Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [384,6,Mod(193,384)]
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([0, 1, 0]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("384.193");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 384 = 2^{7} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 384.d (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: | \(61.5873868082\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} + 338x^{10} + 43555x^{8} + 2692222x^{6} + 81680965x^{4} + 1098257588x^{2} + 4742525956 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{57}\cdot 3^{8} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 193.5 | ||
Root | \(10.8525i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 384.193 |
Dual form | 384.6.d.j.193.8 |
$q$-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 | ||||||||
\(3\) | − 9.00000i | − 0.577350i | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 46.1613i | 0.825758i | 0.910786 | + | 0.412879i | \(0.135477\pi\) | ||||
−0.910786 | + | 0.412879i | \(0.864523\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 59.9278 | 0.462257 | 0.231128 | − | 0.972923i | \(-0.425758\pi\) | ||||
0.231128 | + | 0.972923i | \(0.425758\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −81.0000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 400.065i | 0.996894i | 0.866920 | + | 0.498447i | \(0.166096\pi\) | ||||
−0.866920 | + | 0.498447i | \(0.833904\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 351.898i | − 0.577508i | −0.957403 | − | 0.288754i | \(-0.906759\pi\) | ||||
0.957403 | − | 0.288754i | \(-0.0932410\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 415.451 | 0.476751 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1662.58 | 1.39527 | 0.697636 | − | 0.716452i | \(-0.254235\pi\) | ||||
0.697636 | + | 0.716452i | \(0.254235\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − 564.314i | − 0.358622i | −0.983792 | − | 0.179311i | \(-0.942613\pi\) | ||||
0.983792 | − | 0.179311i | \(-0.0573869\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − 539.350i | − 0.266884i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −3831.57 | −1.51028 | −0.755139 | − | 0.655565i | \(-0.772430\pi\) | ||||
−0.755139 | + | 0.655565i | \(0.772430\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 994.139 | 0.318124 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 729.000i | 0.192450i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 5944.12i | 1.31248i | 0.754552 | + | 0.656240i | \(0.227854\pi\) | ||||
−0.754552 | + | 0.656240i | \(0.772146\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2678.95 | −0.500680 | −0.250340 | − | 0.968158i | \(-0.580542\pi\) | ||||
−0.250340 | + | 0.968158i | \(0.580542\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 3600.59 | 0.575557 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 2766.34i | 0.381712i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 771.803i | 0.0926834i | 0.998926 | + | 0.0463417i | \(0.0147563\pi\) | ||||
−0.998926 | + | 0.0463417i | \(0.985244\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −3167.08 | −0.333425 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −5119.70 | −0.475647 | −0.237824 | − | 0.971308i | \(-0.576434\pi\) | ||||
−0.237824 | + | 0.971308i | \(0.576434\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 9518.90i | − 0.785083i | −0.919734 | − | 0.392541i | \(-0.871596\pi\) | ||||
0.919734 | − | 0.392541i | \(-0.128404\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | − 3739.06i | − 0.275253i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 8138.39 | 0.537395 | 0.268698 | − | 0.963225i | \(-0.413407\pi\) | ||||
0.268698 | + | 0.963225i | \(0.413407\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −13215.7 | −0.786319 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | − 14963.2i | − 0.805561i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 11051.9i | 0.540441i | 0.962799 | + | 0.270220i | \(0.0870966\pi\) | ||||
−0.962799 | + | 0.270220i | \(0.912903\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −18467.5 | −0.823193 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −5078.83 | −0.207051 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 32143.3i | 1.20215i | 0.799191 | + | 0.601077i | \(0.205261\pi\) | ||||
−0.799191 | + | 0.601077i | \(0.794739\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 35454.8i | 1.21997i | 0.792412 | + | 0.609986i | \(0.208825\pi\) | ||||
−0.792412 | + | 0.609986i | \(0.791175\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −4854.15 | −0.154086 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 16244.0 | 0.476882 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 11362.8i | 0.309242i | 0.987974 | + | 0.154621i | \(0.0494157\pi\) | ||||
−0.987974 | + | 0.154621i | \(0.950584\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 34484.1i | 0.871959i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −10394.7 | −0.244719 | −0.122360 | − | 0.992486i | \(-0.539046\pi\) | ||||
−0.122360 | + | 0.992486i | \(0.539046\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −40098.7 | −0.880689 | −0.440345 | − | 0.897829i | \(-0.645144\pi\) | ||||
−0.440345 | + | 0.897829i | \(0.645144\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | − 8947.25i | − 0.183669i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 23975.0i | 0.460821i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 25754.8 | 0.464291 | 0.232146 | − | 0.972681i | \(-0.425425\pi\) | ||||
0.232146 | + | 0.972681i | \(0.425425\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 6561.00 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 2239.75i | 0.0356866i | 0.999841 | + | 0.0178433i | \(0.00568000\pi\) | ||||
−0.999841 | + | 0.0178433i | \(0.994320\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 76746.5i | 1.15216i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 53497.1 | 0.757761 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −15149.4 | −0.202732 | −0.101366 | − | 0.994849i | \(-0.532321\pi\) | ||||
−0.101366 | + | 0.994849i | \(0.532321\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − 21088.5i | − 0.266957i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 24110.6i | 0.289068i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 26049.5 | 0.296135 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 158426. | 1.70961 | 0.854804 | − | 0.518951i | \(-0.173677\pi\) | ||||
0.854804 | + | 0.518951i | \(0.173677\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − 32405.3i | − 0.332298i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 154639.i | 1.50840i | 0.656647 | + | 0.754198i | \(0.271974\pi\) | ||||
−0.656647 | + | 0.754198i | \(0.728026\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 89671.0 | 0.832835 | 0.416417 | − | 0.909174i | \(-0.363286\pi\) | ||||
0.416417 | + | 0.909174i | \(0.363286\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 24897.1 | 0.220382 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 113338.i | 0.957006i | 0.878086 | + | 0.478503i | \(0.158820\pi\) | ||||
−0.878086 | + | 0.478503i | \(0.841180\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 221403.i | 1.78491i | 0.451133 | + | 0.892457i | \(0.351020\pi\) | ||||
−0.451133 | + | 0.892457i | \(0.648980\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 6946.23 | 0.0535108 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −6039.39 | −0.0444936 | −0.0222468 | − | 0.999753i | \(-0.507082\pi\) | ||||
−0.0222468 | + | 0.999753i | \(0.507082\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − 176870.i | − 1.24712i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 28503.7i | 0.192503i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 99634.5 | 0.644974 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 998.858 | 0.00620212 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 46077.3i | 0.274615i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 190145.i | 1.08845i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −328162. | −1.80542 | −0.902711 | − | 0.430247i | \(-0.858427\pi\) | ||||
−0.902711 | + | 0.430247i | \(0.858427\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −85670.1 | −0.453268 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − 176176.i | − 0.896952i | −0.893795 | − | 0.448476i | \(-0.851967\pi\) | ||||
0.893795 | − | 0.448476i | \(-0.148033\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − 33818.1i | − 0.165776i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −33651.6 | −0.158917 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 50245.9 | 0.228718 | 0.114359 | − | 0.993440i | \(-0.463519\pi\) | ||||
0.114359 | + | 0.993440i | \(0.463519\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 364925.i | 1.60201i | 0.598655 | + | 0.801007i | \(0.295702\pi\) | ||||
−0.598655 | + | 0.801007i | \(0.704298\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − 73245.5i | − 0.310265i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 140782. | 0.575715 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −274388. | −1.08379 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 118941.i | 0.453981i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 502438.i | 1.85403i | 0.375023 | + | 0.927016i | \(0.377635\pi\) | ||||
−0.375023 | + | 0.927016i | \(0.622365\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −225684. | −0.805485 | −0.402743 | − | 0.915313i | \(-0.631943\pi\) | ||||
−0.402743 | + | 0.915313i | \(0.631943\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −134669. | −0.465091 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − 123664.i | − 0.413441i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 464228.i | 1.50308i | 0.659688 | + | 0.751539i | \(0.270688\pi\) | ||||
−0.659688 | + | 0.751539i | \(0.729312\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 99467.3 | 0.312024 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −229617. | −0.698136 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 143142.i | − 0.421987i | −0.977487 | − | 0.210994i | \(-0.932330\pi\) | ||||
0.977487 | − | 0.210994i | \(-0.0676699\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 166208.i | 0.475271i | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −170711. | −0.473663 | −0.236831 | − | 0.971551i | \(-0.576109\pi\) | ||||
−0.236831 | + | 0.971551i | \(0.576109\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 247461. | 0.666484 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 45709.5i | 0.119541i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − 38779.6i | − 0.0985118i | −0.998786 | − | 0.0492559i | \(-0.984315\pi\) | ||||
0.998786 | − | 0.0492559i | \(-0.0156850\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 59576.6 | 0.147055 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 289289. | 0.694064 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − 399489.i | − 0.931907i | −0.884809 | − | 0.465954i | \(-0.845711\pi\) | ||||
0.884809 | − | 0.465954i | \(-0.154289\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − 168069.i | − 0.381322i | −0.981656 | − | 0.190661i | \(-0.938937\pi\) | ||||
0.981656 | − | 0.190661i | \(-0.0610632\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 319093. | 0.704351 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −35627.4 | −0.0765340 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 665138.i | 1.39094i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 43687.4i | 0.0889614i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −230781. | −0.457738 | −0.228869 | − | 0.973457i | \(-0.573503\pi\) | ||||
−0.228869 | + | 0.973457i | \(0.573503\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 7236.58 | 0.0139843 | 0.00699214 | − | 0.999976i | \(-0.497774\pi\) | ||||
0.00699214 | + | 0.999976i | \(0.497774\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | − 146196.i | − 0.275328i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 582795.i | − 1.06992i | −0.844878 | − | 0.534959i | \(-0.820327\pi\) | ||||
0.844878 | − | 0.534959i | \(-0.179673\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1.07918e6 | −1.93180 | −0.965899 | − | 0.258920i | \(-0.916633\pi\) | ||||
−0.965899 | + | 0.258920i | \(0.916633\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 102265. | 0.178541 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 356218.i | 0.606703i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − 236332.i | − 0.392769i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 310357. | 0.503426 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 225763. | 0.357508 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − 860927.i | − 1.33125i | −0.746286 | − | 0.665626i | \(-0.768165\pi\) | ||||
0.746286 | − | 0.665626i | \(-0.231835\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 93552.7i | 0.141289i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 439404. | 0.648288 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −160544. | −0.231443 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 360888.i | 0.508466i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − 585057.i | − 0.805781i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −442484. | −0.595848 | −0.297924 | − | 0.954590i | \(-0.596294\pi\) | ||||
−0.297924 | + | 0.954590i | \(0.596294\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −80525.2 | −0.106041 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − 1.25053e6i | − 1.61076i | −0.592761 | − | 0.805378i | \(-0.701962\pi\) | ||||
0.592761 | − | 0.805378i | \(-0.298038\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 508471.i | 0.640734i | 0.947293 | + | 0.320367i | \(0.103806\pi\) | ||||
−0.947293 | + | 0.320367i | \(0.896194\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 215775. | 0.266055 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 1.28856e6 | 1.55495 | 0.777474 | − | 0.628915i | \(-0.216501\pi\) | ||||
0.777474 | + | 0.628915i | \(0.216501\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 375678.i | 0.443758i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − 231793.i | − 0.268059i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1.42040e6 | 1.60848 | 0.804240 | − | 0.594304i | \(-0.202572\pi\) | ||||
0.804240 | + | 0.594304i | \(0.202572\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −196969. | −0.218452 | −0.109226 | − | 0.994017i | \(-0.534837\pi\) | ||||
−0.109226 | + | 0.994017i | \(0.534837\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − 59049.0i | − 0.0641500i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | − 610051.i | − 0.649309i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −198581. | −0.207107 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 20157.8 | 0.0206037 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1.87291e6i | 1.87643i | 0.346052 | + | 0.938215i | \(0.387522\pi\) | ||||
−0.346052 | + | 0.938215i | \(0.612478\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − 1.53288e6i | − 1.50559i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 690719. | 0.665198 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −854792. | −0.807287 | −0.403643 | − | 0.914916i | \(-0.632256\pi\) | ||||
−0.403643 | + | 0.914916i | \(0.632256\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 46252.4i | 0.0428435i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | − 481474.i | − 0.437493i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 1.94301e6 | 1.73215 | 0.866076 | − | 0.499913i | \(-0.166635\pi\) | ||||
0.866076 | + | 0.499913i | \(0.166635\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −510170. | −0.446273 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 136345.i | 0.117047i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − 223635.i | − 0.188434i | −0.995552 | − | 0.0942168i | \(-0.969965\pi\) | ||||
0.995552 | − | 0.0942168i | \(-0.0300347\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.73900e6 | −1.43839 | −0.719196 | − | 0.694807i | \(-0.755490\pi\) | ||||
−0.719196 | + | 0.694807i | \(0.755490\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −189796. | −0.154128 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 397720.i | 0.317136i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − 2.35793e6i | − 1.84642i | −0.384294 | − | 0.923211i | \(-0.625555\pi\) | ||||
0.384294 | − | 0.923211i | \(-0.374445\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 216995. | 0.166893 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −923073. | −0.697382 | −0.348691 | − | 0.937238i | \(-0.613374\pi\) | ||||
−0.348691 | + | 0.937238i | \(0.613374\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 848669.i | − 0.629901i | −0.949108 | − | 0.314951i | \(-0.898012\pi\) | ||||
0.949108 | − | 0.314951i | \(-0.101988\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | − 234445.i | − 0.170974i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −306813. | −0.219871 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.34430e6 | 0.946785 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − 1.42583e6i | − 0.987043i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − 1.09123e6i | − 0.742585i | −0.928516 | − | 0.371293i | \(-0.878915\pi\) | ||||
0.928516 | − | 0.371293i | \(-0.121085\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.48377e6 | −0.992687 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −291648. | −0.191852 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1.34832e6i | 0.872197i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − 570447.i | − 0.362910i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 1.39175e6 | 0.870873 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −1.63664e6 | −1.00740 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 1.55616e6i | − 0.942340i | −0.882042 | − | 0.471170i | \(-0.843832\pi\) | ||||
0.882042 | − | 0.471170i | \(-0.156168\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − 807039.i | − 0.480837i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −457231. | −0.268062 | −0.134031 | − | 0.990977i | \(-0.542792\pi\) | ||||
−0.134031 | + | 0.990977i | \(0.542792\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1.73593e6 | −1.00154 | −0.500772 | − | 0.865579i | \(-0.666951\pi\) | ||||
−0.500772 | + | 0.865579i | \(0.666951\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | − 224074.i | − 0.127237i | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − 450224.i | − 0.251640i | −0.992053 | − | 0.125820i | \(-0.959844\pi\) | ||||
0.992053 | − | 0.125820i | \(-0.0401562\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2.37804e6 | −1.30840 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1.02004e6 | 0.552528 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 938215.i | − 0.500376i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − 349835.i | − 0.183719i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 1.99263e6 | 1.03052 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 487716. | 0.248415 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2.79853e6i | 1.40397i | 0.712189 | + | 0.701987i | \(0.247704\pi\) | ||||
−0.712189 | + | 0.701987i | \(0.752296\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − 62516.0i | − 0.0308945i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −524522. | −0.255359 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.88545e6 | 0.904359 | 0.452180 | − | 0.891927i | \(-0.350647\pi\) | ||||
0.452180 | + | 0.891927i | \(0.350647\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 54354.5i | 0.0256884i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − 1.07176e6i | − 0.499125i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.79919e6 | −0.825738 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −1.59183e6 | −0.720027 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − 841512.i | − 0.375178i | −0.982248 | − | 0.187589i | \(-0.939933\pi\) | ||||
0.982248 | − | 0.187589i | \(-0.0600672\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − 3.05425e6i | − 1.34227i | −0.741333 | − | 0.671137i | \(-0.765806\pi\) | ||||
0.741333 | − | 0.671137i | \(-0.234194\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 256533. | 0.111142 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 3.20066e6 | 1.36711 | 0.683555 | − | 0.729899i | \(-0.260433\pi\) | ||||
0.683555 | + | 0.729899i | \(0.260433\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − 479834.i | − 0.202079i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | − 896710.i | − 0.372376i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 1.95304e6 | 0.799788 | 0.399894 | − | 0.916561i | \(-0.369047\pi\) | ||||
0.399894 | + | 0.916561i | \(0.369047\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 2.15765e6 | 0.871390 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − 8989.72i | − 0.00358080i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − 1.85100e6i | − 0.727236i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −3.31321e6 | −1.28406 | −0.642028 | − | 0.766682i | \(-0.721907\pi\) | ||||
−0.642028 | + | 0.766682i | \(0.721907\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 414696. | 0.158549 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 662317.i | 0.249822i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 3.65917e6i | 1.36179i | 0.732381 | + | 0.680895i | \(0.238409\pi\) | ||||
−0.732381 | + | 0.680895i | \(0.761591\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1.71130e6 | 0.628418 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 2.09172e6 | 0.757968 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − 1.76629e6i | − 0.631631i | −0.948821 | − | 0.315816i | \(-0.897722\pi\) | ||||
0.948821 | − | 0.315816i | \(-0.102278\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 2.95346e6i | 1.04236i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 3.69691e6 | 1.28778 | 0.643890 | − | 0.765118i | \(-0.277320\pi\) | ||||
0.643890 | + | 0.765118i | \(0.277320\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.10672e6 | −0.380526 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 771031.i | 0.261694i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − 669156.i | − 0.224209i | −0.993696 | − | 0.112105i | \(-0.964241\pi\) | ||||
0.993696 | − | 0.112105i | \(-0.0357592\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −6.37027e6 | −2.10725 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −1.58559e6 | −0.517855 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 1.18887e6i | 0.383392i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 2.19806e6i | 0.699945i | 0.936760 | + | 0.349973i | \(0.113809\pi\) | ||||
−0.936760 | + | 0.349973i | \(0.886191\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −304363. | −0.0957105 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −4.54750e6 | −1.41225 | −0.706125 | − | 0.708087i | \(-0.749558\pi\) | ||||
−0.706125 | + | 0.708087i | \(0.749558\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 942717.i | 0.289147i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 302864.i | 0.0917508i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −308771. | −0.0923956 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −1.46461e6 | −0.432926 | −0.216463 | − | 0.976291i | \(-0.569452\pi\) | ||||
−0.216463 | + | 0.976291i | \(0.569452\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − 452213.i | − 0.132050i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 1.92628e6i | 0.555704i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −103390. | −0.0294685 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 3.28432e6 | 0.924923 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 868371.i | 0.241641i | 0.992674 | + | 0.120820i | \(0.0385525\pi\) | ||||
−0.992674 | + | 0.120820i | \(0.961447\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1.31760e6i | 0.362308i | 0.983455 | + | 0.181154i | \(0.0579833\pi\) | ||||
−0.983455 | + | 0.181154i | \(0.942017\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −659210. | −0.179132 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1.65283e6 | 0.443870 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 2.12473e6i | 0.563941i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | − 1.26704e6i | − 0.332389i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 3.26185e6 | 0.845805 | 0.422902 | − | 0.906175i | \(-0.361011\pi\) | ||||
0.422902 | + | 0.906175i | \(0.361011\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −278010. | −0.0712591 | −0.0356295 | − | 0.999365i | \(-0.511344\pi\) | ||||
−0.0356295 | + | 0.999365i | \(0.511344\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 2.46949e6i | 0.625727i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 2.16221e6i | 0.541619i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −2.77446e6 | −0.687096 | −0.343548 | − | 0.939135i | \(-0.611629\pi\) | ||||
−0.343548 | + | 0.939135i | \(0.611629\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.07047e6 | 0.262106 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − 5.97809e6i | − 1.44728i | −0.690176 | − | 0.723641i | \(-0.742467\pi\) | ||||
0.690176 | − | 0.723641i | \(-0.257533\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − 699317.i | − 0.167407i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 4.52194e6 | 1.07043 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −5.68566e6 | −1.33096 | −0.665480 | − | 0.746416i | \(-0.731773\pi\) | ||||
−0.665480 | + | 0.746416i | \(0.731773\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − 2.04821e6i | − 0.474170i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 2.03115e6i | 0.465047i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 973470. | 0.220442 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −2.65598e6 | −0.594886 | −0.297443 | − | 0.954740i | \(-0.596134\pi\) | ||||
−0.297443 | + | 0.954740i | \(0.596134\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 1.21202e6i | 0.268520i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 3.88629e6i | 0.851692i | 0.904796 | + | 0.425846i | \(0.140024\pi\) | ||||
−0.904796 | + | 0.425846i | \(0.859976\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −3.78966e6 | −0.821576 | −0.410788 | − | 0.911731i | \(-0.634746\pi\) | ||||
−0.410788 | + | 0.911731i | \(0.634746\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −1.11297e6 | −0.238700 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − 2.31109e6i | − 0.490371i | −0.969476 | − | 0.245185i | \(-0.921151\pi\) | ||||
0.969476 | − | 0.245185i | \(-0.0788488\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 680948.i | 0.142949i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 4.17805e6 | 0.867803 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 3.80818e6 | 0.782645 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − 561007.i | − 0.114086i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − 895206.i | − 0.180147i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 4.62388e6 | 0.920804 | 0.460402 | − | 0.887710i | \(-0.347705\pi\) | ||||
0.460402 | + | 0.887710i | \(0.347705\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 271596. | 0.0535254 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 2.06656e6i | 0.403069i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 7.31313e6i | 1.41172i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 7.55618e6 | 1.44371 | 0.721855 | − | 0.692044i | \(-0.243290\pi\) | ||||
0.721855 | + | 0.692044i | \(0.243290\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −1.28828e6 | −0.243634 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − 4.40919e6i | − 0.825382i | −0.910871 | − | 0.412691i | \(-0.864589\pi\) | ||||
0.910871 | − | 0.412691i | \(-0.135411\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 9.88255e6i | 1.83127i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 1.49587e6 | 0.274398 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −622934. | −0.113123 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 8.45546e6i | 1.52015i | 0.649837 | + | 0.760074i | \(0.274837\pi\) | ||||
−0.649837 | + | 0.760074i | \(0.725163\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1.53639e6i | 0.273469i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −1.17007e6 | −0.206201 | −0.103100 | − | 0.994671i | \(-0.532876\pi\) | ||||
−0.103100 | + | 0.994671i | \(0.532876\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −7.13833e6 | −1.24557 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − 2.22715e6i | − 0.384795i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 9.48209e6i | 1.62222i | 0.584893 | + | 0.811110i | \(0.301136\pi\) | ||||
−0.584893 | + | 0.811110i | \(0.698864\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2.40302e6 | −0.407105 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 411385. | 0.0690169 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 4.13932e6i | 0.687720i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 3.25589e6i | 0.535726i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −349016. | −0.0568758 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 1.08606e7 | 1.75290 | 0.876451 | − | 0.481491i | \(-0.159905\pi\) | ||||
0.876451 | + | 0.481491i | \(0.159905\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 7.05571e6i | − 1.12794i | −0.825795 | − | 0.563971i | \(-0.809273\pi\) | ||||
0.825795 | − | 0.563971i | \(-0.190727\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | − 536189.i | − 0.0849023i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −4.45396e6 | −0.698585 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 8.24455e6 | 1.28094 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − 2.60360e6i | − 0.400718i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.80161e6i | 0.274690i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −5.23181e6 | −0.790255 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −3.59541e6 | −0.538037 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − 5.28712e6i | − 0.783876i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 2.11215e6i | 0.310264i | 0.987894 | + | 0.155132i | \(0.0495804\pi\) | ||||
−0.987894 | + | 0.155132i | \(0.950420\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −1.51262e6 | −0.220157 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −1.02202e7 | −1.47391 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 9.37947e6i | 1.34032i | 0.742215 | + | 0.670162i | \(0.233775\pi\) | ||||
−0.742215 | + | 0.670162i | \(0.766225\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | − 2.87184e6i | − 0.406657i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 3.35435e6 | 0.470685 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1.54343e6 | 0.214622 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 320646.i | 0.0441869i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − 3.61461e6i | − 0.493655i | −0.969059 | − | 0.246827i | \(-0.920612\pi\) | ||||
0.969059 | − | 0.246827i | \(-0.0793881\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −3.34968e6 | −0.453392 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 5.98625e6 | 0.803059 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 1.04180e7i | 1.38520i | 0.721321 | + | 0.692601i | \(0.243535\pi\) | ||||
−0.721321 | + | 0.692601i | \(0.756465\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − 278786.i | − 0.0367409i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 393186. | 0.0513619 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 7.80034e6 | 1.01003 | 0.505014 | − | 0.863111i | \(-0.331487\pi\) | ||||
0.505014 | + | 0.863111i | \(0.331487\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − 1.13367e7i | − 1.45511i | −0.686049 | − | 0.727555i | \(-0.740657\pi\) | ||||
0.686049 | − | 0.727555i | \(-0.259343\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 2.07703e6i | 0.264275i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −3.80911e6 | −0.480456 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 3.41197e6 | 0.426644 | 0.213322 | − | 0.976982i | \(-0.431572\pi\) | ||||
0.213322 | + | 0.976982i | \(0.431572\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | − 65129.2i | − 0.00807383i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 134224.i | 0.0164964i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −4.42149e6 | −0.538762 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −1.31577e6 | −0.158961 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 9.10881e6i | 1.09111i | 0.838077 | + | 0.545553i | \(0.183680\pi\) | ||||
−0.838077 | + | 0.545553i | \(0.816320\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.51177e6i | 0.179555i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −5.24516e6 | −0.617717 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −5.87052e6 | −0.685551 | −0.342776 | − | 0.939417i | \(-0.611367\pi\) | ||||
−0.342776 | + | 0.939417i | \(0.611367\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 4.59925e6i | 0.532592i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 9.71263e6i | 1.11532i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 9.18159e6 | 1.04556 | 0.522782 | − | 0.852466i | \(-0.324894\pi\) | ||||
0.522782 | + | 0.852466i | \(0.324894\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.01852e7 | 1.15022 | 0.575112 | − | 0.818075i | \(-0.304959\pi\) | ||||
0.575112 | + | 0.818075i | \(0.304959\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − 920388.i | − 0.103081i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 46108.5i | 0.00512145i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 4.74894e6 | 0.523148 | 0.261574 | − | 0.965183i | \(-0.415758\pi\) | ||||
0.261574 | + | 0.965183i | \(0.415758\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 3.20596e6 | 0.350280 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − 2.86388e6i | − 0.310350i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1.16623e6i | 0.125352i | 0.998034 | + | 0.0626760i | \(0.0199635\pi\) | ||||
−0.998034 | + | 0.0626760i | \(0.980037\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −2.12699e6 | −0.226766 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −1.29443e6 | −0.136888 | −0.0684440 | − | 0.997655i | \(-0.521803\pi\) | ||||
−0.0684440 | + | 0.997655i | \(0.521803\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 4.23949e6i | 0.444721i | 0.974965 | + | 0.222360i | \(0.0713762\pi\) | ||||
−0.974965 | + | 0.222360i | \(0.928624\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | − 2.79321e6i | − 0.290653i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −907873. | −0.0937141 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −5.67063e6 | −0.580672 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − 2.03186e6i | − 0.206408i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 1.28318e6i | 0.129319i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.24132e6 | −0.124111 | −0.0620553 | − | 0.998073i | \(-0.519766\pi\) | ||||
−0.0620553 | + | 0.998073i | \(0.519766\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −7.74834e6 | −0.768599 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − 1.51484e7i | − 1.49084i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 4.65056e6i | 0.454105i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 841974. | 0.0815730 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −1.09152e7 | −1.04927 | −0.524635 | − | 0.851327i | \(-0.675798\pi\) | ||||
−0.524635 | + | 0.851327i | \(0.675798\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 1.48054e7i | − 1.41219i | −0.708118 | − | 0.706095i | \(-0.750455\pi\) | ||||
0.708118 | − | 0.706095i | \(-0.249545\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − 3.95464e6i | − 0.374289i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −7.50071e6 | −0.704436 | −0.352218 | − | 0.935918i | \(-0.614572\pi\) | ||||
−0.352218 | + | 0.935918i | \(0.614572\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1.28594e7 | −1.19842 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.44489e6i | 0.133624i | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − 1.84442e7i | − 1.69269i | −0.532638 | − | 0.846343i | \(-0.678799\pi\) | ||||
0.532638 | − | 0.846343i | \(-0.321201\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 8.13252e6 | 0.740665 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 3.24799e6 | 0.293563 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 1.50202e7i | 1.34729i | 0.739055 | + | 0.673645i | \(0.235272\pi\) | ||||
−0.739055 | + | 0.673645i | \(0.764728\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − 1.62211e7i | − 1.44403i | −0.691876 | − | 0.722017i | \(-0.743215\pi\) | ||||
0.691876 | − | 0.722017i | \(-0.256785\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −5.26551e6 | −0.465218 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 1.56109e6 | 0.136890 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 2.27753e7i | − 1.98221i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 3.98236e6i | 0.344013i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −1.41842e7 | −1.21618 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 8.38719e6 | 0.713804 | 0.356902 | − | 0.934142i | \(-0.383833\pi\) | ||||
0.356902 | + | 0.934142i | \(0.383833\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 724727.i | 0.0612231i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − 5.22589e6i | − 0.438216i | −0.975701 | − | 0.219108i | \(-0.929685\pi\) | ||||
0.975701 | − | 0.219108i | \(-0.0703147\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 9.49411e6 | 0.790278 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −1.12548e7 | −0.929970 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 1.61671e7i | 1.32611i | 0.748570 | + | 0.663056i | \(0.230741\pi\) | ||||
−0.748570 | + | 0.663056i | \(0.769259\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 2.31942e6i | 0.188865i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 4.57624e6 | 0.369928 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 3.88915e6 | 0.312109 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 2.38372e7i | 1.89915i | 0.313533 | + | 0.949577i | \(0.398487\pi\) | ||||
−0.313533 | + | 0.949577i | \(0.601513\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | − 1.94198e6i | − 0.153607i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −1.68454e7 | −1.32287 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −8.51189e6 | −0.663658 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | − 1.15971e7i | − 0.897750i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − 9.30715e6i | − 0.715355i | −0.933845 | − | 0.357678i | \(-0.883569\pi\) | ||||
0.933845 | − | 0.357678i | \(-0.116431\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 435539. | 0.0332383 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 3.38110e6 | 0.256204 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 9.26717e6i | 0.697266i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − 5.17752e6i | − 0.386818i | −0.981118 | − | 0.193409i | \(-0.938046\pi\) | ||||
0.981118 | − | 0.193409i | \(-0.0619544\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −2.08614e6 | −0.154764 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 1.02646e7 | 0.756166 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 6.49868e6i | 0.475401i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − 1.27836e7i | − 0.928657i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 3.77696e6 | 0.272471 | 0.136236 | − | 0.990676i | \(-0.456500\pi\) | ||||
0.136236 | + | 0.990676i | \(0.456500\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 5.37378e6 | 0.384983 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 1.77272e6i | 0.126123i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 5.90928e6i | 0.417532i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 2.50517e7 | 1.75793 | 0.878966 | − | 0.476885i | \(-0.158234\pi\) | ||||
0.878966 | + | 0.476885i | \(0.158234\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −531441. | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − 1.58259e7i | − 1.09540i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 2.58312e7i | − 1.77576i | −0.460074 | − | 0.887881i | \(-0.652177\pi\) | ||||
0.460074 | − | 0.887881i | \(-0.347823\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −5.49046e6 | −0.374879 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −4.54587e6 | −0.308282 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − 1.40532e7i | − 0.946593i | −0.880903 | − | 0.473297i | \(-0.843064\pi\) | ||||
0.880903 | − | 0.473297i | \(-0.156936\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 1.78723e6i | 0.119573i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 3.60964e6 | 0.239878 | 0.119939 | − | 0.992781i | \(-0.461730\pi\) | ||||
0.119939 | + | 0.992781i | \(0.461730\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −2.31932e7 | −1.53098 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − 181420.i | − 0.0118955i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 6.79207e6i | 0.442382i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 2.91748e7 | 1.88759 | 0.943795 | − | 0.330531i | \(-0.107228\pi\) | ||||
0.943795 | + | 0.330531i | \(0.107228\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 1.68562e7 | 1.08336 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − 1.04178e7i | − 0.665136i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − 1.12305e7i | − 0.712294i | −0.934430 | − | 0.356147i | \(-0.884090\pi\) | ||||
0.934430 | − | 0.356147i | \(-0.115910\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −1.37959e7 | −0.869251 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1.69614e7 | 1.06170 | 0.530849 | − | 0.847466i | \(-0.321873\pi\) | ||||
0.530849 | + | 0.847466i | \(0.321873\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.32682e7i | 0.825089i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | − 6.21647e6i | − 0.384052i | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 1.13111e7 | 0.694254 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 2.61093e7 | 1.59214 | 0.796068 | − | 0.605208i | \(-0.206910\pi\) | ||||
0.796068 | + | 0.605208i | \(0.206910\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 7.69313e6i | 0.466087i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − 2.28744e7i | − 1.37690i | −0.725286 | − | 0.688448i | \(-0.758292\pi\) | ||||
0.725286 | − | 0.688448i | \(-0.241708\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −2.66325e6 | −0.159279 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 416272. | 0.0247357 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 2.88912e6i | 0.170578i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − 4.15857e6i | − 0.243959i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −4.33327e6 | −0.252587 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −2.14293e7 | −1.24118 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1.44464e6i | 0.0831423i | 0.999136 | + | 0.0415712i | \(0.0132363\pi\) | ||||
−0.999136 | + | 0.0415712i | \(0.986764\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | − 1.74871e7i | − 1.00006i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −361927. | −0.0205674 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.24765e7 | 0.704544 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 4.59153e6i | 0.257656i | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − 5.37136e6i | − 0.299529i | −0.988722 | − | 0.149764i | \(-0.952148\pi\) | ||||
0.988722 | − | 0.149764i | \(-0.0478515\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.35307e7 | 0.749813 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 1.22710e6 | 0.0675772 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − 1.60421e7i | − 0.877954i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − 1.05994e7i | − 0.576491i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −2.01271e6 | −0.108792 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 8.86137e6 | 0.476025 | 0.238012 | − | 0.971262i | \(-0.423504\pi\) | ||||
0.238012 | + | 0.971262i | \(0.423504\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 2.91251e7i | 1.55495i | 0.628915 | + | 0.777474i | \(0.283499\pi\) | ||||
−0.628915 | + | 0.777474i | \(0.716501\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 1.56510e7i | 0.830456i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 6.60763e6 | 0.348459 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −5.37165e6 | −0.281548 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 1.70817e6i | 0.0889857i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − 2.62586e7i | − 1.35961i | −0.733394 | − | 0.679803i | \(-0.762065\pi\) | ||||
0.733394 | − | 0.679803i | \(-0.237935\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1.88150e7 | 0.968287 | 0.484143 | − | 0.874989i | \(-0.339131\pi\) | ||||
0.484143 | + | 0.874989i | \(0.339131\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 3.57948e6 | 0.183099 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − 1.26962e7i | − 0.645520i | −0.946481 | − | 0.322760i | \(-0.895389\pi\) | ||||
0.946481 | − | 0.322760i | \(-0.104611\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − 2.01838e7i | − 1.02004i | −0.860164 | − | 0.510018i | \(-0.829639\pi\) | ||||
0.860164 | − | 0.510018i | \(-0.170361\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −2.12213e7 | −1.06603 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −2.19720e7 | −1.09713 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − 7.88021e6i | − 0.391130i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − 1.95296e6i | − 0.0963560i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −1.27185e7 | −0.623781 | −0.311890 | − | 0.950118i | \(-0.600962\pi\) | ||||
−0.311890 | + | 0.950118i | \(0.600962\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.48215e7 | −0.722605 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 8.30766e6i | 0.402633i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1.14231e7i | 0.550354i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 59859.3 | 0.00286697 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −7.63802e6 | −0.363674 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − 2.95721e6i | − 0.139978i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1.95957e7i | 0.922121i | 0.887369 | + | 0.461060i | \(0.152531\pi\) | ||||
−0.887369 | + | 0.461060i | \(0.847469\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −2.11001e6 | −0.0987117 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 3.68287e7 | 1.71291 | 0.856454 | − | 0.516224i | \(-0.172663\pi\) | ||||
0.856454 | + | 0.516224i | \(0.172663\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − 1.70593e7i | − 0.788823i | −0.918934 | − | 0.394411i | \(-0.870949\pi\) | ||||
0.918934 | − | 0.394411i | \(-0.129051\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 2.76131e6i | 0.126943i | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −3.56411e7 | −1.62901 | −0.814506 | − | 0.580155i | \(-0.802992\pi\) | ||||
−0.814506 | + | 0.580155i | \(0.802992\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1.79012e6 | 0.0813468 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − 1.20987e7i | − 0.546626i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1.03036e7i | 0.462849i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 3.99855e6 | 0.178590 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −1.28325e7 | −0.569869 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1.13949e7i | 0.503144i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − 6.78596e6i | − 0.297929i | −0.988843 | − | 0.148964i | \(-0.952406\pi\) | ||||
0.988843 | − | 0.148964i | \(-0.0475939\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −9.82105e6 | −0.428732 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 6.27597e6 | 0.272421 | 0.136211 | − | 0.990680i | \(-0.456508\pi\) | ||||
0.136211 | + | 0.990680i | \(0.456508\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 2.46975e7i | − 1.06599i | −0.846120 | − | 0.532993i | \(-0.821067\pi\) | ||||
0.846120 | − | 0.532993i | \(-0.178933\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 1.33540e7i | 0.573128i | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −1.04054e6 | −0.0444070 | −0.0222035 | − | 0.999753i | \(-0.507068\pi\) | ||||
−0.0222035 | + | 0.999753i | \(0.507068\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.96660e7 | −0.834569 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 2.62483e6i | 0.110766i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − 4.59261e6i | − 0.192722i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1.84409e7 | 0.769530 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 1.21349e7 | 0.503563 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − 1.59240e7i | − 0.657133i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.83746e7i | 0.754062i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −5.13402e6 | −0.209526 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 7.75829e6 | 0.314880 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 2.41754e7i | 0.975789i | 0.872903 | + | 0.487894i | \(0.162235\pi\) | ||||
−0.872903 | + | 0.487894i | \(0.837765\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | − 1.25258e7i | − 0.502799i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −3.64416e7 | −1.45479 | −0.727396 | − | 0.686217i | \(-0.759270\pi\) | ||||
−0.727396 | + | 0.686217i | \(0.759270\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −896047. | −0.0355758 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 1.47297e7i | 0.581624i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − 1.05579e7i | − 0.414622i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 3.29796e7 | 1.28812 | 0.644060 | − | 0.764975i | \(-0.277249\pi\) | ||||
0.644060 | + | 0.764975i | \(0.277249\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −1.40054e7 | −0.544060 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 3.65789e6i | 0.141327i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 767279.i | 0.0294849i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −7.26335e6 | −0.277612 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −3.83111e7 | −1.45642 | −0.728209 | − | 0.685356i | \(-0.759647\pi\) | ||||
−0.728209 | + | 0.685356i | \(0.759647\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 7.45779e6i | 0.281991i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 4.11508e6i | 0.154765i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −3.07036e7 | −1.14858 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1.48708e7 | 0.553332 | 0.276666 | − | 0.960966i | \(-0.410770\pi\) | ||||
0.276666 | + | 0.960966i | \(0.410770\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 1.56233e7i | 0.578242i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − 2.67852e7i | − 0.986099i | −0.870001 | − | 0.493049i | \(-0.835882\pi\) | ||||
0.870001 | − | 0.493049i | \(-0.164118\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1.96165e7 | 0.718359 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −2.01666e6 | −0.0734605 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 1.24319e7i | − 0.450467i | −0.974305 | − | 0.225233i | \(-0.927686\pi\) | ||||
0.974305 | − | 0.225233i | \(-0.0723145\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1.41106e7i | 0.508605i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −4.05201e6 | −0.145285 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −3.05330e7 | −1.08902 | −0.544511 | − | 0.838753i | \(-0.683285\pi\) | ||||
−0.544511 | + | 0.838753i | \(0.683285\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − 1.06532e7i | − 0.377981i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 2.14023e7i | 0.755407i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 3.01113e6 | 0.105726 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.14524e7 | −0.749319 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − 9.18035e6i | − 0.319002i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 334050.i | 0.0115476i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 3.23903e7 | 1.11391 | 0.556954 | − | 0.830543i | \(-0.311970\pi\) | ||||
0.556954 | + | 0.830543i | \(0.311970\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −8.44394e6 | −0.288892 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 5.00157e7i | 1.70239i | 0.524853 | + | 0.851193i | \(0.324120\pi\) | ||||
−0.524853 | + | 0.851193i | \(0.675880\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 2.18691e7i | 0.740542i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −3.14852e6 | −0.106070 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 621156. | 0.0208192 | 0.0104096 | − | 0.999946i | \(-0.496686\pi\) | ||||
0.0104096 | + | 0.999946i | \(0.496686\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − 6.06076e6i | − 0.202102i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − 1.79336e7i | − 0.594971i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 6.73840e6 | 0.222420 | 0.111210 | − | 0.993797i | \(-0.464527\pi\) | ||||
0.111210 | + | 0.993797i | \(0.464527\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 2.69026e7 | 0.883493 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − 4.38944e6i | − 0.143422i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 3.64723e7i | 1.18569i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1.73933e7 | −0.562597 | −0.281298 | − | 0.959620i | \(-0.590765\pi\) | ||||
−0.281298 | + | 0.959620i | \(0.590765\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 2.51867e7 | 0.810585 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − 4.98163e7i | − 1.59520i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 9.67436e6i | 0.308237i | 0.988052 | + | 0.154118i | \(0.0492537\pi\) | ||||
−0.988052 | + | 0.154118i | \(0.950746\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −562644. | −0.0178369 |
(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 | 384.6.d.j.193.5 | yes | 12 | |
4.3 | odd | 2 | inner | 384.6.d.j.193.11 | yes | 12 | |
8.3 | odd | 2 | inner | 384.6.d.j.193.2 | ✓ | 12 | |
8.5 | even | 2 | inner | 384.6.d.j.193.8 | yes | 12 | |
16.3 | odd | 4 | 768.6.a.be.1.5 | 6 | |||
16.5 | even | 4 | 768.6.a.be.1.2 | 6 | |||
16.11 | odd | 4 | 768.6.a.bf.1.2 | 6 | |||
16.13 | even | 4 | 768.6.a.bf.1.5 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
384.6.d.j.193.2 | ✓ | 12 | 8.3 | odd | 2 | inner | |
384.6.d.j.193.5 | yes | 12 | 1.1 | even | 1 | trivial | |
384.6.d.j.193.8 | yes | 12 | 8.5 | even | 2 | inner | |
384.6.d.j.193.11 | yes | 12 | 4.3 | odd | 2 | inner | |
768.6.a.be.1.2 | 6 | 16.5 | even | 4 | |||
768.6.a.be.1.5 | 6 | 16.3 | odd | 4 | |||
768.6.a.bf.1.2 | 6 | 16.11 | odd | 4 | |||
768.6.a.bf.1.5 | 6 | 16.13 | even | 4 |