Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [441,6,Mod(1,441)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(441, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("441.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 441 = 3^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 441.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(70.7292645375\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{57}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 14 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 7) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-3.27492\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 441.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.725083 | −0.128178 | −0.0640889 | − | 0.997944i | \(-0.520414\pi\) | ||||
−0.0640889 | + | 0.997944i | \(0.520414\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −31.4743 | −0.983570 | ||||||||
\(5\) | −46.7492 | −0.836275 | −0.418137 | − | 0.908384i | \(-0.637317\pi\) | ||||
−0.418137 | + | 0.908384i | \(0.637317\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 46.0241 | 0.254250 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 33.8970 | 0.107192 | ||||||||
\(11\) | −666.090 | −1.65978 | −0.829891 | − | 0.557926i | \(-0.811597\pi\) | ||||
−0.829891 | + | 0.557926i | \(0.811597\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 650.640 | 1.06778 | 0.533890 | − | 0.845554i | \(-0.320729\pi\) | ||||
0.533890 | + | 0.845554i | \(0.320729\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 973.805 | 0.950981 | ||||||||
\(17\) | 1186.89 | 0.996069 | 0.498035 | − | 0.867157i | \(-0.334055\pi\) | ||||
0.498035 | + | 0.867157i | \(0.334055\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1565.05 | 0.994591 | 0.497296 | − | 0.867581i | \(-0.334326\pi\) | ||||
0.497296 | + | 0.867581i | \(0.334326\pi\) | |||||||
\(20\) | 1471.40 | 0.822535 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 482.970 | 0.212747 | ||||||||
\(23\) | 1100.15 | 0.433644 | 0.216822 | − | 0.976211i | \(-0.430431\pi\) | ||||
0.216822 | + | 0.976211i | \(0.430431\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −939.515 | −0.300645 | ||||||||
\(26\) | −471.768 | −0.136866 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2396.72 | −0.529203 | −0.264602 | − | 0.964358i | \(-0.585240\pi\) | ||||
−0.264602 | + | 0.964358i | \(0.585240\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2048.46 | 0.382844 | 0.191422 | − | 0.981508i | \(-0.438690\pi\) | ||||
0.191422 | + | 0.981508i | \(0.438690\pi\) | |||||||
\(32\) | −2178.86 | −0.376144 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −860.596 | −0.127674 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1077.54 | 0.129399 | 0.0646995 | − | 0.997905i | \(-0.479391\pi\) | ||||
0.0646995 | + | 0.997905i | \(0.479391\pi\) | |||||||
\(38\) | −1134.79 | −0.127484 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −2151.59 | −0.212622 | ||||||||
\(41\) | 1098.21 | 0.102029 | 0.0510147 | − | 0.998698i | \(-0.483754\pi\) | ||||
0.0510147 | + | 0.998698i | \(0.483754\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 16564.3 | 1.36616 | 0.683081 | − | 0.730343i | \(-0.260640\pi\) | ||||
0.683081 | + | 0.730343i | \(0.260640\pi\) | |||||||
\(44\) | 20964.7 | 1.63251 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −797.702 | −0.0555835 | ||||||||
\(47\) | −8298.39 | −0.547960 | −0.273980 | − | 0.961735i | \(-0.588340\pi\) | ||||
−0.273980 | + | 0.961735i | \(0.588340\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 681.226 | 0.0385360 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −20478.4 | −1.05024 | ||||||||
\(53\) | −5519.18 | −0.269889 | −0.134944 | − | 0.990853i | \(-0.543086\pi\) | ||||
−0.134944 | + | 0.990853i | \(0.543086\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 31139.1 | 1.38803 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 1737.82 | 0.0678321 | ||||||||
\(59\) | −14230.4 | −0.532216 | −0.266108 | − | 0.963943i | \(-0.585738\pi\) | ||||
−0.266108 | + | 0.963943i | \(0.585738\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 14234.7 | 0.489807 | 0.244904 | − | 0.969547i | \(-0.421244\pi\) | ||||
0.244904 | + | 0.969547i | \(0.421244\pi\) | |||||||
\(62\) | −1485.30 | −0.0490721 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −29581.9 | −0.902768 | ||||||||
\(65\) | −30416.9 | −0.892958 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 19730.4 | 0.536970 | 0.268485 | − | 0.963284i | \(-0.413477\pi\) | ||||
0.268485 | + | 0.963284i | \(0.413477\pi\) | |||||||
\(68\) | −37356.6 | −0.979704 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −64562.7 | −1.51997 | −0.759986 | − | 0.649940i | \(-0.774794\pi\) | ||||
−0.759986 | + | 0.649940i | \(0.774794\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −28567.0 | −0.627418 | −0.313709 | − | 0.949519i | \(-0.601572\pi\) | ||||
−0.313709 | + | 0.949519i | \(0.601572\pi\) | |||||||
\(74\) | −781.309 | −0.0165861 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −49258.8 | −0.978251 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −30633.4 | −0.552239 | −0.276119 | − | 0.961123i | \(-0.589049\pi\) | ||||
−0.276119 | + | 0.961123i | \(0.589049\pi\) | |||||||
\(80\) | −45524.6 | −0.795282 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −796.293 | −0.0130779 | ||||||||
\(83\) | −675.946 | −0.0107700 | −0.00538501 | − | 0.999986i | \(-0.501714\pi\) | ||||
−0.00538501 | + | 0.999986i | \(0.501714\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −55486.3 | −0.832987 | ||||||||
\(86\) | −12010.5 | −0.175111 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −30656.2 | −0.421999 | ||||||||
\(89\) | 125971. | 1.68576 | 0.842882 | − | 0.538098i | \(-0.180857\pi\) | ||||
0.842882 | + | 0.538098i | \(0.180857\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −34626.5 | −0.426520 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 6017.02 | 0.0702363 | ||||||||
\(95\) | −73164.9 | −0.831751 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 22906.8 | 0.247192 | 0.123596 | − | 0.992333i | \(-0.460557\pi\) | ||||
0.123596 | + | 0.992333i | \(0.460557\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 29570.5 | 0.295705 | ||||||||
\(101\) | −181474. | −1.77015 | −0.885077 | − | 0.465444i | \(-0.845895\pi\) | ||||
−0.885077 | + | 0.465444i | \(0.845895\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −64772.0 | −0.601581 | −0.300791 | − | 0.953690i | \(-0.597251\pi\) | ||||
−0.300791 | + | 0.953690i | \(0.597251\pi\) | |||||||
\(104\) | 29945.1 | 0.271483 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 4001.86 | 0.0345938 | ||||||||
\(107\) | 148170. | 1.25112 | 0.625562 | − | 0.780175i | \(-0.284870\pi\) | ||||
0.625562 | + | 0.780175i | \(0.284870\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −111294. | −0.897237 | −0.448618 | − | 0.893723i | \(-0.648084\pi\) | ||||
−0.448618 | + | 0.893723i | \(0.648084\pi\) | |||||||
\(110\) | −22578.5 | −0.177915 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 43175.5 | 0.318084 | 0.159042 | − | 0.987272i | \(-0.449160\pi\) | ||||
0.159042 | + | 0.987272i | \(0.449160\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −51431.2 | −0.362646 | ||||||||
\(116\) | 75435.0 | 0.520509 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 10318.2 | 0.0682182 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 282625. | 1.75488 | ||||||||
\(122\) | −10321.4 | −0.0627824 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −64473.6 | −0.376554 | ||||||||
\(125\) | 190013. | 1.08770 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −131449. | −0.723182 | −0.361591 | − | 0.932337i | \(-0.617766\pi\) | ||||
−0.361591 | + | 0.932337i | \(0.617766\pi\) | |||||||
\(128\) | 91172.8 | 0.491859 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 22054.7 | 0.114457 | ||||||||
\(131\) | −349458. | −1.77916 | −0.889582 | − | 0.456775i | \(-0.849005\pi\) | ||||
−0.889582 | + | 0.456775i | \(0.849005\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −14306.2 | −0.0688276 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 54625.7 | 0.253250 | ||||||||
\(137\) | −386434. | −1.75903 | −0.879516 | − | 0.475869i | \(-0.842134\pi\) | ||||
−0.879516 | + | 0.475869i | \(0.842134\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −17289.3 | −0.0758997 | −0.0379498 | − | 0.999280i | \(-0.512083\pi\) | ||||
−0.0379498 | + | 0.999280i | \(0.512083\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 46813.3 | 0.194827 | ||||||||
\(143\) | −433384. | −1.77228 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 112045. | 0.442559 | ||||||||
\(146\) | 20713.4 | 0.0804210 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −33914.9 | −0.127273 | ||||||||
\(149\) | 112171. | 0.413917 | 0.206959 | − | 0.978350i | \(-0.433643\pi\) | ||||
0.206959 | + | 0.978350i | \(0.433643\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 30495.4 | 0.108841 | 0.0544205 | − | 0.998518i | \(-0.482669\pi\) | ||||
0.0544205 | + | 0.998518i | \(0.482669\pi\) | |||||||
\(152\) | 72030.1 | 0.252874 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −95763.6 | −0.320163 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −523509. | −1.69502 | −0.847510 | − | 0.530780i | \(-0.821899\pi\) | ||||
−0.847510 | + | 0.530780i | \(0.821899\pi\) | |||||||
\(158\) | 22211.7 | 0.0707847 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 101860. | 0.314560 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −439646. | −1.29609 | −0.648043 | − | 0.761604i | \(-0.724412\pi\) | ||||
−0.648043 | + | 0.761604i | \(0.724412\pi\) | |||||||
\(164\) | −34565.3 | −0.100353 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 490.117 | 0.00138048 | ||||||||
\(167\) | 279353. | 0.775107 | 0.387554 | − | 0.921847i | \(-0.373320\pi\) | ||||
0.387554 | + | 0.921847i | \(0.373320\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 52038.8 | 0.140156 | ||||||||
\(170\) | 40232.2 | 0.106770 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −521349. | −1.34372 | ||||||||
\(173\) | 99699.4 | 0.253266 | 0.126633 | − | 0.991950i | \(-0.459583\pi\) | ||||
0.126633 | + | 0.991950i | \(0.459583\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −648641. | −1.57842 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −91339.7 | −0.216077 | ||||||||
\(179\) | −329980. | −0.769760 | −0.384880 | − | 0.922967i | \(-0.625757\pi\) | ||||
−0.384880 | + | 0.922967i | \(0.625757\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 505810. | 1.14760 | 0.573800 | − | 0.818995i | \(-0.305469\pi\) | ||||
0.573800 | + | 0.818995i | \(0.305469\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 50633.5 | 0.110254 | ||||||||
\(185\) | −50374.3 | −0.108213 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −790578. | −1.65326 | ||||||||
\(188\) | 261186. | 0.538958 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 53050.6 | 0.106612 | ||||||||
\(191\) | 63835.6 | 0.126613 | 0.0633067 | − | 0.997994i | \(-0.479835\pi\) | ||||
0.0633067 | + | 0.997994i | \(0.479835\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 469355. | 0.907001 | 0.453501 | − | 0.891256i | \(-0.350175\pi\) | ||||
0.453501 | + | 0.891256i | \(0.350175\pi\) | |||||||
\(194\) | −16609.3 | −0.0316845 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −268021. | −0.492043 | −0.246021 | − | 0.969264i | \(-0.579123\pi\) | ||||
−0.246021 | + | 0.969264i | \(0.579123\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 605167. | 1.08328 | 0.541642 | − | 0.840609i | \(-0.317803\pi\) | ||||
0.541642 | + | 0.840609i | \(0.317803\pi\) | |||||||
\(200\) | −43240.3 | −0.0764388 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 131584. | 0.226894 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −51340.4 | −0.0853246 | ||||||||
\(206\) | 46965.1 | 0.0771094 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 633596. | 1.01544 | ||||||||
\(209\) | −1.04246e6 | −1.65080 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 335389. | 0.518612 | 0.259306 | − | 0.965795i | \(-0.416506\pi\) | ||||
0.259306 | + | 0.965795i | \(0.416506\pi\) | |||||||
\(212\) | 173712. | 0.265455 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −107435. | −0.160366 | ||||||||
\(215\) | −774367. | −1.14249 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 80697.7 | 0.115006 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −980081. | −1.36523 | ||||||||
\(221\) | 772240. | 1.06358 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1.02526e6 | −1.38061 | −0.690305 | − | 0.723518i | \(-0.742524\pi\) | ||||
−0.690305 | + | 0.723518i | \(0.742524\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −31305.8 | −0.0407713 | ||||||||
\(227\) | −504226. | −0.649473 | −0.324736 | − | 0.945805i | \(-0.605276\pi\) | ||||
−0.324736 | + | 0.945805i | \(0.605276\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.11939e6 | 1.41057 | 0.705283 | − | 0.708925i | \(-0.250820\pi\) | ||||
0.705283 | + | 0.708925i | \(0.250820\pi\) | |||||||
\(230\) | 37291.9 | 0.0464831 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −110307. | −0.134550 | ||||||||
\(233\) | −770703. | −0.930031 | −0.465015 | − | 0.885303i | \(-0.653951\pi\) | ||||
−0.465015 | + | 0.885303i | \(0.653951\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 387943. | 0.458245 | ||||||||
\(236\) | 447892. | 0.523472 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 171646. | 0.194374 | 0.0971871 | − | 0.995266i | \(-0.469015\pi\) | ||||
0.0971871 | + | 0.995266i | \(0.469015\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 383779. | 0.425637 | 0.212818 | − | 0.977092i | \(-0.431736\pi\) | ||||
0.212818 | + | 0.977092i | \(0.431736\pi\) | |||||||
\(242\) | −204926. | −0.224936 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −448028. | −0.481760 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.01828e6 | 1.06201 | ||||||||
\(248\) | 94278.3 | 0.0973380 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −137775. | −0.139418 | ||||||||
\(251\) | −1.57046e6 | −1.57342 | −0.786708 | − | 0.617325i | \(-0.788216\pi\) | ||||
−0.786708 | + | 0.617325i | \(0.788216\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −732801. | −0.719755 | ||||||||
\(254\) | 95311.4 | 0.0926959 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 880513. | 0.839723 | ||||||||
\(257\) | 790656. | 0.746715 | 0.373357 | − | 0.927688i | \(-0.378207\pi\) | ||||
0.373357 | + | 0.927688i | \(0.378207\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 957348. | 0.878287 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 253386. | 0.228049 | ||||||||
\(263\) | −464416. | −0.414017 | −0.207008 | − | 0.978339i | \(-0.566373\pi\) | ||||
−0.207008 | + | 0.978339i | \(0.566373\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 258017. | 0.225701 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −621001. | −0.528147 | ||||||||
\(269\) | 1.99959e6 | 1.68484 | 0.842422 | − | 0.538818i | \(-0.181129\pi\) | ||||
0.842422 | + | 0.538818i | \(0.181129\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.61296e6 | −1.33414 | −0.667070 | − | 0.744995i | \(-0.732452\pi\) | ||||
−0.667070 | + | 0.744995i | \(0.732452\pi\) | |||||||
\(272\) | 1.15580e6 | 0.947243 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 280197. | 0.225469 | ||||||||
\(275\) | 625801. | 0.499005 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −2.08119e6 | −1.62972 | −0.814860 | − | 0.579658i | \(-0.803186\pi\) | ||||
−0.814860 | + | 0.579658i | \(0.803186\pi\) | |||||||
\(278\) | 12536.2 | 0.00972865 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 982035. | 0.741927 | 0.370964 | − | 0.928647i | \(-0.379027\pi\) | ||||
0.370964 | + | 0.928647i | \(0.379027\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1.39622e6 | 1.03630 | 0.518152 | − | 0.855289i | \(-0.326620\pi\) | ||||
0.518152 | + | 0.855289i | \(0.326620\pi\) | |||||||
\(284\) | 2.03206e6 | 1.49500 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 314240. | 0.227167 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −11140.3 | −0.00784609 | ||||||||
\(290\) | −81241.7 | −0.0567262 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 899124. | 0.617110 | ||||||||
\(293\) | 2.56205e6 | 1.74348 | 0.871742 | − | 0.489965i | \(-0.162990\pi\) | ||||
0.871742 | + | 0.489965i | \(0.162990\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 665260. | 0.445078 | ||||||||
\(296\) | 49593.0 | 0.0328996 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −81333.0 | −0.0530550 | ||||||||
\(299\) | 715803. | 0.463037 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −22111.7 | −0.0139510 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 1.52405e6 | 0.945838 | ||||||||
\(305\) | −665463. | −0.409613 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 884855. | 0.535829 | 0.267915 | − | 0.963443i | \(-0.413666\pi\) | ||||
0.267915 | + | 0.963443i | \(0.413666\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 69436.5 | 0.0410378 | ||||||||
\(311\) | 1.80120e6 | 1.05599 | 0.527997 | − | 0.849246i | \(-0.322943\pi\) | ||||
0.527997 | + | 0.849246i | \(0.322943\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −950366. | −0.548315 | −0.274158 | − | 0.961685i | \(-0.588399\pi\) | ||||
−0.274158 | + | 0.961685i | \(0.588399\pi\) | |||||||
\(314\) | 379587. | 0.217264 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 964162. | 0.543166 | ||||||||
\(317\) | −3.04277e6 | −1.70068 | −0.850338 | − | 0.526237i | \(-0.823602\pi\) | ||||
−0.850338 | + | 0.526237i | \(0.823602\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.59643e6 | 0.878362 | ||||||||
\(320\) | 1.38293e6 | 0.754962 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.85755e6 | 0.990682 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −611286. | −0.321023 | ||||||||
\(326\) | 318780. | 0.166129 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 50544.1 | 0.0259409 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2.19616e6 | −1.10178 | −0.550889 | − | 0.834579i | \(-0.685711\pi\) | ||||
−0.550889 | + | 0.834579i | \(0.685711\pi\) | |||||||
\(332\) | 21274.9 | 0.0105931 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −202554. | −0.0993515 | ||||||||
\(335\) | −922382. | −0.449054 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −2.41491e6 | −1.15832 | −0.579158 | − | 0.815216i | \(-0.696618\pi\) | ||||
−0.579158 | + | 0.815216i | \(0.696618\pi\) | |||||||
\(338\) | −37732.5 | −0.0179648 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 1.74639e6 | 0.819302 | ||||||||
\(341\) | −1.36446e6 | −0.635438 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 762357. | 0.347346 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −72290.3 | −0.0324631 | ||||||||
\(347\) | 1.08833e6 | 0.485219 | 0.242609 | − | 0.970124i | \(-0.421997\pi\) | ||||
0.242609 | + | 0.970124i | \(0.421997\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −2.79267e6 | −1.22731 | −0.613657 | − | 0.789573i | \(-0.710302\pi\) | ||||
−0.613657 | + | 0.789573i | \(0.710302\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 1.45132e6 | 0.624317 | ||||||||
\(353\) | 2.53134e6 | 1.08122 | 0.540610 | − | 0.841273i | \(-0.318193\pi\) | ||||
0.540610 | + | 0.841273i | \(0.318193\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 3.01825e6 | 1.27111 | ||||||||
\(356\) | −3.96485e6 | −1.65807 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 239263. | 0.0986661 | ||||||||
\(359\) | −1.09028e6 | −0.446480 | −0.223240 | − | 0.974763i | \(-0.571663\pi\) | ||||
−0.223240 | + | 0.974763i | \(0.571663\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −26712.8 | −0.0107883 | ||||||||
\(362\) | −366754. | −0.147097 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1.33548e6 | 0.524694 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −188070. | −0.0728879 | −0.0364439 | − | 0.999336i | \(-0.511603\pi\) | ||||
−0.0364439 | + | 0.999336i | \(0.511603\pi\) | |||||||
\(368\) | 1.07133e6 | 0.412387 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 36525.6 | 0.0138705 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −1.79371e6 | −0.667545 | −0.333772 | − | 0.942654i | \(-0.608322\pi\) | ||||
−0.333772 | + | 0.942654i | \(0.608322\pi\) | |||||||
\(374\) | 573234. | 0.211911 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −381926. | −0.139319 | ||||||||
\(377\) | −1.55940e6 | −0.565073 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 3.58806e6 | 1.28310 | 0.641551 | − | 0.767080i | \(-0.278291\pi\) | ||||
0.641551 | + | 0.767080i | \(0.278291\pi\) | |||||||
\(380\) | 2.30281e6 | 0.818086 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −46286.1 | −0.0162290 | ||||||||
\(383\) | −3.42457e6 | −1.19291 | −0.596457 | − | 0.802645i | \(-0.703425\pi\) | ||||
−0.596457 | + | 0.802645i | \(0.703425\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −340321. | −0.116257 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −720974. | −0.243131 | ||||||||
\(389\) | −8625.27 | −0.00289001 | −0.00144500 | − | 0.999999i | \(-0.500460\pi\) | ||||
−0.00144500 | + | 0.999999i | \(0.500460\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.30576e6 | 0.431940 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 194337. | 0.0630690 | ||||||||
\(395\) | 1.43208e6 | 0.461823 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −1.25709e6 | −0.400306 | −0.200153 | − | 0.979765i | \(-0.564144\pi\) | ||||
−0.200153 | + | 0.979765i | \(0.564144\pi\) | |||||||
\(398\) | −438796. | −0.138853 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −914904. | −0.285908 | ||||||||
\(401\) | −1.42670e6 | −0.443070 | −0.221535 | − | 0.975152i | \(-0.571107\pi\) | ||||
−0.221535 | + | 0.975152i | \(0.571107\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.33281e6 | 0.408794 | ||||||||
\(404\) | 5.71176e6 | 1.74107 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −717741. | −0.214774 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 3.06529e6 | 0.906073 | 0.453036 | − | 0.891492i | \(-0.350341\pi\) | ||||
0.453036 | + | 0.891492i | \(0.350341\pi\) | |||||||
\(410\) | 37226.0 | 0.0109367 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 2.03865e6 | 0.591698 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 31599.9 | 0.00900670 | ||||||||
\(416\) | −1.41765e6 | −0.401640 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 755873. | 0.211596 | ||||||||
\(419\) | −248240. | −0.0690776 | −0.0345388 | − | 0.999403i | \(-0.510996\pi\) | ||||
−0.0345388 | + | 0.999403i | \(0.510996\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 5.96280e6 | 1.63963 | 0.819814 | − | 0.572630i | \(-0.194077\pi\) | ||||
0.819814 | + | 0.572630i | \(0.194077\pi\) | |||||||
\(422\) | −243185. | −0.0664746 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −254015. | −0.0686192 | ||||||||
\(425\) | −1.11510e6 | −0.299463 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −4.66353e6 | −1.23057 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 561481. | 0.146441 | ||||||||
\(431\) | 4.93538e6 | 1.27976 | 0.639879 | − | 0.768476i | \(-0.278985\pi\) | ||||
0.639879 | + | 0.768476i | \(0.278985\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −4.15513e6 | −1.06504 | −0.532519 | − | 0.846418i | \(-0.678755\pi\) | ||||
−0.532519 | + | 0.846418i | \(0.678755\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 3.50291e6 | 0.882496 | ||||||||
\(437\) | 1.72180e6 | 0.431299 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 227955. | 0.0564531 | 0.0282265 | − | 0.999602i | \(-0.491014\pi\) | ||||
0.0282265 | + | 0.999602i | \(0.491014\pi\) | |||||||
\(440\) | 1.43315e6 | 0.352907 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −559938. | −0.136328 | ||||||||
\(443\) | 1.98462e6 | 0.480472 | 0.240236 | − | 0.970715i | \(-0.422775\pi\) | ||||
0.240236 | + | 0.970715i | \(0.422775\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −5.88906e6 | −1.40976 | ||||||||
\(446\) | 743397. | 0.176963 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −2.61077e6 | −0.611157 | −0.305579 | − | 0.952167i | \(-0.598850\pi\) | ||||
−0.305579 | + | 0.952167i | \(0.598850\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −731506. | −0.169347 | ||||||||
\(452\) | −1.35892e6 | −0.312858 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 365606. | 0.0832480 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −4.09917e6 | −0.918132 | −0.459066 | − | 0.888402i | \(-0.651816\pi\) | ||||
−0.459066 | + | 0.888402i | \(0.651816\pi\) | |||||||
\(458\) | −811652. | −0.180803 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 1.61876e6 | 0.356687 | ||||||||
\(461\) | −2.62378e6 | −0.575009 | −0.287505 | − | 0.957779i | \(-0.592826\pi\) | ||||
−0.287505 | + | 0.957779i | \(0.592826\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −4.28563e6 | −0.929100 | −0.464550 | − | 0.885547i | \(-0.653784\pi\) | ||||
−0.464550 | + | 0.885547i | \(0.653784\pi\) | |||||||
\(464\) | −2.33394e6 | −0.503262 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 558824. | 0.119209 | ||||||||
\(467\) | 990118. | 0.210085 | 0.105042 | − | 0.994468i | \(-0.466502\pi\) | ||||
0.105042 | + | 0.994468i | \(0.466502\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −281291. | −0.0587369 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −654942. | −0.135316 | ||||||||
\(473\) | −1.10333e7 | −2.26753 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.47039e6 | −0.299019 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −124457. | −0.0249144 | ||||||||
\(479\) | 2.57976e6 | 0.513737 | 0.256868 | − | 0.966446i | \(-0.417309\pi\) | ||||
0.256868 | + | 0.966446i | \(0.417309\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 701093. | 0.138170 | ||||||||
\(482\) | −278272. | −0.0545571 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −8.89540e6 | −1.72604 | ||||||||
\(485\) | −1.07087e6 | −0.206720 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 3.21474e6 | 0.614219 | 0.307109 | − | 0.951674i | \(-0.400638\pi\) | ||||
0.307109 | + | 0.951674i | \(0.400638\pi\) | |||||||
\(488\) | 655141. | 0.124533 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 7.86108e6 | 1.47156 | 0.735781 | − | 0.677220i | \(-0.236815\pi\) | ||||
0.735781 | + | 0.677220i | \(0.236815\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −2.84465e6 | −0.527123 | ||||||||
\(494\) | −738341. | −0.136125 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 1.99480e6 | 0.364078 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −1.35382e6 | −0.243395 | −0.121697 | − | 0.992567i | \(-0.538834\pi\) | ||||
−0.121697 | + | 0.992567i | \(0.538834\pi\) | |||||||
\(500\) | −5.98051e6 | −1.06983 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 1.13872e6 | 0.201677 | ||||||||
\(503\) | 3.85775e6 | 0.679851 | 0.339926 | − | 0.940452i | \(-0.389598\pi\) | ||||
0.339926 | + | 0.940452i | \(0.389598\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 8.48376e6 | 1.48034 | ||||||||
\(506\) | 531341. | 0.0922565 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 4.13726e6 | 0.711301 | ||||||||
\(509\) | −1.06060e7 | −1.81451 | −0.907253 | − | 0.420585i | \(-0.861825\pi\) | ||||
−0.907253 | + | 0.420585i | \(0.861825\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −3.55598e6 | −0.599493 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −573291. | −0.0957122 | ||||||||
\(515\) | 3.02804e6 | 0.503087 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 5.52747e6 | 0.909495 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −1.39991e6 | −0.227034 | ||||||||
\(521\) | −9.17989e6 | −1.48164 | −0.740821 | − | 0.671703i | \(-0.765563\pi\) | ||||
−0.740821 | + | 0.671703i | \(0.765563\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −9.05585e6 | −1.44769 | −0.723844 | − | 0.689964i | \(-0.757627\pi\) | ||||
−0.723844 | + | 0.689964i | \(0.757627\pi\) | |||||||
\(524\) | 1.09989e7 | 1.74993 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 336740. | 0.0530677 | ||||||||
\(527\) | 2.43130e6 | 0.381339 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −5.22601e6 | −0.811953 | ||||||||
\(530\) | −187084. | −0.0289299 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 714539. | 0.108945 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −6.92681e6 | −1.04628 | ||||||||
\(536\) | 908075. | 0.136524 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −1.44987e6 | −0.215960 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1.21783e7 | 1.78894 | 0.894468 | − | 0.447132i | \(-0.147555\pi\) | ||||
0.894468 | + | 0.447132i | \(0.147555\pi\) | |||||||
\(542\) | 1.16953e6 | 0.171007 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −2.58608e6 | −0.374666 | ||||||||
\(545\) | 5.20292e6 | 0.750336 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −9.00451e6 | −1.28674 | −0.643372 | − | 0.765554i | \(-0.722465\pi\) | ||||
−0.643372 | + | 0.765554i | \(0.722465\pi\) | |||||||
\(548\) | 1.21627e7 | 1.73013 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −453758. | −0.0639613 | ||||||||
\(551\) | −3.75099e6 | −0.526341 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 1.50904e6 | 0.208894 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 544167. | 0.0746527 | ||||||||
\(557\) | −1.54461e6 | −0.210950 | −0.105475 | − | 0.994422i | \(-0.533636\pi\) | ||||
−0.105475 | + | 0.994422i | \(0.533636\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.07774e7 | 1.45876 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −712057. | −0.0950986 | ||||||||
\(563\) | −1.18748e7 | −1.57890 | −0.789449 | − | 0.613816i | \(-0.789634\pi\) | ||||
−0.789449 | + | 0.613816i | \(0.789634\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −2.01842e6 | −0.266005 | ||||||||
\(566\) | −1.01237e6 | −0.132831 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −2.97144e6 | −0.386452 | ||||||||
\(569\) | 1.54308e6 | 0.199806 | 0.0999031 | − | 0.994997i | \(-0.468147\pi\) | ||||
0.0999031 | + | 0.994997i | \(0.468147\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −7.01812e6 | −0.900804 | −0.450402 | − | 0.892826i | \(-0.648719\pi\) | ||||
−0.450402 | + | 0.892826i | \(0.648719\pi\) | |||||||
\(572\) | 1.36404e7 | 1.74317 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1.03361e6 | −0.130373 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 5.37543e6 | 0.672162 | 0.336081 | − | 0.941833i | \(-0.390898\pi\) | ||||
0.336081 | + | 0.941833i | \(0.390898\pi\) | |||||||
\(578\) | 8077.66 | 0.00100569 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −3.52652e6 | −0.435288 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 3.67627e6 | 0.447957 | ||||||||
\(584\) | −1.31477e6 | −0.159521 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −1.85770e6 | −0.223476 | ||||||||
\(587\) | −2.06682e6 | −0.247575 | −0.123788 | − | 0.992309i | \(-0.539504\pi\) | ||||
−0.123788 | + | 0.992309i | \(0.539504\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 3.20594e6 | 0.380774 | ||||||||
\(590\) | −482369. | −0.0570492 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 1.04932e6 | 0.123056 | ||||||||
\(593\) | −5.46947e6 | −0.638717 | −0.319358 | − | 0.947634i | \(-0.603467\pi\) | ||||
−0.319358 | + | 0.947634i | \(0.603467\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −3.53049e6 | −0.407117 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −519016. | −0.0593510 | ||||||||
\(599\) | −1.09943e7 | −1.25199 | −0.625996 | − | 0.779826i | \(-0.715307\pi\) | ||||
−0.625996 | + | 0.779826i | \(0.715307\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1.58788e7 | −1.79322 | −0.896608 | − | 0.442826i | \(-0.853976\pi\) | ||||
−0.896608 | + | 0.442826i | \(0.853976\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −959820. | −0.107053 | ||||||||
\(605\) | −1.32125e7 | −1.46756 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −5.33262e6 | −0.587447 | −0.293724 | − | 0.955890i | \(-0.594895\pi\) | ||||
−0.293724 | + | 0.955890i | \(0.594895\pi\) | |||||||
\(608\) | −3.41003e6 | −0.374110 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 482516. | 0.0525033 | ||||||||
\(611\) | −5.39926e6 | −0.585102 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −8.91838e6 | −0.958594 | −0.479297 | − | 0.877653i | \(-0.659108\pi\) | ||||
−0.479297 | + | 0.877653i | \(0.659108\pi\) | |||||||
\(614\) | −641593. | −0.0686814 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −9.63586e6 | −1.01901 | −0.509504 | − | 0.860468i | \(-0.670171\pi\) | ||||
−0.509504 | + | 0.860468i | \(0.670171\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −1.21747e7 | −1.27712 | −0.638560 | − | 0.769572i | \(-0.720470\pi\) | ||||
−0.638560 | + | 0.769572i | \(0.720470\pi\) | |||||||
\(620\) | 3.01409e6 | 0.314903 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −1.30602e6 | −0.135355 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −5.94695e6 | −0.608968 | ||||||||
\(626\) | 689094. | 0.0702818 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 1.64770e7 | 1.66717 | ||||||||
\(629\) | 1.27893e6 | 0.128890 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.30854e7 | −1.30832 | −0.654161 | − | 0.756356i | \(-0.726978\pi\) | ||||
−0.654161 | + | 0.756356i | \(0.726978\pi\) | |||||||
\(632\) | −1.40987e6 | −0.140407 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 2.20626e6 | 0.217989 | ||||||||
\(635\) | 6.14513e6 | 0.604779 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −1.15754e6 | −0.112586 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −4.26226e6 | −0.411329 | ||||||||
\(641\) | 441107. | 0.0424032 | 0.0212016 | − | 0.999775i | \(-0.493251\pi\) | ||||
0.0212016 | + | 0.999775i | \(0.493251\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 4.18888e6 | 0.399550 | 0.199775 | − | 0.979842i | \(-0.435979\pi\) | ||||
0.199775 | + | 0.979842i | \(0.435979\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −1.34688e6 | −0.126983 | ||||||||
\(647\) | 1.87822e7 | 1.76395 | 0.881973 | − | 0.471300i | \(-0.156215\pi\) | ||||
0.881973 | + | 0.471300i | \(0.156215\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 9.47874e6 | 0.883362 | ||||||||
\(650\) | 443233. | 0.0411480 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 1.38375e7 | 1.27479 | ||||||||
\(653\) | 1.51733e6 | 0.139251 | 0.0696254 | − | 0.997573i | \(-0.477820\pi\) | ||||
0.0696254 | + | 0.997573i | \(0.477820\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1.63368e7 | 1.48787 | ||||||||
\(656\) | 1.06944e6 | 0.0970281 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −1.84809e7 | −1.65772 | −0.828859 | − | 0.559458i | \(-0.811009\pi\) | ||||
−0.828859 | + | 0.559458i | \(0.811009\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.03952e7 | 0.925403 | 0.462702 | − | 0.886514i | \(-0.346880\pi\) | ||||
0.462702 | + | 0.886514i | \(0.346880\pi\) | |||||||
\(662\) | 1.59240e6 | 0.141223 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −31109.8 | −0.00273828 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −2.63676e6 | −0.229486 | ||||||||
\(668\) | −8.79242e6 | −0.762372 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 668803. | 0.0575587 | ||||||||
\(671\) | −9.48162e6 | −0.812973 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1.10398e7 | −0.939556 | −0.469778 | − | 0.882785i | \(-0.655666\pi\) | ||||
−0.469778 | + | 0.882785i | \(0.655666\pi\) | |||||||
\(674\) | 1.75101e6 | 0.148470 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −1.63788e6 | −0.137853 | ||||||||
\(677\) | −8.23485e6 | −0.690532 | −0.345266 | − | 0.938505i | \(-0.612211\pi\) | ||||
−0.345266 | + | 0.938505i | \(0.612211\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −2.55371e6 | −0.211787 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 989343. | 0.0814490 | ||||||||
\(683\) | −1.98437e7 | −1.62768 | −0.813842 | − | 0.581086i | \(-0.802628\pi\) | ||||
−0.813842 | + | 0.581086i | \(0.802628\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1.80655e7 | 1.47103 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 1.61304e7 | 1.29919 | ||||||||
\(689\) | −3.59100e6 | −0.288182 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 2.37019e6 | 0.188837 | 0.0944185 | − | 0.995533i | \(-0.469901\pi\) | ||||
0.0944185 | + | 0.995533i | \(0.469901\pi\) | |||||||
\(692\) | −3.13796e6 | −0.249105 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −789131. | −0.0621943 | ||||||||
\(695\) | 808259. | 0.0634730 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.30346e6 | 0.101628 | ||||||||
\(698\) | 2.02491e6 | 0.157314 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1.56833e7 | 1.20543 | 0.602714 | − | 0.797957i | \(-0.294086\pi\) | ||||
0.602714 | + | 0.797957i | \(0.294086\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.68641e6 | 0.128699 | ||||||||
\(704\) | 1.97042e7 | 1.49840 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −1.83543e6 | −0.138588 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 3.68544e6 | 0.275343 | 0.137671 | − | 0.990478i | \(-0.456038\pi\) | ||||
0.137671 | + | 0.990478i | \(0.456038\pi\) | |||||||
\(710\) | −2.18848e6 | −0.162928 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 5.79772e6 | 0.428605 | ||||||||
\(713\) | 2.25361e6 | 0.166018 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2.02604e7 | 1.48212 | ||||||||
\(716\) | 1.03859e7 | 0.757113 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 790544. | 0.0572289 | ||||||||
\(719\) | −1.56427e7 | −1.12847 | −0.564233 | − | 0.825615i | \(-0.690828\pi\) | ||||
−0.564233 | + | 0.825615i | \(0.690828\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 19369.0 | 0.00138282 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −1.59200e7 | −1.12875 | ||||||||
\(725\) | 2.25175e6 | 0.159102 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −1.85908e7 | −1.30456 | −0.652279 | − | 0.757979i | \(-0.726187\pi\) | ||||
−0.652279 | + | 0.757979i | \(0.726187\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −968335. | −0.0672541 | ||||||||
\(731\) | 1.96601e7 | 1.36079 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −2.49466e7 | −1.71495 | −0.857476 | − | 0.514524i | \(-0.827969\pi\) | ||||
−0.857476 | + | 0.514524i | \(0.827969\pi\) | |||||||
\(734\) | 136367. | 0.00934260 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −2.39708e6 | −0.163113 | ||||||||
\(737\) | −1.31422e7 | −0.891253 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −2.42944e7 | −1.63642 | −0.818211 | − | 0.574918i | \(-0.805034\pi\) | ||||
−0.818211 | + | 0.574918i | \(0.805034\pi\) | |||||||
\(740\) | 1.58549e6 | 0.106435 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −4.16541e6 | −0.276812 | −0.138406 | − | 0.990376i | \(-0.544198\pi\) | ||||
−0.138406 | + | 0.990376i | \(0.544198\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −5.24388e6 | −0.346148 | ||||||||
\(746\) | 1.30059e6 | 0.0855644 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 2.48828e7 | 1.62610 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −2.36434e7 | −1.52972 | −0.764858 | − | 0.644199i | \(-0.777191\pi\) | ||||
−0.764858 | + | 0.644199i | \(0.777191\pi\) | |||||||
\(752\) | −8.08101e6 | −0.521100 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 1.13070e6 | 0.0724298 | ||||||||
\(755\) | −1.42564e6 | −0.0910209 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1.50108e7 | 0.952062 | 0.476031 | − | 0.879429i | \(-0.342075\pi\) | ||||
0.476031 | + | 0.879429i | \(0.342075\pi\) | |||||||
\(758\) | −2.60164e6 | −0.164465 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −3.36735e6 | −0.211472 | ||||||||
\(761\) | 2.92191e6 | 0.182897 | 0.0914483 | − | 0.995810i | \(-0.470850\pi\) | ||||
0.0914483 | + | 0.995810i | \(0.470850\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −2.00918e6 | −0.124533 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 2.48310e6 | 0.152905 | ||||||||
\(767\) | −9.25887e6 | −0.568290 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −1.42847e7 | −0.871073 | −0.435536 | − | 0.900171i | \(-0.643441\pi\) | ||||
−0.435536 | + | 0.900171i | \(0.643441\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −1.47726e7 | −0.892100 | ||||||||
\(773\) | −1.09012e7 | −0.656186 | −0.328093 | − | 0.944645i | \(-0.606406\pi\) | ||||
−0.328093 | + | 0.944645i | \(0.606406\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1.92455e6 | −0.115100 | ||||||||
\(776\) | 1.05426e6 | 0.0628485 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 6254.04 | 0.000370434 0 | ||||||||
\(779\) | 1.71875e6 | 0.101478 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 4.30045e7 | 2.52282 | ||||||||
\(782\) | −946787. | −0.0553650 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 2.44736e7 | 1.41750 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 2.56449e7 | 1.47593 | 0.737963 | − | 0.674841i | \(-0.235788\pi\) | ||||
0.737963 | + | 0.674841i | \(0.235788\pi\) | |||||||
\(788\) | 8.43576e6 | 0.483959 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −1.03838e6 | −0.0591955 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 9.26169e6 | 0.523007 | ||||||||
\(794\) | 911498. | 0.0513103 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −1.90472e7 | −1.06549 | ||||||||
\(797\) | 7.73086e6 | 0.431104 | 0.215552 | − | 0.976492i | \(-0.430845\pi\) | ||||
0.215552 | + | 0.976492i | \(0.430845\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −9.84931e6 | −0.545807 | ||||||||
\(800\) | 2.04707e6 | 0.113086 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 1.03448e6 | 0.0567917 | ||||||||
\(803\) | 1.90282e7 | 1.04138 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −966395. | −0.0523983 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −8.35218e6 | −0.450061 | ||||||||
\(809\) | 1.87811e7 | 1.00890 | 0.504452 | − | 0.863440i | \(-0.331695\pi\) | ||||
0.504452 | + | 0.863440i | \(0.331695\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 9.00729e6 | 0.480886 | 0.240443 | − | 0.970663i | \(-0.422707\pi\) | ||||
0.240443 | + | 0.970663i | \(0.422707\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 520422. | 0.0275293 | ||||||||
\(815\) | 2.05531e7 | 1.08388 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2.59240e7 | 1.35877 | ||||||||
\(818\) | −2.22259e6 | −0.116138 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 1.61590e6 | 0.0839228 | ||||||||
\(821\) | 9.27965e6 | 0.480478 | 0.240239 | − | 0.970714i | \(-0.422774\pi\) | ||||
0.240239 | + | 0.970714i | \(0.422774\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1.08308e7 | −0.557393 | −0.278697 | − | 0.960379i | \(-0.589902\pi\) | ||||
−0.278697 | + | 0.960379i | \(0.589902\pi\) | |||||||
\(824\) | −2.98107e6 | −0.152952 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 2.05230e7 | 1.04346 | 0.521731 | − | 0.853110i | \(-0.325286\pi\) | ||||
0.521731 | + | 0.853110i | \(0.325286\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1.42216e7 | 0.718724 | 0.359362 | − | 0.933198i | \(-0.382994\pi\) | ||||
0.359362 | + | 0.933198i | \(0.382994\pi\) | |||||||
\(830\) | −22912.6 | −0.00115446 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −1.92472e7 | −0.963958 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1.30595e7 | −0.648202 | ||||||||
\(836\) | 3.28108e7 | 1.62368 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 179995. | 0.00885421 | ||||||||
\(839\) | −9.29934e6 | −0.456087 | −0.228043 | − | 0.973651i | \(-0.573233\pi\) | ||||
−0.228043 | + | 0.973651i | \(0.573233\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.47669e7 | −0.719944 | ||||||||
\(842\) | −4.32353e6 | −0.210164 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −1.05561e7 | −0.510092 | ||||||||
\(845\) | −2.43277e6 | −0.117209 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −5.37461e6 | −0.256659 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 808543. | 0.0383845 | ||||||||
\(851\) | 1.18546e6 | 0.0561131 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 3.07436e6 | 0.144671 | 0.0723357 | − | 0.997380i | \(-0.476955\pi\) | ||||
0.0723357 | + | 0.997380i | \(0.476955\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 6.81938e6 | 0.318098 | ||||||||
\(857\) | 3.45835e7 | 1.60848 | 0.804242 | − | 0.594302i | \(-0.202572\pi\) | ||||
0.804242 | + | 0.594302i | \(0.202572\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1.63022e7 | −0.753814 | −0.376907 | − | 0.926251i | \(-0.623012\pi\) | ||||
−0.376907 | + | 0.926251i | \(0.623012\pi\) | |||||||
\(860\) | 2.43726e7 | 1.12372 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −3.57856e6 | −0.164036 | ||||||||
\(863\) | −2.56962e7 | −1.17447 | −0.587235 | − | 0.809416i | \(-0.699784\pi\) | ||||
−0.587235 | + | 0.809416i | \(0.699784\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −4.66087e6 | −0.211800 | ||||||||
\(866\) | 3.01281e6 | 0.136514 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 2.04046e7 | 0.916596 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.28374e7 | 0.573366 | ||||||||
\(872\) | −5.12222e6 | −0.228122 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −1.24844e6 | −0.0552829 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 3.30060e7 | 1.44908 | 0.724542 | − | 0.689230i | \(-0.242051\pi\) | ||||
0.724542 | + | 0.689230i | \(0.242051\pi\) | |||||||
\(878\) | −165286. | −0.00723603 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 3.03235e7 | 1.31999 | ||||||||
\(881\) | 2.26705e6 | 0.0984060 | 0.0492030 | − | 0.998789i | \(-0.484332\pi\) | ||||
0.0492030 | + | 0.998789i | \(0.484332\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1.97779e7 | 0.853649 | 0.426825 | − | 0.904334i | \(-0.359632\pi\) | ||||
0.426825 | + | 0.904334i | \(0.359632\pi\) | |||||||
\(884\) | −2.43057e7 | −1.04611 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −1.43901e6 | −0.0615858 | ||||||||
\(887\) | −36468.3 | −0.00155635 | −0.000778173 | − | 1.00000i | \(-0.500248\pi\) | ||||
−0.000778173 | 1.00000i | \(0.500248\pi\) | ||||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 4.27005e6 | 0.180700 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 3.22692e7 | 1.35793 | ||||||||
\(893\) | −1.29874e7 | −0.544997 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1.54263e7 | 0.643730 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 1.89303e6 | 0.0783367 | ||||||||
\(899\) | −4.90958e6 | −0.202602 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −6.55068e6 | −0.268828 | ||||||||
\(902\) | 530403. | 0.0217065 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 1.98711e6 | 0.0808727 | ||||||||
\(905\) | −2.36462e7 | −0.959709 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1.62298e7 | 0.655079 | 0.327540 | − | 0.944837i | \(-0.393781\pi\) | ||||
0.327540 | + | 0.944837i | \(0.393781\pi\) | |||||||
\(908\) | 1.58702e7 | 0.638802 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 2.61699e7 | 1.04474 | 0.522368 | − | 0.852720i | \(-0.325049\pi\) | ||||
0.522368 | + | 0.852720i | \(0.325049\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 450241. | 0.0178759 | ||||||||
\(914\) | 2.97224e6 | 0.117684 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −3.52320e7 | −1.38739 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 4.05973e6 | 0.158565 | 0.0792826 | − | 0.996852i | \(-0.474737\pi\) | ||||
0.0792826 | + | 0.996852i | \(0.474737\pi\) | |||||||
\(920\) | −2.36708e6 | −0.0922025 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 1.90246e6 | 0.0737034 | ||||||||
\(923\) | −4.20070e7 | −1.62300 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.01237e6 | −0.0389031 | ||||||||
\(926\) | 3.10744e6 | 0.119090 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 5.22212e6 | 0.199057 | ||||||||
\(929\) | 3.69518e6 | 0.140474 | 0.0702370 | − | 0.997530i | \(-0.477624\pi\) | ||||
0.0702370 | + | 0.997530i | \(0.477624\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 2.42573e7 | 0.914751 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −717918. | −0.0269282 | ||||||||
\(935\) | 3.69589e7 | 1.38258 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1.91384e7 | 0.712126 | 0.356063 | − | 0.934462i | \(-0.384119\pi\) | ||||
0.356063 | + | 0.934462i | \(0.384119\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −1.22102e7 | −0.450717 | ||||||||
\(941\) | 1.20954e7 | 0.445294 | 0.222647 | − | 0.974899i | \(-0.428530\pi\) | ||||
0.222647 | + | 0.974899i | \(0.428530\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1.20820e6 | 0.0442445 | ||||||||
\(944\) | −1.38577e7 | −0.506127 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 8.00007e6 | 0.290647 | ||||||||
\(947\) | 1.95969e7 | 0.710087 | 0.355044 | − | 0.934850i | \(-0.384466\pi\) | ||||
0.355044 | + | 0.934850i | \(0.384466\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1.85868e7 | −0.669945 | ||||||||
\(950\) | 1.06615e6 | 0.0383275 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −4.23265e7 | −1.50966 | −0.754832 | − | 0.655918i | \(-0.772282\pi\) | ||||
−0.754832 | + | 0.655918i | \(0.772282\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −2.98426e6 | −0.105884 | ||||||||
\(956\) | −5.40243e6 | −0.191181 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −1.87054e6 | −0.0658496 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.44330e7 | −0.853430 | ||||||||
\(962\) | −508351. | −0.0177103 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −1.20792e7 | −0.418644 | ||||||||
\(965\) | −2.19419e7 | −0.758502 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1.39211e6 | 0.0478749 | 0.0239375 | − | 0.999713i | \(-0.492380\pi\) | ||||
0.0239375 | + | 0.999713i | \(0.492380\pi\) | |||||||
\(968\) | 1.30075e7 | 0.446176 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 776471. | 0.0264970 | ||||||||
\(971\) | 4.41877e7 | 1.50402 | 0.752009 | − | 0.659153i | \(-0.229085\pi\) | ||||
0.752009 | + | 0.659153i | \(0.229085\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −2.33095e6 | −0.0787292 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 1.38619e7 | 0.465798 | ||||||||
\(977\) | 5.60457e7 | 1.87848 | 0.939239 | − | 0.343264i | \(-0.111533\pi\) | ||||
0.939239 | + | 0.343264i | \(0.111533\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −8.39082e7 | −2.79800 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −5.69993e6 | −0.188621 | ||||||||
\(983\) | −5.00560e7 | −1.65224 | −0.826118 | − | 0.563497i | \(-0.809456\pi\) | ||||
−0.826118 | + | 0.563497i | \(0.809456\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1.25298e7 | 0.411483 | ||||||||
\(986\) | 2.06261e6 | 0.0675654 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −3.20497e7 | −1.04456 | ||||||||
\(989\) | 1.82233e7 | 0.592428 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1.59116e7 | 0.514670 | 0.257335 | − | 0.966322i | \(-0.417156\pi\) | ||||
0.257335 | + | 0.966322i | \(0.417156\pi\) | |||||||
\(992\) | −4.46330e6 | −0.144005 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −2.82911e7 | −0.905924 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −4.25995e7 | −1.35727 | −0.678635 | − | 0.734476i | \(-0.737428\pi\) | ||||
−0.678635 | + | 0.734476i | \(0.737428\pi\) | |||||||
\(998\) | 981634. | 0.0311978 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 441.6.a.l.1.2 | 2 | ||
3.2 | odd | 2 | 49.6.a.f.1.1 | 2 | |||
7.6 | odd | 2 | 63.6.a.f.1.2 | 2 | |||
12.11 | even | 2 | 784.6.a.v.1.2 | 2 | |||
21.2 | odd | 6 | 49.6.c.d.18.2 | 4 | |||
21.5 | even | 6 | 49.6.c.e.18.2 | 4 | |||
21.11 | odd | 6 | 49.6.c.d.30.2 | 4 | |||
21.17 | even | 6 | 49.6.c.e.30.2 | 4 | |||
21.20 | even | 2 | 7.6.a.b.1.1 | ✓ | 2 | ||
28.27 | even | 2 | 1008.6.a.bq.1.2 | 2 | |||
84.83 | odd | 2 | 112.6.a.h.1.1 | 2 | |||
105.62 | odd | 4 | 175.6.b.c.99.3 | 4 | |||
105.83 | odd | 4 | 175.6.b.c.99.2 | 4 | |||
105.104 | even | 2 | 175.6.a.c.1.2 | 2 | |||
168.83 | odd | 2 | 448.6.a.u.1.2 | 2 | |||
168.125 | even | 2 | 448.6.a.w.1.1 | 2 | |||
231.230 | odd | 2 | 847.6.a.c.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
7.6.a.b.1.1 | ✓ | 2 | 21.20 | even | 2 | ||
49.6.a.f.1.1 | 2 | 3.2 | odd | 2 | |||
49.6.c.d.18.2 | 4 | 21.2 | odd | 6 | |||
49.6.c.d.30.2 | 4 | 21.11 | odd | 6 | |||
49.6.c.e.18.2 | 4 | 21.5 | even | 6 | |||
49.6.c.e.30.2 | 4 | 21.17 | even | 6 | |||
63.6.a.f.1.2 | 2 | 7.6 | odd | 2 | |||
112.6.a.h.1.1 | 2 | 84.83 | odd | 2 | |||
175.6.a.c.1.2 | 2 | 105.104 | even | 2 | |||
175.6.b.c.99.2 | 4 | 105.83 | odd | 4 | |||
175.6.b.c.99.3 | 4 | 105.62 | odd | 4 | |||
441.6.a.l.1.2 | 2 | 1.1 | even | 1 | trivial | ||
448.6.a.u.1.2 | 2 | 168.83 | odd | 2 | |||
448.6.a.w.1.1 | 2 | 168.125 | even | 2 | |||
784.6.a.v.1.2 | 2 | 12.11 | even | 2 | |||
847.6.a.c.1.2 | 2 | 231.230 | odd | 2 | |||
1008.6.a.bq.1.2 | 2 | 28.27 | even | 2 |