Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [25,6,Mod(1,25)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(25, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("25.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 25 = 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 25.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: | \(4.00959549532\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{241}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 60 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(8.26209\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 25.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −5.26209 | −0.930214 | −0.465107 | − | 0.885254i | \(-0.653984\pi\) | ||||
−0.465107 | + | 0.885254i | \(0.653984\pi\) | |||||||
\(3\) | 25.5242 | 1.63738 | 0.818688 | − | 0.574238i | \(-0.194702\pi\) | ||||
0.818688 | + | 0.574238i | \(0.194702\pi\) | |||||||
\(4\) | −4.31044 | −0.134701 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −134.310 | −1.52311 | ||||||||
\(7\) | 131.048 | 1.01085 | 0.505425 | − | 0.862871i | \(-0.331336\pi\) | ||||
0.505425 | + | 0.862871i | \(0.331336\pi\) | |||||||
\(8\) | 191.069 | 1.05552 | ||||||||
\(9\) | 408.483 | 1.68100 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 290.104 | 0.722891 | 0.361445 | − | 0.932393i | \(-0.382283\pi\) | ||||
0.361445 | + | 0.932393i | \(0.382283\pi\) | |||||||
\(12\) | −110.020 | −0.220557 | ||||||||
\(13\) | 68.3868 | 0.112231 | 0.0561156 | − | 0.998424i | \(-0.482128\pi\) | ||||
0.0561156 | + | 0.998424i | \(0.482128\pi\) | |||||||
\(14\) | −689.588 | −0.940307 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −867.486 | −0.847154 | ||||||||
\(17\) | −310.644 | −0.260700 | −0.130350 | − | 0.991468i | \(-0.541610\pi\) | ||||
−0.130350 | + | 0.991468i | \(0.541610\pi\) | |||||||
\(18\) | −2149.48 | −1.56369 | ||||||||
\(19\) | −2133.35 | −1.35574 | −0.677871 | − | 0.735180i | \(-0.737097\pi\) | ||||
−0.677871 | + | 0.735180i | \(0.737097\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 3344.90 | 1.65514 | ||||||||
\(22\) | −1526.55 | −0.672443 | ||||||||
\(23\) | 873.145 | 0.344165 | 0.172083 | − | 0.985083i | \(-0.444950\pi\) | ||||
0.172083 | + | 0.985083i | \(0.444950\pi\) | |||||||
\(24\) | 4876.87 | 1.72828 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −359.857 | −0.104399 | ||||||||
\(27\) | 4223.83 | 1.11506 | ||||||||
\(28\) | −564.876 | −0.136163 | ||||||||
\(29\) | −2580.97 | −0.569885 | −0.284943 | − | 0.958545i | \(-0.591975\pi\) | ||||
−0.284943 | + | 0.958545i | \(0.591975\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −9086.30 | −1.69818 | −0.849088 | − | 0.528252i | \(-0.822848\pi\) | ||||
−0.849088 | + | 0.528252i | \(0.822848\pi\) | |||||||
\(32\) | −1549.41 | −0.267480 | ||||||||
\(33\) | 7404.67 | 1.18364 | ||||||||
\(34\) | 1634.64 | 0.242507 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −1760.74 | −0.226433 | ||||||||
\(37\) | 3990.64 | 0.479224 | 0.239612 | − | 0.970869i | \(-0.422980\pi\) | ||||
0.239612 | + | 0.970869i | \(0.422980\pi\) | |||||||
\(38\) | 11225.9 | 1.26113 | ||||||||
\(39\) | 1745.52 | 0.183765 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 16981.8 | 1.57770 | 0.788851 | − | 0.614584i | \(-0.210676\pi\) | ||||
0.788851 | + | 0.614584i | \(0.210676\pi\) | |||||||
\(42\) | −17601.2 | −1.53964 | ||||||||
\(43\) | −18017.7 | −1.48603 | −0.743017 | − | 0.669273i | \(-0.766606\pi\) | ||||
−0.743017 | + | 0.669273i | \(0.766606\pi\) | |||||||
\(44\) | −1250.48 | −0.0973742 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −4594.57 | −0.320147 | ||||||||
\(47\) | 24864.7 | 1.64187 | 0.820933 | − | 0.571024i | \(-0.193454\pi\) | ||||
0.820933 | + | 0.571024i | \(0.193454\pi\) | |||||||
\(48\) | −22141.9 | −1.38711 | ||||||||
\(49\) | 366.670 | 0.0218165 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −7928.93 | −0.426864 | ||||||||
\(52\) | −294.777 | −0.0151177 | ||||||||
\(53\) | −7652.91 | −0.374229 | −0.187114 | − | 0.982338i | \(-0.559913\pi\) | ||||
−0.187114 | + | 0.982338i | \(0.559913\pi\) | |||||||
\(54\) | −22226.2 | −1.03724 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 25039.2 | 1.06697 | ||||||||
\(57\) | −54451.9 | −2.21986 | ||||||||
\(58\) | 13581.3 | 0.530116 | ||||||||
\(59\) | −9233.69 | −0.345339 | −0.172669 | − | 0.984980i | \(-0.555239\pi\) | ||||
−0.172669 | + | 0.984980i | \(0.555239\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3326.17 | 0.114451 | 0.0572256 | − | 0.998361i | \(-0.481775\pi\) | ||||
0.0572256 | + | 0.998361i | \(0.481775\pi\) | |||||||
\(62\) | 47812.9 | 1.57967 | ||||||||
\(63\) | 53531.1 | 1.69924 | ||||||||
\(64\) | 35912.7 | 1.09597 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −38964.0 | −1.10104 | ||||||||
\(67\) | −32340.7 | −0.880161 | −0.440080 | − | 0.897958i | \(-0.645050\pi\) | ||||
−0.440080 | + | 0.897958i | \(0.645050\pi\) | |||||||
\(68\) | 1339.01 | 0.0351165 | ||||||||
\(69\) | 22286.3 | 0.563528 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −35885.9 | −0.844847 | −0.422424 | − | 0.906399i | \(-0.638821\pi\) | ||||
−0.422424 | + | 0.906399i | \(0.638821\pi\) | |||||||
\(72\) | 78048.4 | 1.77432 | ||||||||
\(73\) | −26513.6 | −0.582319 | −0.291159 | − | 0.956675i | \(-0.594041\pi\) | ||||
−0.291159 | + | 0.956675i | \(0.594041\pi\) | |||||||
\(74\) | −20999.1 | −0.445781 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 9195.65 | 0.182620 | ||||||||
\(77\) | 38017.7 | 0.730733 | ||||||||
\(78\) | −9185.06 | −0.170941 | ||||||||
\(79\) | 71705.7 | 1.29266 | 0.646332 | − | 0.763056i | \(-0.276302\pi\) | ||||
0.646332 | + | 0.763056i | \(0.276302\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 8548.28 | 0.144766 | ||||||||
\(82\) | −89359.9 | −1.46760 | ||||||||
\(83\) | 39630.1 | 0.631437 | 0.315719 | − | 0.948853i | \(-0.397754\pi\) | ||||
0.315719 | + | 0.948853i | \(0.397754\pi\) | |||||||
\(84\) | −14418.0 | −0.222949 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 94810.8 | 1.38233 | ||||||||
\(87\) | −65877.1 | −0.933117 | ||||||||
\(88\) | 55429.9 | 0.763022 | ||||||||
\(89\) | −117441. | −1.57161 | −0.785806 | − | 0.618473i | \(-0.787752\pi\) | ||||
−0.785806 | + | 0.618473i | \(0.787752\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 8961.98 | 0.113449 | ||||||||
\(92\) | −3763.64 | −0.0463594 | ||||||||
\(93\) | −231920. | −2.78055 | ||||||||
\(94\) | −130840. | −1.52729 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −39547.4 | −0.437966 | ||||||||
\(97\) | 21878.3 | 0.236093 | 0.118047 | − | 0.993008i | \(-0.462337\pi\) | ||||
0.118047 | + | 0.993008i | \(0.462337\pi\) | |||||||
\(98\) | −1929.45 | −0.0202940 | ||||||||
\(99\) | 118503. | 1.21518 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −75072.1 | −0.732276 | −0.366138 | − | 0.930561i | \(-0.619320\pi\) | ||||
−0.366138 | + | 0.930561i | \(0.619320\pi\) | |||||||
\(102\) | 41722.7 | 0.397075 | ||||||||
\(103\) | 47928.6 | 0.445145 | 0.222573 | − | 0.974916i | \(-0.428555\pi\) | ||||
0.222573 | + | 0.974916i | \(0.428555\pi\) | |||||||
\(104\) | 13066.6 | 0.118462 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 40270.3 | 0.348113 | ||||||||
\(107\) | 92012.3 | 0.776938 | 0.388469 | − | 0.921462i | \(-0.373004\pi\) | ||||
0.388469 | + | 0.921462i | \(0.373004\pi\) | |||||||
\(108\) | −18206.6 | −0.150199 | ||||||||
\(109\) | −10647.5 | −0.0858387 | −0.0429194 | − | 0.999079i | \(-0.513666\pi\) | ||||
−0.0429194 | + | 0.999079i | \(0.513666\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 101858. | 0.784670 | ||||||||
\(112\) | −113683. | −0.856346 | ||||||||
\(113\) | 87373.9 | 0.643703 | 0.321852 | − | 0.946790i | \(-0.395695\pi\) | ||||
0.321852 | + | 0.946790i | \(0.395695\pi\) | |||||||
\(114\) | 286531. | 2.06495 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 11125.1 | 0.0767642 | ||||||||
\(117\) | 27934.9 | 0.188661 | ||||||||
\(118\) | 48588.5 | 0.321239 | ||||||||
\(119\) | −40709.4 | −0.263528 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −76890.5 | −0.477429 | ||||||||
\(122\) | −17502.6 | −0.106464 | ||||||||
\(123\) | 433447. | 2.58329 | ||||||||
\(124\) | 39165.9 | 0.228746 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −281685. | −1.58066 | ||||||||
\(127\) | 197379. | 1.08591 | 0.542953 | − | 0.839763i | \(-0.317306\pi\) | ||||
0.542953 | + | 0.839763i | \(0.317306\pi\) | |||||||
\(128\) | −139395. | −0.752005 | ||||||||
\(129\) | −459887. | −2.43320 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −118490. | −0.603258 | −0.301629 | − | 0.953425i | \(-0.597530\pi\) | ||||
−0.301629 | + | 0.953425i | \(0.597530\pi\) | |||||||
\(132\) | −31917.4 | −0.159438 | ||||||||
\(133\) | −279571. | −1.37045 | ||||||||
\(134\) | 170179. | 0.818738 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −59354.3 | −0.275173 | ||||||||
\(137\) | −302570. | −1.37728 | −0.688642 | − | 0.725101i | \(-0.741793\pi\) | ||||
−0.688642 | + | 0.725101i | \(0.741793\pi\) | |||||||
\(138\) | −117272. | −0.524202 | ||||||||
\(139\) | 157190. | 0.690062 | 0.345031 | − | 0.938591i | \(-0.387868\pi\) | ||||
0.345031 | + | 0.938591i | \(0.387868\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 634650. | 2.68835 | ||||||||
\(142\) | 188835. | 0.785889 | ||||||||
\(143\) | 19839.3 | 0.0811309 | ||||||||
\(144\) | −354354. | −1.42407 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 139517. | 0.541681 | ||||||||
\(147\) | 9358.95 | 0.0357218 | ||||||||
\(148\) | −17201.4 | −0.0645520 | ||||||||
\(149\) | 526340. | 1.94223 | 0.971115 | − | 0.238612i | \(-0.0766923\pi\) | ||||
0.971115 | + | 0.238612i | \(0.0766923\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1849.08 | 0.00659954 | 0.00329977 | − | 0.999995i | \(-0.498950\pi\) | ||||
0.00329977 | + | 0.999995i | \(0.498950\pi\) | |||||||
\(152\) | −407616. | −1.43101 | ||||||||
\(153\) | −126893. | −0.438237 | ||||||||
\(154\) | −200052. | −0.679739 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −7523.94 | −0.0247533 | ||||||||
\(157\) | 343342. | 1.11167 | 0.555837 | − | 0.831292i | \(-0.312398\pi\) | ||||
0.555837 | + | 0.831292i | \(0.312398\pi\) | |||||||
\(158\) | −377322. | −1.20246 | ||||||||
\(159\) | −195334. | −0.612753 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 114424. | 0.347899 | ||||||||
\(162\) | −44981.8 | −0.134663 | ||||||||
\(163\) | −267463. | −0.788487 | −0.394243 | − | 0.919006i | \(-0.628993\pi\) | ||||
−0.394243 | + | 0.919006i | \(0.628993\pi\) | |||||||
\(164\) | −73199.1 | −0.212518 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −208537. | −0.587372 | ||||||||
\(167\) | 122968. | 0.341193 | 0.170596 | − | 0.985341i | \(-0.445431\pi\) | ||||
0.170596 | + | 0.985341i | \(0.445431\pi\) | |||||||
\(168\) | 639106. | 1.74703 | ||||||||
\(169\) | −366616. | −0.987404 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −871437. | −2.27901 | ||||||||
\(172\) | 77664.3 | 0.200170 | ||||||||
\(173\) | 288020. | 0.731657 | 0.365829 | − | 0.930682i | \(-0.380786\pi\) | ||||
0.365829 | + | 0.930682i | \(0.380786\pi\) | |||||||
\(174\) | 346651. | 0.867999 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −251662. | −0.612400 | ||||||||
\(177\) | −235682. | −0.565450 | ||||||||
\(178\) | 617986. | 1.46194 | ||||||||
\(179\) | 246177. | 0.574268 | 0.287134 | − | 0.957890i | \(-0.407298\pi\) | ||||
0.287134 | + | 0.957890i | \(0.407298\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 433120. | 0.982678 | 0.491339 | − | 0.870968i | \(-0.336508\pi\) | ||||
0.491339 | + | 0.870968i | \(0.336508\pi\) | |||||||
\(182\) | −47158.7 | −0.105532 | ||||||||
\(183\) | 84897.9 | 0.187400 | ||||||||
\(184\) | 166831. | 0.363272 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 1.22038e6 | 2.58651 | ||||||||
\(187\) | −90119.1 | −0.188457 | ||||||||
\(188\) | −107178. | −0.221161 | ||||||||
\(189\) | 553526. | 1.12715 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −701011. | −1.39040 | −0.695202 | − | 0.718814i | \(-0.744685\pi\) | ||||
−0.695202 | + | 0.718814i | \(0.744685\pi\) | |||||||
\(192\) | 916642. | 1.79451 | ||||||||
\(193\) | 215730. | 0.416887 | 0.208443 | − | 0.978034i | \(-0.433160\pi\) | ||||
0.208443 | + | 0.978034i | \(0.433160\pi\) | |||||||
\(194\) | −115125. | −0.219618 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1580.51 | −0.00293871 | ||||||||
\(197\) | −700484. | −1.28598 | −0.642988 | − | 0.765876i | \(-0.722305\pi\) | ||||
−0.642988 | + | 0.765876i | \(0.722305\pi\) | |||||||
\(198\) | −623572. | −1.13038 | ||||||||
\(199\) | 22097.5 | 0.0395558 | 0.0197779 | − | 0.999804i | \(-0.493704\pi\) | ||||
0.0197779 | + | 0.999804i | \(0.493704\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −825469. | −1.44115 | ||||||||
\(202\) | 395036. | 0.681174 | ||||||||
\(203\) | −338231. | −0.576068 | ||||||||
\(204\) | 34177.1 | 0.0574990 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −252205. | −0.414081 | ||||||||
\(207\) | 356665. | 0.578542 | ||||||||
\(208\) | −59324.6 | −0.0950772 | ||||||||
\(209\) | −618893. | −0.980054 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 910782. | 1.40834 | 0.704172 | − | 0.710030i | \(-0.251319\pi\) | ||||
0.704172 | + | 0.710030i | \(0.251319\pi\) | |||||||
\(212\) | 32987.4 | 0.0504090 | ||||||||
\(213\) | −915958. | −1.38333 | ||||||||
\(214\) | −484177. | −0.722719 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 807042. | 1.17696 | ||||||||
\(217\) | −1.19074e6 | −1.71660 | ||||||||
\(218\) | 56028.3 | 0.0798484 | ||||||||
\(219\) | −676737. | −0.953475 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −21243.9 | −0.0292587 | ||||||||
\(222\) | −535985. | −0.729911 | ||||||||
\(223\) | 132745. | 0.178754 | 0.0893768 | − | 0.995998i | \(-0.471512\pi\) | ||||
0.0893768 | + | 0.995998i | \(0.471512\pi\) | |||||||
\(224\) | −203048. | −0.270382 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −459769. | −0.598782 | ||||||||
\(227\) | −354321. | −0.456386 | −0.228193 | − | 0.973616i | \(-0.573282\pi\) | ||||
−0.228193 | + | 0.973616i | \(0.573282\pi\) | |||||||
\(228\) | 234711. | 0.299018 | ||||||||
\(229\) | 366643. | 0.462013 | 0.231007 | − | 0.972952i | \(-0.425798\pi\) | ||||
0.231007 | + | 0.972952i | \(0.425798\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 970370. | 1.19649 | ||||||||
\(232\) | −493142. | −0.601523 | ||||||||
\(233\) | 1.02388e6 | 1.23555 | 0.617776 | − | 0.786355i | \(-0.288034\pi\) | ||||
0.617776 | + | 0.786355i | \(0.288034\pi\) | |||||||
\(234\) | −146996. | −0.175495 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 39801.2 | 0.0465175 | ||||||||
\(237\) | 1.83023e6 | 2.11658 | ||||||||
\(238\) | 214216. | 0.245138 | ||||||||
\(239\) | 1.19966e6 | 1.35852 | 0.679258 | − | 0.733899i | \(-0.262302\pi\) | ||||
0.679258 | + | 0.733899i | \(0.262302\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −94967.5 | −0.105325 | −0.0526626 | − | 0.998612i | \(-0.516771\pi\) | ||||
−0.0526626 | + | 0.998612i | \(0.516771\pi\) | |||||||
\(242\) | 404604. | 0.444112 | ||||||||
\(243\) | −808203. | −0.878021 | ||||||||
\(244\) | −14337.3 | −0.0154167 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −2.28084e6 | −2.40302 | ||||||||
\(247\) | −145893. | −0.152157 | ||||||||
\(248\) | −1.73611e6 | −1.79245 | ||||||||
\(249\) | 1.01153e6 | 1.03390 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 418053. | 0.418839 | 0.209419 | − | 0.977826i | \(-0.432843\pi\) | ||||
0.209419 | + | 0.977826i | \(0.432843\pi\) | |||||||
\(252\) | −230742. | −0.228890 | ||||||||
\(253\) | 253303. | 0.248794 | ||||||||
\(254\) | −1.03863e6 | −1.01012 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −415700. | −0.396442 | ||||||||
\(257\) | 2.04586e6 | 1.93216 | 0.966079 | − | 0.258246i | \(-0.0831444\pi\) | ||||
0.966079 | + | 0.258246i | \(0.0831444\pi\) | |||||||
\(258\) | 2.41997e6 | 2.26340 | ||||||||
\(259\) | 522967. | 0.484423 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.05428e6 | −0.957978 | ||||||||
\(262\) | 623505. | 0.561160 | ||||||||
\(263\) | 1.64024e6 | 1.46224 | 0.731119 | − | 0.682250i | \(-0.238998\pi\) | ||||
0.731119 | + | 0.682250i | \(0.238998\pi\) | |||||||
\(264\) | 1.41480e6 | 1.24935 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 1.47113e6 | 1.27481 | ||||||||
\(267\) | −2.99759e6 | −2.57332 | ||||||||
\(268\) | 139402. | 0.118559 | ||||||||
\(269\) | −720582. | −0.607160 | −0.303580 | − | 0.952806i | \(-0.598182\pi\) | ||||
−0.303580 | + | 0.952806i | \(0.598182\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.14186e6 | 0.944477 | 0.472238 | − | 0.881471i | \(-0.343446\pi\) | ||||
0.472238 | + | 0.881471i | \(0.343446\pi\) | |||||||
\(272\) | 269479. | 0.220853 | ||||||||
\(273\) | 228747. | 0.185759 | ||||||||
\(274\) | 1.59215e6 | 1.28117 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −96063.7 | −0.0759078 | ||||||||
\(277\) | 377028. | 0.295239 | 0.147620 | − | 0.989044i | \(-0.452839\pi\) | ||||
0.147620 | + | 0.989044i | \(0.452839\pi\) | |||||||
\(278\) | −827148. | −0.641906 | ||||||||
\(279\) | −3.71160e6 | −2.85464 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −617249. | −0.466331 | −0.233166 | − | 0.972437i | \(-0.574908\pi\) | ||||
−0.233166 | + | 0.972437i | \(0.574908\pi\) | |||||||
\(282\) | −3.33958e6 | −2.50075 | ||||||||
\(283\) | −1.25311e6 | −0.930087 | −0.465044 | − | 0.885288i | \(-0.653961\pi\) | ||||
−0.465044 | + | 0.885288i | \(0.653961\pi\) | |||||||
\(284\) | 154684. | 0.113802 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −104396. | −0.0754692 | ||||||||
\(287\) | 2.22544e6 | 1.59482 | ||||||||
\(288\) | −632908. | −0.449635 | ||||||||
\(289\) | −1.32336e6 | −0.932036 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 558425. | 0.386574 | ||||||||
\(292\) | 114285. | 0.0784390 | ||||||||
\(293\) | 818972. | 0.557314 | 0.278657 | − | 0.960391i | \(-0.410111\pi\) | ||||
0.278657 | + | 0.960391i | \(0.410111\pi\) | |||||||
\(294\) | −49247.6 | −0.0332290 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 762487. | 0.505828 | ||||||||
\(297\) | 1.22535e6 | 0.806064 | ||||||||
\(298\) | −2.76965e6 | −1.80669 | ||||||||
\(299\) | 59711.6 | 0.0386261 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2.36119e6 | −1.50216 | ||||||||
\(302\) | −9730.03 | −0.00613899 | ||||||||
\(303\) | −1.91615e6 | −1.19901 | ||||||||
\(304\) | 1.85065e6 | 1.14852 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 667722. | 0.407654 | ||||||||
\(307\) | −136224. | −0.0824915 | −0.0412458 | − | 0.999149i | \(-0.513133\pi\) | ||||
−0.0412458 | + | 0.999149i | \(0.513133\pi\) | |||||||
\(308\) | −163873. | −0.0984306 | ||||||||
\(309\) | 1.22334e6 | 0.728871 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 2.62886e6 | 1.54122 | 0.770612 | − | 0.637304i | \(-0.219950\pi\) | ||||
0.770612 | + | 0.637304i | \(0.219950\pi\) | |||||||
\(312\) | 333514. | 0.193967 | ||||||||
\(313\) | −218161. | −0.125868 | −0.0629341 | − | 0.998018i | \(-0.520046\pi\) | ||||
−0.0629341 | + | 0.998018i | \(0.520046\pi\) | |||||||
\(314\) | −1.80669e6 | −1.03409 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −309083. | −0.174123 | ||||||||
\(317\) | −1.25865e6 | −0.703491 | −0.351745 | − | 0.936096i | \(-0.614412\pi\) | ||||
−0.351745 | + | 0.936096i | \(0.614412\pi\) | |||||||
\(318\) | 1.02787e6 | 0.569992 | ||||||||
\(319\) | −748750. | −0.411965 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 2.34854e6 | 1.27214 | ||||||||
\(322\) | −602110. | −0.323621 | ||||||||
\(323\) | 662711. | 0.353442 | ||||||||
\(324\) | −36846.8 | −0.0195001 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 1.40741e6 | 0.733462 | ||||||||
\(327\) | −271770. | −0.140550 | ||||||||
\(328\) | 3.24470e6 | 1.66529 | ||||||||
\(329\) | 3.25847e6 | 1.65968 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3.21863e6 | −1.61473 | −0.807366 | − | 0.590051i | \(-0.799108\pi\) | ||||
−0.807366 | + | 0.590051i | \(0.799108\pi\) | |||||||
\(332\) | −170823. | −0.0850553 | ||||||||
\(333\) | 1.63011e6 | 0.805576 | ||||||||
\(334\) | −647067. | −0.317382 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −2.90166e6 | −1.40216 | ||||||||
\(337\) | −1.63574e6 | −0.784585 | −0.392293 | − | 0.919840i | \(-0.628318\pi\) | ||||
−0.392293 | + | 0.919840i | \(0.628318\pi\) | |||||||
\(338\) | 1.92917e6 | 0.918498 | ||||||||
\(339\) | 2.23015e6 | 1.05398 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −2.63597e6 | −1.22760 | ||||||||
\(342\) | 4.58558e6 | 2.11996 | ||||||||
\(343\) | −2.15448e6 | −0.988796 | ||||||||
\(344\) | −3.44262e6 | −1.56853 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −1.51559e6 | −0.680598 | ||||||||
\(347\) | 1.83815e6 | 0.819514 | 0.409757 | − | 0.912195i | \(-0.365614\pi\) | ||||
0.409757 | + | 0.912195i | \(0.365614\pi\) | |||||||
\(348\) | 283959. | 0.125692 | ||||||||
\(349\) | −2.53806e6 | −1.11542 | −0.557710 | − | 0.830036i | \(-0.688320\pi\) | ||||
−0.557710 | + | 0.830036i | \(0.688320\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 288854. | 0.125144 | ||||||||
\(352\) | −449491. | −0.193359 | ||||||||
\(353\) | 1.88471e6 | 0.805023 | 0.402511 | − | 0.915415i | \(-0.368137\pi\) | ||||
0.402511 | + | 0.915415i | \(0.368137\pi\) | |||||||
\(354\) | 1.24018e6 | 0.525989 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 506223. | 0.211698 | ||||||||
\(357\) | −1.03907e6 | −0.431495 | ||||||||
\(358\) | −1.29540e6 | −0.534192 | ||||||||
\(359\) | 305057. | 0.124924 | 0.0624619 | − | 0.998047i | \(-0.480105\pi\) | ||||
0.0624619 | + | 0.998047i | \(0.480105\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 2.07507e6 | 0.838039 | ||||||||
\(362\) | −2.27911e6 | −0.914102 | ||||||||
\(363\) | −1.96257e6 | −0.781731 | ||||||||
\(364\) | −38630.0 | −0.0152817 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −446740. | −0.174322 | ||||||||
\(367\) | 727834. | 0.282077 | 0.141038 | − | 0.990004i | \(-0.454956\pi\) | ||||
0.141038 | + | 0.990004i | \(0.454956\pi\) | |||||||
\(368\) | −757441. | −0.291561 | ||||||||
\(369\) | 6.93680e6 | 2.65212 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1.00290e6 | −0.378289 | ||||||||
\(372\) | 999677. | 0.374544 | ||||||||
\(373\) | 4.77676e6 | 1.77771 | 0.888855 | − | 0.458188i | \(-0.151501\pi\) | ||||
0.888855 | + | 0.458188i | \(0.151501\pi\) | |||||||
\(374\) | 474215. | 0.175306 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 4.75086e6 | 1.73302 | ||||||||
\(377\) | −176504. | −0.0639590 | ||||||||
\(378\) | −2.91270e6 | −1.04850 | ||||||||
\(379\) | −701558. | −0.250880 | −0.125440 | − | 0.992101i | \(-0.540034\pi\) | ||||
−0.125440 | + | 0.992101i | \(0.540034\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 5.03794e6 | 1.77804 | ||||||||
\(382\) | 3.68878e6 | 1.29337 | ||||||||
\(383\) | −4.01069e6 | −1.39708 | −0.698541 | − | 0.715570i | \(-0.746167\pi\) | ||||
−0.698541 | + | 0.715570i | \(0.746167\pi\) | |||||||
\(384\) | −3.55793e6 | −1.23132 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −1.13519e6 | −0.387794 | ||||||||
\(387\) | −7.35994e6 | −2.49803 | ||||||||
\(388\) | −94305.0 | −0.0318021 | ||||||||
\(389\) | −4.45952e6 | −1.49422 | −0.747108 | − | 0.664702i | \(-0.768558\pi\) | ||||
−0.747108 | + | 0.664702i | \(0.768558\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −271237. | −0.0897237 | ||||||||
\(392\) | 70059.1 | 0.0230276 | ||||||||
\(393\) | −3.02436e6 | −0.987761 | ||||||||
\(394\) | 3.68601e6 | 1.19623 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −510799. | −0.163686 | ||||||||
\(397\) | −3.36993e6 | −1.07311 | −0.536555 | − | 0.843865i | \(-0.680275\pi\) | ||||
−0.536555 | + | 0.843865i | \(0.680275\pi\) | |||||||
\(398\) | −116279. | −0.0367953 | ||||||||
\(399\) | −7.13583e6 | −2.24395 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −3.00679e6 | −0.933775 | −0.466888 | − | 0.884317i | \(-0.654625\pi\) | ||||
−0.466888 | + | 0.884317i | \(0.654625\pi\) | |||||||
\(402\) | 4.34369e6 | 1.34058 | ||||||||
\(403\) | −621383. | −0.190588 | ||||||||
\(404\) | 323593. | 0.0986384 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 1.77980e6 | 0.535867 | ||||||||
\(407\) | 1.15770e6 | 0.346426 | ||||||||
\(408\) | −1.51497e6 | −0.450561 | ||||||||
\(409\) | −998012. | −0.295004 | −0.147502 | − | 0.989062i | \(-0.547123\pi\) | ||||
−0.147502 | + | 0.989062i | \(0.547123\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −7.72284e6 | −2.25513 | ||||||||
\(412\) | −206593. | −0.0599616 | ||||||||
\(413\) | −1.21006e6 | −0.349085 | ||||||||
\(414\) | −1.87680e6 | −0.538168 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −105959. | −0.0300196 | ||||||||
\(417\) | 4.01215e6 | 1.12989 | ||||||||
\(418\) | 3.25667e6 | 0.911660 | ||||||||
\(419\) | 5.53743e6 | 1.54090 | 0.770448 | − | 0.637503i | \(-0.220033\pi\) | ||||
0.770448 | + | 0.637503i | \(0.220033\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1.98635e6 | 0.546198 | 0.273099 | − | 0.961986i | \(-0.411951\pi\) | ||||
0.273099 | + | 0.961986i | \(0.411951\pi\) | |||||||
\(422\) | −4.79262e6 | −1.31006 | ||||||||
\(423\) | 1.01568e7 | 2.75998 | ||||||||
\(424\) | −1.46223e6 | −0.395004 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 4.81985e6 | 1.28680 | ||||||||
\(427\) | 435890. | 0.115693 | ||||||||
\(428\) | −396613. | −0.104654 | ||||||||
\(429\) | 506382. | 0.132842 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 116512. | 0.0302118 | 0.0151059 | − | 0.999886i | \(-0.495191\pi\) | ||||
0.0151059 | + | 0.999886i | \(0.495191\pi\) | |||||||
\(432\) | −3.66411e6 | −0.944625 | ||||||||
\(433\) | −4.56166e6 | −1.16924 | −0.584619 | − | 0.811308i | \(-0.698756\pi\) | ||||
−0.584619 | + | 0.811308i | \(0.698756\pi\) | |||||||
\(434\) | 6.26580e6 | 1.59681 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 45895.6 | 0.0115626 | ||||||||
\(437\) | −1.86272e6 | −0.466599 | ||||||||
\(438\) | 3.56105e6 | 0.886936 | ||||||||
\(439\) | 2.92172e6 | 0.723565 | 0.361782 | − | 0.932263i | \(-0.382168\pi\) | ||||
0.361782 | + | 0.932263i | \(0.382168\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 149779. | 0.0366736 | ||||||||
\(442\) | 111787. | 0.0272168 | ||||||||
\(443\) | −1.59752e6 | −0.386756 | −0.193378 | − | 0.981124i | \(-0.561944\pi\) | ||||
−0.193378 | + | 0.981124i | \(0.561944\pi\) | |||||||
\(444\) | −439052. | −0.105696 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −698514. | −0.166279 | ||||||||
\(447\) | 1.34344e7 | 3.18016 | ||||||||
\(448\) | 4.70630e6 | 1.10786 | ||||||||
\(449\) | 3.11073e6 | 0.728193 | 0.364096 | − | 0.931361i | \(-0.381378\pi\) | ||||
0.364096 | + | 0.931361i | \(0.381378\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 4.92650e6 | 1.14051 | ||||||||
\(452\) | −376620. | −0.0867076 | ||||||||
\(453\) | 47196.3 | 0.0108059 | ||||||||
\(454\) | 1.86447e6 | 0.424537 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −1.04041e7 | −2.34310 | ||||||||
\(457\) | 6.47145e6 | 1.44948 | 0.724738 | − | 0.689025i | \(-0.241961\pi\) | ||||
0.724738 | + | 0.689025i | \(0.241961\pi\) | |||||||
\(458\) | −1.92931e6 | −0.429771 | ||||||||
\(459\) | −1.31211e6 | −0.290695 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −5.47864e6 | −1.20066 | −0.600330 | − | 0.799752i | \(-0.704964\pi\) | ||||
−0.600330 | + | 0.799752i | \(0.704964\pi\) | |||||||
\(462\) | −5.10617e6 | −1.11299 | ||||||||
\(463\) | 2.35489e6 | 0.510526 | 0.255263 | − | 0.966872i | \(-0.417838\pi\) | ||||
0.255263 | + | 0.966872i | \(0.417838\pi\) | |||||||
\(464\) | 2.23895e6 | 0.482781 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −5.38776e6 | −1.14933 | ||||||||
\(467\) | −4.56027e6 | −0.967606 | −0.483803 | − | 0.875177i | \(-0.660745\pi\) | ||||
−0.483803 | + | 0.875177i | \(0.660745\pi\) | |||||||
\(468\) | −120412. | −0.0254129 | ||||||||
\(469\) | −4.23819e6 | −0.889710 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 8.76351e6 | 1.82023 | ||||||||
\(472\) | −1.76427e6 | −0.364510 | ||||||||
\(473\) | −5.22702e6 | −1.07424 | ||||||||
\(474\) | −9.63082e6 | −1.96887 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 175475. | 0.0354975 | ||||||||
\(477\) | −3.12609e6 | −0.629079 | ||||||||
\(478\) | −6.31274e6 | −1.26371 | ||||||||
\(479\) | −1.88004e6 | −0.374394 | −0.187197 | − | 0.982322i | \(-0.559940\pi\) | ||||
−0.187197 | + | 0.982322i | \(0.559940\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 272907. | 0.0537839 | ||||||||
\(482\) | 499727. | 0.0979751 | ||||||||
\(483\) | 2.92058e6 | 0.569642 | ||||||||
\(484\) | 331431. | 0.0643103 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 4.25283e6 | 0.816747 | ||||||||
\(487\) | 1.69396e6 | 0.323654 | 0.161827 | − | 0.986819i | \(-0.448261\pi\) | ||||
0.161827 | + | 0.986819i | \(0.448261\pi\) | |||||||
\(488\) | 635528. | 0.120805 | ||||||||
\(489\) | −6.82677e6 | −1.29105 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 1.48645e6 | 0.278258 | 0.139129 | − | 0.990274i | \(-0.455570\pi\) | ||||
0.139129 | + | 0.990274i | \(0.455570\pi\) | |||||||
\(492\) | −1.86835e6 | −0.347972 | ||||||||
\(493\) | 801762. | 0.148569 | ||||||||
\(494\) | 767700. | 0.141538 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 7.88224e6 | 1.43862 | ||||||||
\(497\) | −4.70279e6 | −0.854013 | ||||||||
\(498\) | −5.32274e6 | −0.961749 | ||||||||
\(499\) | 7.09934e6 | 1.27634 | 0.638170 | − | 0.769896i | \(-0.279692\pi\) | ||||
0.638170 | + | 0.769896i | \(0.279692\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 3.13865e6 | 0.558661 | ||||||||
\(502\) | −2.19983e6 | −0.389610 | ||||||||
\(503\) | 9.24224e6 | 1.62876 | 0.814381 | − | 0.580331i | \(-0.197077\pi\) | ||||
0.814381 | + | 0.580331i | \(0.197077\pi\) | |||||||
\(504\) | 1.02281e7 | 1.79357 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −1.33290e6 | −0.231431 | ||||||||
\(507\) | −9.35758e6 | −1.61675 | ||||||||
\(508\) | −850790. | −0.146273 | ||||||||
\(509\) | −8.12506e6 | −1.39006 | −0.695028 | − | 0.718983i | \(-0.744608\pi\) | ||||
−0.695028 | + | 0.718983i | \(0.744608\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3.47456e6 | −0.588637 | ||||||||
\(512\) | 6.64807e6 | 1.12078 | ||||||||
\(513\) | −9.01089e6 | −1.51173 | ||||||||
\(514\) | −1.07655e7 | −1.79732 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 1.98232e6 | 0.327754 | ||||||||
\(517\) | 7.21335e6 | 1.18689 | ||||||||
\(518\) | −2.75190e6 | −0.450617 | ||||||||
\(519\) | 7.35148e6 | 1.19800 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 5.06245e6 | 0.817084 | 0.408542 | − | 0.912740i | \(-0.366037\pi\) | ||||
0.408542 | + | 0.912740i | \(0.366037\pi\) | |||||||
\(522\) | 5.54773e6 | 0.891125 | ||||||||
\(523\) | −4.76222e6 | −0.761299 | −0.380649 | − | 0.924719i | \(-0.624300\pi\) | ||||
−0.380649 | + | 0.924719i | \(0.624300\pi\) | |||||||
\(524\) | 510744. | 0.0812596 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −8.63109e6 | −1.36019 | ||||||||
\(527\) | 2.82260e6 | 0.442714 | ||||||||
\(528\) | −6.42345e6 | −1.00273 | ||||||||
\(529\) | −5.67396e6 | −0.881550 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −3.77181e6 | −0.580515 | ||||||||
\(532\) | 1.20508e6 | 0.184601 | ||||||||
\(533\) | 1.16133e6 | 0.177067 | ||||||||
\(534\) | 1.57736e7 | 2.39374 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −6.17929e6 | −0.929023 | ||||||||
\(537\) | 6.28346e6 | 0.940292 | ||||||||
\(538\) | 3.79177e6 | 0.564789 | ||||||||
\(539\) | 106373. | 0.0157709 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −2.89920e6 | −0.425877 | −0.212939 | − | 0.977066i | \(-0.568303\pi\) | ||||
−0.212939 | + | 0.977066i | \(0.568303\pi\) | |||||||
\(542\) | −6.00859e6 | −0.878566 | ||||||||
\(543\) | 1.10550e7 | 1.60901 | ||||||||
\(544\) | 481315. | 0.0697320 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −1.20369e6 | −0.172795 | ||||||||
\(547\) | −5.74434e6 | −0.820866 | −0.410433 | − | 0.911891i | \(-0.634622\pi\) | ||||
−0.410433 | + | 0.911891i | \(0.634622\pi\) | |||||||
\(548\) | 1.30421e6 | 0.185522 | ||||||||
\(549\) | 1.35869e6 | 0.192393 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 5.50610e6 | 0.772618 | ||||||||
\(552\) | 4.25822e6 | 0.594812 | ||||||||
\(553\) | 9.39691e6 | 1.30669 | ||||||||
\(554\) | −1.98395e6 | −0.274636 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −677558. | −0.0929522 | ||||||||
\(557\) | −7.29174e6 | −0.995848 | −0.497924 | − | 0.867221i | \(-0.665904\pi\) | ||||
−0.497924 | + | 0.867221i | \(0.665904\pi\) | |||||||
\(558\) | 1.95308e7 | 2.65542 | ||||||||
\(559\) | −1.23217e6 | −0.166779 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −2.30022e6 | −0.308576 | ||||||||
\(562\) | 3.24802e6 | 0.433788 | ||||||||
\(563\) | 6.65348e6 | 0.884663 | 0.442331 | − | 0.896852i | \(-0.354151\pi\) | ||||
0.442331 | + | 0.896852i | \(0.354151\pi\) | |||||||
\(564\) | −2.73562e6 | −0.362124 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 6.59398e6 | 0.865181 | ||||||||
\(567\) | 1.12024e6 | 0.146336 | ||||||||
\(568\) | −6.85667e6 | −0.891749 | ||||||||
\(569\) | 5.78715e6 | 0.749349 | 0.374675 | − | 0.927156i | \(-0.377754\pi\) | ||||
0.374675 | + | 0.927156i | \(0.377754\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −1.22059e7 | −1.56667 | −0.783336 | − | 0.621599i | \(-0.786483\pi\) | ||||
−0.783336 | + | 0.621599i | \(0.786483\pi\) | |||||||
\(572\) | −85516.1 | −0.0109284 | ||||||||
\(573\) | −1.78927e7 | −2.27662 | ||||||||
\(574\) | −1.17105e7 | −1.48352 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 1.46697e7 | 1.84232 | ||||||||
\(577\) | −1.02981e7 | −1.28771 | −0.643853 | − | 0.765149i | \(-0.722665\pi\) | ||||
−0.643853 | + | 0.765149i | \(0.722665\pi\) | |||||||
\(578\) | 6.96362e6 | 0.866993 | ||||||||
\(579\) | 5.50634e6 | 0.682601 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 5.19346e6 | 0.638288 | ||||||||
\(582\) | −2.93848e6 | −0.359597 | ||||||||
\(583\) | −2.22014e6 | −0.270526 | ||||||||
\(584\) | −5.06591e6 | −0.614647 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −4.30950e6 | −0.518422 | ||||||||
\(587\) | 1.30519e7 | 1.56343 | 0.781715 | − | 0.623636i | \(-0.214345\pi\) | ||||
0.781715 | + | 0.623636i | \(0.214345\pi\) | |||||||
\(588\) | −40341.1 | −0.00481177 | ||||||||
\(589\) | 1.93842e7 | 2.30229 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −1.78793e7 | −2.10563 | ||||||||
\(592\) | −3.46183e6 | −0.405977 | ||||||||
\(593\) | −6.43920e6 | −0.751961 | −0.375980 | − | 0.926628i | \(-0.622694\pi\) | ||||
−0.375980 | + | 0.926628i | \(0.622694\pi\) | |||||||
\(594\) | −6.44791e6 | −0.749812 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −2.26876e6 | −0.261621 | ||||||||
\(597\) | 564020. | 0.0647677 | ||||||||
\(598\) | −314208. | −0.0359305 | ||||||||
\(599\) | −1.00760e7 | −1.14741 | −0.573707 | − | 0.819061i | \(-0.694495\pi\) | ||||
−0.573707 | + | 0.819061i | \(0.694495\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.57050e6 | 0.177358 | 0.0886791 | − | 0.996060i | \(-0.471735\pi\) | ||||
0.0886791 | + | 0.996060i | \(0.471735\pi\) | |||||||
\(602\) | 1.24248e7 | 1.39733 | ||||||||
\(603\) | −1.32106e7 | −1.47955 | ||||||||
\(604\) | −7970.35 | −0.000888966 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 1.00830e7 | 1.11534 | ||||||||
\(607\) | 7.31039e6 | 0.805321 | 0.402660 | − | 0.915349i | \(-0.368086\pi\) | ||||
0.402660 | + | 0.915349i | \(0.368086\pi\) | |||||||
\(608\) | 3.30543e6 | 0.362634 | ||||||||
\(609\) | −8.63308e6 | −0.943241 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.70041e6 | 0.184269 | ||||||||
\(612\) | 546964. | 0.0590310 | ||||||||
\(613\) | −1.31997e7 | −1.41878 | −0.709389 | − | 0.704817i | \(-0.751029\pi\) | ||||
−0.709389 | + | 0.704817i | \(0.751029\pi\) | |||||||
\(614\) | 716825. | 0.0767348 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 7.26399e6 | 0.771300 | ||||||||
\(617\) | −1.02423e7 | −1.08314 | −0.541570 | − | 0.840655i | \(-0.682170\pi\) | ||||
−0.541570 | + | 0.840655i | \(0.682170\pi\) | |||||||
\(618\) | −6.43732e6 | −0.678006 | ||||||||
\(619\) | 1.05614e7 | 1.10788 | 0.553942 | − | 0.832555i | \(-0.313123\pi\) | ||||
0.553942 | + | 0.832555i | \(0.313123\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 3.68802e6 | 0.383764 | ||||||||
\(622\) | −1.38333e7 | −1.43367 | ||||||||
\(623\) | −1.53905e7 | −1.58866 | ||||||||
\(624\) | −1.51421e6 | −0.155677 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 1.14798e6 | 0.117084 | ||||||||
\(627\) | −1.57967e7 | −1.60472 | ||||||||
\(628\) | −1.47995e6 | −0.149744 | ||||||||
\(629\) | −1.23967e6 | −0.124933 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.90535e7 | 1.90503 | 0.952513 | − | 0.304497i | \(-0.0984883\pi\) | ||||
0.952513 | + | 0.304497i | \(0.0984883\pi\) | |||||||
\(632\) | 1.37007e7 | 1.36443 | ||||||||
\(633\) | 2.32470e7 | 2.30599 | ||||||||
\(634\) | 6.62315e6 | 0.654397 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 841976. | 0.0825385 | ||||||||
\(637\) | 25075.4 | 0.00244849 | ||||||||
\(638\) | 3.93999e6 | 0.383216 | ||||||||
\(639\) | −1.46588e7 | −1.42019 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 8.56937e6 | 0.823766 | 0.411883 | − | 0.911237i | \(-0.364871\pi\) | ||||
0.411883 | + | 0.911237i | \(0.364871\pi\) | |||||||
\(642\) | −1.23582e7 | −1.18336 | ||||||||
\(643\) | 1.79513e7 | 1.71226 | 0.856130 | − | 0.516761i | \(-0.172862\pi\) | ||||
0.856130 | + | 0.516761i | \(0.172862\pi\) | |||||||
\(644\) | −493218. | −0.0468624 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −3.48724e6 | −0.328777 | ||||||||
\(647\) | 1.05470e7 | 0.990534 | 0.495267 | − | 0.868741i | \(-0.335070\pi\) | ||||
0.495267 | + | 0.868741i | \(0.335070\pi\) | |||||||
\(648\) | 1.63331e6 | 0.152803 | ||||||||
\(649\) | −2.67873e6 | −0.249642 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −3.03928e7 | −2.81072 | ||||||||
\(652\) | 1.15288e6 | 0.106210 | ||||||||
\(653\) | 1.00324e7 | 0.920712 | 0.460356 | − | 0.887734i | \(-0.347722\pi\) | ||||
0.460356 | + | 0.887734i | \(0.347722\pi\) | |||||||
\(654\) | 1.43008e6 | 0.130742 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −1.47315e7 | −1.33656 | ||||||||
\(657\) | −1.08304e7 | −0.978879 | ||||||||
\(658\) | −1.71464e7 | −1.54386 | ||||||||
\(659\) | −8.99161e6 | −0.806536 | −0.403268 | − | 0.915082i | \(-0.632126\pi\) | ||||
−0.403268 | + | 0.915082i | \(0.632126\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 2.39297e6 | 0.213027 | 0.106513 | − | 0.994311i | \(-0.466031\pi\) | ||||
0.106513 | + | 0.994311i | \(0.466031\pi\) | |||||||
\(662\) | 1.69367e7 | 1.50205 | ||||||||
\(663\) | −542234. | −0.0479074 | ||||||||
\(664\) | 7.57208e6 | 0.666492 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −8.57779e6 | −0.749359 | ||||||||
\(667\) | −2.25356e6 | −0.196135 | ||||||||
\(668\) | −530044. | −0.0459590 | ||||||||
\(669\) | 3.38820e6 | 0.292687 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 964938. | 0.0827357 | ||||||||
\(672\) | −5.18262e6 | −0.442717 | ||||||||
\(673\) | 1.53612e7 | 1.30733 | 0.653666 | − | 0.756783i | \(-0.273230\pi\) | ||||
0.653666 | + | 0.756783i | \(0.273230\pi\) | |||||||
\(674\) | 8.60742e6 | 0.729833 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 1.58028e6 | 0.133004 | ||||||||
\(677\) | 1.16026e7 | 0.972934 | 0.486467 | − | 0.873699i | \(-0.338285\pi\) | ||||
0.486467 | + | 0.873699i | \(0.338285\pi\) | |||||||
\(678\) | −1.17352e7 | −0.980432 | ||||||||
\(679\) | 2.86711e6 | 0.238655 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −9.04375e6 | −0.747275 | ||||||||
\(682\) | 1.38707e7 | 1.14193 | ||||||||
\(683\) | −1.20315e7 | −0.986890 | −0.493445 | − | 0.869777i | \(-0.664263\pi\) | ||||
−0.493445 | + | 0.869777i | \(0.664263\pi\) | |||||||
\(684\) | 3.75627e6 | 0.306985 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 1.13371e7 | 0.919792 | ||||||||
\(687\) | 9.35825e6 | 0.756490 | ||||||||
\(688\) | 1.56301e7 | 1.25890 | ||||||||
\(689\) | −523358. | −0.0420001 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 5.18616e6 | 0.413191 | 0.206595 | − | 0.978426i | \(-0.433762\pi\) | ||||
0.206595 | + | 0.978426i | \(0.433762\pi\) | |||||||
\(692\) | −1.24149e6 | −0.0985550 | ||||||||
\(693\) | 1.55296e7 | 1.22836 | ||||||||
\(694\) | −9.67248e6 | −0.762323 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −1.25870e7 | −0.984919 | ||||||||
\(697\) | −5.27530e6 | −0.411306 | ||||||||
\(698\) | 1.33555e7 | 1.03758 | ||||||||
\(699\) | 2.61338e7 | 2.02306 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 6.00859e6 | 0.461825 | 0.230913 | − | 0.972974i | \(-0.425829\pi\) | ||||
0.230913 | + | 0.972974i | \(0.425829\pi\) | |||||||
\(702\) | −1.51998e6 | −0.116411 | ||||||||
\(703\) | −8.51342e6 | −0.649704 | ||||||||
\(704\) | 1.04184e7 | 0.792265 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −9.91752e6 | −0.748844 | ||||||||
\(707\) | −9.83807e6 | −0.740221 | ||||||||
\(708\) | 1.01589e6 | 0.0761667 | ||||||||
\(709\) | 5.90083e6 | 0.440857 | 0.220429 | − | 0.975403i | \(-0.429254\pi\) | ||||
0.220429 | + | 0.975403i | \(0.429254\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 2.92906e7 | 2.17297 | ||||||||
\(712\) | −2.24393e7 | −1.65886 | ||||||||
\(713\) | −7.93365e6 | −0.584453 | ||||||||
\(714\) | 5.46769e6 | 0.401383 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −1.06113e6 | −0.0773545 | ||||||||
\(717\) | 3.06204e7 | 2.22440 | ||||||||
\(718\) | −1.60524e6 | −0.116206 | ||||||||
\(719\) | −1.36592e7 | −0.985382 | −0.492691 | − | 0.870204i | \(-0.663987\pi\) | ||||
−0.492691 | + | 0.870204i | \(0.663987\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 6.28097e6 | 0.449975 | ||||||||
\(722\) | −1.09192e7 | −0.779556 | ||||||||
\(723\) | −2.42397e6 | −0.172457 | ||||||||
\(724\) | −1.86693e6 | −0.132368 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 1.03272e7 | 0.727178 | ||||||||
\(727\) | −1.11594e7 | −0.783079 | −0.391539 | − | 0.920161i | \(-0.628057\pi\) | ||||
−0.391539 | + | 0.920161i | \(0.628057\pi\) | |||||||
\(728\) | 1.71235e6 | 0.119747 | ||||||||
\(729\) | −2.27059e7 | −1.58242 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 5.59710e6 | 0.387409 | ||||||||
\(732\) | −365947. | −0.0252430 | ||||||||
\(733\) | −1.52510e7 | −1.04843 | −0.524215 | − | 0.851586i | \(-0.675641\pi\) | ||||
−0.524215 | + | 0.851586i | \(0.675641\pi\) | |||||||
\(734\) | −3.82993e6 | −0.262392 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −1.35286e6 | −0.0920573 | ||||||||
\(737\) | −9.38217e6 | −0.636260 | ||||||||
\(738\) | −3.65020e7 | −2.46704 | ||||||||
\(739\) | −1.11820e7 | −0.753196 | −0.376598 | − | 0.926377i | \(-0.622906\pi\) | ||||
−0.376598 | + | 0.926377i | \(0.622906\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −3.72379e6 | −0.249138 | ||||||||
\(742\) | 5.27735e6 | 0.351890 | ||||||||
\(743\) | 7.71450e6 | 0.512667 | 0.256334 | − | 0.966588i | \(-0.417485\pi\) | ||||
0.256334 | + | 0.966588i | \(0.417485\pi\) | |||||||
\(744\) | −4.43127e7 | −2.93492 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −2.51357e7 | −1.65365 | ||||||||
\(747\) | 1.61883e7 | 1.06145 | ||||||||
\(748\) | 388453. | 0.0253854 | ||||||||
\(749\) | 1.20581e7 | 0.785367 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −2.23973e7 | −1.44909 | −0.724545 | − | 0.689228i | \(-0.757950\pi\) | ||||
−0.724545 | + | 0.689228i | \(0.757950\pi\) | |||||||
\(752\) | −2.15698e7 | −1.39091 | ||||||||
\(753\) | 1.06704e7 | 0.685796 | ||||||||
\(754\) | 928780. | 0.0594955 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −2.38594e6 | −0.151829 | ||||||||
\(757\) | 2.57267e7 | 1.63171 | 0.815857 | − | 0.578254i | \(-0.196266\pi\) | ||||
0.815857 | + | 0.578254i | \(0.196266\pi\) | |||||||
\(758\) | 3.69166e6 | 0.233372 | ||||||||
\(759\) | 6.46535e6 | 0.407369 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −1.48340e7 | −0.928533 | −0.464267 | − | 0.885696i | \(-0.653682\pi\) | ||||
−0.464267 | + | 0.885696i | \(0.653682\pi\) | |||||||
\(762\) | −2.65101e7 | −1.65395 | ||||||||
\(763\) | −1.39534e6 | −0.0867700 | ||||||||
\(764\) | 3.02166e6 | 0.187289 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 2.11046e7 | 1.29959 | ||||||||
\(767\) | −631463. | −0.0387578 | ||||||||
\(768\) | −1.06104e7 | −0.649125 | ||||||||
\(769\) | −5.57112e6 | −0.339724 | −0.169862 | − | 0.985468i | \(-0.554332\pi\) | ||||
−0.169862 | + | 0.985468i | \(0.554332\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 5.22188e7 | 3.16367 | ||||||||
\(772\) | −929892. | −0.0561551 | ||||||||
\(773\) | −1.58230e7 | −0.952447 | −0.476224 | − | 0.879324i | \(-0.657995\pi\) | ||||
−0.476224 | + | 0.879324i | \(0.657995\pi\) | |||||||
\(774\) | 3.87287e7 | 2.32370 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 4.18026e6 | 0.249200 | ||||||||
\(777\) | 1.33483e7 | 0.793183 | ||||||||
\(778\) | 2.34664e7 | 1.38994 | ||||||||
\(779\) | −3.62281e7 | −2.13896 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.04107e7 | −0.610732 | ||||||||
\(782\) | 1.42727e6 | 0.0834623 | ||||||||
\(783\) | −1.09016e7 | −0.635454 | ||||||||
\(784\) | −318081. | −0.0184819 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 1.59144e7 | 0.918830 | ||||||||
\(787\) | −1.31529e7 | −0.756981 | −0.378491 | − | 0.925605i | \(-0.623557\pi\) | ||||
−0.378491 | + | 0.925605i | \(0.623557\pi\) | |||||||
\(788\) | 3.01939e6 | 0.173222 | ||||||||
\(789\) | 4.18658e7 | 2.39423 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1.14502e7 | 0.650687 | ||||||||
\(792\) | 2.26422e7 | 1.28264 | ||||||||
\(793\) | 227466. | 0.0128450 | ||||||||
\(794\) | 1.77328e7 | 0.998222 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −95249.7 | −0.00532821 | ||||||||
\(797\) | −2.58443e7 | −1.44118 | −0.720590 | − | 0.693361i | \(-0.756129\pi\) | ||||
−0.720590 | + | 0.693361i | \(0.756129\pi\) | |||||||
\(798\) | 3.75494e7 | 2.08735 | ||||||||
\(799\) | −7.72406e6 | −0.428034 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −4.79728e7 | −2.64188 | ||||||||
\(802\) | 1.58220e7 | 0.868611 | ||||||||
\(803\) | −7.69170e6 | −0.420953 | ||||||||
\(804\) | 3.55813e6 | 0.194125 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 3.26977e6 | 0.177288 | ||||||||
\(807\) | −1.83923e7 | −0.994149 | ||||||||
\(808\) | −1.43439e7 | −0.772929 | ||||||||
\(809\) | 1.78857e7 | 0.960804 | 0.480402 | − | 0.877048i | \(-0.340491\pi\) | ||||
0.480402 | + | 0.877048i | \(0.340491\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1.41608e7 | −0.756026 | −0.378013 | − | 0.925800i | \(-0.623393\pi\) | ||||
−0.378013 | + | 0.925800i | \(0.623393\pi\) | |||||||
\(812\) | 1.45793e6 | 0.0775970 | ||||||||
\(813\) | 2.91451e7 | 1.54646 | ||||||||
\(814\) | −6.09193e6 | −0.322251 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 6.87824e6 | 0.361619 | ||||||||
\(817\) | 3.84380e7 | 2.01468 | ||||||||
\(818\) | 5.25162e6 | 0.274417 | ||||||||
\(819\) | 3.66082e6 | 0.190708 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −3.46248e7 | −1.79279 | −0.896394 | − | 0.443258i | \(-0.853823\pi\) | ||||
−0.896394 | + | 0.443258i | \(0.853823\pi\) | |||||||
\(822\) | 4.06382e7 | 2.09776 | ||||||||
\(823\) | 2.13360e7 | 1.09803 | 0.549015 | − | 0.835813i | \(-0.315003\pi\) | ||||
0.549015 | + | 0.835813i | \(0.315003\pi\) | |||||||
\(824\) | 9.15766e6 | 0.469858 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 6.36744e6 | 0.324724 | ||||||||
\(827\) | −1.59813e6 | −0.0812548 | −0.0406274 | − | 0.999174i | \(-0.512936\pi\) | ||||
−0.0406274 | + | 0.999174i | \(0.512936\pi\) | |||||||
\(828\) | −1.53738e6 | −0.0779303 | ||||||||
\(829\) | −2.53923e7 | −1.28327 | −0.641633 | − | 0.767012i | \(-0.721743\pi\) | ||||
−0.641633 | + | 0.767012i | \(0.721743\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 9.62333e6 | 0.483418 | ||||||||
\(832\) | 2.45595e6 | 0.123002 | ||||||||
\(833\) | −113904. | −0.00568755 | ||||||||
\(834\) | −2.11123e7 | −1.05104 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 2.66770e6 | 0.132014 | ||||||||
\(837\) | −3.83790e7 | −1.89356 | ||||||||
\(838\) | −2.91384e7 | −1.43336 | ||||||||
\(839\) | 1.98528e7 | 0.973681 | 0.486841 | − | 0.873491i | \(-0.338149\pi\) | ||||
0.486841 | + | 0.873491i | \(0.338149\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.38498e7 | −0.675231 | ||||||||
\(842\) | −1.04523e7 | −0.508081 | ||||||||
\(843\) | −1.57548e7 | −0.763560 | ||||||||
\(844\) | −3.92587e6 | −0.189705 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −5.34460e7 | −2.56737 | ||||||||
\(847\) | −1.00764e7 | −0.482609 | ||||||||
\(848\) | 6.63879e6 | 0.317029 | ||||||||
\(849\) | −3.19846e7 | −1.52290 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 3.48441e6 | 0.164932 | ||||||||
\(852\) | 3.94818e6 | 0.186337 | ||||||||
\(853\) | 1.59794e7 | 0.751948 | 0.375974 | − | 0.926630i | \(-0.377308\pi\) | ||||
0.375974 | + | 0.926630i | \(0.377308\pi\) | |||||||
\(854\) | −2.29369e6 | −0.107619 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 1.75807e7 | 0.820070 | ||||||||
\(857\) | −7.00157e6 | −0.325644 | −0.162822 | − | 0.986655i | \(-0.552060\pi\) | ||||
−0.162822 | + | 0.986655i | \(0.552060\pi\) | |||||||
\(858\) | −2.66463e6 | −0.123571 | ||||||||
\(859\) | −7.28414e6 | −0.336818 | −0.168409 | − | 0.985717i | \(-0.553863\pi\) | ||||
−0.168409 | + | 0.985717i | \(0.553863\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 5.68026e7 | 2.61132 | ||||||||
\(862\) | −613094. | −0.0281034 | ||||||||
\(863\) | 1.76361e7 | 0.806075 | 0.403037 | − | 0.915184i | \(-0.367954\pi\) | ||||
0.403037 | + | 0.915184i | \(0.367954\pi\) | |||||||
\(864\) | −6.54444e6 | −0.298255 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 2.40038e7 | 1.08764 | ||||||||
\(867\) | −3.37776e7 | −1.52609 | ||||||||
\(868\) | 5.13263e6 | 0.231228 | ||||||||
\(869\) | 2.08021e7 | 0.934455 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −2.21167e6 | −0.0987816 | ||||||||
\(872\) | −2.03441e6 | −0.0906041 | ||||||||
\(873\) | 8.93692e6 | 0.396874 | ||||||||
\(874\) | 9.80180e6 | 0.434037 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 2.91703e6 | 0.128434 | ||||||||
\(877\) | 2.69004e7 | 1.18102 | 0.590512 | − | 0.807029i | \(-0.298926\pi\) | ||||
0.590512 | + | 0.807029i | \(0.298926\pi\) | |||||||
\(878\) | −1.53743e7 | −0.673070 | ||||||||
\(879\) | 2.09036e7 | 0.912533 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 2.51911e7 | 1.09347 | 0.546735 | − | 0.837306i | \(-0.315870\pi\) | ||||
0.546735 | + | 0.837306i | \(0.315870\pi\) | |||||||
\(882\) | −788148. | −0.0341143 | ||||||||
\(883\) | −3.22126e7 | −1.39035 | −0.695175 | − | 0.718840i | \(-0.744673\pi\) | ||||
−0.695175 | + | 0.718840i | \(0.744673\pi\) | |||||||
\(884\) | 91570.7 | 0.00394117 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 8.40629e6 | 0.359766 | ||||||||
\(887\) | 8.96139e6 | 0.382443 | 0.191221 | − | 0.981547i | \(-0.438755\pi\) | ||||
0.191221 | + | 0.981547i | \(0.438755\pi\) | |||||||
\(888\) | 1.94618e7 | 0.828231 | ||||||||
\(889\) | 2.58662e7 | 1.09769 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 2.47989e6 | 0.104650 | ||||||||
\(892\) | −572187. | −0.0240783 | ||||||||
\(893\) | −5.30449e7 | −2.22595 | ||||||||
\(894\) | −7.06930e7 | −2.95823 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −1.82674e7 | −0.760164 | ||||||||
\(897\) | 1.52409e6 | 0.0632454 | ||||||||
\(898\) | −1.63689e7 | −0.677376 | ||||||||
\(899\) | 2.34514e7 | 0.967765 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2.37733e6 | 0.0975613 | ||||||||
\(902\) | −2.59237e7 | −1.06092 | ||||||||
\(903\) | −6.02675e7 | −2.45960 | ||||||||
\(904\) | 1.66944e7 | 0.679439 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −248351. | −0.0100518 | ||||||||
\(907\) | −5.81689e6 | −0.234786 | −0.117393 | − | 0.993086i | \(-0.537454\pi\) | ||||
−0.117393 | + | 0.993086i | \(0.537454\pi\) | |||||||
\(908\) | 1.52728e6 | 0.0614757 | ||||||||
\(909\) | −3.06657e7 | −1.23096 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −1.96435e7 | −0.784192 | −0.392096 | − | 0.919924i | \(-0.628250\pi\) | ||||
−0.392096 | + | 0.919924i | \(0.628250\pi\) | |||||||
\(912\) | 4.72363e7 | 1.88057 | ||||||||
\(913\) | 1.14969e7 | 0.456460 | ||||||||
\(914\) | −3.40533e7 | −1.34832 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −1.58039e6 | −0.0622337 | ||||||||
\(917\) | −1.55279e7 | −0.609803 | ||||||||
\(918\) | 6.90442e6 | 0.270409 | ||||||||
\(919\) | −89962.4 | −0.00351376 | −0.00175688 | − | 0.999998i | \(-0.500559\pi\) | ||||
−0.00175688 | + | 0.999998i | \(0.500559\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −3.47702e6 | −0.135070 | ||||||||
\(922\) | 2.88291e7 | 1.11687 | ||||||||
\(923\) | −2.45412e6 | −0.0948183 | ||||||||
\(924\) | −4.18272e6 | −0.161168 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −1.23916e7 | −0.474899 | ||||||||
\(927\) | 1.95781e7 | 0.748290 | ||||||||
\(928\) | 3.99898e6 | 0.152433 | ||||||||
\(929\) | 3.65192e7 | 1.38830 | 0.694149 | − | 0.719832i | \(-0.255781\pi\) | ||||
0.694149 | + | 0.719832i | \(0.255781\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −782234. | −0.0295776 | ||||||||
\(932\) | −4.41338e6 | −0.166430 | ||||||||
\(933\) | 6.70994e7 | 2.52357 | ||||||||
\(934\) | 2.39966e7 | 0.900081 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 5.33748e6 | 0.199135 | ||||||||
\(937\) | −3.58659e7 | −1.33454 | −0.667272 | − | 0.744814i | \(-0.732538\pi\) | ||||
−0.667272 | + | 0.744814i | \(0.732538\pi\) | |||||||
\(938\) | 2.23017e7 | 0.827621 | ||||||||
\(939\) | −5.56838e6 | −0.206094 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −3.19693e7 | −1.17695 | −0.588476 | − | 0.808515i | \(-0.700272\pi\) | ||||
−0.588476 | + | 0.808515i | \(0.700272\pi\) | |||||||
\(942\) | −4.61143e7 | −1.69320 | ||||||||
\(943\) | 1.48276e7 | 0.542990 | ||||||||
\(944\) | 8.01010e6 | 0.292555 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 2.75050e7 | 0.999273 | ||||||||
\(947\) | 4.71846e7 | 1.70972 | 0.854861 | − | 0.518858i | \(-0.173643\pi\) | ||||
0.854861 | + | 0.518858i | \(0.173643\pi\) | |||||||
\(948\) | −7.88908e6 | −0.285106 | ||||||||
\(949\) | −1.81318e6 | −0.0653544 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −3.21261e7 | −1.15188 | ||||||||
\(952\) | −7.77829e6 | −0.278158 | ||||||||
\(953\) | 1.65226e6 | 0.0589315 | 0.0294657 | − | 0.999566i | \(-0.490619\pi\) | ||||
0.0294657 | + | 0.999566i | \(0.490619\pi\) | |||||||
\(954\) | 1.64497e7 | 0.585178 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −5.17108e6 | −0.182994 | ||||||||
\(957\) | −1.91112e7 | −0.674541 | ||||||||
\(958\) | 9.89295e6 | 0.348267 | ||||||||
\(959\) | −3.96512e7 | −1.39223 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 5.39316e7 | 1.88380 | ||||||||
\(962\) | −1.43606e6 | −0.0500306 | ||||||||
\(963\) | 3.75855e7 | 1.30603 | ||||||||
\(964\) | 409351. | 0.0141874 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −1.53684e7 | −0.529889 | ||||||||
\(967\) | −3.23040e7 | −1.11094 | −0.555470 | − | 0.831537i | \(-0.687462\pi\) | ||||
−0.555470 | + | 0.831537i | \(0.687462\pi\) | |||||||
\(968\) | −1.46914e7 | −0.503934 | ||||||||
\(969\) | 1.69151e7 | 0.578717 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1.15927e7 | 0.394582 | 0.197291 | − | 0.980345i | \(-0.436786\pi\) | ||||
0.197291 | + | 0.980345i | \(0.436786\pi\) | |||||||
\(972\) | 3.48371e6 | 0.118270 | ||||||||
\(973\) | 2.05995e7 | 0.697549 | ||||||||
\(974\) | −8.91377e6 | −0.301068 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −2.88541e6 | −0.0969579 | ||||||||
\(977\) | 2.58947e7 | 0.867909 | 0.433954 | − | 0.900935i | \(-0.357118\pi\) | ||||
0.433954 | + | 0.900935i | \(0.357118\pi\) | |||||||
\(978\) | 3.59231e7 | 1.20095 | ||||||||
\(979\) | −3.40702e7 | −1.13610 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −4.34935e6 | −0.144295 | ||||||||
\(982\) | −7.82184e6 | −0.258839 | ||||||||
\(983\) | 3.46040e7 | 1.14220 | 0.571101 | − | 0.820880i | \(-0.306517\pi\) | ||||
0.571101 | + | 0.820880i | \(0.306517\pi\) | |||||||
\(984\) | 8.28182e7 | 2.72670 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −4.21894e6 | −0.138201 | ||||||||
\(987\) | 8.31698e7 | 2.71752 | ||||||||
\(988\) | 628861. | 0.0204957 | ||||||||
\(989\) | −1.57321e7 | −0.511441 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −3.71464e7 | −1.20152 | −0.600762 | − | 0.799428i | \(-0.705136\pi\) | ||||
−0.600762 | + | 0.799428i | \(0.705136\pi\) | |||||||
\(992\) | 1.40784e7 | 0.454228 | ||||||||
\(993\) | −8.21528e7 | −2.64393 | ||||||||
\(994\) | 2.47465e7 | 0.794415 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −4.36012e6 | −0.139268 | ||||||||
\(997\) | −2.47350e7 | −0.788086 | −0.394043 | − | 0.919092i | \(-0.628924\pi\) | ||||
−0.394043 | + | 0.919092i | \(0.628924\pi\) | |||||||
\(998\) | −3.73573e7 | −1.18727 | ||||||||
\(999\) | 1.68558e7 | 0.534362 |
(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 | 25.6.a.d.1.1 | yes | 2 | |
3.2 | odd | 2 | 225.6.a.l.1.2 | 2 | |||
4.3 | odd | 2 | 400.6.a.o.1.1 | 2 | |||
5.2 | odd | 4 | 25.6.b.b.24.2 | 4 | |||
5.3 | odd | 4 | 25.6.b.b.24.3 | 4 | |||
5.4 | even | 2 | 25.6.a.b.1.2 | ✓ | 2 | ||
15.2 | even | 4 | 225.6.b.i.199.3 | 4 | |||
15.8 | even | 4 | 225.6.b.i.199.2 | 4 | |||
15.14 | odd | 2 | 225.6.a.s.1.1 | 2 | |||
20.3 | even | 4 | 400.6.c.n.49.1 | 4 | |||
20.7 | even | 4 | 400.6.c.n.49.4 | 4 | |||
20.19 | odd | 2 | 400.6.a.w.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
25.6.a.b.1.2 | ✓ | 2 | 5.4 | even | 2 | ||
25.6.a.d.1.1 | yes | 2 | 1.1 | even | 1 | trivial | |
25.6.b.b.24.2 | 4 | 5.2 | odd | 4 | |||
25.6.b.b.24.3 | 4 | 5.3 | odd | 4 | |||
225.6.a.l.1.2 | 2 | 3.2 | odd | 2 | |||
225.6.a.s.1.1 | 2 | 15.14 | odd | 2 | |||
225.6.b.i.199.2 | 4 | 15.8 | even | 4 | |||
225.6.b.i.199.3 | 4 | 15.2 | even | 4 | |||
400.6.a.o.1.1 | 2 | 4.3 | odd | 2 | |||
400.6.a.w.1.2 | 2 | 20.19 | odd | 2 | |||
400.6.c.n.49.1 | 4 | 20.3 | even | 4 | |||
400.6.c.n.49.4 | 4 | 20.7 | even | 4 |