Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [25,6,Mod(24,25)]
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([1]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("25.24");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 25 = 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 25.b (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(4.00959549532\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(i, \sqrt{241})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 121x^{2} + 3600 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 5^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 24.3 | ||
Root | \(7.26209i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 25.24 |
Dual form | 25.6.b.b.24.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/25\mathbb{Z}\right)^\times\).
\(n\) | \(2\) |
\(\chi(n)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 5.26209i | 0.930214i | 0.885254 | + | 0.465107i | \(0.153984\pi\) | ||||
−0.885254 | + | 0.465107i | \(0.846016\pi\) | |||||||
\(3\) | 25.5242i | 1.63738i | 0.574238 | + | 0.818688i | \(0.305298\pi\) | ||||
−0.574238 | + | 0.818688i | \(0.694702\pi\) | |||||||
\(4\) | 4.31044 | 0.134701 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −134.310 | −1.52311 | ||||||||
\(7\) | − 131.048i | − 1.01085i | −0.862871 | − | 0.505425i | \(-0.831336\pi\) | ||||
0.862871 | − | 0.505425i | \(-0.168664\pi\) | |||||||
\(8\) | 191.069i | 1.05552i | ||||||||
\(9\) | −408.483 | −1.68100 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 290.104 | 0.722891 | 0.361445 | − | 0.932393i | \(-0.382283\pi\) | ||||
0.361445 | + | 0.932393i | \(0.382283\pi\) | |||||||
\(12\) | 110.020i | 0.220557i | ||||||||
\(13\) | 68.3868i | 0.112231i | 0.998424 | + | 0.0561156i | \(0.0178715\pi\) | ||||
−0.998424 | + | 0.0561156i | \(0.982128\pi\) | |||||||
\(14\) | 689.588 | 0.940307 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −867.486 | −0.847154 | ||||||||
\(17\) | 310.644i | 0.260700i | 0.991468 | + | 0.130350i | \(0.0416100\pi\) | ||||
−0.991468 | + | 0.130350i | \(0.958390\pi\) | |||||||
\(18\) | − 2149.48i | − 1.56369i | ||||||||
\(19\) | 2133.35 | 1.35574 | 0.677871 | − | 0.735180i | \(-0.262903\pi\) | ||||
0.677871 | + | 0.735180i | \(0.262903\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 3344.90 | 1.65514 | ||||||||
\(22\) | 1526.55i | 0.672443i | ||||||||
\(23\) | 873.145i | 0.344165i | 0.985083 | + | 0.172083i | \(0.0550496\pi\) | ||||
−0.985083 | + | 0.172083i | \(0.944950\pi\) | |||||||
\(24\) | −4876.87 | −1.72828 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −359.857 | −0.104399 | ||||||||
\(27\) | − 4223.83i | − 1.11506i | ||||||||
\(28\) | − 564.876i | − 0.136163i | ||||||||
\(29\) | 2580.97 | 0.569885 | 0.284943 | − | 0.958545i | \(-0.408025\pi\) | ||||
0.284943 | + | 0.958545i | \(0.408025\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −9086.30 | −1.69818 | −0.849088 | − | 0.528252i | \(-0.822848\pi\) | ||||
−0.849088 | + | 0.528252i | \(0.822848\pi\) | |||||||
\(32\) | 1549.41i | 0.267480i | ||||||||
\(33\) | 7404.67i | 1.18364i | ||||||||
\(34\) | −1634.64 | −0.242507 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −1760.74 | −0.226433 | ||||||||
\(37\) | − 3990.64i | − 0.479224i | −0.970869 | − | 0.239612i | \(-0.922980\pi\) | ||||
0.970869 | − | 0.239612i | \(-0.0770202\pi\) | |||||||
\(38\) | 11225.9i | 1.26113i | ||||||||
\(39\) | −1745.52 | −0.183765 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 16981.8 | 1.57770 | 0.788851 | − | 0.614584i | \(-0.210676\pi\) | ||||
0.788851 | + | 0.614584i | \(0.210676\pi\) | |||||||
\(42\) | 17601.2i | 1.53964i | ||||||||
\(43\) | − 18017.7i | − 1.48603i | −0.669273 | − | 0.743017i | \(-0.733394\pi\) | ||||
0.669273 | − | 0.743017i | \(-0.266606\pi\) | |||||||
\(44\) | 1250.48 | 0.0973742 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −4594.57 | −0.320147 | ||||||||
\(47\) | − 24864.7i | − 1.64187i | −0.571024 | − | 0.820933i | \(-0.693454\pi\) | ||||
0.571024 | − | 0.820933i | \(-0.306546\pi\) | |||||||
\(48\) | − 22141.9i | − 1.38711i | ||||||||
\(49\) | −366.670 | −0.0218165 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −7928.93 | −0.426864 | ||||||||
\(52\) | 294.777i | 0.0151177i | ||||||||
\(53\) | − 7652.91i | − 0.374229i | −0.982338 | − | 0.187114i | \(-0.940087\pi\) | ||||
0.982338 | − | 0.187114i | \(-0.0599135\pi\) | |||||||
\(54\) | 22226.2 | 1.03724 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 25039.2 | 1.06697 | ||||||||
\(57\) | 54451.9i | 2.21986i | ||||||||
\(58\) | 13581.3i | 0.530116i | ||||||||
\(59\) | 9233.69 | 0.345339 | 0.172669 | − | 0.984980i | \(-0.444761\pi\) | ||||
0.172669 | + | 0.984980i | \(0.444761\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3326.17 | 0.114451 | 0.0572256 | − | 0.998361i | \(-0.481775\pi\) | ||||
0.0572256 | + | 0.998361i | \(0.481775\pi\) | |||||||
\(62\) | − 47812.9i | − 1.57967i | ||||||||
\(63\) | 53531.1i | 1.69924i | ||||||||
\(64\) | −35912.7 | −1.09597 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −38964.0 | −1.10104 | ||||||||
\(67\) | 32340.7i | 0.880161i | 0.897958 | + | 0.440080i | \(0.145050\pi\) | ||||
−0.897958 | + | 0.440080i | \(0.854950\pi\) | |||||||
\(68\) | 1339.01i | 0.0351165i | ||||||||
\(69\) | −22286.3 | −0.563528 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −35885.9 | −0.844847 | −0.422424 | − | 0.906399i | \(-0.638821\pi\) | ||||
−0.422424 | + | 0.906399i | \(0.638821\pi\) | |||||||
\(72\) | − 78048.4i | − 1.77432i | ||||||||
\(73\) | − 26513.6i | − 0.582319i | −0.956675 | − | 0.291159i | \(-0.905959\pi\) | ||||
0.956675 | − | 0.291159i | \(-0.0940410\pi\) | |||||||
\(74\) | 20999.1 | 0.445781 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 9195.65 | 0.182620 | ||||||||
\(77\) | − 38017.7i | − 0.730733i | ||||||||
\(78\) | − 9185.06i | − 0.170941i | ||||||||
\(79\) | −71705.7 | −1.29266 | −0.646332 | − | 0.763056i | \(-0.723698\pi\) | ||||
−0.646332 | + | 0.763056i | \(0.723698\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 8548.28 | 0.144766 | ||||||||
\(82\) | 89359.9i | 1.46760i | ||||||||
\(83\) | 39630.1i | 0.631437i | 0.948853 | + | 0.315719i | \(0.102246\pi\) | ||||
−0.948853 | + | 0.315719i | \(0.897754\pi\) | |||||||
\(84\) | 14418.0 | 0.222949 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 94810.8 | 1.38233 | ||||||||
\(87\) | 65877.1i | 0.933117i | ||||||||
\(88\) | 55429.9i | 0.763022i | ||||||||
\(89\) | 117441. | 1.57161 | 0.785806 | − | 0.618473i | \(-0.212248\pi\) | ||||
0.785806 | + | 0.618473i | \(0.212248\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 8961.98 | 0.113449 | ||||||||
\(92\) | 3763.64i | 0.0463594i | ||||||||
\(93\) | − 231920.i | − 2.78055i | ||||||||
\(94\) | 130840. | 1.52729 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −39547.4 | −0.437966 | ||||||||
\(97\) | − 21878.3i | − 0.236093i | −0.993008 | − | 0.118047i | \(-0.962337\pi\) | ||||
0.993008 | − | 0.118047i | \(-0.0376633\pi\) | |||||||
\(98\) | − 1929.45i | − 0.0202940i | ||||||||
\(99\) | −118503. | −1.21518 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −75072.1 | −0.732276 | −0.366138 | − | 0.930561i | \(-0.619320\pi\) | ||||
−0.366138 | + | 0.930561i | \(0.619320\pi\) | |||||||
\(102\) | − 41722.7i | − 0.397075i | ||||||||
\(103\) | 47928.6i | 0.445145i | 0.974916 | + | 0.222573i | \(0.0714455\pi\) | ||||
−0.974916 | + | 0.222573i | \(0.928555\pi\) | |||||||
\(104\) | −13066.6 | −0.118462 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 40270.3 | 0.348113 | ||||||||
\(107\) | − 92012.3i | − 0.776938i | −0.921462 | − | 0.388469i | \(-0.873004\pi\) | ||||
0.921462 | − | 0.388469i | \(-0.126996\pi\) | |||||||
\(108\) | − 18206.6i | − 0.150199i | ||||||||
\(109\) | 10647.5 | 0.0858387 | 0.0429194 | − | 0.999079i | \(-0.486334\pi\) | ||||
0.0429194 | + | 0.999079i | \(0.486334\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 101858. | 0.784670 | ||||||||
\(112\) | 113683.i | 0.856346i | ||||||||
\(113\) | 87373.9i | 0.643703i | 0.946790 | + | 0.321852i | \(0.104305\pi\) | ||||
−0.946790 | + | 0.321852i | \(0.895695\pi\) | |||||||
\(114\) | −286531. | −2.06495 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 11125.1 | 0.0767642 | ||||||||
\(117\) | − 27934.9i | − 0.188661i | ||||||||
\(118\) | 48588.5i | 0.321239i | ||||||||
\(119\) | 40709.4 | 0.263528 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −76890.5 | −0.477429 | ||||||||
\(122\) | 17502.6i | 0.106464i | ||||||||
\(123\) | 433447.i | 2.58329i | ||||||||
\(124\) | −39165.9 | −0.228746 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −281685. | −1.58066 | ||||||||
\(127\) | − 197379.i | − 1.08591i | −0.839763 | − | 0.542953i | \(-0.817306\pi\) | ||||
0.839763 | − | 0.542953i | \(-0.182694\pi\) | |||||||
\(128\) | − 139395.i | − 0.752005i | ||||||||
\(129\) | 459887. | 2.43320 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −118490. | −0.603258 | −0.301629 | − | 0.953425i | \(-0.597530\pi\) | ||||
−0.301629 | + | 0.953425i | \(0.597530\pi\) | |||||||
\(132\) | 31917.4i | 0.159438i | ||||||||
\(133\) | − 279571.i | − 1.37045i | ||||||||
\(134\) | −170179. | −0.818738 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −59354.3 | −0.275173 | ||||||||
\(137\) | 302570.i | 1.37728i | 0.725101 | + | 0.688642i | \(0.241793\pi\) | ||||
−0.725101 | + | 0.688642i | \(0.758207\pi\) | |||||||
\(138\) | − 117272.i | − 0.524202i | ||||||||
\(139\) | −157190. | −0.690062 | −0.345031 | − | 0.938591i | \(-0.612132\pi\) | ||||
−0.345031 | + | 0.938591i | \(0.612132\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 634650. | 2.68835 | ||||||||
\(142\) | − 188835.i | − 0.785889i | ||||||||
\(143\) | 19839.3i | 0.0811309i | ||||||||
\(144\) | 354354. | 1.42407 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 139517. | 0.541681 | ||||||||
\(147\) | − 9358.95i | − 0.0357218i | ||||||||
\(148\) | − 17201.4i | − 0.0645520i | ||||||||
\(149\) | −526340. | −1.94223 | −0.971115 | − | 0.238612i | \(-0.923308\pi\) | ||||
−0.971115 | + | 0.238612i | \(0.923308\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1849.08 | 0.00659954 | 0.00329977 | − | 0.999995i | \(-0.498950\pi\) | ||||
0.00329977 | + | 0.999995i | \(0.498950\pi\) | |||||||
\(152\) | 407616.i | 1.43101i | ||||||||
\(153\) | − 126893.i | − 0.438237i | ||||||||
\(154\) | 200052. | 0.679739 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −7523.94 | −0.0247533 | ||||||||
\(157\) | − 343342.i | − 1.11167i | −0.831292 | − | 0.555837i | \(-0.812398\pi\) | ||||
0.831292 | − | 0.555837i | \(-0.187602\pi\) | |||||||
\(158\) | − 377322.i | − 1.20246i | ||||||||
\(159\) | 195334. | 0.612753 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 114424. | 0.347899 | ||||||||
\(162\) | 44981.8i | 0.134663i | ||||||||
\(163\) | − 267463.i | − 0.788487i | −0.919006 | − | 0.394243i | \(-0.871007\pi\) | ||||
0.919006 | − | 0.394243i | \(-0.128993\pi\) | |||||||
\(164\) | 73199.1 | 0.212518 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −208537. | −0.587372 | ||||||||
\(167\) | − 122968.i | − 0.341193i | −0.985341 | − | 0.170596i | \(-0.945431\pi\) | ||||
0.985341 | − | 0.170596i | \(-0.0545694\pi\) | |||||||
\(168\) | 639106.i | 1.74703i | ||||||||
\(169\) | 366616. | 0.987404 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −871437. | −2.27901 | ||||||||
\(172\) | − 77664.3i | − 0.200170i | ||||||||
\(173\) | 288020.i | 0.731657i | 0.930682 | + | 0.365829i | \(0.119214\pi\) | ||||
−0.930682 | + | 0.365829i | \(0.880786\pi\) | |||||||
\(174\) | −346651. | −0.867999 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −251662. | −0.612400 | ||||||||
\(177\) | 235682.i | 0.565450i | ||||||||
\(178\) | 617986.i | 1.46194i | ||||||||
\(179\) | −246177. | −0.574268 | −0.287134 | − | 0.957890i | \(-0.592702\pi\) | ||||
−0.287134 | + | 0.957890i | \(0.592702\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 433120. | 0.982678 | 0.491339 | − | 0.870968i | \(-0.336508\pi\) | ||||
0.491339 | + | 0.870968i | \(0.336508\pi\) | |||||||
\(182\) | 47158.7i | 0.105532i | ||||||||
\(183\) | 84897.9i | 0.187400i | ||||||||
\(184\) | −166831. | −0.363272 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 1.22038e6 | 2.58651 | ||||||||
\(187\) | 90119.1i | 0.188457i | ||||||||
\(188\) | − 107178.i | − 0.221161i | ||||||||
\(189\) | −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.i | − 1.79451i | ||||||||
\(193\) | 215730.i | 0.416887i | 0.978034 | + | 0.208443i | \(0.0668397\pi\) | ||||
−0.978034 | + | 0.208443i | \(0.933160\pi\) | |||||||
\(194\) | 115125. | 0.219618 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1580.51 | −0.00293871 | ||||||||
\(197\) | 700484.i | 1.28598i | 0.765876 | + | 0.642988i | \(0.222305\pi\) | ||||
−0.765876 | + | 0.642988i | \(0.777695\pi\) | |||||||
\(198\) | − 623572.i | − 1.13038i | ||||||||
\(199\) | −22097.5 | −0.0395558 | −0.0197779 | − | 0.999804i | \(-0.506296\pi\) | ||||
−0.0197779 | + | 0.999804i | \(0.506296\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −825469. | −1.44115 | ||||||||
\(202\) | − 395036.i | − 0.681174i | ||||||||
\(203\) | − 338231.i | − 0.576068i | ||||||||
\(204\) | −34177.1 | −0.0574990 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −252205. | −0.414081 | ||||||||
\(207\) | − 356665.i | − 0.578542i | ||||||||
\(208\) | − 59324.6i | − 0.0950772i | ||||||||
\(209\) | 618893. | 0.980054 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 910782. | 1.40834 | 0.704172 | − | 0.710030i | \(-0.251319\pi\) | ||||
0.704172 | + | 0.710030i | \(0.251319\pi\) | |||||||
\(212\) | − 32987.4i | − 0.0504090i | ||||||||
\(213\) | − 915958.i | − 1.38333i | ||||||||
\(214\) | 484177. | 0.722719 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 807042. | 1.17696 | ||||||||
\(217\) | 1.19074e6i | 1.71660i | ||||||||
\(218\) | 56028.3i | 0.0798484i | ||||||||
\(219\) | 676737. | 0.953475 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −21243.9 | −0.0292587 | ||||||||
\(222\) | 535985.i | 0.729911i | ||||||||
\(223\) | 132745.i | 0.178754i | 0.995998 | + | 0.0893768i | \(0.0284875\pi\) | ||||
−0.995998 | + | 0.0893768i | \(0.971512\pi\) | |||||||
\(224\) | 203048. | 0.270382 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −459769. | −0.598782 | ||||||||
\(227\) | 354321.i | 0.456386i | 0.973616 | + | 0.228193i | \(0.0732817\pi\) | ||||
−0.973616 | + | 0.228193i | \(0.926718\pi\) | |||||||
\(228\) | 234711.i | 0.299018i | ||||||||
\(229\) | −366643. | −0.462013 | −0.231007 | − | 0.972952i | \(-0.574202\pi\) | ||||
−0.231007 | + | 0.972952i | \(0.574202\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 970370. | 1.19649 | ||||||||
\(232\) | 493142.i | 0.601523i | ||||||||
\(233\) | 1.02388e6i | 1.23555i | 0.786355 | + | 0.617776i | \(0.211966\pi\) | ||||
−0.786355 | + | 0.617776i | \(0.788034\pi\) | |||||||
\(234\) | 146996. | 0.175495 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 39801.2 | 0.0465175 | ||||||||
\(237\) | − 1.83023e6i | − 2.11658i | ||||||||
\(238\) | 214216.i | 0.245138i | ||||||||
\(239\) | −1.19966e6 | −1.35852 | −0.679258 | − | 0.733899i | \(-0.737698\pi\) | ||||
−0.679258 | + | 0.733899i | \(0.737698\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −94967.5 | −0.105325 | −0.0526626 | − | 0.998612i | \(-0.516771\pi\) | ||||
−0.0526626 | + | 0.998612i | \(0.516771\pi\) | |||||||
\(242\) | − 404604.i | − 0.444112i | ||||||||
\(243\) | − 808203.i | − 0.878021i | ||||||||
\(244\) | 14337.3 | 0.0154167 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −2.28084e6 | −2.40302 | ||||||||
\(247\) | 145893.i | 0.152157i | ||||||||
\(248\) | − 1.73611e6i | − 1.79245i | ||||||||
\(249\) | −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.i | 0.228890i | ||||||||
\(253\) | 253303.i | 0.248794i | ||||||||
\(254\) | 1.03863e6 | 1.01012 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −415700. | −0.396442 | ||||||||
\(257\) | − 2.04586e6i | − 1.93216i | −0.258246 | − | 0.966079i | \(-0.583144\pi\) | ||||
0.258246 | − | 0.966079i | \(-0.416856\pi\) | |||||||
\(258\) | 2.41997e6i | 2.26340i | ||||||||
\(259\) | −522967. | −0.484423 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.05428e6 | −0.957978 | ||||||||
\(262\) | − 623505.i | − 0.561160i | ||||||||
\(263\) | 1.64024e6i | 1.46224i | 0.682250 | + | 0.731119i | \(0.261002\pi\) | ||||
−0.682250 | + | 0.731119i | \(0.738998\pi\) | |||||||
\(264\) | −1.41480e6 | −1.24935 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 1.47113e6 | 1.27481 | ||||||||
\(267\) | 2.99759e6i | 2.57332i | ||||||||
\(268\) | 139402.i | 0.118559i | ||||||||
\(269\) | 720582. | 0.607160 | 0.303580 | − | 0.952806i | \(-0.401818\pi\) | ||||
0.303580 | + | 0.952806i | \(0.401818\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.14186e6 | 0.944477 | 0.472238 | − | 0.881471i | \(-0.343446\pi\) | ||||
0.472238 | + | 0.881471i | \(0.343446\pi\) | |||||||
\(272\) | − 269479.i | − 0.220853i | ||||||||
\(273\) | 228747.i | 0.185759i | ||||||||
\(274\) | −1.59215e6 | −1.28117 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −96063.7 | −0.0759078 | ||||||||
\(277\) | − 377028.i | − 0.295239i | −0.989044 | − | 0.147620i | \(-0.952839\pi\) | ||||
0.989044 | − | 0.147620i | \(-0.0471612\pi\) | |||||||
\(278\) | − 827148.i | − 0.641906i | ||||||||
\(279\) | 3.71160e6 | 2.85464 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −617249. | −0.466331 | −0.233166 | − | 0.972437i | \(-0.574908\pi\) | ||||
−0.233166 | + | 0.972437i | \(0.574908\pi\) | |||||||
\(282\) | 3.33958e6i | 2.50075i | ||||||||
\(283\) | − 1.25311e6i | − 0.930087i | −0.885288 | − | 0.465044i | \(-0.846039\pi\) | ||||
0.885288 | − | 0.465044i | \(-0.153961\pi\) | |||||||
\(284\) | −154684. | −0.113802 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −104396. | −0.0754692 | ||||||||
\(287\) | − 2.22544e6i | − 1.59482i | ||||||||
\(288\) | − 632908.i | − 0.449635i | ||||||||
\(289\) | 1.32336e6 | 0.932036 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 558425. | 0.386574 | ||||||||
\(292\) | − 114285.i | − 0.0784390i | ||||||||
\(293\) | 818972.i | 0.557314i | 0.960391 | + | 0.278657i | \(0.0898893\pi\) | ||||
−0.960391 | + | 0.278657i | \(0.910111\pi\) | |||||||
\(294\) | 49247.6 | 0.0332290 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 762487. | 0.505828 | ||||||||
\(297\) | − 1.22535e6i | − 0.806064i | ||||||||
\(298\) | − 2.76965e6i | − 1.80669i | ||||||||
\(299\) | −59711.6 | −0.0386261 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2.36119e6 | −1.50216 | ||||||||
\(302\) | 9730.03i | 0.00613899i | ||||||||
\(303\) | − 1.91615e6i | − 1.19901i | ||||||||
\(304\) | −1.85065e6 | −1.14852 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 667722. | 0.407654 | ||||||||
\(307\) | 136224.i | 0.0824915i | 0.999149 | + | 0.0412458i | \(0.0131327\pi\) | ||||
−0.999149 | + | 0.0412458i | \(0.986867\pi\) | |||||||
\(308\) | − 163873.i | − 0.0984306i | ||||||||
\(309\) | −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.i | − 0.193967i | ||||||||
\(313\) | − 218161.i | − 0.125868i | −0.998018 | − | 0.0629341i | \(-0.979954\pi\) | ||||
0.998018 | − | 0.0629341i | \(-0.0200458\pi\) | |||||||
\(314\) | 1.80669e6 | 1.03409 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −309083. | −0.174123 | ||||||||
\(317\) | 1.25865e6i | 0.703491i | 0.936096 | + | 0.351745i | \(0.114412\pi\) | ||||
−0.936096 | + | 0.351745i | \(0.885588\pi\) | |||||||
\(318\) | 1.02787e6i | 0.569992i | ||||||||
\(319\) | 748750. | 0.411965 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 2.34854e6 | 1.27214 | ||||||||
\(322\) | 602110.i | 0.323621i | ||||||||
\(323\) | 662711.i | 0.353442i | ||||||||
\(324\) | 36846.8 | 0.0195001 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 1.40741e6 | 0.733462 | ||||||||
\(327\) | 271770.i | 0.140550i | ||||||||
\(328\) | 3.24470e6i | 1.66529i | ||||||||
\(329\) | −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.i | 0.0850553i | ||||||||
\(333\) | 1.63011e6i | 0.805576i | ||||||||
\(334\) | 647067. | 0.317382 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −2.90166e6 | −1.40216 | ||||||||
\(337\) | 1.63574e6i | 0.784585i | 0.919840 | + | 0.392293i | \(0.128318\pi\) | ||||
−0.919840 | + | 0.392293i | \(0.871682\pi\) | |||||||
\(338\) | 1.92917e6i | 0.918498i | ||||||||
\(339\) | −2.23015e6 | −1.05398 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −2.63597e6 | −1.22760 | ||||||||
\(342\) | − 4.58558e6i | − 2.11996i | ||||||||
\(343\) | − 2.15448e6i | − 0.988796i | ||||||||
\(344\) | 3.44262e6 | 1.56853 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −1.51559e6 | −0.680598 | ||||||||
\(347\) | − 1.83815e6i | − 0.819514i | −0.912195 | − | 0.409757i | \(-0.865614\pi\) | ||||
0.912195 | − | 0.409757i | \(-0.134386\pi\) | |||||||
\(348\) | 283959.i | 0.125692i | ||||||||
\(349\) | 2.53806e6 | 1.11542 | 0.557710 | − | 0.830036i | \(-0.311680\pi\) | ||||
0.557710 | + | 0.830036i | \(0.311680\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 288854. | 0.125144 | ||||||||
\(352\) | 449491.i | 0.193359i | ||||||||
\(353\) | 1.88471e6i | 0.805023i | 0.915415 | + | 0.402511i | \(0.131863\pi\) | ||||
−0.915415 | + | 0.402511i | \(0.868137\pi\) | |||||||
\(354\) | −1.24018e6 | −0.525989 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 506223. | 0.211698 | ||||||||
\(357\) | 1.03907e6i | 0.431495i | ||||||||
\(358\) | − 1.29540e6i | − 0.534192i | ||||||||
\(359\) | −305057. | −0.124924 | −0.0624619 | − | 0.998047i | \(-0.519895\pi\) | ||||
−0.0624619 | + | 0.998047i | \(0.519895\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 2.07507e6 | 0.838039 | ||||||||
\(362\) | 2.27911e6i | 0.914102i | ||||||||
\(363\) | − 1.96257e6i | − 0.781731i | ||||||||
\(364\) | 38630.0 | 0.0152817 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −446740. | −0.174322 | ||||||||
\(367\) | − 727834.i | − 0.282077i | −0.990004 | − | 0.141038i | \(-0.954956\pi\) | ||||
0.990004 | − | 0.141038i | \(-0.0450441\pi\) | |||||||
\(368\) | − 757441.i | − 0.291561i | ||||||||
\(369\) | −6.93680e6 | −2.65212 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1.00290e6 | −0.378289 | ||||||||
\(372\) | − 999677.i | − 0.374544i | ||||||||
\(373\) | 4.77676e6i | 1.77771i | 0.458188 | + | 0.888855i | \(0.348499\pi\) | ||||
−0.458188 | + | 0.888855i | \(0.651501\pi\) | |||||||
\(374\) | −474215. | −0.175306 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 4.75086e6 | 1.73302 | ||||||||
\(377\) | 176504.i | 0.0639590i | ||||||||
\(378\) | − 2.91270e6i | − 1.04850i | ||||||||
\(379\) | 701558. | 0.250880 | 0.125440 | − | 0.992101i | \(-0.459966\pi\) | ||||
0.125440 | + | 0.992101i | \(0.459966\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 5.03794e6 | 1.77804 | ||||||||
\(382\) | − 3.68878e6i | − 1.29337i | ||||||||
\(383\) | − 4.01069e6i | − 1.39708i | −0.715570 | − | 0.698541i | \(-0.753833\pi\) | ||||
0.715570 | − | 0.698541i | \(-0.246167\pi\) | |||||||
\(384\) | 3.55793e6 | 1.23132 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −1.13519e6 | −0.387794 | ||||||||
\(387\) | 7.35994e6i | 2.49803i | ||||||||
\(388\) | − 94305.0i | − 0.0318021i | ||||||||
\(389\) | 4.45952e6 | 1.49422 | 0.747108 | − | 0.664702i | \(-0.231442\pi\) | ||||
0.747108 | + | 0.664702i | \(0.231442\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −271237. | −0.0897237 | ||||||||
\(392\) | − 70059.1i | − 0.0230276i | ||||||||
\(393\) | − 3.02436e6i | − 0.987761i | ||||||||
\(394\) | −3.68601e6 | −1.19623 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −510799. | −0.163686 | ||||||||
\(397\) | 3.36993e6i | 1.07311i | 0.843865 | + | 0.536555i | \(0.180275\pi\) | ||||
−0.843865 | + | 0.536555i | \(0.819725\pi\) | |||||||
\(398\) | − 116279.i | − 0.0367953i | ||||||||
\(399\) | 7.13583e6 | 2.24395 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −3.00679e6 | −0.933775 | −0.466888 | − | 0.884317i | \(-0.654625\pi\) | ||||
−0.466888 | + | 0.884317i | \(0.654625\pi\) | |||||||
\(402\) | − 4.34369e6i | − 1.34058i | ||||||||
\(403\) | − 621383.i | − 0.190588i | ||||||||
\(404\) | −323593. | −0.0986384 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 1.77980e6 | 0.535867 | ||||||||
\(407\) | − 1.15770e6i | − 0.346426i | ||||||||
\(408\) | − 1.51497e6i | − 0.450561i | ||||||||
\(409\) | 998012. | 0.295004 | 0.147502 | − | 0.989062i | \(-0.452877\pi\) | ||||
0.147502 | + | 0.989062i | \(0.452877\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −7.72284e6 | −2.25513 | ||||||||
\(412\) | 206593.i | 0.0599616i | ||||||||
\(413\) | − 1.21006e6i | − 0.349085i | ||||||||
\(414\) | 1.87680e6 | 0.538168 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −105959. | −0.0300196 | ||||||||
\(417\) | − 4.01215e6i | − 1.12989i | ||||||||
\(418\) | 3.25667e6i | 0.911660i | ||||||||
\(419\) | −5.53743e6 | −1.54090 | −0.770448 | − | 0.637503i | \(-0.779967\pi\) | ||||
−0.770448 | + | 0.637503i | \(0.779967\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1.98635e6 | 0.546198 | 0.273099 | − | 0.961986i | \(-0.411951\pi\) | ||||
0.273099 | + | 0.961986i | \(0.411951\pi\) | |||||||
\(422\) | 4.79262e6i | 1.31006i | ||||||||
\(423\) | 1.01568e7i | 2.75998i | ||||||||
\(424\) | 1.46223e6 | 0.395004 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 4.81985e6 | 1.28680 | ||||||||
\(427\) | − 435890.i | − 0.115693i | ||||||||
\(428\) | − 396613.i | − 0.104654i | ||||||||
\(429\) | −506382. | −0.132842 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 116512. | 0.0302118 | 0.0151059 | − | 0.999886i | \(-0.495191\pi\) | ||||
0.0151059 | + | 0.999886i | \(0.495191\pi\) | |||||||
\(432\) | 3.66411e6i | 0.944625i | ||||||||
\(433\) | − 4.56166e6i | − 1.16924i | −0.811308 | − | 0.584619i | \(-0.801244\pi\) | ||||
0.811308 | − | 0.584619i | \(-0.198756\pi\) | |||||||
\(434\) | −6.26580e6 | −1.59681 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 45895.6 | 0.0115626 | ||||||||
\(437\) | 1.86272e6i | 0.466599i | ||||||||
\(438\) | 3.56105e6i | 0.886936i | ||||||||
\(439\) | −2.92172e6 | −0.723565 | −0.361782 | − | 0.932263i | \(-0.617832\pi\) | ||||
−0.361782 | + | 0.932263i | \(0.617832\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 149779. | 0.0366736 | ||||||||
\(442\) | − 111787.i | − 0.0272168i | ||||||||
\(443\) | − 1.59752e6i | − 0.386756i | −0.981124 | − | 0.193378i | \(-0.938056\pi\) | ||||
0.981124 | − | 0.193378i | \(-0.0619444\pi\) | |||||||
\(444\) | 439052. | 0.105696 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −698514. | −0.166279 | ||||||||
\(447\) | − 1.34344e7i | − 3.18016i | ||||||||
\(448\) | 4.70630e6i | 1.10786i | ||||||||
\(449\) | −3.11073e6 | −0.728193 | −0.364096 | − | 0.931361i | \(-0.618622\pi\) | ||||
−0.364096 | + | 0.931361i | \(0.618622\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 4.92650e6 | 1.14051 | ||||||||
\(452\) | 376620.i | 0.0867076i | ||||||||
\(453\) | 47196.3i | 0.0108059i | ||||||||
\(454\) | −1.86447e6 | −0.424537 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −1.04041e7 | −2.34310 | ||||||||
\(457\) | − 6.47145e6i | − 1.44948i | −0.689025 | − | 0.724738i | \(-0.741961\pi\) | ||||
0.689025 | − | 0.724738i | \(-0.258039\pi\) | |||||||
\(458\) | − 1.92931e6i | − 0.429771i | ||||||||
\(459\) | 1.31211e6 | 0.290695 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −5.47864e6 | −1.20066 | −0.600330 | − | 0.799752i | \(-0.704964\pi\) | ||||
−0.600330 | + | 0.799752i | \(0.704964\pi\) | |||||||
\(462\) | 5.10617e6i | 1.11299i | ||||||||
\(463\) | 2.35489e6i | 0.510526i | 0.966872 | + | 0.255263i | \(0.0821621\pi\) | ||||
−0.966872 | + | 0.255263i | \(0.917838\pi\) | |||||||
\(464\) | −2.23895e6 | −0.482781 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −5.38776e6 | −1.14933 | ||||||||
\(467\) | 4.56027e6i | 0.967606i | 0.875177 | + | 0.483803i | \(0.160745\pi\) | ||||
−0.875177 | + | 0.483803i | \(0.839255\pi\) | |||||||
\(468\) | − 120412.i | − 0.0254129i | ||||||||
\(469\) | 4.23819e6 | 0.889710 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 8.76351e6 | 1.82023 | ||||||||
\(472\) | 1.76427e6i | 0.364510i | ||||||||
\(473\) | − 5.22702e6i | − 1.07424i | ||||||||
\(474\) | 9.63082e6 | 1.96887 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 175475. | 0.0354975 | ||||||||
\(477\) | 3.12609e6i | 0.629079i | ||||||||
\(478\) | − 6.31274e6i | − 1.26371i | ||||||||
\(479\) | 1.88004e6 | 0.374394 | 0.187197 | − | 0.982322i | \(-0.440060\pi\) | ||||
0.187197 | + | 0.982322i | \(0.440060\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 272907. | 0.0537839 | ||||||||
\(482\) | − 499727.i | − 0.0979751i | ||||||||
\(483\) | 2.92058e6i | 0.569642i | ||||||||
\(484\) | −331431. | −0.0643103 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 4.25283e6 | 0.816747 | ||||||||
\(487\) | − 1.69396e6i | − 0.323654i | −0.986819 | − | 0.161827i | \(-0.948261\pi\) | ||||
0.986819 | − | 0.161827i | \(-0.0517386\pi\) | |||||||
\(488\) | 635528.i | 0.120805i | ||||||||
\(489\) | 6.82677e6 | 1.29105 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 1.48645e6 | 0.278258 | 0.139129 | − | 0.990274i | \(-0.455570\pi\) | ||||
0.139129 | + | 0.990274i | \(0.455570\pi\) | |||||||
\(492\) | 1.86835e6i | 0.347972i | ||||||||
\(493\) | 801762.i | 0.148569i | ||||||||
\(494\) | −767700. | −0.141538 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 7.88224e6 | 1.43862 | ||||||||
\(497\) | 4.70279e6i | 0.854013i | ||||||||
\(498\) | − 5.32274e6i | − 0.961749i | ||||||||
\(499\) | −7.09934e6 | −1.27634 | −0.638170 | − | 0.769896i | \(-0.720308\pi\) | ||||
−0.638170 | + | 0.769896i | \(0.720308\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 3.13865e6 | 0.558661 | ||||||||
\(502\) | 2.19983e6i | 0.389610i | ||||||||
\(503\) | 9.24224e6i | 1.62876i | 0.580331 | + | 0.814381i | \(0.302923\pi\) | ||||
−0.580331 | + | 0.814381i | \(0.697077\pi\) | |||||||
\(504\) | −1.02281e7 | −1.79357 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −1.33290e6 | −0.231431 | ||||||||
\(507\) | 9.35758e6i | 1.61675i | ||||||||
\(508\) | − 850790.i | − 0.146273i | ||||||||
\(509\) | 8.12506e6 | 1.39006 | 0.695028 | − | 0.718983i | \(-0.255392\pi\) | ||||
0.695028 | + | 0.718983i | \(0.255392\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3.47456e6 | −0.588637 | ||||||||
\(512\) | − 6.64807e6i | − 1.12078i | ||||||||
\(513\) | − 9.01089e6i | − 1.51173i | ||||||||
\(514\) | 1.07655e7 | 1.79732 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 1.98232e6 | 0.327754 | ||||||||
\(517\) | − 7.21335e6i | − 1.18689i | ||||||||
\(518\) | − 2.75190e6i | − 0.450617i | ||||||||
\(519\) | −7.35148e6 | −1.19800 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 5.06245e6 | 0.817084 | 0.408542 | − | 0.912740i | \(-0.366037\pi\) | ||||
0.408542 | + | 0.912740i | \(0.366037\pi\) | |||||||
\(522\) | − 5.54773e6i | − 0.891125i | ||||||||
\(523\) | − 4.76222e6i | − 0.761299i | −0.924719 | − | 0.380649i | \(-0.875700\pi\) | ||||
0.924719 | − | 0.380649i | \(-0.124300\pi\) | |||||||
\(524\) | −510744. | −0.0812596 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −8.63109e6 | −1.36019 | ||||||||
\(527\) | − 2.82260e6i | − 0.442714i | ||||||||
\(528\) | − 6.42345e6i | − 1.00273i | ||||||||
\(529\) | 5.67396e6 | 0.881550 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −3.77181e6 | −0.580515 | ||||||||
\(532\) | − 1.20508e6i | − 0.184601i | ||||||||
\(533\) | 1.16133e6i | 0.177067i | ||||||||
\(534\) | −1.57736e7 | −2.39374 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −6.17929e6 | −0.929023 | ||||||||
\(537\) | − 6.28346e6i | − 0.940292i | ||||||||
\(538\) | 3.79177e6i | 0.564789i | ||||||||
\(539\) | −106373. | −0.0157709 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −2.89920e6 | −0.425877 | −0.212939 | − | 0.977066i | \(-0.568303\pi\) | ||||
−0.212939 | + | 0.977066i | \(0.568303\pi\) | |||||||
\(542\) | 6.00859e6i | 0.878566i | ||||||||
\(543\) | 1.10550e7i | 1.60901i | ||||||||
\(544\) | −481315. | −0.0697320 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −1.20369e6 | −0.172795 | ||||||||
\(547\) | 5.74434e6i | 0.820866i | 0.911891 | + | 0.410433i | \(0.134622\pi\) | ||||
−0.911891 | + | 0.410433i | \(0.865378\pi\) | |||||||
\(548\) | 1.30421e6i | 0.185522i | ||||||||
\(549\) | −1.35869e6 | −0.192393 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 5.50610e6 | 0.772618 | ||||||||
\(552\) | − 4.25822e6i | − 0.594812i | ||||||||
\(553\) | 9.39691e6i | 1.30669i | ||||||||
\(554\) | 1.98395e6 | 0.274636 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −677558. | −0.0929522 | ||||||||
\(557\) | 7.29174e6i | 0.995848i | 0.867221 | + | 0.497924i | \(0.165904\pi\) | ||||
−0.867221 | + | 0.497924i | \(0.834096\pi\) | |||||||
\(558\) | 1.95308e7i | 2.65542i | ||||||||
\(559\) | 1.23217e6 | 0.166779 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −2.30022e6 | −0.308576 | ||||||||
\(562\) | − 3.24802e6i | − 0.433788i | ||||||||
\(563\) | 6.65348e6i | 0.884663i | 0.896852 | + | 0.442331i | \(0.145849\pi\) | ||||
−0.896852 | + | 0.442331i | \(0.854151\pi\) | |||||||
\(564\) | 2.73562e6 | 0.362124 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 6.59398e6 | 0.865181 | ||||||||
\(567\) | − 1.12024e6i | − 0.146336i | ||||||||
\(568\) | − 6.85667e6i | − 0.891749i | ||||||||
\(569\) | −5.78715e6 | −0.749349 | −0.374675 | − | 0.927156i | \(-0.622246\pi\) | ||||
−0.374675 | + | 0.927156i | \(0.622246\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −1.22059e7 | −1.56667 | −0.783336 | − | 0.621599i | \(-0.786483\pi\) | ||||
−0.783336 | + | 0.621599i | \(0.786483\pi\) | |||||||
\(572\) | 85516.1i | 0.0109284i | ||||||||
\(573\) | − 1.78927e7i | − 2.27662i | ||||||||
\(574\) | 1.17105e7 | 1.48352 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 1.46697e7 | 1.84232 | ||||||||
\(577\) | 1.02981e7i | 1.28771i | 0.765149 | + | 0.643853i | \(0.222665\pi\) | ||||
−0.765149 | + | 0.643853i | \(0.777335\pi\) | |||||||
\(578\) | 6.96362e6i | 0.866993i | ||||||||
\(579\) | −5.50634e6 | −0.682601 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 5.19346e6 | 0.638288 | ||||||||
\(582\) | 2.93848e6i | 0.359597i | ||||||||
\(583\) | − 2.22014e6i | − 0.270526i | ||||||||
\(584\) | 5.06591e6 | 0.614647 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −4.30950e6 | −0.518422 | ||||||||
\(587\) | − 1.30519e7i | − 1.56343i | −0.623636 | − | 0.781715i | \(-0.714345\pi\) | ||||
0.623636 | − | 0.781715i | \(-0.285655\pi\) | |||||||
\(588\) | − 40341.1i | − 0.00481177i | ||||||||
\(589\) | −1.93842e7 | −2.30229 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −1.78793e7 | −2.10563 | ||||||||
\(592\) | 3.46183e6i | 0.405977i | ||||||||
\(593\) | − 6.43920e6i | − 0.751961i | −0.926628 | − | 0.375980i | \(-0.877306\pi\) | ||||
0.926628 | − | 0.375980i | \(-0.122694\pi\) | |||||||
\(594\) | 6.44791e6 | 0.749812 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −2.26876e6 | −0.261621 | ||||||||
\(597\) | − 564020.i | − 0.0647677i | ||||||||
\(598\) | − 314208.i | − 0.0359305i | ||||||||
\(599\) | 1.00760e7 | 1.14741 | 0.573707 | − | 0.819061i | \(-0.305505\pi\) | ||||
0.573707 | + | 0.819061i | \(0.305505\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.57050e6 | 0.177358 | 0.0886791 | − | 0.996060i | \(-0.471735\pi\) | ||||
0.0886791 | + | 0.996060i | \(0.471735\pi\) | |||||||
\(602\) | − 1.24248e7i | − 1.39733i | ||||||||
\(603\) | − 1.32106e7i | − 1.47955i | ||||||||
\(604\) | 7970.35 | 0.000888966 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 1.00830e7 | 1.11534 | ||||||||
\(607\) | − 7.31039e6i | − 0.805321i | −0.915349 | − | 0.402660i | \(-0.868086\pi\) | ||||
0.915349 | − | 0.402660i | \(-0.131914\pi\) | |||||||
\(608\) | 3.30543e6i | 0.362634i | ||||||||
\(609\) | 8.63308e6 | 0.943241 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.70041e6 | 0.184269 | ||||||||
\(612\) | − 546964.i | − 0.0590310i | ||||||||
\(613\) | − 1.31997e7i | − 1.41878i | −0.704817 | − | 0.709389i | \(-0.748971\pi\) | ||||
0.704817 | − | 0.709389i | \(-0.251029\pi\) | |||||||
\(614\) | −716825. | −0.0767348 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 7.26399e6 | 0.771300 | ||||||||
\(617\) | 1.02423e7i | 1.08314i | 0.840655 | + | 0.541570i | \(0.182170\pi\) | ||||
−0.840655 | + | 0.541570i | \(0.817830\pi\) | |||||||
\(618\) | − 6.43732e6i | − 0.678006i | ||||||||
\(619\) | −1.05614e7 | −1.10788 | −0.553942 | − | 0.832555i | \(-0.686877\pi\) | ||||
−0.553942 | + | 0.832555i | \(0.686877\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 3.68802e6 | 0.383764 | ||||||||
\(622\) | 1.38333e7i | 1.43367i | ||||||||
\(623\) | − 1.53905e7i | − 1.58866i | ||||||||
\(624\) | 1.51421e6 | 0.155677 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 1.14798e6 | 0.117084 | ||||||||
\(627\) | 1.57967e7i | 1.60472i | ||||||||
\(628\) | − 1.47995e6i | − 0.149744i | ||||||||
\(629\) | 1.23967e6 | 0.124933 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.90535e7 | 1.90503 | 0.952513 | − | 0.304497i | \(-0.0984883\pi\) | ||||
0.952513 | + | 0.304497i | \(0.0984883\pi\) | |||||||
\(632\) | − 1.37007e7i | − 1.36443i | ||||||||
\(633\) | 2.32470e7i | 2.30599i | ||||||||
\(634\) | −6.62315e6 | −0.654397 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 841976. | 0.0825385 | ||||||||
\(637\) | − 25075.4i | − 0.00244849i | ||||||||
\(638\) | 3.93999e6i | 0.383216i | ||||||||
\(639\) | 1.46588e7 | 1.42019 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 8.56937e6 | 0.823766 | 0.411883 | − | 0.911237i | \(-0.364871\pi\) | ||||
0.411883 | + | 0.911237i | \(0.364871\pi\) | |||||||
\(642\) | 1.23582e7i | 1.18336i | ||||||||
\(643\) | 1.79513e7i | 1.71226i | 0.516761 | + | 0.856130i | \(0.327138\pi\) | ||||
−0.516761 | + | 0.856130i | \(0.672862\pi\) | |||||||
\(644\) | 493218. | 0.0468624 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −3.48724e6 | −0.328777 | ||||||||
\(647\) | − 1.05470e7i | − 0.990534i | −0.868741 | − | 0.495267i | \(-0.835070\pi\) | ||||
0.868741 | − | 0.495267i | \(-0.164930\pi\) | |||||||
\(648\) | 1.63331e6i | 0.152803i | ||||||||
\(649\) | 2.67873e6 | 0.249642 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −3.03928e7 | −2.81072 | ||||||||
\(652\) | − 1.15288e6i | − 0.106210i | ||||||||
\(653\) | 1.00324e7i | 0.920712i | 0.887734 | + | 0.460356i | \(0.152278\pi\) | ||||
−0.887734 | + | 0.460356i | \(0.847722\pi\) | |||||||
\(654\) | −1.43008e6 | −0.130742 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −1.47315e7 | −1.33656 | ||||||||
\(657\) | 1.08304e7i | 0.978879i | ||||||||
\(658\) | − 1.71464e7i | − 1.54386i | ||||||||
\(659\) | 8.99161e6 | 0.806536 | 0.403268 | − | 0.915082i | \(-0.367874\pi\) | ||||
0.403268 | + | 0.915082i | \(0.367874\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 2.39297e6 | 0.213027 | 0.106513 | − | 0.994311i | \(-0.466031\pi\) | ||||
0.106513 | + | 0.994311i | \(0.466031\pi\) | |||||||
\(662\) | − 1.69367e7i | − 1.50205i | ||||||||
\(663\) | − 542234.i | − 0.0479074i | ||||||||
\(664\) | −7.57208e6 | −0.666492 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −8.57779e6 | −0.749359 | ||||||||
\(667\) | 2.25356e6i | 0.196135i | ||||||||
\(668\) | − 530044.i | − 0.0459590i | ||||||||
\(669\) | −3.38820e6 | −0.292687 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 964938. | 0.0827357 | ||||||||
\(672\) | 5.18262e6i | 0.442717i | ||||||||
\(673\) | 1.53612e7i | 1.30733i | 0.756783 | + | 0.653666i | \(0.226770\pi\) | ||||
−0.756783 | + | 0.653666i | \(0.773230\pi\) | |||||||
\(674\) | −8.60742e6 | −0.729833 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 1.58028e6 | 0.133004 | ||||||||
\(677\) | − 1.16026e7i | − 0.972934i | −0.873699 | − | 0.486467i | \(-0.838285\pi\) | ||||
0.873699 | − | 0.486467i | \(-0.161715\pi\) | |||||||
\(678\) | − 1.17352e7i | − 0.980432i | ||||||||
\(679\) | −2.86711e6 | −0.238655 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −9.04375e6 | −0.747275 | ||||||||
\(682\) | − 1.38707e7i | − 1.14193i | ||||||||
\(683\) | − 1.20315e7i | − 0.986890i | −0.869777 | − | 0.493445i | \(-0.835737\pi\) | ||||
0.869777 | − | 0.493445i | \(-0.164263\pi\) | |||||||
\(684\) | −3.75627e6 | −0.306985 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 1.13371e7 | 0.919792 | ||||||||
\(687\) | − 9.35825e6i | − 0.756490i | ||||||||
\(688\) | 1.56301e7i | 1.25890i | ||||||||
\(689\) | 523358. | 0.0420001 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 5.18616e6 | 0.413191 | 0.206595 | − | 0.978426i | \(-0.433762\pi\) | ||||
0.206595 | + | 0.978426i | \(0.433762\pi\) | |||||||
\(692\) | 1.24149e6i | 0.0985550i | ||||||||
\(693\) | 1.55296e7i | 1.22836i | ||||||||
\(694\) | 9.67248e6 | 0.762323 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −1.25870e7 | −0.984919 | ||||||||
\(697\) | 5.27530e6i | 0.411306i | ||||||||
\(698\) | 1.33555e7i | 1.03758i | ||||||||
\(699\) | −2.61338e7 | −2.02306 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 6.00859e6 | 0.461825 | 0.230913 | − | 0.972974i | \(-0.425829\pi\) | ||||
0.230913 | + | 0.972974i | \(0.425829\pi\) | |||||||
\(702\) | 1.51998e6i | 0.116411i | ||||||||
\(703\) | − 8.51342e6i | − 0.649704i | ||||||||
\(704\) | −1.04184e7 | −0.792265 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −9.91752e6 | −0.748844 | ||||||||
\(707\) | 9.83807e6i | 0.740221i | ||||||||
\(708\) | 1.01589e6i | 0.0761667i | ||||||||
\(709\) | −5.90083e6 | −0.440857 | −0.220429 | − | 0.975403i | \(-0.570746\pi\) | ||||
−0.220429 | + | 0.975403i | \(0.570746\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 2.92906e7 | 2.17297 | ||||||||
\(712\) | 2.24393e7i | 1.65886i | ||||||||
\(713\) | − 7.93365e6i | − 0.584453i | ||||||||
\(714\) | −5.46769e6 | −0.401383 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −1.06113e6 | −0.0773545 | ||||||||
\(717\) | − 3.06204e7i | − 2.22440i | ||||||||
\(718\) | − 1.60524e6i | − 0.116206i | ||||||||
\(719\) | 1.36592e7 | 0.985382 | 0.492691 | − | 0.870204i | \(-0.336013\pi\) | ||||
0.492691 | + | 0.870204i | \(0.336013\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 6.28097e6 | 0.449975 | ||||||||
\(722\) | 1.09192e7i | 0.779556i | ||||||||
\(723\) | − 2.42397e6i | − 0.172457i | ||||||||
\(724\) | 1.86693e6 | 0.132368 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 1.03272e7 | 0.727178 | ||||||||
\(727\) | 1.11594e7i | 0.783079i | 0.920161 | + | 0.391539i | \(0.128057\pi\) | ||||
−0.920161 | + | 0.391539i | \(0.871943\pi\) | |||||||
\(728\) | 1.71235e6i | 0.119747i | ||||||||
\(729\) | 2.27059e7 | 1.58242 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 5.59710e6 | 0.387409 | ||||||||
\(732\) | 365947.i | 0.0252430i | ||||||||
\(733\) | − 1.52510e7i | − 1.04843i | −0.851586 | − | 0.524215i | \(-0.824359\pi\) | ||||
0.851586 | − | 0.524215i | \(-0.175641\pi\) | |||||||
\(734\) | 3.82993e6 | 0.262392 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −1.35286e6 | −0.0920573 | ||||||||
\(737\) | 9.38217e6i | 0.636260i | ||||||||
\(738\) | − 3.65020e7i | − 2.46704i | ||||||||
\(739\) | 1.11820e7 | 0.753196 | 0.376598 | − | 0.926377i | \(-0.377094\pi\) | ||||
0.376598 | + | 0.926377i | \(0.377094\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −3.72379e6 | −0.249138 | ||||||||
\(742\) | − 5.27735e6i | − 0.351890i | ||||||||
\(743\) | 7.71450e6i | 0.512667i | 0.966588 | + | 0.256334i | \(0.0825146\pi\) | ||||
−0.966588 | + | 0.256334i | \(0.917485\pi\) | |||||||
\(744\) | 4.43127e7 | 2.93492 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −2.51357e7 | −1.65365 | ||||||||
\(747\) | − 1.61883e7i | − 1.06145i | ||||||||
\(748\) | 388453.i | 0.0253854i | ||||||||
\(749\) | −1.20581e7 | −0.785367 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −2.23973e7 | −1.44909 | −0.724545 | − | 0.689228i | \(-0.757950\pi\) | ||||
−0.724545 | + | 0.689228i | \(0.757950\pi\) | |||||||
\(752\) | 2.15698e7i | 1.39091i | ||||||||
\(753\) | 1.06704e7i | 0.685796i | ||||||||
\(754\) | −928780. | −0.0594955 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −2.38594e6 | −0.151829 | ||||||||
\(757\) | − 2.57267e7i | − 1.63171i | −0.578254 | − | 0.815857i | \(-0.696266\pi\) | ||||
0.578254 | − | 0.815857i | \(-0.303734\pi\) | |||||||
\(758\) | 3.69166e6i | 0.233372i | ||||||||
\(759\) | −6.46535e6 | −0.407369 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −1.48340e7 | −0.928533 | −0.464267 | − | 0.885696i | \(-0.653682\pi\) | ||||
−0.464267 | + | 0.885696i | \(0.653682\pi\) | |||||||
\(762\) | 2.65101e7i | 1.65395i | ||||||||
\(763\) | − 1.39534e6i | − 0.0867700i | ||||||||
\(764\) | −3.02166e6 | −0.187289 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 2.11046e7 | 1.29959 | ||||||||
\(767\) | 631463.i | 0.0387578i | ||||||||
\(768\) | − 1.06104e7i | − 0.649125i | ||||||||
\(769\) | 5.57112e6 | 0.339724 | 0.169862 | − | 0.985468i | \(-0.445668\pi\) | ||||
0.169862 | + | 0.985468i | \(0.445668\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 5.22188e7 | 3.16367 | ||||||||
\(772\) | 929892.i | 0.0561551i | ||||||||
\(773\) | − 1.58230e7i | − 0.952447i | −0.879324 | − | 0.476224i | \(-0.842005\pi\) | ||||
0.879324 | − | 0.476224i | \(-0.157995\pi\) | |||||||
\(774\) | −3.87287e7 | −2.32370 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 4.18026e6 | 0.249200 | ||||||||
\(777\) | − 1.33483e7i | − 0.793183i | ||||||||
\(778\) | 2.34664e7i | 1.38994i | ||||||||
\(779\) | 3.62281e7 | 2.13896 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.04107e7 | −0.610732 | ||||||||
\(782\) | − 1.42727e6i | − 0.0834623i | ||||||||
\(783\) | − 1.09016e7i | − 0.635454i | ||||||||
\(784\) | 318081. | 0.0184819 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 1.59144e7 | 0.918830 | ||||||||
\(787\) | 1.31529e7i | 0.756981i | 0.925605 | + | 0.378491i | \(0.123557\pi\) | ||||
−0.925605 | + | 0.378491i | \(0.876443\pi\) | |||||||
\(788\) | 3.01939e6i | 0.173222i | ||||||||
\(789\) | −4.18658e7 | −2.39423 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1.14502e7 | 0.650687 | ||||||||
\(792\) | − 2.26422e7i | − 1.28264i | ||||||||
\(793\) | 227466.i | 0.0128450i | ||||||||
\(794\) | −1.77328e7 | −0.998222 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −95249.7 | −0.00532821 | ||||||||
\(797\) | 2.58443e7i | 1.44118i | 0.693361 | + | 0.720590i | \(0.256129\pi\) | ||||
−0.693361 | + | 0.720590i | \(0.743871\pi\) | |||||||
\(798\) | 3.75494e7i | 2.08735i | ||||||||
\(799\) | 7.72406e6 | 0.428034 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −4.79728e7 | −2.64188 | ||||||||
\(802\) | − 1.58220e7i | − 0.868611i | ||||||||
\(803\) | − 7.69170e6i | − 0.420953i | ||||||||
\(804\) | −3.55813e6 | −0.194125 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 3.26977e6 | 0.177288 | ||||||||
\(807\) | 1.83923e7i | 0.994149i | ||||||||
\(808\) | − 1.43439e7i | − 0.772929i | ||||||||
\(809\) | −1.78857e7 | −0.960804 | −0.480402 | − | 0.877048i | \(-0.659509\pi\) | ||||
−0.480402 | + | 0.877048i | \(0.659509\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1.41608e7 | −0.756026 | −0.378013 | − | 0.925800i | \(-0.623393\pi\) | ||||
−0.378013 | + | 0.925800i | \(0.623393\pi\) | |||||||
\(812\) | − 1.45793e6i | − 0.0775970i | ||||||||
\(813\) | 2.91451e7i | 1.54646i | ||||||||
\(814\) | 6.09193e6 | 0.322251 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 6.87824e6 | 0.361619 | ||||||||
\(817\) | − 3.84380e7i | − 2.01468i | ||||||||
\(818\) | 5.25162e6i | 0.274417i | ||||||||
\(819\) | −3.66082e6 | −0.190708 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −3.46248e7 | −1.79279 | −0.896394 | − | 0.443258i | \(-0.853823\pi\) | ||||
−0.896394 | + | 0.443258i | \(0.853823\pi\) | |||||||
\(822\) | − 4.06382e7i | − 2.09776i | ||||||||
\(823\) | 2.13360e7i | 1.09803i | 0.835813 | + | 0.549015i | \(0.184997\pi\) | ||||
−0.835813 | + | 0.549015i | \(0.815003\pi\) | |||||||
\(824\) | −9.15766e6 | −0.469858 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 6.36744e6 | 0.324724 | ||||||||
\(827\) | 1.59813e6i | 0.0812548i | 0.999174 | + | 0.0406274i | \(0.0129357\pi\) | ||||
−0.999174 | + | 0.0406274i | \(0.987064\pi\) | |||||||
\(828\) | − 1.53738e6i | − 0.0779303i | ||||||||
\(829\) | 2.53923e7 | 1.28327 | 0.641633 | − | 0.767012i | \(-0.278257\pi\) | ||||
0.641633 | + | 0.767012i | \(0.278257\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 9.62333e6 | 0.483418 | ||||||||
\(832\) | − 2.45595e6i | − 0.123002i | ||||||||
\(833\) | − 113904.i | − 0.00568755i | ||||||||
\(834\) | 2.11123e7 | 1.05104 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 2.66770e6 | 0.132014 | ||||||||
\(837\) | 3.83790e7i | 1.89356i | ||||||||
\(838\) | − 2.91384e7i | − 1.43336i | ||||||||
\(839\) | −1.98528e7 | −0.973681 | −0.486841 | − | 0.873491i | \(-0.661851\pi\) | ||||
−0.486841 | + | 0.873491i | \(0.661851\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.38498e7 | −0.675231 | ||||||||
\(842\) | 1.04523e7i | 0.508081i | ||||||||
\(843\) | − 1.57548e7i | − 0.763560i | ||||||||
\(844\) | 3.92587e6 | 0.189705 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −5.34460e7 | −2.56737 | ||||||||
\(847\) | 1.00764e7i | 0.482609i | ||||||||
\(848\) | 6.63879e6i | 0.317029i | ||||||||
\(849\) | 3.19846e7 | 1.52290 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 3.48441e6 | 0.164932 | ||||||||
\(852\) | − 3.94818e6i | − 0.186337i | ||||||||
\(853\) | 1.59794e7i | 0.751948i | 0.926630 | + | 0.375974i | \(0.122692\pi\) | ||||
−0.926630 | + | 0.375974i | \(0.877308\pi\) | |||||||
\(854\) | 2.29369e6 | 0.107619 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 1.75807e7 | 0.820070 | ||||||||
\(857\) | 7.00157e6i | 0.325644i | 0.986655 | + | 0.162822i | \(0.0520597\pi\) | ||||
−0.986655 | + | 0.162822i | \(0.947940\pi\) | |||||||
\(858\) | − 2.66463e6i | − 0.123571i | ||||||||
\(859\) | 7.28414e6 | 0.336818 | 0.168409 | − | 0.985717i | \(-0.446137\pi\) | ||||
0.168409 | + | 0.985717i | \(0.446137\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 5.68026e7 | 2.61132 | ||||||||
\(862\) | 613094.i | 0.0281034i | ||||||||
\(863\) | 1.76361e7i | 0.806075i | 0.915184 | + | 0.403037i | \(0.132046\pi\) | ||||
−0.915184 | + | 0.403037i | \(0.867954\pi\) | |||||||
\(864\) | 6.54444e6 | 0.298255 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 2.40038e7 | 1.08764 | ||||||||
\(867\) | 3.37776e7i | 1.52609i | ||||||||
\(868\) | 5.13263e6i | 0.231228i | ||||||||
\(869\) | −2.08021e7 | −0.934455 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −2.21167e6 | −0.0987816 | ||||||||
\(872\) | 2.03441e6i | 0.0906041i | ||||||||
\(873\) | 8.93692e6i | 0.396874i | ||||||||
\(874\) | −9.80180e6 | −0.434037 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 2.91703e6 | 0.128434 | ||||||||
\(877\) | − 2.69004e7i | − 1.18102i | −0.807029 | − | 0.590512i | \(-0.798926\pi\) | ||||
0.807029 | − | 0.590512i | \(-0.201074\pi\) | |||||||
\(878\) | − 1.53743e7i | − 0.673070i | ||||||||
\(879\) | −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.i | 0.0341143i | ||||||||
\(883\) | − 3.22126e7i | − 1.39035i | −0.718840 | − | 0.695175i | \(-0.755327\pi\) | ||||
0.718840 | − | 0.695175i | \(-0.244673\pi\) | |||||||
\(884\) | −91570.7 | −0.00394117 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 8.40629e6 | 0.359766 | ||||||||
\(887\) | − 8.96139e6i | − 0.382443i | −0.981547 | − | 0.191221i | \(-0.938755\pi\) | ||||
0.981547 | − | 0.191221i | \(-0.0612448\pi\) | |||||||
\(888\) | 1.94618e7i | 0.828231i | ||||||||
\(889\) | −2.58662e7 | −1.09769 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 2.47989e6 | 0.104650 | ||||||||
\(892\) | 572187.i | 0.0240783i | ||||||||
\(893\) | − 5.30449e7i | − 2.22595i | ||||||||
\(894\) | 7.06930e7 | 2.95823 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −1.82674e7 | −0.760164 | ||||||||
\(897\) | − 1.52409e6i | − 0.0632454i | ||||||||
\(898\) | − 1.63689e7i | − 0.677376i | ||||||||
\(899\) | −2.34514e7 | −0.967765 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2.37733e6 | 0.0975613 | ||||||||
\(902\) | 2.59237e7i | 1.06092i | ||||||||
\(903\) | − 6.02675e7i | − 2.45960i | ||||||||
\(904\) | −1.66944e7 | −0.679439 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −248351. | −0.0100518 | ||||||||
\(907\) | 5.81689e6i | 0.234786i | 0.993086 | + | 0.117393i | \(0.0374537\pi\) | ||||
−0.993086 | + | 0.117393i | \(0.962546\pi\) | |||||||
\(908\) | 1.52728e6i | 0.0614757i | ||||||||
\(909\) | 3.06657e7 | 1.23096 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −1.96435e7 | −0.784192 | −0.392096 | − | 0.919924i | \(-0.628250\pi\) | ||||
−0.392096 | + | 0.919924i | \(0.628250\pi\) | |||||||
\(912\) | − 4.72363e7i | − 1.88057i | ||||||||
\(913\) | 1.14969e7i | 0.456460i | ||||||||
\(914\) | 3.40533e7 | 1.34832 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −1.58039e6 | −0.0622337 | ||||||||
\(917\) | 1.55279e7i | 0.609803i | ||||||||
\(918\) | 6.90442e6i | 0.270409i | ||||||||
\(919\) | 89962.4 | 0.00351376 | 0.00175688 | − | 0.999998i | \(-0.499441\pi\) | ||||
0.00175688 | + | 0.999998i | \(0.499441\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −3.47702e6 | −0.135070 | ||||||||
\(922\) | − 2.88291e7i | − 1.11687i | ||||||||
\(923\) | − 2.45412e6i | − 0.0948183i | ||||||||
\(924\) | 4.18272e6 | 0.161168 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −1.23916e7 | −0.474899 | ||||||||
\(927\) | − 1.95781e7i | − 0.748290i | ||||||||
\(928\) | 3.99898e6i | 0.152433i | ||||||||
\(929\) | −3.65192e7 | −1.38830 | −0.694149 | − | 0.719832i | \(-0.744219\pi\) | ||||
−0.694149 | + | 0.719832i | \(0.744219\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −782234. | −0.0295776 | ||||||||
\(932\) | 4.41338e6i | 0.166430i | ||||||||
\(933\) | 6.70994e7i | 2.52357i | ||||||||
\(934\) | −2.39966e7 | −0.900081 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 5.33748e6 | 0.199135 | ||||||||
\(937\) | 3.58659e7i | 1.33454i | 0.744814 | + | 0.667272i | \(0.232538\pi\) | ||||
−0.744814 | + | 0.667272i | \(0.767462\pi\) | |||||||
\(938\) | 2.23017e7i | 0.827621i | ||||||||
\(939\) | 5.56838e6 | 0.206094 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −3.19693e7 | −1.17695 | −0.588476 | − | 0.808515i | \(-0.700272\pi\) | ||||
−0.588476 | + | 0.808515i | \(0.700272\pi\) | |||||||
\(942\) | 4.61143e7i | 1.69320i | ||||||||
\(943\) | 1.48276e7i | 0.542990i | ||||||||
\(944\) | −8.01010e6 | −0.292555 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 2.75050e7 | 0.999273 | ||||||||
\(947\) | − 4.71846e7i | − 1.70972i | −0.518858 | − | 0.854861i | \(-0.673643\pi\) | ||||
0.518858 | − | 0.854861i | \(-0.326357\pi\) | |||||||
\(948\) | − 7.88908e6i | − 0.285106i | ||||||||
\(949\) | 1.81318e6 | 0.0653544 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −3.21261e7 | −1.15188 | ||||||||
\(952\) | 7.77829e6i | 0.278158i | ||||||||
\(953\) | 1.65226e6i | 0.0589315i | 0.999566 | + | 0.0294657i | \(0.00938059\pi\) | ||||
−0.999566 | + | 0.0294657i | \(0.990619\pi\) | |||||||
\(954\) | −1.64497e7 | −0.585178 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −5.17108e6 | −0.182994 | ||||||||
\(957\) | 1.91112e7i | 0.674541i | ||||||||
\(958\) | 9.89295e6i | 0.348267i | ||||||||
\(959\) | 3.96512e7 | 1.39223 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 5.39316e7 | 1.88380 | ||||||||
\(962\) | 1.43606e6i | 0.0500306i | ||||||||
\(963\) | 3.75855e7i | 1.30603i | ||||||||
\(964\) | −409351. | −0.0141874 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −1.53684e7 | −0.529889 | ||||||||
\(967\) | 3.23040e7i | 1.11094i | 0.831537 | + | 0.555470i | \(0.187462\pi\) | ||||
−0.831537 | + | 0.555470i | \(0.812538\pi\) | |||||||
\(968\) | − 1.46914e7i | − 0.503934i | ||||||||
\(969\) | −1.69151e7 | −0.578717 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1.15927e7 | 0.394582 | 0.197291 | − | 0.980345i | \(-0.436786\pi\) | ||||
0.197291 | + | 0.980345i | \(0.436786\pi\) | |||||||
\(972\) | − 3.48371e6i | − 0.118270i | ||||||||
\(973\) | 2.05995e7i | 0.697549i | ||||||||
\(974\) | 8.91377e6 | 0.301068 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −2.88541e6 | −0.0969579 | ||||||||
\(977\) | − 2.58947e7i | − 0.867909i | −0.900935 | − | 0.433954i | \(-0.857118\pi\) | ||||
0.900935 | − | 0.433954i | \(-0.142882\pi\) | |||||||
\(978\) | 3.59231e7i | 1.20095i | ||||||||
\(979\) | 3.40702e7 | 1.13610 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −4.34935e6 | −0.144295 | ||||||||
\(982\) | 7.82184e6i | 0.258839i | ||||||||
\(983\) | 3.46040e7i | 1.14220i | 0.820880 | + | 0.571101i | \(0.193483\pi\) | ||||
−0.820880 | + | 0.571101i | \(0.806517\pi\) | |||||||
\(984\) | −8.28182e7 | −2.72670 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −4.21894e6 | −0.138201 | ||||||||
\(987\) | − 8.31698e7i | − 2.71752i | ||||||||
\(988\) | 628861.i | 0.0204957i | ||||||||
\(989\) | 1.57321e7 | 0.511441 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −3.71464e7 | −1.20152 | −0.600762 | − | 0.799428i | \(-0.705136\pi\) | ||||
−0.600762 | + | 0.799428i | \(0.705136\pi\) | |||||||
\(992\) | − 1.40784e7i | − 0.454228i | ||||||||
\(993\) | − 8.21528e7i | − 2.64393i | ||||||||
\(994\) | −2.47465e7 | −0.794415 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −4.36012e6 | −0.139268 | ||||||||
\(997\) | 2.47350e7i | 0.788086i | 0.919092 | + | 0.394043i | \(0.128924\pi\) | ||||
−0.919092 | + | 0.394043i | \(0.871076\pi\) | |||||||
\(998\) | − 3.73573e7i | − 1.18727i | ||||||||
\(999\) | −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.b.b.24.3 | 4 | ||
3.2 | odd | 2 | 225.6.b.i.199.2 | 4 | |||
4.3 | odd | 2 | 400.6.c.n.49.1 | 4 | |||
5.2 | odd | 4 | 25.6.a.d.1.1 | yes | 2 | ||
5.3 | odd | 4 | 25.6.a.b.1.2 | ✓ | 2 | ||
5.4 | even | 2 | inner | 25.6.b.b.24.2 | 4 | ||
15.2 | even | 4 | 225.6.a.l.1.2 | 2 | |||
15.8 | even | 4 | 225.6.a.s.1.1 | 2 | |||
15.14 | odd | 2 | 225.6.b.i.199.3 | 4 | |||
20.3 | even | 4 | 400.6.a.w.1.2 | 2 | |||
20.7 | even | 4 | 400.6.a.o.1.1 | 2 | |||
20.19 | odd | 2 | 400.6.c.n.49.4 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
25.6.a.b.1.2 | ✓ | 2 | 5.3 | odd | 4 | ||
25.6.a.d.1.1 | yes | 2 | 5.2 | odd | 4 | ||
25.6.b.b.24.2 | 4 | 5.4 | even | 2 | inner | ||
25.6.b.b.24.3 | 4 | 1.1 | even | 1 | trivial | ||
225.6.a.l.1.2 | 2 | 15.2 | even | 4 | |||
225.6.a.s.1.1 | 2 | 15.8 | even | 4 | |||
225.6.b.i.199.2 | 4 | 3.2 | odd | 2 | |||
225.6.b.i.199.3 | 4 | 15.14 | odd | 2 | |||
400.6.a.o.1.1 | 2 | 20.7 | even | 4 | |||
400.6.a.w.1.2 | 2 | 20.3 | even | 4 | |||
400.6.c.n.49.1 | 4 | 4.3 | odd | 2 | |||
400.6.c.n.49.4 | 4 | 20.19 | odd | 2 |