Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [207,6,Mod(206,207)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(207, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("207.206");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 207 = 3^{2} \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 207.c (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(33.1994507013\) |
Analytic rank: | \(0\) |
Dimension: | \(40\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 206.26 | ||
Character | \(\chi\) | \(=\) | 207.206 |
Dual form | 207.6.c.a.206.25 |
$q$-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 \(\left(\mathbb{Z}/207\mathbb{Z}\right)^\times\).
\(n\) | \(28\) | \(47\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 8.84990i | 1.56446i | 0.622992 | + | 0.782228i | \(0.285917\pi\) | ||||
−0.622992 | + | 0.782228i | \(0.714083\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −46.3207 | −1.44752 | ||||||||
\(5\) | 32.1196 | 0.574572 | 0.287286 | − | 0.957845i | \(-0.407247\pi\) | ||||
0.287286 | + | 0.957845i | \(0.407247\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 32.0928i | 0.247550i | 0.992310 | + | 0.123775i | \(0.0395001\pi\) | ||||
−0.992310 | + | 0.123775i | \(0.960500\pi\) | |||||||
\(8\) | − | 126.737i | − | 0.700129i | ||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 284.255i | 0.898893i | ||||||||
\(11\) | −601.231 | −1.49817 | −0.749083 | − | 0.662476i | \(-0.769506\pi\) | ||||
−0.749083 | + | 0.662476i | \(0.769506\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 865.912 | 1.42107 | 0.710534 | − | 0.703662i | \(-0.248453\pi\) | ||||
0.710534 | + | 0.703662i | \(0.248453\pi\) | |||||||
\(14\) | −284.018 | −0.387281 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −360.654 | −0.352201 | ||||||||
\(17\) | −831.109 | −0.697487 | −0.348743 | − | 0.937218i | \(-0.613391\pi\) | ||||
−0.348743 | + | 0.937218i | \(0.613391\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1073.08i | 0.681946i | 0.940073 | + | 0.340973i | \(0.110756\pi\) | ||||
−0.940073 | + | 0.340973i | \(0.889244\pi\) | |||||||
\(20\) | −1487.80 | −0.831706 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | − | 5320.84i | − | 2.34381i | ||||||
\(23\) | −2491.41 | − | 478.774i | −0.982032 | − | 0.188717i | ||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2093.33 | −0.669867 | ||||||||
\(26\) | 7663.23i | 2.22320i | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | − | 1486.56i | − | 0.358334i | ||||||
\(29\) | − | 1742.95i | − | 0.384850i | −0.981312 | − | 0.192425i | \(-0.938365\pi\) | ||
0.981312 | − | 0.192425i | \(-0.0616352\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4617.38 | −0.862962 | −0.431481 | − | 0.902122i | \(-0.642009\pi\) | ||||
−0.431481 | + | 0.902122i | \(0.642009\pi\) | |||||||
\(32\) | − | 7247.33i | − | 1.25113i | ||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | − | 7355.23i | − | 1.09119i | ||||||
\(35\) | 1030.81i | 0.142235i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 14538.9i | − | 1.74594i | −0.487778 | − | 0.872968i | \(-0.662193\pi\) | ||
0.487778 | − | 0.872968i | \(-0.337807\pi\) | |||||||
\(38\) | −9496.69 | −1.06687 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | − | 4070.73i | − | 0.402275i | ||||||
\(41\) | 4605.46i | 0.427872i | 0.976848 | + | 0.213936i | \(0.0686284\pi\) | ||||
−0.976848 | + | 0.213936i | \(0.931372\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 16104.7i | − | 1.32826i | −0.747619 | − | 0.664128i | \(-0.768803\pi\) | ||
0.747619 | − | 0.664128i | \(-0.231197\pi\) | |||||||
\(44\) | 27849.5 | 2.16863 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 4237.10 | − | 22048.7i | 0.295239 | − | 1.53635i | ||||
\(47\) | 6936.30i | 0.458019i | 0.973424 | + | 0.229009i | \(0.0735486\pi\) | ||||
−0.973424 | + | 0.229009i | \(0.926451\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 15777.1 | 0.938719 | ||||||||
\(50\) | − | 18525.8i | − | 1.04798i | ||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −40109.6 | −2.05703 | ||||||||
\(53\) | −11493.3 | −0.562024 | −0.281012 | − | 0.959704i | \(-0.590670\pi\) | ||||
−0.281012 | + | 0.959704i | \(0.590670\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −19311.3 | −0.860804 | ||||||||
\(56\) | 4067.35 | 0.173317 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 15425.0 | 0.602080 | ||||||||
\(59\) | 21495.9i | 0.803945i | 0.915652 | + | 0.401972i | \(0.131675\pi\) | ||||
−0.915652 | + | 0.401972i | \(0.868325\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 3068.46i | − | 0.105583i | −0.998606 | − | 0.0527917i | \(-0.983188\pi\) | ||
0.998606 | − | 0.0527917i | \(-0.0168119\pi\) | |||||||
\(62\) | − | 40863.4i | − | 1.35007i | ||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 52597.2 | 1.60514 | ||||||||
\(65\) | 27812.7 | 0.816506 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 69034.0i | 1.87878i | 0.342848 | + | 0.939391i | \(0.388608\pi\) | ||||
−0.342848 | + | 0.939391i | \(0.611392\pi\) | |||||||
\(68\) | 38497.6 | 1.00963 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −9122.54 | −0.222521 | ||||||||
\(71\) | 5054.68i | 0.119000i | 0.998228 | + | 0.0595001i | \(0.0189507\pi\) | ||||
−0.998228 | + | 0.0595001i | \(0.981049\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 7803.25 | 0.171383 | 0.0856917 | − | 0.996322i | \(-0.472690\pi\) | ||||
0.0856917 | + | 0.996322i | \(0.472690\pi\) | |||||||
\(74\) | 128668. | 2.73144 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | − | 49706.0i | − | 0.987132i | ||||||
\(77\) | − | 19295.2i | − | 0.370871i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 18787.0i | − | 0.338680i | −0.985558 | − | 0.169340i | \(-0.945836\pi\) | ||
0.985558 | − | 0.169340i | \(-0.0541637\pi\) | |||||||
\(80\) | −11584.0 | −0.202365 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −40757.9 | −0.669387 | ||||||||
\(83\) | −60140.1 | −0.958227 | −0.479114 | − | 0.877753i | \(-0.659042\pi\) | ||||
−0.479114 | + | 0.877753i | \(0.659042\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −26694.9 | −0.400756 | ||||||||
\(86\) | 142525. | 2.07800 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 76198.2i | 1.04891i | ||||||||
\(89\) | −29806.7 | −0.398877 | −0.199439 | − | 0.979910i | \(-0.563912\pi\) | ||||
−0.199439 | + | 0.979910i | \(0.563912\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 27789.6i | 0.351786i | ||||||||
\(92\) | 115404. | + | 22177.1i | 1.42151 | + | 0.273172i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −61385.6 | −0.716550 | ||||||||
\(95\) | 34467.0i | 0.391827i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 126459.i | − | 1.36464i | −0.731052 | − | 0.682322i | \(-0.760970\pi\) | ||
0.731052 | − | 0.682322i | \(-0.239030\pi\) | |||||||
\(98\) | 139625.i | 1.46858i | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 96964.8 | 0.969648 | ||||||||
\(101\) | − | 121023.i | − | 1.18050i | −0.807222 | − | 0.590248i | \(-0.799030\pi\) | ||
0.807222 | − | 0.590248i | \(-0.200970\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 42716.5i | − | 0.396737i | −0.980128 | − | 0.198368i | \(-0.936436\pi\) | ||
0.980128 | − | 0.198368i | \(-0.0635642\pi\) | |||||||
\(104\) | − | 109743.i | − | 0.994932i | ||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | − | 101715.i | − | 0.879262i | ||||||
\(107\) | −83454.0 | −0.704673 | −0.352337 | − | 0.935873i | \(-0.614613\pi\) | ||||
−0.352337 | + | 0.935873i | \(0.614613\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 53334.5i | − | 0.429974i | −0.976617 | − | 0.214987i | \(-0.931029\pi\) | ||
0.976617 | − | 0.214987i | \(-0.0689709\pi\) | |||||||
\(110\) | − | 170903.i | − | 1.34669i | ||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | − | 11574.4i | − | 0.0871874i | ||||||
\(113\) | −35211.2 | −0.259409 | −0.129705 | − | 0.991553i | \(-0.541403\pi\) | ||||
−0.129705 | + | 0.991553i | \(0.541403\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −80022.9 | − | 15378.0i | −0.564248 | − | 0.108431i | ||||
\(116\) | 80734.9i | 0.557079i | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −190237. | −1.25774 | ||||||||
\(119\) | − | 26672.6i | − | 0.172663i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 200428. | 1.24450 | ||||||||
\(122\) | 27155.5 | 0.165180 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 213880. | 1.24916 | ||||||||
\(125\) | −167611. | −0.959459 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 189969. | 1.04514 | 0.522569 | − | 0.852597i | \(-0.324974\pi\) | ||||
0.522569 | + | 0.852597i | \(0.324974\pi\) | |||||||
\(128\) | 233566.i | 1.26004i | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 246139.i | 1.27739i | ||||||||
\(131\) | 197216.i | 1.00407i | 0.864847 | + | 0.502036i | \(0.167416\pi\) | ||||
−0.864847 | + | 0.502036i | \(0.832584\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −34438.3 | −0.168816 | ||||||||
\(134\) | −610944. | −2.93927 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 105332.i | 0.488331i | ||||||||
\(137\) | −52017.2 | −0.236780 | −0.118390 | − | 0.992967i | \(-0.537773\pi\) | ||||
−0.118390 | + | 0.992967i | \(0.537773\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −413006. | −1.81309 | −0.906546 | − | 0.422108i | \(-0.861290\pi\) | ||||
−0.906546 | + | 0.422108i | \(0.861290\pi\) | |||||||
\(140\) | − | 47747.7i | − | 0.205889i | ||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −44733.4 | −0.186171 | ||||||||
\(143\) | −520613. | −2.12900 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 55982.9i | − | 0.221124i | ||||||
\(146\) | 69058.0i | 0.268122i | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 673454.i | 2.52728i | ||||||||
\(149\) | −498144. | −1.83818 | −0.919092 | − | 0.394042i | \(-0.871076\pi\) | ||||
−0.919092 | + | 0.394042i | \(0.871076\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −267038. | −0.953083 | −0.476541 | − | 0.879152i | \(-0.658110\pi\) | ||||
−0.476541 | + | 0.879152i | \(0.658110\pi\) | |||||||
\(152\) | 135999. | 0.477450 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 170761. | 0.580211 | ||||||||
\(155\) | −148308. | −0.495834 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 154389.i | 0.499881i | 0.968261 | + | 0.249941i | \(0.0804111\pi\) | ||||
−0.968261 | + | 0.249941i | \(0.919589\pi\) | |||||||
\(158\) | 166263. | 0.529851 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | − | 232781.i | − | 0.718866i | ||||||
\(161\) | 15365.2 | − | 79956.4i | 0.0467169 | − | 0.243102i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 314441. | 0.926981 | 0.463490 | − | 0.886102i | \(-0.346597\pi\) | ||||
0.463490 | + | 0.886102i | \(0.346597\pi\) | |||||||
\(164\) | − | 213328.i | − | 0.619354i | ||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | − | 532233.i | − | 1.49910i | ||||||
\(167\) | 466773.i | 1.29513i | 0.762009 | + | 0.647567i | \(0.224213\pi\) | ||||
−0.762009 | + | 0.647567i | \(0.775787\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 378510. | 1.01944 | ||||||||
\(170\) | − | 236247.i | − | 0.626965i | ||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 745982.i | 1.92268i | ||||||||
\(173\) | 437548.i | 1.11150i | 0.831348 | + | 0.555752i | \(0.187569\pi\) | ||||
−0.831348 | + | 0.555752i | \(0.812431\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 67181.0i | − | 0.165826i | ||||||
\(176\) | 216837. | 0.527656 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | − | 263787.i | − | 0.624026i | ||||||
\(179\) | − | 52237.9i | − | 0.121858i | −0.998142 | − | 0.0609289i | \(-0.980594\pi\) | ||
0.998142 | − | 0.0609289i | \(-0.0194063\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 622329.i | 1.41196i | 0.708230 | + | 0.705982i | \(0.249494\pi\) | ||||
−0.708230 | + | 0.705982i | \(0.750506\pi\) | |||||||
\(182\) | −245935. | −0.550353 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −60678.3 | + | 315754.i | −0.132126 | + | 0.687549i | ||||
\(185\) | − | 466984.i | − | 1.00317i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 499689. | 1.04495 | ||||||||
\(188\) | − | 321294.i | − | 0.662992i | ||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −305029. | −0.612996 | ||||||||
\(191\) | 814655. | 1.61581 | 0.807905 | − | 0.589312i | \(-0.200601\pi\) | ||||
0.807905 | + | 0.589312i | \(0.200601\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −396971. | −0.767124 | −0.383562 | − | 0.923515i | \(-0.625303\pi\) | ||||
−0.383562 | + | 0.923515i | \(0.625303\pi\) | |||||||
\(194\) | 1.11915e6 | 2.13493 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −730804. | −1.35882 | ||||||||
\(197\) | 314623.i | 0.577597i | 0.957390 | + | 0.288799i | \(0.0932558\pi\) | ||||
−0.957390 | + | 0.288799i | \(0.906744\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 188929.i | 0.338194i | 0.985599 | + | 0.169097i | \(0.0540851\pi\) | ||||
−0.985599 | + | 0.169097i | \(0.945915\pi\) | |||||||
\(200\) | 265303.i | 0.468993i | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 1.07104e6 | 1.84683 | ||||||||
\(203\) | 55936.4 | 0.0952695 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 147925.i | 0.245843i | ||||||||
\(206\) | 378036. | 0.620677 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −312294. | −0.500502 | ||||||||
\(209\) | − | 645172.i | − | 1.02167i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 248477. | 0.384220 | 0.192110 | − | 0.981373i | \(-0.438467\pi\) | ||||
0.192110 | + | 0.981373i | \(0.438467\pi\) | |||||||
\(212\) | 532378. | 0.813543 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | − | 738560.i | − | 1.10243i | ||||||
\(215\) | − | 517276.i | − | 0.763179i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 148185.i | − | 0.213626i | ||||||
\(218\) | 472005. | 0.672675 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 894512. | 1.24603 | ||||||||
\(221\) | −719667. | −0.991176 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1.25438e6 | −1.68914 | −0.844571 | − | 0.535443i | \(-0.820145\pi\) | ||||
−0.844571 | + | 0.535443i | \(0.820145\pi\) | |||||||
\(224\) | 232587. | 0.309718 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | − | 311616.i | − | 0.405834i | ||||||
\(227\) | −388100. | −0.499895 | −0.249948 | − | 0.968259i | \(-0.580413\pi\) | ||||
−0.249948 | + | 0.968259i | \(0.580413\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.08193e6i | 1.36336i | 0.731650 | + | 0.681680i | \(0.238750\pi\) | ||||
−0.731650 | + | 0.681680i | \(0.761250\pi\) | |||||||
\(230\) | 136094. | − | 708195.i | 0.169636 | − | 0.882741i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −220897. | −0.269445 | ||||||||
\(233\) | 1.04198e6i | 1.25738i | 0.777654 | + | 0.628692i | \(0.216409\pi\) | ||||
−0.777654 | + | 0.628692i | \(0.783591\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 222791.i | 0.263165i | ||||||||
\(236\) | − | 995707.i | − | 1.16373i | ||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 236050. | 0.270123 | ||||||||
\(239\) | − | 947058.i | − | 1.07246i | −0.844071 | − | 0.536231i | \(-0.819848\pi\) | ||
0.844071 | − | 0.536231i | \(-0.180152\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 168288.i | − | 0.186642i | −0.995636 | − | 0.0933210i | \(-0.970252\pi\) | ||
0.995636 | − | 0.0933210i | \(-0.0297483\pi\) | |||||||
\(242\) | 1.77377e6i | 1.94697i | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 142133.i | 0.152834i | ||||||||
\(245\) | 506752. | 0.539362 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 929196.i | 0.969092i | ||||||||
\(248\) | 585193.i | 0.604185i | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | − | 1.48334e6i | − | 1.50103i | ||||||
\(251\) | 661022. | 0.662264 | 0.331132 | − | 0.943584i | \(-0.392569\pi\) | ||||
0.331132 | + | 0.943584i | \(0.392569\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.49791e6 | + | 287854.i | 1.47125 | + | 0.282729i | ||||
\(254\) | 1.68121e6i | 1.63507i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −383921. | −0.366135 | ||||||||
\(257\) | − | 113921.i | − | 0.107590i | −0.998552 | − | 0.0537949i | \(-0.982868\pi\) | ||
0.998552 | − | 0.0537949i | \(-0.0171317\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 466595. | 0.432206 | ||||||||
\(260\) | −1.28830e6 | −1.18191 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −1.74535e6 | −1.57083 | ||||||||
\(263\) | −1.91611e6 | −1.70817 | −0.854086 | − | 0.520132i | \(-0.825883\pi\) | ||||
−0.854086 | + | 0.520132i | \(0.825883\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −369160. | −0.322923 | ||||||||
\(266\) | − | 304776.i | − | 0.264105i | ||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | − | 3.19771e6i | − | 2.71958i | ||||||
\(269\) | 1.72330e6i | 1.45205i | 0.687669 | + | 0.726024i | \(0.258634\pi\) | ||||
−0.687669 | + | 0.726024i | \(0.741366\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 156049. | 0.129074 | 0.0645369 | − | 0.997915i | \(-0.479443\pi\) | ||||
0.0645369 | + | 0.997915i | \(0.479443\pi\) | |||||||
\(272\) | 299743. | 0.245656 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | − | 460347.i | − | 0.370432i | ||||||
\(275\) | 1.25858e6 | 1.00357 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1.29944e6 | −1.01756 | −0.508778 | − | 0.860898i | \(-0.669903\pi\) | ||||
−0.508778 | + | 0.860898i | \(0.669903\pi\) | |||||||
\(278\) | − | 3.65506e6i | − | 2.83650i | ||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 130641. | 0.0995831 | ||||||||
\(281\) | 1.53841e6 | 1.16227 | 0.581135 | − | 0.813807i | \(-0.302609\pi\) | ||||
0.581135 | + | 0.813807i | \(0.302609\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1.22558e6i | 0.909653i | 0.890580 | + | 0.454827i | \(0.150299\pi\) | ||||
−0.890580 | + | 0.454827i | \(0.849701\pi\) | |||||||
\(284\) | − | 234136.i | − | 0.172256i | ||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | − | 4.60737e6i | − | 3.33072i | ||||||
\(287\) | −147802. | −0.105920 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −729114. | −0.513513 | ||||||||
\(290\) | 495443. | 0.345939 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −361452. | −0.248081 | ||||||||
\(293\) | 38645.9 | 0.0262987 | 0.0131493 | − | 0.999914i | \(-0.495814\pi\) | ||||
0.0131493 | + | 0.999914i | \(0.495814\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 690440.i | 0.461924i | ||||||||
\(296\) | −1.84262e6 | −1.22238 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | − | 4.40852e6i | − | 2.87576i | ||||||
\(299\) | −2.15734e6 | − | 414576.i | −1.39553 | − | 0.268180i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 516846. | 0.328810 | ||||||||
\(302\) | − | 2.36326e6i | − | 1.49106i | ||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | − | 387012.i | − | 0.240182i | ||||||
\(305\) | − | 98557.4i | − | 0.0606652i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2.23002e6 | 1.35040 | 0.675201 | − | 0.737634i | \(-0.264057\pi\) | ||||
0.675201 | + | 0.737634i | \(0.264057\pi\) | |||||||
\(308\) | 893768.i | 0.536844i | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | − | 1.31251e6i | − | 0.775710i | ||||||
\(311\) | 2.62823e6i | 1.54086i | 0.637526 | + | 0.770429i | \(0.279958\pi\) | ||||
−0.637526 | + | 0.770429i | \(0.720042\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 2.55421e6i | − | 1.47366i | −0.676081 | − | 0.736828i | \(-0.736323\pi\) | ||
0.676081 | − | 0.736828i | \(-0.263677\pi\) | |||||||
\(314\) | −1.36633e6 | −0.782042 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 870228.i | 0.490247i | ||||||||
\(317\) | − | 2.08931e6i | − | 1.16776i | −0.811839 | − | 0.583881i | \(-0.801534\pi\) | ||
0.811839 | − | 0.583881i | \(-0.198466\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.04792e6i | 0.576569i | ||||||||
\(320\) | 1.68940e6 | 0.922269 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 707606. | + | 135981.i | 0.380322 | + | 0.0730865i | ||||
\(323\) | − | 891850.i | − | 0.475648i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.81264e6 | −0.951927 | ||||||||
\(326\) | 2.78278e6i | 1.45022i | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 583682. | 0.299566 | ||||||||
\(329\) | −222605. | −0.113383 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 669432. | 0.335843 | 0.167922 | − | 0.985800i | \(-0.446294\pi\) | ||||
0.167922 | + | 0.985800i | \(0.446294\pi\) | |||||||
\(332\) | 2.78573e6 | 1.38706 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −4.13089e6 | −2.02618 | ||||||||
\(335\) | 2.21734e6i | 1.07950i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2.26733e6i | 1.08752i | 0.839239 | + | 0.543762i | \(0.183001\pi\) | ||||
−0.839239 | + | 0.543762i | \(0.816999\pi\) | |||||||
\(338\) | 3.34977e6i | 1.59486i | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 1.23652e6 | 0.580104 | ||||||||
\(341\) | 2.77611e6 | 1.29286 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.04571e6i | 0.479930i | ||||||||
\(344\) | −2.04106e6 | −0.929951 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −3.87226e6 | −1.73890 | ||||||||
\(347\) | − | 1.79403e6i | − | 0.799845i | −0.916549 | − | 0.399922i | \(-0.869037\pi\) | ||
0.916549 | − | 0.399922i | \(-0.130963\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 3.09620e6 | 1.36071 | 0.680355 | − | 0.732882i | \(-0.261825\pi\) | ||||
0.680355 | + | 0.732882i | \(0.261825\pi\) | |||||||
\(350\) | 594545. | 0.259427 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 4.35732e6i | 1.87440i | ||||||||
\(353\) | − | 4.46663e6i | − | 1.90785i | −0.300051 | − | 0.953923i | \(-0.597004\pi\) | ||
0.300051 | − | 0.953923i | \(-0.402996\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 162354.i | 0.0683742i | ||||||||
\(356\) | 1.38067e6 | 0.577384 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 462300. | 0.190641 | ||||||||
\(359\) | 1.24915e6 | 0.511537 | 0.255769 | − | 0.966738i | \(-0.417671\pi\) | ||||
0.255769 | + | 0.966738i | \(0.417671\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.32459e6 | 0.534950 | ||||||||
\(362\) | −5.50755e6 | −2.20896 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | − | 1.28723e6i | − | 0.509218i | ||||||
\(365\) | 250637. | 0.0984721 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1.81423e6i | 0.703117i | 0.936166 | + | 0.351558i | \(0.114348\pi\) | ||||
−0.936166 | + | 0.351558i | \(0.885652\pi\) | |||||||
\(368\) | 898537. | + | 172672.i | 0.345873 | + | 0.0664663i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 4.13276e6 | 1.56941 | ||||||||
\(371\) | − | 368853.i | − | 0.139129i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 4.17985e6i | 1.55557i | 0.628533 | + | 0.777783i | \(0.283656\pi\) | ||||
−0.628533 | + | 0.777783i | \(0.716344\pi\) | |||||||
\(374\) | 4.42220e6i | 1.63478i | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 879085. | 0.320672 | ||||||||
\(377\) | − | 1.50924e6i | − | 0.546898i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 3.05588e6i | 1.09279i | 0.837527 | + | 0.546397i | \(0.184001\pi\) | ||||
−0.837527 | + | 0.546397i | \(0.815999\pi\) | |||||||
\(380\) | − | 1.59654e6i | − | 0.567178i | ||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 7.20962e6i | 2.52786i | ||||||||
\(383\) | 4.23058e6 | 1.47368 | 0.736840 | − | 0.676068i | \(-0.236317\pi\) | ||||
0.736840 | + | 0.676068i | \(0.236317\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | − | 619754.i | − | 0.213092i | ||||||
\(386\) | − | 3.51316e6i | − | 1.20013i | ||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 5.85766e6i | 1.97535i | ||||||||
\(389\) | −3.31466e6 | −1.11062 | −0.555309 | − | 0.831644i | \(-0.687400\pi\) | ||||
−0.555309 | + | 0.831644i | \(0.687400\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.07063e6 | + | 397913.i | 0.684954 | + | 0.131627i | ||||
\(392\) | − | 1.99953e6i | − | 0.657225i | ||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −2.78438e6 | −0.903625 | ||||||||
\(395\) | − | 603430.i | − | 0.194596i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −1.82036e6 | −0.579670 | −0.289835 | − | 0.957077i | \(-0.593601\pi\) | ||||
−0.289835 | + | 0.957077i | \(0.593601\pi\) | |||||||
\(398\) | −1.67200e6 | −0.529089 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 754969. | 0.235928 | ||||||||
\(401\) | 704005. | 0.218633 | 0.109316 | − | 0.994007i | \(-0.465134\pi\) | ||||
0.109316 | + | 0.994007i | \(0.465134\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −3.99824e6 | −1.22633 | ||||||||
\(404\) | 5.60587e6i | 1.70879i | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 495031.i | 0.149045i | ||||||||
\(407\) | 8.74126e6i | 2.61570i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 2.24072e6 | 0.662339 | 0.331169 | − | 0.943571i | \(-0.392557\pi\) | ||||
0.331169 | + | 0.943571i | \(0.392557\pi\) | |||||||
\(410\) | −1.30913e6 | −0.384611 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 1.97866e6i | 0.574285i | ||||||||
\(413\) | −689865. | −0.199017 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1.93167e6 | −0.550571 | ||||||||
\(416\) | − | 6.27555e6i | − | 1.77795i | ||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 5.70971e6 | 1.59835 | ||||||||
\(419\) | −3.56788e6 | −0.992830 | −0.496415 | − | 0.868085i | \(-0.665351\pi\) | ||||
−0.496415 | + | 0.868085i | \(0.665351\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 5.04487e6i | − | 1.38722i | −0.720352 | − | 0.693609i | \(-0.756020\pi\) | ||
0.720352 | − | 0.693609i | \(-0.243980\pi\) | |||||||
\(422\) | 2.19899e6i | 0.601095i | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 1.45663e6i | 0.393490i | ||||||||
\(425\) | 1.73979e6 | 0.467223 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 98475.4 | 0.0261371 | ||||||||
\(428\) | 3.86565e6 | 1.02003 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 4.57784e6 | 1.19396 | ||||||||
\(431\) | 905396. | 0.234772 | 0.117386 | − | 0.993086i | \(-0.462549\pi\) | ||||
0.117386 | + | 0.993086i | \(0.462549\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 477429.i | 0.122374i | 0.998126 | + | 0.0611870i | \(0.0194886\pi\) | ||||
−0.998126 | + | 0.0611870i | \(0.980511\pi\) | |||||||
\(434\) | 1.31142e6 | 0.334209 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 2.47049e6i | 0.622397i | ||||||||
\(437\) | 513764. | − | 2.67349e6i | 0.128695 | − | 0.669692i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −2.09936e6 | −0.519906 | −0.259953 | − | 0.965621i | \(-0.583707\pi\) | ||||
−0.259953 | + | 0.965621i | \(0.583707\pi\) | |||||||
\(440\) | 2.44745e6i | 0.602674i | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | − | 6.36898e6i | − | 1.55065i | ||||||
\(443\) | − | 5.15177e6i | − | 1.24723i | −0.781731 | − | 0.623616i | \(-0.785663\pi\) | ||
0.781731 | − | 0.623616i | \(-0.214337\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −957379. | −0.229184 | ||||||||
\(446\) | − | 1.11011e7i | − | 2.64259i | ||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 1.68799e6i | 0.397353i | ||||||||
\(449\) | − | 188053.i | − | 0.0440216i | −0.999758 | − | 0.0220108i | \(-0.992993\pi\) | ||
0.999758 | − | 0.0220108i | \(-0.00700682\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 2.76895e6i | − | 0.641023i | ||||||
\(452\) | 1.63101e6 | 0.375501 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | − | 3.43464e6i | − | 0.782064i | ||||||
\(455\) | 892588.i | 0.202126i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 3.55643e6i | 0.796569i | 0.917262 | + | 0.398284i | \(0.130394\pi\) | ||||
−0.917262 | + | 0.398284i | \(0.869606\pi\) | |||||||
\(458\) | −9.57498e6 | −2.13292 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 3.70672e6 | + | 712320.i | 0.816761 | + | 0.156957i | ||||
\(461\) | 7.65350e6i | 1.67729i | 0.544680 | + | 0.838644i | \(0.316651\pi\) | ||||
−0.544680 | + | 0.838644i | \(0.683349\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −4.99234e6 | −1.08231 | −0.541155 | − | 0.840923i | \(-0.682013\pi\) | ||||
−0.541155 | + | 0.840923i | \(0.682013\pi\) | |||||||
\(464\) | 628604.i | 0.135545i | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −9.22138e6 | −1.96712 | ||||||||
\(467\) | 482188. | 0.102311 | 0.0511557 | − | 0.998691i | \(-0.483710\pi\) | ||||
0.0511557 | + | 0.998691i | \(0.483710\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −2.21550e6 | −0.465092 | ||||||||
\(470\) | −1.97168e6 | −0.411710 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 2.72433e6 | 0.562865 | ||||||||
\(473\) | 9.68266e6i | 1.98995i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 2.24632e6i | − | 0.456813i | ||||||
\(476\) | 1.23550e6i | 0.249933i | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 8.38137e6 | 1.67782 | ||||||||
\(479\) | −7.22981e6 | −1.43975 | −0.719877 | − | 0.694102i | \(-0.755802\pi\) | ||||
−0.719877 | + | 0.694102i | \(0.755802\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − | 1.25894e7i | − | 2.48109i | ||||||
\(482\) | 1.48933e6 | 0.291993 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −9.28398e6 | −1.80144 | ||||||||
\(485\) | − | 4.06180e6i | − | 0.784086i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 7.95633e6 | 1.52016 | 0.760082 | − | 0.649828i | \(-0.225159\pi\) | ||||
0.760082 | + | 0.649828i | \(0.225159\pi\) | |||||||
\(488\) | −388887. | −0.0739220 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 4.48470e6i | 0.843808i | ||||||||
\(491\) | − | 4.52236e6i | − | 0.846568i | −0.905997 | − | 0.423284i | \(-0.860877\pi\) | ||
0.905997 | − | 0.423284i | \(-0.139123\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1.44859e6i | 0.268427i | ||||||||
\(494\) | −8.22329e6 | −1.51610 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 1.66528e6 | 0.303936 | ||||||||
\(497\) | −162219. | −0.0294585 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 774400. | 0.139224 | 0.0696120 | − | 0.997574i | \(-0.477824\pi\) | ||||
0.0696120 | + | 0.997574i | \(0.477824\pi\) | |||||||
\(500\) | 7.76384e6 | 1.38884 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 5.84997e6i | 1.03608i | ||||||||
\(503\) | −7.87112e6 | −1.38713 | −0.693564 | − | 0.720395i | \(-0.743961\pi\) | ||||
−0.693564 | + | 0.720395i | \(0.743961\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 3.88720e6i | − | 0.678280i | ||||||
\(506\) | −2.54748e6 | + | 1.32564e7i | −0.442317 | + | 2.30170i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −8.79951e6 | −1.51286 | ||||||||
\(509\) | − | 457065.i | − | 0.0781957i | −0.999235 | − | 0.0390979i | \(-0.987552\pi\) | ||
0.999235 | − | 0.0390979i | \(-0.0124484\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 250429.i | 0.0424259i | ||||||||
\(512\) | 4.07644e6i | 0.687237i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 1.00819e6 | 0.168319 | ||||||||
\(515\) | − | 1.37203e6i | − | 0.227954i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 4.17032e6i | − | 0.686188i | ||||||
\(518\) | 4.12932e6i | 0.676168i | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | − | 3.52489e6i | − | 0.571660i | ||||||
\(521\) | −7.34583e6 | −1.18562 | −0.592811 | − | 0.805342i | \(-0.701982\pi\) | ||||
−0.592811 | + | 0.805342i | \(0.701982\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 1.31316e6i | − | 0.209925i | −0.994476 | − | 0.104963i | \(-0.966528\pi\) | ||
0.994476 | − | 0.104963i | \(-0.0334723\pi\) | |||||||
\(524\) | − | 9.13521e6i | − | 1.45342i | ||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | − | 1.69574e7i | − | 2.67236i | ||||||
\(527\) | 3.83755e6 | 0.601904 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 5.97789e6 | + | 2.38564e6i | 0.928772 | + | 0.370652i | ||||
\(530\) | − | 3.26703e6i | − | 0.505200i | ||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 1.59521e6 | 0.244364 | ||||||||
\(533\) | 3.98792e6i | 0.608036i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −2.68051e6 | −0.404886 | ||||||||
\(536\) | 8.74916e6 | 1.31539 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −1.52511e7 | −2.27167 | ||||||||
\(539\) | −9.48566e6 | −1.40636 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1.14053e7 | −1.67538 | −0.837691 | − | 0.546144i | \(-0.816095\pi\) | ||||
−0.837691 | + | 0.546144i | \(0.816095\pi\) | |||||||
\(542\) | 1.38102e6i | 0.201930i | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 6.02333e6i | 0.872648i | ||||||||
\(545\) | − | 1.71308e6i | − | 0.247051i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1.26924e7 | 1.81374 | 0.906869 | − | 0.421413i | \(-0.138466\pi\) | ||||
0.906869 | + | 0.421413i | \(0.138466\pi\) | |||||||
\(548\) | 2.40947e6 | 0.342745 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 1.11383e7i | 1.57004i | ||||||||
\(551\) | 1.87034e6 | 0.262447 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 602928. | 0.0838403 | ||||||||
\(554\) | − | 1.15000e7i | − | 1.59192i | ||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 1.91307e7 | 2.62449 | ||||||||
\(557\) | −968825. | −0.132314 | −0.0661572 | − | 0.997809i | \(-0.521074\pi\) | ||||
−0.0661572 | + | 0.997809i | \(0.521074\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 1.39453e7i | − | 1.88754i | ||||||
\(560\) | − | 371765.i | − | 0.0500954i | ||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 1.36148e7i | 1.81832i | ||||||||
\(563\) | 1.89549e6 | 0.252028 | 0.126014 | − | 0.992028i | \(-0.459782\pi\) | ||||
0.126014 | + | 0.992028i | \(0.459782\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1.13097e6 | −0.149049 | ||||||||
\(566\) | −1.08463e7 | −1.42311 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 640615. | 0.0833156 | ||||||||
\(569\) | 1.10647e7 | 1.43271 | 0.716354 | − | 0.697738i | \(-0.245810\pi\) | ||||
0.716354 | + | 0.697738i | \(0.245810\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 5.95073e6i | − | 0.763801i | −0.924204 | − | 0.381900i | \(-0.875270\pi\) | ||
0.924204 | − | 0.381900i | \(-0.124730\pi\) | |||||||
\(572\) | 2.41152e7 | 3.08177 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | − | 1.30804e6i | − | 0.165707i | ||||||
\(575\) | 5.21535e6 | + | 1.00223e6i | 0.657831 | + | 0.126415i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −9.66464e6 | −1.20850 | −0.604249 | − | 0.796795i | \(-0.706527\pi\) | ||||
−0.604249 | + | 0.796795i | \(0.706527\pi\) | |||||||
\(578\) | − | 6.45259e6i | − | 0.803368i | ||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 2.59317e6i | 0.320082i | ||||||||
\(581\) | − | 1.93006e6i | − | 0.237209i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 6.91014e6 | 0.842006 | ||||||||
\(584\) | − | 988961.i | − | 0.119990i | ||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 342012.i | 0.0411431i | ||||||||
\(587\) | − | 1.06148e7i | − | 1.27150i | −0.771895 | − | 0.635749i | \(-0.780691\pi\) | ||
0.771895 | − | 0.635749i | \(-0.219309\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 4.95484e6i | − | 0.588493i | ||||||
\(590\) | −6.11032e6 | −0.722660 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 5.24352e6i | 0.614920i | ||||||||
\(593\) | 4.26629e6i | 0.498212i | 0.968476 | + | 0.249106i | \(0.0801367\pi\) | ||||
−0.968476 | + | 0.249106i | \(0.919863\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − | 856713.i | − | 0.0992072i | ||||||
\(596\) | 2.30744e7 | 2.66081 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 3.66895e6 | − | 1.90922e7i | 0.419555 | − | 2.18325i | ||||
\(599\) | − | 1.21167e7i | − | 1.37980i | −0.723903 | − | 0.689902i | \(-0.757654\pi\) | ||
0.723903 | − | 0.689902i | \(-0.242346\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1.45959e7 | −1.64833 | −0.824167 | − | 0.566346i | \(-0.808357\pi\) | ||||
−0.824167 | + | 0.566346i | \(0.808357\pi\) | |||||||
\(602\) | 4.57403e6i | 0.514408i | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 1.23694e7 | 1.37961 | ||||||||
\(605\) | 6.43766e6 | 0.715056 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −8.70600e6 | −0.959063 | −0.479531 | − | 0.877525i | \(-0.659193\pi\) | ||||
−0.479531 | + | 0.877525i | \(0.659193\pi\) | |||||||
\(608\) | 7.77700e6 | 0.853204 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 872223. | 0.0949080 | ||||||||
\(611\) | 6.00622e6i | 0.650876i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 1.60427e7i | − | 1.72435i | −0.506610 | − | 0.862175i | \(-0.669102\pi\) | ||
0.506610 | − | 0.862175i | \(-0.330898\pi\) | |||||||
\(614\) | 1.97355e7i | 2.11264i | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −2.44542e6 | −0.259658 | ||||||||
\(617\) | 1.35989e7 | 1.43811 | 0.719053 | − | 0.694955i | \(-0.244576\pi\) | ||||
0.719053 | + | 0.694955i | \(0.244576\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 8.39164e6i | 0.880279i | 0.897929 | + | 0.440139i | \(0.145071\pi\) | ||||
−0.897929 | + | 0.440139i | \(0.854929\pi\) | |||||||
\(620\) | 6.86974e6 | 0.717730 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −2.32596e7 | −2.41060 | ||||||||
\(623\) | − | 956583.i | − | 0.0987421i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.15809e6 | 0.118589 | ||||||||
\(626\) | 2.26045e7 | 2.30547 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | − | 7.15140e6i | − | 0.723589i | ||||||
\(629\) | 1.20834e7i | 1.21777i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 4.63039e6i | − | 0.462961i | −0.972840 | − | 0.231481i | \(-0.925643\pi\) | ||
0.972840 | − | 0.231481i | \(-0.0743570\pi\) | |||||||
\(632\) | −2.38101e6 | −0.237120 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 1.84902e7 | 1.82691 | ||||||||
\(635\) | 6.10172e6 | 0.600507 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.36615e7 | 1.33398 | ||||||||
\(638\) | −9.27398e6 | −0.902016 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 7.50202e6i | 0.723983i | ||||||||
\(641\) | −7.21313e6 | −0.693392 | −0.346696 | − | 0.937978i | \(-0.612696\pi\) | ||||
−0.346696 | + | 0.937978i | \(0.612696\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1.24779e7i | 1.19019i | 0.803657 | + | 0.595093i | \(0.202885\pi\) | ||||
−0.803657 | + | 0.595093i | \(0.797115\pi\) | |||||||
\(644\) | −711727. | + | 3.70364e6i | −0.0676237 | + | 0.351895i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 7.89278e6 | 0.744130 | ||||||||
\(647\) | − | 8.39992e6i | − | 0.788887i | −0.918920 | − | 0.394443i | \(-0.870937\pi\) | ||
0.918920 | − | 0.394443i | \(-0.129063\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 1.29240e7i | − | 1.20444i | ||||||
\(650\) | − | 1.60417e7i | − | 1.48925i | ||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −1.45652e7 | −1.34183 | ||||||||
\(653\) | − | 5.72017e6i | − | 0.524960i | −0.964937 | − | 0.262480i | \(-0.915460\pi\) | ||
0.964937 | − | 0.262480i | \(-0.0845404\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 6.33450e6i | 0.576912i | ||||||||
\(656\) | − | 1.66098e6i | − | 0.150697i | ||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | − | 1.97004e6i | − | 0.177382i | ||||||
\(659\) | −6.18373e6 | −0.554673 | −0.277337 | − | 0.960773i | \(-0.589452\pi\) | ||||
−0.277337 | + | 0.960773i | \(0.589452\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.39119e6i | 0.123846i | 0.998081 | + | 0.0619231i | \(0.0197233\pi\) | ||||
−0.998081 | + | 0.0619231i | \(0.980277\pi\) | |||||||
\(662\) | 5.92441e6i | 0.525412i | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 7.62197e6i | 0.670883i | ||||||||
\(665\) | −1.10614e6 | −0.0969967 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −834481. | + | 4.34241e6i | −0.0726276 | + | 0.377935i | ||||
\(668\) | − | 2.16213e7i | − | 1.87473i | ||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −1.96233e7 | −1.68882 | ||||||||
\(671\) | 1.84485e6i | 0.158181i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1.31993e7 | 1.12335 | 0.561673 | − | 0.827359i | \(-0.310158\pi\) | ||||
0.561673 | + | 0.827359i | \(0.310158\pi\) | |||||||
\(674\) | −2.00656e7 | −1.70138 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −1.75328e7 | −1.47566 | ||||||||
\(677\) | 1.85679e7 | 1.55701 | 0.778503 | − | 0.627640i | \(-0.215979\pi\) | ||||
0.778503 | + | 0.627640i | \(0.215979\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 4.05842e6 | 0.337818 | ||||||||
\(680\) | 3.38322e6i | 0.280581i | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 2.45683e7i | 2.02262i | ||||||||
\(683\) | 1.44272e7i | 1.18339i | 0.806161 | + | 0.591696i | \(0.201542\pi\) | ||||
−0.806161 | + | 0.591696i | \(0.798458\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −1.67077e6 | −0.136047 | ||||||||
\(686\) | −9.25447e6 | −0.750829 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 5.80823e6i | 0.467813i | ||||||||
\(689\) | −9.95218e6 | −0.798675 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1.56581e7 | −1.24751 | −0.623755 | − | 0.781620i | \(-0.714394\pi\) | ||||
−0.623755 | + | 0.781620i | \(0.714394\pi\) | |||||||
\(692\) | − | 2.02676e7i | − | 1.60893i | ||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 1.58770e7 | 1.25132 | ||||||||
\(695\) | −1.32656e7 | −1.04175 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 3.82764e6i | − | 0.298435i | ||||||
\(698\) | 2.74011e7i | 2.12877i | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 3.11187e6i | 0.240036i | ||||||||
\(701\) | −1.87473e6 | −0.144093 | −0.0720465 | − | 0.997401i | \(-0.522953\pi\) | ||||
−0.0720465 | + | 0.997401i | \(0.522953\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.56015e7 | 1.19063 | ||||||||
\(704\) | −3.16231e7 | −2.40477 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 3.95292e7 | 2.98474 | ||||||||
\(707\) | 3.88397e6 | 0.292232 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 4.21563e6i | 0.314954i | 0.987523 | + | 0.157477i | \(0.0503360\pi\) | ||||
−0.987523 | + | 0.157477i | \(0.949664\pi\) | |||||||
\(710\) | −1.43682e6 | −0.106968 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 3.77761e6i | 0.279266i | ||||||||
\(713\) | 1.15038e7 | + | 2.21068e6i | 0.847456 | + | 0.162855i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.67219e7 | −1.22326 | ||||||||
\(716\) | 2.41970e6i | 0.176392i | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 1.10548e7i | 0.800278i | ||||||||
\(719\) | 3.85693e6i | 0.278240i | 0.990276 | + | 0.139120i | \(0.0444273\pi\) | ||||
−0.990276 | + | 0.139120i | \(0.955573\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.37089e6 | 0.0982121 | ||||||||
\(722\) | 1.17225e7i | 0.836906i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | − | 2.88267e7i | − | 2.04385i | ||||||
\(725\) | 3.64859e6i | 0.257798i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1.82196e7i | 1.27850i | 0.768998 | + | 0.639251i | \(0.220756\pi\) | ||||
−0.768998 | + | 0.639251i | \(0.779244\pi\) | |||||||
\(728\) | 3.52196e6 | 0.246295 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 2.21811e6i | 0.154055i | ||||||||
\(731\) | 1.33848e7i | 0.926440i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 2.49993e7i | − | 1.71857i | −0.511495 | − | 0.859286i | \(-0.670908\pi\) | ||
0.511495 | − | 0.859286i | \(-0.329092\pi\) | |||||||
\(734\) | −1.60558e7 | −1.09999 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −3.46983e6 | + | 1.80561e7i | −0.236110 | + | 1.22865i | ||||
\(737\) | − | 4.15054e7i | − | 2.81473i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 2.49012e6 | 0.167729 | 0.0838647 | − | 0.996477i | \(-0.473274\pi\) | ||||
0.0838647 | + | 0.996477i | \(0.473274\pi\) | |||||||
\(740\) | 2.16310e7i | 1.45210i | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 3.26431e6 | 0.217661 | ||||||||
\(743\) | −1.05540e7 | −0.701367 | −0.350684 | − | 0.936494i | \(-0.614051\pi\) | ||||
−0.350684 | + | 0.936494i | \(0.614051\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1.60002e7 | −1.05617 | ||||||||
\(746\) | −3.69912e7 | −2.43362 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −2.31460e7 | −1.51259 | ||||||||
\(749\) | − | 2.67828e6i | − | 0.174442i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.14752e7i | 0.742440i | 0.928545 | + | 0.371220i | \(0.121060\pi\) | ||||
−0.928545 | + | 0.371220i | \(0.878940\pi\) | |||||||
\(752\) | − | 2.50160e6i | − | 0.161315i | ||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 1.33567e7 | 0.855598 | ||||||||
\(755\) | −8.57714e6 | −0.547615 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 2.88533e7i | − | 1.83002i | −0.403433 | − | 0.915009i | \(-0.632183\pi\) | ||
0.403433 | − | 0.915009i | \(-0.367817\pi\) | |||||||
\(758\) | −2.70442e7 | −1.70963 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 4.36824e6 | 0.274329 | ||||||||
\(761\) | − | 1.15175e7i | − | 0.720934i | −0.932772 | − | 0.360467i | \(-0.882617\pi\) | ||
0.932772 | − | 0.360467i | \(-0.117383\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.71166e6 | 0.106440 | ||||||||
\(764\) | −3.77354e7 | −2.33892 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 3.74402e7i | 2.30551i | ||||||||
\(767\) | 1.86136e7i | 1.14246i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 7.23163e6i | 0.440981i | 0.975389 | + | 0.220491i | \(0.0707659\pi\) | ||||
−0.975389 | + | 0.220491i | \(0.929234\pi\) | |||||||
\(770\) | 5.48476e6 | 0.333373 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 1.83880e7 | 1.11043 | ||||||||
\(773\) | 2.66964e7 | 1.60696 | 0.803478 | − | 0.595335i | \(-0.202981\pi\) | ||||
0.803478 | + | 0.595335i | \(0.202981\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 9.66572e6 | 0.578070 | ||||||||
\(776\) | −1.60270e7 | −0.955427 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | − | 2.93344e7i | − | 1.73751i | ||||||
\(779\) | −4.94205e6 | −0.291785 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 3.03903e6i | − | 0.178282i | ||||||
\(782\) | −3.52149e6 | + | 1.83249e7i | −0.205925 | + | 1.07158i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −5.69006e6 | −0.330618 | ||||||||
\(785\) | 4.95890e6i | 0.287218i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1.40550e7i | 0.808897i | 0.914561 | + | 0.404449i | \(0.132537\pi\) | ||||
−0.914561 | + | 0.404449i | \(0.867463\pi\) | |||||||
\(788\) | − | 1.45736e7i | − | 0.836085i | ||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 5.34030e6 | 0.304437 | ||||||||
\(791\) | − | 1.13003e6i | − | 0.0642167i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 2.65701e6i | − | 0.150041i | ||||||
\(794\) | − | 1.61100e7i | − | 0.906869i | ||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | − | 8.75132e6i | − | 0.489543i | ||||||
\(797\) | 2.43756e7 | 1.35928 | 0.679642 | − | 0.733544i | \(-0.262135\pi\) | ||||
0.679642 | + | 0.733544i | \(0.262135\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 5.76482e6i | − | 0.319462i | ||||||
\(800\) | 1.51711e7i | 0.838092i | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 6.23037e6i | 0.342041i | ||||||||
\(803\) | −4.69156e6 | −0.256761 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 493523. | − | 2.56816e6i | 0.0268422 | − | 0.139680i | ||||
\(806\) | − | 3.53841e7i | − | 1.91854i | ||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −1.53381e7 | −0.826499 | ||||||||
\(809\) | 8.73191e6i | 0.469070i | 0.972108 | + | 0.234535i | \(0.0753568\pi\) | ||||
−0.972108 | + | 0.234535i | \(0.924643\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 9.83211e6 | 0.524922 | 0.262461 | − | 0.964943i | \(-0.415466\pi\) | ||||
0.262461 | + | 0.964943i | \(0.415466\pi\) | |||||||
\(812\) | −2.59101e6 | −0.137905 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −7.73593e7 | −4.09215 | ||||||||
\(815\) | 1.00997e7 | 0.532617 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.72817e7 | 0.905798 | ||||||||
\(818\) | 1.98302e7i | 1.03620i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | − | 6.85201e6i | − | 0.355864i | ||||||
\(821\) | − | 1.77459e7i | − | 0.918841i | −0.888219 | − | 0.459421i | \(-0.848057\pi\) | ||
0.888219 | − | 0.459421i | \(-0.151943\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 6.14010e6 | 0.315992 | 0.157996 | − | 0.987440i | \(-0.449497\pi\) | ||||
0.157996 | + | 0.987440i | \(0.449497\pi\) | |||||||
\(824\) | −5.41375e6 | −0.277767 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | − | 6.10524e6i | − | 0.311353i | ||||||
\(827\) | 2.46889e7 | 1.25527 | 0.627637 | − | 0.778506i | \(-0.284022\pi\) | ||||
0.627637 | + | 0.778506i | \(0.284022\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −1.63192e7 | −0.824729 | −0.412364 | − | 0.911019i | \(-0.635297\pi\) | ||||
−0.412364 | + | 0.911019i | \(0.635297\pi\) | |||||||
\(830\) | − | 1.70951e7i | − | 0.861343i | ||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 4.55446e7 | 2.28102 | ||||||||
\(833\) | −1.31125e7 | −0.654744 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1.49925e7i | 0.744147i | ||||||||
\(836\) | 2.98848e7i | 1.47889i | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | − | 3.15754e7i | − | 1.55324i | ||||||
\(839\) | 9.90074e6 | 0.485582 | 0.242791 | − | 0.970079i | \(-0.421937\pi\) | ||||
0.242791 | + | 0.970079i | \(0.421937\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.74733e7 | 0.851891 | ||||||||
\(842\) | 4.46466e7 | 2.17024 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −1.15096e7 | −0.556167 | ||||||||
\(845\) | 1.21576e7 | 0.585740 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 6.43231e6i | 0.308076i | ||||||||
\(848\) | 4.14511e6 | 0.197946 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 1.53970e7i | 0.730950i | ||||||||
\(851\) | −6.96086e6 | + | 3.62224e7i | −0.329487 | + | 1.71456i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −2.20295e7 | −1.03665 | −0.518325 | − | 0.855184i | \(-0.673444\pi\) | ||||
−0.518325 | + | 0.855184i | \(0.673444\pi\) | |||||||
\(854\) | 871498.i | 0.0408904i | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 1.05767e7i | 0.493362i | ||||||||
\(857\) | − | 5.35124e6i | − | 0.248887i | −0.992227 | − | 0.124443i | \(-0.960285\pi\) | ||
0.992227 | − | 0.124443i | \(-0.0397145\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −2.27154e7 | −1.05036 | −0.525180 | − | 0.850991i | \(-0.676002\pi\) | ||||
−0.525180 | + | 0.850991i | \(0.676002\pi\) | |||||||
\(860\) | 2.39606e7i | 1.10472i | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 8.01267e6i | 0.367290i | ||||||||
\(863\) | − | 2.50118e7i | − | 1.14319i | −0.820537 | − | 0.571594i | \(-0.806325\pi\) | ||
0.820537 | − | 0.571594i | \(-0.193675\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1.40539e7i | 0.638639i | ||||||||
\(866\) | −4.22520e6 | −0.191449 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 6.86403e6i | 0.309229i | ||||||||
\(869\) | 1.12953e7i | 0.507399i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 5.97774e7i | 2.66988i | ||||||||
\(872\) | −6.75945e6 | −0.301037 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 2.36601e7 | + | 4.54676e6i | 1.04770 | + | 0.201337i | ||||
\(875\) | − | 5.37910e6i | − | 0.237514i | ||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1.33025e7 | 0.584030 | 0.292015 | − | 0.956414i | \(-0.405674\pi\) | ||||
0.292015 | + | 0.956414i | \(0.405674\pi\) | |||||||
\(878\) | − | 1.85791e7i | − | 0.813370i | ||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 6.96469e6 | 0.303176 | ||||||||
\(881\) | 2.81119e7 | 1.22025 | 0.610127 | − | 0.792304i | \(-0.291119\pi\) | ||||
0.610127 | + | 0.792304i | \(0.291119\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −3.69156e7 | −1.59334 | −0.796668 | − | 0.604417i | \(-0.793406\pi\) | ||||
−0.796668 | + | 0.604417i | \(0.793406\pi\) | |||||||
\(884\) | 3.33355e7 | 1.43475 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 4.55927e7 | 1.95124 | ||||||||
\(887\) | − | 2.10720e7i | − | 0.899283i | −0.893209 | − | 0.449641i | \(-0.851552\pi\) | ||
0.893209 | − | 0.449641i | \(-0.148448\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 6.09665e6i | 0.258724i | ||||||||
\(890\) | − | 8.47271e6i | − | 0.358548i | ||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 5.81037e7 | 2.44507 | ||||||||
\(893\) | −7.44323e6 | −0.312344 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 1.67786e6i | − | 0.0700161i | ||||||
\(896\) | −7.49578e6 | −0.311923 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 1.66425e6 | 0.0688698 | ||||||||
\(899\) | 8.04789e6i | 0.332111i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 9.55219e6 | 0.392004 | ||||||||
\(902\) | 2.45049e7 | 1.00285 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 4.46257e6i | 0.181620i | ||||||||
\(905\) | 1.99889e7i | 0.811275i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 4.67560e6i | 0.188721i | 0.995538 | + | 0.0943603i | \(0.0300806\pi\) | ||||
−0.995538 | + | 0.0943603i | \(0.969919\pi\) | |||||||
\(908\) | 1.79771e7 | 0.723609 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −7.89931e6 | −0.316217 | ||||||||
\(911\) | −2.67198e7 | −1.06669 | −0.533343 | − | 0.845899i | \(-0.679065\pi\) | ||||
−0.533343 | + | 0.845899i | \(0.679065\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 3.61581e7 | 1.43558 | ||||||||
\(914\) | −3.14740e7 | −1.24620 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | − | 5.01158e7i | − | 1.97349i | ||||||
\(917\) | −6.32923e6 | −0.248558 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1.67106e6i | 0.0652685i | 0.999467 | + | 0.0326343i | \(0.0103897\pi\) | ||||
−0.999467 | + | 0.0326343i | \(0.989610\pi\) | |||||||
\(920\) | −1.94896e6 | + | 1.01419e7i | −0.0759160 | + | 0.395046i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −6.77327e7 | −2.62404 | ||||||||
\(923\) | 4.37691e6i | 0.169108i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 3.04348e7i | 1.16954i | ||||||||
\(926\) | − | 4.41817e7i | − | 1.69323i | ||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −1.26318e7 | −0.481498 | ||||||||
\(929\) | − | 3.81445e7i | − | 1.45008i | −0.688705 | − | 0.725041i | \(-0.741821\pi\) | ||
0.688705 | − | 0.725041i | \(-0.258179\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.69301e7i | 0.640155i | ||||||||
\(932\) | − | 4.82651e7i | − | 1.82009i | ||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 4.26732e6i | 0.160062i | ||||||||
\(935\) | 1.60498e7 | 0.600399 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 5.11671e6i | 0.190389i | 0.995459 | + | 0.0951944i | \(0.0303473\pi\) | ||||
−0.995459 | + | 0.0951944i | \(0.969653\pi\) | |||||||
\(938\) | − | 1.96069e7i | − | 0.727616i | ||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | − | 1.03198e7i | − | 0.380937i | ||||||
\(941\) | 1.94139e7 | 0.714725 | 0.357362 | − | 0.933966i | \(-0.383676\pi\) | ||||
0.357362 | + | 0.933966i | \(0.383676\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 2.20498e6 | − | 1.14741e7i | 0.0807467 | − | 0.420184i | ||||
\(944\) | − | 7.75259e6i | − | 0.283150i | ||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −8.56905e7 | −3.11319 | ||||||||
\(947\) | 1.61762e7i | 0.586140i | 0.956091 | + | 0.293070i | \(0.0946768\pi\) | ||||
−0.956091 | + | 0.293070i | \(0.905323\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 6.75693e6 | 0.243548 | ||||||||
\(950\) | 1.98797e7 | 0.714664 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −3.38041e6 | −0.120886 | ||||||||
\(953\) | −1.69946e7 | −0.606148 | −0.303074 | − | 0.952967i | \(-0.598013\pi\) | ||||
−0.303074 | + | 0.952967i | \(0.598013\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 2.61664e7 | 0.928399 | ||||||||
\(956\) | 4.38684e7i | 1.55241i | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | − | 6.39831e7i | − | 2.25243i | ||||||
\(959\) | − | 1.66938e6i | − | 0.0586150i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −7.30894e6 | −0.255297 | ||||||||
\(962\) | 1.11415e8 | 3.88156 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 7.79520e6i | 0.270168i | ||||||||
\(965\) | −1.27505e7 | −0.440768 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −9.47024e6 | −0.325683 | −0.162841 | − | 0.986652i | \(-0.552066\pi\) | ||||
−0.162841 | + | 0.986652i | \(0.552066\pi\) | |||||||
\(968\) | − | 2.54017e7i | − | 0.871312i | ||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 3.59465e7 | 1.22667 | ||||||||
\(971\) | 2.74957e7 | 0.935874 | 0.467937 | − | 0.883762i | \(-0.344997\pi\) | ||||
0.467937 | + | 0.883762i | \(0.344997\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 1.32545e7i | − | 0.448831i | ||||||
\(974\) | 7.04127e7i | 2.37823i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 1.10665e6i | 0.0371866i | ||||||||
\(977\) | 3.33362e7 | 1.11732 | 0.558662 | − | 0.829395i | \(-0.311315\pi\) | ||||
0.558662 | + | 0.829395i | \(0.311315\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1.79207e7 | 0.597585 | ||||||||
\(980\) | −2.34731e7 | −0.780738 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 4.00225e7 | 1.32442 | ||||||||
\(983\) | −3.35806e7 | −1.10842 | −0.554210 | − | 0.832377i | \(-0.686979\pi\) | ||||
−0.554210 | + | 0.832377i | \(0.686979\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1.01056e7i | 0.331871i | ||||||||
\(986\) | −1.28198e7 | −0.419943 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | − | 4.30410e7i | − | 1.40278i | ||||||
\(989\) | −7.71051e6 | + | 4.01234e7i | −0.250664 | + | 1.30439i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1.73879e7 | 0.562422 | 0.281211 | − | 0.959646i | \(-0.409264\pi\) | ||||
0.281211 | + | 0.959646i | \(0.409264\pi\) | |||||||
\(992\) | 3.34637e7i | 1.07968i | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | − | 1.43562e6i | − | 0.0460866i | ||||||
\(995\) | 6.06831e6i | 0.194317i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −4.16006e7 | −1.32544 | −0.662722 | − | 0.748865i | \(-0.730599\pi\) | ||||
−0.662722 | + | 0.748865i | \(0.730599\pi\) | |||||||
\(998\) | 6.85336e6i | 0.217810i | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 207.6.c.a.206.26 | yes | 40 | |
3.2 | odd | 2 | inner | 207.6.c.a.206.15 | ✓ | 40 | |
23.22 | odd | 2 | inner | 207.6.c.a.206.16 | yes | 40 | |
69.68 | even | 2 | inner | 207.6.c.a.206.25 | yes | 40 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
207.6.c.a.206.15 | ✓ | 40 | 3.2 | odd | 2 | inner | |
207.6.c.a.206.16 | yes | 40 | 23.22 | odd | 2 | inner | |
207.6.c.a.206.25 | yes | 40 | 69.68 | even | 2 | inner | |
207.6.c.a.206.26 | yes | 40 | 1.1 | even | 1 | trivial |