Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [825,6,Mod(1,825)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(825, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("825.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 825 = 3 \cdot 5^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 825.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(132.316651346\) |
Analytic rank: | \(1\) |
Dimension: | \(13\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{13} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{13} - 306 x^{11} - 206 x^{10} + 34574 x^{9} + 39928 x^{8} - 1788312 x^{7} - 2591628 x^{6} + 42852537 x^{5} + 63733360 x^{4} - 448113518 x^{3} + \cdots + 522579400 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2^{9}\cdot 3^{2}\cdot 5^{7} \) |
Twist minimal: | no (minimal twist has level 165) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-9.75306\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 825.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −10.7531 | −1.90089 | −0.950445 | − | 0.310892i | \(-0.899372\pi\) | ||||
−0.950445 | + | 0.310892i | \(0.899372\pi\) | |||||||
\(3\) | −9.00000 | −0.577350 | ||||||||
\(4\) | 83.6283 | 2.61338 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 96.7775 | 1.09748 | ||||||||
\(7\) | −41.3813 | −0.319197 | −0.159599 | − | 0.987182i | \(-0.551020\pi\) | ||||
−0.159599 | + | 0.987182i | \(0.551020\pi\) | |||||||
\(8\) | −555.162 | −3.06687 | ||||||||
\(9\) | 81.0000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 121.000 | 0.301511 | ||||||||
\(12\) | −752.654 | −1.50884 | ||||||||
\(13\) | 13.6514 | 0.0224037 | 0.0112019 | − | 0.999937i | \(-0.496434\pi\) | ||||
0.0112019 | + | 0.999937i | \(0.496434\pi\) | |||||||
\(14\) | 444.975 | 0.606759 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 3293.58 | 3.21639 | ||||||||
\(17\) | −1143.92 | −0.960005 | −0.480002 | − | 0.877267i | \(-0.659364\pi\) | ||||
−0.480002 | + | 0.877267i | \(0.659364\pi\) | |||||||
\(18\) | −870.998 | −0.633630 | ||||||||
\(19\) | −1425.16 | −0.905689 | −0.452844 | − | 0.891590i | \(-0.649591\pi\) | ||||
−0.452844 | + | 0.891590i | \(0.649591\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 372.432 | 0.184289 | ||||||||
\(22\) | −1301.12 | −0.573140 | ||||||||
\(23\) | 2533.88 | 0.998770 | 0.499385 | − | 0.866380i | \(-0.333559\pi\) | ||||
0.499385 | + | 0.866380i | \(0.333559\pi\) | |||||||
\(24\) | 4996.46 | 1.77066 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −146.795 | −0.0425870 | ||||||||
\(27\) | −729.000 | −0.192450 | ||||||||
\(28\) | −3460.65 | −0.834185 | ||||||||
\(29\) | 8594.21 | 1.89763 | 0.948814 | − | 0.315837i | \(-0.102285\pi\) | ||||
0.948814 | + | 0.315837i | \(0.102285\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 434.427 | 0.0811918 | 0.0405959 | − | 0.999176i | \(-0.487074\pi\) | ||||
0.0405959 | + | 0.999176i | \(0.487074\pi\) | |||||||
\(32\) | −17650.9 | −3.04714 | ||||||||
\(33\) | −1089.00 | −0.174078 | ||||||||
\(34\) | 12300.6 | 1.82486 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 6773.89 | 0.871128 | ||||||||
\(37\) | −14403.2 | −1.72963 | −0.864815 | − | 0.502090i | \(-0.832564\pi\) | ||||
−0.864815 | + | 0.502090i | \(0.832564\pi\) | |||||||
\(38\) | 15324.8 | 1.72162 | ||||||||
\(39\) | −122.863 | −0.0129348 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 12386.5 | 1.15077 | 0.575387 | − | 0.817881i | \(-0.304851\pi\) | ||||
0.575387 | + | 0.817881i | \(0.304851\pi\) | |||||||
\(42\) | −4004.78 | −0.350312 | ||||||||
\(43\) | 2699.39 | 0.222635 | 0.111318 | − | 0.993785i | \(-0.464493\pi\) | ||||
0.111318 | + | 0.993785i | \(0.464493\pi\) | |||||||
\(44\) | 10119.0 | 0.787965 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −27246.9 | −1.89855 | ||||||||
\(47\) | 1691.93 | 0.111722 | 0.0558608 | − | 0.998439i | \(-0.482210\pi\) | ||||
0.0558608 | + | 0.998439i | \(0.482210\pi\) | |||||||
\(48\) | −29642.3 | −1.85698 | ||||||||
\(49\) | −15094.6 | −0.898113 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 10295.3 | 0.554259 | ||||||||
\(52\) | 1141.65 | 0.0585495 | ||||||||
\(53\) | 9465.19 | 0.462850 | 0.231425 | − | 0.972853i | \(-0.425661\pi\) | ||||
0.231425 | + | 0.972853i | \(0.425661\pi\) | |||||||
\(54\) | 7838.98 | 0.365826 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 22973.3 | 0.978935 | ||||||||
\(57\) | 12826.4 | 0.522900 | ||||||||
\(58\) | −92414.0 | −3.60718 | ||||||||
\(59\) | −41470.4 | −1.55099 | −0.775493 | − | 0.631356i | \(-0.782499\pi\) | ||||
−0.775493 | + | 0.631356i | \(0.782499\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −17867.3 | −0.614802 | −0.307401 | − | 0.951580i | \(-0.599459\pi\) | ||||
−0.307401 | + | 0.951580i | \(0.599459\pi\) | |||||||
\(62\) | −4671.41 | −0.154337 | ||||||||
\(63\) | −3351.88 | −0.106399 | ||||||||
\(64\) | 84406.7 | 2.57589 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 11710.1 | 0.330903 | ||||||||
\(67\) | −51700.6 | −1.40705 | −0.703523 | − | 0.710672i | \(-0.748391\pi\) | ||||
−0.703523 | + | 0.710672i | \(0.748391\pi\) | |||||||
\(68\) | −95664.1 | −2.50886 | ||||||||
\(69\) | −22804.9 | −0.576640 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −16645.8 | −0.391885 | −0.195943 | − | 0.980615i | \(-0.562777\pi\) | ||||
−0.195943 | + | 0.980615i | \(0.562777\pi\) | |||||||
\(72\) | −44968.1 | −1.02229 | ||||||||
\(73\) | 49707.4 | 1.09173 | 0.545863 | − | 0.837874i | \(-0.316202\pi\) | ||||
0.545863 | + | 0.837874i | \(0.316202\pi\) | |||||||
\(74\) | 154878. | 3.28784 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −119184. | −2.36691 | ||||||||
\(77\) | −5007.14 | −0.0962416 | ||||||||
\(78\) | 1321.15 | 0.0245876 | ||||||||
\(79\) | 71497.6 | 1.28891 | 0.644456 | − | 0.764641i | \(-0.277084\pi\) | ||||
0.644456 | + | 0.764641i | \(0.277084\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 6561.00 | 0.111111 | ||||||||
\(82\) | −133193. | −2.18750 | ||||||||
\(83\) | 33539.3 | 0.534390 | 0.267195 | − | 0.963642i | \(-0.413903\pi\) | ||||
0.267195 | + | 0.963642i | \(0.413903\pi\) | |||||||
\(84\) | 31145.8 | 0.481617 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −29026.7 | −0.423205 | ||||||||
\(87\) | −77347.9 | −1.09560 | ||||||||
\(88\) | −67174.6 | −0.924695 | ||||||||
\(89\) | −76978.3 | −1.03013 | −0.515066 | − | 0.857150i | \(-0.672233\pi\) | ||||
−0.515066 | + | 0.857150i | \(0.672233\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −564.914 | −0.00715120 | ||||||||
\(92\) | 211904. | 2.61017 | ||||||||
\(93\) | −3909.84 | −0.0468761 | ||||||||
\(94\) | −18193.4 | −0.212371 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 158858. | 1.75927 | ||||||||
\(97\) | −17713.7 | −0.191152 | −0.0955761 | − | 0.995422i | \(-0.530469\pi\) | ||||
−0.0955761 | + | 0.995422i | \(0.530469\pi\) | |||||||
\(98\) | 162313. | 1.70721 | ||||||||
\(99\) | 9801.00 | 0.100504 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −2788.38 | −0.0271987 | −0.0135994 | − | 0.999908i | \(-0.504329\pi\) | ||||
−0.0135994 | + | 0.999908i | \(0.504329\pi\) | |||||||
\(102\) | −110706. | −1.05359 | ||||||||
\(103\) | −3106.69 | −0.0288539 | −0.0144269 | − | 0.999896i | \(-0.504592\pi\) | ||||
−0.0144269 | + | 0.999896i | \(0.504592\pi\) | |||||||
\(104\) | −7578.76 | −0.0687092 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −101780. | −0.879826 | ||||||||
\(107\) | 21599.2 | 0.182381 | 0.0911904 | − | 0.995833i | \(-0.470933\pi\) | ||||
0.0911904 | + | 0.995833i | \(0.470933\pi\) | |||||||
\(108\) | −60965.0 | −0.502946 | ||||||||
\(109\) | 190632. | 1.53684 | 0.768421 | − | 0.639945i | \(-0.221043\pi\) | ||||
0.768421 | + | 0.639945i | \(0.221043\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 129628. | 0.998603 | ||||||||
\(112\) | −136293. | −1.02666 | ||||||||
\(113\) | 239503. | 1.76447 | 0.882236 | − | 0.470808i | \(-0.156038\pi\) | ||||
0.882236 | + | 0.470808i | \(0.156038\pi\) | |||||||
\(114\) | −137923. | −0.993975 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 718719. | 4.95923 | ||||||||
\(117\) | 1105.77 | 0.00746791 | ||||||||
\(118\) | 445934. | 2.94826 | ||||||||
\(119\) | 47336.9 | 0.306431 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 14641.0 | 0.0909091 | ||||||||
\(122\) | 192129. | 1.16867 | ||||||||
\(123\) | −111479. | −0.664400 | ||||||||
\(124\) | 36330.3 | 0.212185 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 36043.0 | 0.202253 | ||||||||
\(127\) | 112217. | 0.617373 | 0.308687 | − | 0.951164i | \(-0.400111\pi\) | ||||
0.308687 | + | 0.951164i | \(0.400111\pi\) | |||||||
\(128\) | −342801. | −1.84934 | ||||||||
\(129\) | −24294.5 | −0.128539 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 334801. | 1.70455 | 0.852273 | − | 0.523097i | \(-0.175224\pi\) | ||||
0.852273 | + | 0.523097i | \(0.175224\pi\) | |||||||
\(132\) | −91071.2 | −0.454932 | ||||||||
\(133\) | 58974.9 | 0.289093 | ||||||||
\(134\) | 555939. | 2.67464 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 635061. | 2.94420 | ||||||||
\(137\) | −913.914 | −0.00416010 | −0.00208005 | − | 0.999998i | \(-0.500662\pi\) | ||||
−0.00208005 | + | 0.999998i | \(0.500662\pi\) | |||||||
\(138\) | 245222. | 1.09613 | ||||||||
\(139\) | 270355. | 1.18685 | 0.593427 | − | 0.804888i | \(-0.297774\pi\) | ||||
0.593427 | + | 0.804888i | \(0.297774\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −15227.4 | −0.0645025 | ||||||||
\(142\) | 178993. | 0.744931 | ||||||||
\(143\) | 1651.82 | 0.00675498 | ||||||||
\(144\) | 266780. | 1.07213 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −534507. | −2.07525 | ||||||||
\(147\) | 135851. | 0.518526 | ||||||||
\(148\) | −1.20451e6 | −4.52019 | ||||||||
\(149\) | −533592. | −1.96899 | −0.984496 | − | 0.175407i | \(-0.943876\pi\) | ||||
−0.984496 | + | 0.175407i | \(0.943876\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −109266. | −0.389980 | −0.194990 | − | 0.980805i | \(-0.562467\pi\) | ||||
−0.194990 | + | 0.980805i | \(0.562467\pi\) | |||||||
\(152\) | 791193. | 2.77763 | ||||||||
\(153\) | −92657.5 | −0.320002 | ||||||||
\(154\) | 53842.0 | 0.182945 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −10274.8 | −0.0338036 | ||||||||
\(157\) | 362759. | 1.17454 | 0.587272 | − | 0.809390i | \(-0.300202\pi\) | ||||
0.587272 | + | 0.809390i | \(0.300202\pi\) | |||||||
\(158\) | −768818. | −2.45008 | ||||||||
\(159\) | −85186.7 | −0.267226 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −104855. | −0.318805 | ||||||||
\(162\) | −70550.8 | −0.211210 | ||||||||
\(163\) | −339033. | −0.999478 | −0.499739 | − | 0.866176i | \(-0.666571\pi\) | ||||
−0.499739 | + | 0.866176i | \(0.666571\pi\) | |||||||
\(164\) | 1.03586e6 | 3.00742 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −360650. | −1.01582 | ||||||||
\(167\) | −459806. | −1.27580 | −0.637901 | − | 0.770118i | \(-0.720197\pi\) | ||||
−0.637901 | + | 0.770118i | \(0.720197\pi\) | |||||||
\(168\) | −206760. | −0.565188 | ||||||||
\(169\) | −371107. | −0.999498 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −115438. | −0.301896 | ||||||||
\(172\) | 225745. | 0.581831 | ||||||||
\(173\) | 527699. | 1.34051 | 0.670256 | − | 0.742130i | \(-0.266184\pi\) | ||||
0.670256 | + | 0.742130i | \(0.266184\pi\) | |||||||
\(174\) | 831726. | 2.08261 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 398524. | 0.969778 | ||||||||
\(177\) | 373234. | 0.895463 | ||||||||
\(178\) | 827752. | 1.95817 | ||||||||
\(179\) | 789810. | 1.84243 | 0.921213 | − | 0.389059i | \(-0.127200\pi\) | ||||
0.921213 | + | 0.389059i | \(0.127200\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −375428. | −0.851786 | −0.425893 | − | 0.904773i | \(-0.640040\pi\) | ||||
−0.425893 | + | 0.904773i | \(0.640040\pi\) | |||||||
\(182\) | 6074.56 | 0.0135937 | ||||||||
\(183\) | 160806. | 0.354956 | ||||||||
\(184\) | −1.40671e6 | −3.06309 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 42042.7 | 0.0891063 | ||||||||
\(187\) | −138414. | −0.289452 | ||||||||
\(188\) | 141493. | 0.291972 | ||||||||
\(189\) | 30167.0 | 0.0614295 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 339151. | 0.672681 | 0.336341 | − | 0.941740i | \(-0.390811\pi\) | ||||
0.336341 | + | 0.941740i | \(0.390811\pi\) | |||||||
\(192\) | −759660. | −1.48719 | ||||||||
\(193\) | −359337. | −0.694398 | −0.347199 | − | 0.937792i | \(-0.612867\pi\) | ||||
−0.347199 | + | 0.937792i | \(0.612867\pi\) | |||||||
\(194\) | 190476. | 0.363359 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1.26233e6 | −2.34711 | ||||||||
\(197\) | 604048. | 1.10893 | 0.554467 | − | 0.832206i | \(-0.312922\pi\) | ||||
0.554467 | + | 0.832206i | \(0.312922\pi\) | |||||||
\(198\) | −105391. | −0.191047 | ||||||||
\(199\) | −1.03446e6 | −1.85174 | −0.925868 | − | 0.377846i | \(-0.876665\pi\) | ||||
−0.925868 | + | 0.377846i | \(0.876665\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 465305. | 0.812358 | ||||||||
\(202\) | 29983.6 | 0.0517018 | ||||||||
\(203\) | −355639. | −0.605717 | ||||||||
\(204\) | 860976. | 1.44849 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 33406.4 | 0.0548481 | ||||||||
\(207\) | 205244. | 0.332923 | ||||||||
\(208\) | 44962.2 | 0.0720591 | ||||||||
\(209\) | −172444. | −0.273075 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −758371. | −1.17267 | −0.586335 | − | 0.810069i | \(-0.699430\pi\) | ||||
−0.586335 | + | 0.810069i | \(0.699430\pi\) | |||||||
\(212\) | 791558. | 1.20960 | ||||||||
\(213\) | 149812. | 0.226255 | ||||||||
\(214\) | −232258. | −0.346686 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 404713. | 0.590218 | ||||||||
\(217\) | −17977.1 | −0.0259162 | ||||||||
\(218\) | −2.04988e6 | −2.92137 | ||||||||
\(219\) | −447367. | −0.630309 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −15616.2 | −0.0215077 | ||||||||
\(222\) | −1.39390e6 | −1.89823 | ||||||||
\(223\) | 1.08373e6 | 1.45935 | 0.729677 | − | 0.683792i | \(-0.239671\pi\) | ||||
0.729677 | + | 0.683792i | \(0.239671\pi\) | |||||||
\(224\) | 730418. | 0.972638 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −2.57539e6 | −3.35407 | ||||||||
\(227\) | 635159. | 0.818122 | 0.409061 | − | 0.912507i | \(-0.365856\pi\) | ||||
0.409061 | + | 0.912507i | \(0.365856\pi\) | |||||||
\(228\) | 1.07265e6 | 1.36654 | ||||||||
\(229\) | 622829. | 0.784838 | 0.392419 | − | 0.919787i | \(-0.371638\pi\) | ||||
0.392419 | + | 0.919787i | \(0.371638\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 45064.2 | 0.0555651 | ||||||||
\(232\) | −4.77118e6 | −5.81977 | ||||||||
\(233\) | −1.31801e6 | −1.59048 | −0.795239 | − | 0.606296i | \(-0.792655\pi\) | ||||
−0.795239 | + | 0.606296i | \(0.792655\pi\) | |||||||
\(234\) | −11890.4 | −0.0141957 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −3.46810e6 | −4.05332 | ||||||||
\(237\) | −643478. | −0.744154 | ||||||||
\(238\) | −509016. | −0.582491 | ||||||||
\(239\) | −240029. | −0.271812 | −0.135906 | − | 0.990722i | \(-0.543395\pi\) | ||||
−0.135906 | + | 0.990722i | \(0.543395\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 659027. | 0.730904 | 0.365452 | − | 0.930830i | \(-0.380914\pi\) | ||||
0.365452 | + | 0.930830i | \(0.380914\pi\) | |||||||
\(242\) | −157436. | −0.172808 | ||||||||
\(243\) | −59049.0 | −0.0641500 | ||||||||
\(244\) | −1.49422e6 | −1.60671 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 1.19874e6 | 1.26295 | ||||||||
\(247\) | −19455.5 | −0.0202908 | ||||||||
\(248\) | −241177. | −0.249004 | ||||||||
\(249\) | −301854. | −0.308530 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1.72716e6 | 1.73040 | 0.865202 | − | 0.501424i | \(-0.167190\pi\) | ||||
0.865202 | + | 0.501424i | \(0.167190\pi\) | |||||||
\(252\) | −280312. | −0.278062 | ||||||||
\(253\) | 306599. | 0.301141 | ||||||||
\(254\) | −1.20667e6 | −1.17356 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 985142. | 0.939505 | ||||||||
\(257\) | 889184. | 0.839767 | 0.419883 | − | 0.907578i | \(-0.362071\pi\) | ||||
0.419883 | + | 0.907578i | \(0.362071\pi\) | |||||||
\(258\) | 261240. | 0.244338 | ||||||||
\(259\) | 596021. | 0.552093 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 696131. | 0.632542 | ||||||||
\(262\) | −3.60014e6 | −3.24015 | ||||||||
\(263\) | 352666. | 0.314394 | 0.157197 | − | 0.987567i | \(-0.449754\pi\) | ||||
0.157197 | + | 0.987567i | \(0.449754\pi\) | |||||||
\(264\) | 604571. | 0.533873 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −634160. | −0.549535 | ||||||||
\(267\) | 692804. | 0.594747 | ||||||||
\(268\) | −4.32363e6 | −3.67715 | ||||||||
\(269\) | −506736. | −0.426973 | −0.213487 | − | 0.976946i | \(-0.568482\pi\) | ||||
−0.213487 | + | 0.976946i | \(0.568482\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.33528e6 | −1.10446 | −0.552230 | − | 0.833691i | \(-0.686223\pi\) | ||||
−0.552230 | + | 0.833691i | \(0.686223\pi\) | |||||||
\(272\) | −3.76760e6 | −3.08775 | ||||||||
\(273\) | 5084.23 | 0.00412875 | ||||||||
\(274\) | 9827.37 | 0.00790790 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −1.90713e6 | −1.50698 | ||||||||
\(277\) | 1.72199e6 | 1.34844 | 0.674218 | − | 0.738532i | \(-0.264481\pi\) | ||||
0.674218 | + | 0.738532i | \(0.264481\pi\) | |||||||
\(278\) | −2.90714e6 | −2.25608 | ||||||||
\(279\) | 35188.5 | 0.0270639 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1.20590e6 | −0.911061 | −0.455530 | − | 0.890220i | \(-0.650550\pi\) | ||||
−0.455530 | + | 0.890220i | \(0.650550\pi\) | |||||||
\(282\) | 163741. | 0.122612 | ||||||||
\(283\) | −920183. | −0.682980 | −0.341490 | − | 0.939885i | \(-0.610932\pi\) | ||||
−0.341490 | + | 0.939885i | \(0.610932\pi\) | |||||||
\(284\) | −1.39206e6 | −1.02415 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −17762.2 | −0.0128405 | ||||||||
\(287\) | −512571. | −0.367324 | ||||||||
\(288\) | −1.42972e6 | −1.01571 | ||||||||
\(289\) | −111304. | −0.0783911 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 159423. | 0.110362 | ||||||||
\(292\) | 4.15694e6 | 2.85310 | ||||||||
\(293\) | 125447. | 0.0853674 | 0.0426837 | − | 0.999089i | \(-0.486409\pi\) | ||||
0.0426837 | + | 0.999089i | \(0.486409\pi\) | |||||||
\(294\) | −1.46082e6 | −0.985661 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 7.99608e6 | 5.30454 | ||||||||
\(297\) | −88209.0 | −0.0580259 | ||||||||
\(298\) | 5.73775e6 | 3.74284 | ||||||||
\(299\) | 34591.1 | 0.0223762 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −111704. | −0.0710646 | ||||||||
\(302\) | 1.17494e6 | 0.741310 | ||||||||
\(303\) | 25095.4 | 0.0157032 | ||||||||
\(304\) | −4.69388e6 | −2.91305 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 996352. | 0.608288 | ||||||||
\(307\) | −922678. | −0.558733 | −0.279366 | − | 0.960185i | \(-0.590124\pi\) | ||||
−0.279366 | + | 0.960185i | \(0.590124\pi\) | |||||||
\(308\) | −418738. | −0.251516 | ||||||||
\(309\) | 27960.2 | 0.0166588 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −1.60136e6 | −0.938831 | −0.469416 | − | 0.882977i | \(-0.655535\pi\) | ||||
−0.469416 | + | 0.882977i | \(0.655535\pi\) | |||||||
\(312\) | 68208.9 | 0.0396693 | ||||||||
\(313\) | −177127. | −0.102193 | −0.0510967 | − | 0.998694i | \(-0.516272\pi\) | ||||
−0.0510967 | + | 0.998694i | \(0.516272\pi\) | |||||||
\(314\) | −3.90077e6 | −2.23268 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 5.97922e6 | 3.36842 | ||||||||
\(317\) | −578254. | −0.323199 | −0.161600 | − | 0.986856i | \(-0.551665\pi\) | ||||
−0.161600 | + | 0.986856i | \(0.551665\pi\) | |||||||
\(318\) | 916018. | 0.507968 | ||||||||
\(319\) | 1.03990e6 | 0.572156 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −194393. | −0.105298 | ||||||||
\(322\) | 1.12751e6 | 0.606013 | ||||||||
\(323\) | 1.63027e6 | 0.869466 | ||||||||
\(324\) | 548685. | 0.290376 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 3.64565e6 | 1.89990 | ||||||||
\(327\) | −1.71569e6 | −0.887296 | ||||||||
\(328\) | −6.87653e6 | −3.52927 | ||||||||
\(329\) | −70014.2 | −0.0356612 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3.23768e6 | −1.62429 | −0.812145 | − | 0.583456i | \(-0.801700\pi\) | ||||
−0.812145 | + | 0.583456i | \(0.801700\pi\) | |||||||
\(332\) | 2.80483e6 | 1.39657 | ||||||||
\(333\) | −1.16666e6 | −0.576543 | ||||||||
\(334\) | 4.94432e6 | 2.42516 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 1.22663e6 | 0.592744 | ||||||||
\(337\) | −1.82330e6 | −0.874546 | −0.437273 | − | 0.899329i | \(-0.644056\pi\) | ||||
−0.437273 | + | 0.899329i | \(0.644056\pi\) | |||||||
\(338\) | 3.99053e6 | 1.89994 | ||||||||
\(339\) | −2.15553e6 | −1.01872 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 52565.6 | 0.0244802 | ||||||||
\(342\) | 1.24131e6 | 0.573872 | ||||||||
\(343\) | 1.32013e6 | 0.605872 | ||||||||
\(344\) | −1.49860e6 | −0.682792 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −5.67438e6 | −2.54817 | ||||||||
\(347\) | −564150. | −0.251519 | −0.125759 | − | 0.992061i | \(-0.540137\pi\) | ||||
−0.125759 | + | 0.992061i | \(0.540137\pi\) | |||||||
\(348\) | −6.46847e6 | −2.86321 | ||||||||
\(349\) | 2.72653e6 | 1.19825 | 0.599124 | − | 0.800657i | \(-0.295516\pi\) | ||||
0.599124 | + | 0.800657i | \(0.295516\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −9951.90 | −0.00431160 | ||||||||
\(352\) | −2.13576e6 | −0.918747 | ||||||||
\(353\) | −694975. | −0.296847 | −0.148423 | − | 0.988924i | \(-0.547420\pi\) | ||||
−0.148423 | + | 0.988924i | \(0.547420\pi\) | |||||||
\(354\) | −4.01340e6 | −1.70218 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −6.43756e6 | −2.69213 | ||||||||
\(357\) | −426032. | −0.176918 | ||||||||
\(358\) | −8.49287e6 | −3.50225 | ||||||||
\(359\) | −306112. | −0.125356 | −0.0626779 | − | 0.998034i | \(-0.519964\pi\) | ||||
−0.0626779 | + | 0.998034i | \(0.519964\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −445023. | −0.179728 | ||||||||
\(362\) | 4.03700e6 | 1.61915 | ||||||||
\(363\) | −131769. | −0.0524864 | ||||||||
\(364\) | −47242.8 | −0.0186888 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −1.72916e6 | −0.674733 | ||||||||
\(367\) | −1.51571e6 | −0.587423 | −0.293712 | − | 0.955894i | \(-0.594891\pi\) | ||||
−0.293712 | + | 0.955894i | \(0.594891\pi\) | |||||||
\(368\) | 8.34553e6 | 3.21244 | ||||||||
\(369\) | 1.00331e6 | 0.383592 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −391682. | −0.147740 | ||||||||
\(372\) | −326973. | −0.122505 | ||||||||
\(373\) | −1.05811e6 | −0.393783 | −0.196892 | − | 0.980425i | \(-0.563085\pi\) | ||||
−0.196892 | + | 0.980425i | \(0.563085\pi\) | |||||||
\(374\) | 1.48838e6 | 0.550217 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −939294. | −0.342635 | ||||||||
\(377\) | 117323. | 0.0425139 | ||||||||
\(378\) | −324387. | −0.116771 | ||||||||
\(379\) | 812383. | 0.290511 | 0.145256 | − | 0.989394i | \(-0.453600\pi\) | ||||
0.145256 | + | 0.989394i | \(0.453600\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1.00995e6 | −0.356441 | ||||||||
\(382\) | −3.64691e6 | −1.27869 | ||||||||
\(383\) | 1.22178e6 | 0.425593 | 0.212797 | − | 0.977096i | \(-0.431743\pi\) | ||||
0.212797 | + | 0.977096i | \(0.431743\pi\) | |||||||
\(384\) | 3.08521e6 | 1.06772 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 3.86397e6 | 1.31997 | ||||||||
\(387\) | 218650. | 0.0742118 | ||||||||
\(388\) | −1.48136e6 | −0.499554 | ||||||||
\(389\) | −4.08811e6 | −1.36977 | −0.684887 | − | 0.728649i | \(-0.740148\pi\) | ||||
−0.684887 | + | 0.728649i | \(0.740148\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2.89855e6 | −0.958824 | ||||||||
\(392\) | 8.37994e6 | 2.75439 | ||||||||
\(393\) | −3.01321e6 | −0.984120 | ||||||||
\(394\) | −6.49536e6 | −2.10796 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 819641. | 0.262655 | ||||||||
\(397\) | −15256.4 | −0.00485822 | −0.00242911 | − | 0.999997i | \(-0.500773\pi\) | ||||
−0.00242911 | + | 0.999997i | \(0.500773\pi\) | |||||||
\(398\) | 1.11236e7 | 3.51995 | ||||||||
\(399\) | −530774. | −0.166908 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −4.75411e6 | −1.47642 | −0.738208 | − | 0.674574i | \(-0.764328\pi\) | ||||
−0.738208 | + | 0.674574i | \(0.764328\pi\) | |||||||
\(402\) | −5.00345e6 | −1.54420 | ||||||||
\(403\) | 5930.55 | 0.00181900 | ||||||||
\(404\) | −233188. | −0.0710807 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 3.82421e6 | 1.15140 | ||||||||
\(407\) | −1.74278e6 | −0.521503 | ||||||||
\(408\) | −5.71555e6 | −1.69984 | ||||||||
\(409\) | −6.12814e6 | −1.81143 | −0.905713 | − | 0.423891i | \(-0.860664\pi\) | ||||
−0.905713 | + | 0.423891i | \(0.860664\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 8225.23 | 0.00240184 | ||||||||
\(412\) | −259807. | −0.0754063 | ||||||||
\(413\) | 1.71610e6 | 0.495071 | ||||||||
\(414\) | −2.20700e6 | −0.632851 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −240961. | −0.0682673 | ||||||||
\(417\) | −2.43320e6 | −0.685231 | ||||||||
\(418\) | 1.85430e6 | 0.519086 | ||||||||
\(419\) | −3.61815e6 | −1.00682 | −0.503410 | − | 0.864048i | \(-0.667921\pi\) | ||||
−0.503410 | + | 0.864048i | \(0.667921\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1.49527e6 | −0.411164 | −0.205582 | − | 0.978640i | \(-0.565909\pi\) | ||||
−0.205582 | + | 0.978640i | \(0.565909\pi\) | |||||||
\(422\) | 8.15481e6 | 2.22912 | ||||||||
\(423\) | 137046. | 0.0372406 | ||||||||
\(424\) | −5.25471e6 | −1.41950 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −1.61094e6 | −0.430086 | ||||||||
\(427\) | 739374. | 0.196243 | ||||||||
\(428\) | 1.80631e6 | 0.476631 | ||||||||
\(429\) | −14866.4 | −0.00389999 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 538580. | 0.139655 | 0.0698276 | − | 0.997559i | \(-0.477755\pi\) | ||||
0.0698276 | + | 0.997559i | \(0.477755\pi\) | |||||||
\(432\) | −2.40102e6 | −0.618995 | ||||||||
\(433\) | 5.50572e6 | 1.41122 | 0.705610 | − | 0.708600i | \(-0.250673\pi\) | ||||
0.705610 | + | 0.708600i | \(0.250673\pi\) | |||||||
\(434\) | 193309. | 0.0492638 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 1.59422e7 | 4.01636 | ||||||||
\(437\) | −3.61117e6 | −0.904575 | ||||||||
\(438\) | 4.81056e6 | 1.19815 | ||||||||
\(439\) | 4.55179e6 | 1.12725 | 0.563626 | − | 0.826030i | \(-0.309406\pi\) | ||||
0.563626 | + | 0.826030i | \(0.309406\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.22266e6 | −0.299371 | ||||||||
\(442\) | 167921. | 0.0408837 | ||||||||
\(443\) | 1.92800e6 | 0.466764 | 0.233382 | − | 0.972385i | \(-0.425021\pi\) | ||||
0.233382 | + | 0.972385i | \(0.425021\pi\) | |||||||
\(444\) | 1.08406e7 | 2.60973 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −1.16535e7 | −2.77407 | ||||||||
\(447\) | 4.80233e6 | 1.13680 | ||||||||
\(448\) | −3.49286e6 | −0.822216 | ||||||||
\(449\) | 2.25763e6 | 0.528491 | 0.264246 | − | 0.964455i | \(-0.414877\pi\) | ||||
0.264246 | + | 0.964455i | \(0.414877\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.49877e6 | 0.346972 | ||||||||
\(452\) | 2.00292e7 | 4.61124 | ||||||||
\(453\) | 983394. | 0.225155 | ||||||||
\(454\) | −6.82991e6 | −1.55516 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −7.12074e6 | −1.60366 | ||||||||
\(457\) | 1.40364e6 | 0.314388 | 0.157194 | − | 0.987568i | \(-0.449755\pi\) | ||||
0.157194 | + | 0.987568i | \(0.449755\pi\) | |||||||
\(458\) | −6.69732e6 | −1.49189 | ||||||||
\(459\) | 833918. | 0.184753 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 1.28230e6 | 0.281021 | 0.140510 | − | 0.990079i | \(-0.455126\pi\) | ||||
0.140510 | + | 0.990079i | \(0.455126\pi\) | |||||||
\(462\) | −484578. | −0.105623 | ||||||||
\(463\) | 5.16733e6 | 1.12025 | 0.560124 | − | 0.828409i | \(-0.310754\pi\) | ||||
0.560124 | + | 0.828409i | \(0.310754\pi\) | |||||||
\(464\) | 2.83057e7 | 6.10351 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 1.41726e7 | 3.02332 | ||||||||
\(467\) | −1.85528e6 | −0.393657 | −0.196828 | − | 0.980438i | \(-0.563064\pi\) | ||||
−0.196828 | + | 0.980438i | \(0.563064\pi\) | |||||||
\(468\) | 92473.4 | 0.0195165 | ||||||||
\(469\) | 2.13944e6 | 0.449125 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −3.26483e6 | −0.678123 | ||||||||
\(472\) | 2.30228e7 | 4.75667 | ||||||||
\(473\) | 326626. | 0.0671271 | ||||||||
\(474\) | 6.91936e6 | 1.41456 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 3.95870e6 | 0.800821 | ||||||||
\(477\) | 766681. | 0.154283 | ||||||||
\(478\) | 2.58104e6 | 0.516685 | ||||||||
\(479\) | 2.77689e6 | 0.552993 | 0.276497 | − | 0.961015i | \(-0.410827\pi\) | ||||
0.276497 | + | 0.961015i | \(0.410827\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −196624. | −0.0387502 | ||||||||
\(482\) | −7.08655e6 | −1.38937 | ||||||||
\(483\) | 943695. | 0.184062 | ||||||||
\(484\) | 1.22440e6 | 0.237580 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 634957. | 0.121942 | ||||||||
\(487\) | −8.55421e6 | −1.63440 | −0.817198 | − | 0.576356i | \(-0.804474\pi\) | ||||
−0.817198 | + | 0.576356i | \(0.804474\pi\) | |||||||
\(488\) | 9.91927e6 | 1.88552 | ||||||||
\(489\) | 3.05130e6 | 0.577049 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −9.34368e6 | −1.74910 | −0.874550 | − | 0.484936i | \(-0.838843\pi\) | ||||
−0.874550 | + | 0.484936i | \(0.838843\pi\) | |||||||
\(492\) | −9.32278e6 | −1.73633 | ||||||||
\(493\) | −9.83109e6 | −1.82173 | ||||||||
\(494\) | 209206. | 0.0385706 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 1.43082e6 | 0.261144 | ||||||||
\(497\) | 688825. | 0.125089 | ||||||||
\(498\) | 3.24585e6 | 0.586483 | ||||||||
\(499\) | 1.03633e7 | 1.86314 | 0.931569 | − | 0.363564i | \(-0.118440\pi\) | ||||
0.931569 | + | 0.363564i | \(0.118440\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 4.13825e6 | 0.736585 | ||||||||
\(502\) | −1.85722e7 | −3.28931 | ||||||||
\(503\) | −5.19173e6 | −0.914938 | −0.457469 | − | 0.889225i | \(-0.651244\pi\) | ||||
−0.457469 | + | 0.889225i | \(0.651244\pi\) | |||||||
\(504\) | 1.86084e6 | 0.326312 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −3.29688e6 | −0.572435 | ||||||||
\(507\) | 3.33996e6 | 0.577060 | ||||||||
\(508\) | 9.38448e6 | 1.61343 | ||||||||
\(509\) | 591024. | 0.101114 | 0.0505569 | − | 0.998721i | \(-0.483900\pi\) | ||||
0.0505569 | + | 0.998721i | \(0.483900\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2.05696e6 | −0.348476 | ||||||||
\(512\) | 376329. | 0.0634444 | ||||||||
\(513\) | 1.03894e6 | 0.174300 | ||||||||
\(514\) | −9.56145e6 | −1.59630 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −2.03171e6 | −0.335921 | ||||||||
\(517\) | 204723. | 0.0336854 | ||||||||
\(518\) | −6.40905e6 | −1.04947 | ||||||||
\(519\) | −4.74929e6 | −0.773945 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 4.41573e6 | 0.712702 | 0.356351 | − | 0.934352i | \(-0.384021\pi\) | ||||
0.356351 | + | 0.934352i | \(0.384021\pi\) | |||||||
\(522\) | −7.48554e6 | −1.20239 | ||||||||
\(523\) | −7.91473e6 | −1.26527 | −0.632633 | − | 0.774452i | \(-0.718026\pi\) | ||||
−0.632633 | + | 0.774452i | \(0.718026\pi\) | |||||||
\(524\) | 2.79988e7 | 4.45463 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −3.79224e6 | −0.597629 | ||||||||
\(527\) | −496949. | −0.0779445 | ||||||||
\(528\) | −3.58671e6 | −0.559902 | ||||||||
\(529\) | −15819.3 | −0.00245780 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −3.35910e6 | −0.516996 | ||||||||
\(532\) | 4.93197e6 | 0.755512 | ||||||||
\(533\) | 169094. | 0.0257816 | ||||||||
\(534\) | −7.44977e6 | −1.13055 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 2.87022e7 | 4.31522 | ||||||||
\(537\) | −7.10829e6 | −1.06372 | ||||||||
\(538\) | 5.44896e6 | 0.811629 | ||||||||
\(539\) | −1.82645e6 | −0.270791 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1.37134e6 | 0.201443 | 0.100722 | − | 0.994915i | \(-0.467885\pi\) | ||||
0.100722 | + | 0.994915i | \(0.467885\pi\) | |||||||
\(542\) | 1.43584e7 | 2.09946 | ||||||||
\(543\) | 3.37886e6 | 0.491779 | ||||||||
\(544\) | 2.01912e7 | 2.92527 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −54671.0 | −0.00784830 | ||||||||
\(547\) | −7.82390e6 | −1.11803 | −0.559017 | − | 0.829156i | \(-0.688821\pi\) | ||||
−0.559017 | + | 0.829156i | \(0.688821\pi\) | |||||||
\(548\) | −76429.1 | −0.0108719 | ||||||||
\(549\) | −1.44726e6 | −0.204934 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1.22481e7 | −1.71866 | ||||||||
\(552\) | 1.26604e7 | 1.76848 | ||||||||
\(553\) | −2.95866e6 | −0.411417 | ||||||||
\(554\) | −1.85166e7 | −2.56323 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 2.26093e7 | 3.10171 | ||||||||
\(557\) | −8.25549e6 | −1.12747 | −0.563735 | − | 0.825956i | \(-0.690636\pi\) | ||||
−0.563735 | + | 0.825956i | \(0.690636\pi\) | |||||||
\(558\) | −378385. | −0.0514456 | ||||||||
\(559\) | 36850.5 | 0.00498786 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1.24573e6 | 0.167115 | ||||||||
\(562\) | 1.29672e7 | 1.73183 | ||||||||
\(563\) | −1.20969e7 | −1.60843 | −0.804214 | − | 0.594340i | \(-0.797413\pi\) | ||||
−0.804214 | + | 0.594340i | \(0.797413\pi\) | |||||||
\(564\) | −1.27344e6 | −0.168570 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 9.89478e6 | 1.29827 | ||||||||
\(567\) | −271503. | −0.0354663 | ||||||||
\(568\) | 9.24112e6 | 1.20186 | ||||||||
\(569\) | −7.97678e6 | −1.03287 | −0.516437 | − | 0.856325i | \(-0.672742\pi\) | ||||
−0.516437 | + | 0.856325i | \(0.672742\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −8.94027e6 | −1.14752 | −0.573760 | − | 0.819023i | \(-0.694516\pi\) | ||||
−0.573760 | + | 0.819023i | \(0.694516\pi\) | |||||||
\(572\) | 138139. | 0.0176533 | ||||||||
\(573\) | −3.05236e6 | −0.388373 | ||||||||
\(574\) | 5.51171e6 | 0.698242 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 6.83694e6 | 0.858629 | ||||||||
\(577\) | 4.92430e6 | 0.615751 | 0.307875 | − | 0.951427i | \(-0.400382\pi\) | ||||
0.307875 | + | 0.951427i | \(0.400382\pi\) | |||||||
\(578\) | 1.19686e6 | 0.149013 | ||||||||
\(579\) | 3.23403e6 | 0.400911 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1.38790e6 | −0.170576 | ||||||||
\(582\) | −1.71428e6 | −0.209786 | ||||||||
\(583\) | 1.14529e6 | 0.139554 | ||||||||
\(584\) | −2.75957e7 | −3.34818 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −1.34894e6 | −0.162274 | ||||||||
\(587\) | −1.22885e7 | −1.47199 | −0.735993 | − | 0.676989i | \(-0.763285\pi\) | ||||
−0.735993 | + | 0.676989i | \(0.763285\pi\) | |||||||
\(588\) | 1.13610e7 | 1.35511 | ||||||||
\(589\) | −619126. | −0.0735345 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −5.43643e6 | −0.640244 | ||||||||
\(592\) | −4.74380e7 | −5.56317 | ||||||||
\(593\) | 8.20846e6 | 0.958572 | 0.479286 | − | 0.877659i | \(-0.340896\pi\) | ||||
0.479286 | + | 0.877659i | \(0.340896\pi\) | |||||||
\(594\) | 948517. | 0.110301 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −4.46234e7 | −5.14573 | ||||||||
\(597\) | 9.31010e6 | 1.06910 | ||||||||
\(598\) | −371960. | −0.0425347 | ||||||||
\(599\) | −2.00442e6 | −0.228256 | −0.114128 | − | 0.993466i | \(-0.536407\pi\) | ||||
−0.114128 | + | 0.993466i | \(0.536407\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −871399. | −0.0984081 | −0.0492041 | − | 0.998789i | \(-0.515668\pi\) | ||||
−0.0492041 | + | 0.998789i | \(0.515668\pi\) | |||||||
\(602\) | 1.20116e6 | 0.135086 | ||||||||
\(603\) | −4.18775e6 | −0.469015 | ||||||||
\(604\) | −9.13773e6 | −1.01917 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −269853. | −0.0298501 | ||||||||
\(607\) | 1.04538e7 | 1.15160 | 0.575802 | − | 0.817589i | \(-0.304690\pi\) | ||||
0.575802 | + | 0.817589i | \(0.304690\pi\) | |||||||
\(608\) | 2.51554e7 | 2.75976 | ||||||||
\(609\) | 3.20075e6 | 0.349711 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 23097.3 | 0.00250298 | ||||||||
\(612\) | −7.74879e6 | −0.836287 | ||||||||
\(613\) | 5.79441e6 | 0.622814 | 0.311407 | − | 0.950277i | \(-0.399200\pi\) | ||||
0.311407 | + | 0.950277i | \(0.399200\pi\) | |||||||
\(614\) | 9.92161e6 | 1.06209 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 2.77977e6 | 0.295160 | ||||||||
\(617\) | −7.10900e6 | −0.751788 | −0.375894 | − | 0.926663i | \(-0.622664\pi\) | ||||
−0.375894 | + | 0.926663i | \(0.622664\pi\) | |||||||
\(618\) | −300657. | −0.0316665 | ||||||||
\(619\) | −1.13332e7 | −1.18885 | −0.594424 | − | 0.804152i | \(-0.702620\pi\) | ||||
−0.594424 | + | 0.804152i | \(0.702620\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.84720e6 | −0.192213 | ||||||||
\(622\) | 1.72195e7 | 1.78462 | ||||||||
\(623\) | 3.18546e6 | 0.328815 | ||||||||
\(624\) | −404660. | −0.0416034 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 1.90465e6 | 0.194259 | ||||||||
\(627\) | 1.55200e6 | 0.157660 | ||||||||
\(628\) | 3.03369e7 | 3.06953 | ||||||||
\(629\) | 1.64761e7 | 1.66045 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 3.77282e6 | 0.377218 | 0.188609 | − | 0.982052i | \(-0.439602\pi\) | ||||
0.188609 | + | 0.982052i | \(0.439602\pi\) | |||||||
\(632\) | −3.96927e7 | −3.95292 | ||||||||
\(633\) | 6.82534e6 | 0.677041 | ||||||||
\(634\) | 6.21800e6 | 0.614366 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −7.12402e6 | −0.698365 | ||||||||
\(637\) | −206063. | −0.0201211 | ||||||||
\(638\) | −1.11821e7 | −1.08761 | ||||||||
\(639\) | −1.34831e6 | −0.130628 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1.76552e6 | 0.169718 | 0.0848591 | − | 0.996393i | \(-0.472956\pi\) | ||||
0.0848591 | + | 0.996393i | \(0.472956\pi\) | |||||||
\(642\) | 2.09032e6 | 0.200159 | ||||||||
\(643\) | −3.29197e6 | −0.313999 | −0.157000 | − | 0.987599i | \(-0.550182\pi\) | ||||
−0.157000 | + | 0.987599i | \(0.550182\pi\) | |||||||
\(644\) | −8.76885e6 | −0.833159 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −1.75304e7 | −1.65276 | ||||||||
\(647\) | −1.62220e7 | −1.52350 | −0.761752 | − | 0.647868i | \(-0.775661\pi\) | ||||
−0.761752 | + | 0.647868i | \(0.775661\pi\) | |||||||
\(648\) | −3.64242e6 | −0.340763 | ||||||||
\(649\) | −5.01792e6 | −0.467640 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 161794. | 0.0149627 | ||||||||
\(652\) | −2.83528e7 | −2.61202 | ||||||||
\(653\) | −3.42354e6 | −0.314190 | −0.157095 | − | 0.987583i | \(-0.550213\pi\) | ||||
−0.157095 | + | 0.987583i | \(0.550213\pi\) | |||||||
\(654\) | 1.84489e7 | 1.68665 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 4.07961e7 | 3.70134 | ||||||||
\(657\) | 4.02630e6 | 0.363909 | ||||||||
\(658\) | 752867. | 0.0677881 | ||||||||
\(659\) | 5.40108e6 | 0.484470 | 0.242235 | − | 0.970218i | \(-0.422119\pi\) | ||||
0.242235 | + | 0.970218i | \(0.422119\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 4.42083e6 | 0.393550 | 0.196775 | − | 0.980449i | \(-0.436953\pi\) | ||||
0.196775 | + | 0.980449i | \(0.436953\pi\) | |||||||
\(662\) | 3.48149e7 | 3.08760 | ||||||||
\(663\) | 140545. | 0.0124175 | ||||||||
\(664\) | −1.86197e7 | −1.63890 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 1.25451e7 | 1.09595 | ||||||||
\(667\) | 2.17767e7 | 1.89529 | ||||||||
\(668\) | −3.84528e7 | −3.33416 | ||||||||
\(669\) | −9.75360e6 | −0.842558 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −2.16195e6 | −0.185370 | ||||||||
\(672\) | −6.57376e6 | −0.561553 | ||||||||
\(673\) | −1.15029e7 | −0.978969 | −0.489484 | − | 0.872012i | \(-0.662815\pi\) | ||||
−0.489484 | + | 0.872012i | \(0.662815\pi\) | |||||||
\(674\) | 1.96060e7 | 1.66242 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −3.10350e7 | −2.61207 | ||||||||
\(677\) | 2.08105e7 | 1.74506 | 0.872530 | − | 0.488560i | \(-0.162478\pi\) | ||||
0.872530 | + | 0.488560i | \(0.162478\pi\) | |||||||
\(678\) | 2.31785e7 | 1.93647 | ||||||||
\(679\) | 733014. | 0.0610152 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −5.71643e6 | −0.472343 | ||||||||
\(682\) | −565241. | −0.0465343 | ||||||||
\(683\) | −2.29333e7 | −1.88111 | −0.940556 | − | 0.339638i | \(-0.889695\pi\) | ||||
−0.940556 | + | 0.339638i | \(0.889695\pi\) | |||||||
\(684\) | −9.65386e6 | −0.788971 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −1.41954e7 | −1.15170 | ||||||||
\(687\) | −5.60546e6 | −0.453126 | ||||||||
\(688\) | 8.89066e6 | 0.716082 | ||||||||
\(689\) | 129214. | 0.0103696 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1.87802e7 | −1.49626 | −0.748128 | − | 0.663554i | \(-0.769047\pi\) | ||||
−0.748128 | + | 0.663554i | \(0.769047\pi\) | |||||||
\(692\) | 4.41306e7 | 3.50327 | ||||||||
\(693\) | −405578. | −0.0320805 | ||||||||
\(694\) | 6.06634e6 | 0.478110 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 4.29406e7 | 3.36004 | ||||||||
\(697\) | −1.41692e7 | −1.10475 | ||||||||
\(698\) | −2.93185e7 | −2.27774 | ||||||||
\(699\) | 1.18621e7 | 0.918263 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −4.01030e6 | −0.308235 | −0.154118 | − | 0.988053i | \(-0.549253\pi\) | ||||
−0.154118 | + | 0.988053i | \(0.549253\pi\) | |||||||
\(702\) | 107013. | 0.00819588 | ||||||||
\(703\) | 2.05268e7 | 1.56651 | ||||||||
\(704\) | 1.02132e7 | 0.776659 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 7.47310e6 | 0.564273 | ||||||||
\(707\) | 115387. | 0.00868176 | ||||||||
\(708\) | 3.12129e7 | 2.34019 | ||||||||
\(709\) | −326851. | −0.0244193 | −0.0122097 | − | 0.999925i | \(-0.503887\pi\) | ||||
−0.0122097 | + | 0.999925i | \(0.503887\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 5.79130e6 | 0.429638 | ||||||||
\(712\) | 4.27354e7 | 3.15928 | ||||||||
\(713\) | 1.10078e6 | 0.0810919 | ||||||||
\(714\) | 4.58115e6 | 0.336301 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 6.60504e7 | 4.81496 | ||||||||
\(717\) | 2.16026e6 | 0.156931 | ||||||||
\(718\) | 3.29164e6 | 0.238287 | ||||||||
\(719\) | −1.34067e7 | −0.967161 | −0.483581 | − | 0.875300i | \(-0.660664\pi\) | ||||
−0.483581 | + | 0.875300i | \(0.660664\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 128559. | 0.00921008 | ||||||||
\(722\) | 4.78536e6 | 0.341643 | ||||||||
\(723\) | −5.93124e6 | −0.421988 | ||||||||
\(724\) | −3.13964e7 | −2.22604 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 1.41692e6 | 0.0997709 | ||||||||
\(727\) | 2.14838e7 | 1.50756 | 0.753780 | − | 0.657127i | \(-0.228229\pi\) | ||||
0.753780 | + | 0.657127i | \(0.228229\pi\) | |||||||
\(728\) | 313619. | 0.0219318 | ||||||||
\(729\) | 531441. | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −3.08788e6 | −0.213731 | ||||||||
\(732\) | 1.34479e7 | 0.927637 | ||||||||
\(733\) | −8.60145e6 | −0.591305 | −0.295653 | − | 0.955296i | \(-0.595537\pi\) | ||||
−0.295653 | + | 0.955296i | \(0.595537\pi\) | |||||||
\(734\) | 1.62985e7 | 1.11663 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −4.47252e7 | −3.04339 | ||||||||
\(737\) | −6.25577e6 | −0.424240 | ||||||||
\(738\) | −1.07886e7 | −0.729165 | ||||||||
\(739\) | −4.69199e6 | −0.316043 | −0.158022 | − | 0.987436i | \(-0.550512\pi\) | ||||
−0.158022 | + | 0.987436i | \(0.550512\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 175099. | 0.0117149 | ||||||||
\(742\) | 4.21178e6 | 0.280838 | ||||||||
\(743\) | 1.84011e7 | 1.22284 | 0.611422 | − | 0.791305i | \(-0.290598\pi\) | ||||
0.611422 | + | 0.791305i | \(0.290598\pi\) | |||||||
\(744\) | 2.17059e6 | 0.143763 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 1.13779e7 | 0.748539 | ||||||||
\(747\) | 2.71668e6 | 0.178130 | ||||||||
\(748\) | −1.15754e7 | −0.756450 | ||||||||
\(749\) | −893804. | −0.0582154 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 4.90697e6 | 0.317478 | 0.158739 | − | 0.987321i | \(-0.449257\pi\) | ||||
0.158739 | + | 0.987321i | \(0.449257\pi\) | |||||||
\(752\) | 5.57251e6 | 0.359341 | ||||||||
\(753\) | −1.55444e7 | −0.999049 | ||||||||
\(754\) | −1.26158e6 | −0.0808143 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 2.52281e6 | 0.160539 | ||||||||
\(757\) | −1.77340e7 | −1.12478 | −0.562390 | − | 0.826872i | \(-0.690118\pi\) | ||||
−0.562390 | + | 0.826872i | \(0.690118\pi\) | |||||||
\(758\) | −8.73560e6 | −0.552230 | ||||||||
\(759\) | −2.75939e6 | −0.173864 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 7.16267e6 | 0.448346 | 0.224173 | − | 0.974549i | \(-0.428032\pi\) | ||||
0.224173 | + | 0.974549i | \(0.428032\pi\) | |||||||
\(762\) | 1.08600e7 | 0.677554 | ||||||||
\(763\) | −7.88859e6 | −0.490556 | ||||||||
\(764\) | 2.83626e7 | 1.75797 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −1.31378e7 | −0.809006 | ||||||||
\(767\) | −566131. | −0.0347479 | ||||||||
\(768\) | −8.86628e6 | −0.542423 | ||||||||
\(769\) | −1.90012e7 | −1.15869 | −0.579343 | − | 0.815084i | \(-0.696691\pi\) | ||||
−0.579343 | + | 0.815084i | \(0.696691\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −8.00265e6 | −0.484840 | ||||||||
\(772\) | −3.00507e7 | −1.81473 | ||||||||
\(773\) | 6.66234e6 | 0.401031 | 0.200516 | − | 0.979690i | \(-0.435738\pi\) | ||||
0.200516 | + | 0.979690i | \(0.435738\pi\) | |||||||
\(774\) | −2.35116e6 | −0.141068 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 9.83395e6 | 0.586238 | ||||||||
\(777\) | −5.36419e6 | −0.318751 | ||||||||
\(778\) | 4.39597e7 | 2.60379 | ||||||||
\(779\) | −1.76528e7 | −1.04224 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −2.01414e6 | −0.118158 | ||||||||
\(782\) | 3.11683e7 | 1.82262 | ||||||||
\(783\) | −6.26518e6 | −0.365198 | ||||||||
\(784\) | −4.97153e7 | −2.88868 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 3.24012e7 | 1.87070 | ||||||||
\(787\) | 9.20508e6 | 0.529774 | 0.264887 | − | 0.964279i | \(-0.414665\pi\) | ||||
0.264887 | + | 0.964279i | \(0.414665\pi\) | |||||||
\(788\) | 5.05155e7 | 2.89807 | ||||||||
\(789\) | −3.17400e6 | −0.181516 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −9.91094e6 | −0.563214 | ||||||||
\(792\) | −5.44114e6 | −0.308232 | ||||||||
\(793\) | −243915. | −0.0137739 | ||||||||
\(794\) | 164053. | 0.00923494 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −8.65098e7 | −4.83930 | ||||||||
\(797\) | 2.71663e7 | 1.51490 | 0.757450 | − | 0.652893i | \(-0.226445\pi\) | ||||
0.757450 | + | 0.652893i | \(0.226445\pi\) | |||||||
\(798\) | 5.70744e6 | 0.317274 | ||||||||
\(799\) | −1.93543e6 | −0.107253 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −6.23524e6 | −0.343378 | ||||||||
\(802\) | 5.11213e7 | 2.80650 | ||||||||
\(803\) | 6.01460e6 | 0.329168 | ||||||||
\(804\) | 3.89127e7 | 2.12300 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −63771.6 | −0.00345772 | ||||||||
\(807\) | 4.56062e6 | 0.246513 | ||||||||
\(808\) | 1.54800e6 | 0.0834149 | ||||||||
\(809\) | −2.31559e7 | −1.24392 | −0.621958 | − | 0.783051i | \(-0.713662\pi\) | ||||
−0.621958 | + | 0.783051i | \(0.713662\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1.33212e6 | 0.0711200 | 0.0355600 | − | 0.999368i | \(-0.488679\pi\) | ||||
0.0355600 | + | 0.999368i | \(0.488679\pi\) | |||||||
\(812\) | −2.97415e7 | −1.58297 | ||||||||
\(813\) | 1.20176e7 | 0.637661 | ||||||||
\(814\) | 1.87402e7 | 0.991320 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 3.39084e7 | 1.78271 | ||||||||
\(817\) | −3.84705e6 | −0.201638 | ||||||||
\(818\) | 6.58963e7 | 3.44332 | ||||||||
\(819\) | −45758.1 | −0.00238373 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1.06084e7 | 0.549277 | 0.274638 | − | 0.961548i | \(-0.411442\pi\) | ||||
0.274638 | + | 0.961548i | \(0.411442\pi\) | |||||||
\(822\) | −88446.4 | −0.00456563 | ||||||||
\(823\) | −1.83916e7 | −0.946496 | −0.473248 | − | 0.880929i | \(-0.656919\pi\) | ||||
−0.473248 | + | 0.880929i | \(0.656919\pi\) | |||||||
\(824\) | 1.72471e6 | 0.0884910 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −1.84533e7 | −0.941075 | ||||||||
\(827\) | −1.95386e7 | −0.993414 | −0.496707 | − | 0.867918i | \(-0.665458\pi\) | ||||
−0.496707 | + | 0.867918i | \(0.665458\pi\) | |||||||
\(828\) | 1.71642e7 | 0.870057 | ||||||||
\(829\) | −3.37798e7 | −1.70714 | −0.853572 | − | 0.520974i | \(-0.825569\pi\) | ||||
−0.853572 | + | 0.520974i | \(0.825569\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −1.54979e7 | −0.778520 | ||||||||
\(832\) | 1.15227e6 | 0.0577095 | ||||||||
\(833\) | 1.72670e7 | 0.862193 | ||||||||
\(834\) | 2.61643e7 | 1.30255 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −1.44212e7 | −0.713651 | ||||||||
\(837\) | −316697. | −0.0156254 | ||||||||
\(838\) | 3.89062e7 | 1.91385 | ||||||||
\(839\) | 2.77050e7 | 1.35879 | 0.679396 | − | 0.733772i | \(-0.262242\pi\) | ||||
0.679396 | + | 0.733772i | \(0.262242\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 5.33493e7 | 2.60099 | ||||||||
\(842\) | 1.60788e7 | 0.781578 | ||||||||
\(843\) | 1.08531e7 | 0.526001 | ||||||||
\(844\) | −6.34213e7 | −3.06463 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −1.47367e6 | −0.0707902 | ||||||||
\(847\) | −605864. | −0.0290179 | ||||||||
\(848\) | 3.11744e7 | 1.48870 | ||||||||
\(849\) | 8.28165e6 | 0.394319 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −3.64958e7 | −1.72750 | ||||||||
\(852\) | 1.25285e7 | 0.591291 | ||||||||
\(853\) | 1.04555e7 | 0.492007 | 0.246003 | − | 0.969269i | \(-0.420883\pi\) | ||||
0.246003 | + | 0.969269i | \(0.420883\pi\) | |||||||
\(854\) | −7.95053e6 | −0.373037 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −1.19911e7 | −0.559337 | ||||||||
\(857\) | −2.53866e7 | −1.18074 | −0.590369 | − | 0.807134i | \(-0.701018\pi\) | ||||
−0.590369 | + | 0.807134i | \(0.701018\pi\) | |||||||
\(858\) | 159860. | 0.00741345 | ||||||||
\(859\) | 1.84775e6 | 0.0854396 | 0.0427198 | − | 0.999087i | \(-0.486398\pi\) | ||||
0.0427198 | + | 0.999087i | \(0.486398\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 4.61314e6 | 0.212075 | ||||||||
\(862\) | −5.79138e6 | −0.265469 | ||||||||
\(863\) | −2.89194e7 | −1.32179 | −0.660894 | − | 0.750479i | \(-0.729823\pi\) | ||||
−0.660894 | + | 0.750479i | \(0.729823\pi\) | |||||||
\(864\) | 1.28675e7 | 0.586422 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −5.92034e7 | −2.68257 | ||||||||
\(867\) | 1.00174e6 | 0.0452591 | ||||||||
\(868\) | −1.50340e6 | −0.0677289 | ||||||||
\(869\) | 8.65121e6 | 0.388622 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −705788. | −0.0315231 | ||||||||
\(872\) | −1.05832e8 | −4.71329 | ||||||||
\(873\) | −1.43481e6 | −0.0637174 | ||||||||
\(874\) | 3.88312e7 | 1.71950 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −3.74125e7 | −1.64724 | ||||||||
\(877\) | −2.63977e7 | −1.15896 | −0.579478 | − | 0.814988i | \(-0.696743\pi\) | ||||
−0.579478 | + | 0.814988i | \(0.696743\pi\) | |||||||
\(878\) | −4.89457e7 | −2.14278 | ||||||||
\(879\) | −1.12903e6 | −0.0492869 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1.08347e7 | 0.470304 | 0.235152 | − | 0.971959i | \(-0.424441\pi\) | ||||
0.235152 | + | 0.971959i | \(0.424441\pi\) | |||||||
\(882\) | 1.31474e7 | 0.569072 | ||||||||
\(883\) | −2.45316e7 | −1.05883 | −0.529413 | − | 0.848364i | \(-0.677588\pi\) | ||||
−0.529413 | + | 0.848364i | \(0.677588\pi\) | |||||||
\(884\) | −1.30595e6 | −0.0562078 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −2.07319e7 | −0.887268 | ||||||||
\(887\) | −2.84619e7 | −1.21466 | −0.607330 | − | 0.794450i | \(-0.707759\pi\) | ||||
−0.607330 | + | 0.794450i | \(0.707759\pi\) | |||||||
\(888\) | −7.19647e7 | −3.06258 | ||||||||
\(889\) | −4.64367e6 | −0.197064 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 793881. | 0.0335013 | ||||||||
\(892\) | 9.06308e7 | 3.81385 | ||||||||
\(893\) | −2.41127e6 | −0.101185 | ||||||||
\(894\) | −5.16398e7 | −2.16093 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 1.41855e7 | 0.590304 | ||||||||
\(897\) | −311320. | −0.0129189 | ||||||||
\(898\) | −2.42765e7 | −1.00460 | ||||||||
\(899\) | 3.73355e6 | 0.154072 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.08274e7 | −0.444338 | ||||||||
\(902\) | −1.61164e7 | −0.659555 | ||||||||
\(903\) | 1.00534e6 | 0.0410291 | ||||||||
\(904\) | −1.32963e8 | −5.41139 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −1.05745e7 | −0.427995 | ||||||||
\(907\) | −1.85629e7 | −0.749253 | −0.374626 | − | 0.927176i | \(-0.622229\pi\) | ||||
−0.374626 | + | 0.927176i | \(0.622229\pi\) | |||||||
\(908\) | 5.31173e7 | 2.13807 | ||||||||
\(909\) | −225859. | −0.00906625 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 3.93363e7 | 1.57035 | 0.785177 | − | 0.619271i | \(-0.212572\pi\) | ||||
0.785177 | + | 0.619271i | \(0.212572\pi\) | |||||||
\(912\) | 4.22449e7 | 1.68185 | ||||||||
\(913\) | 4.05825e6 | 0.161125 | ||||||||
\(914\) | −1.50935e7 | −0.597617 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 5.20861e7 | 2.05108 | ||||||||
\(917\) | −1.38545e7 | −0.544086 | ||||||||
\(918\) | −8.96717e6 | −0.351195 | ||||||||
\(919\) | 2.72458e7 | 1.06417 | 0.532084 | − | 0.846691i | \(-0.321409\pi\) | ||||
0.532084 | + | 0.846691i | \(0.321409\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 8.30410e6 | 0.322584 | ||||||||
\(922\) | −1.37887e7 | −0.534190 | ||||||||
\(923\) | −227239. | −0.00877969 | ||||||||
\(924\) | 3.76864e6 | 0.145213 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −5.55646e7 | −2.12947 | ||||||||
\(927\) | −251642. | −0.00961796 | ||||||||
\(928\) | −1.51696e8 | −5.78233 | ||||||||
\(929\) | −2.98863e7 | −1.13614 | −0.568071 | − | 0.822980i | \(-0.692310\pi\) | ||||
−0.568071 | + | 0.822980i | \(0.692310\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.15122e7 | 0.813411 | ||||||||
\(932\) | −1.10223e8 | −4.15653 | ||||||||
\(933\) | 1.44122e7 | 0.542035 | ||||||||
\(934\) | 1.99500e7 | 0.748298 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −613880. | −0.0229031 | ||||||||
\(937\) | 3.91979e7 | 1.45852 | 0.729262 | − | 0.684234i | \(-0.239863\pi\) | ||||
0.729262 | + | 0.684234i | \(0.239863\pi\) | |||||||
\(938\) | −2.30055e7 | −0.853737 | ||||||||
\(939\) | 1.59414e6 | 0.0590014 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 2.33041e7 | 0.857941 | 0.428971 | − | 0.903318i | \(-0.358876\pi\) | ||||
0.428971 | + | 0.903318i | \(0.358876\pi\) | |||||||
\(942\) | 3.51069e7 | 1.28904 | ||||||||
\(943\) | 3.13859e7 | 1.14936 | ||||||||
\(944\) | −1.36586e8 | −4.98858 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −3.51223e6 | −0.127601 | ||||||||
\(947\) | −2.41038e7 | −0.873394 | −0.436697 | − | 0.899609i | \(-0.643852\pi\) | ||||
−0.436697 | + | 0.899609i | \(0.643852\pi\) | |||||||
\(948\) | −5.38130e7 | −1.94476 | ||||||||
\(949\) | 678578. | 0.0244587 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 5.20428e6 | 0.186599 | ||||||||
\(952\) | −2.62796e7 | −0.939782 | ||||||||
\(953\) | −3.46893e7 | −1.23727 | −0.618633 | − | 0.785680i | \(-0.712313\pi\) | ||||
−0.618633 | + | 0.785680i | \(0.712313\pi\) | |||||||
\(954\) | −8.24416e6 | −0.293275 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −2.00732e7 | −0.710349 | ||||||||
\(957\) | −9.35909e6 | −0.330334 | ||||||||
\(958\) | −2.98601e7 | −1.05118 | ||||||||
\(959\) | 37819.0 | 0.00132789 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.84404e7 | −0.993408 | ||||||||
\(962\) | 2.11431e6 | 0.0736598 | ||||||||
\(963\) | 1.74954e6 | 0.0607936 | ||||||||
\(964\) | 5.51133e7 | 1.91013 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −1.01476e7 | −0.349882 | ||||||||
\(967\) | −3.99380e7 | −1.37347 | −0.686737 | − | 0.726906i | \(-0.740958\pi\) | ||||
−0.686737 | + | 0.726906i | \(0.740958\pi\) | |||||||
\(968\) | −8.12813e6 | −0.278806 | ||||||||
\(969\) | −1.46724e7 | −0.501986 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −3.25227e6 | −0.110698 | −0.0553488 | − | 0.998467i | \(-0.517627\pi\) | ||||
−0.0553488 | + | 0.998467i | \(0.517627\pi\) | |||||||
\(972\) | −4.93817e6 | −0.167649 | ||||||||
\(973\) | −1.11876e7 | −0.378841 | ||||||||
\(974\) | 9.19839e7 | 3.10681 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −5.88476e7 | −1.97744 | ||||||||
\(977\) | −2.38653e7 | −0.799892 | −0.399946 | − | 0.916539i | \(-0.630971\pi\) | ||||
−0.399946 | + | 0.916539i | \(0.630971\pi\) | |||||||
\(978\) | −3.28108e7 | −1.09691 | ||||||||
\(979\) | −9.31437e6 | −0.310597 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1.54412e7 | 0.512281 | ||||||||
\(982\) | 1.00473e8 | 3.32485 | ||||||||
\(983\) | 2.22870e7 | 0.735645 | 0.367823 | − | 0.929896i | \(-0.380103\pi\) | ||||
0.367823 | + | 0.929896i | \(0.380103\pi\) | |||||||
\(984\) | 6.18888e7 | 2.03763 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 1.05714e8 | 3.46291 | ||||||||
\(987\) | 630128. | 0.0205890 | ||||||||
\(988\) | −1.62703e6 | −0.0530277 | ||||||||
\(989\) | 6.83991e6 | 0.222362 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1.74834e7 | −0.565513 | −0.282756 | − | 0.959192i | \(-0.591249\pi\) | ||||
−0.282756 | + | 0.959192i | \(0.591249\pi\) | |||||||
\(992\) | −7.66803e6 | −0.247403 | ||||||||
\(993\) | 2.91391e7 | 0.937784 | ||||||||
\(994\) | −7.40697e6 | −0.237780 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −2.52435e7 | −0.806308 | ||||||||
\(997\) | −4.50302e7 | −1.43472 | −0.717358 | − | 0.696705i | \(-0.754649\pi\) | ||||
−0.717358 | + | 0.696705i | \(0.754649\pi\) | |||||||
\(998\) | −1.11437e8 | −3.54162 | ||||||||
\(999\) | 1.04999e7 | 0.332868 |
(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 | 825.6.a.v.1.1 | 13 | ||
5.2 | odd | 4 | 165.6.c.b.34.1 | ✓ | 26 | ||
5.3 | odd | 4 | 165.6.c.b.34.26 | yes | 26 | ||
5.4 | even | 2 | 825.6.a.y.1.13 | 13 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
165.6.c.b.34.1 | ✓ | 26 | 5.2 | odd | 4 | ||
165.6.c.b.34.26 | yes | 26 | 5.3 | odd | 4 | ||
825.6.a.v.1.1 | 13 | 1.1 | even | 1 | trivial | ||
825.6.a.y.1.13 | 13 | 5.4 | even | 2 |