Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [49,6,Mod(18,49)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(49, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([4]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("49.18");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 49 = 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 49.c (of order \(3\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(7.85880717084\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\Q(\sqrt{-3}, \sqrt{-19})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 4x^{2} - 5x + 25 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{9}]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | no (minimal twist has level 7) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 18.1 | ||
Root | \(-1.63746 + 1.52274i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 49.18 |
Dual form | 49.6.c.e.30.1 |
$q$-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 \(\left(\mathbb{Z}/49\mathbb{Z}\right)^\times\).
\(n\) | \(3\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −4.13746 | − | 7.16629i | −0.731406 | − | 1.26683i | −0.956282 | − | 0.292445i | \(-0.905531\pi\) |
0.224876 | − | 0.974387i | \(-0.427802\pi\) | |||||||
\(3\) | 12.8248 | − | 22.2131i | 0.822708 | − | 1.42497i | −0.0809501 | − | 0.996718i | \(-0.525795\pi\) |
0.903658 | − | 0.428254i | \(-0.140871\pi\) | |||||||
\(4\) | −18.2371 | + | 31.5876i | −0.569910 | + | 0.987113i | ||||
\(5\) | −14.3746 | − | 24.8975i | −0.257140 | − | 0.445380i | 0.708334 | − | 0.705877i | \(-0.249447\pi\) |
−0.965475 | + | 0.260497i | \(0.916114\pi\) | |||||||
\(6\) | −212.248 | −2.40694 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 37.0241 | 0.204531 | ||||||||
\(9\) | −207.449 | − | 359.311i | −0.853698 | − | 1.47865i | ||||
\(10\) | −118.949 | + | 206.025i | −0.376148 | + | 0.651508i | ||||
\(11\) | 135.045 | − | 233.905i | 0.336509 | − | 0.582850i | −0.647265 | − | 0.762265i | \(-0.724087\pi\) |
0.983773 | + | 0.179415i | \(0.0574205\pi\) | |||||||
\(12\) | 467.773 | + | 810.207i | 0.937740 | + | 1.62421i | ||||
\(13\) | 300.640 | 0.493387 | 0.246694 | − | 0.969094i | \(-0.420656\pi\) | ||||
0.246694 | + | 0.969094i | \(0.420656\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −737.402 | −0.846206 | ||||||||
\(16\) | 430.402 | + | 745.479i | 0.420315 | + | 0.728007i | ||||
\(17\) | −306.553 | + | 530.966i | −0.257267 | + | 0.445599i | −0.965509 | − | 0.260371i | \(-0.916155\pi\) |
0.708242 | + | 0.705970i | \(0.249489\pi\) | |||||||
\(18\) | −1716.62 | + | 2973.27i | −1.24880 | + | 2.16298i | ||||
\(19\) | 850.474 | + | 1473.06i | 0.540477 | + | 0.936134i | 0.998877 | + | 0.0473873i | \(0.0150895\pi\) |
−0.458400 | + | 0.888746i | \(0.651577\pi\) | |||||||
\(20\) | 1048.60 | 0.586188 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −2234.97 | −0.984498 | ||||||||
\(23\) | −1594.08 | − | 2761.02i | −0.628333 | − | 1.08830i | −0.987886 | − | 0.155180i | \(-0.950404\pi\) |
0.359554 | − | 0.933124i | \(-0.382929\pi\) | |||||||
\(24\) | 474.825 | − | 822.421i | 0.168269 | − | 0.291451i | ||||
\(25\) | 1149.24 | − | 1990.55i | 0.367758 | − | 0.636975i | ||||
\(26\) | −1243.88 | − | 2154.47i | −0.360866 | − | 0.625039i | ||||
\(27\) | −4409.07 | −1.16396 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4299.28 | 0.949294 | 0.474647 | − | 0.880176i | \(-0.342576\pi\) | ||||
0.474647 | + | 0.880176i | \(0.342576\pi\) | |||||||
\(30\) | 3050.97 | + | 5284.44i | 0.618920 | + | 1.07200i | ||||
\(31\) | −1014.23 | + | 1756.69i | −0.189553 | + | 0.328316i | −0.945101 | − | 0.326777i | \(-0.894037\pi\) |
0.755548 | + | 0.655093i | \(0.227371\pi\) | |||||||
\(32\) | 4153.93 | − | 7194.82i | 0.717107 | − | 1.24207i | ||||
\(33\) | −3463.83 | − | 5999.54i | −0.553697 | − | 0.959031i | ||||
\(34\) | 5073.40 | 0.752666 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 15133.1 | 1.94612 | ||||||||
\(37\) | −2577.23 | − | 4463.89i | −0.309491 | − | 0.536055i | 0.668760 | − | 0.743478i | \(-0.266825\pi\) |
−0.978251 | + | 0.207424i | \(0.933492\pi\) | |||||||
\(38\) | 7037.60 | − | 12189.5i | 0.790616 | − | 1.36939i | ||||
\(39\) | 3855.63 | − | 6678.14i | 0.405914 | − | 0.703063i | ||||
\(40\) | −532.206 | − | 921.808i | −0.0525932 | − | 0.0910941i | ||||
\(41\) | −7146.21 | −0.663921 | −0.331960 | − | 0.943293i | \(-0.607710\pi\) | ||||
−0.331960 | + | 0.943293i | \(0.607710\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −19584.3 | −1.61524 | −0.807620 | − | 0.589703i | \(-0.799245\pi\) | ||||
−0.807620 | + | 0.589703i | \(0.799245\pi\) | |||||||
\(44\) | 4925.66 | + | 8531.49i | 0.383560 | + | 0.664345i | ||||
\(45\) | −5963.97 | + | 10329.9i | −0.439040 | + | 0.760440i | ||||
\(46\) | −13190.9 | + | 22847.2i | −0.919133 | + | 1.59198i | ||||
\(47\) | −9999.19 | − | 17319.1i | −0.660268 | − | 1.14362i | −0.980545 | − | 0.196294i | \(-0.937109\pi\) |
0.320277 | − | 0.947324i | \(-0.396224\pi\) | |||||||
\(48\) | 22079.2 | 1.38319 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −19019.8 | −1.07592 | ||||||||
\(51\) | 7862.94 | + | 13619.0i | 0.423311 | + | 0.733196i | ||||
\(52\) | −5482.80 | + | 9496.49i | −0.281186 | + | 0.487029i | ||||
\(53\) | −1974.41 | + | 3419.78i | −0.0965489 | + | 0.167228i | −0.910254 | − | 0.414050i | \(-0.864114\pi\) |
0.813705 | + | 0.581278i | \(0.197447\pi\) | |||||||
\(54\) | 18242.4 | + | 31596.7i | 0.851327 | + | 1.47454i | ||||
\(55\) | −7764.86 | −0.346120 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 43628.5 | 1.77862 | ||||||||
\(58\) | −17788.1 | − | 30809.9i | −0.694319 | − | 1.20260i | ||||
\(59\) | 14853.8 | − | 25727.5i | 0.555530 | − | 0.962206i | −0.442332 | − | 0.896851i | \(-0.645849\pi\) |
0.997862 | − | 0.0653544i | \(-0.0208178\pi\) | |||||||
\(60\) | 13448.1 | − | 23292.8i | 0.482262 | − | 0.835301i | ||||
\(61\) | 25259.6 | + | 43751.0i | 0.869165 | + | 1.50544i | 0.862851 | + | 0.505458i | \(0.168677\pi\) |
0.00631412 | + | 0.999980i | \(0.497990\pi\) | |||||||
\(62\) | 16785.3 | 0.554562 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −41201.1 | −1.25736 | ||||||||
\(65\) | −4321.57 | − | 7485.18i | −0.126870 | − | 0.219745i | ||||
\(66\) | −28662.9 | + | 49645.7i | −0.809955 | + | 1.40288i | ||||
\(67\) | −2526.78 | + | 4376.51i | −0.0687671 | + | 0.119108i | −0.898359 | − | 0.439262i | \(-0.855240\pi\) |
0.829592 | + | 0.558370i | \(0.188573\pi\) | |||||||
\(68\) | −11181.3 | − | 19366.6i | −0.293238 | − | 0.507903i | ||||
\(69\) | −81774.5 | −2.06774 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 32853.3 | 0.773453 | 0.386726 | − | 0.922195i | \(-0.373606\pi\) | ||||
0.386726 | + | 0.922195i | \(0.373606\pi\) | |||||||
\(72\) | −7680.59 | − | 13303.2i | −0.174608 | − | 0.302429i | ||||
\(73\) | 5557.48 | − | 9625.84i | 0.122059 | − | 0.211413i | −0.798520 | − | 0.601968i | \(-0.794384\pi\) |
0.920580 | + | 0.390555i | \(0.127717\pi\) | |||||||
\(74\) | −21326.3 | + | 36938.3i | −0.452728 | + | 0.784148i | ||||
\(75\) | −29477.5 | − | 51056.5i | −0.605114 | − | 1.04809i | ||||
\(76\) | −62040.8 | −1.23209 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −63810.0 | −1.18755 | ||||||||
\(79\) | −40944.7 | − | 70918.3i | −0.738125 | − | 1.27847i | −0.953339 | − | 0.301903i | \(-0.902378\pi\) |
0.215214 | − | 0.976567i | \(-0.430955\pi\) | |||||||
\(80\) | 12373.7 | − | 21431.9i | 0.216160 | − | 0.374400i | ||||
\(81\) | −6135.28 | + | 10626.6i | −0.103902 | + | 0.179963i | ||||
\(82\) | 29567.1 | + | 51211.8i | 0.485596 | + | 0.841076i | ||||
\(83\) | 118234. | 1.88385 | 0.941926 | − | 0.335819i | \(-0.109013\pi\) | ||||
0.941926 | + | 0.335819i | \(0.109013\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 17626.3 | 0.264615 | ||||||||
\(86\) | 81029.2 | + | 140347.i | 1.18140 | + | 2.04624i | ||||
\(87\) | 55137.2 | − | 95500.4i | 0.780992 | − | 1.35272i | ||||
\(88\) | 4999.91 | − | 8660.10i | 0.0688265 | − | 0.119211i | ||||
\(89\) | 20847.7 | + | 36109.2i | 0.278986 | + | 0.483218i | 0.971133 | − | 0.238538i | \(-0.0766683\pi\) |
−0.692147 | + | 0.721757i | \(0.743335\pi\) | |||||||
\(90\) | 98702.8 | 1.28447 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 116286. | 1.43237 | ||||||||
\(93\) | 26014.4 | + | 45058.3i | 0.311894 | + | 0.540216i | ||||
\(94\) | −82742.5 | + | 143314.i | −0.965849 | + | 1.67290i | ||||
\(95\) | 24450.4 | − | 42349.4i | 0.277957 | − | 0.481436i | ||||
\(96\) | −106546. | − | 184544.i | −1.17994 | − | 2.04372i | ||||
\(97\) | 43682.8 | 0.471391 | 0.235695 | − | 0.971827i | \(-0.424263\pi\) | ||||
0.235695 | + | 0.971827i | \(0.424263\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −112059. | −1.14911 | ||||||||
\(100\) | 41917.8 | + | 72603.7i | 0.419178 | + | 0.726037i | ||||
\(101\) | −12824.0 | + | 22211.9i | −0.125090 | + | 0.216662i | −0.921768 | − | 0.387742i | \(-0.873255\pi\) |
0.796678 | + | 0.604404i | \(0.206589\pi\) | |||||||
\(102\) | 65065.1 | − | 112696.i | 0.619224 | − | 1.07253i | ||||
\(103\) | 7160.02 | + | 12401.5i | 0.0664999 | + | 0.115181i | 0.897358 | − | 0.441303i | \(-0.145483\pi\) |
−0.830858 | + | 0.556484i | \(0.812150\pi\) | |||||||
\(104\) | 11130.9 | 0.100913 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 32676.1 | 0.282466 | ||||||||
\(107\) | −8600.89 | − | 14897.2i | −0.0726247 | − | 0.125790i | 0.827426 | − | 0.561574i | \(-0.189804\pi\) |
−0.900051 | + | 0.435785i | \(0.856471\pi\) | |||||||
\(108\) | 80408.8 | − | 139272.i | 0.663352 | − | 1.14896i | ||||
\(109\) | 43008.8 | − | 74493.4i | 0.346730 | − | 0.600553i | −0.638937 | − | 0.769259i | \(-0.720625\pi\) |
0.985666 | + | 0.168706i | \(0.0539588\pi\) | |||||||
\(110\) | 32126.8 | + | 55645.2i | 0.253154 | + | 0.438476i | ||||
\(111\) | −132209. | −1.01848 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 137568. | 1.01349 | 0.506745 | − | 0.862096i | \(-0.330848\pi\) | ||||
0.506745 | + | 0.862096i | \(0.330848\pi\) | |||||||
\(114\) | −180511. | − | 312654.i | −1.30089 | − | 2.25321i | ||||
\(115\) | −45828.4 | + | 79377.1i | −0.323139 | + | 0.559694i | ||||
\(116\) | −78406.5 | + | 135804.i | −0.541012 | + | 0.937061i | ||||
\(117\) | −62367.2 | − | 108023.i | −0.421203 | − | 0.729546i | ||||
\(118\) | −245828. | −1.62527 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −27301.6 | −0.173075 | ||||||||
\(121\) | 44051.3 | + | 76299.0i | 0.273524 | + | 0.473757i | ||||
\(122\) | 209021. | − | 362036.i | 1.27143 | − | 2.20217i | ||||
\(123\) | −91648.4 | + | 158740.i | −0.546213 | + | 0.946068i | ||||
\(124\) | −36993.2 | − | 64074.1i | −0.216057 | − | 0.374221i | ||||
\(125\) | −155921. | −0.892542 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −70567.1 | −0.388233 | −0.194117 | − | 0.980978i | \(-0.562184\pi\) | ||||
−0.194117 | + | 0.980978i | \(0.562184\pi\) | |||||||
\(128\) | 37542.1 | + | 65024.8i | 0.202532 | + | 0.350795i | ||||
\(129\) | −251164. | + | 435029.i | −1.32887 | + | 2.30167i | ||||
\(130\) | −35760.6 | + | 61939.2i | −0.185587 | + | 0.321446i | ||||
\(131\) | 86856.2 | + | 150439.i | 0.442204 | + | 0.765920i | 0.997853 | − | 0.0654972i | \(-0.0208633\pi\) |
−0.555649 | + | 0.831417i | \(0.687530\pi\) | |||||||
\(132\) | 252682. | 1.26223 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 41817.8 | 0.201187 | ||||||||
\(135\) | 63378.6 | + | 109775.i | 0.299301 | + | 0.518405i | ||||
\(136\) | −11349.9 | + | 19658.5i | −0.0526190 | + | 0.0911388i | ||||
\(137\) | 994.971 | − | 1723.34i | 0.00452907 | − | 0.00784457i | −0.863752 | − | 0.503917i | \(-0.831892\pi\) |
0.868281 | + | 0.496073i | \(0.165225\pi\) | |||||||
\(138\) | 338339. | + | 586020.i | 1.51236 | + | 2.61948i | ||||
\(139\) | 366409. | 1.60853 | 0.804264 | − | 0.594272i | \(-0.202560\pi\) | ||||
0.804264 | + | 0.594272i | \(0.202560\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −512949. | −2.17283 | ||||||||
\(142\) | −135929. | − | 235437.i | −0.565708 | − | 0.979835i | ||||
\(143\) | 40599.8 | − | 70321.0i | 0.166029 | − | 0.287571i | ||||
\(144\) | 178573. | − | 309297.i | 0.717644 | − | 1.24300i | ||||
\(145\) | −61800.4 | − | 107041.i | −0.244102 | − | 0.422797i | ||||
\(146\) | −91975.4 | −0.357100 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 188005. | 0.705529 | ||||||||
\(149\) | −70359.3 | − | 121866.i | −0.259631 | − | 0.449693i | 0.706512 | − | 0.707701i | \(-0.250267\pi\) |
−0.966143 | + | 0.258007i | \(0.916934\pi\) | |||||||
\(150\) | −243924. | + | 422489.i | −0.885169 | + | 1.53316i | ||||
\(151\) | −25032.3 | + | 43357.2i | −0.0893425 | + | 0.154746i | −0.907233 | − | 0.420628i | \(-0.861810\pi\) |
0.817891 | + | 0.575373i | \(0.195143\pi\) | |||||||
\(152\) | 31488.0 | + | 54538.9i | 0.110544 | + | 0.191468i | ||||
\(153\) | 254376. | 0.878512 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 58316.4 | 0.194967 | ||||||||
\(156\) | 140631. | + | 243580.i | 0.462669 | + | 0.801366i | ||||
\(157\) | 44897.3 | − | 77764.4i | 0.145369 | − | 0.251786i | −0.784142 | − | 0.620582i | \(-0.786896\pi\) |
0.929510 | + | 0.368796i | \(0.120230\pi\) | |||||||
\(158\) | −338814. | + | 586843.i | −1.07974 | + | 1.87016i | ||||
\(159\) | 50642.6 | + | 87715.6i | 0.158863 | + | 0.275159i | ||||
\(160\) | −238844. | −0.737589 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 101538. | 0.303977 | ||||||||
\(163\) | 240615. | + | 416758.i | 0.709339 | + | 1.22861i | 0.965103 | + | 0.261872i | \(0.0843398\pi\) |
−0.255764 | + | 0.966739i | \(0.582327\pi\) | |||||||
\(164\) | 130326. | − | 225732.i | 0.378375 | − | 0.655365i | ||||
\(165\) | −99582.4 | + | 172482.i | −0.284756 | + | 0.493211i | ||||
\(166\) | −489188. | − | 847299.i | −1.37786 | − | 2.38653i | ||||
\(167\) | −86572.7 | −0.240209 | −0.120105 | − | 0.992761i | \(-0.538323\pi\) | ||||
−0.120105 | + | 0.992761i | \(0.538323\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −280909. | −0.756569 | ||||||||
\(170\) | −72928.1 | − | 126315.i | −0.193541 | − | 0.335222i | ||||
\(171\) | 352859. | − | 611170.i | 0.922808 | − | 1.59835i | ||||
\(172\) | 357161. | − | 618622.i | 0.920542 | − | 1.59442i | ||||
\(173\) | 29068.7 | + | 50348.5i | 0.0738432 | + | 0.127900i | 0.900583 | − | 0.434685i | \(-0.143140\pi\) |
−0.826739 | + | 0.562585i | \(0.809807\pi\) | |||||||
\(174\) | −912511. | −2.28489 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 232495. | 0.565759 | ||||||||
\(177\) | −380992. | − | 659898.i | −0.914078 | − | 1.58323i | ||||
\(178\) | 172513. | − | 298801.i | 0.408105 | − | 0.706858i | ||||
\(179\) | 104690. | − | 181328.i | 0.244215 | − | 0.422993i | −0.717695 | − | 0.696357i | \(-0.754803\pi\) |
0.961911 | + | 0.273364i | \(0.0881363\pi\) | |||||||
\(180\) | −217531. | − | 376776.i | −0.500427 | − | 0.866765i | ||||
\(181\) | 278996. | 0.632996 | 0.316498 | − | 0.948593i | \(-0.397493\pi\) | ||||
0.316498 | + | 0.948593i | \(0.397493\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1.29579e6 | 2.86028 | ||||||||
\(184\) | −59019.2 | − | 102224.i | −0.128514 | − | 0.222592i | ||||
\(185\) | −74093.2 | + | 128333.i | −0.159165 | + | 0.275683i | ||||
\(186\) | 215267. | − | 372854.i | 0.456242 | − | 0.790235i | ||||
\(187\) | 82796.9 | + | 143408.i | 0.173145 | + | 0.299896i | ||||
\(188\) | 729426. | 1.50517 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −404651. | −0.813198 | ||||||||
\(191\) | 222566. | + | 385496.i | 0.441444 | + | 0.764604i | 0.997797 | − | 0.0663425i | \(-0.0211330\pi\) |
−0.556353 | + | 0.830946i | \(0.687800\pi\) | |||||||
\(192\) | −528394. | + | 915205.i | −1.03444 | + | 1.79170i | ||||
\(193\) | 363405. | − | 629437.i | 0.702260 | − | 1.21635i | −0.265411 | − | 0.964135i | \(-0.585508\pi\) |
0.967671 | − | 0.252215i | \(-0.0811590\pi\) | |||||||
\(194\) | −180736. | − | 313043.i | −0.344778 | − | 0.597173i | ||||
\(195\) | −221692. | −0.417507 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −364897. | −0.669892 | −0.334946 | − | 0.942237i | \(-0.608718\pi\) | ||||
−0.334946 | + | 0.942237i | \(0.608718\pi\) | |||||||
\(198\) | 463641. | + | 803050.i | 0.840464 | + | 1.45573i | ||||
\(199\) | −144654. | + | 250547.i | −0.258938 | + | 0.448494i | −0.965958 | − | 0.258700i | \(-0.916706\pi\) |
0.707019 | + | 0.707194i | \(0.250039\pi\) | |||||||
\(200\) | 42549.7 | − | 73698.2i | 0.0752179 | − | 0.130281i | ||||
\(201\) | 64810.7 | + | 112255.i | 0.113150 | + | 0.195982i | ||||
\(202\) | 212236. | 0.365965 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −573589. | −0.964997 | ||||||||
\(205\) | 102724. | + | 177923.i | 0.170721 | + | 0.295697i | ||||
\(206\) | 59248.5 | − | 102621.i | 0.0972769 | − | 0.168488i | ||||
\(207\) | −661378. | + | 1.14554e6i | −1.07281 | + | 1.85816i | ||||
\(208\) | 129396. | + | 224120.i | 0.207378 | + | 0.359189i | ||||
\(209\) | 459409. | 0.727501 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 750147. | 1.15995 | 0.579976 | − | 0.814633i | \(-0.303062\pi\) | ||||
0.579976 | + | 0.814633i | \(0.303062\pi\) | |||||||
\(212\) | −72015.1 | − | 124734.i | −0.110048 | − | 0.190609i | ||||
\(213\) | 421336. | − | 729775.i | 0.636326 | − | 1.10215i | ||||
\(214\) | −71171.7 | + | 123273.i | −0.106236 | + | 0.184007i | ||||
\(215\) | 281516. | + | 487600.i | 0.415343 | + | 0.719396i | ||||
\(216\) | −163242. | −0.238066 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −711788. | −1.01440 | ||||||||
\(219\) | −142547. | − | 246898.i | −0.200838 | − | 0.347862i | ||||
\(220\) | 141609. | − | 245273.i | 0.197257 | − | 0.341660i | ||||
\(221\) | −92162.0 | + | 159629.i | −0.126932 | + | 0.219853i | ||||
\(222\) | 547010. | + | 947449.i | 0.744926 | + | 1.29025i | ||||
\(223\) | 534398. | 0.719619 | 0.359810 | − | 0.933026i | \(-0.382842\pi\) | ||||
0.359810 | + | 0.933026i | \(0.382842\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −953635. | −1.25582 | ||||||||
\(226\) | −569180. | − | 985849.i | −0.741273 | − | 1.28392i | ||||
\(227\) | 205312. | − | 355610.i | 0.264453 | − | 0.458047i | −0.702967 | − | 0.711223i | \(-0.748142\pi\) |
0.967420 | + | 0.253176i | \(0.0814751\pi\) | |||||||
\(228\) | −795658. | + | 1.37812e6i | −1.01365 | + | 1.75570i | ||||
\(229\) | −515181. | − | 892320.i | −0.649189 | − | 1.12443i | −0.983317 | − | 0.181901i | \(-0.941775\pi\) |
0.334128 | − | 0.942528i | \(-0.391558\pi\) | |||||||
\(230\) | 758452. | 0.945385 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 159177. | 0.194160 | ||||||||
\(233\) | 59605.5 | + | 103240.i | 0.0719278 | + | 0.124583i | 0.899746 | − | 0.436414i | \(-0.143752\pi\) |
−0.827818 | + | 0.560996i | \(0.810418\pi\) | |||||||
\(234\) | −516084. | + | 893883.i | −0.616142 | + | 1.06719i | ||||
\(235\) | −287469. | + | 497910.i | −0.339563 | + | 0.588141i | ||||
\(236\) | 541781. | + | 938392.i | 0.633204 | + | 1.09674i | ||||
\(237\) | −2.10042e6 | −2.42905 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −254090. | −0.287735 | −0.143868 | − | 0.989597i | \(-0.545954\pi\) | ||||
−0.143868 | + | 0.989597i | \(0.545954\pi\) | |||||||
\(240\) | −317380. | − | 549718.i | −0.355673 | − | 0.616044i | ||||
\(241\) | −706254. | + | 1.22327e6i | −0.783282 | + | 1.35668i | 0.146738 | + | 0.989175i | \(0.453123\pi\) |
−0.930020 | + | 0.367509i | \(0.880211\pi\) | |||||||
\(242\) | 364521. | − | 631368.i | 0.400114 | − | 0.693018i | ||||
\(243\) | −378335. | − | 655296.i | −0.411019 | − | 0.711905i | ||||
\(244\) | −1.84265e6 | −1.98138 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 1.51677e6 | 1.59801 | ||||||||
\(247\) | 255686. | + | 442862.i | 0.266664 | + | 0.461876i | ||||
\(248\) | −37550.9 | + | 65040.0i | −0.0387695 | + | 0.0671508i | ||||
\(249\) | 1.51632e6 | − | 2.62635e6i | 1.54986 | − | 2.68444i | ||||
\(250\) | 645115. | + | 1.11737e6i | 0.652811 | + | 1.13070i | ||||
\(251\) | −1.67542e6 | −1.67857 | −0.839286 | − | 0.543690i | \(-0.817027\pi\) | ||||
−0.839286 | + | 0.543690i | \(0.817027\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −861087. | −0.845758 | ||||||||
\(254\) | 291968. | + | 505704.i | 0.283956 | + | 0.491827i | ||||
\(255\) | 226053. | − | 391535.i | 0.217701 | − | 0.377069i | ||||
\(256\) | −348560. | + | 603724.i | −0.332413 | + | 0.575756i | ||||
\(257\) | −363498. | − | 629597.i | −0.343296 | − | 0.594607i | 0.641746 | − | 0.766917i | \(-0.278210\pi\) |
−0.985043 | + | 0.172310i | \(0.944877\pi\) | |||||||
\(258\) | 4.15672e6 | 3.88778 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 315252. | 0.289217 | ||||||||
\(261\) | −891879. | − | 1.54478e6i | −0.810410 | − | 1.40367i | ||||
\(262\) | 718728. | − | 1.24487e6i | 0.646862 | − | 1.12040i | ||||
\(263\) | 112940. | − | 195618.i | 0.100684 | − | 0.174389i | −0.811283 | − | 0.584654i | \(-0.801230\pi\) |
0.911967 | + | 0.410265i | \(0.134564\pi\) | |||||||
\(264\) | −128245. | − | 222127.i | −0.113248 | − | 0.196152i | ||||
\(265\) | 113525. | 0.0993065 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1.06947e6 | 0.918097 | ||||||||
\(268\) | −92162.4 | − | 159630.i | −0.0783821 | − | 0.135762i | ||||
\(269\) | −902635. | + | 1.56341e6i | −0.760557 | + | 1.31732i | 0.182008 | + | 0.983297i | \(0.441740\pi\) |
−0.942564 | + | 0.334025i | \(0.891593\pi\) | |||||||
\(270\) | 524453. | − | 908379.i | 0.437821 | − | 0.758329i | ||||
\(271\) | 856898. | + | 1.48419e6i | 0.708771 | + | 1.22763i | 0.965313 | + | 0.261094i | \(0.0840833\pi\) |
−0.256543 | + | 0.966533i | \(0.582583\pi\) | |||||||
\(272\) | −527765. | −0.432532 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −16466.6 | −0.0132504 | ||||||||
\(275\) | −310399. | − | 537626.i | −0.247507 | − | 0.428695i | ||||
\(276\) | 1.49133e6 | − | 2.58306e6i | 1.17842 | − | 2.04109i | ||||
\(277\) | −1.11527e6 | + | 1.93171e6i | −0.873338 | + | 1.51267i | −0.0148147 | + | 0.999890i | \(0.504716\pi\) |
−0.858523 | + | 0.512775i | \(0.828617\pi\) | |||||||
\(278\) | −1.51600e6 | − | 2.62579e6i | −1.17649 | − | 2.03774i | ||||
\(279\) | 841600. | 0.647285 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.67140e6 | 1.26274 | 0.631371 | − | 0.775481i | \(-0.282493\pi\) | ||||
0.631371 | + | 0.775481i | \(0.282493\pi\) | |||||||
\(282\) | 2.12230e6 | + | 3.67594e6i | 1.58922 | + | 2.75262i | ||||
\(283\) | 198076. | − | 343078.i | 0.147016 | − | 0.254640i | −0.783107 | − | 0.621887i | \(-0.786366\pi\) |
0.930123 | + | 0.367247i | \(0.119700\pi\) | |||||||
\(284\) | −599151. | + | 1.03776e6i | −0.440799 | + | 0.763486i | ||||
\(285\) | −627141. | − | 1.08624e6i | −0.457355 | − | 0.792162i | ||||
\(286\) | −671920. | −0.485739 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −3.44691e6 | −2.44877 | ||||||||
\(289\) | 521979. | + | 904094.i | 0.367628 | + | 0.636750i | ||||
\(290\) | −511393. | + | 885758.i | −0.357075 | + | 0.618472i | ||||
\(291\) | 560221. | − | 970331.i | 0.387817 | − | 0.671718i | ||||
\(292\) | 202705. | + | 351095.i | 0.139126 | + | 0.240973i | ||||
\(293\) | −929465. | −0.632505 | −0.316252 | − | 0.948675i | \(-0.602425\pi\) | ||||
−0.316252 | + | 0.948675i | \(0.602425\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −854068. | −0.571397 | ||||||||
\(296\) | −95419.5 | − | 165271.i | −0.0633006 | − | 0.109640i | ||||
\(297\) | −595423. | + | 1.03130e6i | −0.391683 | + | 0.678414i | ||||
\(298\) | −582217. | + | 1.00843e6i | −0.379791 | + | 0.657817i | ||||
\(299\) | −479242. | − | 830072.i | −0.310011 | − | 0.536955i | ||||
\(300\) | 2.15034e6 | 1.37944 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 414280. | 0.261383 | ||||||||
\(303\) | 328930. | + | 569724.i | 0.205825 | + | 0.356499i | ||||
\(304\) | −732092. | + | 1.26802e6i | −0.454341 | + | 0.786942i | ||||
\(305\) | 726193. | − | 1.25780e6i | 0.446995 | − | 0.774218i | ||||
\(306\) | −1.05247e6 | − | 1.82293e6i | −0.642549 | − | 1.11293i | ||||
\(307\) | 1.83295e6 | 1.10995 | 0.554976 | − | 0.831866i | \(-0.312727\pi\) | ||||
0.554976 | + | 0.831866i | \(0.312727\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 367302. | 0.218840 | ||||||||
\(310\) | −241282. | − | 417912.i | −0.142600 | − | 0.246991i | ||||
\(311\) | 1.14842e6 | − | 1.98913e6i | 0.673289 | − | 1.16617i | −0.303677 | − | 0.952775i | \(-0.598214\pi\) |
0.976966 | − | 0.213396i | \(-0.0684523\pi\) | |||||||
\(312\) | 142751. | − | 247252.i | 0.0830220 | − | 0.143798i | ||||
\(313\) | 1.71235e6 | + | 2.96588e6i | 0.987943 | + | 1.71117i | 0.628047 | + | 0.778176i | \(0.283855\pi\) |
0.359897 | + | 0.932992i | \(0.382812\pi\) | |||||||
\(314\) | −743043. | −0.425295 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 2.98685e6 | 1.68266 | ||||||||
\(317\) | −1.47153e6 | − | 2.54876e6i | −0.822470 | − | 1.42456i | −0.903837 | − | 0.427876i | \(-0.859262\pi\) |
0.0813671 | − | 0.996684i | \(-0.474071\pi\) | |||||||
\(318\) | 419063. | − | 725839.i | 0.232387 | − | 0.402506i | ||||
\(319\) | 580596. | − | 1.00562e6i | 0.319446 | − | 0.553296i | ||||
\(320\) | 592249. | + | 1.02580e6i | 0.323317 | + | 0.560002i | ||||
\(321\) | −441217. | −0.238996 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1.04286e6 | −0.556187 | ||||||||
\(324\) | −223780. | − | 387598.i | −0.118429 | − | 0.205125i | ||||
\(325\) | 345508. | − | 598437.i | 0.181447 | − | 0.314275i | ||||
\(326\) | 1.99107e6 | − | 3.44863e6i | 1.03763 | − | 1.79723i | ||||
\(327\) | −1.10315e6 | − | 1.91072e6i | −0.570515 | − | 0.988160i | ||||
\(328\) | −264582. | −0.135792 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 1.64807e6 | 0.833089 | ||||||||
\(331\) | −483082. | − | 836722.i | −0.242354 | − | 0.419770i | 0.719030 | − | 0.694979i | \(-0.244586\pi\) |
−0.961384 | + | 0.275209i | \(0.911253\pi\) | |||||||
\(332\) | −2.15625e6 | + | 3.73473e6i | −1.07363 | + | 1.85958i | ||||
\(333\) | −1.06928e6 | + | 1.85205e6i | −0.528424 | + | 0.915257i | ||||
\(334\) | 358191. | + | 620405.i | 0.175691 | + | 0.304305i | ||||
\(335\) | 145286. | 0.0707312 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 136417. | 0.0654327 | 0.0327163 | − | 0.999465i | \(-0.489584\pi\) | ||||
0.0327163 | + | 0.999465i | \(0.489584\pi\) | |||||||
\(338\) | 1.16225e6 | + | 2.01307e6i | 0.553359 | + | 0.958447i | ||||
\(339\) | 1.76427e6 | − | 3.05580e6i | 0.833807 | − | 1.44420i | ||||
\(340\) | −321453. | + | 556773.i | −0.150807 | + | 0.261205i | ||||
\(341\) | 273932. | + | 474465.i | 0.127573 | + | 0.220962i | ||||
\(342\) | −5.83976e6 | −2.69979 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −725091. | −0.330367 | ||||||||
\(345\) | 1.17548e6 | + | 2.03598e6i | 0.531699 | + | 0.920929i | ||||
\(346\) | 240541. | − | 416630.i | 0.108019 | − | 0.187094i | ||||
\(347\) | −177704. | + | 307792.i | −0.0792270 | + | 0.137225i | −0.902917 | − | 0.429816i | \(-0.858579\pi\) |
0.823690 | + | 0.567041i | \(0.191912\pi\) | |||||||
\(348\) | 2.01109e6 | + | 3.48331e6i | 0.890190 | + | 1.54186i | ||||
\(349\) | −140128. | −0.0615830 | −0.0307915 | − | 0.999526i | \(-0.509803\pi\) | ||||
−0.0307915 | + | 0.999526i | \(0.509803\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.32554e6 | −0.574283 | ||||||||
\(352\) | −1.12193e6 | − | 1.94325e6i | −0.482626 | − | 0.835933i | ||||
\(353\) | −1.74071e6 | + | 3.01499e6i | −0.743514 | + | 1.28780i | 0.207373 | + | 0.978262i | \(0.433509\pi\) |
−0.950886 | + | 0.309541i | \(0.899825\pi\) | |||||||
\(354\) | −3.15268e6 | + | 5.46060e6i | −1.33712 | + | 2.31597i | ||||
\(355\) | −472253. | − | 817967.i | −0.198886 | − | 0.344481i | ||||
\(356\) | −1.52081e6 | −0.635988 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −1.73260e6 | −0.714482 | ||||||||
\(359\) | −876427. | − | 1.51802e6i | −0.358905 | − | 0.621642i | 0.628873 | − | 0.777508i | \(-0.283517\pi\) |
−0.987778 | + | 0.155866i | \(0.950183\pi\) | |||||||
\(360\) | −220811. | + | 382455.i | −0.0897974 | + | 0.155534i | ||||
\(361\) | −208563. | + | 361242.i | −0.0842306 | + | 0.145892i | ||||
\(362\) | −1.15433e6 | − | 1.99936e6i | −0.462977 | − | 0.801900i | ||||
\(363\) | 2.25979e6 | 0.900121 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −319546. | −0.125546 | ||||||||
\(366\) | −5.36129e6 | − | 9.28603e6i | −2.09202 | − | 3.62349i | ||||
\(367\) | 884695. | − | 1.53234e6i | 0.342869 | − | 0.593867i | −0.642095 | − | 0.766625i | \(-0.721935\pi\) |
0.984964 | + | 0.172758i | \(0.0552679\pi\) | |||||||
\(368\) | 1.37219e6 | − | 2.37670e6i | 0.528195 | − | 0.914861i | ||||
\(369\) | 1.48247e6 | + | 2.56771e6i | 0.566787 | + | 0.981705i | ||||
\(370\) | 1.22623e6 | 0.465658 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −1.89771e6 | −0.711006 | ||||||||
\(373\) | 2.08106e6 | + | 3.60451e6i | 0.774485 | + | 1.34145i | 0.935083 | + | 0.354428i | \(0.115324\pi\) |
−0.160598 | + | 0.987020i | \(0.551342\pi\) | |||||||
\(374\) | 685137. | − | 1.18669e6i | 0.253279 | − | 0.438691i | ||||
\(375\) | −1.99964e6 | + | 3.46349e6i | −0.734302 | + | 1.27185i | ||||
\(376\) | −370211. | − | 641224.i | −0.135045 | − | 0.233905i | ||||
\(377\) | 1.29253e6 | 0.468369 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 618163. | 0.221057 | 0.110529 | − | 0.993873i | \(-0.464746\pi\) | ||||
0.110529 | + | 0.993873i | \(0.464746\pi\) | |||||||
\(380\) | 891811. | + | 1.54466e6i | 0.316821 | + | 0.548750i | ||||
\(381\) | −905005. | + | 1.56751e6i | −0.319403 | + | 0.553222i | ||||
\(382\) | 1.84172e6 | − | 3.18995e6i | 0.645750 | − | 1.11847i | ||||
\(383\) | 2.05582e6 | + | 3.56078e6i | 0.716123 | + | 1.24036i | 0.962525 | + | 0.271194i | \(0.0874183\pi\) |
−0.246402 | + | 0.969168i | \(0.579248\pi\) | |||||||
\(384\) | 1.92587e6 | 0.666498 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −6.01430e6 | −2.05455 | ||||||||
\(387\) | 4.06273e6 | + | 7.03686e6i | 1.37893 | + | 2.38837i | ||||
\(388\) | −796648. | + | 1.37984e6i | −0.268650 | + | 0.465316i | ||||
\(389\) | −2.31038e6 | + | 4.00169e6i | −0.774122 | + | 1.34082i | 0.161165 | + | 0.986927i | \(0.448475\pi\) |
−0.935287 | + | 0.353891i | \(0.884858\pi\) | |||||||
\(390\) | 917242. | + | 1.58871e6i | 0.305367 | + | 0.528912i | ||||
\(391\) | 1.95468e6 | 0.646596 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 4.45564e6 | 1.45522 | ||||||||
\(394\) | 1.50975e6 | + | 2.61496e6i | 0.489963 | + | 0.848641i | ||||
\(395\) | −1.17713e6 | + | 2.03884e6i | −0.379603 | + | 0.657492i | ||||
\(396\) | 2.04364e6 | − | 3.53969e6i | 0.654888 | − | 1.13430i | ||||
\(397\) | −2.53675e6 | − | 4.39377e6i | −0.807794 | − | 1.39914i | −0.914389 | − | 0.404838i | \(-0.867328\pi\) |
0.106595 | − | 0.994303i | \(-0.466005\pi\) | |||||||
\(398\) | 2.39399e6 | 0.757557 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1.97855e6 | 0.618296 | ||||||||
\(401\) | 740279. | + | 1.28220e6i | 0.229898 | + | 0.398194i | 0.957778 | − | 0.287510i | \(-0.0928275\pi\) |
−0.727880 | + | 0.685705i | \(0.759494\pi\) | |||||||
\(402\) | 536303. | − | 928904.i | 0.165518 | − | 0.286685i | ||||
\(403\) | −304917. | + | 528132.i | −0.0935231 | + | 0.161987i | ||||
\(404\) | −467747. | − | 810162.i | −0.142580 | − | 0.246955i | ||||
\(405\) | 352768. | 0.106869 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −1.39217e6 | −0.416586 | ||||||||
\(408\) | 291118. | + | 504231.i | 0.0865802 | + | 0.149961i | ||||
\(409\) | 2.26690e6 | − | 3.92638e6i | 0.670075 | − | 1.16060i | −0.307808 | − | 0.951449i | \(-0.599595\pi\) |
0.977882 | − | 0.209155i | \(-0.0670713\pi\) | |||||||
\(410\) | 850031. | − | 1.47230e6i | 0.249733 | − | 0.432549i | ||||
\(411\) | −25520.5 | − | 44202.8i | −0.00745220 | − | 0.0129076i | ||||
\(412\) | −522313. | −0.151596 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 1.09457e7 | 3.13865 | ||||||||
\(415\) | −1.69956e6 | − | 2.94373e6i | −0.484415 | − | 0.839031i | ||||
\(416\) | 1.24884e6 | − | 2.16305e6i | 0.353812 | − | 0.612820i | ||||
\(417\) | 4.69910e6 | − | 8.13908e6i | 1.32335 | − | 2.29211i | ||||
\(418\) | −1.90078e6 | − | 3.29226e6i | −0.532099 | − | 0.921622i | ||||
\(419\) | 111026. | 0.0308952 | 0.0154476 | − | 0.999881i | \(-0.495083\pi\) | ||||
0.0154476 | + | 0.999881i | \(0.495083\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1.41151e6 | −0.388132 | −0.194066 | − | 0.980988i | \(-0.562168\pi\) | ||||
−0.194066 | + | 0.980988i | \(0.562168\pi\) | |||||||
\(422\) | −3.10370e6 | − | 5.37577e6i | −0.848396 | − | 1.46947i | ||||
\(423\) | −4.14864e6 | + | 7.18565e6i | −1.12734 | + | 1.95261i | ||||
\(424\) | −73100.7 | + | 126614.i | −0.0197473 | + | 0.0342033i | ||||
\(425\) | 704608. | + | 1.22042e6i | 0.189224 | + | 0.327745i | ||||
\(426\) | −6.97304e6 | −1.86165 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 627422. | 0.165558 | ||||||||
\(429\) | −1.04137e6 | − | 1.80370e6i | −0.273187 | − | 0.473174i | ||||
\(430\) | 2.32952e6 | − | 4.03485e6i | 0.607570 | − | 1.05234i | ||||
\(431\) | −538200. | + | 932189.i | −0.139557 | + | 0.241719i | −0.927329 | − | 0.374248i | \(-0.877901\pi\) |
0.787772 | + | 0.615967i | \(0.211234\pi\) | |||||||
\(432\) | −1.89768e6 | − | 3.28687e6i | −0.489230 | − | 0.847370i | ||||
\(433\) | −310172. | −0.0795029 | −0.0397515 | − | 0.999210i | \(-0.512657\pi\) | ||||
−0.0397515 | + | 0.999210i | \(0.512657\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −3.17030e6 | −0.803298 | ||||||||
\(436\) | 1.56871e6 | + | 2.71709e6i | 0.395210 | + | 0.684523i | ||||
\(437\) | 2.71144e6 | − | 4.69636e6i | 0.679199 | − | 1.17641i | ||||
\(438\) | −1.17956e6 | + | 2.04306e6i | −0.293789 | + | 0.508857i | ||||
\(439\) | −2.83825e6 | − | 4.91599e6i | −0.702893 | − | 1.21745i | −0.967447 | − | 0.253075i | \(-0.918558\pi\) |
0.264553 | − | 0.964371i | \(-0.414775\pi\) | |||||||
\(440\) | −287487. | −0.0707923 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 1.52527e6 | 0.371356 | ||||||||
\(443\) | −2.02983e6 | − | 3.51577e6i | −0.491417 | − | 0.851159i | 0.508534 | − | 0.861042i | \(-0.330188\pi\) |
−0.999951 | + | 0.00988261i | \(0.996854\pi\) | |||||||
\(444\) | 2.41112e6 | − | 4.17618e6i | 0.580445 | − | 1.00536i | ||||
\(445\) | 599354. | − | 1.03811e6i | 0.143477 | − | 0.248510i | ||||
\(446\) | −2.21105e6 | − | 3.82965e6i | −0.526334 | − | 0.911637i | ||||
\(447\) | −3.60936e6 | −0.854401 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −6.96544e6 | −1.63054 | −0.815272 | − | 0.579078i | \(-0.803413\pi\) | ||||
−0.815272 | + | 0.579078i | \(0.803413\pi\) | |||||||
\(450\) | 3.94562e6 | + | 6.83402e6i | 0.918511 | + | 1.59091i | ||||
\(451\) | −965059. | + | 1.67153e6i | −0.223415 | + | 0.386966i | ||||
\(452\) | −2.50884e6 | + | 4.34543e6i | −0.577599 | + | 1.00043i | ||||
\(453\) | 642066. | + | 1.11209e6i | 0.147006 | + | 0.254621i | ||||
\(454\) | −3.39788e6 | −0.773692 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 1.61530e6 | 0.363783 | ||||||||
\(457\) | −897615. | − | 1.55472e6i | −0.201048 | − | 0.348225i | 0.747818 | − | 0.663903i | \(-0.231101\pi\) |
−0.948866 | + | 0.315678i | \(0.897768\pi\) | |||||||
\(458\) | −4.26308e6 | + | 7.38387e6i | −0.949642 | + | 1.64483i | ||||
\(459\) | 1.35162e6 | − | 2.34107e6i | 0.299448 | − | 0.518659i | ||||
\(460\) | −1.67156e6 | − | 2.89522e6i | −0.368321 | − | 0.637950i | ||||
\(461\) | −2.11294e6 | −0.463058 | −0.231529 | − | 0.972828i | \(-0.574373\pi\) | ||||
−0.231529 | + | 0.972828i | \(0.574373\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1.26223e6 | 0.273643 | 0.136822 | − | 0.990596i | \(-0.456311\pi\) | ||||
0.136822 | + | 0.990596i | \(0.456311\pi\) | |||||||
\(464\) | 1.85042e6 | + | 3.20502e6i | 0.399002 | + | 0.691092i | ||||
\(465\) | 747893. | − | 1.29539e6i | 0.160401 | − | 0.277823i | ||||
\(466\) | 493231. | − | 854301.i | 0.105217 | − | 0.182241i | ||||
\(467\) | 1.79463e6 | + | 3.10839e6i | 0.380788 | + | 0.659544i | 0.991175 | − | 0.132559i | \(-0.0423194\pi\) |
−0.610387 | + | 0.792103i | \(0.708986\pi\) | |||||||
\(468\) | 4.54960e6 | 0.960192 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 4.75756e6 | 0.993435 | ||||||||
\(471\) | −1.15159e6 | − | 1.99462e6i | −0.239192 | − | 0.414293i | ||||
\(472\) | 549948. | − | 952538.i | 0.113623 | − | 0.196801i | ||||
\(473\) | −2.64476e6 | + | 4.58086e6i | −0.543542 | + | 0.941443i | ||||
\(474\) | 8.69041e6 | + | 1.50522e7i | 1.77662 | + | 3.07719i | ||||
\(475\) | 3.90960e6 | 0.795058 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1.63835e6 | 0.329694 | ||||||||
\(478\) | 1.05129e6 | + | 1.82088e6i | 0.210451 | + | 0.364512i | ||||
\(479\) | 1.20847e6 | − | 2.09312e6i | 0.240655 | − | 0.416827i | −0.720246 | − | 0.693719i | \(-0.755971\pi\) |
0.960901 | + | 0.276892i | \(0.0893043\pi\) | |||||||
\(480\) | −3.06312e6 | + | 5.30547e6i | −0.606821 | + | 1.05104i | ||||
\(481\) | −774817. | − | 1.34202e6i | −0.152699 | − | 0.264482i | ||||
\(482\) | 1.16884e7 | 2.29159 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −3.21347e6 | −0.623536 | ||||||||
\(485\) | −627922. | − | 1.08759e6i | −0.121214 | − | 0.209948i | ||||
\(486\) | −3.13069e6 | + | 5.42252e6i | −0.601243 | + | 1.04138i | ||||
\(487\) | 2.59701e6 | − | 4.49816e6i | 0.496194 | − | 0.859434i | −0.503796 | − | 0.863823i | \(-0.668064\pi\) |
0.999990 | + | 0.00438895i | \(0.00139705\pi\) | |||||||
\(488\) | 935215. | + | 1.61984e6i | 0.177771 | + | 0.307909i | ||||
\(489\) | 1.23433e7 | 2.33432 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 5.38961e6 | 1.00891 | 0.504456 | − | 0.863437i | \(-0.331693\pi\) | ||||
0.504456 | + | 0.863437i | \(0.331693\pi\) | |||||||
\(492\) | −3.34281e6 | − | 5.78991e6i | −0.622585 | − | 1.07835i | ||||
\(493\) | −1.31796e6 | + | 2.28277e6i | −0.244222 | + | 0.423004i | ||||
\(494\) | 2.11578e6 | − | 3.66464e6i | 0.390080 | − | 0.675638i | ||||
\(495\) | 1.61081e6 | + | 2.79000e6i | 0.295482 | + | 0.511790i | ||||
\(496\) | −1.74610e6 | −0.318688 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −2.50949e7 | −4.53431 | ||||||||
\(499\) | 1.64803e6 | + | 2.85448e6i | 0.296288 | + | 0.513186i | 0.975284 | − | 0.220956i | \(-0.0709178\pi\) |
−0.678996 | + | 0.734142i | \(0.737584\pi\) | |||||||
\(500\) | 2.84355e6 | − | 4.92517e6i | 0.508669 | − | 0.881040i | ||||
\(501\) | −1.11027e6 | + | 1.92305e6i | −0.197622 | + | 0.342292i | ||||
\(502\) | 6.93199e6 | + | 1.20066e7i | 1.22772 | + | 2.12647i | ||||
\(503\) | −1.06512e7 | −1.87706 | −0.938528 | − | 0.345204i | \(-0.887810\pi\) | ||||
−0.938528 | + | 0.345204i | \(0.887810\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 737361. | 0.128662 | ||||||||
\(506\) | 3.56271e6 | + | 6.17080e6i | 0.618592 | + | 1.07143i | ||||
\(507\) | −3.60259e6 | + | 6.23986e6i | −0.622436 | + | 1.07809i | ||||
\(508\) | 1.28694e6 | − | 2.22905e6i | 0.221258 | − | 0.383230i | ||||
\(509\) | 1.37134e6 | + | 2.37523e6i | 0.234612 | + | 0.406360i | 0.959160 | − | 0.282864i | \(-0.0912846\pi\) |
−0.724548 | + | 0.689225i | \(0.757951\pi\) | |||||||
\(510\) | −3.74114e6 | −0.636910 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 8.17130e6 | 1.37758 | ||||||||
\(513\) | −3.74980e6 | − | 6.49485e6i | −0.629093 | − | 1.08962i | ||||
\(514\) | −3.00792e6 | + | 5.20986e6i | −0.502178 | + | 0.869798i | ||||
\(515\) | 205845. | − | 356533.i | 0.0341996 | − | 0.0592355i | ||||
\(516\) | −9.16101e6 | − | 1.58673e7i | −1.51467 | − | 2.62349i | ||||
\(517\) | −5.40136e6 | −0.888744 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 1.49120e6 | 0.243006 | ||||||||
\(520\) | −160002. | − | 277132.i | −0.0259488 | − | 0.0449447i | ||||
\(521\) | −2.48538e6 | + | 4.30481e6i | −0.401143 | + | 0.694800i | −0.993864 | − | 0.110608i | \(-0.964720\pi\) |
0.592721 | + | 0.805408i | \(0.298054\pi\) | |||||||
\(522\) | −7.38023e6 | + | 1.27829e7i | −1.18548 | + | 2.05331i | ||||
\(523\) | −1.20789e6 | − | 2.09213e6i | −0.193096 | − | 0.334453i | 0.753178 | − | 0.657816i | \(-0.228520\pi\) |
−0.946275 | + | 0.323363i | \(0.895186\pi\) | |||||||
\(524\) | −6.33603e6 | −1.00807 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −1.86914e6 | −0.294563 | ||||||||
\(527\) | −621829. | − | 1.07704e6i | −0.0975314 | − | 0.168929i | ||||
\(528\) | 2.98169e6 | − | 5.16443e6i | 0.465454 | − | 0.806190i | ||||
\(529\) | −1.86399e6 | + | 3.22852e6i | −0.289604 | + | 0.501608i | ||||
\(530\) | −469706. | − | 813555.i | −0.0726334 | − | 0.125805i | ||||
\(531\) | −1.23256e7 | −1.89702 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −2.14843e6 | −0.327570 | ||||||||
\(534\) | −4.42487e6 | − | 7.66410e6i | −0.671502 | − | 1.16308i | ||||
\(535\) | −247269. | + | 428282.i | −0.0373495 | + | 0.0646912i | ||||
\(536\) | −93551.7 | + | 162036.i | −0.0140650 | + | 0.0243613i | ||||
\(537\) | −2.68525e6 | − | 4.65099e6i | −0.401836 | − | 0.696000i | ||||
\(538\) | 1.49385e7 | 2.22510 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −4.62337e6 | −0.682299 | ||||||||
\(541\) | −236083. | − | 408907.i | −0.0346794 | − | 0.0600664i | 0.848165 | − | 0.529732i | \(-0.177708\pi\) |
−0.882844 | + | 0.469666i | \(0.844374\pi\) | |||||||
\(542\) | 7.09076e6 | − | 1.22816e7i | 1.03680 | − | 1.79579i | ||||
\(543\) | 3.57805e6 | − | 6.19736e6i | 0.520771 | − | 0.902002i | ||||
\(544\) | 2.54680e6 | + | 4.41119e6i | 0.368976 | + | 0.639085i | ||||
\(545\) | −2.47293e6 | −0.356633 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 7.63716e6 | 1.09135 | 0.545675 | − | 0.837997i | \(-0.316273\pi\) | ||||
0.545675 | + | 0.837997i | \(0.316273\pi\) | |||||||
\(548\) | 36290.8 | + | 62857.5i | 0.00516232 | + | 0.00894141i | ||||
\(549\) | 1.04801e7 | − | 1.81521e7i | 1.48401 | − | 2.57038i | ||||
\(550\) | −2.56852e6 | + | 4.44881e6i | −0.362057 | + | 0.627101i | ||||
\(551\) | 3.65643e6 | + | 6.33312e6i | 0.513071 | + | 0.888666i | ||||
\(552\) | −3.02763e6 | −0.422917 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 1.84576e7 | 2.55506 | ||||||||
\(555\) | 1.90045e6 | + | 3.29168e6i | 0.261893 | + | 0.453613i | ||||
\(556\) | −6.68224e6 | + | 1.15740e7i | −0.916717 | + | 1.58780i | ||||
\(557\) | 2.24404e6 | − | 3.88679e6i | 0.306473 | − | 0.530827i | −0.671115 | − | 0.741353i | \(-0.734184\pi\) |
0.977588 | + | 0.210526i | \(0.0675178\pi\) | |||||||
\(558\) | −3.48209e6 | − | 6.03115e6i | −0.473428 | − | 0.820001i | ||||
\(559\) | −5.88782e6 | −0.796938 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 4.24740e6 | 0.569791 | ||||||||
\(562\) | −6.91535e6 | − | 1.19777e7i | −0.923577 | − | 1.59968i | ||||
\(563\) | 1.08250e6 | − | 1.87494e6i | 0.143932 | − | 0.249297i | −0.785042 | − | 0.619442i | \(-0.787359\pi\) |
0.928974 | + | 0.370145i | \(0.120692\pi\) | |||||||
\(564\) | 9.35471e6 | − | 1.62028e7i | 1.23832 | − | 2.14483i | ||||
\(565\) | −1.97748e6 | − | 3.42509e6i | −0.260609 | − | 0.451389i | ||||
\(566\) | −3.27812e6 | −0.430115 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 1.21637e6 | 0.158195 | ||||||||
\(569\) | 5.66627e6 | + | 9.81426e6i | 0.733696 | + | 1.27080i | 0.955293 | + | 0.295661i | \(0.0955398\pi\) |
−0.221597 | + | 0.975138i | \(0.571127\pi\) | |||||||
\(570\) | −5.18954e6 | + | 8.98855e6i | −0.669024 | + | 1.15878i | ||||
\(571\) | 421887. | − | 730729.i | 0.0541509 | − | 0.0937921i | −0.837679 | − | 0.546162i | \(-0.816088\pi\) |
0.891830 | + | 0.452370i | \(0.149421\pi\) | |||||||
\(572\) | 1.48085e6 | + | 2.56490e6i | 0.189243 | + | 0.327779i | ||||
\(573\) | 1.14174e7 | 1.45272 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −7.32792e6 | −0.924296 | ||||||||
\(576\) | 8.54711e6 | + | 1.48040e7i | 1.07340 | + | 1.85919i | ||||
\(577\) | 1.11892e6 | − | 1.93803e6i | 0.139914 | − | 0.242338i | −0.787550 | − | 0.616251i | \(-0.788651\pi\) |
0.927464 | + | 0.373913i | \(0.121984\pi\) | |||||||
\(578\) | 4.31933e6 | − | 7.48130e6i | 0.537770 | − | 0.931446i | ||||
\(579\) | −9.32117e6 | − | 1.61447e7i | −1.15551 | − | 2.00140i | ||||
\(580\) | 4.50824e6 | 0.556464 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −9.27156e6 | −1.13461 | ||||||||
\(583\) | 533267. | + | 923646.i | 0.0649791 | + | 0.112547i | ||||
\(584\) | 205761. | − | 356388.i | 0.0249649 | − | 0.0432405i | ||||
\(585\) | −1.79301e6 | + | 3.10558e6i | −0.216617 | + | 0.375191i | ||||
\(586\) | 3.84562e6 | + | 6.66081e6i | 0.462618 | + | 0.801278i | ||||
\(587\) | 1.21190e7 | 1.45168 | 0.725839 | − | 0.687864i | \(-0.241452\pi\) | ||||
0.725839 | + | 0.687864i | \(0.241452\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −3.45030e6 | −0.409797 | ||||||||
\(590\) | 3.53367e6 | + | 6.12050e6i | 0.417923 | + | 0.723864i | ||||
\(591\) | −4.67971e6 | + | 8.10550e6i | −0.551125 | + | 0.954577i | ||||
\(592\) | 2.21849e6 | − | 3.84254e6i | 0.260168 | − | 0.450624i | ||||
\(593\) | −4.00084e6 | − | 6.92965e6i | −0.467212 | − | 0.809235i | 0.532086 | − | 0.846690i | \(-0.321408\pi\) |
−0.999298 | + | 0.0374552i | \(0.988075\pi\) | |||||||
\(594\) | 9.85415e6 | 1.14592 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 5.13261e6 | 0.591865 | ||||||||
\(597\) | 3.71029e6 | + | 6.42641e6i | 0.426061 | + | 0.737960i | ||||
\(598\) | −3.96569e6 | + | 6.86878e6i | −0.453488 | + | 0.785465i | ||||
\(599\) | −7.29493e6 | + | 1.26352e7i | −0.830719 | + | 1.43885i | 0.0667499 | + | 0.997770i | \(0.478737\pi\) |
−0.897469 | + | 0.441078i | \(0.854596\pi\) | |||||||
\(600\) | −1.09138e6 | − | 1.89032e6i | −0.123765 | − | 0.214367i | ||||
\(601\) | −8.67178e6 | −0.979314 | −0.489657 | − | 0.871915i | \(-0.662878\pi\) | ||||
−0.489657 | + | 0.871915i | \(0.662878\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 2.09671e6 | 0.234825 | ||||||||
\(604\) | −913034. | − | 1.58142e6i | −0.101834 | − | 0.176382i | ||||
\(605\) | 1.26644e6 | − | 2.19353e6i | 0.140668 | − | 0.243644i | ||||
\(606\) | 2.72187e6 | − | 4.71442e6i | 0.301083 | − | 0.521491i | ||||
\(607\) | 6.65297e6 | + | 1.15233e7i | 0.732898 | + | 1.26942i | 0.955639 | + | 0.294539i | \(0.0951661\pi\) |
−0.222742 | + | 0.974878i | \(0.571501\pi\) | |||||||
\(608\) | 1.41312e7 | 1.55032 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −1.20184e7 | −1.30774 | ||||||||
\(611\) | −3.00615e6 | − | 5.20681e6i | −0.325768 | − | 0.564246i | ||||
\(612\) | −4.63909e6 | + | 8.03513e6i | −0.500673 | + | 0.867191i | ||||
\(613\) | −1.17551e6 | + | 2.03604e6i | −0.126350 | + | 0.218844i | −0.922260 | − | 0.386571i | \(-0.873659\pi\) |
0.795910 | + | 0.605415i | \(0.206993\pi\) | |||||||
\(614\) | −7.58375e6 | − | 1.31354e7i | −0.811826 | − | 1.40612i | ||||
\(615\) | 5.26963e6 | 0.561814 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 9.63523e6 | 1.01894 | 0.509470 | − | 0.860488i | \(-0.329841\pi\) | ||||
0.509470 | + | 0.860488i | \(0.329841\pi\) | |||||||
\(618\) | −1.51970e6 | − | 2.63219e6i | −0.160061 | − | 0.277234i | ||||
\(619\) | 2.43074e6 | − | 4.21016e6i | 0.254983 | − | 0.441644i | −0.709908 | − | 0.704295i | \(-0.751263\pi\) |
0.964891 | + | 0.262651i | \(0.0845967\pi\) | |||||||
\(620\) | −1.06352e6 | + | 1.84208e6i | −0.111114 | + | 0.192455i | ||||
\(621\) | 7.02840e6 | + | 1.21735e7i | 0.731354 | + | 1.26674i | ||||
\(622\) | −1.90062e7 | −1.96979 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 6.63789e6 | 0.682446 | ||||||||
\(625\) | −1.35009e6 | − | 2.33842e6i | −0.138249 | − | 0.239454i | ||||
\(626\) | 1.41696e7 | − | 2.45424e7i | 1.44518 | − | 2.50312i | ||||
\(627\) | 5.89180e6 | − | 1.02049e7i | 0.598521 | − | 1.03667i | ||||
\(628\) | 1.63760e6 | + | 2.83640e6i | 0.165694 | + | 0.286991i | ||||
\(629\) | 3.16023e6 | 0.318487 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −6.59770e6 | −0.659659 | −0.329829 | − | 0.944041i | \(-0.606991\pi\) | ||||
−0.329829 | + | 0.944041i | \(0.606991\pi\) | |||||||
\(632\) | −1.51594e6 | − | 2.62568e6i | −0.150969 | − | 0.261487i | ||||
\(633\) | 9.62045e6 | − | 1.66631e7i | 0.954302 | − | 1.65290i | ||||
\(634\) | −1.21768e7 | + | 2.10908e7i | −1.20312 | + | 2.08386i | ||||
\(635\) | 1.01437e6 | + | 1.75694e6i | 0.0998305 | + | 0.172911i | ||||
\(636\) | −3.69430e6 | −0.362151 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −9.60876e6 | −0.934578 | ||||||||
\(639\) | −6.81538e6 | − | 1.18046e7i | −0.660295 | − | 1.14366i | ||||
\(640\) | 1.07930e6 | − | 1.86941e6i | 0.104158 | − | 0.180407i | ||||
\(641\) | −7.22623e6 | + | 1.25162e7i | −0.694651 | + | 1.20317i | 0.275648 | + | 0.961259i | \(0.411108\pi\) |
−0.970298 | + | 0.241911i | \(0.922226\pi\) | |||||||
\(642\) | 1.82552e6 | + | 3.16189e6i | 0.174803 | + | 0.302767i | ||||
\(643\) | −1.54720e7 | −1.47577 | −0.737886 | − | 0.674926i | \(-0.764176\pi\) | ||||
−0.737886 | + | 0.674926i | \(0.764176\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 1.44415e7 | 1.36683 | ||||||||
\(646\) | 4.31480e6 | + | 7.47345e6i | 0.406798 | + | 0.704596i | ||||
\(647\) | −8.33234e6 | + | 1.44320e7i | −0.782540 | + | 1.35540i | 0.147918 | + | 0.989000i | \(0.452743\pi\) |
−0.930458 | + | 0.366399i | \(0.880590\pi\) | |||||||
\(648\) | −227153. | + | 393441.i | −0.0212511 | + | 0.0368080i | ||||
\(649\) | −4.01186e6 | − | 6.94874e6i | −0.373881 | − | 0.647581i | ||||
\(650\) | −5.71810e6 | −0.530845 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −1.75525e7 | −1.61704 | ||||||||
\(653\) | 6.67253e6 | + | 1.15572e7i | 0.612361 | + | 1.06064i | 0.990841 | + | 0.135031i | \(0.0431133\pi\) |
−0.378481 | + | 0.925609i | \(0.623553\pi\) | |||||||
\(654\) | −9.12851e6 | + | 1.58110e7i | −0.834556 | + | 1.44549i | ||||
\(655\) | 2.49704e6 | − | 4.32501e6i | 0.227417 | − | 0.393898i | ||||
\(656\) | −3.07575e6 | − | 5.32735e6i | −0.279056 | − | 0.483339i | ||||
\(657\) | −4.61157e6 | −0.416807 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −4.00667e6 | −0.359393 | −0.179697 | − | 0.983722i | \(-0.557512\pi\) | ||||
−0.179697 | + | 0.983722i | \(0.557512\pi\) | |||||||
\(660\) | −3.63219e6 | − | 6.29114e6i | −0.324570 | − | 0.562173i | ||||
\(661\) | −5.40024e6 | + | 9.35349e6i | −0.480739 | + | 0.832664i | −0.999756 | − | 0.0220996i | \(-0.992965\pi\) |
0.519017 | + | 0.854764i | \(0.326298\pi\) | |||||||
\(662\) | −3.99746e6 | + | 6.92381e6i | −0.354519 | + | 0.614045i | ||||
\(663\) | 2.36391e6 | + | 4.09441e6i | 0.208856 | + | 0.361749i | ||||
\(664\) | 4.37750e6 | 0.385307 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 1.76965e7 | 1.54597 | ||||||||
\(667\) | −6.85338e6 | − | 1.18704e7i | −0.596472 | − | 1.03312i | ||||
\(668\) | 1.57884e6 | − | 2.73463e6i | 0.136898 | − | 0.237114i | ||||
\(669\) | 6.85352e6 | − | 1.18706e7i | 0.592036 | − | 1.02544i | ||||
\(670\) | −601114. | − | 1.04116e6i | −0.0517332 | − | 0.0896046i | ||||
\(671\) | 1.36447e7 | 1.16993 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1.09119e7 | 0.928676 | 0.464338 | − | 0.885658i | \(-0.346292\pi\) | ||||
0.464338 | + | 0.885658i | \(0.346292\pi\) | |||||||
\(674\) | −564421. | − | 977606.i | −0.0478579 | − | 0.0828923i | ||||
\(675\) | −5.06709e6 | + | 8.77647e6i | −0.428055 | + | 0.741413i | ||||
\(676\) | 5.12297e6 | − | 8.87325e6i | 0.431177 | − | 0.746820i | ||||
\(677\) | 6.78826e6 | + | 1.17576e7i | 0.569229 | + | 0.985933i | 0.996642 | + | 0.0818771i | \(0.0260915\pi\) |
−0.427414 | + | 0.904056i | \(0.640575\pi\) | |||||||
\(678\) | −2.91984e7 | −2.43941 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 652598. | 0.0541219 | ||||||||
\(681\) | −5.26615e6 | − | 9.12123e6i | −0.435136 | − | 0.753678i | ||||
\(682\) | 2.26677e6 | − | 3.92616e6i | 0.186615 | − | 0.323226i | ||||
\(683\) | 6.33631e6 | − | 1.09748e7i | 0.519738 | − | 0.900213i | −0.479999 | − | 0.877269i | \(-0.659363\pi\) |
0.999737 | − | 0.0229436i | \(-0.00730382\pi\) | |||||||
\(684\) | 1.28703e7 | + | 2.22920e7i | 1.05184 | + | 1.82183i | ||||
\(685\) | −57209.2 | −0.00465843 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −2.64283e7 | −2.13637 | ||||||||
\(688\) | −8.42913e6 | − | 1.45997e7i | −0.678909 | − | 1.17591i | ||||
\(689\) | −593585. | + | 1.02812e6i | −0.0476360 | + | 0.0825079i | ||||
\(690\) | 9.72696e6 | − | 1.68476e7i | 0.777776 | − | 1.34715i | ||||
\(691\) | −3.55982e6 | − | 6.16579e6i | −0.283617 | − | 0.491240i | 0.688656 | − | 0.725089i | \(-0.258201\pi\) |
−0.972273 | + | 0.233849i | \(0.924868\pi\) | |||||||
\(692\) | −2.12052e6 | −0.168336 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 2.94097e6 | 0.231789 | ||||||||
\(695\) | −5.26697e6 | − | 9.12267e6i | −0.413618 | − | 0.716407i | ||||
\(696\) | 2.04140e6 | − | 3.53582e6i | 0.159737 | − | 0.276673i | ||||
\(697\) | 2.19069e6 | − | 3.79439e6i | 0.170805 | − | 0.295842i | ||||
\(698\) | 579773. | + | 1.00420e6i | 0.0450422 | + | 0.0780153i | ||||
\(699\) | 3.05770e6 | 0.236702 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −1.00155e7 | −0.769803 | −0.384902 | − | 0.922958i | \(-0.625765\pi\) | ||||
−0.384902 | + | 0.922958i | \(0.625765\pi\) | |||||||
\(702\) | 5.48437e6 | + | 9.49922e6i | 0.420034 | + | 0.727520i | ||||
\(703\) | 4.38373e6 | − | 7.59285e6i | 0.334546 | − | 0.579450i | ||||
\(704\) | −5.56400e6 | + | 9.63713e6i | −0.423112 | + | 0.732851i | ||||
\(705\) | 7.37343e6 | + | 1.27711e7i | 0.558723 | + | 0.967737i | ||||
\(706\) | 2.88084e7 | 2.17524 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 2.77928e7 | 2.08377 | ||||||||
\(709\) | 4.42227e6 | + | 7.65959e6i | 0.330392 | + | 0.572256i | 0.982589 | − | 0.185794i | \(-0.0594857\pi\) |
−0.652197 | + | 0.758050i | \(0.726152\pi\) | |||||||
\(710\) | −3.90786e6 | + | 6.76861e6i | −0.290933 | + | 0.503910i | ||||
\(711\) | −1.69878e7 | + | 2.94238e7i | −1.26027 | + | 2.18285i | ||||
\(712\) | 771866. | + | 1.33691e6i | 0.0570614 | + | 0.0988332i | ||||
\(713\) | 6.46703e6 | 0.476410 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −2.33442e6 | −0.170771 | ||||||||
\(716\) | 3.81849e6 | + | 6.61382e6i | 0.278362 | + | 0.482136i | ||||
\(717\) | −3.25864e6 | + | 5.64413e6i | −0.236722 | + | 0.410015i | ||||
\(718\) | −7.25236e6 | + | 1.25615e7i | −0.525011 | + | 0.909346i | ||||
\(719\) | −3.29043e6 | − | 5.69920e6i | −0.237373 | − | 0.411142i | 0.722587 | − | 0.691280i | \(-0.242953\pi\) |
−0.959960 | + | 0.280139i | \(0.909620\pi\) | |||||||
\(720\) | −1.02676e7 | −0.738141 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 3.45169e6 | 0.246427 | ||||||||
\(723\) | 1.81151e7 | + | 3.13762e7i | 1.28883 | + | 2.23231i | ||||
\(724\) | −5.08808e6 | + | 8.81281e6i | −0.360751 | + | 0.624839i | ||||
\(725\) | 4.94091e6 | − | 8.55791e6i | 0.349110 | − | 0.604676i | ||||
\(726\) | −9.34977e6 | − | 1.61943e7i | −0.658354 | − | 1.14030i | ||||
\(727\) | 1.88401e7 | 1.32205 | 0.661023 | − | 0.750365i | \(-0.270122\pi\) | ||||
0.661023 | + | 0.750365i | \(0.270122\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −2.23900e7 | −1.56040 | ||||||||
\(730\) | 1.32211e6 | + | 2.28996e6i | 0.0918248 | + | 0.159045i | ||||
\(731\) | 6.00363e6 | − | 1.03986e7i | 0.415547 | − | 0.719749i | ||||
\(732\) | −2.36316e7 | + | 4.09311e7i | −1.63010 | + | 2.82342i | ||||
\(733\) | 1.39165e6 | + | 2.41041e6i | 0.0956687 | + | 0.165703i | 0.909887 | − | 0.414855i | \(-0.136168\pi\) |
−0.814219 | + | 0.580558i | \(0.802834\pi\) | |||||||
\(734\) | −1.46416e7 | −1.00311 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −2.64867e7 | −1.80233 | ||||||||
\(737\) | 682457. | + | 1.18205e6i | 0.0462814 | + | 0.0801618i | ||||
\(738\) | 1.22673e7 | − | 2.12476e7i | 0.829104 | − | 1.43605i | ||||
\(739\) | 1.24485e7 | − | 2.15614e7i | 0.838505 | − | 1.45233i | −0.0526394 | − | 0.998614i | \(-0.516763\pi\) |
0.891144 | − | 0.453720i | \(-0.149903\pi\) | |||||||
\(740\) | −2.70249e6 | − | 4.68085e6i | −0.181420 | − | 0.314229i | ||||
\(741\) | 1.31164e7 | 0.877548 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −3.86085e6 | −0.256573 | −0.128286 | − | 0.991737i | \(-0.540948\pi\) | ||||
−0.128286 | + | 0.991737i | \(0.540948\pi\) | |||||||
\(744\) | 963161. | + | 1.66824e6i | 0.0637920 | + | 0.110491i | ||||
\(745\) | −2.02277e6 | + | 3.50354e6i | −0.133523 | + | 0.231269i | ||||
\(746\) | 1.72206e7 | − | 2.98270e7i | 1.13293 | − | 1.96229i | ||||
\(747\) | −2.45275e7 | − | 4.24828e7i | −1.60824 | − | 2.78555i | ||||
\(748\) | −6.03991e6 | −0.394708 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 3.30938e7 | 2.14829 | ||||||||
\(751\) | −3.36368e6 | − | 5.82607e6i | −0.217628 | − | 0.376943i | 0.736454 | − | 0.676488i | \(-0.236499\pi\) |
−0.954082 | + | 0.299544i | \(0.903165\pi\) | |||||||
\(752\) | 8.60736e6 | − | 1.49084e7i | 0.555041 | − | 0.961359i | ||||
\(753\) | −2.14869e7 | + | 3.72164e7i | −1.38097 | + | 2.39192i | ||||
\(754\) | −5.34780e6 | − | 9.26267e6i | −0.342568 | − | 0.593346i | ||||
\(755\) | 1.43932e6 | 0.0918943 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 2.17782e7 | 1.38128 | 0.690642 | − | 0.723197i | \(-0.257328\pi\) | ||||
0.690642 | + | 0.723197i | \(0.257328\pi\) | |||||||
\(758\) | −2.55762e6 | − | 4.42994e6i | −0.161683 | − | 0.280043i | ||||
\(759\) | −1.10432e7 | + | 1.91274e7i | −0.695812 | + | 1.20518i | ||||
\(760\) | 905255. | − | 1.56795e6i | 0.0568508 | − | 0.0984686i | ||||
\(761\) | 1.28537e7 | + | 2.22633e7i | 0.804575 | + | 1.39356i | 0.916578 | + | 0.399856i | \(0.130940\pi\) |
−0.112003 | + | 0.993708i | \(0.535727\pi\) | |||||||
\(762\) | 1.49777e7 | 0.934453 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −1.62359e7 | −1.00633 | ||||||||
\(765\) | −3.65655e6 | − | 6.33333e6i | −0.225901 | − | 0.391272i | ||||
\(766\) | 1.70117e7 | − | 2.94652e7i | 1.04755 | − | 1.81442i | ||||
\(767\) | 4.46564e6 | − | 7.73471e6i | 0.274091 | − | 0.474740i | ||||
\(768\) | 8.94039e6 | + | 1.54852e7i | 0.546957 | + | 0.947358i | ||||
\(769\) | −1.34375e7 | −0.819413 | −0.409706 | − | 0.912217i | \(-0.634369\pi\) | ||||
−0.409706 | + | 0.912217i | \(0.634369\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1.86471e7 | −1.12973 | ||||||||
\(772\) | 1.32549e7 | + | 2.29582e7i | 0.800451 | + | 1.38642i | ||||
\(773\) | −1.52786e7 | + | 2.64633e7i | −0.919674 | + | 1.59292i | −0.119765 | + | 0.992802i | \(0.538214\pi\) |
−0.799910 | + | 0.600121i | \(0.795119\pi\) | |||||||
\(774\) | 3.36188e7 | − | 5.82295e7i | 2.01711 | − | 3.49374i | ||||
\(775\) | 2.33119e6 | + | 4.03773e6i | 0.139419 | + | 0.241481i | ||||
\(776\) | 1.61731e6 | 0.0964140 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 3.82364e7 | 2.26479 | ||||||||
\(779\) | −6.07767e6 | − | 1.05268e7i | −0.358834 | − | 0.621518i | ||||
\(780\) | 4.04303e6 | − | 7.00273e6i | 0.237942 | − | 0.412127i | ||||
\(781\) | 4.43668e6 | − | 7.68455e6i | 0.260274 | − | 0.450807i | ||||
\(782\) | −8.08739e6 | − | 1.40078e7i | −0.472924 | − | 0.819129i | ||||
\(783\) | −1.89558e7 | −1.10494 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −2.58152e6 | −0.149521 | ||||||||
\(786\) | −1.84350e7 | − | 3.19304e7i | −1.06436 | − | 1.84352i | ||||
\(787\) | 1.03836e6 | − | 1.79849e6i | 0.0597602 | − | 0.103508i | −0.834598 | − | 0.550860i | \(-0.814300\pi\) |
0.894358 | + | 0.447353i | \(0.147633\pi\) | |||||||
\(788\) | 6.65467e6 | − | 1.15262e7i | 0.381778 | − | 0.661259i | ||||
\(789\) | −2.89686e6 | − | 5.01751e6i | −0.165666 | − | 0.286943i | ||||
\(790\) | 1.94812e7 | 1.11058 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −4.14890e6 | −0.235028 | ||||||||
\(793\) | 7.59404e6 | + | 1.31533e7i | 0.428835 | + | 0.742764i | ||||
\(794\) | −2.09914e7 | + | 3.63581e7i | −1.18165 | + | 2.04668i | ||||
\(795\) | 1.45593e6 | − | 2.52175e6i | 0.0817003 | − | 0.141509i | ||||
\(796\) | −5.27613e6 | − | 9.13853e6i | −0.295143 | − | 0.511203i | ||||
\(797\) | −5.98563e6 | −0.333783 | −0.166892 | − | 0.985975i | \(-0.553373\pi\) | ||||
−0.166892 | + | 0.985975i | \(0.553373\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.22611e7 | 0.679460 | ||||||||
\(800\) | −9.54775e6 | − | 1.65372e7i | −0.527443 | − | 0.913559i | ||||
\(801\) | 8.64964e6 | − | 1.49816e7i | 0.476340 | − | 0.825045i | ||||
\(802\) | 6.12575e6 | − | 1.06101e7i | 0.336297 | − | 0.582484i | ||||
\(803\) | −1.50102e6 | − | 2.59984e6i | −0.0821481 | − | 0.142285i | ||||
\(804\) | −4.72784e6 | −0.257942 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 5.04633e6 | 0.273614 | ||||||||
\(807\) | 2.31521e7 | + | 4.01007e7i | 1.25143 | + | 2.16754i | ||||
\(808\) | −474798. | + | 822375.i | −0.0255847 | + | 0.0443141i | ||||
\(809\) | −9.84321e6 | + | 1.70489e7i | −0.528769 | + | 0.915854i | 0.470669 | + | 0.882310i | \(0.344013\pi\) |
−0.999437 | + | 0.0335439i | \(0.989321\pi\) | |||||||
\(810\) | −1.45956e6 | − | 2.52804e6i | −0.0781647 | − | 0.135385i | ||||
\(811\) | 8.50101e6 | 0.453856 | 0.226928 | − | 0.973912i | \(-0.427132\pi\) | ||||
0.226928 | + | 0.973912i | \(0.427132\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 4.39580e7 | 2.33245 | ||||||||
\(814\) | 5.76003e6 | + | 9.97666e6i | 0.304694 | + | 0.527745i | ||||
\(815\) | 6.91749e6 | − | 1.19814e7i | 0.364800 | − | 0.631851i | ||||
\(816\) | −6.76845e6 | + | 1.17233e7i | −0.355848 | + | 0.616346i | ||||
\(817\) | −1.66559e7 | − | 2.88489e7i | −0.873000 | − | 1.51208i | ||||
\(818\) | −3.75168e7 | −1.96039 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −7.49355e6 | −0.389182 | ||||||||
\(821\) | 680993. | + | 1.17952e6i | 0.0352602 | + | 0.0610725i | 0.883117 | − | 0.469153i | \(-0.155441\pi\) |
−0.847857 | + | 0.530225i | \(0.822107\pi\) | |||||||
\(822\) | −211180. | + | 365775.i | −0.0109012 | + | 0.0188814i | ||||
\(823\) | 679670. | − | 1.17722e6i | 0.0349783 | − | 0.0605842i | −0.848006 | − | 0.529986i | \(-0.822197\pi\) |
0.882985 | + | 0.469402i | \(0.155530\pi\) | |||||||
\(824\) | 265093. | + | 459155.i | 0.0136013 | + | 0.0235581i | ||||
\(825\) | −1.59231e7 | −0.814505 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1.00727e7 | 0.512132 | 0.256066 | − | 0.966659i | \(-0.417574\pi\) | ||||
0.256066 | + | 0.966659i | \(0.417574\pi\) | |||||||
\(828\) | −2.41233e7 | − | 4.17827e7i | −1.22281 | − | 2.11797i | ||||
\(829\) | 2.81992e6 | − | 4.88425e6i | 0.142512 | − | 0.246837i | −0.785930 | − | 0.618315i | \(-0.787815\pi\) |
0.928442 | + | 0.371478i | \(0.121149\pi\) | |||||||
\(830\) | −1.40638e7 | + | 2.43591e7i | −0.708608 | + | 1.22734i | ||||
\(831\) | 2.86062e7 | + | 4.95474e7i | 1.43700 | + | 2.48896i | ||||
\(832\) | −1.23867e7 | −0.620364 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −7.77693e7 | −3.87163 | ||||||||
\(835\) | 1.24445e6 | + | 2.15544e6i | 0.0617675 | + | 0.106984i | ||||
\(836\) | −8.37830e6 | + | 1.45116e7i | −0.414610 | + | 0.718126i | ||||
\(837\) | 4.47180e6 | − | 7.74539e6i | 0.220632 | − | 0.382146i | ||||
\(838\) | −459366. | − | 795646.i | −0.0225969 | − | 0.0391390i | ||||
\(839\) | −1.16351e7 | −0.570642 | −0.285321 | − | 0.958432i | \(-0.592100\pi\) | ||||
−0.285321 | + | 0.958432i | \(0.592100\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −2.02735e6 | −0.0988413 | ||||||||
\(842\) | 5.84007e6 | + | 1.01153e7i | 0.283882 | + | 0.491698i | ||||
\(843\) | 2.14353e7 | − | 3.71270e7i | 1.03887 | − | 1.79937i | ||||
\(844\) | −1.36805e7 | + | 2.36954e7i | −0.661069 | + | 1.14500i | ||||
\(845\) | 4.03795e6 | + | 6.99393e6i | 0.194545 | + | 0.336961i | ||||
\(846\) | 6.86592e7 | 3.29817 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −3.39916e6 | −0.162324 | ||||||||
\(849\) | −5.08055e6 | − | 8.79977e6i | −0.241903 | − | 0.418989i | ||||
\(850\) | 5.83057e6 | − | 1.00988e7i | 0.276799 | − | 0.479429i | ||||
\(851\) | −8.21660e6 | + | 1.42316e7i | −0.388927 | + | 0.673641i | ||||
\(852\) | 1.53679e7 | + | 2.66180e7i | 0.725297 | + | 1.25625i | ||||
\(853\) | 2.85205e7 | 1.34210 | 0.671049 | − | 0.741413i | \(-0.265844\pi\) | ||||
0.671049 | + | 0.741413i | \(0.265844\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −2.02888e7 | −0.949165 | ||||||||
\(856\) | −318440. | − | 551555.i | −0.0148540 | − | 0.0257279i | ||||
\(857\) | 4.97862e6 | − | 8.62323e6i | 0.231557 | − | 0.401068i | −0.726710 | − | 0.686945i | \(-0.758951\pi\) |
0.958266 | + | 0.285877i | \(0.0922848\pi\) | |||||||
\(858\) | −8.61721e6 | + | 1.49255e7i | −0.399621 | + | 0.692164i | ||||
\(859\) | 7.46610e6 | + | 1.29317e7i | 0.345232 | + | 0.597959i | 0.985396 | − | 0.170279i | \(-0.0544670\pi\) |
−0.640164 | + | 0.768238i | \(0.721134\pi\) | |||||||
\(860\) | −2.05362e7 | −0.946834 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 8.90711e6 | 0.408290 | ||||||||
\(863\) | −1.92467e7 | − | 3.33362e7i | −0.879687 | − | 1.52366i | −0.851685 | − | 0.524055i | \(-0.824419\pi\) |
−0.0280024 | − | 0.999608i | \(-0.508915\pi\) | |||||||
\(864\) | −1.83150e7 | + | 3.17225e7i | −0.834684 | + | 1.44572i | ||||
\(865\) | 835701. | − | 1.44748e6i | 0.0379761 | − | 0.0657766i | ||||
\(866\) | 1.28332e6 | + | 2.22278e6i | 0.0581489 | + | 0.100717i | ||||
\(867\) | 2.67770e7 | 1.20980 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −2.21175e7 | −0.993542 | ||||||||
\(870\) | 1.31170e7 | + | 2.27193e7i | 0.587537 | + | 1.01764i | ||||
\(871\) | −759650. | + | 1.31575e6i | −0.0339288 | + | 0.0587664i | ||||
\(872\) | 1.59236e6 | − | 2.75805e6i | 0.0709170 | − | 0.122832i | ||||
\(873\) | −9.06193e6 | − | 1.56957e7i | −0.402425 | − | 0.697020i | ||||
\(874\) | −4.48739e7 | −1.98708 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 1.03986e7 | 0.457839 | ||||||||
\(877\) | −4.70156e6 | − | 8.14334e6i | −0.206416 | − | 0.357523i | 0.744167 | − | 0.667993i | \(-0.232847\pi\) |
−0.950583 | + | 0.310471i | \(0.899513\pi\) | |||||||
\(878\) | −2.34863e7 | + | 4.06794e7i | −1.02820 | + | 1.78090i | ||||
\(879\) | −1.19202e7 | + | 2.06463e7i | −0.520367 | + | 0.901302i | ||||
\(880\) | −3.34201e6 | − | 5.78854e6i | −0.145479 | − | 0.251978i | ||||
\(881\) | 1.10395e6 | 0.0479194 | 0.0239597 | − | 0.999713i | \(-0.492373\pi\) | ||||
0.0239597 | + | 0.999713i | \(0.492373\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 8.06579e6 | 0.348133 | 0.174067 | − | 0.984734i | \(-0.444309\pi\) | ||||
0.174067 | + | 0.984734i | \(0.444309\pi\) | |||||||
\(884\) | −3.36154e6 | − | 5.82236e6i | −0.144680 | − | 0.250593i | ||||
\(885\) | −1.09532e7 | + | 1.89715e7i | −0.470093 | + | 0.814224i | ||||
\(886\) | −1.67967e7 | + | 2.90927e7i | −0.718851 | + | 1.24509i | ||||
\(887\) | 7.49509e6 | + | 1.29819e7i | 0.319866 | + | 0.554024i | 0.980460 | − | 0.196719i | \(-0.0630288\pi\) |
−0.660594 | + | 0.750743i | \(0.729695\pi\) | |||||||
\(888\) | −4.89493e6 | −0.208312 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −9.91920e6 | −0.419761 | ||||||||
\(891\) | 1.65708e6 | + | 2.87014e6i | 0.0699275 | + | 0.121118i | ||||
\(892\) | −9.74588e6 | + | 1.68804e7i | −0.410118 | + | 0.710346i | ||||
\(893\) | 1.70081e7 | − | 2.94589e7i | 0.713719 | − | 1.23620i | ||||
\(894\) | 1.49336e7 | + | 2.58657e7i | 0.624914 | + | 1.08238i | ||||
\(895\) | −6.01950e6 | −0.251190 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −2.45847e7 | −1.02019 | ||||||||
\(898\) | 2.88192e7 | + | 4.99163e7i | 1.19259 | + | 2.06563i | ||||
\(899\) | −4.36045e6 | + | 7.55252e6i | −0.179942 | + | 0.311668i | ||||
\(900\) | 1.73916e7 | − | 3.01231e7i | 0.715702 | − | 1.23963i | ||||
\(901\) | −1.21052e6 | − | 2.09669e6i | −0.0496776 | − | 0.0860442i | ||||
\(902\) | 1.59716e7 | 0.653629 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 5.09331e6 | 0.207290 | ||||||||
\(905\) | −4.01045e6 | − | 6.94630e6i | −0.162769 | − | 0.281924i | ||||
\(906\) | 5.31304e6 | − | 9.20246e6i | 0.215042 | − | 0.372463i | ||||
\(907\) | −2.06311e6 | + | 3.57341e6i | −0.0832730 | + | 0.144233i | −0.904654 | − | 0.426147i | \(-0.859871\pi\) |
0.821381 | + | 0.570380i | \(0.193204\pi\) | |||||||
\(908\) | 7.48859e6 | + | 1.29706e7i | 0.301429 | + | 0.522091i | ||||
\(909\) | 1.06413e7 | 0.427155 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 4.04272e7 | 1.61391 | 0.806953 | − | 0.590616i | \(-0.201115\pi\) | ||||
0.806953 | + | 0.590616i | \(0.201115\pi\) | |||||||
\(912\) | 1.87778e7 | + | 3.25241e7i | 0.747580 | + | 1.29485i | ||||
\(913\) | 1.59669e7 | − | 2.76555e7i | 0.633933 | − | 1.09800i | ||||
\(914\) | −7.42769e6 | + | 1.28651e7i | −0.294096 | + | 0.509388i | ||||
\(915\) | −1.86265e7 | − | 3.22620e7i | −0.735493 | − | 1.27391i | ||||
\(916\) | 3.75817e7 | 1.47992 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −2.23690e7 | −0.876072 | ||||||||
\(919\) | −1.09273e7 | − | 1.89267e7i | −0.426800 | − | 0.739240i | 0.569786 | − | 0.821793i | \(-0.307026\pi\) |
−0.996587 | + | 0.0825532i | \(0.973693\pi\) | |||||||
\(920\) | −1.69675e6 | + | 2.93886e6i | −0.0660921 | + | 0.114475i | ||||
\(921\) | 2.35071e7 | − | 4.07155e7i | 0.913167 | − | 1.58165i | ||||
\(922\) | 8.74220e6 | + | 1.51419e7i | 0.338683 | + | 0.586616i | ||||
\(923\) | 9.87702e6 | 0.381612 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.18474e7 | −0.455271 | ||||||||
\(926\) | −5.22241e6 | − | 9.04548e6i | −0.200144 | − | 0.346660i | ||||
\(927\) | 2.97067e6 | − | 5.14535e6i | 0.113542 | − | 0.196660i | ||||
\(928\) | 1.78589e7 | − | 3.09325e7i | 0.680746 | − | 1.17909i | ||||
\(929\) | −5.34215e6 | − | 9.25288e6i | −0.203085 | − | 0.351753i | 0.746436 | − | 0.665457i | \(-0.231763\pi\) |
−0.949521 | + | 0.313704i | \(0.898430\pi\) | |||||||
\(930\) | −1.23775e7 | −0.469274 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −4.34813e6 | −0.163970 | ||||||||
\(933\) | −2.94565e7 | − | 5.10202e7i | −1.10784 | − | 1.91884i | ||||
\(934\) | 1.48504e7 | − | 2.57217e7i | 0.557021 | − | 0.964789i | ||||
\(935\) | 2.38034e6 | − | 4.12287e6i | 0.0890451 | − | 0.154231i | ||||
\(936\) | −2.30909e6 | − | 3.99946e6i | −0.0861492 | − | 0.149215i | ||||
\(937\) | −3.99105e7 | −1.48504 | −0.742521 | − | 0.669823i | \(-0.766370\pi\) | ||||
−0.742521 | + | 0.669823i | \(0.766370\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 8.78419e7 | 3.25116 | ||||||||
\(940\) | −1.04852e7 | − | 1.81609e7i | −0.387041 | − | 0.670375i | ||||
\(941\) | −661751. | + | 1.14619e6i | −0.0243624 | + | 0.0421969i | −0.877950 | − | 0.478753i | \(-0.841089\pi\) |
0.853587 | + | 0.520950i | \(0.174422\pi\) | |||||||
\(942\) | −9.52934e6 | + | 1.65053e7i | −0.349893 | + | 0.606033i | ||||
\(943\) | 1.13916e7 | + | 1.97308e7i | 0.417163 | + | 0.722547i | ||||
\(944\) | 2.55724e7 | 0.933990 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 4.37703e7 | 1.59020 | ||||||||
\(947\) | 1.38161e7 | + | 2.39301e7i | 0.500622 | + | 0.867102i | 1.00000 | 0.000718120i | \(0.000228585\pi\) | |
−0.499378 | + | 0.866384i | \(0.666438\pi\) | |||||||
\(948\) | 3.83057e7 | − | 6.63473e7i | 1.38434 | − | 2.39774i | ||||
\(949\) | 1.67080e6 | − | 2.89391e6i | 0.0602225 | − | 0.104308i | ||||
\(950\) | −1.61758e7 | − | 2.80174e7i | −0.581510 | − | 1.00721i | ||||
\(951\) | −7.54879e7 | −2.70661 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −3.07901e7 | −1.09819 | −0.549096 | − | 0.835759i | \(-0.685028\pi\) | ||||
−0.549096 | + | 0.835759i | \(0.685028\pi\) | |||||||
\(954\) | −6.77862e6 | − | 1.17409e7i | −0.241140 | − | 0.417668i | ||||
\(955\) | 6.39859e6 | − | 1.10827e7i | 0.227026 | − | 0.393221i | ||||
\(956\) | 4.63387e6 | − | 8.02610e6i | 0.163983 | − | 0.284027i | ||||
\(957\) | −1.48920e7 | − | 2.57937e7i | −0.525621 | − | 0.910403i | ||||
\(958\) | −1.99999e7 | −0.704068 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 3.03818e7 | 1.06398 | ||||||||
\(961\) | 1.22573e7 | + | 2.12302e7i | 0.428139 | + | 0.741559i | ||||
\(962\) | −6.41154e6 | + | 1.11051e7i | −0.223370 | + | 0.386888i | ||||
\(963\) | −3.56849e6 | + | 6.18080e6i | −0.123999 | + | 0.214773i | ||||
\(964\) | −2.57601e7 | − | 4.46178e7i | −0.892801 | − | 1.54638i | ||||
\(965\) | −2.08952e7 | −0.722318 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 2.92557e6 | 0.100611 | 0.0503055 | − | 0.998734i | \(-0.483981\pi\) | ||||
0.0503055 | + | 0.998734i | \(0.483981\pi\) | |||||||
\(968\) | 1.63096e6 | + | 2.82490e6i | 0.0559441 | + | 0.0968980i | ||||
\(969\) | −1.33744e7 | + | 2.31652e7i | −0.457579 | + | 0.792551i | ||||
\(970\) | −5.19600e6 | + | 8.99974e6i | −0.177313 | + | 0.307115i | ||||
\(971\) | −1.39055e6 | − | 2.40850e6i | −0.0473301 | − | 0.0819781i | 0.841390 | − | 0.540429i | \(-0.181738\pi\) |
−0.888720 | + | 0.458451i | \(0.848405\pi\) | |||||||
\(972\) | 2.75990e7 | 0.936975 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −4.29801e7 | −1.45168 | ||||||||
\(975\) | −8.86210e6 | − | 1.53496e7i | −0.298556 | − | 0.517114i | ||||
\(976\) | −2.17436e7 | + | 3.76610e7i | −0.730646 | + | 1.26552i | ||||
\(977\) | −3.74337e6 | + | 6.48370e6i | −0.125466 | + | 0.217313i | −0.921915 | − | 0.387392i | \(-0.873376\pi\) |
0.796449 | + | 0.604706i | \(0.206709\pi\) | |||||||
\(978\) | −5.10700e7 | − | 8.84558e7i | −1.70733 | − | 2.95719i | ||||
\(979\) | 1.12615e7 | 0.375525 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −3.56884e7 | −1.18401 | ||||||||
\(982\) | −2.22993e7 | − | 3.86235e7i | −0.737925 | − | 1.27812i | ||||
\(983\) | −8.99073e6 | + | 1.55724e7i | −0.296764 | + | 0.514010i | −0.975394 | − | 0.220470i | \(-0.929241\pi\) |
0.678630 | + | 0.734481i | \(0.262574\pi\) | |||||||
\(984\) | −3.39320e6 | + | 5.87719e6i | −0.111718 | + | 0.193500i | ||||
\(985\) | 5.24524e6 | + | 9.08502e6i | 0.172256 | + | 0.298357i | ||||
\(986\) | 2.18120e7 | 0.714501 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −1.86519e7 | −0.607899 | ||||||||
\(989\) | 3.12189e7 | + | 5.40727e7i | 1.01491 | + | 1.75787i | ||||
\(990\) | 1.33293e7 | − | 2.30870e7i | 0.432234 | − | 0.748652i | ||||
\(991\) | −1.86389e7 | + | 3.22835e7i | −0.602888 | + | 1.04423i | 0.389494 | + | 0.921029i | \(0.372650\pi\) |
−0.992381 | + | 0.123203i | \(0.960683\pi\) | |||||||
\(992\) | 8.42606e6 | + | 1.45944e7i | 0.271860 | + | 0.470875i | ||||
\(993\) | −2.47816e7 | −0.797548 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 8.31734e6 | 0.266334 | ||||||||
\(996\) | 5.53067e7 | + | 9.57940e7i | 1.76656 | + | 3.05978i | ||||
\(997\) | −2.43711e7 | + | 4.22119e7i | −0.776492 | + | 1.34492i | 0.157461 | + | 0.987525i | \(0.449669\pi\) |
−0.933952 | + | 0.357398i | \(0.883664\pi\) | |||||||
\(998\) | 1.36373e7 | − | 2.36205e7i | 0.433414 | − | 0.750695i | ||||
\(999\) | 1.13632e7 | + | 1.96816e7i | 0.360235 | + | 0.623946i |
(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 | 49.6.c.e.18.1 | 4 | ||
7.2 | even | 3 | inner | 49.6.c.e.30.1 | 4 | ||
7.3 | odd | 6 | 49.6.a.f.1.2 | 2 | |||
7.4 | even | 3 | 7.6.a.b.1.2 | ✓ | 2 | ||
7.5 | odd | 6 | 49.6.c.d.30.1 | 4 | |||
7.6 | odd | 2 | 49.6.c.d.18.1 | 4 | |||
21.11 | odd | 6 | 63.6.a.f.1.1 | 2 | |||
21.17 | even | 6 | 441.6.a.l.1.1 | 2 | |||
28.3 | even | 6 | 784.6.a.v.1.1 | 2 | |||
28.11 | odd | 6 | 112.6.a.h.1.2 | 2 | |||
35.4 | even | 6 | 175.6.a.c.1.1 | 2 | |||
35.18 | odd | 12 | 175.6.b.c.99.1 | 4 | |||
35.32 | odd | 12 | 175.6.b.c.99.4 | 4 | |||
56.11 | odd | 6 | 448.6.a.u.1.1 | 2 | |||
56.53 | even | 6 | 448.6.a.w.1.2 | 2 | |||
77.32 | odd | 6 | 847.6.a.c.1.1 | 2 | |||
84.11 | even | 6 | 1008.6.a.bq.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
7.6.a.b.1.2 | ✓ | 2 | 7.4 | even | 3 | ||
49.6.a.f.1.2 | 2 | 7.3 | odd | 6 | |||
49.6.c.d.18.1 | 4 | 7.6 | odd | 2 | |||
49.6.c.d.30.1 | 4 | 7.5 | odd | 6 | |||
49.6.c.e.18.1 | 4 | 1.1 | even | 1 | trivial | ||
49.6.c.e.30.1 | 4 | 7.2 | even | 3 | inner | ||
63.6.a.f.1.1 | 2 | 21.11 | odd | 6 | |||
112.6.a.h.1.2 | 2 | 28.11 | odd | 6 | |||
175.6.a.c.1.1 | 2 | 35.4 | even | 6 | |||
175.6.b.c.99.1 | 4 | 35.18 | odd | 12 | |||
175.6.b.c.99.4 | 4 | 35.32 | odd | 12 | |||
441.6.a.l.1.1 | 2 | 21.17 | even | 6 | |||
448.6.a.u.1.1 | 2 | 56.11 | odd | 6 | |||
448.6.a.w.1.2 | 2 | 56.53 | even | 6 | |||
784.6.a.v.1.1 | 2 | 28.3 | even | 6 | |||
847.6.a.c.1.1 | 2 | 77.32 | odd | 6 | |||
1008.6.a.bq.1.1 | 2 | 84.11 | even | 6 |