Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [63,4,Mod(5,63)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(63, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([5, 5]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("63.5");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 63 = 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 63.i (of order \(6\), degree \(2\), 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: | \(3.71712033036\) |
Analytic rank: | \(0\) |
Dimension: | \(44\) |
Relative dimension: | \(22\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 5.22 | ||
Character | \(\chi\) | \(=\) | 63.5 |
Dual form | 63.4.i.a.38.1 |
$q$-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 \(\left(\mathbb{Z}/63\mathbb{Z}\right)^\times\).
\(n\) | \(10\) | \(29\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) | \(e\left(\frac{5}{6}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 5.23841i | 1.85206i | 0.377454 | + | 0.926028i | \(0.376800\pi\) | ||||
−0.377454 | + | 0.926028i | \(0.623200\pi\) | |||||||
\(3\) | −2.33478 | − | 4.64207i | −0.449328 | − | 0.893367i | ||||
\(4\) | −19.4409 | −2.43011 | ||||||||
\(5\) | −6.10572 | − | 10.5754i | −0.546112 | − | 0.945894i | −0.998536 | − | 0.0540908i | \(-0.982774\pi\) |
0.452424 | − | 0.891803i | \(-0.350559\pi\) | |||||||
\(6\) | 24.3171 | − | 12.2305i | 1.65457 | − | 0.832182i | ||||
\(7\) | 18.4237 | − | 1.88889i | 0.994785 | − | 0.101990i | ||||
\(8\) | − | 59.9322i | − | 2.64865i | ||||||
\(9\) | −16.0976 | + | 21.6764i | −0.596208 | + | 0.802830i | ||||
\(10\) | 55.3983 | − | 31.9842i | 1.75185 | − | 1.01143i | ||||
\(11\) | −55.0881 | − | 31.8051i | −1.50997 | − | 0.871783i | −0.999932 | − | 0.0116323i | \(-0.996297\pi\) |
−0.510040 | − | 0.860151i | \(-0.670369\pi\) | |||||||
\(12\) | 45.3902 | + | 90.2461i | 1.09192 | + | 2.17098i | ||||
\(13\) | −13.7938 | − | 7.96386i | −0.294286 | − | 0.169906i | 0.345587 | − | 0.938387i | \(-0.387680\pi\) |
−0.639873 | + | 0.768481i | \(0.721013\pi\) | |||||||
\(14\) | 9.89475 | + | 96.5108i | 0.188892 | + | 1.84240i | ||||
\(15\) | −34.8363 | + | 53.0344i | −0.599646 | + | 0.912895i | ||||
\(16\) | 158.422 | 2.47534 | ||||||||
\(17\) | −17.9283 | − | 31.0528i | −0.255780 | − | 0.443024i | 0.709327 | − | 0.704880i | \(-0.248999\pi\) |
−0.965107 | + | 0.261855i | \(0.915666\pi\) | |||||||
\(18\) | −113.550 | − | 84.3259i | −1.48689 | − | 1.10421i | ||||
\(19\) | −13.8136 | − | 7.97531i | −0.166793 | − | 0.0962979i | 0.414280 | − | 0.910150i | \(-0.364033\pi\) |
−0.581073 | + | 0.813852i | \(0.697367\pi\) | |||||||
\(20\) | 118.701 | + | 205.596i | 1.32711 | + | 2.29863i | ||||
\(21\) | −51.7836 | − | 81.1139i | −0.538100 | − | 0.842881i | ||||
\(22\) | 166.608 | − | 288.574i | 1.61459 | − | 2.79655i | ||||
\(23\) | 39.5226 | − | 22.8184i | 0.358306 | − | 0.206868i | −0.310031 | − | 0.950726i | \(-0.600340\pi\) |
0.668337 | + | 0.743858i | \(0.267006\pi\) | |||||||
\(24\) | −278.209 | + | 139.928i | −2.36622 | + | 1.19011i | ||||
\(25\) | −12.0596 | + | 20.8878i | −0.0964767 | + | 0.167103i | ||||
\(26\) | 41.7179 | − | 72.2576i | 0.314675 | − | 0.545034i | ||||
\(27\) | 138.208 | + | 24.1166i | 0.985115 | + | 0.171898i | ||||
\(28\) | −358.173 | + | 36.7217i | −2.41744 | + | 0.247848i | ||||
\(29\) | −206.656 | + | 119.313i | −1.32328 | + | 0.763996i | −0.984251 | − | 0.176779i | \(-0.943432\pi\) |
−0.339030 | + | 0.940776i | \(0.610099\pi\) | |||||||
\(30\) | −277.816 | − | 182.487i | −1.69073 | − | 1.11058i | ||||
\(31\) | 135.296i | 0.783867i | 0.919994 | + | 0.391933i | \(0.128194\pi\) | ||||
−0.919994 | + | 0.391933i | \(0.871806\pi\) | |||||||
\(32\) | 350.421i | 1.93582i | ||||||||
\(33\) | −19.0231 | + | 329.981i | −0.100348 | + | 1.74068i | ||||
\(34\) | 162.667 | − | 93.9160i | 0.820506 | − | 0.473719i | ||||
\(35\) | −132.466 | − | 183.305i | −0.639736 | − | 0.885263i | ||||
\(36\) | 312.952 | − | 421.409i | 1.44885 | − | 1.95097i | ||||
\(37\) | 18.0766 | − | 31.3095i | 0.0803180 | − | 0.139115i | −0.823069 | − | 0.567942i | \(-0.807740\pi\) |
0.903387 | + | 0.428827i | \(0.141073\pi\) | |||||||
\(38\) | 41.7779 | − | 72.3615i | 0.178349 | − | 0.308910i | ||||
\(39\) | −4.76329 | + | 82.6257i | −0.0195574 | + | 0.339249i | ||||
\(40\) | −633.807 | + | 365.929i | −2.50534 | + | 1.44646i | ||||
\(41\) | 84.5046 | − | 146.366i | 0.321888 | − | 0.557526i | −0.658990 | − | 0.752152i | \(-0.729016\pi\) |
0.980878 | + | 0.194626i | \(0.0623493\pi\) | |||||||
\(42\) | 424.908 | − | 271.263i | 1.56106 | − | 0.996592i | ||||
\(43\) | −37.8895 | − | 65.6266i | −0.134374 | − | 0.232743i | 0.790984 | − | 0.611837i | \(-0.209569\pi\) |
−0.925358 | + | 0.379094i | \(0.876236\pi\) | |||||||
\(44\) | 1070.96 | + | 618.321i | 3.66941 | + | 2.11853i | ||||
\(45\) | 327.525 | + | 37.8889i | 1.08499 | + | 0.125514i | ||||
\(46\) | 119.532 | + | 207.036i | 0.383131 | + | 0.663603i | ||||
\(47\) | 6.93563 | 0.0215248 | 0.0107624 | − | 0.999942i | \(-0.496574\pi\) | ||||
0.0107624 | + | 0.999942i | \(0.496574\pi\) | |||||||
\(48\) | −369.880 | − | 735.405i | −1.11224 | − | 2.21139i | ||||
\(49\) | 335.864 | − | 69.6005i | 0.979196 | − | 0.202917i | ||||
\(50\) | −109.419 | − | 63.1731i | −0.309484 | − | 0.178680i | ||||
\(51\) | −102.291 | + | 155.726i | −0.280854 | + | 0.427569i | ||||
\(52\) | 268.164 | + | 154.825i | 0.715148 | + | 0.412891i | ||||
\(53\) | 33.2929 | − | 19.2216i | 0.0862854 | − | 0.0498169i | −0.456236 | − | 0.889859i | \(-0.650803\pi\) |
0.542522 | + | 0.840042i | \(0.317470\pi\) | |||||||
\(54\) | −126.333 | + | 723.989i | −0.318365 | + | 1.82449i | ||||
\(55\) | 776.773i | 1.90436i | ||||||||
\(56\) | −113.205 | − | 1104.17i | −0.270137 | − | 2.63484i | ||||
\(57\) | −4.77014 | + | 82.7444i | −0.0110846 | + | 0.192277i | ||||
\(58\) | −625.011 | − | 1082.55i | −1.41496 | − | 2.45079i | ||||
\(59\) | −124.484 | −0.274686 | −0.137343 | − | 0.990524i | \(-0.543856\pi\) | ||||
−0.137343 | + | 0.990524i | \(0.543856\pi\) | |||||||
\(60\) | 677.250 | − | 1031.04i | 1.45721 | − | 2.21844i | ||||
\(61\) | − | 514.833i | − | 1.08062i | −0.841467 | − | 0.540308i | \(-0.818308\pi\) | ||
0.841467 | − | 0.540308i | \(-0.181692\pi\) | |||||||
\(62\) | −708.735 | −1.45177 | ||||||||
\(63\) | −255.633 | + | 429.766i | −0.511218 | + | 0.859451i | ||||
\(64\) | −568.272 | −1.10991 | ||||||||
\(65\) | 194.500i | 0.371151i | ||||||||
\(66\) | −1728.57 | − | 99.6507i | −3.22383 | − | 0.185851i | ||||
\(67\) | 335.932 | 0.612547 | 0.306273 | − | 0.951944i | \(-0.400918\pi\) | ||||
0.306273 | + | 0.951944i | \(0.400918\pi\) | |||||||
\(68\) | 348.543 | + | 603.695i | 0.621575 | + | 1.07660i | ||||
\(69\) | −198.201 | − | 130.191i | −0.345806 | − | 0.227147i | ||||
\(70\) | 960.227 | − | 693.909i | 1.63956 | − | 1.18483i | ||||
\(71\) | 716.432i | 1.19753i | 0.800924 | + | 0.598767i | \(0.204342\pi\) | ||||
−0.800924 | + | 0.598767i | \(0.795658\pi\) | |||||||
\(72\) | 1299.11 | + | 964.765i | 2.12642 | + | 1.57915i | ||||
\(73\) | 725.427 | − | 418.826i | 1.16308 | − | 0.671504i | 0.211040 | − | 0.977478i | \(-0.432315\pi\) |
0.952040 | + | 0.305973i | \(0.0989818\pi\) | |||||||
\(74\) | 164.012 | + | 94.6923i | 0.257649 | + | 0.148754i | ||||
\(75\) | 125.119 | + | 7.21301i | 0.192634 | + | 0.0111051i | ||||
\(76\) | 268.550 | + | 155.047i | 0.405326 | + | 0.234015i | ||||
\(77\) | −1075.00 | − | 481.913i | −1.59101 | − | 0.713235i | ||||
\(78\) | −432.827 | − | 24.9521i | −0.628308 | − | 0.0362213i | ||||
\(79\) | −409.854 | −0.583699 | −0.291849 | − | 0.956464i | \(-0.594271\pi\) | ||||
−0.291849 | + | 0.956464i | \(0.594271\pi\) | |||||||
\(80\) | −967.279 | − | 1675.38i | −1.35181 | − | 2.34141i | ||||
\(81\) | −210.734 | − | 697.877i | −0.289072 | − | 0.957307i | ||||
\(82\) | 766.726 | + | 442.670i | 1.03257 | + | 0.596155i | ||||
\(83\) | −135.674 | − | 234.994i | −0.179423 | − | 0.310770i | 0.762260 | − | 0.647271i | \(-0.224090\pi\) |
−0.941683 | + | 0.336501i | \(0.890757\pi\) | |||||||
\(84\) | 1006.72 | + | 1576.93i | 1.30764 | + | 2.04830i | ||||
\(85\) | −218.931 | + | 379.199i | −0.279369 | + | 0.483882i | ||||
\(86\) | 343.779 | − | 198.481i | 0.431054 | − | 0.248869i | ||||
\(87\) | 1036.36 | + | 680.744i | 1.27712 | + | 0.838889i | ||||
\(88\) | −1906.15 | + | 3301.55i | −2.30905 | + | 3.99939i | ||||
\(89\) | 717.489 | − | 1242.73i | 0.854535 | − | 1.48010i | −0.0225404 | − | 0.999746i | \(-0.507175\pi\) |
0.877076 | − | 0.480352i | \(-0.159491\pi\) | |||||||
\(90\) | −198.477 | + | 1715.71i | −0.232459 | + | 2.00946i | ||||
\(91\) | −269.176 | − | 120.669i | −0.310080 | − | 0.139006i | ||||
\(92\) | −768.356 | + | 443.611i | −0.870725 | + | 0.502713i | ||||
\(93\) | 628.053 | − | 315.886i | 0.700280 | − | 0.352214i | ||||
\(94\) | 36.3317i | 0.0398652i | ||||||||
\(95\) | 194.780i | 0.210358i | ||||||||
\(96\) | 1626.68 | − | 818.155i | 1.72940 | − | 0.869818i | ||||
\(97\) | −433.147 | + | 250.077i | −0.453396 | + | 0.261768i | −0.709263 | − | 0.704944i | \(-0.750972\pi\) |
0.255868 | + | 0.966712i | \(0.417639\pi\) | |||||||
\(98\) | 364.596 | + | 1759.39i | 0.375813 | + | 1.81353i | ||||
\(99\) | 1576.21 | − | 682.126i | 1.60015 | − | 0.692487i | ||||
\(100\) | 234.450 | − | 406.078i | 0.234450 | − | 0.406078i | ||||
\(101\) | 918.553 | − | 1590.98i | 0.904945 | − | 1.56741i | 0.0839535 | − | 0.996470i | \(-0.473245\pi\) |
0.820991 | − | 0.570941i | \(-0.193421\pi\) | |||||||
\(102\) | −815.757 | − | 535.840i | −0.791882 | − | 0.520157i | ||||
\(103\) | −582.577 | + | 336.351i | −0.557311 | + | 0.321764i | −0.752066 | − | 0.659088i | \(-0.770942\pi\) |
0.194754 | + | 0.980852i | \(0.437609\pi\) | |||||||
\(104\) | −477.291 | + | 826.693i | −0.450022 | + | 0.779461i | ||||
\(105\) | −541.637 | + | 1042.89i | −0.503413 | + | 0.969293i | ||||
\(106\) | 100.691 | + | 174.402i | 0.0922637 | + | 0.159805i | ||||
\(107\) | −837.754 | − | 483.678i | −0.756904 | − | 0.436999i | 0.0712787 | − | 0.997456i | \(-0.477292\pi\) |
−0.828183 | + | 0.560457i | \(0.810625\pi\) | |||||||
\(108\) | −2686.89 | − | 468.849i | −2.39394 | − | 0.417732i | ||||
\(109\) | −749.801 | − | 1298.69i | −0.658880 | − | 1.14121i | −0.980906 | − | 0.194483i | \(-0.937697\pi\) |
0.322026 | − | 0.946731i | \(-0.395636\pi\) | |||||||
\(110\) | −4069.05 | −3.52699 | ||||||||
\(111\) | −187.546 | − | 10.8118i | −0.160370 | − | 0.00924517i | ||||
\(112\) | 2918.71 | − | 299.241i | 2.46243 | − | 0.252461i | ||||
\(113\) | −1202.80 | − | 694.434i | −1.00132 | − | 0.578114i | −0.0926834 | − | 0.995696i | \(-0.529544\pi\) |
−0.908639 | + | 0.417582i | \(0.862878\pi\) | |||||||
\(114\) | −433.449 | − | 24.9879i | −0.356107 | − | 0.0205292i | ||||
\(115\) | −482.628 | − | 278.646i | −0.391351 | − | 0.225946i | ||||
\(116\) | 4017.59 | − | 2319.56i | 3.21572 | − | 1.85660i | ||||
\(117\) | 394.675 | − | 170.801i | 0.311861 | − | 0.134962i | ||||
\(118\) | − | 652.100i | − | 0.508734i | ||||||
\(119\) | −388.961 | − | 538.243i | −0.299631 | − | 0.414627i | ||||
\(120\) | 3178.47 | + | 2087.82i | 2.41794 | + | 1.58825i | ||||
\(121\) | 1357.63 | + | 2351.49i | 1.02001 | + | 1.76671i | ||||
\(122\) | 2696.90 | 2.00136 | ||||||||
\(123\) | −876.742 | − | 50.5433i | −0.642709 | − | 0.0370515i | ||||
\(124\) | − | 2630.28i | − | 1.90489i | ||||||
\(125\) | −1231.90 | −0.881476 | ||||||||
\(126\) | −2251.29 | − | 1339.11i | −1.59175 | − | 0.946805i | ||||
\(127\) | −404.036 | −0.282302 | −0.141151 | − | 0.989988i | \(-0.545080\pi\) | ||||
−0.141151 | + | 0.989988i | \(0.545080\pi\) | |||||||
\(128\) | − | 173.473i | − | 0.119789i | ||||||
\(129\) | −216.180 | + | 329.110i | −0.147547 | + | 0.224624i | ||||
\(130\) | −1018.87 | −0.687392 | ||||||||
\(131\) | 1367.10 | + | 2367.88i | 0.911786 | + | 1.57926i | 0.811540 | + | 0.584297i | \(0.198630\pi\) |
0.100246 | + | 0.994963i | \(0.468037\pi\) | |||||||
\(132\) | 369.826 | − | 6415.13i | 0.243858 | − | 4.23004i | ||||
\(133\) | −269.562 | − | 120.842i | −0.175745 | − | 0.0787845i | ||||
\(134\) | 1759.75i | 1.13447i | ||||||||
\(135\) | −588.815 | − | 1608.85i | −0.375386 | − | 1.02569i | ||||
\(136\) | −1861.06 | + | 1074.48i | −1.17342 | + | 0.677473i | ||||
\(137\) | 743.037 | + | 428.993i | 0.463372 | + | 0.267528i | 0.713461 | − | 0.700695i | \(-0.247127\pi\) |
−0.250089 | + | 0.968223i | \(0.580460\pi\) | |||||||
\(138\) | 681.993 | − | 1038.26i | 0.420689 | − | 0.640453i | ||||
\(139\) | −2002.26 | − | 1156.01i | −1.22180 | − | 0.705404i | −0.256496 | − | 0.966545i | \(-0.582568\pi\) |
−0.965301 | + | 0.261141i | \(0.915901\pi\) | |||||||
\(140\) | 2575.25 | + | 3563.62i | 1.55463 | + | 2.15129i | ||||
\(141\) | −16.1932 | − | 32.1957i | −0.00967171 | − | 0.0192295i | ||||
\(142\) | −3752.96 | −2.21790 | ||||||||
\(143\) | 506.583 | + | 877.428i | 0.296242 | + | 0.513107i | ||||
\(144\) | −2550.21 | + | 3434.02i | −1.47582 | + | 1.98728i | ||||
\(145\) | 2523.57 | + | 1456.98i | 1.44532 | + | 0.834455i | ||||
\(146\) | 2193.98 | + | 3800.08i | 1.24366 | + | 2.15409i | ||||
\(147\) | −1107.26 | − | 1396.60i | −0.621260 | − | 0.783605i | ||||
\(148\) | −351.425 | + | 608.685i | −0.195182 | + | 0.338065i | ||||
\(149\) | 1647.40 | − | 951.126i | 0.905773 | − | 0.522948i | 0.0267040 | − | 0.999643i | \(-0.491499\pi\) |
0.879069 | + | 0.476695i | \(0.158166\pi\) | |||||||
\(150\) | −37.7847 | + | 655.426i | −0.0205674 | + | 0.356768i | ||||
\(151\) | 768.979 | − | 1331.91i | 0.414428 | − | 0.717810i | −0.580940 | − | 0.813946i | \(-0.697315\pi\) |
0.995368 | + | 0.0961358i | \(0.0306483\pi\) | |||||||
\(152\) | −477.977 | + | 827.881i | −0.255060 | + | 0.441776i | ||||
\(153\) | 961.717 | + | 111.254i | 0.508171 | + | 0.0587866i | ||||
\(154\) | 2524.46 | − | 5631.30i | 1.32095 | − | 2.94664i | ||||
\(155\) | 1430.81 | − | 826.079i | 0.741455 | − | 0.428079i | ||||
\(156\) | 92.6027 | − | 1606.32i | 0.0475266 | − | 0.824413i | ||||
\(157\) | 2910.07i | 1.47929i | 0.672995 | + | 0.739647i | \(0.265007\pi\) | ||||
−0.672995 | + | 0.739647i | \(0.734993\pi\) | |||||||
\(158\) | − | 2146.98i | − | 1.08104i | ||||||
\(159\) | −166.960 | − | 109.669i | −0.0832752 | − | 0.0547003i | ||||
\(160\) | 3705.84 | − | 2139.57i | 1.83108 | − | 1.05717i | ||||
\(161\) | 685.051 | − | 495.053i | 0.335339 | − | 0.242333i | ||||
\(162\) | 3655.76 | − | 1103.91i | 1.77299 | − | 0.535378i | ||||
\(163\) | −1133.65 | + | 1963.54i | −0.544751 | + | 0.943536i | 0.453872 | + | 0.891067i | \(0.350042\pi\) |
−0.998623 | + | 0.0524693i | \(0.983291\pi\) | |||||||
\(164\) | −1642.85 | + | 2845.49i | −0.782224 | + | 1.35485i | ||||
\(165\) | 3605.83 | − | 1813.59i | 1.70130 | − | 0.855685i | ||||
\(166\) | 1230.99 | − | 710.715i | 0.575564 | − | 0.332302i | ||||
\(167\) | −671.601 | + | 1163.25i | −0.311198 | + | 0.539011i | −0.978622 | − | 0.205667i | \(-0.934064\pi\) |
0.667424 | + | 0.744678i | \(0.267397\pi\) | |||||||
\(168\) | −4861.33 | + | 3103.50i | −2.23250 | + | 1.42524i | ||||
\(169\) | −971.654 | − | 1682.95i | −0.442264 | − | 0.766024i | ||||
\(170\) | −1986.40 | − | 1146.85i | −0.896177 | − | 0.517408i | ||||
\(171\) | 395.243 | − | 171.047i | 0.176754 | − | 0.0764928i | ||||
\(172\) | 736.607 | + | 1275.84i | 0.326545 | + | 0.565593i | ||||
\(173\) | 942.516 | 0.414209 | 0.207104 | − | 0.978319i | \(-0.433596\pi\) | ||||
0.207104 | + | 0.978319i | \(0.433596\pi\) | |||||||
\(174\) | −3566.01 | + | 5428.86i | −1.55367 | + | 2.36529i | ||||
\(175\) | −182.727 | + | 407.610i | −0.0789308 | + | 0.176071i | ||||
\(176\) | −8727.16 | − | 5038.63i | −3.73770 | − | 2.15796i | ||||
\(177\) | 290.643 | + | 577.865i | 0.123424 | + | 0.245395i | ||||
\(178\) | 6509.91 | + | 3758.50i | 2.74123 | + | 1.58265i | ||||
\(179\) | 62.9841 | − | 36.3639i | 0.0262997 | − | 0.0151842i | −0.486792 | − | 0.873518i | \(-0.661833\pi\) |
0.513092 | + | 0.858333i | \(0.328500\pi\) | |||||||
\(180\) | −6367.38 | − | 736.594i | −2.63665 | − | 0.305014i | ||||
\(181\) | − | 1860.29i | − | 0.763944i | −0.924174 | − | 0.381972i | \(-0.875245\pi\) | ||
0.924174 | − | 0.381972i | \(-0.124755\pi\) | |||||||
\(182\) | 632.112 | − | 1410.05i | 0.257446 | − | 0.574286i | ||||
\(183\) | −2389.89 | + | 1202.02i | −0.965386 | + | 0.485551i | ||||
\(184\) | −1367.56 | − | 2368.68i | −0.547922 | − | 0.949028i | ||||
\(185\) | −441.481 | −0.175451 | ||||||||
\(186\) | 1654.74 | + | 3290.00i | 0.652319 | + | 1.29696i | ||||
\(187\) | 2280.86i | 0.891939i | ||||||||
\(188\) | −134.835 | −0.0523077 | ||||||||
\(189\) | 2591.85 | + | 183.258i | 0.997510 | + | 0.0705295i | ||||
\(190\) | −1020.34 | −0.389595 | ||||||||
\(191\) | − | 4.08168i | − | 0.00154628i | −1.00000 | 0.000773141i | \(-0.999754\pi\) | |||
1.00000 | 0.000773141i | \(-0.000246098\pi\) | ||||||||
\(192\) | 1326.79 | + | 2637.96i | 0.498712 | + | 0.991553i | ||||
\(193\) | −4402.88 | −1.64211 | −0.821053 | − | 0.570853i | \(-0.806613\pi\) | ||||
−0.821053 | + | 0.570853i | \(0.806613\pi\) | |||||||
\(194\) | −1310.01 | − | 2269.00i | −0.484809 | − | 0.839714i | ||||
\(195\) | 902.884 | − | 454.115i | 0.331574 | − | 0.166769i | ||||
\(196\) | −6529.51 | + | 1353.10i | −2.37956 | + | 0.493111i | ||||
\(197\) | − | 389.909i | − | 0.141014i | −0.997511 | − | 0.0705072i | \(-0.977538\pi\) | ||
0.997511 | − | 0.0705072i | \(-0.0224618\pi\) | |||||||
\(198\) | 3573.25 | + | 8256.82i | 1.28253 | + | 2.96357i | ||||
\(199\) | 912.641 | − | 526.914i | 0.325103 | − | 0.187698i | −0.328562 | − | 0.944482i | \(-0.606564\pi\) |
0.653665 | + | 0.756784i | \(0.273231\pi\) | |||||||
\(200\) | 1251.85 | + | 722.758i | 0.442597 | + | 0.255533i | ||||
\(201\) | −784.327 | − | 1559.42i | −0.275235 | − | 0.547229i | ||||
\(202\) | 8334.20 | + | 4811.75i | 2.90293 | + | 1.67601i | ||||
\(203\) | −3582.00 | + | 2588.54i | −1.23846 | + | 0.894974i | ||||
\(204\) | 1988.62 | − | 3027.46i | 0.682507 | − | 1.03904i | ||||
\(205\) | −2063.85 | −0.703147 | ||||||||
\(206\) | −1761.95 | − | 3051.78i | −0.595925 | − | 1.03217i | ||||
\(207\) | −141.599 | + | 1224.03i | −0.0475450 | + | 0.410995i | ||||
\(208\) | −2185.24 | − | 1261.65i | −0.728457 | − | 0.420575i | ||||
\(209\) | 507.312 | + | 878.689i | 0.167902 | + | 0.290814i | ||||
\(210\) | −5463.09 | − | 2837.32i | −1.79519 | − | 0.932349i | ||||
\(211\) | −561.416 | + | 972.401i | −0.183173 | + | 0.317265i | −0.942959 | − | 0.332908i | \(-0.891970\pi\) |
0.759786 | + | 0.650173i | \(0.225303\pi\) | |||||||
\(212\) | −647.243 | + | 373.686i | −0.209683 | + | 0.121061i | ||||
\(213\) | 3325.73 | − | 1672.71i | 1.06984 | − | 0.538086i | ||||
\(214\) | 2533.70 | − | 4388.50i | 0.809347 | − | 1.40183i | ||||
\(215\) | −462.686 | + | 801.395i | −0.146767 | + | 0.254208i | ||||
\(216\) | 1445.36 | − | 8283.09i | 0.455298 | − | 2.60923i | ||||
\(217\) | 255.558 | + | 2492.65i | 0.0799467 | + | 0.779779i | ||||
\(218\) | 6803.09 | − | 3927.77i | 2.11359 | − | 1.22028i | ||||
\(219\) | −3637.93 | − | 2389.62i | −1.12250 | − | 0.737331i | ||||
\(220\) | − | 15101.2i | − | 4.62782i | ||||||
\(221\) | 571.115i | 0.173834i | ||||||||
\(222\) | 56.6368 | − | 982.441i | 0.0171226 | − | 0.297014i | ||||
\(223\) | 3850.81 | − | 2223.27i | 1.15637 | − | 0.667628i | 0.205935 | − | 0.978566i | \(-0.433976\pi\) |
0.950430 | + | 0.310937i | \(0.100643\pi\) | |||||||
\(224\) | 661.904 | + | 6456.04i | 0.197435 | + | 1.92572i | ||||
\(225\) | −258.642 | − | 597.653i | −0.0766348 | − | 0.177082i | ||||
\(226\) | 3637.73 | − | 6300.73i | 1.07070 | − | 1.85451i | ||||
\(227\) | −23.6177 | + | 40.9071i | −0.00690556 | + | 0.0119608i | −0.869458 | − | 0.494008i | \(-0.835531\pi\) |
0.862552 | + | 0.505968i | \(0.168865\pi\) | |||||||
\(228\) | 92.7358 | − | 1608.63i | 0.0269368 | − | 0.467254i | ||||
\(229\) | −2860.63 | + | 1651.59i | −0.825485 | + | 0.476594i | −0.852304 | − | 0.523046i | \(-0.824795\pi\) |
0.0268193 | + | 0.999640i | \(0.491462\pi\) | |||||||
\(230\) | 1459.66 | − | 2528.20i | 0.418465 | − | 0.724803i | ||||
\(231\) | 272.821 | + | 6115.40i | 0.0777069 | + | 1.74183i | ||||
\(232\) | 7150.70 | + | 12385.4i | 2.02356 | + | 3.50491i | ||||
\(233\) | 4018.91 | + | 2320.32i | 1.12999 | + | 0.652400i | 0.943932 | − | 0.330139i | \(-0.107096\pi\) |
0.186057 | + | 0.982539i | \(0.440429\pi\) | |||||||
\(234\) | 894.726 | + | 2067.47i | 0.249958 | + | 0.577584i | ||||
\(235\) | −42.3470 | − | 73.3472i | −0.0117550 | − | 0.0203602i | ||||
\(236\) | 2420.09 | 0.667519 | ||||||||
\(237\) | 956.919 | + | 1902.57i | 0.262273 | + | 0.521457i | ||||
\(238\) | 2819.53 | − | 2037.54i | 0.767913 | − | 0.554933i | ||||
\(239\) | 3801.25 | + | 2194.65i | 1.02880 | + | 0.593976i | 0.916640 | − | 0.399715i | \(-0.130891\pi\) |
0.112157 | + | 0.993691i | \(0.464224\pi\) | |||||||
\(240\) | −5518.83 | + | 8401.81i | −1.48433 | + | 2.25973i | ||||
\(241\) | −962.435 | − | 555.662i | −0.257244 | − | 0.148520i | 0.365833 | − | 0.930681i | \(-0.380784\pi\) |
−0.623077 | + | 0.782161i | \(0.714118\pi\) | |||||||
\(242\) | −12318.1 | + | 7111.84i | −3.27205 | + | 1.88912i | ||||
\(243\) | −2747.58 | + | 2607.63i | −0.725338 | + | 0.688393i | ||||
\(244\) | 10008.8i | 2.62602i | ||||||||
\(245\) | −2786.75 | − | 3126.94i | −0.726688 | − | 0.815400i | ||||
\(246\) | 264.767 | − | 4592.73i | 0.0686216 | − | 1.19033i | ||||
\(247\) | 127.028 | + | 220.020i | 0.0327232 | + | 0.0566782i | ||||
\(248\) | 8108.58 | 2.07619 | ||||||||
\(249\) | −774.090 | + | 1178.47i | −0.197012 | + | 0.299929i | ||||
\(250\) | − | 6453.19i | − | 1.63254i | ||||||
\(251\) | 1262.49 | 0.317480 | 0.158740 | − | 0.987320i | \(-0.449257\pi\) | ||||
0.158740 | + | 0.987320i | \(0.449257\pi\) | |||||||
\(252\) | 4969.74 | − | 8355.04i | 1.24232 | − | 2.08856i | ||||
\(253\) | −2902.97 | −0.721376 | ||||||||
\(254\) | − | 2116.50i | − | 0.522839i | ||||||
\(255\) | 2271.43 | + | 130.946i | 0.557812 | + | 0.0321574i | ||||
\(256\) | −3637.45 | −0.888049 | ||||||||
\(257\) | −2670.98 | − | 4626.27i | −0.648291 | − | 1.12287i | −0.983531 | − | 0.180741i | \(-0.942151\pi\) |
0.335239 | − | 0.942133i | \(-0.391183\pi\) | |||||||
\(258\) | −1724.01 | − | 1132.44i | −0.416016 | − | 0.273265i | ||||
\(259\) | 273.897 | − | 610.981i | 0.0657108 | − | 0.146581i | ||||
\(260\) | − | 3781.26i | − | 0.901939i | ||||||
\(261\) | 740.395 | − | 6400.23i | 0.175591 | − | 1.51787i | ||||
\(262\) | −12403.9 | + | 7161.42i | −2.92488 | + | 1.68868i | ||||
\(263\) | −900.046 | − | 519.642i | −0.211024 | − | 0.121835i | 0.390763 | − | 0.920491i | \(-0.372211\pi\) |
−0.601787 | + | 0.798657i | \(0.705544\pi\) | |||||||
\(264\) | 19776.5 | + | 1140.09i | 4.61045 | + | 0.265788i | ||||
\(265\) | −406.554 | − | 234.724i | −0.0942430 | − | 0.0544112i | ||||
\(266\) | 633.020 | − | 1412.08i | 0.145913 | − | 0.325489i | ||||
\(267\) | −7444.00 | − | 429.140i | −1.70624 | − | 0.0983630i | ||||
\(268\) | −6530.83 | −1.48856 | ||||||||
\(269\) | 2118.62 | + | 3669.55i | 0.480202 | + | 0.831735i | 0.999742 | − | 0.0227115i | \(-0.00722993\pi\) |
−0.519540 | + | 0.854446i | \(0.673897\pi\) | |||||||
\(270\) | 8427.83 | − | 3084.45i | 1.89964 | − | 0.695236i | ||||
\(271\) | 5981.42 | + | 3453.38i | 1.34076 | + | 0.774087i | 0.986919 | − | 0.161219i | \(-0.0515425\pi\) |
0.353840 | + | 0.935306i | \(0.384876\pi\) | |||||||
\(272\) | −2840.24 | − | 4919.44i | −0.633143 | − | 1.09664i | ||||
\(273\) | 68.3131 | + | 1531.27i | 0.0151447 | + | 0.339474i | ||||
\(274\) | −2247.24 | + | 3892.33i | −0.495477 | + | 0.858191i | ||||
\(275\) | 1328.68 | − | 767.114i | 0.291354 | − | 0.168214i | ||||
\(276\) | 3853.21 | + | 2531.03i | 0.840349 | + | 0.551993i | ||||
\(277\) | 1226.23 | − | 2123.90i | 0.265983 | − | 0.460696i | −0.701838 | − | 0.712337i | \(-0.747637\pi\) |
0.967821 | + | 0.251641i | \(0.0809702\pi\) | |||||||
\(278\) | 6055.63 | − | 10488.7i | 1.30645 | − | 2.26284i | ||||
\(279\) | −2932.73 | − | 2177.94i | −0.629312 | − | 0.467347i | ||||
\(280\) | −10985.9 | + | 7938.95i | −2.34475 | + | 1.69444i | ||||
\(281\) | −7204.13 | + | 4159.31i | −1.52940 | + | 0.883002i | −0.530017 | + | 0.847987i | \(0.677815\pi\) |
−0.999387 | + | 0.0350152i | \(0.988852\pi\) | |||||||
\(282\) | 168.654 | − | 84.8264i | 0.0356142 | − | 0.0179125i | ||||
\(283\) | − | 6851.81i | − | 1.43922i | −0.694381 | − | 0.719608i | \(-0.744322\pi\) | ||
0.694381 | − | 0.719608i | \(-0.255678\pi\) | |||||||
\(284\) | − | 13928.1i | − | 2.91014i | ||||||
\(285\) | 904.182 | − | 454.768i | 0.187927 | − | 0.0945198i | ||||
\(286\) | −4596.33 | + | 2653.69i | −0.950302 | + | 0.548657i | ||||
\(287\) | 1280.42 | − | 2856.23i | 0.263347 | − | 0.587448i | ||||
\(288\) | −7595.86 | − | 5640.94i | −1.55413 | − | 1.15415i | ||||
\(289\) | 1813.65 | − | 3141.33i | 0.369153 | − | 0.639392i | ||||
\(290\) | −7632.28 | + | 13219.5i | −1.54546 | + | 2.67681i | ||||
\(291\) | 2172.18 | + | 1426.82i | 0.437578 | + | 0.287429i | ||||
\(292\) | −14103.0 | + | 8142.35i | −2.82642 | + | 1.63183i | ||||
\(293\) | 388.740 | − | 673.317i | 0.0775100 | − | 0.134251i | −0.824665 | − | 0.565621i | \(-0.808636\pi\) |
0.902175 | + | 0.431370i | \(0.141970\pi\) | |||||||
\(294\) | 7315.98 | − | 5800.27i | 1.45128 | − | 1.15061i | ||||
\(295\) | 760.066 | + | 1316.47i | 0.150009 | + | 0.259824i | ||||
\(296\) | −1876.45 | − | 1083.37i | −0.368467 | − | 0.212735i | ||||
\(297\) | −6846.58 | − | 5724.26i | −1.33764 | − | 1.11837i | ||||
\(298\) | 4982.38 | + | 8629.74i | 0.968529 | + | 1.67754i | ||||
\(299\) | −726.890 | −0.140592 | ||||||||
\(300\) | −2432.43 | − | 140.227i | −0.468122 | − | 0.0269868i | ||||
\(301\) | −822.026 | − | 1137.51i | −0.157411 | − | 0.217825i | ||||
\(302\) | 6977.09 | + | 4028.23i | 1.32943 | + | 0.767544i | ||||
\(303\) | −9530.06 | − | 549.399i | −1.80689 | − | 0.104165i | ||||
\(304\) | −2188.38 | − | 1263.46i | −0.412869 | − | 0.238370i | ||||
\(305\) | −5444.57 | + | 3143.42i | −1.02215 | + | 0.590137i | ||||
\(306\) | −582.793 | + | 5037.87i | −0.108876 | + | 0.941162i | ||||
\(307\) | − | 5502.32i | − | 1.02291i | −0.859309 | − | 0.511456i | \(-0.829106\pi\) | ||
0.859309 | − | 0.511456i | \(-0.170894\pi\) | |||||||
\(308\) | 20899.0 | + | 9368.82i | 3.86634 | + | 1.73324i | ||||
\(309\) | 2921.56 | + | 1919.06i | 0.537869 | + | 0.353306i | ||||
\(310\) | 4327.34 | + | 7495.17i | 0.792827 | + | 1.37322i | ||||
\(311\) | −2147.49 | −0.391554 | −0.195777 | − | 0.980648i | \(-0.562723\pi\) | ||||
−0.195777 | + | 0.980648i | \(0.562723\pi\) | |||||||
\(312\) | 4951.94 | + | 285.474i | 0.898552 | + | 0.0518007i | ||||
\(313\) | 1969.86i | 0.355729i | 0.984055 | + | 0.177864i | \(0.0569188\pi\) | ||||
−0.984055 | + | 0.177864i | \(0.943081\pi\) | |||||||
\(314\) | −15244.1 | −2.73974 | ||||||||
\(315\) | 6105.78 | + | 79.3964i | 1.09213 | + | 0.0142015i | ||||
\(316\) | 7967.94 | 1.41846 | ||||||||
\(317\) | − | 1451.03i | − | 0.257091i | −0.991704 | − | 0.128545i | \(-0.958969\pi\) | ||
0.991704 | − | 0.128545i | \(-0.0410308\pi\) | |||||||
\(318\) | 574.493 | − | 874.603i | 0.101308 | − | 0.154230i | ||||
\(319\) | 15179.1 | 2.66416 | ||||||||
\(320\) | 3469.71 | + | 6009.71i | 0.606133 | + | 1.04985i | ||||
\(321\) | −289.294 | + | 5018.19i | −0.0503016 | + | 0.872549i | ||||
\(322\) | 2593.29 | + | 3588.58i | 0.448815 | + | 0.621067i | ||||
\(323\) | 571.936i | 0.0985244i | ||||||||
\(324\) | 4096.85 | + | 13567.4i | 0.702478 | + | 2.32637i | ||||
\(325\) | 332.695 | − | 192.082i | 0.0567835 | − | 0.0327839i | ||||
\(326\) | −10285.8 | − | 5938.53i | −1.74748 | − | 1.00891i | ||||
\(327\) | −4278.01 | + | 6512.79i | −0.723469 | + | 1.10140i | ||||
\(328\) | −8772.05 | − | 5064.54i | −1.47669 | − | 0.852569i | ||||
\(329\) | 127.780 | − | 13.1006i | 0.0214126 | − | 0.00219532i | ||||
\(330\) | 9500.34 | + | 18888.8i | 1.58478 | + | 3.15090i | ||||
\(331\) | −1188.85 | −0.197417 | −0.0987086 | − | 0.995116i | \(-0.531471\pi\) | ||||
−0.0987086 | + | 0.995116i | \(0.531471\pi\) | |||||||
\(332\) | 2637.62 | + | 4568.50i | 0.436019 | + | 0.755207i | ||||
\(333\) | 387.688 | + | 895.843i | 0.0637994 | + | 0.147423i | ||||
\(334\) | −6093.56 | − | 3518.12i | −0.998279 | − | 0.576356i | ||||
\(335\) | −2051.11 | − | 3552.62i | −0.334519 | − | 0.579404i | ||||
\(336\) | −8203.65 | − | 12850.2i | −1.33198 | − | 2.08642i | ||||
\(337\) | 3178.71 | − | 5505.69i | 0.513814 | − | 0.889952i | −0.486058 | − | 0.873927i | \(-0.661565\pi\) |
0.999872 | − | 0.0160253i | \(-0.00510122\pi\) | |||||||
\(338\) | 8816.00 | − | 5089.92i | 1.41872 | − | 0.819098i | ||||
\(339\) | −415.351 | + | 7204.81i | −0.0665450 | + | 1.15431i | ||||
\(340\) | 4256.22 | − | 7371.98i | 0.678899 | − | 1.17589i | ||||
\(341\) | 4303.11 | − | 7453.20i | 0.683361 | − | 1.18362i | ||||
\(342\) | 896.012 | + | 2070.44i | 0.141669 | + | 0.327359i | ||||
\(343\) | 6056.39 | − | 1916.71i | 0.953394 | − | 0.301727i | ||||
\(344\) | −3933.15 | + | 2270.80i | −0.616456 | + | 0.355911i | ||||
\(345\) | −166.662 | + | 2890.97i | −0.0260080 | + | 0.451144i | ||||
\(346\) | 4937.28i | 0.767138i | ||||||||
\(347\) | 11126.9i | 1.72140i | 0.509115 | + | 0.860698i | \(0.329973\pi\) | ||||
−0.509115 | + | 0.860698i | \(0.670027\pi\) | |||||||
\(348\) | −20147.7 | − | 13234.3i | −3.10354 | − | 2.03860i | ||||
\(349\) | 2318.23 | − | 1338.43i | 0.355564 | − | 0.205285i | −0.311569 | − | 0.950224i | \(-0.600855\pi\) |
0.667133 | + | 0.744938i | \(0.267521\pi\) | |||||||
\(350\) | −2135.23 | − | 957.201i | −0.326093 | − | 0.146184i | ||||
\(351\) | −1714.35 | − | 1433.33i | −0.260699 | − | 0.217964i | ||||
\(352\) | 11145.2 | − | 19304.0i | 1.68761 | − | 2.92303i | ||||
\(353\) | 3764.40 | − | 6520.13i | 0.567589 | − | 0.983092i | −0.429215 | − | 0.903202i | \(-0.641210\pi\) |
0.996804 | − | 0.0798900i | \(-0.0254569\pi\) | |||||||
\(354\) | −3027.09 | + | 1522.51i | −0.454486 | + | 0.228589i | ||||
\(355\) | 7576.57 | − | 4374.33i | 1.13274 | − | 0.653987i | ||||
\(356\) | −13948.6 | + | 24159.7i | −2.07662 | + | 3.59681i | ||||
\(357\) | −1590.42 | + | 3062.26i | −0.235781 | + | 0.453984i | ||||
\(358\) | 190.489 | + | 329.936i | 0.0281219 | + | 0.0487086i | ||||
\(359\) | 9009.61 | + | 5201.70i | 1.32454 | + | 0.764722i | 0.984449 | − | 0.175671i | \(-0.0562094\pi\) |
0.340089 | + | 0.940393i | \(0.389543\pi\) | |||||||
\(360\) | 2270.76 | − | 19629.3i | 0.332444 | − | 2.87376i | ||||
\(361\) | −3302.29 | − | 5719.73i | −0.481453 | − | 0.833902i | ||||
\(362\) | 9744.93 | 1.41487 | ||||||||
\(363\) | 7746.01 | − | 11792.4i | 1.12000 | − | 1.70508i | ||||
\(364\) | 5233.02 | + | 2345.91i | 0.753530 | + | 0.337800i | ||||
\(365\) | −8858.51 | − | 5114.46i | −1.27034 | − | 0.733433i | ||||
\(366\) | −6296.67 | − | 12519.2i | −0.899269 | − | 1.78795i | ||||
\(367\) | −10537.2 | − | 6083.67i | −1.49874 | − | 0.865299i | −0.498743 | − | 0.866750i | \(-0.666205\pi\) |
−0.999999 | + | 0.00145066i | \(0.999538\pi\) | |||||||
\(368\) | 6261.25 | − | 3614.93i | 0.886930 | − | 0.512069i | ||||
\(369\) | 1812.37 | + | 4187.90i | 0.255687 | + | 0.590823i | ||||
\(370\) | − | 2312.66i | − | 0.324944i | ||||||
\(371\) | 577.070 | − | 417.020i | 0.0807546 | − | 0.0583574i | ||||
\(372\) | −12209.9 | + | 6141.11i | −1.70176 | + | 0.855919i | ||||
\(373\) | 1108.39 | + | 1919.79i | 0.153862 | + | 0.266496i | 0.932644 | − | 0.360798i | \(-0.117496\pi\) |
−0.778782 | + | 0.627294i | \(0.784162\pi\) | |||||||
\(374\) | −11948.0 | −1.65192 | ||||||||
\(375\) | 2876.21 | + | 5718.56i | 0.396072 | + | 0.787481i | ||||
\(376\) | − | 415.667i | − | 0.0570117i | ||||||
\(377\) | 3800.77 | 0.519230 | ||||||||
\(378\) | −959.981 | + | 13577.2i | −0.130625 | + | 1.84744i | ||||
\(379\) | −2955.89 | −0.400617 | −0.200308 | − | 0.979733i | \(-0.564194\pi\) | ||||
−0.200308 | + | 0.979733i | \(0.564194\pi\) | |||||||
\(380\) | − | 3786.70i | − | 0.511194i | ||||||
\(381\) | 943.334 | + | 1875.56i | 0.126846 | + | 0.252199i | ||||
\(382\) | 21.3815 | 0.00286380 | ||||||||
\(383\) | −3724.64 | − | 6451.27i | −0.496920 | − | 0.860691i | 0.503074 | − | 0.864244i | \(-0.332202\pi\) |
−0.999994 | + | 0.00355274i | \(0.998869\pi\) | |||||||
\(384\) | −805.276 | + | 405.022i | −0.107016 | + | 0.0538247i | ||||
\(385\) | 1467.24 | + | 14311.0i | 0.194227 | + | 1.89443i | ||||
\(386\) | − | 23064.1i | − | 3.04127i | ||||||
\(387\) | 2032.48 | + | 235.123i | 0.266968 | + | 0.0308836i | ||||
\(388\) | 8420.76 | − | 4861.73i | 1.10180 | − | 0.636126i | ||||
\(389\) | 5221.02 | + | 3014.36i | 0.680505 | + | 0.392890i | 0.800045 | − | 0.599940i | \(-0.204809\pi\) |
−0.119540 | + | 0.992829i | \(0.538142\pi\) | |||||||
\(390\) | 2378.84 | + | 4729.67i | 0.308865 | + | 0.614093i | ||||
\(391\) | −1417.15 | − | 818.193i | −0.183295 | − | 0.105826i | ||||
\(392\) | −4171.31 | − | 20129.1i | −0.537456 | − | 2.59355i | ||||
\(393\) | 7800.01 | − | 11874.7i | 1.00117 | − | 1.52417i | ||||
\(394\) | 2042.50 | 0.261167 | ||||||||
\(395\) | 2502.46 | + | 4334.38i | 0.318765 | + | 0.552117i | ||||
\(396\) | −30642.9 | + | 13261.2i | −3.88855 | + | 1.68282i | ||||
\(397\) | 12778.7 | + | 7377.79i | 1.61548 | + | 0.932696i | 0.988070 | + | 0.154005i | \(0.0492172\pi\) |
0.627407 | + | 0.778691i | \(0.284116\pi\) | |||||||
\(398\) | 2760.19 | + | 4780.79i | 0.347628 | + | 0.602109i | ||||
\(399\) | 68.4112 | + | 1533.47i | 0.00858357 | + | 0.192405i | ||||
\(400\) | −1910.50 | + | 3309.09i | −0.238813 | + | 0.413636i | ||||
\(401\) | −3293.14 | + | 1901.29i | −0.410103 | + | 0.236773i | −0.690834 | − | 0.723013i | \(-0.742756\pi\) |
0.280731 | + | 0.959787i | \(0.409423\pi\) | |||||||
\(402\) | 8168.88 | − | 4108.62i | 1.01350 | − | 0.509750i | ||||
\(403\) | 1077.48 | − | 1866.25i | 0.133184 | − | 0.230681i | ||||
\(404\) | −17857.5 | + | 30930.1i | −2.19912 | + | 3.80899i | ||||
\(405\) | −6093.66 | + | 6489.64i | −0.747645 | + | 0.796229i | ||||
\(406\) | −13559.8 | − | 18764.0i | −1.65754 | − | 2.29370i | ||||
\(407\) | −1991.61 | + | 1149.85i | −0.242556 | + | 0.140040i | ||||
\(408\) | 9333.00 | + | 6130.50i | 1.13248 | + | 0.743884i | ||||
\(409\) | 4356.56i | 0.526694i | 0.964701 | + | 0.263347i | \(0.0848264\pi\) | ||||
−0.964701 | + | 0.263347i | \(0.915174\pi\) | |||||||
\(410\) | − | 10811.3i | − | 1.30227i | ||||||
\(411\) | 256.586 | − | 4450.83i | 0.0307943 | − | 0.534169i | ||||
\(412\) | 11325.8 | − | 6538.98i | 1.35433 | − | 0.781923i | ||||
\(413\) | −2293.46 | + | 235.137i | −0.273254 | + | 0.0280153i | ||||
\(414\) | −6411.97 | − | 741.753i | −0.761187 | − | 0.0880560i | ||||
\(415\) | −1656.77 | + | 2869.61i | −0.195970 | + | 0.339431i | ||||
\(416\) | 2790.70 | − | 4833.64i | 0.328907 | − | 0.569684i | ||||
\(417\) | −691.423 | + | 11993.7i | −0.0811970 | + | 1.40847i | ||||
\(418\) | −4602.93 | + | 2657.50i | −0.538605 | + | 0.310964i | ||||
\(419\) | 4875.07 | − | 8443.88i | 0.568408 | − | 0.984512i | −0.428316 | − | 0.903629i | \(-0.640893\pi\) |
0.996724 | − | 0.0808824i | \(-0.0257738\pi\) | |||||||
\(420\) | 10529.9 | − | 20274.8i | 1.22335 | − | 2.35549i | ||||
\(421\) | 4245.69 | + | 7353.75i | 0.491502 | + | 0.851306i | 0.999952 | − | 0.00978535i | \(-0.00311482\pi\) |
−0.508450 | + | 0.861091i | \(0.669781\pi\) | |||||||
\(422\) | −5093.83 | − | 2940.93i | −0.587592 | − | 0.339246i | ||||
\(423\) | −111.647 | + | 150.340i | −0.0128333 | + | 0.0172808i | ||||
\(424\) | −1151.99 | − | 1995.31i | −0.131948 | − | 0.228540i | ||||
\(425\) | 864.834 | 0.0987074 | ||||||||
\(426\) | 8762.34 | + | 17421.5i | 0.996565 | + | 1.98140i | ||||
\(427\) | −972.460 | − | 9485.11i | −0.110212 | − | 1.07498i | ||||
\(428\) | 16286.7 | + | 9403.14i | 1.83936 | + | 1.06196i | ||||
\(429\) | 2890.32 | − | 4400.20i | 0.325282 | − | 0.495206i | ||||
\(430\) | −4198.04 | − | 2423.74i | −0.470808 | − | 0.271821i | ||||
\(431\) | −3582.61 | + | 2068.42i | −0.400390 | + | 0.231166i | −0.686652 | − | 0.726986i | \(-0.740921\pi\) |
0.286262 | + | 0.958151i | \(0.407587\pi\) | |||||||
\(432\) | 21895.1 | + | 3820.60i | 2.43849 | + | 0.425506i | ||||
\(433\) | 1005.45i | 0.111591i | 0.998442 | + | 0.0557953i | \(0.0177694\pi\) | ||||
−0.998442 | + | 0.0557953i | \(0.982231\pi\) | |||||||
\(434\) | −13057.5 | + | 1338.72i | −1.44419 | + | 0.148066i | ||||
\(435\) | 871.442 | − | 15116.3i | 0.0960516 | − | 1.66614i | ||||
\(436\) | 14576.8 | + | 25247.8i | 1.60115 | + | 2.77328i | ||||
\(437\) | −727.935 | −0.0796839 | ||||||||
\(438\) | 12517.8 | − | 19057.0i | 1.36558 | − | 2.07894i | ||||
\(439\) | − | 8230.57i | − | 0.894814i | −0.894330 | − | 0.447407i | \(-0.852348\pi\) | ||
0.894330 | − | 0.447407i | \(-0.147652\pi\) | |||||||
\(440\) | 46553.7 | 5.04400 | ||||||||
\(441\) | −3897.92 | + | 8400.73i | −0.420897 | + | 0.907109i | ||||
\(442\) | −2991.74 | −0.321951 | ||||||||
\(443\) | 1353.60i | 0.145173i | 0.997362 | + | 0.0725863i | \(0.0231253\pi\) | ||||
−0.997362 | + | 0.0725863i | \(0.976875\pi\) | |||||||
\(444\) | 3646.06 | + | 210.192i | 0.389717 | + | 0.0224668i | ||||
\(445\) | −17523.1 | −1.86669 | ||||||||
\(446\) | 11646.4 | + | 20172.1i | 1.23649 | + | 2.14166i | ||||
\(447\) | −8261.50 | − | 5426.67i | −0.874174 | − | 0.574212i | ||||
\(448\) | −10469.7 | + | 1073.40i | −1.10412 | + | 0.113200i | ||||
\(449\) | 11342.5i | 1.19217i | 0.802922 | + | 0.596084i | \(0.203278\pi\) | ||||
−0.802922 | + | 0.596084i | \(0.796722\pi\) | |||||||
\(450\) | 3130.75 | − | 1354.87i | 0.327967 | − | 0.141932i | ||||
\(451\) | −9310.40 | + | 5375.36i | −0.972084 | + | 0.561233i | ||||
\(452\) | 23383.4 | + | 13500.4i | 2.43333 | + | 1.40488i | ||||
\(453\) | −7978.22 | − | 459.937i | −0.827482 | − | 0.0477036i | ||||
\(454\) | −214.288 | − | 123.719i | −0.0221520 | − | 0.0127895i | ||||
\(455\) | 367.389 | + | 3583.41i | 0.0378538 | + | 0.369215i | ||||
\(456\) | 4959.05 | + | 285.885i | 0.509274 | + | 0.0293592i | ||||
\(457\) | −7267.52 | −0.743895 | −0.371948 | − | 0.928254i | \(-0.621310\pi\) | ||||
−0.371948 | + | 0.928254i | \(0.621310\pi\) | |||||||
\(458\) | −8651.69 | − | 14985.2i | −0.882679 | − | 1.52884i | ||||
\(459\) | −1728.95 | − | 4724.11i | −0.175818 | − | 0.480398i | ||||
\(460\) | 9382.73 | + | 5417.12i | 0.951027 | + | 0.549075i | ||||
\(461\) | −6216.19 | − | 10766.8i | −0.628019 | − | 1.08776i | −0.987949 | − | 0.154782i | \(-0.950533\pi\) |
0.359930 | − | 0.932979i | \(-0.382801\pi\) | |||||||
\(462\) | −32034.9 | + | 1429.15i | −3.22597 | + | 0.143918i | ||||
\(463\) | 1444.49 | − | 2501.94i | 0.144992 | − | 0.251134i | −0.784378 | − | 0.620283i | \(-0.787018\pi\) |
0.929370 | + | 0.369150i | \(0.120351\pi\) | |||||||
\(464\) | −32738.9 | + | 18901.8i | −3.27557 | + | 1.89115i | ||||
\(465\) | −7175.34 | − | 4713.21i | −0.715588 | − | 0.470043i | ||||
\(466\) | −12154.8 | + | 21052.7i | −1.20828 | + | 2.09280i | ||||
\(467\) | −1313.23 | + | 2274.59i | −0.130127 | + | 0.225386i | −0.923725 | − | 0.383055i | \(-0.874872\pi\) |
0.793598 | + | 0.608442i | \(0.208205\pi\) | |||||||
\(468\) | −7672.85 | + | 3320.53i | −0.757858 | + | 0.327973i | ||||
\(469\) | 6189.11 | − | 634.537i | 0.609353 | − | 0.0624738i | ||||
\(470\) | 384.222 | − | 221.831i | 0.0377082 | − | 0.0217708i | ||||
\(471\) | 13508.8 | − | 6794.38i | 1.32155 | − | 0.664689i | ||||
\(472\) | 7460.62i | 0.727548i | ||||||||
\(473\) | 4820.33i | 0.468581i | ||||||||
\(474\) | −9966.45 | + | 5012.73i | −0.965768 | + | 0.485744i | ||||
\(475\) | 333.174 | − | 192.358i | 0.0321833 | − | 0.0185810i | ||||
\(476\) | 7561.77 | + | 10463.9i | 0.728136 | + | 1.00759i | ||||
\(477\) | −119.279 | + | 1031.09i | −0.0114495 | + | 0.0989737i | ||||
\(478\) | −11496.5 | + | 19912.5i | −1.10008 | + | 1.90539i | ||||
\(479\) | 380.831 | − | 659.619i | 0.0363270 | − | 0.0629202i | −0.847290 | − | 0.531130i | \(-0.821768\pi\) |
0.883617 | + | 0.468210i | \(0.155101\pi\) | |||||||
\(480\) | −18584.4 | − | 12207.4i | −1.76720 | − | 1.16081i | ||||
\(481\) | −498.689 | + | 287.918i | −0.0472729 | + | 0.0272930i | ||||
\(482\) | 2910.78 | − | 5041.62i | 0.275068 | − | 0.476431i | ||||
\(483\) | −3897.51 | − | 2024.22i | −0.367170 | − | 0.190694i | ||||
\(484\) | −26393.7 | − | 45715.2i | −2.47874 | − | 4.29331i | ||||
\(485\) | 5289.34 | + | 3053.80i | 0.495210 | + | 0.285909i | ||||
\(486\) | −13659.8 | − | 14392.9i | −1.27494 | − | 1.34337i | ||||
\(487\) | −8677.57 | − | 15030.0i | −0.807430 | − | 1.39851i | −0.914639 | − | 0.404273i | \(-0.867525\pi\) |
0.107209 | − | 0.994237i | \(-0.465809\pi\) | |||||||
\(488\) | −30855.0 | −2.86218 | ||||||||
\(489\) | 11761.7 | + | 678.052i | 1.08770 | + | 0.0627046i | ||||
\(490\) | 16380.2 | − | 14598.1i | 1.51017 | − | 1.34587i | ||||
\(491\) | 17290.8 | + | 9982.86i | 1.58925 | + | 0.917557i | 0.993430 | + | 0.114442i | \(0.0365081\pi\) |
0.595825 | + | 0.803114i | \(0.296825\pi\) | |||||||
\(492\) | 17044.7 | + | 982.609i | 1.56186 | + | 0.0900395i | ||||
\(493\) | 7410.02 | + | 4278.18i | 0.676938 | + | 0.390830i | ||||
\(494\) | −1152.55 | + | 665.427i | −0.104971 | + | 0.0606052i | ||||
\(495\) | −16837.7 | − | 12504.2i | −1.52888 | − | 1.13540i | ||||
\(496\) | 21433.8i | 1.94034i | ||||||||
\(497\) | 1353.26 | + | 13199.3i | 0.122137 | + | 1.19129i | ||||
\(498\) | −6173.29 | − | 4055.00i | −0.555485 | − | 0.364877i | ||||
\(499\) | 770.803 | + | 1335.07i | 0.0691500 | + | 0.119771i | 0.898527 | − | 0.438917i | \(-0.144638\pi\) |
−0.829377 | + | 0.558689i | \(0.811305\pi\) | |||||||
\(500\) | 23949.3 | 2.14209 | ||||||||
\(501\) | 6967.92 | + | 401.694i | 0.621364 | + | 0.0358211i | ||||
\(502\) | 6613.43i | 0.587992i | ||||||||
\(503\) | 578.894 | 0.0513153 | 0.0256577 | − | 0.999671i | \(-0.491832\pi\) | ||||
0.0256577 | + | 0.999671i | \(0.491832\pi\) | |||||||
\(504\) | 25756.8 | + | 15320.6i | 2.27639 | + | 1.35404i | ||||
\(505\) | −22433.7 | −1.97681 | ||||||||
\(506\) | − | 15206.9i | − | 1.33603i | ||||||
\(507\) | −5543.79 | + | 8439.81i | −0.485618 | + | 0.739300i | ||||
\(508\) | 7854.82 | 0.686026 | ||||||||
\(509\) | −4581.00 | − | 7934.52i | −0.398918 | − | 0.690946i | 0.594675 | − | 0.803966i | \(-0.297281\pi\) |
−0.993593 | + | 0.113021i | \(0.963947\pi\) | |||||||
\(510\) | −685.946 | + | 11898.7i | −0.0595573 | + | 1.03310i | ||||
\(511\) | 12573.9 | − | 9086.56i | 1.08853 | − | 0.786626i | ||||
\(512\) | − | 20442.2i | − | 1.76451i | ||||||
\(513\) | −1716.81 | − | 1435.39i | −0.147757 | − | 0.123536i | ||||
\(514\) | 24234.3 | − | 13991.7i | 2.07963 | − | 1.20067i | ||||
\(515\) | 7114.11 | + | 4107.33i | 0.608709 | + | 0.351438i | ||||
\(516\) | 4202.73 | − | 6398.19i | 0.358556 | − | 0.545862i | ||||
\(517\) | −382.071 | − | 220.589i | −0.0325019 | − | 0.0187650i | ||||
\(518\) | 3200.57 | + | 1434.78i | 0.271477 | + | 0.121700i | ||||
\(519\) | −2200.57 | − | 4375.22i | −0.186116 | − | 0.370040i | ||||
\(520\) | 11656.8 | 0.983049 | ||||||||
\(521\) | −6093.28 | − | 10553.9i | −0.512382 | − | 0.887473i | −0.999897 | − | 0.0143576i | \(-0.995430\pi\) |
0.487514 | − | 0.873115i | \(-0.337904\pi\) | |||||||
\(522\) | 33527.0 | + | 3878.49i | 2.81118 | + | 0.325205i | ||||
\(523\) | −8988.68 | − | 5189.62i | −0.751525 | − | 0.433893i | 0.0747195 | − | 0.997205i | \(-0.476194\pi\) |
−0.826245 | + | 0.563311i | \(0.809527\pi\) | |||||||
\(524\) | −26577.6 | − | 46033.8i | −2.21574 | − | 3.83778i | ||||
\(525\) | 2318.78 | − | 103.446i | 0.192762 | − | 0.00859951i | ||||
\(526\) | 2722.10 | − | 4714.81i | 0.225644 | − | 0.390828i | ||||
\(527\) | 4201.32 | − | 2425.63i | 0.347272 | − | 0.200498i | ||||
\(528\) | −3013.67 | + | 52276.2i | −0.248396 | + | 4.30877i | ||||
\(529\) | −5042.14 | + | 8733.24i | −0.414411 | + | 0.717781i | ||||
\(530\) | 1229.58 | − | 2129.69i | 0.100773 | − | 0.174543i | ||||
\(531\) | 2003.90 | − | 2698.37i | 0.163770 | − | 0.220526i | ||||
\(532\) | 5240.54 | + | 2349.28i | 0.427079 | + | 0.191455i | ||||
\(533\) | −2331.28 | + | 1345.97i | −0.189454 | + | 0.109381i | ||||
\(534\) | 2248.01 | − | 38994.7i | 0.182174 | − | 3.16005i | ||||
\(535\) | 11812.8i | 0.954602i | ||||||||
\(536\) | − | 20133.1i | − | 1.62242i | ||||||
\(537\) | −315.857 | − | 207.475i | −0.0253822 | − | 0.0166726i | ||||
\(538\) | −19222.6 | + | 11098.2i | −1.54042 | + | 0.889362i | ||||
\(539\) | −20715.8 | − | 6848.05i | −1.65546 | − | 0.547248i | ||||
\(540\) | 11447.1 | + | 31277.6i | 0.912230 | + | 2.49254i | ||||
\(541\) | 2598.10 | − | 4500.05i | 0.206472 | − | 0.357619i | −0.744129 | − | 0.668036i | \(-0.767135\pi\) |
0.950601 | + | 0.310417i | \(0.100469\pi\) | |||||||
\(542\) | −18090.2 | + | 31333.1i | −1.43365 | + | 2.48316i | ||||
\(543\) | −8635.57 | + | 4343.36i | −0.682482 | + | 0.343262i | ||||
\(544\) | 10881.5 | − | 6282.46i | 0.857615 | − | 0.495144i | ||||
\(545\) | −9156.15 | + | 15858.9i | −0.719645 | + | 1.24646i | ||||
\(546\) | −8021.40 | + | 357.852i | −0.628726 | + | 0.0280488i | ||||
\(547\) | 10154.0 | + | 17587.3i | 0.793703 | + | 1.37473i | 0.923660 | + | 0.383214i | \(0.125183\pi\) |
−0.129957 | + | 0.991520i | \(0.541484\pi\) | |||||||
\(548\) | −14445.3 | − | 8340.01i | −1.12605 | − | 0.650123i | ||||
\(549\) | 11159.7 | + | 8287.58i | 0.867551 | + | 0.644272i | ||||
\(550\) | 4018.46 | + | 6960.17i | 0.311541 | + | 0.539605i | ||||
\(551\) | 3806.24 | 0.294285 | ||||||||
\(552\) | −7802.62 | + | 11878.6i | −0.601633 | + | 0.915920i | ||||
\(553\) | −7551.03 | + | 774.168i | −0.580655 | + | 0.0595316i | ||||
\(554\) | 11125.8 | + | 6423.51i | 0.853235 | + | 0.492615i | ||||
\(555\) | 1030.76 | + | 2049.39i | 0.0788349 | + | 0.156742i | ||||
\(556\) | 38925.8 | + | 22473.8i | 2.96910 | + | 1.71421i | ||||
\(557\) | 8891.43 | − | 5133.47i | 0.676377 | − | 0.390507i | −0.122111 | − | 0.992516i | \(-0.538967\pi\) |
0.798489 | + | 0.602010i | \(0.205633\pi\) | |||||||
\(558\) | 11408.9 | − | 15362.8i | 0.865554 | − | 1.16552i | ||||
\(559\) | 1206.99i | 0.0913241i | ||||||||
\(560\) | −20985.4 | − | 29039.5i | −1.58357 | − | 2.19133i | ||||
\(561\) | 10587.9 | − | 5325.29i | 0.796829 | − | 0.400774i | ||||
\(562\) | −21788.2 | − | 37738.2i | −1.63537 | − | 2.83254i | ||||
\(563\) | 8350.36 | 0.625090 | 0.312545 | − | 0.949903i | \(-0.398818\pi\) | ||||
0.312545 | + | 0.949903i | \(0.398818\pi\) | |||||||
\(564\) | 314.810 | + | 625.913i | 0.0235034 | + | 0.0467300i | ||||
\(565\) | 16960.1i | 1.26286i | ||||||||
\(566\) | 35892.6 | 2.66551 | ||||||||
\(567\) | −5200.70 | − | 12459.4i | −0.385201 | − | 0.922833i | ||||
\(568\) | 42937.3 | 3.17185 | ||||||||
\(569\) | 3165.00i | 0.233188i | 0.993180 | + | 0.116594i | \(0.0371975\pi\) | ||||
−0.993180 | + | 0.116594i | \(0.962802\pi\) | |||||||
\(570\) | 2382.26 | + | 4736.47i | 0.175056 | + | 0.348051i | ||||
\(571\) | −2957.30 | −0.216741 | −0.108371 | − | 0.994111i | \(-0.534563\pi\) | ||||
−0.108371 | + | 0.994111i | \(0.534563\pi\) | |||||||
\(572\) | −9848.45 | − | 17058.0i | −0.719902 | − | 1.24691i | ||||
\(573\) | −18.9474 | + | 9.52982i | −0.00138140 | + | 0.000694788i | ||||
\(574\) | 14962.1 | + | 6707.35i | 1.08799 | + | 0.487734i | ||||
\(575\) | 1100.72i | 0.0798319i | ||||||||
\(576\) | 9147.82 | − | 12318.1i | 0.661735 | − | 0.891066i | ||||
\(577\) | −21694.0 | + | 12525.0i | −1.56522 | + | 0.903681i | −0.568507 | + | 0.822678i | \(0.692479\pi\) |
−0.996714 | + | 0.0810022i | \(0.974188\pi\) | |||||||
\(578\) | 16455.6 | + | 9500.63i | 1.18419 | + | 0.683692i | ||||
\(579\) | 10279.8 | + | 20438.5i | 0.737844 | + | 1.46700i | ||||
\(580\) | −49060.5 | − | 28325.1i | −3.51229 | − | 2.02782i | ||||
\(581\) | −2943.49 | − | 4073.18i | −0.210183 | − | 0.290850i | ||||
\(582\) | −7474.27 | + | 11378.8i | −0.532334 | + | 0.810420i | ||||
\(583\) | −2445.39 | −0.173718 | ||||||||
\(584\) | −25101.1 | − | 43476.4i | −1.77858 | − | 3.08059i | ||||
\(585\) | −4216.07 | − | 3130.99i | −0.297971 | − | 0.221283i | ||||
\(586\) | 3527.11 | + | 2036.38i | 0.248641 | + | 0.143553i | ||||
\(587\) | 6544.89 | + | 11336.1i | 0.460198 | + | 0.797087i | 0.998970 | − | 0.0453646i | \(-0.0144450\pi\) |
−0.538772 | + | 0.842452i | \(0.681112\pi\) | |||||||
\(588\) | 21526.1 | + | 27151.2i | 1.50973 | + | 1.90425i | ||||
\(589\) | 1079.03 | − | 1868.93i | 0.0754847 | − | 0.130743i | ||||
\(590\) | −6896.22 | + | 3981.54i | −0.481209 | + | 0.277826i | ||||
\(591\) | −1809.98 | + | 910.350i | −0.125978 | + | 0.0633618i | ||||
\(592\) | 2863.72 | − | 4960.11i | 0.198814 | − | 0.344357i | ||||
\(593\) | 3549.51 | − | 6147.93i | 0.245803 | − | 0.425743i | −0.716554 | − | 0.697531i | \(-0.754282\pi\) |
0.962357 | + | 0.271789i | \(0.0876151\pi\) | |||||||
\(594\) | 29986.0 | − | 35865.2i | 2.07128 | − | 2.47738i | ||||
\(595\) | −3317.25 | + | 7399.79i | −0.228561 | + | 0.509852i | ||||
\(596\) | −32026.9 | + | 18490.8i | −2.20113 | + | 1.27082i | ||||
\(597\) | −4576.79 | − | 3006.32i | −0.313761 | − | 0.206098i | ||||
\(598\) | − | 3807.75i | − | 0.260385i | ||||||
\(599\) | 16385.4i | 1.11768i | 0.829276 | + | 0.558840i | \(0.188753\pi\) | ||||
−0.829276 | + | 0.558840i | \(0.811247\pi\) | |||||||
\(600\) | 432.291 | − | 7498.67i | 0.0294137 | − | 0.510220i | ||||
\(601\) | 1449.23 | − | 836.712i | 0.0983615 | − | 0.0567890i | −0.450012 | − | 0.893022i | \(-0.648580\pi\) |
0.548374 | + | 0.836233i | \(0.315247\pi\) | |||||||
\(602\) | 5958.77 | − | 4306.11i | 0.403424 | − | 0.291535i | ||||
\(603\) | −5407.70 | + | 7281.80i | −0.365205 | + | 0.491771i | ||||
\(604\) | −14949.7 | + | 25893.6i | −1.00711 | + | 1.74436i | ||||
\(605\) | 16578.7 | − | 28715.1i | 1.11408 | − | 1.92964i | ||||
\(606\) | 2877.98 | − | 49922.3i | 0.192920 | − | 3.34646i | ||||
\(607\) | 8214.09 | − | 4742.41i | 0.549258 | − | 0.317114i | −0.199565 | − | 0.979885i | \(-0.563953\pi\) |
0.748823 | + | 0.662770i | \(0.230619\pi\) | |||||||
\(608\) | 2794.71 | − | 4840.58i | 0.186415 | − | 0.322881i | ||||
\(609\) | 20379.4 | + | 10584.2i | 1.35602 | + | 0.704262i | ||||
\(610\) | −16466.5 | − | 28520.9i | −1.09297 | − | 1.89308i | ||||
\(611\) | −95.6688 | − | 55.2344i | −0.00633444 | − | 0.00365719i | ||||
\(612\) | −18696.7 | − | 2162.88i | −1.23491 | − | 0.142858i | ||||
\(613\) | 791.346 | + | 1370.65i | 0.0521405 | + | 0.0903100i | 0.890918 | − | 0.454165i | \(-0.150062\pi\) |
−0.838777 | + | 0.544475i | \(0.816729\pi\) | |||||||
\(614\) | 28823.4 | 1.89449 | ||||||||
\(615\) | 4818.62 | + | 9580.51i | 0.315944 | + | 0.628168i | ||||
\(616\) | −28882.1 | + | 64427.2i | −1.88911 | + | 4.21404i | ||||
\(617\) | −19948.8 | − | 11517.5i | −1.30164 | − | 0.751500i | −0.320952 | − | 0.947095i | \(-0.604003\pi\) |
−0.980685 | + | 0.195595i | \(0.937336\pi\) | |||||||
\(618\) | −10052.8 | + | 15304.3i | −0.654342 | + | 0.996164i | ||||
\(619\) | 978.859 | + | 565.145i | 0.0635601 | + | 0.0366964i | 0.531443 | − | 0.847094i | \(-0.321650\pi\) |
−0.467883 | + | 0.883790i | \(0.654983\pi\) | |||||||
\(620\) | −27816.3 | + | 16059.7i | −1.80182 | + | 1.04028i | ||||
\(621\) | 6012.64 | − | 2200.53i | 0.388533 | − | 0.142197i | ||||
\(622\) | − | 11249.5i | − | 0.725180i | ||||||
\(623\) | 10871.4 | − | 24250.9i | 0.699124 | − | 1.55953i | ||||
\(624\) | −754.609 | + | 13089.7i | −0.0484111 | + | 0.839756i | ||||
\(625\) | 9029.08 | + | 15638.8i | 0.577861 | + | 1.00088i | ||||
\(626\) | −10318.9 | −0.658830 | ||||||||
\(627\) | 2894.48 | − | 4406.52i | 0.184361 | − | 0.280669i | ||||
\(628\) | − | 56574.5i | − | 3.59485i | ||||||
\(629\) | −1296.33 | −0.0821750 | ||||||||
\(630\) | −415.910 | + | 31984.5i | −0.0263020 | + | 2.02269i | ||||
\(631\) | 6214.42 | 0.392064 | 0.196032 | − | 0.980598i | \(-0.437194\pi\) | ||||
0.196032 | + | 0.980598i | \(0.437194\pi\) | |||||||
\(632\) | 24563.5i | 1.54602i | ||||||||
\(633\) | 5824.73 | + | 335.790i | 0.365738 | + | 0.0210845i | ||||
\(634\) | 7601.06 | 0.476146 | ||||||||
\(635\) | 2466.93 | + | 4272.84i | 0.154169 | + | 0.267028i | ||||
\(636\) | 3245.85 | + | 2132.07i | 0.202368 | + | 0.132928i | ||||
\(637\) | −5187.14 | − | 1714.72i | −0.322640 | − | 0.106656i | ||||
\(638\) | 79514.3i | 4.93417i | ||||||||
\(639\) | −15529.7 | − | 11532.9i | −0.961416 | − | 0.713979i | ||||
\(640\) | −1834.55 | + | 1059.18i | −0.113308 | + | 0.0654184i | ||||
\(641\) | −14285.1 | − | 8247.49i | −0.880228 | − | 0.508200i | −0.00949468 | − | 0.999955i | \(-0.503022\pi\) |
−0.870734 | + | 0.491755i | \(0.836356\pi\) | |||||||
\(642\) | −26287.3 | − | 1515.44i | −1.61601 | − | 0.0931615i | ||||
\(643\) | 11470.6 | + | 6622.54i | 0.703507 | + | 0.406170i | 0.808652 | − | 0.588287i | \(-0.200197\pi\) |
−0.105145 | + | 0.994457i | \(0.533531\pi\) | |||||||
\(644\) | −13318.0 | + | 9624.28i | −0.814912 | + | 0.588897i | ||||
\(645\) | 4800.40 | + | 276.739i | 0.293047 | + | 0.0168939i | ||||
\(646\) | −2996.04 | −0.182473 | ||||||||
\(647\) | 5765.87 | + | 9986.78i | 0.350355 | + | 0.606833i | 0.986312 | − | 0.164892i | \(-0.0527275\pi\) |
−0.635956 | + | 0.771725i | \(0.719394\pi\) | |||||||
\(648\) | −41825.3 | + | 12629.7i | −2.53557 | + | 0.765652i | ||||
\(649\) | 6857.61 | + | 3959.24i | 0.414768 | + | 0.239467i | ||||
\(650\) | 1006.20 | + | 1742.79i | 0.0607177 | + | 0.105166i | ||||
\(651\) | 10974.4 | − | 7006.10i | 0.660706 | − | 0.421799i | ||||
\(652\) | 22039.2 | − | 38173.0i | 1.32381 | − | 2.29290i | ||||
\(653\) | 11889.2 | − | 6864.22i | 0.712495 | − | 0.411359i | −0.0994890 | − | 0.995039i | \(-0.531721\pi\) |
0.811984 | + | 0.583679i | \(0.198387\pi\) | |||||||
\(654\) | −34116.7 | − | 22409.9i | −2.03986 | − | 1.33991i | ||||
\(655\) | 16694.2 | − | 28915.3i | 0.995874 | − | 1.72491i | ||||
\(656\) | 13387.4 | − | 23187.6i | 0.796782 | − | 1.38007i | ||||
\(657\) | −2599.01 | + | 22466.7i | −0.154333 | + | 1.33411i | ||||
\(658\) | 68.6264 | + | 669.363i | 0.00406586 | + | 0.0396573i | ||||
\(659\) | −104.852 | + | 60.5365i | −0.00619797 | + | 0.00357840i | −0.503096 | − | 0.864231i | \(-0.667806\pi\) |
0.496898 | + | 0.867809i | \(0.334472\pi\) | |||||||
\(660\) | −70100.7 | + | 35257.9i | −4.13434 | + | 2.07941i | ||||
\(661\) | − | 27841.9i | − | 1.63831i | −0.573571 | − | 0.819156i | \(-0.694442\pi\) | ||
0.573571 | − | 0.819156i | \(-0.305558\pi\) | |||||||
\(662\) | − | 6227.68i | − | 0.365628i | ||||||
\(663\) | 2651.16 | − | 1333.43i | 0.155298 | − | 0.0781087i | ||||
\(664\) | −14083.7 | + | 8131.23i | −0.823123 | + | 0.475230i | ||||
\(665\) | 367.917 | + | 3588.56i | 0.0214544 | + | 0.209261i | ||||
\(666\) | −4692.79 | + | 2030.87i | −0.273036 | + | 0.118160i | ||||
\(667\) | −5445.07 | + | 9431.14i | −0.316093 | + | 0.547489i | ||||
\(668\) | 13056.5 | − | 22614.6i | 0.756247 | − | 1.30986i | ||||
\(669\) | −19311.4 | − | 12684.9i | −1.11602 | − | 0.733074i | ||||
\(670\) | 18610.1 | − | 10744.5i | 1.07309 | − | 0.619548i | ||||
\(671\) | −16374.3 | + | 28361.2i | −0.942062 | + | 1.63170i | ||||
\(672\) | 28424.0 | − | 18146.0i | 1.63166 | − | 1.04166i | ||||
\(673\) | 10610.3 | + | 18377.6i | 0.607724 | + | 1.05261i | 0.991615 | + | 0.129230i | \(0.0412507\pi\) |
−0.383890 | + | 0.923379i | \(0.625416\pi\) | |||||||
\(674\) | 28841.0 | + | 16651.4i | 1.64824 | + | 0.951613i | ||||
\(675\) | −2170.47 | + | 2596.02i | −0.123765 | + | 0.148031i | ||||
\(676\) | 18889.8 | + | 32718.2i | 1.07475 | + | 1.86152i | ||||
\(677\) | −10357.6 | −0.587997 | −0.293999 | − | 0.955806i | \(-0.594986\pi\) | ||||
−0.293999 | + | 0.955806i | \(0.594986\pi\) | |||||||
\(678\) | −37741.7 | − | 2175.78i | −2.13785 | − | 0.123245i | ||||
\(679\) | −7507.79 | + | 5425.51i | −0.424333 | + | 0.306645i | ||||
\(680\) | 22726.2 | + | 13121.0i | 1.28163 | + | 0.739952i | ||||
\(681\) | 245.036 | + | 14.1261i | 0.0137882 | + | 0.000794878i | ||||
\(682\) | 39042.9 | + | 22541.4i | 2.19213 | + | 1.26562i | ||||
\(683\) | 5821.72 | − | 3361.17i | 0.326152 | − | 0.188304i | −0.327979 | − | 0.944685i | \(-0.606368\pi\) |
0.654131 | + | 0.756381i | \(0.273034\pi\) | |||||||
\(684\) | −7683.88 | + | 3325.30i | −0.429533 | + | 0.185886i | ||||
\(685\) | − | 10477.2i | − | 0.584401i | ||||||
\(686\) | 10040.5 | + | 31725.8i | 0.558816 | + | 1.76574i | ||||
\(687\) | 14345.7 | + | 9423.17i | 0.796687 | + | 0.523314i | ||||
\(688\) | −6002.53 | − | 10396.7i | −0.332623 | − | 0.576119i | ||||
\(689\) | −612.314 | −0.0338567 | ||||||||
\(690\) | −15144.1 | − | 873.042i | −0.835544 | − | 0.0481683i | ||||
\(691\) | 993.374i | 0.0546884i | 0.999626 | + | 0.0273442i | \(0.00870502\pi\) | ||||
−0.999626 | + | 0.0273442i | \(0.991295\pi\) | |||||||
\(692\) | −18323.4 | −1.00657 | ||||||||
\(693\) | 27751.1 | − | 15544.6i | 1.52118 | − | 0.852076i | ||||
\(694\) | −58287.4 | −3.18812 | ||||||||
\(695\) | 28233.0i | 1.54092i | ||||||||
\(696\) | 40798.4 | − | 62111.1i | 2.22193 | − | 3.38264i | ||||
\(697\) | −6060.11 | −0.329330 | ||||||||
\(698\) | 7011.24 | + | 12143.8i | 0.380200 | + | 0.658525i | ||||
\(699\) | 1387.81 | − | 24073.5i | 0.0750958 | − | 1.30264i | ||||
\(700\) | 3552.39 | − | 7924.31i | 0.191811 | − | 0.427872i | ||||
\(701\) | 3345.02i | 0.180228i | 0.995931 | + | 0.0901138i | \(0.0287231\pi\) | ||||
−0.995931 | + | 0.0901138i | \(0.971277\pi\) | |||||||
\(702\) | 7508.35 | − | 8980.47i | 0.403682 | − | 0.482829i | ||||
\(703\) | −499.406 | + | 288.332i | −0.0267930 | + | 0.0154689i | ||||
\(704\) | 31305.0 | + | 18074.0i | 1.67593 | + | 0.967597i | ||||
\(705\) | −241.612 | + | 367.827i | −0.0129073 | + | 0.0196499i | ||||
\(706\) | 34155.1 | + | 19719.5i | 1.82074 | + | 1.05121i | ||||
\(707\) | 13917.9 | − | 31046.8i | 0.740365 | − | 1.65153i | ||||
\(708\) | −5650.37 | − | 11234.2i | −0.299935 | − | 0.596339i | ||||
\(709\) | −5556.67 | −0.294337 | −0.147169 | − | 0.989111i | \(-0.547016\pi\) | ||||
−0.147169 | + | 0.989111i | \(0.547016\pi\) | |||||||
\(710\) | 22914.5 | + | 39689.2i | 1.21122 | + | 2.09790i | ||||
\(711\) | 6597.68 | − | 8884.17i | 0.348006 | − | 0.468611i | ||||
\(712\) | −74479.3 | − | 43000.6i | −3.92027 | − | 2.26337i | ||||
\(713\) | 3087.24 | + | 5347.25i | 0.162157 | + | 0.280864i | ||||
\(714\) | −16041.4 | − | 8331.27i | −0.840804 | − | 0.436681i | ||||
\(715\) | 6186.11 | − | 10714.7i | 0.323563 | − | 0.560427i | ||||
\(716\) | −1224.47 | + | 706.947i | −0.0639113 | + | 0.0368992i | ||||
\(717\) | 1312.65 | − | 22769.7i | 0.0683708 | − | 1.18598i | ||||
\(718\) | −27248.6 | + | 47196.0i | −1.41631 | + | 2.45312i | ||||
\(719\) | 11984.2 | − | 20757.2i | 0.621605 | − | 1.07665i | −0.367582 | − | 0.929991i | \(-0.619814\pi\) |
0.989187 | − | 0.146660i | \(-0.0468524\pi\) | |||||||
\(720\) | 51887.0 | + | 6002.42i | 2.68572 | + | 0.310690i | ||||
\(721\) | −10097.9 | + | 7297.25i | −0.521588 | + | 0.376926i | ||||
\(722\) | 29962.3 | − | 17298.7i | 1.54443 | − | 0.891679i | ||||
\(723\) | −332.349 | + | 5765.04i | −0.0170957 | + | 0.296548i | ||||
\(724\) | 36165.6i | 1.85647i | ||||||||
\(725\) | − | 5755.47i | − | 0.294832i | ||||||
\(726\) | 61773.7 | + | 40576.8i | 3.15790 | + | 2.07430i | ||||
\(727\) | −28778.8 | + | 16615.4i | −1.46815 | + | 0.847637i | −0.999363 | − | 0.0356749i | \(-0.988642\pi\) |
−0.468786 | + | 0.883312i | \(0.655309\pi\) | |||||||
\(728\) | −7231.94 | + | 16132.3i | −0.368178 | + | 0.821294i | ||||
\(729\) | 18519.8 | + | 6666.21i | 0.940902 | + | 0.338678i | ||||
\(730\) | 26791.6 | − | 46404.5i | 1.35836 | − | 2.35275i | ||||
\(731\) | −1358.59 | + | 2353.15i | −0.0687407 | + | 0.119062i | ||||
\(732\) | 46461.6 | − | 23368.4i | 2.34600 | − | 1.17995i | ||||
\(733\) | −19526.7 | + | 11273.7i | −0.983950 | + | 0.568084i | −0.903460 | − | 0.428672i | \(-0.858982\pi\) |
−0.0804895 | + | 0.996755i | \(0.525648\pi\) | |||||||
\(734\) | 31868.7 | − | 55198.2i | 1.60258 | − | 2.77576i | ||||
\(735\) | −8009.05 | + | 20237.0i | −0.401929 | + | 1.01558i | ||||
\(736\) | 7996.04 | + | 13849.5i | 0.400459 | + | 0.693616i | ||||
\(737\) | −18505.9 | − | 10684.4i | −0.924929 | − | 0.534008i | ||||
\(738\) | −21938.0 | + | 9493.95i | −1.09424 | + | 0.473546i | ||||
\(739\) | 10873.2 | + | 18833.0i | 0.541242 | + | 0.937458i | 0.998833 | + | 0.0482957i | \(0.0153790\pi\) |
−0.457591 | + | 0.889163i | \(0.651288\pi\) | |||||||
\(740\) | 8582.80 | 0.426365 | ||||||||
\(741\) | 724.763 | − | 1103.37i | 0.0359310 | − | 0.0547009i | ||||
\(742\) | 2184.52 | + | 3022.93i | 0.108081 | + | 0.149562i | ||||
\(743\) | −22091.4 | − | 12754.5i | −1.09079 | − | 0.629766i | −0.157000 | − | 0.987599i | \(-0.550182\pi\) |
−0.933786 | + | 0.357833i | \(0.883516\pi\) | |||||||
\(744\) | −18931.7 | − | 37640.6i | −0.932891 | − | 1.85480i | ||||
\(745\) | −20117.1 | − | 11614.6i | −0.989307 | − | 0.571176i | ||||
\(746\) | −10056.7 | + | 5806.22i | −0.493567 | + | 0.284961i | ||||
\(747\) | 7277.85 | + | 841.920i | 0.356469 | + | 0.0412373i | ||||
\(748\) | − | 44341.9i | − | 2.16751i | ||||||
\(749\) | −16348.1 | − | 7328.70i | −0.797527 | − | 0.357523i | ||||
\(750\) | −29956.2 | + | 15066.8i | −1.45846 | + | 0.733548i | ||||
\(751\) | −16281.1 | − | 28199.6i | −0.791084 | − | 1.37020i | −0.925296 | − | 0.379245i | \(-0.876184\pi\) |
0.134212 | − | 0.990953i | \(-0.457150\pi\) | |||||||
\(752\) | 1098.76 | 0.0532812 | ||||||||
\(753\) | −2947.63 | − | 5860.56i | −0.142653 | − | 0.283626i | ||||
\(754\) | 19910.0i | 0.961644i | ||||||||
\(755\) | −18780.7 | −0.905297 | ||||||||
\(756\) | −50387.9 | − | 3562.71i | −2.42406 | − | 0.171395i | ||||
\(757\) | −922.082 | −0.0442717 | −0.0221358 | − | 0.999755i | \(-0.507047\pi\) | ||||
−0.0221358 | + | 0.999755i | \(0.507047\pi\) | |||||||
\(758\) | − | 15484.1i | − | 0.741965i | ||||||
\(759\) | 6777.80 | + | 13475.8i | 0.324135 | + | 0.644454i | ||||
\(760\) | 11673.6 | 0.557165 | ||||||||
\(761\) | −5138.37 | − | 8899.92i | −0.244764 | − | 0.423944i | 0.717301 | − | 0.696763i | \(-0.245377\pi\) |
−0.962065 | + | 0.272819i | \(0.912044\pi\) | |||||||
\(762\) | −9824.95 | + | 4941.57i | −0.467087 | + | 0.234927i | ||||
\(763\) | −16267.2 | − | 22510.4i | −0.771837 | − | 1.06806i | ||||
\(764\) | 79.3516i | 0.00375764i | ||||||||
\(765\) | −4695.42 | − | 10849.8i | −0.221913 | − | 0.512780i | ||||
\(766\) | 33794.4 | − | 19511.2i | 1.59405 | − | 0.920324i | ||||
\(767\) | 1717.11 | + | 991.376i | 0.0808362 | + | 0.0466708i | ||||
\(768\) | 8492.64 | + | 16885.3i | 0.399026 | + | 0.793353i | ||||
\(769\) | 30344.0 | + | 17519.1i | 1.42293 | + | 0.821528i | 0.996548 | − | 0.0830156i | \(-0.0264551\pi\) |
0.426380 | + | 0.904544i | \(0.359788\pi\) | |||||||
\(770\) | −74967.0 | + | 7685.98i | −3.50860 | + | 0.359719i | ||||
\(771\) | −15239.3 | + | 23200.2i | −0.711842 | + | 1.08370i | ||||
\(772\) | 85596.0 | 3.99050 | ||||||||
\(773\) | −4927.07 | − | 8533.94i | −0.229256 | − | 0.397082i | 0.728332 | − | 0.685224i | \(-0.240296\pi\) |
−0.957588 | + | 0.288142i | \(0.906962\pi\) | |||||||
\(774\) | −1231.67 | + | 10647.0i | −0.0571982 | + | 0.494441i | ||||
\(775\) | −2826.04 | − | 1631.61i | −0.130986 | − | 0.0756249i | ||||
\(776\) | 14987.7 | + | 25959.4i | 0.693333 | + | 1.20089i | ||||
\(777\) | −3475.70 | + | 155.059i | −0.160476 | + | 0.00715919i | ||||
\(778\) | −15790.4 | + | 27349.9i | −0.727654 | + | 1.26033i | ||||
\(779\) | −2334.63 | + | 1347.90i | −0.107377 | + | 0.0619943i | ||||
\(780\) | −17552.9 | + | 8828.42i | −0.805762 | + | 0.405267i | ||||
\(781\) | 22786.2 | − | 39466.9i | 1.04399 | − | 1.80824i | ||||
\(782\) | 4286.03 | − | 7423.62i | 0.195995 | − | 0.339473i | ||||
\(783\) | −31439.0 | + | 11506.2i | −1.43491 | + | 0.525155i | ||||
\(784\) | 53208.2 | − | 11026.2i | 2.42384 | − | 0.502288i | ||||
\(785\) | 30775.2 | − | 17768.1i | 1.39925 | − | 0.807860i | ||||
\(786\) | 62204.3 | + | 40859.6i | 2.82284 | + | 1.85422i | ||||
\(787\) | 21139.5i | 0.957485i | 0.877955 | + | 0.478742i | \(0.158907\pi\) | ||||
−0.877955 | + | 0.478742i | \(0.841093\pi\) | |||||||
\(788\) | 7580.18i | 0.342681i | ||||||||
\(789\) | −310.805 | + | 5391.32i | −0.0140240 | + | 0.243265i | ||||
\(790\) | −22705.2 | + | 13108.9i | −1.02255 | + | 0.590371i | ||||
\(791\) | −23471.6 | − | 10522.1i | −1.05506 | − | 0.472974i | ||||
\(792\) | −40881.3 | − | 94465.6i | −1.83416 | − | 4.23824i | ||||
\(793\) | −4100.05 | + | 7101.50i | −0.183603 | + | 0.318010i | ||||
\(794\) | −38647.8 | + | 66940.0i | −1.72741 | + | 2.99196i | ||||
\(795\) | −140.391 | + | 2435.28i | −0.00626311 | + | 0.108642i | ||||
\(796\) | −17742.6 | + | 10243.7i | −0.790037 | + | 0.456128i | ||||
\(797\) | 10049.6 | − | 17406.5i | 0.446645 | − | 0.773612i | −0.551520 | − | 0.834161i | \(-0.685952\pi\) |
0.998165 | + | 0.0605498i | \(0.0192854\pi\) | |||||||
\(798\) | −8032.93 | + | 358.366i | −0.356344 | + | 0.0158973i | ||||
\(799\) | −124.344 | − | 215.371i | −0.00550562 | − | 0.00953601i | ||||
\(800\) | −7319.53 | − | 4225.93i | −0.323480 | − | 0.186761i | ||||
\(801\) | 15388.0 | + | 35557.5i | 0.678787 | + | 1.56849i | ||||
\(802\) | −9959.74 | − | 17250.8i | −0.438517 | − | 0.759534i | ||||
\(803\) | −53283.2 | −2.34162 | ||||||||
\(804\) | 15248.0 | + | 30316.5i | 0.668852 | + | 1.32983i | ||||
\(805\) | −9418.12 | − | 4222.05i | −0.412354 | − | 0.184854i | ||||
\(806\) | 9776.16 | + | 5644.27i | 0.427234 | + | 0.246664i | ||||
\(807\) | 12087.8 | − | 18402.4i | 0.527276 | − | 0.802719i | ||||
\(808\) | −95350.9 | − | 55050.9i | −4.15153 | − | 2.39688i | ||||
\(809\) | 25583.5 | − | 14770.7i | 1.11183 | − | 0.641914i | 0.172525 | − | 0.985005i | \(-0.444807\pi\) |
0.939302 | + | 0.343091i | \(0.111474\pi\) | |||||||
\(810\) | −33995.4 | − | 31921.1i | −1.47466 | − | 1.38468i | ||||
\(811\) | − | 13234.7i | − | 0.573036i | −0.958075 | − | 0.286518i | \(-0.907502\pi\) | ||
0.958075 | − | 0.286518i | \(-0.0924978\pi\) | |||||||
\(812\) | 69637.4 | − | 50323.5i | 3.00960 | − | 2.17489i | ||||
\(813\) | 2065.51 | − | 35829.0i | 0.0891029 | − | 1.54561i | ||||
\(814\) | −6023.41 | − | 10432.8i | −0.259362 | − | 0.449227i | ||||
\(815\) | 27687.0 | 1.18998 | ||||||||
\(816\) | −16205.1 | + | 24670.4i | −0.695209 | + | 1.05838i | ||||
\(817\) | 1208.72i | 0.0517599i | ||||||||
\(818\) | −22821.4 | −0.975467 | ||||||||
\(819\) | 6948.75 | − | 3892.28i | 0.296470 | − | 0.166065i | ||||
\(820\) | 40123.0 | 1.70873 | ||||||||
\(821\) | 6483.12i | 0.275594i | 0.990461 | + | 0.137797i | \(0.0440021\pi\) | ||||
−0.990461 | + | 0.137797i | \(0.955998\pi\) | |||||||
\(822\) | 23315.3 | + | 1344.10i | 0.989311 | + | 0.0570329i | ||||
\(823\) | 15499.1 | 0.656459 | 0.328230 | − | 0.944598i | \(-0.393548\pi\) | ||||
0.328230 | + | 0.944598i | \(0.393548\pi\) | |||||||
\(824\) | 20158.3 | + | 34915.1i | 0.852241 | + | 1.47612i | ||||
\(825\) | −6663.17 | − | 4376.79i | −0.281190 | − | 0.184703i | ||||
\(826\) | −1231.74 | − | 12014.1i | −0.0518859 | − | 0.506081i | ||||
\(827\) | − | 7987.02i | − | 0.335835i | −0.985801 | − | 0.167918i | \(-0.946296\pi\) | ||
0.985801 | − | 0.167918i | \(-0.0537043\pi\) | |||||||
\(828\) | 2752.81 | − | 23796.3i | 0.115540 | − | 0.998766i | ||||
\(829\) | 38491.6 | − | 22223.1i | 1.61263 | − | 0.931051i | 0.623870 | − | 0.781528i | \(-0.285559\pi\) |
0.988758 | − | 0.149524i | \(-0.0477740\pi\) | |||||||
\(830\) | −15032.2 | − | 8678.85i | −0.628645 | − | 0.362948i | ||||
\(831\) | −12722.3 | − | 733.427i | −0.531084 | − | 0.0306165i | ||||
\(832\) | 7838.63 | + | 4525.64i | 0.326629 | + | 0.188580i | ||||
\(833\) | −8182.78 | − | 9181.71i | −0.340356 | − | 0.381906i | ||||
\(834\) | −62827.7 | − | 3621.96i | −2.60857 | − | 0.150381i | ||||
\(835\) | 16402.4 | 0.679796 | ||||||||
\(836\) | −9862.60 | − | 17082.5i | −0.408021 | − | 0.706712i | ||||
\(837\) | −3262.88 | + | 18698.9i | −0.134745 | + | 0.772199i | ||||
\(838\) | 44232.5 | + | 25537.6i | 1.82337 | + | 1.05272i | ||||
\(839\) | 8987.71 | + | 15567.2i | 0.369833 | + | 0.640570i | 0.989539 | − | 0.144264i | \(-0.0460815\pi\) |
−0.619706 | + | 0.784834i | \(0.712748\pi\) | |||||||
\(840\) | 62502.7 | + | 32461.5i | 2.56732 | + | 1.33337i | ||||
\(841\) | 16276.8 | − | 28192.2i | 0.667381 | − | 1.15594i | ||||
\(842\) | −38521.9 | + | 22240.6i | −1.57667 | + | 0.910289i | ||||
\(843\) | 36127.9 | + | 23731.0i | 1.47605 | + | 0.969561i | ||||
\(844\) | 10914.4 | − | 18904.4i | 0.445131 | − | 0.770989i | ||||
\(845\) | −11865.3 | + | 20551.3i | −0.483051 | + | 0.836669i | ||||
\(846\) | −787.540 | − | 584.853i | −0.0320049 | − | 0.0237679i | ||||
\(847\) | 29454.3 | + | 40758.7i | 1.19488 | + | 1.65347i | ||||
\(848\) | 5274.31 | − | 3045.13i | 0.213586 | − | 0.123314i | ||||
\(849\) | −31806.6 | + | 15997.5i | −1.28575 | + | 0.646680i | ||||
\(850\) | 4530.36i | 0.182812i | ||||||||
\(851\) | − | 1649.91i | − | 0.0664610i | ||||||
\(852\) | −64655.2 | + | 32519.0i | −2.59982 | + | 1.30761i | ||||
\(853\) | 21062.1 | − | 12160.2i | 0.845431 | − | 0.488110i | −0.0136759 | − | 0.999906i | \(-0.504353\pi\) |
0.859106 | + | 0.511797i | \(0.171020\pi\) | |||||||
\(854\) | 49686.9 | − | 5094.14i | 1.99093 | − | 0.204119i | ||||
\(855\) | −4222.13 | − | 3135.49i | −0.168882 | − | 0.125417i | ||||
\(856\) | −28987.9 | + | 50208.4i | −1.15746 | + | 2.00478i | ||||
\(857\) | −11448.4 | + | 19829.2i | −0.456324 | + | 0.790377i | −0.998763 | − | 0.0497185i | \(-0.984168\pi\) |
0.542439 | + | 0.840095i | \(0.317501\pi\) | |||||||
\(858\) | 23050.0 | + | 15140.7i | 0.917150 | + | 0.602441i | ||||
\(859\) | −7592.10 | + | 4383.30i | −0.301559 | + | 0.174105i | −0.643143 | − | 0.765746i | \(-0.722370\pi\) |
0.341584 | + | 0.939851i | \(0.389037\pi\) | |||||||
\(860\) | 8995.03 | − | 15579.9i | 0.356661 | − | 0.617754i | ||||
\(861\) | −16248.3 | + | 724.871i | −0.643136 | + | 0.0286917i | ||||
\(862\) | −10835.2 | − | 18767.2i | −0.428132 | − | 0.741546i | ||||
\(863\) | −6585.65 | − | 3802.22i | −0.259766 | − | 0.149976i | 0.364462 | − | 0.931218i | \(-0.381253\pi\) |
−0.624228 | + | 0.781242i | \(0.714586\pi\) | |||||||
\(864\) | −8450.96 | + | 48430.9i | −0.332763 | + | 1.90700i | ||||
\(865\) | −5754.73 | − | 9967.49i | −0.226204 | − | 0.391798i | ||||
\(866\) | −5266.95 | −0.206672 | ||||||||
\(867\) | −18816.7 | − | 1084.77i | −0.737082 | − | 0.0424921i | ||||
\(868\) | −4968.29 | − | 48459.4i | −0.194280 | − | 1.89495i | ||||
\(869\) | 22578.1 | + | 13035.5i | 0.881369 | + | 0.508859i | ||||
\(870\) | 79185.5 | + | 4564.97i | 3.08579 | + | 0.177893i | ||||
\(871\) | −4633.78 | − | 2675.32i | −0.180264 | − | 0.104075i | ||||
\(872\) | −77833.6 | + | 44937.2i | −3.02268 | + | 1.74514i | ||||
\(873\) | 1551.85 | − | 13414.7i | 0.0601628 | − | 0.520068i | ||||
\(874\) | − | 3813.22i | − | 0.147579i | ||||||
\(875\) | −22696.1 | + | 2326.92i | −0.876879 | + | 0.0899019i | ||||
\(876\) | 70724.7 | + | 46456.4i | 2.72781 | + | 1.79180i | ||||
\(877\) | 18628.0 | + | 32264.7i | 0.717244 | + | 1.24230i | 0.962087 | + | 0.272741i | \(0.0879302\pi\) |
−0.244843 | + | 0.969563i | \(0.578736\pi\) | |||||||
\(878\) | 43115.1 | 1.65725 | ||||||||
\(879\) | −4033.21 | − | 232.510i | −0.154763 | − | 0.00892194i | ||||
\(880\) | 123058.i | 4.71395i | ||||||||
\(881\) | −1271.30 | −0.0486164 | −0.0243082 | − | 0.999705i | \(-0.507738\pi\) | ||||
−0.0243082 | + | 0.999705i | \(0.507738\pi\) | |||||||
\(882\) | −44006.5 | − | 20418.9i | −1.68002 | − | 0.779525i | ||||
\(883\) | 29075.5 | 1.10812 | 0.554060 | − | 0.832477i | \(-0.313078\pi\) | ||||
0.554060 | + | 0.832477i | \(0.313078\pi\) | |||||||
\(884\) | − | 11103.0i | − | 0.422437i | ||||||
\(885\) | 4336.57 | − | 6601.95i | 0.164715 | − | 0.250760i | ||||
\(886\) | −7090.70 | −0.268868 | ||||||||
\(887\) | 14253.6 | + | 24688.0i | 0.539560 | + | 0.934546i | 0.998928 | + | 0.0462996i | \(0.0147429\pi\) |
−0.459367 | + | 0.888246i | \(0.651924\pi\) | |||||||
\(888\) | −647.976 | + | 11240.0i | −0.0244872 | + | 0.424764i | ||||
\(889\) | −7443.82 | + | 763.177i | −0.280830 | + | 0.0287921i | ||||
\(890\) | − | 91793.3i | − | 3.45721i | ||||||
\(891\) | −10587.2 | + | 45147.2i | −0.398073 | + | 1.69752i | ||||
\(892\) | −74863.3 | + | 43222.4i | −2.81010 | + | 1.62241i | ||||
\(893\) | −95.8063 | − | 55.3138i | −0.00359018 | − | 0.00207279i | ||||
\(894\) | 28427.1 | − | 43277.1i | 1.06347 | − | 1.61902i | ||||
\(895\) | −769.126 | − | 444.055i | −0.0287252 | − | 0.0165845i | ||||
\(896\) | −327.671 | − | 3196.02i | −0.0122173 | − | 0.119165i | ||||
\(897\) | 1697.13 | + | 3374.28i | 0.0631722 | + | 0.125601i | ||||
\(898\) | −59416.4 | −2.20796 | ||||||||
\(899\) | −16142.6 | − | 27959.8i | −0.598871 | − | 1.03728i | ||||
\(900\) | 5028.25 | + | 11618.9i | 0.186231 | + | 0.430330i | ||||
\(901\) | −1193.77 | − | 689.224i | −0.0441402 | − | 0.0254843i | ||||
\(902\) | −28158.3 | − | 48771.7i | −1.03943 | − | 1.80035i | ||||
\(903\) | −3361.17 | + | 6471.75i | −0.123868 | + | 0.238501i | ||||
\(904\) | −41619.0 | + | 72086.1i | −1.53122 | + | 2.65216i | ||||
\(905\) | −19673.3 | + | 11358.4i | −0.722610 | + | 0.417199i | ||||
\(906\) | 2409.34 | − | 41793.2i | 0.0883497 | − | 1.53254i | ||||
\(907\) | −13155.3 | + | 22785.7i | −0.481604 | + | 0.834163i | −0.999777 | − | 0.0211130i | \(-0.993279\pi\) |
0.518173 | + | 0.855276i | \(0.326612\pi\) | |||||||
\(908\) | 459.150 | − | 795.271i | 0.0167813 | − | 0.0290661i | ||||
\(909\) | 19700.2 | + | 45521.9i | 0.718829 | + | 1.66102i | ||||
\(910\) | −18771.4 | + | 1924.53i | −0.683808 | + | 0.0701073i | ||||
\(911\) | −12914.3 | + | 7456.08i | −0.469671 | + | 0.271164i | −0.716102 | − | 0.697996i | \(-0.754075\pi\) |
0.246431 | + | 0.969160i | \(0.420742\pi\) | |||||||
\(912\) | −755.694 | + | 13108.5i | −0.0274381 | + | 0.475950i | ||||
\(913\) | 17260.5i | 0.625673i | ||||||||
\(914\) | − | 38070.2i | − | 1.37774i | ||||||
\(915\) | 27303.8 | + | 17934.9i | 0.986489 | + | 0.647987i | ||||
\(916\) | 55613.3 | − | 32108.4i | 2.00602 | − | 1.15818i | ||||
\(917\) | 29659.7 | + | 41042.9i | 1.06810 | + | 1.47803i | ||||
\(918\) | 24746.8 | − | 9056.94i | 0.889724 | − | 0.325625i | ||||
\(919\) | 17879.8 | − | 30968.8i | 0.641786 | − | 1.11161i | −0.343248 | − | 0.939245i | \(-0.611527\pi\) |
0.985034 | − | 0.172361i | \(-0.0551396\pi\) | |||||||
\(920\) | −16699.8 | + | 28925.0i | −0.598453 | + | 1.03655i | ||||
\(921\) | −25542.2 | + | 12846.7i | −0.913836 | + | 0.459624i | ||||
\(922\) | 56400.7 | − | 32562.9i | 2.01460 | − | 1.16313i | ||||
\(923\) | 5705.57 | − | 9882.33i | 0.203468 | − | 0.352417i | ||||
\(924\) | −5303.89 | − | 118889.i | −0.188837 | − | 4.23285i | ||||
\(925\) | 435.992 | + | 755.160i | 0.0154976 | + | 0.0268427i | ||||
\(926\) | 13106.2 | + | 7566.85i | 0.465114 | + | 0.268534i | ||||
\(927\) | 2087.22 | − | 18042.6i | 0.0739518 | − | 0.639264i | ||||
\(928\) | −41809.8 | − | 72416.7i | −1.47896 | − | 2.56163i | ||||
\(929\) | 34325.5 | 1.21225 | 0.606127 | − | 0.795368i | \(-0.292722\pi\) | ||||
0.606127 | + | 0.795368i | \(0.292722\pi\) | |||||||
\(930\) | 24689.7 | − | 37587.4i | 0.870546 | − | 1.32531i | ||||
\(931\) | −5194.59 | − | 1717.18i | −0.182863 | − | 0.0604495i | ||||
\(932\) | −78131.3 | − | 45109.1i | −2.74600 | − | 1.58541i | ||||
\(933\) | 5013.93 | + | 9968.82i | 0.175936 | + | 0.349801i | ||||
\(934\) | −11915.2 | − | 6879.26i | −0.417428 | − | 0.241002i | ||||
\(935\) | 24121.0 | − | 13926.3i | 0.843680 | − | 0.487099i | ||||
\(936\) | −10236.5 | − | 23653.7i | −0.357468 | − | 0.826012i | ||||
\(937\) | 14515.1i | 0.506071i | 0.967457 | + | 0.253036i | \(0.0814289\pi\) | ||||
−0.967457 | + | 0.253036i | \(0.918571\pi\) | |||||||
\(938\) | 3323.96 | + | 32421.1i | 0.115705 | + | 1.12856i | ||||
\(939\) | 9144.23 | − | 4599.19i | 0.317796 | − | 0.159839i | ||||
\(940\) | 823.265 | + | 1425.94i | 0.0285659 | + | 0.0494776i | ||||
\(941\) | −23852.5 | −0.826323 | −0.413162 | − | 0.910658i | \(-0.635576\pi\) | ||||
−0.413162 | + | 0.910658i | \(0.635576\pi\) | |||||||
\(942\) | 35591.7 | + | 70764.4i | 1.23104 | + | 2.44759i | ||||
\(943\) | − | 7713.04i | − | 0.266353i | ||||||
\(944\) | −19721.0 | −0.679942 | ||||||||
\(945\) | −13887.1 | − | 28528.8i | −0.478039 | − | 0.982055i | ||||
\(946\) | −25250.9 | −0.867839 | ||||||||
\(947\) | − | 41604.5i | − | 1.42763i | −0.700335 | − | 0.713814i | \(-0.746966\pi\) | ||
0.700335 | − | 0.713814i | \(-0.253034\pi\) | |||||||
\(948\) | −18603.4 | − | 36987.7i | −0.637352 | − | 1.26720i | ||||
\(949\) | −13341.9 | −0.456370 | ||||||||
\(950\) | 1007.65 | + | 1745.30i | 0.0344131 | + | 0.0596053i | ||||
\(951\) | −6735.76 | + | 3387.82i | −0.229676 | + | 0.115518i | ||||
\(952\) | −32258.0 | + | 23311.3i | −1.09820 | + | 0.793617i | ||||
\(953\) | 21486.0i | 0.730326i | 0.930944 | + | 0.365163i | \(0.118987\pi\) | ||||
−0.930944 | + | 0.365163i | \(0.881013\pi\) | |||||||
\(954\) | −5401.28 | − | 624.834i | −0.183305 | − | 0.0212052i | ||||
\(955\) | −43.1654 | + | 24.9216i | −0.00146262 | + | 0.000844443i | ||||
\(956\) | −73899.8 | − | 42666.0i | −2.50009 | − | 1.44343i | ||||
\(957\) | −35439.8 | − | 70462.4i | −1.19708 | − | 2.38007i | ||||
\(958\) | 3455.36 | + | 1994.95i | 0.116532 | + | 0.0672797i | ||||
\(959\) | 14499.8 | + | 6500.11i | 0.488241 | + | 0.218873i | ||||
\(960\) | 19796.5 | − | 30138.0i | 0.665551 | − | 1.01323i | ||||
\(961\) | 11486.0 | 0.385553 | ||||||||
\(962\) | −1508.23 | − | 2612.34i | −0.0505482 | − | 0.0875521i | ||||
\(963\) | 23970.2 | − | 10373.5i | 0.802108 | − | 0.347123i | ||||
\(964\) | 18710.6 | + | 10802.6i | 0.625133 | + | 0.360921i | ||||
\(965\) | 26882.7 | + | 46562.3i | 0.896773 | + | 1.55326i | ||||
\(966\) | 10603.7 | − | 20416.8i | 0.353175 | − | 0.680019i | ||||
\(967\) | −8872.69 | + | 15367.9i | −0.295064 | + | 0.511065i | −0.975000 | − | 0.222206i | \(-0.928674\pi\) |
0.679936 | + | 0.733271i | \(0.262007\pi\) | |||||||
\(968\) | 140930. | − | 81366.0i | 4.67940 | − | 2.70165i | ||||
\(969\) | 2654.97 | − | 1335.34i | 0.0880184 | − | 0.0442698i | ||||
\(970\) | −15997.1 | + | 27707.7i | −0.529520 | + | 0.917156i | ||||
\(971\) | −17856.1 | + | 30927.8i | −0.590145 | + | 1.02216i | 0.404067 | + | 0.914729i | \(0.367596\pi\) |
−0.994212 | + | 0.107432i | \(0.965737\pi\) | |||||||
\(972\) | 53415.4 | − | 50694.7i | 1.76265 | − | 1.67287i | ||||
\(973\) | −39072.6 | − | 17515.9i | −1.28737 | − | 0.577115i | ||||
\(974\) | 78733.2 | − | 45456.6i | 2.59012 | − | 1.49541i | ||||
\(975\) | −1668.43 | − | 1095.93i | −0.0548025 | − | 0.0359977i | ||||
\(976\) | − | 81560.7i | − | 2.67489i | ||||||
\(977\) | − | 40832.8i | − | 1.33711i | −0.743662 | − | 0.668555i | \(-0.766913\pi\) | ||
0.743662 | − | 0.668555i | \(-0.233087\pi\) | |||||||
\(978\) | −3551.91 | + | 61612.7i | −0.116133 | + | 2.01447i | ||||
\(979\) | −79050.2 | + | 45639.7i | −2.58065 | + | 1.48994i | ||||
\(980\) | 54176.9 | + | 60790.6i | 1.76594 | + | 1.98152i | ||||
\(981\) | 40221.0 | + | 4652.87i | 1.30903 | + | 0.151432i | ||||
\(982\) | −52294.3 | + | 90576.4i | −1.69937 | + | 2.94339i | ||||
\(983\) | −14795.7 | + | 25626.9i | −0.480070 | + | 0.831506i | −0.999739 | − | 0.0228618i | \(-0.992722\pi\) |
0.519668 | + | 0.854368i | \(0.326056\pi\) | |||||||
\(984\) | −3029.17 | + | 52545.0i | −0.0981367 | + | 1.70231i | ||||
\(985\) | −4123.45 | + | 2380.67i | −0.133385 | + | 0.0770097i | ||||
\(986\) | −22410.8 | + | 38816.7i | −0.723840 | + | 1.25373i | ||||
\(987\) | −359.152 | − | 562.576i | −0.0115825 | − | 0.0181428i | ||||
\(988\) | −2469.55 | − | 4277.38i | −0.0795211 | − | 0.137735i | ||||
\(989\) | −2994.99 | − | 1729.16i | −0.0962944 | − | 0.0555956i | ||||
\(990\) | 65502.1 | − | 88202.5i | 2.10282 | − | 2.83157i | ||||
\(991\) | −21470.6 | − | 37188.1i | −0.688230 | − | 1.19205i | −0.972410 | − | 0.233278i | \(-0.925055\pi\) |
0.284181 | − | 0.958771i | \(-0.408278\pi\) | |||||||
\(992\) | −47410.5 | −1.51742 | ||||||||
\(993\) | 2775.70 | + | 5518.72i | 0.0887052 | + | 0.176366i | ||||
\(994\) | −69143.4 | + | 7088.92i | −2.20633 | + | 0.226204i | ||||
\(995\) | −11144.7 | − | 6434.37i | −0.355085 | − | 0.205008i | ||||
\(996\) | 15049.0 | − | 22910.5i | 0.478761 | − | 0.728861i | ||||
\(997\) | −37664.7 | − | 21745.7i | −1.19644 | − | 0.690767i | −0.236683 | − | 0.971587i | \(-0.576060\pi\) |
−0.959760 | + | 0.280820i | \(0.909394\pi\) | |||||||
\(998\) | −6993.64 | + | 4037.78i | −0.221823 | + | 0.128070i | ||||
\(999\) | 3253.40 | − | 3891.27i | 0.103036 | − | 0.123238i |
(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 | 63.4.i.a.5.22 | ✓ | 44 | |
3.2 | odd | 2 | 189.4.i.a.152.1 | 44 | |||
7.3 | odd | 6 | 63.4.s.a.59.1 | yes | 44 | ||
9.2 | odd | 6 | 63.4.s.a.47.1 | yes | 44 | ||
9.7 | even | 3 | 189.4.s.a.89.22 | 44 | |||
21.17 | even | 6 | 189.4.s.a.17.22 | 44 | |||
63.38 | even | 6 | inner | 63.4.i.a.38.1 | yes | 44 | |
63.52 | odd | 6 | 189.4.i.a.143.22 | 44 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
63.4.i.a.5.22 | ✓ | 44 | 1.1 | even | 1 | trivial | |
63.4.i.a.38.1 | yes | 44 | 63.38 | even | 6 | inner | |
63.4.s.a.47.1 | yes | 44 | 9.2 | odd | 6 | ||
63.4.s.a.59.1 | yes | 44 | 7.3 | odd | 6 | ||
189.4.i.a.143.22 | 44 | 63.52 | odd | 6 | |||
189.4.i.a.152.1 | 44 | 3.2 | odd | 2 | |||
189.4.s.a.17.22 | 44 | 21.17 | even | 6 | |||
189.4.s.a.89.22 | 44 | 9.7 | even | 3 |