Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [378,4,Mod(127,378)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(378, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([4, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("378.127");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 378 = 2 \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 378.f (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: | \(22.3027219822\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 2x^{7} - 2x^{6} + 53x^{5} + 38x^{4} - 166x^{3} + 7x^{2} + 1543x + 2707 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 3^{6} \) |
Twist minimal: | no (minimal twist has level 126) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 253.3 | ||
Root | \(2.52060 - 3.08349i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 378.253 |
Dual form | 378.4.f.b.127.3 |
$q$-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 \(\left(\mathbb{Z}/378\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(325\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | + | 1.73205i | 0.353553 | + | 0.612372i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −2.00000 | + | 3.46410i | −0.250000 | + | 0.433013i | ||||
\(5\) | 2.98310 | − | 5.16688i | 0.266817 | − | 0.462140i | −0.701221 | − | 0.712944i | \(-0.747362\pi\) |
0.968038 | + | 0.250804i | \(0.0806948\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.50000 | + | 6.06218i | 0.188982 | + | 0.327327i | ||||
\(8\) | −8.00000 | −0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 11.9324 | 0.377336 | ||||||||
\(11\) | 3.67432 | + | 6.36411i | 0.100714 | + | 0.174441i | 0.911979 | − | 0.410237i | \(-0.134554\pi\) |
−0.811265 | + | 0.584678i | \(0.801221\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 27.4070 | − | 47.4703i | 0.584718 | − | 1.01276i | −0.410192 | − | 0.911999i | \(-0.634538\pi\) |
0.994910 | − | 0.100763i | \(-0.0321283\pi\) | |||||||
\(14\) | −7.00000 | + | 12.1244i | −0.133631 | + | 0.231455i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −8.00000 | − | 13.8564i | −0.125000 | − | 0.216506i | ||||
\(17\) | 53.3544 | 0.761197 | 0.380598 | − | 0.924740i | \(-0.375718\pi\) | ||||
0.380598 | + | 0.924740i | \(0.375718\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 88.7964 | 1.07217 | 0.536087 | − | 0.844163i | \(-0.319902\pi\) | ||||
0.536087 | + | 0.844163i | \(0.319902\pi\) | |||||||
\(20\) | 11.9324 | + | 20.6675i | 0.133408 | + | 0.231070i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −7.34865 | + | 12.7282i | −0.0712153 | + | 0.123349i | ||||
\(23\) | −98.0698 | + | 169.862i | −0.889086 | + | 1.53994i | −0.0481279 | + | 0.998841i | \(0.515326\pi\) |
−0.840958 | + | 0.541101i | \(0.818008\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 44.7022 | + | 77.4265i | 0.357618 | + | 0.619412i | ||||
\(26\) | 109.628 | 0.826916 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −28.0000 | −0.188982 | ||||||||
\(29\) | −48.8199 | − | 84.5585i | −0.312608 | − | 0.541453i | 0.666318 | − | 0.745667i | \(-0.267869\pi\) |
−0.978926 | + | 0.204215i | \(0.934536\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 82.9760 | − | 143.719i | 0.480740 | − | 0.832666i | −0.519016 | − | 0.854765i | \(-0.673701\pi\) |
0.999756 | + | 0.0220988i | \(0.00703483\pi\) | |||||||
\(32\) | 16.0000 | − | 27.7128i | 0.0883883 | − | 0.153093i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 53.3544 | + | 92.4126i | 0.269124 | + | 0.466136i | ||||
\(35\) | 41.7634 | 0.201694 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 431.884 | 1.91895 | 0.959477 | − | 0.281789i | \(-0.0909277\pi\) | ||||
0.959477 | + | 0.281789i | \(0.0909277\pi\) | |||||||
\(38\) | 88.7964 | + | 153.800i | 0.379070 | + | 0.656569i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −23.8648 | + | 41.3351i | −0.0943339 | + | 0.163391i | ||||
\(41\) | 47.5332 | − | 82.3299i | 0.181059 | − | 0.313604i | −0.761182 | − | 0.648538i | \(-0.775381\pi\) |
0.942242 | + | 0.334934i | \(0.108714\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 187.423 | + | 324.627i | 0.664693 | + | 1.15128i | 0.979368 | + | 0.202083i | \(0.0647711\pi\) |
−0.314675 | + | 0.949199i | \(0.601896\pi\) | |||||||
\(44\) | −29.3946 | −0.100714 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −392.279 | −1.25736 | ||||||||
\(47\) | 57.5647 | + | 99.7049i | 0.178652 | + | 0.309435i | 0.941419 | − | 0.337239i | \(-0.109493\pi\) |
−0.762767 | + | 0.646674i | \(0.776160\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −24.5000 | + | 42.4352i | −0.0714286 | + | 0.123718i | ||||
\(50\) | −89.4044 | + | 154.853i | −0.252874 | + | 0.437990i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 109.628 | + | 189.881i | 0.292359 | + | 0.506381i | ||||
\(53\) | 145.549 | 0.377220 | 0.188610 | − | 0.982052i | \(-0.439602\pi\) | ||||
0.188610 | + | 0.982052i | \(0.439602\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 43.8435 | 0.107488 | ||||||||
\(56\) | −28.0000 | − | 48.4974i | −0.0668153 | − | 0.115728i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 97.6398 | − | 169.117i | 0.221047 | − | 0.382865i | ||||
\(59\) | −202.457 | + | 350.666i | −0.446741 | + | 0.773778i | −0.998172 | − | 0.0604428i | \(-0.980749\pi\) |
0.551431 | + | 0.834221i | \(0.314082\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 288.425 | + | 499.567i | 0.605394 | + | 1.04857i | 0.991989 | + | 0.126324i | \(0.0403177\pi\) |
−0.386595 | + | 0.922250i | \(0.626349\pi\) | |||||||
\(62\) | 331.904 | 0.679869 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 64.0000 | 0.125000 | ||||||||
\(65\) | −163.516 | − | 283.218i | −0.312025 | − | 0.540443i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 21.8954 | − | 37.9239i | 0.0399246 | − | 0.0691514i | −0.845373 | − | 0.534177i | \(-0.820622\pi\) |
0.885297 | + | 0.465026i | \(0.153955\pi\) | |||||||
\(68\) | −106.709 | + | 184.825i | −0.190299 | + | 0.329608i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 41.7634 | + | 72.3364i | 0.0713098 | + | 0.123512i | ||||
\(71\) | −196.885 | −0.329098 | −0.164549 | − | 0.986369i | \(-0.552617\pi\) | ||||
−0.164549 | + | 0.986369i | \(0.552617\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −510.969 | −0.819239 | −0.409619 | − | 0.912257i | \(-0.634338\pi\) | ||||
−0.409619 | + | 0.912257i | \(0.634338\pi\) | |||||||
\(74\) | 431.884 | + | 748.045i | 0.678452 | + | 1.17511i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −177.593 | + | 307.600i | −0.268043 | + | 0.464265i | ||||
\(77\) | −25.7203 | + | 44.5488i | −0.0380662 | + | 0.0659326i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −196.883 | − | 341.011i | −0.280393 | − | 0.485655i | 0.691088 | − | 0.722770i | \(-0.257132\pi\) |
−0.971482 | + | 0.237115i | \(0.923798\pi\) | |||||||
\(80\) | −95.4592 | −0.133408 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 190.133 | 0.256057 | ||||||||
\(83\) | 263.437 | + | 456.286i | 0.348385 | + | 0.603420i | 0.985963 | − | 0.166966i | \(-0.0533969\pi\) |
−0.637578 | + | 0.770386i | \(0.720064\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 159.162 | − | 275.676i | 0.203100 | − | 0.351780i | ||||
\(86\) | −374.847 | + | 649.254i | −0.470009 | + | 0.814080i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −29.3946 | − | 50.9129i | −0.0356076 | − | 0.0616743i | ||||
\(89\) | 589.818 | 0.702479 | 0.351239 | − | 0.936286i | \(-0.385760\pi\) | ||||
0.351239 | + | 0.936286i | \(0.385760\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 383.698 | 0.442005 | ||||||||
\(92\) | −392.279 | − | 679.448i | −0.444543 | − | 0.769971i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −115.129 | + | 199.410i | −0.126326 | + | 0.218804i | ||||
\(95\) | 264.889 | − | 458.800i | 0.286074 | − | 0.495494i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −468.232 | − | 811.002i | −0.490122 | − | 0.848915i | 0.509814 | − | 0.860285i | \(-0.329714\pi\) |
−0.999935 | + | 0.0113693i | \(0.996381\pi\) | |||||||
\(98\) | −98.0000 | −0.101015 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −357.618 | −0.357618 | ||||||||
\(101\) | −213.573 | − | 369.920i | −0.210409 | − | 0.364439i | 0.741433 | − | 0.671026i | \(-0.234146\pi\) |
−0.951843 | + | 0.306587i | \(0.900813\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 997.566 | − | 1727.84i | 0.954302 | − | 1.65290i | 0.218344 | − | 0.975872i | \(-0.429934\pi\) |
0.735958 | − | 0.677028i | \(-0.236732\pi\) | |||||||
\(104\) | −219.256 | + | 379.763i | −0.206729 | + | 0.358065i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 145.549 | + | 252.098i | 0.133368 | + | 0.230999i | ||||
\(107\) | −1866.87 | −1.68671 | −0.843353 | − | 0.537361i | \(-0.819421\pi\) | ||||
−0.843353 | + | 0.537361i | \(0.819421\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −585.651 | −0.514635 | −0.257317 | − | 0.966327i | \(-0.582839\pi\) | ||||
−0.257317 | + | 0.966327i | \(0.582839\pi\) | |||||||
\(110\) | 43.8435 | + | 75.9392i | 0.0380029 | + | 0.0658229i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 56.0000 | − | 96.9948i | 0.0472456 | − | 0.0818317i | ||||
\(113\) | −370.541 | + | 641.795i | −0.308474 | + | 0.534292i | −0.978029 | − | 0.208470i | \(-0.933152\pi\) |
0.669555 | + | 0.742763i | \(0.266485\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 585.104 | + | 1013.43i | 0.474446 | + | 0.821764i | ||||
\(116\) | 390.559 | 0.312608 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −809.830 | −0.631787 | ||||||||
\(119\) | 186.740 | + | 323.444i | 0.143853 | + | 0.249160i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 638.499 | − | 1105.91i | 0.479714 | − | 0.830888i | ||||
\(122\) | −576.850 | + | 999.133i | −0.428078 | + | 0.741453i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 331.904 | + | 574.875i | 0.240370 | + | 0.416333i | ||||
\(125\) | 1279.18 | 0.915307 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −72.9178 | −0.0509481 | −0.0254740 | − | 0.999675i | \(-0.508110\pi\) | ||||
−0.0254740 | + | 0.999675i | \(0.508110\pi\) | |||||||
\(128\) | 64.0000 | + | 110.851i | 0.0441942 | + | 0.0765466i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 327.032 | − | 566.435i | 0.220635 | − | 0.382151i | ||||
\(131\) | 470.494 | − | 814.920i | 0.313796 | − | 0.543510i | −0.665385 | − | 0.746500i | \(-0.731733\pi\) |
0.979181 | + | 0.202990i | \(0.0650659\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 310.787 | + | 538.299i | 0.202622 | + | 0.350951i | ||||
\(134\) | 87.5816 | 0.0564619 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −426.835 | −0.269124 | ||||||||
\(137\) | −896.728 | − | 1553.18i | −0.559216 | − | 0.968591i | −0.997562 | − | 0.0697848i | \(-0.977769\pi\) |
0.438346 | − | 0.898807i | \(-0.355565\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −296.550 | + | 513.639i | −0.180957 | + | 0.313427i | −0.942207 | − | 0.335032i | \(-0.891253\pi\) |
0.761250 | + | 0.648459i | \(0.224586\pi\) | |||||||
\(140\) | −83.5268 | + | 144.673i | −0.0504236 | + | 0.0873363i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −196.885 | − | 341.015i | −0.116354 | − | 0.201531i | ||||
\(143\) | 402.809 | 0.235556 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −582.539 | −0.333636 | ||||||||
\(146\) | −510.969 | − | 885.025i | −0.289645 | − | 0.501679i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −863.768 | + | 1496.09i | −0.479738 | + | 0.830931i | ||||
\(149\) | 1762.35 | − | 3052.49i | 0.968978 | − | 1.67832i | 0.270454 | − | 0.962733i | \(-0.412826\pi\) |
0.698524 | − | 0.715586i | \(-0.253840\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −99.9885 | − | 173.185i | −0.0538871 | − | 0.0933352i | 0.837824 | − | 0.545941i | \(-0.183828\pi\) |
−0.891711 | + | 0.452606i | \(0.850494\pi\) | |||||||
\(152\) | −710.371 | −0.379070 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −102.881 | −0.0538337 | ||||||||
\(155\) | −495.052 | − | 857.455i | −0.256539 | − | 0.444338i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −385.823 | + | 668.266i | −0.196128 | + | 0.339703i | −0.947270 | − | 0.320438i | \(-0.896170\pi\) |
0.751142 | + | 0.660141i | \(0.229503\pi\) | |||||||
\(158\) | 393.766 | − | 682.023i | 0.198268 | − | 0.343410i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −95.4592 | − | 165.340i | −0.0471670 | − | 0.0816956i | ||||
\(161\) | −1372.98 | −0.672086 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −215.179 | −0.103399 | −0.0516996 | − | 0.998663i | \(-0.516464\pi\) | ||||
−0.0516996 | + | 0.998663i | \(0.516464\pi\) | |||||||
\(164\) | 190.133 | + | 329.320i | 0.0905297 | + | 0.156802i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −526.874 | + | 912.572i | −0.246345 | + | 0.426683i | ||||
\(167\) | 185.964 | − | 322.099i | 0.0861695 | − | 0.149250i | −0.819719 | − | 0.572765i | \(-0.805871\pi\) |
0.905889 | + | 0.423515i | \(0.139204\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −403.789 | − | 699.382i | −0.183791 | − | 0.318335i | ||||
\(170\) | 636.647 | 0.287227 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −1499.39 | −0.664693 | ||||||||
\(173\) | −51.3645 | − | 88.9659i | −0.0225732 | − | 0.0390980i | 0.854518 | − | 0.519422i | \(-0.173853\pi\) |
−0.877091 | + | 0.480324i | \(0.840519\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −312.916 | + | 541.986i | −0.135167 | + | 0.234116i | ||||
\(176\) | 58.7892 | − | 101.826i | 0.0251784 | − | 0.0436103i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 589.818 | + | 1021.60i | 0.248364 | + | 0.430179i | ||||
\(179\) | 4299.18 | 1.79517 | 0.897585 | − | 0.440841i | \(-0.145320\pi\) | ||||
0.897585 | + | 0.440841i | \(0.145320\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −3032.50 | −1.24533 | −0.622663 | − | 0.782490i | \(-0.713949\pi\) | ||||
−0.622663 | + | 0.782490i | \(0.713949\pi\) | |||||||
\(182\) | 383.698 | + | 664.585i | 0.156273 | + | 0.270672i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 784.559 | − | 1358.90i | 0.314339 | − | 0.544452i | ||||
\(185\) | 1288.35 | − | 2231.49i | 0.512009 | − | 0.886825i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 196.041 | + | 339.554i | 0.0766629 | + | 0.132784i | ||||
\(188\) | −460.517 | −0.178652 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 1059.55 | 0.404569 | ||||||||
\(191\) | −1246.15 | − | 2158.39i | −0.472084 | − | 0.817674i | 0.527406 | − | 0.849614i | \(-0.323165\pi\) |
−0.999490 | + | 0.0319400i | \(0.989831\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1076.98 | − | 1865.39i | 0.401673 | − | 0.695718i | −0.592255 | − | 0.805751i | \(-0.701762\pi\) |
0.993928 | + | 0.110033i | \(0.0350955\pi\) | |||||||
\(194\) | 936.465 | − | 1622.00i | 0.346568 | − | 0.600274i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −98.0000 | − | 169.741i | −0.0357143 | − | 0.0618590i | ||||
\(197\) | −5115.11 | −1.84993 | −0.924966 | − | 0.380049i | \(-0.875907\pi\) | ||||
−0.924966 | + | 0.380049i | \(0.875907\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −2870.67 | −1.02259 | −0.511297 | − | 0.859404i | \(-0.670835\pi\) | ||||
−0.511297 | + | 0.859404i | \(0.670835\pi\) | |||||||
\(200\) | −357.618 | − | 619.412i | −0.126437 | − | 0.218995i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 427.146 | − | 739.839i | 0.148782 | − | 0.257698i | ||||
\(203\) | 341.739 | − | 591.910i | 0.118155 | − | 0.204650i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −283.593 | − | 491.197i | −0.0966193 | − | 0.167350i | ||||
\(206\) | 3990.26 | 1.34959 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −877.024 | −0.292359 | ||||||||
\(209\) | 326.267 | + | 565.110i | 0.107982 | + | 0.187031i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1100.18 | − | 1905.57i | 0.358956 | − | 0.621730i | −0.628831 | − | 0.777542i | \(-0.716466\pi\) |
0.987787 | + | 0.155812i | \(0.0497995\pi\) | |||||||
\(212\) | −291.098 | + | 504.196i | −0.0943051 | + | 0.163341i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −1866.87 | − | 3233.52i | −0.596340 | − | 1.03289i | ||||
\(215\) | 2236.41 | 0.709405 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1161.66 | 0.363405 | ||||||||
\(218\) | −585.651 | − | 1014.38i | −0.181951 | − | 0.315148i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −87.6870 | + | 151.878i | −0.0268721 | + | 0.0465438i | ||||
\(221\) | 1462.29 | − | 2532.75i | 0.445086 | − | 0.770911i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1494.30 | + | 2588.20i | 0.448724 | + | 0.777213i | 0.998303 | − | 0.0582288i | \(-0.0185453\pi\) |
−0.549579 | + | 0.835442i | \(0.685212\pi\) | |||||||
\(224\) | 224.000 | 0.0668153 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −1482.16 | −0.436248 | ||||||||
\(227\) | 871.858 | + | 1510.10i | 0.254922 | + | 0.441538i | 0.964874 | − | 0.262712i | \(-0.0846169\pi\) |
−0.709952 | + | 0.704250i | \(0.751284\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 812.307 | − | 1406.96i | 0.234405 | − | 0.406001i | −0.724695 | − | 0.689070i | \(-0.758019\pi\) |
0.959100 | + | 0.283069i | \(0.0913525\pi\) | |||||||
\(230\) | −1170.21 | + | 2026.86i | −0.335484 | + | 0.581075i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 390.559 | + | 676.468i | 0.110524 | + | 0.191432i | ||||
\(233\) | −4815.42 | −1.35394 | −0.676972 | − | 0.736009i | \(-0.736708\pi\) | ||||
−0.676972 | + | 0.736009i | \(0.736708\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 686.885 | 0.190670 | ||||||||
\(236\) | −809.830 | − | 1402.67i | −0.223370 | − | 0.386889i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −373.481 | + | 646.888i | −0.101719 | + | 0.176183i | ||||
\(239\) | −1719.02 | + | 2977.42i | −0.465247 | + | 0.805831i | −0.999213 | − | 0.0396751i | \(-0.987368\pi\) |
0.533966 | + | 0.845506i | \(0.320701\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2828.48 | + | 4899.07i | 0.756010 | + | 1.30945i | 0.944871 | + | 0.327444i | \(0.106187\pi\) |
−0.188861 | + | 0.982004i | \(0.560480\pi\) | |||||||
\(242\) | 2553.99 | 0.678417 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −2307.40 | −0.605394 | ||||||||
\(245\) | 146.172 | + | 253.177i | 0.0381167 | + | 0.0660200i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2433.64 | − | 4215.19i | 0.626919 | − | 1.08586i | ||||
\(248\) | −663.808 | + | 1149.75i | −0.169967 | + | 0.294392i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 1279.18 | + | 2215.61i | 0.323610 | + | 0.560509i | ||||
\(251\) | −7375.50 | −1.85473 | −0.927365 | − | 0.374157i | \(-0.877932\pi\) | ||||
−0.927365 | + | 0.374157i | \(0.877932\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1441.36 | −0.358172 | ||||||||
\(254\) | −72.9178 | − | 126.297i | −0.0180129 | − | 0.0311992i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −128.000 | + | 221.703i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | −129.494 | + | 224.291i | −0.0314305 | + | 0.0544392i | −0.881313 | − | 0.472533i | \(-0.843340\pi\) |
0.849882 | + | 0.526973i | \(0.176673\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1511.59 | + | 2618.16i | 0.362648 | + | 0.628125i | ||||
\(260\) | 1308.13 | 0.312025 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 1881.98 | 0.443774 | ||||||||
\(263\) | 2069.48 | + | 3584.45i | 0.485208 | + | 0.840405i | 0.999856 | − | 0.0169970i | \(-0.00541057\pi\) |
−0.514648 | + | 0.857402i | \(0.672077\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 434.187 | − | 752.034i | 0.100649 | − | 0.174329i | ||||
\(266\) | −621.575 | + | 1076.60i | −0.143275 | + | 0.248160i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 87.5816 | + | 151.696i | 0.0199623 | + | 0.0345757i | ||||
\(269\) | −5571.27 | −1.26277 | −0.631387 | − | 0.775468i | \(-0.717514\pi\) | ||||
−0.631387 | + | 0.775468i | \(0.717514\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −7479.10 | −1.67647 | −0.838234 | − | 0.545311i | \(-0.816412\pi\) | ||||
−0.838234 | + | 0.545311i | \(0.816412\pi\) | |||||||
\(272\) | −426.835 | − | 739.301i | −0.0951496 | − | 0.164804i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 1793.46 | − | 3106.36i | 0.395426 | − | 0.684898i | ||||
\(275\) | −328.501 | + | 568.980i | −0.0720340 | + | 0.124766i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −2717.90 | − | 4707.54i | −0.589541 | − | 1.02112i | −0.994292 | − | 0.106688i | \(-0.965975\pi\) |
0.404751 | − | 0.914427i | \(-0.367358\pi\) | |||||||
\(278\) | −1186.20 | −0.255912 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −334.107 | −0.0713098 | ||||||||
\(281\) | 3683.92 | + | 6380.74i | 0.782079 | + | 1.35460i | 0.930729 | + | 0.365711i | \(0.119174\pi\) |
−0.148649 | + | 0.988890i | \(0.547493\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −2897.42 | + | 5018.47i | −0.608599 | + | 1.05412i | 0.382872 | + | 0.923801i | \(0.374935\pi\) |
−0.991472 | + | 0.130324i | \(0.958398\pi\) | |||||||
\(284\) | 393.771 | − | 682.031i | 0.0822746 | − | 0.142504i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 402.809 | + | 697.685i | 0.0832818 | + | 0.144248i | ||||
\(287\) | 665.465 | 0.136868 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −2066.31 | −0.420579 | ||||||||
\(290\) | −582.539 | − | 1008.99i | −0.117958 | − | 0.204309i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 1021.94 | − | 1770.05i | 0.204810 | − | 0.354741i | ||||
\(293\) | −2282.20 | + | 3952.89i | −0.455044 | + | 0.788159i | −0.998691 | − | 0.0511553i | \(-0.983710\pi\) |
0.543647 | + | 0.839314i | \(0.317043\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1207.90 | + | 2092.15i | 0.238396 | + | 0.412914i | ||||
\(296\) | −3455.07 | −0.678452 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 7049.42 | 1.37034 | ||||||||
\(299\) | 5375.60 | + | 9310.82i | 1.03973 | + | 1.80086i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1311.96 | + | 2272.39i | −0.251230 | + | 0.435144i | ||||
\(302\) | 199.977 | − | 346.370i | 0.0381039 | − | 0.0659980i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −710.371 | − | 1230.40i | −0.134022 | − | 0.232132i | ||||
\(305\) | 3441.60 | 0.646117 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 9770.57 | 1.81640 | 0.908202 | − | 0.418533i | \(-0.137455\pi\) | ||||
0.908202 | + | 0.418533i | \(0.137455\pi\) | |||||||
\(308\) | −102.881 | − | 178.195i | −0.0190331 | − | 0.0329663i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 990.103 | − | 1714.91i | 0.181400 | − | 0.314195i | ||||
\(311\) | −2917.06 | + | 5052.50i | −0.531870 | + | 0.921226i | 0.467438 | + | 0.884026i | \(0.345177\pi\) |
−0.999308 | + | 0.0371997i | \(0.988156\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −4032.66 | − | 6984.77i | −0.728241 | − | 1.26135i | −0.957626 | − | 0.288014i | \(-0.907005\pi\) |
0.229385 | − | 0.973336i | \(-0.426328\pi\) | |||||||
\(314\) | −1543.29 | −0.277367 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 1575.06 | 0.280393 | ||||||||
\(317\) | 1216.50 | + | 2107.04i | 0.215538 | + | 0.373323i | 0.953439 | − | 0.301586i | \(-0.0975161\pi\) |
−0.737901 | + | 0.674909i | \(0.764183\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 358.760 | − | 621.391i | 0.0629677 | − | 0.109063i | ||||
\(320\) | 190.918 | − | 330.680i | 0.0333521 | − | 0.0577675i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −1372.98 | − | 2378.07i | −0.237618 | − | 0.411567i | ||||
\(323\) | 4737.68 | 0.816135 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 4900.62 | 0.836422 | ||||||||
\(326\) | −215.179 | − | 372.700i | −0.0365572 | − | 0.0633189i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −380.265 | + | 658.639i | −0.0640142 | + | 0.110876i | ||||
\(329\) | −402.953 | + | 697.934i | −0.0675243 | + | 0.116956i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1455.34 | + | 2520.72i | 0.241670 | + | 0.418584i | 0.961190 | − | 0.275887i | \(-0.0889717\pi\) |
−0.719520 | + | 0.694471i | \(0.755638\pi\) | |||||||
\(332\) | −2107.49 | −0.348385 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 743.855 | 0.121862 | ||||||||
\(335\) | −130.632 | − | 226.262i | −0.0213051 | − | 0.0369015i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −2355.52 | + | 4079.88i | −0.380752 | + | 0.659482i | −0.991170 | − | 0.132598i | \(-0.957668\pi\) |
0.610418 | + | 0.792080i | \(0.291002\pi\) | |||||||
\(338\) | 807.577 | − | 1398.76i | 0.129960 | − | 0.225097i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 636.647 | + | 1102.70i | 0.101550 | + | 0.175890i | ||||
\(341\) | 1219.52 | 0.193668 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −343.000 | −0.0539949 | ||||||||
\(344\) | −1499.39 | − | 2597.02i | −0.235005 | − | 0.407040i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 102.729 | − | 177.932i | 0.0159617 | − | 0.0276465i | ||||
\(347\) | 4201.39 | − | 7277.01i | 0.649977 | − | 1.12579i | −0.333150 | − | 0.942874i | \(-0.608112\pi\) |
0.983128 | − | 0.182920i | \(-0.0585550\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 3161.78 | + | 5476.36i | 0.484946 | + | 0.839951i | 0.999850 | − | 0.0172969i | \(-0.00550604\pi\) |
−0.514905 | + | 0.857247i | \(0.672173\pi\) | |||||||
\(350\) | −1251.66 | −0.191155 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 235.157 | 0.0356076 | ||||||||
\(353\) | 2692.85 | + | 4664.15i | 0.406022 | + | 0.703251i | 0.994440 | − | 0.105306i | \(-0.0335821\pi\) |
−0.588417 | + | 0.808557i | \(0.700249\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −587.329 | + | 1017.28i | −0.0878090 | + | 0.152090i | ||||
\(356\) | −1179.64 | + | 2043.19i | −0.175620 | + | 0.304182i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 4299.18 | + | 7446.39i | 0.634689 | + | 1.09931i | ||||
\(359\) | 11993.9 | 1.76327 | 0.881637 | − | 0.471927i | \(-0.156442\pi\) | ||||
0.881637 | + | 0.471927i | \(0.156442\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1025.80 | 0.149555 | ||||||||
\(362\) | −3032.50 | − | 5252.44i | −0.440289 | − | 0.762603i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −767.396 | + | 1329.17i | −0.110501 | + | 0.191394i | ||||
\(365\) | −1524.27 | + | 2640.12i | −0.218587 | + | 0.378603i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2615.33 | + | 4529.89i | 0.371987 | + | 0.644301i | 0.989871 | − | 0.141968i | \(-0.0453432\pi\) |
−0.617884 | + | 0.786269i | \(0.712010\pi\) | |||||||
\(368\) | 3138.23 | 0.444543 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 5153.41 | 0.724090 | ||||||||
\(371\) | 509.421 | + | 882.343i | 0.0712880 | + | 0.123474i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −4334.34 | + | 7507.30i | −0.601672 | + | 1.04213i | 0.390896 | + | 0.920435i | \(0.372165\pi\) |
−0.992568 | + | 0.121692i | \(0.961168\pi\) | |||||||
\(374\) | −392.083 | + | 679.107i | −0.0542089 | + | 0.0938925i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −460.517 | − | 797.639i | −0.0631632 | − | 0.109402i | ||||
\(377\) | −5352.03 | −0.731150 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −6465.25 | −0.876247 | −0.438123 | − | 0.898915i | \(-0.644357\pi\) | ||||
−0.438123 | + | 0.898915i | \(0.644357\pi\) | |||||||
\(380\) | 1059.55 | + | 1835.20i | 0.143037 | + | 0.247747i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 2492.29 | − | 4316.78i | 0.333814 | − | 0.578183i | ||||
\(383\) | 6827.24 | − | 11825.1i | 0.910850 | − | 1.57764i | 0.0979832 | − | 0.995188i | \(-0.468761\pi\) |
0.812867 | − | 0.582450i | \(-0.197906\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 153.452 | + | 265.787i | 0.0203134 | + | 0.0351838i | ||||
\(386\) | 4307.93 | 0.568051 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 3745.86 | 0.490122 | ||||||||
\(389\) | −4249.25 | − | 7359.92i | −0.553844 | − | 0.959287i | −0.997992 | − | 0.0633332i | \(-0.979827\pi\) |
0.444148 | − | 0.895953i | \(-0.353506\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −5232.46 | + | 9062.88i | −0.676769 | + | 1.17220i | ||||
\(392\) | 196.000 | − | 339.482i | 0.0252538 | − | 0.0437409i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −5115.11 | − | 8859.64i | −0.654050 | − | 1.13285i | ||||
\(395\) | −2349.29 | −0.299254 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 12203.2 | 1.54272 | 0.771360 | − | 0.636399i | \(-0.219577\pi\) | ||||
0.771360 | + | 0.636399i | \(0.219577\pi\) | |||||||
\(398\) | −2870.67 | − | 4972.14i | −0.361541 | − | 0.626208i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 715.235 | − | 1238.82i | 0.0894044 | − | 0.154853i | ||||
\(401\) | 4882.89 | − | 8457.42i | 0.608080 | − | 1.05323i | −0.383477 | − | 0.923551i | \(-0.625273\pi\) |
0.991557 | − | 0.129675i | \(-0.0413933\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −4548.25 | − | 7877.80i | −0.562195 | − | 0.973750i | ||||
\(404\) | 1708.59 | 0.210409 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 1366.96 | 0.167096 | ||||||||
\(407\) | 1586.88 | + | 2748.56i | 0.193265 | + | 0.334744i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 3897.13 | − | 6750.04i | 0.471151 | − | 0.816058i | −0.528304 | − | 0.849055i | \(-0.677172\pi\) |
0.999455 | + | 0.0329971i | \(0.0105052\pi\) | |||||||
\(410\) | 567.185 | − | 982.393i | 0.0683202 | − | 0.118334i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 3990.26 | + | 6911.34i | 0.477151 | + | 0.826450i | ||||
\(413\) | −2834.40 | −0.337704 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 3143.43 | 0.371820 | ||||||||
\(416\) | −877.024 | − | 1519.05i | −0.103365 | − | 0.179033i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −652.533 | + | 1130.22i | −0.0763551 | + | 0.132251i | ||||
\(419\) | −6042.62 | + | 10466.1i | −0.704538 | + | 1.22030i | 0.262320 | + | 0.964981i | \(0.415512\pi\) |
−0.966858 | + | 0.255314i | \(0.917821\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −4925.64 | − | 8531.46i | −0.570217 | − | 0.987644i | −0.996543 | − | 0.0830748i | \(-0.973526\pi\) |
0.426327 | − | 0.904569i | \(-0.359807\pi\) | |||||||
\(422\) | 4400.73 | 0.507640 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −1164.39 | −0.133368 | ||||||||
\(425\) | 2385.06 | + | 4131.05i | 0.272218 | + | 0.471495i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −2018.97 | + | 3496.97i | −0.228817 | + | 0.396323i | ||||
\(428\) | 3733.75 | − | 6467.04i | 0.421676 | − | 0.730365i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 2236.41 | + | 3873.58i | 0.250813 | + | 0.434420i | ||||
\(431\) | 268.348 | 0.0299904 | 0.0149952 | − | 0.999888i | \(-0.495227\pi\) | ||||
0.0149952 | + | 0.999888i | \(0.495227\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −2696.15 | −0.299235 | −0.149617 | − | 0.988744i | \(-0.547804\pi\) | ||||
−0.149617 | + | 0.988744i | \(0.547804\pi\) | |||||||
\(434\) | 1161.66 | + | 2012.06i | 0.128483 | + | 0.222539i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 1171.30 | − | 2028.76i | 0.128659 | − | 0.222843i | ||||
\(437\) | −8708.25 | + | 15083.1i | −0.953254 | + | 1.65108i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 4691.03 | + | 8125.10i | 0.510001 | + | 0.883348i | 0.999933 | + | 0.0115874i | \(0.00368845\pi\) |
−0.489931 | + | 0.871761i | \(0.662978\pi\) | |||||||
\(440\) | −350.748 | −0.0380029 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 5849.14 | 0.629446 | ||||||||
\(443\) | 6343.60 | + | 10987.4i | 0.680347 | + | 1.17839i | 0.974875 | + | 0.222752i | \(0.0715041\pi\) |
−0.294529 | + | 0.955643i | \(0.595163\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1759.49 | − | 3047.52i | 0.187433 | − | 0.324644i | ||||
\(446\) | −2988.59 | + | 5176.39i | −0.317296 | + | 0.549572i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 224.000 | + | 387.979i | 0.0236228 | + | 0.0409159i | ||||
\(449\) | −8285.34 | −0.870845 | −0.435423 | − | 0.900226i | \(-0.643401\pi\) | ||||
−0.435423 | + | 0.900226i | \(0.643401\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 698.609 | 0.0729406 | ||||||||
\(452\) | −1482.16 | − | 2567.18i | −0.154237 | − | 0.267146i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −1743.72 | + | 3020.21i | −0.180257 | + | 0.312214i | ||||
\(455\) | 1144.61 | − | 1982.52i | 0.117934 | − | 0.204268i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −7970.71 | − | 13805.7i | −0.815873 | − | 1.41313i | −0.908699 | − | 0.417451i | \(-0.862923\pi\) |
0.0928263 | − | 0.995682i | \(-0.470410\pi\) | |||||||
\(458\) | 3249.23 | 0.331499 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −4680.84 | −0.474446 | ||||||||
\(461\) | −5159.87 | − | 8937.15i | −0.521299 | − | 0.902917i | −0.999693 | − | 0.0247714i | \(-0.992114\pi\) |
0.478394 | − | 0.878145i | \(-0.341219\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −9235.81 | + | 15996.9i | −0.927050 | + | 1.60570i | −0.138820 | + | 0.990318i | \(0.544331\pi\) |
−0.788230 | + | 0.615381i | \(0.789002\pi\) | |||||||
\(464\) | −781.118 | + | 1352.94i | −0.0781520 | + | 0.135363i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −4815.42 | − | 8340.56i | −0.478691 | − | 0.829118i | ||||
\(467\) | 1991.38 | 0.197324 | 0.0986619 | − | 0.995121i | \(-0.468544\pi\) | ||||
0.0986619 | + | 0.995121i | \(0.468544\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 306.535 | 0.0301802 | ||||||||
\(470\) | 686.885 | + | 1189.72i | 0.0674120 | + | 0.116761i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 1619.66 | − | 2805.33i | 0.157947 | − | 0.273572i | ||||
\(473\) | −1377.31 | + | 2385.57i | −0.133887 | + | 0.231900i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 3969.40 | + | 6875.19i | 0.383428 | + | 0.664117i | ||||
\(476\) | −1493.92 | −0.143853 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −6876.07 | −0.657958 | ||||||||
\(479\) | −3702.84 | − | 6413.51i | −0.353209 | − | 0.611777i | 0.633600 | − | 0.773660i | \(-0.281576\pi\) |
−0.986810 | + | 0.161884i | \(0.948243\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 11836.6 | − | 20501.7i | 1.12205 | − | 1.94344i | ||||
\(482\) | −5656.96 | + | 9798.14i | −0.534580 | + | 0.925919i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 2553.99 | + | 4423.65i | 0.239857 | + | 0.415444i | ||||
\(485\) | −5587.14 | −0.523090 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 7064.90 | 0.657374 | 0.328687 | − | 0.944439i | \(-0.393394\pi\) | ||||
0.328687 | + | 0.944439i | \(0.393394\pi\) | |||||||
\(488\) | −2307.40 | − | 3996.53i | −0.214039 | − | 0.370727i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −292.344 | + | 506.355i | −0.0269526 | + | 0.0466832i | ||||
\(491\) | −2706.72 | + | 4688.17i | −0.248783 | + | 0.430904i | −0.963188 | − | 0.268827i | \(-0.913364\pi\) |
0.714406 | + | 0.699732i | \(0.246697\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −2604.76 | − | 4511.57i | −0.237956 | − | 0.412152i | ||||
\(494\) | 9734.57 | 0.886598 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −2655.23 | −0.240370 | ||||||||
\(497\) | −689.099 | − | 1193.55i | −0.0621938 | − | 0.107723i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −6682.03 | + | 11573.6i | −0.599456 | + | 1.03829i | 0.393445 | + | 0.919348i | \(0.371283\pi\) |
−0.992901 | + | 0.118941i | \(0.962050\pi\) | |||||||
\(500\) | −2558.36 | + | 4431.21i | −0.228827 | + | 0.396339i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −7375.50 | − | 12774.7i | −0.655746 | − | 1.13579i | ||||
\(503\) | 19112.4 | 1.69420 | 0.847098 | − | 0.531437i | \(-0.178348\pi\) | ||||
0.847098 | + | 0.531437i | \(0.178348\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −2548.44 | −0.224563 | ||||||||
\(506\) | −1441.36 | − | 2496.51i | −0.126633 | − | 0.219335i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 145.836 | − | 252.595i | 0.0127370 | − | 0.0220612i | ||||
\(509\) | 9593.67 | − | 16616.7i | 0.835426 | − | 1.44700i | −0.0582574 | − | 0.998302i | \(-0.518554\pi\) |
0.893683 | − | 0.448698i | \(-0.148112\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1788.39 | − | 3097.59i | −0.154822 | − | 0.268159i | ||||
\(512\) | −512.000 | −0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −517.977 | −0.0444494 | ||||||||
\(515\) | −5951.68 | − | 10308.6i | −0.509247 | − | 0.882042i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −423.022 | + | 732.696i | −0.0359855 | + | 0.0623287i | ||||
\(518\) | −3023.19 | + | 5236.31i | −0.256431 | + | 0.444151i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 1308.13 | + | 2265.74i | 0.110318 | + | 0.191076i | ||||
\(521\) | −17848.7 | −1.50089 | −0.750445 | − | 0.660933i | \(-0.770161\pi\) | ||||
−0.750445 | + | 0.660933i | \(0.770161\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −18283.8 | −1.52867 | −0.764334 | − | 0.644821i | \(-0.776932\pi\) | ||||
−0.764334 | + | 0.644821i | \(0.776932\pi\) | |||||||
\(524\) | 1881.98 | + | 3259.68i | 0.156898 | + | 0.271755i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −4138.96 | + | 7168.89i | −0.343094 | + | 0.594256i | ||||
\(527\) | 4427.14 | − | 7668.03i | 0.365938 | − | 0.633823i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −13151.9 | − | 22779.7i | −1.08095 | − | 1.87226i | ||||
\(530\) | 1736.75 | 0.142339 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −2486.30 | −0.202622 | ||||||||
\(533\) | −2605.48 | − | 4512.83i | −0.211737 | − | 0.366740i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −5569.07 | + | 9645.91i | −0.450041 | + | 0.779494i | ||||
\(536\) | −175.163 | + | 303.391i | −0.0141155 | + | 0.0244487i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −5571.27 | − | 9649.72i | −0.446458 | − | 0.773288i | ||||
\(539\) | −360.084 | −0.0287753 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 16801.9 | 1.33525 | 0.667623 | − | 0.744500i | \(-0.267312\pi\) | ||||
0.667623 | + | 0.744500i | \(0.267312\pi\) | |||||||
\(542\) | −7479.10 | − | 12954.2i | −0.592721 | − | 1.02662i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 853.671 | − | 1478.60i | 0.0672809 | − | 0.116534i | ||||
\(545\) | −1747.06 | + | 3025.99i | −0.137313 | + | 0.237833i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −3217.95 | − | 5573.66i | −0.251535 | − | 0.435672i | 0.712414 | − | 0.701760i | \(-0.247602\pi\) |
−0.963949 | + | 0.266088i | \(0.914269\pi\) | |||||||
\(548\) | 7173.83 | 0.559216 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −1314.00 | −0.101871 | ||||||||
\(551\) | −4335.03 | − | 7508.49i | −0.335170 | − | 0.580531i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1378.18 | − | 2387.08i | 0.105979 | − | 0.183560i | ||||
\(554\) | 5435.80 | − | 9415.09i | 0.416869 | − | 0.722038i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −1186.20 | − | 2054.56i | −0.0904784 | − | 0.156713i | ||||
\(557\) | 1258.90 | 0.0957657 | 0.0478829 | − | 0.998853i | \(-0.484753\pi\) | ||||
0.0478829 | + | 0.998853i | \(0.484753\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 20546.9 | 1.55463 | ||||||||
\(560\) | −334.107 | − | 578.691i | −0.0252118 | − | 0.0436681i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −7367.84 | + | 12761.5i | −0.553013 | + | 0.957847i | ||||
\(563\) | 1032.66 | − | 1788.63i | 0.0773030 | − | 0.133893i | −0.824782 | − | 0.565450i | \(-0.808702\pi\) |
0.902085 | + | 0.431557i | \(0.142036\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 2210.72 | + | 3829.08i | 0.164612 | + | 0.285116i | ||||
\(566\) | −11589.7 | −0.860689 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 1575.08 | 0.116354 | ||||||||
\(569\) | 61.9784 | + | 107.350i | 0.00456638 | + | 0.00790920i | 0.868300 | − | 0.496040i | \(-0.165213\pi\) |
−0.863733 | + | 0.503949i | \(0.831880\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 612.046 | − | 1060.10i | 0.0448570 | − | 0.0776946i | −0.842725 | − | 0.538344i | \(-0.819050\pi\) |
0.887582 | + | 0.460649i | \(0.152383\pi\) | |||||||
\(572\) | −805.618 | + | 1395.37i | −0.0588891 | + | 0.101999i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 665.465 | + | 1152.62i | 0.0483902 | + | 0.0838142i | ||||
\(575\) | −17535.8 | −1.27181 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −22288.4 | −1.60811 | −0.804055 | − | 0.594555i | \(-0.797328\pi\) | ||||
−0.804055 | + | 0.594555i | \(0.797328\pi\) | |||||||
\(578\) | −2066.31 | − | 3578.95i | −0.148697 | − | 0.257551i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 1165.08 | − | 2017.97i | 0.0834090 | − | 0.144469i | ||||
\(581\) | −1844.06 | + | 3194.00i | −0.131677 | + | 0.228071i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 534.794 | + | 926.290i | 0.0379912 | + | 0.0658028i | ||||
\(584\) | 4087.75 | 0.289645 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −9128.82 | −0.643529 | ||||||||
\(587\) | −8503.97 | − | 14729.3i | −0.597949 | − | 1.03568i | −0.993123 | − | 0.117073i | \(-0.962649\pi\) |
0.395174 | − | 0.918606i | \(-0.370684\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 7367.97 | − | 12761.7i | 0.515436 | − | 0.892762i | ||||
\(590\) | −2415.80 | + | 4184.29i | −0.168571 | + | 0.291974i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −3455.07 | − | 5984.36i | −0.239869 | − | 0.415466i | ||||
\(593\) | −2043.54 | −0.141515 | −0.0707574 | − | 0.997494i | \(-0.522542\pi\) | ||||
−0.0707574 | + | 0.997494i | \(0.522542\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 2228.26 | 0.153529 | ||||||||
\(596\) | 7049.42 | + | 12210.0i | 0.484489 | + | 0.839160i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −10751.2 | + | 18621.6i | −0.735200 | + | 1.27340i | ||||
\(599\) | 5409.54 | − | 9369.60i | 0.368995 | − | 0.639118i | −0.620414 | − | 0.784275i | \(-0.713035\pi\) |
0.989409 | + | 0.145157i | \(0.0463687\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 2611.91 | + | 4523.95i | 0.177274 | + | 0.307048i | 0.940946 | − | 0.338557i | \(-0.109939\pi\) |
−0.763672 | + | 0.645605i | \(0.776605\pi\) | |||||||
\(602\) | −5247.86 | −0.355294 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 799.908 | 0.0538871 | ||||||||
\(605\) | −3809.41 | − | 6598.10i | −0.255991 | − | 0.443390i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 4311.44 | − | 7467.63i | 0.288296 | − | 0.499344i | −0.685107 | − | 0.728442i | \(-0.740245\pi\) |
0.973403 | + | 0.229099i | \(0.0735779\pi\) | |||||||
\(608\) | 1420.74 | − | 2460.80i | 0.0947676 | − | 0.164142i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 3441.60 | + | 5961.03i | 0.228437 | + | 0.395664i | ||||
\(611\) | 6310.70 | 0.417846 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −1749.52 | −0.115273 | −0.0576366 | − | 0.998338i | \(-0.518356\pi\) | ||||
−0.0576366 | + | 0.998338i | \(0.518356\pi\) | |||||||
\(614\) | 9770.57 | + | 16923.1i | 0.642196 | + | 1.11232i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 205.762 | − | 356.390i | 0.0134584 | − | 0.0233107i | ||||
\(617\) | 1166.01 | − | 2019.59i | 0.0760809 | − | 0.131776i | −0.825475 | − | 0.564439i | \(-0.809093\pi\) |
0.901556 | + | 0.432663i | \(0.142426\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −8104.50 | − | 14037.4i | −0.526248 | − | 0.911488i | −0.999532 | − | 0.0305782i | \(-0.990265\pi\) |
0.473285 | − | 0.880910i | \(-0.343068\pi\) | |||||||
\(620\) | 3960.41 | 0.256539 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −11668.3 | −0.752178 | ||||||||
\(623\) | 2064.36 | + | 3575.58i | 0.132756 | + | 0.229940i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −1771.85 | + | 3068.94i | −0.113399 | + | 0.196412i | ||||
\(626\) | 8065.32 | − | 13969.5i | 0.514944 | − | 0.891909i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −1543.29 | − | 2673.06i | −0.0980639 | − | 0.169852i | ||||
\(629\) | 23042.9 | 1.46070 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −14574.4 | −0.919488 | −0.459744 | − | 0.888052i | \(-0.652059\pi\) | ||||
−0.459744 | + | 0.888052i | \(0.652059\pi\) | |||||||
\(632\) | 1575.06 | + | 2728.09i | 0.0991340 | + | 0.171705i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −2433.01 | + | 4214.09i | −0.152409 | + | 0.263979i | ||||
\(635\) | −217.521 | + | 376.758i | −0.0135938 | + | 0.0235451i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1342.94 | + | 2326.05i | 0.0835312 | + | 0.144680i | ||||
\(638\) | 1435.04 | 0.0890498 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 763.674 | 0.0471670 | ||||||||
\(641\) | 685.232 | + | 1186.86i | 0.0422232 | + | 0.0731327i | 0.886365 | − | 0.462988i | \(-0.153223\pi\) |
−0.844142 | + | 0.536120i | \(0.819889\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1379.94 | − | 2390.12i | 0.0846336 | − | 0.146590i | −0.820601 | − | 0.571501i | \(-0.806361\pi\) |
0.905235 | + | 0.424911i | \(0.139695\pi\) | |||||||
\(644\) | 2745.96 | − | 4756.13i | 0.168021 | − | 0.291022i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 4737.68 | + | 8205.90i | 0.288547 | + | 0.499778i | ||||
\(647\) | 3675.83 | 0.223357 | 0.111678 | − | 0.993744i | \(-0.464377\pi\) | ||||
0.111678 | + | 0.993744i | \(0.464377\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −2975.58 | −0.179972 | ||||||||
\(650\) | 4900.62 | + | 8488.12i | 0.295720 | + | 0.512202i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 430.357 | − | 745.400i | 0.0258498 | − | 0.0447732i | ||||
\(653\) | 4565.83 | − | 7908.26i | 0.273622 | − | 0.473926i | −0.696165 | − | 0.717882i | \(-0.745112\pi\) |
0.969786 | + | 0.243955i | \(0.0784451\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −2807.06 | − | 4861.98i | −0.167452 | − | 0.290035i | ||||
\(656\) | −1521.06 | −0.0905297 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −1611.81 | −0.0954938 | ||||||||
\(659\) | 3378.65 | + | 5851.99i | 0.199717 | + | 0.345920i | 0.948437 | − | 0.316967i | \(-0.102664\pi\) |
−0.748720 | + | 0.662887i | \(0.769331\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −11202.9 | + | 19403.9i | −0.659215 | + | 1.14179i | 0.321604 | + | 0.946874i | \(0.395778\pi\) |
−0.980819 | + | 0.194920i | \(0.937555\pi\) | |||||||
\(662\) | −2910.68 | + | 5041.44i | −0.170886 | + | 0.295983i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −2107.49 | − | 3650.29i | −0.123173 | − | 0.213341i | ||||
\(665\) | 3708.44 | 0.216251 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 19151.0 | 1.11174 | ||||||||
\(668\) | 743.855 | + | 1288.40i | 0.0430848 | + | 0.0746250i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 261.265 | − | 452.524i | 0.0150650 | − | 0.0260933i | ||||
\(671\) | −2119.53 | + | 3671.14i | −0.121943 | + | 0.211211i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 7266.75 | + | 12586.4i | 0.416215 | + | 0.720905i | 0.995555 | − | 0.0941807i | \(-0.0300232\pi\) |
−0.579340 | + | 0.815086i | \(0.696690\pi\) | |||||||
\(674\) | −9422.09 | −0.538465 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 3230.31 | 0.183791 | ||||||||
\(677\) | −14651.4 | − | 25377.0i | −0.831758 | − | 1.44065i | −0.896643 | − | 0.442754i | \(-0.854002\pi\) |
0.0648858 | − | 0.997893i | \(-0.479332\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 3277.63 | − | 5677.02i | 0.185249 | − | 0.320860i | ||||
\(680\) | −1273.29 | + | 2205.41i | −0.0718067 | + | 0.124373i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 1219.52 | + | 2112.28i | 0.0684721 | + | 0.118597i | ||||
\(683\) | 15718.2 | 0.880584 | 0.440292 | − | 0.897855i | \(-0.354875\pi\) | ||||
0.440292 | + | 0.897855i | \(0.354875\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −10700.1 | −0.596833 | ||||||||
\(686\) | −343.000 | − | 594.093i | −0.0190901 | − | 0.0330650i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 2998.78 | − | 5194.03i | 0.166173 | − | 0.287821i | ||||
\(689\) | 3989.06 | − | 6909.26i | 0.220568 | − | 0.382034i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 11677.9 | + | 20226.7i | 0.642906 | + | 1.11355i | 0.984781 | + | 0.173800i | \(0.0556048\pi\) |
−0.341875 | + | 0.939745i | \(0.611062\pi\) | |||||||
\(692\) | 410.916 | 0.0225732 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 16805.5 | 0.919207 | ||||||||
\(695\) | 1769.27 | + | 3064.47i | 0.0965646 | + | 0.167255i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2536.11 | − | 4392.66i | 0.137822 | − | 0.238714i | ||||
\(698\) | −6323.55 | + | 10952.7i | −0.342908 | + | 0.593935i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −1251.66 | − | 2167.94i | −0.0675834 | − | 0.117058i | ||||
\(701\) | −34760.7 | −1.87289 | −0.936445 | − | 0.350815i | \(-0.885904\pi\) | ||||
−0.936445 | + | 0.350815i | \(0.885904\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 38349.7 | 2.05745 | ||||||||
\(704\) | 235.157 | + | 407.303i | 0.0125892 | + | 0.0218051i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −5385.70 | + | 9328.30i | −0.287101 | + | 0.497274i | ||||
\(707\) | 1495.01 | − | 2589.44i | 0.0795272 | − | 0.137745i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 3237.66 | + | 5607.79i | 0.171499 | + | 0.297045i | 0.938944 | − | 0.344070i | \(-0.111806\pi\) |
−0.767445 | + | 0.641115i | \(0.778472\pi\) | |||||||
\(710\) | −2349.32 | −0.124181 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −4718.55 | −0.248364 | ||||||||
\(713\) | 16274.9 | + | 28188.9i | 0.854838 | + | 1.48062i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1201.62 | − | 2081.27i | 0.0628504 | − | 0.108860i | ||||
\(716\) | −8598.35 | + | 14892.8i | −0.448793 | + | 0.777332i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 11993.9 | + | 20774.1i | 0.623412 | + | 1.07978i | ||||
\(719\) | 7178.95 | 0.372364 | 0.186182 | − | 0.982515i | \(-0.440389\pi\) | ||||
0.186182 | + | 0.982515i | \(0.440389\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 13965.9 | 0.721384 | ||||||||
\(722\) | 1025.80 | + | 1776.73i | 0.0528757 | + | 0.0915833i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 6065.00 | − | 10504.9i | 0.311331 | − | 0.539242i | ||||
\(725\) | 4364.71 | − | 7559.91i | 0.223588 | − | 0.387266i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 4077.92 | + | 7063.16i | 0.208035 | + | 0.360328i | 0.951096 | − | 0.308897i | \(-0.0999598\pi\) |
−0.743060 | + | 0.669225i | \(0.766626\pi\) | |||||||
\(728\) | −3069.59 | −0.156273 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −6097.09 | −0.309128 | ||||||||
\(731\) | 9999.87 | + | 17320.3i | 0.505962 | + | 0.876353i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 7672.05 | − | 13288.4i | 0.386594 | − | 0.669601i | −0.605395 | − | 0.795925i | \(-0.706985\pi\) |
0.991989 | + | 0.126325i | \(0.0403181\pi\) | |||||||
\(734\) | −5230.67 | + | 9059.78i | −0.263035 | + | 0.455590i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 3138.23 | + | 5435.58i | 0.157170 | + | 0.272226i | ||||
\(737\) | 321.803 | 0.0160838 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −10730.9 | −0.534155 | −0.267078 | − | 0.963675i | \(-0.586058\pi\) | ||||
−0.267078 | + | 0.963675i | \(0.586058\pi\) | |||||||
\(740\) | 5153.41 | + | 8925.97i | 0.256004 | + | 0.443413i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −1018.84 | + | 1764.69i | −0.0504082 | + | 0.0873096i | ||||
\(743\) | −7772.66 | + | 13462.6i | −0.383783 | + | 0.664732i | −0.991600 | − | 0.129345i | \(-0.958712\pi\) |
0.607816 | + | 0.794078i | \(0.292046\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −10514.6 | − | 18211.8i | −0.517079 | − | 0.895607i | ||||
\(746\) | −17337.4 | −0.850893 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −1568.33 | −0.0766629 | ||||||||
\(749\) | −6534.06 | − | 11317.3i | −0.318757 | − | 0.552104i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1264.26 | − | 2189.76i | 0.0614292 | − | 0.106399i | −0.833675 | − | 0.552255i | \(-0.813767\pi\) |
0.895104 | + | 0.445856i | \(0.147101\pi\) | |||||||
\(752\) | 921.034 | − | 1595.28i | 0.0446631 | − | 0.0773588i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −5352.03 | − | 9269.99i | −0.258501 | − | 0.447736i | ||||
\(755\) | −1193.10 | −0.0575119 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −890.832 | −0.0427712 | −0.0213856 | − | 0.999771i | \(-0.506808\pi\) | ||||
−0.0213856 | + | 0.999771i | \(0.506808\pi\) | |||||||
\(758\) | −6465.25 | − | 11198.1i | −0.309800 | − | 0.536589i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −2119.11 | + | 3670.40i | −0.101142 | + | 0.175184i | ||||
\(761\) | −7254.29 | + | 12564.8i | −0.345556 | + | 0.598520i | −0.985455 | − | 0.169939i | \(-0.945643\pi\) |
0.639899 | + | 0.768459i | \(0.278976\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −2049.78 | − | 3550.32i | −0.0972569 | − | 0.168454i | ||||
\(764\) | 9969.18 | 0.472084 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 27308.9 | 1.28814 | ||||||||
\(767\) | 11097.5 | + | 19221.4i | 0.522435 | + | 0.904884i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −3721.33 | + | 6445.54i | −0.174505 | + | 0.302252i | −0.939990 | − | 0.341202i | \(-0.889166\pi\) |
0.765485 | + | 0.643454i | \(0.222499\pi\) | |||||||
\(770\) | −306.905 | + | 531.574i | −0.0143637 | + | 0.0248787i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 4307.93 | + | 7461.55i | 0.200836 | + | 0.347859i | ||||
\(773\) | 2614.02 | 0.121630 | 0.0608148 | − | 0.998149i | \(-0.480630\pi\) | ||||
0.0608148 | + | 0.998149i | \(0.480630\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 14836.8 | 0.687684 | ||||||||
\(776\) | 3745.86 | + | 6488.02i | 0.173284 | + | 0.300137i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 8498.50 | − | 14719.8i | 0.391627 | − | 0.678318i | ||||
\(779\) | 4220.77 | − | 7310.60i | 0.194127 | − | 0.336238i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −723.420 | − | 1253.00i | −0.0331447 | − | 0.0574083i | ||||
\(782\) | −20929.8 | −0.957096 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 784.000 | 0.0357143 | ||||||||
\(785\) | 2301.90 | + | 3987.01i | 0.104660 | + | 0.181277i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 13238.7 | − | 22930.1i | 0.599629 | − | 1.03859i | −0.393247 | − | 0.919433i | \(-0.628648\pi\) |
0.992876 | − | 0.119155i | \(-0.0380185\pi\) | |||||||
\(788\) | 10230.2 | − | 17719.3i | 0.462483 | − | 0.801044i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −2349.29 | − | 4069.08i | −0.105802 | − | 0.183255i | ||||
\(791\) | −5187.57 | −0.233184 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 31619.5 | 1.41594 | ||||||||
\(794\) | 12203.2 | + | 21136.5i | 0.545434 | + | 0.944719i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 5741.33 | − | 9944.28i | 0.255648 | − | 0.442796i | ||||
\(797\) | 14542.1 | − | 25187.7i | 0.646309 | − | 1.11944i | −0.337689 | − | 0.941258i | \(-0.609645\pi\) |
0.983998 | − | 0.178182i | \(-0.0570215\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 3071.33 | + | 5319.70i | 0.135990 | + | 0.235541i | ||||
\(800\) | 2860.94 | 0.126437 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 19531.6 | 0.859955 | ||||||||
\(803\) | −1877.47 | − | 3251.87i | −0.0825085 | − | 0.142909i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −4095.73 | + | 7094.01i | −0.179324 | + | 0.310598i | ||||
\(806\) | 9096.50 | − | 15755.6i | 0.397532 | − | 0.688545i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 1708.59 | + | 2959.36i | 0.0743909 | + | 0.128849i | ||||
\(809\) | −8808.99 | −0.382828 | −0.191414 | − | 0.981509i | \(-0.561307\pi\) | ||||
−0.191414 | + | 0.981509i | \(0.561307\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −14856.3 | −0.643251 | −0.321625 | − | 0.946867i | \(-0.604229\pi\) | ||||
−0.321625 | + | 0.946867i | \(0.604229\pi\) | |||||||
\(812\) | 1366.96 | + | 2367.64i | 0.0590773 | + | 0.102325i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −3173.76 | + | 5497.12i | −0.136659 | + | 0.236700i | ||||
\(815\) | −641.899 | + | 1111.80i | −0.0275887 | + | 0.0477850i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 16642.5 | + | 28825.7i | 0.712666 | + | 1.23437i | ||||
\(818\) | 15588.5 | 0.666309 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 2268.74 | 0.0966193 | ||||||||
\(821\) | 12778.9 | + | 22133.7i | 0.543223 | + | 0.940890i | 0.998716 | + | 0.0506511i | \(0.0161296\pi\) |
−0.455493 | + | 0.890239i | \(0.650537\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −3718.84 | + | 6441.23i | −0.157510 | + | 0.272815i | −0.933970 | − | 0.357351i | \(-0.883680\pi\) |
0.776460 | + | 0.630166i | \(0.217013\pi\) | |||||||
\(824\) | −7980.53 | + | 13822.7i | −0.337397 | + | 0.584388i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −2834.40 | − | 4909.33i | −0.119397 | − | 0.206801i | ||||
\(827\) | 12890.0 | 0.541995 | 0.270998 | − | 0.962580i | \(-0.412646\pi\) | ||||
0.270998 | + | 0.962580i | \(0.412646\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −8592.44 | −0.359985 | −0.179993 | − | 0.983668i | \(-0.557607\pi\) | ||||
−0.179993 | + | 0.983668i | \(0.557607\pi\) | |||||||
\(830\) | 3143.43 | + | 5444.59i | 0.131458 | + | 0.227692i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 1754.05 | − | 3038.10i | 0.0730898 | − | 0.126595i | ||||
\(833\) | −1307.18 | + | 2264.11i | −0.0543712 | + | 0.0941737i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1109.50 | − | 1921.71i | −0.0459829 | − | 0.0796448i | ||||
\(836\) | −2610.13 | −0.107982 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −24170.5 | −0.996367 | ||||||||
\(839\) | −17776.0 | − | 30789.0i | −0.731462 | − | 1.26693i | −0.956258 | − | 0.292523i | \(-0.905505\pi\) |
0.224797 | − | 0.974406i | \(-0.427828\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 7427.74 | − | 12865.2i | 0.304553 | − | 0.527501i | ||||
\(842\) | 9851.29 | − | 17062.9i | 0.403204 | − | 0.698370i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 4400.73 | + | 7622.29i | 0.179478 | + | 0.310865i | ||||
\(845\) | −4818.17 | −0.196154 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 8938.98 | 0.362629 | ||||||||
\(848\) | −1164.39 | − | 2016.78i | −0.0471526 | − | 0.0816706i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −4770.12 | + | 8262.09i | −0.192487 | + | 0.333397i | ||||
\(851\) | −42354.8 | + | 73360.6i | −1.70611 | + | 2.95508i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 2104.95 | + | 3645.88i | 0.0844926 | + | 0.146345i | 0.905175 | − | 0.425039i | \(-0.139740\pi\) |
−0.820682 | + | 0.571385i | \(0.806406\pi\) | |||||||
\(854\) | −8075.90 | −0.323597 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 14935.0 | 0.596340 | ||||||||
\(857\) | −1438.67 | − | 2491.85i | −0.0573443 | − | 0.0993232i | 0.835928 | − | 0.548839i | \(-0.184930\pi\) |
−0.893272 | + | 0.449516i | \(0.851597\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 2494.94 | − | 4321.37i | 0.0990993 | − | 0.171645i | −0.812213 | − | 0.583361i | \(-0.801737\pi\) |
0.911312 | + | 0.411716i | \(0.135071\pi\) | |||||||
\(860\) | −4472.83 | + | 7747.16i | −0.177351 | + | 0.307181i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 268.348 | + | 464.793i | 0.0106032 | + | 0.0183653i | ||||
\(863\) | 20313.7 | 0.801260 | 0.400630 | − | 0.916240i | \(-0.368791\pi\) | ||||
0.400630 | + | 0.916240i | \(0.368791\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −612.902 | −0.0240917 | ||||||||
\(866\) | −2696.15 | − | 4669.87i | −0.105795 | − | 0.183243i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −2323.33 | + | 4024.12i | −0.0908513 | + | 0.157359i | ||||
\(869\) | 1446.82 | − | 2505.97i | 0.0564788 | − | 0.0978242i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1200.17 | − | 2078.76i | −0.0466893 | − | 0.0808682i | ||||
\(872\) | 4685.21 | 0.181951 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −34833.0 | −1.34810 | ||||||||
\(875\) | 4477.13 | + | 7754.62i | 0.172977 | + | 0.299604i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1966.37 | + | 3405.85i | −0.0757120 | + | 0.131137i | −0.901396 | − | 0.432996i | \(-0.857456\pi\) |
0.825684 | + | 0.564133i | \(0.190790\pi\) | |||||||
\(878\) | −9382.06 | + | 16250.2i | −0.360625 | + | 0.624622i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −350.748 | − | 607.513i | −0.0134360 | − | 0.0232719i | ||||
\(881\) | 36905.8 | 1.41134 | 0.705668 | − | 0.708543i | \(-0.250647\pi\) | ||||
0.705668 | + | 0.708543i | \(0.250647\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −26603.9 | −1.01392 | −0.506960 | − | 0.861970i | \(-0.669231\pi\) | ||||
−0.506960 | + | 0.861970i | \(0.669231\pi\) | |||||||
\(884\) | 5849.14 | + | 10131.0i | 0.222543 | + | 0.385456i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −12687.2 | + | 21974.9i | −0.481078 | + | 0.833251i | ||||
\(887\) | 3983.32 | − | 6899.32i | 0.150786 | − | 0.261168i | −0.780731 | − | 0.624867i | \(-0.785153\pi\) |
0.931517 | + | 0.363699i | \(0.118486\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −255.212 | − | 442.041i | −0.00962828 | − | 0.0166767i | ||||
\(890\) | 7037.95 | 0.265070 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −11954.4 | −0.448724 | ||||||||
\(893\) | 5111.53 | + | 8853.43i | 0.191546 | + | 0.331768i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 12824.9 | − | 22213.3i | 0.478981 | − | 0.829620i | ||||
\(896\) | −448.000 | + | 775.959i | −0.0167038 | + | 0.0289319i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −8285.34 | − | 14350.6i | −0.307890 | − | 0.533282i | ||||
\(899\) | −16203.5 | −0.601132 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 7765.68 | 0.287139 | ||||||||
\(902\) | 698.609 | + | 1210.03i | 0.0257884 | + | 0.0446668i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 2964.33 | − | 5134.36i | 0.109062 | − | 0.188901i | ||||
\(905\) | −9046.25 | + | 15668.6i | −0.332274 | + | 0.575515i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −2900.71 | − | 5024.17i | −0.106192 | − | 0.183930i | 0.808032 | − | 0.589138i | \(-0.200533\pi\) |
−0.914225 | + | 0.405208i | \(0.867199\pi\) | |||||||
\(908\) | −6974.87 | −0.254922 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 4578.44 | 0.166784 | ||||||||
\(911\) | −9314.42 | − | 16133.0i | −0.338749 | − | 0.586731i | 0.645449 | − | 0.763804i | \(-0.276670\pi\) |
−0.984198 | + | 0.177073i | \(0.943337\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1935.90 | + | 3353.08i | −0.0701742 | + | 0.121545i | ||||
\(914\) | 15941.4 | − | 27611.3i | 0.576909 | − | 0.999236i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 3249.23 | + | 5627.83i | 0.117203 | + | 0.203001i | ||||
\(917\) | 6586.92 | 0.237207 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −36920.3 | −1.32523 | −0.662615 | − | 0.748960i | \(-0.730554\pi\) | ||||
−0.662615 | + | 0.748960i | \(0.730554\pi\) | |||||||
\(920\) | −4680.84 | − | 8107.44i | −0.167742 | − | 0.290538i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 10319.7 | − | 17874.3i | 0.368614 | − | 0.638459i | ||||
\(923\) | −5396.04 | + | 9346.21i | −0.192430 | + | 0.333298i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 19306.2 | + | 33439.3i | 0.686252 | + | 1.18862i | ||||
\(926\) | −36943.2 | −1.31105 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −3124.47 | −0.110524 | ||||||||
\(929\) | 11683.8 | + | 20236.9i | 0.412628 | + | 0.714693i | 0.995176 | − | 0.0981030i | \(-0.0312775\pi\) |
−0.582548 | + | 0.812796i | \(0.697944\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2175.51 | + | 3768.10i | −0.0765838 | + | 0.132647i | ||||
\(932\) | 9630.85 | − | 16681.1i | 0.338486 | − | 0.586275i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 1991.38 | + | 3449.18i | 0.0697645 | + | 0.120836i | ||||
\(935\) | 2339.24 | 0.0818198 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −17216.9 | −0.600268 | −0.300134 | − | 0.953897i | \(-0.597031\pi\) | ||||
−0.300134 | + | 0.953897i | \(0.597031\pi\) | |||||||
\(938\) | 306.535 | + | 530.935i | 0.0106703 | + | 0.0184815i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −1373.77 | + | 2379.44i | −0.0476675 | + | 0.0825625i | ||||
\(941\) | −2597.04 | + | 4498.20i | −0.0899692 | + | 0.155831i | −0.907498 | − | 0.420057i | \(-0.862010\pi\) |
0.817529 | + | 0.575888i | \(0.195344\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 9323.14 | + | 16148.2i | 0.321955 | + | 0.557642i | ||||
\(944\) | 6478.64 | 0.223370 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −5509.24 | −0.189345 | ||||||||
\(947\) | −4610.28 | − | 7985.23i | −0.158198 | − | 0.274008i | 0.776021 | − | 0.630707i | \(-0.217235\pi\) |
−0.934219 | + | 0.356700i | \(0.883902\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −14004.1 | + | 24255.9i | −0.479024 | + | 0.829694i | ||||
\(950\) | −7938.79 | + | 13750.4i | −0.271125 | + | 0.469602i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −1493.92 | − | 2587.55i | −0.0508596 | − | 0.0880914i | ||||
\(953\) | −3344.36 | −0.113677 | −0.0568386 | − | 0.998383i | \(-0.518102\pi\) | ||||
−0.0568386 | + | 0.998383i | \(0.518102\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −14869.5 | −0.503840 | ||||||||
\(956\) | −6876.07 | − | 11909.7i | −0.232623 | − | 0.402915i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 7405.69 | − | 12827.0i | 0.249757 | − | 0.432591i | ||||
\(959\) | 6277.10 | − | 10872.3i | 0.211364 | − | 0.366093i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1125.46 | + | 1949.35i | 0.0377785 | + | 0.0654342i | ||||
\(962\) | 47346.6 | 1.58681 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −22627.8 | −0.756010 | ||||||||
\(965\) | −6425.49 | − | 11129.3i | −0.214346 | − | 0.371258i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 17167.6 | − | 29735.2i | 0.570914 | − | 0.988851i | −0.425559 | − | 0.904931i | \(-0.639922\pi\) |
0.996472 | − | 0.0839207i | \(-0.0267442\pi\) | |||||||
\(968\) | −5107.99 | + | 8847.30i | −0.169604 | + | 0.293763i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −5587.14 | − | 9677.21i | −0.184940 | − | 0.320326i | ||||
\(971\) | −31841.4 | −1.05236 | −0.526179 | − | 0.850374i | \(-0.676376\pi\) | ||||
−0.526179 | + | 0.850374i | \(0.676376\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −4151.69 | −0.136791 | ||||||||
\(974\) | 7064.90 | + | 12236.8i | 0.232417 | + | 0.402558i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 4614.80 | − | 7993.07i | 0.151348 | − | 0.262143i | ||||
\(977\) | 14123.0 | − | 24461.8i | 0.462472 | − | 0.801025i | −0.536612 | − | 0.843829i | \(-0.680296\pi\) |
0.999083 | + | 0.0428046i | \(0.0136293\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 2167.18 | + | 3753.67i | 0.0707492 | + | 0.122541i | ||||
\(980\) | −1169.38 | −0.0381167 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −10826.9 | −0.351832 | ||||||||
\(983\) | −4222.78 | − | 7314.07i | −0.137015 | − | 0.237317i | 0.789350 | − | 0.613943i | \(-0.210418\pi\) |
−0.926365 | + | 0.376626i | \(0.877084\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −15258.9 | + | 26429.2i | −0.493593 | + | 0.854928i | ||||
\(986\) | 5209.51 | − | 9023.14i | 0.168260 | − | 0.291436i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 9734.57 | + | 16860.8i | 0.313460 | + | 0.542928i | ||||
\(989\) | −73522.4 | −2.36388 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 26998.8 | 0.865435 | 0.432718 | − | 0.901529i | \(-0.357555\pi\) | ||||
0.432718 | + | 0.901529i | \(0.357555\pi\) | |||||||
\(992\) | −2655.23 | − | 4599.00i | −0.0849836 | − | 0.147196i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 1378.20 | − | 2387.11i | 0.0439776 | − | 0.0761715i | ||||
\(995\) | −8563.49 | + | 14832.4i | −0.272845 | + | 0.472581i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −18784.0 | − | 32534.8i | −0.596684 | − | 1.03349i | −0.993307 | − | 0.115506i | \(-0.963151\pi\) |
0.396623 | − | 0.917982i | \(-0.370182\pi\) | |||||||
\(998\) | −26728.1 | −0.847759 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 378.4.f.b.253.3 | 8 | ||
3.2 | odd | 2 | 126.4.f.b.85.1 | yes | 8 | ||
9.2 | odd | 6 | 126.4.f.b.43.1 | ✓ | 8 | ||
9.4 | even | 3 | 1134.4.a.l.1.2 | 4 | |||
9.5 | odd | 6 | 1134.4.a.o.1.3 | 4 | |||
9.7 | even | 3 | inner | 378.4.f.b.127.3 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
126.4.f.b.43.1 | ✓ | 8 | 9.2 | odd | 6 | ||
126.4.f.b.85.1 | yes | 8 | 3.2 | odd | 2 | ||
378.4.f.b.127.3 | 8 | 9.7 | even | 3 | inner | ||
378.4.f.b.253.3 | 8 | 1.1 | even | 1 | trivial | ||
1134.4.a.l.1.2 | 4 | 9.4 | even | 3 | |||
1134.4.a.o.1.3 | 4 | 9.5 | odd | 6 |