Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [525,4,Mod(274,525)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(525, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("525.274");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 525 = 3 \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 525.d (of order \(2\), degree \(1\), 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: | \(30.9760027530\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 40x^{6} + 488x^{4} + 1945x^{2} + 1936 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 274.3 | ||
Root | \(-3.56826i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 525.274 |
Dual form | 525.4.d.o.274.6 |
$q$-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 \(\left(\mathbb{Z}/525\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(176\) | \(451\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − 2.56826i | − 0.908017i | −0.890997 | − | 0.454008i | \(-0.849994\pi\) | ||||
0.890997 | − | 0.454008i | \(-0.150006\pi\) | |||||||
\(3\) | − 3.00000i | − 0.577350i | ||||||||
\(4\) | 1.40404 | 0.175505 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −7.70478 | −0.524244 | ||||||||
\(7\) | − 7.00000i | − 0.377964i | ||||||||
\(8\) | − 24.1520i | − 1.06738i | ||||||||
\(9\) | −9.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 66.4181 | 1.82053 | 0.910264 | − | 0.414029i | \(-0.135879\pi\) | ||||
0.910264 | + | 0.414029i | \(0.135879\pi\) | |||||||
\(12\) | − 4.21213i | − 0.101328i | ||||||||
\(13\) | − 34.0329i | − 0.726079i | −0.931774 | − | 0.363040i | \(-0.881739\pi\) | ||||
0.931774 | − | 0.363040i | \(-0.118261\pi\) | |||||||
\(14\) | −17.9778 | −0.343198 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −50.7963 | −0.793692 | ||||||||
\(17\) | − 6.12934i | − 0.0874461i | −0.999044 | − | 0.0437231i | \(-0.986078\pi\) | ||||
0.999044 | − | 0.0437231i | \(-0.0139219\pi\) | |||||||
\(18\) | 23.1143i | 0.302672i | ||||||||
\(19\) | 163.424 | 1.97327 | 0.986634 | − | 0.162951i | \(-0.0521013\pi\) | ||||
0.986634 | + | 0.162951i | \(0.0521013\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −21.0000 | −0.218218 | ||||||||
\(22\) | − 170.579i | − 1.65307i | ||||||||
\(23\) | 35.8799i | 0.325282i | 0.986685 | + | 0.162641i | \(0.0520012\pi\) | ||||
−0.986685 | + | 0.162641i | \(0.947999\pi\) | |||||||
\(24\) | −72.4561 | −0.616251 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −87.4053 | −0.659292 | ||||||||
\(27\) | 27.0000i | 0.192450i | ||||||||
\(28\) | − 9.82830i | − 0.0663348i | ||||||||
\(29\) | −27.7256 | −0.177535 | −0.0887676 | − | 0.996052i | \(-0.528293\pi\) | ||||
−0.0887676 | + | 0.996052i | \(0.528293\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 74.3417 | 0.430715 | 0.215358 | − | 0.976535i | \(-0.430908\pi\) | ||||
0.215358 | + | 0.976535i | \(0.430908\pi\) | |||||||
\(32\) | − 62.7581i | − 0.346693i | ||||||||
\(33\) | − 199.254i | − 1.05108i | ||||||||
\(34\) | −15.7417 | −0.0794026 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −12.6364 | −0.0585018 | ||||||||
\(37\) | 260.966i | 1.15953i | 0.814785 | + | 0.579763i | \(0.196855\pi\) | ||||
−0.814785 | + | 0.579763i | \(0.803145\pi\) | |||||||
\(38\) | − 419.716i | − 1.79176i | ||||||||
\(39\) | −102.099 | −0.419202 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −445.485 | −1.69690 | −0.848452 | − | 0.529272i | \(-0.822465\pi\) | ||||
−0.848452 | + | 0.529272i | \(0.822465\pi\) | |||||||
\(42\) | 53.9334i | 0.198146i | ||||||||
\(43\) | − 474.985i | − 1.68452i | −0.539070 | − | 0.842261i | \(-0.681224\pi\) | ||||
0.539070 | − | 0.842261i | \(-0.318776\pi\) | |||||||
\(44\) | 93.2538 | 0.319512 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 92.1489 | 0.295361 | ||||||||
\(47\) | 51.0436i | 0.158414i | 0.996858 | + | 0.0792072i | \(0.0252389\pi\) | ||||
−0.996858 | + | 0.0792072i | \(0.974761\pi\) | |||||||
\(48\) | 152.389i | 0.458239i | ||||||||
\(49\) | −49.0000 | −0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −18.3880 | −0.0504871 | ||||||||
\(52\) | − 47.7837i | − 0.127431i | ||||||||
\(53\) | − 676.667i | − 1.75372i | −0.480742 | − | 0.876862i | \(-0.659633\pi\) | ||||
0.480742 | − | 0.876862i | \(-0.340367\pi\) | |||||||
\(54\) | 69.3430 | 0.174748 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −169.064 | −0.403431 | ||||||||
\(57\) | − 490.273i | − 1.13927i | ||||||||
\(58\) | 71.2066i | 0.161205i | ||||||||
\(59\) | 115.979 | 0.255917 | 0.127959 | − | 0.991779i | \(-0.459158\pi\) | ||||
0.127959 | + | 0.991779i | \(0.459158\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −390.356 | −0.819344 | −0.409672 | − | 0.912233i | \(-0.634357\pi\) | ||||
−0.409672 | + | 0.912233i | \(0.634357\pi\) | |||||||
\(62\) | − 190.929i | − 0.391097i | ||||||||
\(63\) | 63.0000i | 0.125988i | ||||||||
\(64\) | −567.550 | −1.10850 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −511.737 | −0.954400 | ||||||||
\(67\) | 713.721i | 1.30142i | 0.759328 | + | 0.650708i | \(0.225528\pi\) | ||||
−0.759328 | + | 0.650708i | \(0.774472\pi\) | |||||||
\(68\) | − 8.60586i | − 0.0153473i | ||||||||
\(69\) | 107.640 | 0.187801 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 810.524 | 1.35481 | 0.677405 | − | 0.735610i | \(-0.263104\pi\) | ||||
0.677405 | + | 0.735610i | \(0.263104\pi\) | |||||||
\(72\) | 217.368i | 0.355793i | ||||||||
\(73\) | 350.196i | 0.561470i | 0.959785 | + | 0.280735i | \(0.0905782\pi\) | ||||
−0.959785 | + | 0.280735i | \(0.909422\pi\) | |||||||
\(74\) | 670.227 | 1.05287 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 229.455 | 0.346319 | ||||||||
\(77\) | − 464.927i | − 0.688095i | ||||||||
\(78\) | 262.216i | 0.380642i | ||||||||
\(79\) | 50.9307 | 0.0725336 | 0.0362668 | − | 0.999342i | \(-0.488453\pi\) | ||||
0.0362668 | + | 0.999342i | \(0.488453\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 1144.12i | 1.54082i | ||||||||
\(83\) | − 84.8904i | − 0.112264i | −0.998423 | − | 0.0561321i | \(-0.982123\pi\) | ||||
0.998423 | − | 0.0561321i | \(-0.0178768\pi\) | |||||||
\(84\) | −29.4849 | −0.0382984 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −1219.88 | −1.52957 | ||||||||
\(87\) | 83.1769i | 0.102500i | ||||||||
\(88\) | − 1604.13i | − 1.94319i | ||||||||
\(89\) | −1521.82 | −1.81251 | −0.906253 | − | 0.422735i | \(-0.861070\pi\) | ||||
−0.906253 | + | 0.422735i | \(0.861070\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −238.230 | −0.274432 | ||||||||
\(92\) | 50.3769i | 0.0570887i | ||||||||
\(93\) | − 223.025i | − 0.248674i | ||||||||
\(94\) | 131.093 | 0.143843 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −188.274 | −0.200163 | ||||||||
\(97\) | 1232.08i | 1.28968i | 0.764317 | + | 0.644840i | \(0.223076\pi\) | ||||
−0.764317 | + | 0.644840i | \(0.776924\pi\) | |||||||
\(98\) | 125.845i | 0.129717i | ||||||||
\(99\) | −597.763 | −0.606843 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1661.64 | −1.63702 | −0.818510 | − | 0.574492i | \(-0.805200\pi\) | ||||
−0.818510 | + | 0.574492i | \(0.805200\pi\) | |||||||
\(102\) | 47.2252i | 0.0458431i | ||||||||
\(103\) | − 193.631i | − 0.185233i | −0.995702 | − | 0.0926167i | \(-0.970477\pi\) | ||||
0.995702 | − | 0.0926167i | \(-0.0295231\pi\) | |||||||
\(104\) | −821.963 | −0.775001 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1737.86 | −1.59241 | ||||||||
\(107\) | − 921.040i | − 0.832153i | −0.909330 | − | 0.416076i | \(-0.863405\pi\) | ||||
0.909330 | − | 0.416076i | \(-0.136595\pi\) | |||||||
\(108\) | 37.9092i | 0.0337760i | ||||||||
\(109\) | −1304.73 | −1.14652 | −0.573260 | − | 0.819373i | \(-0.694322\pi\) | ||||
−0.573260 | + | 0.819373i | \(0.694322\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 782.897 | 0.669453 | ||||||||
\(112\) | 355.574i | 0.299988i | ||||||||
\(113\) | 237.585i | 0.197789i | 0.995098 | + | 0.0988945i | \(0.0315306\pi\) | ||||
−0.995098 | + | 0.0988945i | \(0.968469\pi\) | |||||||
\(114\) | −1259.15 | −1.03447 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −38.9280 | −0.0311584 | ||||||||
\(117\) | 306.296i | 0.242026i | ||||||||
\(118\) | − 297.863i | − 0.232377i | ||||||||
\(119\) | −42.9054 | −0.0330515 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 3080.36 | 2.31432 | ||||||||
\(122\) | 1002.54i | 0.743978i | ||||||||
\(123\) | 1336.45i | 0.979708i | ||||||||
\(124\) | 104.379 | 0.0755928 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 161.800 | 0.114399 | ||||||||
\(127\) | 1442.31i | 1.00775i | 0.863776 | + | 0.503876i | \(0.168093\pi\) | ||||
−0.863776 | + | 0.503876i | \(0.831907\pi\) | |||||||
\(128\) | 955.550i | 0.659840i | ||||||||
\(129\) | −1424.95 | −0.972559 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 644.035 | 0.429539 | 0.214770 | − | 0.976665i | \(-0.431100\pi\) | ||||
0.214770 | + | 0.976665i | \(0.431100\pi\) | |||||||
\(132\) | − 279.762i | − 0.184471i | ||||||||
\(133\) | − 1143.97i | − 0.745825i | ||||||||
\(134\) | 1833.02 | 1.18171 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −148.036 | −0.0933381 | ||||||||
\(137\) | 355.576i | 0.221744i | 0.993835 | + | 0.110872i | \(0.0353644\pi\) | ||||
−0.993835 | + | 0.110872i | \(0.964636\pi\) | |||||||
\(138\) | − 276.447i | − 0.170527i | ||||||||
\(139\) | 472.016 | 0.288028 | 0.144014 | − | 0.989576i | \(-0.453999\pi\) | ||||
0.144014 | + | 0.989576i | \(0.453999\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 153.131 | 0.0914606 | ||||||||
\(142\) | − 2081.64i | − 1.23019i | ||||||||
\(143\) | − 2260.40i | − 1.32185i | ||||||||
\(144\) | 457.167 | 0.264564 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 899.393 | 0.509824 | ||||||||
\(147\) | 147.000i | 0.0824786i | ||||||||
\(148\) | 366.407i | 0.203503i | ||||||||
\(149\) | 1091.53 | 0.600143 | 0.300072 | − | 0.953917i | \(-0.402989\pi\) | ||||
0.300072 | + | 0.953917i | \(0.402989\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2914.48 | 1.57071 | 0.785354 | − | 0.619047i | \(-0.212481\pi\) | ||||
0.785354 | + | 0.619047i | \(0.212481\pi\) | |||||||
\(152\) | − 3947.03i | − 2.10622i | ||||||||
\(153\) | 55.1641i | 0.0291487i | ||||||||
\(154\) | −1194.05 | −0.624802 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −143.351 | −0.0735722 | ||||||||
\(157\) | 1476.94i | 0.750780i | 0.926867 | + | 0.375390i | \(0.122491\pi\) | ||||
−0.926867 | + | 0.375390i | \(0.877509\pi\) | |||||||
\(158\) | − 130.803i | − 0.0658617i | ||||||||
\(159\) | −2030.00 | −1.01251 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 251.159 | 0.122945 | ||||||||
\(162\) | − 208.029i | − 0.100891i | ||||||||
\(163\) | 2764.56i | 1.32845i | 0.747534 | + | 0.664224i | \(0.231238\pi\) | ||||
−0.747534 | + | 0.664224i | \(0.768762\pi\) | |||||||
\(164\) | −625.480 | −0.297816 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −218.020 | −0.101938 | ||||||||
\(167\) | 255.508i | 0.118394i | 0.998246 | + | 0.0591970i | \(0.0188540\pi\) | ||||
−0.998246 | + | 0.0591970i | \(0.981146\pi\) | |||||||
\(168\) | 507.192i | 0.232921i | ||||||||
\(169\) | 1038.76 | 0.472809 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1470.82 | −0.657756 | ||||||||
\(172\) | − 666.899i | − 0.295643i | ||||||||
\(173\) | − 3850.56i | − 1.69221i | −0.533016 | − | 0.846105i | \(-0.678941\pi\) | ||||
0.533016 | − | 0.846105i | \(-0.321059\pi\) | |||||||
\(174\) | 213.620 | 0.0930717 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −3373.79 | −1.44494 | ||||||||
\(177\) | − 347.936i | − 0.147754i | ||||||||
\(178\) | 3908.44i | 1.64579i | ||||||||
\(179\) | −952.804 | −0.397854 | −0.198927 | − | 0.980014i | \(-0.563746\pi\) | ||||
−0.198927 | + | 0.980014i | \(0.563746\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1648.83 | 0.677109 | 0.338554 | − | 0.940947i | \(-0.390062\pi\) | ||||
0.338554 | + | 0.940947i | \(0.390062\pi\) | |||||||
\(182\) | 611.837i | 0.249189i | ||||||||
\(183\) | 1171.07i | 0.473048i | ||||||||
\(184\) | 866.572 | 0.347199 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −572.787 | −0.225800 | ||||||||
\(187\) | − 407.099i | − 0.159198i | ||||||||
\(188\) | 71.6675i | 0.0278026i | ||||||||
\(189\) | 189.000 | 0.0727393 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 767.536 | 0.290769 | 0.145385 | − | 0.989375i | \(-0.453558\pi\) | ||||
0.145385 | + | 0.989375i | \(0.453558\pi\) | |||||||
\(192\) | 1702.65i | 0.639990i | ||||||||
\(193\) | − 1186.61i | − 0.442561i | −0.975210 | − | 0.221280i | \(-0.928976\pi\) | ||||
0.975210 | − | 0.221280i | \(-0.0710236\pi\) | |||||||
\(194\) | 3164.31 | 1.17105 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −68.7981 | −0.0250722 | ||||||||
\(197\) | − 3614.72i | − 1.30730i | −0.756797 | − | 0.653650i | \(-0.773237\pi\) | ||||
0.756797 | − | 0.653650i | \(-0.226763\pi\) | |||||||
\(198\) | 1535.21i | 0.551023i | ||||||||
\(199\) | 3077.54 | 1.09629 | 0.548144 | − | 0.836384i | \(-0.315335\pi\) | ||||
0.548144 | + | 0.836384i | \(0.315335\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 2141.16 | 0.751373 | ||||||||
\(202\) | 4267.52i | 1.48644i | ||||||||
\(203\) | 194.079i | 0.0671020i | ||||||||
\(204\) | −25.8176 | −0.00886075 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −497.295 | −0.168195 | ||||||||
\(207\) | − 322.919i | − 0.108427i | ||||||||
\(208\) | 1728.75i | 0.576284i | ||||||||
\(209\) | 10854.3 | 3.59239 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 145.901 | 0.0476031 | 0.0238016 | − | 0.999717i | \(-0.492423\pi\) | ||||
0.0238016 | + | 0.999717i | \(0.492423\pi\) | |||||||
\(212\) | − 950.070i | − 0.307788i | ||||||||
\(213\) | − 2431.57i | − 0.782200i | ||||||||
\(214\) | −2365.47 | −0.755609 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 652.105 | 0.205417 | ||||||||
\(217\) | − 520.392i | − 0.162795i | ||||||||
\(218\) | 3350.89i | 1.04106i | ||||||||
\(219\) | 1050.59 | 0.324165 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −208.599 | −0.0634928 | ||||||||
\(222\) | − 2010.68i | − 0.607875i | ||||||||
\(223\) | 3357.30i | 1.00817i | 0.863655 | + | 0.504084i | \(0.168170\pi\) | ||||
−0.863655 | + | 0.504084i | \(0.831830\pi\) | |||||||
\(224\) | −439.306 | −0.131037 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 610.181 | 0.179596 | ||||||||
\(227\) | 636.529i | 0.186114i | 0.995661 | + | 0.0930570i | \(0.0296639\pi\) | ||||
−0.995661 | + | 0.0930570i | \(0.970336\pi\) | |||||||
\(228\) | − 688.364i | − 0.199948i | ||||||||
\(229\) | −3652.17 | −1.05389 | −0.526947 | − | 0.849898i | \(-0.676663\pi\) | ||||
−0.526947 | + | 0.849898i | \(0.676663\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1394.78 | −0.397272 | ||||||||
\(232\) | 669.630i | 0.189497i | ||||||||
\(233\) | 3387.30i | 0.952400i | 0.879337 | + | 0.476200i | \(0.157986\pi\) | ||||
−0.879337 | + | 0.476200i | \(0.842014\pi\) | |||||||
\(234\) | 786.648 | 0.219764 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 162.839 | 0.0449149 | ||||||||
\(237\) | − 152.792i | − 0.0418773i | ||||||||
\(238\) | 110.192i | 0.0300113i | ||||||||
\(239\) | 3382.64 | 0.915502 | 0.457751 | − | 0.889080i | \(-0.348655\pi\) | ||||
0.457751 | + | 0.889080i | \(0.348655\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 5809.63 | 1.55283 | 0.776413 | − | 0.630225i | \(-0.217037\pi\) | ||||
0.776413 | + | 0.630225i | \(0.217037\pi\) | |||||||
\(242\) | − 7911.17i | − 2.10144i | ||||||||
\(243\) | − 243.000i | − 0.0641500i | ||||||||
\(244\) | −548.077 | −0.143799 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 3432.36 | 0.889591 | ||||||||
\(247\) | − 5561.80i | − 1.43275i | ||||||||
\(248\) | − 1795.50i | − 0.459736i | ||||||||
\(249\) | −254.671 | −0.0648158 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −345.006 | −0.0867593 | −0.0433796 | − | 0.999059i | \(-0.513813\pi\) | ||||
−0.0433796 | + | 0.999059i | \(0.513813\pi\) | |||||||
\(252\) | 88.4547i | 0.0221116i | ||||||||
\(253\) | 2383.07i | 0.592184i | ||||||||
\(254\) | 3704.23 | 0.915056 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −2086.30 | −0.509350 | ||||||||
\(257\) | 3142.39i | 0.762712i | 0.924428 | + | 0.381356i | \(0.124543\pi\) | ||||
−0.924428 | + | 0.381356i | \(0.875457\pi\) | |||||||
\(258\) | 3659.65i | 0.883100i | ||||||||
\(259\) | 1826.76 | 0.438260 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 249.531 | 0.0591784 | ||||||||
\(262\) | − 1654.05i | − 0.390029i | ||||||||
\(263\) | − 4949.02i | − 1.16034i | −0.814495 | − | 0.580170i | \(-0.802986\pi\) | ||||
0.814495 | − | 0.580170i | \(-0.197014\pi\) | |||||||
\(264\) | −4812.39 | −1.12190 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −2938.01 | −0.677222 | ||||||||
\(267\) | 4565.47i | 1.04645i | ||||||||
\(268\) | 1002.10i | 0.228406i | ||||||||
\(269\) | 4570.60 | 1.03596 | 0.517982 | − | 0.855391i | \(-0.326683\pi\) | ||||
0.517982 | + | 0.855391i | \(0.326683\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −5338.43 | −1.19663 | −0.598315 | − | 0.801261i | \(-0.704163\pi\) | ||||
−0.598315 | + | 0.801261i | \(0.704163\pi\) | |||||||
\(272\) | 311.348i | 0.0694053i | ||||||||
\(273\) | 714.691i | 0.158443i | ||||||||
\(274\) | 913.213 | 0.201347 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 151.131 | 0.0329602 | ||||||||
\(277\) | − 2225.98i | − 0.482837i | −0.970421 | − | 0.241419i | \(-0.922387\pi\) | ||||
0.970421 | − | 0.241419i | \(-0.0776127\pi\) | |||||||
\(278\) | − 1212.26i | − 0.261534i | ||||||||
\(279\) | −669.076 | −0.143572 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1991.15 | 0.422712 | 0.211356 | − | 0.977409i | \(-0.432212\pi\) | ||||
0.211356 | + | 0.977409i | \(0.432212\pi\) | |||||||
\(282\) | − 393.280i | − 0.0830478i | ||||||||
\(283\) | − 7350.20i | − 1.54390i | −0.635682 | − | 0.771951i | \(-0.719281\pi\) | ||||
0.635682 | − | 0.771951i | \(-0.280719\pi\) | |||||||
\(284\) | 1138.01 | 0.237777 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −5805.29 | −1.20026 | ||||||||
\(287\) | 3118.39i | 0.641369i | ||||||||
\(288\) | 564.823i | 0.115564i | ||||||||
\(289\) | 4875.43 | 0.992353 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 3696.25 | 0.744597 | ||||||||
\(292\) | 491.690i | 0.0985410i | ||||||||
\(293\) | 6250.16i | 1.24621i | 0.782140 | + | 0.623103i | \(0.214128\pi\) | ||||
−0.782140 | + | 0.623103i | \(0.785872\pi\) | |||||||
\(294\) | 377.534 | 0.0748920 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 6302.85 | 1.23765 | ||||||||
\(297\) | 1793.29i | 0.350361i | ||||||||
\(298\) | − 2803.32i | − 0.544940i | ||||||||
\(299\) | 1221.10 | 0.236180 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −3324.89 | −0.636690 | ||||||||
\(302\) | − 7485.13i | − 1.42623i | ||||||||
\(303\) | 4984.91i | 0.945134i | ||||||||
\(304\) | −8301.35 | −1.56617 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 141.676 | 0.0264675 | ||||||||
\(307\) | 1259.29i | 0.234109i | 0.993126 | + | 0.117054i | \(0.0373452\pi\) | ||||
−0.993126 | + | 0.117054i | \(0.962655\pi\) | |||||||
\(308\) | − 652.777i | − 0.120764i | ||||||||
\(309\) | −580.893 | −0.106945 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −6711.92 | −1.22379 | −0.611894 | − | 0.790940i | \(-0.709592\pi\) | ||||
−0.611894 | + | 0.790940i | \(0.709592\pi\) | |||||||
\(312\) | 2465.89i | 0.447447i | ||||||||
\(313\) | 2436.27i | 0.439955i | 0.975505 | + | 0.219978i | \(0.0705984\pi\) | ||||
−0.975505 | + | 0.219978i | \(0.929402\pi\) | |||||||
\(314\) | 3793.16 | 0.681721 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 71.5089 | 0.0127300 | ||||||||
\(317\) | − 1191.81i | − 0.211164i | −0.994411 | − | 0.105582i | \(-0.966330\pi\) | ||||
0.994411 | − | 0.105582i | \(-0.0336705\pi\) | |||||||
\(318\) | 5213.57i | 0.919379i | ||||||||
\(319\) | −1841.48 | −0.323208 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −2763.12 | −0.480443 | ||||||||
\(322\) | − 645.042i | − 0.111636i | ||||||||
\(323\) | − 1001.68i | − 0.172555i | ||||||||
\(324\) | 113.727 | 0.0195006 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 7100.11 | 1.20625 | ||||||||
\(327\) | 3914.20i | 0.661944i | ||||||||
\(328\) | 10759.4i | 1.81124i | ||||||||
\(329\) | 357.305 | 0.0598750 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 5885.63 | 0.977351 | 0.488676 | − | 0.872466i | \(-0.337480\pi\) | ||||
0.488676 | + | 0.872466i | \(0.337480\pi\) | |||||||
\(332\) | − 119.190i | − 0.0197030i | ||||||||
\(333\) | − 2348.69i | − 0.386509i | ||||||||
\(334\) | 656.210 | 0.107504 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 1066.72 | 0.173198 | ||||||||
\(337\) | − 1209.73i | − 0.195544i | −0.995209 | − | 0.0977720i | \(-0.968828\pi\) | ||||
0.995209 | − | 0.0977720i | \(-0.0311716\pi\) | |||||||
\(338\) | − 2667.81i | − 0.429319i | ||||||||
\(339\) | 712.756 | 0.114193 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 4937.63 | 0.784129 | ||||||||
\(342\) | 3777.44i | 0.597254i | ||||||||
\(343\) | 343.000i | 0.0539949i | ||||||||
\(344\) | −11471.8 | −1.79802 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −9889.23 | −1.53656 | ||||||||
\(347\) | 5065.21i | 0.783617i | 0.920047 | + | 0.391808i | \(0.128150\pi\) | ||||
−0.920047 | + | 0.391808i | \(0.871850\pi\) | |||||||
\(348\) | 116.784i | 0.0179893i | ||||||||
\(349\) | −5481.35 | −0.840716 | −0.420358 | − | 0.907358i | \(-0.638096\pi\) | ||||
−0.420358 | + | 0.907358i | \(0.638096\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 918.888 | 0.139734 | ||||||||
\(352\) | − 4168.27i | − 0.631163i | ||||||||
\(353\) | − 602.190i | − 0.0907970i | −0.998969 | − | 0.0453985i | \(-0.985544\pi\) | ||||
0.998969 | − | 0.0453985i | \(-0.0144558\pi\) | |||||||
\(354\) | −893.589 | −0.134163 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −2136.71 | −0.318105 | ||||||||
\(357\) | 128.716i | 0.0190823i | ||||||||
\(358\) | 2447.05i | 0.361259i | ||||||||
\(359\) | −2004.84 | −0.294740 | −0.147370 | − | 0.989081i | \(-0.547081\pi\) | ||||
−0.147370 | + | 0.989081i | \(0.547081\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 19848.5 | 2.89379 | ||||||||
\(362\) | − 4234.63i | − 0.614826i | ||||||||
\(363\) | − 9241.08i | − 1.33617i | ||||||||
\(364\) | −334.486 | −0.0481643 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 3007.61 | 0.429536 | ||||||||
\(367\) | 7770.37i | 1.10520i | 0.833445 | + | 0.552602i | \(0.186365\pi\) | ||||
−0.833445 | + | 0.552602i | \(0.813635\pi\) | |||||||
\(368\) | − 1822.57i | − 0.258174i | ||||||||
\(369\) | 4009.36 | 0.565635 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −4736.67 | −0.662846 | ||||||||
\(372\) | − 313.137i | − 0.0436435i | ||||||||
\(373\) | 7485.06i | 1.03904i | 0.854458 | + | 0.519520i | \(0.173889\pi\) | ||||
−0.854458 | + | 0.519520i | \(0.826111\pi\) | |||||||
\(374\) | −1045.54 | −0.144555 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 1232.81 | 0.169088 | ||||||||
\(377\) | 943.583i | 0.128905i | ||||||||
\(378\) | − 485.401i | − 0.0660485i | ||||||||
\(379\) | 4053.61 | 0.549393 | 0.274697 | − | 0.961531i | \(-0.411423\pi\) | ||||
0.274697 | + | 0.961531i | \(0.411423\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 4326.94 | 0.581826 | ||||||||
\(382\) | − 1971.23i | − 0.264023i | ||||||||
\(383\) | − 4531.33i | − 0.604543i | −0.953222 | − | 0.302272i | \(-0.902255\pi\) | ||||
0.953222 | − | 0.302272i | \(-0.0977450\pi\) | |||||||
\(384\) | 2866.65 | 0.380959 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −3047.53 | −0.401853 | ||||||||
\(387\) | 4274.86i | 0.561507i | ||||||||
\(388\) | 1729.90i | 0.226346i | ||||||||
\(389\) | 1160.19 | 0.151219 | 0.0756093 | − | 0.997138i | \(-0.475910\pi\) | ||||
0.0756093 | + | 0.997138i | \(0.475910\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 219.920 | 0.0284446 | ||||||||
\(392\) | 1183.45i | 0.152483i | ||||||||
\(393\) | − 1932.11i | − 0.247995i | ||||||||
\(394\) | −9283.53 | −1.18705 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −839.285 | −0.106504 | ||||||||
\(397\) | − 6720.74i | − 0.849632i | −0.905280 | − | 0.424816i | \(-0.860339\pi\) | ||||
0.905280 | − | 0.424816i | \(-0.139661\pi\) | |||||||
\(398\) | − 7903.93i | − 0.995448i | ||||||||
\(399\) | −3431.91 | −0.430602 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 2769.06 | 0.344839 | 0.172419 | − | 0.985024i | \(-0.444842\pi\) | ||||
0.172419 | + | 0.985024i | \(0.444842\pi\) | |||||||
\(402\) | − 5499.06i | − 0.682260i | ||||||||
\(403\) | − 2530.07i | − 0.312733i | ||||||||
\(404\) | −2333.01 | −0.287306 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 498.446 | 0.0609297 | ||||||||
\(407\) | 17332.8i | 2.11095i | ||||||||
\(408\) | 444.108i | 0.0538888i | ||||||||
\(409\) | −14438.9 | −1.74561 | −0.872806 | − | 0.488067i | \(-0.837702\pi\) | ||||
−0.872806 | + | 0.488067i | \(0.837702\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 1066.73 | 0.128024 | ||||||||
\(412\) | − 271.866i | − 0.0325095i | ||||||||
\(413\) | − 811.850i | − 0.0967277i | ||||||||
\(414\) | −829.340 | −0.0984537 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −2135.84 | −0.251726 | ||||||||
\(417\) | − 1416.05i | − 0.166293i | ||||||||
\(418\) | − 27876.7i | − 3.26195i | ||||||||
\(419\) | −6396.35 | −0.745780 | −0.372890 | − | 0.927875i | \(-0.621633\pi\) | ||||
−0.372890 | + | 0.927875i | \(0.621633\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −8231.07 | −0.952868 | −0.476434 | − | 0.879210i | \(-0.658071\pi\) | ||||
−0.476434 | + | 0.879210i | \(0.658071\pi\) | |||||||
\(422\) | − 374.712i | − 0.0432244i | ||||||||
\(423\) | − 459.393i | − 0.0528048i | ||||||||
\(424\) | −16342.9 | −1.87189 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −6244.91 | −0.710251 | ||||||||
\(427\) | 2732.49i | 0.309683i | ||||||||
\(428\) | − 1293.18i | − 0.146047i | ||||||||
\(429\) | −6781.20 | −0.763169 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −5975.72 | −0.667843 | −0.333922 | − | 0.942601i | \(-0.608372\pi\) | ||||
−0.333922 | + | 0.942601i | \(0.608372\pi\) | |||||||
\(432\) | − 1371.50i | − 0.152746i | ||||||||
\(433\) | 10912.9i | 1.21118i | 0.795776 | + | 0.605591i | \(0.207063\pi\) | ||||
−0.795776 | + | 0.605591i | \(0.792937\pi\) | |||||||
\(434\) | −1336.50 | −0.147821 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −1831.90 | −0.201221 | ||||||||
\(437\) | 5863.65i | 0.641868i | ||||||||
\(438\) | − 2698.18i | − 0.294347i | ||||||||
\(439\) | −3784.05 | −0.411396 | −0.205698 | − | 0.978616i | \(-0.565946\pi\) | ||||
−0.205698 | + | 0.978616i | \(0.565946\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 441.000 | 0.0476190 | ||||||||
\(442\) | 535.737i | 0.0576526i | ||||||||
\(443\) | − 7869.34i | − 0.843981i | −0.906600 | − | 0.421991i | \(-0.861331\pi\) | ||||
0.906600 | − | 0.421991i | \(-0.138669\pi\) | |||||||
\(444\) | 1099.22 | 0.117493 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 8622.42 | 0.915434 | ||||||||
\(447\) | − 3274.58i | − 0.346493i | ||||||||
\(448\) | 3972.85i | 0.418972i | ||||||||
\(449\) | 15601.8 | 1.63986 | 0.819929 | − | 0.572465i | \(-0.194013\pi\) | ||||
0.819929 | + | 0.572465i | \(0.194013\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −29588.3 | −3.08926 | ||||||||
\(452\) | 333.580i | 0.0347130i | ||||||||
\(453\) | − 8743.43i | − 0.906848i | ||||||||
\(454\) | 1634.77 | 0.168995 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −11841.1 | −1.21603 | ||||||||
\(457\) | 8840.78i | 0.904933i | 0.891781 | + | 0.452466i | \(0.149456\pi\) | ||||
−0.891781 | + | 0.452466i | \(0.850544\pi\) | |||||||
\(458\) | 9379.71i | 0.956954i | ||||||||
\(459\) | 165.492 | 0.0168290 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −10523.7 | −1.06321 | −0.531605 | − | 0.846993i | \(-0.678411\pi\) | ||||
−0.531605 | + | 0.846993i | \(0.678411\pi\) | |||||||
\(462\) | 3582.16i | 0.360729i | ||||||||
\(463\) | 10781.6i | 1.08221i | 0.840954 | + | 0.541107i | \(0.181994\pi\) | ||||
−0.840954 | + | 0.541107i | \(0.818006\pi\) | |||||||
\(464\) | 1408.36 | 0.140908 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 8699.46 | 0.864795 | ||||||||
\(467\) | 5592.55i | 0.554160i | 0.960847 | + | 0.277080i | \(0.0893666\pi\) | ||||
−0.960847 | + | 0.277080i | \(0.910633\pi\) | |||||||
\(468\) | 430.053i | 0.0424769i | ||||||||
\(469\) | 4996.05 | 0.491889 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 4430.82 | 0.433463 | ||||||||
\(472\) | − 2801.12i | − 0.273161i | ||||||||
\(473\) | − 31547.6i | − 3.06672i | ||||||||
\(474\) | −392.410 | −0.0380253 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −60.2410 | −0.00580072 | ||||||||
\(477\) | 6090.01i | 0.584575i | ||||||||
\(478\) | − 8687.51i | − 0.831292i | ||||||||
\(479\) | 7835.28 | 0.747397 | 0.373698 | − | 0.927550i | \(-0.378089\pi\) | ||||
0.373698 | + | 0.927550i | \(0.378089\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 8881.42 | 0.841908 | ||||||||
\(482\) | − 14920.6i | − 1.40999i | ||||||||
\(483\) | − 753.478i | − 0.0709823i | ||||||||
\(484\) | 4324.96 | 0.406176 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −624.087 | −0.0582493 | ||||||||
\(487\) | − 5979.24i | − 0.556356i | −0.960530 | − | 0.278178i | \(-0.910269\pi\) | ||||
0.960530 | − | 0.278178i | \(-0.0897305\pi\) | |||||||
\(488\) | 9427.89i | 0.874550i | ||||||||
\(489\) | 8293.68 | 0.766980 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −1792.66 | −0.164769 | −0.0823846 | − | 0.996601i | \(-0.526254\pi\) | ||||
−0.0823846 | + | 0.996601i | \(0.526254\pi\) | |||||||
\(492\) | 1876.44i | 0.171944i | ||||||||
\(493\) | 169.940i | 0.0155248i | ||||||||
\(494\) | −14284.2 | −1.30096 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −3776.29 | −0.341855 | ||||||||
\(497\) | − 5673.67i | − 0.512070i | ||||||||
\(498\) | 654.061i | 0.0588538i | ||||||||
\(499\) | 20514.4 | 1.84038 | 0.920191 | − | 0.391470i | \(-0.128033\pi\) | ||||
0.920191 | + | 0.391470i | \(0.128033\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 766.523 | 0.0683548 | ||||||||
\(502\) | 886.065i | 0.0787789i | ||||||||
\(503\) | 16294.5i | 1.44441i | 0.691679 | + | 0.722205i | \(0.256871\pi\) | ||||
−0.691679 | + | 0.722205i | \(0.743129\pi\) | |||||||
\(504\) | 1521.58 | 0.134477 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 6120.35 | 0.537713 | ||||||||
\(507\) | − 3116.28i | − 0.272976i | ||||||||
\(508\) | 2025.07i | 0.176866i | ||||||||
\(509\) | −12183.8 | −1.06097 | −0.530487 | − | 0.847693i | \(-0.677991\pi\) | ||||
−0.530487 | + | 0.847693i | \(0.677991\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2451.37 | 0.212216 | ||||||||
\(512\) | 13002.5i | 1.12234i | ||||||||
\(513\) | 4412.46i | 0.379756i | ||||||||
\(514\) | 8070.48 | 0.692555 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −2000.70 | −0.170689 | ||||||||
\(517\) | 3390.22i | 0.288398i | ||||||||
\(518\) | − 4691.59i | − 0.397947i | ||||||||
\(519\) | −11551.7 | −0.976998 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −11251.3 | −0.946116 | −0.473058 | − | 0.881031i | \(-0.656850\pi\) | ||||
−0.473058 | + | 0.881031i | \(0.656850\pi\) | |||||||
\(522\) | − 640.859i | − 0.0537350i | ||||||||
\(523\) | − 13493.7i | − 1.12818i | −0.825713 | − | 0.564090i | \(-0.809227\pi\) | ||||
0.825713 | − | 0.564090i | \(-0.190773\pi\) | |||||||
\(524\) | 904.254 | 0.0753865 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −12710.4 | −1.05361 | ||||||||
\(527\) | − 455.666i | − 0.0376644i | ||||||||
\(528\) | 10121.4i | 0.834236i | ||||||||
\(529\) | 10879.6 | 0.894192 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −1043.81 | −0.0853058 | ||||||||
\(532\) | − 1606.18i | − 0.130896i | ||||||||
\(533\) | 15161.1i | 1.23209i | ||||||||
\(534\) | 11725.3 | 0.950195 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 17237.8 | 1.38910 | ||||||||
\(537\) | 2858.41i | 0.229701i | ||||||||
\(538\) | − 11738.5i | − 0.940673i | ||||||||
\(539\) | −3254.49 | −0.260075 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −18810.8 | −1.49490 | −0.747449 | − | 0.664319i | \(-0.768722\pi\) | ||||
−0.747449 | + | 0.664319i | \(0.768722\pi\) | |||||||
\(542\) | 13710.5i | 1.08656i | ||||||||
\(543\) | − 4946.49i | − 0.390929i | ||||||||
\(544\) | −384.666 | −0.0303169 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 1835.51 | 0.143869 | ||||||||
\(547\) | − 9822.68i | − 0.767801i | −0.923374 | − | 0.383901i | \(-0.874581\pi\) | ||||
0.923374 | − | 0.383901i | \(-0.125419\pi\) | |||||||
\(548\) | 499.245i | 0.0389173i | ||||||||
\(549\) | 3513.20 | 0.273115 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −4531.04 | −0.350324 | ||||||||
\(552\) | − 2599.72i | − 0.200455i | ||||||||
\(553\) | − 356.515i | − 0.0274151i | ||||||||
\(554\) | −5716.89 | −0.438424 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 662.731 | 0.0505504 | ||||||||
\(557\) | − 23627.9i | − 1.79739i | −0.438571 | − | 0.898696i | \(-0.644515\pi\) | ||||
0.438571 | − | 0.898696i | \(-0.355485\pi\) | |||||||
\(558\) | 1718.36i | 0.130366i | ||||||||
\(559\) | −16165.1 | −1.22310 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1221.30 | −0.0919131 | ||||||||
\(562\) | − 5113.79i | − 0.383830i | ||||||||
\(563\) | − 966.441i | − 0.0723457i | −0.999346 | − | 0.0361729i | \(-0.988483\pi\) | ||||
0.999346 | − | 0.0361729i | \(-0.0115167\pi\) | |||||||
\(564\) | 215.002 | 0.0160518 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −18877.2 | −1.40189 | ||||||||
\(567\) | − 567.000i | − 0.0419961i | ||||||||
\(568\) | − 19575.8i | − 1.44610i | ||||||||
\(569\) | −16451.2 | −1.21208 | −0.606038 | − | 0.795435i | \(-0.707242\pi\) | ||||
−0.606038 | + | 0.795435i | \(0.707242\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 37.8467 | 0.00277379 | 0.00138690 | − | 0.999999i | \(-0.499559\pi\) | ||||
0.00138690 | + | 0.999999i | \(0.499559\pi\) | |||||||
\(572\) | − 3173.70i | − 0.231991i | ||||||||
\(573\) | − 2302.61i | − 0.167876i | ||||||||
\(574\) | 8008.85 | 0.582374 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 5107.95 | 0.369498 | ||||||||
\(577\) | 23779.1i | 1.71566i | 0.513933 | + | 0.857830i | \(0.328188\pi\) | ||||
−0.513933 | + | 0.857830i | \(0.671812\pi\) | |||||||
\(578\) | − 12521.4i | − 0.901073i | ||||||||
\(579\) | −3559.84 | −0.255513 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −594.233 | −0.0424319 | ||||||||
\(582\) | − 9492.92i | − 0.676107i | ||||||||
\(583\) | − 44942.9i | − 3.19270i | ||||||||
\(584\) | 8457.93 | 0.599301 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 16052.0 | 1.13158 | ||||||||
\(587\) | 12556.0i | 0.882863i | 0.897295 | + | 0.441432i | \(0.145529\pi\) | ||||
−0.897295 | + | 0.441432i | \(0.854471\pi\) | |||||||
\(588\) | 206.394i | 0.0144754i | ||||||||
\(589\) | 12149.2 | 0.849917 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −10844.2 | −0.754770 | ||||||||
\(592\) | − 13256.1i | − 0.920307i | ||||||||
\(593\) | 26489.2i | 1.83437i | 0.398461 | + | 0.917185i | \(0.369544\pi\) | ||||
−0.398461 | + | 0.917185i | \(0.630456\pi\) | |||||||
\(594\) | 4605.63 | 0.318133 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 1532.55 | 0.105328 | ||||||||
\(597\) | − 9232.63i | − 0.632942i | ||||||||
\(598\) | − 3136.09i | − 0.214456i | ||||||||
\(599\) | −8910.78 | −0.607821 | −0.303910 | − | 0.952701i | \(-0.598292\pi\) | ||||
−0.303910 | + | 0.952701i | \(0.598292\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 2943.50 | 0.199780 | 0.0998902 | − | 0.994998i | \(-0.468151\pi\) | ||||
0.0998902 | + | 0.994998i | \(0.468151\pi\) | |||||||
\(602\) | 8539.18i | 0.578125i | ||||||||
\(603\) | − 6423.49i | − 0.433806i | ||||||||
\(604\) | 4092.05 | 0.275668 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 12802.5 | 0.858198 | ||||||||
\(607\) | − 20445.4i | − 1.36714i | −0.729886 | − | 0.683569i | \(-0.760427\pi\) | ||||
0.729886 | − | 0.683569i | \(-0.239573\pi\) | |||||||
\(608\) | − 10256.2i | − 0.684117i | ||||||||
\(609\) | 582.238 | 0.0387413 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1737.16 | 0.115021 | ||||||||
\(612\) | 77.4528i | 0.00511576i | ||||||||
\(613\) | 19174.7i | 1.26339i | 0.775215 | + | 0.631697i | \(0.217641\pi\) | ||||
−0.775215 | + | 0.631697i | \(0.782359\pi\) | |||||||
\(614\) | 3234.18 | 0.212575 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −11228.9 | −0.734458 | ||||||||
\(617\) | 21445.6i | 1.39930i | 0.714486 | + | 0.699650i | \(0.246661\pi\) | ||||
−0.714486 | + | 0.699650i | \(0.753339\pi\) | |||||||
\(618\) | 1491.88i | 0.0971074i | ||||||||
\(619\) | 17031.2 | 1.10588 | 0.552941 | − | 0.833220i | \(-0.313505\pi\) | ||||
0.552941 | + | 0.833220i | \(0.313505\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −968.757 | −0.0626005 | ||||||||
\(622\) | 17237.9i | 1.11122i | ||||||||
\(623\) | 10652.8i | 0.685063i | ||||||||
\(624\) | 5186.24 | 0.332717 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 6256.97 | 0.399487 | ||||||||
\(627\) | − 32563.0i | − 2.07407i | ||||||||
\(628\) | 2073.69i | 0.131766i | ||||||||
\(629\) | 1599.55 | 0.101396 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 25190.1 | 1.58923 | 0.794614 | − | 0.607115i | \(-0.207673\pi\) | ||||
0.794614 | + | 0.607115i | \(0.207673\pi\) | |||||||
\(632\) | − 1230.08i | − 0.0774208i | ||||||||
\(633\) | − 437.704i | − 0.0274837i | ||||||||
\(634\) | −3060.88 | −0.191740 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −2850.21 | −0.177702 | ||||||||
\(637\) | 1667.61i | 0.103726i | ||||||||
\(638\) | 4729.40i | 0.293478i | ||||||||
\(639\) | −7294.72 | −0.451603 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 11755.1 | 0.724335 | 0.362168 | − | 0.932113i | \(-0.382037\pi\) | ||||
0.362168 | + | 0.932113i | \(0.382037\pi\) | |||||||
\(642\) | 7096.41i | 0.436251i | ||||||||
\(643\) | 24044.2i | 1.47467i | 0.675530 | + | 0.737333i | \(0.263915\pi\) | ||||
−0.675530 | + | 0.737333i | \(0.736085\pi\) | |||||||
\(644\) | 352.639 | 0.0215775 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −2572.58 | −0.156683 | ||||||||
\(647\) | 5138.50i | 0.312234i | 0.987739 | + | 0.156117i | \(0.0498976\pi\) | ||||
−0.987739 | + | 0.156117i | \(0.950102\pi\) | |||||||
\(648\) | − 1956.31i | − 0.118598i | ||||||||
\(649\) | 7703.07 | 0.465905 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1561.18 | −0.0939897 | ||||||||
\(652\) | 3881.56i | 0.233150i | ||||||||
\(653\) | 6665.57i | 0.399455i | 0.979851 | + | 0.199727i | \(0.0640057\pi\) | ||||
−0.979851 | + | 0.199727i | \(0.935994\pi\) | |||||||
\(654\) | 10052.7 | 0.601056 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 22629.0 | 1.34682 | ||||||||
\(657\) | − 3151.76i | − 0.187157i | ||||||||
\(658\) | − 917.653i | − 0.0543675i | ||||||||
\(659\) | −8996.31 | −0.531785 | −0.265893 | − | 0.964003i | \(-0.585667\pi\) | ||||
−0.265893 | + | 0.964003i | \(0.585667\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 24565.6 | 1.44553 | 0.722763 | − | 0.691096i | \(-0.242872\pi\) | ||||
0.722763 | + | 0.691096i | \(0.242872\pi\) | |||||||
\(662\) | − 15115.8i | − 0.887451i | ||||||||
\(663\) | 625.798i | 0.0366576i | ||||||||
\(664\) | −2050.27 | −0.119828 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −6032.05 | −0.350957 | ||||||||
\(667\) | − 994.793i | − 0.0577489i | ||||||||
\(668\) | 358.744i | 0.0207788i | ||||||||
\(669\) | 10071.9 | 0.582066 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −25926.7 | −1.49164 | ||||||||
\(672\) | 1317.92i | 0.0756545i | ||||||||
\(673\) | − 22046.9i | − 1.26277i | −0.775468 | − | 0.631387i | \(-0.782486\pi\) | ||||
0.775468 | − | 0.631387i | \(-0.217514\pi\) | |||||||
\(674\) | −3106.91 | −0.177557 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 1458.47 | 0.0829805 | ||||||||
\(677\) | − 25109.8i | − 1.42548i | −0.701430 | − | 0.712738i | \(-0.747455\pi\) | ||||
0.701430 | − | 0.712738i | \(-0.252545\pi\) | |||||||
\(678\) | − 1830.54i | − 0.103690i | ||||||||
\(679\) | 8624.58 | 0.487453 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1909.59 | 0.107453 | ||||||||
\(682\) | − 12681.1i | − 0.712002i | ||||||||
\(683\) | 20540.1i | 1.15073i | 0.817898 | + | 0.575363i | \(0.195139\pi\) | ||||
−0.817898 | + | 0.575363i | \(0.804861\pi\) | |||||||
\(684\) | −2065.09 | −0.115440 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 880.913 | 0.0490283 | ||||||||
\(687\) | 10956.5i | 0.608466i | ||||||||
\(688\) | 24127.5i | 1.33699i | ||||||||
\(689\) | −23029.0 | −1.27334 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1635.59 | −0.0900446 | −0.0450223 | − | 0.998986i | \(-0.514336\pi\) | ||||
−0.0450223 | + | 0.998986i | \(0.514336\pi\) | |||||||
\(692\) | − 5406.35i | − 0.296992i | ||||||||
\(693\) | 4184.34i | 0.229365i | ||||||||
\(694\) | 13008.8 | 0.711537 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 2008.89 | 0.109406 | ||||||||
\(697\) | 2730.53i | 0.148388i | ||||||||
\(698\) | 14077.5i | 0.763385i | ||||||||
\(699\) | 10161.9 | 0.549868 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 16895.6 | 0.910325 | 0.455163 | − | 0.890408i | \(-0.349581\pi\) | ||||
0.455163 | + | 0.890408i | \(0.349581\pi\) | |||||||
\(702\) | − 2359.94i | − 0.126881i | ||||||||
\(703\) | 42648.1i | 2.28806i | ||||||||
\(704\) | −37695.5 | −2.01805 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −1546.58 | −0.0824452 | ||||||||
\(707\) | 11631.5i | 0.618736i | ||||||||
\(708\) | − 488.517i | − 0.0259316i | ||||||||
\(709\) | 3527.13 | 0.186833 | 0.0934163 | − | 0.995627i | \(-0.470221\pi\) | ||||
0.0934163 | + | 0.995627i | \(0.470221\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −458.376 | −0.0241779 | ||||||||
\(712\) | 36755.1i | 1.93463i | ||||||||
\(713\) | 2667.37i | 0.140104i | ||||||||
\(714\) | 330.577 | 0.0173271 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −1337.78 | −0.0698256 | ||||||||
\(717\) | − 10147.9i | − 0.528566i | ||||||||
\(718\) | 5148.95i | 0.267628i | ||||||||
\(719\) | 35693.3 | 1.85137 | 0.925687 | − | 0.378291i | \(-0.123488\pi\) | ||||
0.925687 | + | 0.378291i | \(0.123488\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1355.42 | −0.0700116 | ||||||||
\(722\) | − 50976.1i | − 2.62761i | ||||||||
\(723\) | − 17428.9i | − 0.896524i | ||||||||
\(724\) | 2315.03 | 0.118836 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −23733.5 | −1.21327 | ||||||||
\(727\) | 18829.9i | 0.960611i | 0.877101 | + | 0.480305i | \(0.159474\pi\) | ||||
−0.877101 | + | 0.480305i | \(0.840526\pi\) | |||||||
\(728\) | 5753.74i | 0.292923i | ||||||||
\(729\) | −729.000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −2911.34 | −0.147305 | ||||||||
\(732\) | 1644.23i | 0.0830225i | ||||||||
\(733\) | − 14895.4i | − 0.750577i | −0.926908 | − | 0.375288i | \(-0.877544\pi\) | ||||
0.926908 | − | 0.375288i | \(-0.122456\pi\) | |||||||
\(734\) | 19956.3 | 1.00354 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 2251.75 | 0.112773 | ||||||||
\(737\) | 47404.0i | 2.36926i | ||||||||
\(738\) | − 10297.1i | − 0.513606i | ||||||||
\(739\) | −8866.34 | −0.441345 | −0.220672 | − | 0.975348i | \(-0.570825\pi\) | ||||
−0.220672 | + | 0.975348i | \(0.570825\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −16685.4 | −0.827198 | ||||||||
\(742\) | 12165.0i | 0.601875i | ||||||||
\(743\) | 14225.4i | 0.702394i | 0.936302 | + | 0.351197i | \(0.114225\pi\) | ||||
−0.936302 | + | 0.351197i | \(0.885775\pi\) | |||||||
\(744\) | −5386.51 | −0.265429 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 19223.6 | 0.943465 | ||||||||
\(747\) | 764.013i | 0.0374214i | ||||||||
\(748\) | − 571.585i | − 0.0279401i | ||||||||
\(749\) | −6447.28 | −0.314524 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 34300.2 | 1.66662 | 0.833311 | − | 0.552804i | \(-0.186442\pi\) | ||||
0.833311 | + | 0.552804i | \(0.186442\pi\) | |||||||
\(752\) | − 2592.83i | − 0.125732i | ||||||||
\(753\) | 1035.02i | 0.0500905i | ||||||||
\(754\) | 2423.37 | 0.117047 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 265.364 | 0.0127661 | ||||||||
\(757\) | 2340.98i | 0.112397i | 0.998420 | + | 0.0561984i | \(0.0178979\pi\) | ||||
−0.998420 | + | 0.0561984i | \(0.982102\pi\) | |||||||
\(758\) | − 10410.7i | − 0.498858i | ||||||||
\(759\) | 7149.22 | 0.341898 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 23894.9 | 1.13823 | 0.569113 | − | 0.822259i | \(-0.307287\pi\) | ||||
0.569113 | + | 0.822259i | \(0.307287\pi\) | |||||||
\(762\) | − 11112.7i | − 0.528308i | ||||||||
\(763\) | 9133.13i | 0.433344i | ||||||||
\(764\) | 1077.65 | 0.0510316 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −11637.6 | −0.548935 | ||||||||
\(767\) | − 3947.09i | − 0.185816i | ||||||||
\(768\) | 6258.89i | 0.294073i | ||||||||
\(769\) | −22951.1 | −1.07625 | −0.538126 | − | 0.842864i | \(-0.680868\pi\) | ||||
−0.538126 | + | 0.842864i | \(0.680868\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 9427.17 | 0.440352 | ||||||||
\(772\) | − 1666.05i | − 0.0776718i | ||||||||
\(773\) | 13526.7i | 0.629393i | 0.949192 | + | 0.314696i | \(0.101903\pi\) | ||||
−0.949192 | + | 0.314696i | \(0.898097\pi\) | |||||||
\(774\) | 10979.0 | 0.509858 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 29757.3 | 1.37658 | ||||||||
\(777\) | − 5480.28i | − 0.253029i | ||||||||
\(778\) | − 2979.67i | − 0.137309i | ||||||||
\(779\) | −72803.1 | −3.34845 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 53833.5 | 2.46647 | ||||||||
\(782\) | − 564.812i | − 0.0258282i | ||||||||
\(783\) | − 748.592i | − 0.0341666i | ||||||||
\(784\) | 2489.02 | 0.113385 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −4962.15 | −0.225183 | ||||||||
\(787\) | 1611.55i | 0.0729929i | 0.999334 | + | 0.0364965i | \(0.0116198\pi\) | ||||
−0.999334 | + | 0.0364965i | \(0.988380\pi\) | |||||||
\(788\) | − 5075.22i | − 0.229438i | ||||||||
\(789\) | −14847.1 | −0.669923 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1663.10 | 0.0747572 | ||||||||
\(792\) | 14437.2i | 0.647731i | ||||||||
\(793\) | 13285.0i | 0.594909i | ||||||||
\(794\) | −17260.6 | −0.771481 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 4321.00 | 0.192404 | ||||||||
\(797\) | 7064.99i | 0.313996i | 0.987599 | + | 0.156998i | \(0.0501816\pi\) | ||||
−0.987599 | + | 0.156998i | \(0.949818\pi\) | |||||||
\(798\) | 8814.03i | 0.390994i | ||||||||
\(799\) | 312.864 | 0.0138527 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 13696.4 | 0.604169 | ||||||||
\(802\) | − 7111.67i | − 0.313119i | ||||||||
\(803\) | 23259.3i | 1.02217i | ||||||||
\(804\) | 3006.29 | 0.131870 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −6497.86 | −0.283967 | ||||||||
\(807\) | − 13711.8i | − 0.598114i | ||||||||
\(808\) | 40131.9i | 1.74732i | ||||||||
\(809\) | 6352.68 | 0.276079 | 0.138040 | − | 0.990427i | \(-0.455920\pi\) | ||||
0.138040 | + | 0.990427i | \(0.455920\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −16809.3 | −0.727810 | −0.363905 | − | 0.931436i | \(-0.618557\pi\) | ||||
−0.363905 | + | 0.931436i | \(0.618557\pi\) | |||||||
\(812\) | 272.496i | 0.0117768i | ||||||||
\(813\) | 16015.3i | 0.690874i | ||||||||
\(814\) | 44515.2 | 1.91678 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 934.044 | 0.0400712 | ||||||||
\(817\) | − 77624.0i | − 3.32401i | ||||||||
\(818\) | 37082.7i | 1.58505i | ||||||||
\(819\) | 2144.07 | 0.0914774 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −41992.9 | −1.78510 | −0.892548 | − | 0.450952i | \(-0.851084\pi\) | ||||
−0.892548 | + | 0.450952i | \(0.851084\pi\) | |||||||
\(822\) | − 2739.64i | − 0.116248i | ||||||||
\(823\) | − 37046.2i | − 1.56908i | −0.620080 | − | 0.784538i | \(-0.712900\pi\) | ||||
0.620080 | − | 0.784538i | \(-0.287100\pi\) | |||||||
\(824\) | −4676.58 | −0.197714 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −2085.04 | −0.0878304 | ||||||||
\(827\) | 14371.8i | 0.604301i | 0.953260 | + | 0.302151i | \(0.0977046\pi\) | ||||
−0.953260 | + | 0.302151i | \(0.902295\pi\) | |||||||
\(828\) | − 453.392i | − 0.0190296i | ||||||||
\(829\) | 43252.1 | 1.81207 | 0.906037 | − | 0.423199i | \(-0.139093\pi\) | ||||
0.906037 | + | 0.423199i | \(0.139093\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −6677.93 | −0.278766 | ||||||||
\(832\) | 19315.4i | 0.804855i | ||||||||
\(833\) | 300.338i | 0.0124923i | ||||||||
\(834\) | −3636.78 | −0.150997 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 15239.9 | 0.630484 | ||||||||
\(837\) | 2007.23i | 0.0828912i | ||||||||
\(838\) | 16427.5i | 0.677181i | ||||||||
\(839\) | 6400.97 | 0.263392 | 0.131696 | − | 0.991290i | \(-0.457958\pi\) | ||||
0.131696 | + | 0.991290i | \(0.457958\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −23620.3 | −0.968481 | ||||||||
\(842\) | 21139.5i | 0.865221i | ||||||||
\(843\) | − 5973.45i | − 0.244053i | ||||||||
\(844\) | 204.852 | 0.00835460 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −1179.84 | −0.0479477 | ||||||||
\(847\) | − 21562.5i | − 0.874731i | ||||||||
\(848\) | 34372.2i | 1.39192i | ||||||||
\(849\) | −22050.6 | −0.891372 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −9363.42 | −0.377173 | ||||||||
\(852\) | − 3414.03i | − 0.137280i | ||||||||
\(853\) | 17772.0i | 0.713368i | 0.934225 | + | 0.356684i | \(0.116093\pi\) | ||||
−0.934225 | + | 0.356684i | \(0.883907\pi\) | |||||||
\(854\) | 7017.75 | 0.281197 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −22245.0 | −0.888222 | ||||||||
\(857\) | − 29094.3i | − 1.15968i | −0.814731 | − | 0.579839i | \(-0.803115\pi\) | ||||
0.814731 | − | 0.579839i | \(-0.196885\pi\) | |||||||
\(858\) | 17415.9i | 0.692970i | ||||||||
\(859\) | 599.045 | 0.0237941 | 0.0118971 | − | 0.999929i | \(-0.496213\pi\) | ||||
0.0118971 | + | 0.999929i | \(0.496213\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 9355.18 | 0.370295 | ||||||||
\(862\) | 15347.2i | 0.606413i | ||||||||
\(863\) | − 19253.4i | − 0.759435i | −0.925103 | − | 0.379717i | \(-0.876021\pi\) | ||||
0.925103 | − | 0.379717i | \(-0.123979\pi\) | |||||||
\(864\) | 1694.47 | 0.0667210 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 28027.2 | 1.09977 | ||||||||
\(867\) | − 14626.3i | − 0.572935i | ||||||||
\(868\) | − 730.653i | − 0.0285714i | ||||||||
\(869\) | 3382.72 | 0.132049 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 24290.0 | 0.944931 | ||||||||
\(872\) | 31511.9i | 1.22377i | ||||||||
\(873\) | − 11088.7i | − 0.429893i | ||||||||
\(874\) | 15059.4 | 0.582827 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 1475.07 | 0.0568927 | ||||||||
\(877\) | − 42907.7i | − 1.65210i | −0.563598 | − | 0.826049i | \(-0.690583\pi\) | ||||
0.563598 | − | 0.826049i | \(-0.309417\pi\) | |||||||
\(878\) | 9718.41i | 0.373554i | ||||||||
\(879\) | 18750.5 | 0.719498 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −5765.54 | −0.220484 | −0.110242 | − | 0.993905i | \(-0.535163\pi\) | ||||
−0.110242 | + | 0.993905i | \(0.535163\pi\) | |||||||
\(882\) | − 1132.60i | − 0.0432389i | ||||||||
\(883\) | − 35426.8i | − 1.35018i | −0.737736 | − | 0.675089i | \(-0.764105\pi\) | ||||
0.737736 | − | 0.675089i | \(-0.235895\pi\) | |||||||
\(884\) | −292.883 | −0.0111433 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −20210.5 | −0.766349 | ||||||||
\(887\) | 24413.1i | 0.924138i | 0.886844 | + | 0.462069i | \(0.152893\pi\) | ||||
−0.886844 | + | 0.462069i | \(0.847107\pi\) | |||||||
\(888\) | − 18908.5i | − 0.714560i | ||||||||
\(889\) | 10096.2 | 0.380895 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 5379.86 | 0.202281 | ||||||||
\(892\) | 4713.80i | 0.176939i | ||||||||
\(893\) | 8341.77i | 0.312594i | ||||||||
\(894\) | −8409.97 | −0.314621 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 6688.85 | 0.249396 | ||||||||
\(897\) | − 3663.29i | − 0.136359i | ||||||||
\(898\) | − 40069.6i | − 1.48902i | ||||||||
\(899\) | −2061.17 | −0.0764671 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −4147.53 | −0.153356 | ||||||||
\(902\) | 75990.3i | 2.80510i | ||||||||
\(903\) | 9974.67i | 0.367593i | ||||||||
\(904\) | 5738.17 | 0.211116 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −22455.4 | −0.823434 | ||||||||
\(907\) | 23459.2i | 0.858818i | 0.903110 | + | 0.429409i | \(0.141278\pi\) | ||||
−0.903110 | + | 0.429409i | \(0.858722\pi\) | |||||||
\(908\) | 893.714i | 0.0326640i | ||||||||
\(909\) | 14954.7 | 0.545674 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −45803.8 | −1.66580 | −0.832902 | − | 0.553421i | \(-0.813322\pi\) | ||||
−0.832902 | + | 0.553421i | \(0.813322\pi\) | |||||||
\(912\) | 24904.1i | 0.904228i | ||||||||
\(913\) | − 5638.25i | − 0.204380i | ||||||||
\(914\) | 22705.4 | 0.821694 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −5127.80 | −0.184964 | ||||||||
\(917\) | − 4508.25i | − 0.162351i | ||||||||
\(918\) | − 425.027i | − 0.0152810i | ||||||||
\(919\) | −33360.4 | −1.19745 | −0.598725 | − | 0.800955i | \(-0.704326\pi\) | ||||
−0.598725 | + | 0.800955i | \(0.704326\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 3777.86 | 0.135163 | ||||||||
\(922\) | 27027.7i | 0.965412i | ||||||||
\(923\) | − 27584.5i | − 0.983700i | ||||||||
\(924\) | −1958.33 | −0.0697233 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 27690.0 | 0.982668 | ||||||||
\(927\) | 1742.68i | 0.0617444i | ||||||||
\(928\) | 1740.01i | 0.0615501i | ||||||||
\(929\) | −11194.3 | −0.395341 | −0.197670 | − | 0.980269i | \(-0.563338\pi\) | ||||
−0.197670 | + | 0.980269i | \(0.563338\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −8007.79 | −0.281895 | ||||||||
\(932\) | 4755.91i | 0.167151i | ||||||||
\(933\) | 20135.8i | 0.706554i | ||||||||
\(934\) | 14363.1 | 0.503186 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 7397.67 | 0.258334 | ||||||||
\(937\) | − 4383.20i | − 0.152821i | −0.997076 | − | 0.0764103i | \(-0.975654\pi\) | ||||
0.997076 | − | 0.0764103i | \(-0.0243459\pi\) | |||||||
\(938\) | − 12831.1i | − 0.446644i | ||||||||
\(939\) | 7308.80 | 0.254008 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −27642.7 | −0.957626 | −0.478813 | − | 0.877917i | \(-0.658933\pi\) | ||||
−0.478813 | + | 0.877917i | \(0.658933\pi\) | |||||||
\(942\) | − 11379.5i | − 0.393592i | ||||||||
\(943\) | − 15984.0i | − 0.551972i | ||||||||
\(944\) | −5891.29 | −0.203120 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −81022.3 | −2.78463 | ||||||||
\(947\) | − 25657.8i | − 0.880428i | −0.897893 | − | 0.440214i | \(-0.854902\pi\) | ||||
0.897893 | − | 0.440214i | \(-0.145098\pi\) | |||||||
\(948\) | − 214.527i | − 0.00734969i | ||||||||
\(949\) | 11918.2 | 0.407672 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −3575.44 | −0.121915 | ||||||||
\(952\) | 1036.25i | 0.0352785i | ||||||||
\(953\) | 48210.6i | 1.63871i | 0.573285 | + | 0.819356i | \(0.305669\pi\) | ||||
−0.573285 | + | 0.819356i | \(0.694331\pi\) | |||||||
\(954\) | 15640.7 | 0.530804 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 4749.38 | 0.160676 | ||||||||
\(957\) | 5524.45i | 0.186604i | ||||||||
\(958\) | − 20123.0i | − 0.678649i | ||||||||
\(959\) | 2489.04 | 0.0838114 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −24264.3 | −0.814484 | ||||||||
\(962\) | − 22809.8i | − 0.764467i | ||||||||
\(963\) | 8289.36i | 0.277384i | ||||||||
\(964\) | 8156.97 | 0.272529 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −1935.13 | −0.0644531 | ||||||||
\(967\) | 17711.5i | 0.589002i | 0.955651 | + | 0.294501i | \(0.0951534\pi\) | ||||
−0.955651 | + | 0.294501i | \(0.904847\pi\) | |||||||
\(968\) | − 74396.9i | − 2.47026i | ||||||||
\(969\) | −3005.05 | −0.0996245 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 35777.8 | 1.18245 | 0.591227 | − | 0.806505i | \(-0.298644\pi\) | ||||
0.591227 | + | 0.806505i | \(0.298644\pi\) | |||||||
\(972\) | − 341.182i | − 0.0112587i | ||||||||
\(973\) | − 3304.11i | − 0.108864i | ||||||||
\(974\) | −15356.2 | −0.505181 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 19828.7 | 0.650307 | ||||||||
\(977\) | − 30436.2i | − 0.996662i | −0.866987 | − | 0.498331i | \(-0.833946\pi\) | ||||
0.866987 | − | 0.498331i | \(-0.166054\pi\) | |||||||
\(978\) | − 21300.3i | − 0.696430i | ||||||||
\(979\) | −101077. | −3.29972 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 11742.6 | 0.382174 | ||||||||
\(982\) | 4604.02i | 0.149613i | ||||||||
\(983\) | − 57841.2i | − 1.87675i | −0.345617 | − | 0.938376i | \(-0.612330\pi\) | ||||
0.345617 | − | 0.938376i | \(-0.387670\pi\) | |||||||
\(984\) | 32278.1 | 1.04572 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 436.450 | 0.0140967 | ||||||||
\(987\) | − 1071.92i | − 0.0345689i | ||||||||
\(988\) | − 7809.01i | − 0.251455i | ||||||||
\(989\) | 17042.4 | 0.547944 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1521.84 | 0.0487819 | 0.0243909 | − | 0.999702i | \(-0.492235\pi\) | ||||
0.0243909 | + | 0.999702i | \(0.492235\pi\) | |||||||
\(992\) | − 4665.54i | − 0.149326i | ||||||||
\(993\) | − 17656.9i | − 0.564274i | ||||||||
\(994\) | −14571.5 | −0.464968 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −357.569 | −0.0113755 | ||||||||
\(997\) | − 46899.5i | − 1.48979i | −0.667181 | − | 0.744896i | \(-0.732499\pi\) | ||||
0.667181 | − | 0.744896i | \(-0.267501\pi\) | |||||||
\(998\) | − 52686.3i | − 1.67110i | ||||||||
\(999\) | −7046.07 | −0.223151 |
(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 | 525.4.d.o.274.3 | 8 | ||
5.2 | odd | 4 | 525.4.a.s.1.4 | ✓ | 4 | ||
5.3 | odd | 4 | 525.4.a.v.1.1 | yes | 4 | ||
5.4 | even | 2 | inner | 525.4.d.o.274.6 | 8 | ||
15.2 | even | 4 | 1575.4.a.bm.1.1 | 4 | |||
15.8 | even | 4 | 1575.4.a.bf.1.4 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
525.4.a.s.1.4 | ✓ | 4 | 5.2 | odd | 4 | ||
525.4.a.v.1.1 | yes | 4 | 5.3 | odd | 4 | ||
525.4.d.o.274.3 | 8 | 1.1 | even | 1 | trivial | ||
525.4.d.o.274.6 | 8 | 5.4 | even | 2 | inner | ||
1575.4.a.bf.1.4 | 4 | 15.8 | even | 4 | |||
1575.4.a.bm.1.1 | 4 | 15.2 | even | 4 |