Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [60,5,Mod(41,60)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(60, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("60.41");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 60 = 2^{2} \cdot 3 \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 60.g (of order \(2\), degree \(1\), 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: | \(6.20219778503\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\sqrt{-5}, \sqrt{34})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 58x^{2} + 1521 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 3\cdot 5 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 41.2 | ||
Root | \(5.83095 - 2.23607i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 60.41 |
Dual form | 60.5.g.b.41.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/60\mathbb{Z}\right)^\times\).
\(n\) | \(31\) | \(37\) | \(41\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −7.91548 | + | 4.28313i | −0.879497 | + | 0.475904i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − | 11.1803i | − | 0.447214i | ||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 7.49286 | 0.152915 | 0.0764577 | − | 0.997073i | \(-0.475639\pi\) | ||||
0.0764577 | + | 0.997073i | \(0.475639\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 44.3095 | − | 67.8061i | 0.547031 | − | 0.837112i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 185.562i | − | 1.53357i | −0.641905 | − | 0.766784i | \(-0.721856\pi\) | ||
0.641905 | − | 0.766784i | \(-0.278144\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 269.886 | 1.59696 | 0.798478 | − | 0.602023i | \(-0.205639\pi\) | ||||
0.798478 | + | 0.602023i | \(0.205639\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 47.8869 | + | 88.4977i | 0.212831 | + | 0.393323i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 438.205i | − | 1.51628i | −0.652091 | − | 0.758141i | \(-0.726108\pi\) | ||
0.652091 | − | 0.758141i | \(-0.273892\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −310.929 | −0.861298 | −0.430649 | − | 0.902520i | \(-0.641715\pi\) | ||||
−0.430649 | + | 0.902520i | \(0.641715\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −59.3095 | + | 32.0929i | −0.134489 | + | 0.0727730i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 436.880i | 0.825860i | 0.910763 | + | 0.412930i | \(0.135495\pi\) | ||||
−0.910763 | + | 0.412930i | \(0.864505\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −125.000 | −0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −60.3083 | + | 726.501i | −0.0827275 | + | 0.996572i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 813.673i | − | 0.967507i | −0.875204 | − | 0.483753i | \(-0.839273\pi\) | ||
0.875204 | − | 0.483753i | \(-0.160727\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −115.714 | −0.120410 | −0.0602051 | − | 0.998186i | \(-0.519175\pi\) | ||||
−0.0602051 | + | 0.998186i | \(0.519175\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 794.786 | + | 1468.81i | 0.729831 | + | 1.34877i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | − | 83.7727i | − | 0.0683859i | ||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −279.914 | −0.204466 | −0.102233 | − | 0.994760i | \(-0.532599\pi\) | ||||
−0.102233 | + | 0.994760i | \(0.532599\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −2136.27 | + | 1155.96i | −1.40452 | + | 0.759998i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 121.131i | − | 0.0720589i | −0.999351 | − | 0.0360295i | \(-0.988529\pi\) | ||
0.999351 | − | 0.0360295i | \(-0.0114710\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1342.71 | 0.726180 | 0.363090 | − | 0.931754i | \(-0.381722\pi\) | ||||
0.363090 | + | 0.931754i | \(0.381722\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −758.095 | − | 495.395i | −0.374368 | − | 0.244640i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 950.856i | 0.430446i | 0.976565 | + | 0.215223i | \(0.0690479\pi\) | ||||
−0.976565 | + | 0.215223i | \(0.930952\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −2344.86 | −0.976617 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1876.89 | + | 3468.60i | 0.721604 | + | 1.33357i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 2299.13i | − | 0.818485i | −0.912426 | − | 0.409243i | \(-0.865793\pi\) | ||
0.912426 | − | 0.409243i | \(-0.134207\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2074.64 | −0.685832 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 2461.15 | − | 1331.75i | 0.757509 | − | 0.409895i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − | 6352.54i | − | 1.82492i | −0.409168 | − | 0.912459i | \(-0.634181\pi\) | ||
0.409168 | − | 0.912459i | \(-0.365819\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5231.86 | 1.40604 | 0.703018 | − | 0.711172i | \(-0.251836\pi\) | ||||
0.703018 | + | 0.711172i | \(0.251836\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 332.005 | − | 508.061i | 0.0836495 | − | 0.128007i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − | 3017.41i | − | 0.714181i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 761.278 | 0.169588 | 0.0847938 | − | 0.996399i | \(-0.472977\pi\) | ||||
0.0847938 | + | 0.996399i | \(0.472977\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −1871.21 | − | 3458.11i | −0.393030 | − | 0.726341i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2084.62i | 0.413533i | 0.978390 | + | 0.206767i | \(0.0662941\pi\) | ||||
−0.978390 | + | 0.206767i | \(0.933706\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 8598.37 | 1.61351 | 0.806753 | − | 0.590889i | \(-0.201223\pi\) | ||||
0.806753 | + | 0.590889i | \(0.201223\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 989.434 | − | 535.392i | 0.175899 | − | 0.0951808i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − | 1390.39i | − | 0.234506i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −8650.21 | −1.38603 | −0.693015 | − | 0.720923i | \(-0.743718\pi\) | ||||
−0.693015 | + | 0.720923i | \(0.743718\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −2634.33 | − | 6008.91i | −0.401514 | − | 0.915853i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 7854.04i | 1.14008i | 0.821615 | + | 0.570042i | \(0.193073\pi\) | ||||
−0.821615 | + | 0.570042i | \(0.806927\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −4899.29 | −0.678102 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 3485.07 | + | 6440.61i | 0.460440 | + | 0.850920i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 9177.21i | 1.15859i | 0.815117 | + | 0.579296i | \(0.196672\pi\) | ||||
−0.815117 | + | 0.579296i | \(0.803328\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2022.21 | 0.244199 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 915.933 | − | 495.620i | 0.105900 | − | 0.0573037i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 3476.29i | 0.385184i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −10936.5 | −1.16235 | −0.581175 | − | 0.813779i | \(-0.697407\pi\) | ||||
−0.581175 | + | 0.813779i | \(0.697407\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −12582.2 | − | 8222.15i | −1.28377 | − | 0.838909i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 9133.76i | 0.895379i | 0.894189 | + | 0.447690i | \(0.147753\pi\) | ||||
−0.894189 | + | 0.447690i | \(0.852247\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 4767.26 | 0.449360 | 0.224680 | − | 0.974433i | \(-0.427866\pi\) | ||||
0.224680 | + | 0.974433i | \(0.427866\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 358.810 | + | 663.101i | 0.0325451 | + | 0.0601452i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1424.04i | 0.124381i | 0.998064 | + | 0.0621906i | \(0.0198087\pi\) | ||||
−0.998064 | + | 0.0621906i | \(0.980191\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 13612.4 | 1.14573 | 0.572865 | − | 0.819649i | \(-0.305832\pi\) | ||||
0.572865 | + | 0.819649i | \(0.305832\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 2215.65 | − | 1198.91i | 0.179828 | − | 0.0973063i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 24150.0i | 1.89130i | 0.325182 | + | 0.945651i | \(0.394574\pi\) | ||||
−0.325182 | + | 0.945651i | \(0.605426\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 4884.46 | 0.369336 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 11958.5 | − | 18299.9i | 0.873585 | − | 1.33683i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − | 3283.41i | − | 0.231863i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −19792.1 | −1.35183 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 518.821 | + | 958.810i | 0.0342931 | + | 0.0633756i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 1397.54i | 0.0894427i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −17779.2 | −1.10231 | −0.551157 | − | 0.834401i | \(-0.685814\pi\) | ||||
−0.551157 | + | 0.834401i | \(0.685814\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −10628.2 | + | 5751.00i | −0.638674 | + | 0.345592i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 19682.8i | − | 1.14695i | −0.819223 | − | 0.573475i | \(-0.805595\pi\) | ||
0.819223 | − | 0.573475i | \(-0.194405\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2329.74 | −0.131706 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 8122.53 | + | 674.267i | 0.445681 | + | 0.0369968i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 24052.6i | 1.28150i | 0.767748 | + | 0.640752i | \(0.221377\pi\) | ||||
−0.767748 | + | 0.640752i | \(0.778623\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 32890.8 | 1.70233 | 0.851167 | − | 0.524895i | \(-0.175896\pi\) | ||||
0.851167 | + | 0.524895i | \(0.175896\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −4072.64 | − | 7526.48i | −0.204851 | − | 0.378576i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 50080.4i | − | 2.44904i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −9097.14 | −0.432682 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 18560.7 | − | 10043.3i | 0.858932 | − | 0.464776i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 5263.83i | 0.237099i | 0.992948 | + | 0.118549i | \(0.0378244\pi\) | ||||
−0.992948 | + | 0.118549i | \(0.962176\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 36541.6 | 1.60263 | 0.801315 | − | 0.598243i | \(-0.204134\pi\) | ||||
0.801315 | + | 0.598243i | \(0.204134\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −29713.0 | − | 19416.7i | −1.26930 | − | 0.829453i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1293.72i | 0.0538491i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2630.88 | 0.106734 | 0.0533669 | − | 0.998575i | \(-0.483005\pi\) | ||||
0.0533669 | + | 0.998575i | \(0.483005\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 9847.46 | + | 18198.7i | 0.389520 | + | 0.719856i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 3273.48i | 0.126287i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −20407.6 | −0.768100 | −0.384050 | − | 0.923312i | \(-0.625471\pi\) | ||||
−0.384050 | + | 0.923312i | \(0.625471\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 16421.8 | − | 8885.97i | 0.603188 | − | 0.326390i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 45547.7i | − | 1.63318i | −0.577220 | − | 0.816588i | \(-0.695863\pi\) | ||
0.577220 | − | 0.816588i | \(-0.304137\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 44277.3 | 1.55027 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −13777.1 | + | 21082.9i | −0.471157 | + | 0.721003i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − | 17995.0i | − | 0.601256i | −0.953742 | − | 0.300628i | \(-0.902804\pi\) | ||
0.953742 | − | 0.300628i | \(-0.0971962\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −936.607 | −0.0305831 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 27208.8 | + | 50283.4i | 0.868486 | + | 1.60501i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 5358.45i | 0.167237i | 0.996498 | + | 0.0836186i | \(0.0266477\pi\) | ||||
−0.996498 | + | 0.0836186i | \(0.973352\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −42560.6 | −1.29912 | −0.649562 | − | 0.760309i | \(-0.725048\pi\) | ||||
−0.649562 | + | 0.760309i | \(0.725048\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −41412.6 | + | 22408.7i | −1.23660 | + | 0.669137i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 3129.54i | 0.0914401i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −81314.1 | −2.32532 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −451.881 | + | 5443.57i | −0.0126503 | + | 0.152391i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 40085.0i | 1.09879i | 0.835562 | + | 0.549396i | \(0.185142\pi\) | ||||
−0.835562 | + | 0.549396i | \(0.814858\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −16107.4 | −0.432425 | −0.216212 | − | 0.976346i | \(-0.569370\pi\) | ||||
−0.216212 | + | 0.976346i | \(0.569370\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 12924.0 | + | 23884.3i | 0.339881 | + | 0.628120i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 6357.91i | 0.163826i | 0.996640 | + | 0.0819128i | \(0.0261029\pi\) | ||||
−0.996640 | + | 0.0819128i | \(0.973897\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 42969.4 | 1.08506 | 0.542529 | − | 0.840037i | \(-0.317467\pi\) | ||||
0.542529 | + | 0.840037i | \(0.317467\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −6025.88 | + | 3260.66i | −0.149152 | + | 0.0807073i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − | 6096.74i | − | 0.147947i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1354.29 | −0.0322257 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 29623.1 | + | 19357.9i | 0.691337 | + | 0.451771i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 57696.4i | 1.32086i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 15301.0 | 0.343681 | 0.171840 | − | 0.985125i | \(-0.445029\pi\) | ||||
0.171840 | + | 0.985125i | \(0.445029\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −8928.72 | − | 16500.8i | −0.196802 | − | 0.363702i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − | 15011.9i | − | 0.324758i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −867.030 | −0.0184126 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −68060.2 | + | 36828.0i | −1.41907 | + | 0.767873i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 118265.i | − | 2.42144i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −6149.72 | −0.123665 | −0.0618324 | − | 0.998087i | \(-0.519694\pi\) | ||||
−0.0618324 | + | 0.998087i | \(0.519694\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −5538.69 | + | 8475.76i | −0.109406 | + | 0.167422i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − | 18408.5i | − | 0.357246i | −0.983918 | − | 0.178623i | \(-0.942836\pi\) | ||
0.983918 | − | 0.178623i | \(-0.0571642\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 78317.1 | 1.49343 | 0.746717 | − | 0.665142i | \(-0.231629\pi\) | ||||
0.746717 | + | 0.665142i | \(0.231629\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 5955.21 | + | 11005.6i | 0.111602 | + | 0.206248i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 12038.2i | 0.221742i | 0.993835 | + | 0.110871i | \(0.0353641\pi\) | ||||
−0.993835 | + | 0.110871i | \(0.964636\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 10630.9 | 0.192501 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 68470.6 | − | 37050.0i | 1.21901 | − | 0.659617i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 50014.8i | − | 0.875593i | −0.899074 | − | 0.437797i | \(-0.855759\pi\) | ||
0.899074 | − | 0.437797i | \(-0.144241\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −45019.3 | −0.775112 | −0.387556 | − | 0.921846i | \(-0.626681\pi\) | ||||
−0.387556 | + | 0.921846i | \(0.626681\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 46589.0 | + | 36280.2i | 0.788988 | + | 0.614408i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 26216.3i | 0.436756i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −83915.2 | −1.37546 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −33639.9 | − | 62168.5i | −0.542571 | − | 1.00270i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 5129.44i | 0.0814184i | 0.999171 | + | 0.0407092i | \(0.0129617\pi\) | ||||
−0.999171 | + | 0.0407092i | \(0.987038\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 81068.1 | 1.26651 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 38780.2 | − | 20984.3i | 0.596389 | − | 0.322711i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 10584.1i | 0.160247i | 0.996785 | + | 0.0801234i | \(0.0255314\pi\) | ||||
−0.996785 | + | 0.0801234i | \(0.974469\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −2097.36 | −0.0312660 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −55172.0 | − | 36053.5i | −0.809912 | − | 0.529256i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 60860.5i | 0.879881i | 0.898027 | + | 0.439940i | \(0.145000\pi\) | ||||
−0.898027 | + | 0.439940i | \(0.855000\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −25705.0 | −0.366038 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −39307.2 | − | 72642.0i | −0.551378 | − | 1.01898i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 116001.i | − | 1.60309i | −0.597932 | − | 0.801547i | \(-0.704011\pi\) | ||
0.597932 | − | 0.801547i | \(-0.295989\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 89298.3 | 1.21592 | 0.607959 | − | 0.793968i | \(-0.291988\pi\) | ||||
0.607959 | + | 0.793968i | \(0.291988\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −16006.8 | + | 8661.42i | −0.214773 | + | 0.116215i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 23195.2i | 0.306714i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 42073.5 | 0.548338 | 0.274169 | − | 0.961681i | \(-0.411597\pi\) | ||||
0.274169 | + | 0.961681i | \(0.411597\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −5127.24 | + | 7846.13i | −0.0658681 | + | 0.100797i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 80101.2i | 1.01444i | 0.861817 | + | 0.507220i | \(0.169327\pi\) | ||||
−0.861817 | + | 0.507220i | \(0.830673\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 60061.3 | 0.749933 | 0.374966 | − | 0.927038i | \(-0.377654\pi\) | ||||
0.374966 | + | 0.927038i | \(0.377654\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −14889.4 | − | 27516.5i | −0.183311 | − | 0.338768i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 907.618i | − | 0.0110189i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −108503. | −1.29911 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 86567.9 | − | 46842.7i | 1.02228 | − | 0.553166i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 50062.0i | − | 0.583140i | −0.956549 | − | 0.291570i | \(-0.905822\pi\) | ||
0.956549 | − | 0.291570i | \(-0.0941776\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −71023.6 | −0.816128 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 134811. | + | 11190.9i | 1.52831 | + | 0.126868i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 117908.i | 1.31886i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 10060.7 | 0.111044 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −39121.1 | − | 72298.1i | −0.426114 | − | 0.787484i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 58493.9i | − | 0.628798i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −37829.6 | −0.401380 | −0.200690 | − | 0.979655i | \(-0.564318\pi\) | ||||
−0.200690 | + | 0.979655i | \(0.564318\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −37735.2 | + | 20418.8i | −0.395211 | + | 0.213852i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 134422.i | 1.38980i | 0.719108 | + | 0.694898i | \(0.244551\pi\) | ||||
−0.719108 | + | 0.694898i | \(0.755449\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 93976.5 | 0.959247 | 0.479623 | − | 0.877474i | \(-0.340773\pi\) | ||||
0.479623 | + | 0.877474i | \(0.340773\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −5680.30 | − | 3711.93i | −0.0572466 | − | 0.0374092i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 193466.i | 1.92524i | 0.270849 | + | 0.962622i | \(0.412696\pi\) | ||||
−0.270849 | + | 0.962622i | \(0.587304\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −150987. | −1.48374 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −6099.35 | − | 11272.0i | −0.0591935 | − | 0.109393i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 136251.i | 1.30597i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −33735.7 | −0.319391 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −107749. | + | 58303.9i | −1.00767 | + | 0.545258i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 7124.63i | 0.0658219i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 47066.4 | 0.429591 | 0.214796 | − | 0.976659i | \(-0.431091\pi\) | ||||
0.214796 | + | 0.976659i | \(0.431091\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −12402.9 | + | 18979.9i | −0.111849 | + | 0.171161i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − | 8511.35i | − | 0.0758418i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −18146.4 | −0.159783 | −0.0798915 | − | 0.996804i | \(-0.525457\pi\) | ||||
−0.0798915 | + | 0.996804i | \(0.525457\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −103438. | − | 191159.i | −0.900078 | − | 1.66340i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 21472.1i | 0.184657i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −35560.0 | −0.302255 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −38662.9 | + | 20920.8i | −0.324830 | + | 0.175768i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − | 38797.0i | − | 0.322210i | −0.986937 | − | 0.161105i | \(-0.948494\pi\) | ||
0.986937 | − | 0.161105i | \(-0.0515059\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 23918.0 | 0.196369 | 0.0981847 | − | 0.995168i | \(-0.468696\pi\) | ||||
0.0981847 | + | 0.995168i | \(0.468696\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −16276.4 | + | 196072.i | −0.132112 | + | 1.59148i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 121919.i | 0.978413i | 0.872168 | + | 0.489207i | \(0.162714\pi\) | ||||
−0.872168 | + | 0.489207i | \(0.837286\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 23306.8 | 0.184938 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 14063.3 | + | 25989.8i | 0.110344 | + | 0.203923i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 54589.0i | − | 0.423561i | −0.977317 | − | 0.211781i | \(-0.932074\pi\) | ||
0.977317 | − | 0.211781i | \(-0.0679262\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −33644.4 | −0.258166 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 156664. | − | 84772.4i | 1.18893 | − | 0.643341i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 96132.7i | − | 0.721582i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 173280. | 1.28652 | 0.643259 | − | 0.765648i | \(-0.277582\pi\) | ||||
0.643259 | + | 0.765648i | \(0.277582\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −8213.43 | − | 5367.26i | −0.0603214 | − | 0.0394185i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 17227.0i | − | 0.125159i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −33117.7 | −0.238036 | −0.119018 | − | 0.992892i | \(-0.537975\pi\) | ||||
−0.119018 | + | 0.992892i | \(0.537975\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −5985.86 | − | 11062.2i | −0.0425661 | − | 0.0786646i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 219599.i | − | 1.54507i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −5342.79 | −0.0371954 | −0.0185977 | − | 0.999827i | \(-0.505920\pi\) | ||||
−0.0185977 | + | 0.999827i | \(0.505920\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 140731. | − | 76150.9i | 0.969483 | − | 0.524596i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 258063.i | − | 1.75925i | −0.475669 | − | 0.879625i | \(-0.657794\pi\) | ||
0.475669 | − | 0.879625i | \(-0.342206\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −15545.0 | −0.104874 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 59494.7 | − | 91043.7i | 0.397243 | − | 0.607894i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 39109.0i | 0.258450i | 0.991615 | + | 0.129225i | \(0.0412490\pi\) | ||||
−0.991615 | + | 0.129225i | \(0.958751\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 191443. | 1.25224 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 84304.1 | + | 155799.i | 0.545838 | + | 1.00874i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 96712.3i | 0.619851i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −39193.5 | −0.248676 | −0.124338 | − | 0.992240i | \(-0.539681\pi\) | ||||
−0.124338 | + | 0.992240i | \(0.539681\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 18441.0 | − | 9978.60i | 0.115835 | − | 0.0626793i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 109754.i | − | 0.682545i | −0.939964 | − | 0.341272i | \(-0.889142\pi\) | ||
0.939964 | − | 0.341272i | \(-0.110858\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −31229.6 | −0.192290 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −67181.7 | + | 29452.7i | −0.409582 | + | 0.179562i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 51941.4i | 0.313563i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −47748.4 | −0.285438 | −0.142719 | − | 0.989763i | \(-0.545585\pi\) | ||||
−0.142719 | + | 0.989763i | \(0.545585\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −103020. | − | 190387.i | −0.609873 | − | 1.12708i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − | 47598.7i | − | 0.279058i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 87810.9 | 0.509861 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −260346. | + | 140876.i | −1.49720 | + | 0.810147i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 305048.i | − | 1.73756i | −0.495197 | − | 0.868781i | \(-0.664904\pi\) | ||
0.495197 | − | 0.868781i | \(-0.335096\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −307155. | −1.73298 | −0.866489 | − | 0.499196i | \(-0.833629\pi\) | ||||
−0.866489 | + | 0.499196i | \(0.833629\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 64473.8 | + | 42132.0i | 0.360332 | + | 0.235468i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 54775.7i | 0.303256i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 39201.5 | 0.215004 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 214501. | + | 396411.i | 1.16551 | + | 2.15393i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 291873.i | − | 1.57123i | −0.618716 | − | 0.785615i | \(-0.712347\pi\) | ||
0.618716 | − | 0.785615i | \(-0.287653\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 227573. | 1.21380 | 0.606898 | − | 0.794780i | \(-0.292414\pi\) | ||||
0.606898 | + | 0.794780i | \(0.292414\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 72008.2 | − | 38964.3i | 0.380543 | − | 0.205915i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − | 135838.i | − | 0.711311i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −85820.5 | −0.445309 | −0.222655 | − | 0.974897i | \(-0.571472\pi\) | ||||
−0.222655 | + | 0.974897i | \(0.571472\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −103899. | + | 158996.i | −0.534240 | + | 0.817538i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 294251.i | 1.49938i | 0.661791 | + | 0.749689i | \(0.269797\pi\) | ||||
−0.661791 | + | 0.749689i | \(0.730203\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 102604. | 0.518138 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −22545.7 | − | 41665.7i | −0.112836 | − | 0.208528i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 10134.9i | − | 0.0502720i | −0.999684 | − | 0.0251360i | \(-0.991998\pi\) | ||
0.999684 | − | 0.0251360i | \(-0.00800188\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −22477.3 | −0.110507 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −289244. | + | 156512.i | −1.40951 | + | 0.762698i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | − | 22609.0i | − | 0.109209i | ||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 171657. | 0.821921 | 0.410960 | − | 0.911653i | \(-0.365193\pi\) | ||||
0.410960 | + | 0.911653i | \(0.365193\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 318357. | + | 26427.4i | 1.51108 | + | 0.125438i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 35926.8i | 0.169051i | 0.996421 | + | 0.0845254i | \(0.0269374\pi\) | ||||
−0.996421 | + | 0.0845254i | \(0.973063\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −284140. | −1.32547 | −0.662735 | − | 0.748854i | \(-0.730605\pi\) | ||||
−0.662735 | + | 0.748854i | \(0.730605\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −5541.20 | − | 10240.4i | −0.0256270 | − | 0.0473601i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 163891.i | 0.751485i | 0.926724 | + | 0.375743i | \(0.122612\pi\) | ||||
−0.926724 | + | 0.375743i | \(0.877388\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 5704.15 | 0.0259325 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −20824.7 | + | 11268.4i | −0.0938722 | + | 0.0507951i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 249155.i | − | 1.11365i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 38866.1 | 0.172260 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −155895. | − | 101873.i | −0.685164 | − | 0.447737i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 192581.i | 0.839347i | 0.907675 | + | 0.419673i | \(0.137855\pi\) | ||||
−0.907675 | + | 0.419673i | \(0.862145\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −75544.9 | −0.326524 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −14020.7 | − | 25911.1i | −0.0601003 | − | 0.111069i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 122274.i | 0.519818i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 58765.7 | 0.247780 | 0.123890 | − | 0.992296i | \(-0.460463\pi\) | ||||
0.123890 | + | 0.992296i | \(0.460463\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 161536. | − | 87408.7i | 0.675542 | − | 0.365542i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 250734.i | 1.04004i | 0.854154 | + | 0.520020i | \(0.174075\pi\) | ||||
−0.854154 | + | 0.520020i | \(0.825925\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −356556. | −1.46701 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −91926.4 | + | 140673.i | −0.375172 | + | 0.574119i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 15619.8i | 0.0632356i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 21438.1 | 0.0860963 | 0.0430482 | − | 0.999073i | \(-0.486293\pi\) | ||||
0.0430482 | + | 0.999073i | \(0.486293\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 195087. | + | 360531.i | 0.777235 | + | 1.43637i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 312093.i | − | 1.23353i | −0.787149 | − | 0.616763i | \(-0.788444\pi\) | ||
0.787149 | − | 0.616763i | \(-0.211556\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 102119. | 0.400426 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −350476. | + | 189646.i | −1.36346 | + | 0.737780i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 365909.i | 1.41233i | 0.708045 | + | 0.706167i | \(0.249577\pi\) | ||||
−0.708045 | + | 0.706167i | \(0.750423\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 64426.4 | 0.246730 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 18751.6 | − | 225890.i | 0.0712530 | − | 0.858346i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − | 53299.6i | − | 0.200960i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 176442. | 0.660119 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 77074.9 | + | 142439.i | 0.286140 | + | 0.528803i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 285210.i | − | 1.05072i | −0.850879 | − | 0.525362i | \(-0.823930\pi\) | ||
0.850879 | − | 0.525362i | \(-0.176070\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −423227. | −1.54729 | −0.773643 | − | 0.633622i | \(-0.781567\pi\) | ||||
−0.773643 | + | 0.633622i | \(0.781567\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 7413.69 | − | 4011.61i | 0.0268977 | − | 0.0145546i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 50706.6i | 0.182576i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 88977.1 | 0.317956 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −430741. | − | 281478.i | −1.52766 | − | 0.998287i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 32691.5i | − | 0.115075i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 15921.3 | 0.0556250 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −22950.9 | − | 42414.7i | −0.0795888 | − | 0.147085i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 435116.i | 1.49771i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −171697. | −0.586636 | −0.293318 | − | 0.956015i | \(-0.594759\pi\) | ||||
−0.293318 | + | 0.956015i | \(0.594759\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 336887. | − | 182293.i | 1.14258 | − | 0.618258i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 152192.i | − | 0.512386i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 302744. | 1.01181 | 0.505907 | − | 0.862588i | \(-0.331158\pi\) | ||||
0.505907 | + | 0.862588i | \(0.331158\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 231821. | − | 354752.i | 0.769145 | − | 1.17701i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 252994.i | 0.833312i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −64814.8 | −0.211945 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −13404.2 | − | 24771.8i | −0.0435167 | − | 0.0804213i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 258715.i | − | 0.833896i | −0.908930 | − | 0.416948i | \(-0.863100\pi\) | ||
0.908930 | − | 0.416948i | \(-0.136900\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 362377. | 1.15968 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 643640. | − | 348279.i | 2.04511 | − | 1.10663i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 7185.47i | 0.0226693i | 0.999936 | + | 0.0113346i | \(0.00360801\pi\) | ||||
−0.999936 | + | 0.0113346i | \(0.996392\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 270006. | 0.845816 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −19738.7 | − | 45023.9i | −0.0613977 | − | 0.140048i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 465206.i | − | 1.43688i | −0.695589 | − | 0.718440i | \(-0.744857\pi\) | ||
0.695589 | − | 0.718440i | \(-0.255143\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −176094. | −0.540099 | −0.270049 | − | 0.962847i | \(-0.587040\pi\) | ||||
−0.270049 | + | 0.962847i | \(0.587040\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −171689. | − | 317292.i | −0.522919 | − | 0.966384i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 54610.0i | − | 0.165172i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 31818.4 | 0.0955712 | 0.0477856 | − | 0.998858i | \(-0.484784\pi\) | ||||
0.0477856 | + | 0.998858i | \(0.484784\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 127498. | − | 68990.1i | 0.380317 | − | 0.205793i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 58849.2i | 0.174337i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −426630. | −1.25520 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −204599. | − | 133700.i | −0.597849 | − | 0.390679i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 7750.43i | 0.0224931i | 0.999937 | + | 0.0112466i | \(0.00357997\pi\) | ||||
−0.999937 | + | 0.0112466i | \(0.996420\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 35978.9 | 0.103709 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −27231.8 | − | 50325.9i | −0.0779652 | − | 0.144084i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 91847.4i | 0.261191i | 0.991436 | + | 0.130595i | \(0.0416889\pi\) | ||||
−0.991436 | + | 0.130595i | \(0.958311\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −36709.6 | −0.103692 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −340123. | + | 184044.i | −0.954305 | + | 0.516383i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 410.933i | − | 0.00114529i | −1.00000 | 0.000572647i | \(-0.999818\pi\) | |||
1.00000 | 0.000572647i | \(-0.000182279\pi\) | ||||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 597721. | 1.65482 | 0.827408 | − | 0.561602i | \(-0.189815\pi\) | ||||
0.827408 | + | 0.561602i | \(0.189815\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 33731.9 | − | 51619.3i | 0.0927696 | − | 0.141964i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 221283.i | 0.604557i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 609937. | 1.65542 | 0.827709 | − | 0.561158i | \(-0.189644\pi\) | ||||
0.827709 | + | 0.561158i | \(0.189644\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 26113.1 | + | 48258.6i | 0.0704084 | + | 0.130119i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 256622.i | 0.687404i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 462712. | 1.23137 | 0.615687 | − | 0.787991i | \(-0.288879\pi\) | ||||
0.615687 | + | 0.787991i | \(0.288879\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 10719.8 | − | 5800.59i | 0.0283424 | − | 0.0153364i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 205753.i | 0.540474i | 0.962794 | + | 0.270237i | \(0.0871021\pi\) | ||||
−0.962794 | + | 0.270237i | \(0.912898\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −467560. | −1.22027 | −0.610135 | − | 0.792298i | \(-0.708885\pi\) | ||||
−0.610135 | + | 0.792298i | \(0.708885\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −317394. | − | 26347.5i | −0.823029 | − | 0.0683213i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 68763.5i | 0.177167i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 15625.0 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −247122. | − | 456695.i | −0.628602 | − | 1.16169i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 122660.i | 0.310028i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −639276. | −1.60557 | −0.802786 | − | 0.596267i | \(-0.796650\pi\) | ||||
−0.802786 | + | 0.596267i | \(0.796650\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −121115. | + | 65536.2i | −0.302266 | + | 0.163559i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 198778.i | 0.492970i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −632843. | −1.55961 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 141350. | + | 92368.6i | 0.346174 | + | 0.226216i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 207410.i | 0.504794i | 0.967624 | + | 0.252397i | \(0.0812189\pi\) | ||||
−0.967624 | + | 0.252397i | \(0.918781\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 396677. | 0.959434 | 0.479717 | − | 0.877423i | \(-0.340739\pi\) | ||||
0.479717 | + | 0.877423i | \(0.340739\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 64298.1 | + | 118827.i | 0.154553 | + | 0.285623i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 287606.i | 0.687052i | 0.939143 | + | 0.343526i | \(0.111621\pi\) | ||||
−0.939143 | + | 0.343526i | \(0.888379\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1.17879e6 | −2.79864 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 6862.96 | − | 3713.61i | 0.0161938 | − | 0.00876262i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 481395.i | 1.12895i | 0.825450 | + | 0.564476i | \(0.190922\pi\) | ||||
−0.825450 | + | 0.564476i | \(0.809078\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −220060. | −0.512931 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 380990. | − | 583022.i | 0.882638 | − | 1.35069i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 300201.i | 0.691260i | 0.938371 | + | 0.345630i | \(0.112335\pi\) | ||||
−0.938371 | + | 0.345630i | \(0.887665\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −84703.8 | −0.193865 | −0.0969327 | − | 0.995291i | \(-0.530903\pi\) | ||||
−0.0969327 | + | 0.995291i | \(0.530903\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 506546. | + | 936127.i | 1.15237 | + | 2.12965i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 26047.3i | 0.0589006i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 355477. | 0.799025 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 48678.0 | − | 26340.1i | 0.108763 | − | 0.0588525i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 970832.i | − | 2.15625i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 440538. | 0.972643 | 0.486322 | − | 0.873780i | \(-0.338338\pi\) | ||||
0.486322 | + | 0.873780i | \(0.338338\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 7538.54 | − | 90812.6i | 0.0165455 | − | 0.199314i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 298268.i | 0.650772i | 0.945581 | + | 0.325386i | \(0.105494\pi\) | ||||
−0.945581 | + | 0.325386i | \(0.894506\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −81945.9 | −0.177741 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 78846.1 | + | 145712.i | 0.170015 | + | 0.314196i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 450549.i | 0.965829i | 0.875668 | + | 0.482915i | \(0.160422\pi\) | ||||
−0.875668 | + | 0.482915i | \(0.839578\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 268916. | 0.573106 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −619917. | + | 335443.i | −1.31347 | + | 0.710731i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 620501.i | − | 1.30709i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 587313. | 1.23002 | 0.615012 | − | 0.788518i | \(-0.289151\pi\) | ||||
0.615012 | + | 0.788518i | \(0.289151\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −94276.7 | − | 61607.4i | −0.196308 | − | 0.128282i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 367730.i | − | 0.761307i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −53080.3 | −0.109262 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −51561.0 | − | 95287.7i | −0.105528 | − | 0.195022i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 521524.i | 1.06130i | 0.847591 | + | 0.530650i | \(0.178052\pi\) | ||||
−0.847591 | + | 0.530650i | \(0.821948\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 87033.3 | 0.176106 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −84148.6 | + | 45533.5i | −0.169304 | + | 0.0916122i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 68438.0i | 0.136917i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −129165. | −0.256951 | −0.128476 | − | 0.991713i | \(-0.541008\pi\) | ||||
−0.128476 | + | 0.991713i | \(0.541008\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −383287. | + | 586537.i | −0.758202 | + | 1.16026i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 50553.2i | − | 0.0994419i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −559916. | −1.09524 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 214220. | + | 395891.i | 0.416698 | + | 0.770082i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − | 747554.i | − | 1.44606i | −0.690819 | − | 0.723028i | \(-0.742750\pi\) | ||
0.690819 | − | 0.723028i | \(-0.257250\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 35720.4 | 0.0687141 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 356349. | − | 192824.i | 0.681709 | − | 0.368879i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 101709.i | 0.193501i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −19031.0 | −0.0360075 | −0.0180037 | − | 0.999838i | \(-0.505731\pi\) | ||||
−0.0180037 | + | 0.999838i | \(0.505731\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −524167. | − | 87628.1i | −0.986312 | − | 0.164888i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 588382.i | − | 1.10109i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −209303. | −0.389553 | −0.194777 | − | 0.980848i | \(-0.562398\pi\) | ||||
−0.194777 | + | 0.980848i | \(0.562398\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −112288. | − | 207514.i | −0.207854 | − | 0.384126i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 141264.i | − | 0.260074i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 247993. | 0.454099 | 0.227049 | − | 0.973883i | \(-0.427092\pi\) | ||||
0.227049 | + | 0.973883i | \(0.427092\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 664228. | − | 359420.i | 1.20971 | − | 0.654585i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 247338.i | 0.448037i | 0.974585 | + | 0.224018i | \(0.0719176\pi\) | ||||
−0.974585 | + | 0.224018i | \(0.928082\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 58851.4 | 0.106034 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 532552. | + | 348009.i | 0.954379 | + | 0.623662i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 10670.1i | 0.0190198i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 146465. | 0.259689 | 0.129845 | − | 0.991534i | \(-0.458552\pi\) | ||||
0.129845 | + | 0.991534i | \(0.458552\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −21970.1 | − | 40602.0i | −0.0387473 | − | 0.0716073i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − | 408547.i | − | 0.716718i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 38708.6 | 0.0675485 | 0.0337742 | − | 0.999429i | \(-0.489247\pi\) | ||||
0.0337742 | + | 0.999429i | \(0.489247\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −641693. | + | 347226.i | −1.11389 | + | 0.602738i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 712289.i | 1.22995i | 0.788547 | + | 0.614974i | \(0.210833\pi\) | ||||
−0.788547 | + | 0.614974i | \(0.789167\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 101996. | 0.175200 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −217085. | + | 332201.i | −0.370943 | + | 0.567647i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 1.71446e6i | − | 2.91432i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −591771. | −1.00069 | −0.500347 | − | 0.865825i | \(-0.666794\pi\) | ||||
−0.500347 | + | 0.865825i | \(0.666794\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −45333.3 | − | 83778.5i | −0.0762620 | − | 0.140937i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 791169.i | − | 1.32407i | −0.749474 | − | 0.662034i | \(-0.769694\pi\) | ||
0.749474 | − | 0.662034i | \(-0.230306\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 14464.3 | 0.0240820 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 16601.6 | − | 8983.26i | 0.0274984 | − | 0.0148796i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 37663.1i | 0.0620642i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 386826. | 0.634181 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 591134. | + | 49071.3i | 0.964190 | + | 0.0800394i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 29414.2i | − | 0.0477329i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 90648.7 | 0.146357 | 0.0731783 | − | 0.997319i | \(-0.476686\pi\) | ||||
0.0731783 | + | 0.997319i | \(0.476686\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −260674. | − | 481740.i | −0.418739 | − | 0.773853i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 180953.i | 0.289209i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.41200e6 | 2.24538 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 203467. | − | 110098.i | 0.321929 | − | 0.174199i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 374938.i | − | 0.590259i | −0.955457 | − | 0.295129i | \(-0.904637\pi\) | ||
0.955457 | − | 0.295129i | \(-0.0953627\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 416670. | 0.652678 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 622271. | + | 406638.i | 0.969872 | + | 0.633786i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − | 1.59553e6i | − | 2.47442i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 36598.6 | 0.0564771 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 496850. | + | 918207.i | 0.762918 | + | 1.40992i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 302871.i | − | 0.462765i | −0.972863 | − | 0.231383i | \(-0.925675\pi\) | ||
0.972863 | − | 0.231383i | \(-0.0743249\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −78720.5 | −0.119687 | −0.0598434 | − | 0.998208i | \(-0.519060\pi\) | ||||
−0.0598434 | + | 0.998208i | \(0.519060\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −706838. | + | 382477.i | −1.06940 | + | 0.578660i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 228164.i | 0.343505i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −417486. | −0.625458 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 89603.4 | − | 137118.i | 0.133585 | − | 0.204422i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 126623.i | − | 0.187856i | −0.995579 | − | 0.0939280i | \(-0.970058\pi\) | ||
0.995579 | − | 0.0939280i | \(-0.0299423\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −574953. | −0.848854 | −0.424427 | − | 0.905462i | \(-0.639524\pi\) | ||||
−0.424427 | + | 0.905462i | \(0.639524\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −99348.2 | − | 183601.i | −0.145966 | − | 0.269754i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 724955.i | 1.05999i | 0.848002 | + | 0.529993i | \(0.177805\pi\) | ||||
−0.848002 | + | 0.529993i | \(0.822195\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 643760. | 0.936732 | 0.468366 | − | 0.883535i | \(-0.344843\pi\) | ||||
0.468366 | + | 0.883535i | \(0.344843\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −333031. | + | 180206.i | −0.482262 | + | 0.260956i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 1.02753e6i | 1.48083i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −509238. | −0.730379 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 6978.53 | − | 84066.5i | 0.00996123 | − | 0.119997i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 639908.i | − | 0.909063i | −0.890731 | − | 0.454531i | \(-0.849807\pi\) | ||
0.890731 | − | 0.454531i | \(-0.150193\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 45217.0 | 0.0639308 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −343084. | − | 634039.i | −0.482776 | − | 0.892197i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − | 495035.i | − | 0.693302i | ||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −148300. | −0.206716 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −475414. | + | 257251.i | −0.659564 | + | 0.356896i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 122289.i | − | 0.168860i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −1.23118e6 | −1.69210 | −0.846048 | − | 0.533107i | \(-0.821024\pi\) | ||||
−0.846048 | + | 0.533107i | \(0.821024\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 235713. | + | 154033.i | 0.322442 | + | 0.210708i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 1.33870e6i | 1.82273i | 0.411597 | + | 0.911366i | \(0.364971\pi\) | ||||
−0.411597 | + | 0.911366i | \(0.635029\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 94388.3 | 0.127918 | 0.0639590 | − | 0.997953i | \(-0.479627\pi\) | ||||
0.0639590 | + | 0.997953i | \(0.479627\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 3887.45 | + | 7184.23i | 0.00524395 | + | 0.00969111i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 774167.i | 1.03947i | 0.854327 | + | 0.519736i | \(0.173970\pi\) | ||||
−0.854327 | + | 0.519736i | \(0.826030\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −201190. | −0.268890 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 858853. | − | 464733.i | 1.14256 | − | 0.618252i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1.60515e6i | 2.12557i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 205458. | 0.270824 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −484593. | + | 741564.i | −0.635841 | + | 0.973017i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 10471.6i | 0.0136772i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1.12546e6 | −1.46329 | −0.731647 | − | 0.681684i | \(-0.761248\pi\) | ||||
−0.731647 | + | 0.681684i | \(0.761248\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 214422. | + | 396264.i | 0.277519 | + | 0.512870i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 474036.i | 0.610745i | 0.952233 | + | 0.305372i | \(0.0987809\pi\) | ||||
−0.952233 | + | 0.305372i | \(0.901219\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 79072.8 | 0.101416 | 0.0507079 | − | 0.998714i | \(-0.483852\pi\) | ||||
0.0507079 | + | 0.998714i | \(0.483852\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 562185. | − | 304203.i | 0.717783 | − | 0.388399i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 366939.i | 0.466387i | 0.972430 | + | 0.233194i | \(0.0749176\pi\) | ||||
−0.972430 | + | 0.233194i | \(0.925082\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −133217. | −0.168561 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.11502e6 | + | 488831.i | −1.40452 | + | 0.615749i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − | 295648.i | − | 0.370742i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 59909.3 | 0.0747907 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −505014. | − | 933295.i | −0.627651 | − | 1.15994i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 94153.6i | 0.116498i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.00749e6 | −1.24105 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −79635.3 | + | 43091.4i | −0.0976630 | + | 0.0528463i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 475842.i | 0.580985i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 418936. | 0.509252 | 0.254626 | − | 0.967040i | \(-0.418048\pi\) | ||||
0.254626 | + | 0.967040i | \(0.418048\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 619325. | + | 404713.i | 0.749533 | + | 0.489800i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 1.16696e6i | − | 1.40611i | −0.711135 | − | 0.703056i | \(-0.751818\pi\) | ||
0.711135 | − | 0.703056i | \(-0.248182\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1.45741e6 | 1.74840 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 250537. | + | 463007.i | 0.299247 | + | 0.553026i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − | 147480.i | − | 0.175386i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 108728. | 0.128739 | 0.0643697 | − | 0.997926i | \(-0.479496\pi\) | ||||
0.0643697 | + | 0.997926i | \(0.479496\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 299440. | − | 162029.i | 0.353013 | − | 0.191018i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 562610.i | 0.660395i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 34989.3 | 0.0408932 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 211235. | − | 323250.i | 0.245814 | − | 0.376165i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 139198.i | − | 0.161288i | −0.996743 | − | 0.0806440i | \(-0.974302\pi\) | ||
0.996743 | − | 0.0806440i | \(-0.0256977\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 729083. | 0.841158 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −575749. | − | 1.06402e6i | −0.661409 | − | 1.22232i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 909120.i | 1.03992i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1.66932e6 | −1.90135 | −0.950673 | − | 0.310196i | \(-0.899605\pi\) | ||||
−0.950673 | + | 0.310196i | \(0.899605\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −743868. | + | 402514.i | −0.843655 | + | 0.456509i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 309587.i | − | 0.349626i | −0.984602 | − | 0.174813i | \(-0.944068\pi\) | ||
0.984602 | − | 0.174813i | \(-0.0559321\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 52919.7 | 0.0595106 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 60860.9 | + | 5052.19i | 0.0681514 | + | 0.00565739i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 200056.i | 0.223076i | 0.993760 | + | 0.111538i | \(0.0355776\pi\) | ||||
−0.993760 | + | 0.111538i | \(0.964422\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 2.32058e6 | 2.57670 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −828640. | − | 1.53137e6i | −0.916231 | − | 1.69325i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 33737.1i | − | 0.0371469i | −0.999827 | − | 0.0185734i | \(-0.994088\pi\) | ||
0.999827 | − | 0.0185734i | \(-0.00591245\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 448164. | 0.491394 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 1.19513e6 | − | 646696.i | 1.30494 | − | 0.706116i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 180222.i | 0.195962i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −910131. | −0.985501 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 96558.6 | + | 63098.5i | 0.104121 | + | 0.0680404i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 180086.i | 0.193386i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −423000. | −0.452363 | −0.226182 | − | 0.974085i | \(-0.572624\pi\) | ||||
−0.226182 | + | 0.974085i | \(0.572624\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −583580. | − | 1.07849e6i | −0.621516 | − | 1.14860i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1.28807e6i | 1.36616i | 0.730344 | + | 0.683080i | \(0.239360\pi\) | ||||
−0.730344 | + | 0.683080i | \(0.760640\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 246446. | 0.260313 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 267034. | − | 144495.i | 0.280904 | − | 0.152000i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 1.20117e6i | − | 1.25839i | −0.777247 | − | 0.629196i | \(-0.783384\pi\) | ||
0.777247 | − | 0.629196i | \(-0.216616\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1.70294e6 | 1.77678 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 603160. | − | 923006.i | 0.626750 | − | 0.959105i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 491587.i | − | 0.508737i | −0.967107 | − | 0.254369i | \(-0.918132\pi\) | ||
0.967107 | − | 0.254369i | \(-0.0818676\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 71083.5 | 0.0732650 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −30515.7 | − | 56394.8i | −0.0313249 | − | 0.0578902i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 586602.i | 0.599723i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −543192. | −0.553103 | −0.276551 | − | 0.960999i | \(-0.589192\pi\) | ||||
−0.276551 | + | 0.960999i | \(0.589192\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −372553. | + | 201592.i | −0.377824 | + | 0.204444i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 480412.i | − | 0.485252i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 853733. | 0.858879 | 0.429439 | − | 0.903096i | \(-0.358711\pi\) | ||||
0.429439 | + | 0.903096i | \(0.358711\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 16881.2 | − | 203358.i | 0.0169150 | − | 0.203765i |
(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 | 60.5.g.b.41.2 | yes | 4 | |
3.2 | odd | 2 | inner | 60.5.g.b.41.1 | ✓ | 4 | |
4.3 | odd | 2 | 240.5.l.c.161.3 | 4 | |||
5.2 | odd | 4 | 300.5.b.d.149.6 | 8 | |||
5.3 | odd | 4 | 300.5.b.d.149.3 | 8 | |||
5.4 | even | 2 | 300.5.g.g.101.3 | 4 | |||
12.11 | even | 2 | 240.5.l.c.161.4 | 4 | |||
15.2 | even | 4 | 300.5.b.d.149.4 | 8 | |||
15.8 | even | 4 | 300.5.b.d.149.5 | 8 | |||
15.14 | odd | 2 | 300.5.g.g.101.4 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
60.5.g.b.41.1 | ✓ | 4 | 3.2 | odd | 2 | inner | |
60.5.g.b.41.2 | yes | 4 | 1.1 | even | 1 | trivial | |
240.5.l.c.161.3 | 4 | 4.3 | odd | 2 | |||
240.5.l.c.161.4 | 4 | 12.11 | even | 2 | |||
300.5.b.d.149.3 | 8 | 5.3 | odd | 4 | |||
300.5.b.d.149.4 | 8 | 15.2 | even | 4 | |||
300.5.b.d.149.5 | 8 | 15.8 | even | 4 | |||
300.5.b.d.149.6 | 8 | 5.2 | odd | 4 | |||
300.5.g.g.101.3 | 4 | 5.4 | even | 2 | |||
300.5.g.g.101.4 | 4 | 15.14 | odd | 2 |