Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [15,5,Mod(11,15)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(15, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("15.11");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 15 = 3 \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 15.c (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: | \(1.55054944626\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{6} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} + 73x^{4} + 1096x^{2} + 180 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 3\cdot 5^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 11.4 | ||
Root | \(0.407512i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 15.11 |
Dual form | 15.5.c.a.11.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/15\mathbb{Z}\right)^\times\).
\(n\) | \(7\) | \(11\) |
\(\chi(n)\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.407512i | 0.101878i | 0.998702 | + | 0.0509390i | \(0.0162214\pi\) | ||||
−0.998702 | + | 0.0509390i | \(0.983779\pi\) | |||||||
\(3\) | 3.21297 | − | 8.40695i | 0.356996 | − | 0.934106i | ||||
\(4\) | 15.8339 | 0.989621 | ||||||||
\(5\) | 11.1803i | 0.447214i | ||||||||
\(6\) | 3.42594 | + | 1.30932i | 0.0951649 | + | 0.0363701i | ||||
\(7\) | −46.9457 | −0.958075 | −0.479038 | − | 0.877794i | \(-0.659014\pi\) | ||||
−0.479038 | + | 0.877794i | \(0.659014\pi\) | |||||||
\(8\) | 12.9727i | 0.202699i | ||||||||
\(9\) | −60.3537 | − | 54.0225i | −0.745107 | − | 0.666945i | ||||
\(10\) | −4.55613 | −0.0455613 | ||||||||
\(11\) | 200.952i | 1.66076i | 0.557198 | + | 0.830379i | \(0.311876\pi\) | ||||
−0.557198 | + | 0.830379i | \(0.688124\pi\) | |||||||
\(12\) | 50.8739 | − | 133.115i | 0.353291 | − | 0.924411i | ||||
\(13\) | −22.3321 | −0.132143 | −0.0660714 | − | 0.997815i | \(-0.521047\pi\) | ||||
−0.0660714 | + | 0.997815i | \(0.521047\pi\) | |||||||
\(14\) | − | 19.1309i | − | 0.0976068i | ||||||
\(15\) | 93.9926 | + | 35.9221i | 0.417745 | + | 0.159654i | ||||
\(16\) | 248.056 | 0.968970 | ||||||||
\(17\) | − | 344.602i | − | 1.19239i | −0.802838 | − | 0.596197i | \(-0.796678\pi\) | ||
0.802838 | − | 0.596197i | \(-0.203322\pi\) | |||||||
\(18\) | 22.0148 | − | 24.5949i | 0.0679471 | − | 0.0759101i | ||||
\(19\) | −59.9990 | −0.166202 | −0.0831011 | − | 0.996541i | \(-0.526482\pi\) | ||||
−0.0831011 | + | 0.996541i | \(0.526482\pi\) | |||||||
\(20\) | 177.029i | 0.442572i | ||||||||
\(21\) | −150.835 | + | 394.670i | −0.342029 | + | 0.894943i | ||||
\(22\) | −81.8903 | −0.169195 | ||||||||
\(23\) | − | 212.905i | − | 0.402467i | −0.979543 | − | 0.201234i | \(-0.935505\pi\) | ||
0.979543 | − | 0.201234i | \(-0.0644951\pi\) | |||||||
\(24\) | 109.061 | + | 41.6809i | 0.189342 | + | 0.0723627i | ||||
\(25\) | −125.000 | −0.200000 | ||||||||
\(26\) | − | 9.10062i | − | 0.0134625i | ||||||
\(27\) | −648.079 | + | 333.818i | −0.888998 | + | 0.457912i | ||||
\(28\) | −743.335 | −0.948131 | ||||||||
\(29\) | − | 578.043i | − | 0.687328i | −0.939093 | − | 0.343664i | \(-0.888332\pi\) | ||
0.939093 | − | 0.343664i | \(-0.111668\pi\) | |||||||
\(30\) | −14.6387 | + | 38.3031i | −0.0162652 | + | 0.0425590i | ||||
\(31\) | 490.110 | 0.510000 | 0.255000 | − | 0.966941i | \(-0.417925\pi\) | ||||
0.255000 | + | 0.966941i | \(0.417925\pi\) | |||||||
\(32\) | 308.650i | 0.301416i | ||||||||
\(33\) | 1689.39 | + | 645.652i | 1.55132 | + | 0.592885i | ||||
\(34\) | 140.429 | 0.121479 | ||||||||
\(35\) | − | 524.869i | − | 0.428464i | ||||||
\(36\) | −955.636 | − | 855.389i | −0.737374 | − | 0.660023i | ||||
\(37\) | 1936.81 | 1.41476 | 0.707382 | − | 0.706832i | \(-0.249876\pi\) | ||||
0.707382 | + | 0.706832i | \(0.249876\pi\) | |||||||
\(38\) | − | 24.4503i | − | 0.0169324i | ||||||
\(39\) | −71.7524 | + | 187.745i | −0.0471745 | + | 0.123435i | ||||
\(40\) | −145.039 | −0.0906496 | ||||||||
\(41\) | − | 1638.25i | − | 0.974567i | −0.873244 | − | 0.487284i | \(-0.837988\pi\) | ||
0.873244 | − | 0.487284i | \(-0.162012\pi\) | |||||||
\(42\) | −160.833 | − | 61.4671i | −0.0911751 | − | 0.0348453i | ||||
\(43\) | −2160.31 | −1.16837 | −0.584183 | − | 0.811622i | \(-0.698585\pi\) | ||||
−0.584183 | + | 0.811622i | \(0.698585\pi\) | |||||||
\(44\) | 3181.86i | 1.64352i | ||||||||
\(45\) | 603.990 | − | 674.775i | 0.298267 | − | 0.333222i | ||||
\(46\) | 86.7615 | 0.0410026 | ||||||||
\(47\) | 2282.28i | 1.03318i | 0.856234 | + | 0.516588i | \(0.172798\pi\) | ||||
−0.856234 | + | 0.516588i | \(0.827202\pi\) | |||||||
\(48\) | 796.997 | − | 2085.40i | 0.345919 | − | 0.905121i | ||||
\(49\) | −197.104 | −0.0820923 | ||||||||
\(50\) | − | 50.9390i | − | 0.0203756i | ||||||
\(51\) | −2897.05 | − | 1107.19i | −1.11382 | − | 0.425680i | ||||
\(52\) | −353.606 | −0.130771 | ||||||||
\(53\) | 2626.84i | 0.935151i | 0.883953 | + | 0.467575i | \(0.154872\pi\) | ||||
−0.883953 | + | 0.467575i | \(0.845128\pi\) | |||||||
\(54\) | −136.035 | − | 264.100i | −0.0466512 | − | 0.0905694i | ||||
\(55\) | −2246.71 | −0.742714 | ||||||||
\(56\) | − | 609.013i | − | 0.194201i | ||||||
\(57\) | −192.775 | + | 504.409i | −0.0593336 | + | 0.155250i | ||||
\(58\) | 235.560 | 0.0700237 | ||||||||
\(59\) | − | 4106.06i | − | 1.17956i | −0.807563 | − | 0.589782i | \(-0.799214\pi\) | ||
0.807563 | − | 0.589782i | \(-0.200786\pi\) | |||||||
\(60\) | 1488.27 | + | 568.788i | 0.413409 | + | 0.157997i | ||||
\(61\) | 4790.63 | 1.28746 | 0.643729 | − | 0.765254i | \(-0.277386\pi\) | ||||
0.643729 | + | 0.765254i | \(0.277386\pi\) | |||||||
\(62\) | 199.726i | 0.0519578i | ||||||||
\(63\) | 2833.34 | + | 2536.12i | 0.713868 | + | 0.638983i | ||||
\(64\) | 3843.12 | 0.938263 | ||||||||
\(65\) | − | 249.681i | − | 0.0590961i | ||||||
\(66\) | −263.111 | + | 688.448i | −0.0604020 | + | 0.158046i | ||||
\(67\) | −1565.70 | −0.348785 | −0.174393 | − | 0.984676i | \(-0.555796\pi\) | ||||
−0.174393 | + | 0.984676i | \(0.555796\pi\) | |||||||
\(68\) | − | 5456.40i | − | 1.18002i | ||||||
\(69\) | −1789.88 | − | 684.058i | −0.375947 | − | 0.143679i | ||||
\(70\) | 213.890 | 0.0436511 | ||||||||
\(71\) | 5372.27i | 1.06571i | 0.846205 | + | 0.532857i | \(0.178882\pi\) | ||||
−0.846205 | + | 0.532857i | \(0.821118\pi\) | |||||||
\(72\) | 700.819 | − | 782.951i | 0.135189 | − | 0.151032i | ||||
\(73\) | −4321.67 | −0.810972 | −0.405486 | − | 0.914101i | \(-0.632898\pi\) | ||||
−0.405486 | + | 0.914101i | \(0.632898\pi\) | |||||||
\(74\) | 789.274i | 0.144133i | ||||||||
\(75\) | −401.621 | + | 1050.87i | −0.0713993 | + | 0.186821i | ||||
\(76\) | −950.020 | −0.164477 | ||||||||
\(77\) | − | 9433.82i | − | 1.59113i | ||||||
\(78\) | −76.5085 | − | 29.2400i | −0.0125754 | − | 0.00480605i | ||||
\(79\) | −4801.14 | −0.769290 | −0.384645 | − | 0.923065i | \(-0.625676\pi\) | ||||
−0.384645 | + | 0.923065i | \(0.625676\pi\) | |||||||
\(80\) | 2773.35i | 0.433337i | ||||||||
\(81\) | 724.132 | + | 6520.92i | 0.110369 | + | 0.993891i | ||||
\(82\) | 667.606 | 0.0992870 | ||||||||
\(83\) | 3384.94i | 0.491354i | 0.969352 | + | 0.245677i | \(0.0790103\pi\) | ||||
−0.969352 | + | 0.245677i | \(0.920990\pi\) | |||||||
\(84\) | −2388.31 | + | 6249.18i | −0.338479 | + | 0.885655i | ||||
\(85\) | 3852.77 | 0.533255 | ||||||||
\(86\) | − | 880.352i | − | 0.119031i | ||||||
\(87\) | −4859.58 | − | 1857.23i | −0.642037 | − | 0.245374i | ||||
\(88\) | −2606.89 | −0.336634 | ||||||||
\(89\) | − | 3446.38i | − | 0.435094i | −0.976050 | − | 0.217547i | \(-0.930194\pi\) | ||
0.976050 | − | 0.217547i | \(-0.0698056\pi\) | |||||||
\(90\) | 274.979 | + | 246.133i | 0.0339480 | + | 0.0303868i | ||||
\(91\) | 1048.40 | 0.126603 | ||||||||
\(92\) | − | 3371.13i | − | 0.398290i | ||||||
\(93\) | 1574.71 | − | 4120.33i | 0.182068 | − | 0.476394i | ||||
\(94\) | −930.059 | −0.105258 | ||||||||
\(95\) | − | 670.809i | − | 0.0743279i | ||||||
\(96\) | 2594.80 | + | 991.681i | 0.281554 | + | 0.107604i | ||||
\(97\) | 5447.68 | 0.578986 | 0.289493 | − | 0.957180i | \(-0.406513\pi\) | ||||
0.289493 | + | 0.957180i | \(0.406513\pi\) | |||||||
\(98\) | − | 80.3221i | − | 0.00836340i | ||||||
\(99\) | 10855.9 | − | 12128.2i | 1.10763 | − | 1.23744i | ||||
\(100\) | −1979.24 | −0.197924 | ||||||||
\(101\) | 7655.22i | 0.750438i | 0.926936 | + | 0.375219i | \(0.122433\pi\) | ||||
−0.926936 | + | 0.375219i | \(0.877567\pi\) | |||||||
\(102\) | 451.195 | − | 1180.58i | 0.0433675 | − | 0.113474i | ||||
\(103\) | 16163.7 | 1.52358 | 0.761790 | − | 0.647824i | \(-0.224321\pi\) | ||||
0.761790 | + | 0.647824i | \(0.224321\pi\) | |||||||
\(104\) | − | 289.708i | − | 0.0267852i | ||||||
\(105\) | −4412.55 | − | 1686.39i | −0.400231 | − | 0.152960i | ||||
\(106\) | −1070.47 | −0.0952713 | ||||||||
\(107\) | 18944.3i | 1.65466i | 0.561713 | + | 0.827332i | \(0.310143\pi\) | ||||
−0.561713 | + | 0.827332i | \(0.689857\pi\) | |||||||
\(108\) | −10261.6 | + | 5285.65i | −0.879771 | + | 0.453159i | ||||
\(109\) | −4373.48 | −0.368107 | −0.184053 | − | 0.982916i | \(-0.558922\pi\) | ||||
−0.184053 | + | 0.982916i | \(0.558922\pi\) | |||||||
\(110\) | − | 915.562i | − | 0.0756663i | ||||||
\(111\) | 6222.91 | − | 16282.7i | 0.505065 | − | 1.32154i | ||||
\(112\) | −11645.2 | −0.928346 | ||||||||
\(113\) | − | 1242.99i | − | 0.0973443i | −0.998815 | − | 0.0486722i | \(-0.984501\pi\) | ||
0.998815 | − | 0.0486722i | \(-0.0154990\pi\) | |||||||
\(114\) | −205.553 | − | 78.5581i | −0.0158166 | − | 0.00604479i | ||||
\(115\) | 2380.35 | 0.179989 | ||||||||
\(116\) | − | 9152.69i | − | 0.680194i | ||||||
\(117\) | 1347.83 | + | 1206.44i | 0.0984605 | + | 0.0881320i | ||||
\(118\) | 1673.27 | 0.120172 | ||||||||
\(119\) | 16177.6i | 1.14240i | ||||||||
\(120\) | −466.007 | + | 1219.34i | −0.0323616 | + | 0.0846763i | ||||
\(121\) | −25740.6 | −1.75812 | ||||||||
\(122\) | 1952.24i | 0.131164i | ||||||||
\(123\) | −13772.7 | − | 5263.64i | −0.910349 | − | 0.347917i | ||||
\(124\) | 7760.36 | 0.504706 | ||||||||
\(125\) | − | 1397.54i | − | 0.0894427i | ||||||
\(126\) | −1033.50 | + | 1154.62i | −0.0650984 | + | 0.0727275i | ||||
\(127\) | 4143.92 | 0.256924 | 0.128462 | − | 0.991714i | \(-0.458996\pi\) | ||||
0.128462 | + | 0.991714i | \(0.458996\pi\) | |||||||
\(128\) | 6504.51i | 0.397004i | ||||||||
\(129\) | −6941.00 | + | 18161.6i | −0.417102 | + | 1.09138i | ||||
\(130\) | 101.748 | 0.00602059 | ||||||||
\(131\) | − | 23414.5i | − | 1.36440i | −0.731166 | − | 0.682200i | \(-0.761023\pi\) | ||
0.731166 | − | 0.682200i | \(-0.238977\pi\) | |||||||
\(132\) | 26749.7 | + | 10223.2i | 1.53522 | + | 0.586731i | ||||
\(133\) | 2816.69 | 0.159234 | ||||||||
\(134\) | − | 638.041i | − | 0.0355336i | ||||||
\(135\) | −3732.20 | − | 7245.75i | −0.204784 | − | 0.397572i | ||||
\(136\) | 4470.42 | 0.241697 | ||||||||
\(137\) | − | 4168.41i | − | 0.222090i | −0.993815 | − | 0.111045i | \(-0.964580\pi\) | ||
0.993815 | − | 0.111045i | \(-0.0354198\pi\) | |||||||
\(138\) | 278.762 | − | 729.400i | 0.0146378 | − | 0.0383008i | ||||
\(139\) | 6702.86 | 0.346921 | 0.173460 | − | 0.984841i | \(-0.444505\pi\) | ||||
0.173460 | + | 0.984841i | \(0.444505\pi\) | |||||||
\(140\) | − | 8310.73i | − | 0.424017i | ||||||
\(141\) | 19187.1 | + | 7332.91i | 0.965095 | + | 0.368840i | ||||
\(142\) | −2189.26 | −0.108573 | ||||||||
\(143\) | − | 4487.68i | − | 0.219457i | ||||||
\(144\) | −14971.1 | − | 13400.6i | −0.721987 | − | 0.646250i | ||||
\(145\) | 6462.72 | 0.307382 | ||||||||
\(146\) | − | 1761.13i | − | 0.0826203i | ||||||
\(147\) | −633.287 | + | 1657.04i | −0.0293067 | + | 0.0766829i | ||||
\(148\) | 30667.3 | 1.40008 | ||||||||
\(149\) | − | 7267.97i | − | 0.327371i | −0.986513 | − | 0.163686i | \(-0.947662\pi\) | ||
0.986513 | − | 0.163686i | \(-0.0523383\pi\) | |||||||
\(150\) | −428.242 | − | 163.665i | −0.0190330 | − | 0.00727402i | ||||
\(151\) | −17022.9 | −0.746584 | −0.373292 | − | 0.927714i | \(-0.621771\pi\) | ||||
−0.373292 | + | 0.927714i | \(0.621771\pi\) | |||||||
\(152\) | − | 778.350i | − | 0.0336890i | ||||||
\(153\) | −18616.3 | + | 20798.0i | −0.795261 | + | 0.888461i | ||||
\(154\) | 3844.40 | 0.162101 | ||||||||
\(155\) | 5479.59i | 0.228079i | ||||||||
\(156\) | −1136.12 | + | 2972.74i | −0.0466849 | + | 0.122154i | ||||
\(157\) | −11560.8 | −0.469017 | −0.234509 | − | 0.972114i | \(-0.575348\pi\) | ||||
−0.234509 | + | 0.972114i | \(0.575348\pi\) | |||||||
\(158\) | − | 1956.52i | − | 0.0783738i | ||||||
\(159\) | 22083.7 | + | 8439.95i | 0.873530 | + | 0.333845i | ||||
\(160\) | −3450.81 | −0.134797 | ||||||||
\(161\) | 9994.98i | 0.385594i | ||||||||
\(162\) | −2657.35 | + | 295.093i | −0.101256 | + | 0.0112442i | ||||
\(163\) | −6066.12 | −0.228316 | −0.114158 | − | 0.993463i | \(-0.536417\pi\) | ||||
−0.114158 | + | 0.993463i | \(0.536417\pi\) | |||||||
\(164\) | − | 25939.9i | − | 0.964452i | ||||||
\(165\) | −7218.61 | + | 18888.0i | −0.265146 | + | 0.693773i | ||||
\(166\) | −1379.40 | −0.0500582 | ||||||||
\(167\) | − | 6974.71i | − | 0.250088i | −0.992151 | − | 0.125044i | \(-0.960093\pi\) | ||
0.992151 | − | 0.125044i | \(-0.0399073\pi\) | |||||||
\(168\) | −5119.94 | − | 1956.74i | −0.181404 | − | 0.0693289i | ||||
\(169\) | −28062.3 | −0.982538 | ||||||||
\(170\) | 1570.05i | 0.0543270i | ||||||||
\(171\) | 3621.16 | + | 3241.30i | 0.123838 | + | 0.110848i | ||||
\(172\) | −34206.2 | −1.15624 | ||||||||
\(173\) | − | 27868.0i | − | 0.931135i | −0.885012 | − | 0.465568i | \(-0.845850\pi\) | ||
0.885012 | − | 0.465568i | \(-0.154150\pi\) | |||||||
\(174\) | 756.845 | − | 1980.34i | 0.0249982 | − | 0.0654095i | ||||
\(175\) | 5868.21 | 0.191615 | ||||||||
\(176\) | 49847.4i | 1.60923i | ||||||||
\(177\) | −34519.4 | − | 13192.6i | −1.10184 | − | 0.421100i | ||||
\(178\) | 1404.44 | 0.0443266 | ||||||||
\(179\) | 22242.5i | 0.694189i | 0.937830 | + | 0.347095i | \(0.112832\pi\) | ||||
−0.937830 | + | 0.347095i | \(0.887168\pi\) | |||||||
\(180\) | 9563.54 | − | 10684.3i | 0.295171 | − | 0.329763i | ||||
\(181\) | 33471.7 | 1.02169 | 0.510847 | − | 0.859672i | \(-0.329332\pi\) | ||||
0.510847 | + | 0.859672i | \(0.329332\pi\) | |||||||
\(182\) | 427.235i | 0.0128980i | ||||||||
\(183\) | 15392.1 | − | 40274.6i | 0.459618 | − | 1.20262i | ||||
\(184\) | 2761.96 | 0.0815796 | ||||||||
\(185\) | 21654.2i | 0.632701i | ||||||||
\(186\) | 1679.08 | + | 641.712i | 0.0485341 | + | 0.0185487i | ||||
\(187\) | 69248.4 | 1.98028 | ||||||||
\(188\) | 36137.5i | 1.02245i | ||||||||
\(189\) | 30424.5 | − | 15671.3i | 0.851726 | − | 0.438714i | ||||
\(190\) | 273.363 | 0.00757238 | ||||||||
\(191\) | − | 602.154i | − | 0.0165060i | −0.999966 | − | 0.00825298i | \(-0.997373\pi\) | ||
0.999966 | − | 0.00825298i | \(-0.00262704\pi\) | |||||||
\(192\) | 12347.8 | − | 32309.0i | 0.334956 | − | 0.876437i | ||||
\(193\) | −27201.4 | −0.730259 | −0.365130 | − | 0.930957i | \(-0.618975\pi\) | ||||
−0.365130 | + | 0.930957i | \(0.618975\pi\) | |||||||
\(194\) | 2220.00i | 0.0589860i | ||||||||
\(195\) | −2099.05 | − | 802.217i | −0.0552020 | − | 0.0210971i | ||||
\(196\) | −3120.92 | −0.0812402 | ||||||||
\(197\) | − | 61640.6i | − | 1.58831i | −0.607717 | − | 0.794154i | \(-0.707915\pi\) | ||
0.607717 | − | 0.794154i | \(-0.292085\pi\) | |||||||
\(198\) | 4942.38 | + | 4423.92i | 0.126068 | + | 0.112844i | ||||
\(199\) | −10712.4 | −0.270507 | −0.135254 | − | 0.990811i | \(-0.543185\pi\) | ||||
−0.135254 | + | 0.990811i | \(0.543185\pi\) | |||||||
\(200\) | − | 1621.59i | − | 0.0405397i | ||||||
\(201\) | −5030.53 | + | 13162.7i | −0.124515 | + | 0.325802i | ||||
\(202\) | −3119.60 | −0.0764532 | ||||||||
\(203\) | 27136.6i | 0.658512i | ||||||||
\(204\) | −45871.7 | − | 17531.2i | −1.10226 | − | 0.421262i | ||||
\(205\) | 18316.2 | 0.435840 | ||||||||
\(206\) | 6586.89i | 0.155219i | ||||||||
\(207\) | −11501.7 | + | 12849.6i | −0.268424 | + | 0.299881i | ||||
\(208\) | −5539.63 | −0.128042 | ||||||||
\(209\) | − | 12056.9i | − | 0.276022i | ||||||
\(210\) | 687.223 | − | 1798.17i | 0.0155833 | − | 0.0407747i | ||||
\(211\) | 19405.1 | 0.435865 | 0.217933 | − | 0.975964i | \(-0.430069\pi\) | ||||
0.217933 | + | 0.975964i | \(0.430069\pi\) | |||||||
\(212\) | 41593.2i | 0.925445i | ||||||||
\(213\) | 45164.4 | + | 17260.9i | 0.995490 | + | 0.380456i | ||||
\(214\) | −7720.02 | −0.168574 | ||||||||
\(215\) | − | 24153.0i | − | 0.522509i | ||||||
\(216\) | −4330.52 | − | 8407.35i | −0.0928182 | − | 0.180199i | ||||
\(217\) | −23008.5 | −0.488618 | ||||||||
\(218\) | − | 1782.25i | − | 0.0375020i | ||||||
\(219\) | −13885.4 | + | 36332.1i | −0.289514 | + | 0.757534i | ||||
\(220\) | −35574.3 | −0.735005 | ||||||||
\(221\) | 7695.70i | 0.157566i | ||||||||
\(222\) | 6635.39 | + | 2535.91i | 0.134636 | + | 0.0514551i | ||||
\(223\) | −60220.2 | −1.21097 | −0.605484 | − | 0.795857i | \(-0.707021\pi\) | ||||
−0.605484 | + | 0.795857i | \(0.707021\pi\) | |||||||
\(224\) | − | 14489.8i | − | 0.288779i | ||||||
\(225\) | 7544.21 | + | 6752.82i | 0.149021 | + | 0.133389i | ||||
\(226\) | 506.534 | 0.00991725 | ||||||||
\(227\) | 52638.3i | 1.02153i | 0.859721 | + | 0.510764i | \(0.170637\pi\) | ||||
−0.859721 | + | 0.510764i | \(0.829363\pi\) | |||||||
\(228\) | −3052.38 | + | 7986.77i | −0.0587177 | + | 0.153639i | ||||
\(229\) | 54102.0 | 1.03167 | 0.515837 | − | 0.856687i | \(-0.327481\pi\) | ||||
0.515837 | + | 0.856687i | \(0.327481\pi\) | |||||||
\(230\) | 970.023i | 0.0183369i | ||||||||
\(231\) | −79309.7 | − | 30310.6i | −1.48629 | − | 0.568028i | ||||
\(232\) | 7498.79 | 0.139321 | ||||||||
\(233\) | − | 82178.1i | − | 1.51372i | −0.653580 | − | 0.756858i | \(-0.726734\pi\) | ||
0.653580 | − | 0.756858i | \(-0.273266\pi\) | |||||||
\(234\) | −491.638 | + | 549.256i | −0.00897871 | + | 0.0100310i | ||||
\(235\) | −25516.7 | −0.462050 | ||||||||
\(236\) | − | 65015.1i | − | 1.16732i | ||||||
\(237\) | −15425.9 | + | 40362.9i | −0.274634 | + | 0.718598i | ||||
\(238\) | −6592.56 | −0.116386 | ||||||||
\(239\) | 44047.8i | 0.771132i | 0.922680 | + | 0.385566i | \(0.125994\pi\) | ||||
−0.922680 | + | 0.385566i | \(0.874006\pi\) | |||||||
\(240\) | 23315.5 | + | 8910.70i | 0.404782 | + | 0.154700i | ||||
\(241\) | 11775.6 | 0.202744 | 0.101372 | − | 0.994849i | \(-0.467677\pi\) | ||||
0.101372 | + | 0.994849i | \(0.467677\pi\) | |||||||
\(242\) | − | 10489.6i | − | 0.179114i | ||||||
\(243\) | 57147.6 | + | 14863.8i | 0.967800 | + | 0.251719i | ||||
\(244\) | 75854.5 | 1.27410 | ||||||||
\(245\) | − | 2203.68i | − | 0.0367128i | ||||||
\(246\) | 2145.00 | − | 5612.53i | 0.0354451 | − | 0.0927446i | ||||
\(247\) | 1339.91 | 0.0219624 | ||||||||
\(248\) | 6358.05i | 0.103376i | ||||||||
\(249\) | 28457.0 | + | 10875.7i | 0.458977 | + | 0.175412i | ||||
\(250\) | 569.516 | 0.00911225 | ||||||||
\(251\) | − | 114693.i | − | 1.82050i | −0.414061 | − | 0.910249i | \(-0.635890\pi\) | ||
0.414061 | − | 0.910249i | \(-0.364110\pi\) | |||||||
\(252\) | 44863.0 | + | 40156.8i | 0.706459 | + | 0.632351i | ||||
\(253\) | 42783.7 | 0.668401 | ||||||||
\(254\) | 1688.70i | 0.0261749i | ||||||||
\(255\) | 12378.8 | − | 32390.0i | 0.190370 | − | 0.498116i | ||||
\(256\) | 58839.3 | 0.897817 | ||||||||
\(257\) | 44360.2i | 0.671626i | 0.941929 | + | 0.335813i | \(0.109011\pi\) | ||||
−0.941929 | + | 0.335813i | \(0.890989\pi\) | |||||||
\(258\) | −7401.08 | − | 2828.54i | −0.111187 | − | 0.0424936i | ||||
\(259\) | −90924.9 | −1.35545 | ||||||||
\(260\) | − | 3953.43i | − | 0.0584827i | ||||||
\(261\) | −31227.3 | + | 34887.0i | −0.458410 | + | 0.512133i | ||||
\(262\) | 9541.68 | 0.139002 | ||||||||
\(263\) | 61162.6i | 0.884249i | 0.896954 | + | 0.442124i | \(0.145775\pi\) | ||||
−0.896954 | + | 0.442124i | \(0.854225\pi\) | |||||||
\(264\) | −8375.86 | + | 21916.0i | −0.120177 | + | 0.314451i | ||||
\(265\) | −29368.9 | −0.418212 | ||||||||
\(266\) | 1147.84i | 0.0162225i | ||||||||
\(267\) | −28973.6 | − | 11073.1i | −0.406424 | − | 0.155327i | ||||
\(268\) | −24791.1 | −0.345165 | ||||||||
\(269\) | − | 54930.0i | − | 0.759110i | −0.925169 | − | 0.379555i | \(-0.876077\pi\) | ||
0.925169 | − | 0.379555i | \(-0.123923\pi\) | |||||||
\(270\) | 2952.73 | − | 1520.92i | 0.0405038 | − | 0.0208630i | ||||
\(271\) | −48199.5 | −0.656302 | −0.328151 | − | 0.944625i | \(-0.606425\pi\) | ||||
−0.328151 | + | 0.944625i | \(0.606425\pi\) | |||||||
\(272\) | − | 85480.7i | − | 1.15539i | ||||||
\(273\) | 3368.47 | − | 8813.82i | 0.0451967 | − | 0.118260i | ||||
\(274\) | 1698.68 | 0.0226261 | ||||||||
\(275\) | − | 25119.0i | − | 0.332152i | ||||||
\(276\) | −28340.9 | − | 10831.3i | −0.372045 | − | 0.142188i | ||||
\(277\) | 101493. | 1.32275 | 0.661375 | − | 0.750056i | \(-0.269973\pi\) | ||||
0.661375 | + | 0.750056i | \(0.269973\pi\) | |||||||
\(278\) | 2731.50i | 0.0353436i | ||||||||
\(279\) | −29579.9 | − | 26477.0i | −0.380004 | − | 0.340142i | ||||
\(280\) | 6808.97 | 0.0868491 | ||||||||
\(281\) | 120902.i | 1.53117i | 0.643337 | + | 0.765583i | \(0.277549\pi\) | ||||
−0.643337 | + | 0.765583i | \(0.722451\pi\) | |||||||
\(282\) | −2988.25 | + | 7818.96i | −0.0375767 | + | 0.0983220i | ||||
\(283\) | −111286. | −1.38953 | −0.694767 | − | 0.719235i | \(-0.744493\pi\) | ||||
−0.694767 | + | 0.719235i | \(0.744493\pi\) | |||||||
\(284\) | 85064.1i | 1.05465i | ||||||||
\(285\) | −5639.46 | − | 2155.29i | −0.0694301 | − | 0.0265348i | ||||
\(286\) | 1828.79 | 0.0223579 | ||||||||
\(287\) | 76908.6i | 0.933708i | ||||||||
\(288\) | 16674.0 | − | 18628.1i | 0.201028 | − | 0.224587i | ||||
\(289\) | −35229.5 | −0.421804 | ||||||||
\(290\) | 2633.64i | 0.0313155i | ||||||||
\(291\) | 17503.2 | − | 45798.4i | 0.206696 | − | 0.540834i | ||||
\(292\) | −68429.1 | −0.802555 | ||||||||
\(293\) | 64072.7i | 0.746342i | 0.927763 | + | 0.373171i | \(0.121730\pi\) | ||||
−0.927763 | + | 0.373171i | \(0.878270\pi\) | |||||||
\(294\) | −675.264 | − | 258.072i | −0.00781230 | − | 0.00298570i | ||||
\(295\) | 45907.1 | 0.527517 | ||||||||
\(296\) | 25125.7i | 0.286771i | ||||||||
\(297\) | −67081.3 | − | 130233.i | −0.760481 | − | 1.47641i | ||||
\(298\) | 2961.79 | 0.0333520 | ||||||||
\(299\) | 4754.63i | 0.0531832i | ||||||||
\(300\) | −6359.24 | + | 16639.4i | −0.0706582 | + | 0.184882i | ||||
\(301\) | 101417. | 1.11938 | ||||||||
\(302\) | − | 6937.02i | − | 0.0760605i | ||||||
\(303\) | 64357.1 | + | 24596.0i | 0.700989 | + | 0.267904i | ||||
\(304\) | −14883.1 | −0.161045 | ||||||||
\(305\) | 53560.9i | 0.575769i | ||||||||
\(306\) | −8475.44 | − | 7586.36i | −0.0905147 | − | 0.0810197i | ||||
\(307\) | 33666.4 | 0.357207 | 0.178604 | − | 0.983921i | \(-0.442842\pi\) | ||||
0.178604 | + | 0.983921i | \(0.442842\pi\) | |||||||
\(308\) | − | 149374.i | − | 1.57462i | ||||||
\(309\) | 51933.3 | − | 135887.i | 0.543913 | − | 1.42318i | ||||
\(310\) | −2233.00 | −0.0232362 | ||||||||
\(311\) | 58424.9i | 0.604056i | 0.953299 | + | 0.302028i | \(0.0976636\pi\) | ||||
−0.953299 | + | 0.302028i | \(0.902336\pi\) | |||||||
\(312\) | −2435.57 | − | 930.824i | −0.0250202 | − | 0.00956221i | ||||
\(313\) | 40228.4 | 0.410624 | 0.205312 | − | 0.978697i | \(-0.434179\pi\) | ||||
0.205312 | + | 0.978697i | \(0.434179\pi\) | |||||||
\(314\) | − | 4711.17i | − | 0.0477826i | ||||||
\(315\) | −28354.7 | + | 31677.7i | −0.285762 | + | 0.319252i | ||||
\(316\) | −76020.9 | −0.761305 | ||||||||
\(317\) | − | 114181.i | − | 1.13625i | −0.822943 | − | 0.568124i | \(-0.807669\pi\) | ||
0.822943 | − | 0.568124i | \(-0.192331\pi\) | |||||||
\(318\) | −3439.38 | + | 8999.38i | −0.0340115 | + | 0.0889935i | ||||
\(319\) | 116159. | 1.14149 | ||||||||
\(320\) | 42967.4i | 0.419604i | ||||||||
\(321\) | 159263. | + | 60867.3i | 1.54563 | + | 0.590709i | ||||
\(322\) | −4073.08 | −0.0392836 | ||||||||
\(323\) | 20675.8i | 0.198178i | ||||||||
\(324\) | 11465.9 | + | 103252.i | 0.109224 | + | 0.983575i | ||||
\(325\) | 2791.52 | 0.0264286 | ||||||||
\(326\) | − | 2472.02i | − | 0.0232604i | ||||||
\(327\) | −14051.8 | + | 36767.6i | −0.131413 | + | 0.343851i | ||||
\(328\) | 21252.5 | 0.197544 | ||||||||
\(329\) | − | 107143.i | − | 0.989860i | ||||||
\(330\) | −7697.08 | − | 2941.67i | −0.0706803 | − | 0.0270126i | ||||
\(331\) | 479.214 | 0.00437395 | 0.00218698 | − | 0.999998i | \(-0.499304\pi\) | ||||
0.00218698 | + | 0.999998i | \(0.499304\pi\) | |||||||
\(332\) | 53596.9i | 0.486254i | ||||||||
\(333\) | −116894. | − | 104631.i | −1.05415 | − | 0.943569i | ||||
\(334\) | 2842.28 | 0.0254785 | ||||||||
\(335\) | − | 17505.0i | − | 0.155981i | ||||||
\(336\) | −37415.6 | + | 97900.4i | −0.331416 | + | 0.867174i | ||||
\(337\) | −139642. | −1.22958 | −0.614790 | − | 0.788691i | \(-0.710759\pi\) | ||||
−0.614790 | + | 0.788691i | \(0.710759\pi\) | |||||||
\(338\) | − | 11435.7i | − | 0.100099i | ||||||
\(339\) | −10449.8 | − | 3993.69i | −0.0909299 | − | 0.0347516i | ||||
\(340\) | 61004.4 | 0.527720 | ||||||||
\(341\) | 98488.4i | 0.846986i | ||||||||
\(342\) | −1320.87 | + | 1475.67i | −0.0112929 | + | 0.0126164i | ||||
\(343\) | 121970. | 1.03673 | ||||||||
\(344\) | − | 28025.1i | − | 0.236826i | ||||||
\(345\) | 7648.00 | − | 20011.5i | 0.0642554 | − | 0.168129i | ||||
\(346\) | 11356.5 | 0.0948623 | ||||||||
\(347\) | − | 131835.i | − | 1.09489i | −0.836842 | − | 0.547445i | \(-0.815600\pi\) | ||
0.836842 | − | 0.547445i | \(-0.184400\pi\) | |||||||
\(348\) | −76946.3 | − | 29407.3i | −0.635373 | − | 0.242827i | ||||
\(349\) | −238053. | −1.95444 | −0.977221 | − | 0.212222i | \(-0.931930\pi\) | ||||
−0.977221 | + | 0.212222i | \(0.931930\pi\) | |||||||
\(350\) | 2391.37i | 0.0195214i | ||||||||
\(351\) | 14473.0 | − | 7454.86i | 0.117475 | − | 0.0605098i | ||||
\(352\) | −62023.7 | −0.500579 | ||||||||
\(353\) | 181533.i | 1.45682i | 0.685142 | + | 0.728410i | \(0.259740\pi\) | ||||
−0.685142 | + | 0.728410i | \(0.740260\pi\) | |||||||
\(354\) | 5376.16 | − | 14067.1i | 0.0429008 | − | 0.112253i | ||||
\(355\) | −60063.8 | −0.476602 | ||||||||
\(356\) | − | 54569.8i | − | 0.430578i | ||||||
\(357\) | 136004. | + | 51978.0i | 1.06713 | + | 0.407834i | ||||
\(358\) | −9064.10 | −0.0707227 | ||||||||
\(359\) | − | 32567.2i | − | 0.252692i | −0.991986 | − | 0.126346i | \(-0.959675\pi\) | ||
0.991986 | − | 0.126346i | \(-0.0403249\pi\) | |||||||
\(360\) | 8753.66 | + | 7835.40i | 0.0675437 | + | 0.0604583i | ||||
\(361\) | −126721. | −0.972377 | ||||||||
\(362\) | 13640.1i | 0.104088i | ||||||||
\(363\) | −82703.8 | + | 216400.i | −0.627643 | + | 1.64227i | ||||
\(364\) | 16600.2 | 0.125289 | ||||||||
\(365\) | − | 48317.8i | − | 0.362678i | ||||||
\(366\) | 16412.4 | + | 6272.49i | 0.122521 | + | 0.0468250i | ||||
\(367\) | 117190. | 0.870076 | 0.435038 | − | 0.900412i | \(-0.356735\pi\) | ||||
0.435038 | + | 0.900412i | \(0.356735\pi\) | |||||||
\(368\) | − | 52812.5i | − | 0.389979i | ||||||
\(369\) | −88502.3 | + | 98874.2i | −0.649983 | + | 0.726157i | ||||
\(370\) | −8824.35 | −0.0644584 | ||||||||
\(371\) | − | 123319.i | − | 0.895945i | ||||||
\(372\) | 24933.8 | − | 65241.0i | 0.180178 | − | 0.471449i | ||||
\(373\) | 155803. | 1.11984 | 0.559922 | − | 0.828546i | \(-0.310831\pi\) | ||||
0.559922 | + | 0.828546i | \(0.310831\pi\) | |||||||
\(374\) | 28219.6i | 0.201747i | ||||||||
\(375\) | −11749.1 | − | 4490.26i | −0.0835490 | − | 0.0319307i | ||||
\(376\) | −29607.4 | −0.209423 | ||||||||
\(377\) | 12908.9i | 0.0908255i | ||||||||
\(378\) | 6386.25 | + | 12398.4i | 0.0446953 | + | 0.0867722i | ||||
\(379\) | 174237. | 1.21301 | 0.606503 | − | 0.795082i | \(-0.292572\pi\) | ||||
0.606503 | + | 0.795082i | \(0.292572\pi\) | |||||||
\(380\) | − | 10621.5i | − | 0.0735564i | ||||||
\(381\) | 13314.3 | − | 34837.8i | 0.0917209 | − | 0.239994i | ||||
\(382\) | 245.385 | 0.00168160 | ||||||||
\(383\) | − | 252899.i | − | 1.72405i | −0.506869 | − | 0.862023i | \(-0.669197\pi\) | ||
0.506869 | − | 0.862023i | \(-0.330803\pi\) | |||||||
\(384\) | 54683.1 | + | 20898.8i | 0.370844 | + | 0.141729i | ||||
\(385\) | 105473. | 0.711576 | ||||||||
\(386\) | − | 11084.9i | − | 0.0743974i | ||||||
\(387\) | 130383. | + | 116705.i | 0.870558 | + | 0.779235i | ||||
\(388\) | 86258.2 | 0.572977 | ||||||||
\(389\) | 125454.i | 0.829058i | 0.910036 | + | 0.414529i | \(0.136054\pi\) | ||||
−0.910036 | + | 0.414529i | \(0.863946\pi\) | |||||||
\(390\) | 326.913 | − | 855.391i | 0.00214933 | − | 0.00562387i | ||||
\(391\) | −73367.5 | −0.479900 | ||||||||
\(392\) | − | 2556.97i | − | 0.0166400i | ||||||
\(393\) | −196844. | − | 75229.9i | −1.27449 | − | 0.487086i | ||||
\(394\) | 25119.3 | 0.161814 | ||||||||
\(395\) | − | 53678.3i | − | 0.344037i | ||||||
\(396\) | 171892. | − | 192037.i | 1.09614 | − | 1.22460i | ||||
\(397\) | −225399. | −1.43012 | −0.715059 | − | 0.699064i | \(-0.753600\pi\) | ||||
−0.715059 | + | 0.699064i | \(0.753600\pi\) | |||||||
\(398\) | − | 4365.42i | − | 0.0275588i | ||||||
\(399\) | 9049.94 | − | 23679.8i | 0.0568460 | − | 0.148742i | ||||
\(400\) | −31007.0 | −0.193794 | ||||||||
\(401\) | − | 128670.i | − | 0.800184i | −0.916475 | − | 0.400092i | \(-0.868978\pi\) | ||
0.916475 | − | 0.400092i | \(-0.131022\pi\) | |||||||
\(402\) | −5363.98 | − | 2050.00i | −0.0331921 | − | 0.0126854i | ||||
\(403\) | −10945.2 | −0.0673928 | ||||||||
\(404\) | 121212.i | 0.742649i | ||||||||
\(405\) | −72906.1 | + | 8096.04i | −0.444481 | + | 0.0493586i | ||||
\(406\) | −11058.5 | −0.0670879 | ||||||||
\(407\) | 389206.i | 2.34958i | ||||||||
\(408\) | 14363.3 | − | 37582.6i | 0.0862849 | − | 0.225770i | ||||
\(409\) | 105708. | 0.631917 | 0.315958 | − | 0.948773i | \(-0.397674\pi\) | ||||
0.315958 | + | 0.948773i | \(0.397674\pi\) | |||||||
\(410\) | 7464.06i | 0.0444025i | ||||||||
\(411\) | −35043.6 | − | 13393.0i | −0.207456 | − | 0.0792854i | ||||
\(412\) | 255934. | 1.50777 | ||||||||
\(413\) | 192762.i | 1.13011i | ||||||||
\(414\) | −5236.37 | − | 4687.08i | −0.0305513 | − | 0.0273465i | ||||
\(415\) | −37844.8 | −0.219740 | ||||||||
\(416\) | − | 6892.80i | − | 0.0398299i | ||||||
\(417\) | 21536.1 | − | 56350.6i | 0.123850 | − | 0.324061i | ||||
\(418\) | 4913.34 | 0.0281206 | ||||||||
\(419\) | − | 157919.i | − | 0.899512i | −0.893151 | − | 0.449756i | \(-0.851511\pi\) | ||
0.893151 | − | 0.449756i | \(-0.148489\pi\) | |||||||
\(420\) | −69867.9 | − | 26702.1i | −0.396077 | − | 0.151373i | ||||
\(421\) | −245033. | −1.38248 | −0.691242 | − | 0.722623i | \(-0.742936\pi\) | ||||
−0.691242 | + | 0.722623i | \(0.742936\pi\) | |||||||
\(422\) | 7907.84i | 0.0444051i | ||||||||
\(423\) | 123295. | − | 137744.i | 0.689071 | − | 0.769826i | ||||
\(424\) | −34077.2 | −0.189554 | ||||||||
\(425\) | 43075.2i | 0.238479i | ||||||||
\(426\) | −7034.04 | + | 18405.0i | −0.0387602 | + | 0.101419i | ||||
\(427\) | −224899. | −1.23348 | ||||||||
\(428\) | 299962.i | 1.63749i | ||||||||
\(429\) | −37727.7 | − | 14418.8i | −0.204996 | − | 0.0783455i | ||||
\(430\) | 9842.64 | 0.0532322 | ||||||||
\(431\) | − | 61385.4i | − | 0.330454i | −0.986256 | − | 0.165227i | \(-0.947164\pi\) | ||
0.986256 | − | 0.165227i | \(-0.0528356\pi\) | |||||||
\(432\) | −160760. | + | 82805.6i | −0.861412 | + | 0.443703i | ||||
\(433\) | 25262.9 | 0.134743 | 0.0673716 | − | 0.997728i | \(-0.478539\pi\) | ||||
0.0673716 | + | 0.997728i | \(0.478539\pi\) | |||||||
\(434\) | − | 9376.26i | − | 0.0497795i | ||||||
\(435\) | 20764.5 | − | 54331.7i | 0.109734 | − | 0.287128i | ||||
\(436\) | −69249.3 | −0.364286 | ||||||||
\(437\) | 12774.1i | 0.0668909i | ||||||||
\(438\) | −14805.8 | − | 5658.47i | −0.0771761 | − | 0.0294952i | ||||
\(439\) | −207087. | −1.07455 | −0.537273 | − | 0.843409i | \(-0.680545\pi\) | ||||
−0.537273 | + | 0.843409i | \(0.680545\pi\) | |||||||
\(440\) | − | 29145.9i | − | 0.150547i | ||||||
\(441\) | 11895.9 | + | 10648.0i | 0.0611675 | + | 0.0547510i | ||||
\(442\) | −3136.09 | −0.0160525 | ||||||||
\(443\) | − | 132568.i | − | 0.675508i | −0.941234 | − | 0.337754i | \(-0.890333\pi\) | ||
0.941234 | − | 0.337754i | \(-0.109667\pi\) | |||||||
\(444\) | 98533.2 | − | 257819.i | 0.499823 | − | 1.30782i | ||||
\(445\) | 38531.7 | 0.194580 | ||||||||
\(446\) | − | 24540.5i | − | 0.123371i | ||||||
\(447\) | −61101.5 | − | 23351.8i | −0.305799 | − | 0.116870i | ||||
\(448\) | −180418. | −0.898926 | ||||||||
\(449\) | 200739.i | 0.995726i | 0.867256 | + | 0.497863i | \(0.165882\pi\) | ||||
−0.867256 | + | 0.497863i | \(0.834118\pi\) | |||||||
\(450\) | −2751.86 | + | 3074.36i | −0.0135894 | + | 0.0151820i | ||||
\(451\) | 329209. | 1.61852 | ||||||||
\(452\) | − | 19681.4i | − | 0.0963340i | ||||||
\(453\) | −54693.9 | + | 143110.i | −0.266528 | + | 0.697388i | ||||
\(454\) | −21450.8 | −0.104071 | ||||||||
\(455\) | 11721.4i | 0.0566185i | ||||||||
\(456\) | −6543.55 | − | 2500.81i | −0.0314691 | − | 0.0120268i | ||||
\(457\) | 396196. | 1.89705 | 0.948523 | − | 0.316709i | \(-0.102578\pi\) | ||||
0.948523 | + | 0.316709i | \(0.102578\pi\) | |||||||
\(458\) | 22047.2i | 0.105105i | ||||||||
\(459\) | 115034. | + | 223329.i | 0.546011 | + | 1.06004i | ||||
\(460\) | 37690.3 | 0.178121 | ||||||||
\(461\) | 182217.i | 0.857405i | 0.903446 | + | 0.428702i | \(0.141029\pi\) | ||||
−0.903446 | + | 0.428702i | \(0.858971\pi\) | |||||||
\(462\) | 12351.9 | − | 32319.7i | 0.0578696 | − | 0.151420i | ||||
\(463\) | 181212. | 0.845329 | 0.422665 | − | 0.906286i | \(-0.361095\pi\) | ||||
0.422665 | + | 0.906286i | \(0.361095\pi\) | |||||||
\(464\) | − | 143387.i | − | 0.666001i | ||||||
\(465\) | 46066.7 | + | 17605.8i | 0.213050 | + | 0.0814233i | ||||
\(466\) | 33488.6 | 0.154214 | ||||||||
\(467\) | − | 370180.i | − | 1.69738i | −0.528889 | − | 0.848691i | \(-0.677391\pi\) | ||
0.528889 | − | 0.848691i | \(-0.322609\pi\) | |||||||
\(468\) | 21341.4 | + | 19102.7i | 0.0974386 | + | 0.0872172i | ||||
\(469\) | 73502.7 | 0.334162 | ||||||||
\(470\) | − | 10398.4i | − | 0.0470728i | ||||||
\(471\) | −37144.5 | + | 97191.1i | −0.167437 | + | 0.438112i | ||||
\(472\) | 53266.8 | 0.239096 | ||||||||
\(473\) | − | 434118.i | − | 1.94037i | ||||||
\(474\) | −16448.4 | − | 6286.24i | −0.0732094 | − | 0.0279792i | ||||
\(475\) | 7499.87 | 0.0332404 | ||||||||
\(476\) | 256155.i | 1.13055i | ||||||||
\(477\) | 141908. | − | 158539.i | 0.623694 | − | 0.696787i | ||||
\(478\) | −17950.0 | −0.0785615 | ||||||||
\(479\) | − | 13652.2i | − | 0.0595020i | −0.999557 | − | 0.0297510i | \(-0.990529\pi\) | ||
0.999557 | − | 0.0297510i | \(-0.00947143\pi\) | |||||||
\(480\) | −11087.3 | + | 29010.8i | −0.0481221 | + | 0.125915i | ||||
\(481\) | −43253.1 | −0.186951 | ||||||||
\(482\) | 4798.68i | 0.0206551i | ||||||||
\(483\) | 84027.3 | + | 32113.6i | 0.360185 | + | 0.137656i | ||||
\(484\) | −407575. | −1.73987 | ||||||||
\(485\) | 60906.9i | 0.258931i | ||||||||
\(486\) | −6057.16 | + | 23288.4i | −0.0256446 | + | 0.0985976i | ||||
\(487\) | −193653. | −0.816521 | −0.408260 | − | 0.912865i | \(-0.633864\pi\) | ||||
−0.408260 | + | 0.912865i | \(0.633864\pi\) | |||||||
\(488\) | 62147.5i | 0.260966i | ||||||||
\(489\) | −19490.2 | + | 50997.6i | −0.0815079 | + | 0.213271i | ||||
\(490\) | 898.029 | 0.00374023 | ||||||||
\(491\) | − | 26447.9i | − | 0.109705i | −0.998494 | − | 0.0548527i | \(-0.982531\pi\) | ||
0.998494 | − | 0.0548527i | \(-0.0174689\pi\) | |||||||
\(492\) | −218075. | − | 83344.1i | −0.900900 | − | 0.344306i | ||||
\(493\) | −199195. | −0.819566 | ||||||||
\(494\) | 546.028i | 0.00223749i | ||||||||
\(495\) | 135597. | + | 121373.i | 0.553401 | + | 0.495349i | ||||
\(496\) | 121575. | 0.494175 | ||||||||
\(497\) | − | 252205.i | − | 1.02103i | ||||||
\(498\) | −4431.98 | + | 11596.6i | −0.0178706 | + | 0.0467597i | ||||
\(499\) | 365043. | 1.46603 | 0.733015 | − | 0.680213i | \(-0.238113\pi\) | ||||
0.733015 | + | 0.680213i | \(0.238113\pi\) | |||||||
\(500\) | − | 22128.6i | − | 0.0885144i | ||||||
\(501\) | −58636.1 | − | 22409.5i | −0.233609 | − | 0.0892806i | ||||
\(502\) | 46738.9 | 0.185469 | ||||||||
\(503\) | 85439.2i | 0.337693i | 0.985642 | + | 0.168846i | \(0.0540041\pi\) | ||||
−0.985642 | + | 0.168846i | \(0.945996\pi\) | |||||||
\(504\) | −32900.4 | + | 36756.2i | −0.129521 | + | 0.144700i | ||||
\(505\) | −85588.0 | −0.335606 | ||||||||
\(506\) | 17434.9i | 0.0680954i | ||||||||
\(507\) | −90163.2 | + | 235918.i | −0.350763 | + | 0.917795i | ||||
\(508\) | 65614.6 | 0.254257 | ||||||||
\(509\) | − | 28412.1i | − | 0.109665i | −0.998496 | − | 0.0548325i | \(-0.982538\pi\) | ||
0.998496 | − | 0.0548325i | \(-0.0174625\pi\) | |||||||
\(510\) | 13199.3 | + | 5044.52i | 0.0507471 | + | 0.0193945i | ||||
\(511\) | 202884. | 0.776972 | ||||||||
\(512\) | 128050.i | 0.488472i | ||||||||
\(513\) | 38884.1 | − | 20028.7i | 0.147753 | − | 0.0761059i | ||||
\(514\) | −18077.3 | −0.0684239 | ||||||||
\(515\) | 180715.i | 0.681366i | ||||||||
\(516\) | −109903. | + | 287570.i | −0.412773 | + | 1.08005i | ||||
\(517\) | −458629. | −1.71586 | ||||||||
\(518\) | − | 37053.0i | − | 0.138091i | ||||||
\(519\) | −234285. | − | 89538.8i | −0.869779 | − | 0.332412i | ||||
\(520\) | 3239.04 | 0.0119787 | ||||||||
\(521\) | − | 2801.47i | − | 0.0103208i | −0.999987 | − | 0.00516038i | \(-0.998357\pi\) | ||
0.999987 | − | 0.00516038i | \(-0.00164261\pi\) | |||||||
\(522\) | −14216.9 | − | 12725.5i | −0.0521751 | − | 0.0467019i | ||||
\(523\) | −524249. | −1.91661 | −0.958306 | − | 0.285743i | \(-0.907760\pi\) | ||||
−0.958306 | + | 0.285743i | \(0.907760\pi\) | |||||||
\(524\) | − | 370743.i | − | 1.35024i | ||||||
\(525\) | 18854.4 | − | 49333.8i | 0.0684059 | − | 0.178989i | ||||
\(526\) | −24924.5 | −0.0900855 | ||||||||
\(527\) | − | 168893.i | − | 0.608121i | ||||||
\(528\) | 419065. | + | 160158.i | 1.50319 | + | 0.574488i | ||||
\(529\) | 234512. | 0.838020 | ||||||||
\(530\) | − | 11968.2i | − | 0.0426066i | ||||||
\(531\) | −221820. | + | 247816.i | −0.786704 | + | 0.878901i | ||||
\(532\) | 44599.3 | 0.157581 | ||||||||
\(533\) | 36585.6i | 0.128782i | ||||||||
\(534\) | 4512.43 | − | 11807.1i | 0.0158244 | − | 0.0414057i | ||||
\(535\) | −211803. | −0.739988 | ||||||||
\(536\) | − | 20311.3i | − | 0.0706983i | ||||||
\(537\) | 186992. | + | 71464.5i | 0.648446 | + | 0.247823i | ||||
\(538\) | 22384.6 | 0.0773367 | ||||||||
\(539\) | − | 39608.3i | − | 0.136335i | ||||||
\(540\) | −59095.3 | − | 114729.i | −0.202659 | − | 0.393445i | ||||
\(541\) | 300315. | 1.02608 | 0.513042 | − | 0.858364i | \(-0.328519\pi\) | ||||
0.513042 | + | 0.858364i | \(0.328519\pi\) | |||||||
\(542\) | − | 19641.9i | − | 0.0668628i | ||||||
\(543\) | 107544. | − | 281395.i | 0.364741 | − | 0.954370i | ||||
\(544\) | 106361. | 0.359406 | ||||||||
\(545\) | − | 48897.0i | − | 0.164622i | ||||||
\(546\) | 3591.74 | + | 1372.69i | 0.0120481 | + | 0.00460455i | ||||
\(547\) | 255317. | 0.853307 | 0.426653 | − | 0.904415i | \(-0.359692\pi\) | ||||
0.426653 | + | 0.904415i | \(0.359692\pi\) | |||||||
\(548\) | − | 66002.4i | − | 0.219785i | ||||||
\(549\) | −289132. | − | 258802.i | −0.959294 | − | 0.858663i | ||||
\(550\) | 10236.3 | 0.0338390 | ||||||||
\(551\) | 34682.0i | 0.114235i | ||||||||
\(552\) | 8874.09 | − | 23219.7i | 0.0291236 | − | 0.0762040i | ||||
\(553\) | 225393. | 0.737037 | ||||||||
\(554\) | 41359.7i | 0.134759i | ||||||||
\(555\) | 182046. | + | 69574.3i | 0.591010 | + | 0.225872i | ||||
\(556\) | 106133. | 0.343320 | ||||||||
\(557\) | 517752.i | 1.66883i | 0.551138 | + | 0.834414i | \(0.314194\pi\) | ||||
−0.551138 | + | 0.834414i | \(0.685806\pi\) | |||||||
\(558\) | 10789.7 | − | 12054.2i | 0.0346530 | − | 0.0387141i | ||||
\(559\) | 48244.3 | 0.154391 | ||||||||
\(560\) | − | 130197.i | − | 0.415169i | ||||||
\(561\) | 222493. | − | 582168.i | 0.706953 | − | 1.84979i | ||||
\(562\) | −49269.2 | −0.155992 | ||||||||
\(563\) | 353826.i | 1.11628i | 0.829747 | + | 0.558139i | \(0.188485\pi\) | ||||
−0.829747 | + | 0.558139i | \(0.811515\pi\) | |||||||
\(564\) | 303807. | + | 116109.i | 0.955078 | + | 0.365012i | ||||
\(565\) | 13897.1 | 0.0435337 | ||||||||
\(566\) | − | 45350.6i | − | 0.141563i | ||||||
\(567\) | −33994.9 | − | 306129.i | −0.105742 | − | 0.952222i | ||||
\(568\) | −69692.9 | −0.216019 | ||||||||
\(569\) | 570557.i | 1.76228i | 0.472857 | + | 0.881139i | \(0.343223\pi\) | ||||
−0.472857 | + | 0.881139i | \(0.656777\pi\) | |||||||
\(570\) | 878.306 | − | 2298.15i | 0.00270331 | − | 0.00707340i | ||||
\(571\) | −108185. | −0.331815 | −0.165908 | − | 0.986141i | \(-0.553055\pi\) | ||||
−0.165908 | + | 0.986141i | \(0.553055\pi\) | |||||||
\(572\) | − | 71057.7i | − | 0.217180i | ||||||
\(573\) | −5062.28 | − | 1934.70i | −0.0154183 | − | 0.00589257i | ||||
\(574\) | −31341.2 | −0.0951244 | ||||||||
\(575\) | 26613.2i | 0.0804935i | ||||||||
\(576\) | −231947. | − | 207615.i | −0.699106 | − | 0.625769i | ||||
\(577\) | 161728. | 0.485772 | 0.242886 | − | 0.970055i | \(-0.421906\pi\) | ||||
0.242886 | + | 0.970055i | \(0.421906\pi\) | |||||||
\(578\) | − | 14356.4i | − | 0.0429725i | ||||||
\(579\) | −87397.3 | + | 228681.i | −0.260700 | + | 0.682139i | ||||
\(580\) | 102330. | 0.304192 | ||||||||
\(581\) | − | 158908.i | − | 0.470754i | ||||||
\(582\) | 18663.4 | + | 7132.78i | 0.0550992 | + | 0.0210578i | ||||
\(583\) | −527868. | −1.55306 | ||||||||
\(584\) | − | 56063.8i | − | 0.164383i | ||||||
\(585\) | −13488.4 | + | 15069.2i | −0.0394138 | + | 0.0440329i | ||||
\(586\) | −26110.4 | −0.0760359 | ||||||||
\(587\) | 61507.6i | 0.178506i | 0.996009 | + | 0.0892529i | \(0.0284479\pi\) | ||||
−0.996009 | + | 0.0892529i | \(0.971552\pi\) | |||||||
\(588\) | −10027.4 | + | 26237.5i | −0.0290025 | + | 0.0758870i | ||||
\(589\) | −29406.1 | −0.0847630 | ||||||||
\(590\) | 18707.7i | 0.0537424i | ||||||||
\(591\) | −518210. | − | 198049.i | −1.48365 | − | 0.567020i | ||||
\(592\) | 480438. | 1.37086 | ||||||||
\(593\) | − | 204770.i | − | 0.582313i | −0.956675 | − | 0.291157i | \(-0.905960\pi\) | ||
0.956675 | − | 0.291157i | \(-0.0940400\pi\) | |||||||
\(594\) | 53071.4 | − | 27336.4i | 0.150414 | − | 0.0774764i | ||||
\(595\) | −180871. | −0.510898 | ||||||||
\(596\) | − | 115081.i | − | 0.323974i | ||||||
\(597\) | −34418.5 | + | 90058.3i | −0.0965702 | + | 0.252683i | ||||
\(598\) | −1937.57 | −0.00541820 | ||||||||
\(599\) | 460558.i | 1.28360i | 0.766871 | + | 0.641801i | \(0.221812\pi\) | ||||
−0.766871 | + | 0.641801i | \(0.778188\pi\) | |||||||
\(600\) | −13632.6 | − | 5210.12i | −0.0378684 | − | 0.0144725i | ||||
\(601\) | −273581. | −0.757419 | −0.378710 | − | 0.925516i | \(-0.623632\pi\) | ||||
−0.378710 | + | 0.925516i | \(0.623632\pi\) | |||||||
\(602\) | 41328.7i | 0.114040i | ||||||||
\(603\) | 94495.5 | + | 84582.9i | 0.259882 | + | 0.232620i | ||||
\(604\) | −269539. | −0.738835 | ||||||||
\(605\) | − | 287789.i | − | 0.786255i | ||||||
\(606\) | −10023.2 | + | 26226.3i | −0.0272935 | + | 0.0714154i | ||||
\(607\) | 6868.44 | 0.0186415 | 0.00932074 | − | 0.999957i | \(-0.497033\pi\) | ||||
0.00932074 | + | 0.999957i | \(0.497033\pi\) | |||||||
\(608\) | − | 18518.7i | − | 0.0500959i | ||||||
\(609\) | 228136. | + | 87189.1i | 0.615120 | + | 0.235086i | ||||
\(610\) | −21826.7 | −0.0586582 | ||||||||
\(611\) | − | 50968.3i | − | 0.136527i | ||||||
\(612\) | −294769. | + | 329314.i | −0.787007 | + | 0.879240i | ||||
\(613\) | 189461. | 0.504196 | 0.252098 | − | 0.967702i | \(-0.418879\pi\) | ||||
0.252098 | + | 0.967702i | \(0.418879\pi\) | |||||||
\(614\) | 13719.5i | 0.0363916i | ||||||||
\(615\) | 58849.2 | − | 153983.i | 0.155593 | − | 0.407120i | ||||
\(616\) | 122382. | 0.322520 | ||||||||
\(617\) | 510628.i | 1.34132i | 0.741763 | + | 0.670662i | \(0.233990\pi\) | ||||
−0.741763 | + | 0.670662i | \(0.766010\pi\) | |||||||
\(618\) | 55375.7 | + | 21163.5i | 0.144991 | + | 0.0554128i | ||||
\(619\) | −466167. | −1.21663 | −0.608317 | − | 0.793694i | \(-0.708155\pi\) | ||||
−0.608317 | + | 0.793694i | \(0.708155\pi\) | |||||||
\(620\) | 86763.5i | 0.225712i | ||||||||
\(621\) | 71071.5 | + | 137979.i | 0.184295 | + | 0.357793i | ||||
\(622\) | −23808.9 | −0.0615400 | ||||||||
\(623\) | 161793.i | 0.416853i | ||||||||
\(624\) | −17798.6 | + | 46571.4i | −0.0457107 | + | 0.119605i | ||||
\(625\) | 15625.0 | 0.0400000 | ||||||||
\(626\) | 16393.6i | 0.0418336i | ||||||||
\(627\) | −101362. | − | 38738.4i | −0.257833 | − | 0.0985388i | ||||
\(628\) | −183053. | −0.464149 | ||||||||
\(629\) | − | 667429.i | − | 1.68696i | ||||||
\(630\) | −12909.1 | − | 11554.9i | −0.0325247 | − | 0.0291129i | ||||
\(631\) | 144471. | 0.362847 | 0.181423 | − | 0.983405i | \(-0.441930\pi\) | ||||
0.181423 | + | 0.983405i | \(0.441930\pi\) | |||||||
\(632\) | − | 62283.8i | − | 0.155934i | ||||||
\(633\) | 62348.1 | − | 163138.i | 0.155602 | − | 0.407144i | ||||
\(634\) | 46530.0 | 0.115759 | ||||||||
\(635\) | 46330.5i | 0.114900i | ||||||||
\(636\) | 349672. | + | 133638.i | 0.864463 | + | 0.330380i | ||||
\(637\) | 4401.74 | 0.0108479 | ||||||||
\(638\) | 47336.1i | 0.116292i | ||||||||
\(639\) | 290223. | − | 324236.i | 0.710773 | − | 0.794071i | ||||
\(640\) | −72722.7 | −0.177546 | ||||||||
\(641\) | − | 536191.i | − | 1.30498i | −0.757798 | − | 0.652490i | \(-0.773725\pi\) | ||
0.757798 | − | 0.652490i | \(-0.226275\pi\) | |||||||
\(642\) | −24804.2 | + | 64901.8i | −0.0601803 | + | 0.157466i | ||||
\(643\) | 382957. | 0.926250 | 0.463125 | − | 0.886293i | \(-0.346728\pi\) | ||||
0.463125 | + | 0.886293i | \(0.346728\pi\) | |||||||
\(644\) | 158260.i | 0.381592i | ||||||||
\(645\) | −203053. | − | 77602.7i | −0.488079 | − | 0.186534i | ||||
\(646\) | −8425.63 | −0.0201900 | ||||||||
\(647\) | − | 320474.i | − | 0.765570i | −0.923838 | − | 0.382785i | \(-0.874965\pi\) | ||
0.923838 | − | 0.382785i | \(-0.125035\pi\) | |||||||
\(648\) | −84594.0 | + | 9393.96i | −0.201460 | + | 0.0223717i | ||||
\(649\) | 825120. | 1.95897 | ||||||||
\(650\) | 1137.58i | 0.00269249i | ||||||||
\(651\) | −73925.7 | + | 193432.i | −0.174435 | + | 0.456421i | ||||
\(652\) | −96050.5 | −0.225946 | ||||||||
\(653\) | 227576.i | 0.533703i | 0.963738 | + | 0.266851i | \(0.0859833\pi\) | ||||
−0.963738 | + | 0.266851i | \(0.914017\pi\) | |||||||
\(654\) | −14983.2 | − | 5726.30i | −0.0350308 | − | 0.0133881i | ||||
\(655\) | 261782. | 0.610178 | ||||||||
\(656\) | − | 406378.i | − | 0.944327i | ||||||
\(657\) | 260829. | + | 233468.i | 0.604261 | + | 0.540874i | ||||
\(658\) | 43662.3 | 0.100845 | ||||||||
\(659\) | − | 531408.i | − | 1.22365i | −0.790993 | − | 0.611825i | \(-0.790436\pi\) | ||
0.790993 | − | 0.611825i | \(-0.209564\pi\) | |||||||
\(660\) | −114299. | + | 299071.i | −0.262394 | + | 0.686573i | ||||
\(661\) | −251100. | −0.574704 | −0.287352 | − | 0.957825i | \(-0.592775\pi\) | ||||
−0.287352 | + | 0.957825i | \(0.592775\pi\) | |||||||
\(662\) | 195.286i | 0.000445610i | ||||||||
\(663\) | 64697.3 | + | 24726.0i | 0.147184 | + | 0.0562506i | ||||
\(664\) | −43911.9 | −0.0995969 | ||||||||
\(665\) | 31491.6i | 0.0712117i | ||||||||
\(666\) | 42638.6 | − | 47635.6i | 0.0961290 | − | 0.107395i | ||||
\(667\) | −123068. | −0.276627 | ||||||||
\(668\) | − | 110437.i | − | 0.247493i | ||||||
\(669\) | −193486. | + | 506269.i | −0.432311 | + | 1.13117i | ||||
\(670\) | 7133.51 | 0.0158911 | ||||||||
\(671\) | 962686.i | 2.13816i | ||||||||
\(672\) | −121815. | − | 46555.1i | −0.269750 | − | 0.103093i | ||||
\(673\) | 532133. | 1.17487 | 0.587435 | − | 0.809271i | \(-0.300138\pi\) | ||||
0.587435 | + | 0.809271i | \(0.300138\pi\) | |||||||
\(674\) | − | 56905.9i | − | 0.125267i | ||||||
\(675\) | 81009.9 | − | 41727.2i | 0.177800 | − | 0.0915824i | ||||
\(676\) | −444336. | −0.972340 | ||||||||
\(677\) | − | 73112.8i | − | 0.159520i | −0.996814 | − | 0.0797602i | \(-0.974585\pi\) | ||
0.996814 | − | 0.0797602i | \(-0.0254154\pi\) | |||||||
\(678\) | 1627.48 | − | 4258.40i | 0.00354042 | − | 0.00926376i | ||||
\(679\) | −255745. | −0.554712 | ||||||||
\(680\) | 49980.9i | 0.108090i | ||||||||
\(681\) | 442528. | + | 169125.i | 0.954216 | + | 0.364682i | ||||
\(682\) | −40135.2 | −0.0862893 | ||||||||
\(683\) | − | 674426.i | − | 1.44575i | −0.690979 | − | 0.722875i | \(-0.742820\pi\) | ||
0.690979 | − | 0.722875i | \(-0.257180\pi\) | |||||||
\(684\) | 57337.2 | + | 51322.5i | 0.122553 | + | 0.109697i | ||||
\(685\) | 46604.3 | 0.0993218 | ||||||||
\(686\) | 49704.2i | 0.105620i | ||||||||
\(687\) | 173828. | − | 454833.i | 0.368304 | − | 0.963692i | ||||
\(688\) | −535878. | −1.13211 | ||||||||
\(689\) | − | 58662.9i | − | 0.123573i | ||||||
\(690\) | 8154.94 | + | 3116.65i | 0.0171286 | + | 0.00654621i | ||||
\(691\) | 617153. | 1.29252 | 0.646259 | − | 0.763118i | \(-0.276333\pi\) | ||||
0.646259 | + | 0.763118i | \(0.276333\pi\) | |||||||
\(692\) | − | 441259.i | − | 0.921471i | ||||||
\(693\) | −509639. | + | 569366.i | −1.06120 | + | 1.18556i | ||||
\(694\) | 53724.2 | 0.111545 | ||||||||
\(695\) | 74940.3i | 0.155148i | ||||||||
\(696\) | 24093.4 | − | 63042.0i | 0.0497369 | − | 0.130140i | ||||
\(697\) | −564543. | −1.16207 | ||||||||
\(698\) | − | 97009.6i | − | 0.199115i | ||||||
\(699\) | −690867. | − | 264036.i | −1.41397 | − | 0.540391i | ||||
\(700\) | 92916.8 | 0.189626 | ||||||||
\(701\) | 154788.i | 0.314993i | 0.987520 | + | 0.157496i | \(0.0503422\pi\) | ||||
−0.987520 | + | 0.157496i | \(0.949658\pi\) | |||||||
\(702\) | 3037.95 | + | 5897.92i | 0.00616462 | + | 0.0119681i | ||||
\(703\) | −116207. | −0.235137 | ||||||||
\(704\) | 772283.i | 1.55823i | ||||||||
\(705\) | −81984.4 | + | 214518.i | −0.164950 | + | 0.431604i | ||||
\(706\) | −73976.9 | −0.148418 | ||||||||
\(707\) | − | 359379.i | − | 0.718976i | ||||||
\(708\) | −546579. | − | 208891.i | −1.09040 | − | 0.416729i | ||||
\(709\) | −480282. | −0.955440 | −0.477720 | − | 0.878512i | \(-0.658537\pi\) | ||||
−0.477720 | + | 0.878512i | \(0.658537\pi\) | |||||||
\(710\) | − | 24476.7i | − | 0.0485553i | ||||||
\(711\) | 289766. | + | 259370.i | 0.573203 | + | 0.513074i | ||||
\(712\) | 44708.9 | 0.0881931 | ||||||||
\(713\) | − | 104347.i | − | 0.205258i | ||||||
\(714\) | −21181.7 | + | 55423.3i | −0.0415493 | + | 0.108717i | ||||
\(715\) | 50173.8 | 0.0981443 | ||||||||
\(716\) | 352187.i | 0.686984i | ||||||||
\(717\) | 370308. | + | 141524.i | 0.720319 | + | 0.275291i | ||||
\(718\) | 13271.5 | 0.0257437 | ||||||||
\(719\) | 99977.2i | 0.193394i | 0.995314 | + | 0.0966971i | \(0.0308278\pi\) | ||||
−0.995314 | + | 0.0966971i | \(0.969172\pi\) | |||||||
\(720\) | 149824. | − | 167382.i | 0.289012 | − | 0.322882i | ||||
\(721\) | −758814. | −1.45970 | ||||||||
\(722\) | − | 51640.4i | − | 0.0990639i | ||||||
\(723\) | 37834.5 | − | 98996.5i | 0.0723788 | − | 0.189384i | ||||
\(724\) | 529989. | 1.01109 | ||||||||
\(725\) | 72255.4i | 0.137466i | ||||||||
\(726\) | −88185.8 | − | 33702.8i | −0.167311 | − | 0.0639430i | ||||
\(727\) | −182930. | −0.346112 | −0.173056 | − | 0.984912i | \(-0.555364\pi\) | ||||
−0.173056 | + | 0.984912i | \(0.555364\pi\) | |||||||
\(728\) | 13600.6i | 0.0256622i | ||||||||
\(729\) | 308572. | − | 432681.i | 0.580633 | − | 0.814165i | ||||
\(730\) | 19690.1 | 0.0369489 | ||||||||
\(731\) | 744446.i | 1.39315i | ||||||||
\(732\) | 243718. | − | 637705.i | 0.454847 | − | 1.19014i | ||||
\(733\) | 671761. | 1.25028 | 0.625139 | − | 0.780513i | \(-0.285042\pi\) | ||||
0.625139 | + | 0.780513i | \(0.285042\pi\) | |||||||
\(734\) | 47756.2i | 0.0886417i | ||||||||
\(735\) | −18526.3 | − | 7080.37i | −0.0342936 | − | 0.0131063i | ||||
\(736\) | 65713.1 | 0.121310 | ||||||||
\(737\) | − | 314630.i | − | 0.579248i | ||||||
\(738\) | −40292.5 | − | 36065.8i | −0.0739795 | − | 0.0662190i | ||||
\(739\) | −209903. | −0.384353 | −0.192176 | − | 0.981360i | \(-0.561555\pi\) | ||||
−0.192176 | + | 0.981360i | \(0.561555\pi\) | |||||||
\(740\) | 342871.i | 0.626135i | ||||||||
\(741\) | 4305.07 | − | 11264.5i | 0.00784051 | − | 0.0205152i | ||||
\(742\) | 50253.9 | 0.0912771 | ||||||||
\(743\) | 980505.i | 1.77612i | 0.459728 | + | 0.888060i | \(0.347947\pi\) | ||||
−0.459728 | + | 0.888060i | \(0.652053\pi\) | |||||||
\(744\) | 53451.9 | + | 20428.2i | 0.0965644 | + | 0.0369050i | ||||
\(745\) | 81258.4 | 0.146405 | ||||||||
\(746\) | 63491.5i | 0.114087i | ||||||||
\(747\) | 182863. | − | 204294.i | 0.327706 | − | 0.366112i | ||||
\(748\) | 1.09647e6 | 1.95973 | ||||||||
\(749\) | − | 889351.i | − | 1.58529i | ||||||
\(750\) | 1829.84 | − | 4787.89i | 0.00325304 | − | 0.00851181i | ||||
\(751\) | 642018. | 1.13833 | 0.569164 | − | 0.822224i | \(-0.307267\pi\) | ||||
0.569164 | + | 0.822224i | \(0.307267\pi\) | |||||||
\(752\) | 566135.i | 1.00112i | ||||||||
\(753\) | −964220. | − | 368506.i | −1.70054 | − | 0.649911i | ||||
\(754\) | −5260.55 | −0.00925312 | ||||||||
\(755\) | − | 190321.i | − | 0.333883i | ||||||
\(756\) | 481740. | − | 248138.i | 0.842886 | − | 0.434160i | ||||
\(757\) | −315426. | −0.550434 | −0.275217 | − | 0.961382i | \(-0.588750\pi\) | ||||
−0.275217 | + | 0.961382i | \(0.588750\pi\) | |||||||
\(758\) | 71003.8i | 0.123579i | ||||||||
\(759\) | 137463. | − | 359680.i | 0.238617 | − | 0.624357i | ||||
\(760\) | 8702.22 | 0.0150662 | ||||||||
\(761\) | − | 843657.i | − | 1.45679i | −0.685158 | − | 0.728394i | \(-0.740267\pi\) | ||
0.685158 | − | 0.728394i | \(-0.259733\pi\) | |||||||
\(762\) | 14196.8 | + | 5425.74i | 0.0244501 | + | 0.00934435i | ||||
\(763\) | 205316. | 0.352674 | ||||||||
\(764\) | − | 9534.47i | − | 0.0163347i | ||||||
\(765\) | −232529. | − | 208136.i | −0.397332 | − | 0.355652i | ||||
\(766\) | 103059. | 0.175643 | ||||||||
\(767\) | 91697.1i | 0.155871i | ||||||||
\(768\) | 189049. | − | 494659.i | 0.320517 | − | 0.838656i | ||||
\(769\) | −326397. | −0.551942 | −0.275971 | − | 0.961166i | \(-0.588999\pi\) | ||||
−0.275971 | + | 0.961166i | \(0.588999\pi\) | |||||||
\(770\) | 42981.7i | 0.0724940i | ||||||||
\(771\) | 372934. | + | 142528.i | 0.627369 | + | 0.239768i | ||||
\(772\) | −430706. | −0.722680 | ||||||||
\(773\) | 702706.i | 1.17602i | 0.808853 | + | 0.588010i | \(0.200089\pi\) | ||||
−0.808853 | + | 0.588010i | \(0.799911\pi\) | |||||||
\(774\) | −47558.8 | + | 53132.5i | −0.0793870 | + | 0.0886907i | ||||
\(775\) | −61263.7 | −0.102000 | ||||||||
\(776\) | 70671.2i | 0.117360i | ||||||||
\(777\) | −292139. | + | 764401.i | −0.483891 | + | 1.26613i | ||||
\(778\) | −51124.0 | −0.0844628 | ||||||||
\(779\) | 98293.2i | 0.161975i | ||||||||
\(780\) | −33236.3 | − | 12702.2i | −0.0546290 | − | 0.0208781i | ||||
\(781\) | −1.07957e6 | −1.76989 | ||||||||
\(782\) | − | 29898.2i | − | 0.0488913i | ||||||
\(783\) | 192961. | + | 374618.i | 0.314736 | + | 0.611033i | ||||
\(784\) | −48892.8 | −0.0795450 | ||||||||
\(785\) | − | 129254.i | − | 0.209751i | ||||||
\(786\) | 30657.1 | − | 80216.5i | 0.0496234 | − | 0.129843i | ||||
\(787\) | 447743. | 0.722902 | 0.361451 | − | 0.932391i | \(-0.382282\pi\) | ||||
0.361451 | + | 0.932391i | \(0.382282\pi\) | |||||||
\(788\) | − | 976013.i | − | 1.57182i | ||||||
\(789\) | 514191. | + | 196513.i | 0.825982 | + | 0.315674i | ||||
\(790\) | 21874.6 | 0.0350498 | ||||||||
\(791\) | 58353.0i | 0.0932632i | ||||||||
\(792\) | 157335. | + | 140831.i | 0.250828 | + | 0.224516i | ||||
\(793\) | −106985. | −0.170128 | ||||||||
\(794\) | − | 91853.0i | − | 0.145698i | ||||||
\(795\) | −94361.5 | + | 246903.i | −0.149300 | + | 0.390654i | ||||
\(796\) | −169619. | −0.267700 | ||||||||
\(797\) | 662789.i | 1.04342i | 0.853123 | + | 0.521710i | \(0.174706\pi\) | ||||
−0.853123 | + | 0.521710i | \(0.825294\pi\) | |||||||
\(798\) | 9649.81 | + | 3687.96i | 0.0151535 | + | 0.00579136i | ||||
\(799\) | 786480. | 1.23195 | ||||||||
\(800\) | − | 38581.2i | − | 0.0602831i | ||||||
\(801\) | −186182. | + | 208002.i | −0.290184 | + | 0.324192i | ||||
\(802\) | 52434.7 | 0.0815212 | ||||||||
\(803\) | − | 868448.i | − | 1.34683i | ||||||
\(804\) | −79653.1 | + | 208418.i | −0.123223 | + | 0.322421i | ||||
\(805\) | −111747. | −0.172443 | ||||||||
\(806\) | − | 4460.30i | − | 0.00686585i | ||||||
\(807\) | −461794. | − | 176488.i | −0.709089 | − | 0.271000i | ||||
\(808\) | −99309.0 | −0.152113 | ||||||||
\(809\) | 1.20479e6i | 1.84084i | 0.390936 | + | 0.920418i | \(0.372152\pi\) | ||||
−0.390936 | + | 0.920418i | \(0.627848\pi\) | |||||||
\(810\) | −3299.24 | − | 29710.1i | −0.00502856 | − | 0.0452829i | ||||
\(811\) | −380108. | −0.577917 | −0.288958 | − | 0.957342i | \(-0.593309\pi\) | ||||
−0.288958 | + | 0.957342i | \(0.593309\pi\) | |||||||
\(812\) | 429679.i | 0.651677i | ||||||||
\(813\) | −154863. | + | 405210.i | −0.234297 | + | 0.613055i | ||||
\(814\) | −158606. | −0.239371 | ||||||||
\(815\) | − | 67821.3i | − | 0.102106i | ||||||
\(816\) | −718632. | − | 274647.i | −1.07926 | − | 0.412472i | ||||
\(817\) | 129616. | 0.194185 | ||||||||
\(818\) | 43077.2i | 0.0643785i | ||||||||
\(819\) | −63274.6 | − | 56637.1i | −0.0943326 | − | 0.0844370i | ||||
\(820\) | 290017. | 0.431316 | ||||||||
\(821\) | − | 1.16909e6i | − | 1.73444i | −0.497923 | − | 0.867221i | \(-0.665904\pi\) | ||
0.497923 | − | 0.867221i | \(-0.334096\pi\) | |||||||
\(822\) | 5457.80 | − | 14280.7i | 0.00807745 | − | 0.0211352i | ||||
\(823\) | −1.04796e6 | −1.54719 | −0.773594 | − | 0.633681i | \(-0.781543\pi\) | ||||
−0.773594 | + | 0.633681i | \(0.781543\pi\) | |||||||
\(824\) | 209687.i | 0.308828i | ||||||||
\(825\) | −211174. | − | 80706.5i | −0.310265 | − | 0.118577i | ||||
\(826\) | −78552.8 | −0.115133 | ||||||||
\(827\) | 9106.01i | 0.0133143i | 0.999978 | + | 0.00665713i | \(0.00211905\pi\) | ||||
−0.999978 | + | 0.00665713i | \(0.997881\pi\) | |||||||
\(828\) | −182117. | + | 203460.i | −0.265638 | + | 0.296769i | ||||
\(829\) | −715146. | −1.04060 | −0.520302 | − | 0.853982i | \(-0.674181\pi\) | ||||
−0.520302 | + | 0.853982i | \(0.674181\pi\) | |||||||
\(830\) | − | 15422.2i | − | 0.0223867i | ||||||
\(831\) | 326094. | − | 853249.i | 0.472217 | − | 1.23559i | ||||
\(832\) | −85825.2 | −0.123985 | ||||||||
\(833\) | 67922.3i | 0.0978863i | ||||||||
\(834\) | 22963.6 | + | 8776.22i | 0.0330147 | + | 0.0126176i | ||||
\(835\) | 77979.7 | 0.111843 | ||||||||
\(836\) | − | 190908.i | − | 0.273157i | ||||||
\(837\) | −317630. | + | 163607.i | −0.453388 | + | 0.233535i | ||||
\(838\) | 64354.1 | 0.0916406 | ||||||||
\(839\) | − | 242894.i | − | 0.345059i | −0.985004 | − | 0.172529i | \(-0.944806\pi\) | ||
0.985004 | − | 0.172529i | \(-0.0551940\pi\) | |||||||
\(840\) | 21877.0 | − | 57242.7i | 0.0310048 | − | 0.0811263i | ||||
\(841\) | 373147. | 0.527580 | ||||||||
\(842\) | − | 99853.9i | − | 0.140845i | ||||||
\(843\) | 1.01642e6 | + | 388456.i | 1.43027 | + | 0.546621i | ||||
\(844\) | 307260. | 0.431341 | ||||||||
\(845\) | − | 313746.i | − | 0.439404i | ||||||
\(846\) | 56132.5 | + | 50244.1i | 0.0784284 | + | 0.0702012i | ||||
\(847\) | 1.20841e6 | 1.68441 | ||||||||
\(848\) | 651604.i | 0.906133i | ||||||||
\(849\) | −357560. | + | 935580.i | −0.496059 | + | 1.29797i | ||||
\(850\) | −17553.7 | −0.0242958 | ||||||||
\(851\) | − | 412357.i | − | 0.569396i | ||||||
\(852\) | 715130. | + | 273308.i | 0.985158 | + | 0.376507i | ||||
\(853\) | 861767. | 1.18438 | 0.592191 | − | 0.805797i | \(-0.298263\pi\) | ||||
0.592191 | + | 0.805797i | \(0.298263\pi\) | |||||||
\(854\) | − | 91649.3i | − | 0.125665i | ||||||
\(855\) | −36238.8 | + | 40485.8i | −0.0495726 | + | 0.0553822i | ||||
\(856\) | −245758. | −0.335398 | ||||||||
\(857\) | − | 525214.i | − | 0.715113i | −0.933891 | − | 0.357557i | \(-0.883610\pi\) | ||
0.933891 | − | 0.357557i | \(-0.116390\pi\) | |||||||
\(858\) | 5875.83 | − | 15374.5i | 0.00798169 | − | 0.0208846i | ||||
\(859\) | 66206.8 | 0.0897256 | 0.0448628 | − | 0.998993i | \(-0.485715\pi\) | ||||
0.0448628 | + | 0.998993i | \(0.485715\pi\) | |||||||
\(860\) | − | 382437.i | − | 0.517086i | ||||||
\(861\) | 646567. | + | 247105.i | 0.872182 | + | 0.333331i | ||||
\(862\) | 25015.3 | 0.0336660 | ||||||||
\(863\) | − | 5062.88i | − | 0.00679792i | −0.999994 | − | 0.00339896i | \(-0.998918\pi\) | ||
0.999994 | − | 0.00339896i | \(-0.00108192\pi\) | |||||||
\(864\) | −103033. | − | 200029.i | −0.138022 | − | 0.267958i | ||||
\(865\) | 311573. | 0.416416 | ||||||||
\(866\) | 10294.9i | 0.0137274i | ||||||||
\(867\) | −113191. | + | 296172.i | −0.150582 | + | 0.394009i | ||||
\(868\) | −364316. | −0.483546 | ||||||||
\(869\) | − | 964797.i | − | 1.27760i | ||||||
\(870\) | 22140.9 | + | 8461.79i | 0.0292520 | + | 0.0111795i | ||||
\(871\) | 34965.3 | 0.0460894 | ||||||||
\(872\) | − | 56735.9i | − | 0.0746148i | ||||||
\(873\) | −328788. | − | 294298.i | −0.431407 | − | 0.386152i | ||||
\(874\) | −5205.60 | −0.00681472 | ||||||||
\(875\) | 65608.6i | 0.0856928i | ||||||||
\(876\) | −219860. | + | 575280.i | −0.286509 | + | 0.749672i | ||||
\(877\) | 1.24871e6 | 1.62354 | 0.811772 | − | 0.583975i | \(-0.198503\pi\) | ||||
0.811772 | + | 0.583975i | \(0.198503\pi\) | |||||||
\(878\) | − | 84390.7i | − | 0.109473i | ||||||
\(879\) | 538656. | + | 205864.i | 0.697162 | + | 0.266441i | ||||
\(880\) | −557311. | −0.719668 | ||||||||
\(881\) | 112260.i | 0.144635i | 0.997382 | + | 0.0723173i | \(0.0230394\pi\) | ||||
−0.997382 | + | 0.0723173i | \(0.976961\pi\) | |||||||
\(882\) | −4339.20 | + | 4847.73i | −0.00557793 | + | 0.00623163i | ||||
\(883\) | −329416. | −0.422496 | −0.211248 | − | 0.977432i | \(-0.567753\pi\) | ||||
−0.211248 | + | 0.977432i | \(0.567753\pi\) | |||||||
\(884\) | 121853.i | 0.155931i | ||||||||
\(885\) | 147498. | − | 385939.i | 0.188322 | − | 0.492756i | ||||
\(886\) | 54023.0 | 0.0688194 | ||||||||
\(887\) | − | 152778.i | − | 0.194185i | −0.995275 | − | 0.0970923i | \(-0.969046\pi\) | ||
0.995275 | − | 0.0970923i | \(-0.0309542\pi\) | |||||||
\(888\) | 211231. | + | 80728.1i | 0.267874 | + | 0.102376i | ||||
\(889\) | −194539. | −0.246152 | ||||||||
\(890\) | 15702.2i | 0.0198234i | ||||||||
\(891\) | −1.31039e6 | + | 145516.i | −1.65061 | + | 0.183296i | ||||
\(892\) | −953523. | −1.19840 | ||||||||
\(893\) | − | 136935.i | − | 0.171716i | ||||||
\(894\) | 9516.13 | − | 24899.6i | 0.0119065 | − | 0.0311543i | ||||
\(895\) | −248679. | −0.310451 | ||||||||
\(896\) | − | 305359.i | − | 0.380360i | ||||||
\(897\) | 39971.9 | + | 15276.5i | 0.0496787 | + | 0.0189862i | ||||
\(898\) | −81803.8 | −0.101443 | ||||||||
\(899\) | − | 283304.i | − | 0.350537i | ||||||
\(900\) | 119455. | + | 106924.i | 0.147475 | + | 0.132005i | ||||
\(901\) | 905213. | 1.11507 | ||||||||
\(902\) | 134157.i | 0.164892i | ||||||||
\(903\) | 325850. | − | 852609.i | 0.399615 | − | 1.04562i | ||||
\(904\) | 16125.0 | 0.0197316 | ||||||||
\(905\) | 374225.i | 0.456916i | ||||||||
\(906\) | −58319.2 | − | 22288.4i | −0.0710486 | − | 0.0271533i | ||||
\(907\) | −1.26534e6 | −1.53813 | −0.769067 | − | 0.639169i | \(-0.779279\pi\) | ||||
−0.769067 | + | 0.639169i | \(0.779279\pi\) | |||||||
\(908\) | 833472.i | 1.01093i | ||||||||
\(909\) | 413554. | − | 462021.i | 0.500501 | − | 0.559157i | ||||
\(910\) | −4776.63 | −0.00576818 | ||||||||
\(911\) | 702340.i | 0.846274i | 0.906066 | + | 0.423137i | \(0.139071\pi\) | ||||
−0.906066 | + | 0.423137i | \(0.860929\pi\) | |||||||
\(912\) | −47819.0 | + | 125122.i | −0.0574925 | + | 0.150433i | ||||
\(913\) | −680210. | −0.816021 | ||||||||
\(914\) | 161455.i | 0.193267i | ||||||||
\(915\) | 450284. | + | 172089.i | 0.537829 | + | 0.205547i | ||||
\(916\) | 856648. | 1.02097 | ||||||||
\(917\) | 1.09921e6i | 1.30720i | ||||||||
\(918\) | −91009.4 | + | 46877.9i | −0.107994 | + | 0.0556266i | ||||
\(919\) | 266756. | 0.315851 | 0.157926 | − | 0.987451i | \(-0.449519\pi\) | ||||
0.157926 | + | 0.987451i | \(0.449519\pi\) | |||||||
\(920\) | 30879.6i | 0.0364835i | ||||||||
\(921\) | 108169. | − | 283032.i | 0.127522 | − | 0.333670i | ||||
\(922\) | −74255.5 | −0.0873507 | ||||||||
\(923\) | − | 119974.i | − | 0.140827i | ||||||
\(924\) | −1.25578e6 | − | 479935.i | −1.47086 | − | 0.562133i | ||||
\(925\) | −242101. | −0.282953 | ||||||||
\(926\) | 73846.3i | 0.0861205i | ||||||||
\(927\) | −975536. | − | 873202.i | −1.13523 | − | 1.01614i | ||||
\(928\) | 178413. | 0.207171 | ||||||||
\(929\) | 1.29140e6i | 1.49634i | 0.663509 | + | 0.748169i | \(0.269067\pi\) | ||||
−0.663509 | + | 0.748169i | \(0.730933\pi\) | |||||||
\(930\) | −7174.56 | + | 18772.7i | −0.00829525 | + | 0.0217051i | ||||
\(931\) | 11826.0 | 0.0136439 | ||||||||
\(932\) | − | 1.30120e6i | − | 1.49800i | ||||||
\(933\) | 491175. | + | 187717.i | 0.564252 | + | 0.215646i | ||||
\(934\) | 150853. | 0.172926 | ||||||||
\(935\) | 774220.i | 0.885608i | ||||||||
\(936\) | −15650.8 | + | 17485.0i | −0.0178642 | + | 0.0199578i | ||||
\(937\) | −399820. | −0.455392 | −0.227696 | − | 0.973732i | \(-0.573119\pi\) | ||||
−0.227696 | + | 0.973732i | \(0.573119\pi\) | |||||||
\(938\) | 29953.2i | 0.0340438i | ||||||||
\(939\) | 129253. | − | 338199.i | 0.146591 | − | 0.383566i | ||||
\(940\) | −404030. | −0.457254 | ||||||||
\(941\) | 1.22439e6i | 1.38274i | 0.722499 | + | 0.691372i | \(0.242993\pi\) | ||||
−0.722499 | + | 0.691372i | \(0.757007\pi\) | |||||||
\(942\) | −39606.6 | − | 15136.8i | −0.0446340 | − | 0.0170582i | ||||
\(943\) | −348791. | −0.392231 | ||||||||
\(944\) | − | 1.01853e6i | − | 1.14296i | ||||||
\(945\) | 175210. | + | 340156.i | 0.196199 | + | 0.380904i | ||||
\(946\) | 176908. | 0.197682 | ||||||||
\(947\) | 699832.i | 0.780358i | 0.920739 | + | 0.390179i | \(0.127587\pi\) | ||||
−0.920739 | + | 0.390179i | \(0.872413\pi\) | |||||||
\(948\) | −244253. | + | 639104.i | −0.271783 | + | 0.711140i | ||||
\(949\) | 96512.2 | 0.107164 | ||||||||
\(950\) | 3056.29i | 0.00338647i | ||||||||
\(951\) | −959910. | − | 366858.i | −1.06138 | − | 0.405637i | ||||
\(952\) | −209867. | −0.231564 | ||||||||
\(953\) | − | 1.25288e6i | − | 1.37950i | −0.724045 | − | 0.689752i | \(-0.757719\pi\) | ||
0.724045 | − | 0.689752i | \(-0.242281\pi\) | |||||||
\(954\) | 64606.7 | + | 57829.4i | 0.0709874 | + | 0.0635407i | ||||
\(955\) | 6732.29 | 0.00738169 | ||||||||
\(956\) | 697451.i | 0.763128i | ||||||||
\(957\) | 373214. | − | 976541.i | 0.407507 | − | 1.06627i | ||||
\(958\) | 5563.43 | 0.00606194 | ||||||||
\(959\) | 195689.i | 0.212779i | ||||||||
\(960\) | 361225. | + | 138053.i | 0.391954 | + | 0.149797i | ||||
\(961\) | −683314. | −0.739900 | ||||||||
\(962\) | − | 17626.2i | − | 0.0190462i | ||||||
\(963\) | 1.02342e6 | − | 1.14336e6i | 1.10357 | − | 1.23290i | ||||
\(964\) | 186453. | 0.200639 | ||||||||
\(965\) | − | 304121.i | − | 0.326582i | ||||||
\(966\) | −13086.7 | + | 34242.2i | −0.0140241 | + | 0.0366950i | ||||
\(967\) | 580972. | 0.621301 | 0.310651 | − | 0.950524i | \(-0.399453\pi\) | ||||
0.310651 | + | 0.950524i | \(0.399453\pi\) | |||||||
\(968\) | − | 333926.i | − | 0.356369i | ||||||
\(969\) | 173820. | + | 66430.6i | 0.185120 | + | 0.0707490i | ||||
\(970\) | −24820.3 | −0.0263793 | ||||||||
\(971\) | 648131.i | 0.687423i | 0.939075 | + | 0.343712i | \(0.111684\pi\) | ||||
−0.939075 | + | 0.343712i | \(0.888316\pi\) | |||||||
\(972\) | 904872. | + | 235352.i | 0.957755 | + | 0.249106i | ||||
\(973\) | −314670. | −0.332376 | ||||||||
\(974\) | − | 78916.2i | − | 0.0831856i | ||||||
\(975\) | 8969.05 | − | 23468.1i | 0.00943490 | − | 0.0246871i | ||||
\(976\) | 1.18835e6 | 1.24751 | ||||||||
\(977\) | − | 1.48636e6i | − | 1.55717i | −0.627539 | − | 0.778585i | \(-0.715938\pi\) | ||
0.627539 | − | 0.778585i | \(-0.284062\pi\) | |||||||
\(978\) | −20782.1 | − | 7942.51i | −0.0217276 | − | 0.00830386i | ||||
\(979\) | 692557. | 0.722587 | ||||||||
\(980\) | − | 34893.0i | − | 0.0363317i | ||||||
\(981\) | 263955. | + | 236266.i | 0.274279 | + | 0.245507i | ||||
\(982\) | 10777.8 | 0.0111766 | ||||||||
\(983\) | 992676.i | 1.02731i | 0.857998 | + | 0.513654i | \(0.171708\pi\) | ||||
−0.857998 | + | 0.513654i | \(0.828292\pi\) | |||||||
\(984\) | 68283.7 | − | 178669.i | 0.0705223 | − | 0.184527i | ||||
\(985\) | 689163. | 0.710313 | ||||||||
\(986\) | − | 81174.3i | − | 0.0834958i | ||||||
\(987\) | −900749. | − | 344248.i | −0.924634 | − | 0.353376i | ||||
\(988\) | 21216.0 | 0.0217345 | ||||||||
\(989\) | 459941.i | 0.470229i | ||||||||
\(990\) | −49461.0 | + | 55257.5i | −0.0504652 | + | 0.0563795i | ||||
\(991\) | 1.60928e6 | 1.63864 | 0.819322 | − | 0.573334i | \(-0.194350\pi\) | ||||
0.819322 | + | 0.573334i | \(0.194350\pi\) | |||||||
\(992\) | 151272.i | 0.153722i | ||||||||
\(993\) | 1539.70 | − | 4028.73i | 0.00156148 | − | 0.00408573i | ||||
\(994\) | 102777. | 0.104021 | ||||||||
\(995\) | − | 119768.i | − | 0.120975i | ||||||
\(996\) | 450587. | + | 172205.i | 0.454213 | + | 0.173591i | ||||
\(997\) | 375625. | 0.377889 | 0.188945 | − | 0.981988i | \(-0.439493\pi\) | ||||
0.188945 | + | 0.981988i | \(0.439493\pi\) | |||||||
\(998\) | 148759.i | 0.149356i | ||||||||
\(999\) | −1.25521e6 | + | 646542.i | −1.25772 | + | 0.647837i |
(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 | 15.5.c.a.11.4 | yes | 6 | |
3.2 | odd | 2 | inner | 15.5.c.a.11.3 | ✓ | 6 | |
4.3 | odd | 2 | 240.5.l.d.161.4 | 6 | |||
5.2 | odd | 4 | 75.5.d.d.74.5 | 12 | |||
5.3 | odd | 4 | 75.5.d.d.74.8 | 12 | |||
5.4 | even | 2 | 75.5.c.i.26.3 | 6 | |||
12.11 | even | 2 | 240.5.l.d.161.3 | 6 | |||
15.2 | even | 4 | 75.5.d.d.74.7 | 12 | |||
15.8 | even | 4 | 75.5.d.d.74.6 | 12 | |||
15.14 | odd | 2 | 75.5.c.i.26.4 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
15.5.c.a.11.3 | ✓ | 6 | 3.2 | odd | 2 | inner | |
15.5.c.a.11.4 | yes | 6 | 1.1 | even | 1 | trivial | |
75.5.c.i.26.3 | 6 | 5.4 | even | 2 | |||
75.5.c.i.26.4 | 6 | 15.14 | odd | 2 | |||
75.5.d.d.74.5 | 12 | 5.2 | odd | 4 | |||
75.5.d.d.74.6 | 12 | 15.8 | even | 4 | |||
75.5.d.d.74.7 | 12 | 15.2 | even | 4 | |||
75.5.d.d.74.8 | 12 | 5.3 | odd | 4 | |||
240.5.l.d.161.3 | 6 | 12.11 | even | 2 | |||
240.5.l.d.161.4 | 6 | 4.3 | odd | 2 |