Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [294,4,Mod(67,294)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(294, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 4]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("294.67");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 294 = 2 \cdot 3 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 294.e (of order \(3\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(17.3465615417\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\Q(\sqrt{2}, \sqrt{-3})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 2x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 79.1 | ||
Root | \(-0.707107 - 1.22474i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 294.79 |
Dual form | 294.4.e.k.67.1 |
$q$-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 \(\left(\mathbb{Z}/294\mathbb{Z}\right)^\times\).
\(n\) | \(197\) | \(199\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | + | 1.73205i | −0.353553 | + | 0.612372i | ||||
\(3\) | −1.50000 | − | 2.59808i | −0.288675 | − | 0.500000i | ||||
\(4\) | −2.00000 | − | 3.46410i | −0.250000 | − | 0.433013i | ||||
\(5\) | −3.70711 | + | 6.42090i | −0.331574 | + | 0.574303i | −0.982821 | − | 0.184563i | \(-0.940913\pi\) |
0.651247 | + | 0.758866i | \(0.274246\pi\) | |||||||
\(6\) | 6.00000 | 0.408248 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 8.00000 | 0.353553 | ||||||||
\(9\) | −4.50000 | + | 7.79423i | −0.166667 | + | 0.288675i | ||||
\(10\) | −7.41421 | − | 12.8418i | −0.234458 | − | 0.406093i | ||||
\(11\) | −5.24264 | − | 9.08052i | −0.143701 | − | 0.248898i | 0.785186 | − | 0.619260i | \(-0.212567\pi\) |
−0.928888 | + | 0.370361i | \(0.879234\pi\) | |||||||
\(12\) | −6.00000 | + | 10.3923i | −0.144338 | + | 0.250000i | ||||
\(13\) | 2.78680 | 0.0594553 | 0.0297276 | − | 0.999558i | \(-0.490536\pi\) | ||||
0.0297276 | + | 0.999558i | \(0.490536\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 22.2426 | 0.382868 | ||||||||
\(16\) | −8.00000 | + | 13.8564i | −0.125000 | + | 0.216506i | ||||
\(17\) | −25.2218 | − | 43.6855i | −0.359835 | − | 0.623252i | 0.628098 | − | 0.778134i | \(-0.283834\pi\) |
−0.987933 | + | 0.154882i | \(0.950500\pi\) | |||||||
\(18\) | −9.00000 | − | 15.5885i | −0.117851 | − | 0.204124i | ||||
\(19\) | −62.5269 | + | 108.300i | −0.754982 | + | 1.30767i | 0.190401 | + | 0.981706i | \(0.439021\pi\) |
−0.945383 | + | 0.325961i | \(0.894312\pi\) | |||||||
\(20\) | 29.6569 | 0.331574 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 20.9706 | 0.203225 | ||||||||
\(23\) | 91.1249 | − | 157.833i | 0.826124 | − | 1.43089i | −0.0749331 | − | 0.997189i | \(-0.523874\pi\) |
0.901057 | − | 0.433700i | \(-0.142792\pi\) | |||||||
\(24\) | −12.0000 | − | 20.7846i | −0.102062 | − | 0.176777i | ||||
\(25\) | 35.0147 | + | 60.6473i | 0.280118 | + | 0.485178i | ||||
\(26\) | −2.78680 | + | 4.82687i | −0.0210206 | + | 0.0364088i | ||||
\(27\) | 27.0000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 156.132 | 0.999758 | 0.499879 | − | 0.866095i | \(-0.333378\pi\) | ||||
0.499879 | + | 0.866095i | \(0.333378\pi\) | |||||||
\(30\) | −22.2426 | + | 38.5254i | −0.135364 | + | 0.234458i | ||||
\(31\) | −69.8162 | − | 120.925i | −0.404496 | − | 0.700607i | 0.589767 | − | 0.807573i | \(-0.299220\pi\) |
−0.994263 | + | 0.106966i | \(0.965886\pi\) | |||||||
\(32\) | −16.0000 | − | 27.7128i | −0.0883883 | − | 0.153093i | ||||
\(33\) | −15.7279 | + | 27.2416i | −0.0829661 | + | 0.143701i | ||||
\(34\) | 100.887 | 0.508883 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 36.0000 | 0.166667 | ||||||||
\(37\) | 197.279 | − | 341.698i | 0.876554 | − | 1.51824i | 0.0214563 | − | 0.999770i | \(-0.493170\pi\) |
0.855098 | − | 0.518467i | \(-0.173497\pi\) | |||||||
\(38\) | −125.054 | − | 216.600i | −0.533853 | − | 0.924660i | ||||
\(39\) | −4.18019 | − | 7.24031i | −0.0171633 | − | 0.0297276i | ||||
\(40\) | −29.6569 | + | 51.3672i | −0.117229 | + | 0.203047i | ||||
\(41\) | 197.605 | 0.752701 | 0.376350 | − | 0.926477i | \(-0.377179\pi\) | ||||
0.376350 | + | 0.926477i | \(0.377179\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 343.294 | 1.21748 | 0.608741 | − | 0.793369i | \(-0.291675\pi\) | ||||
0.608741 | + | 0.793369i | \(0.291675\pi\) | |||||||
\(44\) | −20.9706 | + | 36.3221i | −0.0718507 | + | 0.124449i | ||||
\(45\) | −33.3640 | − | 57.7881i | −0.110525 | − | 0.191434i | ||||
\(46\) | 182.250 | + | 315.666i | 0.584158 | + | 1.01179i | ||||
\(47\) | 305.002 | − | 528.279i | 0.946577 | − | 1.63952i | 0.194015 | − | 0.980999i | \(-0.437849\pi\) |
0.752562 | − | 0.658521i | \(-0.228818\pi\) | |||||||
\(48\) | 48.0000 | 0.144338 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −140.059 | −0.396146 | ||||||||
\(51\) | −75.6655 | + | 131.056i | −0.207751 | + | 0.359835i | ||||
\(52\) | −5.57359 | − | 9.65375i | −0.0148638 | − | 0.0257449i | ||||
\(53\) | 68.7645 | + | 119.104i | 0.178218 | + | 0.308682i | 0.941270 | − | 0.337655i | \(-0.109634\pi\) |
−0.763053 | + | 0.646336i | \(0.776300\pi\) | |||||||
\(54\) | −27.0000 | + | 46.7654i | −0.0680414 | + | 0.117851i | ||||
\(55\) | 77.7401 | 0.190590 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 375.161 | 0.871778 | ||||||||
\(58\) | −156.132 | + | 270.429i | −0.353468 | + | 0.612224i | ||||
\(59\) | −294.718 | − | 510.466i | −0.650322 | − | 1.12639i | −0.983045 | − | 0.183366i | \(-0.941301\pi\) |
0.332723 | − | 0.943025i | \(-0.392033\pi\) | |||||||
\(60\) | −44.4853 | − | 77.0508i | −0.0957171 | − | 0.165787i | ||||
\(61\) | −123.609 | + | 214.097i | −0.259450 | + | 0.449381i | −0.966095 | − | 0.258188i | \(-0.916875\pi\) |
0.706644 | + | 0.707569i | \(0.250208\pi\) | |||||||
\(62\) | 279.265 | 0.572043 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 64.0000 | 0.125000 | ||||||||
\(65\) | −10.3310 | + | 17.8937i | −0.0197138 | + | 0.0341453i | ||||
\(66\) | −31.4558 | − | 54.4831i | −0.0586659 | − | 0.101612i | ||||
\(67\) | 197.823 | + | 342.640i | 0.360716 | + | 0.624778i | 0.988079 | − | 0.153949i | \(-0.0491990\pi\) |
−0.627363 | + | 0.778727i | \(0.715866\pi\) | |||||||
\(68\) | −100.887 | + | 174.742i | −0.179917 | + | 0.311626i | ||||
\(69\) | −546.749 | −0.953926 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 285.661 | 0.477489 | 0.238745 | − | 0.971082i | \(-0.423264\pi\) | ||||
0.238745 | + | 0.971082i | \(0.423264\pi\) | |||||||
\(72\) | −36.0000 | + | 62.3538i | −0.0589256 | + | 0.102062i | ||||
\(73\) | 498.729 | + | 863.823i | 0.799613 | + | 1.38497i | 0.919868 | + | 0.392228i | \(0.128295\pi\) |
−0.120255 | + | 0.992743i | \(0.538371\pi\) | |||||||
\(74\) | 394.558 | + | 683.395i | 0.619817 | + | 1.07356i | ||||
\(75\) | 105.044 | − | 181.942i | 0.161726 | − | 0.280118i | ||||
\(76\) | 500.215 | 0.754982 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 16.7208 | 0.0242725 | ||||||||
\(79\) | 424.132 | − | 734.618i | 0.604033 | − | 1.04622i | −0.388171 | − | 0.921587i | \(-0.626893\pi\) |
0.992204 | − | 0.124628i | \(-0.0397737\pi\) | |||||||
\(80\) | −59.3137 | − | 102.734i | −0.0828934 | − | 0.143576i | ||||
\(81\) | −40.5000 | − | 70.1481i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | −197.605 | + | 342.262i | −0.266120 | + | 0.460933i | ||||
\(83\) | −210.863 | −0.278858 | −0.139429 | − | 0.990232i | \(-0.544527\pi\) | ||||
−0.139429 | + | 0.990232i | \(0.544527\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 374.000 | 0.477247 | ||||||||
\(86\) | −343.294 | + | 594.602i | −0.430445 | + | 0.745553i | ||||
\(87\) | −234.198 | − | 405.643i | −0.288605 | − | 0.499879i | ||||
\(88\) | −41.9411 | − | 72.6442i | −0.0508061 | − | 0.0879988i | ||||
\(89\) | 276.744 | − | 479.334i | 0.329604 | − | 0.570891i | −0.652829 | − | 0.757505i | \(-0.726418\pi\) |
0.982433 | + | 0.186614i | \(0.0597514\pi\) | |||||||
\(90\) | 133.456 | 0.156305 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −728.999 | −0.826124 | ||||||||
\(93\) | −209.449 | + | 362.776i | −0.233536 | + | 0.404496i | ||||
\(94\) | 610.004 | + | 1056.56i | 0.669331 | + | 1.15932i | ||||
\(95\) | −463.588 | − | 802.958i | −0.500664 | − | 0.867176i | ||||
\(96\) | −48.0000 | + | 83.1384i | −0.0510310 | + | 0.0883883i | ||||
\(97\) | −903.910 | −0.946166 | −0.473083 | − | 0.881018i | \(-0.656859\pi\) | ||||
−0.473083 | + | 0.881018i | \(0.656859\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 94.3675 | 0.0958009 | ||||||||
\(100\) | 140.059 | − | 242.589i | 0.140059 | − | 0.242589i | ||||
\(101\) | 156.806 | + | 271.595i | 0.154482 | + | 0.267572i | 0.932870 | − | 0.360212i | \(-0.117296\pi\) |
−0.778388 | + | 0.627784i | \(0.783962\pi\) | |||||||
\(102\) | −151.331 | − | 262.113i | −0.146902 | − | 0.254442i | ||||
\(103\) | −115.487 | + | 200.030i | −0.110479 | + | 0.191355i | −0.915963 | − | 0.401262i | \(-0.868572\pi\) |
0.805485 | + | 0.592617i | \(0.201905\pi\) | |||||||
\(104\) | 22.2944 | 0.0210206 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −275.058 | −0.252038 | ||||||||
\(107\) | −62.7431 | + | 108.674i | −0.0566879 | + | 0.0981863i | −0.892977 | − | 0.450103i | \(-0.851387\pi\) |
0.836289 | + | 0.548289i | \(0.184721\pi\) | |||||||
\(108\) | −54.0000 | − | 93.5307i | −0.0481125 | − | 0.0833333i | ||||
\(109\) | −372.764 | − | 645.646i | −0.327562 | − | 0.567354i | 0.654465 | − | 0.756092i | \(-0.272894\pi\) |
−0.982028 | + | 0.188738i | \(0.939560\pi\) | |||||||
\(110\) | −77.7401 | + | 134.650i | −0.0673839 | + | 0.116712i | ||||
\(111\) | −1183.68 | −1.01216 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1043.76 | −0.868929 | −0.434464 | − | 0.900689i | \(-0.643062\pi\) | ||||
−0.434464 | + | 0.900689i | \(0.643062\pi\) | |||||||
\(114\) | −375.161 | + | 649.799i | −0.308220 | + | 0.533853i | ||||
\(115\) | 675.619 | + | 1170.21i | 0.547842 | + | 0.948890i | ||||
\(116\) | −312.264 | − | 540.857i | −0.249940 | − | 0.432908i | ||||
\(117\) | −12.5406 | + | 21.7209i | −0.00990921 | + | 0.0171633i | ||||
\(118\) | 1178.87 | 0.919694 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 177.941 | 0.135364 | ||||||||
\(121\) | 610.529 | − | 1057.47i | 0.458700 | − | 0.794491i | ||||
\(122\) | −247.217 | − | 428.193i | −0.183459 | − | 0.317760i | ||||
\(123\) | −296.408 | − | 513.393i | −0.217286 | − | 0.376350i | ||||
\(124\) | −279.265 | + | 483.701i | −0.202248 | + | 0.350304i | ||||
\(125\) | −1445.99 | −1.03467 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2080.17 | −1.45343 | −0.726715 | − | 0.686939i | \(-0.758954\pi\) | ||||
−0.726715 | + | 0.686939i | \(0.758954\pi\) | |||||||
\(128\) | −64.0000 | + | 110.851i | −0.0441942 | + | 0.0765466i | ||||
\(129\) | −514.940 | − | 891.903i | −0.351457 | − | 0.608741i | ||||
\(130\) | −20.6619 | − | 35.7875i | −0.0139398 | − | 0.0241444i | ||||
\(131\) | 634.764 | − | 1099.44i | 0.423355 | − | 0.733273i | −0.572910 | − | 0.819618i | \(-0.694186\pi\) |
0.996265 | + | 0.0863453i | \(0.0275188\pi\) | |||||||
\(132\) | 125.823 | 0.0829661 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −791.294 | −0.510129 | ||||||||
\(135\) | −100.092 | + | 173.364i | −0.0638114 | + | 0.110525i | ||||
\(136\) | −201.775 | − | 349.484i | −0.127221 | − | 0.220353i | ||||
\(137\) | −1536.59 | − | 2661.46i | −0.958249 | − | 1.65974i | −0.726752 | − | 0.686900i | \(-0.758971\pi\) |
−0.231497 | − | 0.972836i | \(-0.574362\pi\) | |||||||
\(138\) | 546.749 | − | 946.998i | 0.337264 | − | 0.584158i | ||||
\(139\) | 1013.60 | 0.618504 | 0.309252 | − | 0.950980i | \(-0.399921\pi\) | ||||
0.309252 | + | 0.950980i | \(0.399921\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1830.01 | −1.09301 | ||||||||
\(142\) | −285.661 | + | 494.779i | −0.168818 | + | 0.292401i | ||||
\(143\) | −14.6102 | − | 25.3056i | −0.00854380 | − | 0.0147983i | ||||
\(144\) | −72.0000 | − | 124.708i | −0.0416667 | − | 0.0721688i | ||||
\(145\) | −578.798 | + | 1002.51i | −0.331494 | + | 0.574164i | ||||
\(146\) | −1994.91 | −1.13082 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −1578.23 | −0.876554 | ||||||||
\(149\) | −615.735 | + | 1066.48i | −0.338544 | + | 0.586375i | −0.984159 | − | 0.177288i | \(-0.943268\pi\) |
0.645615 | + | 0.763663i | \(0.276601\pi\) | |||||||
\(150\) | 210.088 | + | 363.884i | 0.114358 | + | 0.198073i | ||||
\(151\) | 1122.37 | + | 1944.00i | 0.604881 | + | 1.04768i | 0.992070 | + | 0.125684i | \(0.0401125\pi\) |
−0.387190 | + | 0.922000i | \(0.626554\pi\) | |||||||
\(152\) | −500.215 | + | 866.398i | −0.266926 | + | 0.462330i | ||||
\(153\) | 453.993 | 0.239890 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1035.26 | 0.536481 | ||||||||
\(156\) | −16.7208 | + | 28.9612i | −0.00858163 | + | 0.0148638i | ||||
\(157\) | 1893.58 | + | 3279.77i | 0.962573 | + | 1.66723i | 0.715998 | + | 0.698102i | \(0.245972\pi\) |
0.246575 | + | 0.969124i | \(0.420695\pi\) | |||||||
\(158\) | 848.264 | + | 1469.24i | 0.427116 | + | 0.739786i | ||||
\(159\) | 206.294 | − | 357.311i | 0.102894 | − | 0.178218i | ||||
\(160\) | 237.255 | 0.117229 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 162.000 | 0.0785674 | ||||||||
\(163\) | 1054.28 | − | 1826.07i | 0.506611 | − | 0.877476i | −0.493360 | − | 0.869825i | \(-0.664231\pi\) |
0.999971 | − | 0.00765060i | \(-0.00243528\pi\) | |||||||
\(164\) | −395.210 | − | 684.524i | −0.188175 | − | 0.325929i | ||||
\(165\) | −116.610 | − | 201.975i | −0.0550187 | − | 0.0952952i | ||||
\(166\) | 210.863 | − | 365.225i | 0.0985912 | − | 0.170765i | ||||
\(167\) | 1502.41 | 0.696170 | 0.348085 | − | 0.937463i | \(-0.386832\pi\) | ||||
0.348085 | + | 0.937463i | \(0.386832\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2189.23 | −0.996465 | ||||||||
\(170\) | −374.000 | + | 647.787i | −0.168732 | + | 0.292253i | ||||
\(171\) | −562.742 | − | 974.698i | −0.251661 | − | 0.435889i | ||||
\(172\) | −686.587 | − | 1189.20i | −0.304371 | − | 0.527186i | ||||
\(173\) | −235.628 | + | 408.120i | −0.103552 | + | 0.179357i | −0.913146 | − | 0.407634i | \(-0.866354\pi\) |
0.809594 | + | 0.586991i | \(0.199687\pi\) | |||||||
\(174\) | 936.792 | 0.408150 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 167.765 | 0.0718507 | ||||||||
\(177\) | −884.153 | + | 1531.40i | −0.375464 | + | 0.650322i | ||||
\(178\) | 553.487 | + | 958.668i | 0.233065 | + | 0.403681i | ||||
\(179\) | −666.244 | − | 1153.97i | −0.278198 | − | 0.481852i | 0.692739 | − | 0.721188i | \(-0.256404\pi\) |
−0.970937 | + | 0.239336i | \(0.923070\pi\) | |||||||
\(180\) | −133.456 | + | 231.152i | −0.0552623 | + | 0.0957171i | ||||
\(181\) | −997.727 | −0.409726 | −0.204863 | − | 0.978791i | \(-0.565675\pi\) | ||||
−0.204863 | + | 0.978791i | \(0.565675\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 741.652 | 0.299587 | ||||||||
\(184\) | 728.999 | − | 1262.66i | 0.292079 | − | 0.505896i | ||||
\(185\) | 1462.67 | + | 2533.42i | 0.581285 | + | 1.00681i | ||||
\(186\) | −418.897 | − | 725.552i | −0.165135 | − | 0.286022i | ||||
\(187\) | −264.458 | + | 458.055i | −0.103418 | + | 0.179124i | ||||
\(188\) | −2440.02 | −0.946577 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 1854.35 | 0.708046 | ||||||||
\(191\) | −613.360 | + | 1062.37i | −0.232362 | + | 0.402463i | −0.958503 | − | 0.285083i | \(-0.907979\pi\) |
0.726141 | + | 0.687546i | \(0.241312\pi\) | |||||||
\(192\) | −96.0000 | − | 166.277i | −0.0360844 | − | 0.0625000i | ||||
\(193\) | 1739.65 | + | 3013.16i | 0.648821 | + | 1.12379i | 0.983405 | + | 0.181425i | \(0.0580709\pi\) |
−0.334584 | + | 0.942366i | \(0.608596\pi\) | |||||||
\(194\) | 903.910 | − | 1565.62i | 0.334520 | − | 0.579406i | ||||
\(195\) | 61.9857 | 0.0227635 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 3193.47 | 1.15495 | 0.577476 | − | 0.816408i | \(-0.304038\pi\) | ||||
0.577476 | + | 0.816408i | \(0.304038\pi\) | |||||||
\(198\) | −94.3675 | + | 163.449i | −0.0338708 | + | 0.0586659i | ||||
\(199\) | −532.574 | − | 922.446i | −0.189715 | − | 0.328595i | 0.755440 | − | 0.655217i | \(-0.227423\pi\) |
−0.945155 | + | 0.326622i | \(0.894090\pi\) | |||||||
\(200\) | 280.118 | + | 485.178i | 0.0990366 | + | 0.171536i | ||||
\(201\) | 593.470 | − | 1027.92i | 0.208259 | − | 0.360716i | ||||
\(202\) | −627.222 | −0.218471 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 605.324 | 0.207751 | ||||||||
\(205\) | −732.543 | + | 1268.80i | −0.249576 | + | 0.432278i | ||||
\(206\) | −230.975 | − | 400.060i | −0.0781203 | − | 0.135308i | ||||
\(207\) | 820.124 | + | 1420.50i | 0.275375 | + | 0.476963i | ||||
\(208\) | −22.2944 | + | 38.6150i | −0.00743191 | + | 0.0128724i | ||||
\(209\) | 1311.22 | 0.433968 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2057.50 | 0.671298 | 0.335649 | − | 0.941987i | \(-0.391044\pi\) | ||||
0.335649 | + | 0.941987i | \(0.391044\pi\) | |||||||
\(212\) | 275.058 | − | 476.414i | 0.0891088 | − | 0.154341i | ||||
\(213\) | −428.492 | − | 742.169i | −0.137839 | − | 0.238745i | ||||
\(214\) | −125.486 | − | 217.348i | −0.0400844 | − | 0.0694282i | ||||
\(215\) | −1272.63 | + | 2204.25i | −0.403685 | + | 0.699204i | ||||
\(216\) | 216.000 | 0.0680414 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 1491.05 | 0.463243 | ||||||||
\(219\) | 1496.19 | − | 2591.47i | 0.461657 | − | 0.799613i | ||||
\(220\) | −155.480 | − | 269.300i | −0.0476476 | − | 0.0825281i | ||||
\(221\) | −70.2881 | − | 121.743i | −0.0213941 | − | 0.0370556i | ||||
\(222\) | 1183.68 | − | 2050.19i | 0.357852 | − | 0.619817i | ||||
\(223\) | 2028.27 | 0.609071 | 0.304536 | − | 0.952501i | \(-0.401499\pi\) | ||||
0.304536 | + | 0.952501i | \(0.401499\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −630.265 | −0.186745 | ||||||||
\(226\) | 1043.76 | − | 1807.85i | 0.307213 | − | 0.532108i | ||||
\(227\) | −1211.98 | − | 2099.21i | −0.354369 | − | 0.613786i | 0.632640 | − | 0.774446i | \(-0.281971\pi\) |
−0.987010 | + | 0.160660i | \(0.948638\pi\) | |||||||
\(228\) | −750.323 | − | 1299.60i | −0.217945 | − | 0.377491i | ||||
\(229\) | 983.584 | − | 1703.62i | 0.283830 | − | 0.491608i | −0.688495 | − | 0.725241i | \(-0.741728\pi\) |
0.972325 | + | 0.233633i | \(0.0750615\pi\) | |||||||
\(230\) | −2702.48 | −0.774766 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 1249.06 | 0.353468 | ||||||||
\(233\) | −2239.17 | + | 3878.35i | −0.629582 | + | 1.09047i | 0.358053 | + | 0.933701i | \(0.383441\pi\) |
−0.987636 | + | 0.156767i | \(0.949893\pi\) | |||||||
\(234\) | −25.0812 | − | 43.4419i | −0.00700687 | − | 0.0121363i | ||||
\(235\) | 2261.35 | + | 3916.77i | 0.627720 | + | 1.08724i | ||||
\(236\) | −1178.87 | + | 2041.86i | −0.325161 | + | 0.563195i | ||||
\(237\) | −2544.79 | −0.697477 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 6116.92 | 1.65553 | 0.827763 | − | 0.561078i | \(-0.189613\pi\) | ||||
0.827763 | + | 0.561078i | \(0.189613\pi\) | |||||||
\(240\) | −177.941 | + | 308.203i | −0.0478585 | + | 0.0828934i | ||||
\(241\) | −3114.19 | − | 5393.94i | −0.832376 | − | 1.44172i | −0.896149 | − | 0.443754i | \(-0.853647\pi\) |
0.0637726 | − | 0.997964i | \(-0.479687\pi\) | |||||||
\(242\) | 1221.06 | + | 2114.94i | 0.324350 | + | 0.561790i | ||||
\(243\) | −121.500 | + | 210.444i | −0.0320750 | + | 0.0555556i | ||||
\(244\) | 988.870 | 0.259450 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 1185.63 | 0.307289 | ||||||||
\(247\) | −174.250 | + | 301.809i | −0.0448876 | + | 0.0777477i | ||||
\(248\) | −558.530 | − | 967.402i | −0.143011 | − | 0.247702i | ||||
\(249\) | 316.294 | + | 547.838i | 0.0804994 | + | 0.139429i | ||||
\(250\) | 1445.99 | − | 2504.53i | 0.365810 | − | 0.633601i | ||||
\(251\) | 5904.42 | 1.48479 | 0.742397 | − | 0.669960i | \(-0.233689\pi\) | ||||
0.742397 | + | 0.669960i | \(0.233689\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1910.94 | −0.474861 | ||||||||
\(254\) | 2080.17 | − | 3602.97i | 0.513865 | − | 0.890041i | ||||
\(255\) | −561.000 | − | 971.681i | −0.137769 | − | 0.238624i | ||||
\(256\) | −128.000 | − | 221.703i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | 204.112 | − | 353.532i | 0.0495414 | − | 0.0858082i | −0.840191 | − | 0.542290i | \(-0.817557\pi\) |
0.889733 | + | 0.456482i | \(0.150891\pi\) | |||||||
\(258\) | 2059.76 | 0.497035 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 82.6476 | 0.0197138 | ||||||||
\(261\) | −702.594 | + | 1216.93i | −0.166626 | + | 0.288605i | ||||
\(262\) | 1269.53 | + | 2198.89i | 0.299357 | + | 0.518502i | ||||
\(263\) | 2313.00 | + | 4006.24i | 0.542304 | + | 0.939298i | 0.998771 | + | 0.0495577i | \(0.0157812\pi\) |
−0.456467 | + | 0.889740i | \(0.650885\pi\) | |||||||
\(264\) | −125.823 | + | 217.932i | −0.0293329 | + | 0.0508061i | ||||
\(265\) | −1019.67 | −0.236369 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −1660.46 | −0.380594 | ||||||||
\(268\) | 791.294 | − | 1370.56i | 0.180358 | − | 0.312389i | ||||
\(269\) | 435.646 | + | 754.562i | 0.0987429 | + | 0.171028i | 0.911165 | − | 0.412043i | \(-0.135185\pi\) |
−0.812422 | + | 0.583070i | \(0.801851\pi\) | |||||||
\(270\) | −200.184 | − | 346.728i | −0.0451215 | − | 0.0781527i | ||||
\(271\) | −3236.17 | + | 5605.22i | −0.725401 | + | 1.25643i | 0.233408 | + | 0.972379i | \(0.425012\pi\) |
−0.958809 | + | 0.284052i | \(0.908321\pi\) | |||||||
\(272\) | 807.098 | 0.179917 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 6146.38 | 1.35517 | ||||||||
\(275\) | 367.139 | − | 635.904i | 0.0805066 | − | 0.139442i | ||||
\(276\) | 1093.50 | + | 1894.00i | 0.238481 | + | 0.413062i | ||||
\(277\) | −2355.94 | − | 4080.61i | −0.511028 | − | 0.885126i | −0.999918 | − | 0.0127811i | \(-0.995932\pi\) |
0.488890 | − | 0.872345i | \(-0.337402\pi\) | |||||||
\(278\) | −1013.60 | + | 1755.60i | −0.218674 | + | 0.378755i | ||||
\(279\) | 1256.69 | 0.269664 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −7165.66 | −1.52124 | −0.760618 | − | 0.649200i | \(-0.775104\pi\) | ||||
−0.760618 | + | 0.649200i | \(0.775104\pi\) | |||||||
\(282\) | 1830.01 | − | 3169.67i | 0.386439 | − | 0.669331i | ||||
\(283\) | −3173.50 | − | 5496.67i | −0.666590 | − | 1.15457i | −0.978851 | − | 0.204572i | \(-0.934420\pi\) |
0.312261 | − | 0.949996i | \(-0.398914\pi\) | |||||||
\(284\) | −571.322 | − | 989.559i | −0.119372 | − | 0.206759i | ||||
\(285\) | −1390.76 | + | 2408.87i | −0.289059 | + | 0.500664i | ||||
\(286\) | 58.4407 | 0.0120828 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 288.000 | 0.0589256 | ||||||||
\(289\) | 1184.22 | − | 2051.13i | 0.241038 | − | 0.417490i | ||||
\(290\) | −1157.60 | − | 2005.02i | −0.234401 | − | 0.405995i | ||||
\(291\) | 1355.86 | + | 2348.43i | 0.273135 | + | 0.473083i | ||||
\(292\) | 1994.91 | − | 3455.29i | 0.399807 | − | 0.692485i | ||||
\(293\) | 9233.78 | 1.84110 | 0.920552 | − | 0.390621i | \(-0.127740\pi\) | ||||
0.920552 | + | 0.390621i | \(0.127740\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 4370.20 | 0.862519 | ||||||||
\(296\) | 1578.23 | − | 2733.58i | 0.309909 | − | 0.536778i | ||||
\(297\) | −141.551 | − | 245.174i | −0.0276554 | − | 0.0479005i | ||||
\(298\) | −1231.47 | − | 2132.97i | −0.239386 | − | 0.414629i | ||||
\(299\) | 253.947 | − | 439.848i | 0.0491174 | − | 0.0850739i | ||||
\(300\) | −840.353 | −0.161726 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −4489.47 | −0.855430 | ||||||||
\(303\) | 470.417 | − | 814.785i | 0.0891905 | − | 0.154482i | ||||
\(304\) | −1000.43 | − | 1732.80i | −0.188745 | − | 0.326917i | ||||
\(305\) | −916.461 | − | 1587.36i | −0.172054 | − | 0.298006i | ||||
\(306\) | −453.993 | + | 786.339i | −0.0848139 | + | 0.146902i | ||||
\(307\) | 6786.53 | 1.26165 | 0.630827 | − | 0.775923i | \(-0.282716\pi\) | ||||
0.630827 | + | 0.775923i | \(0.282716\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 692.924 | 0.127570 | ||||||||
\(310\) | −1035.26 | + | 1793.13i | −0.189675 | + | 0.328526i | ||||
\(311\) | −2568.38 | − | 4448.57i | −0.468295 | − | 0.811111i | 0.531048 | − | 0.847341i | \(-0.321798\pi\) |
−0.999343 | + | 0.0362307i | \(0.988465\pi\) | |||||||
\(312\) | −33.4416 | − | 57.9225i | −0.00606813 | − | 0.0105103i | ||||
\(313\) | 1881.78 | − | 3259.34i | 0.339822 | − | 0.588590i | −0.644577 | − | 0.764540i | \(-0.722966\pi\) |
0.984399 | + | 0.175950i | \(0.0562997\pi\) | |||||||
\(314\) | −7574.31 | −1.36128 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −3393.06 | −0.604033 | ||||||||
\(317\) | 517.473 | − | 896.289i | 0.0916851 | − | 0.158803i | −0.816535 | − | 0.577296i | \(-0.804108\pi\) |
0.908220 | + | 0.418492i | \(0.137441\pi\) | |||||||
\(318\) | 412.587 | + | 714.622i | 0.0727570 | + | 0.126019i | ||||
\(319\) | −818.544 | − | 1417.76i | −0.143667 | − | 0.248838i | ||||
\(320\) | −237.255 | + | 410.937i | −0.0414467 | + | 0.0717878i | ||||
\(321\) | 376.458 | 0.0654575 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 6308.17 | 1.08668 | ||||||||
\(324\) | −162.000 | + | 280.592i | −0.0277778 | + | 0.0481125i | ||||
\(325\) | 97.5789 | + | 169.012i | 0.0166545 | + | 0.0288464i | ||||
\(326\) | 2108.56 | + | 3652.13i | 0.358228 | + | 0.620469i | ||||
\(327\) | −1118.29 | + | 1936.94i | −0.189118 | + | 0.327562i | ||||
\(328\) | 1580.84 | 0.266120 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 466.441 | 0.0778082 | ||||||||
\(331\) | −4400.03 | + | 7621.08i | −0.730657 | + | 1.26554i | 0.225945 | + | 0.974140i | \(0.427453\pi\) |
−0.956603 | + | 0.291395i | \(0.905880\pi\) | |||||||
\(332\) | 421.726 | + | 730.451i | 0.0697145 | + | 0.120749i | ||||
\(333\) | 1775.51 | + | 3075.28i | 0.292185 | + | 0.506079i | ||||
\(334\) | −1502.41 | + | 2602.26i | −0.246133 | + | 0.426315i | ||||
\(335\) | −2933.41 | −0.478416 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −5859.78 | −0.947189 | −0.473595 | − | 0.880743i | \(-0.657044\pi\) | ||||
−0.473595 | + | 0.880743i | \(0.657044\pi\) | |||||||
\(338\) | 2189.23 | − | 3791.86i | 0.352304 | − | 0.610208i | ||||
\(339\) | 1565.64 | + | 2711.78i | 0.250838 | + | 0.434464i | ||||
\(340\) | −748.000 | − | 1295.57i | −0.119312 | − | 0.206654i | ||||
\(341\) | −732.043 | + | 1267.94i | −0.116253 | + | 0.201356i | ||||
\(342\) | 2250.97 | 0.355902 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 2746.35 | 0.430445 | ||||||||
\(345\) | 2026.86 | − | 3510.62i | 0.316297 | − | 0.547842i | ||||
\(346\) | −471.256 | − | 816.239i | −0.0732222 | − | 0.126825i | ||||
\(347\) | −3969.27 | − | 6874.98i | −0.614068 | − | 1.06360i | −0.990547 | − | 0.137172i | \(-0.956199\pi\) |
0.376479 | − | 0.926425i | \(-0.377135\pi\) | |||||||
\(348\) | −936.792 | + | 1622.57i | −0.144303 | + | 0.249940i | ||||
\(349\) | −9927.75 | −1.52269 | −0.761347 | − | 0.648344i | \(-0.775462\pi\) | ||||
−0.761347 | + | 0.648344i | \(0.775462\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 75.2435 | 0.0114422 | ||||||||
\(352\) | −167.765 | + | 290.577i | −0.0254031 | + | 0.0439994i | ||||
\(353\) | 5051.52 | + | 8749.49i | 0.761658 | + | 1.31923i | 0.941996 | + | 0.335625i | \(0.108948\pi\) |
−0.180338 | + | 0.983605i | \(0.557719\pi\) | |||||||
\(354\) | −1768.31 | − | 3062.80i | −0.265493 | − | 0.459847i | ||||
\(355\) | −1058.98 | + | 1834.20i | −0.158323 | + | 0.274223i | ||||
\(356\) | −2213.95 | −0.329604 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 2664.97 | 0.393431 | ||||||||
\(359\) | 2412.64 | − | 4178.81i | 0.354691 | − | 0.614343i | −0.632374 | − | 0.774663i | \(-0.717919\pi\) |
0.987065 | + | 0.160320i | \(0.0512527\pi\) | |||||||
\(360\) | −266.912 | − | 462.305i | −0.0390763 | − | 0.0676822i | ||||
\(361\) | −4389.73 | − | 7603.23i | −0.639996 | − | 1.10850i | ||||
\(362\) | 997.727 | − | 1728.11i | 0.144860 | − | 0.250905i | ||||
\(363\) | −3663.18 | −0.529661 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −7395.36 | −1.06052 | ||||||||
\(366\) | −741.652 | + | 1284.58i | −0.105920 | + | 0.183459i | ||||
\(367\) | −3467.65 | − | 6006.15i | −0.493215 | − | 0.854274i | 0.506754 | − | 0.862091i | \(-0.330845\pi\) |
−0.999969 | + | 0.00781688i | \(0.997512\pi\) | |||||||
\(368\) | 1458.00 | + | 2525.33i | 0.206531 | + | 0.357722i | ||||
\(369\) | −889.223 | + | 1540.18i | −0.125450 | + | 0.217286i | ||||
\(370\) | −5850.68 | −0.822061 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 1675.59 | 0.233536 | ||||||||
\(373\) | −7046.55 | + | 12205.0i | −0.978168 | + | 1.69424i | −0.309110 | + | 0.951026i | \(0.600031\pi\) |
−0.669058 | + | 0.743210i | \(0.733302\pi\) | |||||||
\(374\) | −528.916 | − | 916.109i | −0.0731272 | − | 0.126660i | ||||
\(375\) | 2168.98 | + | 3756.79i | 0.298682 | + | 0.517333i | ||||
\(376\) | 2440.02 | − | 4226.23i | 0.334666 | − | 0.579658i | ||||
\(377\) | 435.108 | 0.0594409 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 5354.17 | 0.725661 | 0.362830 | − | 0.931855i | \(-0.381810\pi\) | ||||
0.362830 | + | 0.931855i | \(0.381810\pi\) | |||||||
\(380\) | −1854.35 | + | 3211.83i | −0.250332 | + | 0.433588i | ||||
\(381\) | 3120.26 | + | 5404.45i | 0.419569 | + | 0.726715i | ||||
\(382\) | −1226.72 | − | 2124.74i | −0.164305 | − | 0.284585i | ||||
\(383\) | 4485.24 | − | 7768.66i | 0.598394 | − | 1.03645i | −0.394664 | − | 0.918825i | \(-0.629139\pi\) |
0.993058 | − | 0.117623i | \(-0.0375276\pi\) | |||||||
\(384\) | 384.000 | 0.0510310 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −6958.58 | −0.917571 | ||||||||
\(387\) | −1544.82 | + | 2675.71i | −0.202914 | + | 0.351457i | ||||
\(388\) | 1807.82 | + | 3131.23i | 0.236542 | + | 0.409702i | ||||
\(389\) | 1851.29 | + | 3206.53i | 0.241296 | + | 0.417937i | 0.961084 | − | 0.276257i | \(-0.0890942\pi\) |
−0.719788 | + | 0.694194i | \(0.755761\pi\) | |||||||
\(390\) | −61.9857 | + | 107.362i | −0.00804812 | + | 0.0139398i | ||||
\(391\) | −9193.34 | −1.18907 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −3808.58 | −0.488849 | ||||||||
\(394\) | −3193.47 | + | 5531.26i | −0.408337 | + | 0.707260i | ||||
\(395\) | 3144.61 | + | 5446.62i | 0.400563 | + | 0.693795i | ||||
\(396\) | −188.735 | − | 326.899i | −0.0239502 | − | 0.0414830i | ||||
\(397\) | 1041.62 | − | 1804.13i | 0.131681 | − | 0.228078i | −0.792644 | − | 0.609685i | \(-0.791296\pi\) |
0.924325 | + | 0.381607i | \(0.124629\pi\) | |||||||
\(398\) | 2130.30 | 0.268297 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −1120.47 | −0.140059 | ||||||||
\(401\) | 5317.01 | − | 9209.33i | 0.662141 | − | 1.14686i | −0.317910 | − | 0.948121i | \(-0.602981\pi\) |
0.980052 | − | 0.198742i | \(-0.0636855\pi\) | |||||||
\(402\) | 1186.94 | + | 2055.84i | 0.147262 | + | 0.255065i | ||||
\(403\) | −194.564 | − | 336.994i | −0.0240494 | − | 0.0416548i | ||||
\(404\) | 627.222 | − | 1086.38i | 0.0772412 | − | 0.133786i | ||||
\(405\) | 600.551 | 0.0736830 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −4137.06 | −0.503848 | ||||||||
\(408\) | −605.324 | + | 1048.45i | −0.0734510 | + | 0.127221i | ||||
\(409\) | 3258.18 | + | 5643.34i | 0.393904 | + | 0.682262i | 0.992961 | − | 0.118445i | \(-0.0377908\pi\) |
−0.599056 | + | 0.800707i | \(0.704458\pi\) | |||||||
\(410\) | −1465.09 | − | 2537.60i | −0.176477 | − | 0.305667i | ||||
\(411\) | −4609.78 | + | 7984.38i | −0.553245 | + | 0.958249i | ||||
\(412\) | 923.899 | 0.110479 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −3280.50 | −0.389439 | ||||||||
\(415\) | 781.691 | − | 1353.93i | 0.0924620 | − | 0.160149i | ||||
\(416\) | −44.5887 | − | 77.2300i | −0.00525515 | − | 0.00910219i | ||||
\(417\) | −1520.39 | − | 2633.40i | −0.178547 | − | 0.309252i | ||||
\(418\) | −1311.22 | + | 2271.11i | −0.153431 | + | 0.265750i | ||||
\(419\) | 6079.92 | 0.708887 | 0.354443 | − | 0.935077i | \(-0.384670\pi\) | ||||
0.354443 | + | 0.935077i | \(0.384670\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −5631.58 | −0.651939 | −0.325969 | − | 0.945380i | \(-0.605691\pi\) | ||||
−0.325969 | + | 0.945380i | \(0.605691\pi\) | |||||||
\(422\) | −2057.50 | + | 3563.69i | −0.237340 | + | 0.411084i | ||||
\(423\) | 2745.02 | + | 4754.51i | 0.315526 | + | 0.546507i | ||||
\(424\) | 550.116 | + | 952.829i | 0.0630094 | + | 0.109136i | ||||
\(425\) | 1766.27 | − | 3059.27i | 0.201592 | − | 0.349168i | ||||
\(426\) | 1713.97 | 0.194934 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 501.945 | 0.0566879 | ||||||||
\(429\) | −43.8305 | + | 75.9167i | −0.00493277 | + | 0.00854380i | ||||
\(430\) | −2545.25 | − | 4408.50i | −0.285449 | − | 0.494412i | ||||
\(431\) | 1868.45 | + | 3236.25i | 0.208817 | + | 0.361681i | 0.951342 | − | 0.308137i | \(-0.0997055\pi\) |
−0.742525 | + | 0.669818i | \(0.766372\pi\) | |||||||
\(432\) | −216.000 | + | 374.123i | −0.0240563 | + | 0.0416667i | ||||
\(433\) | −5757.46 | −0.638998 | −0.319499 | − | 0.947587i | \(-0.603515\pi\) | ||||
−0.319499 | + | 0.947587i | \(0.603515\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 3472.79 | 0.382776 | ||||||||
\(436\) | −1491.05 | + | 2582.58i | −0.163781 | + | 0.283677i | ||||
\(437\) | 11395.5 | + | 19737.6i | 1.24742 | + | 2.16059i | ||||
\(438\) | 2992.37 | + | 5182.94i | 0.326441 | + | 0.565412i | ||||
\(439\) | 4906.38 | − | 8498.10i | 0.533414 | − | 0.923900i | −0.465824 | − | 0.884877i | \(-0.654242\pi\) |
0.999238 | − | 0.0390229i | \(-0.0124245\pi\) | |||||||
\(440\) | 621.921 | 0.0673839 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 281.152 | 0.0302558 | ||||||||
\(443\) | −2915.15 | + | 5049.19i | −0.312648 | + | 0.541522i | −0.978935 | − | 0.204174i | \(-0.934549\pi\) |
0.666287 | + | 0.745695i | \(0.267883\pi\) | |||||||
\(444\) | 2367.35 | + | 4100.37i | 0.253039 | + | 0.438277i | ||||
\(445\) | 2051.84 | + | 3553.89i | 0.218576 | + | 0.378585i | ||||
\(446\) | −2028.27 | + | 3513.06i | −0.215339 | + | 0.372978i | ||||
\(447\) | 3694.41 | 0.390916 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −8674.94 | −0.911794 | −0.455897 | − | 0.890033i | \(-0.650681\pi\) | ||||
−0.455897 | + | 0.890033i | \(0.650681\pi\) | |||||||
\(450\) | 630.265 | − | 1091.65i | 0.0660244 | − | 0.114358i | ||||
\(451\) | −1035.97 | − | 1794.36i | −0.108164 | − | 0.187346i | ||||
\(452\) | 2087.53 | + | 3615.70i | 0.217232 | + | 0.376257i | ||||
\(453\) | 3367.10 | − | 5831.99i | 0.349228 | − | 0.604881i | ||||
\(454\) | 4847.91 | 0.501154 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 3001.29 | 0.308220 | ||||||||
\(457\) | −4553.41 | + | 7886.74i | −0.466082 | + | 0.807278i | −0.999250 | − | 0.0387315i | \(-0.987668\pi\) |
0.533167 | + | 0.846010i | \(0.321002\pi\) | |||||||
\(458\) | 1967.17 | + | 3407.24i | 0.200698 | + | 0.347619i | ||||
\(459\) | −680.989 | − | 1179.51i | −0.0692502 | − | 0.119945i | ||||
\(460\) | 2702.48 | − | 4680.83i | 0.273921 | − | 0.474445i | ||||
\(461\) | −8729.69 | −0.881957 | −0.440979 | − | 0.897518i | \(-0.645369\pi\) | ||||
−0.440979 | + | 0.897518i | \(0.645369\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −1795.62 | −0.180237 | −0.0901184 | − | 0.995931i | \(-0.528725\pi\) | ||||
−0.0901184 | + | 0.995931i | \(0.528725\pi\) | |||||||
\(464\) | −1249.06 | + | 2163.43i | −0.124970 | + | 0.216454i | ||||
\(465\) | −1552.90 | − | 2689.70i | −0.154869 | − | 0.268240i | ||||
\(466\) | −4478.33 | − | 7756.70i | −0.445182 | − | 0.771078i | ||||
\(467\) | −65.2797 | + | 113.068i | −0.00646849 | + | 0.0112038i | −0.869242 | − | 0.494388i | \(-0.835392\pi\) |
0.862773 | + | 0.505591i | \(0.168726\pi\) | |||||||
\(468\) | 100.325 | 0.00990921 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −9045.40 | −0.887730 | ||||||||
\(471\) | 5680.74 | − | 9839.32i | 0.555742 | − | 0.962573i | ||||
\(472\) | −2357.74 | − | 4083.73i | −0.229924 | − | 0.398239i | ||||
\(473\) | −1799.76 | − | 3117.28i | −0.174954 | − | 0.303029i | ||||
\(474\) | 2544.79 | − | 4407.71i | 0.246595 | − | 0.427116i | ||||
\(475\) | −8757.45 | −0.845935 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −1237.76 | −0.118812 | ||||||||
\(478\) | −6116.92 | + | 10594.8i | −0.585317 | + | 1.01380i | ||||
\(479\) | −5922.90 | − | 10258.8i | −0.564978 | − | 0.978570i | −0.997052 | − | 0.0767319i | \(-0.975551\pi\) |
0.432074 | − | 0.901838i | \(-0.357782\pi\) | |||||||
\(480\) | −355.882 | − | 616.406i | −0.0338411 | − | 0.0586145i | ||||
\(481\) | 549.777 | − | 952.242i | 0.0521158 | − | 0.0902671i | ||||
\(482\) | 12456.8 | 1.17716 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −4884.24 | −0.458700 | ||||||||
\(485\) | 3350.89 | − | 5803.91i | 0.313724 | − | 0.543386i | ||||
\(486\) | −243.000 | − | 420.888i | −0.0226805 | − | 0.0392837i | ||||
\(487\) | 2403.61 | + | 4163.17i | 0.223650 | + | 0.387374i | 0.955914 | − | 0.293648i | \(-0.0948693\pi\) |
−0.732263 | + | 0.681022i | \(0.761536\pi\) | |||||||
\(488\) | −988.870 | + | 1712.77i | −0.0917296 | + | 0.158880i | ||||
\(489\) | −6325.68 | −0.584984 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 6068.04 | 0.557733 | 0.278866 | − | 0.960330i | \(-0.410041\pi\) | ||||
0.278866 | + | 0.960330i | \(0.410041\pi\) | |||||||
\(492\) | −1185.63 | + | 2053.57i | −0.108643 | + | 0.188175i | ||||
\(493\) | −3937.93 | − | 6820.70i | −0.359748 | − | 0.623101i | ||||
\(494\) | −348.500 | − | 603.619i | −0.0317404 | − | 0.0549759i | ||||
\(495\) | −349.831 | + | 605.924i | −0.0317651 | + | 0.0550187i | ||||
\(496\) | 2234.12 | 0.202248 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −1265.18 | −0.113843 | ||||||||
\(499\) | 7753.21 | − | 13429.0i | 0.695554 | − | 1.20473i | −0.274440 | − | 0.961604i | \(-0.588492\pi\) |
0.969994 | − | 0.243130i | \(-0.0781742\pi\) | |||||||
\(500\) | 2891.98 | + | 5009.06i | 0.258667 | + | 0.448024i | ||||
\(501\) | −2253.62 | − | 3903.39i | −0.200967 | − | 0.348085i | ||||
\(502\) | −5904.42 | + | 10226.7i | −0.524954 | + | 0.909247i | ||||
\(503\) | −1496.79 | −0.132681 | −0.0663405 | − | 0.997797i | \(-0.521132\pi\) | ||||
−0.0663405 | + | 0.997797i | \(0.521132\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −2325.18 | −0.204889 | ||||||||
\(506\) | 1910.94 | − | 3309.85i | 0.167889 | − | 0.290792i | ||||
\(507\) | 3283.85 | + | 5687.80i | 0.287655 | + | 0.498233i | ||||
\(508\) | 4160.35 | + | 7205.94i | 0.363358 | + | 0.629354i | ||||
\(509\) | 2526.87 | − | 4376.66i | 0.220042 | − | 0.381124i | −0.734778 | − | 0.678307i | \(-0.762714\pi\) |
0.954821 | + | 0.297183i | \(0.0960472\pi\) | |||||||
\(510\) | 2244.00 | 0.194835 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 512.000 | 0.0441942 | ||||||||
\(513\) | −1688.23 | + | 2924.09i | −0.145296 | + | 0.251661i | ||||
\(514\) | 408.223 | + | 707.063i | 0.0350310 | + | 0.0606755i | ||||
\(515\) | −856.248 | − | 1483.07i | −0.0732637 | − | 0.126896i | ||||
\(516\) | −2059.76 | + | 3567.61i | −0.175729 | + | 0.304371i | ||||
\(517\) | −6396.07 | −0.544098 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 1413.77 | 0.119571 | ||||||||
\(520\) | −82.6476 | + | 143.150i | −0.00696988 | + | 0.0120722i | ||||
\(521\) | −4868.36 | − | 8432.25i | −0.409380 | − | 0.709067i | 0.585441 | − | 0.810715i | \(-0.300922\pi\) |
−0.994820 | + | 0.101649i | \(0.967588\pi\) | |||||||
\(522\) | −1405.19 | − | 2433.86i | −0.117823 | − | 0.204075i | ||||
\(523\) | 5898.34 | − | 10216.2i | 0.493148 | − | 0.854157i | −0.506821 | − | 0.862051i | \(-0.669180\pi\) |
0.999969 | + | 0.00789446i | \(0.00251291\pi\) | |||||||
\(524\) | −5078.11 | −0.423355 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −9252.01 | −0.766933 | ||||||||
\(527\) | −3521.79 | + | 6099.91i | −0.291103 | + | 0.504206i | ||||
\(528\) | −251.647 | − | 435.865i | −0.0207415 | − | 0.0359254i | ||||
\(529\) | −10524.0 | − | 18228.1i | −0.864962 | − | 1.49816i | ||||
\(530\) | 1019.67 | − | 1766.12i | 0.0835691 | − | 0.144746i | ||||
\(531\) | 5304.92 | 0.433548 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 550.685 | 0.0447520 | ||||||||
\(534\) | 1660.46 | − | 2876.00i | 0.134560 | − | 0.233065i | ||||
\(535\) | −465.191 | − | 805.734i | −0.0375924 | − | 0.0651120i | ||||
\(536\) | 1582.59 | + | 2741.12i | 0.127532 | + | 0.220893i | ||||
\(537\) | −1998.73 | + | 3461.90i | −0.160617 | + | 0.278198i | ||||
\(538\) | −1742.59 | −0.139644 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 800.735 | 0.0638114 | ||||||||
\(541\) | 2155.41 | − | 3733.28i | 0.171291 | − | 0.296684i | −0.767581 | − | 0.640952i | \(-0.778540\pi\) |
0.938871 | + | 0.344268i | \(0.111873\pi\) | |||||||
\(542\) | −6472.35 | − | 11210.4i | −0.512936 | − | 0.888431i | ||||
\(543\) | 1496.59 | + | 2592.17i | 0.118278 | + | 0.204863i | ||||
\(544\) | −807.098 | + | 1397.94i | −0.0636104 | + | 0.110176i | ||||
\(545\) | 5527.50 | 0.434444 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 17015.9 | 1.33007 | 0.665034 | − | 0.746813i | \(-0.268417\pi\) | ||||
0.665034 | + | 0.746813i | \(0.268417\pi\) | |||||||
\(548\) | −6146.38 | + | 10645.8i | −0.479124 | + | 0.829868i | ||||
\(549\) | −1112.48 | − | 1926.87i | −0.0864835 | − | 0.149794i | ||||
\(550\) | 734.278 | + | 1271.81i | 0.0569268 | + | 0.0986001i | ||||
\(551\) | −9762.45 | + | 16909.1i | −0.754799 | + | 1.30735i | ||||
\(552\) | −4373.99 | −0.337264 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 9423.76 | 0.722703 | ||||||||
\(555\) | 4388.01 | − | 7600.26i | 0.335605 | − | 0.581285i | ||||
\(556\) | −2027.19 | − | 3511.20i | −0.154626 | − | 0.267820i | ||||
\(557\) | −870.588 | − | 1507.90i | −0.0662262 | − | 0.114707i | 0.831011 | − | 0.556256i | \(-0.187763\pi\) |
−0.897237 | + | 0.441549i | \(0.854429\pi\) | |||||||
\(558\) | −1256.69 | + | 2176.65i | −0.0953405 | + | 0.165135i | ||||
\(559\) | 956.689 | 0.0723858 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1586.75 | 0.119416 | ||||||||
\(562\) | 7165.66 | − | 12411.3i | 0.537838 | − | 0.931563i | ||||
\(563\) | −5673.42 | − | 9826.66i | −0.424700 | − | 0.735602i | 0.571692 | − | 0.820468i | \(-0.306287\pi\) |
−0.996392 | + | 0.0848658i | \(0.972954\pi\) | |||||||
\(564\) | 3660.03 | + | 6339.35i | 0.273253 | + | 0.473289i | ||||
\(565\) | 3869.34 | − | 6701.89i | 0.288114 | − | 0.499028i | ||||
\(566\) | 12694.0 | 0.942701 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 2285.29 | 0.168818 | ||||||||
\(569\) | 9208.72 | − | 15950.0i | 0.678470 | − | 1.17514i | −0.296972 | − | 0.954886i | \(-0.595977\pi\) |
0.975442 | − | 0.220258i | \(-0.0706900\pi\) | |||||||
\(570\) | −2781.53 | − | 4817.75i | −0.204395 | − | 0.354023i | ||||
\(571\) | −4999.25 | − | 8658.95i | −0.366396 | − | 0.634616i | 0.622603 | − | 0.782538i | \(-0.286075\pi\) |
−0.988999 | + | 0.147922i | \(0.952742\pi\) | |||||||
\(572\) | −58.4407 | + | 101.222i | −0.00427190 | + | 0.00739915i | ||||
\(573\) | 3680.16 | 0.268309 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 12762.8 | 0.925648 | ||||||||
\(576\) | −288.000 | + | 498.831i | −0.0208333 | + | 0.0360844i | ||||
\(577\) | 700.855 | + | 1213.92i | 0.0505667 | + | 0.0875840i | 0.890201 | − | 0.455568i | \(-0.150564\pi\) |
−0.839634 | + | 0.543152i | \(0.817231\pi\) | |||||||
\(578\) | 2368.44 | + | 4102.26i | 0.170440 | + | 0.295210i | ||||
\(579\) | 5218.94 | − | 9039.47i | 0.374597 | − | 0.648821i | ||||
\(580\) | 4630.38 | 0.331494 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −5423.46 | −0.386271 | ||||||||
\(583\) | 721.015 | − | 1248.83i | 0.0512202 | − | 0.0887160i | ||||
\(584\) | 3989.83 | + | 6910.59i | 0.282706 | + | 0.489661i | ||||
\(585\) | −92.9786 | − | 161.044i | −0.00657127 | − | 0.0113818i | ||||
\(586\) | −9233.78 | + | 15993.4i | −0.650928 | + | 1.12744i | ||||
\(587\) | −10851.3 | −0.763001 | −0.381500 | − | 0.924369i | \(-0.624593\pi\) | ||||
−0.381500 | + | 0.924369i | \(0.624593\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 17461.6 | 1.22155 | ||||||||
\(590\) | −4370.20 | + | 7569.41i | −0.304946 | + | 0.528183i | ||||
\(591\) | −4790.21 | − | 8296.88i | −0.333406 | − | 0.577476i | ||||
\(592\) | 3156.47 | + | 5467.16i | 0.219139 | + | 0.379559i | ||||
\(593\) | −10231.0 | + | 17720.6i | −0.708493 | + | 1.22715i | 0.256923 | + | 0.966432i | \(0.417291\pi\) |
−0.965416 | + | 0.260715i | \(0.916042\pi\) | |||||||
\(594\) | 566.205 | 0.0391106 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 4925.88 | 0.338544 | ||||||||
\(597\) | −1597.72 | + | 2767.34i | −0.109532 | + | 0.189715i | ||||
\(598\) | 507.893 | + | 879.697i | 0.0347313 | + | 0.0601563i | ||||
\(599\) | −4995.21 | − | 8651.96i | −0.340733 | − | 0.590166i | 0.643836 | − | 0.765163i | \(-0.277342\pi\) |
−0.984569 | + | 0.174997i | \(0.944008\pi\) | |||||||
\(600\) | 840.353 | − | 1455.53i | 0.0571788 | − | 0.0990366i | ||||
\(601\) | 17435.9 | 1.18341 | 0.591703 | − | 0.806156i | \(-0.298456\pi\) | ||||
0.591703 | + | 0.806156i | \(0.298456\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −3560.82 | −0.240477 | ||||||||
\(604\) | 4489.47 | − | 7775.99i | 0.302440 | − | 0.523842i | ||||
\(605\) | 4526.60 | + | 7840.29i | 0.304186 | + | 0.526865i | ||||
\(606\) | 940.833 | + | 1629.57i | 0.0630672 | + | 0.109236i | ||||
\(607\) | −8350.16 | + | 14462.9i | −0.558356 | + | 0.967102i | 0.439277 | + | 0.898351i | \(0.355234\pi\) |
−0.997634 | + | 0.0687503i | \(0.978099\pi\) | |||||||
\(608\) | 4001.72 | 0.266926 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 3665.85 | 0.243321 | ||||||||
\(611\) | 849.979 | − | 1472.21i | 0.0562790 | − | 0.0974781i | ||||
\(612\) | −907.986 | − | 1572.68i | −0.0599725 | − | 0.103875i | ||||
\(613\) | 13351.5 | + | 23125.4i | 0.879707 | + | 1.52370i | 0.851662 | + | 0.524091i | \(0.175595\pi\) |
0.0280452 | + | 0.999607i | \(0.491072\pi\) | |||||||
\(614\) | −6786.53 | + | 11754.6i | −0.446062 | + | 0.772602i | ||||
\(615\) | 4395.26 | 0.288185 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 27790.4 | 1.81329 | 0.906645 | − | 0.421894i | \(-0.138635\pi\) | ||||
0.906645 | + | 0.421894i | \(0.138635\pi\) | |||||||
\(618\) | −692.924 | + | 1200.18i | −0.0451028 | + | 0.0781203i | ||||
\(619\) | −868.040 | − | 1503.49i | −0.0563642 | − | 0.0976257i | 0.836467 | − | 0.548018i | \(-0.184617\pi\) |
−0.892831 | + | 0.450392i | \(0.851284\pi\) | |||||||
\(620\) | −2070.53 | − | 3586.26i | −0.134120 | − | 0.232303i | ||||
\(621\) | 2460.37 | − | 4261.49i | 0.158988 | − | 0.275375i | ||||
\(622\) | 10273.5 | 0.662269 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 133.766 | 0.00858163 | ||||||||
\(625\) | 983.599 | − | 1703.64i | 0.0629503 | − | 0.109033i | ||||
\(626\) | 3763.56 | + | 6518.67i | 0.240291 | + | 0.416196i | ||||
\(627\) | −1966.84 | − | 3406.66i | −0.125276 | − | 0.216984i | ||||
\(628\) | 7574.31 | − | 13119.1i | 0.481287 | − | 0.833613i | ||||
\(629\) | −19903.0 | −1.26166 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −8990.27 | −0.567190 | −0.283595 | − | 0.958944i | \(-0.591527\pi\) | ||||
−0.283595 | + | 0.958944i | \(0.591527\pi\) | |||||||
\(632\) | 3393.06 | − | 5876.95i | 0.213558 | − | 0.369893i | ||||
\(633\) | −3086.24 | − | 5345.53i | −0.193787 | − | 0.335649i | ||||
\(634\) | 1034.95 | + | 1792.58i | 0.0648311 | + | 0.112291i | ||||
\(635\) | 7711.43 | − | 13356.6i | 0.481919 | − | 0.834709i | ||||
\(636\) | −1650.35 | −0.102894 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 3274.18 | 0.203175 | ||||||||
\(639\) | −1285.47 | + | 2226.51i | −0.0795815 | + | 0.137839i | ||||
\(640\) | −474.510 | − | 821.875i | −0.0293073 | − | 0.0507617i | ||||
\(641\) | 6884.81 | + | 11924.8i | 0.424233 | + | 0.734794i | 0.996348 | − | 0.0853796i | \(-0.0272103\pi\) |
−0.572115 | + | 0.820173i | \(0.693877\pi\) | |||||||
\(642\) | −376.458 | + | 652.045i | −0.0231427 | + | 0.0400844i | ||||
\(643\) | 26969.9 | 1.65411 | 0.827053 | − | 0.562124i | \(-0.190015\pi\) | ||||
0.827053 | + | 0.562124i | \(0.190015\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 7635.75 | 0.466136 | ||||||||
\(646\) | −6308.17 | + | 10926.1i | −0.384198 | + | 0.665450i | ||||
\(647\) | −12200.9 | − | 21132.5i | −0.741368 | − | 1.28409i | −0.951872 | − | 0.306495i | \(-0.900844\pi\) |
0.210504 | − | 0.977593i | \(-0.432490\pi\) | |||||||
\(648\) | −324.000 | − | 561.184i | −0.0196419 | − | 0.0340207i | ||||
\(649\) | −3090.20 | + | 5352.38i | −0.186904 | + | 0.323728i | ||||
\(650\) | −390.316 | −0.0235530 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −8434.24 | −0.506611 | ||||||||
\(653\) | −7984.79 | + | 13830.1i | −0.478513 | + | 0.828809i | −0.999696 | − | 0.0246357i | \(-0.992157\pi\) |
0.521183 | + | 0.853445i | \(0.325491\pi\) | |||||||
\(654\) | −2236.58 | − | 3873.87i | −0.133727 | − | 0.231621i | ||||
\(655\) | 4706.27 | + | 8151.50i | 0.280747 | + | 0.486268i | ||||
\(656\) | −1580.84 | + | 2738.10i | −0.0940876 | + | 0.162965i | ||||
\(657\) | −8977.11 | −0.533075 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −11596.2 | −0.685467 | −0.342733 | − | 0.939433i | \(-0.611353\pi\) | ||||
−0.342733 | + | 0.939433i | \(0.611353\pi\) | |||||||
\(660\) | −466.441 | + | 807.899i | −0.0275094 | + | 0.0476476i | ||||
\(661\) | −6301.11 | − | 10913.8i | −0.370779 | − | 0.642208i | 0.618907 | − | 0.785464i | \(-0.287576\pi\) |
−0.989686 | + | 0.143257i | \(0.954243\pi\) | |||||||
\(662\) | −8800.06 | − | 15242.2i | −0.516653 | − | 0.894869i | ||||
\(663\) | −210.864 | + | 365.228i | −0.0123519 | + | 0.0213941i | ||||
\(664\) | −1686.90 | −0.0985912 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −7102.05 | −0.413212 | ||||||||
\(667\) | 14227.5 | − | 24642.8i | 0.825924 | − | 1.43054i | ||||
\(668\) | −3004.83 | − | 5204.52i | −0.174042 | − | 0.301450i | ||||
\(669\) | −3042.40 | − | 5269.59i | −0.175824 | − | 0.304536i | ||||
\(670\) | 2933.41 | − | 5080.81i | 0.169146 | − | 0.292969i | ||||
\(671\) | 2592.14 | 0.149134 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 2126.29 | 0.121787 | 0.0608934 | − | 0.998144i | \(-0.480605\pi\) | ||||
0.0608934 | + | 0.998144i | \(0.480605\pi\) | |||||||
\(674\) | 5859.78 | − | 10149.4i | 0.334882 | − | 0.580032i | ||||
\(675\) | 945.397 | + | 1637.48i | 0.0539087 | + | 0.0933726i | ||||
\(676\) | 4378.47 | + | 7583.73i | 0.249116 | + | 0.431482i | ||||
\(677\) | −1309.69 | + | 2268.45i | −0.0743508 | + | 0.128779i | −0.900804 | − | 0.434226i | \(-0.857022\pi\) |
0.826453 | + | 0.563006i | \(0.190355\pi\) | |||||||
\(678\) | −6262.58 | −0.354739 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 2992.00 | 0.168732 | ||||||||
\(681\) | −3635.94 | + | 6297.63i | −0.204595 | + | 0.354369i | ||||
\(682\) | −1464.09 | − | 2535.87i | −0.0822034 | − | 0.142381i | ||||
\(683\) | 14964.9 | + | 25919.9i | 0.838383 | + | 1.45212i | 0.891246 | + | 0.453520i | \(0.149832\pi\) |
−0.0528633 | + | 0.998602i | \(0.516835\pi\) | |||||||
\(684\) | −2250.97 | + | 3898.79i | −0.125830 | + | 0.217945i | ||||
\(685\) | 22785.3 | 1.27092 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −5901.51 | −0.327739 | ||||||||
\(688\) | −2746.35 | + | 4756.81i | −0.152185 | + | 0.263593i | ||||
\(689\) | 191.633 | + | 331.918i | 0.0105960 | + | 0.0183528i | ||||
\(690\) | 4053.72 | + | 7021.24i | 0.223656 | + | 0.387383i | ||||
\(691\) | −3380.45 | + | 5855.11i | −0.186105 | + | 0.322343i | −0.943948 | − | 0.330094i | \(-0.892920\pi\) |
0.757844 | + | 0.652436i | \(0.226253\pi\) | |||||||
\(692\) | 1885.02 | 0.103552 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 15877.1 | 0.868423 | ||||||||
\(695\) | −3757.51 | + | 6508.20i | −0.205080 | + | 0.355209i | ||||
\(696\) | −1873.58 | − | 3245.14i | −0.102037 | − | 0.176734i | ||||
\(697\) | −4983.96 | − | 8632.48i | −0.270848 | − | 0.469122i | ||||
\(698\) | 9927.75 | − | 17195.4i | 0.538354 | − | 0.932456i | ||||
\(699\) | 13435.0 | 0.726979 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 467.205 | 0.0251727 | 0.0125864 | − | 0.999921i | \(-0.495994\pi\) | ||||
0.0125864 | + | 0.999921i | \(0.495994\pi\) | |||||||
\(702\) | −75.2435 | + | 130.326i | −0.00404542 | + | 0.00700687i | ||||
\(703\) | 24670.5 | + | 42730.6i | 1.32357 | + | 2.29248i | ||||
\(704\) | −335.529 | − | 581.153i | −0.0179627 | − | 0.0311123i | ||||
\(705\) | 6784.05 | − | 11750.3i | 0.362414 | − | 0.627720i | ||||
\(706\) | −20206.1 | −1.07715 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 7073.23 | 0.375464 | ||||||||
\(709\) | −4412.32 | + | 7642.36i | −0.233721 | + | 0.404816i | −0.958900 | − | 0.283744i | \(-0.908424\pi\) |
0.725179 | + | 0.688560i | \(0.241757\pi\) | |||||||
\(710\) | −2117.95 | − | 3668.40i | −0.111951 | − | 0.193905i | ||||
\(711\) | 3817.19 | + | 6611.56i | 0.201344 | + | 0.348738i | ||||
\(712\) | 2213.95 | − | 3834.67i | 0.116533 | − | 0.201841i | ||||
\(713\) | −25448.0 | −1.33665 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 216.646 | 0.0113316 | ||||||||
\(716\) | −2664.97 | + | 4615.87i | −0.139099 | + | 0.240926i | ||||
\(717\) | −9175.38 | − | 15892.2i | −0.477909 | − | 0.827763i | ||||
\(718\) | 4825.27 | + | 8357.62i | 0.250804 | + | 0.434406i | ||||
\(719\) | 10549.4 | − | 18272.2i | 0.547188 | − | 0.947757i | −0.451278 | − | 0.892383i | \(-0.649032\pi\) |
0.998466 | − | 0.0553733i | \(-0.0176349\pi\) | |||||||
\(720\) | 1067.65 | 0.0552623 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 17558.9 | 0.905090 | ||||||||
\(723\) | −9342.57 | + | 16181.8i | −0.480573 | + | 0.832376i | ||||
\(724\) | 1995.45 | + | 3456.23i | 0.102432 | + | 0.177417i | ||||
\(725\) | 5466.92 | + | 9468.98i | 0.280050 | + | 0.485061i | ||||
\(726\) | 3663.18 | − | 6344.81i | 0.187263 | − | 0.324350i | ||||
\(727\) | −4616.48 | −0.235510 | −0.117755 | − | 0.993043i | \(-0.537570\pi\) | ||||
−0.117755 | + | 0.993043i | \(0.537570\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 7395.36 | − | 12809.1i | 0.374951 | − | 0.649435i | ||||
\(731\) | −8658.49 | − | 14996.9i | −0.438093 | − | 0.758799i | ||||
\(732\) | −1483.30 | − | 2569.16i | −0.0748969 | − | 0.129725i | ||||
\(733\) | 5344.03 | − | 9256.13i | 0.269285 | − | 0.466416i | −0.699392 | − | 0.714738i | \(-0.746546\pi\) |
0.968678 | + | 0.248322i | \(0.0798791\pi\) | |||||||
\(734\) | 13870.6 | 0.697511 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −5831.99 | −0.292079 | ||||||||
\(737\) | 2074.23 | − | 3592.68i | 0.103671 | − | 0.179563i | ||||
\(738\) | −1778.45 | − | 3080.36i | −0.0887066 | − | 0.153644i | ||||
\(739\) | 7683.78 | + | 13308.7i | 0.382480 | + | 0.662474i | 0.991416 | − | 0.130745i | \(-0.0417369\pi\) |
−0.608936 | + | 0.793219i | \(0.708404\pi\) | |||||||
\(740\) | 5850.68 | − | 10133.7i | 0.290642 | − | 0.503407i | ||||
\(741\) | 1045.50 | 0.0518318 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 6502.58 | 0.321072 | 0.160536 | − | 0.987030i | \(-0.448678\pi\) | ||||
0.160536 | + | 0.987030i | \(0.448678\pi\) | |||||||
\(744\) | −1675.59 | + | 2902.21i | −0.0825673 | + | 0.143011i | ||||
\(745\) | −4565.19 | − | 7907.14i | −0.224504 | − | 0.388853i | ||||
\(746\) | −14093.1 | − | 24410.0i | −0.691669 | − | 1.19801i | ||||
\(747\) | 948.883 | − | 1643.51i | 0.0464763 | − | 0.0804994i | ||||
\(748\) | 2115.66 | 0.103418 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −8675.94 | −0.422401 | ||||||||
\(751\) | 9937.07 | − | 17211.5i | 0.482835 | − | 0.836295i | −0.516971 | − | 0.856003i | \(-0.672940\pi\) |
0.999806 | + | 0.0197085i | \(0.00627380\pi\) | |||||||
\(752\) | 4880.03 | + | 8452.47i | 0.236644 | + | 0.409880i | ||||
\(753\) | −8856.62 | − | 15340.1i | −0.428623 | − | 0.742397i | ||||
\(754\) | −435.108 | + | 753.630i | −0.0210155 | + | 0.0364000i | ||||
\(755\) | −16642.9 | −0.802250 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −15157.8 | −0.727765 | −0.363883 | − | 0.931445i | \(-0.618549\pi\) | ||||
−0.363883 | + | 0.931445i | \(0.618549\pi\) | |||||||
\(758\) | −5354.17 | + | 9273.70i | −0.256560 | + | 0.444375i | ||||
\(759\) | 2866.41 | + | 4964.77i | 0.137081 | + | 0.237430i | ||||
\(760\) | −3708.70 | − | 6423.66i | −0.177012 | − | 0.306593i | ||||
\(761\) | −17609.9 | + | 30501.3i | −0.838842 | + | 1.45292i | 0.0520212 | + | 0.998646i | \(0.483434\pi\) |
−0.890863 | + | 0.454271i | \(0.849900\pi\) | |||||||
\(762\) | −12481.0 | −0.593361 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 4906.88 | 0.232362 | ||||||||
\(765\) | −1683.00 | + | 2915.04i | −0.0795412 | + | 0.137769i | ||||
\(766\) | 8970.47 | + | 15537.3i | 0.423128 | + | 0.732880i | ||||
\(767\) | −821.319 | − | 1422.57i | −0.0386651 | − | 0.0669698i | ||||
\(768\) | −384.000 | + | 665.108i | −0.0180422 | + | 0.0312500i | ||||
\(769\) | −2264.35 | −0.106183 | −0.0530915 | − | 0.998590i | \(-0.516907\pi\) | ||||
−0.0530915 | + | 0.998590i | \(0.516907\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1224.67 | −0.0572054 | ||||||||
\(772\) | 6958.58 | − | 12052.6i | 0.324410 | − | 0.561895i | ||||
\(773\) | 4766.39 | + | 8255.64i | 0.221779 | + | 0.384133i | 0.955348 | − | 0.295482i | \(-0.0954803\pi\) |
−0.733569 | + | 0.679615i | \(0.762147\pi\) | |||||||
\(774\) | −3089.64 | − | 5351.42i | −0.143482 | − | 0.248518i | ||||
\(775\) | 4889.19 | − | 8468.33i | 0.226613 | − | 0.392505i | ||||
\(776\) | −7231.28 | −0.334520 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −7405.16 | −0.341244 | ||||||||
\(779\) | −12355.6 | + | 21400.6i | −0.568276 | + | 0.984282i | ||||
\(780\) | −123.971 | − | 214.725i | −0.00569088 | − | 0.00985690i | ||||
\(781\) | −1497.62 | − | 2593.95i | −0.0686159 | − | 0.118846i | ||||
\(782\) | 9193.34 | − | 15923.3i | 0.420401 | − | 0.728155i | ||||
\(783\) | 4215.56 | 0.192404 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −28078.8 | −1.27666 | ||||||||
\(786\) | 3808.58 | − | 6596.66i | 0.172834 | − | 0.299357i | ||||
\(787\) | 16606.5 | + | 28763.3i | 0.752170 | + | 1.30280i | 0.946769 | + | 0.321913i | \(0.104326\pi\) |
−0.194599 | + | 0.980883i | \(0.562341\pi\) | |||||||
\(788\) | −6386.94 | − | 11062.5i | −0.288738 | − | 0.500109i | ||||
\(789\) | 6939.01 | − | 12018.7i | 0.313099 | − | 0.542304i | ||||
\(790\) | −12578.4 | −0.566481 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 754.940 | 0.0338708 | ||||||||
\(793\) | −344.472 | + | 596.643i | −0.0154257 | + | 0.0267181i | ||||
\(794\) | 2083.24 | + | 3608.27i | 0.0931124 | + | 0.161275i | ||||
\(795\) | 1529.50 | + | 2649.18i | 0.0682339 | + | 0.118185i | ||||
\(796\) | −2130.30 | + | 3689.78i | −0.0948573 | + | 0.164298i | ||||
\(797\) | 42065.6 | 1.86956 | 0.934781 | − | 0.355223i | \(-0.115595\pi\) | ||||
0.934781 | + | 0.355223i | \(0.115595\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −30770.8 | −1.36245 | ||||||||
\(800\) | 1120.47 | − | 1940.71i | 0.0495183 | − | 0.0857682i | ||||
\(801\) | 2490.69 | + | 4314.01i | 0.109868 | + | 0.190297i | ||||
\(802\) | 10634.0 | + | 18418.7i | 0.468205 | + | 0.810954i | ||||
\(803\) | 5229.31 | − | 9057.43i | 0.229811 | − | 0.398044i | ||||
\(804\) | −4747.76 | −0.208259 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 778.255 | 0.0340110 | ||||||||
\(807\) | 1306.94 | − | 2263.69i | 0.0570092 | − | 0.0987429i | ||||
\(808\) | 1254.44 | + | 2172.76i | 0.0546178 | + | 0.0946008i | ||||
\(809\) | 388.780 | + | 673.387i | 0.0168959 | + | 0.0292646i | 0.874350 | − | 0.485296i | \(-0.161288\pi\) |
−0.857454 | + | 0.514561i | \(0.827955\pi\) | |||||||
\(810\) | −600.551 | + | 1040.19i | −0.0260509 | + | 0.0451215i | ||||
\(811\) | 16559.4 | 0.716991 | 0.358496 | − | 0.933531i | \(-0.383290\pi\) | ||||
0.358496 | + | 0.933531i | \(0.383290\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 19417.0 | 0.837620 | ||||||||
\(814\) | 4137.06 | − | 7165.59i | 0.178137 | − | 0.308543i | ||||
\(815\) | 7816.66 | + | 13538.8i | 0.335958 | + | 0.581896i | ||||
\(816\) | −1210.65 | − | 2096.90i | −0.0519377 | − | 0.0899587i | ||||
\(817\) | −21465.1 | + | 37178.6i | −0.919178 | + | 1.59206i | ||||
\(818\) | −13032.7 | −0.557065 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 5860.35 | 0.249576 | ||||||||
\(821\) | −115.612 | + | 200.246i | −0.00491460 | + | 0.00851235i | −0.868472 | − | 0.495738i | \(-0.834898\pi\) |
0.863558 | + | 0.504250i | \(0.168231\pi\) | |||||||
\(822\) | −9219.56 | − | 15968.8i | −0.391203 | − | 0.677584i | ||||
\(823\) | 2611.43 | + | 4523.13i | 0.110606 | + | 0.191575i | 0.916015 | − | 0.401145i | \(-0.131388\pi\) |
−0.805409 | + | 0.592720i | \(0.798054\pi\) | |||||||
\(824\) | −923.899 | + | 1600.24i | −0.0390601 | + | 0.0676541i | ||||
\(825\) | −2202.84 | −0.0929611 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −46225.5 | −1.94367 | −0.971836 | − | 0.235658i | \(-0.924275\pi\) | ||||
−0.971836 | + | 0.235658i | \(0.924275\pi\) | |||||||
\(828\) | 3280.50 | − | 5681.99i | 0.137687 | − | 0.238481i | ||||
\(829\) | 19797.1 | + | 34289.6i | 0.829410 | + | 1.43658i | 0.898502 | + | 0.438970i | \(0.144657\pi\) |
−0.0690913 | + | 0.997610i | \(0.522010\pi\) | |||||||
\(830\) | 1563.38 | + | 2707.86i | 0.0653805 | + | 0.113242i | ||||
\(831\) | −7067.82 | + | 12241.8i | −0.295042 | + | 0.511028i | ||||
\(832\) | 178.355 | 0.00743191 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 6081.58 | 0.252503 | ||||||||
\(835\) | −5569.61 | + | 9646.85i | −0.230832 | + | 0.399812i | ||||
\(836\) | −2622.45 | − | 4542.22i | −0.108492 | − | 0.187914i | ||||
\(837\) | −1885.04 | − | 3264.98i | −0.0778452 | − | 0.134832i | ||||
\(838\) | −6079.92 | + | 10530.7i | −0.250629 | + | 0.434103i | ||||
\(839\) | −45737.6 | −1.88205 | −0.941023 | − | 0.338344i | \(-0.890133\pi\) | ||||
−0.941023 | + | 0.338344i | \(0.890133\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −11.7878 | −0.000483326 | ||||||||
\(842\) | 5631.58 | − | 9754.18i | 0.230495 | − | 0.399229i | ||||
\(843\) | 10748.5 | + | 18616.9i | 0.439143 | + | 0.760618i | ||||
\(844\) | −4114.99 | − | 7127.37i | −0.167824 | − | 0.290680i | ||||
\(845\) | 8115.72 | − | 14056.8i | 0.330402 | − | 0.572272i | ||||
\(846\) | −10980.1 | −0.446221 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −2200.46 | −0.0891088 | ||||||||
\(849\) | −9520.50 | + | 16490.0i | −0.384856 | + | 0.666590i | ||||
\(850\) | 3532.54 | + | 6118.54i | 0.142547 | + | 0.246899i | ||||
\(851\) | −35954.1 | − | 62274.3i | −1.44828 | − | 2.50850i | ||||
\(852\) | −1713.97 | + | 2968.68i | −0.0689196 | + | 0.119372i | ||||
\(853\) | −8795.55 | −0.353053 | −0.176526 | − | 0.984296i | \(-0.556486\pi\) | ||||
−0.176526 | + | 0.984296i | \(0.556486\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 8344.58 | 0.333776 | ||||||||
\(856\) | −501.945 | + | 869.394i | −0.0200422 | + | 0.0347141i | ||||
\(857\) | −15127.5 | − | 26201.6i | −0.602969 | − | 1.04437i | −0.992369 | − | 0.123305i | \(-0.960651\pi\) |
0.389400 | − | 0.921069i | \(-0.372683\pi\) | |||||||
\(858\) | −87.6610 | − | 151.833i | −0.00348799 | − | 0.00604138i | ||||
\(859\) | −22496.7 | + | 38965.5i | −0.893573 | + | 1.54771i | −0.0580118 | + | 0.998316i | \(0.518476\pi\) |
−0.835561 | + | 0.549398i | \(0.814857\pi\) | |||||||
\(860\) | 10181.0 | 0.403685 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −7473.79 | −0.295311 | ||||||||
\(863\) | −22333.9 | + | 38683.5i | −0.880946 | + | 1.52584i | −0.0306555 | + | 0.999530i | \(0.509759\pi\) |
−0.850291 | + | 0.526313i | \(0.823574\pi\) | |||||||
\(864\) | −432.000 | − | 748.246i | −0.0170103 | − | 0.0294628i | ||||
\(865\) | −1747.00 | − | 3025.89i | −0.0686701 | − | 0.118940i | ||||
\(866\) | 5757.46 | − | 9972.22i | 0.225920 | − | 0.391305i | ||||
\(867\) | −7105.31 | −0.278327 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −8894.29 | −0.347201 | ||||||||
\(870\) | −3472.79 | + | 6015.05i | −0.135332 | + | 0.234401i | ||||
\(871\) | 551.294 | + | 954.868i | 0.0214465 | + | 0.0371464i | ||||
\(872\) | −2982.11 | − | 5165.16i | −0.115811 | − | 0.200590i | ||||
\(873\) | 4067.59 | − | 7045.28i | 0.157694 | − | 0.273135i | ||||
\(874\) | −45582.1 | −1.76411 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −11969.5 | −0.461657 | ||||||||
\(877\) | −2993.42 | + | 5184.76i | −0.115257 | + | 0.199631i | −0.917883 | − | 0.396852i | \(-0.870103\pi\) |
0.802625 | + | 0.596484i | \(0.203436\pi\) | |||||||
\(878\) | 9812.76 | + | 16996.2i | 0.377181 | + | 0.653296i | ||||
\(879\) | −13850.7 | − | 23990.1i | −0.531481 | − | 0.920552i | ||||
\(880\) | −621.921 | + | 1077.20i | −0.0238238 | + | 0.0412640i | ||||
\(881\) | 37911.8 | 1.44981 | 0.724904 | − | 0.688850i | \(-0.241884\pi\) | ||||
0.724904 | + | 0.688850i | \(0.241884\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −16293.6 | −0.620978 | −0.310489 | − | 0.950577i | \(-0.600493\pi\) | ||||
−0.310489 | + | 0.950577i | \(0.600493\pi\) | |||||||
\(884\) | −281.152 | + | 486.970i | −0.0106970 | + | 0.0185278i | ||||
\(885\) | −6555.30 | − | 11354.1i | −0.248988 | − | 0.431259i | ||||
\(886\) | −5830.30 | − | 10098.4i | −0.221075 | − | 0.382914i | ||||
\(887\) | −4426.71 | + | 7667.28i | −0.167570 | + | 0.290239i | −0.937565 | − | 0.347811i | \(-0.886925\pi\) |
0.769995 | + | 0.638050i | \(0.220259\pi\) | |||||||
\(888\) | −9469.40 | −0.357852 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −8207.35 | −0.309113 | ||||||||
\(891\) | −424.654 | + | 735.522i | −0.0159668 | + | 0.0276554i | ||||
\(892\) | −4056.54 | − | 7026.12i | −0.152268 | − | 0.263735i | ||||
\(893\) | 38141.7 | + | 66063.3i | 1.42930 | + | 2.47562i | ||||
\(894\) | −3694.41 | + | 6398.91i | −0.138210 | + | 0.239386i | ||||
\(895\) | 9879.34 | 0.368972 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −1523.68 | −0.0567159 | ||||||||
\(898\) | 8674.94 | − | 15025.4i | 0.322368 | − | 0.558358i | ||||
\(899\) | −10900.6 | − | 18880.3i | −0.404398 | − | 0.700438i | ||||
\(900\) | 1260.53 | + | 2183.30i | 0.0466863 | + | 0.0808630i | ||||
\(901\) | 3468.73 | − | 6008.02i | 0.128258 | − | 0.222149i | ||||
\(902\) | 4143.89 | 0.152967 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −8350.10 | −0.307213 | ||||||||
\(905\) | 3698.68 | − | 6406.30i | 0.135854 | − | 0.235307i | ||||
\(906\) | 6734.21 | + | 11664.0i | 0.246941 | + | 0.427715i | ||||
\(907\) | −8331.23 | − | 14430.1i | −0.304999 | − | 0.528274i | 0.672262 | − | 0.740313i | \(-0.265323\pi\) |
−0.977261 | + | 0.212039i | \(0.931989\pi\) | |||||||
\(908\) | −4847.91 | + | 8396.83i | −0.177185 | + | 0.306893i | ||||
\(909\) | −2822.50 | −0.102988 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −29071.2 | −1.05727 | −0.528635 | − | 0.848849i | \(-0.677296\pi\) | ||||
−0.528635 | + | 0.848849i | \(0.677296\pi\) | |||||||
\(912\) | −3001.29 | + | 5198.39i | −0.108972 | + | 0.188745i | ||||
\(913\) | 1105.48 | + | 1914.74i | 0.0400723 | + | 0.0694072i | ||||
\(914\) | −9106.82 | − | 15773.5i | −0.329570 | − | 0.570832i | ||||
\(915\) | −2749.38 | + | 4762.07i | −0.0993353 | + | 0.172054i | ||||
\(916\) | −7868.67 | −0.283830 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 2723.96 | 0.0979346 | ||||||||
\(919\) | −3986.70 | + | 6905.16i | −0.143100 | + | 0.247857i | −0.928663 | − | 0.370926i | \(-0.879040\pi\) |
0.785562 | + | 0.618782i | \(0.212374\pi\) | |||||||
\(920\) | 5404.96 | + | 9361.66i | 0.193691 | + | 0.335483i | ||||
\(921\) | −10179.8 | − | 17631.9i | −0.364208 | − | 0.630827i | ||||
\(922\) | 8729.69 | − | 15120.3i | 0.311819 | − | 0.540086i | ||||
\(923\) | 796.079 | 0.0283892 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 27630.7 | 0.982154 | ||||||||
\(926\) | 1795.62 | − | 3110.11i | 0.0637233 | − | 0.110372i | ||||
\(927\) | −1039.39 | − | 1800.27i | −0.0368262 | − | 0.0637849i | ||||
\(928\) | −2498.11 | − | 4326.86i | −0.0883670 | − | 0.153056i | ||||
\(929\) | −15070.7 | + | 26103.3i | −0.532244 | + | 0.921874i | 0.467047 | + | 0.884233i | \(0.345318\pi\) |
−0.999291 | + | 0.0376418i | \(0.988015\pi\) | |||||||
\(930\) | 6211.59 | 0.219017 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 17913.3 | 0.629582 | ||||||||
\(933\) | −7705.15 | + | 13345.7i | −0.270370 | + | 0.468295i | ||||
\(934\) | −130.559 | − | 226.136i | −0.00457391 | − | 0.00792225i | ||||
\(935\) | −1960.75 | − | 3396.11i | −0.0685811 | − | 0.118786i | ||||
\(936\) | −100.325 | + | 173.767i | −0.00350343 | + | 0.00606813i | ||||
\(937\) | 1126.37 | 0.0392709 | 0.0196354 | − | 0.999807i | \(-0.493749\pi\) | ||||
0.0196354 | + | 0.999807i | \(0.493749\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −11290.7 | −0.392393 | ||||||||
\(940\) | 9045.40 | − | 15667.1i | 0.313860 | − | 0.543622i | ||||
\(941\) | 5166.64 | + | 8948.89i | 0.178988 | + | 0.310016i | 0.941534 | − | 0.336917i | \(-0.109384\pi\) |
−0.762546 | + | 0.646934i | \(0.776051\pi\) | |||||||
\(942\) | 11361.5 | + | 19678.6i | 0.392969 | + | 0.680642i | ||||
\(943\) | 18006.7 | − | 31188.6i | 0.621824 | − | 1.07703i | ||||
\(944\) | 9430.97 | 0.325161 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 7199.06 | 0.247422 | ||||||||
\(947\) | −12405.1 | + | 21486.3i | −0.425673 | + | 0.737288i | −0.996483 | − | 0.0837944i | \(-0.973296\pi\) |
0.570810 | + | 0.821082i | \(0.306629\pi\) | |||||||
\(948\) | 5089.58 | + | 8815.42i | 0.174369 | + | 0.302016i | ||||
\(949\) | 1389.85 | + | 2407.30i | 0.0475412 | + | 0.0823438i | ||||
\(950\) | 8757.45 | − | 15168.3i | 0.299083 | − | 0.518028i | ||||
\(951\) | −3104.84 | −0.105869 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −15048.6 | −0.511513 | −0.255757 | − | 0.966741i | \(-0.582325\pi\) | ||||
−0.255757 | + | 0.966741i | \(0.582325\pi\) | |||||||
\(954\) | 1237.76 | − | 2143.87i | 0.0420063 | − | 0.0727570i | ||||
\(955\) | −4547.58 | − | 7876.65i | −0.154090 | − | 0.266893i | ||||
\(956\) | −12233.8 | − | 21189.6i | −0.413881 | − | 0.716864i | ||||
\(957\) | −2455.63 | + | 4253.28i | −0.0829460 | + | 0.143667i | ||||
\(958\) | 23691.6 | 0.798999 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 1423.53 | 0.0478585 | ||||||||
\(961\) | 5146.89 | − | 8914.67i | 0.172767 | − | 0.299240i | ||||
\(962\) | 1099.55 | + | 1904.48i | 0.0368514 | + | 0.0638285i | ||||
\(963\) | −564.688 | − | 978.068i | −0.0188960 | − | 0.0327288i | ||||
\(964\) | −12456.8 | + | 21575.7i | −0.416188 | + | 0.720859i | ||||
\(965\) | −25796.2 | −0.860528 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −15619.9 | −0.519442 | −0.259721 | − | 0.965684i | \(-0.583631\pi\) | ||||
−0.259721 | + | 0.965684i | \(0.583631\pi\) | |||||||
\(968\) | 4884.24 | − | 8459.74i | 0.162175 | − | 0.280895i | ||||
\(969\) | −9462.26 | − | 16389.1i | −0.313696 | − | 0.543338i | ||||
\(970\) | 6701.78 | + | 11607.8i | 0.221836 | + | 0.384232i | ||||
\(971\) | 12416.5 | − | 21506.0i | 0.410365 | − | 0.710773i | −0.584565 | − | 0.811347i | \(-0.698735\pi\) |
0.994930 | + | 0.100574i | \(0.0320680\pi\) | |||||||
\(972\) | 972.000 | 0.0320750 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −9614.42 | −0.316289 | ||||||||
\(975\) | 292.737 | − | 507.035i | 0.00961546 | − | 0.0166545i | ||||
\(976\) | −1977.74 | − | 3425.54i | −0.0648626 | − | 0.112345i | ||||
\(977\) | −19328.4 | − | 33477.8i | −0.632928 | − | 1.09626i | −0.986950 | − | 0.161026i | \(-0.948520\pi\) |
0.354022 | − | 0.935237i | \(-0.384814\pi\) | |||||||
\(978\) | 6325.68 | − | 10956.4i | 0.206823 | − | 0.358228i | ||||
\(979\) | −5803.47 | −0.189458 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 6709.75 | 0.218375 | ||||||||
\(982\) | −6068.04 | + | 10510.2i | −0.197188 | + | 0.341540i | ||||
\(983\) | −13332.1 | − | 23091.8i | −0.432581 | − | 0.749252i | 0.564514 | − | 0.825424i | \(-0.309064\pi\) |
−0.997095 | + | 0.0761716i | \(0.975730\pi\) | |||||||
\(984\) | −2371.26 | − | 4107.15i | −0.0768222 | − | 0.133060i | ||||
\(985\) | −11838.5 | + | 20505.0i | −0.382952 | + | 0.663292i | ||||
\(986\) | 15751.7 | 0.508760 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 1394.00 | 0.0448876 | ||||||||
\(989\) | 31282.6 | − | 54183.0i | 1.00579 | − | 1.74208i | ||||
\(990\) | −699.661 | − | 1211.85i | −0.0224613 | − | 0.0389041i | ||||
\(991\) | −13614.1 | − | 23580.3i | −0.436393 | − | 0.755855i | 0.561015 | − | 0.827806i | \(-0.310411\pi\) |
−0.997408 | + | 0.0719507i | \(0.977078\pi\) | |||||||
\(992\) | −2234.12 | + | 3869.61i | −0.0715054 | + | 0.123851i | ||||
\(993\) | 26400.2 | 0.843690 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 7897.24 | 0.251617 | ||||||||
\(996\) | 1265.18 | − | 2191.35i | 0.0402497 | − | 0.0697145i | ||||
\(997\) | −2581.46 | − | 4471.22i | −0.0820016 | − | 0.142031i | 0.822108 | − | 0.569332i | \(-0.192798\pi\) |
−0.904110 | + | 0.427301i | \(0.859465\pi\) | |||||||
\(998\) | 15506.4 | + | 26857.9i | 0.491831 | + | 0.851876i | ||||
\(999\) | 5326.54 | − | 9225.84i | 0.168693 | − | 0.292185i |
(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 | 294.4.e.k.79.1 | 4 | ||
3.2 | odd | 2 | 882.4.g.bk.667.2 | 4 | |||
7.2 | even | 3 | 294.4.a.o.1.2 | yes | 2 | ||
7.3 | odd | 6 | 294.4.e.m.67.2 | 4 | |||
7.4 | even | 3 | inner | 294.4.e.k.67.1 | 4 | ||
7.5 | odd | 6 | 294.4.a.l.1.1 | ✓ | 2 | ||
7.6 | odd | 2 | 294.4.e.m.79.2 | 4 | |||
21.2 | odd | 6 | 882.4.a.t.1.1 | 2 | |||
21.5 | even | 6 | 882.4.a.bb.1.2 | 2 | |||
21.11 | odd | 6 | 882.4.g.bk.361.2 | 4 | |||
21.17 | even | 6 | 882.4.g.be.361.1 | 4 | |||
21.20 | even | 2 | 882.4.g.be.667.1 | 4 | |||
28.19 | even | 6 | 2352.4.a.bw.1.1 | 2 | |||
28.23 | odd | 6 | 2352.4.a.bu.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
294.4.a.l.1.1 | ✓ | 2 | 7.5 | odd | 6 | ||
294.4.a.o.1.2 | yes | 2 | 7.2 | even | 3 | ||
294.4.e.k.67.1 | 4 | 7.4 | even | 3 | inner | ||
294.4.e.k.79.1 | 4 | 1.1 | even | 1 | trivial | ||
294.4.e.m.67.2 | 4 | 7.3 | odd | 6 | |||
294.4.e.m.79.2 | 4 | 7.6 | odd | 2 | |||
882.4.a.t.1.1 | 2 | 21.2 | odd | 6 | |||
882.4.a.bb.1.2 | 2 | 21.5 | even | 6 | |||
882.4.g.be.361.1 | 4 | 21.17 | even | 6 | |||
882.4.g.be.667.1 | 4 | 21.20 | even | 2 | |||
882.4.g.bk.361.2 | 4 | 21.11 | odd | 6 | |||
882.4.g.bk.667.2 | 4 | 3.2 | odd | 2 | |||
2352.4.a.bu.1.2 | 2 | 28.23 | odd | 6 | |||
2352.4.a.bw.1.1 | 2 | 28.19 | even | 6 |