Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1450,4,Mod(1,1450)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1450, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1450.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1450 = 2 \cdot 5^{2} \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1450.a (trivial) |
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: | yes |
Analytic conductor: | \(85.5527695083\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{6}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 6 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 58) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-2.44949\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1450.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.00000 | 0.707107 | ||||||||
\(3\) | −1.44949 | −0.278954 | −0.139477 | − | 0.990225i | \(-0.544542\pi\) | ||||
−0.139477 | + | 0.990225i | \(0.544542\pi\) | |||||||
\(4\) | 4.00000 | 0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −2.89898 | −0.197251 | ||||||||
\(7\) | −11.5959 | −0.626121 | −0.313060 | − | 0.949733i | \(-0.601354\pi\) | ||||
−0.313060 | + | 0.949733i | \(0.601354\pi\) | |||||||
\(8\) | 8.00000 | 0.353553 | ||||||||
\(9\) | −24.8990 | −0.922184 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −37.6515 | −1.03203 | −0.516017 | − | 0.856579i | \(-0.672586\pi\) | ||||
−0.516017 | + | 0.856579i | \(0.672586\pi\) | |||||||
\(12\) | −5.79796 | −0.139477 | ||||||||
\(13\) | 44.5959 | 0.951437 | 0.475719 | − | 0.879598i | \(-0.342188\pi\) | ||||
0.475719 | + | 0.879598i | \(0.342188\pi\) | |||||||
\(14\) | −23.1918 | −0.442734 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 16.0000 | 0.250000 | ||||||||
\(17\) | 61.1918 | 0.873012 | 0.436506 | − | 0.899701i | \(-0.356216\pi\) | ||||
0.436506 | + | 0.899701i | \(0.356216\pi\) | |||||||
\(18\) | −49.7980 | −0.652083 | ||||||||
\(19\) | 63.7980 | 0.770329 | 0.385165 | − | 0.922848i | \(-0.374145\pi\) | ||||
0.385165 | + | 0.922848i | \(0.374145\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 16.8082 | 0.174659 | ||||||||
\(22\) | −75.3031 | −0.729758 | ||||||||
\(23\) | −177.060 | −1.60520 | −0.802600 | − | 0.596517i | \(-0.796551\pi\) | ||||
−0.802600 | + | 0.596517i | \(0.796551\pi\) | |||||||
\(24\) | −11.5959 | −0.0986253 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 89.1918 | 0.672768 | ||||||||
\(27\) | 75.2270 | 0.536202 | ||||||||
\(28\) | −46.3837 | −0.313060 | ||||||||
\(29\) | 29.0000 | 0.185695 | ||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −233.994 | −1.35570 | −0.677849 | − | 0.735201i | \(-0.737088\pi\) | ||||
−0.677849 | + | 0.735201i | \(0.737088\pi\) | |||||||
\(32\) | 32.0000 | 0.176777 | ||||||||
\(33\) | 54.5755 | 0.287890 | ||||||||
\(34\) | 122.384 | 0.617313 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −99.5959 | −0.461092 | ||||||||
\(37\) | −10.2020 | −0.0453299 | −0.0226649 | − | 0.999743i | \(-0.507215\pi\) | ||||
−0.0226649 | + | 0.999743i | \(0.507215\pi\) | |||||||
\(38\) | 127.596 | 0.544705 | ||||||||
\(39\) | −64.6413 | −0.265408 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 347.959 | 1.32542 | 0.662708 | − | 0.748877i | \(-0.269407\pi\) | ||||
0.662708 | + | 0.748877i | \(0.269407\pi\) | |||||||
\(42\) | 33.6163 | 0.123503 | ||||||||
\(43\) | 194.823 | 0.690935 | 0.345468 | − | 0.938431i | \(-0.387720\pi\) | ||||
0.345468 | + | 0.938431i | \(0.387720\pi\) | |||||||
\(44\) | −150.606 | −0.516017 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −354.120 | −1.13505 | ||||||||
\(47\) | 14.5005 | 0.0450025 | 0.0225013 | − | 0.999747i | \(-0.492837\pi\) | ||||
0.0225013 | + | 0.999747i | \(0.492837\pi\) | |||||||
\(48\) | −23.1918 | −0.0697386 | ||||||||
\(49\) | −208.535 | −0.607973 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −88.6969 | −0.243531 | ||||||||
\(52\) | 178.384 | 0.475719 | ||||||||
\(53\) | 606.373 | 1.57154 | 0.785772 | − | 0.618517i | \(-0.212266\pi\) | ||||
0.785772 | + | 0.618517i | \(0.212266\pi\) | |||||||
\(54\) | 150.454 | 0.379152 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −92.7673 | −0.221367 | ||||||||
\(57\) | −92.4745 | −0.214887 | ||||||||
\(58\) | 58.0000 | 0.131306 | ||||||||
\(59\) | −702.372 | −1.54985 | −0.774925 | − | 0.632054i | \(-0.782212\pi\) | ||||
−0.774925 | + | 0.632054i | \(0.782212\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 543.394 | 1.14056 | 0.570282 | − | 0.821449i | \(-0.306834\pi\) | ||||
0.570282 | + | 0.821449i | \(0.306834\pi\) | |||||||
\(62\) | −467.989 | −0.958623 | ||||||||
\(63\) | 288.727 | 0.577399 | ||||||||
\(64\) | 64.0000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 109.151 | 0.203569 | ||||||||
\(67\) | 407.010 | 0.742152 | 0.371076 | − | 0.928602i | \(-0.378989\pi\) | ||||
0.371076 | + | 0.928602i | \(0.378989\pi\) | |||||||
\(68\) | 244.767 | 0.436506 | ||||||||
\(69\) | 256.647 | 0.447778 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 314.717 | 0.526057 | 0.263029 | − | 0.964788i | \(-0.415279\pi\) | ||||
0.263029 | + | 0.964788i | \(0.415279\pi\) | |||||||
\(72\) | −199.192 | −0.326041 | ||||||||
\(73\) | 859.110 | 1.37741 | 0.688707 | − | 0.725040i | \(-0.258179\pi\) | ||||
0.688707 | + | 0.725040i | \(0.258179\pi\) | |||||||
\(74\) | −20.4041 | −0.0320531 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 255.192 | 0.385165 | ||||||||
\(77\) | 436.604 | 0.646177 | ||||||||
\(78\) | −129.283 | −0.187672 | ||||||||
\(79\) | 725.266 | 1.03290 | 0.516448 | − | 0.856319i | \(-0.327254\pi\) | ||||
0.516448 | + | 0.856319i | \(0.327254\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 563.232 | 0.772609 | ||||||||
\(82\) | 695.918 | 0.937211 | ||||||||
\(83\) | 820.919 | 1.08563 | 0.542817 | − | 0.839851i | \(-0.317358\pi\) | ||||
0.542817 | + | 0.839851i | \(0.317358\pi\) | |||||||
\(84\) | 67.2327 | 0.0873296 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 389.646 | 0.488565 | ||||||||
\(87\) | −42.0352 | −0.0518005 | ||||||||
\(88\) | −301.212 | −0.364879 | ||||||||
\(89\) | −648.363 | −0.772206 | −0.386103 | − | 0.922456i | \(-0.626179\pi\) | ||||
−0.386103 | + | 0.922456i | \(0.626179\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −517.131 | −0.595714 | ||||||||
\(92\) | −708.241 | −0.802600 | ||||||||
\(93\) | 339.172 | 0.378178 | ||||||||
\(94\) | 29.0010 | 0.0318216 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −46.3837 | −0.0493126 | ||||||||
\(97\) | 60.9490 | 0.0637983 | 0.0318991 | − | 0.999491i | \(-0.489844\pi\) | ||||
0.0318991 | + | 0.999491i | \(0.489844\pi\) | |||||||
\(98\) | −417.069 | −0.429902 | ||||||||
\(99\) | 937.485 | 0.951725 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1100.16 | 1.08386 | 0.541930 | − | 0.840423i | \(-0.317694\pi\) | ||||
0.541930 | + | 0.840423i | \(0.317694\pi\) | |||||||
\(102\) | −177.394 | −0.172202 | ||||||||
\(103\) | −747.930 | −0.715492 | −0.357746 | − | 0.933819i | \(-0.616455\pi\) | ||||
−0.357746 | + | 0.933819i | \(0.616455\pi\) | |||||||
\(104\) | 356.767 | 0.336384 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1212.75 | 1.11125 | ||||||||
\(107\) | −176.059 | −0.159068 | −0.0795340 | − | 0.996832i | \(-0.525343\pi\) | ||||
−0.0795340 | + | 0.996832i | \(0.525343\pi\) | |||||||
\(108\) | 300.908 | 0.268101 | ||||||||
\(109\) | 173.856 | 0.152774 | 0.0763871 | − | 0.997078i | \(-0.475662\pi\) | ||||
0.0763871 | + | 0.997078i | \(0.475662\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 14.7878 | 0.0126450 | ||||||||
\(112\) | −185.535 | −0.156530 | ||||||||
\(113\) | 1707.65 | 1.42161 | 0.710807 | − | 0.703387i | \(-0.248330\pi\) | ||||
0.710807 | + | 0.703387i | \(0.248330\pi\) | |||||||
\(114\) | −184.949 | −0.151948 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 116.000 | 0.0928477 | ||||||||
\(117\) | −1110.39 | −0.877400 | ||||||||
\(118\) | −1404.74 | −1.09591 | ||||||||
\(119\) | −709.576 | −0.546611 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 86.6378 | 0.0650922 | ||||||||
\(122\) | 1086.79 | 0.806501 | ||||||||
\(123\) | −504.363 | −0.369731 | ||||||||
\(124\) | −935.978 | −0.677849 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 577.453 | 0.408283 | ||||||||
\(127\) | 881.473 | 0.615891 | 0.307945 | − | 0.951404i | \(-0.400359\pi\) | ||||
0.307945 | + | 0.951404i | \(0.400359\pi\) | |||||||
\(128\) | 128.000 | 0.0883883 | ||||||||
\(129\) | −282.394 | −0.192739 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2025.49 | 1.35090 | 0.675451 | − | 0.737405i | \(-0.263949\pi\) | ||||
0.675451 | + | 0.737405i | \(0.263949\pi\) | |||||||
\(132\) | 218.302 | 0.143945 | ||||||||
\(133\) | −739.796 | −0.482319 | ||||||||
\(134\) | 814.020 | 0.524781 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 489.535 | 0.308656 | ||||||||
\(137\) | −1594.32 | −0.994248 | −0.497124 | − | 0.867679i | \(-0.665611\pi\) | ||||
−0.497124 | + | 0.867679i | \(0.665611\pi\) | |||||||
\(138\) | 513.294 | 0.316627 | ||||||||
\(139\) | −2855.40 | −1.74239 | −0.871195 | − | 0.490938i | \(-0.836654\pi\) | ||||
−0.871195 | + | 0.490938i | \(0.836654\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −21.0183 | −0.0125536 | ||||||||
\(142\) | 629.435 | 0.371979 | ||||||||
\(143\) | −1679.10 | −0.981915 | ||||||||
\(144\) | −398.384 | −0.230546 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 1718.22 | 0.973979 | ||||||||
\(147\) | 302.269 | 0.169597 | ||||||||
\(148\) | −40.8082 | −0.0226649 | ||||||||
\(149\) | −18.3755 | −0.0101032 | −0.00505162 | − | 0.999987i | \(-0.501608\pi\) | ||||
−0.00505162 | + | 0.999987i | \(0.501608\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −778.806 | −0.419724 | −0.209862 | − | 0.977731i | \(-0.567301\pi\) | ||||
−0.209862 | + | 0.977731i | \(0.567301\pi\) | |||||||
\(152\) | 510.384 | 0.272353 | ||||||||
\(153\) | −1523.61 | −0.805078 | ||||||||
\(154\) | 873.208 | 0.456916 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −258.565 | −0.132704 | ||||||||
\(157\) | 511.896 | 0.260215 | 0.130107 | − | 0.991500i | \(-0.458468\pi\) | ||||
0.130107 | + | 0.991500i | \(0.458468\pi\) | |||||||
\(158\) | 1450.53 | 0.730368 | ||||||||
\(159\) | −878.932 | −0.438389 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2053.18 | 1.00505 | ||||||||
\(162\) | 1126.46 | 0.546317 | ||||||||
\(163\) | 1451.59 | 0.697529 | 0.348764 | − | 0.937210i | \(-0.386601\pi\) | ||||
0.348764 | + | 0.937210i | \(0.386601\pi\) | |||||||
\(164\) | 1391.84 | 0.662708 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 1641.84 | 0.767659 | ||||||||
\(167\) | −600.374 | −0.278194 | −0.139097 | − | 0.990279i | \(-0.544420\pi\) | ||||
−0.139097 | + | 0.990279i | \(0.544420\pi\) | |||||||
\(168\) | 134.465 | 0.0617513 | ||||||||
\(169\) | −208.204 | −0.0947675 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1588.50 | −0.710386 | ||||||||
\(172\) | 779.292 | 0.345468 | ||||||||
\(173\) | 2574.20 | 1.13129 | 0.565644 | − | 0.824650i | \(-0.308628\pi\) | ||||
0.565644 | + | 0.824650i | \(0.308628\pi\) | |||||||
\(174\) | −84.0704 | −0.0366285 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −602.424 | −0.258008 | ||||||||
\(177\) | 1018.08 | 0.432337 | ||||||||
\(178\) | −1296.73 | −0.546032 | ||||||||
\(179\) | 3828.72 | 1.59872 | 0.799362 | − | 0.600850i | \(-0.205171\pi\) | ||||
0.799362 | + | 0.600850i | \(0.205171\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2075.64 | 0.852381 | 0.426190 | − | 0.904633i | \(-0.359855\pi\) | ||||
0.426190 | + | 0.904633i | \(0.359855\pi\) | |||||||
\(182\) | −1034.26 | −0.421234 | ||||||||
\(183\) | −787.644 | −0.318166 | ||||||||
\(184\) | −1416.48 | −0.567524 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 678.345 | 0.267412 | ||||||||
\(187\) | −2303.97 | −0.900977 | ||||||||
\(188\) | 58.0021 | 0.0225013 | ||||||||
\(189\) | −872.327 | −0.335727 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 4070.08 | 1.54189 | 0.770944 | − | 0.636902i | \(-0.219785\pi\) | ||||
0.770944 | + | 0.636902i | \(0.219785\pi\) | |||||||
\(192\) | −92.7673 | −0.0348693 | ||||||||
\(193\) | −2373.24 | −0.885129 | −0.442565 | − | 0.896737i | \(-0.645931\pi\) | ||||
−0.442565 | + | 0.896737i | \(0.645931\pi\) | |||||||
\(194\) | 121.898 | 0.0451122 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −834.139 | −0.303986 | ||||||||
\(197\) | 3108.58 | 1.12425 | 0.562125 | − | 0.827052i | \(-0.309984\pi\) | ||||
0.562125 | + | 0.827052i | \(0.309984\pi\) | |||||||
\(198\) | 1874.97 | 0.672971 | ||||||||
\(199\) | −4048.30 | −1.44209 | −0.721046 | − | 0.692887i | \(-0.756338\pi\) | ||||
−0.721046 | + | 0.692887i | \(0.756338\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −589.957 | −0.207027 | ||||||||
\(202\) | 2200.32 | 0.766405 | ||||||||
\(203\) | −336.282 | −0.116268 | ||||||||
\(204\) | −354.788 | −0.121765 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −1495.86 | −0.505929 | ||||||||
\(207\) | 4408.62 | 1.48029 | ||||||||
\(208\) | 713.535 | 0.237859 | ||||||||
\(209\) | −2402.09 | −0.795005 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3591.66 | 1.17185 | 0.585924 | − | 0.810366i | \(-0.300732\pi\) | ||||
0.585924 | + | 0.810366i | \(0.300732\pi\) | |||||||
\(212\) | 2425.49 | 0.785772 | ||||||||
\(213\) | −456.180 | −0.146746 | ||||||||
\(214\) | −352.118 | −0.112478 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 601.816 | 0.189576 | ||||||||
\(217\) | 2713.38 | 0.848830 | ||||||||
\(218\) | 347.712 | 0.108028 | ||||||||
\(219\) | −1245.27 | −0.384236 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2728.91 | 0.830616 | ||||||||
\(222\) | 29.5755 | 0.00894134 | ||||||||
\(223\) | 772.085 | 0.231850 | 0.115925 | − | 0.993258i | \(-0.463017\pi\) | ||||
0.115925 | + | 0.993258i | \(0.463017\pi\) | |||||||
\(224\) | −371.069 | −0.110684 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 3415.31 | 1.00523 | ||||||||
\(227\) | 4435.16 | 1.29679 | 0.648397 | − | 0.761303i | \(-0.275440\pi\) | ||||
0.648397 | + | 0.761303i | \(0.275440\pi\) | |||||||
\(228\) | −369.898 | −0.107443 | ||||||||
\(229\) | 2213.12 | 0.638634 | 0.319317 | − | 0.947648i | \(-0.396546\pi\) | ||||
0.319317 | + | 0.947648i | \(0.396546\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −632.853 | −0.180254 | ||||||||
\(232\) | 232.000 | 0.0656532 | ||||||||
\(233\) | 2980.41 | 0.837998 | 0.418999 | − | 0.907987i | \(-0.362381\pi\) | ||||
0.418999 | + | 0.907987i | \(0.362381\pi\) | |||||||
\(234\) | −2220.79 | −0.620416 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −2809.49 | −0.774925 | ||||||||
\(237\) | −1051.27 | −0.288131 | ||||||||
\(238\) | −1419.15 | −0.386512 | ||||||||
\(239\) | −557.093 | −0.150775 | −0.0753877 | − | 0.997154i | \(-0.524019\pi\) | ||||
−0.0753877 | + | 0.997154i | \(0.524019\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −4168.65 | −1.11422 | −0.557109 | − | 0.830439i | \(-0.688089\pi\) | ||||
−0.557109 | + | 0.830439i | \(0.688089\pi\) | |||||||
\(242\) | 173.276 | 0.0460272 | ||||||||
\(243\) | −2847.53 | −0.751724 | ||||||||
\(244\) | 2173.58 | 0.570282 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −1008.73 | −0.261439 | ||||||||
\(247\) | 2845.13 | 0.732920 | ||||||||
\(248\) | −1871.96 | −0.479312 | ||||||||
\(249\) | −1189.91 | −0.302842 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −7132.56 | −1.79364 | −0.896819 | − | 0.442398i | \(-0.854128\pi\) | ||||
−0.896819 | + | 0.442398i | \(0.854128\pi\) | |||||||
\(252\) | 1154.91 | 0.288699 | ||||||||
\(253\) | 6666.59 | 1.65662 | ||||||||
\(254\) | 1762.95 | 0.435501 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 256.000 | 0.0625000 | ||||||||
\(257\) | −5564.76 | −1.35066 | −0.675331 | − | 0.737514i | \(-0.735999\pi\) | ||||
−0.675331 | + | 0.737514i | \(0.735999\pi\) | |||||||
\(258\) | −564.788 | −0.136287 | ||||||||
\(259\) | 118.302 | 0.0283820 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −722.070 | −0.171245 | ||||||||
\(262\) | 4050.98 | 0.955231 | ||||||||
\(263\) | −7188.72 | −1.68546 | −0.842729 | − | 0.538338i | \(-0.819053\pi\) | ||||
−0.842729 | + | 0.538338i | \(0.819053\pi\) | |||||||
\(264\) | 436.604 | 0.101785 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −1479.59 | −0.341051 | ||||||||
\(267\) | 939.796 | 0.215410 | ||||||||
\(268\) | 1628.04 | 0.371076 | ||||||||
\(269\) | 3184.38 | 0.721765 | 0.360883 | − | 0.932611i | \(-0.382476\pi\) | ||||
0.360883 | + | 0.932611i | \(0.382476\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1732.34 | 0.388311 | 0.194155 | − | 0.980971i | \(-0.437803\pi\) | ||||
0.194155 | + | 0.980971i | \(0.437803\pi\) | |||||||
\(272\) | 979.069 | 0.218253 | ||||||||
\(273\) | 749.576 | 0.166177 | ||||||||
\(274\) | −3188.64 | −0.703040 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 1026.59 | 0.223889 | ||||||||
\(277\) | −6061.31 | −1.31476 | −0.657381 | − | 0.753558i | \(-0.728336\pi\) | ||||
−0.657381 | + | 0.753558i | \(0.728336\pi\) | |||||||
\(278\) | −5710.81 | −1.23206 | ||||||||
\(279\) | 5826.22 | 1.25020 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 6183.75 | 1.31278 | 0.656391 | − | 0.754421i | \(-0.272082\pi\) | ||||
0.656391 | + | 0.754421i | \(0.272082\pi\) | |||||||
\(282\) | −42.0367 | −0.00887677 | ||||||||
\(283\) | 9076.75 | 1.90656 | 0.953281 | − | 0.302086i | \(-0.0976829\pi\) | ||||
0.953281 | + | 0.302086i | \(0.0976829\pi\) | |||||||
\(284\) | 1258.87 | 0.263029 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −3358.21 | −0.694318 | ||||||||
\(287\) | −4034.91 | −0.829871 | ||||||||
\(288\) | −796.767 | −0.163021 | ||||||||
\(289\) | −1168.56 | −0.237850 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −88.3449 | −0.0177968 | ||||||||
\(292\) | 3436.44 | 0.688707 | ||||||||
\(293\) | 3636.66 | 0.725105 | 0.362553 | − | 0.931963i | \(-0.381905\pi\) | ||||
0.362553 | + | 0.931963i | \(0.381905\pi\) | |||||||
\(294\) | 604.538 | 0.119923 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −81.6163 | −0.0160265 | ||||||||
\(297\) | −2832.41 | −0.553378 | ||||||||
\(298\) | −36.7511 | −0.00714407 | ||||||||
\(299\) | −7896.16 | −1.52725 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2259.15 | −0.432609 | ||||||||
\(302\) | −1557.61 | −0.296790 | ||||||||
\(303\) | −1594.67 | −0.302348 | ||||||||
\(304\) | 1020.77 | 0.192582 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −3047.23 | −0.569276 | ||||||||
\(307\) | 4619.06 | 0.858708 | 0.429354 | − | 0.903136i | \(-0.358741\pi\) | ||||
0.429354 | + | 0.903136i | \(0.358741\pi\) | |||||||
\(308\) | 1746.42 | 0.323089 | ||||||||
\(309\) | 1084.12 | 0.199590 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 8094.07 | 1.47580 | 0.737898 | − | 0.674912i | \(-0.235818\pi\) | ||||
0.737898 | + | 0.674912i | \(0.235818\pi\) | |||||||
\(312\) | −517.131 | −0.0938358 | ||||||||
\(313\) | −6901.79 | −1.24637 | −0.623183 | − | 0.782076i | \(-0.714161\pi\) | ||||
−0.623183 | + | 0.782076i | \(0.714161\pi\) | |||||||
\(314\) | 1023.79 | 0.184000 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 2901.06 | 0.516448 | ||||||||
\(317\) | 6119.75 | 1.08429 | 0.542144 | − | 0.840286i | \(-0.317613\pi\) | ||||
0.542144 | + | 0.840286i | \(0.317613\pi\) | |||||||
\(318\) | −1757.86 | −0.309988 | ||||||||
\(319\) | −1091.89 | −0.191644 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 255.196 | 0.0443727 | ||||||||
\(322\) | 4106.35 | 0.710677 | ||||||||
\(323\) | 3903.91 | 0.672506 | ||||||||
\(324\) | 2252.93 | 0.386304 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 2903.18 | 0.493227 | ||||||||
\(327\) | −252.003 | −0.0426171 | ||||||||
\(328\) | 2783.67 | 0.468606 | ||||||||
\(329\) | −168.147 | −0.0281770 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 198.924 | 0.0330328 | 0.0165164 | − | 0.999864i | \(-0.494742\pi\) | ||||
0.0165164 | + | 0.999864i | \(0.494742\pi\) | |||||||
\(332\) | 3283.68 | 0.542817 | ||||||||
\(333\) | 254.020 | 0.0418025 | ||||||||
\(334\) | −1200.75 | −0.196713 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 268.931 | 0.0436648 | ||||||||
\(337\) | −2102.43 | −0.339841 | −0.169921 | − | 0.985458i | \(-0.554351\pi\) | ||||
−0.169921 | + | 0.985458i | \(0.554351\pi\) | |||||||
\(338\) | −416.408 | −0.0670107 | ||||||||
\(339\) | −2475.23 | −0.396566 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 8810.25 | 1.39912 | ||||||||
\(342\) | −3177.01 | −0.502318 | ||||||||
\(343\) | 6395.55 | 1.00679 | ||||||||
\(344\) | 1558.58 | 0.244283 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 5148.40 | 0.799941 | ||||||||
\(347\) | −6543.83 | −1.01237 | −0.506183 | − | 0.862426i | \(-0.668944\pi\) | ||||
−0.506183 | + | 0.862426i | \(0.668944\pi\) | |||||||
\(348\) | −168.141 | −0.0259003 | ||||||||
\(349\) | 793.427 | 0.121694 | 0.0608469 | − | 0.998147i | \(-0.480620\pi\) | ||||
0.0608469 | + | 0.998147i | \(0.480620\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 3354.82 | 0.510162 | ||||||||
\(352\) | −1204.85 | −0.182439 | ||||||||
\(353\) | −7378.84 | −1.11257 | −0.556284 | − | 0.830992i | \(-0.687773\pi\) | ||||
−0.556284 | + | 0.830992i | \(0.687773\pi\) | |||||||
\(354\) | 2036.16 | 0.305709 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −2593.45 | −0.386103 | ||||||||
\(357\) | 1028.52 | 0.152479 | ||||||||
\(358\) | 7657.43 | 1.13047 | ||||||||
\(359\) | −7142.97 | −1.05012 | −0.525058 | − | 0.851066i | \(-0.675956\pi\) | ||||
−0.525058 | + | 0.851066i | \(0.675956\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2788.82 | −0.406593 | ||||||||
\(362\) | 4151.28 | 0.602724 | ||||||||
\(363\) | −125.581 | −0.0181578 | ||||||||
\(364\) | −2068.52 | −0.297857 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −1575.29 | −0.224977 | ||||||||
\(367\) | 1806.47 | 0.256940 | 0.128470 | − | 0.991713i | \(-0.458993\pi\) | ||||
0.128470 | + | 0.991713i | \(0.458993\pi\) | |||||||
\(368\) | −2832.96 | −0.401300 | ||||||||
\(369\) | −8663.83 | −1.22228 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −7031.46 | −0.983976 | ||||||||
\(372\) | 1356.69 | 0.189089 | ||||||||
\(373\) | −9396.05 | −1.30431 | −0.652157 | − | 0.758084i | \(-0.726136\pi\) | ||||
−0.652157 | + | 0.758084i | \(0.726136\pi\) | |||||||
\(374\) | −4607.93 | −0.637087 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 116.004 | 0.0159108 | ||||||||
\(377\) | 1293.28 | 0.176677 | ||||||||
\(378\) | −1744.65 | −0.237395 | ||||||||
\(379\) | −421.482 | −0.0571242 | −0.0285621 | − | 0.999592i | \(-0.509093\pi\) | ||||
−0.0285621 | + | 0.999592i | \(0.509093\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1277.69 | −0.171805 | ||||||||
\(382\) | 8140.16 | 1.09028 | ||||||||
\(383\) | −3189.84 | −0.425570 | −0.212785 | − | 0.977099i | \(-0.568253\pi\) | ||||
−0.212785 | + | 0.977099i | \(0.568253\pi\) | |||||||
\(384\) | −185.535 | −0.0246563 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −4746.49 | −0.625881 | ||||||||
\(387\) | −4850.89 | −0.637170 | ||||||||
\(388\) | 243.796 | 0.0318991 | ||||||||
\(389\) | −4110.96 | −0.535820 | −0.267910 | − | 0.963444i | \(-0.586333\pi\) | ||||
−0.267910 | + | 0.963444i | \(0.586333\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −10834.6 | −1.40136 | ||||||||
\(392\) | −1668.28 | −0.214951 | ||||||||
\(393\) | −2935.93 | −0.376840 | ||||||||
\(394\) | 6217.17 | 0.794965 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 3749.94 | 0.475862 | ||||||||
\(397\) | 827.505 | 0.104613 | 0.0523064 | − | 0.998631i | \(-0.483343\pi\) | ||||
0.0523064 | + | 0.998631i | \(0.483343\pi\) | |||||||
\(398\) | −8096.60 | −1.01971 | ||||||||
\(399\) | 1072.33 | 0.134545 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 675.145 | 0.0840776 | 0.0420388 | − | 0.999116i | \(-0.486615\pi\) | ||||
0.0420388 | + | 0.999116i | \(0.486615\pi\) | |||||||
\(402\) | −1179.91 | −0.146390 | ||||||||
\(403\) | −10435.2 | −1.28986 | ||||||||
\(404\) | 4400.64 | 0.541930 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −672.563 | −0.0822137 | ||||||||
\(407\) | 384.122 | 0.0467819 | ||||||||
\(408\) | −709.576 | −0.0861010 | ||||||||
\(409\) | 764.847 | 0.0924676 | 0.0462338 | − | 0.998931i | \(-0.485278\pi\) | ||||
0.0462338 | + | 0.998931i | \(0.485278\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 2310.95 | 0.277350 | ||||||||
\(412\) | −2991.72 | −0.357746 | ||||||||
\(413\) | 8144.65 | 0.970393 | ||||||||
\(414\) | 8817.24 | 1.04672 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 1427.07 | 0.168192 | ||||||||
\(417\) | 4138.88 | 0.486047 | ||||||||
\(418\) | −4804.18 | −0.562154 | ||||||||
\(419\) | −2573.33 | −0.300037 | −0.150019 | − | 0.988683i | \(-0.547933\pi\) | ||||
−0.150019 | + | 0.988683i | \(0.547933\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 14287.4 | 1.65398 | 0.826992 | − | 0.562213i | \(-0.190050\pi\) | ||||
0.826992 | + | 0.562213i | \(0.190050\pi\) | |||||||
\(422\) | 7183.32 | 0.828622 | ||||||||
\(423\) | −361.048 | −0.0415006 | ||||||||
\(424\) | 4850.99 | 0.555625 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −912.359 | −0.103765 | ||||||||
\(427\) | −6301.15 | −0.714131 | ||||||||
\(428\) | −704.237 | −0.0795340 | ||||||||
\(429\) | 2433.84 | 0.273909 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −11283.2 | −1.26100 | −0.630500 | − | 0.776189i | \(-0.717150\pi\) | ||||
−0.630500 | + | 0.776189i | \(0.717150\pi\) | |||||||
\(432\) | 1203.63 | 0.134050 | ||||||||
\(433\) | −8069.64 | −0.895617 | −0.447809 | − | 0.894129i | \(-0.647795\pi\) | ||||
−0.447809 | + | 0.894129i | \(0.647795\pi\) | |||||||
\(434\) | 5426.76 | 0.600214 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 695.424 | 0.0763871 | ||||||||
\(437\) | −11296.1 | −1.23653 | ||||||||
\(438\) | −2490.54 | −0.271696 | ||||||||
\(439\) | −7819.42 | −0.850116 | −0.425058 | − | 0.905166i | \(-0.639746\pi\) | ||||
−0.425058 | + | 0.905166i | \(0.639746\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 5192.30 | 0.560663 | ||||||||
\(442\) | 5457.81 | 0.587334 | ||||||||
\(443\) | 10153.4 | 1.08894 | 0.544472 | − | 0.838779i | \(-0.316730\pi\) | ||||
0.544472 | + | 0.838779i | \(0.316730\pi\) | |||||||
\(444\) | 59.1510 | 0.00632248 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 1544.17 | 0.163943 | ||||||||
\(447\) | 26.6351 | 0.00281834 | ||||||||
\(448\) | −742.139 | −0.0782651 | ||||||||
\(449\) | 13608.3 | 1.43033 | 0.715163 | − | 0.698958i | \(-0.246353\pi\) | ||||
0.715163 | + | 0.698958i | \(0.246353\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −13101.2 | −1.36787 | ||||||||
\(452\) | 6830.61 | 0.710807 | ||||||||
\(453\) | 1128.87 | 0.117084 | ||||||||
\(454\) | 8870.32 | 0.916971 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −739.796 | −0.0759739 | ||||||||
\(457\) | 1882.55 | 0.192696 | 0.0963479 | − | 0.995348i | \(-0.469284\pi\) | ||||
0.0963479 | + | 0.995348i | \(0.469284\pi\) | |||||||
\(458\) | 4426.24 | 0.451583 | ||||||||
\(459\) | 4603.28 | 0.468111 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −13947.2 | −1.40908 | −0.704542 | − | 0.709662i | \(-0.748847\pi\) | ||||
−0.704542 | + | 0.709662i | \(0.748847\pi\) | |||||||
\(462\) | −1265.71 | −0.127459 | ||||||||
\(463\) | 12454.8 | 1.25016 | 0.625079 | − | 0.780562i | \(-0.285067\pi\) | ||||
0.625079 | + | 0.780562i | \(0.285067\pi\) | |||||||
\(464\) | 464.000 | 0.0464238 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 5960.83 | 0.592554 | ||||||||
\(467\) | 6561.59 | 0.650180 | 0.325090 | − | 0.945683i | \(-0.394605\pi\) | ||||
0.325090 | + | 0.945683i | \(0.394605\pi\) | |||||||
\(468\) | −4441.57 | −0.438700 | ||||||||
\(469\) | −4719.66 | −0.464677 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −741.988 | −0.0725881 | ||||||||
\(472\) | −5618.98 | −0.547954 | ||||||||
\(473\) | −7335.38 | −0.713068 | ||||||||
\(474\) | −2102.53 | −0.203739 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −2838.30 | −0.273305 | ||||||||
\(477\) | −15098.1 | −1.44925 | ||||||||
\(478\) | −1114.19 | −0.106614 | ||||||||
\(479\) | −17407.5 | −1.66048 | −0.830240 | − | 0.557406i | \(-0.811797\pi\) | ||||
−0.830240 | + | 0.557406i | \(0.811797\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −454.969 | −0.0431285 | ||||||||
\(482\) | −8337.31 | −0.787871 | ||||||||
\(483\) | −2976.06 | −0.280363 | ||||||||
\(484\) | 346.551 | 0.0325461 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −5695.06 | −0.531549 | ||||||||
\(487\) | 2544.79 | 0.236787 | 0.118393 | − | 0.992967i | \(-0.462226\pi\) | ||||
0.118393 | + | 0.992967i | \(0.462226\pi\) | |||||||
\(488\) | 4347.15 | 0.403251 | ||||||||
\(489\) | −2104.06 | −0.194579 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 2712.89 | 0.249351 | 0.124675 | − | 0.992198i | \(-0.460211\pi\) | ||||
0.124675 | + | 0.992198i | \(0.460211\pi\) | |||||||
\(492\) | −2017.45 | −0.184865 | ||||||||
\(493\) | 1774.56 | 0.162114 | ||||||||
\(494\) | 5690.26 | 0.518253 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −3743.91 | −0.338924 | ||||||||
\(497\) | −3649.44 | −0.329375 | ||||||||
\(498\) | −2379.83 | −0.214142 | ||||||||
\(499\) | 4583.79 | 0.411220 | 0.205610 | − | 0.978634i | \(-0.434082\pi\) | ||||
0.205610 | + | 0.978634i | \(0.434082\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 870.237 | 0.0776034 | ||||||||
\(502\) | −14265.1 | −1.26829 | ||||||||
\(503\) | 1950.19 | 0.172872 | 0.0864359 | − | 0.996257i | \(-0.472452\pi\) | ||||
0.0864359 | + | 0.996257i | \(0.472452\pi\) | |||||||
\(504\) | 2309.81 | 0.204141 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 13333.2 | 1.17141 | ||||||||
\(507\) | 301.790 | 0.0264358 | ||||||||
\(508\) | 3525.89 | 0.307945 | ||||||||
\(509\) | −8853.80 | −0.770997 | −0.385499 | − | 0.922708i | \(-0.625971\pi\) | ||||
−0.385499 | + | 0.922708i | \(0.625971\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −9962.17 | −0.862428 | ||||||||
\(512\) | 512.000 | 0.0441942 | ||||||||
\(513\) | 4799.33 | 0.413052 | ||||||||
\(514\) | −11129.5 | −0.955063 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −1129.58 | −0.0963697 | ||||||||
\(517\) | −545.967 | −0.0464441 | ||||||||
\(518\) | 236.604 | 0.0200691 | ||||||||
\(519\) | −3731.28 | −0.315578 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −19939.5 | −1.67671 | −0.838355 | − | 0.545125i | \(-0.816482\pi\) | ||||
−0.838355 | + | 0.545125i | \(0.816482\pi\) | |||||||
\(522\) | −1444.14 | −0.121089 | ||||||||
\(523\) | 12185.8 | 1.01883 | 0.509416 | − | 0.860520i | \(-0.329862\pi\) | ||||
0.509416 | + | 0.860520i | \(0.329862\pi\) | |||||||
\(524\) | 8101.97 | 0.675451 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −14377.4 | −1.19180 | ||||||||
\(527\) | −14318.5 | −1.18354 | ||||||||
\(528\) | 873.208 | 0.0719725 | ||||||||
\(529\) | 19183.3 | 1.57667 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 17488.4 | 1.42925 | ||||||||
\(532\) | −2959.18 | −0.241160 | ||||||||
\(533\) | 15517.6 | 1.26105 | ||||||||
\(534\) | 1879.59 | 0.152318 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 3256.08 | 0.262390 | ||||||||
\(537\) | −5549.68 | −0.445971 | ||||||||
\(538\) | 6368.75 | 0.510365 | ||||||||
\(539\) | 7851.65 | 0.627448 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 700.188 | 0.0556440 | 0.0278220 | − | 0.999613i | \(-0.491143\pi\) | ||||
0.0278220 | + | 0.999613i | \(0.491143\pi\) | |||||||
\(542\) | 3464.68 | 0.274577 | ||||||||
\(543\) | −3008.62 | −0.237775 | ||||||||
\(544\) | 1958.14 | 0.154328 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 1499.15 | 0.117505 | ||||||||
\(547\) | −10664.2 | −0.833576 | −0.416788 | − | 0.909004i | \(-0.636844\pi\) | ||||
−0.416788 | + | 0.909004i | \(0.636844\pi\) | |||||||
\(548\) | −6377.28 | −0.497124 | ||||||||
\(549\) | −13530.0 | −1.05181 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1850.14 | 0.143047 | ||||||||
\(552\) | 2053.18 | 0.158313 | ||||||||
\(553\) | −8410.12 | −0.646718 | ||||||||
\(554\) | −12122.6 | −0.929677 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −11421.6 | −0.871195 | ||||||||
\(557\) | −8410.60 | −0.639800 | −0.319900 | − | 0.947451i | \(-0.603649\pi\) | ||||
−0.319900 | + | 0.947451i | \(0.603649\pi\) | |||||||
\(558\) | 11652.4 | 0.884027 | ||||||||
\(559\) | 8688.31 | 0.657382 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 3339.58 | 0.251332 | ||||||||
\(562\) | 12367.5 | 0.928277 | ||||||||
\(563\) | −8770.15 | −0.656515 | −0.328257 | − | 0.944588i | \(-0.606461\pi\) | ||||
−0.328257 | + | 0.944588i | \(0.606461\pi\) | |||||||
\(564\) | −84.0734 | −0.00627682 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 18153.5 | 1.34814 | ||||||||
\(567\) | −6531.19 | −0.483746 | ||||||||
\(568\) | 2517.74 | 0.185989 | ||||||||
\(569\) | −10493.4 | −0.773125 | −0.386562 | − | 0.922263i | \(-0.626338\pi\) | ||||
−0.386562 | + | 0.922263i | \(0.626338\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −2517.50 | −0.184508 | −0.0922542 | − | 0.995735i | \(-0.529407\pi\) | ||||
−0.0922542 | + | 0.995735i | \(0.529407\pi\) | |||||||
\(572\) | −6716.42 | −0.490957 | ||||||||
\(573\) | −5899.54 | −0.430117 | ||||||||
\(574\) | −8069.81 | −0.586807 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −1593.53 | −0.115273 | ||||||||
\(577\) | −1394.88 | −0.100641 | −0.0503203 | − | 0.998733i | \(-0.516024\pi\) | ||||
−0.0503203 | + | 0.998733i | \(0.516024\pi\) | |||||||
\(578\) | −2337.12 | −0.168186 | ||||||||
\(579\) | 3439.99 | 0.246911 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −9519.31 | −0.679738 | ||||||||
\(582\) | −176.690 | −0.0125842 | ||||||||
\(583\) | −22830.9 | −1.62188 | ||||||||
\(584\) | 6872.88 | 0.486989 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 7273.31 | 0.512727 | ||||||||
\(587\) | −24391.0 | −1.71504 | −0.857518 | − | 0.514455i | \(-0.827994\pi\) | ||||
−0.857518 | + | 0.514455i | \(0.827994\pi\) | |||||||
\(588\) | 1209.08 | 0.0847984 | ||||||||
\(589\) | −14928.4 | −1.04433 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −4505.86 | −0.313615 | ||||||||
\(592\) | −163.233 | −0.0113325 | ||||||||
\(593\) | 16089.4 | 1.11418 | 0.557092 | − | 0.830451i | \(-0.311917\pi\) | ||||
0.557092 | + | 0.830451i | \(0.311917\pi\) | |||||||
\(594\) | −5664.83 | −0.391297 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −73.5021 | −0.00505162 | ||||||||
\(597\) | 5867.97 | 0.402278 | ||||||||
\(598\) | −15792.3 | −1.07993 | ||||||||
\(599\) | −19228.2 | −1.31159 | −0.655796 | − | 0.754938i | \(-0.727667\pi\) | ||||
−0.655796 | + | 0.754938i | \(0.727667\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −2345.94 | −0.159223 | −0.0796115 | − | 0.996826i | \(-0.525368\pi\) | ||||
−0.0796115 | + | 0.996826i | \(0.525368\pi\) | |||||||
\(602\) | −4518.30 | −0.305901 | ||||||||
\(603\) | −10134.1 | −0.684401 | ||||||||
\(604\) | −3115.22 | −0.209862 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −3189.34 | −0.213792 | ||||||||
\(607\) | 4621.11 | 0.309004 | 0.154502 | − | 0.987993i | \(-0.450623\pi\) | ||||
0.154502 | + | 0.987993i | \(0.450623\pi\) | |||||||
\(608\) | 2041.53 | 0.136176 | ||||||||
\(609\) | 487.437 | 0.0324334 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 646.664 | 0.0428170 | ||||||||
\(612\) | −6094.46 | −0.402539 | ||||||||
\(613\) | 10464.8 | 0.689511 | 0.344755 | − | 0.938693i | \(-0.387962\pi\) | ||||
0.344755 | + | 0.938693i | \(0.387962\pi\) | |||||||
\(614\) | 9238.11 | 0.607198 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 3492.83 | 0.228458 | ||||||||
\(617\) | 11873.3 | 0.774718 | 0.387359 | − | 0.921929i | \(-0.373387\pi\) | ||||
0.387359 | + | 0.921929i | \(0.373387\pi\) | |||||||
\(618\) | 2168.23 | 0.141131 | ||||||||
\(619\) | 13102.2 | 0.850762 | 0.425381 | − | 0.905014i | \(-0.360140\pi\) | ||||
0.425381 | + | 0.905014i | \(0.360140\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −13319.7 | −0.860711 | ||||||||
\(622\) | 16188.1 | 1.04355 | ||||||||
\(623\) | 7518.37 | 0.483494 | ||||||||
\(624\) | −1034.26 | −0.0663519 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −13803.6 | −0.881313 | ||||||||
\(627\) | 3481.81 | 0.221770 | ||||||||
\(628\) | 2047.58 | 0.130107 | ||||||||
\(629\) | −624.282 | −0.0395735 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 12279.7 | 0.774719 | 0.387359 | − | 0.921929i | \(-0.373387\pi\) | ||||
0.387359 | + | 0.921929i | \(0.373387\pi\) | |||||||
\(632\) | 5802.13 | 0.365184 | ||||||||
\(633\) | −5206.07 | −0.326892 | ||||||||
\(634\) | 12239.5 | 0.766707 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −3515.73 | −0.219195 | ||||||||
\(637\) | −9299.80 | −0.578448 | ||||||||
\(638\) | −2183.79 | −0.135513 | ||||||||
\(639\) | −7836.14 | −0.485122 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 17054.4 | 1.05087 | 0.525435 | − | 0.850834i | \(-0.323903\pi\) | ||||
0.525435 | + | 0.850834i | \(0.323903\pi\) | |||||||
\(642\) | 510.392 | 0.0313763 | ||||||||
\(643\) | 20697.3 | 1.26940 | 0.634698 | − | 0.772761i | \(-0.281125\pi\) | ||||
0.634698 | + | 0.772761i | \(0.281125\pi\) | |||||||
\(644\) | 8212.70 | 0.502525 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 7807.83 | 0.475534 | ||||||||
\(647\) | 10613.6 | 0.644924 | 0.322462 | − | 0.946582i | \(-0.395490\pi\) | ||||
0.322462 | + | 0.946582i | \(0.395490\pi\) | |||||||
\(648\) | 4505.85 | 0.273158 | ||||||||
\(649\) | 26445.4 | 1.59950 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −3933.02 | −0.236785 | ||||||||
\(652\) | 5806.35 | 0.348764 | ||||||||
\(653\) | 10019.4 | 0.600441 | 0.300220 | − | 0.953870i | \(-0.402940\pi\) | ||||
0.300220 | + | 0.953870i | \(0.402940\pi\) | |||||||
\(654\) | −504.005 | −0.0301348 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 5567.35 | 0.331354 | ||||||||
\(657\) | −21391.0 | −1.27023 | ||||||||
\(658\) | −336.294 | −0.0199241 | ||||||||
\(659\) | 2400.70 | 0.141909 | 0.0709545 | − | 0.997480i | \(-0.477395\pi\) | ||||
0.0709545 | + | 0.997480i | \(0.477395\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −5037.05 | −0.296397 | −0.148199 | − | 0.988958i | \(-0.547347\pi\) | ||||
−0.148199 | + | 0.988958i | \(0.547347\pi\) | |||||||
\(662\) | 397.848 | 0.0233577 | ||||||||
\(663\) | −3955.52 | −0.231704 | ||||||||
\(664\) | 6567.36 | 0.383830 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 508.041 | 0.0295588 | ||||||||
\(667\) | −5134.75 | −0.298078 | ||||||||
\(668\) | −2401.50 | −0.139097 | ||||||||
\(669\) | −1119.13 | −0.0646757 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −20459.6 | −1.17710 | ||||||||
\(672\) | 537.861 | 0.0308757 | ||||||||
\(673\) | 20842.1 | 1.19377 | 0.596884 | − | 0.802328i | \(-0.296405\pi\) | ||||
0.596884 | + | 0.802328i | \(0.296405\pi\) | |||||||
\(674\) | −4204.85 | −0.240304 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −832.816 | −0.0473837 | ||||||||
\(677\) | 23394.0 | 1.32807 | 0.664037 | − | 0.747700i | \(-0.268842\pi\) | ||||
0.664037 | + | 0.747700i | \(0.268842\pi\) | |||||||
\(678\) | −4950.45 | −0.280414 | ||||||||
\(679\) | −706.759 | −0.0399454 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −6428.72 | −0.361746 | ||||||||
\(682\) | 17620.5 | 0.989331 | ||||||||
\(683\) | 8567.11 | 0.479958 | 0.239979 | − | 0.970778i | \(-0.422859\pi\) | ||||
0.239979 | + | 0.970778i | \(0.422859\pi\) | |||||||
\(684\) | −6354.02 | −0.355193 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 12791.1 | 0.711905 | ||||||||
\(687\) | −3207.90 | −0.178150 | ||||||||
\(688\) | 3117.17 | 0.172734 | ||||||||
\(689\) | 27041.8 | 1.49522 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −11987.6 | −0.659959 | −0.329979 | − | 0.943988i | \(-0.607042\pi\) | ||||
−0.329979 | + | 0.943988i | \(0.607042\pi\) | |||||||
\(692\) | 10296.8 | 0.565644 | ||||||||
\(693\) | −10871.0 | −0.595895 | ||||||||
\(694\) | −13087.7 | −0.715851 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −336.282 | −0.0183143 | ||||||||
\(697\) | 21292.3 | 1.15710 | ||||||||
\(698\) | 1586.85 | 0.0860505 | ||||||||
\(699\) | −4320.08 | −0.233763 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 19429.6 | 1.04686 | 0.523428 | − | 0.852070i | \(-0.324653\pi\) | ||||
0.523428 | + | 0.852070i | \(0.324653\pi\) | |||||||
\(702\) | 6709.64 | 0.360739 | ||||||||
\(703\) | −650.869 | −0.0349189 | ||||||||
\(704\) | −2409.70 | −0.129004 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −14757.7 | −0.786704 | ||||||||
\(707\) | −12757.4 | −0.678628 | ||||||||
\(708\) | 4072.33 | 0.216169 | ||||||||
\(709\) | −804.014 | −0.0425887 | −0.0212944 | − | 0.999773i | \(-0.506779\pi\) | ||||
−0.0212944 | + | 0.999773i | \(0.506779\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −18058.4 | −0.952521 | ||||||||
\(712\) | −5186.91 | −0.273016 | ||||||||
\(713\) | 41431.1 | 2.17617 | ||||||||
\(714\) | 2057.04 | 0.107819 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 15314.9 | 0.799362 | ||||||||
\(717\) | 807.500 | 0.0420595 | ||||||||
\(718\) | −14285.9 | −0.742544 | ||||||||
\(719\) | 4975.94 | 0.258096 | 0.129048 | − | 0.991638i | \(-0.458808\pi\) | ||||
0.129048 | + | 0.991638i | \(0.458808\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 8672.93 | 0.447984 | ||||||||
\(722\) | −5577.64 | −0.287505 | ||||||||
\(723\) | 6042.42 | 0.310816 | ||||||||
\(724\) | 8302.55 | 0.426190 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −251.161 | −0.0128395 | ||||||||
\(727\) | 3761.32 | 0.191884 | 0.0959419 | − | 0.995387i | \(-0.469414\pi\) | ||||
0.0959419 | + | 0.995387i | \(0.469414\pi\) | |||||||
\(728\) | −4137.04 | −0.210617 | ||||||||
\(729\) | −11079.8 | −0.562912 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 11921.6 | 0.603195 | ||||||||
\(732\) | −3150.58 | −0.159083 | ||||||||
\(733\) | −21439.2 | −1.08032 | −0.540161 | − | 0.841562i | \(-0.681637\pi\) | ||||
−0.540161 | + | 0.841562i | \(0.681637\pi\) | |||||||
\(734\) | 3612.94 | 0.181684 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −5665.93 | −0.283762 | ||||||||
\(737\) | −15324.6 | −0.765926 | ||||||||
\(738\) | −17327.7 | −0.864282 | ||||||||
\(739\) | 22000.3 | 1.09512 | 0.547561 | − | 0.836766i | \(-0.315556\pi\) | ||||
0.547561 | + | 0.836766i | \(0.315556\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −4123.98 | −0.204451 | ||||||||
\(742\) | −14062.9 | −0.695776 | ||||||||
\(743\) | 13371.8 | 0.660246 | 0.330123 | − | 0.943938i | \(-0.392910\pi\) | ||||
0.330123 | + | 0.943938i | \(0.392910\pi\) | |||||||
\(744\) | 2713.38 | 0.133706 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −18792.1 | −0.922289 | ||||||||
\(747\) | −20440.1 | −1.00115 | ||||||||
\(748\) | −9215.87 | −0.450489 | ||||||||
\(749\) | 2041.57 | 0.0995958 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −17764.8 | −0.863178 | −0.431589 | − | 0.902070i | \(-0.642047\pi\) | ||||
−0.431589 | + | 0.902070i | \(0.642047\pi\) | |||||||
\(752\) | 232.008 | 0.0112506 | ||||||||
\(753\) | 10338.6 | 0.500343 | ||||||||
\(754\) | 2586.56 | 0.124930 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −3489.31 | −0.167864 | ||||||||
\(757\) | −33266.1 | −1.59719 | −0.798597 | − | 0.601867i | \(-0.794424\pi\) | ||||
−0.798597 | + | 0.601867i | \(0.794424\pi\) | |||||||
\(758\) | −842.963 | −0.0403929 | ||||||||
\(759\) | −9663.15 | −0.462121 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −25327.3 | −1.20646 | −0.603228 | − | 0.797569i | \(-0.706119\pi\) | ||||
−0.603228 | + | 0.797569i | \(0.706119\pi\) | |||||||
\(762\) | −2555.37 | −0.121485 | ||||||||
\(763\) | −2016.02 | −0.0956551 | ||||||||
\(764\) | 16280.3 | 0.770944 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −6379.69 | −0.300924 | ||||||||
\(767\) | −31322.9 | −1.47458 | ||||||||
\(768\) | −371.069 | −0.0174347 | ||||||||
\(769\) | −9587.28 | −0.449579 | −0.224789 | − | 0.974407i | \(-0.572169\pi\) | ||||
−0.224789 | + | 0.974407i | \(0.572169\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 8066.07 | 0.376773 | ||||||||
\(772\) | −9492.98 | −0.442565 | ||||||||
\(773\) | −2825.54 | −0.131472 | −0.0657359 | − | 0.997837i | \(-0.520939\pi\) | ||||
−0.0657359 | + | 0.997837i | \(0.520939\pi\) | |||||||
\(774\) | −9701.79 | −0.450547 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 487.592 | 0.0225561 | ||||||||
\(777\) | −171.478 | −0.00791728 | ||||||||
\(778\) | −8221.92 | −0.378882 | ||||||||
\(779\) | 22199.1 | 1.02101 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −11849.6 | −0.542909 | ||||||||
\(782\) | −21669.3 | −0.990910 | ||||||||
\(783\) | 2181.58 | 0.0995702 | ||||||||
\(784\) | −3336.55 | −0.151993 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −5871.86 | −0.266466 | ||||||||
\(787\) | −2132.09 | −0.0965702 | −0.0482851 | − | 0.998834i | \(-0.515376\pi\) | ||||
−0.0482851 | + | 0.998834i | \(0.515376\pi\) | |||||||
\(788\) | 12434.3 | 0.562125 | ||||||||
\(789\) | 10420.0 | 0.470166 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −19801.8 | −0.890103 | ||||||||
\(792\) | 7499.88 | 0.336486 | ||||||||
\(793\) | 24233.1 | 1.08518 | ||||||||
\(794\) | 1655.01 | 0.0739724 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −16193.2 | −0.721046 | ||||||||
\(797\) | −5443.62 | −0.241936 | −0.120968 | − | 0.992656i | \(-0.538600\pi\) | ||||
−0.120968 | + | 0.992656i | \(0.538600\pi\) | |||||||
\(798\) | 2144.65 | 0.0951377 | ||||||||
\(799\) | 887.313 | 0.0392877 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 16143.6 | 0.712117 | ||||||||
\(802\) | 1350.29 | 0.0594519 | ||||||||
\(803\) | −32346.8 | −1.42154 | ||||||||
\(804\) | −2359.83 | −0.103513 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −20870.4 | −0.912070 | ||||||||
\(807\) | −4615.72 | −0.201340 | ||||||||
\(808\) | 8801.27 | 0.383203 | ||||||||
\(809\) | 41193.5 | 1.79022 | 0.895109 | − | 0.445847i | \(-0.147098\pi\) | ||||
0.895109 | + | 0.445847i | \(0.147098\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −18225.9 | −0.789145 | −0.394572 | − | 0.918865i | \(-0.629107\pi\) | ||||
−0.394572 | + | 0.918865i | \(0.629107\pi\) | |||||||
\(812\) | −1345.13 | −0.0581338 | ||||||||
\(813\) | −2511.01 | −0.108321 | ||||||||
\(814\) | 768.245 | 0.0330798 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −1419.15 | −0.0608826 | ||||||||
\(817\) | 12429.3 | 0.532248 | ||||||||
\(818\) | 1529.69 | 0.0653845 | ||||||||
\(819\) | 12876.0 | 0.549359 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 46061.7 | 1.95806 | 0.979029 | − | 0.203720i | \(-0.0653033\pi\) | ||||
0.979029 | + | 0.203720i | \(0.0653033\pi\) | |||||||
\(822\) | 4621.90 | 0.196116 | ||||||||
\(823\) | −40166.3 | −1.70122 | −0.850612 | − | 0.525793i | \(-0.823769\pi\) | ||||
−0.850612 | + | 0.525793i | \(0.823769\pi\) | |||||||
\(824\) | −5983.44 | −0.252965 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 16289.3 | 0.686171 | ||||||||
\(827\) | 23994.5 | 1.00891 | 0.504457 | − | 0.863437i | \(-0.331693\pi\) | ||||
0.504457 | + | 0.863437i | \(0.331693\pi\) | |||||||
\(828\) | 17634.5 | 0.740145 | ||||||||
\(829\) | −13549.6 | −0.567668 | −0.283834 | − | 0.958873i | \(-0.591606\pi\) | ||||
−0.283834 | + | 0.958873i | \(0.591606\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 8785.81 | 0.366759 | ||||||||
\(832\) | 2854.14 | 0.118930 | ||||||||
\(833\) | −12760.6 | −0.530767 | ||||||||
\(834\) | 8277.75 | 0.343687 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −9608.36 | −0.397503 | ||||||||
\(837\) | −17602.7 | −0.726928 | ||||||||
\(838\) | −5146.67 | −0.212158 | ||||||||
\(839\) | 34768.5 | 1.43068 | 0.715341 | − | 0.698776i | \(-0.246271\pi\) | ||||
0.715341 | + | 0.698776i | \(0.246271\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 841.000 | 0.0344828 | ||||||||
\(842\) | 28574.9 | 1.16954 | ||||||||
\(843\) | −8963.29 | −0.366207 | ||||||||
\(844\) | 14366.6 | 0.585924 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −722.096 | −0.0293454 | ||||||||
\(847\) | −1004.64 | −0.0407556 | ||||||||
\(848\) | 9701.98 | 0.392886 | ||||||||
\(849\) | −13156.7 | −0.531844 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1806.38 | 0.0727635 | ||||||||
\(852\) | −1824.72 | −0.0733730 | ||||||||
\(853\) | −4691.07 | −0.188299 | −0.0941496 | − | 0.995558i | \(-0.530013\pi\) | ||||
−0.0941496 | + | 0.995558i | \(0.530013\pi\) | |||||||
\(854\) | −12602.3 | −0.504967 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −1408.47 | −0.0562391 | ||||||||
\(857\) | 14362.7 | 0.572485 | 0.286242 | − | 0.958157i | \(-0.407594\pi\) | ||||
0.286242 | + | 0.958157i | \(0.407594\pi\) | |||||||
\(858\) | 4867.69 | 0.193683 | ||||||||
\(859\) | 1392.43 | 0.0553073 | 0.0276537 | − | 0.999618i | \(-0.491196\pi\) | ||||
0.0276537 | + | 0.999618i | \(0.491196\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 5848.55 | 0.231496 | ||||||||
\(862\) | −22566.3 | −0.891661 | ||||||||
\(863\) | −19162.2 | −0.755840 | −0.377920 | − | 0.925838i | \(-0.623361\pi\) | ||||
−0.377920 | + | 0.925838i | \(0.623361\pi\) | |||||||
\(864\) | 2407.27 | 0.0947880 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −16139.3 | −0.633297 | ||||||||
\(867\) | 1693.81 | 0.0663494 | ||||||||
\(868\) | 10853.5 | 0.424415 | ||||||||
\(869\) | −27307.4 | −1.06598 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 18151.0 | 0.706111 | ||||||||
\(872\) | 1390.85 | 0.0540139 | ||||||||
\(873\) | −1517.57 | −0.0588338 | ||||||||
\(874\) | −22592.2 | −0.874361 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −4981.09 | −0.192118 | ||||||||
\(877\) | 6509.75 | 0.250649 | 0.125324 | − | 0.992116i | \(-0.460003\pi\) | ||||
0.125324 | + | 0.992116i | \(0.460003\pi\) | |||||||
\(878\) | −15638.8 | −0.601122 | ||||||||
\(879\) | −5271.30 | −0.202271 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −589.496 | −0.0225433 | −0.0112716 | − | 0.999936i | \(-0.503588\pi\) | ||||
−0.0112716 | + | 0.999936i | \(0.503588\pi\) | |||||||
\(882\) | 10384.6 | 0.396449 | ||||||||
\(883\) | 3903.57 | 0.148772 | 0.0743859 | − | 0.997230i | \(-0.476300\pi\) | ||||
0.0743859 | + | 0.997230i | \(0.476300\pi\) | |||||||
\(884\) | 10915.6 | 0.415308 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 20306.8 | 0.770000 | ||||||||
\(887\) | 24136.6 | 0.913674 | 0.456837 | − | 0.889550i | \(-0.348982\pi\) | ||||
0.456837 | + | 0.889550i | \(0.348982\pi\) | |||||||
\(888\) | 118.302 | 0.00447067 | ||||||||
\(889\) | −10221.5 | −0.385622 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −21206.5 | −0.797358 | ||||||||
\(892\) | 3088.34 | 0.115925 | ||||||||
\(893\) | 925.103 | 0.0346667 | ||||||||
\(894\) | 53.2703 | 0.00199287 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −1484.28 | −0.0553418 | ||||||||
\(897\) | 11445.4 | 0.426032 | ||||||||
\(898\) | 27216.6 | 1.01139 | ||||||||
\(899\) | −6785.84 | −0.251747 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 37105.1 | 1.37198 | ||||||||
\(902\) | −26202.4 | −0.967233 | ||||||||
\(903\) | 3274.62 | 0.120678 | ||||||||
\(904\) | 13661.2 | 0.502617 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 2257.74 | 0.0827908 | ||||||||
\(907\) | −22174.3 | −0.811781 | −0.405890 | − | 0.913922i | \(-0.633038\pi\) | ||||
−0.405890 | + | 0.913922i | \(0.633038\pi\) | |||||||
\(908\) | 17740.6 | 0.648397 | ||||||||
\(909\) | −27392.8 | −0.999519 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −46956.1 | −1.70771 | −0.853856 | − | 0.520509i | \(-0.825742\pi\) | ||||
−0.853856 | + | 0.520509i | \(0.825742\pi\) | |||||||
\(912\) | −1479.59 | −0.0537217 | ||||||||
\(913\) | −30908.9 | −1.12041 | ||||||||
\(914\) | 3765.10 | 0.136257 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 8852.49 | 0.319317 | ||||||||
\(917\) | −23487.4 | −0.845827 | ||||||||
\(918\) | 9206.56 | 0.331004 | ||||||||
\(919\) | −37166.4 | −1.33407 | −0.667033 | − | 0.745028i | \(-0.732436\pi\) | ||||
−0.667033 | + | 0.745028i | \(0.732436\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −6695.27 | −0.239540 | ||||||||
\(922\) | −27894.5 | −0.996373 | ||||||||
\(923\) | 14035.1 | 0.500511 | ||||||||
\(924\) | −2531.41 | −0.0901270 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 24909.6 | 0.883995 | ||||||||
\(927\) | 18622.7 | 0.659816 | ||||||||
\(928\) | 928.000 | 0.0328266 | ||||||||
\(929\) | 29571.7 | 1.04437 | 0.522183 | − | 0.852833i | \(-0.325118\pi\) | ||||
0.522183 | + | 0.852833i | \(0.325118\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −13304.1 | −0.468339 | ||||||||
\(932\) | 11921.7 | 0.418999 | ||||||||
\(933\) | −11732.3 | −0.411680 | ||||||||
\(934\) | 13123.2 | 0.459747 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −8883.14 | −0.310208 | ||||||||
\(937\) | −8691.51 | −0.303030 | −0.151515 | − | 0.988455i | \(-0.548415\pi\) | ||||
−0.151515 | + | 0.988455i | \(0.548415\pi\) | |||||||
\(938\) | −9439.31 | −0.328576 | ||||||||
\(939\) | 10004.1 | 0.347679 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −2862.43 | −0.0991632 | −0.0495816 | − | 0.998770i | \(-0.515789\pi\) | ||||
−0.0495816 | + | 0.998770i | \(0.515789\pi\) | |||||||
\(942\) | −1483.98 | −0.0513275 | ||||||||
\(943\) | −61609.7 | −2.12756 | ||||||||
\(944\) | −11238.0 | −0.387462 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −14670.8 | −0.504215 | ||||||||
\(947\) | −36997.8 | −1.26955 | −0.634777 | − | 0.772695i | \(-0.718908\pi\) | ||||
−0.634777 | + | 0.772695i | \(0.718908\pi\) | |||||||
\(948\) | −4205.06 | −0.144065 | ||||||||
\(949\) | 38312.8 | 1.31052 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −8870.51 | −0.302467 | ||||||||
\(952\) | −5676.60 | −0.193256 | ||||||||
\(953\) | −20998.8 | −0.713764 | −0.356882 | − | 0.934150i | \(-0.616160\pi\) | ||||
−0.356882 | + | 0.934150i | \(0.616160\pi\) | |||||||
\(954\) | −30196.2 | −1.02478 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −2228.37 | −0.0753877 | ||||||||
\(957\) | 1582.69 | 0.0534599 | ||||||||
\(958\) | −34815.0 | −1.17414 | ||||||||
\(959\) | 18487.6 | 0.622519 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 24962.4 | 0.837917 | ||||||||
\(962\) | −909.939 | −0.0304965 | ||||||||
\(963\) | 4383.69 | 0.146690 | ||||||||
\(964\) | −16674.6 | −0.557109 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −5952.11 | −0.198247 | ||||||||
\(967\) | 30803.0 | 1.02436 | 0.512181 | − | 0.858878i | \(-0.328838\pi\) | ||||
0.512181 | + | 0.858878i | \(0.328838\pi\) | |||||||
\(968\) | 693.102 | 0.0230136 | ||||||||
\(969\) | −5658.68 | −0.187599 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −755.015 | −0.0249532 | −0.0124766 | − | 0.999922i | \(-0.503972\pi\) | ||||
−0.0124766 | + | 0.999922i | \(0.503972\pi\) | |||||||
\(972\) | −11390.1 | −0.375862 | ||||||||
\(973\) | 33111.0 | 1.09095 | ||||||||
\(974\) | 5089.57 | 0.167434 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 8694.30 | 0.285141 | ||||||||
\(977\) | 44011.7 | 1.44121 | 0.720603 | − | 0.693348i | \(-0.243865\pi\) | ||||
0.720603 | + | 0.693348i | \(0.243865\pi\) | |||||||
\(978\) | −4208.12 | −0.137588 | ||||||||
\(979\) | 24411.9 | 0.796943 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −4328.84 | −0.140886 | ||||||||
\(982\) | 5425.79 | 0.176318 | ||||||||
\(983\) | 36334.8 | 1.17894 | 0.589471 | − | 0.807790i | \(-0.299336\pi\) | ||||
0.589471 | + | 0.807790i | \(0.299336\pi\) | |||||||
\(984\) | −4034.91 | −0.130720 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 3549.13 | 0.114632 | ||||||||
\(987\) | 243.727 | 0.00786010 | ||||||||
\(988\) | 11380.5 | 0.366460 | ||||||||
\(989\) | −34495.4 | −1.10909 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 9848.60 | 0.315692 | 0.157846 | − | 0.987464i | \(-0.449545\pi\) | ||||
0.157846 | + | 0.987464i | \(0.449545\pi\) | |||||||
\(992\) | −7487.82 | −0.239656 | ||||||||
\(993\) | −288.338 | −0.00921464 | ||||||||
\(994\) | −7298.87 | −0.232904 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −4759.66 | −0.151421 | ||||||||
\(997\) | −3378.02 | −0.107305 | −0.0536525 | − | 0.998560i | \(-0.517086\pi\) | ||||
−0.0536525 | + | 0.998560i | \(0.517086\pi\) | |||||||
\(998\) | 9167.59 | 0.290777 | ||||||||
\(999\) | −767.469 | −0.0243060 |
(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 | 1450.4.a.g.1.1 | 2 | ||
5.4 | even | 2 | 58.4.a.c.1.2 | ✓ | 2 | ||
15.14 | odd | 2 | 522.4.a.j.1.2 | 2 | |||
20.19 | odd | 2 | 464.4.a.e.1.1 | 2 | |||
40.19 | odd | 2 | 1856.4.a.i.1.2 | 2 | |||
40.29 | even | 2 | 1856.4.a.l.1.1 | 2 | |||
145.144 | even | 2 | 1682.4.a.c.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
58.4.a.c.1.2 | ✓ | 2 | 5.4 | even | 2 | ||
464.4.a.e.1.1 | 2 | 20.19 | odd | 2 | |||
522.4.a.j.1.2 | 2 | 15.14 | odd | 2 | |||
1450.4.a.g.1.1 | 2 | 1.1 | even | 1 | trivial | ||
1682.4.a.c.1.1 | 2 | 145.144 | even | 2 | |||
1856.4.a.i.1.2 | 2 | 40.19 | odd | 2 | |||
1856.4.a.l.1.1 | 2 | 40.29 | even | 2 |