Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1045,4,Mod(1,1045)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1045, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("1045.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1045 = 5 \cdot 11 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1045.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: | \(61.6569959560\) |
Analytic rank: | \(1\) |
Dimension: | \(20\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{20} - x^{19} - 105 x^{18} + 103 x^{17} + 4500 x^{16} - 4345 x^{15} - 101844 x^{14} + 95592 x^{13} + 1317797 x^{12} - 1160501 x^{11} - 9914845 x^{10} + 7570653 x^{9} + \cdots + 150528 \)
|
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.9 | ||
Root | \(0.783853\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1045.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.783853 | −0.277134 | −0.138567 | − | 0.990353i | \(-0.544250\pi\) | ||||
−0.138567 | + | 0.990353i | \(0.544250\pi\) | |||||||
\(3\) | 0.0603595 | 0.0116162 | 0.00580810 | − | 0.999983i | \(-0.498151\pi\) | ||||
0.00580810 | + | 0.999983i | \(0.498151\pi\) | |||||||
\(4\) | −7.38557 | −0.923197 | ||||||||
\(5\) | −5.00000 | −0.447214 | ||||||||
\(6\) | −0.0473130 | −0.00321924 | ||||||||
\(7\) | −1.09978 | −0.0593827 | −0.0296913 | − | 0.999559i | \(-0.509452\pi\) | ||||
−0.0296913 | + | 0.999559i | \(0.509452\pi\) | |||||||
\(8\) | 12.0600 | 0.532983 | ||||||||
\(9\) | −26.9964 | −0.999865 | ||||||||
\(10\) | 3.91926 | 0.123938 | ||||||||
\(11\) | −11.0000 | −0.301511 | ||||||||
\(12\) | −0.445790 | −0.0107240 | ||||||||
\(13\) | −22.1285 | −0.472104 | −0.236052 | − | 0.971740i | \(-0.575854\pi\) | ||||
−0.236052 | + | 0.971740i | \(0.575854\pi\) | |||||||
\(14\) | 0.862068 | 0.0164569 | ||||||||
\(15\) | −0.301798 | −0.00519492 | ||||||||
\(16\) | 49.6313 | 0.775489 | ||||||||
\(17\) | 88.1083 | 1.25702 | 0.628512 | − | 0.777800i | \(-0.283664\pi\) | ||||
0.628512 | + | 0.777800i | \(0.283664\pi\) | |||||||
\(18\) | 21.1612 | 0.277096 | ||||||||
\(19\) | 19.0000 | 0.229416 | ||||||||
\(20\) | 36.9279 | 0.412866 | ||||||||
\(21\) | −0.0663823 | −0.000689801 0 | ||||||||
\(22\) | 8.62238 | 0.0835590 | ||||||||
\(23\) | 168.327 | 1.52603 | 0.763015 | − | 0.646381i | \(-0.223718\pi\) | ||||
0.763015 | + | 0.646381i | \(0.223718\pi\) | |||||||
\(24\) | 0.727938 | 0.00619123 | ||||||||
\(25\) | 25.0000 | 0.200000 | ||||||||
\(26\) | 17.3455 | 0.130836 | ||||||||
\(27\) | −3.25919 | −0.0232308 | ||||||||
\(28\) | 8.12252 | 0.0548219 | ||||||||
\(29\) | 214.076 | 1.37079 | 0.685395 | − | 0.728171i | \(-0.259629\pi\) | ||||
0.685395 | + | 0.728171i | \(0.259629\pi\) | |||||||
\(30\) | 0.236565 | 0.00143969 | ||||||||
\(31\) | −36.7173 | −0.212730 | −0.106365 | − | 0.994327i | \(-0.533921\pi\) | ||||
−0.106365 | + | 0.994327i | \(0.533921\pi\) | |||||||
\(32\) | −135.384 | −0.747897 | ||||||||
\(33\) | −0.663955 | −0.00350241 | ||||||||
\(34\) | −69.0640 | −0.348364 | ||||||||
\(35\) | 5.49891 | 0.0265567 | ||||||||
\(36\) | 199.384 | 0.923072 | ||||||||
\(37\) | −218.260 | −0.969778 | −0.484889 | − | 0.874576i | \(-0.661140\pi\) | ||||
−0.484889 | + | 0.874576i | \(0.661140\pi\) | |||||||
\(38\) | −14.8932 | −0.0635789 | ||||||||
\(39\) | −1.33567 | −0.00548405 | ||||||||
\(40\) | −60.3001 | −0.238357 | ||||||||
\(41\) | 28.0068 | 0.106681 | 0.0533406 | − | 0.998576i | \(-0.483013\pi\) | ||||
0.0533406 | + | 0.998576i | \(0.483013\pi\) | |||||||
\(42\) | 0.0520340 | 0.000191167 0 | ||||||||
\(43\) | −376.154 | −1.33402 | −0.667011 | − | 0.745048i | \(-0.732427\pi\) | ||||
−0.667011 | + | 0.745048i | \(0.732427\pi\) | |||||||
\(44\) | 81.2413 | 0.278354 | ||||||||
\(45\) | 134.982 | 0.447153 | ||||||||
\(46\) | −131.944 | −0.422915 | ||||||||
\(47\) | −249.449 | −0.774168 | −0.387084 | − | 0.922044i | \(-0.626518\pi\) | ||||
−0.387084 | + | 0.922044i | \(0.626518\pi\) | |||||||
\(48\) | 2.99572 | 0.00900823 | ||||||||
\(49\) | −341.790 | −0.996474 | ||||||||
\(50\) | −19.5963 | −0.0554268 | ||||||||
\(51\) | 5.31818 | 0.0146018 | ||||||||
\(52\) | 163.432 | 0.435845 | ||||||||
\(53\) | 446.371 | 1.15686 | 0.578432 | − | 0.815731i | \(-0.303665\pi\) | ||||
0.578432 | + | 0.815731i | \(0.303665\pi\) | |||||||
\(54\) | 2.55473 | 0.00643805 | ||||||||
\(55\) | 55.0000 | 0.134840 | ||||||||
\(56\) | −13.2634 | −0.0316499 | ||||||||
\(57\) | 1.14683 | 0.00266494 | ||||||||
\(58\) | −167.804 | −0.379893 | ||||||||
\(59\) | 826.710 | 1.82421 | 0.912106 | − | 0.409955i | \(-0.134456\pi\) | ||||
0.912106 | + | 0.409955i | \(0.134456\pi\) | |||||||
\(60\) | 2.22895 | 0.00479593 | ||||||||
\(61\) | 349.824 | 0.734269 | 0.367134 | − | 0.930168i | \(-0.380339\pi\) | ||||
0.367134 | + | 0.930168i | \(0.380339\pi\) | |||||||
\(62\) | 28.7809 | 0.0589546 | ||||||||
\(63\) | 29.6901 | 0.0593746 | ||||||||
\(64\) | −290.929 | −0.568222 | ||||||||
\(65\) | 110.643 | 0.211131 | ||||||||
\(66\) | 0.520443 | 0.000970638 0 | ||||||||
\(67\) | −340.516 | −0.620906 | −0.310453 | − | 0.950589i | \(-0.600481\pi\) | ||||
−0.310453 | + | 0.950589i | \(0.600481\pi\) | |||||||
\(68\) | −650.731 | −1.16048 | ||||||||
\(69\) | 10.1602 | 0.0177267 | ||||||||
\(70\) | −4.31034 | −0.00735977 | ||||||||
\(71\) | −1068.42 | −1.78588 | −0.892942 | − | 0.450172i | \(-0.851363\pi\) | ||||
−0.892942 | + | 0.450172i | \(0.851363\pi\) | |||||||
\(72\) | −325.577 | −0.532911 | ||||||||
\(73\) | −99.5645 | −0.159632 | −0.0798161 | − | 0.996810i | \(-0.525433\pi\) | ||||
−0.0798161 | + | 0.996810i | \(0.525433\pi\) | |||||||
\(74\) | 171.084 | 0.268758 | ||||||||
\(75\) | 1.50899 | 0.00232324 | ||||||||
\(76\) | −140.326 | −0.211796 | ||||||||
\(77\) | 12.0976 | 0.0179045 | ||||||||
\(78\) | 1.04697 | 0.00151982 | ||||||||
\(79\) | 1027.99 | 1.46402 | 0.732012 | − | 0.681292i | \(-0.238582\pi\) | ||||
0.732012 | + | 0.681292i | \(0.238582\pi\) | |||||||
\(80\) | −248.157 | −0.346809 | ||||||||
\(81\) | 728.705 | 0.999595 | ||||||||
\(82\) | −21.9532 | −0.0295650 | ||||||||
\(83\) | 609.027 | 0.805414 | 0.402707 | − | 0.915329i | \(-0.368069\pi\) | ||||
0.402707 | + | 0.915329i | \(0.368069\pi\) | |||||||
\(84\) | 0.490272 | 0.000636822 0 | ||||||||
\(85\) | −440.542 | −0.562158 | ||||||||
\(86\) | 294.849 | 0.369703 | ||||||||
\(87\) | 12.9215 | 0.0159234 | ||||||||
\(88\) | −132.660 | −0.160700 | ||||||||
\(89\) | 175.527 | 0.209055 | 0.104527 | − | 0.994522i | \(-0.466667\pi\) | ||||
0.104527 | + | 0.994522i | \(0.466667\pi\) | |||||||
\(90\) | −105.806 | −0.123921 | ||||||||
\(91\) | 24.3366 | 0.0280348 | ||||||||
\(92\) | −1243.19 | −1.40883 | ||||||||
\(93\) | −2.21624 | −0.00247111 | ||||||||
\(94\) | 195.531 | 0.214548 | ||||||||
\(95\) | −95.0000 | −0.102598 | ||||||||
\(96\) | −8.17171 | −0.00868772 | ||||||||
\(97\) | 38.6274 | 0.0404332 | 0.0202166 | − | 0.999796i | \(-0.493564\pi\) | ||||
0.0202166 | + | 0.999796i | \(0.493564\pi\) | |||||||
\(98\) | 267.913 | 0.276157 | ||||||||
\(99\) | 296.960 | 0.301471 | ||||||||
\(100\) | −184.639 | −0.184639 | ||||||||
\(101\) | −592.060 | −0.583289 | −0.291644 | − | 0.956527i | \(-0.594202\pi\) | ||||
−0.291644 | + | 0.956527i | \(0.594202\pi\) | |||||||
\(102\) | −4.16867 | −0.00404666 | ||||||||
\(103\) | 886.258 | 0.847821 | 0.423910 | − | 0.905704i | \(-0.360657\pi\) | ||||
0.423910 | + | 0.905704i | \(0.360657\pi\) | |||||||
\(104\) | −266.871 | −0.251623 | ||||||||
\(105\) | 0.331912 | 0.000308488 0 | ||||||||
\(106\) | −349.889 | −0.320606 | ||||||||
\(107\) | −1745.46 | −1.57701 | −0.788506 | − | 0.615027i | \(-0.789145\pi\) | ||||
−0.788506 | + | 0.615027i | \(0.789145\pi\) | |||||||
\(108\) | 24.0710 | 0.0214466 | ||||||||
\(109\) | −1923.93 | −1.69063 | −0.845316 | − | 0.534266i | \(-0.820588\pi\) | ||||
−0.845316 | + | 0.534266i | \(0.820588\pi\) | |||||||
\(110\) | −43.1119 | −0.0373687 | ||||||||
\(111\) | −13.1741 | −0.0112651 | ||||||||
\(112\) | −54.5836 | −0.0460506 | ||||||||
\(113\) | −720.292 | −0.599641 | −0.299820 | − | 0.953996i | \(-0.596927\pi\) | ||||
−0.299820 | + | 0.953996i | \(0.596927\pi\) | |||||||
\(114\) | −0.898947 | −0.000738545 0 | ||||||||
\(115\) | −841.637 | −0.682461 | ||||||||
\(116\) | −1581.08 | −1.26551 | ||||||||
\(117\) | 597.390 | 0.472040 | ||||||||
\(118\) | −648.019 | −0.505551 | ||||||||
\(119\) | −96.9000 | −0.0746454 | ||||||||
\(120\) | −3.63969 | −0.00276880 | ||||||||
\(121\) | 121.000 | 0.0909091 | ||||||||
\(122\) | −274.211 | −0.203491 | ||||||||
\(123\) | 1.69048 | 0.00123923 | ||||||||
\(124\) | 271.178 | 0.196391 | ||||||||
\(125\) | −125.000 | −0.0894427 | ||||||||
\(126\) | −23.2727 | −0.0164547 | ||||||||
\(127\) | −1879.77 | −1.31341 | −0.656704 | − | 0.754149i | \(-0.728050\pi\) | ||||
−0.656704 | + | 0.754149i | \(0.728050\pi\) | |||||||
\(128\) | 1311.12 | 0.905371 | ||||||||
\(129\) | −22.7045 | −0.0154963 | ||||||||
\(130\) | −86.7276 | −0.0585117 | ||||||||
\(131\) | −77.2212 | −0.0515027 | −0.0257513 | − | 0.999668i | \(-0.508198\pi\) | ||||
−0.0257513 | + | 0.999668i | \(0.508198\pi\) | |||||||
\(132\) | 4.90369 | 0.00323342 | ||||||||
\(133\) | −20.8959 | −0.0136233 | ||||||||
\(134\) | 266.915 | 0.172074 | ||||||||
\(135\) | 16.2960 | 0.0103891 | ||||||||
\(136\) | 1062.59 | 0.669972 | ||||||||
\(137\) | −244.748 | −0.152629 | −0.0763147 | − | 0.997084i | \(-0.524315\pi\) | ||||
−0.0763147 | + | 0.997084i | \(0.524315\pi\) | |||||||
\(138\) | −7.96407 | −0.00491266 | ||||||||
\(139\) | −1554.03 | −0.948279 | −0.474139 | − | 0.880450i | \(-0.657241\pi\) | ||||
−0.474139 | + | 0.880450i | \(0.657241\pi\) | |||||||
\(140\) | −40.6126 | −0.0245171 | ||||||||
\(141\) | −15.0566 | −0.00899289 | ||||||||
\(142\) | 837.482 | 0.494929 | ||||||||
\(143\) | 243.414 | 0.142345 | ||||||||
\(144\) | −1339.86 | −0.775385 | ||||||||
\(145\) | −1070.38 | −0.613036 | ||||||||
\(146\) | 78.0440 | 0.0442395 | ||||||||
\(147\) | −20.6303 | −0.0115752 | ||||||||
\(148\) | 1611.98 | 0.895296 | ||||||||
\(149\) | −1846.74 | −1.01538 | −0.507688 | − | 0.861541i | \(-0.669500\pi\) | ||||
−0.507688 | + | 0.861541i | \(0.669500\pi\) | |||||||
\(150\) | −1.18282 | −0.000643848 0 | ||||||||
\(151\) | −1013.96 | −0.546458 | −0.273229 | − | 0.961949i | \(-0.588092\pi\) | ||||
−0.273229 | + | 0.961949i | \(0.588092\pi\) | |||||||
\(152\) | 229.141 | 0.122275 | ||||||||
\(153\) | −2378.60 | −1.25685 | ||||||||
\(154\) | −9.48274 | −0.00496196 | ||||||||
\(155\) | 183.586 | 0.0951355 | ||||||||
\(156\) | 9.86468 | 0.00506286 | ||||||||
\(157\) | −3340.56 | −1.69812 | −0.849062 | − | 0.528293i | \(-0.822832\pi\) | ||||
−0.849062 | + | 0.528293i | \(0.822832\pi\) | |||||||
\(158\) | −805.793 | −0.405731 | ||||||||
\(159\) | 26.9428 | 0.0134384 | ||||||||
\(160\) | 676.919 | 0.334470 | ||||||||
\(161\) | −185.123 | −0.0906197 | ||||||||
\(162\) | −571.197 | −0.277022 | ||||||||
\(163\) | 720.474 | 0.346208 | 0.173104 | − | 0.984904i | \(-0.444620\pi\) | ||||
0.173104 | + | 0.984904i | \(0.444620\pi\) | |||||||
\(164\) | −206.846 | −0.0984878 | ||||||||
\(165\) | 3.31977 | 0.00156633 | ||||||||
\(166\) | −477.388 | −0.223208 | ||||||||
\(167\) | −278.976 | −0.129268 | −0.0646342 | − | 0.997909i | \(-0.520588\pi\) | ||||
−0.0646342 | + | 0.997909i | \(0.520588\pi\) | |||||||
\(168\) | −0.800573 | −0.000367652 0 | ||||||||
\(169\) | −1707.33 | −0.777118 | ||||||||
\(170\) | 345.320 | 0.155793 | ||||||||
\(171\) | −512.931 | −0.229385 | ||||||||
\(172\) | 2778.11 | 1.23157 | ||||||||
\(173\) | −228.531 | −0.100433 | −0.0502165 | − | 0.998738i | \(-0.515991\pi\) | ||||
−0.0502165 | + | 0.998738i | \(0.515991\pi\) | |||||||
\(174\) | −10.1286 | −0.00441291 | ||||||||
\(175\) | −27.4946 | −0.0118765 | ||||||||
\(176\) | −545.944 | −0.233819 | ||||||||
\(177\) | 49.8998 | 0.0211904 | ||||||||
\(178\) | −137.588 | −0.0579361 | ||||||||
\(179\) | 3443.47 | 1.43786 | 0.718930 | − | 0.695083i | \(-0.244632\pi\) | ||||
0.718930 | + | 0.695083i | \(0.244632\pi\) | |||||||
\(180\) | −996.918 | −0.412810 | ||||||||
\(181\) | 3327.36 | 1.36641 | 0.683207 | − | 0.730225i | \(-0.260585\pi\) | ||||
0.683207 | + | 0.730225i | \(0.260585\pi\) | |||||||
\(182\) | −19.0763 | −0.00776939 | ||||||||
\(183\) | 21.1152 | 0.00852941 | ||||||||
\(184\) | 2030.03 | 0.813348 | ||||||||
\(185\) | 1091.30 | 0.433698 | ||||||||
\(186\) | 1.73720 | 0.000684828 0 | ||||||||
\(187\) | −969.192 | −0.379007 | ||||||||
\(188\) | 1842.32 | 0.714709 | ||||||||
\(189\) | 3.58440 | 0.00137951 | ||||||||
\(190\) | 74.4660 | 0.0284333 | ||||||||
\(191\) | 1998.23 | 0.757000 | 0.378500 | − | 0.925601i | \(-0.376440\pi\) | ||||
0.378500 | + | 0.925601i | \(0.376440\pi\) | |||||||
\(192\) | −17.5604 | −0.00660057 | ||||||||
\(193\) | −1524.15 | −0.568448 | −0.284224 | − | 0.958758i | \(-0.591736\pi\) | ||||
−0.284224 | + | 0.958758i | \(0.591736\pi\) | |||||||
\(194\) | −30.2782 | −0.0112054 | ||||||||
\(195\) | 6.67834 | 0.00245254 | ||||||||
\(196\) | 2524.32 | 0.919941 | ||||||||
\(197\) | −281.245 | −0.101715 | −0.0508575 | − | 0.998706i | \(-0.516195\pi\) | ||||
−0.0508575 | + | 0.998706i | \(0.516195\pi\) | |||||||
\(198\) | −232.773 | −0.0835477 | ||||||||
\(199\) | −3911.67 | −1.39342 | −0.696711 | − | 0.717352i | \(-0.745354\pi\) | ||||
−0.696711 | + | 0.717352i | \(0.745354\pi\) | |||||||
\(200\) | 301.501 | 0.106597 | ||||||||
\(201\) | −20.5534 | −0.00721256 | ||||||||
\(202\) | 464.088 | 0.161649 | ||||||||
\(203\) | −235.437 | −0.0814012 | ||||||||
\(204\) | −39.2778 | −0.0134804 | ||||||||
\(205\) | −140.034 | −0.0477093 | ||||||||
\(206\) | −694.696 | −0.234960 | ||||||||
\(207\) | −4544.23 | −1.52582 | ||||||||
\(208\) | −1098.27 | −0.366112 | ||||||||
\(209\) | −209.000 | −0.0691714 | ||||||||
\(210\) | −0.260170 | −8.54925e−5 0 | ||||||||
\(211\) | 297.386 | 0.0970279 | 0.0485139 | − | 0.998823i | \(-0.484551\pi\) | ||||
0.0485139 | + | 0.998823i | \(0.484551\pi\) | |||||||
\(212\) | −3296.71 | −1.06801 | ||||||||
\(213\) | −64.4891 | −0.0207452 | ||||||||
\(214\) | 1368.19 | 0.437043 | ||||||||
\(215\) | 1880.77 | 0.596593 | ||||||||
\(216\) | −39.3060 | −0.0123816 | ||||||||
\(217\) | 40.3810 | 0.0126324 | ||||||||
\(218\) | 1508.08 | 0.468532 | ||||||||
\(219\) | −6.00967 | −0.00185432 | ||||||||
\(220\) | −406.207 | −0.124484 | ||||||||
\(221\) | −1949.71 | −0.593446 | ||||||||
\(222\) | 10.3266 | 0.00312195 | ||||||||
\(223\) | 2419.03 | 0.726413 | 0.363206 | − | 0.931709i | \(-0.381682\pi\) | ||||
0.363206 | + | 0.931709i | \(0.381682\pi\) | |||||||
\(224\) | 148.893 | 0.0444121 | ||||||||
\(225\) | −674.909 | −0.199973 | ||||||||
\(226\) | 564.603 | 0.166181 | ||||||||
\(227\) | −3083.26 | −0.901512 | −0.450756 | − | 0.892647i | \(-0.648846\pi\) | ||||
−0.450756 | + | 0.892647i | \(0.648846\pi\) | |||||||
\(228\) | −8.47001 | −0.00246026 | ||||||||
\(229\) | 1552.11 | 0.447887 | 0.223944 | − | 0.974602i | \(-0.428107\pi\) | ||||
0.223944 | + | 0.974602i | \(0.428107\pi\) | |||||||
\(230\) | 659.720 | 0.189133 | ||||||||
\(231\) | 0.730206 | 0.000207983 0 | ||||||||
\(232\) | 2581.76 | 0.730608 | ||||||||
\(233\) | 1396.79 | 0.392733 | 0.196366 | − | 0.980531i | \(-0.437086\pi\) | ||||
0.196366 | + | 0.980531i | \(0.437086\pi\) | |||||||
\(234\) | −468.266 | −0.130818 | ||||||||
\(235\) | 1247.25 | 0.346218 | ||||||||
\(236\) | −6105.73 | −1.68411 | ||||||||
\(237\) | 62.0490 | 0.0170064 | ||||||||
\(238\) | 75.9553 | 0.0206868 | ||||||||
\(239\) | 2918.42 | 0.789861 | 0.394930 | − | 0.918711i | \(-0.370769\pi\) | ||||
0.394930 | + | 0.918711i | \(0.370769\pi\) | |||||||
\(240\) | −14.9786 | −0.00402861 | ||||||||
\(241\) | −2402.93 | −0.642267 | −0.321133 | − | 0.947034i | \(-0.604064\pi\) | ||||
−0.321133 | + | 0.947034i | \(0.604064\pi\) | |||||||
\(242\) | −94.8462 | −0.0251940 | ||||||||
\(243\) | 131.983 | 0.0348423 | ||||||||
\(244\) | −2583.65 | −0.677875 | ||||||||
\(245\) | 1708.95 | 0.445637 | ||||||||
\(246\) | −1.32509 | −0.000343433 0 | ||||||||
\(247\) | −420.442 | −0.108308 | ||||||||
\(248\) | −442.811 | −0.113381 | ||||||||
\(249\) | 36.7606 | 0.00935585 | ||||||||
\(250\) | 97.9816 | 0.0247876 | ||||||||
\(251\) | 4142.81 | 1.04180 | 0.520900 | − | 0.853617i | \(-0.325596\pi\) | ||||
0.520900 | + | 0.853617i | \(0.325596\pi\) | |||||||
\(252\) | −219.279 | −0.0548145 | ||||||||
\(253\) | −1851.60 | −0.460115 | ||||||||
\(254\) | 1473.46 | 0.363990 | ||||||||
\(255\) | −26.5909 | −0.00653014 | ||||||||
\(256\) | 1299.71 | 0.317313 | ||||||||
\(257\) | −2926.38 | −0.710283 | −0.355142 | − | 0.934813i | \(-0.615567\pi\) | ||||
−0.355142 | + | 0.934813i | \(0.615567\pi\) | |||||||
\(258\) | 17.7970 | 0.00429454 | ||||||||
\(259\) | 240.039 | 0.0575880 | ||||||||
\(260\) | −817.160 | −0.194916 | ||||||||
\(261\) | −5779.27 | −1.37061 | ||||||||
\(262\) | 60.5301 | 0.0142731 | ||||||||
\(263\) | −2387.23 | −0.559707 | −0.279853 | − | 0.960043i | \(-0.590286\pi\) | ||||
−0.279853 | + | 0.960043i | \(0.590286\pi\) | |||||||
\(264\) | −8.00731 | −0.00186673 | ||||||||
\(265\) | −2231.86 | −0.517365 | ||||||||
\(266\) | 16.3793 | 0.00377548 | ||||||||
\(267\) | 10.5947 | 0.00242842 | ||||||||
\(268\) | 2514.91 | 0.573218 | ||||||||
\(269\) | −5830.08 | −1.32144 | −0.660718 | − | 0.750634i | \(-0.729748\pi\) | ||||
−0.660718 | + | 0.750634i | \(0.729748\pi\) | |||||||
\(270\) | −12.7736 | −0.00287918 | ||||||||
\(271\) | −6575.21 | −1.47386 | −0.736930 | − | 0.675970i | \(-0.763725\pi\) | ||||
−0.736930 | + | 0.675970i | \(0.763725\pi\) | |||||||
\(272\) | 4372.93 | 0.974809 | ||||||||
\(273\) | 1.46894 | 0.000325658 0 | ||||||||
\(274\) | 191.846 | 0.0422988 | ||||||||
\(275\) | −275.000 | −0.0603023 | ||||||||
\(276\) | −75.0386 | −0.0163652 | ||||||||
\(277\) | 5770.55 | 1.25169 | 0.625846 | − | 0.779947i | \(-0.284754\pi\) | ||||
0.625846 | + | 0.779947i | \(0.284754\pi\) | |||||||
\(278\) | 1218.13 | 0.262800 | ||||||||
\(279\) | 991.232 | 0.212701 | ||||||||
\(280\) | 66.3170 | 0.0141543 | ||||||||
\(281\) | 372.824 | 0.0791488 | 0.0395744 | − | 0.999217i | \(-0.487400\pi\) | ||||
0.0395744 | + | 0.999217i | \(0.487400\pi\) | |||||||
\(282\) | 11.8022 | 0.00249223 | ||||||||
\(283\) | 1853.03 | 0.389226 | 0.194613 | − | 0.980880i | \(-0.437655\pi\) | ||||
0.194613 | + | 0.980880i | \(0.437655\pi\) | |||||||
\(284\) | 7890.87 | 1.64872 | ||||||||
\(285\) | −5.73416 | −0.00119180 | ||||||||
\(286\) | −190.801 | −0.0394486 | ||||||||
\(287\) | −30.8014 | −0.00633501 | ||||||||
\(288\) | 3654.87 | 0.747796 | ||||||||
\(289\) | 2850.08 | 0.580109 | ||||||||
\(290\) | 839.021 | 0.169893 | ||||||||
\(291\) | 2.33153 | 0.000469680 0 | ||||||||
\(292\) | 735.341 | 0.147372 | ||||||||
\(293\) | −3682.91 | −0.734328 | −0.367164 | − | 0.930156i | \(-0.619671\pi\) | ||||
−0.367164 | + | 0.930156i | \(0.619671\pi\) | |||||||
\(294\) | 16.1711 | 0.00320789 | ||||||||
\(295\) | −4133.55 | −0.815812 | ||||||||
\(296\) | −2632.23 | −0.516875 | ||||||||
\(297\) | 35.8511 | 0.00700436 | ||||||||
\(298\) | 1447.57 | 0.281395 | ||||||||
\(299\) | −3724.84 | −0.720445 | ||||||||
\(300\) | −11.1447 | −0.00214481 | ||||||||
\(301\) | 413.688 | 0.0792178 | ||||||||
\(302\) | 794.798 | 0.151442 | ||||||||
\(303\) | −35.7364 | −0.00677559 | ||||||||
\(304\) | 942.995 | 0.177909 | ||||||||
\(305\) | −1749.12 | −0.328375 | ||||||||
\(306\) | 1864.48 | 0.348317 | ||||||||
\(307\) | −4358.02 | −0.810180 | −0.405090 | − | 0.914277i | \(-0.632760\pi\) | ||||
−0.405090 | + | 0.914277i | \(0.632760\pi\) | |||||||
\(308\) | −89.3478 | −0.0165294 | ||||||||
\(309\) | 53.4941 | 0.00984845 | ||||||||
\(310\) | −143.905 | −0.0263653 | ||||||||
\(311\) | −467.150 | −0.0851756 | −0.0425878 | − | 0.999093i | \(-0.513560\pi\) | ||||
−0.0425878 | + | 0.999093i | \(0.513560\pi\) | |||||||
\(312\) | −16.1082 | −0.00292291 | ||||||||
\(313\) | 8790.72 | 1.58748 | 0.793740 | − | 0.608258i | \(-0.208131\pi\) | ||||
0.793740 | + | 0.608258i | \(0.208131\pi\) | |||||||
\(314\) | 2618.51 | 0.470608 | ||||||||
\(315\) | −148.451 | −0.0265531 | ||||||||
\(316\) | −7592.29 | −1.35158 | ||||||||
\(317\) | 636.066 | 0.112697 | 0.0563486 | − | 0.998411i | \(-0.482054\pi\) | ||||
0.0563486 | + | 0.998411i | \(0.482054\pi\) | |||||||
\(318\) | −21.1192 | −0.00372422 | ||||||||
\(319\) | −2354.84 | −0.413309 | ||||||||
\(320\) | 1454.65 | 0.254116 | ||||||||
\(321\) | −105.355 | −0.0183189 | ||||||||
\(322\) | 145.110 | 0.0251138 | ||||||||
\(323\) | 1674.06 | 0.288381 | ||||||||
\(324\) | −5381.90 | −0.922823 | ||||||||
\(325\) | −553.214 | −0.0944208 | ||||||||
\(326\) | −564.746 | −0.0959459 | ||||||||
\(327\) | −116.127 | −0.0196387 | ||||||||
\(328\) | 337.763 | 0.0568593 | ||||||||
\(329\) | 274.340 | 0.0459721 | ||||||||
\(330\) | −2.60221 | −0.000434082 0 | ||||||||
\(331\) | −8584.94 | −1.42559 | −0.712796 | − | 0.701371i | \(-0.752572\pi\) | ||||
−0.712796 | + | 0.701371i | \(0.752572\pi\) | |||||||
\(332\) | −4498.01 | −0.743556 | ||||||||
\(333\) | 5892.24 | 0.969647 | ||||||||
\(334\) | 218.676 | 0.0358246 | ||||||||
\(335\) | 1702.58 | 0.277677 | ||||||||
\(336\) | −3.29464 | −0.000534933 0 | ||||||||
\(337\) | −1382.13 | −0.223411 | −0.111706 | − | 0.993741i | \(-0.535631\pi\) | ||||
−0.111706 | + | 0.993741i | \(0.535631\pi\) | |||||||
\(338\) | 1338.29 | 0.215366 | ||||||||
\(339\) | −43.4765 | −0.00696554 | ||||||||
\(340\) | 3253.65 | 0.518983 | ||||||||
\(341\) | 403.890 | 0.0641404 | ||||||||
\(342\) | 402.062 | 0.0635703 | ||||||||
\(343\) | 753.120 | 0.118556 | ||||||||
\(344\) | −4536.43 | −0.711011 | ||||||||
\(345\) | −50.8008 | −0.00792760 | ||||||||
\(346\) | 179.135 | 0.0278334 | ||||||||
\(347\) | 11869.6 | 1.83629 | 0.918143 | − | 0.396249i | \(-0.129688\pi\) | ||||
0.918143 | + | 0.396249i | \(0.129688\pi\) | |||||||
\(348\) | −95.4329 | −0.0147004 | ||||||||
\(349\) | −413.020 | −0.0633481 | −0.0316740 | − | 0.999498i | \(-0.510084\pi\) | ||||
−0.0316740 | + | 0.999498i | \(0.510084\pi\) | |||||||
\(350\) | 21.5517 | 0.00329139 | ||||||||
\(351\) | 72.1212 | 0.0109674 | ||||||||
\(352\) | 1489.22 | 0.225500 | ||||||||
\(353\) | −3256.96 | −0.491078 | −0.245539 | − | 0.969387i | \(-0.578965\pi\) | ||||
−0.245539 | + | 0.969387i | \(0.578965\pi\) | |||||||
\(354\) | −39.1141 | −0.00587258 | ||||||||
\(355\) | 5342.08 | 0.798672 | ||||||||
\(356\) | −1296.37 | −0.192999 | ||||||||
\(357\) | −5.84884 | −0.000867096 0 | ||||||||
\(358\) | −2699.17 | −0.398479 | ||||||||
\(359\) | −5256.97 | −0.772848 | −0.386424 | − | 0.922321i | \(-0.626290\pi\) | ||||
−0.386424 | + | 0.922321i | \(0.626290\pi\) | |||||||
\(360\) | 1627.88 | 0.238325 | ||||||||
\(361\) | 361.000 | 0.0526316 | ||||||||
\(362\) | −2608.16 | −0.378680 | ||||||||
\(363\) | 7.30350 | 0.00105602 | ||||||||
\(364\) | −179.740 | −0.0258816 | ||||||||
\(365\) | 497.823 | 0.0713897 | ||||||||
\(366\) | −16.5512 | −0.00236379 | ||||||||
\(367\) | 1958.55 | 0.278571 | 0.139286 | − | 0.990252i | \(-0.455519\pi\) | ||||
0.139286 | + | 0.990252i | \(0.455519\pi\) | |||||||
\(368\) | 8354.31 | 1.18342 | ||||||||
\(369\) | −756.082 | −0.106667 | ||||||||
\(370\) | −855.420 | −0.120192 | ||||||||
\(371\) | −490.911 | −0.0686977 | ||||||||
\(372\) | 16.3682 | 0.00228132 | ||||||||
\(373\) | −5965.31 | −0.828076 | −0.414038 | − | 0.910260i | \(-0.635882\pi\) | ||||
−0.414038 | + | 0.910260i | \(0.635882\pi\) | |||||||
\(374\) | 759.704 | 0.105036 | ||||||||
\(375\) | −7.54494 | −0.00103898 | ||||||||
\(376\) | −3008.36 | −0.412618 | ||||||||
\(377\) | −4737.19 | −0.647156 | ||||||||
\(378\) | −2.80965 | −0.000382308 0 | ||||||||
\(379\) | 375.676 | 0.0509161 | 0.0254580 | − | 0.999676i | \(-0.491896\pi\) | ||||
0.0254580 | + | 0.999676i | \(0.491896\pi\) | |||||||
\(380\) | 701.630 | 0.0947180 | ||||||||
\(381\) | −113.462 | −0.0152568 | ||||||||
\(382\) | −1566.32 | −0.209790 | ||||||||
\(383\) | 292.289 | 0.0389954 | 0.0194977 | − | 0.999810i | \(-0.493793\pi\) | ||||
0.0194977 | + | 0.999810i | \(0.493793\pi\) | |||||||
\(384\) | 79.1384 | 0.0105170 | ||||||||
\(385\) | −60.4880 | −0.00800716 | ||||||||
\(386\) | 1194.71 | 0.157536 | ||||||||
\(387\) | 10154.8 | 1.33384 | ||||||||
\(388\) | −285.286 | −0.0373278 | ||||||||
\(389\) | −6104.86 | −0.795704 | −0.397852 | − | 0.917450i | \(-0.630244\pi\) | ||||
−0.397852 | + | 0.917450i | \(0.630244\pi\) | |||||||
\(390\) | −5.23484 | −0.000679683 0 | ||||||||
\(391\) | 14831.0 | 1.91826 | ||||||||
\(392\) | −4122.00 | −0.531104 | ||||||||
\(393\) | −4.66104 | −0.000598265 0 | ||||||||
\(394\) | 220.455 | 0.0281887 | ||||||||
\(395\) | −5139.95 | −0.654731 | ||||||||
\(396\) | −2193.22 | −0.278317 | ||||||||
\(397\) | 2537.19 | 0.320751 | 0.160375 | − | 0.987056i | \(-0.448730\pi\) | ||||
0.160375 | + | 0.987056i | \(0.448730\pi\) | |||||||
\(398\) | 3066.17 | 0.386164 | ||||||||
\(399\) | −1.26126 | −0.000158251 0 | ||||||||
\(400\) | 1240.78 | 0.155098 | ||||||||
\(401\) | −2019.82 | −0.251534 | −0.125767 | − | 0.992060i | \(-0.540139\pi\) | ||||
−0.125767 | + | 0.992060i | \(0.540139\pi\) | |||||||
\(402\) | 16.1108 | 0.00199884 | ||||||||
\(403\) | 812.500 | 0.100430 | ||||||||
\(404\) | 4372.70 | 0.538490 | ||||||||
\(405\) | −3643.52 | −0.447033 | ||||||||
\(406\) | 184.548 | 0.0225590 | ||||||||
\(407\) | 2400.86 | 0.292399 | ||||||||
\(408\) | 64.1374 | 0.00778253 | ||||||||
\(409\) | −5930.91 | −0.717029 | −0.358514 | − | 0.933524i | \(-0.616717\pi\) | ||||
−0.358514 | + | 0.933524i | \(0.616717\pi\) | |||||||
\(410\) | 109.766 | 0.0132219 | ||||||||
\(411\) | −14.7729 | −0.00177297 | ||||||||
\(412\) | −6545.52 | −0.782706 | ||||||||
\(413\) | −909.201 | −0.108327 | ||||||||
\(414\) | 3562.00 | 0.422857 | ||||||||
\(415\) | −3045.14 | −0.360192 | ||||||||
\(416\) | 2995.85 | 0.353085 | ||||||||
\(417\) | −93.8003 | −0.0110154 | ||||||||
\(418\) | 163.825 | 0.0191697 | ||||||||
\(419\) | 13939.9 | 1.62532 | 0.812658 | − | 0.582741i | \(-0.198020\pi\) | ||||
0.812658 | + | 0.582741i | \(0.198020\pi\) | |||||||
\(420\) | −2.45136 | −0.000284795 0 | ||||||||
\(421\) | −11207.9 | −1.29748 | −0.648738 | − | 0.761012i | \(-0.724703\pi\) | ||||
−0.648738 | + | 0.761012i | \(0.724703\pi\) | |||||||
\(422\) | −233.107 | −0.0268897 | ||||||||
\(423\) | 6734.22 | 0.774063 | ||||||||
\(424\) | 5383.25 | 0.616589 | ||||||||
\(425\) | 2202.71 | 0.251405 | ||||||||
\(426\) | 50.5500 | 0.00574919 | ||||||||
\(427\) | −384.730 | −0.0436028 | ||||||||
\(428\) | 12891.2 | 1.45589 | ||||||||
\(429\) | 14.6924 | 0.00165350 | ||||||||
\(430\) | −1474.25 | −0.165336 | ||||||||
\(431\) | 2686.39 | 0.300230 | 0.150115 | − | 0.988669i | \(-0.452036\pi\) | ||||
0.150115 | + | 0.988669i | \(0.452036\pi\) | |||||||
\(432\) | −161.758 | −0.0180153 | ||||||||
\(433\) | 5824.77 | 0.646468 | 0.323234 | − | 0.946319i | \(-0.395230\pi\) | ||||
0.323234 | + | 0.946319i | \(0.395230\pi\) | |||||||
\(434\) | −31.6528 | −0.00350088 | ||||||||
\(435\) | −64.6077 | −0.00712115 | ||||||||
\(436\) | 14209.3 | 1.56079 | ||||||||
\(437\) | 3198.22 | 0.350095 | ||||||||
\(438\) | 4.71070 | 0.000513894 0 | ||||||||
\(439\) | −16128.4 | −1.75346 | −0.876728 | − | 0.480986i | \(-0.840279\pi\) | ||||
−0.876728 | + | 0.480986i | \(0.840279\pi\) | |||||||
\(440\) | 663.302 | 0.0718674 | ||||||||
\(441\) | 9227.10 | 0.996339 | ||||||||
\(442\) | 1528.29 | 0.164464 | ||||||||
\(443\) | −16147.4 | −1.73179 | −0.865896 | − | 0.500224i | \(-0.833251\pi\) | ||||
−0.865896 | + | 0.500224i | \(0.833251\pi\) | |||||||
\(444\) | 97.2983 | 0.0103999 | ||||||||
\(445\) | −877.637 | −0.0934921 | ||||||||
\(446\) | −1896.16 | −0.201314 | ||||||||
\(447\) | −111.468 | −0.0117948 | ||||||||
\(448\) | 319.959 | 0.0337425 | ||||||||
\(449\) | 10233.4 | 1.07560 | 0.537801 | − | 0.843072i | \(-0.319255\pi\) | ||||
0.537801 | + | 0.843072i | \(0.319255\pi\) | |||||||
\(450\) | 529.029 | 0.0554193 | ||||||||
\(451\) | −308.075 | −0.0321656 | ||||||||
\(452\) | 5319.77 | 0.553586 | ||||||||
\(453\) | −61.2023 | −0.00634776 | ||||||||
\(454\) | 2416.82 | 0.249840 | ||||||||
\(455\) | −121.683 | −0.0125375 | ||||||||
\(456\) | 13.8308 | 0.00142037 | ||||||||
\(457\) | 6256.80 | 0.640439 | 0.320220 | − | 0.947343i | \(-0.396243\pi\) | ||||
0.320220 | + | 0.947343i | \(0.396243\pi\) | |||||||
\(458\) | −1216.62 | −0.124125 | ||||||||
\(459\) | −287.162 | −0.0292017 | ||||||||
\(460\) | 6215.97 | 0.630046 | ||||||||
\(461\) | 11010.4 | 1.11238 | 0.556189 | − | 0.831056i | \(-0.312263\pi\) | ||||
0.556189 | + | 0.831056i | \(0.312263\pi\) | |||||||
\(462\) | −0.572374 | −5.76391e−5 0 | ||||||||
\(463\) | 16642.0 | 1.67046 | 0.835228 | − | 0.549904i | \(-0.185336\pi\) | ||||
0.835228 | + | 0.549904i | \(0.185336\pi\) | |||||||
\(464\) | 10624.9 | 1.06303 | ||||||||
\(465\) | 11.0812 | 0.00110511 | ||||||||
\(466\) | −1094.88 | −0.108840 | ||||||||
\(467\) | −6140.06 | −0.608411 | −0.304206 | − | 0.952606i | \(-0.598391\pi\) | ||||
−0.304206 | + | 0.952606i | \(0.598391\pi\) | |||||||
\(468\) | −4412.07 | −0.435786 | ||||||||
\(469\) | 374.494 | 0.0368710 | ||||||||
\(470\) | −977.657 | −0.0959488 | ||||||||
\(471\) | −201.635 | −0.0197258 | ||||||||
\(472\) | 9970.15 | 0.972274 | ||||||||
\(473\) | 4137.70 | 0.402223 | ||||||||
\(474\) | −48.6373 | −0.00471305 | ||||||||
\(475\) | 475.000 | 0.0458831 | ||||||||
\(476\) | 715.662 | 0.0689124 | ||||||||
\(477\) | −12050.4 | −1.15671 | ||||||||
\(478\) | −2287.61 | −0.218897 | ||||||||
\(479\) | −2999.01 | −0.286072 | −0.143036 | − | 0.989718i | \(-0.545686\pi\) | ||||
−0.143036 | + | 0.989718i | \(0.545686\pi\) | |||||||
\(480\) | 40.8585 | 0.00388527 | ||||||||
\(481\) | 4829.79 | 0.457836 | ||||||||
\(482\) | 1883.54 | 0.177994 | ||||||||
\(483\) | −11.1740 | −0.00105266 | ||||||||
\(484\) | −893.655 | −0.0839270 | ||||||||
\(485\) | −193.137 | −0.0180823 | ||||||||
\(486\) | −103.455 | −0.00965599 | ||||||||
\(487\) | 13804.2 | 1.28445 | 0.642224 | − | 0.766517i | \(-0.278012\pi\) | ||||
0.642224 | + | 0.766517i | \(0.278012\pi\) | |||||||
\(488\) | 4218.89 | 0.391353 | ||||||||
\(489\) | 43.4875 | 0.00402162 | ||||||||
\(490\) | −1339.57 | −0.123501 | ||||||||
\(491\) | 1097.44 | 0.100869 | 0.0504346 | − | 0.998727i | \(-0.483939\pi\) | ||||
0.0504346 | + | 0.998727i | \(0.483939\pi\) | |||||||
\(492\) | −12.4852 | −0.00114405 | ||||||||
\(493\) | 18861.9 | 1.72312 | ||||||||
\(494\) | 329.565 | 0.0300158 | ||||||||
\(495\) | −1484.80 | −0.134822 | ||||||||
\(496\) | −1822.33 | −0.164969 | ||||||||
\(497\) | 1175.03 | 0.106051 | ||||||||
\(498\) | −28.8149 | −0.00259282 | ||||||||
\(499\) | −11098.7 | −0.995679 | −0.497840 | − | 0.867269i | \(-0.665873\pi\) | ||||
−0.497840 | + | 0.867269i | \(0.665873\pi\) | |||||||
\(500\) | 923.197 | 0.0825732 | ||||||||
\(501\) | −16.8389 | −0.00150161 | ||||||||
\(502\) | −3247.36 | −0.288718 | ||||||||
\(503\) | 6753.57 | 0.598662 | 0.299331 | − | 0.954149i | \(-0.403237\pi\) | ||||
0.299331 | + | 0.954149i | \(0.403237\pi\) | |||||||
\(504\) | 358.064 | 0.0316457 | ||||||||
\(505\) | 2960.30 | 0.260855 | ||||||||
\(506\) | 1451.38 | 0.127514 | ||||||||
\(507\) | −103.053 | −0.00902715 | ||||||||
\(508\) | 13883.2 | 1.21253 | ||||||||
\(509\) | −10002.2 | −0.870997 | −0.435499 | − | 0.900189i | \(-0.643428\pi\) | ||||
−0.435499 | + | 0.900189i | \(0.643428\pi\) | |||||||
\(510\) | 20.8433 | 0.00180972 | ||||||||
\(511\) | 109.499 | 0.00947938 | ||||||||
\(512\) | −11507.7 | −0.993309 | ||||||||
\(513\) | −61.9247 | −0.00532952 | ||||||||
\(514\) | 2293.85 | 0.196843 | ||||||||
\(515\) | −4431.29 | −0.379157 | ||||||||
\(516\) | 167.686 | 0.0143061 | ||||||||
\(517\) | 2743.94 | 0.233420 | ||||||||
\(518\) | −188.155 | −0.0159596 | ||||||||
\(519\) | −13.7940 | −0.00116665 | ||||||||
\(520\) | 1334.35 | 0.112529 | ||||||||
\(521\) | −107.338 | −0.00902602 | −0.00451301 | − | 0.999990i | \(-0.501437\pi\) | ||||
−0.00451301 | + | 0.999990i | \(0.501437\pi\) | |||||||
\(522\) | 4530.10 | 0.379841 | ||||||||
\(523\) | 9371.01 | 0.783491 | 0.391745 | − | 0.920074i | \(-0.371871\pi\) | ||||
0.391745 | + | 0.920074i | \(0.371871\pi\) | |||||||
\(524\) | 570.323 | 0.0475471 | ||||||||
\(525\) | −1.65956 | −0.000137960 0 | ||||||||
\(526\) | 1871.24 | 0.155114 | ||||||||
\(527\) | −3235.10 | −0.267406 | ||||||||
\(528\) | −32.9529 | −0.00271608 | ||||||||
\(529\) | 16167.1 | 1.32877 | ||||||||
\(530\) | 1749.45 | 0.143379 | ||||||||
\(531\) | −22318.2 | −1.82397 | ||||||||
\(532\) | 154.328 | 0.0125770 | ||||||||
\(533\) | −619.750 | −0.0503646 | ||||||||
\(534\) | −8.30472 | −0.000672997 0 | ||||||||
\(535\) | 8727.31 | 0.705261 | ||||||||
\(536\) | −4106.63 | −0.330932 | ||||||||
\(537\) | 207.846 | 0.0167025 | ||||||||
\(538\) | 4569.92 | 0.366215 | ||||||||
\(539\) | 3759.70 | 0.300448 | ||||||||
\(540\) | −120.355 | −0.00959122 | ||||||||
\(541\) | −3851.36 | −0.306068 | −0.153034 | − | 0.988221i | \(-0.548904\pi\) | ||||
−0.153034 | + | 0.988221i | \(0.548904\pi\) | |||||||
\(542\) | 5154.00 | 0.408456 | ||||||||
\(543\) | 200.838 | 0.0158725 | ||||||||
\(544\) | −11928.4 | −0.940125 | ||||||||
\(545\) | 9619.64 | 0.756074 | ||||||||
\(546\) | −1.15144 | −9.02508e−5 0 | ||||||||
\(547\) | 572.812 | 0.0447746 | 0.0223873 | − | 0.999749i | \(-0.492873\pi\) | ||||
0.0223873 | + | 0.999749i | \(0.492873\pi\) | |||||||
\(548\) | 1807.60 | 0.140907 | ||||||||
\(549\) | −9443.98 | −0.734170 | ||||||||
\(550\) | 215.560 | 0.0167118 | ||||||||
\(551\) | 4067.45 | 0.314481 | ||||||||
\(552\) | 122.532 | 0.00944801 | ||||||||
\(553\) | −1130.56 | −0.0869376 | ||||||||
\(554\) | −4523.26 | −0.346886 | ||||||||
\(555\) | 65.8705 | 0.00503792 | ||||||||
\(556\) | 11477.4 | 0.875448 | ||||||||
\(557\) | −21782.7 | −1.65703 | −0.828513 | − | 0.559971i | \(-0.810812\pi\) | ||||
−0.828513 | + | 0.559971i | \(0.810812\pi\) | |||||||
\(558\) | −776.980 | −0.0589466 | ||||||||
\(559\) | 8323.74 | 0.629798 | ||||||||
\(560\) | 272.918 | 0.0205945 | ||||||||
\(561\) | −58.4999 | −0.00440262 | ||||||||
\(562\) | −292.239 | −0.0219348 | ||||||||
\(563\) | 7408.62 | 0.554593 | 0.277297 | − | 0.960784i | \(-0.410562\pi\) | ||||
0.277297 | + | 0.960784i | \(0.410562\pi\) | |||||||
\(564\) | 111.202 | 0.00830220 | ||||||||
\(565\) | 3601.46 | 0.268168 | ||||||||
\(566\) | −1452.50 | −0.107868 | ||||||||
\(567\) | −801.417 | −0.0593586 | ||||||||
\(568\) | −12885.1 | −0.951846 | ||||||||
\(569\) | 2367.61 | 0.174438 | 0.0872190 | − | 0.996189i | \(-0.472202\pi\) | ||||
0.0872190 | + | 0.996189i | \(0.472202\pi\) | |||||||
\(570\) | 4.49473 | 0.000330287 0 | ||||||||
\(571\) | −22777.5 | −1.66937 | −0.834683 | − | 0.550731i | \(-0.814349\pi\) | ||||
−0.834683 | + | 0.550731i | \(0.814349\pi\) | |||||||
\(572\) | −1797.75 | −0.131412 | ||||||||
\(573\) | 120.612 | 0.00879346 | ||||||||
\(574\) | 24.1438 | 0.00175565 | ||||||||
\(575\) | 4208.18 | 0.305206 | ||||||||
\(576\) | 7854.03 | 0.568145 | ||||||||
\(577\) | −16073.0 | −1.15967 | −0.579833 | − | 0.814735i | \(-0.696882\pi\) | ||||
−0.579833 | + | 0.814735i | \(0.696882\pi\) | |||||||
\(578\) | −2234.04 | −0.160768 | ||||||||
\(579\) | −91.9967 | −0.00660320 | ||||||||
\(580\) | 7905.38 | 0.565953 | ||||||||
\(581\) | −669.797 | −0.0478276 | ||||||||
\(582\) | −1.82758 | −0.000130164 0 | ||||||||
\(583\) | −4910.08 | −0.348808 | ||||||||
\(584\) | −1200.75 | −0.0850812 | ||||||||
\(585\) | −2986.95 | −0.211103 | ||||||||
\(586\) | 2886.86 | 0.203507 | ||||||||
\(587\) | −14991.8 | −1.05413 | −0.527067 | − | 0.849823i | \(-0.676708\pi\) | ||||
−0.527067 | + | 0.849823i | \(0.676708\pi\) | |||||||
\(588\) | 152.367 | 0.0106862 | ||||||||
\(589\) | −697.628 | −0.0488035 | ||||||||
\(590\) | 3240.10 | 0.226089 | ||||||||
\(591\) | −16.9758 | −0.00118154 | ||||||||
\(592\) | −10832.6 | −0.752053 | ||||||||
\(593\) | 8315.72 | 0.575861 | 0.287930 | − | 0.957651i | \(-0.407033\pi\) | ||||
0.287930 | + | 0.957651i | \(0.407033\pi\) | |||||||
\(594\) | −28.1020 | −0.00194114 | ||||||||
\(595\) | 484.500 | 0.0333824 | ||||||||
\(596\) | 13639.2 | 0.937391 | ||||||||
\(597\) | −236.106 | −0.0161863 | ||||||||
\(598\) | 2919.73 | 0.199660 | ||||||||
\(599\) | −18674.7 | −1.27383 | −0.636916 | − | 0.770933i | \(-0.719790\pi\) | ||||
−0.636916 | + | 0.770933i | \(0.719790\pi\) | |||||||
\(600\) | 18.1984 | 0.00123825 | ||||||||
\(601\) | −807.103 | −0.0547794 | −0.0273897 | − | 0.999625i | \(-0.508719\pi\) | ||||
−0.0273897 | + | 0.999625i | \(0.508719\pi\) | |||||||
\(602\) | −324.270 | −0.0219539 | ||||||||
\(603\) | 9192.70 | 0.620822 | ||||||||
\(604\) | 7488.70 | 0.504488 | ||||||||
\(605\) | −605.000 | −0.0406558 | ||||||||
\(606\) | 28.0121 | 0.00187775 | ||||||||
\(607\) | 16324.2 | 1.09156 | 0.545782 | − | 0.837927i | \(-0.316233\pi\) | ||||
0.545782 | + | 0.837927i | \(0.316233\pi\) | |||||||
\(608\) | −2572.29 | −0.171579 | ||||||||
\(609\) | −14.2109 | −0.000945572 0 | ||||||||
\(610\) | 1371.05 | 0.0910038 | ||||||||
\(611\) | 5519.95 | 0.365488 | ||||||||
\(612\) | 17567.4 | 1.16032 | ||||||||
\(613\) | −824.080 | −0.0542973 | −0.0271487 | − | 0.999631i | \(-0.508643\pi\) | ||||
−0.0271487 | + | 0.999631i | \(0.508643\pi\) | |||||||
\(614\) | 3416.04 | 0.224528 | ||||||||
\(615\) | −8.45239 | −0.000554200 0 | ||||||||
\(616\) | 145.897 | 0.00954282 | ||||||||
\(617\) | −15112.5 | −0.986070 | −0.493035 | − | 0.870009i | \(-0.664113\pi\) | ||||
−0.493035 | + | 0.870009i | \(0.664113\pi\) | |||||||
\(618\) | −41.9315 | −0.00272934 | ||||||||
\(619\) | 3574.05 | 0.232073 | 0.116036 | − | 0.993245i | \(-0.462981\pi\) | ||||
0.116036 | + | 0.993245i | \(0.462981\pi\) | |||||||
\(620\) | −1355.89 | −0.0878288 | ||||||||
\(621\) | −548.612 | −0.0354509 | ||||||||
\(622\) | 366.177 | 0.0236051 | ||||||||
\(623\) | −193.042 | −0.0124142 | ||||||||
\(624\) | −66.2910 | −0.00425283 | ||||||||
\(625\) | 625.000 | 0.0400000 | ||||||||
\(626\) | −6890.63 | −0.439944 | ||||||||
\(627\) | −12.6151 | −0.000803509 0 | ||||||||
\(628\) | 24671.9 | 1.56770 | ||||||||
\(629\) | −19230.6 | −1.21903 | ||||||||
\(630\) | 116.363 | 0.00735878 | ||||||||
\(631\) | 1678.56 | 0.105899 | 0.0529495 | − | 0.998597i | \(-0.483138\pi\) | ||||
0.0529495 | + | 0.998597i | \(0.483138\pi\) | |||||||
\(632\) | 12397.6 | 0.780300 | ||||||||
\(633\) | 17.9501 | 0.00112709 | ||||||||
\(634\) | −498.582 | −0.0312322 | ||||||||
\(635\) | 9398.86 | 0.587374 | ||||||||
\(636\) | −198.988 | −0.0124063 | ||||||||
\(637\) | 7563.33 | 0.470439 | ||||||||
\(638\) | 1845.85 | 0.114542 | ||||||||
\(639\) | 28843.4 | 1.78564 | ||||||||
\(640\) | −6555.58 | −0.404894 | ||||||||
\(641\) | 2186.08 | 0.134704 | 0.0673518 | − | 0.997729i | \(-0.478545\pi\) | ||||
0.0673518 | + | 0.997729i | \(0.478545\pi\) | |||||||
\(642\) | 82.5831 | 0.00507678 | ||||||||
\(643\) | −22353.0 | −1.37094 | −0.685472 | − | 0.728099i | \(-0.740404\pi\) | ||||
−0.685472 | + | 0.728099i | \(0.740404\pi\) | |||||||
\(644\) | 1367.24 | 0.0836598 | ||||||||
\(645\) | 113.522 | 0.00693014 | ||||||||
\(646\) | −1312.22 | −0.0799202 | ||||||||
\(647\) | 848.196 | 0.0515394 | 0.0257697 | − | 0.999668i | \(-0.491796\pi\) | ||||
0.0257697 | + | 0.999668i | \(0.491796\pi\) | |||||||
\(648\) | 8788.20 | 0.532767 | ||||||||
\(649\) | −9093.81 | −0.550021 | ||||||||
\(650\) | 433.638 | 0.0261672 | ||||||||
\(651\) | 2.43738 | 0.000146741 0 | ||||||||
\(652\) | −5321.12 | −0.319618 | ||||||||
\(653\) | 20748.5 | 1.24341 | 0.621707 | − | 0.783250i | \(-0.286439\pi\) | ||||
0.621707 | + | 0.783250i | \(0.286439\pi\) | |||||||
\(654\) | 91.0268 | 0.00544255 | ||||||||
\(655\) | 386.106 | 0.0230327 | ||||||||
\(656\) | 1390.01 | 0.0827301 | ||||||||
\(657\) | 2687.88 | 0.159611 | ||||||||
\(658\) | −215.042 | −0.0127404 | ||||||||
\(659\) | −5565.49 | −0.328984 | −0.164492 | − | 0.986378i | \(-0.552599\pi\) | ||||
−0.164492 | + | 0.986378i | \(0.552599\pi\) | |||||||
\(660\) | −24.5184 | −0.00144603 | ||||||||
\(661\) | −6981.39 | −0.410809 | −0.205404 | − | 0.978677i | \(-0.565851\pi\) | ||||
−0.205404 | + | 0.978677i | \(0.565851\pi\) | |||||||
\(662\) | 6729.33 | 0.395080 | ||||||||
\(663\) | −117.684 | −0.00689359 | ||||||||
\(664\) | 7344.88 | 0.429272 | ||||||||
\(665\) | 104.479 | 0.00609253 | ||||||||
\(666\) | −4618.65 | −0.268722 | ||||||||
\(667\) | 36034.9 | 2.09187 | ||||||||
\(668\) | 2060.40 | 0.119340 | ||||||||
\(669\) | 146.011 | 0.00843816 | ||||||||
\(670\) | −1334.57 | −0.0769538 | ||||||||
\(671\) | −3848.07 | −0.221390 | ||||||||
\(672\) | 8.98710 | 0.000515900 0 | ||||||||
\(673\) | 15367.4 | 0.880192 | 0.440096 | − | 0.897951i | \(-0.354944\pi\) | ||||
0.440096 | + | 0.897951i | \(0.354944\pi\) | |||||||
\(674\) | 1083.39 | 0.0619148 | ||||||||
\(675\) | −81.4799 | −0.00464617 | ||||||||
\(676\) | 12609.6 | 0.717433 | ||||||||
\(677\) | −20345.3 | −1.15500 | −0.577500 | − | 0.816391i | \(-0.695972\pi\) | ||||
−0.577500 | + | 0.816391i | \(0.695972\pi\) | |||||||
\(678\) | 34.0792 | 0.00193039 | ||||||||
\(679\) | −42.4818 | −0.00240103 | ||||||||
\(680\) | −5312.94 | −0.299621 | ||||||||
\(681\) | −186.104 | −0.0104721 | ||||||||
\(682\) | −316.590 | −0.0177755 | ||||||||
\(683\) | −17653.0 | −0.988982 | −0.494491 | − | 0.869183i | \(-0.664645\pi\) | ||||
−0.494491 | + | 0.869183i | \(0.664645\pi\) | |||||||
\(684\) | 3788.29 | 0.211767 | ||||||||
\(685\) | 1223.74 | 0.0682579 | ||||||||
\(686\) | −590.336 | −0.0328559 | ||||||||
\(687\) | 93.6845 | 0.00520275 | ||||||||
\(688\) | −18669.0 | −1.03452 | ||||||||
\(689\) | −9877.54 | −0.546160 | ||||||||
\(690\) | 39.8204 | 0.00219701 | ||||||||
\(691\) | −27619.5 | −1.52054 | −0.760272 | − | 0.649605i | \(-0.774934\pi\) | ||||
−0.760272 | + | 0.649605i | \(0.774934\pi\) | |||||||
\(692\) | 1687.83 | 0.0927194 | ||||||||
\(693\) | −326.591 | −0.0179021 | ||||||||
\(694\) | −9303.99 | −0.508897 | ||||||||
\(695\) | 7770.13 | 0.424083 | ||||||||
\(696\) | 155.834 | 0.00848689 | ||||||||
\(697\) | 2467.63 | 0.134101 | ||||||||
\(698\) | 323.747 | 0.0175559 | ||||||||
\(699\) | 84.3095 | 0.00456206 | ||||||||
\(700\) | 203.063 | 0.0109644 | ||||||||
\(701\) | −10809.2 | −0.582393 | −0.291196 | − | 0.956663i | \(-0.594053\pi\) | ||||
−0.291196 | + | 0.956663i | \(0.594053\pi\) | |||||||
\(702\) | −56.5324 | −0.00303943 | ||||||||
\(703\) | −4146.95 | −0.222482 | ||||||||
\(704\) | 3200.22 | 0.171325 | ||||||||
\(705\) | 75.2831 | 0.00402174 | ||||||||
\(706\) | 2552.98 | 0.136094 | ||||||||
\(707\) | 651.137 | 0.0346372 | ||||||||
\(708\) | −368.539 | −0.0195629 | ||||||||
\(709\) | −14360.2 | −0.760663 | −0.380331 | − | 0.924850i | \(-0.624190\pi\) | ||||
−0.380331 | + | 0.924850i | \(0.624190\pi\) | |||||||
\(710\) | −4187.41 | −0.221339 | ||||||||
\(711\) | −27752.0 | −1.46383 | ||||||||
\(712\) | 2116.86 | 0.111423 | ||||||||
\(713\) | −6180.52 | −0.324632 | ||||||||
\(714\) | 4.58463 | 0.000240302 0 | ||||||||
\(715\) | −1217.07 | −0.0636585 | ||||||||
\(716\) | −25432.0 | −1.32743 | ||||||||
\(717\) | 176.154 | 0.00917518 | ||||||||
\(718\) | 4120.69 | 0.214182 | ||||||||
\(719\) | 19614.5 | 1.01738 | 0.508690 | − | 0.860950i | \(-0.330130\pi\) | ||||
0.508690 | + | 0.860950i | \(0.330130\pi\) | |||||||
\(720\) | 6699.32 | 0.346763 | ||||||||
\(721\) | −974.690 | −0.0503459 | ||||||||
\(722\) | −282.971 | −0.0145860 | ||||||||
\(723\) | −145.040 | −0.00746070 | ||||||||
\(724\) | −24574.5 | −1.26147 | ||||||||
\(725\) | 5351.90 | 0.274158 | ||||||||
\(726\) | −5.72487 | −0.000292658 0 | ||||||||
\(727\) | 7497.02 | 0.382461 | 0.191231 | − | 0.981545i | \(-0.438752\pi\) | ||||
0.191231 | + | 0.981545i | \(0.438752\pi\) | |||||||
\(728\) | 293.500 | 0.0149421 | ||||||||
\(729\) | −19667.1 | −0.999190 | ||||||||
\(730\) | −390.220 | −0.0197845 | ||||||||
\(731\) | −33142.3 | −1.67690 | ||||||||
\(732\) | −155.948 | −0.00787433 | ||||||||
\(733\) | 21328.5 | 1.07474 | 0.537371 | − | 0.843346i | \(-0.319418\pi\) | ||||
0.537371 | + | 0.843346i | \(0.319418\pi\) | |||||||
\(734\) | −1535.22 | −0.0772016 | ||||||||
\(735\) | 103.152 | 0.00517660 | ||||||||
\(736\) | −22788.8 | −1.14131 | ||||||||
\(737\) | 3745.68 | 0.187210 | ||||||||
\(738\) | 592.657 | 0.0295610 | ||||||||
\(739\) | 13437.4 | 0.668879 | 0.334440 | − | 0.942417i | \(-0.391453\pi\) | ||||
0.334440 | + | 0.942417i | \(0.391453\pi\) | |||||||
\(740\) | −8059.89 | −0.400389 | ||||||||
\(741\) | −25.3777 | −0.00125813 | ||||||||
\(742\) | 384.802 | 0.0190384 | ||||||||
\(743\) | −3760.57 | −0.185682 | −0.0928411 | − | 0.995681i | \(-0.529595\pi\) | ||||
−0.0928411 | + | 0.995681i | \(0.529595\pi\) | |||||||
\(744\) | −26.7279 | −0.00131706 | ||||||||
\(745\) | 9233.70 | 0.454090 | ||||||||
\(746\) | 4675.93 | 0.229488 | ||||||||
\(747\) | −16441.5 | −0.805306 | ||||||||
\(748\) | 7158.04 | 0.349898 | ||||||||
\(749\) | 1919.63 | 0.0936471 | ||||||||
\(750\) | 5.91412 | 0.000287938 0 | ||||||||
\(751\) | −27004.2 | −1.31211 | −0.656056 | − | 0.754712i | \(-0.727777\pi\) | ||||
−0.656056 | + | 0.754712i | \(0.727777\pi\) | |||||||
\(752\) | −12380.5 | −0.600359 | ||||||||
\(753\) | 250.058 | 0.0121018 | ||||||||
\(754\) | 3713.26 | 0.179349 | ||||||||
\(755\) | 5069.82 | 0.244383 | ||||||||
\(756\) | −26.4729 | −0.00127356 | ||||||||
\(757\) | 4049.74 | 0.194439 | 0.0972195 | − | 0.995263i | \(-0.469005\pi\) | ||||
0.0972195 | + | 0.995263i | \(0.469005\pi\) | |||||||
\(758\) | −294.475 | −0.0141106 | ||||||||
\(759\) | −111.762 | −0.00534479 | ||||||||
\(760\) | −1145.70 | −0.0546829 | ||||||||
\(761\) | −25094.8 | −1.19538 | −0.597692 | − | 0.801726i | \(-0.703915\pi\) | ||||
−0.597692 | + | 0.801726i | \(0.703915\pi\) | |||||||
\(762\) | 88.9376 | 0.00422818 | ||||||||
\(763\) | 2115.90 | 0.100394 | ||||||||
\(764\) | −14758.1 | −0.698860 | ||||||||
\(765\) | 11893.0 | 0.562082 | ||||||||
\(766\) | −229.111 | −0.0108070 | ||||||||
\(767\) | −18293.9 | −0.861218 | ||||||||
\(768\) | 78.4500 | 0.00368597 | ||||||||
\(769\) | 12245.3 | 0.574224 | 0.287112 | − | 0.957897i | \(-0.407305\pi\) | ||||
0.287112 | + | 0.957897i | \(0.407305\pi\) | |||||||
\(770\) | 47.4137 | 0.00221905 | ||||||||
\(771\) | −176.635 | −0.00825079 | ||||||||
\(772\) | 11256.7 | 0.524789 | ||||||||
\(773\) | 4554.29 | 0.211910 | 0.105955 | − | 0.994371i | \(-0.466210\pi\) | ||||
0.105955 | + | 0.994371i | \(0.466210\pi\) | |||||||
\(774\) | −7959.86 | −0.369653 | ||||||||
\(775\) | −917.932 | −0.0425459 | ||||||||
\(776\) | 465.848 | 0.0215502 | ||||||||
\(777\) | 14.4886 | 0.000668954 0 | ||||||||
\(778\) | 4785.32 | 0.220517 | ||||||||
\(779\) | 532.129 | 0.0244743 | ||||||||
\(780\) | −49.3234 | −0.00226418 | ||||||||
\(781\) | 11752.6 | 0.538464 | ||||||||
\(782\) | −11625.4 | −0.531614 | ||||||||
\(783\) | −697.716 | −0.0318446 | ||||||||
\(784\) | −16963.5 | −0.772755 | ||||||||
\(785\) | 16702.8 | 0.759424 | ||||||||
\(786\) | 3.65357 | 0.000165800 0 | ||||||||
\(787\) | 4110.23 | 0.186167 | 0.0930837 | − | 0.995658i | \(-0.470328\pi\) | ||||
0.0930837 | + | 0.995658i | \(0.470328\pi\) | |||||||
\(788\) | 2077.15 | 0.0939030 | ||||||||
\(789\) | −144.092 | −0.00650167 | ||||||||
\(790\) | 4028.96 | 0.181448 | ||||||||
\(791\) | 792.165 | 0.0356083 | ||||||||
\(792\) | 3581.34 | 0.160679 | ||||||||
\(793\) | −7741.10 | −0.346651 | ||||||||
\(794\) | −1988.79 | −0.0888909 | ||||||||
\(795\) | −134.714 | −0.00600982 | ||||||||
\(796\) | 28889.9 | 1.28640 | ||||||||
\(797\) | 28046.0 | 1.24647 | 0.623237 | − | 0.782033i | \(-0.285817\pi\) | ||||
0.623237 | + | 0.782033i | \(0.285817\pi\) | |||||||
\(798\) | 0.988646 | 4.38567e−5 0 | ||||||||
\(799\) | −21978.5 | −0.973148 | ||||||||
\(800\) | −3384.60 | −0.149579 | ||||||||
\(801\) | −4738.60 | −0.209026 | ||||||||
\(802\) | 1583.25 | 0.0697087 | ||||||||
\(803\) | 1095.21 | 0.0481309 | ||||||||
\(804\) | 151.799 | 0.00665861 | ||||||||
\(805\) | 925.617 | 0.0405264 | ||||||||
\(806\) | −636.880 | −0.0278327 | ||||||||
\(807\) | −351.901 | −0.0153501 | ||||||||
\(808\) | −7140.26 | −0.310883 | ||||||||
\(809\) | −12876.7 | −0.559607 | −0.279803 | − | 0.960057i | \(-0.590269\pi\) | ||||
−0.279803 | + | 0.960057i | \(0.590269\pi\) | |||||||
\(810\) | 2855.99 | 0.123888 | ||||||||
\(811\) | 2515.04 | 0.108896 | 0.0544482 | − | 0.998517i | \(-0.482660\pi\) | ||||
0.0544482 | + | 0.998517i | \(0.482660\pi\) | |||||||
\(812\) | 1738.84 | 0.0751493 | ||||||||
\(813\) | −396.877 | −0.0171206 | ||||||||
\(814\) | −1881.92 | −0.0810337 | ||||||||
\(815\) | −3602.37 | −0.154829 | ||||||||
\(816\) | 263.948 | 0.0113236 | ||||||||
\(817\) | −7146.93 | −0.306046 | ||||||||
\(818\) | 4648.96 | 0.198713 | ||||||||
\(819\) | −656.999 | −0.0280310 | ||||||||
\(820\) | 1034.23 | 0.0440451 | ||||||||
\(821\) | −39018.8 | −1.65867 | −0.829333 | − | 0.558754i | \(-0.811280\pi\) | ||||
−0.829333 | + | 0.558754i | \(0.811280\pi\) | |||||||
\(822\) | 11.5798 | 0.000491351 0 | ||||||||
\(823\) | −3391.84 | −0.143660 | −0.0718299 | − | 0.997417i | \(-0.522884\pi\) | ||||
−0.0718299 | + | 0.997417i | \(0.522884\pi\) | |||||||
\(824\) | 10688.3 | 0.451874 | ||||||||
\(825\) | −16.5989 | −0.000700483 0 | ||||||||
\(826\) | 712.680 | 0.0300210 | ||||||||
\(827\) | −36397.7 | −1.53044 | −0.765220 | − | 0.643769i | \(-0.777370\pi\) | ||||
−0.765220 | + | 0.643769i | \(0.777370\pi\) | |||||||
\(828\) | 33561.7 | 1.40864 | ||||||||
\(829\) | −25754.4 | −1.07899 | −0.539497 | − | 0.841987i | \(-0.681386\pi\) | ||||
−0.539497 | + | 0.841987i | \(0.681386\pi\) | |||||||
\(830\) | 2386.94 | 0.0998215 | ||||||||
\(831\) | 348.308 | 0.0145399 | ||||||||
\(832\) | 6437.85 | 0.268260 | ||||||||
\(833\) | −30114.6 | −1.25259 | ||||||||
\(834\) | 73.5256 | 0.00305274 | ||||||||
\(835\) | 1394.88 | 0.0578105 | ||||||||
\(836\) | 1543.59 | 0.0638589 | ||||||||
\(837\) | 119.669 | 0.00494188 | ||||||||
\(838\) | −10926.8 | −0.450430 | ||||||||
\(839\) | −26723.0 | −1.09962 | −0.549809 | − | 0.835290i | \(-0.685300\pi\) | ||||
−0.549809 | + | 0.835290i | \(0.685300\pi\) | |||||||
\(840\) | 4.00286 | 0.000164419 0 | ||||||||
\(841\) | 21439.6 | 0.879067 | ||||||||
\(842\) | 8785.31 | 0.359575 | ||||||||
\(843\) | 22.5035 | 0.000919408 0 | ||||||||
\(844\) | −2196.36 | −0.0895758 | ||||||||
\(845\) | 8536.64 | 0.347538 | ||||||||
\(846\) | −5278.64 | −0.214519 | ||||||||
\(847\) | −133.074 | −0.00539842 | ||||||||
\(848\) | 22154.0 | 0.897136 | ||||||||
\(849\) | 111.848 | 0.00452133 | ||||||||
\(850\) | −1726.60 | −0.0696728 | ||||||||
\(851\) | −36739.2 | −1.47991 | ||||||||
\(852\) | 476.289 | 0.0191519 | ||||||||
\(853\) | 31404.1 | 1.26056 | 0.630279 | − | 0.776368i | \(-0.282940\pi\) | ||||
0.630279 | + | 0.776368i | \(0.282940\pi\) | |||||||
\(854\) | 301.572 | 0.0120838 | ||||||||
\(855\) | 2564.65 | 0.102584 | ||||||||
\(856\) | −21050.3 | −0.840520 | ||||||||
\(857\) | −19490.7 | −0.776884 | −0.388442 | − | 0.921473i | \(-0.626987\pi\) | ||||
−0.388442 | + | 0.921473i | \(0.626987\pi\) | |||||||
\(858\) | −11.5166 | −0.000458242 0 | ||||||||
\(859\) | −2031.11 | −0.0806758 | −0.0403379 | − | 0.999186i | \(-0.512843\pi\) | ||||
−0.0403379 | + | 0.999186i | \(0.512843\pi\) | |||||||
\(860\) | −13890.6 | −0.550773 | ||||||||
\(861\) | −1.85916 | −7.35888e−5 0 | ||||||||
\(862\) | −2105.74 | −0.0832038 | ||||||||
\(863\) | −31486.2 | −1.24195 | −0.620975 | − | 0.783830i | \(-0.713263\pi\) | ||||
−0.620975 | + | 0.783830i | \(0.713263\pi\) | |||||||
\(864\) | 441.242 | 0.0173743 | ||||||||
\(865\) | 1142.66 | 0.0449150 | ||||||||
\(866\) | −4565.77 | −0.179158 | ||||||||
\(867\) | 172.029 | 0.00673866 | ||||||||
\(868\) | −298.237 | −0.0116622 | ||||||||
\(869\) | −11307.9 | −0.441420 | ||||||||
\(870\) | 50.6429 | 0.00197351 | ||||||||
\(871\) | 7535.13 | 0.293132 | ||||||||
\(872\) | −23202.6 | −0.901078 | ||||||||
\(873\) | −1042.80 | −0.0404278 | ||||||||
\(874\) | −2506.93 | −0.0970232 | ||||||||
\(875\) | 137.473 | 0.00531135 | ||||||||
\(876\) | 44.3849 | 0.00171190 | ||||||||
\(877\) | −16898.1 | −0.650638 | −0.325319 | − | 0.945604i | \(-0.605472\pi\) | ||||
−0.325319 | + | 0.945604i | \(0.605472\pi\) | |||||||
\(878\) | 12642.3 | 0.485942 | ||||||||
\(879\) | −222.299 | −0.00853009 | ||||||||
\(880\) | 2729.72 | 0.104567 | ||||||||
\(881\) | 25394.8 | 0.971138 | 0.485569 | − | 0.874198i | \(-0.338612\pi\) | ||||
0.485569 | + | 0.874198i | \(0.338612\pi\) | |||||||
\(882\) | −7232.69 | −0.276119 | ||||||||
\(883\) | −19200.4 | −0.731762 | −0.365881 | − | 0.930662i | \(-0.619232\pi\) | ||||
−0.365881 | + | 0.930662i | \(0.619232\pi\) | |||||||
\(884\) | 14399.7 | 0.547868 | ||||||||
\(885\) | −249.499 | −0.00947664 | ||||||||
\(886\) | 12657.2 | 0.479938 | ||||||||
\(887\) | 41952.3 | 1.58807 | 0.794036 | − | 0.607871i | \(-0.207976\pi\) | ||||
0.794036 | + | 0.607871i | \(0.207976\pi\) | |||||||
\(888\) | −158.880 | −0.00600412 | ||||||||
\(889\) | 2067.34 | 0.0779936 | ||||||||
\(890\) | 687.938 | 0.0259098 | ||||||||
\(891\) | −8015.75 | −0.301389 | ||||||||
\(892\) | −17865.9 | −0.670622 | ||||||||
\(893\) | −4739.53 | −0.177606 | ||||||||
\(894\) | 87.3748 | 0.00326874 | ||||||||
\(895\) | −17217.3 | −0.643030 | ||||||||
\(896\) | −1441.94 | −0.0537633 | ||||||||
\(897\) | −224.830 | −0.00836883 | ||||||||
\(898\) | −8021.50 | −0.298086 | ||||||||
\(899\) | −7860.29 | −0.291608 | ||||||||
\(900\) | 4984.59 | 0.184614 | ||||||||
\(901\) | 39329.0 | 1.45421 | ||||||||
\(902\) | 241.485 | 0.00891418 | ||||||||
\(903\) | 24.9700 | 0.000920209 0 | ||||||||
\(904\) | −8686.75 | −0.319598 | ||||||||
\(905\) | −16636.8 | −0.611079 | ||||||||
\(906\) | 47.9736 | 0.00175918 | ||||||||
\(907\) | 7143.32 | 0.261511 | 0.130755 | − | 0.991415i | \(-0.458260\pi\) | ||||
0.130755 | + | 0.991415i | \(0.458260\pi\) | |||||||
\(908\) | 22771.7 | 0.832273 | ||||||||
\(909\) | 15983.5 | 0.583210 | ||||||||
\(910\) | 95.3815 | 0.00347458 | ||||||||
\(911\) | −19674.4 | −0.715522 | −0.357761 | − | 0.933813i | \(-0.616460\pi\) | ||||
−0.357761 | + | 0.933813i | \(0.616460\pi\) | |||||||
\(912\) | 56.9187 | 0.00206663 | ||||||||
\(913\) | −6699.30 | −0.242842 | ||||||||
\(914\) | −4904.41 | −0.177487 | ||||||||
\(915\) | −105.576 | −0.00381447 | ||||||||
\(916\) | −11463.2 | −0.413488 | ||||||||
\(917\) | 84.9265 | 0.00305837 | ||||||||
\(918\) | 225.093 | 0.00809278 | ||||||||
\(919\) | 30418.3 | 1.09185 | 0.545924 | − | 0.837835i | \(-0.316179\pi\) | ||||
0.545924 | + | 0.837835i | \(0.316179\pi\) | |||||||
\(920\) | −10150.2 | −0.363740 | ||||||||
\(921\) | −263.048 | −0.00941121 | ||||||||
\(922\) | −8630.54 | −0.308277 | ||||||||
\(923\) | 23642.5 | 0.843123 | ||||||||
\(924\) | −5.39299 | −0.000192009 0 | ||||||||
\(925\) | −5456.51 | −0.193956 | ||||||||
\(926\) | −13044.9 | −0.462940 | ||||||||
\(927\) | −23925.7 | −0.847707 | ||||||||
\(928\) | −28982.5 | −1.02521 | ||||||||
\(929\) | 20882.8 | 0.737504 | 0.368752 | − | 0.929528i | \(-0.379785\pi\) | ||||
0.368752 | + | 0.929528i | \(0.379785\pi\) | |||||||
\(930\) | −8.68602 | −0.000306264 0 | ||||||||
\(931\) | −6494.02 | −0.228607 | ||||||||
\(932\) | −10316.1 | −0.362570 | ||||||||
\(933\) | −28.1969 | −0.000989417 0 | ||||||||
\(934\) | 4812.90 | 0.168611 | ||||||||
\(935\) | 4845.96 | 0.169497 | ||||||||
\(936\) | 7204.54 | 0.251590 | ||||||||
\(937\) | −49312.2 | −1.71927 | −0.859636 | − | 0.510907i | \(-0.829310\pi\) | ||||
−0.859636 | + | 0.510907i | \(0.829310\pi\) | |||||||
\(938\) | −293.548 | −0.0102182 | ||||||||
\(939\) | 530.604 | 0.0184405 | ||||||||
\(940\) | −9211.62 | −0.319628 | ||||||||
\(941\) | 20987.9 | 0.727083 | 0.363542 | − | 0.931578i | \(-0.381567\pi\) | ||||
0.363542 | + | 0.931578i | \(0.381567\pi\) | |||||||
\(942\) | 158.052 | 0.00546667 | ||||||||
\(943\) | 4714.31 | 0.162799 | ||||||||
\(944\) | 41030.7 | 1.41466 | ||||||||
\(945\) | −17.9220 | −0.000616935 0 | ||||||||
\(946\) | −3243.34 | −0.111470 | ||||||||
\(947\) | −50485.8 | −1.73238 | −0.866192 | − | 0.499711i | \(-0.833440\pi\) | ||||
−0.866192 | + | 0.499711i | \(0.833440\pi\) | |||||||
\(948\) | −458.267 | −0.0157002 | ||||||||
\(949\) | 2203.22 | 0.0753630 | ||||||||
\(950\) | −372.330 | −0.0127158 | ||||||||
\(951\) | 38.3926 | 0.00130911 | ||||||||
\(952\) | −1168.62 | −0.0397847 | ||||||||
\(953\) | 35925.7 | 1.22114 | 0.610570 | − | 0.791962i | \(-0.290940\pi\) | ||||
0.610570 | + | 0.791962i | \(0.290940\pi\) | |||||||
\(954\) | 9445.74 | 0.320563 | ||||||||
\(955\) | −9991.16 | −0.338541 | ||||||||
\(956\) | −21554.2 | −0.729197 | ||||||||
\(957\) | −142.137 | −0.00480108 | ||||||||
\(958\) | 2350.78 | 0.0792802 | ||||||||
\(959\) | 269.169 | 0.00906354 | ||||||||
\(960\) | 87.8018 | 0.00295187 | ||||||||
\(961\) | −28442.8 | −0.954746 | ||||||||
\(962\) | −3785.84 | −0.126882 | ||||||||
\(963\) | 47121.1 | 1.57680 | ||||||||
\(964\) | 17747.0 | 0.592939 | ||||||||
\(965\) | 7620.73 | 0.254218 | ||||||||
\(966\) | 8.75874 | 0.000291727 0 | ||||||||
\(967\) | −13309.2 | −0.442600 | −0.221300 | − | 0.975206i | \(-0.571030\pi\) | ||||
−0.221300 | + | 0.975206i | \(0.571030\pi\) | |||||||
\(968\) | 1459.26 | 0.0484530 | ||||||||
\(969\) | 101.045 | 0.00334989 | ||||||||
\(970\) | 151.391 | 0.00501121 | ||||||||
\(971\) | −15424.5 | −0.509781 | −0.254890 | − | 0.966970i | \(-0.582039\pi\) | ||||
−0.254890 | + | 0.966970i | \(0.582039\pi\) | |||||||
\(972\) | −974.767 | −0.0321663 | ||||||||
\(973\) | 1709.09 | 0.0563113 | ||||||||
\(974\) | −10820.4 | −0.355964 | ||||||||
\(975\) | −33.3917 | −0.00109681 | ||||||||
\(976\) | 17362.2 | 0.569418 | ||||||||
\(977\) | 31101.5 | 1.01845 | 0.509224 | − | 0.860634i | \(-0.329932\pi\) | ||||
0.509224 | + | 0.860634i | \(0.329932\pi\) | |||||||
\(978\) | −34.0878 | −0.00111453 | ||||||||
\(979\) | −1930.80 | −0.0630323 | ||||||||
\(980\) | −12621.6 | −0.411410 | ||||||||
\(981\) | 51939.1 | 1.69040 | ||||||||
\(982\) | −860.231 | −0.0279543 | ||||||||
\(983\) | 6010.71 | 0.195027 | 0.0975136 | − | 0.995234i | \(-0.468911\pi\) | ||||
0.0975136 | + | 0.995234i | \(0.468911\pi\) | |||||||
\(984\) | 20.3872 | 0.000660488 0 | ||||||||
\(985\) | 1406.22 | 0.0454884 | ||||||||
\(986\) | −14784.9 | −0.477534 | ||||||||
\(987\) | 16.5590 | 0.000534021 0 | ||||||||
\(988\) | 3105.21 | 0.0999897 | ||||||||
\(989\) | −63317.0 | −2.03576 | ||||||||
\(990\) | 1163.86 | 0.0373637 | ||||||||
\(991\) | −19192.5 | −0.615208 | −0.307604 | − | 0.951515i | \(-0.599527\pi\) | ||||
−0.307604 | + | 0.951515i | \(0.599527\pi\) | |||||||
\(992\) | 4970.93 | 0.159100 | ||||||||
\(993\) | −518.183 | −0.0165600 | ||||||||
\(994\) | −921.047 | −0.0293902 | ||||||||
\(995\) | 19558.3 | 0.623157 | ||||||||
\(996\) | −271.498 | −0.00863729 | ||||||||
\(997\) | 53233.1 | 1.69098 | 0.845490 | − | 0.533990i | \(-0.179308\pi\) | ||||
0.845490 | + | 0.533990i | \(0.179308\pi\) | |||||||
\(998\) | 8699.71 | 0.275936 | ||||||||
\(999\) | 711.353 | 0.0225287 |
(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 | 1045.4.a.c.1.9 | ✓ | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1045.4.a.c.1.9 | ✓ | 20 | 1.1 | even | 1 | trivial |