Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [405,4,Mod(136,405)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(405, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([4, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("405.136");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 405 = 3^{4} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 405.e (of order \(3\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(23.8957735523\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Relative dimension: | \(3\) over \(\Q(\zeta_{3})\) |
Coefficient field: | 6.0.95327307.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 3x^{5} + 20x^{4} - 35x^{3} + 85x^{2} - 68x + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 3^{3} \) |
Twist minimal: | no (minimal twist has level 135) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 271.3 | ||
Root | \(0.500000 + 0.0280269i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 405.271 |
Dual form | 405.4.e.t.136.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/405\mathbb{Z}\right)^\times\).
\(n\) | \(82\) | \(326\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.60034 | + | 4.50391i | 0.919357 | + | 1.59237i | 0.800393 | + | 0.599475i | \(0.204624\pi\) |
0.118964 | + | 0.992899i | \(0.462043\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −9.52349 | + | 16.4952i | −1.19044 | + | 2.06190i | ||||
\(5\) | −2.50000 | + | 4.33013i | −0.223607 | + | 0.387298i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −12.2007 | − | 21.1322i | −0.658774 | − | 1.14103i | −0.980933 | − | 0.194345i | \(-0.937742\pi\) |
0.322159 | − | 0.946686i | \(-0.395591\pi\) | |||||||
\(8\) | −57.4517 | −2.53903 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −26.0034 | −0.822298 | ||||||||
\(11\) | −14.4919 | − | 25.1008i | −0.397226 | − | 0.688015i | 0.596157 | − | 0.802868i | \(-0.296694\pi\) |
−0.993383 | + | 0.114853i | \(0.963360\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 32.6960 | − | 56.6311i | 0.697556 | − | 1.20820i | −0.271756 | − | 0.962366i | \(-0.587604\pi\) |
0.969311 | − | 0.245836i | \(-0.0790625\pi\) | |||||||
\(14\) | 63.4517 | − | 109.902i | 1.21130 | − | 2.09803i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −73.2057 | − | 126.796i | −1.14384 | − | 1.98119i | ||||
\(17\) | −68.1718 | −0.972593 | −0.486296 | − | 0.873794i | \(-0.661653\pi\) | ||||
−0.486296 | + | 0.873794i | \(0.661653\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 104.424 | 1.26087 | 0.630435 | − | 0.776242i | \(-0.282876\pi\) | ||||
0.630435 | + | 0.776242i | \(0.282876\pi\) | |||||||
\(20\) | −47.6174 | − | 82.4758i | −0.532379 | − | 0.922108i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 75.3678 | − | 130.541i | 0.730385 | − | 1.26506i | ||||
\(23\) | −77.4033 | + | 134.067i | −0.701727 | + | 1.21543i | 0.266133 | + | 0.963936i | \(0.414254\pi\) |
−0.967860 | + | 0.251490i | \(0.919080\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −12.5000 | − | 21.6506i | −0.100000 | − | 0.173205i | ||||
\(26\) | 340.082 | 2.56521 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 464.772 | 3.13691 | ||||||||
\(29\) | −102.829 | − | 178.105i | −0.658443 | − | 1.14046i | −0.981019 | − | 0.193913i | \(-0.937882\pi\) |
0.322576 | − | 0.946544i | \(-0.395451\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 9.12485 | − | 15.8047i | 0.0528668 | − | 0.0915680i | −0.838381 | − | 0.545085i | \(-0.816497\pi\) |
0.891248 | + | 0.453517i | \(0.149831\pi\) | |||||||
\(32\) | 150.912 | − | 261.387i | 0.833679 | − | 1.44397i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −177.269 | − | 307.040i | −0.894160 | − | 1.54873i | ||||
\(35\) | 122.007 | 0.589226 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −337.613 | −1.50009 | −0.750044 | − | 0.661387i | \(-0.769968\pi\) | ||||
−0.750044 | + | 0.661387i | \(0.769968\pi\) | |||||||
\(38\) | 271.538 | + | 470.317i | 1.15919 | + | 2.00778i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 143.629 | − | 248.773i | 0.567744 | − | 0.983362i | ||||
\(41\) | −97.9845 | + | 169.714i | −0.373234 | + | 0.646461i | −0.990061 | − | 0.140638i | \(-0.955085\pi\) |
0.616827 | + | 0.787099i | \(0.288418\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −167.441 | − | 290.016i | −0.593826 | − | 1.02854i | −0.993711 | − | 0.111971i | \(-0.964284\pi\) |
0.399886 | − | 0.916565i | \(-0.369050\pi\) | |||||||
\(44\) | 552.055 | 1.89149 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −805.098 | −2.58055 | ||||||||
\(47\) | −2.50199 | − | 4.33358i | −0.00776496 | − | 0.0134493i | 0.862117 | − | 0.506710i | \(-0.169138\pi\) |
−0.869882 | + | 0.493260i | \(0.835805\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −126.213 | + | 218.607i | −0.367967 | + | 0.637338i | ||||
\(50\) | 65.0084 | − | 112.598i | 0.183871 | − | 0.318475i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 622.759 | + | 1078.65i | 1.66079 | + | 2.87657i | ||||
\(53\) | 319.965 | 0.829256 | 0.414628 | − | 0.909991i | \(-0.363912\pi\) | ||||
0.414628 | + | 0.909991i | \(0.363912\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 144.919 | 0.355289 | ||||||||
\(56\) | 700.949 | + | 1214.08i | 1.67265 | + | 2.89711i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 534.779 | − | 926.265i | 1.21069 | − | 2.09697i | ||||
\(59\) | 215.305 | − | 372.920i | 0.475091 | − | 0.822882i | −0.524502 | − | 0.851409i | \(-0.675749\pi\) |
0.999593 | + | 0.0285276i | \(0.00908184\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −297.291 | − | 514.922i | −0.624002 | − | 1.08080i | −0.988733 | − | 0.149691i | \(-0.952172\pi\) |
0.364730 | − | 0.931113i | \(-0.381161\pi\) | |||||||
\(62\) | 94.9106 | 0.194414 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 398.396 | 0.778118 | ||||||||
\(65\) | 163.480 | + | 283.155i | 0.311956 | + | 0.540324i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −97.9382 | + | 169.634i | −0.178583 | + | 0.309315i | −0.941395 | − | 0.337305i | \(-0.890485\pi\) |
0.762812 | + | 0.646620i | \(0.223818\pi\) | |||||||
\(68\) | 649.233 | − | 1124.50i | 1.15781 | − | 2.00538i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 317.258 | + | 549.508i | 0.541709 | + | 0.938267i | ||||
\(71\) | −425.955 | −0.711994 | −0.355997 | − | 0.934487i | \(-0.615859\pi\) | ||||
−0.355997 | + | 0.934487i | \(0.615859\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 929.193 | 1.48978 | 0.744889 | − | 0.667188i | \(-0.232502\pi\) | ||||
0.744889 | + | 0.667188i | \(0.232502\pi\) | |||||||
\(74\) | −877.908 | − | 1520.58i | −1.37912 | − | 2.38870i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −994.482 | + | 1722.49i | −1.50099 | + | 2.59978i | ||||
\(77\) | −353.623 | + | 612.492i | −0.523364 | + | 0.906493i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −12.2148 | − | 21.1567i | −0.0173959 | − | 0.0301305i | 0.857196 | − | 0.514990i | \(-0.172204\pi\) |
−0.874592 | + | 0.484859i | \(0.838871\pi\) | |||||||
\(80\) | 732.057 | 1.02308 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −1019.17 | −1.37254 | ||||||||
\(83\) | −272.929 | − | 472.727i | −0.360938 | − | 0.625164i | 0.627177 | − | 0.778877i | \(-0.284210\pi\) |
−0.988116 | + | 0.153713i | \(0.950877\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 170.429 | − | 295.192i | 0.217478 | − | 0.376684i | ||||
\(86\) | 870.805 | − | 1508.28i | 1.09188 | − | 1.89118i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 832.586 | + | 1442.08i | 1.00857 | + | 1.74689i | ||||
\(89\) | 84.1332 | 0.100203 | 0.0501017 | − | 0.998744i | \(-0.484045\pi\) | ||||
0.0501017 | + | 0.998744i | \(0.484045\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1595.65 | −1.83813 | ||||||||
\(92\) | −1474.30 | − | 2553.56i | −1.67072 | − | 2.89377i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 13.0120 | − | 22.5375i | 0.0142775 | − | 0.0247294i | ||||
\(95\) | −261.060 | + | 452.170i | −0.281939 | + | 0.488333i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −413.807 | − | 716.734i | −0.433152 | − | 0.750241i | 0.563991 | − | 0.825781i | \(-0.309265\pi\) |
−0.997143 | + | 0.0755403i | \(0.975932\pi\) | |||||||
\(98\) | −1312.78 | −1.35317 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 476.174 | 0.476174 | ||||||||
\(101\) | 411.788 | + | 713.238i | 0.405688 | + | 0.702671i | 0.994401 | − | 0.105670i | \(-0.0336988\pi\) |
−0.588714 | + | 0.808342i | \(0.700365\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −585.595 | + | 1014.28i | −0.560198 | + | 0.970291i | 0.437281 | + | 0.899325i | \(0.355941\pi\) |
−0.997479 | + | 0.0709659i | \(0.977392\pi\) | |||||||
\(104\) | −1878.44 | + | 3253.55i | −1.77111 | + | 3.06766i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 832.016 | + | 1441.09i | 0.762383 | + | 1.32049i | ||||
\(107\) | −1023.21 | −0.924460 | −0.462230 | − | 0.886760i | \(-0.652951\pi\) | ||||
−0.462230 | + | 0.886760i | \(0.652951\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −403.647 | −0.354700 | −0.177350 | − | 0.984148i | \(-0.556753\pi\) | ||||
−0.177350 | + | 0.984148i | \(0.556753\pi\) | |||||||
\(110\) | 376.839 | + | 652.704i | 0.326638 | + | 0.565754i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −1786.32 | + | 3093.99i | −1.50706 | + | 2.61031i | ||||
\(113\) | 541.102 | − | 937.216i | 0.450465 | − | 0.780229i | −0.547950 | − | 0.836511i | \(-0.684591\pi\) |
0.998415 | + | 0.0562825i | \(0.0179247\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −387.017 | − | 670.333i | −0.313822 | − | 0.543555i | ||||
\(116\) | 3917.16 | 3.13534 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 2239.46 | 1.74711 | ||||||||
\(119\) | 831.741 | + | 1440.62i | 0.640719 | + | 1.10976i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 245.468 | − | 425.162i | 0.184423 | − | 0.319431i | ||||
\(122\) | 1546.11 | − | 2677.94i | 1.14736 | − | 1.98729i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 173.801 | + | 301.032i | 0.125869 | + | 0.218012i | ||||
\(125\) | 125.000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −774.132 | −0.540890 | −0.270445 | − | 0.962735i | \(-0.587171\pi\) | ||||
−0.270445 | + | 0.962735i | \(0.587171\pi\) | |||||||
\(128\) | −171.332 | − | 296.756i | −0.118311 | − | 0.204920i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −850.204 | + | 1472.60i | −0.573599 | + | 0.993503i | ||||
\(131\) | −607.019 | + | 1051.39i | −0.404851 | + | 0.701222i | −0.994304 | − | 0.106580i | \(-0.966010\pi\) |
0.589453 | + | 0.807802i | \(0.299343\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1274.04 | − | 2206.71i | −0.830629 | − | 1.43869i | ||||
\(134\) | −1018.69 | −0.656726 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 3916.58 | 2.46944 | ||||||||
\(137\) | 1150.07 | + | 1991.99i | 0.717207 | + | 1.24224i | 0.962102 | + | 0.272690i | \(0.0879133\pi\) |
−0.244895 | + | 0.969550i | \(0.578753\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 677.963 | − | 1174.27i | 0.413698 | − | 0.716546i | −0.581593 | − | 0.813480i | \(-0.697570\pi\) |
0.995291 | + | 0.0969339i | \(0.0309035\pi\) | |||||||
\(140\) | −1161.93 | + | 2012.52i | −0.701435 | + | 1.21492i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −1107.63 | − | 1918.47i | −0.654577 | − | 1.13376i | ||||
\(143\) | −1895.31 | −1.10835 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1028.29 | 0.588929 | ||||||||
\(146\) | 2416.21 | + | 4185.00i | 1.36964 | + | 2.37228i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 3215.26 | − | 5568.99i | 1.78576 | − | 3.09303i | ||||
\(149\) | 129.923 | − | 225.032i | 0.0714340 | − | 0.123727i | −0.828096 | − | 0.560586i | \(-0.810576\pi\) |
0.899530 | + | 0.436859i | \(0.143909\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 254.152 | + | 440.204i | 0.136971 | + | 0.237240i | 0.926349 | − | 0.376667i | \(-0.122930\pi\) |
−0.789378 | + | 0.613908i | \(0.789597\pi\) | |||||||
\(152\) | −5999.34 | −3.20139 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −3678.15 | −1.92463 | ||||||||
\(155\) | 45.6242 | + | 79.0235i | 0.0236428 | + | 0.0409504i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 11.6526 | − | 20.1829i | 0.00592342 | − | 0.0102597i | −0.863049 | − | 0.505121i | \(-0.831448\pi\) |
0.868972 | + | 0.494861i | \(0.164781\pi\) | |||||||
\(158\) | 63.5252 | − | 110.029i | 0.0319860 | − | 0.0554014i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 754.560 | + | 1306.94i | 0.372833 | + | 0.645765i | ||||
\(161\) | 3777.49 | 1.84912 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −4032.10 | −1.93754 | −0.968769 | − | 0.247964i | \(-0.920238\pi\) | ||||
−0.968769 | + | 0.247964i | \(0.920238\pi\) | |||||||
\(164\) | −1866.31 | − | 3232.54i | −0.888623 | − | 1.53914i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 1419.42 | − | 2458.50i | 0.663663 | − | 1.14950i | ||||
\(167\) | −335.955 | + | 581.892i | −0.155671 | + | 0.269630i | −0.933303 | − | 0.359090i | \(-0.883087\pi\) |
0.777632 | + | 0.628719i | \(0.216421\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1039.55 | − | 1800.56i | −0.473169 | − | 0.819552i | ||||
\(170\) | 1772.69 | 0.799761 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 6378.49 | 2.82765 | ||||||||
\(173\) | 816.764 | + | 1414.68i | 0.358944 | + | 0.621710i | 0.987785 | − | 0.155825i | \(-0.0498034\pi\) |
−0.628840 | + | 0.777534i | \(0.716470\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −305.017 | + | 528.305i | −0.131755 | + | 0.228206i | ||||
\(176\) | −2121.78 | + | 3675.04i | −0.908725 | + | 1.57396i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 218.775 | + | 378.929i | 0.0921227 | + | 0.159561i | ||||
\(179\) | −341.260 | −0.142497 | −0.0712485 | − | 0.997459i | \(-0.522698\pi\) | ||||
−0.0712485 | + | 0.997459i | \(0.522698\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1695.92 | −0.696447 | −0.348223 | − | 0.937412i | \(-0.613215\pi\) | ||||
−0.348223 | + | 0.937412i | \(0.613215\pi\) | |||||||
\(182\) | −4149.23 | − | 7186.67i | −1.68990 | − | 2.92699i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 4446.95 | − | 7702.34i | 1.78170 | − | 3.08600i | ||||
\(185\) | 844.033 | − | 1461.91i | 0.335430 | − | 0.580982i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 987.941 | + | 1711.16i | 0.386339 | + | 0.669159i | ||||
\(188\) | 95.3107 | 0.0369747 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −2715.38 | −1.03681 | ||||||||
\(191\) | −363.226 | − | 629.125i | −0.137603 | − | 0.238335i | 0.788986 | − | 0.614411i | \(-0.210606\pi\) |
−0.926589 | + | 0.376076i | \(0.877273\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2123.63 | + | 3678.24i | −0.792032 | + | 1.37184i | 0.132674 | + | 0.991160i | \(0.457644\pi\) |
−0.924707 | + | 0.380681i | \(0.875690\pi\) | |||||||
\(194\) | 2152.07 | − | 3727.50i | 0.796442 | − | 1.37948i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −2403.97 | − | 4163.80i | −0.876082 | − | 1.51742i | ||||
\(197\) | −2678.52 | −0.968713 | −0.484357 | − | 0.874871i | \(-0.660946\pi\) | ||||
−0.484357 | + | 0.874871i | \(0.660946\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1486.48 | 0.529517 | 0.264759 | − | 0.964315i | \(-0.414708\pi\) | ||||
0.264759 | + | 0.964315i | \(0.414708\pi\) | |||||||
\(200\) | 718.146 | + | 1243.87i | 0.253903 | + | 0.439773i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −2141.57 | + | 3709.31i | −0.745944 | + | 1.29201i | ||||
\(203\) | −2509.16 | + | 4346.00i | −0.867530 | + | 1.50261i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −489.923 | − | 848.571i | −0.166915 | − | 0.289106i | ||||
\(206\) | −6090.97 | −2.06009 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −9574.12 | −3.19157 | ||||||||
\(209\) | −1513.31 | − | 2621.13i | −0.500850 | − | 0.867498i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2413.71 | − | 4180.66i | 0.787519 | − | 1.36402i | −0.139964 | − | 0.990157i | \(-0.544699\pi\) |
0.927483 | − | 0.373866i | \(-0.121968\pi\) | |||||||
\(212\) | −3047.18 | + | 5277.87i | −0.987176 | + | 1.70984i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −2660.68 | − | 4608.44i | −0.849909 | − | 1.47209i | ||||
\(215\) | 1674.41 | 0.531134 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −445.317 | −0.139309 | ||||||||
\(218\) | −1049.62 | − | 1817.99i | −0.326096 | − | 0.564815i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −1380.14 | + | 2390.47i | −0.422949 | + | 0.732570i | ||||
\(221\) | −2228.94 | + | 3860.64i | −0.678438 | + | 1.17509i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1387.24 | − | 2402.77i | −0.416576 | − | 0.721532i | 0.579016 | − | 0.815316i | \(-0.303437\pi\) |
−0.995593 | + | 0.0937845i | \(0.970104\pi\) | |||||||
\(224\) | −7364.91 | −2.19683 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 5628.19 | 1.65655 | ||||||||
\(227\) | −2550.67 | − | 4417.89i | −0.745788 | − | 1.29174i | −0.949826 | − | 0.312779i | \(-0.898740\pi\) |
0.204038 | − | 0.978963i | \(-0.434593\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2048.91 | − | 3548.82i | 0.591249 | − | 1.02407i | −0.402816 | − | 0.915281i | \(-0.631968\pi\) |
0.994065 | − | 0.108792i | \(-0.0346983\pi\) | |||||||
\(230\) | 2012.75 | − | 3486.18i | 0.577028 | − | 0.999443i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 5907.69 | + | 10232.4i | 1.67181 | + | 2.89565i | ||||
\(233\) | −357.613 | −0.100549 | −0.0502747 | − | 0.998735i | \(-0.516010\pi\) | ||||
−0.0502747 | + | 0.998735i | \(0.516010\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 25.0199 | 0.00694519 | ||||||||
\(236\) | 4100.91 | + | 7102.99i | 1.13113 | + | 1.95918i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −4325.61 | + | 7492.18i | −1.17810 | + | 2.04053i | ||||
\(239\) | −175.841 | + | 304.566i | −0.0475909 | + | 0.0824298i | −0.888840 | − | 0.458219i | \(-0.848488\pi\) |
0.841249 | + | 0.540648i | \(0.181821\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3082.76 | + | 5339.51i | 0.823976 | + | 1.42717i | 0.902699 | + | 0.430273i | \(0.141583\pi\) |
−0.0787225 | + | 0.996897i | \(0.525084\pi\) | |||||||
\(242\) | 2553.19 | 0.678204 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 11325.0 | 2.97134 | ||||||||
\(245\) | −631.064 | − | 1093.03i | −0.164560 | − | 0.285026i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3414.25 | − | 5913.65i | 0.879528 | − | 1.52339i | ||||
\(248\) | −524.238 | + | 908.006i | −0.134230 | + | 0.232494i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 325.042 | + | 562.989i | 0.0822298 | + | 0.142426i | ||||
\(251\) | −3245.53 | −0.816160 | −0.408080 | − | 0.912946i | \(-0.633802\pi\) | ||||
−0.408080 | + | 0.912946i | \(0.633802\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 4486.90 | 1.11498 | ||||||||
\(254\) | −2013.00 | − | 3486.62i | −0.497271 | − | 0.861299i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 2484.63 | − | 4303.50i | 0.606598 | − | 1.05066i | ||||
\(257\) | 1776.10 | − | 3076.29i | 0.431089 | − | 0.746668i | −0.565878 | − | 0.824489i | \(-0.691463\pi\) |
0.996967 | + | 0.0778206i | \(0.0247961\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 4119.11 | + | 7134.51i | 0.988220 | + | 1.71165i | ||||
\(260\) | −6227.59 | −1.48546 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −6313.81 | −1.48881 | ||||||||
\(263\) | 2208.29 | + | 3824.88i | 0.517754 | + | 0.896776i | 0.999787 | + | 0.0206232i | \(0.00656503\pi\) |
−0.482033 | + | 0.876153i | \(0.660102\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −799.913 | + | 1385.49i | −0.185427 | + | 0.321170i | ||||
\(266\) | 6625.89 | − | 11476.4i | 1.52729 | − | 2.64534i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −1865.43 | − | 3231.01i | −0.425183 | − | 0.736439i | ||||
\(269\) | 3419.93 | 0.775155 | 0.387578 | − | 0.921837i | \(-0.373312\pi\) | ||||
0.387578 | + | 0.921837i | \(0.373312\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 716.407 | 0.160585 | 0.0802927 | − | 0.996771i | \(-0.474415\pi\) | ||||
0.0802927 | + | 0.996771i | \(0.474415\pi\) | |||||||
\(272\) | 4990.56 | + | 8643.91i | 1.11249 | + | 1.92689i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −5981.15 | + | 10359.7i | −1.31874 | + | 2.28412i | ||||
\(275\) | −362.298 | + | 627.519i | −0.0794451 | + | 0.137603i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −328.764 | − | 569.437i | −0.0713124 | − | 0.123517i | 0.828164 | − | 0.560485i | \(-0.189385\pi\) |
−0.899477 | + | 0.436969i | \(0.856052\pi\) | |||||||
\(278\) | 7051.72 | 1.52135 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −7009.49 | −1.49606 | ||||||||
\(281\) | 756.957 | + | 1311.09i | 0.160698 | + | 0.278338i | 0.935119 | − | 0.354333i | \(-0.115292\pi\) |
−0.774421 | + | 0.632671i | \(0.781959\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1953.19 | + | 3383.03i | −0.410266 | + | 0.710601i | −0.994919 | − | 0.100682i | \(-0.967897\pi\) |
0.584653 | + | 0.811284i | \(0.301231\pi\) | |||||||
\(284\) | 4056.58 | − | 7026.20i | 0.847584 | − | 1.46806i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −4928.44 | − | 8536.31i | −1.01897 | − | 1.76491i | ||||
\(287\) | 4781.91 | 0.983509 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −265.611 | −0.0540629 | ||||||||
\(290\) | 2673.90 | + | 4631.32i | 0.541436 | + | 0.937795i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −8849.16 | + | 15327.2i | −1.77349 | + | 3.07177i | ||||
\(293\) | −4024.38 | + | 6970.43i | −0.802413 | + | 1.38982i | 0.115611 | + | 0.993295i | \(0.463117\pi\) |
−0.918024 | + | 0.396525i | \(0.870216\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1076.53 | + | 1864.60i | 0.212467 | + | 0.368004i | ||||
\(296\) | 19396.4 | 3.80877 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 1351.37 | 0.262693 | ||||||||
\(299\) | 5061.55 | + | 8766.87i | 0.978987 | + | 1.69566i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −4085.78 | + | 7076.78i | −0.782394 | + | 1.35515i | ||||
\(302\) | −1321.76 | + | 2289.35i | −0.251850 | + | 0.436217i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −7644.44 | − | 13240.6i | −1.44223 | − | 2.49802i | ||||
\(305\) | 2972.91 | 0.558125 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 101.564 | 0.0188814 | 0.00944068 | − | 0.999955i | \(-0.496995\pi\) | ||||
0.00944068 | + | 0.999955i | \(0.496995\pi\) | |||||||
\(308\) | −6735.44 | − | 11666.1i | −1.24606 | − | 2.15824i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −237.277 | + | 410.975i | −0.0434723 | + | 0.0752962i | ||||
\(311\) | −3842.29 | + | 6655.05i | −0.700567 | + | 1.21342i | 0.267700 | + | 0.963502i | \(0.413736\pi\) |
−0.968268 | + | 0.249916i | \(0.919597\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 672.575 | + | 1164.93i | 0.121457 | + | 0.210370i | 0.920343 | − | 0.391113i | \(-0.127910\pi\) |
−0.798885 | + | 0.601484i | \(0.794577\pi\) | |||||||
\(314\) | 121.202 | 0.0217830 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 465.310 | 0.0828346 | ||||||||
\(317\) | 3811.17 | + | 6601.13i | 0.675257 | + | 1.16958i | 0.976394 | + | 0.215998i | \(0.0693006\pi\) |
−0.301137 | + | 0.953581i | \(0.597366\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2980.38 | + | 5162.17i | −0.523101 | + | 0.906037i | ||||
\(320\) | −995.991 | + | 1725.11i | −0.173993 | + | 0.301364i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 9822.74 | + | 17013.5i | 1.70000 | + | 2.94449i | ||||
\(323\) | −7118.78 | −1.22631 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1634.80 | −0.279022 | ||||||||
\(326\) | −10484.8 | − | 18160.2i | −1.78129 | − | 3.08528i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 5629.37 | − | 9750.36i | 0.947653 | − | 1.64138i | ||||
\(329\) | −61.0519 | + | 105.745i | −0.0102307 | + | 0.0177201i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 3292.54 | + | 5702.85i | 0.546751 | + | 0.947000i | 0.998494 | + | 0.0548525i | \(0.0174689\pi\) |
−0.451744 | + | 0.892148i | \(0.649198\pi\) | |||||||
\(332\) | 10397.0 | 1.71870 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −3494.39 | −0.572468 | ||||||||
\(335\) | −489.691 | − | 848.170i | −0.0798647 | − | 0.138330i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1473.47 | − | 2552.13i | 0.238175 | − | 0.412532i | −0.722015 | − | 0.691877i | \(-0.756784\pi\) |
0.960191 | + | 0.279345i | \(0.0901174\pi\) | |||||||
\(338\) | 5406.36 | − | 9364.10i | 0.870022 | − | 1.50692i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 3246.16 | + | 5622.52i | 0.517788 | + | 0.896835i | ||||
\(341\) | −528.947 | −0.0840002 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −2210.14 | −0.347919 | ||||||||
\(344\) | 9619.76 | + | 16661.9i | 1.50774 | + | 2.61148i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −4247.72 | + | 7357.26i | −0.659996 | + | 1.14315i | ||||
\(347\) | 4246.74 | − | 7355.57i | 0.656994 | − | 1.13795i | −0.324396 | − | 0.945921i | \(-0.605161\pi\) |
0.981390 | − | 0.192025i | \(-0.0615056\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −2823.27 | − | 4890.05i | −0.433027 | − | 0.750024i | 0.564106 | − | 0.825703i | \(-0.309221\pi\) |
−0.997132 | + | 0.0756785i | \(0.975888\pi\) | |||||||
\(350\) | −3172.58 | −0.484519 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −8748.03 | −1.32464 | ||||||||
\(353\) | −610.966 | − | 1058.22i | −0.0921202 | − | 0.159557i | 0.816283 | − | 0.577652i | \(-0.196031\pi\) |
−0.908403 | + | 0.418096i | \(0.862698\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1064.89 | − | 1844.44i | 0.159207 | − | 0.275754i | ||||
\(356\) | −801.242 | + | 1387.79i | −0.119286 | + | 0.206609i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −887.390 | − | 1537.00i | −0.131006 | − | 0.226908i | ||||
\(359\) | 4151.44 | 0.610319 | 0.305160 | − | 0.952301i | \(-0.401290\pi\) | ||||
0.305160 | + | 0.952301i | \(0.401290\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 4045.41 | 0.589796 | ||||||||
\(362\) | −4409.96 | − | 7638.28i | −0.640283 | − | 1.10900i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 15196.2 | − | 26320.5i | 2.18817 | − | 3.79003i | ||||
\(365\) | −2322.98 | + | 4023.52i | −0.333125 | + | 0.576989i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 3519.36 | + | 6095.70i | 0.500569 | + | 0.867011i | 1.00000 | 0.000657484i | \(0.000209284\pi\) | |
−0.499430 | + | 0.866354i | \(0.666457\pi\) | |||||||
\(368\) | 22665.5 | 3.21065 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 8779.08 | 1.23352 | ||||||||
\(371\) | −3903.79 | − | 6761.56i | −0.546293 | − | 0.946207i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 3559.78 | − | 6165.72i | 0.494152 | − | 0.855896i | −0.505826 | − | 0.862636i | \(-0.668812\pi\) |
0.999977 | + | 0.00674002i | \(0.00214543\pi\) | |||||||
\(374\) | −5137.95 | + | 8899.20i | −0.710367 | + | 1.23039i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 143.744 | + | 248.971i | 0.0197154 | + | 0.0341482i | ||||
\(377\) | −13448.4 | −1.83720 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 3372.29 | 0.457053 | 0.228526 | − | 0.973538i | \(-0.426609\pi\) | ||||
0.228526 | + | 0.973538i | \(0.426609\pi\) | |||||||
\(380\) | −4972.41 | − | 8612.47i | −0.671261 | − | 1.16266i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 1889.02 | − | 3271.87i | 0.253012 | − | 0.438229i | ||||
\(383\) | 1979.32 | − | 3428.28i | 0.264069 | − | 0.457381i | −0.703250 | − | 0.710942i | \(-0.748269\pi\) |
0.967319 | + | 0.253562i | \(0.0816021\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1768.11 | − | 3062.46i | −0.234056 | − | 0.405396i | ||||
\(386\) | −22088.6 | −2.91264 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 15763.5 | 2.06256 | ||||||||
\(389\) | 4827.00 | + | 8360.61i | 0.629148 | + | 1.08972i | 0.987723 | + | 0.156216i | \(0.0499296\pi\) |
−0.358574 | + | 0.933501i | \(0.616737\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 5276.72 | − | 9139.55i | 0.682494 | − | 1.18211i | ||||
\(392\) | 7251.13 | − | 12559.3i | 0.934279 | − | 1.61822i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −6965.04 | − | 12063.8i | −0.890594 | − | 1.54255i | ||||
\(395\) | 122.148 | 0.0155593 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 10928.3 | 1.38155 | 0.690776 | − | 0.723068i | \(-0.257269\pi\) | ||||
0.690776 | + | 0.723068i | \(0.257269\pi\) | |||||||
\(398\) | 3865.35 | + | 6694.99i | 0.486816 | + | 0.843189i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −1830.14 | + | 3169.90i | −0.228768 | + | 0.396237i | ||||
\(401\) | 2042.78 | − | 3538.21i | 0.254393 | − | 0.440622i | −0.710337 | − | 0.703862i | \(-0.751458\pi\) |
0.964731 | + | 0.263239i | \(0.0847909\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −596.691 | − | 1033.50i | −0.0737551 | − | 0.127748i | ||||
\(404\) | −15686.6 | −1.93178 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −26098.7 | −3.19028 | ||||||||
\(407\) | 4892.67 | + | 8474.35i | 0.595874 | + | 1.03208i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −5078.13 | + | 8795.57i | −0.613930 | + | 1.06336i | 0.376642 | + | 0.926359i | \(0.377079\pi\) |
−0.990571 | + | 0.136998i | \(0.956255\pi\) | |||||||
\(410\) | 2547.93 | − | 4413.14i | 0.306910 | − | 0.531584i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −11153.8 | − | 19319.0i | −1.33376 | − | 2.31014i | ||||
\(413\) | −10507.5 | −1.25191 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 2729.29 | 0.322833 | ||||||||
\(416\) | −9868.43 | − | 17092.6i | −1.16308 | − | 2.01451i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 7870.22 | − | 13631.6i | 0.920921 | − | 1.59508i | ||||
\(419\) | 7939.41 | − | 13751.5i | 0.925693 | − | 1.60335i | 0.135250 | − | 0.990811i | \(-0.456816\pi\) |
0.790443 | − | 0.612536i | \(-0.209851\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1139.92 | + | 1974.40i | 0.131963 | + | 0.228567i | 0.924433 | − | 0.381344i | \(-0.124539\pi\) |
−0.792470 | + | 0.609911i | \(0.791205\pi\) | |||||||
\(422\) | 25105.8 | 2.89604 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −18382.5 | −2.10551 | ||||||||
\(425\) | 852.147 | + | 1475.96i | 0.0972593 | + | 0.168458i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −7254.29 | + | 12564.8i | −0.822154 | + | 1.42401i | ||||
\(428\) | 9744.51 | − | 16878.0i | 1.10051 | − | 1.90614i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 4354.03 | + | 7541.39i | 0.488302 | + | 0.845763i | ||||
\(431\) | 1947.38 | 0.217638 | 0.108819 | − | 0.994062i | \(-0.465293\pi\) | ||||
0.108819 | + | 0.994062i | \(0.465293\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 12636.2 | 1.40244 | 0.701219 | − | 0.712946i | \(-0.252639\pi\) | ||||
0.701219 | + | 0.712946i | \(0.252639\pi\) | |||||||
\(434\) | −1157.97 | − | 2005.67i | −0.128075 | − | 0.221832i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 3844.12 | − | 6658.22i | 0.422248 | − | 0.731355i | ||||
\(437\) | −8082.78 | + | 13999.8i | −0.884787 | + | 1.53250i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 7924.92 | + | 13726.4i | 0.861585 | + | 1.49231i | 0.870399 | + | 0.492347i | \(0.163861\pi\) |
−0.00881399 | + | 0.999961i | \(0.502806\pi\) | |||||||
\(440\) | −8325.86 | −0.902090 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −23184.0 | −2.49491 | ||||||||
\(443\) | −8727.78 | − | 15117.0i | −0.936048 | − | 1.62128i | −0.772754 | − | 0.634706i | \(-0.781121\pi\) |
−0.163294 | − | 0.986577i | \(-0.552212\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −210.333 | + | 364.308i | −0.0224062 | + | 0.0388086i | ||||
\(446\) | 7214.59 | − | 12496.0i | 0.765965 | − | 1.32669i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −4860.70 | − | 8418.99i | −0.512604 | − | 0.887857i | ||||
\(449\) | 16068.1 | 1.68887 | 0.844435 | − | 0.535658i | \(-0.179936\pi\) | ||||
0.844435 | + | 0.535658i | \(0.179936\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 5679.94 | 0.593033 | ||||||||
\(452\) | 10306.4 | + | 17851.1i | 1.07250 | + | 1.85762i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 13265.2 | − | 22976.0i | 1.37129 | − | 2.37515i | ||||
\(455\) | 3989.13 | − | 6909.37i | 0.411018 | − | 0.711904i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −5945.86 | − | 10298.5i | −0.608612 | − | 1.05415i | −0.991469 | − | 0.130339i | \(-0.958393\pi\) |
0.382858 | − | 0.923807i | \(-0.374940\pi\) | |||||||
\(458\) | 21311.4 | 2.17428 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 14743.0 | 1.49434 | ||||||||
\(461\) | −1401.11 | − | 2426.80i | −0.141554 | − | 0.245179i | 0.786528 | − | 0.617555i | \(-0.211877\pi\) |
−0.928082 | + | 0.372376i | \(0.878543\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 6466.66 | − | 11200.6i | 0.649096 | − | 1.12427i | −0.334244 | − | 0.942487i | \(-0.608481\pi\) |
0.983339 | − | 0.181780i | \(-0.0581859\pi\) | |||||||
\(464\) | −15055.3 | + | 26076.6i | −1.50631 | + | 2.60900i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −929.915 | − | 1610.66i | −0.0924409 | − | 0.160112i | ||||
\(467\) | −5748.11 | −0.569573 | −0.284787 | − | 0.958591i | \(-0.591923\pi\) | ||||
−0.284787 | + | 0.958591i | \(0.591923\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 4779.65 | 0.470583 | ||||||||
\(470\) | 65.0602 | + | 112.688i | 0.00638511 | + | 0.0110593i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −12369.6 | + | 21424.9i | −1.20627 | + | 2.08932i | ||||
\(473\) | −4853.09 | + | 8405.79i | −0.471766 | + | 0.817122i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1305.30 | − | 2260.85i | −0.126087 | − | 0.218389i | ||||
\(476\) | −31684.3 | −3.05094 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −1828.98 | −0.175012 | ||||||||
\(479\) | −5608.66 | − | 9714.48i | −0.535002 | − | 0.926651i | −0.999163 | − | 0.0409004i | \(-0.986977\pi\) |
0.464161 | − | 0.885751i | \(-0.346356\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −11038.6 | + | 19119.4i | −1.04640 | + | 1.81241i | ||||
\(482\) | −16032.4 | + | 27769.0i | −1.51506 | + | 2.62416i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 4675.42 | + | 8098.06i | 0.439089 | + | 0.760524i | ||||
\(485\) | 4138.07 | 0.387423 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −8905.12 | −0.828603 | −0.414301 | − | 0.910140i | \(-0.635974\pi\) | ||||
−0.414301 | + | 0.910140i | \(0.635974\pi\) | |||||||
\(488\) | 17079.8 | + | 29583.1i | 1.58436 | + | 2.74419i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 3281.95 | − | 5684.51i | 0.302579 | − | 0.524082i | ||||
\(491\) | −3276.55 | + | 5675.15i | −0.301158 | + | 0.521621i | −0.976399 | − | 0.215976i | \(-0.930707\pi\) |
0.675240 | + | 0.737598i | \(0.264040\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 7010.03 | + | 12141.7i | 0.640397 | + | 1.10920i | ||||
\(494\) | 35512.8 | 3.23440 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −2671.96 | −0.241884 | ||||||||
\(497\) | 5196.94 | + | 9001.37i | 0.469044 | + | 0.812407i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 2305.04 | − | 3992.45i | 0.206789 | − | 0.358170i | −0.743912 | − | 0.668278i | \(-0.767032\pi\) |
0.950701 | + | 0.310108i | \(0.100365\pi\) | |||||||
\(500\) | −1190.44 | + | 2061.90i | −0.106476 | + | 0.184422i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −8439.47 | − | 14617.6i | −0.750343 | − | 1.29963i | ||||
\(503\) | −13069.1 | −1.15850 | −0.579249 | − | 0.815151i | \(-0.696654\pi\) | ||||
−0.579249 | + | 0.815151i | \(0.696654\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −4117.88 | −0.362858 | ||||||||
\(506\) | 11667.4 | + | 20208.6i | 1.02506 | + | 1.77546i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 7372.43 | − | 12769.4i | 0.643895 | − | 1.11526i | ||||
\(509\) | 7965.40 | − | 13796.5i | 0.693635 | − | 1.20141i | −0.277004 | − | 0.960869i | \(-0.589341\pi\) |
0.970639 | − | 0.240542i | \(-0.0773252\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −11336.8 | − | 19635.9i | −0.981428 | − | 1.69988i | ||||
\(512\) | 23102.1 | 1.99410 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 18473.8 | 1.58530 | ||||||||
\(515\) | −2927.97 | − | 5071.40i | −0.250528 | − | 0.433927i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −72.5174 | + | 125.604i | −0.00616888 | + | 0.0106848i | ||||
\(518\) | −21422.1 | + | 37104.2i | −1.81705 | + | 3.14723i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −9392.19 | − | 16267.7i | −0.792067 | − | 1.37190i | ||||
\(521\) | −3654.38 | −0.307296 | −0.153648 | − | 0.988126i | \(-0.549102\pi\) | ||||
−0.153648 | + | 0.988126i | \(0.549102\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −5138.66 | −0.429633 | −0.214816 | − | 0.976654i | \(-0.568915\pi\) | ||||
−0.214816 | + | 0.976654i | \(0.568915\pi\) | |||||||
\(524\) | −11561.9 | − | 20025.7i | −0.963898 | − | 1.66952i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −11484.6 | + | 19891.9i | −0.952002 | + | 1.64892i | ||||
\(527\) | −622.057 | + | 1077.43i | −0.0514179 | + | 0.0890584i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −5899.05 | − | 10217.5i | −0.484840 | − | 0.839768i | ||||
\(530\) | −8320.16 | −0.681896 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 48533.4 | 3.95524 | ||||||||
\(533\) | 6407.39 | + | 11097.9i | 0.520704 | + | 0.901885i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 2558.02 | − | 4430.62i | 0.206716 | − | 0.358042i | ||||
\(536\) | 5626.71 | − | 9745.75i | 0.453427 | − | 0.785359i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 8892.96 | + | 15403.1i | 0.712645 | + | 1.23434i | ||||
\(539\) | 7316.27 | 0.584664 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 6932.06 | 0.550892 | 0.275446 | − | 0.961317i | \(-0.411175\pi\) | ||||
0.275446 | + | 0.961317i | \(0.411175\pi\) | |||||||
\(542\) | 1862.90 | + | 3226.64i | 0.147635 | + | 0.255712i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −10287.9 | + | 17819.2i | −0.810831 | + | 1.40440i | ||||
\(545\) | 1009.12 | − | 1747.84i | 0.0793134 | − | 0.137375i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1711.56 | + | 2964.50i | 0.133786 | + | 0.231724i | 0.925133 | − | 0.379643i | \(-0.123953\pi\) |
−0.791347 | + | 0.611367i | \(0.790620\pi\) | |||||||
\(548\) | −43810.8 | −3.41516 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −3768.39 | −0.292154 | ||||||||
\(551\) | −10737.8 | − | 18598.4i | −0.830211 | − | 1.43797i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −298.058 | + | 516.251i | −0.0229199 | + | 0.0396984i | ||||
\(554\) | 1709.79 | − | 2961.45i | 0.131123 | − | 0.227112i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 12913.1 | + | 22366.2i | 0.984962 | + | 1.70600i | ||||
\(557\) | 24489.2 | 1.86291 | 0.931455 | − | 0.363856i | \(-0.118540\pi\) | ||||
0.931455 | + | 0.363856i | \(0.118540\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −21898.6 | −1.65691 | ||||||||
\(560\) | −8931.59 | − | 15470.0i | −0.673979 | − | 1.16737i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −3936.68 | + | 6818.54i | −0.295479 | + | 0.511784i | ||||
\(563\) | −5026.54 | + | 8706.22i | −0.376276 | + | 0.651729i | −0.990517 | − | 0.137389i | \(-0.956129\pi\) |
0.614241 | + | 0.789118i | \(0.289462\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 2705.51 | + | 4686.08i | 0.201454 | + | 0.348929i | ||||
\(566\) | −20315.8 | −1.50872 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 24471.8 | 1.80777 | ||||||||
\(569\) | −3335.23 | − | 5776.78i | −0.245729 | − | 0.425616i | 0.716607 | − | 0.697477i | \(-0.245694\pi\) |
−0.962336 | + | 0.271861i | \(0.912361\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −2316.78 | + | 4012.77i | −0.169797 | + | 0.294097i | −0.938348 | − | 0.345691i | \(-0.887645\pi\) |
0.768551 | + | 0.639788i | \(0.220978\pi\) | |||||||
\(572\) | 18050.0 | − | 31263.5i | 1.31942 | − | 2.28530i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 12434.6 | + | 21537.3i | 0.904196 | + | 1.56611i | ||||
\(575\) | 3870.17 | 0.280691 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 7045.15 | 0.508307 | 0.254154 | − | 0.967164i | \(-0.418203\pi\) | ||||
0.254154 | + | 0.967164i | \(0.418203\pi\) | |||||||
\(578\) | −690.677 | − | 1196.29i | −0.0497031 | − | 0.0860883i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −9792.89 | + | 16961.8i | −0.701082 | + | 1.21431i | ||||
\(581\) | −6659.84 | + | 11535.2i | −0.475554 | + | 0.823683i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −4636.91 | − | 8031.37i | −0.329402 | − | 0.570541i | ||||
\(584\) | −53383.7 | −3.78259 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −41859.0 | −2.95082 | ||||||||
\(587\) | −4000.53 | − | 6929.12i | −0.281294 | − | 0.487216i | 0.690410 | − | 0.723419i | \(-0.257430\pi\) |
−0.971704 | + | 0.236203i | \(0.924097\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 952.855 | − | 1650.39i | 0.0666582 | − | 0.115455i | ||||
\(590\) | −5598.66 | + | 9697.16i | −0.390666 | + | 0.676654i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 24715.2 | + | 42808.0i | 1.71586 | + | 2.97196i | ||||
\(593\) | −6747.53 | −0.467265 | −0.233632 | − | 0.972325i | \(-0.575061\pi\) | ||||
−0.233632 | + | 0.972325i | \(0.575061\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −8317.41 | −0.573077 | ||||||||
\(596\) | 2474.63 | + | 4286.19i | 0.170075 | + | 0.294579i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −26323.5 | + | 45593.6i | −1.80008 | + | 3.11783i | ||||
\(599\) | 10773.6 | − | 18660.5i | 0.734890 | − | 1.27287i | −0.219881 | − | 0.975527i | \(-0.570567\pi\) |
0.954771 | − | 0.297341i | \(-0.0960998\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 6077.53 | + | 10526.6i | 0.412492 | + | 0.714456i | 0.995162 | − | 0.0982525i | \(-0.0313253\pi\) |
−0.582670 | + | 0.812709i | \(0.697992\pi\) | |||||||
\(602\) | −42497.6 | −2.87720 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −9681.64 | −0.652219 | ||||||||
\(605\) | 1227.34 | + | 2125.81i | 0.0824767 | + | 0.142854i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −8174.47 | + | 14158.6i | −0.546608 | + | 0.946754i | 0.451895 | + | 0.892071i | \(0.350748\pi\) |
−0.998504 | + | 0.0546827i | \(0.982585\pi\) | |||||||
\(608\) | 15758.9 | − | 27295.2i | 1.05116 | − | 1.82067i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 7730.55 | + | 13389.7i | 0.513116 | + | 0.888743i | ||||
\(611\) | −327.220 | −0.0216660 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −29955.5 | −1.97372 | −0.986859 | − | 0.161581i | \(-0.948341\pi\) | ||||
−0.986859 | + | 0.161581i | \(0.948341\pi\) | |||||||
\(614\) | 264.101 | + | 457.437i | 0.0173587 | + | 0.0300662i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 20316.2 | − | 35188.7i | 1.32884 | − | 2.30161i | ||||
\(617\) | 1079.87 | − | 1870.39i | 0.0704603 | − | 0.122041i | −0.828643 | − | 0.559778i | \(-0.810887\pi\) |
0.899103 | + | 0.437737i | \(0.144220\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −11050.4 | − | 19139.9i | −0.717535 | − | 1.24281i | −0.961974 | − | 0.273142i | \(-0.911937\pi\) |
0.244439 | − | 0.969665i | \(-0.421396\pi\) | |||||||
\(620\) | −1738.01 | −0.112581 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −39965.0 | −2.57629 | ||||||||
\(623\) | −1026.48 | − | 1777.92i | −0.0660114 | − | 0.114335i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −312.500 | + | 541.266i | −0.0200000 | + | 0.0346410i | ||||
\(626\) | −3497.84 | + | 6058.44i | −0.223326 | + | 0.386811i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 221.946 | + | 384.422i | 0.0141029 | + | 0.0244269i | ||||
\(629\) | 23015.7 | 1.45898 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 18360.1 | 1.15833 | 0.579164 | − | 0.815211i | \(-0.303379\pi\) | ||||
0.579164 | + | 0.815211i | \(0.303379\pi\) | |||||||
\(632\) | 701.761 | + | 1215.49i | 0.0441686 | + | 0.0765023i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −19820.6 | + | 34330.3i | −1.24160 | + | 2.15052i | ||||
\(635\) | 1935.33 | − | 3352.09i | 0.120947 | − | 0.209486i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 8253.29 | + | 14295.1i | 0.513355 | + | 0.889157i | ||||
\(638\) | −30999.9 | −1.92367 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 1713.32 | 0.105820 | ||||||||
\(641\) | −10532.3 | − | 18242.4i | −0.648985 | − | 1.12407i | −0.983366 | − | 0.181636i | \(-0.941861\pi\) |
0.334381 | − | 0.942438i | \(-0.391473\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 5269.57 | − | 9127.16i | 0.323190 | − | 0.559782i | −0.657954 | − | 0.753058i | \(-0.728578\pi\) |
0.981144 | + | 0.193276i | \(0.0619112\pi\) | |||||||
\(644\) | −35974.9 | + | 62310.3i | −2.20126 | + | 3.81269i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −18511.2 | − | 32062.4i | −1.12742 | − | 1.95275i | ||||
\(647\) | −22553.4 | −1.37043 | −0.685213 | − | 0.728343i | \(-0.740291\pi\) | ||||
−0.685213 | + | 0.728343i | \(0.740291\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −12480.8 | −0.754873 | ||||||||
\(650\) | −4251.02 | − | 7362.99i | −0.256521 | − | 0.444308i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 38399.7 | − | 66510.2i | 2.30652 | − | 3.99500i | ||||
\(653\) | 11312.0 | − | 19593.0i | 0.677908 | − | 1.17417i | −0.297702 | − | 0.954659i | \(-0.596220\pi\) |
0.975610 | − | 0.219512i | \(-0.0704464\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −3035.09 | − | 5256.94i | −0.181055 | − | 0.313596i | ||||
\(656\) | 28692.1 | 1.70768 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −635.022 | −0.0376227 | ||||||||
\(659\) | 3188.30 | + | 5522.29i | 0.188465 | + | 0.326431i | 0.944739 | − | 0.327824i | \(-0.106315\pi\) |
−0.756274 | + | 0.654255i | \(0.772982\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 11048.8 | − | 19137.0i | 0.650146 | − | 1.12609i | −0.332941 | − | 0.942948i | \(-0.608041\pi\) |
0.983087 | − | 0.183139i | \(-0.0586258\pi\) | |||||||
\(662\) | −17123.4 | + | 29658.7i | −1.00532 | + | 1.74126i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 15680.2 | + | 27159.0i | 0.916433 | + | 1.58731i | ||||
\(665\) | 12740.4 | 0.742938 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 31837.2 | 1.84819 | ||||||||
\(668\) | −6398.93 | − | 11083.3i | −0.370632 | − | 0.641953i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 2546.72 | − | 4411.05i | 0.146848 | − | 0.254349i | ||||
\(671\) | −8616.63 | + | 14924.4i | −0.495740 | + | 0.858646i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −12016.5 | − | 20813.2i | −0.688264 | − | 1.19211i | −0.972399 | − | 0.233323i | \(-0.925040\pi\) |
0.284136 | − | 0.958784i | \(-0.408293\pi\) | |||||||
\(674\) | 15326.1 | 0.875873 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 39600.6 | 2.25311 | ||||||||
\(677\) | 89.8191 | + | 155.571i | 0.00509901 | + | 0.00883175i | 0.868564 | − | 0.495578i | \(-0.165044\pi\) |
−0.863465 | + | 0.504409i | \(0.831710\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −10097.4 | + | 17489.3i | −0.570698 | + | 0.988478i | ||||
\(680\) | −9791.45 | + | 16959.3i | −0.552184 | + | 0.956411i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −1375.44 | − | 2382.33i | −0.0772262 | − | 0.133760i | ||||
\(683\) | 30434.2 | 1.70502 | 0.852511 | − | 0.522709i | \(-0.175079\pi\) | ||||
0.852511 | + | 0.522709i | \(0.175079\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −11500.7 | −0.641490 | ||||||||
\(686\) | −5747.11 | − | 9954.28i | −0.319862 | − | 0.554018i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −24515.3 | + | 42461.7i | −1.35848 | + | 2.35296i | ||||
\(689\) | 10461.6 | − | 18120.0i | 0.578453 | − | 1.00191i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −4896.36 | − | 8480.75i | −0.269561 | − | 0.466893i | 0.699188 | − | 0.714938i | \(-0.253545\pi\) |
−0.968748 | + | 0.248045i | \(0.920212\pi\) | |||||||
\(692\) | −31113.7 | −1.70920 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 44171.8 | 2.41605 | ||||||||
\(695\) | 3389.81 | + | 5871.33i | 0.185011 | + | 0.320449i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 6679.78 | − | 11569.7i | 0.363005 | − | 0.628743i | ||||
\(698\) | 14682.9 | − | 25431.5i | 0.796212 | − | 1.37908i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −5809.65 | − | 10062.6i | −0.313691 | − | 0.543329i | ||||
\(701\) | −8130.47 | −0.438065 | −0.219032 | − | 0.975718i | \(-0.570290\pi\) | ||||
−0.219032 | + | 0.975718i | \(0.570290\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −35255.0 | −1.89142 | ||||||||
\(704\) | −5773.54 | − | 10000.1i | −0.309089 | − | 0.535357i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 3177.43 | − | 5503.47i | 0.169383 | − | 0.293379i | ||||
\(707\) | 10048.2 | − | 17404.0i | 0.534513 | − | 0.925804i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 2429.98 | + | 4208.84i | 0.128716 | + | 0.222943i | 0.923179 | − | 0.384369i | \(-0.125581\pi\) |
−0.794463 | + | 0.607312i | \(0.792248\pi\) | |||||||
\(710\) | 11076.3 | 0.585472 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −4833.59 | −0.254419 | ||||||||
\(713\) | 1412.59 | + | 2446.67i | 0.0741961 | + | 0.128511i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 4738.28 | − | 8206.94i | 0.247834 | − | 0.429262i | ||||
\(716\) | 3249.98 | − | 5629.13i | 0.169633 | − | 0.293814i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 10795.1 | + | 18697.7i | 0.561101 | + | 0.971856i | ||||
\(719\) | −19463.0 | −1.00952 | −0.504762 | − | 0.863259i | \(-0.668420\pi\) | ||||
−0.504762 | + | 0.863259i | \(0.668420\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 28578.6 | 1.47618 | ||||||||
\(722\) | 10519.4 | + | 18220.2i | 0.542233 | + | 0.939175i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 16151.1 | − | 27974.5i | 0.829075 | − | 1.43600i | ||||
\(725\) | −2570.72 | + | 4452.62i | −0.131689 | + | 0.228091i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −1216.33 | − | 2106.75i | −0.0620512 | − | 0.107476i | 0.833331 | − | 0.552774i | \(-0.186431\pi\) |
−0.895382 | + | 0.445299i | \(0.853098\pi\) | |||||||
\(728\) | 91672.8 | 4.66706 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −24162.1 | −1.22504 | ||||||||
\(731\) | 11414.7 | + | 19770.9i | 0.577551 | + | 1.00035i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 8983.79 | − | 15560.4i | 0.452693 | − | 0.784087i | −0.545859 | − | 0.837877i | \(-0.683797\pi\) |
0.998552 | + | 0.0537895i | \(0.0171300\pi\) | |||||||
\(734\) | −18303.0 | + | 31701.8i | −0.920404 | + | 1.59419i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 23362.2 | + | 40464.5i | 1.17003 | + | 2.02655i | ||||
\(737\) | 5677.26 | 0.283751 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 23473.0 | 1.16843 | 0.584214 | − | 0.811599i | \(-0.301403\pi\) | ||||
0.584214 | + | 0.811599i | \(0.301403\pi\) | |||||||
\(740\) | 16076.3 | + | 27844.9i | 0.798616 | + | 1.38324i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 20302.3 | − | 35164.6i | 1.00448 | − | 1.73980i | ||||
\(743\) | −16779.6 | + | 29063.2i | −0.828512 | + | 1.43503i | 0.0706932 | + | 0.997498i | \(0.477479\pi\) |
−0.899205 | + | 0.437527i | \(0.855854\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 649.613 | + | 1125.16i | 0.0319463 | + | 0.0553325i | ||||
\(746\) | 37026.5 | 1.81721 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −37634.6 | −1.83965 | ||||||||
\(749\) | 12483.8 | + | 21622.6i | 0.609011 | + | 1.05484i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 3891.38 | − | 6740.06i | 0.189079 | − | 0.327495i | −0.755864 | − | 0.654728i | \(-0.772783\pi\) |
0.944943 | + | 0.327234i | \(0.106116\pi\) | |||||||
\(752\) | −366.320 | + | 634.485i | −0.0177637 | + | 0.0307677i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −34970.2 | − | 60570.2i | −1.68905 | − | 2.92551i | ||||
\(755\) | −2541.52 | −0.122510 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −38154.3 | −1.83189 | −0.915946 | − | 0.401300i | \(-0.868558\pi\) | ||||
−0.915946 | + | 0.401300i | \(0.868558\pi\) | |||||||
\(758\) | 8769.09 | + | 15188.5i | 0.420195 | + | 0.727799i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 14998.4 | − | 25977.9i | 0.715852 | − | 1.23989i | ||||
\(761\) | 9933.56 | − | 17205.4i | 0.473182 | − | 0.819575i | −0.526347 | − | 0.850270i | \(-0.676439\pi\) |
0.999529 | + | 0.0306951i | \(0.00977209\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 4924.76 | + | 8529.93i | 0.233667 | + | 0.404724i | ||||
\(764\) | 13836.7 | 0.655228 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 20587.5 | 0.971094 | ||||||||
\(767\) | −14079.2 | − | 24385.9i | −0.662805 | − | 1.14801i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 7855.40 | − | 13605.9i | 0.368365 | − | 0.638027i | −0.620945 | − | 0.783854i | \(-0.713251\pi\) |
0.989310 | + | 0.145827i | \(0.0465843\pi\) | |||||||
\(770\) | 9195.37 | − | 15926.9i | 0.430361 | − | 0.745408i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −40448.7 | − | 70059.3i | −1.88573 | − | 3.26618i | ||||
\(773\) | −25811.9 | −1.20102 | −0.600510 | − | 0.799617i | \(-0.705036\pi\) | ||||
−0.600510 | + | 0.799617i | \(0.705036\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −456.242 | −0.0211467 | ||||||||
\(776\) | 23773.9 | + | 41177.6i | 1.09978 | + | 1.90488i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −25103.6 | + | 43480.8i | −1.15682 | + | 2.00368i | ||||
\(779\) | −10232.0 | + | 17722.3i | −0.470600 | + | 0.815104i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 6172.92 | + | 10691.8i | 0.282822 | + | 0.489863i | ||||
\(782\) | 54885.0 | 2.50982 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 36958.0 | 1.68358 | ||||||||
\(785\) | 58.2629 | + | 100.914i | 0.00264903 | + | 0.00458826i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 14621.3 | − | 25324.8i | 0.662252 | − | 1.14705i | −0.317770 | − | 0.948168i | \(-0.602934\pi\) |
0.980023 | − | 0.198887i | \(-0.0637326\pi\) | |||||||
\(788\) | 25508.8 | − | 44182.6i | 1.15319 | − | 1.99739i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 317.626 | + | 550.144i | 0.0143046 | + | 0.0247763i | ||||
\(791\) | −26407.2 | −1.18702 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −38880.8 | −1.74111 | ||||||||
\(794\) | 28417.3 | + | 49220.2i | 1.27014 | + | 2.19995i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −14156.5 | + | 24519.8i | −0.630356 | + | 1.09181i | ||||
\(797\) | 16286.9 | − | 28209.7i | 0.723853 | − | 1.25375i | −0.235592 | − | 0.971852i | \(-0.575703\pi\) |
0.959445 | − | 0.281898i | \(-0.0909638\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 170.565 | + | 295.428i | 0.00755214 | + | 0.0130807i | ||||
\(800\) | −7545.60 | −0.333472 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 21247.7 | 0.935514 | ||||||||
\(803\) | −13465.8 | − | 23323.5i | −0.591778 | − | 1.02499i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −9443.73 | + | 16357.0i | −0.413475 | + | 0.716160i | ||||
\(806\) | 3103.19 | − | 5374.89i | 0.135615 | − | 0.234891i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −23657.9 | − | 40976.7i | −1.03005 | − | 1.78410i | ||||
\(809\) | 34644.9 | 1.50562 | 0.752812 | − | 0.658236i | \(-0.228697\pi\) | ||||
0.752812 | + | 0.658236i | \(0.228697\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −29057.9 | −1.25815 | −0.629077 | − | 0.777343i | \(-0.716567\pi\) | ||||
−0.629077 | + | 0.777343i | \(0.716567\pi\) | |||||||
\(812\) | −47791.9 | − | 82778.1i | −2.06548 | − | 3.57751i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −25445.2 | + | 44072.3i | −1.09564 | + | 1.89771i | ||||
\(815\) | 10080.3 | − | 17459.5i | 0.433247 | − | 0.750405i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −17484.9 | − | 30284.7i | −0.748738 | − | 1.29685i | ||||
\(818\) | −52819.3 | −2.25768 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 18663.1 | 0.794809 | ||||||||
\(821\) | 23354.8 | + | 40451.6i | 0.992798 | + | 1.71958i | 0.600150 | + | 0.799887i | \(0.295107\pi\) |
0.392647 | + | 0.919689i | \(0.371559\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1734.05 | − | 3003.46i | 0.0734450 | − | 0.127210i | −0.826964 | − | 0.562255i | \(-0.809934\pi\) |
0.900409 | + | 0.435044i | \(0.143267\pi\) | |||||||
\(824\) | 33643.4 | − | 58272.1i | 1.42236 | − | 2.46360i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −27323.0 | − | 47324.8i | −1.15095 | − | 1.99351i | ||||
\(827\) | −42454.9 | −1.78513 | −0.892564 | − | 0.450920i | \(-0.851096\pi\) | ||||
−0.892564 | + | 0.450920i | \(0.851096\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −3933.47 | −0.164795 | −0.0823975 | − | 0.996600i | \(-0.526258\pi\) | ||||
−0.0823975 | + | 0.996600i | \(0.526258\pi\) | |||||||
\(830\) | 7097.08 | + | 12292.5i | 0.296799 | + | 0.514071i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 13026.0 | − | 22561.6i | 0.542781 | − | 0.940124i | ||||
\(833\) | 8604.14 | − | 14902.8i | 0.357882 | − | 0.619870i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1679.78 | − | 2909.46i | −0.0696181 | − | 0.120582i | ||||
\(836\) | 57647.9 | 2.38492 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 82580.5 | 3.40417 | ||||||||
\(839\) | −16479.8 | − | 28543.8i | −0.678123 | − | 1.17454i | −0.975546 | − | 0.219797i | \(-0.929460\pi\) |
0.297423 | − | 0.954746i | \(-0.403873\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −8953.05 | + | 15507.1i | −0.367094 | + | 0.635825i | ||||
\(842\) | −5928.36 | + | 10268.2i | −0.242642 | + | 0.420269i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 45973.8 | + | 79629.0i | 1.87498 | + | 3.24756i | ||||
\(845\) | 10395.5 | 0.423215 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −11979.5 | −0.485974 | ||||||||
\(848\) | −23423.3 | − | 40570.3i | −0.948536 | − | 1.64291i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −4431.74 | + | 7675.99i | −0.178832 | + | 0.309746i | ||||
\(851\) | 26132.4 | − | 45262.6i | 1.05265 | − | 1.82325i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −19422.9 | − | 33641.5i | −0.779634 | − | 1.35037i | −0.932153 | − | 0.362066i | \(-0.882072\pi\) |
0.152518 | − | 0.988301i | \(-0.451262\pi\) | |||||||
\(854\) | −75454.3 | −3.02341 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 58785.0 | 2.34723 | ||||||||
\(857\) | −14652.6 | − | 25379.1i | −0.584043 | − | 1.01159i | −0.994994 | − | 0.0999343i | \(-0.968137\pi\) |
0.410951 | − | 0.911657i | \(-0.365197\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 454.830 | − | 787.788i | 0.0180659 | − | 0.0312910i | −0.856851 | − | 0.515564i | \(-0.827582\pi\) |
0.874917 | + | 0.484273i | \(0.160916\pi\) | |||||||
\(860\) | −15946.2 | + | 27619.7i | −0.632281 | + | 1.09514i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 5063.83 | + | 8770.81i | 0.200087 | + | 0.346560i | ||||
\(863\) | −47998.0 | −1.89324 | −0.946622 | − | 0.322346i | \(-0.895529\pi\) | ||||
−0.946622 | + | 0.322346i | \(0.895529\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −8167.64 | −0.321050 | ||||||||
\(866\) | 32858.3 | + | 56912.2i | 1.28934 | + | 2.23321i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 4240.97 | − | 7345.58i | 0.165839 | − | 0.287241i | ||||
\(869\) | −354.032 | + | 613.202i | −0.0138202 | + | 0.0239372i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 6404.37 | + | 11092.7i | 0.249143 | + | 0.431529i | ||||
\(872\) | 23190.2 | 0.900594 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −84071.7 | −3.25374 | ||||||||
\(875\) | −1525.08 | − | 2641.52i | −0.0589226 | − | 0.102057i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1629.01 | + | 2821.52i | −0.0627225 | + | 0.108639i | −0.895681 | − | 0.444696i | \(-0.853312\pi\) |
0.832959 | + | 0.553335i | \(0.186645\pi\) | |||||||
\(878\) | −41214.9 | + | 71386.3i | −1.58421 | + | 2.74393i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −10608.9 | − | 18375.2i | −0.406394 | − | 0.703895i | ||||
\(881\) | 33380.2 | 1.27651 | 0.638256 | − | 0.769824i | \(-0.279656\pi\) | ||||
0.638256 | + | 0.769824i | \(0.279656\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 33714.6 | 1.28492 | 0.642460 | − | 0.766319i | \(-0.277914\pi\) | ||||
0.642460 | + | 0.766319i | \(0.277914\pi\) | |||||||
\(884\) | −42454.6 | − | 73533.5i | −1.61527 | − | 2.79774i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 45390.3 | − | 78618.3i | 1.72113 | − | 2.98108i | ||||
\(887\) | −3109.40 | + | 5385.64i | −0.117704 | + | 0.203869i | −0.918857 | − | 0.394590i | \(-0.870887\pi\) |
0.801153 | + | 0.598459i | \(0.204220\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 9444.92 | + | 16359.1i | 0.356325 | + | 0.617172i | ||||
\(890\) | −2187.75 | −0.0823971 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 52845.5 | 1.98363 | ||||||||
\(893\) | −261.268 | − | 452.530i | −0.00979061 | − | 0.0169578i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 853.149 | − | 1477.70i | 0.0318633 | − | 0.0551888i | ||||
\(896\) | −4180.73 | + | 7241.24i | −0.155880 | + | 0.269992i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 41782.6 | + | 72369.5i | 1.55268 | + | 2.68931i | ||||
\(899\) | −3753.19 | −0.139239 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −21812.6 | −0.806529 | ||||||||
\(902\) | 14769.7 | + | 25582.0i | 0.545209 | + | 0.944330i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −31087.2 | + | 53844.6i | −1.14374 | + | 1.98102i | ||||
\(905\) | 4239.80 | − | 7343.56i | 0.155730 | − | 0.269733i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 11439.3 | + | 19813.5i | 0.418783 | + | 0.725354i | 0.995817 | − | 0.0913663i | \(-0.0291234\pi\) |
−0.577034 | + | 0.816720i | \(0.695790\pi\) | |||||||
\(908\) | 97165.0 | 3.55125 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 41492.3 | 1.51149 | ||||||||
\(911\) | −15072.4 | − | 26106.2i | −0.548157 | − | 0.949435i | −0.998401 | − | 0.0565298i | \(-0.981996\pi\) |
0.450244 | − | 0.892905i | \(-0.351337\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −7910.55 | + | 13701.5i | −0.286748 | + | 0.496662i | ||||
\(914\) | 30922.4 | − | 53559.2i | 1.11906 | − | 1.93827i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 39025.6 | + | 67594.3i | 1.40769 | + | 2.43819i | ||||
\(917\) | 29624.1 | 1.06682 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 3803.52 | 0.136525 | 0.0682625 | − | 0.997667i | \(-0.478254\pi\) | ||||
0.0682625 | + | 0.997667i | \(0.478254\pi\) | |||||||
\(920\) | 22234.8 | + | 38511.7i | 0.796802 | + | 1.38010i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 7286.74 | − | 12621.0i | 0.260277 | − | 0.450814i | ||||
\(923\) | −13927.0 | + | 24122.3i | −0.496656 | + | 0.860233i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 4220.17 | + | 7309.54i | 0.150009 | + | 0.259823i | ||||
\(926\) | 67262.0 | 2.38700 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −62072.5 | −2.19572 | ||||||||
\(929\) | 62.9925 | + | 109.106i | 0.00222467 | + | 0.00385324i | 0.867136 | − | 0.498072i | \(-0.165959\pi\) |
−0.864911 | + | 0.501925i | \(0.832625\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −13179.7 | + | 22827.8i | −0.463959 | + | 0.803601i | ||||
\(932\) | 3405.73 | − | 5898.89i | 0.119698 | − | 0.207322i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −14947.0 | − | 25889.0i | −0.523642 | − | 0.906974i | ||||
\(935\) | −9879.41 | −0.345552 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 28107.9 | 0.979984 | 0.489992 | − | 0.871727i | \(-0.337000\pi\) | ||||
0.489992 | + | 0.871727i | \(0.337000\pi\) | |||||||
\(938\) | 12428.7 | + | 21527.1i | 0.432634 | + | 0.749344i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −238.277 | + | 412.708i | −0.00826780 | + | 0.0143203i | ||||
\(941\) | −24597.5 | + | 42604.0i | −0.852130 | + | 1.47593i | 0.0271524 | + | 0.999631i | \(0.491356\pi\) |
−0.879282 | + | 0.476301i | \(0.841977\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −15168.7 | − | 26272.9i | −0.523817 | − | 0.907277i | ||||
\(944\) | −63046.3 | −2.17371 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −50478.6 | −1.73488 | ||||||||
\(947\) | −7249.02 | − | 12555.7i | −0.248745 | − | 0.430839i | 0.714433 | − | 0.699704i | \(-0.246685\pi\) |
−0.963178 | + | 0.268865i | \(0.913351\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 30380.9 | − | 52621.2i | 1.03920 | − | 1.79995i | ||||
\(950\) | 6788.45 | − | 11757.9i | 0.231838 | − | 0.401556i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −47784.9 | − | 82765.9i | −1.62680 | − | 2.81771i | ||||
\(953\) | −3201.79 | −0.108831 | −0.0544155 | − | 0.998518i | \(-0.517330\pi\) | ||||
−0.0544155 | + | 0.998518i | \(0.517330\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 3632.26 | 0.123075 | ||||||||
\(956\) | −3349.24 | − | 5801.06i | −0.113308 | − | 0.196255i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 29168.8 | − | 50521.8i | 0.983717 | − | 1.70385i | ||||
\(959\) | 28063.3 | − | 48607.1i | 0.944956 | − | 1.63671i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 14729.0 | + | 25511.3i | 0.494410 | + | 0.856344i | ||||
\(962\) | −114816. | −3.84805 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −117435. | −3.92356 | ||||||||
\(965\) | −10618.2 | − | 18391.2i | −0.354208 | − | 0.613506i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −28891.0 | + | 50040.6i | −0.960776 | + | 1.66411i | −0.240217 | + | 0.970719i | \(0.577219\pi\) |
−0.720559 | + | 0.693394i | \(0.756115\pi\) | |||||||
\(968\) | −14102.5 | + | 24426.3i | −0.468257 | + | 0.811044i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 10760.4 | + | 18637.5i | 0.356180 | + | 0.616921i | ||||
\(971\) | −2611.60 | −0.0863133 | −0.0431566 | − | 0.999068i | \(-0.513741\pi\) | ||||
−0.0431566 | + | 0.999068i | \(0.513741\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −33086.4 | −1.09013 | ||||||||
\(974\) | −23156.3 | − | 40107.9i | −0.761782 | − | 1.31945i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −43526.7 | + | 75390.5i | −1.42752 | + | 2.47253i | ||||
\(977\) | −16799.1 | + | 29097.0i | −0.550104 | + | 0.952809i | 0.448162 | + | 0.893952i | \(0.352079\pi\) |
−0.998266 | + | 0.0588563i | \(0.981255\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1219.25 | − | 2111.81i | −0.0398034 | − | 0.0689415i | ||||
\(980\) | 24039.7 | 0.783592 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −34080.5 | −1.10749 | ||||||||
\(983\) | −19742.4 | − | 34194.9i | −0.640575 | − | 1.10951i | −0.985305 | − | 0.170807i | \(-0.945363\pi\) |
0.344729 | − | 0.938702i | \(-0.387971\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 6696.30 | − | 11598.3i | 0.216611 | − | 0.375181i | ||||
\(986\) | −36456.8 | + | 63145.1i | −1.17751 | + | 2.03950i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 65031.1 | + | 112637.i | 2.09404 | + | 3.62699i | ||||
\(989\) | 51841.9 | 1.66681 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 39918.6 | 1.27957 | 0.639786 | − | 0.768553i | \(-0.279023\pi\) | ||||
0.639786 | + | 0.768553i | \(0.279023\pi\) | |||||||
\(992\) | −2754.10 | − | 4770.24i | −0.0881479 | − | 0.152677i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −27027.6 | + | 46813.1i | −0.862437 | + | 1.49379i | ||||
\(995\) | −3716.21 | + | 6436.66i | −0.118404 | + | 0.205081i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 12835.1 | + | 22231.1i | 0.407716 | + | 0.706185i | 0.994633 | − | 0.103462i | \(-0.0329920\pi\) |
−0.586917 | + | 0.809647i | \(0.699659\pi\) | |||||||
\(998\) | 23975.6 | 0.760454 | ||||||||
\(999\) | 0 | 0 |
(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 | 405.4.e.t.271.3 | 6 | ||
3.2 | odd | 2 | 405.4.e.r.271.1 | 6 | |||
9.2 | odd | 6 | 405.4.e.r.136.1 | 6 | |||
9.4 | even | 3 | 135.4.a.f.1.1 | ✓ | 3 | ||
9.5 | odd | 6 | 135.4.a.g.1.3 | yes | 3 | ||
9.7 | even | 3 | inner | 405.4.e.t.136.3 | 6 | ||
36.23 | even | 6 | 2160.4.a.be.1.1 | 3 | |||
36.31 | odd | 6 | 2160.4.a.bm.1.1 | 3 | |||
45.4 | even | 6 | 675.4.a.r.1.3 | 3 | |||
45.13 | odd | 12 | 675.4.b.l.649.6 | 6 | |||
45.14 | odd | 6 | 675.4.a.q.1.1 | 3 | |||
45.22 | odd | 12 | 675.4.b.l.649.1 | 6 | |||
45.23 | even | 12 | 675.4.b.k.649.1 | 6 | |||
45.32 | even | 12 | 675.4.b.k.649.6 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
135.4.a.f.1.1 | ✓ | 3 | 9.4 | even | 3 | ||
135.4.a.g.1.3 | yes | 3 | 9.5 | odd | 6 | ||
405.4.e.r.136.1 | 6 | 9.2 | odd | 6 | |||
405.4.e.r.271.1 | 6 | 3.2 | odd | 2 | |||
405.4.e.t.136.3 | 6 | 9.7 | even | 3 | inner | ||
405.4.e.t.271.3 | 6 | 1.1 | even | 1 | trivial | ||
675.4.a.q.1.1 | 3 | 45.14 | odd | 6 | |||
675.4.a.r.1.3 | 3 | 45.4 | even | 6 | |||
675.4.b.k.649.1 | 6 | 45.23 | even | 12 | |||
675.4.b.k.649.6 | 6 | 45.32 | even | 12 | |||
675.4.b.l.649.1 | 6 | 45.22 | odd | 12 | |||
675.4.b.l.649.6 | 6 | 45.13 | odd | 12 | |||
2160.4.a.be.1.1 | 3 | 36.23 | even | 6 | |||
2160.4.a.bm.1.1 | 3 | 36.31 | odd | 6 |