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: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.7 | ||
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.96820 | −1.04942 | −0.524709 | − | 0.851282i | \(-0.675826\pi\) | ||||
−0.524709 | + | 0.851282i | \(0.675826\pi\) | |||||||
\(3\) | 4.96634 | 0.955772 | 0.477886 | − | 0.878422i | \(-0.341403\pi\) | ||||
0.477886 | + | 0.878422i | \(0.341403\pi\) | |||||||
\(4\) | 0.810213 | 0.101277 | ||||||||
\(5\) | 5.00000 | 0.447214 | ||||||||
\(6\) | −14.7411 | −1.00300 | ||||||||
\(7\) | 12.3435 | 0.666488 | 0.333244 | − | 0.942841i | \(-0.391857\pi\) | ||||
0.333244 | + | 0.942841i | \(0.391857\pi\) | |||||||
\(8\) | 21.3407 | 0.943136 | ||||||||
\(9\) | −2.33550 | −0.0864999 | ||||||||
\(10\) | −14.8410 | −0.469314 | ||||||||
\(11\) | −11.0000 | −0.301511 | ||||||||
\(12\) | 4.02379 | 0.0967974 | ||||||||
\(13\) | 49.0109 | 1.04563 | 0.522815 | − | 0.852446i | \(-0.324882\pi\) | ||||
0.522815 | + | 0.852446i | \(0.324882\pi\) | |||||||
\(14\) | −36.6381 | −0.699425 | ||||||||
\(15\) | 24.8317 | 0.427434 | ||||||||
\(16\) | −69.8253 | −1.09102 | ||||||||
\(17\) | 111.557 | 1.59157 | 0.795784 | − | 0.605580i | \(-0.207059\pi\) | ||||
0.795784 | + | 0.605580i | \(0.207059\pi\) | |||||||
\(18\) | 6.93223 | 0.0907745 | ||||||||
\(19\) | 19.0000 | 0.229416 | ||||||||
\(20\) | 4.05107 | 0.0452923 | ||||||||
\(21\) | 61.3022 | 0.637011 | ||||||||
\(22\) | 32.6502 | 0.316411 | ||||||||
\(23\) | −130.782 | −1.18565 | −0.592823 | − | 0.805333i | \(-0.701986\pi\) | ||||
−0.592823 | + | 0.805333i | \(0.701986\pi\) | |||||||
\(24\) | 105.985 | 0.901423 | ||||||||
\(25\) | 25.0000 | 0.200000 | ||||||||
\(26\) | −145.474 | −1.09730 | ||||||||
\(27\) | −145.690 | −1.03845 | ||||||||
\(28\) | 10.0009 | 0.0674997 | ||||||||
\(29\) | 166.706 | 1.06747 | 0.533734 | − | 0.845652i | \(-0.320788\pi\) | ||||
0.533734 | + | 0.845652i | \(0.320788\pi\) | |||||||
\(30\) | −73.7054 | −0.448557 | ||||||||
\(31\) | 122.487 | 0.709656 | 0.354828 | − | 0.934932i | \(-0.384539\pi\) | ||||
0.354828 | + | 0.934932i | \(0.384539\pi\) | |||||||
\(32\) | 36.5296 | 0.201799 | ||||||||
\(33\) | −54.6297 | −0.288176 | ||||||||
\(34\) | −331.125 | −1.67022 | ||||||||
\(35\) | 61.7177 | 0.298063 | ||||||||
\(36\) | −1.89225 | −0.00876043 | ||||||||
\(37\) | 155.438 | 0.690642 | 0.345321 | − | 0.938485i | \(-0.387770\pi\) | ||||
0.345321 | + | 0.938485i | \(0.387770\pi\) | |||||||
\(38\) | −56.3958 | −0.240753 | ||||||||
\(39\) | 243.405 | 0.999383 | ||||||||
\(40\) | 106.704 | 0.421783 | ||||||||
\(41\) | 371.603 | 1.41548 | 0.707739 | − | 0.706474i | \(-0.249715\pi\) | ||||
0.707739 | + | 0.706474i | \(0.249715\pi\) | |||||||
\(42\) | −181.957 | −0.668490 | ||||||||
\(43\) | −89.9580 | −0.319034 | −0.159517 | − | 0.987195i | \(-0.550994\pi\) | ||||
−0.159517 | + | 0.987195i | \(0.550994\pi\) | |||||||
\(44\) | −8.91235 | −0.0305361 | ||||||||
\(45\) | −11.6775 | −0.0386839 | ||||||||
\(46\) | 388.186 | 1.24424 | ||||||||
\(47\) | −361.877 | −1.12309 | −0.561544 | − | 0.827447i | \(-0.689792\pi\) | ||||
−0.561544 | + | 0.827447i | \(0.689792\pi\) | |||||||
\(48\) | −346.776 | −1.04277 | ||||||||
\(49\) | −190.637 | −0.555793 | ||||||||
\(50\) | −74.2050 | −0.209883 | ||||||||
\(51\) | 554.032 | 1.52118 | ||||||||
\(52\) | 39.7093 | 0.105898 | ||||||||
\(53\) | −350.798 | −0.909167 | −0.454583 | − | 0.890704i | \(-0.650212\pi\) | ||||
−0.454583 | + | 0.890704i | \(0.650212\pi\) | |||||||
\(54\) | 432.437 | 1.08976 | ||||||||
\(55\) | −55.0000 | −0.134840 | ||||||||
\(56\) | 263.420 | 0.628589 | ||||||||
\(57\) | 94.3604 | 0.219269 | ||||||||
\(58\) | −494.818 | −1.12022 | ||||||||
\(59\) | 796.573 | 1.75771 | 0.878855 | − | 0.477088i | \(-0.158308\pi\) | ||||
0.878855 | + | 0.477088i | \(0.158308\pi\) | |||||||
\(60\) | 20.1190 | 0.0432891 | ||||||||
\(61\) | −226.206 | −0.474798 | −0.237399 | − | 0.971412i | \(-0.576295\pi\) | ||||
−0.237399 | + | 0.971412i | \(0.576295\pi\) | |||||||
\(62\) | −363.566 | −0.744725 | ||||||||
\(63\) | −28.8283 | −0.0576512 | ||||||||
\(64\) | 450.175 | 0.879248 | ||||||||
\(65\) | 245.055 | 0.467620 | ||||||||
\(66\) | 162.152 | 0.302417 | ||||||||
\(67\) | 351.549 | 0.641023 | 0.320512 | − | 0.947245i | \(-0.396145\pi\) | ||||
0.320512 | + | 0.947245i | \(0.396145\pi\) | |||||||
\(68\) | 90.3854 | 0.161189 | ||||||||
\(69\) | −649.505 | −1.13321 | ||||||||
\(70\) | −183.190 | −0.312792 | ||||||||
\(71\) | 394.348 | 0.659162 | 0.329581 | − | 0.944127i | \(-0.393092\pi\) | ||||
0.329581 | + | 0.944127i | \(0.393092\pi\) | |||||||
\(72\) | −49.8412 | −0.0815812 | ||||||||
\(73\) | 66.2672 | 0.106246 | 0.0531232 | − | 0.998588i | \(-0.483082\pi\) | ||||
0.0531232 | + | 0.998588i | \(0.483082\pi\) | |||||||
\(74\) | −461.370 | −0.724772 | ||||||||
\(75\) | 124.158 | 0.191154 | ||||||||
\(76\) | 15.3941 | 0.0232345 | ||||||||
\(77\) | −135.779 | −0.200954 | ||||||||
\(78\) | −722.474 | −1.04877 | ||||||||
\(79\) | 8.71831 | 0.0124163 | 0.00620814 | − | 0.999981i | \(-0.498024\pi\) | ||||
0.00620814 | + | 0.999981i | \(0.498024\pi\) | |||||||
\(80\) | −349.126 | −0.487919 | ||||||||
\(81\) | −660.487 | −0.906018 | ||||||||
\(82\) | −1102.99 | −1.48543 | ||||||||
\(83\) | 50.2961 | 0.0665146 | 0.0332573 | − | 0.999447i | \(-0.489412\pi\) | ||||
0.0332573 | + | 0.999447i | \(0.489412\pi\) | |||||||
\(84\) | 49.6678 | 0.0645144 | ||||||||
\(85\) | 557.787 | 0.711771 | ||||||||
\(86\) | 267.013 | 0.334800 | ||||||||
\(87\) | 827.920 | 1.02026 | ||||||||
\(88\) | −234.748 | −0.284366 | ||||||||
\(89\) | −1609.37 | −1.91677 | −0.958386 | − | 0.285474i | \(-0.907849\pi\) | ||||
−0.958386 | + | 0.285474i | \(0.907849\pi\) | |||||||
\(90\) | 34.6611 | 0.0405956 | ||||||||
\(91\) | 604.968 | 0.696900 | ||||||||
\(92\) | −105.961 | −0.120078 | ||||||||
\(93\) | 608.312 | 0.678269 | ||||||||
\(94\) | 1074.12 | 1.17859 | ||||||||
\(95\) | 95.0000 | 0.102598 | ||||||||
\(96\) | 181.418 | 0.192874 | ||||||||
\(97\) | 364.255 | 0.381283 | 0.190642 | − | 0.981660i | \(-0.438943\pi\) | ||||
0.190642 | + | 0.981660i | \(0.438943\pi\) | |||||||
\(98\) | 565.849 | 0.583259 | ||||||||
\(99\) | 25.6905 | 0.0260807 | ||||||||
\(100\) | 20.2553 | 0.0202553 | ||||||||
\(101\) | −439.512 | −0.433001 | −0.216500 | − | 0.976283i | \(-0.569464\pi\) | ||||
−0.216500 | + | 0.976283i | \(0.569464\pi\) | |||||||
\(102\) | −1644.48 | −1.59635 | ||||||||
\(103\) | 1014.51 | 0.970508 | 0.485254 | − | 0.874373i | \(-0.338727\pi\) | ||||
0.485254 | + | 0.874373i | \(0.338727\pi\) | |||||||
\(104\) | 1045.93 | 0.986170 | ||||||||
\(105\) | 306.511 | 0.284880 | ||||||||
\(106\) | 1041.24 | 0.954095 | ||||||||
\(107\) | 290.378 | 0.262354 | 0.131177 | − | 0.991359i | \(-0.458124\pi\) | ||||
0.131177 | + | 0.991359i | \(0.458124\pi\) | |||||||
\(108\) | −118.040 | −0.105170 | ||||||||
\(109\) | −1731.86 | −1.52185 | −0.760925 | − | 0.648840i | \(-0.775254\pi\) | ||||
−0.760925 | + | 0.648840i | \(0.775254\pi\) | |||||||
\(110\) | 163.251 | 0.141503 | ||||||||
\(111\) | 771.955 | 0.660097 | ||||||||
\(112\) | −861.891 | −0.727152 | ||||||||
\(113\) | 1650.43 | 1.37397 | 0.686987 | − | 0.726670i | \(-0.258933\pi\) | ||||
0.686987 | + | 0.726670i | \(0.258933\pi\) | |||||||
\(114\) | −280.081 | −0.230105 | ||||||||
\(115\) | −653.908 | −0.530237 | ||||||||
\(116\) | 135.068 | 0.108110 | ||||||||
\(117\) | −114.465 | −0.0904468 | ||||||||
\(118\) | −2364.39 | −1.84457 | ||||||||
\(119\) | 1377.01 | 1.06076 | ||||||||
\(120\) | 529.926 | 0.403129 | ||||||||
\(121\) | 121.000 | 0.0909091 | ||||||||
\(122\) | 671.425 | 0.498262 | ||||||||
\(123\) | 1845.50 | 1.35287 | ||||||||
\(124\) | 99.2407 | 0.0718716 | ||||||||
\(125\) | 125.000 | 0.0894427 | ||||||||
\(126\) | 85.5682 | 0.0605002 | ||||||||
\(127\) | −1213.81 | −0.848097 | −0.424049 | − | 0.905639i | \(-0.639391\pi\) | ||||
−0.424049 | + | 0.905639i | \(0.639391\pi\) | |||||||
\(128\) | −1628.45 | −1.12450 | ||||||||
\(129\) | −446.762 | −0.304924 | ||||||||
\(130\) | −727.371 | −0.490728 | ||||||||
\(131\) | 1411.47 | 0.941381 | 0.470690 | − | 0.882298i | \(-0.344005\pi\) | ||||
0.470690 | + | 0.882298i | \(0.344005\pi\) | |||||||
\(132\) | −44.2617 | −0.0291855 | ||||||||
\(133\) | 234.527 | 0.152903 | ||||||||
\(134\) | −1043.47 | −0.672701 | ||||||||
\(135\) | −728.450 | −0.464407 | ||||||||
\(136\) | 2380.72 | 1.50106 | ||||||||
\(137\) | −134.868 | −0.0841064 | −0.0420532 | − | 0.999115i | \(-0.513390\pi\) | ||||
−0.0420532 | + | 0.999115i | \(0.513390\pi\) | |||||||
\(138\) | 1927.86 | 1.18921 | ||||||||
\(139\) | 2129.24 | 1.29928 | 0.649639 | − | 0.760242i | \(-0.274920\pi\) | ||||
0.649639 | + | 0.760242i | \(0.274920\pi\) | |||||||
\(140\) | 50.0045 | 0.0301868 | ||||||||
\(141\) | −1797.20 | −1.07342 | ||||||||
\(142\) | −1170.50 | −0.691736 | ||||||||
\(143\) | −539.120 | −0.315269 | ||||||||
\(144\) | 163.077 | 0.0943731 | ||||||||
\(145\) | 833.531 | 0.477386 | ||||||||
\(146\) | −196.694 | −0.111497 | ||||||||
\(147\) | −946.768 | −0.531212 | ||||||||
\(148\) | 125.938 | 0.0699460 | ||||||||
\(149\) | −2633.56 | −1.44798 | −0.723992 | − | 0.689808i | \(-0.757695\pi\) | ||||
−0.723992 | + | 0.689808i | \(0.757695\pi\) | |||||||
\(150\) | −368.527 | −0.200601 | ||||||||
\(151\) | 2922.55 | 1.57506 | 0.787528 | − | 0.616278i | \(-0.211360\pi\) | ||||
0.787528 | + | 0.616278i | \(0.211360\pi\) | |||||||
\(152\) | 405.474 | 0.216370 | ||||||||
\(153\) | −260.542 | −0.137671 | ||||||||
\(154\) | 403.019 | 0.210884 | ||||||||
\(155\) | 612.436 | 0.317368 | ||||||||
\(156\) | 197.210 | 0.101214 | ||||||||
\(157\) | 2201.17 | 1.11893 | 0.559465 | − | 0.828854i | \(-0.311007\pi\) | ||||
0.559465 | + | 0.828854i | \(0.311007\pi\) | |||||||
\(158\) | −25.8777 | −0.0130299 | ||||||||
\(159\) | −1742.18 | −0.868956 | ||||||||
\(160\) | 182.648 | 0.0902473 | ||||||||
\(161\) | −1614.31 | −0.790219 | ||||||||
\(162\) | 1960.46 | 0.950791 | ||||||||
\(163\) | −3088.46 | −1.48409 | −0.742045 | − | 0.670350i | \(-0.766144\pi\) | ||||
−0.742045 | + | 0.670350i | \(0.766144\pi\) | |||||||
\(164\) | 301.077 | 0.143355 | ||||||||
\(165\) | −273.149 | −0.128876 | ||||||||
\(166\) | −149.289 | −0.0698016 | ||||||||
\(167\) | 1053.79 | 0.488290 | 0.244145 | − | 0.969739i | \(-0.421493\pi\) | ||||
0.244145 | + | 0.969739i | \(0.421493\pi\) | |||||||
\(168\) | 1308.23 | 0.600788 | ||||||||
\(169\) | 205.068 | 0.0933402 | ||||||||
\(170\) | −1655.62 | −0.746945 | ||||||||
\(171\) | −44.3745 | −0.0198444 | ||||||||
\(172\) | −72.8852 | −0.0323107 | ||||||||
\(173\) | 3.86971 | 0.00170063 | 0.000850313 | − | 1.00000i | \(-0.499729\pi\) | ||||
0.000850313 | 1.00000i | \(0.499729\pi\) | ||||||||
\(174\) | −2457.43 | −1.07067 | ||||||||
\(175\) | 308.588 | 0.133298 | ||||||||
\(176\) | 768.078 | 0.328955 | ||||||||
\(177\) | 3956.05 | 1.67997 | ||||||||
\(178\) | 4776.93 | 2.01149 | ||||||||
\(179\) | 1333.10 | 0.556649 | 0.278325 | − | 0.960487i | \(-0.410221\pi\) | ||||
0.278325 | + | 0.960487i | \(0.410221\pi\) | |||||||
\(180\) | −9.46126 | −0.00391778 | ||||||||
\(181\) | 2050.05 | 0.841873 | 0.420936 | − | 0.907090i | \(-0.361702\pi\) | ||||
0.420936 | + | 0.907090i | \(0.361702\pi\) | |||||||
\(182\) | −1795.67 | −0.731339 | ||||||||
\(183\) | −1123.41 | −0.453799 | ||||||||
\(184\) | −2790.97 | −1.11822 | ||||||||
\(185\) | 777.188 | 0.308865 | ||||||||
\(186\) | −1805.59 | −0.711788 | ||||||||
\(187\) | −1227.13 | −0.479876 | ||||||||
\(188\) | −293.197 | −0.113743 | ||||||||
\(189\) | −1798.33 | −0.692112 | ||||||||
\(190\) | −281.979 | −0.107668 | ||||||||
\(191\) | 308.046 | 0.116699 | 0.0583493 | − | 0.998296i | \(-0.481416\pi\) | ||||
0.0583493 | + | 0.998296i | \(0.481416\pi\) | |||||||
\(192\) | 2235.72 | 0.840361 | ||||||||
\(193\) | −3538.67 | −1.31979 | −0.659893 | − | 0.751360i | \(-0.729398\pi\) | ||||
−0.659893 | + | 0.751360i | \(0.729398\pi\) | |||||||
\(194\) | −1081.18 | −0.400125 | ||||||||
\(195\) | 1217.02 | 0.446938 | ||||||||
\(196\) | −154.457 | −0.0562889 | ||||||||
\(197\) | 1458.84 | 0.527604 | 0.263802 | − | 0.964577i | \(-0.415024\pi\) | ||||
0.263802 | + | 0.964577i | \(0.415024\pi\) | |||||||
\(198\) | −76.2545 | −0.0273695 | ||||||||
\(199\) | 1616.84 | 0.575955 | 0.287977 | − | 0.957637i | \(-0.407017\pi\) | ||||
0.287977 | + | 0.957637i | \(0.407017\pi\) | |||||||
\(200\) | 533.518 | 0.188627 | ||||||||
\(201\) | 1745.91 | 0.612672 | ||||||||
\(202\) | 1304.56 | 0.454399 | ||||||||
\(203\) | 2057.75 | 0.711455 | ||||||||
\(204\) | 448.884 | 0.154060 | ||||||||
\(205\) | 1858.01 | 0.633021 | ||||||||
\(206\) | −3011.26 | −1.01847 | ||||||||
\(207\) | 305.440 | 0.102558 | ||||||||
\(208\) | −3422.20 | −1.14080 | ||||||||
\(209\) | −209.000 | −0.0691714 | ||||||||
\(210\) | −909.786 | −0.298958 | ||||||||
\(211\) | 2464.17 | 0.803982 | 0.401991 | − | 0.915644i | \(-0.368318\pi\) | ||||
0.401991 | + | 0.915644i | \(0.368318\pi\) | |||||||
\(212\) | −284.221 | −0.0920774 | ||||||||
\(213\) | 1958.47 | 0.630009 | ||||||||
\(214\) | −861.900 | −0.275319 | ||||||||
\(215\) | −449.790 | −0.142676 | ||||||||
\(216\) | −3109.13 | −0.979396 | ||||||||
\(217\) | 1511.92 | 0.472978 | ||||||||
\(218\) | 5140.49 | 1.59706 | ||||||||
\(219\) | 329.105 | 0.101547 | ||||||||
\(220\) | −44.5617 | −0.0136561 | ||||||||
\(221\) | 5467.53 | 1.66419 | ||||||||
\(222\) | −2291.32 | −0.692717 | ||||||||
\(223\) | 5519.02 | 1.65731 | 0.828657 | − | 0.559757i | \(-0.189105\pi\) | ||||
0.828657 | + | 0.559757i | \(0.189105\pi\) | |||||||
\(224\) | 450.904 | 0.134497 | ||||||||
\(225\) | −58.3875 | −0.0173000 | ||||||||
\(226\) | −4898.80 | −1.44187 | ||||||||
\(227\) | 5681.83 | 1.66130 | 0.830652 | − | 0.556792i | \(-0.187968\pi\) | ||||
0.830652 | + | 0.556792i | \(0.187968\pi\) | |||||||
\(228\) | 76.4521 | 0.0222069 | ||||||||
\(229\) | −299.705 | −0.0864849 | −0.0432425 | − | 0.999065i | \(-0.513769\pi\) | ||||
−0.0432425 | + | 0.999065i | \(0.513769\pi\) | |||||||
\(230\) | 1940.93 | 0.556440 | ||||||||
\(231\) | −674.324 | −0.192066 | ||||||||
\(232\) | 3557.63 | 1.00677 | ||||||||
\(233\) | 6789.92 | 1.90911 | 0.954555 | − | 0.298035i | \(-0.0963312\pi\) | ||||
0.954555 | + | 0.298035i | \(0.0963312\pi\) | |||||||
\(234\) | 339.755 | 0.0949165 | ||||||||
\(235\) | −1809.38 | −0.502260 | ||||||||
\(236\) | 645.394 | 0.178015 | ||||||||
\(237\) | 43.2981 | 0.0118671 | ||||||||
\(238\) | −4087.25 | −1.11318 | ||||||||
\(239\) | −2319.42 | −0.627744 | −0.313872 | − | 0.949465i | \(-0.601626\pi\) | ||||
−0.313872 | + | 0.949465i | \(0.601626\pi\) | |||||||
\(240\) | −1733.88 | −0.466339 | ||||||||
\(241\) | 5623.61 | 1.50311 | 0.751553 | − | 0.659673i | \(-0.229305\pi\) | ||||
0.751553 | + | 0.659673i | \(0.229305\pi\) | |||||||
\(242\) | −359.152 | −0.0954016 | ||||||||
\(243\) | 653.428 | 0.172500 | ||||||||
\(244\) | −183.275 | −0.0480860 | ||||||||
\(245\) | −953.185 | −0.248558 | ||||||||
\(246\) | −5477.83 | −1.41973 | ||||||||
\(247\) | 931.207 | 0.239884 | ||||||||
\(248\) | 2613.96 | 0.669302 | ||||||||
\(249\) | 249.787 | 0.0635728 | ||||||||
\(250\) | −371.025 | −0.0938627 | ||||||||
\(251\) | 547.078 | 0.137575 | 0.0687873 | − | 0.997631i | \(-0.478087\pi\) | ||||
0.0687873 | + | 0.997631i | \(0.478087\pi\) | |||||||
\(252\) | −23.3571 | −0.00583872 | ||||||||
\(253\) | 1438.60 | 0.357485 | ||||||||
\(254\) | 3602.83 | 0.890008 | ||||||||
\(255\) | 2770.16 | 0.680291 | ||||||||
\(256\) | 1232.15 | 0.300819 | ||||||||
\(257\) | −2778.02 | −0.674273 | −0.337136 | − | 0.941456i | \(-0.609458\pi\) | ||||
−0.337136 | + | 0.941456i | \(0.609458\pi\) | |||||||
\(258\) | 1326.08 | 0.319993 | ||||||||
\(259\) | 1918.65 | 0.460305 | ||||||||
\(260\) | 198.546 | 0.0473590 | ||||||||
\(261\) | −389.342 | −0.0923359 | ||||||||
\(262\) | −4189.53 | −0.987901 | ||||||||
\(263\) | 3801.03 | 0.891184 | 0.445592 | − | 0.895236i | \(-0.352993\pi\) | ||||
0.445592 | + | 0.895236i | \(0.352993\pi\) | |||||||
\(264\) | −1165.84 | −0.271789 | ||||||||
\(265\) | −1753.99 | −0.406592 | ||||||||
\(266\) | −696.124 | −0.160459 | ||||||||
\(267\) | −7992.67 | −1.83200 | ||||||||
\(268\) | 284.830 | 0.0649207 | ||||||||
\(269\) | 4107.29 | 0.930951 | 0.465475 | − | 0.885061i | \(-0.345883\pi\) | ||||
0.465475 | + | 0.885061i | \(0.345883\pi\) | |||||||
\(270\) | 2162.19 | 0.487357 | ||||||||
\(271\) | 600.647 | 0.134637 | 0.0673187 | − | 0.997732i | \(-0.478556\pi\) | ||||
0.0673187 | + | 0.997732i | \(0.478556\pi\) | |||||||
\(272\) | −7789.53 | −1.73643 | ||||||||
\(273\) | 3004.47 | 0.666077 | ||||||||
\(274\) | 400.316 | 0.0882627 | ||||||||
\(275\) | −275.000 | −0.0603023 | ||||||||
\(276\) | −526.238 | −0.114767 | ||||||||
\(277\) | 380.251 | 0.0824804 | 0.0412402 | − | 0.999149i | \(-0.486869\pi\) | ||||
0.0412402 | + | 0.999149i | \(0.486869\pi\) | |||||||
\(278\) | −6320.01 | −1.36349 | ||||||||
\(279\) | −286.068 | −0.0613852 | ||||||||
\(280\) | 1317.10 | 0.281114 | ||||||||
\(281\) | 6090.74 | 1.29304 | 0.646518 | − | 0.762899i | \(-0.276224\pi\) | ||||
0.646518 | + | 0.762899i | \(0.276224\pi\) | |||||||
\(282\) | 5334.45 | 1.12646 | ||||||||
\(283\) | −3547.77 | −0.745205 | −0.372602 | − | 0.927991i | \(-0.621534\pi\) | ||||
−0.372602 | + | 0.927991i | \(0.621534\pi\) | |||||||
\(284\) | 319.506 | 0.0667578 | ||||||||
\(285\) | 471.802 | 0.0980601 | ||||||||
\(286\) | 1600.22 | 0.330849 | ||||||||
\(287\) | 4586.89 | 0.943400 | ||||||||
\(288\) | −85.3147 | −0.0174556 | ||||||||
\(289\) | 7532.07 | 1.53309 | ||||||||
\(290\) | −2474.09 | −0.500977 | ||||||||
\(291\) | 1809.01 | 0.364420 | ||||||||
\(292\) | 53.6906 | 0.0107603 | ||||||||
\(293\) | 8555.29 | 1.70582 | 0.852910 | − | 0.522058i | \(-0.174836\pi\) | ||||
0.852910 | + | 0.522058i | \(0.174836\pi\) | |||||||
\(294\) | 2810.20 | 0.557463 | ||||||||
\(295\) | 3982.86 | 0.786072 | ||||||||
\(296\) | 3317.15 | 0.651370 | ||||||||
\(297\) | 1602.59 | 0.313103 | ||||||||
\(298\) | 7816.94 | 1.51954 | ||||||||
\(299\) | −6409.72 | −1.23975 | ||||||||
\(300\) | 100.595 | 0.0193595 | ||||||||
\(301\) | −1110.40 | −0.212633 | ||||||||
\(302\) | −8674.71 | −1.65289 | ||||||||
\(303\) | −2182.77 | −0.413850 | ||||||||
\(304\) | −1326.68 | −0.250297 | ||||||||
\(305\) | −1131.03 | −0.212336 | ||||||||
\(306\) | 773.342 | 0.144474 | ||||||||
\(307\) | 2883.54 | 0.536066 | 0.268033 | − | 0.963410i | \(-0.413626\pi\) | ||||
0.268033 | + | 0.963410i | \(0.413626\pi\) | |||||||
\(308\) | −110.010 | −0.0203519 | ||||||||
\(309\) | 5038.38 | 0.927584 | ||||||||
\(310\) | −1817.83 | −0.333051 | ||||||||
\(311\) | 5156.90 | 0.940260 | 0.470130 | − | 0.882597i | \(-0.344207\pi\) | ||||
0.470130 | + | 0.882597i | \(0.344207\pi\) | |||||||
\(312\) | 5194.43 | 0.942554 | ||||||||
\(313\) | −1234.96 | −0.223016 | −0.111508 | − | 0.993764i | \(-0.535568\pi\) | ||||
−0.111508 | + | 0.993764i | \(0.535568\pi\) | |||||||
\(314\) | −6533.50 | −1.17423 | ||||||||
\(315\) | −144.142 | −0.0257824 | ||||||||
\(316\) | 7.06369 | 0.00125748 | ||||||||
\(317\) | −755.101 | −0.133788 | −0.0668939 | − | 0.997760i | \(-0.521309\pi\) | ||||
−0.0668939 | + | 0.997760i | \(0.521309\pi\) | |||||||
\(318\) | 5171.14 | 0.911897 | ||||||||
\(319\) | −1833.77 | −0.321854 | ||||||||
\(320\) | 2250.88 | 0.393212 | ||||||||
\(321\) | 1442.11 | 0.250751 | ||||||||
\(322\) | 4791.59 | 0.829269 | ||||||||
\(323\) | 2119.59 | 0.365131 | ||||||||
\(324\) | −535.135 | −0.0917585 | ||||||||
\(325\) | 1225.27 | 0.209126 | ||||||||
\(326\) | 9167.17 | 1.55743 | ||||||||
\(327\) | −8600.98 | −1.45454 | ||||||||
\(328\) | 7930.27 | 1.33499 | ||||||||
\(329\) | −4466.84 | −0.748525 | ||||||||
\(330\) | 810.760 | 0.135245 | ||||||||
\(331\) | 1503.38 | 0.249648 | 0.124824 | − | 0.992179i | \(-0.460163\pi\) | ||||
0.124824 | + | 0.992179i | \(0.460163\pi\) | |||||||
\(332\) | 40.7506 | 0.00673638 | ||||||||
\(333\) | −363.024 | −0.0597405 | ||||||||
\(334\) | −3127.85 | −0.512420 | ||||||||
\(335\) | 1757.75 | 0.286674 | ||||||||
\(336\) | −4280.44 | −0.694992 | ||||||||
\(337\) | −9713.15 | −1.57006 | −0.785028 | − | 0.619460i | \(-0.787351\pi\) | ||||
−0.785028 | + | 0.619460i | \(0.787351\pi\) | |||||||
\(338\) | −608.684 | −0.0979528 | ||||||||
\(339\) | 8196.58 | 1.31321 | ||||||||
\(340\) | 451.927 | 0.0720858 | ||||||||
\(341\) | −1347.36 | −0.213969 | ||||||||
\(342\) | 131.712 | 0.0208251 | ||||||||
\(343\) | −6586.97 | −1.03692 | ||||||||
\(344\) | −1919.77 | −0.300893 | ||||||||
\(345\) | −3247.53 | −0.506785 | ||||||||
\(346\) | −11.4861 | −0.00178467 | ||||||||
\(347\) | −5948.83 | −0.920317 | −0.460158 | − | 0.887837i | \(-0.652207\pi\) | ||||
−0.460158 | + | 0.887837i | \(0.652207\pi\) | |||||||
\(348\) | 670.792 | 0.103328 | ||||||||
\(349\) | −6838.37 | −1.04885 | −0.524426 | − | 0.851456i | \(-0.675720\pi\) | ||||
−0.524426 | + | 0.851456i | \(0.675720\pi\) | |||||||
\(350\) | −915.952 | −0.139885 | ||||||||
\(351\) | −7140.40 | −1.08583 | ||||||||
\(352\) | −401.825 | −0.0608447 | ||||||||
\(353\) | −7855.74 | −1.18447 | −0.592236 | − | 0.805765i | \(-0.701755\pi\) | ||||
−0.592236 | + | 0.805765i | \(0.701755\pi\) | |||||||
\(354\) | −11742.3 | −1.76299 | ||||||||
\(355\) | 1971.74 | 0.294786 | ||||||||
\(356\) | −1303.93 | −0.194124 | ||||||||
\(357\) | 6838.71 | 1.01385 | ||||||||
\(358\) | −3956.89 | −0.584157 | ||||||||
\(359\) | 1894.17 | 0.278469 | 0.139234 | − | 0.990259i | \(-0.455536\pi\) | ||||
0.139234 | + | 0.990259i | \(0.455536\pi\) | |||||||
\(360\) | −249.206 | −0.0364842 | ||||||||
\(361\) | 361.000 | 0.0526316 | ||||||||
\(362\) | −6084.96 | −0.883476 | ||||||||
\(363\) | 600.927 | 0.0868884 | ||||||||
\(364\) | 490.153 | 0.0705797 | ||||||||
\(365\) | 331.336 | 0.0475148 | ||||||||
\(366\) | 3334.52 | 0.476225 | ||||||||
\(367\) | −5254.00 | −0.747294 | −0.373647 | − | 0.927571i | \(-0.621893\pi\) | ||||
−0.373647 | + | 0.927571i | \(0.621893\pi\) | |||||||
\(368\) | 9131.86 | 1.29356 | ||||||||
\(369\) | −867.877 | −0.122439 | ||||||||
\(370\) | −2306.85 | −0.324128 | ||||||||
\(371\) | −4330.09 | −0.605949 | ||||||||
\(372\) | 492.863 | 0.0686929 | ||||||||
\(373\) | −6049.41 | −0.839750 | −0.419875 | − | 0.907582i | \(-0.637926\pi\) | ||||
−0.419875 | + | 0.907582i | \(0.637926\pi\) | |||||||
\(374\) | 3642.37 | 0.503590 | ||||||||
\(375\) | 620.792 | 0.0854868 | ||||||||
\(376\) | −7722.71 | −1.05922 | ||||||||
\(377\) | 8170.43 | 1.11618 | ||||||||
\(378\) | 5337.80 | 0.726315 | ||||||||
\(379\) | −12697.6 | −1.72092 | −0.860461 | − | 0.509516i | \(-0.829825\pi\) | ||||
−0.860461 | + | 0.509516i | \(0.829825\pi\) | |||||||
\(380\) | 76.9703 | 0.0103908 | ||||||||
\(381\) | −6028.20 | −0.810587 | ||||||||
\(382\) | −914.343 | −0.122466 | ||||||||
\(383\) | 2321.97 | 0.309784 | 0.154892 | − | 0.987931i | \(-0.450497\pi\) | ||||
0.154892 | + | 0.987931i | \(0.450497\pi\) | |||||||
\(384\) | −8087.41 | −1.07476 | ||||||||
\(385\) | −678.895 | −0.0898693 | ||||||||
\(386\) | 10503.5 | 1.38501 | ||||||||
\(387\) | 210.097 | 0.0275964 | ||||||||
\(388\) | 295.124 | 0.0386151 | ||||||||
\(389\) | −9082.50 | −1.18381 | −0.591904 | − | 0.806009i | \(-0.701624\pi\) | ||||
−0.591904 | + | 0.806009i | \(0.701624\pi\) | |||||||
\(390\) | −3612.37 | −0.469024 | ||||||||
\(391\) | −14589.7 | −1.88704 | ||||||||
\(392\) | −4068.33 | −0.524188 | ||||||||
\(393\) | 7009.85 | 0.899745 | ||||||||
\(394\) | −4330.12 | −0.553676 | ||||||||
\(395\) | 43.5915 | 0.00555273 | ||||||||
\(396\) | 20.8148 | 0.00264137 | ||||||||
\(397\) | −12122.8 | −1.53256 | −0.766280 | − | 0.642507i | \(-0.777894\pi\) | ||||
−0.766280 | + | 0.642507i | \(0.777894\pi\) | |||||||
\(398\) | −4799.12 | −0.604417 | ||||||||
\(399\) | 1164.74 | 0.146140 | ||||||||
\(400\) | −1745.63 | −0.218204 | ||||||||
\(401\) | 5048.00 | 0.628641 | 0.314320 | − | 0.949317i | \(-0.398223\pi\) | ||||
0.314320 | + | 0.949317i | \(0.398223\pi\) | |||||||
\(402\) | −5182.21 | −0.642949 | ||||||||
\(403\) | 6003.20 | 0.742037 | ||||||||
\(404\) | −356.099 | −0.0438529 | ||||||||
\(405\) | −3302.44 | −0.405183 | ||||||||
\(406\) | −6107.80 | −0.746613 | ||||||||
\(407\) | −1709.81 | −0.208237 | ||||||||
\(408\) | 11823.4 | 1.43468 | ||||||||
\(409\) | −11630.4 | −1.40607 | −0.703037 | − | 0.711153i | \(-0.748173\pi\) | ||||
−0.703037 | + | 0.711153i | \(0.748173\pi\) | |||||||
\(410\) | −5514.96 | −0.664303 | ||||||||
\(411\) | −669.801 | −0.0803865 | ||||||||
\(412\) | 821.967 | 0.0982898 | ||||||||
\(413\) | 9832.53 | 1.17149 | ||||||||
\(414\) | −906.607 | −0.107626 | ||||||||
\(415\) | 251.481 | 0.0297462 | ||||||||
\(416\) | 1790.35 | 0.211007 | ||||||||
\(417\) | 10574.5 | 1.24181 | ||||||||
\(418\) | 620.354 | 0.0725897 | ||||||||
\(419\) | 1088.03 | 0.126859 | 0.0634294 | − | 0.997986i | \(-0.479796\pi\) | ||||
0.0634294 | + | 0.997986i | \(0.479796\pi\) | |||||||
\(420\) | 248.339 | 0.0288517 | ||||||||
\(421\) | 2024.61 | 0.234378 | 0.117189 | − | 0.993110i | \(-0.462612\pi\) | ||||
0.117189 | + | 0.993110i | \(0.462612\pi\) | |||||||
\(422\) | −7314.14 | −0.843712 | ||||||||
\(423\) | 845.162 | 0.0971470 | ||||||||
\(424\) | −7486.29 | −0.857467 | ||||||||
\(425\) | 2788.94 | 0.318314 | ||||||||
\(426\) | −5813.12 | −0.661142 | ||||||||
\(427\) | −2792.18 | −0.316448 | ||||||||
\(428\) | 235.268 | 0.0265703 | ||||||||
\(429\) | −2677.45 | −0.301325 | ||||||||
\(430\) | 1335.07 | 0.149727 | ||||||||
\(431\) | −2423.36 | −0.270833 | −0.135417 | − | 0.990789i | \(-0.543237\pi\) | ||||
−0.135417 | + | 0.990789i | \(0.543237\pi\) | |||||||
\(432\) | 10172.8 | 1.13297 | ||||||||
\(433\) | −420.532 | −0.0466732 | −0.0233366 | − | 0.999728i | \(-0.507429\pi\) | ||||
−0.0233366 | + | 0.999728i | \(0.507429\pi\) | |||||||
\(434\) | −4487.69 | −0.496351 | ||||||||
\(435\) | 4139.60 | 0.456272 | ||||||||
\(436\) | −1403.17 | −0.154128 | ||||||||
\(437\) | −2484.85 | −0.272006 | ||||||||
\(438\) | −976.850 | −0.106566 | ||||||||
\(439\) | 4331.19 | 0.470880 | 0.235440 | − | 0.971889i | \(-0.424347\pi\) | ||||
0.235440 | + | 0.971889i | \(0.424347\pi\) | |||||||
\(440\) | −1173.74 | −0.127172 | ||||||||
\(441\) | 445.232 | 0.0480761 | ||||||||
\(442\) | −16228.7 | −1.74643 | ||||||||
\(443\) | −991.151 | −0.106300 | −0.0531501 | − | 0.998587i | \(-0.516926\pi\) | ||||
−0.0531501 | + | 0.998587i | \(0.516926\pi\) | |||||||
\(444\) | 625.448 | 0.0668524 | ||||||||
\(445\) | −8046.84 | −0.857207 | ||||||||
\(446\) | −16381.6 | −1.73921 | ||||||||
\(447\) | −13079.2 | −1.38394 | ||||||||
\(448\) | 5556.75 | 0.586009 | ||||||||
\(449\) | −12736.5 | −1.33870 | −0.669348 | − | 0.742949i | \(-0.733426\pi\) | ||||
−0.669348 | + | 0.742949i | \(0.733426\pi\) | |||||||
\(450\) | 173.306 | 0.0181549 | ||||||||
\(451\) | −4087.63 | −0.426783 | ||||||||
\(452\) | 1337.20 | 0.139152 | ||||||||
\(453\) | 14514.4 | 1.50540 | ||||||||
\(454\) | −16864.8 | −1.74340 | ||||||||
\(455\) | 3024.84 | 0.311663 | ||||||||
\(456\) | 2013.72 | 0.206801 | ||||||||
\(457\) | −8939.19 | −0.915006 | −0.457503 | − | 0.889208i | \(-0.651256\pi\) | ||||
−0.457503 | + | 0.889208i | \(0.651256\pi\) | |||||||
\(458\) | 889.584 | 0.0907588 | ||||||||
\(459\) | −16252.8 | −1.65276 | ||||||||
\(460\) | −529.805 | −0.0537006 | ||||||||
\(461\) | 17730.6 | 1.79132 | 0.895659 | − | 0.444742i | \(-0.146705\pi\) | ||||
0.895659 | + | 0.444742i | \(0.146705\pi\) | |||||||
\(462\) | 2001.53 | 0.201557 | ||||||||
\(463\) | 4021.06 | 0.403617 | 0.201808 | − | 0.979425i | \(-0.435318\pi\) | ||||
0.201808 | + | 0.979425i | \(0.435318\pi\) | |||||||
\(464\) | −11640.3 | −1.16463 | ||||||||
\(465\) | 3041.56 | 0.303331 | ||||||||
\(466\) | −20153.9 | −2.00345 | ||||||||
\(467\) | −7007.69 | −0.694384 | −0.347192 | − | 0.937794i | \(-0.612865\pi\) | ||||
−0.347192 | + | 0.937794i | \(0.612865\pi\) | |||||||
\(468\) | −92.7410 | −0.00916016 | ||||||||
\(469\) | 4339.36 | 0.427235 | ||||||||
\(470\) | 5370.61 | 0.527081 | ||||||||
\(471\) | 10931.7 | 1.06944 | ||||||||
\(472\) | 16999.4 | 1.65776 | ||||||||
\(473\) | 989.538 | 0.0961924 | ||||||||
\(474\) | −128.517 | −0.0124536 | ||||||||
\(475\) | 475.000 | 0.0458831 | ||||||||
\(476\) | 1115.68 | 0.107430 | ||||||||
\(477\) | 819.288 | 0.0786428 | ||||||||
\(478\) | 6884.51 | 0.658766 | ||||||||
\(479\) | 8123.23 | 0.774864 | 0.387432 | − | 0.921898i | \(-0.373362\pi\) | ||||
0.387432 | + | 0.921898i | \(0.373362\pi\) | |||||||
\(480\) | 907.090 | 0.0862559 | ||||||||
\(481\) | 7618.13 | 0.722156 | ||||||||
\(482\) | −16692.0 | −1.57738 | ||||||||
\(483\) | −8017.19 | −0.755269 | ||||||||
\(484\) | 98.0358 | 0.00920697 | ||||||||
\(485\) | 1821.27 | 0.170515 | ||||||||
\(486\) | −1939.51 | −0.181024 | ||||||||
\(487\) | 4955.39 | 0.461089 | 0.230544 | − | 0.973062i | \(-0.425949\pi\) | ||||
0.230544 | + | 0.973062i | \(0.425949\pi\) | |||||||
\(488\) | −4827.40 | −0.447799 | ||||||||
\(489\) | −15338.3 | −1.41845 | ||||||||
\(490\) | 2829.24 | 0.260841 | ||||||||
\(491\) | −11923.8 | −1.09596 | −0.547979 | − | 0.836492i | \(-0.684602\pi\) | ||||
−0.547979 | + | 0.836492i | \(0.684602\pi\) | |||||||
\(492\) | 1495.25 | 0.137015 | ||||||||
\(493\) | 18597.3 | 1.69895 | ||||||||
\(494\) | −2764.01 | −0.251738 | ||||||||
\(495\) | 128.452 | 0.0116636 | ||||||||
\(496\) | −8552.69 | −0.774249 | ||||||||
\(497\) | 4867.65 | 0.439324 | ||||||||
\(498\) | −741.419 | −0.0667144 | ||||||||
\(499\) | 7173.44 | 0.643542 | 0.321771 | − | 0.946818i | \(-0.395722\pi\) | ||||
0.321771 | + | 0.946818i | \(0.395722\pi\) | |||||||
\(500\) | 101.277 | 0.00905846 | ||||||||
\(501\) | 5233.46 | 0.466694 | ||||||||
\(502\) | −1623.84 | −0.144373 | ||||||||
\(503\) | −15095.3 | −1.33811 | −0.669053 | − | 0.743214i | \(-0.733300\pi\) | ||||
−0.669053 | + | 0.743214i | \(0.733300\pi\) | |||||||
\(504\) | −615.217 | −0.0543729 | ||||||||
\(505\) | −2197.56 | −0.193644 | ||||||||
\(506\) | −4270.04 | −0.375151 | ||||||||
\(507\) | 1018.44 | 0.0892119 | ||||||||
\(508\) | −983.446 | −0.0858925 | ||||||||
\(509\) | −4027.53 | −0.350721 | −0.175361 | − | 0.984504i | \(-0.556109\pi\) | ||||
−0.175361 | + | 0.984504i | \(0.556109\pi\) | |||||||
\(510\) | −8222.39 | −0.713909 | ||||||||
\(511\) | 817.972 | 0.0708120 | ||||||||
\(512\) | 9370.29 | 0.808813 | ||||||||
\(513\) | −2768.11 | −0.238236 | ||||||||
\(514\) | 8245.72 | 0.707593 | ||||||||
\(515\) | 5072.53 | 0.434024 | ||||||||
\(516\) | −361.973 | −0.0308817 | ||||||||
\(517\) | 3980.64 | 0.338624 | ||||||||
\(518\) | −5694.93 | −0.483052 | ||||||||
\(519\) | 19.2183 | 0.00162541 | ||||||||
\(520\) | 5229.64 | 0.441029 | ||||||||
\(521\) | −20995.4 | −1.76550 | −0.882750 | − | 0.469843i | \(-0.844311\pi\) | ||||
−0.882750 | + | 0.469843i | \(0.844311\pi\) | |||||||
\(522\) | 1155.65 | 0.0968989 | ||||||||
\(523\) | 575.393 | 0.0481074 | 0.0240537 | − | 0.999711i | \(-0.492343\pi\) | ||||
0.0240537 | + | 0.999711i | \(0.492343\pi\) | |||||||
\(524\) | 1143.59 | 0.0953399 | ||||||||
\(525\) | 1532.55 | 0.127402 | ||||||||
\(526\) | −11282.2 | −0.935224 | ||||||||
\(527\) | 13664.4 | 1.12947 | ||||||||
\(528\) | 3814.53 | 0.314406 | ||||||||
\(529\) | 4936.82 | 0.405755 | ||||||||
\(530\) | 5206.20 | 0.426684 | ||||||||
\(531\) | −1860.39 | −0.152042 | ||||||||
\(532\) | 190.017 | 0.0154855 | ||||||||
\(533\) | 18212.6 | 1.48006 | ||||||||
\(534\) | 23723.8 | 1.92253 | ||||||||
\(535\) | 1451.89 | 0.117328 | ||||||||
\(536\) | 7502.31 | 0.604572 | ||||||||
\(537\) | 6620.60 | 0.532030 | ||||||||
\(538\) | −12191.3 | −0.976956 | ||||||||
\(539\) | 2097.01 | 0.167578 | ||||||||
\(540\) | −590.200 | −0.0470336 | ||||||||
\(541\) | −18785.9 | −1.49292 | −0.746460 | − | 0.665431i | \(-0.768248\pi\) | ||||
−0.746460 | + | 0.665431i | \(0.768248\pi\) | |||||||
\(542\) | −1782.84 | −0.141291 | ||||||||
\(543\) | 10181.2 | 0.804638 | ||||||||
\(544\) | 4075.14 | 0.321177 | ||||||||
\(545\) | −8659.28 | −0.680592 | ||||||||
\(546\) | −8917.88 | −0.698993 | ||||||||
\(547\) | 11138.9 | 0.870689 | 0.435344 | − | 0.900264i | \(-0.356627\pi\) | ||||
0.435344 | + | 0.900264i | \(0.356627\pi\) | |||||||
\(548\) | −109.272 | −0.00851801 | ||||||||
\(549\) | 528.304 | 0.0410700 | ||||||||
\(550\) | 816.255 | 0.0632822 | ||||||||
\(551\) | 3167.42 | 0.244894 | ||||||||
\(552\) | −13860.9 | −1.06877 | ||||||||
\(553\) | 107.615 | 0.00827531 | ||||||||
\(554\) | −1128.66 | −0.0865564 | ||||||||
\(555\) | 3859.78 | 0.295204 | ||||||||
\(556\) | 1725.14 | 0.131587 | ||||||||
\(557\) | 13011.2 | 0.989769 | 0.494884 | − | 0.868959i | \(-0.335210\pi\) | ||||
0.494884 | + | 0.868959i | \(0.335210\pi\) | |||||||
\(558\) | 849.108 | 0.0644187 | ||||||||
\(559\) | −4408.92 | −0.333591 | ||||||||
\(560\) | −4309.45 | −0.325192 | ||||||||
\(561\) | −6094.35 | −0.458652 | ||||||||
\(562\) | −18078.5 | −1.35693 | ||||||||
\(563\) | −4192.52 | −0.313843 | −0.156922 | − | 0.987611i | \(-0.550157\pi\) | ||||
−0.156922 | + | 0.987611i | \(0.550157\pi\) | |||||||
\(564\) | −1456.12 | −0.108712 | ||||||||
\(565\) | 8252.13 | 0.614460 | ||||||||
\(566\) | 10530.5 | 0.782031 | ||||||||
\(567\) | −8152.75 | −0.603850 | ||||||||
\(568\) | 8415.68 | 0.621679 | ||||||||
\(569\) | 17949.6 | 1.32247 | 0.661237 | − | 0.750177i | \(-0.270032\pi\) | ||||
0.661237 | + | 0.750177i | \(0.270032\pi\) | |||||||
\(570\) | −1400.40 | −0.102906 | ||||||||
\(571\) | 13377.3 | 0.980422 | 0.490211 | − | 0.871604i | \(-0.336920\pi\) | ||||
0.490211 | + | 0.871604i | \(0.336920\pi\) | |||||||
\(572\) | −436.802 | −0.0319294 | ||||||||
\(573\) | 1529.86 | 0.111537 | ||||||||
\(574\) | −13614.8 | −0.990020 | ||||||||
\(575\) | −3269.54 | −0.237129 | ||||||||
\(576\) | −1051.38 | −0.0760549 | ||||||||
\(577\) | −18895.1 | −1.36328 | −0.681642 | − | 0.731686i | \(-0.738734\pi\) | ||||
−0.681642 | + | 0.731686i | \(0.738734\pi\) | |||||||
\(578\) | −22356.7 | −1.60885 | ||||||||
\(579\) | −17574.2 | −1.26141 | ||||||||
\(580\) | 675.338 | 0.0483481 | ||||||||
\(581\) | 620.832 | 0.0443312 | ||||||||
\(582\) | −5369.51 | −0.382428 | ||||||||
\(583\) | 3858.78 | 0.274124 | ||||||||
\(584\) | 1414.19 | 0.100205 | ||||||||
\(585\) | −572.324 | −0.0404491 | ||||||||
\(586\) | −25393.8 | −1.79012 | ||||||||
\(587\) | 6401.83 | 0.450140 | 0.225070 | − | 0.974343i | \(-0.427739\pi\) | ||||
0.225070 | + | 0.974343i | \(0.427739\pi\) | |||||||
\(588\) | −767.084 | −0.0537993 | ||||||||
\(589\) | 2327.26 | 0.162806 | ||||||||
\(590\) | −11821.9 | −0.824918 | ||||||||
\(591\) | 7245.08 | 0.504269 | ||||||||
\(592\) | −10853.5 | −0.753504 | ||||||||
\(593\) | 21186.0 | 1.46713 | 0.733563 | − | 0.679622i | \(-0.237856\pi\) | ||||
0.733563 | + | 0.679622i | \(0.237856\pi\) | |||||||
\(594\) | −4756.81 | −0.328576 | ||||||||
\(595\) | 6885.07 | 0.474387 | ||||||||
\(596\) | −2133.75 | −0.146647 | ||||||||
\(597\) | 8029.79 | 0.550482 | ||||||||
\(598\) | 19025.3 | 1.30101 | ||||||||
\(599\) | −7743.91 | −0.528226 | −0.264113 | − | 0.964492i | \(-0.585079\pi\) | ||||
−0.264113 | + | 0.964492i | \(0.585079\pi\) | |||||||
\(600\) | 2649.63 | 0.180285 | ||||||||
\(601\) | −26444.1 | −1.79480 | −0.897402 | − | 0.441215i | \(-0.854548\pi\) | ||||
−0.897402 | + | 0.441215i | \(0.854548\pi\) | |||||||
\(602\) | 3295.89 | 0.223140 | ||||||||
\(603\) | −821.042 | −0.0554485 | ||||||||
\(604\) | 2367.89 | 0.159517 | ||||||||
\(605\) | 605.000 | 0.0406558 | ||||||||
\(606\) | 6478.89 | 0.434302 | ||||||||
\(607\) | −19007.7 | −1.27100 | −0.635502 | − | 0.772099i | \(-0.719207\pi\) | ||||
−0.635502 | + | 0.772099i | \(0.719207\pi\) | |||||||
\(608\) | 694.061 | 0.0462959 | ||||||||
\(609\) | 10219.5 | 0.679989 | ||||||||
\(610\) | 3357.12 | 0.222829 | ||||||||
\(611\) | −17735.9 | −1.17433 | ||||||||
\(612\) | −211.095 | −0.0139428 | ||||||||
\(613\) | −21420.1 | −1.41134 | −0.705668 | − | 0.708543i | \(-0.749353\pi\) | ||||
−0.705668 | + | 0.708543i | \(0.749353\pi\) | |||||||
\(614\) | −8558.91 | −0.562556 | ||||||||
\(615\) | 9227.52 | 0.605024 | ||||||||
\(616\) | −2897.62 | −0.189527 | ||||||||
\(617\) | −11062.6 | −0.721819 | −0.360909 | − | 0.932601i | \(-0.617534\pi\) | ||||
−0.360909 | + | 0.932601i | \(0.617534\pi\) | |||||||
\(618\) | −14954.9 | −0.973423 | ||||||||
\(619\) | 12693.6 | 0.824228 | 0.412114 | − | 0.911132i | \(-0.364790\pi\) | ||||
0.412114 | + | 0.911132i | \(0.364790\pi\) | |||||||
\(620\) | 496.204 | 0.0321420 | ||||||||
\(621\) | 19053.6 | 1.23123 | ||||||||
\(622\) | −15306.7 | −0.986725 | ||||||||
\(623\) | −19865.3 | −1.27751 | ||||||||
\(624\) | −16995.8 | −1.09035 | ||||||||
\(625\) | 625.000 | 0.0400000 | ||||||||
\(626\) | 3665.60 | 0.234037 | ||||||||
\(627\) | −1037.96 | −0.0661121 | ||||||||
\(628\) | 1783.41 | 0.113322 | ||||||||
\(629\) | 17340.2 | 1.09920 | ||||||||
\(630\) | 427.841 | 0.0270565 | ||||||||
\(631\) | −5174.69 | −0.326468 | −0.163234 | − | 0.986587i | \(-0.552193\pi\) | ||||
−0.163234 | + | 0.986587i | \(0.552193\pi\) | |||||||
\(632\) | 186.055 | 0.0117102 | ||||||||
\(633\) | 12237.9 | 0.768423 | ||||||||
\(634\) | 2241.29 | 0.140399 | ||||||||
\(635\) | −6069.06 | −0.379281 | ||||||||
\(636\) | −1411.54 | −0.0880050 | ||||||||
\(637\) | −9343.29 | −0.581153 | ||||||||
\(638\) | 5442.99 | 0.337759 | ||||||||
\(639\) | −920.999 | −0.0570175 | ||||||||
\(640\) | −8142.23 | −0.502891 | ||||||||
\(641\) | −13763.7 | −0.848099 | −0.424050 | − | 0.905639i | \(-0.639392\pi\) | ||||
−0.424050 | + | 0.905639i | \(0.639392\pi\) | |||||||
\(642\) | −4280.48 | −0.263142 | ||||||||
\(643\) | −851.193 | −0.0522049 | −0.0261025 | − | 0.999659i | \(-0.508310\pi\) | ||||
−0.0261025 | + | 0.999659i | \(0.508310\pi\) | |||||||
\(644\) | −1307.93 | −0.0800307 | ||||||||
\(645\) | −2233.81 | −0.136366 | ||||||||
\(646\) | −6291.37 | −0.383175 | ||||||||
\(647\) | 18529.5 | 1.12592 | 0.562958 | − | 0.826485i | \(-0.309663\pi\) | ||||
0.562958 | + | 0.826485i | \(0.309663\pi\) | |||||||
\(648\) | −14095.3 | −0.854498 | ||||||||
\(649\) | −8762.30 | −0.529970 | ||||||||
\(650\) | −3636.85 | −0.219460 | ||||||||
\(651\) | 7508.73 | 0.452059 | ||||||||
\(652\) | −2502.31 | −0.150304 | ||||||||
\(653\) | −9605.15 | −0.575618 | −0.287809 | − | 0.957688i | \(-0.592927\pi\) | ||||
−0.287809 | + | 0.957688i | \(0.592927\pi\) | |||||||
\(654\) | 25529.4 | 1.52642 | ||||||||
\(655\) | 7057.36 | 0.420998 | ||||||||
\(656\) | −25947.3 | −1.54431 | ||||||||
\(657\) | −154.767 | −0.00919031 | ||||||||
\(658\) | 13258.5 | 0.785515 | ||||||||
\(659\) | −2619.07 | −0.154817 | −0.0774084 | − | 0.996999i | \(-0.524665\pi\) | ||||
−0.0774084 | + | 0.996999i | \(0.524665\pi\) | |||||||
\(660\) | −221.309 | −0.0130522 | ||||||||
\(661\) | −31931.9 | −1.87898 | −0.939492 | − | 0.342571i | \(-0.888702\pi\) | ||||
−0.939492 | + | 0.342571i | \(0.888702\pi\) | |||||||
\(662\) | −4462.35 | −0.261985 | ||||||||
\(663\) | 27153.6 | 1.59059 | ||||||||
\(664\) | 1073.36 | 0.0627323 | ||||||||
\(665\) | 1172.64 | 0.0683803 | ||||||||
\(666\) | 1077.53 | 0.0626927 | ||||||||
\(667\) | −21802.1 | −1.26564 | ||||||||
\(668\) | 853.792 | 0.0494524 | ||||||||
\(669\) | 27409.3 | 1.58401 | ||||||||
\(670\) | −5217.34 | −0.300841 | ||||||||
\(671\) | 2488.27 | 0.143157 | ||||||||
\(672\) | 2239.34 | 0.128548 | ||||||||
\(673\) | 12767.5 | 0.731279 | 0.365640 | − | 0.930757i | \(-0.380850\pi\) | ||||
0.365640 | + | 0.930757i | \(0.380850\pi\) | |||||||
\(674\) | 28830.6 | 1.64764 | ||||||||
\(675\) | −3642.25 | −0.207689 | ||||||||
\(676\) | 166.149 | 0.00945318 | ||||||||
\(677\) | 9984.20 | 0.566801 | 0.283400 | − | 0.959002i | \(-0.408537\pi\) | ||||
0.283400 | + | 0.959002i | \(0.408537\pi\) | |||||||
\(678\) | −24329.1 | −1.37810 | ||||||||
\(679\) | 4496.19 | 0.254121 | ||||||||
\(680\) | 11903.6 | 0.671297 | ||||||||
\(681\) | 28217.9 | 1.58783 | ||||||||
\(682\) | 3999.23 | 0.224543 | ||||||||
\(683\) | 14756.0 | 0.826680 | 0.413340 | − | 0.910577i | \(-0.364362\pi\) | ||||
0.413340 | + | 0.910577i | \(0.364362\pi\) | |||||||
\(684\) | −35.9528 | −0.00200978 | ||||||||
\(685\) | −674.341 | −0.0376135 | ||||||||
\(686\) | 19551.4 | 1.08816 | ||||||||
\(687\) | −1488.43 | −0.0826599 | ||||||||
\(688\) | 6281.34 | 0.348073 | ||||||||
\(689\) | −17192.9 | −0.950651 | ||||||||
\(690\) | 9639.31 | 0.531829 | ||||||||
\(691\) | −9238.09 | −0.508587 | −0.254293 | − | 0.967127i | \(-0.581843\pi\) | ||||
−0.254293 | + | 0.967127i | \(0.581843\pi\) | |||||||
\(692\) | 3.13529 | 0.000172234 0 | ||||||||
\(693\) | 317.111 | 0.0173825 | ||||||||
\(694\) | 17657.3 | 0.965796 | ||||||||
\(695\) | 10646.2 | 0.581055 | ||||||||
\(696\) | 17668.4 | 0.962240 | ||||||||
\(697\) | 41455.1 | 2.25283 | ||||||||
\(698\) | 20297.6 | 1.10068 | ||||||||
\(699\) | 33721.0 | 1.82467 | ||||||||
\(700\) | 250.023 | 0.0134999 | ||||||||
\(701\) | 16977.6 | 0.914744 | 0.457372 | − | 0.889275i | \(-0.348791\pi\) | ||||
0.457372 | + | 0.889275i | \(0.348791\pi\) | |||||||
\(702\) | 21194.1 | 1.13949 | ||||||||
\(703\) | 2953.31 | 0.158444 | ||||||||
\(704\) | −4951.93 | −0.265103 | ||||||||
\(705\) | −8986.01 | −0.480046 | ||||||||
\(706\) | 23317.4 | 1.24301 | ||||||||
\(707\) | −5425.14 | −0.288590 | ||||||||
\(708\) | 3205.24 | 0.170142 | ||||||||
\(709\) | −29166.9 | −1.54497 | −0.772487 | − | 0.635031i | \(-0.780987\pi\) | ||||
−0.772487 | + | 0.635031i | \(0.780987\pi\) | |||||||
\(710\) | −5852.52 | −0.309354 | ||||||||
\(711\) | −20.3616 | −0.00107401 | ||||||||
\(712\) | −34345.1 | −1.80778 | ||||||||
\(713\) | −16019.1 | −0.841400 | ||||||||
\(714\) | −20298.7 | −1.06395 | ||||||||
\(715\) | −2695.60 | −0.140993 | ||||||||
\(716\) | 1080.09 | 0.0563756 | ||||||||
\(717\) | −11519.0 | −0.599980 | ||||||||
\(718\) | −5622.26 | −0.292230 | ||||||||
\(719\) | −21673.4 | −1.12417 | −0.562086 | − | 0.827079i | \(-0.690001\pi\) | ||||
−0.562086 | + | 0.827079i | \(0.690001\pi\) | |||||||
\(720\) | 815.384 | 0.0422049 | ||||||||
\(721\) | 12522.6 | 0.646832 | ||||||||
\(722\) | −1071.52 | −0.0552325 | ||||||||
\(723\) | 27928.7 | 1.43663 | ||||||||
\(724\) | 1660.98 | 0.0852621 | ||||||||
\(725\) | 4167.66 | 0.213494 | ||||||||
\(726\) | −1783.67 | −0.0911822 | ||||||||
\(727\) | 10695.3 | 0.545621 | 0.272811 | − | 0.962068i | \(-0.412047\pi\) | ||||
0.272811 | + | 0.962068i | \(0.412047\pi\) | |||||||
\(728\) | 12910.5 | 0.657271 | ||||||||
\(729\) | 21078.3 | 1.07089 | ||||||||
\(730\) | −983.471 | −0.0498629 | ||||||||
\(731\) | −10035.5 | −0.507765 | ||||||||
\(732\) | −910.206 | −0.0459593 | ||||||||
\(733\) | −16807.3 | −0.846920 | −0.423460 | − | 0.905915i | \(-0.639185\pi\) | ||||
−0.423460 | + | 0.905915i | \(0.639185\pi\) | |||||||
\(734\) | 15594.9 | 0.784223 | ||||||||
\(735\) | −4733.84 | −0.237565 | ||||||||
\(736\) | −4777.39 | −0.239262 | ||||||||
\(737\) | −3867.04 | −0.193276 | ||||||||
\(738\) | 2576.03 | 0.128489 | ||||||||
\(739\) | −37222.2 | −1.85283 | −0.926414 | − | 0.376507i | \(-0.877125\pi\) | ||||
−0.926414 | + | 0.376507i | \(0.877125\pi\) | |||||||
\(740\) | 629.688 | 0.0312808 | ||||||||
\(741\) | 4624.69 | 0.229274 | ||||||||
\(742\) | 12852.6 | 0.635893 | ||||||||
\(743\) | −6844.95 | −0.337977 | −0.168988 | − | 0.985618i | \(-0.554050\pi\) | ||||
−0.168988 | + | 0.985618i | \(0.554050\pi\) | |||||||
\(744\) | 12981.8 | 0.639700 | ||||||||
\(745\) | −13167.8 | −0.647559 | ||||||||
\(746\) | 17955.9 | 0.881248 | ||||||||
\(747\) | −117.466 | −0.00575351 | ||||||||
\(748\) | −994.239 | −0.0486002 | ||||||||
\(749\) | 3584.29 | 0.174856 | ||||||||
\(750\) | −1842.64 | −0.0897114 | ||||||||
\(751\) | 31094.6 | 1.51086 | 0.755432 | − | 0.655227i | \(-0.227427\pi\) | ||||
0.755432 | + | 0.655227i | \(0.227427\pi\) | |||||||
\(752\) | 25268.1 | 1.22531 | ||||||||
\(753\) | 2716.97 | 0.131490 | ||||||||
\(754\) | −24251.5 | −1.17133 | ||||||||
\(755\) | 14612.7 | 0.704387 | ||||||||
\(756\) | −1457.03 | −0.0700948 | ||||||||
\(757\) | 18226.0 | 0.875077 | 0.437539 | − | 0.899200i | \(-0.355850\pi\) | ||||
0.437539 | + | 0.899200i | \(0.355850\pi\) | |||||||
\(758\) | 37688.9 | 1.80597 | ||||||||
\(759\) | 7144.56 | 0.341675 | ||||||||
\(760\) | 2027.37 | 0.0967637 | ||||||||
\(761\) | −11885.6 | −0.566165 | −0.283083 | − | 0.959096i | \(-0.591357\pi\) | ||||
−0.283083 | + | 0.959096i | \(0.591357\pi\) | |||||||
\(762\) | 17892.9 | 0.850644 | ||||||||
\(763\) | −21377.2 | −1.01430 | ||||||||
\(764\) | 249.583 | 0.0118189 | ||||||||
\(765\) | −1302.71 | −0.0615681 | ||||||||
\(766\) | −6892.07 | −0.325092 | ||||||||
\(767\) | 39040.7 | 1.83791 | ||||||||
\(768\) | 6119.29 | 0.287514 | ||||||||
\(769\) | −6216.53 | −0.291513 | −0.145757 | − | 0.989320i | \(-0.546562\pi\) | ||||
−0.145757 | + | 0.989320i | \(0.546562\pi\) | |||||||
\(770\) | 2015.10 | 0.0943104 | ||||||||
\(771\) | −13796.6 | −0.644451 | ||||||||
\(772\) | −2867.07 | −0.133664 | ||||||||
\(773\) | −21129.9 | −0.983171 | −0.491586 | − | 0.870829i | \(-0.663583\pi\) | ||||
−0.491586 | + | 0.870829i | \(0.663583\pi\) | |||||||
\(774\) | −623.609 | −0.0289602 | ||||||||
\(775\) | 3062.18 | 0.141931 | ||||||||
\(776\) | 7773.46 | 0.359602 | ||||||||
\(777\) | 9528.66 | 0.439947 | ||||||||
\(778\) | 26958.7 | 1.24231 | ||||||||
\(779\) | 7060.45 | 0.324733 | ||||||||
\(780\) | 986.049 | 0.0452644 | ||||||||
\(781\) | −4337.83 | −0.198745 | ||||||||
\(782\) | 43305.0 | 1.98029 | ||||||||
\(783\) | −24287.4 | −1.10851 | ||||||||
\(784\) | 13311.3 | 0.606381 | ||||||||
\(785\) | 11005.8 | 0.500401 | ||||||||
\(786\) | −20806.6 | −0.944208 | ||||||||
\(787\) | −21928.0 | −0.993198 | −0.496599 | − | 0.867980i | \(-0.665418\pi\) | ||||
−0.496599 | + | 0.867980i | \(0.665418\pi\) | |||||||
\(788\) | 1181.97 | 0.0534339 | ||||||||
\(789\) | 18877.2 | 0.851769 | ||||||||
\(790\) | −129.388 | −0.00582713 | ||||||||
\(791\) | 20372.1 | 0.915738 | ||||||||
\(792\) | 548.253 | 0.0245977 | ||||||||
\(793\) | −11086.6 | −0.496463 | ||||||||
\(794\) | 35982.9 | 1.60829 | ||||||||
\(795\) | −8710.91 | −0.388609 | ||||||||
\(796\) | 1309.99 | 0.0583308 | ||||||||
\(797\) | 39641.4 | 1.76182 | 0.880909 | − | 0.473286i | \(-0.156932\pi\) | ||||
0.880909 | + | 0.473286i | \(0.156932\pi\) | |||||||
\(798\) | −3457.19 | −0.153362 | ||||||||
\(799\) | −40370.0 | −1.78747 | ||||||||
\(800\) | 913.239 | 0.0403598 | ||||||||
\(801\) | 3758.68 | 0.165801 | ||||||||
\(802\) | −14983.5 | −0.659706 | ||||||||
\(803\) | −728.939 | −0.0320345 | ||||||||
\(804\) | 1414.56 | 0.0620494 | ||||||||
\(805\) | −8071.54 | −0.353397 | ||||||||
\(806\) | −17818.7 | −0.778706 | ||||||||
\(807\) | 20398.2 | 0.889777 | ||||||||
\(808\) | −9379.51 | −0.408379 | ||||||||
\(809\) | 14982.9 | 0.651139 | 0.325570 | − | 0.945518i | \(-0.394444\pi\) | ||||
0.325570 | + | 0.945518i | \(0.394444\pi\) | |||||||
\(810\) | 9802.29 | 0.425207 | ||||||||
\(811\) | 20606.0 | 0.892200 | 0.446100 | − | 0.894983i | \(-0.352813\pi\) | ||||
0.446100 | + | 0.894983i | \(0.352813\pi\) | |||||||
\(812\) | 1667.21 | 0.0720538 | ||||||||
\(813\) | 2983.02 | 0.128683 | ||||||||
\(814\) | 5075.07 | 0.218527 | ||||||||
\(815\) | −15442.3 | −0.663706 | ||||||||
\(816\) | −38685.4 | −1.65963 | ||||||||
\(817\) | −1709.20 | −0.0731915 | ||||||||
\(818\) | 34521.3 | 1.47556 | ||||||||
\(819\) | −1412.90 | −0.0602818 | ||||||||
\(820\) | 1505.39 | 0.0641103 | ||||||||
\(821\) | 39159.7 | 1.66466 | 0.832329 | − | 0.554282i | \(-0.187007\pi\) | ||||
0.832329 | + | 0.554282i | \(0.187007\pi\) | |||||||
\(822\) | 1988.10 | 0.0843590 | ||||||||
\(823\) | 31720.7 | 1.34352 | 0.671759 | − | 0.740770i | \(-0.265539\pi\) | ||||
0.671759 | + | 0.740770i | \(0.265539\pi\) | |||||||
\(824\) | 21650.3 | 0.915321 | ||||||||
\(825\) | −1365.74 | −0.0576352 | ||||||||
\(826\) | −29184.9 | −1.22939 | ||||||||
\(827\) | 6144.79 | 0.258374 | 0.129187 | − | 0.991620i | \(-0.458763\pi\) | ||||
0.129187 | + | 0.991620i | \(0.458763\pi\) | |||||||
\(828\) | 247.472 | 0.0103868 | ||||||||
\(829\) | −6843.18 | −0.286699 | −0.143349 | − | 0.989672i | \(-0.545787\pi\) | ||||
−0.143349 | + | 0.989672i | \(0.545787\pi\) | |||||||
\(830\) | −746.445 | −0.0312162 | ||||||||
\(831\) | 1888.46 | 0.0788325 | ||||||||
\(832\) | 22063.5 | 0.919367 | ||||||||
\(833\) | −21267.0 | −0.884583 | ||||||||
\(834\) | −31387.3 | −1.30318 | ||||||||
\(835\) | 5268.93 | 0.218370 | ||||||||
\(836\) | −169.335 | −0.00700545 | ||||||||
\(837\) | −17845.1 | −0.736940 | ||||||||
\(838\) | −3229.50 | −0.133128 | ||||||||
\(839\) | 37368.0 | 1.53765 | 0.768824 | − | 0.639461i | \(-0.220842\pi\) | ||||
0.768824 | + | 0.639461i | \(0.220842\pi\) | |||||||
\(840\) | 6541.16 | 0.268680 | ||||||||
\(841\) | 3401.99 | 0.139489 | ||||||||
\(842\) | −6009.44 | −0.245961 | ||||||||
\(843\) | 30248.7 | 1.23585 | ||||||||
\(844\) | 1996.50 | 0.0814246 | ||||||||
\(845\) | 1025.34 | 0.0417430 | ||||||||
\(846\) | −2508.61 | −0.101948 | ||||||||
\(847\) | 1493.57 | 0.0605899 | ||||||||
\(848\) | 24494.6 | 0.991919 | ||||||||
\(849\) | −17619.4 | −0.712246 | ||||||||
\(850\) | −8278.12 | −0.334044 | ||||||||
\(851\) | −20328.4 | −0.818857 | ||||||||
\(852\) | 1586.78 | 0.0638052 | ||||||||
\(853\) | −38570.1 | −1.54820 | −0.774101 | − | 0.633062i | \(-0.781798\pi\) | ||||
−0.774101 | + | 0.633062i | \(0.781798\pi\) | |||||||
\(854\) | 8287.75 | 0.332086 | ||||||||
\(855\) | −221.872 | −0.00887471 | ||||||||
\(856\) | 6196.87 | 0.247436 | ||||||||
\(857\) | 27103.7 | 1.08033 | 0.540167 | − | 0.841558i | \(-0.318361\pi\) | ||||
0.540167 | + | 0.841558i | \(0.318361\pi\) | |||||||
\(858\) | 7947.21 | 0.316216 | ||||||||
\(859\) | 16004.5 | 0.635701 | 0.317851 | − | 0.948141i | \(-0.397039\pi\) | ||||
0.317851 | + | 0.948141i | \(0.397039\pi\) | |||||||
\(860\) | −364.426 | −0.0144498 | ||||||||
\(861\) | 22780.1 | 0.901675 | ||||||||
\(862\) | 7193.02 | 0.284217 | ||||||||
\(863\) | 34355.0 | 1.35511 | 0.677554 | − | 0.735473i | \(-0.263040\pi\) | ||||
0.677554 | + | 0.735473i | \(0.263040\pi\) | |||||||
\(864\) | −5321.99 | −0.209558 | ||||||||
\(865\) | 19.3485 | 0.000760543 0 | ||||||||
\(866\) | 1248.22 | 0.0489797 | ||||||||
\(867\) | 37406.8 | 1.46528 | ||||||||
\(868\) | 1224.98 | 0.0479016 | ||||||||
\(869\) | −95.9014 | −0.00374365 | ||||||||
\(870\) | −12287.2 | −0.478820 | ||||||||
\(871\) | 17229.7 | 0.670273 | ||||||||
\(872\) | −36959.0 | −1.43531 | ||||||||
\(873\) | −850.716 | −0.0329810 | ||||||||
\(874\) | 7375.53 | 0.285447 | ||||||||
\(875\) | 1542.94 | 0.0596125 | ||||||||
\(876\) | 266.645 | 0.0102844 | ||||||||
\(877\) | −24142.3 | −0.929563 | −0.464782 | − | 0.885425i | \(-0.653867\pi\) | ||||
−0.464782 | + | 0.885425i | \(0.653867\pi\) | |||||||
\(878\) | −12855.8 | −0.494149 | ||||||||
\(879\) | 42488.4 | 1.63037 | ||||||||
\(880\) | 3840.39 | 0.147113 | ||||||||
\(881\) | −20489.9 | −0.783567 | −0.391784 | − | 0.920057i | \(-0.628142\pi\) | ||||
−0.391784 | + | 0.920057i | \(0.628142\pi\) | |||||||
\(882\) | −1321.54 | −0.0504519 | ||||||||
\(883\) | −23422.6 | −0.892677 | −0.446338 | − | 0.894864i | \(-0.647272\pi\) | ||||
−0.446338 | + | 0.894864i | \(0.647272\pi\) | |||||||
\(884\) | 4429.87 | 0.168544 | ||||||||
\(885\) | 19780.2 | 0.751306 | ||||||||
\(886\) | 2941.93 | 0.111553 | ||||||||
\(887\) | −13832.1 | −0.523602 | −0.261801 | − | 0.965122i | \(-0.584316\pi\) | ||||
−0.261801 | + | 0.965122i | \(0.584316\pi\) | |||||||
\(888\) | 16474.1 | 0.622561 | ||||||||
\(889\) | −14982.7 | −0.565247 | ||||||||
\(890\) | 23884.6 | 0.899568 | ||||||||
\(891\) | 7265.36 | 0.273175 | ||||||||
\(892\) | 4471.59 | 0.167847 | ||||||||
\(893\) | −6875.66 | −0.257654 | ||||||||
\(894\) | 38821.5 | 1.45233 | ||||||||
\(895\) | 6665.48 | 0.248941 | ||||||||
\(896\) | −20100.8 | −0.749465 | ||||||||
\(897\) | −31832.8 | −1.18491 | ||||||||
\(898\) | 37804.6 | 1.40485 | ||||||||
\(899\) | 20419.4 | 0.757535 | ||||||||
\(900\) | −47.3063 | −0.00175209 | ||||||||
\(901\) | −39134.1 | −1.44700 | ||||||||
\(902\) | 12132.9 | 0.447873 | ||||||||
\(903\) | −5514.62 | −0.203228 | ||||||||
\(904\) | 35221.3 | 1.29584 | ||||||||
\(905\) | 10250.2 | 0.376497 | ||||||||
\(906\) | −43081.5 | −1.57979 | ||||||||
\(907\) | −10084.8 | −0.369194 | −0.184597 | − | 0.982814i | \(-0.559098\pi\) | ||||
−0.184597 | + | 0.982814i | \(0.559098\pi\) | |||||||
\(908\) | 4603.49 | 0.168251 | ||||||||
\(909\) | 1026.48 | 0.0374546 | ||||||||
\(910\) | −8978.33 | −0.327065 | ||||||||
\(911\) | −40909.4 | −1.48780 | −0.743901 | − | 0.668289i | \(-0.767027\pi\) | ||||
−0.743901 | + | 0.668289i | \(0.767027\pi\) | |||||||
\(912\) | −6588.74 | −0.239227 | ||||||||
\(913\) | −553.257 | −0.0200549 | ||||||||
\(914\) | 26533.3 | 0.960223 | ||||||||
\(915\) | −5617.07 | −0.202945 | ||||||||
\(916\) | −242.825 | −0.00875891 | ||||||||
\(917\) | 17422.6 | 0.627419 | ||||||||
\(918\) | 48241.6 | 1.73443 | ||||||||
\(919\) | −29353.2 | −1.05361 | −0.526807 | − | 0.849985i | \(-0.676611\pi\) | ||||
−0.526807 | + | 0.849985i | \(0.676611\pi\) | |||||||
\(920\) | −13954.9 | −0.500085 | ||||||||
\(921\) | 14320.6 | 0.512356 | ||||||||
\(922\) | −52628.0 | −1.87984 | ||||||||
\(923\) | 19327.4 | 0.689239 | ||||||||
\(924\) | −546.346 | −0.0194518 | ||||||||
\(925\) | 3885.94 | 0.138128 | ||||||||
\(926\) | −11935.3 | −0.423562 | ||||||||
\(927\) | −2369.38 | −0.0839489 | ||||||||
\(928\) | 6089.71 | 0.215414 | ||||||||
\(929\) | 36206.4 | 1.27868 | 0.639340 | − | 0.768924i | \(-0.279207\pi\) | ||||
0.639340 | + | 0.768924i | \(0.279207\pi\) | |||||||
\(930\) | −9027.96 | −0.318321 | ||||||||
\(931\) | −3622.10 | −0.127508 | ||||||||
\(932\) | 5501.29 | 0.193348 | ||||||||
\(933\) | 25610.9 | 0.898674 | ||||||||
\(934\) | 20800.2 | 0.728698 | ||||||||
\(935\) | −6135.66 | −0.214607 | ||||||||
\(936\) | −2442.76 | −0.0853037 | ||||||||
\(937\) | −22248.1 | −0.775682 | −0.387841 | − | 0.921726i | \(-0.626779\pi\) | ||||
−0.387841 | + | 0.921726i | \(0.626779\pi\) | |||||||
\(938\) | −12880.1 | −0.448347 | ||||||||
\(939\) | −6133.22 | −0.213152 | ||||||||
\(940\) | −1465.99 | −0.0508672 | ||||||||
\(941\) | −53751.2 | −1.86210 | −0.931052 | − | 0.364888i | \(-0.881107\pi\) | ||||
−0.931052 | + | 0.364888i | \(0.881107\pi\) | |||||||
\(942\) | −32447.6 | −1.12229 | ||||||||
\(943\) | −48598.8 | −1.67825 | ||||||||
\(944\) | −55620.9 | −1.91770 | ||||||||
\(945\) | −8991.65 | −0.309522 | ||||||||
\(946\) | −2937.15 | −0.100946 | ||||||||
\(947\) | 3011.55 | 0.103339 | 0.0516696 | − | 0.998664i | \(-0.483546\pi\) | ||||
0.0516696 | + | 0.998664i | \(0.483546\pi\) | |||||||
\(948\) | 35.0807 | 0.00120186 | ||||||||
\(949\) | 3247.81 | 0.111094 | ||||||||
\(950\) | −1409.90 | −0.0481506 | ||||||||
\(951\) | −3750.09 | −0.127871 | ||||||||
\(952\) | 29386.5 | 1.00044 | ||||||||
\(953\) | 35562.8 | 1.20881 | 0.604404 | − | 0.796678i | \(-0.293411\pi\) | ||||
0.604404 | + | 0.796678i | \(0.293411\pi\) | |||||||
\(954\) | −2431.81 | −0.0825292 | ||||||||
\(955\) | 1540.23 | 0.0521892 | ||||||||
\(956\) | −1879.23 | −0.0635759 | ||||||||
\(957\) | −9107.12 | −0.307619 | ||||||||
\(958\) | −24111.4 | −0.813156 | ||||||||
\(959\) | −1664.75 | −0.0560559 | ||||||||
\(960\) | 11178.6 | 0.375821 | ||||||||
\(961\) | −14787.9 | −0.496388 | ||||||||
\(962\) | −22612.1 | −0.757843 | ||||||||
\(963\) | −678.177 | −0.0226936 | ||||||||
\(964\) | 4556.32 | 0.152230 | ||||||||
\(965\) | −17693.3 | −0.590226 | ||||||||
\(966\) | 23796.6 | 0.792592 | ||||||||
\(967\) | −10743.1 | −0.357263 | −0.178631 | − | 0.983916i | \(-0.557167\pi\) | ||||
−0.178631 | + | 0.983916i | \(0.557167\pi\) | |||||||
\(968\) | 2582.23 | 0.0857396 | ||||||||
\(969\) | 10526.6 | 0.348982 | ||||||||
\(970\) | −5405.90 | −0.178941 | ||||||||
\(971\) | 34154.2 | 1.12880 | 0.564398 | − | 0.825503i | \(-0.309108\pi\) | ||||
0.564398 | + | 0.825503i | \(0.309108\pi\) | |||||||
\(972\) | 529.416 | 0.0174702 | ||||||||
\(973\) | 26282.4 | 0.865954 | ||||||||
\(974\) | −14708.6 | −0.483874 | ||||||||
\(975\) | 6085.12 | 0.199877 | ||||||||
\(976\) | 15794.9 | 0.518014 | ||||||||
\(977\) | −6108.45 | −0.200027 | −0.100014 | − | 0.994986i | \(-0.531889\pi\) | ||||
−0.100014 | + | 0.994986i | \(0.531889\pi\) | |||||||
\(978\) | 45527.2 | 1.48855 | ||||||||
\(979\) | 17703.1 | 0.577929 | ||||||||
\(980\) | −772.284 | −0.0251732 | ||||||||
\(981\) | 4044.74 | 0.131640 | ||||||||
\(982\) | 35392.3 | 1.15012 | ||||||||
\(983\) | −43151.9 | −1.40014 | −0.700068 | − | 0.714076i | \(-0.746847\pi\) | ||||
−0.700068 | + | 0.714076i | \(0.746847\pi\) | |||||||
\(984\) | 39384.4 | 1.27594 | ||||||||
\(985\) | 7294.19 | 0.235951 | ||||||||
\(986\) | −55200.6 | −1.78291 | ||||||||
\(987\) | −22183.8 | −0.715419 | ||||||||
\(988\) | 754.477 | 0.0242946 | ||||||||
\(989\) | 11764.9 | 0.378261 | ||||||||
\(990\) | −381.272 | −0.0122400 | ||||||||
\(991\) | −14240.0 | −0.456458 | −0.228229 | − | 0.973607i | \(-0.573293\pi\) | ||||
−0.228229 | + | 0.973607i | \(0.573293\pi\) | |||||||
\(992\) | 4474.40 | 0.143208 | ||||||||
\(993\) | 7466.31 | 0.238607 | ||||||||
\(994\) | −14448.2 | −0.461034 | ||||||||
\(995\) | 8084.22 | 0.257575 | ||||||||
\(996\) | 202.381 | 0.00643844 | ||||||||
\(997\) | 30650.8 | 0.973640 | 0.486820 | − | 0.873502i | \(-0.338157\pi\) | ||||
0.486820 | + | 0.873502i | \(0.338157\pi\) | |||||||
\(998\) | −21292.2 | −0.675344 | ||||||||
\(999\) | −22645.7 | −0.717195 |
(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.h.1.7 | ✓ | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1045.4.a.h.1.7 | ✓ | 24 | 1.1 | even | 1 | trivial |