Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [147,4,Mod(146,147)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(147, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("147.146");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 147 = 3 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 147.c (of order \(2\), degree \(1\), 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: | \(8.67328077084\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 146.9 | ||
Character | \(\chi\) | \(=\) | 147.146 |
Dual form | 147.4.c.b.146.15 |
$q$-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 \(\left(\mathbb{Z}/147\mathbb{Z}\right)^\times\).
\(n\) | \(50\) | \(52\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 1.05015i | − | 0.371285i | −0.982617 | − | 0.185643i | \(-0.940563\pi\) | ||
0.982617 | − | 0.185643i | \(-0.0594367\pi\) | |||||||
\(3\) | −4.50851 | + | 2.58329i | −0.867663 | + | 0.497154i | ||||
\(4\) | 6.89718 | 0.862147 | ||||||||
\(5\) | −10.2305 | −0.915044 | −0.457522 | − | 0.889198i | \(-0.651263\pi\) | ||||
−0.457522 | + | 0.889198i | \(0.651263\pi\) | |||||||
\(6\) | 2.71285 | + | 4.73462i | 0.184586 | + | 0.322150i | ||||
\(7\) | 0 | 0 | ||||||||
\(8\) | − | 15.6443i | − | 0.691388i | ||||||
\(9\) | 13.6533 | − | 23.2935i | 0.505677 | − | 0.862723i | ||||
\(10\) | 10.7436i | 0.339742i | ||||||||
\(11\) | 24.0632i | 0.659574i | 0.944055 | + | 0.329787i | \(0.106977\pi\) | ||||
−0.944055 | + | 0.329787i | \(0.893023\pi\) | |||||||
\(12\) | −31.0960 | + | 17.8174i | −0.748053 | + | 0.428620i | ||||
\(13\) | − | 49.4354i | − | 1.05468i | −0.849653 | − | 0.527342i | \(-0.823189\pi\) | ||
0.849653 | − | 0.527342i | \(-0.176811\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 46.1243 | − | 26.4283i | 0.793950 | − | 0.454918i | ||||
\(16\) | 38.7485 | 0.605445 | ||||||||
\(17\) | 125.761 | 1.79421 | 0.897106 | − | 0.441815i | \(-0.145665\pi\) | ||||
0.897106 | + | 0.441815i | \(0.145665\pi\) | |||||||
\(18\) | −24.4618 | − | 14.3380i | −0.320316 | − | 0.187750i | ||||
\(19\) | − | 95.5681i | − | 1.15394i | −0.816766 | − | 0.576969i | \(-0.804235\pi\) | ||
0.816766 | − | 0.576969i | \(-0.195765\pi\) | |||||||
\(20\) | −70.5616 | −0.788903 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 25.2700 | 0.244890 | ||||||||
\(23\) | − | 185.716i | − | 1.68367i | −0.539736 | − | 0.841834i | \(-0.681476\pi\) | ||
0.539736 | − | 0.841834i | \(-0.318524\pi\) | |||||||
\(24\) | 40.4138 | + | 70.5325i | 0.343726 | + | 0.599891i | ||||
\(25\) | −20.3367 | −0.162694 | ||||||||
\(26\) | −51.9147 | −0.391589 | ||||||||
\(27\) | −1.38202 | + | 140.289i | −0.00985074 | + | 0.999951i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 40.6873i | − | 0.260533i | −0.991479 | − | 0.130266i | \(-0.958417\pi\) | ||
0.991479 | − | 0.130266i | \(-0.0415832\pi\) | |||||||
\(30\) | −27.7538 | − | 48.4376i | −0.168904 | − | 0.294782i | ||||
\(31\) | − | 37.5677i | − | 0.217656i | −0.994061 | − | 0.108828i | \(-0.965290\pi\) | ||
0.994061 | − | 0.108828i | \(-0.0347098\pi\) | |||||||
\(32\) | − | 165.846i | − | 0.916181i | ||||||
\(33\) | −62.1620 | − | 108.489i | −0.327910 | − | 0.572288i | ||||
\(34\) | − | 132.069i | − | 0.666165i | ||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 94.1690 | − | 160.660i | 0.435968 | − | 0.743794i | ||||
\(37\) | 283.290 | 1.25872 | 0.629358 | − | 0.777115i | \(-0.283318\pi\) | ||||
0.629358 | + | 0.777115i | \(0.283318\pi\) | |||||||
\(38\) | −100.361 | −0.428440 | ||||||||
\(39\) | 127.706 | + | 222.880i | 0.524340 | + | 0.915110i | ||||
\(40\) | 160.049i | 0.632651i | ||||||||
\(41\) | 166.685 | 0.634923 | 0.317462 | − | 0.948271i | \(-0.397170\pi\) | ||||
0.317462 | + | 0.948271i | \(0.397170\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −411.667 | −1.45997 | −0.729984 | − | 0.683464i | \(-0.760473\pi\) | ||||
−0.729984 | + | 0.683464i | \(0.760473\pi\) | |||||||
\(44\) | 165.968i | 0.568650i | ||||||||
\(45\) | −139.680 | + | 238.305i | −0.462716 | + | 0.789430i | ||||
\(46\) | −195.030 | −0.625121 | ||||||||
\(47\) | 15.1056 | 0.0468805 | 0.0234402 | − | 0.999725i | \(-0.492538\pi\) | ||||
0.0234402 | + | 0.999725i | \(0.492538\pi\) | |||||||
\(48\) | −174.698 | + | 100.098i | −0.525322 | + | 0.300999i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 21.3567i | 0.0604058i | ||||||||
\(51\) | −566.996 | + | 324.878i | −1.55677 | + | 0.891999i | ||||
\(52\) | − | 340.964i | − | 0.909293i | ||||||
\(53\) | 190.230i | 0.493020i | 0.969140 | + | 0.246510i | \(0.0792838\pi\) | ||||
−0.969140 | + | 0.246510i | \(0.920716\pi\) | |||||||
\(54\) | 147.325 | + | 1.45133i | 0.371267 | + | 0.00365744i | ||||
\(55\) | − | 246.178i | − | 0.603540i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 246.880 | + | 430.869i | 0.573684 | + | 1.00123i | ||||
\(58\) | −42.7279 | −0.0967320 | ||||||||
\(59\) | −94.7330 | −0.209037 | −0.104519 | − | 0.994523i | \(-0.533330\pi\) | ||||
−0.104519 | + | 0.994523i | \(0.533330\pi\) | |||||||
\(60\) | 318.128 | − | 182.281i | 0.684502 | − | 0.392206i | ||||
\(61\) | 412.161i | 0.865111i | 0.901607 | + | 0.432555i | \(0.142388\pi\) | ||||
−0.901607 | + | 0.432555i | \(0.857612\pi\) | |||||||
\(62\) | −39.4518 | −0.0808126 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 135.824 | 0.265281 | ||||||||
\(65\) | 505.749i | 0.965083i | ||||||||
\(66\) | −113.930 | + | 65.2797i | −0.212482 | + | 0.121748i | ||||
\(67\) | −88.7656 | −0.161857 | −0.0809287 | − | 0.996720i | \(-0.525789\pi\) | ||||
−0.0809287 | + | 0.996720i | \(0.525789\pi\) | |||||||
\(68\) | 867.398 | 1.54688 | ||||||||
\(69\) | 479.756 | + | 837.300i | 0.837042 | + | 1.46086i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1064.80i | 1.77984i | 0.456118 | + | 0.889920i | \(0.349240\pi\) | ||||
−0.456118 | + | 0.889920i | \(0.650760\pi\) | |||||||
\(72\) | −364.411 | − | 213.596i | −0.596476 | − | 0.349619i | ||||
\(73\) | − | 828.400i | − | 1.32818i | −0.747654 | − | 0.664088i | \(-0.768820\pi\) | ||
0.747654 | − | 0.664088i | \(-0.231180\pi\) | |||||||
\(74\) | − | 297.497i | − | 0.467343i | ||||||
\(75\) | 91.6883 | − | 52.5356i | 0.141163 | − | 0.0808839i | ||||
\(76\) | − | 659.150i | − | 0.994864i | ||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 234.058 | − | 134.111i | 0.339767 | − | 0.194680i | ||||
\(79\) | 256.515 | 0.365319 | 0.182659 | − | 0.983176i | \(-0.441529\pi\) | ||||
0.182659 | + | 0.983176i | \(0.441529\pi\) | |||||||
\(80\) | −396.417 | −0.554009 | ||||||||
\(81\) | −356.177 | − | 636.065i | −0.488582 | − | 0.872518i | ||||
\(82\) | − | 175.045i | − | 0.235738i | ||||||
\(83\) | 97.2939 | 0.128667 | 0.0643337 | − | 0.997928i | \(-0.479508\pi\) | ||||
0.0643337 | + | 0.997928i | \(0.479508\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1286.60 | −1.64178 | ||||||||
\(86\) | 432.314i | 0.542065i | ||||||||
\(87\) | 105.107 | + | 183.439i | 0.129525 | + | 0.226054i | ||||
\(88\) | 376.452 | 0.456022 | ||||||||
\(89\) | −899.046 | −1.07077 | −0.535386 | − | 0.844608i | \(-0.679834\pi\) | ||||
−0.535386 | + | 0.844608i | \(0.679834\pi\) | |||||||
\(90\) | 250.256 | + | 146.685i | 0.293104 | + | 0.171800i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | − | 1280.91i | − | 1.45157i | ||||||
\(93\) | 97.0480 | + | 169.374i | 0.108209 | + | 0.188852i | ||||
\(94\) | − | 15.8632i | − | 0.0174060i | ||||||
\(95\) | 977.710i | 1.05590i | ||||||||
\(96\) | 428.429 | + | 747.720i | 0.455483 | + | 0.794936i | ||||
\(97\) | − | 398.892i | − | 0.417540i | −0.977965 | − | 0.208770i | \(-0.933054\pi\) | ||
0.977965 | − | 0.208770i | \(-0.0669460\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 560.516 | + | 328.541i | 0.569030 | + | 0.333531i | ||||
\(100\) | −140.266 | −0.140266 | ||||||||
\(101\) | −57.2539 | −0.0564057 | −0.0282028 | − | 0.999602i | \(-0.508978\pi\) | ||||
−0.0282028 | + | 0.999602i | \(0.508978\pi\) | |||||||
\(102\) | 341.171 | + | 595.433i | 0.331186 | + | 0.578006i | ||||
\(103\) | − | 740.200i | − | 0.708098i | −0.935227 | − | 0.354049i | \(-0.884805\pi\) | ||
0.935227 | − | 0.354049i | \(-0.115195\pi\) | |||||||
\(104\) | −773.383 | −0.729196 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 199.770 | 0.183051 | ||||||||
\(107\) | − | 862.638i | − | 0.779386i | −0.920945 | − | 0.389693i | \(-0.872581\pi\) | ||
0.920945 | − | 0.389693i | \(-0.127419\pi\) | |||||||
\(108\) | −9.53205 | + | 967.600i | −0.00849279 | + | 0.862105i | ||||
\(109\) | −657.058 | −0.577383 | −0.288691 | − | 0.957422i | \(-0.593220\pi\) | ||||
−0.288691 | + | 0.957422i | \(0.593220\pi\) | |||||||
\(110\) | −258.525 | −0.224085 | ||||||||
\(111\) | −1277.21 | + | 731.818i | −1.09214 | + | 0.625776i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 884.317i | − | 0.736190i | −0.929788 | − | 0.368095i | \(-0.880010\pi\) | ||
0.929788 | − | 0.368095i | \(-0.119990\pi\) | |||||||
\(114\) | 452.479 | − | 259.262i | 0.371742 | − | 0.213001i | ||||
\(115\) | 1899.96i | 1.54063i | ||||||||
\(116\) | − | 280.628i | − | 0.224618i | ||||||
\(117\) | −1151.52 | − | 674.954i | −0.909901 | − | 0.533329i | ||||
\(118\) | 99.4842i | 0.0776124i | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −413.453 | − | 721.584i | −0.314524 | − | 0.548927i | ||||
\(121\) | 751.964 | 0.564962 | ||||||||
\(122\) | 432.832 | 0.321203 | ||||||||
\(123\) | −751.501 | + | 430.595i | −0.550899 | + | 0.315654i | ||||
\(124\) | − | 259.111i | − | 0.187652i | ||||||
\(125\) | 1486.87 | 1.06392 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1004.76 | 0.702028 | 0.351014 | − | 0.936370i | \(-0.385837\pi\) | ||||
0.351014 | + | 0.936370i | \(0.385837\pi\) | |||||||
\(128\) | − | 1469.41i | − | 1.01468i | ||||||
\(129\) | 1856.00 | − | 1063.45i | 1.26676 | − | 0.725829i | ||||
\(130\) | 531.114 | 0.358321 | ||||||||
\(131\) | −712.639 | −0.475294 | −0.237647 | − | 0.971352i | \(-0.576376\pi\) | ||||
−0.237647 | + | 0.971352i | \(0.576376\pi\) | |||||||
\(132\) | −428.743 | − | 748.268i | −0.282706 | − | 0.493396i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 93.2175i | 0.0600953i | ||||||||
\(135\) | 14.1388 | − | 1435.23i | 0.00901387 | − | 0.915000i | ||||
\(136\) | − | 1967.45i | − | 1.24050i | ||||||
\(137\) | − | 1359.68i | − | 0.847921i | −0.905681 | − | 0.423961i | \(-0.860639\pi\) | ||
0.905681 | − | 0.423961i | \(-0.139361\pi\) | |||||||
\(138\) | 879.293 | − | 503.818i | 0.542394 | − | 0.310781i | ||||
\(139\) | 213.266i | 0.130137i | 0.997881 | + | 0.0650684i | \(0.0207266\pi\) | ||||
−0.997881 | + | 0.0650684i | \(0.979273\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −68.1039 | + | 39.0222i | −0.0406765 | + | 0.0233068i | ||||
\(142\) | 1118.20 | 0.660828 | ||||||||
\(143\) | 1189.57 | 0.695643 | ||||||||
\(144\) | 529.043 | − | 902.589i | 0.306159 | − | 0.522331i | ||||
\(145\) | 416.252i | 0.238399i | ||||||||
\(146\) | −869.947 | −0.493132 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 1953.90 | 1.08520 | ||||||||
\(149\) | − | 1522.90i | − | 0.837319i | −0.908143 | − | 0.418660i | \(-0.862500\pi\) | ||
0.908143 | − | 0.418660i | \(-0.137500\pi\) | |||||||
\(150\) | −55.1704 | − | 96.2868i | −0.0300310 | − | 0.0524119i | ||||
\(151\) | 410.715 | 0.221348 | 0.110674 | − | 0.993857i | \(-0.464699\pi\) | ||||
0.110674 | + | 0.993857i | \(0.464699\pi\) | |||||||
\(152\) | −1495.10 | −0.797819 | ||||||||
\(153\) | 1717.05 | − | 2929.43i | 0.907291 | − | 1.54791i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 384.336i | 0.199165i | ||||||||
\(156\) | 880.809 | + | 1537.24i | 0.452059 | + | 0.788960i | ||||
\(157\) | 2184.75i | 1.11059i | 0.831655 | + | 0.555293i | \(0.187394\pi\) | ||||
−0.831655 | + | 0.555293i | \(0.812606\pi\) | |||||||
\(158\) | − | 269.380i | − | 0.135637i | ||||||
\(159\) | −491.417 | − | 857.651i | −0.245107 | − | 0.427775i | ||||
\(160\) | 1696.69i | 0.838346i | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −667.966 | + | 374.040i | −0.323953 | + | 0.181403i | ||||
\(163\) | −1593.25 | −0.765600 | −0.382800 | − | 0.923831i | \(-0.625040\pi\) | ||||
−0.382800 | + | 0.923831i | \(0.625040\pi\) | |||||||
\(164\) | 1149.66 | 0.547397 | ||||||||
\(165\) | 635.949 | + | 1109.90i | 0.300052 | + | 0.523669i | ||||
\(166\) | − | 102.173i | − | 0.0477723i | ||||||
\(167\) | −1297.31 | −0.601129 | −0.300564 | − | 0.953762i | \(-0.597175\pi\) | ||||
−0.300564 | + | 0.953762i | \(0.597175\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −246.854 | −0.112360 | ||||||||
\(170\) | 1351.13i | 0.609570i | ||||||||
\(171\) | −2226.12 | − | 1304.82i | −0.995529 | − | 0.583519i | ||||
\(172\) | −2839.34 | −1.25871 | ||||||||
\(173\) | 3229.49 | 1.41927 | 0.709635 | − | 0.704570i | \(-0.248860\pi\) | ||||
0.709635 | + | 0.704570i | \(0.248860\pi\) | |||||||
\(174\) | 192.639 | − | 110.378i | 0.0839307 | − | 0.0480906i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 932.411i | 0.399336i | ||||||||
\(177\) | 427.104 | − | 244.722i | 0.181374 | − | 0.103924i | ||||
\(178\) | 944.136i | 0.397562i | ||||||||
\(179\) | 3521.41i | 1.47040i | 0.677848 | + | 0.735202i | \(0.262913\pi\) | ||||
−0.677848 | + | 0.735202i | \(0.737087\pi\) | |||||||
\(180\) | −963.397 | + | 1643.63i | −0.398930 | + | 0.680605i | ||||
\(181\) | 3143.01i | 1.29071i | 0.763883 | + | 0.645354i | \(0.223290\pi\) | ||||
−0.763883 | + | 0.645354i | \(0.776710\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1064.73 | − | 1858.23i | −0.430093 | − | 0.750624i | ||||
\(184\) | −2905.39 | −1.16407 | ||||||||
\(185\) | −2898.20 | −1.15178 | ||||||||
\(186\) | 177.869 | − | 101.915i | 0.0701181 | − | 0.0401763i | ||||
\(187\) | 3026.22i | 1.18342i | ||||||||
\(188\) | 104.186 | 0.0404179 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 1026.75 | 0.392042 | ||||||||
\(191\) | 4480.24i | 1.69727i | 0.528978 | + | 0.848636i | \(0.322576\pi\) | ||||
−0.528978 | + | 0.848636i | \(0.677424\pi\) | |||||||
\(192\) | −612.362 | + | 350.871i | −0.230174 | + | 0.131885i | ||||
\(193\) | 5217.77 | 1.94603 | 0.973013 | − | 0.230751i | \(-0.0741182\pi\) | ||||
0.973013 | + | 0.230751i | \(0.0741182\pi\) | |||||||
\(194\) | −418.898 | −0.155026 | ||||||||
\(195\) | −1306.49 | − | 2280.17i | −0.479795 | − | 0.837367i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 474.082i | 0.171457i | 0.996319 | + | 0.0857283i | \(0.0273217\pi\) | ||||
−0.996319 | + | 0.0857283i | \(0.972678\pi\) | |||||||
\(198\) | 345.018 | − | 588.628i | 0.123835 | − | 0.211272i | ||||
\(199\) | 1055.13i | 0.375860i | 0.982182 | + | 0.187930i | \(0.0601778\pi\) | ||||
−0.982182 | + | 0.187930i | \(0.939822\pi\) | |||||||
\(200\) | 318.154i | 0.112485i | ||||||||
\(201\) | 400.200 | − | 229.307i | 0.140438 | − | 0.0804680i | ||||
\(202\) | 60.1253i | 0.0209426i | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −3910.67 | + | 2240.74i | −1.34217 | + | 0.769035i | ||||
\(205\) | −1705.27 | −0.580983 | ||||||||
\(206\) | −777.324 | −0.262906 | ||||||||
\(207\) | −4325.97 | − | 2535.62i | −1.45254 | − | 0.851392i | ||||
\(208\) | − | 1915.55i | − | 0.638554i | ||||||
\(209\) | 2299.67 | 0.761108 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1367.40 | −0.446141 | −0.223070 | − | 0.974802i | \(-0.571608\pi\) | ||||
−0.223070 | + | 0.974802i | \(0.571608\pi\) | |||||||
\(212\) | 1312.05i | 0.425056i | ||||||||
\(213\) | −2750.68 | − | 4800.66i | −0.884853 | − | 1.54430i | ||||
\(214\) | −905.902 | −0.289375 | ||||||||
\(215\) | 4211.56 | 1.33594 | ||||||||
\(216\) | 2194.73 | + | 21.6208i | 0.691354 | + | 0.00681069i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 690.012i | 0.214374i | ||||||||
\(219\) | 2139.99 | + | 3734.85i | 0.660308 | + | 1.15241i | ||||
\(220\) | − | 1697.94i | − | 0.520340i | ||||||
\(221\) | − | 6217.06i | − | 1.89233i | ||||||
\(222\) | 768.521 | + | 1341.27i | 0.232341 | + | 0.405496i | ||||
\(223\) | 1165.04i | 0.349852i | 0.984582 | + | 0.174926i | \(0.0559686\pi\) | ||||
−0.984582 | + | 0.174926i | \(0.944031\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −277.663 | + | 473.714i | −0.0822705 | + | 0.140360i | ||||
\(226\) | −928.668 | −0.273337 | ||||||||
\(227\) | 1508.20 | 0.440981 | 0.220491 | − | 0.975389i | \(-0.429234\pi\) | ||||
0.220491 | + | 0.975389i | \(0.429234\pi\) | |||||||
\(228\) | 1702.77 | + | 2971.78i | 0.494600 | + | 0.863207i | ||||
\(229\) | − | 2678.95i | − | 0.773056i | −0.922278 | − | 0.386528i | \(-0.873674\pi\) | ||
0.922278 | − | 0.386528i | \(-0.126326\pi\) | |||||||
\(230\) | 1995.25 | 0.572014 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −636.526 | −0.180129 | ||||||||
\(233\) | − | 1651.83i | − | 0.464443i | −0.972663 | − | 0.232221i | \(-0.925401\pi\) | ||
0.972663 | − | 0.232221i | \(-0.0745994\pi\) | |||||||
\(234\) | −708.805 | + | 1209.28i | −0.198017 | + | 0.337833i | ||||
\(235\) | −154.538 | −0.0428977 | ||||||||
\(236\) | −653.390 | −0.180221 | ||||||||
\(237\) | −1156.50 | + | 662.651i | −0.316973 | + | 0.181620i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1945.85i | 0.526638i | 0.964709 | + | 0.263319i | \(0.0848172\pi\) | ||||
−0.964709 | + | 0.263319i | \(0.915183\pi\) | |||||||
\(240\) | 1787.25 | − | 1024.06i | 0.480693 | − | 0.275428i | ||||
\(241\) | 480.849i | 0.128524i | 0.997933 | + | 0.0642618i | \(0.0204693\pi\) | ||||
−0.997933 | + | 0.0642618i | \(0.979531\pi\) | |||||||
\(242\) | − | 789.678i | − | 0.209762i | ||||||
\(243\) | 3248.96 | + | 1947.60i | 0.857700 | + | 0.514151i | ||||
\(244\) | 2842.74i | 0.745853i | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 452.191 | + | 789.192i | 0.117198 | + | 0.204541i | ||||
\(247\) | −4724.44 | −1.21704 | ||||||||
\(248\) | −587.720 | −0.150485 | ||||||||
\(249\) | −438.650 | + | 251.338i | −0.111640 | + | 0.0639674i | ||||
\(250\) | − | 1561.44i | − | 0.395017i | ||||||
\(251\) | −5108.84 | −1.28473 | −0.642364 | − | 0.766400i | \(-0.722046\pi\) | ||||
−0.642364 | + | 0.766400i | \(0.722046\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 4468.90 | 1.11050 | ||||||||
\(254\) | − | 1055.15i | − | 0.260653i | ||||||
\(255\) | 5800.66 | − | 3323.66i | 1.42451 | − | 0.816219i | ||||
\(256\) | −456.513 | −0.111453 | ||||||||
\(257\) | −1656.10 | −0.401963 | −0.200982 | − | 0.979595i | \(-0.564413\pi\) | ||||
−0.200982 | + | 0.979595i | \(0.564413\pi\) | |||||||
\(258\) | −1116.79 | − | 1949.09i | −0.269489 | − | 0.470329i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 3488.24i | 0.832044i | ||||||||
\(261\) | −947.751 | − | 555.515i | −0.224768 | − | 0.131745i | ||||
\(262\) | 748.380i | 0.176470i | ||||||||
\(263\) | 1496.85i | 0.350950i | 0.984484 | + | 0.175475i | \(0.0561462\pi\) | ||||
−0.984484 | + | 0.175475i | \(0.943854\pi\) | |||||||
\(264\) | −1697.24 | + | 972.483i | −0.395673 | + | 0.226713i | ||||
\(265\) | − | 1946.15i | − | 0.451135i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 4053.35 | − | 2322.49i | 0.929068 | − | 0.532338i | ||||
\(268\) | −612.232 | −0.139545 | ||||||||
\(269\) | −2373.66 | −0.538009 | −0.269005 | − | 0.963139i | \(-0.586695\pi\) | ||||
−0.269005 | + | 0.963139i | \(0.586695\pi\) | |||||||
\(270\) | −1507.21 | − | 14.8479i | −0.339726 | − | 0.00334672i | ||||
\(271\) | 5846.44i | 1.31050i | 0.755412 | + | 0.655251i | \(0.227437\pi\) | ||||
−0.755412 | + | 0.655251i | \(0.772563\pi\) | |||||||
\(272\) | 4873.06 | 1.08630 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −1427.87 | −0.314821 | ||||||||
\(275\) | − | 489.366i | − | 0.107309i | ||||||
\(276\) | 3308.97 | + | 5775.01i | 0.721653 | + | 1.25947i | ||||
\(277\) | 2501.87 | 0.542681 | 0.271341 | − | 0.962483i | \(-0.412533\pi\) | ||||
0.271341 | + | 0.962483i | \(0.412533\pi\) | |||||||
\(278\) | 223.962 | 0.0483179 | ||||||||
\(279\) | −875.083 | − | 512.921i | −0.187777 | − | 0.110064i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 8088.74i | − | 1.71720i | −0.512645 | − | 0.858601i | \(-0.671334\pi\) | ||
0.512645 | − | 0.858601i | \(-0.328666\pi\) | |||||||
\(282\) | 40.9793 | + | 71.5195i | 0.00865347 | + | 0.0151026i | ||||
\(283\) | 4331.83i | 0.909895i | 0.890518 | + | 0.454947i | \(0.150342\pi\) | ||||
−0.890518 | + | 0.454947i | \(0.849658\pi\) | |||||||
\(284\) | 7344.12i | 1.53448i | ||||||||
\(285\) | −2525.70 | − | 4408.01i | −0.524947 | − | 0.916169i | ||||
\(286\) | − | 1249.23i | − | 0.258282i | ||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −3863.15 | − | 2264.35i | −0.790410 | − | 0.463291i | ||||
\(289\) | 10902.9 | 2.21920 | ||||||||
\(290\) | 437.128 | 0.0885140 | ||||||||
\(291\) | 1030.45 | + | 1798.41i | 0.207581 | + | 0.362284i | ||||
\(292\) | − | 5713.62i | − | 1.14508i | ||||||
\(293\) | −4715.26 | −0.940164 | −0.470082 | − | 0.882623i | \(-0.655776\pi\) | ||||
−0.470082 | + | 0.882623i | \(0.655776\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 969.166 | 0.191278 | ||||||||
\(296\) | − | 4431.87i | − | 0.870261i | ||||||
\(297\) | −3375.81 | − | 33.2558i | −0.659542 | − | 0.00649730i | ||||
\(298\) | −1599.28 | −0.310884 | ||||||||
\(299\) | −9180.91 | −1.77574 | ||||||||
\(300\) | 632.391 | − | 362.347i | 0.121704 | − | 0.0697338i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | − | 431.314i | − | 0.0821832i | ||||||
\(303\) | 258.129 | − | 147.903i | 0.0489411 | − | 0.0280423i | ||||
\(304\) | − | 3703.12i | − | 0.698646i | ||||||
\(305\) | − | 4216.61i | − | 0.791615i | ||||||
\(306\) | −3076.35 | − | 1803.17i | −0.574716 | − | 0.336864i | ||||
\(307\) | − | 4540.05i | − | 0.844020i | −0.906591 | − | 0.422010i | \(-0.861325\pi\) | ||
0.906591 | − | 0.422010i | \(-0.138675\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1912.15 | + | 3337.20i | 0.352033 | + | 0.614390i | ||||
\(310\) | 403.612 | 0.0739471 | ||||||||
\(311\) | 5248.33 | 0.956932 | 0.478466 | − | 0.878106i | \(-0.341193\pi\) | ||||
0.478466 | + | 0.878106i | \(0.341193\pi\) | |||||||
\(312\) | 3486.80 | − | 1997.87i | 0.632696 | − | 0.362522i | ||||
\(313\) | 6079.22i | 1.09782i | 0.835881 | + | 0.548910i | \(0.184957\pi\) | ||||
−0.835881 | + | 0.548910i | \(0.815043\pi\) | |||||||
\(314\) | 2294.32 | 0.412344 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 1769.23 | 0.314959 | ||||||||
\(317\) | − | 4335.82i | − | 0.768215i | −0.923288 | − | 0.384107i | \(-0.874509\pi\) | ||
0.923288 | − | 0.384107i | \(-0.125491\pi\) | |||||||
\(318\) | −900.666 | + | 516.064i | −0.158826 | + | 0.0910044i | ||||
\(319\) | 979.066 | 0.171841 | ||||||||
\(320\) | −1389.55 | −0.242744 | ||||||||
\(321\) | 2228.44 | + | 3889.21i | 0.387475 | + | 0.676244i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 12018.8i | − | 2.07041i | ||||||
\(324\) | −2456.61 | − | 4387.06i | −0.421230 | − | 0.752239i | ||||
\(325\) | 1005.35i | 0.171591i | ||||||||
\(326\) | 1673.16i | 0.284256i | ||||||||
\(327\) | 2962.35 | − | 1697.37i | 0.500974 | − | 0.287048i | ||||
\(328\) | − | 2607.68i | − | 0.438978i | ||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 1165.56 | − | 667.844i | 0.194431 | − | 0.111405i | ||||
\(331\) | 6270.17 | 1.04121 | 0.520603 | − | 0.853799i | \(-0.325707\pi\) | ||||
0.520603 | + | 0.853799i | \(0.325707\pi\) | |||||||
\(332\) | 671.053 | 0.110930 | ||||||||
\(333\) | 3867.83 | − | 6598.81i | 0.636504 | − | 1.08592i | ||||
\(334\) | 1362.37i | 0.223190i | ||||||||
\(335\) | 908.117 | 0.148107 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −5320.37 | −0.859997 | −0.429999 | − | 0.902830i | \(-0.641486\pi\) | ||||
−0.429999 | + | 0.902830i | \(0.641486\pi\) | |||||||
\(338\) | 259.235i | 0.0417175i | ||||||||
\(339\) | 2284.44 | + | 3986.95i | 0.366000 | + | 0.638765i | ||||
\(340\) | −8873.93 | −1.41546 | ||||||||
\(341\) | 903.997 | 0.143561 | ||||||||
\(342\) | −1370.26 | + | 2337.76i | −0.216652 | + | 0.369625i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 6440.25i | 1.00940i | ||||||||
\(345\) | −4908.15 | − | 8566.00i | −0.765930 | − | 1.33675i | ||||
\(346\) | − | 3391.46i | − | 0.526954i | ||||||
\(347\) | 4815.66i | 0.745009i | 0.928030 | + | 0.372504i | \(0.121501\pi\) | ||||
−0.928030 | + | 0.372504i | \(0.878499\pi\) | |||||||
\(348\) | 724.942 | + | 1265.21i | 0.111669 | + | 0.194892i | ||||
\(349\) | 5201.69i | 0.797822i | 0.916990 | + | 0.398911i | \(0.130612\pi\) | ||||
−0.916990 | + | 0.398911i | \(0.869388\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 6935.25 | + | 68.3207i | 1.05463 | + | 0.0103894i | ||||
\(352\) | 3990.79 | 0.604289 | ||||||||
\(353\) | 637.734 | 0.0961563 | 0.0480782 | − | 0.998844i | \(-0.484690\pi\) | ||||
0.0480782 | + | 0.998844i | \(0.484690\pi\) | |||||||
\(354\) | −256.996 | − | 448.525i | −0.0385853 | − | 0.0673413i | ||||
\(355\) | − | 10893.4i | − | 1.62863i | ||||||
\(356\) | −6200.88 | −0.923163 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 3698.02 | 0.545939 | ||||||||
\(359\) | 5518.37i | 0.811277i | 0.914034 | + | 0.405638i | \(0.132951\pi\) | ||||
−0.914034 | + | 0.405638i | \(0.867049\pi\) | |||||||
\(360\) | 3728.11 | + | 2185.20i | 0.545802 | + | 0.319917i | ||||
\(361\) | −2274.26 | −0.331573 | ||||||||
\(362\) | 3300.64 | 0.479221 | ||||||||
\(363\) | −3390.23 | + | 1942.54i | −0.490196 | + | 0.280873i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 8474.95i | 1.21534i | ||||||||
\(366\) | −1951.42 | + | 1118.13i | −0.278696 | + | 0.159687i | ||||
\(367\) | − | 2594.14i | − | 0.368973i | −0.982835 | − | 0.184486i | \(-0.940938\pi\) | ||
0.982835 | − | 0.184486i | \(-0.0590622\pi\) | |||||||
\(368\) | − | 7196.20i | − | 1.01937i | ||||||
\(369\) | 2275.80 | − | 3882.69i | 0.321066 | − | 0.547763i | ||||
\(370\) | 3043.55i | 0.427640i | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 669.357 | + | 1168.20i | 0.0932918 | + | 0.162819i | ||||
\(373\) | −5173.83 | −0.718206 | −0.359103 | − | 0.933298i | \(-0.616917\pi\) | ||||
−0.359103 | + | 0.933298i | \(0.616917\pi\) | |||||||
\(374\) | 3177.99 | 0.439385 | ||||||||
\(375\) | −6703.56 | + | 3841.01i | −0.923120 | + | 0.528930i | ||||
\(376\) | − | 236.317i | − | 0.0324126i | ||||||
\(377\) | −2011.39 | −0.274780 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −14088.2 | −1.90940 | −0.954700 | − | 0.297568i | \(-0.903824\pi\) | ||||
−0.954700 | + | 0.297568i | \(0.903824\pi\) | |||||||
\(380\) | 6743.44i | 0.910345i | ||||||||
\(381\) | −4529.95 | + | 2595.57i | −0.609124 | + | 0.349016i | ||||
\(382\) | 4704.94 | 0.630172 | ||||||||
\(383\) | 7732.32 | 1.03160 | 0.515801 | − | 0.856709i | \(-0.327495\pi\) | ||||
0.515801 | + | 0.856709i | \(0.327495\pi\) | |||||||
\(384\) | 3795.90 | + | 6624.83i | 0.504450 | + | 0.880396i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | − | 5479.45i | − | 0.722531i | ||||||
\(387\) | −5620.60 | + | 9589.18i | −0.738272 | + | 1.25955i | ||||
\(388\) | − | 2751.23i | − | 0.359981i | ||||||
\(389\) | 731.955i | 0.0954025i | 0.998862 | + | 0.0477013i | \(0.0151895\pi\) | ||||
−0.998862 | + | 0.0477013i | \(0.984810\pi\) | |||||||
\(390\) | −2394.53 | + | 1372.02i | −0.310902 | + | 0.178141i | ||||
\(391\) | − | 23355.8i | − | 3.02086i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 3212.94 | − | 1840.95i | 0.412395 | − | 0.236294i | ||||
\(394\) | 497.859 | 0.0636593 | ||||||||
\(395\) | −2624.28 | −0.334283 | ||||||||
\(396\) | 3865.98 | + | 2266.00i | 0.490588 | + | 0.287553i | ||||
\(397\) | 14564.1i | 1.84119i | 0.390518 | + | 0.920595i | \(0.372296\pi\) | ||||
−0.390518 | + | 0.920595i | \(0.627704\pi\) | |||||||
\(398\) | 1108.05 | 0.139551 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −788.018 | −0.0985022 | ||||||||
\(401\) | − | 5909.89i | − | 0.735975i | −0.929831 | − | 0.367988i | \(-0.880047\pi\) | ||
0.929831 | − | 0.367988i | \(-0.119953\pi\) | |||||||
\(402\) | −240.807 | − | 420.272i | −0.0298766 | − | 0.0521424i | ||||
\(403\) | −1857.17 | −0.229559 | ||||||||
\(404\) | −394.890 | −0.0486300 | ||||||||
\(405\) | 3643.87 | + | 6507.27i | 0.447075 | + | 0.798392i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 6816.84i | 0.830217i | ||||||||
\(408\) | 5082.49 | + | 8870.27i | 0.616717 | + | 1.07633i | ||||
\(409\) | − | 8054.46i | − | 0.973759i | −0.873469 | − | 0.486880i | \(-0.838135\pi\) | ||
0.873469 | − | 0.486880i | \(-0.161865\pi\) | |||||||
\(410\) | 1790.80i | 0.215710i | ||||||||
\(411\) | 3512.44 | + | 6130.12i | 0.421547 | + | 0.735709i | ||||
\(412\) | − | 5105.29i | − | 0.610485i | ||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −2662.79 | + | 4542.93i | −0.316109 | + | 0.539307i | ||||
\(415\) | −995.366 | −0.117736 | ||||||||
\(416\) | −8198.68 | −0.966282 | ||||||||
\(417\) | −550.928 | − | 961.513i | −0.0646980 | − | 0.112915i | ||||
\(418\) | − | 2415.01i | − | 0.282588i | ||||||
\(419\) | 13850.2 | 1.61486 | 0.807428 | − | 0.589966i | \(-0.200859\pi\) | ||||
0.807428 | + | 0.589966i | \(0.200859\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2365.25 | −0.273813 | −0.136906 | − | 0.990584i | \(-0.543716\pi\) | ||||
−0.136906 | + | 0.990584i | \(0.543716\pi\) | |||||||
\(422\) | 1435.98i | 0.165645i | ||||||||
\(423\) | 206.241 | − | 351.863i | 0.0237064 | − | 0.0404449i | ||||
\(424\) | 2976.01 | 0.340868 | ||||||||
\(425\) | −2557.58 | −0.291907 | ||||||||
\(426\) | −5041.43 | + | 2888.64i | −0.573376 | + | 0.328533i | ||||
\(427\) | 0 | 0 | ||||||||
\(428\) | − | 5949.77i | − | 0.671946i | ||||||
\(429\) | −5363.19 | + | 3073.00i | −0.603583 | + | 0.345841i | ||||
\(430\) | − | 4422.79i | − | 0.496013i | ||||||
\(431\) | 194.891i | 0.0217809i | 0.999941 | + | 0.0108905i | \(0.00346661\pi\) | ||||
−0.999941 | + | 0.0108905i | \(0.996533\pi\) | |||||||
\(432\) | −53.5512 | + | 5436.00i | −0.00596409 | + | 0.605416i | ||||
\(433\) | 7716.01i | 0.856369i | 0.903691 | + | 0.428185i | \(0.140847\pi\) | ||||
−0.903691 | + | 0.428185i | \(0.859153\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −1075.30 | − | 1876.68i | −0.118521 | − | 0.206850i | ||||
\(436\) | −4531.85 | −0.497789 | ||||||||
\(437\) | −17748.5 | −1.94285 | ||||||||
\(438\) | 3922.16 | − | 2247.32i | 0.427873 | − | 0.245163i | ||||
\(439\) | − | 7595.59i | − | 0.825781i | −0.910781 | − | 0.412891i | \(-0.864519\pi\) | ||
0.910781 | − | 0.412891i | \(-0.135481\pi\) | |||||||
\(440\) | −3851.29 | −0.417280 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −6528.86 | −0.702594 | ||||||||
\(443\) | 10116.7i | 1.08501i | 0.840053 | + | 0.542505i | \(0.182524\pi\) | ||||
−0.840053 | + | 0.542505i | \(0.817476\pi\) | |||||||
\(444\) | −8809.16 | + | 5047.48i | −0.941587 | + | 0.539511i | ||||
\(445\) | 9197.69 | 0.979803 | ||||||||
\(446\) | 1223.47 | 0.129895 | ||||||||
\(447\) | 3934.08 | + | 6865.99i | 0.416276 | + | 0.726511i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 18315.5i | 1.92509i | 0.271131 | + | 0.962543i | \(0.412602\pi\) | ||||
−0.271131 | + | 0.962543i | \(0.587398\pi\) | |||||||
\(450\) | 497.473 | + | 291.589i | 0.0521135 | + | 0.0305458i | ||||
\(451\) | 4010.97i | 0.418779i | ||||||||
\(452\) | − | 6099.29i | − | 0.634705i | ||||||
\(453\) | −1851.71 | + | 1061.00i | −0.192055 | + | 0.110044i | ||||
\(454\) | − | 1583.84i | − | 0.163730i | ||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 6740.66 | − | 3862.26i | 0.692237 | − | 0.396638i | ||||
\(457\) | 5171.83 | 0.529383 | 0.264692 | − | 0.964333i | \(-0.414730\pi\) | ||||
0.264692 | + | 0.964333i | \(0.414730\pi\) | |||||||
\(458\) | −2813.31 | −0.287024 | ||||||||
\(459\) | −173.805 | + | 17643.0i | −0.0176743 | + | 1.79413i | ||||
\(460\) | 13104.4i | 1.32825i | ||||||||
\(461\) | 7960.73 | 0.804269 | 0.402135 | − | 0.915581i | \(-0.368268\pi\) | ||||
0.402135 | + | 0.915581i | \(0.368268\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1659.53 | 0.166577 | 0.0832883 | − | 0.996525i | \(-0.473458\pi\) | ||||
0.0832883 | + | 0.996525i | \(0.473458\pi\) | |||||||
\(464\) | − | 1576.57i | − | 0.157738i | ||||||
\(465\) | −992.850 | − | 1732.78i | −0.0990157 | − | 0.172808i | ||||
\(466\) | −1734.68 | −0.172441 | ||||||||
\(467\) | 6925.40 | 0.686230 | 0.343115 | − | 0.939293i | \(-0.388518\pi\) | ||||
0.343115 | + | 0.939293i | \(0.388518\pi\) | |||||||
\(468\) | −7942.26 | − | 4655.28i | −0.784468 | − | 0.459808i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 162.289i | 0.0159273i | ||||||||
\(471\) | −5643.83 | − | 9849.95i | −0.552131 | − | 0.963613i | ||||
\(472\) | 1482.03i | 0.144526i | ||||||||
\(473\) | − | 9906.01i | − | 0.962958i | ||||||
\(474\) | 695.885 | + | 1214.50i | 0.0674327 | + | 0.117688i | ||||
\(475\) | 1943.54i | 0.187739i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 4431.12 | + | 2597.26i | 0.425339 | + | 0.249309i | ||||
\(478\) | 2043.44 | 0.195533 | ||||||||
\(479\) | 19425.3 | 1.85295 | 0.926474 | − | 0.376358i | \(-0.122824\pi\) | ||||
0.926474 | + | 0.376358i | \(0.122824\pi\) | |||||||
\(480\) | −4383.04 | − | 7649.55i | −0.416787 | − | 0.727401i | ||||
\(481\) | − | 14004.5i | − | 1.32755i | ||||||
\(482\) | 504.965 | 0.0477190 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 5186.43 | 0.487080 | ||||||||
\(485\) | 4080.87i | 0.382067i | ||||||||
\(486\) | 2045.28 | − | 3411.91i | 0.190897 | − | 0.318451i | ||||
\(487\) | −9624.35 | −0.895525 | −0.447763 | − | 0.894152i | \(-0.647779\pi\) | ||||
−0.447763 | + | 0.894152i | \(0.647779\pi\) | |||||||
\(488\) | 6447.97 | 0.598127 | ||||||||
\(489\) | 7183.17 | − | 4115.82i | 0.664283 | − | 0.380621i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 448.247i | 0.0411998i | 0.999788 | + | 0.0205999i | \(0.00655762\pi\) | ||||
−0.999788 | + | 0.0205999i | \(0.993442\pi\) | |||||||
\(492\) | −5183.24 | + | 2969.89i | −0.474956 | + | 0.272141i | ||||
\(493\) | − | 5116.89i | − | 0.467451i | ||||||
\(494\) | 4961.39i | 0.451869i | ||||||||
\(495\) | −5734.36 | − | 3361.14i | −0.520688 | − | 0.305196i | ||||
\(496\) | − | 1455.69i | − | 0.131779i | ||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 263.943 | + | 460.650i | 0.0237502 | + | 0.0414502i | ||||
\(499\) | −13858.2 | −1.24324 | −0.621620 | − | 0.783319i | \(-0.713525\pi\) | ||||
−0.621620 | + | 0.783319i | \(0.713525\pi\) | |||||||
\(500\) | 10255.2 | 0.917253 | ||||||||
\(501\) | 5848.91 | − | 3351.31i | 0.521577 | − | 0.298853i | ||||
\(502\) | 5365.06i | 0.477001i | ||||||||
\(503\) | −17853.2 | −1.58258 | −0.791288 | − | 0.611443i | \(-0.790589\pi\) | ||||
−0.791288 | + | 0.611443i | \(0.790589\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 585.736 | 0.0516137 | ||||||||
\(506\) | − | 4693.04i | − | 0.412314i | ||||||
\(507\) | 1112.94 | − | 637.695i | 0.0974903 | − | 0.0558600i | ||||
\(508\) | 6929.98 | 0.605252 | ||||||||
\(509\) | −9982.92 | −0.869322 | −0.434661 | − | 0.900594i | \(-0.643132\pi\) | ||||
−0.434661 | + | 0.900594i | \(0.643132\pi\) | |||||||
\(510\) | −3490.35 | − | 6091.58i | −0.303050 | − | 0.528901i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | − | 11275.8i | − | 0.973295i | ||||||
\(513\) | 13407.2 | + | 132.077i | 1.15388 | + | 0.0113671i | ||||
\(514\) | 1739.16i | 0.149243i | ||||||||
\(515\) | 7572.62i | 0.647941i | ||||||||
\(516\) | 12801.2 | − | 7334.83i | 1.09213 | − | 0.625771i | ||||
\(517\) | 363.489i | 0.0309212i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −14560.2 | + | 8342.70i | −1.23145 | + | 0.705595i | ||||
\(520\) | 7912.10 | 0.667247 | ||||||||
\(521\) | 12630.5 | 1.06210 | 0.531048 | − | 0.847342i | \(-0.321798\pi\) | ||||
0.531048 | + | 0.847342i | \(0.321798\pi\) | |||||||
\(522\) | −583.376 | + | 995.284i | −0.0489151 | + | 0.0834529i | ||||
\(523\) | 11669.0i | 0.975622i | 0.872949 | + | 0.487811i | \(0.162205\pi\) | ||||
−0.872949 | + | 0.487811i | \(0.837795\pi\) | |||||||
\(524\) | −4915.20 | −0.409774 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 1571.93 | 0.130303 | ||||||||
\(527\) | − | 4724.56i | − | 0.390522i | ||||||
\(528\) | −2408.68 | − | 4203.78i | −0.198531 | − | 0.346489i | ||||
\(529\) | −22323.3 | −1.83474 | ||||||||
\(530\) | −2043.75 | −0.167500 | ||||||||
\(531\) | −1293.41 | + | 2206.67i | −0.105705 | + | 0.180341i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 8240.14i | − | 0.669644i | ||||||
\(534\) | −2438.97 | − | 4256.64i | −0.197649 | − | 0.344949i | ||||
\(535\) | 8825.22i | 0.713173i | ||||||||
\(536\) | 1388.68i | 0.111906i | ||||||||
\(537\) | −9096.80 | − | 15876.3i | −0.731016 | − | 1.27581i | ||||
\(538\) | 2492.71i | 0.199755i | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 97.5177 | − | 9899.04i | 0.00777128 | − | 0.788865i | ||||
\(541\) | 19740.4 | 1.56877 | 0.784385 | − | 0.620274i | \(-0.212979\pi\) | ||||
0.784385 | + | 0.620274i | \(0.212979\pi\) | |||||||
\(542\) | 6139.66 | 0.486570 | ||||||||
\(543\) | −8119.30 | − | 14170.3i | −0.641680 | − | 1.11990i | ||||
\(544\) | − | 20857.1i | − | 1.64382i | ||||||
\(545\) | 6722.04 | 0.528331 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 7949.55 | 0.621386 | 0.310693 | − | 0.950510i | \(-0.399439\pi\) | ||||
0.310693 | + | 0.950510i | \(0.399439\pi\) | |||||||
\(548\) | − | 9377.95i | − | 0.731033i | ||||||
\(549\) | 9600.67 | + | 5627.34i | 0.746351 | + | 0.437466i | ||||
\(550\) | −513.910 | −0.0398421 | ||||||||
\(551\) | −3888.41 | −0.300639 | ||||||||
\(552\) | 13099.0 | − | 7505.46i | 1.01002 | − | 0.578721i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | − | 2627.34i | − | 0.201489i | ||||||
\(555\) | 13066.5 | − | 7486.87i | 0.999358 | − | 0.572612i | ||||
\(556\) | 1470.94i | 0.112197i | ||||||||
\(557\) | 9866.11i | 0.750522i | 0.926919 | + | 0.375261i | \(0.122447\pi\) | ||||
−0.926919 | + | 0.375261i | \(0.877553\pi\) | |||||||
\(558\) | −538.646 | + | 918.971i | −0.0408651 | + | 0.0697189i | ||||
\(559\) | 20350.9i | 1.53981i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −7817.58 | − | 13643.7i | −0.588340 | − | 1.02681i | ||||
\(562\) | −8494.42 | −0.637572 | ||||||||
\(563\) | −9237.69 | −0.691514 | −0.345757 | − | 0.938324i | \(-0.612378\pi\) | ||||
−0.345757 | + | 0.938324i | \(0.612378\pi\) | |||||||
\(564\) | −469.724 | + | 269.143i | −0.0350691 | + | 0.0200939i | ||||
\(565\) | 9047.01i | 0.673647i | ||||||||
\(566\) | 4549.08 | 0.337831 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 16658.1 | 1.23056 | ||||||||
\(569\) | − | 12586.1i | − | 0.927308i | −0.886016 | − | 0.463654i | \(-0.846538\pi\) | ||
0.886016 | − | 0.463654i | \(-0.153462\pi\) | |||||||
\(570\) | −4629.09 | + | 2652.38i | −0.340160 | + | 0.194905i | ||||
\(571\) | 20675.9 | 1.51534 | 0.757669 | − | 0.652640i | \(-0.226338\pi\) | ||||
0.757669 | + | 0.652640i | \(0.226338\pi\) | |||||||
\(572\) | 8204.68 | 0.599747 | ||||||||
\(573\) | −11573.7 | − | 20199.2i | −0.843805 | − | 1.47266i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 3776.85i | 0.273923i | ||||||||
\(576\) | 1854.44 | − | 3163.81i | 0.134146 | − | 0.228864i | ||||
\(577\) | 15543.6i | 1.12147i | 0.827996 | + | 0.560734i | \(0.189481\pi\) | ||||
−0.827996 | + | 0.560734i | \(0.810519\pi\) | |||||||
\(578\) | − | 11449.7i | − | 0.823955i | ||||||
\(579\) | −23524.3 | + | 13479.0i | −1.68849 | + | 0.967474i | ||||
\(580\) | 2870.96i | 0.205535i | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 1888.60 | − | 1082.13i | 0.134511 | − | 0.0770719i | ||||
\(583\) | −4577.53 | −0.325183 | ||||||||
\(584\) | −12959.8 | −0.918285 | ||||||||
\(585\) | 11780.7 | + | 6905.12i | 0.832600 | + | 0.488020i | ||||
\(586\) | 4951.74i | 0.349069i | ||||||||
\(587\) | −13650.3 | −0.959811 | −0.479905 | − | 0.877320i | \(-0.659329\pi\) | ||||
−0.479905 | + | 0.877320i | \(0.659329\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −3590.27 | −0.251162 | ||||||||
\(590\) | − | 1017.77i | − | 0.0710188i | ||||||
\(591\) | −1224.69 | − | 2137.40i | −0.0852402 | − | 0.148766i | ||||
\(592\) | 10977.0 | 0.762084 | ||||||||
\(593\) | −24799.6 | −1.71736 | −0.858682 | − | 0.512508i | \(-0.828716\pi\) | ||||
−0.858682 | + | 0.512508i | \(0.828716\pi\) | |||||||
\(594\) | −34.9237 | + | 3545.11i | −0.00241235 | + | 0.244878i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | − | 10503.7i | − | 0.721892i | ||||||
\(597\) | −2725.70 | − | 4757.06i | −0.186860 | − | 0.326120i | ||||
\(598\) | 9641.37i | 0.659306i | ||||||||
\(599\) | 7543.35i | 0.514545i | 0.966339 | + | 0.257273i | \(0.0828239\pi\) | ||||
−0.966339 | + | 0.257273i | \(0.917176\pi\) | |||||||
\(600\) | −821.884 | − | 1434.40i | −0.0559221 | − | 0.0975987i | ||||
\(601\) | 17481.2i | 1.18648i | 0.805027 | + | 0.593239i | \(0.202151\pi\) | ||||
−0.805027 | + | 0.593239i | \(0.797849\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −1211.94 | + | 2067.66i | −0.0818475 | + | 0.139638i | ||||
\(604\) | 2832.78 | 0.190835 | ||||||||
\(605\) | −7692.97 | −0.516965 | ||||||||
\(606\) | −155.321 | − | 271.075i | −0.0104117 | − | 0.0181711i | ||||
\(607\) | − | 25695.5i | − | 1.71820i | −0.511806 | − | 0.859101i | \(-0.671023\pi\) | ||
0.511806 | − | 0.859101i | \(-0.328977\pi\) | |||||||
\(608\) | −15849.6 | −1.05722 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −4428.09 | −0.293915 | ||||||||
\(611\) | − | 746.752i | − | 0.0494441i | ||||||
\(612\) | 11842.8 | − | 20204.8i | 0.782219 | − | 1.33452i | ||||
\(613\) | −7168.60 | −0.472328 | −0.236164 | − | 0.971713i | \(-0.575890\pi\) | ||||
−0.236164 | + | 0.971713i | \(0.575890\pi\) | |||||||
\(614\) | −4767.75 | −0.313372 | ||||||||
\(615\) | 7688.24 | − | 4405.21i | 0.504097 | − | 0.288838i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 10280.7i | − | 0.670805i | −0.942075 | − | 0.335402i | \(-0.891128\pi\) | ||
0.942075 | − | 0.335402i | \(-0.108872\pi\) | |||||||
\(618\) | 3504.57 | − | 2008.05i | 0.228114 | − | 0.130705i | ||||
\(619\) | 4548.35i | 0.295337i | 0.989037 | + | 0.147668i | \(0.0471769\pi\) | ||||
−0.989037 | + | 0.147668i | \(0.952823\pi\) | |||||||
\(620\) | 2650.83i | 0.171710i | ||||||||
\(621\) | 26053.9 | + | 256.663i | 1.68359 | + | 0.0165854i | ||||
\(622\) | − | 5511.56i | − | 0.355295i | ||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 4948.40 | + | 8636.25i | 0.317459 | + | 0.554049i | ||||
\(625\) | −12669.3 | −0.810837 | ||||||||
\(626\) | 6384.11 | 0.407605 | ||||||||
\(627\) | −10368.1 | + | 5940.71i | −0.660385 | + | 0.378388i | ||||
\(628\) | 15068.6i | 0.957488i | ||||||||
\(629\) | 35626.9 | 2.25840 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 18015.7 | 1.13660 | 0.568298 | − | 0.822823i | \(-0.307602\pi\) | ||||
0.568298 | + | 0.822823i | \(0.307602\pi\) | |||||||
\(632\) | − | 4013.00i | − | 0.252577i | ||||||
\(633\) | 6164.93 | − | 3532.38i | 0.387099 | − | 0.221800i | ||||
\(634\) | −4553.28 | −0.285227 | ||||||||
\(635\) | −10279.2 | −0.642387 | ||||||||
\(636\) | −3389.39 | − | 5915.37i | −0.211318 | − | 0.368805i | ||||
\(637\) | 0 | 0 | ||||||||
\(638\) | − | 1028.17i | − | 0.0638019i | ||||||
\(639\) | 24803.0 | + | 14538.0i | 1.53551 | + | 0.900023i | ||||
\(640\) | 15032.8i | 0.928473i | ||||||||
\(641\) | − | 1117.06i | − | 0.0688321i | −0.999408 | − | 0.0344161i | \(-0.989043\pi\) | ||
0.999408 | − | 0.0344161i | \(-0.0109571\pi\) | |||||||
\(642\) | 4084.27 | − | 2340.20i | 0.251080 | − | 0.143864i | ||||
\(643\) | − | 11689.0i | − | 0.716907i | −0.933548 | − | 0.358453i | \(-0.883304\pi\) | ||
0.933548 | − | 0.358453i | \(-0.116696\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −18987.9 | + | 10879.7i | −1.15914 | + | 0.664165i | ||||
\(646\) | −12621.6 | −0.768713 | ||||||||
\(647\) | 10088.7 | 0.613025 | 0.306513 | − | 0.951867i | \(-0.400838\pi\) | ||||
0.306513 | + | 0.951867i | \(0.400838\pi\) | |||||||
\(648\) | −9950.81 | + | 5572.14i | −0.603248 | + | 0.337800i | ||||
\(649\) | − | 2279.58i | − | 0.137875i | ||||||
\(650\) | 1055.78 | 0.0637091 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −10988.9 | −0.660060 | ||||||||
\(653\) | 20037.7i | 1.20082i | 0.799693 | + | 0.600409i | \(0.204995\pi\) | ||||
−0.799693 | + | 0.600409i | \(0.795005\pi\) | |||||||
\(654\) | −1782.50 | − | 3110.92i | −0.106577 | − | 0.186004i | ||||
\(655\) | 7290.66 | 0.434915 | ||||||||
\(656\) | 6458.80 | 0.384411 | ||||||||
\(657\) | −19296.4 | − | 11310.4i | −1.14585 | − | 0.671628i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 11752.2i | 0.694691i | 0.937737 | + | 0.347345i | \(0.112917\pi\) | ||||
−0.937737 | + | 0.347345i | \(0.887083\pi\) | |||||||
\(660\) | 4386.25 | + | 7655.16i | 0.258689 | + | 0.451480i | ||||
\(661\) | − | 22013.0i | − | 1.29532i | −0.761930 | − | 0.647659i | \(-0.775748\pi\) | ||
0.761930 | − | 0.647659i | \(-0.224252\pi\) | |||||||
\(662\) | − | 6584.64i | − | 0.386585i | ||||||
\(663\) | 16060.4 | + | 28029.6i | 0.940778 | + | 1.64190i | ||||
\(664\) | − | 1522.10i | − | 0.0889590i | ||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −6929.76 | − | 4061.81i | −0.403188 | − | 0.236324i | ||||
\(667\) | −7556.27 | −0.438651 | ||||||||
\(668\) | −8947.75 | −0.518262 | ||||||||
\(669\) | −3009.63 | − | 5252.60i | −0.173930 | − | 0.303553i | ||||
\(670\) | − | 953.662i | − | 0.0549898i | ||||||
\(671\) | −9917.89 | −0.570605 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 24243.2 | 1.38857 | 0.694283 | − | 0.719702i | \(-0.255721\pi\) | ||||
0.694283 | + | 0.719702i | \(0.255721\pi\) | |||||||
\(674\) | 5587.20i | 0.319304i | ||||||||
\(675\) | 28.1058 | − | 2853.03i | 0.00160266 | − | 0.162686i | ||||
\(676\) | −1702.60 | −0.0968706 | ||||||||
\(677\) | 29061.2 | 1.64979 | 0.824897 | − | 0.565283i | \(-0.191233\pi\) | ||||
0.824897 | + | 0.565283i | \(0.191233\pi\) | |||||||
\(678\) | 4186.91 | − | 2399.02i | 0.237164 | − | 0.135890i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 20128.0i | 1.13511i | ||||||||
\(681\) | −6799.73 | + | 3896.11i | −0.382623 | + | 0.219235i | ||||
\(682\) | − | 949.335i | − | 0.0533019i | ||||||
\(683\) | − | 12078.4i | − | 0.676673i | −0.941025 | − | 0.338337i | \(-0.890136\pi\) | ||
0.941025 | − | 0.338337i | \(-0.109864\pi\) | |||||||
\(684\) | −15353.9 | − | 8999.55i | −0.858293 | − | 0.503080i | ||||
\(685\) | 13910.2i | 0.775886i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 6920.49 | + | 12078.1i | 0.384328 | + | 0.670752i | ||||
\(688\) | −15951.5 | −0.883931 | ||||||||
\(689\) | 9404.07 | 0.519980 | ||||||||
\(690\) | −8995.62 | + | 5154.31i | −0.496315 | + | 0.284379i | ||||
\(691\) | − | 5338.80i | − | 0.293918i | −0.989143 | − | 0.146959i | \(-0.953051\pi\) | ||
0.989143 | − | 0.146959i | \(-0.0469486\pi\) | |||||||
\(692\) | 22274.4 | 1.22362 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 5057.18 | 0.276611 | ||||||||
\(695\) | − | 2181.82i | − | 0.119081i | ||||||
\(696\) | 2869.78 | − | 1644.33i | 0.156291 | − | 0.0895518i | ||||
\(697\) | 20962.6 | 1.13919 | ||||||||
\(698\) | 5462.57 | 0.296220 | ||||||||
\(699\) | 4267.16 | + | 7447.30i | 0.230899 | + | 0.402980i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 11322.3i | 0.610038i | 0.952346 | + | 0.305019i | \(0.0986628\pi\) | ||||
−0.952346 | + | 0.305019i | \(0.901337\pi\) | |||||||
\(702\) | 71.7472 | − | 7283.08i | 0.00385744 | − | 0.391570i | ||||
\(703\) | − | 27073.4i | − | 1.45248i | ||||||
\(704\) | 3268.35i | 0.174972i | ||||||||
\(705\) | 696.737 | − | 399.217i | 0.0372208 | − | 0.0213268i | ||||
\(706\) | − | 669.719i | − | 0.0357014i | ||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 2945.81 | − | 1687.89i | 0.156371 | − | 0.0895974i | ||||
\(709\) | −16036.7 | −0.849466 | −0.424733 | − | 0.905319i | \(-0.639632\pi\) | ||||
−0.424733 | + | 0.905319i | \(0.639632\pi\) | |||||||
\(710\) | −11439.8 | −0.604687 | ||||||||
\(711\) | 3502.27 | − | 5975.14i | 0.184733 | − | 0.315169i | ||||
\(712\) | 14065.0i | 0.740318i | ||||||||
\(713\) | −6976.90 | −0.366461 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −12169.9 | −0.636544 | ||||||||
\(716\) | 24287.8i | 1.26770i | ||||||||
\(717\) | −5026.68 | − | 8772.87i | −0.261820 | − | 0.456944i | ||||
\(718\) | 5795.13 | 0.301215 | ||||||||
\(719\) | 20243.8 | 1.05002 | 0.525011 | − | 0.851096i | \(-0.324061\pi\) | ||||
0.525011 | + | 0.851096i | \(0.324061\pi\) | |||||||
\(720\) | −5412.38 | + | 9233.94i | −0.280149 | + | 0.477956i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 2388.32i | 0.123108i | ||||||||
\(723\) | −1242.17 | − | 2167.91i | −0.0638960 | − | 0.111515i | ||||
\(724\) | 21677.9i | 1.11278i | ||||||||
\(725\) | 827.448i | 0.0423871i | ||||||||
\(726\) | 2039.96 | + | 3560.27i | 0.104284 | + | 0.182003i | ||||
\(727\) | 23697.2i | 1.20892i | 0.796637 | + | 0.604458i | \(0.206610\pi\) | ||||
−0.796637 | + | 0.604458i | \(0.793390\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −19679.2 | − | 387.766i | −0.999806 | − | 0.0197005i | ||||
\(730\) | 8900.00 | 0.451238 | ||||||||
\(731\) | −51771.8 | −2.61949 | ||||||||
\(732\) | −7343.62 | − | 12816.5i | −0.370803 | − | 0.647148i | ||||
\(733\) | − | 7895.50i | − | 0.397854i | −0.980014 | − | 0.198927i | \(-0.936254\pi\) | ||
0.980014 | − | 0.198927i | \(-0.0637457\pi\) | |||||||
\(734\) | −2724.24 | −0.136994 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −30800.3 | −1.54254 | ||||||||
\(737\) | − | 2135.98i | − | 0.106757i | ||||||
\(738\) | −4077.42 | − | 2389.94i | −0.203376 | − | 0.119207i | ||||
\(739\) | −23190.3 | −1.15436 | −0.577178 | − | 0.816619i | \(-0.695846\pi\) | ||||
−0.577178 | + | 0.816619i | \(0.695846\pi\) | |||||||
\(740\) | −19989.4 | −0.993005 | ||||||||
\(741\) | 21300.2 | − | 12204.6i | 1.05598 | − | 0.605056i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 24811.0i | − | 1.22507i | −0.790443 | − | 0.612536i | \(-0.790150\pi\) | ||
0.790443 | − | 0.612536i | \(-0.209850\pi\) | |||||||
\(744\) | 2649.74 | − | 1518.25i | 0.130570 | − | 0.0748142i | ||||
\(745\) | 15580.0i | 0.766184i | ||||||||
\(746\) | 5433.32i | 0.266659i | ||||||||
\(747\) | 1328.38 | − | 2266.32i | 0.0650641 | − | 0.111004i | ||||
\(748\) | 20872.4i | 1.02028i | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 4033.65 | + | 7039.76i | 0.196384 | + | 0.342741i | ||||
\(751\) | −26673.5 | −1.29605 | −0.648023 | − | 0.761621i | \(-0.724404\pi\) | ||||
−0.648023 | + | 0.761621i | \(0.724404\pi\) | |||||||
\(752\) | 585.321 | 0.0283836 | ||||||||
\(753\) | 23033.2 | − | 13197.6i | 1.11471 | − | 0.638707i | ||||
\(754\) | 2112.27i | 0.102022i | ||||||||
\(755\) | −4201.83 | −0.202543 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1543.03 | −0.0740853 | −0.0370426 | − | 0.999314i | \(-0.511794\pi\) | ||||
−0.0370426 | + | 0.999314i | \(0.511794\pi\) | |||||||
\(758\) | 14794.8i | 0.708932i | ||||||||
\(759\) | −20148.1 | + | 11544.5i | −0.963543 | + | 0.552091i | ||||
\(760\) | 15295.6 | 0.730039 | ||||||||
\(761\) | 15291.5 | 0.728405 | 0.364202 | − | 0.931320i | \(-0.381342\pi\) | ||||
0.364202 | + | 0.931320i | \(0.381342\pi\) | |||||||
\(762\) | 2725.75 | + | 4757.14i | 0.129584 | + | 0.226159i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 30901.0i | 1.46330i | ||||||||
\(765\) | −17566.3 | + | 29969.5i | −0.830212 | + | 1.41640i | ||||
\(766\) | − | 8120.13i | − | 0.383018i | ||||||
\(767\) | 4683.16i | 0.220468i | ||||||||
\(768\) | 2058.19 | − | 1179.30i | 0.0967039 | − | 0.0554095i | ||||
\(769\) | − | 30749.1i | − | 1.44193i | −0.692973 | − | 0.720963i | \(-0.743700\pi\) | ||
0.692973 | − | 0.720963i | \(-0.256300\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 7466.53 | − | 4278.17i | 0.348768 | − | 0.199837i | ||||
\(772\) | 35987.9 | 1.67776 | ||||||||
\(773\) | 16417.4 | 0.763899 | 0.381949 | − | 0.924183i | \(-0.375253\pi\) | ||||
0.381949 | + | 0.924183i | \(0.375253\pi\) | |||||||
\(774\) | 10070.1 | + | 5902.49i | 0.467652 | + | 0.274109i | ||||
\(775\) | 764.003i | 0.0354114i | ||||||||
\(776\) | −6240.40 | −0.288682 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 768.665 | 0.0354216 | ||||||||
\(779\) | − | 15929.8i | − | 0.732662i | ||||||
\(780\) | −9011.12 | − | 15726.7i | −0.413654 | − | 0.721933i | ||||
\(781\) | −25622.5 | −1.17394 | ||||||||
\(782\) | −24527.2 | −1.12160 | ||||||||
\(783\) | 5708.00 | + | 56.2308i | 0.260520 | + | 0.00256644i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 22351.1i | − | 1.01623i | ||||||
\(786\) | −1933.28 | − | 3374.08i | −0.0877326 | − | 0.153116i | ||||
\(787\) | 4625.39i | 0.209501i | 0.994499 | + | 0.104751i | \(0.0334044\pi\) | ||||
−0.994499 | + | 0.104751i | \(0.966596\pi\) | |||||||
\(788\) | 3269.83i | 0.147821i | ||||||||
\(789\) | −3866.80 | − | 6748.57i | −0.174476 | − | 0.304506i | ||||
\(790\) | 2755.89i | 0.124114i | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 5139.80 | − | 8768.89i | 0.230599 | − | 0.393420i | ||||
\(793\) | 20375.3 | 0.912419 | ||||||||
\(794\) | 15294.6 | 0.683607 | ||||||||
\(795\) | 5027.45 | + | 8774.21i | 0.224283 | + | 0.391433i | ||||
\(796\) | 7277.42i | 0.324047i | ||||||||
\(797\) | −10959.4 | −0.487079 | −0.243539 | − | 0.969891i | \(-0.578309\pi\) | ||||
−0.243539 | + | 0.969891i | \(0.578309\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1899.71 | 0.0841136 | ||||||||
\(800\) | 3372.78i | 0.149057i | ||||||||
\(801\) | −12274.9 | + | 20941.9i | −0.541464 | + | 0.923779i | ||||
\(802\) | −6206.29 | −0.273257 | ||||||||
\(803\) | 19933.9 | 0.876031 | ||||||||
\(804\) | 2760.25 | − | 1581.57i | 0.121078 | − | 0.0693752i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 1950.31i | 0.0852318i | ||||||||
\(807\) | 10701.7 | − | 6131.84i | 0.466811 | − | 0.267473i | ||||
\(808\) | 895.698i | 0.0389982i | ||||||||
\(809\) | 24280.4i | 1.05519i | 0.849495 | + | 0.527597i | \(0.176907\pi\) | ||||
−0.849495 | + | 0.527597i | \(0.823093\pi\) | |||||||
\(810\) | 6833.63 | − | 3826.62i | 0.296431 | − | 0.165992i | ||||
\(811\) | − | 14278.5i | − | 0.618233i | −0.951024 | − | 0.309116i | \(-0.899967\pi\) | ||
0.951024 | − | 0.309116i | \(-0.100033\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −15103.0 | − | 26358.7i | −0.651520 | − | 1.13707i | ||||
\(814\) | 7158.73 | 0.308247 | ||||||||
\(815\) | 16299.7 | 0.700558 | ||||||||
\(816\) | −21970.2 | + | 12588.5i | −0.942539 | + | 0.540056i | ||||
\(817\) | 39342.2i | 1.68471i | ||||||||
\(818\) | −8458.42 | −0.361542 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −11761.6 | −0.500893 | ||||||||
\(821\) | 13397.3i | 0.569514i | 0.958600 | + | 0.284757i | \(0.0919128\pi\) | ||||
−0.958600 | + | 0.284757i | \(0.908087\pi\) | |||||||
\(822\) | 6437.57 | − | 3688.60i | 0.273158 | − | 0.156514i | ||||
\(823\) | 13534.6 | 0.573252 | 0.286626 | − | 0.958043i | \(-0.407466\pi\) | ||||
0.286626 | + | 0.958043i | \(0.407466\pi\) | |||||||
\(824\) | −11579.9 | −0.489570 | ||||||||
\(825\) | 1264.17 | + | 2206.31i | 0.0533489 | + | 0.0931078i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 9455.93i | − | 0.397600i | −0.980040 | − | 0.198800i | \(-0.936296\pi\) | ||
0.980040 | − | 0.198800i | \(-0.0637044\pi\) | |||||||
\(828\) | −29837.0 | − | 17488.7i | −1.25230 | − | 0.734025i | ||||
\(829\) | − | 39689.0i | − | 1.66279i | −0.555680 | − | 0.831396i | \(-0.687542\pi\) | ||
0.555680 | − | 0.831396i | \(-0.312458\pi\) | |||||||
\(830\) | 1045.29i | 0.0437138i | ||||||||
\(831\) | −11279.7 | + | 6463.04i | −0.470864 | + | 0.269796i | ||||
\(832\) | − | 6714.49i | − | 0.279787i | ||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −1009.74 | + | 578.559i | −0.0419236 | + | 0.0240214i | ||||
\(835\) | 13272.1 | 0.550060 | ||||||||
\(836\) | 15861.2 | 0.656187 | ||||||||
\(837\) | 5270.34 | + | 51.9193i | 0.217646 | + | 0.00214408i | ||||
\(838\) | − | 14544.8i | − | 0.599573i | ||||||
\(839\) | 2668.41 | 0.109802 | 0.0549009 | − | 0.998492i | \(-0.482516\pi\) | ||||
0.0549009 | + | 0.998492i | \(0.482516\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 22733.5 | 0.932123 | ||||||||
\(842\) | 2483.88i | 0.101663i | ||||||||
\(843\) | 20895.5 | + | 36468.1i | 0.853713 | + | 1.48995i | ||||
\(844\) | −9431.20 | −0.384639 | ||||||||
\(845\) | 2525.44 | 0.102814 | ||||||||
\(846\) | −369.511 | − | 216.585i | −0.0150166 | − | 0.00880183i | ||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 7371.11i | 0.298496i | ||||||||
\(849\) | −11190.3 | − | 19530.1i | −0.452358 | − | 0.789482i | ||||
\(850\) | 2685.85i | 0.108381i | ||||||||
\(851\) | − | 52611.3i | − | 2.11926i | ||||||
\(852\) | −18972.0 | − | 33111.0i | −0.762874 | − | 1.33141i | ||||
\(853\) | − | 22152.8i | − | 0.889211i | −0.895726 | − | 0.444606i | \(-0.853344\pi\) | ||
0.895726 | − | 0.444606i | \(-0.146656\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 22774.3 | + | 13348.9i | 0.910953 | + | 0.533946i | ||||
\(856\) | −13495.4 | −0.538858 | ||||||||
\(857\) | 22498.6 | 0.896778 | 0.448389 | − | 0.893839i | \(-0.351998\pi\) | ||||
0.448389 | + | 0.893839i | \(0.351998\pi\) | |||||||
\(858\) | 3227.12 | + | 5632.17i | 0.128406 | + | 0.224102i | ||||
\(859\) | − | 31093.1i | − | 1.23502i | −0.786563 | − | 0.617511i | \(-0.788141\pi\) | ||
0.786563 | − | 0.617511i | \(-0.211859\pi\) | |||||||
\(860\) | 29047.9 | 1.15177 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 204.665 | 0.00808693 | ||||||||
\(863\) | − | 31827.4i | − | 1.25541i | −0.778451 | − | 0.627705i | \(-0.783994\pi\) | ||
0.778451 | − | 0.627705i | \(-0.216006\pi\) | |||||||
\(864\) | 23266.5 | + | 229.203i | 0.916136 | + | 0.00902506i | ||||
\(865\) | −33039.3 | −1.29869 | ||||||||
\(866\) | 8103.00 | 0.317957 | ||||||||
\(867\) | −49155.9 | + | 28165.4i | −1.92551 | + | 1.10328i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 6172.56i | 0.240955i | ||||||||
\(870\) | −1970.80 | + | 1129.23i | −0.0768003 | + | 0.0440051i | ||||
\(871\) | 4388.16i | 0.170708i | ||||||||
\(872\) | 10279.2i | 0.399196i | ||||||||
\(873\) | −9291.60 | − | 5446.18i | −0.360221 | − | 0.211140i | ||||
\(874\) | 18638.6i | 0.721351i | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 14759.9 | + | 25759.9i | 0.569283 | + | 0.993546i | ||||
\(877\) | 26294.3 | 1.01242 | 0.506212 | − | 0.862409i | \(-0.331045\pi\) | ||||
0.506212 | + | 0.862409i | \(0.331045\pi\) | |||||||
\(878\) | −7976.54 | −0.306600 | ||||||||
\(879\) | 21258.8 | − | 12180.9i | 0.815745 | − | 0.467406i | ||||
\(880\) | − | 9539.04i | − | 0.365410i | ||||||
\(881\) | −30578.4 | −1.16937 | −0.584684 | − | 0.811261i | \(-0.698781\pi\) | ||||
−0.584684 | + | 0.811261i | \(0.698781\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 15673.3 | 0.597336 | 0.298668 | − | 0.954357i | \(-0.403458\pi\) | ||||
0.298668 | + | 0.954357i | \(0.403458\pi\) | |||||||
\(884\) | − | 42880.1i | − | 1.63147i | ||||||
\(885\) | −4369.49 | + | 2503.63i | −0.165965 | + | 0.0950946i | ||||
\(886\) | 10624.1 | 0.402848 | ||||||||
\(887\) | −28236.5 | −1.06887 | −0.534436 | − | 0.845209i | \(-0.679476\pi\) | ||||
−0.534436 | + | 0.845209i | \(0.679476\pi\) | |||||||
\(888\) | 11448.8 | + | 19981.1i | 0.432654 | + | 0.755093i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | − | 9658.99i | − | 0.363787i | ||||||
\(891\) | 15305.7 | − | 8570.74i | 0.575490 | − | 0.322256i | ||||
\(892\) | 8035.50i | 0.301624i | ||||||||
\(893\) | − | 1443.62i | − | 0.0540972i | ||||||
\(894\) | 7210.34 | − | 4131.38i | 0.269743 | − | 0.154557i | ||||
\(895\) | − | 36025.8i | − | 1.34548i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 41392.2 | − | 23716.9i | 1.54074 | − | 0.882815i | ||||
\(898\) | 19234.1 | 0.714756 | ||||||||
\(899\) | −1528.53 | −0.0567066 | ||||||||
\(900\) | −1915.09 | + | 3267.29i | −0.0709293 | + | 0.121011i | ||||
\(901\) | 23923.5i | 0.884582i | ||||||||
\(902\) | 4212.14 | 0.155487 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −13834.5 | −0.508993 | ||||||||
\(905\) | − | 32154.6i | − | 1.18106i | ||||||
\(906\) | 1114.21 | + | 1944.58i | 0.0408577 | + | 0.0713073i | ||||
\(907\) | 44831.2 | 1.64123 | 0.820615 | − | 0.571482i | \(-0.193631\pi\) | ||||
0.820615 | + | 0.571482i | \(0.193631\pi\) | |||||||
\(908\) | 10402.3 | 0.380191 | ||||||||
\(909\) | −781.702 | + | 1333.64i | −0.0285230 | + | 0.0486625i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 3062.53i | 0.111379i | 0.998448 | + | 0.0556895i | \(0.0177357\pi\) | ||||
−0.998448 | + | 0.0556895i | \(0.982264\pi\) | |||||||
\(912\) | 9566.21 | + | 16695.5i | 0.347334 | + | 0.606189i | ||||
\(913\) | 2341.20i | 0.0848657i | ||||||||
\(914\) | − | 5431.22i | − | 0.196552i | ||||||
\(915\) | 10892.7 | + | 19010.6i | 0.393554 | + | 0.686854i | ||||
\(916\) | − | 18477.2i | − | 0.666488i | ||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 18527.8 | + | 182.522i | 0.666132 | + | 0.00656222i | ||||
\(919\) | 8419.65 | 0.302218 | 0.151109 | − | 0.988517i | \(-0.451715\pi\) | ||||
0.151109 | + | 0.988517i | \(0.451715\pi\) | |||||||
\(920\) | 29723.7 | 1.06517 | ||||||||
\(921\) | 11728.2 | + | 20468.8i | 0.419608 | + | 0.732325i | ||||
\(922\) | − | 8359.99i | − | 0.298613i | ||||||
\(923\) | 52638.8 | 1.87717 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −5761.19 | −0.204786 | ||||||||
\(926\) | − | 1742.76i | − | 0.0618475i | ||||||
\(927\) | −17241.9 | − | 10106.2i | −0.610892 | − | 0.358069i | ||||
\(928\) | −6747.85 | −0.238695 | ||||||||
\(929\) | −35888.4 | −1.26745 | −0.633725 | − | 0.773558i | \(-0.718475\pi\) | ||||
−0.633725 | + | 0.773558i | \(0.718475\pi\) | |||||||
\(930\) | −1819.69 | + | 1042.64i | −0.0641612 | + | 0.0367631i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | − | 11393.0i | − | 0.400418i | ||||||
\(933\) | −23662.2 | + | 13557.9i | −0.830294 | + | 0.475742i | ||||
\(934\) | − | 7272.73i | − | 0.254787i | ||||||
\(935\) | − | 30959.7i | − | 1.08288i | ||||||
\(936\) | −10559.2 | + | 18014.8i | −0.368737 | + | 0.629094i | ||||
\(937\) | − | 1758.68i | − | 0.0613165i | −0.999530 | − | 0.0306583i | \(-0.990240\pi\) | ||
0.999530 | − | 0.0306583i | \(-0.00976035\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −15704.4 | − | 27408.2i | −0.545785 | − | 0.952538i | ||||
\(940\) | −1065.88 | −0.0369842 | ||||||||
\(941\) | 2698.83 | 0.0934957 | 0.0467478 | − | 0.998907i | \(-0.485114\pi\) | ||||
0.0467478 | + | 0.998907i | \(0.485114\pi\) | |||||||
\(942\) | −10344.0 | + | 5926.89i | −0.357775 | + | 0.204998i | ||||
\(943\) | − | 30956.0i | − | 1.06900i | ||||||
\(944\) | −3670.76 | −0.126560 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −10402.8 | −0.357532 | ||||||||
\(947\) | − | 6850.74i | − | 0.235078i | −0.993068 | − | 0.117539i | \(-0.962499\pi\) | ||
0.993068 | − | 0.117539i | \(-0.0375005\pi\) | |||||||
\(948\) | −7976.58 | + | 4570.42i | −0.273278 | + | 0.156583i | ||||
\(949\) | −40952.3 | −1.40081 | ||||||||
\(950\) | 2041.02 | 0.0697046 | ||||||||
\(951\) | 11200.7 | + | 19548.1i | 0.381921 | + | 0.666551i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 24475.9i | − | 0.831953i | −0.909375 | − | 0.415977i | \(-0.863440\pi\) | ||
0.909375 | − | 0.415977i | \(-0.136560\pi\) | |||||||
\(954\) | 2727.52 | − | 4653.35i | 0.0925646 | − | 0.157922i | ||||
\(955\) | − | 45835.1i | − | 1.55308i | ||||||
\(956\) | 13420.9i | 0.454040i | ||||||||
\(957\) | −4414.13 | + | 2529.21i | −0.149100 | + | 0.0854312i | ||||
\(958\) | − | 20399.5i | − | 0.687973i | ||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 6264.78 | − | 3589.59i | 0.210620 | − | 0.120681i | ||||
\(961\) | 28379.7 | 0.952626 | ||||||||
\(962\) | −14706.9 | −0.492899 | ||||||||
\(963\) | −20093.9 | − | 11777.8i | −0.672395 | − | 0.394117i | ||||
\(964\) | 3316.50i | 0.110806i | ||||||||
\(965\) | −53380.4 | −1.78070 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −49080.8 | −1.63220 | −0.816098 | − | 0.577914i | \(-0.803867\pi\) | ||||
−0.816098 | + | 0.577914i | \(0.803867\pi\) | |||||||
\(968\) | − | 11764.0i | − | 0.390608i | ||||||
\(969\) | 31047.9 | + | 54186.7i | 1.02931 | + | 1.79642i | ||||
\(970\) | 4285.54 | 0.141856 | ||||||||
\(971\) | −14730.9 | −0.486855 | −0.243427 | − | 0.969919i | \(-0.578272\pi\) | ||||
−0.243427 | + | 0.969919i | \(0.578272\pi\) | |||||||
\(972\) | 22408.7 | + | 13432.9i | 0.739464 | + | 0.443273i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 10107.0i | 0.332495i | ||||||||
\(975\) | −2597.12 | − | 4532.64i | −0.0853070 | − | 0.148883i | ||||
\(976\) | 15970.6i | 0.523777i | ||||||||
\(977\) | 38879.7i | 1.27315i | 0.771213 | + | 0.636577i | \(0.219650\pi\) | ||||
−0.771213 | + | 0.636577i | \(0.780350\pi\) | |||||||
\(978\) | −4322.24 | − | 7543.43i | −0.141319 | − | 0.246638i | ||||
\(979\) | − | 21633.9i | − | 0.706253i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −8970.99 | + | 15305.2i | −0.291969 | + | 0.498122i | ||||
\(982\) | 470.728 | 0.0152969 | ||||||||
\(983\) | −36156.1 | −1.17314 | −0.586572 | − | 0.809897i | \(-0.699523\pi\) | ||||
−0.586572 | + | 0.809897i | \(0.699523\pi\) | |||||||
\(984\) | 6736.37 | + | 11756.7i | 0.218240 | + | 0.380885i | ||||
\(985\) | − | 4850.10i | − | 0.156890i | ||||||
\(986\) | −5373.52 | −0.173558 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −32585.3 | −1.04927 | ||||||||
\(989\) | 76453.0i | 2.45810i | ||||||||
\(990\) | −3529.71 | + | 6021.96i | −0.113315 | + | 0.193324i | ||||
\(991\) | 15576.7 | 0.499305 | 0.249652 | − | 0.968336i | \(-0.419684\pi\) | ||||
0.249652 | + | 0.968336i | \(0.419684\pi\) | |||||||
\(992\) | −6230.46 | −0.199413 | ||||||||
\(993\) | −28269.1 | + | 16197.6i | −0.903416 | + | 0.517640i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 10794.5i | − | 0.343929i | ||||||
\(996\) | −3025.45 | + | 1733.52i | −0.0962500 | + | 0.0551493i | ||||
\(997\) | 23135.4i | 0.734910i | 0.930041 | + | 0.367455i | \(0.119771\pi\) | ||||
−0.930041 | + | 0.367455i | \(0.880229\pi\) | |||||||
\(998\) | 14553.2i | 0.461597i | ||||||||
\(999\) | −391.512 | + | 39742.5i | −0.0123993 | + | 1.25866i |
(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 | 147.4.c.b.146.9 | ✓ | 24 | |
3.2 | odd | 2 | inner | 147.4.c.b.146.16 | yes | 24 | |
7.2 | even | 3 | 147.4.g.e.80.10 | 48 | |||
7.3 | odd | 6 | 147.4.g.e.68.15 | 48 | |||
7.4 | even | 3 | 147.4.g.e.68.16 | 48 | |||
7.5 | odd | 6 | 147.4.g.e.80.9 | 48 | |||
7.6 | odd | 2 | inner | 147.4.c.b.146.10 | yes | 24 | |
21.2 | odd | 6 | 147.4.g.e.80.15 | 48 | |||
21.5 | even | 6 | 147.4.g.e.80.16 | 48 | |||
21.11 | odd | 6 | 147.4.g.e.68.9 | 48 | |||
21.17 | even | 6 | 147.4.g.e.68.10 | 48 | |||
21.20 | even | 2 | inner | 147.4.c.b.146.15 | yes | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
147.4.c.b.146.9 | ✓ | 24 | 1.1 | even | 1 | trivial | |
147.4.c.b.146.10 | yes | 24 | 7.6 | odd | 2 | inner | |
147.4.c.b.146.15 | yes | 24 | 21.20 | even | 2 | inner | |
147.4.c.b.146.16 | yes | 24 | 3.2 | odd | 2 | inner | |
147.4.g.e.68.9 | 48 | 21.11 | odd | 6 | |||
147.4.g.e.68.10 | 48 | 21.17 | even | 6 | |||
147.4.g.e.68.15 | 48 | 7.3 | odd | 6 | |||
147.4.g.e.68.16 | 48 | 7.4 | even | 3 | |||
147.4.g.e.80.9 | 48 | 7.5 | odd | 6 | |||
147.4.g.e.80.10 | 48 | 7.2 | even | 3 | |||
147.4.g.e.80.15 | 48 | 21.2 | odd | 6 | |||
147.4.g.e.80.16 | 48 | 21.5 | even | 6 |