Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [136,4,Mod(69,136)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(136, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("136.69");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 136 = 2^{3} \cdot 17 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 136.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: | \(8.02425976078\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 69.8 | ||
Character | \(\chi\) | \(=\) | 136.69 |
Dual form | 136.4.c.b.69.7 |
$q$-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 \(\left(\mathbb{Z}/136\mathbb{Z}\right)^\times\).
\(n\) | \(69\) | \(103\) | \(105\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.85990 | + | 2.13091i | −0.657573 | + | 0.753391i | ||||
\(3\) | 3.39972i | 0.654277i | 0.944976 | + | 0.327139i | \(0.106084\pi\) | ||||
−0.944976 | + | 0.327139i | \(0.893916\pi\) | |||||||
\(4\) | −1.08156 | − | 7.92655i | −0.135195 | − | 0.990819i | ||||
\(5\) | 21.1389i | 1.89072i | 0.326030 | + | 0.945359i | \(0.394289\pi\) | ||||
−0.326030 | + | 0.945359i | \(0.605711\pi\) | |||||||
\(6\) | −7.24451 | − | 6.32314i | −0.492926 | − | 0.430235i | ||||
\(7\) | 36.0029 | 1.94397 | 0.971987 | − | 0.235034i | \(-0.0755201\pi\) | ||||
0.971987 | + | 0.235034i | \(0.0755201\pi\) | |||||||
\(8\) | 18.9024 | + | 12.4379i | 0.835374 | + | 0.549681i | ||||
\(9\) | 15.4419 | 0.571921 | ||||||||
\(10\) | −45.0451 | − | 39.3162i | −1.42445 | − | 1.24329i | ||||
\(11\) | 1.32292i | 0.0362614i | 0.999836 | + | 0.0181307i | \(0.00577149\pi\) | ||||
−0.999836 | + | 0.0181307i | \(0.994229\pi\) | |||||||
\(12\) | 26.9481 | − | 3.67701i | 0.648270 | − | 0.0884551i | ||||
\(13\) | 22.9931i | 0.490549i | 0.969454 | + | 0.245274i | \(0.0788781\pi\) | ||||
−0.969454 | + | 0.245274i | \(0.921122\pi\) | |||||||
\(14\) | −66.9617 | + | 76.7190i | −1.27831 | + | 1.46457i | ||||
\(15\) | −71.8664 | −1.23705 | ||||||||
\(16\) | −61.6605 | + | 17.1461i | −0.963445 | + | 0.267908i | ||||
\(17\) | 17.0000 | 0.242536 | ||||||||
\(18\) | −28.7203 | + | 32.9053i | −0.376080 | + | 0.430880i | ||||
\(19\) | − | 50.4607i | − | 0.609288i | −0.952466 | − | 0.304644i | \(-0.901462\pi\) | ||
0.952466 | − | 0.304644i | \(-0.0985375\pi\) | |||||||
\(20\) | 167.558 | − | 22.8630i | 1.87336 | − | 0.255616i | ||||
\(21\) | 122.400i | 1.27190i | ||||||||
\(22\) | −2.81902 | − | 2.46049i | −0.0273190 | − | 0.0238445i | ||||
\(23\) | 44.6733 | 0.405001 | 0.202501 | − | 0.979282i | \(-0.435093\pi\) | ||||
0.202501 | + | 0.979282i | \(0.435093\pi\) | |||||||
\(24\) | −42.2853 | + | 64.2628i | −0.359644 | + | 0.546566i | ||||
\(25\) | −321.852 | −2.57482 | ||||||||
\(26\) | −48.9962 | − | 42.7648i | −0.369575 | − | 0.322572i | ||||
\(27\) | 144.291i | 1.02847i | ||||||||
\(28\) | −38.9393 | − | 285.379i | −0.262816 | − | 1.92613i | ||||
\(29\) | − | 74.4837i | − | 0.476940i | −0.971150 | − | 0.238470i | \(-0.923354\pi\) | ||
0.971150 | − | 0.238470i | \(-0.0766459\pi\) | |||||||
\(30\) | 133.664 | − | 153.141i | 0.813454 | − | 0.931985i | ||||
\(31\) | −160.995 | −0.932759 | −0.466379 | − | 0.884585i | \(-0.654442\pi\) | ||||
−0.466379 | + | 0.884585i | \(0.654442\pi\) | |||||||
\(32\) | 78.1453 | − | 163.283i | 0.431696 | − | 0.902019i | ||||
\(33\) | −4.49756 | −0.0237250 | ||||||||
\(34\) | −31.6183 | + | 36.2255i | −0.159485 | + | 0.182724i | ||||
\(35\) | 761.061i | 3.67551i | ||||||||
\(36\) | −16.7013 | − | 122.401i | −0.0773209 | − | 0.566671i | ||||
\(37\) | − | 371.209i | − | 1.64936i | −0.565599 | − | 0.824681i | \(-0.691355\pi\) | ||
0.565599 | − | 0.824681i | \(-0.308645\pi\) | |||||||
\(38\) | 107.527 | + | 93.8517i | 0.459032 | + | 0.400652i | ||||
\(39\) | −78.1702 | −0.320955 | ||||||||
\(40\) | −262.923 | + | 399.575i | −1.03929 | + | 1.57946i | ||||
\(41\) | −264.139 | −1.00614 | −0.503068 | − | 0.864247i | \(-0.667795\pi\) | ||||
−0.503068 | + | 0.864247i | \(0.667795\pi\) | |||||||
\(42\) | −260.823 | − | 227.651i | −0.958236 | − | 0.836366i | ||||
\(43\) | − | 144.753i | − | 0.513362i | −0.966496 | − | 0.256681i | \(-0.917371\pi\) | ||
0.966496 | − | 0.256681i | \(-0.0826289\pi\) | |||||||
\(44\) | 10.4862 | − | 1.43082i | 0.0359285 | − | 0.00490236i | ||||
\(45\) | 326.424i | 1.08134i | ||||||||
\(46\) | −83.0878 | + | 95.1948i | −0.266318 | + | 0.305124i | ||||
\(47\) | 445.614 | 1.38297 | 0.691484 | − | 0.722392i | \(-0.256957\pi\) | ||||
0.691484 | + | 0.722392i | \(0.256957\pi\) | |||||||
\(48\) | −58.2920 | − | 209.629i | −0.175286 | − | 0.630360i | ||||
\(49\) | 953.209 | 2.77904 | ||||||||
\(50\) | 598.612 | − | 685.838i | 1.69313 | − | 1.93984i | ||||
\(51\) | 57.7953i | 0.158686i | ||||||||
\(52\) | 182.256 | − | 24.8684i | 0.486045 | − | 0.0663198i | ||||
\(53\) | − | 243.350i | − | 0.630693i | −0.948977 | − | 0.315346i | \(-0.897879\pi\) | ||
0.948977 | − | 0.315346i | \(-0.102121\pi\) | |||||||
\(54\) | −307.471 | − | 268.366i | −0.774841 | − | 0.676296i | ||||
\(55\) | −27.9650 | −0.0685601 | ||||||||
\(56\) | 680.540 | + | 447.799i | 1.62395 | + | 1.06857i | ||||
\(57\) | 171.552 | 0.398643 | ||||||||
\(58\) | 158.718 | + | 138.532i | 0.359322 | + | 0.313623i | ||||
\(59\) | 404.638i | 0.892871i | 0.894816 | + | 0.446436i | \(0.147307\pi\) | ||||
−0.894816 | + | 0.446436i | \(0.852693\pi\) | |||||||
\(60\) | 77.7278 | + | 569.652i | 0.167244 | + | 1.22570i | ||||
\(61\) | − | 474.840i | − | 0.996673i | −0.866984 | − | 0.498336i | \(-0.833944\pi\) | ||
0.866984 | − | 0.498336i | \(-0.166056\pi\) | |||||||
\(62\) | 299.434 | − | 343.066i | 0.613357 | − | 0.702732i | ||||
\(63\) | 555.952 | 1.11180 | ||||||||
\(64\) | 202.599 | + | 470.210i | 0.395701 | + | 0.918379i | ||||
\(65\) | −486.048 | −0.927490 | ||||||||
\(66\) | 8.36500 | − | 9.58390i | 0.0156009 | − | 0.0178742i | ||||
\(67\) | 424.323i | 0.773721i | 0.922138 | + | 0.386860i | \(0.126440\pi\) | ||||
−0.922138 | + | 0.386860i | \(0.873560\pi\) | |||||||
\(68\) | −18.3865 | − | 134.751i | −0.0327896 | − | 0.240309i | ||||
\(69\) | 151.877i | 0.264983i | ||||||||
\(70\) | −1621.75 | − | 1415.50i | −2.76909 | − | 2.41692i | ||||
\(71\) | −54.9686 | −0.0918812 | −0.0459406 | − | 0.998944i | \(-0.514629\pi\) | ||||
−0.0459406 | + | 0.998944i | \(0.514629\pi\) | |||||||
\(72\) | 291.888 | + | 192.064i | 0.477768 | + | 0.314374i | ||||
\(73\) | −648.234 | −1.03932 | −0.519658 | − | 0.854375i | \(-0.673940\pi\) | ||||
−0.519658 | + | 0.854375i | \(0.673940\pi\) | |||||||
\(74\) | 791.013 | + | 690.411i | 1.24261 | + | 1.08458i | ||||
\(75\) | − | 1094.21i | − | 1.68464i | ||||||
\(76\) | −399.979 | + | 54.5763i | −0.603694 | + | 0.0823728i | ||||
\(77\) | 47.6289i | 0.0704912i | ||||||||
\(78\) | 145.389 | − | 166.574i | 0.211051 | − | 0.241805i | ||||
\(79\) | −157.149 | −0.223806 | −0.111903 | − | 0.993719i | \(-0.535695\pi\) | ||||
−0.111903 | + | 0.993719i | \(0.535695\pi\) | |||||||
\(80\) | −362.449 | − | 1303.43i | −0.506538 | − | 1.82160i | ||||
\(81\) | −73.6178 | −0.100985 | ||||||||
\(82\) | 491.271 | − | 562.856i | 0.661607 | − | 0.758013i | ||||
\(83\) | − | 523.315i | − | 0.692064i | −0.938223 | − | 0.346032i | \(-0.887529\pi\) | ||
0.938223 | − | 0.346032i | \(-0.112471\pi\) | |||||||
\(84\) | 970.210 | − | 132.383i | 1.26022 | − | 0.171954i | ||||
\(85\) | 359.361i | 0.458567i | ||||||||
\(86\) | 308.455 | + | 269.225i | 0.386762 | + | 0.337573i | ||||
\(87\) | 253.224 | 0.312051 | ||||||||
\(88\) | −16.4543 | + | 25.0063i | −0.0199322 | + | 0.0302918i | ||||
\(89\) | −603.481 | −0.718751 | −0.359376 | − | 0.933193i | \(-0.617010\pi\) | ||||
−0.359376 | + | 0.933193i | \(0.617010\pi\) | |||||||
\(90\) | −695.580 | − | 607.115i | −0.814673 | − | 0.711062i | ||||
\(91\) | 827.818i | 0.953615i | ||||||||
\(92\) | −48.3169 | − | 354.105i | −0.0547542 | − | 0.401283i | ||||
\(93\) | − | 547.338i | − | 0.610283i | ||||||
\(94\) | −828.796 | + | 949.563i | −0.909402 | + | 1.04191i | ||||
\(95\) | 1066.68 | 1.15199 | ||||||||
\(96\) | 555.117 | + | 265.673i | 0.590171 | + | 0.282449i | ||||
\(97\) | −142.748 | −0.149422 | −0.0747108 | − | 0.997205i | \(-0.523803\pi\) | ||||
−0.0747108 | + | 0.997205i | \(0.523803\pi\) | |||||||
\(98\) | −1772.87 | + | 2031.20i | −1.82742 | + | 2.09370i | ||||
\(99\) | 20.4283i | 0.0207387i | ||||||||
\(100\) | 348.103 | + | 2551.18i | 0.348103 | + | 2.55118i | ||||
\(101\) | 850.033i | 0.837440i | 0.908115 | + | 0.418720i | \(0.137521\pi\) | ||||
−0.908115 | + | 0.418720i | \(0.862479\pi\) | |||||||
\(102\) | −123.157 | − | 107.493i | −0.119552 | − | 0.104347i | ||||
\(103\) | 1264.69 | 1.20984 | 0.604920 | − | 0.796287i | \(-0.293205\pi\) | ||||
0.604920 | + | 0.796287i | \(0.293205\pi\) | |||||||
\(104\) | −285.985 | + | 434.624i | −0.269646 | + | 0.409792i | ||||
\(105\) | −2587.40 | −2.40480 | ||||||||
\(106\) | 518.557 | + | 452.606i | 0.475158 | + | 0.414726i | ||||
\(107\) | − | 565.627i | − | 0.511040i | −0.966804 | − | 0.255520i | \(-0.917753\pi\) | ||
0.966804 | − | 0.255520i | \(-0.0822466\pi\) | |||||||
\(108\) | 1143.73 | − | 156.059i | 1.01903 | − | 0.139044i | ||||
\(109\) | − | 1351.13i | − | 1.18730i | −0.804725 | − | 0.593648i | \(-0.797687\pi\) | ||
0.804725 | − | 0.593648i | \(-0.202313\pi\) | |||||||
\(110\) | 52.0121 | − | 59.5910i | 0.0450833 | − | 0.0516525i | ||||
\(111\) | 1262.01 | 1.07914 | ||||||||
\(112\) | −2219.96 | + | 617.309i | −1.87291 | + | 0.520806i | ||||
\(113\) | −454.029 | −0.377978 | −0.188989 | − | 0.981979i | \(-0.560521\pi\) | ||||
−0.188989 | + | 0.981979i | \(0.560521\pi\) | |||||||
\(114\) | −319.070 | + | 365.563i | −0.262137 | + | 0.300334i | ||||
\(115\) | 944.344i | 0.765743i | ||||||||
\(116\) | −590.399 | + | 80.5586i | −0.472562 | + | 0.0644800i | ||||
\(117\) | 355.056i | 0.280555i | ||||||||
\(118\) | −862.248 | − | 752.586i | −0.672681 | − | 0.587128i | ||||
\(119\) | 612.049 | 0.471483 | ||||||||
\(120\) | −1358.44 | − | 893.864i | −1.03340 | − | 0.679986i | ||||
\(121\) | 1329.25 | 0.998685 | ||||||||
\(122\) | 1011.84 | + | 883.154i | 0.750884 | + | 0.655385i | ||||
\(123\) | − | 897.999i | − | 0.658291i | ||||||
\(124\) | 174.126 | + | 1276.13i | 0.126104 | + | 0.924195i | ||||
\(125\) | − | 4161.23i | − | 2.97754i | ||||||
\(126\) | −1034.01 | + | 1184.68i | −0.731090 | + | 0.837620i | ||||
\(127\) | −2229.88 | −1.55803 | −0.779015 | − | 0.627005i | \(-0.784281\pi\) | ||||
−0.779015 | + | 0.627005i | \(0.784281\pi\) | |||||||
\(128\) | −1378.79 | − | 442.823i | −0.952101 | − | 0.305784i | ||||
\(129\) | 492.119 | 0.335881 | ||||||||
\(130\) | 904.000 | − | 1035.73i | 0.609893 | − | 0.698762i | ||||
\(131\) | 1673.41i | 1.11608i | 0.829815 | + | 0.558039i | \(0.188446\pi\) | ||||
−0.829815 | + | 0.558039i | \(0.811554\pi\) | |||||||
\(132\) | 4.86438 | + | 35.6501i | 0.00320750 | + | 0.0235072i | ||||
\(133\) | − | 1816.73i | − | 1.18444i | ||||||
\(134\) | −904.194 | − | 789.197i | −0.582914 | − | 0.508778i | ||||
\(135\) | −3050.14 | −1.94455 | ||||||||
\(136\) | 321.340 | + | 211.444i | 0.202608 | + | 0.133317i | ||||
\(137\) | −1174.82 | −0.732642 | −0.366321 | − | 0.930489i | \(-0.619383\pi\) | ||||
−0.366321 | + | 0.930489i | \(0.619383\pi\) | |||||||
\(138\) | −323.636 | − | 282.476i | −0.199636 | − | 0.174246i | ||||
\(139\) | − | 1715.44i | − | 1.04677i | −0.852096 | − | 0.523386i | \(-0.824669\pi\) | ||
0.852096 | − | 0.523386i | \(-0.175331\pi\) | |||||||
\(140\) | 6032.59 | − | 823.134i | 3.64176 | − | 0.496911i | ||||
\(141\) | 1514.96i | 0.904844i | ||||||||
\(142\) | 102.236 | − | 117.133i | 0.0604186 | − | 0.0692225i | ||||
\(143\) | −30.4180 | −0.0177880 | ||||||||
\(144\) | −952.153 | + | 264.768i | −0.551014 | + | 0.153222i | ||||
\(145\) | 1574.50 | 0.901760 | ||||||||
\(146\) | 1205.65 | − | 1381.33i | 0.683426 | − | 0.783010i | ||||
\(147\) | 3240.65i | 1.81826i | ||||||||
\(148\) | −2942.41 | + | 401.485i | −1.63422 | + | 0.222986i | ||||
\(149\) | − | 339.712i | − | 0.186781i | −0.995630 | − | 0.0933903i | \(-0.970230\pi\) | ||
0.995630 | − | 0.0933903i | \(-0.0297704\pi\) | |||||||
\(150\) | 2331.66 | + | 2035.12i | 1.26920 | + | 1.10778i | ||||
\(151\) | 430.149 | 0.231821 | 0.115911 | − | 0.993260i | \(-0.463021\pi\) | ||||
0.115911 | + | 0.993260i | \(0.463021\pi\) | |||||||
\(152\) | 627.623 | − | 953.826i | 0.334914 | − | 0.508984i | ||||
\(153\) | 262.512 | 0.138711 | ||||||||
\(154\) | −101.493 | − | 88.5849i | −0.0531074 | − | 0.0463531i | ||||
\(155\) | − | 3403.25i | − | 1.76358i | ||||||
\(156\) | 84.5458 | + | 619.620i | 0.0433915 | + | 0.318008i | ||||
\(157\) | 3283.54i | 1.66914i | 0.550903 | + | 0.834569i | \(0.314283\pi\) | ||||
−0.550903 | + | 0.834569i | \(0.685717\pi\) | |||||||
\(158\) | 292.281 | − | 334.871i | 0.147169 | − | 0.168613i | ||||
\(159\) | 827.323 | 0.412648 | ||||||||
\(160\) | 3451.62 | + | 1651.91i | 1.70546 | + | 0.816216i | ||||
\(161\) | 1608.37 | 0.787312 | ||||||||
\(162\) | 136.922 | − | 156.873i | 0.0664048 | − | 0.0760809i | ||||
\(163\) | 2209.15i | 1.06156i | 0.847511 | + | 0.530778i | \(0.178100\pi\) | ||||
−0.847511 | + | 0.530778i | \(0.821900\pi\) | |||||||
\(164\) | 285.682 | + | 2093.71i | 0.136025 | + | 0.996898i | ||||
\(165\) | − | 95.0734i | − | 0.0448573i | ||||||
\(166\) | 1115.14 | + | 973.313i | 0.521395 | + | 0.455083i | ||||
\(167\) | 1939.29 | 0.898604 | 0.449302 | − | 0.893380i | \(-0.351673\pi\) | ||||
0.449302 | + | 0.893380i | \(0.351673\pi\) | |||||||
\(168\) | −1522.39 | + | 2313.65i | −0.699139 | + | 1.06251i | ||||
\(169\) | 1668.32 | 0.759362 | ||||||||
\(170\) | −765.766 | − | 668.375i | −0.345480 | − | 0.301541i | ||||
\(171\) | − | 779.208i | − | 0.348465i | ||||||
\(172\) | −1147.39 | + | 156.559i | −0.508649 | + | 0.0694040i | ||||
\(173\) | − | 1119.29i | − | 0.491895i | −0.969283 | − | 0.245947i | \(-0.920901\pi\) | ||
0.969283 | − | 0.245947i | \(-0.0790990\pi\) | |||||||
\(174\) | −470.971 | + | 539.598i | −0.205197 | + | 0.235097i | ||||
\(175\) | −11587.6 | −5.00538 | ||||||||
\(176\) | −22.6829 | − | 81.5718i | −0.00971470 | − | 0.0349358i | ||||
\(177\) | −1375.66 | −0.584185 | ||||||||
\(178\) | 1122.41 | − | 1285.96i | 0.472632 | − | 0.541500i | ||||
\(179\) | − | 1139.87i | − | 0.475964i | −0.971270 | − | 0.237982i | \(-0.923514\pi\) | ||
0.971270 | − | 0.237982i | \(-0.0764859\pi\) | |||||||
\(180\) | 2587.42 | − | 353.047i | 1.07141 | − | 0.146192i | ||||
\(181\) | − | 1793.25i | − | 0.736414i | −0.929744 | − | 0.368207i | \(-0.879972\pi\) | ||
0.929744 | − | 0.368207i | \(-0.120028\pi\) | |||||||
\(182\) | −1764.01 | − | 1539.66i | −0.718444 | − | 0.627071i | ||||
\(183\) | 1614.33 | 0.652100 | ||||||||
\(184\) | 844.431 | + | 555.641i | 0.338328 | + | 0.222622i | ||||
\(185\) | 7846.94 | 3.11848 | ||||||||
\(186\) | 1166.33 | + | 1017.99i | 0.459781 | + | 0.401306i | ||||
\(187\) | 22.4896i | 0.00879467i | ||||||||
\(188\) | −481.958 | − | 3532.18i | −0.186970 | − | 1.37027i | ||||
\(189\) | 5194.88i | 1.99932i | ||||||||
\(190\) | −1983.92 | + | 2273.00i | −0.757519 | + | 0.867901i | ||||
\(191\) | 3846.25 | 1.45709 | 0.728547 | − | 0.684996i | \(-0.240196\pi\) | ||||
0.728547 | + | 0.684996i | \(0.240196\pi\) | |||||||
\(192\) | −1598.59 | + | 688.780i | −0.600875 | + | 0.258898i | ||||
\(193\) | 1572.91 | 0.586635 | 0.293317 | − | 0.956015i | \(-0.405241\pi\) | ||||
0.293317 | + | 0.956015i | \(0.405241\pi\) | |||||||
\(194\) | 265.497 | − | 304.184i | 0.0982557 | − | 0.112573i | ||||
\(195\) | − | 1652.43i | − | 0.606836i | ||||||
\(196\) | −1030.95 | − | 7555.66i | −0.375712 | − | 2.75352i | ||||
\(197\) | 1503.79i | 0.543859i | 0.962317 | + | 0.271930i | \(0.0876618\pi\) | ||||
−0.962317 | + | 0.271930i | \(0.912338\pi\) | |||||||
\(198\) | −43.5310 | − | 37.9946i | −0.0156243 | − | 0.0136372i | ||||
\(199\) | 1541.82 | 0.549230 | 0.274615 | − | 0.961554i | \(-0.411450\pi\) | ||||
0.274615 | + | 0.961554i | \(0.411450\pi\) | |||||||
\(200\) | −6083.77 | − | 4003.15i | −2.15094 | − | 1.41533i | ||||
\(201\) | −1442.58 | −0.506228 | ||||||||
\(202\) | −1811.34 | − | 1580.97i | −0.630920 | − | 0.550678i | ||||
\(203\) | − | 2681.63i | − | 0.927160i | ||||||
\(204\) | 458.118 | − | 62.5091i | 0.157229 | − | 0.0214535i | ||||
\(205\) | − | 5583.60i | − | 1.90232i | ||||||
\(206\) | −2352.19 | + | 2694.94i | −0.795558 | + | 0.911482i | ||||
\(207\) | 689.840 | 0.231629 | ||||||||
\(208\) | −394.242 | − | 1417.76i | −0.131422 | − | 0.472617i | ||||
\(209\) | 66.7554 | 0.0220936 | ||||||||
\(210\) | 4812.30 | − | 5513.51i | 1.58133 | − | 1.81176i | ||||
\(211\) | − | 2123.21i | − | 0.692740i | −0.938098 | − | 0.346370i | \(-0.887414\pi\) | ||
0.938098 | − | 0.346370i | \(-0.112586\pi\) | |||||||
\(212\) | −1928.93 | + | 263.198i | −0.624902 | + | 0.0852665i | ||||
\(213\) | − | 186.878i | − | 0.0601158i | ||||||
\(214\) | 1205.30 | + | 1052.01i | 0.385013 | + | 0.336046i | ||||
\(215\) | 3059.91 | 0.970623 | ||||||||
\(216\) | −1794.67 | + | 2727.44i | −0.565332 | + | 0.859160i | ||||
\(217\) | −5796.28 | −1.81326 | ||||||||
\(218\) | 2879.15 | + | 2512.97i | 0.894497 | + | 0.780734i | ||||
\(219\) | − | 2203.82i | − | 0.680000i | ||||||
\(220\) | 30.2459 | + | 221.666i | 0.00926898 | + | 0.0679306i | ||||
\(221\) | 390.883i | 0.118976i | ||||||||
\(222\) | −2347.21 | + | 2689.23i | −0.709613 | + | 0.813014i | ||||
\(223\) | 5201.04 | 1.56183 | 0.780914 | − | 0.624638i | \(-0.214754\pi\) | ||||
0.780914 | + | 0.624638i | \(0.214754\pi\) | |||||||
\(224\) | 2813.46 | − | 5878.66i | 0.839206 | − | 1.75350i | ||||
\(225\) | −4970.00 | −1.47259 | ||||||||
\(226\) | 844.448 | − | 967.496i | 0.248548 | − | 0.284765i | ||||
\(227\) | 3554.85i | 1.03940i | 0.854349 | + | 0.519699i | \(0.173956\pi\) | ||||
−0.854349 | + | 0.519699i | \(0.826044\pi\) | |||||||
\(228\) | −185.544 | − | 1359.82i | −0.0538946 | − | 0.394983i | ||||
\(229\) | 3915.44i | 1.12987i | 0.825136 | + | 0.564934i | \(0.191098\pi\) | ||||
−0.825136 | + | 0.564934i | \(0.808902\pi\) | |||||||
\(230\) | −2012.31 | − | 1756.38i | −0.576904 | − | 0.503532i | ||||
\(231\) | −161.925 | −0.0461208 | ||||||||
\(232\) | 926.418 | − | 1407.92i | 0.262165 | − | 0.398424i | ||||
\(233\) | 1060.07 | 0.298059 | 0.149029 | − | 0.988833i | \(-0.452385\pi\) | ||||
0.149029 | + | 0.988833i | \(0.452385\pi\) | |||||||
\(234\) | −756.594 | − | 660.369i | −0.211368 | − | 0.184486i | ||||
\(235\) | 9419.78i | 2.61480i | ||||||||
\(236\) | 3207.39 | − | 437.641i | 0.884674 | − | 0.120712i | ||||
\(237\) | − | 534.263i | − | 0.146431i | ||||||
\(238\) | −1138.35 | + | 1304.22i | −0.310035 | + | 0.355211i | ||||
\(239\) | −4204.93 | −1.13805 | −0.569026 | − | 0.822320i | \(-0.692680\pi\) | ||||
−0.569026 | + | 0.822320i | \(0.692680\pi\) | |||||||
\(240\) | 4431.31 | − | 1232.23i | 1.19183 | − | 0.331416i | ||||
\(241\) | −371.702 | −0.0993503 | −0.0496752 | − | 0.998765i | \(-0.515819\pi\) | ||||
−0.0496752 | + | 0.998765i | \(0.515819\pi\) | |||||||
\(242\) | −2472.27 | + | 2832.51i | −0.656709 | + | 0.752400i | ||||
\(243\) | 3645.57i | 0.962400i | ||||||||
\(244\) | −3763.84 | + | 513.568i | −0.987522 | + | 0.134745i | ||||
\(245\) | 20149.8i | 5.25438i | ||||||||
\(246\) | 1913.56 | + | 1670.19i | 0.495951 | + | 0.432875i | ||||
\(247\) | 1160.25 | 0.298886 | ||||||||
\(248\) | −3043.18 | − | 2002.43i | −0.779203 | − | 0.512720i | ||||
\(249\) | 1779.13 | 0.452802 | ||||||||
\(250\) | 8867.22 | + | 7739.47i | 2.24325 | + | 1.95795i | ||||
\(251\) | 24.8057i | 0.00623793i | 0.999995 | + | 0.00311896i | \(0.000992799\pi\) | ||||
−0.999995 | + | 0.00311896i | \(0.999007\pi\) | |||||||
\(252\) | −601.296 | − | 4406.79i | −0.150310 | − | 1.10159i | ||||
\(253\) | 59.0992i | 0.0146859i | ||||||||
\(254\) | 4147.35 | − | 4751.68i | 1.02452 | − | 1.17381i | ||||
\(255\) | −1221.73 | −0.300030 | ||||||||
\(256\) | 3508.02 | − | 2114.47i | 0.856451 | − | 0.516228i | ||||
\(257\) | −2671.29 | −0.648368 | −0.324184 | − | 0.945994i | \(-0.605090\pi\) | ||||
−0.324184 | + | 0.945994i | \(0.605090\pi\) | |||||||
\(258\) | −915.291 | + | 1048.66i | −0.220866 | + | 0.253050i | ||||
\(259\) | − | 13364.6i | − | 3.20632i | ||||||
\(260\) | 525.691 | + | 3852.69i | 0.125392 | + | 0.918975i | ||||
\(261\) | − | 1150.17i | − | 0.272772i | ||||||
\(262\) | −3565.88 | − | 3112.37i | −0.840843 | − | 0.733903i | ||||
\(263\) | −6352.11 | −1.48931 | −0.744654 | − | 0.667450i | \(-0.767386\pi\) | ||||
−0.744654 | + | 0.667450i | \(0.767386\pi\) | |||||||
\(264\) | −85.0145 | − | 55.9400i | −0.0198192 | − | 0.0130412i | ||||
\(265\) | 5144.15 | 1.19246 | ||||||||
\(266\) | 3871.29 | + | 3378.93i | 0.892347 | + | 0.778856i | ||||
\(267\) | − | 2051.67i | − | 0.470263i | ||||||
\(268\) | 3363.42 | − | 458.931i | 0.766617 | − | 0.104603i | ||||
\(269\) | 2258.87i | 0.511991i | 0.966678 | + | 0.255995i | \(0.0824032\pi\) | ||||
−0.966678 | + | 0.255995i | \(0.917597\pi\) | |||||||
\(270\) | 5672.95 | − | 6499.58i | 1.27869 | − | 1.46501i | ||||
\(271\) | 4013.00 | 0.899530 | 0.449765 | − | 0.893147i | \(-0.351508\pi\) | ||||
0.449765 | + | 0.893147i | \(0.351508\pi\) | |||||||
\(272\) | −1048.23 | + | 291.484i | −0.233670 | + | 0.0649772i | ||||
\(273\) | −2814.35 | −0.623928 | ||||||||
\(274\) | 2185.05 | − | 2503.44i | 0.481766 | − | 0.551966i | ||||
\(275\) | − | 425.784i | − | 0.0933664i | ||||||
\(276\) | 1203.86 | − | 164.264i | 0.262550 | − | 0.0358244i | ||||
\(277\) | − | 3812.62i | − | 0.826997i | −0.910505 | − | 0.413498i | \(-0.864307\pi\) | ||
0.910505 | − | 0.413498i | \(-0.135693\pi\) | |||||||
\(278\) | 3655.44 | + | 3190.53i | 0.788628 | + | 0.688329i | ||||
\(279\) | −2486.06 | −0.533465 | ||||||||
\(280\) | −9465.98 | + | 14385.9i | −2.02036 | + | 3.07043i | ||||
\(281\) | −2293.65 | −0.486931 | −0.243466 | − | 0.969909i | \(-0.578284\pi\) | ||||
−0.243466 | + | 0.969909i | \(0.578284\pi\) | |||||||
\(282\) | −3228.25 | − | 2817.68i | −0.681701 | − | 0.595001i | ||||
\(283\) | − | 3018.72i | − | 0.634079i | −0.948412 | − | 0.317039i | \(-0.897311\pi\) | ||
0.948412 | − | 0.317039i | \(-0.102689\pi\) | |||||||
\(284\) | 59.4518 | + | 435.711i | 0.0124219 | + | 0.0910377i | ||||
\(285\) | 3626.43i | 0.753723i | ||||||||
\(286\) | 56.5744 | − | 64.8180i | 0.0116969 | − | 0.0134013i | ||||
\(287\) | −9509.76 | −1.95590 | ||||||||
\(288\) | 1206.71 | − | 2521.39i | 0.246896 | − | 0.515884i | ||||
\(289\) | 289.000 | 0.0588235 | ||||||||
\(290\) | −2928.41 | + | 3355.12i | −0.592973 | + | 0.679378i | ||||
\(291\) | − | 485.305i | − | 0.0977632i | ||||||
\(292\) | 701.104 | + | 5138.26i | 0.140510 | + | 1.02977i | ||||
\(293\) | − | 2099.19i | − | 0.418552i | −0.977857 | − | 0.209276i | \(-0.932889\pi\) | ||
0.977857 | − | 0.209276i | \(-0.0671108\pi\) | |||||||
\(294\) | −6905.53 | − | 6027.28i | −1.36986 | − | 1.19564i | ||||
\(295\) | −8553.60 | −1.68817 | ||||||||
\(296\) | 4617.05 | − | 7016.73i | 0.906623 | − | 1.37783i | ||||
\(297\) | −190.885 | −0.0372938 | ||||||||
\(298\) | 723.896 | + | 631.830i | 0.140719 | + | 0.122822i | ||||
\(299\) | 1027.18i | 0.198673i | ||||||||
\(300\) | −8673.30 | + | 1183.45i | −1.66918 | + | 0.227756i | ||||
\(301\) | − | 5211.51i | − | 0.997962i | ||||||
\(302\) | −800.033 | + | 916.609i | −0.152440 | + | 0.174652i | ||||
\(303\) | −2889.88 | −0.547918 | ||||||||
\(304\) | 865.204 | + | 3111.43i | 0.163233 | + | 0.587015i | ||||
\(305\) | 10037.6 | 1.88443 | ||||||||
\(306\) | −488.245 | + | 559.389i | −0.0912128 | + | 0.104504i | ||||
\(307\) | − | 2231.40i | − | 0.414829i | −0.978253 | − | 0.207415i | \(-0.933495\pi\) | ||
0.978253 | − | 0.207415i | \(-0.0665049\pi\) | |||||||
\(308\) | 377.533 | − | 51.5136i | 0.0698440 | − | 0.00953006i | ||||
\(309\) | 4299.59i | 0.791570i | ||||||||
\(310\) | 7252.02 | + | 6329.70i | 1.32867 | + | 1.15969i | ||||
\(311\) | 1662.17 | 0.303064 | 0.151532 | − | 0.988452i | \(-0.451579\pi\) | ||||
0.151532 | + | 0.988452i | \(0.451579\pi\) | |||||||
\(312\) | −1477.60 | − | 972.270i | −0.268118 | − | 0.176423i | ||||
\(313\) | −815.145 | −0.147204 | −0.0736018 | − | 0.997288i | \(-0.523449\pi\) | ||||
−0.0736018 | + | 0.997288i | \(0.523449\pi\) | |||||||
\(314\) | −6996.92 | − | 6107.04i | −1.25751 | − | 1.09758i | ||||
\(315\) | 11752.2i | 2.10210i | ||||||||
\(316\) | 169.966 | + | 1245.65i | 0.0302574 | + | 0.221751i | ||||
\(317\) | 5671.98i | 1.00495i | 0.864591 | + | 0.502477i | \(0.167578\pi\) | ||||
−0.864591 | + | 0.502477i | \(0.832422\pi\) | |||||||
\(318\) | −1538.74 | + | 1762.95i | −0.271346 | + | 0.310885i | ||||
\(319\) | 98.5359 | 0.0172945 | ||||||||
\(320\) | −9939.72 | + | 4282.71i | −1.73640 | + | 0.748159i | ||||
\(321\) | 1922.98 | 0.334362 | ||||||||
\(322\) | −2991.40 | + | 3427.29i | −0.517715 | + | 0.593153i | ||||
\(323\) | − | 857.832i | − | 0.147774i | ||||||
\(324\) | 79.6222 | + | 583.536i | 0.0136526 | + | 0.100058i | ||||
\(325\) | − | 7400.38i | − | 1.26307i | ||||||
\(326\) | −4707.50 | − | 4108.79i | −0.799767 | − | 0.698051i | ||||
\(327\) | 4593.48 | 0.776820 | ||||||||
\(328\) | −4992.85 | − | 3285.32i | −0.840500 | − | 0.553054i | ||||
\(329\) | 16043.4 | 2.68845 | ||||||||
\(330\) | 202.593 | + | 176.827i | 0.0337951 | + | 0.0294969i | ||||
\(331\) | 626.406i | 0.104019i | 0.998647 | + | 0.0520096i | \(0.0165627\pi\) | ||||
−0.998647 | + | 0.0520096i | \(0.983437\pi\) | |||||||
\(332\) | −4148.09 | + | 565.997i | −0.685710 | + | 0.0935637i | ||||
\(333\) | − | 5732.16i | − | 0.943305i | ||||||
\(334\) | −3606.88 | + | 4132.46i | −0.590898 | + | 0.677000i | ||||
\(335\) | −8969.71 | −1.46289 | ||||||||
\(336\) | −2098.68 | − | 7547.24i | −0.340751 | − | 1.22540i | ||||
\(337\) | −8153.84 | −1.31801 | −0.659003 | − | 0.752140i | \(-0.729022\pi\) | ||||
−0.659003 | + | 0.752140i | \(0.729022\pi\) | |||||||
\(338\) | −3102.90 | + | 3555.04i | −0.499336 | + | 0.572096i | ||||
\(339\) | − | 1543.57i | − | 0.247302i | ||||||
\(340\) | 2848.49 | − | 388.671i | 0.454357 | − | 0.0619960i | ||||
\(341\) | − | 212.983i | − | 0.0338231i | ||||||
\(342\) | 1660.42 | + | 1449.25i | 0.262530 | + | 0.229141i | ||||
\(343\) | 21969.3 | 3.45840 | ||||||||
\(344\) | 1800.41 | − | 2736.17i | 0.282185 | − | 0.428849i | ||||
\(345\) | −3210.51 | −0.501008 | ||||||||
\(346\) | 2385.10 | + | 2081.76i | 0.370589 | + | 0.323457i | ||||
\(347\) | − | 1514.80i | − | 0.234348i | −0.993111 | − | 0.117174i | \(-0.962617\pi\) | ||
0.993111 | − | 0.117174i | \(-0.0373835\pi\) | |||||||
\(348\) | −273.877 | − | 2007.19i | −0.0421878 | − | 0.309186i | ||||
\(349\) | 10015.4i | 1.53614i | 0.640364 | + | 0.768072i | \(0.278784\pi\) | ||||
−0.640364 | + | 0.768072i | \(0.721216\pi\) | |||||||
\(350\) | 21551.8 | − | 24692.2i | 3.29140 | − | 3.77101i | ||||
\(351\) | −3317.69 | −0.504516 | ||||||||
\(352\) | 216.010 | + | 103.380i | 0.0327084 | + | 0.0156539i | ||||
\(353\) | 399.079 | 0.0601723 | 0.0300862 | − | 0.999547i | \(-0.490422\pi\) | ||||
0.0300862 | + | 0.999547i | \(0.490422\pi\) | |||||||
\(354\) | 2558.58 | − | 2931.40i | 0.384145 | − | 0.440120i | ||||
\(355\) | − | 1161.97i | − | 0.173722i | ||||||
\(356\) | 652.701 | + | 4783.52i | 0.0971716 | + | 0.712152i | ||||
\(357\) | 2080.80i | 0.308481i | ||||||||
\(358\) | 2428.95 | + | 2120.03i | 0.358587 | + | 0.312981i | ||||
\(359\) | −4123.65 | −0.606234 | −0.303117 | − | 0.952953i | \(-0.598027\pi\) | ||||
−0.303117 | + | 0.952953i | \(0.598027\pi\) | |||||||
\(360\) | −4060.02 | + | 6170.18i | −0.594394 | + | 0.903326i | ||||
\(361\) | 4312.72 | 0.628768 | ||||||||
\(362\) | 3821.25 | + | 3335.25i | 0.554808 | + | 0.484246i | ||||
\(363\) | 4519.08i | 0.653417i | ||||||||
\(364\) | 6561.74 | − | 895.336i | 0.944859 | − | 0.128924i | ||||
\(365\) | − | 13702.9i | − | 1.96505i | ||||||
\(366\) | −3002.48 | + | 3439.98i | −0.428804 | + | 0.491286i | ||||
\(367\) | −6635.21 | −0.943747 | −0.471873 | − | 0.881666i | \(-0.656422\pi\) | ||||
−0.471873 | + | 0.881666i | \(0.656422\pi\) | |||||||
\(368\) | −2754.58 | + | 765.973i | −0.390196 | + | 0.108503i | ||||
\(369\) | −4078.80 | −0.575430 | ||||||||
\(370\) | −14594.5 | + | 16721.1i | −2.05063 | + | 2.34943i | ||||
\(371\) | − | 8761.31i | − | 1.22605i | ||||||
\(372\) | −4338.50 | + | 591.979i | −0.604680 | + | 0.0825072i | ||||
\(373\) | − | 12174.1i | − | 1.68995i | −0.534804 | − | 0.844976i | \(-0.679615\pi\) | ||
0.534804 | − | 0.844976i | \(-0.320385\pi\) | |||||||
\(374\) | −47.9234 | − | 41.8284i | −0.00662583 | − | 0.00578314i | ||||
\(375\) | 14147.1 | 1.94813 | ||||||||
\(376\) | 8423.16 | + | 5542.49i | 1.15530 | + | 0.760191i | ||||
\(377\) | 1712.61 | 0.233963 | ||||||||
\(378\) | −11069.8 | − | 9661.95i | −1.50627 | − | 1.31470i | ||||
\(379\) | 11223.2i | 1.52110i | 0.649277 | + | 0.760552i | \(0.275071\pi\) | ||||
−0.649277 | + | 0.760552i | \(0.724929\pi\) | |||||||
\(380\) | −1153.68 | − | 8455.11i | −0.155744 | − | 1.14142i | ||||
\(381\) | − | 7580.98i | − | 1.01938i | ||||||
\(382\) | −7153.64 | + | 8196.02i | −0.958146 | + | 1.09776i | ||||
\(383\) | −736.925 | −0.0983162 | −0.0491581 | − | 0.998791i | \(-0.515654\pi\) | ||||
−0.0491581 | + | 0.998791i | \(0.515654\pi\) | |||||||
\(384\) | 1505.48 | − | 4687.50i | 0.200068 | − | 0.622938i | ||||
\(385\) | −1006.82 | −0.133279 | ||||||||
\(386\) | −2925.45 | + | 3351.73i | −0.385755 | + | 0.441965i | ||||
\(387\) | − | 2235.25i | − | 0.293603i | ||||||
\(388\) | 154.391 | + | 1131.50i | 0.0202011 | + | 0.148050i | ||||
\(389\) | − | 12516.4i | − | 1.63138i | −0.578487 | − | 0.815691i | \(-0.696357\pi\) | ||
0.578487 | − | 0.815691i | \(-0.303643\pi\) | |||||||
\(390\) | 3521.18 | + | 3073.35i | 0.457184 | + | 0.399039i | ||||
\(391\) | 759.446 | 0.0982272 | ||||||||
\(392\) | 18017.9 | + | 11855.9i | 2.32154 | + | 1.52758i | ||||
\(393\) | −5689.12 | −0.730225 | ||||||||
\(394\) | −3204.43 | − | 2796.89i | −0.409739 | − | 0.357627i | ||||
\(395\) | − | 3321.95i | − | 0.423154i | ||||||
\(396\) | 161.926 | − | 22.0945i | 0.0205482 | − | 0.00280376i | ||||
\(397\) | − | 6952.37i | − | 0.878916i | −0.898263 | − | 0.439458i | \(-0.855171\pi\) | ||
0.898263 | − | 0.439458i | \(-0.144829\pi\) | |||||||
\(398\) | −2867.63 | + | 3285.48i | −0.361159 | + | 0.413785i | ||||
\(399\) | 6176.39 | 0.774953 | ||||||||
\(400\) | 19845.6 | − | 5518.51i | 2.48069 | − | 0.689813i | ||||
\(401\) | −14778.4 | −1.84040 | −0.920198 | − | 0.391454i | \(-0.871972\pi\) | ||||
−0.920198 | + | 0.391454i | \(0.871972\pi\) | |||||||
\(402\) | 2683.05 | − | 3074.01i | 0.332882 | − | 0.381387i | ||||
\(403\) | − | 3701.77i | − | 0.457564i | ||||||
\(404\) | 6737.83 | − | 919.362i | 0.829752 | − | 0.113218i | ||||
\(405\) | − | 1556.20i | − | 0.190934i | ||||||
\(406\) | 5714.31 | + | 4987.56i | 0.698514 | + | 0.609676i | ||||
\(407\) | 491.079 | 0.0598081 | ||||||||
\(408\) | −718.850 | + | 1092.47i | −0.0872265 | + | 0.132562i | ||||
\(409\) | −1871.27 | −0.226231 | −0.113115 | − | 0.993582i | \(-0.536083\pi\) | ||||
−0.113115 | + | 0.993582i | \(0.536083\pi\) | |||||||
\(410\) | 11898.1 | + | 10384.9i | 1.43319 | + | 1.25091i | ||||
\(411\) | − | 3994.08i | − | 0.479351i | ||||||
\(412\) | −1367.84 | − | 10024.6i | −0.163564 | − | 1.19873i | ||||
\(413\) | 14568.2i | 1.73572i | ||||||||
\(414\) | −1283.03 | + | 1469.99i | −0.152313 | + | 0.174507i | ||||
\(415\) | 11062.3 | 1.30850 | ||||||||
\(416\) | 3754.38 | + | 1796.80i | 0.442485 | + | 0.211768i | ||||
\(417\) | 5832.01 | 0.684879 | ||||||||
\(418\) | −124.158 | + | 142.250i | −0.0145282 | + | 0.0166451i | ||||
\(419\) | − | 1709.40i | − | 0.199308i | −0.995022 | − | 0.0996538i | \(-0.968226\pi\) | ||
0.995022 | − | 0.0996538i | \(-0.0317735\pi\) | |||||||
\(420\) | 2798.43 | + | 20509.1i | 0.325117 | + | 2.38272i | ||||
\(421\) | 3736.71i | 0.432580i | 0.976329 | + | 0.216290i | \(0.0693956\pi\) | ||||
−0.976329 | + | 0.216290i | \(0.930604\pi\) | |||||||
\(422\) | 4524.38 | + | 3948.96i | 0.521904 | + | 0.455527i | ||||
\(423\) | 6881.11 | 0.790948 | ||||||||
\(424\) | 3026.76 | − | 4599.89i | 0.346680 | − | 0.526864i | ||||
\(425\) | −5471.49 | −0.624485 | ||||||||
\(426\) | 398.220 | + | 347.574i | 0.0452907 | + | 0.0395305i | ||||
\(427\) | − | 17095.6i | − | 1.93751i | ||||||
\(428\) | −4483.47 | + | 611.760i | −0.506348 | + | 0.0690901i | ||||
\(429\) | − | 103.413i | − | 0.0116383i | ||||||
\(430\) | −5691.11 | + | 6520.39i | −0.638256 | + | 0.731258i | ||||
\(431\) | −1214.16 | −0.135694 | −0.0678468 | − | 0.997696i | \(-0.521613\pi\) | ||||
−0.0678468 | + | 0.997696i | \(0.521613\pi\) | |||||||
\(432\) | −2474.02 | − | 8897.03i | −0.275536 | − | 0.990876i | ||||
\(433\) | 4290.25 | 0.476158 | 0.238079 | − | 0.971246i | \(-0.423482\pi\) | ||||
0.238079 | + | 0.971246i | \(0.423482\pi\) | |||||||
\(434\) | 10780.5 | − | 12351.4i | 1.19235 | − | 1.36609i | ||||
\(435\) | 5352.87i | 0.590001i | ||||||||
\(436\) | −10709.8 | + | 1461.33i | −1.17639 | + | 0.160517i | ||||
\(437\) | − | 2254.25i | − | 0.246762i | ||||||
\(438\) | 4696.13 | + | 4098.87i | 0.512306 | + | 0.447150i | ||||
\(439\) | 7584.89 | 0.824617 | 0.412309 | − | 0.911044i | \(-0.364723\pi\) | ||||
0.412309 | + | 0.911044i | \(0.364723\pi\) | |||||||
\(440\) | −528.605 | − | 347.825i | −0.0572733 | − | 0.0376862i | ||||
\(441\) | 14719.3 | 1.58939 | ||||||||
\(442\) | −832.936 | − | 727.002i | −0.0896351 | − | 0.0782352i | ||||
\(443\) | 12323.7i | 1.32171i | 0.750514 | + | 0.660854i | \(0.229806\pi\) | ||||
−0.750514 | + | 0.660854i | \(0.770194\pi\) | |||||||
\(444\) | −1364.94 | − | 10003.4i | −0.145894 | − | 1.06923i | ||||
\(445\) | − | 12756.9i | − | 1.35896i | ||||||
\(446\) | −9673.41 | + | 11083.0i | −1.02702 | + | 1.17667i | ||||
\(447\) | 1154.93 | 0.122206 | ||||||||
\(448\) | 7294.15 | + | 16928.9i | 0.769233 | + | 1.78531i | ||||
\(449\) | −10994.8 | −1.15563 | −0.577815 | − | 0.816168i | \(-0.696094\pi\) | ||||
−0.577815 | + | 0.816168i | \(0.696094\pi\) | |||||||
\(450\) | 9243.69 | − | 10590.6i | 0.968338 | − | 1.10944i | ||||
\(451\) | − | 349.434i | − | 0.0364838i | ||||||
\(452\) | 491.060 | + | 3598.89i | 0.0511007 | + | 0.374508i | ||||
\(453\) | 1462.39i | 0.151675i | ||||||||
\(454\) | −7575.06 | − | 6611.65i | −0.783073 | − | 0.683481i | ||||
\(455\) | −17499.1 | −1.80302 | ||||||||
\(456\) | 3242.75 | + | 2133.75i | 0.333017 | + | 0.219127i | ||||
\(457\) | −15812.8 | −1.61858 | −0.809289 | − | 0.587411i | \(-0.800147\pi\) | ||||
−0.809289 | + | 0.587411i | \(0.800147\pi\) | |||||||
\(458\) | −8343.46 | − | 7282.33i | −0.851232 | − | 0.742971i | ||||
\(459\) | 2452.94i | 0.249441i | ||||||||
\(460\) | 7485.39 | − | 1021.36i | 0.758713 | − | 0.103525i | ||||
\(461\) | 5226.08i | 0.527988i | 0.964524 | + | 0.263994i | \(0.0850400\pi\) | ||||
−0.964524 | + | 0.263994i | \(0.914960\pi\) | |||||||
\(462\) | 301.164 | − | 345.048i | 0.0303278 | − | 0.0347470i | ||||
\(463\) | 10585.7 | 1.06254 | 0.531272 | − | 0.847202i | \(-0.321714\pi\) | ||||
0.531272 | + | 0.847202i | \(0.321714\pi\) | |||||||
\(464\) | 1277.10 | + | 4592.70i | 0.127776 | + | 0.459506i | ||||
\(465\) | 11570.1 | 1.15387 | ||||||||
\(466\) | −1971.63 | + | 2258.92i | −0.195995 | + | 0.224555i | ||||
\(467\) | − | 12269.4i | − | 1.21576i | −0.794029 | − | 0.607880i | \(-0.792020\pi\) | ||
0.794029 | − | 0.607880i | \(-0.207980\pi\) | |||||||
\(468\) | 2814.37 | − | 384.015i | 0.277980 | − | 0.0379297i | ||||
\(469\) | 15276.9i | 1.50409i | ||||||||
\(470\) | −20072.7 | − | 17519.8i | −1.96997 | − | 1.71942i | ||||
\(471\) | −11163.1 | −1.09208 | ||||||||
\(472\) | −5032.84 | + | 7648.62i | −0.490795 | + | 0.745882i | ||||
\(473\) | 191.496 | 0.0186152 | ||||||||
\(474\) | 1138.47 | + | 993.675i | 0.110320 | + | 0.0962891i | ||||
\(475\) | 16240.9i | 1.56881i | ||||||||
\(476\) | −661.969 | − | 4851.44i | −0.0637422 | − | 0.467154i | ||||
\(477\) | − | 3757.78i | − | 0.360706i | ||||||
\(478\) | 7820.74 | − | 8960.33i | 0.748352 | − | 0.857398i | ||||
\(479\) | −10339.1 | −0.986235 | −0.493118 | − | 0.869963i | \(-0.664143\pi\) | ||||
−0.493118 | + | 0.869963i | \(0.664143\pi\) | |||||||
\(480\) | −5616.02 | + | 11734.5i | −0.534032 | + | 1.11585i | ||||
\(481\) | 8535.24 | 0.809092 | ||||||||
\(482\) | 691.327 | − | 792.063i | 0.0653301 | − | 0.0748496i | ||||
\(483\) | 5468.01i | 0.515120i | ||||||||
\(484\) | −1437.66 | − | 10536.4i | −0.135017 | − | 0.989516i | ||||
\(485\) | − | 3017.54i | − | 0.282514i | ||||||
\(486\) | −7768.38 | − | 6780.38i | −0.725063 | − | 0.632849i | ||||
\(487\) | 5138.18 | 0.478097 | 0.239049 | − | 0.971008i | \(-0.423164\pi\) | ||||
0.239049 | + | 0.971008i | \(0.423164\pi\) | |||||||
\(488\) | 5906.00 | − | 8975.60i | 0.547852 | − | 0.832595i | ||||
\(489\) | −7510.49 | −0.694552 | ||||||||
\(490\) | −42937.4 | − | 37476.5i | −3.95860 | − | 3.45514i | ||||
\(491\) | 8771.11i | 0.806180i | 0.915160 | + | 0.403090i | \(0.132064\pi\) | ||||
−0.915160 | + | 0.403090i | \(0.867936\pi\) | |||||||
\(492\) | −7118.03 | + | 971.240i | −0.652248 | + | 0.0889977i | ||||
\(493\) | − | 1266.22i | − | 0.115675i | ||||||
\(494\) | −2157.94 | + | 2472.38i | −0.196539 | + | 0.225178i | ||||
\(495\) | −431.832 | −0.0392110 | ||||||||
\(496\) | 9927.01 | − | 2760.43i | 0.898662 | − | 0.249893i | ||||
\(497\) | −1979.03 | −0.178615 | ||||||||
\(498\) | −3309.00 | + | 3791.16i | −0.297750 | + | 0.341137i | ||||
\(499\) | − | 10907.2i | − | 0.978502i | −0.872143 | − | 0.489251i | \(-0.837270\pi\) | ||
0.872143 | − | 0.489251i | \(-0.162730\pi\) | |||||||
\(500\) | −32984.2 | + | 4500.63i | −2.95020 | + | 0.402548i | ||||
\(501\) | 6593.06i | 0.587936i | ||||||||
\(502\) | −52.8587 | − | 46.1360i | −0.00469960 | − | 0.00410189i | ||||
\(503\) | 18065.6 | 1.60140 | 0.800700 | − | 0.599066i | \(-0.204461\pi\) | ||||
0.800700 | + | 0.599066i | \(0.204461\pi\) | |||||||
\(504\) | 10508.8 | + | 6914.86i | 0.928770 | + | 0.611136i | ||||
\(505\) | −17968.7 | −1.58336 | ||||||||
\(506\) | −125.935 | − | 109.918i | −0.0110642 | − | 0.00965705i | ||||
\(507\) | 5671.82i | 0.496833i | ||||||||
\(508\) | 2411.75 | + | 17675.3i | 0.210638 | + | 1.54373i | ||||
\(509\) | 21694.5i | 1.88918i | 0.328249 | + | 0.944591i | \(0.393541\pi\) | ||||
−0.328249 | + | 0.944591i | \(0.606459\pi\) | |||||||
\(510\) | 2272.29 | − | 2603.39i | 0.197291 | − | 0.226040i | ||||
\(511\) | −23338.3 | −2.02040 | ||||||||
\(512\) | −2018.81 | + | 11408.0i | −0.174257 | + | 0.984700i | ||||
\(513\) | 7281.01 | 0.626636 | ||||||||
\(514\) | 4968.33 | − | 5692.29i | 0.426350 | − | 0.488475i | ||||
\(515\) | 26734.1i | 2.28747i | ||||||||
\(516\) | −532.256 | − | 3900.81i | −0.0454095 | − | 0.332797i | ||||
\(517\) | 589.511i | 0.0501483i | ||||||||
\(518\) | 28478.8 | + | 24856.8i | 2.41561 | + | 2.10839i | ||||
\(519\) | 3805.27 | 0.321836 | ||||||||
\(520\) | −9187.46 | − | 6045.40i | −0.774802 | − | 0.509824i | ||||
\(521\) | −16531.5 | −1.39013 | −0.695065 | − | 0.718947i | \(-0.744624\pi\) | ||||
−0.695065 | + | 0.718947i | \(0.744624\pi\) | |||||||
\(522\) | 2450.90 | + | 2139.19i | 0.205504 | + | 0.179368i | ||||
\(523\) | − | 21109.8i | − | 1.76495i | −0.470361 | − | 0.882474i | \(-0.655876\pi\) | ||
0.470361 | − | 0.882474i | \(-0.344124\pi\) | |||||||
\(524\) | 13264.4 | − | 1809.89i | 1.10583 | − | 0.150888i | ||||
\(525\) | − | 39394.7i | − | 3.27491i | ||||||
\(526\) | 11814.3 | − | 13535.8i | 0.979329 | − | 1.12203i | ||||
\(527\) | −2736.91 | −0.226227 | ||||||||
\(528\) | 277.322 | − | 77.1156i | 0.0228577 | − | 0.00635611i | ||||
\(529\) | −10171.3 | −0.835974 | ||||||||
\(530\) | −9567.59 | + | 10961.7i | −0.784131 | + | 0.898390i | ||||
\(531\) | 6248.37i | 0.510652i | ||||||||
\(532\) | −14400.4 | + | 1964.91i | −1.17357 | + | 0.160131i | ||||
\(533\) | − | 6073.37i | − | 0.493559i | ||||||
\(534\) | 4371.92 | + | 3815.89i | 0.354291 | + | 0.309232i | ||||
\(535\) | 11956.7 | 0.966233 | ||||||||
\(536\) | −5277.67 | + | 8020.71i | −0.425300 | + | 0.646347i | ||||
\(537\) | 3875.23 | 0.311412 | ||||||||
\(538\) | −4813.44 | − | 4201.26i | −0.385729 | − | 0.336671i | ||||
\(539\) | 1261.02i | 0.100772i | ||||||||
\(540\) | 3298.91 | + | 24177.1i | 0.262894 | + | 1.92670i | ||||
\(541\) | 1140.05i | 0.0905998i | 0.998973 | + | 0.0452999i | \(0.0144243\pi\) | ||||
−0.998973 | + | 0.0452999i | \(0.985576\pi\) | |||||||
\(542\) | −7463.77 | + | 8551.35i | −0.591507 | + | 0.677697i | ||||
\(543\) | 6096.54 | 0.481819 | ||||||||
\(544\) | 1328.47 | − | 2775.81i | 0.104702 | − | 0.218772i | ||||
\(545\) | 28561.5 | 2.24484 | ||||||||
\(546\) | 5234.41 | − | 5997.14i | 0.410279 | − | 0.470062i | ||||
\(547\) | 1815.52i | 0.141913i | 0.997479 | + | 0.0709563i | \(0.0226051\pi\) | ||||
−0.997479 | + | 0.0709563i | \(0.977395\pi\) | |||||||
\(548\) | 1270.64 | + | 9312.30i | 0.0990496 | + | 0.725916i | ||||
\(549\) | − | 7332.42i | − | 0.570018i | ||||||
\(550\) | 907.308 | + | 791.915i | 0.0703414 | + | 0.0613952i | ||||
\(551\) | −3758.50 | −0.290594 | ||||||||
\(552\) | −1889.02 | + | 2870.83i | −0.145656 | + | 0.221360i | ||||
\(553\) | −5657.82 | −0.435072 | ||||||||
\(554\) | 8124.35 | + | 7091.08i | 0.623051 | + | 0.543811i | ||||
\(555\) | 26677.4i | 2.04035i | ||||||||
\(556\) | −13597.5 | + | 1855.35i | −1.03716 | + | 0.141518i | ||||
\(557\) | 12853.9i | 0.977803i | 0.872339 | + | 0.488901i | \(0.162602\pi\) | ||||
−0.872339 | + | 0.488901i | \(0.837398\pi\) | |||||||
\(558\) | 4623.82 | − | 5297.58i | 0.350792 | − | 0.401907i | ||||
\(559\) | 3328.31 | 0.251829 | ||||||||
\(560\) | −13049.2 | − | 46927.4i | −0.984697 | − | 3.54115i | ||||
\(561\) | −76.4585 | −0.00575415 | ||||||||
\(562\) | 4265.96 | − | 4887.57i | 0.320193 | − | 0.366850i | ||||
\(563\) | 7349.70i | 0.550183i | 0.961418 | + | 0.275091i | \(0.0887081\pi\) | ||||
−0.961418 | + | 0.275091i | \(0.911292\pi\) | |||||||
\(564\) | 12008.4 | − | 1638.53i | 0.896536 | − | 0.122330i | ||||
\(565\) | − | 9597.67i | − | 0.714650i | ||||||
\(566\) | 6432.62 | + | 5614.51i | 0.477709 | + | 0.416953i | ||||
\(567\) | −2650.46 | −0.196312 | ||||||||
\(568\) | −1039.04 | − | 683.692i | −0.0767552 | − | 0.0505054i | ||||
\(569\) | 1835.93 | 0.135266 | 0.0676328 | − | 0.997710i | \(-0.478455\pi\) | ||||
0.0676328 | + | 0.997710i | \(0.478455\pi\) | |||||||
\(570\) | −7727.59 | − | 6744.78i | −0.567848 | − | 0.495628i | ||||
\(571\) | 8306.81i | 0.608808i | 0.952543 | + | 0.304404i | \(0.0984572\pi\) | ||||
−0.952543 | + | 0.304404i | \(0.901543\pi\) | |||||||
\(572\) | 32.8989 | + | 241.110i | 0.00240485 | + | 0.0176247i | ||||
\(573\) | 13076.2i | 0.953344i | ||||||||
\(574\) | 17687.2 | − | 20264.5i | 1.28615 | − | 1.47356i | ||||
\(575\) | −14378.2 | −1.04280 | ||||||||
\(576\) | 3128.51 | + | 7260.93i | 0.226310 | + | 0.525241i | ||||
\(577\) | −20957.8 | −1.51210 | −0.756051 | − | 0.654513i | \(-0.772874\pi\) | ||||
−0.756051 | + | 0.654513i | \(0.772874\pi\) | |||||||
\(578\) | −537.510 | + | 615.833i | −0.0386808 | + | 0.0443171i | ||||
\(579\) | 5347.46i | 0.383822i | ||||||||
\(580\) | −1702.92 | − | 12480.4i | −0.121914 | − | 0.893481i | ||||
\(581\) | − | 18840.9i | − | 1.34535i | ||||||
\(582\) | 1034.14 | + | 902.618i | 0.0736539 | + | 0.0642865i | ||||
\(583\) | 321.932 | 0.0228698 | ||||||||
\(584\) | −12253.2 | − | 8062.64i | −0.868217 | − | 0.571292i | ||||
\(585\) | −7505.50 | −0.530451 | ||||||||
\(586\) | 4473.18 | + | 3904.27i | 0.315333 | + | 0.275229i | ||||
\(587\) | − | 1119.97i | − | 0.0787500i | −0.999225 | − | 0.0393750i | \(-0.987463\pi\) | ||
0.999225 | − | 0.0393750i | \(-0.0125367\pi\) | |||||||
\(588\) | 25687.2 | − | 3504.96i | 1.80157 | − | 0.245820i | ||||
\(589\) | 8123.91i | 0.568319i | ||||||||
\(590\) | 15908.8 | − | 18227.0i | 1.11009 | − | 1.27185i | ||||
\(591\) | −5112.46 | −0.355835 | ||||||||
\(592\) | 6364.78 | + | 22888.9i | 0.441877 | + | 1.58907i | ||||
\(593\) | −17060.2 | −1.18141 | −0.590707 | − | 0.806886i | \(-0.701151\pi\) | ||||
−0.590707 | + | 0.806886i | \(0.701151\pi\) | |||||||
\(594\) | 355.026 | − | 406.759i | 0.0245234 | − | 0.0280968i | ||||
\(595\) | 12938.0i | 0.891442i | ||||||||
\(596\) | −2692.75 | + | 367.419i | −0.185066 | + | 0.0252518i | ||||
\(597\) | 5241.77i | 0.359349i | ||||||||
\(598\) | −2188.82 | − | 1910.44i | −0.149678 | − | 0.130642i | ||||
\(599\) | 14554.2 | 0.992769 | 0.496385 | − | 0.868103i | \(-0.334661\pi\) | ||||
0.496385 | + | 0.868103i | \(0.334661\pi\) | |||||||
\(600\) | 13609.6 | − | 20683.1i | 0.926018 | − | 1.40731i | ||||
\(601\) | −15344.2 | −1.04143 | −0.520717 | − | 0.853730i | \(-0.674335\pi\) | ||||
−0.520717 | + | 0.853730i | \(0.674335\pi\) | |||||||
\(602\) | 11105.3 | + | 9692.88i | 0.751855 | + | 0.656233i | ||||
\(603\) | 6552.34i | 0.442507i | ||||||||
\(604\) | −465.232 | − | 3409.60i | −0.0313411 | − | 0.229693i | ||||
\(605\) | 28098.9i | 1.88823i | ||||||||
\(606\) | 5374.88 | − | 6158.07i | 0.360296 | − | 0.412796i | ||||
\(607\) | 17195.4 | 1.14982 | 0.574908 | − | 0.818218i | \(-0.305038\pi\) | ||||
0.574908 | + | 0.818218i | \(0.305038\pi\) | |||||||
\(608\) | −8239.37 | − | 3943.27i | −0.549590 | − | 0.263027i | ||||
\(609\) | 9116.80 | 0.606620 | ||||||||
\(610\) | −18668.9 | + | 21389.2i | −1.23915 | + | 1.41971i | ||||
\(611\) | 10246.0i | 0.678413i | ||||||||
\(612\) | −283.923 | − | 2080.81i | −0.0187531 | − | 0.137438i | ||||
\(613\) | − | 5210.05i | − | 0.343282i | −0.985160 | − | 0.171641i | \(-0.945093\pi\) | ||
0.985160 | − | 0.171641i | \(-0.0549070\pi\) | |||||||
\(614\) | 4754.91 | + | 4150.17i | 0.312529 | + | 0.272781i | ||||
\(615\) | 18982.7 | 1.24464 | ||||||||
\(616\) | −592.402 | + | 900.299i | −0.0387477 | + | 0.0588865i | ||||
\(617\) | −9605.27 | −0.626732 | −0.313366 | − | 0.949632i | \(-0.601457\pi\) | ||||
−0.313366 | + | 0.949632i | \(0.601457\pi\) | |||||||
\(618\) | −9162.04 | − | 7996.80i | −0.596362 | − | 0.520515i | ||||
\(619\) | 10970.5i | 0.712345i | 0.934420 | + | 0.356172i | \(0.115918\pi\) | ||||
−0.934420 | + | 0.356172i | \(0.884082\pi\) | |||||||
\(620\) | −26976.0 | + | 3680.82i | −1.74739 | + | 0.238428i | ||||
\(621\) | 6445.94i | 0.416533i | ||||||||
\(622\) | −3091.46 | + | 3541.93i | −0.199286 | + | 0.228325i | ||||
\(623\) | −21727.1 | −1.39723 | ||||||||
\(624\) | 4820.01 | − | 1340.31i | 0.309222 | − | 0.0859863i | ||||
\(625\) | 47732.3 | 3.05487 | ||||||||
\(626\) | 1516.09 | − | 1737.00i | 0.0967971 | − | 0.110902i | ||||
\(627\) | 226.950i | 0.0144554i | ||||||||
\(628\) | 26027.1 | − | 3551.34i | 1.65381 | − | 0.225659i | ||||
\(629\) | − | 6310.55i | − | 0.400029i | ||||||
\(630\) | −25042.9 | − | 21857.9i | −1.58370 | − | 1.38229i | ||||
\(631\) | 21720.1 | 1.37031 | 0.685154 | − | 0.728398i | \(-0.259735\pi\) | ||||
0.685154 | + | 0.728398i | \(0.259735\pi\) | |||||||
\(632\) | −2970.49 | − | 1954.60i | −0.186962 | − | 0.123022i | ||||
\(633\) | 7218.34 | 0.453244 | ||||||||
\(634\) | −12086.5 | − | 10549.3i | −0.757123 | − | 0.660831i | ||||
\(635\) | − | 47137.2i | − | 2.94580i | ||||||
\(636\) | −894.800 | − | 6557.82i | −0.0557879 | − | 0.408859i | ||||
\(637\) | 21917.2i | 1.36325i | ||||||||
\(638\) | −183.267 | + | 209.971i | −0.0113724 | + | 0.0130295i | ||||
\(639\) | −848.818 | −0.0525488 | ||||||||
\(640\) | 9360.78 | − | 29146.1i | 0.578152 | − | 1.80015i | ||||
\(641\) | 21736.8 | 1.33939 | 0.669696 | − | 0.742635i | \(-0.266424\pi\) | ||||
0.669696 | + | 0.742635i | \(0.266424\pi\) | |||||||
\(642\) | −3576.54 | + | 4097.69i | −0.219867 | + | 0.251905i | ||||
\(643\) | − | 16220.6i | − | 0.994831i | −0.867513 | − | 0.497415i | \(-0.834283\pi\) | ||
0.867513 | − | 0.497415i | \(-0.165717\pi\) | |||||||
\(644\) | −1739.55 | − | 12748.8i | −0.106441 | − | 0.780084i | ||||
\(645\) | 10402.8i | 0.635056i | ||||||||
\(646\) | 1827.96 | + | 1595.48i | 0.111332 | + | 0.0971723i | ||||
\(647\) | 11372.7 | 0.691045 | 0.345523 | − | 0.938410i | \(-0.387702\pi\) | ||||
0.345523 | + | 0.938410i | \(0.387702\pi\) | |||||||
\(648\) | −1391.55 | − | 915.649i | −0.0843600 | − | 0.0555094i | ||||
\(649\) | −535.303 | −0.0323767 | ||||||||
\(650\) | 15769.5 | + | 13763.9i | 0.951588 | + | 0.830564i | ||||
\(651\) | − | 19705.8i | − | 1.18637i | ||||||
\(652\) | 17510.9 | − | 2389.33i | 1.05181 | − | 0.143517i | ||||
\(653\) | − | 2019.60i | − | 0.121031i | −0.998167 | − | 0.0605155i | \(-0.980726\pi\) | ||
0.998167 | − | 0.0605155i | \(-0.0192745\pi\) | |||||||
\(654\) | −8543.41 | + | 9788.31i | −0.510816 | + | 0.585249i | ||||
\(655\) | −35374.0 | −2.11019 | ||||||||
\(656\) | 16286.9 | − | 4528.95i | 0.969355 | − | 0.269551i | ||||
\(657\) | −10009.9 | −0.594407 | ||||||||
\(658\) | −29839.1 | + | 34187.0i | −1.76785 | + | 2.02546i | ||||
\(659\) | − | 2381.04i | − | 0.140747i | −0.997521 | − | 0.0703734i | \(-0.977581\pi\) | ||
0.997521 | − | 0.0703734i | \(-0.0224191\pi\) | |||||||
\(660\) | −753.604 | + | 102.828i | −0.0444454 | + | 0.00606448i | ||||
\(661\) | − | 10353.6i | − | 0.609239i | −0.952474 | − | 0.304619i | \(-0.901471\pi\) | ||
0.952474 | − | 0.304619i | \(-0.0985292\pi\) | |||||||
\(662\) | −1334.82 | − | 1165.05i | −0.0783672 | − | 0.0684003i | ||||
\(663\) | −1328.89 | −0.0778430 | ||||||||
\(664\) | 6508.93 | − | 9891.90i | 0.380415 | − | 0.578133i | ||||
\(665\) | 38403.7 | 2.23944 | ||||||||
\(666\) | 12214.7 | + | 10661.2i | 0.710677 | + | 0.620292i | ||||
\(667\) | − | 3327.43i | − | 0.193161i | ||||||
\(668\) | −2097.46 | − | 15371.9i | −0.121487 | − | 0.890354i | ||||
\(669\) | 17682.1i | 1.02187i | ||||||||
\(670\) | 16682.7 | − | 19113.7i | 0.961956 | − | 1.10213i | ||||
\(671\) | 628.175 | 0.0361407 | ||||||||
\(672\) | 19985.8 | + | 9564.99i | 1.14728 | + | 0.549074i | ||||
\(673\) | −9430.32 | −0.540137 | −0.270068 | − | 0.962841i | \(-0.587046\pi\) | ||||
−0.270068 | + | 0.962841i | \(0.587046\pi\) | |||||||
\(674\) | 15165.3 | − | 17375.1i | 0.866686 | − | 0.992974i | ||||
\(675\) | − | 46440.3i | − | 2.64813i | ||||||
\(676\) | −1804.39 | − | 13224.0i | −0.102662 | − | 0.752390i | ||||
\(677\) | 23598.4i | 1.33967i | 0.742508 | + | 0.669837i | \(0.233636\pi\) | ||||
−0.742508 | + | 0.669837i | \(0.766364\pi\) | |||||||
\(678\) | 3289.22 | + | 2870.89i | 0.186315 | + | 0.162619i | ||||
\(679\) | −5139.36 | −0.290472 | ||||||||
\(680\) | −4469.68 | + | 6792.77i | −0.252066 | + | 0.383075i | ||||
\(681\) | −12085.5 | −0.680055 | ||||||||
\(682\) | 453.848 | + | 396.127i | 0.0254820 | + | 0.0222412i | ||||
\(683\) | − | 15278.0i | − | 0.855923i | −0.903797 | − | 0.427961i | \(-0.859232\pi\) | ||
0.903797 | − | 0.427961i | \(-0.140768\pi\) | |||||||
\(684\) | −6176.43 | + | 842.760i | −0.345266 | + | 0.0471107i | ||||
\(685\) | − | 24834.5i | − | 1.38522i | ||||||
\(686\) | −40860.7 | + | 46814.6i | −2.27415 | + | 2.60553i | ||||
\(687\) | −13311.4 | −0.739247 | ||||||||
\(688\) | 2481.94 | + | 8925.51i | 0.137534 | + | 0.494596i | ||||
\(689\) | 5595.37 | 0.309386 | ||||||||
\(690\) | 5971.22 | − | 6841.30i | 0.329450 | − | 0.377455i | ||||
\(691\) | − | 9266.06i | − | 0.510127i | −0.966924 | − | 0.255063i | \(-0.917904\pi\) | ||
0.966924 | − | 0.255063i | \(-0.0820963\pi\) | |||||||
\(692\) | −8872.08 | + | 1210.58i | −0.487379 | + | 0.0665018i | ||||
\(693\) | 735.480i | 0.0403154i | ||||||||
\(694\) | 3227.90 | + | 2817.37i | 0.176555 | + | 0.154101i | ||||
\(695\) | 36262.4 | 1.97915 | ||||||||
\(696\) | 4786.53 | + | 3149.57i | 0.260680 | + | 0.171529i | ||||
\(697\) | −4490.36 | −0.244024 | ||||||||
\(698\) | −21342.0 | − | 18627.7i | −1.15732 | − | 1.01013i | ||||
\(699\) | 3603.95i | 0.195013i | ||||||||
\(700\) | 12532.7 | + | 91849.8i | 0.676703 | + | 4.95942i | ||||
\(701\) | 677.706i | 0.0365144i | 0.999833 | + | 0.0182572i | \(0.00581177\pi\) | ||||
−0.999833 | + | 0.0182572i | \(0.994188\pi\) | |||||||
\(702\) | 6170.56 | − | 7069.70i | 0.331756 | − | 0.380098i | ||||
\(703\) | −18731.5 | −1.00494 | ||||||||
\(704\) | −622.050 | + | 268.022i | −0.0333017 | + | 0.0143487i | ||||
\(705\) | −32024.6 | −1.71081 | ||||||||
\(706\) | −742.246 | + | 850.402i | −0.0395677 | + | 0.0453333i | ||||
\(707\) | 30603.7i | 1.62796i | ||||||||
\(708\) | 1487.86 | + | 10904.2i | 0.0789790 | + | 0.578822i | ||||
\(709\) | − | 21334.8i | − | 1.13011i | −0.825055 | − | 0.565053i | \(-0.808856\pi\) | ||
0.825055 | − | 0.565053i | \(-0.191144\pi\) | |||||||
\(710\) | 2476.06 | + | 2161.15i | 0.130880 | + | 0.114235i | ||||
\(711\) | −2426.68 | −0.127999 | ||||||||
\(712\) | −11407.2 | − | 7506.02i | −0.600426 | − | 0.395084i | ||||
\(713\) | −7192.17 | −0.377768 | ||||||||
\(714\) | −4434.00 | − | 3870.07i | −0.232406 | − | 0.202849i | ||||
\(715\) | − | 643.002i | − | 0.0336321i | ||||||
\(716\) | −9035.20 | + | 1232.83i | −0.471594 | + | 0.0643480i | ||||
\(717\) | − | 14295.6i | − | 0.744602i | ||||||
\(718\) | 7669.57 | − | 8787.14i | 0.398643 | − | 0.456731i | ||||
\(719\) | 36141.9 | 1.87464 | 0.937318 | − | 0.348474i | \(-0.113300\pi\) | ||||
0.937318 | + | 0.348474i | \(0.113300\pi\) | |||||||
\(720\) | −5596.90 | − | 20127.4i | −0.289700 | − | 1.04181i | ||||
\(721\) | 45532.5 | 2.35190 | ||||||||
\(722\) | −8021.22 | + | 9190.02i | −0.413461 | + | 0.473708i | ||||
\(723\) | − | 1263.68i | − | 0.0650026i | ||||||
\(724\) | −14214.3 | + | 1939.50i | −0.729653 | + | 0.0995596i | ||||
\(725\) | 23972.7i | 1.22803i | ||||||||
\(726\) | −9629.76 | − | 8405.03i | −0.492278 | − | 0.429669i | ||||
\(727\) | −36614.9 | −1.86791 | −0.933956 | − | 0.357387i | \(-0.883668\pi\) | ||||
−0.933956 | + | 0.357387i | \(0.883668\pi\) | |||||||
\(728\) | −10296.3 | + | 15647.7i | −0.524184 | + | 0.796625i | ||||
\(729\) | −14381.6 | −0.730661 | ||||||||
\(730\) | 29199.7 | + | 25486.1i | 1.48045 | + | 1.29217i | ||||
\(731\) | − | 2460.79i | − | 0.124509i | ||||||
\(732\) | −1745.99 | − | 12796.0i | −0.0881608 | − | 0.646113i | ||||
\(733\) | − | 23692.7i | − | 1.19387i | −0.802289 | − | 0.596936i | \(-0.796385\pi\) | ||
0.802289 | − | 0.596936i | \(-0.203615\pi\) | |||||||
\(734\) | 12340.8 | − | 14139.0i | 0.620583 | − | 0.711010i | ||||
\(735\) | −68503.7 | −3.43782 | ||||||||
\(736\) | 3491.01 | − | 7294.39i | 0.174837 | − | 0.365319i | ||||
\(737\) | −561.345 | −0.0280562 | ||||||||
\(738\) | 7586.15 | − | 8691.55i | 0.378387 | − | 0.433524i | ||||
\(739\) | 19337.2i | 0.962558i | 0.876567 | + | 0.481279i | \(0.159828\pi\) | ||||
−0.876567 | + | 0.481279i | \(0.840172\pi\) | |||||||
\(740\) | −8486.94 | − | 62199.2i | −0.421603 | − | 3.08985i | ||||
\(741\) | 3944.52i | 0.195554i | ||||||||
\(742\) | 18669.6 | + | 16295.1i | 0.923695 | + | 0.806218i | ||||
\(743\) | −3141.98 | −0.155139 | −0.0775693 | − | 0.996987i | \(-0.524716\pi\) | ||||
−0.0775693 | + | 0.996987i | \(0.524716\pi\) | |||||||
\(744\) | 6807.72 | − | 10346.0i | 0.335461 | − | 0.509815i | ||||
\(745\) | 7181.13 | 0.353149 | ||||||||
\(746\) | 25942.0 | + | 22642.6i | 1.27319 | + | 1.11127i | ||||
\(747\) | − | 8080.97i | − | 0.395806i | ||||||
\(748\) | 178.265 | − | 24.3239i | 0.00871393 | − | 0.00118900i | ||||
\(749\) | − | 20364.2i | − | 0.993448i | ||||||
\(750\) | −26312.1 | + | 30146.1i | −1.28104 | + | 1.46771i | ||||
\(751\) | −14579.1 | −0.708387 | −0.354194 | − | 0.935172i | \(-0.615245\pi\) | ||||
−0.354194 | + | 0.935172i | \(0.615245\pi\) | |||||||
\(752\) | −27476.7 | + | 7640.54i | −1.33241 | + | 0.370508i | ||||
\(753\) | −84.3324 | −0.00408133 | ||||||||
\(754\) | −3185.28 | + | 3649.42i | −0.153848 | + | 0.176265i | ||||
\(755\) | 9092.87i | 0.438309i | ||||||||
\(756\) | 41177.5 | − | 5618.58i | 1.98097 | − | 0.270299i | ||||
\(757\) | 26557.2i | 1.27508i | 0.770416 | + | 0.637541i | \(0.220048\pi\) | ||||
−0.770416 | + | 0.637541i | \(0.779952\pi\) | |||||||
\(758\) | −23915.7 | − | 20874.0i | −1.14599 | − | 1.00024i | ||||
\(759\) | −200.921 | −0.00960865 | ||||||||
\(760\) | 20162.8 | + | 13267.3i | 0.962345 | + | 0.633229i | ||||
\(761\) | 25342.3 | 1.20717 | 0.603585 | − | 0.797299i | \(-0.293739\pi\) | ||||
0.603585 | + | 0.797299i | \(0.293739\pi\) | |||||||
\(762\) | 16154.4 | + | 14099.8i | 0.767994 | + | 0.670320i | ||||
\(763\) | − | 48644.8i | − | 2.30807i | ||||||
\(764\) | −4159.95 | − | 30487.5i | −0.196992 | − | 1.44372i | ||||
\(765\) | 5549.21i | 0.262264i | ||||||||
\(766\) | 1370.61 | − | 1570.32i | 0.0646501 | − | 0.0740705i | ||||
\(767\) | −9303.88 | −0.437997 | ||||||||
\(768\) | 7188.62 | + | 11926.3i | 0.337757 | + | 0.560356i | ||||
\(769\) | 8237.67 | 0.386291 | 0.193146 | − | 0.981170i | \(-0.438131\pi\) | ||||
0.193146 | + | 0.981170i | \(0.438131\pi\) | |||||||
\(770\) | 1872.59 | − | 2145.45i | 0.0876407 | − | 0.100411i | ||||
\(771\) | − | 9081.66i | − | 0.424213i | ||||||
\(772\) | −1701.20 | − | 12467.8i | −0.0793101 | − | 0.581249i | ||||
\(773\) | − | 26852.0i | − | 1.24942i | −0.780858 | − | 0.624709i | \(-0.785218\pi\) | ||
0.780858 | − | 0.624709i | \(-0.214782\pi\) | |||||||
\(774\) | 4763.12 | + | 4157.34i | 0.221197 | + | 0.193065i | ||||
\(775\) | 51816.5 | 2.40168 | ||||||||
\(776\) | −2698.28 | − | 1775.49i | −0.124823 | − | 0.0821343i | ||||
\(777\) | 45436.0 | 2.09782 | ||||||||
\(778\) | 26671.4 | + | 23279.3i | 1.22907 | + | 1.07275i | ||||
\(779\) | 13328.6i | 0.613026i | ||||||||
\(780\) | −13098.1 | + | 1787.20i | −0.601264 | + | 0.0820412i | ||||
\(781\) | − | 72.7189i | − | 0.00333174i | ||||||
\(782\) | −1412.49 | + | 1618.31i | −0.0645916 | + | 0.0740035i | ||||
\(783\) | 10747.3 | 0.490520 | ||||||||
\(784\) | −58775.3 | + | 16343.8i | −2.67745 | + | 0.744525i | ||||
\(785\) | −69410.3 | −3.15587 | ||||||||
\(786\) | 10581.2 | − | 12123.0i | 0.480176 | − | 0.550145i | ||||
\(787\) | 14269.9i | 0.646339i | 0.946341 | + | 0.323169i | \(0.104748\pi\) | ||||
−0.946341 | + | 0.323169i | \(0.895252\pi\) | |||||||
\(788\) | 11919.8 | − | 1626.44i | 0.538866 | − | 0.0735271i | ||||
\(789\) | − | 21595.4i | − | 0.974421i | ||||||
\(790\) | 7078.79 | + | 6178.50i | 0.318800 | + | 0.278254i | ||||
\(791\) | −16346.4 | −0.734779 | ||||||||
\(792\) | −254.085 | + | 386.144i | −0.0113996 | + | 0.0173245i | ||||
\(793\) | 10918.0 | 0.488917 | ||||||||
\(794\) | 14814.9 | + | 12930.7i | 0.662167 | + | 0.577951i | ||||
\(795\) | 17488.7i | 0.780201i | ||||||||
\(796\) | −1667.57 | − | 12221.3i | −0.0742533 | − | 0.544188i | ||||
\(797\) | 5985.21i | 0.266006i | 0.991116 | + | 0.133003i | \(0.0424620\pi\) | ||||
−0.991116 | + | 0.133003i | \(0.957538\pi\) | |||||||
\(798\) | −11487.4 | + | 13161.3i | −0.509588 | + | 0.583842i | ||||
\(799\) | 7575.43 | 0.335419 | ||||||||
\(800\) | −25151.3 | + | 52553.0i | −1.11154 | + | 2.32253i | ||||
\(801\) | −9318.88 | −0.411069 | ||||||||
\(802\) | 27486.3 | − | 31491.5i | 1.21019 | − | 1.38654i | ||||
\(803\) | − | 857.561i | − | 0.0376870i | ||||||
\(804\) | 1560.24 | + | 11434.7i | 0.0684395 | + | 0.501580i | ||||
\(805\) | 33999.1i | 1.48859i | ||||||||
\(806\) | 7888.14 | + | 6884.91i | 0.344724 | + | 0.300882i | ||||
\(807\) | −7679.52 | −0.334984 | ||||||||
\(808\) | −10572.6 | + | 16067.6i | −0.460325 | + | 0.699576i | ||||
\(809\) | 24655.1 | 1.07148 | 0.535739 | − | 0.844384i | \(-0.320033\pi\) | ||||
0.535739 | + | 0.844384i | \(0.320033\pi\) | |||||||
\(810\) | 3316.12 | + | 2894.37i | 0.143848 | + | 0.125553i | ||||
\(811\) | 1336.11i | 0.0578511i | 0.999582 | + | 0.0289255i | \(0.00920857\pi\) | ||||
−0.999582 | + | 0.0289255i | \(0.990791\pi\) | |||||||
\(812\) | −21256.1 | + | 2900.34i | −0.918648 | + | 0.125347i | ||||
\(813\) | 13643.1i | 0.588542i | ||||||||
\(814\) | −913.357 | + | 1046.45i | −0.0393282 | + | 0.0450589i | ||||
\(815\) | −46698.9 | −2.00711 | ||||||||
\(816\) | −990.964 | − | 3563.69i | −0.0425131 | − | 0.152885i | ||||
\(817\) | −7304.31 | −0.312785 | ||||||||
\(818\) | 3480.37 | − | 3987.51i | 0.148763 | − | 0.170440i | ||||
\(819\) | 12783.1i | 0.545393i | ||||||||
\(820\) | −44258.7 | + | 6039.00i | −1.88485 | + | 0.257184i | ||||
\(821\) | 23963.6i | 1.01868i | 0.860565 | + | 0.509340i | \(0.170111\pi\) | ||||
−0.860565 | + | 0.509340i | \(0.829889\pi\) | |||||||
\(822\) | 8511.02 | + | 7428.58i | 0.361139 | + | 0.315208i | ||||
\(823\) | −32712.5 | −1.38552 | −0.692762 | − | 0.721167i | \(-0.743606\pi\) | ||||
−0.692762 | + | 0.721167i | \(0.743606\pi\) | |||||||
\(824\) | 23905.6 | + | 15730.0i | 1.01067 | + | 0.665026i | ||||
\(825\) | 1447.55 | 0.0610875 | ||||||||
\(826\) | −31043.4 | − | 27095.3i | −1.30767 | − | 1.14136i | ||||
\(827\) | − | 41923.9i | − | 1.76280i | −0.472368 | − | 0.881401i | \(-0.656601\pi\) | ||
0.472368 | − | 0.881401i | \(-0.343399\pi\) | |||||||
\(828\) | −746.103 | − | 5468.05i | −0.0313151 | − | 0.229502i | ||||
\(829\) | − | 21043.1i | − | 0.881615i | −0.897602 | − | 0.440807i | \(-0.854692\pi\) | ||
0.897602 | − | 0.440807i | \(-0.145308\pi\) | |||||||
\(830\) | −20574.7 | + | 23572.8i | −0.860434 | + | 0.985811i | ||||
\(831\) | 12961.9 | 0.541085 | ||||||||
\(832\) | −10811.6 | + | 4658.38i | −0.450510 | + | 0.194111i | ||||
\(833\) | 16204.6 | 0.674015 | ||||||||
\(834\) | −10846.9 | + | 12427.5i | −0.450358 | + | 0.515982i | ||||
\(835\) | 40994.5i | 1.69901i | ||||||||
\(836\) | −72.2000 | − | 529.140i | −0.00298695 | − | 0.0218908i | ||||
\(837\) | − | 23230.1i | − | 0.959317i | ||||||
\(838\) | 3642.59 | + | 3179.32i | 0.150156 | + | 0.131059i | ||||
\(839\) | 15634.6 | 0.643345 | 0.321673 | − | 0.946851i | \(-0.395755\pi\) | ||||
0.321673 | + | 0.946851i | \(0.395755\pi\) | |||||||
\(840\) | −48907.9 | − | 32181.7i | −2.00891 | − | 1.32187i | ||||
\(841\) | 18841.2 | 0.772528 | ||||||||
\(842\) | −7962.59 | − | 6949.90i | −0.325902 | − | 0.284453i | ||||
\(843\) | − | 7797.78i | − | 0.318588i | ||||||
\(844\) | −16829.8 | + | 2296.39i | −0.686380 | + | 0.0936550i | ||||
\(845\) | 35266.4i | 1.43574i | ||||||||
\(846\) | −12798.2 | + | 14663.0i | −0.520106 | + | 0.595893i | ||||
\(847\) | 47856.9 | 1.94142 | ||||||||
\(848\) | 4172.50 | + | 15005.1i | 0.168967 | + | 0.607637i | ||||
\(849\) | 10262.8 | 0.414863 | ||||||||
\(850\) | 10176.4 | − | 11659.3i | 0.410645 | − | 0.470481i | ||||
\(851\) | − | 16583.1i | − | 0.667993i | ||||||
\(852\) | −1481.30 | + | 202.120i | −0.0595639 | + | 0.00812736i | ||||
\(853\) | − | 49098.9i | − | 1.97083i | −0.170178 | − | 0.985413i | \(-0.554434\pi\) | ||
0.170178 | − | 0.985413i | \(-0.445566\pi\) | |||||||
\(854\) | 36429.2 | + | 31796.1i | 1.45970 | + | 1.27405i | ||||
\(855\) | 16471.6 | 0.658849 | ||||||||
\(856\) | 7035.20 | − | 10691.7i | 0.280909 | − | 0.426910i | ||||
\(857\) | 30953.5 | 1.23378 | 0.616890 | − | 0.787049i | \(-0.288392\pi\) | ||||
0.616890 | + | 0.787049i | \(0.288392\pi\) | |||||||
\(858\) | 220.363 | + | 192.337i | 0.00876816 | + | 0.00765301i | ||||
\(859\) | 31986.2i | 1.27049i | 0.772309 | + | 0.635246i | \(0.219101\pi\) | ||||
−0.772309 | + | 0.635246i | \(0.780899\pi\) | |||||||
\(860\) | −3309.47 | − | 24254.5i | −0.131223 | − | 0.961712i | ||||
\(861\) | − | 32330.6i | − | 1.27970i | ||||||
\(862\) | 2258.21 | − | 2587.26i | 0.0892285 | − | 0.102230i | ||||
\(863\) | 5417.61 | 0.213694 | 0.106847 | − | 0.994275i | \(-0.465925\pi\) | ||||
0.106847 | + | 0.994275i | \(0.465925\pi\) | |||||||
\(864\) | 23560.2 | + | 11275.6i | 0.927702 | + | 0.443988i | ||||
\(865\) | 23660.5 | 0.930035 | ||||||||
\(866\) | −7979.43 | + | 9142.15i | −0.313109 | + | 0.358733i | ||||
\(867\) | 982.520i | 0.0384869i | ||||||||
\(868\) | 6269.03 | + | 45944.5i | 0.245144 | + | 1.79661i | ||||
\(869\) | − | 207.895i | − | 0.00811550i | ||||||
\(870\) | −11406.5 | − | 9955.79i | −0.444501 | − | 0.387969i | ||||
\(871\) | −9756.50 | −0.379548 | ||||||||
\(872\) | 16805.2 | − | 25539.6i | 0.652634 | − | 0.991836i | ||||
\(873\) | −2204.30 | −0.0854574 | ||||||||
\(874\) | 4803.60 | + | 4192.67i | 0.185909 | + | 0.162264i | ||||
\(875\) | − | 149817.i | − | 5.78826i | ||||||
\(876\) | −17468.7 | + | 2383.56i | −0.673757 | + | 0.0919327i | ||||
\(877\) | 38749.6i | 1.49200i | 0.665948 | + | 0.745998i | \(0.268027\pi\) | ||||
−0.665948 | + | 0.745998i | \(0.731973\pi\) | |||||||
\(878\) | −14107.1 | + | 16162.7i | −0.542246 | + | 0.621259i | ||||
\(879\) | 7136.66 | 0.273849 | ||||||||
\(880\) | 1724.34 | − | 479.491i | 0.0660538 | − | 0.0183678i | ||||
\(881\) | −33654.7 | −1.28701 | −0.643506 | − | 0.765441i | \(-0.722521\pi\) | ||||
−0.643506 | + | 0.765441i | \(0.722521\pi\) | |||||||
\(882\) | −27376.5 | + | 31365.6i | −1.04514 | + | 1.19743i | ||||
\(883\) | − | 2077.27i | − | 0.0791682i | −0.999216 | − | 0.0395841i | \(-0.987397\pi\) | ||
0.999216 | − | 0.0395841i | \(-0.0126033\pi\) | |||||||
\(884\) | 3098.35 | − | 422.763i | 0.117883 | − | 0.0160849i | ||||
\(885\) | − | 29079.9i | − | 1.10453i | ||||||
\(886\) | −26260.7 | − | 22920.8i | −0.995763 | − | 0.869120i | ||||
\(887\) | −29795.2 | −1.12787 | −0.563936 | − | 0.825818i | \(-0.690714\pi\) | ||||
−0.563936 | + | 0.825818i | \(0.690714\pi\) | |||||||
\(888\) | 23854.9 | + | 15696.7i | 0.901486 | + | 0.593183i | ||||
\(889\) | −80282.2 | −3.02877 | ||||||||
\(890\) | 27183.8 | + | 23726.6i | 1.02383 | + | 0.893613i | ||||
\(891\) | − | 97.3904i | − | 0.00366184i | ||||||
\(892\) | −5625.24 | − | 41226.3i | −0.211151 | − | 1.54749i | ||||
\(893\) | − | 22486.0i | − | 0.842625i | ||||||
\(894\) | −2148.05 | + | 2461.05i | −0.0803595 | + | 0.0920690i | ||||
\(895\) | 24095.5 | 0.899914 | ||||||||
\(896\) | −49640.4 | − | 15942.9i | −1.85086 | − | 0.594437i | ||||
\(897\) | −3492.12 | −0.129987 | ||||||||
\(898\) | 20449.2 | − | 23429.0i | 0.759911 | − | 0.870641i | ||||
\(899\) | 11991.5i | 0.444870i | ||||||||
\(900\) | 5375.36 | + | 39395.0i | 0.199087 | + | 1.45907i | ||||
\(901\) | − | 4136.95i | − | 0.152965i | ||||||
\(902\) | 744.613 | + | 649.912i | 0.0274866 | + | 0.0239908i | ||||
\(903\) | 17717.7 | 0.652944 | ||||||||
\(904\) | −8582.23 | − | 5647.16i | −0.315753 | − | 0.207767i | ||||
\(905\) | 37907.2 | 1.39235 | ||||||||
\(906\) | −3116.22 | − | 2719.89i | −0.114271 | − | 0.0997377i | ||||
\(907\) | 28087.5i | 1.02826i | 0.857713 | + | 0.514130i | \(0.171885\pi\) | ||||
−0.857713 | + | 0.514130i | \(0.828115\pi\) | |||||||
\(908\) | 28177.7 | − | 3844.78i | 1.02986 | − | 0.140522i | ||||
\(909\) | 13126.1i | 0.478950i | ||||||||
\(910\) | 32546.6 | − | 37289.1i | 1.18562 | − | 1.35838i | ||||
\(911\) | −42586.7 | −1.54880 | −0.774401 | − | 0.632695i | \(-0.781949\pi\) | ||||
−0.774401 | + | 0.632695i | \(0.781949\pi\) | |||||||
\(912\) | −10578.0 | + | 2941.45i | −0.384071 | + | 0.106800i | ||||
\(913\) | 692.304 | 0.0250952 | ||||||||
\(914\) | 29410.1 | − | 33695.6i | 1.06433 | − | 1.21942i | ||||
\(915\) | 34125.0i | 1.23294i | ||||||||
\(916\) | 31036.0 | − | 4234.79i | 1.11949 | − | 0.152753i | ||||
\(917\) | 60247.5i | 2.16963i | ||||||||
\(918\) | −5227.00 | − | 4562.22i | −0.187927 | − | 0.164026i | ||||
\(919\) | −5275.59 | −0.189364 | −0.0946820 | − | 0.995508i | \(-0.530183\pi\) | ||||
−0.0946820 | + | 0.995508i | \(0.530183\pi\) | |||||||
\(920\) | −11745.6 | + | 17850.3i | −0.420915 | + | 0.639682i | ||||
\(921\) | 7586.14 | 0.271413 | ||||||||
\(922\) | −11136.3 | − | 9719.97i | −0.397782 | − | 0.347191i | ||||
\(923\) | − | 1263.90i | − | 0.0450722i | ||||||
\(924\) | 175.132 | + | 1283.51i | 0.00623530 | + | 0.0456973i | ||||
\(925\) | 119474.i | 4.24680i | ||||||||
\(926\) | −19688.2 | + | 22557.1i | −0.698700 | + | 0.800510i | ||||
\(927\) | 19529.2 | 0.691933 | ||||||||
\(928\) | −12161.9 | − | 5820.55i | −0.430209 | − | 0.205893i | ||||
\(929\) | −21538.2 | −0.760651 | −0.380326 | − | 0.924853i | \(-0.624188\pi\) | ||||
−0.380326 | + | 0.924853i | \(0.624188\pi\) | |||||||
\(930\) | −21519.2 | + | 24654.9i | −0.758756 | + | 0.869317i | ||||
\(931\) | − | 48099.6i | − | 1.69323i | ||||||
\(932\) | −1146.53 | − | 8402.72i | −0.0402961 | − | 0.295322i | ||||
\(933\) | 5650.90i | 0.198288i | ||||||||
\(934\) | 26145.0 | + | 22819.8i | 0.915943 | + | 0.799451i | ||||
\(935\) | −475.405 | −0.0166283 | ||||||||
\(936\) | −4416.15 | + | 6711.41i | −0.154216 | + | 0.234369i | ||||
\(937\) | 27121.0 | 0.945576 | 0.472788 | − | 0.881176i | \(-0.343248\pi\) | ||||
0.472788 | + | 0.881176i | \(0.343248\pi\) | |||||||
\(938\) | −32553.6 | − | 28413.4i | −1.13317 | − | 0.989051i | ||||
\(939\) | − | 2771.27i | − | 0.0963119i | ||||||
\(940\) | 74666.3 | − | 10188.1i | 2.59080 | − | 0.353508i | ||||
\(941\) | 37778.5i | 1.30876i | 0.756166 | + | 0.654380i | \(0.227070\pi\) | ||||
−0.756166 | + | 0.654380i | \(0.772930\pi\) | |||||||
\(942\) | 20762.3 | − | 23787.6i | 0.718122 | − | 0.822762i | ||||
\(943\) | −11799.9 | −0.407486 | ||||||||
\(944\) | −6937.96 | − | 24950.2i | −0.239207 | − | 0.860232i | ||||
\(945\) | −109814. | −3.78016 | ||||||||
\(946\) | −356.163 | + | 408.061i | −0.0122409 | + | 0.0140245i | ||||
\(947\) | − | 34635.6i | − | 1.18850i | −0.804281 | − | 0.594249i | \(-0.797449\pi\) | ||
0.804281 | − | 0.594249i | \(-0.202551\pi\) | |||||||
\(948\) | −4234.87 | + | 577.838i | −0.145087 | + | 0.0197967i | ||||
\(949\) | − | 14904.9i | − | 0.509835i | ||||||
\(950\) | −34607.9 | − | 30206.4i | −1.18192 | − | 1.03160i | ||||
\(951\) | −19283.2 | −0.657518 | ||||||||
\(952\) | 11569.2 | + | 7612.59i | 0.393865 | + | 0.259165i | ||||
\(953\) | 17330.3 | 0.589069 | 0.294534 | − | 0.955641i | \(-0.404835\pi\) | ||||
0.294534 | + | 0.955641i | \(0.404835\pi\) | |||||||
\(954\) | 8007.50 | + | 6989.09i | 0.271753 | + | 0.237191i | ||||
\(955\) | 81305.5i | 2.75496i | ||||||||
\(956\) | 4547.89 | + | 33330.6i | 0.153859 | + | 1.12760i | ||||
\(957\) | 334.995i | 0.0113154i | ||||||||
\(958\) | 19229.7 | − | 22031.7i | 0.648522 | − | 0.743020i | ||||
\(959\) | −42297.1 | −1.42424 | ||||||||
\(960\) | −14560.0 | − | 33792.3i | −0.489504 | − | 1.13609i | ||||
\(961\) | −3871.66 | −0.129961 | ||||||||
\(962\) | −15874.7 | + | 18187.8i | −0.532037 | + | 0.609563i | ||||
\(963\) | − | 8734.35i | − | 0.292275i | ||||||
\(964\) | 402.018 | + | 2946.31i | 0.0134317 | + | 0.0984382i | ||||
\(965\) | 33249.5i | 1.10916i | ||||||||
\(966\) | −11651.8 | − | 10169.9i | −0.388087 | − | 0.338729i | ||||
\(967\) | 10669.2 | 0.354808 | 0.177404 | − | 0.984138i | \(-0.443230\pi\) | ||||
0.177404 | + | 0.984138i | \(0.443230\pi\) | |||||||
\(968\) | 25126.0 | + | 16533.0i | 0.834276 | + | 0.548958i | ||||
\(969\) | 2916.39 | 0.0966852 | ||||||||
\(970\) | 6430.11 | + | 5612.32i | 0.212844 | + | 0.185774i | ||||
\(971\) | − | 34329.6i | − | 1.13459i | −0.823514 | − | 0.567296i | \(-0.807990\pi\) | ||
0.823514 | − | 0.567296i | \(-0.192010\pi\) | |||||||
\(972\) | 28896.8 | − | 3942.90i | 0.953565 | − | 0.130112i | ||||
\(973\) | − | 61760.7i | − | 2.03490i | ||||||
\(974\) | −9556.49 | + | 10949.0i | −0.314384 | + | 0.360194i | ||||
\(975\) | 25159.2 | 0.826401 | ||||||||
\(976\) | 8141.65 | + | 29278.9i | 0.267016 | + | 0.960239i | ||||
\(977\) | 474.154 | 0.0155266 | 0.00776332 | − | 0.999970i | \(-0.497529\pi\) | ||||
0.00776332 | + | 0.999970i | \(0.497529\pi\) | |||||||
\(978\) | 13968.7 | − | 16004.2i | 0.456719 | − | 0.523269i | ||||
\(979\) | − | 798.356i | − | 0.0260629i | ||||||
\(980\) | 159718. | − | 21793.2i | 5.20614 | − | 0.710366i | ||||
\(981\) | − | 20864.1i | − | 0.679040i | ||||||
\(982\) | −18690.5 | − | 16313.4i | −0.607369 | − | 0.530123i | ||||
\(983\) | 9073.76 | 0.294413 | 0.147207 | − | 0.989106i | \(-0.452972\pi\) | ||||
0.147207 | + | 0.989106i | \(0.452972\pi\) | |||||||
\(984\) | 11169.2 | − | 16974.3i | 0.361850 | − | 0.549920i | ||||
\(985\) | −31788.4 | −1.02829 | ||||||||
\(986\) | 2698.21 | + | 2355.04i | 0.0871485 | + | 0.0760648i | ||||
\(987\) | 54543.1i | 1.75899i | ||||||||
\(988\) | −1254.88 | − | 9196.76i | −0.0404079 | − | 0.296142i | ||||
\(989\) | − | 6466.57i | − | 0.207912i | ||||||
\(990\) | 803.164 | − | 920.196i | 0.0257841 | − | 0.0295412i | ||||
\(991\) | −24588.7 | −0.788178 | −0.394089 | − | 0.919072i | \(-0.628940\pi\) | ||||
−0.394089 | + | 0.919072i | \(0.628940\pi\) | |||||||
\(992\) | −12581.0 | + | 26287.7i | −0.402668 | + | 0.841366i | ||||
\(993\) | −2129.61 | −0.0680574 | ||||||||
\(994\) | 3680.79 | − | 4217.13i | 0.117452 | − | 0.134567i | ||||
\(995\) | 32592.4i | 1.03844i | ||||||||
\(996\) | −1924.23 | − | 14102.3i | −0.0612166 | − | 0.448645i | ||||
\(997\) | − | 40948.3i | − | 1.30075i | −0.759614 | − | 0.650374i | \(-0.774612\pi\) | ||
0.759614 | − | 0.650374i | \(-0.225388\pi\) | |||||||
\(998\) | 23242.2 | + | 20286.2i | 0.737194 | + | 0.643437i | ||||
\(999\) | 53562.0 | 1.69632 |
(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 | 136.4.c.b.69.8 | yes | 24 | |
4.3 | odd | 2 | 544.4.c.a.273.10 | 24 | |||
8.3 | odd | 2 | 544.4.c.a.273.15 | 24 | |||
8.5 | even | 2 | inner | 136.4.c.b.69.7 | ✓ | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
136.4.c.b.69.7 | ✓ | 24 | 8.5 | even | 2 | inner | |
136.4.c.b.69.8 | yes | 24 | 1.1 | even | 1 | trivial | |
544.4.c.a.273.10 | 24 | 4.3 | odd | 2 | |||
544.4.c.a.273.15 | 24 | 8.3 | odd | 2 |