Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [210,3,Mod(83,210)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(210, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 3, 2]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("210.83");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 210 = 2 \cdot 3 \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 210.k (of order \(4\), degree \(2\), 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: | \(5.72208555157\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Relative dimension: | \(16\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 167.12 | ||
Character | \(\chi\) | \(=\) | 210.167 |
Dual form | 210.3.k.a.83.12 |
$q$-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 \(\left(\mathbb{Z}/210\mathbb{Z}\right)^\times\).
\(n\) | \(31\) | \(71\) | \(127\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(e\left(\frac{1}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | + | 1.00000i | −0.500000 | + | 0.500000i | ||||
\(3\) | 2.14733 | − | 2.09499i | 0.715775 | − | 0.698331i | ||||
\(4\) | − | 2.00000i | − | 0.500000i | ||||||
\(5\) | 1.13661 | + | 4.86910i | 0.227322 | + | 0.973820i | ||||
\(6\) | −0.0523328 | + | 4.24232i | −0.00872213 | + | 0.707053i | ||||
\(7\) | 2.31291 | + | 6.60685i | 0.330415 | + | 0.943836i | ||||
\(8\) | 2.00000 | + | 2.00000i | 0.250000 | + | 0.250000i | ||||
\(9\) | 0.222012 | − | 8.99726i | 0.0246680 | − | 0.999696i | ||||
\(10\) | −6.00571 | − | 3.73249i | −0.600571 | − | 0.373249i | ||||
\(11\) | 16.9733i | 1.54303i | 0.636213 | + | 0.771513i | \(0.280500\pi\) | ||||
−0.636213 | + | 0.771513i | \(0.719500\pi\) | |||||||
\(12\) | −4.18999 | − | 4.29465i | −0.349165 | − | 0.357888i | ||||
\(13\) | −10.2231 | − | 10.2231i | −0.786392 | − | 0.786392i | 0.194509 | − | 0.980901i | \(-0.437689\pi\) |
−0.980901 | + | 0.194509i | \(0.937689\pi\) | |||||||
\(14\) | −8.91976 | − | 4.29394i | −0.637126 | − | 0.306710i | ||||
\(15\) | 12.6414 | + | 8.07434i | 0.842760 | + | 0.538290i | ||||
\(16\) | −4.00000 | −0.250000 | ||||||||
\(17\) | 8.79877 | + | 8.79877i | 0.517575 | + | 0.517575i | 0.916837 | − | 0.399262i | \(-0.130734\pi\) |
−0.399262 | + | 0.916837i | \(0.630734\pi\) | |||||||
\(18\) | 8.77525 | + | 9.21927i | 0.487514 | + | 0.512182i | ||||
\(19\) | 24.7369 | 1.30194 | 0.650972 | − | 0.759102i | \(-0.274361\pi\) | ||||
0.650972 | + | 0.759102i | \(0.274361\pi\) | |||||||
\(20\) | 9.73820 | − | 2.27322i | 0.486910 | − | 0.113661i | ||||
\(21\) | 18.8079 | + | 9.34153i | 0.895613 | + | 0.444835i | ||||
\(22\) | −16.9733 | − | 16.9733i | −0.771513 | − | 0.771513i | ||||
\(23\) | 19.2569 | + | 19.2569i | 0.837258 | + | 0.837258i | 0.988497 | − | 0.151239i | \(-0.0483263\pi\) |
−0.151239 | + | 0.988497i | \(0.548326\pi\) | |||||||
\(24\) | 8.48464 | + | 0.104666i | 0.353526 | + | 0.00436106i | ||||
\(25\) | −22.4162 | + | 11.0685i | −0.896649 | + | 0.442742i | ||||
\(26\) | 20.4462 | 0.786392 | ||||||||
\(27\) | −18.3725 | − | 19.7852i | −0.680462 | − | 0.732784i | ||||
\(28\) | 13.2137 | − | 4.62582i | 0.471918 | − | 0.165208i | ||||
\(29\) | 1.67978 | 0.0579235 | 0.0289618 | − | 0.999581i | \(-0.490780\pi\) | ||||
0.0289618 | + | 0.999581i | \(0.490780\pi\) | |||||||
\(30\) | −20.7157 | + | 4.56706i | −0.690525 | + | 0.152235i | ||||
\(31\) | − | 36.8991i | − | 1.19029i | −0.803616 | − | 0.595147i | \(-0.797094\pi\) | ||
0.803616 | − | 0.595147i | \(-0.202906\pi\) | |||||||
\(32\) | 4.00000 | − | 4.00000i | 0.125000 | − | 0.125000i | ||||
\(33\) | 35.5589 | + | 36.4472i | 1.07754 | + | 1.10446i | ||||
\(34\) | −17.5975 | −0.517575 | ||||||||
\(35\) | −29.5405 | + | 18.7712i | −0.844015 | + | 0.536320i | ||||
\(36\) | −17.9945 | − | 0.444025i | −0.499848 | − | 0.0123340i | ||||
\(37\) | 40.5381 | + | 40.5381i | 1.09562 | + | 1.09562i | 0.994916 | + | 0.100708i | \(0.0321107\pi\) |
0.100708 | + | 0.994916i | \(0.467889\pi\) | |||||||
\(38\) | −24.7369 | + | 24.7369i | −0.650972 | + | 0.650972i | ||||
\(39\) | −43.3696 | − | 0.535003i | −1.11204 | − | 0.0137180i | ||||
\(40\) | −7.46497 | + | 12.0114i | −0.186624 | + | 0.300285i | ||||
\(41\) | 0.885911 | 0.0216076 | 0.0108038 | − | 0.999942i | \(-0.496561\pi\) | ||||
0.0108038 | + | 0.999942i | \(0.496561\pi\) | |||||||
\(42\) | −28.1494 | + | 9.46634i | −0.670224 | + | 0.225389i | ||||
\(43\) | −9.87427 | + | 9.87427i | −0.229634 | + | 0.229634i | −0.812540 | − | 0.582906i | \(-0.801916\pi\) |
0.582906 | + | 0.812540i | \(0.301916\pi\) | |||||||
\(44\) | 33.9466 | 0.771513 | ||||||||
\(45\) | 44.0609 | − | 9.14540i | 0.979131 | − | 0.203231i | ||||
\(46\) | −38.5139 | −0.837258 | ||||||||
\(47\) | −33.7538 | − | 33.7538i | −0.718165 | − | 0.718165i | 0.250064 | − | 0.968229i | \(-0.419548\pi\) |
−0.968229 | + | 0.250064i | \(0.919548\pi\) | |||||||
\(48\) | −8.58930 | + | 8.37997i | −0.178944 | + | 0.174583i | ||||
\(49\) | −38.3009 | + | 30.5621i | −0.781651 | + | 0.623716i | ||||
\(50\) | 11.3477 | − | 33.4848i | 0.226954 | − | 0.669696i | ||||
\(51\) | 37.3272 | + | 0.460464i | 0.731906 | + | 0.00902871i | ||||
\(52\) | −20.4462 | + | 20.4462i | −0.393196 | + | 0.393196i | ||||
\(53\) | −11.9694 | − | 11.9694i | −0.225838 | − | 0.225838i | 0.585113 | − | 0.810952i | \(-0.301050\pi\) |
−0.810952 | + | 0.585113i | \(0.801050\pi\) | |||||||
\(54\) | 38.1576 | + | 1.41270i | 0.706623 | + | 0.0261611i | ||||
\(55\) | −82.6446 | + | 19.2920i | −1.50263 | + | 0.350765i | ||||
\(56\) | −8.58788 | + | 17.8395i | −0.153355 | + | 0.318563i | ||||
\(57\) | 53.1183 | − | 51.8237i | 0.931899 | − | 0.909188i | ||||
\(58\) | −1.67978 | + | 1.67978i | −0.0289618 | + | 0.0289618i | ||||
\(59\) | − | 50.5136i | − | 0.856162i | −0.903740 | − | 0.428081i | \(-0.859190\pi\) | ||
0.903740 | − | 0.428081i | \(-0.140810\pi\) | |||||||
\(60\) | 16.1487 | − | 25.2828i | 0.269145 | − | 0.421380i | ||||
\(61\) | − | 80.6872i | − | 1.32274i | −0.750059 | − | 0.661370i | \(-0.769975\pi\) | ||
0.750059 | − | 0.661370i | \(-0.230025\pi\) | |||||||
\(62\) | 36.8991 | + | 36.8991i | 0.595147 | + | 0.595147i | ||||
\(63\) | 59.9570 | − | 19.3430i | 0.951699 | − | 0.307032i | ||||
\(64\) | 8.00000i | 0.125000i | ||||||||
\(65\) | 38.1575 | − | 61.3969i | 0.587039 | − | 0.944568i | ||||
\(66\) | −72.0061 | − | 0.888260i | −1.09100 | − | 0.0134585i | ||||
\(67\) | −4.46192 | − | 4.46192i | −0.0665959 | − | 0.0665959i | 0.673024 | − | 0.739620i | \(-0.264995\pi\) |
−0.739620 | + | 0.673024i | \(0.764995\pi\) | |||||||
\(68\) | 17.5975 | − | 17.5975i | 0.258787 | − | 0.258787i | ||||
\(69\) | 81.6941 | + | 1.00777i | 1.18397 | + | 0.0146053i | ||||
\(70\) | 10.7693 | − | 48.3117i | 0.153847 | − | 0.690167i | ||||
\(71\) | − | 137.180i | − | 1.93212i | −0.258322 | − | 0.966059i | \(-0.583169\pi\) | ||
0.258322 | − | 0.966059i | \(-0.416831\pi\) | |||||||
\(72\) | 18.4385 | − | 17.5505i | 0.256091 | − | 0.243757i | ||||
\(73\) | 53.3244 | + | 53.3244i | 0.730471 | + | 0.730471i | 0.970713 | − | 0.240242i | \(-0.0772268\pi\) |
−0.240242 | + | 0.970713i | \(0.577227\pi\) | |||||||
\(74\) | −81.0762 | −1.09562 | ||||||||
\(75\) | −24.9464 | + | 70.7296i | −0.332619 | + | 0.943061i | ||||
\(76\) | − | 49.4739i | − | 0.650972i | ||||||
\(77\) | −112.140 | + | 39.2577i | −1.45636 | + | 0.509840i | ||||
\(78\) | 43.9046 | − | 42.8346i | 0.562880 | − | 0.549162i | ||||
\(79\) | − | 127.936i | − | 1.61944i | −0.586816 | − | 0.809721i | \(-0.699619\pi\) | ||
0.586816 | − | 0.809721i | \(-0.300381\pi\) | |||||||
\(80\) | −4.54645 | − | 19.4764i | −0.0568306 | − | 0.243455i | ||||
\(81\) | −80.9014 | − | 3.99500i | −0.998783 | − | 0.0493210i | ||||
\(82\) | −0.885911 | + | 0.885911i | −0.0108038 | + | 0.0108038i | ||||
\(83\) | −60.0077 | + | 60.0077i | −0.722985 | + | 0.722985i | −0.969212 | − | 0.246227i | \(-0.920809\pi\) |
0.246227 | + | 0.969212i | \(0.420809\pi\) | |||||||
\(84\) | 18.6831 | − | 37.6157i | 0.222417 | − | 0.447806i | ||||
\(85\) | −32.8413 | + | 52.8429i | −0.386368 | + | 0.621681i | ||||
\(86\) | − | 19.7485i | − | 0.229634i | ||||||
\(87\) | 3.60704 | − | 3.51913i | 0.0414602 | − | 0.0404498i | ||||
\(88\) | −33.9466 | + | 33.9466i | −0.385757 | + | 0.385757i | ||||
\(89\) | 51.3826i | 0.577332i | 0.957430 | + | 0.288666i | \(0.0932117\pi\) | ||||
−0.957430 | + | 0.288666i | \(0.906788\pi\) | |||||||
\(90\) | −34.9155 | + | 53.2063i | −0.387950 | + | 0.591181i | ||||
\(91\) | 43.8974 | − | 91.1875i | 0.482388 | − | 1.00206i | ||||
\(92\) | 38.5139 | − | 38.5139i | 0.418629 | − | 0.418629i | ||||
\(93\) | −77.3034 | − | 79.2345i | −0.831220 | − | 0.851984i | ||||
\(94\) | 67.5075 | 0.718165 | ||||||||
\(95\) | 28.1163 | + | 120.447i | 0.295961 | + | 1.26786i | ||||
\(96\) | 0.209331 | − | 16.9693i | 0.00218053 | − | 0.176763i | ||||
\(97\) | −0.274025 | + | 0.274025i | −0.00282500 | + | 0.00282500i | −0.708518 | − | 0.705693i | \(-0.750636\pi\) |
0.705693 | + | 0.708518i | \(0.250636\pi\) | |||||||
\(98\) | 7.73884 | − | 68.8630i | 0.0789678 | − | 0.702683i | ||||
\(99\) | 152.713 | + | 3.76828i | 1.54256 | + | 0.0380634i | ||||
\(100\) | 22.1371 | + | 44.8325i | 0.221371 | + | 0.448325i | ||||
\(101\) | −21.6785 | −0.214638 | −0.107319 | − | 0.994225i | \(-0.534227\pi\) | ||||
−0.107319 | + | 0.994225i | \(0.534227\pi\) | |||||||
\(102\) | −37.7877 | + | 36.8667i | −0.370467 | + | 0.361438i | ||||
\(103\) | −49.4148 | − | 49.4148i | −0.479755 | − | 0.479755i | 0.425298 | − | 0.905053i | \(-0.360169\pi\) |
−0.905053 | + | 0.425298i | \(0.860169\pi\) | |||||||
\(104\) | − | 40.8924i | − | 0.393196i | ||||||
\(105\) | −24.1076 | + | 102.195i | −0.229596 | + | 0.973286i | ||||
\(106\) | 23.9389 | 0.225838 | ||||||||
\(107\) | −42.7088 | + | 42.7088i | −0.399147 | + | 0.399147i | −0.877932 | − | 0.478785i | \(-0.841077\pi\) |
0.478785 | + | 0.877932i | \(0.341077\pi\) | |||||||
\(108\) | −39.5703 | + | 36.7449i | −0.366392 | + | 0.340231i | ||||
\(109\) | − | 69.1171i | − | 0.634102i | −0.948408 | − | 0.317051i | \(-0.897307\pi\) | ||
0.948408 | − | 0.317051i | \(-0.102693\pi\) | |||||||
\(110\) | 63.3526 | − | 101.937i | 0.575933 | − | 0.926697i | ||||
\(111\) | 171.975 | + | 2.12147i | 1.54933 | + | 0.0191123i | ||||
\(112\) | −9.25163 | − | 26.4274i | −0.0826039 | − | 0.235959i | ||||
\(113\) | 58.1205 | + | 58.1205i | 0.514341 | + | 0.514341i | 0.915853 | − | 0.401513i | \(-0.131515\pi\) |
−0.401513 | + | 0.915853i | \(0.631515\pi\) | |||||||
\(114\) | −1.29455 | + | 104.942i | −0.0113557 | + | 0.920544i | ||||
\(115\) | −71.8763 | + | 115.652i | −0.625011 | + | 1.00567i | ||||
\(116\) | − | 3.35956i | − | 0.0289618i | ||||||
\(117\) | −94.2495 | + | 89.7102i | −0.805551 | + | 0.766754i | ||||
\(118\) | 50.5136 | + | 50.5136i | 0.428081 | + | 0.428081i | ||||
\(119\) | −37.7814 | + | 78.4829i | −0.317491 | + | 0.659520i | ||||
\(120\) | 9.13411 | + | 41.4315i | 0.0761176 | + | 0.345262i | ||||
\(121\) | −167.093 | −1.38093 | ||||||||
\(122\) | 80.6872 | + | 80.6872i | 0.661370 | + | 0.661370i | ||||
\(123\) | 1.90234 | − | 1.85598i | 0.0154662 | − | 0.0150892i | ||||
\(124\) | −73.7983 | −0.595147 | ||||||||
\(125\) | −79.3724 | − | 96.5662i | −0.634979 | − | 0.772529i | ||||
\(126\) | −40.6140 | + | 79.3001i | −0.322333 | + | 0.629366i | ||||
\(127\) | −7.40218 | − | 7.40218i | −0.0582849 | − | 0.0582849i | 0.677364 | − | 0.735648i | \(-0.263122\pi\) |
−0.735648 | + | 0.677364i | \(0.763122\pi\) | |||||||
\(128\) | −8.00000 | − | 8.00000i | −0.0625000 | − | 0.0625000i | ||||
\(129\) | −0.516748 | + | 41.8898i | −0.00400580 | + | 0.324727i | ||||
\(130\) | 23.2394 | + | 99.5545i | 0.178764 | + | 0.765804i | ||||
\(131\) | −16.3631 | −0.124909 | −0.0624544 | − | 0.998048i | \(-0.519893\pi\) | ||||
−0.0624544 | + | 0.998048i | \(0.519893\pi\) | |||||||
\(132\) | 72.8944 | − | 71.1179i | 0.552230 | − | 0.538772i | ||||
\(133\) | 57.2143 | + | 163.433i | 0.430183 | + | 1.22882i | ||||
\(134\) | 8.92385 | 0.0665959 | ||||||||
\(135\) | 75.4535 | − | 111.945i | 0.558915 | − | 0.829225i | ||||
\(136\) | 35.1951i | 0.258787i | ||||||||
\(137\) | −102.022 | + | 102.022i | −0.744688 | + | 0.744688i | −0.973476 | − | 0.228788i | \(-0.926524\pi\) |
0.228788 | + | 0.973476i | \(0.426524\pi\) | |||||||
\(138\) | −82.7018 | + | 80.6863i | −0.599289 | + | 0.584683i | ||||
\(139\) | 80.5228 | 0.579300 | 0.289650 | − | 0.957133i | \(-0.406461\pi\) | ||||
0.289650 | + | 0.957133i | \(0.406461\pi\) | |||||||
\(140\) | 37.5424 | + | 59.0810i | 0.268160 | + | 0.422007i | ||||
\(141\) | −143.194 | − | 1.76643i | −1.01556 | − | 0.0125279i | ||||
\(142\) | 137.180 | + | 137.180i | 0.966059 | + | 0.966059i | ||||
\(143\) | 173.520 | − | 173.520i | 1.21342 | − | 1.21342i | ||||
\(144\) | −0.888049 | + | 35.9890i | −0.00616701 | + | 0.249924i | ||||
\(145\) | 1.90926 | + | 8.17902i | 0.0131673 | + | 0.0564071i | ||||
\(146\) | −106.649 | −0.730471 | ||||||||
\(147\) | −18.2172 | + | 145.867i | −0.123927 | + | 0.992291i | ||||
\(148\) | 81.0762 | − | 81.0762i | 0.547812 | − | 0.547812i | ||||
\(149\) | 140.338 | 0.941864 | 0.470932 | − | 0.882170i | \(-0.343918\pi\) | ||||
0.470932 | + | 0.882170i | \(0.343918\pi\) | |||||||
\(150\) | −45.7832 | − | 95.6760i | −0.305221 | − | 0.637840i | ||||
\(151\) | 32.6929 | 0.216509 | 0.108255 | − | 0.994123i | \(-0.465474\pi\) | ||||
0.108255 | + | 0.994123i | \(0.465474\pi\) | |||||||
\(152\) | 49.4739 | + | 49.4739i | 0.325486 | + | 0.325486i | ||||
\(153\) | 81.1183 | − | 77.2114i | 0.530185 | − | 0.504650i | ||||
\(154\) | 72.8823 | − | 151.398i | 0.473262 | − | 0.983102i | ||||
\(155\) | 179.666 | − | 41.9400i | 1.15913 | − | 0.270581i | ||||
\(156\) | −1.07001 | + | 86.7392i | −0.00685901 | + | 0.556021i | ||||
\(157\) | −17.9885 | + | 17.9885i | −0.114576 | + | 0.114576i | −0.762070 | − | 0.647494i | \(-0.775817\pi\) |
0.647494 | + | 0.762070i | \(0.275817\pi\) | |||||||
\(158\) | 127.936 | + | 127.936i | 0.809721 | + | 0.809721i | ||||
\(159\) | −50.7781 | − | 0.626394i | −0.319359 | − | 0.00393958i | ||||
\(160\) | 24.0228 | + | 14.9299i | 0.150143 | + | 0.0933121i | ||||
\(161\) | −82.6882 | + | 171.767i | −0.513591 | + | 1.06688i | ||||
\(162\) | 84.8964 | − | 76.9064i | 0.524052 | − | 0.474731i | ||||
\(163\) | 90.3636 | − | 90.3636i | 0.554378 | − | 0.554378i | −0.373324 | − | 0.927701i | \(-0.621782\pi\) |
0.927701 | + | 0.373324i | \(0.121782\pi\) | |||||||
\(164\) | − | 1.77182i | − | 0.0108038i | ||||||
\(165\) | −137.048 | + | 214.566i | −0.830595 | + | 1.30040i | ||||
\(166\) | − | 120.015i | − | 0.722985i | ||||||
\(167\) | −11.1296 | − | 11.1296i | −0.0666444 | − | 0.0666444i | 0.672999 | − | 0.739643i | \(-0.265006\pi\) |
−0.739643 | + | 0.672999i | \(0.765006\pi\) | |||||||
\(168\) | 18.9327 | + | 56.2988i | 0.112694 | + | 0.335112i | ||||
\(169\) | 40.0232i | 0.236824i | ||||||||
\(170\) | −20.0016 | − | 85.6842i | −0.117656 | − | 0.504024i | ||||
\(171\) | 5.49190 | − | 222.565i | 0.0321164 | − | 1.30155i | ||||
\(172\) | 19.7485 | + | 19.7485i | 0.114817 | + | 0.114817i | ||||
\(173\) | 143.704 | − | 143.704i | 0.830661 | − | 0.830661i | −0.156946 | − | 0.987607i | \(-0.550165\pi\) |
0.987607 | + | 0.156946i | \(0.0501648\pi\) | |||||||
\(174\) | −0.0879077 | + | 7.12617i | −0.000505216 | + | 0.0409550i | ||||
\(175\) | −124.975 | − | 122.500i | −0.714142 | − | 0.700001i | ||||
\(176\) | − | 67.8932i | − | 0.385757i | ||||||
\(177\) | −105.826 | − | 108.469i | −0.597884 | − | 0.612819i | ||||
\(178\) | −51.3826 | − | 51.3826i | −0.288666 | − | 0.288666i | ||||
\(179\) | −334.691 | −1.86978 | −0.934891 | − | 0.354936i | \(-0.884503\pi\) | ||||
−0.934891 | + | 0.354936i | \(0.884503\pi\) | |||||||
\(180\) | −18.2908 | − | 88.1218i | −0.101616 | − | 0.489565i | ||||
\(181\) | 99.3599i | 0.548949i | 0.961594 | + | 0.274475i | \(0.0885040\pi\) | ||||
−0.961594 | + | 0.274475i | \(0.911496\pi\) | |||||||
\(182\) | 47.2901 | + | 135.085i | 0.259836 | + | 0.742224i | ||||
\(183\) | −169.039 | − | 173.262i | −0.923711 | − | 0.946785i | ||||
\(184\) | 77.0278i | 0.418629i | ||||||||
\(185\) | −151.308 | + | 243.460i | −0.817880 | + | 1.31600i | ||||
\(186\) | 156.538 | + | 1.93103i | 0.841602 | + | 0.0103819i | ||||
\(187\) | −149.344 | + | 149.344i | −0.798632 | + | 0.798632i | ||||
\(188\) | −67.5075 | + | 67.5075i | −0.359083 | + | 0.359083i | ||||
\(189\) | 88.2238 | − | 167.145i | 0.466792 | − | 0.884367i | ||||
\(190\) | −148.563 | − | 92.3303i | −0.781910 | − | 0.485949i | ||||
\(191\) | 41.5022i | 0.217289i | 0.994081 | + | 0.108645i | \(0.0346510\pi\) | ||||
−0.994081 | + | 0.108645i | \(0.965349\pi\) | |||||||
\(192\) | 16.7599 | + | 17.1786i | 0.0872914 | + | 0.0894719i | ||||
\(193\) | 112.254 | − | 112.254i | 0.581626 | − | 0.581626i | −0.353724 | − | 0.935350i | \(-0.615085\pi\) |
0.935350 | + | 0.353724i | \(0.115085\pi\) | |||||||
\(194\) | − | 0.548049i | − | 0.00282500i | ||||||
\(195\) | −46.6894 | − | 211.779i | −0.239433 | − | 1.08605i | ||||
\(196\) | 61.1241 | + | 76.6018i | 0.311858 | + | 0.390826i | ||||
\(197\) | 177.771 | − | 177.771i | 0.902388 | − | 0.902388i | −0.0932539 | − | 0.995642i | \(-0.529727\pi\) |
0.995642 | + | 0.0932539i | \(0.0297268\pi\) | |||||||
\(198\) | −156.481 | + | 148.945i | −0.790310 | + | 0.752247i | ||||
\(199\) | 79.5223 | 0.399609 | 0.199805 | − | 0.979836i | \(-0.435969\pi\) | ||||
0.199805 | + | 0.979836i | \(0.435969\pi\) | |||||||
\(200\) | −66.9696 | − | 22.6954i | −0.334848 | − | 0.113477i | ||||
\(201\) | −18.9289 | − | 0.233505i | −0.0941736 | − | 0.00116172i | ||||
\(202\) | 21.6785 | − | 21.6785i | 0.107319 | − | 0.107319i | ||||
\(203\) | 3.88518 | + | 11.0981i | 0.0191388 | + | 0.0546703i | ||||
\(204\) | 0.920928 | − | 74.6544i | 0.00451435 | − | 0.365953i | ||||
\(205\) | 1.00694 | + | 4.31359i | 0.00491189 | + | 0.0210419i | ||||
\(206\) | 98.8296 | 0.479755 | ||||||||
\(207\) | 177.535 | − | 168.984i | 0.857657 | − | 0.816350i | ||||
\(208\) | 40.8924 | + | 40.8924i | 0.196598 | + | 0.196598i | ||||
\(209\) | 419.867i | 2.00894i | ||||||||
\(210\) | −78.0875 | − | 126.303i | −0.371845 | − | 0.601441i | ||||
\(211\) | 398.914 | 1.89059 | 0.945294 | − | 0.326220i | \(-0.105775\pi\) | ||||
0.945294 | + | 0.326220i | \(0.105775\pi\) | |||||||
\(212\) | −23.9389 | + | 23.9389i | −0.112919 | + | 0.112919i | ||||
\(213\) | −287.392 | − | 294.571i | −1.34926 | − | 1.38296i | ||||
\(214\) | − | 85.4175i | − | 0.399147i | ||||||
\(215\) | −59.3020 | − | 36.8556i | −0.275823 | − | 0.171421i | ||||
\(216\) | 2.82540 | − | 76.3152i | 0.0130805 | − | 0.353311i | ||||
\(217\) | 243.787 | − | 85.3443i | 1.12344 | − | 0.393292i | ||||
\(218\) | 69.1171 | + | 69.1171i | 0.317051 | + | 0.317051i | ||||
\(219\) | 226.219 | + | 2.79061i | 1.03296 | + | 0.0127425i | ||||
\(220\) | 38.5841 | + | 165.289i | 0.175382 | + | 0.751315i | ||||
\(221\) | − | 179.901i | − | 0.814033i | ||||||
\(222\) | −174.097 | + | 169.854i | −0.784220 | + | 0.765108i | ||||
\(223\) | 162.636 | + | 162.636i | 0.729308 | + | 0.729308i | 0.970482 | − | 0.241174i | \(-0.0775325\pi\) |
−0.241174 | + | 0.970482i | \(0.577532\pi\) | |||||||
\(224\) | 35.6790 | + | 17.1758i | 0.159281 | + | 0.0766775i | ||||
\(225\) | 94.6100 | + | 204.142i | 0.420489 | + | 0.907298i | ||||
\(226\) | −116.241 | −0.514341 | ||||||||
\(227\) | −255.602 | − | 255.602i | −1.12600 | − | 1.12600i | −0.990821 | − | 0.135179i | \(-0.956839\pi\) |
−0.135179 | − | 0.990821i | \(-0.543161\pi\) | |||||||
\(228\) | −103.647 | − | 106.237i | −0.454594 | − | 0.465950i | ||||
\(229\) | 188.516 | 0.823212 | 0.411606 | − | 0.911362i | \(-0.364968\pi\) | ||||
0.411606 | + | 0.911362i | \(0.364968\pi\) | |||||||
\(230\) | −43.7753 | − | 187.528i | −0.190328 | − | 0.815338i | ||||
\(231\) | −158.557 | + | 319.231i | −0.686392 | + | 1.38195i | ||||
\(232\) | 3.35956 | + | 3.35956i | 0.0144809 | + | 0.0144809i | ||||
\(233\) | 16.7394 | + | 16.7394i | 0.0718429 | + | 0.0718429i | 0.742115 | − | 0.670272i | \(-0.233823\pi\) |
−0.670272 | + | 0.742115i | \(0.733823\pi\) | |||||||
\(234\) | 4.53930 | − | 183.960i | 0.0193987 | − | 0.786152i | ||||
\(235\) | 125.985 | − | 202.715i | 0.536108 | − | 0.862618i | ||||
\(236\) | −101.027 | −0.428081 | ||||||||
\(237\) | −268.025 | − | 274.720i | −1.13091 | − | 1.15916i | ||||
\(238\) | −40.7015 | − | 116.264i | −0.171015 | − | 0.488506i | ||||
\(239\) | −93.1494 | −0.389746 | −0.194873 | − | 0.980828i | \(-0.562430\pi\) | ||||
−0.194873 | + | 0.980828i | \(0.562430\pi\) | |||||||
\(240\) | −50.5656 | − | 32.2974i | −0.210690 | − | 0.134572i | ||||
\(241\) | 443.888i | 1.84186i | 0.389729 | + | 0.920929i | \(0.372569\pi\) | ||||
−0.389729 | + | 0.920929i | \(0.627431\pi\) | |||||||
\(242\) | 167.093 | − | 167.093i | 0.690466 | − | 0.690466i | ||||
\(243\) | −182.091 | + | 160.909i | −0.749346 | + | 0.662178i | ||||
\(244\) | −161.374 | −0.661370 | ||||||||
\(245\) | −192.343 | − | 151.754i | −0.785073 | − | 0.619403i | ||||
\(246\) | −0.0463622 | + | 3.75831i | −0.000188464 | + | 0.0152777i | ||||
\(247\) | −252.888 | − | 252.888i | −1.02384 | − | 1.02384i | ||||
\(248\) | 73.7983 | − | 73.7983i | 0.297574 | − | 0.297574i | ||||
\(249\) | −3.14037 | + | 254.572i | −0.0126119 | + | 1.02238i | ||||
\(250\) | 175.939 | + | 17.1938i | 0.703754 | + | 0.0687750i | ||||
\(251\) | 387.377 | 1.54334 | 0.771668 | − | 0.636026i | \(-0.219423\pi\) | ||||
0.771668 | + | 0.636026i | \(0.219423\pi\) | |||||||
\(252\) | −38.6861 | − | 119.914i | −0.153516 | − | 0.475850i | ||||
\(253\) | −326.854 | + | 326.854i | −1.29191 | + | 1.29191i | ||||
\(254\) | 14.8044 | 0.0582849 | ||||||||
\(255\) | 40.1845 | + | 182.273i | 0.157586 | + | 0.714796i | ||||
\(256\) | 16.0000 | 0.0625000 | ||||||||
\(257\) | 181.485 | + | 181.485i | 0.706167 | + | 0.706167i | 0.965727 | − | 0.259560i | \(-0.0835776\pi\) |
−0.259560 | + | 0.965727i | \(0.583578\pi\) | |||||||
\(258\) | −41.3730 | − | 42.4065i | −0.160361 | − | 0.164366i | ||||
\(259\) | −174.068 | + | 361.590i | −0.672078 | + | 1.39610i | ||||
\(260\) | −122.794 | − | 76.3151i | −0.472284 | − | 0.293520i | ||||
\(261\) | 0.372932 | − | 15.1134i | 0.00142886 | − | 0.0579059i | ||||
\(262\) | 16.3631 | − | 16.3631i | 0.0624544 | − | 0.0624544i | ||||
\(263\) | 181.005 | + | 181.005i | 0.688233 | + | 0.688233i | 0.961841 | − | 0.273608i | \(-0.0882171\pi\) |
−0.273608 | + | 0.961841i | \(0.588217\pi\) | |||||||
\(264\) | −1.77652 | + | 144.012i | −0.00672924 | + | 0.545501i | ||||
\(265\) | 44.6757 | − | 71.8849i | 0.168588 | − | 0.271264i | ||||
\(266\) | −220.648 | − | 106.219i | −0.829502 | − | 0.399319i | ||||
\(267\) | 107.646 | + | 110.335i | 0.403169 | + | 0.413240i | ||||
\(268\) | −8.92385 | + | 8.92385i | −0.0332979 | + | 0.0332979i | ||||
\(269\) | 197.175i | 0.732994i | 0.930419 | + | 0.366497i | \(0.119443\pi\) | ||||
−0.930419 | + | 0.366497i | \(0.880557\pi\) | |||||||
\(270\) | 36.4918 | + | 187.399i | 0.135155 | + | 0.694070i | ||||
\(271\) | − | 311.811i | − | 1.15059i | −0.817945 | − | 0.575296i | \(-0.804887\pi\) | ||
0.817945 | − | 0.575296i | \(-0.195113\pi\) | |||||||
\(272\) | −35.1951 | − | 35.1951i | −0.129394 | − | 0.129394i | ||||
\(273\) | −96.7752 | − | 287.774i | −0.354488 | − | 1.05412i | ||||
\(274\) | − | 204.044i | − | 0.744688i | ||||||
\(275\) | −187.870 | − | 380.477i | −0.683163 | − | 1.38355i | ||||
\(276\) | 2.01554 | − | 163.388i | 0.00730267 | − | 0.591986i | ||||
\(277\) | 161.718 | + | 161.718i | 0.583820 | + | 0.583820i | 0.935951 | − | 0.352131i | \(-0.114543\pi\) |
−0.352131 | + | 0.935951i | \(0.614543\pi\) | |||||||
\(278\) | −80.5228 | + | 80.5228i | −0.289650 | + | 0.289650i | ||||
\(279\) | −331.991 | − | 8.19206i | −1.18993 | − | 0.0293622i | ||||
\(280\) | −96.6234 | − | 21.5386i | −0.345084 | − | 0.0769237i | ||||
\(281\) | − | 182.531i | − | 0.649576i | −0.945787 | − | 0.324788i | \(-0.894707\pi\) | ||
0.945787 | − | 0.324788i | \(-0.105293\pi\) | |||||||
\(282\) | 144.961 | − | 141.428i | 0.514045 | − | 0.501517i | ||||
\(283\) | 13.2471 | + | 13.2471i | 0.0468095 | + | 0.0468095i | 0.730124 | − | 0.683315i | \(-0.239462\pi\) |
−0.683315 | + | 0.730124i | \(0.739462\pi\) | |||||||
\(284\) | −274.361 | −0.966059 | ||||||||
\(285\) | 312.710 | + | 199.735i | 1.09723 | + | 0.700823i | ||||
\(286\) | 347.039i | 1.21342i | ||||||||
\(287\) | 2.04903 | + | 5.85308i | 0.00713948 | + | 0.0203940i | ||||
\(288\) | −35.1010 | − | 36.8771i | −0.121878 | − | 0.128045i | ||||
\(289\) | − | 134.163i | − | 0.464233i | ||||||
\(290\) | −10.0883 | − | 6.26976i | −0.0347872 | − | 0.0216199i | ||||
\(291\) | −0.0143405 | + | 1.16250i | −4.92800e−5 | + | 0.00399485i | ||||
\(292\) | 106.649 | − | 106.649i | 0.365236 | − | 0.365236i | ||||
\(293\) | −45.8307 | + | 45.8307i | −0.156419 | + | 0.156419i | −0.780978 | − | 0.624559i | \(-0.785279\pi\) |
0.624559 | + | 0.780978i | \(0.285279\pi\) | |||||||
\(294\) | −127.650 | − | 164.084i | −0.434182 | − | 0.558109i | ||||
\(295\) | 245.955 | − | 57.4143i | 0.833747 | − | 0.194625i | ||||
\(296\) | 162.152i | 0.547812i | ||||||||
\(297\) | 335.819 | − | 311.841i | 1.13070 | − | 1.04997i | ||||
\(298\) | −140.338 | + | 140.338i | −0.470932 | + | 0.470932i | ||||
\(299\) | − | 393.731i | − | 1.31683i | ||||||
\(300\) | 141.459 | + | 49.8928i | 0.471531 | + | 0.166309i | ||||
\(301\) | −88.0761 | − | 42.3995i | −0.292612 | − | 0.140862i | ||||
\(302\) | −32.6929 | + | 32.6929i | −0.108255 | + | 0.108255i | ||||
\(303\) | −46.5508 | + | 45.4163i | −0.153633 | + | 0.149889i | ||||
\(304\) | −98.9478 | −0.325486 | ||||||||
\(305\) | 392.874 | − | 91.7100i | 1.28811 | − | 0.300689i | ||||
\(306\) | −3.90687 | + | 158.330i | −0.0127675 | + | 0.517417i | ||||
\(307\) | 273.273 | − | 273.273i | 0.890140 | − | 0.890140i | −0.104396 | − | 0.994536i | \(-0.533291\pi\) |
0.994536 | + | 0.104396i | \(0.0332909\pi\) | |||||||
\(308\) | 78.5153 | + | 224.280i | 0.254920 | + | 0.728182i | ||||
\(309\) | −209.633 | − | 2.58601i | −0.678425 | − | 0.00836898i | ||||
\(310\) | −137.726 | + | 221.606i | −0.444276 | + | 0.714857i | ||||
\(311\) | −408.594 | −1.31381 | −0.656903 | − | 0.753975i | \(-0.728134\pi\) | ||||
−0.656903 | + | 0.753975i | \(0.728134\pi\) | |||||||
\(312\) | −85.6692 | − | 87.8092i | −0.274581 | − | 0.281440i | ||||
\(313\) | −269.726 | − | 269.726i | −0.861746 | − | 0.861746i | 0.129795 | − | 0.991541i | \(-0.458568\pi\) |
−0.991541 | + | 0.129795i | \(0.958568\pi\) | |||||||
\(314\) | − | 35.9770i | − | 0.114576i | ||||||
\(315\) | 162.331 | + | 269.951i | 0.515337 | + | 0.856988i | ||||
\(316\) | −255.872 | −0.809721 | ||||||||
\(317\) | −265.401 | + | 265.401i | −0.837227 | + | 0.837227i | −0.988493 | − | 0.151266i | \(-0.951665\pi\) |
0.151266 | + | 0.988493i | \(0.451665\pi\) | |||||||
\(318\) | 51.4045 | − | 50.1517i | 0.161649 | − | 0.157710i | ||||
\(319\) | 28.5114i | 0.0893776i | ||||||||
\(320\) | −38.9528 | + | 9.09290i | −0.121727 | + | 0.0284153i | ||||
\(321\) | −2.23507 | + | 181.184i | −0.00696283 | + | 0.564437i | ||||
\(322\) | −89.0791 | − | 254.455i | −0.276643 | − | 0.790234i | ||||
\(323\) | 217.655 | + | 217.655i | 0.673854 | + | 0.673854i | ||||
\(324\) | −7.99001 | + | 161.803i | −0.0246605 | + | 0.499391i | ||||
\(325\) | 342.318 | + | 116.008i | 1.05329 | + | 0.356949i | ||||
\(326\) | 180.727i | 0.554378i | ||||||||
\(327\) | −144.800 | − | 148.417i | −0.442813 | − | 0.453875i | ||||
\(328\) | 1.77182 | + | 1.77182i | 0.00540189 | + | 0.00540189i | ||||
\(329\) | 144.937 | − | 301.075i | 0.440537 | − | 0.915123i | ||||
\(330\) | −77.5180 | − | 351.614i | −0.234903 | − | 1.06550i | ||||
\(331\) | 383.355 | 1.15817 | 0.579086 | − | 0.815266i | \(-0.303409\pi\) | ||||
0.579086 | + | 0.815266i | \(0.303409\pi\) | |||||||
\(332\) | 120.015 | + | 120.015i | 0.361492 | + | 0.361492i | ||||
\(333\) | 373.732 | − | 355.732i | 1.12232 | − | 1.06826i | ||||
\(334\) | 22.2592 | 0.0666444 | ||||||||
\(335\) | 16.6541 | − | 26.7970i | 0.0497136 | − | 0.0799911i | ||||
\(336\) | −75.2315 | − | 37.3661i | −0.223903 | − | 0.111209i | ||||
\(337\) | −207.675 | − | 207.675i | −0.616246 | − | 0.616246i | 0.328321 | − | 0.944566i | \(-0.393517\pi\) |
−0.944566 | + | 0.328321i | \(0.893517\pi\) | |||||||
\(338\) | −40.0232 | − | 40.0232i | −0.118412 | − | 0.118412i | ||||
\(339\) | 246.566 | + | 3.04161i | 0.727333 | + | 0.00897229i | ||||
\(340\) | 105.686 | + | 65.6826i | 0.310840 | + | 0.193184i | ||||
\(341\) | 626.300 | 1.83666 | ||||||||
\(342\) | 217.073 | + | 228.057i | 0.634716 | + | 0.666832i | ||||
\(343\) | −290.505 | − | 182.361i | −0.846955 | − | 0.531665i | ||||
\(344\) | −39.4971 | −0.114817 | ||||||||
\(345\) | 87.9475 | + | 398.922i | 0.254920 | + | 1.15630i | ||||
\(346\) | 287.409i | 0.830661i | ||||||||
\(347\) | −41.3813 | + | 41.3813i | −0.119254 | + | 0.119254i | −0.764215 | − | 0.644961i | \(-0.776874\pi\) |
0.644961 | + | 0.764215i | \(0.276874\pi\) | |||||||
\(348\) | −7.03826 | − | 7.21408i | −0.0202249 | − | 0.0207301i | ||||
\(349\) | −565.082 | −1.61915 | −0.809573 | − | 0.587019i | \(-0.800302\pi\) | ||||
−0.809573 | + | 0.587019i | \(0.800302\pi\) | |||||||
\(350\) | 247.475 | − | 2.47482i | 0.707071 | − | 0.00707091i | ||||
\(351\) | −14.4421 | + | 390.089i | −0.0411457 | + | 1.11136i | ||||
\(352\) | 67.8932 | + | 67.8932i | 0.192878 | + | 0.192878i | ||||
\(353\) | 121.484 | − | 121.484i | 0.344146 | − | 0.344146i | −0.513778 | − | 0.857923i | \(-0.671754\pi\) |
0.857923 | + | 0.513778i | \(0.171754\pi\) | |||||||
\(354\) | 214.295 | + | 2.64351i | 0.605352 | + | 0.00746756i | ||||
\(355\) | 667.945 | − | 155.921i | 1.88153 | − | 0.439214i | ||||
\(356\) | 102.765 | 0.288666 | ||||||||
\(357\) | 83.2921 | + | 247.680i | 0.233311 | + | 0.693782i | ||||
\(358\) | 334.691 | − | 334.691i | 0.934891 | − | 0.934891i | ||||
\(359\) | −129.751 | −0.361424 | −0.180712 | − | 0.983536i | \(-0.557840\pi\) | ||||
−0.180712 | + | 0.983536i | \(0.557840\pi\) | |||||||
\(360\) | 106.413 | + | 69.8310i | 0.295590 | + | 0.193975i | ||||
\(361\) | 250.916 | 0.695059 | ||||||||
\(362\) | −99.3599 | − | 99.3599i | −0.274475 | − | 0.274475i | ||||
\(363\) | −358.802 | + | 350.058i | −0.988437 | + | 0.964347i | ||||
\(364\) | −182.375 | − | 87.7947i | −0.501030 | − | 0.241194i | ||||
\(365\) | −199.033 | + | 320.251i | −0.545295 | + | 0.877399i | ||||
\(366\) | 342.301 | + | 4.22258i | 0.935248 | + | 0.0115371i | ||||
\(367\) | −476.739 | + | 476.739i | −1.29902 | + | 1.29902i | −0.369976 | + | 0.929041i | \(0.620634\pi\) |
−0.929041 | + | 0.369976i | \(0.879366\pi\) | |||||||
\(368\) | −77.0278 | − | 77.0278i | −0.209315 | − | 0.209315i | ||||
\(369\) | 0.196683 | − | 7.97077i | 0.000533016 | − | 0.0216010i | ||||
\(370\) | −92.1521 | − | 394.768i | −0.249060 | − | 1.06694i | ||||
\(371\) | 51.3960 | − | 106.764i | 0.138534 | − | 0.287775i | ||||
\(372\) | −158.469 | + | 154.607i | −0.425992 | + | 0.415610i | ||||
\(373\) | 76.1479 | − | 76.1479i | 0.204150 | − | 0.204150i | −0.597626 | − | 0.801775i | \(-0.703889\pi\) |
0.801775 | + | 0.597626i | \(0.203889\pi\) | |||||||
\(374\) | − | 298.688i | − | 0.798632i | ||||||
\(375\) | −372.744 | − | 41.0744i | −0.993983 | − | 0.109532i | ||||
\(376\) | − | 135.015i | − | 0.359083i | ||||||
\(377\) | −17.1726 | − | 17.1726i | −0.0455506 | − | 0.0455506i | ||||
\(378\) | 78.9216 | + | 255.369i | 0.208787 | + | 0.675580i | ||||
\(379\) | 390.814i | 1.03117i | 0.856838 | + | 0.515585i | \(0.172426\pi\) | ||||
−0.856838 | + | 0.515585i | \(0.827574\pi\) | |||||||
\(380\) | 240.893 | − | 56.2326i | 0.633929 | − | 0.147981i | ||||
\(381\) | −31.4024 | − | 0.387377i | −0.0824210 | − | 0.00101674i | ||||
\(382\) | −41.5022 | − | 41.5022i | −0.108645 | − | 0.108645i | ||||
\(383\) | −62.8508 | + | 62.8508i | −0.164101 | + | 0.164101i | −0.784381 | − | 0.620280i | \(-0.787019\pi\) |
0.620280 | + | 0.784381i | \(0.287019\pi\) | |||||||
\(384\) | −33.9385 | − | 0.418662i | −0.0883816 | − | 0.00109027i | ||||
\(385\) | −318.609 | − | 501.400i | −0.827556 | − | 1.30234i | ||||
\(386\) | 224.508i | 0.581626i | ||||||||
\(387\) | 86.6492 | + | 91.0336i | 0.223900 | + | 0.235229i | ||||
\(388\) | 0.548049 | + | 0.548049i | 0.00141250 | + | 0.00141250i | ||||
\(389\) | 24.2532 | 0.0623476 | 0.0311738 | − | 0.999514i | \(-0.490075\pi\) | ||||
0.0311738 | + | 0.999514i | \(0.490075\pi\) | |||||||
\(390\) | 258.468 | + | 165.090i | 0.662739 | + | 0.423306i | ||||
\(391\) | 338.875i | 0.866688i | ||||||||
\(392\) | −137.726 | − | 15.4777i | −0.351342 | − | 0.0394839i | ||||
\(393\) | −35.1368 | + | 34.2805i | −0.0894066 | + | 0.0872277i | ||||
\(394\) | 355.541i | 0.902388i | ||||||||
\(395\) | 622.932 | − | 145.413i | 1.57704 | − | 0.368135i | ||||
\(396\) | 7.53656 | − | 305.426i | 0.0190317 | − | 0.771279i | ||||
\(397\) | −176.911 | + | 176.911i | −0.445618 | + | 0.445618i | −0.893895 | − | 0.448277i | \(-0.852038\pi\) |
0.448277 | + | 0.893895i | \(0.352038\pi\) | |||||||
\(398\) | −79.5223 | + | 79.5223i | −0.199805 | + | 0.199805i | ||||
\(399\) | 465.249 | + | 231.081i | 1.16604 | + | 0.579150i | ||||
\(400\) | 89.6649 | − | 44.2742i | 0.224162 | − | 0.110685i | ||||
\(401\) | 48.5936i | 0.121181i | 0.998163 | + | 0.0605905i | \(0.0192984\pi\) | ||||
−0.998163 | + | 0.0605905i | \(0.980702\pi\) | |||||||
\(402\) | 19.1624 | − | 18.6954i | 0.0476677 | − | 0.0465060i | ||||
\(403\) | −377.223 | + | 377.223i | −0.936038 | + | 0.936038i | ||||
\(404\) | 43.3570i | 0.107319i | ||||||||
\(405\) | −72.5015 | − | 398.458i | −0.179016 | − | 0.983846i | ||||
\(406\) | −14.9833 | − | 7.21289i | −0.0369046 | − | 0.0177657i | ||||
\(407\) | −688.065 | + | 688.065i | −1.69058 | + | 1.69058i | ||||
\(408\) | 73.7334 | + | 75.5753i | 0.180719 | + | 0.185234i | ||||
\(409\) | −143.848 | −0.351706 | −0.175853 | − | 0.984416i | \(-0.556268\pi\) | ||||
−0.175853 | + | 0.984416i | \(0.556268\pi\) | |||||||
\(410\) | −5.32052 | − | 3.30665i | −0.0129769 | − | 0.00806500i | ||||
\(411\) | −5.33910 | + | 432.811i | −0.0129905 | + | 1.05307i | ||||
\(412\) | −98.8296 | + | 98.8296i | −0.239878 | + | 0.239878i | ||||
\(413\) | 333.735 | − | 116.833i | 0.808076 | − | 0.282889i | ||||
\(414\) | −8.55055 | + | 346.519i | −0.0206535 | + | 0.837003i | ||||
\(415\) | −360.389 | − | 223.978i | −0.868407 | − | 0.539706i | ||||
\(416\) | −81.7847 | −0.196598 | ||||||||
\(417\) | 172.909 | − | 168.695i | 0.414649 | − | 0.404543i | ||||
\(418\) | −419.867 | − | 419.867i | −1.00447 | − | 1.00447i | ||||
\(419\) | 80.8927i | 0.193061i | 0.995330 | + | 0.0965306i | \(0.0307746\pi\) | ||||
−0.995330 | + | 0.0965306i | \(0.969225\pi\) | |||||||
\(420\) | 204.390 | + | 48.2152i | 0.486643 | + | 0.114798i | ||||
\(421\) | −194.231 | −0.461355 | −0.230678 | − | 0.973030i | \(-0.574094\pi\) | ||||
−0.230678 | + | 0.973030i | \(0.574094\pi\) | |||||||
\(422\) | −398.914 | + | 398.914i | −0.945294 | + | 0.945294i | ||||
\(423\) | −311.185 | + | 296.198i | −0.735662 | + | 0.700231i | ||||
\(424\) | − | 47.8777i | − | 0.112919i | ||||||
\(425\) | −294.625 | − | 99.8456i | −0.693235 | − | 0.234931i | ||||
\(426\) | 581.963 | + | 7.17903i | 1.36611 | + | 0.0168522i | ||||
\(427\) | 533.088 | − | 186.622i | 1.24845 | − | 0.437054i | ||||
\(428\) | 85.4175 | + | 85.4175i | 0.199574 | + | 0.199574i | ||||
\(429\) | 9.08076 | − | 736.125i | 0.0211673 | − | 1.71591i | ||||
\(430\) | 96.1576 | − | 22.4464i | 0.223622 | − | 0.0522010i | ||||
\(431\) | − | 577.019i | − | 1.33879i | −0.742906 | − | 0.669396i | \(-0.766553\pi\) | ||
0.742906 | − | 0.669396i | \(-0.233447\pi\) | |||||||
\(432\) | 73.4899 | + | 79.1406i | 0.170115 | + | 0.183196i | ||||
\(433\) | 42.9015 | + | 42.9015i | 0.0990797 | + | 0.0990797i | 0.754909 | − | 0.655829i | \(-0.227681\pi\) |
−0.655829 | + | 0.754909i | \(0.727681\pi\) | |||||||
\(434\) | −158.443 | + | 329.131i | −0.365075 | + | 0.758367i | ||||
\(435\) | 21.2348 | + | 13.5631i | 0.0488156 | + | 0.0311796i | ||||
\(436\) | −138.234 | −0.317051 | ||||||||
\(437\) | 476.358 | + | 476.358i | 1.09006 | + | 1.09006i | ||||
\(438\) | −229.010 | + | 223.428i | −0.522853 | + | 0.510110i | ||||
\(439\) | 73.7420 | 0.167977 | 0.0839886 | − | 0.996467i | \(-0.473234\pi\) | ||||
0.0839886 | + | 0.996467i | \(0.473234\pi\) | |||||||
\(440\) | −203.873 | − | 126.705i | −0.463349 | − | 0.287966i | ||||
\(441\) | 266.472 | + | 351.388i | 0.604244 | + | 0.796799i | ||||
\(442\) | 179.901 | + | 179.901i | 0.407017 | + | 0.407017i | ||||
\(443\) | 10.4996 | + | 10.4996i | 0.0237011 | + | 0.0237011i | 0.718858 | − | 0.695157i | \(-0.244665\pi\) |
−0.695157 | + | 0.718858i | \(0.744665\pi\) | |||||||
\(444\) | 4.24294 | − | 343.951i | 0.00955617 | − | 0.774664i | ||||
\(445\) | −250.187 | + | 58.4020i | −0.562217 | + | 0.131241i | ||||
\(446\) | −325.271 | −0.729308 | ||||||||
\(447\) | 301.351 | − | 294.006i | 0.674163 | − | 0.657732i | ||||
\(448\) | −52.8548 | + | 18.5033i | −0.117979 | + | 0.0413019i | ||||
\(449\) | −284.237 | −0.633044 | −0.316522 | − | 0.948585i | \(-0.602515\pi\) | ||||
−0.316522 | + | 0.948585i | \(0.602515\pi\) | |||||||
\(450\) | −298.752 | − | 109.532i | −0.663893 | − | 0.243405i | ||||
\(451\) | 15.0368i | 0.0333411i | ||||||||
\(452\) | 116.241 | − | 116.241i | 0.257170 | − | 0.257170i | ||||
\(453\) | 70.2023 | − | 68.4914i | 0.154972 | − | 0.151195i | ||||
\(454\) | 511.204 | 1.12600 | ||||||||
\(455\) | 493.895 | + | 110.096i | 1.08548 | + | 0.241969i | ||||
\(456\) | 209.884 | + | 2.58911i | 0.460272 | + | 0.00567786i | ||||
\(457\) | −117.076 | − | 117.076i | −0.256184 | − | 0.256184i | 0.567316 | − | 0.823500i | \(-0.307982\pi\) |
−0.823500 | + | 0.567316i | \(0.807982\pi\) | |||||||
\(458\) | −188.516 | + | 188.516i | −0.411606 | + | 0.411606i | ||||
\(459\) | 12.4300 | − | 335.740i | 0.0270806 | − | 0.731460i | ||||
\(460\) | 231.303 | + | 143.753i | 0.502833 | + | 0.312505i | ||||
\(461\) | −221.554 | −0.480594 | −0.240297 | − | 0.970699i | \(-0.577245\pi\) | ||||
−0.240297 | + | 0.970699i | \(0.577245\pi\) | |||||||
\(462\) | −160.675 | − | 477.788i | −0.347781 | − | 1.03417i | ||||
\(463\) | −315.054 | + | 315.054i | −0.680462 | + | 0.680462i | −0.960104 | − | 0.279642i | \(-0.909784\pi\) |
0.279642 | + | 0.960104i | \(0.409784\pi\) | |||||||
\(464\) | −6.71913 | −0.0144809 | ||||||||
\(465\) | 297.936 | − | 466.457i | 0.640723 | − | 1.00313i | ||||
\(466\) | −33.4788 | −0.0718429 | ||||||||
\(467\) | −229.349 | − | 229.349i | −0.491111 | − | 0.491111i | 0.417545 | − | 0.908656i | \(-0.362891\pi\) |
−0.908656 | + | 0.417545i | \(0.862891\pi\) | |||||||
\(468\) | 179.420 | + | 188.499i | 0.383377 | + | 0.402776i | ||||
\(469\) | 19.1592 | − | 39.7993i | 0.0408513 | − | 0.0848599i | ||||
\(470\) | 76.7299 | + | 328.701i | 0.163255 | + | 0.699363i | ||||
\(471\) | −0.941388 | + | 76.3129i | −0.00199870 | + | 0.162023i | ||||
\(472\) | 101.027 | − | 101.027i | 0.214041 | − | 0.214041i | ||||
\(473\) | −167.599 | − | 167.599i | −0.354332 | − | 0.354332i | ||||
\(474\) | 542.745 | + | 6.69524i | 1.14503 | + | 0.0141250i | ||||
\(475\) | −554.509 | + | 273.802i | −1.16739 | + | 0.576425i | ||||
\(476\) | 156.966 | + | 75.5628i | 0.329760 | + | 0.158745i | ||||
\(477\) | −110.349 | + | 105.035i | −0.231341 | + | 0.220199i | ||||
\(478\) | 93.1494 | − | 93.1494i | 0.194873 | − | 0.194873i | ||||
\(479\) | − | 166.037i | − | 0.346633i | −0.984866 | − | 0.173316i | \(-0.944552\pi\) | ||
0.984866 | − | 0.173316i | \(-0.0554483\pi\) | |||||||
\(480\) | 82.8630 | − | 18.2682i | 0.172631 | − | 0.0380588i | ||||
\(481\) | − | 828.849i | − | 1.72318i | ||||||
\(482\) | −443.888 | − | 443.888i | −0.920929 | − | 0.920929i | ||||
\(483\) | 182.293 | + | 542.071i | 0.377418 | + | 1.12230i | ||||
\(484\) | 334.185i | 0.690466i | ||||||||
\(485\) | −1.64571 | − | 1.02279i | −0.00339322 | − | 0.00210885i | ||||
\(486\) | 21.1819 | − | 343.000i | 0.0435841 | − | 0.705762i | ||||
\(487\) | −639.073 | − | 639.073i | −1.31226 | − | 1.31226i | −0.919743 | − | 0.392521i | \(-0.871603\pi\) |
−0.392521 | − | 0.919743i | \(-0.628397\pi\) | |||||||
\(488\) | 161.374 | − | 161.374i | 0.330685 | − | 0.330685i | ||||
\(489\) | 4.72898 | − | 383.351i | 0.00967071 | − | 0.783949i | ||||
\(490\) | 344.097 | − | 40.5893i | 0.702238 | − | 0.0828353i | ||||
\(491\) | − | 148.567i | − | 0.302581i | −0.988489 | − | 0.151291i | \(-0.951657\pi\) | ||
0.988489 | − | 0.151291i | \(-0.0483429\pi\) | |||||||
\(492\) | −3.71195 | − | 3.80468i | −0.00754462 | − | 0.00773308i | ||||
\(493\) | 14.7800 | + | 14.7800i | 0.0299798 | + | 0.0299798i | ||||
\(494\) | 505.776 | 1.02384 | ||||||||
\(495\) | 155.227 | + | 747.858i | 0.313591 | + | 1.51083i | ||||
\(496\) | 147.597i | 0.297574i | ||||||||
\(497\) | 906.330 | − | 317.286i | 1.82360 | − | 0.638402i | ||||
\(498\) | −251.431 | − | 257.712i | −0.504882 | − | 0.517494i | ||||
\(499\) | 471.498i | 0.944885i | 0.881361 | + | 0.472443i | \(0.156628\pi\) | ||||
−0.881361 | + | 0.472443i | \(0.843372\pi\) | |||||||
\(500\) | −193.132 | + | 158.745i | −0.386265 | + | 0.317490i | ||||
\(501\) | −47.2153 | − | 0.582443i | −0.0942422 | − | 0.00116256i | ||||
\(502\) | −387.377 | + | 387.377i | −0.771668 | + | 0.771668i | ||||
\(503\) | 40.7334 | − | 40.7334i | 0.0809810 | − | 0.0809810i | −0.665456 | − | 0.746437i | \(-0.731763\pi\) |
0.746437 | + | 0.665456i | \(0.231763\pi\) | |||||||
\(504\) | 158.600 | + | 81.2280i | 0.314683 | + | 0.161167i | ||||
\(505\) | −24.6400 | − | 105.555i | −0.0487921 | − | 0.209019i | ||||
\(506\) | − | 653.707i | − | 1.29191i | ||||||
\(507\) | 83.8483 | + | 85.9428i | 0.165381 | + | 0.169512i | ||||
\(508\) | −14.8044 | + | 14.8044i | −0.0291424 | + | 0.0291424i | ||||
\(509\) | 834.832i | 1.64014i | 0.572263 | + | 0.820070i | \(0.306066\pi\) | ||||
−0.572263 | + | 0.820070i | \(0.693934\pi\) | |||||||
\(510\) | −222.458 | − | 142.089i | −0.436191 | − | 0.278605i | ||||
\(511\) | −228.972 | + | 475.641i | −0.448086 | + | 0.930803i | ||||
\(512\) | −16.0000 | + | 16.0000i | −0.0312500 | + | 0.0312500i | ||||
\(513\) | −454.479 | − | 489.424i | −0.885923 | − | 0.954044i | ||||
\(514\) | −362.970 | −0.706167 | ||||||||
\(515\) | 184.440 | − | 296.771i | 0.358136 | − | 0.576254i | ||||
\(516\) | 83.7796 | + | 1.03350i | 0.162364 | + | 0.00200290i | ||||
\(517\) | 572.913 | − | 572.913i | 1.10815 | − | 1.10815i | ||||
\(518\) | −187.522 | − | 535.658i | −0.362011 | − | 1.03409i | ||||
\(519\) | 7.52045 | − | 609.640i | 0.0144903 | − | 1.17464i | ||||
\(520\) | 199.109 | − | 46.4788i | 0.382902 | − | 0.0893822i | ||||
\(521\) | −690.826 | −1.32596 | −0.662980 | − | 0.748637i | \(-0.730709\pi\) | ||||
−0.662980 | + | 0.748637i | \(0.730709\pi\) | |||||||
\(522\) | 14.7405 | + | 15.4864i | 0.0282385 | + | 0.0296674i | ||||
\(523\) | −560.737 | − | 560.737i | −1.07216 | − | 1.07216i | −0.997186 | − | 0.0749699i | \(-0.976114\pi\) |
−0.0749699 | − | 0.997186i | \(-0.523886\pi\) | |||||||
\(524\) | 32.7261i | 0.0624544i | ||||||||
\(525\) | −524.999 | − | 1.22605i | −0.999997 | − | 0.00233532i | ||||
\(526\) | −362.011 | −0.688233 | ||||||||
\(527\) | 324.667 | − | 324.667i | 0.616067 | − | 0.616067i | ||||
\(528\) | −142.236 | − | 145.789i | −0.269386 | − | 0.276115i | ||||
\(529\) | 212.659i | 0.402003i | ||||||||
\(530\) | 27.2092 | + | 116.561i | 0.0513381 | + | 0.219926i | ||||
\(531\) | −454.484 | − | 11.2146i | −0.855902 | − | 0.0211198i | ||||
\(532\) | 326.866 | − | 114.429i | 0.614411 | − | 0.215091i | ||||
\(533\) | −9.05675 | − | 9.05675i | −0.0169920 | − | 0.0169920i | ||||
\(534\) | −217.981 | − | 2.68899i | −0.408204 | − | 0.00503557i | ||||
\(535\) | −256.496 | − | 159.410i | −0.479433 | − | 0.297962i | ||||
\(536\) | − | 17.8477i | − | 0.0332979i | ||||||
\(537\) | −718.690 | + | 701.175i | −1.33834 | + | 1.30573i | ||||
\(538\) | −197.175 | − | 197.175i | −0.366497 | − | 0.366497i | ||||
\(539\) | −518.739 | − | 650.093i | −0.962410 | − | 1.20611i | ||||
\(540\) | −223.891 | − | 150.907i | −0.414612 | − | 0.279457i | ||||
\(541\) | 655.178 | 1.21105 | 0.605525 | − | 0.795827i | \(-0.292963\pi\) | ||||
0.605525 | + | 0.795827i | \(0.292963\pi\) | |||||||
\(542\) | 311.811 | + | 311.811i | 0.575296 | + | 0.575296i | ||||
\(543\) | 208.158 | + | 213.358i | 0.383348 | + | 0.392924i | ||||
\(544\) | 70.3902 | 0.129394 | ||||||||
\(545\) | 336.538 | − | 78.5594i | 0.617501 | − | 0.144146i | ||||
\(546\) | 384.549 | + | 190.999i | 0.704302 | + | 0.349814i | ||||
\(547\) | 253.750 | + | 253.750i | 0.463894 | + | 0.463894i | 0.899929 | − | 0.436036i | \(-0.143618\pi\) |
−0.436036 | + | 0.899929i | \(0.643618\pi\) | |||||||
\(548\) | 204.044 | + | 204.044i | 0.372344 | + | 0.372344i | ||||
\(549\) | −725.964 | − | 17.9135i | −1.32234 | − | 0.0326294i | ||||
\(550\) | 568.347 | + | 192.607i | 1.03336 | + | 0.350195i | ||||
\(551\) | 41.5527 | 0.0754132 | ||||||||
\(552\) | 161.373 | + | 165.404i | 0.292342 | + | 0.299644i | ||||
\(553\) | 845.253 | − | 295.904i | 1.52849 | − | 0.535088i | ||||
\(554\) | −323.436 | −0.583820 | ||||||||
\(555\) | 185.140 | + | 839.776i | 0.333585 | + | 1.51311i | ||||
\(556\) | − | 161.046i | − | 0.289650i | ||||||
\(557\) | 468.602 | − | 468.602i | 0.841296 | − | 0.841296i | −0.147731 | − | 0.989028i | \(-0.547197\pi\) |
0.989028 | + | 0.147731i | \(0.0471971\pi\) | |||||||
\(558\) | 340.183 | − | 323.799i | 0.609647 | − | 0.580285i | ||||
\(559\) | 201.891 | 0.361165 | ||||||||
\(560\) | 118.162 | − | 75.0848i | 0.211004 | − | 0.134080i | ||||
\(561\) | −7.81559 | + | 633.565i | −0.0139315 | + | 1.12935i | ||||
\(562\) | 182.531 | + | 182.531i | 0.324788 | + | 0.324788i | ||||
\(563\) | 10.9862 | − | 10.9862i | 0.0195137 | − | 0.0195137i | −0.697283 | − | 0.716796i | \(-0.745608\pi\) |
0.716796 | + | 0.697283i | \(0.245608\pi\) | |||||||
\(564\) | −3.53286 | + | 286.388i | −0.00626393 | + | 0.507781i | ||||
\(565\) | −216.934 | + | 349.055i | −0.383954 | + | 0.617796i | ||||
\(566\) | −26.4942 | −0.0468095 | ||||||||
\(567\) | −160.723 | − | 543.744i | −0.283462 | − | 0.958983i | ||||
\(568\) | 274.361 | − | 274.361i | 0.483029 | − | 0.483029i | ||||
\(569\) | 122.993 | 0.216157 | 0.108079 | − | 0.994142i | \(-0.465530\pi\) | ||||
0.108079 | + | 0.994142i | \(0.465530\pi\) | |||||||
\(570\) | −512.444 | + | 112.975i | −0.899025 | + | 0.198202i | ||||
\(571\) | −863.540 | −1.51233 | −0.756164 | − | 0.654382i | \(-0.772929\pi\) | ||||
−0.756164 | + | 0.654382i | \(0.772929\pi\) | |||||||
\(572\) | −347.039 | − | 347.039i | −0.606712 | − | 0.606712i | ||||
\(573\) | 86.9469 | + | 89.1188i | 0.151740 | + | 0.155530i | ||||
\(574\) | −7.90211 | − | 3.80405i | −0.0137667 | − | 0.00662726i | ||||
\(575\) | −644.814 | − | 218.522i | −1.12142 | − | 0.380037i | ||||
\(576\) | 71.9781 | + | 1.77610i | 0.124962 | + | 0.00308350i | ||||
\(577\) | −604.940 | + | 604.940i | −1.04842 | + | 1.04842i | −0.0496572 | + | 0.998766i | \(0.515813\pi\) |
−0.998766 | + | 0.0496572i | \(0.984187\pi\) | |||||||
\(578\) | 134.163 | + | 134.163i | 0.232116 | + | 0.232116i | ||||
\(579\) | 5.87455 | − | 476.216i | 0.0101460 | − | 0.822481i | ||||
\(580\) | 16.3580 | − | 3.81852i | 0.0282035 | − | 0.00658366i | ||||
\(581\) | −535.254 | − | 257.670i | −0.921264 | − | 0.443493i | ||||
\(582\) | −1.14816 | − | 1.17684i | −0.00197278 | − | 0.00202206i | ||||
\(583\) | 203.161 | − | 203.161i | 0.348475 | − | 0.348475i | ||||
\(584\) | 213.298i | 0.365236i | ||||||||
\(585\) | −543.933 | − | 356.944i | −0.929799 | − | 0.610161i | ||||
\(586\) | − | 91.6614i | − | 0.156419i | ||||||
\(587\) | 354.852 | + | 354.852i | 0.604518 | + | 0.604518i | 0.941508 | − | 0.336990i | \(-0.109409\pi\) |
−0.336990 | + | 0.941508i | \(0.609409\pi\) | |||||||
\(588\) | 291.734 | + | 36.4344i | 0.496146 | + | 0.0619633i | ||||
\(589\) | − | 912.772i | − | 1.54970i | ||||||
\(590\) | −188.541 | + | 303.370i | −0.319561 | + | 0.514186i | ||||
\(591\) | 9.30322 | − | 754.159i | 0.0157415 | − | 1.27607i | ||||
\(592\) | −162.152 | − | 162.152i | −0.273906 | − | 0.273906i | ||||
\(593\) | −420.895 | + | 420.895i | −0.709772 | + | 0.709772i | −0.966487 | − | 0.256715i | \(-0.917360\pi\) |
0.256715 | + | 0.966487i | \(0.417360\pi\) | |||||||
\(594\) | −23.9781 | + | 647.661i | −0.0403672 | + | 1.09034i | ||||
\(595\) | −425.084 | − | 94.7568i | −0.714426 | − | 0.159255i | ||||
\(596\) | − | 280.675i | − | 0.470932i | ||||||
\(597\) | 170.760 | − | 166.599i | 0.286030 | − | 0.279060i | ||||
\(598\) | 393.731 | + | 393.731i | 0.658413 | + | 0.658413i | ||||
\(599\) | 761.718 | 1.27165 | 0.635824 | − | 0.771834i | \(-0.280660\pi\) | ||||
0.635824 | + | 0.771834i | \(0.280660\pi\) | |||||||
\(600\) | −191.352 | + | 91.5664i | −0.318920 | + | 0.152611i | ||||
\(601\) | 348.645i | 0.580109i | 0.957010 | + | 0.290054i | \(0.0936734\pi\) | ||||
−0.957010 | + | 0.290054i | \(0.906327\pi\) | |||||||
\(602\) | 130.476 | − | 45.6766i | 0.216737 | − | 0.0758747i | ||||
\(603\) | −41.1357 | + | 39.1545i | −0.0682184 | + | 0.0649328i | ||||
\(604\) | − | 65.3858i | − | 0.108255i | ||||||
\(605\) | −189.920 | − | 813.591i | −0.313917 | − | 1.34478i | ||||
\(606\) | 1.13449 | − | 91.9670i | 0.00187210 | − | 0.151761i | ||||
\(607\) | −520.469 | + | 520.469i | −0.857444 | + | 0.857444i | −0.991036 | − | 0.133592i | \(-0.957349\pi\) |
0.133592 | + | 0.991036i | \(0.457349\pi\) | |||||||
\(608\) | 98.9478 | − | 98.9478i | 0.162743 | − | 0.162743i | ||||
\(609\) | 31.5931 | + | 15.6917i | 0.0518770 | + | 0.0257664i | ||||
\(610\) | −301.164 | + | 484.584i | −0.493711 | + | 0.794400i | ||||
\(611\) | 690.136i | 1.12952i | ||||||||
\(612\) | −154.423 | − | 162.237i | −0.252325 | − | 0.265092i | ||||
\(613\) | 82.1048 | − | 82.1048i | 0.133939 | − | 0.133939i | −0.636959 | − | 0.770898i | \(-0.719808\pi\) |
0.770898 | + | 0.636959i | \(0.219808\pi\) | |||||||
\(614\) | 546.546i | 0.890140i | ||||||||
\(615\) | 11.1992 | + | 7.15315i | 0.0182100 | + | 0.0116311i | ||||
\(616\) | −302.795 | − | 145.765i | −0.491551 | − | 0.236631i | ||||
\(617\) | −186.511 | + | 186.511i | −0.302286 | + | 0.302286i | −0.841908 | − | 0.539621i | \(-0.818567\pi\) |
0.539621 | + | 0.841908i | \(0.318567\pi\) | |||||||
\(618\) | 212.219 | − | 207.047i | 0.343397 | − | 0.335028i | ||||
\(619\) | 608.262 | 0.982652 | 0.491326 | − | 0.870976i | \(-0.336512\pi\) | ||||
0.491326 | + | 0.870976i | \(0.336512\pi\) | |||||||
\(620\) | −83.8800 | − | 359.331i | −0.135290 | − | 0.579566i | ||||
\(621\) | 27.2042 | − | 734.799i | 0.0438072 | − | 1.18325i | ||||
\(622\) | 408.594 | − | 408.594i | 0.656903 | − | 0.656903i | ||||
\(623\) | −339.477 | + | 118.843i | −0.544907 | + | 0.190759i | ||||
\(624\) | 173.478 | + | 2.14001i | 0.278010 | + | 0.00342950i | ||||
\(625\) | 379.974 | − | 496.230i | 0.607959 | − | 0.793968i | ||||
\(626\) | 539.453 | 0.861746 | ||||||||
\(627\) | 879.619 | + | 901.592i | 1.40290 | + | 1.43795i | ||||
\(628\) | 35.9770 | + | 35.9770i | 0.0572882 | + | 0.0572882i | ||||
\(629\) | 713.371i | 1.13413i | ||||||||
\(630\) | −432.282 | − | 107.620i | −0.686162 | − | 0.170826i | ||||
\(631\) | 180.633 | 0.286265 | 0.143132 | − | 0.989704i | \(-0.454283\pi\) | ||||
0.143132 | + | 0.989704i | \(0.454283\pi\) | |||||||
\(632\) | 255.872 | − | 255.872i | 0.404860 | − | 0.404860i | ||||
\(633\) | 856.598 | − | 835.722i | 1.35324 | − | 1.32026i | ||||
\(634\) | − | 530.802i | − | 0.837227i | ||||||
\(635\) | 27.6285 | − | 44.4553i | 0.0435095 | − | 0.0700084i | ||||
\(636\) | −1.25279 | + | 101.556i | −0.00196979 | + | 0.159680i | ||||
\(637\) | 703.993 | + | 79.1149i | 1.10517 | + | 0.124199i | ||||
\(638\) | −28.5114 | − | 28.5114i | −0.0446888 | − | 0.0446888i | ||||
\(639\) | −1234.25 | − | 30.4557i | −1.93153 | − | 0.0476615i | ||||
\(640\) | 29.8599 | − | 48.0457i | 0.0466561 | − | 0.0750714i | ||||
\(641\) | 1036.40i | 1.61685i | 0.588597 | + | 0.808427i | \(0.299681\pi\) | ||||
−0.588597 | + | 0.808427i | \(0.700319\pi\) | |||||||
\(642\) | −178.949 | − | 183.419i | −0.278737 | − | 0.285700i | ||||
\(643\) | 639.514 | + | 639.514i | 0.994579 | + | 0.994579i | 0.999985 | − | 0.00540613i | \(-0.00172083\pi\) |
−0.00540613 | + | 0.999985i | \(0.501721\pi\) | |||||||
\(644\) | 343.534 | + | 165.376i | 0.533439 | + | 0.256796i | ||||
\(645\) | −204.553 | + | 45.0963i | −0.317136 | + | 0.0699168i | ||||
\(646\) | −435.309 | −0.673854 | ||||||||
\(647\) | −659.438 | − | 659.438i | −1.01922 | − | 1.01922i | −0.999812 | − | 0.0194122i | \(-0.993821\pi\) |
−0.0194122 | − | 0.999812i | \(-0.506179\pi\) | |||||||
\(648\) | −153.813 | − | 169.793i | −0.237365 | − | 0.262026i | ||||
\(649\) | 857.382 | 1.32108 | ||||||||
\(650\) | −458.326 | + | 226.310i | −0.705117 | + | 0.348169i | ||||
\(651\) | 344.694 | − | 693.994i | 0.529485 | − | 1.06604i | ||||
\(652\) | −180.727 | − | 180.727i | −0.277189 | − | 0.277189i | ||||
\(653\) | 334.285 | + | 334.285i | 0.511921 | + | 0.511921i | 0.915115 | − | 0.403194i | \(-0.132100\pi\) |
−0.403194 | + | 0.915115i | \(0.632100\pi\) | |||||||
\(654\) | 293.217 | + | 3.61709i | 0.448344 | + | 0.00553072i | ||||
\(655\) | −18.5984 | − | 79.6733i | −0.0283946 | − | 0.121639i | ||||
\(656\) | −3.54364 | −0.00540189 | ||||||||
\(657\) | 491.612 | − | 467.935i | 0.748268 | − | 0.712229i | ||||
\(658\) | 156.139 | + | 446.012i | 0.237293 | + | 0.677830i | ||||
\(659\) | −231.047 | −0.350602 | −0.175301 | − | 0.984515i | \(-0.556090\pi\) | ||||
−0.175301 | + | 0.984515i | \(0.556090\pi\) | |||||||
\(660\) | 429.132 | + | 274.096i | 0.650201 | + | 0.415298i | ||||
\(661\) | − | 513.220i | − | 0.776429i | −0.921569 | − | 0.388215i | \(-0.873092\pi\) | ||
0.921569 | − | 0.388215i | \(-0.126908\pi\) | |||||||
\(662\) | −383.355 | + | 383.355i | −0.579086 | + | 0.579086i | ||||
\(663\) | −376.892 | − | 386.307i | −0.568464 | − | 0.582665i | ||||
\(664\) | −240.031 | −0.361492 | ||||||||
\(665\) | −730.742 | + | 464.342i | −1.09886 | + | 0.698259i | ||||
\(666\) | −17.9999 | + | 729.463i | −0.0270269 | + | 1.09529i | ||||
\(667\) | 32.3475 | + | 32.3475i | 0.0484970 | + | 0.0484970i | ||||
\(668\) | −22.2592 | + | 22.2592i | −0.0333222 | + | 0.0333222i | ||||
\(669\) | 689.952 | + | 8.51117i | 1.03132 | + | 0.0127222i | ||||
\(670\) | 10.1430 | + | 43.4511i | 0.0151387 | + | 0.0648524i | ||||
\(671\) | 1369.53 | 2.04102 | ||||||||
\(672\) | 112.598 | − | 37.8653i | 0.167556 | − | 0.0563472i | ||||
\(673\) | −98.5465 | + | 98.5465i | −0.146429 | + | 0.146429i | −0.776521 | − | 0.630092i | \(-0.783017\pi\) |
0.630092 | + | 0.776521i | \(0.283017\pi\) | |||||||
\(674\) | 415.350 | 0.616246 | ||||||||
\(675\) | 630.834 | + | 240.152i | 0.934569 | + | 0.355781i | ||||
\(676\) | 80.0464 | 0.118412 | ||||||||
\(677\) | 856.497 | + | 856.497i | 1.26514 | + | 1.26514i | 0.948571 | + | 0.316565i | \(0.102529\pi\) |
0.316565 | + | 0.948571i | \(0.397471\pi\) | |||||||
\(678\) | −249.607 | + | 243.524i | −0.368152 | + | 0.359180i | ||||
\(679\) | −2.44423 | − | 1.17665i | −0.00359976 | − | 0.00173291i | ||||
\(680\) | −171.368 | + | 40.0032i | −0.252012 | + | 0.0588282i | ||||
\(681\) | −1084.35 | − | 13.3764i | −1.59228 | − | 0.0196422i | ||||
\(682\) | −626.300 | + | 626.300i | −0.918329 | + | 0.918329i | ||||
\(683\) | −423.420 | − | 423.420i | −0.619941 | − | 0.619941i | 0.325575 | − | 0.945516i | \(-0.394442\pi\) |
−0.945516 | + | 0.325575i | \(0.894442\pi\) | |||||||
\(684\) | −445.129 | − | 10.9838i | −0.650774 | − | 0.0160582i | ||||
\(685\) | −612.716 | − | 380.796i | −0.894476 | − | 0.555907i | ||||
\(686\) | 472.867 | − | 108.144i | 0.689310 | − | 0.157645i | ||||
\(687\) | 404.804 | − | 394.939i | 0.589235 | − | 0.574874i | ||||
\(688\) | 39.4971 | − | 39.4971i | 0.0574085 | − | 0.0574085i | ||||
\(689\) | 244.729i | 0.355195i | ||||||||
\(690\) | −486.869 | − | 310.974i | −0.705608 | − | 0.450687i | ||||
\(691\) | − | 785.969i | − | 1.13744i | −0.822532 | − | 0.568718i | \(-0.807439\pi\) | ||
0.822532 | − | 0.568718i | \(-0.192561\pi\) | |||||||
\(692\) | −287.409 | − | 287.409i | −0.415331 | − | 0.415331i | ||||
\(693\) | 328.315 | + | 1017.67i | 0.473759 | + | 1.46850i | ||||
\(694\) | − | 82.7625i | − | 0.119254i | ||||||
\(695\) | 91.5231 | + | 392.073i | 0.131688 | + | 0.564134i | ||||
\(696\) | 14.2523 | + | 0.175815i | 0.0204775 | + | 0.000252608i | ||||
\(697\) | 7.79493 | + | 7.79493i | 0.0111835 | + | 0.0111835i | ||||
\(698\) | 565.082 | − | 565.082i | 0.809573 | − | 0.809573i | ||||
\(699\) | 71.0138 | + | 0.876019i | 0.101593 | + | 0.00125325i | ||||
\(700\) | −245.000 | + | 249.950i | −0.350000 | + | 0.357071i | ||||
\(701\) | 462.898i | 0.660340i | 0.943922 | + | 0.330170i | \(0.107106\pi\) | ||||
−0.943922 | + | 0.330170i | \(0.892894\pi\) | |||||||
\(702\) | −375.647 | − | 404.531i | −0.535109 | − | 0.576255i | ||||
\(703\) | 1002.79 | + | 1002.79i | 1.42644 | + | 1.42644i | ||||
\(704\) | −135.786 | −0.192878 | ||||||||
\(705\) | −154.155 | − | 699.234i | −0.218660 | − | 0.991822i | ||||
\(706\) | 242.967i | 0.344146i | ||||||||
\(707\) | −50.1403 | − | 143.226i | −0.0709199 | − | 0.202583i | ||||
\(708\) | −216.938 | + | 211.651i | −0.306410 | + | 0.298942i | ||||
\(709\) | 946.923i | 1.33558i | 0.744352 | + | 0.667788i | \(0.232759\pi\) | ||||
−0.744352 | + | 0.667788i | \(0.767241\pi\) | |||||||
\(710\) | −512.024 | + | 823.865i | −0.721160 | + | 1.16037i | ||||
\(711\) | −1151.07 | − | 28.4033i | −1.61895 | − | 0.0399484i | ||||
\(712\) | −102.765 | + | 102.765i | −0.144333 | + | 0.144333i | ||||
\(713\) | 710.565 | − | 710.565i | 0.996584 | − | 0.996584i | ||||
\(714\) | −330.972 | − | 164.388i | −0.463547 | − | 0.230235i | ||||
\(715\) | 1042.11 | + | 647.659i | 1.45749 | + | 0.905817i | ||||
\(716\) | 669.382i | 0.934891i | ||||||||
\(717\) | −200.022 | + | 195.147i | −0.278971 | + | 0.272172i | ||||
\(718\) | 129.751 | − | 129.751i | 0.180712 | − | 0.180712i | ||||
\(719\) | − | 713.422i | − | 0.992242i | −0.868254 | − | 0.496121i | \(-0.834757\pi\) | ||
0.868254 | − | 0.496121i | \(-0.165243\pi\) | |||||||
\(720\) | −176.244 | + | 36.5816i | −0.244783 | + | 0.0508078i | ||||
\(721\) | 212.184 | − | 440.768i | 0.294292 | − | 0.611329i | ||||
\(722\) | −250.916 | + | 250.916i | −0.347530 | + | 0.347530i | ||||
\(723\) | 929.942 | + | 953.172i | 1.28623 | + | 1.31836i | ||||
\(724\) | 198.720 | 0.274475 | ||||||||
\(725\) | −37.6544 | + | 18.5928i | −0.0519371 | + | 0.0256452i | ||||
\(726\) | 8.74443 | − | 708.861i | 0.0120447 | − | 0.976392i | ||||
\(727\) | −521.776 | + | 521.776i | −0.717711 | + | 0.717711i | −0.968136 | − | 0.250425i | \(-0.919430\pi\) |
0.250425 | + | 0.968136i | \(0.419430\pi\) | |||||||
\(728\) | 270.170 | − | 94.5803i | 0.371112 | − | 0.129918i | ||||
\(729\) | −53.9052 | + | 727.004i | −0.0739440 | + | 0.997262i | ||||
\(730\) | −121.218 | − | 519.283i | −0.166052 | − | 0.711347i | ||||
\(731\) | −173.763 | −0.237706 | ||||||||
\(732\) | −346.523 | + | 338.078i | −0.473393 | + | 0.461855i | ||||
\(733\) | −121.904 | − | 121.904i | −0.166309 | − | 0.166309i | 0.619046 | − | 0.785355i | \(-0.287519\pi\) |
−0.785355 | + | 0.619046i | \(0.787519\pi\) | |||||||
\(734\) | − | 953.479i | − | 1.29902i | ||||||
\(735\) | −730.946 | + | 77.0926i | −0.994484 | + | 0.104888i | ||||
\(736\) | 154.056 | 0.209315 | ||||||||
\(737\) | 75.7335 | − | 75.7335i | 0.102759 | − | 0.102759i | ||||
\(738\) | 7.77409 | + | 8.16745i | 0.0105340 | + | 0.0110670i | ||||
\(739\) | 708.172i | 0.958284i | 0.877737 | + | 0.479142i | \(0.159052\pi\) | ||||
−0.877737 | + | 0.479142i | \(0.840948\pi\) | |||||||
\(740\) | 486.920 | + | 302.616i | 0.658000 | + | 0.408940i | ||||
\(741\) | −1072.83 | − | 13.2343i | −1.44782 | − | 0.0178601i | ||||
\(742\) | 55.3684 | + | 158.160i | 0.0746205 | + | 0.213154i | ||||
\(743\) | 212.648 | + | 212.648i | 0.286202 | + | 0.286202i | 0.835576 | − | 0.549374i | \(-0.185134\pi\) |
−0.549374 | + | 0.835576i | \(0.685134\pi\) | |||||||
\(744\) | 3.86207 | − | 313.076i | 0.00519095 | − | 0.420801i | ||||
\(745\) | 159.509 | + | 683.318i | 0.214107 | + | 0.917205i | ||||
\(746\) | 152.296i | 0.204150i | ||||||||
\(747\) | 526.583 | + | 553.228i | 0.704930 | + | 0.740599i | ||||
\(748\) | 298.688 | + | 298.688i | 0.399316 | + | 0.399316i | ||||
\(749\) | −380.952 | − | 183.389i | −0.508614 | − | 0.244845i | ||||
\(750\) | 413.818 | − | 331.669i | 0.551757 | − | 0.442226i | ||||
\(751\) | −588.834 | −0.784067 | −0.392034 | − | 0.919951i | \(-0.628228\pi\) | ||||
−0.392034 | + | 0.919951i | \(0.628228\pi\) | |||||||
\(752\) | 135.015 | + | 135.015i | 0.179541 | + | 0.179541i | ||||
\(753\) | 831.825 | − | 811.552i | 1.10468 | − | 1.07776i | ||||
\(754\) | 34.3451 | 0.0455506 | ||||||||
\(755\) | 37.1591 | + | 159.185i | 0.0492174 | + | 0.210841i | ||||
\(756\) | −334.291 | − | 176.448i | −0.442183 | − | 0.233396i | ||||
\(757\) | −627.004 | − | 627.004i | −0.828275 | − | 0.828275i | 0.159003 | − | 0.987278i | \(-0.449172\pi\) |
−0.987278 | + | 0.159003i | \(0.949172\pi\) | |||||||
\(758\) | −390.814 | − | 390.814i | −0.515585 | − | 0.515585i | ||||
\(759\) | −17.1052 | + | 1386.62i | −0.0225364 | + | 1.82690i | ||||
\(760\) | −184.661 | + | 297.126i | −0.242974 | + | 0.390955i | ||||
\(761\) | −1055.93 | −1.38756 | −0.693780 | − | 0.720187i | \(-0.744056\pi\) | ||||
−0.693780 | + | 0.720187i | \(0.744056\pi\) | |||||||
\(762\) | 31.7898 | − | 31.0150i | 0.0417189 | − | 0.0407021i | ||||
\(763\) | 456.647 | − | 159.862i | 0.598488 | − | 0.209517i | ||||
\(764\) | 83.0045 | 0.108645 | ||||||||
\(765\) | 468.150 | + | 307.213i | 0.611961 | + | 0.401586i | ||||
\(766\) | − | 125.702i | − | 0.164101i | ||||||
\(767\) | −516.405 | + | 516.405i | −0.673279 | + | 0.673279i | ||||
\(768\) | 34.3572 | − | 33.5199i | 0.0447359 | − | 0.0436457i | ||||
\(769\) | 102.288 | 0.133014 | 0.0665072 | − | 0.997786i | \(-0.478814\pi\) | ||||
0.0665072 | + | 0.997786i | \(0.478814\pi\) | |||||||
\(770\) | 820.009 | + | 182.791i | 1.06495 | + | 0.237391i | ||||
\(771\) | 769.916 | + | 9.49760i | 0.998594 | + | 0.0123186i | ||||
\(772\) | −224.508 | − | 224.508i | −0.290813 | − | 0.290813i | ||||
\(773\) | −64.6043 | + | 64.6043i | −0.0835761 | + | 0.0835761i | −0.747659 | − | 0.664083i | \(-0.768822\pi\) |
0.664083 | + | 0.747659i | \(0.268822\pi\) | |||||||
\(774\) | −177.683 | − | 4.38442i | −0.229564 | − | 0.00566462i | ||||
\(775\) | 408.420 | + | 827.140i | 0.526994 | + | 1.06728i | ||||
\(776\) | −1.09610 | −0.00141250 | ||||||||
\(777\) | 383.747 | + | 1141.12i | 0.493883 | + | 1.46863i | ||||
\(778\) | −24.2532 | + | 24.2532i | −0.0311738 | + | 0.0311738i | ||||
\(779\) | 21.9147 | 0.0281319 | ||||||||
\(780\) | −423.558 | + | 93.3789i | −0.543023 | + | 0.119716i | ||||
\(781\) | 2328.40 | 2.98131 | ||||||||
\(782\) | −338.875 | − | 338.875i | −0.433344 | − | 0.433344i | ||||
\(783\) | −30.8617 | − | 33.2348i | −0.0394147 | − | 0.0424454i | ||||
\(784\) | 153.204 | − | 122.248i | 0.195413 | − | 0.155929i | ||||
\(785\) | −108.034 | − | 67.1418i | −0.137623 | − | 0.0855310i | ||||
\(786\) | 0.856324 | − | 69.4173i | 0.00108947 | − | 0.0883171i | ||||
\(787\) | 370.534 | − | 370.534i | 0.470819 | − | 0.470819i | −0.431361 | − | 0.902180i | \(-0.641966\pi\) |
0.902180 | + | 0.431361i | \(0.141966\pi\) | |||||||
\(788\) | −355.541 | − | 355.541i | −0.451194 | − | 0.451194i | ||||
\(789\) | 767.882 | + | 9.47251i | 0.973235 | + | 0.0120057i | ||||
\(790\) | −477.519 | + | 768.346i | −0.604454 | + | 0.972589i | ||||
\(791\) | −249.566 | + | 518.421i | −0.315507 | + | 0.655399i | ||||
\(792\) | 297.890 | + | 312.963i | 0.376123 | + | 0.395155i | ||||
\(793\) | −824.873 | + | 824.873i | −1.04019 | + | 1.04019i | ||||
\(794\) | − | 353.821i | − | 0.445618i | ||||||
\(795\) | −54.6651 | − | 247.956i | −0.0687611 | − | 0.311894i | ||||
\(796\) | − | 159.045i | − | 0.199805i | ||||||
\(797\) | 331.906 | + | 331.906i | 0.416444 | + | 0.416444i | 0.883976 | − | 0.467532i | \(-0.154857\pi\) |
−0.467532 | + | 0.883976i | \(0.654857\pi\) | |||||||
\(798\) | −696.330 | + | 234.168i | −0.872594 | + | 0.293444i | ||||
\(799\) | − | 593.983i | − | 0.743408i | ||||||
\(800\) | −45.3907 | + | 133.939i | −0.0567384 | + | 0.167424i | ||||
\(801\) | 462.302 | + | 11.4076i | 0.577157 | + | 0.0142416i | ||||
\(802\) | −48.5936 | − | 48.5936i | −0.0605905 | − | 0.0605905i | ||||
\(803\) | −905.091 | + | 905.091i | −1.12714 | + | 1.12714i | ||||
\(804\) | −0.467010 | + | 37.8578i | −0.000580858 | + | 0.0470868i | ||||
\(805\) | −930.336 | − | 207.384i | −1.15570 | − | 0.257620i | ||||
\(806\) | − | 754.447i | − | 0.936038i | ||||||
\(807\) | 413.081 | + | 423.400i | 0.511873 | + | 0.524659i | ||||
\(808\) | −43.3570 | − | 43.3570i | −0.0536596 | − | 0.0536596i | ||||
\(809\) | 79.9556 | 0.0988327 | 0.0494163 | − | 0.998778i | \(-0.484264\pi\) | ||||
0.0494163 | + | 0.998778i | \(0.484264\pi\) | |||||||
\(810\) | 470.959 | + | 325.956i | 0.581431 | + | 0.402415i | ||||
\(811\) | − | 601.430i | − | 0.741591i | −0.928715 | − | 0.370795i | \(-0.879085\pi\) | ||
0.928715 | − | 0.370795i | \(-0.120915\pi\) | |||||||
\(812\) | 22.1961 | − | 7.77036i | 0.0273351 | − | 0.00956941i | ||||
\(813\) | −653.241 | − | 669.559i | −0.803494 | − | 0.823565i | ||||
\(814\) | − | 1376.13i | − | 1.69058i | ||||||
\(815\) | 542.697 | + | 337.281i | 0.665886 | + | 0.413841i | ||||
\(816\) | −149.309 | − | 1.84186i | −0.182976 | − | 0.00225718i | ||||
\(817\) | −244.259 | + | 244.259i | −0.298971 | + | 0.298971i | ||||
\(818\) | 143.848 | − | 143.848i | 0.175853 | − | 0.175853i | ||||
\(819\) | −810.692 | − | 415.201i | −0.989856 | − | 0.506961i | ||||
\(820\) | 8.62717 | − | 2.01387i | 0.0105209 | − | 0.00245594i | ||||
\(821\) | − | 1419.78i | − | 1.72933i | −0.502353 | − | 0.864663i | \(-0.667532\pi\) | ||
0.502353 | − | 0.864663i | \(-0.332468\pi\) | |||||||
\(822\) | −427.472 | − | 438.150i | −0.520038 | − | 0.533029i | ||||
\(823\) | −197.094 | + | 197.094i | −0.239482 | + | 0.239482i | −0.816636 | − | 0.577153i | \(-0.804163\pi\) |
0.577153 | + | 0.816636i | \(0.304163\pi\) | |||||||
\(824\) | − | 197.659i | − | 0.239878i | ||||||
\(825\) | −1200.51 | − | 423.423i | −1.45517 | − | 0.513240i | ||||
\(826\) | −216.902 | + | 450.569i | −0.262594 | + | 0.545483i | ||||
\(827\) | 718.394 | − | 718.394i | 0.868675 | − | 0.868675i | −0.123651 | − | 0.992326i | \(-0.539460\pi\) |
0.992326 | + | 0.123651i | \(0.0394604\pi\) | |||||||
\(828\) | −337.969 | − | 355.070i | −0.408175 | − | 0.428828i | ||||
\(829\) | 671.129 | 0.809565 | 0.404782 | − | 0.914413i | \(-0.367347\pi\) | ||||
0.404782 | + | 0.914413i | \(0.367347\pi\) | |||||||
\(830\) | 584.367 | − | 136.411i | 0.704057 | − | 0.164351i | ||||
\(831\) | 686.060 | + | 8.46316i | 0.825584 | + | 0.0101843i | ||||
\(832\) | 81.7847 | − | 81.7847i | 0.0982990 | − | 0.0982990i | ||||
\(833\) | −605.910 | − | 68.0923i | −0.727383 | − | 0.0817435i | ||||
\(834\) | −4.21398 | + | 341.603i | −0.00505273 | + | 0.409596i | ||||
\(835\) | 41.5411 | − | 66.8412i | 0.0497498 | − | 0.0800494i | ||||
\(836\) | 839.735 | 1.00447 | ||||||||
\(837\) | −730.056 | + | 677.928i | −0.872229 | + | 0.809950i | ||||
\(838\) | −80.8927 | − | 80.8927i | −0.0965306 | − | 0.0965306i | ||||
\(839\) | − | 1507.60i | − | 1.79690i | −0.439077 | − | 0.898449i | \(-0.644695\pi\) | ||
0.439077 | − | 0.898449i | \(-0.355305\pi\) | |||||||
\(840\) | −252.605 | + | 156.175i | −0.300720 | + | 0.185923i | ||||
\(841\) | −838.178 | −0.996645 | ||||||||
\(842\) | 194.231 | − | 194.231i | 0.230678 | − | 0.230678i | ||||
\(843\) | −382.401 | − | 391.953i | −0.453619 | − | 0.464951i | ||||
\(844\) | − | 797.828i | − | 0.945294i | ||||||
\(845\) | −194.877 | + | 45.4908i | −0.230624 | + | 0.0538353i | ||||
\(846\) | 14.9875 | − | 607.383i | 0.0177157 | − | 0.717947i | ||||
\(847\) | −386.470 | − | 1103.96i | −0.456281 | − | 1.30337i | ||||
\(848\) | 47.8777 | + | 47.8777i | 0.0564596 | + | 0.0564596i | ||||
\(849\) | 56.1984 | + | 0.693257i | 0.0661936 | + | 0.000816557i | ||||
\(850\) | 394.471 | − | 194.779i | 0.464083 | − | 0.229152i | ||||
\(851\) | 1561.28i | 1.83464i | ||||||||
\(852\) | −589.142 | + | 574.784i | −0.691481 | + | 0.674629i | ||||
\(853\) | 702.377 | + | 702.377i | 0.823420 | + | 0.823420i | 0.986597 | − | 0.163177i | \(-0.0521742\pi\) |
−0.163177 | + | 0.986597i | \(0.552174\pi\) | |||||||
\(854\) | −346.466 | + | 719.710i | −0.405698 | + | 0.842752i | ||||
\(855\) | 1089.93 | − | 226.229i | 1.27477 | − | 0.264595i | ||||
\(856\) | −170.835 | −0.199574 | ||||||||
\(857\) | −933.376 | − | 933.376i | −1.08912 | − | 1.08912i | −0.995619 | − | 0.0935014i | \(-0.970194\pi\) |
−0.0935014 | − | 0.995619i | \(-0.529806\pi\) | |||||||
\(858\) | 727.044 | + | 745.206i | 0.847371 | + | 0.868538i | ||||
\(859\) | 1132.05 | 1.31787 | 0.658934 | − | 0.752201i | \(-0.271008\pi\) | ||||
0.658934 | + | 0.752201i | \(0.271008\pi\) | |||||||
\(860\) | −73.7111 | + | 118.604i | −0.0857106 | + | 0.137912i | ||||
\(861\) | 16.6621 | + | 8.27576i | 0.0193520 | + | 0.00961180i | ||||
\(862\) | 577.019 | + | 577.019i | 0.669396 | + | 0.669396i | ||||
\(863\) | −158.115 | − | 158.115i | −0.183216 | − | 0.183216i | 0.609540 | − | 0.792755i | \(-0.291354\pi\) |
−0.792755 | + | 0.609540i | \(0.791354\pi\) | |||||||
\(864\) | −152.630 | − | 5.65079i | −0.176656 | − | 0.00654027i | ||||
\(865\) | 863.047 | + | 536.375i | 0.997742 | + | 0.620086i | ||||
\(866\) | −85.8030 | −0.0990797 | ||||||||
\(867\) | −281.071 | − | 288.092i | −0.324188 | − | 0.332286i | ||||
\(868\) | −170.689 | − | 487.574i | −0.196646 | − | 0.561721i | ||||
\(869\) | 2171.49 | 2.49884 | ||||||||
\(870\) | −34.7979 | + | 7.67166i | −0.0399976 | + | 0.00881800i | ||||
\(871\) | 91.2293i | 0.104741i | ||||||||
\(872\) | 138.234 | − | 138.234i | 0.158526 | − | 0.158526i | ||||
\(873\) | 2.40464 | + | 2.52631i | 0.00275445 | + | 0.00289382i | ||||
\(874\) | −952.716 | −1.09006 | ||||||||
\(875\) | 454.417 | − | 747.750i | 0.519334 | − | 0.854572i | ||||
\(876\) | 5.58123 | − | 452.438i | 0.00637126 | − | 0.516482i | ||||
\(877\) | 809.948 | + | 809.948i | 0.923544 | + | 0.923544i | 0.997278 | − | 0.0737339i | \(-0.0234915\pi\) |
−0.0737339 | + | 0.997278i | \(0.523492\pi\) | |||||||
\(878\) | −73.7420 | + | 73.7420i | −0.0839886 | + | 0.0839886i | ||||
\(879\) | −2.39845 | + | 194.428i | −0.00272861 | + | 0.221193i | ||||
\(880\) | 330.579 | − | 77.1682i | 0.375657 | − | 0.0876911i | ||||
\(881\) | −779.133 | −0.884373 | −0.442187 | − | 0.896923i | \(-0.645797\pi\) | ||||
−0.442187 | + | 0.896923i | \(0.645797\pi\) | |||||||
\(882\) | −617.860 | − | 84.9168i | −0.700522 | − | 0.0962776i | ||||
\(883\) | 1131.33 | − | 1131.33i | 1.28124 | − | 1.28124i | 0.341272 | − | 0.939965i | \(-0.389142\pi\) |
0.939965 | − | 0.341272i | \(-0.110858\pi\) | |||||||
\(884\) | −359.803 | −0.407017 | ||||||||
\(885\) | 407.864 | − | 638.562i | 0.460863 | − | 0.721539i | ||||
\(886\) | −20.9992 | −0.0237011 | ||||||||
\(887\) | 146.694 | + | 146.694i | 0.165382 | + | 0.165382i | 0.784946 | − | 0.619564i | \(-0.212691\pi\) |
−0.619564 | + | 0.784946i | \(0.712691\pi\) | |||||||
\(888\) | 339.708 | + | 348.194i | 0.382554 | + | 0.392110i | ||||
\(889\) | 31.7845 | − | 66.0257i | 0.0357531 | − | 0.0742696i | ||||
\(890\) | 191.785 | − | 308.589i | 0.215488 | − | 0.346729i | ||||
\(891\) | 67.8084 | − | 1373.16i | 0.0761037 | − | 1.54115i | ||||
\(892\) | 325.271 | − | 325.271i | 0.364654 | − | 0.364654i | ||||
\(893\) | −834.965 | − | 834.965i | −0.935011 | − | 0.935011i | ||||
\(894\) | −7.34426 | + | 595.357i | −0.00821506 | + | 0.665947i | ||||
\(895\) | −380.414 | − | 1629.64i | −0.425043 | − | 1.82083i | ||||
\(896\) | 34.3515 | − | 71.3581i | 0.0383388 | − | 0.0796407i | ||||
\(897\) | −824.863 | − | 845.468i | −0.919580 | − | 0.942551i | ||||
\(898\) | 284.237 | − | 284.237i | 0.316522 | − | 0.316522i | ||||
\(899\) | − | 61.9825i | − | 0.0689461i | ||||||
\(900\) | 408.284 | − | 189.220i | 0.453649 | − | 0.210244i | ||||
\(901\) | − | 210.633i | − | 0.233776i | ||||||
\(902\) | −15.0368 | − | 15.0368i | −0.0166705 | − | 0.0166705i | ||||
\(903\) | −277.955 | + | 93.4732i | −0.307813 | + | 0.103514i | ||||
\(904\) | 232.482i | 0.257170i | ||||||||
\(905\) | −483.793 | + | 112.934i | −0.534578 | + | 0.124789i | ||||
\(906\) | −1.71091 | + | 138.694i | −0.00188842 | + | 0.153084i | ||||
\(907\) | 517.383 | + | 517.383i | 0.570434 | + | 0.570434i | 0.932250 | − | 0.361816i | \(-0.117843\pi\) |
−0.361816 | + | 0.932250i | \(0.617843\pi\) | |||||||
\(908\) | −511.204 | + | 511.204i | −0.563000 | + | 0.563000i | ||||
\(909\) | −4.81289 | + | 195.047i | −0.00529471 | + | 0.214573i | ||||
\(910\) | −603.991 | + | 383.799i | −0.663726 | + | 0.421758i | ||||
\(911\) | − | 1374.39i | − | 1.50866i | −0.656495 | − | 0.754330i | \(-0.727962\pi\) | ||
0.656495 | − | 0.754330i | \(-0.272038\pi\) | |||||||
\(912\) | −212.473 | + | 207.295i | −0.232975 | + | 0.227297i | ||||
\(913\) | −1018.53 | − | 1018.53i | −1.11558 | − | 1.11558i | ||||
\(914\) | 234.152 | 0.256184 | ||||||||
\(915\) | 651.496 | − | 1020.00i | 0.712018 | − | 1.11475i | ||||
\(916\) | − | 377.031i | − | 0.411606i | ||||||
\(917\) | −37.8462 | − | 108.108i | −0.0412718 | − | 0.117893i | ||||
\(918\) | 323.310 | + | 348.170i | 0.352190 | + | 0.379270i | ||||
\(919\) | 252.031i | 0.274245i | 0.990554 | + | 0.137122i | \(0.0437854\pi\) | ||||
−0.990554 | + | 0.137122i | \(0.956215\pi\) | |||||||
\(920\) | −375.056 | + | 87.5507i | −0.407669 | + | 0.0951638i | ||||
\(921\) | 14.3011 | − | 1159.31i | 0.0155278 | − | 1.25875i | ||||
\(922\) | 221.554 | − | 221.554i | 0.240297 | − | 0.240297i | ||||
\(923\) | −1402.41 | + | 1402.41i | −1.51940 | + | 1.51940i | ||||
\(924\) | 638.463 | + | 317.113i | 0.690977 | + | 0.343196i | ||||
\(925\) | −1357.41 | − | 460.013i | −1.46747 | − | 0.497311i | ||||
\(926\) | − | 630.108i | − | 0.680462i | ||||||
\(927\) | −455.569 | + | 433.627i | −0.491444 | + | 0.467775i | ||||
\(928\) | 6.71913 | − | 6.71913i | 0.00724044 | − | 0.00724044i | ||||
\(929\) | − | 837.498i | − | 0.901504i | −0.892649 | − | 0.450752i | \(-0.851156\pi\) | ||
0.892649 | − | 0.450752i | \(-0.148844\pi\) | |||||||
\(930\) | 168.520 | + | 764.393i | 0.181205 | + | 0.821928i | ||||
\(931\) | −947.447 | + | 756.012i | −1.01767 | + | 0.812043i | ||||
\(932\) | 33.4788 | − | 33.4788i | 0.0359214 | − | 0.0359214i | ||||
\(933\) | −877.384 | + | 856.001i | −0.940390 | + | 0.917472i | ||||
\(934\) | 458.698 | 0.491111 | ||||||||
\(935\) | −896.918 | − | 557.425i | −0.959270 | − | 0.596176i | ||||
\(936\) | −367.919 | − | 9.07861i | −0.393076 | − | 0.00969937i | ||||
\(937\) | −324.135 | + | 324.135i | −0.345929 | + | 0.345929i | −0.858591 | − | 0.512662i | \(-0.828660\pi\) |
0.512662 | + | 0.858591i | \(0.328660\pi\) | |||||||
\(938\) | 20.6400 | + | 58.9585i | 0.0220043 | + | 0.0628556i | ||||
\(939\) | −1144.26 | − | 14.1155i | −1.21860 | − | 0.0150325i | ||||
\(940\) | −405.431 | − | 251.971i | −0.431309 | − | 0.268054i | ||||
\(941\) | 194.663 | 0.206868 | 0.103434 | − | 0.994636i | \(-0.467017\pi\) | ||||
0.103434 | + | 0.994636i | \(0.467017\pi\) | |||||||
\(942\) | −75.3715 | − | 77.2543i | −0.0800122 | − | 0.0820109i | ||||
\(943\) | 17.0599 | + | 17.0599i | 0.0180911 | + | 0.0180911i | ||||
\(944\) | 202.054i | 0.214041i | ||||||||
\(945\) | 914.123 | + | 239.591i | 0.967326 | + | 0.253535i | ||||
\(946\) | 335.198 | 0.354332 | ||||||||
\(947\) | −53.7161 | + | 53.7161i | −0.0567223 | + | 0.0567223i | −0.734899 | − | 0.678177i | \(-0.762770\pi\) |
0.678177 | + | 0.734899i | \(0.262770\pi\) | |||||||
\(948\) | −549.440 | + | 536.049i | −0.579578 | + | 0.565453i | ||||
\(949\) | − | 1090.28i | − | 1.14887i | ||||||
\(950\) | 280.707 | − | 828.311i | 0.295481 | − | 0.871906i | ||||
\(951\) | −13.8892 | + | 1125.91i | −0.0146048 | + | 1.18393i | ||||
\(952\) | −232.529 | + | 81.4030i | −0.244253 | + | 0.0855074i | ||||
\(953\) | 0.875943 | + | 0.875943i | 0.000919142 | + | 0.000919142i | 0.707566 | − | 0.706647i | \(-0.249793\pi\) |
−0.706647 | + | 0.707566i | \(0.749793\pi\) | |||||||
\(954\) | 5.31472 | − | 215.384i | 0.00557099 | − | 0.225770i | ||||
\(955\) | −202.078 | + | 47.1719i | −0.211600 | + | 0.0493947i | ||||
\(956\) | 186.299i | 0.194873i | ||||||||
\(957\) | 59.7313 | + | 61.2233i | 0.0624151 | + | 0.0639742i | ||||
\(958\) | 166.037 | + | 166.037i | 0.173316 | + | 0.173316i | ||||
\(959\) | −910.013 | − | 438.077i | −0.948919 | − | 0.456806i | ||||
\(960\) | −64.5947 | + | 101.131i | −0.0672862 | + | 0.105345i | ||||
\(961\) | −400.547 | −0.416802 | ||||||||
\(962\) | 828.849 | + | 828.849i | 0.861589 | + | 0.861589i | ||||
\(963\) | 374.780 | + | 393.744i | 0.389180 | + | 0.408872i | ||||
\(964\) | 887.776 | 0.920929 | ||||||||
\(965\) | 674.164 | + | 418.986i | 0.698615 | + | 0.434182i | ||||
\(966\) | −724.364 | − | 359.779i | −0.749859 | − | 0.372442i | ||||
\(967\) | 552.816 | + | 552.816i | 0.571682 | + | 0.571682i | 0.932598 | − | 0.360916i | \(-0.117536\pi\) |
−0.360916 | + | 0.932598i | \(0.617536\pi\) | |||||||
\(968\) | −334.185 | − | 334.185i | −0.345233 | − | 0.345233i | ||||
\(969\) | 923.360 | + | 11.3905i | 0.952900 | + | 0.0117549i | ||||
\(970\) | 2.66851 | − | 0.622920i | 0.00275104 | − | 0.000642185i | ||||
\(971\) | −333.064 | −0.343012 | −0.171506 | − | 0.985183i | \(-0.554863\pi\) | ||||
−0.171506 | + | 0.985183i | \(0.554863\pi\) | |||||||
\(972\) | 321.819 | + | 364.182i | 0.331089 | + | 0.374673i | ||||
\(973\) | 186.242 | + | 532.002i | 0.191410 | + | 0.546764i | ||||
\(974\) | 1278.15 | 1.31226 | ||||||||
\(975\) | 978.105 | − | 468.046i | 1.00318 | − | 0.480047i | ||||
\(976\) | 322.749i | 0.330685i | ||||||||
\(977\) | −206.855 | + | 206.855i | −0.211724 | + | 0.211724i | −0.805000 | − | 0.593275i | \(-0.797835\pi\) |
0.593275 | + | 0.805000i | \(0.297835\pi\) | |||||||
\(978\) | 378.622 | + | 388.080i | 0.387139 | + | 0.396810i | ||||
\(979\) | −872.131 | −0.890839 | ||||||||
\(980\) | −303.507 | + | 384.686i | −0.309701 | + | 0.392537i | ||||
\(981\) | −621.865 | − | 15.3449i | −0.633909 | − | 0.0156421i | ||||
\(982\) | 148.567 | + | 148.567i | 0.151291 | + | 0.151291i | ||||
\(983\) | −583.925 | + | 583.925i | −0.594023 | + | 0.594023i | −0.938716 | − | 0.344692i | \(-0.887983\pi\) |
0.344692 | + | 0.938716i | \(0.387983\pi\) | |||||||
\(984\) | 7.51663 | + | 0.0927243i | 0.00763885 | + | 9.42320e-5i | ||||
\(985\) | 1067.64 | + | 663.526i | 1.08390 | + | 0.673630i | ||||
\(986\) | −29.5600 | −0.0299798 | ||||||||
\(987\) | −319.525 | − | 950.148i | −0.323733 | − | 0.962663i | ||||
\(988\) | −505.776 | + | 505.776i | −0.511919 | + | 0.511919i | ||||
\(989\) | −380.296 | −0.384526 | ||||||||
\(990\) | −903.086 | − | 592.631i | −0.912208 | − | 0.598617i | ||||
\(991\) | −905.597 | −0.913821 | −0.456911 | − | 0.889513i | \(-0.651044\pi\) | ||||
−0.456911 | + | 0.889513i | \(0.651044\pi\) | |||||||
\(992\) | −147.597 | − | 147.597i | −0.148787 | − | 0.148787i | ||||
\(993\) | 823.188 | − | 803.126i | 0.828991 | − | 0.808788i | ||||
\(994\) | −589.044 | + | 1223.62i | −0.592600 | + | 1.23100i | ||||
\(995\) | 90.3860 | + | 387.202i | 0.0908402 | + | 0.389147i | ||||
\(996\) | 509.144 | + | 6.28074i | 0.511188 | + | 0.00630596i | ||||
\(997\) | 528.385 | − | 528.385i | 0.529975 | − | 0.529975i | −0.390590 | − | 0.920565i | \(-0.627729\pi\) |
0.920565 | + | 0.390590i | \(0.127729\pi\) | |||||||
\(998\) | −471.498 | − | 471.498i | −0.472443 | − | 0.472443i | ||||
\(999\) | 57.2681 | − | 1546.84i | 0.0573254 | − | 1.54839i |
(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 | 210.3.k.a.167.12 | yes | 32 | |
3.2 | odd | 2 | 210.3.k.b.167.4 | yes | 32 | ||
5.3 | odd | 4 | 210.3.k.b.83.13 | yes | 32 | ||
7.6 | odd | 2 | inner | 210.3.k.a.167.5 | yes | 32 | |
15.8 | even | 4 | inner | 210.3.k.a.83.5 | ✓ | 32 | |
21.20 | even | 2 | 210.3.k.b.167.13 | yes | 32 | ||
35.13 | even | 4 | 210.3.k.b.83.4 | yes | 32 | ||
105.83 | odd | 4 | inner | 210.3.k.a.83.12 | yes | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
210.3.k.a.83.5 | ✓ | 32 | 15.8 | even | 4 | inner | |
210.3.k.a.83.12 | yes | 32 | 105.83 | odd | 4 | inner | |
210.3.k.a.167.5 | yes | 32 | 7.6 | odd | 2 | inner | |
210.3.k.a.167.12 | yes | 32 | 1.1 | even | 1 | trivial | |
210.3.k.b.83.4 | yes | 32 | 35.13 | even | 4 | ||
210.3.k.b.83.13 | yes | 32 | 5.3 | odd | 4 | ||
210.3.k.b.167.4 | yes | 32 | 3.2 | odd | 2 | ||
210.3.k.b.167.13 | yes | 32 | 21.20 | even | 2 |