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 | 83.5 | ||
Character | \(\chi\) | \(=\) | 210.83 |
Dual form | 210.3.k.a.167.5 |
$q$-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 \(\left(\mathbb{Z}/210\mathbb{Z}\right)^\times\).
\(n\) | \(31\) | \(71\) | \(127\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(e\left(\frac{3}{4}\right)\) |
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 | ||||
\(7\) | 6.60685 | − | 2.31291i | 0.943836 | − | 0.330415i | ||||
\(8\) | 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 | \(-0.719500\pi\) | ||
0.636213 | − | 0.771513i | \(-0.280500\pi\) | |||||||
\(12\) | 4.18999 | − | 4.29465i | 0.349165 | − | 0.357888i | ||||
\(13\) | 10.2231 | − | 10.2231i | 0.786392 | − | 0.786392i | −0.194509 | − | 0.980901i | \(-0.562311\pi\) |
0.980901 | + | 0.194509i | \(0.0623114\pi\) | |||||||
\(14\) | −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 | \(-0.869266\pi\) |
0.399262 | + | 0.916837i | \(0.369266\pi\) | |||||||
\(18\) | 8.77525 | − | 9.21927i | 0.487514 | − | 0.512182i | ||||
\(19\) | −24.7369 | −1.30194 | −0.650972 | − | 0.759102i | \(-0.725639\pi\) | ||||
−0.650972 | + | 0.759102i | \(0.725639\pi\) | |||||||
\(20\) | −9.73820 | − | 2.27322i | −0.486910 | − | 0.113661i | ||||
\(21\) | −19.0326 | − | 8.87473i | −0.906313 | − | 0.422606i | ||||
\(22\) | −16.9733 | + | 16.9733i | −0.771513 | + | 0.771513i | ||||
\(23\) | 19.2569 | − | 19.2569i | 0.837258 | − | 0.837258i | −0.151239 | − | 0.988497i | \(-0.548326\pi\) |
0.988497 | + | 0.151239i | \(0.0483263\pi\) | |||||||
\(24\) | −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 | ||||
\(28\) | 4.62582 | + | 13.2137i | 0.165208 | + | 0.471918i | ||||
\(29\) | 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 | ||||||||
\(35\) | 3.75235 | + | 34.7983i | 0.107210 | + | 0.994236i | ||||
\(36\) | −17.9945 | + | 0.444025i | −0.499848 | + | 0.0123340i | ||||
\(37\) | 40.5381 | − | 40.5381i | 1.09562 | − | 1.09562i | 0.100708 | − | 0.994916i | \(-0.467889\pi\) |
0.994916 | − | 0.100708i | \(-0.0321107\pi\) | |||||||
\(38\) | 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 | \(-0.503439\pi\) | ||||
−0.0108038 | + | 0.999942i | \(0.503439\pi\) | |||||||
\(42\) | 10.1578 | + | 27.9073i | 0.241853 | + | 0.664460i | ||||
\(43\) | −9.87427 | − | 9.87427i | −0.229634 | − | 0.229634i | 0.582906 | − | 0.812540i | \(-0.301916\pi\) |
−0.812540 | + | 0.582906i | \(0.801916\pi\) | |||||||
\(44\) | 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 | \(-0.580452\pi\) |
0.968229 | + | 0.250064i | \(0.0804517\pi\) | |||||||
\(48\) | 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 | −0.810952 | − | 0.585113i | \(-0.801050\pi\) |
0.585113 | + | 0.810952i | \(0.301050\pi\) | |||||||
\(54\) | −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 | ||||
\(63\) | 22.2766 | + | 58.9301i | 0.353597 | + | 0.935398i | ||||
\(64\) | − | 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 | −0.739620 | − | 0.673024i | \(-0.764995\pi\) |
0.673024 | + | 0.739620i | \(0.264995\pi\) | |||||||
\(68\) | −17.5975 | − | 17.5975i | −0.258787 | − | 0.258787i | ||||
\(69\) | −81.6941 | + | 1.00777i | −1.18397 | + | 0.0146053i | ||||
\(70\) | 31.0459 | − | 38.5506i | 0.443513 | − | 0.550723i | ||||
\(71\) | 137.180i | 1.93212i | 0.258322 | + | 0.966059i | \(0.416831\pi\) | ||||
−0.258322 | + | 0.966059i | \(0.583169\pi\) | |||||||
\(72\) | 18.4385 | + | 17.5505i | 0.256091 | + | 0.243757i | ||||
\(73\) | −53.3244 | + | 53.3244i | −0.730471 | + | 0.730471i | −0.970713 | − | 0.240242i | \(-0.922773\pi\) |
0.240242 | + | 0.970713i | \(0.422773\pi\) | |||||||
\(74\) | −81.0762 | −1.09562 | ||||||||
\(75\) | 24.9464 | + | 70.7296i | 0.332619 | + | 0.943061i | ||||
\(76\) | − | 49.4739i | − | 0.650972i | ||||||
\(77\) | −39.2577 | − | 112.140i | −0.509840 | − | 1.45636i | ||||
\(78\) | 43.9046 | + | 42.8346i | 0.562880 | + | 0.549162i | ||||
\(79\) | 127.936i | 1.61944i | 0.586816 | + | 0.809721i | \(0.300381\pi\) | ||||
−0.586816 | + | 0.809721i | \(0.699619\pi\) | |||||||
\(80\) | 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 | \(-0.0791910\pi\) |
−0.246227 | + | 0.969212i | \(0.579191\pi\) | |||||||
\(84\) | 17.7495 | − | 38.0652i | 0.211303 | − | 0.453157i | ||||
\(85\) | −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 | \(-0.249364\pi\) |
−0.705693 | + | 0.708518i | \(0.749364\pi\) | |||||||
\(98\) | −68.8630 | − | 7.73884i | −0.702683 | − | 0.0789678i | ||||
\(99\) | 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 | \(-0.465773\pi\) | ||||
0.107319 | + | 0.994225i | \(0.465773\pi\) | |||||||
\(102\) | −37.7877 | − | 36.8667i | −0.370467 | − | 0.361438i | ||||
\(103\) | 49.4148 | − | 49.4148i | 0.479755 | − | 0.479755i | −0.425298 | − | 0.905053i | \(-0.639831\pi\) |
0.905053 | + | 0.425298i | \(0.139831\pi\) | |||||||
\(104\) | − | 40.8924i | − | 0.393196i | ||||||
\(105\) | 64.8446 | − | 82.5844i | 0.617568 | − | 0.786518i | ||||
\(106\) | 23.9389 | 0.225838 | ||||||||
\(107\) | −42.7088 | − | 42.7088i | −0.399147 | − | 0.399147i | 0.478785 | − | 0.877932i | \(-0.341077\pi\) |
−0.877932 | + | 0.478785i | \(0.841077\pi\) | |||||||
\(108\) | 39.5703 | + | 36.7449i | 0.366392 | + | 0.340231i | ||||
\(109\) | 69.1171i | 0.634102i | 0.948408 | + | 0.317051i | \(0.102693\pi\) | ||||
−0.948408 | + | 0.317051i | \(0.897307\pi\) | |||||||
\(110\) | −63.3526 | − | 101.937i | −0.575933 | − | 0.926697i | ||||
\(111\) | −171.975 | + | 2.12147i | −1.54933 | + | 0.0191123i | ||||
\(112\) | −26.4274 | + | 9.25163i | −0.235959 | + | 0.0826039i | ||||
\(113\) | 58.1205 | − | 58.1205i | 0.514341 | − | 0.514341i | −0.401513 | − | 0.915853i | \(-0.631515\pi\) |
0.915853 | + | 0.401513i | \(0.131515\pi\) | |||||||
\(114\) | −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 | ||||
\(126\) | 36.6534 | − | 81.2067i | 0.290900 | − | 0.644498i | ||||
\(127\) | −7.40218 | + | 7.40218i | −0.0582849 | + | 0.0582849i | −0.735648 | − | 0.677364i | \(-0.763122\pi\) |
0.677364 | + | 0.735648i | \(0.263122\pi\) | |||||||
\(128\) | −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 | \(-0.480107\pi\) | ||||
0.0624544 | + | 0.998048i | \(0.480107\pi\) | |||||||
\(132\) | −72.8944 | − | 71.1179i | −0.552230 | − | 0.538772i | ||||
\(133\) | −163.433 | + | 57.2143i | −1.22882 | + | 0.430183i | ||||
\(134\) | 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 | 0.228788 | − | 0.973476i | \(-0.426524\pi\) |
−0.973476 | + | 0.228788i | \(0.926524\pi\) | |||||||
\(138\) | 82.7018 | + | 80.6863i | 0.599289 | + | 0.584683i | ||||
\(139\) | −80.5228 | −0.579300 | −0.289650 | − | 0.957133i | \(-0.593539\pi\) | ||||
−0.289650 | + | 0.957133i | \(0.593539\pi\) | |||||||
\(140\) | −69.5965 | + | 7.50470i | −0.497118 | + | 0.0536050i | ||||
\(141\) | −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 | ||||||||
\(147\) | −146.272 | − | 14.6134i | −0.995046 | − | 0.0994110i | ||||
\(148\) | 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 | \(-0.224183\pi\) |
−0.647494 | + | 0.762070i | \(0.724183\pi\) | |||||||
\(158\) | 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 | 0.927701 | − | 0.373324i | \(-0.121782\pi\) |
−0.373324 | + | 0.927701i | \(0.621782\pi\) | |||||||
\(164\) | − | 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 | \(-0.734994\pi\) |
0.739643 | + | 0.672999i | \(0.234994\pi\) | |||||||
\(168\) | −55.8146 | + | 20.3157i | −0.332230 | + | 0.120927i | ||||
\(169\) | − | 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 | \(-0.449835\pi\) |
−0.987607 | + | 0.156946i | \(0.949835\pi\) | |||||||
\(174\) | 0.0879077 | + | 7.12617i | 0.000505216 | + | 0.0409550i | ||||
\(175\) | −173.701 | − | 21.2816i | −0.992578 | − | 0.121609i | ||||
\(176\) | 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 | \(0.911496\pi\) | |||||||
\(182\) | −135.085 | + | 47.2901i | −0.742224 | + | 0.259836i | ||||
\(183\) | −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 | ||||
\(189\) | 75.6228 | − | 173.211i | 0.400121 | − | 0.916462i | ||||
\(190\) | −148.563 | + | 92.3303i | −0.781910 | + | 0.485949i | ||||
\(191\) | − | 41.5022i | − | 0.217289i | −0.994081 | − | 0.108645i | \(-0.965349\pi\) | ||
0.994081 | − | 0.108645i | \(-0.0346510\pi\) | |||||||
\(192\) | −16.7599 | + | 17.1786i | −0.0872914 | + | 0.0894719i | ||||
\(193\) | 112.254 | + | 112.254i | 0.581626 | + | 0.581626i | 0.935350 | − | 0.353724i | \(-0.115085\pi\) |
−0.353724 | + | 0.935350i | \(0.615085\pi\) | |||||||
\(194\) | − | 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 | 0.995642 | − | 0.0932539i | \(-0.0297268\pi\) |
−0.0932539 | + | 0.995642i | \(0.529727\pi\) | |||||||
\(198\) | −156.481 | − | 148.945i | −0.790310 | − | 0.752247i | ||||
\(199\) | −79.5223 | −0.399609 | −0.199805 | − | 0.979836i | \(-0.564031\pi\) | ||||
−0.199805 | + | 0.979836i | \(0.564031\pi\) | |||||||
\(200\) | −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 | ||||
\(203\) | 11.0981 | − | 3.88518i | 0.0546703 | − | 0.0191388i | ||||
\(204\) | 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 | ||||||||
\(210\) | −147.429 | + | 17.7398i | −0.702043 | + | 0.0844750i | ||||
\(211\) | 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 | ||||
\(217\) | −85.3443 | − | 243.787i | −0.393292 | − | 1.12344i | ||||
\(218\) | 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 | \(-0.922468\pi\) |
0.241174 | + | 0.970482i | \(0.422468\pi\) | |||||||
\(224\) | 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 | 0.135179 | − | 0.990821i | \(-0.456839\pi\) |
0.990821 | − | 0.135179i | \(-0.0431610\pi\) | |||||||
\(228\) | −103.647 | + | 106.237i | −0.454594 | + | 0.465950i | ||||
\(229\) | −188.516 | −0.823212 | −0.411606 | − | 0.911362i | \(-0.635032\pi\) | ||||
−0.411606 | + | 0.911362i | \(0.635032\pi\) | |||||||
\(230\) | 43.7753 | − | 187.528i | 0.190328 | − | 0.815338i | ||||
\(231\) | −150.633 | + | 323.046i | −0.652093 | + | 1.39847i | ||||
\(232\) | 3.35956 | − | 3.35956i | 0.0144809 | − | 0.0144809i | ||||
\(233\) | 16.7394 | − | 16.7394i | 0.0718429 | − | 0.0718429i | −0.670272 | − | 0.742115i | \(-0.733823\pi\) |
0.742115 | + | 0.670272i | \(0.233823\pi\) | |||||||
\(234\) | −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 | ||||
\(238\) | 116.264 | − | 40.7015i | 0.488506 | − | 0.171015i | ||||
\(239\) | −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 | ||||||||
\(245\) | 105.276 | + | 221.228i | 0.429700 | + | 0.902972i | ||||
\(246\) | −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 | \(-0.780577\pi\) | ||||
−0.771668 | + | 0.636026i | \(0.780577\pi\) | |||||||
\(252\) | −117.860 | + | 44.5533i | −0.467699 | + | 0.176799i | ||||
\(253\) | −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 | \(-0.916422\pi\) |
0.259560 | + | 0.965727i | \(0.416422\pi\) | |||||||
\(258\) | 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 | −0.273608 | − | 0.961841i | \(-0.588217\pi\) |
0.961841 | + | 0.273608i | \(0.0882171\pi\) | |||||||
\(264\) | 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 | ||||
\(273\) | −285.299 | + | 103.845i | −1.04505 | + | 0.380383i | ||||
\(274\) | 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 | −0.352131 | − | 0.935951i | \(-0.614543\pi\) |
0.935951 | + | 0.352131i | \(0.114543\pi\) | |||||||
\(278\) | 80.5228 | + | 80.5228i | 0.289650 | + | 0.289650i | ||||
\(279\) | 331.991 | − | 8.19206i | 1.18993 | − | 0.0293622i | ||||
\(280\) | 77.1013 | + | 62.0918i | 0.275362 | + | 0.221757i | ||||
\(281\) | 182.531i | 0.649576i | 0.945787 | + | 0.324788i | \(0.105293\pi\) | ||||
−0.945787 | + | 0.324788i | \(0.894707\pi\) | |||||||
\(282\) | 144.961 | + | 141.428i | 0.514045 | + | 0.501517i | ||||
\(283\) | −13.2471 | + | 13.2471i | −0.0468095 | + | 0.0468095i | −0.730124 | − | 0.683315i | \(-0.760538\pi\) |
0.683315 | + | 0.730124i | \(0.260538\pi\) | |||||||
\(284\) | −274.361 | −0.966059 | ||||||||
\(285\) | −312.710 | + | 199.735i | −1.09723 | + | 0.700823i | ||||
\(286\) | 347.039i | 1.21342i | ||||||||
\(287\) | −5.85308 | + | 2.04903i | −0.0203940 | + | 0.00713948i | ||||
\(288\) | −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 | \(-0.214721\pi\) |
−0.624559 | + | 0.780978i | \(0.714721\pi\) | |||||||
\(294\) | 131.658 | + | 160.885i | 0.447818 | + | 0.547229i | ||||
\(295\) | 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 | \(-0.466709\pi\) |
−0.994536 | + | 0.104396i | \(0.966709\pi\) | |||||||
\(308\) | 224.280 | − | 78.5153i | 0.728182 | − | 0.254920i | ||||
\(309\) | −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 | \(-0.271866\pi\) | ||||
0.656903 | + | 0.753975i | \(0.271866\pi\) | |||||||
\(312\) | −85.6692 | + | 87.8092i | −0.274581 | + | 0.281440i | ||||
\(313\) | 269.726 | − | 269.726i | 0.861746 | − | 0.861746i | −0.129795 | − | 0.991541i | \(-0.541432\pi\) |
0.991541 | + | 0.129795i | \(0.0414320\pi\) | |||||||
\(314\) | − | 35.9770i | − | 0.114576i | ||||||
\(315\) | −312.256 | + | 41.4865i | −0.991289 | + | 0.131703i | ||||
\(316\) | −255.872 | −0.809721 | ||||||||
\(317\) | −265.401 | − | 265.401i | −0.837227 | − | 0.837227i | 0.151266 | − | 0.988493i | \(-0.451665\pi\) |
−0.988493 | + | 0.151266i | \(0.951665\pi\) | |||||||
\(318\) | −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 | ||||
\(322\) | −254.455 | + | 89.0791i | −0.790234 | + | 0.276643i | ||||
\(323\) | 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 | ||||
\(336\) | 76.1303 | + | 35.4989i | 0.226578 | + | 0.105652i | ||||
\(337\) | −207.675 | + | 207.675i | −0.616246 | + | 0.616246i | −0.944566 | − | 0.328321i | \(-0.893517\pi\) |
0.328321 | + | 0.944566i | \(0.393517\pi\) | |||||||
\(338\) | −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 | ||||
\(343\) | 182.361 | − | 290.505i | 0.531665 | − | 0.846955i | ||||
\(344\) | −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 | 0.644961 | − | 0.764215i | \(-0.276874\pi\) |
−0.764215 | + | 0.644961i | \(0.776874\pi\) | |||||||
\(348\) | 7.03826 | − | 7.21408i | 0.0202249 | − | 0.0207301i | ||||
\(349\) | 565.082 | 1.61915 | 0.809573 | − | 0.587019i | \(-0.199698\pi\) | ||||
0.809573 | + | 0.587019i | \(0.199698\pi\) | |||||||
\(350\) | 152.420 | + | 194.983i | 0.435485 | + | 0.557094i | ||||
\(351\) | −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 | \(-0.328246\pi\) |
−0.857923 | + | 0.513778i | \(0.828246\pi\) | |||||||
\(354\) | 214.295 | − | 2.64351i | 0.605352 | − | 0.00746756i | ||||
\(355\) | −667.945 | − | 155.921i | −1.88153 | − | 0.439214i | ||||
\(356\) | −102.765 | −0.288666 | ||||||||
\(357\) | 245.550 | − | 89.3766i | 0.687815 | − | 0.250355i | ||||
\(358\) | 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 | 0.929041 | + | 0.369976i | \(0.120634\pi\) |
0.369976 | + | 0.929041i | \(0.379366\pi\) | |||||||
\(368\) | −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 | 0.801775 | − | 0.597626i | \(-0.203889\pi\) |
−0.597626 | + | 0.801775i | \(0.703889\pi\) | |||||||
\(374\) | − | 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 | ||||
\(378\) | −248.834 | + | 97.5886i | −0.658292 | + | 0.258171i | ||||
\(379\) | − | 390.814i | − | 1.03117i | −0.856838 | − | 0.515585i | \(-0.827574\pi\) | ||
0.856838 | − | 0.515585i | \(-0.172426\pi\) | |||||||
\(380\) | 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 | \(-0.212981\pi\) |
−0.620280 | + | 0.784381i | \(0.712981\pi\) | |||||||
\(384\) | 33.9385 | − | 0.418662i | 0.0883816 | − | 0.00109027i | ||||
\(385\) | 590.641 | − | 63.6898i | 1.53413 | − | 0.165428i | ||||
\(386\) | − | 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 | ||||||||
\(392\) | 15.4777 | − | 137.726i | 0.0394839 | − | 0.351342i | ||||
\(393\) | −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 | \(-0.147962\pi\) |
−0.448277 | + | 0.893895i | \(0.647962\pi\) | |||||||
\(398\) | 79.5223 | + | 79.5223i | 0.199805 | + | 0.199805i | ||||
\(399\) | 470.808 | + | 219.534i | 1.17997 | + | 0.550210i | ||||
\(400\) | 89.6649 | + | 44.2742i | 0.224162 | + | 0.110685i | ||||
\(401\) | − | 48.5936i | − | 0.121181i | −0.998163 | − | 0.0605905i | \(-0.980702\pi\) | ||
0.998163 | − | 0.0605905i | \(-0.0192984\pi\) | |||||||
\(402\) | −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 | \(-0.443732\pi\) | ||||
0.175853 | + | 0.984416i | \(0.443732\pi\) | |||||||
\(410\) | −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 | ||||
\(413\) | −116.833 | − | 333.735i | −0.282889 | − | 0.808076i | ||||
\(414\) | −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 | \(0.969225\pi\) | |||||||
\(420\) | 165.169 | + | 129.689i | 0.393259 | + | 0.308784i | ||||
\(421\) | −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 | ||||
\(427\) | −186.622 | − | 533.088i | −0.437054 | − | 1.24845i | ||||
\(428\) | 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 | \(0.233447\pi\) | ||||
−0.742906 | + | 0.669396i | \(0.766553\pi\) | |||||||
\(432\) | −73.4899 | + | 79.1406i | −0.170115 | + | 0.183196i | ||||
\(433\) | −42.9015 | + | 42.9015i | −0.0990797 | + | 0.0990797i | −0.754909 | − | 0.655829i | \(-0.772319\pi\) |
0.655829 | + | 0.754909i | \(0.272319\pi\) | |||||||
\(434\) | −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 | \(-0.526766\pi\) | ||||
−0.0839886 | + | 0.996467i | \(0.526766\pi\) | |||||||
\(440\) | 203.873 | − | 126.705i | 0.463349 | − | 0.287966i | ||||
\(441\) | 283.478 | + | 337.818i | 0.642808 | + | 0.766028i | ||||
\(442\) | 179.901 | − | 179.901i | 0.407017 | − | 0.407017i | ||||
\(443\) | 10.4996 | − | 10.4996i | 0.0237011 | − | 0.0237011i | −0.695157 | − | 0.718858i | \(-0.744665\pi\) |
0.718858 | + | 0.695157i | \(0.244665\pi\) | |||||||
\(444\) | −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 | ||||
\(448\) | −18.5033 | − | 52.8548i | −0.0413019 | − | 0.117979i | ||||
\(449\) | −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 | ||||||||
\(455\) | 394.107 | + | 317.385i | 0.866168 | + | 0.697550i | ||||
\(456\) | 209.884 | − | 2.58911i | 0.460272 | − | 0.00567786i | ||||
\(457\) | −117.076 | + | 117.076i | −0.256184 | + | 0.256184i | −0.823500 | − | 0.567316i | \(-0.807982\pi\) |
0.567316 | + | 0.823500i | \(0.307982\pi\) | |||||||
\(458\) | 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 | \(-0.422755\pi\) | ||||
0.240297 | + | 0.970699i | \(0.422755\pi\) | |||||||
\(462\) | 473.679 | − | 172.412i | 1.02528 | − | 0.373186i | ||||
\(463\) | −315.054 | − | 315.054i | −0.680462 | − | 0.680462i | 0.279642 | − | 0.960104i | \(-0.409784\pi\) |
−0.960104 | + | 0.279642i | \(0.909784\pi\) | |||||||
\(464\) | −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 | \(-0.637109\pi\) |
0.908656 | + | 0.417545i | \(0.137109\pi\) | |||||||
\(468\) | −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 | ||||
\(483\) | −537.409 | + | 195.609i | −1.11265 | + | 0.404988i | ||||
\(484\) | − | 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 | −0.392521 | + | 0.919743i | \(0.628397\pi\) |
−0.919743 | + | 0.392521i | \(0.871603\pi\) | |||||||
\(488\) | −161.374 | − | 161.374i | −0.330685 | − | 0.330685i | ||||
\(489\) | −4.72898 | − | 383.351i | −0.00967071 | − | 0.783949i | ||||
\(490\) | 115.952 | − | 326.505i | 0.236636 | − | 0.666336i | ||||
\(491\) | 148.567i | 0.302581i | 0.988489 | + | 0.151291i | \(0.0483429\pi\) | ||||
−0.988489 | + | 0.151291i | \(0.951657\pi\) | |||||||
\(492\) | −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 | ||||||||
\(497\) | 317.286 | + | 906.330i | 0.638402 | + | 1.82360i | ||||
\(498\) | −251.431 | + | 257.712i | −0.504882 | + | 0.517494i | ||||
\(499\) | − | 471.498i | − | 0.944885i | −0.881361 | − | 0.472443i | \(-0.843372\pi\) | ||
0.881361 | − | 0.472443i | \(-0.156628\pi\) | |||||||
\(500\) | 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 | \(-0.268237\pi\) |
−0.746437 | + | 0.665456i | \(0.768237\pi\) | |||||||
\(504\) | 162.413 | + | 73.3068i | 0.322249 | + | 0.145450i | ||||
\(505\) | −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 | ||||
\(518\) | −535.658 | + | 187.522i | −1.03409 | + | 0.362011i | ||||
\(519\) | 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 | \(-0.269291\pi\) | ||||
0.662980 | + | 0.748637i | \(0.269291\pi\) | |||||||
\(522\) | 14.7405 | − | 15.4864i | 0.0282385 | − | 0.0296674i | ||||
\(523\) | 560.737 | − | 560.737i | 1.07216 | − | 1.07216i | 0.0749699 | − | 0.997186i | \(-0.476114\pi\) |
0.997186 | − | 0.0749699i | \(-0.0238861\pi\) | |||||||
\(524\) | 32.7261i | 0.0624544i | ||||||||
\(525\) | 328.408 | + | 409.601i | 0.625539 | + | 0.780193i | ||||
\(526\) | −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 | ||||
\(532\) | −114.429 | − | 326.866i | −0.215091 | − | 0.614411i | ||||
\(533\) | −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 | ||||
\(546\) | 389.144 | + | 181.454i | 0.712717 | + | 0.332334i | ||||
\(547\) | 253.750 | − | 253.750i | 0.463894 | − | 0.463894i | −0.436036 | − | 0.899929i | \(-0.643618\pi\) |
0.899929 | + | 0.436036i | \(0.143618\pi\) | |||||||
\(548\) | 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 | ||||
\(553\) | 295.904 | + | 845.253i | 0.535088 | + | 1.52849i | ||||
\(554\) | −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 | 0.989028 | − | 0.147731i | \(-0.0471971\pi\) |
−0.147731 | + | 0.989028i | \(0.547197\pi\) | |||||||
\(558\) | −340.183 | − | 323.799i | −0.609647 | − | 0.580285i | ||||
\(559\) | −201.891 | −0.361165 | ||||||||
\(560\) | −15.0094 | − | 139.193i | −0.0268025 | − | 0.248559i | ||||
\(561\) | −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 | \(-0.254392\pi\) |
−0.716796 | + | 0.697283i | \(0.754392\pi\) | |||||||
\(564\) | −3.53286 | − | 286.388i | −0.00626393 | − | 0.507781i | ||||
\(565\) | 216.934 | + | 349.055i | 0.383954 | + | 0.617796i | ||||
\(566\) | 26.4942 | 0.0468095 | ||||||||
\(567\) | −525.263 | + | 213.512i | −0.926390 | + | 0.376564i | ||||
\(568\) | 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 | 0.998766 | + | 0.0496572i | \(0.0158129\pi\) |
0.0496572 | + | 0.998766i | \(0.484187\pi\) | |||||||
\(578\) | 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 | \(-0.890591\pi\) |
0.336990 | + | 0.941508i | \(0.390591\pi\) | |||||||
\(588\) | 29.2268 | − | 292.544i | 0.0497055 | − | 0.497523i | ||||
\(589\) | 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 | \(-0.0826403\pi\) |
−0.256715 | + | 0.966487i | \(0.582640\pi\) | |||||||
\(594\) | 23.9781 | + | 647.661i | 0.0403672 | + | 1.09034i | ||||
\(595\) | −339.198 | − | 273.166i | −0.570081 | − | 0.459102i | ||||
\(596\) | 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 | \(0.906327\pi\) | |||||||
\(602\) | 45.6766 | + | 130.476i | 0.0758747 | + | 0.216737i | ||||
\(603\) | −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 | \(-0.0426512\pi\) |
−0.133592 | + | 0.991036i | \(0.542651\pi\) | |||||||
\(608\) | −98.9478 | − | 98.9478i | −0.162743 | − | 0.162743i | ||||
\(609\) | −31.9706 | − | 14.9076i | −0.0524969 | − | 0.0244789i | ||||
\(610\) | −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 | 0.770898 | − | 0.636959i | \(-0.219808\pi\) |
−0.636959 | + | 0.770898i | \(0.719808\pi\) | |||||||
\(614\) | 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 | 0.539621 | − | 0.841908i | \(-0.318567\pi\) |
−0.841908 | + | 0.539621i | \(0.818567\pi\) | |||||||
\(618\) | 212.219 | + | 207.047i | 0.343397 | + | 0.335028i | ||||
\(619\) | −608.262 | −0.982652 | −0.491326 | − | 0.870976i | \(-0.663488\pi\) | ||||
−0.491326 | + | 0.870976i | \(0.663488\pi\) | |||||||
\(620\) | −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 | ||||
\(623\) | 118.843 | + | 339.477i | 0.190759 | + | 0.544907i | ||||
\(624\) | 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 | ||||||||
\(630\) | 353.743 | + | 270.770i | 0.561496 | + | 0.429793i | ||||
\(631\) | 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 | ||||
\(637\) | 79.1149 | − | 703.993i | 0.124199 | − | 1.10517i | ||||
\(638\) | −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 | \(-0.700319\pi\) | ||
0.588597 | − | 0.808427i | \(-0.299681\pi\) | |||||||
\(642\) | 178.949 | − | 183.419i | 0.278737 | − | 0.285700i | ||||
\(643\) | −639.514 | + | 639.514i | −0.994579 | + | 0.994579i | −0.999985 | − | 0.00540613i | \(-0.998279\pi\) |
0.00540613 | + | 0.999985i | \(0.498279\pi\) | |||||||
\(644\) | 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 | 0.0194122 | − | 0.999812i | \(-0.493821\pi\) |
0.999812 | − | 0.0194122i | \(-0.00617949\pi\) | |||||||
\(648\) | −153.813 | + | 169.793i | −0.237365 | + | 0.262026i | ||||
\(649\) | −857.382 | −1.32108 | ||||||||
\(650\) | 458.326 | + | 226.310i | 0.705117 | + | 0.348169i | ||||
\(651\) | −327.470 | + | 702.286i | −0.503026 | + | 1.07878i | ||||
\(652\) | −180.727 | + | 180.727i | −0.277189 | + | 0.277189i | ||||
\(653\) | 334.285 | − | 334.285i | 0.511921 | − | 0.511921i | −0.403194 | − | 0.915115i | \(-0.632100\pi\) |
0.915115 | + | 0.403194i | \(0.132100\pi\) | |||||||
\(654\) | −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 | ||||
\(658\) | −446.012 | + | 156.139i | −0.677830 | + | 0.237293i | ||||
\(659\) | −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 | ||||||||
\(665\) | −92.8217 | − | 860.803i | −0.139582 | − | 1.29444i | ||||
\(666\) | −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 | ||||||||
\(672\) | −40.6314 | − | 111.629i | −0.0604634 | − | 0.166115i | ||||
\(673\) | −98.5465 | − | 98.5465i | −0.146429 | − | 0.146429i | 0.630092 | − | 0.776521i | \(-0.283017\pi\) |
−0.776521 | + | 0.630092i | \(0.783017\pi\) | |||||||
\(674\) | 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 | −0.316565 | + | 0.948571i | \(0.602529\pi\) |
−0.948571 | + | 0.316565i | \(0.897471\pi\) | |||||||
\(678\) | 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 | −0.945516 | − | 0.325575i | \(-0.894442\pi\) |
0.325575 | + | 0.945516i | \(0.394442\pi\) | |||||||
\(684\) | 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 | ||||
\(693\) | 1000.24 | − | 378.108i | 1.44334 | − | 0.545610i | ||||
\(694\) | 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 | ||||
\(700\) | 42.5631 | − | 347.402i | 0.0608045 | − | 0.496289i | ||||
\(701\) | − | 462.898i | − | 0.660340i | −0.943922 | − | 0.330170i | \(-0.892894\pi\) | ||
0.943922 | − | 0.330170i | \(-0.107106\pi\) | |||||||
\(702\) | −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 | ||||||||
\(707\) | 143.226 | − | 50.1403i | 0.202583 | − | 0.0709199i | ||||
\(708\) | −216.938 | − | 211.651i | −0.306410 | − | 0.298942i | ||||
\(709\) | − | 946.923i | − | 1.33558i | −0.744352 | − | 0.667788i | \(-0.767241\pi\) | ||
0.744352 | − | 0.667788i | \(-0.232759\pi\) | |||||||
\(710\) | 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 | ||||
\(714\) | −334.927 | − | 156.174i | −0.469085 | − | 0.218730i | ||||
\(715\) | 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 | \(-0.0805702\pi\) |
−0.250425 | + | 0.968136i | \(0.580570\pi\) | |||||||
\(728\) | −94.5803 | − | 270.170i | −0.129918 | − | 0.371112i | ||||
\(729\) | −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 | \(-0.712481\pi\) |
0.785355 | + | 0.619046i | \(0.212481\pi\) | |||||||
\(734\) | − | 953.479i | − | 1.29902i | ||||||
\(735\) | 237.408 | − | 695.602i | 0.323005 | − | 0.946397i | ||||
\(736\) | 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 | \(-0.840948\pi\) | ||
0.877737 | − | 0.479142i | \(-0.159052\pi\) | |||||||
\(740\) | −486.920 | + | 302.616i | −0.658000 | + | 0.408940i | ||||
\(741\) | 1072.83 | − | 13.2343i | 1.44782 | − | 0.0178601i | ||||
\(742\) | 158.160 | − | 55.3684i | 0.213154 | − | 0.0746205i | ||||
\(743\) | 212.648 | − | 212.648i | 0.286202 | − | 0.286202i | −0.549374 | − | 0.835576i | \(-0.685134\pi\) |
0.835576 | + | 0.549374i | \(0.185134\pi\) | |||||||
\(744\) | 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 | ||||
\(756\) | 346.423 | + | 151.246i | 0.458231 | + | 0.200060i | ||||
\(757\) | −627.004 | + | 627.004i | −0.828275 | + | 0.828275i | −0.987278 | − | 0.159003i | \(-0.949172\pi\) |
0.159003 | + | 0.987278i | \(0.449172\pi\) | |||||||
\(758\) | −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 | \(-0.255944\pi\) | ||||
0.693780 | + | 0.720187i | \(0.255944\pi\) | |||||||
\(762\) | −31.7898 | − | 31.0150i | −0.0417189 | − | 0.0407021i | ||||
\(763\) | 159.862 | + | 456.647i | 0.209517 | + | 0.598488i | ||||
\(764\) | 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 | \(-0.521186\pi\) | ||||
−0.0665072 | + | 0.997786i | \(0.521186\pi\) | |||||||
\(770\) | −654.331 | − | 526.952i | −0.849781 | − | 0.684353i | ||||
\(771\) | 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 | \(-0.231178\pi\) |
−0.664083 | + | 0.747659i | \(0.731178\pi\) | |||||||
\(774\) | −177.683 | + | 4.38442i | −0.229564 | + | 0.00566462i | ||||
\(775\) | −408.420 | + | 827.140i | −0.526994 | + | 1.06728i | ||||
\(776\) | 1.09610 | 0.00141250 | ||||||||
\(777\) | −1131.31 | + | 411.780i | −1.45600 | + | 0.529961i | ||||
\(778\) | −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 | \(-0.358034\pi\) |
−0.902180 | + | 0.431361i | \(0.858034\pi\) | |||||||
\(788\) | −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 | \(-0.845143\pi\) |
0.467532 | + | 0.883976i | \(0.345143\pi\) | |||||||
\(798\) | −251.274 | − | 690.342i | −0.314880 | − | 0.865090i | ||||
\(799\) | 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 | ||||
\(805\) | 742.367 | + | 597.849i | 0.922195 | + | 0.742670i | ||||
\(806\) | 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 | \(-0.120915\pi\) | |||||||
\(812\) | 7.77036 | + | 22.1961i | 0.00956941 | + | 0.0273351i | ||||
\(813\) | −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 | ||||
\(819\) | 830.183 | + | 374.711i | 1.01366 | + | 0.457523i | ||||
\(820\) | 8.62717 | + | 2.01387i | 0.0105209 | + | 0.00245594i | ||||
\(821\) | 1419.78i | 1.72933i | 0.502353 | + | 0.864663i | \(0.332468\pi\) | ||||
−0.502353 | + | 0.864663i | \(0.667532\pi\) | |||||||
\(822\) | 427.472 | − | 438.150i | 0.520038 | − | 0.533029i | ||||
\(823\) | −197.094 | − | 197.094i | −0.239482 | − | 0.239482i | 0.577153 | − | 0.816636i | \(-0.304163\pi\) |
−0.816636 | + | 0.577153i | \(0.804163\pi\) | |||||||
\(824\) | − | 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 | 0.992326 | − | 0.123651i | \(-0.0394604\pi\) |
−0.123651 | + | 0.992326i | \(0.539460\pi\) | |||||||
\(828\) | −337.969 | + | 355.070i | −0.408175 | + | 0.428828i | ||||
\(829\) | −671.129 | −0.809565 | −0.404782 | − | 0.914413i | \(-0.632653\pi\) | ||||
−0.404782 | + | 0.914413i | \(0.632653\pi\) | |||||||
\(830\) | 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 | ||||
\(833\) | −68.0923 | + | 605.910i | −0.0817435 | + | 0.727383i | ||||
\(834\) | −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 | \(-0.355305\pi\) | |||||||
\(840\) | −35.4795 | − | 294.858i | −0.0422375 | − | 0.351021i | ||||
\(841\) | −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 | ||||
\(847\) | −1103.96 | + | 386.470i | −1.30337 | + | 0.456281i | ||||
\(848\) | 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 | \(-0.947826\pi\) |
0.163177 | + | 0.986597i | \(0.447826\pi\) | |||||||
\(854\) | −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 | 0.0935014 | − | 0.995619i | \(-0.470194\pi\) |
0.995619 | − | 0.0935014i | \(-0.0298060\pi\) | |||||||
\(858\) | 727.044 | − | 745.206i | 0.847371 | − | 0.868538i | ||||
\(859\) | −1132.05 | −1.31787 | −0.658934 | − | 0.752201i | \(-0.728992\pi\) | ||||
−0.658934 | + | 0.752201i | \(0.728992\pi\) | |||||||
\(860\) | 73.7111 | + | 118.604i | 0.0857106 | + | 0.137912i | ||||
\(861\) | 16.8612 | + | 7.86222i | 0.0195832 | + | 0.00913150i | ||||
\(862\) | 577.019 | − | 577.019i | 0.669396 | − | 0.669396i | ||||
\(863\) | −158.115 | + | 158.115i | −0.183216 | + | 0.183216i | −0.792755 | − | 0.609540i | \(-0.791354\pi\) |
0.609540 | + | 0.792755i | \(0.291354\pi\) | |||||||
\(864\) | 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 | ||||
\(868\) | 487.574 | − | 170.689i | 0.561721 | − | 0.196646i | ||||
\(869\) | 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 | ||||||||
\(875\) | 301.053 | − | 821.579i | 0.344060 | − | 0.938948i | ||||
\(876\) | 5.58123 | + | 452.438i | 0.00637126 | + | 0.516482i | ||||
\(877\) | 809.948 | − | 809.948i | 0.923544 | − | 0.923544i | −0.0737339 | − | 0.997278i | \(-0.523492\pi\) |
0.997278 | + | 0.0737339i | \(0.0234915\pi\) | |||||||
\(878\) | 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 | \(-0.354203\pi\) | ||||
0.442187 | + | 0.896923i | \(0.354203\pi\) | |||||||
\(882\) | 54.3400 | − | 621.296i | 0.0616099 | − | 0.704418i | ||||
\(883\) | 1131.33 | + | 1131.33i | 1.28124 | + | 1.28124i | 0.939965 | + | 0.341272i | \(0.110858\pi\) |
0.341272 | + | 0.939965i | \(0.389142\pi\) | |||||||
\(884\) | −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 | \(-0.787309\pi\) |
0.619564 | + | 0.784946i | \(0.287309\pi\) | |||||||
\(888\) | −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 | ||||
\(903\) | 100.301 | + | 275.564i | 0.111076 | + | 0.305165i | ||||
\(904\) | − | 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 | −0.361816 | − | 0.932250i | \(-0.617843\pi\) |
0.932250 | + | 0.361816i | \(0.117843\pi\) | |||||||
\(908\) | 511.204 | + | 511.204i | 0.563000 | + | 0.563000i | ||||
\(909\) | 4.81289 | + | 195.047i | 0.00529471 | + | 0.214573i | ||||
\(910\) | −76.7213 | − | 711.492i | −0.0843091 | − | 0.781859i | ||||
\(911\) | 1374.39i | 1.50866i | 0.656495 | + | 0.754330i | \(0.272038\pi\) | ||||
−0.656495 | + | 0.754330i | \(0.727962\pi\) | |||||||
\(912\) | −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 | ||||||
\(917\) | 108.108 | − | 37.8462i | 0.117893 | − | 0.0412718i | ||||
\(918\) | 323.310 | − | 348.170i | 0.352190 | − | 0.379270i | ||||
\(919\) | − | 252.031i | − | 0.274245i | −0.990554 | − | 0.137122i | \(-0.956215\pi\) | ||
0.990554 | − | 0.137122i | \(-0.0437854\pi\) | |||||||
\(920\) | 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 | ||||
\(924\) | −646.091 | − | 301.267i | −0.699233 | − | 0.326046i | ||||
\(925\) | −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 | \(-0.171340\pi\) |
−0.512662 | + | 0.858591i | \(0.671340\pi\) | |||||||
\(938\) | 58.9585 | − | 20.6400i | 0.0628556 | − | 0.0220043i | ||||
\(939\) | −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 | \(-0.532983\pi\) | ||||
−0.103434 | + | 0.994636i | \(0.532983\pi\) | |||||||
\(942\) | −75.3715 | + | 77.2543i | −0.0800122 | + | 0.0820109i | ||||
\(943\) | −17.0599 | + | 17.0599i | −0.0180911 | + | 0.0180911i | ||||
\(944\) | 202.054i | 0.214041i | ||||||||
\(945\) | 757.429 | + | 565.089i | 0.801513 | + | 0.597978i | ||||
\(946\) | 335.198 | 0.354332 | ||||||||
\(947\) | −53.7161 | − | 53.7161i | −0.0567223 | − | 0.0567223i | 0.678177 | − | 0.734899i | \(-0.262770\pi\) |
−0.734899 | + | 0.678177i | \(0.762770\pi\) | |||||||
\(948\) | 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 | ||||
\(952\) | 81.4030 | + | 232.529i | 0.0855074 | + | 0.244253i | ||||
\(953\) | 0.875943 | − | 0.875943i | 0.000919142 | − | 0.000919142i | −0.706647 | − | 0.707566i | \(-0.749793\pi\) |
0.707566 | + | 0.706647i | \(0.249793\pi\) | |||||||
\(954\) | 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 | ||||
\(966\) | 733.018 | + | 341.800i | 0.758818 | + | 0.353831i | ||||
\(967\) | 552.816 | − | 552.816i | 0.571682 | − | 0.571682i | −0.360916 | − | 0.932598i | \(-0.617536\pi\) |
0.932598 | + | 0.360916i | \(0.117536\pi\) | |||||||
\(968\) | −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 | \(-0.445137\pi\) | ||||
0.171506 | + | 0.985183i | \(0.445137\pi\) | |||||||
\(972\) | −321.819 | + | 364.182i | −0.331089 | + | 0.374673i | ||||
\(973\) | −532.002 | + | 186.242i | −0.546764 | + | 0.191410i | ||||
\(974\) | 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 | 0.593275 | − | 0.805000i | \(-0.297835\pi\) |
−0.805000 | + | 0.593275i | \(0.797835\pi\) | |||||||
\(978\) | −378.622 | + | 388.080i | −0.387139 | + | 0.396810i | ||||
\(979\) | 872.131 | 0.890839 | ||||||||
\(980\) | −442.456 | + | 210.553i | −0.451486 | + | 0.214850i | ||||
\(981\) | −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 | \(-0.112017\pi\) |
−0.344692 | + | 0.938716i | \(0.612017\pi\) | |||||||
\(984\) | 7.51663 | − | 0.0927243i | 0.00763885 | − | 9.42320e-5i | ||||
\(985\) | −1067.64 | + | 663.526i | −1.08390 | + | 0.673630i | ||||
\(986\) | 29.5600 | 0.0299798 | ||||||||
\(987\) | −941.977 | + | 342.866i | −0.954384 | + | 0.347382i | ||||
\(988\) | −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 | \(-0.372271\pi\) |
−0.920565 | + | 0.390590i | \(0.872271\pi\) | |||||||
\(998\) | −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.83.5 | ✓ | 32 | |
3.2 | odd | 2 | 210.3.k.b.83.13 | yes | 32 | ||
5.2 | odd | 4 | 210.3.k.b.167.4 | yes | 32 | ||
7.6 | odd | 2 | inner | 210.3.k.a.83.12 | yes | 32 | |
15.2 | even | 4 | inner | 210.3.k.a.167.12 | yes | 32 | |
21.20 | even | 2 | 210.3.k.b.83.4 | yes | 32 | ||
35.27 | even | 4 | 210.3.k.b.167.13 | yes | 32 | ||
105.62 | odd | 4 | inner | 210.3.k.a.167.5 | yes | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
210.3.k.a.83.5 | ✓ | 32 | 1.1 | even | 1 | trivial | |
210.3.k.a.83.12 | yes | 32 | 7.6 | odd | 2 | inner | |
210.3.k.a.167.5 | yes | 32 | 105.62 | odd | 4 | inner | |
210.3.k.a.167.12 | yes | 32 | 15.2 | even | 4 | inner | |
210.3.k.b.83.4 | yes | 32 | 21.20 | even | 2 | ||
210.3.k.b.83.13 | yes | 32 | 3.2 | odd | 2 | ||
210.3.k.b.167.4 | yes | 32 | 5.2 | odd | 4 | ||
210.3.k.b.167.13 | yes | 32 | 35.27 | even | 4 |