Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2646,2,Mod(1549,2646)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2646, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([2, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2646.1549");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2646 = 2 \cdot 3^{3} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2646.e (of order \(3\), degree \(2\), not 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: | \(21.1284163748\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Relative dimension: | \(3\) over \(\Q(\zeta_{3})\) |
Coefficient field: | 6.0.309123.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 3x^{5} + 10x^{4} - 15x^{3} + 19x^{2} - 12x + 3 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | no (minimal twist has level 126) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 2125.3 | ||
Root | \(0.500000 + 1.41036i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2646.2125 |
Dual form | 2646.2.e.p.1549.3 |
$q$-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 \(\left(\mathbb{Z}/2646\mathbb{Z}\right)^\times\).
\(n\) | \(785\) | \(1081\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{2}{3}\right)\) |
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 | 0.707107 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 1.59097 | − | 2.75564i | 0.711504 | − | 1.23236i | −0.252788 | − | 0.967522i | \(-0.581348\pi\) |
0.964292 | − | 0.264840i | \(-0.0853191\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 1.59097 | − | 2.75564i | 0.503109 | − | 0.871411i | ||||
\(11\) | 1.59097 | + | 2.75564i | 0.479696 | + | 0.830858i | 0.999729 | − | 0.0232884i | \(-0.00741361\pi\) |
−0.520033 | + | 0.854146i | \(0.674080\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.85185 | − | 4.93955i | −0.790960 | − | 1.36998i | −0.925373 | − | 0.379058i | \(-0.876248\pi\) |
0.134412 | − | 0.990925i | \(-0.457085\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −0.760877 | + | 1.31788i | −0.184540 | + | 0.319632i | −0.943421 | − | 0.331596i | \(-0.892413\pi\) |
0.758882 | + | 0.651229i | \(0.225746\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.641315 | + | 1.11079i | 0.147128 | + | 0.254833i | 0.930165 | − | 0.367142i | \(-0.119664\pi\) |
−0.783037 | + | 0.621975i | \(0.786330\pi\) | |||||||
\(20\) | 1.59097 | − | 2.75564i | 0.355752 | − | 0.616181i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1.59097 | + | 2.75564i | 0.339196 | + | 0.587505i | ||||
\(23\) | 1.11956 | − | 1.93914i | 0.233445 | − | 0.404338i | −0.725375 | − | 0.688354i | \(-0.758334\pi\) |
0.958820 | + | 0.284016i | \(0.0916669\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.56238 | − | 4.43818i | −0.512476 | − | 0.887635i | ||||
\(26\) | −2.85185 | − | 4.93955i | −0.559293 | − | 0.968725i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.54063 | − | 6.13255i | 0.657478 | − | 1.13879i | −0.323788 | − | 0.946130i | \(-0.604957\pi\) |
0.981266 | − | 0.192656i | \(-0.0617101\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 9.42107 | 1.69207 | 0.846037 | − | 0.533125i | \(-0.178982\pi\) | ||||
0.846037 | + | 0.533125i | \(0.178982\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −0.760877 | + | 1.31788i | −0.130489 | + | 0.226014i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.500000 | + | 0.866025i | 0.0821995 | + | 0.142374i | 0.904194 | − | 0.427121i | \(-0.140472\pi\) |
−0.821995 | + | 0.569495i | \(0.807139\pi\) | |||||||
\(38\) | 0.641315 | + | 1.11079i | 0.104035 | + | 0.180194i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1.59097 | − | 2.75564i | 0.251555 | − | 0.435706i | ||||
\(41\) | −2.80150 | − | 4.85235i | −0.437522 | − | 0.757810i | 0.559976 | − | 0.828509i | \(-0.310810\pi\) |
−0.997498 | + | 0.0706992i | \(0.977477\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.41423 | − | 5.91362i | 0.520665 | − | 0.901819i | −0.479046 | − | 0.877790i | \(-0.659017\pi\) |
0.999711 | − | 0.0240288i | \(-0.00764935\pi\) | |||||||
\(44\) | 1.59097 | + | 2.75564i | 0.239848 | + | 0.415429i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.11956 | − | 1.93914i | 0.165070 | − | 0.285910i | ||||
\(47\) | −5.82846 | −0.850168 | −0.425084 | − | 0.905154i | \(-0.639755\pi\) | ||||
−0.425084 | + | 0.905154i | \(0.639755\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −2.56238 | − | 4.43818i | −0.362375 | − | 0.627653i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −2.85185 | − | 4.93955i | −0.395480 | − | 0.684992i | ||||
\(53\) | −1.02859 | + | 1.78157i | −0.141288 | + | 0.244717i | −0.927982 | − | 0.372626i | \(-0.878458\pi\) |
0.786694 | + | 0.617343i | \(0.211791\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 10.1248 | 1.36522 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 3.54063 | − | 6.13255i | 0.464907 | − | 0.805243i | ||||
\(59\) | −1.12476 | −0.146432 | −0.0732159 | − | 0.997316i | \(-0.523326\pi\) | ||||
−0.0732159 | + | 0.997316i | \(0.523326\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.12476 | −0.400085 | −0.200042 | − | 0.979787i | \(-0.564108\pi\) | ||||
−0.200042 | + | 0.979787i | \(0.564108\pi\) | |||||||
\(62\) | 9.42107 | 1.19648 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −18.1488 | −2.25109 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 10.9669 | 1.33982 | 0.669910 | − | 0.742442i | \(-0.266333\pi\) | ||||
0.669910 | + | 0.742442i | \(0.266333\pi\) | |||||||
\(68\) | −0.760877 | + | 1.31788i | −0.0922699 | + | 0.159816i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −8.69002 | −1.03132 | −0.515658 | − | 0.856794i | \(-0.672452\pi\) | ||||
−0.515658 | + | 0.856794i | \(0.672452\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.48345 | − | 4.30146i | 0.290666 | − | 0.503448i | −0.683302 | − | 0.730136i | \(-0.739457\pi\) |
0.973967 | + | 0.226689i | \(0.0727899\pi\) | |||||||
\(74\) | 0.500000 | + | 0.866025i | 0.0581238 | + | 0.100673i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0.641315 | + | 1.11079i | 0.0735639 | + | 0.127416i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −4.13844 | −0.465610 | −0.232805 | − | 0.972523i | \(-0.574790\pi\) | ||||
−0.232805 | + | 0.972523i | \(0.574790\pi\) | |||||||
\(80\) | 1.59097 | − | 2.75564i | 0.177876 | − | 0.308090i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −2.80150 | − | 4.85235i | −0.309374 | − | 0.535852i | ||||
\(83\) | −4.03379 | + | 6.98673i | −0.442766 | + | 0.766893i | −0.997894 | − | 0.0648718i | \(-0.979336\pi\) |
0.555127 | + | 0.831765i | \(0.312669\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.42107 | + | 4.19341i | 0.262602 | + | 0.454839i | ||||
\(86\) | 3.41423 | − | 5.91362i | 0.368166 | − | 0.637682i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 1.59097 | + | 2.75564i | 0.169598 | + | 0.293753i | ||||
\(89\) | 0.112725 | + | 0.195246i | 0.0119488 | + | 0.0206960i | 0.871938 | − | 0.489616i | \(-0.162863\pi\) |
−0.859989 | + | 0.510312i | \(0.829530\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 1.11956 | − | 1.93914i | 0.116722 | − | 0.202169i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −5.82846 | −0.601160 | ||||||||
\(95\) | 4.08126 | 0.418728 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −7.42107 | + | 12.8537i | −0.753495 | + | 1.30509i | 0.192624 | + | 0.981273i | \(0.438300\pi\) |
−0.946119 | + | 0.323819i | \(0.895033\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −2.56238 | − | 4.43818i | −0.256238 | − | 0.443818i | ||||
\(101\) | −9.29467 | − | 16.0988i | −0.924854 | − | 1.60189i | −0.791796 | − | 0.610786i | \(-0.790854\pi\) |
−0.133058 | − | 0.991108i | \(-0.542480\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −0.141315 | + | 0.244765i | −0.0139242 | + | 0.0241174i | −0.872904 | − | 0.487893i | \(-0.837766\pi\) |
0.858979 | + | 0.512010i | \(0.171099\pi\) | |||||||
\(104\) | −2.85185 | − | 4.93955i | −0.279647 | − | 0.484362i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1.02859 | + | 1.78157i | −0.0999055 | + | 0.173041i | ||||
\(107\) | −5.68878 | − | 9.85326i | −0.549955 | − | 0.952550i | −0.998277 | − | 0.0586780i | \(-0.981311\pi\) |
0.448322 | − | 0.893872i | \(-0.352022\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −2.21053 | + | 3.82876i | −0.211731 | + | 0.366728i | −0.952256 | − | 0.305300i | \(-0.901243\pi\) |
0.740526 | + | 0.672028i | \(0.234577\pi\) | |||||||
\(110\) | 10.1248 | 0.965358 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1.60752 | + | 2.78431i | 0.151223 | + | 0.261926i | 0.931677 | − | 0.363287i | \(-0.118345\pi\) |
−0.780454 | + | 0.625213i | \(0.785012\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −3.56238 | − | 6.17023i | −0.332194 | − | 0.575377i | ||||
\(116\) | 3.54063 | − | 6.13255i | 0.328739 | − | 0.569393i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −1.12476 | −0.103543 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0.437618 | − | 0.757977i | 0.0397835 | − | 0.0689070i | ||||
\(122\) | −3.12476 | −0.282903 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 9.42107 | 0.846037 | ||||||||
\(125\) | −0.396990 | −0.0355079 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 20.1053 | 1.78406 | 0.892030 | − | 0.451976i | \(-0.149281\pi\) | ||||
0.892030 | + | 0.451976i | \(0.149281\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −18.1488 | −1.59176 | ||||||||
\(131\) | −3.18194 | + | 5.51129i | −0.278008 | + | 0.481523i | −0.970890 | − | 0.239528i | \(-0.923007\pi\) |
0.692882 | + | 0.721051i | \(0.256341\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 10.9669 | 0.947396 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −0.760877 | + | 1.31788i | −0.0652446 | + | 0.113007i | ||||
\(137\) | 1.37072 | + | 2.37416i | 0.117109 | + | 0.202838i | 0.918621 | − | 0.395140i | \(-0.129304\pi\) |
−0.801512 | + | 0.597979i | \(0.795971\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 3.98345 | + | 6.89953i | 0.337872 | + | 0.585211i | 0.984032 | − | 0.177991i | \(-0.0569597\pi\) |
−0.646161 | + | 0.763202i | \(0.723626\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −8.69002 | −0.729251 | ||||||||
\(143\) | 9.07442 | − | 15.7174i | 0.758841 | − | 1.31435i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −11.2661 | − | 19.5134i | −0.935597 | − | 1.62050i | ||||
\(146\) | 2.48345 | − | 4.30146i | 0.205532 | − | 0.355991i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0.500000 | + | 0.866025i | 0.0410997 | + | 0.0711868i | ||||
\(149\) | −11.6300 | + | 20.1437i | −0.952764 | + | 1.65024i | −0.213360 | + | 0.976974i | \(0.568441\pi\) |
−0.739404 | + | 0.673262i | \(0.764893\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 4.06238 | + | 7.03625i | 0.330592 | + | 0.572602i | 0.982628 | − | 0.185586i | \(-0.0594183\pi\) |
−0.652036 | + | 0.758188i | \(0.726085\pi\) | |||||||
\(152\) | 0.641315 | + | 1.11079i | 0.0520175 | + | 0.0900970i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 14.9887 | − | 25.9611i | 1.20392 | − | 2.08525i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 11.2632 | 0.898901 | 0.449451 | − | 0.893305i | \(-0.351620\pi\) | ||||
0.449451 | + | 0.893305i | \(0.351620\pi\) | |||||||
\(158\) | −4.13844 | −0.329236 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 1.59097 | − | 2.75564i | 0.125777 | − | 0.217853i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1.99028 | − | 3.44727i | −0.155891 | − | 0.270011i | 0.777492 | − | 0.628893i | \(-0.216492\pi\) |
−0.933383 | + | 0.358881i | \(0.883158\pi\) | |||||||
\(164\) | −2.80150 | − | 4.85235i | −0.218761 | − | 0.378905i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −4.03379 | + | 6.98673i | −0.313083 | + | 0.542276i | ||||
\(167\) | 2.61956 | + | 4.53721i | 0.202708 | + | 0.351100i | 0.949400 | − | 0.314070i | \(-0.101693\pi\) |
−0.746692 | + | 0.665170i | \(0.768359\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −9.76608 | + | 16.9153i | −0.751237 | + | 1.30118i | ||||
\(170\) | 2.42107 | + | 4.19341i | 0.185687 | + | 0.321620i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 3.41423 | − | 5.91362i | 0.260333 | − | 0.450909i | ||||
\(173\) | 2.55159 | 0.193994 | 0.0969968 | − | 0.995285i | \(-0.469076\pi\) | ||||
0.0969968 | + | 0.995285i | \(0.469076\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 1.59097 | + | 2.75564i | 0.119924 | + | 0.207714i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0.112725 | + | 0.195246i | 0.00844910 | + | 0.0146343i | ||||
\(179\) | −3.51887 | + | 6.09487i | −0.263013 | + | 0.455552i | −0.967041 | − | 0.254620i | \(-0.918050\pi\) |
0.704028 | + | 0.710172i | \(0.251383\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 12.9669 | 0.963822 | 0.481911 | − | 0.876220i | \(-0.339943\pi\) | ||||
0.481911 | + | 0.876220i | \(0.339943\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 1.11956 | − | 1.93914i | 0.0825352 | − | 0.142955i | ||||
\(185\) | 3.18194 | 0.233941 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −4.84213 | −0.354092 | ||||||||
\(188\) | −5.82846 | −0.425084 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 4.08126 | 0.296085 | ||||||||
\(191\) | −1.98057 | −0.143309 | −0.0716545 | − | 0.997430i | \(-0.522828\pi\) | ||||
−0.0716545 | + | 0.997430i | \(0.522828\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −4.54583 | −0.327216 | −0.163608 | − | 0.986525i | \(-0.552313\pi\) | ||||
−0.163608 | + | 0.986525i | \(0.552313\pi\) | |||||||
\(194\) | −7.42107 | + | 12.8537i | −0.532802 | + | 0.922839i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 21.8148 | 1.55424 | 0.777120 | − | 0.629353i | \(-0.216680\pi\) | ||||
0.777120 | + | 0.629353i | \(0.216680\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −6.14132 | + | 10.6371i | −0.435346 | + | 0.754042i | −0.997324 | − | 0.0731106i | \(-0.976707\pi\) |
0.561978 | + | 0.827152i | \(0.310041\pi\) | |||||||
\(200\) | −2.56238 | − | 4.43818i | −0.181188 | − | 0.313826i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −9.29467 | − | 16.0988i | −0.653971 | − | 1.13271i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −17.8285 | −1.24519 | ||||||||
\(206\) | −0.141315 | + | 0.244765i | −0.00984589 | + | 0.0170536i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −2.85185 | − | 4.93955i | −0.197740 | − | 0.342496i | ||||
\(209\) | −2.04063 | + | 3.53447i | −0.141153 | + | 0.244485i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −8.32846 | − | 14.4253i | −0.573355 | − | 0.993080i | −0.996218 | − | 0.0868863i | \(-0.972308\pi\) |
0.422863 | − | 0.906193i | \(-0.361025\pi\) | |||||||
\(212\) | −1.02859 | + | 1.78157i | −0.0706438 | + | 0.122359i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −5.68878 | − | 9.85326i | −0.388877 | − | 0.673555i | ||||
\(215\) | −10.8639 | − | 18.8168i | −0.740911 | − | 1.28330i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −2.21053 | + | 3.82876i | −0.149716 | + | 0.259316i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 10.1248 | 0.682611 | ||||||||
\(221\) | 8.67962 | 0.583854 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 5.32846 | − | 9.22916i | 0.356820 | − | 0.618031i | −0.630608 | − | 0.776102i | \(-0.717194\pi\) |
0.987428 | + | 0.158071i | \(0.0505276\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 1.60752 | + | 2.78431i | 0.106931 | + | 0.185210i | ||||
\(227\) | 7.25404 | + | 12.5644i | 0.481468 | + | 0.833926i | 0.999774 | − | 0.0212688i | \(-0.00677059\pi\) |
−0.518306 | + | 0.855195i | \(0.673437\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 5.12476 | − | 8.87635i | 0.338654 | − | 0.586566i | −0.645526 | − | 0.763738i | \(-0.723362\pi\) |
0.984180 | + | 0.177173i | \(0.0566951\pi\) | |||||||
\(230\) | −3.56238 | − | 6.17023i | −0.234896 | − | 0.406853i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 3.54063 | − | 6.13255i | 0.232454 | − | 0.402622i | ||||
\(233\) | −0.540628 | − | 0.936396i | −0.0354177 | − | 0.0613453i | 0.847773 | − | 0.530359i | \(-0.177943\pi\) |
−0.883191 | + | 0.469014i | \(0.844610\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −9.27292 | + | 16.0612i | −0.604898 | + | 1.04771i | ||||
\(236\) | −1.12476 | −0.0732159 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 6.16019 | + | 10.6698i | 0.398470 | + | 0.690170i | 0.993537 | − | 0.113506i | \(-0.0362081\pi\) |
−0.595068 | + | 0.803676i | \(0.702875\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −6.50000 | − | 11.2583i | −0.418702 | − | 0.725213i | 0.577107 | − | 0.816668i | \(-0.304181\pi\) |
−0.995809 | + | 0.0914555i | \(0.970848\pi\) | |||||||
\(242\) | 0.437618 | − | 0.757977i | 0.0281312 | − | 0.0487246i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −3.12476 | −0.200042 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3.65787 | − | 6.33561i | 0.232744 | − | 0.403125i | ||||
\(248\) | 9.42107 | 0.598238 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −0.396990 | −0.0251079 | ||||||||
\(251\) | 5.11109 | 0.322609 | 0.161305 | − | 0.986905i | \(-0.448430\pi\) | ||||
0.161305 | + | 0.986905i | \(0.448430\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 7.12476 | 0.447930 | ||||||||
\(254\) | 20.1053 | 1.26152 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −3.83009 | + | 6.63392i | −0.238915 | + | 0.413813i | −0.960403 | − | 0.278614i | \(-0.910125\pi\) |
0.721488 | + | 0.692427i | \(0.243458\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −18.1488 | −1.12554 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −3.18194 | + | 5.51129i | −0.196581 | + | 0.340488i | ||||
\(263\) | −1.54746 | − | 2.68029i | −0.0954208 | − | 0.165274i | 0.814363 | − | 0.580355i | \(-0.197086\pi\) |
−0.909784 | + | 0.415082i | \(0.863753\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 3.27292 | + | 5.66886i | 0.201054 | + | 0.348235i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 10.9669 | 0.669910 | ||||||||
\(269\) | −13.4451 | + | 23.2877i | −0.819765 | + | 1.41987i | 0.0860906 | + | 0.996287i | \(0.472563\pi\) |
−0.905855 | + | 0.423587i | \(0.860771\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 11.1082 | + | 19.2400i | 0.674776 | + | 1.16875i | 0.976534 | + | 0.215362i | \(0.0690930\pi\) |
−0.301759 | + | 0.953384i | \(0.597574\pi\) | |||||||
\(272\) | −0.760877 | + | 1.31788i | −0.0461349 | + | 0.0799080i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 1.37072 | + | 2.37416i | 0.0828084 | + | 0.143428i | ||||
\(275\) | 8.15335 | − | 14.1220i | 0.491666 | − | 0.851590i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 7.31875 | + | 12.6764i | 0.439741 | + | 0.761653i | 0.997669 | − | 0.0682357i | \(-0.0217370\pi\) |
−0.557928 | + | 0.829889i | \(0.688404\pi\) | |||||||
\(278\) | 3.98345 | + | 6.89953i | 0.238911 | + | 0.413807i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −11.6992 | + | 20.2636i | −0.697915 | + | 1.20882i | 0.271273 | + | 0.962502i | \(0.412555\pi\) |
−0.969188 | + | 0.246322i | \(0.920778\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 26.1248 | 1.55296 | 0.776478 | − | 0.630144i | \(-0.217004\pi\) | ||||
0.776478 | + | 0.630144i | \(0.217004\pi\) | |||||||
\(284\) | −8.69002 | −0.515658 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 9.07442 | − | 15.7174i | 0.536582 | − | 0.929387i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 7.34213 | + | 12.7169i | 0.431890 | + | 0.748056i | ||||
\(290\) | −11.2661 | − | 19.5134i | −0.661567 | − | 1.14587i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 2.48345 | − | 4.30146i | 0.145333 | − | 0.251724i | ||||
\(293\) | 12.9315 | + | 22.3980i | 0.755465 | + | 1.30850i | 0.945143 | + | 0.326657i | \(0.105922\pi\) |
−0.189678 | + | 0.981846i | \(0.560745\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.78947 | + | 3.09945i | −0.104187 | + | 0.180457i | ||||
\(296\) | 0.500000 | + | 0.866025i | 0.0290619 | + | 0.0503367i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −11.6300 | + | 20.1437i | −0.673706 | + | 1.16689i | ||||
\(299\) | −12.7713 | −0.738582 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 4.06238 | + | 7.03625i | 0.233764 | + | 0.404891i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0.641315 | + | 1.11079i | 0.0367819 | + | 0.0637082i | ||||
\(305\) | −4.97141 | + | 8.61073i | −0.284662 | + | 0.493049i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −3.53216 | −0.201591 | −0.100795 | − | 0.994907i | \(-0.532139\pi\) | ||||
−0.100795 | + | 0.994907i | \(0.532139\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 14.9887 | − | 25.9611i | 0.851298 | − | 1.47449i | ||||
\(311\) | 1.70370 | 0.0966078 | 0.0483039 | − | 0.998833i | \(-0.484618\pi\) | ||||
0.0483039 | + | 0.998833i | \(0.484618\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2.84213 | 0.160647 | 0.0803234 | − | 0.996769i | \(-0.474405\pi\) | ||||
0.0803234 | + | 0.996769i | \(0.474405\pi\) | |||||||
\(314\) | 11.2632 | 0.635619 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −4.13844 | −0.232805 | ||||||||
\(317\) | 24.9201 | 1.39965 | 0.699827 | − | 0.714313i | \(-0.253261\pi\) | ||||
0.699827 | + | 0.714313i | \(0.253261\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 22.5322 | 1.26156 | ||||||||
\(320\) | 1.59097 | − | 2.75564i | 0.0889380 | − | 0.154045i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1.95185 | −0.108604 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −14.6150 | + | 25.3140i | −0.810697 | + | 1.40417i | ||||
\(326\) | −1.99028 | − | 3.44727i | −0.110232 | − | 0.190927i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −2.80150 | − | 4.85235i | −0.154687 | − | 0.267926i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −7.17154 | −0.394183 | −0.197092 | − | 0.980385i | \(-0.563150\pi\) | ||||
−0.197092 | + | 0.980385i | \(0.563150\pi\) | |||||||
\(332\) | −4.03379 | + | 6.98673i | −0.221383 | + | 0.383447i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 2.61956 | + | 4.53721i | 0.143336 | + | 0.248265i | ||||
\(335\) | 17.4480 | − | 30.2209i | 0.953287 | − | 1.65114i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −10.9211 | − | 18.9158i | −0.594908 | − | 1.03041i | −0.993560 | − | 0.113309i | \(-0.963855\pi\) |
0.398651 | − | 0.917103i | \(-0.369478\pi\) | |||||||
\(338\) | −9.76608 | + | 16.9153i | −0.531205 | + | 0.920073i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 2.42107 | + | 4.19341i | 0.131301 | + | 0.227420i | ||||
\(341\) | 14.9887 | + | 25.9611i | 0.811681 | + | 1.40587i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 3.41423 | − | 5.91362i | 0.184083 | − | 0.318841i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 2.55159 | 0.137174 | ||||||||
\(347\) | 2.11109 | 0.113329 | 0.0566646 | − | 0.998393i | \(-0.481953\pi\) | ||||
0.0566646 | + | 0.998393i | \(0.481953\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −18.1082 | + | 31.3643i | −0.969310 | + | 1.67889i | −0.271751 | + | 0.962368i | \(0.587603\pi\) |
−0.697559 | + | 0.716527i | \(0.745731\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 1.59097 | + | 2.75564i | 0.0847991 | + | 0.146876i | ||||
\(353\) | 5.24433 | + | 9.08344i | 0.279127 | + | 0.483463i | 0.971168 | − | 0.238396i | \(-0.0766215\pi\) |
−0.692041 | + | 0.721858i | \(0.743288\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −13.8256 | + | 23.9466i | −0.733786 | + | 1.27095i | ||||
\(356\) | 0.112725 | + | 0.195246i | 0.00597442 | + | 0.0103480i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −3.51887 | + | 6.09487i | −0.185978 | + | 0.322124i | ||||
\(359\) | −16.2209 | − | 28.0955i | −0.856108 | − | 1.48282i | −0.875613 | − | 0.483013i | \(-0.839542\pi\) |
0.0195047 | − | 0.999810i | \(-0.493791\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 8.67743 | − | 15.0297i | 0.456707 | − | 0.791039i | ||||
\(362\) | 12.9669 | 0.681525 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −7.90219 | − | 13.6870i | −0.413620 | − | 0.716410i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −9.05555 | − | 15.6847i | −0.472696 | − | 0.818733i | 0.526816 | − | 0.849979i | \(-0.323386\pi\) |
−0.999512 | + | 0.0312465i | \(0.990052\pi\) | |||||||
\(368\) | 1.11956 | − | 1.93914i | 0.0583612 | − | 0.101085i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 3.18194 | 0.165421 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 5.83530 | − | 10.1070i | 0.302140 | − | 0.523322i | −0.674480 | − | 0.738293i | \(-0.735632\pi\) |
0.976621 | + | 0.214971i | \(0.0689656\pi\) | |||||||
\(374\) | −4.84213 | −0.250381 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −5.82846 | −0.300580 | ||||||||
\(377\) | −40.3893 | −2.08016 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 14.2690 | 0.732947 | 0.366474 | − | 0.930428i | \(-0.380565\pi\) | ||||
0.366474 | + | 0.930428i | \(0.380565\pi\) | |||||||
\(380\) | 4.08126 | 0.209364 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −1.98057 | −0.101335 | ||||||||
\(383\) | 0.824893 | − | 1.42876i | 0.0421501 | − | 0.0730061i | −0.844181 | − | 0.536059i | \(-0.819913\pi\) |
0.886331 | + | 0.463053i | \(0.153246\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −4.54583 | −0.231377 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −7.42107 | + | 12.8537i | −0.376748 | + | 0.652546i | ||||
\(389\) | −16.0338 | − | 27.7713i | −0.812946 | − | 1.40806i | −0.910794 | − | 0.412862i | \(-0.864529\pi\) |
0.0978483 | − | 0.995201i | \(-0.468804\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.70370 | + | 2.95089i | 0.0861596 | + | 0.149233i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 21.8148 | 1.09901 | ||||||||
\(395\) | −6.58414 | + | 11.4041i | −0.331284 | + | 0.573800i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 18.9669 | + | 32.8516i | 0.951921 | + | 1.64878i | 0.741261 | + | 0.671217i | \(0.234228\pi\) |
0.210660 | + | 0.977559i | \(0.432439\pi\) | |||||||
\(398\) | −6.14132 | + | 10.6371i | −0.307836 | + | 0.533188i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −2.56238 | − | 4.43818i | −0.128119 | − | 0.221909i | ||||
\(401\) | 5.30959 | − | 9.19647i | 0.265148 | − | 0.459250i | −0.702454 | − | 0.711729i | \(-0.747913\pi\) |
0.967602 | + | 0.252479i | \(0.0812458\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −26.8675 | − | 46.5358i | −1.33836 | − | 2.31811i | ||||
\(404\) | −9.29467 | − | 16.0988i | −0.462427 | − | 0.800947i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −1.59097 | + | 2.75564i | −0.0788615 | + | 0.136592i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −5.54583 | −0.274224 | −0.137112 | − | 0.990556i | \(-0.543782\pi\) | ||||
−0.137112 | + | 0.990556i | \(0.543782\pi\) | |||||||
\(410\) | −17.8285 | −0.880485 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −0.141315 | + | 0.244765i | −0.00696209 | + | 0.0120587i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 12.8353 | + | 22.2314i | 0.630060 | + | 1.09130i | ||||
\(416\) | −2.85185 | − | 4.93955i | −0.139823 | − | 0.242181i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −2.04063 | + | 3.53447i | −0.0998104 | + | 0.172877i | ||||
\(419\) | 2.77455 | + | 4.80566i | 0.135546 | + | 0.234772i | 0.925806 | − | 0.378000i | \(-0.123388\pi\) |
−0.790260 | + | 0.612772i | \(0.790055\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −3.42107 | + | 5.92546i | −0.166733 | + | 0.288789i | −0.937269 | − | 0.348606i | \(-0.886655\pi\) |
0.770537 | + | 0.637396i | \(0.219988\pi\) | |||||||
\(422\) | −8.32846 | − | 14.4253i | −0.405423 | − | 0.702213i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −1.02859 | + | 1.78157i | −0.0499527 | + | 0.0865207i | ||||
\(425\) | 7.79863 | 0.378289 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −5.68878 | − | 9.85326i | −0.274978 | − | 0.476275i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −10.8639 | − | 18.8168i | −0.523903 | − | 0.907427i | ||||
\(431\) | −16.5539 | + | 28.6722i | −0.797374 | + | 1.38109i | 0.123947 | + | 0.992289i | \(0.460445\pi\) |
−0.921321 | + | 0.388803i | \(0.872889\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 12.1111 | 0.582022 | 0.291011 | − | 0.956720i | \(-0.406008\pi\) | ||||
0.291011 | + | 0.956720i | \(0.406008\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −2.21053 | + | 3.82876i | −0.105865 | + | 0.183364i | ||||
\(437\) | 2.87197 | 0.137385 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 8.83422 | 0.421634 | 0.210817 | − | 0.977526i | \(-0.432388\pi\) | ||||
0.210817 | + | 0.977526i | \(0.432388\pi\) | |||||||
\(440\) | 10.1248 | 0.482679 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 8.67962 | 0.412847 | ||||||||
\(443\) | −17.5185 | −0.832328 | −0.416164 | − | 0.909290i | \(-0.636626\pi\) | ||||
−0.416164 | + | 0.909290i | \(0.636626\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0.717370 | 0.0340066 | ||||||||
\(446\) | 5.32846 | − | 9.22916i | 0.252310 | − | 0.437014i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −31.2301 | −1.47384 | −0.736920 | − | 0.675980i | \(-0.763720\pi\) | ||||
−0.736920 | + | 0.675980i | \(0.763720\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 8.91423 | − | 15.4399i | 0.419755 | − | 0.727036i | ||||
\(452\) | 1.60752 | + | 2.78431i | 0.0756115 | + | 0.130963i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 7.25404 | + | 12.5644i | 0.340449 | + | 0.589675i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −32.1248 | −1.50273 | −0.751367 | − | 0.659885i | \(-0.770605\pi\) | ||||
−0.751367 | + | 0.659885i | \(0.770605\pi\) | |||||||
\(458\) | 5.12476 | − | 8.87635i | 0.239464 | − | 0.414765i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −3.56238 | − | 6.17023i | −0.166097 | − | 0.287688i | ||||
\(461\) | 1.23229 | − | 2.13438i | 0.0573933 | − | 0.0994081i | −0.835901 | − | 0.548880i | \(-0.815054\pi\) |
0.893295 | + | 0.449472i | \(0.148388\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 15.1735 | + | 26.2812i | 0.705171 | + | 1.22139i | 0.966630 | + | 0.256177i | \(0.0824631\pi\) |
−0.261459 | + | 0.965215i | \(0.584204\pi\) | |||||||
\(464\) | 3.54063 | − | 6.13255i | 0.164370 | − | 0.284696i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −0.540628 | − | 0.936396i | −0.0250441 | − | 0.0433777i | ||||
\(467\) | −7.98181 | − | 13.8249i | −0.369354 | − | 0.639740i | 0.620110 | − | 0.784515i | \(-0.287088\pi\) |
−0.989465 | + | 0.144774i | \(0.953754\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −9.27292 | + | 16.0612i | −0.427728 | + | 0.740846i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −1.12476 | −0.0517714 | ||||||||
\(473\) | 21.7278 | 0.999044 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 3.28659 | − | 5.69254i | 0.150799 | − | 0.261192i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 6.16019 | + | 10.6698i | 0.281761 | + | 0.488024i | ||||
\(479\) | 11.5865 | + | 20.0683i | 0.529399 | + | 0.916946i | 0.999412 | + | 0.0342863i | \(0.0109158\pi\) |
−0.470013 | + | 0.882659i | \(0.655751\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.85185 | − | 4.93955i | 0.130033 | − | 0.225224i | ||||
\(482\) | −6.50000 | − | 11.2583i | −0.296067 | − | 0.512803i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0.437618 | − | 0.757977i | 0.0198917 | − | 0.0344535i | ||||
\(485\) | 23.6134 | + | 40.8996i | 1.07223 | + | 1.85716i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 1.70658 | − | 2.95588i | 0.0773323 | − | 0.133943i | −0.824766 | − | 0.565474i | \(-0.808693\pi\) |
0.902098 | + | 0.431531i | \(0.142026\pi\) | |||||||
\(488\) | −3.12476 | −0.141451 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 9.58414 | + | 16.6002i | 0.432526 | + | 0.749157i | 0.997090 | − | 0.0762323i | \(-0.0242890\pi\) |
−0.564564 | + | 0.825389i | \(0.690956\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 5.38796 | + | 9.33223i | 0.242662 | + | 0.420302i | ||||
\(494\) | 3.65787 | − | 6.33561i | 0.164575 | − | 0.285053i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 9.42107 | 0.423018 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −20.5848 | + | 35.6540i | −0.921503 | + | 1.59609i | −0.124413 | + | 0.992231i | \(0.539705\pi\) |
−0.797090 | + | 0.603860i | \(0.793629\pi\) | |||||||
\(500\) | −0.396990 | −0.0177539 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 5.11109 | 0.228119 | ||||||||
\(503\) | −26.4542 | −1.17953 | −0.589767 | − | 0.807574i | \(-0.700780\pi\) | ||||
−0.589767 | + | 0.807574i | \(0.700780\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −59.1502 | −2.63215 | ||||||||
\(506\) | 7.12476 | 0.316734 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 20.1053 | 0.892030 | ||||||||
\(509\) | −6.38564 | + | 11.0603i | −0.283039 | + | 0.490237i | −0.972132 | − | 0.234436i | \(-0.924676\pi\) |
0.689093 | + | 0.724673i | \(0.258009\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −3.83009 | + | 6.63392i | −0.168938 | + | 0.292610i | ||||
\(515\) | 0.449657 | + | 0.778828i | 0.0198142 | + | 0.0343193i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −9.27292 | − | 16.0612i | −0.407822 | − | 0.706369i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −18.1488 | −0.795879 | ||||||||
\(521\) | −3.40615 | + | 5.89962i | −0.149226 | + | 0.258467i | −0.930942 | − | 0.365168i | \(-0.881012\pi\) |
0.781716 | + | 0.623635i | \(0.214345\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −14.7535 | − | 25.5538i | −0.645125 | − | 1.11739i | −0.984273 | − | 0.176656i | \(-0.943472\pi\) |
0.339148 | − | 0.940733i | \(-0.389861\pi\) | |||||||
\(524\) | −3.18194 | + | 5.51129i | −0.139004 | + | 0.240762i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −1.54746 | − | 2.68029i | −0.0674727 | − | 0.116866i | ||||
\(527\) | −7.16827 | + | 12.4158i | −0.312255 | + | 0.540841i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 8.99316 | + | 15.5766i | 0.391007 | + | 0.677244i | ||||
\(530\) | 3.27292 | + | 5.66886i | 0.142166 | + | 0.246239i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −15.9789 | + | 27.6763i | −0.692125 | + | 1.19879i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −36.2028 | −1.56518 | ||||||||
\(536\) | 10.9669 | 0.473698 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −13.4451 | + | 23.2877i | −0.579661 | + | 1.00400i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 14.7008 | + | 25.4626i | 0.632038 | + | 1.09472i | 0.987135 | + | 0.159892i | \(0.0511145\pi\) |
−0.355097 | + | 0.934829i | \(0.615552\pi\) | |||||||
\(542\) | 11.1082 | + | 19.2400i | 0.477139 | + | 0.826428i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −0.760877 | + | 1.31788i | −0.0326223 | + | 0.0565035i | ||||
\(545\) | 7.03379 | + | 12.1829i | 0.301295 | + | 0.521857i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 17.6150 | − | 30.5102i | 0.753165 | − | 1.30452i | −0.193116 | − | 0.981176i | \(-0.561859\pi\) |
0.946281 | − | 0.323344i | \(-0.104807\pi\) | |||||||
\(548\) | 1.37072 | + | 2.37416i | 0.0585544 | + | 0.101419i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 8.15335 | − | 14.1220i | 0.347660 | − | 0.602165i | ||||
\(551\) | 9.08263 | 0.386933 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 7.31875 | + | 12.6764i | 0.310944 | + | 0.538570i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 3.98345 | + | 6.89953i | 0.168936 | + | 0.292605i | ||||
\(557\) | 3.36909 | − | 5.83543i | 0.142753 | − | 0.247255i | −0.785779 | − | 0.618507i | \(-0.787738\pi\) |
0.928532 | + | 0.371252i | \(0.121071\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −38.9475 | −1.64730 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −11.6992 | + | 20.2636i | −0.493500 | + | 0.854768i | ||||
\(563\) | −1.45993 | −0.0615286 | −0.0307643 | − | 0.999527i | \(-0.509794\pi\) | ||||
−0.0307643 | + | 0.999527i | \(0.509794\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 10.2301 | 0.430383 | ||||||||
\(566\) | 26.1248 | 1.09811 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −8.69002 | −0.364625 | ||||||||
\(569\) | −19.5653 | −0.820218 | −0.410109 | − | 0.912036i | \(-0.634509\pi\) | ||||
−0.410109 | + | 0.912036i | \(0.634509\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −21.9259 | −0.917569 | −0.458785 | − | 0.888547i | \(-0.651715\pi\) | ||||
−0.458785 | + | 0.888547i | \(0.651715\pi\) | |||||||
\(572\) | 9.07442 | − | 15.7174i | 0.379421 | − | 0.657176i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −11.4750 | −0.478540 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −12.3655 | + | 21.4177i | −0.514783 | + | 0.891631i | 0.485069 | + | 0.874476i | \(0.338794\pi\) |
−0.999853 | + | 0.0171554i | \(0.994539\pi\) | |||||||
\(578\) | 7.34213 | + | 12.7169i | 0.305392 | + | 0.528955i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −11.2661 | − | 19.5134i | −0.467798 | − | 0.810251i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −6.54583 | −0.271101 | ||||||||
\(584\) | 2.48345 | − | 4.30146i | 0.102766 | − | 0.177996i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 12.9315 | + | 22.3980i | 0.534194 | + | 0.925251i | ||||
\(587\) | −18.0796 | + | 31.3148i | −0.746226 | + | 1.29250i | 0.203394 | + | 0.979097i | \(0.434803\pi\) |
−0.949620 | + | 0.313404i | \(0.898531\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 6.04187 | + | 10.4648i | 0.248951 | + | 0.431196i | ||||
\(590\) | −1.78947 | + | 3.09945i | −0.0736712 | + | 0.127602i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0.500000 | + | 0.866025i | 0.0205499 | + | 0.0355934i | ||||
\(593\) | −7.55391 | − | 13.0838i | −0.310202 | − | 0.537285i | 0.668204 | − | 0.743978i | \(-0.267063\pi\) |
−0.978406 | + | 0.206693i | \(0.933730\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −11.6300 | + | 20.1437i | −0.476382 | + | 0.825118i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −12.7713 | −0.522256 | ||||||||
\(599\) | 5.45417 | 0.222851 | 0.111426 | − | 0.993773i | \(-0.464458\pi\) | ||||
0.111426 | + | 0.993773i | \(0.464458\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 3.36840 | − | 5.83424i | 0.137400 | − | 0.237984i | −0.789112 | − | 0.614250i | \(-0.789459\pi\) |
0.926512 | + | 0.376266i | \(0.122792\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 4.06238 | + | 7.03625i | 0.165296 | + | 0.286301i | ||||
\(605\) | −1.39248 | − | 2.41184i | −0.0566122 | − | 0.0980553i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 3.33530 | − | 5.77690i | 0.135376 | − | 0.234477i | −0.790365 | − | 0.612636i | \(-0.790109\pi\) |
0.925741 | + | 0.378159i | \(0.123443\pi\) | |||||||
\(608\) | 0.641315 | + | 1.11079i | 0.0260088 | + | 0.0450485i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −4.97141 | + | 8.61073i | −0.201287 | + | 0.348638i | ||||
\(611\) | 16.6219 | + | 28.7899i | 0.672449 | + | 1.16472i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 0.654988 | − | 1.13447i | 0.0264547 | − | 0.0458209i | −0.852495 | − | 0.522735i | \(-0.824912\pi\) |
0.878950 | + | 0.476915i | \(0.158245\pi\) | |||||||
\(614\) | −3.53216 | −0.142546 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −17.2483 | − | 29.8749i | −0.694390 | − | 1.20272i | −0.970386 | − | 0.241560i | \(-0.922341\pi\) |
0.275996 | − | 0.961159i | \(-0.410992\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −8.22421 | − | 14.2447i | −0.330559 | − | 0.572545i | 0.652063 | − | 0.758165i | \(-0.273904\pi\) |
−0.982622 | + | 0.185620i | \(0.940571\pi\) | |||||||
\(620\) | 14.9887 | − | 25.9611i | 0.601959 | − | 1.04262i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 1.70370 | 0.0683120 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 12.1803 | − | 21.0969i | 0.487212 | − | 0.843877i | ||||
\(626\) | 2.84213 | 0.113594 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 11.2632 | 0.449451 | ||||||||
\(629\) | −1.52175 | −0.0606763 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −30.0118 | −1.19475 | −0.597375 | − | 0.801962i | \(-0.703790\pi\) | ||||
−0.597375 | + | 0.801962i | \(0.703790\pi\) | |||||||
\(632\) | −4.13844 | −0.164618 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 24.9201 | 0.989704 | ||||||||
\(635\) | 31.9870 | − | 55.4031i | 1.26937 | − | 2.19861i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 22.5322 | 0.892057 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 1.59097 | − | 2.75564i | 0.0628887 | − | 0.108926i | ||||
\(641\) | 13.9497 | + | 24.1615i | 0.550978 | + | 0.954322i | 0.998204 | + | 0.0599014i | \(0.0190786\pi\) |
−0.447226 | + | 0.894421i | \(0.647588\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −14.2524 | − | 24.6859i | −0.562060 | − | 0.973516i | −0.997317 | − | 0.0732100i | \(-0.976676\pi\) |
0.435257 | − | 0.900306i | \(-0.356658\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −1.95185 | −0.0767944 | ||||||||
\(647\) | 8.35705 | − | 14.4748i | 0.328550 | − | 0.569065i | −0.653675 | − | 0.756776i | \(-0.726774\pi\) |
0.982224 | + | 0.187711i | \(0.0601069\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1.78947 | − | 3.09945i | −0.0702427 | − | 0.121664i | ||||
\(650\) | −14.6150 | + | 25.3140i | −0.573249 | + | 0.992897i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −1.99028 | − | 3.44727i | −0.0779456 | − | 0.135006i | ||||
\(653\) | 19.0825 | − | 33.0519i | 0.746756 | − | 1.29342i | −0.202614 | − | 0.979259i | \(-0.564944\pi\) |
0.949370 | − | 0.314161i | \(-0.101723\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 10.1248 | + | 17.5366i | 0.395607 | + | 0.685212i | ||||
\(656\) | −2.80150 | − | 4.85235i | −0.109380 | − | 0.189452i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −4.37072 | + | 7.57031i | −0.170259 | + | 0.294898i | −0.938510 | − | 0.345251i | \(-0.887794\pi\) |
0.768251 | + | 0.640148i | \(0.221127\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 20.0837 | 0.781167 | 0.390584 | − | 0.920567i | \(-0.372273\pi\) | ||||
0.390584 | + | 0.920567i | \(0.372273\pi\) | |||||||
\(662\) | −7.17154 | −0.278730 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −4.03379 | + | 6.98673i | −0.156541 | + | 0.271138i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −7.92790 | − | 13.7315i | −0.306970 | − | 0.531687i | ||||
\(668\) | 2.61956 | + | 4.53721i | 0.101354 | + | 0.175550i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 17.4480 | − | 30.2209i | 0.674076 | − | 1.16753i | ||||
\(671\) | −4.97141 | − | 8.61073i | −0.191919 | − | 0.332414i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −17.0264 | + | 29.4906i | −0.656319 | + | 1.13678i | 0.325242 | + | 0.945631i | \(0.394554\pi\) |
−0.981561 | + | 0.191148i | \(0.938779\pi\) | |||||||
\(674\) | −10.9211 | − | 18.9158i | −0.420664 | − | 0.728611i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −9.76608 | + | 16.9153i | −0.375618 | + | 0.650590i | ||||
\(677\) | −0.717370 | −0.0275708 | −0.0137854 | − | 0.999905i | \(-0.504388\pi\) | ||||
−0.0137854 | + | 0.999905i | \(0.504388\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 2.42107 | + | 4.19341i | 0.0928437 | + | 0.160810i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 14.9887 | + | 25.9611i | 0.573945 | + | 0.994102i | ||||
\(683\) | 10.5270 | − | 18.2332i | 0.402803 | − | 0.697675i | −0.591260 | − | 0.806481i | \(-0.701369\pi\) |
0.994063 | + | 0.108806i | \(0.0347027\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 8.72313 | 0.333294 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 3.41423 | − | 5.91362i | 0.130166 | − | 0.225455i | ||||
\(689\) | 11.7335 | 0.447012 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −5.84789 | −0.222464 | −0.111232 | − | 0.993794i | \(-0.535480\pi\) | ||||
−0.111232 | + | 0.993794i | \(0.535480\pi\) | |||||||
\(692\) | 2.55159 | 0.0969968 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 2.11109 | 0.0801359 | ||||||||
\(695\) | 25.3502 | 0.961588 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 8.52640 | 0.322960 | ||||||||
\(698\) | −18.1082 | + | 31.3643i | −0.685406 | + | 1.18716i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −10.2711 | −0.387935 | −0.193967 | − | 0.981008i | \(-0.562136\pi\) | ||||
−0.193967 | + | 0.981008i | \(0.562136\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −0.641315 | + | 1.11079i | −0.0241877 | + | 0.0418942i | ||||
\(704\) | 1.59097 | + | 2.75564i | 0.0599620 | + | 0.103857i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 5.24433 | + | 9.08344i | 0.197373 | + | 0.341860i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 43.4854 | 1.63313 | 0.816564 | − | 0.577255i | \(-0.195876\pi\) | ||||
0.816564 | + | 0.577255i | \(0.195876\pi\) | |||||||
\(710\) | −13.8256 | + | 23.9466i | −0.518865 | + | 0.898700i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0.112725 | + | 0.195246i | 0.00422455 | + | 0.00731714i | ||||
\(713\) | 10.5475 | − | 18.2687i | 0.395006 | − | 0.684170i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −28.8743 | − | 50.0117i | −1.07984 | − | 1.87033i | ||||
\(716\) | −3.51887 | + | 6.09487i | −0.131507 | + | 0.227776i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −16.2209 | − | 28.0955i | −0.605360 | − | 1.04851i | ||||
\(719\) | 25.4412 | + | 44.0654i | 0.948796 | + | 1.64336i | 0.747966 | + | 0.663737i | \(0.231031\pi\) |
0.200830 | + | 0.979626i | \(0.435636\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 8.67743 | − | 15.0297i | 0.322941 | − | 0.559349i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 12.9669 | 0.481911 | ||||||||
\(725\) | −36.2898 | −1.34777 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −6.07210 | + | 10.5172i | −0.225202 | + | 0.390061i | −0.956380 | − | 0.292126i | \(-0.905637\pi\) |
0.731178 | + | 0.682186i | \(0.238971\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −7.90219 | − | 13.6870i | −0.292473 | − | 0.506579i | ||||
\(731\) | 5.19562 | + | 8.99907i | 0.192167 | + | 0.332843i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −23.0848 | + | 39.9841i | −0.852657 | + | 1.47685i | 0.0261440 | + | 0.999658i | \(0.491677\pi\) |
−0.878801 | + | 0.477188i | \(0.841656\pi\) | |||||||
\(734\) | −9.05555 | − | 15.6847i | −0.334246 | − | 0.578932i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.11956 | − | 1.93914i | 0.0412676 | − | 0.0714776i | ||||
\(737\) | 17.4480 | + | 30.2209i | 0.642706 | + | 1.11320i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −2.49604 | + | 4.32327i | −0.0918184 | + | 0.159034i | −0.908276 | − | 0.418371i | \(-0.862601\pi\) |
0.816458 | + | 0.577405i | \(0.195935\pi\) | |||||||
\(740\) | 3.18194 | 0.116971 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 15.7060 | + | 27.2036i | 0.576198 | + | 0.998004i | 0.995910 | + | 0.0903470i | \(0.0287976\pi\) |
−0.419712 | + | 0.907657i | \(0.637869\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 37.0059 | + | 64.0961i | 1.35579 | + | 2.34830i | ||||
\(746\) | 5.83530 | − | 10.1070i | 0.213645 | − | 0.370045i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −4.84213 | −0.177046 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.64815 | + | 2.85468i | −0.0601419 | + | 0.104169i | −0.894529 | − | 0.447010i | \(-0.852489\pi\) |
0.834387 | + | 0.551179i | \(0.185822\pi\) | |||||||
\(752\) | −5.82846 | −0.212542 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −40.3893 | −1.47089 | ||||||||
\(755\) | 25.8525 | 0.940870 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −10.1384 | −0.368488 | −0.184244 | − | 0.982881i | \(-0.558984\pi\) | ||||
−0.184244 | + | 0.982881i | \(0.558984\pi\) | |||||||
\(758\) | 14.2690 | 0.518272 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 4.08126 | 0.148043 | ||||||||
\(761\) | −7.03379 | + | 12.1829i | −0.254975 | + | 0.441629i | −0.964889 | − | 0.262659i | \(-0.915400\pi\) |
0.709914 | + | 0.704288i | \(0.248734\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −1.98057 | −0.0716545 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0.824893 | − | 1.42876i | 0.0298046 | − | 0.0516231i | ||||
\(767\) | 3.20765 | + | 5.55582i | 0.115822 | + | 0.200609i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −11.3461 | − | 19.6520i | −0.409151 | − | 0.708669i | 0.585644 | − | 0.810568i | \(-0.300842\pi\) |
−0.994795 | + | 0.101899i | \(0.967508\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −4.54583 | −0.163608 | ||||||||
\(773\) | 0.327772 | − | 0.567717i | 0.0117891 | − | 0.0204194i | −0.860071 | − | 0.510175i | \(-0.829581\pi\) |
0.871860 | + | 0.489756i | \(0.162914\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −24.1404 | − | 41.8123i | −0.867148 | − | 1.50194i | ||||
\(776\) | −7.42107 | + | 12.8537i | −0.266401 | + | 0.461420i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −16.0338 | − | 27.7713i | −0.574839 | − | 0.995651i | ||||
\(779\) | 3.59329 | − | 6.22377i | 0.128743 | − | 0.222990i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −13.8256 | − | 23.9466i | −0.494718 | − | 0.856877i | ||||
\(782\) | 1.70370 | + | 2.95089i | 0.0609241 | + | 0.105524i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 17.9194 | − | 31.0374i | 0.639572 | − | 1.10777i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −0.540073 | −0.0192515 | −0.00962576 | − | 0.999954i | \(-0.503064\pi\) | ||||
−0.00962576 | + | 0.999954i | \(0.503064\pi\) | |||||||
\(788\) | 21.8148 | 0.777120 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −6.58414 | + | 11.4041i | −0.234253 | + | 0.405738i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 8.91135 | + | 15.4349i | 0.316451 | + | 0.548110i | ||||
\(794\) | 18.9669 | + | 32.8516i | 0.673110 | + | 1.16586i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −6.14132 | + | 10.6371i | −0.217673 | + | 0.377021i | ||||
\(797\) | −12.5550 | − | 21.7459i | −0.444721 | − | 0.770279i | 0.553312 | − | 0.832974i | \(-0.313364\pi\) |
−0.998033 | + | 0.0626954i | \(0.980030\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 4.43474 | − | 7.68119i | 0.156890 | − | 0.271741i | ||||
\(800\) | −2.56238 | − | 4.43818i | −0.0905939 | − | 0.156913i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 5.30959 | − | 9.19647i | 0.187488 | − | 0.324739i | ||||
\(803\) | 15.8044 | 0.557725 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −26.8675 | − | 46.5358i | −0.946366 | − | 1.63915i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −9.29467 | − | 16.0988i | −0.326985 | − | 0.566355i | ||||
\(809\) | 14.5865 | − | 25.2645i | 0.512833 | − | 0.888252i | −0.487057 | − | 0.873370i | \(-0.661929\pi\) |
0.999889 | − | 0.0148817i | \(-0.00473717\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 15.4290 | 0.541785 | 0.270892 | − | 0.962610i | \(-0.412681\pi\) | ||||
0.270892 | + | 0.962610i | \(0.412681\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −1.59097 | + | 2.75564i | −0.0557635 | + | 0.0965853i | ||||
\(815\) | −12.6659 | −0.443669 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 8.75839 | 0.306417 | ||||||||
\(818\) | −5.54583 | −0.193905 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −17.8285 | −0.622597 | ||||||||
\(821\) | −8.48727 | −0.296208 | −0.148104 | − | 0.988972i | \(-0.547317\pi\) | ||||
−0.148104 | + | 0.988972i | \(0.547317\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 29.0974 | 1.01427 | 0.507136 | − | 0.861866i | \(-0.330704\pi\) | ||||
0.507136 | + | 0.861866i | \(0.330704\pi\) | |||||||
\(824\) | −0.141315 | + | 0.244765i | −0.00492294 | + | 0.00852679i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 25.9396 | 0.902007 | 0.451003 | − | 0.892522i | \(-0.351066\pi\) | ||||
0.451003 | + | 0.892522i | \(0.351066\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −3.10821 | + | 5.38358i | −0.107953 | + | 0.186979i | −0.914941 | − | 0.403588i | \(-0.867763\pi\) |
0.806988 | + | 0.590568i | \(0.201096\pi\) | |||||||
\(830\) | 12.8353 | + | 22.2314i | 0.445520 | + | 0.771663i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −2.85185 | − | 4.93955i | −0.0988701 | − | 0.171248i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 16.6706 | 0.576910 | ||||||||
\(836\) | −2.04063 | + | 3.53447i | −0.0705766 | + | 0.122242i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 2.77455 | + | 4.80566i | 0.0958452 | + | 0.166009i | ||||
\(839\) | 21.2947 | − | 36.8834i | 0.735174 | − | 1.27336i | −0.219474 | − | 0.975618i | \(-0.570434\pi\) |
0.954647 | − | 0.297740i | \(-0.0962327\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −10.5721 | − | 18.3114i | −0.364555 | − | 0.631428i | ||||
\(842\) | −3.42107 | + | 5.92546i | −0.117898 | + | 0.204205i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −8.32846 | − | 14.4253i | −0.286677 | − | 0.496540i | ||||
\(845\) | 31.0751 | + | 53.8237i | 1.06902 | + | 1.85159i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −1.02859 | + | 1.78157i | −0.0353219 | + | 0.0611794i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 7.79863 | 0.267491 | ||||||||
\(851\) | 2.23912 | 0.0767562 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 10.6969 | − | 18.5275i | 0.366254 | − | 0.634370i | −0.622723 | − | 0.782442i | \(-0.713974\pi\) |
0.988976 | + | 0.148073i | \(0.0473070\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −5.68878 | − | 9.85326i | −0.194438 | − | 0.336777i | ||||
\(857\) | 18.4218 | + | 31.9074i | 0.629275 | + | 1.08994i | 0.987697 | + | 0.156377i | \(0.0499815\pi\) |
−0.358422 | + | 0.933560i | \(0.616685\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −8.81875 | + | 15.2745i | −0.300892 | + | 0.521160i | −0.976338 | − | 0.216249i | \(-0.930618\pi\) |
0.675446 | + | 0.737409i | \(0.263951\pi\) | |||||||
\(860\) | −10.8639 | − | 18.8168i | −0.370455 | − | 0.641648i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −16.5539 | + | 28.6722i | −0.563828 | + | 0.976579i | ||||
\(863\) | 0.380438 | + | 0.658939i | 0.0129503 | + | 0.0224305i | 0.872428 | − | 0.488743i | \(-0.162544\pi\) |
−0.859478 | + | 0.511173i | \(0.829211\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 4.05950 | − | 7.03127i | 0.138027 | − | 0.239070i | ||||
\(866\) | 12.1111 | 0.411552 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −6.58414 | − | 11.4041i | −0.223351 | − | 0.386856i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −31.2759 | − | 54.1715i | −1.05974 | − | 1.83553i | ||||
\(872\) | −2.21053 | + | 3.82876i | −0.0748581 | + | 0.129658i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 2.87197 | 0.0971457 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 20.7495 | − | 35.9392i | 0.700662 | − | 1.21358i | −0.267573 | − | 0.963538i | \(-0.586222\pi\) |
0.968234 | − | 0.250044i | \(-0.0804451\pi\) | |||||||
\(878\) | 8.83422 | 0.298140 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 10.1248 | 0.341306 | ||||||||
\(881\) | 8.35486 | 0.281482 | 0.140741 | − | 0.990046i | \(-0.455051\pi\) | ||||
0.140741 | + | 0.990046i | \(0.455051\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 35.6181 | 1.19864 | 0.599322 | − | 0.800508i | \(-0.295437\pi\) | ||||
0.599322 | + | 0.800508i | \(0.295437\pi\) | |||||||
\(884\) | 8.67962 | 0.291927 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −17.5185 | −0.588545 | ||||||||
\(887\) | 18.5550 | − | 32.1382i | 0.623016 | − | 1.07909i | −0.365905 | − | 0.930652i | \(-0.619241\pi\) |
0.988921 | − | 0.148443i | \(-0.0474260\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0.717370 | 0.0240463 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 5.32846 | − | 9.22916i | 0.178410 | − | 0.309015i | ||||
\(893\) | −3.73788 | − | 6.47420i | −0.125083 | − | 0.216651i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 11.1969 | + | 19.3935i | 0.374270 | + | 0.648254i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −31.2301 | −1.04216 | ||||||||
\(899\) | 33.3565 | − | 57.7751i | 1.11250 | − | 1.92691i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.56526 | − | 2.71111i | −0.0521464 | − | 0.0903202i | ||||
\(902\) | 8.91423 | − | 15.4399i | 0.296811 | − | 0.514092i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 1.60752 | + | 2.78431i | 0.0534654 | + | 0.0926048i | ||||
\(905\) | 20.6300 | − | 35.7321i | 0.685763 | − | 1.18778i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 24.0751 | + | 41.6993i | 0.799401 | + | 1.38460i | 0.920007 | + | 0.391902i | \(0.128183\pi\) |
−0.120606 | + | 0.992700i | \(0.538484\pi\) | |||||||
\(908\) | 7.25404 | + | 12.5644i | 0.240734 | + | 0.416963i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −17.4428 | + | 30.2119i | −0.577906 | + | 1.00096i | 0.417813 | + | 0.908533i | \(0.362797\pi\) |
−0.995719 | + | 0.0924301i | \(0.970537\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −25.6706 | −0.849573 | ||||||||
\(914\) | −32.1248 | −1.06259 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 5.12476 | − | 8.87635i | 0.169327 | − | 0.293283i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −25.8675 | − | 44.8037i | −0.853289 | − | 1.47794i | −0.878224 | − | 0.478250i | \(-0.841271\pi\) |
0.0249351 | − | 0.999689i | \(-0.492062\pi\) | |||||||
\(920\) | −3.56238 | − | 6.17023i | −0.117448 | − | 0.203426i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 1.23229 | − | 2.13438i | 0.0405832 | − | 0.0702922i | ||||
\(923\) | 24.7826 | + | 42.9248i | 0.815730 | + | 1.41289i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2.56238 | − | 4.43818i | 0.0842506 | − | 0.145926i | ||||
\(926\) | 15.1735 | + | 26.2812i | 0.498631 | + | 0.863655i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 3.54063 | − | 6.13255i | 0.116227 | − | 0.201311i | ||||
\(929\) | −50.8285 | −1.66763 | −0.833814 | − | 0.552046i | \(-0.813847\pi\) | ||||
−0.833814 | + | 0.552046i | \(0.813847\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −0.540628 | − | 0.936396i | −0.0177089 | − | 0.0306727i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −7.98181 | − | 13.8249i | −0.261173 | − | 0.452365i | ||||
\(935\) | −7.70370 | + | 13.3432i | −0.251938 | + | 0.436369i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −2.54583 | −0.0831686 | −0.0415843 | − | 0.999135i | \(-0.513241\pi\) | ||||
−0.0415843 | + | 0.999135i | \(0.513241\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −9.27292 | + | 16.0612i | −0.302449 | + | 0.523857i | ||||
\(941\) | 1.15787 | 0.0377454 | 0.0188727 | − | 0.999822i | \(-0.493992\pi\) | ||||
0.0188727 | + | 0.999822i | \(0.493992\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −12.5458 | −0.408548 | ||||||||
\(944\) | −1.12476 | −0.0366079 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 21.7278 | 0.706431 | ||||||||
\(947\) | −9.81479 | −0.318938 | −0.159469 | − | 0.987203i | \(-0.550978\pi\) | ||||
−0.159469 | + | 0.987203i | \(0.550978\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −28.3297 | −0.919620 | ||||||||
\(950\) | 3.28659 | − | 5.69254i | 0.106631 | − | 0.184690i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −6.53791 | −0.211784 | −0.105892 | − | 0.994378i | \(-0.533770\pi\) | ||||
−0.105892 | + | 0.994378i | \(0.533770\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −3.15103 | + | 5.45774i | −0.101965 | + | 0.176608i | ||||
\(956\) | 6.16019 | + | 10.6698i | 0.199235 | + | 0.345085i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 11.5865 | + | 20.0683i | 0.374341 | + | 0.648378i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 57.7565 | 1.86311 | ||||||||
\(962\) | 2.85185 | − | 4.93955i | 0.0919473 | − | 0.159257i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −6.50000 | − | 11.2583i | −0.209351 | − | 0.362606i | ||||
\(965\) | −7.23229 | + | 12.5267i | −0.232816 | + | 0.403248i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 14.4445 | + | 25.0185i | 0.464502 | + | 0.804542i | 0.999179 | − | 0.0405151i | \(-0.0128999\pi\) |
−0.534677 | + | 0.845057i | \(0.679567\pi\) | |||||||
\(968\) | 0.437618 | − | 0.757977i | 0.0140656 | − | 0.0243623i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 23.6134 | + | 40.8996i | 0.758181 | + | 1.31321i | ||||
\(971\) | 2.66827 | + | 4.62158i | 0.0856289 | + | 0.148314i | 0.905659 | − | 0.424007i | \(-0.139377\pi\) |
−0.820030 | + | 0.572320i | \(0.806043\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 1.70658 | − | 2.95588i | 0.0546822 | − | 0.0947124i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −3.12476 | −0.100021 | ||||||||
\(977\) | 48.0722 | 1.53797 | 0.768983 | − | 0.639269i | \(-0.220763\pi\) | ||||
0.768983 | + | 0.639269i | \(0.220763\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −0.358685 | + | 0.621261i | −0.0114636 | + | 0.0198556i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 9.58414 | + | 16.6002i | 0.305842 | + | 0.529734i | ||||
\(983\) | −14.7313 | − | 25.5154i | −0.469857 | − | 0.813816i | 0.529549 | − | 0.848279i | \(-0.322361\pi\) |
−0.999406 | + | 0.0344634i | \(0.989028\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 34.7067 | − | 60.1138i | 1.10585 | − | 1.91538i | ||||
\(986\) | 5.38796 | + | 9.33223i | 0.171588 | + | 0.297199i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 3.65787 | − | 6.33561i | 0.116372 | − | 0.201563i | ||||
\(989\) | −7.64488 | − | 13.2413i | −0.243093 | − | 0.421050i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 15.4142 | − | 26.6982i | 0.489649 | − | 0.848097i | −0.510280 | − | 0.860008i | \(-0.670458\pi\) |
0.999929 | + | 0.0119112i | \(0.00379153\pi\) | |||||||
\(992\) | 9.42107 | 0.299119 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 19.5413 | + | 33.8466i | 0.619501 | + | 1.07301i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 2.77292 | + | 4.80283i | 0.0878191 | + | 0.152107i | 0.906589 | − | 0.422015i | \(-0.138677\pi\) |
−0.818770 | + | 0.574122i | \(0.805344\pi\) | |||||||
\(998\) | −20.5848 | + | 35.6540i | −0.651601 | + | 1.12861i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))