Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [804,2,Mod(41,804)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(804, base_ring=CyclotomicField(66))
chi = DirichletCharacter(H, H._module([0, 33, 53]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("804.41");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 804 = 2^{2} \cdot 3 \cdot 67 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 804.ba (of order \(66\), degree \(20\), 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: | \(6.41997232251\) |
Analytic rank: | \(0\) |
Dimension: | \(440\) |
Relative dimension: | \(22\) over \(\Q(\zeta_{66})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{66}]$ |
Embedding invariants
Embedding label | 353.14 | ||
Character | \(\chi\) | \(=\) | 804.353 |
Dual form | 804.2.ba.b.41.14 |
$q$-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 \(\left(\mathbb{Z}/804\mathbb{Z}\right)^\times\).
\(n\) | \(269\) | \(337\) | \(403\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{13}{66}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0.399410 | + | 1.68537i | 0.230599 | + | 0.973049i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.202812 | + | 1.41059i | 0.0907002 | + | 0.630834i | 0.983571 | + | 0.180521i | \(0.0577784\pi\) |
−0.892871 | + | 0.450313i | \(0.851312\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.147283 | + | 1.54242i | −0.0556679 | + | 0.582980i | 0.924005 | + | 0.382380i | \(0.124895\pi\) |
−0.979673 | + | 0.200600i | \(0.935711\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.68094 | + | 1.34631i | −0.893648 | + | 0.448769i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.41940 | + | 0.968583i | 0.729477 | + | 0.292039i | 0.706515 | − | 0.707698i | \(-0.250266\pi\) |
0.0229619 | + | 0.999736i | \(0.492690\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.91962 | + | 2.01323i | −0.532405 | + | 0.558371i | −0.933920 | − | 0.357482i | \(-0.883635\pi\) |
0.401515 | + | 0.915853i | \(0.368484\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −2.29636 | + | 0.905215i | −0.592917 | + | 0.233726i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −3.53951 | − | 1.22504i | −0.858458 | − | 0.297115i | −0.137846 | − | 0.990454i | \(-0.544018\pi\) |
−0.720612 | + | 0.693339i | \(0.756139\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.0830309 | + | 0.00792849i | −0.0190486 | + | 0.00181892i | −0.104576 | − | 0.994517i | \(-0.533349\pi\) |
0.0855274 | + | 0.996336i | \(0.472742\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.65838 | + | 0.367831i | −0.580105 | + | 0.0802673i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −0.357259 | − | 0.0170183i | −0.0744936 | − | 0.00354857i | 0.0103020 | − | 0.999947i | \(-0.496721\pi\) |
−0.0847956 | + | 0.996398i | \(0.527024\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.84884 | − | 0.836495i | 0.569768 | − | 0.167299i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −3.33982 | − | 3.98065i | −0.642748 | − | 0.766077i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2.14642 | − | 1.23924i | −0.398581 | − | 0.230121i | 0.287291 | − | 0.957843i | \(-0.407245\pi\) |
−0.685872 | + | 0.727723i | \(0.740579\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.40107 | + | 2.51817i | 0.431245 | + | 0.452277i | 0.903120 | − | 0.429389i | \(-0.141271\pi\) |
−0.471875 | + | 0.881666i | \(0.656422\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −0.666088 | + | 4.46445i | −0.115951 | + | 0.777161i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −2.20559 | + | 0.105065i | −0.372813 | + | 0.0177593i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.28486 | + | 5.68954i | 0.540027 | + | 0.935354i | 0.998902 | + | 0.0468534i | \(0.0149193\pi\) |
−0.458875 | + | 0.888501i | \(0.651747\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −4.15976 | − | 2.43116i | −0.666094 | − | 0.389297i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.45686 | + | 0.280786i | −0.227523 | + | 0.0438514i | −0.301738 | − | 0.953391i | \(-0.597567\pi\) |
0.0742156 | + | 0.997242i | \(0.476355\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −6.93510 | + | 6.00930i | −1.05759 | + | 0.916409i | −0.996654 | − | 0.0817323i | \(-0.973955\pi\) |
−0.0609383 | + | 0.998142i | \(0.519409\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −2.44281 | − | 3.50866i | −0.364153 | − | 0.523040i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −5.86207 | − | 11.3708i | −0.855071 | − | 1.65861i | −0.747355 | − | 0.664425i | \(-0.768677\pi\) |
−0.107716 | − | 0.994182i | \(-0.534354\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 4.51613 | + | 0.870413i | 0.645162 | + | 0.124345i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0.650925 | − | 6.45468i | 0.0911478 | − | 0.903836i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −1.34621 | + | 1.55361i | −0.184916 | + | 0.213405i | −0.840637 | − | 0.541598i | \(-0.817819\pi\) |
0.655721 | + | 0.755003i | \(0.272365\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −0.875587 | + | 3.60922i | −0.118064 | + | 0.486667i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −0.0465258 | − | 0.136771i | −0.00616249 | − | 0.0181158i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0.862133 | − | 2.93616i | 0.112240 | − | 0.382255i | −0.884144 | − | 0.467214i | \(-0.845258\pi\) |
0.996384 | + | 0.0849590i | \(0.0270759\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.16017 | + | 10.3916i | 0.532655 | + | 1.33051i | 0.913864 | + | 0.406020i | \(0.133084\pi\) |
−0.381209 | + | 0.924489i | \(0.624492\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.68171 | − | 4.33343i | −0.211876 | − | 0.545961i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −3.22916 | − | 2.29948i | −0.400529 | − | 0.285215i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 8.16291 | − | 0.605750i | 0.997258 | − | 0.0740041i | ||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −0.114010 | − | 0.608910i | −0.0137252 | − | 0.0733042i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −3.54925 | + | 1.22841i | −0.421219 | + | 0.145785i | −0.529451 | − | 0.848340i | \(-0.677602\pi\) |
0.108232 | + | 0.994126i | \(0.465481\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −3.48722 | + | 1.39607i | −0.408148 | + | 0.163398i | −0.566646 | − | 0.823962i | \(-0.691759\pi\) |
0.158498 | + | 0.987359i | \(0.449335\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 2.54766 | + | 4.46724i | 0.294178 | + | 0.515833i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1.85030 | + | 3.58908i | −0.210861 | + | 0.409014i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −2.37878 | − | 0.577087i | −0.267634 | − | 0.0649273i | 0.0996961 | − | 0.995018i | \(-0.468213\pi\) |
−0.367330 | + | 0.930091i | \(0.619728\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 5.37492 | − | 7.21874i | 0.597213 | − | 0.802082i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −3.35310 | − | 4.26381i | −0.368051 | − | 0.468014i | 0.566388 | − | 0.824139i | \(-0.308340\pi\) |
−0.934439 | + | 0.356124i | \(0.884098\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.01017 | − | 5.24124i | 0.109568 | − | 0.568493i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 1.23127 | − | 4.11248i | 0.132006 | − | 0.440904i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 4.10997 | + | 6.39524i | 0.435656 | + | 0.677894i | 0.987778 | − | 0.155870i | \(-0.0498180\pi\) |
−0.552122 | + | 0.833763i | \(0.686182\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.82253 | − | 3.25737i | −0.295881 | − | 0.341465i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −3.28504 | + | 5.05248i | −0.340643 | + | 0.523917i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −0.0280235 | − | 0.115514i | −0.00287515 | − | 0.0118515i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.05636 | − | 0.609890i | 0.107257 | − | 0.0619250i | −0.445412 | − | 0.895326i | \(-0.646943\pi\) |
0.552669 | + | 0.833401i | \(0.313609\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −7.79029 | + | 0.660540i | −0.782954 | + | 0.0663868i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 6.68674 | + | 9.39021i | 0.665355 | + | 0.934360i | 0.999968 | − | 0.00799517i | \(-0.00254497\pi\) |
−0.334613 | + | 0.942356i | \(0.608606\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0.528083 | − | 0.503526i | 0.0520335 | − | 0.0496139i | −0.663616 | − | 0.748073i | \(-0.730979\pi\) |
0.715650 | + | 0.698459i | \(0.246131\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −1.05801 | − | 3.67527i | −0.103251 | − | 0.358670i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 6.25579 | + | 0.899446i | 0.604770 | + | 0.0869527i | 0.437896 | − | 0.899026i | \(-0.355724\pi\) |
0.166874 | + | 0.985978i | \(0.446633\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 3.35712 | + | 11.4333i | 0.321554 | + | 1.09511i | 0.948692 | + | 0.316203i | \(0.102408\pi\) |
−0.627138 | + | 0.778908i | \(0.715774\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −8.27697 | + | 7.80865i | −0.785616 | + | 0.741165i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 6.30125 | + | 4.95536i | 0.592772 | + | 0.466161i | 0.868919 | − | 0.494954i | \(-0.164815\pi\) |
−0.276147 | + | 0.961115i | \(0.589058\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −0.0484505 | − | 0.507396i | −0.00451803 | − | 0.0473149i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 2.43595 | − | 7.98176i | 0.225204 | − | 0.737914i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 2.41083 | − | 5.27899i | 0.221001 | − | 0.483924i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −3.04572 | − | 2.90409i | −0.276883 | − | 0.264008i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −1.05511 | − | 2.34319i | −0.0951361 | − | 0.211278i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 4.71775 | + | 10.3304i | 0.421969 | + | 0.923983i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 11.8766 | + | 1.13408i | 1.05388 | + | 0.100633i | 0.607586 | − | 0.794254i | \(-0.292138\pi\) |
0.446292 | + | 0.894887i | \(0.352744\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −12.8978 | − | 9.28804i | −1.13559 | − | 0.817766i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 3.67671 | − | 5.72108i | 0.321236 | − | 0.499853i | −0.642653 | − | 0.766157i | \(-0.722166\pi\) |
0.963889 | + | 0.266305i | \(0.0858027\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − | 0.129236i | − | 0.0112062i | ||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 4.93771 | − | 5.51843i | 0.424970 | − | 0.474951i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1.14559 | − | 0.736228i | −0.0978746 | − | 0.0629002i | 0.490788 | − | 0.871279i | \(-0.336709\pi\) |
−0.588663 | + | 0.808379i | \(0.700345\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 10.8784 | − | 1.56408i | 0.922694 | − | 0.132663i | 0.335436 | − | 0.942063i | \(-0.391116\pi\) |
0.587258 | + | 0.809400i | \(0.300207\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 16.8227 | − | 14.4214i | 1.41673 | − | 1.21450i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −6.59431 | + | 3.01152i | −0.551444 | + | 0.251836i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.31273 | − | 3.27905i | 0.109017 | − | 0.272310i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0.336818 | + | 7.95900i | 0.0277803 | + | 0.656448i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 15.7872 | + | 7.20977i | 1.29334 | + | 0.590648i | 0.938822 | − | 0.344403i | \(-0.111919\pi\) |
0.354516 | + | 0.935050i | \(0.384646\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0.992148 | − | 2.86662i | 0.0807399 | − | 0.233283i | −0.897405 | − | 0.441208i | \(-0.854550\pi\) |
0.978145 | + | 0.207926i | \(0.0666712\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 11.1385 | − | 1.48101i | 0.900495 | − | 0.119733i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −3.06514 | + | 3.89764i | −0.246198 | + | 0.313066i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0.328555 | − | 6.89723i | 0.0262216 | − | 0.550459i | −0.947090 | − | 0.320969i | \(-0.895991\pi\) |
0.973311 | − | 0.229489i | \(-0.0737056\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −3.15610 | − | 1.64834i | −0.250295 | − | 0.130722i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0.0788676 | − | 0.548536i | 0.00621564 | − | 0.0432307i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 3.61487 | − | 6.26113i | 0.283138 | − | 0.490410i | −0.689018 | − | 0.724744i | \(-0.741958\pi\) |
0.972156 | + | 0.234335i | \(0.0752912\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −6.43259 | − | 0.0341313i | −0.500776 | − | 0.00265712i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 2.39412 | − | 1.70485i | 0.185263 | − | 0.131925i | −0.483663 | − | 0.875254i | \(-0.660694\pi\) |
0.668925 | + | 0.743329i | \(0.266755\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0.250374 | + | 5.25600i | 0.0192596 | + | 0.404308i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0.211927 | − | 0.133041i | 0.0162065 | − | 0.0101739i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −5.89177 | + | 1.42933i | −0.447943 | + | 0.108670i | −0.453384 | − | 0.891315i | \(-0.649783\pi\) |
0.00544065 | + | 0.999985i | \(0.498268\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0.870640 | + | 4.51731i | 0.0658142 | + | 0.341477i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 5.29285 | + | 0.280284i | 0.397835 | + | 0.0210675i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 4.82757 | − | 3.10249i | 0.360829 | − | 0.231891i | −0.347647 | − | 0.937626i | \(-0.613019\pi\) |
0.708476 | + | 0.705735i | \(0.249383\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 20.1033 | − | 10.3640i | 1.49427 | − | 0.770348i | 0.498915 | − | 0.866651i | \(-0.333732\pi\) |
0.995352 | + | 0.0963033i | \(0.0307019\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −15.8521 | + | 11.1619i | −1.17182 | + | 0.825114i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −7.35939 | + | 5.78748i | −0.541073 | + | 0.425504i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −7.37695 | − | 6.39217i | −0.539456 | − | 0.467442i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 6.63174 | − | 4.56512i | 0.482388 | − | 0.332064i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 24.0016 | + | 12.3737i | 1.73669 | + | 0.895328i | 0.966166 | + | 0.257921i | \(0.0830374\pi\) |
0.770527 | + | 0.637407i | \(0.219993\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2.62247 | + | 0.770026i | 0.188769 | + | 0.0554277i | 0.374751 | − | 0.927126i | \(-0.377728\pi\) |
−0.185981 | + | 0.982553i | \(0.559546\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 2.58571 | − | 6.36077i | 0.185167 | − | 0.455504i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −0.305616 | − | 0.883020i | −0.0217743 | − | 0.0629126i | 0.933590 | − | 0.358343i | \(-0.116658\pi\) |
−0.955364 | + | 0.295430i | \(0.904537\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 0.0656217 | − | 0.0921528i | 0.00465180 | − | 0.00653254i | −0.812244 | − | 0.583319i | \(-0.801754\pi\) |
0.816895 | + | 0.576786i | \(0.195693\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 4.28126 | + | 13.5156i | 0.301977 | + | 0.953315i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 2.22756 | − | 3.12817i | 0.156344 | − | 0.219555i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −0.691541 | − | 1.99808i | −0.0482993 | − | 0.139552i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0.980702 | − | 0.435354i | 0.0681635 | − | 0.0302592i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −0.208565 | − | 0.0612401i | −0.0144267 | − | 0.00423607i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −18.2747 | − | 9.42126i | −1.25808 | − | 0.648587i | −0.305305 | − | 0.952255i | \(-0.598758\pi\) |
−0.952778 | + | 0.303668i | \(0.901789\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −3.48793 | − | 5.49117i | −0.238989 | − | 0.376248i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −9.88316 | − | 8.56381i | −0.674026 | − | 0.584047i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −4.23772 | + | 3.33258i | −0.287675 | + | 0.226230i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −3.74572 | − | 5.31965i | −0.253113 | − | 0.359468i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 9.26079 | − | 4.77427i | 0.622948 | − | 0.321152i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −5.19600 | + | 3.33927i | −0.347950 | + | 0.223614i | −0.702928 | − | 0.711261i | \(-0.748125\pi\) |
0.354979 | + | 0.934874i | \(0.384488\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −6.51140 | + | 6.07801i | −0.434093 | + | 0.405200i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −4.20062 | − | 21.7949i | −0.278805 | − | 1.44658i | −0.803509 | − | 0.595292i | \(-0.797036\pi\) |
0.524704 | − | 0.851285i | \(-0.324176\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 4.93842 | − | 1.19805i | 0.326340 | − | 0.0791693i | −0.0692419 | − | 0.997600i | \(-0.522058\pi\) |
0.395582 | + | 0.918431i | \(0.370543\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −6.78796 | − | 1.68493i | −0.446615 | − | 0.110860i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −0.859288 | − | 18.0387i | −0.0562938 | − | 1.18175i | −0.833505 | − | 0.552512i | \(-0.813669\pi\) |
0.777211 | − | 0.629240i | \(-0.216634\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 14.8507 | − | 10.5751i | 0.968750 | − | 0.689844i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0.0224955 | − | 4.23962i | 0.00146124 | − | 0.275393i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −11.4331 | + | 19.8027i | −0.739545 | + | 1.28093i | 0.213156 | + | 0.977018i | \(0.431626\pi\) |
−0.952700 | + | 0.303911i | \(0.901707\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2.88317 | + | 20.0529i | −0.185722 | + | 1.29172i | 0.657213 | + | 0.753705i | \(0.271735\pi\) |
−0.842934 | + | 0.538017i | \(0.819174\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 14.3130 | + | 6.17549i | 0.918182 | + | 0.396158i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −0.311869 | + | 6.54693i | −0.0199246 | + | 0.418268i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.143425 | − | 0.182380i | 0.00912595 | − | 0.0116046i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 5.84684 | − | 7.35422i | 0.370529 | − | 0.466055i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 2.54986 | − | 7.36734i | 0.160946 | − | 0.465022i | −0.835477 | − | 0.549525i | \(-0.814809\pi\) |
0.996423 | + | 0.0845023i | \(0.0269300\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −0.847869 | − | 0.387209i | −0.0533050 | − | 0.0243436i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 9.23690 | − | 0.390898i | 0.578437 | − | 0.0244790i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 10.2940 | − | 25.7132i | 0.642122 | − | 1.60394i | −0.146602 | − | 0.989196i | \(-0.546834\pi\) |
0.788724 | − | 0.614748i | \(-0.210742\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −9.25947 | + | 4.22866i | −0.575355 | + | 0.262756i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 7.42284 | + | 0.432586i | 0.459462 | + | 0.0267764i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −6.22844 | + | 0.895514i | −0.384062 | + | 0.0552198i | −0.331642 | − | 0.943405i | \(-0.607603\pi\) |
−0.0524201 | + | 0.998625i | \(0.516693\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2.46453 | − | 1.58386i | −0.151395 | − | 0.0972957i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −9.13678 | + | 9.48114i | −0.559162 | + | 0.580236i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 13.0797i | − | 0.797486i | −0.917063 | − | 0.398743i | \(-0.869447\pi\) | ||
0.917063 | − | 0.398743i | \(-0.130553\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 4.10696 | − | 6.39055i | 0.249480 | − | 0.388199i | −0.693815 | − | 0.720153i | \(-0.744072\pi\) |
0.943295 | + | 0.331954i | \(0.107708\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 4.36253 | − | 6.05803i | 0.264032 | − | 0.366649i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 7.70270 | + | 0.735519i | 0.464491 | + | 0.0443535i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 6.98148 | + | 15.2873i | 0.419477 | + | 0.918526i | 0.994919 | + | 0.100683i | \(0.0321028\pi\) |
−0.575442 | + | 0.817843i | \(0.695170\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −9.82737 | − | 3.51850i | −0.588349 | − | 0.210647i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 14.5570 | + | 13.8800i | 0.868396 | + | 0.828013i | 0.986291 | − | 0.165012i | \(-0.0527664\pi\) |
−0.117896 | + | 0.993026i | \(0.537615\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 0.488456 | − | 1.06957i | 0.0290357 | − | 0.0635793i | −0.894558 | − | 0.446951i | \(-0.852510\pi\) |
0.923594 | + | 0.383372i | \(0.125237\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0.183492 | − | 0.0933675i | 0.0108691 | − | 0.00553061i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −0.218519 | − | 2.28844i | −0.0128988 | − | 0.135082i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −2.33548 | − | 1.83664i | −0.137381 | − | 0.108038i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1.44981 | + | 1.53676i | 0.0849894 | + | 0.0900866i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −0.126387 | − | 0.430435i | −0.00738362 | − | 0.0251463i | 0.955719 | − | 0.294282i | \(-0.0950803\pi\) |
−0.963102 | + | 0.269135i | \(0.913262\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 4.31656 | + | 0.620627i | 0.251320 | + | 0.0361343i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −4.22477 | − | 12.8657i | −0.245146 | − | 0.746543i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0.720061 | − | 0.686577i | 0.0416422 | − | 0.0397058i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −8.24744 | − | 11.5819i | −0.475375 | − | 0.667570i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −13.1552 | + | 15.0202i | −0.755748 | + | 0.862886i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −13.8145 | + | 7.97583i | −0.791018 | + | 0.456694i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −7.26725 | − | 29.9560i | −0.414764 | − | 1.70968i | −0.669623 | − | 0.742701i | \(-0.733544\pi\) |
0.254859 | − | 0.966978i | \(-0.417971\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1.05955 | + | 0.688902i | 0.0602756 | + | 0.0391903i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −4.38634 | − | 5.06210i | −0.248726 | − | 0.287045i | 0.617633 | − | 0.786466i | \(-0.288092\pi\) |
−0.866360 | + | 0.499421i | \(0.833546\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 10.4654 | + | 16.2844i | 0.591538 | + | 0.920450i | 0.999971 | + | 0.00766215i | \(0.00243896\pi\) |
−0.408433 | + | 0.912788i | \(0.633925\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 5.77161 | − | 3.25107i | 0.325194 | − | 0.183177i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −1.11635 | + | 5.79218i | −0.0627005 | + | 0.325321i | −0.999713 | − | 0.0239760i | \(-0.992367\pi\) |
0.937012 | + | 0.349297i | \(0.113580\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −3.99276 | − | 5.07721i | −0.223552 | − | 0.284269i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0.982721 | + | 10.9026i | 0.0548502 | + | 0.608522i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0.303602 | + | 0.0736529i | 0.0168928 | + | 0.00409816i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −3.78462 | + | 7.34113i | −0.209933 | + | 0.407213i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −17.9285 | + | 10.2246i | −0.991447 | + | 0.565419i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 18.4020 | − | 7.36705i | 1.01453 | − | 0.406158i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −0.801830 | + | 0.277516i | −0.0440726 | + | 0.0152537i | −0.349015 | − | 0.937117i | \(-0.613484\pi\) |
0.304943 | + | 0.952371i | \(0.401363\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −16.4664 | − | 10.8309i | −0.902352 | − | 0.593530i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 2.51000 | + | 11.3916i | 0.137136 | + | 0.622392i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −3.49556 | − | 2.48918i | −0.190415 | − | 0.135594i | 0.480874 | − | 0.876790i | \(-0.340320\pi\) |
−0.671289 | + | 0.741196i | \(0.734259\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −5.83484 | + | 12.5992i | −0.316905 | + | 0.684293i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 3.37010 | + | 8.41811i | 0.182501 | + | 0.455866i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −5.06338 | + | 17.2443i | −0.273397 | + | 0.931104i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0.835799 | − | 0.284316i | 0.0449979 | − | 0.0153070i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −5.13930 | + | 21.1845i | −0.275892 | + | 1.13724i | 0.650145 | + | 0.759810i | \(0.274708\pi\) |
−0.926037 | + | 0.377433i | \(0.876807\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −11.2600 | + | 12.9947i | −0.602732 | + | 0.695590i | −0.972333 | − | 0.233601i | \(-0.924949\pi\) |
0.369600 | + | 0.929191i | \(0.379495\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 14.4252 | + | 0.917488i | 0.769958 | + | 0.0489719i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −33.7883 | − | 6.51216i | −1.79837 | − | 0.346607i | −0.823147 | − | 0.567829i | \(-0.807784\pi\) |
−0.975224 | + | 0.221221i | \(0.928996\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −2.45261 | − | 4.75740i | −0.130171 | − | 0.252496i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 9.85996 | + | 1.95467i | 0.521844 | + | 0.103452i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −9.21787 | + | 7.98733i | −0.486501 | + | 0.421555i | −0.863263 | − | 0.504755i | \(-0.831583\pi\) |
0.376762 | + | 0.926310i | \(0.377037\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.6498 | + | 3.59446i | −0.981569 | + | 0.189182i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 3.67797 | − | 6.29308i | 0.193043 | − | 0.330301i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −2.67653 | − | 4.63589i | −0.140096 | − | 0.242653i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −12.5256 | + | 0.596669i | −0.653832 | + | 0.0311459i | −0.371877 | − | 0.928282i | \(-0.621286\pi\) |
−0.281955 | + | 0.959428i | \(0.590983\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 3.52772 | − | 2.71414i | 0.183646 | − | 0.141293i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −2.19805 | − | 2.30525i | −0.114117 | − | 0.119682i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 17.8677 | + | 10.3159i | 0.925152 | + | 0.534137i | 0.885275 | − | 0.465068i | \(-0.153970\pi\) |
0.0398769 | + | 0.999205i | \(0.487303\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −15.5263 | + | 12.0772i | −0.801774 | + | 0.623666i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 6.61519 | − | 1.94239i | 0.340700 | − | 0.100038i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 3.61034 | + | 0.171982i | 0.185451 | + | 0.00883410i | 0.140102 | − | 0.990137i | \(-0.455257\pi\) |
0.0453489 | + | 0.998971i | \(0.485560\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 2.83229 | + | 20.4694i | 0.145103 | + | 1.04868i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −33.6647 | + | 3.21459i | −1.72019 | + | 0.164258i | −0.907952 | − | 0.419075i | \(-0.862355\pi\) |
−0.812234 | + | 0.583332i | \(0.801749\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −5.43798 | − | 1.88210i | −0.277145 | − | 0.0959208i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 10.5023 | − | 25.4474i | 0.533860 | − | 1.29356i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −5.78914 | + | 6.07148i | −0.293521 | + | 0.307836i | −0.853938 | − | 0.520374i | \(-0.825792\pi\) |
0.560417 | + | 0.828211i | \(0.310641\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.24367 | + | 0.497891i | 0.0628952 | + | 0.0251795i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 11.1106 | + | 3.91157i | 0.560458 | + | 0.197312i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0.331586 | − | 3.47252i | 0.0166839 | − | 0.174722i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −0.615406 | − | 4.28024i | −0.0308864 | − | 0.214819i | 0.968533 | − | 0.248884i | \(-0.0800638\pi\) |
−0.999420 | + | 0.0340648i | \(0.989155\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0.217811 | − | 0.0516182i | 0.0109042 | − | 0.00258414i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −8.18648 | −0.408813 | −0.204407 | − | 0.978886i | \(-0.565526\pi\) | ||||
−0.204407 | + | 0.978886i | \(0.565526\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −9.67881 | −0.482136 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 11.2728 | + | 6.11775i | 0.560148 | + | 0.303993i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 2.43660 | + | 16.9469i | 0.120778 | + | 0.840029i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 0.349654 | − | 3.66174i | 0.0172893 | − | 0.181062i | −0.982702 | − | 0.185193i | \(-0.940709\pi\) |
0.999991 | + | 0.00413133i | \(0.00131505\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0.783255 | − | 2.22480i | 0.0386351 | − | 0.109741i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 4.40181 | + | 1.76222i | 0.216599 | + | 0.0867131i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 5.33444 | − | 5.59460i | 0.261857 | − | 0.274628i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 6.98099 | + | 17.7094i | 0.341860 | + | 0.867234i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 19.7012 | + | 6.81865i | 0.962466 | + | 0.333113i | 0.762716 | − | 0.646734i | \(-0.223866\pi\) |
0.199750 | + | 0.979847i | \(0.435987\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2.93353 | + | 0.280118i | −0.142972 | + | 0.0136521i | −0.166296 | − | 0.986076i | \(-0.553181\pi\) |
0.0233249 | + | 0.999728i | \(0.492575\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 31.0245 | + | 22.5924i | 1.50846 | + | 1.09848i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −11.1082 | − | 0.529151i | −0.538829 | − | 0.0256676i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −16.6409 | + | 4.88622i | −0.805312 | + | 0.236461i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −7.70935 | − | 9.91102i | −0.372211 | − | 0.478508i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0.139674 | + | 0.0806411i | 0.00672788 | + | 0.00388434i | 0.503360 | − | 0.864077i | \(-0.332097\pi\) |
−0.496632 | + | 0.867961i | \(0.665430\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −9.23625 | − | 9.68670i | −0.443866 | − | 0.465513i | 0.463352 | − | 0.886174i | \(-0.346647\pi\) |
−0.907218 | + | 0.420661i | \(0.861798\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 6.05074 | + | 0.902758i | 0.290111 | + | 0.0432840i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0.0297984 | − | 0.00141947i | 0.00142545 | − | 6.79027e-5i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 10.2184 | + | 17.6988i | 0.487699 | + | 0.844719i | 0.999900 | − | 0.0141468i | \(-0.00450321\pi\) |
−0.512201 | + | 0.858865i | \(0.671170\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −13.2793 | + | 3.74657i | −0.632349 | + | 0.178408i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −2.47875 | + | 0.477739i | −0.117769 | + | 0.0226981i | −0.247795 | − | 0.968812i | \(-0.579706\pi\) |
0.130026 | + | 0.991511i | \(0.458494\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −8.18749 | + | 7.09450i | −0.388124 | + | 0.336312i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −5.84557 | + | 29.4869i | −0.276486 | + | 1.39468i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −15.3573 | − | 29.7891i | −0.724757 | − | 1.40583i | −0.906380 | − | 0.422464i | \(-0.861165\pi\) |
0.181623 | − | 0.983368i | \(-0.441865\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −3.79668 | − | 0.731751i | −0.178779 | − | 0.0344568i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 5.22760 | + | 0.527180i | 0.245614 | + | 0.0247691i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 4.02236 | − | 4.64206i | 0.188571 | − | 0.217623i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 1.47064 | − | 6.06204i | 0.0687935 | − | 0.283571i | −0.927016 | − | 0.375021i | \(-0.877635\pi\) |
0.995810 | + | 0.0914510i | \(0.0291505\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 6.94488 | + | 18.1810i | 0.324159 | + | 0.848615i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 0.207098 | − | 0.705312i | 0.00964552 | − | 0.0328496i | −0.954530 | − | 0.298116i | \(-0.903642\pi\) |
0.964175 | + | 0.265266i | \(0.0854599\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 2.50929 | + | 6.26790i | 0.116616 | + | 0.291294i | 0.975180 | − | 0.221413i | \(-0.0710670\pi\) |
−0.858564 | + | 0.512707i | \(0.828643\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −7.79321 | − | 3.60913i | −0.361401 | − | 0.167370i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −16.6138 | − | 11.8307i | −0.768796 | − | 0.547457i | 0.127010 | − | 0.991901i | \(-0.459462\pi\) |
−0.895807 | + | 0.444444i | \(0.853401\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −0.267940 | + | 12.6799i | −0.0123723 | + | 0.585501i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 11.7556 | − | 2.20108i | 0.541670 | − | 0.101420i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −22.5993 | + | 7.82169i | −1.03912 | + | 0.359642i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −0.229910 | + | 0.0920419i | −0.0105490 | + | 0.00422317i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1.51748 | − | 5.97756i | 0.0694807 | − | 0.273694i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 9.11674 | − | 17.6840i | 0.416554 | − | 0.808003i | −0.583437 | − | 0.812158i | \(-0.698292\pi\) |
0.999991 | + | 0.00415563i | \(0.00132278\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −17.7600 | − | 4.30854i | −0.809788 | − | 0.196452i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0.955987 | − | 0.0861696i | 0.0434989 | − | 0.00392085i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 1.07455 | + | 1.36640i | 0.0487926 | + | 0.0620449i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −1.09713 | + | 5.69243i | −0.0497155 | + | 0.257949i | −0.998279 | − | 0.0586373i | \(-0.981324\pi\) |
0.948564 | + | 0.316586i | \(0.102537\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 11.9961 | + | 3.59163i | 0.542484 | + | 0.162419i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 18.9279 | + | 29.4524i | 0.854204 | + | 1.32917i | 0.942889 | + | 0.333108i | \(0.108097\pi\) |
−0.0886844 | + | 0.996060i | \(0.528266\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 6.07918 | + | 7.01575i | 0.273793 | + | 0.315973i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −2.51171 | − | 10.8549i | −0.112893 | − | 0.487893i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −1.37198 | − | 5.65536i | −0.0615416 | − | 0.253678i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 29.2314 | − | 16.8767i | 1.30858 | − | 0.755507i | 0.326718 | − | 0.945122i | \(-0.394057\pi\) |
0.981859 | + | 0.189615i | \(0.0607240\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 3.82953 | + | 3.35405i | 0.171091 | + | 0.149848i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 9.88721 | + | 13.8846i | 0.440849 | + | 0.619086i | 0.973895 | − | 0.227001i | \(-0.0728920\pi\) |
−0.533046 | + | 0.846086i | \(0.678953\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −11.8896 | + | 11.3367i | −0.529079 | + | 0.504475i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −8.75831 | + | 2.52127i | −0.388970 | + | 0.111974i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −27.9399 | − | 4.01716i | −1.23842 | − | 0.178057i | −0.508179 | − | 0.861251i | \(-0.669681\pi\) |
−0.730237 | + | 0.683194i | \(0.760590\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.63972 | − | 5.58437i | −0.0725369 | − | 0.247038i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0.308869 | + | 0.304038i | 0.0136369 | + | 0.0134236i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0.817369 | + | 0.642786i | 0.0360176 | + | 0.0283245i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −3.16912 | − | 33.1885i | −0.139378 | − | 1.45963i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −4.76218 | − | 9.35893i | −0.209036 | − | 0.410811i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 5.69828 | − | 12.4775i | 0.249646 | − | 0.546649i | −0.742774 | − | 0.669543i | \(-0.766490\pi\) |
0.992420 | + | 0.122894i | \(0.0392174\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 0.277148 | + | 0.264260i | 0.0121188 | + | 0.0115553i | 0.696114 | − | 0.717931i | \(-0.254911\pi\) |
−0.683995 | + | 0.729486i | \(0.739759\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −7.26560 | + | 3.27161i | −0.317097 | + | 0.142785i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −5.41377 | − | 11.8545i | −0.235827 | − | 0.516390i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.7685 | − | 2.17413i | −0.989935 | − | 0.0945274i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 1.64163 | + | 9.03236i | 0.0712408 | + | 0.391971i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 2.23131 | − | 3.47199i | 0.0966489 | − | 0.150389i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 9.00675i | 0.389396i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 7.15702 | + | 6.89708i | 0.308848 | + | 0.297631i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 10.0833 | + | 6.48013i | 0.434317 | + | 0.279119i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −16.3582 | + | 2.35195i | −0.703294 | + | 0.101118i | −0.484678 | − | 0.874693i | \(-0.661063\pi\) |
−0.218616 | + | 0.975811i | \(0.570154\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 25.4966 | + | 29.7420i | 1.09416 | + | 1.27635i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −15.4468 | + | 7.05432i | −0.661669 | + | 0.302174i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1.10381 | − | 2.75718i | 0.0471955 | − | 0.117889i | −0.902897 | − | 0.429857i | \(-0.858564\pi\) |
0.950093 | + | 0.311968i | \(0.100988\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −25.1435 | − | 22.2584i | −1.07310 | − | 0.949967i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0.188045 | + | 0.0858772i | 0.00801098 | + | 0.00365849i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1.24047 | − | 3.58409i | 0.0527500 | − | 0.152411i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −12.6935 | − | 10.0917i | −0.538807 | − | 0.428369i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −24.7197 | + | 31.4337i | −1.04741 | + | 1.33189i | −0.106094 | + | 0.994356i | \(0.533834\pi\) |
−0.941314 | + | 0.337531i | \(0.890408\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.21460 | − | 25.4975i | 0.0513720 | − | 1.07843i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 7.82674 | − | 14.9860i | 0.330445 | − | 0.632709i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 3.39797 | − | 23.6334i | 0.143208 | − | 0.996030i | −0.783807 | − | 0.621005i | \(-0.786725\pi\) |
0.927014 | − | 0.375026i | \(-0.122366\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −5.71200 | + | 9.89348i | −0.240306 | + | 0.416222i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 10.3427 | + | 9.35359i | 0.434353 | + | 0.392814i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −0.941694 | + | 0.670577i | −0.0394778 | + | 0.0281120i | −0.599626 | − | 0.800281i | \(-0.704684\pi\) |
0.560148 | + | 0.828393i | \(0.310744\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −2.14806 | − | 45.0934i | −0.0898936 | − | 1.88710i | −0.372742 | − | 0.927935i | \(-0.621582\pi\) |
0.282848 | − | 0.959165i | \(-0.408721\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −11.2678 | + | 45.3937i | −0.470717 | + | 1.89635i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1.03201 | + | 0.250362i | −0.0430377 | + | 0.0104408i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −5.19434 | − | 26.9508i | −0.216243 | − | 1.12198i | −0.914022 | − | 0.405664i | \(-0.867040\pi\) |
0.697779 | − | 0.716313i | \(-0.254172\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −0.250340 | + | 4.72739i | −0.0104038 | + | 0.196463i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 7.07045 | − | 4.54390i | 0.293332 | − | 0.188513i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −4.76183 | + | 2.45489i | −0.197215 | + | 0.101671i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 11.7530 | + | 1.81733i | 0.485927 | + | 0.0751372i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −2.28824 | + | 1.79949i | −0.0944459 | + | 0.0742730i | −0.664265 | − | 0.747497i | \(-0.731256\pi\) |
0.569820 | + | 0.821770i | \(0.307013\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −0.219328 | − | 0.190049i | −0.00903727 | − | 0.00783084i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1.36615 | − | 0.867763i | 0.0561959 | − | 0.0356950i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 8.77838 | + | 4.52557i | 0.360485 | + | 0.185843i | 0.628948 | − | 0.777447i | \(-0.283486\pi\) |
−0.268464 | + | 0.963290i | \(0.586516\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 7.93542 | + | 2.33005i | 0.325321 | + | 0.0955227i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0.181522 | + | 0.0737902i | 0.00742918 | + | 0.00302003i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −12.1844 | − | 35.2044i | −0.497839 | − | 1.43841i | −0.861920 | − | 0.507045i | \(-0.830738\pi\) |
0.364080 | − | 0.931368i | \(-0.381383\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −7.04162 | + | 9.88857i | −0.287234 | + | 0.403363i | −0.932831 | − | 0.360315i | \(-0.882669\pi\) |
0.645597 | + | 0.763678i | \(0.276609\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −21.0688 | + | 12.6138i | −0.857987 | + | 0.513672i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 3.47876 | − | 4.88524i | 0.141432 | − | 0.198613i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 3.42463 | + | 9.89481i | 0.139001 | + | 0.401618i | 0.992919 | − | 0.118789i | \(-0.0379014\pi\) |
−0.853918 | + | 0.520407i | \(0.825780\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 6.16183 | + | 2.50484i | 0.249690 | + | 0.101501i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 34.1451 | + | 10.0259i | 1.38136 | + | 0.405604i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −27.7057 | − | 14.2833i | −1.11902 | − | 0.576896i | −0.203464 | − | 0.979082i | \(-0.565220\pi\) |
−0.915558 | + | 0.402187i | \(0.868250\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 3.09129 | − | 1.96355i | 0.124653 | − | 0.0791781i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 29.9576 | + | 25.9584i | 1.20605 | + | 1.04505i | 0.997754 | + | 0.0669789i | \(0.0213360\pi\) |
0.208292 | + | 0.978067i | \(0.433209\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 20.8262 | − | 16.3779i | 0.837075 | − | 0.658283i | −0.104709 | − | 0.994503i | \(-0.533391\pi\) |
0.941783 | + | 0.336220i | \(0.109149\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.12543 | + | 1.47896i | 0.0451621 | + | 0.0593487i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −10.4695 | + | 5.39739i | −0.419451 | + | 0.216242i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −1.12631 | + | 0.723833i | −0.0450522 | + | 0.0289533i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0.0199095 | − | 0.375968i | 0.000795109 | − | 0.0150147i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −4.65689 | − | 24.1623i | −0.185682 | − | 0.963412i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 28.0316 | − | 6.80039i | 1.11592 | − | 0.270719i | 0.364931 | − | 0.931034i | \(-0.381092\pi\) |
0.750989 | + | 0.660315i | \(0.229577\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 8.57922 | − | 34.5626i | 0.340994 | − | 1.37374i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0.809000 | + | 16.9830i | 0.0321042 | + | 0.673950i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −10.4216 | + | 7.42117i | −0.412918 | + | 0.294038i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 7.86153 | − | 8.07167i | 0.310997 | − | 0.319310i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −4.54237 | + | 7.86762i | −0.179413 | + | 0.310752i | −0.941680 | − | 0.336511i | \(-0.890753\pi\) |
0.762267 | + | 0.647263i | \(0.224087\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 4.62181 | − | 32.1454i | 0.182267 | − | 1.26769i | −0.669120 | − | 0.743154i | \(-0.733329\pi\) |
0.851387 | − | 0.524538i | \(-0.175762\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 10.4858 | − | 20.0773i | 0.412876 | − | 0.790541i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 2.07032 | − | 43.4613i | 0.0813926 | − | 1.70864i | −0.476867 | − | 0.878975i | \(-0.658228\pi\) |
0.558260 | − | 0.829666i | \(-0.311469\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 4.92976 | − | 6.26870i | 0.193510 | − | 0.246068i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −7.30921 | − | 5.81106i | −0.286471 | − | 0.227753i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 13.5176 | − | 39.0564i | 0.528983 | − | 1.52840i | −0.291411 | − | 0.956598i | \(-0.594125\pi\) |
0.820394 | − | 0.571798i | \(-0.193754\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 8.81576 | + | 4.02602i | 0.344460 | + | 0.157310i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 7.46949 | − | 8.43765i | 0.291413 | − | 0.329184i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 15.5343 | − | 38.8029i | 0.605132 | − | 1.51155i | −0.236576 | − | 0.971613i | \(-0.576025\pi\) |
0.841708 | − | 0.539933i | \(-0.181551\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 27.5555 | − | 12.5842i | 1.07178 | − | 0.489468i | 0.200222 | − | 0.979751i | \(-0.435834\pi\) |
0.871563 | + | 0.490283i | \(0.163107\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 11.7453 | + | 13.7010i | 0.456148 | + | 0.532101i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0.182299 | − | 0.0262107i | 0.00706926 | − | 0.00101641i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0.745739 | + | 0.479257i | 0.0288751 | + | 0.0185569i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −7.70323 | − | 7.42344i | −0.297824 | − | 0.287007i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 29.1709i | 1.12613i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −25.0388 | + | 38.9611i | −0.965174 | + | 1.50184i | −0.103343 | + | 0.994646i | \(0.532954\pi\) |
−0.861832 | + | 0.507195i | \(0.830683\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −12.8444 | − | 8.54651i | −0.494381 | − | 0.328955i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 21.2689 | + | 2.03094i | 0.817432 | + | 0.0780553i | 0.495391 | − | 0.868670i | \(-0.335025\pi\) |
0.322041 | + | 0.946726i | \(0.395631\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0.785123 | + | 1.71918i | 0.0301302 | + | 0.0659760i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 35.0547 | − | 15.7847i | 1.34330 | − | 0.604870i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 5.96693 | + | 5.68946i | 0.228318 | + | 0.217701i | 0.795599 | − | 0.605823i | \(-0.207156\pi\) |
−0.567281 | + | 0.823524i | \(0.692005\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0.806174 | − | 1.76527i | 0.0308023 | − | 0.0674477i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 3.99161 | + | 7.84456i | 0.152289 | + | 0.299288i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −0.543575 | − | 5.69257i | −0.0207086 | − | 0.216870i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −11.6624 | − | 9.17143i | −0.443659 | − | 0.348898i | 0.371203 | − | 0.928552i | \(-0.378945\pi\) |
−0.814863 | + | 0.579654i | \(0.803188\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0.128549 | − | 12.1132i | 0.00488317 | − | 0.460142i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 4.41254 | + | 15.0277i | 0.167377 | + | 0.570034i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 5.50053 | + | 0.790857i | 0.208347 | + | 0.0299558i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 30.0586 | − | 8.65303i | 1.13692 | − | 0.327288i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 2.13427 | − | 2.03502i | 0.0806103 | − | 0.0768618i | −0.648703 | − | 0.761042i | \(-0.724688\pi\) |
0.729313 | + | 0.684180i | \(0.239840\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −0.317854 | − | 0.446364i | −0.0119881 | − | 0.0168349i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 23.7545 | + | 20.8051i | 0.894645 | + | 0.783564i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −15.4685 | + | 8.93074i | −0.581753 | + | 0.335875i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1.26490 | + | 5.21399i | 0.0475043 | + | 0.195815i | 0.990619 | − | 0.136652i | \(-0.0436341\pi\) |
−0.943115 | + | 0.332467i | \(0.892119\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 7.15432 | − | 1.65543i | 0.268308 | − | 0.0620836i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −0.814948 | − | 0.940501i | −0.0305201 | − | 0.0352220i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −5.58542 | − | 8.69108i | −0.208883 | − | 0.325028i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −37.9413 | − | 11.3596i | −1.41695 | − | 0.424232i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −6.71790 | + | 34.8558i | −0.250535 | + | 1.29990i | 0.610768 | + | 0.791810i | \(0.290861\pi\) |
−0.861303 | + | 0.508092i | \(0.830351\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0.698871 | + | 0.888687i | 0.0260273 | + | 0.0330964i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −34.9481 | + | 3.15011i | −1.29974 | + | 0.117154i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −7.15144 | − | 1.73492i | −0.265598 | − | 0.0644333i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 4.27368 | − | 8.28979i | 0.158502 | − | 0.307451i | −0.796190 | − | 0.605047i | \(-0.793154\pi\) |
0.954692 | + | 0.297596i | \(0.0961847\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −4.69123 | + | 26.5893i | −0.173749 | + | 0.984790i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 31.9085 | − | 12.7742i | 1.18018 | − | 0.472472i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −37.0304 | + | 12.8163i | −1.36775 | + | 0.473382i | −0.909597 | − | 0.415493i | \(-0.863609\pi\) |
−0.458151 | + | 0.888874i | \(0.651488\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −11.1586 | + | 2.08929i | −0.411590 | + | 0.0770647i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 20.3361 | + | 6.44090i | 0.749089 | + | 0.237254i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −4.98582 | − | 3.55039i | −0.183406 | − | 0.130603i | 0.484666 | − | 0.874699i | \(-0.338941\pi\) |
−0.668073 | + | 0.744096i | \(0.732880\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0.364664 | + | 0.168881i | 0.0133963 | + | 0.00620398i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 16.6185 | + | 41.5110i | 0.609674 | + | 1.52289i | 0.835937 | + | 0.548825i | \(0.184925\pi\) |
−0.226263 | + | 0.974066i | \(0.572651\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −6.96818 | + | 23.7315i | −0.255295 | + | 0.869453i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 14.7299 | + | 6.91675i | 0.538938 | + | 0.253071i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −2.30870 | + | 9.51658i | −0.0843580 | + | 0.347728i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 25.8809 | − | 29.8682i | 0.944408 | − | 1.08990i | −0.0514223 | − | 0.998677i | \(-0.516375\pi\) |
0.995830 | − | 0.0912277i | \(-0.0290791\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 13.4351 | + | 1.35487i | 0.489603 | + | 0.0493743i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 4.24484 | + | 0.818127i | 0.154486 | + | 0.0297747i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −12.3112 | − | 23.8803i | −0.447457 | − | 0.867946i | −0.999419 | − | 0.0340765i | \(-0.989151\pi\) |
0.551962 | − | 0.833869i | \(-0.313879\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0.313943 | − | 1.58363i | 0.0113954 | − | 0.0574820i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 25.0471 | − | 21.7035i | 0.907958 | − | 0.786750i | −0.0695652 | − | 0.997577i | \(-0.522161\pi\) |
0.977523 | + | 0.210827i | \(0.0676157\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −18.1294 | + | 3.49416i | −0.656329 | + | 0.126497i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 4.34812 | + | 15.4115i | 0.157206 | + | 0.557203i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 4.25621 | + | 7.37197i | 0.153683 | + | 0.266186i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 3.40997 | − | 0.162437i | 0.122966 | − | 0.00585762i | 0.0139916 | − | 0.999902i | \(-0.495546\pi\) |
0.108975 | + | 0.994044i | \(0.465243\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 47.4477 | + | 7.07911i | 1.70879 | + | 0.254948i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −11.5079 | − | 12.0691i | −0.413910 | − | 0.434096i | 0.483466 | − | 0.875363i | \(-0.339378\pi\) |
−0.897376 | + | 0.441267i | \(0.854529\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 8.94671 | + | 5.16538i | 0.321375 | + | 0.185546i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −10.8252 | − | 13.9167i | −0.388351 | − | 0.499257i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0.118738 | − | 0.0348646i | 0.00425422 | − | 0.00124915i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −9.77688 | − | 0.465730i | −0.349844 | − | 0.0166651i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 2.23569 | + | 12.6830i | 0.0798969 | + | 0.453254i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 9.79578 | − | 0.935384i | 0.349626 | − | 0.0333853i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −19.8262 | − | 6.86191i | −0.706727 | − | 0.244601i | −0.0500221 | − | 0.998748i | \(-0.515929\pi\) |
−0.656705 | + | 0.754147i | \(0.728050\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −3.99697 | − | 10.1395i | −0.142296 | − | 0.360977i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −8.57132 | + | 8.98934i | −0.304761 | + | 0.319624i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −28.9067 | − | 11.5725i | −1.02651 | − | 0.410951i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 1.68503 | − | 4.78626i | 0.0597619 | − | 0.169751i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −0.315915 | + | 3.30841i | −0.0111903 | + | 0.117190i | −0.999341 | − | 0.0362963i | \(-0.988444\pi\) |
0.988151 | + | 0.153486i | \(0.0490501\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 6.81918 | + | 47.4284i | 0.241245 | + | 1.67790i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −19.6285 | − | 11.6120i | −0.693540 | − | 0.410290i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −9.78919 | −0.345453 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0.789754 | 0.0278352 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 22.0442 | − | 5.22418i | 0.775993 | − | 0.183900i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 7.37705 | + | 51.3085i | 0.259363 | + | 1.80391i | 0.537386 | + | 0.843337i | \(0.319412\pi\) |
−0.278022 | + | 0.960575i | \(0.589679\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 4.74317 | − | 49.6727i | 0.166555 | − | 1.74424i | −0.396688 | − | 0.917953i | \(-0.629841\pi\) |
0.563244 | − | 0.826291i | \(-0.309553\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 12.4108 | + | 4.36930i | 0.435266 | + | 0.153238i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 9.56501 | + | 3.82925i | 0.335048 | + | 0.134133i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0.528183 | − | 0.553942i | 0.0184788 | − | 0.0193800i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 11.9525 | + | 4.93284i | 0.417653 | + | 0.172367i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 35.8686 | + | 12.4142i | 1.25182 | + | 0.433260i | 0.870952 | − | 0.491368i | \(-0.163503\pi\) |
0.380871 | + | 0.924628i | \(0.375624\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 40.2095 | − | 3.83954i | 1.40161 | − | 0.133838i | 0.633298 | − | 0.773908i | \(-0.281701\pi\) |
0.768317 | + | 0.640070i | \(0.221095\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 1.83691 | + | 13.2757i | 0.0639531 | + | 0.462200i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 38.4021 | + | 1.82932i | 1.33537 | + | 0.0636115i | 0.703075 | − | 0.711116i | \(-0.251810\pi\) |
0.632296 | + | 0.774727i | \(0.282113\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −10.8813 | + | 3.19504i | −0.377924 | + | 0.110968i | −0.465177 | − | 0.885218i | \(-0.654009\pi\) |
0.0872531 | + | 0.996186i | \(0.472191\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −22.9763 | + | 17.8723i | −0.797039 | + | 0.619982i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −14.9186 | − | 8.61326i | −0.516899 | − | 0.298432i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 2.89039 | + | 3.03135i | 0.100026 | + | 0.104904i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 2.00483 | − | 17.9681i | 0.0692970 | − | 0.621068i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 17.8042 | − | 0.848117i | 0.614668 | − | 0.0292803i | 0.262060 | − | 0.965051i | \(-0.415598\pi\) |
0.352608 | + | 0.935771i | \(0.385295\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −11.4286 | − | 19.7949i | −0.394089 | − | 0.682582i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −17.5788 | + | 30.0777i | −0.605446 | + | 1.03593i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −7.36328 | + | 1.41916i | −0.253304 | + | 0.0488204i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 4.92791 | − | 4.27006i | 0.169325 | − | 0.146721i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 1.99771 | + | 0.396033i | 0.0685614 | + | 0.0135918i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1.07672 | − | 2.08854i | −0.0369094 | − | 0.0715942i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 38.8301 | + | 7.48389i | 1.32952 | + | 0.256244i | 0.804046 | − | 0.594567i | \(-0.202677\pi\) |
0.525472 | + | 0.850811i | \(0.323889\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0.230647 | + | 0.271959i | 0.00788796 | + | 0.00930082i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 10.3061 | − | 11.8939i | 0.352050 | − | 0.406287i | −0.551911 | − | 0.833903i | \(-0.686101\pi\) |
0.903960 | + | 0.427616i | \(0.140646\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −0.141362 | + | 0.582702i | −0.00482321 | + | 0.0198815i | −0.974172 | − | 0.225806i | \(-0.927499\pi\) |
0.969349 | + | 0.245687i | \(0.0790137\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 3.76959 | − | 1.28231i | 0.128467 | − | 0.0437010i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −15.1957 | + | 51.7517i | −0.517267 | + | 1.76165i | 0.121859 | + | 0.992547i | \(0.461114\pi\) |
−0.639126 | + | 0.769102i | \(0.720704\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −3.21112 | − | 8.02098i | −0.109181 | − | 0.272721i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 2.16260 | − | 4.66971i | 0.0734459 | − | 0.158592i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −5.19628 | − | 3.70025i | −0.176272 | − | 0.125522i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −14.4501 | + | 17.5967i | −0.489624 | + | 0.596240i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −2.01094 | + | 3.05727i | −0.0680602 | + | 0.103473i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −16.6287 | + | 5.75526i | −0.562154 | + | 0.194563i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 49.3682 | − | 19.7641i | 1.66705 | − | 0.667385i | 0.669870 | − | 0.742478i | \(-0.266350\pi\) |
0.997176 | + | 0.0750936i | \(0.0239255\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0.674962 | − | 0.384929i | 0.0227659 | − | 0.0129833i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 19.0945 | − | 37.0381i | 0.643310 | − | 1.24785i | −0.311392 | − | 0.950282i | \(-0.600795\pi\) |
0.954702 | − | 0.297565i | \(-0.0961745\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 44.2066 | + | 10.7244i | 1.48767 | + | 0.360905i | 0.895556 | − | 0.444949i | \(-0.146778\pi\) |
0.592114 | + | 0.805854i | \(0.298293\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0.678088 | + | 7.52288i | 0.0227937 | + | 0.252879i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −17.0181 | − | 21.6403i | −0.571411 | − | 0.726609i | 0.411352 | − | 0.911477i | \(-0.365057\pi\) |
−0.982763 | + | 0.184868i | \(0.940814\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −3.49845 | + | 18.1517i | −0.117334 | + | 0.608788i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 19.9960 | − | 12.2590i | 0.669893 | − | 0.410692i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0.576887 | + | 0.897653i | 0.0193048 | + | 0.0300388i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 5.35542 | + | 6.18049i | 0.179012 | + | 0.206591i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 1.44473 | + | 0.939344i | 0.0482383 | + | 0.0313638i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −2.03310 | − | 8.38057i | −0.0678078 | − | 0.279508i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 6.66816 | − | 3.84986i | 0.222149 | − | 0.128258i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 16.2257 | − | 18.5259i | 0.539957 | − | 0.616504i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 18.6965 | + | 26.2555i | 0.621492 | + | 0.872763i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −31.5127 | + | 30.0473i | −1.04636 | + | 0.997705i | −0.999999 | − | 0.00121963i | \(-0.999612\pi\) |
−0.0463636 | + | 0.998925i | \(0.514763\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −30.5689 | − | 16.1722i | −1.01390 | − | 0.536399i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −46.1549 | − | 6.63607i | −1.52918 | − | 0.219863i | −0.674209 | − | 0.738540i | \(-0.735515\pi\) |
−0.854970 | + | 0.518677i | \(0.826425\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −3.98264 | − | 13.5636i | −0.131806 | − | 0.448891i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −18.9599 | − | 20.0970i | −0.626794 | − | 0.664386i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 8.28279 | + | 6.51366i | 0.273522 | + | 0.215100i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1.69859 | − | 17.7885i | −0.0560315 | − | 0.586788i | −0.979270 | − | 0.202560i | \(-0.935074\pi\) |
0.923238 | − | 0.384228i | \(-0.125532\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 47.5843 | − | 24.2127i | 1.56796 | − | 0.797836i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 4.34013 | − | 9.50355i | 0.142857 | − | 0.312813i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 14.1173 | + | 13.4608i | 0.464174 | + | 0.442589i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −0.737860 | + | 2.06089i | −0.0242345 | + | 0.0676884i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −6.72664 | − | 14.7293i | −0.220694 | − | 0.483252i | 0.766606 | − | 0.642117i | \(-0.221944\pi\) |
−0.987300 | + | 0.158865i | \(0.949216\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −0.381880 | − | 0.0364651i | −0.0125156 | − | 0.00119509i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 6.77957 | − | 9.41445i | 0.221953 | − | 0.308215i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 7.52058 | − | 11.7022i | 0.245949 | − | 0.382704i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 36.9927i | − | 1.20850i | −0.796795 | − | 0.604250i | \(-0.793473\pi\) | ||
0.796795 | − | 0.604250i | \(-0.206527\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −23.2653 | + | 24.1422i | −0.759235 | + | 0.787850i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −30.1623 | − | 19.3842i | −0.983264 | − | 0.631905i | −0.0529219 | − | 0.998599i | \(-0.516853\pi\) |
−0.930342 | + | 0.366693i | \(0.880490\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0.525253 | − | 0.0755199i | 0.0171046 | − | 0.00245927i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 7.78450 | + | 8.42880i | 0.253230 | + | 0.274189i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 5.10967 | − | 2.33351i | 0.166042 | − | 0.0758289i | −0.330660 | − | 0.943750i | \(-0.607271\pi\) |
0.496702 | + | 0.867921i | \(0.334544\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 3.88350 | − | 9.70051i | 0.126064 | − | 0.314892i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −10.2078 | + | 0.431988i | −0.331012 | + | 0.0140082i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 6.34797 | + | 2.89902i | 0.205631 | + | 0.0939084i | 0.515568 | − | 0.856849i | \(-0.327581\pi\) |
−0.309937 | + | 0.950757i | \(0.600308\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −12.5863 | + | 36.3659i | −0.407285 | + | 1.17677i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 6.96223 | − | 8.75716i | 0.225057 | − | 0.283079i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 1.30430 | − | 1.65855i | 0.0421180 | − | 0.0535574i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 0.898997 | − | 18.8723i | 0.0289999 | − | 0.608783i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −17.9823 | + | 6.01084i | −0.579473 | + | 0.193697i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −0.554322 | + | 3.85539i | −0.0178443 | + | 0.124109i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 13.9889 | − | 24.2294i | 0.449852 | − | 0.779166i | −0.548524 | − | 0.836135i | \(-0.684810\pi\) |
0.998376 | + | 0.0569685i | \(0.0181435\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −0.00287107 | + | 0.541099i | −9.22321e−5 | + | 0.0173826i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −28.3879 | + | 20.2149i | −0.911010 | + | 0.648728i | −0.936394 | − | 0.350950i | \(-0.885859\pi\) |
0.0253837 | + | 0.999678i | \(0.491919\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0.810259 | + | 17.0094i | 0.0259757 | + | 0.545297i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −13.8841 | − | 3.44636i | −0.444648 | − | 0.110372i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 20.0489 | − | 4.86380i | 0.641420 | − | 0.155607i | 0.0981593 | − | 0.995171i | \(-0.468705\pi\) |
0.543261 | + | 0.839564i | \(0.317189\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 3.74935 | + | 19.4535i | 0.119830 | + | 0.621736i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −24.3930 | − | 26.1323i | −0.778808 | − | 0.834341i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −23.1987 | + | 14.9089i | −0.739923 | + | 0.475520i | −0.855516 | − | 0.517777i | \(-0.826760\pi\) |
0.115592 | + | 0.993297i | \(0.463123\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1.18360 | − | 0.610186i | 0.0377125 | − | 0.0194421i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 19.7661 | + | 28.0717i | 0.629163 | + | 0.893532i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 2.57989 | − | 2.02885i | 0.0820358 | − | 0.0645137i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −16.2720 | − | 14.0997i | −0.516896 | − | 0.447893i | 0.356930 | − | 0.934131i | \(-0.383823\pi\) |
−0.873826 | + | 0.486238i | \(0.838369\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −0.787976 | − | 1.24054i | −0.0250057 | − | 0.0393673i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0.143299 | + | 0.0738755i | 0.00454287 | + | 0.00234201i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 12.1773 | + | 3.57558i | 0.385659 | + | 0.113240i | 0.468814 | − | 0.883297i | \(-0.344681\pi\) |
−0.0831548 | + | 0.996537i | \(0.526500\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 11.6773 | − | 32.0779i | 0.369452 | − | 1.01490i |
(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 | 804.2.ba.b.353.14 | yes | 440 | |
3.2 | odd | 2 | inner | 804.2.ba.b.353.2 | yes | 440 | |
67.41 | odd | 66 | inner | 804.2.ba.b.41.2 | ✓ | 440 | |
201.41 | even | 66 | inner | 804.2.ba.b.41.14 | yes | 440 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
804.2.ba.b.41.2 | ✓ | 440 | 67.41 | odd | 66 | inner | |
804.2.ba.b.41.14 | yes | 440 | 201.41 | even | 66 | inner | |
804.2.ba.b.353.2 | yes | 440 | 3.2 | odd | 2 | inner | |
804.2.ba.b.353.14 | yes | 440 | 1.1 | even | 1 | trivial |