Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [128,4,Mod(17,128)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(128, base_ring=CyclotomicField(8))
chi = DirichletCharacter(H, H._module([0, 7]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("128.17");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 128 = 2^{7} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 128.g (of order \(8\), degree \(4\), 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: | \(7.55224448073\) |
Analytic rank: | \(0\) |
Dimension: | \(44\) |
Relative dimension: | \(11\) over \(\Q(\zeta_{8})\) |
Twist minimal: | no (minimal twist has level 32) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{8}]$ |
Embedding invariants
Embedding label | 113.4 | ||
Character | \(\chi\) | \(=\) | 128.113 |
Dual form | 128.4.g.a.17.4 |
$q$-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 \(\left(\mathbb{Z}/128\mathbb{Z}\right)^\times\).
\(n\) | \(5\) | \(127\) |
\(\chi(n)\) | \(e\left(\frac{1}{8}\right)\) | \(1\) |
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 | ||||||||
\(3\) | −1.64064 | − | 3.96085i | −0.315741 | − | 0.762266i | −0.999471 | − | 0.0325307i | \(-0.989643\pi\) |
0.683730 | − | 0.729735i | \(-0.260357\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −11.8087 | − | 4.89132i | −1.05620 | − | 0.437493i | −0.214099 | − | 0.976812i | \(-0.568682\pi\) |
−0.842101 | + | 0.539319i | \(0.818682\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 5.11236 | + | 5.11236i | 0.276042 | + | 0.276042i | 0.831527 | − | 0.555485i | \(-0.187467\pi\) |
−0.555485 | + | 0.831527i | \(0.687467\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 6.09524 | − | 6.09524i | 0.225750 | − | 0.225750i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −15.2446 | + | 36.8038i | −0.417858 | + | 1.00880i | 0.565110 | + | 0.825016i | \(0.308834\pi\) |
−0.982967 | + | 0.183781i | \(0.941166\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −73.4903 | + | 30.4407i | −1.56789 | + | 0.649440i | −0.986437 | − | 0.164142i | \(-0.947515\pi\) |
−0.581450 | + | 0.813582i | \(0.697515\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 54.7973i | 0.943240i | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 66.8708i | 0.954033i | 0.878894 | + | 0.477016i | \(0.158282\pi\) | ||||
−0.878894 | + | 0.477016i | \(0.841718\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 37.0353 | − | 15.3405i | 0.447184 | − | 0.185230i | −0.147715 | − | 0.989030i | \(-0.547192\pi\) |
0.594899 | + | 0.803800i | \(0.297192\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 11.8618 | − | 28.6368i | 0.123260 | − | 0.297575i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −30.1143 | + | 30.1143i | −0.273012 | + | 0.273012i | −0.830311 | − | 0.557300i | \(-0.811837\pi\) |
0.557300 | + | 0.830311i | \(0.311837\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 27.1316 | + | 27.1316i | 0.217053 | + | 0.217053i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −141.085 | − | 58.4395i | −1.00563 | − | 0.416544i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 64.4434 | + | 155.580i | 0.412649 | + | 0.996224i | 0.984424 | + | 0.175813i | \(0.0562553\pi\) |
−0.571774 | + | 0.820411i | \(0.693745\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −219.132 | −1.26959 | −0.634796 | − | 0.772680i | \(-0.718916\pi\) | ||||
−0.634796 | + | 0.772680i | \(0.718916\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 170.785 | 0.900907 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −35.3641 | − | 85.3765i | −0.170789 | − | 0.412322i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −286.081 | − | 118.499i | −1.27112 | − | 0.526515i | −0.357816 | − | 0.933792i | \(-0.616478\pi\) |
−0.913305 | + | 0.407277i | \(0.866478\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 241.142 | + | 241.142i | 0.990092 | + | 0.990092i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 64.2737 | − | 64.2737i | 0.244826 | − | 0.244826i | −0.574017 | − | 0.818843i | \(-0.694616\pi\) |
0.818843 | + | 0.574017i | \(0.194616\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 200.870 | − | 484.942i | 0.712380 | − | 1.71984i | 0.0184123 | − | 0.999830i | \(-0.494139\pi\) |
0.693967 | − | 0.720006i | \(-0.255861\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −101.791 | + | 42.1630i | −0.337201 | + | 0.139673i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 392.444i | 1.21795i | 0.793188 | + | 0.608977i | \(0.208420\pi\) | ||||
−0.793188 | + | 0.608977i | \(0.791580\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | − | 290.727i | − | 0.847602i | ||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 264.865 | − | 109.711i | 0.727227 | − | 0.301227i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 107.214 | − | 258.838i | 0.277868 | − | 0.670833i | −0.721908 | − | 0.691989i | \(-0.756735\pi\) |
0.999776 | + | 0.0211562i | \(0.00673472\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 360.038 | − | 360.038i | 0.882683 | − | 0.882683i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −121.523 | − | 121.523i | −0.282388 | − | 0.282388i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −237.764 | − | 98.4852i | −0.524649 | − | 0.217317i | 0.104609 | − | 0.994513i | \(-0.466641\pi\) |
−0.629258 | + | 0.777197i | \(0.716641\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −43.9101 | − | 106.008i | −0.0921658 | − | 0.222508i | 0.871074 | − | 0.491153i | \(-0.163424\pi\) |
−0.963239 | + | 0.268645i | \(0.913424\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 62.3222 | 0.124633 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1016.72 | 1.94013 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 333.028 | + | 804.000i | 0.607251 | + | 1.46603i | 0.865978 | + | 0.500083i | \(0.166697\pi\) |
−0.258727 | + | 0.965951i | \(0.583303\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 168.685 | + | 69.8717i | 0.294309 | + | 0.121907i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −387.445 | − | 387.445i | −0.647624 | − | 0.647624i | 0.304794 | − | 0.952418i | \(-0.401412\pi\) |
−0.952418 | + | 0.304794i | \(0.901412\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −518.132 | + | 518.132i | −0.830723 | + | 0.830723i | −0.987616 | − | 0.156892i | \(-0.949852\pi\) |
0.156892 | + | 0.987616i | \(0.449852\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 62.9512 | − | 151.978i | 0.0969197 | − | 0.233985i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −266.091 | + | 110.218i | −0.393816 | + | 0.163124i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 214.985i | − | 0.306173i | −0.988213 | − | 0.153086i | \(-0.951079\pi\) | ||
0.988213 | − | 0.153086i | \(-0.0489213\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 421.957i | 0.578816i | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −436.657 | + | 180.869i | −0.577462 | + | 0.239193i | −0.652246 | − | 0.758007i | \(-0.726173\pi\) |
0.0747842 | + | 0.997200i | \(0.476173\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 327.086 | − | 789.656i | 0.417382 | − | 1.00765i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 510.501 | − | 510.501i | 0.629097 | − | 0.629097i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −877.926 | − | 877.926i | −1.04562 | − | 1.04562i | −0.998909 | − | 0.0467087i | \(-0.985127\pi\) |
−0.0467087 | − | 0.998909i | \(-0.514873\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −531.333 | − | 220.085i | −0.612075 | − | 0.253530i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 359.517 | + | 867.951i | 0.400862 | + | 0.967767i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −512.374 | −0.553352 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 43.7563 | 0.0458019 | 0.0229009 | − | 0.999738i | \(-0.492710\pi\) | ||||
0.0229009 | + | 0.999738i | \(0.492710\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 131.408 | + | 317.248i | 0.133404 | + | 0.322067i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 427.453 | + | 177.057i | 0.421120 | + | 0.174434i | 0.583172 | − | 0.812349i | \(-0.301811\pi\) |
−0.162052 | + | 0.986782i | \(0.551811\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −570.431 | − | 570.431i | −0.545691 | − | 0.545691i | 0.379500 | − | 0.925192i | \(-0.376096\pi\) |
−0.925192 | + | 0.379500i | \(0.876096\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −280.144 | + | 280.144i | −0.260374 | + | 0.260374i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −398.490 | + | 962.041i | −0.360033 | + | 0.869196i | 0.635261 | + | 0.772297i | \(0.280892\pi\) |
−0.995294 | + | 0.0968989i | \(0.969108\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −129.224 | + | 53.5263i | −0.113554 | + | 0.0470357i | −0.438737 | − | 0.898615i | \(-0.644574\pi\) |
0.325183 | + | 0.945651i | \(0.394574\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1327.54i | 1.13517i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 772.521i | 0.643121i | 0.946889 | + | 0.321561i | \(0.104207\pi\) | ||||
−0.946889 | + | 0.321561i | \(0.895793\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 502.909 | − | 208.312i | 0.407796 | − | 0.168915i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −262.398 | + | 633.484i | −0.207339 | + | 0.500561i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −341.868 | + | 341.868i | −0.263353 | + | 0.263353i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −180.963 | − | 180.963i | −0.135960 | − | 0.135960i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −360.028 | − | 149.129i | −0.263924 | − | 0.109321i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 423.735 | + | 1022.99i | 0.303200 | + | 0.731990i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −485.865 | −0.339477 | −0.169738 | − | 0.985489i | \(-0.554292\pi\) | ||||
−0.169738 | + | 0.985489i | \(0.554292\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −2250.34 | −1.53590 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 764.762 | + | 1846.30i | 0.510058 | + | 1.23139i | 0.943850 | + | 0.330375i | \(0.107175\pi\) |
−0.433792 | + | 0.901013i | \(0.642825\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 267.765 | + | 110.912i | 0.174572 | + | 0.0723103i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1380.19 | + | 1380.19i | 0.879908 | + | 0.879908i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1360.64 | + | 1360.64i | −0.848519 | + | 0.848519i | −0.989948 | − | 0.141430i | \(-0.954830\pi\) |
0.141430 | + | 0.989948i | \(0.454830\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −76.8204 | + | 185.461i | −0.0468764 | + | 0.113170i | −0.945583 | − | 0.325380i | \(-0.894508\pi\) |
0.898707 | + | 0.438550i | \(0.144508\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1554.41 | − | 643.859i | 0.928405 | − | 0.384558i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 3168.78i | − | 1.85305i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 2152.41i | − | 1.23274i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −1151.53 | + | 476.978i | −0.646098 | + | 0.267623i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 687.916 | − | 1660.78i | 0.378230 | − | 0.913128i | −0.614068 | − | 0.789253i | \(-0.710468\pi\) |
0.992298 | − | 0.123875i | \(-0.0395321\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1133.92 | − | 1133.92i | 0.611107 | − | 0.611107i | −0.332128 | − | 0.943235i | \(-0.607766\pi\) |
0.943235 | + | 0.332128i | \(0.107766\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 407.594 | + | 407.594i | 0.215373 | + | 0.215373i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2587.67 | + | 1071.85i | 1.34094 | + | 0.555437i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −368.347 | − | 889.267i | −0.187244 | − | 0.452046i | 0.802183 | − | 0.597078i | \(-0.203672\pi\) |
−0.989427 | + | 0.145032i | \(0.953672\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −1201.12 | −0.599087 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −307.911 | −0.150725 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −988.667 | − | 2386.85i | −0.475082 | − | 1.14695i | −0.961889 | − | 0.273440i | \(-0.911839\pi\) |
0.486807 | − | 0.873509i | \(-0.338161\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −2016.75 | − | 835.365i | −0.951538 | − | 0.394140i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −373.791 | − | 373.791i | −0.173202 | − | 0.173202i | 0.615182 | − | 0.788385i | \(-0.289082\pi\) |
−0.788385 | + | 0.615182i | \(0.789082\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2920.67 | − | 2920.67i | 1.32939 | − | 1.32939i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 132.235 | − | 319.244i | 0.0591361 | − | 0.142767i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −71.8748 | + | 29.7715i | −0.0315870 | + | 0.0130837i | −0.398421 | − | 0.917203i | \(-0.630442\pi\) |
0.366834 | + | 0.930286i | \(0.380442\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 277.414i | 0.119831i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 1103.33i | 0.468538i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 1660.73 | − | 687.899i | 0.693459 | − | 0.287240i | −0.00798155 | − | 0.999968i | \(-0.502541\pi\) |
0.701440 | + | 0.712728i | \(0.252541\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −757.224 | + | 1828.10i | −0.310962 | + | 0.750728i | 0.688708 | + | 0.725038i | \(0.258178\pi\) |
−0.999670 | + | 0.0256892i | \(0.991822\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −347.843 | + | 347.843i | −0.140510 | + | 0.140510i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 2798.63 | + | 2798.63i | 1.11221 | + | 1.11221i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2461.10 | − | 1019.42i | −0.962426 | − | 0.398650i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −422.516 | − | 1020.04i | −0.162611 | − | 0.392578i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 3023.78 | 1.14551 | 0.572757 | − | 0.819725i | \(-0.305874\pi\) | ||||
0.572757 | + | 0.819725i | \(0.305874\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2155.34 | 0.803860 | 0.401930 | − | 0.915670i | \(-0.368339\pi\) | ||||
0.401930 | + | 0.915670i | \(0.368339\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −1668.07 | − | 4027.07i | −0.612578 | − | 1.47889i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 2832.03 | + | 1173.07i | 1.02423 | + | 0.424251i | 0.830628 | − | 0.556828i | \(-0.187982\pi\) |
0.193606 | + | 0.981079i | \(0.437982\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −751.482 | − | 751.482i | −0.267694 | − | 0.267694i | 0.560476 | − | 0.828171i | \(-0.310618\pi\) |
−0.828171 | + | 0.560476i | \(0.810618\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 2638.15 | − | 2638.15i | 0.925774 | − | 0.925774i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −465.924 | + | 1124.84i | −0.161091 | + | 0.388908i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1073.37 | + | 444.605i | −0.365695 | + | 0.151476i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 367.108i | 0.123265i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1596.90i | 0.528517i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 469.343 | − | 194.408i | 0.153132 | − | 0.0634295i | −0.304801 | − | 0.952416i | \(-0.598590\pi\) |
0.457933 | + | 0.888987i | \(0.348590\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −898.956 | + | 2170.27i | −0.289180 | + | 0.698143i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −4744.01 | + | 4744.01i | −1.50483 | + | 1.50483i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1120.29 | − | 1120.29i | −0.350460 | − | 0.350460i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 2902.31 | + | 1202.18i | 0.895525 | + | 0.370939i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −2035.59 | − | 4914.35i | −0.619587 | − | 1.49582i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 6411.24 | 1.92524 | 0.962619 | − | 0.270857i | \(-0.0873072\pi\) | ||||
0.962619 | + | 0.270857i | \(0.0873072\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 330.748 | 0.0979993 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −139.729 | − | 337.336i | −0.0408553 | − | 0.0986334i | 0.902135 | − | 0.431455i | \(-0.141999\pi\) |
−0.942990 | + | 0.332821i | \(0.891999\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −2169.11 | − | 898.477i | −0.625935 | − | 0.259271i | 0.0470898 | − | 0.998891i | \(-0.485005\pi\) |
−0.673025 | + | 0.739620i | \(0.735005\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 873.117 | + | 873.117i | 0.248688 | + | 0.248688i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −1442.89 | + | 1442.89i | −0.405696 | + | 0.405696i | −0.880235 | − | 0.474539i | \(-0.842615\pi\) |
0.474539 | + | 0.880235i | \(0.342615\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1919.57 | − | 4634.25i | 0.532846 | − | 1.28640i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −851.522 | + | 352.712i | −0.233385 | + | 0.0966713i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 2049.94i | 0.554811i | 0.960753 | + | 0.277406i | \(0.0894746\pi\) | ||||
−0.960753 | + | 0.277406i | \(0.910525\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 3964.18i | − | 1.05956i | −0.848134 | − | 0.529782i | \(-0.822274\pi\) | ||
0.848134 | − | 0.529782i | \(-0.177726\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −2138.00 | + | 885.588i | −0.564414 | + | 0.233788i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −1422.04 | + | 3433.11i | −0.370820 | + | 0.895238i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2254.76 | + | 2254.76i | −0.580838 | + | 0.580838i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 1432.79 | + | 1432.79i | 0.364657 | + | 0.364657i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 3653.50 | + | 1513.33i | 0.918754 | + | 0.380560i | 0.791401 | − | 0.611297i | \(-0.209352\pi\) |
0.127353 | + | 0.991858i | \(0.459352\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −649.240 | − | 1567.41i | −0.161334 | − | 0.389494i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −3664.34 | −0.899882 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −6137.79 | −1.48975 | −0.744873 | − | 0.667206i | \(-0.767490\pi\) | ||||
−0.744873 | + | 0.667206i | \(0.767490\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −856.743 | − | 2068.36i | −0.205542 | − | 0.496223i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1341.10 | + | 555.500i | 0.318053 | + | 0.131742i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −1379.24 | − | 1379.24i | −0.323374 | − | 0.323374i | 0.526686 | − | 0.850060i | \(-0.323434\pi\) |
−0.850060 | + | 0.526686i | \(0.823434\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2532.12 | + | 2532.12i | −0.586969 | + | 0.586969i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −2036.97 | + | 4917.69i | −0.466894 | + | 1.12718i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 136.201 | − | 56.4164i | 0.0308711 | − | 0.0127872i | −0.367194 | − | 0.930144i | \(-0.619682\pi\) |
0.398066 | + | 0.917357i | \(0.369682\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1576.16i | 0.353302i | 0.984274 | + | 0.176651i | \(0.0565264\pi\) | ||||
−0.984274 | + | 0.176651i | \(0.943474\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 2465.61i | 0.546614i | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1412.16 | + | 584.936i | −0.309660 | + | 0.128265i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1137.39 | + | 2745.89i | −0.246711 | + | 0.595613i | −0.997921 | − | 0.0644505i | \(-0.979471\pi\) |
0.751210 | + | 0.660063i | \(0.229471\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −1335.67 | + | 1335.67i | −0.286610 | + | 0.286610i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 346.910 | + | 346.910i | 0.0736474 | + | 0.0736474i | 0.742971 | − | 0.669324i | \(-0.233416\pi\) |
−0.669324 | + | 0.742971i | \(0.733416\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −2926.90 | − | 1212.36i | −0.614791 | − | 0.254655i | 0.0534844 | − | 0.998569i | \(-0.482967\pi\) |
−0.668275 | + | 0.743914i | \(0.732967\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 840.620 | + | 2029.44i | 0.174716 | + | 0.421802i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 657.181 | 0.135164 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 441.294 | 0.0898217 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −71.7883 | − | 173.312i | −0.0144615 | − | 0.0349132i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 551.934 | + | 228.618i | 0.110049 | + | 0.0455837i | 0.437029 | − | 0.899448i | \(-0.356031\pi\) |
−0.326980 | + | 0.945031i | \(0.606031\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2325.96 | + | 2325.96i | 0.459060 | + | 0.459060i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 4301.59 | − | 4301.59i | 0.840416 | − | 0.840416i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1296.41 | − | 3129.81i | 0.250747 | − | 0.605357i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 3506.12 | − | 1452.28i | 0.671393 | − | 0.278100i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − | 1983.56i | − | 0.376081i | ||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 1466.60i | 0.275335i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −3795.75 | + | 1572.25i | −0.705651 | + | 0.292290i | −0.706503 | − | 0.707710i | \(-0.749729\pi\) |
0.000852873 | 1.00000i | \(0.499729\pi\) | ||||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1323.52 | + | 3195.26i | −0.243665 | + | 0.588259i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 2922.48 | − | 2922.48i | 0.532857 | − | 0.532857i | −0.388565 | − | 0.921421i | \(-0.627029\pi\) |
0.921421 | + | 0.388565i | \(0.127029\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 4410.61 | + | 4410.61i | 0.796493 | + | 0.796493i | 0.982541 | − | 0.186048i | \(-0.0595678\pi\) |
−0.186048 | + | 0.982541i | \(0.559568\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −735.943 | − | 304.838i | −0.131637 | − | 0.0545259i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −823.383 | − | 1987.82i | −0.145886 | − | 0.352199i | 0.833998 | − | 0.551767i | \(-0.186046\pi\) |
−0.979884 | + | 0.199568i | \(0.936046\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −6708.36 | −1.17742 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 4464.28 | 0.776236 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1025.83 | + | 2476.58i | 0.176715 | + | 0.426628i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −2819.82 | − | 1168.01i | −0.481278 | − | 0.199352i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 424.019 | + | 424.019i | 0.0717074 | + | 0.0717074i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −2006.32 | + | 2006.32i | −0.336206 | + | 0.336206i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2294.33 | + | 5539.00i | −0.380990 | + | 0.919791i | 0.610785 | + | 0.791797i | \(0.290854\pi\) |
−0.991775 | + | 0.127995i | \(0.959146\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −2466.01 | + | 1021.46i | −0.405816 | + | 0.168094i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − | 11123.1i | − | 1.81409i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 4177.18i | − | 0.675209i | −0.941288 | − | 0.337604i | \(-0.890383\pi\) | ||
0.941288 | − | 0.337604i | \(-0.109617\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 3059.84 | − | 1267.43i | 0.490229 | − | 0.203060i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 3340.60 | − | 8064.91i | 0.530509 | − | 1.28076i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 3239.85 | − | 3239.85i | 0.510015 | − | 0.510015i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −1650.18 | − | 1650.18i | −0.257516 | − | 0.257516i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 6068.09 | + | 2513.48i | 0.938767 | + | 0.388850i | 0.798998 | − | 0.601334i | \(-0.205364\pi\) |
0.139769 | + | 0.990184i | \(0.455364\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 3219.82 | + | 7773.32i | 0.493848 | + | 1.19225i | 0.952747 | + | 0.303765i | \(0.0982438\pi\) |
−0.458899 | + | 0.888488i | \(0.651756\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 12147.3 | 1.84723 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −10007.7 | −1.50895 | −0.754473 | − | 0.656331i | \(-0.772107\pi\) | ||||
−0.754473 | + | 0.656331i | \(0.772107\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2680.10 | + | 6470.34i | 0.400690 | + | 0.967352i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 1914.97 | + | 793.206i | 0.283896 | + | 0.117594i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −3853.86 | − | 3853.86i | −0.566572 | − | 0.566572i | 0.364595 | − | 0.931166i | \(-0.381208\pi\) |
−0.931166 | + | 0.364595i | \(0.881208\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3713.76 | + | 3713.76i | −0.541443 | + | 0.541443i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −419.873 | + | 1013.66i | −0.0607097 | + | 0.146566i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 8652.81 | − | 3584.11i | 1.24085 | − | 0.513975i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2274.12i | 0.323456i | 0.986835 | + | 0.161728i | \(0.0517067\pi\) | ||||
−0.986835 | + | 0.161728i | \(0.948293\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | − | 783.528i | − | 0.110539i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1871.39 | − | 775.156i | 0.261881 | − | 0.108475i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 4974.80 | − | 12010.2i | 0.690577 | − | 1.66720i | −0.0530384 | − | 0.998592i | \(-0.516891\pi\) |
0.743615 | − | 0.668608i | \(-0.233109\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 3356.70 | − | 3356.70i | 0.462238 | − | 0.462238i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −9471.92 | − | 9471.92i | −1.29398 | − | 1.29398i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −10078.6 | − | 4174.70i | −1.36597 | − | 0.565805i | −0.425280 | − | 0.905062i | \(-0.639824\pi\) |
−0.940694 | + | 0.339257i | \(0.889824\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 797.128 | + | 1924.44i | 0.107187 | + | 0.258771i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −14593.3 | −1.94695 | −0.973477 | − | 0.228784i | \(-0.926525\pi\) | ||||
−0.973477 | + | 0.228784i | \(0.926525\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 3681.29 | 0.487314 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −1731.49 | − | 4180.19i | −0.227433 | − | 0.549072i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 5607.97 | + | 2322.90i | 0.730939 | + | 0.302765i | 0.716938 | − | 0.697137i | \(-0.245543\pi\) |
0.0140014 | + | 0.999902i | \(0.495543\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2013.77 | − | 2013.77i | −0.260462 | − | 0.260462i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 6058.21 | − | 6058.21i | 0.777599 | − | 0.777599i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −1051.56 | + | 2538.69i | −0.133948 | + | 0.323380i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −1428.80 | + | 591.828i | −0.180628 | + | 0.0748187i | −0.471165 | − | 0.882045i | \(-0.656166\pi\) |
0.290536 | + | 0.956864i | \(0.406166\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | − | 1242.54i | − | 0.155902i | ||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 7265.44i | 0.904786i | 0.891819 | + | 0.452393i | \(0.149429\pi\) | ||||
−0.891819 | + | 0.452393i | \(0.850571\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 16104.1 | − | 6670.54i | 1.99058 | − | 0.824524i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 2063.92 | − | 4982.75i | 0.253228 | − | 0.611346i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 8722.41 | − | 8722.41i | 1.06229 | − | 1.06229i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −7223.12 | − | 7223.12i | −0.873252 | − | 0.873252i | 0.119573 | − | 0.992825i | \(-0.461847\pi\) |
−0.992825 | + | 0.119573i | \(0.961847\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 7621.59 | + | 3156.97i | 0.914709 | + | 0.378885i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −712.046 | − | 1719.03i | −0.0848365 | − | 0.204813i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 6041.03 | 0.714561 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 860.618 | 0.101066 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 3225.87 | + | 7787.95i | 0.376120 | + | 0.908034i | 0.992685 | + | 0.120730i | \(0.0385235\pi\) |
−0.616566 | + | 0.787304i | \(0.711476\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1956.30 | + | 810.327i | 0.226471 | + | 0.0938074i | 0.493034 | − | 0.870010i | \(-0.335888\pi\) |
−0.266563 | + | 0.963818i | \(0.585888\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 2392.04 | + | 2392.04i | 0.274953 | + | 0.274953i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −1814.31 | + | 1814.31i | −0.207076 | + | 0.207076i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 317.469 | − | 766.438i | 0.0359799 | − | 0.0868631i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −12551.1 | + | 5198.82i | −1.41252 | + | 0.585085i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 10185.7i | 1.13835i | 0.822216 | + | 0.569175i | \(0.192737\pi\) | ||||
−0.822216 | + | 0.569175i | \(0.807263\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 4456.20i | 0.494576i | 0.968942 | + | 0.247288i | \(0.0795394\pi\) | ||||
−0.968942 | + | 0.247288i | \(0.920461\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −8525.37 | + | 3531.32i | −0.939678 | + | 0.389227i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −653.325 | + | 1577.27i | −0.0715166 | + | 0.172656i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −2494.47 | + | 2494.47i | −0.271195 | + | 0.271195i | −0.829581 | − | 0.558386i | \(-0.811421\pi\) |
0.558386 | + | 0.829581i | \(0.311421\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1772.05 | − | 1772.05i | −0.191346 | − | 0.191346i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −13843.2 | − | 5734.06i | −1.48468 | − | 0.614974i | −0.514526 | − | 0.857475i | \(-0.672032\pi\) |
−0.970151 | + | 0.242501i | \(0.922032\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 6072.93 | + | 14661.4i | 0.646932 | + | 1.56183i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −7706.71 | −0.815469 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 6724.60 | 0.706801 | 0.353400 | − | 0.935472i | \(-0.385025\pi\) | ||||
0.353400 | + | 0.935472i | \(0.385025\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1385.69 | + | 3345.35i | 0.144677 | + | 0.349282i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −6351.64 | − | 2630.94i | −0.658778 | − | 0.272875i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 5197.83 | + | 5197.83i | 0.535556 | + | 0.535556i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −12569.7 | + | 12569.7i | −1.28662 | + | 1.28662i | −0.349795 | + | 0.936826i | \(0.613749\pi\) |
−0.936826 | + | 0.349795i | \(0.886251\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 3907.90 | − | 9434.49i | 0.397396 | − | 0.959400i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 5822.39 | − | 2411.71i | 0.588234 | − | 0.243654i | −0.0686568 | − | 0.997640i | \(-0.521871\pi\) |
0.656891 | + | 0.753986i | \(0.271871\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 15045.1i | 1.51016i | 0.655634 | + | 0.755079i | \(0.272402\pi\) | ||||
−0.655634 | + | 0.755079i | \(0.727598\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | − | 12007.9i | − | 1.19753i | ||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −12797.5 | + | 5300.90i | −1.26809 | + | 0.525260i | −0.912383 | − | 0.409337i | \(-0.865760\pi\) |
−0.355708 | + | 0.934597i | \(0.615760\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −2407.78 | + | 5812.90i | −0.237060 | + | 0.572313i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −2917.93 | + | 2917.93i | −0.285459 | + | 0.285459i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 14785.5 | + | 14785.5i | 1.43729 | + | 1.43729i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1421.04 | + | 588.616i | 0.137267 | + | 0.0568580i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −924.184 | − | 2231.18i | −0.0887117 | − | 0.214169i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −5991.54 | −0.571525 | −0.285762 | − | 0.958301i | \(-0.592247\pi\) | ||||
−0.285762 | + | 0.958301i | \(0.592247\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 24631.4 | 2.33491 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 505.170 | + | 1219.59i | 0.0475902 | + | 0.114893i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −516.705 | − | 214.026i | −0.0483760 | − | 0.0200380i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −6120.86 | − | 6120.86i | −0.569534 | − | 0.569534i | 0.362464 | − | 0.931998i | \(-0.381936\pi\) |
−0.931998 | + | 0.362464i | \(0.881936\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −7831.92 | + | 7831.92i | −0.724278 | + | 0.724278i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 7107.17 | − | 17158.2i | 0.653242 | − | 1.57707i | −0.154803 | − | 0.987945i | \(-0.549474\pi\) |
0.808045 | − | 0.589121i | \(-0.200526\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −10403.8 | + | 4309.38i | −0.950430 | + | 0.393681i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | − | 4389.04i | − | 0.398531i | ||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 3961.52i | − | 0.357543i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −276.250 | + | 114.426i | −0.0247828 | + | 0.0102654i | −0.395040 | − | 0.918664i | \(-0.629269\pi\) |
0.370258 | + | 0.928929i | \(0.379269\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −867.274 | + | 2093.78i | −0.0773392 | + | 0.186713i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −3966.95 | + | 3966.95i | −0.351645 | + | 0.351645i | −0.860721 | − | 0.509076i | \(-0.829987\pi\) |
0.509076 | + | 0.860721i | \(0.329987\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −4181.61 | − | 4181.61i | −0.368474 | − | 0.368474i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −16360.1 | − | 6776.58i | −1.43309 | − | 0.593606i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −4067.11 | − | 9818.87i | −0.354168 | − | 0.855037i | −0.996096 | − | 0.0882726i | \(-0.971865\pi\) |
0.641928 | − | 0.766765i | \(-0.278135\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −5297.76 | −0.458629 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −6121.64 | −0.526856 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 3945.88 | + | 9526.19i | 0.337624 | + | 0.815095i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −14443.4 | − | 5982.67i | −1.22867 | − | 0.508931i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 235.841 | + | 235.841i | 0.0199466 | + | 0.0199466i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 9171.85 | − | 9171.85i | 0.771259 | − | 0.771259i | −0.207067 | − | 0.978327i | \(-0.566392\pi\) |
0.978327 | + | 0.207067i | \(0.0663919\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −6048.17 | + | 14601.6i | −0.505675 | + | 1.22081i | 0.440676 | + | 0.897666i | \(0.354739\pi\) |
−0.946351 | + | 0.323140i | \(0.895261\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 1098.79 | − | 455.135i | 0.0913434 | − | 0.0378357i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 14653.6i | − | 1.21123i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 10353.3i | 0.850929i | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −2049.52 | + | 848.940i | −0.167499 | + | 0.0693802i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −2766.96 | + | 6680.03i | −0.224860 | + | 0.542860i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 9411.29 | − | 9411.29i | 0.760534 | − | 0.760534i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −5449.33 | − | 5449.33i | −0.437907 | − | 0.437907i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 10699.9 | + | 4432.04i | 0.855059 | + | 0.354177i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1872.33 | + | 4520.21i | 0.148795 | + | 0.359222i | 0.980650 | − | 0.195771i | \(-0.0627210\pi\) |
−0.831855 | + | 0.554993i | \(0.812721\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 8483.17 | 0.670437 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 1787.78 | 0.140514 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1131.56 | + | 2731.83i | 0.0884499 | + | 0.213537i | 0.961914 | − | 0.273351i | \(-0.0881320\pi\) |
−0.873464 | + | 0.486888i | \(0.838132\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −913.789 | − | 378.504i | −0.0710375 | − | 0.0294247i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 4773.36 | + | 4773.36i | 0.369060 | + | 0.369060i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1099.08 | − | 1099.08i | 0.0845165 | − | 0.0845165i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 6493.41 | − | 15676.5i | 0.496630 | − | 1.19897i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −4125.91 | + | 1709.01i | −0.313861 | + | 0.130005i | −0.534053 | − | 0.845451i | \(-0.679332\pi\) |
0.220192 | + | 0.975457i | \(0.429332\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 41753.1i | 3.15916i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 11420.6i | 0.859494i | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 13629.3 | − | 5645.44i | 1.02026 | − | 0.422605i | 0.191072 | − | 0.981576i | \(-0.438804\pi\) |
0.829187 | + | 0.558971i | \(0.188804\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 3778.65 | − | 9122.46i | 0.281361 | − | 0.679265i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −2157.20 | + | 2157.20i | −0.159777 | + | 0.159777i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −1198.17 | − | 1198.17i | −0.0882777 | − | 0.0882777i | 0.661589 | − | 0.749867i | \(-0.269882\pi\) |
−0.749867 | + | 0.661589i | \(0.769882\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −1981.86 | − | 820.913i | −0.145251 | − | 0.0601649i | 0.308874 | − | 0.951103i | \(-0.400048\pi\) |
−0.454125 | + | 0.890938i | \(0.650048\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −4960.93 | − | 11976.7i | −0.361685 | − | 0.873186i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1634.10 | −0.118516 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 1653.54 | 0.119303 | 0.0596515 | − | 0.998219i | \(-0.481001\pi\) | ||||
0.0596515 | + | 0.998219i | \(0.481001\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −3536.14 | − | 8536.99i | −0.253812 | − | 0.612755i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −3157.02 | − | 1307.68i | −0.225431 | − | 0.0933765i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 7891.78 | + | 7891.78i | 0.560625 | + | 0.560625i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 6197.14 | − | 6197.14i | 0.437983 | − | 0.437983i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −5748.28 | + | 13877.6i | −0.404186 | + | 0.975790i | 0.582453 | + | 0.812865i | \(0.302093\pi\) |
−0.986638 | + | 0.162926i | \(0.947907\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −8115.65 | + | 3361.61i | −0.567741 | + | 0.235166i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − | 13141.8i | − | 0.914692i | ||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 10098.5i | − | 0.699322i | −0.936876 | − | 0.349661i | \(-0.886297\pi\) | ||
0.936876 | − | 0.349661i | \(-0.113703\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 5709.19 | − | 2364.83i | 0.393368 | − | 0.162938i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −1743.60 | + | 4209.42i | −0.119532 | + | 0.288576i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −15005.1 | + | 15005.1i | −1.02353 | + | 1.02353i | −0.0238107 | + | 0.999716i | \(0.507580\pi\) |
−0.999716 | + | 0.0238107i | \(0.992420\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 11177.5 | + | 11177.5i | 0.758632 | + | 0.758632i | 0.976073 | − | 0.217442i | \(-0.0697712\pi\) |
−0.217442 | + | 0.976073i | \(0.569771\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 6930.46 | + | 2870.69i | 0.468043 | + | 0.193870i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 1251.79 | + | 3022.08i | 0.0841197 | + | 0.203083i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 16418.5 | 1.09787 | 0.548935 | − | 0.835865i | \(-0.315033\pi\) | ||||
0.548935 | + | 0.835865i | \(0.315033\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 5219.73 | 0.347314 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −11946.3 | − | 28840.8i | −0.790989 | − | 1.90962i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −954.545 | − | 395.385i | −0.0628935 | − | 0.0260513i | 0.351015 | − | 0.936370i | \(-0.385837\pi\) |
−0.413908 | + | 0.910319i | \(0.635837\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 3522.03 | + | 3522.03i | 0.230930 | + | 0.230930i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 7933.23 | − | 7933.23i | 0.517633 | − | 0.517633i | −0.399221 | − | 0.916855i | \(-0.630719\pi\) |
0.916855 | + | 0.399221i | \(0.130719\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 5475.77 | − | 13219.7i | 0.355557 | − | 0.858391i | −0.640356 | − | 0.768078i | \(-0.721213\pi\) |
0.995913 | − | 0.0903128i | \(-0.0287867\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 6008.56 | − | 2488.83i | 0.388269 | − | 0.160826i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − | 8976.55i | − | 0.577268i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | − | 18949.0i | − | 1.21274i | ||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 6325.10 | − | 2619.94i | 0.402871 | − | 0.166875i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 7924.11 | − | 19130.5i | 0.502313 | − | 1.21269i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 14339.1 | − | 14339.1i | 0.904647 | − | 0.904647i | −0.0911870 | − | 0.995834i | \(-0.529066\pi\) |
0.995834 | + | 0.0911870i | \(0.0290661\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −1540.04 | − | 1540.04i | −0.0967002 | − | 0.0967002i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 5737.42 | + | 2376.52i | 0.358555 | + | 0.148519i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 8849.94 | + | 21365.6i | 0.550467 | + | 1.32894i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −4723.15 | −0.292402 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −8662.28 | −0.533759 | −0.266879 | − | 0.963730i | \(-0.585993\pi\) | ||||
−0.266879 | + | 0.963730i | \(0.585993\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −3070.12 | − | 7411.92i | −0.188295 | − | 0.454584i | 0.801337 | − | 0.598214i | \(-0.204123\pi\) |
−0.989632 | + | 0.143630i | \(0.954123\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 26573.5 | + | 11007.1i | 1.62222 | + | 0.671945i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −16839.6 | − | 16839.6i | −1.02323 | − | 1.02323i | −0.999724 | − | 0.0235089i | \(-0.992516\pi\) |
−0.0235089 | − | 0.999724i | \(-0.507484\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 7249.27 | − | 7249.27i | 0.438457 | − | 0.438457i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −2599.30 | + | 6275.26i | −0.156489 | + | 0.377799i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 5431.53 | − | 2249.81i | 0.325501 | − | 0.134827i | −0.213948 | − | 0.976845i | \(-0.568632\pi\) |
0.539449 | + | 0.842018i | \(0.318632\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 25543.0i | − | 1.52374i | ||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 6316.28i | 0.375071i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −6283.92 | + | 2602.88i | −0.371452 | + | 0.153860i | −0.560597 | − | 0.828089i | \(-0.689428\pi\) |
0.189145 | + | 0.981949i | \(0.439428\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −6288.29 | + | 15181.3i | −0.370024 | + | 0.893318i | 0.623721 | + | 0.781647i | \(0.285620\pi\) |
−0.993745 | + | 0.111671i | \(0.964380\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −16125.4 | + | 16125.4i | −0.944580 | + | 0.944580i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −2619.44 | − | 2619.44i | −0.152748 | − | 0.152748i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −6625.86 | − | 2744.52i | −0.384639 | − | 0.159323i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −10518.5 | − | 25394.0i | −0.607877 | − | 1.46754i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 4570.91 | 0.262978 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −22750.9 | −1.30309 | −0.651546 | − | 0.758609i | \(-0.725879\pi\) | ||||
−0.651546 | + | 0.758609i | \(0.725879\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −2242.32 | − | 5413.44i | −0.127862 | − | 0.308686i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 18090.7 | + | 7493.42i | 1.02701 | + | 0.425400i | 0.831631 | − | 0.555329i | \(-0.187408\pi\) |
0.195375 | + | 0.980729i | \(0.437408\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 223.698 | + | 223.698i | 0.0126432 | + | 0.0126432i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −1106.89 | + | 1106.89i | −0.0622852 | + | 0.0622852i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −4949.33 | + | 11948.7i | −0.277278 | + | 0.669408i | −0.999758 | − | 0.0219835i | \(-0.993002\pi\) |
0.722481 | + | 0.691391i | \(0.243002\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 22722.6 | − | 9412.02i | 1.26743 | − | 0.524985i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 10065.6i | 0.558991i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 22285.7i | 1.23225i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 8985.78 | − | 3722.03i | 0.494696 | − | 0.204910i | −0.121365 | − | 0.992608i | \(-0.538727\pi\) |
0.616062 | + | 0.787698i | \(0.288727\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −950.080 | + | 2293.69i | −0.0520787 | + | 0.125729i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 1814.30 | − | 1814.30i | 0.0990218 | − | 0.0990218i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 4298.04 | + | 4298.04i | 0.233572 | + | 0.233572i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 8082.35 | + | 3347.82i | 0.437343 | + | 0.181153i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −5041.79 | − | 12172.0i | −0.271649 | − | 0.655818i | 0.727905 | − | 0.685678i | \(-0.240494\pi\) |
−0.999554 | + | 0.0298593i | \(0.990494\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −12413.0 | −0.665951 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −21504.9 | −1.14882 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 1280.12 | + | 3090.47i | 0.0680958 | + | 0.164398i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −29815.3 | − | 12349.9i | −1.57932 | − | 0.654176i | −0.591014 | − | 0.806661i | \(-0.701272\pi\) |
−0.988306 | + | 0.152486i | \(0.951272\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1310.38 | − | 1310.38i | −0.0691185 | − | 0.0691185i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 6599.03 | − | 6599.03i | 0.346614 | − | 0.346614i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −15499.5 | + | 37419.1i | −0.810697 | + | 1.95720i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 8119.52 | − | 3363.22i | 0.422914 | − | 0.175177i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − | 35519.5i | − | 1.84236i | −0.389141 | − | 0.921178i | \(-0.627228\pi\) | ||
0.389141 | − | 0.921178i | \(-0.372772\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 5832.50i | − | 0.301267i | ||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −15701.5 | + | 6503.78i | −0.807670 | + | 0.334548i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −2472.69 | + | 5969.60i | −0.126667 | + | 0.305800i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 6873.52 | − | 6873.52i | 0.350653 | − | 0.350653i | −0.509699 | − | 0.860353i | \(-0.670243\pi\) |
0.860353 | + | 0.509699i | \(0.170243\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 15071.3 | + | 15071.3i | 0.765702 | + | 0.765702i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 32428.5 | + | 13432.3i | 1.64078 | + | 0.679634i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 6189.58 | + | 14943.0i | 0.311893 | + | 0.752975i | 0.999635 | + | 0.0270204i | \(0.00860190\pi\) |
−0.687742 | + | 0.725955i | \(0.741398\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 15931.1 | 0.799492 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −34667.2 | −1.73268 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 8349.16 | + | 20156.7i | 0.415601 | + | 1.00335i | 0.983607 | + | 0.180325i | \(0.0577148\pi\) |
−0.568007 | + | 0.823024i | \(0.692285\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 12630.0 | + | 5231.53i | 0.626148 | + | 0.259359i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 6318.96 | + | 6318.96i | 0.312006 | + | 0.312006i | 0.845686 | − | 0.533680i | \(-0.179191\pi\) |
−0.533680 | + | 0.845686i | \(0.679191\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −16246.8 | + | 16246.8i | −0.798974 | + | 0.798974i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −1559.09 | + | 3763.97i | −0.0763642 | + | 0.184360i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −6955.53 | + | 2881.07i | −0.339318 | + | 0.140550i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 4475.99i | 0.217485i | 0.994070 | + | 0.108742i | \(0.0346824\pi\) | ||||
−0.994070 | + | 0.108742i | \(0.965318\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − | 16953.8i | − | 0.820493i | ||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −18936.5 | + | 7843.74i | −0.912806 | + | 0.378097i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −8674.08 | + | 20941.1i | −0.416466 | + | 1.00544i | 0.566897 | + | 0.823788i | \(0.308144\pi\) |
−0.983363 | + | 0.181650i | \(0.941856\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −5143.09 | + | 5143.09i | −0.245958 | + | 0.245958i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −6136.35 | − | 6136.35i | −0.292303 | − | 0.292303i | 0.545686 | − | 0.837989i | \(-0.316269\pi\) |
−0.837989 | + | 0.545686i | \(0.816269\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −934.286 | − | 386.994i | −0.0443295 | − | 0.0183619i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −2819.48 | − | 6806.82i | −0.133253 | − | 0.321701i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 20471.3 | 0.963725 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 13154.1 | 0.616838 | 0.308419 | − | 0.951251i | \(-0.400200\pi\) | ||||
0.308419 | + | 0.951251i | \(0.400200\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 10069.9 | + | 24310.9i | 0.470374 | + | 1.13558i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −14475.7 | − | 5996.05i | −0.673552 | − | 0.278995i | 0.0195763 | − | 0.999808i | \(-0.493768\pi\) |
−0.693129 | + | 0.720814i | \(0.743768\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −5945.42 | − | 5945.42i | −0.275569 | − | 0.275569i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −6786.86 | + | 6786.86i | −0.313356 | + | 0.313356i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1394.41 | − | 3366.39i | 0.0641332 | − | 0.154831i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 20165.9 | − | 8353.00i | 0.923936 | − | 0.382707i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − | 25716.1i | − | 1.17371i | ||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 12302.8i | 0.559369i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −29783.0 | + | 12336.5i | −1.34898 | + | 0.558768i | −0.936010 | − | 0.351975i | \(-0.885510\pi\) |
−0.412975 | + | 0.910742i | \(0.635510\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −3200.12 | + | 7725.78i | −0.144395 | + | 0.348599i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −3949.41 | + | 3949.41i | −0.177528 | + | 0.177528i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 6453.93 | + | 6453.93i | 0.289011 | + | 0.289011i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 14183.6 | + | 5875.05i | 0.632756 | + | 0.262096i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −179.018 | − | 432.187i | −0.00795626 | − | 0.0192081i | 0.919851 | − | 0.392267i | \(-0.128309\pi\) |
−0.927808 | + | 0.373059i | \(0.878309\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −26243.1 | −1.16197 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −10702.3 | −0.472096 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −11170.5 | − | 26968.0i | −0.490907 | − | 1.18516i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 3636.02 | + | 1506.09i | 0.159196 | + | 0.0659412i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −446.914 | − | 446.914i | −0.0194946 | − | 0.0194946i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −1696.33 | + | 1696.33i | −0.0737205 | + | 0.0737205i | −0.743006 | − | 0.669285i | \(-0.766600\pi\) |
0.669285 | + | 0.743006i | \(0.266600\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 9036.86 | − | 21816.9i | 0.391279 | − | 0.944631i | −0.598383 | − | 0.801210i | \(-0.704190\pi\) |
0.989662 | − | 0.143421i | \(-0.0458102\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 6242.93 | − | 2585.91i | 0.269310 | − | 0.111552i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 33021.5i | 1.41925i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 21041.5i | − | 0.901037i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −4580.07 | + | 1897.13i | −0.195410 | + | 0.0809415i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −14759.0 | + | 35631.4i | −0.627397 | + | 1.51467i | 0.215450 | + | 0.976515i | \(0.430878\pi\) |
−0.842846 | + | 0.538155i | \(0.819122\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −26350.3 | + | 26350.3i | −1.11606 | + | 1.11606i | −0.123742 | + | 0.992314i | \(0.539489\pi\) |
−0.992314 | + | 0.123742i | \(0.960511\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 4633.69 | + | 4633.69i | 0.195545 | + | 0.195545i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −15258.6 | − | 6320.31i | −0.641587 | − | 0.265754i | 0.0380800 | − | 0.999275i | \(-0.487876\pi\) |
−0.679667 | + | 0.733521i | \(0.737876\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −12319.9 | − | 29742.8i | −0.516148 | − | 1.24609i | −0.940252 | − | 0.340479i | \(-0.889411\pi\) |
0.424104 | − | 0.905614i | \(-0.360589\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 12742.1 | 0.531912 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 19441.2 | 0.808640 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 2585.65 | + | 6242.31i | 0.107162 | + | 0.258711i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 30916.4 | + | 12806.0i | 1.27673 | + | 0.528841i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 17943.3 | + | 17943.3i | 0.738347 | + | 0.738347i | 0.972258 | − | 0.233911i | \(-0.0751524\pi\) |
−0.233911 | + | 0.972258i | \(0.575152\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −2806.57 | + | 2806.57i | −0.115075 | + | 0.115075i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 804.905 | − | 1943.21i | 0.0328854 | − | 0.0793924i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −48775.2 | + | 20203.4i | −1.98570 | + | 0.822505i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 1850.30i | − | 0.0750614i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 13582.0i | 0.549039i | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 12183.7 | − | 5046.64i | 0.490776 | − | 0.203286i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 12194.4 | − | 29439.9i | 0.489482 | − | 1.18171i | −0.465500 | − | 0.885048i | \(-0.654125\pi\) |
0.954981 | − | 0.296666i | \(-0.0958747\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −3123.04 | + | 3123.04i | −0.124919 | + | 0.124919i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −26988.2 | − | 26988.2i | −1.07573 | − | 1.07573i | −0.996887 | − | 0.0788412i | \(-0.974878\pi\) |
−0.0788412 | − | 0.996887i | \(-0.525122\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −9332.38 | − | 3865.60i | −0.370683 | − | 0.153542i | 0.189562 | − | 0.981869i | \(-0.439293\pi\) |
−0.560245 | + | 0.828327i | \(0.689293\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −1078.20 | − | 2603.00i | −0.0426769 | − | 0.103031i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 42549.4 | 1.67833 | 0.839164 | − | 0.543878i | \(-0.183044\pi\) | ||||
0.839164 | + | 0.543878i | \(0.183044\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 994.369 | 0.0390862 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −724.003 | − | 1747.90i | −0.0283604 | − | 0.0684680i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 7912.26 | + | 3277.36i | 0.308866 | + | 0.127937i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −48948.6 | − | 48948.6i | −1.90420 | − | 1.90420i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 266.705 | − | 266.705i | 0.0103398 | − | 0.0103398i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −3063.59 | + | 7396.17i | −0.118364 | + | 0.285756i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 29966.3 | − | 12412.4i | 1.15381 | − | 0.477923i | 0.277999 | − | 0.960581i | \(-0.410329\pi\) |
0.875809 | + | 0.482659i | \(0.160329\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | − | 2561.21i | − | 0.0982792i | ||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 14567.6i | 0.557088i | 0.960423 | + | 0.278544i | \(0.0898519\pi\) | ||||
−0.960423 | + | 0.278544i | \(0.910148\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 43111.8 | − | 17857.5i | 1.64306 | − | 0.680580i | 0.646462 | − | 0.762946i | \(-0.276248\pi\) |
0.996602 | + | 0.0823661i | \(0.0262477\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 5396.72 | − | 13028.8i | 0.204982 | − | 0.494870i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 3731.29 | − | 3731.29i | 0.141245 | − | 0.141245i | −0.632949 | − | 0.774194i | \(-0.718156\pi\) |
0.774194 | + | 0.632949i | \(0.218156\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −2483.92 | − | 2483.92i | −0.0937097 | − | 0.0937097i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −15529.6 | − | 6432.58i | −0.583908 | − | 0.241863i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 6020.31 | + | 14534.3i | 0.225601 | + | 0.544649i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −22975.8 | −0.858097 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −14523.7 | −0.540614 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −14121.6 | − | 34092.6i | −0.523896 | − | 1.26480i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 17308.7 | + | 7169.50i | 0.639996 | + | 0.265095i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −11504.5 | − | 11504.5i | −0.423973 | − | 0.423973i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 17883.6 | − | 17883.6i | 0.656876 | − | 0.656876i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −2716.64 | + | 6558.56i | −0.0994538 | + | 0.240103i | −0.965773 | − | 0.259387i | \(-0.916479\pi\) |
0.866320 | + | 0.499490i | \(0.166479\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 3684.63 | − | 1526.22i | 0.134446 | − | 0.0556894i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 26795.2i | 0.974496i | 0.873264 | + | 0.487248i | \(0.161999\pi\) | ||||
−0.873264 | + | 0.487248i | \(0.838001\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 18827.9i | − | 0.682491i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 5808.97 | − | 2406.15i | 0.209878 | − | 0.0869345i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −5529.21 | + | 13348.7i | −0.199117 | + | 0.480712i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 39104.1 | − | 39104.1i | 1.40362 | − | 1.40362i | 0.615423 | − | 0.788197i | \(-0.288985\pi\) |
0.788197 | − | 0.615423i | \(-0.211015\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 12454.9 | + | 12454.9i | 0.445605 | + | 0.445605i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 40267.6 | + | 16679.4i | 1.43599 | + | 0.594808i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −4546.79 | − | 10976.9i | −0.161619 | − | 0.390183i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −6953.83 | −0.246379 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 48932.6 | 1.72812 | 0.864061 | − | 0.503386i | \(-0.167913\pi\) | ||||
0.864061 | + | 0.503386i | \(0.167913\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −4459.92 | − | 10767.2i | −0.157001 | − | 0.379034i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −16370.2 | − | 6780.77i | −0.574423 | − | 0.237934i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 24076.1 | + | 24076.1i | 0.842108 | + | 0.842108i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 3286.41 | − | 3286.41i | 0.114581 | − | 0.114581i | −0.647492 | − | 0.762072i | \(-0.724182\pi\) |
0.762072 | + | 0.647492i | \(0.224182\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 10233.5 | − | 24706.0i | 0.355654 | − | 0.858625i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −12857.9 | + | 5325.93i | −0.445438 | + | 0.184506i | −0.594116 | − | 0.804379i | \(-0.702498\pi\) |
0.148678 | + | 0.988886i | \(0.452498\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 3871.12i | 0.133681i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 14112.0i | 0.485782i | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −24989.2 | + | 10350.8i | −0.857485 | + | 0.355182i | −0.767723 | − | 0.640781i | \(-0.778611\pi\) |
−0.0897616 | + | 0.995963i | \(0.528611\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 22305.4 | − | 53850.0i | 0.762975 | − | 1.84199i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −6522.59 | + | 6522.59i | −0.222407 | + | 0.222407i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 16871.9 | + | 16871.9i | 0.573488 | + | 0.573488i | 0.933101 | − | 0.359614i | \(-0.117092\pi\) |
−0.359614 | + | 0.933101i | \(0.617092\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −35706.9 | − | 14790.3i | −1.20989 | − | 0.501154i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 11006.0 | + | 26570.8i | 0.371759 | + | 0.897504i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −13912.1 | −0.468453 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 18228.0 | 0.611864 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 3434.98 | + | 8292.77i | 0.114943 | + | 0.277498i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −25451.8 | − | 10542.5i | −0.849038 | − | 0.351683i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 20339.3 | + | 20339.3i | 0.676388 | + | 0.676388i | 0.959181 | − | 0.282793i | \(-0.0912610\pi\) |
−0.282793 | + | 0.959181i | \(0.591261\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 8126.35 | − | 8126.35i | 0.269408 | − | 0.269408i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 9157.64 | − | 22108.5i | 0.302660 | − | 0.730685i | −0.697244 | − | 0.716834i | \(-0.745591\pi\) |
0.999904 | − | 0.0138517i | \(-0.00440928\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1340.88 | + | 555.410i | −0.0441794 | + | 0.0182997i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 13085.1i | 0.429805i | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 13599.6i | − | 0.445334i | −0.974895 | − | 0.222667i | \(-0.928524\pi\) | ||
0.974895 | − | 0.222667i | \(-0.0714762\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 45694.7 | − | 18927.4i | 1.49173 | − | 0.617897i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −461.395 | + | 1113.91i | −0.0150165 | + | 0.0362531i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −19227.9 | + | 19227.9i | −0.623882 | + | 0.623882i | −0.946522 | − | 0.322640i | \(-0.895430\pi\) |
0.322640 | + | 0.946522i | \(0.395430\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −27704.7 | − | 27704.7i | −0.896189 | − | 0.896189i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 11238.4 | + | 4655.08i | 0.362433 | + | 0.150125i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 8554.66 | + | 20652.8i | 0.275048 | + | 0.664024i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 10267.1 | 0.329106 | 0.164553 | − | 0.986368i | \(-0.447382\pi\) | ||||
0.164553 | + | 0.986368i | \(0.447382\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 25703.3 | 0.821420 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 5198.28 | + | 12549.8i | 0.165625 | + | 0.399853i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −47357.4 | − | 19616.1i | −1.50434 | − | 0.623117i | −0.529957 | − | 0.848025i | \(-0.677792\pi\) |
−0.974380 | + | 0.224908i | \(0.927792\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 33436.9 | + | 33436.9i | 1.05895 | + | 1.05895i |
(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 | 128.4.g.a.113.4 | 44 | ||
4.3 | odd | 2 | 32.4.g.a.5.11 | ✓ | 44 | ||
8.3 | odd | 2 | 256.4.g.b.225.4 | 44 | |||
8.5 | even | 2 | 256.4.g.a.225.8 | 44 | |||
32.3 | odd | 8 | 256.4.g.b.33.4 | 44 | |||
32.13 | even | 8 | inner | 128.4.g.a.17.4 | 44 | ||
32.19 | odd | 8 | 32.4.g.a.13.11 | yes | 44 | ||
32.29 | even | 8 | 256.4.g.a.33.8 | 44 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
32.4.g.a.5.11 | ✓ | 44 | 4.3 | odd | 2 | ||
32.4.g.a.13.11 | yes | 44 | 32.19 | odd | 8 | ||
128.4.g.a.17.4 | 44 | 32.13 | even | 8 | inner | ||
128.4.g.a.113.4 | 44 | 1.1 | even | 1 | trivial | ||
256.4.g.a.33.8 | 44 | 32.29 | even | 8 | |||
256.4.g.a.225.8 | 44 | 8.5 | even | 2 | |||
256.4.g.b.33.4 | 44 | 32.3 | odd | 8 | |||
256.4.g.b.225.4 | 44 | 8.3 | odd | 2 |