Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1638,2,Mod(127,1638)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1638, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1638.127");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1638 = 2 \cdot 3^{2} \cdot 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1638.bj (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(13.0794958511\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 6 x^{11} + 39 x^{10} - 140 x^{9} + 460 x^{8} - 1066 x^{7} + 2127 x^{6} - 3172 x^{5} + \cdots + 169 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 182) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 127.5 | ||
Root | \(0.500000 - 0.613147i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1638.127 |
Dual form | 1638.2.bj.g.1135.5 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1638\mathbb{Z}\right)^\times\).
\(n\) | \(379\) | \(703\) | \(911\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) | \(1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.866025 | − | 0.500000i | 0.612372 | − | 0.353553i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0.500000 | − | 0.866025i | 0.250000 | − | 0.433013i | ||||
\(5\) | 1.14776i | 0.513292i | 0.966505 | + | 0.256646i | \(0.0826174\pi\) | ||||
−0.966505 | + | 0.256646i | \(0.917383\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.866025 | − | 0.500000i | −0.327327 | − | 0.188982i | ||||
\(8\) | − | 1.00000i | − | 0.353553i | ||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0.573878 | + | 0.993985i | 0.181476 | + | 0.314326i | ||||
\(11\) | −3.84935 | + | 2.22243i | −1.16062 | + | 0.670086i | −0.951453 | − | 0.307793i | \(-0.900410\pi\) |
−0.209170 | + | 0.977879i | \(0.567076\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.54343 | − | 0.666437i | −0.982769 | − | 0.184837i | ||||
\(14\) | −1.00000 | −0.267261 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | −1.35488 | + | 2.34672i | −0.328606 | + | 0.569163i | −0.982236 | − | 0.187652i | \(-0.939912\pi\) |
0.653629 | + | 0.756815i | \(0.273246\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 5.68371 | + | 3.28149i | 1.30393 | + | 0.752826i | 0.981076 | − | 0.193623i | \(-0.0620237\pi\) |
0.322856 | + | 0.946448i | \(0.395357\pi\) | |||||||
\(20\) | 0.993985 | + | 0.573878i | 0.222262 | + | 0.128323i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −2.22243 | + | 3.84935i | −0.473823 | + | 0.820685i | ||||
\(23\) | 1.04000 | + | 1.80133i | 0.216855 | + | 0.375603i | 0.953845 | − | 0.300300i | \(-0.0970869\pi\) |
−0.736990 | + | 0.675904i | \(0.763754\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3.68266 | 0.736531 | ||||||||
\(26\) | −3.40191 | + | 1.19456i | −0.667170 | + | 0.234273i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −0.866025 | + | 0.500000i | −0.163663 | + | 0.0944911i | ||||
\(29\) | 3.59960 | + | 6.23469i | 0.668428 | + | 1.15775i | 0.978344 | + | 0.206988i | \(0.0663660\pi\) |
−0.309915 | + | 0.950764i | \(0.600301\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 7.90895i | 1.42049i | 0.703955 | + | 0.710245i | \(0.251416\pi\) | ||||
−0.703955 | + | 0.710245i | \(0.748584\pi\) | |||||||
\(32\) | −0.866025 | − | 0.500000i | −0.153093 | − | 0.0883883i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 2.70976i | 0.464720i | ||||||||
\(35\) | 0.573878 | − | 0.993985i | 0.0970030 | − | 0.168014i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −8.35199 | + | 4.82202i | −1.37306 | + | 0.792736i | −0.991312 | − | 0.131532i | \(-0.958011\pi\) |
−0.381746 | + | 0.924267i | \(0.624677\pi\) | |||||||
\(38\) | 6.56298 | 1.06466 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1.14776 | 0.181476 | ||||||||
\(41\) | 8.22266 | − | 4.74735i | 1.28416 | − | 0.741412i | 0.306556 | − | 0.951852i | \(-0.400823\pi\) |
0.977607 | + | 0.210441i | \(0.0674898\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.70160 | + | 2.94725i | −0.259491 | + | 0.449452i | −0.966106 | − | 0.258147i | \(-0.916888\pi\) |
0.706614 | + | 0.707599i | \(0.250222\pi\) | |||||||
\(44\) | 4.44485i | 0.670086i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.80133 | + | 1.04000i | 0.265592 | + | 0.153339i | ||||
\(47\) | 1.67435i | 0.244229i | 0.992516 | + | 0.122114i | \(0.0389674\pi\) | ||||
−0.992516 | + | 0.122114i | \(0.961033\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0.500000 | + | 0.866025i | 0.0714286 | + | 0.123718i | ||||
\(50\) | 3.18927 | − | 1.84133i | 0.451032 | − | 0.260403i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −2.34886 | + | 2.73548i | −0.325729 | + | 0.379342i | ||||
\(53\) | −13.2815 | −1.82436 | −0.912180 | − | 0.409789i | \(-0.865602\pi\) | ||||
−0.912180 | + | 0.409789i | \(0.865602\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2.55080 | − | 4.41812i | −0.343950 | − | 0.595739i | ||||
\(56\) | −0.500000 | + | 0.866025i | −0.0668153 | + | 0.115728i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 6.23469 | + | 3.59960i | 0.818654 | + | 0.472650i | ||||
\(59\) | −0.0586805 | − | 0.0338792i | −0.00763956 | − | 0.00441070i | 0.496175 | − | 0.868222i | \(-0.334737\pi\) |
−0.503815 | + | 0.863812i | \(0.668071\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.05023 | + | 7.01521i | −0.518579 | + | 0.898205i | 0.481188 | + | 0.876617i | \(0.340205\pi\) |
−0.999767 | + | 0.0215878i | \(0.993128\pi\) | |||||||
\(62\) | 3.95448 | + | 6.84935i | 0.502219 | + | 0.869869i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 0.764907 | − | 4.06699i | 0.0948751 | − | 0.504447i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −0.444700 | + | 0.256747i | −0.0543287 | + | 0.0313667i | −0.526918 | − | 0.849916i | \(-0.676653\pi\) |
0.472590 | + | 0.881283i | \(0.343319\pi\) | |||||||
\(68\) | 1.35488 | + | 2.34672i | 0.164303 | + | 0.284582i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | − | 1.14776i | − | 0.137183i | ||||||
\(71\) | −9.34208 | − | 5.39365i | −1.10870 | − | 0.640109i | −0.170208 | − | 0.985408i | \(-0.554444\pi\) |
−0.938493 | + | 0.345300i | \(0.887777\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 8.02452i | − | 0.939199i | −0.882880 | − | 0.469599i | \(-0.844398\pi\) | ||
0.882880 | − | 0.469599i | \(-0.155602\pi\) | |||||||
\(74\) | −4.82202 | + | 8.35199i | −0.560549 | + | 0.970899i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 5.68371 | − | 3.28149i | 0.651966 | − | 0.376413i | ||||
\(77\) | 4.44485 | 0.506538 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 10.7404 | 1.20839 | 0.604193 | − | 0.796838i | \(-0.293496\pi\) | ||||
0.604193 | + | 0.796838i | \(0.293496\pi\) | |||||||
\(80\) | 0.993985 | − | 0.573878i | 0.111131 | − | 0.0641615i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 4.74735 | − | 8.22266i | 0.524257 | − | 0.908040i | ||||
\(83\) | − | 15.3479i | − | 1.68465i | −0.538967 | − | 0.842327i | \(-0.681185\pi\) | ||
0.538967 | − | 0.842327i | \(-0.318815\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.69346 | − | 1.55507i | −0.292147 | − | 0.168671i | ||||
\(86\) | 3.40320i | 0.366976i | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 2.22243 | + | 3.84935i | 0.236911 | + | 0.410342i | ||||
\(89\) | −9.40465 | + | 5.42978i | −0.996891 | + | 0.575555i | −0.907327 | − | 0.420426i | \(-0.861881\pi\) |
−0.0895643 | + | 0.995981i | \(0.528547\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.73548 | + | 2.34886i | 0.286756 | + | 0.246228i | ||||
\(92\) | 2.08000 | 0.216855 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0.837173 | + | 1.45003i | 0.0863478 | + | 0.149559i | ||||
\(95\) | −3.76635 | + | 6.52351i | −0.386419 | + | 0.669298i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.84198 | + | 1.06347i | 0.187025 | + | 0.107979i | 0.590589 | − | 0.806973i | \(-0.298895\pi\) |
−0.403564 | + | 0.914951i | \(0.632229\pi\) | |||||||
\(98\) | 0.866025 | + | 0.500000i | 0.0874818 | + | 0.0505076i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 1.84133 | − | 3.18927i | 0.184133 | − | 0.318927i | ||||
\(101\) | 3.00944 | + | 5.21251i | 0.299451 | + | 0.518664i | 0.976010 | − | 0.217724i | \(-0.0698633\pi\) |
−0.676560 | + | 0.736388i | \(0.736530\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 5.75670 | 0.567224 | 0.283612 | − | 0.958939i | \(-0.408467\pi\) | ||||
0.283612 | + | 0.958939i | \(0.408467\pi\) | |||||||
\(104\) | −0.666437 | + | 3.54343i | −0.0653496 | + | 0.347461i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −11.5022 | + | 6.64077i | −1.11719 | + | 0.645009i | ||||
\(107\) | −2.77468 | − | 4.80589i | −0.268239 | − | 0.464603i | 0.700168 | − | 0.713978i | \(-0.253108\pi\) |
−0.968407 | + | 0.249375i | \(0.919775\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 7.96986i | 0.763374i | 0.924292 | + | 0.381687i | \(0.124657\pi\) | ||||
−0.924292 | + | 0.381687i | \(0.875343\pi\) | |||||||
\(110\) | −4.41812 | − | 2.55080i | −0.421251 | − | 0.243209i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 1.00000i | 0.0944911i | ||||||||
\(113\) | −2.18535 | + | 3.78514i | −0.205580 | + | 0.356076i | −0.950318 | − | 0.311282i | \(-0.899242\pi\) |
0.744737 | + | 0.667358i | \(0.232575\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2.06749 | + | 1.19366i | −0.192794 | + | 0.111310i | ||||
\(116\) | 7.19919 | 0.668428 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −0.0677585 | −0.00623767 | ||||||||
\(119\) | 2.34672 | − | 1.35488i | 0.215123 | − | 0.124202i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 4.37835 | − | 7.58352i | 0.398032 | − | 0.689411i | ||||
\(122\) | 8.10046i | 0.733382i | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 6.84935 | + | 3.95448i | 0.615090 | + | 0.355122i | ||||
\(125\) | 9.96557i | 0.891347i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 3.43247 | + | 5.94522i | 0.304583 | + | 0.527553i | 0.977168 | − | 0.212467i | \(-0.0681497\pi\) |
−0.672586 | + | 0.740019i | \(0.734816\pi\) | |||||||
\(128\) | −0.866025 | + | 0.500000i | −0.0765466 | + | 0.0441942i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −1.37106 | − | 3.90457i | −0.120250 | − | 0.342453i | ||||
\(131\) | 16.1996 | 1.41537 | 0.707683 | − | 0.706530i | \(-0.249741\pi\) | ||||
0.707683 | + | 0.706530i | \(0.249741\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −3.28149 | − | 5.68371i | −0.284541 | − | 0.492840i | ||||
\(134\) | −0.256747 | + | 0.444700i | −0.0221796 | + | 0.0384162i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 2.34672 | + | 1.35488i | 0.201230 | + | 0.116180i | ||||
\(137\) | −4.50527 | − | 2.60112i | −0.384911 | − | 0.222229i | 0.295042 | − | 0.955484i | \(-0.404666\pi\) |
−0.679953 | + | 0.733256i | \(0.738000\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2.87013 | + | 4.97122i | −0.243442 | + | 0.421653i | −0.961692 | − | 0.274131i | \(-0.911610\pi\) |
0.718251 | + | 0.695784i | \(0.244943\pi\) | |||||||
\(140\) | −0.573878 | − | 0.993985i | −0.0485015 | − | 0.0840071i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −10.7873 | −0.905250 | ||||||||
\(143\) | 15.1210 | − | 5.30964i | 1.26448 | − | 0.444015i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −7.15589 | + | 4.13146i | −0.594265 | + | 0.343099i | ||||
\(146\) | −4.01226 | − | 6.94944i | −0.332057 | − | 0.575140i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 9.64405i | 0.792736i | ||||||||
\(149\) | −2.62042 | − | 1.51290i | −0.214673 | − | 0.123941i | 0.388808 | − | 0.921319i | \(-0.372887\pi\) |
−0.603481 | + | 0.797377i | \(0.706220\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 1.27030i | − | 0.103376i | −0.998663 | − | 0.0516879i | \(-0.983540\pi\) | ||
0.998663 | − | 0.0516879i | \(-0.0164601\pi\) | |||||||
\(152\) | 3.28149 | − | 5.68371i | 0.266164 | − | 0.461010i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 3.84935 | − | 2.22243i | 0.310190 | − | 0.179088i | ||||
\(155\) | −9.07754 | −0.729126 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −4.11859 | −0.328699 | −0.164350 | − | 0.986402i | \(-0.552553\pi\) | ||||
−0.164350 | + | 0.986402i | \(0.552553\pi\) | |||||||
\(158\) | 9.30143 | − | 5.37018i | 0.739982 | − | 0.427229i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0.573878 | − | 0.993985i | 0.0453690 | − | 0.0785814i | ||||
\(161\) | − | 2.08000i | − | 0.163927i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −9.71606 | − | 5.60957i | −0.761021 | − | 0.439376i | 0.0686413 | − | 0.997641i | \(-0.478134\pi\) |
−0.829662 | + | 0.558266i | \(0.811467\pi\) | |||||||
\(164\) | − | 9.49471i | − | 0.741412i | ||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −7.67396 | − | 13.2917i | −0.595615 | − | 1.03164i | ||||
\(167\) | 3.46184 | − | 1.99869i | 0.267885 | − | 0.154664i | −0.360041 | − | 0.932936i | \(-0.617237\pi\) |
0.627926 | + | 0.778273i | \(0.283904\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 12.1117 | + | 4.72294i | 0.931671 | + | 0.363303i | ||||
\(170\) | −3.11014 | −0.238537 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 1.70160 | + | 2.94725i | 0.129746 | + | 0.224726i | ||||
\(173\) | 6.08396 | − | 10.5377i | 0.462555 | − | 0.801168i | −0.536533 | − | 0.843879i | \(-0.680266\pi\) |
0.999087 | + | 0.0427113i | \(0.0135996\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −3.18927 | − | 1.84133i | −0.241087 | − | 0.139191i | ||||
\(176\) | 3.84935 | + | 2.22243i | 0.290156 | + | 0.167522i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −5.42978 | + | 9.40465i | −0.406979 | + | 0.704909i | ||||
\(179\) | 5.93554 | + | 10.2806i | 0.443643 | + | 0.768412i | 0.997957 | − | 0.0638960i | \(-0.0203526\pi\) |
−0.554314 | + | 0.832308i | \(0.687019\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −4.79134 | −0.356137 | −0.178069 | − | 0.984018i | \(-0.556985\pi\) | ||||
−0.178069 | + | 0.984018i | \(0.556985\pi\) | |||||||
\(182\) | 3.54343 | + | 0.666437i | 0.262656 | + | 0.0493996i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 1.80133 | − | 1.04000i | 0.132796 | − | 0.0766697i | ||||
\(185\) | −5.53450 | − | 9.58604i | −0.406905 | − | 0.704780i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 12.0445i | − | 0.880779i | ||||||
\(188\) | 1.45003 | + | 0.837173i | 0.105754 | + | 0.0610571i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 7.53270i | 0.546479i | ||||||||
\(191\) | 7.79263 | − | 13.4972i | 0.563855 | − | 0.976625i | −0.433300 | − | 0.901250i | \(-0.642651\pi\) |
0.997155 | − | 0.0753756i | \(-0.0240156\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −15.2295 | + | 8.79275i | −1.09624 | + | 0.632916i | −0.935231 | − | 0.354037i | \(-0.884809\pi\) |
−0.161011 | + | 0.986953i | \(0.551475\pi\) | |||||||
\(194\) | 2.12694 | 0.152705 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.00000 | 0.0714286 | ||||||||
\(197\) | 0.458833 | − | 0.264907i | 0.0326905 | − | 0.0188739i | −0.483566 | − | 0.875308i | \(-0.660659\pi\) |
0.516256 | + | 0.856434i | \(0.327325\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 12.5732 | − | 21.7775i | 0.891294 | − | 1.54377i | 0.0529680 | − | 0.998596i | \(-0.483132\pi\) |
0.838326 | − | 0.545170i | \(-0.183535\pi\) | |||||||
\(200\) | − | 3.68266i | − | 0.260403i | ||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 5.21251 | + | 3.00944i | 0.366751 | + | 0.211744i | ||||
\(203\) | − | 7.19919i | − | 0.505284i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 5.44880 | + | 9.43760i | 0.380561 | + | 0.659150i | ||||
\(206\) | 4.98545 | − | 2.87835i | 0.347352 | − | 0.200544i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 1.19456 | + | 3.40191i | 0.0828279 | + | 0.235880i | ||||
\(209\) | −29.1715 | −2.01783 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2.72085 | − | 4.71265i | −0.187311 | − | 0.324432i | 0.757042 | − | 0.653366i | \(-0.226644\pi\) |
−0.944353 | + | 0.328934i | \(0.893311\pi\) | |||||||
\(212\) | −6.64077 | + | 11.5022i | −0.456090 | + | 0.789971i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −4.80589 | − | 2.77468i | −0.328524 | − | 0.189673i | ||||
\(215\) | −3.38273 | − | 1.95302i | −0.230700 | − | 0.133195i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 3.95448 | − | 6.84935i | 0.268447 | − | 0.464964i | ||||
\(218\) | 3.98493 | + | 6.90210i | 0.269893 | + | 0.467469i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −5.10160 | −0.343950 | ||||||||
\(221\) | 6.36485 | − | 7.41248i | 0.428146 | − | 0.498617i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 8.00684 | − | 4.62275i | 0.536177 | − | 0.309562i | −0.207351 | − | 0.978267i | \(-0.566484\pi\) |
0.743528 | + | 0.668704i | \(0.233151\pi\) | |||||||
\(224\) | 0.500000 | + | 0.866025i | 0.0334077 | + | 0.0578638i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 4.37070i | 0.290735i | ||||||||
\(227\) | 1.30318 | + | 0.752389i | 0.0864948 | + | 0.0499378i | 0.542624 | − | 0.839976i | \(-0.317431\pi\) |
−0.456129 | + | 0.889914i | \(0.650764\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 25.4380i | − | 1.68099i | −0.541818 | − | 0.840496i | \(-0.682264\pi\) | ||
0.541818 | − | 0.840496i | \(-0.317736\pi\) | |||||||
\(230\) | −1.19366 | + | 2.06749i | −0.0787079 | + | 0.136326i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 6.23469 | − | 3.59960i | 0.409327 | − | 0.236325i | ||||
\(233\) | −12.1004 | −0.792724 | −0.396362 | − | 0.918094i | \(-0.629727\pi\) | ||||
−0.396362 | + | 0.918094i | \(0.629727\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1.92174 | −0.125361 | ||||||||
\(236\) | −0.0586805 | + | 0.0338792i | −0.00381978 | + | 0.00220535i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 1.35488 | − | 2.34672i | 0.0878238 | − | 0.152115i | ||||
\(239\) | 5.57964i | 0.360917i | 0.983583 | + | 0.180458i | \(0.0577581\pi\) | ||||
−0.983583 | + | 0.180458i | \(0.942242\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 20.1291 | + | 11.6215i | 1.29663 | + | 0.748608i | 0.979820 | − | 0.199882i | \(-0.0640559\pi\) |
0.316807 | + | 0.948490i | \(0.397389\pi\) | |||||||
\(242\) | − | 8.75670i | − | 0.562902i | ||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 4.05023 | + | 7.01521i | 0.259290 | + | 0.449103i | ||||
\(245\) | −0.993985 | + | 0.573878i | −0.0635034 | + | 0.0366637i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −17.9529 | − | 15.4156i | −1.14231 | − | 0.980868i | ||||
\(248\) | 7.90895 | 0.502219 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 4.98278 | + | 8.63043i | 0.315139 | + | 0.545837i | ||||
\(251\) | 11.8707 | − | 20.5607i | 0.749273 | − | 1.29778i | −0.198898 | − | 0.980020i | \(-0.563736\pi\) |
0.948171 | − | 0.317760i | \(-0.102930\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −8.00664 | − | 4.62264i | −0.503373 | − | 0.290623i | ||||
\(254\) | 5.94522 | + | 3.43247i | 0.373036 | + | 0.215372i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | −3.50520 | − | 6.07118i | −0.218648 | − | 0.378710i | 0.735747 | − | 0.677257i | \(-0.236831\pi\) |
−0.954395 | + | 0.298547i | \(0.903498\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 9.64405 | 0.599252 | ||||||||
\(260\) | −3.13966 | − | 2.69592i | −0.194713 | − | 0.167194i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 14.0293 | − | 8.09980i | 0.866731 | − | 0.500407i | ||||
\(263\) | 15.4226 | + | 26.7127i | 0.950998 | + | 1.64718i | 0.743270 | + | 0.668991i | \(0.233274\pi\) |
0.207728 | + | 0.978187i | \(0.433393\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 15.2440i | − | 0.936429i | ||||||
\(266\) | −5.68371 | − | 3.28149i | −0.348491 | − | 0.201201i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0.513495i | 0.0313667i | ||||||||
\(269\) | −2.81595 | + | 4.87737i | −0.171692 | + | 0.297379i | −0.939011 | − | 0.343886i | \(-0.888257\pi\) |
0.767320 | + | 0.641265i | \(0.221590\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2.60224 | + | 1.50240i | −0.158075 | + | 0.0912645i | −0.576951 | − | 0.816779i | \(-0.695758\pi\) |
0.418876 | + | 0.908043i | \(0.362424\pi\) | |||||||
\(272\) | 2.70976 | 0.164303 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −5.20224 | −0.314279 | ||||||||
\(275\) | −14.1759 | + | 8.18443i | −0.854836 | + | 0.493540i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −12.0866 | + | 20.9346i | −0.726214 | + | 1.25784i | 0.232259 | + | 0.972654i | \(0.425388\pi\) |
−0.958473 | + | 0.285185i | \(0.907945\pi\) | |||||||
\(278\) | 5.74027i | 0.344278i | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −0.993985 | − | 0.573878i | −0.0594020 | − | 0.0342958i | ||||
\(281\) | − | 1.74575i | − | 0.104143i | −0.998643 | − | 0.0520713i | \(-0.983418\pi\) | ||
0.998643 | − | 0.0520713i | \(-0.0165823\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 13.0572 | + | 22.6156i | 0.776167 | + | 1.34436i | 0.934136 | + | 0.356917i | \(0.116172\pi\) |
−0.157969 | + | 0.987444i | \(0.550495\pi\) | |||||||
\(284\) | −9.34208 | + | 5.39365i | −0.554350 | + | 0.320054i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 10.4404 | − | 12.1588i | 0.617351 | − | 0.718964i | ||||
\(287\) | −9.49471 | −0.560455 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 4.82861 | + | 8.36339i | 0.284036 | + | 0.491964i | ||||
\(290\) | −4.13146 | + | 7.15589i | −0.242608 | + | 0.420209i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −6.94944 | − | 4.01226i | −0.406685 | − | 0.234800i | ||||
\(293\) | 4.89767 | + | 2.82767i | 0.286125 | + | 0.165194i | 0.636193 | − | 0.771530i | \(-0.280508\pi\) |
−0.350068 | + | 0.936724i | \(0.613841\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0.0388851 | − | 0.0673509i | 0.00226398 | − | 0.00392132i | ||||
\(296\) | 4.82202 | + | 8.35199i | 0.280274 | + | 0.485449i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −3.02580 | −0.175280 | ||||||||
\(299\) | −2.48468 | − | 7.07597i | −0.143693 | − | 0.409214i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.94725 | − | 1.70160i | 0.169877 | − | 0.0980785i | ||||
\(302\) | −0.635151 | − | 1.10011i | −0.0365489 | − | 0.0633045i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | − | 6.56298i | − | 0.376413i | ||||||
\(305\) | −8.05174 | − | 4.64868i | −0.461041 | − | 0.266182i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 20.4767i | − | 1.16867i | −0.811514 | − | 0.584333i | \(-0.801356\pi\) | ||
0.811514 | − | 0.584333i | \(-0.198644\pi\) | |||||||
\(308\) | 2.22243 | − | 3.84935i | 0.126634 | − | 0.219337i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −7.86138 | + | 4.53877i | −0.446497 | + | 0.257785i | ||||
\(311\) | −1.23712 | −0.0701506 | −0.0350753 | − | 0.999385i | \(-0.511167\pi\) | ||||
−0.0350753 | + | 0.999385i | \(0.511167\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −9.01151 | −0.509361 | −0.254680 | − | 0.967025i | \(-0.581970\pi\) | ||||
−0.254680 | + | 0.967025i | \(0.581970\pi\) | |||||||
\(314\) | −3.56680 | + | 2.05930i | −0.201286 | + | 0.116213i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 5.37018 | − | 9.30143i | 0.302096 | − | 0.523246i | ||||
\(317\) | 0.580644i | 0.0326122i | 0.999867 | + | 0.0163061i | \(0.00519062\pi\) | ||||
−0.999867 | + | 0.0163061i | \(0.994809\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −27.7122 | − | 15.9997i | −1.55159 | − | 0.895810i | ||||
\(320\) | − | 1.14776i | − | 0.0641615i | ||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −1.04000 | − | 1.80133i | −0.0579569 | − | 0.100384i | ||||
\(323\) | −15.4015 | + | 8.89204i | −0.856961 | + | 0.494767i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −13.0492 | − | 2.45426i | −0.723841 | − | 0.136138i | ||||
\(326\) | −11.2191 | −0.621371 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −4.74735 | − | 8.22266i | −0.262129 | − | 0.454020i | ||||
\(329\) | 0.837173 | − | 1.45003i | 0.0461549 | − | 0.0799426i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −27.1632 | − | 15.6827i | −1.49303 | − | 0.861999i | −0.493058 | − | 0.869996i | \(-0.664121\pi\) |
−0.999968 | + | 0.00799735i | \(0.997454\pi\) | |||||||
\(332\) | −13.2917 | − | 7.67396i | −0.729477 | − | 0.421163i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 1.99869 | − | 3.46184i | 0.109364 | − | 0.189423i | ||||
\(335\) | −0.294683 | − | 0.510406i | −0.0161003 | − | 0.0278865i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 9.43033 | 0.513703 | 0.256851 | − | 0.966451i | \(-0.417315\pi\) | ||||
0.256851 | + | 0.966451i | \(0.417315\pi\) | |||||||
\(338\) | 12.8505 | − | 1.96567i | 0.698977 | − | 0.106919i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −2.69346 | + | 1.55507i | −0.146073 | + | 0.0843355i | ||||
\(341\) | −17.5771 | − | 30.4444i | −0.951851 | − | 1.64865i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 1.00000i | − | 0.0539949i | ||||||
\(344\) | 2.94725 | + | 1.70160i | 0.158905 | + | 0.0917440i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | − | 12.1679i | − | 0.654151i | ||||||
\(347\) | 3.23650 | − | 5.60578i | 0.173744 | − | 0.300934i | −0.765982 | − | 0.642862i | \(-0.777747\pi\) |
0.939726 | + | 0.341928i | \(0.111080\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 8.57811 | − | 4.95258i | 0.459176 | − | 0.265105i | −0.252522 | − | 0.967591i | \(-0.581260\pi\) |
0.711698 | + | 0.702486i | \(0.247927\pi\) | |||||||
\(350\) | −3.68266 | −0.196846 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 4.44485 | 0.236911 | ||||||||
\(353\) | −24.9206 | + | 14.3879i | −1.32639 | + | 0.765790i | −0.984739 | − | 0.174037i | \(-0.944319\pi\) |
−0.341649 | + | 0.939828i | \(0.610985\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 6.19059 | − | 10.7224i | 0.328562 | − | 0.569087i | ||||
\(356\) | 10.8596i | 0.575555i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 10.2806 | + | 5.93554i | 0.543349 | + | 0.313703i | ||||
\(359\) | − | 12.1382i | − | 0.640631i | −0.947311 | − | 0.320315i | \(-0.896211\pi\) | ||
0.947311 | − | 0.320315i | \(-0.103789\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 12.0364 | + | 20.8476i | 0.633493 | + | 1.09724i | ||||
\(362\) | −4.14942 | + | 2.39567i | −0.218089 | + | 0.125914i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 3.40191 | − | 1.19456i | 0.178309 | − | 0.0626120i | ||||
\(365\) | 9.21019 | 0.482083 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 13.5388 | + | 23.4498i | 0.706717 | + | 1.22407i | 0.966068 | + | 0.258287i | \(0.0831580\pi\) |
−0.259351 | + | 0.965783i | \(0.583509\pi\) | |||||||
\(368\) | 1.04000 | − | 1.80133i | 0.0542137 | − | 0.0939008i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −9.58604 | − | 5.53450i | −0.498354 | − | 0.287725i | ||||
\(371\) | 11.5022 | + | 6.64077i | 0.597162 | + | 0.344772i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 7.81661 | − | 13.5388i | 0.404729 | − | 0.701010i | −0.589561 | − | 0.807724i | \(-0.700699\pi\) |
0.994290 | + | 0.106713i | \(0.0340327\pi\) | |||||||
\(374\) | −6.02223 | − | 10.4308i | −0.311402 | − | 0.539365i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 1.67435 | 0.0863478 | ||||||||
\(377\) | −8.59987 | − | 24.4910i | −0.442916 | − | 1.26135i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −32.3295 | + | 18.6654i | −1.66065 | + | 0.958778i | −0.688249 | + | 0.725475i | \(0.741620\pi\) |
−0.972404 | + | 0.233304i | \(0.925046\pi\) | |||||||
\(380\) | 3.76635 | + | 6.52351i | 0.193210 | + | 0.334649i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | − | 15.5853i | − | 0.797411i | ||||||
\(383\) | 32.8193 | + | 18.9482i | 1.67699 | + | 0.968209i | 0.963565 | + | 0.267473i | \(0.0861886\pi\) |
0.713421 | + | 0.700736i | \(0.247145\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 5.10160i | 0.260002i | ||||||||
\(386\) | −8.79275 | + | 15.2295i | −0.447539 | + | 0.775160i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 1.84198 | − | 1.06347i | 0.0935124 | − | 0.0539894i | ||||
\(389\) | 10.1053 | 0.512361 | 0.256180 | − | 0.966629i | \(-0.417536\pi\) | ||||
0.256180 | + | 0.966629i | \(0.417536\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −5.63629 | −0.285039 | ||||||||
\(392\) | 0.866025 | − | 0.500000i | 0.0437409 | − | 0.0252538i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0.264907 | − | 0.458833i | 0.0133458 | − | 0.0231157i | ||||
\(395\) | 12.3273i | 0.620254i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 4.77041 | + | 2.75419i | 0.239420 | + | 0.138229i | 0.614910 | − | 0.788597i | \(-0.289192\pi\) |
−0.375490 | + | 0.926826i | \(0.622526\pi\) | |||||||
\(398\) | − | 25.1465i | − | 1.26048i | ||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −1.84133 | − | 3.18927i | −0.0920664 | − | 0.159464i | ||||
\(401\) | 23.1657 | − | 13.3747i | 1.15684 | − | 0.667903i | 0.206296 | − | 0.978490i | \(-0.433859\pi\) |
0.950545 | + | 0.310587i | \(0.100526\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 5.27082 | − | 28.0248i | 0.262558 | − | 1.39601i | ||||
\(404\) | 6.01888 | 0.299451 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −3.59960 | − | 6.23469i | −0.178645 | − | 0.309422i | ||||
\(407\) | 21.4332 | − | 37.1233i | 1.06240 | − | 1.84014i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −27.7124 | − | 15.9998i | −1.37029 | − | 0.791137i | −0.379325 | − | 0.925264i | \(-0.623844\pi\) |
−0.990964 | + | 0.134127i | \(0.957177\pi\) | |||||||
\(410\) | 9.43760 | + | 5.44880i | 0.466090 | + | 0.269097i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 2.87835 | − | 4.98545i | 0.141806 | − | 0.245615i | ||||
\(413\) | 0.0338792 | + | 0.0586805i | 0.00166709 | + | 0.00288748i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 17.6157 | 0.864719 | ||||||||
\(416\) | 2.73548 | + | 2.34886i | 0.134118 | + | 0.115163i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −25.2632 | + | 14.5857i | −1.23567 | + | 0.713412i | ||||
\(419\) | 5.84782 | + | 10.1287i | 0.285685 | + | 0.494821i | 0.972775 | − | 0.231751i | \(-0.0744456\pi\) |
−0.687090 | + | 0.726572i | \(0.741112\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 25.8565i | 1.26017i | 0.776527 | + | 0.630084i | \(0.216979\pi\) | ||||
−0.776527 | + | 0.630084i | \(0.783021\pi\) | |||||||
\(422\) | −4.71265 | − | 2.72085i | −0.229408 | − | 0.132449i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 13.2815i | 0.645009i | ||||||||
\(425\) | −4.98956 | + | 8.64216i | −0.242029 | + | 0.419206i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 7.01521 | − | 4.05023i | 0.339490 | − | 0.196004i | ||||
\(428\) | −5.54937 | −0.268239 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −3.90604 | −0.188366 | ||||||||
\(431\) | −9.27186 | + | 5.35311i | −0.446610 | + | 0.257850i | −0.706397 | − | 0.707816i | \(-0.749681\pi\) |
0.259788 | + | 0.965666i | \(0.416347\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 11.2150 | − | 19.4249i | 0.538956 | − | 0.933500i | −0.460004 | − | 0.887917i | \(-0.652152\pi\) |
0.998961 | − | 0.0455830i | \(-0.0145146\pi\) | |||||||
\(434\) | − | 7.90895i | − | 0.379642i | ||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 6.90210 | + | 3.98493i | 0.330551 | + | 0.190843i | ||||
\(437\) | 13.6510i | 0.653015i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −6.35913 | − | 11.0143i | −0.303505 | − | 0.525686i | 0.673423 | − | 0.739258i | \(-0.264823\pi\) |
−0.976927 | + | 0.213572i | \(0.931490\pi\) | |||||||
\(440\) | −4.41812 | + | 2.55080i | −0.210625 | + | 0.121605i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 1.80588 | − | 9.60182i | 0.0858972 | − | 0.456712i | ||||
\(443\) | 7.86448 | 0.373653 | 0.186826 | − | 0.982393i | \(-0.440180\pi\) | ||||
0.186826 | + | 0.982393i | \(0.440180\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −6.23206 | − | 10.7942i | −0.295428 | − | 0.511696i | ||||
\(446\) | 4.62275 | − | 8.00684i | 0.218893 | − | 0.379135i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0.866025 | + | 0.500000i | 0.0409159 | + | 0.0236228i | ||||
\(449\) | 14.5815 | + | 8.41864i | 0.688144 | + | 0.397300i | 0.802916 | − | 0.596092i | \(-0.203280\pi\) |
−0.114772 | + | 0.993392i | \(0.536614\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −21.1013 | + | 36.5485i | −0.993620 | + | 1.72100i | ||||
\(452\) | 2.18535 | + | 3.78514i | 0.102790 | + | 0.178038i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 1.50478 | 0.0706227 | ||||||||
\(455\) | −2.69592 | + | 3.13966i | −0.126387 | + | 0.147189i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 7.96539 | − | 4.59882i | 0.372605 | − | 0.215124i | −0.301991 | − | 0.953311i | \(-0.597651\pi\) |
0.674596 | + | 0.738187i | \(0.264318\pi\) | |||||||
\(458\) | −12.7190 | − | 22.0300i | −0.594320 | − | 1.02939i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 2.38733i | 0.111310i | ||||||||
\(461\) | 18.8812 | + | 10.9010i | 0.879383 | + | 0.507712i | 0.870455 | − | 0.492248i | \(-0.163825\pi\) |
0.00892828 | + | 0.999960i | \(0.497158\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 26.0636i | 1.21128i | 0.795740 | + | 0.605638i | \(0.207082\pi\) | ||||
−0.795740 | + | 0.605638i | \(0.792918\pi\) | |||||||
\(464\) | 3.59960 | − | 6.23469i | 0.167107 | − | 0.289438i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −10.4793 | + | 6.05020i | −0.485442 | + | 0.280270i | ||||
\(467\) | −28.6668 | −1.32654 | −0.663271 | − | 0.748379i | \(-0.730832\pi\) | ||||
−0.663271 | + | 0.748379i | \(0.730832\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0.513495 | 0.0237110 | ||||||||
\(470\) | −1.66428 | + | 0.960870i | −0.0767673 | + | 0.0443216i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −0.0338792 | + | 0.0586805i | −0.00155942 | + | 0.00270099i | ||||
\(473\) | − | 15.1267i | − | 0.695526i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 20.9312 | + | 12.0846i | 0.960387 | + | 0.554480i | ||||
\(476\) | − | 2.70976i | − | 0.124202i | ||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 2.78982 | + | 4.83211i | 0.127603 | + | 0.221015i | ||||
\(479\) | 15.5679 | − | 8.98812i | 0.711315 | − | 0.410678i | −0.100233 | − | 0.994964i | \(-0.531959\pi\) |
0.811548 | + | 0.584286i | \(0.198625\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 32.8082 | − | 11.5204i | 1.49593 | − | 0.525285i | ||||
\(482\) | 23.2430 | 1.05869 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −4.37835 | − | 7.58352i | −0.199016 | − | 0.344706i | ||||
\(485\) | −1.22060 | + | 2.11414i | −0.0554247 | + | 0.0959983i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 18.9847 | + | 10.9608i | 0.860278 | + | 0.496681i | 0.864105 | − | 0.503311i | \(-0.167885\pi\) |
−0.00382768 | + | 0.999993i | \(0.501218\pi\) | |||||||
\(488\) | 7.01521 | + | 4.05023i | 0.317564 | + | 0.183345i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −0.573878 | + | 0.993985i | −0.0259252 | + | 0.0449037i | ||||
\(491\) | 10.8003 | + | 18.7067i | 0.487411 | + | 0.844221i | 0.999895 | − | 0.0144759i | \(-0.00460798\pi\) |
−0.512484 | + | 0.858697i | \(0.671275\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −19.5081 | −0.878599 | ||||||||
\(494\) | −23.2554 | − | 4.37382i | −1.04631 | − | 0.196787i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 6.84935 | − | 3.95448i | 0.307545 | − | 0.177561i | ||||
\(497\) | 5.39365 | + | 9.34208i | 0.241938 | + | 0.419049i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 38.6105i | − | 1.72844i | −0.503112 | − | 0.864221i | \(-0.667812\pi\) | ||
0.503112 | − | 0.864221i | \(-0.332188\pi\) | |||||||
\(500\) | 8.63043 | + | 4.98278i | 0.385965 | + | 0.222837i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | − | 23.7414i | − | 1.05963i | ||||||
\(503\) | −4.73503 | + | 8.20132i | −0.211125 | + | 0.365679i | −0.952067 | − | 0.305890i | \(-0.901046\pi\) |
0.740942 | + | 0.671569i | \(0.234379\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −5.98268 | + | 3.45410i | −0.266226 | + | 0.153706i | ||||
\(506\) | −9.24528 | −0.411003 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 6.86494 | 0.304583 | ||||||||
\(509\) | −11.3043 | + | 6.52651i | −0.501052 | + | 0.289283i | −0.729148 | − | 0.684356i | \(-0.760083\pi\) |
0.228096 | + | 0.973639i | \(0.426750\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −4.01226 | + | 6.94944i | −0.177492 | + | 0.307425i | ||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −6.07118 | − | 3.50520i | −0.267788 | − | 0.154608i | ||||
\(515\) | 6.60728i | 0.291152i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −3.72111 | − | 6.44515i | −0.163654 | − | 0.283457i | ||||
\(518\) | 8.35199 | − | 4.82202i | 0.366965 | − | 0.211868i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −4.06699 | − | 0.764907i | −0.178349 | − | 0.0335434i | ||||
\(521\) | −10.3444 | −0.453196 | −0.226598 | − | 0.973988i | \(-0.572760\pi\) | ||||
−0.226598 | + | 0.973988i | \(0.572760\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 1.06684 | + | 1.84782i | 0.0466497 | + | 0.0807996i | 0.888407 | − | 0.459056i | \(-0.151812\pi\) |
−0.841758 | + | 0.539855i | \(0.818479\pi\) | |||||||
\(524\) | 8.09980 | − | 14.0293i | 0.353841 | − | 0.612871i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 26.7127 | + | 15.4226i | 1.16473 | + | 0.672457i | ||||
\(527\) | −18.5601 | − | 10.7157i | −0.808490 | − | 0.466782i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 9.33681 | − | 16.1718i | 0.405948 | − | 0.703123i | ||||
\(530\) | −7.62198 | − | 13.2017i | −0.331078 | − | 0.573444i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −6.56298 | −0.284541 | ||||||||
\(533\) | −32.3002 | + | 11.3420i | −1.39908 | + | 0.491277i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 5.51599 | − | 3.18466i | 0.238477 | − | 0.137685i | ||||
\(536\) | 0.256747 | + | 0.444700i | 0.0110898 | + | 0.0192081i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 5.63191i | 0.242809i | ||||||||
\(539\) | −3.84935 | − | 2.22243i | −0.165803 | − | 0.0957266i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 8.41225i | 0.361671i | 0.983513 | + | 0.180836i | \(0.0578802\pi\) | ||||
−0.983513 | + | 0.180836i | \(0.942120\pi\) | |||||||
\(542\) | −1.50240 | + | 2.60224i | −0.0645338 | + | 0.111776i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 2.34672 | − | 1.35488i | 0.100615 | − | 0.0580900i | ||||
\(545\) | −9.14745 | −0.391834 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −1.00730 | −0.0430692 | −0.0215346 | − | 0.999768i | \(-0.506855\pi\) | ||||
−0.0215346 | + | 0.999768i | \(0.506855\pi\) | |||||||
\(548\) | −4.50527 | + | 2.60112i | −0.192456 | + | 0.111114i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −8.18443 | + | 14.1759i | −0.348985 | + | 0.604460i | ||||
\(551\) | 47.2482i | 2.01284i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −9.30143 | − | 5.37018i | −0.395537 | − | 0.228363i | ||||
\(554\) | 24.1732i | 1.02702i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 2.87013 | + | 4.97122i | 0.121721 | + | 0.210827i | ||||
\(557\) | −37.9237 | + | 21.8953i | −1.60688 | + | 0.927732i | −0.616816 | + | 0.787108i | \(0.711578\pi\) |
−0.990063 | + | 0.140624i | \(0.955089\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 7.99365 | − | 9.30937i | 0.338095 | − | 0.393744i | ||||
\(560\) | −1.14776 | −0.0485015 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −0.872873 | − | 1.51186i | −0.0368199 | − | 0.0637740i | ||||
\(563\) | −2.11334 | + | 3.66041i | −0.0890665 | + | 0.154268i | −0.907117 | − | 0.420879i | \(-0.861722\pi\) |
0.818050 | + | 0.575147i | \(0.195055\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −4.34441 | − | 2.50825i | −0.182771 | − | 0.105523i | ||||
\(566\) | 22.6156 | + | 13.0572i | 0.950607 | + | 0.548833i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −5.39365 | + | 9.34208i | −0.226313 | + | 0.391985i | ||||
\(569\) | −4.71320 | − | 8.16349i | −0.197587 | − | 0.342231i | 0.750158 | − | 0.661258i | \(-0.229977\pi\) |
−0.947746 | + | 0.319027i | \(0.896644\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 25.5304 | 1.06842 | 0.534208 | − | 0.845353i | \(-0.320610\pi\) | ||||
0.534208 | + | 0.845353i | \(0.320610\pi\) | |||||||
\(572\) | 2.96222 | − | 15.7500i | 0.123856 | − | 0.658540i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −8.22266 | + | 4.74735i | −0.343207 | + | 0.198151i | ||||
\(575\) | 3.82996 | + | 6.63368i | 0.159720 | + | 0.276644i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 31.7623i | − | 1.32228i | −0.750262 | − | 0.661141i | \(-0.770073\pi\) | ||
0.750262 | − | 0.661141i | \(-0.229927\pi\) | |||||||
\(578\) | 8.36339 | + | 4.82861i | 0.347871 | + | 0.200844i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 8.26291i | 0.343099i | ||||||||
\(581\) | −7.67396 | + | 13.2917i | −0.318370 | + | 0.551432i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 51.1254 | − | 29.5172i | 2.11740 | − | 1.22248i | ||||
\(584\) | −8.02452 | −0.332057 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 5.65535 | 0.233620 | ||||||||
\(587\) | 29.7429 | − | 17.1721i | 1.22762 | − | 0.708768i | 0.261090 | − | 0.965314i | \(-0.415918\pi\) |
0.966532 | + | 0.256546i | \(0.0825846\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −25.9532 | + | 44.9522i | −1.06938 | + | 1.85222i | ||||
\(590\) | − | 0.0777701i | − | 0.00320175i | ||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 8.35199 | + | 4.82202i | 0.343265 | + | 0.198184i | ||||
\(593\) | 15.1751i | 0.623168i | 0.950219 | + | 0.311584i | \(0.100860\pi\) | ||||
−0.950219 | + | 0.311584i | \(0.899140\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.55507 | + | 2.69346i | 0.0637516 | + | 0.110421i | ||||
\(596\) | −2.62042 | + | 1.51290i | −0.107336 | + | 0.0619707i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −5.68978 | − | 4.88563i | −0.232673 | − | 0.199788i | ||||
\(599\) | −7.48641 | −0.305886 | −0.152943 | − | 0.988235i | \(-0.548875\pi\) | ||||
−0.152943 | + | 0.988235i | \(0.548875\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −18.2071 | − | 31.5356i | −0.742683 | − | 1.28637i | −0.951269 | − | 0.308361i | \(-0.900219\pi\) |
0.208586 | − | 0.978004i | \(-0.433114\pi\) | |||||||
\(602\) | 1.70160 | − | 2.94725i | 0.0693520 | − | 0.120121i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −1.10011 | − | 0.635151i | −0.0447630 | − | 0.0258439i | ||||
\(605\) | 8.70403 | + | 5.02527i | 0.353869 | + | 0.204306i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −2.26168 | + | 3.91735i | −0.0917989 | + | 0.159000i | −0.908268 | − | 0.418389i | \(-0.862595\pi\) |
0.816469 | + | 0.577389i | \(0.195928\pi\) | |||||||
\(608\) | −3.28149 | − | 5.68371i | −0.133082 | − | 0.230505i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −9.29735 | −0.376439 | ||||||||
\(611\) | 1.11585 | − | 5.93292i | 0.0451424 | − | 0.240020i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −34.8434 | + | 20.1168i | −1.40731 | + | 0.812512i | −0.995128 | − | 0.0985892i | \(-0.968567\pi\) |
−0.412183 | + | 0.911101i | \(0.635234\pi\) | |||||||
\(614\) | −10.2383 | − | 17.7333i | −0.413186 | − | 0.715659i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | − | 4.44485i | − | 0.179088i | ||||||
\(617\) | 34.2107 | + | 19.7516i | 1.37727 | + | 0.795168i | 0.991830 | − | 0.127565i | \(-0.0407162\pi\) |
0.385440 | + | 0.922733i | \(0.374050\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 22.9229i | 0.921348i | 0.887569 | + | 0.460674i | \(0.152392\pi\) | ||||
−0.887569 | + | 0.460674i | \(0.847608\pi\) | |||||||
\(620\) | −4.53877 | + | 7.86138i | −0.182281 | + | 0.315721i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −1.07138 | + | 0.618559i | −0.0429583 | + | 0.0248020i | ||||
\(623\) | 10.8596 | 0.435079 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 6.97525 | 0.279010 | ||||||||
\(626\) | −7.80420 | + | 4.50576i | −0.311918 | + | 0.180086i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −2.05930 | + | 3.56680i | −0.0821748 | + | 0.142331i | ||||
\(629\) | − | 26.1330i | − | 1.04199i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 3.11897 | + | 1.80074i | 0.124164 | + | 0.0716862i | 0.560796 | − | 0.827954i | \(-0.310495\pi\) |
−0.436632 | + | 0.899640i | \(0.643829\pi\) | |||||||
\(632\) | − | 10.7404i | − | 0.427229i | ||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0.290322 | + | 0.502852i | 0.0115302 | + | 0.0199708i | ||||
\(635\) | −6.82365 | + | 3.93964i | −0.270788 | + | 0.156340i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.19456 | − | 3.40191i | −0.0473302 | − | 0.134789i | ||||
\(638\) | −31.9993 | −1.26687 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −0.573878 | − | 0.993985i | −0.0226845 | − | 0.0392907i | ||||
\(641\) | −2.60928 | + | 4.51940i | −0.103060 | + | 0.178506i | −0.912944 | − | 0.408085i | \(-0.866197\pi\) |
0.809884 | + | 0.586590i | \(0.199530\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 18.1006 | + | 10.4504i | 0.713820 | + | 0.412124i | 0.812474 | − | 0.582998i | \(-0.198120\pi\) |
−0.0986540 | + | 0.995122i | \(0.531454\pi\) | |||||||
\(644\) | −1.80133 | − | 1.04000i | −0.0709824 | − | 0.0409817i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −8.89204 | + | 15.4015i | −0.349853 | + | 0.605963i | ||||
\(647\) | 3.81055 | + | 6.60007i | 0.149808 | + | 0.259476i | 0.931156 | − | 0.364620i | \(-0.118801\pi\) |
−0.781348 | + | 0.624095i | \(0.785468\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0.301176 | 0.0118222 | ||||||||
\(650\) | −12.5281 | + | 4.39916i | −0.491392 | + | 0.172549i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −9.71606 | + | 5.60957i | −0.380510 | + | 0.219688i | ||||
\(653\) | −12.8910 | − | 22.3278i | −0.504462 | − | 0.873755i | −0.999987 | − | 0.00516051i | \(-0.998357\pi\) |
0.495524 | − | 0.868594i | \(-0.334976\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 18.5932i | 0.726495i | ||||||||
\(656\) | −8.22266 | − | 4.74735i | −0.321041 | − | 0.185353i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | − | 1.67435i | − | 0.0652728i | ||||||
\(659\) | 7.82964 | − | 13.5613i | 0.305000 | − | 0.528275i | −0.672262 | − | 0.740314i | \(-0.734677\pi\) |
0.977261 | + | 0.212039i | \(0.0680103\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −27.4434 | + | 15.8444i | −1.06742 | + | 0.616277i | −0.927476 | − | 0.373881i | \(-0.878027\pi\) |
−0.139947 | + | 0.990159i | \(0.544693\pi\) | |||||||
\(662\) | −31.3654 | −1.21905 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −15.3479 | −0.595615 | ||||||||
\(665\) | 6.52351 | − | 3.76635i | 0.252971 | − | 0.146053i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −7.48715 | + | 12.9681i | −0.289904 | + | 0.502128i | ||||
\(668\) | − | 3.99739i | − | 0.154664i | ||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −0.510406 | − | 0.294683i | −0.0197187 | − | 0.0113846i | ||||
\(671\) | − | 36.0054i | − | 1.38997i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 8.38642 | + | 14.5257i | 0.323273 | + | 0.559925i | 0.981161 | − | 0.193190i | \(-0.0618835\pi\) |
−0.657889 | + | 0.753115i | \(0.728550\pi\) | |||||||
\(674\) | 8.16690 | − | 4.71516i | 0.314577 | − | 0.181621i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 10.1460 | − | 8.12759i | 0.390233 | − | 0.312600i | ||||
\(677\) | 8.34791 | 0.320836 | 0.160418 | − | 0.987049i | \(-0.448716\pi\) | ||||
0.160418 | + | 0.987049i | \(0.448716\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1.06347 | − | 1.84198i | −0.0408122 | − | 0.0706887i | ||||
\(680\) | −1.55507 | + | 2.69346i | −0.0596342 | + | 0.103289i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −30.4444 | − | 17.5771i | −1.16577 | − | 0.673060i | ||||
\(683\) | 23.5376 | + | 13.5895i | 0.900642 | + | 0.519986i | 0.877408 | − | 0.479744i | \(-0.159270\pi\) |
0.0232337 | + | 0.999730i | \(0.492604\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 2.98545 | − | 5.17095i | 0.114068 | − | 0.197572i | ||||
\(686\) | −0.500000 | − | 0.866025i | −0.0190901 | − | 0.0330650i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 3.40320 | 0.129746 | ||||||||
\(689\) | 47.0622 | + | 8.85132i | 1.79293 | + | 0.337208i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 22.7403 | − | 13.1291i | 0.865080 | − | 0.499454i | −0.000629844 | − | 1.00000i | \(-0.500200\pi\) |
0.865710 | + | 0.500545i | \(0.166867\pi\) | |||||||
\(692\) | −6.08396 | − | 10.5377i | −0.231277 | − | 0.400584i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | − | 6.47300i | − | 0.245712i | ||||||
\(695\) | −5.70574 | − | 3.29421i | −0.216431 | − | 0.124957i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 25.7284i | 0.974531i | ||||||||
\(698\) | 4.95258 | − | 8.57811i | 0.187458 | − | 0.324686i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −3.18927 | + | 1.84133i | −0.120543 | + | 0.0695957i | ||||
\(701\) | 26.4443 | 0.998786 | 0.499393 | − | 0.866376i | \(-0.333556\pi\) | ||||
0.499393 | + | 0.866376i | \(0.333556\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −63.2937 | −2.38717 | ||||||||
\(704\) | 3.84935 | − | 2.22243i | 0.145078 | − | 0.0837608i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −14.3879 | + | 24.9206i | −0.541496 | + | 0.937898i | ||||
\(707\) | − | 6.01888i | − | 0.226363i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 10.0688 | + | 5.81322i | 0.378141 | + | 0.218320i | 0.677009 | − | 0.735975i | \(-0.263276\pi\) |
−0.298868 | + | 0.954294i | \(0.596609\pi\) | |||||||
\(710\) | − | 12.3812i | − | 0.464658i | ||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 5.42978 | + | 9.40465i | 0.203490 | + | 0.352454i | ||||
\(713\) | −14.2466 | + | 8.22530i | −0.533541 | + | 0.308040i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 6.09417 | + | 17.3552i | 0.227909 | + | 0.649048i | ||||
\(716\) | 11.8711 | 0.443643 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −6.06911 | − | 10.5120i | −0.226497 | − | 0.392305i | ||||
\(719\) | 22.4379 | − | 38.8636i | 0.836793 | − | 1.44937i | −0.0557687 | − | 0.998444i | \(-0.517761\pi\) |
0.892562 | − | 0.450925i | \(-0.148906\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −4.98545 | − | 2.87835i | −0.185668 | − | 0.107195i | ||||
\(722\) | 20.8476 | + | 12.0364i | 0.775867 | + | 0.447947i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −2.39567 | + | 4.14942i | −0.0890344 | + | 0.154212i | ||||
\(725\) | 13.2561 | + | 22.9602i | 0.492319 | + | 0.852721i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 19.5156 | 0.723793 | 0.361896 | − | 0.932218i | \(-0.382129\pi\) | ||||
0.361896 | + | 0.932218i | \(0.382129\pi\) | |||||||
\(728\) | 2.34886 | − | 2.73548i | 0.0870547 | − | 0.101384i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 7.97626 | − | 4.60509i | 0.295214 | − | 0.170442i | ||||
\(731\) | −4.61092 | − | 7.98635i | −0.170541 | − | 0.295386i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 10.7037i | − | 0.395349i | −0.980268 | − | 0.197675i | \(-0.936661\pi\) | ||
0.980268 | − | 0.197675i | \(-0.0633390\pi\) | |||||||
\(734\) | 23.4498 | + | 13.5388i | 0.865548 | + | 0.499725i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | − | 2.08000i | − | 0.0766697i | ||||||
\(737\) | 1.14120 | − | 1.97662i | 0.0420368 | − | 0.0728099i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 0.413619 | − | 0.238803i | 0.0152152 | − | 0.00878452i | −0.492373 | − | 0.870384i | \(-0.663870\pi\) |
0.507588 | + | 0.861600i | \(0.330537\pi\) | |||||||
\(740\) | −11.0690 | −0.406905 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 13.2815 | 0.487581 | ||||||||
\(743\) | −8.43019 | + | 4.86717i | −0.309274 | + | 0.178559i | −0.646601 | − | 0.762828i | \(-0.723810\pi\) |
0.337328 | + | 0.941387i | \(0.390477\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1.73644 | − | 3.00760i | 0.0636181 | − | 0.110190i | ||||
\(746\) | − | 15.6332i | − | 0.572373i | ||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −10.4308 | − | 6.02223i | −0.381388 | − | 0.220195i | ||||
\(749\) | 5.54937i | 0.202769i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 18.1084 | + | 31.3646i | 0.660784 | + | 1.14451i | 0.980410 | + | 0.196967i | \(0.0631093\pi\) |
−0.319626 | + | 0.947544i | \(0.603557\pi\) | |||||||
\(752\) | 1.45003 | − | 0.837173i | 0.0528770 | − | 0.0305286i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −19.6932 | − | 16.9099i | −0.717185 | − | 0.615823i | ||||
\(755\) | 1.45800 | 0.0530619 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −23.2347 | − | 40.2436i | −0.844479 | − | 1.46268i | −0.886073 | − | 0.463545i | \(-0.846577\pi\) |
0.0415945 | − | 0.999135i | \(-0.486756\pi\) | |||||||
\(758\) | −18.6654 | + | 32.3295i | −0.677959 | + | 1.17426i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 6.52351 | + | 3.76635i | 0.236632 | + | 0.136620i | ||||
\(761\) | −18.5037 | − | 10.6831i | −0.670760 | − | 0.387263i | 0.125605 | − | 0.992080i | \(-0.459913\pi\) |
−0.796365 | + | 0.604817i | \(0.793246\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 3.98493 | − | 6.90210i | 0.144264 | − | 0.249873i | ||||
\(764\) | −7.79263 | − | 13.4972i | −0.281927 | − | 0.488313i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 37.8964 | 1.36925 | ||||||||
\(767\) | 0.185352 | + | 0.159155i | 0.00669266 | + | 0.00574677i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −39.8297 | + | 22.9957i | −1.43630 | + | 0.829246i | −0.997590 | − | 0.0693848i | \(-0.977896\pi\) |
−0.438706 | + | 0.898631i | \(0.644563\pi\) | |||||||
\(770\) | 2.55080 | + | 4.41812i | 0.0919245 | + | 0.159218i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 17.5855i | 0.632916i | ||||||||
\(773\) | −17.2754 | − | 9.97393i | −0.621351 | − | 0.358737i | 0.156044 | − | 0.987750i | \(-0.450126\pi\) |
−0.777395 | + | 0.629013i | \(0.783459\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 29.1260i | 1.04624i | ||||||||
\(776\) | 1.06347 | − | 1.84198i | 0.0381763 | − | 0.0661233i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 8.75147 | − | 5.05267i | 0.313756 | − | 0.181147i | ||||
\(779\) | 62.3136 | 2.23262 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 47.9479 | 1.71571 | ||||||||
\(782\) | −4.88117 | + | 2.81814i | −0.174550 | + | 0.100777i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0.500000 | − | 0.866025i | 0.0178571 | − | 0.0309295i | ||||
\(785\) | − | 4.72714i | − | 0.168719i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 38.0726 | + | 21.9812i | 1.35714 | + | 0.783546i | 0.989238 | − | 0.146318i | \(-0.0467421\pi\) |
0.367904 | + | 0.929864i | \(0.380075\pi\) | |||||||
\(788\) | − | 0.529815i | − | 0.0188739i | ||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 6.16365 | + | 10.6758i | 0.219293 | + | 0.379827i | ||||
\(791\) | 3.78514 | − | 2.18535i | 0.134584 | − | 0.0777021i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 19.0269 | − | 22.1586i | 0.675665 | − | 0.786876i | ||||
\(794\) | 5.50839 | 0.195485 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −12.5732 | − | 21.7775i | −0.445647 | − | 0.771883i | ||||
\(797\) | −15.9862 | + | 27.6889i | −0.566260 | + | 0.980792i | 0.430671 | + | 0.902509i | \(0.358277\pi\) |
−0.996931 | + | 0.0782827i | \(0.975056\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −3.92922 | − | 2.26854i | −0.139006 | − | 0.0802551i | ||||
\(800\) | −3.18927 | − | 1.84133i | −0.112758 | − | 0.0651008i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 13.3747 | − | 23.1657i | 0.472278 | − | 0.818010i | ||||
\(803\) | 17.8339 | + | 30.8892i | 0.629345 | + | 1.09006i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 2.38733 | 0.0841423 | ||||||||
\(806\) | −9.44772 | − | 26.9056i | −0.332782 | − | 0.947709i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 5.21251 | − | 3.00944i | 0.183375 | − | 0.105872i | ||||
\(809\) | −14.0866 | − | 24.3986i | −0.495257 | − | 0.857811i | 0.504728 | − | 0.863279i | \(-0.331593\pi\) |
−0.999985 | + | 0.00546789i | \(0.998260\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 39.0534i | 1.37135i | 0.727908 | + | 0.685675i | \(0.240493\pi\) | ||||
−0.727908 | + | 0.685675i | \(0.759507\pi\) | |||||||
\(812\) | −6.23469 | − | 3.59960i | −0.218795 | − | 0.126321i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | − | 42.8663i | − | 1.50246i | ||||||
\(815\) | 6.43842 | − | 11.1517i | 0.225528 | − | 0.390626i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −19.3428 | + | 11.1676i | −0.676718 | + | 0.390703i | ||||
\(818\) | −31.9995 | −1.11884 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 10.8976 | 0.380561 | ||||||||
\(821\) | −20.4243 | + | 11.7920i | −0.712812 | + | 0.411542i | −0.812101 | − | 0.583516i | \(-0.801676\pi\) |
0.0992893 | + | 0.995059i | \(0.468343\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 12.3566 | − | 21.4023i | 0.430725 | − | 0.746038i | −0.566211 | − | 0.824260i | \(-0.691591\pi\) |
0.996936 | + | 0.0782228i | \(0.0249245\pi\) | |||||||
\(824\) | − | 5.75670i | − | 0.200544i | ||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0.0586805 | + | 0.0338792i | 0.00204176 | + | 0.00117881i | ||||
\(827\) | − | 45.2456i | − | 1.57334i | −0.617371 | − | 0.786672i | \(-0.711802\pi\) | ||
0.617371 | − | 0.786672i | \(-0.288198\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 22.4064 | + | 38.8091i | 0.778208 | + | 1.34790i | 0.932974 | + | 0.359945i | \(0.117204\pi\) |
−0.154765 | + | 0.987951i | \(0.549462\pi\) | |||||||
\(830\) | 15.2556 | − | 8.80783i | 0.529530 | − | 0.305724i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 3.54343 | + | 0.666437i | 0.122846 | + | 0.0231046i | ||||
\(833\) | −2.70976 | −0.0938875 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 2.29401 | + | 3.97334i | 0.0793875 | + | 0.137503i | ||||
\(836\) | −14.5857 | + | 25.2632i | −0.504458 | + | 0.873747i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 10.1287 | + | 5.84782i | 0.349891 | + | 0.202010i | ||||
\(839\) | 26.7511 | + | 15.4447i | 0.923550 | + | 0.533212i | 0.884766 | − | 0.466036i | \(-0.154318\pi\) |
0.0387839 | + | 0.999248i | \(0.487652\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −11.4142 | + | 19.7700i | −0.393593 | + | 0.681723i | ||||
\(842\) | 12.9282 | + | 22.3924i | 0.445536 | + | 0.771692i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −5.44170 | −0.187311 | ||||||||
\(845\) | −5.42078 | + | 13.9013i | −0.186481 | + | 0.478219i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −7.58352 | + | 4.37835i | −0.260573 | + | 0.150442i | ||||
\(848\) | 6.64077 | + | 11.5022i | 0.228045 | + | 0.394986i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 9.97911i | 0.342281i | ||||||||
\(851\) | −17.3721 | − | 10.0298i | −0.595508 | − | 0.343817i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 27.9201i | − | 0.955965i | −0.878369 | − | 0.477982i | \(-0.841368\pi\) | ||
0.878369 | − | 0.477982i | \(-0.158632\pi\) | |||||||
\(854\) | 4.05023 | − | 7.01521i | 0.138596 | − | 0.240055i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −4.80589 | + | 2.77468i | −0.164262 | + | 0.0948367i | ||||
\(857\) | 17.5921 | 0.600935 | 0.300468 | − | 0.953792i | \(-0.402857\pi\) | ||||
0.300468 | + | 0.953792i | \(0.402857\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 22.1337 | 0.755193 | 0.377596 | − | 0.925970i | \(-0.376751\pi\) | ||||
0.377596 | + | 0.925970i | \(0.376751\pi\) | |||||||
\(860\) | −3.38273 | + | 1.95302i | −0.115350 | + | 0.0665974i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −5.35311 | + | 9.27186i | −0.182328 | + | 0.315801i | ||||
\(863\) | 4.58867i | 0.156200i | 0.996946 | + | 0.0781000i | \(0.0248854\pi\) | ||||
−0.996946 | + | 0.0781000i | \(0.975115\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 12.0947 | + | 6.98289i | 0.411233 | + | 0.237426i | ||||
\(866\) | − | 22.4299i | − | 0.762199i | ||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −3.95448 | − | 6.84935i | −0.134224 | − | 0.232482i | ||||
\(869\) | −41.3434 | + | 23.8697i | −1.40248 | + | 0.809722i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.74687 | − | 0.613401i | 0.0591903 | − | 0.0207843i | ||||
\(872\) | 7.96986 | 0.269893 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 6.82549 | + | 11.8221i | 0.230876 | + | 0.399888i | ||||
\(875\) | 4.98278 | − | 8.63043i | 0.168449 | − | 0.291762i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −34.6248 | − | 19.9906i | −1.16920 | − | 0.675035i | −0.215705 | − | 0.976459i | \(-0.569205\pi\) |
−0.953490 | + | 0.301423i | \(0.902538\pi\) | |||||||
\(878\) | −11.0143 | − | 6.35913i | −0.371716 | − | 0.214610i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −2.55080 | + | 4.41812i | −0.0859875 | + | 0.148935i | ||||
\(881\) | 23.9548 | + | 41.4910i | 0.807058 | + | 1.39787i | 0.914893 | + | 0.403697i | \(0.132275\pi\) |
−0.107834 | + | 0.994169i | \(0.534392\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 34.0091 | 1.14450 | 0.572248 | − | 0.820080i | \(-0.306071\pi\) | ||||
0.572248 | + | 0.820080i | \(0.306071\pi\) | |||||||
\(884\) | −3.23697 | − | 9.21837i | −0.108871 | − | 0.310047i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 6.81084 | − | 3.93224i | 0.228815 | − | 0.132106i | ||||
\(887\) | 1.88672 | + | 3.26789i | 0.0633497 | + | 0.109725i | 0.895961 | − | 0.444133i | \(-0.146488\pi\) |
−0.832611 | + | 0.553858i | \(0.813155\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 6.86494i | − | 0.230243i | ||||||
\(890\) | −10.7942 | − | 6.23206i | −0.361824 | − | 0.208899i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | − | 9.24550i | − | 0.309562i | ||||||
\(893\) | −5.49435 | + | 9.51650i | −0.183862 | + | 0.318457i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −11.7997 | + | 6.81254i | −0.394419 | + | 0.227718i | ||||
\(896\) | 1.00000 | 0.0334077 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 16.8373 | 0.561867 | ||||||||
\(899\) | −49.3098 | + | 28.4690i | −1.64457 | + | 0.949496i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 17.9949 | − | 31.1681i | 0.599497 | − | 1.03836i | ||||
\(902\) | 42.2025i | 1.40519i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 3.78514 | + | 2.18535i | 0.125892 | + | 0.0726837i | ||||
\(905\) | − | 5.49929i | − | 0.182802i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 7.13753 | + | 12.3626i | 0.236998 | + | 0.410492i | 0.959851 | − | 0.280509i | \(-0.0905032\pi\) |
−0.722854 | + | 0.691001i | \(0.757170\pi\) | |||||||
\(908\) | 1.30318 | − | 0.752389i | 0.0432474 | − | 0.0249689i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −0.764907 | + | 4.06699i | −0.0253564 | + | 0.134819i | ||||
\(911\) | −17.4161 | −0.577020 | −0.288510 | − | 0.957477i | \(-0.593160\pi\) | ||||
−0.288510 | + | 0.957477i | \(0.593160\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 34.1096 | + | 59.0796i | 1.12886 | + | 1.95525i | ||||
\(914\) | 4.59882 | − | 7.96539i | 0.152115 | − | 0.263472i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −22.0300 | − | 12.7190i | −0.727891 | − | 0.420248i | ||||
\(917\) | −14.0293 | − | 8.09980i | −0.463287 | − | 0.267479i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −18.1179 | + | 31.3811i | −0.597654 | + | 1.03517i | 0.395512 | + | 0.918461i | \(0.370567\pi\) |
−0.993166 | + | 0.116707i | \(0.962766\pi\) | |||||||
\(920\) | 1.19366 | + | 2.06749i | 0.0393539 | + | 0.0681630i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 21.8021 | 0.718013 | ||||||||
\(923\) | 29.5084 | + | 25.3379i | 0.971281 | + | 0.834007i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −30.7575 | + | 17.7579i | −1.01130 | + | 0.583875i | ||||
\(926\) | 13.0318 | + | 22.5717i | 0.428251 | + | 0.741752i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | − | 7.19919i | − | 0.236325i | ||||||
\(929\) | 12.4656 | + | 7.19701i | 0.408983 | + | 0.236126i | 0.690353 | − | 0.723473i | \(-0.257455\pi\) |
−0.281370 | + | 0.959599i | \(0.590789\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 6.56298i | 0.215093i | ||||||||
\(932\) | −6.05020 | + | 10.4793i | −0.198181 | + | 0.343260i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −24.8262 | + | 14.3334i | −0.812338 | + | 0.469004i | ||||
\(935\) | 13.8241 | 0.452097 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −6.25633 | −0.204385 | −0.102193 | − | 0.994765i | \(-0.532586\pi\) | ||||
−0.102193 | + | 0.994765i | \(0.532586\pi\) | |||||||
\(938\) | 0.444700 | − | 0.256747i | 0.0145200 | − | 0.00838310i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −0.960870 | + | 1.66428i | −0.0313401 | + | 0.0542827i | ||||
\(941\) | 29.1506i | 0.950284i | 0.879909 | + | 0.475142i | \(0.157603\pi\) | ||||
−0.879909 | + | 0.475142i | \(0.842397\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 17.1031 | + | 9.87448i | 0.556954 | + | 0.321557i | ||||
\(944\) | 0.0677585i | 0.00220535i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −7.56335 | − | 13.1001i | −0.245906 | − | 0.425921i | ||||
\(947\) | 9.43915 | − | 5.44970i | 0.306731 | − | 0.177091i | −0.338732 | − | 0.940883i | \(-0.609998\pi\) |
0.645463 | + | 0.763792i | \(0.276665\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −5.34784 | + | 28.4343i | −0.173598 | + | 0.923016i | ||||
\(950\) | 24.1692 | 0.784153 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −1.35488 | − | 2.34672i | −0.0439119 | − | 0.0760576i | ||||
\(953\) | −13.7652 | + | 23.8421i | −0.445900 | + | 0.772321i | −0.998114 | − | 0.0613812i | \(-0.980449\pi\) |
0.552215 | + | 0.833702i | \(0.313783\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 15.4915 | + | 8.94403i | 0.501294 | + | 0.289422i | ||||
\(956\) | 4.83211 | + | 2.78982i | 0.156282 | + | 0.0902292i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 8.98812 | − | 15.5679i | 0.290393 | − | 0.502975i | ||||
\(959\) | 2.60112 | + | 4.50527i | 0.0839945 | + | 0.145483i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −31.5515 | −1.01779 | ||||||||
\(962\) | 22.6526 | − | 26.3811i | 0.730348 | − | 0.850560i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 20.1291 | − | 11.6215i | 0.648314 | − | 0.374304i | ||||
\(965\) | −10.0919 | − | 17.4797i | −0.324870 | − | 0.562692i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 21.0297i | − | 0.676271i | −0.941097 | − | 0.338135i | \(-0.890204\pi\) | ||
0.941097 | − | 0.338135i | \(-0.109796\pi\) | |||||||
\(968\) | −7.58352 | − | 4.37835i | −0.243744 | − | 0.140725i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 2.44120i | 0.0783823i | ||||||||
\(971\) | 2.18410 | − | 3.78297i | 0.0700911 | − | 0.121401i | −0.828850 | − | 0.559471i | \(-0.811004\pi\) |
0.898941 | + | 0.438070i | \(0.144338\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 4.97122 | − | 2.87013i | 0.159370 | − | 0.0920123i | ||||
\(974\) | 21.9216 | 0.702414 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 8.10046 | 0.259290 | ||||||||
\(977\) | 46.8829 | − | 27.0679i | 1.49992 | − | 0.865978i | 0.499918 | − | 0.866073i | \(-0.333363\pi\) |
1.00000 | 9.46999e-5i | \(3.01439e-5\pi\) | ||||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 24.1346 | − | 41.8023i | 0.771344 | − | 1.33601i | ||||
\(980\) | 1.14776i | 0.0366637i | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 18.7067 | + | 10.8003i | 0.596954 | + | 0.344652i | ||||
\(983\) | 44.3574i | 1.41478i | 0.706823 | + | 0.707391i | \(0.250128\pi\) | ||||
−0.706823 | + | 0.707391i | \(0.749872\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0.304049 | + | 0.526628i | 0.00968780 | + | 0.0167798i | ||||
\(986\) | −16.8945 | + | 9.75404i | −0.538030 | + | 0.310632i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −22.3267 | + | 7.83988i | −0.710307 | + | 0.249420i | ||||
\(989\) | −7.07864 | −0.225088 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −13.6936 | − | 23.7181i | −0.434992 | − | 0.753429i | 0.562303 | − | 0.826932i | \(-0.309916\pi\) |
−0.997295 | + | 0.0735026i | \(0.976582\pi\) | |||||||
\(992\) | 3.95448 | − | 6.84935i | 0.125555 | − | 0.217467i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 9.34208 | + | 5.39365i | 0.296313 | + | 0.171076i | ||||
\(995\) | 24.9952 | + | 14.4310i | 0.792402 | + | 0.457494i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 22.9017 | − | 39.6669i | 0.725303 | − | 1.25626i | −0.233546 | − | 0.972346i | \(-0.575033\pi\) |
0.958849 | − | 0.283916i | \(-0.0916338\pi\) | |||||||
\(998\) | −19.3052 | − | 33.4377i | −0.611097 | − | 1.05845i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1638.2.bj.g.127.5 | 12 | ||
3.2 | odd | 2 | 182.2.m.b.127.2 | yes | 12 | ||
12.11 | even | 2 | 1456.2.cc.d.673.4 | 12 | |||
13.4 | even | 6 | inner | 1638.2.bj.g.1135.5 | 12 | ||
21.2 | odd | 6 | 1274.2.v.e.361.5 | 12 | |||
21.5 | even | 6 | 1274.2.v.d.361.5 | 12 | |||
21.11 | odd | 6 | 1274.2.o.d.569.2 | 12 | |||
21.17 | even | 6 | 1274.2.o.e.569.2 | 12 | |||
21.20 | even | 2 | 1274.2.m.c.491.2 | 12 | |||
39.2 | even | 12 | 2366.2.a.bf.1.4 | 6 | |||
39.11 | even | 12 | 2366.2.a.bh.1.4 | 6 | |||
39.17 | odd | 6 | 182.2.m.b.43.2 | ✓ | 12 | ||
39.23 | odd | 6 | 2366.2.d.r.337.10 | 12 | |||
39.29 | odd | 6 | 2366.2.d.r.337.4 | 12 | |||
156.95 | even | 6 | 1456.2.cc.d.225.4 | 12 | |||
273.17 | even | 6 | 1274.2.v.d.667.5 | 12 | |||
273.95 | odd | 6 | 1274.2.v.e.667.5 | 12 | |||
273.173 | even | 6 | 1274.2.o.e.459.5 | 12 | |||
273.212 | odd | 6 | 1274.2.o.d.459.5 | 12 | |||
273.251 | even | 6 | 1274.2.m.c.589.2 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
182.2.m.b.43.2 | ✓ | 12 | 39.17 | odd | 6 | ||
182.2.m.b.127.2 | yes | 12 | 3.2 | odd | 2 | ||
1274.2.m.c.491.2 | 12 | 21.20 | even | 2 | |||
1274.2.m.c.589.2 | 12 | 273.251 | even | 6 | |||
1274.2.o.d.459.5 | 12 | 273.212 | odd | 6 | |||
1274.2.o.d.569.2 | 12 | 21.11 | odd | 6 | |||
1274.2.o.e.459.5 | 12 | 273.173 | even | 6 | |||
1274.2.o.e.569.2 | 12 | 21.17 | even | 6 | |||
1274.2.v.d.361.5 | 12 | 21.5 | even | 6 | |||
1274.2.v.d.667.5 | 12 | 273.17 | even | 6 | |||
1274.2.v.e.361.5 | 12 | 21.2 | odd | 6 | |||
1274.2.v.e.667.5 | 12 | 273.95 | odd | 6 | |||
1456.2.cc.d.225.4 | 12 | 156.95 | even | 6 | |||
1456.2.cc.d.673.4 | 12 | 12.11 | even | 2 | |||
1638.2.bj.g.127.5 | 12 | 1.1 | even | 1 | trivial | ||
1638.2.bj.g.1135.5 | 12 | 13.4 | even | 6 | inner | ||
2366.2.a.bf.1.4 | 6 | 39.2 | even | 12 | |||
2366.2.a.bh.1.4 | 6 | 39.11 | even | 12 | |||
2366.2.d.r.337.4 | 12 | 39.29 | odd | 6 | |||
2366.2.d.r.337.10 | 12 | 39.23 | odd | 6 |