Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [968,2,Mod(9,968)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(968, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 0, 6]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("968.9");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 968 = 2^{3} \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 968.i (of order \(5\), 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: | \(7.72951891566\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\zeta_{10})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} + x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 88) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 81.1 | ||
Root | \(0.809017 - 0.587785i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 968.81 |
Dual form | 968.2.i.i.729.1 |
$q$-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 \(\left(\mathbb{Z}/968\mathbb{Z}\right)^\times\).
\(n\) | \(485\) | \(727\) | \(849\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{1}{5}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −0.927051 | + | 2.85317i | −0.535233 | + | 1.64728i | 0.207912 | + | 0.978148i | \(0.433333\pi\) |
−0.743145 | + | 0.669131i | \(0.766667\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.42705 | − | 1.76336i | 1.08541 | − | 0.788597i | 0.106792 | − | 0.994281i | \(-0.465942\pi\) |
0.978618 | + | 0.205685i | \(0.0659421\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.618034 | + | 1.90211i | 0.233595 | + | 0.718931i | 0.997305 | + | 0.0733714i | \(0.0233759\pi\) |
−0.763710 | + | 0.645560i | \(0.776624\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −4.85410 | − | 3.52671i | −1.61803 | − | 1.17557i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0 | 0 | 0.587785 | − | 0.809017i | \(-0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.78115 | + | 8.55951i | 0.718091 | + | 2.21006i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −4.85410 | + | 3.52671i | −1.17729 | + | 0.855353i | −0.991864 | − | 0.127304i | \(-0.959367\pi\) |
−0.185429 | + | 0.982658i | \(0.559367\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.23607 | + | 3.80423i | −0.283573 | + | 0.872749i | 0.703249 | + | 0.710943i | \(0.251732\pi\) |
−0.986823 | + | 0.161806i | \(0.948268\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −6.00000 | −1.30931 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 1.00000 | 0.208514 | 0.104257 | − | 0.994550i | \(-0.466753\pi\) | ||||
0.104257 | + | 0.994550i | \(0.466753\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.23607 | − | 3.80423i | 0.247214 | − | 0.760845i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 7.28115 | − | 5.29007i | 1.40126 | − | 1.01807i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.47214 | + | 7.60845i | 0.459064 | + | 1.41285i | 0.866297 | + | 0.499530i | \(0.166494\pi\) |
−0.407233 | + | 0.913324i | \(0.633506\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.66312 | + | 4.11450i | 1.01713 | + | 0.738985i | 0.965692 | − | 0.259691i | \(-0.0836207\pi\) |
0.0514344 | + | 0.998676i | \(0.483621\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 4.85410 | + | 3.52671i | 0.820493 | + | 0.596123i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −0.309017 | − | 0.951057i | −0.0508021 | − | 0.156353i | 0.922437 | − | 0.386148i | \(-0.126194\pi\) |
−0.973239 | + | 0.229795i | \(0.926194\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.23607 | + | 3.80423i | −0.193041 | + | 0.594120i | 0.806952 | + | 0.590616i | \(0.201115\pi\) |
−0.999994 | + | 0.00350392i | \(0.998885\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −6.00000 | −0.914991 | −0.457496 | − | 0.889212i | \(-0.651253\pi\) | ||||
−0.457496 | + | 0.889212i | \(0.651253\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −18.0000 | −2.68328 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −2.47214 | + | 7.60845i | −0.360598 | + | 1.10981i | 0.592094 | + | 0.805869i | \(0.298301\pi\) |
−0.952692 | + | 0.303938i | \(0.901699\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 2.42705 | − | 1.76336i | 0.346722 | − | 0.251908i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −5.56231 | − | 17.1190i | −0.778879 | − | 2.39714i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −1.61803 | − | 1.17557i | −0.222254 | − | 0.161477i | 0.471087 | − | 0.882087i | \(-0.343862\pi\) |
−0.693341 | + | 0.720610i | \(0.743862\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −9.70820 | − | 7.05342i | −1.28588 | − | 0.934249i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −0.309017 | − | 0.951057i | −0.0402306 | − | 0.123817i | 0.928924 | − | 0.370270i | \(-0.120735\pi\) |
−0.969155 | + | 0.246453i | \(0.920735\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.23607 | − | 2.35114i | 0.414336 | − | 0.301033i | −0.361019 | − | 0.932559i | \(-0.617571\pi\) |
0.775355 | + | 0.631526i | \(0.217571\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 3.70820 | − | 11.4127i | 0.467190 | − | 1.43786i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −5.00000 | −0.610847 | −0.305424 | − | 0.952217i | \(-0.598798\pi\) | ||||
−0.305424 | + | 0.952217i | \(0.598798\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −0.927051 | + | 2.85317i | −0.111604 | + | 0.343481i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −2.42705 | + | 1.76336i | −0.288038 | + | 0.209272i | −0.722416 | − | 0.691459i | \(-0.756968\pi\) |
0.434378 | + | 0.900731i | \(0.356968\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −4.94427 | − | 15.2169i | −0.578683 | − | 1.78100i | −0.623280 | − | 0.781999i | \(-0.714200\pi\) |
0.0445966 | − | 0.999005i | \(-0.485800\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 9.70820 | + | 7.05342i | 1.12101 | + | 0.814459i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.61803 | + | 1.17557i | 0.182043 | + | 0.132262i | 0.675075 | − | 0.737749i | \(-0.264111\pi\) |
−0.493032 | + | 0.870011i | \(0.664111\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 2.78115 | + | 8.55951i | 0.309017 | + | 0.951057i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −1.61803 | + | 1.17557i | −0.177602 | + | 0.129036i | −0.673035 | − | 0.739611i | \(-0.735010\pi\) |
0.495432 | + | 0.868646i | \(0.335010\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −5.56231 | + | 17.1190i | −0.603317 | + | 1.85682i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −24.0000 | −2.57307 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 15.0000 | 1.59000 | 0.794998 | − | 0.606612i | \(-0.207472\pi\) | ||||
0.794998 | + | 0.606612i | \(0.207472\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −16.9894 | + | 12.3435i | −1.76171 | + | 1.27996i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 3.70820 | + | 11.4127i | 0.380454 | + | 1.17092i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 5.66312 | + | 4.11450i | 0.575003 | + | 0.417764i | 0.836919 | − | 0.547327i | \(-0.184354\pi\) |
−0.261916 | + | 0.965091i | \(0.584354\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −8.09017 | − | 5.87785i | −0.805002 | − | 0.584868i | 0.107375 | − | 0.994219i | \(-0.465755\pi\) |
−0.912377 | + | 0.409350i | \(0.865755\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −4.94427 | − | 15.2169i | −0.487174 | − | 1.49937i | −0.828808 | − | 0.559533i | \(-0.810980\pi\) |
0.341634 | − | 0.939833i | \(-0.389020\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −14.5623 | + | 10.5801i | −1.42114 | + | 1.03252i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −0.618034 | + | 1.90211i | −0.0597476 | + | 0.183884i | −0.976476 | − | 0.215627i | \(-0.930820\pi\) |
0.916728 | + | 0.399512i | \(0.130820\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 14.0000 | 1.34096 | 0.670478 | − | 0.741929i | \(-0.266089\pi\) | ||||
0.670478 | + | 0.741929i | \(0.266089\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 3.00000 | 0.284747 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −2.16312 | + | 6.65740i | −0.203489 | + | 0.626275i | 0.796283 | + | 0.604924i | \(0.206797\pi\) |
−0.999772 | + | 0.0213507i | \(0.993203\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.42705 | − | 1.76336i | 0.226324 | − | 0.164434i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −9.70820 | − | 7.05342i | −0.889950 | − | 0.646586i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −9.70820 | − | 7.05342i | −0.875359 | − | 0.635986i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0.927051 | + | 2.85317i | 0.0829180 | + | 0.255195i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 3.23607 | − | 2.35114i | 0.287155 | − | 0.208630i | −0.434877 | − | 0.900490i | \(-0.643208\pi\) |
0.722032 | + | 0.691860i | \(0.243208\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 5.56231 | − | 17.1190i | 0.489734 | − | 1.50725i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2.00000 | 0.174741 | 0.0873704 | − | 0.996176i | \(-0.472154\pi\) | ||||
0.0873704 | + | 0.996176i | \(0.472154\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −8.00000 | −0.693688 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 8.34346 | − | 25.6785i | 0.718091 | − | 2.21006i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 12.1353 | − | 8.81678i | 1.03678 | − | 0.753268i | 0.0671295 | − | 0.997744i | \(-0.478616\pi\) |
0.969655 | + | 0.244476i | \(0.0786159\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 6.79837 | + | 20.9232i | 0.576631 | + | 1.77469i | 0.630559 | + | 0.776142i | \(0.282826\pi\) |
−0.0539282 | + | 0.998545i | \(0.517174\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −19.4164 | − | 14.1068i | −1.63516 | − | 1.18801i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 19.4164 | + | 14.1068i | 1.61244 | + | 1.17151i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 2.78115 | + | 8.55951i | 0.229386 | + | 0.705976i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 14.5623 | − | 10.5801i | 1.19299 | − | 0.866758i | 0.199413 | − | 0.979915i | \(-0.436096\pi\) |
0.993577 | + | 0.113157i | \(0.0360963\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 5.56231 | − | 17.1190i | 0.452654 | − | 1.39313i | −0.421213 | − | 0.906962i | \(-0.638396\pi\) |
0.873867 | − | 0.486164i | \(-0.161604\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 36.0000 | 2.91043 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 21.0000 | 1.68676 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −3.39919 | + | 10.4616i | −0.271285 | + | 0.834928i | 0.718894 | + | 0.695120i | \(0.244649\pi\) |
−0.990179 | + | 0.139808i | \(0.955351\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 4.85410 | − | 3.52671i | 0.384955 | − | 0.279686i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0.618034 | + | 1.90211i | 0.0487079 | + | 0.149908i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 3.23607 | + | 2.35114i | 0.253468 | + | 0.184156i | 0.707263 | − | 0.706951i | \(-0.249930\pi\) |
−0.453794 | + | 0.891107i | \(0.649930\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 12.9443 | + | 9.40456i | 1.00166 | + | 0.727747i | 0.962443 | − | 0.271484i | \(-0.0875143\pi\) |
0.0392148 | + | 0.999231i | \(0.487514\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −4.01722 | − | 12.3637i | −0.309017 | − | 0.951057i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 19.4164 | − | 14.1068i | 1.48481 | − | 1.07878i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −5.56231 | + | 17.1190i | −0.422894 | + | 1.30153i | 0.482102 | + | 0.876115i | \(0.339873\pi\) |
−0.904996 | + | 0.425420i | \(0.860127\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 8.00000 | 0.604743 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 3.00000 | 0.225494 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −1.54508 | + | 4.75528i | −0.115485 | + | 0.355427i | −0.992048 | − | 0.125861i | \(-0.959831\pi\) |
0.876563 | + | 0.481287i | \(0.159831\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 4.04508 | − | 2.93893i | 0.300669 | − | 0.218449i | −0.427213 | − | 0.904151i | \(-0.640505\pi\) |
0.727882 | + | 0.685702i | \(0.240505\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 3.70820 | + | 11.4127i | 0.274118 | + | 0.843649i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −2.42705 | − | 1.76336i | −0.178440 | − | 0.129644i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 14.5623 | + | 10.5801i | 1.05925 | + | 0.769592i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −2.78115 | − | 8.55951i | −0.201237 | − | 0.619344i | −0.999847 | − | 0.0174951i | \(-0.994431\pi\) |
0.798610 | − | 0.601849i | \(-0.205569\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 3.23607 | − | 2.35114i | 0.232937 | − | 0.169239i | −0.465194 | − | 0.885209i | \(-0.654015\pi\) |
0.698131 | + | 0.715970i | \(0.254015\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −6.00000 | −0.427482 | −0.213741 | − | 0.976890i | \(-0.568565\pi\) | ||||
−0.213741 | + | 0.976890i | \(0.568565\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 8.00000 | 0.567105 | 0.283552 | − | 0.958957i | \(-0.408487\pi\) | ||||
0.283552 | + | 0.958957i | \(0.408487\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 4.63525 | − | 14.2658i | 0.326946 | − | 1.00624i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −12.9443 | + | 9.40456i | −0.908510 | + | 0.660071i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 3.70820 | + | 11.4127i | 0.258992 | + | 0.797096i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −4.85410 | − | 3.52671i | −0.337383 | − | 0.245123i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 16.1803 | + | 11.7557i | 1.11390 | + | 0.809296i | 0.983273 | − | 0.182135i | \(-0.0583009\pi\) |
0.130627 | + | 0.991432i | \(0.458301\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −2.78115 | − | 8.55951i | −0.190561 | − | 0.586488i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −14.5623 | + | 10.5801i | −0.993141 | + | 0.721559i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −4.32624 | + | 13.3148i | −0.293684 | + | 0.903867i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 48.0000 | 3.24354 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 8.96149 | − | 27.5806i | 0.600106 | − | 1.84694i | 0.0726433 | − | 0.997358i | \(-0.476857\pi\) |
0.527463 | − | 0.849578i | \(-0.323143\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −19.4164 | + | 14.1068i | −1.29443 | + | 0.940456i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −5.56231 | − | 17.1190i | −0.369183 | − | 1.13623i | −0.947320 | − | 0.320289i | \(-0.896220\pi\) |
0.578137 | − | 0.815940i | \(-0.303780\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 16.9894 | + | 12.3435i | 1.12269 | + | 0.815681i | 0.984614 | − | 0.174741i | \(-0.0559089\pi\) |
0.138074 | + | 0.990422i | \(0.455909\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −12.9443 | − | 9.40456i | −0.848007 | − | 0.616113i | 0.0765885 | − | 0.997063i | \(-0.475597\pi\) |
−0.924596 | + | 0.380949i | \(0.875597\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 7.41641 | + | 22.8254i | 0.483793 | + | 1.48896i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −4.85410 | + | 3.52671i | −0.315308 | + | 0.229085i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 0.618034 | − | 1.90211i | 0.0399773 | − | 0.123037i | −0.929076 | − | 0.369889i | \(-0.879396\pi\) |
0.969053 | + | 0.246851i | \(0.0793959\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 2.78115 | − | 8.55951i | 0.177681 | − | 0.546847i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −1.85410 | − | 5.70634i | −0.117499 | − | 0.361625i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 10.5172 | + | 7.64121i | 0.663841 | + | 0.482309i | 0.867958 | − | 0.496638i | \(-0.165432\pi\) |
−0.204117 | + | 0.978947i | \(0.565432\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −43.6869 | − | 31.7404i | −2.73578 | − | 1.98766i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −3.09017 | − | 9.51057i | −0.192760 | − | 0.593253i | −0.999995 | − | 0.00302385i | \(-0.999037\pi\) |
0.807236 | − | 0.590229i | \(-0.200963\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.61803 | − | 1.17557i | 0.100540 | − | 0.0730464i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 14.8328 | − | 45.6507i | 0.918128 | − | 2.82571i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −14.0000 | −0.863277 | −0.431638 | − | 0.902047i | \(-0.642064\pi\) | ||||
−0.431638 | + | 0.902047i | \(0.642064\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −6.00000 | −0.368577 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −13.9058 | + | 42.7975i | −0.851019 | + | 2.61917i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −21.0344 | + | 15.2824i | −1.28249 | + | 0.931785i | −0.999625 | − | 0.0273737i | \(-0.991286\pi\) |
−0.282867 | + | 0.959159i | \(0.591286\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0 | 0 | 0.951057 | − | 0.309017i | \(-0.100000\pi\) | ||||
−0.951057 | + | 0.309017i | \(0.900000\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1.61803 | − | 1.17557i | −0.0972182 | − | 0.0706332i | 0.538114 | − | 0.842872i | \(-0.319137\pi\) |
−0.635332 | + | 0.772239i | \(0.719137\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −12.9787 | − | 39.9444i | −0.777015 | − | 2.39141i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 4.85410 | − | 3.52671i | 0.289571 | − | 0.210386i | −0.433510 | − | 0.901149i | \(-0.642725\pi\) |
0.723081 | + | 0.690763i | \(0.242725\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1.23607 | + | 3.80423i | −0.0734766 | + | 0.226138i | −0.981050 | − | 0.193756i | \(-0.937933\pi\) |
0.907573 | + | 0.419894i | \(0.137933\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −36.0000 | −2.13246 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −8.00000 | −0.472225 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 5.87132 | − | 18.0701i | 0.345372 | − | 1.06295i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −16.9894 | + | 12.3435i | −0.995934 | + | 0.723588i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −3.70820 | − | 11.4127i | −0.216636 | − | 0.666736i | −0.999033 | − | 0.0439568i | \(-0.986004\pi\) |
0.782398 | − | 0.622779i | \(-0.213996\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −2.42705 | − | 1.76336i | −0.141308 | − | 0.102667i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −3.70820 | − | 11.4127i | −0.213737 | − | 0.657816i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 24.2705 | − | 17.6336i | 1.39430 | − | 1.01302i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 3.70820 | − | 11.4127i | 0.212331 | − | 0.653488i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 4.00000 | 0.228292 | 0.114146 | − | 0.993464i | \(-0.463587\pi\) | ||||
0.114146 | + | 0.993464i | \(0.463587\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 48.0000 | 2.73062 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −3.70820 | + | 11.4127i | −0.210273 | + | 0.647154i | 0.789183 | + | 0.614159i | \(0.210505\pi\) |
−0.999456 | + | 0.0329949i | \(0.989495\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 7.28115 | − | 5.29007i | 0.411555 | − | 0.299012i | −0.362676 | − | 0.931915i | \(-0.618137\pi\) |
0.774231 | + | 0.632903i | \(0.218137\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −11.1246 | − | 34.2380i | −0.626801 | − | 1.92909i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 12.1353 | + | 8.81678i | 0.681584 | + | 0.495200i | 0.873883 | − | 0.486137i | \(-0.161594\pi\) |
−0.192299 | + | 0.981336i | \(0.561594\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −4.85410 | − | 3.52671i | −0.270930 | − | 0.196842i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −7.41641 | − | 22.8254i | −0.412660 | − | 1.27004i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −12.9787 | + | 39.9444i | −0.717725 | + | 2.20893i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −16.0000 | −0.882109 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −35.0000 | −1.92377 | −0.961887 | − | 0.273447i | \(-0.911836\pi\) | ||||
−0.961887 | + | 0.273447i | \(0.911836\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −1.85410 | + | 5.70634i | −0.101604 | + | 0.312705i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −12.1353 | + | 8.81678i | −0.663020 | + | 0.481712i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 3.09017 | + | 9.51057i | 0.168332 | + | 0.518073i | 0.999266 | − | 0.0382973i | \(-0.0121934\pi\) |
−0.830934 | + | 0.556371i | \(0.812193\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −16.9894 | − | 12.3435i | −0.922735 | − | 0.670406i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 16.1803 | + | 11.7557i | 0.873656 | + | 0.634748i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 2.78115 | + | 8.55951i | 0.149732 | + | 0.460828i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −25.8885 | + | 18.8091i | −1.38977 | + | 1.00973i | −0.393879 | + | 0.919162i | \(0.628867\pi\) |
−0.995891 | + | 0.0905647i | \(0.971133\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 4.32624 | − | 13.3148i | 0.231578 | − | 0.712724i | −0.765979 | − | 0.642866i | \(-0.777745\pi\) |
0.997557 | − | 0.0698585i | \(-0.0222548\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 3.00000 | 0.159674 | 0.0798369 | − | 0.996808i | \(-0.474560\pi\) | ||||
0.0798369 | + | 0.996808i | \(0.474560\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −2.78115 | + | 8.55951i | −0.147608 | + | 0.454292i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 29.1246 | − | 21.1603i | 1.54144 | − | 1.11992i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −7.41641 | − | 22.8254i | −0.391423 | − | 1.20468i | −0.931712 | − | 0.363197i | \(-0.881685\pi\) |
0.540289 | − | 0.841479i | \(-0.318315\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 2.42705 | + | 1.76336i | 0.127740 | + | 0.0928082i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −38.8328 | − | 28.2137i | −2.03260 | − | 1.47677i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 10.1976 | + | 31.3849i | 0.532308 | + | 1.63828i | 0.749394 | + | 0.662124i | \(0.230345\pi\) |
−0.217086 | + | 0.976153i | \(0.569655\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 19.4164 | − | 14.1068i | 1.01078 | − | 0.734373i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.23607 | − | 3.80423i | 0.0641735 | − | 0.197506i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 22.0000 | 1.13912 | 0.569558 | − | 0.821951i | \(-0.307114\pi\) | ||||
0.569558 | + | 0.821951i | \(0.307114\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −9.00000 | −0.464758 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −20.2254 | + | 14.6946i | −1.03891 | + | 0.754813i | −0.970073 | − | 0.242815i | \(-0.921929\pi\) |
−0.0688378 | + | 0.997628i | \(0.521929\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 3.70820 | + | 11.4127i | 0.189977 | + | 0.584689i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −0.809017 | − | 0.587785i | −0.0413388 | − | 0.0300344i | 0.566924 | − | 0.823770i | \(-0.308133\pi\) |
−0.608263 | + | 0.793736i | \(0.708133\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 29.1246 | + | 21.1603i | 1.48049 | + | 1.07564i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 4.01722 | + | 12.3637i | 0.203681 | + | 0.626866i | 0.999765 | + | 0.0216798i | \(0.00690144\pi\) |
−0.796084 | + | 0.605186i | \(0.793099\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −4.85410 | + | 3.52671i | −0.245482 | + | 0.178353i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −1.85410 | + | 5.70634i | −0.0935271 | + | 0.287847i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 6.00000 | 0.301893 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −26.0000 | −1.30490 | −0.652451 | − | 0.757831i | \(-0.726259\pi\) | ||||
−0.652451 | + | 0.757831i | \(0.726259\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 7.41641 | − | 22.8254i | 0.371285 | − | 1.14270i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 4.85410 | − | 3.52671i | 0.242402 | − | 0.176116i | −0.459951 | − | 0.887945i | \(-0.652133\pi\) |
0.702353 | + | 0.711829i | \(0.252133\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 21.8435 | + | 15.8702i | 1.08541 | + | 0.788597i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 27.5066 | + | 19.9847i | 1.36011 | + | 0.988180i | 0.998438 | + | 0.0558755i | \(0.0177950\pi\) |
0.361675 | + | 0.932304i | \(0.382205\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 13.9058 | + | 42.7975i | 0.685921 | + | 2.11105i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 1.61803 | − | 1.17557i | 0.0796182 | − | 0.0578460i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1.85410 | + | 5.70634i | −0.0910143 | + | 0.280113i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −66.0000 | −3.23203 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −28.0000 | −1.36789 | −0.683945 | − | 0.729534i | \(-0.739737\pi\) | ||||
−0.683945 | + | 0.729534i | \(0.739737\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 9.27051 | − | 28.5317i | 0.451817 | − | 1.39055i | −0.423015 | − | 0.906123i | \(-0.639028\pi\) |
0.874832 | − | 0.484427i | \(-0.160972\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 38.8328 | − | 28.2137i | 1.88812 | − | 1.37180i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 7.41641 | + | 22.8254i | 0.359749 | + | 1.10719i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 6.47214 | + | 4.70228i | 0.313209 | + | 0.227559i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −21.0344 | − | 15.2824i | −1.01319 | − | 0.736128i | −0.0483169 | − | 0.998832i | \(-0.515386\pi\) |
−0.964876 | + | 0.262704i | \(0.915386\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 4.01722 | + | 12.3637i | 0.193055 | + | 0.594163i | 0.999994 | + | 0.00352765i | \(0.00112289\pi\) |
−0.806938 | + | 0.590636i | \(0.798877\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −58.2492 | + | 42.3205i | −2.79284 | + | 2.02911i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −1.23607 | + | 3.80423i | −0.0591292 | + | 0.181981i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 32.0000 | 1.52728 | 0.763638 | − | 0.645644i | \(-0.223411\pi\) | ||||
0.763638 | + | 0.645644i | \(0.223411\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −18.0000 | −0.857143 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −2.78115 | + | 8.55951i | −0.132137 | + | 0.406675i | −0.995134 | − | 0.0985344i | \(-0.968585\pi\) |
0.862997 | + | 0.505209i | \(0.168585\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 36.4058 | − | 26.4503i | 1.72580 | − | 1.25387i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 16.6869 | + | 51.3571i | 0.789264 | + | 2.42911i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 16.9894 | + | 12.3435i | 0.801777 | + | 0.582525i | 0.911435 | − | 0.411444i | \(-0.134975\pi\) |
−0.109658 | + | 0.993969i | \(0.534975\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 43.6869 | + | 31.7404i | 2.05259 | + | 1.49129i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 9.70820 | − | 7.05342i | 0.454131 | − | 0.329945i | −0.337094 | − | 0.941471i | \(-0.609444\pi\) |
0.791224 | + | 0.611526i | \(0.209444\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −16.6869 | + | 51.3571i | −0.778879 | + | 2.39714i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 28.0000 | 1.30409 | 0.652045 | − | 0.758180i | \(-0.273911\pi\) | ||||
0.652045 | + | 0.758180i | \(0.273911\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 27.0000 | 1.25480 | 0.627398 | − | 0.778699i | \(-0.284120\pi\) | ||||
0.627398 | + | 0.778699i | \(0.284120\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −19.4681 | + | 59.9166i | −0.902810 | + | 2.77856i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 26.6976 | − | 19.3969i | 1.23542 | − | 0.897582i | 0.238132 | − | 0.971233i | \(-0.423465\pi\) |
0.997284 | + | 0.0736508i | \(0.0234650\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −3.09017 | − | 9.51057i | −0.142691 | − | 0.439157i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −26.6976 | − | 19.3969i | −1.23016 | − | 0.893763i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 12.9443 | + | 9.40456i | 0.593924 | + | 0.431511i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 3.70820 | + | 11.4127i | 0.169787 | + | 0.522551i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 6.47214 | − | 4.70228i | 0.295719 | − | 0.214853i | −0.430025 | − | 0.902817i | \(-0.641495\pi\) |
0.725745 | + | 0.687964i | \(0.241495\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −6.00000 | −0.273009 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 21.0000 | 0.953561 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 2.78115 | − | 8.55951i | 0.126026 | − | 0.387868i | −0.868061 | − | 0.496458i | \(-0.834634\pi\) |
0.994087 | + | 0.108590i | \(0.0346336\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −9.70820 | + | 7.05342i | −0.439020 | + | 0.318967i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −2.47214 | − | 7.60845i | −0.111566 | − | 0.343365i | 0.879649 | − | 0.475623i | \(-0.157777\pi\) |
−0.991215 | + | 0.132258i | \(0.957777\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −38.8328 | − | 28.2137i | −1.74894 | − | 1.27068i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −4.85410 | − | 3.52671i | −0.217736 | − | 0.158195i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −6.18034 | − | 19.0211i | −0.276670 | − | 0.851503i | −0.988773 | − | 0.149427i | \(-0.952257\pi\) |
0.712103 | − | 0.702075i | \(-0.247743\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −38.8328 | + | 28.2137i | −1.73492 | + | 1.26049i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 9.27051 | − | 28.5317i | 0.413352 | − | 1.27217i | −0.500365 | − | 0.865814i | \(-0.666801\pi\) |
0.913717 | − | 0.406351i | \(-0.133199\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −30.0000 | −1.33498 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 39.0000 | 1.73205 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −4.01722 | + | 12.3637i | −0.178060 | + | 0.548013i | −0.999760 | − | 0.0219076i | \(-0.993026\pi\) |
0.821700 | + | 0.569921i | \(0.193026\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 25.8885 | − | 18.8091i | 1.14524 | − | 0.832067i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 11.1246 | + | 34.2380i | 0.491164 | + | 1.51165i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −38.8328 | − | 28.2137i | −1.71118 | − | 1.24324i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −43.6869 | − | 31.7404i | −1.91764 | − | 1.39325i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 11.4336 | + | 35.1891i | 0.500916 | + | 1.54166i | 0.807529 | + | 0.589828i | \(0.200804\pi\) |
−0.306613 | + | 0.951834i | \(0.599196\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 35.5967 | − | 25.8626i | 1.55654 | − | 1.13089i | 0.617759 | − | 0.786367i | \(-0.288041\pi\) |
0.938778 | − | 0.344523i | \(-0.111959\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −7.41641 | + | 22.8254i | −0.323679 | + | 0.996180i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −42.0000 | −1.82955 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.0000 | −0.956522 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −1.85410 | + | 5.70634i | −0.0804612 | + | 0.247634i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1.85410 | + | 5.70634i | 0.0801598 | + | 0.246707i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −12.1353 | − | 8.81678i | −0.523675 | − | 0.380472i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 9.70820 | + | 7.05342i | 0.417388 | + | 0.303250i | 0.776586 | − | 0.630011i | \(-0.216950\pi\) |
−0.359198 | + | 0.933261i | \(0.616950\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 4.63525 | + | 14.2658i | 0.198918 | + | 0.612206i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 33.9787 | − | 24.6870i | 1.45549 | − | 1.05747i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 0 | 0 | −0.951057 | − | 0.309017i | \(-0.900000\pi\) | ||||
0.951057 | + | 0.309017i | \(0.100000\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −24.0000 | −1.02430 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −32.0000 | −1.36325 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1.23607 | + | 3.80423i | −0.0525630 | + | 0.161772i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 7.28115 | − | 5.29007i | 0.309068 | − | 0.224551i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −12.9787 | − | 39.9444i | −0.549926 | − | 1.69250i | −0.708981 | − | 0.705228i | \(-0.750845\pi\) |
0.159055 | − | 0.987270i | \(-0.449155\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −9.70820 | − | 7.05342i | −0.409152 | − | 0.297266i | 0.364106 | − | 0.931357i | \(-0.381374\pi\) |
−0.773258 | + | 0.634091i | \(0.781374\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 6.48936 | + | 19.9722i | 0.273009 | + | 0.840236i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −14.5623 | + | 10.5801i | −0.611559 | + | 0.444324i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 7.41641 | − | 22.8254i | 0.310912 | − | 0.956889i | −0.666493 | − | 0.745512i | \(-0.732205\pi\) |
0.977405 | − | 0.211377i | \(-0.0677948\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 4.00000 | 0.167395 | 0.0836974 | − | 0.996491i | \(-0.473327\pi\) | ||||
0.0836974 | + | 0.996491i | \(0.473327\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 27.0000 | 1.12794 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1.23607 | − | 3.80423i | 0.0515476 | − | 0.158647i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 18.6074 | − | 13.5191i | 0.774636 | − | 0.562806i | −0.128728 | − | 0.991680i | \(-0.541090\pi\) |
0.903364 | + | 0.428874i | \(0.141090\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 3.70820 | + | 11.4127i | 0.154108 | + | 0.474295i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −3.23607 | − | 2.35114i | −0.134255 | − | 0.0975418i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 3.70820 | + | 11.4127i | 0.153054 | + | 0.471052i | 0.997959 | − | 0.0638654i | \(-0.0203428\pi\) |
−0.844905 | + | 0.534917i | \(0.820343\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −22.6525 | + | 16.4580i | −0.933379 | + | 0.678140i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 5.56231 | − | 17.1190i | 0.228803 | − | 0.704182i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 4.00000 | 0.164260 | 0.0821302 | − | 0.996622i | \(-0.473828\pi\) | ||||
0.0821302 | + | 0.996622i | \(0.473828\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −36.0000 | −1.47586 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −7.41641 | + | 22.8254i | −0.303533 | + | 0.934180i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −38.8328 | + | 28.2137i | −1.58667 | + | 1.15278i | −0.678155 | + | 0.734919i | \(0.737220\pi\) |
−0.908511 | + | 0.417861i | \(0.862780\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −11.7426 | − | 36.1401i | −0.478993 | − | 1.47419i | −0.840497 | − | 0.541817i | \(-0.817737\pi\) |
0.361504 | − | 0.932371i | \(-0.382263\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 24.2705 | + | 17.6336i | 0.988372 | + | 0.718094i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −14.5623 | − | 10.5801i | −0.591066 | − | 0.429434i | 0.251631 | − | 0.967823i | \(-0.419033\pi\) |
−0.842696 | + | 0.538389i | \(0.819033\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −14.8328 | − | 45.6507i | −0.601056 | − | 1.84986i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 4.94427 | − | 15.2169i | 0.199697 | − | 0.614605i | −0.800192 | − | 0.599744i | \(-0.795269\pi\) |
0.999890 | − | 0.0148615i | \(-0.00473072\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −36.0000 | −1.45166 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 18.0000 | 0.724653 | 0.362326 | − | 0.932051i | \(-0.381983\pi\) | ||||
0.362326 | + | 0.932051i | \(0.381983\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −0.927051 | + | 2.85317i | −0.0372613 | + | 0.114679i | −0.967957 | − | 0.251116i | \(-0.919203\pi\) |
0.930696 | + | 0.365794i | \(0.119203\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 7.28115 | − | 5.29007i | 0.292183 | − | 0.212283i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 9.27051 | + | 28.5317i | 0.371415 | + | 1.14310i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 23.4615 | + | 17.0458i | 0.938460 | + | 0.681831i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 4.85410 | + | 3.52671i | 0.193546 | + | 0.140619i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 2.78115 | + | 8.55951i | 0.110716 | + | 0.340749i | 0.991029 | − | 0.133644i | \(-0.0426678\pi\) |
−0.880313 | + | 0.474392i | \(0.842668\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −48.5410 | + | 35.2671i | −1.92933 | + | 1.40174i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 3.70820 | − | 11.4127i | 0.147156 | − | 0.452898i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 18.0000 | 0.712069 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −2.78115 | + | 8.55951i | −0.109849 | + | 0.338080i | −0.990838 | − | 0.135057i | \(-0.956878\pi\) |
0.880989 | + | 0.473137i | \(0.156878\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −5.66312 | + | 4.11450i | −0.223332 | + | 0.162260i | −0.693825 | − | 0.720144i | \(-0.744076\pi\) |
0.470493 | + | 0.882403i | \(0.344076\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −16.6869 | − | 51.3571i | −0.657047 | − | 2.02218i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −12.1353 | − | 8.81678i | −0.477086 | − | 0.346623i | 0.323110 | − | 0.946361i | \(-0.395271\pi\) |
−0.800196 | + | 0.599738i | \(0.795271\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −33.9787 | − | 24.6870i | −1.33173 | − | 0.967559i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 3.39919 | + | 10.4616i | 0.133020 | + | 0.409395i | 0.995277 | − | 0.0970771i | \(-0.0309494\pi\) |
−0.862256 | + | 0.506472i | \(0.830949\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 4.85410 | − | 3.52671i | 0.189665 | − | 0.137800i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −29.6656 | + | 91.3014i | −1.15737 | + | 3.56201i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −22.0000 | −0.856998 | −0.428499 | − | 0.903542i | \(-0.640958\pi\) | ||||
−0.428499 | + | 0.903542i | \(0.640958\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −7.00000 | −0.272268 | −0.136134 | − | 0.990690i | \(-0.543468\pi\) | ||||
−0.136134 | + | 0.990690i | \(0.543468\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −19.4164 | + | 14.1068i | −0.752936 | + | 0.547040i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 2.47214 | + | 7.60845i | 0.0957215 | + | 0.294600i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 70.3845 | + | 51.1373i | 2.72122 | + | 1.97708i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −27.5066 | − | 19.9847i | −1.06030 | − | 0.770354i | −0.0861567 | − | 0.996282i | \(-0.527459\pi\) |
−0.974144 | + | 0.225928i | \(0.927459\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −11.1246 | − | 34.2380i | −0.428187 | − | 1.31782i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −24.2705 | + | 17.6336i | −0.932791 | + | 0.677713i | −0.946675 | − | 0.322191i | \(-0.895581\pi\) |
0.0138832 | + | 0.999904i | \(0.495581\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −4.32624 | + | 13.3148i | −0.166026 | + | 0.510975i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 54.0000 | 2.06928 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 8.00000 | 0.306111 | 0.153056 | − | 0.988218i | \(-0.451089\pi\) | ||||
0.153056 | + | 0.988218i | \(0.451089\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 13.9058 | − | 42.7975i | 0.531312 | − | 1.63521i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −50.9681 | + | 37.0305i | −1.94455 | + | 1.41280i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 23.4615 | + | 17.0458i | 0.892517 | + | 0.648452i | 0.936533 | − | 0.350579i | \(-0.114015\pi\) |
−0.0440159 | + | 0.999031i | \(0.514015\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 53.3951 | + | 38.7938i | 2.02539 | + | 1.47153i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −7.41641 | − | 22.8254i | −0.280916 | − | 0.864572i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 38.8328 | − | 28.2137i | 1.46879 | − | 1.06714i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 3.09017 | − | 9.51057i | 0.116714 | − | 0.359209i | −0.875587 | − | 0.483061i | \(-0.839525\pi\) |
0.992301 | + | 0.123852i | \(0.0395248\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 4.00000 | 0.150863 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −72.0000 | −2.71168 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 6.18034 | − | 19.0211i | 0.232436 | − | 0.715363i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −15.3713 | + | 11.1679i | −0.577282 | + | 0.419420i | −0.837743 | − | 0.546064i | \(-0.816125\pi\) |
0.260461 | + | 0.965484i | \(0.416125\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −3.70820 | − | 11.4127i | −0.139069 | − | 0.428009i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 5.66312 | + | 4.11450i | 0.212085 | + | 0.154089i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 4.85410 | + | 3.52671i | 0.181280 | + | 0.131707i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −7.10739 | − | 21.8743i | −0.265061 | − | 0.815774i | −0.991679 | − | 0.128732i | \(-0.958909\pi\) |
0.726618 | − | 0.687041i | \(-0.241091\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 25.8885 | − | 18.8091i | 0.964140 | − | 0.700489i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 32.0000 | 1.18845 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −35.0000 | −1.29808 | −0.649039 | − | 0.760755i | \(-0.724829\pi\) | ||||
−0.649039 | + | 0.760755i | \(0.724829\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −8.34346 | + | 25.6785i | −0.309017 | + | 0.951057i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 29.1246 | − | 21.1603i | 1.07721 | − | 0.782641i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −1.23607 | − | 3.80423i | −0.0456552 | − | 0.140512i | 0.925630 | − | 0.378429i | \(-0.123536\pi\) |
−0.971286 | + | 0.237917i | \(0.923536\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 21.8435 | + | 15.8702i | 0.805708 | + | 0.585381i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −21.0344 | − | 15.2824i | −0.773764 | − | 0.562173i | 0.129337 | − | 0.991601i | \(-0.458715\pi\) |
−0.903101 | + | 0.429428i | \(0.858715\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −29.1246 | + | 21.1603i | −1.06848 | + | 0.776295i | −0.975638 | − | 0.219386i | \(-0.929595\pi\) |
−0.0928402 | + | 0.995681i | \(0.529595\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 16.6869 | − | 51.3571i | 0.611361 | − | 1.88158i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 12.0000 | 0.439057 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −4.00000 | −0.146157 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 7.10739 | − | 21.8743i | 0.259352 | − | 0.798205i | −0.733588 | − | 0.679594i | \(-0.762156\pi\) |
0.992941 | − | 0.118611i | \(-0.0378440\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −31.5517 | + | 22.9236i | −1.14981 | + | 0.835383i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −16.6869 | − | 51.3571i | −0.607299 | − | 1.86907i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −8.09017 | − | 5.87785i | −0.294042 | − | 0.213634i | 0.430977 | − | 0.902363i | \(-0.358169\pi\) |
−0.725019 | + | 0.688729i | \(0.758169\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 0 | 0 | 0.587785 | − | 0.809017i | \(-0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 8.65248 | + | 26.6296i | 0.313241 | + | 0.964056i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 87.3738 | − | 63.4808i | 3.15901 | − | 2.29515i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −16.0000 | −0.576975 | −0.288487 | − | 0.957484i | \(-0.593152\pi\) | ||||
−0.288487 | + | 0.957484i | \(0.593152\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 30.0000 | 1.08042 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −1.85410 | + | 5.70634i | −0.0666874 | + | 0.205243i | −0.978847 | − | 0.204591i | \(-0.934413\pi\) |
0.912160 | + | 0.409834i | \(0.134413\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 22.6525 | − | 16.4580i | 0.813701 | − | 0.591188i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 1.85410 | + | 5.70634i | 0.0665155 | + | 0.204714i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −12.9443 | − | 9.40456i | −0.463777 | − | 0.336953i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 58.2492 | + | 42.3205i | 2.08166 | + | 1.51241i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 10.1976 | + | 31.3849i | 0.363967 | + | 1.12017i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 19.4164 | − | 14.1068i | 0.692120 | − | 0.502855i | −0.185236 | − | 0.982694i | \(-0.559305\pi\) |
0.877356 | + | 0.479839i | \(0.159305\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 12.9787 | − | 39.9444i | 0.462054 | − | 1.42206i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −14.0000 | −0.497783 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 5.56231 | − | 17.1190i | 0.197275 | − | 0.607149i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −0.809017 | + | 0.587785i | −0.0286569 | + | 0.0208204i | −0.602021 | − | 0.798480i | \(-0.705638\pi\) |
0.573365 | + | 0.819300i | \(0.305638\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −14.8328 | − | 45.6507i | −0.524747 | − | 1.61501i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −72.8115 | − | 52.9007i | −2.57267 | − | 1.86915i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 4.85410 | + | 3.52671i | 0.171085 | + | 0.124300i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −24.1033 | − | 74.1824i | −0.848477 | − | 2.61134i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 9.70820 | − | 7.05342i | 0.341322 | − | 0.247985i | −0.403897 | − | 0.914804i | \(-0.632345\pi\) |
0.745220 | + | 0.666819i | \(0.232345\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 8.03444 | − | 24.7275i | 0.282127 | − | 0.868299i | −0.705118 | − | 0.709090i | \(-0.749106\pi\) |
0.987245 | − | 0.159208i | \(-0.0508942\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 12.0000 | 0.420342 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 7.41641 | − | 22.8254i | 0.259467 | − | 0.798558i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 10.5066 | + | 32.3359i | 0.366682 | + | 1.12853i | 0.948921 | + | 0.315514i | \(0.102177\pi\) |
−0.582239 | + | 0.813018i | \(0.697823\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 25.0795 | + | 18.2213i | 0.874217 | + | 0.635156i | 0.931715 | − | 0.363190i | \(-0.118312\pi\) |
−0.0574979 | + | 0.998346i | \(0.518312\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −12.9443 | − | 9.40456i | −0.450116 | − | 0.327029i | 0.339525 | − | 0.940597i | \(-0.389734\pi\) |
−0.789642 | + | 0.613568i | \(0.789734\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −10.8156 | − | 33.2870i | −0.375641 | − | 1.15610i | −0.943045 | − | 0.332665i | \(-0.892052\pi\) |
0.567404 | − | 0.823440i | \(-0.307948\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 4.85410 | − | 3.52671i | 0.168387 | − | 0.122340i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −5.56231 | + | 17.1190i | −0.192722 | + | 0.593139i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 48.0000 | 1.66111 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 63.0000 | 2.17760 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 6.48936 | − | 19.9722i | 0.224037 | − | 0.689516i | −0.774350 | − | 0.632757i | \(-0.781923\pi\) |
0.998388 | − | 0.0567594i | \(-0.0180768\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.3156 | + | 20.5725i | −0.976400 | + | 0.709396i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 5.56231 | + | 17.1190i | 0.191576 | + | 0.589610i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −31.5517 | − | 22.9236i | −1.08541 | − | 0.788597i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −9.70820 | − | 7.05342i | −0.333185 | − | 0.242073i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −0.309017 | − | 0.951057i | −0.0105930 | − | 0.0326018i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −21.0344 | + | 15.2824i | −0.720206 | + | 0.523260i | −0.886450 | − | 0.462825i | \(-0.846836\pi\) |
0.166244 | + | 0.986085i | \(0.446836\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 22.2492 | − | 68.4761i | 0.760907 | − | 2.34183i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 24.0000 | 0.819824 | 0.409912 | − | 0.912125i | \(-0.365559\pi\) | ||||
0.409912 | + | 0.912125i | \(0.365559\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 11.0000 | 0.375315 | 0.187658 | − | 0.982235i | \(-0.439910\pi\) | ||||
0.187658 | + | 0.982235i | \(0.439910\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 7.41641 | − | 22.8254i | 0.252751 | − | 0.777886i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 12.9443 | − | 9.40456i | 0.440628 | − | 0.320135i | −0.345256 | − | 0.938508i | \(-0.612208\pi\) |
0.785884 | + | 0.618373i | \(0.212208\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 16.6869 | + | 51.3571i | 0.567372 | + | 1.74619i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 46.1140 | + | 33.5038i | 1.56611 | + | 1.13785i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −12.9787 | − | 39.9444i | −0.439263 | − | 1.35191i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −4.85410 | + | 3.52671i | −0.164099 | + | 0.119225i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −17.3050 | + | 53.2592i | −0.584347 | + | 1.79843i | 0.0175315 | + | 0.999846i | \(0.494419\pi\) |
−0.601878 | + | 0.798588i | \(0.705581\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 36.0000 | 1.21425 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −19.0000 | −0.640126 | −0.320063 | − | 0.947396i | \(-0.603704\pi\) | ||||
−0.320063 | + | 0.947396i | \(0.603704\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −8.65248 | + | 26.6296i | −0.291179 | + | 0.896157i | 0.693299 | + | 0.720650i | \(0.256156\pi\) |
−0.984478 | + | 0.175507i | \(0.943844\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 7.28115 | − | 5.29007i | 0.244753 | − | 0.177824i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 10.5066 | + | 32.3359i | 0.352776 | + | 1.08573i | 0.957288 | + | 0.289137i | \(0.0933684\pi\) |
−0.604511 | + | 0.796597i | \(0.706632\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 6.47214 | + | 4.70228i | 0.217068 | + | 0.157709i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −25.8885 | − | 18.8091i | −0.866327 | − | 0.629423i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 4.63525 | + | 14.2658i | 0.154939 | + | 0.476855i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −17.3050 | + | 53.2592i | −0.577152 | + | 1.77629i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 12.0000 | 0.399778 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 36.0000 | 1.19800 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 4.63525 | − | 14.2658i | 0.154081 | − | 0.474213i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −22.6525 | + | 16.4580i | −0.752163 | + | 0.546478i | −0.896497 | − | 0.443051i | \(-0.853896\pi\) |
0.144333 | + | 0.989529i | \(0.453896\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 18.5410 | + | 57.0634i | 0.614967 | + | 1.89267i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −29.1246 | − | 21.1603i | −0.964941 | − | 0.701071i | −0.0106483 | − | 0.999943i | \(-0.503390\pi\) |
−0.954293 | + | 0.298872i | \(0.903390\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 29.1246 | + | 21.1603i | 0.962830 | + | 0.699537i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 1.23607 | + | 3.80423i | 0.0408186 | + | 0.125627i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −40.4508 | + | 29.3893i | −1.33435 | + | 0.969462i | −0.334719 | + | 0.942318i | \(0.608641\pi\) |
−0.999632 | + | 0.0271443i | \(0.991359\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −3.70820 | + | 11.4127i | −0.122189 | + | 0.376061i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −4.00000 | −0.131519 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −29.6656 | + | 91.3014i | −0.974347 | + | 2.99873i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 17.7984 | − | 12.9313i | 0.583946 | − | 0.424261i | −0.256199 | − | 0.966624i | \(-0.582470\pi\) |
0.840144 | + | 0.542363i | \(0.182470\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 3.70820 | + | 11.4127i | 0.121531 | + | 0.374035i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −29.1246 | − | 21.1603i | −0.953497 | − | 0.692756i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 3.23607 | + | 2.35114i | 0.105718 | + | 0.0768084i | 0.639388 | − | 0.768884i | \(-0.279188\pi\) |
−0.533670 | + | 0.845693i | \(0.679188\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 8.34346 | + | 25.6785i | 0.272278 | + | 0.837987i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 8.09017 | − | 5.87785i | 0.263732 | − | 0.191613i | −0.448059 | − | 0.894004i | \(-0.647884\pi\) |
0.711791 | + | 0.702392i | \(0.247884\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1.23607 | + | 3.80423i | −0.0402519 | + | 0.123883i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 54.0000 | 1.75662 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 47.0000 | 1.52729 | 0.763647 | − | 0.645634i | \(-0.223407\pi\) | ||||
0.763647 | + | 0.645634i | \(0.223407\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −36.4058 | + | 26.4503i | −1.18054 | + | 0.857711i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 10.5066 | + | 32.3359i | 0.340341 | + | 1.04746i | 0.964031 | + | 0.265791i | \(0.0856331\pi\) |
−0.623689 | + | 0.781672i | \(0.714367\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −21.8435 | − | 15.8702i | −0.706838 | − | 0.513548i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 24.2705 | + | 17.6336i | 0.783736 | + | 0.569417i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 5.56231 | + | 17.1190i | 0.179429 | + | 0.552226i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 9.70820 | − | 7.05342i | 0.312842 | − | 0.227293i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 3.70820 | − | 11.4127i | 0.119371 | − | 0.367387i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 8.00000 | 0.257263 | 0.128631 | − | 0.991692i | \(-0.458942\pi\) | ||||
0.128631 | + | 0.991692i | \(0.458942\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 72.0000 | 2.31297 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 16.3779 | − | 50.4060i | 0.525592 | − | 1.61761i | −0.237551 | − | 0.971375i | \(-0.576345\pi\) |
0.763143 | − | 0.646230i | \(-0.223655\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −35.5967 | + | 25.8626i | −1.14118 | + | 0.829115i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 8.89919 | + | 6.46564i | 0.284710 | + | 0.206854i | 0.720969 | − | 0.692967i | \(-0.243697\pi\) |
−0.436259 | + | 0.899821i | \(0.643697\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −67.9574 | − | 49.3740i | −2.16971 | − | 1.57639i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 7.72542 | + | 23.7764i | 0.246403 | + | 0.758350i | 0.995403 | + | 0.0957796i | \(0.0305344\pi\) |
−0.749000 | + | 0.662570i | \(0.769466\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −14.5623 | + | 10.5801i | −0.463994 | + | 0.337111i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 14.8328 | − | 45.6507i | 0.472134 | − | 1.45308i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −6.00000 | −0.190789 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 16.0000 | 0.508257 | 0.254128 | − | 0.967170i | \(-0.418211\pi\) | ||||
0.254128 | + | 0.967170i | \(0.418211\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 32.4468 | − | 99.8609i | 1.02967 | − | 3.16899i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 19.4164 | − | 14.1068i | 0.615542 | − | 0.447217i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −0.618034 | − | 1.90211i | −0.0195733 | − | 0.0602405i | 0.940793 | − | 0.338982i | \(-0.110083\pi\) |
−0.960366 | + | 0.278742i | \(0.910083\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −7.28115 | − | 5.29007i | −0.230365 | − | 0.167370i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))