Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [575,2,Mod(24,575)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(575, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("575.24");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 575 = 5^{2} \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 575.b (of order \(2\), degree \(1\), 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: | \(4.59139811622\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(i, \sqrt{5})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 3x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 23) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 24.2 | ||
Root | \(-0.618034i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 575.24 |
Dual form | 575.2.b.d.24.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/575\mathbb{Z}\right)^\times\).
\(n\) | \(51\) | \(277\) |
\(\chi(n)\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − 0.618034i | − 0.437016i | −0.975835 | − | 0.218508i | \(-0.929881\pi\) | ||||
0.975835 | − | 0.218508i | \(-0.0701190\pi\) | |||||||
\(3\) | − 2.23607i | − 1.29099i | −0.763763 | − | 0.645497i | \(-0.776650\pi\) | ||||
0.763763 | − | 0.645497i | \(-0.223350\pi\) | |||||||
\(4\) | 1.61803 | 0.809017 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −1.38197 | −0.564185 | ||||||||
\(7\) | − 3.23607i | − 1.22312i | −0.791199 | − | 0.611559i | \(-0.790543\pi\) | ||||
0.791199 | − | 0.611559i | \(-0.209457\pi\) | |||||||
\(8\) | − 2.23607i | − 0.790569i | ||||||||
\(9\) | −2.00000 | −0.666667 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −5.23607 | −1.57873 | −0.789367 | − | 0.613922i | \(-0.789591\pi\) | ||||
−0.789367 | + | 0.613922i | \(0.789591\pi\) | |||||||
\(12\) | − 3.61803i | − 1.04444i | ||||||||
\(13\) | 3.00000i | 0.832050i | 0.909353 | + | 0.416025i | \(0.136577\pi\) | ||||
−0.909353 | + | 0.416025i | \(0.863423\pi\) | |||||||
\(14\) | −2.00000 | −0.534522 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.85410 | 0.463525 | ||||||||
\(17\) | − 0.763932i | − 0.185281i | −0.995700 | − | 0.0926404i | \(-0.970469\pi\) | ||||
0.995700 | − | 0.0926404i | \(-0.0295307\pi\) | |||||||
\(18\) | 1.23607i | 0.291344i | ||||||||
\(19\) | 2.00000 | 0.458831 | 0.229416 | − | 0.973329i | \(-0.426318\pi\) | ||||
0.229416 | + | 0.973329i | \(0.426318\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −7.23607 | −1.57904 | ||||||||
\(22\) | 3.23607i | 0.689932i | ||||||||
\(23\) | 1.00000i | 0.208514i | ||||||||
\(24\) | −5.00000 | −1.02062 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 1.85410 | 0.363619 | ||||||||
\(27\) | − 2.23607i | − 0.430331i | ||||||||
\(28\) | − 5.23607i | − 0.989524i | ||||||||
\(29\) | 3.00000 | 0.557086 | 0.278543 | − | 0.960424i | \(-0.410149\pi\) | ||||
0.278543 | + | 0.960424i | \(0.410149\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.70820 | 1.20483 | 0.602414 | − | 0.798183i | \(-0.294205\pi\) | ||||
0.602414 | + | 0.798183i | \(0.294205\pi\) | |||||||
\(32\) | − 5.61803i | − 0.993137i | ||||||||
\(33\) | 11.7082i | 2.03814i | ||||||||
\(34\) | −0.472136 | −0.0809706 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −3.23607 | −0.539345 | ||||||||
\(37\) | 1.23607i | 0.203208i | 0.994825 | + | 0.101604i | \(0.0323975\pi\) | ||||
−0.994825 | + | 0.101604i | \(0.967602\pi\) | |||||||
\(38\) | − 1.23607i | − 0.200517i | ||||||||
\(39\) | 6.70820 | 1.07417 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −3.47214 | −0.542257 | −0.271128 | − | 0.962543i | \(-0.587397\pi\) | ||||
−0.271128 | + | 0.962543i | \(0.587397\pi\) | |||||||
\(42\) | 4.47214i | 0.690066i | ||||||||
\(43\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(44\) | −8.47214 | −1.27722 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0.618034 | 0.0911241 | ||||||||
\(47\) | 2.23607i | 0.326164i | 0.986613 | + | 0.163082i | \(0.0521435\pi\) | ||||
−0.986613 | + | 0.163082i | \(0.947856\pi\) | |||||||
\(48\) | − 4.14590i | − 0.598409i | ||||||||
\(49\) | −3.47214 | −0.496019 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.70820 | −0.239196 | ||||||||
\(52\) | 4.85410i | 0.673143i | ||||||||
\(53\) | 0.472136i | 0.0648529i | 0.999474 | + | 0.0324264i | \(0.0103235\pi\) | ||||
−0.999474 | + | 0.0324264i | \(0.989677\pi\) | |||||||
\(54\) | −1.38197 | −0.188062 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −7.23607 | −0.966960 | ||||||||
\(57\) | − 4.47214i | − 0.592349i | ||||||||
\(58\) | − 1.85410i | − 0.243456i | ||||||||
\(59\) | −6.47214 | −0.842600 | −0.421300 | − | 0.906921i | \(-0.638426\pi\) | ||||
−0.421300 | + | 0.906921i | \(0.638426\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −6.94427 | −0.889123 | −0.444561 | − | 0.895748i | \(-0.646640\pi\) | ||||
−0.444561 | + | 0.895748i | \(0.646640\pi\) | |||||||
\(62\) | − 4.14590i | − 0.526530i | ||||||||
\(63\) | 6.47214i | 0.815412i | ||||||||
\(64\) | 0.236068 | 0.0295085 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 7.23607 | 0.890698 | ||||||||
\(67\) | 2.76393i | 0.337668i | 0.985644 | + | 0.168834i | \(0.0540002\pi\) | ||||
−0.985644 | + | 0.168834i | \(0.946000\pi\) | |||||||
\(68\) | − 1.23607i | − 0.149895i | ||||||||
\(69\) | 2.23607 | 0.269191 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 12.2361 | 1.45215 | 0.726077 | − | 0.687613i | \(-0.241342\pi\) | ||||
0.726077 | + | 0.687613i | \(0.241342\pi\) | |||||||
\(72\) | 4.47214i | 0.527046i | ||||||||
\(73\) | 6.52786i | 0.764029i | 0.924156 | + | 0.382014i | \(0.124770\pi\) | ||||
−0.924156 | + | 0.382014i | \(0.875230\pi\) | |||||||
\(74\) | 0.763932 | 0.0888053 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 3.23607 | 0.371202 | ||||||||
\(77\) | 16.9443i | 1.93098i | ||||||||
\(78\) | − 4.14590i | − 0.469431i | ||||||||
\(79\) | 10.9443 | 1.23133 | 0.615663 | − | 0.788009i | \(-0.288888\pi\) | ||||
0.615663 | + | 0.788009i | \(0.288888\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −11.0000 | −1.22222 | ||||||||
\(82\) | 2.14590i | 0.236975i | ||||||||
\(83\) | − 8.76393i | − 0.961967i | −0.876730 | − | 0.480983i | \(-0.840280\pi\) | ||||
0.876730 | − | 0.480983i | \(-0.159720\pi\) | |||||||
\(84\) | −11.7082 | −1.27747 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − 6.70820i | − 0.719195i | ||||||||
\(88\) | 11.7082i | 1.24810i | ||||||||
\(89\) | 10.4721 | 1.11004 | 0.555022 | − | 0.831836i | \(-0.312710\pi\) | ||||
0.555022 | + | 0.831836i | \(0.312710\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 9.70820 | 1.01770 | ||||||||
\(92\) | 1.61803i | 0.168692i | ||||||||
\(93\) | − 15.0000i | − 1.55543i | ||||||||
\(94\) | 1.38197 | 0.142539 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −12.5623 | −1.28213 | ||||||||
\(97\) | − 17.7082i | − 1.79800i | −0.437953 | − | 0.898998i | \(-0.644296\pi\) | ||||
0.437953 | − | 0.898998i | \(-0.355704\pi\) | |||||||
\(98\) | 2.14590i | 0.216768i | ||||||||
\(99\) | 10.4721 | 1.05249 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 4.47214 | 0.444994 | 0.222497 | − | 0.974933i | \(-0.428579\pi\) | ||||
0.222497 | + | 0.974933i | \(0.428579\pi\) | |||||||
\(102\) | 1.05573i | 0.104533i | ||||||||
\(103\) | − 4.18034i | − 0.411901i | −0.978562 | − | 0.205951i | \(-0.933971\pi\) | ||||
0.978562 | − | 0.205951i | \(-0.0660286\pi\) | |||||||
\(104\) | 6.70820 | 0.657794 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0.291796 | 0.0283417 | ||||||||
\(107\) | − 13.4164i | − 1.29701i | −0.761209 | − | 0.648507i | \(-0.775394\pi\) | ||||
0.761209 | − | 0.648507i | \(-0.224606\pi\) | |||||||
\(108\) | − 3.61803i | − 0.348145i | ||||||||
\(109\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 2.76393 | 0.262341 | ||||||||
\(112\) | − 6.00000i | − 0.566947i | ||||||||
\(113\) | 8.76393i | 0.824441i | 0.911084 | + | 0.412221i | \(0.135247\pi\) | ||||
−0.911084 | + | 0.412221i | \(0.864753\pi\) | |||||||
\(114\) | −2.76393 | −0.258866 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 4.85410 | 0.450692 | ||||||||
\(117\) | − 6.00000i | − 0.554700i | ||||||||
\(118\) | 4.00000i | 0.368230i | ||||||||
\(119\) | −2.47214 | −0.226620 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 16.4164 | 1.49240 | ||||||||
\(122\) | 4.29180i | 0.388561i | ||||||||
\(123\) | 7.76393i | 0.700050i | ||||||||
\(124\) | 10.8541 | 0.974727 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 4.00000 | 0.356348 | ||||||||
\(127\) | 7.29180i | 0.647042i | 0.946221 | + | 0.323521i | \(0.104867\pi\) | ||||
−0.946221 | + | 0.323521i | \(0.895133\pi\) | |||||||
\(128\) | − 11.3820i | − 1.00603i | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 18.7082 | 1.63454 | 0.817272 | − | 0.576253i | \(-0.195486\pi\) | ||||
0.817272 | + | 0.576253i | \(0.195486\pi\) | |||||||
\(132\) | 18.9443i | 1.64889i | ||||||||
\(133\) | − 6.47214i | − 0.561205i | ||||||||
\(134\) | 1.70820 | 0.147566 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −1.70820 | −0.146477 | ||||||||
\(137\) | 21.8885i | 1.87006i | 0.354563 | + | 0.935032i | \(0.384630\pi\) | ||||
−0.354563 | + | 0.935032i | \(0.615370\pi\) | |||||||
\(138\) | − 1.38197i | − 0.117641i | ||||||||
\(139\) | 10.7082 | 0.908258 | 0.454129 | − | 0.890936i | \(-0.349951\pi\) | ||||
0.454129 | + | 0.890936i | \(0.349951\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 5.00000 | 0.421076 | ||||||||
\(142\) | − 7.56231i | − 0.634615i | ||||||||
\(143\) | − 15.7082i | − 1.31359i | ||||||||
\(144\) | −3.70820 | −0.309017 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 4.03444 | 0.333893 | ||||||||
\(147\) | 7.76393i | 0.640358i | ||||||||
\(148\) | 2.00000i | 0.164399i | ||||||||
\(149\) | −23.8885 | −1.95703 | −0.978513 | − | 0.206186i | \(-0.933895\pi\) | ||||
−0.978513 | + | 0.206186i | \(0.933895\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 4.23607 | 0.344726 | 0.172363 | − | 0.985033i | \(-0.444860\pi\) | ||||
0.172363 | + | 0.985033i | \(0.444860\pi\) | |||||||
\(152\) | − 4.47214i | − 0.362738i | ||||||||
\(153\) | 1.52786i | 0.123520i | ||||||||
\(154\) | 10.4721 | 0.843869 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 10.8541 | 0.869024 | ||||||||
\(157\) | 11.4164i | 0.911129i | 0.890203 | + | 0.455564i | \(0.150562\pi\) | ||||
−0.890203 | + | 0.455564i | \(0.849438\pi\) | |||||||
\(158\) | − 6.76393i | − 0.538110i | ||||||||
\(159\) | 1.05573 | 0.0837247 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 3.23607 | 0.255038 | ||||||||
\(162\) | 6.79837i | 0.534131i | ||||||||
\(163\) | − 5.76393i | − 0.451466i | −0.974189 | − | 0.225733i | \(-0.927522\pi\) | ||||
0.974189 | − | 0.225733i | \(-0.0724777\pi\) | |||||||
\(164\) | −5.61803 | −0.438695 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −5.41641 | −0.420395 | ||||||||
\(167\) | − 1.52786i | − 0.118230i | −0.998251 | − | 0.0591148i | \(-0.981172\pi\) | ||||
0.998251 | − | 0.0591148i | \(-0.0188278\pi\) | |||||||
\(168\) | 16.1803i | 1.24834i | ||||||||
\(169\) | 4.00000 | 0.307692 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −4.00000 | −0.305888 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 22.9443i | 1.74442i | 0.489131 | + | 0.872210i | \(0.337314\pi\) | ||||
−0.489131 | + | 0.872210i | \(0.662686\pi\) | |||||||
\(174\) | −4.14590 | −0.314300 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −9.70820 | −0.731783 | ||||||||
\(177\) | 14.4721i | 1.08779i | ||||||||
\(178\) | − 6.47214i | − 0.485107i | ||||||||
\(179\) | −0.708204 | −0.0529336 | −0.0264668 | − | 0.999650i | \(-0.508426\pi\) | ||||
−0.0264668 | + | 0.999650i | \(0.508426\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 16.6525 | 1.23777 | 0.618884 | − | 0.785482i | \(-0.287585\pi\) | ||||
0.618884 | + | 0.785482i | \(0.287585\pi\) | |||||||
\(182\) | − 6.00000i | − 0.444750i | ||||||||
\(183\) | 15.5279i | 1.14785i | ||||||||
\(184\) | 2.23607 | 0.164845 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −9.27051 | −0.679747 | ||||||||
\(187\) | 4.00000i | 0.292509i | ||||||||
\(188\) | 3.61803i | 0.263872i | ||||||||
\(189\) | −7.23607 | −0.526346 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −26.1803 | −1.89434 | −0.947171 | − | 0.320728i | \(-0.896073\pi\) | ||||
−0.947171 | + | 0.320728i | \(0.896073\pi\) | |||||||
\(192\) | − 0.527864i | − 0.0380953i | ||||||||
\(193\) | 9.94427i | 0.715804i | 0.933759 | + | 0.357902i | \(0.116508\pi\) | ||||
−0.933759 | + | 0.357902i | \(0.883492\pi\) | |||||||
\(194\) | −10.9443 | −0.785753 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −5.61803 | −0.401288 | ||||||||
\(197\) | 1.47214i | 0.104885i | 0.998624 | + | 0.0524427i | \(0.0167007\pi\) | ||||
−0.998624 | + | 0.0524427i | \(0.983299\pi\) | |||||||
\(198\) | − 6.47214i | − 0.459955i | ||||||||
\(199\) | 12.2918 | 0.871342 | 0.435671 | − | 0.900106i | \(-0.356511\pi\) | ||||
0.435671 | + | 0.900106i | \(0.356511\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 6.18034 | 0.435928 | ||||||||
\(202\) | − 2.76393i | − 0.194470i | ||||||||
\(203\) | − 9.70820i | − 0.681382i | ||||||||
\(204\) | −2.76393 | −0.193514 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −2.58359 | −0.180007 | ||||||||
\(207\) | − 2.00000i | − 0.139010i | ||||||||
\(208\) | 5.56231i | 0.385677i | ||||||||
\(209\) | −10.4721 | −0.724373 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −23.4164 | −1.61205 | −0.806026 | − | 0.591880i | \(-0.798386\pi\) | ||||
−0.806026 | + | 0.591880i | \(0.798386\pi\) | |||||||
\(212\) | 0.763932i | 0.0524671i | ||||||||
\(213\) | − 27.3607i | − 1.87472i | ||||||||
\(214\) | −8.29180 | −0.566816 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −5.00000 | −0.340207 | ||||||||
\(217\) | − 21.7082i | − 1.47365i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 14.5967 | 0.986357 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2.29180 | 0.154163 | ||||||||
\(222\) | − 1.70820i | − 0.114647i | ||||||||
\(223\) | 4.00000i | 0.267860i | 0.990991 | + | 0.133930i | \(0.0427597\pi\) | ||||
−0.990991 | + | 0.133930i | \(0.957240\pi\) | |||||||
\(224\) | −18.1803 | −1.21473 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 5.41641 | 0.360294 | ||||||||
\(227\) | 12.1803i | 0.808438i | 0.914662 | + | 0.404219i | \(0.132457\pi\) | ||||
−0.914662 | + | 0.404219i | \(0.867543\pi\) | |||||||
\(228\) | − 7.23607i | − 0.479220i | ||||||||
\(229\) | 12.0000 | 0.792982 | 0.396491 | − | 0.918039i | \(-0.370228\pi\) | ||||
0.396491 | + | 0.918039i | \(0.370228\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 37.8885 | 2.49288 | ||||||||
\(232\) | − 6.70820i | − 0.440415i | ||||||||
\(233\) | − 6.52786i | − 0.427655i | −0.976871 | − | 0.213827i | \(-0.931407\pi\) | ||||
0.976871 | − | 0.213827i | \(-0.0685930\pi\) | |||||||
\(234\) | −3.70820 | −0.242413 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −10.4721 | −0.681678 | ||||||||
\(237\) | − 24.4721i | − 1.58964i | ||||||||
\(238\) | 1.52786i | 0.0990367i | ||||||||
\(239\) | −13.7639 | −0.890315 | −0.445157 | − | 0.895452i | \(-0.646852\pi\) | ||||
−0.445157 | + | 0.895452i | \(0.646852\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −23.1246 | −1.48959 | −0.744794 | − | 0.667295i | \(-0.767452\pi\) | ||||
−0.744794 | + | 0.667295i | \(0.767452\pi\) | |||||||
\(242\) | − 10.1459i | − 0.652203i | ||||||||
\(243\) | 17.8885i | 1.14755i | ||||||||
\(244\) | −11.2361 | −0.719316 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 4.79837 | 0.305933 | ||||||||
\(247\) | 6.00000i | 0.381771i | ||||||||
\(248\) | − 15.0000i | − 0.952501i | ||||||||
\(249\) | −19.5967 | −1.24189 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 2.29180 | 0.144657 | 0.0723284 | − | 0.997381i | \(-0.476957\pi\) | ||||
0.0723284 | + | 0.997381i | \(0.476957\pi\) | |||||||
\(252\) | 10.4721i | 0.659683i | ||||||||
\(253\) | − 5.23607i | − 0.329189i | ||||||||
\(254\) | 4.50658 | 0.282768 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −6.56231 | −0.410144 | ||||||||
\(257\) | 7.47214i | 0.466099i | 0.972465 | + | 0.233050i | \(0.0748704\pi\) | ||||
−0.972465 | + | 0.233050i | \(0.925130\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 4.00000 | 0.248548 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −6.00000 | −0.371391 | ||||||||
\(262\) | − 11.5623i | − 0.714322i | ||||||||
\(263\) | 2.94427i | 0.181552i | 0.995871 | + | 0.0907758i | \(0.0289347\pi\) | ||||
−0.995871 | + | 0.0907758i | \(0.971065\pi\) | |||||||
\(264\) | 26.1803 | 1.61129 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −4.00000 | −0.245256 | ||||||||
\(267\) | − 23.4164i | − 1.43306i | ||||||||
\(268\) | 4.47214i | 0.273179i | ||||||||
\(269\) | 7.94427 | 0.484371 | 0.242185 | − | 0.970230i | \(-0.422136\pi\) | ||||
0.242185 | + | 0.970230i | \(0.422136\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 8.00000 | 0.485965 | 0.242983 | − | 0.970031i | \(-0.421874\pi\) | ||||
0.242983 | + | 0.970031i | \(0.421874\pi\) | |||||||
\(272\) | − 1.41641i | − 0.0858823i | ||||||||
\(273\) | − 21.7082i | − 1.31384i | ||||||||
\(274\) | 13.5279 | 0.817248 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 3.61803 | 0.217780 | ||||||||
\(277\) | − 15.4721i | − 0.929631i | −0.885408 | − | 0.464815i | \(-0.846121\pi\) | ||||
0.885408 | − | 0.464815i | \(-0.153879\pi\) | |||||||
\(278\) | − 6.61803i | − 0.396923i | ||||||||
\(279\) | −13.4164 | −0.803219 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −8.76393 | −0.522812 | −0.261406 | − | 0.965229i | \(-0.584186\pi\) | ||||
−0.261406 | + | 0.965229i | \(0.584186\pi\) | |||||||
\(282\) | − 3.09017i | − 0.184017i | ||||||||
\(283\) | 27.7082i | 1.64708i | 0.567257 | + | 0.823541i | \(0.308005\pi\) | ||||
−0.567257 | + | 0.823541i | \(0.691995\pi\) | |||||||
\(284\) | 19.7984 | 1.17482 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −9.70820 | −0.574058 | ||||||||
\(287\) | 11.2361i | 0.663244i | ||||||||
\(288\) | 11.2361i | 0.662092i | ||||||||
\(289\) | 16.4164 | 0.965671 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −39.5967 | −2.32120 | ||||||||
\(292\) | 10.5623i | 0.618112i | ||||||||
\(293\) | − 1.52786i | − 0.0892588i | −0.999004 | − | 0.0446294i | \(-0.985789\pi\) | ||||
0.999004 | − | 0.0446294i | \(-0.0142107\pi\) | |||||||
\(294\) | 4.79837 | 0.279847 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 2.76393 | 0.160650 | ||||||||
\(297\) | 11.7082i | 0.679379i | ||||||||
\(298\) | 14.7639i | 0.855252i | ||||||||
\(299\) | −3.00000 | −0.173494 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | − 2.61803i | − 0.150651i | ||||||||
\(303\) | − 10.0000i | − 0.574485i | ||||||||
\(304\) | 3.70820 | 0.212680 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0.944272 | 0.0539804 | ||||||||
\(307\) | − 9.52786i | − 0.543784i | −0.962328 | − | 0.271892i | \(-0.912351\pi\) | ||||
0.962328 | − | 0.271892i | \(-0.0876493\pi\) | |||||||
\(308\) | 27.4164i | 1.56219i | ||||||||
\(309\) | −9.34752 | −0.531762 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 13.1803 | 0.747389 | 0.373694 | − | 0.927552i | \(-0.378091\pi\) | ||||
0.373694 | + | 0.927552i | \(0.378091\pi\) | |||||||
\(312\) | − 15.0000i | − 0.849208i | ||||||||
\(313\) | 24.3607i | 1.37695i | 0.725261 | + | 0.688474i | \(0.241719\pi\) | ||||
−0.725261 | + | 0.688474i | \(0.758281\pi\) | |||||||
\(314\) | 7.05573 | 0.398178 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 17.7082 | 0.996164 | ||||||||
\(317\) | − 25.4164i | − 1.42753i | −0.700386 | − | 0.713764i | \(-0.746989\pi\) | ||||
0.700386 | − | 0.713764i | \(-0.253011\pi\) | |||||||
\(318\) | − 0.652476i | − 0.0365890i | ||||||||
\(319\) | −15.7082 | −0.879491 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −30.0000 | −1.67444 | ||||||||
\(322\) | − 2.00000i | − 0.111456i | ||||||||
\(323\) | − 1.52786i | − 0.0850126i | ||||||||
\(324\) | −17.7984 | −0.988799 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −3.56231 | −0.197298 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 7.76393i | 0.428691i | ||||||||
\(329\) | 7.23607 | 0.398937 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −19.6525 | −1.08020 | −0.540099 | − | 0.841602i | \(-0.681613\pi\) | ||||
−0.540099 | + | 0.841602i | \(0.681613\pi\) | |||||||
\(332\) | − 14.1803i | − 0.778247i | ||||||||
\(333\) | − 2.47214i | − 0.135472i | ||||||||
\(334\) | −0.944272 | −0.0516683 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −13.4164 | −0.731925 | ||||||||
\(337\) | − 23.4164i | − 1.27557i | −0.770213 | − | 0.637787i | \(-0.779850\pi\) | ||||
0.770213 | − | 0.637787i | \(-0.220150\pi\) | |||||||
\(338\) | − 2.47214i | − 0.134466i | ||||||||
\(339\) | 19.5967 | 1.06435 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −35.1246 | −1.90210 | ||||||||
\(342\) | 2.47214i | 0.133678i | ||||||||
\(343\) | − 11.4164i | − 0.616428i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 14.1803 | 0.762340 | ||||||||
\(347\) | 9.88854i | 0.530845i | 0.964132 | + | 0.265422i | \(0.0855114\pi\) | ||||
−0.964132 | + | 0.265422i | \(0.914489\pi\) | |||||||
\(348\) | − 10.8541i | − 0.581841i | ||||||||
\(349\) | −24.4164 | −1.30698 | −0.653490 | − | 0.756935i | \(-0.726696\pi\) | ||||
−0.653490 | + | 0.756935i | \(0.726696\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 6.70820 | 0.358057 | ||||||||
\(352\) | 29.4164i | 1.56790i | ||||||||
\(353\) | 9.36068i | 0.498219i | 0.968475 | + | 0.249109i | \(0.0801379\pi\) | ||||
−0.968475 | + | 0.249109i | \(0.919862\pi\) | |||||||
\(354\) | 8.94427 | 0.475383 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 16.9443 | 0.898045 | ||||||||
\(357\) | 5.52786i | 0.292566i | ||||||||
\(358\) | 0.437694i | 0.0231329i | ||||||||
\(359\) | 19.8885 | 1.04968 | 0.524839 | − | 0.851202i | \(-0.324126\pi\) | ||||
0.524839 | + | 0.851202i | \(0.324126\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −15.0000 | −0.789474 | ||||||||
\(362\) | − 10.2918i | − 0.540925i | ||||||||
\(363\) | − 36.7082i | − 1.92668i | ||||||||
\(364\) | 15.7082 | 0.823334 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 9.59675 | 0.501630 | ||||||||
\(367\) | 4.18034i | 0.218212i | 0.994030 | + | 0.109106i | \(0.0347988\pi\) | ||||
−0.994030 | + | 0.109106i | \(0.965201\pi\) | |||||||
\(368\) | 1.85410i | 0.0966517i | ||||||||
\(369\) | 6.94427 | 0.361504 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.52786 | 0.0793227 | ||||||||
\(372\) | − 24.2705i | − 1.25837i | ||||||||
\(373\) | 7.70820i | 0.399116i | 0.979886 | + | 0.199558i | \(0.0639506\pi\) | ||||
−0.979886 | + | 0.199558i | \(0.936049\pi\) | |||||||
\(374\) | 2.47214 | 0.127831 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 5.00000 | 0.257855 | ||||||||
\(377\) | 9.00000i | 0.463524i | ||||||||
\(378\) | 4.47214i | 0.230022i | ||||||||
\(379\) | −24.3607 | −1.25132 | −0.625662 | − | 0.780094i | \(-0.715171\pi\) | ||||
−0.625662 | + | 0.780094i | \(0.715171\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 16.3050 | 0.835328 | ||||||||
\(382\) | 16.1803i | 0.827858i | ||||||||
\(383\) | 7.05573i | 0.360531i | 0.983618 | + | 0.180265i | \(0.0576957\pi\) | ||||
−0.983618 | + | 0.180265i | \(0.942304\pi\) | |||||||
\(384\) | −25.4508 | −1.29878 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 6.14590 | 0.312818 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | − 28.6525i | − 1.45461i | ||||||||
\(389\) | −25.5279 | −1.29431 | −0.647157 | − | 0.762357i | \(-0.724042\pi\) | ||||
−0.647157 | + | 0.762357i | \(0.724042\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0.763932 | 0.0386337 | ||||||||
\(392\) | 7.76393i | 0.392138i | ||||||||
\(393\) | − 41.8328i | − 2.11019i | ||||||||
\(394\) | 0.909830 | 0.0458366 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 16.9443 | 0.851482 | ||||||||
\(397\) | 24.4164i | 1.22542i | 0.790306 | + | 0.612712i | \(0.209922\pi\) | ||||
−0.790306 | + | 0.612712i | \(0.790078\pi\) | |||||||
\(398\) | − 7.59675i | − 0.380791i | ||||||||
\(399\) | −14.4721 | −0.724513 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −14.1803 | −0.708132 | −0.354066 | − | 0.935220i | \(-0.615201\pi\) | ||||
−0.354066 | + | 0.935220i | \(0.615201\pi\) | |||||||
\(402\) | − 3.81966i | − 0.190507i | ||||||||
\(403\) | 20.1246i | 1.00248i | ||||||||
\(404\) | 7.23607 | 0.360008 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −6.00000 | −0.297775 | ||||||||
\(407\) | − 6.47214i | − 0.320812i | ||||||||
\(408\) | 3.81966i | 0.189101i | ||||||||
\(409\) | −21.3607 | −1.05622 | −0.528109 | − | 0.849177i | \(-0.677099\pi\) | ||||
−0.528109 | + | 0.849177i | \(0.677099\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 48.9443 | 2.41424 | ||||||||
\(412\) | − 6.76393i | − 0.333235i | ||||||||
\(413\) | 20.9443i | 1.03060i | ||||||||
\(414\) | −1.23607 | −0.0607494 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 16.8541 | 0.826340 | ||||||||
\(417\) | − 23.9443i | − 1.17256i | ||||||||
\(418\) | 6.47214i | 0.316563i | ||||||||
\(419\) | 4.58359 | 0.223923 | 0.111962 | − | 0.993713i | \(-0.464287\pi\) | ||||
0.111962 | + | 0.993713i | \(0.464287\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −10.2918 | −0.501591 | −0.250796 | − | 0.968040i | \(-0.580692\pi\) | ||||
−0.250796 | + | 0.968040i | \(0.580692\pi\) | |||||||
\(422\) | 14.4721i | 0.704493i | ||||||||
\(423\) | − 4.47214i | − 0.217443i | ||||||||
\(424\) | 1.05573 | 0.0512707 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −16.9098 | −0.819284 | ||||||||
\(427\) | 22.4721i | 1.08750i | ||||||||
\(428\) | − 21.7082i | − 1.04931i | ||||||||
\(429\) | −35.1246 | −1.69583 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −17.5279 | −0.844288 | −0.422144 | − | 0.906529i | \(-0.638722\pi\) | ||||
−0.422144 | + | 0.906529i | \(0.638722\pi\) | |||||||
\(432\) | − 4.14590i | − 0.199470i | ||||||||
\(433\) | 17.8197i | 0.856358i | 0.903694 | + | 0.428179i | \(0.140845\pi\) | ||||
−0.903694 | + | 0.428179i | \(0.859155\pi\) | |||||||
\(434\) | −13.4164 | −0.644008 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 2.00000i | 0.0956730i | ||||||||
\(438\) | − 9.02129i | − 0.431054i | ||||||||
\(439\) | 18.7082 | 0.892894 | 0.446447 | − | 0.894810i | \(-0.352689\pi\) | ||||
0.446447 | + | 0.894810i | \(0.352689\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 6.94427 | 0.330680 | ||||||||
\(442\) | − 1.41641i | − 0.0673717i | ||||||||
\(443\) | 38.1246i | 1.81135i | 0.423967 | + | 0.905677i | \(0.360637\pi\) | ||||
−0.423967 | + | 0.905677i | \(0.639363\pi\) | |||||||
\(444\) | 4.47214 | 0.212238 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 2.47214 | 0.117059 | ||||||||
\(447\) | 53.4164i | 2.52651i | ||||||||
\(448\) | − 0.763932i | − 0.0360924i | ||||||||
\(449\) | 14.9443 | 0.705264 | 0.352632 | − | 0.935762i | \(-0.385287\pi\) | ||||
0.352632 | + | 0.935762i | \(0.385287\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 18.1803 | 0.856079 | ||||||||
\(452\) | 14.1803i | 0.666987i | ||||||||
\(453\) | − 9.47214i | − 0.445040i | ||||||||
\(454\) | 7.52786 | 0.353300 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −10.0000 | −0.468293 | ||||||||
\(457\) | 5.12461i | 0.239719i | 0.992791 | + | 0.119860i | \(0.0382444\pi\) | ||||
−0.992791 | + | 0.119860i | \(0.961756\pi\) | |||||||
\(458\) | − 7.41641i | − 0.346546i | ||||||||
\(459\) | −1.70820 | −0.0797321 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −1.47214 | −0.0685642 | −0.0342821 | − | 0.999412i | \(-0.510914\pi\) | ||||
−0.0342821 | + | 0.999412i | \(0.510914\pi\) | |||||||
\(462\) | − 23.4164i | − 1.08943i | ||||||||
\(463\) | − 20.0000i | − 0.929479i | −0.885448 | − | 0.464739i | \(-0.846148\pi\) | ||||
0.885448 | − | 0.464739i | \(-0.153852\pi\) | |||||||
\(464\) | 5.56231 | 0.258224 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −4.03444 | −0.186892 | ||||||||
\(467\) | 13.0557i | 0.604147i | 0.953285 | + | 0.302074i | \(0.0976788\pi\) | ||||
−0.953285 | + | 0.302074i | \(0.902321\pi\) | |||||||
\(468\) | − 9.70820i | − 0.448762i | ||||||||
\(469\) | 8.94427 | 0.413008 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 25.5279 | 1.17626 | ||||||||
\(472\) | 14.4721i | 0.666134i | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | −15.1246 | −0.694696 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −4.00000 | −0.183340 | ||||||||
\(477\) | − 0.944272i | − 0.0432352i | ||||||||
\(478\) | 8.50658i | 0.389082i | ||||||||
\(479\) | −31.5967 | −1.44369 | −0.721846 | − | 0.692054i | \(-0.756706\pi\) | ||||
−0.721846 | + | 0.692054i | \(0.756706\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3.70820 | −0.169080 | ||||||||
\(482\) | 14.2918i | 0.650973i | ||||||||
\(483\) | − 7.23607i | − 0.329252i | ||||||||
\(484\) | 26.5623 | 1.20738 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 11.0557 | 0.501498 | ||||||||
\(487\) | 14.7082i | 0.666492i | 0.942840 | + | 0.333246i | \(0.108144\pi\) | ||||
−0.942840 | + | 0.333246i | \(0.891856\pi\) | |||||||
\(488\) | 15.5279i | 0.702913i | ||||||||
\(489\) | −12.8885 | −0.582840 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 8.34752 | 0.376718 | 0.188359 | − | 0.982100i | \(-0.439683\pi\) | ||||
0.188359 | + | 0.982100i | \(0.439683\pi\) | |||||||
\(492\) | 12.5623i | 0.566352i | ||||||||
\(493\) | − 2.29180i | − 0.103217i | ||||||||
\(494\) | 3.70820 | 0.166840 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 12.4377 | 0.558469 | ||||||||
\(497\) | − 39.5967i | − 1.77616i | ||||||||
\(498\) | 12.1115i | 0.542727i | ||||||||
\(499\) | −19.2918 | −0.863619 | −0.431810 | − | 0.901965i | \(-0.642125\pi\) | ||||
−0.431810 | + | 0.901965i | \(0.642125\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −3.41641 | −0.152634 | ||||||||
\(502\) | − 1.41641i | − 0.0632174i | ||||||||
\(503\) | − 26.9443i | − 1.20139i | −0.799480 | − | 0.600693i | \(-0.794891\pi\) | ||||
0.799480 | − | 0.600693i | \(-0.205109\pi\) | |||||||
\(504\) | 14.4721 | 0.644640 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −3.23607 | −0.143861 | ||||||||
\(507\) | − 8.94427i | − 0.397229i | ||||||||
\(508\) | 11.7984i | 0.523468i | ||||||||
\(509\) | 28.3050 | 1.25459 | 0.627297 | − | 0.778780i | \(-0.284161\pi\) | ||||
0.627297 | + | 0.778780i | \(0.284161\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 21.1246 | 0.934498 | ||||||||
\(512\) | − 18.7082i | − 0.826794i | ||||||||
\(513\) | − 4.47214i | − 0.197450i | ||||||||
\(514\) | 4.61803 | 0.203693 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − 11.7082i | − 0.514926i | ||||||||
\(518\) | − 2.47214i | − 0.108619i | ||||||||
\(519\) | 51.3050 | 2.25204 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 31.4164 | 1.37638 | 0.688189 | − | 0.725532i | \(-0.258406\pi\) | ||||
0.688189 | + | 0.725532i | \(0.258406\pi\) | |||||||
\(522\) | 3.70820i | 0.162304i | ||||||||
\(523\) | 41.1246i | 1.79825i | 0.437688 | + | 0.899127i | \(0.355797\pi\) | ||||
−0.437688 | + | 0.899127i | \(0.644203\pi\) | |||||||
\(524\) | 30.2705 | 1.32237 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 1.81966 | 0.0793410 | ||||||||
\(527\) | − 5.12461i | − 0.223232i | ||||||||
\(528\) | 21.7082i | 0.944728i | ||||||||
\(529\) | −1.00000 | −0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 12.9443 | 0.561734 | ||||||||
\(532\) | − 10.4721i | − 0.454025i | ||||||||
\(533\) | − 10.4164i | − 0.451185i | ||||||||
\(534\) | −14.4721 | −0.626271 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 6.18034 | 0.266950 | ||||||||
\(537\) | 1.58359i | 0.0683370i | ||||||||
\(538\) | − 4.90983i | − 0.211678i | ||||||||
\(539\) | 18.1803 | 0.783083 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −34.4164 | −1.47968 | −0.739838 | − | 0.672785i | \(-0.765098\pi\) | ||||
−0.739838 | + | 0.672785i | \(0.765098\pi\) | |||||||
\(542\) | − 4.94427i | − 0.212375i | ||||||||
\(543\) | − 37.2361i | − 1.59795i | ||||||||
\(544\) | −4.29180 | −0.184009 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −13.4164 | −0.574169 | ||||||||
\(547\) | 29.5410i | 1.26308i | 0.775342 | + | 0.631541i | \(0.217577\pi\) | ||||
−0.775342 | + | 0.631541i | \(0.782423\pi\) | |||||||
\(548\) | 35.4164i | 1.51291i | ||||||||
\(549\) | 13.8885 | 0.592749 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 6.00000 | 0.255609 | ||||||||
\(552\) | − 5.00000i | − 0.212814i | ||||||||
\(553\) | − 35.4164i | − 1.50606i | ||||||||
\(554\) | −9.56231 | −0.406263 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 17.3262 | 0.734796 | ||||||||
\(557\) | 7.41641i | 0.314243i | 0.987579 | + | 0.157122i | \(0.0502215\pi\) | ||||
−0.987579 | + | 0.157122i | \(0.949779\pi\) | |||||||
\(558\) | 8.29180i | 0.351020i | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 8.94427 | 0.377627 | ||||||||
\(562\) | 5.41641i | 0.228477i | ||||||||
\(563\) | − 32.9443i | − 1.38844i | −0.719765 | − | 0.694218i | \(-0.755750\pi\) | ||||
0.719765 | − | 0.694218i | \(-0.244250\pi\) | |||||||
\(564\) | 8.09017 | 0.340658 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 17.1246 | 0.719801 | ||||||||
\(567\) | 35.5967i | 1.49492i | ||||||||
\(568\) | − 27.3607i | − 1.14803i | ||||||||
\(569\) | 22.1803 | 0.929848 | 0.464924 | − | 0.885351i | \(-0.346082\pi\) | ||||
0.464924 | + | 0.885351i | \(0.346082\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −14.2918 | −0.598093 | −0.299047 | − | 0.954239i | \(-0.596669\pi\) | ||||
−0.299047 | + | 0.954239i | \(0.596669\pi\) | |||||||
\(572\) | − 25.4164i | − 1.06271i | ||||||||
\(573\) | 58.5410i | 2.44559i | ||||||||
\(574\) | 6.94427 | 0.289848 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −0.472136 | −0.0196723 | ||||||||
\(577\) | − 22.8885i | − 0.952863i | −0.879212 | − | 0.476431i | \(-0.841930\pi\) | ||||
0.879212 | − | 0.476431i | \(-0.158070\pi\) | |||||||
\(578\) | − 10.1459i | − 0.422014i | ||||||||
\(579\) | 22.2361 | 0.924099 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −28.3607 | −1.17660 | ||||||||
\(582\) | 24.4721i | 1.01440i | ||||||||
\(583\) | − 2.47214i | − 0.102385i | ||||||||
\(584\) | 14.5967 | 0.604018 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −0.944272 | −0.0390075 | ||||||||
\(587\) | 24.7082i | 1.01982i | 0.860229 | + | 0.509908i | \(0.170321\pi\) | ||||
−0.860229 | + | 0.509908i | \(0.829679\pi\) | |||||||
\(588\) | 12.5623i | 0.518061i | ||||||||
\(589\) | 13.4164 | 0.552813 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 3.29180 | 0.135406 | ||||||||
\(592\) | 2.29180i | 0.0941922i | ||||||||
\(593\) | − 2.94427i | − 0.120907i | −0.998171 | − | 0.0604534i | \(-0.980745\pi\) | ||||
0.998171 | − | 0.0604534i | \(-0.0192546\pi\) | |||||||
\(594\) | 7.23607 | 0.296899 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −38.6525 | −1.58327 | ||||||||
\(597\) | − 27.4853i | − 1.12490i | ||||||||
\(598\) | 1.85410i | 0.0758199i | ||||||||
\(599\) | −33.8885 | −1.38465 | −0.692324 | − | 0.721587i | \(-0.743413\pi\) | ||||
−0.692324 | + | 0.721587i | \(0.743413\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 46.8885 | 1.91262 | 0.956312 | − | 0.292349i | \(-0.0944368\pi\) | ||||
0.956312 | + | 0.292349i | \(0.0944368\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − 5.52786i | − 0.225112i | ||||||||
\(604\) | 6.85410 | 0.278889 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −6.18034 | −0.251059 | ||||||||
\(607\) | − 26.4721i | − 1.07447i | −0.843432 | − | 0.537235i | \(-0.819469\pi\) | ||||
0.843432 | − | 0.537235i | \(-0.180531\pi\) | |||||||
\(608\) | − 11.2361i | − 0.455683i | ||||||||
\(609\) | −21.7082 | −0.879661 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −6.70820 | −0.271385 | ||||||||
\(612\) | 2.47214i | 0.0999302i | ||||||||
\(613\) | 5.70820i | 0.230552i | 0.993333 | + | 0.115276i | \(0.0367753\pi\) | ||||
−0.993333 | + | 0.115276i | \(0.963225\pi\) | |||||||
\(614\) | −5.88854 | −0.237642 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 37.8885 | 1.52657 | ||||||||
\(617\) | 7.52786i | 0.303060i | 0.988453 | + | 0.151530i | \(0.0484201\pi\) | ||||
−0.988453 | + | 0.151530i | \(0.951580\pi\) | |||||||
\(618\) | 5.77709i | 0.232389i | ||||||||
\(619\) | −19.4164 | −0.780411 | −0.390206 | − | 0.920728i | \(-0.627596\pi\) | ||||
−0.390206 | + | 0.920728i | \(0.627596\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 2.23607 | 0.0897303 | ||||||||
\(622\) | − 8.14590i | − 0.326621i | ||||||||
\(623\) | − 33.8885i | − 1.35772i | ||||||||
\(624\) | 12.4377 | 0.497906 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 15.0557 | 0.601748 | ||||||||
\(627\) | 23.4164i | 0.935161i | ||||||||
\(628\) | 18.4721i | 0.737118i | ||||||||
\(629\) | 0.944272 | 0.0376506 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 12.3607 | 0.492071 | 0.246035 | − | 0.969261i | \(-0.420872\pi\) | ||||
0.246035 | + | 0.969261i | \(0.420872\pi\) | |||||||
\(632\) | − 24.4721i | − 0.973449i | ||||||||
\(633\) | 52.3607i | 2.08115i | ||||||||
\(634\) | −15.7082 | −0.623852 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 1.70820 | 0.0677347 | ||||||||
\(637\) | − 10.4164i | − 0.412713i | ||||||||
\(638\) | 9.70820i | 0.384351i | ||||||||
\(639\) | −24.4721 | −0.968103 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −17.3050 | −0.683504 | −0.341752 | − | 0.939790i | \(-0.611020\pi\) | ||||
−0.341752 | + | 0.939790i | \(0.611020\pi\) | |||||||
\(642\) | 18.5410i | 0.731756i | ||||||||
\(643\) | − 29.5967i | − 1.16718i | −0.812048 | − | 0.583591i | \(-0.801647\pi\) | ||||
0.812048 | − | 0.583591i | \(-0.198353\pi\) | |||||||
\(644\) | 5.23607 | 0.206330 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −0.944272 | −0.0371519 | ||||||||
\(647\) | − 6.70820i | − 0.263727i | −0.991268 | − | 0.131863i | \(-0.957904\pi\) | ||||
0.991268 | − | 0.131863i | \(-0.0420960\pi\) | |||||||
\(648\) | 24.5967i | 0.966252i | ||||||||
\(649\) | 33.8885 | 1.33024 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −48.5410 | −1.90247 | ||||||||
\(652\) | − 9.32624i | − 0.365244i | ||||||||
\(653\) | − 38.3050i | − 1.49899i | −0.662011 | − | 0.749494i | \(-0.730297\pi\) | ||||
0.662011 | − | 0.749494i | \(-0.269703\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −6.43769 | −0.251350 | ||||||||
\(657\) | − 13.0557i | − 0.509352i | ||||||||
\(658\) | − 4.47214i | − 0.174342i | ||||||||
\(659\) | 10.6525 | 0.414962 | 0.207481 | − | 0.978239i | \(-0.433474\pi\) | ||||
0.207481 | + | 0.978239i | \(0.433474\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −22.9443 | −0.892429 | −0.446214 | − | 0.894926i | \(-0.647228\pi\) | ||||
−0.446214 | + | 0.894926i | \(0.647228\pi\) | |||||||
\(662\) | 12.1459i | 0.472064i | ||||||||
\(663\) | − 5.12461i | − 0.199023i | ||||||||
\(664\) | −19.5967 | −0.760501 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −1.52786 | −0.0592035 | ||||||||
\(667\) | 3.00000i | 0.116160i | ||||||||
\(668\) | − 2.47214i | − 0.0956498i | ||||||||
\(669\) | 8.94427 | 0.345806 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 36.3607 | 1.40369 | ||||||||
\(672\) | 40.6525i | 1.56820i | ||||||||
\(673\) | 3.00000i | 0.115642i | 0.998327 | + | 0.0578208i | \(0.0184152\pi\) | ||||
−0.998327 | + | 0.0578208i | \(0.981585\pi\) | |||||||
\(674\) | −14.4721 | −0.557446 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 6.47214 | 0.248928 | ||||||||
\(677\) | − 18.0000i | − 0.691796i | −0.938272 | − | 0.345898i | \(-0.887574\pi\) | ||||
0.938272 | − | 0.345898i | \(-0.112426\pi\) | |||||||
\(678\) | − 12.1115i | − 0.465138i | ||||||||
\(679\) | −57.3050 | −2.19916 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 27.2361 | 1.04369 | ||||||||
\(682\) | 21.7082i | 0.831250i | ||||||||
\(683\) | 26.5967i | 1.01770i | 0.860856 | + | 0.508848i | \(0.169929\pi\) | ||||
−0.860856 | + | 0.508848i | \(0.830071\pi\) | |||||||
\(684\) | −6.47214 | −0.247468 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −7.05573 | −0.269389 | ||||||||
\(687\) | − 26.8328i | − 1.02374i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −1.41641 | −0.0539608 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 7.05573 | 0.268413 | 0.134206 | − | 0.990953i | \(-0.457152\pi\) | ||||
0.134206 | + | 0.990953i | \(0.457152\pi\) | |||||||
\(692\) | 37.1246i | 1.41127i | ||||||||
\(693\) | − 33.8885i | − 1.28732i | ||||||||
\(694\) | 6.11146 | 0.231988 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −15.0000 | −0.568574 | ||||||||
\(697\) | 2.65248i | 0.100470i | ||||||||
\(698\) | 15.0902i | 0.571171i | ||||||||
\(699\) | −14.5967 | −0.552100 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −3.81966 | −0.144267 | −0.0721333 | − | 0.997395i | \(-0.522981\pi\) | ||||
−0.0721333 | + | 0.997395i | \(0.522981\pi\) | |||||||
\(702\) | − 4.14590i | − 0.156477i | ||||||||
\(703\) | 2.47214i | 0.0932384i | ||||||||
\(704\) | −1.23607 | −0.0465861 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 5.78522 | 0.217730 | ||||||||
\(707\) | − 14.4721i | − 0.544281i | ||||||||
\(708\) | 23.4164i | 0.880042i | ||||||||
\(709\) | 42.0689 | 1.57993 | 0.789965 | − | 0.613152i | \(-0.210099\pi\) | ||||
0.789965 | + | 0.613152i | \(0.210099\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −21.8885 | −0.820885 | ||||||||
\(712\) | − 23.4164i | − 0.877567i | ||||||||
\(713\) | 6.70820i | 0.251224i | ||||||||
\(714\) | 3.41641 | 0.127856 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −1.14590 | −0.0428242 | ||||||||
\(717\) | 30.7771i | 1.14939i | ||||||||
\(718\) | − 12.2918i | − 0.458726i | ||||||||
\(719\) | 3.05573 | 0.113959 | 0.0569797 | − | 0.998375i | \(-0.481853\pi\) | ||||
0.0569797 | + | 0.998375i | \(0.481853\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −13.5279 | −0.503804 | ||||||||
\(722\) | 9.27051i | 0.345013i | ||||||||
\(723\) | 51.7082i | 1.92305i | ||||||||
\(724\) | 26.9443 | 1.00138 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −22.6869 | −0.841990 | ||||||||
\(727\) | 27.7082i | 1.02764i | 0.857898 | + | 0.513820i | \(0.171770\pi\) | ||||
−0.857898 | + | 0.513820i | \(0.828230\pi\) | |||||||
\(728\) | − 21.7082i | − 0.804560i | ||||||||
\(729\) | 7.00000 | 0.259259 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 25.1246i | 0.928632i | ||||||||
\(733\) | − 31.2361i | − 1.15373i | −0.816839 | − | 0.576865i | \(-0.804276\pi\) | ||||
0.816839 | − | 0.576865i | \(-0.195724\pi\) | |||||||
\(734\) | 2.58359 | 0.0953621 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 5.61803 | 0.207083 | ||||||||
\(737\) | − 14.4721i | − 0.533088i | ||||||||
\(738\) | − 4.29180i | − 0.157983i | ||||||||
\(739\) | −26.8197 | −0.986577 | −0.493289 | − | 0.869866i | \(-0.664205\pi\) | ||||
−0.493289 | + | 0.869866i | \(0.664205\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 13.4164 | 0.492864 | ||||||||
\(742\) | − 0.944272i | − 0.0346653i | ||||||||
\(743\) | 41.1246i | 1.50872i | 0.656463 | + | 0.754358i | \(0.272052\pi\) | ||||
−0.656463 | + | 0.754358i | \(0.727948\pi\) | |||||||
\(744\) | −33.5410 | −1.22967 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 4.76393 | 0.174420 | ||||||||
\(747\) | 17.5279i | 0.641311i | ||||||||
\(748\) | 6.47214i | 0.236645i | ||||||||
\(749\) | −43.4164 | −1.58640 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 0.360680 | 0.0131614 | 0.00658070 | − | 0.999978i | \(-0.497905\pi\) | ||||
0.00658070 | + | 0.999978i | \(0.497905\pi\) | |||||||
\(752\) | 4.14590i | 0.151185i | ||||||||
\(753\) | − 5.12461i | − 0.186751i | ||||||||
\(754\) | 5.56231 | 0.202567 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −11.7082 | −0.425823 | ||||||||
\(757\) | − 1.59675i | − 0.0580348i | −0.999579 | − | 0.0290174i | \(-0.990762\pi\) | ||||
0.999579 | − | 0.0290174i | \(-0.00923782\pi\) | |||||||
\(758\) | 15.0557i | 0.546849i | ||||||||
\(759\) | −11.7082 | −0.424981 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 46.3050 | 1.67855 | 0.839277 | − | 0.543705i | \(-0.182979\pi\) | ||||
0.839277 | + | 0.543705i | \(0.182979\pi\) | |||||||
\(762\) | − 10.0770i | − 0.365052i | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −42.3607 | −1.53256 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 4.36068 | 0.157558 | ||||||||
\(767\) | − 19.4164i | − 0.701086i | ||||||||
\(768\) | 14.6738i | 0.529494i | ||||||||
\(769\) | 23.1246 | 0.833895 | 0.416947 | − | 0.908931i | \(-0.363100\pi\) | ||||
0.416947 | + | 0.908931i | \(0.363100\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 16.7082 | 0.601731 | ||||||||
\(772\) | 16.0902i | 0.579098i | ||||||||
\(773\) | − 5.52786i | − 0.198823i | −0.995046 | − | 0.0994117i | \(-0.968304\pi\) | ||||
0.995046 | − | 0.0994117i | \(-0.0316961\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −39.5967 | −1.42144 | ||||||||
\(777\) | − 8.94427i | − 0.320874i | ||||||||
\(778\) | 15.7771i | 0.565636i | ||||||||
\(779\) | −6.94427 | −0.248804 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −64.0689 | −2.29256 | ||||||||
\(782\) | − 0.472136i | − 0.0168835i | ||||||||
\(783\) | − 6.70820i | − 0.239732i | ||||||||
\(784\) | −6.43769 | −0.229918 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −25.8541 | −0.922185 | ||||||||
\(787\) | − 24.5836i | − 0.876310i | −0.898899 | − | 0.438155i | \(-0.855632\pi\) | ||||
0.898899 | − | 0.438155i | \(-0.144368\pi\) | |||||||
\(788\) | 2.38197i | 0.0848540i | ||||||||
\(789\) | 6.58359 | 0.234382 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 28.3607 | 1.00839 | ||||||||
\(792\) | − 23.4164i | − 0.832066i | ||||||||
\(793\) | − 20.8328i | − 0.739795i | ||||||||
\(794\) | 15.0902 | 0.535530 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 19.8885 | 0.704931 | ||||||||
\(797\) | 34.3607i | 1.21712i | 0.793509 | + | 0.608559i | \(0.208252\pi\) | ||||
−0.793509 | + | 0.608559i | \(0.791748\pi\) | |||||||
\(798\) | 8.94427i | 0.316624i | ||||||||
\(799\) | 1.70820 | 0.0604319 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −20.9443 | −0.740029 | ||||||||
\(802\) | 8.76393i | 0.309465i | ||||||||
\(803\) | − 34.1803i | − 1.20620i | ||||||||
\(804\) | 10.0000 | 0.352673 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 12.4377 | 0.438099 | ||||||||
\(807\) | − 17.7639i | − 0.625320i | ||||||||
\(808\) | − 10.0000i | − 0.351799i | ||||||||
\(809\) | −12.1115 | −0.425816 | −0.212908 | − | 0.977072i | \(-0.568293\pi\) | ||||
−0.212908 | + | 0.977072i | \(0.568293\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −24.3475 | −0.854957 | −0.427479 | − | 0.904025i | \(-0.640598\pi\) | ||||
−0.427479 | + | 0.904025i | \(0.640598\pi\) | |||||||
\(812\) | − 15.7082i | − 0.551250i | ||||||||
\(813\) | − 17.8885i | − 0.627379i | ||||||||
\(814\) | −4.00000 | −0.140200 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −3.16718 | −0.110874 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 13.2016i | 0.461584i | ||||||||
\(819\) | −19.4164 | −0.678464 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −38.9443 | −1.35916 | −0.679582 | − | 0.733599i | \(-0.737839\pi\) | ||||
−0.679582 | + | 0.733599i | \(0.737839\pi\) | |||||||
\(822\) | − 30.2492i | − 1.05506i | ||||||||
\(823\) | − 39.5410i | − 1.37831i | −0.724612 | − | 0.689157i | \(-0.757981\pi\) | ||||
0.724612 | − | 0.689157i | \(-0.242019\pi\) | |||||||
\(824\) | −9.34752 | −0.325636 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 12.9443 | 0.450389 | ||||||||
\(827\) | − 1.52786i | − 0.0531290i | −0.999647 | − | 0.0265645i | \(-0.991543\pi\) | ||||
0.999647 | − | 0.0265645i | \(-0.00845674\pi\) | |||||||
\(828\) | − 3.23607i | − 0.112461i | ||||||||
\(829\) | −40.2492 | −1.39791 | −0.698957 | − | 0.715164i | \(-0.746352\pi\) | ||||
−0.698957 | + | 0.715164i | \(0.746352\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −34.5967 | −1.20015 | ||||||||
\(832\) | 0.708204i | 0.0245526i | ||||||||
\(833\) | 2.65248i | 0.0919028i | ||||||||
\(834\) | −14.7984 | −0.512426 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −16.9443 | −0.586030 | ||||||||
\(837\) | − 15.0000i | − 0.518476i | ||||||||
\(838\) | − 2.83282i | − 0.0978580i | ||||||||
\(839\) | 41.1246 | 1.41978 | 0.709890 | − | 0.704313i | \(-0.248745\pi\) | ||||
0.709890 | + | 0.704313i | \(0.248745\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −20.0000 | −0.689655 | ||||||||
\(842\) | 6.36068i | 0.219204i | ||||||||
\(843\) | 19.5967i | 0.674948i | ||||||||
\(844\) | −37.8885 | −1.30418 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −2.76393 | −0.0950259 | ||||||||
\(847\) | − 53.1246i | − 1.82538i | ||||||||
\(848\) | 0.875388i | 0.0300610i | ||||||||
\(849\) | 61.9574 | 2.12637 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1.23607 | −0.0423719 | ||||||||
\(852\) | − 44.2705i | − 1.51668i | ||||||||
\(853\) | − 10.5836i | − 0.362375i | −0.983449 | − | 0.181188i | \(-0.942006\pi\) | ||||
0.983449 | − | 0.181188i | \(-0.0579941\pi\) | |||||||
\(854\) | 13.8885 | 0.475256 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −30.0000 | −1.02538 | ||||||||
\(857\) | − 1.47214i | − 0.0502872i | −0.999684 | − | 0.0251436i | \(-0.991996\pi\) | ||||
0.999684 | − | 0.0251436i | \(-0.00800430\pi\) | |||||||
\(858\) | 21.7082i | 0.741106i | ||||||||
\(859\) | 16.7082 | 0.570077 | 0.285038 | − | 0.958516i | \(-0.407994\pi\) | ||||
0.285038 | + | 0.958516i | \(0.407994\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 25.1246 | 0.856244 | ||||||||
\(862\) | 10.8328i | 0.368967i | ||||||||
\(863\) | − 21.5410i | − 0.733265i | −0.930366 | − | 0.366632i | \(-0.880511\pi\) | ||||
0.930366 | − | 0.366632i | \(-0.119489\pi\) | |||||||
\(864\) | −12.5623 | −0.427378 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 11.0132 | 0.374242 | ||||||||
\(867\) | − 36.7082i | − 1.24668i | ||||||||
\(868\) | − 35.1246i | − 1.19221i | ||||||||
\(869\) | −57.3050 | −1.94394 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −8.29180 | −0.280957 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 35.4164i | 1.19866i | ||||||||
\(874\) | 1.23607 | 0.0418106 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 23.6180 | 0.797979 | ||||||||
\(877\) | 36.4721i | 1.23158i | 0.787912 | + | 0.615788i | \(0.211162\pi\) | ||||
−0.787912 | + | 0.615788i | \(0.788838\pi\) | |||||||
\(878\) | − 11.5623i | − 0.390209i | ||||||||
\(879\) | −3.41641 | −0.115233 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 44.1803 | 1.48847 | 0.744237 | − | 0.667916i | \(-0.232813\pi\) | ||||
0.744237 | + | 0.667916i | \(0.232813\pi\) | |||||||
\(882\) | − 4.29180i | − 0.144512i | ||||||||
\(883\) | 4.00000i | 0.134611i | 0.997732 | + | 0.0673054i | \(0.0214402\pi\) | ||||
−0.997732 | + | 0.0673054i | \(0.978560\pi\) | |||||||
\(884\) | 3.70820 | 0.124720 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 23.5623 | 0.791591 | ||||||||
\(887\) | − 23.0689i | − 0.774577i | −0.921959 | − | 0.387289i | \(-0.873412\pi\) | ||||
0.921959 | − | 0.387289i | \(-0.126588\pi\) | |||||||
\(888\) | − 6.18034i | − 0.207399i | ||||||||
\(889\) | 23.5967 | 0.791410 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 57.5967 | 1.92956 | ||||||||
\(892\) | 6.47214i | 0.216703i | ||||||||
\(893\) | 4.47214i | 0.149654i | ||||||||
\(894\) | 33.0132 | 1.10413 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −36.8328 | −1.23050 | ||||||||
\(897\) | 6.70820i | 0.223980i | ||||||||
\(898\) | − 9.23607i | − 0.308212i | ||||||||
\(899\) | 20.1246 | 0.671193 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0.360680 | 0.0120160 | ||||||||
\(902\) | − 11.2361i | − 0.374120i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 19.5967 | 0.651778 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −5.85410 | −0.194490 | ||||||||
\(907\) | 40.2492i | 1.33645i | 0.743958 | + | 0.668227i | \(0.232946\pi\) | ||||
−0.743958 | + | 0.668227i | \(0.767054\pi\) | |||||||
\(908\) | 19.7082i | 0.654040i | ||||||||
\(909\) | −8.94427 | −0.296663 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 31.3050 | 1.03718 | 0.518590 | − | 0.855023i | \(-0.326457\pi\) | ||||
0.518590 | + | 0.855023i | \(0.326457\pi\) | |||||||
\(912\) | − 8.29180i | − 0.274569i | ||||||||
\(913\) | 45.8885i | 1.51869i | ||||||||
\(914\) | 3.16718 | 0.104761 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 19.4164 | 0.641536 | ||||||||
\(917\) | − 60.5410i | − 1.99924i | ||||||||
\(918\) | 1.05573i | 0.0348442i | ||||||||
\(919\) | −41.1246 | −1.35658 | −0.678288 | − | 0.734796i | \(-0.737278\pi\) | ||||
−0.678288 | + | 0.734796i | \(0.737278\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −21.3050 | −0.702022 | ||||||||
\(922\) | 0.909830i | 0.0299637i | ||||||||
\(923\) | 36.7082i | 1.20827i | ||||||||
\(924\) | 61.3050 | 2.01678 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −12.3607 | −0.406197 | ||||||||
\(927\) | 8.36068i | 0.274601i | ||||||||
\(928\) | − 16.8541i | − 0.553263i | ||||||||
\(929\) | 24.0557 | 0.789243 | 0.394621 | − | 0.918844i | \(-0.370876\pi\) | ||||
0.394621 | + | 0.918844i | \(0.370876\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −6.94427 | −0.227589 | ||||||||
\(932\) | − 10.5623i | − 0.345980i | ||||||||
\(933\) | − 29.4721i | − 0.964874i | ||||||||
\(934\) | 8.06888 | 0.264022 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −13.4164 | −0.438529 | ||||||||
\(937\) | − 34.1803i | − 1.11662i | −0.829631 | − | 0.558312i | \(-0.811449\pi\) | ||||
0.829631 | − | 0.558312i | \(-0.188551\pi\) | |||||||
\(938\) | − 5.52786i | − 0.180491i | ||||||||
\(939\) | 54.4721 | 1.77763 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 6.65248 | 0.216865 | 0.108432 | − | 0.994104i | \(-0.465417\pi\) | ||||
0.108432 | + | 0.994104i | \(0.465417\pi\) | |||||||
\(942\) | − 15.7771i | − 0.514045i | ||||||||
\(943\) | − 3.47214i | − 0.113068i | ||||||||
\(944\) | −12.0000 | −0.390567 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 10.8197i | 0.351592i | 0.984427 | + | 0.175796i | \(0.0562499\pi\) | ||||
−0.984427 | + | 0.175796i | \(0.943750\pi\) | |||||||
\(948\) | − 39.5967i | − 1.28604i | ||||||||
\(949\) | −19.5836 | −0.635710 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −56.8328 | −1.84293 | ||||||||
\(952\) | 5.52786i | 0.179159i | ||||||||
\(953\) | 20.4721i | 0.663158i | 0.943428 | + | 0.331579i | \(0.107581\pi\) | ||||
−0.943428 | + | 0.331579i | \(0.892419\pi\) | |||||||
\(954\) | −0.583592 | −0.0188945 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −22.2705 | −0.720280 | ||||||||
\(957\) | 35.1246i | 1.13542i | ||||||||
\(958\) | 19.5279i | 0.630917i | ||||||||
\(959\) | 70.8328 | 2.28731 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 14.0000 | 0.451613 | ||||||||
\(962\) | 2.29180i | 0.0738905i | ||||||||
\(963\) | 26.8328i | 0.864675i | ||||||||
\(964\) | −37.4164 | −1.20510 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −4.47214 | −0.143889 | ||||||||
\(967\) | − 27.5410i | − 0.885659i | −0.896606 | − | 0.442830i | \(-0.853975\pi\) | ||||
0.896606 | − | 0.442830i | \(-0.146025\pi\) | |||||||
\(968\) | − 36.7082i | − 1.17985i | ||||||||
\(969\) | −3.41641 | −0.109751 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 16.4721 | 0.528616 | 0.264308 | − | 0.964438i | \(-0.414856\pi\) | ||||
0.264308 | + | 0.964438i | \(0.414856\pi\) | |||||||
\(972\) | 28.9443i | 0.928388i | ||||||||
\(973\) | − 34.6525i | − 1.11091i | ||||||||
\(974\) | 9.09017 | 0.291268 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −12.8754 | −0.412131 | ||||||||
\(977\) | 23.3475i | 0.746953i | 0.927640 | + | 0.373477i | \(0.121834\pi\) | ||||
−0.927640 | + | 0.373477i | \(0.878166\pi\) | |||||||
\(978\) | 7.96556i | 0.254710i | ||||||||
\(979\) | −54.8328 | −1.75246 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | − 5.15905i | − 0.164632i | ||||||||
\(983\) | − 40.4721i | − 1.29086i | −0.763819 | − | 0.645430i | \(-0.776678\pi\) | ||||
0.763819 | − | 0.645430i | \(-0.223322\pi\) | |||||||
\(984\) | 17.3607 | 0.553438 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −1.41641 | −0.0451076 | ||||||||
\(987\) | − 16.1803i | − 0.515026i | ||||||||
\(988\) | 9.70820i | 0.308859i | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 24.0000 | 0.762385 | 0.381193 | − | 0.924496i | \(-0.375513\pi\) | ||||
0.381193 | + | 0.924496i | \(0.375513\pi\) | |||||||
\(992\) | − 37.6869i | − 1.19656i | ||||||||
\(993\) | 43.9443i | 1.39453i | ||||||||
\(994\) | −24.4721 | −0.776209 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −31.7082 | −1.00471 | ||||||||
\(997\) | − 16.8328i | − 0.533101i | −0.963821 | − | 0.266550i | \(-0.914116\pi\) | ||||
0.963821 | − | 0.266550i | \(-0.0858838\pi\) | |||||||
\(998\) | 11.9230i | 0.377416i | ||||||||
\(999\) | 2.76393 | 0.0874469 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))