Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8303,2,Mod(1,8303)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8303, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8303.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8303 = 19^{2} \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8303.a (trivial) |
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: | yes |
Analytic conductor: | \(66.2997887983\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{10})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x - 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 23) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-0.618034\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8303.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.618034 | −0.437016 | −0.218508 | − | 0.975835i | \(-0.570119\pi\) | ||||
−0.218508 | + | 0.975835i | \(0.570119\pi\) | |||||||
\(3\) | 2.23607 | 1.29099 | 0.645497 | − | 0.763763i | \(-0.276650\pi\) | ||||
0.645497 | + | 0.763763i | \(0.276650\pi\) | |||||||
\(4\) | −1.61803 | −0.809017 | ||||||||
\(5\) | 1.23607 | 0.552786 | 0.276393 | − | 0.961045i | \(-0.410861\pi\) | ||||
0.276393 | + | 0.961045i | \(0.410861\pi\) | |||||||
\(6\) | −1.38197 | −0.564185 | ||||||||
\(7\) | 3.23607 | 1.22312 | 0.611559 | − | 0.791199i | \(-0.290543\pi\) | ||||
0.611559 | + | 0.791199i | \(0.290543\pi\) | |||||||
\(8\) | 2.23607 | 0.790569 | ||||||||
\(9\) | 2.00000 | 0.666667 | ||||||||
\(10\) | −0.763932 | −0.241577 | ||||||||
\(11\) | −5.23607 | −1.57873 | −0.789367 | − | 0.613922i | \(-0.789591\pi\) | ||||
−0.789367 | + | 0.613922i | \(0.789591\pi\) | |||||||
\(12\) | −3.61803 | −1.04444 | ||||||||
\(13\) | −3.00000 | −0.832050 | −0.416025 | − | 0.909353i | \(-0.636577\pi\) | ||||
−0.416025 | + | 0.909353i | \(0.636577\pi\) | |||||||
\(14\) | −2.00000 | −0.534522 | ||||||||
\(15\) | 2.76393 | 0.713644 | ||||||||
\(16\) | 1.85410 | 0.463525 | ||||||||
\(17\) | 0.763932 | 0.185281 | 0.0926404 | − | 0.995700i | \(-0.470469\pi\) | ||||
0.0926404 | + | 0.995700i | \(0.470469\pi\) | |||||||
\(18\) | −1.23607 | −0.291344 | ||||||||
\(19\) | 0 | 0 | ||||||||
\(20\) | −2.00000 | −0.447214 | ||||||||
\(21\) | 7.23607 | 1.57904 | ||||||||
\(22\) | 3.23607 | 0.689932 | ||||||||
\(23\) | 1.00000 | 0.208514 | ||||||||
\(24\) | 5.00000 | 1.02062 | ||||||||
\(25\) | −3.47214 | −0.694427 | ||||||||
\(26\) | 1.85410 | 0.363619 | ||||||||
\(27\) | −2.23607 | −0.430331 | ||||||||
\(28\) | −5.23607 | −0.989524 | ||||||||
\(29\) | 3.00000 | 0.557086 | 0.278543 | − | 0.960424i | \(-0.410149\pi\) | ||||
0.278543 | + | 0.960424i | \(0.410149\pi\) | |||||||
\(30\) | −1.70820 | −0.311874 | ||||||||
\(31\) | −6.70820 | −1.20483 | −0.602414 | − | 0.798183i | \(-0.705795\pi\) | ||||
−0.602414 | + | 0.798183i | \(0.705795\pi\) | |||||||
\(32\) | −5.61803 | −0.993137 | ||||||||
\(33\) | −11.7082 | −2.03814 | ||||||||
\(34\) | −0.472136 | −0.0809706 | ||||||||
\(35\) | 4.00000 | 0.676123 | ||||||||
\(36\) | −3.23607 | −0.539345 | ||||||||
\(37\) | 1.23607 | 0.203208 | 0.101604 | − | 0.994825i | \(-0.467602\pi\) | ||||
0.101604 | + | 0.994825i | \(0.467602\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −6.70820 | −1.07417 | ||||||||
\(40\) | 2.76393 | 0.437016 | ||||||||
\(41\) | 3.47214 | 0.542257 | 0.271128 | − | 0.962543i | \(-0.412603\pi\) | ||||
0.271128 | + | 0.962543i | \(0.412603\pi\) | |||||||
\(42\) | −4.47214 | −0.690066 | ||||||||
\(43\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(44\) | 8.47214 | 1.27722 | ||||||||
\(45\) | 2.47214 | 0.368524 | ||||||||
\(46\) | −0.618034 | −0.0911241 | ||||||||
\(47\) | −2.23607 | −0.326164 | −0.163082 | − | 0.986613i | \(-0.552144\pi\) | ||||
−0.163082 | + | 0.986613i | \(0.552144\pi\) | |||||||
\(48\) | 4.14590 | 0.598409 | ||||||||
\(49\) | 3.47214 | 0.496019 | ||||||||
\(50\) | 2.14590 | 0.303476 | ||||||||
\(51\) | 1.70820 | 0.239196 | ||||||||
\(52\) | 4.85410 | 0.673143 | ||||||||
\(53\) | −0.472136 | −0.0648529 | −0.0324264 | − | 0.999474i | \(-0.510323\pi\) | ||||
−0.0324264 | + | 0.999474i | \(0.510323\pi\) | |||||||
\(54\) | 1.38197 | 0.188062 | ||||||||
\(55\) | −6.47214 | −0.872703 | ||||||||
\(56\) | 7.23607 | 0.966960 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −1.85410 | −0.243456 | ||||||||
\(59\) | −6.47214 | −0.842600 | −0.421300 | − | 0.906921i | \(-0.638426\pi\) | ||||
−0.421300 | + | 0.906921i | \(0.638426\pi\) | |||||||
\(60\) | −4.47214 | −0.577350 | ||||||||
\(61\) | −6.94427 | −0.889123 | −0.444561 | − | 0.895748i | \(-0.646640\pi\) | ||||
−0.444561 | + | 0.895748i | \(0.646640\pi\) | |||||||
\(62\) | 4.14590 | 0.526530 | ||||||||
\(63\) | 6.47214 | 0.815412 | ||||||||
\(64\) | −0.236068 | −0.0295085 | ||||||||
\(65\) | −3.70820 | −0.459946 | ||||||||
\(66\) | 7.23607 | 0.890698 | ||||||||
\(67\) | 2.76393 | 0.337668 | 0.168834 | − | 0.985644i | \(-0.446000\pi\) | ||||
0.168834 | + | 0.985644i | \(0.446000\pi\) | |||||||
\(68\) | −1.23607 | −0.149895 | ||||||||
\(69\) | 2.23607 | 0.269191 | ||||||||
\(70\) | −2.47214 | −0.295477 | ||||||||
\(71\) | −12.2361 | −1.45215 | −0.726077 | − | 0.687613i | \(-0.758658\pi\) | ||||
−0.726077 | + | 0.687613i | \(0.758658\pi\) | |||||||
\(72\) | 4.47214 | 0.527046 | ||||||||
\(73\) | 6.52786 | 0.764029 | 0.382014 | − | 0.924156i | \(-0.375230\pi\) | ||||
0.382014 | + | 0.924156i | \(0.375230\pi\) | |||||||
\(74\) | −0.763932 | −0.0888053 | ||||||||
\(75\) | −7.76393 | −0.896502 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −16.9443 | −1.93098 | ||||||||
\(78\) | 4.14590 | 0.469431 | ||||||||
\(79\) | 10.9443 | 1.23133 | 0.615663 | − | 0.788009i | \(-0.288888\pi\) | ||||
0.615663 | + | 0.788009i | \(0.288888\pi\) | |||||||
\(80\) | 2.29180 | 0.256231 | ||||||||
\(81\) | −11.0000 | −1.22222 | ||||||||
\(82\) | −2.14590 | −0.236975 | ||||||||
\(83\) | −8.76393 | −0.961967 | −0.480983 | − | 0.876730i | \(-0.659720\pi\) | ||||
−0.480983 | + | 0.876730i | \(0.659720\pi\) | |||||||
\(84\) | −11.7082 | −1.27747 | ||||||||
\(85\) | 0.944272 | 0.102421 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 6.70820 | 0.719195 | ||||||||
\(88\) | −11.7082 | −1.24810 | ||||||||
\(89\) | 10.4721 | 1.11004 | 0.555022 | − | 0.831836i | \(-0.312710\pi\) | ||||
0.555022 | + | 0.831836i | \(0.312710\pi\) | |||||||
\(90\) | −1.52786 | −0.161051 | ||||||||
\(91\) | −9.70820 | −1.01770 | ||||||||
\(92\) | −1.61803 | −0.168692 | ||||||||
\(93\) | −15.0000 | −1.55543 | ||||||||
\(94\) | 1.38197 | 0.142539 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −12.5623 | −1.28213 | ||||||||
\(97\) | −17.7082 | −1.79800 | −0.898998 | − | 0.437953i | \(-0.855704\pi\) | ||||
−0.898998 | + | 0.437953i | \(0.855704\pi\) | |||||||
\(98\) | −2.14590 | −0.216768 | ||||||||
\(99\) | −10.4721 | −1.05249 | ||||||||
\(100\) | 5.61803 | 0.561803 | ||||||||
\(101\) | 4.47214 | 0.444994 | 0.222497 | − | 0.974933i | \(-0.428579\pi\) | ||||
0.222497 | + | 0.974933i | \(0.428579\pi\) | |||||||
\(102\) | −1.05573 | −0.104533 | ||||||||
\(103\) | 4.18034 | 0.411901 | 0.205951 | − | 0.978562i | \(-0.433971\pi\) | ||||
0.205951 | + | 0.978562i | \(0.433971\pi\) | |||||||
\(104\) | −6.70820 | −0.657794 | ||||||||
\(105\) | 8.94427 | 0.872872 | ||||||||
\(106\) | 0.291796 | 0.0283417 | ||||||||
\(107\) | −13.4164 | −1.29701 | −0.648507 | − | 0.761209i | \(-0.724606\pi\) | ||||
−0.648507 | + | 0.761209i | \(0.724606\pi\) | |||||||
\(108\) | 3.61803 | 0.348145 | ||||||||
\(109\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(110\) | 4.00000 | 0.381385 | ||||||||
\(111\) | 2.76393 | 0.262341 | ||||||||
\(112\) | 6.00000 | 0.566947 | ||||||||
\(113\) | −8.76393 | −0.824441 | −0.412221 | − | 0.911084i | \(-0.635247\pi\) | ||||
−0.412221 | + | 0.911084i | \(0.635247\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.23607 | 0.115264 | ||||||||
\(116\) | −4.85410 | −0.450692 | ||||||||
\(117\) | −6.00000 | −0.554700 | ||||||||
\(118\) | 4.00000 | 0.368230 | ||||||||
\(119\) | 2.47214 | 0.226620 | ||||||||
\(120\) | 6.18034 | 0.564185 | ||||||||
\(121\) | 16.4164 | 1.49240 | ||||||||
\(122\) | 4.29180 | 0.388561 | ||||||||
\(123\) | 7.76393 | 0.700050 | ||||||||
\(124\) | 10.8541 | 0.974727 | ||||||||
\(125\) | −10.4721 | −0.936656 | ||||||||
\(126\) | −4.00000 | −0.356348 | ||||||||
\(127\) | 7.29180 | 0.647042 | 0.323521 | − | 0.946221i | \(-0.395133\pi\) | ||||
0.323521 | + | 0.946221i | \(0.395133\pi\) | |||||||
\(128\) | 11.3820 | 1.00603 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 2.29180 | 0.201004 | ||||||||
\(131\) | 18.7082 | 1.63454 | 0.817272 | − | 0.576253i | \(-0.195486\pi\) | ||||
0.817272 | + | 0.576253i | \(0.195486\pi\) | |||||||
\(132\) | 18.9443 | 1.64889 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −1.70820 | −0.147566 | ||||||||
\(135\) | −2.76393 | −0.237881 | ||||||||
\(136\) | 1.70820 | 0.146477 | ||||||||
\(137\) | −21.8885 | −1.87006 | −0.935032 | − | 0.354563i | \(-0.884630\pi\) | ||||
−0.935032 | + | 0.354563i | \(0.884630\pi\) | |||||||
\(138\) | −1.38197 | −0.117641 | ||||||||
\(139\) | −10.7082 | −0.908258 | −0.454129 | − | 0.890936i | \(-0.650049\pi\) | ||||
−0.454129 | + | 0.890936i | \(0.650049\pi\) | |||||||
\(140\) | −6.47214 | −0.546995 | ||||||||
\(141\) | −5.00000 | −0.421076 | ||||||||
\(142\) | 7.56231 | 0.634615 | ||||||||
\(143\) | 15.7082 | 1.31359 | ||||||||
\(144\) | 3.70820 | 0.309017 | ||||||||
\(145\) | 3.70820 | 0.307950 | ||||||||
\(146\) | −4.03444 | −0.333893 | ||||||||
\(147\) | 7.76393 | 0.640358 | ||||||||
\(148\) | −2.00000 | −0.164399 | ||||||||
\(149\) | 23.8885 | 1.95703 | 0.978513 | − | 0.206186i | \(-0.0661051\pi\) | ||||
0.978513 | + | 0.206186i | \(0.0661051\pi\) | |||||||
\(150\) | 4.79837 | 0.391786 | ||||||||
\(151\) | −4.23607 | −0.344726 | −0.172363 | − | 0.985033i | \(-0.555140\pi\) | ||||
−0.172363 | + | 0.985033i | \(0.555140\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 1.52786 | 0.123520 | ||||||||
\(154\) | 10.4721 | 0.843869 | ||||||||
\(155\) | −8.29180 | −0.666013 | ||||||||
\(156\) | 10.8541 | 0.869024 | ||||||||
\(157\) | −11.4164 | −0.911129 | −0.455564 | − | 0.890203i | \(-0.650562\pi\) | ||||
−0.455564 | + | 0.890203i | \(0.650562\pi\) | |||||||
\(158\) | −6.76393 | −0.538110 | ||||||||
\(159\) | −1.05573 | −0.0837247 | ||||||||
\(160\) | −6.94427 | −0.548993 | ||||||||
\(161\) | 3.23607 | 0.255038 | ||||||||
\(162\) | 6.79837 | 0.534131 | ||||||||
\(163\) | −5.76393 | −0.451466 | −0.225733 | − | 0.974189i | \(-0.572478\pi\) | ||||
−0.225733 | + | 0.974189i | \(0.572478\pi\) | |||||||
\(164\) | −5.61803 | −0.438695 | ||||||||
\(165\) | −14.4721 | −1.12665 | ||||||||
\(166\) | 5.41641 | 0.420395 | ||||||||
\(167\) | −1.52786 | −0.118230 | −0.0591148 | − | 0.998251i | \(-0.518828\pi\) | ||||
−0.0591148 | + | 0.998251i | \(0.518828\pi\) | |||||||
\(168\) | 16.1803 | 1.24834 | ||||||||
\(169\) | −4.00000 | −0.307692 | ||||||||
\(170\) | −0.583592 | −0.0447595 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −22.9443 | −1.74442 | −0.872210 | − | 0.489131i | \(-0.837314\pi\) | ||||
−0.872210 | + | 0.489131i | \(0.837314\pi\) | |||||||
\(174\) | −4.14590 | −0.314300 | ||||||||
\(175\) | −11.2361 | −0.849367 | ||||||||
\(176\) | −9.70820 | −0.731783 | ||||||||
\(177\) | −14.4721 | −1.08779 | ||||||||
\(178\) | −6.47214 | −0.485107 | ||||||||
\(179\) | −0.708204 | −0.0529336 | −0.0264668 | − | 0.999650i | \(-0.508426\pi\) | ||||
−0.0264668 | + | 0.999650i | \(0.508426\pi\) | |||||||
\(180\) | −4.00000 | −0.298142 | ||||||||
\(181\) | −16.6525 | −1.23777 | −0.618884 | − | 0.785482i | \(-0.712415\pi\) | ||||
−0.618884 | + | 0.785482i | \(0.712415\pi\) | |||||||
\(182\) | 6.00000 | 0.444750 | ||||||||
\(183\) | −15.5279 | −1.14785 | ||||||||
\(184\) | 2.23607 | 0.164845 | ||||||||
\(185\) | 1.52786 | 0.112331 | ||||||||
\(186\) | 9.27051 | 0.679747 | ||||||||
\(187\) | −4.00000 | −0.292509 | ||||||||
\(188\) | 3.61803 | 0.263872 | ||||||||
\(189\) | −7.23607 | −0.526346 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −26.1803 | −1.89434 | −0.947171 | − | 0.320728i | \(-0.896073\pi\) | ||||
−0.947171 | + | 0.320728i | \(0.896073\pi\) | |||||||
\(192\) | −0.527864 | −0.0380953 | ||||||||
\(193\) | −9.94427 | −0.715804 | −0.357902 | − | 0.933759i | \(-0.616508\pi\) | ||||
−0.357902 | + | 0.933759i | \(0.616508\pi\) | |||||||
\(194\) | 10.9443 | 0.785753 | ||||||||
\(195\) | −8.29180 | −0.593788 | ||||||||
\(196\) | −5.61803 | −0.401288 | ||||||||
\(197\) | −1.47214 | −0.104885 | −0.0524427 | − | 0.998624i | \(-0.516701\pi\) | ||||
−0.0524427 | + | 0.998624i | \(0.516701\pi\) | |||||||
\(198\) | 6.47214 | 0.459955 | ||||||||
\(199\) | −12.2918 | −0.871342 | −0.435671 | − | 0.900106i | \(-0.643489\pi\) | ||||
−0.435671 | + | 0.900106i | \(0.643489\pi\) | |||||||
\(200\) | −7.76393 | −0.548993 | ||||||||
\(201\) | 6.18034 | 0.435928 | ||||||||
\(202\) | −2.76393 | −0.194470 | ||||||||
\(203\) | 9.70820 | 0.681382 | ||||||||
\(204\) | −2.76393 | −0.193514 | ||||||||
\(205\) | 4.29180 | 0.299752 | ||||||||
\(206\) | −2.58359 | −0.180007 | ||||||||
\(207\) | 2.00000 | 0.139010 | ||||||||
\(208\) | −5.56231 | −0.385677 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | −5.52786 | −0.381459 | ||||||||
\(211\) | 23.4164 | 1.61205 | 0.806026 | − | 0.591880i | \(-0.201614\pi\) | ||||
0.806026 | + | 0.591880i | \(0.201614\pi\) | |||||||
\(212\) | 0.763932 | 0.0524671 | ||||||||
\(213\) | −27.3607 | −1.87472 | ||||||||
\(214\) | 8.29180 | 0.566816 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −5.00000 | −0.340207 | ||||||||
\(217\) | −21.7082 | −1.47365 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 14.5967 | 0.986357 | ||||||||
\(220\) | 10.4721 | 0.706031 | ||||||||
\(221\) | −2.29180 | −0.154163 | ||||||||
\(222\) | −1.70820 | −0.114647 | ||||||||
\(223\) | −4.00000 | −0.267860 | −0.133930 | − | 0.990991i | \(-0.542760\pi\) | ||||
−0.133930 | + | 0.990991i | \(0.542760\pi\) | |||||||
\(224\) | −18.1803 | −1.21473 | ||||||||
\(225\) | −6.94427 | −0.462951 | ||||||||
\(226\) | 5.41641 | 0.360294 | ||||||||
\(227\) | 12.1803 | 0.808438 | 0.404219 | − | 0.914662i | \(-0.367543\pi\) | ||||
0.404219 | + | 0.914662i | \(0.367543\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −12.0000 | −0.792982 | −0.396491 | − | 0.918039i | \(-0.629772\pi\) | ||||
−0.396491 | + | 0.918039i | \(0.629772\pi\) | |||||||
\(230\) | −0.763932 | −0.0503722 | ||||||||
\(231\) | −37.8885 | −2.49288 | ||||||||
\(232\) | 6.70820 | 0.440415 | ||||||||
\(233\) | −6.52786 | −0.427655 | −0.213827 | − | 0.976871i | \(-0.568593\pi\) | ||||
−0.213827 | + | 0.976871i | \(0.568593\pi\) | |||||||
\(234\) | 3.70820 | 0.242413 | ||||||||
\(235\) | −2.76393 | −0.180299 | ||||||||
\(236\) | 10.4721 | 0.681678 | ||||||||
\(237\) | 24.4721 | 1.58964 | ||||||||
\(238\) | −1.52786 | −0.0990367 | ||||||||
\(239\) | 13.7639 | 0.890315 | 0.445157 | − | 0.895452i | \(-0.353148\pi\) | ||||
0.445157 | + | 0.895452i | \(0.353148\pi\) | |||||||
\(240\) | 5.12461 | 0.330792 | ||||||||
\(241\) | 23.1246 | 1.48959 | 0.744794 | − | 0.667295i | \(-0.232548\pi\) | ||||
0.744794 | + | 0.667295i | \(0.232548\pi\) | |||||||
\(242\) | −10.1459 | −0.652203 | ||||||||
\(243\) | −17.8885 | −1.14755 | ||||||||
\(244\) | 11.2361 | 0.719316 | ||||||||
\(245\) | 4.29180 | 0.274193 | ||||||||
\(246\) | −4.79837 | −0.305933 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −15.0000 | −0.952501 | ||||||||
\(249\) | −19.5967 | −1.24189 | ||||||||
\(250\) | 6.47214 | 0.409334 | ||||||||
\(251\) | 2.29180 | 0.144657 | 0.0723284 | − | 0.997381i | \(-0.476957\pi\) | ||||
0.0723284 | + | 0.997381i | \(0.476957\pi\) | |||||||
\(252\) | −10.4721 | −0.659683 | ||||||||
\(253\) | −5.23607 | −0.329189 | ||||||||
\(254\) | −4.50658 | −0.282768 | ||||||||
\(255\) | 2.11146 | 0.132225 | ||||||||
\(256\) | −6.56231 | −0.410144 | ||||||||
\(257\) | 7.47214 | 0.466099 | 0.233050 | − | 0.972465i | \(-0.425130\pi\) | ||||
0.233050 | + | 0.972465i | \(0.425130\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 4.00000 | 0.248548 | ||||||||
\(260\) | 6.00000 | 0.372104 | ||||||||
\(261\) | 6.00000 | 0.371391 | ||||||||
\(262\) | −11.5623 | −0.714322 | ||||||||
\(263\) | 2.94427 | 0.181552 | 0.0907758 | − | 0.995871i | \(-0.471065\pi\) | ||||
0.0907758 | + | 0.995871i | \(0.471065\pi\) | |||||||
\(264\) | −26.1803 | −1.61129 | ||||||||
\(265\) | −0.583592 | −0.0358498 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 23.4164 | 1.43306 | ||||||||
\(268\) | −4.47214 | −0.273179 | ||||||||
\(269\) | 7.94427 | 0.484371 | 0.242185 | − | 0.970230i | \(-0.422136\pi\) | ||||
0.242185 | + | 0.970230i | \(0.422136\pi\) | |||||||
\(270\) | 1.70820 | 0.103958 | ||||||||
\(271\) | 8.00000 | 0.485965 | 0.242983 | − | 0.970031i | \(-0.421874\pi\) | ||||
0.242983 | + | 0.970031i | \(0.421874\pi\) | |||||||
\(272\) | 1.41641 | 0.0858823 | ||||||||
\(273\) | −21.7082 | −1.31384 | ||||||||
\(274\) | 13.5279 | 0.817248 | ||||||||
\(275\) | 18.1803 | 1.09632 | ||||||||
\(276\) | −3.61803 | −0.217780 | ||||||||
\(277\) | 15.4721 | 0.929631 | 0.464815 | − | 0.885408i | \(-0.346121\pi\) | ||||
0.464815 | + | 0.885408i | \(0.346121\pi\) | |||||||
\(278\) | 6.61803 | 0.396923 | ||||||||
\(279\) | −13.4164 | −0.803219 | ||||||||
\(280\) | 8.94427 | 0.534522 | ||||||||
\(281\) | 8.76393 | 0.522812 | 0.261406 | − | 0.965229i | \(-0.415814\pi\) | ||||
0.261406 | + | 0.965229i | \(0.415814\pi\) | |||||||
\(282\) | 3.09017 | 0.184017 | ||||||||
\(283\) | 27.7082 | 1.64708 | 0.823541 | − | 0.567257i | \(-0.191995\pi\) | ||||
0.823541 | + | 0.567257i | \(0.191995\pi\) | |||||||
\(284\) | 19.7984 | 1.17482 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −9.70820 | −0.574058 | ||||||||
\(287\) | 11.2361 | 0.663244 | ||||||||
\(288\) | −11.2361 | −0.662092 | ||||||||
\(289\) | −16.4164 | −0.965671 | ||||||||
\(290\) | −2.29180 | −0.134579 | ||||||||
\(291\) | −39.5967 | −2.32120 | ||||||||
\(292\) | −10.5623 | −0.618112 | ||||||||
\(293\) | 1.52786 | 0.0892588 | 0.0446294 | − | 0.999004i | \(-0.485789\pi\) | ||||
0.0446294 | + | 0.999004i | \(0.485789\pi\) | |||||||
\(294\) | −4.79837 | −0.279847 | ||||||||
\(295\) | −8.00000 | −0.465778 | ||||||||
\(296\) | 2.76393 | 0.160650 | ||||||||
\(297\) | 11.7082 | 0.679379 | ||||||||
\(298\) | −14.7639 | −0.855252 | ||||||||
\(299\) | −3.00000 | −0.173494 | ||||||||
\(300\) | 12.5623 | 0.725285 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 2.61803 | 0.150651 | ||||||||
\(303\) | 10.0000 | 0.574485 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −8.58359 | −0.491495 | ||||||||
\(306\) | −0.944272 | −0.0539804 | ||||||||
\(307\) | −9.52786 | −0.543784 | −0.271892 | − | 0.962328i | \(-0.587649\pi\) | ||||
−0.271892 | + | 0.962328i | \(0.587649\pi\) | |||||||
\(308\) | 27.4164 | 1.56219 | ||||||||
\(309\) | 9.34752 | 0.531762 | ||||||||
\(310\) | 5.12461 | 0.291058 | ||||||||
\(311\) | 13.1803 | 0.747389 | 0.373694 | − | 0.927552i | \(-0.378091\pi\) | ||||
0.373694 | + | 0.927552i | \(0.378091\pi\) | |||||||
\(312\) | −15.0000 | −0.849208 | ||||||||
\(313\) | 24.3607 | 1.37695 | 0.688474 | − | 0.725261i | \(-0.258281\pi\) | ||||
0.688474 | + | 0.725261i | \(0.258281\pi\) | |||||||
\(314\) | 7.05573 | 0.398178 | ||||||||
\(315\) | 8.00000 | 0.450749 | ||||||||
\(316\) | −17.7082 | −0.996164 | ||||||||
\(317\) | −25.4164 | −1.42753 | −0.713764 | − | 0.700386i | \(-0.753011\pi\) | ||||
−0.713764 | + | 0.700386i | \(0.753011\pi\) | |||||||
\(318\) | 0.652476 | 0.0365890 | ||||||||
\(319\) | −15.7082 | −0.879491 | ||||||||
\(320\) | −0.291796 | −0.0163119 | ||||||||
\(321\) | −30.0000 | −1.67444 | ||||||||
\(322\) | −2.00000 | −0.111456 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 17.7984 | 0.988799 | ||||||||
\(325\) | 10.4164 | 0.577798 | ||||||||
\(326\) | 3.56231 | 0.197298 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 7.76393 | 0.428691 | ||||||||
\(329\) | −7.23607 | −0.398937 | ||||||||
\(330\) | 8.94427 | 0.492366 | ||||||||
\(331\) | 19.6525 | 1.08020 | 0.540099 | − | 0.841602i | \(-0.318387\pi\) | ||||
0.540099 | + | 0.841602i | \(0.318387\pi\) | |||||||
\(332\) | 14.1803 | 0.778247 | ||||||||
\(333\) | 2.47214 | 0.135472 | ||||||||
\(334\) | 0.944272 | 0.0516683 | ||||||||
\(335\) | 3.41641 | 0.186658 | ||||||||
\(336\) | 13.4164 | 0.731925 | ||||||||
\(337\) | −23.4164 | −1.27557 | −0.637787 | − | 0.770213i | \(-0.720150\pi\) | ||||
−0.637787 | + | 0.770213i | \(0.720150\pi\) | |||||||
\(338\) | 2.47214 | 0.134466 | ||||||||
\(339\) | −19.5967 | −1.06435 | ||||||||
\(340\) | −1.52786 | −0.0828601 | ||||||||
\(341\) | 35.1246 | 1.90210 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −11.4164 | −0.616428 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 2.76393 | 0.148805 | ||||||||
\(346\) | 14.1803 | 0.762340 | ||||||||
\(347\) | −9.88854 | −0.530845 | −0.265422 | − | 0.964132i | \(-0.585511\pi\) | ||||
−0.265422 | + | 0.964132i | \(0.585511\pi\) | |||||||
\(348\) | −10.8541 | −0.581841 | ||||||||
\(349\) | 24.4164 | 1.30698 | 0.653490 | − | 0.756935i | \(-0.273304\pi\) | ||||
0.653490 | + | 0.756935i | \(0.273304\pi\) | |||||||
\(350\) | 6.94427 | 0.371187 | ||||||||
\(351\) | 6.70820 | 0.358057 | ||||||||
\(352\) | 29.4164 | 1.56790 | ||||||||
\(353\) | 9.36068 | 0.498219 | 0.249109 | − | 0.968475i | \(-0.419862\pi\) | ||||
0.249109 | + | 0.968475i | \(0.419862\pi\) | |||||||
\(354\) | 8.94427 | 0.475383 | ||||||||
\(355\) | −15.1246 | −0.802731 | ||||||||
\(356\) | −16.9443 | −0.898045 | ||||||||
\(357\) | 5.52786 | 0.292566 | ||||||||
\(358\) | 0.437694 | 0.0231329 | ||||||||
\(359\) | −19.8885 | −1.04968 | −0.524839 | − | 0.851202i | \(-0.675874\pi\) | ||||
−0.524839 | + | 0.851202i | \(0.675874\pi\) | |||||||
\(360\) | 5.52786 | 0.291344 | ||||||||
\(361\) | 0 | 0 | ||||||||
\(362\) | 10.2918 | 0.540925 | ||||||||
\(363\) | 36.7082 | 1.92668 | ||||||||
\(364\) | 15.7082 | 0.823334 | ||||||||
\(365\) | 8.06888 | 0.422345 | ||||||||
\(366\) | 9.59675 | 0.501630 | ||||||||
\(367\) | −4.18034 | −0.218212 | −0.109106 | − | 0.994030i | \(-0.534799\pi\) | ||||
−0.109106 | + | 0.994030i | \(0.534799\pi\) | |||||||
\(368\) | 1.85410 | 0.0966517 | ||||||||
\(369\) | 6.94427 | 0.361504 | ||||||||
\(370\) | −0.944272 | −0.0490904 | ||||||||
\(371\) | −1.52786 | −0.0793227 | ||||||||
\(372\) | 24.2705 | 1.25837 | ||||||||
\(373\) | −7.70820 | −0.399116 | −0.199558 | − | 0.979886i | \(-0.563951\pi\) | ||||
−0.199558 | + | 0.979886i | \(0.563951\pi\) | |||||||
\(374\) | 2.47214 | 0.127831 | ||||||||
\(375\) | −23.4164 | −1.20922 | ||||||||
\(376\) | −5.00000 | −0.257855 | ||||||||
\(377\) | −9.00000 | −0.463524 | ||||||||
\(378\) | 4.47214 | 0.230022 | ||||||||
\(379\) | −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 | ||||||||
\(382\) | 16.1803 | 0.827858 | ||||||||
\(383\) | −7.05573 | −0.360531 | −0.180265 | − | 0.983618i | \(-0.557696\pi\) | ||||
−0.180265 | + | 0.983618i | \(0.557696\pi\) | |||||||
\(384\) | 25.4508 | 1.29878 | ||||||||
\(385\) | −20.9443 | −1.06742 | ||||||||
\(386\) | 6.14590 | 0.312818 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 28.6525 | 1.45461 | ||||||||
\(389\) | 25.5279 | 1.29431 | 0.647157 | − | 0.762357i | \(-0.275958\pi\) | ||||
0.647157 | + | 0.762357i | \(0.275958\pi\) | |||||||
\(390\) | 5.12461 | 0.259495 | ||||||||
\(391\) | 0.763932 | 0.0386337 | ||||||||
\(392\) | 7.76393 | 0.392138 | ||||||||
\(393\) | 41.8328 | 2.11019 | ||||||||
\(394\) | 0.909830 | 0.0458366 | ||||||||
\(395\) | 13.5279 | 0.680661 | ||||||||
\(396\) | 16.9443 | 0.851482 | ||||||||
\(397\) | −24.4164 | −1.22542 | −0.612712 | − | 0.790306i | \(-0.709922\pi\) | ||||
−0.612712 | + | 0.790306i | \(0.709922\pi\) | |||||||
\(398\) | 7.59675 | 0.380791 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −6.43769 | −0.321885 | ||||||||
\(401\) | 14.1803 | 0.708132 | 0.354066 | − | 0.935220i | \(-0.384799\pi\) | ||||
0.354066 | + | 0.935220i | \(0.384799\pi\) | |||||||
\(402\) | −3.81966 | −0.190507 | ||||||||
\(403\) | 20.1246 | 1.00248 | ||||||||
\(404\) | −7.23607 | −0.360008 | ||||||||
\(405\) | −13.5967 | −0.675628 | ||||||||
\(406\) | −6.00000 | −0.297775 | ||||||||
\(407\) | −6.47214 | −0.320812 | ||||||||
\(408\) | 3.81966 | 0.189101 | ||||||||
\(409\) | −21.3607 | −1.05622 | −0.528109 | − | 0.849177i | \(-0.677099\pi\) | ||||
−0.528109 | + | 0.849177i | \(0.677099\pi\) | |||||||
\(410\) | −2.65248 | −0.130996 | ||||||||
\(411\) | −48.9443 | −2.41424 | ||||||||
\(412\) | −6.76393 | −0.333235 | ||||||||
\(413\) | −20.9443 | −1.03060 | ||||||||
\(414\) | −1.23607 | −0.0607494 | ||||||||
\(415\) | −10.8328 | −0.531762 | ||||||||
\(416\) | 16.8541 | 0.826340 | ||||||||
\(417\) | −23.9443 | −1.17256 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −4.58359 | −0.223923 | −0.111962 | − | 0.993713i | \(-0.535713\pi\) | ||||
−0.111962 | + | 0.993713i | \(0.535713\pi\) | |||||||
\(420\) | −14.4721 | −0.706168 | ||||||||
\(421\) | 10.2918 | 0.501591 | 0.250796 | − | 0.968040i | \(-0.419308\pi\) | ||||
0.250796 | + | 0.968040i | \(0.419308\pi\) | |||||||
\(422\) | −14.4721 | −0.704493 | ||||||||
\(423\) | −4.47214 | −0.217443 | ||||||||
\(424\) | −1.05573 | −0.0512707 | ||||||||
\(425\) | −2.65248 | −0.128664 | ||||||||
\(426\) | 16.9098 | 0.819284 | ||||||||
\(427\) | −22.4721 | −1.08750 | ||||||||
\(428\) | 21.7082 | 1.04931 | ||||||||
\(429\) | 35.1246 | 1.69583 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 17.5279 | 0.844288 | 0.422144 | − | 0.906529i | \(-0.361278\pi\) | ||||
0.422144 | + | 0.906529i | \(0.361278\pi\) | |||||||
\(432\) | −4.14590 | −0.199470 | ||||||||
\(433\) | −17.8197 | −0.856358 | −0.428179 | − | 0.903694i | \(-0.640845\pi\) | ||||
−0.428179 | + | 0.903694i | \(0.640845\pi\) | |||||||
\(434\) | 13.4164 | 0.644008 | ||||||||
\(435\) | 8.29180 | 0.397561 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | −9.02129 | −0.431054 | ||||||||
\(439\) | 18.7082 | 0.892894 | 0.446447 | − | 0.894810i | \(-0.352689\pi\) | ||||
0.446447 | + | 0.894810i | \(0.352689\pi\) | |||||||
\(440\) | −14.4721 | −0.689932 | ||||||||
\(441\) | 6.94427 | 0.330680 | ||||||||
\(442\) | 1.41641 | 0.0673717 | ||||||||
\(443\) | 38.1246 | 1.81135 | 0.905677 | − | 0.423967i | \(-0.139363\pi\) | ||||
0.905677 | + | 0.423967i | \(0.139363\pi\) | |||||||
\(444\) | −4.47214 | −0.212238 | ||||||||
\(445\) | 12.9443 | 0.613617 | ||||||||
\(446\) | 2.47214 | 0.117059 | ||||||||
\(447\) | 53.4164 | 2.52651 | ||||||||
\(448\) | −0.763932 | −0.0360924 | ||||||||
\(449\) | 14.9443 | 0.705264 | 0.352632 | − | 0.935762i | \(-0.385287\pi\) | ||||
0.352632 | + | 0.935762i | \(0.385287\pi\) | |||||||
\(450\) | 4.29180 | 0.202317 | ||||||||
\(451\) | −18.1803 | −0.856079 | ||||||||
\(452\) | 14.1803 | 0.666987 | ||||||||
\(453\) | −9.47214 | −0.445040 | ||||||||
\(454\) | −7.52786 | −0.353300 | ||||||||
\(455\) | −12.0000 | −0.562569 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −5.12461 | −0.239719 | −0.119860 | − | 0.992791i | \(-0.538244\pi\) | ||||
−0.119860 | + | 0.992791i | \(0.538244\pi\) | |||||||
\(458\) | 7.41641 | 0.346546 | ||||||||
\(459\) | −1.70820 | −0.0797321 | ||||||||
\(460\) | −2.00000 | −0.0932505 | ||||||||
\(461\) | −1.47214 | −0.0685642 | −0.0342821 | − | 0.999412i | \(-0.510914\pi\) | ||||
−0.0342821 | + | 0.999412i | \(0.510914\pi\) | |||||||
\(462\) | 23.4164 | 1.08943 | ||||||||
\(463\) | −20.0000 | −0.929479 | −0.464739 | − | 0.885448i | \(-0.653852\pi\) | ||||
−0.464739 | + | 0.885448i | \(0.653852\pi\) | |||||||
\(464\) | 5.56231 | 0.258224 | ||||||||
\(465\) | −18.5410 | −0.859819 | ||||||||
\(466\) | 4.03444 | 0.186892 | ||||||||
\(467\) | −13.0557 | −0.604147 | −0.302074 | − | 0.953285i | \(-0.597679\pi\) | ||||
−0.302074 | + | 0.953285i | \(0.597679\pi\) | |||||||
\(468\) | 9.70820 | 0.448762 | ||||||||
\(469\) | 8.94427 | 0.413008 | ||||||||
\(470\) | 1.70820 | 0.0787936 | ||||||||
\(471\) | −25.5279 | −1.17626 | ||||||||
\(472\) | −14.4721 | −0.666134 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | −15.1246 | −0.694696 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −4.00000 | −0.183340 | ||||||||
\(477\) | −0.944272 | −0.0432352 | ||||||||
\(478\) | −8.50658 | −0.389082 | ||||||||
\(479\) | 31.5967 | 1.44369 | 0.721846 | − | 0.692054i | \(-0.243294\pi\) | ||||
0.721846 | + | 0.692054i | \(0.243294\pi\) | |||||||
\(480\) | −15.5279 | −0.708747 | ||||||||
\(481\) | −3.70820 | −0.169080 | ||||||||
\(482\) | −14.2918 | −0.650973 | ||||||||
\(483\) | 7.23607 | 0.329252 | ||||||||
\(484\) | −26.5623 | −1.20738 | ||||||||
\(485\) | −21.8885 | −0.993908 | ||||||||
\(486\) | 11.0557 | 0.501498 | ||||||||
\(487\) | 14.7082 | 0.666492 | 0.333246 | − | 0.942840i | \(-0.391856\pi\) | ||||
0.333246 | + | 0.942840i | \(0.391856\pi\) | |||||||
\(488\) | −15.5279 | −0.702913 | ||||||||
\(489\) | −12.8885 | −0.582840 | ||||||||
\(490\) | −2.65248 | −0.119827 | ||||||||
\(491\) | 8.34752 | 0.376718 | 0.188359 | − | 0.982100i | \(-0.439683\pi\) | ||||
0.188359 | + | 0.982100i | \(0.439683\pi\) | |||||||
\(492\) | −12.5623 | −0.566352 | ||||||||
\(493\) | 2.29180 | 0.103217 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −12.9443 | −0.581802 | ||||||||
\(496\) | −12.4377 | −0.558469 | ||||||||
\(497\) | −39.5967 | −1.77616 | ||||||||
\(498\) | 12.1115 | 0.542727 | ||||||||
\(499\) | 19.2918 | 0.863619 | 0.431810 | − | 0.901965i | \(-0.357875\pi\) | ||||
0.431810 | + | 0.901965i | \(0.357875\pi\) | |||||||
\(500\) | 16.9443 | 0.757771 | ||||||||
\(501\) | −3.41641 | −0.152634 | ||||||||
\(502\) | −1.41641 | −0.0632174 | ||||||||
\(503\) | −26.9443 | −1.20139 | −0.600693 | − | 0.799480i | \(-0.705109\pi\) | ||||
−0.600693 | + | 0.799480i | \(0.705109\pi\) | |||||||
\(504\) | 14.4721 | 0.644640 | ||||||||
\(505\) | 5.52786 | 0.245987 | ||||||||
\(506\) | 3.23607 | 0.143861 | ||||||||
\(507\) | −8.94427 | −0.397229 | ||||||||
\(508\) | −11.7984 | −0.523468 | ||||||||
\(509\) | 28.3050 | 1.25459 | 0.627297 | − | 0.778780i | \(-0.284161\pi\) | ||||
0.627297 | + | 0.778780i | \(0.284161\pi\) | |||||||
\(510\) | −1.30495 | −0.0577842 | ||||||||
\(511\) | 21.1246 | 0.934498 | ||||||||
\(512\) | −18.7082 | −0.826794 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −4.61803 | −0.203693 | ||||||||
\(515\) | 5.16718 | 0.227693 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 11.7082 | 0.514926 | ||||||||
\(518\) | −2.47214 | −0.108619 | ||||||||
\(519\) | −51.3050 | −2.25204 | ||||||||
\(520\) | −8.29180 | −0.363619 | ||||||||
\(521\) | −31.4164 | −1.37638 | −0.688189 | − | 0.725532i | \(-0.741594\pi\) | ||||
−0.688189 | + | 0.725532i | \(0.741594\pi\) | |||||||
\(522\) | −3.70820 | −0.162304 | ||||||||
\(523\) | −41.1246 | −1.79825 | −0.899127 | − | 0.437688i | \(-0.855797\pi\) | ||||
−0.899127 | + | 0.437688i | \(0.855797\pi\) | |||||||
\(524\) | −30.2705 | −1.32237 | ||||||||
\(525\) | −25.1246 | −1.09653 | ||||||||
\(526\) | −1.81966 | −0.0793410 | ||||||||
\(527\) | −5.12461 | −0.223232 | ||||||||
\(528\) | −21.7082 | −0.944728 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 0.360680 | 0.0156669 | ||||||||
\(531\) | −12.9443 | −0.561734 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −10.4164 | −0.451185 | ||||||||
\(534\) | −14.4721 | −0.626271 | ||||||||
\(535\) | −16.5836 | −0.716971 | ||||||||
\(536\) | 6.18034 | 0.266950 | ||||||||
\(537\) | −1.58359 | −0.0683370 | ||||||||
\(538\) | −4.90983 | −0.211678 | ||||||||
\(539\) | −18.1803 | −0.783083 | ||||||||
\(540\) | 4.47214 | 0.192450 | ||||||||
\(541\) | −34.4164 | −1.47968 | −0.739838 | − | 0.672785i | \(-0.765098\pi\) | ||||
−0.739838 | + | 0.672785i | \(0.765098\pi\) | |||||||
\(542\) | −4.94427 | −0.212375 | ||||||||
\(543\) | −37.2361 | −1.59795 | ||||||||
\(544\) | −4.29180 | −0.184009 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 13.4164 | 0.574169 | ||||||||
\(547\) | 29.5410 | 1.26308 | 0.631541 | − | 0.775342i | \(-0.282423\pi\) | ||||
0.631541 | + | 0.775342i | \(0.282423\pi\) | |||||||
\(548\) | 35.4164 | 1.51291 | ||||||||
\(549\) | −13.8885 | −0.592749 | ||||||||
\(550\) | −11.2361 | −0.479108 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 5.00000 | 0.212814 | ||||||||
\(553\) | 35.4164 | 1.50606 | ||||||||
\(554\) | −9.56231 | −0.406263 | ||||||||
\(555\) | 3.41641 | 0.145018 | ||||||||
\(556\) | 17.3262 | 0.734796 | ||||||||
\(557\) | −7.41641 | −0.314243 | −0.157122 | − | 0.987579i | \(-0.550221\pi\) | ||||
−0.157122 | + | 0.987579i | \(0.550221\pi\) | |||||||
\(558\) | 8.29180 | 0.351020 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 7.41641 | 0.313400 | ||||||||
\(561\) | −8.94427 | −0.377627 | ||||||||
\(562\) | −5.41641 | −0.228477 | ||||||||
\(563\) | 32.9443 | 1.38844 | 0.694218 | − | 0.719765i | \(-0.255750\pi\) | ||||
0.694218 | + | 0.719765i | \(0.255750\pi\) | |||||||
\(564\) | 8.09017 | 0.340658 | ||||||||
\(565\) | −10.8328 | −0.455740 | ||||||||
\(566\) | −17.1246 | −0.719801 | ||||||||
\(567\) | −35.5967 | −1.49492 | ||||||||
\(568\) | −27.3607 | −1.14803 | ||||||||
\(569\) | 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 | \(0.596669\pi\) | |||||||
\(572\) | −25.4164 | −1.06271 | ||||||||
\(573\) | −58.5410 | −2.44559 | ||||||||
\(574\) | −6.94427 | −0.289848 | ||||||||
\(575\) | −3.47214 | −0.144798 | ||||||||
\(576\) | −0.472136 | −0.0196723 | ||||||||
\(577\) | 22.8885 | 0.952863 | 0.476431 | − | 0.879212i | \(-0.341930\pi\) | ||||
0.476431 | + | 0.879212i | \(0.341930\pi\) | |||||||
\(578\) | 10.1459 | 0.422014 | ||||||||
\(579\) | −22.2361 | −0.924099 | ||||||||
\(580\) | −6.00000 | −0.249136 | ||||||||
\(581\) | −28.3607 | −1.17660 | ||||||||
\(582\) | 24.4721 | 1.01440 | ||||||||
\(583\) | 2.47214 | 0.102385 | ||||||||
\(584\) | 14.5967 | 0.604018 | ||||||||
\(585\) | −7.41641 | −0.306631 | ||||||||
\(586\) | −0.944272 | −0.0390075 | ||||||||
\(587\) | −24.7082 | −1.01982 | −0.509908 | − | 0.860229i | \(-0.670321\pi\) | ||||
−0.509908 | + | 0.860229i | \(0.670321\pi\) | |||||||
\(588\) | −12.5623 | −0.518061 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 4.94427 | 0.203552 | ||||||||
\(591\) | −3.29180 | −0.135406 | ||||||||
\(592\) | 2.29180 | 0.0941922 | ||||||||
\(593\) | −2.94427 | −0.120907 | −0.0604534 | − | 0.998171i | \(-0.519255\pi\) | ||||
−0.0604534 | + | 0.998171i | \(0.519255\pi\) | |||||||
\(594\) | −7.23607 | −0.296899 | ||||||||
\(595\) | 3.05573 | 0.125273 | ||||||||
\(596\) | −38.6525 | −1.58327 | ||||||||
\(597\) | −27.4853 | −1.12490 | ||||||||
\(598\) | 1.85410 | 0.0758199 | ||||||||
\(599\) | −33.8885 | −1.38465 | −0.692324 | − | 0.721587i | \(-0.743413\pi\) | ||||
−0.692324 | + | 0.721587i | \(0.743413\pi\) | |||||||
\(600\) | −17.3607 | −0.708747 | ||||||||
\(601\) | −46.8885 | −1.91262 | −0.956312 | − | 0.292349i | \(-0.905563\pi\) | ||||
−0.956312 | + | 0.292349i | \(0.905563\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 5.52786 | 0.225112 | ||||||||
\(604\) | 6.85410 | 0.278889 | ||||||||
\(605\) | 20.2918 | 0.824979 | ||||||||
\(606\) | −6.18034 | −0.251059 | ||||||||
\(607\) | −26.4721 | −1.07447 | −0.537235 | − | 0.843432i | \(-0.680531\pi\) | ||||
−0.537235 | + | 0.843432i | \(0.680531\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 21.7082 | 0.879661 | ||||||||
\(610\) | 5.30495 | 0.214791 | ||||||||
\(611\) | 6.70820 | 0.271385 | ||||||||
\(612\) | −2.47214 | −0.0999302 | ||||||||
\(613\) | 5.70820 | 0.230552 | 0.115276 | − | 0.993333i | \(-0.463225\pi\) | ||||
0.115276 | + | 0.993333i | \(0.463225\pi\) | |||||||
\(614\) | 5.88854 | 0.237642 | ||||||||
\(615\) | 9.59675 | 0.386978 | ||||||||
\(616\) | −37.8885 | −1.52657 | ||||||||
\(617\) | −7.52786 | −0.303060 | −0.151530 | − | 0.988453i | \(-0.548420\pi\) | ||||
−0.151530 | + | 0.988453i | \(0.548420\pi\) | |||||||
\(618\) | −5.77709 | −0.232389 | ||||||||
\(619\) | 19.4164 | 0.780411 | 0.390206 | − | 0.920728i | \(-0.372404\pi\) | ||||
0.390206 | + | 0.920728i | \(0.372404\pi\) | |||||||
\(620\) | 13.4164 | 0.538816 | ||||||||
\(621\) | −2.23607 | −0.0897303 | ||||||||
\(622\) | −8.14590 | −0.326621 | ||||||||
\(623\) | 33.8885 | 1.35772 | ||||||||
\(624\) | −12.4377 | −0.497906 | ||||||||
\(625\) | 4.41641 | 0.176656 | ||||||||
\(626\) | −15.0557 | −0.601748 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 18.4721 | 0.737118 | ||||||||
\(629\) | 0.944272 | 0.0376506 | ||||||||
\(630\) | −4.94427 | −0.196985 | ||||||||
\(631\) | 12.3607 | 0.492071 | 0.246035 | − | 0.969261i | \(-0.420872\pi\) | ||||
0.246035 | + | 0.969261i | \(0.420872\pi\) | |||||||
\(632\) | 24.4721 | 0.973449 | ||||||||
\(633\) | 52.3607 | 2.08115 | ||||||||
\(634\) | 15.7082 | 0.623852 | ||||||||
\(635\) | 9.01316 | 0.357676 | ||||||||
\(636\) | 1.70820 | 0.0677347 | ||||||||
\(637\) | −10.4164 | −0.412713 | ||||||||
\(638\) | 9.70820 | 0.384351 | ||||||||
\(639\) | −24.4721 | −0.968103 | ||||||||
\(640\) | 14.0689 | 0.556121 | ||||||||
\(641\) | 17.3050 | 0.683504 | 0.341752 | − | 0.939790i | \(-0.388980\pi\) | ||||
0.341752 | + | 0.939790i | \(0.388980\pi\) | |||||||
\(642\) | 18.5410 | 0.731756 | ||||||||
\(643\) | −29.5967 | −1.16718 | −0.583591 | − | 0.812048i | \(-0.698353\pi\) | ||||
−0.583591 | + | 0.812048i | \(0.698353\pi\) | |||||||
\(644\) | −5.23607 | −0.206330 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 6.70820 | 0.263727 | 0.131863 | − | 0.991268i | \(-0.457904\pi\) | ||||
0.131863 | + | 0.991268i | \(0.457904\pi\) | |||||||
\(648\) | −24.5967 | −0.966252 | ||||||||
\(649\) | 33.8885 | 1.33024 | ||||||||
\(650\) | −6.43769 | −0.252507 | ||||||||
\(651\) | −48.5410 | −1.90247 | ||||||||
\(652\) | 9.32624 | 0.365244 | ||||||||
\(653\) | −38.3050 | −1.49899 | −0.749494 | − | 0.662011i | \(-0.769703\pi\) | ||||
−0.749494 | + | 0.662011i | \(0.769703\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 23.1246 | 0.903553 | ||||||||
\(656\) | 6.43769 | 0.251350 | ||||||||
\(657\) | 13.0557 | 0.509352 | ||||||||
\(658\) | 4.47214 | 0.174342 | ||||||||
\(659\) | 10.6525 | 0.414962 | 0.207481 | − | 0.978239i | \(-0.433474\pi\) | ||||
0.207481 | + | 0.978239i | \(0.433474\pi\) | |||||||
\(660\) | 23.4164 | 0.911482 | ||||||||
\(661\) | 22.9443 | 0.892429 | 0.446214 | − | 0.894926i | \(-0.352772\pi\) | ||||
0.446214 | + | 0.894926i | \(0.352772\pi\) | |||||||
\(662\) | −12.1459 | −0.472064 | ||||||||
\(663\) | −5.12461 | −0.199023 | ||||||||
\(664\) | −19.5967 | −0.760501 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −1.52786 | −0.0592035 | ||||||||
\(667\) | 3.00000 | 0.116160 | ||||||||
\(668\) | 2.47214 | 0.0956498 | ||||||||
\(669\) | −8.94427 | −0.345806 | ||||||||
\(670\) | −2.11146 | −0.0815727 | ||||||||
\(671\) | 36.3607 | 1.40369 | ||||||||
\(672\) | −40.6525 | −1.56820 | ||||||||
\(673\) | −3.00000 | −0.115642 | −0.0578208 | − | 0.998327i | \(-0.518415\pi\) | ||||
−0.0578208 | + | 0.998327i | \(0.518415\pi\) | |||||||
\(674\) | 14.4721 | 0.557446 | ||||||||
\(675\) | 7.76393 | 0.298834 | ||||||||
\(676\) | 6.47214 | 0.248928 | ||||||||
\(677\) | −18.0000 | −0.691796 | −0.345898 | − | 0.938272i | \(-0.612426\pi\) | ||||
−0.345898 | + | 0.938272i | \(0.612426\pi\) | |||||||
\(678\) | 12.1115 | 0.465138 | ||||||||
\(679\) | −57.3050 | −2.19916 | ||||||||
\(680\) | 2.11146 | 0.0809706 | ||||||||
\(681\) | 27.2361 | 1.04369 | ||||||||
\(682\) | −21.7082 | −0.831250 | ||||||||
\(683\) | −26.5967 | −1.01770 | −0.508848 | − | 0.860856i | \(-0.669929\pi\) | ||||
−0.508848 | + | 0.860856i | \(0.669929\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −27.0557 | −1.03375 | ||||||||
\(686\) | 7.05573 | 0.269389 | ||||||||
\(687\) | −26.8328 | −1.02374 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 1.41641 | 0.0539608 | ||||||||
\(690\) | −1.70820 | −0.0650302 | ||||||||
\(691\) | 7.05573 | 0.268413 | 0.134206 | − | 0.990953i | \(-0.457152\pi\) | ||||
0.134206 | + | 0.990953i | \(0.457152\pi\) | |||||||
\(692\) | 37.1246 | 1.41127 | ||||||||
\(693\) | −33.8885 | −1.28732 | ||||||||
\(694\) | 6.11146 | 0.231988 | ||||||||
\(695\) | −13.2361 | −0.502073 | ||||||||
\(696\) | 15.0000 | 0.568574 | ||||||||
\(697\) | 2.65248 | 0.100470 | ||||||||
\(698\) | −15.0902 | −0.571171 | ||||||||
\(699\) | −14.5967 | −0.552100 | ||||||||
\(700\) | 18.1803 | 0.687152 | ||||||||
\(701\) | −3.81966 | −0.144267 | −0.0721333 | − | 0.997395i | \(-0.522981\pi\) | ||||
−0.0721333 | + | 0.997395i | \(0.522981\pi\) | |||||||
\(702\) | −4.14590 | −0.156477 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 1.23607 | 0.0465861 | ||||||||
\(705\) | −6.18034 | −0.232765 | ||||||||
\(706\) | −5.78522 | −0.217730 | ||||||||
\(707\) | 14.4721 | 0.544281 | ||||||||
\(708\) | 23.4164 | 0.880042 | ||||||||
\(709\) | −42.0689 | −1.57993 | −0.789965 | − | 0.613152i | \(-0.789901\pi\) | ||||
−0.789965 | + | 0.613152i | \(0.789901\pi\) | |||||||
\(710\) | 9.34752 | 0.350806 | ||||||||
\(711\) | 21.8885 | 0.820885 | ||||||||
\(712\) | 23.4164 | 0.877567 | ||||||||
\(713\) | −6.70820 | −0.251224 | ||||||||
\(714\) | −3.41641 | −0.127856 | ||||||||
\(715\) | 19.4164 | 0.726132 | ||||||||
\(716\) | 1.14590 | 0.0428242 | ||||||||
\(717\) | 30.7771 | 1.14939 | ||||||||
\(718\) | 12.2918 | 0.458726 | ||||||||
\(719\) | −3.05573 | −0.113959 | −0.0569797 | − | 0.998375i | \(-0.518147\pi\) | ||||
−0.0569797 | + | 0.998375i | \(0.518147\pi\) | |||||||
\(720\) | 4.58359 | 0.170820 | ||||||||
\(721\) | 13.5279 | 0.503804 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 51.7082 | 1.92305 | ||||||||
\(724\) | 26.9443 | 1.00138 | ||||||||
\(725\) | −10.4164 | −0.386856 | ||||||||
\(726\) | −22.6869 | −0.841990 | ||||||||
\(727\) | −27.7082 | −1.02764 | −0.513820 | − | 0.857898i | \(-0.671770\pi\) | ||||
−0.513820 | + | 0.857898i | \(0.671770\pi\) | |||||||
\(728\) | −21.7082 | −0.804560 | ||||||||
\(729\) | −7.00000 | −0.259259 | ||||||||
\(730\) | −4.98684 | −0.184571 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 25.1246 | 0.928632 | ||||||||
\(733\) | −31.2361 | −1.15373 | −0.576865 | − | 0.816839i | \(-0.695724\pi\) | ||||
−0.576865 | + | 0.816839i | \(0.695724\pi\) | |||||||
\(734\) | 2.58359 | 0.0953621 | ||||||||
\(735\) | 9.59675 | 0.353981 | ||||||||
\(736\) | −5.61803 | −0.207083 | ||||||||
\(737\) | −14.4721 | −0.533088 | ||||||||
\(738\) | −4.29180 | −0.157983 | ||||||||
\(739\) | 26.8197 | 0.986577 | 0.493289 | − | 0.869866i | \(-0.335795\pi\) | ||||
0.493289 | + | 0.869866i | \(0.335795\pi\) | |||||||
\(740\) | −2.47214 | −0.0908775 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0.944272 | 0.0346653 | ||||||||
\(743\) | −41.1246 | −1.50872 | −0.754358 | − | 0.656463i | \(-0.772052\pi\) | ||||
−0.754358 | + | 0.656463i | \(0.772052\pi\) | |||||||
\(744\) | −33.5410 | −1.22967 | ||||||||
\(745\) | 29.5279 | 1.08182 | ||||||||
\(746\) | 4.76393 | 0.174420 | ||||||||
\(747\) | −17.5279 | −0.641311 | ||||||||
\(748\) | 6.47214 | 0.236645 | ||||||||
\(749\) | −43.4164 | −1.58640 | ||||||||
\(750\) | 14.4721 | 0.528448 | ||||||||
\(751\) | −0.360680 | −0.0131614 | −0.00658070 | − | 0.999978i | \(-0.502095\pi\) | ||||
−0.00658070 | + | 0.999978i | \(0.502095\pi\) | |||||||
\(752\) | −4.14590 | −0.151185 | ||||||||
\(753\) | 5.12461 | 0.186751 | ||||||||
\(754\) | 5.56231 | 0.202567 | ||||||||
\(755\) | −5.23607 | −0.190560 | ||||||||
\(756\) | 11.7082 | 0.425823 | ||||||||
\(757\) | 1.59675 | 0.0580348 | 0.0290174 | − | 0.999579i | \(-0.490762\pi\) | ||||
0.0290174 | + | 0.999579i | \(0.490762\pi\) | |||||||
\(758\) | 15.0557 | 0.546849 | ||||||||
\(759\) | −11.7082 | −0.424981 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 46.3050 | 1.67855 | 0.839277 | − | 0.543705i | \(-0.182979\pi\) | ||||
0.839277 | + | 0.543705i | \(0.182979\pi\) | |||||||
\(762\) | −10.0770 | −0.365052 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 42.3607 | 1.53256 | ||||||||
\(765\) | 1.88854 | 0.0682804 | ||||||||
\(766\) | 4.36068 | 0.157558 | ||||||||
\(767\) | 19.4164 | 0.701086 | ||||||||
\(768\) | −14.6738 | −0.529494 | ||||||||
\(769\) | −23.1246 | −0.833895 | −0.416947 | − | 0.908931i | \(-0.636900\pi\) | ||||
−0.416947 | + | 0.908931i | \(0.636900\pi\) | |||||||
\(770\) | 12.9443 | 0.466479 | ||||||||
\(771\) | 16.7082 | 0.601731 | ||||||||
\(772\) | 16.0902 | 0.579098 | ||||||||
\(773\) | 5.52786 | 0.198823 | 0.0994117 | − | 0.995046i | \(-0.468304\pi\) | ||||
0.0994117 | + | 0.995046i | \(0.468304\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 23.2918 | 0.836666 | ||||||||
\(776\) | −39.5967 | −1.42144 | ||||||||
\(777\) | 8.94427 | 0.320874 | ||||||||
\(778\) | −15.7771 | −0.565636 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 13.4164 | 0.480384 | ||||||||
\(781\) | 64.0689 | 2.29256 | ||||||||
\(782\) | −0.472136 | −0.0168835 | ||||||||
\(783\) | −6.70820 | −0.239732 | ||||||||
\(784\) | 6.43769 | 0.229918 | ||||||||
\(785\) | −14.1115 | −0.503659 | ||||||||
\(786\) | −25.8541 | −0.922185 | ||||||||
\(787\) | −24.5836 | −0.876310 | −0.438155 | − | 0.898899i | \(-0.644368\pi\) | ||||
−0.438155 | + | 0.898899i | \(0.644368\pi\) | |||||||
\(788\) | 2.38197 | 0.0848540 | ||||||||
\(789\) | 6.58359 | 0.234382 | ||||||||
\(790\) | −8.36068 | −0.297460 | ||||||||
\(791\) | −28.3607 | −1.00839 | ||||||||
\(792\) | −23.4164 | −0.832066 | ||||||||
\(793\) | 20.8328 | 0.739795 | ||||||||
\(794\) | 15.0902 | 0.535530 | ||||||||
\(795\) | −1.30495 | −0.0462819 | ||||||||
\(796\) | 19.8885 | 0.704931 | ||||||||
\(797\) | 34.3607 | 1.21712 | 0.608559 | − | 0.793509i | \(-0.291748\pi\) | ||||
0.608559 | + | 0.793509i | \(0.291748\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1.70820 | −0.0604319 | ||||||||
\(800\) | 19.5066 | 0.689662 | ||||||||
\(801\) | 20.9443 | 0.740029 | ||||||||
\(802\) | −8.76393 | −0.309465 | ||||||||
\(803\) | −34.1803 | −1.20620 | ||||||||
\(804\) | −10.0000 | −0.352673 | ||||||||
\(805\) | 4.00000 | 0.140981 | ||||||||
\(806\) | −12.4377 | −0.438099 | ||||||||
\(807\) | 17.7639 | 0.625320 | ||||||||
\(808\) | 10.0000 | 0.351799 | ||||||||
\(809\) | 12.1115 | 0.425816 | 0.212908 | − | 0.977072i | \(-0.431707\pi\) | ||||
0.212908 | + | 0.977072i | \(0.431707\pi\) | |||||||
\(810\) | 8.40325 | 0.295260 | ||||||||
\(811\) | 24.3475 | 0.854957 | 0.427479 | − | 0.904025i | \(-0.359402\pi\) | ||||
0.427479 | + | 0.904025i | \(0.359402\pi\) | |||||||
\(812\) | −15.7082 | −0.551250 | ||||||||
\(813\) | 17.8885 | 0.627379 | ||||||||
\(814\) | 4.00000 | 0.140200 | ||||||||
\(815\) | −7.12461 | −0.249564 | ||||||||
\(816\) | 3.16718 | 0.110874 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 13.2016 | 0.461584 | ||||||||
\(819\) | −19.4164 | −0.678464 | ||||||||
\(820\) | −6.94427 | −0.242504 | ||||||||
\(821\) | −38.9443 | −1.35916 | −0.679582 | − | 0.733599i | \(-0.737839\pi\) | ||||
−0.679582 | + | 0.733599i | \(0.737839\pi\) | |||||||
\(822\) | 30.2492 | 1.05506 | ||||||||
\(823\) | −39.5410 | −1.37831 | −0.689157 | − | 0.724612i | \(-0.742019\pi\) | ||||
−0.689157 | + | 0.724612i | \(0.742019\pi\) | |||||||
\(824\) | 9.34752 | 0.325636 | ||||||||
\(825\) | 40.6525 | 1.41534 | ||||||||
\(826\) | 12.9443 | 0.450389 | ||||||||
\(827\) | −1.52786 | −0.0531290 | −0.0265645 | − | 0.999647i | \(-0.508457\pi\) | ||||
−0.0265645 | + | 0.999647i | \(0.508457\pi\) | |||||||
\(828\) | −3.23607 | −0.112461 | ||||||||
\(829\) | −40.2492 | −1.39791 | −0.698957 | − | 0.715164i | \(-0.746352\pi\) | ||||
−0.698957 | + | 0.715164i | \(0.746352\pi\) | |||||||
\(830\) | 6.69505 | 0.232389 | ||||||||
\(831\) | 34.5967 | 1.20015 | ||||||||
\(832\) | 0.708204 | 0.0245526 | ||||||||
\(833\) | 2.65248 | 0.0919028 | ||||||||
\(834\) | 14.7984 | 0.512426 | ||||||||
\(835\) | −1.88854 | −0.0653558 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 15.0000 | 0.518476 | ||||||||
\(838\) | 2.83282 | 0.0978580 | ||||||||
\(839\) | 41.1246 | 1.41978 | 0.709890 | − | 0.704313i | \(-0.248745\pi\) | ||||
0.709890 | + | 0.704313i | \(0.248745\pi\) | |||||||
\(840\) | 20.0000 | 0.690066 | ||||||||
\(841\) | −20.0000 | −0.689655 | ||||||||
\(842\) | −6.36068 | −0.219204 | ||||||||
\(843\) | 19.5967 | 0.674948 | ||||||||
\(844\) | −37.8885 | −1.30418 | ||||||||
\(845\) | −4.94427 | −0.170088 | ||||||||
\(846\) | 2.76393 | 0.0950259 | ||||||||
\(847\) | 53.1246 | 1.82538 | ||||||||
\(848\) | −0.875388 | −0.0300610 | ||||||||
\(849\) | 61.9574 | 2.12637 | ||||||||
\(850\) | 1.63932 | 0.0562282 | ||||||||
\(851\) | 1.23607 | 0.0423719 | ||||||||
\(852\) | 44.2705 | 1.51668 | ||||||||
\(853\) | −10.5836 | −0.362375 | −0.181188 | − | 0.983449i | \(-0.557994\pi\) | ||||
−0.181188 | + | 0.983449i | \(0.557994\pi\) | |||||||
\(854\) | 13.8885 | 0.475256 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −30.0000 | −1.02538 | ||||||||
\(857\) | −1.47214 | −0.0502872 | −0.0251436 | − | 0.999684i | \(-0.508004\pi\) | ||||
−0.0251436 | + | 0.999684i | \(0.508004\pi\) | |||||||
\(858\) | −21.7082 | −0.741106 | ||||||||
\(859\) | −16.7082 | −0.570077 | −0.285038 | − | 0.958516i | \(-0.592006\pi\) | ||||
−0.285038 | + | 0.958516i | \(0.592006\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 25.1246 | 0.856244 | ||||||||
\(862\) | −10.8328 | −0.368967 | ||||||||
\(863\) | 21.5410 | 0.733265 | 0.366632 | − | 0.930366i | \(-0.380511\pi\) | ||||
0.366632 | + | 0.930366i | \(0.380511\pi\) | |||||||
\(864\) | 12.5623 | 0.427378 | ||||||||
\(865\) | −28.3607 | −0.964292 | ||||||||
\(866\) | 11.0132 | 0.374242 | ||||||||
\(867\) | −36.7082 | −1.24668 | ||||||||
\(868\) | 35.1246 | 1.19221 | ||||||||
\(869\) | −57.3050 | −1.94394 | ||||||||
\(870\) | −5.12461 | −0.173741 | ||||||||
\(871\) | −8.29180 | −0.280957 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −35.4164 | −1.19866 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −33.8885 | −1.14564 | ||||||||
\(876\) | −23.6180 | −0.797979 | ||||||||
\(877\) | 36.4721 | 1.23158 | 0.615788 | − | 0.787912i | \(-0.288838\pi\) | ||||
0.615788 | + | 0.787912i | \(0.288838\pi\) | |||||||
\(878\) | −11.5623 | −0.390209 | ||||||||
\(879\) | 3.41641 | 0.115233 | ||||||||
\(880\) | −12.0000 | −0.404520 | ||||||||
\(881\) | 44.1803 | 1.48847 | 0.744237 | − | 0.667916i | \(-0.232813\pi\) | ||||
0.744237 | + | 0.667916i | \(0.232813\pi\) | |||||||
\(882\) | −4.29180 | −0.144512 | ||||||||
\(883\) | 4.00000 | 0.134611 | 0.0673054 | − | 0.997732i | \(-0.478560\pi\) | ||||
0.0673054 | + | 0.997732i | \(0.478560\pi\) | |||||||
\(884\) | 3.70820 | 0.124720 | ||||||||
\(885\) | −17.8885 | −0.601317 | ||||||||
\(886\) | −23.5623 | −0.791591 | ||||||||
\(887\) | −23.0689 | −0.774577 | −0.387289 | − | 0.921959i | \(-0.626588\pi\) | ||||
−0.387289 | + | 0.921959i | \(0.626588\pi\) | |||||||
\(888\) | 6.18034 | 0.207399 | ||||||||
\(889\) | 23.5967 | 0.791410 | ||||||||
\(890\) | −8.00000 | −0.268161 | ||||||||
\(891\) | 57.5967 | 1.92956 | ||||||||
\(892\) | 6.47214 | 0.216703 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | −33.0132 | −1.10413 | ||||||||
\(895\) | −0.875388 | −0.0292610 | ||||||||
\(896\) | 36.8328 | 1.23050 | ||||||||
\(897\) | −6.70820 | −0.223980 | ||||||||
\(898\) | −9.23607 | −0.308212 | ||||||||
\(899\) | −20.1246 | −0.671193 | ||||||||
\(900\) | 11.2361 | 0.374536 | ||||||||
\(901\) | −0.360680 | −0.0120160 | ||||||||
\(902\) | 11.2361 | 0.374120 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −19.5967 | −0.651778 | ||||||||
\(905\) | −20.5836 | −0.684222 | ||||||||
\(906\) | 5.85410 | 0.194490 | ||||||||
\(907\) | 40.2492 | 1.33645 | 0.668227 | − | 0.743958i | \(-0.267054\pi\) | ||||
0.668227 | + | 0.743958i | \(0.267054\pi\) | |||||||
\(908\) | −19.7082 | −0.654040 | ||||||||
\(909\) | 8.94427 | 0.296663 | ||||||||
\(910\) | 7.41641 | 0.245852 | ||||||||
\(911\) | −31.3050 | −1.03718 | −0.518590 | − | 0.855023i | \(-0.673543\pi\) | ||||
−0.518590 | + | 0.855023i | \(0.673543\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 45.8885 | 1.51869 | ||||||||
\(914\) | 3.16718 | 0.104761 | ||||||||
\(915\) | −19.1935 | −0.634517 | ||||||||
\(916\) | 19.4164 | 0.641536 | ||||||||
\(917\) | 60.5410 | 1.99924 | ||||||||
\(918\) | 1.05573 | 0.0348442 | ||||||||
\(919\) | 41.1246 | 1.35658 | 0.678288 | − | 0.734796i | \(-0.262722\pi\) | ||||
0.678288 | + | 0.734796i | \(0.262722\pi\) | |||||||
\(920\) | 2.76393 | 0.0911241 | ||||||||
\(921\) | −21.3050 | −0.702022 | ||||||||
\(922\) | 0.909830 | 0.0299637 | ||||||||
\(923\) | 36.7082 | 1.20827 | ||||||||
\(924\) | 61.3050 | 2.01678 | ||||||||
\(925\) | −4.29180 | −0.141113 | ||||||||
\(926\) | 12.3607 | 0.406197 | ||||||||
\(927\) | 8.36068 | 0.274601 | ||||||||
\(928\) | −16.8541 | −0.553263 | ||||||||
\(929\) | −24.0557 | −0.789243 | −0.394621 | − | 0.918844i | \(-0.629124\pi\) | ||||
−0.394621 | + | 0.918844i | \(0.629124\pi\) | |||||||
\(930\) | 11.4590 | 0.375755 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 10.5623 | 0.345980 | ||||||||
\(933\) | 29.4721 | 0.964874 | ||||||||
\(934\) | 8.06888 | 0.264022 | ||||||||
\(935\) | −4.94427 | −0.161695 | ||||||||
\(936\) | −13.4164 | −0.438529 | ||||||||
\(937\) | 34.1803 | 1.11662 | 0.558312 | − | 0.829631i | \(-0.311449\pi\) | ||||
0.558312 | + | 0.829631i | \(0.311449\pi\) | |||||||
\(938\) | −5.52786 | −0.180491 | ||||||||
\(939\) | 54.4721 | 1.77763 | ||||||||
\(940\) | 4.47214 | 0.145865 | ||||||||
\(941\) | −6.65248 | −0.216865 | −0.108432 | − | 0.994104i | \(-0.534583\pi\) | ||||
−0.108432 | + | 0.994104i | \(0.534583\pi\) | |||||||
\(942\) | 15.7771 | 0.514045 | ||||||||
\(943\) | 3.47214 | 0.113068 | ||||||||
\(944\) | −12.0000 | −0.390567 | ||||||||
\(945\) | −8.94427 | −0.290957 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −10.8197 | −0.351592 | −0.175796 | − | 0.984427i | \(-0.556250\pi\) | ||||
−0.175796 | + | 0.984427i | \(0.556250\pi\) | |||||||
\(948\) | −39.5967 | −1.28604 | ||||||||
\(949\) | −19.5836 | −0.635710 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −56.8328 | −1.84293 | ||||||||
\(952\) | 5.52786 | 0.179159 | ||||||||
\(953\) | −20.4721 | −0.663158 | −0.331579 | − | 0.943428i | \(-0.607581\pi\) | ||||
−0.331579 | + | 0.943428i | \(0.607581\pi\) | |||||||
\(954\) | 0.583592 | 0.0188945 | ||||||||
\(955\) | −32.3607 | −1.04717 | ||||||||
\(956\) | −22.2705 | −0.720280 | ||||||||
\(957\) | −35.1246 | −1.13542 | ||||||||
\(958\) | −19.5279 | −0.630917 | ||||||||
\(959\) | −70.8328 | −2.28731 | ||||||||
\(960\) | −0.652476 | −0.0210586 | ||||||||
\(961\) | 14.0000 | 0.451613 | ||||||||
\(962\) | 2.29180 | 0.0738905 | ||||||||
\(963\) | −26.8328 | −0.864675 | ||||||||
\(964\) | −37.4164 | −1.20510 | ||||||||
\(965\) | −12.2918 | −0.395687 | ||||||||
\(966\) | −4.47214 | −0.143889 | ||||||||
\(967\) | 27.5410 | 0.885659 | 0.442830 | − | 0.896606i | \(-0.353975\pi\) | ||||
0.442830 | + | 0.896606i | \(0.353975\pi\) | |||||||
\(968\) | 36.7082 | 1.17985 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 13.5279 | 0.434354 | ||||||||
\(971\) | −16.4721 | −0.528616 | −0.264308 | − | 0.964438i | \(-0.585144\pi\) | ||||
−0.264308 | + | 0.964438i | \(0.585144\pi\) | |||||||
\(972\) | 28.9443 | 0.928388 | ||||||||
\(973\) | −34.6525 | −1.11091 | ||||||||
\(974\) | −9.09017 | −0.291268 | ||||||||
\(975\) | 23.2918 | 0.745934 | ||||||||
\(976\) | −12.8754 | −0.412131 | ||||||||
\(977\) | 23.3475 | 0.746953 | 0.373477 | − | 0.927640i | \(-0.378166\pi\) | ||||
0.373477 | + | 0.927640i | \(0.378166\pi\) | |||||||
\(978\) | 7.96556 | 0.254710 | ||||||||
\(979\) | −54.8328 | −1.75246 | ||||||||
\(980\) | −6.94427 | −0.221827 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −5.15905 | −0.164632 | ||||||||
\(983\) | 40.4721 | 1.29086 | 0.645430 | − | 0.763819i | \(-0.276678\pi\) | ||||
0.645430 | + | 0.763819i | \(0.276678\pi\) | |||||||
\(984\) | 17.3607 | 0.553438 | ||||||||
\(985\) | −1.81966 | −0.0579792 | ||||||||
\(986\) | −1.41641 | −0.0451076 | ||||||||
\(987\) | −16.1803 | −0.515026 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0 | 0 | ||||||||
\(990\) | 8.00000 | 0.254257 | ||||||||
\(991\) | −24.0000 | −0.762385 | −0.381193 | − | 0.924496i | \(-0.624487\pi\) | ||||
−0.381193 | + | 0.924496i | \(0.624487\pi\) | |||||||
\(992\) | 37.6869 | 1.19656 | ||||||||
\(993\) | 43.9443 | 1.39453 | ||||||||
\(994\) | 24.4721 | 0.776209 | ||||||||
\(995\) | −15.1935 | −0.481666 | ||||||||
\(996\) | 31.7082 | 1.00471 | ||||||||
\(997\) | 16.8328 | 0.533101 | 0.266550 | − | 0.963821i | \(-0.414116\pi\) | ||||
0.266550 | + | 0.963821i | \(0.414116\pi\) | |||||||
\(998\) | −11.9230 | −0.377416 | ||||||||
\(999\) | −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 \(a_p\))