Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6018,2,Mod(1,6018)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6018, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("6018.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6018 = 2 \cdot 3 \cdot 17 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6018.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: | \(48.0539719364\) |
Analytic rank: | \(1\) |
Dimension: | \(10\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - 2x^{9} - 33x^{8} + 53x^{7} + 356x^{6} - 433x^{5} - 1296x^{4} + 1135x^{3} + 930x^{2} - 186x - 104 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(4.05993\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6018.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −4.05993 | −1.81566 | −0.907828 | − | 0.419343i | \(-0.862261\pi\) | ||||
−0.907828 | + | 0.419343i | \(0.862261\pi\) | |||||||
\(6\) | −1.00000 | −0.408248 | ||||||||
\(7\) | 4.32251 | 1.63376 | 0.816878 | − | 0.576811i | \(-0.195703\pi\) | ||||
0.816878 | + | 0.576811i | \(0.195703\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 4.05993 | 1.28386 | ||||||||
\(11\) | −0.174683 | −0.0526689 | −0.0263344 | − | 0.999653i | \(-0.508383\pi\) | ||||
−0.0263344 | + | 0.999653i | \(0.508383\pi\) | |||||||
\(12\) | 1.00000 | 0.288675 | ||||||||
\(13\) | −3.57932 | −0.992726 | −0.496363 | − | 0.868115i | \(-0.665331\pi\) | ||||
−0.496363 | + | 0.868115i | \(0.665331\pi\) | |||||||
\(14\) | −4.32251 | −1.15524 | ||||||||
\(15\) | −4.05993 | −1.04827 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −1.00000 | −0.242536 | ||||||||
\(18\) | −1.00000 | −0.235702 | ||||||||
\(19\) | 4.32911 | 0.993167 | 0.496583 | − | 0.867989i | \(-0.334588\pi\) | ||||
0.496583 | + | 0.867989i | \(0.334588\pi\) | |||||||
\(20\) | −4.05993 | −0.907828 | ||||||||
\(21\) | 4.32251 | 0.943249 | ||||||||
\(22\) | 0.174683 | 0.0372425 | ||||||||
\(23\) | −0.966068 | −0.201439 | −0.100720 | − | 0.994915i | \(-0.532114\pi\) | ||||
−0.100720 | + | 0.994915i | \(0.532114\pi\) | |||||||
\(24\) | −1.00000 | −0.204124 | ||||||||
\(25\) | 11.4830 | 2.29661 | ||||||||
\(26\) | 3.57932 | 0.701963 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 4.32251 | 0.816878 | ||||||||
\(29\) | −2.78244 | −0.516686 | −0.258343 | − | 0.966053i | \(-0.583176\pi\) | ||||
−0.258343 | + | 0.966053i | \(0.583176\pi\) | |||||||
\(30\) | 4.05993 | 0.741238 | ||||||||
\(31\) | −8.94938 | −1.60736 | −0.803678 | − | 0.595064i | \(-0.797127\pi\) | ||||
−0.803678 | + | 0.595064i | \(0.797127\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −0.174683 | −0.0304084 | ||||||||
\(34\) | 1.00000 | 0.171499 | ||||||||
\(35\) | −17.5491 | −2.96634 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 9.05465 | 1.48858 | 0.744288 | − | 0.667859i | \(-0.232789\pi\) | ||||
0.744288 | + | 0.667859i | \(0.232789\pi\) | |||||||
\(38\) | −4.32911 | −0.702275 | ||||||||
\(39\) | −3.57932 | −0.573150 | ||||||||
\(40\) | 4.05993 | 0.641931 | ||||||||
\(41\) | −1.49587 | −0.233616 | −0.116808 | − | 0.993155i | \(-0.537266\pi\) | ||||
−0.116808 | + | 0.993155i | \(0.537266\pi\) | |||||||
\(42\) | −4.32251 | −0.666978 | ||||||||
\(43\) | −7.81727 | −1.19212 | −0.596062 | − | 0.802939i | \(-0.703269\pi\) | ||||
−0.596062 | + | 0.802939i | \(0.703269\pi\) | |||||||
\(44\) | −0.174683 | −0.0263344 | ||||||||
\(45\) | −4.05993 | −0.605219 | ||||||||
\(46\) | 0.966068 | 0.142439 | ||||||||
\(47\) | −10.9910 | −1.60320 | −0.801602 | − | 0.597857i | \(-0.796019\pi\) | ||||
−0.801602 | + | 0.597857i | \(0.796019\pi\) | |||||||
\(48\) | 1.00000 | 0.144338 | ||||||||
\(49\) | 11.6841 | 1.66916 | ||||||||
\(50\) | −11.4830 | −1.62395 | ||||||||
\(51\) | −1.00000 | −0.140028 | ||||||||
\(52\) | −3.57932 | −0.496363 | ||||||||
\(53\) | 8.25436 | 1.13382 | 0.566912 | − | 0.823779i | \(-0.308138\pi\) | ||||
0.566912 | + | 0.823779i | \(0.308138\pi\) | |||||||
\(54\) | −1.00000 | −0.136083 | ||||||||
\(55\) | 0.709201 | 0.0956286 | ||||||||
\(56\) | −4.32251 | −0.577620 | ||||||||
\(57\) | 4.32911 | 0.573405 | ||||||||
\(58\) | 2.78244 | 0.365352 | ||||||||
\(59\) | 1.00000 | 0.130189 | ||||||||
\(60\) | −4.05993 | −0.524135 | ||||||||
\(61\) | −13.2963 | −1.70242 | −0.851208 | − | 0.524828i | \(-0.824130\pi\) | ||||
−0.851208 | + | 0.524828i | \(0.824130\pi\) | |||||||
\(62\) | 8.94938 | 1.13657 | ||||||||
\(63\) | 4.32251 | 0.544585 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 14.5318 | 1.80245 | ||||||||
\(66\) | 0.174683 | 0.0215020 | ||||||||
\(67\) | 10.6386 | 1.29971 | 0.649857 | − | 0.760057i | \(-0.274829\pi\) | ||||
0.649857 | + | 0.760057i | \(0.274829\pi\) | |||||||
\(68\) | −1.00000 | −0.121268 | ||||||||
\(69\) | −0.966068 | −0.116301 | ||||||||
\(70\) | 17.5491 | 2.09752 | ||||||||
\(71\) | −11.5730 | −1.37346 | −0.686730 | − | 0.726912i | \(-0.740955\pi\) | ||||
−0.686730 | + | 0.726912i | \(0.740955\pi\) | |||||||
\(72\) | −1.00000 | −0.117851 | ||||||||
\(73\) | 15.4034 | 1.80283 | 0.901413 | − | 0.432959i | \(-0.142531\pi\) | ||||
0.901413 | + | 0.432959i | \(0.142531\pi\) | |||||||
\(74\) | −9.05465 | −1.05258 | ||||||||
\(75\) | 11.4830 | 1.32595 | ||||||||
\(76\) | 4.32911 | 0.496583 | ||||||||
\(77\) | −0.755069 | −0.0860481 | ||||||||
\(78\) | 3.57932 | 0.405279 | ||||||||
\(79\) | −10.6346 | −1.19648 | −0.598241 | − | 0.801316i | \(-0.704133\pi\) | ||||
−0.598241 | + | 0.801316i | \(0.704133\pi\) | |||||||
\(80\) | −4.05993 | −0.453914 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 1.49587 | 0.165191 | ||||||||
\(83\) | 13.5213 | 1.48416 | 0.742080 | − | 0.670311i | \(-0.233839\pi\) | ||||
0.742080 | + | 0.670311i | \(0.233839\pi\) | |||||||
\(84\) | 4.32251 | 0.471625 | ||||||||
\(85\) | 4.05993 | 0.440361 | ||||||||
\(86\) | 7.81727 | 0.842958 | ||||||||
\(87\) | −2.78244 | −0.298309 | ||||||||
\(88\) | 0.174683 | 0.0186213 | ||||||||
\(89\) | 6.06380 | 0.642761 | 0.321381 | − | 0.946950i | \(-0.395853\pi\) | ||||
0.321381 | + | 0.946950i | \(0.395853\pi\) | |||||||
\(90\) | 4.05993 | 0.427954 | ||||||||
\(91\) | −15.4717 | −1.62187 | ||||||||
\(92\) | −0.966068 | −0.100720 | ||||||||
\(93\) | −8.94938 | −0.928008 | ||||||||
\(94\) | 10.9910 | 1.13364 | ||||||||
\(95\) | −17.5759 | −1.80325 | ||||||||
\(96\) | −1.00000 | −0.102062 | ||||||||
\(97\) | −12.2431 | −1.24310 | −0.621551 | − | 0.783374i | \(-0.713497\pi\) | ||||
−0.621551 | + | 0.783374i | \(0.713497\pi\) | |||||||
\(98\) | −11.6841 | −1.18027 | ||||||||
\(99\) | −0.174683 | −0.0175563 | ||||||||
\(100\) | 11.4830 | 1.14830 | ||||||||
\(101\) | 12.6064 | 1.25438 | 0.627192 | − | 0.778865i | \(-0.284204\pi\) | ||||
0.627192 | + | 0.778865i | \(0.284204\pi\) | |||||||
\(102\) | 1.00000 | 0.0990148 | ||||||||
\(103\) | 5.09638 | 0.502161 | 0.251080 | − | 0.967966i | \(-0.419214\pi\) | ||||
0.251080 | + | 0.967966i | \(0.419214\pi\) | |||||||
\(104\) | 3.57932 | 0.350982 | ||||||||
\(105\) | −17.5491 | −1.71262 | ||||||||
\(106\) | −8.25436 | −0.801734 | ||||||||
\(107\) | −12.2482 | −1.18408 | −0.592038 | − | 0.805910i | \(-0.701676\pi\) | ||||
−0.592038 | + | 0.805910i | \(0.701676\pi\) | |||||||
\(108\) | 1.00000 | 0.0962250 | ||||||||
\(109\) | −16.4156 | −1.57233 | −0.786164 | − | 0.618018i | \(-0.787936\pi\) | ||||
−0.786164 | + | 0.618018i | \(0.787936\pi\) | |||||||
\(110\) | −0.709201 | −0.0676196 | ||||||||
\(111\) | 9.05465 | 0.859429 | ||||||||
\(112\) | 4.32251 | 0.408439 | ||||||||
\(113\) | −10.7707 | −1.01323 | −0.506613 | − | 0.862174i | \(-0.669103\pi\) | ||||
−0.506613 | + | 0.862174i | \(0.669103\pi\) | |||||||
\(114\) | −4.32911 | −0.405459 | ||||||||
\(115\) | 3.92217 | 0.365744 | ||||||||
\(116\) | −2.78244 | −0.258343 | ||||||||
\(117\) | −3.57932 | −0.330909 | ||||||||
\(118\) | −1.00000 | −0.0920575 | ||||||||
\(119\) | −4.32251 | −0.396244 | ||||||||
\(120\) | 4.05993 | 0.370619 | ||||||||
\(121\) | −10.9695 | −0.997226 | ||||||||
\(122\) | 13.2963 | 1.20379 | ||||||||
\(123\) | −1.49587 | −0.134878 | ||||||||
\(124\) | −8.94938 | −0.803678 | ||||||||
\(125\) | −26.3207 | −2.35419 | ||||||||
\(126\) | −4.32251 | −0.385080 | ||||||||
\(127\) | −2.14110 | −0.189992 | −0.0949959 | − | 0.995478i | \(-0.530284\pi\) | ||||
−0.0949959 | + | 0.995478i | \(0.530284\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −7.81727 | −0.688273 | ||||||||
\(130\) | −14.5318 | −1.27452 | ||||||||
\(131\) | 13.7267 | 1.19931 | 0.599653 | − | 0.800260i | \(-0.295305\pi\) | ||||
0.599653 | + | 0.800260i | \(0.295305\pi\) | |||||||
\(132\) | −0.174683 | −0.0152042 | ||||||||
\(133\) | 18.7126 | 1.62259 | ||||||||
\(134\) | −10.6386 | −0.919036 | ||||||||
\(135\) | −4.05993 | −0.349423 | ||||||||
\(136\) | 1.00000 | 0.0857493 | ||||||||
\(137\) | 10.8186 | 0.924296 | 0.462148 | − | 0.886803i | \(-0.347079\pi\) | ||||
0.462148 | + | 0.886803i | \(0.347079\pi\) | |||||||
\(138\) | 0.966068 | 0.0822372 | ||||||||
\(139\) | −3.78704 | −0.321212 | −0.160606 | − | 0.987019i | \(-0.551345\pi\) | ||||
−0.160606 | + | 0.987019i | \(0.551345\pi\) | |||||||
\(140\) | −17.5491 | −1.48317 | ||||||||
\(141\) | −10.9910 | −0.925611 | ||||||||
\(142\) | 11.5730 | 0.971183 | ||||||||
\(143\) | 0.625247 | 0.0522858 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 11.2965 | 0.938123 | ||||||||
\(146\) | −15.4034 | −1.27479 | ||||||||
\(147\) | 11.6841 | 0.963688 | ||||||||
\(148\) | 9.05465 | 0.744288 | ||||||||
\(149\) | −21.9080 | −1.79478 | −0.897388 | − | 0.441242i | \(-0.854538\pi\) | ||||
−0.897388 | + | 0.441242i | \(0.854538\pi\) | |||||||
\(150\) | −11.4830 | −0.937586 | ||||||||
\(151\) | −5.89511 | −0.479737 | −0.239869 | − | 0.970805i | \(-0.577104\pi\) | ||||
−0.239869 | + | 0.970805i | \(0.577104\pi\) | |||||||
\(152\) | −4.32911 | −0.351138 | ||||||||
\(153\) | −1.00000 | −0.0808452 | ||||||||
\(154\) | 0.755069 | 0.0608452 | ||||||||
\(155\) | 36.3339 | 2.91841 | ||||||||
\(156\) | −3.57932 | −0.286575 | ||||||||
\(157\) | 2.64550 | 0.211134 | 0.105567 | − | 0.994412i | \(-0.466334\pi\) | ||||
0.105567 | + | 0.994412i | \(0.466334\pi\) | |||||||
\(158\) | 10.6346 | 0.846040 | ||||||||
\(159\) | 8.25436 | 0.654613 | ||||||||
\(160\) | 4.05993 | 0.320966 | ||||||||
\(161\) | −4.17584 | −0.329102 | ||||||||
\(162\) | −1.00000 | −0.0785674 | ||||||||
\(163\) | −7.83285 | −0.613516 | −0.306758 | − | 0.951788i | \(-0.599244\pi\) | ||||
−0.306758 | + | 0.951788i | \(0.599244\pi\) | |||||||
\(164\) | −1.49587 | −0.116808 | ||||||||
\(165\) | 0.709201 | 0.0552112 | ||||||||
\(166\) | −13.5213 | −1.04946 | ||||||||
\(167\) | −11.8583 | −0.917623 | −0.458811 | − | 0.888534i | \(-0.651725\pi\) | ||||
−0.458811 | + | 0.888534i | \(0.651725\pi\) | |||||||
\(168\) | −4.32251 | −0.333489 | ||||||||
\(169\) | −0.188447 | −0.0144959 | ||||||||
\(170\) | −4.05993 | −0.311382 | ||||||||
\(171\) | 4.32911 | 0.331056 | ||||||||
\(172\) | −7.81727 | −0.596062 | ||||||||
\(173\) | −5.47185 | −0.416017 | −0.208008 | − | 0.978127i | \(-0.566698\pi\) | ||||
−0.208008 | + | 0.978127i | \(0.566698\pi\) | |||||||
\(174\) | 2.78244 | 0.210936 | ||||||||
\(175\) | 49.6355 | 3.75209 | ||||||||
\(176\) | −0.174683 | −0.0131672 | ||||||||
\(177\) | 1.00000 | 0.0751646 | ||||||||
\(178\) | −6.06380 | −0.454501 | ||||||||
\(179\) | 21.4193 | 1.60095 | 0.800476 | − | 0.599365i | \(-0.204580\pi\) | ||||
0.800476 | + | 0.599365i | \(0.204580\pi\) | |||||||
\(180\) | −4.05993 | −0.302609 | ||||||||
\(181\) | 21.9957 | 1.63493 | 0.817464 | − | 0.575980i | \(-0.195380\pi\) | ||||
0.817464 | + | 0.575980i | \(0.195380\pi\) | |||||||
\(182\) | 15.4717 | 1.14684 | ||||||||
\(183\) | −13.2963 | −0.982891 | ||||||||
\(184\) | 0.966068 | 0.0712195 | ||||||||
\(185\) | −36.7613 | −2.70274 | ||||||||
\(186\) | 8.94938 | 0.656201 | ||||||||
\(187\) | 0.174683 | 0.0127741 | ||||||||
\(188\) | −10.9910 | −0.801602 | ||||||||
\(189\) | 4.32251 | 0.314416 | ||||||||
\(190\) | 17.5759 | 1.27509 | ||||||||
\(191\) | −7.81869 | −0.565740 | −0.282870 | − | 0.959158i | \(-0.591287\pi\) | ||||
−0.282870 | + | 0.959158i | \(0.591287\pi\) | |||||||
\(192\) | 1.00000 | 0.0721688 | ||||||||
\(193\) | 2.50888 | 0.180593 | 0.0902964 | − | 0.995915i | \(-0.471219\pi\) | ||||
0.0902964 | + | 0.995915i | \(0.471219\pi\) | |||||||
\(194\) | 12.2431 | 0.879005 | ||||||||
\(195\) | 14.5318 | 1.04064 | ||||||||
\(196\) | 11.6841 | 0.834579 | ||||||||
\(197\) | 18.4106 | 1.31170 | 0.655852 | − | 0.754889i | \(-0.272309\pi\) | ||||
0.655852 | + | 0.754889i | \(0.272309\pi\) | |||||||
\(198\) | 0.174683 | 0.0124142 | ||||||||
\(199\) | 6.35539 | 0.450522 | 0.225261 | − | 0.974299i | \(-0.427677\pi\) | ||||
0.225261 | + | 0.974299i | \(0.427677\pi\) | |||||||
\(200\) | −11.4830 | −0.811973 | ||||||||
\(201\) | 10.6386 | 0.750390 | ||||||||
\(202\) | −12.6064 | −0.886983 | ||||||||
\(203\) | −12.0271 | −0.844138 | ||||||||
\(204\) | −1.00000 | −0.0700140 | ||||||||
\(205\) | 6.07313 | 0.424166 | ||||||||
\(206\) | −5.09638 | −0.355081 | ||||||||
\(207\) | −0.966068 | −0.0671464 | ||||||||
\(208\) | −3.57932 | −0.248181 | ||||||||
\(209\) | −0.756222 | −0.0523090 | ||||||||
\(210\) | 17.5491 | 1.21100 | ||||||||
\(211\) | −13.0469 | −0.898183 | −0.449091 | − | 0.893486i | \(-0.648252\pi\) | ||||
−0.449091 | + | 0.893486i | \(0.648252\pi\) | |||||||
\(212\) | 8.25436 | 0.566912 | ||||||||
\(213\) | −11.5730 | −0.792968 | ||||||||
\(214\) | 12.2482 | 0.837268 | ||||||||
\(215\) | 31.7376 | 2.16449 | ||||||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | −38.6838 | −2.62603 | ||||||||
\(218\) | 16.4156 | 1.11180 | ||||||||
\(219\) | 15.4034 | 1.04086 | ||||||||
\(220\) | 0.709201 | 0.0478143 | ||||||||
\(221\) | 3.57932 | 0.240771 | ||||||||
\(222\) | −9.05465 | −0.607708 | ||||||||
\(223\) | −3.72942 | −0.249740 | −0.124870 | − | 0.992173i | \(-0.539851\pi\) | ||||
−0.124870 | + | 0.992173i | \(0.539851\pi\) | |||||||
\(224\) | −4.32251 | −0.288810 | ||||||||
\(225\) | 11.4830 | 0.765536 | ||||||||
\(226\) | 10.7707 | 0.716458 | ||||||||
\(227\) | −19.9745 | −1.32575 | −0.662877 | − | 0.748729i | \(-0.730665\pi\) | ||||
−0.662877 | + | 0.748729i | \(0.730665\pi\) | |||||||
\(228\) | 4.32911 | 0.286703 | ||||||||
\(229\) | −18.9899 | −1.25489 | −0.627445 | − | 0.778661i | \(-0.715899\pi\) | ||||
−0.627445 | + | 0.778661i | \(0.715899\pi\) | |||||||
\(230\) | −3.92217 | −0.258620 | ||||||||
\(231\) | −0.755069 | −0.0496799 | ||||||||
\(232\) | 2.78244 | 0.182676 | ||||||||
\(233\) | −28.4041 | −1.86081 | −0.930406 | − | 0.366530i | \(-0.880546\pi\) | ||||
−0.930406 | + | 0.366530i | \(0.880546\pi\) | |||||||
\(234\) | 3.57932 | 0.233988 | ||||||||
\(235\) | 44.6228 | 2.91087 | ||||||||
\(236\) | 1.00000 | 0.0650945 | ||||||||
\(237\) | −10.6346 | −0.690789 | ||||||||
\(238\) | 4.32251 | 0.280187 | ||||||||
\(239\) | −8.49338 | −0.549391 | −0.274696 | − | 0.961531i | \(-0.588577\pi\) | ||||
−0.274696 | + | 0.961531i | \(0.588577\pi\) | |||||||
\(240\) | −4.05993 | −0.262067 | ||||||||
\(241\) | 12.2957 | 0.792038 | 0.396019 | − | 0.918242i | \(-0.370391\pi\) | ||||
0.396019 | + | 0.918242i | \(0.370391\pi\) | |||||||
\(242\) | 10.9695 | 0.705145 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | −13.2963 | −0.851208 | ||||||||
\(245\) | −47.4366 | −3.03062 | ||||||||
\(246\) | 1.49587 | 0.0953732 | ||||||||
\(247\) | −15.4953 | −0.985942 | ||||||||
\(248\) | 8.94938 | 0.568286 | ||||||||
\(249\) | 13.5213 | 0.856881 | ||||||||
\(250\) | 26.3207 | 1.66466 | ||||||||
\(251\) | 9.25024 | 0.583870 | 0.291935 | − | 0.956438i | \(-0.405701\pi\) | ||||
0.291935 | + | 0.956438i | \(0.405701\pi\) | |||||||
\(252\) | 4.32251 | 0.272293 | ||||||||
\(253\) | 0.168756 | 0.0106096 | ||||||||
\(254\) | 2.14110 | 0.134345 | ||||||||
\(255\) | 4.05993 | 0.254243 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −23.1257 | −1.44254 | −0.721270 | − | 0.692654i | \(-0.756441\pi\) | ||||
−0.721270 | + | 0.692654i | \(0.756441\pi\) | |||||||
\(258\) | 7.81727 | 0.486682 | ||||||||
\(259\) | 39.1388 | 2.43197 | ||||||||
\(260\) | 14.5318 | 0.901224 | ||||||||
\(261\) | −2.78244 | −0.172229 | ||||||||
\(262\) | −13.7267 | −0.848038 | ||||||||
\(263\) | −16.1148 | −0.993681 | −0.496840 | − | 0.867842i | \(-0.665507\pi\) | ||||
−0.496840 | + | 0.867842i | \(0.665507\pi\) | |||||||
\(264\) | 0.174683 | 0.0107510 | ||||||||
\(265\) | −33.5121 | −2.05863 | ||||||||
\(266\) | −18.7126 | −1.14735 | ||||||||
\(267\) | 6.06380 | 0.371098 | ||||||||
\(268\) | 10.6386 | 0.649857 | ||||||||
\(269\) | 18.7529 | 1.14339 | 0.571693 | − | 0.820467i | \(-0.306287\pi\) | ||||
0.571693 | + | 0.820467i | \(0.306287\pi\) | |||||||
\(270\) | 4.05993 | 0.247079 | ||||||||
\(271\) | −7.10047 | −0.431323 | −0.215661 | − | 0.976468i | \(-0.569191\pi\) | ||||
−0.215661 | + | 0.976468i | \(0.569191\pi\) | |||||||
\(272\) | −1.00000 | −0.0606339 | ||||||||
\(273\) | −15.4717 | −0.936388 | ||||||||
\(274\) | −10.8186 | −0.653576 | ||||||||
\(275\) | −2.00589 | −0.120960 | ||||||||
\(276\) | −0.966068 | −0.0581504 | ||||||||
\(277\) | −9.73472 | −0.584903 | −0.292451 | − | 0.956280i | \(-0.594471\pi\) | ||||
−0.292451 | + | 0.956280i | \(0.594471\pi\) | |||||||
\(278\) | 3.78704 | 0.227131 | ||||||||
\(279\) | −8.94938 | −0.535786 | ||||||||
\(280\) | 17.5491 | 1.04876 | ||||||||
\(281\) | −11.3620 | −0.677799 | −0.338899 | − | 0.940823i | \(-0.610055\pi\) | ||||
−0.338899 | + | 0.940823i | \(0.610055\pi\) | |||||||
\(282\) | 10.9910 | 0.654506 | ||||||||
\(283\) | −2.28586 | −0.135880 | −0.0679402 | − | 0.997689i | \(-0.521643\pi\) | ||||
−0.0679402 | + | 0.997689i | \(0.521643\pi\) | |||||||
\(284\) | −11.5730 | −0.686730 | ||||||||
\(285\) | −17.5759 | −1.04111 | ||||||||
\(286\) | −0.625247 | −0.0369716 | ||||||||
\(287\) | −6.46591 | −0.381671 | ||||||||
\(288\) | −1.00000 | −0.0589256 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | −11.2965 | −0.663353 | ||||||||
\(291\) | −12.2431 | −0.717705 | ||||||||
\(292\) | 15.4034 | 0.901413 | ||||||||
\(293\) | −11.8171 | −0.690362 | −0.345181 | − | 0.938536i | \(-0.612182\pi\) | ||||
−0.345181 | + | 0.938536i | \(0.612182\pi\) | |||||||
\(294\) | −11.6841 | −0.681431 | ||||||||
\(295\) | −4.05993 | −0.236378 | ||||||||
\(296\) | −9.05465 | −0.526291 | ||||||||
\(297\) | −0.174683 | −0.0101361 | ||||||||
\(298\) | 21.9080 | 1.26910 | ||||||||
\(299\) | 3.45787 | 0.199974 | ||||||||
\(300\) | 11.4830 | 0.662973 | ||||||||
\(301\) | −33.7903 | −1.94764 | ||||||||
\(302\) | 5.89511 | 0.339225 | ||||||||
\(303\) | 12.6064 | 0.724219 | ||||||||
\(304\) | 4.32911 | 0.248292 | ||||||||
\(305\) | 53.9821 | 3.09100 | ||||||||
\(306\) | 1.00000 | 0.0571662 | ||||||||
\(307\) | −21.0755 | −1.20284 | −0.601422 | − | 0.798932i | \(-0.705399\pi\) | ||||
−0.601422 | + | 0.798932i | \(0.705399\pi\) | |||||||
\(308\) | −0.755069 | −0.0430240 | ||||||||
\(309\) | 5.09638 | 0.289923 | ||||||||
\(310\) | −36.3339 | −2.06363 | ||||||||
\(311\) | 2.89958 | 0.164420 | 0.0822101 | − | 0.996615i | \(-0.473802\pi\) | ||||
0.0822101 | + | 0.996615i | \(0.473802\pi\) | |||||||
\(312\) | 3.57932 | 0.202639 | ||||||||
\(313\) | 13.0246 | 0.736192 | 0.368096 | − | 0.929788i | \(-0.380010\pi\) | ||||
0.368096 | + | 0.929788i | \(0.380010\pi\) | |||||||
\(314\) | −2.64550 | −0.149294 | ||||||||
\(315\) | −17.5491 | −0.988779 | ||||||||
\(316\) | −10.6346 | −0.598241 | ||||||||
\(317\) | 8.38129 | 0.470740 | 0.235370 | − | 0.971906i | \(-0.424370\pi\) | ||||
0.235370 | + | 0.971906i | \(0.424370\pi\) | |||||||
\(318\) | −8.25436 | −0.462881 | ||||||||
\(319\) | 0.486044 | 0.0272133 | ||||||||
\(320\) | −4.05993 | −0.226957 | ||||||||
\(321\) | −12.2482 | −0.683626 | ||||||||
\(322\) | 4.17584 | 0.232710 | ||||||||
\(323\) | −4.32911 | −0.240878 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | −41.1015 | −2.27990 | ||||||||
\(326\) | 7.83285 | 0.433821 | ||||||||
\(327\) | −16.4156 | −0.907784 | ||||||||
\(328\) | 1.49587 | 0.0825956 | ||||||||
\(329\) | −47.5088 | −2.61924 | ||||||||
\(330\) | −0.709201 | −0.0390402 | ||||||||
\(331\) | 17.9828 | 0.988427 | 0.494213 | − | 0.869341i | \(-0.335456\pi\) | ||||
0.494213 | + | 0.869341i | \(0.335456\pi\) | |||||||
\(332\) | 13.5213 | 0.742080 | ||||||||
\(333\) | 9.05465 | 0.496192 | ||||||||
\(334\) | 11.8583 | 0.648857 | ||||||||
\(335\) | −43.1920 | −2.35983 | ||||||||
\(336\) | 4.32251 | 0.235812 | ||||||||
\(337\) | −2.98634 | −0.162676 | −0.0813382 | − | 0.996687i | \(-0.525919\pi\) | ||||
−0.0813382 | + | 0.996687i | \(0.525919\pi\) | |||||||
\(338\) | 0.188447 | 0.0102501 | ||||||||
\(339\) | −10.7707 | −0.584986 | ||||||||
\(340\) | 4.05993 | 0.220181 | ||||||||
\(341\) | 1.56330 | 0.0846577 | ||||||||
\(342\) | −4.32911 | −0.234092 | ||||||||
\(343\) | 20.2471 | 1.09324 | ||||||||
\(344\) | 7.81727 | 0.421479 | ||||||||
\(345\) | 3.92217 | 0.211162 | ||||||||
\(346\) | 5.47185 | 0.294168 | ||||||||
\(347\) | −0.244347 | −0.0131172 | −0.00655861 | − | 0.999978i | \(-0.502088\pi\) | ||||
−0.00655861 | + | 0.999978i | \(0.502088\pi\) | |||||||
\(348\) | −2.78244 | −0.149154 | ||||||||
\(349\) | −21.9939 | −1.17731 | −0.588654 | − | 0.808385i | \(-0.700342\pi\) | ||||
−0.588654 | + | 0.808385i | \(0.700342\pi\) | |||||||
\(350\) | −49.6355 | −2.65313 | ||||||||
\(351\) | −3.57932 | −0.191050 | ||||||||
\(352\) | 0.174683 | 0.00931063 | ||||||||
\(353\) | −31.3154 | −1.66675 | −0.833375 | − | 0.552708i | \(-0.813595\pi\) | ||||
−0.833375 | + | 0.552708i | \(0.813595\pi\) | |||||||
\(354\) | −1.00000 | −0.0531494 | ||||||||
\(355\) | 46.9855 | 2.49373 | ||||||||
\(356\) | 6.06380 | 0.321381 | ||||||||
\(357\) | −4.32251 | −0.228772 | ||||||||
\(358\) | −21.4193 | −1.13204 | ||||||||
\(359\) | 12.1113 | 0.639213 | 0.319606 | − | 0.947550i | \(-0.396449\pi\) | ||||
0.319606 | + | 0.947550i | \(0.396449\pi\) | |||||||
\(360\) | 4.05993 | 0.213977 | ||||||||
\(361\) | −0.258768 | −0.0136194 | ||||||||
\(362\) | −21.9957 | −1.15607 | ||||||||
\(363\) | −10.9695 | −0.575749 | ||||||||
\(364\) | −15.4717 | −0.810936 | ||||||||
\(365\) | −62.5366 | −3.27331 | ||||||||
\(366\) | 13.2963 | 0.695009 | ||||||||
\(367\) | −16.1209 | −0.841505 | −0.420752 | − | 0.907176i | \(-0.638234\pi\) | ||||
−0.420752 | + | 0.907176i | \(0.638234\pi\) | |||||||
\(368\) | −0.966068 | −0.0503598 | ||||||||
\(369\) | −1.49587 | −0.0778719 | ||||||||
\(370\) | 36.7613 | 1.91113 | ||||||||
\(371\) | 35.6795 | 1.85239 | ||||||||
\(372\) | −8.94938 | −0.464004 | ||||||||
\(373\) | 14.4822 | 0.749859 | 0.374930 | − | 0.927053i | \(-0.377667\pi\) | ||||
0.374930 | + | 0.927053i | \(0.377667\pi\) | |||||||
\(374\) | −0.174683 | −0.00903264 | ||||||||
\(375\) | −26.3207 | −1.35919 | ||||||||
\(376\) | 10.9910 | 0.566819 | ||||||||
\(377\) | 9.95924 | 0.512927 | ||||||||
\(378\) | −4.32251 | −0.222326 | ||||||||
\(379\) | −29.1541 | −1.49755 | −0.748773 | − | 0.662827i | \(-0.769357\pi\) | ||||
−0.748773 | + | 0.662827i | \(0.769357\pi\) | |||||||
\(380\) | −17.5759 | −0.901625 | ||||||||
\(381\) | −2.14110 | −0.109692 | ||||||||
\(382\) | 7.81869 | 0.400039 | ||||||||
\(383\) | −4.49641 | −0.229756 | −0.114878 | − | 0.993380i | \(-0.536648\pi\) | ||||
−0.114878 | + | 0.993380i | \(0.536648\pi\) | |||||||
\(384\) | −1.00000 | −0.0510310 | ||||||||
\(385\) | 3.06553 | 0.156234 | ||||||||
\(386\) | −2.50888 | −0.127698 | ||||||||
\(387\) | −7.81727 | −0.397374 | ||||||||
\(388\) | −12.2431 | −0.621551 | ||||||||
\(389\) | 15.4343 | 0.782552 | 0.391276 | − | 0.920273i | \(-0.372034\pi\) | ||||
0.391276 | + | 0.920273i | \(0.372034\pi\) | |||||||
\(390\) | −14.5318 | −0.735846 | ||||||||
\(391\) | 0.966068 | 0.0488561 | ||||||||
\(392\) | −11.6841 | −0.590136 | ||||||||
\(393\) | 13.7267 | 0.692420 | ||||||||
\(394\) | −18.4106 | −0.927515 | ||||||||
\(395\) | 43.1756 | 2.17240 | ||||||||
\(396\) | −0.174683 | −0.00877815 | ||||||||
\(397\) | −6.00696 | −0.301481 | −0.150740 | − | 0.988573i | \(-0.548166\pi\) | ||||
−0.150740 | + | 0.988573i | \(0.548166\pi\) | |||||||
\(398\) | −6.35539 | −0.318567 | ||||||||
\(399\) | 18.7126 | 0.936804 | ||||||||
\(400\) | 11.4830 | 0.574152 | ||||||||
\(401\) | −12.5444 | −0.626435 | −0.313218 | − | 0.949681i | \(-0.601407\pi\) | ||||
−0.313218 | + | 0.949681i | \(0.601407\pi\) | |||||||
\(402\) | −10.6386 | −0.530606 | ||||||||
\(403\) | 32.0327 | 1.59566 | ||||||||
\(404\) | 12.6064 | 0.627192 | ||||||||
\(405\) | −4.05993 | −0.201740 | ||||||||
\(406\) | 12.0271 | 0.596896 | ||||||||
\(407\) | −1.58169 | −0.0784016 | ||||||||
\(408\) | 1.00000 | 0.0495074 | ||||||||
\(409\) | −13.1148 | −0.648487 | −0.324244 | − | 0.945974i | \(-0.605110\pi\) | ||||
−0.324244 | + | 0.945974i | \(0.605110\pi\) | |||||||
\(410\) | −6.07313 | −0.299930 | ||||||||
\(411\) | 10.8186 | 0.533642 | ||||||||
\(412\) | 5.09638 | 0.251080 | ||||||||
\(413\) | 4.32251 | 0.212697 | ||||||||
\(414\) | 0.966068 | 0.0474796 | ||||||||
\(415\) | −54.8957 | −2.69473 | ||||||||
\(416\) | 3.57932 | 0.175491 | ||||||||
\(417\) | −3.78704 | −0.185452 | ||||||||
\(418\) | 0.756222 | 0.0369880 | ||||||||
\(419\) | −9.76811 | −0.477203 | −0.238602 | − | 0.971118i | \(-0.576689\pi\) | ||||
−0.238602 | + | 0.971118i | \(0.576689\pi\) | |||||||
\(420\) | −17.5491 | −0.856308 | ||||||||
\(421\) | −24.1206 | −1.17556 | −0.587782 | − | 0.809019i | \(-0.699999\pi\) | ||||
−0.587782 | + | 0.809019i | \(0.699999\pi\) | |||||||
\(422\) | 13.0469 | 0.635111 | ||||||||
\(423\) | −10.9910 | −0.534402 | ||||||||
\(424\) | −8.25436 | −0.400867 | ||||||||
\(425\) | −11.4830 | −0.557009 | ||||||||
\(426\) | 11.5730 | 0.560713 | ||||||||
\(427\) | −57.4734 | −2.78133 | ||||||||
\(428\) | −12.2482 | −0.592038 | ||||||||
\(429\) | 0.625247 | 0.0301872 | ||||||||
\(430\) | −31.7376 | −1.53052 | ||||||||
\(431\) | −37.0961 | −1.78686 | −0.893429 | − | 0.449204i | \(-0.851708\pi\) | ||||
−0.893429 | + | 0.449204i | \(0.851708\pi\) | |||||||
\(432\) | 1.00000 | 0.0481125 | ||||||||
\(433\) | 17.3365 | 0.833137 | 0.416569 | − | 0.909104i | \(-0.363233\pi\) | ||||
0.416569 | + | 0.909104i | \(0.363233\pi\) | |||||||
\(434\) | 38.6838 | 1.85688 | ||||||||
\(435\) | 11.2965 | 0.541626 | ||||||||
\(436\) | −16.4156 | −0.786164 | ||||||||
\(437\) | −4.18222 | −0.200063 | ||||||||
\(438\) | −15.4034 | −0.736001 | ||||||||
\(439\) | 12.8971 | 0.615544 | 0.307772 | − | 0.951460i | \(-0.400417\pi\) | ||||
0.307772 | + | 0.951460i | \(0.400417\pi\) | |||||||
\(440\) | −0.709201 | −0.0338098 | ||||||||
\(441\) | 11.6841 | 0.556386 | ||||||||
\(442\) | −3.57932 | −0.170251 | ||||||||
\(443\) | −1.74694 | −0.0829998 | −0.0414999 | − | 0.999139i | \(-0.513214\pi\) | ||||
−0.0414999 | + | 0.999139i | \(0.513214\pi\) | |||||||
\(444\) | 9.05465 | 0.429715 | ||||||||
\(445\) | −24.6186 | −1.16703 | ||||||||
\(446\) | 3.72942 | 0.176593 | ||||||||
\(447\) | −21.9080 | −1.03621 | ||||||||
\(448\) | 4.32251 | 0.204219 | ||||||||
\(449\) | 34.4503 | 1.62581 | 0.812905 | − | 0.582397i | \(-0.197885\pi\) | ||||
0.812905 | + | 0.582397i | \(0.197885\pi\) | |||||||
\(450\) | −11.4830 | −0.541315 | ||||||||
\(451\) | 0.261303 | 0.0123043 | ||||||||
\(452\) | −10.7707 | −0.506613 | ||||||||
\(453\) | −5.89511 | −0.276976 | ||||||||
\(454\) | 19.9745 | 0.937449 | ||||||||
\(455\) | 62.8139 | 2.94476 | ||||||||
\(456\) | −4.32911 | −0.202729 | ||||||||
\(457\) | −29.6667 | −1.38775 | −0.693874 | − | 0.720096i | \(-0.744098\pi\) | ||||
−0.693874 | + | 0.720096i | \(0.744098\pi\) | |||||||
\(458\) | 18.9899 | 0.887341 | ||||||||
\(459\) | −1.00000 | −0.0466760 | ||||||||
\(460\) | 3.92217 | 0.182872 | ||||||||
\(461\) | 12.1391 | 0.565373 | 0.282686 | − | 0.959212i | \(-0.408774\pi\) | ||||
0.282686 | + | 0.959212i | \(0.408774\pi\) | |||||||
\(462\) | 0.755069 | 0.0351290 | ||||||||
\(463\) | −8.82748 | −0.410248 | −0.205124 | − | 0.978736i | \(-0.565760\pi\) | ||||
−0.205124 | + | 0.978736i | \(0.565760\pi\) | |||||||
\(464\) | −2.78244 | −0.129171 | ||||||||
\(465\) | 36.3339 | 1.68494 | ||||||||
\(466\) | 28.4041 | 1.31579 | ||||||||
\(467\) | −5.50907 | −0.254929 | −0.127465 | − | 0.991843i | \(-0.540684\pi\) | ||||
−0.127465 | + | 0.991843i | \(0.540684\pi\) | |||||||
\(468\) | −3.57932 | −0.165454 | ||||||||
\(469\) | 45.9855 | 2.12341 | ||||||||
\(470\) | −44.6228 | −2.05829 | ||||||||
\(471\) | 2.64550 | 0.121898 | ||||||||
\(472\) | −1.00000 | −0.0460287 | ||||||||
\(473\) | 1.36554 | 0.0627878 | ||||||||
\(474\) | 10.6346 | 0.488462 | ||||||||
\(475\) | 49.7114 | 2.28091 | ||||||||
\(476\) | −4.32251 | −0.198122 | ||||||||
\(477\) | 8.25436 | 0.377941 | ||||||||
\(478\) | 8.49338 | 0.388478 | ||||||||
\(479\) | 36.9263 | 1.68721 | 0.843603 | − | 0.536967i | \(-0.180430\pi\) | ||||
0.843603 | + | 0.536967i | \(0.180430\pi\) | |||||||
\(480\) | 4.05993 | 0.185310 | ||||||||
\(481\) | −32.4095 | −1.47775 | ||||||||
\(482\) | −12.2957 | −0.560055 | ||||||||
\(483\) | −4.17584 | −0.190007 | ||||||||
\(484\) | −10.9695 | −0.498613 | ||||||||
\(485\) | 49.7062 | 2.25704 | ||||||||
\(486\) | −1.00000 | −0.0453609 | ||||||||
\(487\) | −2.28081 | −0.103353 | −0.0516766 | − | 0.998664i | \(-0.516457\pi\) | ||||
−0.0516766 | + | 0.998664i | \(0.516457\pi\) | |||||||
\(488\) | 13.2963 | 0.601895 | ||||||||
\(489\) | −7.83285 | −0.354214 | ||||||||
\(490\) | 47.4366 | 2.14297 | ||||||||
\(491\) | −31.6406 | −1.42792 | −0.713959 | − | 0.700187i | \(-0.753100\pi\) | ||||
−0.713959 | + | 0.700187i | \(0.753100\pi\) | |||||||
\(492\) | −1.49587 | −0.0674390 | ||||||||
\(493\) | 2.78244 | 0.125315 | ||||||||
\(494\) | 15.4953 | 0.697166 | ||||||||
\(495\) | 0.709201 | 0.0318762 | ||||||||
\(496\) | −8.94938 | −0.401839 | ||||||||
\(497\) | −50.0244 | −2.24390 | ||||||||
\(498\) | −13.5213 | −0.605906 | ||||||||
\(499\) | −23.7710 | −1.06414 | −0.532068 | − | 0.846701i | \(-0.678585\pi\) | ||||
−0.532068 | + | 0.846701i | \(0.678585\pi\) | |||||||
\(500\) | −26.3207 | −1.17710 | ||||||||
\(501\) | −11.8583 | −0.529790 | ||||||||
\(502\) | −9.25024 | −0.412859 | ||||||||
\(503\) | 13.4171 | 0.598240 | 0.299120 | − | 0.954216i | \(-0.403307\pi\) | ||||
0.299120 | + | 0.954216i | \(0.403307\pi\) | |||||||
\(504\) | −4.32251 | −0.192540 | ||||||||
\(505\) | −51.1811 | −2.27753 | ||||||||
\(506\) | −0.168756 | −0.00750210 | ||||||||
\(507\) | −0.188447 | −0.00836921 | ||||||||
\(508\) | −2.14110 | −0.0949959 | ||||||||
\(509\) | 30.4803 | 1.35101 | 0.675507 | − | 0.737354i | \(-0.263925\pi\) | ||||
0.675507 | + | 0.737354i | \(0.263925\pi\) | |||||||
\(510\) | −4.05993 | −0.179777 | ||||||||
\(511\) | 66.5812 | 2.94538 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 4.32911 | 0.191135 | ||||||||
\(514\) | 23.1257 | 1.02003 | ||||||||
\(515\) | −20.6909 | −0.911751 | ||||||||
\(516\) | −7.81727 | −0.344136 | ||||||||
\(517\) | 1.91994 | 0.0844390 | ||||||||
\(518\) | −39.1388 | −1.71966 | ||||||||
\(519\) | −5.47185 | −0.240188 | ||||||||
\(520\) | −14.5318 | −0.637262 | ||||||||
\(521\) | 6.64178 | 0.290982 | 0.145491 | − | 0.989360i | \(-0.453524\pi\) | ||||
0.145491 | + | 0.989360i | \(0.453524\pi\) | |||||||
\(522\) | 2.78244 | 0.121784 | ||||||||
\(523\) | 44.3127 | 1.93766 | 0.968829 | − | 0.247732i | \(-0.0796853\pi\) | ||||
0.968829 | + | 0.247732i | \(0.0796853\pi\) | |||||||
\(524\) | 13.7267 | 0.599653 | ||||||||
\(525\) | 49.6355 | 2.16627 | ||||||||
\(526\) | 16.1148 | 0.702638 | ||||||||
\(527\) | 8.94938 | 0.389841 | ||||||||
\(528\) | −0.174683 | −0.00760210 | ||||||||
\(529\) | −22.0667 | −0.959422 | ||||||||
\(530\) | 33.5121 | 1.45567 | ||||||||
\(531\) | 1.00000 | 0.0433963 | ||||||||
\(532\) | 18.7126 | 0.811296 | ||||||||
\(533\) | 5.35420 | 0.231916 | ||||||||
\(534\) | −6.06380 | −0.262406 | ||||||||
\(535\) | 49.7267 | 2.14987 | ||||||||
\(536\) | −10.6386 | −0.459518 | ||||||||
\(537\) | 21.4193 | 0.924310 | ||||||||
\(538\) | −18.7529 | −0.808497 | ||||||||
\(539\) | −2.04101 | −0.0879127 | ||||||||
\(540\) | −4.05993 | −0.174712 | ||||||||
\(541\) | −12.3021 | −0.528908 | −0.264454 | − | 0.964398i | \(-0.585192\pi\) | ||||
−0.264454 | + | 0.964398i | \(0.585192\pi\) | |||||||
\(542\) | 7.10047 | 0.304991 | ||||||||
\(543\) | 21.9957 | 0.943926 | ||||||||
\(544\) | 1.00000 | 0.0428746 | ||||||||
\(545\) | 66.6461 | 2.85481 | ||||||||
\(546\) | 15.4717 | 0.662126 | ||||||||
\(547\) | −27.4914 | −1.17545 | −0.587723 | − | 0.809062i | \(-0.699975\pi\) | ||||
−0.587723 | + | 0.809062i | \(0.699975\pi\) | |||||||
\(548\) | 10.8186 | 0.462148 | ||||||||
\(549\) | −13.2963 | −0.567472 | ||||||||
\(550\) | 2.00589 | 0.0855314 | ||||||||
\(551\) | −12.0455 | −0.513155 | ||||||||
\(552\) | 0.966068 | 0.0411186 | ||||||||
\(553\) | −45.9680 | −1.95476 | ||||||||
\(554\) | 9.73472 | 0.413589 | ||||||||
\(555\) | −36.7613 | −1.56043 | ||||||||
\(556\) | −3.78704 | −0.160606 | ||||||||
\(557\) | 4.85946 | 0.205902 | 0.102951 | − | 0.994686i | \(-0.467172\pi\) | ||||
0.102951 | + | 0.994686i | \(0.467172\pi\) | |||||||
\(558\) | 8.94938 | 0.378858 | ||||||||
\(559\) | 27.9805 | 1.18345 | ||||||||
\(560\) | −17.5491 | −0.741585 | ||||||||
\(561\) | 0.174683 | 0.00737512 | ||||||||
\(562\) | 11.3620 | 0.479276 | ||||||||
\(563\) | −4.05063 | −0.170714 | −0.0853568 | − | 0.996350i | \(-0.527203\pi\) | ||||
−0.0853568 | + | 0.996350i | \(0.527203\pi\) | |||||||
\(564\) | −10.9910 | −0.462805 | ||||||||
\(565\) | 43.7284 | 1.83967 | ||||||||
\(566\) | 2.28586 | 0.0960819 | ||||||||
\(567\) | 4.32251 | 0.181528 | ||||||||
\(568\) | 11.5730 | 0.485592 | ||||||||
\(569\) | −34.7391 | −1.45634 | −0.728168 | − | 0.685398i | \(-0.759628\pi\) | ||||
−0.728168 | + | 0.685398i | \(0.759628\pi\) | |||||||
\(570\) | 17.5759 | 0.736174 | ||||||||
\(571\) | −18.6043 | −0.778565 | −0.389283 | − | 0.921118i | \(-0.627277\pi\) | ||||
−0.389283 | + | 0.921118i | \(0.627277\pi\) | |||||||
\(572\) | 0.625247 | 0.0261429 | ||||||||
\(573\) | −7.81869 | −0.326630 | ||||||||
\(574\) | 6.46591 | 0.269882 | ||||||||
\(575\) | −11.0934 | −0.462626 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | −8.88899 | −0.370054 | −0.185027 | − | 0.982733i | \(-0.559237\pi\) | ||||
−0.185027 | + | 0.982733i | \(0.559237\pi\) | |||||||
\(578\) | −1.00000 | −0.0415945 | ||||||||
\(579\) | 2.50888 | 0.104265 | ||||||||
\(580\) | 11.2965 | 0.469062 | ||||||||
\(581\) | 58.4462 | 2.42476 | ||||||||
\(582\) | 12.2431 | 0.507494 | ||||||||
\(583\) | −1.44190 | −0.0597172 | ||||||||
\(584\) | −15.4034 | −0.637396 | ||||||||
\(585\) | 14.5318 | 0.600816 | ||||||||
\(586\) | 11.8171 | 0.488160 | ||||||||
\(587\) | −15.6963 | −0.647854 | −0.323927 | − | 0.946082i | \(-0.605003\pi\) | ||||
−0.323927 | + | 0.946082i | \(0.605003\pi\) | |||||||
\(588\) | 11.6841 | 0.481844 | ||||||||
\(589\) | −38.7429 | −1.59637 | ||||||||
\(590\) | 4.05993 | 0.167145 | ||||||||
\(591\) | 18.4106 | 0.757313 | ||||||||
\(592\) | 9.05465 | 0.372144 | ||||||||
\(593\) | 2.75499 | 0.113134 | 0.0565668 | − | 0.998399i | \(-0.481985\pi\) | ||||
0.0565668 | + | 0.998399i | \(0.481985\pi\) | |||||||
\(594\) | 0.174683 | 0.00716733 | ||||||||
\(595\) | 17.5491 | 0.719443 | ||||||||
\(596\) | −21.9080 | −0.897388 | ||||||||
\(597\) | 6.35539 | 0.260109 | ||||||||
\(598\) | −3.45787 | −0.141403 | ||||||||
\(599\) | −34.9824 | −1.42934 | −0.714671 | − | 0.699461i | \(-0.753423\pi\) | ||||
−0.714671 | + | 0.699461i | \(0.753423\pi\) | |||||||
\(600\) | −11.4830 | −0.468793 | ||||||||
\(601\) | −33.4111 | −1.36287 | −0.681434 | − | 0.731879i | \(-0.738643\pi\) | ||||
−0.681434 | + | 0.731879i | \(0.738643\pi\) | |||||||
\(602\) | 33.7903 | 1.37719 | ||||||||
\(603\) | 10.6386 | 0.433238 | ||||||||
\(604\) | −5.89511 | −0.239869 | ||||||||
\(605\) | 44.5353 | 1.81062 | ||||||||
\(606\) | −12.6064 | −0.512100 | ||||||||
\(607\) | 40.1724 | 1.63055 | 0.815274 | − | 0.579076i | \(-0.196586\pi\) | ||||
0.815274 | + | 0.579076i | \(0.196586\pi\) | |||||||
\(608\) | −4.32911 | −0.175569 | ||||||||
\(609\) | −12.0271 | −0.487363 | ||||||||
\(610\) | −53.9821 | −2.18567 | ||||||||
\(611\) | 39.3404 | 1.59154 | ||||||||
\(612\) | −1.00000 | −0.0404226 | ||||||||
\(613\) | 27.2179 | 1.09932 | 0.549661 | − | 0.835388i | \(-0.314757\pi\) | ||||
0.549661 | + | 0.835388i | \(0.314757\pi\) | |||||||
\(614\) | 21.0755 | 0.850539 | ||||||||
\(615\) | 6.07313 | 0.244892 | ||||||||
\(616\) | 0.755069 | 0.0304226 | ||||||||
\(617\) | 5.10001 | 0.205319 | 0.102659 | − | 0.994717i | \(-0.467265\pi\) | ||||
0.102659 | + | 0.994717i | \(0.467265\pi\) | |||||||
\(618\) | −5.09638 | −0.205006 | ||||||||
\(619\) | −47.9346 | −1.92665 | −0.963327 | − | 0.268331i | \(-0.913528\pi\) | ||||
−0.963327 | + | 0.268331i | \(0.913528\pi\) | |||||||
\(620\) | 36.3339 | 1.45920 | ||||||||
\(621\) | −0.966068 | −0.0387670 | ||||||||
\(622\) | −2.89958 | −0.116263 | ||||||||
\(623\) | 26.2108 | 1.05011 | ||||||||
\(624\) | −3.57932 | −0.143288 | ||||||||
\(625\) | 49.4449 | 1.97780 | ||||||||
\(626\) | −13.0246 | −0.520567 | ||||||||
\(627\) | −0.756222 | −0.0302006 | ||||||||
\(628\) | 2.64550 | 0.105567 | ||||||||
\(629\) | −9.05465 | −0.361033 | ||||||||
\(630\) | 17.5491 | 0.699173 | ||||||||
\(631\) | −14.0892 | −0.560880 | −0.280440 | − | 0.959871i | \(-0.590480\pi\) | ||||
−0.280440 | + | 0.959871i | \(0.590480\pi\) | |||||||
\(632\) | 10.6346 | 0.423020 | ||||||||
\(633\) | −13.0469 | −0.518566 | ||||||||
\(634\) | −8.38129 | −0.332864 | ||||||||
\(635\) | 8.69271 | 0.344960 | ||||||||
\(636\) | 8.25436 | 0.327307 | ||||||||
\(637\) | −41.8212 | −1.65702 | ||||||||
\(638\) | −0.486044 | −0.0192427 | ||||||||
\(639\) | −11.5730 | −0.457820 | ||||||||
\(640\) | 4.05993 | 0.160483 | ||||||||
\(641\) | 34.5870 | 1.36611 | 0.683053 | − | 0.730369i | \(-0.260652\pi\) | ||||
0.683053 | + | 0.730369i | \(0.260652\pi\) | |||||||
\(642\) | 12.2482 | 0.483397 | ||||||||
\(643\) | 42.9143 | 1.69238 | 0.846188 | − | 0.532884i | \(-0.178892\pi\) | ||||
0.846188 | + | 0.532884i | \(0.178892\pi\) | |||||||
\(644\) | −4.17584 | −0.164551 | ||||||||
\(645\) | 31.7376 | 1.24967 | ||||||||
\(646\) | 4.32911 | 0.170327 | ||||||||
\(647\) | 11.6391 | 0.457578 | 0.228789 | − | 0.973476i | \(-0.426523\pi\) | ||||
0.228789 | + | 0.973476i | \(0.426523\pi\) | |||||||
\(648\) | −1.00000 | −0.0392837 | ||||||||
\(649\) | −0.174683 | −0.00685691 | ||||||||
\(650\) | 41.1015 | 1.61213 | ||||||||
\(651\) | −38.6838 | −1.51614 | ||||||||
\(652\) | −7.83285 | −0.306758 | ||||||||
\(653\) | −20.8139 | −0.814511 | −0.407256 | − | 0.913314i | \(-0.633514\pi\) | ||||
−0.407256 | + | 0.913314i | \(0.633514\pi\) | |||||||
\(654\) | 16.4156 | 0.641900 | ||||||||
\(655\) | −55.7294 | −2.17753 | ||||||||
\(656\) | −1.49587 | −0.0584039 | ||||||||
\(657\) | 15.4034 | 0.600942 | ||||||||
\(658\) | 47.5088 | 1.85209 | ||||||||
\(659\) | −29.1730 | −1.13642 | −0.568209 | − | 0.822884i | \(-0.692364\pi\) | ||||
−0.568209 | + | 0.822884i | \(0.692364\pi\) | |||||||
\(660\) | 0.709201 | 0.0276056 | ||||||||
\(661\) | 47.5780 | 1.85057 | 0.925286 | − | 0.379271i | \(-0.123825\pi\) | ||||
0.925286 | + | 0.379271i | \(0.123825\pi\) | |||||||
\(662\) | −17.9828 | −0.698923 | ||||||||
\(663\) | 3.57932 | 0.139009 | ||||||||
\(664\) | −13.5213 | −0.524730 | ||||||||
\(665\) | −75.9720 | −2.94607 | ||||||||
\(666\) | −9.05465 | −0.350861 | ||||||||
\(667\) | 2.68802 | 0.104081 | ||||||||
\(668\) | −11.8583 | −0.458811 | ||||||||
\(669\) | −3.72942 | −0.144188 | ||||||||
\(670\) | 43.1920 | 1.66865 | ||||||||
\(671\) | 2.32264 | 0.0896644 | ||||||||
\(672\) | −4.32251 | −0.166744 | ||||||||
\(673\) | 30.4302 | 1.17300 | 0.586499 | − | 0.809950i | \(-0.300506\pi\) | ||||
0.586499 | + | 0.809950i | \(0.300506\pi\) | |||||||
\(674\) | 2.98634 | 0.115030 | ||||||||
\(675\) | 11.4830 | 0.441982 | ||||||||
\(676\) | −0.188447 | −0.00724794 | ||||||||
\(677\) | −37.7621 | −1.45131 | −0.725657 | − | 0.688056i | \(-0.758464\pi\) | ||||
−0.725657 | + | 0.688056i | \(0.758464\pi\) | |||||||
\(678\) | 10.7707 | 0.413647 | ||||||||
\(679\) | −52.9211 | −2.03092 | ||||||||
\(680\) | −4.05993 | −0.155691 | ||||||||
\(681\) | −19.9745 | −0.765424 | ||||||||
\(682\) | −1.56330 | −0.0598620 | ||||||||
\(683\) | 8.07878 | 0.309126 | 0.154563 | − | 0.987983i | \(-0.450603\pi\) | ||||
0.154563 | + | 0.987983i | \(0.450603\pi\) | |||||||
\(684\) | 4.32911 | 0.165528 | ||||||||
\(685\) | −43.9228 | −1.67820 | ||||||||
\(686\) | −20.2471 | −0.773037 | ||||||||
\(687\) | −18.9899 | −0.724511 | ||||||||
\(688\) | −7.81727 | −0.298031 | ||||||||
\(689\) | −29.5450 | −1.12558 | ||||||||
\(690\) | −3.92217 | −0.149314 | ||||||||
\(691\) | 11.6530 | 0.443300 | 0.221650 | − | 0.975126i | \(-0.428856\pi\) | ||||
0.221650 | + | 0.975126i | \(0.428856\pi\) | |||||||
\(692\) | −5.47185 | −0.208008 | ||||||||
\(693\) | −0.755069 | −0.0286827 | ||||||||
\(694\) | 0.244347 | 0.00927527 | ||||||||
\(695\) | 15.3751 | 0.583211 | ||||||||
\(696\) | 2.78244 | 0.105468 | ||||||||
\(697\) | 1.49587 | 0.0566601 | ||||||||
\(698\) | 21.9939 | 0.832483 | ||||||||
\(699\) | −28.4041 | −1.07434 | ||||||||
\(700\) | 49.6355 | 1.87605 | ||||||||
\(701\) | 5.88109 | 0.222126 | 0.111063 | − | 0.993813i | \(-0.464574\pi\) | ||||
0.111063 | + | 0.993813i | \(0.464574\pi\) | |||||||
\(702\) | 3.57932 | 0.135093 | ||||||||
\(703\) | 39.1986 | 1.47840 | ||||||||
\(704\) | −0.174683 | −0.00658361 | ||||||||
\(705\) | 44.6228 | 1.68059 | ||||||||
\(706\) | 31.3154 | 1.17857 | ||||||||
\(707\) | 54.4913 | 2.04936 | ||||||||
\(708\) | 1.00000 | 0.0375823 | ||||||||
\(709\) | −19.6916 | −0.739535 | −0.369768 | − | 0.929124i | \(-0.620563\pi\) | ||||
−0.369768 | + | 0.929124i | \(0.620563\pi\) | |||||||
\(710\) | −46.9855 | −1.76334 | ||||||||
\(711\) | −10.6346 | −0.398827 | ||||||||
\(712\) | −6.06380 | −0.227250 | ||||||||
\(713\) | 8.64571 | 0.323784 | ||||||||
\(714\) | 4.32251 | 0.161766 | ||||||||
\(715\) | −2.53846 | −0.0949329 | ||||||||
\(716\) | 21.4193 | 0.800476 | ||||||||
\(717\) | −8.49338 | −0.317191 | ||||||||
\(718\) | −12.1113 | −0.451992 | ||||||||
\(719\) | −35.7611 | −1.33366 | −0.666832 | − | 0.745208i | \(-0.732350\pi\) | ||||
−0.666832 | + | 0.745208i | \(0.732350\pi\) | |||||||
\(720\) | −4.05993 | −0.151305 | ||||||||
\(721\) | 22.0291 | 0.820408 | ||||||||
\(722\) | 0.258768 | 0.00963034 | ||||||||
\(723\) | 12.2957 | 0.457283 | ||||||||
\(724\) | 21.9957 | 0.817464 | ||||||||
\(725\) | −31.9508 | −1.18662 | ||||||||
\(726\) | 10.9695 | 0.407116 | ||||||||
\(727\) | −21.5900 | −0.800728 | −0.400364 | − | 0.916356i | \(-0.631116\pi\) | ||||
−0.400364 | + | 0.916356i | \(0.631116\pi\) | |||||||
\(728\) | 15.4717 | 0.573418 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 62.5366 | 2.31458 | ||||||||
\(731\) | 7.81727 | 0.289132 | ||||||||
\(732\) | −13.2963 | −0.491445 | ||||||||
\(733\) | −8.04904 | −0.297298 | −0.148649 | − | 0.988890i | \(-0.547492\pi\) | ||||
−0.148649 | + | 0.988890i | \(0.547492\pi\) | |||||||
\(734\) | 16.1209 | 0.595034 | ||||||||
\(735\) | −47.4366 | −1.74973 | ||||||||
\(736\) | 0.966068 | 0.0356097 | ||||||||
\(737\) | −1.85838 | −0.0684545 | ||||||||
\(738\) | 1.49587 | 0.0550637 | ||||||||
\(739\) | 9.69286 | 0.356558 | 0.178279 | − | 0.983980i | \(-0.442947\pi\) | ||||
0.178279 | + | 0.983980i | \(0.442947\pi\) | |||||||
\(740\) | −36.7613 | −1.35137 | ||||||||
\(741\) | −15.4953 | −0.569234 | ||||||||
\(742\) | −35.6795 | −1.30984 | ||||||||
\(743\) | 1.09730 | 0.0402560 | 0.0201280 | − | 0.999797i | \(-0.493593\pi\) | ||||
0.0201280 | + | 0.999797i | \(0.493593\pi\) | |||||||
\(744\) | 8.94938 | 0.328100 | ||||||||
\(745\) | 88.9451 | 3.25870 | ||||||||
\(746\) | −14.4822 | −0.530231 | ||||||||
\(747\) | 13.5213 | 0.494720 | ||||||||
\(748\) | 0.174683 | 0.00638704 | ||||||||
\(749\) | −52.9428 | −1.93449 | ||||||||
\(750\) | 26.3207 | 0.961095 | ||||||||
\(751\) | −50.7608 | −1.85229 | −0.926144 | − | 0.377170i | \(-0.876897\pi\) | ||||
−0.926144 | + | 0.377170i | \(0.876897\pi\) | |||||||
\(752\) | −10.9910 | −0.400801 | ||||||||
\(753\) | 9.25024 | 0.337098 | ||||||||
\(754\) | −9.95924 | −0.362694 | ||||||||
\(755\) | 23.9337 | 0.871037 | ||||||||
\(756\) | 4.32251 | 0.157208 | ||||||||
\(757\) | −33.1847 | −1.20612 | −0.603058 | − | 0.797697i | \(-0.706051\pi\) | ||||
−0.603058 | + | 0.797697i | \(0.706051\pi\) | |||||||
\(758\) | 29.1541 | 1.05892 | ||||||||
\(759\) | 0.168756 | 0.00612544 | ||||||||
\(760\) | 17.5759 | 0.637545 | ||||||||
\(761\) | −26.2199 | −0.950472 | −0.475236 | − | 0.879858i | \(-0.657637\pi\) | ||||
−0.475236 | + | 0.879858i | \(0.657637\pi\) | |||||||
\(762\) | 2.14110 | 0.0775638 | ||||||||
\(763\) | −70.9565 | −2.56880 | ||||||||
\(764\) | −7.81869 | −0.282870 | ||||||||
\(765\) | 4.05993 | 0.146787 | ||||||||
\(766\) | 4.49641 | 0.162462 | ||||||||
\(767\) | −3.57932 | −0.129242 | ||||||||
\(768\) | 1.00000 | 0.0360844 | ||||||||
\(769\) | 21.1662 | 0.763272 | 0.381636 | − | 0.924313i | \(-0.375361\pi\) | ||||
0.381636 | + | 0.924313i | \(0.375361\pi\) | |||||||
\(770\) | −3.06553 | −0.110474 | ||||||||
\(771\) | −23.1257 | −0.832851 | ||||||||
\(772\) | 2.50888 | 0.0902964 | ||||||||
\(773\) | 5.77405 | 0.207678 | 0.103839 | − | 0.994594i | \(-0.466887\pi\) | ||||
0.103839 | + | 0.994594i | \(0.466887\pi\) | |||||||
\(774\) | 7.81727 | 0.280986 | ||||||||
\(775\) | −102.766 | −3.69147 | ||||||||
\(776\) | 12.2431 | 0.439503 | ||||||||
\(777\) | 39.1388 | 1.40410 | ||||||||
\(778\) | −15.4343 | −0.553348 | ||||||||
\(779\) | −6.47579 | −0.232019 | ||||||||
\(780\) | 14.5318 | 0.520322 | ||||||||
\(781\) | 2.02160 | 0.0723387 | ||||||||
\(782\) | −0.966068 | −0.0345465 | ||||||||
\(783\) | −2.78244 | −0.0994362 | ||||||||
\(784\) | 11.6841 | 0.417289 | ||||||||
\(785\) | −10.7405 | −0.383346 | ||||||||
\(786\) | −13.7267 | −0.489615 | ||||||||
\(787\) | −6.03223 | −0.215026 | −0.107513 | − | 0.994204i | \(-0.534289\pi\) | ||||
−0.107513 | + | 0.994204i | \(0.534289\pi\) | |||||||
\(788\) | 18.4106 | 0.655852 | ||||||||
\(789\) | −16.1148 | −0.573702 | ||||||||
\(790\) | −43.1756 | −1.53612 | ||||||||
\(791\) | −46.5566 | −1.65536 | ||||||||
\(792\) | 0.174683 | 0.00620709 | ||||||||
\(793\) | 47.5918 | 1.69003 | ||||||||
\(794\) | 6.00696 | 0.213179 | ||||||||
\(795\) | −33.5121 | −1.18855 | ||||||||
\(796\) | 6.35539 | 0.225261 | ||||||||
\(797\) | 43.2926 | 1.53350 | 0.766751 | − | 0.641944i | \(-0.221872\pi\) | ||||
0.766751 | + | 0.641944i | \(0.221872\pi\) | |||||||
\(798\) | −18.7126 | −0.662420 | ||||||||
\(799\) | 10.9910 | 0.388834 | ||||||||
\(800\) | −11.4830 | −0.405987 | ||||||||
\(801\) | 6.06380 | 0.214254 | ||||||||
\(802\) | 12.5444 | 0.442957 | ||||||||
\(803\) | −2.69070 | −0.0949529 | ||||||||
\(804\) | 10.6386 | 0.375195 | ||||||||
\(805\) | 16.9536 | 0.597536 | ||||||||
\(806\) | −32.0327 | −1.12830 | ||||||||
\(807\) | 18.7529 | 0.660135 | ||||||||
\(808\) | −12.6064 | −0.443492 | ||||||||
\(809\) | 19.3752 | 0.681196 | 0.340598 | − | 0.940209i | \(-0.389371\pi\) | ||||
0.340598 | + | 0.940209i | \(0.389371\pi\) | |||||||
\(810\) | 4.05993 | 0.142651 | ||||||||
\(811\) | −0.993961 | −0.0349027 | −0.0174513 | − | 0.999848i | \(-0.505555\pi\) | ||||
−0.0174513 | + | 0.999848i | \(0.505555\pi\) | |||||||
\(812\) | −12.0271 | −0.422069 | ||||||||
\(813\) | −7.10047 | −0.249024 | ||||||||
\(814\) | 1.58169 | 0.0554383 | ||||||||
\(815\) | 31.8008 | 1.11393 | ||||||||
\(816\) | −1.00000 | −0.0350070 | ||||||||
\(817\) | −33.8419 | −1.18398 | ||||||||
\(818\) | 13.1148 | 0.458550 | ||||||||
\(819\) | −15.4717 | −0.540624 | ||||||||
\(820\) | 6.07313 | 0.212083 | ||||||||
\(821\) | 47.2114 | 1.64769 | 0.823845 | − | 0.566815i | \(-0.191825\pi\) | ||||
0.823845 | + | 0.566815i | \(0.191825\pi\) | |||||||
\(822\) | −10.8186 | −0.377342 | ||||||||
\(823\) | −0.437840 | −0.0152621 | −0.00763107 | − | 0.999971i | \(-0.502429\pi\) | ||||
−0.00763107 | + | 0.999971i | \(0.502429\pi\) | |||||||
\(824\) | −5.09638 | −0.177541 | ||||||||
\(825\) | −2.00589 | −0.0698361 | ||||||||
\(826\) | −4.32251 | −0.150399 | ||||||||
\(827\) | 13.0771 | 0.454734 | 0.227367 | − | 0.973809i | \(-0.426988\pi\) | ||||
0.227367 | + | 0.973809i | \(0.426988\pi\) | |||||||
\(828\) | −0.966068 | −0.0335732 | ||||||||
\(829\) | 19.7507 | 0.685971 | 0.342985 | − | 0.939341i | \(-0.388562\pi\) | ||||
0.342985 | + | 0.939341i | \(0.388562\pi\) | |||||||
\(830\) | 54.8957 | 1.90546 | ||||||||
\(831\) | −9.73472 | −0.337694 | ||||||||
\(832\) | −3.57932 | −0.124091 | ||||||||
\(833\) | −11.6841 | −0.404830 | ||||||||
\(834\) | 3.78704 | 0.131134 | ||||||||
\(835\) | 48.1439 | 1.66609 | ||||||||
\(836\) | −0.756222 | −0.0261545 | ||||||||
\(837\) | −8.94938 | −0.309336 | ||||||||
\(838\) | 9.76811 | 0.337434 | ||||||||
\(839\) | 5.25854 | 0.181545 | 0.0907724 | − | 0.995872i | \(-0.471066\pi\) | ||||
0.0907724 | + | 0.995872i | \(0.471066\pi\) | |||||||
\(840\) | 17.5491 | 0.605501 | ||||||||
\(841\) | −21.2580 | −0.733036 | ||||||||
\(842\) | 24.1206 | 0.831250 | ||||||||
\(843\) | −11.3620 | −0.391327 | ||||||||
\(844\) | −13.0469 | −0.449091 | ||||||||
\(845\) | 0.765080 | 0.0263195 | ||||||||
\(846\) | 10.9910 | 0.377879 | ||||||||
\(847\) | −47.4157 | −1.62922 | ||||||||
\(848\) | 8.25436 | 0.283456 | ||||||||
\(849\) | −2.28586 | −0.0784506 | ||||||||
\(850\) | 11.4830 | 0.393865 | ||||||||
\(851\) | −8.74741 | −0.299857 | ||||||||
\(852\) | −11.5730 | −0.396484 | ||||||||
\(853\) | 17.0886 | 0.585101 | 0.292551 | − | 0.956250i | \(-0.405496\pi\) | ||||
0.292551 | + | 0.956250i | \(0.405496\pi\) | |||||||
\(854\) | 57.4734 | 1.96670 | ||||||||
\(855\) | −17.5759 | −0.601083 | ||||||||
\(856\) | 12.2482 | 0.418634 | ||||||||
\(857\) | −6.88810 | −0.235293 | −0.117647 | − | 0.993056i | \(-0.537535\pi\) | ||||
−0.117647 | + | 0.993056i | \(0.537535\pi\) | |||||||
\(858\) | −0.625247 | −0.0213456 | ||||||||
\(859\) | 21.2091 | 0.723645 | 0.361822 | − | 0.932247i | \(-0.382155\pi\) | ||||
0.361822 | + | 0.932247i | \(0.382155\pi\) | |||||||
\(860\) | 31.7376 | 1.08224 | ||||||||
\(861\) | −6.46591 | −0.220358 | ||||||||
\(862\) | 37.0961 | 1.26350 | ||||||||
\(863\) | 24.6734 | 0.839893 | 0.419947 | − | 0.907549i | \(-0.362049\pi\) | ||||
0.419947 | + | 0.907549i | \(0.362049\pi\) | |||||||
\(864\) | −1.00000 | −0.0340207 | ||||||||
\(865\) | 22.2153 | 0.755344 | ||||||||
\(866\) | −17.3365 | −0.589117 | ||||||||
\(867\) | 1.00000 | 0.0339618 | ||||||||
\(868\) | −38.6838 | −1.31301 | ||||||||
\(869\) | 1.85768 | 0.0630174 | ||||||||
\(870\) | −11.2965 | −0.382987 | ||||||||
\(871\) | −38.0790 | −1.29026 | ||||||||
\(872\) | 16.4156 | 0.555902 | ||||||||
\(873\) | −12.2431 | −0.414367 | ||||||||
\(874\) | 4.18222 | 0.141466 | ||||||||
\(875\) | −113.771 | −3.84617 | ||||||||
\(876\) | 15.4034 | 0.520431 | ||||||||
\(877\) | −16.4095 | −0.554109 | −0.277054 | − | 0.960854i | \(-0.589358\pi\) | ||||
−0.277054 | + | 0.960854i | \(0.589358\pi\) | |||||||
\(878\) | −12.8971 | −0.435255 | ||||||||
\(879\) | −11.8171 | −0.398581 | ||||||||
\(880\) | 0.709201 | 0.0239071 | ||||||||
\(881\) | 29.4247 | 0.991344 | 0.495672 | − | 0.868510i | \(-0.334922\pi\) | ||||
0.495672 | + | 0.868510i | \(0.334922\pi\) | |||||||
\(882\) | −11.6841 | −0.393424 | ||||||||
\(883\) | −9.91701 | −0.333734 | −0.166867 | − | 0.985979i | \(-0.553365\pi\) | ||||
−0.166867 | + | 0.985979i | \(0.553365\pi\) | |||||||
\(884\) | 3.57932 | 0.120386 | ||||||||
\(885\) | −4.05993 | −0.136473 | ||||||||
\(886\) | 1.74694 | 0.0586897 | ||||||||
\(887\) | −9.92272 | −0.333172 | −0.166586 | − | 0.986027i | \(-0.553274\pi\) | ||||
−0.166586 | + | 0.986027i | \(0.553274\pi\) | |||||||
\(888\) | −9.05465 | −0.303854 | ||||||||
\(889\) | −9.25493 | −0.310400 | ||||||||
\(890\) | 24.6186 | 0.825217 | ||||||||
\(891\) | −0.174683 | −0.00585210 | ||||||||
\(892\) | −3.72942 | −0.124870 | ||||||||
\(893\) | −47.5814 | −1.59225 | ||||||||
\(894\) | 21.9080 | 0.732714 | ||||||||
\(895\) | −86.9608 | −2.90678 | ||||||||
\(896\) | −4.32251 | −0.144405 | ||||||||
\(897\) | 3.45787 | 0.115455 | ||||||||
\(898\) | −34.4503 | −1.14962 | ||||||||
\(899\) | 24.9011 | 0.830498 | ||||||||
\(900\) | 11.4830 | 0.382768 | ||||||||
\(901\) | −8.25436 | −0.274993 | ||||||||
\(902\) | −0.261303 | −0.00870044 | ||||||||
\(903\) | −33.7903 | −1.12447 | ||||||||
\(904\) | 10.7707 | 0.358229 | ||||||||
\(905\) | −89.3010 | −2.96847 | ||||||||
\(906\) | 5.89511 | 0.195852 | ||||||||
\(907\) | 37.0105 | 1.22891 | 0.614457 | − | 0.788950i | \(-0.289375\pi\) | ||||
0.614457 | + | 0.788950i | \(0.289375\pi\) | |||||||
\(908\) | −19.9745 | −0.662877 | ||||||||
\(909\) | 12.6064 | 0.418128 | ||||||||
\(910\) | −62.8139 | −2.08226 | ||||||||
\(911\) | 38.7884 | 1.28512 | 0.642559 | − | 0.766236i | \(-0.277873\pi\) | ||||
0.642559 | + | 0.766236i | \(0.277873\pi\) | |||||||
\(912\) | 4.32911 | 0.143351 | ||||||||
\(913\) | −2.36195 | −0.0781691 | ||||||||
\(914\) | 29.6667 | 0.981286 | ||||||||
\(915\) | 53.9821 | 1.78459 | ||||||||
\(916\) | −18.9899 | −0.627445 | ||||||||
\(917\) | 59.3338 | 1.95937 | ||||||||
\(918\) | 1.00000 | 0.0330049 | ||||||||
\(919\) | −35.8518 | −1.18264 | −0.591321 | − | 0.806436i | \(-0.701393\pi\) | ||||
−0.591321 | + | 0.806436i | \(0.701393\pi\) | |||||||
\(920\) | −3.92217 | −0.129310 | ||||||||
\(921\) | −21.0755 | −0.694462 | ||||||||
\(922\) | −12.1391 | −0.399779 | ||||||||
\(923\) | 41.4235 | 1.36347 | ||||||||
\(924\) | −0.755069 | −0.0248399 | ||||||||
\(925\) | 103.975 | 3.41867 | ||||||||
\(926\) | 8.82748 | 0.290089 | ||||||||
\(927\) | 5.09638 | 0.167387 | ||||||||
\(928\) | 2.78244 | 0.0913380 | ||||||||
\(929\) | 29.3173 | 0.961871 | 0.480935 | − | 0.876756i | \(-0.340297\pi\) | ||||
0.480935 | + | 0.876756i | \(0.340297\pi\) | |||||||
\(930\) | −36.3339 | −1.19143 | ||||||||
\(931\) | 50.5818 | 1.65775 | ||||||||
\(932\) | −28.4041 | −0.930406 | ||||||||
\(933\) | 2.89958 | 0.0949280 | ||||||||
\(934\) | 5.50907 | 0.180262 | ||||||||
\(935\) | −0.709201 | −0.0231933 | ||||||||
\(936\) | 3.57932 | 0.116994 | ||||||||
\(937\) | −6.99549 | −0.228533 | −0.114266 | − | 0.993450i | \(-0.536452\pi\) | ||||
−0.114266 | + | 0.993450i | \(0.536452\pi\) | |||||||
\(938\) | −45.9855 | −1.50148 | ||||||||
\(939\) | 13.0246 | 0.425041 | ||||||||
\(940\) | 44.6228 | 1.45543 | ||||||||
\(941\) | −22.1704 | −0.722733 | −0.361367 | − | 0.932424i | \(-0.617690\pi\) | ||||
−0.361367 | + | 0.932424i | \(0.617690\pi\) | |||||||
\(942\) | −2.64550 | −0.0861950 | ||||||||
\(943\) | 1.44511 | 0.0470593 | ||||||||
\(944\) | 1.00000 | 0.0325472 | ||||||||
\(945\) | −17.5491 | −0.570872 | ||||||||
\(946\) | −1.36554 | −0.0443977 | ||||||||
\(947\) | 10.6628 | 0.346496 | 0.173248 | − | 0.984878i | \(-0.444574\pi\) | ||||
0.173248 | + | 0.984878i | \(0.444574\pi\) | |||||||
\(948\) | −10.6346 | −0.345395 | ||||||||
\(949\) | −55.1336 | −1.78971 | ||||||||
\(950\) | −49.7114 | −1.61285 | ||||||||
\(951\) | 8.38129 | 0.271782 | ||||||||
\(952\) | 4.32251 | 0.140093 | ||||||||
\(953\) | −55.5462 | −1.79932 | −0.899659 | − | 0.436593i | \(-0.856185\pi\) | ||||
−0.899659 | + | 0.436593i | \(0.856185\pi\) | |||||||
\(954\) | −8.25436 | −0.267245 | ||||||||
\(955\) | 31.7433 | 1.02719 | ||||||||
\(956\) | −8.49338 | −0.274696 | ||||||||
\(957\) | 0.486044 | 0.0157116 | ||||||||
\(958\) | −36.9263 | −1.19304 | ||||||||
\(959\) | 46.7635 | 1.51007 | ||||||||
\(960\) | −4.05993 | −0.131034 | ||||||||
\(961\) | 49.0914 | 1.58360 | ||||||||
\(962\) | 32.4095 | 1.04492 | ||||||||
\(963\) | −12.2482 | −0.394692 | ||||||||
\(964\) | 12.2957 | 0.396019 | ||||||||
\(965\) | −10.1859 | −0.327894 | ||||||||
\(966\) | 4.17584 | 0.134355 | ||||||||
\(967\) | 0.737989 | 0.0237321 | 0.0118661 | − | 0.999930i | \(-0.496223\pi\) | ||||
0.0118661 | + | 0.999930i | \(0.496223\pi\) | |||||||
\(968\) | 10.9695 | 0.352573 | ||||||||
\(969\) | −4.32911 | −0.139071 | ||||||||
\(970\) | −49.7062 | −1.59597 | ||||||||
\(971\) | 35.3988 | 1.13600 | 0.568001 | − | 0.823028i | \(-0.307717\pi\) | ||||
0.568001 | + | 0.823028i | \(0.307717\pi\) | |||||||
\(972\) | 1.00000 | 0.0320750 | ||||||||
\(973\) | −16.3695 | −0.524782 | ||||||||
\(974\) | 2.28081 | 0.0730818 | ||||||||
\(975\) | −41.1015 | −1.31630 | ||||||||
\(976\) | −13.2963 | −0.425604 | ||||||||
\(977\) | 44.1495 | 1.41247 | 0.706233 | − | 0.707979i | \(-0.250393\pi\) | ||||
0.706233 | + | 0.707979i | \(0.250393\pi\) | |||||||
\(978\) | 7.83285 | 0.250467 | ||||||||
\(979\) | −1.05924 | −0.0338535 | ||||||||
\(980\) | −47.4366 | −1.51531 | ||||||||
\(981\) | −16.4156 | −0.524109 | ||||||||
\(982\) | 31.6406 | 1.00969 | ||||||||
\(983\) | 37.1477 | 1.18483 | 0.592413 | − | 0.805634i | \(-0.298175\pi\) | ||||
0.592413 | + | 0.805634i | \(0.298175\pi\) | |||||||
\(984\) | 1.49587 | 0.0476866 | ||||||||
\(985\) | −74.7459 | −2.38160 | ||||||||
\(986\) | −2.78244 | −0.0886108 | ||||||||
\(987\) | −47.5088 | −1.51222 | ||||||||
\(988\) | −15.4953 | −0.492971 | ||||||||
\(989\) | 7.55202 | 0.240140 | ||||||||
\(990\) | −0.709201 | −0.0225399 | ||||||||
\(991\) | −44.9443 | −1.42770 | −0.713852 | − | 0.700297i | \(-0.753051\pi\) | ||||
−0.713852 | + | 0.700297i | \(0.753051\pi\) | |||||||
\(992\) | 8.94938 | 0.284143 | ||||||||
\(993\) | 17.9828 | 0.570668 | ||||||||
\(994\) | 50.0244 | 1.58668 | ||||||||
\(995\) | −25.8024 | −0.817992 | ||||||||
\(996\) | 13.5213 | 0.428440 | ||||||||
\(997\) | −31.0541 | −0.983492 | −0.491746 | − | 0.870739i | \(-0.663641\pi\) | ||||
−0.491746 | + | 0.870739i | \(0.663641\pi\) | |||||||
\(998\) | 23.7710 | 0.752458 | ||||||||
\(999\) | 9.05465 | 0.286476 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 6018.2.a.y.1.1 | ✓ | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6018.2.a.y.1.1 | ✓ | 10 | 1.1 | even | 1 | trivial |