Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6010,2,Mod(1,6010)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6010, 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("6010.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6010 = 2 \cdot 5 \cdot 601 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6010.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: | \(47.9900916148\) |
Analytic rank: | \(1\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 8 x^{15} + 9 x^{14} + 75 x^{13} - 178 x^{12} - 232 x^{11} + 872 x^{10} + 228 x^{9} - 1986 x^{8} + \cdots - 10 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Root | \(-0.981279\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 6010.1 |
$q$-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 | ||||||||
\(3\) | −1.98128 | −1.14389 | −0.571946 | − | 0.820291i | \(-0.693811\pi\) | ||||
−0.571946 | + | 0.820291i | \(0.693811\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | −1.98128 | −0.808854 | ||||||||
\(7\) | −4.22080 | −1.59531 | −0.797657 | − | 0.603111i | \(-0.793927\pi\) | ||||
−0.797657 | + | 0.603111i | \(0.793927\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 0.925466 | 0.308489 | ||||||||
\(10\) | 1.00000 | 0.316228 | ||||||||
\(11\) | 0.530338 | 0.159903 | 0.0799515 | − | 0.996799i | \(-0.474523\pi\) | ||||
0.0799515 | + | 0.996799i | \(0.474523\pi\) | |||||||
\(12\) | −1.98128 | −0.571946 | ||||||||
\(13\) | −0.100776 | −0.0279502 | −0.0139751 | − | 0.999902i | \(-0.504449\pi\) | ||||
−0.0139751 | + | 0.999902i | \(0.504449\pi\) | |||||||
\(14\) | −4.22080 | −1.12806 | ||||||||
\(15\) | −1.98128 | −0.511564 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −3.01879 | −0.732163 | −0.366082 | − | 0.930583i | \(-0.619301\pi\) | ||||
−0.366082 | + | 0.930583i | \(0.619301\pi\) | |||||||
\(18\) | 0.925466 | 0.218134 | ||||||||
\(19\) | −1.24304 | −0.285172 | −0.142586 | − | 0.989782i | \(-0.545542\pi\) | ||||
−0.142586 | + | 0.989782i | \(0.545542\pi\) | |||||||
\(20\) | 1.00000 | 0.223607 | ||||||||
\(21\) | 8.36259 | 1.82487 | ||||||||
\(22\) | 0.530338 | 0.113069 | ||||||||
\(23\) | 8.77835 | 1.83041 | 0.915206 | − | 0.402986i | \(-0.132028\pi\) | ||||
0.915206 | + | 0.402986i | \(0.132028\pi\) | |||||||
\(24\) | −1.98128 | −0.404427 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −0.100776 | −0.0197638 | ||||||||
\(27\) | 4.11023 | 0.791014 | ||||||||
\(28\) | −4.22080 | −0.797657 | ||||||||
\(29\) | 1.18004 | 0.219128 | 0.109564 | − | 0.993980i | \(-0.465054\pi\) | ||||
0.109564 | + | 0.993980i | \(0.465054\pi\) | |||||||
\(30\) | −1.98128 | −0.361730 | ||||||||
\(31\) | 3.73228 | 0.670337 | 0.335168 | − | 0.942158i | \(-0.391207\pi\) | ||||
0.335168 | + | 0.942158i | \(0.391207\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | −1.05075 | −0.182912 | ||||||||
\(34\) | −3.01879 | −0.517717 | ||||||||
\(35\) | −4.22080 | −0.713446 | ||||||||
\(36\) | 0.925466 | 0.154244 | ||||||||
\(37\) | 5.95866 | 0.979597 | 0.489798 | − | 0.871836i | \(-0.337070\pi\) | ||||
0.489798 | + | 0.871836i | \(0.337070\pi\) | |||||||
\(38\) | −1.24304 | −0.201647 | ||||||||
\(39\) | 0.199665 | 0.0319720 | ||||||||
\(40\) | 1.00000 | 0.158114 | ||||||||
\(41\) | −10.4027 | −1.62463 | −0.812317 | − | 0.583216i | \(-0.801794\pi\) | ||||
−0.812317 | + | 0.583216i | \(0.801794\pi\) | |||||||
\(42\) | 8.36259 | 1.29038 | ||||||||
\(43\) | 9.82863 | 1.49885 | 0.749426 | − | 0.662088i | \(-0.230329\pi\) | ||||
0.749426 | + | 0.662088i | \(0.230329\pi\) | |||||||
\(44\) | 0.530338 | 0.0799515 | ||||||||
\(45\) | 0.925466 | 0.137960 | ||||||||
\(46\) | 8.77835 | 1.29430 | ||||||||
\(47\) | −2.60238 | −0.379596 | −0.189798 | − | 0.981823i | \(-0.560783\pi\) | ||||
−0.189798 | + | 0.981823i | \(0.560783\pi\) | |||||||
\(48\) | −1.98128 | −0.285973 | ||||||||
\(49\) | 10.8152 | 1.54503 | ||||||||
\(50\) | 1.00000 | 0.141421 | ||||||||
\(51\) | 5.98106 | 0.837515 | ||||||||
\(52\) | −0.100776 | −0.0139751 | ||||||||
\(53\) | 6.07027 | 0.833815 | 0.416908 | − | 0.908949i | \(-0.363114\pi\) | ||||
0.416908 | + | 0.908949i | \(0.363114\pi\) | |||||||
\(54\) | 4.11023 | 0.559332 | ||||||||
\(55\) | 0.530338 | 0.0715108 | ||||||||
\(56\) | −4.22080 | −0.564029 | ||||||||
\(57\) | 2.46280 | 0.326206 | ||||||||
\(58\) | 1.18004 | 0.154947 | ||||||||
\(59\) | −11.8884 | −1.54773 | −0.773866 | − | 0.633349i | \(-0.781680\pi\) | ||||
−0.773866 | + | 0.633349i | \(0.781680\pi\) | |||||||
\(60\) | −1.98128 | −0.255782 | ||||||||
\(61\) | −9.97802 | −1.27755 | −0.638777 | − | 0.769392i | \(-0.720559\pi\) | ||||
−0.638777 | + | 0.769392i | \(0.720559\pi\) | |||||||
\(62\) | 3.73228 | 0.474000 | ||||||||
\(63\) | −3.90621 | −0.492136 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −0.100776 | −0.0124997 | ||||||||
\(66\) | −1.05075 | −0.129338 | ||||||||
\(67\) | −7.26948 | −0.888109 | −0.444054 | − | 0.896000i | \(-0.646460\pi\) | ||||
−0.444054 | + | 0.896000i | \(0.646460\pi\) | |||||||
\(68\) | −3.01879 | −0.366082 | ||||||||
\(69\) | −17.3924 | −2.09379 | ||||||||
\(70\) | −4.22080 | −0.504483 | ||||||||
\(71\) | 15.6832 | 1.86125 | 0.930624 | − | 0.365976i | \(-0.119265\pi\) | ||||
0.930624 | + | 0.365976i | \(0.119265\pi\) | |||||||
\(72\) | 0.925466 | 0.109067 | ||||||||
\(73\) | −15.2789 | −1.78826 | −0.894128 | − | 0.447812i | \(-0.852203\pi\) | ||||
−0.894128 | + | 0.447812i | \(0.852203\pi\) | |||||||
\(74\) | 5.95866 | 0.692680 | ||||||||
\(75\) | −1.98128 | −0.228778 | ||||||||
\(76\) | −1.24304 | −0.142586 | ||||||||
\(77\) | −2.23845 | −0.255096 | ||||||||
\(78\) | 0.199665 | 0.0226076 | ||||||||
\(79\) | −8.86443 | −0.997326 | −0.498663 | − | 0.866796i | \(-0.666175\pi\) | ||||
−0.498663 | + | 0.866796i | \(0.666175\pi\) | |||||||
\(80\) | 1.00000 | 0.111803 | ||||||||
\(81\) | −10.9199 | −1.21332 | ||||||||
\(82\) | −10.4027 | −1.14879 | ||||||||
\(83\) | −10.8435 | −1.19022 | −0.595112 | − | 0.803643i | \(-0.702892\pi\) | ||||
−0.595112 | + | 0.803643i | \(0.702892\pi\) | |||||||
\(84\) | 8.36259 | 0.912433 | ||||||||
\(85\) | −3.01879 | −0.327433 | ||||||||
\(86\) | 9.82863 | 1.05985 | ||||||||
\(87\) | −2.33799 | −0.250659 | ||||||||
\(88\) | 0.530338 | 0.0565343 | ||||||||
\(89\) | −12.3021 | −1.30402 | −0.652012 | − | 0.758209i | \(-0.726075\pi\) | ||||
−0.652012 | + | 0.758209i | \(0.726075\pi\) | |||||||
\(90\) | 0.925466 | 0.0975527 | ||||||||
\(91\) | 0.425356 | 0.0445894 | ||||||||
\(92\) | 8.77835 | 0.915206 | ||||||||
\(93\) | −7.39468 | −0.766793 | ||||||||
\(94\) | −2.60238 | −0.268415 | ||||||||
\(95\) | −1.24304 | −0.127533 | ||||||||
\(96\) | −1.98128 | −0.202213 | ||||||||
\(97\) | 9.19718 | 0.933832 | 0.466916 | − | 0.884302i | \(-0.345365\pi\) | ||||
0.466916 | + | 0.884302i | \(0.345365\pi\) | |||||||
\(98\) | 10.8152 | 1.09250 | ||||||||
\(99\) | 0.490810 | 0.0493283 | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | −0.696428 | −0.0692972 | −0.0346486 | − | 0.999400i | \(-0.511031\pi\) | ||||
−0.0346486 | + | 0.999400i | \(0.511031\pi\) | |||||||
\(102\) | 5.98106 | 0.592213 | ||||||||
\(103\) | −0.109262 | −0.0107659 | −0.00538294 | − | 0.999986i | \(-0.501713\pi\) | ||||
−0.00538294 | + | 0.999986i | \(0.501713\pi\) | |||||||
\(104\) | −0.100776 | −0.00988190 | ||||||||
\(105\) | 8.36259 | 0.816105 | ||||||||
\(106\) | 6.07027 | 0.589596 | ||||||||
\(107\) | −11.7250 | −1.13350 | −0.566749 | − | 0.823890i | \(-0.691799\pi\) | ||||
−0.566749 | + | 0.823890i | \(0.691799\pi\) | |||||||
\(108\) | 4.11023 | 0.395507 | ||||||||
\(109\) | −7.56174 | −0.724283 | −0.362141 | − | 0.932123i | \(-0.617954\pi\) | ||||
−0.362141 | + | 0.932123i | \(0.617954\pi\) | |||||||
\(110\) | 0.530338 | 0.0505658 | ||||||||
\(111\) | −11.8058 | −1.12055 | ||||||||
\(112\) | −4.22080 | −0.398828 | ||||||||
\(113\) | −9.90909 | −0.932169 | −0.466084 | − | 0.884740i | \(-0.654336\pi\) | ||||
−0.466084 | + | 0.884740i | \(0.654336\pi\) | |||||||
\(114\) | 2.46280 | 0.230662 | ||||||||
\(115\) | 8.77835 | 0.818585 | ||||||||
\(116\) | 1.18004 | 0.109564 | ||||||||
\(117\) | −0.0932647 | −0.00862233 | ||||||||
\(118\) | −11.8884 | −1.09441 | ||||||||
\(119\) | 12.7417 | 1.16803 | ||||||||
\(120\) | −1.98128 | −0.180865 | ||||||||
\(121\) | −10.7187 | −0.974431 | ||||||||
\(122\) | −9.97802 | −0.903367 | ||||||||
\(123\) | 20.6107 | 1.85841 | ||||||||
\(124\) | 3.73228 | 0.335168 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | −3.90621 | −0.347993 | ||||||||
\(127\) | 10.1010 | 0.896323 | 0.448162 | − | 0.893953i | \(-0.352079\pi\) | ||||
0.448162 | + | 0.893953i | \(0.352079\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | −19.4733 | −1.71453 | ||||||||
\(130\) | −0.100776 | −0.00883864 | ||||||||
\(131\) | 15.1653 | 1.32499 | 0.662497 | − | 0.749064i | \(-0.269497\pi\) | ||||
0.662497 | + | 0.749064i | \(0.269497\pi\) | |||||||
\(132\) | −1.05075 | −0.0914559 | ||||||||
\(133\) | 5.24661 | 0.454939 | ||||||||
\(134\) | −7.26948 | −0.627988 | ||||||||
\(135\) | 4.11023 | 0.353752 | ||||||||
\(136\) | −3.01879 | −0.258859 | ||||||||
\(137\) | 6.86463 | 0.586485 | 0.293242 | − | 0.956038i | \(-0.405266\pi\) | ||||
0.293242 | + | 0.956038i | \(0.405266\pi\) | |||||||
\(138\) | −17.3924 | −1.48054 | ||||||||
\(139\) | −5.33765 | −0.452734 | −0.226367 | − | 0.974042i | \(-0.572685\pi\) | ||||
−0.226367 | + | 0.974042i | \(0.572685\pi\) | |||||||
\(140\) | −4.22080 | −0.356723 | ||||||||
\(141\) | 5.15604 | 0.434217 | ||||||||
\(142\) | 15.6832 | 1.31610 | ||||||||
\(143\) | −0.0534454 | −0.00446933 | ||||||||
\(144\) | 0.925466 | 0.0771222 | ||||||||
\(145\) | 1.18004 | 0.0979972 | ||||||||
\(146\) | −15.2789 | −1.26449 | ||||||||
\(147\) | −21.4279 | −1.76734 | ||||||||
\(148\) | 5.95866 | 0.489798 | ||||||||
\(149\) | 2.94235 | 0.241046 | 0.120523 | − | 0.992711i | \(-0.461543\pi\) | ||||
0.120523 | + | 0.992711i | \(0.461543\pi\) | |||||||
\(150\) | −1.98128 | −0.161771 | ||||||||
\(151\) | 10.3478 | 0.842094 | 0.421047 | − | 0.907039i | \(-0.361663\pi\) | ||||
0.421047 | + | 0.907039i | \(0.361663\pi\) | |||||||
\(152\) | −1.24304 | −0.100823 | ||||||||
\(153\) | −2.79378 | −0.225864 | ||||||||
\(154\) | −2.23845 | −0.180380 | ||||||||
\(155\) | 3.73228 | 0.299784 | ||||||||
\(156\) | 0.199665 | 0.0159860 | ||||||||
\(157\) | 10.7164 | 0.855264 | 0.427632 | − | 0.903953i | \(-0.359348\pi\) | ||||
0.427632 | + | 0.903953i | \(0.359348\pi\) | |||||||
\(158\) | −8.86443 | −0.705216 | ||||||||
\(159\) | −12.0269 | −0.953795 | ||||||||
\(160\) | 1.00000 | 0.0790569 | ||||||||
\(161\) | −37.0517 | −2.92008 | ||||||||
\(162\) | −10.9199 | −0.857949 | ||||||||
\(163\) | −0.373966 | −0.0292913 | −0.0146457 | − | 0.999893i | \(-0.504662\pi\) | ||||
−0.0146457 | + | 0.999893i | \(0.504662\pi\) | |||||||
\(164\) | −10.4027 | −0.812317 | ||||||||
\(165\) | −1.05075 | −0.0818006 | ||||||||
\(166\) | −10.8435 | −0.841615 | ||||||||
\(167\) | −5.64002 | −0.436438 | −0.218219 | − | 0.975900i | \(-0.570025\pi\) | ||||
−0.218219 | + | 0.975900i | \(0.570025\pi\) | |||||||
\(168\) | 8.36259 | 0.645188 | ||||||||
\(169\) | −12.9898 | −0.999219 | ||||||||
\(170\) | −3.01879 | −0.231530 | ||||||||
\(171\) | −1.15039 | −0.0879723 | ||||||||
\(172\) | 9.82863 | 0.749426 | ||||||||
\(173\) | −7.93500 | −0.603287 | −0.301643 | − | 0.953421i | \(-0.597535\pi\) | ||||
−0.301643 | + | 0.953421i | \(0.597535\pi\) | |||||||
\(174\) | −2.33799 | −0.177243 | ||||||||
\(175\) | −4.22080 | −0.319063 | ||||||||
\(176\) | 0.530338 | 0.0399758 | ||||||||
\(177\) | 23.5542 | 1.77044 | ||||||||
\(178\) | −12.3021 | −0.922084 | ||||||||
\(179\) | −20.4271 | −1.52679 | −0.763395 | − | 0.645932i | \(-0.776469\pi\) | ||||
−0.763395 | + | 0.645932i | \(0.776469\pi\) | |||||||
\(180\) | 0.925466 | 0.0689802 | ||||||||
\(181\) | −16.1239 | −1.19848 | −0.599238 | − | 0.800571i | \(-0.704530\pi\) | ||||
−0.599238 | + | 0.800571i | \(0.704530\pi\) | |||||||
\(182\) | 0.425356 | 0.0315295 | ||||||||
\(183\) | 19.7692 | 1.46138 | ||||||||
\(184\) | 8.77835 | 0.647148 | ||||||||
\(185\) | 5.95866 | 0.438089 | ||||||||
\(186\) | −7.39468 | −0.542204 | ||||||||
\(187\) | −1.60098 | −0.117075 | ||||||||
\(188\) | −2.60238 | −0.189798 | ||||||||
\(189\) | −17.3485 | −1.26192 | ||||||||
\(190\) | −1.24304 | −0.0901792 | ||||||||
\(191\) | −9.40217 | −0.680317 | −0.340158 | − | 0.940368i | \(-0.610481\pi\) | ||||
−0.340158 | + | 0.940368i | \(0.610481\pi\) | |||||||
\(192\) | −1.98128 | −0.142986 | ||||||||
\(193\) | 10.0203 | 0.721276 | 0.360638 | − | 0.932706i | \(-0.382559\pi\) | ||||
0.360638 | + | 0.932706i | \(0.382559\pi\) | |||||||
\(194\) | 9.19718 | 0.660319 | ||||||||
\(195\) | 0.199665 | 0.0142983 | ||||||||
\(196\) | 10.8152 | 0.772513 | ||||||||
\(197\) | −3.88607 | −0.276871 | −0.138436 | − | 0.990371i | \(-0.544207\pi\) | ||||
−0.138436 | + | 0.990371i | \(0.544207\pi\) | |||||||
\(198\) | 0.490810 | 0.0348804 | ||||||||
\(199\) | −12.8979 | −0.914310 | −0.457155 | − | 0.889387i | \(-0.651132\pi\) | ||||
−0.457155 | + | 0.889387i | \(0.651132\pi\) | |||||||
\(200\) | 1.00000 | 0.0707107 | ||||||||
\(201\) | 14.4029 | 1.01590 | ||||||||
\(202\) | −0.696428 | −0.0490005 | ||||||||
\(203\) | −4.98073 | −0.349579 | ||||||||
\(204\) | 5.98106 | 0.418758 | ||||||||
\(205\) | −10.4027 | −0.726559 | ||||||||
\(206\) | −0.109262 | −0.00761262 | ||||||||
\(207\) | 8.12406 | 0.564661 | ||||||||
\(208\) | −0.100776 | −0.00698756 | ||||||||
\(209\) | −0.659229 | −0.0455998 | ||||||||
\(210\) | 8.36259 | 0.577073 | ||||||||
\(211\) | −18.4433 | −1.26969 | −0.634843 | − | 0.772641i | \(-0.718935\pi\) | ||||
−0.634843 | + | 0.772641i | \(0.718935\pi\) | |||||||
\(212\) | 6.07027 | 0.416908 | ||||||||
\(213\) | −31.0727 | −2.12907 | ||||||||
\(214\) | −11.7250 | −0.801504 | ||||||||
\(215\) | 9.82863 | 0.670307 | ||||||||
\(216\) | 4.11023 | 0.279666 | ||||||||
\(217\) | −15.7532 | −1.06940 | ||||||||
\(218\) | −7.56174 | −0.512145 | ||||||||
\(219\) | 30.2717 | 2.04557 | ||||||||
\(220\) | 0.530338 | 0.0357554 | ||||||||
\(221\) | 0.304221 | 0.0204641 | ||||||||
\(222\) | −11.8058 | −0.792351 | ||||||||
\(223\) | 22.0052 | 1.47358 | 0.736789 | − | 0.676122i | \(-0.236341\pi\) | ||||
0.736789 | + | 0.676122i | \(0.236341\pi\) | |||||||
\(224\) | −4.22080 | −0.282014 | ||||||||
\(225\) | 0.925466 | 0.0616977 | ||||||||
\(226\) | −9.90909 | −0.659143 | ||||||||
\(227\) | −14.6503 | −0.972376 | −0.486188 | − | 0.873854i | \(-0.661613\pi\) | ||||
−0.486188 | + | 0.873854i | \(0.661613\pi\) | |||||||
\(228\) | 2.46280 | 0.163103 | ||||||||
\(229\) | −17.3362 | −1.14561 | −0.572805 | − | 0.819692i | \(-0.694145\pi\) | ||||
−0.572805 | + | 0.819692i | \(0.694145\pi\) | |||||||
\(230\) | 8.77835 | 0.578827 | ||||||||
\(231\) | 4.43500 | 0.291802 | ||||||||
\(232\) | 1.18004 | 0.0774736 | ||||||||
\(233\) | 12.0048 | 0.786459 | 0.393230 | − | 0.919440i | \(-0.371358\pi\) | ||||
0.393230 | + | 0.919440i | \(0.371358\pi\) | |||||||
\(234\) | −0.0932647 | −0.00609691 | ||||||||
\(235\) | −2.60238 | −0.169761 | ||||||||
\(236\) | −11.8884 | −0.773866 | ||||||||
\(237\) | 17.5629 | 1.14083 | ||||||||
\(238\) | 12.7417 | 0.825922 | ||||||||
\(239\) | 27.5016 | 1.77893 | 0.889467 | − | 0.457000i | \(-0.151076\pi\) | ||||
0.889467 | + | 0.457000i | \(0.151076\pi\) | |||||||
\(240\) | −1.98128 | −0.127891 | ||||||||
\(241\) | −13.2419 | −0.852983 | −0.426491 | − | 0.904492i | \(-0.640251\pi\) | ||||
−0.426491 | + | 0.904492i | \(0.640251\pi\) | |||||||
\(242\) | −10.7187 | −0.689027 | ||||||||
\(243\) | 9.30470 | 0.596897 | ||||||||
\(244\) | −9.97802 | −0.638777 | ||||||||
\(245\) | 10.8152 | 0.690957 | ||||||||
\(246\) | 20.6107 | 1.31409 | ||||||||
\(247\) | 0.125268 | 0.00797062 | ||||||||
\(248\) | 3.73228 | 0.237000 | ||||||||
\(249\) | 21.4839 | 1.36149 | ||||||||
\(250\) | 1.00000 | 0.0632456 | ||||||||
\(251\) | −3.04529 | −0.192217 | −0.0961084 | − | 0.995371i | \(-0.530640\pi\) | ||||
−0.0961084 | + | 0.995371i | \(0.530640\pi\) | |||||||
\(252\) | −3.90621 | −0.246068 | ||||||||
\(253\) | 4.65549 | 0.292688 | ||||||||
\(254\) | 10.1010 | 0.633796 | ||||||||
\(255\) | 5.98106 | 0.374548 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −17.9678 | −1.12080 | −0.560401 | − | 0.828222i | \(-0.689353\pi\) | ||||
−0.560401 | + | 0.828222i | \(0.689353\pi\) | |||||||
\(258\) | −19.4733 | −1.21235 | ||||||||
\(259\) | −25.1503 | −1.56276 | ||||||||
\(260\) | −0.100776 | −0.00624986 | ||||||||
\(261\) | 1.09209 | 0.0675986 | ||||||||
\(262\) | 15.1653 | 0.936913 | ||||||||
\(263\) | 0.207779 | 0.0128122 | 0.00640610 | − | 0.999979i | \(-0.497961\pi\) | ||||
0.00640610 | + | 0.999979i | \(0.497961\pi\) | |||||||
\(264\) | −1.05075 | −0.0646691 | ||||||||
\(265\) | 6.07027 | 0.372894 | ||||||||
\(266\) | 5.24661 | 0.321690 | ||||||||
\(267\) | 24.3740 | 1.49166 | ||||||||
\(268\) | −7.26948 | −0.444054 | ||||||||
\(269\) | 32.4104 | 1.97610 | 0.988048 | − | 0.154148i | \(-0.0492633\pi\) | ||||
0.988048 | + | 0.154148i | \(0.0492633\pi\) | |||||||
\(270\) | 4.11023 | 0.250141 | ||||||||
\(271\) | 2.36018 | 0.143371 | 0.0716853 | − | 0.997427i | \(-0.477162\pi\) | ||||
0.0716853 | + | 0.997427i | \(0.477162\pi\) | |||||||
\(272\) | −3.01879 | −0.183041 | ||||||||
\(273\) | −0.842748 | −0.0510054 | ||||||||
\(274\) | 6.86463 | 0.414707 | ||||||||
\(275\) | 0.530338 | 0.0319806 | ||||||||
\(276\) | −17.3924 | −1.04690 | ||||||||
\(277\) | −7.91946 | −0.475834 | −0.237917 | − | 0.971285i | \(-0.576465\pi\) | ||||
−0.237917 | + | 0.971285i | \(0.576465\pi\) | |||||||
\(278\) | −5.33765 | −0.320131 | ||||||||
\(279\) | 3.45409 | 0.206791 | ||||||||
\(280\) | −4.22080 | −0.252241 | ||||||||
\(281\) | 15.4693 | 0.922820 | 0.461410 | − | 0.887187i | \(-0.347344\pi\) | ||||
0.461410 | + | 0.887187i | \(0.347344\pi\) | |||||||
\(282\) | 5.15604 | 0.307038 | ||||||||
\(283\) | 30.3044 | 1.80141 | 0.900706 | − | 0.434429i | \(-0.143050\pi\) | ||||
0.900706 | + | 0.434429i | \(0.143050\pi\) | |||||||
\(284\) | 15.6832 | 0.930624 | ||||||||
\(285\) | 2.46280 | 0.145884 | ||||||||
\(286\) | −0.0534454 | −0.00316029 | ||||||||
\(287\) | 43.9079 | 2.59180 | ||||||||
\(288\) | 0.925466 | 0.0545336 | ||||||||
\(289\) | −7.88693 | −0.463937 | ||||||||
\(290\) | 1.18004 | 0.0692945 | ||||||||
\(291\) | −18.2222 | −1.06820 | ||||||||
\(292\) | −15.2789 | −0.894128 | ||||||||
\(293\) | 11.2466 | 0.657034 | 0.328517 | − | 0.944498i | \(-0.393451\pi\) | ||||
0.328517 | + | 0.944498i | \(0.393451\pi\) | |||||||
\(294\) | −21.4279 | −1.24970 | ||||||||
\(295\) | −11.8884 | −0.692167 | ||||||||
\(296\) | 5.95866 | 0.346340 | ||||||||
\(297\) | 2.17981 | 0.126486 | ||||||||
\(298\) | 2.94235 | 0.170446 | ||||||||
\(299\) | −0.884647 | −0.0511604 | ||||||||
\(300\) | −1.98128 | −0.114389 | ||||||||
\(301\) | −41.4847 | −2.39114 | ||||||||
\(302\) | 10.3478 | 0.595451 | ||||||||
\(303\) | 1.37982 | 0.0792685 | ||||||||
\(304\) | −1.24304 | −0.0712929 | ||||||||
\(305\) | −9.97802 | −0.571340 | ||||||||
\(306\) | −2.79378 | −0.159710 | ||||||||
\(307\) | −13.5263 | −0.771986 | −0.385993 | − | 0.922502i | \(-0.626141\pi\) | ||||
−0.385993 | + | 0.922502i | \(0.626141\pi\) | |||||||
\(308\) | −2.23845 | −0.127548 | ||||||||
\(309\) | 0.216478 | 0.0123150 | ||||||||
\(310\) | 3.73228 | 0.211979 | ||||||||
\(311\) | −19.4234 | −1.10140 | −0.550699 | − | 0.834704i | \(-0.685639\pi\) | ||||
−0.550699 | + | 0.834704i | \(0.685639\pi\) | |||||||
\(312\) | 0.199665 | 0.0113038 | ||||||||
\(313\) | −24.8018 | −1.40188 | −0.700942 | − | 0.713219i | \(-0.747237\pi\) | ||||
−0.700942 | + | 0.713219i | \(0.747237\pi\) | |||||||
\(314\) | 10.7164 | 0.604763 | ||||||||
\(315\) | −3.90621 | −0.220090 | ||||||||
\(316\) | −8.86443 | −0.498663 | ||||||||
\(317\) | −18.3022 | −1.02795 | −0.513977 | − | 0.857804i | \(-0.671828\pi\) | ||||
−0.513977 | + | 0.857804i | \(0.671828\pi\) | |||||||
\(318\) | −12.0269 | −0.674435 | ||||||||
\(319\) | 0.625822 | 0.0350393 | ||||||||
\(320\) | 1.00000 | 0.0559017 | ||||||||
\(321\) | 23.2305 | 1.29660 | ||||||||
\(322\) | −37.0517 | −2.06481 | ||||||||
\(323\) | 3.75246 | 0.208792 | ||||||||
\(324\) | −10.9199 | −0.606662 | ||||||||
\(325\) | −0.100776 | −0.00559005 | ||||||||
\(326\) | −0.373966 | −0.0207121 | ||||||||
\(327\) | 14.9819 | 0.828501 | ||||||||
\(328\) | −10.4027 | −0.574395 | ||||||||
\(329\) | 10.9841 | 0.605575 | ||||||||
\(330\) | −1.05075 | −0.0578418 | ||||||||
\(331\) | −8.11182 | −0.445866 | −0.222933 | − | 0.974834i | \(-0.571563\pi\) | ||||
−0.222933 | + | 0.974834i | \(0.571563\pi\) | |||||||
\(332\) | −10.8435 | −0.595112 | ||||||||
\(333\) | 5.51453 | 0.302195 | ||||||||
\(334\) | −5.64002 | −0.308608 | ||||||||
\(335\) | −7.26948 | −0.397174 | ||||||||
\(336\) | 8.36259 | 0.456217 | ||||||||
\(337\) | −5.34930 | −0.291395 | −0.145697 | − | 0.989329i | \(-0.546543\pi\) | ||||
−0.145697 | + | 0.989329i | \(0.546543\pi\) | |||||||
\(338\) | −12.9898 | −0.706554 | ||||||||
\(339\) | 19.6327 | 1.06630 | ||||||||
\(340\) | −3.01879 | −0.163717 | ||||||||
\(341\) | 1.97937 | 0.107189 | ||||||||
\(342\) | −1.15039 | −0.0622058 | ||||||||
\(343\) | −16.1031 | −0.869488 | ||||||||
\(344\) | 9.82863 | 0.529924 | ||||||||
\(345\) | −17.3924 | −0.936373 | ||||||||
\(346\) | −7.93500 | −0.426588 | ||||||||
\(347\) | −5.05294 | −0.271256 | −0.135628 | − | 0.990760i | \(-0.543305\pi\) | ||||
−0.135628 | + | 0.990760i | \(0.543305\pi\) | |||||||
\(348\) | −2.33799 | −0.125330 | ||||||||
\(349\) | −21.1201 | −1.13053 | −0.565267 | − | 0.824908i | \(-0.691227\pi\) | ||||
−0.565267 | + | 0.824908i | \(0.691227\pi\) | |||||||
\(350\) | −4.22080 | −0.225611 | ||||||||
\(351\) | −0.414213 | −0.0221090 | ||||||||
\(352\) | 0.530338 | 0.0282671 | ||||||||
\(353\) | 18.4134 | 0.980044 | 0.490022 | − | 0.871710i | \(-0.336989\pi\) | ||||
0.490022 | + | 0.871710i | \(0.336989\pi\) | |||||||
\(354\) | 23.5542 | 1.25189 | ||||||||
\(355\) | 15.6832 | 0.832376 | ||||||||
\(356\) | −12.3021 | −0.652012 | ||||||||
\(357\) | −25.2449 | −1.33610 | ||||||||
\(358\) | −20.4271 | −1.07960 | ||||||||
\(359\) | −2.92099 | −0.154164 | −0.0770819 | − | 0.997025i | \(-0.524560\pi\) | ||||
−0.0770819 | + | 0.997025i | \(0.524560\pi\) | |||||||
\(360\) | 0.925466 | 0.0487763 | ||||||||
\(361\) | −17.4549 | −0.918677 | ||||||||
\(362\) | −16.1239 | −0.847451 | ||||||||
\(363\) | 21.2368 | 1.11464 | ||||||||
\(364\) | 0.425356 | 0.0222947 | ||||||||
\(365\) | −15.2789 | −0.799732 | ||||||||
\(366\) | 19.7692 | 1.03335 | ||||||||
\(367\) | 13.5315 | 0.706339 | 0.353169 | − | 0.935559i | \(-0.385104\pi\) | ||||
0.353169 | + | 0.935559i | \(0.385104\pi\) | |||||||
\(368\) | 8.77835 | 0.457603 | ||||||||
\(369\) | −9.62738 | −0.501181 | ||||||||
\(370\) | 5.95866 | 0.309776 | ||||||||
\(371\) | −25.6214 | −1.33020 | ||||||||
\(372\) | −7.39468 | −0.383396 | ||||||||
\(373\) | 11.7727 | 0.609569 | 0.304785 | − | 0.952421i | \(-0.401416\pi\) | ||||
0.304785 | + | 0.952421i | \(0.401416\pi\) | |||||||
\(374\) | −1.60098 | −0.0827846 | ||||||||
\(375\) | −1.98128 | −0.102313 | ||||||||
\(376\) | −2.60238 | −0.134207 | ||||||||
\(377\) | −0.118920 | −0.00612469 | ||||||||
\(378\) | −17.3485 | −0.892309 | ||||||||
\(379\) | 16.1520 | 0.829674 | 0.414837 | − | 0.909896i | \(-0.363839\pi\) | ||||
0.414837 | + | 0.909896i | \(0.363839\pi\) | |||||||
\(380\) | −1.24304 | −0.0637664 | ||||||||
\(381\) | −20.0130 | −1.02530 | ||||||||
\(382\) | −9.40217 | −0.481057 | ||||||||
\(383\) | 5.99445 | 0.306302 | 0.153151 | − | 0.988203i | \(-0.451058\pi\) | ||||
0.153151 | + | 0.988203i | \(0.451058\pi\) | |||||||
\(384\) | −1.98128 | −0.101107 | ||||||||
\(385\) | −2.23845 | −0.114082 | ||||||||
\(386\) | 10.0203 | 0.510019 | ||||||||
\(387\) | 9.09606 | 0.462379 | ||||||||
\(388\) | 9.19718 | 0.466916 | ||||||||
\(389\) | 7.07504 | 0.358719 | 0.179360 | − | 0.983784i | \(-0.442597\pi\) | ||||
0.179360 | + | 0.983784i | \(0.442597\pi\) | |||||||
\(390\) | 0.199665 | 0.0101104 | ||||||||
\(391\) | −26.4999 | −1.34016 | ||||||||
\(392\) | 10.8152 | 0.546249 | ||||||||
\(393\) | −30.0466 | −1.51565 | ||||||||
\(394\) | −3.88607 | −0.195778 | ||||||||
\(395\) | −8.86443 | −0.446018 | ||||||||
\(396\) | 0.490810 | 0.0246641 | ||||||||
\(397\) | 1.12705 | 0.0565649 | 0.0282824 | − | 0.999600i | \(-0.490996\pi\) | ||||
0.0282824 | + | 0.999600i | \(0.490996\pi\) | |||||||
\(398\) | −12.8979 | −0.646515 | ||||||||
\(399\) | −10.3950 | −0.520400 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | −18.1263 | −0.905184 | −0.452592 | − | 0.891718i | \(-0.649501\pi\) | ||||
−0.452592 | + | 0.891718i | \(0.649501\pi\) | |||||||
\(402\) | 14.4029 | 0.718350 | ||||||||
\(403\) | −0.376124 | −0.0187361 | ||||||||
\(404\) | −0.696428 | −0.0346486 | ||||||||
\(405\) | −10.9199 | −0.542615 | ||||||||
\(406\) | −4.98073 | −0.247189 | ||||||||
\(407\) | 3.16010 | 0.156641 | ||||||||
\(408\) | 5.98106 | 0.296106 | ||||||||
\(409\) | −8.94909 | −0.442504 | −0.221252 | − | 0.975217i | \(-0.571014\pi\) | ||||
−0.221252 | + | 0.975217i | \(0.571014\pi\) | |||||||
\(410\) | −10.4027 | −0.513755 | ||||||||
\(411\) | −13.6007 | −0.670875 | ||||||||
\(412\) | −0.109262 | −0.00538294 | ||||||||
\(413\) | 50.1784 | 2.46912 | ||||||||
\(414\) | 8.12406 | 0.399276 | ||||||||
\(415\) | −10.8435 | −0.532284 | ||||||||
\(416\) | −0.100776 | −0.00494095 | ||||||||
\(417\) | 10.5754 | 0.517878 | ||||||||
\(418\) | −0.659229 | −0.0322440 | ||||||||
\(419\) | 18.7687 | 0.916911 | 0.458456 | − | 0.888717i | \(-0.348403\pi\) | ||||
0.458456 | + | 0.888717i | \(0.348403\pi\) | |||||||
\(420\) | 8.36259 | 0.408053 | ||||||||
\(421\) | −15.5120 | −0.756010 | −0.378005 | − | 0.925803i | \(-0.623390\pi\) | ||||
−0.378005 | + | 0.925803i | \(0.623390\pi\) | |||||||
\(422\) | −18.4433 | −0.897804 | ||||||||
\(423\) | −2.40841 | −0.117101 | ||||||||
\(424\) | 6.07027 | 0.294798 | ||||||||
\(425\) | −3.01879 | −0.146433 | ||||||||
\(426\) | −31.0727 | −1.50548 | ||||||||
\(427\) | 42.1153 | 2.03810 | ||||||||
\(428\) | −11.7250 | −0.566749 | ||||||||
\(429\) | 0.105890 | 0.00511243 | ||||||||
\(430\) | 9.82863 | 0.473979 | ||||||||
\(431\) | 6.46497 | 0.311407 | 0.155703 | − | 0.987804i | \(-0.450236\pi\) | ||||
0.155703 | + | 0.987804i | \(0.450236\pi\) | |||||||
\(432\) | 4.11023 | 0.197754 | ||||||||
\(433\) | −20.4238 | −0.981507 | −0.490754 | − | 0.871298i | \(-0.663278\pi\) | ||||
−0.490754 | + | 0.871298i | \(0.663278\pi\) | |||||||
\(434\) | −15.7532 | −0.756178 | ||||||||
\(435\) | −2.33799 | −0.112098 | ||||||||
\(436\) | −7.56174 | −0.362141 | ||||||||
\(437\) | −10.9118 | −0.521982 | ||||||||
\(438\) | 30.2717 | 1.44644 | ||||||||
\(439\) | 18.6018 | 0.887816 | 0.443908 | − | 0.896072i | \(-0.353592\pi\) | ||||
0.443908 | + | 0.896072i | \(0.353592\pi\) | |||||||
\(440\) | 0.530338 | 0.0252829 | ||||||||
\(441\) | 10.0091 | 0.476623 | ||||||||
\(442\) | 0.304221 | 0.0144703 | ||||||||
\(443\) | 12.2738 | 0.583147 | 0.291573 | − | 0.956548i | \(-0.405821\pi\) | ||||
0.291573 | + | 0.956548i | \(0.405821\pi\) | |||||||
\(444\) | −11.8058 | −0.560276 | ||||||||
\(445\) | −12.3021 | −0.583177 | ||||||||
\(446\) | 22.0052 | 1.04198 | ||||||||
\(447\) | −5.82961 | −0.275731 | ||||||||
\(448\) | −4.22080 | −0.199414 | ||||||||
\(449\) | −27.2626 | −1.28660 | −0.643301 | − | 0.765613i | \(-0.722436\pi\) | ||||
−0.643301 | + | 0.765613i | \(0.722436\pi\) | |||||||
\(450\) | 0.925466 | 0.0436269 | ||||||||
\(451\) | −5.51697 | −0.259784 | ||||||||
\(452\) | −9.90909 | −0.466084 | ||||||||
\(453\) | −20.5019 | −0.963265 | ||||||||
\(454\) | −14.6503 | −0.687573 | ||||||||
\(455\) | 0.425356 | 0.0199410 | ||||||||
\(456\) | 2.46280 | 0.115331 | ||||||||
\(457\) | −19.2314 | −0.899606 | −0.449803 | − | 0.893128i | \(-0.648506\pi\) | ||||
−0.449803 | + | 0.893128i | \(0.648506\pi\) | |||||||
\(458\) | −17.3362 | −0.810069 | ||||||||
\(459\) | −12.4079 | −0.579151 | ||||||||
\(460\) | 8.77835 | 0.409293 | ||||||||
\(461\) | 11.5699 | 0.538862 | 0.269431 | − | 0.963020i | \(-0.413164\pi\) | ||||
0.269431 | + | 0.963020i | \(0.413164\pi\) | |||||||
\(462\) | 4.43500 | 0.206335 | ||||||||
\(463\) | −0.00174954 | −8.13082e−5 0 | −4.06541e−5 | − | 1.00000i | \(-0.500013\pi\) | ||||
−4.06541e−5 | 1.00000i | \(0.500013\pi\) | ||||||||
\(464\) | 1.18004 | 0.0547821 | ||||||||
\(465\) | −7.39468 | −0.342920 | ||||||||
\(466\) | 12.0048 | 0.556111 | ||||||||
\(467\) | −32.4183 | −1.50014 | −0.750070 | − | 0.661358i | \(-0.769980\pi\) | ||||
−0.750070 | + | 0.661358i | \(0.769980\pi\) | |||||||
\(468\) | −0.0932647 | −0.00431116 | ||||||||
\(469\) | 30.6831 | 1.41681 | ||||||||
\(470\) | −2.60238 | −0.120039 | ||||||||
\(471\) | −21.2322 | −0.978329 | ||||||||
\(472\) | −11.8884 | −0.547206 | ||||||||
\(473\) | 5.21250 | 0.239671 | ||||||||
\(474\) | 17.5629 | 0.806691 | ||||||||
\(475\) | −1.24304 | −0.0570344 | ||||||||
\(476\) | 12.7417 | 0.584015 | ||||||||
\(477\) | 5.61783 | 0.257223 | ||||||||
\(478\) | 27.5016 | 1.25790 | ||||||||
\(479\) | 6.16045 | 0.281478 | 0.140739 | − | 0.990047i | \(-0.455052\pi\) | ||||
0.140739 | + | 0.990047i | \(0.455052\pi\) | |||||||
\(480\) | −1.98128 | −0.0904326 | ||||||||
\(481\) | −0.600489 | −0.0273800 | ||||||||
\(482\) | −13.2419 | −0.603150 | ||||||||
\(483\) | 73.4097 | 3.34026 | ||||||||
\(484\) | −10.7187 | −0.487216 | ||||||||
\(485\) | 9.19718 | 0.417622 | ||||||||
\(486\) | 9.30470 | 0.422070 | ||||||||
\(487\) | −24.9602 | −1.13105 | −0.565527 | − | 0.824730i | \(-0.691327\pi\) | ||||
−0.565527 | + | 0.824730i | \(0.691327\pi\) | |||||||
\(488\) | −9.97802 | −0.451684 | ||||||||
\(489\) | 0.740932 | 0.0335061 | ||||||||
\(490\) | 10.8152 | 0.488580 | ||||||||
\(491\) | 15.8961 | 0.717382 | 0.358691 | − | 0.933456i | \(-0.383223\pi\) | ||||
0.358691 | + | 0.933456i | \(0.383223\pi\) | |||||||
\(492\) | 20.6107 | 0.929203 | ||||||||
\(493\) | −3.56230 | −0.160438 | ||||||||
\(494\) | 0.125268 | 0.00563608 | ||||||||
\(495\) | 0.490810 | 0.0220603 | ||||||||
\(496\) | 3.73228 | 0.167584 | ||||||||
\(497\) | −66.1955 | −2.96928 | ||||||||
\(498\) | 21.4839 | 0.962717 | ||||||||
\(499\) | −3.29567 | −0.147535 | −0.0737673 | − | 0.997275i | \(-0.523502\pi\) | ||||
−0.0737673 | + | 0.997275i | \(0.523502\pi\) | |||||||
\(500\) | 1.00000 | 0.0447214 | ||||||||
\(501\) | 11.1745 | 0.499238 | ||||||||
\(502\) | −3.04529 | −0.135918 | ||||||||
\(503\) | 25.1867 | 1.12302 | 0.561509 | − | 0.827471i | \(-0.310221\pi\) | ||||
0.561509 | + | 0.827471i | \(0.310221\pi\) | |||||||
\(504\) | −3.90621 | −0.173996 | ||||||||
\(505\) | −0.696428 | −0.0309907 | ||||||||
\(506\) | 4.65549 | 0.206962 | ||||||||
\(507\) | 25.7365 | 1.14300 | ||||||||
\(508\) | 10.1010 | 0.448162 | ||||||||
\(509\) | 20.5352 | 0.910207 | 0.455104 | − | 0.890438i | \(-0.349602\pi\) | ||||
0.455104 | + | 0.890438i | \(0.349602\pi\) | |||||||
\(510\) | 5.98106 | 0.264846 | ||||||||
\(511\) | 64.4891 | 2.85283 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −5.10916 | −0.225575 | ||||||||
\(514\) | −17.9678 | −0.792526 | ||||||||
\(515\) | −0.109262 | −0.00481464 | ||||||||
\(516\) | −19.4733 | −0.857263 | ||||||||
\(517\) | −1.38014 | −0.0606986 | ||||||||
\(518\) | −25.1503 | −1.10504 | ||||||||
\(519\) | 15.7215 | 0.690095 | ||||||||
\(520\) | −0.100776 | −0.00441932 | ||||||||
\(521\) | −0.894877 | −0.0392053 | −0.0196026 | − | 0.999808i | \(-0.506240\pi\) | ||||
−0.0196026 | + | 0.999808i | \(0.506240\pi\) | |||||||
\(522\) | 1.09209 | 0.0477995 | ||||||||
\(523\) | 22.9521 | 1.00362 | 0.501812 | − | 0.864977i | \(-0.332667\pi\) | ||||
0.501812 | + | 0.864977i | \(0.332667\pi\) | |||||||
\(524\) | 15.1653 | 0.662497 | ||||||||
\(525\) | 8.36259 | 0.364973 | ||||||||
\(526\) | 0.207779 | 0.00905959 | ||||||||
\(527\) | −11.2669 | −0.490796 | ||||||||
\(528\) | −1.05075 | −0.0457279 | ||||||||
\(529\) | 54.0594 | 2.35041 | ||||||||
\(530\) | 6.07027 | 0.263676 | ||||||||
\(531\) | −11.0023 | −0.477458 | ||||||||
\(532\) | 5.24661 | 0.227469 | ||||||||
\(533\) | 1.04835 | 0.0454089 | ||||||||
\(534\) | 24.3740 | 1.05476 | ||||||||
\(535\) | −11.7250 | −0.506916 | ||||||||
\(536\) | −7.26948 | −0.313994 | ||||||||
\(537\) | 40.4717 | 1.74648 | ||||||||
\(538\) | 32.4104 | 1.39731 | ||||||||
\(539\) | 5.73571 | 0.247054 | ||||||||
\(540\) | 4.11023 | 0.176876 | ||||||||
\(541\) | −34.2710 | −1.47343 | −0.736714 | − | 0.676205i | \(-0.763623\pi\) | ||||
−0.736714 | + | 0.676205i | \(0.763623\pi\) | |||||||
\(542\) | 2.36018 | 0.101378 | ||||||||
\(543\) | 31.9459 | 1.37093 | ||||||||
\(544\) | −3.01879 | −0.129429 | ||||||||
\(545\) | −7.56174 | −0.323909 | ||||||||
\(546\) | −0.842748 | −0.0360663 | ||||||||
\(547\) | −28.2684 | −1.20867 | −0.604334 | − | 0.796731i | \(-0.706561\pi\) | ||||
−0.604334 | + | 0.796731i | \(0.706561\pi\) | |||||||
\(548\) | 6.86463 | 0.293242 | ||||||||
\(549\) | −9.23431 | −0.394111 | ||||||||
\(550\) | 0.530338 | 0.0226137 | ||||||||
\(551\) | −1.46683 | −0.0624893 | ||||||||
\(552\) | −17.3924 | −0.740268 | ||||||||
\(553\) | 37.4150 | 1.59105 | ||||||||
\(554\) | −7.91946 | −0.336466 | ||||||||
\(555\) | −11.8058 | −0.501126 | ||||||||
\(556\) | −5.33765 | −0.226367 | ||||||||
\(557\) | −32.4389 | −1.37448 | −0.687241 | − | 0.726430i | \(-0.741178\pi\) | ||||
−0.687241 | + | 0.726430i | \(0.741178\pi\) | |||||||
\(558\) | 3.45409 | 0.146223 | ||||||||
\(559\) | −0.990490 | −0.0418933 | ||||||||
\(560\) | −4.22080 | −0.178362 | ||||||||
\(561\) | 3.17198 | 0.133921 | ||||||||
\(562\) | 15.4693 | 0.652532 | ||||||||
\(563\) | −19.8704 | −0.837437 | −0.418718 | − | 0.908116i | \(-0.637521\pi\) | ||||
−0.418718 | + | 0.908116i | \(0.637521\pi\) | |||||||
\(564\) | 5.15604 | 0.217108 | ||||||||
\(565\) | −9.90909 | −0.416878 | ||||||||
\(566\) | 30.3044 | 1.27379 | ||||||||
\(567\) | 46.0908 | 1.93563 | ||||||||
\(568\) | 15.6832 | 0.658051 | ||||||||
\(569\) | −19.7541 | −0.828136 | −0.414068 | − | 0.910246i | \(-0.635893\pi\) | ||||
−0.414068 | + | 0.910246i | \(0.635893\pi\) | |||||||
\(570\) | 2.46280 | 0.103155 | ||||||||
\(571\) | −44.2621 | −1.85231 | −0.926156 | − | 0.377140i | \(-0.876908\pi\) | ||||
−0.926156 | + | 0.377140i | \(0.876908\pi\) | |||||||
\(572\) | −0.0534454 | −0.00223466 | ||||||||
\(573\) | 18.6283 | 0.778209 | ||||||||
\(574\) | 43.9079 | 1.83268 | ||||||||
\(575\) | 8.77835 | 0.366082 | ||||||||
\(576\) | 0.925466 | 0.0385611 | ||||||||
\(577\) | −46.1403 | −1.92085 | −0.960423 | − | 0.278544i | \(-0.910148\pi\) | ||||
−0.960423 | + | 0.278544i | \(0.910148\pi\) | |||||||
\(578\) | −7.88693 | −0.328053 | ||||||||
\(579\) | −19.8530 | −0.825062 | ||||||||
\(580\) | 1.18004 | 0.0489986 | ||||||||
\(581\) | 45.7681 | 1.89878 | ||||||||
\(582\) | −18.2222 | −0.755333 | ||||||||
\(583\) | 3.21930 | 0.133330 | ||||||||
\(584\) | −15.2789 | −0.632244 | ||||||||
\(585\) | −0.0932647 | −0.00385602 | ||||||||
\(586\) | 11.2466 | 0.464593 | ||||||||
\(587\) | −10.3313 | −0.426419 | −0.213210 | − | 0.977006i | \(-0.568392\pi\) | ||||
−0.213210 | + | 0.977006i | \(0.568392\pi\) | |||||||
\(588\) | −21.4279 | −0.883672 | ||||||||
\(589\) | −4.63935 | −0.191161 | ||||||||
\(590\) | −11.8884 | −0.489436 | ||||||||
\(591\) | 7.69939 | 0.316711 | ||||||||
\(592\) | 5.95866 | 0.244899 | ||||||||
\(593\) | −14.6996 | −0.603640 | −0.301820 | − | 0.953365i | \(-0.597594\pi\) | ||||
−0.301820 | + | 0.953365i | \(0.597594\pi\) | |||||||
\(594\) | 2.17981 | 0.0894388 | ||||||||
\(595\) | 12.7417 | 0.522359 | ||||||||
\(596\) | 2.94235 | 0.120523 | ||||||||
\(597\) | 25.5544 | 1.04587 | ||||||||
\(598\) | −0.884647 | −0.0361759 | ||||||||
\(599\) | −16.2736 | −0.664922 | −0.332461 | − | 0.943117i | \(-0.607879\pi\) | ||||
−0.332461 | + | 0.943117i | \(0.607879\pi\) | |||||||
\(600\) | −1.98128 | −0.0808854 | ||||||||
\(601\) | −1.00000 | −0.0407909 | ||||||||
\(602\) | −41.4847 | −1.69079 | ||||||||
\(603\) | −6.72766 | −0.273971 | ||||||||
\(604\) | 10.3478 | 0.421047 | ||||||||
\(605\) | −10.7187 | −0.435779 | ||||||||
\(606\) | 1.37982 | 0.0560513 | ||||||||
\(607\) | 8.74412 | 0.354913 | 0.177456 | − | 0.984129i | \(-0.443213\pi\) | ||||
0.177456 | + | 0.984129i | \(0.443213\pi\) | |||||||
\(608\) | −1.24304 | −0.0504117 | ||||||||
\(609\) | 9.86822 | 0.399880 | ||||||||
\(610\) | −9.97802 | −0.403998 | ||||||||
\(611\) | 0.262257 | 0.0106098 | ||||||||
\(612\) | −2.79378 | −0.112932 | ||||||||
\(613\) | 30.3287 | 1.22497 | 0.612483 | − | 0.790484i | \(-0.290171\pi\) | ||||
0.612483 | + | 0.790484i | \(0.290171\pi\) | |||||||
\(614\) | −13.5263 | −0.545877 | ||||||||
\(615\) | 20.6107 | 0.831105 | ||||||||
\(616\) | −2.23845 | −0.0901899 | ||||||||
\(617\) | 21.6643 | 0.872172 | 0.436086 | − | 0.899905i | \(-0.356364\pi\) | ||||
0.436086 | + | 0.899905i | \(0.356364\pi\) | |||||||
\(618\) | 0.216478 | 0.00870801 | ||||||||
\(619\) | −8.68872 | −0.349229 | −0.174615 | − | 0.984637i | \(-0.555868\pi\) | ||||
−0.174615 | + | 0.984637i | \(0.555868\pi\) | |||||||
\(620\) | 3.73228 | 0.149892 | ||||||||
\(621\) | 36.0810 | 1.44788 | ||||||||
\(622\) | −19.4234 | −0.778806 | ||||||||
\(623\) | 51.9249 | 2.08033 | ||||||||
\(624\) | 0.199665 | 0.00799301 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −24.8018 | −0.991281 | ||||||||
\(627\) | 1.30612 | 0.0521613 | ||||||||
\(628\) | 10.7164 | 0.427632 | ||||||||
\(629\) | −17.9879 | −0.717225 | ||||||||
\(630\) | −3.90621 | −0.155627 | ||||||||
\(631\) | 20.6798 | 0.823248 | 0.411624 | − | 0.911354i | \(-0.364962\pi\) | ||||
0.411624 | + | 0.911354i | \(0.364962\pi\) | |||||||
\(632\) | −8.86443 | −0.352608 | ||||||||
\(633\) | 36.5412 | 1.45238 | ||||||||
\(634\) | −18.3022 | −0.726874 | ||||||||
\(635\) | 10.1010 | 0.400848 | ||||||||
\(636\) | −12.0269 | −0.476897 | ||||||||
\(637\) | −1.08991 | −0.0431838 | ||||||||
\(638\) | 0.625822 | 0.0247765 | ||||||||
\(639\) | 14.5142 | 0.574174 | ||||||||
\(640\) | 1.00000 | 0.0395285 | ||||||||
\(641\) | −0.615269 | −0.0243016 | −0.0121508 | − | 0.999926i | \(-0.503868\pi\) | ||||
−0.0121508 | + | 0.999926i | \(0.503868\pi\) | |||||||
\(642\) | 23.2305 | 0.916834 | ||||||||
\(643\) | −8.45656 | −0.333494 | −0.166747 | − | 0.986000i | \(-0.553326\pi\) | ||||
−0.166747 | + | 0.986000i | \(0.553326\pi\) | |||||||
\(644\) | −37.0517 | −1.46004 | ||||||||
\(645\) | −19.4733 | −0.766759 | ||||||||
\(646\) | 3.75246 | 0.147638 | ||||||||
\(647\) | 33.2576 | 1.30749 | 0.653745 | − | 0.756715i | \(-0.273197\pi\) | ||||
0.653745 | + | 0.756715i | \(0.273197\pi\) | |||||||
\(648\) | −10.9199 | −0.428975 | ||||||||
\(649\) | −6.30485 | −0.247487 | ||||||||
\(650\) | −0.100776 | −0.00395276 | ||||||||
\(651\) | 31.2115 | 1.22328 | ||||||||
\(652\) | −0.373966 | −0.0146457 | ||||||||
\(653\) | −28.3789 | −1.11055 | −0.555277 | − | 0.831666i | \(-0.687388\pi\) | ||||
−0.555277 | + | 0.831666i | \(0.687388\pi\) | |||||||
\(654\) | 14.9819 | 0.585839 | ||||||||
\(655\) | 15.1653 | 0.592556 | ||||||||
\(656\) | −10.4027 | −0.406159 | ||||||||
\(657\) | −14.1401 | −0.551656 | ||||||||
\(658\) | 10.9841 | 0.428206 | ||||||||
\(659\) | −33.8124 | −1.31714 | −0.658572 | − | 0.752518i | \(-0.728839\pi\) | ||||
−0.658572 | + | 0.752518i | \(0.728839\pi\) | |||||||
\(660\) | −1.05075 | −0.0409003 | ||||||||
\(661\) | −34.6501 | −1.34773 | −0.673866 | − | 0.738853i | \(-0.735368\pi\) | ||||
−0.673866 | + | 0.738853i | \(0.735368\pi\) | |||||||
\(662\) | −8.11182 | −0.315275 | ||||||||
\(663\) | −0.602747 | −0.0234087 | ||||||||
\(664\) | −10.8435 | −0.420808 | ||||||||
\(665\) | 5.24661 | 0.203455 | ||||||||
\(666\) | 5.51453 | 0.213684 | ||||||||
\(667\) | 10.3588 | 0.401095 | ||||||||
\(668\) | −5.64002 | −0.218219 | ||||||||
\(669\) | −43.5985 | −1.68562 | ||||||||
\(670\) | −7.26948 | −0.280845 | ||||||||
\(671\) | −5.29173 | −0.204285 | ||||||||
\(672\) | 8.36259 | 0.322594 | ||||||||
\(673\) | 33.9018 | 1.30682 | 0.653409 | − | 0.757005i | \(-0.273338\pi\) | ||||
0.653409 | + | 0.757005i | \(0.273338\pi\) | |||||||
\(674\) | −5.34930 | −0.206047 | ||||||||
\(675\) | 4.11023 | 0.158203 | ||||||||
\(676\) | −12.9898 | −0.499609 | ||||||||
\(677\) | −8.49652 | −0.326548 | −0.163274 | − | 0.986581i | \(-0.552205\pi\) | ||||
−0.163274 | + | 0.986581i | \(0.552205\pi\) | |||||||
\(678\) | 19.6327 | 0.753988 | ||||||||
\(679\) | −38.8195 | −1.48975 | ||||||||
\(680\) | −3.01879 | −0.115765 | ||||||||
\(681\) | 29.0264 | 1.11229 | ||||||||
\(682\) | 1.97937 | 0.0757940 | ||||||||
\(683\) | 42.8371 | 1.63912 | 0.819558 | − | 0.572996i | \(-0.194219\pi\) | ||||
0.819558 | + | 0.572996i | \(0.194219\pi\) | |||||||
\(684\) | −1.15039 | −0.0439861 | ||||||||
\(685\) | 6.86463 | 0.262284 | ||||||||
\(686\) | −16.1031 | −0.614821 | ||||||||
\(687\) | 34.3479 | 1.31045 | ||||||||
\(688\) | 9.82863 | 0.374713 | ||||||||
\(689\) | −0.611737 | −0.0233053 | ||||||||
\(690\) | −17.3924 | −0.662116 | ||||||||
\(691\) | 24.9210 | 0.948040 | 0.474020 | − | 0.880514i | \(-0.342802\pi\) | ||||
0.474020 | + | 0.880514i | \(0.342802\pi\) | |||||||
\(692\) | −7.93500 | −0.301643 | ||||||||
\(693\) | −2.07161 | −0.0786941 | ||||||||
\(694\) | −5.05294 | −0.191807 | ||||||||
\(695\) | −5.33765 | −0.202469 | ||||||||
\(696\) | −2.33799 | −0.0886214 | ||||||||
\(697\) | 31.4036 | 1.18950 | ||||||||
\(698\) | −21.1201 | −0.799409 | ||||||||
\(699\) | −23.7848 | −0.899624 | ||||||||
\(700\) | −4.22080 | −0.159531 | ||||||||
\(701\) | 12.9906 | 0.490647 | 0.245323 | − | 0.969441i | \(-0.421106\pi\) | ||||
0.245323 | + | 0.969441i | \(0.421106\pi\) | |||||||
\(702\) | −0.414213 | −0.0156334 | ||||||||
\(703\) | −7.40682 | −0.279353 | ||||||||
\(704\) | 0.530338 | 0.0199879 | ||||||||
\(705\) | 5.15604 | 0.194188 | ||||||||
\(706\) | 18.4134 | 0.692996 | ||||||||
\(707\) | 2.93949 | 0.110551 | ||||||||
\(708\) | 23.5542 | 0.885220 | ||||||||
\(709\) | 35.0433 | 1.31608 | 0.658039 | − | 0.752984i | \(-0.271386\pi\) | ||||
0.658039 | + | 0.752984i | \(0.271386\pi\) | |||||||
\(710\) | 15.6832 | 0.588578 | ||||||||
\(711\) | −8.20372 | −0.307664 | ||||||||
\(712\) | −12.3021 | −0.461042 | ||||||||
\(713\) | 32.7632 | 1.22699 | ||||||||
\(714\) | −25.2449 | −0.944765 | ||||||||
\(715\) | −0.0534454 | −0.00199874 | ||||||||
\(716\) | −20.4271 | −0.763395 | ||||||||
\(717\) | −54.4884 | −2.03491 | ||||||||
\(718\) | −2.92099 | −0.109010 | ||||||||
\(719\) | −16.5186 | −0.616039 | −0.308019 | − | 0.951380i | \(-0.599666\pi\) | ||||
−0.308019 | + | 0.951380i | \(0.599666\pi\) | |||||||
\(720\) | 0.925466 | 0.0344901 | ||||||||
\(721\) | 0.461172 | 0.0171749 | ||||||||
\(722\) | −17.4549 | −0.649603 | ||||||||
\(723\) | 26.2358 | 0.975720 | ||||||||
\(724\) | −16.1239 | −0.599238 | ||||||||
\(725\) | 1.18004 | 0.0438257 | ||||||||
\(726\) | 21.2368 | 0.788172 | ||||||||
\(727\) | 32.1976 | 1.19414 | 0.597072 | − | 0.802187i | \(-0.296331\pi\) | ||||
0.597072 | + | 0.802187i | \(0.296331\pi\) | |||||||
\(728\) | 0.425356 | 0.0157647 | ||||||||
\(729\) | 14.3245 | 0.530538 | ||||||||
\(730\) | −15.2789 | −0.565496 | ||||||||
\(731\) | −29.6705 | −1.09740 | ||||||||
\(732\) | 19.7692 | 0.730692 | ||||||||
\(733\) | −48.4593 | −1.78989 | −0.894943 | − | 0.446181i | \(-0.852784\pi\) | ||||
−0.894943 | + | 0.446181i | \(0.852784\pi\) | |||||||
\(734\) | 13.5315 | 0.499457 | ||||||||
\(735\) | −21.4279 | −0.790380 | ||||||||
\(736\) | 8.77835 | 0.323574 | ||||||||
\(737\) | −3.85529 | −0.142011 | ||||||||
\(738\) | −9.62738 | −0.354389 | ||||||||
\(739\) | 29.2098 | 1.07450 | 0.537250 | − | 0.843423i | \(-0.319463\pi\) | ||||
0.537250 | + | 0.843423i | \(0.319463\pi\) | |||||||
\(740\) | 5.95866 | 0.219045 | ||||||||
\(741\) | −0.248191 | −0.00911752 | ||||||||
\(742\) | −25.6214 | −0.940591 | ||||||||
\(743\) | −32.6377 | −1.19736 | −0.598681 | − | 0.800988i | \(-0.704308\pi\) | ||||
−0.598681 | + | 0.800988i | \(0.704308\pi\) | |||||||
\(744\) | −7.39468 | −0.271102 | ||||||||
\(745\) | 2.94235 | 0.107799 | ||||||||
\(746\) | 11.7727 | 0.431031 | ||||||||
\(747\) | −10.0352 | −0.367170 | ||||||||
\(748\) | −1.60098 | −0.0585375 | ||||||||
\(749\) | 49.4889 | 1.80829 | ||||||||
\(750\) | −1.98128 | −0.0723461 | ||||||||
\(751\) | 38.0341 | 1.38789 | 0.693943 | − | 0.720030i | \(-0.255872\pi\) | ||||
0.693943 | + | 0.720030i | \(0.255872\pi\) | |||||||
\(752\) | −2.60238 | −0.0948990 | ||||||||
\(753\) | 6.03356 | 0.219875 | ||||||||
\(754\) | −0.118920 | −0.00433081 | ||||||||
\(755\) | 10.3478 | 0.376596 | ||||||||
\(756\) | −17.3485 | −0.630958 | ||||||||
\(757\) | −13.0065 | −0.472730 | −0.236365 | − | 0.971664i | \(-0.575956\pi\) | ||||
−0.236365 | + | 0.971664i | \(0.575956\pi\) | |||||||
\(758\) | 16.1520 | 0.586668 | ||||||||
\(759\) | −9.22383 | −0.334804 | ||||||||
\(760\) | −1.24304 | −0.0450896 | ||||||||
\(761\) | −11.1052 | −0.402564 | −0.201282 | − | 0.979533i | \(-0.564511\pi\) | ||||
−0.201282 | + | 0.979533i | \(0.564511\pi\) | |||||||
\(762\) | −20.0130 | −0.724994 | ||||||||
\(763\) | 31.9166 | 1.15546 | ||||||||
\(764\) | −9.40217 | −0.340158 | ||||||||
\(765\) | −2.79378 | −0.101009 | ||||||||
\(766\) | 5.99445 | 0.216588 | ||||||||
\(767\) | 1.19806 | 0.0432595 | ||||||||
\(768\) | −1.98128 | −0.0714932 | ||||||||
\(769\) | 38.0655 | 1.37268 | 0.686338 | − | 0.727283i | \(-0.259217\pi\) | ||||
0.686338 | + | 0.727283i | \(0.259217\pi\) | |||||||
\(770\) | −2.23845 | −0.0806683 | ||||||||
\(771\) | 35.5992 | 1.28208 | ||||||||
\(772\) | 10.0203 | 0.360638 | ||||||||
\(773\) | 13.3518 | 0.480231 | 0.240115 | − | 0.970744i | \(-0.422815\pi\) | ||||
0.240115 | + | 0.970744i | \(0.422815\pi\) | |||||||
\(774\) | 9.09606 | 0.326951 | ||||||||
\(775\) | 3.73228 | 0.134067 | ||||||||
\(776\) | 9.19718 | 0.330159 | ||||||||
\(777\) | 49.8298 | 1.78763 | ||||||||
\(778\) | 7.07504 | 0.253653 | ||||||||
\(779\) | 12.9310 | 0.463300 | ||||||||
\(780\) | 0.199665 | 0.00714917 | ||||||||
\(781\) | 8.31738 | 0.297619 | ||||||||
\(782\) | −26.4999 | −0.947636 | ||||||||
\(783\) | 4.85025 | 0.173334 | ||||||||
\(784\) | 10.8152 | 0.386257 | ||||||||
\(785\) | 10.7164 | 0.382486 | ||||||||
\(786\) | −30.0466 | −1.07173 | ||||||||
\(787\) | −42.7857 | −1.52515 | −0.762573 | − | 0.646903i | \(-0.776064\pi\) | ||||
−0.762573 | + | 0.646903i | \(0.776064\pi\) | |||||||
\(788\) | −3.88607 | −0.138436 | ||||||||
\(789\) | −0.411668 | −0.0146558 | ||||||||
\(790\) | −8.86443 | −0.315382 | ||||||||
\(791\) | 41.8243 | 1.48710 | ||||||||
\(792\) | 0.490810 | 0.0174402 | ||||||||
\(793\) | 1.00554 | 0.0357079 | ||||||||
\(794\) | 1.12705 | 0.0399974 | ||||||||
\(795\) | −12.0269 | −0.426550 | ||||||||
\(796\) | −12.8979 | −0.457155 | ||||||||
\(797\) | 25.1817 | 0.891981 | 0.445991 | − | 0.895038i | \(-0.352851\pi\) | ||||
0.445991 | + | 0.895038i | \(0.352851\pi\) | |||||||
\(798\) | −10.3950 | −0.367979 | ||||||||
\(799\) | 7.85602 | 0.277926 | ||||||||
\(800\) | 1.00000 | 0.0353553 | ||||||||
\(801\) | −11.3852 | −0.402277 | ||||||||
\(802\) | −18.1263 | −0.640062 | ||||||||
\(803\) | −8.10296 | −0.285947 | ||||||||
\(804\) | 14.4029 | 0.507950 | ||||||||
\(805\) | −37.0517 | −1.30590 | ||||||||
\(806\) | −0.376124 | −0.0132484 | ||||||||
\(807\) | −64.2140 | −2.26044 | ||||||||
\(808\) | −0.696428 | −0.0245003 | ||||||||
\(809\) | −40.4736 | −1.42298 | −0.711488 | − | 0.702699i | \(-0.751978\pi\) | ||||
−0.711488 | + | 0.702699i | \(0.751978\pi\) | |||||||
\(810\) | −10.9199 | −0.383687 | ||||||||
\(811\) | 31.3771 | 1.10180 | 0.550899 | − | 0.834572i | \(-0.314285\pi\) | ||||
0.550899 | + | 0.834572i | \(0.314285\pi\) | |||||||
\(812\) | −4.98073 | −0.174789 | ||||||||
\(813\) | −4.67617 | −0.164000 | ||||||||
\(814\) | 3.16010 | 0.110762 | ||||||||
\(815\) | −0.373966 | −0.0130995 | ||||||||
\(816\) | 5.98106 | 0.209379 | ||||||||
\(817\) | −12.2173 | −0.427430 | ||||||||
\(818\) | −8.94909 | −0.312897 | ||||||||
\(819\) | 0.393652 | 0.0137553 | ||||||||
\(820\) | −10.4027 | −0.363279 | ||||||||
\(821\) | −42.4491 | −1.48148 | −0.740742 | − | 0.671789i | \(-0.765526\pi\) | ||||
−0.740742 | + | 0.671789i | \(0.765526\pi\) | |||||||
\(822\) | −13.6007 | −0.474380 | ||||||||
\(823\) | −51.7268 | −1.80308 | −0.901541 | − | 0.432693i | \(-0.857563\pi\) | ||||
−0.901541 | + | 0.432693i | \(0.857563\pi\) | |||||||
\(824\) | −0.109262 | −0.00380631 | ||||||||
\(825\) | −1.05075 | −0.0365824 | ||||||||
\(826\) | 50.1784 | 1.74593 | ||||||||
\(827\) | −31.4371 | −1.09318 | −0.546588 | − | 0.837401i | \(-0.684074\pi\) | ||||
−0.546588 | + | 0.837401i | \(0.684074\pi\) | |||||||
\(828\) | 8.12406 | 0.282331 | ||||||||
\(829\) | −18.9051 | −0.656601 | −0.328300 | − | 0.944573i | \(-0.606476\pi\) | ||||
−0.328300 | + | 0.944573i | \(0.606476\pi\) | |||||||
\(830\) | −10.8435 | −0.376382 | ||||||||
\(831\) | 15.6907 | 0.544303 | ||||||||
\(832\) | −0.100776 | −0.00349378 | ||||||||
\(833\) | −32.6487 | −1.13121 | ||||||||
\(834\) | 10.5754 | 0.366195 | ||||||||
\(835\) | −5.64002 | −0.195181 | ||||||||
\(836\) | −0.659229 | −0.0227999 | ||||||||
\(837\) | 15.3405 | 0.530246 | ||||||||
\(838\) | 18.7687 | 0.648354 | ||||||||
\(839\) | −3.25070 | −0.112227 | −0.0561133 | − | 0.998424i | \(-0.517871\pi\) | ||||
−0.0561133 | + | 0.998424i | \(0.517871\pi\) | |||||||
\(840\) | 8.36259 | 0.288537 | ||||||||
\(841\) | −27.6075 | −0.951983 | ||||||||
\(842\) | −15.5120 | −0.534580 | ||||||||
\(843\) | −30.6490 | −1.05561 | ||||||||
\(844\) | −18.4433 | −0.634843 | ||||||||
\(845\) | −12.9898 | −0.446864 | ||||||||
\(846\) | −2.40841 | −0.0828030 | ||||||||
\(847\) | 45.2417 | 1.55452 | ||||||||
\(848\) | 6.07027 | 0.208454 | ||||||||
\(849\) | −60.0416 | −2.06062 | ||||||||
\(850\) | −3.01879 | −0.103543 | ||||||||
\(851\) | 52.3071 | 1.79307 | ||||||||
\(852\) | −31.0727 | −1.06453 | ||||||||
\(853\) | 24.1730 | 0.827668 | 0.413834 | − | 0.910352i | \(-0.364189\pi\) | ||||
0.413834 | + | 0.910352i | \(0.364189\pi\) | |||||||
\(854\) | 42.1153 | 1.44115 | ||||||||
\(855\) | −1.15039 | −0.0393424 | ||||||||
\(856\) | −11.7250 | −0.400752 | ||||||||
\(857\) | 39.8298 | 1.36056 | 0.680279 | − | 0.732953i | \(-0.261858\pi\) | ||||
0.680279 | + | 0.732953i | \(0.261858\pi\) | |||||||
\(858\) | 0.105890 | 0.00361503 | ||||||||
\(859\) | −43.0036 | −1.46726 | −0.733632 | − | 0.679547i | \(-0.762176\pi\) | ||||
−0.733632 | + | 0.679547i | \(0.762176\pi\) | |||||||
\(860\) | 9.82863 | 0.335154 | ||||||||
\(861\) | −86.9938 | −2.96474 | ||||||||
\(862\) | 6.46497 | 0.220198 | ||||||||
\(863\) | −7.04963 | −0.239972 | −0.119986 | − | 0.992776i | \(-0.538285\pi\) | ||||
−0.119986 | + | 0.992776i | \(0.538285\pi\) | |||||||
\(864\) | 4.11023 | 0.139833 | ||||||||
\(865\) | −7.93500 | −0.269798 | ||||||||
\(866\) | −20.4238 | −0.694030 | ||||||||
\(867\) | 15.6262 | 0.530694 | ||||||||
\(868\) | −15.7532 | −0.534699 | ||||||||
\(869\) | −4.70115 | −0.159475 | ||||||||
\(870\) | −2.33799 | −0.0792654 | ||||||||
\(871\) | 0.732589 | 0.0248228 | ||||||||
\(872\) | −7.56174 | −0.256073 | ||||||||
\(873\) | 8.51167 | 0.288076 | ||||||||
\(874\) | −10.9118 | −0.369097 | ||||||||
\(875\) | −4.22080 | −0.142689 | ||||||||
\(876\) | 30.2717 | 1.02279 | ||||||||
\(877\) | −12.8520 | −0.433980 | −0.216990 | − | 0.976174i | \(-0.569624\pi\) | ||||
−0.216990 | + | 0.976174i | \(0.569624\pi\) | |||||||
\(878\) | 18.6018 | 0.627781 | ||||||||
\(879\) | −22.2827 | −0.751575 | ||||||||
\(880\) | 0.530338 | 0.0178777 | ||||||||
\(881\) | 43.2443 | 1.45694 | 0.728469 | − | 0.685079i | \(-0.240232\pi\) | ||||
0.728469 | + | 0.685079i | \(0.240232\pi\) | |||||||
\(882\) | 10.0091 | 0.337023 | ||||||||
\(883\) | −12.6452 | −0.425544 | −0.212772 | − | 0.977102i | \(-0.568249\pi\) | ||||
−0.212772 | + | 0.977102i | \(0.568249\pi\) | |||||||
\(884\) | 0.304221 | 0.0102321 | ||||||||
\(885\) | 23.5542 | 0.791764 | ||||||||
\(886\) | 12.2738 | 0.412347 | ||||||||
\(887\) | 38.0927 | 1.27903 | 0.639514 | − | 0.768780i | \(-0.279136\pi\) | ||||
0.639514 | + | 0.768780i | \(0.279136\pi\) | |||||||
\(888\) | −11.8058 | −0.396175 | ||||||||
\(889\) | −42.6345 | −1.42992 | ||||||||
\(890\) | −12.3021 | −0.412369 | ||||||||
\(891\) | −5.79125 | −0.194014 | ||||||||
\(892\) | 22.0052 | 0.736789 | ||||||||
\(893\) | 3.23485 | 0.108250 | ||||||||
\(894\) | −5.82961 | −0.194971 | ||||||||
\(895\) | −20.4271 | −0.682801 | ||||||||
\(896\) | −4.22080 | −0.141007 | ||||||||
\(897\) | 1.75273 | 0.0585220 | ||||||||
\(898\) | −27.2626 | −0.909765 | ||||||||
\(899\) | 4.40425 | 0.146890 | ||||||||
\(900\) | 0.925466 | 0.0308489 | ||||||||
\(901\) | −18.3248 | −0.610489 | ||||||||
\(902\) | −5.51697 | −0.183695 | ||||||||
\(903\) | 82.1928 | 2.73521 | ||||||||
\(904\) | −9.90909 | −0.329571 | ||||||||
\(905\) | −16.1239 | −0.535975 | ||||||||
\(906\) | −20.5019 | −0.681131 | ||||||||
\(907\) | 32.2222 | 1.06992 | 0.534960 | − | 0.844877i | \(-0.320327\pi\) | ||||
0.534960 | + | 0.844877i | \(0.320327\pi\) | |||||||
\(908\) | −14.6503 | −0.486188 | ||||||||
\(909\) | −0.644521 | −0.0213774 | ||||||||
\(910\) | 0.425356 | 0.0141004 | ||||||||
\(911\) | −13.2276 | −0.438250 | −0.219125 | − | 0.975697i | \(-0.570320\pi\) | ||||
−0.219125 | + | 0.975697i | \(0.570320\pi\) | |||||||
\(912\) | 2.46280 | 0.0815514 | ||||||||
\(913\) | −5.75070 | −0.190320 | ||||||||
\(914\) | −19.2314 | −0.636118 | ||||||||
\(915\) | 19.7692 | 0.653551 | ||||||||
\(916\) | −17.3362 | −0.572805 | ||||||||
\(917\) | −64.0096 | −2.11378 | ||||||||
\(918\) | −12.4079 | −0.409522 | ||||||||
\(919\) | 59.8759 | 1.97512 | 0.987561 | − | 0.157235i | \(-0.0502579\pi\) | ||||
0.987561 | + | 0.157235i | \(0.0502579\pi\) | |||||||
\(920\) | 8.77835 | 0.289414 | ||||||||
\(921\) | 26.7994 | 0.883069 | ||||||||
\(922\) | 11.5699 | 0.381033 | ||||||||
\(923\) | −1.58049 | −0.0520223 | ||||||||
\(924\) | 4.43500 | 0.145901 | ||||||||
\(925\) | 5.95866 | 0.195919 | ||||||||
\(926\) | −0.00174954 | −5.74936e−5 0 | ||||||||
\(927\) | −0.101118 | −0.00332115 | ||||||||
\(928\) | 1.18004 | 0.0387368 | ||||||||
\(929\) | 1.14314 | 0.0375051 | 0.0187526 | − | 0.999824i | \(-0.494031\pi\) | ||||
0.0187526 | + | 0.999824i | \(0.494031\pi\) | |||||||
\(930\) | −7.39468 | −0.242481 | ||||||||
\(931\) | −13.4437 | −0.440598 | ||||||||
\(932\) | 12.0048 | 0.393230 | ||||||||
\(933\) | 38.4831 | 1.25988 | ||||||||
\(934\) | −32.4183 | −1.06076 | ||||||||
\(935\) | −1.60098 | −0.0523576 | ||||||||
\(936\) | −0.0932647 | −0.00304845 | ||||||||
\(937\) | −7.60417 | −0.248418 | −0.124209 | − | 0.992256i | \(-0.539639\pi\) | ||||
−0.124209 | + | 0.992256i | \(0.539639\pi\) | |||||||
\(938\) | 30.6831 | 1.00184 | ||||||||
\(939\) | 49.1394 | 1.60360 | ||||||||
\(940\) | −2.60238 | −0.0848803 | ||||||||
\(941\) | 35.7215 | 1.16449 | 0.582244 | − | 0.813014i | \(-0.302175\pi\) | ||||
0.582244 | + | 0.813014i | \(0.302175\pi\) | |||||||
\(942\) | −21.2322 | −0.691783 | ||||||||
\(943\) | −91.3189 | −2.97375 | ||||||||
\(944\) | −11.8884 | −0.386933 | ||||||||
\(945\) | −17.3485 | −0.564346 | ||||||||
\(946\) | 5.21250 | 0.169473 | ||||||||
\(947\) | −20.1569 | −0.655013 | −0.327506 | − | 0.944849i | \(-0.606208\pi\) | ||||
−0.327506 | + | 0.944849i | \(0.606208\pi\) | |||||||
\(948\) | 17.5629 | 0.570416 | ||||||||
\(949\) | 1.53974 | 0.0499821 | ||||||||
\(950\) | −1.24304 | −0.0403294 | ||||||||
\(951\) | 36.2618 | 1.17587 | ||||||||
\(952\) | 12.7417 | 0.412961 | ||||||||
\(953\) | 46.2528 | 1.49827 | 0.749137 | − | 0.662415i | \(-0.230468\pi\) | ||||
0.749137 | + | 0.662415i | \(0.230468\pi\) | |||||||
\(954\) | 5.61783 | 0.181884 | ||||||||
\(955\) | −9.40217 | −0.304247 | ||||||||
\(956\) | 27.5016 | 0.889467 | ||||||||
\(957\) | −1.23993 | −0.0400812 | ||||||||
\(958\) | 6.16045 | 0.199035 | ||||||||
\(959\) | −28.9742 | −0.935627 | ||||||||
\(960\) | −1.98128 | −0.0639455 | ||||||||
\(961\) | −17.0701 | −0.550649 | ||||||||
\(962\) | −0.600489 | −0.0193606 | ||||||||
\(963\) | −10.8511 | −0.349671 | ||||||||
\(964\) | −13.2419 | −0.426491 | ||||||||
\(965\) | 10.0203 | 0.322565 | ||||||||
\(966\) | 73.4097 | 2.36192 | ||||||||
\(967\) | −20.8826 | −0.671538 | −0.335769 | − | 0.941944i | \(-0.608996\pi\) | ||||
−0.335769 | + | 0.941944i | \(0.608996\pi\) | |||||||
\(968\) | −10.7187 | −0.344513 | ||||||||
\(969\) | −7.43466 | −0.238836 | ||||||||
\(970\) | 9.19718 | 0.295304 | ||||||||
\(971\) | −43.3521 | −1.39123 | −0.695617 | − | 0.718413i | \(-0.744869\pi\) | ||||
−0.695617 | + | 0.718413i | \(0.744869\pi\) | |||||||
\(972\) | 9.30470 | 0.298448 | ||||||||
\(973\) | 22.5292 | 0.722252 | ||||||||
\(974\) | −24.9602 | −0.799776 | ||||||||
\(975\) | 0.199665 | 0.00639441 | ||||||||
\(976\) | −9.97802 | −0.319389 | ||||||||
\(977\) | −40.2151 | −1.28659 | −0.643297 | − | 0.765617i | \(-0.722434\pi\) | ||||
−0.643297 | + | 0.765617i | \(0.722434\pi\) | |||||||
\(978\) | 0.740932 | 0.0236924 | ||||||||
\(979\) | −6.52430 | −0.208517 | ||||||||
\(980\) | 10.8152 | 0.345478 | ||||||||
\(981\) | −6.99813 | −0.223433 | ||||||||
\(982\) | 15.8961 | 0.507266 | ||||||||
\(983\) | −13.3486 | −0.425754 | −0.212877 | − | 0.977079i | \(-0.568283\pi\) | ||||
−0.212877 | + | 0.977079i | \(0.568283\pi\) | |||||||
\(984\) | 20.6107 | 0.657046 | ||||||||
\(985\) | −3.88607 | −0.123821 | ||||||||
\(986\) | −3.56230 | −0.113447 | ||||||||
\(987\) | −21.7626 | −0.692712 | ||||||||
\(988\) | 0.125268 | 0.00398531 | ||||||||
\(989\) | 86.2792 | 2.74352 | ||||||||
\(990\) | 0.490810 | 0.0155990 | ||||||||
\(991\) | −35.3546 | −1.12308 | −0.561538 | − | 0.827451i | \(-0.689790\pi\) | ||||
−0.561538 | + | 0.827451i | \(0.689790\pi\) | |||||||
\(992\) | 3.73228 | 0.118500 | ||||||||
\(993\) | 16.0718 | 0.510023 | ||||||||
\(994\) | −66.1955 | −2.09959 | ||||||||
\(995\) | −12.8979 | −0.408892 | ||||||||
\(996\) | 21.4839 | 0.680744 | ||||||||
\(997\) | 46.6368 | 1.47700 | 0.738501 | − | 0.674253i | \(-0.235534\pi\) | ||||
0.738501 | + | 0.674253i | \(0.235534\pi\) | |||||||
\(998\) | −3.29567 | −0.104323 | ||||||||
\(999\) | 24.4914 | 0.774875 |
(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 | 6010.2.a.c.1.5 | ✓ | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6010.2.a.c.1.5 | ✓ | 16 | 1.1 | even | 1 | trivial |