Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4013,2,Mod(1,4013)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4013, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4013.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4013 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4013.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: | \(32.0439663311\) |
Analytic rank: | \(0\) |
Dimension: | \(176\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Character | \(\chi\) | \(=\) | 4013.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.69276 | −1.90407 | −0.952035 | − | 0.305989i | \(-0.901013\pi\) | ||||
−0.952035 | + | 0.305989i | \(0.901013\pi\) | |||||||
\(3\) | −0.212283 | −0.122562 | −0.0612808 | − | 0.998121i | \(-0.519519\pi\) | ||||
−0.0612808 | + | 0.998121i | \(0.519519\pi\) | |||||||
\(4\) | 5.25096 | 2.62548 | ||||||||
\(5\) | −3.83789 | −1.71636 | −0.858179 | − | 0.513351i | \(-0.828404\pi\) | ||||
−0.858179 | + | 0.513351i | \(0.828404\pi\) | |||||||
\(6\) | 0.571627 | 0.233366 | ||||||||
\(7\) | 2.56921 | 0.971069 | 0.485534 | − | 0.874218i | \(-0.338625\pi\) | ||||
0.485534 | + | 0.874218i | \(0.338625\pi\) | |||||||
\(8\) | −8.75407 | −3.09503 | ||||||||
\(9\) | −2.95494 | −0.984979 | ||||||||
\(10\) | 10.3345 | 3.26806 | ||||||||
\(11\) | 2.31259 | 0.697271 | 0.348636 | − | 0.937258i | \(-0.386645\pi\) | ||||
0.348636 | + | 0.937258i | \(0.386645\pi\) | |||||||
\(12\) | −1.11469 | −0.321783 | ||||||||
\(13\) | 3.08100 | 0.854517 | 0.427258 | − | 0.904130i | \(-0.359479\pi\) | ||||
0.427258 | + | 0.904130i | \(0.359479\pi\) | |||||||
\(14\) | −6.91826 | −1.84898 | ||||||||
\(15\) | 0.814718 | 0.210359 | ||||||||
\(16\) | 13.0707 | 3.26767 | ||||||||
\(17\) | 0.494885 | 0.120027 | 0.0600136 | − | 0.998198i | \(-0.480886\pi\) | ||||
0.0600136 | + | 0.998198i | \(0.480886\pi\) | |||||||
\(18\) | 7.95694 | 1.87547 | ||||||||
\(19\) | 6.67887 | 1.53224 | 0.766119 | − | 0.642699i | \(-0.222185\pi\) | ||||
0.766119 | + | 0.642699i | \(0.222185\pi\) | |||||||
\(20\) | −20.1526 | −4.50626 | ||||||||
\(21\) | −0.545398 | −0.119016 | ||||||||
\(22\) | −6.22725 | −1.32765 | ||||||||
\(23\) | 8.86376 | 1.84822 | 0.924111 | − | 0.382125i | \(-0.124808\pi\) | ||||
0.924111 | + | 0.382125i | \(0.124808\pi\) | |||||||
\(24\) | 1.85834 | 0.379332 | ||||||||
\(25\) | 9.72941 | 1.94588 | ||||||||
\(26\) | −8.29641 | −1.62706 | ||||||||
\(27\) | 1.26413 | 0.243282 | ||||||||
\(28\) | 13.4908 | 2.54952 | ||||||||
\(29\) | −2.15522 | −0.400215 | −0.200108 | − | 0.979774i | \(-0.564129\pi\) | ||||
−0.200108 | + | 0.979774i | \(0.564129\pi\) | |||||||
\(30\) | −2.19384 | −0.400539 | ||||||||
\(31\) | 0.634048 | 0.113878 | 0.0569392 | − | 0.998378i | \(-0.481866\pi\) | ||||
0.0569392 | + | 0.998378i | \(0.481866\pi\) | |||||||
\(32\) | −17.6881 | −3.12685 | ||||||||
\(33\) | −0.490923 | −0.0854587 | ||||||||
\(34\) | −1.33261 | −0.228540 | ||||||||
\(35\) | −9.86033 | −1.66670 | ||||||||
\(36\) | −15.5163 | −2.58604 | ||||||||
\(37\) | 3.65718 | 0.601237 | 0.300619 | − | 0.953744i | \(-0.402807\pi\) | ||||
0.300619 | + | 0.953744i | \(0.402807\pi\) | |||||||
\(38\) | −17.9846 | −2.91749 | ||||||||
\(39\) | −0.654044 | −0.104731 | ||||||||
\(40\) | 33.5972 | 5.31218 | ||||||||
\(41\) | 9.17637 | 1.43311 | 0.716554 | − | 0.697531i | \(-0.245718\pi\) | ||||
0.716554 | + | 0.697531i | \(0.245718\pi\) | |||||||
\(42\) | 1.46863 | 0.226614 | ||||||||
\(43\) | 7.81894 | 1.19238 | 0.596188 | − | 0.802845i | \(-0.296681\pi\) | ||||
0.596188 | + | 0.802845i | \(0.296681\pi\) | |||||||
\(44\) | 12.1433 | 1.83067 | ||||||||
\(45\) | 11.3407 | 1.69058 | ||||||||
\(46\) | −23.8680 | −3.51914 | ||||||||
\(47\) | −6.82433 | −0.995431 | −0.497715 | − | 0.867340i | \(-0.665828\pi\) | ||||
−0.497715 | + | 0.867340i | \(0.665828\pi\) | |||||||
\(48\) | −2.77468 | −0.400491 | ||||||||
\(49\) | −0.399181 | −0.0570259 | ||||||||
\(50\) | −26.1990 | −3.70509 | ||||||||
\(51\) | −0.105056 | −0.0147107 | ||||||||
\(52\) | 16.1782 | 2.24352 | ||||||||
\(53\) | −11.3666 | −1.56133 | −0.780663 | − | 0.624952i | \(-0.785118\pi\) | ||||
−0.780663 | + | 0.624952i | \(0.785118\pi\) | |||||||
\(54\) | −3.40400 | −0.463226 | ||||||||
\(55\) | −8.87546 | −1.19677 | ||||||||
\(56\) | −22.4910 | −3.00549 | ||||||||
\(57\) | −1.41781 | −0.187793 | ||||||||
\(58\) | 5.80351 | 0.762038 | ||||||||
\(59\) | −1.47305 | −0.191775 | −0.0958877 | − | 0.995392i | \(-0.530569\pi\) | ||||
−0.0958877 | + | 0.995392i | \(0.530569\pi\) | |||||||
\(60\) | 4.27806 | 0.552295 | ||||||||
\(61\) | −4.25610 | −0.544938 | −0.272469 | − | 0.962165i | \(-0.587840\pi\) | ||||
−0.272469 | + | 0.962165i | \(0.587840\pi\) | |||||||
\(62\) | −1.70734 | −0.216833 | ||||||||
\(63\) | −7.59184 | −0.956482 | ||||||||
\(64\) | 21.4885 | 2.68606 | ||||||||
\(65\) | −11.8246 | −1.46666 | ||||||||
\(66\) | 1.32194 | 0.162719 | ||||||||
\(67\) | −2.72727 | −0.333189 | −0.166594 | − | 0.986026i | \(-0.553277\pi\) | ||||
−0.166594 | + | 0.986026i | \(0.553277\pi\) | |||||||
\(68\) | 2.59862 | 0.315129 | ||||||||
\(69\) | −1.88162 | −0.226521 | ||||||||
\(70\) | 26.5515 | 3.17351 | ||||||||
\(71\) | 12.2667 | 1.45579 | 0.727897 | − | 0.685686i | \(-0.240498\pi\) | ||||
0.727897 | + | 0.685686i | \(0.240498\pi\) | |||||||
\(72\) | 25.8677 | 3.04854 | ||||||||
\(73\) | −4.18062 | −0.489304 | −0.244652 | − | 0.969611i | \(-0.578674\pi\) | ||||
−0.244652 | + | 0.969611i | \(0.578674\pi\) | |||||||
\(74\) | −9.84792 | −1.14480 | ||||||||
\(75\) | −2.06539 | −0.238490 | ||||||||
\(76\) | 35.0705 | 4.02286 | ||||||||
\(77\) | 5.94151 | 0.677098 | ||||||||
\(78\) | 1.76119 | 0.199415 | ||||||||
\(79\) | −4.70363 | −0.529199 | −0.264600 | − | 0.964358i | \(-0.585240\pi\) | ||||
−0.264600 | + | 0.964358i | \(0.585240\pi\) | |||||||
\(80\) | −50.1639 | −5.60850 | ||||||||
\(81\) | 8.59645 | 0.955162 | ||||||||
\(82\) | −24.7098 | −2.72874 | ||||||||
\(83\) | 0.123219 | 0.0135250 | 0.00676251 | − | 0.999977i | \(-0.497847\pi\) | ||||
0.00676251 | + | 0.999977i | \(0.497847\pi\) | |||||||
\(84\) | −2.86387 | −0.312474 | ||||||||
\(85\) | −1.89932 | −0.206010 | ||||||||
\(86\) | −21.0545 | −2.27037 | ||||||||
\(87\) | 0.457517 | 0.0490510 | ||||||||
\(88\) | −20.2446 | −2.15808 | ||||||||
\(89\) | 2.64071 | 0.279915 | 0.139957 | − | 0.990158i | \(-0.455303\pi\) | ||||
0.139957 | + | 0.990158i | \(0.455303\pi\) | |||||||
\(90\) | −30.5379 | −3.21897 | ||||||||
\(91\) | 7.91573 | 0.829794 | ||||||||
\(92\) | 46.5433 | 4.85247 | ||||||||
\(93\) | −0.134598 | −0.0139571 | ||||||||
\(94\) | 18.3763 | 1.89537 | ||||||||
\(95\) | −25.6328 | −2.62987 | ||||||||
\(96\) | 3.75489 | 0.383231 | ||||||||
\(97\) | −18.0692 | −1.83465 | −0.917325 | − | 0.398139i | \(-0.869656\pi\) | ||||
−0.917325 | + | 0.398139i | \(0.869656\pi\) | |||||||
\(98\) | 1.07490 | 0.108581 | ||||||||
\(99\) | −6.83355 | −0.686797 | ||||||||
\(100\) | 51.0888 | 5.10888 | ||||||||
\(101\) | 7.00335 | 0.696859 | 0.348430 | − | 0.937335i | \(-0.386715\pi\) | ||||
0.348430 | + | 0.937335i | \(0.386715\pi\) | |||||||
\(102\) | 0.282890 | 0.0280103 | ||||||||
\(103\) | 1.59986 | 0.157639 | 0.0788194 | − | 0.996889i | \(-0.474885\pi\) | ||||
0.0788194 | + | 0.996889i | \(0.474885\pi\) | |||||||
\(104\) | −26.9713 | −2.64476 | ||||||||
\(105\) | 2.09318 | 0.204273 | ||||||||
\(106\) | 30.6076 | 2.97287 | ||||||||
\(107\) | 11.7474 | 1.13566 | 0.567832 | − | 0.823145i | \(-0.307782\pi\) | ||||
0.567832 | + | 0.823145i | \(0.307782\pi\) | |||||||
\(108\) | 6.63791 | 0.638733 | ||||||||
\(109\) | −10.5930 | −1.01462 | −0.507311 | − | 0.861763i | \(-0.669361\pi\) | ||||
−0.507311 | + | 0.861763i | \(0.669361\pi\) | |||||||
\(110\) | 23.8995 | 2.27873 | ||||||||
\(111\) | −0.776357 | −0.0736886 | ||||||||
\(112\) | 33.5813 | 3.17314 | ||||||||
\(113\) | 17.4276 | 1.63945 | 0.819724 | − | 0.572759i | \(-0.194127\pi\) | ||||
0.819724 | + | 0.572759i | \(0.194127\pi\) | |||||||
\(114\) | 3.81782 | 0.357572 | ||||||||
\(115\) | −34.0181 | −3.17221 | ||||||||
\(116\) | −11.3170 | −1.05076 | ||||||||
\(117\) | −9.10417 | −0.841681 | ||||||||
\(118\) | 3.96658 | 0.365154 | ||||||||
\(119\) | 1.27146 | 0.116555 | ||||||||
\(120\) | −7.13210 | −0.651069 | ||||||||
\(121\) | −5.65194 | −0.513813 | ||||||||
\(122\) | 11.4607 | 1.03760 | ||||||||
\(123\) | −1.94799 | −0.175644 | ||||||||
\(124\) | 3.32937 | 0.298986 | ||||||||
\(125\) | −18.1510 | −1.62347 | ||||||||
\(126\) | 20.4430 | 1.82121 | ||||||||
\(127\) | −2.42321 | −0.215025 | −0.107512 | − | 0.994204i | \(-0.534289\pi\) | ||||
−0.107512 | + | 0.994204i | \(0.534289\pi\) | |||||||
\(128\) | −22.4872 | −1.98760 | ||||||||
\(129\) | −1.65983 | −0.146140 | ||||||||
\(130\) | 31.8407 | 2.79262 | ||||||||
\(131\) | 1.23473 | 0.107879 | 0.0539396 | − | 0.998544i | \(-0.482822\pi\) | ||||
0.0539396 | + | 0.998544i | \(0.482822\pi\) | |||||||
\(132\) | −2.57782 | −0.224370 | ||||||||
\(133\) | 17.1594 | 1.48791 | ||||||||
\(134\) | 7.34388 | 0.634415 | ||||||||
\(135\) | −4.85160 | −0.417559 | ||||||||
\(136\) | −4.33226 | −0.371488 | ||||||||
\(137\) | 11.9408 | 1.02017 | 0.510084 | − | 0.860125i | \(-0.329614\pi\) | ||||
0.510084 | + | 0.860125i | \(0.329614\pi\) | |||||||
\(138\) | 5.06676 | 0.431312 | ||||||||
\(139\) | 10.1442 | 0.860423 | 0.430211 | − | 0.902728i | \(-0.358439\pi\) | ||||
0.430211 | + | 0.902728i | \(0.358439\pi\) | |||||||
\(140\) | −51.7763 | −4.37589 | ||||||||
\(141\) | 1.44869 | 0.122002 | ||||||||
\(142\) | −33.0314 | −2.77193 | ||||||||
\(143\) | 7.12509 | 0.595830 | ||||||||
\(144\) | −38.6231 | −3.21859 | ||||||||
\(145\) | 8.27152 | 0.686912 | ||||||||
\(146\) | 11.2574 | 0.931669 | ||||||||
\(147\) | 0.0847393 | 0.00698918 | ||||||||
\(148\) | 19.2037 | 1.57854 | ||||||||
\(149\) | −4.03799 | −0.330805 | −0.165403 | − | 0.986226i | \(-0.552892\pi\) | ||||
−0.165403 | + | 0.986226i | \(0.552892\pi\) | |||||||
\(150\) | 5.56159 | 0.454102 | ||||||||
\(151\) | −20.5812 | −1.67487 | −0.837436 | − | 0.546535i | \(-0.815946\pi\) | ||||
−0.837436 | + | 0.546535i | \(0.815946\pi\) | |||||||
\(152\) | −58.4673 | −4.74232 | ||||||||
\(153\) | −1.46235 | −0.118224 | ||||||||
\(154\) | −15.9991 | −1.28924 | ||||||||
\(155\) | −2.43341 | −0.195456 | ||||||||
\(156\) | −3.43436 | −0.274969 | ||||||||
\(157\) | −4.67486 | −0.373094 | −0.186547 | − | 0.982446i | \(-0.559730\pi\) | ||||
−0.186547 | + | 0.982446i | \(0.559730\pi\) | |||||||
\(158\) | 12.6657 | 1.00763 | ||||||||
\(159\) | 2.41294 | 0.191359 | ||||||||
\(160\) | 67.8851 | 5.36679 | ||||||||
\(161\) | 22.7728 | 1.79475 | ||||||||
\(162\) | −23.1482 | −1.81869 | ||||||||
\(163\) | 22.8843 | 1.79243 | 0.896217 | − | 0.443615i | \(-0.146304\pi\) | ||||
0.896217 | + | 0.443615i | \(0.146304\pi\) | |||||||
\(164\) | 48.1848 | 3.76260 | ||||||||
\(165\) | 1.88411 | 0.146678 | ||||||||
\(166\) | −0.331799 | −0.0257526 | ||||||||
\(167\) | 12.4072 | 0.960096 | 0.480048 | − | 0.877242i | \(-0.340619\pi\) | ||||
0.480048 | + | 0.877242i | \(0.340619\pi\) | |||||||
\(168\) | 4.77446 | 0.368357 | ||||||||
\(169\) | −3.50741 | −0.269801 | ||||||||
\(170\) | 5.11440 | 0.392257 | ||||||||
\(171\) | −19.7356 | −1.50922 | ||||||||
\(172\) | 41.0569 | 3.13056 | ||||||||
\(173\) | 13.3188 | 1.01261 | 0.506303 | − | 0.862356i | \(-0.331012\pi\) | ||||
0.506303 | + | 0.862356i | \(0.331012\pi\) | |||||||
\(174\) | −1.23198 | −0.0933965 | ||||||||
\(175\) | 24.9969 | 1.88958 | ||||||||
\(176\) | 30.2271 | 2.27846 | ||||||||
\(177\) | 0.312704 | 0.0235043 | ||||||||
\(178\) | −7.11080 | −0.532977 | ||||||||
\(179\) | 5.09849 | 0.381079 | 0.190540 | − | 0.981680i | \(-0.438976\pi\) | ||||
0.190540 | + | 0.981680i | \(0.438976\pi\) | |||||||
\(180\) | 59.5497 | 4.43857 | ||||||||
\(181\) | 18.9132 | 1.40580 | 0.702902 | − | 0.711286i | \(-0.251887\pi\) | ||||
0.702902 | + | 0.711286i | \(0.251887\pi\) | |||||||
\(182\) | −21.3152 | −1.57999 | ||||||||
\(183\) | 0.903497 | 0.0667884 | ||||||||
\(184\) | −77.5940 | −5.72030 | ||||||||
\(185\) | −14.0359 | −1.03194 | ||||||||
\(186\) | 0.362439 | 0.0265753 | ||||||||
\(187\) | 1.14447 | 0.0836916 | ||||||||
\(188\) | −35.8343 | −2.61349 | ||||||||
\(189\) | 3.24781 | 0.236244 | ||||||||
\(190\) | 69.0229 | 5.00745 | ||||||||
\(191\) | −22.0090 | −1.59252 | −0.796259 | − | 0.604955i | \(-0.793191\pi\) | ||||
−0.796259 | + | 0.604955i | \(0.793191\pi\) | |||||||
\(192\) | −4.56164 | −0.329208 | ||||||||
\(193\) | −9.42002 | −0.678068 | −0.339034 | − | 0.940774i | \(-0.610100\pi\) | ||||
−0.339034 | + | 0.940774i | \(0.610100\pi\) | |||||||
\(194\) | 48.6561 | 3.49330 | ||||||||
\(195\) | 2.51015 | 0.179756 | ||||||||
\(196\) | −2.09609 | −0.149720 | ||||||||
\(197\) | 0.134865 | 0.00960876 | 0.00480438 | − | 0.999988i | \(-0.498471\pi\) | ||||
0.00480438 | + | 0.999988i | \(0.498471\pi\) | |||||||
\(198\) | 18.4011 | 1.30771 | ||||||||
\(199\) | −23.5042 | −1.66617 | −0.833084 | − | 0.553147i | \(-0.813427\pi\) | ||||
−0.833084 | + | 0.553147i | \(0.813427\pi\) | |||||||
\(200\) | −85.1719 | −6.02256 | ||||||||
\(201\) | 0.578952 | 0.0408361 | ||||||||
\(202\) | −18.8584 | −1.32687 | ||||||||
\(203\) | −5.53722 | −0.388636 | ||||||||
\(204\) | −0.551643 | −0.0386228 | ||||||||
\(205\) | −35.2179 | −2.45973 | ||||||||
\(206\) | −4.30804 | −0.300155 | ||||||||
\(207\) | −26.1918 | −1.82046 | ||||||||
\(208\) | 40.2709 | 2.79228 | ||||||||
\(209\) | 15.4455 | 1.06839 | ||||||||
\(210\) | −5.63643 | −0.388951 | ||||||||
\(211\) | −15.3602 | −1.05744 | −0.528722 | − | 0.848795i | \(-0.677328\pi\) | ||||
−0.528722 | + | 0.848795i | \(0.677328\pi\) | |||||||
\(212\) | −59.6857 | −4.09923 | ||||||||
\(213\) | −2.60402 | −0.178424 | ||||||||
\(214\) | −31.6329 | −2.16238 | ||||||||
\(215\) | −30.0082 | −2.04654 | ||||||||
\(216\) | −11.0663 | −0.752966 | ||||||||
\(217\) | 1.62900 | 0.110584 | ||||||||
\(218\) | 28.5244 | 1.93191 | ||||||||
\(219\) | 0.887473 | 0.0599699 | ||||||||
\(220\) | −46.6047 | −3.14209 | ||||||||
\(221\) | 1.52474 | 0.102565 | ||||||||
\(222\) | 2.09054 | 0.140308 | ||||||||
\(223\) | 17.8160 | 1.19305 | 0.596523 | − | 0.802596i | \(-0.296548\pi\) | ||||
0.596523 | + | 0.802596i | \(0.296548\pi\) | |||||||
\(224\) | −45.4444 | −3.03638 | ||||||||
\(225\) | −28.7498 | −1.91665 | ||||||||
\(226\) | −46.9283 | −3.12162 | ||||||||
\(227\) | −8.74547 | −0.580458 | −0.290229 | − | 0.956957i | \(-0.593731\pi\) | ||||
−0.290229 | + | 0.956957i | \(0.593731\pi\) | |||||||
\(228\) | −7.44486 | −0.493048 | ||||||||
\(229\) | 20.0980 | 1.32811 | 0.664057 | − | 0.747682i | \(-0.268833\pi\) | ||||
0.664057 | + | 0.747682i | \(0.268833\pi\) | |||||||
\(230\) | 91.6027 | 6.04011 | ||||||||
\(231\) | −1.26128 | −0.0829862 | ||||||||
\(232\) | 18.8670 | 1.23868 | ||||||||
\(233\) | −2.66778 | −0.174772 | −0.0873861 | − | 0.996175i | \(-0.527851\pi\) | ||||
−0.0873861 | + | 0.996175i | \(0.527851\pi\) | |||||||
\(234\) | 24.5154 | 1.60262 | ||||||||
\(235\) | 26.1910 | 1.70851 | ||||||||
\(236\) | −7.73496 | −0.503503 | ||||||||
\(237\) | 0.998499 | 0.0648595 | ||||||||
\(238\) | −3.42374 | −0.221928 | ||||||||
\(239\) | −3.37713 | −0.218448 | −0.109224 | − | 0.994017i | \(-0.534837\pi\) | ||||
−0.109224 | + | 0.994017i | \(0.534837\pi\) | |||||||
\(240\) | 10.6489 | 0.687386 | ||||||||
\(241\) | 18.0039 | 1.15973 | 0.579865 | − | 0.814712i | \(-0.303105\pi\) | ||||
0.579865 | + | 0.814712i | \(0.303105\pi\) | |||||||
\(242\) | 15.2193 | 0.978335 | ||||||||
\(243\) | −5.61727 | −0.360348 | ||||||||
\(244\) | −22.3486 | −1.43072 | ||||||||
\(245\) | 1.53201 | 0.0978767 | ||||||||
\(246\) | 5.24546 | 0.334438 | ||||||||
\(247\) | 20.5776 | 1.30932 | ||||||||
\(248\) | −5.55050 | −0.352457 | ||||||||
\(249\) | −0.0261572 | −0.00165765 | ||||||||
\(250\) | 48.8762 | 3.09120 | ||||||||
\(251\) | −17.3166 | −1.09301 | −0.546506 | − | 0.837455i | \(-0.684042\pi\) | ||||
−0.546506 | + | 0.837455i | \(0.684042\pi\) | |||||||
\(252\) | −39.8645 | −2.51123 | ||||||||
\(253\) | 20.4982 | 1.28871 | ||||||||
\(254\) | 6.52512 | 0.409422 | ||||||||
\(255\) | 0.403192 | 0.0252489 | ||||||||
\(256\) | 17.5756 | 1.09847 | ||||||||
\(257\) | 2.99678 | 0.186934 | 0.0934671 | − | 0.995622i | \(-0.470205\pi\) | ||||
0.0934671 | + | 0.995622i | \(0.470205\pi\) | |||||||
\(258\) | 4.46951 | 0.278260 | ||||||||
\(259\) | 9.39606 | 0.583843 | ||||||||
\(260\) | −62.0903 | −3.85068 | ||||||||
\(261\) | 6.36855 | 0.394203 | ||||||||
\(262\) | −3.32484 | −0.205410 | ||||||||
\(263\) | 2.80380 | 0.172890 | 0.0864448 | − | 0.996257i | \(-0.472449\pi\) | ||||
0.0864448 | + | 0.996257i | \(0.472449\pi\) | |||||||
\(264\) | 4.29757 | 0.264497 | ||||||||
\(265\) | 43.6239 | 2.67979 | ||||||||
\(266\) | −46.2061 | −2.83308 | ||||||||
\(267\) | −0.560577 | −0.0343068 | ||||||||
\(268\) | −14.3208 | −0.874781 | ||||||||
\(269\) | 7.41569 | 0.452143 | 0.226071 | − | 0.974111i | \(-0.427412\pi\) | ||||
0.226071 | + | 0.974111i | \(0.427412\pi\) | |||||||
\(270\) | 13.0642 | 0.795061 | ||||||||
\(271\) | −26.7479 | −1.62482 | −0.812410 | − | 0.583087i | \(-0.801845\pi\) | ||||
−0.812410 | + | 0.583087i | \(0.801845\pi\) | |||||||
\(272\) | 6.46849 | 0.392210 | ||||||||
\(273\) | −1.68037 | −0.101701 | ||||||||
\(274\) | −32.1536 | −1.94247 | ||||||||
\(275\) | 22.5001 | 1.35681 | ||||||||
\(276\) | −9.88034 | −0.594727 | ||||||||
\(277\) | 3.99925 | 0.240292 | 0.120146 | − | 0.992756i | \(-0.461664\pi\) | ||||
0.120146 | + | 0.992756i | \(0.461664\pi\) | |||||||
\(278\) | −27.3160 | −1.63830 | ||||||||
\(279\) | −1.87357 | −0.112168 | ||||||||
\(280\) | 86.3181 | 5.15849 | ||||||||
\(281\) | 0.114544 | 0.00683314 | 0.00341657 | − | 0.999994i | \(-0.498912\pi\) | ||||
0.00341657 | + | 0.999994i | \(0.498912\pi\) | |||||||
\(282\) | −3.90097 | −0.232299 | ||||||||
\(283\) | −18.4299 | −1.09555 | −0.547773 | − | 0.836627i | \(-0.684524\pi\) | ||||
−0.547773 | + | 0.836627i | \(0.684524\pi\) | |||||||
\(284\) | 64.4122 | 3.82216 | ||||||||
\(285\) | 5.44140 | 0.322321 | ||||||||
\(286\) | −19.1862 | −1.13450 | ||||||||
\(287\) | 23.5760 | 1.39165 | ||||||||
\(288\) | 52.2673 | 3.07988 | ||||||||
\(289\) | −16.7551 | −0.985593 | ||||||||
\(290\) | −22.2732 | −1.30793 | ||||||||
\(291\) | 3.83578 | 0.224858 | ||||||||
\(292\) | −21.9523 | −1.28466 | ||||||||
\(293\) | 8.03920 | 0.469655 | 0.234827 | − | 0.972037i | \(-0.424547\pi\) | ||||
0.234827 | + | 0.972037i | \(0.424547\pi\) | |||||||
\(294\) | −0.228183 | −0.0133079 | ||||||||
\(295\) | 5.65342 | 0.329155 | ||||||||
\(296\) | −32.0152 | −1.86085 | ||||||||
\(297\) | 2.92341 | 0.169634 | ||||||||
\(298\) | 10.8733 | 0.629876 | ||||||||
\(299\) | 27.3093 | 1.57934 | ||||||||
\(300\) | −10.8453 | −0.626152 | ||||||||
\(301\) | 20.0885 | 1.15788 | ||||||||
\(302\) | 55.4202 | 3.18907 | ||||||||
\(303\) | −1.48669 | −0.0854082 | ||||||||
\(304\) | 87.2975 | 5.00685 | ||||||||
\(305\) | 16.3344 | 0.935307 | ||||||||
\(306\) | 3.93777 | 0.225107 | ||||||||
\(307\) | −5.15724 | −0.294339 | −0.147169 | − | 0.989111i | \(-0.547016\pi\) | ||||
−0.147169 | + | 0.989111i | \(0.547016\pi\) | |||||||
\(308\) | 31.1987 | 1.77771 | ||||||||
\(309\) | −0.339623 | −0.0193204 | ||||||||
\(310\) | 6.55259 | 0.372162 | ||||||||
\(311\) | 3.61155 | 0.204792 | 0.102396 | − | 0.994744i | \(-0.467349\pi\) | ||||
0.102396 | + | 0.994744i | \(0.467349\pi\) | |||||||
\(312\) | 5.72555 | 0.324145 | ||||||||
\(313\) | 26.2965 | 1.48637 | 0.743184 | − | 0.669087i | \(-0.233315\pi\) | ||||
0.743184 | + | 0.669087i | \(0.233315\pi\) | |||||||
\(314\) | 12.5883 | 0.710397 | ||||||||
\(315\) | 29.1367 | 1.64166 | ||||||||
\(316\) | −24.6986 | −1.38940 | ||||||||
\(317\) | −31.9969 | −1.79712 | −0.898562 | − | 0.438847i | \(-0.855387\pi\) | ||||
−0.898562 | + | 0.438847i | \(0.855387\pi\) | |||||||
\(318\) | −6.49747 | −0.364360 | ||||||||
\(319\) | −4.98415 | −0.279059 | ||||||||
\(320\) | −82.4706 | −4.61024 | ||||||||
\(321\) | −2.49377 | −0.139189 | ||||||||
\(322\) | −61.3218 | −3.41733 | ||||||||
\(323\) | 3.30527 | 0.183910 | ||||||||
\(324\) | 45.1397 | 2.50776 | ||||||||
\(325\) | 29.9763 | 1.66279 | ||||||||
\(326\) | −61.6219 | −3.41292 | ||||||||
\(327\) | 2.24871 | 0.124354 | ||||||||
\(328\) | −80.3306 | −4.43552 | ||||||||
\(329\) | −17.5331 | −0.966631 | ||||||||
\(330\) | −5.07345 | −0.279284 | ||||||||
\(331\) | −8.79971 | −0.483676 | −0.241838 | − | 0.970317i | \(-0.577750\pi\) | ||||
−0.241838 | + | 0.970317i | \(0.577750\pi\) | |||||||
\(332\) | 0.647018 | 0.0355097 | ||||||||
\(333\) | −10.8067 | −0.592206 | ||||||||
\(334\) | −33.4096 | −1.82809 | ||||||||
\(335\) | 10.4670 | 0.571871 | ||||||||
\(336\) | −7.12874 | −0.388904 | ||||||||
\(337\) | 32.3009 | 1.75954 | 0.879771 | − | 0.475398i | \(-0.157696\pi\) | ||||
0.879771 | + | 0.475398i | \(0.157696\pi\) | |||||||
\(338\) | 9.44463 | 0.513720 | ||||||||
\(339\) | −3.69957 | −0.200933 | ||||||||
\(340\) | −9.97324 | −0.540875 | ||||||||
\(341\) | 1.46629 | 0.0794042 | ||||||||
\(342\) | 53.1433 | 2.87366 | ||||||||
\(343\) | −19.0100 | −1.02644 | ||||||||
\(344\) | −68.4475 | −3.69044 | ||||||||
\(345\) | 7.22147 | 0.388791 | ||||||||
\(346\) | −35.8642 | −1.92807 | ||||||||
\(347\) | −19.8800 | −1.06721 | −0.533607 | − | 0.845732i | \(-0.679164\pi\) | ||||
−0.533607 | + | 0.845732i | \(0.679164\pi\) | |||||||
\(348\) | 2.40241 | 0.128782 | ||||||||
\(349\) | 27.4836 | 1.47116 | 0.735582 | − | 0.677436i | \(-0.236909\pi\) | ||||
0.735582 | + | 0.677436i | \(0.236909\pi\) | |||||||
\(350\) | −67.3106 | −3.59790 | ||||||||
\(351\) | 3.89479 | 0.207889 | ||||||||
\(352\) | −40.9053 | −2.18026 | ||||||||
\(353\) | 7.79486 | 0.414879 | 0.207439 | − | 0.978248i | \(-0.433487\pi\) | ||||
0.207439 | + | 0.978248i | \(0.433487\pi\) | |||||||
\(354\) | −0.842038 | −0.0447538 | ||||||||
\(355\) | −47.0784 | −2.49866 | ||||||||
\(356\) | 13.8663 | 0.734911 | ||||||||
\(357\) | −0.269910 | −0.0142851 | ||||||||
\(358\) | −13.7290 | −0.725601 | ||||||||
\(359\) | 1.36466 | 0.0720239 | 0.0360119 | − | 0.999351i | \(-0.488535\pi\) | ||||
0.0360119 | + | 0.999351i | \(0.488535\pi\) | |||||||
\(360\) | −99.2775 | −5.23238 | ||||||||
\(361\) | 25.6073 | 1.34775 | ||||||||
\(362\) | −50.9286 | −2.67675 | ||||||||
\(363\) | 1.19981 | 0.0629737 | ||||||||
\(364\) | 41.5652 | 2.17861 | ||||||||
\(365\) | 16.0447 | 0.839820 | ||||||||
\(366\) | −2.43290 | −0.127170 | ||||||||
\(367\) | 30.2734 | 1.58026 | 0.790128 | − | 0.612941i | \(-0.210014\pi\) | ||||
0.790128 | + | 0.612941i | \(0.210014\pi\) | |||||||
\(368\) | 115.855 | 6.03939 | ||||||||
\(369\) | −27.1156 | −1.41158 | ||||||||
\(370\) | 37.7952 | 1.96488 | ||||||||
\(371\) | −29.2032 | −1.51615 | ||||||||
\(372\) | −0.706767 | −0.0366442 | ||||||||
\(373\) | 30.9004 | 1.59996 | 0.799981 | − | 0.600025i | \(-0.204843\pi\) | ||||
0.799981 | + | 0.600025i | \(0.204843\pi\) | |||||||
\(374\) | −3.08177 | −0.159355 | ||||||||
\(375\) | 3.85314 | 0.198975 | ||||||||
\(376\) | 59.7407 | 3.08089 | ||||||||
\(377\) | −6.64026 | −0.341991 | ||||||||
\(378\) | −8.74558 | −0.449824 | ||||||||
\(379\) | −1.67349 | −0.0859616 | −0.0429808 | − | 0.999076i | \(-0.513685\pi\) | ||||
−0.0429808 | + | 0.999076i | \(0.513685\pi\) | |||||||
\(380\) | −134.597 | −6.90467 | ||||||||
\(381\) | 0.514405 | 0.0263538 | ||||||||
\(382\) | 59.2651 | 3.03227 | ||||||||
\(383\) | −11.5094 | −0.588105 | −0.294052 | − | 0.955789i | \(-0.595004\pi\) | ||||
−0.294052 | + | 0.955789i | \(0.595004\pi\) | |||||||
\(384\) | 4.77364 | 0.243604 | ||||||||
\(385\) | −22.8029 | −1.16214 | ||||||||
\(386\) | 25.3659 | 1.29109 | ||||||||
\(387\) | −23.1045 | −1.17447 | ||||||||
\(388\) | −94.8808 | −4.81684 | ||||||||
\(389\) | −28.6354 | −1.45187 | −0.725935 | − | 0.687763i | \(-0.758593\pi\) | ||||
−0.725935 | + | 0.687763i | \(0.758593\pi\) | |||||||
\(390\) | −6.75924 | −0.342267 | ||||||||
\(391\) | 4.38654 | 0.221837 | ||||||||
\(392\) | 3.49446 | 0.176497 | ||||||||
\(393\) | −0.262113 | −0.0132218 | ||||||||
\(394\) | −0.363160 | −0.0182957 | ||||||||
\(395\) | 18.0520 | 0.908295 | ||||||||
\(396\) | −35.8827 | −1.80317 | ||||||||
\(397\) | 3.64723 | 0.183049 | 0.0915245 | − | 0.995803i | \(-0.470826\pi\) | ||||
0.0915245 | + | 0.995803i | \(0.470826\pi\) | |||||||
\(398\) | 63.2912 | 3.17250 | ||||||||
\(399\) | −3.64264 | −0.182360 | ||||||||
\(400\) | 127.170 | 6.35851 | ||||||||
\(401\) | −6.52520 | −0.325853 | −0.162926 | − | 0.986638i | \(-0.552093\pi\) | ||||
−0.162926 | + | 0.986638i | \(0.552093\pi\) | |||||||
\(402\) | −1.55898 | −0.0777548 | ||||||||
\(403\) | 1.95351 | 0.0973110 | ||||||||
\(404\) | 36.7743 | 1.82959 | ||||||||
\(405\) | −32.9923 | −1.63940 | ||||||||
\(406\) | 14.9104 | 0.739991 | ||||||||
\(407\) | 8.45756 | 0.419225 | ||||||||
\(408\) | 0.919664 | 0.0455302 | ||||||||
\(409\) | −32.6804 | −1.61594 | −0.807970 | − | 0.589223i | \(-0.799434\pi\) | ||||
−0.807970 | + | 0.589223i | \(0.799434\pi\) | |||||||
\(410\) | 94.8334 | 4.68349 | ||||||||
\(411\) | −2.53482 | −0.125033 | ||||||||
\(412\) | 8.40080 | 0.413878 | ||||||||
\(413\) | −3.78458 | −0.186227 | ||||||||
\(414\) | 70.5284 | 3.46628 | ||||||||
\(415\) | −0.472901 | −0.0232138 | ||||||||
\(416\) | −54.4972 | −2.67194 | ||||||||
\(417\) | −2.15345 | −0.105455 | ||||||||
\(418\) | −41.5910 | −2.03428 | ||||||||
\(419\) | 6.02994 | 0.294582 | 0.147291 | − | 0.989093i | \(-0.452945\pi\) | ||||
0.147291 | + | 0.989093i | \(0.452945\pi\) | |||||||
\(420\) | 10.9912 | 0.536316 | ||||||||
\(421\) | 17.1353 | 0.835125 | 0.417562 | − | 0.908648i | \(-0.362885\pi\) | ||||
0.417562 | + | 0.908648i | \(0.362885\pi\) | |||||||
\(422\) | 41.3615 | 2.01345 | ||||||||
\(423\) | 20.1655 | 0.980478 | ||||||||
\(424\) | 99.5042 | 4.83235 | ||||||||
\(425\) | 4.81494 | 0.233559 | ||||||||
\(426\) | 7.01200 | 0.339733 | ||||||||
\(427\) | −10.9348 | −0.529172 | ||||||||
\(428\) | 61.6851 | 2.98166 | ||||||||
\(429\) | −1.51253 | −0.0730259 | ||||||||
\(430\) | 80.8050 | 3.89676 | ||||||||
\(431\) | −26.1267 | −1.25848 | −0.629241 | − | 0.777211i | \(-0.716634\pi\) | ||||
−0.629241 | + | 0.777211i | \(0.716634\pi\) | |||||||
\(432\) | 16.5231 | 0.794967 | ||||||||
\(433\) | 11.5088 | 0.553078 | 0.276539 | − | 0.961003i | \(-0.410812\pi\) | ||||
0.276539 | + | 0.961003i | \(0.410812\pi\) | |||||||
\(434\) | −4.38651 | −0.210559 | ||||||||
\(435\) | −1.75590 | −0.0841890 | ||||||||
\(436\) | −55.6233 | −2.66387 | ||||||||
\(437\) | 59.1999 | 2.83191 | ||||||||
\(438\) | −2.38975 | −0.114187 | ||||||||
\(439\) | 29.8291 | 1.42367 | 0.711833 | − | 0.702349i | \(-0.247865\pi\) | ||||
0.711833 | + | 0.702349i | \(0.247865\pi\) | |||||||
\(440\) | 77.6964 | 3.70403 | ||||||||
\(441\) | 1.17955 | 0.0561692 | ||||||||
\(442\) | −4.10577 | −0.195292 | ||||||||
\(443\) | 31.6635 | 1.50438 | 0.752188 | − | 0.658948i | \(-0.228998\pi\) | ||||
0.752188 | + | 0.658948i | \(0.228998\pi\) | |||||||
\(444\) | −4.07662 | −0.193468 | ||||||||
\(445\) | −10.1348 | −0.480434 | ||||||||
\(446\) | −47.9742 | −2.27164 | ||||||||
\(447\) | 0.857196 | 0.0405440 | ||||||||
\(448\) | 55.2084 | 2.60835 | ||||||||
\(449\) | 32.0724 | 1.51359 | 0.756794 | − | 0.653653i | \(-0.226764\pi\) | ||||
0.756794 | + | 0.653653i | \(0.226764\pi\) | |||||||
\(450\) | 77.4163 | 3.64944 | ||||||||
\(451\) | 21.2212 | 0.999265 | ||||||||
\(452\) | 91.5115 | 4.30434 | ||||||||
\(453\) | 4.36903 | 0.205275 | ||||||||
\(454\) | 23.5495 | 1.10523 | ||||||||
\(455\) | −30.3797 | −1.42422 | ||||||||
\(456\) | 12.4116 | 0.581226 | ||||||||
\(457\) | 22.3672 | 1.04629 | 0.523147 | − | 0.852242i | \(-0.324758\pi\) | ||||
0.523147 | + | 0.852242i | \(0.324758\pi\) | |||||||
\(458\) | −54.1192 | −2.52882 | ||||||||
\(459\) | 0.625599 | 0.0292005 | ||||||||
\(460\) | −178.628 | −8.32857 | ||||||||
\(461\) | 31.6791 | 1.47544 | 0.737721 | − | 0.675105i | \(-0.235902\pi\) | ||||
0.737721 | + | 0.675105i | \(0.235902\pi\) | |||||||
\(462\) | 3.39633 | 0.158012 | ||||||||
\(463\) | 15.7833 | 0.733510 | 0.366755 | − | 0.930318i | \(-0.380469\pi\) | ||||
0.366755 | + | 0.930318i | \(0.380469\pi\) | |||||||
\(464\) | −28.1703 | −1.30777 | ||||||||
\(465\) | 0.516571 | 0.0239554 | ||||||||
\(466\) | 7.18370 | 0.332778 | ||||||||
\(467\) | 42.9220 | 1.98619 | 0.993097 | − | 0.117300i | \(-0.0374239\pi\) | ||||
0.993097 | + | 0.117300i | \(0.0374239\pi\) | |||||||
\(468\) | −47.8057 | −2.20982 | ||||||||
\(469\) | −7.00691 | −0.323549 | ||||||||
\(470\) | −70.5262 | −3.25313 | ||||||||
\(471\) | 0.992392 | 0.0457270 | ||||||||
\(472\) | 12.8952 | 0.593551 | ||||||||
\(473\) | 18.0820 | 0.831410 | ||||||||
\(474\) | −2.68872 | −0.123497 | ||||||||
\(475\) | 64.9814 | 2.98155 | ||||||||
\(476\) | 6.67640 | 0.306012 | ||||||||
\(477\) | 33.5876 | 1.53787 | ||||||||
\(478\) | 9.09381 | 0.415941 | ||||||||
\(479\) | −24.0204 | −1.09752 | −0.548760 | − | 0.835980i | \(-0.684900\pi\) | ||||
−0.548760 | + | 0.835980i | \(0.684900\pi\) | |||||||
\(480\) | −14.4108 | −0.657762 | ||||||||
\(481\) | 11.2678 | 0.513767 | ||||||||
\(482\) | −48.4801 | −2.20821 | ||||||||
\(483\) | −4.83428 | −0.219967 | ||||||||
\(484\) | −29.6781 | −1.34901 | ||||||||
\(485\) | 69.3477 | 3.14892 | ||||||||
\(486\) | 15.1260 | 0.686128 | ||||||||
\(487\) | 7.47270 | 0.338620 | 0.169310 | − | 0.985563i | \(-0.445846\pi\) | ||||
0.169310 | + | 0.985563i | \(0.445846\pi\) | |||||||
\(488\) | 37.2582 | 1.68660 | ||||||||
\(489\) | −4.85794 | −0.219684 | ||||||||
\(490\) | −4.12535 | −0.186364 | ||||||||
\(491\) | 11.5032 | 0.519132 | 0.259566 | − | 0.965725i | \(-0.416421\pi\) | ||||
0.259566 | + | 0.965725i | \(0.416421\pi\) | |||||||
\(492\) | −10.2288 | −0.461150 | ||||||||
\(493\) | −1.06659 | −0.0480367 | ||||||||
\(494\) | −55.4106 | −2.49304 | ||||||||
\(495\) | 26.2264 | 1.17879 | ||||||||
\(496\) | 8.28745 | 0.372118 | ||||||||
\(497\) | 31.5158 | 1.41368 | ||||||||
\(498\) | 0.0704352 | 0.00315628 | ||||||||
\(499\) | −27.1099 | −1.21361 | −0.606804 | − | 0.794852i | \(-0.707549\pi\) | ||||
−0.606804 | + | 0.794852i | \(0.707549\pi\) | |||||||
\(500\) | −95.3100 | −4.26239 | ||||||||
\(501\) | −2.63383 | −0.117671 | ||||||||
\(502\) | 46.6294 | 2.08117 | ||||||||
\(503\) | −21.8364 | −0.973637 | −0.486819 | − | 0.873503i | \(-0.661843\pi\) | ||||
−0.486819 | + | 0.873503i | \(0.661843\pi\) | |||||||
\(504\) | 66.4595 | 2.96034 | ||||||||
\(505\) | −26.8781 | −1.19606 | ||||||||
\(506\) | −55.1968 | −2.45380 | ||||||||
\(507\) | 0.744564 | 0.0330672 | ||||||||
\(508\) | −12.7242 | −0.564544 | ||||||||
\(509\) | −6.85343 | −0.303773 | −0.151886 | − | 0.988398i | \(-0.548535\pi\) | ||||
−0.151886 | + | 0.988398i | \(0.548535\pi\) | |||||||
\(510\) | −1.08570 | −0.0480756 | ||||||||
\(511\) | −10.7409 | −0.475148 | ||||||||
\(512\) | −2.35252 | −0.103968 | ||||||||
\(513\) | 8.44296 | 0.372766 | ||||||||
\(514\) | −8.06962 | −0.355936 | ||||||||
\(515\) | −6.14008 | −0.270564 | ||||||||
\(516\) | −8.71569 | −0.383687 | ||||||||
\(517\) | −15.7819 | −0.694085 | ||||||||
\(518\) | −25.3013 | −1.11168 | ||||||||
\(519\) | −2.82734 | −0.124107 | ||||||||
\(520\) | 103.513 | 4.53935 | ||||||||
\(521\) | 17.0675 | 0.747740 | 0.373870 | − | 0.927481i | \(-0.378031\pi\) | ||||
0.373870 | + | 0.927481i | \(0.378031\pi\) | |||||||
\(522\) | −17.1490 | −0.750591 | ||||||||
\(523\) | 6.49693 | 0.284091 | 0.142045 | − | 0.989860i | \(-0.454632\pi\) | ||||
0.142045 | + | 0.989860i | \(0.454632\pi\) | |||||||
\(524\) | 6.48354 | 0.283235 | ||||||||
\(525\) | −5.30640 | −0.231590 | ||||||||
\(526\) | −7.54996 | −0.329194 | ||||||||
\(527\) | 0.313781 | 0.0136685 | ||||||||
\(528\) | −6.41670 | −0.279251 | ||||||||
\(529\) | 55.5662 | 2.41592 | ||||||||
\(530\) | −117.469 | −5.10251 | ||||||||
\(531\) | 4.35278 | 0.188895 | ||||||||
\(532\) | 90.1033 | 3.90647 | ||||||||
\(533\) | 28.2724 | 1.22462 | ||||||||
\(534\) | 1.50950 | 0.0653225 | ||||||||
\(535\) | −45.0852 | −1.94920 | ||||||||
\(536\) | 23.8747 | 1.03123 | ||||||||
\(537\) | −1.08232 | −0.0467056 | ||||||||
\(538\) | −19.9687 | −0.860911 | ||||||||
\(539\) | −0.923141 | −0.0397625 | ||||||||
\(540\) | −25.4756 | −1.09629 | ||||||||
\(541\) | 40.2835 | 1.73192 | 0.865961 | − | 0.500111i | \(-0.166708\pi\) | ||||
0.865961 | + | 0.500111i | \(0.166708\pi\) | |||||||
\(542\) | 72.0257 | 3.09377 | ||||||||
\(543\) | −4.01494 | −0.172298 | ||||||||
\(544\) | −8.75359 | −0.375307 | ||||||||
\(545\) | 40.6547 | 1.74146 | ||||||||
\(546\) | 4.52485 | 0.193646 | ||||||||
\(547\) | 28.5300 | 1.21986 | 0.609928 | − | 0.792457i | \(-0.291198\pi\) | ||||
0.609928 | + | 0.792457i | \(0.291198\pi\) | |||||||
\(548\) | 62.7005 | 2.67843 | ||||||||
\(549\) | 12.5765 | 0.536752 | ||||||||
\(550\) | −60.5874 | −2.58346 | ||||||||
\(551\) | −14.3945 | −0.613225 | ||||||||
\(552\) | 16.4719 | 0.701089 | ||||||||
\(553\) | −12.0846 | −0.513889 | ||||||||
\(554\) | −10.7690 | −0.457533 | ||||||||
\(555\) | 2.97957 | 0.126476 | ||||||||
\(556\) | 53.2670 | 2.25902 | ||||||||
\(557\) | −36.9379 | −1.56511 | −0.782555 | − | 0.622582i | \(-0.786084\pi\) | ||||
−0.782555 | + | 0.622582i | \(0.786084\pi\) | |||||||
\(558\) | 5.04508 | 0.213575 | ||||||||
\(559\) | 24.0902 | 1.01891 | ||||||||
\(560\) | −128.881 | −5.44623 | ||||||||
\(561\) | −0.242950 | −0.0102574 | ||||||||
\(562\) | −0.308440 | −0.0130108 | ||||||||
\(563\) | −23.5729 | −0.993478 | −0.496739 | − | 0.867900i | \(-0.665469\pi\) | ||||
−0.496739 | + | 0.867900i | \(0.665469\pi\) | |||||||
\(564\) | 7.60701 | 0.320313 | ||||||||
\(565\) | −66.8851 | −2.81388 | ||||||||
\(566\) | 49.6275 | 2.08600 | ||||||||
\(567\) | 22.0861 | 0.927527 | ||||||||
\(568\) | −107.384 | −4.50573 | ||||||||
\(569\) | −21.7507 | −0.911838 | −0.455919 | − | 0.890021i | \(-0.650689\pi\) | ||||
−0.455919 | + | 0.890021i | \(0.650689\pi\) | |||||||
\(570\) | −14.6524 | −0.613721 | ||||||||
\(571\) | 18.4990 | 0.774158 | 0.387079 | − | 0.922047i | \(-0.373484\pi\) | ||||
0.387079 | + | 0.922047i | \(0.373484\pi\) | |||||||
\(572\) | 37.4136 | 1.56434 | ||||||||
\(573\) | 4.67214 | 0.195182 | ||||||||
\(574\) | −63.4845 | −2.64979 | ||||||||
\(575\) | 86.2391 | 3.59642 | ||||||||
\(576\) | −63.4972 | −2.64572 | ||||||||
\(577\) | −34.6022 | −1.44051 | −0.720255 | − | 0.693709i | \(-0.755975\pi\) | ||||
−0.720255 | + | 0.693709i | \(0.755975\pi\) | |||||||
\(578\) | 45.1175 | 1.87664 | ||||||||
\(579\) | 1.99971 | 0.0831050 | ||||||||
\(580\) | 43.4334 | 1.80348 | ||||||||
\(581\) | 0.316575 | 0.0131337 | ||||||||
\(582\) | −10.3288 | −0.428145 | ||||||||
\(583\) | −26.2863 | −1.08867 | ||||||||
\(584\) | 36.5974 | 1.51441 | ||||||||
\(585\) | 34.9408 | 1.44462 | ||||||||
\(586\) | −21.6476 | −0.894256 | ||||||||
\(587\) | 35.8441 | 1.47945 | 0.739723 | − | 0.672911i | \(-0.234956\pi\) | ||||
0.739723 | + | 0.672911i | \(0.234956\pi\) | |||||||
\(588\) | 0.444963 | 0.0183500 | ||||||||
\(589\) | 4.23472 | 0.174489 | ||||||||
\(590\) | −15.2233 | −0.626734 | ||||||||
\(591\) | −0.0286296 | −0.00117766 | ||||||||
\(592\) | 47.8019 | 1.96465 | ||||||||
\(593\) | 6.29377 | 0.258454 | 0.129227 | − | 0.991615i | \(-0.458750\pi\) | ||||
0.129227 | + | 0.991615i | \(0.458750\pi\) | |||||||
\(594\) | −7.87205 | −0.322994 | ||||||||
\(595\) | −4.87973 | −0.200050 | ||||||||
\(596\) | −21.2033 | −0.868523 | ||||||||
\(597\) | 4.98953 | 0.204208 | ||||||||
\(598\) | −73.5374 | −3.00717 | ||||||||
\(599\) | 12.0416 | 0.492007 | 0.246004 | − | 0.969269i | \(-0.420882\pi\) | ||||
0.246004 | + | 0.969269i | \(0.420882\pi\) | |||||||
\(600\) | 18.0805 | 0.738135 | ||||||||
\(601\) | −11.8147 | −0.481930 | −0.240965 | − | 0.970534i | \(-0.577464\pi\) | ||||
−0.240965 | + | 0.970534i | \(0.577464\pi\) | |||||||
\(602\) | −54.0934 | −2.20468 | ||||||||
\(603\) | 8.05890 | 0.328184 | ||||||||
\(604\) | −108.071 | −4.39735 | ||||||||
\(605\) | 21.6915 | 0.881886 | ||||||||
\(606\) | 4.00330 | 0.162623 | ||||||||
\(607\) | 36.7972 | 1.49355 | 0.746777 | − | 0.665075i | \(-0.231600\pi\) | ||||
0.746777 | + | 0.665075i | \(0.231600\pi\) | |||||||
\(608\) | −118.137 | −4.79107 | ||||||||
\(609\) | 1.17546 | 0.0476319 | ||||||||
\(610\) | −43.9848 | −1.78089 | ||||||||
\(611\) | −21.0258 | −0.850612 | ||||||||
\(612\) | −7.67877 | −0.310396 | ||||||||
\(613\) | −28.9840 | −1.17065 | −0.585325 | − | 0.810798i | \(-0.699033\pi\) | ||||
−0.585325 | + | 0.810798i | \(0.699033\pi\) | |||||||
\(614\) | 13.8872 | 0.560442 | ||||||||
\(615\) | 7.47616 | 0.301468 | ||||||||
\(616\) | −52.0124 | −2.09564 | ||||||||
\(617\) | −18.3585 | −0.739085 | −0.369542 | − | 0.929214i | \(-0.620486\pi\) | ||||
−0.369542 | + | 0.929214i | \(0.620486\pi\) | |||||||
\(618\) | 0.914522 | 0.0367875 | ||||||||
\(619\) | −10.2532 | −0.412111 | −0.206056 | − | 0.978540i | \(-0.566063\pi\) | ||||
−0.206056 | + | 0.978540i | \(0.566063\pi\) | |||||||
\(620\) | −12.7777 | −0.513166 | ||||||||
\(621\) | 11.2049 | 0.449639 | ||||||||
\(622\) | −9.72504 | −0.389938 | ||||||||
\(623\) | 6.78453 | 0.271816 | ||||||||
\(624\) | −8.54881 | −0.342226 | ||||||||
\(625\) | 21.0143 | 0.840574 | ||||||||
\(626\) | −70.8103 | −2.83015 | ||||||||
\(627\) | −3.27881 | −0.130943 | ||||||||
\(628\) | −24.5475 | −0.979552 | ||||||||
\(629\) | 1.80989 | 0.0721649 | ||||||||
\(630\) | −78.4581 | −3.12584 | ||||||||
\(631\) | 24.1928 | 0.963101 | 0.481551 | − | 0.876418i | \(-0.340074\pi\) | ||||
0.481551 | + | 0.876418i | \(0.340074\pi\) | |||||||
\(632\) | 41.1759 | 1.63789 | ||||||||
\(633\) | 3.26072 | 0.129602 | ||||||||
\(634\) | 86.1600 | 3.42185 | ||||||||
\(635\) | 9.30000 | 0.369059 | ||||||||
\(636\) | 12.6703 | 0.502408 | ||||||||
\(637\) | −1.22988 | −0.0487295 | ||||||||
\(638\) | 13.4211 | 0.531347 | ||||||||
\(639\) | −36.2474 | −1.43393 | ||||||||
\(640\) | 86.3034 | 3.41144 | ||||||||
\(641\) | −19.7245 | −0.779069 | −0.389535 | − | 0.921012i | \(-0.627364\pi\) | ||||
−0.389535 | + | 0.921012i | \(0.627364\pi\) | |||||||
\(642\) | 6.71513 | 0.265025 | ||||||||
\(643\) | −13.1272 | −0.517685 | −0.258842 | − | 0.965920i | \(-0.583341\pi\) | ||||
−0.258842 | + | 0.965920i | \(0.583341\pi\) | |||||||
\(644\) | 119.579 | 4.71208 | ||||||||
\(645\) | 6.37023 | 0.250828 | ||||||||
\(646\) | −8.90031 | −0.350178 | ||||||||
\(647\) | −2.68577 | −0.105589 | −0.0527943 | − | 0.998605i | \(-0.516813\pi\) | ||||
−0.0527943 | + | 0.998605i | \(0.516813\pi\) | |||||||
\(648\) | −75.2540 | −2.95626 | ||||||||
\(649\) | −3.40657 | −0.133719 | ||||||||
\(650\) | −80.7191 | −3.16607 | ||||||||
\(651\) | −0.345809 | −0.0135533 | ||||||||
\(652\) | 120.165 | 4.70601 | ||||||||
\(653\) | 42.5622 | 1.66559 | 0.832793 | − | 0.553584i | \(-0.186740\pi\) | ||||
0.832793 | + | 0.553584i | \(0.186740\pi\) | |||||||
\(654\) | −6.05523 | −0.236778 | ||||||||
\(655\) | −4.73877 | −0.185159 | ||||||||
\(656\) | 119.942 | 4.68293 | ||||||||
\(657\) | 12.3535 | 0.481954 | ||||||||
\(658\) | 47.2125 | 1.84053 | ||||||||
\(659\) | −29.3377 | −1.14284 | −0.571418 | − | 0.820659i | \(-0.693606\pi\) | ||||
−0.571418 | + | 0.820659i | \(0.693606\pi\) | |||||||
\(660\) | 9.89338 | 0.385099 | ||||||||
\(661\) | 26.6044 | 1.03479 | 0.517396 | − | 0.855746i | \(-0.326901\pi\) | ||||
0.517396 | + | 0.855746i | \(0.326901\pi\) | |||||||
\(662\) | 23.6955 | 0.920953 | ||||||||
\(663\) | −0.323677 | −0.0125706 | ||||||||
\(664\) | −1.07867 | −0.0418604 | ||||||||
\(665\) | −65.8559 | −2.55378 | ||||||||
\(666\) | 29.1000 | 1.12760 | ||||||||
\(667\) | −19.1034 | −0.739686 | ||||||||
\(668\) | 65.1496 | 2.52072 | ||||||||
\(669\) | −3.78203 | −0.146222 | ||||||||
\(670\) | −28.1850 | −1.08888 | ||||||||
\(671\) | −9.84260 | −0.379969 | ||||||||
\(672\) | 9.64707 | 0.372144 | ||||||||
\(673\) | 27.3260 | 1.05334 | 0.526670 | − | 0.850070i | \(-0.323440\pi\) | ||||
0.526670 | + | 0.850070i | \(0.323440\pi\) | |||||||
\(674\) | −86.9786 | −3.35029 | ||||||||
\(675\) | 12.2992 | 0.473398 | ||||||||
\(676\) | −18.4173 | −0.708358 | ||||||||
\(677\) | 0.296493 | 0.0113951 | 0.00569757 | − | 0.999984i | \(-0.498186\pi\) | ||||
0.00569757 | + | 0.999984i | \(0.498186\pi\) | |||||||
\(678\) | 9.96207 | 0.382591 | ||||||||
\(679\) | −46.4235 | −1.78157 | ||||||||
\(680\) | 16.6267 | 0.637606 | ||||||||
\(681\) | 1.85651 | 0.0711418 | ||||||||
\(682\) | −3.94838 | −0.151191 | ||||||||
\(683\) | 31.6912 | 1.21263 | 0.606315 | − | 0.795225i | \(-0.292647\pi\) | ||||
0.606315 | + | 0.795225i | \(0.292647\pi\) | |||||||
\(684\) | −103.631 | −3.96243 | ||||||||
\(685\) | −45.8273 | −1.75097 | ||||||||
\(686\) | 51.1894 | 1.95442 | ||||||||
\(687\) | −4.26647 | −0.162776 | ||||||||
\(688\) | 102.199 | 3.89630 | ||||||||
\(689\) | −35.0206 | −1.33418 | ||||||||
\(690\) | −19.4457 | −0.740285 | ||||||||
\(691\) | 2.21915 | 0.0844205 | 0.0422103 | − | 0.999109i | \(-0.486560\pi\) | ||||
0.0422103 | + | 0.999109i | \(0.486560\pi\) | |||||||
\(692\) | 69.9363 | 2.65858 | ||||||||
\(693\) | −17.5568 | −0.666927 | ||||||||
\(694\) | 53.5321 | 2.03205 | ||||||||
\(695\) | −38.9325 | −1.47679 | ||||||||
\(696\) | −4.00514 | −0.151814 | ||||||||
\(697\) | 4.54125 | 0.172012 | ||||||||
\(698\) | −74.0068 | −2.80120 | ||||||||
\(699\) | 0.566324 | 0.0214203 | ||||||||
\(700\) | 131.258 | 4.96107 | ||||||||
\(701\) | −25.7608 | −0.972973 | −0.486487 | − | 0.873688i | \(-0.661722\pi\) | ||||
−0.486487 | + | 0.873688i | \(0.661722\pi\) | |||||||
\(702\) | −10.4877 | −0.395834 | ||||||||
\(703\) | 24.4258 | 0.921238 | ||||||||
\(704\) | 49.6941 | 1.87292 | ||||||||
\(705\) | −5.55991 | −0.209398 | ||||||||
\(706\) | −20.9897 | −0.789958 | ||||||||
\(707\) | 17.9930 | 0.676698 | ||||||||
\(708\) | 1.64200 | 0.0617101 | ||||||||
\(709\) | 5.41832 | 0.203489 | 0.101745 | − | 0.994811i | \(-0.467558\pi\) | ||||
0.101745 | + | 0.994811i | \(0.467558\pi\) | |||||||
\(710\) | 126.771 | 4.75763 | ||||||||
\(711\) | 13.8989 | 0.521250 | ||||||||
\(712\) | −23.1170 | −0.866345 | ||||||||
\(713\) | 5.62005 | 0.210473 | ||||||||
\(714\) | 0.726802 | 0.0271999 | ||||||||
\(715\) | −27.3453 | −1.02266 | ||||||||
\(716\) | 26.7720 | 1.00052 | ||||||||
\(717\) | 0.716907 | 0.0267734 | ||||||||
\(718\) | −3.67470 | −0.137139 | ||||||||
\(719\) | −0.452797 | −0.0168865 | −0.00844324 | − | 0.999964i | \(-0.502688\pi\) | ||||
−0.00844324 | + | 0.999964i | \(0.502688\pi\) | |||||||
\(720\) | 148.231 | 5.52425 | ||||||||
\(721\) | 4.11037 | 0.153078 | ||||||||
\(722\) | −68.9543 | −2.56621 | ||||||||
\(723\) | −3.82191 | −0.142138 | ||||||||
\(724\) | 99.3124 | 3.69091 | ||||||||
\(725\) | −20.9691 | −0.778771 | ||||||||
\(726\) | −3.23080 | −0.119906 | ||||||||
\(727\) | 36.8824 | 1.36789 | 0.683945 | − | 0.729533i | \(-0.260263\pi\) | ||||
0.683945 | + | 0.729533i | \(0.260263\pi\) | |||||||
\(728\) | −69.2949 | −2.56824 | ||||||||
\(729\) | −24.5969 | −0.910997 | ||||||||
\(730\) | −43.2047 | −1.59908 | ||||||||
\(731\) | 3.86947 | 0.143118 | ||||||||
\(732\) | 4.74423 | 0.175352 | ||||||||
\(733\) | −1.45650 | −0.0537969 | −0.0268984 | − | 0.999638i | \(-0.508563\pi\) | ||||
−0.0268984 | + | 0.999638i | \(0.508563\pi\) | |||||||
\(734\) | −81.5190 | −3.00892 | ||||||||
\(735\) | −0.325220 | −0.0119959 | ||||||||
\(736\) | −156.783 | −5.77911 | ||||||||
\(737\) | −6.30704 | −0.232323 | ||||||||
\(738\) | 73.0158 | 2.68775 | ||||||||
\(739\) | −21.7336 | −0.799484 | −0.399742 | − | 0.916628i | \(-0.630900\pi\) | ||||
−0.399742 | + | 0.916628i | \(0.630900\pi\) | |||||||
\(740\) | −73.7019 | −2.70933 | ||||||||
\(741\) | −4.36828 | −0.160473 | ||||||||
\(742\) | 78.6372 | 2.88686 | ||||||||
\(743\) | −22.9147 | −0.840660 | −0.420330 | − | 0.907371i | \(-0.638086\pi\) | ||||
−0.420330 | + | 0.907371i | \(0.638086\pi\) | |||||||
\(744\) | 1.17828 | 0.0431977 | ||||||||
\(745\) | 15.4974 | 0.567780 | ||||||||
\(746\) | −83.2074 | −3.04644 | ||||||||
\(747\) | −0.364104 | −0.0133219 | ||||||||
\(748\) | 6.00955 | 0.219731 | ||||||||
\(749\) | 30.1815 | 1.10281 | ||||||||
\(750\) | −10.3756 | −0.378862 | ||||||||
\(751\) | −27.2152 | −0.993096 | −0.496548 | − | 0.868009i | \(-0.665399\pi\) | ||||
−0.496548 | + | 0.868009i | \(0.665399\pi\) | |||||||
\(752\) | −89.1987 | −3.25274 | ||||||||
\(753\) | 3.67601 | 0.133961 | ||||||||
\(754\) | 17.8806 | 0.651174 | ||||||||
\(755\) | 78.9883 | 2.87468 | ||||||||
\(756\) | 17.0541 | 0.620253 | ||||||||
\(757\) | −35.8836 | −1.30421 | −0.652105 | − | 0.758129i | \(-0.726114\pi\) | ||||
−0.652105 | + | 0.758129i | \(0.726114\pi\) | |||||||
\(758\) | 4.50632 | 0.163677 | ||||||||
\(759\) | −4.35142 | −0.157947 | ||||||||
\(760\) | 224.391 | 8.13952 | ||||||||
\(761\) | −53.4913 | −1.93906 | −0.969529 | − | 0.244978i | \(-0.921219\pi\) | ||||
−0.969529 | + | 0.244978i | \(0.921219\pi\) | |||||||
\(762\) | −1.38517 | −0.0501794 | ||||||||
\(763\) | −27.2155 | −0.985268 | ||||||||
\(764\) | −115.569 | −4.18113 | ||||||||
\(765\) | 5.61235 | 0.202915 | ||||||||
\(766\) | 30.9922 | 1.11979 | ||||||||
\(767\) | −4.53849 | −0.163875 | ||||||||
\(768\) | −3.73100 | −0.134631 | ||||||||
\(769\) | −11.4276 | −0.412088 | −0.206044 | − | 0.978543i | \(-0.566059\pi\) | ||||
−0.206044 | + | 0.978543i | \(0.566059\pi\) | |||||||
\(770\) | 61.4027 | 2.21280 | ||||||||
\(771\) | −0.636165 | −0.0229109 | ||||||||
\(772\) | −49.4642 | −1.78025 | ||||||||
\(773\) | 19.2055 | 0.690774 | 0.345387 | − | 0.938460i | \(-0.387748\pi\) | ||||
0.345387 | + | 0.938460i | \(0.387748\pi\) | |||||||
\(774\) | 62.2148 | 2.23626 | ||||||||
\(775\) | 6.16892 | 0.221594 | ||||||||
\(776\) | 158.179 | 5.67830 | ||||||||
\(777\) | −1.99462 | −0.0715566 | ||||||||
\(778\) | 77.1082 | 2.76446 | ||||||||
\(779\) | 61.2878 | 2.19586 | ||||||||
\(780\) | 13.1807 | 0.471945 | ||||||||
\(781\) | 28.3679 | 1.01508 | ||||||||
\(782\) | −11.8119 | −0.422393 | ||||||||
\(783\) | −2.72449 | −0.0973652 | ||||||||
\(784\) | −5.21757 | −0.186342 | ||||||||
\(785\) | 17.9416 | 0.640363 | ||||||||
\(786\) | 0.705807 | 0.0251753 | ||||||||
\(787\) | −23.4461 | −0.835763 | −0.417882 | − | 0.908501i | \(-0.637227\pi\) | ||||
−0.417882 | + | 0.908501i | \(0.637227\pi\) | |||||||
\(788\) | 0.708173 | 0.0252276 | ||||||||
\(789\) | −0.595199 | −0.0211896 | ||||||||
\(790\) | −48.6097 | −1.72946 | ||||||||
\(791\) | 44.7750 | 1.59202 | ||||||||
\(792\) | 59.8214 | 2.12566 | ||||||||
\(793\) | −13.1131 | −0.465658 | ||||||||
\(794\) | −9.82111 | −0.348538 | ||||||||
\(795\) | −9.26060 | −0.328440 | ||||||||
\(796\) | −123.420 | −4.37449 | ||||||||
\(797\) | 7.75286 | 0.274620 | 0.137310 | − | 0.990528i | \(-0.456154\pi\) | ||||
0.137310 | + | 0.990528i | \(0.456154\pi\) | |||||||
\(798\) | 9.80877 | 0.347227 | ||||||||
\(799\) | −3.37726 | −0.119479 | ||||||||
\(800\) | −172.095 | −6.08448 | ||||||||
\(801\) | −7.80313 | −0.275710 | ||||||||
\(802\) | 17.5708 | 0.620446 | ||||||||
\(803\) | −9.66804 | −0.341178 | ||||||||
\(804\) | 3.04006 | 0.107215 | ||||||||
\(805\) | −87.3996 | −3.08043 | ||||||||
\(806\) | −5.26032 | −0.185287 | ||||||||
\(807\) | −1.57422 | −0.0554153 | ||||||||
\(808\) | −61.3078 | −2.15680 | ||||||||
\(809\) | 23.6375 | 0.831049 | 0.415525 | − | 0.909582i | \(-0.363598\pi\) | ||||
0.415525 | + | 0.909582i | \(0.363598\pi\) | |||||||
\(810\) | 88.8403 | 3.12153 | ||||||||
\(811\) | 16.1854 | 0.568346 | 0.284173 | − | 0.958773i | \(-0.408281\pi\) | ||||
0.284173 | + | 0.958773i | \(0.408281\pi\) | |||||||
\(812\) | −29.0757 | −1.02036 | ||||||||
\(813\) | 5.67812 | 0.199140 | ||||||||
\(814\) | −22.7742 | −0.798235 | ||||||||
\(815\) | −87.8274 | −3.07646 | ||||||||
\(816\) | −1.37315 | −0.0480699 | ||||||||
\(817\) | 52.2216 | 1.82700 | ||||||||
\(818\) | 88.0005 | 3.07686 | ||||||||
\(819\) | −23.3905 | −0.817330 | ||||||||
\(820\) | −184.928 | −6.45797 | ||||||||
\(821\) | −50.9450 | −1.77799 | −0.888996 | − | 0.457916i | \(-0.848596\pi\) | ||||
−0.888996 | + | 0.457916i | \(0.848596\pi\) | |||||||
\(822\) | 6.82566 | 0.238072 | ||||||||
\(823\) | 22.1304 | 0.771418 | 0.385709 | − | 0.922621i | \(-0.373957\pi\) | ||||
0.385709 | + | 0.922621i | \(0.373957\pi\) | |||||||
\(824\) | −14.0053 | −0.487897 | ||||||||
\(825\) | −4.77639 | −0.166292 | ||||||||
\(826\) | 10.1910 | 0.354589 | ||||||||
\(827\) | 15.6426 | 0.543946 | 0.271973 | − | 0.962305i | \(-0.412324\pi\) | ||||
0.271973 | + | 0.962305i | \(0.412324\pi\) | |||||||
\(828\) | −137.532 | −4.77958 | ||||||||
\(829\) | −7.36837 | −0.255914 | −0.127957 | − | 0.991780i | \(-0.540842\pi\) | ||||
−0.127957 | + | 0.991780i | \(0.540842\pi\) | |||||||
\(830\) | 1.27341 | 0.0442006 | ||||||||
\(831\) | −0.848973 | −0.0294506 | ||||||||
\(832\) | 66.2062 | 2.29529 | ||||||||
\(833\) | −0.197549 | −0.00684466 | ||||||||
\(834\) | 5.79872 | 0.200793 | ||||||||
\(835\) | −47.6174 | −1.64787 | ||||||||
\(836\) | 81.1036 | 2.80503 | ||||||||
\(837\) | 0.801520 | 0.0277046 | ||||||||
\(838\) | −16.2372 | −0.560904 | ||||||||
\(839\) | −49.1602 | −1.69720 | −0.848600 | − | 0.529035i | \(-0.822554\pi\) | ||||
−0.848600 | + | 0.529035i | \(0.822554\pi\) | |||||||
\(840\) | −18.3238 | −0.632233 | ||||||||
\(841\) | −24.3550 | −0.839828 | ||||||||
\(842\) | −46.1413 | −1.59014 | ||||||||
\(843\) | −0.0243158 | −0.000837480 0 | ||||||||
\(844\) | −80.6561 | −2.77630 | ||||||||
\(845\) | 13.4611 | 0.463075 | ||||||||
\(846\) | −54.3008 | −1.86690 | ||||||||
\(847\) | −14.5210 | −0.498947 | ||||||||
\(848\) | −148.570 | −5.10190 | ||||||||
\(849\) | 3.91236 | 0.134272 | ||||||||
\(850\) | −12.9655 | −0.444712 | ||||||||
\(851\) | 32.4164 | 1.11122 | ||||||||
\(852\) | −13.6736 | −0.468450 | ||||||||
\(853\) | −23.0639 | −0.789694 | −0.394847 | − | 0.918747i | \(-0.629202\pi\) | ||||
−0.394847 | + | 0.918747i | \(0.629202\pi\) | |||||||
\(854\) | 29.4448 | 1.00758 | ||||||||
\(855\) | 75.7432 | 2.59036 | ||||||||
\(856\) | −102.837 | −3.51491 | ||||||||
\(857\) | 54.7957 | 1.87179 | 0.935893 | − | 0.352283i | \(-0.114595\pi\) | ||||
0.935893 | + | 0.352283i | \(0.114595\pi\) | |||||||
\(858\) | 4.07290 | 0.139046 | ||||||||
\(859\) | 4.43429 | 0.151296 | 0.0756481 | − | 0.997135i | \(-0.475897\pi\) | ||||
0.0756481 | + | 0.997135i | \(0.475897\pi\) | |||||||
\(860\) | −157.572 | −5.37316 | ||||||||
\(861\) | −5.00478 | −0.170562 | ||||||||
\(862\) | 70.3531 | 2.39624 | ||||||||
\(863\) | 15.8507 | 0.539565 | 0.269782 | − | 0.962921i | \(-0.413048\pi\) | ||||
0.269782 | + | 0.962921i | \(0.413048\pi\) | |||||||
\(864\) | −22.3601 | −0.760706 | ||||||||
\(865\) | −51.1159 | −1.73799 | ||||||||
\(866\) | −30.9905 | −1.05310 | ||||||||
\(867\) | 3.55682 | 0.120796 | ||||||||
\(868\) | 8.55382 | 0.290336 | ||||||||
\(869\) | −10.8775 | −0.368996 | ||||||||
\(870\) | 4.72822 | 0.160302 | ||||||||
\(871\) | −8.40272 | −0.284715 | ||||||||
\(872\) | 92.7316 | 3.14029 | ||||||||
\(873\) | 53.3934 | 1.80709 | ||||||||
\(874\) | −159.411 | −5.39216 | ||||||||
\(875\) | −46.6335 | −1.57650 | ||||||||
\(876\) | 4.66009 | 0.157450 | ||||||||
\(877\) | −56.8995 | −1.92136 | −0.960680 | − | 0.277660i | \(-0.910441\pi\) | ||||
−0.960680 | + | 0.277660i | \(0.910441\pi\) | |||||||
\(878\) | −80.3227 | −2.71076 | ||||||||
\(879\) | −1.70658 | −0.0575616 | ||||||||
\(880\) | −116.008 | −3.91064 | ||||||||
\(881\) | −36.3670 | −1.22523 | −0.612617 | − | 0.790380i | \(-0.709883\pi\) | ||||
−0.612617 | + | 0.790380i | \(0.709883\pi\) | |||||||
\(882\) | −3.17626 | −0.106950 | ||||||||
\(883\) | 44.1168 | 1.48465 | 0.742325 | − | 0.670040i | \(-0.233723\pi\) | ||||
0.742325 | + | 0.670040i | \(0.233723\pi\) | |||||||
\(884\) | 8.00637 | 0.269283 | ||||||||
\(885\) | −1.20012 | −0.0403417 | ||||||||
\(886\) | −85.2621 | −2.86444 | ||||||||
\(887\) | −15.2649 | −0.512546 | −0.256273 | − | 0.966604i | \(-0.582495\pi\) | ||||
−0.256273 | + | 0.966604i | \(0.582495\pi\) | |||||||
\(888\) | 6.79629 | 0.228068 | ||||||||
\(889\) | −6.22572 | −0.208804 | ||||||||
\(890\) | 27.2905 | 0.914779 | ||||||||
\(891\) | 19.8801 | 0.666007 | ||||||||
\(892\) | 93.5511 | 3.13232 | ||||||||
\(893\) | −45.5788 | −1.52524 | ||||||||
\(894\) | −2.30823 | −0.0771986 | ||||||||
\(895\) | −19.5675 | −0.654068 | ||||||||
\(896\) | −57.7742 | −1.93010 | ||||||||
\(897\) | −5.79729 | −0.193566 | ||||||||
\(898\) | −86.3632 | −2.88198 | ||||||||
\(899\) | −1.36652 | −0.0455759 | ||||||||
\(900\) | −150.964 | −5.03214 | ||||||||
\(901\) | −5.62517 | −0.187402 | ||||||||
\(902\) | −57.1435 | −1.90267 | ||||||||
\(903\) | −4.26443 | −0.141911 | ||||||||
\(904\) | −152.562 | −5.07414 | ||||||||
\(905\) | −72.5867 | −2.41286 | ||||||||
\(906\) | −11.7648 | −0.390858 | ||||||||
\(907\) | 23.8486 | 0.791881 | 0.395941 | − | 0.918276i | \(-0.370419\pi\) | ||||
0.395941 | + | 0.918276i | \(0.370419\pi\) | |||||||
\(908\) | −45.9222 | −1.52398 | ||||||||
\(909\) | −20.6945 | −0.686392 | ||||||||
\(910\) | 81.8054 | 2.71182 | ||||||||
\(911\) | −0.356916 | −0.0118251 | −0.00591257 | − | 0.999983i | \(-0.501882\pi\) | ||||
−0.00591257 | + | 0.999983i | \(0.501882\pi\) | |||||||
\(912\) | −18.5318 | −0.613648 | ||||||||
\(913\) | 0.284954 | 0.00943061 | ||||||||
\(914\) | −60.2296 | −1.99222 | ||||||||
\(915\) | −3.46752 | −0.114633 | ||||||||
\(916\) | 105.534 | 3.48694 | ||||||||
\(917\) | 3.17229 | 0.104758 | ||||||||
\(918\) | −1.68459 | −0.0555998 | ||||||||
\(919\) | −3.89679 | −0.128543 | −0.0642717 | − | 0.997932i | \(-0.520472\pi\) | ||||
−0.0642717 | + | 0.997932i | \(0.520472\pi\) | |||||||
\(920\) | 297.797 | 9.81808 | ||||||||
\(921\) | 1.09479 | 0.0360746 | ||||||||
\(922\) | −85.3043 | −2.80935 | ||||||||
\(923\) | 37.7939 | 1.24400 | ||||||||
\(924\) | −6.62294 | −0.217879 | ||||||||
\(925\) | 35.5822 | 1.16994 | ||||||||
\(926\) | −42.5006 | −1.39665 | ||||||||
\(927\) | −4.72748 | −0.155271 | ||||||||
\(928\) | 38.1219 | 1.25141 | ||||||||
\(929\) | −16.6041 | −0.544762 | −0.272381 | − | 0.962189i | \(-0.587811\pi\) | ||||
−0.272381 | + | 0.962189i | \(0.587811\pi\) | |||||||
\(930\) | −1.39100 | −0.0456128 | ||||||||
\(931\) | −2.66608 | −0.0873771 | ||||||||
\(932\) | −14.0084 | −0.458861 | ||||||||
\(933\) | −0.766670 | −0.0250996 | ||||||||
\(934\) | −115.579 | −3.78185 | ||||||||
\(935\) | −4.39233 | −0.143645 | ||||||||
\(936\) | 79.6985 | 2.60503 | ||||||||
\(937\) | −40.2957 | −1.31640 | −0.658202 | − | 0.752841i | \(-0.728683\pi\) | ||||
−0.658202 | + | 0.752841i | \(0.728683\pi\) | |||||||
\(938\) | 18.8679 | 0.616060 | ||||||||
\(939\) | −5.58230 | −0.182172 | ||||||||
\(940\) | 137.528 | 4.48567 | ||||||||
\(941\) | 37.7868 | 1.23182 | 0.615908 | − | 0.787818i | \(-0.288789\pi\) | ||||
0.615908 | + | 0.787818i | \(0.288789\pi\) | |||||||
\(942\) | −2.67227 | −0.0870674 | ||||||||
\(943\) | 81.3371 | 2.64870 | ||||||||
\(944\) | −19.2538 | −0.626659 | ||||||||
\(945\) | −12.4647 | −0.405478 | ||||||||
\(946\) | −48.6904 | −1.58306 | ||||||||
\(947\) | −50.1060 | −1.62823 | −0.814114 | − | 0.580706i | \(-0.802777\pi\) | ||||
−0.814114 | + | 0.580706i | \(0.802777\pi\) | |||||||
\(948\) | 5.24308 | 0.170287 | ||||||||
\(949\) | −12.8805 | −0.418118 | ||||||||
\(950\) | −174.979 | −5.67708 | ||||||||
\(951\) | 6.79239 | 0.220258 | ||||||||
\(952\) | −11.1305 | −0.360741 | ||||||||
\(953\) | −31.9329 | −1.03441 | −0.517204 | − | 0.855862i | \(-0.673027\pi\) | ||||
−0.517204 | + | 0.855862i | \(0.673027\pi\) | |||||||
\(954\) | −90.4435 | −2.92822 | ||||||||
\(955\) | 84.4683 | 2.73333 | ||||||||
\(956\) | −17.7332 | −0.573532 | ||||||||
\(957\) | 1.05805 | 0.0342019 | ||||||||
\(958\) | 64.6812 | 2.08975 | ||||||||
\(959\) | 30.6783 | 0.990653 | ||||||||
\(960\) | 17.5071 | 0.565039 | ||||||||
\(961\) | −30.5980 | −0.987032 | ||||||||
\(962\) | −30.3415 | −0.978249 | ||||||||
\(963\) | −34.7128 | −1.11860 | ||||||||
\(964\) | 94.5376 | 3.04485 | ||||||||
\(965\) | 36.1530 | 1.16381 | ||||||||
\(966\) | 13.0176 | 0.418833 | ||||||||
\(967\) | 48.7518 | 1.56775 | 0.783876 | − | 0.620918i | \(-0.213240\pi\) | ||||
0.783876 | + | 0.620918i | \(0.213240\pi\) | |||||||
\(968\) | 49.4775 | 1.59027 | ||||||||
\(969\) | −0.701653 | −0.0225403 | ||||||||
\(970\) | −186.737 | −5.99575 | ||||||||
\(971\) | 3.75936 | 0.120644 | 0.0603219 | − | 0.998179i | \(-0.480787\pi\) | ||||
0.0603219 | + | 0.998179i | \(0.480787\pi\) | |||||||
\(972\) | −29.4961 | −0.946088 | ||||||||
\(973\) | 26.0626 | 0.835529 | ||||||||
\(974\) | −20.1222 | −0.644756 | ||||||||
\(975\) | −6.36346 | −0.203794 | ||||||||
\(976\) | −55.6302 | −1.78068 | ||||||||
\(977\) | 19.2510 | 0.615893 | 0.307946 | − | 0.951404i | \(-0.400358\pi\) | ||||
0.307946 | + | 0.951404i | \(0.400358\pi\) | |||||||
\(978\) | 13.0813 | 0.418293 | ||||||||
\(979\) | 6.10687 | 0.195177 | ||||||||
\(980\) | 8.04455 | 0.256974 | ||||||||
\(981\) | 31.3016 | 0.999382 | ||||||||
\(982\) | −30.9753 | −0.988463 | ||||||||
\(983\) | −20.2320 | −0.645302 | −0.322651 | − | 0.946518i | \(-0.604574\pi\) | ||||
−0.322651 | + | 0.946518i | \(0.604574\pi\) | |||||||
\(984\) | 17.0528 | 0.543624 | ||||||||
\(985\) | −0.517599 | −0.0164921 | ||||||||
\(986\) | 2.87207 | 0.0914653 | ||||||||
\(987\) | 3.72198 | 0.118472 | ||||||||
\(988\) | 108.052 | 3.43760 | ||||||||
\(989\) | 69.3051 | 2.20378 | ||||||||
\(990\) | −70.6215 | −2.24450 | ||||||||
\(991\) | 35.1450 | 1.11642 | 0.558208 | − | 0.829701i | \(-0.311489\pi\) | ||||
0.558208 | + | 0.829701i | \(0.311489\pi\) | |||||||
\(992\) | −11.2151 | −0.356081 | ||||||||
\(993\) | 1.86803 | 0.0592801 | ||||||||
\(994\) | −84.8645 | −2.69174 | ||||||||
\(995\) | 90.2065 | 2.85974 | ||||||||
\(996\) | −0.137351 | −0.00435213 | ||||||||
\(997\) | −1.98283 | −0.0627967 | −0.0313984 | − | 0.999507i | \(-0.509996\pi\) | ||||
−0.0313984 | + | 0.999507i | \(0.509996\pi\) | |||||||
\(998\) | 73.0006 | 2.31079 | ||||||||
\(999\) | 4.62316 | 0.146270 |
(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 | 4013.2.a.c.1.4 | ✓ | 176 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4013.2.a.c.1.4 | ✓ | 176 | 1.1 | even | 1 | trivial |