Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4033,2,Mod(1,4033)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4033, 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("4033.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4033 = 37 \cdot 109 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4033.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: | \(32.2036671352\) |
Analytic rank: | \(1\) |
Dimension: | \(77\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.18 | ||
Character | \(\chi\) | \(=\) | 4033.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.78823 | −1.26447 | −0.632236 | − | 0.774776i | \(-0.717863\pi\) | ||||
−0.632236 | + | 0.774776i | \(0.717863\pi\) | |||||||
\(3\) | 2.78240 | 1.60642 | 0.803208 | − | 0.595698i | \(-0.203125\pi\) | ||||
0.803208 | + | 0.595698i | \(0.203125\pi\) | |||||||
\(4\) | 1.19778 | 0.598891 | ||||||||
\(5\) | −2.10202 | −0.940050 | −0.470025 | − | 0.882653i | \(-0.655755\pi\) | ||||
−0.470025 | + | 0.882653i | \(0.655755\pi\) | |||||||
\(6\) | −4.97558 | −2.03127 | ||||||||
\(7\) | −2.70114 | −1.02094 | −0.510468 | − | 0.859897i | \(-0.670528\pi\) | ||||
−0.510468 | + | 0.859897i | \(0.670528\pi\) | |||||||
\(8\) | 1.43455 | 0.507191 | ||||||||
\(9\) | 4.74173 | 1.58058 | ||||||||
\(10\) | 3.75890 | 1.18867 | ||||||||
\(11\) | 3.93666 | 1.18695 | 0.593474 | − | 0.804853i | \(-0.297756\pi\) | ||||
0.593474 | + | 0.804853i | \(0.297756\pi\) | |||||||
\(12\) | 3.33270 | 0.962069 | ||||||||
\(13\) | −6.77398 | −1.87877 | −0.939383 | − | 0.342871i | \(-0.888601\pi\) | ||||
−0.939383 | + | 0.342871i | \(0.888601\pi\) | |||||||
\(14\) | 4.83028 | 1.29095 | ||||||||
\(15\) | −5.84864 | −1.51011 | ||||||||
\(16\) | −4.96088 | −1.24022 | ||||||||
\(17\) | 6.00146 | 1.45557 | 0.727784 | − | 0.685807i | \(-0.240551\pi\) | ||||
0.727784 | + | 0.685807i | \(0.240551\pi\) | |||||||
\(18\) | −8.47932 | −1.99859 | ||||||||
\(19\) | −3.18902 | −0.731612 | −0.365806 | − | 0.930691i | \(-0.619207\pi\) | ||||
−0.365806 | + | 0.930691i | \(0.619207\pi\) | |||||||
\(20\) | −2.51776 | −0.562988 | ||||||||
\(21\) | −7.51565 | −1.64005 | ||||||||
\(22\) | −7.03967 | −1.50086 | ||||||||
\(23\) | −0.759006 | −0.158264 | −0.0791318 | − | 0.996864i | \(-0.525215\pi\) | ||||
−0.0791318 | + | 0.996864i | \(0.525215\pi\) | |||||||
\(24\) | 3.99149 | 0.814760 | ||||||||
\(25\) | −0.581526 | −0.116305 | ||||||||
\(26\) | 12.1135 | 2.37565 | ||||||||
\(27\) | 4.84617 | 0.932646 | ||||||||
\(28\) | −3.23538 | −0.611430 | ||||||||
\(29\) | 4.13153 | 0.767205 | 0.383602 | − | 0.923498i | \(-0.374683\pi\) | ||||
0.383602 | + | 0.923498i | \(0.374683\pi\) | |||||||
\(30\) | 10.4587 | 1.90950 | ||||||||
\(31\) | 7.00483 | 1.25810 | 0.629052 | − | 0.777363i | \(-0.283443\pi\) | ||||
0.629052 | + | 0.777363i | \(0.283443\pi\) | |||||||
\(32\) | 6.00211 | 1.06103 | ||||||||
\(33\) | 10.9533 | 1.90673 | ||||||||
\(34\) | −10.7320 | −1.84052 | ||||||||
\(35\) | 5.67785 | 0.959732 | ||||||||
\(36\) | 5.67956 | 0.946593 | ||||||||
\(37\) | 1.00000 | 0.164399 | ||||||||
\(38\) | 5.70272 | 0.925104 | ||||||||
\(39\) | −18.8479 | −3.01808 | ||||||||
\(40\) | −3.01545 | −0.476785 | ||||||||
\(41\) | 9.83180 | 1.53547 | 0.767735 | − | 0.640768i | \(-0.221384\pi\) | ||||
0.767735 | + | 0.640768i | \(0.221384\pi\) | |||||||
\(42\) | 13.4397 | 2.07380 | ||||||||
\(43\) | −6.90597 | −1.05315 | −0.526575 | − | 0.850129i | \(-0.676524\pi\) | ||||
−0.526575 | + | 0.850129i | \(0.676524\pi\) | |||||||
\(44\) | 4.71526 | 0.710852 | ||||||||
\(45\) | −9.96719 | −1.48582 | ||||||||
\(46\) | 1.35728 | 0.200120 | ||||||||
\(47\) | −4.59077 | −0.669633 | −0.334817 | − | 0.942283i | \(-0.608674\pi\) | ||||
−0.334817 | + | 0.942283i | \(0.608674\pi\) | |||||||
\(48\) | −13.8031 | −1.99231 | ||||||||
\(49\) | 0.296181 | 0.0423115 | ||||||||
\(50\) | 1.03991 | 0.147065 | ||||||||
\(51\) | 16.6984 | 2.33825 | ||||||||
\(52\) | −8.11376 | −1.12518 | ||||||||
\(53\) | −9.99885 | −1.37345 | −0.686724 | − | 0.726918i | \(-0.740952\pi\) | ||||
−0.686724 | + | 0.726918i | \(0.740952\pi\) | |||||||
\(54\) | −8.66609 | −1.17931 | ||||||||
\(55\) | −8.27492 | −1.11579 | ||||||||
\(56\) | −3.87494 | −0.517810 | ||||||||
\(57\) | −8.87313 | −1.17527 | ||||||||
\(58\) | −7.38814 | −0.970110 | ||||||||
\(59\) | 9.15037 | 1.19128 | 0.595638 | − | 0.803253i | \(-0.296899\pi\) | ||||
0.595638 | + | 0.803253i | \(0.296899\pi\) | |||||||
\(60\) | −7.00540 | −0.904393 | ||||||||
\(61\) | −0.435289 | −0.0557330 | −0.0278665 | − | 0.999612i | \(-0.508871\pi\) | ||||
−0.0278665 | + | 0.999612i | \(0.508871\pi\) | |||||||
\(62\) | −12.5263 | −1.59084 | ||||||||
\(63\) | −12.8081 | −1.61367 | ||||||||
\(64\) | −0.811423 | −0.101428 | ||||||||
\(65\) | 14.2390 | 1.76613 | ||||||||
\(66\) | −19.5871 | −2.41101 | ||||||||
\(67\) | −10.5871 | −1.29343 | −0.646713 | − | 0.762734i | \(-0.723857\pi\) | ||||
−0.646713 | + | 0.762734i | \(0.723857\pi\) | |||||||
\(68\) | 7.18844 | 0.871726 | ||||||||
\(69\) | −2.11185 | −0.254237 | ||||||||
\(70\) | −10.1533 | −1.21355 | ||||||||
\(71\) | −16.1503 | −1.91669 | −0.958345 | − | 0.285615i | \(-0.907802\pi\) | ||||
−0.958345 | + | 0.285615i | \(0.907802\pi\) | |||||||
\(72\) | 6.80226 | 0.801654 | ||||||||
\(73\) | −0.259503 | −0.0303725 | −0.0151862 | − | 0.999885i | \(-0.504834\pi\) | ||||
−0.0151862 | + | 0.999885i | \(0.504834\pi\) | |||||||
\(74\) | −1.78823 | −0.207878 | ||||||||
\(75\) | −1.61804 | −0.186835 | ||||||||
\(76\) | −3.81976 | −0.438156 | ||||||||
\(77\) | −10.6335 | −1.21180 | ||||||||
\(78\) | 33.7045 | 3.81628 | ||||||||
\(79\) | 3.43324 | 0.386269 | 0.193135 | − | 0.981172i | \(-0.438135\pi\) | ||||
0.193135 | + | 0.981172i | \(0.438135\pi\) | |||||||
\(80\) | 10.4279 | 1.16587 | ||||||||
\(81\) | −0.741213 | −0.0823570 | ||||||||
\(82\) | −17.5816 | −1.94156 | ||||||||
\(83\) | −5.22693 | −0.573731 | −0.286865 | − | 0.957971i | \(-0.592613\pi\) | ||||
−0.286865 | + | 0.957971i | \(0.592613\pi\) | |||||||
\(84\) | −9.00212 | −0.982211 | ||||||||
\(85\) | −12.6152 | −1.36831 | ||||||||
\(86\) | 12.3495 | 1.33168 | ||||||||
\(87\) | 11.4955 | 1.23245 | ||||||||
\(88\) | 5.64735 | 0.602009 | ||||||||
\(89\) | 7.31595 | 0.775490 | 0.387745 | − | 0.921767i | \(-0.373254\pi\) | ||||
0.387745 | + | 0.921767i | \(0.373254\pi\) | |||||||
\(90\) | 17.8237 | 1.87878 | ||||||||
\(91\) | 18.2975 | 1.91810 | ||||||||
\(92\) | −0.909124 | −0.0947827 | ||||||||
\(93\) | 19.4902 | 2.02104 | ||||||||
\(94\) | 8.20938 | 0.846733 | ||||||||
\(95\) | 6.70338 | 0.687753 | ||||||||
\(96\) | 16.7003 | 1.70446 | ||||||||
\(97\) | 0.841504 | 0.0854418 | 0.0427209 | − | 0.999087i | \(-0.486397\pi\) | ||||
0.0427209 | + | 0.999087i | \(0.486397\pi\) | |||||||
\(98\) | −0.529640 | −0.0535017 | ||||||||
\(99\) | 18.6666 | 1.87606 | ||||||||
\(100\) | −0.696542 | −0.0696542 | ||||||||
\(101\) | −1.18872 | −0.118282 | −0.0591408 | − | 0.998250i | \(-0.518836\pi\) | ||||
−0.0591408 | + | 0.998250i | \(0.518836\pi\) | |||||||
\(102\) | −29.8607 | −2.95665 | ||||||||
\(103\) | −6.76122 | −0.666203 | −0.333101 | − | 0.942891i | \(-0.608095\pi\) | ||||
−0.333101 | + | 0.942891i | \(0.608095\pi\) | |||||||
\(104\) | −9.71764 | −0.952893 | ||||||||
\(105\) | 15.7980 | 1.54173 | ||||||||
\(106\) | 17.8803 | 1.73669 | ||||||||
\(107\) | −7.45845 | −0.721035 | −0.360518 | − | 0.932752i | \(-0.617400\pi\) | ||||
−0.360518 | + | 0.932752i | \(0.617400\pi\) | |||||||
\(108\) | 5.80466 | 0.558553 | ||||||||
\(109\) | 1.00000 | 0.0957826 | ||||||||
\(110\) | 14.7975 | 1.41089 | ||||||||
\(111\) | 2.78240 | 0.264093 | ||||||||
\(112\) | 13.4001 | 1.26619 | ||||||||
\(113\) | 2.80653 | 0.264016 | 0.132008 | − | 0.991249i | \(-0.457858\pi\) | ||||
0.132008 | + | 0.991249i | \(0.457858\pi\) | |||||||
\(114\) | 15.8672 | 1.48610 | ||||||||
\(115\) | 1.59544 | 0.148776 | ||||||||
\(116\) | 4.94867 | 0.459472 | ||||||||
\(117\) | −32.1204 | −2.96953 | ||||||||
\(118\) | −16.3630 | −1.50634 | ||||||||
\(119\) | −16.2108 | −1.48604 | ||||||||
\(120\) | −8.39019 | −0.765916 | ||||||||
\(121\) | 4.49729 | 0.408844 | ||||||||
\(122\) | 0.778398 | 0.0704729 | ||||||||
\(123\) | 27.3560 | 2.46660 | ||||||||
\(124\) | 8.39026 | 0.753468 | ||||||||
\(125\) | 11.7325 | 1.04938 | ||||||||
\(126\) | 22.9039 | 2.04044 | ||||||||
\(127\) | −14.1158 | −1.25257 | −0.626286 | − | 0.779593i | \(-0.715426\pi\) | ||||
−0.626286 | + | 0.779593i | \(0.715426\pi\) | |||||||
\(128\) | −10.5532 | −0.932781 | ||||||||
\(129\) | −19.2151 | −1.69180 | ||||||||
\(130\) | −25.4627 | −2.23323 | ||||||||
\(131\) | 3.59864 | 0.314414 | 0.157207 | − | 0.987566i | \(-0.449751\pi\) | ||||
0.157207 | + | 0.987566i | \(0.449751\pi\) | |||||||
\(132\) | 13.1197 | 1.14193 | ||||||||
\(133\) | 8.61402 | 0.746930 | ||||||||
\(134\) | 18.9323 | 1.63550 | ||||||||
\(135\) | −10.1867 | −0.876734 | ||||||||
\(136\) | 8.60941 | 0.738251 | ||||||||
\(137\) | −9.05309 | −0.773457 | −0.386729 | − | 0.922194i | \(-0.626395\pi\) | ||||
−0.386729 | + | 0.922194i | \(0.626395\pi\) | |||||||
\(138\) | 3.77649 | 0.321476 | ||||||||
\(139\) | −13.3809 | −1.13495 | −0.567475 | − | 0.823391i | \(-0.692080\pi\) | ||||
−0.567475 | + | 0.823391i | \(0.692080\pi\) | |||||||
\(140\) | 6.80083 | 0.574775 | ||||||||
\(141\) | −12.7734 | −1.07571 | ||||||||
\(142\) | 28.8805 | 2.42360 | ||||||||
\(143\) | −26.6669 | −2.23000 | ||||||||
\(144\) | −23.5231 | −1.96026 | ||||||||
\(145\) | −8.68453 | −0.721211 | ||||||||
\(146\) | 0.464052 | 0.0384052 | ||||||||
\(147\) | 0.824091 | 0.0679699 | ||||||||
\(148\) | 1.19778 | 0.0984571 | ||||||||
\(149\) | −7.79199 | −0.638345 | −0.319172 | − | 0.947697i | \(-0.603405\pi\) | ||||
−0.319172 | + | 0.947697i | \(0.603405\pi\) | |||||||
\(150\) | 2.89343 | 0.236247 | ||||||||
\(151\) | −23.6795 | −1.92701 | −0.963504 | − | 0.267693i | \(-0.913739\pi\) | ||||
−0.963504 | + | 0.267693i | \(0.913739\pi\) | |||||||
\(152\) | −4.57483 | −0.371067 | ||||||||
\(153\) | 28.4573 | 2.30063 | ||||||||
\(154\) | 19.0152 | 1.53229 | ||||||||
\(155\) | −14.7243 | −1.18268 | ||||||||
\(156\) | −22.5757 | −1.80750 | ||||||||
\(157\) | 4.77220 | 0.380863 | 0.190432 | − | 0.981700i | \(-0.439011\pi\) | ||||
0.190432 | + | 0.981700i | \(0.439011\pi\) | |||||||
\(158\) | −6.13943 | −0.488427 | ||||||||
\(159\) | −27.8208 | −2.20633 | ||||||||
\(160\) | −12.6165 | −0.997425 | ||||||||
\(161\) | 2.05018 | 0.161577 | ||||||||
\(162\) | 1.32546 | 0.104138 | ||||||||
\(163\) | −4.12655 | −0.323216 | −0.161608 | − | 0.986855i | \(-0.551668\pi\) | ||||
−0.161608 | + | 0.986855i | \(0.551668\pi\) | |||||||
\(164\) | 11.7764 | 0.919579 | ||||||||
\(165\) | −23.0241 | −1.79242 | ||||||||
\(166\) | 9.34698 | 0.725467 | ||||||||
\(167\) | 16.5259 | 1.27881 | 0.639406 | − | 0.768869i | \(-0.279180\pi\) | ||||
0.639406 | + | 0.768869i | \(0.279180\pi\) | |||||||
\(168\) | −10.7816 | −0.831819 | ||||||||
\(169\) | 32.8869 | 2.52976 | ||||||||
\(170\) | 22.5589 | 1.73019 | ||||||||
\(171\) | −15.1215 | −1.15637 | ||||||||
\(172\) | −8.27185 | −0.630722 | ||||||||
\(173\) | −19.3852 | −1.47383 | −0.736917 | − | 0.675984i | \(-0.763719\pi\) | ||||
−0.736917 | + | 0.675984i | \(0.763719\pi\) | |||||||
\(174\) | −20.5567 | −1.55840 | ||||||||
\(175\) | 1.57079 | 0.118740 | ||||||||
\(176\) | −19.5293 | −1.47208 | ||||||||
\(177\) | 25.4599 | 1.91369 | ||||||||
\(178\) | −13.0826 | −0.980586 | ||||||||
\(179\) | 8.10242 | 0.605604 | 0.302802 | − | 0.953054i | \(-0.402078\pi\) | ||||
0.302802 | + | 0.953054i | \(0.402078\pi\) | |||||||
\(180\) | −11.9385 | −0.889845 | ||||||||
\(181\) | −11.9563 | −0.888706 | −0.444353 | − | 0.895852i | \(-0.646566\pi\) | ||||
−0.444353 | + | 0.895852i | \(0.646566\pi\) | |||||||
\(182\) | −32.7202 | −2.42539 | ||||||||
\(183\) | −1.21115 | −0.0895305 | ||||||||
\(184\) | −1.08883 | −0.0802699 | ||||||||
\(185\) | −2.10202 | −0.154543 | ||||||||
\(186\) | −34.8531 | −2.55555 | ||||||||
\(187\) | 23.6257 | 1.72768 | ||||||||
\(188\) | −5.49875 | −0.401037 | ||||||||
\(189\) | −13.0902 | −0.952172 | ||||||||
\(190\) | −11.9872 | −0.869644 | ||||||||
\(191\) | 7.48022 | 0.541250 | 0.270625 | − | 0.962685i | \(-0.412770\pi\) | ||||
0.270625 | + | 0.962685i | \(0.412770\pi\) | |||||||
\(192\) | −2.25770 | −0.162935 | ||||||||
\(193\) | 0.175460 | 0.0126299 | 0.00631494 | − | 0.999980i | \(-0.497990\pi\) | ||||
0.00631494 | + | 0.999980i | \(0.497990\pi\) | |||||||
\(194\) | −1.50481 | −0.108039 | ||||||||
\(195\) | 39.6186 | 2.83715 | ||||||||
\(196\) | 0.354760 | 0.0253400 | ||||||||
\(197\) | −6.85264 | −0.488230 | −0.244115 | − | 0.969746i | \(-0.578498\pi\) | ||||
−0.244115 | + | 0.969746i | \(0.578498\pi\) | |||||||
\(198\) | −33.3802 | −2.37223 | ||||||||
\(199\) | −13.0809 | −0.927280 | −0.463640 | − | 0.886024i | \(-0.653457\pi\) | ||||
−0.463640 | + | 0.886024i | \(0.653457\pi\) | |||||||
\(200\) | −0.834230 | −0.0589890 | ||||||||
\(201\) | −29.4576 | −2.07778 | ||||||||
\(202\) | 2.12570 | 0.149564 | ||||||||
\(203\) | −11.1598 | −0.783268 | ||||||||
\(204\) | 20.0011 | 1.40036 | ||||||||
\(205\) | −20.6666 | −1.44342 | ||||||||
\(206\) | 12.0906 | 0.842395 | ||||||||
\(207\) | −3.59900 | −0.250148 | ||||||||
\(208\) | 33.6049 | 2.33008 | ||||||||
\(209\) | −12.5541 | −0.868386 | ||||||||
\(210\) | −28.2506 | −1.94947 | ||||||||
\(211\) | 11.4402 | 0.787577 | 0.393789 | − | 0.919201i | \(-0.371164\pi\) | ||||
0.393789 | + | 0.919201i | \(0.371164\pi\) | |||||||
\(212\) | −11.9765 | −0.822546 | ||||||||
\(213\) | −44.9366 | −3.07900 | ||||||||
\(214\) | 13.3375 | 0.911730 | ||||||||
\(215\) | 14.5165 | 0.990014 | ||||||||
\(216\) | 6.95209 | 0.473030 | ||||||||
\(217\) | −18.9211 | −1.28444 | ||||||||
\(218\) | −1.78823 | −0.121115 | ||||||||
\(219\) | −0.722039 | −0.0487909 | ||||||||
\(220\) | −9.91156 | −0.668237 | ||||||||
\(221\) | −40.6538 | −2.73467 | ||||||||
\(222\) | −4.97558 | −0.333939 | ||||||||
\(223\) | −5.31659 | −0.356025 | −0.178013 | − | 0.984028i | \(-0.556967\pi\) | ||||
−0.178013 | + | 0.984028i | \(0.556967\pi\) | |||||||
\(224\) | −16.2126 | −1.08325 | ||||||||
\(225\) | −2.75744 | −0.183829 | ||||||||
\(226\) | −5.01873 | −0.333841 | ||||||||
\(227\) | −16.6263 | −1.10352 | −0.551762 | − | 0.834001i | \(-0.686044\pi\) | ||||
−0.551762 | + | 0.834001i | \(0.686044\pi\) | |||||||
\(228\) | −10.6281 | −0.703862 | ||||||||
\(229\) | 10.9037 | 0.720535 | 0.360267 | − | 0.932849i | \(-0.382685\pi\) | ||||
0.360267 | + | 0.932849i | \(0.382685\pi\) | |||||||
\(230\) | −2.85302 | −0.188123 | ||||||||
\(231\) | −29.5866 | −1.94665 | ||||||||
\(232\) | 5.92689 | 0.389120 | ||||||||
\(233\) | 20.1429 | 1.31961 | 0.659804 | − | 0.751438i | \(-0.270639\pi\) | ||||
0.659804 | + | 0.751438i | \(0.270639\pi\) | |||||||
\(234\) | 57.4388 | 3.75489 | ||||||||
\(235\) | 9.64988 | 0.629489 | ||||||||
\(236\) | 10.9602 | 0.713445 | ||||||||
\(237\) | 9.55262 | 0.620509 | ||||||||
\(238\) | 28.9887 | 1.87906 | ||||||||
\(239\) | −0.657911 | −0.0425567 | −0.0212784 | − | 0.999774i | \(-0.506774\pi\) | ||||
−0.0212784 | + | 0.999774i | \(0.506774\pi\) | |||||||
\(240\) | 29.0144 | 1.87287 | ||||||||
\(241\) | −14.2570 | −0.918375 | −0.459188 | − | 0.888339i | \(-0.651859\pi\) | ||||
−0.459188 | + | 0.888339i | \(0.651859\pi\) | |||||||
\(242\) | −8.04221 | −0.516973 | ||||||||
\(243\) | −16.6009 | −1.06495 | ||||||||
\(244\) | −0.521381 | −0.0333780 | ||||||||
\(245\) | −0.622576 | −0.0397749 | ||||||||
\(246\) | −48.9189 | −3.11895 | ||||||||
\(247\) | 21.6024 | 1.37453 | ||||||||
\(248\) | 10.0488 | 0.638099 | ||||||||
\(249\) | −14.5434 | −0.921650 | ||||||||
\(250\) | −20.9804 | −1.32692 | ||||||||
\(251\) | −12.1221 | −0.765139 | −0.382569 | − | 0.923927i | \(-0.624961\pi\) | ||||
−0.382569 | + | 0.923927i | \(0.624961\pi\) | |||||||
\(252\) | −15.3413 | −0.966411 | ||||||||
\(253\) | −2.98795 | −0.187851 | ||||||||
\(254\) | 25.2423 | 1.58384 | ||||||||
\(255\) | −35.1004 | −2.19807 | ||||||||
\(256\) | 20.4945 | 1.28090 | ||||||||
\(257\) | −31.4020 | −1.95880 | −0.979402 | − | 0.201920i | \(-0.935282\pi\) | ||||
−0.979402 | + | 0.201920i | \(0.935282\pi\) | |||||||
\(258\) | 34.3612 | 2.13923 | ||||||||
\(259\) | −2.70114 | −0.167841 | ||||||||
\(260\) | 17.0553 | 1.05772 | ||||||||
\(261\) | 19.5906 | 1.21263 | ||||||||
\(262\) | −6.43521 | −0.397569 | ||||||||
\(263\) | −2.41584 | −0.148967 | −0.0744836 | − | 0.997222i | \(-0.523731\pi\) | ||||
−0.0744836 | + | 0.997222i | \(0.523731\pi\) | |||||||
\(264\) | 15.7132 | 0.967078 | ||||||||
\(265\) | 21.0178 | 1.29111 | ||||||||
\(266\) | −15.4039 | −0.944473 | ||||||||
\(267\) | 20.3559 | 1.24576 | ||||||||
\(268\) | −12.6811 | −0.774621 | ||||||||
\(269\) | 22.9177 | 1.39732 | 0.698658 | − | 0.715456i | \(-0.253781\pi\) | ||||
0.698658 | + | 0.715456i | \(0.253781\pi\) | |||||||
\(270\) | 18.2163 | 1.10861 | ||||||||
\(271\) | −7.54401 | −0.458266 | −0.229133 | − | 0.973395i | \(-0.573589\pi\) | ||||
−0.229133 | + | 0.973395i | \(0.573589\pi\) | |||||||
\(272\) | −29.7725 | −1.80522 | ||||||||
\(273\) | 50.9109 | 3.08127 | ||||||||
\(274\) | 16.1890 | 0.978016 | ||||||||
\(275\) | −2.28927 | −0.138048 | ||||||||
\(276\) | −2.52954 | −0.152260 | ||||||||
\(277\) | −23.6157 | −1.41893 | −0.709466 | − | 0.704740i | \(-0.751064\pi\) | ||||
−0.709466 | + | 0.704740i | \(0.751064\pi\) | |||||||
\(278\) | 23.9281 | 1.43511 | ||||||||
\(279\) | 33.2150 | 1.98853 | ||||||||
\(280\) | 8.14518 | 0.486767 | ||||||||
\(281\) | −4.78297 | −0.285328 | −0.142664 | − | 0.989771i | \(-0.545567\pi\) | ||||
−0.142664 | + | 0.989771i | \(0.545567\pi\) | |||||||
\(282\) | 22.8417 | 1.36021 | ||||||||
\(283\) | −2.65441 | −0.157788 | −0.0788941 | − | 0.996883i | \(-0.525139\pi\) | ||||
−0.0788941 | + | 0.996883i | \(0.525139\pi\) | |||||||
\(284\) | −19.3446 | −1.14789 | ||||||||
\(285\) | 18.6515 | 1.10482 | ||||||||
\(286\) | 47.6866 | 2.81977 | ||||||||
\(287\) | −26.5571 | −1.56762 | ||||||||
\(288\) | 28.4604 | 1.67704 | ||||||||
\(289\) | 19.0175 | 1.11868 | ||||||||
\(290\) | 15.5300 | 0.911952 | ||||||||
\(291\) | 2.34140 | 0.137255 | ||||||||
\(292\) | −0.310828 | −0.0181898 | ||||||||
\(293\) | 3.88314 | 0.226855 | 0.113428 | − | 0.993546i | \(-0.463817\pi\) | ||||
0.113428 | + | 0.993546i | \(0.463817\pi\) | |||||||
\(294\) | −1.47367 | −0.0859461 | ||||||||
\(295\) | −19.2342 | −1.11986 | ||||||||
\(296\) | 1.43455 | 0.0833817 | ||||||||
\(297\) | 19.0777 | 1.10700 | ||||||||
\(298\) | 13.9339 | 0.807169 | ||||||||
\(299\) | 5.14149 | 0.297340 | ||||||||
\(300\) | −1.93806 | −0.111894 | ||||||||
\(301\) | 18.6540 | 1.07520 | ||||||||
\(302\) | 42.3445 | 2.43665 | ||||||||
\(303\) | −3.30748 | −0.190010 | ||||||||
\(304\) | 15.8204 | 0.907361 | ||||||||
\(305\) | 0.914984 | 0.0523918 | ||||||||
\(306\) | −50.8883 | −2.90909 | ||||||||
\(307\) | −16.3745 | −0.934544 | −0.467272 | − | 0.884114i | \(-0.654763\pi\) | ||||
−0.467272 | + | 0.884114i | \(0.654763\pi\) | |||||||
\(308\) | −12.7366 | −0.725735 | ||||||||
\(309\) | −18.8124 | −1.07020 | ||||||||
\(310\) | 26.3304 | 1.49547 | ||||||||
\(311\) | −32.0913 | −1.81973 | −0.909865 | − | 0.414904i | \(-0.863815\pi\) | ||||
−0.909865 | + | 0.414904i | \(0.863815\pi\) | |||||||
\(312\) | −27.0383 | −1.53074 | ||||||||
\(313\) | 26.2680 | 1.48475 | 0.742376 | − | 0.669983i | \(-0.233699\pi\) | ||||
0.742376 | + | 0.669983i | \(0.233699\pi\) | |||||||
\(314\) | −8.53381 | −0.481591 | ||||||||
\(315\) | 26.9228 | 1.51693 | ||||||||
\(316\) | 4.11227 | 0.231333 | ||||||||
\(317\) | 21.0135 | 1.18023 | 0.590117 | − | 0.807317i | \(-0.299081\pi\) | ||||
0.590117 | + | 0.807317i | \(0.299081\pi\) | |||||||
\(318\) | 49.7501 | 2.78984 | ||||||||
\(319\) | 16.2644 | 0.910632 | ||||||||
\(320\) | 1.70562 | 0.0953473 | ||||||||
\(321\) | −20.7524 | −1.15828 | ||||||||
\(322\) | −3.66621 | −0.204310 | ||||||||
\(323\) | −19.1388 | −1.06491 | ||||||||
\(324\) | −0.887812 | −0.0493229 | ||||||||
\(325\) | 3.93925 | 0.218510 | ||||||||
\(326\) | 7.37924 | 0.408698 | ||||||||
\(327\) | 2.78240 | 0.153867 | ||||||||
\(328\) | 14.1042 | 0.778776 | ||||||||
\(329\) | 12.4003 | 0.683653 | ||||||||
\(330\) | 41.1725 | 2.26647 | ||||||||
\(331\) | −21.4714 | −1.18017 | −0.590086 | − | 0.807340i | \(-0.700906\pi\) | ||||
−0.590086 | + | 0.807340i | \(0.700906\pi\) | |||||||
\(332\) | −6.26073 | −0.343602 | ||||||||
\(333\) | 4.74173 | 0.259845 | ||||||||
\(334\) | −29.5522 | −1.61702 | ||||||||
\(335\) | 22.2544 | 1.21589 | ||||||||
\(336\) | 37.2843 | 2.03402 | ||||||||
\(337\) | −14.6881 | −0.800113 | −0.400056 | − | 0.916491i | \(-0.631009\pi\) | ||||
−0.400056 | + | 0.916491i | \(0.631009\pi\) | |||||||
\(338\) | −58.8094 | −3.19881 | ||||||||
\(339\) | 7.80887 | 0.424119 | ||||||||
\(340\) | −15.1102 | −0.819467 | ||||||||
\(341\) | 27.5756 | 1.49330 | ||||||||
\(342\) | 27.0408 | 1.46220 | ||||||||
\(343\) | 18.1080 | 0.977739 | ||||||||
\(344\) | −9.90698 | −0.534148 | ||||||||
\(345\) | 4.43915 | 0.238996 | ||||||||
\(346\) | 34.6654 | 1.86362 | ||||||||
\(347\) | 36.8520 | 1.97832 | 0.989158 | − | 0.146854i | \(-0.0469147\pi\) | ||||
0.989158 | + | 0.146854i | \(0.0469147\pi\) | |||||||
\(348\) | 13.7692 | 0.738104 | ||||||||
\(349\) | 26.8690 | 1.43826 | 0.719132 | − | 0.694873i | \(-0.244540\pi\) | ||||
0.719132 | + | 0.694873i | \(0.244540\pi\) | |||||||
\(350\) | −2.80893 | −0.150144 | ||||||||
\(351\) | −32.8279 | −1.75222 | ||||||||
\(352\) | 23.6283 | 1.25939 | ||||||||
\(353\) | −36.0355 | −1.91797 | −0.958987 | − | 0.283449i | \(-0.908521\pi\) | ||||
−0.958987 | + | 0.283449i | \(0.908521\pi\) | |||||||
\(354\) | −45.5284 | −2.41980 | ||||||||
\(355\) | 33.9482 | 1.80178 | ||||||||
\(356\) | 8.76292 | 0.464434 | ||||||||
\(357\) | −45.1049 | −2.38720 | ||||||||
\(358\) | −14.4890 | −0.765769 | ||||||||
\(359\) | 18.5854 | 0.980898 | 0.490449 | − | 0.871470i | \(-0.336833\pi\) | ||||
0.490449 | + | 0.871470i | \(0.336833\pi\) | |||||||
\(360\) | −14.2985 | −0.753595 | ||||||||
\(361\) | −8.83012 | −0.464743 | ||||||||
\(362\) | 21.3807 | 1.12375 | ||||||||
\(363\) | 12.5132 | 0.656775 | ||||||||
\(364\) | 21.9164 | 1.14873 | ||||||||
\(365\) | 0.545479 | 0.0285517 | ||||||||
\(366\) | 2.16581 | 0.113209 | ||||||||
\(367\) | −14.0103 | −0.731330 | −0.365665 | − | 0.930746i | \(-0.619158\pi\) | ||||
−0.365665 | + | 0.930746i | \(0.619158\pi\) | |||||||
\(368\) | 3.76534 | 0.196282 | ||||||||
\(369\) | 46.6197 | 2.42692 | ||||||||
\(370\) | 3.75890 | 0.195416 | ||||||||
\(371\) | 27.0083 | 1.40220 | ||||||||
\(372\) | 23.3450 | 1.21038 | ||||||||
\(373\) | 7.74637 | 0.401092 | 0.200546 | − | 0.979684i | \(-0.435728\pi\) | ||||
0.200546 | + | 0.979684i | \(0.435728\pi\) | |||||||
\(374\) | −42.2483 | −2.18461 | ||||||||
\(375\) | 32.6443 | 1.68575 | ||||||||
\(376\) | −6.58571 | −0.339632 | ||||||||
\(377\) | −27.9869 | −1.44140 | ||||||||
\(378\) | 23.4084 | 1.20400 | ||||||||
\(379\) | 32.9230 | 1.69114 | 0.845569 | − | 0.533866i | \(-0.179261\pi\) | ||||
0.845569 | + | 0.533866i | \(0.179261\pi\) | |||||||
\(380\) | 8.02919 | 0.411889 | ||||||||
\(381\) | −39.2757 | −2.01215 | ||||||||
\(382\) | −13.3764 | −0.684396 | ||||||||
\(383\) | 0.823920 | 0.0421003 | 0.0210502 | − | 0.999778i | \(-0.493299\pi\) | ||||
0.0210502 | + | 0.999778i | \(0.493299\pi\) | |||||||
\(384\) | −29.3632 | −1.49844 | ||||||||
\(385\) | 22.3518 | 1.13915 | ||||||||
\(386\) | −0.313763 | −0.0159701 | ||||||||
\(387\) | −32.7462 | −1.66458 | ||||||||
\(388\) | 1.00794 | 0.0511703 | ||||||||
\(389\) | −14.1751 | −0.718704 | −0.359352 | − | 0.933202i | \(-0.617002\pi\) | ||||
−0.359352 | + | 0.933202i | \(0.617002\pi\) | |||||||
\(390\) | −70.8474 | −3.58750 | ||||||||
\(391\) | −4.55514 | −0.230363 | ||||||||
\(392\) | 0.424887 | 0.0214600 | ||||||||
\(393\) | 10.0128 | 0.505081 | ||||||||
\(394\) | 12.2541 | 0.617354 | ||||||||
\(395\) | −7.21672 | −0.363113 | ||||||||
\(396\) | 22.3585 | 1.12356 | ||||||||
\(397\) | 21.1231 | 1.06014 | 0.530068 | − | 0.847955i | \(-0.322166\pi\) | ||||
0.530068 | + | 0.847955i | \(0.322166\pi\) | |||||||
\(398\) | 23.3917 | 1.17252 | ||||||||
\(399\) | 23.9676 | 1.19988 | ||||||||
\(400\) | 2.88488 | 0.144244 | ||||||||
\(401\) | −15.0252 | −0.750322 | −0.375161 | − | 0.926960i | \(-0.622413\pi\) | ||||
−0.375161 | + | 0.926960i | \(0.622413\pi\) | |||||||
\(402\) | 52.6771 | 2.62730 | ||||||||
\(403\) | −47.4506 | −2.36368 | ||||||||
\(404\) | −1.42382 | −0.0708378 | ||||||||
\(405\) | 1.55804 | 0.0774198 | ||||||||
\(406\) | 19.9564 | 0.990421 | ||||||||
\(407\) | 3.93666 | 0.195133 | ||||||||
\(408\) | 23.9548 | 1.18594 | ||||||||
\(409\) | −12.1723 | −0.601882 | −0.300941 | − | 0.953643i | \(-0.597301\pi\) | ||||
−0.300941 | + | 0.953643i | \(0.597301\pi\) | |||||||
\(410\) | 36.9567 | 1.82516 | ||||||||
\(411\) | −25.1893 | −1.24250 | ||||||||
\(412\) | −8.09847 | −0.398983 | ||||||||
\(413\) | −24.7165 | −1.21622 | ||||||||
\(414\) | 6.43585 | 0.316305 | ||||||||
\(415\) | 10.9871 | 0.539336 | ||||||||
\(416\) | −40.6582 | −1.99343 | ||||||||
\(417\) | −37.2308 | −1.82320 | ||||||||
\(418\) | 22.4497 | 1.09805 | ||||||||
\(419\) | 3.62103 | 0.176899 | 0.0884495 | − | 0.996081i | \(-0.471809\pi\) | ||||
0.0884495 | + | 0.996081i | \(0.471809\pi\) | |||||||
\(420\) | 18.9226 | 0.923328 | ||||||||
\(421\) | 3.23248 | 0.157542 | 0.0787708 | − | 0.996893i | \(-0.474900\pi\) | ||||
0.0787708 | + | 0.996893i | \(0.474900\pi\) | |||||||
\(422\) | −20.4578 | −0.995870 | ||||||||
\(423\) | −21.7682 | −1.05841 | ||||||||
\(424\) | −14.3439 | −0.696601 | ||||||||
\(425\) | −3.49000 | −0.169290 | ||||||||
\(426\) | 80.3571 | 3.89331 | ||||||||
\(427\) | 1.17578 | 0.0568999 | ||||||||
\(428\) | −8.93360 | −0.431822 | ||||||||
\(429\) | −74.1978 | −3.58230 | ||||||||
\(430\) | −25.9588 | −1.25185 | ||||||||
\(431\) | 2.25650 | 0.108692 | 0.0543458 | − | 0.998522i | \(-0.482693\pi\) | ||||
0.0543458 | + | 0.998522i | \(0.482693\pi\) | |||||||
\(432\) | −24.0413 | −1.15669 | ||||||||
\(433\) | −31.5848 | −1.51787 | −0.758934 | − | 0.651168i | \(-0.774279\pi\) | ||||
−0.758934 | + | 0.651168i | \(0.774279\pi\) | |||||||
\(434\) | 33.8353 | 1.62415 | ||||||||
\(435\) | −24.1638 | −1.15857 | ||||||||
\(436\) | 1.19778 | 0.0573634 | ||||||||
\(437\) | 2.42049 | 0.115788 | ||||||||
\(438\) | 1.29118 | 0.0616947 | ||||||||
\(439\) | 13.0297 | 0.621875 | 0.310938 | − | 0.950430i | \(-0.399357\pi\) | ||||
0.310938 | + | 0.950430i | \(0.399357\pi\) | |||||||
\(440\) | −11.8708 | −0.565919 | ||||||||
\(441\) | 1.40441 | 0.0668765 | ||||||||
\(442\) | 72.6985 | 3.45791 | ||||||||
\(443\) | −33.0720 | −1.57130 | −0.785649 | − | 0.618672i | \(-0.787671\pi\) | ||||
−0.785649 | + | 0.618672i | \(0.787671\pi\) | |||||||
\(444\) | 3.33270 | 0.158163 | ||||||||
\(445\) | −15.3783 | −0.728999 | ||||||||
\(446\) | 9.50731 | 0.450184 | ||||||||
\(447\) | −21.6804 | −1.02545 | ||||||||
\(448\) | 2.19177 | 0.103551 | ||||||||
\(449\) | 9.55322 | 0.450844 | 0.225422 | − | 0.974261i | \(-0.427624\pi\) | ||||
0.225422 | + | 0.974261i | \(0.427624\pi\) | |||||||
\(450\) | 4.93095 | 0.232447 | ||||||||
\(451\) | 38.7045 | 1.82252 | ||||||||
\(452\) | 3.36161 | 0.158117 | ||||||||
\(453\) | −65.8857 | −3.09558 | ||||||||
\(454\) | 29.7317 | 1.39538 | ||||||||
\(455\) | −38.4617 | −1.80311 | ||||||||
\(456\) | −12.7290 | −0.596089 | ||||||||
\(457\) | −16.8717 | −0.789227 | −0.394614 | − | 0.918847i | \(-0.629122\pi\) | ||||
−0.394614 | + | 0.918847i | \(0.629122\pi\) | |||||||
\(458\) | −19.4983 | −0.911096 | ||||||||
\(459\) | 29.0841 | 1.35753 | ||||||||
\(460\) | 1.91099 | 0.0891005 | ||||||||
\(461\) | 12.4727 | 0.580913 | 0.290456 | − | 0.956888i | \(-0.406193\pi\) | ||||
0.290456 | + | 0.956888i | \(0.406193\pi\) | |||||||
\(462\) | 52.9077 | 2.46149 | ||||||||
\(463\) | −7.20181 | −0.334696 | −0.167348 | − | 0.985898i | \(-0.553520\pi\) | ||||
−0.167348 | + | 0.985898i | \(0.553520\pi\) | |||||||
\(464\) | −20.4960 | −0.951503 | ||||||||
\(465\) | −40.9687 | −1.89988 | ||||||||
\(466\) | −36.0203 | −1.66861 | ||||||||
\(467\) | 31.6042 | 1.46247 | 0.731234 | − | 0.682126i | \(-0.238945\pi\) | ||||
0.731234 | + | 0.682126i | \(0.238945\pi\) | |||||||
\(468\) | −38.4732 | −1.77843 | ||||||||
\(469\) | 28.5974 | 1.32051 | ||||||||
\(470\) | −17.2563 | −0.795972 | ||||||||
\(471\) | 13.2782 | 0.611825 | ||||||||
\(472\) | 13.1267 | 0.604205 | ||||||||
\(473\) | −27.1864 | −1.25003 | ||||||||
\(474\) | −17.0823 | −0.784617 | ||||||||
\(475\) | 1.85450 | 0.0850904 | ||||||||
\(476\) | −19.4170 | −0.889977 | ||||||||
\(477\) | −47.4118 | −2.17084 | ||||||||
\(478\) | 1.17650 | 0.0538118 | ||||||||
\(479\) | −30.7261 | −1.40391 | −0.701956 | − | 0.712220i | \(-0.747690\pi\) | ||||
−0.701956 | + | 0.712220i | \(0.747690\pi\) | |||||||
\(480\) | −35.1042 | −1.60228 | ||||||||
\(481\) | −6.77398 | −0.308867 | ||||||||
\(482\) | 25.4949 | 1.16126 | ||||||||
\(483\) | 5.70442 | 0.259560 | ||||||||
\(484\) | 5.38677 | 0.244853 | ||||||||
\(485\) | −1.76886 | −0.0803196 | ||||||||
\(486\) | 29.6862 | 1.34659 | ||||||||
\(487\) | −20.5462 | −0.931039 | −0.465520 | − | 0.885038i | \(-0.654133\pi\) | ||||
−0.465520 | + | 0.885038i | \(0.654133\pi\) | |||||||
\(488\) | −0.624445 | −0.0282673 | ||||||||
\(489\) | −11.4817 | −0.519220 | ||||||||
\(490\) | 1.11331 | 0.0502943 | ||||||||
\(491\) | −25.3948 | −1.14605 | −0.573025 | − | 0.819538i | \(-0.694230\pi\) | ||||
−0.573025 | + | 0.819538i | \(0.694230\pi\) | |||||||
\(492\) | 32.7665 | 1.47723 | ||||||||
\(493\) | 24.7952 | 1.11672 | ||||||||
\(494\) | −38.6302 | −1.73805 | ||||||||
\(495\) | −39.2374 | −1.76359 | ||||||||
\(496\) | −34.7501 | −1.56033 | ||||||||
\(497\) | 43.6243 | 1.95682 | ||||||||
\(498\) | 26.0070 | 1.16540 | ||||||||
\(499\) | −11.5170 | −0.515570 | −0.257785 | − | 0.966202i | \(-0.582993\pi\) | ||||
−0.257785 | + | 0.966202i | \(0.582993\pi\) | |||||||
\(500\) | 14.0529 | 0.628466 | ||||||||
\(501\) | 45.9816 | 2.05431 | ||||||||
\(502\) | 21.6771 | 0.967497 | ||||||||
\(503\) | 43.6694 | 1.94712 | 0.973562 | − | 0.228423i | \(-0.0733569\pi\) | ||||
0.973562 | + | 0.228423i | \(0.0733569\pi\) | |||||||
\(504\) | −18.3739 | −0.818438 | ||||||||
\(505\) | 2.49870 | 0.111191 | ||||||||
\(506\) | 5.34315 | 0.237532 | ||||||||
\(507\) | 91.5043 | 4.06385 | ||||||||
\(508\) | −16.9076 | −0.750155 | ||||||||
\(509\) | 24.5143 | 1.08658 | 0.543288 | − | 0.839546i | \(-0.317179\pi\) | ||||
0.543288 | + | 0.839546i | \(0.317179\pi\) | |||||||
\(510\) | 62.7677 | 2.77940 | ||||||||
\(511\) | 0.700954 | 0.0310084 | ||||||||
\(512\) | −15.5425 | −0.686887 | ||||||||
\(513\) | −15.4546 | −0.682335 | ||||||||
\(514\) | 56.1542 | 2.47685 | ||||||||
\(515\) | 14.2122 | 0.626264 | ||||||||
\(516\) | −23.0155 | −1.01320 | ||||||||
\(517\) | −18.0723 | −0.794820 | ||||||||
\(518\) | 4.83028 | 0.212230 | ||||||||
\(519\) | −53.9374 | −2.36759 | ||||||||
\(520\) | 20.4266 | 0.895767 | ||||||||
\(521\) | −37.2286 | −1.63102 | −0.815508 | − | 0.578746i | \(-0.803542\pi\) | ||||
−0.815508 | + | 0.578746i | \(0.803542\pi\) | |||||||
\(522\) | −35.0325 | −1.53333 | ||||||||
\(523\) | −1.64243 | −0.0718184 | −0.0359092 | − | 0.999355i | \(-0.511433\pi\) | ||||
−0.0359092 | + | 0.999355i | \(0.511433\pi\) | |||||||
\(524\) | 4.31039 | 0.188300 | ||||||||
\(525\) | 4.37055 | 0.190746 | ||||||||
\(526\) | 4.32009 | 0.188365 | ||||||||
\(527\) | 42.0392 | 1.83126 | ||||||||
\(528\) | −54.3383 | −2.36477 | ||||||||
\(529\) | −22.4239 | −0.974953 | ||||||||
\(530\) | −37.5847 | −1.63257 | ||||||||
\(531\) | 43.3885 | 1.88290 | ||||||||
\(532\) | 10.3177 | 0.447330 | ||||||||
\(533\) | −66.6005 | −2.88479 | ||||||||
\(534\) | −36.4011 | −1.57523 | ||||||||
\(535\) | 15.6778 | 0.677810 | ||||||||
\(536\) | −15.1878 | −0.656014 | ||||||||
\(537\) | 22.5441 | 0.972852 | ||||||||
\(538\) | −40.9822 | −1.76687 | ||||||||
\(539\) | 1.16596 | 0.0502215 | ||||||||
\(540\) | −12.2015 | −0.525068 | ||||||||
\(541\) | 33.9018 | 1.45755 | 0.728776 | − | 0.684752i | \(-0.240089\pi\) | ||||
0.728776 | + | 0.684752i | \(0.240089\pi\) | |||||||
\(542\) | 13.4905 | 0.579465 | ||||||||
\(543\) | −33.2672 | −1.42763 | ||||||||
\(544\) | 36.0214 | 1.54441 | ||||||||
\(545\) | −2.10202 | −0.0900405 | ||||||||
\(546\) | −91.0406 | −3.89618 | ||||||||
\(547\) | 5.57659 | 0.238438 | 0.119219 | − | 0.992868i | \(-0.461961\pi\) | ||||
0.119219 | + | 0.992868i | \(0.461961\pi\) | |||||||
\(548\) | −10.8436 | −0.463217 | ||||||||
\(549\) | −2.06402 | −0.0880902 | ||||||||
\(550\) | 4.09375 | 0.174558 | ||||||||
\(551\) | −13.1755 | −0.561297 | ||||||||
\(552\) | −3.02957 | −0.128947 | ||||||||
\(553\) | −9.27367 | −0.394356 | ||||||||
\(554\) | 42.2305 | 1.79420 | ||||||||
\(555\) | −5.84864 | −0.248261 | ||||||||
\(556\) | −16.0274 | −0.679711 | ||||||||
\(557\) | −15.9952 | −0.677739 | −0.338869 | − | 0.940833i | \(-0.610044\pi\) | ||||
−0.338869 | + | 0.940833i | \(0.610044\pi\) | |||||||
\(558\) | −59.3962 | −2.51444 | ||||||||
\(559\) | 46.7809 | 1.97862 | ||||||||
\(560\) | −28.1671 | −1.19028 | ||||||||
\(561\) | 65.7360 | 2.77538 | ||||||||
\(562\) | 8.55307 | 0.360790 | ||||||||
\(563\) | −26.7907 | −1.12909 | −0.564546 | − | 0.825402i | \(-0.690949\pi\) | ||||
−0.564546 | + | 0.825402i | \(0.690949\pi\) | |||||||
\(564\) | −15.2997 | −0.644233 | ||||||||
\(565\) | −5.89937 | −0.248188 | ||||||||
\(566\) | 4.74670 | 0.199519 | ||||||||
\(567\) | 2.00212 | 0.0840813 | ||||||||
\(568\) | −23.1685 | −0.972128 | ||||||||
\(569\) | 12.7764 | 0.535613 | 0.267807 | − | 0.963473i | \(-0.413701\pi\) | ||||
0.267807 | + | 0.963473i | \(0.413701\pi\) | |||||||
\(570\) | −33.3532 | −1.39701 | ||||||||
\(571\) | 28.4365 | 1.19003 | 0.595015 | − | 0.803715i | \(-0.297146\pi\) | ||||
0.595015 | + | 0.803715i | \(0.297146\pi\) | |||||||
\(572\) | −31.9411 | −1.33552 | ||||||||
\(573\) | 20.8129 | 0.869473 | ||||||||
\(574\) | 47.4903 | 1.98221 | ||||||||
\(575\) | 0.441382 | 0.0184069 | ||||||||
\(576\) | −3.84754 | −0.160314 | ||||||||
\(577\) | 11.2263 | 0.467358 | 0.233679 | − | 0.972314i | \(-0.424924\pi\) | ||||
0.233679 | + | 0.972314i | \(0.424924\pi\) | |||||||
\(578\) | −34.0077 | −1.41453 | ||||||||
\(579\) | 0.488199 | 0.0202888 | ||||||||
\(580\) | −10.4022 | −0.431927 | ||||||||
\(581\) | 14.1187 | 0.585742 | ||||||||
\(582\) | −4.18697 | −0.173555 | ||||||||
\(583\) | −39.3621 | −1.63021 | ||||||||
\(584\) | −0.372270 | −0.0154047 | ||||||||
\(585\) | 67.5176 | 2.79151 | ||||||||
\(586\) | −6.94396 | −0.286852 | ||||||||
\(587\) | −19.0259 | −0.785282 | −0.392641 | − | 0.919692i | \(-0.628438\pi\) | ||||
−0.392641 | + | 0.919692i | \(0.628438\pi\) | |||||||
\(588\) | 0.987082 | 0.0407066 | ||||||||
\(589\) | −22.3386 | −0.920445 | ||||||||
\(590\) | 34.3953 | 1.41603 | ||||||||
\(591\) | −19.0668 | −0.784302 | ||||||||
\(592\) | −4.96088 | −0.203891 | ||||||||
\(593\) | 11.6814 | 0.479700 | 0.239850 | − | 0.970810i | \(-0.422902\pi\) | ||||
0.239850 | + | 0.970810i | \(0.422902\pi\) | |||||||
\(594\) | −34.1154 | −1.39977 | ||||||||
\(595\) | 34.0754 | 1.39695 | ||||||||
\(596\) | −9.33311 | −0.382299 | ||||||||
\(597\) | −36.3962 | −1.48960 | ||||||||
\(598\) | −9.19419 | −0.375978 | ||||||||
\(599\) | 4.17039 | 0.170397 | 0.0851987 | − | 0.996364i | \(-0.472847\pi\) | ||||
0.0851987 | + | 0.996364i | \(0.472847\pi\) | |||||||
\(600\) | −2.32116 | −0.0947609 | ||||||||
\(601\) | −3.93243 | −0.160407 | −0.0802036 | − | 0.996779i | \(-0.525557\pi\) | ||||
−0.0802036 | + | 0.996779i | \(0.525557\pi\) | |||||||
\(602\) | −33.3577 | −1.35956 | ||||||||
\(603\) | −50.2013 | −2.04436 | ||||||||
\(604\) | −28.3629 | −1.15407 | ||||||||
\(605\) | −9.45338 | −0.384334 | ||||||||
\(606\) | 5.91454 | 0.240262 | ||||||||
\(607\) | 10.4646 | 0.424747 | 0.212373 | − | 0.977189i | \(-0.431881\pi\) | ||||
0.212373 | + | 0.977189i | \(0.431881\pi\) | |||||||
\(608\) | −19.1409 | −0.776266 | ||||||||
\(609\) | −31.0511 | −1.25825 | ||||||||
\(610\) | −1.63621 | −0.0662481 | ||||||||
\(611\) | 31.0978 | 1.25808 | ||||||||
\(612\) | 34.0856 | 1.37783 | ||||||||
\(613\) | 25.1831 | 1.01714 | 0.508568 | − | 0.861022i | \(-0.330175\pi\) | ||||
0.508568 | + | 0.861022i | \(0.330175\pi\) | |||||||
\(614\) | 29.2815 | 1.18171 | ||||||||
\(615\) | −57.5027 | −2.31873 | ||||||||
\(616\) | −15.2543 | −0.614613 | ||||||||
\(617\) | 26.3726 | 1.06172 | 0.530860 | − | 0.847459i | \(-0.321869\pi\) | ||||
0.530860 | + | 0.847459i | \(0.321869\pi\) | |||||||
\(618\) | 33.6410 | 1.35324 | ||||||||
\(619\) | −7.11938 | −0.286152 | −0.143076 | − | 0.989712i | \(-0.545699\pi\) | ||||
−0.143076 | + | 0.989712i | \(0.545699\pi\) | |||||||
\(620\) | −17.6365 | −0.708298 | ||||||||
\(621\) | −3.67827 | −0.147604 | ||||||||
\(622\) | 57.3868 | 2.30100 | ||||||||
\(623\) | −19.7614 | −0.791726 | ||||||||
\(624\) | 93.5022 | 3.74308 | ||||||||
\(625\) | −21.7542 | −0.870168 | ||||||||
\(626\) | −46.9733 | −1.87743 | ||||||||
\(627\) | −34.9305 | −1.39499 | ||||||||
\(628\) | 5.71606 | 0.228096 | ||||||||
\(629\) | 6.00146 | 0.239294 | ||||||||
\(630\) | −48.1443 | −1.91811 | ||||||||
\(631\) | −29.3342 | −1.16777 | −0.583887 | − | 0.811835i | \(-0.698469\pi\) | ||||
−0.583887 | + | 0.811835i | \(0.698469\pi\) | |||||||
\(632\) | 4.92516 | 0.195912 | ||||||||
\(633\) | 31.8312 | 1.26518 | ||||||||
\(634\) | −37.5770 | −1.49237 | ||||||||
\(635\) | 29.6716 | 1.17748 | ||||||||
\(636\) | −33.3232 | −1.32135 | ||||||||
\(637\) | −2.00632 | −0.0794934 | ||||||||
\(638\) | −29.0846 | −1.15147 | ||||||||
\(639\) | −76.5803 | −3.02947 | ||||||||
\(640\) | 22.1830 | 0.876861 | ||||||||
\(641\) | −14.2890 | −0.564381 | −0.282190 | − | 0.959358i | \(-0.591061\pi\) | ||||
−0.282190 | + | 0.959358i | \(0.591061\pi\) | |||||||
\(642\) | 37.1101 | 1.46462 | ||||||||
\(643\) | −10.6239 | −0.418966 | −0.209483 | − | 0.977812i | \(-0.567178\pi\) | ||||
−0.209483 | + | 0.977812i | \(0.567178\pi\) | |||||||
\(644\) | 2.45567 | 0.0967671 | ||||||||
\(645\) | 40.3905 | 1.59038 | ||||||||
\(646\) | 34.2247 | 1.34655 | ||||||||
\(647\) | 36.9129 | 1.45120 | 0.725598 | − | 0.688119i | \(-0.241563\pi\) | ||||
0.725598 | + | 0.688119i | \(0.241563\pi\) | |||||||
\(648\) | −1.06331 | −0.0417708 | ||||||||
\(649\) | 36.0219 | 1.41398 | ||||||||
\(650\) | −7.04430 | −0.276300 | ||||||||
\(651\) | −52.6459 | −2.06335 | ||||||||
\(652\) | −4.94271 | −0.193571 | ||||||||
\(653\) | −32.4831 | −1.27116 | −0.635580 | − | 0.772035i | \(-0.719239\pi\) | ||||
−0.635580 | + | 0.772035i | \(0.719239\pi\) | |||||||
\(654\) | −4.97558 | −0.194560 | ||||||||
\(655\) | −7.56440 | −0.295565 | ||||||||
\(656\) | −48.7744 | −1.90432 | ||||||||
\(657\) | −1.23049 | −0.0480060 | ||||||||
\(658\) | −22.1747 | −0.864461 | ||||||||
\(659\) | 7.88394 | 0.307115 | 0.153557 | − | 0.988140i | \(-0.450927\pi\) | ||||
0.153557 | + | 0.988140i | \(0.450927\pi\) | |||||||
\(660\) | −27.5779 | −1.07347 | ||||||||
\(661\) | 5.11501 | 0.198951 | 0.0994754 | − | 0.995040i | \(-0.468284\pi\) | ||||
0.0994754 | + | 0.995040i | \(0.468284\pi\) | |||||||
\(662\) | 38.3958 | 1.49230 | ||||||||
\(663\) | −113.115 | −4.39302 | ||||||||
\(664\) | −7.49831 | −0.290991 | ||||||||
\(665\) | −18.1068 | −0.702152 | ||||||||
\(666\) | −8.47932 | −0.328567 | ||||||||
\(667\) | −3.13585 | −0.121421 | ||||||||
\(668\) | 19.7944 | 0.765870 | ||||||||
\(669\) | −14.7929 | −0.571925 | ||||||||
\(670\) | −39.7960 | −1.53745 | ||||||||
\(671\) | −1.71358 | −0.0661522 | ||||||||
\(672\) | −45.1098 | −1.74015 | ||||||||
\(673\) | −7.50326 | −0.289229 | −0.144615 | − | 0.989488i | \(-0.546194\pi\) | ||||
−0.144615 | + | 0.989488i | \(0.546194\pi\) | |||||||
\(674\) | 26.2658 | 1.01172 | ||||||||
\(675\) | −2.81818 | −0.108472 | ||||||||
\(676\) | 39.3913 | 1.51505 | ||||||||
\(677\) | −15.5864 | −0.599033 | −0.299516 | − | 0.954091i | \(-0.596825\pi\) | ||||
−0.299516 | + | 0.954091i | \(0.596825\pi\) | |||||||
\(678\) | −13.9641 | −0.536287 | ||||||||
\(679\) | −2.27302 | −0.0872307 | ||||||||
\(680\) | −18.0971 | −0.693993 | ||||||||
\(681\) | −46.2609 | −1.77272 | ||||||||
\(682\) | −49.3117 | −1.88824 | ||||||||
\(683\) | 6.82105 | 0.261000 | 0.130500 | − | 0.991448i | \(-0.458342\pi\) | ||||
0.130500 | + | 0.991448i | \(0.458342\pi\) | |||||||
\(684\) | −18.1122 | −0.692539 | ||||||||
\(685\) | 19.0297 | 0.727089 | ||||||||
\(686\) | −32.3813 | −1.23632 | ||||||||
\(687\) | 30.3383 | 1.15748 | ||||||||
\(688\) | 34.2597 | 1.30614 | ||||||||
\(689\) | 67.7321 | 2.58039 | ||||||||
\(690\) | −7.93824 | −0.302204 | ||||||||
\(691\) | −21.8120 | −0.829768 | −0.414884 | − | 0.909874i | \(-0.636178\pi\) | ||||
−0.414884 | + | 0.909874i | \(0.636178\pi\) | |||||||
\(692\) | −23.2193 | −0.882666 | ||||||||
\(693\) | −50.4211 | −1.91534 | ||||||||
\(694\) | −65.8999 | −2.50153 | ||||||||
\(695\) | 28.1268 | 1.06691 | ||||||||
\(696\) | 16.4910 | 0.625088 | ||||||||
\(697\) | 59.0051 | 2.23498 | ||||||||
\(698\) | −48.0481 | −1.81865 | ||||||||
\(699\) | 56.0456 | 2.11984 | ||||||||
\(700\) | 1.88146 | 0.0711125 | ||||||||
\(701\) | 19.3683 | 0.731530 | 0.365765 | − | 0.930707i | \(-0.380807\pi\) | ||||
0.365765 | + | 0.930707i | \(0.380807\pi\) | |||||||
\(702\) | 58.7039 | 2.21564 | ||||||||
\(703\) | −3.18902 | −0.120276 | ||||||||
\(704\) | −3.19429 | −0.120390 | ||||||||
\(705\) | 26.8498 | 1.01122 | ||||||||
\(706\) | 64.4399 | 2.42523 | ||||||||
\(707\) | 3.21089 | 0.120758 | ||||||||
\(708\) | 30.4955 | 1.14609 | ||||||||
\(709\) | −7.76462 | −0.291607 | −0.145803 | − | 0.989314i | \(-0.546577\pi\) | ||||
−0.145803 | + | 0.989314i | \(0.546577\pi\) | |||||||
\(710\) | −60.7074 | −2.27831 | ||||||||
\(711\) | 16.2795 | 0.610528 | ||||||||
\(712\) | 10.4951 | 0.393321 | ||||||||
\(713\) | −5.31670 | −0.199112 | ||||||||
\(714\) | 80.6581 | 3.01855 | ||||||||
\(715\) | 56.0542 | 2.09631 | ||||||||
\(716\) | 9.70494 | 0.362691 | ||||||||
\(717\) | −1.83057 | −0.0683639 | ||||||||
\(718\) | −33.2350 | −1.24032 | ||||||||
\(719\) | −25.8127 | −0.962650 | −0.481325 | − | 0.876542i | \(-0.659844\pi\) | ||||
−0.481325 | + | 0.876542i | \(0.659844\pi\) | |||||||
\(720\) | 49.4460 | 1.84275 | ||||||||
\(721\) | 18.2630 | 0.680151 | ||||||||
\(722\) | 15.7903 | 0.587655 | ||||||||
\(723\) | −39.6687 | −1.47529 | ||||||||
\(724\) | −14.3211 | −0.532238 | ||||||||
\(725\) | −2.40259 | −0.0892300 | ||||||||
\(726\) | −22.3766 | −0.830474 | ||||||||
\(727\) | −12.4894 | −0.463204 | −0.231602 | − | 0.972811i | \(-0.574397\pi\) | ||||
−0.231602 | + | 0.972811i | \(0.574397\pi\) | |||||||
\(728\) | 26.2487 | 0.972843 | ||||||||
\(729\) | −43.9665 | −1.62839 | ||||||||
\(730\) | −0.975444 | −0.0361028 | ||||||||
\(731\) | −41.4459 | −1.53293 | ||||||||
\(732\) | −1.45069 | −0.0536190 | ||||||||
\(733\) | 35.6254 | 1.31585 | 0.657927 | − | 0.753081i | \(-0.271433\pi\) | ||||
0.657927 | + | 0.753081i | \(0.271433\pi\) | |||||||
\(734\) | 25.0536 | 0.924747 | ||||||||
\(735\) | −1.73225 | −0.0638951 | ||||||||
\(736\) | −4.55564 | −0.167923 | ||||||||
\(737\) | −41.6780 | −1.53523 | ||||||||
\(738\) | −83.3670 | −3.06878 | ||||||||
\(739\) | 28.5841 | 1.05148 | 0.525741 | − | 0.850644i | \(-0.323788\pi\) | ||||
0.525741 | + | 0.850644i | \(0.323788\pi\) | |||||||
\(740\) | −2.51776 | −0.0925546 | ||||||||
\(741\) | 60.1064 | 2.20807 | ||||||||
\(742\) | −48.2973 | −1.77305 | ||||||||
\(743\) | 8.02060 | 0.294247 | 0.147124 | − | 0.989118i | \(-0.452999\pi\) | ||||
0.147124 | + | 0.989118i | \(0.452999\pi\) | |||||||
\(744\) | 27.9597 | 1.02505 | ||||||||
\(745\) | 16.3789 | 0.600076 | ||||||||
\(746\) | −13.8523 | −0.507170 | ||||||||
\(747\) | −24.7847 | −0.906824 | ||||||||
\(748\) | 28.2984 | 1.03469 | ||||||||
\(749\) | 20.1463 | 0.736131 | ||||||||
\(750\) | −58.3757 | −2.13158 | ||||||||
\(751\) | −30.1413 | −1.09987 | −0.549936 | − | 0.835207i | \(-0.685348\pi\) | ||||
−0.549936 | + | 0.835207i | \(0.685348\pi\) | |||||||
\(752\) | 22.7743 | 0.830493 | ||||||||
\(753\) | −33.7284 | −1.22913 | ||||||||
\(754\) | 50.0471 | 1.82261 | ||||||||
\(755\) | 49.7747 | 1.81149 | ||||||||
\(756\) | −15.6792 | −0.570248 | ||||||||
\(757\) | −47.4022 | −1.72286 | −0.861431 | − | 0.507875i | \(-0.830431\pi\) | ||||
−0.861431 | + | 0.507875i | \(0.830431\pi\) | |||||||
\(758\) | −58.8740 | −2.13840 | ||||||||
\(759\) | −8.31365 | −0.301766 | ||||||||
\(760\) | 9.61636 | 0.348822 | ||||||||
\(761\) | 41.3674 | 1.49957 | 0.749784 | − | 0.661683i | \(-0.230157\pi\) | ||||
0.749784 | + | 0.661683i | \(0.230157\pi\) | |||||||
\(762\) | 70.2341 | 2.54431 | ||||||||
\(763\) | −2.70114 | −0.0977880 | ||||||||
\(764\) | 8.95968 | 0.324150 | ||||||||
\(765\) | −59.8176 | −2.16271 | ||||||||
\(766\) | −1.47336 | −0.0532347 | ||||||||
\(767\) | −61.9844 | −2.23813 | ||||||||
\(768\) | 57.0237 | 2.05767 | ||||||||
\(769\) | −50.6174 | −1.82531 | −0.912656 | − | 0.408729i | \(-0.865972\pi\) | ||||
−0.912656 | + | 0.408729i | \(0.865972\pi\) | |||||||
\(770\) | −39.9702 | −1.44043 | ||||||||
\(771\) | −87.3728 | −3.14666 | ||||||||
\(772\) | 0.210163 | 0.00756392 | ||||||||
\(773\) | 47.8950 | 1.72266 | 0.861332 | − | 0.508042i | \(-0.169631\pi\) | ||||
0.861332 | + | 0.508042i | \(0.169631\pi\) | |||||||
\(774\) | 58.5579 | 2.10482 | ||||||||
\(775\) | −4.07349 | −0.146324 | ||||||||
\(776\) | 1.20718 | 0.0433353 | ||||||||
\(777\) | −7.51565 | −0.269623 | ||||||||
\(778\) | 25.3483 | 0.908782 | ||||||||
\(779\) | −31.3539 | −1.12337 | ||||||||
\(780\) | 47.4545 | 1.69914 | ||||||||
\(781\) | −63.5783 | −2.27501 | ||||||||
\(782\) | 8.14566 | 0.291288 | ||||||||
\(783\) | 20.0221 | 0.715531 | ||||||||
\(784\) | −1.46932 | −0.0524756 | ||||||||
\(785\) | −10.0312 | −0.358030 | ||||||||
\(786\) | −17.9053 | −0.638661 | ||||||||
\(787\) | 22.3680 | 0.797333 | 0.398667 | − | 0.917096i | \(-0.369473\pi\) | ||||
0.398667 | + | 0.917096i | \(0.369473\pi\) | |||||||
\(788\) | −8.20797 | −0.292397 | ||||||||
\(789\) | −6.72183 | −0.239304 | ||||||||
\(790\) | 12.9052 | 0.459146 | ||||||||
\(791\) | −7.58083 | −0.269543 | ||||||||
\(792\) | 26.7782 | 0.951521 | ||||||||
\(793\) | 2.94864 | 0.104709 | ||||||||
\(794\) | −37.7730 | −1.34051 | ||||||||
\(795\) | 58.4797 | 2.07406 | ||||||||
\(796\) | −15.6681 | −0.555340 | ||||||||
\(797\) | 35.1360 | 1.24458 | 0.622290 | − | 0.782787i | \(-0.286202\pi\) | ||||
0.622290 | + | 0.782787i | \(0.286202\pi\) | |||||||
\(798\) | −42.8597 | −1.51722 | ||||||||
\(799\) | −27.5513 | −0.974696 | ||||||||
\(800\) | −3.49039 | −0.123404 | ||||||||
\(801\) | 34.6903 | 1.22572 | ||||||||
\(802\) | 26.8686 | 0.948762 | ||||||||
\(803\) | −1.02157 | −0.0360506 | ||||||||
\(804\) | −35.2838 | −1.24436 | ||||||||
\(805\) | −4.30952 | −0.151891 | ||||||||
\(806\) | 84.8528 | 2.98881 | ||||||||
\(807\) | 63.7661 | 2.24467 | ||||||||
\(808\) | −1.70528 | −0.0599914 | ||||||||
\(809\) | 7.04084 | 0.247543 | 0.123771 | − | 0.992311i | \(-0.460501\pi\) | ||||
0.123771 | + | 0.992311i | \(0.460501\pi\) | |||||||
\(810\) | −2.78615 | −0.0978952 | ||||||||
\(811\) | 26.9729 | 0.947146 | 0.473573 | − | 0.880755i | \(-0.342964\pi\) | ||||
0.473573 | + | 0.880755i | \(0.342964\pi\) | |||||||
\(812\) | −13.3671 | −0.469092 | ||||||||
\(813\) | −20.9904 | −0.736166 | ||||||||
\(814\) | −7.03967 | −0.246740 | ||||||||
\(815\) | 8.67408 | 0.303840 | ||||||||
\(816\) | −82.8389 | −2.89994 | ||||||||
\(817\) | 22.0233 | 0.770498 | ||||||||
\(818\) | 21.7670 | 0.761064 | ||||||||
\(819\) | 86.7618 | 3.03170 | ||||||||
\(820\) | −24.7541 | −0.864451 | ||||||||
\(821\) | 46.4733 | 1.62193 | 0.810964 | − | 0.585096i | \(-0.198943\pi\) | ||||
0.810964 | + | 0.585096i | \(0.198943\pi\) | |||||||
\(822\) | 45.0443 | 1.57110 | ||||||||
\(823\) | 7.03604 | 0.245261 | 0.122630 | − | 0.992452i | \(-0.460867\pi\) | ||||
0.122630 | + | 0.992452i | \(0.460867\pi\) | |||||||
\(824\) | −9.69933 | −0.337892 | ||||||||
\(825\) | −6.36966 | −0.221763 | ||||||||
\(826\) | 44.1988 | 1.53787 | ||||||||
\(827\) | 50.5036 | 1.75618 | 0.878091 | − | 0.478494i | \(-0.158817\pi\) | ||||
0.878091 | + | 0.478494i | \(0.158817\pi\) | |||||||
\(828\) | −4.31081 | −0.149811 | ||||||||
\(829\) | −13.4652 | −0.467665 | −0.233832 | − | 0.972277i | \(-0.575127\pi\) | ||||
−0.233832 | + | 0.972277i | \(0.575127\pi\) | |||||||
\(830\) | −19.6475 | −0.681975 | ||||||||
\(831\) | −65.7083 | −2.27940 | ||||||||
\(832\) | 5.49656 | 0.190559 | ||||||||
\(833\) | 1.77751 | 0.0615872 | ||||||||
\(834\) | 66.5775 | 2.30539 | ||||||||
\(835\) | −34.7377 | −1.20215 | ||||||||
\(836\) | −15.0371 | −0.520069 | ||||||||
\(837\) | 33.9466 | 1.17337 | ||||||||
\(838\) | −6.47525 | −0.223684 | ||||||||
\(839\) | −12.3017 | −0.424703 | −0.212351 | − | 0.977193i | \(-0.568112\pi\) | ||||
−0.212351 | + | 0.977193i | \(0.568112\pi\) | |||||||
\(840\) | 22.6631 | 0.781952 | ||||||||
\(841\) | −11.9305 | −0.411396 | ||||||||
\(842\) | −5.78044 | −0.199207 | ||||||||
\(843\) | −13.3081 | −0.458356 | ||||||||
\(844\) | 13.7029 | 0.471673 | ||||||||
\(845\) | −69.1287 | −2.37810 | ||||||||
\(846\) | 38.9266 | 1.33833 | ||||||||
\(847\) | −12.1478 | −0.417404 | ||||||||
\(848\) | 49.6031 | 1.70338 | ||||||||
\(849\) | −7.38561 | −0.253474 | ||||||||
\(850\) | 6.24095 | 0.214063 | ||||||||
\(851\) | −0.759006 | −0.0260184 | ||||||||
\(852\) | −53.8242 | −1.84399 | ||||||||
\(853\) | 35.2408 | 1.20662 | 0.603311 | − | 0.797506i | \(-0.293848\pi\) | ||||
0.603311 | + | 0.797506i | \(0.293848\pi\) | |||||||
\(854\) | −2.10257 | −0.0719483 | ||||||||
\(855\) | 31.7856 | 1.08704 | ||||||||
\(856\) | −10.6995 | −0.365703 | ||||||||
\(857\) | 7.60745 | 0.259866 | 0.129933 | − | 0.991523i | \(-0.458524\pi\) | ||||
0.129933 | + | 0.991523i | \(0.458524\pi\) | |||||||
\(858\) | 132.683 | 4.52972 | ||||||||
\(859\) | 56.1782 | 1.91678 | 0.958388 | − | 0.285470i | \(-0.0921497\pi\) | ||||
0.958388 | + | 0.285470i | \(0.0921497\pi\) | |||||||
\(860\) | 17.3876 | 0.592911 | ||||||||
\(861\) | −73.8924 | −2.51825 | ||||||||
\(862\) | −4.03514 | −0.137438 | ||||||||
\(863\) | 42.7233 | 1.45432 | 0.727159 | − | 0.686469i | \(-0.240840\pi\) | ||||
0.727159 | + | 0.686469i | \(0.240840\pi\) | |||||||
\(864\) | 29.0873 | 0.989569 | ||||||||
\(865\) | 40.7481 | 1.38548 | ||||||||
\(866\) | 56.4810 | 1.91930 | ||||||||
\(867\) | 52.9142 | 1.79706 | ||||||||
\(868\) | −22.6633 | −0.769243 | ||||||||
\(869\) | 13.5155 | 0.458481 | ||||||||
\(870\) | 43.2106 | 1.46498 | ||||||||
\(871\) | 71.7171 | 2.43004 | ||||||||
\(872\) | 1.43455 | 0.0485801 | ||||||||
\(873\) | 3.99018 | 0.135047 | ||||||||
\(874\) | −4.32840 | −0.146410 | ||||||||
\(875\) | −31.6911 | −1.07135 | ||||||||
\(876\) | −0.864846 | −0.0292204 | ||||||||
\(877\) | 57.9878 | 1.95811 | 0.979054 | − | 0.203601i | \(-0.0652645\pi\) | ||||
0.979054 | + | 0.203601i | \(0.0652645\pi\) | |||||||
\(878\) | −23.3002 | −0.786344 | ||||||||
\(879\) | 10.8044 | 0.364424 | ||||||||
\(880\) | 41.0509 | 1.38383 | ||||||||
\(881\) | −49.4646 | −1.66650 | −0.833252 | − | 0.552893i | \(-0.813524\pi\) | ||||
−0.833252 | + | 0.552893i | \(0.813524\pi\) | |||||||
\(882\) | −2.51141 | −0.0845635 | ||||||||
\(883\) | −2.51710 | −0.0847070 | −0.0423535 | − | 0.999103i | \(-0.513486\pi\) | ||||
−0.0423535 | + | 0.999103i | \(0.513486\pi\) | |||||||
\(884\) | −48.6944 | −1.63777 | ||||||||
\(885\) | −53.5172 | −1.79896 | ||||||||
\(886\) | 59.1405 | 1.98686 | ||||||||
\(887\) | −19.6261 | −0.658981 | −0.329490 | − | 0.944159i | \(-0.606877\pi\) | ||||
−0.329490 | + | 0.944159i | \(0.606877\pi\) | |||||||
\(888\) | 3.99149 | 0.133946 | ||||||||
\(889\) | 38.1287 | 1.27880 | ||||||||
\(890\) | 27.4999 | 0.921800 | ||||||||
\(891\) | −2.91790 | −0.0977535 | ||||||||
\(892\) | −6.36812 | −0.213220 | ||||||||
\(893\) | 14.6401 | 0.489912 | ||||||||
\(894\) | 38.7696 | 1.29665 | ||||||||
\(895\) | −17.0314 | −0.569298 | ||||||||
\(896\) | 28.5058 | 0.952310 | ||||||||
\(897\) | 14.3057 | 0.477652 | ||||||||
\(898\) | −17.0834 | −0.570080 | ||||||||
\(899\) | 28.9406 | 0.965224 | ||||||||
\(900\) | −3.30281 | −0.110094 | ||||||||
\(901\) | −60.0077 | −1.99915 | ||||||||
\(902\) | −69.2126 | −2.30453 | ||||||||
\(903\) | 51.9028 | 1.72722 | ||||||||
\(904\) | 4.02611 | 0.133906 | ||||||||
\(905\) | 25.1324 | 0.835429 | ||||||||
\(906\) | 117.819 | 3.91428 | ||||||||
\(907\) | 24.4150 | 0.810687 | 0.405344 | − | 0.914164i | \(-0.367152\pi\) | ||||
0.405344 | + | 0.914164i | \(0.367152\pi\) | |||||||
\(908\) | −19.9147 | −0.660891 | ||||||||
\(909\) | −5.63656 | −0.186953 | ||||||||
\(910\) | 68.7785 | 2.27998 | ||||||||
\(911\) | −46.4723 | −1.53970 | −0.769848 | − | 0.638228i | \(-0.779668\pi\) | ||||
−0.769848 | + | 0.638228i | \(0.779668\pi\) | |||||||
\(912\) | 44.0185 | 1.45760 | ||||||||
\(913\) | −20.5767 | −0.680988 | ||||||||
\(914\) | 30.1706 | 0.997956 | ||||||||
\(915\) | 2.54585 | 0.0841631 | ||||||||
\(916\) | 13.0602 | 0.431522 | ||||||||
\(917\) | −9.72044 | −0.320997 | ||||||||
\(918\) | −52.0092 | −1.71656 | ||||||||
\(919\) | 12.8499 | 0.423880 | 0.211940 | − | 0.977283i | \(-0.432022\pi\) | ||||
0.211940 | + | 0.977283i | \(0.432022\pi\) | |||||||
\(920\) | 2.28875 | 0.0754577 | ||||||||
\(921\) | −45.5604 | −1.50127 | ||||||||
\(922\) | −22.3042 | −0.734549 | ||||||||
\(923\) | 109.402 | 3.60101 | ||||||||
\(924\) | −35.4383 | −1.16583 | ||||||||
\(925\) | −0.581526 | −0.0191205 | ||||||||
\(926\) | 12.8785 | 0.423214 | ||||||||
\(927\) | −32.0598 | −1.05298 | ||||||||
\(928\) | 24.7979 | 0.814030 | ||||||||
\(929\) | −32.3342 | −1.06085 | −0.530426 | − | 0.847732i | \(-0.677968\pi\) | ||||
−0.530426 | + | 0.847732i | \(0.677968\pi\) | |||||||
\(930\) | 73.2617 | 2.40235 | ||||||||
\(931\) | −0.944527 | −0.0309556 | ||||||||
\(932\) | 24.1268 | 0.790301 | ||||||||
\(933\) | −89.2907 | −2.92325 | ||||||||
\(934\) | −56.5158 | −1.84925 | ||||||||
\(935\) | −49.6616 | −1.62411 | ||||||||
\(936\) | −46.0784 | −1.50612 | ||||||||
\(937\) | 1.44495 | 0.0472044 | 0.0236022 | − | 0.999721i | \(-0.492486\pi\) | ||||
0.0236022 | + | 0.999721i | \(0.492486\pi\) | |||||||
\(938\) | −51.1389 | −1.66974 | ||||||||
\(939\) | 73.0878 | 2.38513 | ||||||||
\(940\) | 11.5585 | 0.376995 | ||||||||
\(941\) | 30.5512 | 0.995941 | 0.497971 | − | 0.867194i | \(-0.334079\pi\) | ||||
0.497971 | + | 0.867194i | \(0.334079\pi\) | |||||||
\(942\) | −23.7444 | −0.773636 | ||||||||
\(943\) | −7.46239 | −0.243009 | ||||||||
\(944\) | −45.3939 | −1.47745 | ||||||||
\(945\) | 27.5158 | 0.895090 | ||||||||
\(946\) | 48.6157 | 1.58063 | ||||||||
\(947\) | 26.2437 | 0.852806 | 0.426403 | − | 0.904533i | \(-0.359781\pi\) | ||||
0.426403 | + | 0.904533i | \(0.359781\pi\) | |||||||
\(948\) | 11.4420 | 0.371618 | ||||||||
\(949\) | 1.75787 | 0.0570628 | ||||||||
\(950\) | −3.31628 | −0.107594 | ||||||||
\(951\) | 58.4678 | 1.89595 | ||||||||
\(952\) | −23.2553 | −0.753707 | ||||||||
\(953\) | −18.7506 | −0.607392 | −0.303696 | − | 0.952769i | \(-0.598221\pi\) | ||||
−0.303696 | + | 0.952769i | \(0.598221\pi\) | |||||||
\(954\) | 84.7835 | 2.74497 | ||||||||
\(955\) | −15.7235 | −0.508802 | ||||||||
\(956\) | −0.788034 | −0.0254869 | ||||||||
\(957\) | 45.2540 | 1.46285 | ||||||||
\(958\) | 54.9455 | 1.77521 | ||||||||
\(959\) | 24.4537 | 0.789651 | ||||||||
\(960\) | 4.74572 | 0.153167 | ||||||||
\(961\) | 18.0676 | 0.582827 | ||||||||
\(962\) | 12.1135 | 0.390554 | ||||||||
\(963\) | −35.3659 | −1.13965 | ||||||||
\(964\) | −17.0768 | −0.550007 | ||||||||
\(965\) | −0.368820 | −0.0118727 | ||||||||
\(966\) | −10.2008 | −0.328207 | ||||||||
\(967\) | 43.9447 | 1.41317 | 0.706584 | − | 0.707630i | \(-0.250235\pi\) | ||||
0.706584 | + | 0.707630i | \(0.250235\pi\) | |||||||
\(968\) | 6.45160 | 0.207362 | ||||||||
\(969\) | −53.2517 | −1.71069 | ||||||||
\(970\) | 3.16313 | 0.101562 | ||||||||
\(971\) | −11.6688 | −0.374471 | −0.187236 | − | 0.982315i | \(-0.559953\pi\) | ||||
−0.187236 | + | 0.982315i | \(0.559953\pi\) | |||||||
\(972\) | −19.8842 | −0.637787 | ||||||||
\(973\) | 36.1436 | 1.15871 | ||||||||
\(974\) | 36.7415 | 1.17727 | ||||||||
\(975\) | 10.9606 | 0.351019 | ||||||||
\(976\) | 2.15942 | 0.0691212 | ||||||||
\(977\) | −19.8935 | −0.636448 | −0.318224 | − | 0.948016i | \(-0.603086\pi\) | ||||
−0.318224 | + | 0.948016i | \(0.603086\pi\) | |||||||
\(978\) | 20.5320 | 0.656540 | ||||||||
\(979\) | 28.8004 | 0.920466 | ||||||||
\(980\) | −0.745711 | −0.0238209 | ||||||||
\(981\) | 4.74173 | 0.151392 | ||||||||
\(982\) | 45.4118 | 1.44915 | ||||||||
\(983\) | 31.8038 | 1.01438 | 0.507192 | − | 0.861833i | \(-0.330683\pi\) | ||||
0.507192 | + | 0.861833i | \(0.330683\pi\) | |||||||
\(984\) | 39.2436 | 1.25104 | ||||||||
\(985\) | 14.4044 | 0.458961 | ||||||||
\(986\) | −44.3396 | −1.41206 | ||||||||
\(987\) | 34.5027 | 1.09823 | ||||||||
\(988\) | 25.8750 | 0.823193 | ||||||||
\(989\) | 5.24167 | 0.166675 | ||||||||
\(990\) | 70.1657 | 2.23001 | ||||||||
\(991\) | −41.5154 | −1.31878 | −0.659390 | − | 0.751801i | \(-0.729185\pi\) | ||||
−0.659390 | + | 0.751801i | \(0.729185\pi\) | |||||||
\(992\) | 42.0438 | 1.33489 | ||||||||
\(993\) | −59.7418 | −1.89585 | ||||||||
\(994\) | −78.0105 | −2.47434 | ||||||||
\(995\) | 27.4963 | 0.871690 | ||||||||
\(996\) | −17.4198 | −0.551968 | ||||||||
\(997\) | −41.5377 | −1.31551 | −0.657756 | − | 0.753231i | \(-0.728494\pi\) | ||||
−0.657756 | + | 0.753231i | \(0.728494\pi\) | |||||||
\(998\) | 20.5950 | 0.651924 | ||||||||
\(999\) | 4.84617 | 0.153326 |
(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 | 4033.2.a.c.1.18 | ✓ | 77 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4033.2.a.c.1.18 | ✓ | 77 | 1.1 | even | 1 | trivial |