Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4598,2,Mod(1,4598)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4598, 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("4598.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4598 = 2 \cdot 11^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4598.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: | \(36.7152148494\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.258228.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 2x^{3} - 12x^{2} + 6x + 24 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(4.19461\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4598.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | −3.19461 | −1.84441 | −0.922205 | − | 0.386700i | \(-0.873615\pi\) | ||||
−0.922205 | + | 0.386700i | \(0.873615\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −4.19461 | −1.87589 | −0.937944 | − | 0.346787i | \(-0.887273\pi\) | ||||
−0.937944 | + | 0.346787i | \(0.887273\pi\) | |||||||
\(6\) | 3.19461 | 1.30420 | ||||||||
\(7\) | −1.32286 | −0.499995 | −0.249997 | − | 0.968247i | \(-0.580430\pi\) | ||||
−0.249997 | + | 0.968247i | \(0.580430\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 7.20555 | 2.40185 | ||||||||
\(10\) | 4.19461 | 1.32645 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | −3.19461 | −0.922205 | ||||||||
\(13\) | 3.52841 | 0.978606 | 0.489303 | − | 0.872114i | \(-0.337251\pi\) | ||||
0.489303 | + | 0.872114i | \(0.337251\pi\) | |||||||
\(14\) | 1.32286 | 0.353550 | ||||||||
\(15\) | 13.4002 | 3.45991 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 2.32286 | 0.563377 | 0.281688 | − | 0.959506i | \(-0.409106\pi\) | ||||
0.281688 | + | 0.959506i | \(0.409106\pi\) | |||||||
\(18\) | −7.20555 | −1.69837 | ||||||||
\(19\) | −1.00000 | −0.229416 | ||||||||
\(20\) | −4.19461 | −0.937944 | ||||||||
\(21\) | 4.22603 | 0.922195 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.52841 | 0.527211 | 0.263605 | − | 0.964631i | \(-0.415088\pi\) | ||||
0.263605 | + | 0.964631i | \(0.415088\pi\) | |||||||
\(24\) | 3.19461 | 0.652098 | ||||||||
\(25\) | 12.5948 | 2.51896 | ||||||||
\(26\) | −3.52841 | −0.691979 | ||||||||
\(27\) | −13.4351 | −2.58559 | ||||||||
\(28\) | −1.32286 | −0.249997 | ||||||||
\(29\) | 10.4002 | 1.93126 | 0.965631 | − | 0.259916i | \(-0.0836949\pi\) | ||||
0.965631 | + | 0.259916i | \(0.0836949\pi\) | |||||||
\(30\) | −13.4002 | −2.44652 | ||||||||
\(31\) | −6.38923 | −1.14754 | −0.573769 | − | 0.819017i | \(-0.694519\pi\) | ||||
−0.573769 | + | 0.819017i | \(0.694519\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −2.32286 | −0.398367 | ||||||||
\(35\) | 5.54889 | 0.937934 | ||||||||
\(36\) | 7.20555 | 1.20093 | ||||||||
\(37\) | 7.84034 | 1.28894 | 0.644472 | − | 0.764628i | \(-0.277077\pi\) | ||||
0.644472 | + | 0.764628i | \(0.277077\pi\) | |||||||
\(38\) | 1.00000 | 0.162221 | ||||||||
\(39\) | −11.2719 | −1.80495 | ||||||||
\(40\) | 4.19461 | 0.663227 | ||||||||
\(41\) | −2.34334 | −0.365968 | −0.182984 | − | 0.983116i | \(-0.558576\pi\) | ||||
−0.182984 | + | 0.983116i | \(0.558576\pi\) | |||||||
\(42\) | −4.22603 | −0.652091 | ||||||||
\(43\) | 11.4461 | 1.74551 | 0.872753 | − | 0.488161i | \(-0.162332\pi\) | ||||
0.872753 | + | 0.488161i | \(0.162332\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −30.2245 | −4.50560 | ||||||||
\(46\) | −2.52841 | −0.372794 | ||||||||
\(47\) | −6.20555 | −0.905173 | −0.452586 | − | 0.891721i | \(-0.649499\pi\) | ||||
−0.452586 | + | 0.891721i | \(0.649499\pi\) | |||||||
\(48\) | −3.19461 | −0.461103 | ||||||||
\(49\) | −5.25004 | −0.750005 | ||||||||
\(50\) | −12.5948 | −1.78117 | ||||||||
\(51\) | −7.42064 | −1.03910 | ||||||||
\(52\) | 3.52841 | 0.489303 | ||||||||
\(53\) | 4.40017 | 0.604409 | 0.302205 | − | 0.953243i | \(-0.402277\pi\) | ||||
0.302205 | + | 0.953243i | \(0.402277\pi\) | |||||||
\(54\) | 13.4351 | 1.82829 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 1.32286 | 0.176775 | ||||||||
\(57\) | 3.19461 | 0.423137 | ||||||||
\(58\) | −10.4002 | −1.36561 | ||||||||
\(59\) | −6.72303 | −0.875264 | −0.437632 | − | 0.899154i | \(-0.644183\pi\) | ||||
−0.437632 | + | 0.899154i | \(0.644183\pi\) | |||||||
\(60\) | 13.4002 | 1.72995 | ||||||||
\(61\) | 8.60572 | 1.10185 | 0.550925 | − | 0.834555i | \(-0.314275\pi\) | ||||
0.550925 | + | 0.834555i | \(0.314275\pi\) | |||||||
\(62\) | 6.38923 | 0.811433 | ||||||||
\(63\) | −9.53195 | −1.20091 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −14.8003 | −1.83576 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 6.21509 | 0.759294 | 0.379647 | − | 0.925131i | \(-0.376045\pi\) | ||||
0.379647 | + | 0.925131i | \(0.376045\pi\) | |||||||
\(68\) | 2.32286 | 0.281688 | ||||||||
\(69\) | −8.07730 | −0.972393 | ||||||||
\(70\) | −5.54889 | −0.663219 | ||||||||
\(71\) | −10.7326 | −1.27372 | −0.636861 | − | 0.770979i | \(-0.719767\pi\) | ||||
−0.636861 | + | 0.770979i | \(0.719767\pi\) | |||||||
\(72\) | −7.20555 | −0.849183 | ||||||||
\(73\) | 1.67714 | 0.196294 | 0.0981471 | − | 0.995172i | \(-0.468708\pi\) | ||||
0.0981471 | + | 0.995172i | \(0.468708\pi\) | |||||||
\(74\) | −7.84034 | −0.911420 | ||||||||
\(75\) | −40.2354 | −4.64599 | ||||||||
\(76\) | −1.00000 | −0.114708 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 11.2719 | 1.27629 | ||||||||
\(79\) | −5.65666 | −0.636424 | −0.318212 | − | 0.948020i | \(-0.603082\pi\) | ||||
−0.318212 | + | 0.948020i | \(0.603082\pi\) | |||||||
\(80\) | −4.19461 | −0.468972 | ||||||||
\(81\) | 21.3033 | 2.36704 | ||||||||
\(82\) | 2.34334 | 0.258778 | ||||||||
\(83\) | 1.80539 | 0.198167 | 0.0990835 | − | 0.995079i | \(-0.468409\pi\) | ||||
0.0990835 | + | 0.995079i | \(0.468409\pi\) | |||||||
\(84\) | 4.22603 | 0.461098 | ||||||||
\(85\) | −9.74350 | −1.05683 | ||||||||
\(86\) | −11.4461 | −1.23426 | ||||||||
\(87\) | −33.2245 | −3.56204 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 6.04589 | 0.640863 | 0.320431 | − | 0.947272i | \(-0.396172\pi\) | ||||
0.320431 | + | 0.947272i | \(0.396172\pi\) | |||||||
\(90\) | 30.2245 | 3.18594 | ||||||||
\(91\) | −4.66760 | −0.489298 | ||||||||
\(92\) | 2.52841 | 0.263605 | ||||||||
\(93\) | 20.4111 | 2.11653 | ||||||||
\(94\) | 6.20555 | 0.640054 | ||||||||
\(95\) | 4.19461 | 0.430358 | ||||||||
\(96\) | 3.19461 | 0.326049 | ||||||||
\(97\) | −10.0000 | −1.01535 | −0.507673 | − | 0.861550i | \(-0.669494\pi\) | ||||
−0.507673 | + | 0.861550i | \(0.669494\pi\) | |||||||
\(98\) | 5.25004 | 0.530334 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 12.5948 | 1.25948 | ||||||||
\(101\) | −18.9949 | −1.89007 | −0.945034 | − | 0.326973i | \(-0.893972\pi\) | ||||
−0.945034 | + | 0.326973i | \(0.893972\pi\) | |||||||
\(102\) | 7.42064 | 0.734753 | ||||||||
\(103\) | 20.0459 | 1.97518 | 0.987590 | − | 0.157054i | \(-0.0501996\pi\) | ||||
0.987590 | + | 0.157054i | \(0.0501996\pi\) | |||||||
\(104\) | −3.52841 | −0.345989 | ||||||||
\(105\) | −17.7266 | −1.72994 | ||||||||
\(106\) | −4.40017 | −0.427382 | ||||||||
\(107\) | −0.849872 | −0.0821603 | −0.0410801 | − | 0.999156i | \(-0.513080\pi\) | ||||
−0.0410801 | + | 0.999156i | \(0.513080\pi\) | |||||||
\(108\) | −13.4351 | −1.29279 | ||||||||
\(109\) | −8.72303 | −0.835514 | −0.417757 | − | 0.908559i | \(-0.637184\pi\) | ||||
−0.417757 | + | 0.908559i | \(0.637184\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −25.0468 | −2.37734 | ||||||||
\(112\) | −1.32286 | −0.124999 | ||||||||
\(113\) | 3.65666 | 0.343990 | 0.171995 | − | 0.985098i | \(-0.444979\pi\) | ||||
0.171995 | + | 0.985098i | \(0.444979\pi\) | |||||||
\(114\) | −3.19461 | −0.299203 | ||||||||
\(115\) | −10.6057 | −0.988988 | ||||||||
\(116\) | 10.4002 | 0.965631 | ||||||||
\(117\) | 25.4242 | 2.35047 | ||||||||
\(118\) | 6.72303 | 0.618905 | ||||||||
\(119\) | −3.07282 | −0.281685 | ||||||||
\(120\) | −13.4002 | −1.22326 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | −8.60572 | −0.779125 | ||||||||
\(123\) | 7.48606 | 0.674995 | ||||||||
\(124\) | −6.38923 | −0.573769 | ||||||||
\(125\) | −31.8572 | −2.84939 | ||||||||
\(126\) | 9.53195 | 0.849173 | ||||||||
\(127\) | 0.256496 | 0.0227603 | 0.0113802 | − | 0.999935i | \(-0.496377\pi\) | ||||
0.0113802 | + | 0.999935i | \(0.496377\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −36.5657 | −3.21943 | ||||||||
\(130\) | 14.8003 | 1.29807 | ||||||||
\(131\) | 3.70255 | 0.323493 | 0.161747 | − | 0.986832i | \(-0.448287\pi\) | ||||
0.161747 | + | 0.986832i | \(0.448287\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.32286 | 0.114707 | ||||||||
\(134\) | −6.21509 | −0.536902 | ||||||||
\(135\) | 56.3551 | 4.85028 | ||||||||
\(136\) | −2.32286 | −0.199184 | ||||||||
\(137\) | −5.12319 | −0.437704 | −0.218852 | − | 0.975758i | \(-0.570231\pi\) | ||||
−0.218852 | + | 0.975758i | \(0.570231\pi\) | |||||||
\(138\) | 8.07730 | 0.687586 | ||||||||
\(139\) | −6.36735 | −0.540071 | −0.270036 | − | 0.962850i | \(-0.587035\pi\) | ||||
−0.270036 | + | 0.962850i | \(0.587035\pi\) | |||||||
\(140\) | 5.54889 | 0.468967 | ||||||||
\(141\) | 19.8243 | 1.66951 | ||||||||
\(142\) | 10.7326 | 0.900657 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 7.20555 | 0.600463 | ||||||||
\(145\) | −43.6247 | −3.62283 | ||||||||
\(146\) | −1.67714 | −0.138801 | ||||||||
\(147\) | 16.7718 | 1.38332 | ||||||||
\(148\) | 7.84034 | 0.644472 | ||||||||
\(149\) | 13.7244 | 1.12435 | 0.562175 | − | 0.827019i | \(-0.309965\pi\) | ||||
0.562175 | + | 0.827019i | \(0.309965\pi\) | |||||||
\(150\) | 40.2354 | 3.28521 | ||||||||
\(151\) | 4.98906 | 0.406004 | 0.203002 | − | 0.979178i | \(-0.434930\pi\) | ||||
0.203002 | + | 0.979178i | \(0.434930\pi\) | |||||||
\(152\) | 1.00000 | 0.0811107 | ||||||||
\(153\) | 16.7375 | 1.35315 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 26.8003 | 2.15265 | ||||||||
\(156\) | −11.2719 | −0.902476 | ||||||||
\(157\) | 2.04000 | 0.162810 | 0.0814050 | − | 0.996681i | \(-0.474059\pi\) | ||||
0.0814050 | + | 0.996681i | \(0.474059\pi\) | |||||||
\(158\) | 5.65666 | 0.450020 | ||||||||
\(159\) | −14.0568 | −1.11478 | ||||||||
\(160\) | 4.19461 | 0.331613 | ||||||||
\(161\) | −3.34474 | −0.263603 | ||||||||
\(162\) | −21.3033 | −1.67375 | ||||||||
\(163\) | 6.15461 | 0.482066 | 0.241033 | − | 0.970517i | \(-0.422514\pi\) | ||||
0.241033 | + | 0.970517i | \(0.422514\pi\) | |||||||
\(164\) | −2.34334 | −0.182984 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −1.80539 | −0.140125 | ||||||||
\(167\) | −3.74350 | −0.289681 | −0.144841 | − | 0.989455i | \(-0.546267\pi\) | ||||
−0.144841 | + | 0.989455i | \(0.546267\pi\) | |||||||
\(168\) | −4.22603 | −0.326045 | ||||||||
\(169\) | −0.550294 | −0.0423303 | ||||||||
\(170\) | 9.74350 | 0.747293 | ||||||||
\(171\) | −7.20555 | −0.551022 | ||||||||
\(172\) | 11.4461 | 0.872753 | ||||||||
\(173\) | −9.08684 | −0.690860 | −0.345430 | − | 0.938445i | \(-0.612267\pi\) | ||||
−0.345430 | + | 0.938445i | \(0.612267\pi\) | |||||||
\(174\) | 33.2245 | 2.51874 | ||||||||
\(175\) | −16.6611 | −1.25946 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 21.4775 | 1.61435 | ||||||||
\(178\) | −6.04589 | −0.453158 | ||||||||
\(179\) | 8.76751 | 0.655315 | 0.327657 | − | 0.944797i | \(-0.393741\pi\) | ||||
0.327657 | + | 0.944797i | \(0.393741\pi\) | |||||||
\(180\) | −30.2245 | −2.25280 | ||||||||
\(181\) | 19.6807 | 1.46285 | 0.731426 | − | 0.681920i | \(-0.238855\pi\) | ||||
0.731426 | + | 0.681920i | \(0.238855\pi\) | |||||||
\(182\) | 4.66760 | 0.345986 | ||||||||
\(183\) | −27.4919 | −2.03226 | ||||||||
\(184\) | −2.52841 | −0.186397 | ||||||||
\(185\) | −32.8872 | −2.41791 | ||||||||
\(186\) | −20.4111 | −1.49661 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −6.20555 | −0.452586 | ||||||||
\(189\) | 17.7728 | 1.29278 | ||||||||
\(190\) | −4.19461 | −0.304309 | ||||||||
\(191\) | −9.47747 | −0.685766 | −0.342883 | − | 0.939378i | \(-0.611403\pi\) | ||||
−0.342883 | + | 0.939378i | \(0.611403\pi\) | |||||||
\(192\) | −3.19461 | −0.230551 | ||||||||
\(193\) | −8.00000 | −0.575853 | −0.287926 | − | 0.957653i | \(-0.592966\pi\) | ||||
−0.287926 | + | 0.957653i | \(0.592966\pi\) | |||||||
\(194\) | 10.0000 | 0.717958 | ||||||||
\(195\) | 47.2813 | 3.38589 | ||||||||
\(196\) | −5.25004 | −0.375003 | ||||||||
\(197\) | 24.5438 | 1.74868 | 0.874338 | − | 0.485318i | \(-0.161296\pi\) | ||||
0.874338 | + | 0.485318i | \(0.161296\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 20.1991 | 1.43188 | 0.715938 | − | 0.698164i | \(-0.245999\pi\) | ||||
0.715938 | + | 0.698164i | \(0.245999\pi\) | |||||||
\(200\) | −12.5948 | −0.890585 | ||||||||
\(201\) | −19.8548 | −1.40045 | ||||||||
\(202\) | 18.9949 | 1.33648 | ||||||||
\(203\) | −13.7580 | −0.965621 | ||||||||
\(204\) | −7.42064 | −0.519549 | ||||||||
\(205\) | 9.82940 | 0.686515 | ||||||||
\(206\) | −20.0459 | −1.39666 | ||||||||
\(207\) | 18.2186 | 1.26628 | ||||||||
\(208\) | 3.52841 | 0.244652 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 17.7266 | 1.22325 | ||||||||
\(211\) | −1.88129 | −0.129513 | −0.0647566 | − | 0.997901i | \(-0.520627\pi\) | ||||
−0.0647566 | + | 0.997901i | \(0.520627\pi\) | |||||||
\(212\) | 4.40017 | 0.302205 | ||||||||
\(213\) | 34.2864 | 2.34926 | ||||||||
\(214\) | 0.849872 | 0.0580961 | ||||||||
\(215\) | −48.0118 | −3.27438 | ||||||||
\(216\) | 13.4351 | 0.914144 | ||||||||
\(217\) | 8.45206 | 0.573763 | ||||||||
\(218\) | 8.72303 | 0.590798 | ||||||||
\(219\) | −5.35781 | −0.362047 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 8.19602 | 0.551324 | ||||||||
\(222\) | 25.0468 | 1.68103 | ||||||||
\(223\) | 20.0868 | 1.34511 | 0.672557 | − | 0.740045i | \(-0.265196\pi\) | ||||
0.672557 | + | 0.740045i | \(0.265196\pi\) | |||||||
\(224\) | 1.32286 | 0.0883874 | ||||||||
\(225\) | 90.7523 | 6.05016 | ||||||||
\(226\) | −3.65666 | −0.243238 | ||||||||
\(227\) | −3.55029 | −0.235641 | −0.117821 | − | 0.993035i | \(-0.537591\pi\) | ||||
−0.117821 | + | 0.993035i | \(0.537591\pi\) | |||||||
\(228\) | 3.19461 | 0.211568 | ||||||||
\(229\) | 7.72162 | 0.510259 | 0.255130 | − | 0.966907i | \(-0.417882\pi\) | ||||
0.255130 | + | 0.966907i | \(0.417882\pi\) | |||||||
\(230\) | 10.6057 | 0.699320 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −10.4002 | −0.682804 | ||||||||
\(233\) | 21.9081 | 1.43525 | 0.717624 | − | 0.696431i | \(-0.245230\pi\) | ||||
0.717624 | + | 0.696431i | \(0.245230\pi\) | |||||||
\(234\) | −25.4242 | −1.66203 | ||||||||
\(235\) | 26.0299 | 1.69800 | ||||||||
\(236\) | −6.72303 | −0.437632 | ||||||||
\(237\) | 18.0708 | 1.17383 | ||||||||
\(238\) | 3.07282 | 0.199182 | ||||||||
\(239\) | −17.6676 | −1.14282 | −0.571411 | − | 0.820664i | \(-0.693604\pi\) | ||||
−0.571411 | + | 0.820664i | \(0.693604\pi\) | |||||||
\(240\) | 13.4002 | 0.864977 | ||||||||
\(241\) | −17.0999 | −1.10150 | −0.550751 | − | 0.834670i | \(-0.685659\pi\) | ||||
−0.550751 | + | 0.834670i | \(0.685659\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −27.7506 | −1.78020 | ||||||||
\(244\) | 8.60572 | 0.550925 | ||||||||
\(245\) | 22.0219 | 1.40693 | ||||||||
\(246\) | −7.48606 | −0.477294 | ||||||||
\(247\) | −3.52841 | −0.224508 | ||||||||
\(248\) | 6.38923 | 0.405716 | ||||||||
\(249\) | −5.76751 | −0.365501 | ||||||||
\(250\) | 31.8572 | 2.01482 | ||||||||
\(251\) | 13.4461 | 0.848707 | 0.424354 | − | 0.905497i | \(-0.360501\pi\) | ||||
0.424354 | + | 0.905497i | \(0.360501\pi\) | |||||||
\(252\) | −9.53195 | −0.600456 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −0.256496 | −0.0160940 | ||||||||
\(255\) | 31.1267 | 1.94923 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 10.1546 | 0.633427 | 0.316714 | − | 0.948521i | \(-0.397421\pi\) | ||||
0.316714 | + | 0.948521i | \(0.397421\pi\) | |||||||
\(258\) | 36.5657 | 2.27648 | ||||||||
\(259\) | −10.3717 | −0.644465 | ||||||||
\(260\) | −14.8003 | −0.917878 | ||||||||
\(261\) | 74.9389 | 4.63860 | ||||||||
\(262\) | −3.70255 | −0.228744 | ||||||||
\(263\) | −24.9081 | −1.53590 | −0.767950 | − | 0.640510i | \(-0.778723\pi\) | ||||
−0.767950 | + | 0.640510i | \(0.778723\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −18.4570 | −1.13380 | ||||||||
\(266\) | −1.32286 | −0.0811098 | ||||||||
\(267\) | −19.3143 | −1.18201 | ||||||||
\(268\) | 6.21509 | 0.379647 | ||||||||
\(269\) | −29.4761 | −1.79719 | −0.898594 | − | 0.438781i | \(-0.855410\pi\) | ||||
−0.898594 | + | 0.438781i | \(0.855410\pi\) | |||||||
\(270\) | −56.3551 | −3.42966 | ||||||||
\(271\) | 2.99046 | 0.181658 | 0.0908289 | − | 0.995867i | \(-0.471048\pi\) | ||||
0.0908289 | + | 0.995867i | \(0.471048\pi\) | |||||||
\(272\) | 2.32286 | 0.140844 | ||||||||
\(273\) | 14.9112 | 0.902466 | ||||||||
\(274\) | 5.12319 | 0.309503 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −8.07730 | −0.486197 | ||||||||
\(277\) | 16.8622 | 1.01315 | 0.506576 | − | 0.862195i | \(-0.330911\pi\) | ||||
0.506576 | + | 0.862195i | \(0.330911\pi\) | |||||||
\(278\) | 6.36735 | 0.381888 | ||||||||
\(279\) | −46.0379 | −2.75622 | ||||||||
\(280\) | −5.54889 | −0.331610 | ||||||||
\(281\) | 0.989060 | 0.0590024 | 0.0295012 | − | 0.999565i | \(-0.490608\pi\) | ||||
0.0295012 | + | 0.999565i | \(0.490608\pi\) | |||||||
\(282\) | −19.8243 | −1.18052 | ||||||||
\(283\) | 5.97812 | 0.355362 | 0.177681 | − | 0.984088i | \(-0.443140\pi\) | ||||
0.177681 | + | 0.984088i | \(0.443140\pi\) | |||||||
\(284\) | −10.7326 | −0.636861 | ||||||||
\(285\) | −13.4002 | −0.793757 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 3.09991 | 0.182982 | ||||||||
\(288\) | −7.20555 | −0.424591 | ||||||||
\(289\) | −11.6043 | −0.682607 | ||||||||
\(290\) | 43.6247 | 2.56173 | ||||||||
\(291\) | 31.9461 | 1.87272 | ||||||||
\(292\) | 1.67714 | 0.0981471 | ||||||||
\(293\) | −14.5489 | −0.849955 | −0.424978 | − | 0.905204i | \(-0.639718\pi\) | ||||
−0.424978 | + | 0.905204i | \(0.639718\pi\) | |||||||
\(294\) | −16.7718 | −0.978154 | ||||||||
\(295\) | 28.2005 | 1.64190 | ||||||||
\(296\) | −7.84034 | −0.455710 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −13.7244 | −0.795035 | ||||||||
\(299\) | 8.92129 | 0.515932 | ||||||||
\(300\) | −40.2354 | −2.32299 | ||||||||
\(301\) | −15.1415 | −0.872744 | ||||||||
\(302\) | −4.98906 | −0.287088 | ||||||||
\(303\) | 60.6815 | 3.48606 | ||||||||
\(304\) | −1.00000 | −0.0573539 | ||||||||
\(305\) | −36.0977 | −2.06695 | ||||||||
\(306\) | −16.7375 | −0.956819 | ||||||||
\(307\) | −9.69161 | −0.553129 | −0.276565 | − | 0.960995i | \(-0.589196\pi\) | ||||
−0.276565 | + | 0.960995i | \(0.589196\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −64.0389 | −3.64304 | ||||||||
\(310\) | −26.8003 | −1.52216 | ||||||||
\(311\) | −18.8229 | −1.06735 | −0.533675 | − | 0.845689i | \(-0.679190\pi\) | ||||
−0.533675 | + | 0.845689i | \(0.679190\pi\) | |||||||
\(312\) | 11.2719 | 0.638147 | ||||||||
\(313\) | 27.1800 | 1.53631 | 0.768153 | − | 0.640267i | \(-0.221176\pi\) | ||||
0.768153 | + | 0.640267i | \(0.221176\pi\) | |||||||
\(314\) | −2.04000 | −0.115124 | ||||||||
\(315\) | 39.9828 | 2.25278 | ||||||||
\(316\) | −5.65666 | −0.318212 | ||||||||
\(317\) | −14.3697 | −0.807083 | −0.403541 | − | 0.914961i | \(-0.632221\pi\) | ||||
−0.403541 | + | 0.914961i | \(0.632221\pi\) | |||||||
\(318\) | 14.0568 | 0.788268 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | −4.19461 | −0.234486 | ||||||||
\(321\) | 2.71501 | 0.151537 | ||||||||
\(322\) | 3.34474 | 0.186395 | ||||||||
\(323\) | −2.32286 | −0.129247 | ||||||||
\(324\) | 21.3033 | 1.18352 | ||||||||
\(325\) | 44.4396 | 2.46507 | ||||||||
\(326\) | −6.15461 | −0.340872 | ||||||||
\(327\) | 27.8667 | 1.54103 | ||||||||
\(328\) | 2.34334 | 0.129389 | ||||||||
\(329\) | 8.20909 | 0.452582 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 18.9635 | 1.04233 | 0.521165 | − | 0.853456i | \(-0.325498\pi\) | ||||
0.521165 | + | 0.853456i | \(0.325498\pi\) | |||||||
\(332\) | 1.80539 | 0.0990835 | ||||||||
\(333\) | 56.4940 | 3.09585 | ||||||||
\(334\) | 3.74350 | 0.204835 | ||||||||
\(335\) | −26.0699 | −1.42435 | ||||||||
\(336\) | 4.22603 | 0.230549 | ||||||||
\(337\) | −30.1595 | −1.64290 | −0.821448 | − | 0.570284i | \(-0.806833\pi\) | ||||
−0.821448 | + | 0.570284i | \(0.806833\pi\) | |||||||
\(338\) | 0.550294 | 0.0299320 | ||||||||
\(339\) | −11.6816 | −0.634459 | ||||||||
\(340\) | −9.74350 | −0.528416 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 7.20555 | 0.389632 | ||||||||
\(343\) | 16.2051 | 0.874993 | ||||||||
\(344\) | −11.4461 | −0.617130 | ||||||||
\(345\) | 33.8812 | 1.82410 | ||||||||
\(346\) | 9.08684 | 0.488512 | ||||||||
\(347\) | −23.5997 | −1.26690 | −0.633450 | − | 0.773784i | \(-0.718362\pi\) | ||||
−0.633450 | + | 0.773784i | \(0.718362\pi\) | |||||||
\(348\) | −33.2245 | −1.78102 | ||||||||
\(349\) | 29.2086 | 1.56350 | 0.781751 | − | 0.623591i | \(-0.214327\pi\) | ||||
0.781751 | + | 0.623591i | \(0.214327\pi\) | |||||||
\(350\) | 16.6611 | 0.890576 | ||||||||
\(351\) | −47.4046 | −2.53027 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −10.2274 | −0.544351 | −0.272176 | − | 0.962248i | \(-0.587743\pi\) | ||||
−0.272176 | + | 0.962248i | \(0.587743\pi\) | |||||||
\(354\) | −21.4775 | −1.14151 | ||||||||
\(355\) | 45.0190 | 2.38936 | ||||||||
\(356\) | 6.04589 | 0.320431 | ||||||||
\(357\) | 9.81648 | 0.519543 | ||||||||
\(358\) | −8.76751 | −0.463377 | ||||||||
\(359\) | −0.876807 | −0.0462761 | −0.0231380 | − | 0.999732i | \(-0.507366\pi\) | ||||
−0.0231380 | + | 0.999732i | \(0.507366\pi\) | |||||||
\(360\) | 30.2245 | 1.59297 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | −19.6807 | −1.03439 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −4.66760 | −0.244649 | ||||||||
\(365\) | −7.03495 | −0.368226 | ||||||||
\(366\) | 27.4919 | 1.43703 | ||||||||
\(367\) | 10.5030 | 0.548252 | 0.274126 | − | 0.961694i | \(-0.411611\pi\) | ||||
0.274126 | + | 0.961694i | \(0.411611\pi\) | |||||||
\(368\) | 2.52841 | 0.131803 | ||||||||
\(369\) | −16.8850 | −0.879000 | ||||||||
\(370\) | 32.8872 | 1.70972 | ||||||||
\(371\) | −5.82081 | −0.302201 | ||||||||
\(372\) | 20.4111 | 1.05827 | ||||||||
\(373\) | −34.9249 | −1.80834 | −0.904172 | − | 0.427168i | \(-0.859511\pi\) | ||||
−0.904172 | + | 0.427168i | \(0.859511\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 101.771 | 5.25545 | ||||||||
\(376\) | 6.20555 | 0.320027 | ||||||||
\(377\) | 36.6961 | 1.88994 | ||||||||
\(378\) | −17.7728 | −0.914134 | ||||||||
\(379\) | −13.9695 | −0.717567 | −0.358783 | − | 0.933421i | \(-0.616808\pi\) | ||||
−0.358783 | + | 0.933421i | \(0.616808\pi\) | |||||||
\(380\) | 4.19461 | 0.215179 | ||||||||
\(381\) | −0.819406 | −0.0419794 | ||||||||
\(382\) | 9.47747 | 0.484910 | ||||||||
\(383\) | 35.3223 | 1.80488 | 0.902442 | − | 0.430811i | \(-0.141772\pi\) | ||||
0.902442 | + | 0.430811i | \(0.141772\pi\) | |||||||
\(384\) | 3.19461 | 0.163024 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 8.00000 | 0.407189 | ||||||||
\(387\) | 82.4752 | 4.19245 | ||||||||
\(388\) | −10.0000 | −0.507673 | ||||||||
\(389\) | 12.5838 | 0.638026 | 0.319013 | − | 0.947750i | \(-0.396649\pi\) | ||||
0.319013 | + | 0.947750i | \(0.396649\pi\) | |||||||
\(390\) | −47.2813 | −2.39418 | ||||||||
\(391\) | 5.87315 | 0.297018 | ||||||||
\(392\) | 5.25004 | 0.265167 | ||||||||
\(393\) | −11.8282 | −0.596655 | ||||||||
\(394\) | −24.5438 | −1.23650 | ||||||||
\(395\) | 23.7275 | 1.19386 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 0.924098 | 0.0463792 | 0.0231896 | − | 0.999731i | \(-0.492618\pi\) | ||||
0.0231896 | + | 0.999731i | \(0.492618\pi\) | |||||||
\(398\) | −20.1991 | −1.01249 | ||||||||
\(399\) | −4.22603 | −0.211566 | ||||||||
\(400\) | 12.5948 | 0.629739 | ||||||||
\(401\) | −2.30238 | −0.114976 | −0.0574878 | − | 0.998346i | \(-0.518309\pi\) | ||||
−0.0574878 | + | 0.998346i | \(0.518309\pi\) | |||||||
\(402\) | 19.8548 | 0.990268 | ||||||||
\(403\) | −22.5438 | −1.12299 | ||||||||
\(404\) | −18.9949 | −0.945034 | ||||||||
\(405\) | −89.3592 | −4.44030 | ||||||||
\(406\) | 13.7580 | 0.682797 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 7.42064 | 0.367377 | ||||||||
\(409\) | 11.4870 | 0.567996 | 0.283998 | − | 0.958825i | \(-0.408339\pi\) | ||||
0.283998 | + | 0.958825i | \(0.408339\pi\) | |||||||
\(410\) | −9.82940 | −0.485439 | ||||||||
\(411\) | 16.3666 | 0.807306 | ||||||||
\(412\) | 20.0459 | 0.987590 | ||||||||
\(413\) | 8.89363 | 0.437627 | ||||||||
\(414\) | −18.2186 | −0.895396 | ||||||||
\(415\) | −7.57290 | −0.371739 | ||||||||
\(416\) | −3.52841 | −0.172995 | ||||||||
\(417\) | 20.3412 | 0.996113 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 6.21369 | 0.303558 | 0.151779 | − | 0.988414i | \(-0.451500\pi\) | ||||
0.151779 | + | 0.988414i | \(0.451500\pi\) | |||||||
\(420\) | −17.7266 | −0.864968 | ||||||||
\(421\) | 12.5934 | 0.613764 | 0.306882 | − | 0.951748i | \(-0.400714\pi\) | ||||
0.306882 | + | 0.951748i | \(0.400714\pi\) | |||||||
\(422\) | 1.88129 | 0.0915797 | ||||||||
\(423\) | −44.7144 | −2.17409 | ||||||||
\(424\) | −4.40017 | −0.213691 | ||||||||
\(425\) | 29.2559 | 1.41912 | ||||||||
\(426\) | −34.2864 | −1.66118 | ||||||||
\(427\) | −11.3842 | −0.550919 | ||||||||
\(428\) | −0.849872 | −0.0410801 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 48.0118 | 2.31533 | ||||||||
\(431\) | −24.4570 | −1.17805 | −0.589026 | − | 0.808114i | \(-0.700488\pi\) | ||||
−0.589026 | + | 0.808114i | \(0.700488\pi\) | |||||||
\(432\) | −13.4351 | −0.646397 | ||||||||
\(433\) | 16.3892 | 0.787616 | 0.393808 | − | 0.919193i | \(-0.371157\pi\) | ||||
0.393808 | + | 0.919193i | \(0.371157\pi\) | |||||||
\(434\) | −8.45206 | −0.405712 | ||||||||
\(435\) | 139.364 | 6.68199 | ||||||||
\(436\) | −8.72303 | −0.417757 | ||||||||
\(437\) | −2.52841 | −0.120950 | ||||||||
\(438\) | 5.35781 | 0.256006 | ||||||||
\(439\) | 31.8353 | 1.51942 | 0.759708 | − | 0.650265i | \(-0.225342\pi\) | ||||
0.759708 | + | 0.650265i | \(0.225342\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −37.8294 | −1.80140 | ||||||||
\(442\) | −8.19602 | −0.389845 | ||||||||
\(443\) | −14.7594 | −0.701239 | −0.350620 | − | 0.936518i | \(-0.614029\pi\) | ||||
−0.350620 | + | 0.936518i | \(0.614029\pi\) | |||||||
\(444\) | −25.0468 | −1.18867 | ||||||||
\(445\) | −25.3602 | −1.20219 | ||||||||
\(446\) | −20.0868 | −0.951140 | ||||||||
\(447\) | −43.8442 | −2.07376 | ||||||||
\(448\) | −1.32286 | −0.0624993 | ||||||||
\(449\) | 1.44605 | 0.0682435 | 0.0341218 | − | 0.999418i | \(-0.489137\pi\) | ||||
0.0341218 | + | 0.999418i | \(0.489137\pi\) | |||||||
\(450\) | −90.7523 | −4.27811 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 3.65666 | 0.171995 | ||||||||
\(453\) | −15.9381 | −0.748838 | ||||||||
\(454\) | 3.55029 | 0.166624 | ||||||||
\(455\) | 19.5788 | 0.917868 | ||||||||
\(456\) | −3.19461 | −0.149601 | ||||||||
\(457\) | −9.58524 | −0.448379 | −0.224189 | − | 0.974546i | \(-0.571973\pi\) | ||||
−0.224189 | + | 0.974546i | \(0.571973\pi\) | |||||||
\(458\) | −7.72162 | −0.360808 | ||||||||
\(459\) | −31.2079 | −1.45666 | ||||||||
\(460\) | −10.6057 | −0.494494 | ||||||||
\(461\) | 9.91624 | 0.461845 | 0.230923 | − | 0.972972i | \(-0.425826\pi\) | ||||
0.230923 | + | 0.972972i | \(0.425826\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 3.22743 | 0.149992 | 0.0749958 | − | 0.997184i | \(-0.476106\pi\) | ||||
0.0749958 | + | 0.997184i | \(0.476106\pi\) | |||||||
\(464\) | 10.4002 | 0.482816 | ||||||||
\(465\) | −85.6167 | −3.97038 | ||||||||
\(466\) | −21.9081 | −1.01487 | ||||||||
\(467\) | 36.0118 | 1.66643 | 0.833213 | − | 0.552952i | \(-0.186499\pi\) | ||||
0.833213 | + | 0.552952i | \(0.186499\pi\) | |||||||
\(468\) | 25.4242 | 1.17523 | ||||||||
\(469\) | −8.22170 | −0.379643 | ||||||||
\(470\) | −26.0299 | −1.20067 | ||||||||
\(471\) | −6.51702 | −0.300288 | ||||||||
\(472\) | 6.72303 | 0.309452 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | −18.0708 | −0.830021 | ||||||||
\(475\) | −12.5948 | −0.577888 | ||||||||
\(476\) | −3.07282 | −0.140843 | ||||||||
\(477\) | 31.7056 | 1.45170 | ||||||||
\(478\) | 17.6676 | 0.808097 | ||||||||
\(479\) | 7.68668 | 0.351213 | 0.175607 | − | 0.984460i | \(-0.443811\pi\) | ||||
0.175607 | + | 0.984460i | \(0.443811\pi\) | |||||||
\(480\) | −13.4002 | −0.611631 | ||||||||
\(481\) | 27.6640 | 1.26137 | ||||||||
\(482\) | 17.0999 | 0.778880 | ||||||||
\(483\) | 10.6852 | 0.486191 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 41.9461 | 1.90468 | ||||||||
\(486\) | 27.7506 | 1.25879 | ||||||||
\(487\) | −34.6356 | −1.56949 | −0.784745 | − | 0.619819i | \(-0.787206\pi\) | ||||
−0.784745 | + | 0.619819i | \(0.787206\pi\) | |||||||
\(488\) | −8.60572 | −0.389563 | ||||||||
\(489\) | −19.6616 | −0.889128 | ||||||||
\(490\) | −22.0219 | −0.994847 | ||||||||
\(491\) | −33.1458 | −1.49585 | −0.747924 | − | 0.663784i | \(-0.768949\pi\) | ||||
−0.747924 | + | 0.663784i | \(0.768949\pi\) | |||||||
\(492\) | 7.48606 | 0.337498 | ||||||||
\(493\) | 24.1581 | 1.08803 | ||||||||
\(494\) | 3.52841 | 0.158751 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −6.38923 | −0.286885 | ||||||||
\(497\) | 14.1977 | 0.636854 | ||||||||
\(498\) | 5.76751 | 0.258448 | ||||||||
\(499\) | −22.9949 | −1.02940 | −0.514698 | − | 0.857372i | \(-0.672096\pi\) | ||||
−0.514698 | + | 0.857372i | \(0.672096\pi\) | |||||||
\(500\) | −31.8572 | −1.42470 | ||||||||
\(501\) | 11.9590 | 0.534291 | ||||||||
\(502\) | −13.4461 | −0.600127 | ||||||||
\(503\) | −7.30098 | −0.325535 | −0.162767 | − | 0.986664i | \(-0.552042\pi\) | ||||
−0.162767 | + | 0.986664i | \(0.552042\pi\) | |||||||
\(504\) | 9.53195 | 0.424587 | ||||||||
\(505\) | 79.6764 | 3.54556 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 1.75798 | 0.0780744 | ||||||||
\(508\) | 0.256496 | 0.0113802 | ||||||||
\(509\) | −38.3213 | −1.69856 | −0.849282 | − | 0.527940i | \(-0.822965\pi\) | ||||
−0.849282 | + | 0.527940i | \(0.822965\pi\) | |||||||
\(510\) | −31.1267 | −1.37831 | ||||||||
\(511\) | −2.21862 | −0.0981461 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 13.4351 | 0.593175 | ||||||||
\(514\) | −10.1546 | −0.447901 | ||||||||
\(515\) | −84.0847 | −3.70522 | ||||||||
\(516\) | −36.5657 | −1.60972 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 10.3717 | 0.455705 | ||||||||
\(519\) | 29.0289 | 1.27423 | ||||||||
\(520\) | 14.8003 | 0.649037 | ||||||||
\(521\) | 8.17649 | 0.358219 | 0.179109 | − | 0.983829i | \(-0.442678\pi\) | ||||
0.179109 | + | 0.983829i | \(0.442678\pi\) | |||||||
\(522\) | −74.9389 | −3.27999 | ||||||||
\(523\) | −24.3806 | −1.06609 | −0.533045 | − | 0.846087i | \(-0.678953\pi\) | ||||
−0.533045 | + | 0.846087i | \(0.678953\pi\) | |||||||
\(524\) | 3.70255 | 0.161747 | ||||||||
\(525\) | 53.2259 | 2.32297 | ||||||||
\(526\) | 24.9081 | 1.08604 | ||||||||
\(527\) | −14.8413 | −0.646497 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −16.6071 | −0.722049 | ||||||||
\(530\) | 18.4570 | 0.801721 | ||||||||
\(531\) | −48.4431 | −2.10225 | ||||||||
\(532\) | 1.32286 | 0.0573533 | ||||||||
\(533\) | −8.26827 | −0.358138 | ||||||||
\(534\) | 19.3143 | 0.835810 | ||||||||
\(535\) | 3.56489 | 0.154123 | ||||||||
\(536\) | −6.21509 | −0.268451 | ||||||||
\(537\) | −28.0088 | −1.20867 | ||||||||
\(538\) | 29.4761 | 1.27080 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 56.3551 | 2.42514 | ||||||||
\(541\) | 41.5788 | 1.78761 | 0.893806 | − | 0.448454i | \(-0.148025\pi\) | ||||
0.893806 | + | 0.448454i | \(0.148025\pi\) | |||||||
\(542\) | −2.99046 | −0.128451 | ||||||||
\(543\) | −62.8721 | −2.69810 | ||||||||
\(544\) | −2.32286 | −0.0995919 | ||||||||
\(545\) | 36.5897 | 1.56733 | ||||||||
\(546\) | −14.9112 | −0.638140 | ||||||||
\(547\) | 6.05778 | 0.259012 | 0.129506 | − | 0.991579i | \(-0.458661\pi\) | ||||
0.129506 | + | 0.991579i | \(0.458661\pi\) | |||||||
\(548\) | −5.12319 | −0.218852 | ||||||||
\(549\) | 62.0090 | 2.64648 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −10.4002 | −0.443062 | ||||||||
\(552\) | 8.07730 | 0.343793 | ||||||||
\(553\) | 7.48298 | 0.318209 | ||||||||
\(554\) | −16.8622 | −0.716407 | ||||||||
\(555\) | 105.062 | 4.45962 | ||||||||
\(556\) | −6.36735 | −0.270036 | ||||||||
\(557\) | 30.0527 | 1.27337 | 0.636687 | − | 0.771122i | \(-0.280304\pi\) | ||||
0.636687 | + | 0.771122i | \(0.280304\pi\) | |||||||
\(558\) | 46.0379 | 1.94894 | ||||||||
\(559\) | 40.3864 | 1.70816 | ||||||||
\(560\) | 5.54889 | 0.234483 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −0.989060 | −0.0417210 | ||||||||
\(563\) | 29.4410 | 1.24079 | 0.620395 | − | 0.784289i | \(-0.286972\pi\) | ||||
0.620395 | + | 0.784289i | \(0.286972\pi\) | |||||||
\(564\) | 19.8243 | 0.834755 | ||||||||
\(565\) | −15.3383 | −0.645286 | ||||||||
\(566\) | −5.97812 | −0.251279 | ||||||||
\(567\) | −28.1814 | −1.18351 | ||||||||
\(568\) | 10.7326 | 0.450328 | ||||||||
\(569\) | 30.5438 | 1.28046 | 0.640232 | − | 0.768182i | \(-0.278838\pi\) | ||||
0.640232 | + | 0.768182i | \(0.278838\pi\) | |||||||
\(570\) | 13.4002 | 0.561271 | ||||||||
\(571\) | −2.95399 | −0.123621 | −0.0618104 | − | 0.998088i | \(-0.519687\pi\) | ||||
−0.0618104 | + | 0.998088i | \(0.519687\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 30.2769 | 1.26483 | ||||||||
\(574\) | −3.09991 | −0.129388 | ||||||||
\(575\) | 31.8448 | 1.32802 | ||||||||
\(576\) | 7.20555 | 0.300231 | ||||||||
\(577\) | −4.69021 | −0.195256 | −0.0976280 | − | 0.995223i | \(-0.531126\pi\) | ||||
−0.0976280 | + | 0.995223i | \(0.531126\pi\) | |||||||
\(578\) | 11.6043 | 0.482676 | ||||||||
\(579\) | 25.5569 | 1.06211 | ||||||||
\(580\) | −43.6247 | −1.81142 | ||||||||
\(581\) | −2.38828 | −0.0990824 | ||||||||
\(582\) | −31.9461 | −1.32421 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −1.67714 | −0.0694005 | ||||||||
\(585\) | −106.645 | −4.40921 | ||||||||
\(586\) | 14.5489 | 0.601009 | ||||||||
\(587\) | −11.8273 | −0.488164 | −0.244082 | − | 0.969755i | \(-0.578487\pi\) | ||||
−0.244082 | + | 0.969755i | \(0.578487\pi\) | |||||||
\(588\) | 16.7718 | 0.691659 | ||||||||
\(589\) | 6.38923 | 0.263263 | ||||||||
\(590\) | −28.2005 | −1.16100 | ||||||||
\(591\) | −78.4081 | −3.22528 | ||||||||
\(592\) | 7.84034 | 0.322236 | ||||||||
\(593\) | 24.9621 | 1.02507 | 0.512536 | − | 0.858666i | \(-0.328706\pi\) | ||||
0.512536 | + | 0.858666i | \(0.328706\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 12.8893 | 0.528410 | ||||||||
\(596\) | 13.7244 | 0.562175 | ||||||||
\(597\) | −64.5283 | −2.64097 | ||||||||
\(598\) | −8.92129 | −0.364819 | ||||||||
\(599\) | −27.0131 | −1.10372 | −0.551862 | − | 0.833935i | \(-0.686083\pi\) | ||||
−0.551862 | + | 0.833935i | \(0.686083\pi\) | |||||||
\(600\) | 40.2354 | 1.64261 | ||||||||
\(601\) | −7.24343 | −0.295466 | −0.147733 | − | 0.989027i | \(-0.547198\pi\) | ||||
−0.147733 | + | 0.989027i | \(0.547198\pi\) | |||||||
\(602\) | 15.1415 | 0.617123 | ||||||||
\(603\) | 44.7832 | 1.82371 | ||||||||
\(604\) | 4.98906 | 0.203002 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −60.6815 | −2.46502 | ||||||||
\(607\) | −27.4411 | −1.11380 | −0.556900 | − | 0.830579i | \(-0.688009\pi\) | ||||
−0.556900 | + | 0.830579i | \(0.688009\pi\) | |||||||
\(608\) | 1.00000 | 0.0405554 | ||||||||
\(609\) | 43.9514 | 1.78100 | ||||||||
\(610\) | 36.0977 | 1.46155 | ||||||||
\(611\) | −21.8958 | −0.885808 | ||||||||
\(612\) | 16.7375 | 0.676573 | ||||||||
\(613\) | 1.97011 | 0.0795718 | 0.0397859 | − | 0.999208i | \(-0.487332\pi\) | ||||
0.0397859 | + | 0.999208i | \(0.487332\pi\) | |||||||
\(614\) | 9.69161 | 0.391122 | ||||||||
\(615\) | −31.4011 | −1.26622 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 2.42110 | 0.0974696 | 0.0487348 | − | 0.998812i | \(-0.484481\pi\) | ||||
0.0487348 | + | 0.998812i | \(0.484481\pi\) | |||||||
\(618\) | 64.0389 | 2.57602 | ||||||||
\(619\) | 38.0118 | 1.52782 | 0.763911 | − | 0.645322i | \(-0.223277\pi\) | ||||
0.763911 | + | 0.645322i | \(0.223277\pi\) | |||||||
\(620\) | 26.8003 | 1.07633 | ||||||||
\(621\) | −33.9695 | −1.36315 | ||||||||
\(622\) | 18.8229 | 0.754731 | ||||||||
\(623\) | −7.99787 | −0.320428 | ||||||||
\(624\) | −11.2719 | −0.451238 | ||||||||
\(625\) | 70.6546 | 2.82618 | ||||||||
\(626\) | −27.1800 | −1.08633 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 2.04000 | 0.0814050 | ||||||||
\(629\) | 18.2120 | 0.726160 | ||||||||
\(630\) | −39.9828 | −1.59295 | ||||||||
\(631\) | 27.2873 | 1.08629 | 0.543146 | − | 0.839638i | \(-0.317233\pi\) | ||||
0.543146 | + | 0.839638i | \(0.317233\pi\) | |||||||
\(632\) | 5.65666 | 0.225010 | ||||||||
\(633\) | 6.00999 | 0.238876 | ||||||||
\(634\) | 14.3697 | 0.570694 | ||||||||
\(635\) | −1.07590 | −0.0426959 | ||||||||
\(636\) | −14.0568 | −0.557389 | ||||||||
\(637\) | −18.5243 | −0.733960 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −77.3341 | −3.05929 | ||||||||
\(640\) | 4.19461 | 0.165807 | ||||||||
\(641\) | 0.589724 | 0.0232927 | 0.0116464 | − | 0.999932i | \(-0.496293\pi\) | ||||
0.0116464 | + | 0.999932i | \(0.496293\pi\) | |||||||
\(642\) | −2.71501 | −0.107153 | ||||||||
\(643\) | 11.1197 | 0.438517 | 0.219258 | − | 0.975667i | \(-0.429636\pi\) | ||||
0.219258 | + | 0.975667i | \(0.429636\pi\) | |||||||
\(644\) | −3.34474 | −0.131801 | ||||||||
\(645\) | 153.379 | 6.03929 | ||||||||
\(646\) | 2.32286 | 0.0913918 | ||||||||
\(647\) | 9.19837 | 0.361625 | 0.180813 | − | 0.983518i | \(-0.442127\pi\) | ||||
0.180813 | + | 0.983518i | \(0.442127\pi\) | |||||||
\(648\) | −21.3033 | −0.836874 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | −44.4396 | −1.74306 | ||||||||
\(651\) | −27.0011 | −1.05825 | ||||||||
\(652\) | 6.15461 | 0.241033 | ||||||||
\(653\) | −12.9940 | −0.508494 | −0.254247 | − | 0.967139i | \(-0.581828\pi\) | ||||
−0.254247 | + | 0.967139i | \(0.581828\pi\) | |||||||
\(654\) | −27.8667 | −1.08967 | ||||||||
\(655\) | −15.5308 | −0.606837 | ||||||||
\(656\) | −2.34334 | −0.0914920 | ||||||||
\(657\) | 12.0847 | 0.471470 | ||||||||
\(658\) | −8.20909 | −0.320023 | ||||||||
\(659\) | 2.11012 | 0.0821988 | 0.0410994 | − | 0.999155i | \(-0.486914\pi\) | ||||
0.0410994 | + | 0.999155i | \(0.486914\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 7.58665 | 0.295086 | 0.147543 | − | 0.989056i | \(-0.452863\pi\) | ||||
0.147543 | + | 0.989056i | \(0.452863\pi\) | |||||||
\(662\) | −18.9635 | −0.737038 | ||||||||
\(663\) | −26.1831 | −1.01687 | ||||||||
\(664\) | −1.80539 | −0.0700626 | ||||||||
\(665\) | −5.54889 | −0.215177 | ||||||||
\(666\) | −56.4940 | −2.18910 | ||||||||
\(667\) | 26.2959 | 1.01818 | ||||||||
\(668\) | −3.74350 | −0.144841 | ||||||||
\(669\) | −64.1697 | −2.48094 | ||||||||
\(670\) | 26.0699 | 1.00717 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | −4.22603 | −0.163023 | ||||||||
\(673\) | −33.2792 | −1.28282 | −0.641410 | − | 0.767199i | \(-0.721650\pi\) | ||||
−0.641410 | + | 0.767199i | \(0.721650\pi\) | |||||||
\(674\) | 30.1595 | 1.16170 | ||||||||
\(675\) | −169.212 | −6.51298 | ||||||||
\(676\) | −0.550294 | −0.0211651 | ||||||||
\(677\) | 0.160391 | 0.00616431 | 0.00308216 | − | 0.999995i | \(-0.499019\pi\) | ||||
0.00308216 | + | 0.999995i | \(0.499019\pi\) | |||||||
\(678\) | 11.6816 | 0.448630 | ||||||||
\(679\) | 13.2286 | 0.507668 | ||||||||
\(680\) | 9.74350 | 0.373646 | ||||||||
\(681\) | 11.3418 | 0.434619 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 4.60477 | 0.176197 | 0.0880983 | − | 0.996112i | \(-0.471921\pi\) | ||||
0.0880983 | + | 0.996112i | \(0.471921\pi\) | |||||||
\(684\) | −7.20555 | −0.275511 | ||||||||
\(685\) | 21.4898 | 0.821084 | ||||||||
\(686\) | −16.2051 | −0.618714 | ||||||||
\(687\) | −24.6676 | −0.941128 | ||||||||
\(688\) | 11.4461 | 0.436377 | ||||||||
\(689\) | 15.5256 | 0.591479 | ||||||||
\(690\) | −33.8812 | −1.28983 | ||||||||
\(691\) | 6.54008 | 0.248796 | 0.124398 | − | 0.992232i | \(-0.460300\pi\) | ||||
0.124398 | + | 0.992232i | \(0.460300\pi\) | |||||||
\(692\) | −9.08684 | −0.345430 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 23.5997 | 0.895833 | ||||||||
\(695\) | 26.7086 | 1.01311 | ||||||||
\(696\) | 33.2245 | 1.25937 | ||||||||
\(697\) | −5.44325 | −0.206178 | ||||||||
\(698\) | −29.2086 | −1.10556 | ||||||||
\(699\) | −69.9879 | −2.64719 | ||||||||
\(700\) | −16.6611 | −0.629732 | ||||||||
\(701\) | 12.3455 | 0.466282 | 0.233141 | − | 0.972443i | \(-0.425100\pi\) | ||||
0.233141 | + | 0.972443i | \(0.425100\pi\) | |||||||
\(702\) | 47.4046 | 1.78917 | ||||||||
\(703\) | −7.84034 | −0.295704 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −83.1554 | −3.13182 | ||||||||
\(706\) | 10.2274 | 0.384915 | ||||||||
\(707\) | 25.1277 | 0.945023 | ||||||||
\(708\) | 21.4775 | 0.807173 | ||||||||
\(709\) | −26.2464 | −0.985704 | −0.492852 | − | 0.870113i | \(-0.664046\pi\) | ||||
−0.492852 | + | 0.870113i | \(0.664046\pi\) | |||||||
\(710\) | −45.0190 | −1.68953 | ||||||||
\(711\) | −40.7594 | −1.52860 | ||||||||
\(712\) | −6.04589 | −0.226579 | ||||||||
\(713\) | −16.1546 | −0.604995 | ||||||||
\(714\) | −9.81648 | −0.367373 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 8.76751 | 0.327657 | ||||||||
\(717\) | 56.4412 | 2.10783 | ||||||||
\(718\) | 0.876807 | 0.0327221 | ||||||||
\(719\) | 5.61032 | 0.209230 | 0.104615 | − | 0.994513i | \(-0.466639\pi\) | ||||
0.104615 | + | 0.994513i | \(0.466639\pi\) | |||||||
\(720\) | −30.2245 | −1.12640 | ||||||||
\(721\) | −26.5179 | −0.987579 | ||||||||
\(722\) | −1.00000 | −0.0372161 | ||||||||
\(723\) | 54.6276 | 2.03162 | ||||||||
\(724\) | 19.6807 | 0.731426 | ||||||||
\(725\) | 130.988 | 4.86476 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −9.17060 | −0.340119 | −0.170059 | − | 0.985434i | \(-0.554396\pi\) | ||||
−0.170059 | + | 0.985434i | \(0.554396\pi\) | |||||||
\(728\) | 4.66760 | 0.172993 | ||||||||
\(729\) | 24.7423 | 0.916382 | ||||||||
\(730\) | 7.03495 | 0.260375 | ||||||||
\(731\) | 26.5876 | 0.983378 | ||||||||
\(732\) | −27.4919 | −1.01613 | ||||||||
\(733\) | −26.9140 | −0.994091 | −0.497045 | − | 0.867725i | \(-0.665582\pi\) | ||||
−0.497045 | + | 0.867725i | \(0.665582\pi\) | |||||||
\(734\) | −10.5030 | −0.387673 | ||||||||
\(735\) | −70.3514 | −2.59495 | ||||||||
\(736\) | −2.52841 | −0.0931986 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 16.8850 | 0.621547 | ||||||||
\(739\) | −43.4032 | −1.59661 | −0.798307 | − | 0.602251i | \(-0.794271\pi\) | ||||
−0.798307 | + | 0.602251i | \(0.794271\pi\) | |||||||
\(740\) | −32.8872 | −1.20896 | ||||||||
\(741\) | 11.2719 | 0.414084 | ||||||||
\(742\) | 5.82081 | 0.213689 | ||||||||
\(743\) | −18.0671 | −0.662817 | −0.331409 | − | 0.943487i | \(-0.607524\pi\) | ||||
−0.331409 | + | 0.943487i | \(0.607524\pi\) | |||||||
\(744\) | −20.4111 | −0.748307 | ||||||||
\(745\) | −57.5687 | −2.10915 | ||||||||
\(746\) | 34.9249 | 1.27869 | ||||||||
\(747\) | 13.0088 | 0.475967 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 1.12426 | 0.0410797 | ||||||||
\(750\) | −101.771 | −3.71616 | ||||||||
\(751\) | −44.0336 | −1.60681 | −0.803405 | − | 0.595432i | \(-0.796981\pi\) | ||||
−0.803405 | + | 0.595432i | \(0.796981\pi\) | |||||||
\(752\) | −6.20555 | −0.226293 | ||||||||
\(753\) | −42.9549 | −1.56537 | ||||||||
\(754\) | −36.6961 | −1.33639 | ||||||||
\(755\) | −20.9272 | −0.761618 | ||||||||
\(756\) | 17.7728 | 0.646390 | ||||||||
\(757\) | 19.5489 | 0.710517 | 0.355258 | − | 0.934768i | \(-0.384393\pi\) | ||||
0.355258 | + | 0.934768i | \(0.384393\pi\) | |||||||
\(758\) | 13.9695 | 0.507396 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −4.19461 | −0.152155 | ||||||||
\(761\) | 36.8548 | 1.33599 | 0.667993 | − | 0.744168i | \(-0.267154\pi\) | ||||
0.667993 | + | 0.744168i | \(0.267154\pi\) | |||||||
\(762\) | 0.819406 | 0.0296839 | ||||||||
\(763\) | 11.5394 | 0.417753 | ||||||||
\(764\) | −9.47747 | −0.342883 | ||||||||
\(765\) | −70.2073 | −2.53835 | ||||||||
\(766\) | −35.3223 | −1.27625 | ||||||||
\(767\) | −23.7216 | −0.856538 | ||||||||
\(768\) | −3.19461 | −0.115276 | ||||||||
\(769\) | 6.09778 | 0.219892 | 0.109946 | − | 0.993938i | \(-0.464932\pi\) | ||||
0.109946 | + | 0.993938i | \(0.464932\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −32.4400 | −1.16830 | ||||||||
\(772\) | −8.00000 | −0.287926 | ||||||||
\(773\) | 3.70407 | 0.133226 | 0.0666131 | − | 0.997779i | \(-0.478781\pi\) | ||||
0.0666131 | + | 0.997779i | \(0.478781\pi\) | |||||||
\(774\) | −82.4752 | −2.96451 | ||||||||
\(775\) | −80.4709 | −2.89060 | ||||||||
\(776\) | 10.0000 | 0.358979 | ||||||||
\(777\) | 33.1335 | 1.18866 | ||||||||
\(778\) | −12.5838 | −0.451152 | ||||||||
\(779\) | 2.34334 | 0.0839588 | ||||||||
\(780\) | 47.2813 | 1.69294 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | −5.87315 | −0.210024 | ||||||||
\(783\) | −139.727 | −4.99345 | ||||||||
\(784\) | −5.25004 | −0.187501 | ||||||||
\(785\) | −8.55702 | −0.305413 | ||||||||
\(786\) | 11.8282 | 0.421899 | ||||||||
\(787\) | 6.14367 | 0.218998 | 0.109499 | − | 0.993987i | \(-0.465075\pi\) | ||||
0.109499 | + | 0.993987i | \(0.465075\pi\) | |||||||
\(788\) | 24.5438 | 0.874338 | ||||||||
\(789\) | 79.5718 | 2.83283 | ||||||||
\(790\) | −23.7275 | −0.844187 | ||||||||
\(791\) | −4.83726 | −0.171993 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 30.3645 | 1.07828 | ||||||||
\(794\) | −0.924098 | −0.0327950 | ||||||||
\(795\) | 58.9630 | 2.09120 | ||||||||
\(796\) | 20.1991 | 0.715938 | ||||||||
\(797\) | 11.3957 | 0.403656 | 0.201828 | − | 0.979421i | \(-0.435312\pi\) | ||||
0.201828 | + | 0.979421i | \(0.435312\pi\) | |||||||
\(798\) | 4.22603 | 0.149600 | ||||||||
\(799\) | −14.4146 | −0.509953 | ||||||||
\(800\) | −12.5948 | −0.445293 | ||||||||
\(801\) | 43.5640 | 1.53926 | ||||||||
\(802\) | 2.30238 | 0.0813000 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | −19.8548 | −0.700225 | ||||||||
\(805\) | 14.0299 | 0.494489 | ||||||||
\(806\) | 22.5438 | 0.794073 | ||||||||
\(807\) | 94.1646 | 3.31475 | ||||||||
\(808\) | 18.9949 | 0.668240 | ||||||||
\(809\) | 2.18367 | 0.0767739 | 0.0383869 | − | 0.999263i | \(-0.487778\pi\) | ||||
0.0383869 | + | 0.999263i | \(0.487778\pi\) | |||||||
\(810\) | 89.3592 | 3.13976 | ||||||||
\(811\) | −41.8142 | −1.46830 | −0.734148 | − | 0.678989i | \(-0.762418\pi\) | ||||
−0.734148 | + | 0.678989i | \(0.762418\pi\) | |||||||
\(812\) | −13.7580 | −0.482810 | ||||||||
\(813\) | −9.55337 | −0.335051 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −25.8162 | −0.904302 | ||||||||
\(816\) | −7.42064 | −0.259774 | ||||||||
\(817\) | −11.4461 | −0.400447 | ||||||||
\(818\) | −11.4870 | −0.401634 | ||||||||
\(819\) | −33.6327 | −1.17522 | ||||||||
\(820\) | 9.82940 | 0.343257 | ||||||||
\(821\) | 7.65974 | 0.267327 | 0.133663 | − | 0.991027i | \(-0.457326\pi\) | ||||
0.133663 | + | 0.991027i | \(0.457326\pi\) | |||||||
\(822\) | −16.3666 | −0.570851 | ||||||||
\(823\) | −13.8893 | −0.484151 | −0.242075 | − | 0.970257i | \(-0.577828\pi\) | ||||
−0.242075 | + | 0.970257i | \(0.577828\pi\) | |||||||
\(824\) | −20.0459 | −0.698332 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −8.89363 | −0.309449 | ||||||||
\(827\) | 29.3887 | 1.02194 | 0.510972 | − | 0.859597i | \(-0.329286\pi\) | ||||
0.510972 | + | 0.859597i | \(0.329286\pi\) | |||||||
\(828\) | 18.2186 | 0.633141 | ||||||||
\(829\) | 8.60432 | 0.298840 | 0.149420 | − | 0.988774i | \(-0.452259\pi\) | ||||
0.149420 | + | 0.988774i | \(0.452259\pi\) | |||||||
\(830\) | 7.57290 | 0.262859 | ||||||||
\(831\) | −53.8683 | −1.86867 | ||||||||
\(832\) | 3.52841 | 0.122326 | ||||||||
\(833\) | −12.1951 | −0.422536 | ||||||||
\(834\) | −20.3412 | −0.704358 | ||||||||
\(835\) | 15.7026 | 0.543409 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 85.8400 | 2.96706 | ||||||||
\(838\) | −6.21369 | −0.214648 | ||||||||
\(839\) | 0.815377 | 0.0281499 | 0.0140750 | − | 0.999901i | \(-0.495520\pi\) | ||||
0.0140750 | + | 0.999901i | \(0.495520\pi\) | |||||||
\(840\) | 17.7266 | 0.611624 | ||||||||
\(841\) | 79.1635 | 2.72977 | ||||||||
\(842\) | −12.5934 | −0.433996 | ||||||||
\(843\) | −3.15966 | −0.108825 | ||||||||
\(844\) | −1.88129 | −0.0647566 | ||||||||
\(845\) | 2.30827 | 0.0794069 | ||||||||
\(846\) | 44.7144 | 1.53731 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 4.40017 | 0.151102 | ||||||||
\(849\) | −19.0978 | −0.655434 | ||||||||
\(850\) | −29.2559 | −1.00347 | ||||||||
\(851\) | 19.8236 | 0.679545 | ||||||||
\(852\) | 34.2864 | 1.17463 | ||||||||
\(853\) | 6.70856 | 0.229697 | 0.114848 | − | 0.993383i | \(-0.463362\pi\) | ||||
0.114848 | + | 0.993383i | \(0.463362\pi\) | |||||||
\(854\) | 11.3842 | 0.389558 | ||||||||
\(855\) | 30.2245 | 1.03366 | ||||||||
\(856\) | 0.849872 | 0.0290480 | ||||||||
\(857\) | −17.6416 | −0.602626 | −0.301313 | − | 0.953525i | \(-0.597425\pi\) | ||||
−0.301313 | + | 0.953525i | \(0.597425\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 36.3520 | 1.24032 | 0.620158 | − | 0.784477i | \(-0.287069\pi\) | ||||
0.620158 | + | 0.784477i | \(0.287069\pi\) | |||||||
\(860\) | −48.0118 | −1.63719 | ||||||||
\(861\) | −9.90302 | −0.337494 | ||||||||
\(862\) | 24.4570 | 0.833009 | ||||||||
\(863\) | 24.1984 | 0.823722 | 0.411861 | − | 0.911247i | \(-0.364879\pi\) | ||||
0.411861 | + | 0.911247i | \(0.364879\pi\) | |||||||
\(864\) | 13.4351 | 0.457072 | ||||||||
\(865\) | 38.1158 | 1.29598 | ||||||||
\(866\) | −16.3892 | −0.556929 | ||||||||
\(867\) | 37.0713 | 1.25901 | ||||||||
\(868\) | 8.45206 | 0.286882 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | −139.364 | −4.72488 | ||||||||
\(871\) | 21.9294 | 0.743050 | ||||||||
\(872\) | 8.72303 | 0.295399 | ||||||||
\(873\) | −72.0555 | −2.43871 | ||||||||
\(874\) | 2.52841 | 0.0855249 | ||||||||
\(875\) | 42.1426 | 1.42468 | ||||||||
\(876\) | −5.35781 | −0.181024 | ||||||||
\(877\) | −43.3477 | −1.46375 | −0.731874 | − | 0.681440i | \(-0.761354\pi\) | ||||
−0.731874 | + | 0.681440i | \(0.761354\pi\) | |||||||
\(878\) | −31.8353 | −1.07439 | ||||||||
\(879\) | 46.4781 | 1.56767 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1.34121 | 0.0451865 | 0.0225932 | − | 0.999745i | \(-0.492808\pi\) | ||||
0.0225932 | + | 0.999745i | \(0.492808\pi\) | |||||||
\(882\) | 37.8294 | 1.27378 | ||||||||
\(883\) | 41.2924 | 1.38960 | 0.694800 | − | 0.719203i | \(-0.255493\pi\) | ||||
0.694800 | + | 0.719203i | \(0.255493\pi\) | |||||||
\(884\) | 8.19602 | 0.275662 | ||||||||
\(885\) | −90.0897 | −3.02833 | ||||||||
\(886\) | 14.7594 | 0.495851 | ||||||||
\(887\) | 8.18142 | 0.274705 | 0.137353 | − | 0.990522i | \(-0.456141\pi\) | ||||
0.137353 | + | 0.990522i | \(0.456141\pi\) | |||||||
\(888\) | 25.0468 | 0.840517 | ||||||||
\(889\) | −0.339309 | −0.0113800 | ||||||||
\(890\) | 25.3602 | 0.850075 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 20.0868 | 0.672557 | ||||||||
\(893\) | 6.20555 | 0.207661 | ||||||||
\(894\) | 43.8442 | 1.46637 | ||||||||
\(895\) | −36.7763 | −1.22930 | ||||||||
\(896\) | 1.32286 | 0.0441937 | ||||||||
\(897\) | −28.5001 | −0.951590 | ||||||||
\(898\) | −1.44605 | −0.0482555 | ||||||||
\(899\) | −66.4490 | −2.21620 | ||||||||
\(900\) | 90.7523 | 3.02508 | ||||||||
\(901\) | 10.2210 | 0.340510 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 48.3714 | 1.60970 | ||||||||
\(904\) | −3.65666 | −0.121619 | ||||||||
\(905\) | −82.5528 | −2.74415 | ||||||||
\(906\) | 15.9381 | 0.529508 | ||||||||
\(907\) | −4.76398 | −0.158185 | −0.0790927 | − | 0.996867i | \(-0.525202\pi\) | ||||
−0.0790927 | + | 0.996867i | \(0.525202\pi\) | |||||||
\(908\) | −3.55029 | −0.117821 | ||||||||
\(909\) | −136.869 | −4.53966 | ||||||||
\(910\) | −19.5788 | −0.649030 | ||||||||
\(911\) | 10.5589 | 0.349831 | 0.174916 | − | 0.984583i | \(-0.444035\pi\) | ||||
0.174916 | + | 0.984583i | \(0.444035\pi\) | |||||||
\(912\) | 3.19461 | 0.105784 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 9.58524 | 0.317052 | ||||||||
\(915\) | 115.318 | 3.81230 | ||||||||
\(916\) | 7.72162 | 0.255130 | ||||||||
\(917\) | −4.89796 | −0.161745 | ||||||||
\(918\) | 31.2079 | 1.03001 | ||||||||
\(919\) | 37.5764 | 1.23953 | 0.619766 | − | 0.784787i | \(-0.287227\pi\) | ||||
0.619766 | + | 0.784787i | \(0.287227\pi\) | |||||||
\(920\) | 10.6057 | 0.349660 | ||||||||
\(921\) | 30.9609 | 1.02020 | ||||||||
\(922\) | −9.91624 | −0.326574 | ||||||||
\(923\) | −37.8689 | −1.24647 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 98.7473 | 3.24679 | ||||||||
\(926\) | −3.22743 | −0.106060 | ||||||||
\(927\) | 144.442 | 4.74409 | ||||||||
\(928\) | −10.4002 | −0.341402 | ||||||||
\(929\) | −4.07590 | −0.133726 | −0.0668630 | − | 0.997762i | \(-0.521299\pi\) | ||||
−0.0668630 | + | 0.997762i | \(0.521299\pi\) | |||||||
\(930\) | 85.6167 | 2.80748 | ||||||||
\(931\) | 5.25004 | 0.172063 | ||||||||
\(932\) | 21.9081 | 0.717624 | ||||||||
\(933\) | 60.1320 | 1.96863 | ||||||||
\(934\) | −36.0118 | −1.17834 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −25.4242 | −0.831015 | ||||||||
\(937\) | −54.4273 | −1.77806 | −0.889030 | − | 0.457848i | \(-0.848620\pi\) | ||||
−0.889030 | + | 0.457848i | \(0.848620\pi\) | |||||||
\(938\) | 8.22170 | 0.268448 | ||||||||
\(939\) | −86.8297 | −2.83358 | ||||||||
\(940\) | 26.0299 | 0.849002 | ||||||||
\(941\) | −26.7152 | −0.870890 | −0.435445 | − | 0.900215i | \(-0.643409\pi\) | ||||
−0.435445 | + | 0.900215i | \(0.643409\pi\) | |||||||
\(942\) | 6.51702 | 0.212336 | ||||||||
\(943\) | −5.92493 | −0.192942 | ||||||||
\(944\) | −6.72303 | −0.218816 | ||||||||
\(945\) | −74.5500 | −2.42511 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 56.9448 | 1.85046 | 0.925229 | − | 0.379409i | \(-0.123873\pi\) | ||||
0.925229 | + | 0.379409i | \(0.123873\pi\) | |||||||
\(948\) | 18.0708 | 0.586914 | ||||||||
\(949\) | 5.91764 | 0.192095 | ||||||||
\(950\) | 12.5948 | 0.408629 | ||||||||
\(951\) | 45.9056 | 1.48859 | ||||||||
\(952\) | 3.07282 | 0.0995908 | ||||||||
\(953\) | −0.764553 | −0.0247663 | −0.0123832 | − | 0.999923i | \(-0.503942\pi\) | ||||
−0.0123832 | + | 0.999923i | \(0.503942\pi\) | |||||||
\(954\) | −31.7056 | −1.02651 | ||||||||
\(955\) | 39.7543 | 1.28642 | ||||||||
\(956\) | −17.6676 | −0.571411 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −7.68668 | −0.248345 | ||||||||
\(959\) | 6.77727 | 0.218850 | ||||||||
\(960\) | 13.4002 | 0.432489 | ||||||||
\(961\) | 9.82221 | 0.316846 | ||||||||
\(962\) | −27.6640 | −0.891922 | ||||||||
\(963\) | −6.12380 | −0.197337 | ||||||||
\(964\) | −17.0999 | −0.550751 | ||||||||
\(965\) | 33.5569 | 1.08023 | ||||||||
\(966\) | −10.6852 | −0.343789 | ||||||||
\(967\) | −26.5510 | −0.853823 | −0.426912 | − | 0.904293i | \(-0.640398\pi\) | ||||
−0.426912 | + | 0.904293i | \(0.640398\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 7.42064 | 0.238385 | ||||||||
\(970\) | −41.9461 | −1.34681 | ||||||||
\(971\) | −35.6335 | −1.14353 | −0.571766 | − | 0.820416i | \(-0.693742\pi\) | ||||
−0.571766 | + | 0.820416i | \(0.693742\pi\) | |||||||
\(972\) | −27.7506 | −0.890100 | ||||||||
\(973\) | 8.42312 | 0.270033 | ||||||||
\(974\) | 34.6356 | 1.10980 | ||||||||
\(975\) | −141.967 | −4.54659 | ||||||||
\(976\) | 8.60572 | 0.275462 | ||||||||
\(977\) | 23.8544 | 0.763168 | 0.381584 | − | 0.924334i | \(-0.375379\pi\) | ||||
0.381584 | + | 0.924334i | \(0.375379\pi\) | |||||||
\(978\) | 19.6616 | 0.628709 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 22.0219 | 0.703463 | ||||||||
\(981\) | −62.8542 | −2.00678 | ||||||||
\(982\) | 33.1458 | 1.05772 | ||||||||
\(983\) | −21.5520 | −0.687401 | −0.343701 | − | 0.939079i | \(-0.611681\pi\) | ||||
−0.343701 | + | 0.939079i | \(0.611681\pi\) | |||||||
\(984\) | −7.48606 | −0.238647 | ||||||||
\(985\) | −102.952 | −3.28032 | ||||||||
\(986\) | −24.1581 | −0.769352 | ||||||||
\(987\) | −26.2249 | −0.834746 | ||||||||
\(988\) | −3.52841 | −0.112254 | ||||||||
\(989\) | 28.9404 | 0.920250 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 14.0049 | 0.444881 | 0.222441 | − | 0.974946i | \(-0.428598\pi\) | ||||
0.222441 | + | 0.974946i | \(0.428598\pi\) | |||||||
\(992\) | 6.38923 | 0.202858 | ||||||||
\(993\) | −60.5811 | −1.92248 | ||||||||
\(994\) | −14.1977 | −0.450323 | ||||||||
\(995\) | −84.7274 | −2.68604 | ||||||||
\(996\) | −5.76751 | −0.182751 | ||||||||
\(997\) | 47.2733 | 1.49716 | 0.748581 | − | 0.663044i | \(-0.230736\pi\) | ||||
0.748581 | + | 0.663044i | \(0.230736\pi\) | |||||||
\(998\) | 22.9949 | 0.727892 | ||||||||
\(999\) | −105.336 | −3.33268 |
(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 | 4598.2.a.bs.1.1 | ✓ | 4 | |
11.10 | odd | 2 | 4598.2.a.bv.1.1 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4598.2.a.bs.1.1 | ✓ | 4 | 1.1 | even | 1 | trivial | |
4598.2.a.bv.1.1 | yes | 4 | 11.10 | odd | 2 |