Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [370,2,Mod(1,370)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(370, 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("370.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 370 = 2 \cdot 5 \cdot 37 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 370.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: | \(2.95446487479\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.892.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 8x + 10 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-2.91729\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 370.1 |
$q$-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 | ||||||||
\(3\) | 0.406728 | 0.234825 | 0.117412 | − | 0.993083i | \(-0.462540\pi\) | ||||
0.117412 | + | 0.993083i | \(0.462540\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0.406728 | 0.166046 | ||||||||
\(7\) | 2.91729 | 1.10263 | 0.551315 | − | 0.834297i | \(-0.314126\pi\) | ||||
0.551315 | + | 0.834297i | \(0.314126\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | −2.83457 | −0.944857 | ||||||||
\(10\) | −1.00000 | −0.316228 | ||||||||
\(11\) | 6.51056 | 1.96301 | 0.981503 | − | 0.191444i | \(-0.0613171\pi\) | ||||
0.981503 | + | 0.191444i | \(0.0613171\pi\) | |||||||
\(12\) | 0.406728 | 0.117412 | ||||||||
\(13\) | −0.813457 | −0.225612 | −0.112806 | − | 0.993617i | \(-0.535984\pi\) | ||||
−0.112806 | + | 0.993617i | \(0.535984\pi\) | |||||||
\(14\) | 2.91729 | 0.779677 | ||||||||
\(15\) | −0.406728 | −0.105017 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −2.51056 | −0.608900 | −0.304450 | − | 0.952528i | \(-0.598473\pi\) | ||||
−0.304450 | + | 0.952528i | \(0.598473\pi\) | |||||||
\(18\) | −2.83457 | −0.668115 | ||||||||
\(19\) | 0.406728 | 0.0933099 | 0.0466550 | − | 0.998911i | \(-0.485144\pi\) | ||||
0.0466550 | + | 0.998911i | \(0.485144\pi\) | |||||||
\(20\) | −1.00000 | −0.223607 | ||||||||
\(21\) | 1.18654 | 0.258925 | ||||||||
\(22\) | 6.51056 | 1.38806 | ||||||||
\(23\) | 5.02112 | 1.04697 | 0.523487 | − | 0.852033i | \(-0.324631\pi\) | ||||
0.523487 | + | 0.852033i | \(0.324631\pi\) | |||||||
\(24\) | 0.406728 | 0.0830231 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −0.813457 | −0.159532 | ||||||||
\(27\) | −2.37309 | −0.456701 | ||||||||
\(28\) | 2.91729 | 0.551315 | ||||||||
\(29\) | −5.32401 | −0.988645 | −0.494322 | − | 0.869279i | \(-0.664584\pi\) | ||||
−0.494322 | + | 0.869279i | \(0.664584\pi\) | |||||||
\(30\) | −0.406728 | −0.0742581 | ||||||||
\(31\) | −8.75186 | −1.57188 | −0.785940 | − | 0.618303i | \(-0.787821\pi\) | ||||
−0.785940 | + | 0.618303i | \(0.787821\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 2.64803 | 0.460963 | ||||||||
\(34\) | −2.51056 | −0.430557 | ||||||||
\(35\) | −2.91729 | −0.493111 | ||||||||
\(36\) | −2.83457 | −0.472429 | ||||||||
\(37\) | −1.00000 | −0.164399 | ||||||||
\(38\) | 0.406728 | 0.0659801 | ||||||||
\(39\) | −0.330856 | −0.0529794 | ||||||||
\(40\) | −1.00000 | −0.158114 | ||||||||
\(41\) | 6.34513 | 0.990943 | 0.495471 | − | 0.868624i | \(-0.334995\pi\) | ||||
0.495471 | + | 0.868624i | \(0.334995\pi\) | |||||||
\(42\) | 1.18654 | 0.183088 | ||||||||
\(43\) | −7.32401 | −1.11690 | −0.558451 | − | 0.829538i | \(-0.688604\pi\) | ||||
−0.558451 | + | 0.829538i | \(0.688604\pi\) | |||||||
\(44\) | 6.51056 | 0.981503 | ||||||||
\(45\) | 2.83457 | 0.422553 | ||||||||
\(46\) | 5.02112 | 0.740323 | ||||||||
\(47\) | −5.42784 | −0.791732 | −0.395866 | − | 0.918308i | \(-0.629556\pi\) | ||||
−0.395866 | + | 0.918308i | \(0.629556\pi\) | |||||||
\(48\) | 0.406728 | 0.0587062 | ||||||||
\(49\) | 1.51056 | 0.215794 | ||||||||
\(50\) | 1.00000 | 0.141421 | ||||||||
\(51\) | −1.02112 | −0.142985 | ||||||||
\(52\) | −0.813457 | −0.112806 | ||||||||
\(53\) | −2.34513 | −0.322128 | −0.161064 | − | 0.986944i | \(-0.551493\pi\) | ||||
−0.161064 | + | 0.986944i | \(0.551493\pi\) | |||||||
\(54\) | −2.37309 | −0.322936 | ||||||||
\(55\) | −6.51056 | −0.877883 | ||||||||
\(56\) | 2.91729 | 0.389839 | ||||||||
\(57\) | 0.165428 | 0.0219115 | ||||||||
\(58\) | −5.32401 | −0.699077 | ||||||||
\(59\) | −1.42784 | −0.185889 | −0.0929447 | − | 0.995671i | \(-0.529628\pi\) | ||||
−0.0929447 | + | 0.995671i | \(0.529628\pi\) | |||||||
\(60\) | −0.406728 | −0.0525084 | ||||||||
\(61\) | −1.32401 | −0.169523 | −0.0847613 | − | 0.996401i | \(-0.527013\pi\) | ||||
−0.0847613 | + | 0.996401i | \(0.527013\pi\) | |||||||
\(62\) | −8.75186 | −1.11149 | ||||||||
\(63\) | −8.26926 | −1.04183 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0.813457 | 0.100897 | ||||||||
\(66\) | 2.64803 | 0.325950 | ||||||||
\(67\) | −5.42784 | −0.663117 | −0.331558 | − | 0.943435i | \(-0.607574\pi\) | ||||
−0.331558 | + | 0.943435i | \(0.607574\pi\) | |||||||
\(68\) | −2.51056 | −0.304450 | ||||||||
\(69\) | 2.04223 | 0.245856 | ||||||||
\(70\) | −2.91729 | −0.348682 | ||||||||
\(71\) | 14.6480 | 1.73840 | 0.869201 | − | 0.494460i | \(-0.164634\pi\) | ||||
0.869201 | + | 0.494460i | \(0.164634\pi\) | |||||||
\(72\) | −2.83457 | −0.334058 | ||||||||
\(73\) | −11.0211 | −1.28992 | −0.644962 | − | 0.764215i | \(-0.723127\pi\) | ||||
−0.644962 | + | 0.764215i | \(0.723127\pi\) | |||||||
\(74\) | −1.00000 | −0.116248 | ||||||||
\(75\) | 0.406728 | 0.0469650 | ||||||||
\(76\) | 0.406728 | 0.0466550 | ||||||||
\(77\) | 18.9932 | 2.16447 | ||||||||
\(78\) | −0.330856 | −0.0374621 | ||||||||
\(79\) | −1.75870 | −0.197869 | −0.0989346 | − | 0.995094i | \(-0.531543\pi\) | ||||
−0.0989346 | + | 0.995094i | \(0.531543\pi\) | |||||||
\(80\) | −1.00000 | −0.111803 | ||||||||
\(81\) | 7.53851 | 0.837613 | ||||||||
\(82\) | 6.34513 | 0.700702 | ||||||||
\(83\) | −7.05476 | −0.774360 | −0.387180 | − | 0.922004i | \(-0.626551\pi\) | ||||
−0.387180 | + | 0.922004i | \(0.626551\pi\) | |||||||
\(84\) | 1.18654 | 0.129462 | ||||||||
\(85\) | 2.51056 | 0.272308 | ||||||||
\(86\) | −7.32401 | −0.789769 | ||||||||
\(87\) | −2.16543 | −0.232158 | ||||||||
\(88\) | 6.51056 | 0.694028 | ||||||||
\(89\) | 6.00000 | 0.635999 | 0.317999 | − | 0.948091i | \(-0.396989\pi\) | ||||
0.317999 | + | 0.948091i | \(0.396989\pi\) | |||||||
\(90\) | 2.83457 | 0.298790 | ||||||||
\(91\) | −2.37309 | −0.248767 | ||||||||
\(92\) | 5.02112 | 0.523487 | ||||||||
\(93\) | −3.55963 | −0.369116 | ||||||||
\(94\) | −5.42784 | −0.559839 | ||||||||
\(95\) | −0.406728 | −0.0417295 | ||||||||
\(96\) | 0.406728 | 0.0415115 | ||||||||
\(97\) | 2.34513 | 0.238112 | 0.119056 | − | 0.992888i | \(-0.462013\pi\) | ||||
0.119056 | + | 0.992888i | \(0.462013\pi\) | |||||||
\(98\) | 1.51056 | 0.152589 | ||||||||
\(99\) | −18.4546 | −1.85476 | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | −8.20766 | −0.816693 | −0.408346 | − | 0.912827i | \(-0.633894\pi\) | ||||
−0.408346 | + | 0.912827i | \(0.633894\pi\) | |||||||
\(102\) | −1.02112 | −0.101105 | ||||||||
\(103\) | −8.81346 | −0.868416 | −0.434208 | − | 0.900813i | \(-0.642972\pi\) | ||||
−0.434208 | + | 0.900813i | \(0.642972\pi\) | |||||||
\(104\) | −0.813457 | −0.0797660 | ||||||||
\(105\) | −1.18654 | −0.115795 | ||||||||
\(106\) | −2.34513 | −0.227779 | ||||||||
\(107\) | 15.2624 | 1.47547 | 0.737737 | − | 0.675089i | \(-0.235895\pi\) | ||||
0.737737 | + | 0.675089i | \(0.235895\pi\) | |||||||
\(108\) | −2.37309 | −0.228350 | ||||||||
\(109\) | 4.30290 | 0.412143 | 0.206072 | − | 0.978537i | \(-0.433932\pi\) | ||||
0.206072 | + | 0.978537i | \(0.433932\pi\) | |||||||
\(110\) | −6.51056 | −0.620757 | ||||||||
\(111\) | −0.406728 | −0.0386050 | ||||||||
\(112\) | 2.91729 | 0.275658 | ||||||||
\(113\) | −9.15859 | −0.861567 | −0.430784 | − | 0.902455i | \(-0.641763\pi\) | ||||
−0.430784 | + | 0.902455i | \(0.641763\pi\) | |||||||
\(114\) | 0.165428 | 0.0154938 | ||||||||
\(115\) | −5.02112 | −0.468221 | ||||||||
\(116\) | −5.32401 | −0.494322 | ||||||||
\(117\) | 2.30580 | 0.213171 | ||||||||
\(118\) | −1.42784 | −0.131444 | ||||||||
\(119\) | −7.32401 | −0.671391 | ||||||||
\(120\) | −0.406728 | −0.0371291 | ||||||||
\(121\) | 31.3874 | 2.85340 | ||||||||
\(122\) | −1.32401 | −0.119871 | ||||||||
\(123\) | 2.58074 | 0.232698 | ||||||||
\(124\) | −8.75186 | −0.785940 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | −8.26926 | −0.736684 | ||||||||
\(127\) | −8.61439 | −0.764403 | −0.382202 | − | 0.924079i | \(-0.624834\pi\) | ||||
−0.382202 | + | 0.924079i | \(0.624834\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | −2.97888 | −0.262276 | ||||||||
\(130\) | 0.813457 | 0.0713449 | ||||||||
\(131\) | 13.4278 | 1.17320 | 0.586598 | − | 0.809878i | \(-0.300467\pi\) | ||||
0.586598 | + | 0.809878i | \(0.300467\pi\) | |||||||
\(132\) | 2.64803 | 0.230481 | ||||||||
\(133\) | 1.18654 | 0.102886 | ||||||||
\(134\) | −5.42784 | −0.468894 | ||||||||
\(135\) | 2.37309 | 0.204243 | ||||||||
\(136\) | −2.51056 | −0.215279 | ||||||||
\(137\) | −14.6903 | −1.25507 | −0.627537 | − | 0.778587i | \(-0.715937\pi\) | ||||
−0.627537 | + | 0.778587i | \(0.715937\pi\) | |||||||
\(138\) | 2.04223 | 0.173846 | ||||||||
\(139\) | 17.3662 | 1.47299 | 0.736493 | − | 0.676445i | \(-0.236481\pi\) | ||||
0.736493 | + | 0.676445i | \(0.236481\pi\) | |||||||
\(140\) | −2.91729 | −0.246556 | ||||||||
\(141\) | −2.20766 | −0.185918 | ||||||||
\(142\) | 14.6480 | 1.22924 | ||||||||
\(143\) | −5.29606 | −0.442879 | ||||||||
\(144\) | −2.83457 | −0.236214 | ||||||||
\(145\) | 5.32401 | 0.442135 | ||||||||
\(146\) | −11.0211 | −0.912114 | ||||||||
\(147\) | 0.614387 | 0.0506738 | ||||||||
\(148\) | −1.00000 | −0.0821995 | ||||||||
\(149\) | −0.207658 | −0.0170120 | −0.00850601 | − | 0.999964i | \(-0.502708\pi\) | ||||
−0.00850601 | + | 0.999964i | \(0.502708\pi\) | |||||||
\(150\) | 0.406728 | 0.0332092 | ||||||||
\(151\) | 0.813457 | 0.0661982 | 0.0330991 | − | 0.999452i | \(-0.489462\pi\) | ||||
0.0330991 | + | 0.999452i | \(0.489462\pi\) | |||||||
\(152\) | 0.406728 | 0.0329900 | ||||||||
\(153\) | 7.11636 | 0.575323 | ||||||||
\(154\) | 18.9932 | 1.53051 | ||||||||
\(155\) | 8.75186 | 0.702966 | ||||||||
\(156\) | −0.330856 | −0.0264897 | ||||||||
\(157\) | 5.32401 | 0.424903 | 0.212451 | − | 0.977172i | \(-0.431855\pi\) | ||||
0.212451 | + | 0.977172i | \(0.431855\pi\) | |||||||
\(158\) | −1.75870 | −0.139915 | ||||||||
\(159\) | −0.953831 | −0.0756437 | ||||||||
\(160\) | −1.00000 | −0.0790569 | ||||||||
\(161\) | 14.6480 | 1.15443 | ||||||||
\(162\) | 7.53851 | 0.592282 | ||||||||
\(163\) | 15.2008 | 1.19062 | 0.595310 | − | 0.803496i | \(-0.297029\pi\) | ||||
0.595310 | + | 0.803496i | \(0.297029\pi\) | |||||||
\(164\) | 6.34513 | 0.495471 | ||||||||
\(165\) | −2.64803 | −0.206149 | ||||||||
\(166\) | −7.05476 | −0.547555 | ||||||||
\(167\) | −12.4826 | −0.965933 | −0.482966 | − | 0.875639i | \(-0.660441\pi\) | ||||
−0.482966 | + | 0.875639i | \(0.660441\pi\) | |||||||
\(168\) | 1.18654 | 0.0915438 | ||||||||
\(169\) | −12.3383 | −0.949099 | ||||||||
\(170\) | 2.51056 | 0.192551 | ||||||||
\(171\) | −1.15290 | −0.0881645 | ||||||||
\(172\) | −7.32401 | −0.558451 | ||||||||
\(173\) | 23.0354 | 1.75135 | 0.875674 | − | 0.482903i | \(-0.160417\pi\) | ||||
0.875674 | + | 0.482903i | \(0.160417\pi\) | |||||||
\(174\) | −2.16543 | −0.164161 | ||||||||
\(175\) | 2.91729 | 0.220526 | ||||||||
\(176\) | 6.51056 | 0.490752 | ||||||||
\(177\) | −0.580745 | −0.0436514 | ||||||||
\(178\) | 6.00000 | 0.449719 | ||||||||
\(179\) | 24.2835 | 1.81504 | 0.907518 | − | 0.420013i | \(-0.137974\pi\) | ||||
0.907518 | + | 0.420013i | \(0.137974\pi\) | |||||||
\(180\) | 2.83457 | 0.211277 | ||||||||
\(181\) | 2.16543 | 0.160955 | 0.0804775 | − | 0.996756i | \(-0.474355\pi\) | ||||
0.0804775 | + | 0.996756i | \(0.474355\pi\) | |||||||
\(182\) | −2.37309 | −0.175905 | ||||||||
\(183\) | −0.538514 | −0.0398081 | ||||||||
\(184\) | 5.02112 | 0.370162 | ||||||||
\(185\) | 1.00000 | 0.0735215 | ||||||||
\(186\) | −3.55963 | −0.261005 | ||||||||
\(187\) | −16.3451 | −1.19527 | ||||||||
\(188\) | −5.42784 | −0.395866 | ||||||||
\(189\) | −6.92297 | −0.503572 | ||||||||
\(190\) | −0.406728 | −0.0295072 | ||||||||
\(191\) | −19.3326 | −1.39886 | −0.699429 | − | 0.714702i | \(-0.746562\pi\) | ||||
−0.699429 | + | 0.714702i | \(0.746562\pi\) | |||||||
\(192\) | 0.406728 | 0.0293531 | ||||||||
\(193\) | −20.0422 | −1.44267 | −0.721336 | − | 0.692586i | \(-0.756471\pi\) | ||||
−0.721336 | + | 0.692586i | \(0.756471\pi\) | |||||||
\(194\) | 2.34513 | 0.168370 | ||||||||
\(195\) | 0.330856 | 0.0236931 | ||||||||
\(196\) | 1.51056 | 0.107897 | ||||||||
\(197\) | 15.6269 | 1.11337 | 0.556686 | − | 0.830723i | \(-0.312073\pi\) | ||||
0.556686 | + | 0.830723i | \(0.312073\pi\) | |||||||
\(198\) | −18.4546 | −1.31151 | ||||||||
\(199\) | 20.2835 | 1.43786 | 0.718931 | − | 0.695082i | \(-0.244632\pi\) | ||||
0.718931 | + | 0.695082i | \(0.244632\pi\) | |||||||
\(200\) | 1.00000 | 0.0707107 | ||||||||
\(201\) | −2.20766 | −0.155716 | ||||||||
\(202\) | −8.20766 | −0.577489 | ||||||||
\(203\) | −15.5317 | −1.09011 | ||||||||
\(204\) | −1.02112 | −0.0714924 | ||||||||
\(205\) | −6.34513 | −0.443163 | ||||||||
\(206\) | −8.81346 | −0.614063 | ||||||||
\(207\) | −14.2327 | −0.989242 | ||||||||
\(208\) | −0.813457 | −0.0564031 | ||||||||
\(209\) | 2.64803 | 0.183168 | ||||||||
\(210\) | −1.18654 | −0.0818793 | ||||||||
\(211\) | 18.7182 | 1.28862 | 0.644308 | − | 0.764766i | \(-0.277146\pi\) | ||||
0.644308 | + | 0.764766i | \(0.277146\pi\) | |||||||
\(212\) | −2.34513 | −0.161064 | ||||||||
\(213\) | 5.95777 | 0.408220 | ||||||||
\(214\) | 15.2624 | 1.04332 | ||||||||
\(215\) | 7.32401 | 0.499494 | ||||||||
\(216\) | −2.37309 | −0.161468 | ||||||||
\(217\) | −25.5317 | −1.73320 | ||||||||
\(218\) | 4.30290 | 0.291429 | ||||||||
\(219\) | −4.48260 | −0.302906 | ||||||||
\(220\) | −6.51056 | −0.438942 | ||||||||
\(221\) | 2.04223 | 0.137375 | ||||||||
\(222\) | −0.406728 | −0.0272978 | ||||||||
\(223\) | −15.7307 | −1.05341 | −0.526704 | − | 0.850049i | \(-0.676572\pi\) | ||||
−0.526704 | + | 0.850049i | \(0.676572\pi\) | |||||||
\(224\) | 2.91729 | 0.194919 | ||||||||
\(225\) | −2.83457 | −0.188971 | ||||||||
\(226\) | −9.15859 | −0.609220 | ||||||||
\(227\) | 12.8836 | 0.855117 | 0.427559 | − | 0.903988i | \(-0.359374\pi\) | ||||
0.427559 | + | 0.903988i | \(0.359374\pi\) | |||||||
\(228\) | 0.165428 | 0.0109557 | ||||||||
\(229\) | 5.25383 | 0.347183 | 0.173591 | − | 0.984818i | \(-0.444463\pi\) | ||||
0.173591 | + | 0.984818i | \(0.444463\pi\) | |||||||
\(230\) | −5.02112 | −0.331083 | ||||||||
\(231\) | 7.72506 | 0.508271 | ||||||||
\(232\) | −5.32401 | −0.349539 | ||||||||
\(233\) | 28.3172 | 1.85512 | 0.927560 | − | 0.373675i | \(-0.121902\pi\) | ||||
0.927560 | + | 0.373675i | \(0.121902\pi\) | |||||||
\(234\) | 2.30580 | 0.150735 | ||||||||
\(235\) | 5.42784 | 0.354073 | ||||||||
\(236\) | −1.42784 | −0.0929447 | ||||||||
\(237\) | −0.715313 | −0.0464646 | ||||||||
\(238\) | −7.32401 | −0.474745 | ||||||||
\(239\) | 14.3788 | 0.930085 | 0.465043 | − | 0.885288i | \(-0.346039\pi\) | ||||
0.465043 | + | 0.885288i | \(0.346039\pi\) | |||||||
\(240\) | −0.406728 | −0.0262542 | ||||||||
\(241\) | 18.2749 | 1.17719 | 0.588596 | − | 0.808427i | \(-0.299681\pi\) | ||||
0.588596 | + | 0.808427i | \(0.299681\pi\) | |||||||
\(242\) | 31.3874 | 2.01766 | ||||||||
\(243\) | 10.1854 | 0.653393 | ||||||||
\(244\) | −1.32401 | −0.0847613 | ||||||||
\(245\) | −1.51056 | −0.0965060 | ||||||||
\(246\) | 2.58074 | 0.164542 | ||||||||
\(247\) | −0.330856 | −0.0210519 | ||||||||
\(248\) | −8.75186 | −0.555744 | ||||||||
\(249\) | −2.86937 | −0.181839 | ||||||||
\(250\) | −1.00000 | −0.0632456 | ||||||||
\(251\) | −1.22019 | −0.0770174 | −0.0385087 | − | 0.999258i | \(-0.512261\pi\) | ||||
−0.0385087 | + | 0.999258i | \(0.512261\pi\) | |||||||
\(252\) | −8.26926 | −0.520914 | ||||||||
\(253\) | 32.6903 | 2.05522 | ||||||||
\(254\) | −8.61439 | −0.540515 | ||||||||
\(255\) | 1.02112 | 0.0639447 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 27.1306 | 1.69236 | 0.846181 | − | 0.532895i | \(-0.178896\pi\) | ||||
0.846181 | + | 0.532895i | \(0.178896\pi\) | |||||||
\(258\) | −2.97888 | −0.185457 | ||||||||
\(259\) | −2.91729 | −0.181271 | ||||||||
\(260\) | 0.813457 | 0.0504485 | ||||||||
\(261\) | 15.0913 | 0.934128 | ||||||||
\(262\) | 13.4278 | 0.829575 | ||||||||
\(263\) | −20.2133 | −1.24641 | −0.623204 | − | 0.782059i | \(-0.714169\pi\) | ||||
−0.623204 | + | 0.782059i | \(0.714169\pi\) | |||||||
\(264\) | 2.64803 | 0.162975 | ||||||||
\(265\) | 2.34513 | 0.144060 | ||||||||
\(266\) | 1.18654 | 0.0727516 | ||||||||
\(267\) | 2.44037 | 0.149348 | ||||||||
\(268\) | −5.42784 | −0.331558 | ||||||||
\(269\) | −0.207658 | −0.0126611 | −0.00633057 | − | 0.999980i | \(-0.502015\pi\) | ||||
−0.00633057 | + | 0.999980i | \(0.502015\pi\) | |||||||
\(270\) | 2.37309 | 0.144421 | ||||||||
\(271\) | −30.6480 | −1.86174 | −0.930868 | − | 0.365357i | \(-0.880947\pi\) | ||||
−0.930868 | + | 0.365357i | \(0.880947\pi\) | |||||||
\(272\) | −2.51056 | −0.152225 | ||||||||
\(273\) | −0.965202 | −0.0584167 | ||||||||
\(274\) | −14.6903 | −0.887471 | ||||||||
\(275\) | 6.51056 | 0.392601 | ||||||||
\(276\) | 2.04223 | 0.122928 | ||||||||
\(277\) | −16.8135 | −1.01022 | −0.505111 | − | 0.863054i | \(-0.668549\pi\) | ||||
−0.505111 | + | 0.863054i | \(0.668549\pi\) | |||||||
\(278\) | 17.3662 | 1.04156 | ||||||||
\(279\) | 24.8078 | 1.48520 | ||||||||
\(280\) | −2.91729 | −0.174341 | ||||||||
\(281\) | −14.2749 | −0.851572 | −0.425786 | − | 0.904824i | \(-0.640002\pi\) | ||||
−0.425786 | + | 0.904824i | \(0.640002\pi\) | |||||||
\(282\) | −2.20766 | −0.131464 | ||||||||
\(283\) | −13.2288 | −0.786369 | −0.393184 | − | 0.919460i | \(-0.628627\pi\) | ||||
−0.393184 | + | 0.919460i | \(0.628627\pi\) | |||||||
\(284\) | 14.6480 | 0.869201 | ||||||||
\(285\) | −0.165428 | −0.00979911 | ||||||||
\(286\) | −5.29606 | −0.313162 | ||||||||
\(287\) | 18.5106 | 1.09264 | ||||||||
\(288\) | −2.83457 | −0.167029 | ||||||||
\(289\) | −10.6971 | −0.629241 | ||||||||
\(290\) | 5.32401 | 0.312637 | ||||||||
\(291\) | 0.953831 | 0.0559146 | ||||||||
\(292\) | −11.0211 | −0.644962 | ||||||||
\(293\) | 2.34513 | 0.137004 | 0.0685020 | − | 0.997651i | \(-0.478178\pi\) | ||||
0.0685020 | + | 0.997651i | \(0.478178\pi\) | |||||||
\(294\) | 0.614387 | 0.0358318 | ||||||||
\(295\) | 1.42784 | 0.0831323 | ||||||||
\(296\) | −1.00000 | −0.0581238 | ||||||||
\(297\) | −15.4501 | −0.896507 | ||||||||
\(298\) | −0.207658 | −0.0120293 | ||||||||
\(299\) | −4.08446 | −0.236210 | ||||||||
\(300\) | 0.406728 | 0.0234825 | ||||||||
\(301\) | −21.3662 | −1.23153 | ||||||||
\(302\) | 0.813457 | 0.0468092 | ||||||||
\(303\) | −3.33829 | −0.191780 | ||||||||
\(304\) | 0.406728 | 0.0233275 | ||||||||
\(305\) | 1.32401 | 0.0758128 | ||||||||
\(306\) | 7.11636 | 0.406815 | ||||||||
\(307\) | −23.2624 | −1.32766 | −0.663828 | − | 0.747885i | \(-0.731069\pi\) | ||||
−0.663828 | + | 0.747885i | \(0.731069\pi\) | |||||||
\(308\) | 18.9932 | 1.08224 | ||||||||
\(309\) | −3.58468 | −0.203926 | ||||||||
\(310\) | 8.75186 | 0.497072 | ||||||||
\(311\) | −31.3999 | −1.78052 | −0.890262 | − | 0.455449i | \(-0.849479\pi\) | ||||
−0.890262 | + | 0.455449i | \(0.849479\pi\) | |||||||
\(312\) | −0.330856 | −0.0187310 | ||||||||
\(313\) | −8.04223 | −0.454574 | −0.227287 | − | 0.973828i | \(-0.572986\pi\) | ||||
−0.227287 | + | 0.973828i | \(0.572986\pi\) | |||||||
\(314\) | 5.32401 | 0.300452 | ||||||||
\(315\) | 8.26926 | 0.465920 | ||||||||
\(316\) | −1.75870 | −0.0989346 | ||||||||
\(317\) | −12.3029 | −0.691000 | −0.345500 | − | 0.938419i | \(-0.612291\pi\) | ||||
−0.345500 | + | 0.938419i | \(0.612291\pi\) | |||||||
\(318\) | −0.953831 | −0.0534882 | ||||||||
\(319\) | −34.6623 | −1.94072 | ||||||||
\(320\) | −1.00000 | −0.0559017 | ||||||||
\(321\) | 6.20766 | 0.346478 | ||||||||
\(322\) | 14.6480 | 0.816303 | ||||||||
\(323\) | −1.02112 | −0.0568164 | ||||||||
\(324\) | 7.53851 | 0.418806 | ||||||||
\(325\) | −0.813457 | −0.0451225 | ||||||||
\(326\) | 15.2008 | 0.841895 | ||||||||
\(327\) | 1.75011 | 0.0967814 | ||||||||
\(328\) | 6.34513 | 0.350351 | ||||||||
\(329\) | −15.8346 | −0.872988 | ||||||||
\(330\) | −2.64803 | −0.145769 | ||||||||
\(331\) | −6.77981 | −0.372652 | −0.186326 | − | 0.982488i | \(-0.559658\pi\) | ||||
−0.186326 | + | 0.982488i | \(0.559658\pi\) | |||||||
\(332\) | −7.05476 | −0.387180 | ||||||||
\(333\) | 2.83457 | 0.155334 | ||||||||
\(334\) | −12.4826 | −0.683018 | ||||||||
\(335\) | 5.42784 | 0.296555 | ||||||||
\(336\) | 1.18654 | 0.0647312 | ||||||||
\(337\) | 10.6903 | 0.582336 | 0.291168 | − | 0.956672i | \(-0.405956\pi\) | ||||
0.291168 | + | 0.956672i | \(0.405956\pi\) | |||||||
\(338\) | −12.3383 | −0.671114 | ||||||||
\(339\) | −3.72506 | −0.202317 | ||||||||
\(340\) | 2.51056 | 0.136154 | ||||||||
\(341\) | −56.9795 | −3.08561 | ||||||||
\(342\) | −1.15290 | −0.0623417 | ||||||||
\(343\) | −16.0143 | −0.864689 | ||||||||
\(344\) | −7.32401 | −0.394884 | ||||||||
\(345\) | −2.04223 | −0.109950 | ||||||||
\(346\) | 23.0354 | 1.23839 | ||||||||
\(347\) | 5.62691 | 0.302069 | 0.151034 | − | 0.988529i | \(-0.451740\pi\) | ||||
0.151034 | + | 0.988529i | \(0.451740\pi\) | |||||||
\(348\) | −2.16543 | −0.116079 | ||||||||
\(349\) | 15.1306 | 0.809924 | 0.404962 | − | 0.914334i | \(-0.367285\pi\) | ||||
0.404962 | + | 0.914334i | \(0.367285\pi\) | |||||||
\(350\) | 2.91729 | 0.155935 | ||||||||
\(351\) | 1.93040 | 0.103037 | ||||||||
\(352\) | 6.51056 | 0.347014 | ||||||||
\(353\) | 35.7816 | 1.90446 | 0.952230 | − | 0.305381i | \(-0.0987839\pi\) | ||||
0.952230 | + | 0.305381i | \(0.0987839\pi\) | |||||||
\(354\) | −0.580745 | −0.0308662 | ||||||||
\(355\) | −14.6480 | −0.777437 | ||||||||
\(356\) | 6.00000 | 0.317999 | ||||||||
\(357\) | −2.97888 | −0.157659 | ||||||||
\(358\) | 24.2835 | 1.28342 | ||||||||
\(359\) | 4.48260 | 0.236583 | 0.118291 | − | 0.992979i | \(-0.462258\pi\) | ||||
0.118291 | + | 0.992979i | \(0.462258\pi\) | |||||||
\(360\) | 2.83457 | 0.149395 | ||||||||
\(361\) | −18.8346 | −0.991293 | ||||||||
\(362\) | 2.16543 | 0.113812 | ||||||||
\(363\) | 12.7661 | 0.670048 | ||||||||
\(364\) | −2.37309 | −0.124384 | ||||||||
\(365\) | 11.0211 | 0.576872 | ||||||||
\(366\) | −0.538514 | −0.0281486 | ||||||||
\(367\) | −21.5653 | −1.12570 | −0.562850 | − | 0.826559i | \(-0.690295\pi\) | ||||
−0.562850 | + | 0.826559i | \(0.690295\pi\) | |||||||
\(368\) | 5.02112 | 0.261744 | ||||||||
\(369\) | −17.9857 | −0.936300 | ||||||||
\(370\) | 1.00000 | 0.0519875 | ||||||||
\(371\) | −6.84141 | −0.355188 | ||||||||
\(372\) | −3.55963 | −0.184558 | ||||||||
\(373\) | 16.9230 | 0.876238 | 0.438119 | − | 0.898917i | \(-0.355645\pi\) | ||||
0.438119 | + | 0.898917i | \(0.355645\pi\) | |||||||
\(374\) | −16.3451 | −0.845187 | ||||||||
\(375\) | −0.406728 | −0.0210034 | ||||||||
\(376\) | −5.42784 | −0.279920 | ||||||||
\(377\) | 4.33086 | 0.223050 | ||||||||
\(378\) | −6.92297 | −0.356079 | ||||||||
\(379\) | 31.2710 | 1.60628 | 0.803142 | − | 0.595788i | \(-0.203160\pi\) | ||||
0.803142 | + | 0.595788i | \(0.203160\pi\) | |||||||
\(380\) | −0.406728 | −0.0208647 | ||||||||
\(381\) | −3.50372 | −0.179501 | ||||||||
\(382\) | −19.3326 | −0.989142 | ||||||||
\(383\) | 1.62691 | 0.0831314 | 0.0415657 | − | 0.999136i | \(-0.486765\pi\) | ||||
0.0415657 | + | 0.999136i | \(0.486765\pi\) | |||||||
\(384\) | 0.406728 | 0.0207558 | ||||||||
\(385\) | −18.9932 | −0.967981 | ||||||||
\(386\) | −20.0422 | −1.02012 | ||||||||
\(387\) | 20.7604 | 1.05531 | ||||||||
\(388\) | 2.34513 | 0.119056 | ||||||||
\(389\) | −31.6412 | −1.60427 | −0.802136 | − | 0.597141i | \(-0.796303\pi\) | ||||
−0.802136 | + | 0.597141i | \(0.796303\pi\) | |||||||
\(390\) | 0.330856 | 0.0167535 | ||||||||
\(391\) | −12.6058 | −0.637503 | ||||||||
\(392\) | 1.51056 | 0.0762947 | ||||||||
\(393\) | 5.46149 | 0.275496 | ||||||||
\(394\) | 15.6269 | 0.787273 | ||||||||
\(395\) | 1.75870 | 0.0884898 | ||||||||
\(396\) | −18.4546 | −0.927381 | ||||||||
\(397\) | −39.2961 | −1.97221 | −0.986106 | − | 0.166116i | \(-0.946878\pi\) | ||||
−0.986106 | + | 0.166116i | \(0.946878\pi\) | |||||||
\(398\) | 20.2835 | 1.01672 | ||||||||
\(399\) | 0.482601 | 0.0241603 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | −9.66914 | −0.482854 | −0.241427 | − | 0.970419i | \(-0.577615\pi\) | ||||
−0.241427 | + | 0.970419i | \(0.577615\pi\) | |||||||
\(402\) | −2.20766 | −0.110108 | ||||||||
\(403\) | 7.11926 | 0.354636 | ||||||||
\(404\) | −8.20766 | −0.408346 | ||||||||
\(405\) | −7.53851 | −0.374592 | ||||||||
\(406\) | −15.5317 | −0.770824 | ||||||||
\(407\) | −6.51056 | −0.322716 | ||||||||
\(408\) | −1.02112 | −0.0505527 | ||||||||
\(409\) | −26.2749 | −1.29921 | −0.649606 | − | 0.760271i | \(-0.725066\pi\) | ||||
−0.649606 | + | 0.760271i | \(0.725066\pi\) | |||||||
\(410\) | −6.34513 | −0.313364 | ||||||||
\(411\) | −5.97495 | −0.294722 | ||||||||
\(412\) | −8.81346 | −0.434208 | ||||||||
\(413\) | −4.16543 | −0.204967 | ||||||||
\(414\) | −14.2327 | −0.699500 | ||||||||
\(415\) | 7.05476 | 0.346304 | ||||||||
\(416\) | −0.813457 | −0.0398830 | ||||||||
\(417\) | 7.06335 | 0.345894 | ||||||||
\(418\) | 2.64803 | 0.129519 | ||||||||
\(419\) | −30.1940 | −1.47507 | −0.737536 | − | 0.675308i | \(-0.764011\pi\) | ||||
−0.737536 | + | 0.675308i | \(0.764011\pi\) | |||||||
\(420\) | −1.18654 | −0.0578974 | ||||||||
\(421\) | 22.0000 | 1.07221 | 0.536107 | − | 0.844150i | \(-0.319894\pi\) | ||||
0.536107 | + | 0.844150i | \(0.319894\pi\) | |||||||
\(422\) | 18.7182 | 0.911188 | ||||||||
\(423\) | 15.3856 | 0.748074 | ||||||||
\(424\) | −2.34513 | −0.113890 | ||||||||
\(425\) | −2.51056 | −0.121780 | ||||||||
\(426\) | 5.95777 | 0.288655 | ||||||||
\(427\) | −3.86253 | −0.186921 | ||||||||
\(428\) | 15.2624 | 0.737737 | ||||||||
\(429\) | −2.15406 | −0.103999 | ||||||||
\(430\) | 7.32401 | 0.353195 | ||||||||
\(431\) | 25.5653 | 1.23144 | 0.615719 | − | 0.787966i | \(-0.288866\pi\) | ||||
0.615719 | + | 0.787966i | \(0.288866\pi\) | |||||||
\(432\) | −2.37309 | −0.114175 | ||||||||
\(433\) | 32.0422 | 1.53985 | 0.769926 | − | 0.638134i | \(-0.220293\pi\) | ||||
0.769926 | + | 0.638134i | \(0.220293\pi\) | |||||||
\(434\) | −25.5317 | −1.22556 | ||||||||
\(435\) | 2.16543 | 0.103824 | ||||||||
\(436\) | 4.30290 | 0.206072 | ||||||||
\(437\) | 2.04223 | 0.0976931 | ||||||||
\(438\) | −4.48260 | −0.214187 | ||||||||
\(439\) | 3.93840 | 0.187970 | 0.0939848 | − | 0.995574i | \(-0.470039\pi\) | ||||
0.0939848 | + | 0.995574i | \(0.470039\pi\) | |||||||
\(440\) | −6.51056 | −0.310379 | ||||||||
\(441\) | −4.28178 | −0.203894 | ||||||||
\(442\) | 2.04223 | 0.0971390 | ||||||||
\(443\) | −0.0758724 | −0.00360481 | −0.00180240 | − | 0.999998i | \(-0.500574\pi\) | ||||
−0.00180240 | + | 0.999998i | \(0.500574\pi\) | |||||||
\(444\) | −0.406728 | −0.0193025 | ||||||||
\(445\) | −6.00000 | −0.284427 | ||||||||
\(446\) | −15.7307 | −0.744872 | ||||||||
\(447\) | −0.0844605 | −0.00399485 | ||||||||
\(448\) | 2.91729 | 0.137829 | ||||||||
\(449\) | 19.2961 | 0.910637 | 0.455319 | − | 0.890329i | \(-0.349525\pi\) | ||||
0.455319 | + | 0.890329i | \(0.349525\pi\) | |||||||
\(450\) | −2.83457 | −0.133623 | ||||||||
\(451\) | 41.3103 | 1.94523 | ||||||||
\(452\) | −9.15859 | −0.430784 | ||||||||
\(453\) | 0.330856 | 0.0155450 | ||||||||
\(454\) | 12.8836 | 0.604659 | ||||||||
\(455\) | 2.37309 | 0.111252 | ||||||||
\(456\) | 0.165428 | 0.00774688 | ||||||||
\(457\) | 3.00684 | 0.140654 | 0.0703271 | − | 0.997524i | \(-0.477596\pi\) | ||||
0.0703271 | + | 0.997524i | \(0.477596\pi\) | |||||||
\(458\) | 5.25383 | 0.245495 | ||||||||
\(459\) | 5.95777 | 0.278085 | ||||||||
\(460\) | −5.02112 | −0.234111 | ||||||||
\(461\) | −0.633755 | −0.0295169 | −0.0147585 | − | 0.999891i | \(-0.504698\pi\) | ||||
−0.0147585 | + | 0.999891i | \(0.504698\pi\) | |||||||
\(462\) | 7.72506 | 0.359402 | ||||||||
\(463\) | 18.0422 | 0.838494 | 0.419247 | − | 0.907872i | \(-0.362294\pi\) | ||||
0.419247 | + | 0.907872i | \(0.362294\pi\) | |||||||
\(464\) | −5.32401 | −0.247161 | ||||||||
\(465\) | 3.55963 | 0.165074 | ||||||||
\(466\) | 28.3172 | 1.31177 | ||||||||
\(467\) | −23.4758 | −1.08633 | −0.543164 | − | 0.839626i | \(-0.682774\pi\) | ||||
−0.543164 | + | 0.839626i | \(0.682774\pi\) | |||||||
\(468\) | 2.30580 | 0.106586 | ||||||||
\(469\) | −15.8346 | −0.731173 | ||||||||
\(470\) | 5.42784 | 0.250368 | ||||||||
\(471\) | 2.16543 | 0.0997777 | ||||||||
\(472\) | −1.42784 | −0.0657218 | ||||||||
\(473\) | −47.6834 | −2.19249 | ||||||||
\(474\) | −0.715313 | −0.0328554 | ||||||||
\(475\) | 0.406728 | 0.0186620 | ||||||||
\(476\) | −7.32401 | −0.335696 | ||||||||
\(477\) | 6.64744 | 0.304365 | ||||||||
\(478\) | 14.3788 | 0.657670 | ||||||||
\(479\) | −8.19907 | −0.374625 | −0.187313 | − | 0.982300i | \(-0.559978\pi\) | ||||
−0.187313 | + | 0.982300i | \(0.559978\pi\) | |||||||
\(480\) | −0.406728 | −0.0185645 | ||||||||
\(481\) | 0.813457 | 0.0370904 | ||||||||
\(482\) | 18.2749 | 0.832401 | ||||||||
\(483\) | 5.95777 | 0.271088 | ||||||||
\(484\) | 31.3874 | 1.42670 | ||||||||
\(485\) | −2.34513 | −0.106487 | ||||||||
\(486\) | 10.1854 | 0.462019 | ||||||||
\(487\) | 0.953831 | 0.0432222 | 0.0216111 | − | 0.999766i | \(-0.493120\pi\) | ||||
0.0216111 | + | 0.999766i | \(0.493120\pi\) | |||||||
\(488\) | −1.32401 | −0.0599353 | ||||||||
\(489\) | 6.18260 | 0.279587 | ||||||||
\(490\) | −1.51056 | −0.0682400 | ||||||||
\(491\) | 19.3383 | 0.872725 | 0.436362 | − | 0.899771i | \(-0.356267\pi\) | ||||
0.436362 | + | 0.899771i | \(0.356267\pi\) | |||||||
\(492\) | 2.58074 | 0.116349 | ||||||||
\(493\) | 13.3662 | 0.601985 | ||||||||
\(494\) | −0.330856 | −0.0148859 | ||||||||
\(495\) | 18.4546 | 0.829475 | ||||||||
\(496\) | −8.75186 | −0.392970 | ||||||||
\(497\) | 42.7325 | 1.91681 | ||||||||
\(498\) | −2.86937 | −0.128580 | ||||||||
\(499\) | −5.63550 | −0.252280 | −0.126140 | − | 0.992012i | \(-0.540259\pi\) | ||||
−0.126140 | + | 0.992012i | \(0.540259\pi\) | |||||||
\(500\) | −1.00000 | −0.0447214 | ||||||||
\(501\) | −5.07703 | −0.226825 | ||||||||
\(502\) | −1.22019 | −0.0544595 | ||||||||
\(503\) | −33.6269 | −1.49935 | −0.749675 | − | 0.661806i | \(-0.769790\pi\) | ||||
−0.749675 | + | 0.661806i | \(0.769790\pi\) | |||||||
\(504\) | −8.26926 | −0.368342 | ||||||||
\(505\) | 8.20766 | 0.365236 | ||||||||
\(506\) | 32.6903 | 1.45326 | ||||||||
\(507\) | −5.01833 | −0.222872 | ||||||||
\(508\) | −8.61439 | −0.382202 | ||||||||
\(509\) | −18.6903 | −0.828431 | −0.414216 | − | 0.910179i | \(-0.635944\pi\) | ||||
−0.414216 | + | 0.910179i | \(0.635944\pi\) | |||||||
\(510\) | 1.02112 | 0.0452157 | ||||||||
\(511\) | −32.1517 | −1.42231 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −0.965202 | −0.0426147 | ||||||||
\(514\) | 27.1306 | 1.19668 | ||||||||
\(515\) | 8.81346 | 0.388367 | ||||||||
\(516\) | −2.97888 | −0.131138 | ||||||||
\(517\) | −35.3383 | −1.55418 | ||||||||
\(518\) | −2.91729 | −0.128178 | ||||||||
\(519\) | 9.36915 | 0.411260 | ||||||||
\(520\) | 0.813457 | 0.0356724 | ||||||||
\(521\) | 25.1586 | 1.10222 | 0.551109 | − | 0.834433i | \(-0.314205\pi\) | ||||
0.551109 | + | 0.834433i | \(0.314205\pi\) | |||||||
\(522\) | 15.0913 | 0.660528 | ||||||||
\(523\) | −7.25383 | −0.317188 | −0.158594 | − | 0.987344i | \(-0.550696\pi\) | ||||
−0.158594 | + | 0.987344i | \(0.550696\pi\) | |||||||
\(524\) | 13.4278 | 0.586598 | ||||||||
\(525\) | 1.18654 | 0.0517850 | ||||||||
\(526\) | −20.2133 | −0.881344 | ||||||||
\(527\) | 21.9720 | 0.957117 | ||||||||
\(528\) | 2.64803 | 0.115241 | ||||||||
\(529\) | 2.21160 | 0.0961564 | ||||||||
\(530\) | 2.34513 | 0.101866 | ||||||||
\(531\) | 4.04733 | 0.175639 | ||||||||
\(532\) | 1.18654 | 0.0514432 | ||||||||
\(533\) | −5.16149 | −0.223569 | ||||||||
\(534\) | 2.44037 | 0.105605 | ||||||||
\(535\) | −15.2624 | −0.659852 | ||||||||
\(536\) | −5.42784 | −0.234447 | ||||||||
\(537\) | 9.87680 | 0.426215 | ||||||||
\(538\) | −0.207658 | −0.00895278 | ||||||||
\(539\) | 9.83457 | 0.423605 | ||||||||
\(540\) | 2.37309 | 0.102121 | ||||||||
\(541\) | 16.0422 | 0.689709 | 0.344855 | − | 0.938656i | \(-0.387928\pi\) | ||||
0.344855 | + | 0.938656i | \(0.387928\pi\) | |||||||
\(542\) | −30.6480 | −1.31645 | ||||||||
\(543\) | 0.880741 | 0.0377962 | ||||||||
\(544\) | −2.51056 | −0.107639 | ||||||||
\(545\) | −4.30290 | −0.184316 | ||||||||
\(546\) | −0.965202 | −0.0413068 | ||||||||
\(547\) | 16.0143 | 0.684721 | 0.342360 | − | 0.939569i | \(-0.388774\pi\) | ||||
0.342360 | + | 0.939569i | \(0.388774\pi\) | |||||||
\(548\) | −14.6903 | −0.627537 | ||||||||
\(549\) | 3.75301 | 0.160175 | ||||||||
\(550\) | 6.51056 | 0.277611 | ||||||||
\(551\) | −2.16543 | −0.0922503 | ||||||||
\(552\) | 2.04223 | 0.0869231 | ||||||||
\(553\) | −5.13063 | −0.218177 | ||||||||
\(554\) | −16.8135 | −0.714335 | ||||||||
\(555\) | 0.406728 | 0.0172647 | ||||||||
\(556\) | 17.3662 | 0.736493 | ||||||||
\(557\) | −10.8557 | −0.459970 | −0.229985 | − | 0.973194i | \(-0.573868\pi\) | ||||
−0.229985 | + | 0.973194i | \(0.573868\pi\) | |||||||
\(558\) | 24.8078 | 1.05020 | ||||||||
\(559\) | 5.95777 | 0.251987 | ||||||||
\(560\) | −2.91729 | −0.123278 | ||||||||
\(561\) | −6.64803 | −0.280680 | ||||||||
\(562\) | −14.2749 | −0.602152 | ||||||||
\(563\) | 31.0776 | 1.30977 | 0.654883 | − | 0.755731i | \(-0.272718\pi\) | ||||
0.654883 | + | 0.755731i | \(0.272718\pi\) | |||||||
\(564\) | −2.20766 | −0.0929592 | ||||||||
\(565\) | 9.15859 | 0.385305 | ||||||||
\(566\) | −13.2288 | −0.556047 | ||||||||
\(567\) | 21.9920 | 0.923577 | ||||||||
\(568\) | 14.6480 | 0.614618 | ||||||||
\(569\) | 30.0845 | 1.26121 | 0.630603 | − | 0.776105i | \(-0.282808\pi\) | ||||
0.630603 | + | 0.776105i | \(0.282808\pi\) | |||||||
\(570\) | −0.165428 | −0.00692902 | ||||||||
\(571\) | 5.55673 | 0.232542 | 0.116271 | − | 0.993218i | \(-0.462906\pi\) | ||||
0.116271 | + | 0.993218i | \(0.462906\pi\) | |||||||
\(572\) | −5.29606 | −0.221439 | ||||||||
\(573\) | −7.86312 | −0.328487 | ||||||||
\(574\) | 18.5106 | 0.772616 | ||||||||
\(575\) | 5.02112 | 0.209395 | ||||||||
\(576\) | −2.83457 | −0.118107 | ||||||||
\(577\) | −22.2499 | −0.926275 | −0.463137 | − | 0.886286i | \(-0.653276\pi\) | ||||
−0.463137 | + | 0.886286i | \(0.653276\pi\) | |||||||
\(578\) | −10.6971 | −0.444941 | ||||||||
\(579\) | −8.15174 | −0.338775 | ||||||||
\(580\) | 5.32401 | 0.221068 | ||||||||
\(581\) | −20.5807 | −0.853833 | ||||||||
\(582\) | 0.953831 | 0.0395376 | ||||||||
\(583\) | −15.2681 | −0.632340 | ||||||||
\(584\) | −11.0211 | −0.456057 | ||||||||
\(585\) | −2.30580 | −0.0953332 | ||||||||
\(586\) | 2.34513 | 0.0968764 | ||||||||
\(587\) | 45.3103 | 1.87016 | 0.935079 | − | 0.354440i | \(-0.115328\pi\) | ||||
0.935079 | + | 0.354440i | \(0.115328\pi\) | |||||||
\(588\) | 0.614387 | 0.0253369 | ||||||||
\(589\) | −3.55963 | −0.146672 | ||||||||
\(590\) | 1.42784 | 0.0587834 | ||||||||
\(591\) | 6.35591 | 0.261447 | ||||||||
\(592\) | −1.00000 | −0.0410997 | ||||||||
\(593\) | −0.232712 | −0.00955635 | −0.00477817 | − | 0.999989i | \(-0.501521\pi\) | ||||
−0.00477817 | + | 0.999989i | \(0.501521\pi\) | |||||||
\(594\) | −15.4501 | −0.633926 | ||||||||
\(595\) | 7.32401 | 0.300255 | ||||||||
\(596\) | −0.207658 | −0.00850601 | ||||||||
\(597\) | 8.24989 | 0.337645 | ||||||||
\(598\) | −4.08446 | −0.167026 | ||||||||
\(599\) | 43.4056 | 1.77350 | 0.886752 | − | 0.462246i | \(-0.152956\pi\) | ||||
0.886752 | + | 0.462246i | \(0.152956\pi\) | |||||||
\(600\) | 0.406728 | 0.0166046 | ||||||||
\(601\) | 35.5317 | 1.44937 | 0.724684 | − | 0.689082i | \(-0.241986\pi\) | ||||
0.724684 | + | 0.689082i | \(0.241986\pi\) | |||||||
\(602\) | −21.3662 | −0.870823 | ||||||||
\(603\) | 15.3856 | 0.626551 | ||||||||
\(604\) | 0.813457 | 0.0330991 | ||||||||
\(605\) | −31.3874 | −1.27608 | ||||||||
\(606\) | −3.33829 | −0.135609 | ||||||||
\(607\) | 26.7325 | 1.08504 | 0.542519 | − | 0.840043i | \(-0.317471\pi\) | ||||
0.542519 | + | 0.840043i | \(0.317471\pi\) | |||||||
\(608\) | 0.406728 | 0.0164950 | ||||||||
\(609\) | −6.31717 | −0.255985 | ||||||||
\(610\) | 1.32401 | 0.0536078 | ||||||||
\(611\) | 4.41532 | 0.178625 | ||||||||
\(612\) | 7.11636 | 0.287662 | ||||||||
\(613\) | 48.0565 | 1.94098 | 0.970492 | − | 0.241134i | \(-0.0775192\pi\) | ||||
0.970492 | + | 0.241134i | \(0.0775192\pi\) | |||||||
\(614\) | −23.2624 | −0.938795 | ||||||||
\(615\) | −2.58074 | −0.104066 | ||||||||
\(616\) | 18.9932 | 0.765256 | ||||||||
\(617\) | 12.9789 | 0.522510 | 0.261255 | − | 0.965270i | \(-0.415864\pi\) | ||||
0.261255 | + | 0.965270i | \(0.415864\pi\) | |||||||
\(618\) | −3.58468 | −0.144197 | ||||||||
\(619\) | 25.3662 | 1.01956 | 0.509778 | − | 0.860306i | \(-0.329728\pi\) | ||||
0.509778 | + | 0.860306i | \(0.329728\pi\) | |||||||
\(620\) | 8.75186 | 0.351483 | ||||||||
\(621\) | −11.9155 | −0.478154 | ||||||||
\(622\) | −31.3999 | −1.25902 | ||||||||
\(623\) | 17.5037 | 0.701272 | ||||||||
\(624\) | −0.330856 | −0.0132448 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −8.04223 | −0.321432 | ||||||||
\(627\) | 1.07703 | 0.0430124 | ||||||||
\(628\) | 5.32401 | 0.212451 | ||||||||
\(629\) | 2.51056 | 0.100102 | ||||||||
\(630\) | 8.26926 | 0.329455 | ||||||||
\(631\) | −31.6075 | −1.25828 | −0.629138 | − | 0.777293i | \(-0.716592\pi\) | ||||
−0.629138 | + | 0.777293i | \(0.716592\pi\) | |||||||
\(632\) | −1.75870 | −0.0699573 | ||||||||
\(633\) | 7.61323 | 0.302599 | ||||||||
\(634\) | −12.3029 | −0.488611 | ||||||||
\(635\) | 8.61439 | 0.341852 | ||||||||
\(636\) | −0.953831 | −0.0378219 | ||||||||
\(637\) | −1.22877 | −0.0486858 | ||||||||
\(638\) | −34.6623 | −1.37229 | ||||||||
\(639\) | −41.5209 | −1.64254 | ||||||||
\(640\) | −1.00000 | −0.0395285 | ||||||||
\(641\) | −23.8625 | −0.942513 | −0.471257 | − | 0.881996i | \(-0.656199\pi\) | ||||
−0.471257 | + | 0.881996i | \(0.656199\pi\) | |||||||
\(642\) | 6.20766 | 0.244997 | ||||||||
\(643\) | 32.8277 | 1.29460 | 0.647300 | − | 0.762236i | \(-0.275898\pi\) | ||||
0.647300 | + | 0.762236i | \(0.275898\pi\) | |||||||
\(644\) | 14.6480 | 0.577213 | ||||||||
\(645\) | 2.97888 | 0.117293 | ||||||||
\(646\) | −1.02112 | −0.0401752 | ||||||||
\(647\) | −13.9578 | −0.548737 | −0.274368 | − | 0.961625i | \(-0.588469\pi\) | ||||
−0.274368 | + | 0.961625i | \(0.588469\pi\) | |||||||
\(648\) | 7.53851 | 0.296141 | ||||||||
\(649\) | −9.29606 | −0.364902 | ||||||||
\(650\) | −0.813457 | −0.0319064 | ||||||||
\(651\) | −10.3845 | −0.406999 | ||||||||
\(652\) | 15.2008 | 0.595310 | ||||||||
\(653\) | 28.5921 | 1.11890 | 0.559448 | − | 0.828865i | \(-0.311013\pi\) | ||||
0.559448 | + | 0.828865i | \(0.311013\pi\) | |||||||
\(654\) | 1.75011 | 0.0684348 | ||||||||
\(655\) | −13.4278 | −0.524669 | ||||||||
\(656\) | 6.34513 | 0.247736 | ||||||||
\(657\) | 31.2401 | 1.21879 | ||||||||
\(658\) | −15.8346 | −0.617296 | ||||||||
\(659\) | −5.62691 | −0.219193 | −0.109597 | − | 0.993976i | \(-0.534956\pi\) | ||||
−0.109597 | + | 0.993976i | \(0.534956\pi\) | |||||||
\(660\) | −2.64803 | −0.103074 | ||||||||
\(661\) | 13.3240 | 0.518244 | 0.259122 | − | 0.965845i | \(-0.416567\pi\) | ||||
0.259122 | + | 0.965845i | \(0.416567\pi\) | |||||||
\(662\) | −6.77981 | −0.263505 | ||||||||
\(663\) | 0.830633 | 0.0322591 | ||||||||
\(664\) | −7.05476 | −0.273778 | ||||||||
\(665\) | −1.18654 | −0.0460122 | ||||||||
\(666\) | 2.83457 | 0.109837 | ||||||||
\(667\) | −26.7325 | −1.03509 | ||||||||
\(668\) | −12.4826 | −0.482966 | ||||||||
\(669\) | −6.39814 | −0.247366 | ||||||||
\(670\) | 5.42784 | 0.209696 | ||||||||
\(671\) | −8.62007 | −0.332774 | ||||||||
\(672\) | 1.18654 | 0.0457719 | ||||||||
\(673\) | 29.6691 | 1.14366 | 0.571831 | − | 0.820372i | \(-0.306233\pi\) | ||||
0.571831 | + | 0.820372i | \(0.306233\pi\) | |||||||
\(674\) | 10.6903 | 0.411773 | ||||||||
\(675\) | −2.37309 | −0.0913401 | ||||||||
\(676\) | −12.3383 | −0.474550 | ||||||||
\(677\) | −1.25383 | −0.0481885 | −0.0240943 | − | 0.999710i | \(-0.507670\pi\) | ||||
−0.0240943 | + | 0.999710i | \(0.507670\pi\) | |||||||
\(678\) | −3.72506 | −0.143060 | ||||||||
\(679\) | 6.84141 | 0.262549 | ||||||||
\(680\) | 2.51056 | 0.0962755 | ||||||||
\(681\) | 5.24014 | 0.200803 | ||||||||
\(682\) | −56.9795 | −2.18186 | ||||||||
\(683\) | −4.76045 | −0.182153 | −0.0910767 | − | 0.995844i | \(-0.529031\pi\) | ||||
−0.0910767 | + | 0.995844i | \(0.529031\pi\) | |||||||
\(684\) | −1.15290 | −0.0440823 | ||||||||
\(685\) | 14.6903 | 0.561286 | ||||||||
\(686\) | −16.0143 | −0.611428 | ||||||||
\(687\) | 2.13688 | 0.0815271 | ||||||||
\(688\) | −7.32401 | −0.279225 | ||||||||
\(689\) | 1.90766 | 0.0726761 | ||||||||
\(690\) | −2.04223 | −0.0777464 | ||||||||
\(691\) | −20.2219 | −0.769279 | −0.384639 | − | 0.923067i | \(-0.625674\pi\) | ||||
−0.384639 | + | 0.923067i | \(0.625674\pi\) | |||||||
\(692\) | 23.0354 | 0.875674 | ||||||||
\(693\) | −53.8375 | −2.04512 | ||||||||
\(694\) | 5.62691 | 0.213595 | ||||||||
\(695\) | −17.3662 | −0.658739 | ||||||||
\(696\) | −2.16543 | −0.0820803 | ||||||||
\(697\) | −15.9298 | −0.603385 | ||||||||
\(698\) | 15.1306 | 0.572703 | ||||||||
\(699\) | 11.5174 | 0.435628 | ||||||||
\(700\) | 2.91729 | 0.110263 | ||||||||
\(701\) | −22.0845 | −0.834119 | −0.417059 | − | 0.908879i | \(-0.636939\pi\) | ||||
−0.417059 | + | 0.908879i | \(0.636939\pi\) | |||||||
\(702\) | 1.93040 | 0.0728584 | ||||||||
\(703\) | −0.406728 | −0.0153401 | ||||||||
\(704\) | 6.51056 | 0.245376 | ||||||||
\(705\) | 2.20766 | 0.0831452 | ||||||||
\(706\) | 35.7816 | 1.34666 | ||||||||
\(707\) | −23.9441 | −0.900510 | ||||||||
\(708\) | −0.580745 | −0.0218257 | ||||||||
\(709\) | 5.59896 | 0.210273 | 0.105137 | − | 0.994458i | \(-0.466472\pi\) | ||||
0.105137 | + | 0.994458i | \(0.466472\pi\) | |||||||
\(710\) | −14.6480 | −0.549731 | ||||||||
\(711\) | 4.98516 | 0.186958 | ||||||||
\(712\) | 6.00000 | 0.224860 | ||||||||
\(713\) | −43.9441 | −1.64572 | ||||||||
\(714\) | −2.97888 | −0.111482 | ||||||||
\(715\) | 5.29606 | 0.198061 | ||||||||
\(716\) | 24.2835 | 0.907518 | ||||||||
\(717\) | 5.84826 | 0.218407 | ||||||||
\(718\) | 4.48260 | 0.167289 | ||||||||
\(719\) | 40.2921 | 1.50264 | 0.751321 | − | 0.659937i | \(-0.229417\pi\) | ||||
0.751321 | + | 0.659937i | \(0.229417\pi\) | |||||||
\(720\) | 2.83457 | 0.105638 | ||||||||
\(721\) | −25.7114 | −0.957542 | ||||||||
\(722\) | −18.8346 | −0.700950 | ||||||||
\(723\) | 7.43294 | 0.276434 | ||||||||
\(724\) | 2.16543 | 0.0804775 | ||||||||
\(725\) | −5.32401 | −0.197729 | ||||||||
\(726\) | 12.7661 | 0.473796 | ||||||||
\(727\) | 11.2538 | 0.417381 | 0.208691 | − | 0.977982i | \(-0.433080\pi\) | ||||
0.208691 | + | 0.977982i | \(0.433080\pi\) | |||||||
\(728\) | −2.37309 | −0.0879524 | ||||||||
\(729\) | −18.4729 | −0.684180 | ||||||||
\(730\) | 11.0211 | 0.407910 | ||||||||
\(731\) | 18.3874 | 0.680081 | ||||||||
\(732\) | −0.538514 | −0.0199041 | ||||||||
\(733\) | −42.2892 | −1.56199 | −0.780994 | − | 0.624539i | \(-0.785287\pi\) | ||||
−0.780994 | + | 0.624539i | \(0.785287\pi\) | |||||||
\(734\) | −21.5653 | −0.795990 | ||||||||
\(735\) | −0.614387 | −0.0226620 | ||||||||
\(736\) | 5.02112 | 0.185081 | ||||||||
\(737\) | −35.3383 | −1.30170 | ||||||||
\(738\) | −17.9857 | −0.662064 | ||||||||
\(739\) | −29.3103 | −1.07820 | −0.539099 | − | 0.842242i | \(-0.681235\pi\) | ||||
−0.539099 | + | 0.842242i | \(0.681235\pi\) | |||||||
\(740\) | 1.00000 | 0.0367607 | ||||||||
\(741\) | −0.134569 | −0.00494350 | ||||||||
\(742\) | −6.84141 | −0.251156 | ||||||||
\(743\) | −4.39245 | −0.161144 | −0.0805718 | − | 0.996749i | \(-0.525675\pi\) | ||||
−0.0805718 | + | 0.996749i | \(0.525675\pi\) | |||||||
\(744\) | −3.55963 | −0.130502 | ||||||||
\(745\) | 0.207658 | 0.00760801 | ||||||||
\(746\) | 16.9230 | 0.619594 | ||||||||
\(747\) | 19.9972 | 0.731660 | ||||||||
\(748\) | −16.3451 | −0.597637 | ||||||||
\(749\) | 44.5248 | 1.62690 | ||||||||
\(750\) | −0.406728 | −0.0148516 | ||||||||
\(751\) | 2.58074 | 0.0941727 | 0.0470864 | − | 0.998891i | \(-0.485006\pi\) | ||||
0.0470864 | + | 0.998891i | \(0.485006\pi\) | |||||||
\(752\) | −5.42784 | −0.197933 | ||||||||
\(753\) | −0.496284 | −0.0180856 | ||||||||
\(754\) | 4.33086 | 0.157720 | ||||||||
\(755\) | −0.813457 | −0.0296047 | ||||||||
\(756\) | −6.92297 | −0.251786 | ||||||||
\(757\) | 27.3805 | 0.995162 | 0.497581 | − | 0.867418i | \(-0.334222\pi\) | ||||
0.497581 | + | 0.867418i | \(0.334222\pi\) | |||||||
\(758\) | 31.2710 | 1.13581 | ||||||||
\(759\) | 13.2961 | 0.482616 | ||||||||
\(760\) | −0.406728 | −0.0147536 | ||||||||
\(761\) | −42.9509 | −1.55697 | −0.778485 | − | 0.627663i | \(-0.784011\pi\) | ||||
−0.778485 | + | 0.627663i | \(0.784011\pi\) | |||||||
\(762\) | −3.50372 | −0.126926 | ||||||||
\(763\) | 12.5528 | 0.454441 | ||||||||
\(764\) | −19.3326 | −0.699429 | ||||||||
\(765\) | −7.11636 | −0.257292 | ||||||||
\(766\) | 1.62691 | 0.0587828 | ||||||||
\(767\) | 1.16149 | 0.0419389 | ||||||||
\(768\) | 0.406728 | 0.0146765 | ||||||||
\(769\) | −13.0633 | −0.471076 | −0.235538 | − | 0.971865i | \(-0.575685\pi\) | ||||
−0.235538 | + | 0.971865i | \(0.575685\pi\) | |||||||
\(770\) | −18.9932 | −0.684466 | ||||||||
\(771\) | 11.0348 | 0.397409 | ||||||||
\(772\) | −20.0422 | −0.721336 | ||||||||
\(773\) | −15.3662 | −0.552685 | −0.276343 | − | 0.961059i | \(-0.589122\pi\) | ||||
−0.276343 | + | 0.961059i | \(0.589122\pi\) | |||||||
\(774\) | 20.7604 | 0.746219 | ||||||||
\(775\) | −8.75186 | −0.314376 | ||||||||
\(776\) | 2.34513 | 0.0841852 | ||||||||
\(777\) | −1.18654 | −0.0425670 | ||||||||
\(778\) | −31.6412 | −1.13439 | ||||||||
\(779\) | 2.58074 | 0.0924648 | ||||||||
\(780\) | 0.330856 | 0.0118465 | ||||||||
\(781\) | 95.3668 | 3.41249 | ||||||||
\(782\) | −12.6058 | −0.450782 | ||||||||
\(783\) | 12.6343 | 0.451515 | ||||||||
\(784\) | 1.51056 | 0.0539485 | ||||||||
\(785\) | −5.32401 | −0.190022 | ||||||||
\(786\) | 5.46149 | 0.194805 | ||||||||
\(787\) | 10.9316 | 0.389668 | 0.194834 | − | 0.980836i | \(-0.437583\pi\) | ||||
0.194834 | + | 0.980836i | \(0.437583\pi\) | |||||||
\(788\) | 15.6269 | 0.556686 | ||||||||
\(789\) | −8.22134 | −0.292688 | ||||||||
\(790\) | 1.75870 | 0.0625717 | ||||||||
\(791\) | −26.7182 | −0.949990 | ||||||||
\(792\) | −18.4546 | −0.655757 | ||||||||
\(793\) | 1.07703 | 0.0382464 | ||||||||
\(794\) | −39.2961 | −1.39456 | ||||||||
\(795\) | 0.953831 | 0.0338289 | ||||||||
\(796\) | 20.2835 | 0.718931 | ||||||||
\(797\) | −24.2921 | −0.860471 | −0.430235 | − | 0.902717i | \(-0.641569\pi\) | ||||
−0.430235 | + | 0.902717i | \(0.641569\pi\) | |||||||
\(798\) | 0.482601 | 0.0170839 | ||||||||
\(799\) | 13.6269 | 0.482086 | ||||||||
\(800\) | 1.00000 | 0.0353553 | ||||||||
\(801\) | −17.0074 | −0.600928 | ||||||||
\(802\) | −9.66914 | −0.341429 | ||||||||
\(803\) | −71.7536 | −2.53213 | ||||||||
\(804\) | −2.20766 | −0.0778581 | ||||||||
\(805\) | −14.6480 | −0.516275 | ||||||||
\(806\) | 7.11926 | 0.250765 | ||||||||
\(807\) | −0.0844605 | −0.00297315 | ||||||||
\(808\) | −8.20766 | −0.288744 | ||||||||
\(809\) | −40.0422 | −1.40781 | −0.703905 | − | 0.710294i | \(-0.748562\pi\) | ||||
−0.703905 | + | 0.710294i | \(0.748562\pi\) | |||||||
\(810\) | −7.53851 | −0.264876 | ||||||||
\(811\) | −40.6343 | −1.42686 | −0.713432 | − | 0.700724i | \(-0.752860\pi\) | ||||
−0.713432 | + | 0.700724i | \(0.752860\pi\) | |||||||
\(812\) | −15.5317 | −0.545055 | ||||||||
\(813\) | −12.4654 | −0.437182 | ||||||||
\(814\) | −6.51056 | −0.228195 | ||||||||
\(815\) | −15.2008 | −0.532461 | ||||||||
\(816\) | −1.02112 | −0.0357462 | ||||||||
\(817\) | −2.97888 | −0.104218 | ||||||||
\(818\) | −26.2749 | −0.918682 | ||||||||
\(819\) | 6.72668 | 0.235049 | ||||||||
\(820\) | −6.34513 | −0.221582 | ||||||||
\(821\) | −41.4787 | −1.44762 | −0.723808 | − | 0.690002i | \(-0.757610\pi\) | ||||
−0.723808 | + | 0.690002i | \(0.757610\pi\) | |||||||
\(822\) | −5.97495 | −0.208400 | ||||||||
\(823\) | −5.27610 | −0.183913 | −0.0919566 | − | 0.995763i | \(-0.529312\pi\) | ||||
−0.0919566 | + | 0.995763i | \(0.529312\pi\) | |||||||
\(824\) | −8.81346 | −0.307031 | ||||||||
\(825\) | 2.64803 | 0.0921925 | ||||||||
\(826\) | −4.16543 | −0.144934 | ||||||||
\(827\) | 1.76438 | 0.0613537 | 0.0306768 | − | 0.999529i | \(-0.490234\pi\) | ||||
0.0306768 | + | 0.999529i | \(0.490234\pi\) | |||||||
\(828\) | −14.2327 | −0.494621 | ||||||||
\(829\) | 16.3029 | 0.566223 | 0.283112 | − | 0.959087i | \(-0.408633\pi\) | ||||
0.283112 | + | 0.959087i | \(0.408633\pi\) | |||||||
\(830\) | 7.05476 | 0.244874 | ||||||||
\(831\) | −6.83851 | −0.237225 | ||||||||
\(832\) | −0.813457 | −0.0282015 | ||||||||
\(833\) | −3.79234 | −0.131397 | ||||||||
\(834\) | 7.06335 | 0.244584 | ||||||||
\(835\) | 12.4826 | 0.431978 | ||||||||
\(836\) | 2.64803 | 0.0915840 | ||||||||
\(837\) | 20.7689 | 0.717879 | ||||||||
\(838\) | −30.1940 | −1.04303 | ||||||||
\(839\) | 14.3731 | 0.496214 | 0.248107 | − | 0.968733i | \(-0.420192\pi\) | ||||
0.248107 | + | 0.968733i | \(0.420192\pi\) | |||||||
\(840\) | −1.18654 | −0.0409396 | ||||||||
\(841\) | −0.654870 | −0.0225817 | ||||||||
\(842\) | 22.0000 | 0.758170 | ||||||||
\(843\) | −5.80602 | −0.199970 | ||||||||
\(844\) | 18.7182 | 0.644308 | ||||||||
\(845\) | 12.3383 | 0.424450 | ||||||||
\(846\) | 15.3856 | 0.528968 | ||||||||
\(847\) | 91.5659 | 3.14624 | ||||||||
\(848\) | −2.34513 | −0.0805321 | ||||||||
\(849\) | −5.38052 | −0.184659 | ||||||||
\(850\) | −2.51056 | −0.0861114 | ||||||||
\(851\) | −5.02112 | −0.172122 | ||||||||
\(852\) | 5.95777 | 0.204110 | ||||||||
\(853\) | 43.2961 | 1.48243 | 0.741214 | − | 0.671268i | \(-0.234250\pi\) | ||||
0.741214 | + | 0.671268i | \(0.234250\pi\) | |||||||
\(854\) | −3.86253 | −0.132173 | ||||||||
\(855\) | 1.15290 | 0.0394284 | ||||||||
\(856\) | 15.2624 | 0.521659 | ||||||||
\(857\) | −49.0776 | −1.67646 | −0.838230 | − | 0.545317i | \(-0.816409\pi\) | ||||
−0.838230 | + | 0.545317i | \(0.816409\pi\) | |||||||
\(858\) | −2.15406 | −0.0735383 | ||||||||
\(859\) | 15.5374 | 0.530128 | 0.265064 | − | 0.964231i | \(-0.414607\pi\) | ||||
0.265064 | + | 0.964231i | \(0.414607\pi\) | |||||||
\(860\) | 7.32401 | 0.249747 | ||||||||
\(861\) | 7.52877 | 0.256580 | ||||||||
\(862\) | 25.5653 | 0.870758 | ||||||||
\(863\) | −36.0901 | −1.22852 | −0.614261 | − | 0.789103i | \(-0.710546\pi\) | ||||
−0.614261 | + | 0.789103i | \(0.710546\pi\) | |||||||
\(864\) | −2.37309 | −0.0807340 | ||||||||
\(865\) | −23.0354 | −0.783227 | ||||||||
\(866\) | 32.0422 | 1.08884 | ||||||||
\(867\) | −4.35081 | −0.147761 | ||||||||
\(868\) | −25.5317 | −0.866601 | ||||||||
\(869\) | −11.4501 | −0.388419 | ||||||||
\(870\) | 2.16543 | 0.0734149 | ||||||||
\(871\) | 4.41532 | 0.149607 | ||||||||
\(872\) | 4.30290 | 0.145715 | ||||||||
\(873\) | −6.64744 | −0.224982 | ||||||||
\(874\) | 2.04223 | 0.0690795 | ||||||||
\(875\) | −2.91729 | −0.0986223 | ||||||||
\(876\) | −4.48260 | −0.151453 | ||||||||
\(877\) | 29.3240 | 0.990202 | 0.495101 | − | 0.868836i | \(-0.335131\pi\) | ||||
0.495101 | + | 0.868836i | \(0.335131\pi\) | |||||||
\(878\) | 3.93840 | 0.132915 | ||||||||
\(879\) | 0.953831 | 0.0321719 | ||||||||
\(880\) | −6.51056 | −0.219471 | ||||||||
\(881\) | 23.8066 | 0.802065 | 0.401033 | − | 0.916064i | \(-0.368651\pi\) | ||||
0.401033 | + | 0.916064i | \(0.368651\pi\) | |||||||
\(882\) | −4.28178 | −0.144175 | ||||||||
\(883\) | −3.94699 | −0.132827 | −0.0664134 | − | 0.997792i | \(-0.521156\pi\) | ||||
−0.0664134 | + | 0.997792i | \(0.521156\pi\) | |||||||
\(884\) | 2.04223 | 0.0686876 | ||||||||
\(885\) | 0.580745 | 0.0195215 | ||||||||
\(886\) | −0.0758724 | −0.00254898 | ||||||||
\(887\) | 1.96346 | 0.0659264 | 0.0329632 | − | 0.999457i | \(-0.489506\pi\) | ||||
0.0329632 | + | 0.999457i | \(0.489506\pi\) | |||||||
\(888\) | −0.406728 | −0.0136489 | ||||||||
\(889\) | −25.1306 | −0.842854 | ||||||||
\(890\) | −6.00000 | −0.201120 | ||||||||
\(891\) | 49.0799 | 1.64424 | ||||||||
\(892\) | −15.7307 | −0.526704 | ||||||||
\(893\) | −2.20766 | −0.0738765 | ||||||||
\(894\) | −0.0844605 | −0.00282478 | ||||||||
\(895\) | −24.2835 | −0.811709 | ||||||||
\(896\) | 2.91729 | 0.0974597 | ||||||||
\(897\) | −1.66127 | −0.0554681 | ||||||||
\(898\) | 19.2961 | 0.643918 | ||||||||
\(899\) | 46.5950 | 1.55403 | ||||||||
\(900\) | −2.83457 | −0.0944857 | ||||||||
\(901\) | 5.88758 | 0.196144 | ||||||||
\(902\) | 41.3103 | 1.37548 | ||||||||
\(903\) | −8.69026 | −0.289194 | ||||||||
\(904\) | −9.15859 | −0.304610 | ||||||||
\(905\) | −2.16543 | −0.0719813 | ||||||||
\(906\) | 0.330856 | 0.0109920 | ||||||||
\(907\) | 5.89049 | 0.195590 | 0.0977952 | − | 0.995207i | \(-0.468821\pi\) | ||||
0.0977952 | + | 0.995207i | \(0.468821\pi\) | |||||||
\(908\) | 12.8836 | 0.427559 | ||||||||
\(909\) | 23.2652 | 0.771658 | ||||||||
\(910\) | 2.37309 | 0.0786670 | ||||||||
\(911\) | −27.9527 | −0.926113 | −0.463057 | − | 0.886329i | \(-0.653247\pi\) | ||||
−0.463057 | + | 0.886329i | \(0.653247\pi\) | |||||||
\(912\) | 0.165428 | 0.00547787 | ||||||||
\(913\) | −45.9304 | −1.52007 | ||||||||
\(914\) | 3.00684 | 0.0994575 | ||||||||
\(915\) | 0.538514 | 0.0178027 | ||||||||
\(916\) | 5.25383 | 0.173591 | ||||||||
\(917\) | 39.1729 | 1.29360 | ||||||||
\(918\) | 5.95777 | 0.196636 | ||||||||
\(919\) | 17.7587 | 0.585805 | 0.292903 | − | 0.956142i | \(-0.405379\pi\) | ||||
0.292903 | + | 0.956142i | \(0.405379\pi\) | |||||||
\(920\) | −5.02112 | −0.165541 | ||||||||
\(921\) | −9.46149 | −0.311767 | ||||||||
\(922\) | −0.633755 | −0.0208716 | ||||||||
\(923\) | −11.9155 | −0.392205 | ||||||||
\(924\) | 7.72506 | 0.254136 | ||||||||
\(925\) | −1.00000 | −0.0328798 | ||||||||
\(926\) | 18.0422 | 0.592904 | ||||||||
\(927\) | 24.9824 | 0.820529 | ||||||||
\(928\) | −5.32401 | −0.174769 | ||||||||
\(929\) | 34.2892 | 1.12499 | 0.562496 | − | 0.826800i | \(-0.309841\pi\) | ||||
0.562496 | + | 0.826800i | \(0.309841\pi\) | |||||||
\(930\) | 3.55963 | 0.116725 | ||||||||
\(931\) | 0.614387 | 0.0201357 | ||||||||
\(932\) | 28.3172 | 0.927560 | ||||||||
\(933\) | −12.7712 | −0.418111 | ||||||||
\(934\) | −23.4758 | −0.768150 | ||||||||
\(935\) | 16.3451 | 0.534543 | ||||||||
\(936\) | 2.30580 | 0.0753675 | ||||||||
\(937\) | −14.0845 | −0.460119 | −0.230060 | − | 0.973177i | \(-0.573892\pi\) | ||||
−0.230060 | + | 0.973177i | \(0.573892\pi\) | |||||||
\(938\) | −15.8346 | −0.517017 | ||||||||
\(939\) | −3.27100 | −0.106745 | ||||||||
\(940\) | 5.42784 | 0.177037 | ||||||||
\(941\) | 14.2499 | 0.464533 | 0.232267 | − | 0.972652i | \(-0.425386\pi\) | ||||
0.232267 | + | 0.972652i | \(0.425386\pi\) | |||||||
\(942\) | 2.16543 | 0.0705535 | ||||||||
\(943\) | 31.8596 | 1.03749 | ||||||||
\(944\) | −1.42784 | −0.0464723 | ||||||||
\(945\) | 6.92297 | 0.225204 | ||||||||
\(946\) | −47.6834 | −1.55032 | ||||||||
\(947\) | −29.8203 | −0.969029 | −0.484515 | − | 0.874783i | \(-0.661004\pi\) | ||||
−0.484515 | + | 0.874783i | \(0.661004\pi\) | |||||||
\(948\) | −0.715313 | −0.0232323 | ||||||||
\(949\) | 8.96520 | 0.291023 | ||||||||
\(950\) | 0.406728 | 0.0131960 | ||||||||
\(951\) | −5.00394 | −0.162264 | ||||||||
\(952\) | −7.32401 | −0.237373 | ||||||||
\(953\) | 8.64803 | 0.280137 | 0.140069 | − | 0.990142i | \(-0.455268\pi\) | ||||
0.140069 | + | 0.990142i | \(0.455268\pi\) | |||||||
\(954\) | 6.64744 | 0.215219 | ||||||||
\(955\) | 19.3326 | 0.625588 | ||||||||
\(956\) | 14.3788 | 0.465043 | ||||||||
\(957\) | −14.0981 | −0.455728 | ||||||||
\(958\) | −8.19907 | −0.264900 | ||||||||
\(959\) | −42.8557 | −1.38388 | ||||||||
\(960\) | −0.406728 | −0.0131271 | ||||||||
\(961\) | 45.5950 | 1.47081 | ||||||||
\(962\) | 0.813457 | 0.0262269 | ||||||||
\(963\) | −43.2624 | −1.39411 | ||||||||
\(964\) | 18.2749 | 0.588596 | ||||||||
\(965\) | 20.0422 | 0.645182 | ||||||||
\(966\) | 5.95777 | 0.191688 | ||||||||
\(967\) | −45.0325 | −1.44815 | −0.724074 | − | 0.689723i | \(-0.757732\pi\) | ||||
−0.724074 | + | 0.689723i | \(0.757732\pi\) | |||||||
\(968\) | 31.3874 | 1.00883 | ||||||||
\(969\) | −0.415317 | −0.0133419 | ||||||||
\(970\) | −2.34513 | −0.0752976 | ||||||||
\(971\) | 26.3029 | 0.844100 | 0.422050 | − | 0.906573i | \(-0.361311\pi\) | ||||
0.422050 | + | 0.906573i | \(0.361311\pi\) | |||||||
\(972\) | 10.1854 | 0.326696 | ||||||||
\(973\) | 50.6623 | 1.62416 | ||||||||
\(974\) | 0.953831 | 0.0305627 | ||||||||
\(975\) | −0.330856 | −0.0105959 | ||||||||
\(976\) | −1.32401 | −0.0423807 | ||||||||
\(977\) | 25.6549 | 0.820772 | 0.410386 | − | 0.911912i | \(-0.365394\pi\) | ||||
0.410386 | + | 0.911912i | \(0.365394\pi\) | |||||||
\(978\) | 6.18260 | 0.197698 | ||||||||
\(979\) | 39.0633 | 1.24847 | ||||||||
\(980\) | −1.51056 | −0.0482530 | ||||||||
\(981\) | −12.1969 | −0.389416 | ||||||||
\(982\) | 19.3383 | 0.617110 | ||||||||
\(983\) | −55.3611 | −1.76575 | −0.882873 | − | 0.469611i | \(-0.844394\pi\) | ||||
−0.882873 | + | 0.469611i | \(0.844394\pi\) | |||||||
\(984\) | 2.58074 | 0.0822711 | ||||||||
\(985\) | −15.6269 | −0.497915 | ||||||||
\(986\) | 13.3662 | 0.425668 | ||||||||
\(987\) | −6.44037 | −0.204999 | ||||||||
\(988\) | −0.330856 | −0.0105259 | ||||||||
\(989\) | −36.7747 | −1.16937 | ||||||||
\(990\) | 18.4546 | 0.586527 | ||||||||
\(991\) | −3.24814 | −0.103181 | −0.0515903 | − | 0.998668i | \(-0.516429\pi\) | ||||
−0.0515903 | + | 0.998668i | \(0.516429\pi\) | |||||||
\(992\) | −8.75186 | −0.277872 | ||||||||
\(993\) | −2.75754 | −0.0875080 | ||||||||
\(994\) | 42.7325 | 1.35539 | ||||||||
\(995\) | −20.2835 | −0.643031 | ||||||||
\(996\) | −2.86937 | −0.0909195 | ||||||||
\(997\) | −12.6480 | −0.400567 | −0.200284 | − | 0.979738i | \(-0.564186\pi\) | ||||
−0.200284 | + | 0.979738i | \(0.564186\pi\) | |||||||
\(998\) | −5.63550 | −0.178389 | ||||||||
\(999\) | 2.37309 | 0.0750811 |
(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 | 370.2.a.g.1.2 | ✓ | 3 | |
3.2 | odd | 2 | 3330.2.a.bg.1.3 | 3 | |||
4.3 | odd | 2 | 2960.2.a.u.1.2 | 3 | |||
5.2 | odd | 4 | 1850.2.b.o.149.5 | 6 | |||
5.3 | odd | 4 | 1850.2.b.o.149.2 | 6 | |||
5.4 | even | 2 | 1850.2.a.z.1.2 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
370.2.a.g.1.2 | ✓ | 3 | 1.1 | even | 1 | trivial | |
1850.2.a.z.1.2 | 3 | 5.4 | even | 2 | |||
1850.2.b.o.149.2 | 6 | 5.3 | odd | 4 | |||
1850.2.b.o.149.5 | 6 | 5.2 | odd | 4 | |||
2960.2.a.u.1.2 | 3 | 4.3 | odd | 2 | |||
3330.2.a.bg.1.3 | 3 | 3.2 | odd | 2 |