Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1850,2,Mod(149,1850)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1850, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1850.149");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1850 = 2 \cdot 5^{2} \cdot 37 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1850.b (of order \(2\), degree \(1\), not minimal) |
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: | no |
Analytic conductor: | \(14.7723243739\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.0.3182656.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 2x^{3} + 25x^{2} - 10x + 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 370) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 149.5 | ||
Root | \(0.203364 + 0.203364i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1850.149 |
Dual form | 1850.2.b.o.149.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1850\mathbb{Z}\right)^\times\).
\(n\) | \(1001\) | \(1777\) |
\(\chi(n)\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000i | 0.707107i | ||||||||
\(3\) | − 0.406728i | − 0.234825i | −0.993083 | − | 0.117412i | \(-0.962540\pi\) | ||||
0.993083 | − | 0.117412i | \(-0.0374599\pi\) | |||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0.406728 | 0.166046 | ||||||||
\(7\) | 2.91729i | 1.10263i | 0.834297 | + | 0.551315i | \(0.185874\pi\) | ||||
−0.834297 | + | 0.551315i | \(0.814126\pi\) | |||||||
\(8\) | − 1.00000i | − 0.353553i | ||||||||
\(9\) | 2.83457 | 0.944857 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 6.51056 | 1.96301 | 0.981503 | − | 0.191444i | \(-0.0613171\pi\) | ||||
0.981503 | + | 0.191444i | \(0.0613171\pi\) | |||||||
\(12\) | 0.406728i | 0.117412i | ||||||||
\(13\) | 0.813457i | 0.225612i | 0.993617 | + | 0.112806i | \(0.0359839\pi\) | ||||
−0.993617 | + | 0.112806i | \(0.964016\pi\) | |||||||
\(14\) | −2.91729 | −0.779677 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | − 2.51056i | − 0.608900i | −0.952528 | − | 0.304450i | \(-0.901527\pi\) | ||||
0.952528 | − | 0.304450i | \(-0.0984726\pi\) | |||||||
\(18\) | 2.83457i | 0.668115i | ||||||||
\(19\) | −0.406728 | −0.0933099 | −0.0466550 | − | 0.998911i | \(-0.514856\pi\) | ||||
−0.0466550 | + | 0.998911i | \(0.514856\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.18654 | 0.258925 | ||||||||
\(22\) | 6.51056i | 1.38806i | ||||||||
\(23\) | − 5.02112i | − 1.04697i | −0.852033 | − | 0.523487i | \(-0.824631\pi\) | ||||
0.852033 | − | 0.523487i | \(-0.175369\pi\) | |||||||
\(24\) | −0.406728 | −0.0830231 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −0.813457 | −0.159532 | ||||||||
\(27\) | − 2.37309i | − 0.456701i | ||||||||
\(28\) | − 2.91729i | − 0.551315i | ||||||||
\(29\) | 5.32401 | 0.988645 | 0.494322 | − | 0.869279i | \(-0.335416\pi\) | ||||
0.494322 | + | 0.869279i | \(0.335416\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −8.75186 | −1.57188 | −0.785940 | − | 0.618303i | \(-0.787821\pi\) | ||||
−0.785940 | + | 0.618303i | \(0.787821\pi\) | |||||||
\(32\) | 1.00000i | 0.176777i | ||||||||
\(33\) | − 2.64803i | − 0.460963i | ||||||||
\(34\) | 2.51056 | 0.430557 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −2.83457 | −0.472429 | ||||||||
\(37\) | − 1.00000i | − 0.164399i | ||||||||
\(38\) | − 0.406728i | − 0.0659801i | ||||||||
\(39\) | 0.330856 | 0.0529794 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 6.34513 | 0.990943 | 0.495471 | − | 0.868624i | \(-0.334995\pi\) | ||||
0.495471 | + | 0.868624i | \(0.334995\pi\) | |||||||
\(42\) | 1.18654i | 0.183088i | ||||||||
\(43\) | 7.32401i | 1.11690i | 0.829538 | + | 0.558451i | \(0.188604\pi\) | ||||
−0.829538 | + | 0.558451i | \(0.811396\pi\) | |||||||
\(44\) | −6.51056 | −0.981503 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 5.02112 | 0.740323 | ||||||||
\(47\) | − 5.42784i | − 0.791732i | −0.918308 | − | 0.395866i | \(-0.870444\pi\) | ||||
0.918308 | − | 0.395866i | \(-0.129556\pi\) | |||||||
\(48\) | − 0.406728i | − 0.0587062i | ||||||||
\(49\) | −1.51056 | −0.215794 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.02112 | −0.142985 | ||||||||
\(52\) | − 0.813457i | − 0.112806i | ||||||||
\(53\) | 2.34513i | 0.322128i | 0.986944 | + | 0.161064i | \(0.0514926\pi\) | ||||
−0.986944 | + | 0.161064i | \(0.948507\pi\) | |||||||
\(54\) | 2.37309 | 0.322936 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 2.91729 | 0.389839 | ||||||||
\(57\) | 0.165428i | 0.0219115i | ||||||||
\(58\) | 5.32401i | 0.699077i | ||||||||
\(59\) | 1.42784 | 0.185889 | 0.0929447 | − | 0.995671i | \(-0.470372\pi\) | ||||
0.0929447 | + | 0.995671i | \(0.470372\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.32401 | −0.169523 | −0.0847613 | − | 0.996401i | \(-0.527013\pi\) | ||||
−0.0847613 | + | 0.996401i | \(0.527013\pi\) | |||||||
\(62\) | − 8.75186i | − 1.11149i | ||||||||
\(63\) | 8.26926i | 1.04183i | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 2.64803 | 0.325950 | ||||||||
\(67\) | − 5.42784i | − 0.663117i | −0.943435 | − | 0.331558i | \(-0.892426\pi\) | ||||
0.943435 | − | 0.331558i | \(-0.107574\pi\) | |||||||
\(68\) | 2.51056i | 0.304450i | ||||||||
\(69\) | −2.04223 | −0.245856 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 14.6480 | 1.73840 | 0.869201 | − | 0.494460i | \(-0.164634\pi\) | ||||
0.869201 | + | 0.494460i | \(0.164634\pi\) | |||||||
\(72\) | − 2.83457i | − 0.334058i | ||||||||
\(73\) | 11.0211i | 1.28992i | 0.764215 | + | 0.644962i | \(0.223127\pi\) | ||||
−0.764215 | + | 0.644962i | \(0.776873\pi\) | |||||||
\(74\) | 1.00000 | 0.116248 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0.406728 | 0.0466550 | ||||||||
\(77\) | 18.9932i | 2.16447i | ||||||||
\(78\) | 0.330856i | 0.0374621i | ||||||||
\(79\) | 1.75870 | 0.197869 | 0.0989346 | − | 0.995094i | \(-0.468457\pi\) | ||||
0.0989346 | + | 0.995094i | \(0.468457\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 7.53851 | 0.837613 | ||||||||
\(82\) | 6.34513i | 0.700702i | ||||||||
\(83\) | 7.05476i | 0.774360i | 0.922004 | + | 0.387180i | \(0.126551\pi\) | ||||
−0.922004 | + | 0.387180i | \(0.873449\pi\) | |||||||
\(84\) | −1.18654 | −0.129462 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −7.32401 | −0.789769 | ||||||||
\(87\) | − 2.16543i | − 0.232158i | ||||||||
\(88\) | − 6.51056i | − 0.694028i | ||||||||
\(89\) | −6.00000 | −0.635999 | −0.317999 | − | 0.948091i | \(-0.603011\pi\) | ||||
−0.317999 | + | 0.948091i | \(0.603011\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.37309 | −0.248767 | ||||||||
\(92\) | 5.02112i | 0.523487i | ||||||||
\(93\) | 3.55963i | 0.369116i | ||||||||
\(94\) | 5.42784 | 0.559839 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0.406728 | 0.0415115 | ||||||||
\(97\) | 2.34513i | 0.238112i | 0.992888 | + | 0.119056i | \(0.0379868\pi\) | ||||
−0.992888 | + | 0.119056i | \(0.962013\pi\) | |||||||
\(98\) | − 1.51056i | − 0.152589i | ||||||||
\(99\) | 18.4546 | 1.85476 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −8.20766 | −0.816693 | −0.408346 | − | 0.912827i | \(-0.633894\pi\) | ||||
−0.408346 | + | 0.912827i | \(0.633894\pi\) | |||||||
\(102\) | − 1.02112i | − 0.101105i | ||||||||
\(103\) | 8.81346i | 0.868416i | 0.900813 | + | 0.434208i | \(0.142972\pi\) | ||||
−0.900813 | + | 0.434208i | \(0.857028\pi\) | |||||||
\(104\) | 0.813457 | 0.0797660 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −2.34513 | −0.227779 | ||||||||
\(107\) | 15.2624i | 1.47547i | 0.675089 | + | 0.737737i | \(0.264105\pi\) | ||||
−0.675089 | + | 0.737737i | \(0.735895\pi\) | |||||||
\(108\) | 2.37309i | 0.228350i | ||||||||
\(109\) | −4.30290 | −0.412143 | −0.206072 | − | 0.978537i | \(-0.566068\pi\) | ||||
−0.206072 | + | 0.978537i | \(0.566068\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −0.406728 | −0.0386050 | ||||||||
\(112\) | 2.91729i | 0.275658i | ||||||||
\(113\) | 9.15859i | 0.861567i | 0.902455 | + | 0.430784i | \(0.141763\pi\) | ||||
−0.902455 | + | 0.430784i | \(0.858237\pi\) | |||||||
\(114\) | −0.165428 | −0.0154938 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −5.32401 | −0.494322 | ||||||||
\(117\) | 2.30580i | 0.213171i | ||||||||
\(118\) | 1.42784i | 0.131444i | ||||||||
\(119\) | 7.32401 | 0.671391 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 31.3874 | 2.85340 | ||||||||
\(122\) | − 1.32401i | − 0.119871i | ||||||||
\(123\) | − 2.58074i | − 0.232698i | ||||||||
\(124\) | 8.75186 | 0.785940 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −8.26926 | −0.736684 | ||||||||
\(127\) | − 8.61439i | − 0.764403i | −0.924079 | − | 0.382202i | \(-0.875166\pi\) | ||||
0.924079 | − | 0.382202i | \(-0.124834\pi\) | |||||||
\(128\) | − 1.00000i | − 0.0883883i | ||||||||
\(129\) | 2.97888 | 0.262276 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 13.4278 | 1.17320 | 0.586598 | − | 0.809878i | \(-0.300467\pi\) | ||||
0.586598 | + | 0.809878i | \(0.300467\pi\) | |||||||
\(132\) | 2.64803i | 0.230481i | ||||||||
\(133\) | − 1.18654i | − 0.102886i | ||||||||
\(134\) | 5.42784 | 0.468894 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −2.51056 | −0.215279 | ||||||||
\(137\) | − 14.6903i | − 1.25507i | −0.778587 | − | 0.627537i | \(-0.784063\pi\) | ||||
0.778587 | − | 0.627537i | \(-0.215937\pi\) | |||||||
\(138\) | − 2.04223i | − 0.173846i | ||||||||
\(139\) | −17.3662 | −1.47299 | −0.736493 | − | 0.676445i | \(-0.763519\pi\) | ||||
−0.736493 | + | 0.676445i | \(0.763519\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −2.20766 | −0.185918 | ||||||||
\(142\) | 14.6480i | 1.22924i | ||||||||
\(143\) | 5.29606i | 0.442879i | ||||||||
\(144\) | 2.83457 | 0.236214 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −11.0211 | −0.912114 | ||||||||
\(147\) | 0.614387i | 0.0506738i | ||||||||
\(148\) | 1.00000i | 0.0821995i | ||||||||
\(149\) | 0.207658 | 0.0170120 | 0.00850601 | − | 0.999964i | \(-0.497292\pi\) | ||||
0.00850601 | + | 0.999964i | \(0.497292\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0.813457 | 0.0661982 | 0.0330991 | − | 0.999452i | \(-0.489462\pi\) | ||||
0.0330991 | + | 0.999452i | \(0.489462\pi\) | |||||||
\(152\) | 0.406728i | 0.0329900i | ||||||||
\(153\) | − 7.11636i | − 0.575323i | ||||||||
\(154\) | −18.9932 | −1.53051 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −0.330856 | −0.0264897 | ||||||||
\(157\) | 5.32401i | 0.424903i | 0.977172 | + | 0.212451i | \(0.0681447\pi\) | ||||
−0.977172 | + | 0.212451i | \(0.931855\pi\) | |||||||
\(158\) | 1.75870i | 0.139915i | ||||||||
\(159\) | 0.953831 | 0.0756437 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 14.6480 | 1.15443 | ||||||||
\(162\) | 7.53851i | 0.592282i | ||||||||
\(163\) | − 15.2008i | − 1.19062i | −0.803496 | − | 0.595310i | \(-0.797029\pi\) | ||||
0.803496 | − | 0.595310i | \(-0.202971\pi\) | |||||||
\(164\) | −6.34513 | −0.495471 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −7.05476 | −0.547555 | ||||||||
\(167\) | − 12.4826i | − 0.965933i | −0.875639 | − | 0.482966i | \(-0.839559\pi\) | ||||
0.875639 | − | 0.482966i | \(-0.160441\pi\) | |||||||
\(168\) | − 1.18654i | − 0.0915438i | ||||||||
\(169\) | 12.3383 | 0.949099 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.15290 | −0.0881645 | ||||||||
\(172\) | − 7.32401i | − 0.558451i | ||||||||
\(173\) | − 23.0354i | − 1.75135i | −0.482903 | − | 0.875674i | \(-0.660417\pi\) | ||||
0.482903 | − | 0.875674i | \(-0.339583\pi\) | |||||||
\(174\) | 2.16543 | 0.164161 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 6.51056 | 0.490752 | ||||||||
\(177\) | − 0.580745i | − 0.0436514i | ||||||||
\(178\) | − 6.00000i | − 0.449719i | ||||||||
\(179\) | −24.2835 | −1.81504 | −0.907518 | − | 0.420013i | \(-0.862026\pi\) | ||||
−0.907518 | + | 0.420013i | \(0.862026\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2.16543 | 0.160955 | 0.0804775 | − | 0.996756i | \(-0.474355\pi\) | ||||
0.0804775 | + | 0.996756i | \(0.474355\pi\) | |||||||
\(182\) | − 2.37309i | − 0.175905i | ||||||||
\(183\) | 0.538514i | 0.0398081i | ||||||||
\(184\) | −5.02112 | −0.370162 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −3.55963 | −0.261005 | ||||||||
\(187\) | − 16.3451i | − 1.19527i | ||||||||
\(188\) | 5.42784i | 0.395866i | ||||||||
\(189\) | 6.92297 | 0.503572 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −19.3326 | −1.39886 | −0.699429 | − | 0.714702i | \(-0.746562\pi\) | ||||
−0.699429 | + | 0.714702i | \(0.746562\pi\) | |||||||
\(192\) | 0.406728i | 0.0293531i | ||||||||
\(193\) | 20.0422i | 1.44267i | 0.692586 | + | 0.721336i | \(0.256471\pi\) | ||||
−0.692586 | + | 0.721336i | \(0.743529\pi\) | |||||||
\(194\) | −2.34513 | −0.168370 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.51056 | 0.107897 | ||||||||
\(197\) | 15.6269i | 1.11337i | 0.830723 | + | 0.556686i | \(0.187927\pi\) | ||||
−0.830723 | + | 0.556686i | \(0.812073\pi\) | |||||||
\(198\) | 18.4546i | 1.31151i | ||||||||
\(199\) | −20.2835 | −1.43786 | −0.718931 | − | 0.695082i | \(-0.755368\pi\) | ||||
−0.718931 | + | 0.695082i | \(0.755368\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −2.20766 | −0.155716 | ||||||||
\(202\) | − 8.20766i | − 0.577489i | ||||||||
\(203\) | 15.5317i | 1.09011i | ||||||||
\(204\) | 1.02112 | 0.0714924 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −8.81346 | −0.614063 | ||||||||
\(207\) | − 14.2327i | − 0.989242i | ||||||||
\(208\) | 0.813457i | 0.0564031i | ||||||||
\(209\) | −2.64803 | −0.183168 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 18.7182 | 1.28862 | 0.644308 | − | 0.764766i | \(-0.277146\pi\) | ||||
0.644308 | + | 0.764766i | \(0.277146\pi\) | |||||||
\(212\) | − 2.34513i | − 0.161064i | ||||||||
\(213\) | − 5.95777i | − 0.408220i | ||||||||
\(214\) | −15.2624 | −1.04332 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −2.37309 | −0.161468 | ||||||||
\(217\) | − 25.5317i | − 1.73320i | ||||||||
\(218\) | − 4.30290i | − 0.291429i | ||||||||
\(219\) | 4.48260 | 0.302906 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2.04223 | 0.137375 | ||||||||
\(222\) | − 0.406728i | − 0.0272978i | ||||||||
\(223\) | 15.7307i | 1.05341i | 0.850049 | + | 0.526704i | \(0.176572\pi\) | ||||
−0.850049 | + | 0.526704i | \(0.823428\pi\) | |||||||
\(224\) | −2.91729 | −0.194919 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −9.15859 | −0.609220 | ||||||||
\(227\) | 12.8836i | 0.855117i | 0.903988 | + | 0.427559i | \(0.140626\pi\) | ||||
−0.903988 | + | 0.427559i | \(0.859374\pi\) | |||||||
\(228\) | − 0.165428i | − 0.0109557i | ||||||||
\(229\) | −5.25383 | −0.347183 | −0.173591 | − | 0.984818i | \(-0.555537\pi\) | ||||
−0.173591 | + | 0.984818i | \(0.555537\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 7.72506 | 0.508271 | ||||||||
\(232\) | − 5.32401i | − 0.349539i | ||||||||
\(233\) | − 28.3172i | − 1.85512i | −0.373675 | − | 0.927560i | \(-0.621902\pi\) | ||||
0.373675 | − | 0.927560i | \(-0.378098\pi\) | |||||||
\(234\) | −2.30580 | −0.150735 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −1.42784 | −0.0929447 | ||||||||
\(237\) | − 0.715313i | − 0.0464646i | ||||||||
\(238\) | 7.32401i | 0.474745i | ||||||||
\(239\) | −14.3788 | −0.930085 | −0.465043 | − | 0.885288i | \(-0.653961\pi\) | ||||
−0.465043 | + | 0.885288i | \(0.653961\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 18.2749 | 1.17719 | 0.588596 | − | 0.808427i | \(-0.299681\pi\) | ||||
0.588596 | + | 0.808427i | \(0.299681\pi\) | |||||||
\(242\) | 31.3874i | 2.01766i | ||||||||
\(243\) | − 10.1854i | − 0.653393i | ||||||||
\(244\) | 1.32401 | 0.0847613 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 2.58074 | 0.164542 | ||||||||
\(247\) | − 0.330856i | − 0.0210519i | ||||||||
\(248\) | 8.75186i | 0.555744i | ||||||||
\(249\) | 2.86937 | 0.181839 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1.22019 | −0.0770174 | −0.0385087 | − | 0.999258i | \(-0.512261\pi\) | ||||
−0.0385087 | + | 0.999258i | \(0.512261\pi\) | |||||||
\(252\) | − 8.26926i | − 0.520914i | ||||||||
\(253\) | − 32.6903i | − 2.05522i | ||||||||
\(254\) | 8.61439 | 0.540515 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 27.1306i | 1.69236i | 0.532895 | + | 0.846181i | \(0.321104\pi\) | ||||
−0.532895 | + | 0.846181i | \(0.678896\pi\) | |||||||
\(258\) | 2.97888i | 0.185457i | ||||||||
\(259\) | 2.91729 | 0.181271 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 15.0913 | 0.934128 | ||||||||
\(262\) | 13.4278i | 0.829575i | ||||||||
\(263\) | 20.2133i | 1.24641i | 0.782059 | + | 0.623204i | \(0.214169\pi\) | ||||
−0.782059 | + | 0.623204i | \(0.785831\pi\) | |||||||
\(264\) | −2.64803 | −0.162975 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 1.18654 | 0.0727516 | ||||||||
\(267\) | 2.44037i | 0.149348i | ||||||||
\(268\) | 5.42784i | 0.331558i | ||||||||
\(269\) | 0.207658 | 0.0126611 | 0.00633057 | − | 0.999980i | \(-0.497985\pi\) | ||||
0.00633057 | + | 0.999980i | \(0.497985\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −30.6480 | −1.86174 | −0.930868 | − | 0.365357i | \(-0.880947\pi\) | ||||
−0.930868 | + | 0.365357i | \(0.880947\pi\) | |||||||
\(272\) | − 2.51056i | − 0.152225i | ||||||||
\(273\) | 0.965202i | 0.0584167i | ||||||||
\(274\) | 14.6903 | 0.887471 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 2.04223 | 0.122928 | ||||||||
\(277\) | − 16.8135i | − 1.01022i | −0.863054 | − | 0.505111i | \(-0.831451\pi\) | ||||
0.863054 | − | 0.505111i | \(-0.168549\pi\) | |||||||
\(278\) | − 17.3662i | − 1.04156i | ||||||||
\(279\) | −24.8078 | −1.48520 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −14.2749 | −0.851572 | −0.425786 | − | 0.904824i | \(-0.640002\pi\) | ||||
−0.425786 | + | 0.904824i | \(0.640002\pi\) | |||||||
\(282\) | − 2.20766i | − 0.131464i | ||||||||
\(283\) | 13.2288i | 0.786369i | 0.919460 | + | 0.393184i | \(0.128627\pi\) | ||||
−0.919460 | + | 0.393184i | \(0.871373\pi\) | |||||||
\(284\) | −14.6480 | −0.869201 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −5.29606 | −0.313162 | ||||||||
\(287\) | 18.5106i | 1.09264i | ||||||||
\(288\) | 2.83457i | 0.167029i | ||||||||
\(289\) | 10.6971 | 0.629241 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0.953831 | 0.0559146 | ||||||||
\(292\) | − 11.0211i | − 0.644962i | ||||||||
\(293\) | − 2.34513i | − 0.137004i | −0.997651 | − | 0.0685020i | \(-0.978178\pi\) | ||||
0.997651 | − | 0.0685020i | \(-0.0218219\pi\) | |||||||
\(294\) | −0.614387 | −0.0358318 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −1.00000 | −0.0581238 | ||||||||
\(297\) | − 15.4501i | − 0.896507i | ||||||||
\(298\) | 0.207658i | 0.0120293i | ||||||||
\(299\) | 4.08446 | 0.236210 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −21.3662 | −1.23153 | ||||||||
\(302\) | 0.813457i | 0.0468092i | ||||||||
\(303\) | 3.33829i | 0.191780i | ||||||||
\(304\) | −0.406728 | −0.0233275 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 7.11636 | 0.406815 | ||||||||
\(307\) | − 23.2624i | − 1.32766i | −0.747885 | − | 0.663828i | \(-0.768931\pi\) | ||||
0.747885 | − | 0.663828i | \(-0.231069\pi\) | |||||||
\(308\) | − 18.9932i | − 1.08224i | ||||||||
\(309\) | 3.58468 | 0.203926 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −31.3999 | −1.78052 | −0.890262 | − | 0.455449i | \(-0.849479\pi\) | ||||
−0.890262 | + | 0.455449i | \(0.849479\pi\) | |||||||
\(312\) | − 0.330856i | − 0.0187310i | ||||||||
\(313\) | 8.04223i | 0.454574i | 0.973828 | + | 0.227287i | \(0.0729855\pi\) | ||||
−0.973828 | + | 0.227287i | \(0.927014\pi\) | |||||||
\(314\) | −5.32401 | −0.300452 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1.75870 | −0.0989346 | ||||||||
\(317\) | − 12.3029i | − 0.691000i | −0.938419 | − | 0.345500i | \(-0.887709\pi\) | ||||
0.938419 | − | 0.345500i | \(-0.112291\pi\) | |||||||
\(318\) | 0.953831i | 0.0534882i | ||||||||
\(319\) | 34.6623 | 1.94072 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 6.20766 | 0.346478 | ||||||||
\(322\) | 14.6480i | 0.816303i | ||||||||
\(323\) | 1.02112i | 0.0568164i | ||||||||
\(324\) | −7.53851 | −0.418806 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 15.2008 | 0.841895 | ||||||||
\(327\) | 1.75011i | 0.0967814i | ||||||||
\(328\) | − 6.34513i | − 0.350351i | ||||||||
\(329\) | 15.8346 | 0.872988 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −6.77981 | −0.372652 | −0.186326 | − | 0.982488i | \(-0.559658\pi\) | ||||
−0.186326 | + | 0.982488i | \(0.559658\pi\) | |||||||
\(332\) | − 7.05476i | − 0.387180i | ||||||||
\(333\) | − 2.83457i | − 0.155334i | ||||||||
\(334\) | 12.4826 | 0.683018 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 1.18654 | 0.0647312 | ||||||||
\(337\) | 10.6903i | 0.582336i | 0.956672 | + | 0.291168i | \(0.0940438\pi\) | ||||
−0.956672 | + | 0.291168i | \(0.905956\pi\) | |||||||
\(338\) | 12.3383i | 0.671114i | ||||||||
\(339\) | 3.72506 | 0.202317 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −56.9795 | −3.08561 | ||||||||
\(342\) | − 1.15290i | − 0.0623417i | ||||||||
\(343\) | 16.0143i | 0.864689i | ||||||||
\(344\) | 7.32401 | 0.394884 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 23.0354 | 1.23839 | ||||||||
\(347\) | 5.62691i | 0.302069i | 0.988529 | + | 0.151034i | \(0.0482604\pi\) | ||||
−0.988529 | + | 0.151034i | \(0.951740\pi\) | |||||||
\(348\) | 2.16543i | 0.116079i | ||||||||
\(349\) | −15.1306 | −0.809924 | −0.404962 | − | 0.914334i | \(-0.632715\pi\) | ||||
−0.404962 | + | 0.914334i | \(0.632715\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.93040 | 0.103037 | ||||||||
\(352\) | 6.51056i | 0.347014i | ||||||||
\(353\) | − 35.7816i | − 1.90446i | −0.305381 | − | 0.952230i | \(-0.598784\pi\) | ||||
0.305381 | − | 0.952230i | \(-0.401216\pi\) | |||||||
\(354\) | 0.580745 | 0.0308662 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 6.00000 | 0.317999 | ||||||||
\(357\) | − 2.97888i | − 0.157659i | ||||||||
\(358\) | − 24.2835i | − 1.28342i | ||||||||
\(359\) | −4.48260 | −0.236583 | −0.118291 | − | 0.992979i | \(-0.537742\pi\) | ||||
−0.118291 | + | 0.992979i | \(0.537742\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.8346 | −0.991293 | ||||||||
\(362\) | 2.16543i | 0.113812i | ||||||||
\(363\) | − 12.7661i | − 0.670048i | ||||||||
\(364\) | 2.37309 | 0.124384 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −0.538514 | −0.0281486 | ||||||||
\(367\) | − 21.5653i | − 1.12570i | −0.826559 | − | 0.562850i | \(-0.809705\pi\) | ||||
0.826559 | − | 0.562850i | \(-0.190295\pi\) | |||||||
\(368\) | − 5.02112i | − 0.261744i | ||||||||
\(369\) | 17.9857 | 0.936300 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −6.84141 | −0.355188 | ||||||||
\(372\) | − 3.55963i | − 0.184558i | ||||||||
\(373\) | − 16.9230i | − 0.876238i | −0.898917 | − | 0.438119i | \(-0.855645\pi\) | ||||
0.898917 | − | 0.438119i | \(-0.144355\pi\) | |||||||
\(374\) | 16.3451 | 0.845187 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −5.42784 | −0.279920 | ||||||||
\(377\) | 4.33086i | 0.223050i | ||||||||
\(378\) | 6.92297i | 0.356079i | ||||||||
\(379\) | −31.2710 | −1.60628 | −0.803142 | − | 0.595788i | \(-0.796840\pi\) | ||||
−0.803142 | + | 0.595788i | \(0.796840\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −3.50372 | −0.179501 | ||||||||
\(382\) | − 19.3326i | − 0.989142i | ||||||||
\(383\) | − 1.62691i | − 0.0831314i | −0.999136 | − | 0.0415657i | \(-0.986765\pi\) | ||||
0.999136 | − | 0.0415657i | \(-0.0132346\pi\) | |||||||
\(384\) | −0.406728 | −0.0207558 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −20.0422 | −1.02012 | ||||||||
\(387\) | 20.7604i | 1.05531i | ||||||||
\(388\) | − 2.34513i | − 0.119056i | ||||||||
\(389\) | 31.6412 | 1.60427 | 0.802136 | − | 0.597141i | \(-0.203697\pi\) | ||||
0.802136 | + | 0.597141i | \(0.203697\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −12.6058 | −0.637503 | ||||||||
\(392\) | 1.51056i | 0.0762947i | ||||||||
\(393\) | − 5.46149i | − 0.275496i | ||||||||
\(394\) | −15.6269 | −0.787273 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −18.4546 | −0.927381 | ||||||||
\(397\) | − 39.2961i | − 1.97221i | −0.166116 | − | 0.986106i | \(-0.553122\pi\) | ||||
0.166116 | − | 0.986106i | \(-0.446878\pi\) | |||||||
\(398\) | − 20.2835i | − 1.01672i | ||||||||
\(399\) | −0.482601 | −0.0241603 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −9.66914 | −0.482854 | −0.241427 | − | 0.970419i | \(-0.577615\pi\) | ||||
−0.241427 | + | 0.970419i | \(0.577615\pi\) | |||||||
\(402\) | − 2.20766i | − 0.110108i | ||||||||
\(403\) | − 7.11926i | − 0.354636i | ||||||||
\(404\) | 8.20766 | 0.408346 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −15.5317 | −0.770824 | ||||||||
\(407\) | − 6.51056i | − 0.322716i | ||||||||
\(408\) | 1.02112i | 0.0505527i | ||||||||
\(409\) | 26.2749 | 1.29921 | 0.649606 | − | 0.760271i | \(-0.274934\pi\) | ||||
0.649606 | + | 0.760271i | \(0.274934\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −5.97495 | −0.294722 | ||||||||
\(412\) | − 8.81346i | − 0.434208i | ||||||||
\(413\) | 4.16543i | 0.204967i | ||||||||
\(414\) | 14.2327 | 0.699500 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −0.813457 | −0.0398830 | ||||||||
\(417\) | 7.06335i | 0.345894i | ||||||||
\(418\) | − 2.64803i | − 0.129519i | ||||||||
\(419\) | 30.1940 | 1.47507 | 0.737536 | − | 0.675308i | \(-0.235989\pi\) | ||||
0.737536 | + | 0.675308i | \(0.235989\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 22.0000 | 1.07221 | 0.536107 | − | 0.844150i | \(-0.319894\pi\) | ||||
0.536107 | + | 0.844150i | \(0.319894\pi\) | |||||||
\(422\) | 18.7182i | 0.911188i | ||||||||
\(423\) | − 15.3856i | − 0.748074i | ||||||||
\(424\) | 2.34513 | 0.113890 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 5.95777 | 0.288655 | ||||||||
\(427\) | − 3.86253i | − 0.186921i | ||||||||
\(428\) | − 15.2624i | − 0.737737i | ||||||||
\(429\) | 2.15406 | 0.103999 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 25.5653 | 1.23144 | 0.615719 | − | 0.787966i | \(-0.288866\pi\) | ||||
0.615719 | + | 0.787966i | \(0.288866\pi\) | |||||||
\(432\) | − 2.37309i | − 0.114175i | ||||||||
\(433\) | − 32.0422i | − 1.53985i | −0.638134 | − | 0.769926i | \(-0.720293\pi\) | ||||
0.638134 | − | 0.769926i | \(-0.279707\pi\) | |||||||
\(434\) | 25.5317 | 1.22556 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 4.30290 | 0.206072 | ||||||||
\(437\) | 2.04223i | 0.0976931i | ||||||||
\(438\) | 4.48260i | 0.214187i | ||||||||
\(439\) | −3.93840 | −0.187970 | −0.0939848 | − | 0.995574i | \(-0.529961\pi\) | ||||
−0.0939848 | + | 0.995574i | \(0.529961\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −4.28178 | −0.203894 | ||||||||
\(442\) | 2.04223i | 0.0971390i | ||||||||
\(443\) | 0.0758724i | 0.00360481i | 0.999998 | + | 0.00180240i | \(0.000573723\pi\) | ||||
−0.999998 | + | 0.00180240i | \(0.999426\pi\) | |||||||
\(444\) | 0.406728 | 0.0193025 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −15.7307 | −0.744872 | ||||||||
\(447\) | − 0.0844605i | − 0.00399485i | ||||||||
\(448\) | − 2.91729i | − 0.137829i | ||||||||
\(449\) | −19.2961 | −0.910637 | −0.455319 | − | 0.890329i | \(-0.650475\pi\) | ||||
−0.455319 | + | 0.890329i | \(0.650475\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 41.3103 | 1.94523 | ||||||||
\(452\) | − 9.15859i | − 0.430784i | ||||||||
\(453\) | − 0.330856i | − 0.0155450i | ||||||||
\(454\) | −12.8836 | −0.604659 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0.165428 | 0.00774688 | ||||||||
\(457\) | 3.00684i | 0.140654i | 0.997524 | + | 0.0703271i | \(0.0224043\pi\) | ||||
−0.997524 | + | 0.0703271i | \(0.977596\pi\) | |||||||
\(458\) | − 5.25383i | − 0.245495i | ||||||||
\(459\) | −5.95777 | −0.278085 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −0.633755 | −0.0295169 | −0.0147585 | − | 0.999891i | \(-0.504698\pi\) | ||||
−0.0147585 | + | 0.999891i | \(0.504698\pi\) | |||||||
\(462\) | 7.72506i | 0.359402i | ||||||||
\(463\) | − 18.0422i | − 0.838494i | −0.907872 | − | 0.419247i | \(-0.862294\pi\) | ||||
0.907872 | − | 0.419247i | \(-0.137706\pi\) | |||||||
\(464\) | 5.32401 | 0.247161 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 28.3172 | 1.31177 | ||||||||
\(467\) | − 23.4758i | − 1.08633i | −0.839626 | − | 0.543164i | \(-0.817226\pi\) | ||||
0.839626 | − | 0.543164i | \(-0.182774\pi\) | |||||||
\(468\) | − 2.30580i | − 0.106586i | ||||||||
\(469\) | 15.8346 | 0.731173 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 2.16543 | 0.0997777 | ||||||||
\(472\) | − 1.42784i | − 0.0657218i | ||||||||
\(473\) | 47.6834i | 2.19249i | ||||||||
\(474\) | 0.715313 | 0.0328554 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −7.32401 | −0.335696 | ||||||||
\(477\) | 6.64744i | 0.304365i | ||||||||
\(478\) | − 14.3788i | − 0.657670i | ||||||||
\(479\) | 8.19907 | 0.374625 | 0.187313 | − | 0.982300i | \(-0.440022\pi\) | ||||
0.187313 | + | 0.982300i | \(0.440022\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0.813457 | 0.0370904 | ||||||||
\(482\) | 18.2749i | 0.832401i | ||||||||
\(483\) | − 5.95777i | − 0.271088i | ||||||||
\(484\) | −31.3874 | −1.42670 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 10.1854 | 0.462019 | ||||||||
\(487\) | 0.953831i | 0.0432222i | 0.999766 | + | 0.0216111i | \(0.00687956\pi\) | ||||
−0.999766 | + | 0.0216111i | \(0.993120\pi\) | |||||||
\(488\) | 1.32401i | 0.0599353i | ||||||||
\(489\) | −6.18260 | −0.279587 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 19.3383 | 0.872725 | 0.436362 | − | 0.899771i | \(-0.356267\pi\) | ||||
0.436362 | + | 0.899771i | \(0.356267\pi\) | |||||||
\(492\) | 2.58074i | 0.116349i | ||||||||
\(493\) | − 13.3662i | − 0.601985i | ||||||||
\(494\) | 0.330856 | 0.0148859 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −8.75186 | −0.392970 | ||||||||
\(497\) | 42.7325i | 1.91681i | ||||||||
\(498\) | 2.86937i | 0.128580i | ||||||||
\(499\) | 5.63550 | 0.252280 | 0.126140 | − | 0.992012i | \(-0.459741\pi\) | ||||
0.126140 | + | 0.992012i | \(0.459741\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −5.07703 | −0.226825 | ||||||||
\(502\) | − 1.22019i | − 0.0544595i | ||||||||
\(503\) | 33.6269i | 1.49935i | 0.661806 | + | 0.749675i | \(0.269790\pi\) | ||||
−0.661806 | + | 0.749675i | \(0.730210\pi\) | |||||||
\(504\) | 8.26926 | 0.368342 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 32.6903 | 1.45326 | ||||||||
\(507\) | − 5.01833i | − 0.222872i | ||||||||
\(508\) | 8.61439i | 0.382202i | ||||||||
\(509\) | 18.6903 | 0.828431 | 0.414216 | − | 0.910179i | \(-0.364056\pi\) | ||||
0.414216 | + | 0.910179i | \(0.364056\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −32.1517 | −1.42231 | ||||||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | 0.965202i | 0.0426147i | ||||||||
\(514\) | −27.1306 | −1.19668 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −2.97888 | −0.131138 | ||||||||
\(517\) | − 35.3383i | − 1.55418i | ||||||||
\(518\) | 2.91729i | 0.128178i | ||||||||
\(519\) | −9.36915 | −0.411260 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 25.1586 | 1.10222 | 0.551109 | − | 0.834433i | \(-0.314205\pi\) | ||||
0.551109 | + | 0.834433i | \(0.314205\pi\) | |||||||
\(522\) | 15.0913i | 0.660528i | ||||||||
\(523\) | 7.25383i | 0.317188i | 0.987344 | + | 0.158594i | \(0.0506960\pi\) | ||||
−0.987344 | + | 0.158594i | \(0.949304\pi\) | |||||||
\(524\) | −13.4278 | −0.586598 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −20.2133 | −0.881344 | ||||||||
\(527\) | 21.9720i | 0.957117i | ||||||||
\(528\) | − 2.64803i | − 0.115241i | ||||||||
\(529\) | −2.21160 | −0.0961564 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 4.04733 | 0.175639 | ||||||||
\(532\) | 1.18654i | 0.0514432i | ||||||||
\(533\) | 5.16149i | 0.223569i | ||||||||
\(534\) | −2.44037 | −0.105605 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −5.42784 | −0.234447 | ||||||||
\(537\) | 9.87680i | 0.426215i | ||||||||
\(538\) | 0.207658i | 0.00895278i | ||||||||
\(539\) | −9.83457 | −0.423605 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 16.0422 | 0.689709 | 0.344855 | − | 0.938656i | \(-0.387928\pi\) | ||||
0.344855 | + | 0.938656i | \(0.387928\pi\) | |||||||
\(542\) | − 30.6480i | − 1.31645i | ||||||||
\(543\) | − 0.880741i | − 0.0377962i | ||||||||
\(544\) | 2.51056 | 0.107639 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −0.965202 | −0.0413068 | ||||||||
\(547\) | 16.0143i | 0.684721i | 0.939569 | + | 0.342360i | \(0.111226\pi\) | ||||
−0.939569 | + | 0.342360i | \(0.888774\pi\) | |||||||
\(548\) | 14.6903i | 0.627537i | ||||||||
\(549\) | −3.75301 | −0.160175 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −2.16543 | −0.0922503 | ||||||||
\(552\) | 2.04223i | 0.0869231i | ||||||||
\(553\) | 5.13063i | 0.218177i | ||||||||
\(554\) | 16.8135 | 0.714335 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 17.3662 | 0.736493 | ||||||||
\(557\) | − 10.8557i | − 0.459970i | −0.973194 | − | 0.229985i | \(-0.926132\pi\) | ||||
0.973194 | − | 0.229985i | \(-0.0738678\pi\) | |||||||
\(558\) | − 24.8078i | − 1.05020i | ||||||||
\(559\) | −5.95777 | −0.251987 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −6.64803 | −0.280680 | ||||||||
\(562\) | − 14.2749i | − 0.602152i | ||||||||
\(563\) | − 31.0776i | − 1.30977i | −0.755731 | − | 0.654883i | \(-0.772718\pi\) | ||||
0.755731 | − | 0.654883i | \(-0.227282\pi\) | |||||||
\(564\) | 2.20766 | 0.0929592 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −13.2288 | −0.556047 | ||||||||
\(567\) | 21.9920i | 0.923577i | ||||||||
\(568\) | − 14.6480i | − 0.614618i | ||||||||
\(569\) | −30.0845 | −1.26121 | −0.630603 | − | 0.776105i | \(-0.717192\pi\) | ||||
−0.630603 | + | 0.776105i | \(0.717192\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 5.55673 | 0.232542 | 0.116271 | − | 0.993218i | \(-0.462906\pi\) | ||||
0.116271 | + | 0.993218i | \(0.462906\pi\) | |||||||
\(572\) | − 5.29606i | − 0.221439i | ||||||||
\(573\) | 7.86312i | 0.328487i | ||||||||
\(574\) | −18.5106 | −0.772616 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −2.83457 | −0.118107 | ||||||||
\(577\) | − 22.2499i | − 0.926275i | −0.886286 | − | 0.463137i | \(-0.846724\pi\) | ||||
0.886286 | − | 0.463137i | \(-0.153276\pi\) | |||||||
\(578\) | 10.6971i | 0.444941i | ||||||||
\(579\) | 8.15174 | 0.338775 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −20.5807 | −0.853833 | ||||||||
\(582\) | 0.953831i | 0.0395376i | ||||||||
\(583\) | 15.2681i | 0.632340i | ||||||||
\(584\) | 11.0211 | 0.456057 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 2.34513 | 0.0968764 | ||||||||
\(587\) | 45.3103i | 1.87016i | 0.354440 | + | 0.935079i | \(0.384672\pi\) | ||||
−0.354440 | + | 0.935079i | \(0.615328\pi\) | |||||||
\(588\) | − 0.614387i | − 0.0253369i | ||||||||
\(589\) | 3.55963 | 0.146672 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 6.35591 | 0.261447 | ||||||||
\(592\) | − 1.00000i | − 0.0410997i | ||||||||
\(593\) | 0.232712i | 0.00955635i | 0.999989 | + | 0.00477817i | \(0.00152095\pi\) | ||||
−0.999989 | + | 0.00477817i | \(0.998479\pi\) | |||||||
\(594\) | 15.4501 | 0.633926 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −0.207658 | −0.00850601 | ||||||||
\(597\) | 8.24989i | 0.337645i | ||||||||
\(598\) | 4.08446i | 0.167026i | ||||||||
\(599\) | −43.4056 | −1.77350 | −0.886752 | − | 0.462246i | \(-0.847044\pi\) | ||||
−0.886752 | + | 0.462246i | \(0.847044\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 35.5317 | 1.44937 | 0.724684 | − | 0.689082i | \(-0.241986\pi\) | ||||
0.724684 | + | 0.689082i | \(0.241986\pi\) | |||||||
\(602\) | − 21.3662i | − 0.870823i | ||||||||
\(603\) | − 15.3856i | − 0.626551i | ||||||||
\(604\) | −0.813457 | −0.0330991 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −3.33829 | −0.135609 | ||||||||
\(607\) | 26.7325i | 1.08504i | 0.840043 | + | 0.542519i | \(0.182529\pi\) | ||||
−0.840043 | + | 0.542519i | \(0.817471\pi\) | |||||||
\(608\) | − 0.406728i | − 0.0164950i | ||||||||
\(609\) | 6.31717 | 0.255985 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 4.41532 | 0.178625 | ||||||||
\(612\) | 7.11636i | 0.287662i | ||||||||
\(613\) | − 48.0565i | − 1.94098i | −0.241134 | − | 0.970492i | \(-0.577519\pi\) | ||||
0.241134 | − | 0.970492i | \(-0.422481\pi\) | |||||||
\(614\) | 23.2624 | 0.938795 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 18.9932 | 0.765256 | ||||||||
\(617\) | 12.9789i | 0.522510i | 0.965270 | + | 0.261255i | \(0.0841364\pi\) | ||||
−0.965270 | + | 0.261255i | \(0.915864\pi\) | |||||||
\(618\) | 3.58468i | 0.144197i | ||||||||
\(619\) | −25.3662 | −1.01956 | −0.509778 | − | 0.860306i | \(-0.670272\pi\) | ||||
−0.509778 | + | 0.860306i | \(0.670272\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −11.9155 | −0.478154 | ||||||||
\(622\) | − 31.3999i | − 1.25902i | ||||||||
\(623\) | − 17.5037i | − 0.701272i | ||||||||
\(624\) | 0.330856 | 0.0132448 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −8.04223 | −0.321432 | ||||||||
\(627\) | 1.07703i | 0.0430124i | ||||||||
\(628\) | − 5.32401i | − 0.212451i | ||||||||
\(629\) | −2.51056 | −0.100102 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −31.6075 | −1.25828 | −0.629138 | − | 0.777293i | \(-0.716592\pi\) | ||||
−0.629138 | + | 0.777293i | \(0.716592\pi\) | |||||||
\(632\) | − 1.75870i | − 0.0699573i | ||||||||
\(633\) | − 7.61323i | − 0.302599i | ||||||||
\(634\) | 12.3029 | 0.488611 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −0.953831 | −0.0378219 | ||||||||
\(637\) | − 1.22877i | − 0.0486858i | ||||||||
\(638\) | 34.6623i | 1.37229i | ||||||||
\(639\) | 41.5209 | 1.64254 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −23.8625 | −0.942513 | −0.471257 | − | 0.881996i | \(-0.656199\pi\) | ||||
−0.471257 | + | 0.881996i | \(0.656199\pi\) | |||||||
\(642\) | 6.20766i | 0.244997i | ||||||||
\(643\) | − 32.8277i | − 1.29460i | −0.762236 | − | 0.647300i | \(-0.775898\pi\) | ||||
0.762236 | − | 0.647300i | \(-0.224102\pi\) | |||||||
\(644\) | −14.6480 | −0.577213 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −1.02112 | −0.0401752 | ||||||||
\(647\) | − 13.9578i | − 0.548737i | −0.961625 | − | 0.274368i | \(-0.911531\pi\) | ||||
0.961625 | − | 0.274368i | \(-0.0884687\pi\) | |||||||
\(648\) | − 7.53851i | − 0.296141i | ||||||||
\(649\) | 9.29606 | 0.364902 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −10.3845 | −0.406999 | ||||||||
\(652\) | 15.2008i | 0.595310i | ||||||||
\(653\) | − 28.5921i | − 1.11890i | −0.828865 | − | 0.559448i | \(-0.811013\pi\) | ||||
0.828865 | − | 0.559448i | \(-0.188987\pi\) | |||||||
\(654\) | −1.75011 | −0.0684348 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 6.34513 | 0.247736 | ||||||||
\(657\) | 31.2401i | 1.21879i | ||||||||
\(658\) | 15.8346i | 0.617296i | ||||||||
\(659\) | 5.62691 | 0.219193 | 0.109597 | − | 0.993976i | \(-0.465044\pi\) | ||||
0.109597 | + | 0.993976i | \(0.465044\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 13.3240 | 0.518244 | 0.259122 | − | 0.965845i | \(-0.416567\pi\) | ||||
0.259122 | + | 0.965845i | \(0.416567\pi\) | |||||||
\(662\) | − 6.77981i | − 0.263505i | ||||||||
\(663\) | − 0.830633i | − 0.0322591i | ||||||||
\(664\) | 7.05476 | 0.273778 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 2.83457 | 0.109837 | ||||||||
\(667\) | − 26.7325i | − 1.03509i | ||||||||
\(668\) | 12.4826i | 0.482966i | ||||||||
\(669\) | 6.39814 | 0.247366 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −8.62007 | −0.332774 | ||||||||
\(672\) | 1.18654i | 0.0457719i | ||||||||
\(673\) | − 29.6691i | − 1.14366i | −0.820372 | − | 0.571831i | \(-0.806233\pi\) | ||||
0.820372 | − | 0.571831i | \(-0.193767\pi\) | |||||||
\(674\) | −10.6903 | −0.411773 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −12.3383 | −0.474550 | ||||||||
\(677\) | − 1.25383i | − 0.0481885i | −0.999710 | − | 0.0240943i | \(-0.992330\pi\) | ||||
0.999710 | − | 0.0240943i | \(-0.00767018\pi\) | |||||||
\(678\) | 3.72506i | 0.143060i | ||||||||
\(679\) | −6.84141 | −0.262549 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 5.24014 | 0.200803 | ||||||||
\(682\) | − 56.9795i | − 2.18186i | ||||||||
\(683\) | 4.76045i | 0.182153i | 0.995844 | + | 0.0910767i | \(0.0290308\pi\) | ||||
−0.995844 | + | 0.0910767i | \(0.970969\pi\) | |||||||
\(684\) | 1.15290 | 0.0440823 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −16.0143 | −0.611428 | ||||||||
\(687\) | 2.13688i | 0.0815271i | ||||||||
\(688\) | 7.32401i | 0.279225i | ||||||||
\(689\) | −1.90766 | −0.0726761 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −20.2219 | −0.769279 | −0.384639 | − | 0.923067i | \(-0.625674\pi\) | ||||
−0.384639 | + | 0.923067i | \(0.625674\pi\) | |||||||
\(692\) | 23.0354i | 0.875674i | ||||||||
\(693\) | 53.8375i | 2.04512i | ||||||||
\(694\) | −5.62691 | −0.213595 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −2.16543 | −0.0820803 | ||||||||
\(697\) | − 15.9298i | − 0.603385i | ||||||||
\(698\) | − 15.1306i | − 0.572703i | ||||||||
\(699\) | −11.5174 | −0.435628 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −22.0845 | −0.834119 | −0.417059 | − | 0.908879i | \(-0.636939\pi\) | ||||
−0.417059 | + | 0.908879i | \(0.636939\pi\) | |||||||
\(702\) | 1.93040i | 0.0728584i | ||||||||
\(703\) | 0.406728i | 0.0153401i | ||||||||
\(704\) | −6.51056 | −0.245376 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 35.7816 | 1.34666 | ||||||||
\(707\) | − 23.9441i | − 0.900510i | ||||||||
\(708\) | 0.580745i | 0.0218257i | ||||||||
\(709\) | −5.59896 | −0.210273 | −0.105137 | − | 0.994458i | \(-0.533528\pi\) | ||||
−0.105137 | + | 0.994458i | \(0.533528\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 4.98516 | 0.186958 | ||||||||
\(712\) | 6.00000i | 0.224860i | ||||||||
\(713\) | 43.9441i | 1.64572i | ||||||||
\(714\) | 2.97888 | 0.111482 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 24.2835 | 0.907518 | ||||||||
\(717\) | 5.84826i | 0.218407i | ||||||||
\(718\) | − 4.48260i | − 0.167289i | ||||||||
\(719\) | −40.2921 | −1.50264 | −0.751321 | − | 0.659937i | \(-0.770583\pi\) | ||||
−0.751321 | + | 0.659937i | \(0.770583\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −25.7114 | −0.957542 | ||||||||
\(722\) | − 18.8346i | − 0.700950i | ||||||||
\(723\) | − 7.43294i | − 0.276434i | ||||||||
\(724\) | −2.16543 | −0.0804775 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 12.7661 | 0.473796 | ||||||||
\(727\) | 11.2538i | 0.417381i | 0.977982 | + | 0.208691i | \(0.0669202\pi\) | ||||
−0.977982 | + | 0.208691i | \(0.933080\pi\) | |||||||
\(728\) | 2.37309i | 0.0879524i | ||||||||
\(729\) | 18.4729 | 0.684180 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 18.3874 | 0.680081 | ||||||||
\(732\) | − 0.538514i | − 0.0199041i | ||||||||
\(733\) | 42.2892i | 1.56199i | 0.624539 | + | 0.780994i | \(0.285287\pi\) | ||||
−0.624539 | + | 0.780994i | \(0.714713\pi\) | |||||||
\(734\) | 21.5653 | 0.795990 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 5.02112 | 0.185081 | ||||||||
\(737\) | − 35.3383i | − 1.30170i | ||||||||
\(738\) | 17.9857i | 0.662064i | ||||||||
\(739\) | 29.3103 | 1.07820 | 0.539099 | − | 0.842242i | \(-0.318765\pi\) | ||||
0.539099 | + | 0.842242i | \(0.318765\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −0.134569 | −0.00494350 | ||||||||
\(742\) | − 6.84141i | − 0.251156i | ||||||||
\(743\) | 4.39245i | 0.161144i | 0.996749 | + | 0.0805718i | \(0.0256746\pi\) | ||||
−0.996749 | + | 0.0805718i | \(0.974325\pi\) | |||||||
\(744\) | 3.55963 | 0.130502 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 16.9230 | 0.619594 | ||||||||
\(747\) | 19.9972i | 0.731660i | ||||||||
\(748\) | 16.3451i | 0.597637i | ||||||||
\(749\) | −44.5248 | −1.62690 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 2.58074 | 0.0941727 | 0.0470864 | − | 0.998891i | \(-0.485006\pi\) | ||||
0.0470864 | + | 0.998891i | \(0.485006\pi\) | |||||||
\(752\) | − 5.42784i | − 0.197933i | ||||||||
\(753\) | 0.496284i | 0.0180856i | ||||||||
\(754\) | −4.33086 | −0.157720 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −6.92297 | −0.251786 | ||||||||
\(757\) | 27.3805i | 0.995162i | 0.867418 | + | 0.497581i | \(0.165778\pi\) | ||||
−0.867418 | + | 0.497581i | \(0.834222\pi\) | |||||||
\(758\) | − 31.2710i | − 1.13581i | ||||||||
\(759\) | −13.2961 | −0.482616 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −42.9509 | −1.55697 | −0.778485 | − | 0.627663i | \(-0.784011\pi\) | ||||
−0.778485 | + | 0.627663i | \(0.784011\pi\) | |||||||
\(762\) | − 3.50372i | − 0.126926i | ||||||||
\(763\) | − 12.5528i | − 0.454441i | ||||||||
\(764\) | 19.3326 | 0.699429 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 1.62691 | 0.0587828 | ||||||||
\(767\) | 1.16149i | 0.0419389i | ||||||||
\(768\) | − 0.406728i | − 0.0146765i | ||||||||
\(769\) | 13.0633 | 0.471076 | 0.235538 | − | 0.971865i | \(-0.424315\pi\) | ||||
0.235538 | + | 0.971865i | \(0.424315\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 11.0348 | 0.397409 | ||||||||
\(772\) | − 20.0422i | − 0.721336i | ||||||||
\(773\) | 15.3662i | 0.552685i | 0.961059 | + | 0.276343i | \(0.0891225\pi\) | ||||
−0.961059 | + | 0.276343i | \(0.910878\pi\) | |||||||
\(774\) | −20.7604 | −0.746219 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 2.34513 | 0.0841852 | ||||||||
\(777\) | − 1.18654i | − 0.0425670i | ||||||||
\(778\) | 31.6412i | 1.13439i | ||||||||
\(779\) | −2.58074 | −0.0924648 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 95.3668 | 3.41249 | ||||||||
\(782\) | − 12.6058i | − 0.450782i | ||||||||
\(783\) | − 12.6343i | − 0.451515i | ||||||||
\(784\) | −1.51056 | −0.0539485 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 5.46149 | 0.194805 | ||||||||
\(787\) | 10.9316i | 0.389668i | 0.980836 | + | 0.194834i | \(0.0624168\pi\) | ||||
−0.980836 | + | 0.194834i | \(0.937583\pi\) | |||||||
\(788\) | − 15.6269i | − 0.556686i | ||||||||
\(789\) | 8.22134 | 0.292688 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −26.7182 | −0.949990 | ||||||||
\(792\) | − 18.4546i | − 0.655757i | ||||||||
\(793\) | − 1.07703i | − 0.0382464i | ||||||||
\(794\) | 39.2961 | 1.39456 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 20.2835 | 0.718931 | ||||||||
\(797\) | − 24.2921i | − 0.860471i | −0.902717 | − | 0.430235i | \(-0.858431\pi\) | ||||
0.902717 | − | 0.430235i | \(-0.141569\pi\) | |||||||
\(798\) | − 0.482601i | − 0.0170839i | ||||||||
\(799\) | −13.6269 | −0.482086 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −17.0074 | −0.600928 | ||||||||
\(802\) | − 9.66914i | − 0.341429i | ||||||||
\(803\) | 71.7536i | 2.53213i | ||||||||
\(804\) | 2.20766 | 0.0778581 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 7.11926 | 0.250765 | ||||||||
\(807\) | − 0.0844605i | − 0.00297315i | ||||||||
\(808\) | 8.20766i | 0.288744i | ||||||||
\(809\) | 40.0422 | 1.40781 | 0.703905 | − | 0.710294i | \(-0.251438\pi\) | ||||
0.703905 | + | 0.710294i | \(0.251438\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −40.6343 | −1.42686 | −0.713432 | − | 0.700724i | \(-0.752860\pi\) | ||||
−0.713432 | + | 0.700724i | \(0.752860\pi\) | |||||||
\(812\) | − 15.5317i | − 0.545055i | ||||||||
\(813\) | 12.4654i | 0.437182i | ||||||||
\(814\) | 6.51056 | 0.228195 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −1.02112 | −0.0357462 | ||||||||
\(817\) | − 2.97888i | − 0.104218i | ||||||||
\(818\) | 26.2749i | 0.918682i | ||||||||
\(819\) | −6.72668 | −0.235049 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −41.4787 | −1.44762 | −0.723808 | − | 0.690002i | \(-0.757610\pi\) | ||||
−0.723808 | + | 0.690002i | \(0.757610\pi\) | |||||||
\(822\) | − 5.97495i | − 0.208400i | ||||||||
\(823\) | 5.27610i | 0.183913i | 0.995763 | + | 0.0919566i | \(0.0293121\pi\) | ||||
−0.995763 | + | 0.0919566i | \(0.970688\pi\) | |||||||
\(824\) | 8.81346 | 0.307031 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −4.16543 | −0.144934 | ||||||||
\(827\) | 1.76438i | 0.0613537i | 0.999529 | + | 0.0306768i | \(0.00976627\pi\) | ||||
−0.999529 | + | 0.0306768i | \(0.990234\pi\) | |||||||
\(828\) | 14.2327i | 0.494621i | ||||||||
\(829\) | −16.3029 | −0.566223 | −0.283112 | − | 0.959087i | \(-0.591367\pi\) | ||||
−0.283112 | + | 0.959087i | \(0.591367\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −6.83851 | −0.237225 | ||||||||
\(832\) | − 0.813457i | − 0.0282015i | ||||||||
\(833\) | 3.79234i | 0.131397i | ||||||||
\(834\) | −7.06335 | −0.244584 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 2.64803 | 0.0915840 | ||||||||
\(837\) | 20.7689i | 0.717879i | ||||||||
\(838\) | 30.1940i | 1.04303i | ||||||||
\(839\) | −14.3731 | −0.496214 | −0.248107 | − | 0.968733i | \(-0.579808\pi\) | ||||
−0.248107 | + | 0.968733i | \(0.579808\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −0.654870 | −0.0225817 | ||||||||
\(842\) | 22.0000i | 0.758170i | ||||||||
\(843\) | 5.80602i | 0.199970i | ||||||||
\(844\) | −18.7182 | −0.644308 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 15.3856 | 0.528968 | ||||||||
\(847\) | 91.5659i | 3.14624i | ||||||||
\(848\) | 2.34513i | 0.0805321i | ||||||||
\(849\) | 5.38052 | 0.184659 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −5.02112 | −0.172122 | ||||||||
\(852\) | 5.95777i | 0.204110i | ||||||||
\(853\) | − 43.2961i | − 1.48243i | −0.671268 | − | 0.741214i | \(-0.734250\pi\) | ||||
0.671268 | − | 0.741214i | \(-0.265750\pi\) | |||||||
\(854\) | 3.86253 | 0.132173 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 15.2624 | 0.521659 | ||||||||
\(857\) | − 49.0776i | − 1.67646i | −0.545317 | − | 0.838230i | \(-0.683591\pi\) | ||||
0.545317 | − | 0.838230i | \(-0.316409\pi\) | |||||||
\(858\) | 2.15406i | 0.0735383i | ||||||||
\(859\) | −15.5374 | −0.530128 | −0.265064 | − | 0.964231i | \(-0.585393\pi\) | ||||
−0.265064 | + | 0.964231i | \(0.585393\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 7.52877 | 0.256580 | ||||||||
\(862\) | 25.5653i | 0.870758i | ||||||||
\(863\) | 36.0901i | 1.22852i | 0.789103 | + | 0.614261i | \(0.210546\pi\) | ||||
−0.789103 | + | 0.614261i | \(0.789454\pi\) | |||||||
\(864\) | 2.37309 | 0.0807340 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 32.0422 | 1.08884 | ||||||||
\(867\) | − 4.35081i | − 0.147761i | ||||||||
\(868\) | 25.5317i | 0.866601i | ||||||||
\(869\) | 11.4501 | 0.388419 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 4.41532 | 0.149607 | ||||||||
\(872\) | 4.30290i | 0.145715i | ||||||||
\(873\) | 6.64744i | 0.224982i | ||||||||
\(874\) | −2.04223 | −0.0690795 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −4.48260 | −0.151453 | ||||||||
\(877\) | 29.3240i | 0.990202i | 0.868836 | + | 0.495101i | \(0.164869\pi\) | ||||
−0.868836 | + | 0.495101i | \(0.835131\pi\) | |||||||
\(878\) | − 3.93840i | − 0.132915i | ||||||||
\(879\) | −0.953831 | −0.0321719 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 23.8066 | 0.802065 | 0.401033 | − | 0.916064i | \(-0.368651\pi\) | ||||
0.401033 | + | 0.916064i | \(0.368651\pi\) | |||||||
\(882\) | − 4.28178i | − 0.144175i | ||||||||
\(883\) | 3.94699i | 0.132827i | 0.997792 | + | 0.0664134i | \(0.0211556\pi\) | ||||
−0.997792 | + | 0.0664134i | \(0.978844\pi\) | |||||||
\(884\) | −2.04223 | −0.0686876 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −0.0758724 | −0.00254898 | ||||||||
\(887\) | 1.96346i | 0.0659264i | 0.999457 | + | 0.0329632i | \(0.0104944\pi\) | ||||
−0.999457 | + | 0.0329632i | \(0.989506\pi\) | |||||||
\(888\) | 0.406728i | 0.0136489i | ||||||||
\(889\) | 25.1306 | 0.842854 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 49.0799 | 1.64424 | ||||||||
\(892\) | − 15.7307i | − 0.526704i | ||||||||
\(893\) | 2.20766i | 0.0738765i | ||||||||
\(894\) | 0.0844605 | 0.00282478 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 2.91729 | 0.0974597 | ||||||||
\(897\) | − 1.66127i | − 0.0554681i | ||||||||
\(898\) | − 19.2961i | − 0.643918i | ||||||||
\(899\) | −46.5950 | −1.55403 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 5.88758 | 0.196144 | ||||||||
\(902\) | 41.3103i | 1.37548i | ||||||||
\(903\) | 8.69026i | 0.289194i | ||||||||
\(904\) | 9.15859 | 0.304610 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0.330856 | 0.0109920 | ||||||||
\(907\) | 5.89049i | 0.195590i | 0.995207 | + | 0.0977952i | \(0.0311790\pi\) | ||||
−0.995207 | + | 0.0977952i | \(0.968821\pi\) | |||||||
\(908\) | − 12.8836i | − 0.427559i | ||||||||
\(909\) | −23.2652 | −0.771658 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −27.9527 | −0.926113 | −0.463057 | − | 0.886329i | \(-0.653247\pi\) | ||||
−0.463057 | + | 0.886329i | \(0.653247\pi\) | |||||||
\(912\) | 0.165428i | 0.00547787i | ||||||||
\(913\) | 45.9304i | 1.52007i | ||||||||
\(914\) | −3.00684 | −0.0994575 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 5.25383 | 0.173591 | ||||||||
\(917\) | 39.1729i | 1.29360i | ||||||||
\(918\) | − 5.95777i | − 0.196636i | ||||||||
\(919\) | −17.7587 | −0.585805 | −0.292903 | − | 0.956142i | \(-0.594621\pi\) | ||||
−0.292903 | + | 0.956142i | \(0.594621\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −9.46149 | −0.311767 | ||||||||
\(922\) | − 0.633755i | − 0.0208716i | ||||||||
\(923\) | 11.9155i | 0.392205i | ||||||||
\(924\) | −7.72506 | −0.254136 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 18.0422 | 0.592904 | ||||||||
\(927\) | 24.9824i | 0.820529i | ||||||||
\(928\) | 5.32401i | 0.174769i | ||||||||
\(929\) | −34.2892 | −1.12499 | −0.562496 | − | 0.826800i | \(-0.690159\pi\) | ||||
−0.562496 | + | 0.826800i | \(0.690159\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0.614387 | 0.0201357 | ||||||||
\(932\) | 28.3172i | 0.927560i | ||||||||
\(933\) | 12.7712i | 0.418111i | ||||||||
\(934\) | 23.4758 | 0.768150 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 2.30580 | 0.0753675 | ||||||||
\(937\) | − 14.0845i | − 0.460119i | −0.973177 | − | 0.230060i | \(-0.926108\pi\) | ||||
0.973177 | − | 0.230060i | \(-0.0738921\pi\) | |||||||
\(938\) | 15.8346i | 0.517017i | ||||||||
\(939\) | 3.27100 | 0.106745 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 14.2499 | 0.464533 | 0.232267 | − | 0.972652i | \(-0.425386\pi\) | ||||
0.232267 | + | 0.972652i | \(0.425386\pi\) | |||||||
\(942\) | 2.16543i | 0.0705535i | ||||||||
\(943\) | − 31.8596i | − 1.03749i | ||||||||
\(944\) | 1.42784 | 0.0464723 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −47.6834 | −1.55032 | ||||||||
\(947\) | − 29.8203i | − 0.969029i | −0.874783 | − | 0.484515i | \(-0.838996\pi\) | ||||
0.874783 | − | 0.484515i | \(-0.161004\pi\) | |||||||
\(948\) | 0.715313i | 0.0232323i | ||||||||
\(949\) | −8.96520 | −0.291023 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −5.00394 | −0.162264 | ||||||||
\(952\) | − 7.32401i | − 0.237373i | ||||||||
\(953\) | − 8.64803i | − 0.280137i | −0.990142 | − | 0.140069i | \(-0.955268\pi\) | ||||
0.990142 | − | 0.140069i | \(-0.0447323\pi\) | |||||||
\(954\) | −6.64744 | −0.215219 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 14.3788 | 0.465043 | ||||||||
\(957\) | − 14.0981i | − 0.455728i | ||||||||
\(958\) | 8.19907i | 0.264900i | ||||||||
\(959\) | 42.8557 | 1.38388 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 45.5950 | 1.47081 | ||||||||
\(962\) | 0.813457i | 0.0262269i | ||||||||
\(963\) | 43.2624i | 1.39411i | ||||||||
\(964\) | −18.2749 | −0.588596 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 5.95777 | 0.191688 | ||||||||
\(967\) | − 45.0325i | − 1.44815i | −0.689723 | − | 0.724074i | \(-0.742268\pi\) | ||||
0.689723 | − | 0.724074i | \(-0.257732\pi\) | |||||||
\(968\) | − 31.3874i | − 1.00883i | ||||||||
\(969\) | 0.415317 | 0.0133419 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 26.3029 | 0.844100 | 0.422050 | − | 0.906573i | \(-0.361311\pi\) | ||||
0.422050 | + | 0.906573i | \(0.361311\pi\) | |||||||
\(972\) | 10.1854i | 0.326696i | ||||||||
\(973\) | − 50.6623i | − 1.62416i | ||||||||
\(974\) | −0.953831 | −0.0305627 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −1.32401 | −0.0423807 | ||||||||
\(977\) | 25.6549i | 0.820772i | 0.911912 | + | 0.410386i | \(0.134606\pi\) | ||||
−0.911912 | + | 0.410386i | \(0.865394\pi\) | |||||||
\(978\) | − 6.18260i | − 0.197698i | ||||||||
\(979\) | −39.0633 | −1.24847 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −12.1969 | −0.389416 | ||||||||
\(982\) | 19.3383i | 0.617110i | ||||||||
\(983\) | 55.3611i | 1.76575i | 0.469611 | + | 0.882873i | \(0.344394\pi\) | ||||
−0.469611 | + | 0.882873i | \(0.655606\pi\) | |||||||
\(984\) | −2.58074 | −0.0822711 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 13.3662 | 0.425668 | ||||||||
\(987\) | − 6.44037i | − 0.204999i | ||||||||
\(988\) | 0.330856i | 0.0105259i | ||||||||
\(989\) | 36.7747 | 1.16937 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −3.24814 | −0.103181 | −0.0515903 | − | 0.998668i | \(-0.516429\pi\) | ||||
−0.0515903 | + | 0.998668i | \(0.516429\pi\) | |||||||
\(992\) | − 8.75186i | − 0.277872i | ||||||||
\(993\) | 2.75754i | 0.0875080i | ||||||||
\(994\) | −42.7325 | −1.35539 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −2.86937 | −0.0909195 | ||||||||
\(997\) | − 12.6480i | − 0.400567i | −0.979738 | − | 0.200284i | \(-0.935814\pi\) | ||||
0.979738 | − | 0.200284i | \(-0.0641863\pi\) | |||||||
\(998\) | 5.63550i | 0.178389i | ||||||||
\(999\) | −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 | 1850.2.b.o.149.5 | 6 | ||
5.2 | odd | 4 | 1850.2.a.z.1.2 | 3 | |||
5.3 | odd | 4 | 370.2.a.g.1.2 | ✓ | 3 | ||
5.4 | even | 2 | inner | 1850.2.b.o.149.2 | 6 | ||
15.8 | even | 4 | 3330.2.a.bg.1.3 | 3 | |||
20.3 | even | 4 | 2960.2.a.u.1.2 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
370.2.a.g.1.2 | ✓ | 3 | 5.3 | odd | 4 | ||
1850.2.a.z.1.2 | 3 | 5.2 | odd | 4 | |||
1850.2.b.o.149.2 | 6 | 5.4 | even | 2 | inner | ||
1850.2.b.o.149.5 | 6 | 1.1 | even | 1 | trivial | ||
2960.2.a.u.1.2 | 3 | 20.3 | even | 4 | |||
3330.2.a.bg.1.3 | 3 | 15.8 | even | 4 |