Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1875,2,Mod(1249,1875)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1875, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1875.1249");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1875 = 3 \cdot 5^{4} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1875.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: | \(14.9719503790\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 20x^{14} + 156x^{12} + 610x^{10} + 1286x^{8} + 1440x^{6} + 761x^{4} + 130x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{8} \) |
Twist minimal: | no (minimal twist has level 75) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1249.2 | ||
Root | \(1.35083i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1875.1249 |
Dual form | 1875.2.b.h.1249.15 |
$q$-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 \(\left(\mathbb{Z}/1875\mathbb{Z}\right)^\times\).
\(n\) | \(626\) | \(1252\) |
\(\chi(n)\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − 2.35083i | − 1.66229i | −0.556058 | − | 0.831144i | \(-0.687687\pi\) | ||||
0.556058 | − | 0.831144i | \(-0.312313\pi\) | |||||||
\(3\) | − 1.00000i | − 0.577350i | ||||||||
\(4\) | −3.52640 | −1.76320 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −2.35083 | −0.959722 | ||||||||
\(7\) | − 3.48189i | − 1.31603i | −0.753005 | − | 0.658015i | \(-0.771396\pi\) | ||||
0.753005 | − | 0.658015i | \(-0.228604\pi\) | |||||||
\(8\) | 3.58831i | 1.26866i | ||||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.93111 | 0.883762 | 0.441881 | − | 0.897074i | \(-0.354311\pi\) | ||||
0.441881 | + | 0.897074i | \(0.354311\pi\) | |||||||
\(12\) | 3.52640i | 1.01798i | ||||||||
\(13\) | − 1.87575i | − 0.520239i | −0.965576 | − | 0.260119i | \(-0.916238\pi\) | ||||
0.965576 | − | 0.260119i | \(-0.0837619\pi\) | |||||||
\(14\) | −8.18532 | −2.18762 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.38270 | 0.345674 | ||||||||
\(17\) | − 6.78566i | − 1.64576i | −0.568212 | − | 0.822882i | \(-0.692365\pi\) | ||||
0.568212 | − | 0.822882i | \(-0.307635\pi\) | |||||||
\(18\) | 2.35083i | 0.554096i | ||||||||
\(19\) | 2.94950 | 0.676662 | 0.338331 | − | 0.941027i | \(-0.390138\pi\) | ||||
0.338331 | + | 0.941027i | \(0.390138\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −3.48189 | −0.759810 | ||||||||
\(22\) | − 6.89053i | − 1.46907i | ||||||||
\(23\) | − 5.49019i | − 1.14478i | −0.819980 | − | 0.572392i | \(-0.806015\pi\) | ||||
0.819980 | − | 0.572392i | \(-0.193985\pi\) | |||||||
\(24\) | 3.58831 | 0.732460 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −4.40956 | −0.864786 | ||||||||
\(27\) | 1.00000i | 0.192450i | ||||||||
\(28\) | 12.2785i | 2.32042i | ||||||||
\(29\) | −2.55593 | −0.474625 | −0.237313 | − | 0.971433i | \(-0.576267\pi\) | ||||
−0.237313 | + | 0.971433i | \(0.576267\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.418084 | 0.0750901 | 0.0375451 | − | 0.999295i | \(-0.488046\pi\) | ||||
0.0375451 | + | 0.999295i | \(0.488046\pi\) | |||||||
\(32\) | 3.92613i | 0.694048i | ||||||||
\(33\) | − 2.93111i | − 0.510240i | ||||||||
\(34\) | −15.9519 | −2.73573 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 3.52640 | 0.587733 | ||||||||
\(37\) | − 5.23959i | − 0.861383i | −0.902499 | − | 0.430691i | \(-0.858270\pi\) | ||||
0.902499 | − | 0.430691i | \(-0.141730\pi\) | |||||||
\(38\) | − 6.93377i | − 1.12481i | ||||||||
\(39\) | −1.87575 | −0.300360 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.67869 | 0.262167 | 0.131084 | − | 0.991371i | \(-0.458154\pi\) | ||||
0.131084 | + | 0.991371i | \(0.458154\pi\) | |||||||
\(42\) | 8.18532i | 1.26302i | ||||||||
\(43\) | 10.9233i | 1.66578i | 0.553436 | + | 0.832892i | \(0.313316\pi\) | ||||
−0.553436 | + | 0.832892i | \(0.686684\pi\) | |||||||
\(44\) | −10.3363 | −1.55825 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −12.9065 | −1.90296 | ||||||||
\(47\) | 7.49178i | 1.09279i | 0.837528 | + | 0.546394i | \(0.184000\pi\) | ||||
−0.837528 | + | 0.546394i | \(0.816000\pi\) | |||||||
\(48\) | − 1.38270i | − 0.199575i | ||||||||
\(49\) | −5.12353 | −0.731933 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −6.78566 | −0.950183 | ||||||||
\(52\) | 6.61463i | 0.917285i | ||||||||
\(53\) | 3.70953i | 0.509543i | 0.967001 | + | 0.254771i | \(0.0820002\pi\) | ||||
−0.967001 | + | 0.254771i | \(0.918000\pi\) | |||||||
\(54\) | 2.35083 | 0.319907 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 12.4941 | 1.66959 | ||||||||
\(57\) | − 2.94950i | − 0.390671i | ||||||||
\(58\) | 6.00857i | 0.788964i | ||||||||
\(59\) | 7.10854 | 0.925453 | 0.462727 | − | 0.886501i | \(-0.346871\pi\) | ||||
0.462727 | + | 0.886501i | \(0.346871\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −6.43710 | −0.824186 | −0.412093 | − | 0.911142i | \(-0.635202\pi\) | ||||
−0.412093 | + | 0.911142i | \(0.635202\pi\) | |||||||
\(62\) | − 0.982844i | − 0.124821i | ||||||||
\(63\) | 3.48189i | 0.438676i | ||||||||
\(64\) | 11.9951 | 1.49938 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −6.89053 | −0.848166 | ||||||||
\(67\) | − 10.0415i | − 1.22677i | −0.789786 | − | 0.613383i | \(-0.789808\pi\) | ||||
0.789786 | − | 0.613383i | \(-0.210192\pi\) | |||||||
\(68\) | 23.9290i | 2.90181i | ||||||||
\(69\) | −5.49019 | −0.660942 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 0.728602 | 0.0864691 | 0.0432346 | − | 0.999065i | \(-0.486234\pi\) | ||||
0.0432346 | + | 0.999065i | \(0.486234\pi\) | |||||||
\(72\) | − 3.58831i | − 0.422886i | ||||||||
\(73\) | − 3.59269i | − 0.420492i | −0.977648 | − | 0.210246i | \(-0.932573\pi\) | ||||
0.977648 | − | 0.210246i | \(-0.0674266\pi\) | |||||||
\(74\) | −12.3174 | −1.43187 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −10.4011 | −1.19309 | ||||||||
\(77\) | − 10.2058i | − 1.16306i | ||||||||
\(78\) | 4.40956i | 0.499285i | ||||||||
\(79\) | −3.07265 | −0.345700 | −0.172850 | − | 0.984948i | \(-0.555298\pi\) | ||||
−0.172850 | + | 0.984948i | \(0.555298\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | − 3.94632i | − 0.435798i | ||||||||
\(83\) | 10.1152i | 1.11029i | 0.831753 | + | 0.555146i | \(0.187338\pi\) | ||||
−0.831753 | + | 0.555146i | \(0.812662\pi\) | |||||||
\(84\) | 12.2785 | 1.33970 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 25.6788 | 2.76901 | ||||||||
\(87\) | 2.55593i | 0.274025i | ||||||||
\(88\) | 10.5177i | 1.12119i | ||||||||
\(89\) | −0.287512 | −0.0304762 | −0.0152381 | − | 0.999884i | \(-0.504851\pi\) | ||||
−0.0152381 | + | 0.999884i | \(0.504851\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −6.53114 | −0.684649 | ||||||||
\(92\) | 19.3606i | 2.01848i | ||||||||
\(93\) | − 0.418084i | − 0.0433533i | ||||||||
\(94\) | 17.6119 | 1.81653 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 3.92613 | 0.400709 | ||||||||
\(97\) | 10.4090i | 1.05688i | 0.848971 | + | 0.528439i | \(0.177222\pi\) | ||||
−0.848971 | + | 0.528439i | \(0.822778\pi\) | |||||||
\(98\) | 12.0446i | 1.21668i | ||||||||
\(99\) | −2.93111 | −0.294587 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 7.65744 | 0.761943 | 0.380972 | − | 0.924587i | \(-0.375590\pi\) | ||||
0.380972 | + | 0.924587i | \(0.375590\pi\) | |||||||
\(102\) | 15.9519i | 1.57948i | ||||||||
\(103\) | − 2.98602i | − 0.294221i | −0.989120 | − | 0.147111i | \(-0.953003\pi\) | ||||
0.989120 | − | 0.147111i | \(-0.0469974\pi\) | |||||||
\(104\) | 6.73076 | 0.660005 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 8.72047 | 0.847007 | ||||||||
\(107\) | 7.07213i | 0.683689i | 0.939757 | + | 0.341844i | \(0.111052\pi\) | ||||
−0.939757 | + | 0.341844i | \(0.888948\pi\) | |||||||
\(108\) | − 3.52640i | − 0.339328i | ||||||||
\(109\) | 13.3022 | 1.27412 | 0.637058 | − | 0.770816i | \(-0.280151\pi\) | ||||
0.637058 | + | 0.770816i | \(0.280151\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −5.23959 | −0.497320 | ||||||||
\(112\) | − 4.81440i | − 0.454918i | ||||||||
\(113\) | 10.0233i | 0.942911i | 0.881890 | + | 0.471456i | \(0.156271\pi\) | ||||
−0.881890 | + | 0.471456i | \(0.843729\pi\) | |||||||
\(114\) | −6.93377 | −0.649407 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 9.01325 | 0.836859 | ||||||||
\(117\) | 1.87575i | 0.173413i | ||||||||
\(118\) | − 16.7110i | − 1.53837i | ||||||||
\(119\) | −23.6269 | −2.16587 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2.40861 | −0.218965 | ||||||||
\(122\) | 15.1325i | 1.37003i | ||||||||
\(123\) | − 1.67869i | − 0.151362i | ||||||||
\(124\) | −1.47433 | −0.132399 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 8.18532 | 0.729206 | ||||||||
\(127\) | − 10.5730i | − 0.938205i | −0.883144 | − | 0.469103i | \(-0.844577\pi\) | ||||
0.883144 | − | 0.469103i | \(-0.155423\pi\) | |||||||
\(128\) | − 20.3461i | − 1.79836i | ||||||||
\(129\) | 10.9233 | 0.961741 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −9.02608 | −0.788612 | −0.394306 | − | 0.918979i | \(-0.629015\pi\) | ||||
−0.394306 | + | 0.918979i | \(0.629015\pi\) | |||||||
\(132\) | 10.3363i | 0.899656i | ||||||||
\(133\) | − 10.2698i | − 0.890507i | ||||||||
\(134\) | −23.6059 | −2.03924 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 24.3490 | 2.08791 | ||||||||
\(137\) | 19.6646i | 1.68006i | 0.542541 | + | 0.840029i | \(0.317462\pi\) | ||||
−0.542541 | + | 0.840029i | \(0.682538\pi\) | |||||||
\(138\) | 12.9065i | 1.09868i | ||||||||
\(139\) | 11.6520 | 0.988310 | 0.494155 | − | 0.869374i | \(-0.335478\pi\) | ||||
0.494155 | + | 0.869374i | \(0.335478\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 7.49178 | 0.630922 | ||||||||
\(142\) | − 1.71282i | − 0.143737i | ||||||||
\(143\) | − 5.49801i | − 0.459767i | ||||||||
\(144\) | −1.38270 | −0.115225 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −8.44580 | −0.698979 | ||||||||
\(147\) | 5.12353i | 0.422582i | ||||||||
\(148\) | 18.4769i | 1.51879i | ||||||||
\(149\) | 7.33020 | 0.600513 | 0.300257 | − | 0.953858i | \(-0.402928\pi\) | ||||
0.300257 | + | 0.953858i | \(0.402928\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −16.7358 | −1.36194 | −0.680968 | − | 0.732313i | \(-0.738441\pi\) | ||||
−0.680968 | + | 0.732313i | \(0.738441\pi\) | |||||||
\(152\) | 10.5837i | 0.858453i | ||||||||
\(153\) | 6.78566i | 0.548588i | ||||||||
\(154\) | −23.9921 | −1.93333 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 6.61463 | 0.529595 | ||||||||
\(157\) | − 7.88635i | − 0.629399i | −0.949191 | − | 0.314700i | \(-0.898096\pi\) | ||||
0.949191 | − | 0.314700i | \(-0.101904\pi\) | |||||||
\(158\) | 7.22328i | 0.574653i | ||||||||
\(159\) | 3.70953 | 0.294185 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −19.1162 | −1.50657 | ||||||||
\(162\) | − 2.35083i | − 0.184699i | ||||||||
\(163\) | − 9.93992i | − 0.778555i | −0.921121 | − | 0.389277i | \(-0.872725\pi\) | ||||
0.921121 | − | 0.389277i | \(-0.127275\pi\) | |||||||
\(164\) | −5.91973 | −0.462254 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 23.7792 | 1.84563 | ||||||||
\(167\) | − 5.57767i | − 0.431613i | −0.976436 | − | 0.215806i | \(-0.930762\pi\) | ||||
0.976436 | − | 0.215806i | \(-0.0692380\pi\) | |||||||
\(168\) | − 12.4941i | − 0.963939i | ||||||||
\(169\) | 9.48157 | 0.729352 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2.94950 | −0.225554 | ||||||||
\(172\) | − 38.5198i | − 2.93711i | ||||||||
\(173\) | 16.5682i | 1.25966i | 0.776734 | + | 0.629828i | \(0.216875\pi\) | ||||
−0.776734 | + | 0.629828i | \(0.783125\pi\) | |||||||
\(174\) | 6.00857 | 0.455508 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 4.05284 | 0.305494 | ||||||||
\(177\) | − 7.10854i | − 0.534311i | ||||||||
\(178\) | 0.675892i | 0.0506602i | ||||||||
\(179\) | 5.36021 | 0.400641 | 0.200321 | − | 0.979730i | \(-0.435802\pi\) | ||||
0.200321 | + | 0.979730i | \(0.435802\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −0.327745 | −0.0243611 | −0.0121805 | − | 0.999926i | \(-0.503877\pi\) | ||||
−0.0121805 | + | 0.999926i | \(0.503877\pi\) | |||||||
\(182\) | 15.3536i | 1.13808i | ||||||||
\(183\) | 6.43710i | 0.475844i | ||||||||
\(184\) | 19.7005 | 1.45234 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −0.982844 | −0.0720656 | ||||||||
\(187\) | − 19.8895i | − 1.45446i | ||||||||
\(188\) | − 26.4190i | − 1.92680i | ||||||||
\(189\) | 3.48189 | 0.253270 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −3.46992 | −0.251074 | −0.125537 | − | 0.992089i | \(-0.540065\pi\) | ||||
−0.125537 | + | 0.992089i | \(0.540065\pi\) | |||||||
\(192\) | − 11.9951i | − 0.865668i | ||||||||
\(193\) | − 24.3134i | − 1.75012i | −0.484018 | − | 0.875058i | \(-0.660823\pi\) | ||||
0.484018 | − | 0.875058i | \(-0.339177\pi\) | |||||||
\(194\) | 24.4699 | 1.75684 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 18.0676 | 1.29055 | ||||||||
\(197\) | − 14.9561i | − 1.06558i | −0.846248 | − | 0.532789i | \(-0.821144\pi\) | ||||
0.846248 | − | 0.532789i | \(-0.178856\pi\) | |||||||
\(198\) | 6.89053i | 0.489689i | ||||||||
\(199\) | 11.3251 | 0.802817 | 0.401408 | − | 0.915899i | \(-0.368521\pi\) | ||||
0.401408 | + | 0.915899i | \(0.368521\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −10.0415 | −0.708274 | ||||||||
\(202\) | − 18.0013i | − 1.26657i | ||||||||
\(203\) | 8.89948i | 0.624621i | ||||||||
\(204\) | 23.9290 | 1.67536 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −7.01963 | −0.489081 | ||||||||
\(207\) | 5.49019i | 0.381595i | ||||||||
\(208\) | − 2.59359i | − 0.179833i | ||||||||
\(209\) | 8.64530 | 0.598008 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 7.54283 | 0.519270 | 0.259635 | − | 0.965707i | \(-0.416398\pi\) | ||||
0.259635 | + | 0.965707i | \(0.416398\pi\) | |||||||
\(212\) | − 13.0813i | − 0.898426i | ||||||||
\(213\) | − 0.728602i | − 0.0499230i | ||||||||
\(214\) | 16.6254 | 1.13649 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −3.58831 | −0.244153 | ||||||||
\(217\) | − 1.45572i | − 0.0988208i | ||||||||
\(218\) | − 31.2711i | − 2.11795i | ||||||||
\(219\) | −3.59269 | −0.242771 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −12.7282 | −0.856190 | ||||||||
\(222\) | 12.3174i | 0.826688i | ||||||||
\(223\) | − 7.79539i | − 0.522018i | −0.965336 | − | 0.261009i | \(-0.915945\pi\) | ||||
0.965336 | − | 0.261009i | \(-0.0840553\pi\) | |||||||
\(224\) | 13.6703 | 0.913387 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 23.5630 | 1.56739 | ||||||||
\(227\) | 12.8319i | 0.851686i | 0.904797 | + | 0.425843i | \(0.140022\pi\) | ||||
−0.904797 | + | 0.425843i | \(0.859978\pi\) | |||||||
\(228\) | 10.4011i | 0.688831i | ||||||||
\(229\) | 14.5033 | 0.958405 | 0.479203 | − | 0.877704i | \(-0.340926\pi\) | ||||
0.479203 | + | 0.877704i | \(0.340926\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −10.2058 | −0.671491 | ||||||||
\(232\) | − 9.17148i | − 0.602137i | ||||||||
\(233\) | 11.3970i | 0.746646i | 0.927702 | + | 0.373323i | \(0.121782\pi\) | ||||
−0.927702 | + | 0.373323i | \(0.878218\pi\) | |||||||
\(234\) | 4.40956 | 0.288262 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −25.0676 | −1.63176 | ||||||||
\(237\) | 3.07265i | 0.199590i | ||||||||
\(238\) | 55.5428i | 3.60031i | ||||||||
\(239\) | −6.90072 | −0.446371 | −0.223185 | − | 0.974776i | \(-0.571646\pi\) | ||||
−0.223185 | + | 0.974776i | \(0.571646\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −28.4467 | −1.83242 | −0.916208 | − | 0.400704i | \(-0.868766\pi\) | ||||
−0.916208 | + | 0.400704i | \(0.868766\pi\) | |||||||
\(242\) | 5.66224i | 0.363982i | ||||||||
\(243\) | − 1.00000i | − 0.0641500i | ||||||||
\(244\) | 22.6998 | 1.45320 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −3.94632 | −0.251608 | ||||||||
\(247\) | − 5.53252i | − 0.352026i | ||||||||
\(248\) | 1.50021i | 0.0952637i | ||||||||
\(249\) | 10.1152 | 0.641028 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −12.3258 | −0.777999 | −0.389000 | − | 0.921238i | \(-0.627179\pi\) | ||||
−0.389000 | + | 0.921238i | \(0.627179\pi\) | |||||||
\(252\) | − 12.2785i | − 0.773474i | ||||||||
\(253\) | − 16.0923i | − 1.01172i | ||||||||
\(254\) | −24.8554 | −1.55957 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −23.8400 | −1.49000 | ||||||||
\(257\) | − 20.8274i | − 1.29918i | −0.760285 | − | 0.649590i | \(-0.774941\pi\) | ||||
0.760285 | − | 0.649590i | \(-0.225059\pi\) | |||||||
\(258\) | − 25.6788i | − 1.59869i | ||||||||
\(259\) | −18.2437 | −1.13361 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2.55593 | 0.158208 | ||||||||
\(262\) | 21.2188i | 1.31090i | ||||||||
\(263\) | 2.23517i | 0.137826i | 0.997623 | + | 0.0689131i | \(0.0219531\pi\) | ||||
−0.997623 | + | 0.0689131i | \(0.978047\pi\) | |||||||
\(264\) | 10.5177 | 0.647320 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −24.1426 | −1.48028 | ||||||||
\(267\) | 0.287512i | 0.0175955i | ||||||||
\(268\) | 35.4104i | 2.16303i | ||||||||
\(269\) | 19.3036 | 1.17696 | 0.588482 | − | 0.808511i | \(-0.299726\pi\) | ||||
0.588482 | + | 0.808511i | \(0.299726\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −11.9411 | −0.725372 | −0.362686 | − | 0.931911i | \(-0.618140\pi\) | ||||
−0.362686 | + | 0.931911i | \(0.618140\pi\) | |||||||
\(272\) | − 9.38252i | − 0.568899i | ||||||||
\(273\) | 6.53114i | 0.395282i | ||||||||
\(274\) | 46.2281 | 2.79274 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 19.3606 | 1.16537 | ||||||||
\(277\) | − 26.1466i | − 1.57100i | −0.618863 | − | 0.785499i | \(-0.712406\pi\) | ||||
0.618863 | − | 0.785499i | \(-0.287594\pi\) | |||||||
\(278\) | − 27.3919i | − 1.64285i | ||||||||
\(279\) | −0.418084 | −0.0250300 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 10.1219 | 0.603820 | 0.301910 | − | 0.953336i | \(-0.402376\pi\) | ||||
0.301910 | + | 0.953336i | \(0.402376\pi\) | |||||||
\(282\) | − 17.6119i | − 1.04877i | ||||||||
\(283\) | − 31.8638i | − 1.89410i | −0.321081 | − | 0.947052i | \(-0.604046\pi\) | ||||
0.321081 | − | 0.947052i | \(-0.395954\pi\) | |||||||
\(284\) | −2.56934 | −0.152462 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −12.9249 | −0.764265 | ||||||||
\(287\) | − 5.84501i | − 0.345020i | ||||||||
\(288\) | − 3.92613i | − 0.231349i | ||||||||
\(289\) | −29.0452 | −1.70854 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 10.4090 | 0.610189 | ||||||||
\(292\) | 12.6693i | 0.741412i | ||||||||
\(293\) | 16.6235i | 0.971153i | 0.874194 | + | 0.485576i | \(0.161390\pi\) | ||||
−0.874194 | + | 0.485576i | \(0.838610\pi\) | |||||||
\(294\) | 12.0446 | 0.702453 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 18.8012 | 1.09280 | ||||||||
\(297\) | 2.93111i | 0.170080i | ||||||||
\(298\) | − 17.2320i | − 0.998225i | ||||||||
\(299\) | −10.2982 | −0.595561 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 38.0336 | 2.19222 | ||||||||
\(302\) | 39.3429i | 2.26393i | ||||||||
\(303\) | − 7.65744i | − 0.439908i | ||||||||
\(304\) | 4.07827 | 0.233905 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 15.9519 | 0.911911 | ||||||||
\(307\) | 14.1643i | 0.808402i | 0.914670 | + | 0.404201i | \(0.132450\pi\) | ||||
−0.914670 | + | 0.404201i | \(0.867550\pi\) | |||||||
\(308\) | 35.9897i | 2.05070i | ||||||||
\(309\) | −2.98602 | −0.169869 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 15.0500 | 0.853406 | 0.426703 | − | 0.904392i | \(-0.359675\pi\) | ||||
0.426703 | + | 0.904392i | \(0.359675\pi\) | |||||||
\(312\) | − 6.73076i | − 0.381054i | ||||||||
\(313\) | − 3.57476i | − 0.202057i | −0.994884 | − | 0.101029i | \(-0.967787\pi\) | ||||
0.994884 | − | 0.101029i | \(-0.0322134\pi\) | |||||||
\(314\) | −18.5395 | −1.04624 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 10.8354 | 0.609539 | ||||||||
\(317\) | − 12.7820i | − 0.717907i | −0.933355 | − | 0.358954i | \(-0.883134\pi\) | ||||
0.933355 | − | 0.358954i | \(-0.116866\pi\) | |||||||
\(318\) | − 8.72047i | − 0.489020i | ||||||||
\(319\) | −7.49172 | −0.419456 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 7.07213 | 0.394728 | ||||||||
\(322\) | 44.9390i | 2.50435i | ||||||||
\(323\) | − 20.0143i | − 1.11363i | ||||||||
\(324\) | −3.52640 | −0.195911 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −23.3671 | −1.29418 | ||||||||
\(327\) | − 13.3022i | − 0.735612i | ||||||||
\(328\) | 6.02366i | 0.332601i | ||||||||
\(329\) | 26.0855 | 1.43814 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4.70504 | 0.258612 | 0.129306 | − | 0.991605i | \(-0.458725\pi\) | ||||
0.129306 | + | 0.991605i | \(0.458725\pi\) | |||||||
\(332\) | − 35.6704i | − 1.95767i | ||||||||
\(333\) | 5.23959i | 0.287128i | ||||||||
\(334\) | −13.1121 | −0.717465 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −4.81440 | −0.262647 | ||||||||
\(337\) | 17.4048i | 0.948098i | 0.880499 | + | 0.474049i | \(0.157208\pi\) | ||||
−0.880499 | + | 0.474049i | \(0.842792\pi\) | |||||||
\(338\) | − 22.2896i | − 1.21239i | ||||||||
\(339\) | 10.0233 | 0.544390 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1.22545 | 0.0663618 | ||||||||
\(342\) | 6.93377i | 0.374936i | ||||||||
\(343\) | − 6.53364i | − 0.352783i | ||||||||
\(344\) | −39.1961 | −2.11331 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 38.9490 | 2.09391 | ||||||||
\(347\) | − 14.0106i | − 0.752130i | −0.926593 | − | 0.376065i | \(-0.877277\pi\) | ||||
0.926593 | − | 0.376065i | \(-0.122723\pi\) | |||||||
\(348\) | − 9.01325i | − 0.483161i | ||||||||
\(349\) | −35.9459 | −1.92414 | −0.962069 | − | 0.272806i | \(-0.912048\pi\) | ||||
−0.962069 | + | 0.272806i | \(0.912048\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.87575 | 0.100120 | ||||||||
\(352\) | 11.5079i | 0.613373i | ||||||||
\(353\) | 8.80198i | 0.468482i | 0.972179 | + | 0.234241i | \(0.0752605\pi\) | ||||
−0.972179 | + | 0.234241i | \(0.924740\pi\) | |||||||
\(354\) | −16.7110 | −0.888178 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 1.01388 | 0.0537357 | ||||||||
\(357\) | 23.6269i | 1.25047i | ||||||||
\(358\) | − 12.6009i | − 0.665981i | ||||||||
\(359\) | −6.02962 | −0.318231 | −0.159116 | − | 0.987260i | \(-0.550864\pi\) | ||||
−0.159116 | + | 0.987260i | \(0.550864\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −10.3004 | −0.542129 | ||||||||
\(362\) | 0.770472i | 0.0404951i | ||||||||
\(363\) | 2.40861i | 0.126419i | ||||||||
\(364\) | 23.0314 | 1.20717 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 15.1325 | 0.790989 | ||||||||
\(367\) | − 28.7662i | − 1.50158i | −0.660539 | − | 0.750792i | \(-0.729672\pi\) | ||||
0.660539 | − | 0.750792i | \(-0.270328\pi\) | |||||||
\(368\) | − 7.59128i | − 0.395723i | ||||||||
\(369\) | −1.67869 | −0.0873891 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 12.9162 | 0.670574 | ||||||||
\(372\) | 1.47433i | 0.0764405i | ||||||||
\(373\) | 33.6000i | 1.73974i | 0.493278 | + | 0.869872i | \(0.335799\pi\) | ||||
−0.493278 | + | 0.869872i | \(0.664201\pi\) | |||||||
\(374\) | −46.7568 | −2.41774 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −26.8828 | −1.38637 | ||||||||
\(377\) | 4.79429i | 0.246918i | ||||||||
\(378\) | − 8.18532i | − 0.421008i | ||||||||
\(379\) | −4.63403 | −0.238034 | −0.119017 | − | 0.992892i | \(-0.537974\pi\) | ||||
−0.119017 | + | 0.992892i | \(0.537974\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −10.5730 | −0.541673 | ||||||||
\(382\) | 8.15718i | 0.417358i | ||||||||
\(383\) | − 12.9058i | − 0.659453i | −0.944076 | − | 0.329727i | \(-0.893043\pi\) | ||||
0.944076 | − | 0.329727i | \(-0.106957\pi\) | |||||||
\(384\) | −20.3461 | −1.03828 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −57.1567 | −2.90920 | ||||||||
\(387\) | − 10.9233i | − 0.555261i | ||||||||
\(388\) | − 36.7064i | − 1.86349i | ||||||||
\(389\) | 17.5246 | 0.888532 | 0.444266 | − | 0.895895i | \(-0.353465\pi\) | ||||
0.444266 | + | 0.895895i | \(0.353465\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −37.2546 | −1.88405 | ||||||||
\(392\) | − 18.3848i | − 0.928573i | ||||||||
\(393\) | 9.02608i | 0.455305i | ||||||||
\(394\) | −35.1593 | −1.77130 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 10.3363 | 0.519416 | ||||||||
\(397\) | 27.0176i | 1.35597i | 0.735074 | + | 0.677987i | \(0.237147\pi\) | ||||
−0.735074 | + | 0.677987i | \(0.762853\pi\) | |||||||
\(398\) | − 26.6234i | − 1.33451i | ||||||||
\(399\) | −10.2698 | −0.514134 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −15.9792 | −0.797965 | −0.398983 | − | 0.916958i | \(-0.630637\pi\) | ||||
−0.398983 | + | 0.916958i | \(0.630637\pi\) | |||||||
\(402\) | 23.6059i | 1.17735i | ||||||||
\(403\) | − 0.784220i | − 0.0390648i | ||||||||
\(404\) | −27.0032 | −1.34346 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 20.9212 | 1.03830 | ||||||||
\(407\) | − 15.3578i | − 0.761258i | ||||||||
\(408\) | − 24.3490i | − 1.20546i | ||||||||
\(409\) | 30.9962 | 1.53266 | 0.766331 | − | 0.642446i | \(-0.222080\pi\) | ||||
0.766331 | + | 0.642446i | \(0.222080\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 19.6646 | 0.969982 | ||||||||
\(412\) | 10.5299i | 0.518771i | ||||||||
\(413\) | − 24.7511i | − 1.21792i | ||||||||
\(414\) | 12.9065 | 0.634321 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 7.36442 | 0.361070 | ||||||||
\(417\) | − 11.6520i | − 0.570601i | ||||||||
\(418\) | − 20.3236i | − 0.994061i | ||||||||
\(419\) | −25.9153 | −1.26605 | −0.633024 | − | 0.774132i | \(-0.718186\pi\) | ||||
−0.633024 | + | 0.774132i | \(0.718186\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3.92646 | 0.191364 | 0.0956821 | − | 0.995412i | \(-0.469497\pi\) | ||||
0.0956821 | + | 0.995412i | \(0.469497\pi\) | |||||||
\(422\) | − 17.7319i | − 0.863176i | ||||||||
\(423\) | − 7.49178i | − 0.364263i | ||||||||
\(424\) | −13.3109 | −0.646436 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −1.71282 | −0.0829863 | ||||||||
\(427\) | 22.4132i | 1.08465i | ||||||||
\(428\) | − 24.9392i | − 1.20548i | ||||||||
\(429\) | −5.49801 | −0.265447 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −35.4632 | −1.70820 | −0.854101 | − | 0.520108i | \(-0.825892\pi\) | ||||
−0.854101 | + | 0.520108i | \(0.825892\pi\) | |||||||
\(432\) | 1.38270i | 0.0665251i | ||||||||
\(433\) | 10.0959i | 0.485178i | 0.970129 | + | 0.242589i | \(0.0779967\pi\) | ||||
−0.970129 | + | 0.242589i | \(0.922003\pi\) | |||||||
\(434\) | −3.42215 | −0.164269 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −46.9088 | −2.24652 | ||||||||
\(437\) | − 16.1933i | − 0.774632i | ||||||||
\(438\) | 8.44580i | 0.403556i | ||||||||
\(439\) | −7.10560 | −0.339132 | −0.169566 | − | 0.985519i | \(-0.554237\pi\) | ||||
−0.169566 | + | 0.985519i | \(0.554237\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 5.12353 | 0.243978 | ||||||||
\(442\) | 29.9218i | 1.42323i | ||||||||
\(443\) | 20.6841i | 0.982733i | 0.870953 | + | 0.491366i | \(0.163502\pi\) | ||||
−0.870953 | + | 0.491366i | \(0.836498\pi\) | |||||||
\(444\) | 18.4769 | 0.876874 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −18.3256 | −0.867744 | ||||||||
\(447\) | − 7.33020i | − 0.346706i | ||||||||
\(448\) | − 41.7654i | − 1.97323i | ||||||||
\(449\) | −19.4940 | −0.919980 | −0.459990 | − | 0.887924i | \(-0.652147\pi\) | ||||
−0.459990 | + | 0.887924i | \(0.652147\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 4.92042 | 0.231694 | ||||||||
\(452\) | − 35.3461i | − 1.66254i | ||||||||
\(453\) | 16.7358i | 0.786314i | ||||||||
\(454\) | 30.1657 | 1.41575 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 10.5837 | 0.495628 | ||||||||
\(457\) | 4.34194i | 0.203107i | 0.994830 | + | 0.101554i | \(0.0323813\pi\) | ||||
−0.994830 | + | 0.101554i | \(0.967619\pi\) | |||||||
\(458\) | − 34.0948i | − 1.59315i | ||||||||
\(459\) | 6.78566 | 0.316728 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 11.7897 | 0.549102 | 0.274551 | − | 0.961573i | \(-0.411471\pi\) | ||||
0.274551 | + | 0.961573i | \(0.411471\pi\) | |||||||
\(462\) | 23.9921i | 1.11621i | ||||||||
\(463\) | − 9.07870i | − 0.421923i | −0.977494 | − | 0.210962i | \(-0.932341\pi\) | ||||
0.977494 | − | 0.210962i | \(-0.0676595\pi\) | |||||||
\(464\) | −3.53409 | −0.164066 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 26.7925 | 1.24114 | ||||||||
\(467\) | 34.9181i | 1.61582i | 0.589307 | + | 0.807910i | \(0.299401\pi\) | ||||
−0.589307 | + | 0.807910i | \(0.700599\pi\) | |||||||
\(468\) | − 6.61463i | − 0.305762i | ||||||||
\(469\) | −34.9634 | −1.61446 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −7.88635 | −0.363384 | ||||||||
\(472\) | 25.5076i | 1.17408i | ||||||||
\(473\) | 32.0173i | 1.47216i | ||||||||
\(474\) | 7.22328 | 0.331776 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 83.3179 | 3.81887 | ||||||||
\(477\) | − 3.70953i | − 0.169848i | ||||||||
\(478\) | 16.2224i | 0.741996i | ||||||||
\(479\) | 8.64649 | 0.395068 | 0.197534 | − | 0.980296i | \(-0.436707\pi\) | ||||
0.197534 | + | 0.980296i | \(0.436707\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −9.82814 | −0.448125 | ||||||||
\(482\) | 66.8734i | 3.04600i | ||||||||
\(483\) | 19.1162i | 0.869819i | ||||||||
\(484\) | 8.49373 | 0.386079 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −2.35083 | −0.106636 | ||||||||
\(487\) | − 2.84462i | − 0.128902i | −0.997921 | − | 0.0644510i | \(-0.979470\pi\) | ||||
0.997921 | − | 0.0644510i | \(-0.0205296\pi\) | |||||||
\(488\) | − 23.0983i | − 1.04561i | ||||||||
\(489\) | −9.93992 | −0.449499 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 36.8041 | 1.66095 | 0.830473 | − | 0.557059i | \(-0.188070\pi\) | ||||
0.830473 | + | 0.557059i | \(0.188070\pi\) | |||||||
\(492\) | 5.91973i | 0.266882i | ||||||||
\(493\) | 17.3437i | 0.781121i | ||||||||
\(494\) | −13.0060 | −0.585168 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0.578084 | 0.0259567 | ||||||||
\(497\) | − 2.53691i | − 0.113796i | ||||||||
\(498\) | − 23.7792i | − 1.06557i | ||||||||
\(499\) | −5.85775 | −0.262229 | −0.131114 | − | 0.991367i | \(-0.541856\pi\) | ||||
−0.131114 | + | 0.991367i | \(0.541856\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −5.57767 | −0.249192 | ||||||||
\(502\) | 28.9759i | 1.29326i | ||||||||
\(503\) | − 30.2874i | − 1.35045i | −0.737613 | − | 0.675223i | \(-0.764047\pi\) | ||||
0.737613 | − | 0.675223i | \(-0.235953\pi\) | |||||||
\(504\) | −12.4941 | −0.556530 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −37.8304 | −1.68177 | ||||||||
\(507\) | − 9.48157i | − 0.421091i | ||||||||
\(508\) | 37.2848i | 1.65424i | ||||||||
\(509\) | −15.1430 | −0.671201 | −0.335601 | − | 0.942004i | \(-0.608939\pi\) | ||||
−0.335601 | + | 0.942004i | \(0.608939\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −12.5093 | −0.553380 | ||||||||
\(512\) | 15.3517i | 0.678457i | ||||||||
\(513\) | 2.94950i | 0.130224i | ||||||||
\(514\) | −48.9618 | −2.15961 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −38.5198 | −1.69574 | ||||||||
\(517\) | 21.9592i | 0.965765i | ||||||||
\(518\) | 42.8877i | 1.88438i | ||||||||
\(519\) | 16.5682 | 0.727263 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 39.0832 | 1.71227 | 0.856134 | − | 0.516754i | \(-0.172860\pi\) | ||||
0.856134 | + | 0.516754i | \(0.172860\pi\) | |||||||
\(522\) | − 6.00857i | − 0.262988i | ||||||||
\(523\) | − 38.7976i | − 1.69650i | −0.529594 | − | 0.848251i | \(-0.677656\pi\) | ||||
0.529594 | − | 0.848251i | \(-0.322344\pi\) | |||||||
\(524\) | 31.8296 | 1.39048 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 5.25449 | 0.229107 | ||||||||
\(527\) | − 2.83698i | − 0.123581i | ||||||||
\(528\) | − 4.05284i | − 0.176377i | ||||||||
\(529\) | −7.14224 | −0.310532 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −7.10854 | −0.308484 | ||||||||
\(532\) | 36.2155i | 1.57014i | ||||||||
\(533\) | − 3.14880i | − 0.136390i | ||||||||
\(534\) | 0.675892 | 0.0292487 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 36.0320 | 1.55635 | ||||||||
\(537\) | − 5.36021i | − 0.231310i | ||||||||
\(538\) | − 45.3796i | − 1.95645i | ||||||||
\(539\) | −15.0176 | −0.646855 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 14.2280 | 0.611710 | 0.305855 | − | 0.952078i | \(-0.401058\pi\) | ||||
0.305855 | + | 0.952078i | \(0.401058\pi\) | |||||||
\(542\) | 28.0716i | 1.20578i | ||||||||
\(543\) | 0.327745i | 0.0140649i | ||||||||
\(544\) | 26.6414 | 1.14224 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 15.3536 | 0.657073 | ||||||||
\(547\) | − 39.3229i | − 1.68133i | −0.541559 | − | 0.840663i | \(-0.682166\pi\) | ||||
0.541559 | − | 0.840663i | \(-0.317834\pi\) | |||||||
\(548\) | − 69.3452i | − 2.96228i | ||||||||
\(549\) | 6.43710 | 0.274729 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −7.53873 | −0.321161 | ||||||||
\(552\) | − 19.7005i | − 0.838509i | ||||||||
\(553\) | 10.6986i | 0.454952i | ||||||||
\(554\) | −61.4662 | −2.61145 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −41.0896 | −1.74259 | ||||||||
\(557\) | − 35.3849i | − 1.49931i | −0.661830 | − | 0.749654i | \(-0.730220\pi\) | ||||
0.661830 | − | 0.749654i | \(-0.269780\pi\) | |||||||
\(558\) | 0.982844i | 0.0416071i | ||||||||
\(559\) | 20.4893 | 0.866605 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −19.8895 | −0.839735 | ||||||||
\(562\) | − 23.7948i | − 1.00372i | ||||||||
\(563\) | 15.0386i | 0.633800i | 0.948459 | + | 0.316900i | \(0.102642\pi\) | ||||
−0.948459 | + | 0.316900i | \(0.897358\pi\) | |||||||
\(564\) | −26.4190 | −1.11244 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −74.9063 | −3.14855 | ||||||||
\(567\) | − 3.48189i | − 0.146225i | ||||||||
\(568\) | 2.61445i | 0.109700i | ||||||||
\(569\) | 2.72409 | 0.114200 | 0.0570998 | − | 0.998368i | \(-0.481815\pi\) | ||||
0.0570998 | + | 0.998368i | \(0.481815\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 12.6236 | 0.528282 | 0.264141 | − | 0.964484i | \(-0.414912\pi\) | ||||
0.264141 | + | 0.964484i | \(0.414912\pi\) | |||||||
\(572\) | 19.3882i | 0.810661i | ||||||||
\(573\) | 3.46992i | 0.144958i | ||||||||
\(574\) | −13.7406 | −0.573522 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −11.9951 | −0.499794 | ||||||||
\(577\) | 23.5844i | 0.981831i | 0.871207 | + | 0.490915i | \(0.163338\pi\) | ||||
−0.871207 | + | 0.490915i | \(0.836662\pi\) | |||||||
\(578\) | 68.2803i | 2.84009i | ||||||||
\(579\) | −24.3134 | −1.01043 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 35.2201 | 1.46118 | ||||||||
\(582\) | − 24.4699i | − 1.01431i | ||||||||
\(583\) | 10.8730i | 0.450315i | ||||||||
\(584\) | 12.8917 | 0.533461 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 39.0789 | 1.61434 | ||||||||
\(587\) | 22.6772i | 0.935988i | 0.883732 | + | 0.467994i | \(0.155023\pi\) | ||||
−0.883732 | + | 0.467994i | \(0.844977\pi\) | |||||||
\(588\) | − 18.0676i | − 0.745097i | ||||||||
\(589\) | 1.23314 | 0.0508106 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −14.9561 | −0.615212 | ||||||||
\(592\) | − 7.24477i | − 0.297758i | ||||||||
\(593\) | − 8.74287i | − 0.359027i | −0.983756 | − | 0.179513i | \(-0.942548\pi\) | ||||
0.983756 | − | 0.179513i | \(-0.0574523\pi\) | |||||||
\(594\) | 6.89053 | 0.282722 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −25.8492 | −1.05882 | ||||||||
\(597\) | − 11.3251i | − 0.463506i | ||||||||
\(598\) | 24.2094i | 0.989994i | ||||||||
\(599\) | −16.3209 | −0.666854 | −0.333427 | − | 0.942776i | \(-0.608205\pi\) | ||||
−0.333427 | + | 0.942776i | \(0.608205\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 36.2713 | 1.47954 | 0.739768 | − | 0.672862i | \(-0.234935\pi\) | ||||
0.739768 | + | 0.672862i | \(0.234935\pi\) | |||||||
\(602\) | − 89.4105i | − 3.64410i | ||||||||
\(603\) | 10.0415i | 0.408922i | ||||||||
\(604\) | 59.0170 | 2.40137 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −18.0013 | −0.731254 | ||||||||
\(607\) | 16.6820i | 0.677102i | 0.940948 | + | 0.338551i | \(0.109937\pi\) | ||||
−0.940948 | + | 0.338551i | \(0.890063\pi\) | |||||||
\(608\) | 11.5801i | 0.469636i | ||||||||
\(609\) | 8.89948 | 0.360625 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 14.0527 | 0.568511 | ||||||||
\(612\) | − 23.9290i | − 0.967271i | ||||||||
\(613\) | 24.7967i | 1.00153i | 0.865583 | + | 0.500765i | \(0.166948\pi\) | ||||
−0.865583 | + | 0.500765i | \(0.833052\pi\) | |||||||
\(614\) | 33.2980 | 1.34380 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 36.6215 | 1.47552 | ||||||||
\(617\) | − 27.9669i | − 1.12591i | −0.826489 | − | 0.562953i | \(-0.809665\pi\) | ||||
0.826489 | − | 0.562953i | \(-0.190335\pi\) | |||||||
\(618\) | 7.01963i | 0.282371i | ||||||||
\(619\) | −27.2686 | −1.09602 | −0.548009 | − | 0.836473i | \(-0.684614\pi\) | ||||
−0.548009 | + | 0.836473i | \(0.684614\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 5.49019 | 0.220314 | ||||||||
\(622\) | − 35.3799i | − 1.41861i | ||||||||
\(623\) | 1.00108i | 0.0401076i | ||||||||
\(624\) | −2.59359 | −0.103827 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −8.40365 | −0.335878 | ||||||||
\(627\) | − 8.64530i | − 0.345260i | ||||||||
\(628\) | 27.8104i | 1.10976i | ||||||||
\(629\) | −35.5541 | −1.41763 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 42.2603 | 1.68235 | 0.841177 | − | 0.540759i | \(-0.181863\pi\) | ||||
0.841177 | + | 0.540759i | \(0.181863\pi\) | |||||||
\(632\) | − 11.0256i | − 0.438575i | ||||||||
\(633\) | − 7.54283i | − 0.299801i | ||||||||
\(634\) | −30.0482 | −1.19337 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −13.0813 | −0.518707 | ||||||||
\(637\) | 9.61045i | 0.380780i | ||||||||
\(638\) | 17.6118i | 0.697256i | ||||||||
\(639\) | −0.728602 | −0.0288230 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 45.8456 | 1.81079 | 0.905396 | − | 0.424569i | \(-0.139574\pi\) | ||||
0.905396 | + | 0.424569i | \(0.139574\pi\) | |||||||
\(642\) | − 16.6254i | − 0.656151i | ||||||||
\(643\) | − 46.6710i | − 1.84052i | −0.391304 | − | 0.920261i | \(-0.627976\pi\) | ||||
0.391304 | − | 0.920261i | \(-0.372024\pi\) | |||||||
\(644\) | 67.4115 | 2.65639 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −47.0502 | −1.85117 | ||||||||
\(647\) | 12.1264i | 0.476740i | 0.971174 | + | 0.238370i | \(0.0766131\pi\) | ||||
−0.971174 | + | 0.238370i | \(0.923387\pi\) | |||||||
\(648\) | 3.58831i | 0.140962i | ||||||||
\(649\) | 20.8359 | 0.817880 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1.45572 | −0.0570542 | ||||||||
\(652\) | 35.0521i | 1.37275i | ||||||||
\(653\) | − 1.72017i | − 0.0673154i | −0.999433 | − | 0.0336577i | \(-0.989284\pi\) | ||||
0.999433 | − | 0.0336577i | \(-0.0107156\pi\) | |||||||
\(654\) | −31.2711 | −1.22280 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 2.32112 | 0.0906246 | ||||||||
\(657\) | 3.59269i | 0.140164i | ||||||||
\(658\) | − 61.3226i | − 2.39060i | ||||||||
\(659\) | −5.47947 | −0.213450 | −0.106725 | − | 0.994289i | \(-0.534036\pi\) | ||||
−0.106725 | + | 0.994289i | \(0.534036\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 0.797448 | 0.0310171 | 0.0155086 | − | 0.999880i | \(-0.495063\pi\) | ||||
0.0155086 | + | 0.999880i | \(0.495063\pi\) | |||||||
\(662\) | − 11.0607i | − 0.429888i | ||||||||
\(663\) | 12.7282i | 0.494322i | ||||||||
\(664\) | −36.2966 | −1.40858 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 12.3174 | 0.477289 | ||||||||
\(667\) | 14.0326i | 0.543344i | ||||||||
\(668\) | 19.6691i | 0.761020i | ||||||||
\(669\) | −7.79539 | −0.301387 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −18.8678 | −0.728384 | ||||||||
\(672\) | − 13.6703i | − 0.527344i | ||||||||
\(673\) | − 51.3280i | − 1.97855i | −0.146074 | − | 0.989274i | \(-0.546664\pi\) | ||||
0.146074 | − | 0.989274i | \(-0.453336\pi\) | |||||||
\(674\) | 40.9156 | 1.57601 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −33.4358 | −1.28599 | ||||||||
\(677\) | − 15.0929i | − 0.580069i | −0.957016 | − | 0.290034i | \(-0.906333\pi\) | ||||
0.957016 | − | 0.290034i | \(-0.0936667\pi\) | |||||||
\(678\) | − 23.5630i | − 0.904933i | ||||||||
\(679\) | 36.2431 | 1.39088 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 12.8319 | 0.491721 | ||||||||
\(682\) | − 2.88082i | − 0.110312i | ||||||||
\(683\) | − 10.8602i | − 0.415555i | −0.978176 | − | 0.207777i | \(-0.933377\pi\) | ||||
0.978176 | − | 0.207777i | \(-0.0666229\pi\) | |||||||
\(684\) | 10.4011 | 0.397697 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −15.3595 | −0.586428 | ||||||||
\(687\) | − 14.5033i | − 0.553336i | ||||||||
\(688\) | 15.1036i | 0.575819i | ||||||||
\(689\) | 6.95814 | 0.265084 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 8.44552 | 0.321283 | 0.160641 | − | 0.987013i | \(-0.448644\pi\) | ||||
0.160641 | + | 0.987013i | \(0.448644\pi\) | |||||||
\(692\) | − 58.4261i | − 2.22103i | ||||||||
\(693\) | 10.2058i | 0.387686i | ||||||||
\(694\) | −32.9366 | −1.25026 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −9.17148 | −0.347644 | ||||||||
\(697\) | − 11.3910i | − 0.431466i | ||||||||
\(698\) | 84.5026i | 3.19847i | ||||||||
\(699\) | 11.3970 | 0.431076 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 48.9399 | 1.84843 | 0.924216 | − | 0.381869i | \(-0.124719\pi\) | ||||
0.924216 | + | 0.381869i | \(0.124719\pi\) | |||||||
\(702\) | − 4.40956i | − 0.166428i | ||||||||
\(703\) | − 15.4542i | − 0.582865i | ||||||||
\(704\) | 35.1588 | 1.32510 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 20.6920 | 0.778752 | ||||||||
\(707\) | − 26.6623i | − 1.00274i | ||||||||
\(708\) | 25.0676i | 0.942097i | ||||||||
\(709\) | −24.7834 | −0.930762 | −0.465381 | − | 0.885111i | \(-0.654083\pi\) | ||||
−0.465381 | + | 0.885111i | \(0.654083\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 3.07265 | 0.115233 | ||||||||
\(712\) | − 1.03168i | − 0.0386639i | ||||||||
\(713\) | − 2.29536i | − 0.0859620i | ||||||||
\(714\) | 55.5428 | 2.07864 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −18.9023 | −0.706410 | ||||||||
\(717\) | 6.90072i | 0.257712i | ||||||||
\(718\) | 14.1746i | 0.528992i | ||||||||
\(719\) | 18.2171 | 0.679382 | 0.339691 | − | 0.940537i | \(-0.389678\pi\) | ||||
0.339691 | + | 0.940537i | \(0.389678\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −10.3970 | −0.387204 | ||||||||
\(722\) | 24.2146i | 0.901174i | ||||||||
\(723\) | 28.4467i | 1.05795i | ||||||||
\(724\) | 1.15576 | 0.0429534 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 5.66224 | 0.210145 | ||||||||
\(727\) | − 16.6699i | − 0.618253i | −0.951021 | − | 0.309127i | \(-0.899963\pi\) | ||||
0.951021 | − | 0.309127i | \(-0.100037\pi\) | |||||||
\(728\) | − 23.4357i | − 0.868586i | ||||||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 74.1216 | 2.74149 | ||||||||
\(732\) | − 22.6998i | − 0.839008i | ||||||||
\(733\) | 20.0644i | 0.741094i | 0.928814 | + | 0.370547i | \(0.120830\pi\) | ||||
−0.928814 | + | 0.370547i | \(0.879170\pi\) | |||||||
\(734\) | −67.6245 | −2.49606 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 21.5552 | 0.794535 | ||||||||
\(737\) | − 29.4328i | − 1.08417i | ||||||||
\(738\) | 3.94632i | 0.145266i | ||||||||
\(739\) | 34.0571 | 1.25281 | 0.626406 | − | 0.779497i | \(-0.284525\pi\) | ||||
0.626406 | + | 0.779497i | \(0.284525\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −5.53252 | −0.203242 | ||||||||
\(742\) | − 30.3637i | − 1.11469i | ||||||||
\(743\) | − 38.5355i | − 1.41373i | −0.707348 | − | 0.706865i | \(-0.750109\pi\) | ||||
0.707348 | − | 0.706865i | \(-0.249891\pi\) | |||||||
\(744\) | 1.50021 | 0.0550005 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 78.9880 | 2.89195 | ||||||||
\(747\) | − 10.1152i | − 0.370097i | ||||||||
\(748\) | 70.1383i | 2.56451i | ||||||||
\(749\) | 24.6244 | 0.899754 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −36.0351 | −1.31494 | −0.657470 | − | 0.753481i | \(-0.728373\pi\) | ||||
−0.657470 | + | 0.753481i | \(0.728373\pi\) | |||||||
\(752\) | 10.3589i | 0.377749i | ||||||||
\(753\) | 12.3258i | 0.449178i | ||||||||
\(754\) | 11.2706 | 0.410449 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −12.2785 | −0.446566 | ||||||||
\(757\) | − 35.0131i | − 1.27257i | −0.771453 | − | 0.636287i | \(-0.780470\pi\) | ||||
0.771453 | − | 0.636287i | \(-0.219530\pi\) | |||||||
\(758\) | 10.8938i | 0.395681i | ||||||||
\(759\) | −16.0923 | −0.584115 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 31.3577 | 1.13672 | 0.568358 | − | 0.822781i | \(-0.307579\pi\) | ||||
0.568358 | + | 0.822781i | \(0.307579\pi\) | |||||||
\(762\) | 24.8554i | 0.900416i | ||||||||
\(763\) | − 46.3166i | − 1.67678i | ||||||||
\(764\) | 12.2363 | 0.442694 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −30.3392 | −1.09620 | ||||||||
\(767\) | − 13.3338i | − 0.481456i | ||||||||
\(768\) | 23.8400i | 0.860253i | ||||||||
\(769\) | −2.39815 | −0.0864793 | −0.0432397 | − | 0.999065i | \(-0.513768\pi\) | ||||
−0.0432397 | + | 0.999065i | \(0.513768\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −20.8274 | −0.750082 | ||||||||
\(772\) | 85.7388i | 3.08581i | ||||||||
\(773\) | − 10.9226i | − 0.392858i | −0.980518 | − | 0.196429i | \(-0.937065\pi\) | ||||
0.980518 | − | 0.196429i | \(-0.0629345\pi\) | |||||||
\(774\) | −25.6788 | −0.923004 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −37.3508 | −1.34082 | ||||||||
\(777\) | 18.2437i | 0.654487i | ||||||||
\(778\) | − 41.1973i | − 1.47700i | ||||||||
\(779\) | 4.95130 | 0.177399 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2.13561 | 0.0764181 | ||||||||
\(782\) | 87.5792i | 3.13183i | ||||||||
\(783\) | − 2.55593i | − 0.0913417i | ||||||||
\(784\) | −7.08430 | −0.253011 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 21.2188 | 0.756848 | ||||||||
\(787\) | − 11.5724i | − 0.412511i | −0.978498 | − | 0.206256i | \(-0.933872\pi\) | ||||
0.978498 | − | 0.206256i | \(-0.0661278\pi\) | |||||||
\(788\) | 52.7412i | 1.87883i | ||||||||
\(789\) | 2.23517 | 0.0795740 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 34.8999 | 1.24090 | ||||||||
\(792\) | − 10.5177i | − 0.373731i | ||||||||
\(793\) | 12.0744i | 0.428773i | ||||||||
\(794\) | 63.5137 | 2.25402 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −39.9369 | −1.41553 | ||||||||
\(797\) | − 21.8923i | − 0.775467i | −0.921772 | − | 0.387733i | \(-0.873258\pi\) | ||||
0.921772 | − | 0.387733i | \(-0.126742\pi\) | |||||||
\(798\) | 24.1426i | 0.854639i | ||||||||
\(799\) | 50.8367 | 1.79847 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0.287512 | 0.0101587 | ||||||||
\(802\) | 37.5645i | 1.32645i | ||||||||
\(803\) | − 10.5306i | − 0.371615i | ||||||||
\(804\) | 35.4104 | 1.24883 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −1.84357 | −0.0649369 | ||||||||
\(807\) | − 19.3036i | − 0.679520i | ||||||||
\(808\) | 27.4772i | 0.966646i | ||||||||
\(809\) | 21.5498 | 0.757652 | 0.378826 | − | 0.925468i | \(-0.376328\pi\) | ||||
0.378826 | + | 0.925468i | \(0.376328\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −43.9615 | −1.54370 | −0.771848 | − | 0.635807i | \(-0.780667\pi\) | ||||
−0.771848 | + | 0.635807i | \(0.780667\pi\) | |||||||
\(812\) | − 31.3831i | − 1.10133i | ||||||||
\(813\) | 11.9411i | 0.418794i | ||||||||
\(814\) | −36.1036 | −1.26543 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −9.38252 | −0.328454 | ||||||||
\(817\) | 32.2182i | 1.12717i | ||||||||
\(818\) | − 72.8667i | − 2.54772i | ||||||||
\(819\) | 6.53114 | 0.228216 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 33.5061 | 1.16937 | 0.584686 | − | 0.811260i | \(-0.301218\pi\) | ||||
0.584686 | + | 0.811260i | \(0.301218\pi\) | |||||||
\(822\) | − 46.2281i | − 1.61239i | ||||||||
\(823\) | 55.9860i | 1.95155i | 0.218781 | + | 0.975774i | \(0.429792\pi\) | ||||
−0.218781 | + | 0.975774i | \(0.570208\pi\) | |||||||
\(824\) | 10.7148 | 0.373266 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −58.1857 | −2.02454 | ||||||||
\(827\) | 40.8100i | 1.41910i | 0.704653 | + | 0.709552i | \(0.251103\pi\) | ||||
−0.704653 | + | 0.709552i | \(0.748897\pi\) | |||||||
\(828\) | − 19.3606i | − 0.672828i | ||||||||
\(829\) | −0.122914 | −0.00426896 | −0.00213448 | − | 0.999998i | \(-0.500679\pi\) | ||||
−0.00213448 | + | 0.999998i | \(0.500679\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −26.1466 | −0.907016 | ||||||||
\(832\) | − 22.4997i | − 0.780036i | ||||||||
\(833\) | 34.7666i | 1.20459i | ||||||||
\(834\) | −27.3919 | −0.948503 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −30.4868 | −1.05441 | ||||||||
\(837\) | 0.418084i | 0.0144511i | ||||||||
\(838\) | 60.9226i | 2.10454i | ||||||||
\(839\) | −14.8083 | −0.511241 | −0.255620 | − | 0.966777i | \(-0.582280\pi\) | ||||
−0.255620 | + | 0.966777i | \(0.582280\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −22.4672 | −0.774731 | ||||||||
\(842\) | − 9.23045i | − 0.318102i | ||||||||
\(843\) | − 10.1219i | − 0.348616i | ||||||||
\(844\) | −26.5990 | −0.915577 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −17.6119 | −0.605509 | ||||||||
\(847\) | 8.38651i | 0.288164i | ||||||||
\(848\) | 5.12916i | 0.176136i | ||||||||
\(849\) | −31.8638 | −1.09356 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −28.7664 | −0.986098 | ||||||||
\(852\) | 2.56934i | 0.0880242i | ||||||||
\(853\) | 7.26474i | 0.248740i | 0.992236 | + | 0.124370i | \(0.0396910\pi\) | ||||
−0.992236 | + | 0.124370i | \(0.960309\pi\) | |||||||
\(854\) | 52.6897 | 1.80301 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −25.3770 | −0.867367 | ||||||||
\(857\) | 26.8175i | 0.916068i | 0.888935 | + | 0.458034i | \(0.151446\pi\) | ||||
−0.888935 | + | 0.458034i | \(0.848554\pi\) | |||||||
\(858\) | 12.9249i | 0.441249i | ||||||||
\(859\) | 20.6038 | 0.702991 | 0.351496 | − | 0.936190i | \(-0.385673\pi\) | ||||
0.351496 | + | 0.936190i | \(0.385673\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −5.84501 | −0.199197 | ||||||||
\(862\) | 83.3679i | 2.83952i | ||||||||
\(863\) | 13.7488i | 0.468015i | 0.972235 | + | 0.234008i | \(0.0751840\pi\) | ||||
−0.972235 | + | 0.234008i | \(0.924816\pi\) | |||||||
\(864\) | −3.92613 | −0.133570 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 23.7338 | 0.806506 | ||||||||
\(867\) | 29.0452i | 0.986427i | ||||||||
\(868\) | 5.13346i | 0.174241i | ||||||||
\(869\) | −9.00627 | −0.305517 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −18.8353 | −0.638211 | ||||||||
\(872\) | 47.7323i | 1.61642i | ||||||||
\(873\) | − 10.4090i | − 0.352293i | ||||||||
\(874\) | −38.0678 | −1.28766 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 12.6693 | 0.428055 | ||||||||
\(877\) | − 22.0430i | − 0.744339i | −0.928165 | − | 0.372170i | \(-0.878614\pi\) | ||||
0.928165 | − | 0.372170i | \(-0.121386\pi\) | |||||||
\(878\) | 16.7041i | 0.563735i | ||||||||
\(879\) | 16.6235 | 0.560695 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −9.03929 | −0.304541 | −0.152271 | − | 0.988339i | \(-0.548659\pi\) | ||||
−0.152271 | + | 0.988339i | \(0.548659\pi\) | |||||||
\(882\) | − 12.0446i | − 0.405561i | ||||||||
\(883\) | − 1.60120i | − 0.0538848i | −0.999637 | − | 0.0269424i | \(-0.991423\pi\) | ||||
0.999637 | − | 0.0269424i | \(-0.00857708\pi\) | |||||||
\(884\) | 44.8847 | 1.50963 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 48.6249 | 1.63358 | ||||||||
\(887\) | − 17.4253i | − 0.585083i | −0.956253 | − | 0.292541i | \(-0.905499\pi\) | ||||
0.956253 | − | 0.292541i | \(-0.0945009\pi\) | |||||||
\(888\) | − 18.8012i | − 0.630929i | ||||||||
\(889\) | −36.8141 | −1.23471 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 2.93111 | 0.0981958 | ||||||||
\(892\) | 27.4897i | 0.920423i | ||||||||
\(893\) | 22.0970i | 0.739448i | ||||||||
\(894\) | −17.2320 | −0.576326 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −70.8427 | −2.36669 | ||||||||
\(897\) | 10.2982i | 0.343847i | ||||||||
\(898\) | 45.8272i | 1.52927i | ||||||||
\(899\) | −1.06860 | −0.0356397 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 25.1716 | 0.838588 | ||||||||
\(902\) | − 11.5671i | − 0.385141i | ||||||||
\(903\) | − 38.0336i | − 1.26568i | ||||||||
\(904\) | −35.9666 | −1.19623 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 39.3429 | 1.30708 | ||||||||
\(907\) | 20.8690i | 0.692942i | 0.938061 | + | 0.346471i | \(0.112620\pi\) | ||||
−0.938061 | + | 0.346471i | \(0.887380\pi\) | |||||||
\(908\) | − 45.2506i | − 1.50169i | ||||||||
\(909\) | −7.65744 | −0.253981 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 49.1748 | 1.62923 | 0.814617 | − | 0.580000i | \(-0.196947\pi\) | ||||
0.814617 | + | 0.580000i | \(0.196947\pi\) | |||||||
\(912\) | − 4.07827i | − 0.135045i | ||||||||
\(913\) | 29.6489i | 0.981234i | ||||||||
\(914\) | 10.2072 | 0.337623 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −51.1445 | −1.68986 | ||||||||
\(917\) | 31.4278i | 1.03784i | ||||||||
\(918\) | − 15.9519i | − 0.526492i | ||||||||
\(919\) | 11.1959 | 0.369318 | 0.184659 | − | 0.982803i | \(-0.440882\pi\) | ||||
0.184659 | + | 0.982803i | \(0.440882\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 14.1643 | 0.466731 | ||||||||
\(922\) | − 27.7156i | − 0.912765i | ||||||||
\(923\) | − 1.36667i | − 0.0449846i | ||||||||
\(924\) | 35.9897 | 1.18397 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −21.3425 | −0.701357 | ||||||||
\(927\) | 2.98602i | 0.0980738i | ||||||||
\(928\) | − 10.0349i | − 0.329413i | ||||||||
\(929\) | −48.2290 | −1.58234 | −0.791171 | − | 0.611596i | \(-0.790528\pi\) | ||||
−0.791171 | + | 0.611596i | \(0.790528\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −15.1119 | −0.495271 | ||||||||
\(932\) | − 40.1906i | − 1.31649i | ||||||||
\(933\) | − 15.0500i | − 0.492714i | ||||||||
\(934\) | 82.0866 | 2.68596 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −6.73076 | −0.220002 | ||||||||
\(937\) | − 50.5397i | − 1.65106i | −0.564359 | − | 0.825529i | \(-0.690877\pi\) | ||||
0.564359 | − | 0.825529i | \(-0.309123\pi\) | |||||||
\(938\) | 82.1930i | 2.68370i | ||||||||
\(939\) | −3.57476 | −0.116658 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −38.1644 | −1.24412 | −0.622061 | − | 0.782969i | \(-0.713705\pi\) | ||||
−0.622061 | + | 0.782969i | \(0.713705\pi\) | |||||||
\(942\) | 18.5395i | 0.604049i | ||||||||
\(943\) | − 9.21634i | − 0.300125i | ||||||||
\(944\) | 9.82896 | 0.319906 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 75.2672 | 2.44715 | ||||||||
\(947\) | − 24.5190i | − 0.796759i | −0.917221 | − | 0.398380i | \(-0.869573\pi\) | ||||
0.917221 | − | 0.398380i | \(-0.130427\pi\) | |||||||
\(948\) | − 10.8354i | − 0.351917i | ||||||||
\(949\) | −6.73897 | −0.218756 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −12.7820 | −0.414484 | ||||||||
\(952\) | − 84.7806i | − 2.74775i | ||||||||
\(953\) | 13.0019i | 0.421173i | 0.977575 | + | 0.210586i | \(0.0675373\pi\) | ||||
−0.977575 | + | 0.210586i | \(0.932463\pi\) | |||||||
\(954\) | −8.72047 | −0.282336 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 24.3347 | 0.787041 | ||||||||
\(957\) | 7.49172i | 0.242173i | ||||||||
\(958\) | − 20.3264i | − 0.656717i | ||||||||
\(959\) | 68.4698 | 2.21101 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.8252 | −0.994361 | ||||||||
\(962\) | 23.1043i | 0.744912i | ||||||||
\(963\) | − 7.07213i | − 0.227896i | ||||||||
\(964\) | 100.315 | 3.23091 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 44.9390 | 1.44589 | ||||||||
\(967\) | 43.3212i | 1.39312i | 0.717500 | + | 0.696559i | \(0.245286\pi\) | ||||
−0.717500 | + | 0.696559i | \(0.754714\pi\) | |||||||
\(968\) | − 8.64284i | − 0.277791i | ||||||||
\(969\) | −20.0143 | −0.642952 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −29.5324 | −0.947741 | −0.473870 | − | 0.880595i | \(-0.657143\pi\) | ||||
−0.473870 | + | 0.880595i | \(0.657143\pi\) | |||||||
\(972\) | 3.52640i | 0.113109i | ||||||||
\(973\) | − 40.5709i | − 1.30064i | ||||||||
\(974\) | −6.68721 | −0.214272 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −8.90056 | −0.284900 | ||||||||
\(977\) | 60.6153i | 1.93926i | 0.244583 | + | 0.969628i | \(0.421349\pi\) | ||||
−0.244583 | + | 0.969628i | \(0.578651\pi\) | |||||||
\(978\) | 23.3671i | 0.747196i | ||||||||
\(979\) | −0.842729 | −0.0269337 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −13.3022 | −0.424706 | ||||||||
\(982\) | − 86.5202i | − 2.76097i | ||||||||
\(983\) | − 40.2796i | − 1.28472i | −0.766404 | − | 0.642359i | \(-0.777956\pi\) | ||||
0.766404 | − | 0.642359i | \(-0.222044\pi\) | |||||||
\(984\) | 6.02366 | 0.192027 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 40.7721 | 1.29845 | ||||||||
\(987\) | − 26.0855i | − 0.830311i | ||||||||
\(988\) | 19.5099i | 0.620692i | ||||||||
\(989\) | 59.9709 | 1.90696 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 38.1495 | 1.21186 | 0.605930 | − | 0.795518i | \(-0.292801\pi\) | ||||
0.605930 | + | 0.795518i | \(0.292801\pi\) | |||||||
\(992\) | 1.64145i | 0.0521161i | ||||||||
\(993\) | − 4.70504i | − 0.149310i | ||||||||
\(994\) | −5.96384 | −0.189162 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −35.6704 | −1.13026 | ||||||||
\(997\) | − 26.5777i | − 0.841724i | −0.907125 | − | 0.420862i | \(-0.861728\pi\) | ||||
0.907125 | − | 0.420862i | \(-0.138272\pi\) | |||||||
\(998\) | 13.7706i | 0.435900i | ||||||||
\(999\) | 5.23959 | 0.165773 |
(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 | 1875.2.b.h.1249.2 | 16 | ||
5.2 | odd | 4 | 1875.2.a.p.1.7 | 8 | |||
5.3 | odd | 4 | 1875.2.a.m.1.2 | 8 | |||
5.4 | even | 2 | inner | 1875.2.b.h.1249.15 | 16 | ||
15.2 | even | 4 | 5625.2.a.t.1.2 | 8 | |||
15.8 | even | 4 | 5625.2.a.bd.1.7 | 8 | |||
25.2 | odd | 20 | 375.2.g.d.226.4 | 16 | |||
25.9 | even | 10 | 75.2.i.a.19.1 | yes | 16 | ||
25.11 | even | 5 | 75.2.i.a.4.1 | ✓ | 16 | ||
25.12 | odd | 20 | 375.2.g.d.151.4 | 16 | |||
25.13 | odd | 20 | 375.2.g.e.151.1 | 16 | |||
25.14 | even | 10 | 375.2.i.c.274.4 | 16 | |||
25.16 | even | 5 | 375.2.i.c.349.4 | 16 | |||
25.23 | odd | 20 | 375.2.g.e.226.1 | 16 | |||
75.11 | odd | 10 | 225.2.m.b.154.4 | 16 | |||
75.59 | odd | 10 | 225.2.m.b.19.4 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
75.2.i.a.4.1 | ✓ | 16 | 25.11 | even | 5 | ||
75.2.i.a.19.1 | yes | 16 | 25.9 | even | 10 | ||
225.2.m.b.19.4 | 16 | 75.59 | odd | 10 | |||
225.2.m.b.154.4 | 16 | 75.11 | odd | 10 | |||
375.2.g.d.151.4 | 16 | 25.12 | odd | 20 | |||
375.2.g.d.226.4 | 16 | 25.2 | odd | 20 | |||
375.2.g.e.151.1 | 16 | 25.13 | odd | 20 | |||
375.2.g.e.226.1 | 16 | 25.23 | odd | 20 | |||
375.2.i.c.274.4 | 16 | 25.14 | even | 10 | |||
375.2.i.c.349.4 | 16 | 25.16 | even | 5 | |||
1875.2.a.m.1.2 | 8 | 5.3 | odd | 4 | |||
1875.2.a.p.1.7 | 8 | 5.2 | odd | 4 | |||
1875.2.b.h.1249.2 | 16 | 1.1 | even | 1 | trivial | ||
1875.2.b.h.1249.15 | 16 | 5.4 | even | 2 | inner | ||
5625.2.a.t.1.2 | 8 | 15.2 | even | 4 | |||
5625.2.a.bd.1.7 | 8 | 15.8 | even | 4 |