Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6036,2,Mod(1,6036)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6036, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6036.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6036 = 2^{2} \cdot 3 \cdot 503 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6036.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(48.1977026600\) |
Analytic rank: | \(0\) |
Dimension: | \(26\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.19 | ||
Character | \(\chi\) | \(=\) | 6036.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.09204 | 0.935591 | 0.467795 | − | 0.883837i | \(-0.345048\pi\) | ||||
0.467795 | + | 0.883837i | \(0.345048\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.11995 | −0.423303 | −0.211652 | − | 0.977345i | \(-0.567884\pi\) | ||||
−0.211652 | + | 0.977345i | \(0.567884\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.05871 | −0.922234 | −0.461117 | − | 0.887339i | \(-0.652551\pi\) | ||||
−0.461117 | + | 0.887339i | \(0.652551\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −6.80855 | −1.88835 | −0.944177 | − | 0.329440i | \(-0.893140\pi\) | ||||
−0.944177 | + | 0.329440i | \(0.893140\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −2.09204 | −0.540164 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 6.88548 | 1.66997 | 0.834987 | − | 0.550270i | \(-0.185475\pi\) | ||||
0.834987 | + | 0.550270i | \(0.185475\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −6.06064 | −1.39041 | −0.695203 | − | 0.718813i | \(-0.744686\pi\) | ||||
−0.695203 | + | 0.718813i | \(0.744686\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.11995 | 0.244394 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −0.508351 | −0.105998 | −0.0529992 | − | 0.998595i | \(-0.516878\pi\) | ||||
−0.0529992 | + | 0.998595i | \(0.516878\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.623348 | −0.124670 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −4.52700 | −0.840643 | −0.420322 | − | 0.907375i | \(-0.638083\pi\) | ||||
−0.420322 | + | 0.907375i | \(0.638083\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.62475 | 0.291814 | 0.145907 | − | 0.989298i | \(-0.453390\pi\) | ||||
0.145907 | + | 0.989298i | \(0.453390\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 3.05871 | 0.532452 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −2.34300 | −0.396039 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.52706 | 0.744244 | 0.372122 | − | 0.928184i | \(-0.378630\pi\) | ||||
0.372122 | + | 0.928184i | \(0.378630\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 6.80855 | 1.09024 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.40458 | 0.531707 | 0.265853 | − | 0.964014i | \(-0.414346\pi\) | ||||
0.265853 | + | 0.964014i | \(0.414346\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −7.55017 | −1.15139 | −0.575695 | − | 0.817664i | \(-0.695269\pi\) | ||||
−0.575695 | + | 0.817664i | \(0.695269\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 2.09204 | 0.311864 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 12.9657 | 1.89125 | 0.945624 | − | 0.325262i | \(-0.105452\pi\) | ||||
0.945624 | + | 0.325262i | \(0.105452\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.74570 | −0.820815 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −6.88548 | −0.964159 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 5.82613 | 0.800281 | 0.400140 | − | 0.916454i | \(-0.368961\pi\) | ||||
0.400140 | + | 0.916454i | \(0.368961\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −6.39895 | −0.862834 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 6.06064 | 0.802752 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 7.98329 | 1.03934 | 0.519668 | − | 0.854368i | \(-0.326056\pi\) | ||||
0.519668 | + | 0.854368i | \(0.326056\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −11.2818 | −1.44449 | −0.722244 | − | 0.691638i | \(-0.756889\pi\) | ||||
−0.722244 | + | 0.691638i | \(0.756889\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.11995 | −0.141101 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −14.2438 | −1.76673 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 7.90749 | 0.966054 | 0.483027 | − | 0.875605i | \(-0.339537\pi\) | ||||
0.483027 | + | 0.875605i | \(0.339537\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0.508351 | 0.0611982 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 3.42324 | 0.406263 | 0.203132 | − | 0.979151i | \(-0.434888\pi\) | ||||
0.203132 | + | 0.979151i | \(0.434888\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 14.4660 | 1.69311 | 0.846556 | − | 0.532299i | \(-0.178672\pi\) | ||||
0.846556 | + | 0.532299i | \(0.178672\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0.623348 | 0.0719780 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 3.42561 | 0.390385 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −4.06975 | −0.457883 | −0.228941 | − | 0.973440i | \(-0.573526\pi\) | ||||
−0.228941 | + | 0.973440i | \(0.573526\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −4.08357 | −0.448230 | −0.224115 | − | 0.974563i | \(-0.571949\pi\) | ||||
−0.224115 | + | 0.974563i | \(0.571949\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 14.4047 | 1.56241 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 4.52700 | 0.485346 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 17.2613 | 1.82969 | 0.914845 | − | 0.403806i | \(-0.132313\pi\) | ||||
0.914845 | + | 0.403806i | \(0.132313\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 7.62527 | 0.799346 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −1.62475 | −0.168479 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −12.6791 | −1.30085 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 14.8285 | 1.50561 | 0.752804 | − | 0.658244i | \(-0.228701\pi\) | ||||
0.752804 | + | 0.658244i | \(0.228701\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −3.05871 | −0.307411 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 15.0157 | 1.49412 | 0.747060 | − | 0.664757i | \(-0.231465\pi\) | ||||
0.747060 | + | 0.664757i | \(0.231465\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −3.48792 | −0.343675 | −0.171838 | − | 0.985125i | \(-0.554970\pi\) | ||||
−0.171838 | + | 0.985125i | \(0.554970\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 2.34300 | 0.228653 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −2.50472 | −0.242140 | −0.121070 | − | 0.992644i | \(-0.538633\pi\) | ||||
−0.121070 | + | 0.992644i | \(0.538633\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 15.5936 | 1.49359 | 0.746796 | − | 0.665054i | \(-0.231591\pi\) | ||||
0.746796 | + | 0.665054i | \(0.231591\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −4.52706 | −0.429689 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 16.8534 | 1.58543 | 0.792716 | − | 0.609591i | \(-0.208666\pi\) | ||||
0.792716 | + | 0.609591i | \(0.208666\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.06349 | −0.0991712 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −6.80855 | −0.629451 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −7.71142 | −0.706905 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.64432 | −0.149484 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −3.40458 | −0.306981 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −11.7643 | −1.05223 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 13.5676 | 1.20393 | 0.601964 | − | 0.798523i | \(-0.294385\pi\) | ||||
0.601964 | + | 0.798523i | \(0.294385\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 7.55017 | 0.664756 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −15.4825 | −1.35272 | −0.676358 | − | 0.736573i | \(-0.736443\pi\) | ||||
−0.676358 | + | 0.736573i | \(0.736443\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 6.78764 | 0.588563 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −2.09204 | −0.180055 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1.68605 | −0.144049 | −0.0720245 | − | 0.997403i | \(-0.522946\pi\) | ||||
−0.0720245 | + | 0.997403i | \(0.522946\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −21.0299 | −1.78374 | −0.891868 | − | 0.452297i | \(-0.850605\pi\) | ||||
−0.891868 | + | 0.452297i | \(0.850605\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −12.9657 | −1.09191 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 20.8254 | 1.74150 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −9.47069 | −0.786498 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 5.74570 | 0.473897 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 15.5986 | 1.27788 | 0.638942 | − | 0.769255i | \(-0.279372\pi\) | ||||
0.638942 | + | 0.769255i | \(0.279372\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −12.9393 | −1.05299 | −0.526494 | − | 0.850179i | \(-0.676494\pi\) | ||||
−0.526494 | + | 0.850179i | \(0.676494\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 6.88548 | 0.556658 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 3.39905 | 0.273018 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −21.1717 | −1.68969 | −0.844844 | − | 0.535012i | \(-0.820307\pi\) | ||||
−0.844844 | + | 0.535012i | \(0.820307\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −5.82613 | −0.462042 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0.569330 | 0.0448695 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 3.09855 | 0.242697 | 0.121349 | − | 0.992610i | \(-0.461278\pi\) | ||||
0.121349 | + | 0.992610i | \(0.461278\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 6.39895 | 0.498158 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −0.274953 | −0.0212765 | −0.0106383 | − | 0.999943i | \(-0.503386\pi\) | ||||
−0.0106383 | + | 0.999943i | \(0.503386\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 33.3564 | 2.56588 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −6.06064 | −0.463469 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −16.5216 | −1.25612 | −0.628058 | − | 0.778166i | \(-0.716150\pi\) | ||||
−0.628058 | + | 0.778166i | \(0.716150\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0.698122 | 0.0527730 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −7.98329 | −0.600061 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 13.5841 | 1.01532 | 0.507662 | − | 0.861556i | \(-0.330510\pi\) | ||||
0.507662 | + | 0.861556i | \(0.330510\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −3.00685 | −0.223498 | −0.111749 | − | 0.993736i | \(-0.535645\pi\) | ||||
−0.111749 | + | 0.993736i | \(0.535645\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 11.2818 | 0.833976 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 9.47081 | 0.696308 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −21.0606 | −1.54011 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1.11995 | 0.0814647 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 6.40033 | 0.463111 | 0.231556 | − | 0.972822i | \(-0.425618\pi\) | ||||
0.231556 | + | 0.972822i | \(0.425618\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −10.8903 | −0.783899 | −0.391949 | − | 0.919987i | \(-0.628199\pi\) | ||||
−0.391949 | + | 0.919987i | \(0.628199\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 14.2438 | 1.02002 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 12.6911 | 0.904207 | 0.452103 | − | 0.891966i | \(-0.350674\pi\) | ||||
0.452103 | + | 0.891966i | \(0.350674\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 18.7361 | 1.32817 | 0.664085 | − | 0.747657i | \(-0.268821\pi\) | ||||
0.664085 | + | 0.747657i | \(0.268821\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −7.90749 | −0.557752 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 5.07004 | 0.355847 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 7.12254 | 0.497460 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −0.508351 | −0.0353328 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 18.5377 | 1.28228 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −9.31292 | −0.641128 | −0.320564 | − | 0.947227i | \(-0.603872\pi\) | ||||
−0.320564 | + | 0.947227i | \(0.603872\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −3.42324 | −0.234556 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −15.7953 | −1.07723 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.81965 | −0.123526 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −14.4660 | −0.977519 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −46.8801 | −3.15350 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 3.37856 | 0.226245 | 0.113123 | − | 0.993581i | \(-0.463915\pi\) | ||||
0.113123 | + | 0.993581i | \(0.463915\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −0.623348 | −0.0415565 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 14.9597 | 0.992912 | 0.496456 | − | 0.868062i | \(-0.334634\pi\) | ||||
0.496456 | + | 0.868062i | \(0.334634\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 18.6901 | 1.23508 | 0.617538 | − | 0.786541i | \(-0.288130\pi\) | ||||
0.617538 | + | 0.786541i | \(0.288130\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −3.42561 | −0.225389 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 2.10866 | 0.138143 | 0.0690713 | − | 0.997612i | \(-0.477996\pi\) | ||||
0.0690713 | + | 0.997612i | \(0.477996\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 27.1249 | 1.76943 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 4.06975 | 0.264359 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −7.09270 | −0.458789 | −0.229394 | − | 0.973334i | \(-0.573675\pi\) | ||||
−0.229394 | + | 0.973334i | \(0.573675\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 6.11396 | 0.393835 | 0.196917 | − | 0.980420i | \(-0.436907\pi\) | ||||
0.196917 | + | 0.980420i | \(0.436907\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −12.0203 | −0.767947 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 41.2642 | 2.62558 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 4.08357 | 0.258786 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 2.80434 | 0.177008 | 0.0885040 | − | 0.996076i | \(-0.471791\pi\) | ||||
0.0885040 | + | 0.996076i | \(0.471791\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.55489 | 0.0977554 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −14.4047 | −0.902059 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −25.2183 | −1.57308 | −0.786538 | − | 0.617542i | \(-0.788129\pi\) | ||||
−0.786538 | + | 0.617542i | \(0.788129\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −5.07010 | −0.315041 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −4.52700 | −0.280214 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 13.6148 | 0.839526 | 0.419763 | − | 0.907634i | \(-0.362113\pi\) | ||||
0.419763 | + | 0.907634i | \(0.362113\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 12.1885 | 0.748735 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −17.2613 | −1.05637 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −7.70251 | −0.469631 | −0.234815 | − | 0.972040i | \(-0.575449\pi\) | ||||
−0.234815 | + | 0.972040i | \(0.575449\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −25.8369 | −1.56948 | −0.784741 | − | 0.619824i | \(-0.787204\pi\) | ||||
−0.784741 | + | 0.619824i | \(0.787204\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −7.62527 | −0.461502 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1.90664 | 0.114975 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 5.94164 | 0.356999 | 0.178499 | − | 0.983940i | \(-0.442876\pi\) | ||||
0.178499 | + | 0.983940i | \(0.442876\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 1.62475 | 0.0972712 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −5.87340 | −0.350378 | −0.175189 | − | 0.984535i | \(-0.556054\pi\) | ||||
−0.175189 | + | 0.984535i | \(0.556054\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −22.8593 | −1.35884 | −0.679422 | − | 0.733747i | \(-0.737770\pi\) | ||||
−0.679422 | + | 0.733747i | \(0.737770\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 12.6791 | 0.751047 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −3.81298 | −0.225073 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 30.4098 | 1.78881 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −14.8285 | −0.869264 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 10.1271 | 0.591630 | 0.295815 | − | 0.955245i | \(-0.404409\pi\) | ||||
0.295815 | + | 0.955245i | \(0.404409\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 16.7014 | 0.972394 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 3.05871 | 0.177484 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 3.46113 | 0.200162 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 8.45585 | 0.487387 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −15.0157 | −0.862630 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −23.6021 | −1.35145 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −9.08360 | −0.518429 | −0.259214 | − | 0.965820i | \(-0.583464\pi\) | ||||
−0.259214 | + | 0.965820i | \(0.583464\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 3.48792 | 0.198421 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 28.1435 | 1.59587 | 0.797937 | − | 0.602741i | \(-0.205925\pi\) | ||||
0.797937 | + | 0.602741i | \(0.205925\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2.15160 | 0.121616 | 0.0608078 | − | 0.998149i | \(-0.480632\pi\) | ||||
0.0608078 | + | 0.998149i | \(0.480632\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −2.34300 | −0.132013 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −17.9505 | −1.00820 | −0.504100 | − | 0.863645i | \(-0.668176\pi\) | ||||
−0.504100 | + | 0.863645i | \(0.668176\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 13.8468 | 0.775270 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 2.50472 | 0.139800 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −41.7304 | −2.32194 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 4.24410 | 0.235420 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −15.5936 | −0.862325 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −14.5210 | −0.800571 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −0.828334 | −0.0455293 | −0.0227647 | − | 0.999741i | \(-0.507247\pi\) | ||||
−0.0227647 | + | 0.999741i | \(0.507247\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 4.52706 | 0.248081 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 16.5428 | 0.903831 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 15.9706 | 0.869974 | 0.434987 | − | 0.900437i | \(-0.356753\pi\) | ||||
0.434987 | + | 0.900437i | \(0.356753\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −16.8534 | −0.915350 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −4.96963 | −0.269121 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 14.2746 | 0.770756 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 1.06349 | 0.0572565 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −2.09974 | −0.112720 | −0.0563599 | − | 0.998411i | \(-0.517949\pi\) | ||||
−0.0563599 | + | 0.998411i | \(0.517949\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 12.0394 | 0.644452 | 0.322226 | − | 0.946663i | \(-0.395569\pi\) | ||||
0.322226 | + | 0.946663i | \(0.395569\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 6.80855 | 0.363414 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −4.61169 | −0.245456 | −0.122728 | − | 0.992440i | \(-0.539164\pi\) | ||||
−0.122728 | + | 0.992440i | \(0.539164\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 7.16157 | 0.380096 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 7.71142 | 0.408132 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −5.45226 | −0.287759 | −0.143880 | − | 0.989595i | \(-0.545958\pi\) | ||||
−0.143880 | + | 0.989595i | \(0.545958\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 17.7314 | 0.933231 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 1.64432 | 0.0863044 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 30.2634 | 1.58406 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 16.4642 | 0.859422 | 0.429711 | − | 0.902967i | \(-0.358615\pi\) | ||||
0.429711 | + | 0.902967i | \(0.358615\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 3.40458 | 0.177236 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −6.52500 | −0.338761 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −14.1213 | −0.731171 | −0.365586 | − | 0.930778i | \(-0.619131\pi\) | ||||
−0.365586 | + | 0.930778i | \(0.619131\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 11.7643 | 0.607506 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 30.8223 | 1.58743 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1.80636 | −0.0927863 | −0.0463932 | − | 0.998923i | \(-0.514773\pi\) | ||||
−0.0463932 | + | 0.998923i | \(0.514773\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −13.5676 | −0.695088 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −36.3146 | −1.85559 | −0.927794 | − | 0.373092i | \(-0.878298\pi\) | ||||
−0.927794 | + | 0.373092i | \(0.878298\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 7.16653 | 0.365240 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −7.55017 | −0.383797 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −16.2430 | −0.823553 | −0.411776 | − | 0.911285i | \(-0.635091\pi\) | ||||
−0.411776 | + | 0.911285i | \(0.635091\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −3.50024 | −0.177015 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 15.4825 | 0.780991 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −8.51410 | −0.428391 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 33.4869 | 1.68066 | 0.840329 | − | 0.542077i | \(-0.182362\pi\) | ||||
0.840329 | + | 0.542077i | \(0.182362\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −6.78764 | −0.339807 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 17.4558 | 0.871703 | 0.435852 | − | 0.900019i | \(-0.356447\pi\) | ||||
0.435852 | + | 0.900019i | \(0.356447\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −11.0622 | −0.551047 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 2.09204 | 0.103955 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −13.8469 | −0.686367 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1.44472 | 0.0714369 | 0.0357185 | − | 0.999362i | \(-0.488628\pi\) | ||||
0.0357185 | + | 0.999362i | \(0.488628\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 1.68605 | 0.0831667 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −8.94093 | −0.439954 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −8.54302 | −0.419360 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 21.0299 | 1.02984 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 25.1475 | 1.22854 | 0.614268 | − | 0.789097i | \(-0.289451\pi\) | ||||
0.614268 | + | 0.789097i | \(0.289451\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 38.5780 | 1.88017 | 0.940087 | − | 0.340934i | \(-0.110743\pi\) | ||||
0.940087 | + | 0.340934i | \(0.110743\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 12.9657 | 0.630416 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −4.29205 | −0.208195 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 12.6351 | 0.611456 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −20.8254 | −1.00546 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 34.3908 | 1.65655 | 0.828273 | − | 0.560324i | \(-0.189324\pi\) | ||||
0.828273 | + | 0.560324i | \(0.189324\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 1.64164 | 0.0788923 | 0.0394461 | − | 0.999222i | \(-0.487441\pi\) | ||||
0.0394461 | + | 0.999222i | \(0.487441\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 9.47069 | 0.454085 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 3.08093 | 0.147381 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −9.97093 | −0.475887 | −0.237943 | − | 0.971279i | \(-0.576473\pi\) | ||||
−0.237943 | + | 0.971279i | \(0.576473\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −5.74570 | −0.273605 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 16.2845 | 0.773700 | 0.386850 | − | 0.922143i | \(-0.373563\pi\) | ||||
0.386850 | + | 0.922143i | \(0.373563\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 36.1113 | 1.71184 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −15.5986 | −0.737787 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 0.982830 | 0.0463826 | 0.0231913 | − | 0.999731i | \(-0.492617\pi\) | ||||
0.0231913 | + | 0.999731i | \(0.492617\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −10.4136 | −0.490358 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 12.9393 | 0.607943 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 15.9524 | 0.747861 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −4.74202 | −0.221823 | −0.110911 | − | 0.993830i | \(-0.535377\pi\) | ||||
−0.110911 | + | 0.993830i | \(0.535377\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −6.88548 | −0.321386 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 11.4949 | 0.535369 | 0.267685 | − | 0.963507i | \(-0.413742\pi\) | ||||
0.267685 | + | 0.963507i | \(0.413742\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 20.8843 | 0.970575 | 0.485287 | − | 0.874355i | \(-0.338715\pi\) | ||||
0.485287 | + | 0.874355i | \(0.338715\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −3.39905 | −0.157627 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 0.744771 | 0.0344639 | 0.0172320 | − | 0.999852i | \(-0.494515\pi\) | ||||
0.0172320 | + | 0.999852i | \(0.494515\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −8.85603 | −0.408934 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 21.1717 | 0.975542 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 23.0938 | 1.06185 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 3.77789 | 0.173341 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 5.82613 | 0.266760 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 8.84492 | 0.404135 | 0.202067 | − | 0.979372i | \(-0.435234\pi\) | ||||
0.202067 | + | 0.979372i | \(0.435234\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −30.8227 | −1.40540 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −0.569330 | −0.0259054 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 31.0219 | 1.40863 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −25.2217 | −1.14290 | −0.571452 | − | 0.820635i | \(-0.693620\pi\) | ||||
−0.571452 | + | 0.820635i | \(0.693620\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −3.09855 | −0.140121 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 19.7997 | 0.893546 | 0.446773 | − | 0.894647i | \(-0.352573\pi\) | ||||
0.446773 | + | 0.894647i | \(0.352573\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −31.1706 | −1.40385 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −6.39895 | −0.287611 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −3.83387 | −0.171973 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 19.6848 | 0.881212 | 0.440606 | − | 0.897701i | \(-0.354764\pi\) | ||||
0.440606 | + | 0.897701i | \(0.354764\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0.274953 | 0.0122840 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −1.00000 | −0.0445878 | ||||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 31.4136 | 1.39788 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −33.3564 | −1.48141 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 16.0171 | 0.709947 | 0.354974 | − | 0.934876i | \(-0.384490\pi\) | ||||
0.354974 | + | 0.934876i | \(0.384490\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −16.2012 | −0.716700 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 6.06064 | 0.267584 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −7.29689 | −0.321540 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −39.6584 | −1.74417 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 16.5216 | 0.725219 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −22.9713 | −1.00639 | −0.503195 | − | 0.864173i | \(-0.667842\pi\) | ||||
−0.503195 | + | 0.864173i | \(0.667842\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 40.4831 | 1.77020 | 0.885101 | − | 0.465399i | \(-0.154089\pi\) | ||||
0.885101 | + | 0.465399i | \(0.154089\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −0.698122 | −0.0304685 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 11.1872 | 0.487321 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.7416 | −0.988764 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 7.98329 | 0.346445 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −23.1803 | −1.00405 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −5.23998 | −0.226544 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −13.5841 | −0.586198 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 17.5744 | 0.756983 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 32.0601 | 1.37837 | 0.689186 | − | 0.724584i | \(-0.257968\pi\) | ||||
0.689186 | + | 0.724584i | \(0.257968\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 3.00685 | 0.129036 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 32.6224 | 1.39739 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −6.90685 | −0.295316 | −0.147658 | − | 0.989039i | \(-0.547173\pi\) | ||||
−0.147658 | + | 0.989039i | \(0.547173\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −11.2818 | −0.481496 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 27.4365 | 1.16884 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 4.55794 | 0.193823 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −9.47081 | −0.402013 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 34.8776 | 1.47781 | 0.738906 | − | 0.673808i | \(-0.235343\pi\) | ||||
0.738906 | + | 0.673808i | \(0.235343\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 51.4058 | 2.17423 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 21.0606 | 0.889181 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 41.8681 | 1.76453 | 0.882264 | − | 0.470755i | \(-0.156018\pi\) | ||||
0.882264 | + | 0.470755i | \(0.156018\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 35.2580 | 1.48332 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −1.11995 | −0.0470337 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 5.52575 | 0.231651 | 0.115826 | − | 0.993270i | \(-0.463049\pi\) | ||||
0.115826 | + | 0.993270i | \(0.463049\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −22.8981 | −0.958256 | −0.479128 | − | 0.877745i | \(-0.659047\pi\) | ||||
−0.479128 | + | 0.877745i | \(0.659047\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −6.40033 | −0.267378 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0.316879 | 0.0132148 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −10.1018 | −0.420543 | −0.210272 | − | 0.977643i | \(-0.567435\pi\) | ||||
−0.210272 | + | 0.977643i | \(0.567435\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 10.8903 | 0.452584 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 4.57342 | 0.189737 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −17.8204 | −0.738046 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −14.2438 | −0.588909 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −4.81788 | −0.198855 | −0.0994275 | − | 0.995045i | \(-0.531701\pi\) | ||||
−0.0994275 | + | 0.995045i | \(0.531701\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −9.84702 | −0.405740 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −12.6911 | −0.522044 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −23.7096 | −0.973636 | −0.486818 | − | 0.873504i | \(-0.661842\pi\) | ||||
−0.486818 | + | 0.873504i | \(0.661842\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −16.1326 | −0.661374 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −18.7361 | −0.766819 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 10.3607 | 0.423325 | 0.211662 | − | 0.977343i | \(-0.432112\pi\) | ||||
0.211662 | + | 0.977343i | \(0.432112\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −34.9778 | −1.42677 | −0.713387 | − | 0.700770i | \(-0.752840\pi\) | ||||
−0.713387 | + | 0.700770i | \(0.752840\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 7.90749 | 0.322018 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −3.43999 | −0.139856 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −12.7927 | −0.519241 | −0.259620 | − | 0.965711i | \(-0.583597\pi\) | ||||
−0.259620 | + | 0.965711i | \(0.583597\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −5.07004 | −0.205448 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −88.2780 | −3.57134 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 18.4144 | 0.743749 | 0.371874 | − | 0.928283i | \(-0.378715\pi\) | ||||
0.371874 | + | 0.928283i | \(0.378715\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −7.12254 | −0.287209 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −2.35116 | −0.0946540 | −0.0473270 | − | 0.998879i | \(-0.515070\pi\) | ||||
−0.0473270 | + | 0.998879i | \(0.515070\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 28.4460 | 1.14334 | 0.571671 | − | 0.820483i | \(-0.306296\pi\) | ||||
0.571671 | + | 0.820483i | \(0.306296\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0.508351 | 0.0203994 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −19.3318 | −0.774513 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −21.4947 | −0.859788 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −18.5377 | −0.740325 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 31.1709 | 1.24287 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 12.6592 | 0.503955 | 0.251977 | − | 0.967733i | \(-0.418919\pi\) | ||||
0.251977 | + | 0.967733i | \(0.418919\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 9.31292 | 0.370155 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 28.3840 | 1.12638 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 39.1199 | 1.54999 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 3.42324 | 0.135421 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 14.8200 | 0.585353 | 0.292677 | − | 0.956211i | \(-0.405454\pi\) | ||||
0.292677 | + | 0.956211i | \(0.405454\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −43.9859 | −1.73463 | −0.867316 | − | 0.497757i | \(-0.834157\pi\) | ||||
−0.867316 | + | 0.497757i | \(0.834157\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 15.7953 | 0.621939 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −39.1606 | −1.53956 | −0.769781 | − | 0.638308i | \(-0.779635\pi\) | ||||
−0.769781 | + | 0.638308i | \(0.779635\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −24.4185 | −0.958512 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.81965 | 0.0713175 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 2.24871 | 0.0879989 | 0.0439994 | − | 0.999032i | \(-0.485990\pi\) | ||||
0.0439994 | + | 0.999032i | \(0.485990\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −32.3902 | −1.26559 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 14.4660 | 0.564371 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −3.93412 | −0.153251 | −0.0766257 | − | 0.997060i | \(-0.524415\pi\) | ||||
−0.0766257 | + | 0.997060i | \(0.524415\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 20.4901 | 0.796971 | 0.398486 | − | 0.917175i | \(-0.369536\pi\) | ||||
0.398486 | + | 0.917175i | \(0.369536\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 46.8801 | 1.82067 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 14.2001 | 0.550655 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 2.30130 | 0.0891069 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −3.37856 | −0.130623 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 34.5078 | 1.33216 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −31.4063 | −1.21062 | −0.605312 | − | 0.795988i | \(-0.706952\pi\) | ||||
−0.605312 | + | 0.795988i | \(0.706952\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0.623348 | 0.0239927 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 30.0000 | 1.15299 | 0.576496 | − | 0.817100i | \(-0.304420\pi\) | ||||
0.576496 | + | 0.817100i | \(0.304420\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −16.6073 | −0.637329 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −14.9597 | −0.573258 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −15.7273 | −0.601790 | −0.300895 | − | 0.953657i | \(-0.597285\pi\) | ||||
−0.300895 | + | 0.953657i | \(0.597285\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −3.52729 | −0.134771 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −18.6901 | −0.713071 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −39.6675 | −1.51121 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 28.4104 | 1.08078 | 0.540392 | − | 0.841414i | \(-0.318276\pi\) | ||||
0.540392 | + | 0.841414i | \(0.318276\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 3.42561 | 0.130128 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −43.9956 | −1.66885 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 23.4422 | 0.887936 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −2.10866 | −0.0797567 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 8.57137 | 0.323736 | 0.161868 | − | 0.986812i | \(-0.448248\pi\) | ||||
0.161868 | + | 0.986812i | \(0.448248\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −27.4369 | −1.03480 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −27.1249 | −1.02158 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −16.8169 | −0.632466 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 25.5151 | 0.958240 | 0.479120 | − | 0.877749i | \(-0.340956\pi\) | ||||
0.479120 | + | 0.877749i | \(0.340956\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −4.06975 | −0.152628 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −0.825942 | −0.0309318 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 43.5676 | 1.62934 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 7.09270 | 0.264882 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −41.0285 | −1.53011 | −0.765053 | − | 0.643968i | \(-0.777287\pi\) | ||||
−0.765053 | + | 0.643968i | \(0.777287\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 3.90632 | 0.145479 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −6.11396 | −0.227380 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 2.82190 | 0.104803 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −3.91694 | −0.145271 | −0.0726356 | − | 0.997359i | \(-0.523141\pi\) | ||||
−0.0726356 | + | 0.997359i | \(0.523141\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −51.9865 | −1.92279 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −14.5673 | −0.538057 | −0.269028 | − | 0.963132i | \(-0.586703\pi\) | ||||
−0.269028 | + | 0.963132i | \(0.586703\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 12.0203 | 0.443374 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −24.1867 | −0.890928 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 43.9158 | 1.61547 | 0.807734 | − | 0.589547i | \(-0.200694\pi\) | ||||
0.807734 | + | 0.589547i | \(0.200694\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −41.2642 | −1.51588 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −9.07407 | −0.332895 | −0.166448 | − | 0.986050i | \(-0.553230\pi\) | ||||
−0.166448 | + | 0.986050i | \(0.553230\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 32.6329 | 1.19558 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −4.08357 | −0.149410 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 2.80517 | 0.102499 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 6.65730 | 0.242929 | 0.121464 | − | 0.992596i | \(-0.461241\pi\) | ||||
0.121464 | + | 0.992596i | \(0.461241\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −2.80434 | −0.102196 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −27.0697 | −0.985166 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −19.6664 | −0.714788 | −0.357394 | − | 0.933954i | \(-0.616335\pi\) | ||||
−0.357394 | + | 0.933954i | \(0.616335\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −1.55489 | −0.0564391 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 5.81481 | 0.210787 | 0.105393 | − | 0.994431i | \(-0.466390\pi\) | ||||
0.105393 | + | 0.994431i | \(0.466390\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −17.4641 | −0.632242 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 14.4047 | 0.520804 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −54.3547 | −1.96263 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −6.58954 | −0.237625 | −0.118813 | − | 0.992917i | \(-0.537909\pi\) | ||||
−0.118813 | + | 0.992917i | \(0.537909\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 25.2183 | 0.908216 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 19.8195 | 0.712857 | 0.356429 | − | 0.934323i | \(-0.383994\pi\) | ||||
0.356429 | + | 0.934323i | \(0.383994\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1.01278 | −0.0363803 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 5.07010 | 0.181889 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −20.6340 | −0.739288 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −10.4707 | −0.374670 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 4.52700 | 0.161782 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −44.2922 | −1.58086 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 17.6843 | 0.630376 | 0.315188 | − | 0.949029i | \(-0.397932\pi\) | ||||
0.315188 | + | 0.949029i | \(0.397932\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −13.6148 | −0.484701 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −18.8750 | −0.671118 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 76.8129 | 2.72770 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −12.1885 | −0.432283 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −40.7996 | −1.44520 | −0.722598 | − | 0.691269i | \(-0.757052\pi\) | ||||
−0.722598 | + | 0.691269i | \(0.757052\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 89.2753 | 3.15833 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 17.2613 | 0.609897 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −44.2471 | −1.56145 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1.19106 | 0.0419795 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 7.70251 | 0.271141 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −2.95407 | −0.103859 | −0.0519297 | − | 0.998651i | \(-0.516537\pi\) | ||||
−0.0519297 | + | 0.998651i | \(0.516537\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 6.87439 | 0.241392 | 0.120696 | − | 0.992689i | \(-0.461487\pi\) | ||||
0.120696 | + | 0.992689i | \(0.461487\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 25.8369 | 0.906141 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 6.48231 | 0.227065 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 45.7589 | 1.60090 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 7.62527 | 0.266449 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −27.1421 | −0.947267 | −0.473634 | − | 0.880722i | \(-0.657058\pi\) | ||||
−0.473634 | + | 0.880722i | \(0.657058\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −9.66658 | −0.336956 | −0.168478 | − | 0.985705i | \(-0.553885\pi\) | ||||
−0.168478 | + | 0.985705i | \(0.553885\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −1.90664 | −0.0663806 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −30.2680 | −1.05252 | −0.526260 | − | 0.850324i | \(-0.676406\pi\) | ||||
−0.526260 | + | 0.850324i | \(0.676406\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −18.0675 | −0.627512 | −0.313756 | − | 0.949504i | \(-0.601587\pi\) | ||||
−0.313756 | + | 0.949504i | \(0.601587\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −5.94164 | −0.206113 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −39.5619 | −1.37074 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −0.575215 | −0.0199061 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −1.62475 | −0.0561595 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 13.9450 | 0.481434 | 0.240717 | − | 0.970595i | \(-0.422617\pi\) | ||||
0.240717 | + | 0.970595i | \(0.422617\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −8.50626 | −0.293319 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 5.87340 | 0.202291 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 69.7831 | 2.40061 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.84156 | 0.0632769 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 22.8593 | 0.784529 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −2.30133 | −0.0788887 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 23.9459 | 0.819891 | 0.409946 | − | 0.912110i | \(-0.365548\pi\) | ||||
0.409946 | + | 0.912110i | \(0.365548\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −12.6791 | −0.433617 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 12.0017 | 0.409971 | 0.204985 | − | 0.978765i | \(-0.434285\pi\) | ||||
0.204985 | + | 0.978765i | \(0.434285\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 8.27441 | 0.282319 | 0.141160 | − | 0.989987i | \(-0.454917\pi\) | ||||
0.141160 | + | 0.989987i | \(0.454917\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 3.81298 | 0.129946 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −20.6687 | −0.703569 | −0.351785 | − | 0.936081i | \(-0.614425\pi\) | ||||
−0.351785 | + | 0.936081i | \(0.614425\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −34.5640 | −1.17521 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −30.4098 | −1.03277 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 12.4482 | 0.422275 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −53.8386 | −1.82425 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 14.8285 | 0.501870 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 13.1755 | 0.445412 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −52.8954 | −1.78615 | −0.893075 | − | 0.449908i | \(-0.851457\pi\) | ||||
−0.893075 | + | 0.449908i | \(0.851457\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −10.1271 | −0.341578 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 48.1444 | 1.62203 | 0.811013 | − | 0.585029i | \(-0.198917\pi\) | ||||
0.811013 | + | 0.585029i | \(0.198917\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −24.7916 | −0.834304 | −0.417152 | − | 0.908837i | \(-0.636972\pi\) | ||||
−0.417152 | + | 0.908837i | \(0.636972\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −16.7014 | −0.561412 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −32.0672 | −1.07671 | −0.538355 | − | 0.842718i | \(-0.680954\pi\) | ||||
−0.538355 | + | 0.842718i | \(0.680954\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −15.1951 | −0.509626 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −3.05871 | −0.102470 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −78.5807 | −2.62960 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 28.4186 | 0.949928 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −3.46113 | −0.115564 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −7.35524 | −0.245311 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 40.1157 | 1.33645 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −8.45585 | −0.281393 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −6.29047 | −0.209102 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 10.3373 | 0.343245 | 0.171623 | − | 0.985163i | \(-0.445099\pi\) | ||||
0.171623 | + | 0.985163i | \(0.445099\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 15.0157 | 0.498040 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 28.4505 | 0.942608 | 0.471304 | − | 0.881971i | \(-0.343783\pi\) | ||||
0.471304 | + | 0.881971i | \(0.343783\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 12.4904 | 0.413374 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 23.6021 | 0.780260 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 17.3397 | 0.572609 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −36.6977 | −1.21055 | −0.605273 | − | 0.796018i | \(-0.706936\pi\) | ||||
−0.605273 | + | 0.796018i | \(0.706936\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 9.08360 | 0.299315 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −23.3073 | −0.767169 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −2.82193 | −0.0927846 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −3.48792 | −0.114558 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 24.0358 | 0.788589 | 0.394295 | − | 0.918984i | \(-0.370989\pi\) | ||||
0.394295 | + | 0.918984i | \(0.370989\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 34.8226 | 1.14127 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −28.1435 | −0.921378 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −44.0598 | −1.44091 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 40.6241 | 1.32713 | 0.663566 | − | 0.748118i | \(-0.269042\pi\) | ||||
0.663566 | + | 0.748118i | \(0.269042\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −2.15160 | −0.0702148 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −17.9401 | −0.584832 | −0.292416 | − | 0.956291i | \(-0.594459\pi\) | ||||
−0.292416 | + | 0.956291i | \(0.594459\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1.73072 | −0.0563601 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 2.34300 | 0.0762176 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 35.4771 | 1.15285 | 0.576426 | − | 0.817149i | \(-0.304447\pi\) | ||||
0.576426 | + | 0.817149i | \(0.304447\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −98.4923 | −3.19719 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 17.9505 | 0.582084 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −56.9687 | −1.84540 | −0.922699 | − | 0.385521i | \(-0.874022\pi\) | ||||
−0.922699 | + | 0.385521i | \(0.874022\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 13.3898 | 0.433283 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −13.8468 | −0.447602 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 1.88830 | 0.0609764 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −28.3602 | −0.914845 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −2.50472 | −0.0807134 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −22.7829 | −0.733408 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 31.2070 | 1.00355 | 0.501775 | − | 0.864998i | \(-0.332681\pi\) | ||||
0.501775 | + | 0.864998i | \(0.332681\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 41.7304 | 1.34057 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 54.2592 | 1.74126 | 0.870630 | − | 0.491938i | \(-0.163711\pi\) | ||||
0.870630 | + | 0.491938i | \(0.163711\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 23.5526 | 0.755061 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −4.24410 | −0.135920 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −3.73365 | −0.119450 | −0.0597251 | − | 0.998215i | \(-0.519022\pi\) | ||||
−0.0597251 | + | 0.998215i | \(0.519022\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −52.7971 | −1.68740 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 15.5936 | 0.497864 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 48.4077 | 1.54397 | 0.771983 | − | 0.635643i | \(-0.219265\pi\) | ||||
0.771983 | + | 0.635643i | \(0.219265\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 26.5505 | 0.845968 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 14.5210 | 0.462210 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 3.83814 | 0.122046 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −32.3082 | −1.02631 | −0.513153 | − | 0.858297i | \(-0.671523\pi\) | ||||
−0.513153 | + | 0.858297i | \(0.671523\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0.828334 | 0.0262864 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 39.1968 | 1.24262 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 34.4280 | 1.09035 | 0.545173 | − | 0.838323i | \(-0.316464\pi\) | ||||
0.545173 | + | 0.838323i | \(0.316464\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −4.52706 | −0.143230 |
(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 | 6036.2.a.i.1.19 | ✓ | 26 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6036.2.a.i.1.19 | ✓ | 26 | 1.1 | even | 1 | trivial |