Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2025,2,Mod(1,2025)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2025, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2025.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2025 = 3^{4} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2025.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: | \(16.1697064093\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.11661.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 2x^{3} - 4x^{2} + 5x + 3 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 225) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Root | \(-1.63372\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2025.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.63372 | 1.86232 | 0.931162 | − | 0.364606i | \(-0.118796\pi\) | ||||
0.931162 | + | 0.364606i | \(0.118796\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 4.93650 | 2.46825 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.79743 | −0.679364 | −0.339682 | − | 0.940540i | \(-0.610319\pi\) | ||||
−0.339682 | + | 0.940540i | \(0.610319\pi\) | |||||||
\(8\) | 7.73393 | 2.73436 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.80812 | 0.545170 | 0.272585 | − | 0.962132i | \(-0.412121\pi\) | ||||
0.272585 | + | 0.962132i | \(0.412121\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.97183 | 0.546887 | 0.273443 | − | 0.961888i | \(-0.411837\pi\) | ||||
0.273443 | + | 0.961888i | \(0.411837\pi\) | |||||||
\(14\) | −4.73393 | −1.26520 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 10.4960 | 2.62401 | ||||||||
\(17\) | 4.80812 | 1.16614 | 0.583071 | − | 0.812421i | \(-0.301851\pi\) | ||||
0.583071 | + | 0.812421i | \(0.301851\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.96467 | 0.680142 | 0.340071 | − | 0.940400i | \(-0.389549\pi\) | ||||
0.340071 | + | 0.940400i | \(0.389549\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 4.76210 | 1.01528 | ||||||||
\(23\) | −1.73393 | −0.361549 | −0.180774 | − | 0.983525i | \(-0.557860\pi\) | ||||
−0.180774 | + | 0.983525i | \(0.557860\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 5.19325 | 1.01848 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −8.87300 | −1.67684 | ||||||||
\(29\) | −7.36765 | −1.36814 | −0.684069 | − | 0.729417i | \(-0.739791\pi\) | ||||
−0.684069 | + | 0.729417i | \(0.739791\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.62303 | −0.471110 | −0.235555 | − | 0.971861i | \(-0.575691\pi\) | ||||
−0.235555 | + | 0.971861i | \(0.575691\pi\) | |||||||
\(32\) | 12.1758 | 2.15239 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 12.6633 | 2.17173 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 11.6351 | 1.91280 | 0.956399 | − | 0.292063i | \(-0.0943417\pi\) | ||||
0.956399 | + | 0.292063i | \(0.0943417\pi\) | |||||||
\(38\) | 7.80812 | 1.26664 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2.46648 | −0.385199 | −0.192600 | − | 0.981277i | \(-0.561692\pi\) | ||||
−0.192600 | + | 0.981277i | \(0.561692\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −7.27814 | −1.10991 | −0.554953 | − | 0.831882i | \(-0.687264\pi\) | ||||
−0.554953 | + | 0.831882i | \(0.687264\pi\) | |||||||
\(44\) | 8.92580 | 1.34562 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −4.56668 | −0.673321 | ||||||||
\(47\) | 6.29208 | 0.917794 | 0.458897 | − | 0.888489i | \(-0.348245\pi\) | ||||
0.458897 | + | 0.888489i | \(0.348245\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −3.76926 | −0.538465 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 9.73393 | 1.34985 | ||||||||
\(53\) | 1.72540 | 0.237001 | 0.118501 | − | 0.992954i | \(-0.462191\pi\) | ||||
0.118501 | + | 0.992954i | \(0.462191\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −13.9012 | −1.85762 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −19.4044 | −2.54792 | ||||||||
\(59\) | 11.0260 | 1.43546 | 0.717732 | − | 0.696320i | \(-0.245180\pi\) | ||||
0.717732 | + | 0.696320i | \(0.245180\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −12.6704 | −1.62228 | −0.811141 | − | 0.584851i | \(-0.801153\pi\) | ||||
−0.811141 | + | 0.584851i | \(0.801153\pi\) | |||||||
\(62\) | −6.90833 | −0.877358 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 11.0756 | 1.38445 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 9.10374 | 1.11220 | 0.556100 | − | 0.831116i | \(-0.312297\pi\) | ||||
0.556100 | + | 0.831116i | \(0.312297\pi\) | |||||||
\(68\) | 23.7353 | 2.87833 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.27460 | 0.151268 | 0.0756338 | − | 0.997136i | \(-0.475902\pi\) | ||||
0.0756338 | + | 0.997136i | \(0.475902\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −3.58770 | −0.419908 | −0.209954 | − | 0.977711i | \(-0.567331\pi\) | ||||
−0.209954 | + | 0.977711i | \(0.567331\pi\) | |||||||
\(74\) | 30.6436 | 3.56225 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 14.6351 | 1.67876 | ||||||||
\(77\) | −3.24997 | −0.370369 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.11090 | 0.237495 | 0.118747 | − | 0.992924i | \(-0.462112\pi\) | ||||
0.118747 | + | 0.992924i | \(0.462112\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −6.49602 | −0.717366 | ||||||||
\(83\) | 1.09883 | 0.120612 | 0.0603061 | − | 0.998180i | \(-0.480792\pi\) | ||||
0.0603061 | + | 0.998180i | \(0.480792\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −19.1686 | −2.06701 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 13.9839 | 1.49069 | ||||||||
\(89\) | −13.2935 | −1.40910 | −0.704552 | − | 0.709653i | \(-0.748852\pi\) | ||||
−0.704552 | + | 0.709653i | \(0.748852\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3.54422 | −0.371535 | ||||||||
\(92\) | −8.55953 | −0.892392 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 16.5716 | 1.70923 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −3.83276 | −0.389157 | −0.194579 | − | 0.980887i | \(-0.562334\pi\) | ||||
−0.194579 | + | 0.980887i | \(0.562334\pi\) | |||||||
\(98\) | −9.92718 | −1.00280 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 6.55237 | 0.651985 | 0.325993 | − | 0.945372i | \(-0.394302\pi\) | ||||
0.325993 | + | 0.945372i | \(0.394302\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −8.07557 | −0.795710 | −0.397855 | − | 0.917448i | \(-0.630245\pi\) | ||||
−0.397855 | + | 0.917448i | \(0.630245\pi\) | |||||||
\(104\) | 15.2500 | 1.49538 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 4.54422 | 0.441373 | ||||||||
\(107\) | −8.97674 | −0.867814 | −0.433907 | − | 0.900958i | \(-0.642865\pi\) | ||||
−0.433907 | + | 0.900958i | \(0.642865\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −6.34164 | −0.607419 | −0.303710 | − | 0.952765i | \(-0.598225\pi\) | ||||
−0.303710 | + | 0.952765i | \(0.598225\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −18.8658 | −1.78265 | ||||||||
\(113\) | −14.9025 | −1.40191 | −0.700957 | − | 0.713204i | \(-0.747243\pi\) | ||||
−0.700957 | + | 0.713204i | \(0.747243\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −36.3704 | −3.37691 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 29.0394 | 2.67330 | ||||||||
\(119\) | −8.64225 | −0.792234 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7.73069 | −0.702790 | ||||||||
\(122\) | −33.3704 | −3.02121 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −12.9486 | −1.16282 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 3.62303 | 0.321492 | 0.160746 | − | 0.986996i | \(-0.448610\pi\) | ||||
0.160746 | + | 0.986996i | \(0.448610\pi\) | |||||||
\(128\) | 4.81844 | 0.425894 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 7.29345 | 0.637232 | 0.318616 | − | 0.947884i | \(-0.396782\pi\) | ||||
0.318616 | + | 0.947884i | \(0.396782\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −5.32878 | −0.462064 | ||||||||
\(134\) | 23.9767 | 2.07127 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 37.1857 | 3.18865 | ||||||||
\(137\) | −7.12621 | −0.608833 | −0.304417 | − | 0.952539i | \(-0.598461\pi\) | ||||
−0.304417 | + | 0.952539i | \(0.598461\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −14.7107 | −1.24774 | −0.623871 | − | 0.781527i | \(-0.714441\pi\) | ||||
−0.623871 | + | 0.781527i | \(0.714441\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 3.35695 | 0.281709 | ||||||||
\(143\) | 3.56531 | 0.298146 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −9.44900 | −0.782005 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 57.4366 | 4.72126 | ||||||||
\(149\) | −0.565309 | −0.0463119 | −0.0231560 | − | 0.999732i | \(-0.507371\pi\) | ||||
−0.0231560 | + | 0.999732i | \(0.507371\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 0.153385 | 0.0124823 | 0.00624115 | − | 0.999981i | \(-0.498013\pi\) | ||||
0.00624115 | + | 0.999981i | \(0.498013\pi\) | |||||||
\(152\) | 22.9285 | 1.85975 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −8.55953 | −0.689746 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −11.4607 | −0.914663 | −0.457332 | − | 0.889296i | \(-0.651195\pi\) | ||||
−0.457332 | + | 0.889296i | \(0.651195\pi\) | |||||||
\(158\) | 5.55953 | 0.442292 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 3.11661 | 0.245623 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −22.0595 | −1.72783 | −0.863915 | − | 0.503637i | \(-0.831995\pi\) | ||||
−0.863915 | + | 0.503637i | \(0.831995\pi\) | |||||||
\(164\) | −12.1758 | −0.950768 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 2.89401 | 0.224619 | ||||||||
\(167\) | 17.0684 | 1.32079 | 0.660397 | − | 0.750917i | \(-0.270388\pi\) | ||||
0.660397 | + | 0.750917i | \(0.270388\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −9.11189 | −0.700915 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −35.9285 | −2.73953 | ||||||||
\(173\) | 11.9447 | 0.908135 | 0.454067 | − | 0.890967i | \(-0.349972\pi\) | ||||
0.454067 | + | 0.890967i | \(0.349972\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 18.9781 | 1.43053 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −35.0113 | −2.62421 | ||||||||
\(179\) | 8.54921 | 0.638998 | 0.319499 | − | 0.947587i | \(-0.396485\pi\) | ||||
0.319499 | + | 0.947587i | \(0.396485\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −10.5524 | −0.784351 | −0.392176 | − | 0.919890i | \(-0.628277\pi\) | ||||
−0.392176 | + | 0.919890i | \(0.628277\pi\) | |||||||
\(182\) | −9.33449 | −0.691918 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −13.4101 | −0.988603 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 8.69368 | 0.635745 | ||||||||
\(188\) | 31.0608 | 2.26534 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −17.3372 | −1.25448 | −0.627239 | − | 0.778827i | \(-0.715815\pi\) | ||||
−0.627239 | + | 0.778827i | \(0.715815\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1.55953 | 0.112257 | 0.0561286 | − | 0.998424i | \(-0.482124\pi\) | ||||
0.0561286 | + | 0.998424i | \(0.482124\pi\) | |||||||
\(194\) | −10.0944 | −0.724737 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −18.6069 | −1.32907 | ||||||||
\(197\) | 17.9767 | 1.28079 | 0.640395 | − | 0.768046i | \(-0.278771\pi\) | ||||
0.640395 | + | 0.768046i | \(0.278771\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 11.0225 | 0.781362 | 0.390681 | − | 0.920526i | \(-0.372240\pi\) | ||||
0.390681 | + | 0.920526i | \(0.372240\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 17.2571 | 1.21421 | ||||||||
\(203\) | 13.2428 | 0.929463 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −21.2688 | −1.48187 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 20.6964 | 1.43503 | ||||||||
\(209\) | 5.36049 | 0.370793 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −23.9285 | −1.64731 | −0.823655 | − | 0.567092i | \(-0.808068\pi\) | ||||
−0.823655 | + | 0.567092i | \(0.808068\pi\) | |||||||
\(212\) | 8.51742 | 0.584979 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −23.6423 | −1.61615 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 4.71470 | 0.320055 | ||||||||
\(218\) | −16.7021 | −1.13121 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 9.48079 | 0.637747 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 21.7107 | 1.45385 | 0.726927 | − | 0.686715i | \(-0.240948\pi\) | ||||
0.726927 | + | 0.686715i | \(0.240948\pi\) | |||||||
\(224\) | −21.8851 | −1.46226 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −39.2492 | −2.61082 | ||||||||
\(227\) | 14.1002 | 0.935863 | 0.467932 | − | 0.883765i | \(-0.344999\pi\) | ||||
0.467932 | + | 0.883765i | \(0.344999\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 3.67758 | 0.243021 | 0.121511 | − | 0.992590i | \(-0.461226\pi\) | ||||
0.121511 | + | 0.992590i | \(0.461226\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −56.9809 | −3.74098 | ||||||||
\(233\) | −5.34164 | −0.349943 | −0.174971 | − | 0.984574i | \(-0.555983\pi\) | ||||
−0.174971 | + | 0.984574i | \(0.555983\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 54.4299 | 3.54308 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −22.7613 | −1.47540 | ||||||||
\(239\) | −22.0335 | −1.42523 | −0.712613 | − | 0.701557i | \(-0.752488\pi\) | ||||
−0.712613 | + | 0.701557i | \(0.752488\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −18.6472 | −1.20117 | −0.600585 | − | 0.799561i | \(-0.705066\pi\) | ||||
−0.600585 | + | 0.799561i | \(0.705066\pi\) | |||||||
\(242\) | −20.3605 | −1.30882 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −62.5475 | −4.00420 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 5.84582 | 0.371961 | ||||||||
\(248\) | −20.2863 | −1.28818 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 14.6929 | 0.927407 | 0.463704 | − | 0.885990i | \(-0.346520\pi\) | ||||
0.463704 | + | 0.885990i | \(0.346520\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −3.13515 | −0.197105 | ||||||||
\(254\) | 9.54205 | 0.598721 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −9.46070 | −0.591294 | ||||||||
\(257\) | 22.2089 | 1.38536 | 0.692678 | − | 0.721247i | \(-0.256431\pi\) | ||||
0.692678 | + | 0.721247i | \(0.256431\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −20.9132 | −1.29949 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 19.2089 | 1.18673 | ||||||||
\(263\) | 5.74001 | 0.353944 | 0.176972 | − | 0.984216i | \(-0.443370\pi\) | ||||
0.176972 | + | 0.984216i | \(0.443370\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −14.0345 | −0.860513 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 44.9406 | 2.74519 | ||||||||
\(269\) | −15.6162 | −0.952139 | −0.476070 | − | 0.879408i | \(-0.657939\pi\) | ||||
−0.476070 | + | 0.879408i | \(0.657939\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −6.75315 | −0.410225 | −0.205112 | − | 0.978738i | \(-0.565756\pi\) | ||||
−0.205112 | + | 0.978738i | \(0.565756\pi\) | |||||||
\(272\) | 50.4662 | 3.05996 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −18.7685 | −1.13384 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 30.2966 | 1.82034 | 0.910172 | − | 0.414230i | \(-0.135949\pi\) | ||||
0.910172 | + | 0.414230i | \(0.135949\pi\) | |||||||
\(278\) | −38.7438 | −2.32370 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 18.6351 | 1.11168 | 0.555838 | − | 0.831290i | \(-0.312397\pi\) | ||||
0.555838 | + | 0.831290i | \(0.312397\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −5.67366 | −0.337264 | −0.168632 | − | 0.985679i | \(-0.553935\pi\) | ||||
−0.168632 | + | 0.985679i | \(0.553935\pi\) | |||||||
\(284\) | 6.29208 | 0.373366 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 9.39004 | 0.555245 | ||||||||
\(287\) | 4.43332 | 0.261690 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 6.11806 | 0.359886 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −17.7107 | −1.03644 | ||||||||
\(293\) | 18.2773 | 1.06777 | 0.533887 | − | 0.845556i | \(-0.320731\pi\) | ||||
0.533887 | + | 0.845556i | \(0.320731\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 89.9850 | 5.23027 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −1.48887 | −0.0862478 | ||||||||
\(299\) | −3.41900 | −0.197726 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 13.0819 | 0.754030 | ||||||||
\(302\) | 0.403974 | 0.0232461 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 31.1173 | 1.78470 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −15.5050 | −0.884915 | −0.442458 | − | 0.896789i | \(-0.645893\pi\) | ||||
−0.442458 | + | 0.896789i | \(0.645893\pi\) | |||||||
\(308\) | −16.0435 | −0.914162 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 30.4464 | 1.72646 | 0.863228 | − | 0.504814i | \(-0.168439\pi\) | ||||
0.863228 | + | 0.504814i | \(0.168439\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −6.94936 | −0.392801 | −0.196401 | − | 0.980524i | \(-0.562925\pi\) | ||||
−0.196401 | + | 0.980524i | \(0.562925\pi\) | |||||||
\(314\) | −30.1843 | −1.70340 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 10.4205 | 0.586196 | ||||||||
\(317\) | −16.1451 | −0.906797 | −0.453398 | − | 0.891308i | \(-0.649788\pi\) | ||||
−0.453398 | + | 0.891308i | \(0.649788\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −13.3216 | −0.745868 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 8.20828 | 0.457430 | ||||||||
\(323\) | 14.2545 | 0.793142 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −58.0985 | −3.21778 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −19.0756 | −1.05327 | ||||||||
\(329\) | −11.3096 | −0.623516 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 12.6222 | 0.693781 | 0.346890 | − | 0.937906i | \(-0.387238\pi\) | ||||
0.346890 | + | 0.937906i | \(0.387238\pi\) | |||||||
\(332\) | 5.42437 | 0.297701 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 44.9535 | 2.45975 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −6.92040 | −0.376978 | −0.188489 | − | 0.982075i | \(-0.560359\pi\) | ||||
−0.188489 | + | 0.982075i | \(0.560359\pi\) | |||||||
\(338\) | −23.9982 | −1.30533 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −4.74276 | −0.256835 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 19.3570 | 1.04518 | ||||||||
\(344\) | −56.2886 | −3.03488 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 31.4589 | 1.69124 | ||||||||
\(347\) | 13.8063 | 0.741163 | 0.370581 | − | 0.928800i | \(-0.379158\pi\) | ||||
0.370581 | + | 0.928800i | \(0.379158\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 6.56768 | 0.351560 | 0.175780 | − | 0.984429i | \(-0.443755\pi\) | ||||
0.175780 | + | 0.984429i | \(0.443755\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 22.0153 | 1.17342 | ||||||||
\(353\) | −3.52499 | −0.187616 | −0.0938082 | − | 0.995590i | \(-0.529904\pi\) | ||||
−0.0938082 | + | 0.995590i | \(0.529904\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −65.6231 | −3.47802 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 22.5162 | 1.19002 | ||||||||
\(359\) | 22.9285 | 1.21012 | 0.605061 | − | 0.796179i | \(-0.293149\pi\) | ||||
0.605061 | + | 0.796179i | \(0.293149\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −10.2107 | −0.537407 | ||||||||
\(362\) | −27.7920 | −1.46072 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −17.4960 | −0.917041 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 4.17931 | 0.218158 | 0.109079 | − | 0.994033i | \(-0.465210\pi\) | ||||
0.109079 | + | 0.994033i | \(0.465210\pi\) | |||||||
\(368\) | −18.1993 | −0.948706 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −3.10127 | −0.161010 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 6.84091 | 0.354209 | 0.177104 | − | 0.984192i | \(-0.443327\pi\) | ||||
0.177104 | + | 0.984192i | \(0.443327\pi\) | |||||||
\(374\) | 22.8968 | 1.18396 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 48.6625 | 2.50958 | ||||||||
\(377\) | −14.5277 | −0.748217 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −12.7764 | −0.656280 | −0.328140 | − | 0.944629i | \(-0.606422\pi\) | ||||
−0.328140 | + | 0.944629i | \(0.606422\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −45.6615 | −2.33624 | ||||||||
\(383\) | 7.53459 | 0.385000 | 0.192500 | − | 0.981297i | \(-0.438341\pi\) | ||||
0.192500 | + | 0.981297i | \(0.438341\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 4.10736 | 0.209059 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −18.9204 | −0.960538 | ||||||||
\(389\) | 5.45175 | 0.276415 | 0.138207 | − | 0.990403i | \(-0.455866\pi\) | ||||
0.138207 | + | 0.990403i | \(0.455866\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −8.33693 | −0.421617 | ||||||||
\(392\) | −29.1511 | −1.47235 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 47.3458 | 2.38525 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −5.64549 | −0.283339 | −0.141670 | − | 0.989914i | \(-0.545247\pi\) | ||||
−0.141670 | + | 0.989914i | \(0.545247\pi\) | |||||||
\(398\) | 29.0301 | 1.45515 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −5.50418 | −0.274865 | −0.137433 | − | 0.990511i | \(-0.543885\pi\) | ||||
−0.137433 | + | 0.990511i | \(0.543885\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −5.17216 | −0.257643 | ||||||||
\(404\) | 32.3458 | 1.60926 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 34.8779 | 1.73096 | ||||||||
\(407\) | 21.0377 | 1.04280 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 32.8530 | 1.62448 | 0.812238 | − | 0.583327i | \(-0.198249\pi\) | ||||
0.812238 | + | 0.583327i | \(0.198249\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −39.8650 | −1.96401 | ||||||||
\(413\) | −19.8184 | −0.975202 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 24.0085 | 1.17712 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 14.1181 | 0.690537 | ||||||||
\(419\) | 22.8591 | 1.11674 | 0.558369 | − | 0.829593i | \(-0.311427\pi\) | ||||
0.558369 | + | 0.829593i | \(0.311427\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 17.9414 | 0.874411 | 0.437205 | − | 0.899362i | \(-0.355968\pi\) | ||||
0.437205 | + | 0.899362i | \(0.355968\pi\) | |||||||
\(422\) | −63.0212 | −3.06782 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 13.3441 | 0.648046 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 22.7742 | 1.10212 | ||||||||
\(428\) | −44.3137 | −2.14198 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −6.18871 | −0.298100 | −0.149050 | − | 0.988830i | \(-0.547622\pi\) | ||||
−0.149050 | + | 0.988830i | \(0.547622\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −3.11806 | −0.149844 | −0.0749221 | − | 0.997189i | \(-0.523871\pi\) | ||||
−0.0749221 | + | 0.997189i | \(0.523871\pi\) | |||||||
\(434\) | 12.4172 | 0.596045 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −31.3055 | −1.49926 | ||||||||
\(437\) | −5.14052 | −0.245904 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 13.5099 | 0.644792 | 0.322396 | − | 0.946605i | \(-0.395512\pi\) | ||||
0.322396 | + | 0.946605i | \(0.395512\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 24.9698 | 1.18769 | ||||||||
\(443\) | −24.2773 | −1.15345 | −0.576726 | − | 0.816938i | \(-0.695670\pi\) | ||||
−0.576726 | + | 0.816938i | \(0.695670\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 57.1799 | 2.70755 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −19.9075 | −0.940543 | ||||||||
\(449\) | −24.1437 | −1.13941 | −0.569705 | − | 0.821849i | \(-0.692943\pi\) | ||||
−0.569705 | + | 0.821849i | \(0.692943\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −4.45970 | −0.209999 | ||||||||
\(452\) | −73.5664 | −3.46027 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 37.1360 | 1.74288 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −2.82157 | −0.131987 | −0.0659937 | − | 0.997820i | \(-0.521022\pi\) | ||||
−0.0659937 | + | 0.997820i | \(0.521022\pi\) | |||||||
\(458\) | 9.68573 | 0.452585 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 21.4572 | 0.999363 | 0.499681 | − | 0.866209i | \(-0.333450\pi\) | ||||
0.499681 | + | 0.866209i | \(0.333450\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −19.8033 | −0.920339 | −0.460170 | − | 0.887831i | \(-0.652211\pi\) | ||||
−0.460170 | + | 0.887831i | \(0.652211\pi\) | |||||||
\(464\) | −77.3310 | −3.59000 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −14.0684 | −0.651707 | ||||||||
\(467\) | 22.7210 | 1.05140 | 0.525701 | − | 0.850669i | \(-0.323803\pi\) | ||||
0.525701 | + | 0.850669i | \(0.323803\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −16.3633 | −0.755588 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 85.2743 | 3.92507 | ||||||||
\(473\) | −13.1598 | −0.605088 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −42.6625 | −1.95543 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −58.0300 | −2.65423 | ||||||||
\(479\) | 21.2880 | 0.972672 | 0.486336 | − | 0.873772i | \(-0.338333\pi\) | ||||
0.486336 | + | 0.873772i | \(0.338333\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 22.9424 | 1.04608 | ||||||||
\(482\) | −49.1115 | −2.23697 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −38.1625 | −1.73466 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −9.58690 | −0.434424 | −0.217212 | − | 0.976124i | \(-0.569696\pi\) | ||||
−0.217212 | + | 0.976124i | \(0.569696\pi\) | |||||||
\(488\) | −97.9921 | −4.43590 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −37.8443 | −1.70789 | −0.853945 | − | 0.520363i | \(-0.825797\pi\) | ||||
−0.853945 | + | 0.520363i | \(0.825797\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −35.4246 | −1.59544 | ||||||||
\(494\) | 15.3963 | 0.692711 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −27.5314 | −1.23619 | ||||||||
\(497\) | −2.29101 | −0.102766 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 16.9253 | 0.757681 | 0.378840 | − | 0.925462i | \(-0.376323\pi\) | ||||
0.378840 | + | 0.925462i | \(0.376323\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 38.6970 | 1.72713 | ||||||||
\(503\) | 40.4168 | 1.80210 | 0.901048 | − | 0.433719i | \(-0.142799\pi\) | ||||
0.901048 | + | 0.433719i | \(0.142799\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −8.25713 | −0.367074 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 17.8851 | 0.793522 | ||||||||
\(509\) | −41.4067 | −1.83532 | −0.917660 | − | 0.397366i | \(-0.869924\pi\) | ||||
−0.917660 | + | 0.397366i | \(0.869924\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 6.44863 | 0.285270 | ||||||||
\(512\) | −34.5537 | −1.52707 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 58.4922 | 2.57998 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 11.3769 | 0.500354 | ||||||||
\(518\) | −55.0797 | −2.42006 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −17.0301 | −0.746103 | −0.373052 | − | 0.927811i | \(-0.621689\pi\) | ||||
−0.373052 | + | 0.927811i | \(0.621689\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 9.57651 | 0.418751 | 0.209376 | − | 0.977835i | \(-0.432857\pi\) | ||||
0.209376 | + | 0.977835i | \(0.432857\pi\) | |||||||
\(524\) | 36.0041 | 1.57285 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 15.1176 | 0.659159 | ||||||||
\(527\) | −12.6118 | −0.549380 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −19.9935 | −0.869283 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −26.3055 | −1.14049 | ||||||||
\(533\) | −4.86347 | −0.210660 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 70.4077 | 3.04115 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −41.1289 | −1.77319 | ||||||||
\(539\) | −6.81528 | −0.293555 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −0.833751 | −0.0358458 | −0.0179229 | − | 0.999839i | \(-0.505705\pi\) | ||||
−0.0179229 | + | 0.999839i | \(0.505705\pi\) | |||||||
\(542\) | −17.7859 | −0.763971 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 58.5426 | 2.50999 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −28.3270 | −1.21117 | −0.605587 | − | 0.795779i | \(-0.707062\pi\) | ||||
−0.605587 | + | 0.795779i | \(0.707062\pi\) | |||||||
\(548\) | −35.1785 | −1.50275 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −21.8427 | −0.930529 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −3.79419 | −0.161345 | ||||||||
\(554\) | 79.7928 | 3.39007 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −72.6192 | −3.07974 | ||||||||
\(557\) | 11.5042 | 0.487448 | 0.243724 | − | 0.969845i | \(-0.421631\pi\) | ||||
0.243724 | + | 0.969845i | \(0.421631\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −14.3512 | −0.606993 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 49.0797 | 2.07030 | ||||||||
\(563\) | 33.0059 | 1.39103 | 0.695517 | − | 0.718510i | \(-0.255176\pi\) | ||||
0.695517 | + | 0.718510i | \(0.255176\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −14.9429 | −0.628095 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 9.85769 | 0.413619 | ||||||||
\(569\) | −27.0088 | −1.13227 | −0.566135 | − | 0.824313i | \(-0.691562\pi\) | ||||
−0.566135 | + | 0.824313i | \(0.691562\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −24.4244 | −1.02213 | −0.511064 | − | 0.859543i | \(-0.670749\pi\) | ||||
−0.511064 | + | 0.859543i | \(0.670749\pi\) | |||||||
\(572\) | 17.6001 | 0.735899 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 11.6761 | 0.487352 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 14.7976 | 0.616033 | 0.308017 | − | 0.951381i | \(-0.400335\pi\) | ||||
0.308017 | + | 0.951381i | \(0.400335\pi\) | |||||||
\(578\) | 16.1133 | 0.670224 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1.97507 | −0.0819396 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 3.11973 | 0.129206 | ||||||||
\(584\) | −27.7470 | −1.14818 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 48.1375 | 1.98854 | ||||||||
\(587\) | 30.5780 | 1.26209 | 0.631044 | − | 0.775747i | \(-0.282627\pi\) | ||||
0.631044 | + | 0.775747i | \(0.282627\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −7.77641 | −0.320421 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 122.122 | 5.01919 | ||||||||
\(593\) | −5.09990 | −0.209428 | −0.104714 | − | 0.994502i | \(-0.533393\pi\) | ||||
−0.104714 | + | 0.994502i | \(0.533393\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −2.79065 | −0.114309 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −9.00471 | −0.368230 | ||||||||
\(599\) | −0.565309 | −0.0230979 | −0.0115490 | − | 0.999933i | \(-0.503676\pi\) | ||||
−0.0115490 | + | 0.999933i | \(0.503676\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −11.0096 | −0.449091 | −0.224546 | − | 0.974464i | \(-0.572090\pi\) | ||||
−0.224546 | + | 0.974464i | \(0.572090\pi\) | |||||||
\(602\) | 34.4542 | 1.40425 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0.757185 | 0.0308094 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −19.0983 | −0.775174 | −0.387587 | − | 0.921833i | \(-0.626691\pi\) | ||||
−0.387587 | + | 0.921833i | \(0.626691\pi\) | |||||||
\(608\) | 36.0972 | 1.46393 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 12.4069 | 0.501929 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 9.33918 | 0.377206 | 0.188603 | − | 0.982053i | \(-0.439604\pi\) | ||||
0.188603 | + | 0.982053i | \(0.439604\pi\) | |||||||
\(614\) | −40.8358 | −1.64800 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −25.1350 | −1.01272 | ||||||||
\(617\) | −24.4154 | −0.982928 | −0.491464 | − | 0.870898i | \(-0.663538\pi\) | ||||
−0.491464 | + | 0.870898i | \(0.663538\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 39.4863 | 1.58709 | 0.793544 | − | 0.608513i | \(-0.208234\pi\) | ||||
0.793544 | + | 0.608513i | \(0.208234\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 80.1874 | 3.21522 | ||||||||
\(623\) | 23.8940 | 0.957293 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −18.3027 | −0.731523 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −56.5757 | −2.25762 | ||||||||
\(629\) | 55.9430 | 2.23059 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 42.1634 | 1.67850 | 0.839249 | − | 0.543747i | \(-0.182995\pi\) | ||||
0.839249 | + | 0.543747i | \(0.182995\pi\) | |||||||
\(632\) | 16.3255 | 0.649395 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −42.5216 | −1.68875 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −7.43232 | −0.294479 | ||||||||
\(638\) | −35.0855 | −1.38905 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 35.3155 | 1.39488 | 0.697438 | − | 0.716645i | \(-0.254323\pi\) | ||||
0.697438 | + | 0.716645i | \(0.254323\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 14.1954 | 0.559813 | 0.279906 | − | 0.960027i | \(-0.409697\pi\) | ||||
0.279906 | + | 0.960027i | \(0.409697\pi\) | |||||||
\(644\) | 15.3851 | 0.606259 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 37.5424 | 1.47709 | ||||||||
\(647\) | 17.4897 | 0.687593 | 0.343796 | − | 0.939044i | \(-0.388287\pi\) | ||||
0.343796 | + | 0.939044i | \(0.388287\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 19.9364 | 0.782572 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −108.897 | −4.26472 | ||||||||
\(653\) | −10.9772 | −0.429569 | −0.214785 | − | 0.976661i | \(-0.568905\pi\) | ||||
−0.214785 | + | 0.976661i | \(0.568905\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −25.8882 | −1.01077 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −29.7862 | −1.16119 | ||||||||
\(659\) | −15.7876 | −0.614998 | −0.307499 | − | 0.951548i | \(-0.599492\pi\) | ||||
−0.307499 | + | 0.951548i | \(0.599492\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 49.8932 | 1.94062 | 0.970311 | − | 0.241862i | \(-0.0777581\pi\) | ||||
0.970311 | + | 0.241862i | \(0.0777581\pi\) | |||||||
\(662\) | 33.2435 | 1.29204 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 8.49827 | 0.329797 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 12.7750 | 0.494649 | ||||||||
\(668\) | 84.2582 | 3.26005 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −22.9097 | −0.884419 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 28.8395 | 1.11168 | 0.555840 | − | 0.831289i | \(-0.312397\pi\) | ||||
0.555840 | + | 0.831289i | \(0.312397\pi\) | |||||||
\(674\) | −18.2264 | −0.702055 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −44.9809 | −1.73003 | ||||||||
\(677\) | 10.4636 | 0.402150 | 0.201075 | − | 0.979576i | \(-0.435557\pi\) | ||||
0.201075 | + | 0.979576i | \(0.435557\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 6.88910 | 0.264379 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −12.4911 | −0.478309 | ||||||||
\(683\) | −16.1875 | −0.619396 | −0.309698 | − | 0.950835i | \(-0.600228\pi\) | ||||
−0.309698 | + | 0.950835i | \(0.600228\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 50.9809 | 1.94646 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −76.3916 | −2.91240 | ||||||||
\(689\) | 3.40218 | 0.129613 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 9.88362 | 0.375991 | 0.187995 | − | 0.982170i | \(-0.439801\pi\) | ||||
0.187995 | + | 0.982170i | \(0.439801\pi\) | |||||||
\(692\) | 58.9648 | 2.24150 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 36.3621 | 1.38029 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −11.8591 | −0.449197 | ||||||||
\(698\) | 17.2974 | 0.654718 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 43.9692 | 1.66069 | 0.830346 | − | 0.557248i | \(-0.188143\pi\) | ||||
0.830346 | + | 0.557248i | \(0.188143\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 34.4942 | 1.30097 | ||||||||
\(704\) | 20.0260 | 0.754758 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −9.28385 | −0.349402 | ||||||||
\(707\) | −11.7774 | −0.442935 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 25.2260 | 0.947384 | 0.473692 | − | 0.880691i | \(-0.342921\pi\) | ||||
0.473692 | + | 0.880691i | \(0.342921\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −102.811 | −3.85299 | ||||||||
\(713\) | 4.54814 | 0.170329 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 42.2032 | 1.57721 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 60.3875 | 2.25364 | ||||||||
\(719\) | −36.8600 | −1.37465 | −0.687323 | − | 0.726352i | \(-0.741214\pi\) | ||||
−0.687323 | + | 0.726352i | \(0.741214\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 14.5153 | 0.540576 | ||||||||
\(722\) | −26.8922 | −1.00082 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −52.0918 | −1.93598 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −38.2451 | −1.41843 | −0.709217 | − | 0.704990i | \(-0.750951\pi\) | ||||
−0.709217 | + | 0.704990i | \(0.750951\pi\) | |||||||
\(728\) | −27.4107 | −1.01591 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −34.9942 | −1.29431 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 39.5832 | 1.46204 | 0.731020 | − | 0.682356i | \(-0.239045\pi\) | ||||
0.731020 | + | 0.682356i | \(0.239045\pi\) | |||||||
\(734\) | 11.0072 | 0.406282 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −21.1119 | −0.778195 | ||||||||
\(737\) | 16.4607 | 0.606338 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −8.24773 | −0.303398 | −0.151699 | − | 0.988427i | \(-0.548474\pi\) | ||||
−0.151699 | + | 0.988427i | \(0.548474\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −8.16790 | −0.299853 | ||||||||
\(743\) | 1.30818 | 0.0479925 | 0.0239963 | − | 0.999712i | \(-0.492361\pi\) | ||||
0.0239963 | + | 0.999712i | \(0.492361\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 18.0171 | 0.659651 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 42.9164 | 1.56918 | ||||||||
\(749\) | 16.1350 | 0.589562 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 28.4468 | 1.03804 | 0.519020 | − | 0.854762i | \(-0.326297\pi\) | ||||
0.519020 | + | 0.854762i | \(0.326297\pi\) | |||||||
\(752\) | 66.0418 | 2.40830 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −38.2620 | −1.39342 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −38.2012 | −1.38845 | −0.694223 | − | 0.719760i | \(-0.744252\pi\) | ||||
−0.694223 | + | 0.719760i | \(0.744252\pi\) | |||||||
\(758\) | −33.6495 | −1.22221 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 22.1904 | 0.804401 | 0.402200 | − | 0.915552i | \(-0.368245\pi\) | ||||
0.402200 | + | 0.915552i | \(0.368245\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 11.3986 | 0.412659 | ||||||||
\(764\) | −85.5852 | −3.09637 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 19.8440 | 0.716994 | ||||||||
\(767\) | 21.7414 | 0.785036 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −16.9130 | −0.609900 | −0.304950 | − | 0.952368i | \(-0.598640\pi\) | ||||
−0.304950 | + | 0.952368i | \(0.598640\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 7.69860 | 0.277079 | ||||||||
\(773\) | −38.6464 | −1.39001 | −0.695007 | − | 0.719003i | \(-0.744599\pi\) | ||||
−0.695007 | + | 0.719003i | \(0.744599\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −29.6423 | −1.06409 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 14.3584 | 0.514774 | ||||||||
\(779\) | −7.31230 | −0.261990 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2.30464 | 0.0824665 | ||||||||
\(782\) | −21.9572 | −0.785187 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −39.5622 | −1.41294 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 10.9147 | 0.389067 | 0.194533 | − | 0.980896i | \(-0.437681\pi\) | ||||
0.194533 | + | 0.980896i | \(0.437681\pi\) | |||||||
\(788\) | 88.7422 | 3.16131 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 26.7862 | 0.952409 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −24.9839 | −0.887204 | ||||||||
\(794\) | −14.8687 | −0.527669 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 54.4124 | 1.92860 | ||||||||
\(797\) | −2.92550 | −0.103627 | −0.0518133 | − | 0.998657i | \(-0.516500\pi\) | ||||
−0.0518133 | + | 0.998657i | \(0.516500\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 30.2531 | 1.07028 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −14.4965 | −0.511888 | ||||||||
\(803\) | −6.48700 | −0.228921 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −13.6220 | −0.479816 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 50.6755 | 1.78276 | ||||||||
\(809\) | −37.9241 | −1.33334 | −0.666671 | − | 0.745352i | \(-0.732281\pi\) | ||||
−0.666671 | + | 0.745352i | \(0.732281\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 19.5050 | 0.684912 | 0.342456 | − | 0.939534i | \(-0.388741\pi\) | ||||
0.342456 | + | 0.939534i | \(0.388741\pi\) | |||||||
\(812\) | 65.3731 | 2.29415 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 55.4075 | 1.94203 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −21.5773 | −0.754894 | ||||||||
\(818\) | 86.5257 | 3.02530 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 44.7524 | 1.56187 | 0.780934 | − | 0.624613i | \(-0.214743\pi\) | ||||
0.780934 | + | 0.624613i | \(0.214743\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −35.8994 | −1.25137 | −0.625687 | − | 0.780074i | \(-0.715181\pi\) | ||||
−0.625687 | + | 0.780074i | \(0.715181\pi\) | |||||||
\(824\) | −62.4559 | −2.17575 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −52.1963 | −1.81614 | ||||||||
\(827\) | −16.2717 | −0.565822 | −0.282911 | − | 0.959146i | \(-0.591300\pi\) | ||||
−0.282911 | + | 0.959146i | \(0.591300\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −20.6592 | −0.717525 | −0.358762 | − | 0.933429i | \(-0.616801\pi\) | ||||
−0.358762 | + | 0.933429i | \(0.616801\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 21.8391 | 0.757135 | ||||||||
\(833\) | −18.1230 | −0.627926 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 26.4621 | 0.915210 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 60.2044 | 2.07973 | ||||||||
\(839\) | −12.2367 | −0.422459 | −0.211229 | − | 0.977437i | \(-0.567747\pi\) | ||||
−0.211229 | + | 0.977437i | \(0.567747\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 25.2823 | 0.871802 | ||||||||
\(842\) | 47.2527 | 1.62844 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −118.123 | −4.06597 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 13.8953 | 0.477450 | ||||||||
\(848\) | 18.1098 | 0.621893 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −20.1744 | −0.691570 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 16.4293 | 0.562528 | 0.281264 | − | 0.959630i | \(-0.409246\pi\) | ||||
0.281264 | + | 0.959630i | \(0.409246\pi\) | |||||||
\(854\) | 59.9809 | 2.05250 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −69.4255 | −2.37291 | ||||||||
\(857\) | 49.0897 | 1.67687 | 0.838436 | − | 0.545000i | \(-0.183470\pi\) | ||||
0.838436 | + | 0.545000i | \(0.183470\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 41.0908 | 1.40200 | 0.700999 | − | 0.713162i | \(-0.252738\pi\) | ||||
0.700999 | + | 0.713162i | \(0.252738\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −16.2994 | −0.555158 | ||||||||
\(863\) | 47.8366 | 1.62838 | 0.814188 | − | 0.580601i | \(-0.197183\pi\) | ||||
0.814188 | + | 0.580601i | \(0.197183\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −8.21210 | −0.279058 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 23.2741 | 0.789975 | ||||||||
\(869\) | 3.81677 | 0.129475 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 17.9510 | 0.608247 | ||||||||
\(872\) | −49.0458 | −1.66090 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −13.5387 | −0.457954 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −11.3772 | −0.384180 | −0.192090 | − | 0.981377i | \(-0.561527\pi\) | ||||
−0.192090 | + | 0.981377i | \(0.561527\pi\) | |||||||
\(878\) | 35.5813 | 1.20081 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −43.9924 | −1.48214 | −0.741071 | − | 0.671426i | \(-0.765682\pi\) | ||||
−0.741071 | + | 0.671426i | \(0.765682\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 37.6820 | 1.26810 | 0.634051 | − | 0.773291i | \(-0.281391\pi\) | ||||
0.634051 | + | 0.773291i | \(0.281391\pi\) | |||||||
\(884\) | 46.8019 | 1.57412 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −63.9398 | −2.14810 | ||||||||
\(887\) | −33.2833 | −1.11754 | −0.558771 | − | 0.829322i | \(-0.688727\pi\) | ||||
−0.558771 | + | 0.829322i | \(0.688727\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −6.51213 | −0.218410 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 107.175 | 3.58847 | ||||||||
\(893\) | 18.6539 | 0.624230 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −8.66080 | −0.289337 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −63.5878 | −2.12195 | ||||||||
\(899\) | 19.3255 | 0.644543 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 8.29592 | 0.276377 | ||||||||
\(902\) | −11.7456 | −0.391086 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −115.255 | −3.83333 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −14.0784 | −0.467464 | −0.233732 | − | 0.972301i | \(-0.575094\pi\) | ||||
−0.233732 | + | 0.972301i | \(0.575094\pi\) | |||||||
\(908\) | 69.6056 | 2.30994 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 7.31522 | 0.242364 | 0.121182 | − | 0.992630i | \(-0.461332\pi\) | ||||
0.121182 | + | 0.992630i | \(0.461332\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1.98682 | 0.0657542 | ||||||||
\(914\) | −7.43123 | −0.245803 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 18.1544 | 0.599838 | ||||||||
\(917\) | −13.1094 | −0.432912 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 4.44684 | 0.146688 | 0.0733438 | − | 0.997307i | \(-0.476633\pi\) | ||||
0.0733438 | + | 0.997307i | \(0.476633\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 56.5124 | 1.86114 | ||||||||
\(923\) | 2.51330 | 0.0827262 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −52.1565 | −1.71397 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −89.7068 | −2.94477 | ||||||||
\(929\) | 13.1133 | 0.430232 | 0.215116 | − | 0.976588i | \(-0.430987\pi\) | ||||
0.215116 | + | 0.976588i | \(0.430987\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −11.1746 | −0.366233 | ||||||||
\(932\) | −26.3690 | −0.863746 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 59.8408 | 1.95805 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −33.5187 | −1.09501 | −0.547504 | − | 0.836803i | \(-0.684422\pi\) | ||||
−0.547504 | + | 0.836803i | \(0.684422\pi\) | |||||||
\(938\) | −43.0964 | −1.40715 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1.79076 | 0.0583772 | 0.0291886 | − | 0.999574i | \(-0.490708\pi\) | ||||
0.0291886 | + | 0.999574i | \(0.490708\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 4.27669 | 0.139268 | ||||||||
\(944\) | 115.729 | 3.76667 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −34.6592 | −1.12687 | ||||||||
\(947\) | −52.6350 | −1.71041 | −0.855204 | − | 0.518292i | \(-0.826568\pi\) | ||||
−0.855204 | + | 0.518292i | \(0.826568\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −7.07432 | −0.229642 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −66.8386 | −2.16625 | ||||||||
\(953\) | −18.4072 | −0.596268 | −0.298134 | − | 0.954524i | \(-0.596364\pi\) | ||||
−0.298134 | + | 0.954524i | \(0.596364\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −108.768 | −3.51781 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 56.0666 | 1.81143 | ||||||||
\(959\) | 12.8088 | 0.413619 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −24.1197 | −0.778056 | ||||||||
\(962\) | 60.4240 | 1.94815 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −92.0517 | −2.96479 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −6.09579 | −0.196027 | −0.0980137 | − | 0.995185i | \(-0.531249\pi\) | ||||
−0.0980137 | + | 0.995185i | \(0.531249\pi\) | |||||||
\(968\) | −59.7886 | −1.92168 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −34.1077 | −1.09457 | −0.547283 | − | 0.836947i | \(-0.684338\pi\) | ||||
−0.547283 | + | 0.836947i | \(0.684338\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 26.4414 | 0.847671 | ||||||||
\(974\) | −25.2493 | −0.809038 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −132.989 | −4.25688 | ||||||||
\(977\) | 48.7914 | 1.56098 | 0.780488 | − | 0.625171i | \(-0.214971\pi\) | ||||
0.780488 | + | 0.625171i | \(0.214971\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −24.0362 | −0.768201 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −99.6715 | −3.18065 | ||||||||
\(983\) | 33.4172 | 1.06584 | 0.532922 | − | 0.846164i | \(-0.321094\pi\) | ||||
0.532922 | + | 0.846164i | \(0.321094\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −93.2985 | −2.97123 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 28.8579 | 0.918092 | ||||||||
\(989\) | 12.6198 | 0.401285 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −19.3512 | −0.614713 | −0.307356 | − | 0.951595i | \(-0.599444\pi\) | ||||
−0.307356 | + | 0.951595i | \(0.599444\pi\) | |||||||
\(992\) | −31.9374 | −1.01401 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −6.03388 | −0.191383 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 39.5442 | 1.25238 | 0.626189 | − | 0.779671i | \(-0.284614\pi\) | ||||
0.626189 | + | 0.779671i | \(0.284614\pi\) | |||||||
\(998\) | 44.5766 | 1.41105 | ||||||||
\(999\) | 0 | 0 |
(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 | 2025.2.a.y.1.4 | 4 | ||
3.2 | odd | 2 | 2025.2.a.p.1.1 | 4 | |||
5.2 | odd | 4 | 2025.2.b.n.649.8 | 8 | |||
5.3 | odd | 4 | 2025.2.b.n.649.1 | 8 | |||
5.4 | even | 2 | 2025.2.a.q.1.1 | 4 | |||
9.2 | odd | 6 | 675.2.e.e.226.4 | 8 | |||
9.4 | even | 3 | 225.2.e.c.151.1 | yes | 8 | ||
9.5 | odd | 6 | 675.2.e.e.451.4 | 8 | |||
9.7 | even | 3 | 225.2.e.c.76.1 | ✓ | 8 | ||
15.2 | even | 4 | 2025.2.b.o.649.1 | 8 | |||
15.8 | even | 4 | 2025.2.b.o.649.8 | 8 | |||
15.14 | odd | 2 | 2025.2.a.z.1.4 | 4 | |||
45.2 | even | 12 | 675.2.k.c.199.1 | 16 | |||
45.4 | even | 6 | 225.2.e.e.151.4 | yes | 8 | ||
45.7 | odd | 12 | 225.2.k.c.49.8 | 16 | |||
45.13 | odd | 12 | 225.2.k.c.124.8 | 16 | |||
45.14 | odd | 6 | 675.2.e.c.451.1 | 8 | |||
45.22 | odd | 12 | 225.2.k.c.124.1 | 16 | |||
45.23 | even | 12 | 675.2.k.c.424.1 | 16 | |||
45.29 | odd | 6 | 675.2.e.c.226.1 | 8 | |||
45.32 | even | 12 | 675.2.k.c.424.8 | 16 | |||
45.34 | even | 6 | 225.2.e.e.76.4 | yes | 8 | ||
45.38 | even | 12 | 675.2.k.c.199.8 | 16 | |||
45.43 | odd | 12 | 225.2.k.c.49.1 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
225.2.e.c.76.1 | ✓ | 8 | 9.7 | even | 3 | ||
225.2.e.c.151.1 | yes | 8 | 9.4 | even | 3 | ||
225.2.e.e.76.4 | yes | 8 | 45.34 | even | 6 | ||
225.2.e.e.151.4 | yes | 8 | 45.4 | even | 6 | ||
225.2.k.c.49.1 | 16 | 45.43 | odd | 12 | |||
225.2.k.c.49.8 | 16 | 45.7 | odd | 12 | |||
225.2.k.c.124.1 | 16 | 45.22 | odd | 12 | |||
225.2.k.c.124.8 | 16 | 45.13 | odd | 12 | |||
675.2.e.c.226.1 | 8 | 45.29 | odd | 6 | |||
675.2.e.c.451.1 | 8 | 45.14 | odd | 6 | |||
675.2.e.e.226.4 | 8 | 9.2 | odd | 6 | |||
675.2.e.e.451.4 | 8 | 9.5 | odd | 6 | |||
675.2.k.c.199.1 | 16 | 45.2 | even | 12 | |||
675.2.k.c.199.8 | 16 | 45.38 | even | 12 | |||
675.2.k.c.424.1 | 16 | 45.23 | even | 12 | |||
675.2.k.c.424.8 | 16 | 45.32 | even | 12 | |||
2025.2.a.p.1.1 | 4 | 3.2 | odd | 2 | |||
2025.2.a.q.1.1 | 4 | 5.4 | even | 2 | |||
2025.2.a.y.1.4 | 4 | 1.1 | even | 1 | trivial | ||
2025.2.a.z.1.4 | 4 | 15.14 | odd | 2 | |||
2025.2.b.n.649.1 | 8 | 5.3 | odd | 4 | |||
2025.2.b.n.649.8 | 8 | 5.2 | odd | 4 | |||
2025.2.b.o.649.1 | 8 | 15.2 | even | 4 | |||
2025.2.b.o.649.8 | 8 | 15.8 | even | 4 |