Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6001,2,Mod(1,6001)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6001, 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("6001.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6001 = 17 \cdot 353 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6001.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: | \(47.9182262530\) |
Analytic rank: | \(0\) |
Dimension: | \(121\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.14 | ||
Character | \(\chi\) | \(=\) | 6001.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.25245 | −1.59272 | −0.796361 | − | 0.604821i | \(-0.793245\pi\) | ||||
−0.796361 | + | 0.604821i | \(0.793245\pi\) | |||||||
\(3\) | −3.40363 | −1.96508 | −0.982542 | − | 0.186041i | \(-0.940434\pi\) | ||||
−0.982542 | + | 0.186041i | \(0.940434\pi\) | |||||||
\(4\) | 3.07353 | 1.53677 | ||||||||
\(5\) | −2.33953 | −1.04627 | −0.523134 | − | 0.852251i | \(-0.675237\pi\) | ||||
−0.523134 | + | 0.852251i | \(0.675237\pi\) | |||||||
\(6\) | 7.66650 | 3.12983 | ||||||||
\(7\) | 2.81637 | 1.06449 | 0.532243 | − | 0.846591i | \(-0.321349\pi\) | ||||
0.532243 | + | 0.846591i | \(0.321349\pi\) | |||||||
\(8\) | −2.41808 | −0.854920 | ||||||||
\(9\) | 8.58466 | 2.86155 | ||||||||
\(10\) | 5.26966 | 1.66641 | ||||||||
\(11\) | 1.91833 | 0.578399 | 0.289199 | − | 0.957269i | \(-0.406611\pi\) | ||||
0.289199 | + | 0.957269i | \(0.406611\pi\) | |||||||
\(12\) | −10.4612 | −3.01987 | ||||||||
\(13\) | −4.71647 | −1.30811 | −0.654057 | − | 0.756445i | \(-0.726934\pi\) | ||||
−0.654057 | + | 0.756445i | \(0.726934\pi\) | |||||||
\(14\) | −6.34373 | −1.69543 | ||||||||
\(15\) | 7.96287 | 2.05600 | ||||||||
\(16\) | −0.700463 | −0.175116 | ||||||||
\(17\) | 1.00000 | 0.242536 | ||||||||
\(18\) | −19.3365 | −4.55766 | ||||||||
\(19\) | −2.11506 | −0.485227 | −0.242613 | − | 0.970123i | \(-0.578005\pi\) | ||||
−0.242613 | + | 0.970123i | \(0.578005\pi\) | |||||||
\(20\) | −7.19061 | −1.60787 | ||||||||
\(21\) | −9.58586 | −2.09181 | ||||||||
\(22\) | −4.32095 | −0.921229 | ||||||||
\(23\) | −5.88844 | −1.22782 | −0.613912 | − | 0.789374i | \(-0.710405\pi\) | ||||
−0.613912 | + | 0.789374i | \(0.710405\pi\) | |||||||
\(24\) | 8.23023 | 1.67999 | ||||||||
\(25\) | 0.473377 | 0.0946755 | ||||||||
\(26\) | 10.6236 | 2.08346 | ||||||||
\(27\) | −19.0081 | −3.65811 | ||||||||
\(28\) | 8.65620 | 1.63587 | ||||||||
\(29\) | 6.32875 | 1.17522 | 0.587610 | − | 0.809145i | \(-0.300069\pi\) | ||||
0.587610 | + | 0.809145i | \(0.300069\pi\) | |||||||
\(30\) | −17.9360 | −3.27464 | ||||||||
\(31\) | 6.02410 | 1.08196 | 0.540980 | − | 0.841035i | \(-0.318053\pi\) | ||||
0.540980 | + | 0.841035i | \(0.318053\pi\) | |||||||
\(32\) | 6.41392 | 1.13383 | ||||||||
\(33\) | −6.52928 | −1.13660 | ||||||||
\(34\) | −2.25245 | −0.386292 | ||||||||
\(35\) | −6.58896 | −1.11374 | ||||||||
\(36\) | 26.3852 | 4.39754 | ||||||||
\(37\) | −6.28639 | −1.03348 | −0.516738 | − | 0.856144i | \(-0.672854\pi\) | ||||
−0.516738 | + | 0.856144i | \(0.672854\pi\) | |||||||
\(38\) | 4.76406 | 0.772832 | ||||||||
\(39\) | 16.0531 | 2.57055 | ||||||||
\(40\) | 5.65716 | 0.894475 | ||||||||
\(41\) | 1.40476 | 0.219386 | 0.109693 | − | 0.993965i | \(-0.465013\pi\) | ||||
0.109693 | + | 0.993965i | \(0.465013\pi\) | |||||||
\(42\) | 21.5917 | 3.33167 | ||||||||
\(43\) | −4.35602 | −0.664286 | −0.332143 | − | 0.943229i | \(-0.607772\pi\) | ||||
−0.332143 | + | 0.943229i | \(0.607772\pi\) | |||||||
\(44\) | 5.89606 | 0.888864 | ||||||||
\(45\) | −20.0840 | −2.99395 | ||||||||
\(46\) | 13.2634 | 1.95558 | ||||||||
\(47\) | 0.504651 | 0.0736109 | 0.0368054 | − | 0.999322i | \(-0.488282\pi\) | ||||
0.0368054 | + | 0.999322i | \(0.488282\pi\) | |||||||
\(48\) | 2.38411 | 0.344117 | ||||||||
\(49\) | 0.931923 | 0.133132 | ||||||||
\(50\) | −1.06626 | −0.150792 | ||||||||
\(51\) | −3.40363 | −0.476603 | ||||||||
\(52\) | −14.4962 | −2.01027 | ||||||||
\(53\) | −3.90983 | −0.537056 | −0.268528 | − | 0.963272i | \(-0.586537\pi\) | ||||
−0.268528 | + | 0.963272i | \(0.586537\pi\) | |||||||
\(54\) | 42.8148 | 5.82636 | ||||||||
\(55\) | −4.48799 | −0.605160 | ||||||||
\(56\) | −6.81020 | −0.910051 | ||||||||
\(57\) | 7.19886 | 0.953512 | ||||||||
\(58\) | −14.2552 | −1.87180 | ||||||||
\(59\) | 5.35540 | 0.697214 | 0.348607 | − | 0.937269i | \(-0.386655\pi\) | ||||
0.348607 | + | 0.937269i | \(0.386655\pi\) | |||||||
\(60\) | 24.4741 | 3.15960 | ||||||||
\(61\) | 7.70600 | 0.986652 | 0.493326 | − | 0.869845i | \(-0.335781\pi\) | ||||
0.493326 | + | 0.869845i | \(0.335781\pi\) | |||||||
\(62\) | −13.5690 | −1.72326 | ||||||||
\(63\) | 24.1776 | 3.04609 | ||||||||
\(64\) | −13.0461 | −1.63076 | ||||||||
\(65\) | 11.0343 | 1.36864 | ||||||||
\(66\) | 14.7069 | 1.81029 | ||||||||
\(67\) | 6.86600 | 0.838816 | 0.419408 | − | 0.907798i | \(-0.362238\pi\) | ||||
0.419408 | + | 0.907798i | \(0.362238\pi\) | |||||||
\(68\) | 3.07353 | 0.372721 | ||||||||
\(69\) | 20.0420 | 2.41278 | ||||||||
\(70\) | 14.8413 | 1.77388 | ||||||||
\(71\) | 0.718934 | 0.0853218 | 0.0426609 | − | 0.999090i | \(-0.486416\pi\) | ||||
0.0426609 | + | 0.999090i | \(0.486416\pi\) | |||||||
\(72\) | −20.7584 | −2.44640 | ||||||||
\(73\) | −6.38377 | −0.747163 | −0.373582 | − | 0.927597i | \(-0.621870\pi\) | ||||
−0.373582 | + | 0.927597i | \(0.621870\pi\) | |||||||
\(74\) | 14.1598 | 1.64604 | ||||||||
\(75\) | −1.61120 | −0.186045 | ||||||||
\(76\) | −6.50069 | −0.745680 | ||||||||
\(77\) | 5.40273 | 0.615698 | ||||||||
\(78\) | −36.1588 | −4.09418 | ||||||||
\(79\) | −11.0359 | −1.24164 | −0.620819 | − | 0.783954i | \(-0.713200\pi\) | ||||
−0.620819 | + | 0.783954i | \(0.713200\pi\) | |||||||
\(80\) | 1.63875 | 0.183218 | ||||||||
\(81\) | 38.9425 | 4.32694 | ||||||||
\(82\) | −3.16415 | −0.349422 | ||||||||
\(83\) | 11.9956 | 1.31669 | 0.658346 | − | 0.752715i | \(-0.271256\pi\) | ||||
0.658346 | + | 0.752715i | \(0.271256\pi\) | |||||||
\(84\) | −29.4624 | −3.21462 | ||||||||
\(85\) | −2.33953 | −0.253757 | ||||||||
\(86\) | 9.81171 | 1.05802 | ||||||||
\(87\) | −21.5407 | −2.30940 | ||||||||
\(88\) | −4.63868 | −0.494485 | ||||||||
\(89\) | 5.28593 | 0.560308 | 0.280154 | − | 0.959955i | \(-0.409614\pi\) | ||||
0.280154 | + | 0.959955i | \(0.409614\pi\) | |||||||
\(90\) | 45.2383 | 4.76854 | ||||||||
\(91\) | −13.2833 | −1.39247 | ||||||||
\(92\) | −18.0983 | −1.88688 | ||||||||
\(93\) | −20.5038 | −2.12614 | ||||||||
\(94\) | −1.13670 | −0.117242 | ||||||||
\(95\) | 4.94822 | 0.507677 | ||||||||
\(96\) | −21.8306 | −2.22807 | ||||||||
\(97\) | 17.3091 | 1.75748 | 0.878738 | − | 0.477304i | \(-0.158386\pi\) | ||||
0.878738 | + | 0.477304i | \(0.158386\pi\) | |||||||
\(98\) | −2.09911 | −0.212042 | ||||||||
\(99\) | 16.4682 | 1.65512 | ||||||||
\(100\) | 1.45494 | 0.145494 | ||||||||
\(101\) | −2.02067 | −0.201064 | −0.100532 | − | 0.994934i | \(-0.532054\pi\) | ||||
−0.100532 | + | 0.994934i | \(0.532054\pi\) | |||||||
\(102\) | 7.66650 | 0.759096 | ||||||||
\(103\) | 10.6820 | 1.05253 | 0.526267 | − | 0.850320i | \(-0.323591\pi\) | ||||
0.526267 | + | 0.850320i | \(0.323591\pi\) | |||||||
\(104\) | 11.4048 | 1.11833 | ||||||||
\(105\) | 22.4264 | 2.18859 | ||||||||
\(106\) | 8.80669 | 0.855381 | ||||||||
\(107\) | −15.5427 | −1.50257 | −0.751285 | − | 0.659978i | \(-0.770565\pi\) | ||||
−0.751285 | + | 0.659978i | \(0.770565\pi\) | |||||||
\(108\) | −58.4220 | −5.62166 | ||||||||
\(109\) | −2.08085 | −0.199309 | −0.0996545 | − | 0.995022i | \(-0.531774\pi\) | ||||
−0.0996545 | + | 0.995022i | \(0.531774\pi\) | |||||||
\(110\) | 10.1090 | 0.963852 | ||||||||
\(111\) | 21.3965 | 2.03087 | ||||||||
\(112\) | −1.97276 | −0.186408 | ||||||||
\(113\) | −3.39374 | −0.319256 | −0.159628 | − | 0.987177i | \(-0.551030\pi\) | ||||
−0.159628 | + | 0.987177i | \(0.551030\pi\) | |||||||
\(114\) | −16.2151 | −1.51868 | ||||||||
\(115\) | 13.7762 | 1.28463 | ||||||||
\(116\) | 19.4516 | 1.80604 | ||||||||
\(117\) | −40.4893 | −3.74324 | ||||||||
\(118\) | −12.0628 | −1.11047 | ||||||||
\(119\) | 2.81637 | 0.258176 | ||||||||
\(120\) | −19.2548 | −1.75772 | ||||||||
\(121\) | −7.32000 | −0.665455 | ||||||||
\(122\) | −17.3574 | −1.57146 | ||||||||
\(123\) | −4.78127 | −0.431113 | ||||||||
\(124\) | 18.5153 | 1.66272 | ||||||||
\(125\) | 10.5901 | 0.947212 | ||||||||
\(126\) | −54.4588 | −4.85157 | ||||||||
\(127\) | −5.77986 | −0.512880 | −0.256440 | − | 0.966560i | \(-0.582550\pi\) | ||||
−0.256440 | + | 0.966560i | \(0.582550\pi\) | |||||||
\(128\) | 16.5579 | 1.46352 | ||||||||
\(129\) | 14.8262 | 1.30538 | ||||||||
\(130\) | −24.8542 | −2.17986 | ||||||||
\(131\) | −8.16177 | −0.713097 | −0.356548 | − | 0.934277i | \(-0.616047\pi\) | ||||
−0.356548 | + | 0.934277i | \(0.616047\pi\) | |||||||
\(132\) | −20.0680 | −1.74669 | ||||||||
\(133\) | −5.95677 | −0.516518 | ||||||||
\(134\) | −15.4653 | −1.33600 | ||||||||
\(135\) | 44.4699 | 3.82736 | ||||||||
\(136\) | −2.41808 | −0.207349 | ||||||||
\(137\) | 11.4961 | 0.982179 | 0.491089 | − | 0.871109i | \(-0.336599\pi\) | ||||
0.491089 | + | 0.871109i | \(0.336599\pi\) | |||||||
\(138\) | −45.1437 | −3.84289 | ||||||||
\(139\) | −14.8888 | −1.26285 | −0.631425 | − | 0.775437i | \(-0.717530\pi\) | ||||
−0.631425 | + | 0.775437i | \(0.717530\pi\) | |||||||
\(140\) | −20.2514 | −1.71155 | ||||||||
\(141\) | −1.71764 | −0.144652 | ||||||||
\(142\) | −1.61936 | −0.135894 | ||||||||
\(143\) | −9.04776 | −0.756612 | ||||||||
\(144\) | −6.01324 | −0.501103 | ||||||||
\(145\) | −14.8063 | −1.22959 | ||||||||
\(146\) | 14.3791 | 1.19002 | ||||||||
\(147\) | −3.17192 | −0.261615 | ||||||||
\(148\) | −19.3214 | −1.58821 | ||||||||
\(149\) | −22.0689 | −1.80796 | −0.903979 | − | 0.427577i | \(-0.859367\pi\) | ||||
−0.903979 | + | 0.427577i | \(0.859367\pi\) | |||||||
\(150\) | 3.62915 | 0.296319 | ||||||||
\(151\) | −12.5067 | −1.01778 | −0.508890 | − | 0.860831i | \(-0.669944\pi\) | ||||
−0.508890 | + | 0.860831i | \(0.669944\pi\) | |||||||
\(152\) | 5.11437 | 0.414830 | ||||||||
\(153\) | 8.58466 | 0.694029 | ||||||||
\(154\) | −12.1694 | −0.980636 | ||||||||
\(155\) | −14.0935 | −1.13202 | ||||||||
\(156\) | 49.3397 | 3.95034 | ||||||||
\(157\) | −12.0096 | −0.958471 | −0.479236 | − | 0.877686i | \(-0.659086\pi\) | ||||
−0.479236 | + | 0.877686i | \(0.659086\pi\) | |||||||
\(158\) | 24.8578 | 1.97758 | ||||||||
\(159\) | 13.3076 | 1.05536 | ||||||||
\(160\) | −15.0055 | −1.18629 | ||||||||
\(161\) | −16.5840 | −1.30700 | ||||||||
\(162\) | −87.7160 | −6.89162 | ||||||||
\(163\) | −14.5070 | −1.13627 | −0.568137 | − | 0.822934i | \(-0.692336\pi\) | ||||
−0.568137 | + | 0.822934i | \(0.692336\pi\) | |||||||
\(164\) | 4.31757 | 0.337146 | ||||||||
\(165\) | 15.2754 | 1.18919 | ||||||||
\(166\) | −27.0196 | −2.09713 | ||||||||
\(167\) | 17.6656 | 1.36701 | 0.683504 | − | 0.729947i | \(-0.260455\pi\) | ||||
0.683504 | + | 0.729947i | \(0.260455\pi\) | |||||||
\(168\) | 23.1794 | 1.78833 | ||||||||
\(169\) | 9.24512 | 0.711163 | ||||||||
\(170\) | 5.26966 | 0.404165 | ||||||||
\(171\) | −18.1570 | −1.38850 | ||||||||
\(172\) | −13.3884 | −1.02085 | ||||||||
\(173\) | 19.4602 | 1.47953 | 0.739766 | − | 0.672864i | \(-0.234936\pi\) | ||||
0.739766 | + | 0.672864i | \(0.234936\pi\) | |||||||
\(174\) | 48.5193 | 3.67824 | ||||||||
\(175\) | 1.33320 | 0.100781 | ||||||||
\(176\) | −1.34372 | −0.101287 | ||||||||
\(177\) | −18.2278 | −1.37008 | ||||||||
\(178\) | −11.9063 | −0.892415 | ||||||||
\(179\) | 22.1857 | 1.65824 | 0.829119 | − | 0.559072i | \(-0.188842\pi\) | ||||
0.829119 | + | 0.559072i | \(0.188842\pi\) | |||||||
\(180\) | −61.7289 | −4.60100 | ||||||||
\(181\) | −4.67189 | −0.347259 | −0.173629 | − | 0.984811i | \(-0.555549\pi\) | ||||
−0.173629 | + | 0.984811i | \(0.555549\pi\) | |||||||
\(182\) | 29.9200 | 2.21782 | ||||||||
\(183\) | −26.2283 | −1.93885 | ||||||||
\(184\) | 14.2387 | 1.04969 | ||||||||
\(185\) | 14.7072 | 1.08129 | ||||||||
\(186\) | 46.1837 | 3.38636 | ||||||||
\(187\) | 1.91833 | 0.140282 | ||||||||
\(188\) | 1.55106 | 0.113123 | ||||||||
\(189\) | −53.5338 | −3.89401 | ||||||||
\(190\) | −11.1456 | −0.808589 | ||||||||
\(191\) | 1.57262 | 0.113791 | 0.0568956 | − | 0.998380i | \(-0.481880\pi\) | ||||
0.0568956 | + | 0.998380i | \(0.481880\pi\) | |||||||
\(192\) | 44.4040 | 3.20459 | ||||||||
\(193\) | −24.5542 | −1.76745 | −0.883725 | − | 0.468006i | \(-0.844972\pi\) | ||||
−0.883725 | + | 0.468006i | \(0.844972\pi\) | |||||||
\(194\) | −38.9880 | −2.79917 | ||||||||
\(195\) | −37.5566 | −2.68949 | ||||||||
\(196\) | 2.86429 | 0.204592 | ||||||||
\(197\) | −3.58665 | −0.255538 | −0.127769 | − | 0.991804i | \(-0.540782\pi\) | ||||
−0.127769 | + | 0.991804i | \(0.540782\pi\) | |||||||
\(198\) | −37.0939 | −2.63615 | ||||||||
\(199\) | 15.0746 | 1.06861 | 0.534306 | − | 0.845291i | \(-0.320573\pi\) | ||||
0.534306 | + | 0.845291i | \(0.320573\pi\) | |||||||
\(200\) | −1.14466 | −0.0809399 | ||||||||
\(201\) | −23.3693 | −1.64834 | ||||||||
\(202\) | 4.55145 | 0.320239 | ||||||||
\(203\) | 17.8241 | 1.25101 | ||||||||
\(204\) | −10.4612 | −0.732427 | ||||||||
\(205\) | −3.28647 | −0.229537 | ||||||||
\(206\) | −24.0608 | −1.67639 | ||||||||
\(207\) | −50.5503 | −3.51349 | ||||||||
\(208\) | 3.30372 | 0.229071 | ||||||||
\(209\) | −4.05738 | −0.280655 | ||||||||
\(210\) | −50.5142 | −3.48581 | ||||||||
\(211\) | 14.3476 | 0.987730 | 0.493865 | − | 0.869539i | \(-0.335584\pi\) | ||||
0.493865 | + | 0.869539i | \(0.335584\pi\) | |||||||
\(212\) | −12.0170 | −0.825329 | ||||||||
\(213\) | −2.44698 | −0.167665 | ||||||||
\(214\) | 35.0092 | 2.39318 | ||||||||
\(215\) | 10.1910 | 0.695021 | ||||||||
\(216\) | 45.9631 | 3.12739 | ||||||||
\(217\) | 16.9661 | 1.15173 | ||||||||
\(218\) | 4.68700 | 0.317444 | ||||||||
\(219\) | 21.7280 | 1.46824 | ||||||||
\(220\) | −13.7940 | −0.929989 | ||||||||
\(221\) | −4.71647 | −0.317264 | ||||||||
\(222\) | −48.1946 | −3.23461 | ||||||||
\(223\) | 11.7569 | 0.787302 | 0.393651 | − | 0.919260i | \(-0.371212\pi\) | ||||
0.393651 | + | 0.919260i | \(0.371212\pi\) | |||||||
\(224\) | 18.0639 | 1.20695 | ||||||||
\(225\) | 4.06379 | 0.270919 | ||||||||
\(226\) | 7.64423 | 0.508487 | ||||||||
\(227\) | −22.2907 | −1.47949 | −0.739744 | − | 0.672889i | \(-0.765053\pi\) | ||||
−0.739744 | + | 0.672889i | \(0.765053\pi\) | |||||||
\(228\) | 22.1259 | 1.46532 | ||||||||
\(229\) | −6.04812 | −0.399671 | −0.199836 | − | 0.979829i | \(-0.564041\pi\) | ||||
−0.199836 | + | 0.979829i | \(0.564041\pi\) | |||||||
\(230\) | −31.0301 | −2.04606 | ||||||||
\(231\) | −18.3889 | −1.20990 | ||||||||
\(232\) | −15.3034 | −1.00472 | ||||||||
\(233\) | −5.98731 | −0.392241 | −0.196121 | − | 0.980580i | \(-0.562834\pi\) | ||||
−0.196121 | + | 0.980580i | \(0.562834\pi\) | |||||||
\(234\) | 91.2002 | 5.96195 | ||||||||
\(235\) | −1.18064 | −0.0770167 | ||||||||
\(236\) | 16.4600 | 1.07145 | ||||||||
\(237\) | 37.5621 | 2.43992 | ||||||||
\(238\) | −6.34373 | −0.411203 | ||||||||
\(239\) | −13.2808 | −0.859065 | −0.429533 | − | 0.903051i | \(-0.641322\pi\) | ||||
−0.429533 | + | 0.903051i | \(0.641322\pi\) | |||||||
\(240\) | −5.57769 | −0.360039 | ||||||||
\(241\) | −15.1893 | −0.978428 | −0.489214 | − | 0.872164i | \(-0.662716\pi\) | ||||
−0.489214 | + | 0.872164i | \(0.662716\pi\) | |||||||
\(242\) | 16.4879 | 1.05988 | ||||||||
\(243\) | −75.5213 | −4.84469 | ||||||||
\(244\) | 23.6846 | 1.51625 | ||||||||
\(245\) | −2.18026 | −0.139291 | ||||||||
\(246\) | 10.7696 | 0.686643 | ||||||||
\(247\) | 9.97560 | 0.634732 | ||||||||
\(248\) | −14.5667 | −0.924989 | ||||||||
\(249\) | −40.8286 | −2.58741 | ||||||||
\(250\) | −23.8538 | −1.50865 | ||||||||
\(251\) | −10.7655 | −0.679513 | −0.339756 | − | 0.940513i | \(-0.610345\pi\) | ||||
−0.339756 | + | 0.940513i | \(0.610345\pi\) | |||||||
\(252\) | 74.3105 | 4.68112 | ||||||||
\(253\) | −11.2960 | −0.710172 | ||||||||
\(254\) | 13.0189 | 0.816875 | ||||||||
\(255\) | 7.96287 | 0.498654 | ||||||||
\(256\) | −11.2036 | −0.700222 | ||||||||
\(257\) | 26.8539 | 1.67510 | 0.837551 | − | 0.546359i | \(-0.183986\pi\) | ||||
0.837551 | + | 0.546359i | \(0.183986\pi\) | |||||||
\(258\) | −33.3954 | −2.07911 | ||||||||
\(259\) | −17.7048 | −1.10012 | ||||||||
\(260\) | 33.9143 | 2.10328 | ||||||||
\(261\) | 54.3302 | 3.36295 | ||||||||
\(262\) | 18.3840 | 1.13577 | ||||||||
\(263\) | 10.9656 | 0.676167 | 0.338084 | − | 0.941116i | \(-0.390221\pi\) | ||||
0.338084 | + | 0.941116i | \(0.390221\pi\) | |||||||
\(264\) | 15.7883 | 0.971704 | ||||||||
\(265\) | 9.14713 | 0.561904 | ||||||||
\(266\) | 13.4173 | 0.822669 | ||||||||
\(267\) | −17.9913 | −1.10105 | ||||||||
\(268\) | 21.1029 | 1.28906 | ||||||||
\(269\) | 25.7016 | 1.56706 | 0.783528 | − | 0.621357i | \(-0.213418\pi\) | ||||
0.783528 | + | 0.621357i | \(0.213418\pi\) | |||||||
\(270\) | −100.166 | −6.09593 | ||||||||
\(271\) | 19.5897 | 1.18999 | 0.594995 | − | 0.803729i | \(-0.297154\pi\) | ||||
0.594995 | + | 0.803729i | \(0.297154\pi\) | |||||||
\(272\) | −0.700463 | −0.0424718 | ||||||||
\(273\) | 45.2114 | 2.73632 | ||||||||
\(274\) | −25.8944 | −1.56434 | ||||||||
\(275\) | 0.908095 | 0.0547602 | ||||||||
\(276\) | 61.5999 | 3.70788 | ||||||||
\(277\) | 10.5097 | 0.631466 | 0.315733 | − | 0.948848i | \(-0.397750\pi\) | ||||
0.315733 | + | 0.948848i | \(0.397750\pi\) | |||||||
\(278\) | 33.5362 | 2.01137 | ||||||||
\(279\) | 51.7149 | 3.09609 | ||||||||
\(280\) | 15.9326 | 0.952156 | ||||||||
\(281\) | −4.74110 | −0.282830 | −0.141415 | − | 0.989950i | \(-0.545165\pi\) | ||||
−0.141415 | + | 0.989950i | \(0.545165\pi\) | |||||||
\(282\) | 3.86890 | 0.230390 | ||||||||
\(283\) | 19.3457 | 1.14998 | 0.574990 | − | 0.818160i | \(-0.305006\pi\) | ||||
0.574990 | + | 0.818160i | \(0.305006\pi\) | |||||||
\(284\) | 2.20967 | 0.131120 | ||||||||
\(285\) | −16.8419 | −0.997628 | ||||||||
\(286\) | 20.3796 | 1.20507 | ||||||||
\(287\) | 3.95631 | 0.233534 | ||||||||
\(288\) | 55.0613 | 3.24452 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | 33.3504 | 1.95840 | ||||||||
\(291\) | −58.9138 | −3.45359 | ||||||||
\(292\) | −19.6207 | −1.14822 | ||||||||
\(293\) | −15.5157 | −0.906437 | −0.453218 | − | 0.891400i | \(-0.649724\pi\) | ||||
−0.453218 | + | 0.891400i | \(0.649724\pi\) | |||||||
\(294\) | 7.14458 | 0.416680 | ||||||||
\(295\) | −12.5291 | −0.729472 | ||||||||
\(296\) | 15.2010 | 0.883539 | ||||||||
\(297\) | −36.4639 | −2.11585 | ||||||||
\(298\) | 49.7092 | 2.87958 | ||||||||
\(299\) | 27.7727 | 1.60613 | ||||||||
\(300\) | −4.95207 | −0.285908 | ||||||||
\(301\) | −12.2681 | −0.707124 | ||||||||
\(302\) | 28.1707 | 1.62104 | ||||||||
\(303\) | 6.87759 | 0.395107 | ||||||||
\(304\) | 1.48152 | 0.0849709 | ||||||||
\(305\) | −18.0284 | −1.03230 | ||||||||
\(306\) | −19.3365 | −1.10540 | ||||||||
\(307\) | −31.2132 | −1.78143 | −0.890715 | − | 0.454562i | \(-0.849796\pi\) | ||||
−0.890715 | + | 0.454562i | \(0.849796\pi\) | |||||||
\(308\) | 16.6055 | 0.946184 | ||||||||
\(309\) | −36.3577 | −2.06832 | ||||||||
\(310\) | 31.7450 | 1.80299 | ||||||||
\(311\) | −2.59411 | −0.147098 | −0.0735492 | − | 0.997292i | \(-0.523433\pi\) | ||||
−0.0735492 | + | 0.997292i | \(0.523433\pi\) | |||||||
\(312\) | −38.8177 | −2.19762 | ||||||||
\(313\) | −8.42346 | −0.476122 | −0.238061 | − | 0.971250i | \(-0.576512\pi\) | ||||
−0.238061 | + | 0.971250i | \(0.576512\pi\) | |||||||
\(314\) | 27.0510 | 1.52658 | ||||||||
\(315\) | −56.5640 | −3.18702 | ||||||||
\(316\) | −33.9192 | −1.90811 | ||||||||
\(317\) | 9.58978 | 0.538615 | 0.269308 | − | 0.963054i | \(-0.413205\pi\) | ||||
0.269308 | + | 0.963054i | \(0.413205\pi\) | |||||||
\(318\) | −29.9747 | −1.68090 | ||||||||
\(319\) | 12.1406 | 0.679746 | ||||||||
\(320\) | 30.5217 | 1.70621 | ||||||||
\(321\) | 52.9015 | 2.95268 | ||||||||
\(322\) | 37.3547 | 2.08169 | ||||||||
\(323\) | −2.11506 | −0.117685 | ||||||||
\(324\) | 119.691 | 6.64950 | ||||||||
\(325\) | −2.23267 | −0.123846 | ||||||||
\(326\) | 32.6762 | 1.80977 | ||||||||
\(327\) | 7.08242 | 0.391659 | ||||||||
\(328\) | −3.39682 | −0.187558 | ||||||||
\(329\) | 1.42128 | 0.0783578 | ||||||||
\(330\) | −34.4071 | −1.89405 | ||||||||
\(331\) | −28.8689 | −1.58678 | −0.793390 | − | 0.608714i | \(-0.791686\pi\) | ||||
−0.793390 | + | 0.608714i | \(0.791686\pi\) | |||||||
\(332\) | 36.8690 | 2.02345 | ||||||||
\(333\) | −53.9665 | −2.95735 | ||||||||
\(334\) | −39.7910 | −2.17727 | ||||||||
\(335\) | −16.0632 | −0.877626 | ||||||||
\(336\) | 6.71454 | 0.366308 | ||||||||
\(337\) | 1.63256 | 0.0889310 | 0.0444655 | − | 0.999011i | \(-0.485842\pi\) | ||||
0.0444655 | + | 0.999011i | \(0.485842\pi\) | |||||||
\(338\) | −20.8242 | −1.13269 | ||||||||
\(339\) | 11.5510 | 0.627365 | ||||||||
\(340\) | −7.19061 | −0.389965 | ||||||||
\(341\) | 11.5562 | 0.625804 | ||||||||
\(342\) | 40.8978 | 2.21150 | ||||||||
\(343\) | −17.0899 | −0.922770 | ||||||||
\(344\) | 10.5332 | 0.567911 | ||||||||
\(345\) | −46.8889 | −2.52441 | ||||||||
\(346\) | −43.8332 | −2.35649 | ||||||||
\(347\) | 8.59351 | 0.461324 | 0.230662 | − | 0.973034i | \(-0.425911\pi\) | ||||
0.230662 | + | 0.973034i | \(0.425911\pi\) | |||||||
\(348\) | −66.2060 | −3.54902 | ||||||||
\(349\) | 14.8116 | 0.792845 | 0.396423 | − | 0.918068i | \(-0.370252\pi\) | ||||
0.396423 | + | 0.918068i | \(0.370252\pi\) | |||||||
\(350\) | −3.00298 | −0.160516 | ||||||||
\(351\) | 89.6512 | 4.78523 | ||||||||
\(352\) | 12.3040 | 0.655806 | ||||||||
\(353\) | −1.00000 | −0.0532246 | ||||||||
\(354\) | 41.0572 | 2.18216 | ||||||||
\(355\) | −1.68197 | −0.0892694 | ||||||||
\(356\) | 16.2465 | 0.861062 | ||||||||
\(357\) | −9.58586 | −0.507337 | ||||||||
\(358\) | −49.9722 | −2.64111 | ||||||||
\(359\) | −12.1624 | −0.641905 | −0.320952 | − | 0.947095i | \(-0.604003\pi\) | ||||
−0.320952 | + | 0.947095i | \(0.604003\pi\) | |||||||
\(360\) | 48.5648 | 2.55959 | ||||||||
\(361\) | −14.5265 | −0.764555 | ||||||||
\(362\) | 10.5232 | 0.553087 | ||||||||
\(363\) | 24.9145 | 1.30767 | ||||||||
\(364\) | −40.8267 | −2.13990 | ||||||||
\(365\) | 14.9350 | 0.781733 | ||||||||
\(366\) | 59.0780 | 3.08806 | ||||||||
\(367\) | −18.2751 | −0.953952 | −0.476976 | − | 0.878916i | \(-0.658267\pi\) | ||||
−0.476976 | + | 0.878916i | \(0.658267\pi\) | |||||||
\(368\) | 4.12463 | 0.215011 | ||||||||
\(369\) | 12.0594 | 0.627786 | ||||||||
\(370\) | −33.1271 | −1.72220 | ||||||||
\(371\) | −11.0115 | −0.571689 | ||||||||
\(372\) | −63.0190 | −3.26738 | ||||||||
\(373\) | 1.43315 | 0.0742056 | 0.0371028 | − | 0.999311i | \(-0.488187\pi\) | ||||
0.0371028 | + | 0.999311i | \(0.488187\pi\) | |||||||
\(374\) | −4.32095 | −0.223431 | ||||||||
\(375\) | −36.0449 | −1.86135 | ||||||||
\(376\) | −1.22029 | −0.0629314 | ||||||||
\(377\) | −29.8494 | −1.53732 | ||||||||
\(378\) | 120.582 | 6.20208 | ||||||||
\(379\) | 12.0412 | 0.618516 | 0.309258 | − | 0.950978i | \(-0.399919\pi\) | ||||
0.309258 | + | 0.950978i | \(0.399919\pi\) | |||||||
\(380\) | 15.2085 | 0.780181 | ||||||||
\(381\) | 19.6725 | 1.00785 | ||||||||
\(382\) | −3.54226 | −0.181238 | ||||||||
\(383\) | −6.19285 | −0.316440 | −0.158220 | − | 0.987404i | \(-0.550576\pi\) | ||||
−0.158220 | + | 0.987404i | \(0.550576\pi\) | |||||||
\(384\) | −56.3568 | −2.87594 | ||||||||
\(385\) | −12.6398 | −0.644185 | ||||||||
\(386\) | 55.3071 | 2.81506 | ||||||||
\(387\) | −37.3949 | −1.90089 | ||||||||
\(388\) | 53.2002 | 2.70083 | ||||||||
\(389\) | −12.1637 | −0.616723 | −0.308361 | − | 0.951269i | \(-0.599781\pi\) | ||||
−0.308361 | + | 0.951269i | \(0.599781\pi\) | |||||||
\(390\) | 84.5945 | 4.28361 | ||||||||
\(391\) | −5.88844 | −0.297791 | ||||||||
\(392\) | −2.25346 | −0.113817 | ||||||||
\(393\) | 27.7796 | 1.40130 | ||||||||
\(394\) | 8.07876 | 0.407002 | ||||||||
\(395\) | 25.8188 | 1.29908 | ||||||||
\(396\) | 50.6157 | 2.54353 | ||||||||
\(397\) | −23.4312 | −1.17598 | −0.587990 | − | 0.808868i | \(-0.700081\pi\) | ||||
−0.587990 | + | 0.808868i | \(0.700081\pi\) | |||||||
\(398\) | −33.9548 | −1.70200 | ||||||||
\(399\) | 20.2746 | 1.01500 | ||||||||
\(400\) | −0.331583 | −0.0165792 | ||||||||
\(401\) | 29.0965 | 1.45301 | 0.726504 | − | 0.687162i | \(-0.241144\pi\) | ||||
0.726504 | + | 0.687162i | \(0.241144\pi\) | |||||||
\(402\) | 52.6382 | 2.62535 | ||||||||
\(403\) | −28.4125 | −1.41533 | ||||||||
\(404\) | −6.21058 | −0.308988 | ||||||||
\(405\) | −91.1069 | −4.52714 | ||||||||
\(406\) | −40.1479 | −1.99250 | ||||||||
\(407\) | −12.0594 | −0.597761 | ||||||||
\(408\) | 8.23023 | 0.407457 | ||||||||
\(409\) | −5.84381 | −0.288958 | −0.144479 | − | 0.989508i | \(-0.546151\pi\) | ||||
−0.144479 | + | 0.989508i | \(0.546151\pi\) | |||||||
\(410\) | 7.40260 | 0.365588 | ||||||||
\(411\) | −39.1284 | −1.93006 | ||||||||
\(412\) | 32.8316 | 1.61750 | ||||||||
\(413\) | 15.0828 | 0.742175 | ||||||||
\(414\) | 113.862 | 5.59601 | ||||||||
\(415\) | −28.0641 | −1.37761 | ||||||||
\(416\) | −30.2511 | −1.48318 | ||||||||
\(417\) | 50.6758 | 2.48161 | ||||||||
\(418\) | 9.13904 | 0.447005 | ||||||||
\(419\) | −20.0852 | −0.981224 | −0.490612 | − | 0.871378i | \(-0.663227\pi\) | ||||
−0.490612 | + | 0.871378i | \(0.663227\pi\) | |||||||
\(420\) | 68.9281 | 3.36335 | ||||||||
\(421\) | −23.8848 | −1.16407 | −0.582037 | − | 0.813162i | \(-0.697744\pi\) | ||||
−0.582037 | + | 0.813162i | \(0.697744\pi\) | |||||||
\(422\) | −32.3173 | −1.57318 | ||||||||
\(423\) | 4.33226 | 0.210642 | ||||||||
\(424\) | 9.45427 | 0.459140 | ||||||||
\(425\) | 0.473377 | 0.0229622 | ||||||||
\(426\) | 5.51171 | 0.267043 | ||||||||
\(427\) | 21.7029 | 1.05028 | ||||||||
\(428\) | −47.7710 | −2.30910 | ||||||||
\(429\) | 30.7952 | 1.48681 | ||||||||
\(430\) | −22.9547 | −1.10698 | ||||||||
\(431\) | −15.6286 | −0.752801 | −0.376401 | − | 0.926457i | \(-0.622838\pi\) | ||||
−0.376401 | + | 0.926457i | \(0.622838\pi\) | |||||||
\(432\) | 13.3145 | 0.640593 | ||||||||
\(433\) | 15.3464 | 0.737500 | 0.368750 | − | 0.929529i | \(-0.379786\pi\) | ||||
0.368750 | + | 0.929529i | \(0.379786\pi\) | |||||||
\(434\) | −38.2152 | −1.83439 | ||||||||
\(435\) | 50.3950 | 2.41625 | ||||||||
\(436\) | −6.39555 | −0.306291 | ||||||||
\(437\) | 12.4544 | 0.595774 | ||||||||
\(438\) | −48.9411 | −2.33850 | ||||||||
\(439\) | 19.1595 | 0.914434 | 0.457217 | − | 0.889355i | \(-0.348846\pi\) | ||||
0.457217 | + | 0.889355i | \(0.348846\pi\) | |||||||
\(440\) | 10.8523 | 0.517363 | ||||||||
\(441\) | 8.00024 | 0.380964 | ||||||||
\(442\) | 10.6236 | 0.505314 | ||||||||
\(443\) | 7.16237 | 0.340295 | 0.170147 | − | 0.985419i | \(-0.445576\pi\) | ||||
0.170147 | + | 0.985419i | \(0.445576\pi\) | |||||||
\(444\) | 65.7629 | 3.12097 | ||||||||
\(445\) | −12.3666 | −0.586232 | ||||||||
\(446\) | −26.4819 | −1.25395 | ||||||||
\(447\) | 75.1144 | 3.55279 | ||||||||
\(448\) | −36.7426 | −1.73592 | ||||||||
\(449\) | 26.3422 | 1.24317 | 0.621584 | − | 0.783348i | \(-0.286490\pi\) | ||||
0.621584 | + | 0.783348i | \(0.286490\pi\) | |||||||
\(450\) | −9.15348 | −0.431499 | ||||||||
\(451\) | 2.69479 | 0.126893 | ||||||||
\(452\) | −10.4308 | −0.490622 | ||||||||
\(453\) | 42.5681 | 2.00002 | ||||||||
\(454\) | 50.2088 | 2.35641 | ||||||||
\(455\) | 31.0767 | 1.45690 | ||||||||
\(456\) | −17.4074 | −0.815176 | ||||||||
\(457\) | 19.3598 | 0.905614 | 0.452807 | − | 0.891609i | \(-0.350423\pi\) | ||||
0.452807 | + | 0.891609i | \(0.350423\pi\) | |||||||
\(458\) | 13.6231 | 0.636565 | ||||||||
\(459\) | −19.0081 | −0.887222 | ||||||||
\(460\) | 42.3414 | 1.97418 | ||||||||
\(461\) | −31.9895 | −1.48990 | −0.744951 | − | 0.667120i | \(-0.767527\pi\) | ||||
−0.744951 | + | 0.667120i | \(0.767527\pi\) | |||||||
\(462\) | 41.4200 | 1.92703 | ||||||||
\(463\) | 27.1119 | 1.26000 | 0.629999 | − | 0.776596i | \(-0.283055\pi\) | ||||
0.629999 | + | 0.776596i | \(0.283055\pi\) | |||||||
\(464\) | −4.43306 | −0.205799 | ||||||||
\(465\) | 47.9691 | 2.22451 | ||||||||
\(466\) | 13.4861 | 0.624732 | ||||||||
\(467\) | −7.76730 | −0.359428 | −0.179714 | − | 0.983719i | \(-0.557517\pi\) | ||||
−0.179714 | + | 0.983719i | \(0.557517\pi\) | |||||||
\(468\) | −124.445 | −5.75249 | ||||||||
\(469\) | 19.3372 | 0.892908 | ||||||||
\(470\) | 2.65934 | 0.122666 | ||||||||
\(471\) | 40.8762 | 1.88348 | ||||||||
\(472\) | −12.9498 | −0.596062 | ||||||||
\(473\) | −8.35628 | −0.384222 | ||||||||
\(474\) | −84.6068 | −3.88612 | ||||||||
\(475\) | −1.00122 | −0.0459391 | ||||||||
\(476\) | 8.65620 | 0.396756 | ||||||||
\(477\) | −33.5645 | −1.53681 | ||||||||
\(478\) | 29.9144 | 1.36825 | ||||||||
\(479\) | 20.0416 | 0.915723 | 0.457861 | − | 0.889024i | \(-0.348616\pi\) | ||||
0.457861 | + | 0.889024i | \(0.348616\pi\) | |||||||
\(480\) | 51.0732 | 2.33116 | ||||||||
\(481\) | 29.6496 | 1.35190 | ||||||||
\(482\) | 34.2131 | 1.55836 | ||||||||
\(483\) | 56.4457 | 2.56837 | ||||||||
\(484\) | −22.4983 | −1.02265 | ||||||||
\(485\) | −40.4952 | −1.83879 | ||||||||
\(486\) | 170.108 | 7.71625 | ||||||||
\(487\) | −37.4645 | −1.69768 | −0.848840 | − | 0.528650i | \(-0.822698\pi\) | ||||
−0.848840 | + | 0.528650i | \(0.822698\pi\) | |||||||
\(488\) | −18.6337 | −0.843508 | ||||||||
\(489\) | 49.3763 | 2.23287 | ||||||||
\(490\) | 4.91092 | 0.221853 | ||||||||
\(491\) | 6.41698 | 0.289594 | 0.144797 | − | 0.989461i | \(-0.453747\pi\) | ||||
0.144797 | + | 0.989461i | \(0.453747\pi\) | |||||||
\(492\) | −14.6954 | −0.662519 | ||||||||
\(493\) | 6.32875 | 0.285033 | ||||||||
\(494\) | −22.4695 | −1.01095 | ||||||||
\(495\) | −38.5279 | −1.73170 | ||||||||
\(496\) | −4.21966 | −0.189468 | ||||||||
\(497\) | 2.02478 | 0.0908239 | ||||||||
\(498\) | 91.9645 | 4.12103 | ||||||||
\(499\) | 23.2208 | 1.03950 | 0.519752 | − | 0.854317i | \(-0.326024\pi\) | ||||
0.519752 | + | 0.854317i | \(0.326024\pi\) | |||||||
\(500\) | 32.5492 | 1.45564 | ||||||||
\(501\) | −60.1272 | −2.68629 | ||||||||
\(502\) | 24.2488 | 1.08228 | ||||||||
\(503\) | 37.5766 | 1.67546 | 0.837729 | − | 0.546087i | \(-0.183883\pi\) | ||||
0.837729 | + | 0.546087i | \(0.183883\pi\) | |||||||
\(504\) | −58.4633 | −2.60416 | ||||||||
\(505\) | 4.72740 | 0.210366 | ||||||||
\(506\) | 25.4436 | 1.13111 | ||||||||
\(507\) | −31.4669 | −1.39750 | ||||||||
\(508\) | −17.7646 | −0.788176 | ||||||||
\(509\) | 6.85844 | 0.303995 | 0.151998 | − | 0.988381i | \(-0.451429\pi\) | ||||
0.151998 | + | 0.988381i | \(0.451429\pi\) | |||||||
\(510\) | −17.9360 | −0.794218 | ||||||||
\(511\) | −17.9790 | −0.795345 | ||||||||
\(512\) | −7.88026 | −0.348262 | ||||||||
\(513\) | 40.2032 | 1.77501 | ||||||||
\(514\) | −60.4872 | −2.66797 | ||||||||
\(515\) | −24.9909 | −1.10123 | ||||||||
\(516\) | 45.5689 | 2.00606 | ||||||||
\(517\) | 0.968088 | 0.0425765 | ||||||||
\(518\) | 39.8791 | 1.75219 | ||||||||
\(519\) | −66.2353 | −2.90741 | ||||||||
\(520\) | −26.6818 | −1.17008 | ||||||||
\(521\) | 25.4863 | 1.11657 | 0.558287 | − | 0.829648i | \(-0.311459\pi\) | ||||
0.558287 | + | 0.829648i | \(0.311459\pi\) | |||||||
\(522\) | −122.376 | −5.35626 | ||||||||
\(523\) | 10.9109 | 0.477102 | 0.238551 | − | 0.971130i | \(-0.423328\pi\) | ||||
0.238551 | + | 0.971130i | \(0.423328\pi\) | |||||||
\(524\) | −25.0855 | −1.09586 | ||||||||
\(525\) | −4.53773 | −0.198043 | ||||||||
\(526\) | −24.6994 | −1.07695 | ||||||||
\(527\) | 6.02410 | 0.262414 | ||||||||
\(528\) | 4.57352 | 0.199037 | ||||||||
\(529\) | 11.6737 | 0.507553 | ||||||||
\(530\) | −20.6035 | −0.894957 | ||||||||
\(531\) | 45.9743 | 1.99512 | ||||||||
\(532\) | −18.3083 | −0.793767 | ||||||||
\(533\) | −6.62550 | −0.286982 | ||||||||
\(534\) | 40.5246 | 1.75367 | ||||||||
\(535\) | 36.3625 | 1.57209 | ||||||||
\(536\) | −16.6025 | −0.717120 | ||||||||
\(537\) | −75.5119 | −3.25858 | ||||||||
\(538\) | −57.8916 | −2.49588 | ||||||||
\(539\) | 1.78774 | 0.0770033 | ||||||||
\(540\) | 136.680 | 5.88176 | ||||||||
\(541\) | −2.19008 | −0.0941589 | −0.0470794 | − | 0.998891i | \(-0.514991\pi\) | ||||
−0.0470794 | + | 0.998891i | \(0.514991\pi\) | |||||||
\(542\) | −44.1248 | −1.89532 | ||||||||
\(543\) | 15.9014 | 0.682393 | ||||||||
\(544\) | 6.41392 | 0.274994 | ||||||||
\(545\) | 4.86819 | 0.208531 | ||||||||
\(546\) | −101.837 | −4.35820 | ||||||||
\(547\) | 19.9862 | 0.854546 | 0.427273 | − | 0.904123i | \(-0.359474\pi\) | ||||
0.427273 | + | 0.904123i | \(0.359474\pi\) | |||||||
\(548\) | 35.3337 | 1.50938 | ||||||||
\(549\) | 66.1534 | 2.82336 | ||||||||
\(550\) | −2.04544 | −0.0872178 | ||||||||
\(551\) | −13.3857 | −0.570248 | ||||||||
\(552\) | −48.4632 | −2.06273 | ||||||||
\(553\) | −31.0812 | −1.32171 | ||||||||
\(554\) | −23.6726 | −1.00575 | ||||||||
\(555\) | −50.0577 | −2.12483 | ||||||||
\(556\) | −45.7611 | −1.94070 | ||||||||
\(557\) | −33.2761 | −1.40995 | −0.704976 | − | 0.709231i | \(-0.749042\pi\) | ||||
−0.704976 | + | 0.709231i | \(0.749042\pi\) | |||||||
\(558\) | −116.485 | −4.93121 | ||||||||
\(559\) | 20.5450 | 0.868962 | ||||||||
\(560\) | 4.61532 | 0.195033 | ||||||||
\(561\) | −6.52928 | −0.275667 | ||||||||
\(562\) | 10.6791 | 0.450470 | ||||||||
\(563\) | 9.27010 | 0.390688 | 0.195344 | − | 0.980735i | \(-0.437418\pi\) | ||||
0.195344 | + | 0.980735i | \(0.437418\pi\) | |||||||
\(564\) | −5.27923 | −0.222296 | ||||||||
\(565\) | 7.93974 | 0.334027 | ||||||||
\(566\) | −43.5752 | −1.83160 | ||||||||
\(567\) | 109.676 | 4.60597 | ||||||||
\(568\) | −1.73844 | −0.0729433 | ||||||||
\(569\) | −2.11662 | −0.0887334 | −0.0443667 | − | 0.999015i | \(-0.514127\pi\) | ||||
−0.0443667 | + | 0.999015i | \(0.514127\pi\) | |||||||
\(570\) | 37.9355 | 1.58895 | ||||||||
\(571\) | 33.3929 | 1.39745 | 0.698724 | − | 0.715391i | \(-0.253751\pi\) | ||||
0.698724 | + | 0.715391i | \(0.253751\pi\) | |||||||
\(572\) | −27.8086 | −1.16274 | ||||||||
\(573\) | −5.35262 | −0.223609 | ||||||||
\(574\) | −8.91140 | −0.371955 | ||||||||
\(575\) | −2.78745 | −0.116245 | ||||||||
\(576\) | −111.996 | −4.66652 | ||||||||
\(577\) | −33.8918 | −1.41093 | −0.705467 | − | 0.708743i | \(-0.749263\pi\) | ||||
−0.705467 | + | 0.708743i | \(0.749263\pi\) | |||||||
\(578\) | −2.25245 | −0.0936896 | ||||||||
\(579\) | 83.5733 | 3.47319 | ||||||||
\(580\) | −45.5075 | −1.88960 | ||||||||
\(581\) | 33.7841 | 1.40160 | ||||||||
\(582\) | 132.700 | 5.50061 | ||||||||
\(583\) | −7.50034 | −0.310632 | ||||||||
\(584\) | 15.4365 | 0.638765 | ||||||||
\(585\) | 94.7258 | 3.91643 | ||||||||
\(586\) | 34.9483 | 1.44370 | ||||||||
\(587\) | −40.0112 | −1.65144 | −0.825719 | − | 0.564082i | \(-0.809230\pi\) | ||||
−0.825719 | + | 0.564082i | \(0.809230\pi\) | |||||||
\(588\) | −9.74899 | −0.402041 | ||||||||
\(589\) | −12.7413 | −0.524996 | ||||||||
\(590\) | 28.2212 | 1.16185 | ||||||||
\(591\) | 12.2076 | 0.502155 | ||||||||
\(592\) | 4.40338 | 0.180978 | ||||||||
\(593\) | −42.0638 | −1.72735 | −0.863677 | − | 0.504046i | \(-0.831844\pi\) | ||||
−0.863677 | + | 0.504046i | \(0.831844\pi\) | |||||||
\(594\) | 82.1330 | 3.36996 | ||||||||
\(595\) | −6.58896 | −0.270121 | ||||||||
\(596\) | −67.8296 | −2.77841 | ||||||||
\(597\) | −51.3084 | −2.09991 | ||||||||
\(598\) | −62.5566 | −2.55813 | ||||||||
\(599\) | 32.0738 | 1.31050 | 0.655250 | − | 0.755412i | \(-0.272563\pi\) | ||||
0.655250 | + | 0.755412i | \(0.272563\pi\) | |||||||
\(600\) | 3.89601 | 0.159054 | ||||||||
\(601\) | −41.0256 | −1.67347 | −0.836734 | − | 0.547609i | \(-0.815538\pi\) | ||||
−0.836734 | + | 0.547609i | \(0.815538\pi\) | |||||||
\(602\) | 27.6334 | 1.12625 | ||||||||
\(603\) | 58.9423 | 2.40032 | ||||||||
\(604\) | −38.4397 | −1.56409 | ||||||||
\(605\) | 17.1253 | 0.696244 | ||||||||
\(606\) | −15.4914 | −0.629296 | ||||||||
\(607\) | 45.1361 | 1.83202 | 0.916008 | − | 0.401160i | \(-0.131393\pi\) | ||||
0.916008 | + | 0.401160i | \(0.131393\pi\) | |||||||
\(608\) | −13.5658 | −0.550165 | ||||||||
\(609\) | −60.6665 | −2.45833 | ||||||||
\(610\) | 40.6080 | 1.64417 | ||||||||
\(611\) | −2.38017 | −0.0962915 | ||||||||
\(612\) | 26.3852 | 1.06656 | ||||||||
\(613\) | −9.24592 | −0.373439 | −0.186720 | − | 0.982413i | \(-0.559786\pi\) | ||||
−0.186720 | + | 0.982413i | \(0.559786\pi\) | |||||||
\(614\) | 70.3061 | 2.83732 | ||||||||
\(615\) | 11.1859 | 0.451059 | ||||||||
\(616\) | −13.0642 | −0.526372 | ||||||||
\(617\) | 28.9428 | 1.16519 | 0.582597 | − | 0.812761i | \(-0.302037\pi\) | ||||
0.582597 | + | 0.812761i | \(0.302037\pi\) | |||||||
\(618\) | 81.8939 | 3.29425 | ||||||||
\(619\) | −3.29173 | −0.132306 | −0.0661528 | − | 0.997810i | \(-0.521072\pi\) | ||||
−0.0661528 | + | 0.997810i | \(0.521072\pi\) | |||||||
\(620\) | −43.3169 | −1.73965 | ||||||||
\(621\) | 111.928 | 4.49152 | ||||||||
\(622\) | 5.84310 | 0.234287 | ||||||||
\(623\) | 14.8871 | 0.596440 | ||||||||
\(624\) | −11.2446 | −0.450145 | ||||||||
\(625\) | −27.1428 | −1.08571 | ||||||||
\(626\) | 18.9734 | 0.758330 | ||||||||
\(627\) | 13.8098 | 0.551510 | ||||||||
\(628\) | −36.9119 | −1.47295 | ||||||||
\(629\) | −6.28639 | −0.250655 | ||||||||
\(630\) | 127.408 | 5.07604 | ||||||||
\(631\) | −45.3961 | −1.80719 | −0.903595 | − | 0.428388i | \(-0.859081\pi\) | ||||
−0.903595 | + | 0.428388i | \(0.859081\pi\) | |||||||
\(632\) | 26.6857 | 1.06150 | ||||||||
\(633\) | −48.8339 | −1.94097 | ||||||||
\(634\) | −21.6005 | −0.857865 | ||||||||
\(635\) | 13.5221 | 0.536609 | ||||||||
\(636\) | 40.9013 | 1.62184 | ||||||||
\(637\) | −4.39539 | −0.174152 | ||||||||
\(638\) | −27.3462 | −1.08265 | ||||||||
\(639\) | 6.17181 | 0.244153 | ||||||||
\(640\) | −38.7375 | −1.53124 | ||||||||
\(641\) | 20.1778 | 0.796975 | 0.398487 | − | 0.917174i | \(-0.369535\pi\) | ||||
0.398487 | + | 0.917174i | \(0.369535\pi\) | |||||||
\(642\) | −119.158 | −4.70279 | ||||||||
\(643\) | −3.98062 | −0.156980 | −0.0784902 | − | 0.996915i | \(-0.525010\pi\) | ||||
−0.0784902 | + | 0.996915i | \(0.525010\pi\) | |||||||
\(644\) | −50.9715 | −2.00856 | ||||||||
\(645\) | −34.6864 | −1.36577 | ||||||||
\(646\) | 4.76406 | 0.187439 | ||||||||
\(647\) | 5.09085 | 0.200142 | 0.100071 | − | 0.994980i | \(-0.468093\pi\) | ||||
0.100071 | + | 0.994980i | \(0.468093\pi\) | |||||||
\(648\) | −94.1660 | −3.69919 | ||||||||
\(649\) | 10.2734 | 0.403268 | ||||||||
\(650\) | 5.02898 | 0.197253 | ||||||||
\(651\) | −57.7461 | −2.26325 | ||||||||
\(652\) | −44.5876 | −1.74619 | ||||||||
\(653\) | −24.4843 | −0.958146 | −0.479073 | − | 0.877775i | \(-0.659027\pi\) | ||||
−0.479073 | + | 0.877775i | \(0.659027\pi\) | |||||||
\(654\) | −15.9528 | −0.623804 | ||||||||
\(655\) | 19.0947 | 0.746090 | ||||||||
\(656\) | −0.983981 | −0.0384180 | ||||||||
\(657\) | −54.8025 | −2.13805 | ||||||||
\(658\) | −3.20137 | −0.124802 | ||||||||
\(659\) | 33.0011 | 1.28554 | 0.642770 | − | 0.766059i | \(-0.277785\pi\) | ||||
0.642770 | + | 0.766059i | \(0.277785\pi\) | |||||||
\(660\) | 46.9495 | 1.82751 | ||||||||
\(661\) | −25.5147 | −0.992408 | −0.496204 | − | 0.868206i | \(-0.665273\pi\) | ||||
−0.496204 | + | 0.868206i | \(0.665273\pi\) | |||||||
\(662\) | 65.0258 | 2.52730 | ||||||||
\(663\) | 16.0531 | 0.623451 | ||||||||
\(664\) | −29.0064 | −1.12567 | ||||||||
\(665\) | 13.9360 | 0.540416 | ||||||||
\(666\) | 121.557 | 4.71024 | ||||||||
\(667\) | −37.2665 | −1.44296 | ||||||||
\(668\) | 54.2959 | 2.10077 | ||||||||
\(669\) | −40.0161 | −1.54711 | ||||||||
\(670\) | 36.1815 | 1.39781 | ||||||||
\(671\) | 14.7827 | 0.570678 | ||||||||
\(672\) | −61.4829 | −2.37175 | ||||||||
\(673\) | −42.7605 | −1.64830 | −0.824149 | − | 0.566373i | \(-0.808346\pi\) | ||||
−0.824149 | + | 0.566373i | \(0.808346\pi\) | |||||||
\(674\) | −3.67725 | −0.141642 | ||||||||
\(675\) | −8.99801 | −0.346333 | ||||||||
\(676\) | 28.4152 | 1.09289 | ||||||||
\(677\) | 12.2154 | 0.469475 | 0.234738 | − | 0.972059i | \(-0.424577\pi\) | ||||
0.234738 | + | 0.972059i | \(0.424577\pi\) | |||||||
\(678\) | −26.0181 | −0.999219 | ||||||||
\(679\) | 48.7489 | 1.87081 | ||||||||
\(680\) | 5.65716 | 0.216942 | ||||||||
\(681\) | 75.8693 | 2.90732 | ||||||||
\(682\) | −26.0298 | −0.996733 | ||||||||
\(683\) | −9.86422 | −0.377444 | −0.188722 | − | 0.982031i | \(-0.560435\pi\) | ||||
−0.188722 | + | 0.982031i | \(0.560435\pi\) | |||||||
\(684\) | −55.8063 | −2.13381 | ||||||||
\(685\) | −26.8954 | −1.02762 | ||||||||
\(686\) | 38.4942 | 1.46972 | ||||||||
\(687\) | 20.5855 | 0.785387 | ||||||||
\(688\) | 3.05123 | 0.116327 | ||||||||
\(689\) | 18.4406 | 0.702530 | ||||||||
\(690\) | 105.615 | 4.02069 | ||||||||
\(691\) | 12.1041 | 0.460463 | 0.230232 | − | 0.973136i | \(-0.426052\pi\) | ||||
0.230232 | + | 0.973136i | \(0.426052\pi\) | |||||||
\(692\) | 59.8116 | 2.27370 | ||||||||
\(693\) | 46.3806 | 1.76185 | ||||||||
\(694\) | −19.3564 | −0.734761 | ||||||||
\(695\) | 34.8327 | 1.32128 | ||||||||
\(696\) | 52.0871 | 1.97436 | ||||||||
\(697\) | 1.40476 | 0.0532090 | ||||||||
\(698\) | −33.3623 | −1.26278 | ||||||||
\(699\) | 20.3785 | 0.770787 | ||||||||
\(700\) | 4.09765 | 0.154876 | ||||||||
\(701\) | −42.6567 | −1.61112 | −0.805561 | − | 0.592513i | \(-0.798136\pi\) | ||||
−0.805561 | + | 0.592513i | \(0.798136\pi\) | |||||||
\(702\) | −201.935 | −7.62154 | ||||||||
\(703\) | 13.2961 | 0.501470 | ||||||||
\(704\) | −25.0268 | −0.943231 | ||||||||
\(705\) | 4.01847 | 0.151344 | ||||||||
\(706\) | 2.25245 | 0.0847721 | ||||||||
\(707\) | −5.69094 | −0.214030 | ||||||||
\(708\) | −56.0237 | −2.10550 | ||||||||
\(709\) | −3.78495 | −0.142147 | −0.0710733 | − | 0.997471i | \(-0.522642\pi\) | ||||
−0.0710733 | + | 0.997471i | \(0.522642\pi\) | |||||||
\(710\) | 3.78854 | 0.142181 | ||||||||
\(711\) | −94.7396 | −3.55301 | ||||||||
\(712\) | −12.7818 | −0.479018 | ||||||||
\(713\) | −35.4725 | −1.32846 | ||||||||
\(714\) | 21.5917 | 0.808048 | ||||||||
\(715\) | 21.1675 | 0.791618 | ||||||||
\(716\) | 68.1885 | 2.54832 | ||||||||
\(717\) | 45.2030 | 1.68814 | ||||||||
\(718\) | 27.3951 | 1.02238 | ||||||||
\(719\) | 24.3854 | 0.909421 | 0.454710 | − | 0.890639i | \(-0.349743\pi\) | ||||
0.454710 | + | 0.890639i | \(0.349743\pi\) | |||||||
\(720\) | 14.0681 | 0.524288 | ||||||||
\(721\) | 30.0846 | 1.12041 | ||||||||
\(722\) | 32.7203 | 1.21772 | ||||||||
\(723\) | 51.6986 | 1.92269 | ||||||||
\(724\) | −14.3592 | −0.533656 | ||||||||
\(725\) | 2.99589 | 0.111264 | ||||||||
\(726\) | −56.1188 | −2.08276 | ||||||||
\(727\) | 6.19986 | 0.229940 | 0.114970 | − | 0.993369i | \(-0.463323\pi\) | ||||
0.114970 | + | 0.993369i | \(0.463323\pi\) | |||||||
\(728\) | 32.1201 | 1.19045 | ||||||||
\(729\) | 140.219 | 5.19328 | ||||||||
\(730\) | −33.6403 | −1.24508 | ||||||||
\(731\) | −4.35602 | −0.161113 | ||||||||
\(732\) | −80.6136 | −2.97957 | ||||||||
\(733\) | −22.3792 | −0.826594 | −0.413297 | − | 0.910596i | \(-0.635623\pi\) | ||||
−0.413297 | + | 0.910596i | \(0.635623\pi\) | |||||||
\(734\) | 41.1638 | 1.51938 | ||||||||
\(735\) | 7.42078 | 0.273719 | ||||||||
\(736\) | −37.7680 | −1.39215 | ||||||||
\(737\) | 13.1713 | 0.485170 | ||||||||
\(738\) | −27.1631 | −0.999889 | ||||||||
\(739\) | 21.0870 | 0.775699 | 0.387850 | − | 0.921723i | \(-0.373218\pi\) | ||||
0.387850 | + | 0.921723i | \(0.373218\pi\) | |||||||
\(740\) | 45.2029 | 1.66169 | ||||||||
\(741\) | −33.9532 | −1.24730 | ||||||||
\(742\) | 24.8029 | 0.910542 | ||||||||
\(743\) | −35.9850 | −1.32016 | −0.660081 | − | 0.751195i | \(-0.729478\pi\) | ||||
−0.660081 | + | 0.751195i | \(0.729478\pi\) | |||||||
\(744\) | 49.5797 | 1.81768 | ||||||||
\(745\) | 51.6308 | 1.89161 | ||||||||
\(746\) | −3.22810 | −0.118189 | ||||||||
\(747\) | 102.979 | 3.76779 | ||||||||
\(748\) | 5.89606 | 0.215581 | ||||||||
\(749\) | −43.7739 | −1.59947 | ||||||||
\(750\) | 81.1893 | 2.96462 | ||||||||
\(751\) | 0.317378 | 0.0115813 | 0.00579064 | − | 0.999983i | \(-0.498157\pi\) | ||||
0.00579064 | + | 0.999983i | \(0.498157\pi\) | |||||||
\(752\) | −0.353489 | −0.0128904 | ||||||||
\(753\) | 36.6417 | 1.33530 | ||||||||
\(754\) | 67.2343 | 2.44853 | ||||||||
\(755\) | 29.2597 | 1.06487 | ||||||||
\(756\) | −164.538 | −5.98418 | ||||||||
\(757\) | 1.42769 | 0.0518901 | 0.0259451 | − | 0.999663i | \(-0.491741\pi\) | ||||
0.0259451 | + | 0.999663i | \(0.491741\pi\) | |||||||
\(758\) | −27.1223 | −0.985125 | ||||||||
\(759\) | 38.4473 | 1.39555 | ||||||||
\(760\) | −11.9652 | −0.434023 | ||||||||
\(761\) | 7.38254 | 0.267617 | 0.133808 | − | 0.991007i | \(-0.457279\pi\) | ||||
0.133808 | + | 0.991007i | \(0.457279\pi\) | |||||||
\(762\) | −44.3113 | −1.60523 | ||||||||
\(763\) | −5.86043 | −0.212162 | ||||||||
\(764\) | 4.83351 | 0.174870 | ||||||||
\(765\) | −20.0840 | −0.726140 | ||||||||
\(766\) | 13.9491 | 0.504001 | ||||||||
\(767\) | −25.2586 | −0.912035 | ||||||||
\(768\) | 38.1327 | 1.37600 | ||||||||
\(769\) | −23.5794 | −0.850295 | −0.425148 | − | 0.905124i | \(-0.639778\pi\) | ||||
−0.425148 | + | 0.905124i | \(0.639778\pi\) | |||||||
\(770\) | 28.4706 | 1.02601 | ||||||||
\(771\) | −91.4007 | −3.29172 | ||||||||
\(772\) | −75.4681 | −2.71616 | ||||||||
\(773\) | 47.2890 | 1.70087 | 0.850433 | − | 0.526083i | \(-0.176340\pi\) | ||||
0.850433 | + | 0.526083i | \(0.176340\pi\) | |||||||
\(774\) | 84.2302 | 3.02759 | ||||||||
\(775\) | 2.85167 | 0.102435 | ||||||||
\(776\) | −41.8549 | −1.50250 | ||||||||
\(777\) | 60.2604 | 2.16183 | ||||||||
\(778\) | 27.3981 | 0.982268 | ||||||||
\(779\) | −2.97114 | −0.106452 | ||||||||
\(780\) | −115.432 | −4.13311 | ||||||||
\(781\) | 1.37916 | 0.0493500 | ||||||||
\(782\) | 13.2634 | 0.474299 | ||||||||
\(783\) | −120.298 | −4.29908 | ||||||||
\(784\) | −0.652777 | −0.0233135 | ||||||||
\(785\) | 28.0968 | 1.00282 | ||||||||
\(786\) | −62.5722 | −2.23188 | ||||||||
\(787\) | 48.6628 | 1.73464 | 0.867320 | − | 0.497751i | \(-0.165841\pi\) | ||||
0.867320 | + | 0.497751i | \(0.165841\pi\) | |||||||
\(788\) | −11.0237 | −0.392703 | ||||||||
\(789\) | −37.3228 | −1.32873 | ||||||||
\(790\) | −58.1556 | −2.06908 | ||||||||
\(791\) | −9.55802 | −0.339844 | ||||||||
\(792\) | −39.8215 | −1.41500 | ||||||||
\(793\) | −36.3451 | −1.29065 | ||||||||
\(794\) | 52.7777 | 1.87301 | ||||||||
\(795\) | −31.1334 | −1.10419 | ||||||||
\(796\) | 46.3324 | 1.64221 | ||||||||
\(797\) | −37.6676 | −1.33425 | −0.667127 | − | 0.744944i | \(-0.732476\pi\) | ||||
−0.667127 | + | 0.744944i | \(0.732476\pi\) | |||||||
\(798\) | −45.6676 | −1.61661 | ||||||||
\(799\) | 0.504651 | 0.0178533 | ||||||||
\(800\) | 3.03620 | 0.107346 | ||||||||
\(801\) | 45.3780 | 1.60335 | ||||||||
\(802\) | −65.5383 | −2.31424 | ||||||||
\(803\) | −12.2462 | −0.432158 | ||||||||
\(804\) | −71.8263 | −2.53312 | ||||||||
\(805\) | 38.7987 | 1.36747 | ||||||||
\(806\) | 63.9977 | 2.25422 | ||||||||
\(807\) | −87.4787 | −3.07939 | ||||||||
\(808\) | 4.88613 | 0.171893 | ||||||||
\(809\) | 48.9458 | 1.72084 | 0.860421 | − | 0.509583i | \(-0.170200\pi\) | ||||
0.860421 | + | 0.509583i | \(0.170200\pi\) | |||||||
\(810\) | 205.214 | 7.21048 | ||||||||
\(811\) | 0.323004 | 0.0113422 | 0.00567110 | − | 0.999984i | \(-0.498195\pi\) | ||||
0.00567110 | + | 0.999984i | \(0.498195\pi\) | |||||||
\(812\) | 54.7829 | 1.92250 | ||||||||
\(813\) | −66.6760 | −2.33843 | ||||||||
\(814\) | 27.1632 | 0.952068 | ||||||||
\(815\) | 33.9394 | 1.18885 | ||||||||
\(816\) | 2.38411 | 0.0834607 | ||||||||
\(817\) | 9.21321 | 0.322330 | ||||||||
\(818\) | 13.1629 | 0.460230 | ||||||||
\(819\) | −114.033 | −3.98463 | ||||||||
\(820\) | −10.1011 | −0.352744 | ||||||||
\(821\) | 27.4230 | 0.957071 | 0.478535 | − | 0.878068i | \(-0.341168\pi\) | ||||
0.478535 | + | 0.878068i | \(0.341168\pi\) | |||||||
\(822\) | 88.1349 | 3.07406 | ||||||||
\(823\) | 35.6827 | 1.24382 | 0.621911 | − | 0.783088i | \(-0.286356\pi\) | ||||
0.621911 | + | 0.783088i | \(0.286356\pi\) | |||||||
\(824\) | −25.8300 | −0.899832 | ||||||||
\(825\) | −3.09081 | −0.107608 | ||||||||
\(826\) | −33.9732 | −1.18208 | ||||||||
\(827\) | −9.97304 | −0.346797 | −0.173398 | − | 0.984852i | \(-0.555475\pi\) | ||||
−0.173398 | + | 0.984852i | \(0.555475\pi\) | |||||||
\(828\) | −155.368 | −5.39941 | ||||||||
\(829\) | 31.8550 | 1.10637 | 0.553185 | − | 0.833059i | \(-0.313412\pi\) | ||||
0.553185 | + | 0.833059i | \(0.313412\pi\) | |||||||
\(830\) | 63.2130 | 2.19415 | ||||||||
\(831\) | −35.7711 | −1.24088 | ||||||||
\(832\) | 61.5316 | 2.13322 | ||||||||
\(833\) | 0.931923 | 0.0322892 | ||||||||
\(834\) | −114.145 | −3.95251 | ||||||||
\(835\) | −41.3292 | −1.43026 | ||||||||
\(836\) | −12.4705 | −0.431301 | ||||||||
\(837\) | −114.507 | −3.95793 | ||||||||
\(838\) | 45.2408 | 1.56282 | ||||||||
\(839\) | 42.8148 | 1.47813 | 0.739065 | − | 0.673634i | \(-0.235268\pi\) | ||||
0.739065 | + | 0.673634i | \(0.235268\pi\) | |||||||
\(840\) | −54.2287 | −1.87107 | ||||||||
\(841\) | 11.0531 | 0.381141 | ||||||||
\(842\) | 53.7993 | 1.85405 | ||||||||
\(843\) | 16.1369 | 0.555785 | ||||||||
\(844\) | 44.0978 | 1.51791 | ||||||||
\(845\) | −21.6292 | −0.744067 | ||||||||
\(846\) | −9.75820 | −0.335494 | ||||||||
\(847\) | −20.6158 | −0.708368 | ||||||||
\(848\) | 2.73869 | 0.0940469 | ||||||||
\(849\) | −65.8454 | −2.25981 | ||||||||
\(850\) | −1.06626 | −0.0365724 | ||||||||
\(851\) | 37.0170 | 1.26893 | ||||||||
\(852\) | −7.52088 | −0.257661 | ||||||||
\(853\) | 43.9031 | 1.50321 | 0.751607 | − | 0.659611i | \(-0.229279\pi\) | ||||
0.751607 | + | 0.659611i | \(0.229279\pi\) | |||||||
\(854\) | −48.8847 | −1.67280 | ||||||||
\(855\) | 42.4789 | 1.45275 | ||||||||
\(856\) | 37.5835 | 1.28458 | ||||||||
\(857\) | 3.30783 | 0.112993 | 0.0564966 | − | 0.998403i | \(-0.482007\pi\) | ||||
0.0564966 | + | 0.998403i | \(0.482007\pi\) | |||||||
\(858\) | −69.3646 | −2.36807 | ||||||||
\(859\) | 3.95602 | 0.134978 | 0.0674889 | − | 0.997720i | \(-0.478501\pi\) | ||||
0.0674889 | + | 0.997720i | \(0.478501\pi\) | |||||||
\(860\) | 31.3224 | 1.06808 | ||||||||
\(861\) | −13.4658 | −0.458914 | ||||||||
\(862\) | 35.2026 | 1.19900 | ||||||||
\(863\) | 6.61363 | 0.225131 | 0.112565 | − | 0.993644i | \(-0.464093\pi\) | ||||
0.112565 | + | 0.993644i | \(0.464093\pi\) | |||||||
\(864\) | −121.916 | −4.14768 | ||||||||
\(865\) | −45.5277 | −1.54799 | ||||||||
\(866\) | −34.5669 | −1.17463 | ||||||||
\(867\) | −3.40363 | −0.115593 | ||||||||
\(868\) | 52.1458 | 1.76994 | ||||||||
\(869\) | −21.1705 | −0.718162 | ||||||||
\(870\) | −113.512 | −3.84842 | ||||||||
\(871\) | −32.3833 | −1.09727 | ||||||||
\(872\) | 5.03165 | 0.170393 | ||||||||
\(873\) | 148.593 | 5.02912 | ||||||||
\(874\) | −28.0529 | −0.948902 | ||||||||
\(875\) | 29.8257 | 1.00829 | ||||||||
\(876\) | 66.7816 | 2.25634 | ||||||||
\(877\) | −42.6371 | −1.43975 | −0.719877 | − | 0.694102i | \(-0.755802\pi\) | ||||
−0.719877 | + | 0.694102i | \(0.755802\pi\) | |||||||
\(878\) | −43.1559 | −1.45644 | ||||||||
\(879\) | 52.8096 | 1.78122 | ||||||||
\(880\) | 3.14367 | 0.105973 | ||||||||
\(881\) | −34.7636 | −1.17121 | −0.585607 | − | 0.810595i | \(-0.699144\pi\) | ||||
−0.585607 | + | 0.810595i | \(0.699144\pi\) | |||||||
\(882\) | −18.0202 | −0.606770 | ||||||||
\(883\) | 36.0538 | 1.21331 | 0.606653 | − | 0.794967i | \(-0.292512\pi\) | ||||
0.606653 | + | 0.794967i | \(0.292512\pi\) | |||||||
\(884\) | −14.4962 | −0.487561 | ||||||||
\(885\) | 42.6443 | 1.43347 | ||||||||
\(886\) | −16.1329 | −0.541995 | ||||||||
\(887\) | −49.7192 | −1.66941 | −0.834703 | − | 0.550700i | \(-0.814361\pi\) | ||||
−0.834703 | + | 0.550700i | \(0.814361\pi\) | |||||||
\(888\) | −51.7384 | −1.73623 | ||||||||
\(889\) | −16.2782 | −0.545954 | ||||||||
\(890\) | 27.8551 | 0.933705 | ||||||||
\(891\) | 74.7046 | 2.50270 | ||||||||
\(892\) | 36.1353 | 1.20990 | ||||||||
\(893\) | −1.06736 | −0.0357180 | ||||||||
\(894\) | −169.191 | −5.65861 | ||||||||
\(895\) | −51.9040 | −1.73496 | ||||||||
\(896\) | 46.6330 | 1.55790 | ||||||||
\(897\) | −94.5278 | −3.15619 | ||||||||
\(898\) | −59.3346 | −1.98002 | ||||||||
\(899\) | 38.1250 | 1.27154 | ||||||||
\(900\) | 12.4902 | 0.416339 | ||||||||
\(901\) | −3.90983 | −0.130255 | ||||||||
\(902\) | −6.06989 | −0.202105 | ||||||||
\(903\) | 41.7561 | 1.38956 | ||||||||
\(904\) | 8.20633 | 0.272938 | ||||||||
\(905\) | 10.9300 | 0.363326 | ||||||||
\(906\) | −95.8826 | −3.18549 | ||||||||
\(907\) | 10.9067 | 0.362150 | 0.181075 | − | 0.983469i | \(-0.442042\pi\) | ||||
0.181075 | + | 0.983469i | \(0.442042\pi\) | |||||||
\(908\) | −68.5113 | −2.27363 | ||||||||
\(909\) | −17.3467 | −0.575355 | ||||||||
\(910\) | −69.9986 | −2.32043 | ||||||||
\(911\) | 1.32015 | 0.0437384 | 0.0218692 | − | 0.999761i | \(-0.493038\pi\) | ||||
0.0218692 | + | 0.999761i | \(0.493038\pi\) | |||||||
\(912\) | −5.04253 | −0.166975 | ||||||||
\(913\) | 23.0116 | 0.761573 | ||||||||
\(914\) | −43.6070 | −1.44239 | ||||||||
\(915\) | 61.3618 | 2.02856 | ||||||||
\(916\) | −18.5891 | −0.614201 | ||||||||
\(917\) | −22.9865 | −0.759082 | ||||||||
\(918\) | 42.8148 | 1.41310 | ||||||||
\(919\) | −43.7446 | −1.44300 | −0.721501 | − | 0.692414i | \(-0.756547\pi\) | ||||
−0.721501 | + | 0.692414i | \(0.756547\pi\) | |||||||
\(920\) | −33.3118 | −1.09826 | ||||||||
\(921\) | 106.238 | 3.50066 | ||||||||
\(922\) | 72.0548 | 2.37300 | ||||||||
\(923\) | −3.39084 | −0.111611 | ||||||||
\(924\) | −56.5188 | −1.85933 | ||||||||
\(925\) | −2.97583 | −0.0978448 | ||||||||
\(926\) | −61.0683 | −2.00683 | ||||||||
\(927\) | 91.7018 | 3.01188 | ||||||||
\(928\) | 40.5921 | 1.33250 | ||||||||
\(929\) | 6.81195 | 0.223493 | 0.111746 | − | 0.993737i | \(-0.464356\pi\) | ||||
0.111746 | + | 0.993737i | \(0.464356\pi\) | |||||||
\(930\) | −108.048 | −3.54303 | ||||||||
\(931\) | −1.97107 | −0.0645991 | ||||||||
\(932\) | −18.4022 | −0.602783 | ||||||||
\(933\) | 8.82938 | 0.289061 | ||||||||
\(934\) | 17.4955 | 0.572469 | ||||||||
\(935\) | −4.48799 | −0.146773 | ||||||||
\(936\) | 97.9064 | 3.20017 | ||||||||
\(937\) | 6.33273 | 0.206881 | 0.103441 | − | 0.994636i | \(-0.467015\pi\) | ||||
0.103441 | + | 0.994636i | \(0.467015\pi\) | |||||||
\(938\) | −43.5560 | −1.42216 | ||||||||
\(939\) | 28.6703 | 0.935620 | ||||||||
\(940\) | −3.62875 | −0.118357 | ||||||||
\(941\) | 37.0263 | 1.20702 | 0.603511 | − | 0.797355i | \(-0.293768\pi\) | ||||
0.603511 | + | 0.797355i | \(0.293768\pi\) | |||||||
\(942\) | −92.0716 | −2.99986 | ||||||||
\(943\) | −8.27183 | −0.269368 | ||||||||
\(944\) | −3.75126 | −0.122093 | ||||||||
\(945\) | 125.244 | 4.07418 | ||||||||
\(946\) | 18.8221 | 0.611960 | ||||||||
\(947\) | 55.4292 | 1.80121 | 0.900603 | − | 0.434643i | \(-0.143125\pi\) | ||||
0.900603 | + | 0.434643i | \(0.143125\pi\) | |||||||
\(948\) | 115.448 | 3.74959 | ||||||||
\(949\) | 30.1089 | 0.977375 | ||||||||
\(950\) | 2.25520 | 0.0731682 | ||||||||
\(951\) | −32.6400 | −1.05842 | ||||||||
\(952\) | −6.81020 | −0.220720 | ||||||||
\(953\) | −16.3276 | −0.528902 | −0.264451 | − | 0.964399i | \(-0.585191\pi\) | ||||
−0.264451 | + | 0.964399i | \(0.585191\pi\) | |||||||
\(954\) | 75.6025 | 2.44772 | ||||||||
\(955\) | −3.67919 | −0.119056 | ||||||||
\(956\) | −40.8191 | −1.32018 | ||||||||
\(957\) | −41.3222 | −1.33576 | ||||||||
\(958\) | −45.1426 | −1.45849 | ||||||||
\(959\) | 32.3773 | 1.04552 | ||||||||
\(960\) | −103.884 | −3.35285 | ||||||||
\(961\) | 5.28975 | 0.170637 | ||||||||
\(962\) | −66.7842 | −2.15321 | ||||||||
\(963\) | −133.429 | −4.29969 | ||||||||
\(964\) | −46.6847 | −1.50361 | ||||||||
\(965\) | 57.4452 | 1.84923 | ||||||||
\(966\) | −127.141 | −4.09070 | ||||||||
\(967\) | −20.1035 | −0.646484 | −0.323242 | − | 0.946316i | \(-0.604773\pi\) | ||||
−0.323242 | + | 0.946316i | \(0.604773\pi\) | |||||||
\(968\) | 17.7003 | 0.568910 | ||||||||
\(969\) | 7.19886 | 0.231261 | ||||||||
\(970\) | 91.2134 | 2.92868 | ||||||||
\(971\) | −28.3035 | −0.908302 | −0.454151 | − | 0.890925i | \(-0.650057\pi\) | ||||
−0.454151 | + | 0.890925i | \(0.650057\pi\) | |||||||
\(972\) | −232.117 | −7.44516 | ||||||||
\(973\) | −41.9323 | −1.34429 | ||||||||
\(974\) | 84.3870 | 2.70393 | ||||||||
\(975\) | 7.59918 | 0.243368 | ||||||||
\(976\) | −5.39777 | −0.172778 | ||||||||
\(977\) | −23.3419 | −0.746774 | −0.373387 | − | 0.927676i | \(-0.621804\pi\) | ||||
−0.373387 | + | 0.927676i | \(0.621804\pi\) | |||||||
\(978\) | −111.218 | −3.55635 | ||||||||
\(979\) | 10.1402 | 0.324081 | ||||||||
\(980\) | −6.70109 | −0.214058 | ||||||||
\(981\) | −17.8634 | −0.570334 | ||||||||
\(982\) | −14.4539 | −0.461244 | ||||||||
\(983\) | 25.0797 | 0.799918 | 0.399959 | − | 0.916533i | \(-0.369024\pi\) | ||||
0.399959 | + | 0.916533i | \(0.369024\pi\) | |||||||
\(984\) | 11.5615 | 0.368567 | ||||||||
\(985\) | 8.39107 | 0.267362 | ||||||||
\(986\) | −14.2552 | −0.453978 | ||||||||
\(987\) | −4.83751 | −0.153980 | ||||||||
\(988\) | 30.6603 | 0.975435 | ||||||||
\(989\) | 25.6501 | 0.815627 | ||||||||
\(990\) | 86.7821 | 2.75812 | ||||||||
\(991\) | 49.7530 | 1.58045 | 0.790227 | − | 0.612814i | \(-0.209962\pi\) | ||||
0.790227 | + | 0.612814i | \(0.209962\pi\) | |||||||
\(992\) | 38.6381 | 1.22676 | ||||||||
\(993\) | 98.2590 | 3.11816 | ||||||||
\(994\) | −4.56072 | −0.144657 | ||||||||
\(995\) | −35.2675 | −1.11805 | ||||||||
\(996\) | −125.488 | −3.97624 | ||||||||
\(997\) | −2.77539 | −0.0878974 | −0.0439487 | − | 0.999034i | \(-0.513994\pi\) | ||||
−0.0439487 | + | 0.999034i | \(0.513994\pi\) | |||||||
\(998\) | −52.3036 | −1.65564 | ||||||||
\(999\) | 119.492 | 3.78057 |
(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 | 6001.2.a.d.1.14 | ✓ | 121 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6001.2.a.d.1.14 | ✓ | 121 | 1.1 | even | 1 | trivial |