Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [671,2,Mod(1,671)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(671, 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("671.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 671 = 11 \cdot 61 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 671.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: | \(5.35796197563\) |
Analytic rank: | \(0\) |
Dimension: | \(21\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.8 | ||
Character | \(\chi\) | \(=\) | 671.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.29453 | −0.915373 | −0.457686 | − | 0.889114i | \(-0.651322\pi\) | ||||
−0.457686 | + | 0.889114i | \(0.651322\pi\) | |||||||
\(3\) | 3.40741 | 1.96727 | 0.983634 | − | 0.180179i | \(-0.0576679\pi\) | ||||
0.983634 | + | 0.180179i | \(0.0576679\pi\) | |||||||
\(4\) | −0.324186 | −0.162093 | ||||||||
\(5\) | 2.94198 | 1.31569 | 0.657847 | − | 0.753152i | \(-0.271467\pi\) | ||||
0.657847 | + | 0.753152i | \(0.271467\pi\) | |||||||
\(6\) | −4.41100 | −1.80078 | ||||||||
\(7\) | −0.962580 | −0.363821 | −0.181911 | − | 0.983315i | \(-0.558228\pi\) | ||||
−0.181911 | + | 0.983315i | \(0.558228\pi\) | |||||||
\(8\) | 3.00873 | 1.06375 | ||||||||
\(9\) | 8.61042 | 2.87014 | ||||||||
\(10\) | −3.80849 | −1.20435 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | −1.10463 | −0.318880 | ||||||||
\(13\) | −1.22524 | −0.339820 | −0.169910 | − | 0.985460i | \(-0.554348\pi\) | ||||
−0.169910 | + | 0.985460i | \(0.554348\pi\) | |||||||
\(14\) | 1.24609 | 0.333032 | ||||||||
\(15\) | 10.0245 | 2.58832 | ||||||||
\(16\) | −3.24653 | −0.811633 | ||||||||
\(17\) | 4.62899 | 1.12269 | 0.561347 | − | 0.827580i | \(-0.310283\pi\) | ||||
0.561347 | + | 0.827580i | \(0.310283\pi\) | |||||||
\(18\) | −11.1465 | −2.62725 | ||||||||
\(19\) | −5.94052 | −1.36285 | −0.681424 | − | 0.731889i | \(-0.738639\pi\) | ||||
−0.681424 | + | 0.731889i | \(0.738639\pi\) | |||||||
\(20\) | −0.953749 | −0.213265 | ||||||||
\(21\) | −3.27990 | −0.715733 | ||||||||
\(22\) | 1.29453 | 0.275995 | ||||||||
\(23\) | −0.745508 | −0.155449 | −0.0777246 | − | 0.996975i | \(-0.524765\pi\) | ||||
−0.0777246 | + | 0.996975i | \(0.524765\pi\) | |||||||
\(24\) | 10.2520 | 2.09268 | ||||||||
\(25\) | 3.65525 | 0.731050 | ||||||||
\(26\) | 1.58611 | 0.311062 | ||||||||
\(27\) | 19.1170 | 3.67907 | ||||||||
\(28\) | 0.312055 | 0.0589728 | ||||||||
\(29\) | −2.48163 | −0.460826 | −0.230413 | − | 0.973093i | \(-0.574008\pi\) | ||||
−0.230413 | + | 0.973093i | \(0.574008\pi\) | |||||||
\(30\) | −12.9771 | −2.36928 | ||||||||
\(31\) | −7.01525 | −1.25998 | −0.629988 | − | 0.776605i | \(-0.716940\pi\) | ||||
−0.629988 | + | 0.776605i | \(0.716940\pi\) | |||||||
\(32\) | −1.81473 | −0.320802 | ||||||||
\(33\) | −3.40741 | −0.593153 | ||||||||
\(34\) | −5.99237 | −1.02768 | ||||||||
\(35\) | −2.83189 | −0.478677 | ||||||||
\(36\) | −2.79138 | −0.465230 | ||||||||
\(37\) | 8.66581 | 1.42465 | 0.712325 | − | 0.701849i | \(-0.247642\pi\) | ||||
0.712325 | + | 0.701849i | \(0.247642\pi\) | |||||||
\(38\) | 7.69019 | 1.24751 | ||||||||
\(39\) | −4.17488 | −0.668516 | ||||||||
\(40\) | 8.85164 | 1.39957 | ||||||||
\(41\) | 4.87491 | 0.761333 | 0.380666 | − | 0.924712i | \(-0.375695\pi\) | ||||
0.380666 | + | 0.924712i | \(0.375695\pi\) | |||||||
\(42\) | 4.24594 | 0.655163 | ||||||||
\(43\) | −7.47335 | −1.13968 | −0.569838 | − | 0.821757i | \(-0.692994\pi\) | ||||
−0.569838 | + | 0.821757i | \(0.692994\pi\) | |||||||
\(44\) | 0.324186 | 0.0488729 | ||||||||
\(45\) | 25.3317 | 3.77623 | ||||||||
\(46\) | 0.965085 | 0.142294 | ||||||||
\(47\) | 5.10409 | 0.744508 | 0.372254 | − | 0.928131i | \(-0.378585\pi\) | ||||
0.372254 | + | 0.928131i | \(0.378585\pi\) | |||||||
\(48\) | −11.0623 | −1.59670 | ||||||||
\(49\) | −6.07344 | −0.867634 | ||||||||
\(50\) | −4.73184 | −0.669183 | ||||||||
\(51\) | 15.7728 | 2.20864 | ||||||||
\(52\) | 0.397205 | 0.0550824 | ||||||||
\(53\) | −12.5071 | −1.71799 | −0.858994 | − | 0.511986i | \(-0.828910\pi\) | ||||
−0.858994 | + | 0.511986i | \(0.828910\pi\) | |||||||
\(54\) | −24.7476 | −3.36772 | ||||||||
\(55\) | −2.94198 | −0.396697 | ||||||||
\(56\) | −2.89615 | −0.387014 | ||||||||
\(57\) | −20.2418 | −2.68109 | ||||||||
\(58\) | 3.21254 | 0.421828 | ||||||||
\(59\) | −4.29739 | −0.559473 | −0.279736 | − | 0.960077i | \(-0.590247\pi\) | ||||
−0.279736 | + | 0.960077i | \(0.590247\pi\) | |||||||
\(60\) | −3.24981 | −0.419549 | ||||||||
\(61\) | 1.00000 | 0.128037 | ||||||||
\(62\) | 9.08147 | 1.15335 | ||||||||
\(63\) | −8.28822 | −1.04422 | ||||||||
\(64\) | 8.84229 | 1.10529 | ||||||||
\(65\) | −3.60462 | −0.447099 | ||||||||
\(66\) | 4.41100 | 0.542956 | ||||||||
\(67\) | −6.70005 | −0.818542 | −0.409271 | − | 0.912413i | \(-0.634217\pi\) | ||||
−0.409271 | + | 0.912413i | \(0.634217\pi\) | |||||||
\(68\) | −1.50065 | −0.181981 | ||||||||
\(69\) | −2.54025 | −0.305810 | ||||||||
\(70\) | 3.66597 | 0.438168 | ||||||||
\(71\) | −5.44678 | −0.646414 | −0.323207 | − | 0.946328i | \(-0.604761\pi\) | ||||
−0.323207 | + | 0.946328i | \(0.604761\pi\) | |||||||
\(72\) | 25.9065 | 3.05311 | ||||||||
\(73\) | 13.4494 | 1.57413 | 0.787064 | − | 0.616872i | \(-0.211600\pi\) | ||||
0.787064 | + | 0.616872i | \(0.211600\pi\) | |||||||
\(74\) | −11.2182 | −1.30409 | ||||||||
\(75\) | 12.4549 | 1.43817 | ||||||||
\(76\) | 1.92583 | 0.220908 | ||||||||
\(77\) | 0.962580 | 0.109696 | ||||||||
\(78\) | 5.40452 | 0.611942 | ||||||||
\(79\) | −3.09980 | −0.348754 | −0.174377 | − | 0.984679i | \(-0.555791\pi\) | ||||
−0.174377 | + | 0.984679i | \(0.555791\pi\) | |||||||
\(80\) | −9.55123 | −1.06786 | ||||||||
\(81\) | 39.3081 | 4.36757 | ||||||||
\(82\) | −6.31073 | −0.696903 | ||||||||
\(83\) | 11.8714 | 1.30306 | 0.651528 | − | 0.758624i | \(-0.274128\pi\) | ||||
0.651528 | + | 0.758624i | \(0.274128\pi\) | |||||||
\(84\) | 1.06330 | 0.116015 | ||||||||
\(85\) | 13.6184 | 1.47712 | ||||||||
\(86\) | 9.67450 | 1.04323 | ||||||||
\(87\) | −8.45591 | −0.906569 | ||||||||
\(88\) | −3.00873 | −0.320732 | ||||||||
\(89\) | 13.7818 | 1.46087 | 0.730433 | − | 0.682984i | \(-0.239318\pi\) | ||||
0.730433 | + | 0.682984i | \(0.239318\pi\) | |||||||
\(90\) | −32.7927 | −3.45665 | ||||||||
\(91\) | 1.17939 | 0.123634 | ||||||||
\(92\) | 0.241683 | 0.0251972 | ||||||||
\(93\) | −23.9038 | −2.47871 | ||||||||
\(94\) | −6.60741 | −0.681503 | ||||||||
\(95\) | −17.4769 | −1.79309 | ||||||||
\(96\) | −6.18352 | −0.631103 | ||||||||
\(97\) | 16.5554 | 1.68095 | 0.840475 | − | 0.541850i | \(-0.182276\pi\) | ||||
0.840475 | + | 0.541850i | \(0.182276\pi\) | |||||||
\(98\) | 7.86226 | 0.794209 | ||||||||
\(99\) | −8.61042 | −0.865380 | ||||||||
\(100\) | −1.18498 | −0.118498 | ||||||||
\(101\) | 0.888072 | 0.0883665 | 0.0441832 | − | 0.999023i | \(-0.485931\pi\) | ||||
0.0441832 | + | 0.999023i | \(0.485931\pi\) | |||||||
\(102\) | −20.4185 | −2.02173 | ||||||||
\(103\) | −2.85528 | −0.281339 | −0.140670 | − | 0.990057i | \(-0.544926\pi\) | ||||
−0.140670 | + | 0.990057i | \(0.544926\pi\) | |||||||
\(104\) | −3.68641 | −0.361483 | ||||||||
\(105\) | −9.64941 | −0.941686 | ||||||||
\(106\) | 16.1909 | 1.57260 | ||||||||
\(107\) | −3.10491 | −0.300163 | −0.150081 | − | 0.988674i | \(-0.547954\pi\) | ||||
−0.150081 | + | 0.988674i | \(0.547954\pi\) | |||||||
\(108\) | −6.19746 | −0.596351 | ||||||||
\(109\) | −0.543978 | −0.0521037 | −0.0260518 | − | 0.999661i | \(-0.508293\pi\) | ||||
−0.0260518 | + | 0.999661i | \(0.508293\pi\) | |||||||
\(110\) | 3.80849 | 0.363125 | ||||||||
\(111\) | 29.5280 | 2.80267 | ||||||||
\(112\) | 3.12505 | 0.295289 | ||||||||
\(113\) | −8.55519 | −0.804804 | −0.402402 | − | 0.915463i | \(-0.631825\pi\) | ||||
−0.402402 | + | 0.915463i | \(0.631825\pi\) | |||||||
\(114\) | 26.2036 | 2.45419 | ||||||||
\(115\) | −2.19327 | −0.204524 | ||||||||
\(116\) | 0.804508 | 0.0746967 | ||||||||
\(117\) | −10.5498 | −0.975331 | ||||||||
\(118\) | 5.56311 | 0.512126 | ||||||||
\(119\) | −4.45577 | −0.408460 | ||||||||
\(120\) | 30.1611 | 2.75332 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | −1.29453 | −0.117201 | ||||||||
\(123\) | 16.6108 | 1.49775 | ||||||||
\(124\) | 2.27425 | 0.204233 | ||||||||
\(125\) | −3.95623 | −0.353856 | ||||||||
\(126\) | 10.7294 | 0.955848 | ||||||||
\(127\) | 8.12429 | 0.720914 | 0.360457 | − | 0.932776i | \(-0.382621\pi\) | ||||
0.360457 | + | 0.932776i | \(0.382621\pi\) | |||||||
\(128\) | −7.81717 | −0.690947 | ||||||||
\(129\) | −25.4648 | −2.24205 | ||||||||
\(130\) | 4.66630 | 0.409262 | ||||||||
\(131\) | −20.2316 | −1.76765 | −0.883823 | − | 0.467821i | \(-0.845039\pi\) | ||||
−0.883823 | + | 0.467821i | \(0.845039\pi\) | |||||||
\(132\) | 1.10463 | 0.0961460 | ||||||||
\(133\) | 5.71823 | 0.495833 | ||||||||
\(134\) | 8.67344 | 0.749271 | ||||||||
\(135\) | 56.2418 | 4.84053 | ||||||||
\(136\) | 13.9274 | 1.19426 | ||||||||
\(137\) | −5.35686 | −0.457668 | −0.228834 | − | 0.973465i | \(-0.573491\pi\) | ||||
−0.228834 | + | 0.973465i | \(0.573491\pi\) | |||||||
\(138\) | 3.28844 | 0.279930 | ||||||||
\(139\) | −7.84674 | −0.665552 | −0.332776 | − | 0.943006i | \(-0.607985\pi\) | ||||
−0.332776 | + | 0.943006i | \(0.607985\pi\) | |||||||
\(140\) | 0.918060 | 0.0775902 | ||||||||
\(141\) | 17.3917 | 1.46465 | ||||||||
\(142\) | 7.05103 | 0.591709 | ||||||||
\(143\) | 1.22524 | 0.102460 | ||||||||
\(144\) | −27.9540 | −2.32950 | ||||||||
\(145\) | −7.30089 | −0.606306 | ||||||||
\(146\) | −17.4106 | −1.44091 | ||||||||
\(147\) | −20.6947 | −1.70687 | ||||||||
\(148\) | −2.80934 | −0.230926 | ||||||||
\(149\) | −21.4540 | −1.75758 | −0.878792 | − | 0.477205i | \(-0.841650\pi\) | ||||
−0.878792 | + | 0.477205i | \(0.841650\pi\) | |||||||
\(150\) | −16.1233 | −1.31646 | ||||||||
\(151\) | 1.98491 | 0.161530 | 0.0807649 | − | 0.996733i | \(-0.474264\pi\) | ||||
0.0807649 | + | 0.996733i | \(0.474264\pi\) | |||||||
\(152\) | −17.8734 | −1.44973 | ||||||||
\(153\) | 39.8575 | 3.22229 | ||||||||
\(154\) | −1.24609 | −0.100413 | ||||||||
\(155\) | −20.6387 | −1.65774 | ||||||||
\(156\) | 1.35344 | 0.108362 | ||||||||
\(157\) | −6.43117 | −0.513263 | −0.256631 | − | 0.966509i | \(-0.582613\pi\) | ||||
−0.256631 | + | 0.966509i | \(0.582613\pi\) | |||||||
\(158\) | 4.01279 | 0.319240 | ||||||||
\(159\) | −42.6169 | −3.37974 | ||||||||
\(160\) | −5.33889 | −0.422077 | ||||||||
\(161\) | 0.717612 | 0.0565557 | ||||||||
\(162\) | −50.8856 | −3.99795 | ||||||||
\(163\) | 5.86870 | 0.459672 | 0.229836 | − | 0.973229i | \(-0.426181\pi\) | ||||
0.229836 | + | 0.973229i | \(0.426181\pi\) | |||||||
\(164\) | −1.58038 | −0.123407 | ||||||||
\(165\) | −10.0245 | −0.780408 | ||||||||
\(166\) | −15.3679 | −1.19278 | ||||||||
\(167\) | 7.77784 | 0.601867 | 0.300934 | − | 0.953645i | \(-0.402702\pi\) | ||||
0.300934 | + | 0.953645i | \(0.402702\pi\) | |||||||
\(168\) | −9.86835 | −0.761360 | ||||||||
\(169\) | −11.4988 | −0.884523 | ||||||||
\(170\) | −17.6294 | −1.35212 | ||||||||
\(171\) | −51.1504 | −3.91157 | ||||||||
\(172\) | 2.42276 | 0.184733 | ||||||||
\(173\) | 1.52361 | 0.115838 | 0.0579189 | − | 0.998321i | \(-0.481554\pi\) | ||||
0.0579189 | + | 0.998321i | \(0.481554\pi\) | |||||||
\(174\) | 10.9464 | 0.829848 | ||||||||
\(175\) | −3.51847 | −0.265971 | ||||||||
\(176\) | 3.24653 | 0.244717 | ||||||||
\(177\) | −14.6430 | −1.10063 | ||||||||
\(178\) | −17.8410 | −1.33724 | ||||||||
\(179\) | −14.1271 | −1.05591 | −0.527953 | − | 0.849274i | \(-0.677040\pi\) | ||||
−0.527953 | + | 0.849274i | \(0.677040\pi\) | |||||||
\(180\) | −8.21218 | −0.612100 | ||||||||
\(181\) | −6.80507 | −0.505816 | −0.252908 | − | 0.967490i | \(-0.581387\pi\) | ||||
−0.252908 | + | 0.967490i | \(0.581387\pi\) | |||||||
\(182\) | −1.52676 | −0.113171 | ||||||||
\(183\) | 3.40741 | 0.251883 | ||||||||
\(184\) | −2.24304 | −0.165359 | ||||||||
\(185\) | 25.4947 | 1.87440 | ||||||||
\(186\) | 30.9443 | 2.26894 | ||||||||
\(187\) | −4.62899 | −0.338505 | ||||||||
\(188\) | −1.65468 | −0.120680 | ||||||||
\(189\) | −18.4016 | −1.33852 | ||||||||
\(190\) | 22.6244 | 1.64135 | ||||||||
\(191\) | 18.7503 | 1.35673 | 0.678364 | − | 0.734726i | \(-0.262689\pi\) | ||||
0.678364 | + | 0.734726i | \(0.262689\pi\) | |||||||
\(192\) | 30.1293 | 2.17439 | ||||||||
\(193\) | 15.7510 | 1.13378 | 0.566891 | − | 0.823793i | \(-0.308146\pi\) | ||||
0.566891 | + | 0.823793i | \(0.308146\pi\) | |||||||
\(194\) | −21.4316 | −1.53870 | ||||||||
\(195\) | −12.2824 | −0.879563 | ||||||||
\(196\) | 1.96892 | 0.140637 | ||||||||
\(197\) | −19.6194 | −1.39782 | −0.698910 | − | 0.715209i | \(-0.746331\pi\) | ||||
−0.698910 | + | 0.715209i | \(0.746331\pi\) | |||||||
\(198\) | 11.1465 | 0.792145 | ||||||||
\(199\) | 3.05553 | 0.216601 | 0.108300 | − | 0.994118i | \(-0.465459\pi\) | ||||
0.108300 | + | 0.994118i | \(0.465459\pi\) | |||||||
\(200\) | 10.9977 | 0.777653 | ||||||||
\(201\) | −22.8298 | −1.61029 | ||||||||
\(202\) | −1.14964 | −0.0808883 | ||||||||
\(203\) | 2.38876 | 0.167658 | ||||||||
\(204\) | −5.11334 | −0.358005 | ||||||||
\(205\) | 14.3419 | 1.00168 | ||||||||
\(206\) | 3.69625 | 0.257530 | ||||||||
\(207\) | −6.41914 | −0.446161 | ||||||||
\(208\) | 3.97777 | 0.275809 | ||||||||
\(209\) | 5.94052 | 0.410914 | ||||||||
\(210\) | 12.4915 | 0.861993 | ||||||||
\(211\) | −13.2527 | −0.912353 | −0.456177 | − | 0.889889i | \(-0.650781\pi\) | ||||
−0.456177 | + | 0.889889i | \(0.650781\pi\) | |||||||
\(212\) | 4.05464 | 0.278474 | ||||||||
\(213\) | −18.5594 | −1.27167 | ||||||||
\(214\) | 4.01940 | 0.274761 | ||||||||
\(215\) | −21.9865 | −1.49946 | ||||||||
\(216\) | 57.5180 | 3.91360 | ||||||||
\(217\) | 6.75274 | 0.458406 | ||||||||
\(218\) | 0.704197 | 0.0476943 | ||||||||
\(219\) | 45.8274 | 3.09673 | ||||||||
\(220\) | 0.953749 | 0.0643017 | ||||||||
\(221\) | −5.67161 | −0.381514 | ||||||||
\(222\) | −38.2249 | −2.56549 | ||||||||
\(223\) | −25.8228 | −1.72922 | −0.864612 | − | 0.502440i | \(-0.832436\pi\) | ||||
−0.864612 | + | 0.502440i | \(0.832436\pi\) | |||||||
\(224\) | 1.74682 | 0.116714 | ||||||||
\(225\) | 31.4732 | 2.09822 | ||||||||
\(226\) | 11.0750 | 0.736696 | ||||||||
\(227\) | 20.5042 | 1.36091 | 0.680454 | − | 0.732790i | \(-0.261782\pi\) | ||||
0.680454 | + | 0.732790i | \(0.261782\pi\) | |||||||
\(228\) | 6.56210 | 0.434586 | ||||||||
\(229\) | −14.1285 | −0.933639 | −0.466819 | − | 0.884353i | \(-0.654600\pi\) | ||||
−0.466819 | + | 0.884353i | \(0.654600\pi\) | |||||||
\(230\) | 2.83926 | 0.187215 | ||||||||
\(231\) | 3.27990 | 0.215802 | ||||||||
\(232\) | −7.46655 | −0.490203 | ||||||||
\(233\) | −23.5630 | −1.54366 | −0.771832 | − | 0.635826i | \(-0.780659\pi\) | ||||
−0.771832 | + | 0.635826i | \(0.780659\pi\) | |||||||
\(234\) | 13.6571 | 0.892791 | ||||||||
\(235\) | 15.0161 | 0.979545 | ||||||||
\(236\) | 1.39315 | 0.0906866 | ||||||||
\(237\) | −10.5623 | −0.686093 | ||||||||
\(238\) | 5.76814 | 0.373893 | ||||||||
\(239\) | 0.840460 | 0.0543649 | 0.0271824 | − | 0.999630i | \(-0.491346\pi\) | ||||
0.0271824 | + | 0.999630i | \(0.491346\pi\) | |||||||
\(240\) | −32.5449 | −2.10077 | ||||||||
\(241\) | −0.326981 | −0.0210627 | −0.0105313 | − | 0.999945i | \(-0.503352\pi\) | ||||
−0.0105313 | + | 0.999945i | \(0.503352\pi\) | |||||||
\(242\) | −1.29453 | −0.0832157 | ||||||||
\(243\) | 76.5878 | 4.91311 | ||||||||
\(244\) | −0.324186 | −0.0207539 | ||||||||
\(245\) | −17.8679 | −1.14154 | ||||||||
\(246\) | −21.5032 | −1.37099 | ||||||||
\(247\) | 7.27855 | 0.463123 | ||||||||
\(248\) | −21.1070 | −1.34030 | ||||||||
\(249\) | 40.4507 | 2.56346 | ||||||||
\(250\) | 5.12147 | 0.323910 | ||||||||
\(251\) | −6.54627 | −0.413197 | −0.206598 | − | 0.978426i | \(-0.566239\pi\) | ||||
−0.206598 | + | 0.978426i | \(0.566239\pi\) | |||||||
\(252\) | 2.68693 | 0.169260 | ||||||||
\(253\) | 0.745508 | 0.0468697 | ||||||||
\(254\) | −10.5172 | −0.659905 | ||||||||
\(255\) | 46.4034 | 2.90589 | ||||||||
\(256\) | −7.56499 | −0.472812 | ||||||||
\(257\) | 14.6146 | 0.911631 | 0.455816 | − | 0.890074i | \(-0.349348\pi\) | ||||
0.455816 | + | 0.890074i | \(0.349348\pi\) | |||||||
\(258\) | 32.9650 | 2.05231 | ||||||||
\(259\) | −8.34154 | −0.518318 | ||||||||
\(260\) | 1.16857 | 0.0724716 | ||||||||
\(261\) | −21.3678 | −1.32264 | ||||||||
\(262\) | 26.1905 | 1.61805 | ||||||||
\(263\) | 7.05354 | 0.434940 | 0.217470 | − | 0.976067i | \(-0.430220\pi\) | ||||
0.217470 | + | 0.976067i | \(0.430220\pi\) | |||||||
\(264\) | −10.2520 | −0.630966 | ||||||||
\(265\) | −36.7958 | −2.26035 | ||||||||
\(266\) | −7.40243 | −0.453872 | ||||||||
\(267\) | 46.9601 | 2.87391 | ||||||||
\(268\) | 2.17206 | 0.132680 | ||||||||
\(269\) | −5.31730 | −0.324201 | −0.162101 | − | 0.986774i | \(-0.551827\pi\) | ||||
−0.162101 | + | 0.986774i | \(0.551827\pi\) | |||||||
\(270\) | −72.8069 | −4.43089 | ||||||||
\(271\) | 29.6220 | 1.79941 | 0.899704 | − | 0.436501i | \(-0.143782\pi\) | ||||
0.899704 | + | 0.436501i | \(0.143782\pi\) | |||||||
\(272\) | −15.0282 | −0.911216 | ||||||||
\(273\) | 4.01866 | 0.243220 | ||||||||
\(274\) | 6.93463 | 0.418937 | ||||||||
\(275\) | −3.65525 | −0.220420 | ||||||||
\(276\) | 0.823514 | 0.0495697 | ||||||||
\(277\) | −3.25940 | −0.195838 | −0.0979192 | − | 0.995194i | \(-0.531219\pi\) | ||||
−0.0979192 | + | 0.995194i | \(0.531219\pi\) | |||||||
\(278\) | 10.1579 | 0.609228 | ||||||||
\(279\) | −60.4043 | −3.61631 | ||||||||
\(280\) | −8.52041 | −0.509192 | ||||||||
\(281\) | 8.69897 | 0.518937 | 0.259468 | − | 0.965752i | \(-0.416453\pi\) | ||||
0.259468 | + | 0.965752i | \(0.416453\pi\) | |||||||
\(282\) | −22.5141 | −1.34070 | ||||||||
\(283\) | 24.9271 | 1.48176 | 0.740881 | − | 0.671637i | \(-0.234408\pi\) | ||||
0.740881 | + | 0.671637i | \(0.234408\pi\) | |||||||
\(284\) | 1.76577 | 0.104779 | ||||||||
\(285\) | −59.5509 | −3.52749 | ||||||||
\(286\) | −1.58611 | −0.0937886 | ||||||||
\(287\) | −4.69249 | −0.276989 | ||||||||
\(288\) | −15.6256 | −0.920746 | ||||||||
\(289\) | 4.42753 | 0.260443 | ||||||||
\(290\) | 9.45124 | 0.554996 | ||||||||
\(291\) | 56.4111 | 3.30688 | ||||||||
\(292\) | −4.36009 | −0.255155 | ||||||||
\(293\) | −23.5261 | −1.37441 | −0.687204 | − | 0.726464i | \(-0.741162\pi\) | ||||
−0.687204 | + | 0.726464i | \(0.741162\pi\) | |||||||
\(294\) | 26.7899 | 1.56242 | ||||||||
\(295\) | −12.6428 | −0.736095 | ||||||||
\(296\) | 26.0731 | 1.51547 | ||||||||
\(297\) | −19.1170 | −1.10928 | ||||||||
\(298\) | 27.7729 | 1.60884 | ||||||||
\(299\) | 0.913425 | 0.0528247 | ||||||||
\(300\) | −4.03771 | −0.233117 | ||||||||
\(301\) | 7.19370 | 0.414638 | ||||||||
\(302\) | −2.56953 | −0.147860 | ||||||||
\(303\) | 3.02602 | 0.173841 | ||||||||
\(304\) | 19.2861 | 1.10613 | ||||||||
\(305\) | 2.94198 | 0.168457 | ||||||||
\(306\) | −51.5969 | −2.94960 | ||||||||
\(307\) | 11.8721 | 0.677576 | 0.338788 | − | 0.940863i | \(-0.389983\pi\) | ||||
0.338788 | + | 0.940863i | \(0.389983\pi\) | |||||||
\(308\) | −0.312055 | −0.0177810 | ||||||||
\(309\) | −9.72910 | −0.553469 | ||||||||
\(310\) | 26.7175 | 1.51745 | ||||||||
\(311\) | −4.11507 | −0.233344 | −0.116672 | − | 0.993170i | \(-0.537223\pi\) | ||||
−0.116672 | + | 0.993170i | \(0.537223\pi\) | |||||||
\(312\) | −12.5611 | −0.711133 | ||||||||
\(313\) | −6.63578 | −0.375077 | −0.187538 | − | 0.982257i | \(-0.560051\pi\) | ||||
−0.187538 | + | 0.982257i | \(0.560051\pi\) | |||||||
\(314\) | 8.32535 | 0.469827 | ||||||||
\(315\) | −24.3838 | −1.37387 | ||||||||
\(316\) | 1.00491 | 0.0565306 | ||||||||
\(317\) | 16.6483 | 0.935061 | 0.467530 | − | 0.883977i | \(-0.345144\pi\) | ||||
0.467530 | + | 0.883977i | \(0.345144\pi\) | |||||||
\(318\) | 55.1690 | 3.09372 | ||||||||
\(319\) | 2.48163 | 0.138944 | ||||||||
\(320\) | 26.0138 | 1.45422 | ||||||||
\(321\) | −10.5797 | −0.590500 | ||||||||
\(322\) | −0.928971 | −0.0517695 | ||||||||
\(323\) | −27.4986 | −1.53006 | ||||||||
\(324\) | −12.7431 | −0.707953 | ||||||||
\(325\) | −4.47855 | −0.248425 | ||||||||
\(326\) | −7.59722 | −0.420771 | ||||||||
\(327\) | −1.85356 | −0.102502 | ||||||||
\(328\) | 14.6673 | 0.809866 | ||||||||
\(329\) | −4.91310 | −0.270868 | ||||||||
\(330\) | 12.9771 | 0.714364 | ||||||||
\(331\) | −3.64936 | −0.200587 | −0.100293 | − | 0.994958i | \(-0.531978\pi\) | ||||
−0.100293 | + | 0.994958i | \(0.531978\pi\) | |||||||
\(332\) | −3.84855 | −0.211216 | ||||||||
\(333\) | 74.6163 | 4.08895 | ||||||||
\(334\) | −10.0687 | −0.550933 | ||||||||
\(335\) | −19.7114 | −1.07695 | ||||||||
\(336\) | 10.6483 | 0.580913 | ||||||||
\(337\) | 28.4702 | 1.55087 | 0.775436 | − | 0.631427i | \(-0.217530\pi\) | ||||
0.775436 | + | 0.631427i | \(0.217530\pi\) | |||||||
\(338\) | 14.8856 | 0.809668 | ||||||||
\(339\) | −29.1510 | −1.58327 | ||||||||
\(340\) | −4.41489 | −0.239431 | ||||||||
\(341\) | 7.01525 | 0.379897 | ||||||||
\(342\) | 66.2158 | 3.58054 | ||||||||
\(343\) | 12.5842 | 0.679485 | ||||||||
\(344\) | −22.4853 | −1.21233 | ||||||||
\(345\) | −7.47337 | −0.402353 | ||||||||
\(346\) | −1.97236 | −0.106035 | ||||||||
\(347\) | 5.92554 | 0.318100 | 0.159050 | − | 0.987271i | \(-0.449157\pi\) | ||||
0.159050 | + | 0.987271i | \(0.449157\pi\) | |||||||
\(348\) | 2.74129 | 0.146948 | ||||||||
\(349\) | −2.60651 | −0.139523 | −0.0697616 | − | 0.997564i | \(-0.522224\pi\) | ||||
−0.0697616 | + | 0.997564i | \(0.522224\pi\) | |||||||
\(350\) | 4.55477 | 0.243463 | ||||||||
\(351\) | −23.4229 | −1.25022 | ||||||||
\(352\) | 1.81473 | 0.0967253 | ||||||||
\(353\) | 9.84606 | 0.524053 | 0.262026 | − | 0.965061i | \(-0.415609\pi\) | ||||
0.262026 | + | 0.965061i | \(0.415609\pi\) | |||||||
\(354\) | 18.9558 | 1.00749 | ||||||||
\(355\) | −16.0243 | −0.850482 | ||||||||
\(356\) | −4.46786 | −0.236796 | ||||||||
\(357\) | −15.1826 | −0.803550 | ||||||||
\(358\) | 18.2879 | 0.966547 | ||||||||
\(359\) | 25.4699 | 1.34425 | 0.672125 | − | 0.740438i | \(-0.265382\pi\) | ||||
0.672125 | + | 0.740438i | \(0.265382\pi\) | |||||||
\(360\) | 76.2163 | 4.01695 | ||||||||
\(361\) | 16.2898 | 0.857356 | ||||||||
\(362\) | 8.80938 | 0.463011 | ||||||||
\(363\) | 3.40741 | 0.178842 | ||||||||
\(364\) | −0.382341 | −0.0200401 | ||||||||
\(365\) | 39.5677 | 2.07107 | ||||||||
\(366\) | −4.41100 | −0.230567 | ||||||||
\(367\) | 13.5461 | 0.707102 | 0.353551 | − | 0.935415i | \(-0.384974\pi\) | ||||
0.353551 | + | 0.935415i | \(0.384974\pi\) | |||||||
\(368\) | 2.42032 | 0.126168 | ||||||||
\(369\) | 41.9750 | 2.18513 | ||||||||
\(370\) | −33.0037 | −1.71578 | ||||||||
\(371\) | 12.0391 | 0.625040 | ||||||||
\(372\) | 7.74928 | 0.401782 | ||||||||
\(373\) | −37.1332 | −1.92269 | −0.961343 | − | 0.275354i | \(-0.911205\pi\) | ||||
−0.961343 | + | 0.275354i | \(0.911205\pi\) | |||||||
\(374\) | 5.99237 | 0.309858 | ||||||||
\(375\) | −13.4805 | −0.696130 | ||||||||
\(376\) | 15.3569 | 0.791969 | ||||||||
\(377\) | 3.04058 | 0.156598 | ||||||||
\(378\) | 23.8215 | 1.22525 | ||||||||
\(379\) | 21.3790 | 1.09817 | 0.549083 | − | 0.835768i | \(-0.314977\pi\) | ||||
0.549083 | + | 0.835768i | \(0.314977\pi\) | |||||||
\(380\) | 5.66576 | 0.290648 | ||||||||
\(381\) | 27.6828 | 1.41823 | ||||||||
\(382\) | −24.2729 | −1.24191 | ||||||||
\(383\) | −20.5316 | −1.04912 | −0.524558 | − | 0.851375i | \(-0.675770\pi\) | ||||
−0.524558 | + | 0.851375i | \(0.675770\pi\) | |||||||
\(384\) | −26.6363 | −1.35928 | ||||||||
\(385\) | 2.83189 | 0.144327 | ||||||||
\(386\) | −20.3902 | −1.03783 | ||||||||
\(387\) | −64.3487 | −3.27103 | ||||||||
\(388\) | −5.36704 | −0.272470 | ||||||||
\(389\) | −2.54805 | −0.129191 | −0.0645957 | − | 0.997912i | \(-0.520576\pi\) | ||||
−0.0645957 | + | 0.997912i | \(0.520576\pi\) | |||||||
\(390\) | 15.9000 | 0.805128 | ||||||||
\(391\) | −3.45095 | −0.174522 | ||||||||
\(392\) | −18.2734 | −0.922944 | ||||||||
\(393\) | −68.9374 | −3.47743 | ||||||||
\(394\) | 25.3979 | 1.27953 | ||||||||
\(395\) | −9.11954 | −0.458854 | ||||||||
\(396\) | 2.79138 | 0.140272 | ||||||||
\(397\) | −9.93497 | −0.498622 | −0.249311 | − | 0.968424i | \(-0.580204\pi\) | ||||
−0.249311 | + | 0.968424i | \(0.580204\pi\) | |||||||
\(398\) | −3.95549 | −0.198271 | ||||||||
\(399\) | 19.4843 | 0.975436 | ||||||||
\(400\) | −11.8669 | −0.593344 | ||||||||
\(401\) | −10.3974 | −0.519223 | −0.259612 | − | 0.965713i | \(-0.583595\pi\) | ||||
−0.259612 | + | 0.965713i | \(0.583595\pi\) | |||||||
\(402\) | 29.5539 | 1.47402 | ||||||||
\(403\) | 8.59535 | 0.428165 | ||||||||
\(404\) | −0.287901 | −0.0143236 | ||||||||
\(405\) | 115.644 | 5.74638 | ||||||||
\(406\) | −3.09233 | −0.153470 | ||||||||
\(407\) | −8.66581 | −0.429548 | ||||||||
\(408\) | 47.4563 | 2.34944 | ||||||||
\(409\) | 3.14695 | 0.155607 | 0.0778033 | − | 0.996969i | \(-0.475209\pi\) | ||||
0.0778033 | + | 0.996969i | \(0.475209\pi\) | |||||||
\(410\) | −18.5660 | −0.916911 | ||||||||
\(411\) | −18.2530 | −0.900355 | ||||||||
\(412\) | 0.925642 | 0.0456031 | ||||||||
\(413\) | 4.13658 | 0.203548 | ||||||||
\(414\) | 8.30979 | 0.408404 | ||||||||
\(415\) | 34.9255 | 1.71442 | ||||||||
\(416\) | 2.22347 | 0.109015 | ||||||||
\(417\) | −26.7370 | −1.30932 | ||||||||
\(418\) | −7.69019 | −0.376140 | ||||||||
\(419\) | 31.9845 | 1.56254 | 0.781272 | − | 0.624190i | \(-0.214571\pi\) | ||||
0.781272 | + | 0.624190i | \(0.214571\pi\) | |||||||
\(420\) | 3.12820 | 0.152641 | ||||||||
\(421\) | 17.1307 | 0.834898 | 0.417449 | − | 0.908700i | \(-0.362924\pi\) | ||||
0.417449 | + | 0.908700i | \(0.362924\pi\) | |||||||
\(422\) | 17.1560 | 0.835143 | ||||||||
\(423\) | 43.9484 | 2.13684 | ||||||||
\(424\) | −37.6307 | −1.82751 | ||||||||
\(425\) | 16.9201 | 0.820745 | ||||||||
\(426\) | 24.0257 | 1.16405 | ||||||||
\(427\) | −0.962580 | −0.0465825 | ||||||||
\(428\) | 1.00657 | 0.0486543 | ||||||||
\(429\) | 4.17488 | 0.201565 | ||||||||
\(430\) | 28.4622 | 1.37257 | ||||||||
\(431\) | −34.2444 | −1.64949 | −0.824747 | − | 0.565501i | \(-0.808683\pi\) | ||||
−0.824747 | + | 0.565501i | \(0.808683\pi\) | |||||||
\(432\) | −62.0639 | −2.98605 | ||||||||
\(433\) | −0.831844 | −0.0399759 | −0.0199879 | − | 0.999800i | \(-0.506363\pi\) | ||||
−0.0199879 | + | 0.999800i | \(0.506363\pi\) | |||||||
\(434\) | −8.74164 | −0.419612 | ||||||||
\(435\) | −24.8771 | −1.19277 | ||||||||
\(436\) | 0.176350 | 0.00844564 | ||||||||
\(437\) | 4.42871 | 0.211854 | ||||||||
\(438\) | −59.3251 | −2.83466 | ||||||||
\(439\) | 23.0292 | 1.09913 | 0.549563 | − | 0.835452i | \(-0.314794\pi\) | ||||
0.549563 | + | 0.835452i | \(0.314794\pi\) | |||||||
\(440\) | −8.85164 | −0.421985 | ||||||||
\(441\) | −52.2949 | −2.49023 | ||||||||
\(442\) | 7.34208 | 0.349227 | ||||||||
\(443\) | −4.09693 | −0.194651 | −0.0973255 | − | 0.995253i | \(-0.531029\pi\) | ||||
−0.0973255 | + | 0.995253i | \(0.531029\pi\) | |||||||
\(444\) | −9.57255 | −0.454293 | ||||||||
\(445\) | 40.5457 | 1.92205 | ||||||||
\(446\) | 33.4285 | 1.58288 | ||||||||
\(447\) | −73.1027 | −3.45764 | ||||||||
\(448\) | −8.51141 | −0.402126 | ||||||||
\(449\) | 38.8738 | 1.83457 | 0.917285 | − | 0.398231i | \(-0.130376\pi\) | ||||
0.917285 | + | 0.398231i | \(0.130376\pi\) | |||||||
\(450\) | −40.7431 | −1.92065 | ||||||||
\(451\) | −4.87491 | −0.229550 | ||||||||
\(452\) | 2.77347 | 0.130453 | ||||||||
\(453\) | 6.76340 | 0.317772 | ||||||||
\(454\) | −26.5433 | −1.24574 | ||||||||
\(455\) | 3.46974 | 0.162664 | ||||||||
\(456\) | −60.9021 | −2.85200 | ||||||||
\(457\) | 28.7219 | 1.34355 | 0.671777 | − | 0.740753i | \(-0.265531\pi\) | ||||
0.671777 | + | 0.740753i | \(0.265531\pi\) | |||||||
\(458\) | 18.2898 | 0.854628 | ||||||||
\(459\) | 88.4924 | 4.13047 | ||||||||
\(460\) | 0.711028 | 0.0331518 | ||||||||
\(461\) | 36.1721 | 1.68470 | 0.842351 | − | 0.538929i | \(-0.181171\pi\) | ||||
0.842351 | + | 0.538929i | \(0.181171\pi\) | |||||||
\(462\) | −4.24594 | −0.197539 | ||||||||
\(463\) | −19.3506 | −0.899298 | −0.449649 | − | 0.893205i | \(-0.648451\pi\) | ||||
−0.449649 | + | 0.893205i | \(0.648451\pi\) | |||||||
\(464\) | 8.05668 | 0.374022 | ||||||||
\(465\) | −70.3245 | −3.26122 | ||||||||
\(466\) | 30.5031 | 1.41303 | ||||||||
\(467\) | 28.6014 | 1.32352 | 0.661758 | − | 0.749718i | \(-0.269811\pi\) | ||||
0.661758 | + | 0.749718i | \(0.269811\pi\) | |||||||
\(468\) | 3.42010 | 0.158094 | ||||||||
\(469\) | 6.44934 | 0.297803 | ||||||||
\(470\) | −19.4389 | −0.896649 | ||||||||
\(471\) | −21.9136 | −1.00973 | ||||||||
\(472\) | −12.9297 | −0.595138 | ||||||||
\(473\) | 7.47335 | 0.343625 | ||||||||
\(474\) | 13.6732 | 0.628031 | ||||||||
\(475\) | −21.7141 | −0.996310 | ||||||||
\(476\) | 1.44450 | 0.0662085 | ||||||||
\(477\) | −107.692 | −4.93087 | ||||||||
\(478\) | −1.08800 | −0.0497641 | ||||||||
\(479\) | −5.94666 | −0.271710 | −0.135855 | − | 0.990729i | \(-0.543378\pi\) | ||||
−0.135855 | + | 0.990729i | \(0.543378\pi\) | |||||||
\(480\) | −18.1918 | −0.830338 | ||||||||
\(481\) | −10.6177 | −0.484125 | ||||||||
\(482\) | 0.423287 | 0.0192802 | ||||||||
\(483\) | 2.44519 | 0.111260 | ||||||||
\(484\) | −0.324186 | −0.0147357 | ||||||||
\(485\) | 48.7058 | 2.21162 | ||||||||
\(486\) | −99.1454 | −4.49733 | ||||||||
\(487\) | −15.9869 | −0.724436 | −0.362218 | − | 0.932093i | \(-0.617980\pi\) | ||||
−0.362218 | + | 0.932093i | \(0.617980\pi\) | |||||||
\(488\) | 3.00873 | 0.136199 | ||||||||
\(489\) | 19.9970 | 0.904297 | ||||||||
\(490\) | 23.1306 | 1.04494 | ||||||||
\(491\) | −14.3736 | −0.648671 | −0.324335 | − | 0.945942i | \(-0.605141\pi\) | ||||
−0.324335 | + | 0.945942i | \(0.605141\pi\) | |||||||
\(492\) | −5.38499 | −0.242774 | ||||||||
\(493\) | −11.4874 | −0.517367 | ||||||||
\(494\) | −9.42231 | −0.423930 | ||||||||
\(495\) | −25.3317 | −1.13858 | ||||||||
\(496\) | 22.7752 | 1.02264 | ||||||||
\(497\) | 5.24296 | 0.235179 | ||||||||
\(498\) | −52.3648 | −2.34652 | ||||||||
\(499\) | −27.4728 | −1.22985 | −0.614925 | − | 0.788586i | \(-0.710814\pi\) | ||||
−0.614925 | + | 0.788586i | \(0.710814\pi\) | |||||||
\(500\) | 1.28256 | 0.0573577 | ||||||||
\(501\) | 26.5023 | 1.18403 | ||||||||
\(502\) | 8.47436 | 0.378229 | ||||||||
\(503\) | 12.4426 | 0.554787 | 0.277393 | − | 0.960756i | \(-0.410530\pi\) | ||||
0.277393 | + | 0.960756i | \(0.410530\pi\) | |||||||
\(504\) | −24.9371 | −1.11078 | ||||||||
\(505\) | 2.61269 | 0.116263 | ||||||||
\(506\) | −0.965085 | −0.0429033 | ||||||||
\(507\) | −39.1811 | −1.74009 | ||||||||
\(508\) | −2.63378 | −0.116855 | ||||||||
\(509\) | 8.43341 | 0.373804 | 0.186902 | − | 0.982379i | \(-0.440155\pi\) | ||||
0.186902 | + | 0.982379i | \(0.440155\pi\) | |||||||
\(510\) | −60.0707 | −2.65998 | ||||||||
\(511\) | −12.9461 | −0.572701 | ||||||||
\(512\) | 25.4275 | 1.12375 | ||||||||
\(513\) | −113.565 | −5.01401 | ||||||||
\(514\) | −18.9190 | −0.834482 | ||||||||
\(515\) | −8.40018 | −0.370156 | ||||||||
\(516\) | 8.25532 | 0.363420 | ||||||||
\(517\) | −5.10409 | −0.224478 | ||||||||
\(518\) | 10.7984 | 0.474454 | ||||||||
\(519\) | 5.19156 | 0.227884 | ||||||||
\(520\) | −10.8454 | −0.475600 | ||||||||
\(521\) | 32.9612 | 1.44406 | 0.722029 | − | 0.691863i | \(-0.243210\pi\) | ||||
0.722029 | + | 0.691863i | \(0.243210\pi\) | |||||||
\(522\) | 27.6614 | 1.21071 | ||||||||
\(523\) | 35.4687 | 1.55094 | 0.775469 | − | 0.631386i | \(-0.217514\pi\) | ||||
0.775469 | + | 0.631386i | \(0.217514\pi\) | |||||||
\(524\) | 6.55881 | 0.286523 | ||||||||
\(525\) | −11.9889 | −0.523236 | ||||||||
\(526\) | −9.13104 | −0.398132 | ||||||||
\(527\) | −32.4735 | −1.41457 | ||||||||
\(528\) | 11.0623 | 0.481423 | ||||||||
\(529\) | −22.4442 | −0.975836 | ||||||||
\(530\) | 47.6333 | 2.06906 | ||||||||
\(531\) | −37.0024 | −1.60577 | ||||||||
\(532\) | −1.85377 | −0.0803711 | ||||||||
\(533\) | −5.97292 | −0.258716 | ||||||||
\(534\) | −60.7914 | −2.63070 | ||||||||
\(535\) | −9.13457 | −0.394922 | ||||||||
\(536\) | −20.1587 | −0.870722 | ||||||||
\(537\) | −48.1366 | −2.07725 | ||||||||
\(538\) | 6.88341 | 0.296765 | ||||||||
\(539\) | 6.07344 | 0.261602 | ||||||||
\(540\) | −18.2328 | −0.784616 | ||||||||
\(541\) | 34.5067 | 1.48356 | 0.741779 | − | 0.670645i | \(-0.233982\pi\) | ||||
0.741779 | + | 0.670645i | \(0.233982\pi\) | |||||||
\(542\) | −38.3466 | −1.64713 | ||||||||
\(543\) | −23.1876 | −0.995076 | ||||||||
\(544\) | −8.40035 | −0.360162 | ||||||||
\(545\) | −1.60037 | −0.0685525 | ||||||||
\(546\) | −5.20228 | −0.222637 | ||||||||
\(547\) | −21.0533 | −0.900172 | −0.450086 | − | 0.892985i | \(-0.648607\pi\) | ||||
−0.450086 | + | 0.892985i | \(0.648607\pi\) | |||||||
\(548\) | 1.73662 | 0.0741848 | ||||||||
\(549\) | 8.61042 | 0.367484 | ||||||||
\(550\) | 4.73184 | 0.201766 | ||||||||
\(551\) | 14.7421 | 0.628036 | ||||||||
\(552\) | −7.64294 | −0.325305 | ||||||||
\(553\) | 2.98380 | 0.126884 | ||||||||
\(554\) | 4.21940 | 0.179265 | ||||||||
\(555\) | 86.8707 | 3.68745 | ||||||||
\(556\) | 2.54380 | 0.107881 | ||||||||
\(557\) | 2.07457 | 0.0879023 | 0.0439512 | − | 0.999034i | \(-0.486005\pi\) | ||||
0.0439512 | + | 0.999034i | \(0.486005\pi\) | |||||||
\(558\) | 78.1953 | 3.31027 | ||||||||
\(559\) | 9.15663 | 0.387284 | ||||||||
\(560\) | 9.19382 | 0.388510 | ||||||||
\(561\) | −15.7728 | −0.665930 | ||||||||
\(562\) | −11.2611 | −0.475021 | ||||||||
\(563\) | 5.85850 | 0.246906 | 0.123453 | − | 0.992350i | \(-0.460603\pi\) | ||||
0.123453 | + | 0.992350i | \(0.460603\pi\) | |||||||
\(564\) | −5.63815 | −0.237409 | ||||||||
\(565\) | −25.1692 | −1.05888 | ||||||||
\(566\) | −32.2689 | −1.35636 | ||||||||
\(567\) | −37.8372 | −1.58901 | ||||||||
\(568\) | −16.3879 | −0.687621 | ||||||||
\(569\) | −0.644417 | −0.0270154 | −0.0135077 | − | 0.999909i | \(-0.504300\pi\) | ||||
−0.0135077 | + | 0.999909i | \(0.504300\pi\) | |||||||
\(570\) | 77.0905 | 3.22897 | ||||||||
\(571\) | −16.3535 | −0.684374 | −0.342187 | − | 0.939632i | \(-0.611168\pi\) | ||||
−0.342187 | + | 0.939632i | \(0.611168\pi\) | |||||||
\(572\) | −0.397205 | −0.0166080 | ||||||||
\(573\) | 63.8901 | 2.66905 | ||||||||
\(574\) | 6.07458 | 0.253548 | ||||||||
\(575\) | −2.72502 | −0.113641 | ||||||||
\(576\) | 76.1358 | 3.17233 | ||||||||
\(577\) | −0.157078 | −0.00653926 | −0.00326963 | − | 0.999995i | \(-0.501041\pi\) | ||||
−0.00326963 | + | 0.999995i | \(0.501041\pi\) | |||||||
\(578\) | −5.73158 | −0.238402 | ||||||||
\(579\) | 53.6701 | 2.23045 | ||||||||
\(580\) | 2.36685 | 0.0982780 | ||||||||
\(581\) | −11.4272 | −0.474080 | ||||||||
\(582\) | −73.0260 | −3.02703 | ||||||||
\(583\) | 12.5071 | 0.517993 | ||||||||
\(584\) | 40.4655 | 1.67448 | ||||||||
\(585\) | −31.0373 | −1.28324 | ||||||||
\(586\) | 30.4553 | 1.25810 | ||||||||
\(587\) | −6.89197 | −0.284462 | −0.142231 | − | 0.989833i | \(-0.545428\pi\) | ||||
−0.142231 | + | 0.989833i | \(0.545428\pi\) | |||||||
\(588\) | 6.70893 | 0.276671 | ||||||||
\(589\) | 41.6742 | 1.71716 | ||||||||
\(590\) | 16.3666 | 0.673801 | ||||||||
\(591\) | −66.8511 | −2.74989 | ||||||||
\(592\) | −28.1338 | −1.15629 | ||||||||
\(593\) | −19.9356 | −0.818658 | −0.409329 | − | 0.912387i | \(-0.634237\pi\) | ||||
−0.409329 | + | 0.912387i | \(0.634237\pi\) | |||||||
\(594\) | 24.7476 | 1.01541 | ||||||||
\(595\) | −13.1088 | −0.537408 | ||||||||
\(596\) | 6.95510 | 0.284892 | ||||||||
\(597\) | 10.4114 | 0.426112 | ||||||||
\(598\) | −1.18246 | −0.0483543 | ||||||||
\(599\) | 34.3967 | 1.40541 | 0.702706 | − | 0.711480i | \(-0.251975\pi\) | ||||
0.702706 | + | 0.711480i | \(0.251975\pi\) | |||||||
\(600\) | 37.4735 | 1.52985 | ||||||||
\(601\) | 8.45470 | 0.344874 | 0.172437 | − | 0.985021i | \(-0.444836\pi\) | ||||
0.172437 | + | 0.985021i | \(0.444836\pi\) | |||||||
\(602\) | −9.31248 | −0.379548 | ||||||||
\(603\) | −57.6903 | −2.34933 | ||||||||
\(604\) | −0.643480 | −0.0261828 | ||||||||
\(605\) | 2.94198 | 0.119609 | ||||||||
\(606\) | −3.91729 | −0.159129 | ||||||||
\(607\) | −9.29798 | −0.377393 | −0.188697 | − | 0.982035i | \(-0.560426\pi\) | ||||
−0.188697 | + | 0.982035i | \(0.560426\pi\) | |||||||
\(608\) | 10.7804 | 0.437204 | ||||||||
\(609\) | 8.13949 | 0.329829 | ||||||||
\(610\) | −3.80849 | −0.154201 | ||||||||
\(611\) | −6.25373 | −0.252999 | ||||||||
\(612\) | −12.9213 | −0.522311 | ||||||||
\(613\) | −38.5718 | −1.55790 | −0.778950 | − | 0.627086i | \(-0.784247\pi\) | ||||
−0.778950 | + | 0.627086i | \(0.784247\pi\) | |||||||
\(614\) | −15.3688 | −0.620234 | ||||||||
\(615\) | 48.8686 | 1.97057 | ||||||||
\(616\) | 2.89615 | 0.116689 | ||||||||
\(617\) | −8.66174 | −0.348709 | −0.174354 | − | 0.984683i | \(-0.555784\pi\) | ||||
−0.174354 | + | 0.984683i | \(0.555784\pi\) | |||||||
\(618\) | 12.5946 | 0.506630 | ||||||||
\(619\) | 27.0814 | 1.08849 | 0.544247 | − | 0.838925i | \(-0.316815\pi\) | ||||
0.544247 | + | 0.838925i | \(0.316815\pi\) | |||||||
\(620\) | 6.69079 | 0.268708 | ||||||||
\(621\) | −14.2519 | −0.571908 | ||||||||
\(622\) | 5.32709 | 0.213597 | ||||||||
\(623\) | −13.2661 | −0.531494 | ||||||||
\(624\) | 13.5539 | 0.542590 | ||||||||
\(625\) | −29.9154 | −1.19662 | ||||||||
\(626\) | 8.59023 | 0.343335 | ||||||||
\(627\) | 20.2418 | 0.808378 | ||||||||
\(628\) | 2.08489 | 0.0831963 | ||||||||
\(629\) | 40.1139 | 1.59945 | ||||||||
\(630\) | 31.5656 | 1.25760 | ||||||||
\(631\) | 0.783379 | 0.0311858 | 0.0155929 | − | 0.999878i | \(-0.495036\pi\) | ||||
0.0155929 | + | 0.999878i | \(0.495036\pi\) | |||||||
\(632\) | −9.32646 | −0.370987 | ||||||||
\(633\) | −45.1573 | −1.79484 | ||||||||
\(634\) | −21.5517 | −0.855929 | ||||||||
\(635\) | 23.9015 | 0.948502 | ||||||||
\(636\) | 13.8158 | 0.547832 | ||||||||
\(637\) | 7.44141 | 0.294839 | ||||||||
\(638\) | −3.21254 | −0.127186 | ||||||||
\(639\) | −46.8991 | −1.85530 | ||||||||
\(640\) | −22.9980 | −0.909074 | ||||||||
\(641\) | −5.68122 | −0.224395 | −0.112197 | − | 0.993686i | \(-0.535789\pi\) | ||||
−0.112197 | + | 0.993686i | \(0.535789\pi\) | |||||||
\(642\) | 13.6957 | 0.540528 | ||||||||
\(643\) | −3.46757 | −0.136747 | −0.0683737 | − | 0.997660i | \(-0.521781\pi\) | ||||
−0.0683737 | + | 0.997660i | \(0.521781\pi\) | |||||||
\(644\) | −0.232640 | −0.00916729 | ||||||||
\(645\) | −74.9168 | −2.94985 | ||||||||
\(646\) | 35.5978 | 1.40058 | ||||||||
\(647\) | −27.6703 | −1.08783 | −0.543916 | − | 0.839139i | \(-0.683059\pi\) | ||||
−0.543916 | + | 0.839139i | \(0.683059\pi\) | |||||||
\(648\) | 118.268 | 4.64599 | ||||||||
\(649\) | 4.29739 | 0.168687 | ||||||||
\(650\) | 5.79762 | 0.227401 | ||||||||
\(651\) | 23.0093 | 0.901807 | ||||||||
\(652\) | −1.90255 | −0.0745096 | ||||||||
\(653\) | 9.74591 | 0.381387 | 0.190693 | − | 0.981650i | \(-0.438926\pi\) | ||||
0.190693 | + | 0.981650i | \(0.438926\pi\) | |||||||
\(654\) | 2.39949 | 0.0938274 | ||||||||
\(655\) | −59.5211 | −2.32568 | ||||||||
\(656\) | −15.8265 | −0.617923 | ||||||||
\(657\) | 115.805 | 4.51797 | ||||||||
\(658\) | 6.36016 | 0.247945 | ||||||||
\(659\) | −6.98292 | −0.272016 | −0.136008 | − | 0.990708i | \(-0.543427\pi\) | ||||
−0.136008 | + | 0.990708i | \(0.543427\pi\) | |||||||
\(660\) | 3.24981 | 0.126499 | ||||||||
\(661\) | 16.5002 | 0.641783 | 0.320891 | − | 0.947116i | \(-0.396018\pi\) | ||||
0.320891 | + | 0.947116i | \(0.396018\pi\) | |||||||
\(662\) | 4.72421 | 0.183612 | ||||||||
\(663\) | −19.3255 | −0.750540 | ||||||||
\(664\) | 35.7179 | 1.38612 | ||||||||
\(665\) | 16.8229 | 0.652364 | ||||||||
\(666\) | −96.5933 | −3.74291 | ||||||||
\(667\) | 1.85007 | 0.0716351 | ||||||||
\(668\) | −2.52147 | −0.0975585 | ||||||||
\(669\) | −87.9889 | −3.40185 | ||||||||
\(670\) | 25.5171 | 0.985811 | ||||||||
\(671\) | −1.00000 | −0.0386046 | ||||||||
\(672\) | 5.95213 | 0.229608 | ||||||||
\(673\) | 37.4769 | 1.44463 | 0.722314 | − | 0.691566i | \(-0.243079\pi\) | ||||
0.722314 | + | 0.691566i | \(0.243079\pi\) | |||||||
\(674\) | −36.8556 | −1.41963 | ||||||||
\(675\) | 69.8774 | 2.68958 | ||||||||
\(676\) | 3.72775 | 0.143375 | ||||||||
\(677\) | 30.4331 | 1.16964 | 0.584820 | − | 0.811163i | \(-0.301165\pi\) | ||||
0.584820 | + | 0.811163i | \(0.301165\pi\) | |||||||
\(678\) | 37.7369 | 1.44928 | ||||||||
\(679\) | −15.9359 | −0.611565 | ||||||||
\(680\) | 40.9741 | 1.57129 | ||||||||
\(681\) | 69.8660 | 2.67727 | ||||||||
\(682\) | −9.08147 | −0.347747 | ||||||||
\(683\) | 36.6336 | 1.40174 | 0.700872 | − | 0.713287i | \(-0.252794\pi\) | ||||
0.700872 | + | 0.713287i | \(0.252794\pi\) | |||||||
\(684\) | 16.5822 | 0.634038 | ||||||||
\(685\) | −15.7598 | −0.602151 | ||||||||
\(686\) | −16.2907 | −0.621982 | ||||||||
\(687\) | −48.1416 | −1.83672 | ||||||||
\(688\) | 24.2625 | 0.924998 | ||||||||
\(689\) | 15.3242 | 0.583806 | ||||||||
\(690\) | 9.67452 | 0.368303 | ||||||||
\(691\) | 22.3610 | 0.850653 | 0.425327 | − | 0.905040i | \(-0.360159\pi\) | ||||
0.425327 | + | 0.905040i | \(0.360159\pi\) | |||||||
\(692\) | −0.493933 | −0.0187765 | ||||||||
\(693\) | 8.28822 | 0.314844 | ||||||||
\(694\) | −7.67081 | −0.291180 | ||||||||
\(695\) | −23.0850 | −0.875663 | ||||||||
\(696\) | −25.4416 | −0.964361 | ||||||||
\(697\) | 22.5659 | 0.854744 | ||||||||
\(698\) | 3.37421 | 0.127716 | ||||||||
\(699\) | −80.2888 | −3.03680 | ||||||||
\(700\) | 1.14064 | 0.0431121 | ||||||||
\(701\) | −7.55175 | −0.285226 | −0.142613 | − | 0.989779i | \(-0.545550\pi\) | ||||
−0.142613 | + | 0.989779i | \(0.545550\pi\) | |||||||
\(702\) | 30.3217 | 1.14442 | ||||||||
\(703\) | −51.4794 | −1.94158 | ||||||||
\(704\) | −8.84229 | −0.333256 | ||||||||
\(705\) | 51.1661 | 1.92703 | ||||||||
\(706\) | −12.7460 | −0.479704 | ||||||||
\(707\) | −0.854841 | −0.0321496 | ||||||||
\(708\) | 4.74704 | 0.178405 | ||||||||
\(709\) | 43.6759 | 1.64028 | 0.820141 | − | 0.572161i | \(-0.193895\pi\) | ||||
0.820141 | + | 0.572161i | \(0.193895\pi\) | |||||||
\(710\) | 20.7440 | 0.778508 | ||||||||
\(711\) | −26.6906 | −1.00097 | ||||||||
\(712\) | 41.4657 | 1.55399 | ||||||||
\(713\) | 5.22993 | 0.195862 | ||||||||
\(714\) | 19.6544 | 0.735547 | ||||||||
\(715\) | 3.60462 | 0.134805 | ||||||||
\(716\) | 4.57979 | 0.171155 | ||||||||
\(717\) | 2.86379 | 0.106950 | ||||||||
\(718\) | −32.9716 | −1.23049 | ||||||||
\(719\) | 7.45445 | 0.278004 | 0.139002 | − | 0.990292i | \(-0.455611\pi\) | ||||
0.139002 | + | 0.990292i | \(0.455611\pi\) | |||||||
\(720\) | −82.2402 | −3.06491 | ||||||||
\(721\) | 2.74843 | 0.102357 | ||||||||
\(722\) | −21.0876 | −0.784800 | ||||||||
\(723\) | −1.11416 | −0.0414359 | ||||||||
\(724\) | 2.20611 | 0.0819893 | ||||||||
\(725\) | −9.07096 | −0.336887 | ||||||||
\(726\) | −4.41100 | −0.163708 | ||||||||
\(727\) | −41.2110 | −1.52843 | −0.764215 | − | 0.644961i | \(-0.776873\pi\) | ||||
−0.764215 | + | 0.644961i | \(0.776873\pi\) | |||||||
\(728\) | 3.54847 | 0.131515 | ||||||||
\(729\) | 143.041 | 5.29783 | ||||||||
\(730\) | −51.2217 | −1.89580 | ||||||||
\(731\) | −34.5941 | −1.27951 | ||||||||
\(732\) | −1.10463 | −0.0408284 | ||||||||
\(733\) | 5.91454 | 0.218458 | 0.109229 | − | 0.994017i | \(-0.465162\pi\) | ||||
0.109229 | + | 0.994017i | \(0.465162\pi\) | |||||||
\(734\) | −17.5359 | −0.647262 | ||||||||
\(735\) | −60.8833 | −2.24572 | ||||||||
\(736\) | 1.35290 | 0.0498684 | ||||||||
\(737\) | 6.70005 | 0.246800 | ||||||||
\(738\) | −54.3380 | −2.00021 | ||||||||
\(739\) | −50.8314 | −1.86986 | −0.934932 | − | 0.354826i | \(-0.884540\pi\) | ||||
−0.934932 | + | 0.354826i | \(0.884540\pi\) | |||||||
\(740\) | −8.26501 | −0.303828 | ||||||||
\(741\) | 24.8010 | 0.911087 | ||||||||
\(742\) | −15.5850 | −0.572145 | ||||||||
\(743\) | −1.25274 | −0.0459585 | −0.0229793 | − | 0.999736i | \(-0.507315\pi\) | ||||
−0.0229793 | + | 0.999736i | \(0.507315\pi\) | |||||||
\(744\) | −71.9202 | −2.63672 | ||||||||
\(745\) | −63.1174 | −2.31244 | ||||||||
\(746\) | 48.0702 | 1.75997 | ||||||||
\(747\) | 102.218 | 3.73996 | ||||||||
\(748\) | 1.50065 | 0.0548693 | ||||||||
\(749\) | 2.98872 | 0.109205 | ||||||||
\(750\) | 17.4509 | 0.637219 | ||||||||
\(751\) | 47.7300 | 1.74169 | 0.870846 | − | 0.491555i | \(-0.163571\pi\) | ||||
0.870846 | + | 0.491555i | \(0.163571\pi\) | |||||||
\(752\) | −16.5706 | −0.604267 | ||||||||
\(753\) | −22.3058 | −0.812869 | ||||||||
\(754\) | −3.93613 | −0.143345 | ||||||||
\(755\) | 5.83957 | 0.212524 | ||||||||
\(756\) | 5.96556 | 0.216965 | ||||||||
\(757\) | 45.7727 | 1.66364 | 0.831819 | − | 0.555047i | \(-0.187300\pi\) | ||||
0.831819 | + | 0.555047i | \(0.187300\pi\) | |||||||
\(758\) | −27.6758 | −1.00523 | ||||||||
\(759\) | 2.54025 | 0.0922053 | ||||||||
\(760\) | −52.5833 | −1.90740 | ||||||||
\(761\) | 19.6606 | 0.712698 | 0.356349 | − | 0.934353i | \(-0.384022\pi\) | ||||
0.356349 | + | 0.934353i | \(0.384022\pi\) | |||||||
\(762\) | −35.8362 | −1.29821 | ||||||||
\(763\) | 0.523623 | 0.0189564 | ||||||||
\(764\) | −6.07860 | −0.219916 | ||||||||
\(765\) | 117.260 | 4.23955 | ||||||||
\(766\) | 26.5788 | 0.960333 | ||||||||
\(767\) | 5.26532 | 0.190120 | ||||||||
\(768\) | −25.7770 | −0.930148 | ||||||||
\(769\) | −5.37674 | −0.193890 | −0.0969451 | − | 0.995290i | \(-0.530907\pi\) | ||||
−0.0969451 | + | 0.995290i | \(0.530907\pi\) | |||||||
\(770\) | −3.66597 | −0.132113 | ||||||||
\(771\) | 49.7978 | 1.79342 | ||||||||
\(772\) | −5.10625 | −0.183778 | ||||||||
\(773\) | 10.1558 | 0.365277 | 0.182639 | − | 0.983180i | \(-0.441536\pi\) | ||||
0.182639 | + | 0.983180i | \(0.441536\pi\) | |||||||
\(774\) | 83.3015 | 2.99421 | ||||||||
\(775\) | −25.6425 | −0.921105 | ||||||||
\(776\) | 49.8109 | 1.78811 | ||||||||
\(777\) | −28.4230 | −1.01967 | ||||||||
\(778\) | 3.29854 | 0.118258 | ||||||||
\(779\) | −28.9595 | −1.03758 | ||||||||
\(780\) | 3.98179 | 0.142571 | ||||||||
\(781\) | 5.44678 | 0.194901 | ||||||||
\(782\) | 4.46737 | 0.159753 | ||||||||
\(783\) | −47.4412 | −1.69541 | ||||||||
\(784\) | 19.7176 | 0.704200 | ||||||||
\(785\) | −18.9204 | −0.675297 | ||||||||
\(786\) | 89.2417 | 3.18315 | ||||||||
\(787\) | 38.1398 | 1.35954 | 0.679768 | − | 0.733427i | \(-0.262081\pi\) | ||||
0.679768 | + | 0.733427i | \(0.262081\pi\) | |||||||
\(788\) | 6.36032 | 0.226577 | ||||||||
\(789\) | 24.0343 | 0.855644 | ||||||||
\(790\) | 11.8055 | 0.420022 | ||||||||
\(791\) | 8.23505 | 0.292805 | ||||||||
\(792\) | −25.9065 | −0.920547 | ||||||||
\(793\) | −1.22524 | −0.0435095 | ||||||||
\(794\) | 12.8611 | 0.456425 | ||||||||
\(795\) | −125.378 | −4.44670 | ||||||||
\(796\) | −0.990561 | −0.0351095 | ||||||||
\(797\) | −38.8028 | −1.37446 | −0.687232 | − | 0.726438i | \(-0.741174\pi\) | ||||
−0.687232 | + | 0.726438i | \(0.741174\pi\) | |||||||
\(798\) | −25.2231 | −0.892888 | ||||||||
\(799\) | 23.6268 | 0.835855 | ||||||||
\(800\) | −6.63328 | −0.234522 | ||||||||
\(801\) | 118.667 | 4.19289 | ||||||||
\(802\) | 13.4598 | 0.475283 | ||||||||
\(803\) | −13.4494 | −0.474617 | ||||||||
\(804\) | 7.40111 | 0.261017 | ||||||||
\(805\) | 2.11120 | 0.0744100 | ||||||||
\(806\) | −11.1270 | −0.391930 | ||||||||
\(807\) | −18.1182 | −0.637791 | ||||||||
\(808\) | 2.67197 | 0.0939997 | ||||||||
\(809\) | 4.44997 | 0.156453 | 0.0782263 | − | 0.996936i | \(-0.475074\pi\) | ||||
0.0782263 | + | 0.996936i | \(0.475074\pi\) | |||||||
\(810\) | −149.705 | −5.26008 | ||||||||
\(811\) | 31.9572 | 1.12217 | 0.561084 | − | 0.827759i | \(-0.310384\pi\) | ||||
0.561084 | + | 0.827759i | \(0.310384\pi\) | |||||||
\(812\) | −0.774404 | −0.0271762 | ||||||||
\(813\) | 100.934 | 3.53992 | ||||||||
\(814\) | 11.2182 | 0.393197 | ||||||||
\(815\) | 17.2656 | 0.604787 | ||||||||
\(816\) | −51.2070 | −1.79260 | ||||||||
\(817\) | 44.3956 | 1.55321 | ||||||||
\(818\) | −4.07383 | −0.142438 | ||||||||
\(819\) | 10.1550 | 0.354846 | ||||||||
\(820\) | −4.64944 | −0.162365 | ||||||||
\(821\) | 14.8173 | 0.517126 | 0.258563 | − | 0.965994i | \(-0.416751\pi\) | ||||
0.258563 | + | 0.965994i | \(0.416751\pi\) | |||||||
\(822\) | 23.6291 | 0.824160 | ||||||||
\(823\) | −7.72139 | −0.269151 | −0.134575 | − | 0.990903i | \(-0.542967\pi\) | ||||
−0.134575 | + | 0.990903i | \(0.542967\pi\) | |||||||
\(824\) | −8.59078 | −0.299274 | ||||||||
\(825\) | −12.4549 | −0.433625 | ||||||||
\(826\) | −5.35494 | −0.186322 | ||||||||
\(827\) | −27.3551 | −0.951230 | −0.475615 | − | 0.879654i | \(-0.657774\pi\) | ||||
−0.475615 | + | 0.879654i | \(0.657774\pi\) | |||||||
\(828\) | 2.08100 | 0.0723196 | ||||||||
\(829\) | −27.3766 | −0.950829 | −0.475415 | − | 0.879762i | \(-0.657702\pi\) | ||||
−0.475415 | + | 0.879762i | \(0.657702\pi\) | |||||||
\(830\) | −45.2121 | −1.56934 | ||||||||
\(831\) | −11.1061 | −0.385266 | ||||||||
\(832\) | −10.8339 | −0.375598 | ||||||||
\(833\) | −28.1139 | −0.974088 | ||||||||
\(834\) | 34.6120 | 1.19851 | ||||||||
\(835\) | 22.8823 | 0.791873 | ||||||||
\(836\) | −1.92583 | −0.0666063 | ||||||||
\(837\) | −134.111 | −4.63554 | ||||||||
\(838\) | −41.4050 | −1.43031 | ||||||||
\(839\) | −36.1380 | −1.24762 | −0.623812 | − | 0.781575i | \(-0.714417\pi\) | ||||
−0.623812 | + | 0.781575i | \(0.714417\pi\) | |||||||
\(840\) | −29.0325 | −1.00172 | ||||||||
\(841\) | −22.8415 | −0.787639 | ||||||||
\(842\) | −22.1762 | −0.764243 | ||||||||
\(843\) | 29.6409 | 1.02089 | ||||||||
\(844\) | 4.29634 | 0.147886 | ||||||||
\(845\) | −33.8292 | −1.16376 | ||||||||
\(846\) | −56.8926 | −1.95601 | ||||||||
\(847\) | −0.962580 | −0.0330746 | ||||||||
\(848\) | 40.6048 | 1.39438 | ||||||||
\(849\) | 84.9367 | 2.91502 | ||||||||
\(850\) | −21.9036 | −0.751288 | ||||||||
\(851\) | −6.46044 | −0.221461 | ||||||||
\(852\) | 6.01670 | 0.206129 | ||||||||
\(853\) | −13.5704 | −0.464642 | −0.232321 | − | 0.972639i | \(-0.574632\pi\) | ||||
−0.232321 | + | 0.972639i | \(0.574632\pi\) | |||||||
\(854\) | 1.24609 | 0.0426404 | ||||||||
\(855\) | −150.483 | −5.14643 | ||||||||
\(856\) | −9.34184 | −0.319297 | ||||||||
\(857\) | 6.06053 | 0.207024 | 0.103512 | − | 0.994628i | \(-0.466992\pi\) | ||||
0.103512 | + | 0.994628i | \(0.466992\pi\) | |||||||
\(858\) | −5.40452 | −0.184507 | ||||||||
\(859\) | 9.74217 | 0.332399 | 0.166199 | − | 0.986092i | \(-0.446850\pi\) | ||||
0.166199 | + | 0.986092i | \(0.446850\pi\) | |||||||
\(860\) | 7.12770 | 0.243053 | ||||||||
\(861\) | −15.9892 | −0.544911 | ||||||||
\(862\) | 44.3305 | 1.50990 | ||||||||
\(863\) | 18.4875 | 0.629324 | 0.314662 | − | 0.949204i | \(-0.398109\pi\) | ||||
0.314662 | + | 0.949204i | \(0.398109\pi\) | |||||||
\(864\) | −34.6922 | −1.18025 | ||||||||
\(865\) | 4.48243 | 0.152407 | ||||||||
\(866\) | 1.07685 | 0.0365928 | ||||||||
\(867\) | 15.0864 | 0.512360 | ||||||||
\(868\) | −2.18914 | −0.0743044 | ||||||||
\(869\) | 3.09980 | 0.105153 | ||||||||
\(870\) | 32.2042 | 1.09183 | ||||||||
\(871\) | 8.20916 | 0.278157 | ||||||||
\(872\) | −1.63669 | −0.0554252 | ||||||||
\(873\) | 142.549 | 4.82457 | ||||||||
\(874\) | −5.73311 | −0.193925 | ||||||||
\(875\) | 3.80819 | 0.128740 | ||||||||
\(876\) | −14.8566 | −0.501958 | ||||||||
\(877\) | −19.7849 | −0.668087 | −0.334044 | − | 0.942558i | \(-0.608413\pi\) | ||||
−0.334044 | + | 0.942558i | \(0.608413\pi\) | |||||||
\(878\) | −29.8121 | −1.00611 | ||||||||
\(879\) | −80.1629 | −2.70383 | ||||||||
\(880\) | 9.55123 | 0.321972 | ||||||||
\(881\) | −1.52612 | −0.0514164 | −0.0257082 | − | 0.999669i | \(-0.508184\pi\) | ||||
−0.0257082 | + | 0.999669i | \(0.508184\pi\) | |||||||
\(882\) | 67.6974 | 2.27949 | ||||||||
\(883\) | −25.3892 | −0.854413 | −0.427207 | − | 0.904154i | \(-0.640502\pi\) | ||||
−0.427207 | + | 0.904154i | \(0.640502\pi\) | |||||||
\(884\) | 1.83866 | 0.0618407 | ||||||||
\(885\) | −43.0793 | −1.44809 | ||||||||
\(886\) | 5.30361 | 0.178178 | ||||||||
\(887\) | 36.2066 | 1.21570 | 0.607849 | − | 0.794053i | \(-0.292033\pi\) | ||||
0.607849 | + | 0.794053i | \(0.292033\pi\) | |||||||
\(888\) | 88.8418 | 2.98133 | ||||||||
\(889\) | −7.82028 | −0.262284 | ||||||||
\(890\) | −52.4878 | −1.75939 | ||||||||
\(891\) | −39.3081 | −1.31687 | ||||||||
\(892\) | 8.37140 | 0.280295 | ||||||||
\(893\) | −30.3210 | −1.01465 | ||||||||
\(894\) | 94.6338 | 3.16503 | ||||||||
\(895\) | −41.5615 | −1.38925 | ||||||||
\(896\) | 7.52465 | 0.251381 | ||||||||
\(897\) | 3.11241 | 0.103920 | ||||||||
\(898\) | −50.3235 | −1.67932 | ||||||||
\(899\) | 17.4092 | 0.580630 | ||||||||
\(900\) | −10.2032 | −0.340106 | ||||||||
\(901\) | −57.8954 | −1.92878 | ||||||||
\(902\) | 6.31073 | 0.210124 | ||||||||
\(903\) | 24.5119 | 0.815704 | ||||||||
\(904\) | −25.7403 | −0.856109 | ||||||||
\(905\) | −20.0204 | −0.665500 | ||||||||
\(906\) | −8.75544 | −0.290880 | ||||||||
\(907\) | −32.1998 | −1.06918 | −0.534589 | − | 0.845112i | \(-0.679534\pi\) | ||||
−0.534589 | + | 0.845112i | \(0.679534\pi\) | |||||||
\(908\) | −6.64716 | −0.220594 | ||||||||
\(909\) | 7.64668 | 0.253624 | ||||||||
\(910\) | −4.49169 | −0.148898 | ||||||||
\(911\) | −42.9132 | −1.42178 | −0.710889 | − | 0.703305i | \(-0.751707\pi\) | ||||
−0.710889 | + | 0.703305i | \(0.751707\pi\) | |||||||
\(912\) | 65.7155 | 2.17606 | ||||||||
\(913\) | −11.8714 | −0.392886 | ||||||||
\(914\) | −37.1815 | −1.22985 | ||||||||
\(915\) | 10.0245 | 0.331401 | ||||||||
\(916\) | 4.58027 | 0.151336 | ||||||||
\(917\) | 19.4746 | 0.643107 | ||||||||
\(918\) | −114.556 | −3.78092 | ||||||||
\(919\) | 8.99125 | 0.296594 | 0.148297 | − | 0.988943i | \(-0.452621\pi\) | ||||
0.148297 | + | 0.988943i | \(0.452621\pi\) | |||||||
\(920\) | −6.59897 | −0.217562 | ||||||||
\(921\) | 40.4530 | 1.33297 | ||||||||
\(922\) | −46.8259 | −1.54213 | ||||||||
\(923\) | 6.67360 | 0.219664 | ||||||||
\(924\) | −1.06330 | −0.0349800 | ||||||||
\(925\) | 31.6757 | 1.04149 | ||||||||
\(926\) | 25.0500 | 0.823193 | ||||||||
\(927\) | −24.5852 | −0.807483 | ||||||||
\(928\) | 4.50348 | 0.147834 | ||||||||
\(929\) | 9.98673 | 0.327654 | 0.163827 | − | 0.986489i | \(-0.447616\pi\) | ||||
0.163827 | + | 0.986489i | \(0.447616\pi\) | |||||||
\(930\) | 91.0374 | 2.98523 | ||||||||
\(931\) | 36.0794 | 1.18245 | ||||||||
\(932\) | 7.63880 | 0.250217 | ||||||||
\(933\) | −14.0217 | −0.459050 | ||||||||
\(934\) | −37.0255 | −1.21151 | ||||||||
\(935\) | −13.6184 | −0.445369 | ||||||||
\(936\) | −31.7416 | −1.03751 | ||||||||
\(937\) | −50.8038 | −1.65969 | −0.829844 | − | 0.557995i | \(-0.811571\pi\) | ||||
−0.829844 | + | 0.557995i | \(0.811571\pi\) | |||||||
\(938\) | −8.34888 | −0.272600 | ||||||||
\(939\) | −22.6108 | −0.737876 | ||||||||
\(940\) | −4.86802 | −0.158777 | ||||||||
\(941\) | 45.3227 | 1.47748 | 0.738739 | − | 0.673991i | \(-0.235421\pi\) | ||||
0.738739 | + | 0.673991i | \(0.235421\pi\) | |||||||
\(942\) | 28.3679 | 0.924275 | ||||||||
\(943\) | −3.63429 | −0.118349 | ||||||||
\(944\) | 13.9516 | 0.454086 | ||||||||
\(945\) | −54.1373 | −1.76109 | ||||||||
\(946\) | −9.67450 | −0.314545 | ||||||||
\(947\) | −16.2837 | −0.529150 | −0.264575 | − | 0.964365i | \(-0.585232\pi\) | ||||
−0.264575 | + | 0.964365i | \(0.585232\pi\) | |||||||
\(948\) | 3.42414 | 0.111211 | ||||||||
\(949\) | −16.4787 | −0.534920 | ||||||||
\(950\) | 28.1096 | 0.911995 | ||||||||
\(951\) | 56.7275 | 1.83951 | ||||||||
\(952\) | −13.4062 | −0.434498 | ||||||||
\(953\) | −44.2183 | −1.43237 | −0.716185 | − | 0.697910i | \(-0.754113\pi\) | ||||
−0.716185 | + | 0.697910i | \(0.754113\pi\) | |||||||
\(954\) | 139.410 | 4.51358 | ||||||||
\(955\) | 55.1632 | 1.78504 | ||||||||
\(956\) | −0.272466 | −0.00881216 | ||||||||
\(957\) | 8.45591 | 0.273341 | ||||||||
\(958\) | 7.69815 | 0.248716 | ||||||||
\(959\) | 5.15641 | 0.166509 | ||||||||
\(960\) | 88.6397 | 2.86083 | ||||||||
\(961\) | 18.2137 | 0.587540 | ||||||||
\(962\) | 13.7449 | 0.443154 | ||||||||
\(963\) | −26.7346 | −0.861509 | ||||||||
\(964\) | 0.106003 | 0.00341411 | ||||||||
\(965\) | 46.3391 | 1.49171 | ||||||||
\(966\) | −3.16538 | −0.101845 | ||||||||
\(967\) | −27.9526 | −0.898896 | −0.449448 | − | 0.893306i | \(-0.648379\pi\) | ||||
−0.449448 | + | 0.893306i | \(0.648379\pi\) | |||||||
\(968\) | 3.00873 | 0.0967044 | ||||||||
\(969\) | −93.6989 | −3.01004 | ||||||||
\(970\) | −63.0512 | −2.02445 | ||||||||
\(971\) | 36.4599 | 1.17005 | 0.585027 | − | 0.811014i | \(-0.301084\pi\) | ||||
0.585027 | + | 0.811014i | \(0.301084\pi\) | |||||||
\(972\) | −24.8287 | −0.796381 | ||||||||
\(973\) | 7.55312 | 0.242142 | ||||||||
\(974\) | 20.6956 | 0.663129 | ||||||||
\(975\) | −15.2602 | −0.488719 | ||||||||
\(976\) | −3.24653 | −0.103919 | ||||||||
\(977\) | 46.8173 | 1.49782 | 0.748910 | − | 0.662672i | \(-0.230578\pi\) | ||||
0.748910 | + | 0.662672i | \(0.230578\pi\) | |||||||
\(978\) | −25.8868 | −0.827769 | ||||||||
\(979\) | −13.7818 | −0.440468 | ||||||||
\(980\) | 5.79254 | 0.185036 | ||||||||
\(981\) | −4.68388 | −0.149545 | ||||||||
\(982\) | 18.6071 | 0.593775 | ||||||||
\(983\) | −0.591052 | −0.0188516 | −0.00942582 | − | 0.999956i | \(-0.503000\pi\) | ||||
−0.00942582 | + | 0.999956i | \(0.503000\pi\) | |||||||
\(984\) | 49.9775 | 1.59322 | ||||||||
\(985\) | −57.7197 | −1.83910 | ||||||||
\(986\) | 14.8708 | 0.473584 | ||||||||
\(987\) | −16.7409 | −0.532869 | ||||||||
\(988\) | −2.35960 | −0.0750690 | ||||||||
\(989\) | 5.57145 | 0.177162 | ||||||||
\(990\) | 32.7927 | 1.04222 | ||||||||
\(991\) | −12.8064 | −0.406809 | −0.203405 | − | 0.979095i | \(-0.565201\pi\) | ||||
−0.203405 | + | 0.979095i | \(0.565201\pi\) | |||||||
\(992\) | 12.7308 | 0.404202 | ||||||||
\(993\) | −12.4349 | −0.394608 | ||||||||
\(994\) | −6.78718 | −0.215276 | ||||||||
\(995\) | 8.98932 | 0.284981 | ||||||||
\(996\) | −13.1136 | −0.415519 | ||||||||
\(997\) | 59.2470 | 1.87637 | 0.938186 | − | 0.346131i | \(-0.112505\pi\) | ||||
0.938186 | + | 0.346131i | \(0.112505\pi\) | |||||||
\(998\) | 35.5644 | 1.12577 | ||||||||
\(999\) | 165.664 | 5.24139 |
(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 | 671.2.a.d.1.8 | ✓ | 21 | |
3.2 | odd | 2 | 6039.2.a.l.1.14 | 21 | |||
11.10 | odd | 2 | 7381.2.a.j.1.14 | 21 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
671.2.a.d.1.8 | ✓ | 21 | 1.1 | even | 1 | trivial | |
6039.2.a.l.1.14 | 21 | 3.2 | odd | 2 | |||
7381.2.a.j.1.14 | 21 | 11.10 | odd | 2 |