Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6017,2,Mod(1,6017)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6017, 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("6017.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6017 = 11 \cdot 547 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6017.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(48.0459868962\) |
Analytic rank: | \(0\) |
Dimension: | \(121\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.15 | ||
Character | \(\chi\) | \(=\) | 6017.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.29477 | −1.62265 | −0.811323 | − | 0.584598i | \(-0.801252\pi\) | ||||
−0.811323 | + | 0.584598i | \(0.801252\pi\) | |||||||
\(3\) | 3.40179 | 1.96403 | 0.982013 | − | 0.188811i | \(-0.0604634\pi\) | ||||
0.982013 | + | 0.188811i | \(0.0604634\pi\) | |||||||
\(4\) | 3.26597 | 1.63298 | ||||||||
\(5\) | 3.88142 | 1.73582 | 0.867912 | − | 0.496718i | \(-0.165462\pi\) | ||||
0.867912 | + | 0.496718i | \(0.165462\pi\) | |||||||
\(6\) | −7.80633 | −3.18692 | ||||||||
\(7\) | 2.49357 | 0.942482 | 0.471241 | − | 0.882005i | \(-0.343806\pi\) | ||||
0.471241 | + | 0.882005i | \(0.343806\pi\) | |||||||
\(8\) | −2.90510 | −1.02711 | ||||||||
\(9\) | 8.57220 | 2.85740 | ||||||||
\(10\) | −8.90697 | −2.81663 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | 11.1101 | 3.20722 | ||||||||
\(13\) | −3.83894 | −1.06473 | −0.532365 | − | 0.846515i | \(-0.678697\pi\) | ||||
−0.532365 | + | 0.846515i | \(0.678697\pi\) | |||||||
\(14\) | −5.72217 | −1.52931 | ||||||||
\(15\) | 13.2038 | 3.40921 | ||||||||
\(16\) | 0.134602 | 0.0336505 | ||||||||
\(17\) | −0.384749 | −0.0933154 | −0.0466577 | − | 0.998911i | \(-0.514857\pi\) | ||||
−0.0466577 | + | 0.998911i | \(0.514857\pi\) | |||||||
\(18\) | −19.6712 | −4.63655 | ||||||||
\(19\) | −3.93567 | −0.902906 | −0.451453 | − | 0.892295i | \(-0.649094\pi\) | ||||
−0.451453 | + | 0.892295i | \(0.649094\pi\) | |||||||
\(20\) | 12.6766 | 2.83457 | ||||||||
\(21\) | 8.48262 | 1.85106 | ||||||||
\(22\) | 2.29477 | 0.489246 | ||||||||
\(23\) | −1.53652 | −0.320386 | −0.160193 | − | 0.987086i | \(-0.551212\pi\) | ||||
−0.160193 | + | 0.987086i | \(0.551212\pi\) | |||||||
\(24\) | −9.88255 | −2.01727 | ||||||||
\(25\) | 10.0654 | 2.01309 | ||||||||
\(26\) | 8.80948 | 1.72768 | ||||||||
\(27\) | 18.9555 | 3.64799 | ||||||||
\(28\) | 8.14392 | 1.53906 | ||||||||
\(29\) | 9.23562 | 1.71501 | 0.857506 | − | 0.514474i | \(-0.172013\pi\) | ||||
0.857506 | + | 0.514474i | \(0.172013\pi\) | |||||||
\(30\) | −30.2997 | −5.53194 | ||||||||
\(31\) | −2.04469 | −0.367236 | −0.183618 | − | 0.982998i | \(-0.558781\pi\) | ||||
−0.183618 | + | 0.982998i | \(0.558781\pi\) | |||||||
\(32\) | 5.50132 | 0.972505 | ||||||||
\(33\) | −3.40179 | −0.592176 | ||||||||
\(34\) | 0.882911 | 0.151418 | ||||||||
\(35\) | 9.67860 | 1.63598 | ||||||||
\(36\) | 27.9965 | 4.66609 | ||||||||
\(37\) | 4.79025 | 0.787512 | 0.393756 | − | 0.919215i | \(-0.371175\pi\) | ||||
0.393756 | + | 0.919215i | \(0.371175\pi\) | |||||||
\(38\) | 9.03147 | 1.46510 | ||||||||
\(39\) | −13.0593 | −2.09116 | ||||||||
\(40\) | −11.2759 | −1.78288 | ||||||||
\(41\) | −8.74208 | −1.36528 | −0.682642 | − | 0.730753i | \(-0.739169\pi\) | ||||
−0.682642 | + | 0.730753i | \(0.739169\pi\) | |||||||
\(42\) | −19.4657 | −3.00362 | ||||||||
\(43\) | −4.80553 | −0.732837 | −0.366418 | − | 0.930450i | \(-0.619416\pi\) | ||||
−0.366418 | + | 0.930450i | \(0.619416\pi\) | |||||||
\(44\) | −3.26597 | −0.492363 | ||||||||
\(45\) | 33.2723 | 4.95995 | ||||||||
\(46\) | 3.52595 | 0.519873 | ||||||||
\(47\) | 1.56722 | 0.228602 | 0.114301 | − | 0.993446i | \(-0.463537\pi\) | ||||
0.114301 | + | 0.993446i | \(0.463537\pi\) | |||||||
\(48\) | 0.457889 | 0.0660906 | ||||||||
\(49\) | −0.782100 | −0.111729 | ||||||||
\(50\) | −23.0978 | −3.26653 | ||||||||
\(51\) | −1.30884 | −0.183274 | ||||||||
\(52\) | −12.5378 | −1.73869 | ||||||||
\(53\) | −1.13491 | −0.155892 | −0.0779461 | − | 0.996958i | \(-0.524836\pi\) | ||||
−0.0779461 | + | 0.996958i | \(0.524836\pi\) | |||||||
\(54\) | −43.4985 | −5.91939 | ||||||||
\(55\) | −3.88142 | −0.523371 | ||||||||
\(56\) | −7.24408 | −0.968030 | ||||||||
\(57\) | −13.3884 | −1.77333 | ||||||||
\(58\) | −21.1936 | −2.78286 | ||||||||
\(59\) | −9.39532 | −1.22317 | −0.611583 | − | 0.791180i | \(-0.709467\pi\) | ||||
−0.611583 | + | 0.791180i | \(0.709467\pi\) | |||||||
\(60\) | 43.1231 | 5.56717 | ||||||||
\(61\) | 13.5181 | 1.73082 | 0.865409 | − | 0.501066i | \(-0.167059\pi\) | ||||
0.865409 | + | 0.501066i | \(0.167059\pi\) | |||||||
\(62\) | 4.69208 | 0.595895 | ||||||||
\(63\) | 21.3754 | 2.69305 | ||||||||
\(64\) | −12.8935 | −1.61168 | ||||||||
\(65\) | −14.9005 | −1.84818 | ||||||||
\(66\) | 7.80633 | 0.960893 | ||||||||
\(67\) | 3.81781 | 0.466420 | 0.233210 | − | 0.972426i | \(-0.425077\pi\) | ||||
0.233210 | + | 0.972426i | \(0.425077\pi\) | |||||||
\(68\) | −1.25658 | −0.152383 | ||||||||
\(69\) | −5.22691 | −0.629247 | ||||||||
\(70\) | −22.2102 | −2.65462 | ||||||||
\(71\) | 7.77422 | 0.922630 | 0.461315 | − | 0.887236i | \(-0.347378\pi\) | ||||
0.461315 | + | 0.887236i | \(0.347378\pi\) | |||||||
\(72\) | −24.9031 | −2.93486 | ||||||||
\(73\) | −2.25867 | −0.264358 | −0.132179 | − | 0.991226i | \(-0.542197\pi\) | ||||
−0.132179 | + | 0.991226i | \(0.542197\pi\) | |||||||
\(74\) | −10.9925 | −1.27785 | ||||||||
\(75\) | 34.2405 | 3.95375 | ||||||||
\(76\) | −12.8538 | −1.47443 | ||||||||
\(77\) | −2.49357 | −0.284169 | ||||||||
\(78\) | 29.9680 | 3.39321 | ||||||||
\(79\) | 0.175607 | 0.0197574 | 0.00987869 | − | 0.999951i | \(-0.496855\pi\) | ||||
0.00987869 | + | 0.999951i | \(0.496855\pi\) | |||||||
\(80\) | 0.522448 | 0.0584114 | ||||||||
\(81\) | 38.7661 | 4.30734 | ||||||||
\(82\) | 20.0611 | 2.21537 | ||||||||
\(83\) | 7.26733 | 0.797693 | 0.398846 | − | 0.917018i | \(-0.369411\pi\) | ||||
0.398846 | + | 0.917018i | \(0.369411\pi\) | |||||||
\(84\) | 27.7039 | 3.02275 | ||||||||
\(85\) | −1.49337 | −0.161979 | ||||||||
\(86\) | 11.0276 | 1.18914 | ||||||||
\(87\) | 31.4177 | 3.36833 | ||||||||
\(88\) | 2.90510 | 0.309685 | ||||||||
\(89\) | 13.1294 | 1.39172 | 0.695858 | − | 0.718180i | \(-0.255024\pi\) | ||||
0.695858 | + | 0.718180i | \(0.255024\pi\) | |||||||
\(90\) | −76.3523 | −8.04824 | ||||||||
\(91\) | −9.57267 | −1.00349 | ||||||||
\(92\) | −5.01821 | −0.523185 | ||||||||
\(93\) | −6.95560 | −0.721262 | ||||||||
\(94\) | −3.59640 | −0.370940 | ||||||||
\(95\) | −15.2760 | −1.56729 | ||||||||
\(96\) | 18.7144 | 1.91003 | ||||||||
\(97\) | 1.38802 | 0.140932 | 0.0704659 | − | 0.997514i | \(-0.477551\pi\) | ||||
0.0704659 | + | 0.997514i | \(0.477551\pi\) | |||||||
\(98\) | 1.79474 | 0.181296 | ||||||||
\(99\) | −8.57220 | −0.861539 | ||||||||
\(100\) | 32.8733 | 3.28733 | ||||||||
\(101\) | −12.3538 | −1.22925 | −0.614623 | − | 0.788821i | \(-0.710692\pi\) | ||||
−0.614623 | + | 0.788821i | \(0.710692\pi\) | |||||||
\(102\) | 3.00348 | 0.297389 | ||||||||
\(103\) | −15.3186 | −1.50939 | −0.754693 | − | 0.656078i | \(-0.772214\pi\) | ||||
−0.754693 | + | 0.656078i | \(0.772214\pi\) | |||||||
\(104\) | 11.1525 | 1.09359 | ||||||||
\(105\) | 32.9246 | 3.21311 | ||||||||
\(106\) | 2.60436 | 0.252958 | ||||||||
\(107\) | 13.0770 | 1.26420 | 0.632102 | − | 0.774885i | \(-0.282192\pi\) | ||||
0.632102 | + | 0.774885i | \(0.282192\pi\) | |||||||
\(108\) | 61.9080 | 5.95710 | ||||||||
\(109\) | −4.82160 | −0.461826 | −0.230913 | − | 0.972974i | \(-0.574171\pi\) | ||||
−0.230913 | + | 0.972974i | \(0.574171\pi\) | |||||||
\(110\) | 8.90697 | 0.849246 | ||||||||
\(111\) | 16.2954 | 1.54669 | ||||||||
\(112\) | 0.335640 | 0.0317150 | ||||||||
\(113\) | −6.17374 | −0.580777 | −0.290389 | − | 0.956909i | \(-0.593785\pi\) | ||||
−0.290389 | + | 0.956909i | \(0.593785\pi\) | |||||||
\(114\) | 30.7232 | 2.87749 | ||||||||
\(115\) | −5.96387 | −0.556134 | ||||||||
\(116\) | 30.1632 | 2.80059 | ||||||||
\(117\) | −32.9082 | −3.04236 | ||||||||
\(118\) | 21.5601 | 1.98477 | ||||||||
\(119\) | −0.959400 | −0.0879481 | ||||||||
\(120\) | −38.3583 | −3.50162 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | −31.0210 | −2.80851 | ||||||||
\(123\) | −29.7388 | −2.68145 | ||||||||
\(124\) | −6.67787 | −0.599691 | ||||||||
\(125\) | 19.6611 | 1.75854 | ||||||||
\(126\) | −49.0516 | −4.36987 | ||||||||
\(127\) | −16.3730 | −1.45287 | −0.726433 | − | 0.687237i | \(-0.758823\pi\) | ||||
−0.726433 | + | 0.687237i | \(0.758823\pi\) | |||||||
\(128\) | 18.5849 | 1.64269 | ||||||||
\(129\) | −16.3474 | −1.43931 | ||||||||
\(130\) | 34.1933 | 2.99895 | ||||||||
\(131\) | 12.8407 | 1.12190 | 0.560949 | − | 0.827851i | \(-0.310436\pi\) | ||||
0.560949 | + | 0.827851i | \(0.310436\pi\) | |||||||
\(132\) | −11.1101 | −0.967014 | ||||||||
\(133\) | −9.81389 | −0.850972 | ||||||||
\(134\) | −8.76099 | −0.756835 | ||||||||
\(135\) | 73.5742 | 6.33226 | ||||||||
\(136\) | 1.11774 | 0.0958450 | ||||||||
\(137\) | 3.33500 | 0.284928 | 0.142464 | − | 0.989800i | \(-0.454497\pi\) | ||||
0.142464 | + | 0.989800i | \(0.454497\pi\) | |||||||
\(138\) | 11.9946 | 1.02104 | ||||||||
\(139\) | 21.1148 | 1.79094 | 0.895469 | − | 0.445124i | \(-0.146841\pi\) | ||||
0.895469 | + | 0.445124i | \(0.146841\pi\) | |||||||
\(140\) | 31.6100 | 2.67153 | ||||||||
\(141\) | 5.33135 | 0.448980 | ||||||||
\(142\) | −17.8400 | −1.49710 | ||||||||
\(143\) | 3.83894 | 0.321028 | ||||||||
\(144\) | 1.15384 | 0.0961531 | ||||||||
\(145\) | 35.8473 | 2.97696 | ||||||||
\(146\) | 5.18314 | 0.428959 | ||||||||
\(147\) | −2.66054 | −0.219438 | ||||||||
\(148\) | 15.6448 | 1.28599 | ||||||||
\(149\) | 2.53645 | 0.207794 | 0.103897 | − | 0.994588i | \(-0.466869\pi\) | ||||
0.103897 | + | 0.994588i | \(0.466869\pi\) | |||||||
\(150\) | −78.5741 | −6.41555 | ||||||||
\(151\) | 11.8290 | 0.962633 | 0.481316 | − | 0.876547i | \(-0.340159\pi\) | ||||
0.481316 | + | 0.876547i | \(0.340159\pi\) | |||||||
\(152\) | 11.4335 | 0.927382 | ||||||||
\(153\) | −3.29815 | −0.266640 | ||||||||
\(154\) | 5.72217 | 0.461106 | ||||||||
\(155\) | −7.93628 | −0.637458 | ||||||||
\(156\) | −42.6512 | −3.41483 | ||||||||
\(157\) | −0.934206 | −0.0745578 | −0.0372789 | − | 0.999305i | \(-0.511869\pi\) | ||||
−0.0372789 | + | 0.999305i | \(0.511869\pi\) | |||||||
\(158\) | −0.402978 | −0.0320592 | ||||||||
\(159\) | −3.86074 | −0.306177 | ||||||||
\(160\) | 21.3529 | 1.68810 | ||||||||
\(161\) | −3.83141 | −0.301958 | ||||||||
\(162\) | −88.9592 | −6.98929 | ||||||||
\(163\) | 11.2630 | 0.882190 | 0.441095 | − | 0.897460i | \(-0.354590\pi\) | ||||
0.441095 | + | 0.897460i | \(0.354590\pi\) | |||||||
\(164\) | −28.5513 | −2.22949 | ||||||||
\(165\) | −13.2038 | −1.02791 | ||||||||
\(166\) | −16.6768 | −1.29437 | ||||||||
\(167\) | 19.1049 | 1.47838 | 0.739189 | − | 0.673498i | \(-0.235209\pi\) | ||||
0.739189 | + | 0.673498i | \(0.235209\pi\) | |||||||
\(168\) | −24.6429 | −1.90124 | ||||||||
\(169\) | 1.73744 | 0.133649 | ||||||||
\(170\) | 3.42695 | 0.262835 | ||||||||
\(171\) | −33.7374 | −2.57996 | ||||||||
\(172\) | −15.6947 | −1.19671 | ||||||||
\(173\) | −24.3308 | −1.84983 | −0.924917 | − | 0.380170i | \(-0.875865\pi\) | ||||
−0.924917 | + | 0.380170i | \(0.875865\pi\) | |||||||
\(174\) | −72.0964 | −5.46561 | ||||||||
\(175\) | 25.0989 | 1.89730 | ||||||||
\(176\) | −0.134602 | −0.0101460 | ||||||||
\(177\) | −31.9609 | −2.40233 | ||||||||
\(178\) | −30.1290 | −2.25826 | ||||||||
\(179\) | −5.61541 | −0.419716 | −0.209858 | − | 0.977732i | \(-0.567300\pi\) | ||||
−0.209858 | + | 0.977732i | \(0.567300\pi\) | |||||||
\(180\) | 108.666 | 8.09951 | ||||||||
\(181\) | −5.22545 | −0.388404 | −0.194202 | − | 0.980962i | \(-0.562212\pi\) | ||||
−0.194202 | + | 0.980962i | \(0.562212\pi\) | |||||||
\(182\) | 21.9671 | 1.62831 | ||||||||
\(183\) | 45.9859 | 3.39937 | ||||||||
\(184\) | 4.46374 | 0.329071 | ||||||||
\(185\) | 18.5930 | 1.36698 | ||||||||
\(186\) | 15.9615 | 1.17035 | ||||||||
\(187\) | 0.384749 | 0.0281357 | ||||||||
\(188\) | 5.11847 | 0.373303 | ||||||||
\(189\) | 47.2669 | 3.43816 | ||||||||
\(190\) | 35.0549 | 2.54315 | ||||||||
\(191\) | −20.4724 | −1.48133 | −0.740665 | − | 0.671874i | \(-0.765490\pi\) | ||||
−0.740665 | + | 0.671874i | \(0.765490\pi\) | |||||||
\(192\) | −43.8609 | −3.16539 | ||||||||
\(193\) | 20.9183 | 1.50574 | 0.752868 | − | 0.658172i | \(-0.228670\pi\) | ||||
0.752868 | + | 0.658172i | \(0.228670\pi\) | |||||||
\(194\) | −3.18518 | −0.228682 | ||||||||
\(195\) | −50.6885 | −3.62988 | ||||||||
\(196\) | −2.55431 | −0.182451 | ||||||||
\(197\) | 0.277697 | 0.0197851 | 0.00989254 | − | 0.999951i | \(-0.496851\pi\) | ||||
0.00989254 | + | 0.999951i | \(0.496851\pi\) | |||||||
\(198\) | 19.6712 | 1.39797 | ||||||||
\(199\) | 6.96795 | 0.493945 | 0.246972 | − | 0.969023i | \(-0.420564\pi\) | ||||
0.246972 | + | 0.969023i | \(0.420564\pi\) | |||||||
\(200\) | −29.2411 | −2.06766 | ||||||||
\(201\) | 12.9874 | 0.916061 | ||||||||
\(202\) | 28.3490 | 1.99463 | ||||||||
\(203\) | 23.0297 | 1.61637 | ||||||||
\(204\) | −4.27462 | −0.299283 | ||||||||
\(205\) | −33.9317 | −2.36989 | ||||||||
\(206\) | 35.1526 | 2.44920 | ||||||||
\(207\) | −13.1713 | −0.915471 | ||||||||
\(208\) | −0.516729 | −0.0358287 | ||||||||
\(209\) | 3.93567 | 0.272236 | ||||||||
\(210\) | −75.5544 | −5.21375 | ||||||||
\(211\) | −0.833253 | −0.0573635 | −0.0286817 | − | 0.999589i | \(-0.509131\pi\) | ||||
−0.0286817 | + | 0.999589i | \(0.509131\pi\) | |||||||
\(212\) | −3.70659 | −0.254569 | ||||||||
\(213\) | 26.4463 | 1.81207 | ||||||||
\(214\) | −30.0088 | −2.05136 | ||||||||
\(215\) | −18.6523 | −1.27208 | ||||||||
\(216\) | −55.0676 | −3.74688 | ||||||||
\(217\) | −5.09857 | −0.346113 | ||||||||
\(218\) | 11.0645 | 0.749380 | ||||||||
\(219\) | −7.68354 | −0.519206 | ||||||||
\(220\) | −12.6766 | −0.854655 | ||||||||
\(221\) | 1.47703 | 0.0993557 | ||||||||
\(222\) | −37.3943 | −2.50974 | ||||||||
\(223\) | 23.8089 | 1.59436 | 0.797182 | − | 0.603738i | \(-0.206323\pi\) | ||||
0.797182 | + | 0.603738i | \(0.206323\pi\) | |||||||
\(224\) | 13.7179 | 0.916568 | ||||||||
\(225\) | 86.2829 | 5.75219 | ||||||||
\(226\) | 14.1673 | 0.942396 | ||||||||
\(227\) | −7.45079 | −0.494526 | −0.247263 | − | 0.968948i | \(-0.579531\pi\) | ||||
−0.247263 | + | 0.968948i | \(0.579531\pi\) | |||||||
\(228\) | −43.7259 | −2.89582 | ||||||||
\(229\) | −9.43985 | −0.623803 | −0.311901 | − | 0.950115i | \(-0.600966\pi\) | ||||
−0.311901 | + | 0.950115i | \(0.600966\pi\) | |||||||
\(230\) | 13.6857 | 0.902408 | ||||||||
\(231\) | −8.48262 | −0.558115 | ||||||||
\(232\) | −26.8304 | −1.76150 | ||||||||
\(233\) | −29.3067 | −1.91995 | −0.959974 | − | 0.280089i | \(-0.909636\pi\) | ||||
−0.959974 | + | 0.280089i | \(0.909636\pi\) | |||||||
\(234\) | 75.5166 | 4.93668 | ||||||||
\(235\) | 6.08303 | 0.396813 | ||||||||
\(236\) | −30.6848 | −1.99741 | ||||||||
\(237\) | 0.597380 | 0.0388040 | ||||||||
\(238\) | 2.20160 | 0.142709 | ||||||||
\(239\) | −15.4508 | −0.999430 | −0.499715 | − | 0.866190i | \(-0.666562\pi\) | ||||
−0.499715 | + | 0.866190i | \(0.666562\pi\) | |||||||
\(240\) | 1.77726 | 0.114722 | ||||||||
\(241\) | −13.3069 | −0.857175 | −0.428588 | − | 0.903500i | \(-0.640989\pi\) | ||||
−0.428588 | + | 0.903500i | \(0.640989\pi\) | |||||||
\(242\) | −2.29477 | −0.147513 | ||||||||
\(243\) | 75.0077 | 4.81175 | ||||||||
\(244\) | 44.1497 | 2.82640 | ||||||||
\(245\) | −3.03566 | −0.193941 | ||||||||
\(246\) | 68.2436 | 4.35105 | ||||||||
\(247\) | 15.1088 | 0.961351 | ||||||||
\(248\) | 5.94001 | 0.377191 | ||||||||
\(249\) | 24.7220 | 1.56669 | ||||||||
\(250\) | −45.1176 | −2.85349 | ||||||||
\(251\) | 21.1815 | 1.33696 | 0.668481 | − | 0.743729i | \(-0.266945\pi\) | ||||
0.668481 | + | 0.743729i | \(0.266945\pi\) | |||||||
\(252\) | 69.8113 | 4.39770 | ||||||||
\(253\) | 1.53652 | 0.0966000 | ||||||||
\(254\) | 37.5722 | 2.35749 | ||||||||
\(255\) | −5.08015 | −0.318131 | ||||||||
\(256\) | −16.8611 | −1.05382 | ||||||||
\(257\) | −23.0580 | −1.43832 | −0.719158 | − | 0.694846i | \(-0.755472\pi\) | ||||
−0.719158 | + | 0.694846i | \(0.755472\pi\) | |||||||
\(258\) | 37.5136 | 2.33549 | ||||||||
\(259\) | 11.9448 | 0.742216 | ||||||||
\(260\) | −48.6646 | −3.01805 | ||||||||
\(261\) | 79.1697 | 4.90048 | ||||||||
\(262\) | −29.4665 | −1.82044 | ||||||||
\(263\) | 11.6442 | 0.718011 | 0.359005 | − | 0.933336i | \(-0.383116\pi\) | ||||
0.359005 | + | 0.933336i | \(0.383116\pi\) | |||||||
\(264\) | 9.88255 | 0.608229 | ||||||||
\(265\) | −4.40507 | −0.270602 | ||||||||
\(266\) | 22.5206 | 1.38083 | ||||||||
\(267\) | 44.6636 | 2.73337 | ||||||||
\(268\) | 12.4688 | 0.761655 | ||||||||
\(269\) | −18.9028 | −1.15252 | −0.576262 | − | 0.817265i | \(-0.695489\pi\) | ||||
−0.576262 | + | 0.817265i | \(0.695489\pi\) | |||||||
\(270\) | −168.836 | −10.2750 | ||||||||
\(271\) | 17.8487 | 1.08423 | 0.542117 | − | 0.840303i | \(-0.317623\pi\) | ||||
0.542117 | + | 0.840303i | \(0.317623\pi\) | |||||||
\(272\) | −0.0517881 | −0.00314012 | ||||||||
\(273\) | −32.5642 | −1.97088 | ||||||||
\(274\) | −7.65306 | −0.462338 | ||||||||
\(275\) | −10.0654 | −0.606968 | ||||||||
\(276\) | −17.0709 | −1.02755 | ||||||||
\(277\) | −14.5671 | −0.875250 | −0.437625 | − | 0.899158i | \(-0.644180\pi\) | ||||
−0.437625 | + | 0.899158i | \(0.644180\pi\) | |||||||
\(278\) | −48.4537 | −2.90606 | ||||||||
\(279\) | −17.5275 | −1.04934 | ||||||||
\(280\) | −28.1173 | −1.68033 | ||||||||
\(281\) | 13.8882 | 0.828502 | 0.414251 | − | 0.910163i | \(-0.364044\pi\) | ||||
0.414251 | + | 0.910163i | \(0.364044\pi\) | |||||||
\(282\) | −12.2342 | −0.728537 | ||||||||
\(283\) | 24.8296 | 1.47597 | 0.737983 | − | 0.674819i | \(-0.235778\pi\) | ||||
0.737983 | + | 0.674819i | \(0.235778\pi\) | |||||||
\(284\) | 25.3903 | 1.50664 | ||||||||
\(285\) | −51.9658 | −3.07819 | ||||||||
\(286\) | −8.80948 | −0.520915 | ||||||||
\(287\) | −21.7990 | −1.28675 | ||||||||
\(288\) | 47.1584 | 2.77884 | ||||||||
\(289\) | −16.8520 | −0.991292 | ||||||||
\(290\) | −82.2614 | −4.83055 | ||||||||
\(291\) | 4.72175 | 0.276794 | ||||||||
\(292\) | −7.37675 | −0.431692 | ||||||||
\(293\) | 2.17646 | 0.127150 | 0.0635750 | − | 0.997977i | \(-0.479750\pi\) | ||||
0.0635750 | + | 0.997977i | \(0.479750\pi\) | |||||||
\(294\) | 6.10533 | 0.356070 | ||||||||
\(295\) | −36.4672 | −2.12320 | ||||||||
\(296\) | −13.9162 | −0.808860 | ||||||||
\(297\) | −18.9555 | −1.09991 | ||||||||
\(298\) | −5.82056 | −0.337176 | ||||||||
\(299\) | 5.89859 | 0.341124 | ||||||||
\(300\) | 111.828 | 6.45641 | ||||||||
\(301\) | −11.9829 | −0.690685 | ||||||||
\(302\) | −27.1449 | −1.56201 | ||||||||
\(303\) | −42.0250 | −2.41427 | ||||||||
\(304\) | −0.529750 | −0.0303833 | ||||||||
\(305\) | 52.4695 | 3.00440 | ||||||||
\(306\) | 7.56849 | 0.432662 | ||||||||
\(307\) | −11.6506 | −0.664932 | −0.332466 | − | 0.943115i | \(-0.607881\pi\) | ||||
−0.332466 | + | 0.943115i | \(0.607881\pi\) | |||||||
\(308\) | −8.14392 | −0.464043 | ||||||||
\(309\) | −52.1107 | −2.96447 | ||||||||
\(310\) | 18.2119 | 1.03437 | ||||||||
\(311\) | −22.8376 | −1.29500 | −0.647500 | − | 0.762065i | \(-0.724185\pi\) | ||||
−0.647500 | + | 0.762065i | \(0.724185\pi\) | |||||||
\(312\) | 37.9385 | 2.14784 | ||||||||
\(313\) | 21.5645 | 1.21890 | 0.609450 | − | 0.792825i | \(-0.291390\pi\) | ||||
0.609450 | + | 0.792825i | \(0.291390\pi\) | |||||||
\(314\) | 2.14379 | 0.120981 | ||||||||
\(315\) | 82.9669 | 4.67466 | ||||||||
\(316\) | 0.573528 | 0.0322635 | ||||||||
\(317\) | −7.46570 | −0.419316 | −0.209658 | − | 0.977775i | \(-0.567235\pi\) | ||||
−0.209658 | + | 0.977775i | \(0.567235\pi\) | |||||||
\(318\) | 8.85951 | 0.496816 | ||||||||
\(319\) | −9.23562 | −0.517096 | ||||||||
\(320\) | −50.0450 | −2.79760 | ||||||||
\(321\) | 44.4854 | 2.48293 | ||||||||
\(322\) | 8.79221 | 0.489971 | ||||||||
\(323\) | 1.51425 | 0.0842550 | ||||||||
\(324\) | 126.609 | 7.03381 | ||||||||
\(325\) | −38.6405 | −2.14339 | ||||||||
\(326\) | −25.8461 | −1.43148 | ||||||||
\(327\) | −16.4021 | −0.907038 | ||||||||
\(328\) | 25.3966 | 1.40229 | ||||||||
\(329\) | 3.90797 | 0.215453 | ||||||||
\(330\) | 30.2997 | 1.66794 | ||||||||
\(331\) | −17.8599 | −0.981671 | −0.490835 | − | 0.871252i | \(-0.663308\pi\) | ||||
−0.490835 | + | 0.871252i | \(0.663308\pi\) | |||||||
\(332\) | 23.7348 | 1.30262 | ||||||||
\(333\) | 41.0630 | 2.25024 | ||||||||
\(334\) | −43.8412 | −2.39889 | ||||||||
\(335\) | 14.8185 | 0.809623 | ||||||||
\(336\) | 1.14178 | 0.0622891 | ||||||||
\(337\) | −3.85714 | −0.210112 | −0.105056 | − | 0.994466i | \(-0.533502\pi\) | ||||
−0.105056 | + | 0.994466i | \(0.533502\pi\) | |||||||
\(338\) | −3.98703 | −0.216866 | ||||||||
\(339\) | −21.0018 | −1.14066 | ||||||||
\(340\) | −4.87731 | −0.264509 | ||||||||
\(341\) | 2.04469 | 0.110726 | ||||||||
\(342\) | 77.4196 | 4.18637 | ||||||||
\(343\) | −19.4052 | −1.04778 | ||||||||
\(344\) | 13.9606 | 0.752703 | ||||||||
\(345\) | −20.2879 | −1.09226 | ||||||||
\(346\) | 55.8335 | 3.00163 | ||||||||
\(347\) | −7.65766 | −0.411084 | −0.205542 | − | 0.978648i | \(-0.565896\pi\) | ||||
−0.205542 | + | 0.978648i | \(0.565896\pi\) | |||||||
\(348\) | 102.609 | 5.50043 | ||||||||
\(349\) | −20.8804 | −1.11770 | −0.558850 | − | 0.829269i | \(-0.688757\pi\) | ||||
−0.558850 | + | 0.829269i | \(0.688757\pi\) | |||||||
\(350\) | −57.5961 | −3.07864 | ||||||||
\(351\) | −72.7690 | −3.88412 | ||||||||
\(352\) | −5.50132 | −0.293221 | ||||||||
\(353\) | −31.5101 | −1.67711 | −0.838557 | − | 0.544815i | \(-0.816600\pi\) | ||||
−0.838557 | + | 0.544815i | \(0.816600\pi\) | |||||||
\(354\) | 73.3430 | 3.89814 | ||||||||
\(355\) | 30.1750 | 1.60152 | ||||||||
\(356\) | 42.8802 | 2.27265 | ||||||||
\(357\) | −3.26368 | −0.172732 | ||||||||
\(358\) | 12.8861 | 0.681051 | ||||||||
\(359\) | −21.7079 | −1.14570 | −0.572850 | − | 0.819661i | \(-0.694162\pi\) | ||||
−0.572850 | + | 0.819661i | \(0.694162\pi\) | |||||||
\(360\) | −96.6595 | −5.09440 | ||||||||
\(361\) | −3.51046 | −0.184761 | ||||||||
\(362\) | 11.9912 | 0.630243 | ||||||||
\(363\) | 3.40179 | 0.178548 | ||||||||
\(364\) | −31.2640 | −1.63868 | ||||||||
\(365\) | −8.76686 | −0.458879 | ||||||||
\(366\) | −105.527 | −5.51598 | ||||||||
\(367\) | −22.1398 | −1.15569 | −0.577845 | − | 0.816147i | \(-0.696106\pi\) | ||||
−0.577845 | + | 0.816147i | \(0.696106\pi\) | |||||||
\(368\) | −0.206819 | −0.0107812 | ||||||||
\(369\) | −74.9389 | −3.90116 | ||||||||
\(370\) | −42.6666 | −2.21813 | ||||||||
\(371\) | −2.82999 | −0.146926 | ||||||||
\(372\) | −22.7167 | −1.17781 | ||||||||
\(373\) | −22.1036 | −1.14448 | −0.572240 | − | 0.820086i | \(-0.693925\pi\) | ||||
−0.572240 | + | 0.820086i | \(0.693925\pi\) | |||||||
\(374\) | −0.882911 | −0.0456542 | ||||||||
\(375\) | 66.8829 | 3.45382 | ||||||||
\(376\) | −4.55292 | −0.234799 | ||||||||
\(377\) | −35.4550 | −1.82602 | ||||||||
\(378\) | −108.467 | −5.57892 | ||||||||
\(379\) | −14.6258 | −0.751278 | −0.375639 | − | 0.926766i | \(-0.622577\pi\) | ||||
−0.375639 | + | 0.926766i | \(0.622577\pi\) | |||||||
\(380\) | −49.8909 | −2.55935 | ||||||||
\(381\) | −55.6975 | −2.85347 | ||||||||
\(382\) | 46.9794 | 2.40368 | ||||||||
\(383\) | −10.0580 | −0.513940 | −0.256970 | − | 0.966419i | \(-0.582724\pi\) | ||||
−0.256970 | + | 0.966419i | \(0.582724\pi\) | |||||||
\(384\) | 63.2219 | 3.22628 | ||||||||
\(385\) | −9.67860 | −0.493267 | ||||||||
\(386\) | −48.0028 | −2.44328 | ||||||||
\(387\) | −41.1940 | −2.09401 | ||||||||
\(388\) | 4.53322 | 0.230139 | ||||||||
\(389\) | 9.82753 | 0.498276 | 0.249138 | − | 0.968468i | \(-0.419853\pi\) | ||||
0.249138 | + | 0.968468i | \(0.419853\pi\) | |||||||
\(390\) | 116.319 | 5.89002 | ||||||||
\(391\) | 0.591174 | 0.0298970 | ||||||||
\(392\) | 2.27208 | 0.114757 | ||||||||
\(393\) | 43.6814 | 2.20344 | ||||||||
\(394\) | −0.637250 | −0.0321042 | ||||||||
\(395\) | 0.681606 | 0.0342953 | ||||||||
\(396\) | −27.9965 | −1.40688 | ||||||||
\(397\) | −2.24596 | −0.112721 | −0.0563606 | − | 0.998410i | \(-0.517950\pi\) | ||||
−0.0563606 | + | 0.998410i | \(0.517950\pi\) | |||||||
\(398\) | −15.9898 | −0.801498 | ||||||||
\(399\) | −33.3848 | −1.67133 | ||||||||
\(400\) | 1.35483 | 0.0677414 | ||||||||
\(401\) | 7.15542 | 0.357325 | 0.178662 | − | 0.983910i | \(-0.442823\pi\) | ||||
0.178662 | + | 0.983910i | \(0.442823\pi\) | |||||||
\(402\) | −29.8031 | −1.48644 | ||||||||
\(403\) | 7.84942 | 0.391007 | ||||||||
\(404\) | −40.3470 | −2.00734 | ||||||||
\(405\) | 150.467 | 7.47679 | ||||||||
\(406\) | −52.8478 | −2.62279 | ||||||||
\(407\) | −4.79025 | −0.237444 | ||||||||
\(408\) | 3.80231 | 0.188242 | ||||||||
\(409\) | 14.1397 | 0.699162 | 0.349581 | − | 0.936906i | \(-0.386324\pi\) | ||||
0.349581 | + | 0.936906i | \(0.386324\pi\) | |||||||
\(410\) | 77.8654 | 3.84550 | ||||||||
\(411\) | 11.3450 | 0.559607 | ||||||||
\(412\) | −50.0300 | −2.46480 | ||||||||
\(413\) | −23.4279 | −1.15281 | ||||||||
\(414\) | 30.2252 | 1.48549 | ||||||||
\(415\) | 28.2076 | 1.38465 | ||||||||
\(416\) | −21.1192 | −1.03545 | ||||||||
\(417\) | 71.8283 | 3.51745 | ||||||||
\(418\) | −9.03147 | −0.441743 | ||||||||
\(419\) | −17.2268 | −0.841584 | −0.420792 | − | 0.907157i | \(-0.638248\pi\) | ||||
−0.420792 | + | 0.907157i | \(0.638248\pi\) | |||||||
\(420\) | 107.531 | 5.24696 | ||||||||
\(421\) | 17.0202 | 0.829513 | 0.414756 | − | 0.909932i | \(-0.363867\pi\) | ||||
0.414756 | + | 0.909932i | \(0.363867\pi\) | |||||||
\(422\) | 1.91212 | 0.0930807 | ||||||||
\(423\) | 13.4345 | 0.653208 | ||||||||
\(424\) | 3.29703 | 0.160118 | ||||||||
\(425\) | −3.87267 | −0.187852 | ||||||||
\(426\) | −60.6881 | −2.94035 | ||||||||
\(427\) | 33.7084 | 1.63126 | ||||||||
\(428\) | 42.7091 | 2.06442 | ||||||||
\(429\) | 13.0593 | 0.630508 | ||||||||
\(430\) | 42.8027 | 2.06413 | ||||||||
\(431\) | −24.8064 | −1.19488 | −0.597442 | − | 0.801912i | \(-0.703816\pi\) | ||||
−0.597442 | + | 0.801912i | \(0.703816\pi\) | |||||||
\(432\) | 2.55145 | 0.122757 | ||||||||
\(433\) | 12.5758 | 0.604356 | 0.302178 | − | 0.953252i | \(-0.402286\pi\) | ||||
0.302178 | + | 0.953252i | \(0.402286\pi\) | |||||||
\(434\) | 11.7000 | 0.561620 | ||||||||
\(435\) | 121.945 | 5.84683 | ||||||||
\(436\) | −15.7472 | −0.754154 | ||||||||
\(437\) | 6.04723 | 0.289278 | ||||||||
\(438\) | 17.6320 | 0.842488 | ||||||||
\(439\) | 1.56351 | 0.0746222 | 0.0373111 | − | 0.999304i | \(-0.488121\pi\) | ||||
0.0373111 | + | 0.999304i | \(0.488121\pi\) | |||||||
\(440\) | 11.2759 | 0.537558 | ||||||||
\(441\) | −6.70432 | −0.319253 | ||||||||
\(442\) | −3.38944 | −0.161219 | ||||||||
\(443\) | −24.4177 | −1.16012 | −0.580061 | − | 0.814573i | \(-0.696971\pi\) | ||||
−0.580061 | + | 0.814573i | \(0.696971\pi\) | |||||||
\(444\) | 53.2204 | 2.52573 | ||||||||
\(445\) | 50.9608 | 2.41577 | ||||||||
\(446\) | −54.6360 | −2.58709 | ||||||||
\(447\) | 8.62847 | 0.408113 | ||||||||
\(448\) | −32.1508 | −1.51898 | ||||||||
\(449\) | 7.71052 | 0.363882 | 0.181941 | − | 0.983309i | \(-0.441762\pi\) | ||||
0.181941 | + | 0.983309i | \(0.441762\pi\) | |||||||
\(450\) | −197.999 | −9.33378 | ||||||||
\(451\) | 8.74208 | 0.411649 | ||||||||
\(452\) | −20.1632 | −0.948399 | ||||||||
\(453\) | 40.2399 | 1.89064 | ||||||||
\(454\) | 17.0978 | 0.802442 | ||||||||
\(455\) | −37.1555 | −1.74188 | ||||||||
\(456\) | 38.8945 | 1.82140 | ||||||||
\(457\) | −30.8822 | −1.44461 | −0.722304 | − | 0.691576i | \(-0.756917\pi\) | ||||
−0.722304 | + | 0.691576i | \(0.756917\pi\) | |||||||
\(458\) | 21.6623 | 1.01221 | ||||||||
\(459\) | −7.29311 | −0.340413 | ||||||||
\(460\) | −19.4778 | −0.908157 | ||||||||
\(461\) | −35.7065 | −1.66302 | −0.831509 | − | 0.555512i | \(-0.812522\pi\) | ||||
−0.831509 | + | 0.555512i | \(0.812522\pi\) | |||||||
\(462\) | 19.4657 | 0.905624 | ||||||||
\(463\) | −18.0308 | −0.837965 | −0.418982 | − | 0.907994i | \(-0.637613\pi\) | ||||
−0.418982 | + | 0.907994i | \(0.637613\pi\) | |||||||
\(464\) | 1.24314 | 0.0577111 | ||||||||
\(465\) | −26.9976 | −1.25198 | ||||||||
\(466\) | 67.2522 | 3.11540 | ||||||||
\(467\) | 28.4992 | 1.31879 | 0.659393 | − | 0.751799i | \(-0.270813\pi\) | ||||
0.659393 | + | 0.751799i | \(0.270813\pi\) | |||||||
\(468\) | −107.477 | −4.96812 | ||||||||
\(469\) | 9.51998 | 0.439592 | ||||||||
\(470\) | −13.9591 | −0.643887 | ||||||||
\(471\) | −3.17798 | −0.146433 | ||||||||
\(472\) | 27.2943 | 1.25632 | ||||||||
\(473\) | 4.80553 | 0.220959 | ||||||||
\(474\) | −1.37085 | −0.0629652 | ||||||||
\(475\) | −39.6143 | −1.81763 | ||||||||
\(476\) | −3.13337 | −0.143618 | ||||||||
\(477\) | −9.72870 | −0.445447 | ||||||||
\(478\) | 35.4561 | 1.62172 | ||||||||
\(479\) | −36.5478 | −1.66991 | −0.834955 | − | 0.550318i | \(-0.814507\pi\) | ||||
−0.834955 | + | 0.550318i | \(0.814507\pi\) | |||||||
\(480\) | 72.6383 | 3.31547 | ||||||||
\(481\) | −18.3895 | −0.838488 | ||||||||
\(482\) | 30.5363 | 1.39089 | ||||||||
\(483\) | −13.0337 | −0.593053 | ||||||||
\(484\) | 3.26597 | 0.148453 | ||||||||
\(485\) | 5.38748 | 0.244633 | ||||||||
\(486\) | −172.125 | −7.80777 | ||||||||
\(487\) | 38.8696 | 1.76135 | 0.880675 | − | 0.473721i | \(-0.157089\pi\) | ||||
0.880675 | + | 0.473721i | \(0.157089\pi\) | |||||||
\(488\) | −39.2715 | −1.77774 | ||||||||
\(489\) | 38.3146 | 1.73264 | ||||||||
\(490\) | 6.96614 | 0.314698 | ||||||||
\(491\) | 37.0059 | 1.67005 | 0.835027 | − | 0.550209i | \(-0.185452\pi\) | ||||
0.835027 | + | 0.550209i | \(0.185452\pi\) | |||||||
\(492\) | −97.1258 | −4.37877 | ||||||||
\(493\) | −3.55340 | −0.160037 | ||||||||
\(494\) | −34.6712 | −1.55993 | ||||||||
\(495\) | −33.2723 | −1.49548 | ||||||||
\(496\) | −0.275219 | −0.0123577 | ||||||||
\(497\) | 19.3856 | 0.869562 | ||||||||
\(498\) | −56.7312 | −2.54218 | ||||||||
\(499\) | 22.4957 | 1.00705 | 0.503524 | − | 0.863981i | \(-0.332037\pi\) | ||||
0.503524 | + | 0.863981i | \(0.332037\pi\) | |||||||
\(500\) | 64.2123 | 2.87166 | ||||||||
\(501\) | 64.9908 | 2.90357 | ||||||||
\(502\) | −48.6066 | −2.16942 | ||||||||
\(503\) | −12.8176 | −0.571509 | −0.285754 | − | 0.958303i | \(-0.592244\pi\) | ||||
−0.285754 | + | 0.958303i | \(0.592244\pi\) | |||||||
\(504\) | −62.0977 | −2.76605 | ||||||||
\(505\) | −47.9502 | −2.13375 | ||||||||
\(506\) | −3.52595 | −0.156748 | ||||||||
\(507\) | 5.91042 | 0.262491 | ||||||||
\(508\) | −53.4736 | −2.37251 | ||||||||
\(509\) | 9.11722 | 0.404114 | 0.202057 | − | 0.979374i | \(-0.435237\pi\) | ||||
0.202057 | + | 0.979374i | \(0.435237\pi\) | |||||||
\(510\) | 11.6578 | 0.516215 | ||||||||
\(511\) | −5.63216 | −0.249152 | ||||||||
\(512\) | 1.52256 | 0.0672881 | ||||||||
\(513\) | −74.6027 | −3.29379 | ||||||||
\(514\) | 52.9127 | 2.33388 | ||||||||
\(515\) | −59.4579 | −2.62003 | ||||||||
\(516\) | −53.3902 | −2.35037 | ||||||||
\(517\) | −1.56722 | −0.0689261 | ||||||||
\(518\) | −27.4106 | −1.20435 | ||||||||
\(519\) | −82.7682 | −3.63312 | ||||||||
\(520\) | 43.2875 | 1.89828 | ||||||||
\(521\) | −15.6808 | −0.686986 | −0.343493 | − | 0.939155i | \(-0.611610\pi\) | ||||
−0.343493 | + | 0.939155i | \(0.611610\pi\) | |||||||
\(522\) | −181.676 | −7.95175 | ||||||||
\(523\) | −3.13344 | −0.137016 | −0.0685078 | − | 0.997651i | \(-0.521824\pi\) | ||||
−0.0685078 | + | 0.997651i | \(0.521824\pi\) | |||||||
\(524\) | 41.9373 | 1.83204 | ||||||||
\(525\) | 85.3812 | 3.72634 | ||||||||
\(526\) | −26.7207 | −1.16508 | ||||||||
\(527\) | 0.786691 | 0.0342688 | ||||||||
\(528\) | −0.457889 | −0.0199271 | ||||||||
\(529\) | −20.6391 | −0.897353 | ||||||||
\(530\) | 10.1086 | 0.439091 | ||||||||
\(531\) | −80.5386 | −3.49508 | ||||||||
\(532\) | −32.0518 | −1.38962 | ||||||||
\(533\) | 33.5603 | 1.45366 | ||||||||
\(534\) | −102.493 | −4.43529 | ||||||||
\(535\) | 50.7574 | 2.19444 | ||||||||
\(536\) | −11.0911 | −0.479063 | ||||||||
\(537\) | −19.1025 | −0.824333 | ||||||||
\(538\) | 43.3775 | 1.87014 | ||||||||
\(539\) | 0.782100 | 0.0336874 | ||||||||
\(540\) | 240.291 | 10.3405 | ||||||||
\(541\) | 25.8455 | 1.11119 | 0.555593 | − | 0.831455i | \(-0.312491\pi\) | ||||
0.555593 | + | 0.831455i | \(0.312491\pi\) | |||||||
\(542\) | −40.9588 | −1.75933 | ||||||||
\(543\) | −17.7759 | −0.762837 | ||||||||
\(544\) | −2.11663 | −0.0907497 | ||||||||
\(545\) | −18.7147 | −0.801649 | ||||||||
\(546\) | 74.7274 | 3.19804 | ||||||||
\(547\) | 1.00000 | 0.0427569 | ||||||||
\(548\) | 10.8920 | 0.465283 | ||||||||
\(549\) | 115.880 | 4.94564 | ||||||||
\(550\) | 23.0978 | 0.984895 | ||||||||
\(551\) | −36.3484 | −1.54849 | ||||||||
\(552\) | 15.1847 | 0.646304 | ||||||||
\(553\) | 0.437890 | 0.0186210 | ||||||||
\(554\) | 33.4280 | 1.42022 | ||||||||
\(555\) | 63.2495 | 2.68479 | ||||||||
\(556\) | 68.9604 | 2.92457 | ||||||||
\(557\) | 28.1466 | 1.19261 | 0.596304 | − | 0.802758i | \(-0.296635\pi\) | ||||
0.596304 | + | 0.802758i | \(0.296635\pi\) | |||||||
\(558\) | 40.2215 | 1.70271 | ||||||||
\(559\) | 18.4481 | 0.780273 | ||||||||
\(560\) | 1.30276 | 0.0550517 | ||||||||
\(561\) | 1.30884 | 0.0552592 | ||||||||
\(562\) | −31.8703 | −1.34437 | ||||||||
\(563\) | 19.7853 | 0.833851 | 0.416926 | − | 0.908941i | \(-0.363108\pi\) | ||||
0.416926 | + | 0.908941i | \(0.363108\pi\) | |||||||
\(564\) | 17.4120 | 0.733177 | ||||||||
\(565\) | −23.9629 | −1.00813 | ||||||||
\(566\) | −56.9782 | −2.39497 | ||||||||
\(567\) | 96.6660 | 4.05959 | ||||||||
\(568\) | −22.5849 | −0.947641 | ||||||||
\(569\) | −12.0280 | −0.504240 | −0.252120 | − | 0.967696i | \(-0.581128\pi\) | ||||
−0.252120 | + | 0.967696i | \(0.581128\pi\) | |||||||
\(570\) | 119.250 | 4.99482 | ||||||||
\(571\) | 14.3454 | 0.600338 | 0.300169 | − | 0.953886i | \(-0.402957\pi\) | ||||
0.300169 | + | 0.953886i | \(0.402957\pi\) | |||||||
\(572\) | 12.5378 | 0.524233 | ||||||||
\(573\) | −69.6429 | −2.90937 | ||||||||
\(574\) | 50.0237 | 2.08795 | ||||||||
\(575\) | −15.4657 | −0.644964 | ||||||||
\(576\) | −110.525 | −4.60522 | ||||||||
\(577\) | −6.41702 | −0.267144 | −0.133572 | − | 0.991039i | \(-0.542645\pi\) | ||||
−0.133572 | + | 0.991039i | \(0.542645\pi\) | |||||||
\(578\) | 38.6714 | 1.60852 | ||||||||
\(579\) | 71.1599 | 2.95730 | ||||||||
\(580\) | 117.076 | 4.86132 | ||||||||
\(581\) | 18.1216 | 0.751811 | ||||||||
\(582\) | −10.8353 | −0.449138 | ||||||||
\(583\) | 1.13491 | 0.0470033 | ||||||||
\(584\) | 6.56167 | 0.271524 | ||||||||
\(585\) | −127.730 | −5.28100 | ||||||||
\(586\) | −4.99447 | −0.206320 | ||||||||
\(587\) | −2.72214 | −0.112355 | −0.0561773 | − | 0.998421i | \(-0.517891\pi\) | ||||
−0.0561773 | + | 0.998421i | \(0.517891\pi\) | |||||||
\(588\) | −8.68925 | −0.358338 | ||||||||
\(589\) | 8.04722 | 0.331580 | ||||||||
\(590\) | 83.6838 | 3.44521 | ||||||||
\(591\) | 0.944668 | 0.0388584 | ||||||||
\(592\) | 0.644778 | 0.0265002 | ||||||||
\(593\) | −27.0454 | −1.11062 | −0.555311 | − | 0.831643i | \(-0.687401\pi\) | ||||
−0.555311 | + | 0.831643i | \(0.687401\pi\) | |||||||
\(594\) | 43.4985 | 1.78476 | ||||||||
\(595\) | −3.72384 | −0.152662 | ||||||||
\(596\) | 8.28395 | 0.339324 | ||||||||
\(597\) | 23.7035 | 0.970120 | ||||||||
\(598\) | −13.5359 | −0.553524 | ||||||||
\(599\) | −46.5407 | −1.90160 | −0.950800 | − | 0.309805i | \(-0.899736\pi\) | ||||
−0.950800 | + | 0.309805i | \(0.899736\pi\) | |||||||
\(600\) | −99.4721 | −4.06093 | ||||||||
\(601\) | −24.2496 | −0.989160 | −0.494580 | − | 0.869132i | \(-0.664678\pi\) | ||||
−0.494580 | + | 0.869132i | \(0.664678\pi\) | |||||||
\(602\) | 27.4981 | 1.12074 | ||||||||
\(603\) | 32.7270 | 1.33275 | ||||||||
\(604\) | 38.6332 | 1.57196 | ||||||||
\(605\) | 3.88142 | 0.157802 | ||||||||
\(606\) | 96.4376 | 3.91751 | ||||||||
\(607\) | −19.7787 | −0.802794 | −0.401397 | − | 0.915904i | \(-0.631475\pi\) | ||||
−0.401397 | + | 0.915904i | \(0.631475\pi\) | |||||||
\(608\) | −21.6514 | −0.878080 | ||||||||
\(609\) | 78.3423 | 3.17459 | ||||||||
\(610\) | −120.405 | −4.87507 | ||||||||
\(611\) | −6.01645 | −0.243399 | ||||||||
\(612\) | −10.7716 | −0.435418 | ||||||||
\(613\) | 22.1445 | 0.894408 | 0.447204 | − | 0.894432i | \(-0.352420\pi\) | ||||
0.447204 | + | 0.894432i | \(0.352420\pi\) | |||||||
\(614\) | 26.7353 | 1.07895 | ||||||||
\(615\) | −115.429 | −4.65453 | ||||||||
\(616\) | 7.24408 | 0.291872 | ||||||||
\(617\) | −32.3709 | −1.30320 | −0.651601 | − | 0.758562i | \(-0.725902\pi\) | ||||
−0.651601 | + | 0.758562i | \(0.725902\pi\) | |||||||
\(618\) | 119.582 | 4.81029 | ||||||||
\(619\) | −16.0701 | −0.645910 | −0.322955 | − | 0.946414i | \(-0.604676\pi\) | ||||
−0.322955 | + | 0.946414i | \(0.604676\pi\) | |||||||
\(620\) | −25.9196 | −1.04096 | ||||||||
\(621\) | −29.1254 | −1.16876 | ||||||||
\(622\) | 52.4070 | 2.10133 | ||||||||
\(623\) | 32.7391 | 1.31167 | ||||||||
\(624\) | −1.75781 | −0.0703686 | ||||||||
\(625\) | 25.9857 | 1.03943 | ||||||||
\(626\) | −49.4856 | −1.97784 | ||||||||
\(627\) | 13.3884 | 0.534679 | ||||||||
\(628\) | −3.05109 | −0.121752 | ||||||||
\(629\) | −1.84305 | −0.0734870 | ||||||||
\(630\) | −190.390 | −7.58532 | ||||||||
\(631\) | 38.9934 | 1.55230 | 0.776151 | − | 0.630547i | \(-0.217170\pi\) | ||||
0.776151 | + | 0.630547i | \(0.217170\pi\) | |||||||
\(632\) | −0.510157 | −0.0202930 | ||||||||
\(633\) | −2.83455 | −0.112663 | ||||||||
\(634\) | 17.1321 | 0.680401 | ||||||||
\(635\) | −63.5504 | −2.52192 | ||||||||
\(636\) | −12.6090 | −0.499981 | ||||||||
\(637\) | 3.00243 | 0.118961 | ||||||||
\(638\) | 21.1936 | 0.839064 | ||||||||
\(639\) | 66.6422 | 2.63632 | ||||||||
\(640\) | 72.1358 | 2.85142 | ||||||||
\(641\) | −6.83403 | −0.269928 | −0.134964 | − | 0.990851i | \(-0.543092\pi\) | ||||
−0.134964 | + | 0.990851i | \(0.543092\pi\) | |||||||
\(642\) | −102.084 | −4.02892 | ||||||||
\(643\) | −35.0196 | −1.38104 | −0.690520 | − | 0.723314i | \(-0.742618\pi\) | ||||
−0.690520 | + | 0.723314i | \(0.742618\pi\) | |||||||
\(644\) | −12.5133 | −0.493092 | ||||||||
\(645\) | −63.4513 | −2.49839 | ||||||||
\(646\) | −3.47485 | −0.136716 | ||||||||
\(647\) | 36.9174 | 1.45137 | 0.725686 | − | 0.688026i | \(-0.241522\pi\) | ||||
0.725686 | + | 0.688026i | \(0.241522\pi\) | |||||||
\(648\) | −112.619 | −4.42410 | ||||||||
\(649\) | 9.39532 | 0.368799 | ||||||||
\(650\) | 88.6711 | 3.47797 | ||||||||
\(651\) | −17.3443 | −0.679776 | ||||||||
\(652\) | 36.7847 | 1.44060 | ||||||||
\(653\) | −20.5073 | −0.802514 | −0.401257 | − | 0.915966i | \(-0.631427\pi\) | ||||
−0.401257 | + | 0.915966i | \(0.631427\pi\) | |||||||
\(654\) | 37.6390 | 1.47180 | ||||||||
\(655\) | 49.8402 | 1.94742 | ||||||||
\(656\) | −1.17670 | −0.0459425 | ||||||||
\(657\) | −19.3618 | −0.755376 | ||||||||
\(658\) | −8.96788 | −0.349604 | ||||||||
\(659\) | −16.3098 | −0.635339 | −0.317669 | − | 0.948202i | \(-0.602900\pi\) | ||||
−0.317669 | + | 0.948202i | \(0.602900\pi\) | |||||||
\(660\) | −43.1231 | −1.67857 | ||||||||
\(661\) | −38.6304 | −1.50255 | −0.751274 | − | 0.659991i | \(-0.770560\pi\) | ||||
−0.751274 | + | 0.659991i | \(0.770560\pi\) | |||||||
\(662\) | 40.9844 | 1.59291 | ||||||||
\(663\) | 5.02455 | 0.195137 | ||||||||
\(664\) | −21.1123 | −0.819317 | ||||||||
\(665\) | −38.0918 | −1.47714 | ||||||||
\(666\) | −94.2301 | −3.65134 | ||||||||
\(667\) | −14.1907 | −0.549466 | ||||||||
\(668\) | 62.3958 | 2.41417 | ||||||||
\(669\) | 80.9931 | 3.13138 | ||||||||
\(670\) | −34.0051 | −1.31373 | ||||||||
\(671\) | −13.5181 | −0.521861 | ||||||||
\(672\) | 46.6656 | 1.80016 | ||||||||
\(673\) | −26.1730 | −1.00889 | −0.504447 | − | 0.863443i | \(-0.668304\pi\) | ||||
−0.504447 | + | 0.863443i | \(0.668304\pi\) | |||||||
\(674\) | 8.85126 | 0.340938 | ||||||||
\(675\) | 190.795 | 7.34371 | ||||||||
\(676\) | 5.67443 | 0.218247 | ||||||||
\(677\) | −30.7469 | −1.18170 | −0.590849 | − | 0.806782i | \(-0.701207\pi\) | ||||
−0.590849 | + | 0.806782i | \(0.701207\pi\) | |||||||
\(678\) | 48.1943 | 1.85089 | ||||||||
\(679\) | 3.46112 | 0.132826 | ||||||||
\(680\) | 4.33840 | 0.166370 | ||||||||
\(681\) | −25.3461 | −0.971263 | ||||||||
\(682\) | −4.69208 | −0.179669 | ||||||||
\(683\) | −51.5321 | −1.97182 | −0.985910 | − | 0.167279i | \(-0.946502\pi\) | ||||
−0.985910 | + | 0.167279i | \(0.946502\pi\) | |||||||
\(684\) | −110.185 | −4.21304 | ||||||||
\(685\) | 12.9445 | 0.494586 | ||||||||
\(686\) | 44.5305 | 1.70018 | ||||||||
\(687\) | −32.1124 | −1.22517 | ||||||||
\(688\) | −0.646835 | −0.0246604 | ||||||||
\(689\) | 4.35686 | 0.165983 | ||||||||
\(690\) | 46.5559 | 1.77235 | ||||||||
\(691\) | 24.2843 | 0.923820 | 0.461910 | − | 0.886927i | \(-0.347164\pi\) | ||||
0.461910 | + | 0.886927i | \(0.347164\pi\) | |||||||
\(692\) | −79.4634 | −3.02075 | ||||||||
\(693\) | −21.3754 | −0.811985 | ||||||||
\(694\) | 17.5726 | 0.667045 | ||||||||
\(695\) | 81.9556 | 3.10875 | ||||||||
\(696\) | −91.2715 | −3.45964 | ||||||||
\(697\) | 3.36351 | 0.127402 | ||||||||
\(698\) | 47.9156 | 1.81363 | ||||||||
\(699\) | −99.6955 | −3.77083 | ||||||||
\(700\) | 81.9720 | 3.09825 | ||||||||
\(701\) | 7.92748 | 0.299417 | 0.149708 | − | 0.988730i | \(-0.452167\pi\) | ||||
0.149708 | + | 0.988730i | \(0.452167\pi\) | |||||||
\(702\) | 166.988 | 6.30255 | ||||||||
\(703\) | −18.8529 | −0.711049 | ||||||||
\(704\) | 12.8935 | 0.485941 | ||||||||
\(705\) | 20.6932 | 0.779351 | ||||||||
\(706\) | 72.3084 | 2.72136 | ||||||||
\(707\) | −30.8050 | −1.15854 | ||||||||
\(708\) | −104.383 | −3.92297 | ||||||||
\(709\) | 0.355524 | 0.0133520 | 0.00667599 | − | 0.999978i | \(-0.497875\pi\) | ||||
0.00667599 | + | 0.999978i | \(0.497875\pi\) | |||||||
\(710\) | −69.2447 | −2.59871 | ||||||||
\(711\) | 1.50534 | 0.0564548 | ||||||||
\(712\) | −38.1423 | −1.42944 | ||||||||
\(713\) | 3.14169 | 0.117657 | ||||||||
\(714\) | 7.48940 | 0.280284 | ||||||||
\(715\) | 14.9005 | 0.557248 | ||||||||
\(716\) | −18.3398 | −0.685389 | ||||||||
\(717\) | −52.5605 | −1.96291 | ||||||||
\(718\) | 49.8146 | 1.85907 | ||||||||
\(719\) | −25.6548 | −0.956761 | −0.478381 | − | 0.878153i | \(-0.658776\pi\) | ||||
−0.478381 | + | 0.878153i | \(0.658776\pi\) | |||||||
\(720\) | 4.47853 | 0.166905 | ||||||||
\(721\) | −38.1980 | −1.42257 | ||||||||
\(722\) | 8.05570 | 0.299802 | ||||||||
\(723\) | −45.2675 | −1.68351 | ||||||||
\(724\) | −17.0661 | −0.634258 | ||||||||
\(725\) | 92.9605 | 3.45247 | ||||||||
\(726\) | −7.80633 | −0.289720 | ||||||||
\(727\) | 37.4547 | 1.38912 | 0.694560 | − | 0.719435i | \(-0.255599\pi\) | ||||
0.694560 | + | 0.719435i | \(0.255599\pi\) | |||||||
\(728\) | 27.8096 | 1.03069 | ||||||||
\(729\) | 138.863 | 5.14306 | ||||||||
\(730\) | 20.1179 | 0.744598 | ||||||||
\(731\) | 1.84893 | 0.0683850 | ||||||||
\(732\) | 150.188 | 5.55112 | ||||||||
\(733\) | −0.881589 | −0.0325622 | −0.0162811 | − | 0.999867i | \(-0.505183\pi\) | ||||
−0.0162811 | + | 0.999867i | \(0.505183\pi\) | |||||||
\(734\) | 50.8058 | 1.87528 | ||||||||
\(735\) | −10.3267 | −0.380906 | ||||||||
\(736\) | −8.45287 | −0.311577 | ||||||||
\(737\) | −3.81781 | −0.140631 | ||||||||
\(738\) | 171.968 | 6.33021 | ||||||||
\(739\) | −18.9331 | −0.696466 | −0.348233 | − | 0.937408i | \(-0.613218\pi\) | ||||
−0.348233 | + | 0.937408i | \(0.613218\pi\) | |||||||
\(740\) | 60.7240 | 2.23226 | ||||||||
\(741\) | 51.3971 | 1.88812 | ||||||||
\(742\) | 6.49417 | 0.238408 | ||||||||
\(743\) | −4.13373 | −0.151652 | −0.0758259 | − | 0.997121i | \(-0.524159\pi\) | ||||
−0.0758259 | + | 0.997121i | \(0.524159\pi\) | |||||||
\(744\) | 20.2067 | 0.740814 | ||||||||
\(745\) | 9.84502 | 0.360694 | ||||||||
\(746\) | 50.7226 | 1.85709 | ||||||||
\(747\) | 62.2970 | 2.27933 | ||||||||
\(748\) | 1.25658 | 0.0459451 | ||||||||
\(749\) | 32.6085 | 1.19149 | ||||||||
\(750\) | −153.481 | −5.60432 | ||||||||
\(751\) | 19.7061 | 0.719085 | 0.359543 | − | 0.933129i | \(-0.382933\pi\) | ||||
0.359543 | + | 0.933129i | \(0.382933\pi\) | |||||||
\(752\) | 0.210951 | 0.00769258 | ||||||||
\(753\) | 72.0550 | 2.62583 | ||||||||
\(754\) | 81.3610 | 2.96299 | ||||||||
\(755\) | 45.9134 | 1.67096 | ||||||||
\(756\) | 154.372 | 5.61446 | ||||||||
\(757\) | 16.6576 | 0.605429 | 0.302715 | − | 0.953081i | \(-0.402107\pi\) | ||||
0.302715 | + | 0.953081i | \(0.402107\pi\) | |||||||
\(758\) | 33.5629 | 1.21906 | ||||||||
\(759\) | 5.22691 | 0.189725 | ||||||||
\(760\) | 44.3783 | 1.60977 | ||||||||
\(761\) | −29.8931 | −1.08362 | −0.541812 | − | 0.840500i | \(-0.682261\pi\) | ||||
−0.541812 | + | 0.840500i | \(0.682261\pi\) | |||||||
\(762\) | 127.813 | 4.63017 | ||||||||
\(763\) | −12.0230 | −0.435262 | ||||||||
\(764\) | −66.8622 | −2.41899 | ||||||||
\(765\) | −12.8015 | −0.462840 | ||||||||
\(766\) | 23.0808 | 0.833943 | ||||||||
\(767\) | 36.0680 | 1.30234 | ||||||||
\(768\) | −57.3580 | −2.06973 | ||||||||
\(769\) | −3.67393 | −0.132485 | −0.0662427 | − | 0.997804i | \(-0.521101\pi\) | ||||
−0.0662427 | + | 0.997804i | \(0.521101\pi\) | |||||||
\(770\) | 22.2102 | 0.800398 | ||||||||
\(771\) | −78.4385 | −2.82489 | ||||||||
\(772\) | 68.3186 | 2.45884 | ||||||||
\(773\) | 12.8806 | 0.463284 | 0.231642 | − | 0.972801i | \(-0.425590\pi\) | ||||
0.231642 | + | 0.972801i | \(0.425590\pi\) | |||||||
\(774\) | 94.5308 | 3.39784 | ||||||||
\(775\) | −20.5806 | −0.739278 | ||||||||
\(776\) | −4.03233 | −0.144752 | ||||||||
\(777\) | 40.6339 | 1.45773 | ||||||||
\(778\) | −22.5519 | −0.808525 | ||||||||
\(779\) | 34.4060 | 1.23272 | ||||||||
\(780\) | −165.547 | −5.92754 | ||||||||
\(781\) | −7.77422 | −0.278183 | ||||||||
\(782\) | −1.35661 | −0.0485122 | ||||||||
\(783\) | 175.066 | 6.25634 | ||||||||
\(784\) | −0.105272 | −0.00375973 | ||||||||
\(785\) | −3.62605 | −0.129419 | ||||||||
\(786\) | −100.239 | −3.57540 | ||||||||
\(787\) | 45.3111 | 1.61517 | 0.807583 | − | 0.589754i | \(-0.200775\pi\) | ||||
0.807583 | + | 0.589754i | \(0.200775\pi\) | |||||||
\(788\) | 0.906949 | 0.0323087 | ||||||||
\(789\) | 39.6111 | 1.41019 | ||||||||
\(790\) | −1.56413 | −0.0556492 | ||||||||
\(791\) | −15.3947 | −0.547372 | ||||||||
\(792\) | 24.9031 | 0.884893 | ||||||||
\(793\) | −51.8952 | −1.84285 | ||||||||
\(794\) | 5.15395 | 0.182907 | ||||||||
\(795\) | −14.9852 | −0.531469 | ||||||||
\(796\) | 22.7571 | 0.806603 | ||||||||
\(797\) | −5.84557 | −0.207061 | −0.103530 | − | 0.994626i | \(-0.533014\pi\) | ||||
−0.103530 | + | 0.994626i | \(0.533014\pi\) | |||||||
\(798\) | 76.6105 | 2.71198 | ||||||||
\(799\) | −0.602985 | −0.0213321 | ||||||||
\(800\) | 55.3731 | 1.95774 | ||||||||
\(801\) | 112.548 | 3.97669 | ||||||||
\(802\) | −16.4200 | −0.579812 | ||||||||
\(803\) | 2.25867 | 0.0797069 | ||||||||
\(804\) | 42.4164 | 1.49591 | ||||||||
\(805\) | −14.8713 | −0.524146 | ||||||||
\(806\) | −18.0126 | −0.634467 | ||||||||
\(807\) | −64.3034 | −2.26359 | ||||||||
\(808\) | 35.8889 | 1.26257 | ||||||||
\(809\) | 13.0053 | 0.457242 | 0.228621 | − | 0.973515i | \(-0.426578\pi\) | ||||
0.228621 | + | 0.973515i | \(0.426578\pi\) | |||||||
\(810\) | −345.288 | −12.1322 | ||||||||
\(811\) | 13.4655 | 0.472838 | 0.236419 | − | 0.971651i | \(-0.424026\pi\) | ||||
0.236419 | + | 0.971651i | \(0.424026\pi\) | |||||||
\(812\) | 75.2142 | 2.63950 | ||||||||
\(813\) | 60.7178 | 2.12947 | ||||||||
\(814\) | 10.9925 | 0.385287 | ||||||||
\(815\) | 43.7166 | 1.53133 | ||||||||
\(816\) | −0.176172 | −0.00616727 | ||||||||
\(817\) | 18.9130 | 0.661683 | ||||||||
\(818\) | −32.4473 | −1.13449 | ||||||||
\(819\) | −82.0588 | −2.86737 | ||||||||
\(820\) | −110.820 | −3.86999 | ||||||||
\(821\) | 37.2586 | 1.30034 | 0.650168 | − | 0.759791i | \(-0.274699\pi\) | ||||
0.650168 | + | 0.759791i | \(0.274699\pi\) | |||||||
\(822\) | −26.0341 | −0.908045 | ||||||||
\(823\) | −9.63528 | −0.335865 | −0.167932 | − | 0.985799i | \(-0.553709\pi\) | ||||
−0.167932 | + | 0.985799i | \(0.553709\pi\) | |||||||
\(824\) | 44.5020 | 1.55030 | ||||||||
\(825\) | −34.2405 | −1.19210 | ||||||||
\(826\) | 53.7616 | 1.87061 | ||||||||
\(827\) | 2.81571 | 0.0979120 | 0.0489560 | − | 0.998801i | \(-0.484411\pi\) | ||||
0.0489560 | + | 0.998801i | \(0.484411\pi\) | |||||||
\(828\) | −43.0171 | −1.49495 | ||||||||
\(829\) | 35.6028 | 1.23654 | 0.618268 | − | 0.785968i | \(-0.287835\pi\) | ||||
0.618268 | + | 0.785968i | \(0.287835\pi\) | |||||||
\(830\) | −64.7298 | −2.24681 | ||||||||
\(831\) | −49.5541 | −1.71901 | ||||||||
\(832\) | 49.4972 | 1.71601 | ||||||||
\(833\) | 0.300913 | 0.0104260 | ||||||||
\(834\) | −164.829 | −5.70758 | ||||||||
\(835\) | 74.1540 | 2.56621 | ||||||||
\(836\) | 12.8538 | 0.444557 | ||||||||
\(837\) | −38.7580 | −1.33967 | ||||||||
\(838\) | 39.5315 | 1.36559 | ||||||||
\(839\) | 47.8060 | 1.65045 | 0.825223 | − | 0.564808i | \(-0.191050\pi\) | ||||
0.825223 | + | 0.564808i | \(0.191050\pi\) | |||||||
\(840\) | −95.6493 | −3.30021 | ||||||||
\(841\) | 56.2967 | 1.94127 | ||||||||
\(842\) | −39.0574 | −1.34601 | ||||||||
\(843\) | 47.2449 | 1.62720 | ||||||||
\(844\) | −2.72137 | −0.0936736 | ||||||||
\(845\) | 6.74374 | 0.231992 | ||||||||
\(846\) | −30.8291 | −1.05993 | ||||||||
\(847\) | 2.49357 | 0.0856801 | ||||||||
\(848\) | −0.152762 | −0.00524586 | ||||||||
\(849\) | 84.4652 | 2.89884 | ||||||||
\(850\) | 8.88688 | 0.304817 | ||||||||
\(851\) | −7.36030 | −0.252308 | ||||||||
\(852\) | 86.3727 | 2.95908 | ||||||||
\(853\) | 8.48535 | 0.290533 | 0.145266 | − | 0.989393i | \(-0.453596\pi\) | ||||
0.145266 | + | 0.989393i | \(0.453596\pi\) | |||||||
\(854\) | −77.3530 | −2.64697 | ||||||||
\(855\) | −130.949 | −4.47836 | ||||||||
\(856\) | −37.9901 | −1.29847 | ||||||||
\(857\) | −21.2334 | −0.725320 | −0.362660 | − | 0.931922i | \(-0.618131\pi\) | ||||
−0.362660 | + | 0.931922i | \(0.618131\pi\) | |||||||
\(858\) | −29.9680 | −1.02309 | ||||||||
\(859\) | −0.364795 | −0.0124467 | −0.00622333 | − | 0.999981i | \(-0.501981\pi\) | ||||
−0.00622333 | + | 0.999981i | \(0.501981\pi\) | |||||||
\(860\) | −60.9178 | −2.07728 | ||||||||
\(861\) | −74.1557 | −2.52722 | ||||||||
\(862\) | 56.9250 | 1.93887 | ||||||||
\(863\) | 51.2218 | 1.74361 | 0.871806 | − | 0.489852i | \(-0.162949\pi\) | ||||
0.871806 | + | 0.489852i | \(0.162949\pi\) | |||||||
\(864\) | 104.280 | 3.54768 | ||||||||
\(865\) | −94.4379 | −3.21098 | ||||||||
\(866\) | −28.8586 | −0.980656 | ||||||||
\(867\) | −57.3269 | −1.94692 | ||||||||
\(868\) | −16.6518 | −0.565197 | ||||||||
\(869\) | −0.175607 | −0.00595707 | ||||||||
\(870\) | −279.836 | −9.48734 | ||||||||
\(871\) | −14.6563 | −0.496611 | ||||||||
\(872\) | 14.0072 | 0.474345 | ||||||||
\(873\) | 11.8984 | 0.402699 | ||||||||
\(874\) | −13.8770 | −0.469397 | ||||||||
\(875\) | 49.0263 | 1.65739 | ||||||||
\(876\) | −25.0942 | −0.847854 | ||||||||
\(877\) | −34.6400 | −1.16971 | −0.584855 | − | 0.811138i | \(-0.698849\pi\) | ||||
−0.584855 | + | 0.811138i | \(0.698849\pi\) | |||||||
\(878\) | −3.58789 | −0.121085 | ||||||||
\(879\) | 7.40386 | 0.249726 | ||||||||
\(880\) | −0.522448 | −0.0176117 | ||||||||
\(881\) | −53.6224 | −1.80658 | −0.903292 | − | 0.429027i | \(-0.858857\pi\) | ||||
−0.903292 | + | 0.429027i | \(0.858857\pi\) | |||||||
\(882\) | 15.3849 | 0.518036 | ||||||||
\(883\) | −42.9478 | −1.44531 | −0.722655 | − | 0.691209i | \(-0.757078\pi\) | ||||
−0.722655 | + | 0.691209i | \(0.757078\pi\) | |||||||
\(884\) | 4.82393 | 0.162246 | ||||||||
\(885\) | −124.054 | −4.17003 | ||||||||
\(886\) | 56.0331 | 1.88247 | ||||||||
\(887\) | −29.5095 | −0.990832 | −0.495416 | − | 0.868656i | \(-0.664984\pi\) | ||||
−0.495416 | + | 0.868656i | \(0.664984\pi\) | |||||||
\(888\) | −47.3399 | −1.58862 | ||||||||
\(889\) | −40.8272 | −1.36930 | ||||||||
\(890\) | −116.943 | −3.91995 | ||||||||
\(891\) | −38.7661 | −1.29871 | ||||||||
\(892\) | 77.7592 | 2.60357 | ||||||||
\(893\) | −6.16805 | −0.206406 | ||||||||
\(894\) | −19.8004 | −0.662223 | ||||||||
\(895\) | −21.7958 | −0.728553 | ||||||||
\(896\) | 46.3427 | 1.54820 | ||||||||
\(897\) | 20.0658 | 0.669977 | ||||||||
\(898\) | −17.6939 | −0.590452 | ||||||||
\(899\) | −18.8839 | −0.629815 | ||||||||
\(900\) | 281.797 | 9.39323 | ||||||||
\(901\) | 0.436657 | 0.0145472 | ||||||||
\(902\) | −20.0611 | −0.667960 | ||||||||
\(903\) | −40.7635 | −1.35652 | ||||||||
\(904\) | 17.9353 | 0.596521 | ||||||||
\(905\) | −20.2822 | −0.674202 | ||||||||
\(906\) | −92.3413 | −3.06783 | ||||||||
\(907\) | −31.3851 | −1.04212 | −0.521062 | − | 0.853519i | \(-0.674464\pi\) | ||||
−0.521062 | + | 0.853519i | \(0.674464\pi\) | |||||||
\(908\) | −24.3340 | −0.807553 | ||||||||
\(909\) | −105.899 | −3.51245 | ||||||||
\(910\) | 85.2634 | 2.82645 | ||||||||
\(911\) | 36.9332 | 1.22365 | 0.611825 | − | 0.790993i | \(-0.290436\pi\) | ||||
0.611825 | + | 0.790993i | \(0.290436\pi\) | |||||||
\(912\) | −1.80210 | −0.0596736 | ||||||||
\(913\) | −7.26733 | −0.240513 | ||||||||
\(914\) | 70.8675 | 2.34409 | ||||||||
\(915\) | 178.491 | 5.90072 | ||||||||
\(916\) | −30.8302 | −1.01866 | ||||||||
\(917\) | 32.0192 | 1.05737 | ||||||||
\(918\) | 16.7360 | 0.552371 | ||||||||
\(919\) | 38.1897 | 1.25976 | 0.629880 | − | 0.776692i | \(-0.283104\pi\) | ||||
0.629880 | + | 0.776692i | \(0.283104\pi\) | |||||||
\(920\) | 17.3256 | 0.571209 | ||||||||
\(921\) | −39.6328 | −1.30594 | ||||||||
\(922\) | 81.9382 | 2.69849 | ||||||||
\(923\) | −29.8447 | −0.982352 | ||||||||
\(924\) | −27.7039 | −0.911393 | ||||||||
\(925\) | 48.2159 | 1.58533 | ||||||||
\(926\) | 41.3766 | 1.35972 | ||||||||
\(927\) | −131.314 | −4.31292 | ||||||||
\(928\) | 50.8081 | 1.66786 | ||||||||
\(929\) | 43.7914 | 1.43675 | 0.718375 | − | 0.695656i | \(-0.244886\pi\) | ||||
0.718375 | + | 0.695656i | \(0.244886\pi\) | |||||||
\(930\) | 61.9533 | 2.03153 | ||||||||
\(931\) | 3.07809 | 0.100880 | ||||||||
\(932\) | −95.7148 | −3.13524 | ||||||||
\(933\) | −77.6887 | −2.54341 | ||||||||
\(934\) | −65.3991 | −2.13992 | ||||||||
\(935\) | 1.49337 | 0.0488386 | ||||||||
\(936\) | 95.6015 | 3.12483 | ||||||||
\(937\) | 14.9844 | 0.489520 | 0.244760 | − | 0.969584i | \(-0.421291\pi\) | ||||
0.244760 | + | 0.969584i | \(0.421291\pi\) | |||||||
\(938\) | −21.8462 | −0.713303 | ||||||||
\(939\) | 73.3581 | 2.39395 | ||||||||
\(940\) | 19.8670 | 0.647989 | ||||||||
\(941\) | −37.6535 | −1.22747 | −0.613734 | − | 0.789513i | \(-0.710333\pi\) | ||||
−0.613734 | + | 0.789513i | \(0.710333\pi\) | |||||||
\(942\) | 7.29273 | 0.237610 | ||||||||
\(943\) | 13.4324 | 0.437418 | ||||||||
\(944\) | −1.26463 | −0.0411602 | ||||||||
\(945\) | 183.463 | 5.96804 | ||||||||
\(946\) | −11.0276 | −0.358538 | ||||||||
\(947\) | −26.8790 | −0.873451 | −0.436726 | − | 0.899595i | \(-0.643862\pi\) | ||||
−0.436726 | + | 0.899595i | \(0.643862\pi\) | |||||||
\(948\) | 1.95102 | 0.0633663 | ||||||||
\(949\) | 8.67091 | 0.281470 | ||||||||
\(950\) | 90.9056 | 2.94937 | ||||||||
\(951\) | −25.3968 | −0.823547 | ||||||||
\(952\) | 2.78715 | 0.0903322 | ||||||||
\(953\) | −5.36078 | −0.173653 | −0.0868264 | − | 0.996223i | \(-0.527673\pi\) | ||||
−0.0868264 | + | 0.996223i | \(0.527673\pi\) | |||||||
\(954\) | 22.3251 | 0.722803 | ||||||||
\(955\) | −79.4620 | −2.57133 | ||||||||
\(956\) | −50.4618 | −1.63205 | ||||||||
\(957\) | −31.4177 | −1.01559 | ||||||||
\(958\) | 83.8687 | 2.70968 | ||||||||
\(959\) | 8.31607 | 0.268540 | ||||||||
\(960\) | −170.243 | −5.49456 | ||||||||
\(961\) | −26.8193 | −0.865138 | ||||||||
\(962\) | 42.1996 | 1.36057 | ||||||||
\(963\) | 112.099 | 3.61234 | ||||||||
\(964\) | −43.4600 | −1.39975 | ||||||||
\(965\) | 81.1929 | 2.61369 | ||||||||
\(966\) | 29.9093 | 0.962316 | ||||||||
\(967\) | 61.4434 | 1.97589 | 0.987944 | − | 0.154813i | \(-0.0494774\pi\) | ||||
0.987944 | + | 0.154813i | \(0.0494774\pi\) | |||||||
\(968\) | −2.90510 | −0.0933735 | ||||||||
\(969\) | 5.15116 | 0.165479 | ||||||||
\(970\) | −12.3630 | −0.396953 | ||||||||
\(971\) | 7.78462 | 0.249820 | 0.124910 | − | 0.992168i | \(-0.460136\pi\) | ||||
0.124910 | + | 0.992168i | \(0.460136\pi\) | |||||||
\(972\) | 244.973 | 7.85750 | ||||||||
\(973\) | 52.6514 | 1.68793 | ||||||||
\(974\) | −89.1968 | −2.85805 | ||||||||
\(975\) | −131.447 | −4.20968 | ||||||||
\(976\) | 1.81957 | 0.0582430 | ||||||||
\(977\) | −29.2487 | −0.935750 | −0.467875 | − | 0.883795i | \(-0.654980\pi\) | ||||
−0.467875 | + | 0.883795i | \(0.654980\pi\) | |||||||
\(978\) | −87.9231 | −2.81147 | ||||||||
\(979\) | −13.1294 | −0.419618 | ||||||||
\(980\) | −9.91436 | −0.316703 | ||||||||
\(981\) | −41.3318 | −1.31962 | ||||||||
\(982\) | −84.9200 | −2.70991 | ||||||||
\(983\) | −41.7342 | −1.33111 | −0.665557 | − | 0.746347i | \(-0.731806\pi\) | ||||
−0.665557 | + | 0.746347i | \(0.731806\pi\) | |||||||
\(984\) | 86.3941 | 2.75414 | ||||||||
\(985\) | 1.07786 | 0.0343434 | ||||||||
\(986\) | 8.15423 | 0.259684 | ||||||||
\(987\) | 13.2941 | 0.423156 | ||||||||
\(988\) | 49.3449 | 1.56987 | ||||||||
\(989\) | 7.38378 | 0.234791 | ||||||||
\(990\) | 76.3523 | 2.42664 | ||||||||
\(991\) | −37.9590 | −1.20581 | −0.602904 | − | 0.797814i | \(-0.705990\pi\) | ||||
−0.602904 | + | 0.797814i | \(0.705990\pi\) | |||||||
\(992\) | −11.2485 | −0.357139 | ||||||||
\(993\) | −60.7558 | −1.92803 | ||||||||
\(994\) | −44.4854 | −1.41099 | ||||||||
\(995\) | 27.0455 | 0.857401 | ||||||||
\(996\) | 80.7411 | 2.55838 | ||||||||
\(997\) | 54.0626 | 1.71218 | 0.856090 | − | 0.516827i | \(-0.172887\pi\) | ||||
0.856090 | + | 0.516827i | \(0.172887\pi\) | |||||||
\(998\) | −51.6225 | −1.63408 | ||||||||
\(999\) | 90.8015 | 2.87283 |
(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 | 6017.2.a.f.1.15 | ✓ | 121 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6017.2.a.f.1.15 | ✓ | 121 | 1.1 | even | 1 | trivial |