Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4033,2,Mod(1,4033)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4033, 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("4033.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4033 = 37 \cdot 109 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4033.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: | \(32.2036671352\) |
Analytic rank: | \(0\) |
Dimension: | \(82\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.18 | ||
Character | \(\chi\) | \(=\) | 4033.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.58741 | −1.12247 | −0.561234 | − | 0.827657i | \(-0.689673\pi\) | ||||
−0.561234 | + | 0.827657i | \(0.689673\pi\) | |||||||
\(3\) | −1.76709 | −1.02023 | −0.510114 | − | 0.860107i | \(-0.670397\pi\) | ||||
−0.510114 | + | 0.860107i | \(0.670397\pi\) | |||||||
\(4\) | 0.519871 | 0.259935 | ||||||||
\(5\) | 4.42213 | 1.97764 | 0.988818 | − | 0.149126i | \(-0.0476459\pi\) | ||||
0.988818 | + | 0.149126i | \(0.0476459\pi\) | |||||||
\(6\) | 2.80509 | 1.14517 | ||||||||
\(7\) | 5.11364 | 1.93277 | 0.966387 | − | 0.257092i | \(-0.0827643\pi\) | ||||
0.966387 | + | 0.257092i | \(0.0827643\pi\) | |||||||
\(8\) | 2.34957 | 0.830699 | ||||||||
\(9\) | 0.122598 | 0.0408662 | ||||||||
\(10\) | −7.01973 | −2.21983 | ||||||||
\(11\) | 2.77837 | 0.837711 | 0.418856 | − | 0.908053i | \(-0.362431\pi\) | ||||
0.418856 | + | 0.908053i | \(0.362431\pi\) | |||||||
\(12\) | −0.918658 | −0.265194 | ||||||||
\(13\) | 3.42651 | 0.950342 | 0.475171 | − | 0.879893i | \(-0.342386\pi\) | ||||
0.475171 | + | 0.879893i | \(0.342386\pi\) | |||||||
\(14\) | −8.11744 | −2.16948 | ||||||||
\(15\) | −7.81429 | −2.01764 | ||||||||
\(16\) | −4.76948 | −1.19237 | ||||||||
\(17\) | −1.72760 | −0.419004 | −0.209502 | − | 0.977808i | \(-0.567184\pi\) | ||||
−0.209502 | + | 0.977808i | \(0.567184\pi\) | |||||||
\(18\) | −0.194614 | −0.0458710 | ||||||||
\(19\) | −0.486137 | −0.111527 | −0.0557637 | − | 0.998444i | \(-0.517759\pi\) | ||||
−0.0557637 | + | 0.998444i | \(0.517759\pi\) | |||||||
\(20\) | 2.29894 | 0.514058 | ||||||||
\(21\) | −9.03625 | −1.97187 | ||||||||
\(22\) | −4.41042 | −0.940304 | ||||||||
\(23\) | −1.12174 | −0.233898 | −0.116949 | − | 0.993138i | \(-0.537311\pi\) | ||||
−0.116949 | + | 0.993138i | \(0.537311\pi\) | |||||||
\(24\) | −4.15190 | −0.847503 | ||||||||
\(25\) | 14.5552 | 2.91105 | ||||||||
\(26\) | −5.43927 | −1.06673 | ||||||||
\(27\) | 5.08462 | 0.978536 | ||||||||
\(28\) | 2.65843 | 0.502397 | ||||||||
\(29\) | −5.83305 | −1.08317 | −0.541585 | − | 0.840646i | \(-0.682176\pi\) | ||||
−0.541585 | + | 0.840646i | \(0.682176\pi\) | |||||||
\(30\) | 12.4045 | 2.26474 | ||||||||
\(31\) | −1.64580 | −0.295595 | −0.147797 | − | 0.989018i | \(-0.547218\pi\) | ||||
−0.147797 | + | 0.989018i | \(0.547218\pi\) | |||||||
\(32\) | 2.87197 | 0.507698 | ||||||||
\(33\) | −4.90963 | −0.854657 | ||||||||
\(34\) | 2.74241 | 0.470319 | ||||||||
\(35\) | 22.6132 | 3.82232 | ||||||||
\(36\) | 0.0637354 | 0.0106226 | ||||||||
\(37\) | −1.00000 | −0.164399 | ||||||||
\(38\) | 0.771699 | 0.125186 | ||||||||
\(39\) | −6.05494 | −0.969566 | ||||||||
\(40\) | 10.3901 | 1.64282 | ||||||||
\(41\) | 11.7093 | 1.82869 | 0.914345 | − | 0.404935i | \(-0.132706\pi\) | ||||
0.914345 | + | 0.404935i | \(0.132706\pi\) | |||||||
\(42\) | 14.3442 | 2.21336 | ||||||||
\(43\) | −10.9423 | −1.66868 | −0.834340 | − | 0.551250i | \(-0.814151\pi\) | ||||
−0.834340 | + | 0.551250i | \(0.814151\pi\) | |||||||
\(44\) | 1.44440 | 0.217751 | ||||||||
\(45\) | 0.542146 | 0.0808184 | ||||||||
\(46\) | 1.78066 | 0.262544 | ||||||||
\(47\) | 8.57759 | 1.25117 | 0.625585 | − | 0.780156i | \(-0.284860\pi\) | ||||
0.625585 | + | 0.780156i | \(0.284860\pi\) | |||||||
\(48\) | 8.42808 | 1.21649 | ||||||||
\(49\) | 19.1493 | 2.73561 | ||||||||
\(50\) | −23.1051 | −3.26756 | ||||||||
\(51\) | 3.05282 | 0.427480 | ||||||||
\(52\) | 1.78134 | 0.247028 | ||||||||
\(53\) | −6.03514 | −0.828990 | −0.414495 | − | 0.910052i | \(-0.636042\pi\) | ||||
−0.414495 | + | 0.910052i | \(0.636042\pi\) | |||||||
\(54\) | −8.07138 | −1.09838 | ||||||||
\(55\) | 12.2863 | 1.65669 | ||||||||
\(56\) | 12.0149 | 1.60555 | ||||||||
\(57\) | 0.859047 | 0.113784 | ||||||||
\(58\) | 9.25944 | 1.21582 | ||||||||
\(59\) | 10.6848 | 1.39105 | 0.695523 | − | 0.718504i | \(-0.255173\pi\) | ||||
0.695523 | + | 0.718504i | \(0.255173\pi\) | |||||||
\(60\) | −4.06242 | −0.524457 | ||||||||
\(61\) | −6.45823 | −0.826892 | −0.413446 | − | 0.910529i | \(-0.635675\pi\) | ||||
−0.413446 | + | 0.910529i | \(0.635675\pi\) | |||||||
\(62\) | 2.61256 | 0.331796 | ||||||||
\(63\) | 0.626924 | 0.0789850 | ||||||||
\(64\) | 4.97996 | 0.622494 | ||||||||
\(65\) | 15.1525 | 1.87943 | ||||||||
\(66\) | 7.79360 | 0.959325 | ||||||||
\(67\) | 9.21587 | 1.12590 | 0.562949 | − | 0.826492i | \(-0.309667\pi\) | ||||
0.562949 | + | 0.826492i | \(0.309667\pi\) | |||||||
\(68\) | −0.898128 | −0.108914 | ||||||||
\(69\) | 1.98221 | 0.238630 | ||||||||
\(70\) | −35.8964 | −4.29044 | ||||||||
\(71\) | −5.14194 | −0.610236 | −0.305118 | − | 0.952314i | \(-0.598696\pi\) | ||||
−0.305118 | + | 0.952314i | \(0.598696\pi\) | |||||||
\(72\) | 0.288054 | 0.0339475 | ||||||||
\(73\) | −6.51491 | −0.762513 | −0.381256 | − | 0.924469i | \(-0.624508\pi\) | ||||
−0.381256 | + | 0.924469i | \(0.624508\pi\) | |||||||
\(74\) | 1.58741 | 0.184533 | ||||||||
\(75\) | −25.7204 | −2.96993 | ||||||||
\(76\) | −0.252729 | −0.0289899 | ||||||||
\(77\) | 14.2076 | 1.61911 | ||||||||
\(78\) | 9.61167 | 1.08831 | ||||||||
\(79\) | 9.01818 | 1.01462 | 0.507312 | − | 0.861762i | \(-0.330639\pi\) | ||||
0.507312 | + | 0.861762i | \(0.330639\pi\) | |||||||
\(80\) | −21.0912 | −2.35807 | ||||||||
\(81\) | −9.35277 | −1.03920 | ||||||||
\(82\) | −18.5875 | −2.05265 | ||||||||
\(83\) | −4.19788 | −0.460777 | −0.230388 | − | 0.973099i | \(-0.574000\pi\) | ||||
−0.230388 | + | 0.973099i | \(0.574000\pi\) | |||||||
\(84\) | −4.69768 | −0.512559 | ||||||||
\(85\) | −7.63966 | −0.828638 | ||||||||
\(86\) | 17.3699 | 1.87304 | ||||||||
\(87\) | 10.3075 | 1.10508 | ||||||||
\(88\) | 6.52799 | 0.695886 | ||||||||
\(89\) | 13.6231 | 1.44405 | 0.722023 | − | 0.691869i | \(-0.243213\pi\) | ||||
0.722023 | + | 0.691869i | \(0.243213\pi\) | |||||||
\(90\) | −0.860609 | −0.0907161 | ||||||||
\(91\) | 17.5219 | 1.83680 | ||||||||
\(92\) | −0.583159 | −0.0607985 | ||||||||
\(93\) | 2.90828 | 0.301574 | ||||||||
\(94\) | −13.6162 | −1.40440 | ||||||||
\(95\) | −2.14976 | −0.220561 | ||||||||
\(96\) | −5.07502 | −0.517968 | ||||||||
\(97\) | 4.16270 | 0.422658 | 0.211329 | − | 0.977415i | \(-0.432221\pi\) | ||||
0.211329 | + | 0.977415i | \(0.432221\pi\) | |||||||
\(98\) | −30.3978 | −3.07064 | ||||||||
\(99\) | 0.340624 | 0.0342340 | ||||||||
\(100\) | 7.56684 | 0.756684 | ||||||||
\(101\) | −14.3403 | −1.42691 | −0.713457 | − | 0.700699i | \(-0.752872\pi\) | ||||
−0.713457 | + | 0.700699i | \(0.752872\pi\) | |||||||
\(102\) | −4.84607 | −0.479833 | ||||||||
\(103\) | −6.59348 | −0.649675 | −0.324838 | − | 0.945770i | \(-0.605310\pi\) | ||||
−0.324838 | + | 0.945770i | \(0.605310\pi\) | |||||||
\(104\) | 8.05083 | 0.789448 | ||||||||
\(105\) | −39.9595 | −3.89964 | ||||||||
\(106\) | 9.58024 | 0.930515 | ||||||||
\(107\) | −12.4197 | −1.20066 | −0.600328 | − | 0.799754i | \(-0.704963\pi\) | ||||
−0.600328 | + | 0.799754i | \(0.704963\pi\) | |||||||
\(108\) | 2.64335 | 0.254356 | ||||||||
\(109\) | 1.00000 | 0.0957826 | ||||||||
\(110\) | −19.5034 | −1.85958 | ||||||||
\(111\) | 1.76709 | 0.167725 | ||||||||
\(112\) | −24.3894 | −2.30458 | ||||||||
\(113\) | 6.88445 | 0.647634 | 0.323817 | − | 0.946120i | \(-0.395034\pi\) | ||||
0.323817 | + | 0.946120i | \(0.395034\pi\) | |||||||
\(114\) | −1.36366 | −0.127718 | ||||||||
\(115\) | −4.96047 | −0.462566 | ||||||||
\(116\) | −3.03243 | −0.281554 | ||||||||
\(117\) | 0.420085 | 0.0388368 | ||||||||
\(118\) | −16.9612 | −1.56141 | ||||||||
\(119\) | −8.83431 | −0.809840 | ||||||||
\(120\) | −18.3602 | −1.67605 | ||||||||
\(121\) | −3.28064 | −0.298240 | ||||||||
\(122\) | 10.2519 | 0.928160 | ||||||||
\(123\) | −20.6914 | −1.86568 | ||||||||
\(124\) | −0.855605 | −0.0768356 | ||||||||
\(125\) | 42.2545 | 3.77935 | ||||||||
\(126\) | −0.995186 | −0.0886582 | ||||||||
\(127\) | −1.11615 | −0.0990420 | −0.0495210 | − | 0.998773i | \(-0.515769\pi\) | ||||
−0.0495210 | + | 0.998773i | \(0.515769\pi\) | |||||||
\(128\) | −13.6492 | −1.20643 | ||||||||
\(129\) | 19.3359 | 1.70243 | ||||||||
\(130\) | −24.0532 | −2.10960 | ||||||||
\(131\) | 6.75498 | 0.590185 | 0.295093 | − | 0.955469i | \(-0.404649\pi\) | ||||
0.295093 | + | 0.955469i | \(0.404649\pi\) | |||||||
\(132\) | −2.55237 | −0.222156 | ||||||||
\(133\) | −2.48593 | −0.215557 | ||||||||
\(134\) | −14.6294 | −1.26378 | ||||||||
\(135\) | 22.4849 | 1.93519 | ||||||||
\(136\) | −4.05912 | −0.348066 | ||||||||
\(137\) | −1.65774 | −0.141630 | −0.0708151 | − | 0.997489i | \(-0.522560\pi\) | ||||
−0.0708151 | + | 0.997489i | \(0.522560\pi\) | |||||||
\(138\) | −3.14658 | −0.267854 | ||||||||
\(139\) | 3.91965 | 0.332461 | 0.166230 | − | 0.986087i | \(-0.446840\pi\) | ||||
0.166230 | + | 0.986087i | \(0.446840\pi\) | |||||||
\(140\) | 11.7559 | 0.993558 | ||||||||
\(141\) | −15.1574 | −1.27648 | ||||||||
\(142\) | 8.16237 | 0.684971 | ||||||||
\(143\) | 9.52012 | 0.796112 | ||||||||
\(144\) | −0.584730 | −0.0487275 | ||||||||
\(145\) | −25.7945 | −2.14212 | ||||||||
\(146\) | 10.3418 | 0.855896 | ||||||||
\(147\) | −33.8385 | −2.79095 | ||||||||
\(148\) | −0.519871 | −0.0427331 | ||||||||
\(149\) | −20.7255 | −1.69790 | −0.848949 | − | 0.528474i | \(-0.822764\pi\) | ||||
−0.848949 | + | 0.528474i | \(0.822764\pi\) | |||||||
\(150\) | 40.8288 | 3.33366 | ||||||||
\(151\) | −3.07484 | −0.250227 | −0.125114 | − | 0.992142i | \(-0.539930\pi\) | ||||
−0.125114 | + | 0.992142i | \(0.539930\pi\) | |||||||
\(152\) | −1.14221 | −0.0926458 | ||||||||
\(153\) | −0.211801 | −0.0171231 | ||||||||
\(154\) | −22.5533 | −1.81740 | ||||||||
\(155\) | −7.27795 | −0.584579 | ||||||||
\(156\) | −3.14779 | −0.252025 | ||||||||
\(157\) | −0.520753 | −0.0415606 | −0.0207803 | − | 0.999784i | \(-0.506615\pi\) | ||||
−0.0207803 | + | 0.999784i | \(0.506615\pi\) | |||||||
\(158\) | −14.3155 | −1.13888 | ||||||||
\(159\) | 10.6646 | 0.845759 | ||||||||
\(160\) | 12.7002 | 1.00404 | ||||||||
\(161\) | −5.73616 | −0.452073 | ||||||||
\(162\) | 14.8467 | 1.16646 | ||||||||
\(163\) | 7.29872 | 0.571680 | 0.285840 | − | 0.958277i | \(-0.407727\pi\) | ||||
0.285840 | + | 0.958277i | \(0.407727\pi\) | |||||||
\(164\) | 6.08734 | 0.475342 | ||||||||
\(165\) | −21.7110 | −1.69020 | ||||||||
\(166\) | 6.66375 | 0.517207 | ||||||||
\(167\) | −10.1775 | −0.787561 | −0.393781 | − | 0.919204i | \(-0.628833\pi\) | ||||
−0.393781 | + | 0.919204i | \(0.628833\pi\) | |||||||
\(168\) | −21.2313 | −1.63803 | ||||||||
\(169\) | −1.25905 | −0.0968497 | ||||||||
\(170\) | 12.1273 | 0.930120 | ||||||||
\(171\) | −0.0595997 | −0.00455770 | ||||||||
\(172\) | −5.68857 | −0.433749 | ||||||||
\(173\) | −19.8165 | −1.50662 | −0.753309 | − | 0.657667i | \(-0.771544\pi\) | ||||
−0.753309 | + | 0.657667i | \(0.771544\pi\) | |||||||
\(174\) | −16.3622 | −1.24042 | ||||||||
\(175\) | 74.4302 | 5.62639 | ||||||||
\(176\) | −13.2514 | −0.998861 | ||||||||
\(177\) | −18.8810 | −1.41919 | ||||||||
\(178\) | −21.6254 | −1.62090 | ||||||||
\(179\) | 10.1010 | 0.754981 | 0.377491 | − | 0.926013i | \(-0.376787\pi\) | ||||
0.377491 | + | 0.926013i | \(0.376787\pi\) | |||||||
\(180\) | 0.281846 | 0.0210076 | ||||||||
\(181\) | −11.3631 | −0.844616 | −0.422308 | − | 0.906452i | \(-0.638780\pi\) | ||||
−0.422308 | + | 0.906452i | \(0.638780\pi\) | |||||||
\(182\) | −27.8145 | −2.06175 | ||||||||
\(183\) | 11.4123 | 0.843619 | ||||||||
\(184\) | −2.63560 | −0.194299 | ||||||||
\(185\) | −4.42213 | −0.325121 | ||||||||
\(186\) | −4.61663 | −0.338508 | ||||||||
\(187\) | −4.79991 | −0.351004 | ||||||||
\(188\) | 4.45924 | 0.325224 | ||||||||
\(189\) | 26.0009 | 1.89129 | ||||||||
\(190\) | 3.41255 | 0.247573 | ||||||||
\(191\) | 11.5261 | 0.833998 | 0.416999 | − | 0.908907i | \(-0.363082\pi\) | ||||
0.416999 | + | 0.908907i | \(0.363082\pi\) | |||||||
\(192\) | −8.80002 | −0.635087 | ||||||||
\(193\) | 19.2702 | 1.38710 | 0.693549 | − | 0.720410i | \(-0.256046\pi\) | ||||
0.693549 | + | 0.720410i | \(0.256046\pi\) | |||||||
\(194\) | −6.60792 | −0.474421 | ||||||||
\(195\) | −26.7757 | −1.91745 | ||||||||
\(196\) | 9.95517 | 0.711083 | ||||||||
\(197\) | 12.7645 | 0.909432 | 0.454716 | − | 0.890637i | \(-0.349741\pi\) | ||||
0.454716 | + | 0.890637i | \(0.349741\pi\) | |||||||
\(198\) | −0.540711 | −0.0384266 | ||||||||
\(199\) | −8.52369 | −0.604229 | −0.302114 | − | 0.953272i | \(-0.597692\pi\) | ||||
−0.302114 | + | 0.953272i | \(0.597692\pi\) | |||||||
\(200\) | 34.1986 | 2.41820 | ||||||||
\(201\) | −16.2852 | −1.14867 | ||||||||
\(202\) | 22.7639 | 1.60167 | ||||||||
\(203\) | −29.8281 | −2.09352 | ||||||||
\(204\) | 1.58707 | 0.111117 | ||||||||
\(205\) | 51.7802 | 3.61649 | ||||||||
\(206\) | 10.4666 | 0.729240 | ||||||||
\(207\) | −0.137523 | −0.00955853 | ||||||||
\(208\) | −16.3426 | −1.13316 | ||||||||
\(209\) | −1.35067 | −0.0934278 | ||||||||
\(210\) | 63.4321 | 4.37723 | ||||||||
\(211\) | 25.2348 | 1.73724 | 0.868618 | − | 0.495483i | \(-0.165009\pi\) | ||||
0.868618 | + | 0.495483i | \(0.165009\pi\) | |||||||
\(212\) | −3.13749 | −0.215484 | ||||||||
\(213\) | 9.08626 | 0.622581 | ||||||||
\(214\) | 19.7151 | 1.34770 | ||||||||
\(215\) | −48.3881 | −3.30004 | ||||||||
\(216\) | 11.9467 | 0.812869 | ||||||||
\(217\) | −8.41604 | −0.571318 | ||||||||
\(218\) | −1.58741 | −0.107513 | ||||||||
\(219\) | 11.5124 | 0.777937 | ||||||||
\(220\) | 6.38731 | 0.430632 | ||||||||
\(221\) | −5.91963 | −0.398197 | ||||||||
\(222\) | −2.80509 | −0.188265 | ||||||||
\(223\) | 21.7036 | 1.45338 | 0.726692 | − | 0.686964i | \(-0.241057\pi\) | ||||
0.726692 | + | 0.686964i | \(0.241057\pi\) | |||||||
\(224\) | 14.6862 | 0.981265 | ||||||||
\(225\) | 1.78445 | 0.118963 | ||||||||
\(226\) | −10.9284 | −0.726949 | ||||||||
\(227\) | −27.4608 | −1.82264 | −0.911318 | − | 0.411704i | \(-0.864934\pi\) | ||||
−0.911318 | + | 0.411704i | \(0.864934\pi\) | |||||||
\(228\) | 0.446593 | 0.0295764 | ||||||||
\(229\) | 13.8667 | 0.916337 | 0.458169 | − | 0.888865i | \(-0.348506\pi\) | ||||
0.458169 | + | 0.888865i | \(0.348506\pi\) | |||||||
\(230\) | 7.87430 | 0.519216 | ||||||||
\(231\) | −25.1061 | −1.65186 | ||||||||
\(232\) | −13.7052 | −0.899788 | ||||||||
\(233\) | 11.6555 | 0.763574 | 0.381787 | − | 0.924250i | \(-0.375309\pi\) | ||||
0.381787 | + | 0.924250i | \(0.375309\pi\) | |||||||
\(234\) | −0.666847 | −0.0435931 | ||||||||
\(235\) | 37.9312 | 2.47436 | ||||||||
\(236\) | 5.55473 | 0.361582 | ||||||||
\(237\) | −15.9359 | −1.03515 | ||||||||
\(238\) | 14.0237 | 0.909020 | ||||||||
\(239\) | −13.3886 | −0.866039 | −0.433020 | − | 0.901385i | \(-0.642552\pi\) | ||||
−0.433020 | + | 0.901385i | \(0.642552\pi\) | |||||||
\(240\) | 37.2701 | 2.40577 | ||||||||
\(241\) | −18.1093 | −1.16652 | −0.583261 | − | 0.812285i | \(-0.698223\pi\) | ||||
−0.583261 | + | 0.812285i | \(0.698223\pi\) | |||||||
\(242\) | 5.20772 | 0.334765 | ||||||||
\(243\) | 1.27329 | 0.0816818 | ||||||||
\(244\) | −3.35745 | −0.214939 | ||||||||
\(245\) | 84.6807 | 5.41005 | ||||||||
\(246\) | 32.8458 | 2.09417 | ||||||||
\(247\) | −1.66575 | −0.105989 | ||||||||
\(248\) | −3.86693 | −0.245550 | ||||||||
\(249\) | 7.41802 | 0.470098 | ||||||||
\(250\) | −67.0752 | −4.24221 | ||||||||
\(251\) | 1.12054 | 0.0707276 | 0.0353638 | − | 0.999375i | \(-0.488741\pi\) | ||||
0.0353638 | + | 0.999375i | \(0.488741\pi\) | |||||||
\(252\) | 0.325920 | 0.0205310 | ||||||||
\(253\) | −3.11661 | −0.195939 | ||||||||
\(254\) | 1.77178 | 0.111172 | ||||||||
\(255\) | 13.5000 | 0.845400 | ||||||||
\(256\) | 11.7069 | 0.731683 | ||||||||
\(257\) | 19.0728 | 1.18973 | 0.594864 | − | 0.803826i | \(-0.297206\pi\) | ||||
0.594864 | + | 0.803826i | \(0.297206\pi\) | |||||||
\(258\) | −30.6941 | −1.91093 | ||||||||
\(259\) | −5.11364 | −0.317746 | ||||||||
\(260\) | 7.87732 | 0.488531 | ||||||||
\(261\) | −0.715123 | −0.0442650 | ||||||||
\(262\) | −10.7229 | −0.662465 | ||||||||
\(263\) | 5.92816 | 0.365546 | 0.182773 | − | 0.983155i | \(-0.441493\pi\) | ||||
0.182773 | + | 0.983155i | \(0.441493\pi\) | |||||||
\(264\) | −11.5355 | −0.709963 | ||||||||
\(265\) | −26.6882 | −1.63944 | ||||||||
\(266\) | 3.94619 | 0.241956 | ||||||||
\(267\) | −24.0732 | −1.47326 | ||||||||
\(268\) | 4.79106 | 0.292661 | ||||||||
\(269\) | 4.87237 | 0.297073 | 0.148537 | − | 0.988907i | \(-0.452544\pi\) | ||||
0.148537 | + | 0.988907i | \(0.452544\pi\) | |||||||
\(270\) | −35.6927 | −2.17219 | ||||||||
\(271\) | −28.0688 | −1.70506 | −0.852529 | − | 0.522679i | \(-0.824932\pi\) | ||||
−0.852529 | + | 0.522679i | \(0.824932\pi\) | |||||||
\(272\) | 8.23974 | 0.499608 | ||||||||
\(273\) | −30.9628 | −1.87395 | ||||||||
\(274\) | 2.63151 | 0.158975 | ||||||||
\(275\) | 40.4399 | 2.43862 | ||||||||
\(276\) | 1.03049 | 0.0620284 | ||||||||
\(277\) | −12.2931 | −0.738624 | −0.369312 | − | 0.929306i | \(-0.620407\pi\) | ||||
−0.369312 | + | 0.929306i | \(0.620407\pi\) | |||||||
\(278\) | −6.22210 | −0.373177 | ||||||||
\(279\) | −0.201773 | −0.0120798 | ||||||||
\(280\) | 53.1313 | 3.17520 | ||||||||
\(281\) | −10.3174 | −0.615486 | −0.307743 | − | 0.951470i | \(-0.599574\pi\) | ||||
−0.307743 | + | 0.951470i | \(0.599574\pi\) | |||||||
\(282\) | 24.0609 | 1.43281 | ||||||||
\(283\) | −13.3640 | −0.794407 | −0.397203 | − | 0.917731i | \(-0.630019\pi\) | ||||
−0.397203 | + | 0.917731i | \(0.630019\pi\) | |||||||
\(284\) | −2.67315 | −0.158622 | ||||||||
\(285\) | 3.79882 | 0.225022 | ||||||||
\(286\) | −15.1123 | −0.893611 | ||||||||
\(287\) | 59.8773 | 3.53445 | ||||||||
\(288\) | 0.352099 | 0.0207476 | ||||||||
\(289\) | −14.0154 | −0.824436 | ||||||||
\(290\) | 40.9464 | 2.40446 | ||||||||
\(291\) | −7.35586 | −0.431208 | ||||||||
\(292\) | −3.38691 | −0.198204 | ||||||||
\(293\) | −9.31413 | −0.544138 | −0.272069 | − | 0.962278i | \(-0.587708\pi\) | ||||
−0.272069 | + | 0.962278i | \(0.587708\pi\) | |||||||
\(294\) | 53.7156 | 3.13276 | ||||||||
\(295\) | 47.2497 | 2.75098 | ||||||||
\(296\) | −2.34957 | −0.136566 | ||||||||
\(297\) | 14.1270 | 0.819730 | ||||||||
\(298\) | 32.8999 | 1.90584 | ||||||||
\(299\) | −3.84364 | −0.222284 | ||||||||
\(300\) | −13.3713 | −0.771991 | ||||||||
\(301\) | −55.9548 | −3.22518 | ||||||||
\(302\) | 4.88103 | 0.280872 | ||||||||
\(303\) | 25.3406 | 1.45578 | ||||||||
\(304\) | 2.31862 | 0.132982 | ||||||||
\(305\) | −28.5591 | −1.63529 | ||||||||
\(306\) | 0.336215 | 0.0192201 | ||||||||
\(307\) | −20.7612 | −1.18490 | −0.592451 | − | 0.805606i | \(-0.701840\pi\) | ||||
−0.592451 | + | 0.805606i | \(0.701840\pi\) | |||||||
\(308\) | 7.38612 | 0.420863 | ||||||||
\(309\) | 11.6513 | 0.662817 | ||||||||
\(310\) | 11.5531 | 0.656172 | ||||||||
\(311\) | 19.7030 | 1.11726 | 0.558628 | − | 0.829418i | \(-0.311328\pi\) | ||||
0.558628 | + | 0.829418i | \(0.311328\pi\) | |||||||
\(312\) | −14.2265 | −0.805418 | ||||||||
\(313\) | −19.9593 | −1.12816 | −0.564082 | − | 0.825719i | \(-0.690770\pi\) | ||||
−0.564082 | + | 0.825719i | \(0.690770\pi\) | |||||||
\(314\) | 0.826648 | 0.0466504 | ||||||||
\(315\) | 2.77234 | 0.156204 | ||||||||
\(316\) | 4.68829 | 0.263737 | ||||||||
\(317\) | −13.5256 | −0.759675 | −0.379838 | − | 0.925053i | \(-0.624020\pi\) | ||||
−0.379838 | + | 0.925053i | \(0.624020\pi\) | |||||||
\(318\) | −16.9291 | −0.949338 | ||||||||
\(319\) | −16.2064 | −0.907384 | ||||||||
\(320\) | 22.0220 | 1.23107 | ||||||||
\(321\) | 21.9467 | 1.22494 | ||||||||
\(322\) | 9.10564 | 0.507437 | ||||||||
\(323\) | 0.839849 | 0.0467305 | ||||||||
\(324\) | −4.86223 | −0.270124 | ||||||||
\(325\) | 49.8736 | 2.76649 | ||||||||
\(326\) | −11.5861 | −0.641692 | ||||||||
\(327\) | −1.76709 | −0.0977202 | ||||||||
\(328\) | 27.5119 | 1.51909 | ||||||||
\(329\) | 43.8627 | 2.41823 | ||||||||
\(330\) | 34.4643 | 1.89720 | ||||||||
\(331\) | 17.7616 | 0.976268 | 0.488134 | − | 0.872769i | \(-0.337678\pi\) | ||||
0.488134 | + | 0.872769i | \(0.337678\pi\) | |||||||
\(332\) | −2.18235 | −0.119772 | ||||||||
\(333\) | −0.122598 | −0.00671835 | ||||||||
\(334\) | 16.1559 | 0.884013 | ||||||||
\(335\) | 40.7538 | 2.22662 | ||||||||
\(336\) | 43.0982 | 2.35120 | ||||||||
\(337\) | 21.8009 | 1.18757 | 0.593786 | − | 0.804623i | \(-0.297633\pi\) | ||||
0.593786 | + | 0.804623i | \(0.297633\pi\) | |||||||
\(338\) | 1.99862 | 0.108711 | ||||||||
\(339\) | −12.1654 | −0.660735 | ||||||||
\(340\) | −3.97164 | −0.215392 | ||||||||
\(341\) | −4.57266 | −0.247623 | ||||||||
\(342\) | 0.0946091 | 0.00511587 | ||||||||
\(343\) | 62.1272 | 3.35455 | ||||||||
\(344\) | −25.7096 | −1.38617 | ||||||||
\(345\) | 8.76558 | 0.471923 | ||||||||
\(346\) | 31.4569 | 1.69113 | ||||||||
\(347\) | 3.17023 | 0.170187 | 0.0850933 | − | 0.996373i | \(-0.472881\pi\) | ||||
0.0850933 | + | 0.996373i | \(0.472881\pi\) | |||||||
\(348\) | 5.35857 | 0.287250 | ||||||||
\(349\) | −5.31212 | −0.284351 | −0.142176 | − | 0.989841i | \(-0.545410\pi\) | ||||
−0.142176 | + | 0.989841i | \(0.545410\pi\) | |||||||
\(350\) | −118.151 | −6.31545 | ||||||||
\(351\) | 17.4225 | 0.929944 | ||||||||
\(352\) | 7.97941 | 0.425304 | ||||||||
\(353\) | 11.1143 | 0.591556 | 0.295778 | − | 0.955257i | \(-0.404421\pi\) | ||||
0.295778 | + | 0.955257i | \(0.404421\pi\) | |||||||
\(354\) | 29.9719 | 1.59299 | ||||||||
\(355\) | −22.7383 | −1.20683 | ||||||||
\(356\) | 7.08225 | 0.375359 | ||||||||
\(357\) | 15.6110 | 0.826222 | ||||||||
\(358\) | −16.0344 | −0.847443 | ||||||||
\(359\) | 6.58045 | 0.347303 | 0.173651 | − | 0.984807i | \(-0.444443\pi\) | ||||
0.173651 | + | 0.984807i | \(0.444443\pi\) | |||||||
\(360\) | 1.27381 | 0.0671358 | ||||||||
\(361\) | −18.7637 | −0.987562 | ||||||||
\(362\) | 18.0380 | 0.948055 | ||||||||
\(363\) | 5.79718 | 0.304273 | ||||||||
\(364\) | 9.10914 | 0.477449 | ||||||||
\(365\) | −28.8098 | −1.50797 | ||||||||
\(366\) | −18.1159 | −0.946936 | ||||||||
\(367\) | −1.92109 | −0.100280 | −0.0501401 | − | 0.998742i | \(-0.515967\pi\) | ||||
−0.0501401 | + | 0.998742i | \(0.515967\pi\) | |||||||
\(368\) | 5.35010 | 0.278893 | ||||||||
\(369\) | 1.43555 | 0.0747316 | ||||||||
\(370\) | 7.01973 | 0.364939 | ||||||||
\(371\) | −30.8615 | −1.60225 | ||||||||
\(372\) | 1.51193 | 0.0783899 | ||||||||
\(373\) | 9.79966 | 0.507407 | 0.253703 | − | 0.967282i | \(-0.418351\pi\) | ||||
0.253703 | + | 0.967282i | \(0.418351\pi\) | |||||||
\(374\) | 7.61943 | 0.393991 | ||||||||
\(375\) | −74.6674 | −3.85581 | ||||||||
\(376\) | 20.1537 | 1.03935 | ||||||||
\(377\) | −19.9870 | −1.02938 | ||||||||
\(378\) | −41.2741 | −2.12291 | ||||||||
\(379\) | 11.4383 | 0.587545 | 0.293772 | − | 0.955875i | \(-0.405089\pi\) | ||||
0.293772 | + | 0.955875i | \(0.405089\pi\) | |||||||
\(380\) | −1.11760 | −0.0573316 | ||||||||
\(381\) | 1.97233 | 0.101045 | ||||||||
\(382\) | −18.2966 | −0.936136 | ||||||||
\(383\) | 24.8518 | 1.26987 | 0.634933 | − | 0.772567i | \(-0.281027\pi\) | ||||
0.634933 | + | 0.772567i | \(0.281027\pi\) | |||||||
\(384\) | 24.1193 | 1.23083 | ||||||||
\(385\) | 62.8279 | 3.20200 | ||||||||
\(386\) | −30.5897 | −1.55697 | ||||||||
\(387\) | −1.34150 | −0.0681925 | ||||||||
\(388\) | 2.16407 | 0.109864 | ||||||||
\(389\) | 14.9924 | 0.760145 | 0.380072 | − | 0.924957i | \(-0.375899\pi\) | ||||
0.380072 | + | 0.924957i | \(0.375899\pi\) | |||||||
\(390\) | 42.5041 | 2.15228 | ||||||||
\(391\) | 1.93791 | 0.0980044 | ||||||||
\(392\) | 44.9927 | 2.27247 | ||||||||
\(393\) | −11.9366 | −0.602124 | ||||||||
\(394\) | −20.2625 | −1.02081 | ||||||||
\(395\) | 39.8796 | 2.00656 | ||||||||
\(396\) | 0.177081 | 0.00889864 | ||||||||
\(397\) | −20.8047 | −1.04416 | −0.522080 | − | 0.852897i | \(-0.674844\pi\) | ||||
−0.522080 | + | 0.852897i | \(0.674844\pi\) | |||||||
\(398\) | 13.5306 | 0.678228 | ||||||||
\(399\) | 4.39285 | 0.219918 | ||||||||
\(400\) | −69.4208 | −3.47104 | ||||||||
\(401\) | −23.0011 | −1.14862 | −0.574310 | − | 0.818638i | \(-0.694730\pi\) | ||||
−0.574310 | + | 0.818638i | \(0.694730\pi\) | |||||||
\(402\) | 25.8514 | 1.28935 | ||||||||
\(403\) | −5.63936 | −0.280916 | ||||||||
\(404\) | −7.45511 | −0.370906 | ||||||||
\(405\) | −41.3591 | −2.05515 | ||||||||
\(406\) | 47.3494 | 2.34991 | ||||||||
\(407\) | −2.77837 | −0.137719 | ||||||||
\(408\) | 7.17281 | 0.355107 | ||||||||
\(409\) | −28.7199 | −1.42011 | −0.710053 | − | 0.704148i | \(-0.751329\pi\) | ||||
−0.710053 | + | 0.704148i | \(0.751329\pi\) | |||||||
\(410\) | −82.1964 | −4.05939 | ||||||||
\(411\) | 2.92937 | 0.144495 | ||||||||
\(412\) | −3.42776 | −0.168874 | ||||||||
\(413\) | 54.6384 | 2.68858 | ||||||||
\(414\) | 0.218306 | 0.0107291 | ||||||||
\(415\) | −18.5636 | −0.911249 | ||||||||
\(416\) | 9.84083 | 0.482486 | ||||||||
\(417\) | −6.92637 | −0.339186 | ||||||||
\(418\) | 2.14407 | 0.104870 | ||||||||
\(419\) | 7.51258 | 0.367013 | 0.183507 | − | 0.983018i | \(-0.441255\pi\) | ||||
0.183507 | + | 0.983018i | \(0.441255\pi\) | |||||||
\(420\) | −20.7738 | −1.01366 | ||||||||
\(421\) | −0.630207 | −0.0307144 | −0.0153572 | − | 0.999882i | \(-0.504889\pi\) | ||||
−0.0153572 | + | 0.999882i | \(0.504889\pi\) | |||||||
\(422\) | −40.0580 | −1.94999 | ||||||||
\(423\) | 1.05160 | 0.0511305 | ||||||||
\(424\) | −14.1800 | −0.688641 | ||||||||
\(425\) | −25.1456 | −1.21974 | ||||||||
\(426\) | −14.4236 | −0.698827 | ||||||||
\(427\) | −33.0251 | −1.59820 | ||||||||
\(428\) | −6.45663 | −0.312093 | ||||||||
\(429\) | −16.8229 | −0.812216 | ||||||||
\(430\) | 76.8118 | 3.70419 | ||||||||
\(431\) | 5.39531 | 0.259883 | 0.129941 | − | 0.991522i | \(-0.458521\pi\) | ||||
0.129941 | + | 0.991522i | \(0.458521\pi\) | |||||||
\(432\) | −24.2510 | −1.16678 | ||||||||
\(433\) | −17.1859 | −0.825902 | −0.412951 | − | 0.910753i | \(-0.635502\pi\) | ||||
−0.412951 | + | 0.910753i | \(0.635502\pi\) | |||||||
\(434\) | 13.3597 | 0.641287 | ||||||||
\(435\) | 45.5811 | 2.18545 | ||||||||
\(436\) | 0.519871 | 0.0248973 | ||||||||
\(437\) | 0.545318 | 0.0260861 | ||||||||
\(438\) | −18.2749 | −0.873210 | ||||||||
\(439\) | 23.4994 | 1.12157 | 0.560784 | − | 0.827962i | \(-0.310500\pi\) | ||||
0.560784 | + | 0.827962i | \(0.310500\pi\) | |||||||
\(440\) | 28.8676 | 1.37621 | ||||||||
\(441\) | 2.34768 | 0.111794 | ||||||||
\(442\) | 9.39688 | 0.446964 | ||||||||
\(443\) | −9.77816 | −0.464574 | −0.232287 | − | 0.972647i | \(-0.574621\pi\) | ||||
−0.232287 | + | 0.972647i | \(0.574621\pi\) | |||||||
\(444\) | 0.918658 | 0.0435976 | ||||||||
\(445\) | 60.2431 | 2.85580 | ||||||||
\(446\) | −34.4526 | −1.63138 | ||||||||
\(447\) | 36.6238 | 1.73224 | ||||||||
\(448\) | 25.4657 | 1.20314 | ||||||||
\(449\) | 19.2866 | 0.910190 | 0.455095 | − | 0.890443i | \(-0.349605\pi\) | ||||
0.455095 | + | 0.890443i | \(0.349605\pi\) | |||||||
\(450\) | −2.83265 | −0.133533 | ||||||||
\(451\) | 32.5329 | 1.53191 | ||||||||
\(452\) | 3.57902 | 0.168343 | ||||||||
\(453\) | 5.43351 | 0.255289 | ||||||||
\(454\) | 43.5915 | 2.04585 | ||||||||
\(455\) | 77.4842 | 3.63252 | ||||||||
\(456\) | 2.01839 | 0.0945199 | ||||||||
\(457\) | −23.4362 | −1.09630 | −0.548149 | − | 0.836381i | \(-0.684667\pi\) | ||||
−0.548149 | + | 0.836381i | \(0.684667\pi\) | |||||||
\(458\) | −22.0121 | −1.02856 | ||||||||
\(459\) | −8.78418 | −0.410010 | ||||||||
\(460\) | −2.57880 | −0.120237 | ||||||||
\(461\) | −31.1498 | −1.45079 | −0.725396 | − | 0.688332i | \(-0.758343\pi\) | ||||
−0.725396 | + | 0.688332i | \(0.758343\pi\) | |||||||
\(462\) | 39.8536 | 1.85416 | ||||||||
\(463\) | −6.53567 | −0.303739 | −0.151869 | − | 0.988401i | \(-0.548529\pi\) | ||||
−0.151869 | + | 0.988401i | \(0.548529\pi\) | |||||||
\(464\) | 27.8206 | 1.29154 | ||||||||
\(465\) | 12.8608 | 0.596404 | ||||||||
\(466\) | −18.5020 | −0.857088 | ||||||||
\(467\) | 41.4275 | 1.91703 | 0.958517 | − | 0.285035i | \(-0.0920051\pi\) | ||||
0.958517 | + | 0.285035i | \(0.0920051\pi\) | |||||||
\(468\) | 0.218390 | 0.0100951 | ||||||||
\(469\) | 47.1266 | 2.17611 | ||||||||
\(470\) | −60.2124 | −2.77739 | ||||||||
\(471\) | 0.920215 | 0.0424013 | ||||||||
\(472\) | 25.1048 | 1.15554 | ||||||||
\(473\) | −30.4017 | −1.39787 | ||||||||
\(474\) | 25.2968 | 1.16192 | ||||||||
\(475\) | −7.07584 | −0.324662 | ||||||||
\(476\) | −4.59270 | −0.210506 | ||||||||
\(477\) | −0.739899 | −0.0338776 | ||||||||
\(478\) | 21.2533 | 0.972102 | ||||||||
\(479\) | 8.54881 | 0.390605 | 0.195303 | − | 0.980743i | \(-0.437431\pi\) | ||||
0.195303 | + | 0.980743i | \(0.437431\pi\) | |||||||
\(480\) | −22.4424 | −1.02435 | ||||||||
\(481\) | −3.42651 | −0.156235 | ||||||||
\(482\) | 28.7469 | 1.30938 | ||||||||
\(483\) | 10.1363 | 0.461218 | ||||||||
\(484\) | −1.70551 | −0.0775231 | ||||||||
\(485\) | 18.4080 | 0.835865 | ||||||||
\(486\) | −2.02124 | −0.0916853 | ||||||||
\(487\) | −4.08692 | −0.185196 | −0.0925981 | − | 0.995704i | \(-0.529517\pi\) | ||||
−0.0925981 | + | 0.995704i | \(0.529517\pi\) | |||||||
\(488\) | −15.1741 | −0.686898 | ||||||||
\(489\) | −12.8975 | −0.583244 | ||||||||
\(490\) | −134.423 | −6.07261 | ||||||||
\(491\) | 3.91957 | 0.176888 | 0.0884438 | − | 0.996081i | \(-0.471811\pi\) | ||||
0.0884438 | + | 0.996081i | \(0.471811\pi\) | |||||||
\(492\) | −10.7569 | −0.484957 | ||||||||
\(493\) | 10.0772 | 0.453853 | ||||||||
\(494\) | 2.64423 | 0.118970 | ||||||||
\(495\) | 1.50629 | 0.0677025 | ||||||||
\(496\) | 7.84962 | 0.352458 | ||||||||
\(497\) | −26.2940 | −1.17945 | ||||||||
\(498\) | −11.7754 | −0.527670 | ||||||||
\(499\) | −18.9502 | −0.848329 | −0.424164 | − | 0.905585i | \(-0.639432\pi\) | ||||
−0.424164 | + | 0.905585i | \(0.639432\pi\) | |||||||
\(500\) | 21.9669 | 0.982389 | ||||||||
\(501\) | 17.9846 | 0.803492 | ||||||||
\(502\) | −1.77875 | −0.0793895 | ||||||||
\(503\) | 14.0224 | 0.625227 | 0.312614 | − | 0.949880i | \(-0.398795\pi\) | ||||
0.312614 | + | 0.949880i | \(0.398795\pi\) | |||||||
\(504\) | 1.47300 | 0.0656128 | ||||||||
\(505\) | −63.4147 | −2.82192 | ||||||||
\(506\) | 4.94733 | 0.219936 | ||||||||
\(507\) | 2.22485 | 0.0988089 | ||||||||
\(508\) | −0.580252 | −0.0257445 | ||||||||
\(509\) | −20.1107 | −0.891389 | −0.445695 | − | 0.895185i | \(-0.647043\pi\) | ||||
−0.445695 | + | 0.895185i | \(0.647043\pi\) | |||||||
\(510\) | −21.4300 | −0.948935 | ||||||||
\(511\) | −33.3149 | −1.47376 | ||||||||
\(512\) | 8.71466 | 0.385137 | ||||||||
\(513\) | −2.47182 | −0.109134 | ||||||||
\(514\) | −30.2764 | −1.33543 | ||||||||
\(515\) | −29.1572 | −1.28482 | ||||||||
\(516\) | 10.0522 | 0.442523 | ||||||||
\(517\) | 23.8318 | 1.04812 | ||||||||
\(518\) | 8.11744 | 0.356660 | ||||||||
\(519\) | 35.0174 | 1.53709 | ||||||||
\(520\) | 35.6018 | 1.56124 | ||||||||
\(521\) | 20.1187 | 0.881417 | 0.440709 | − | 0.897650i | \(-0.354727\pi\) | ||||
0.440709 | + | 0.897650i | \(0.354727\pi\) | |||||||
\(522\) | 1.13519 | 0.0496861 | ||||||||
\(523\) | −15.9364 | −0.696852 | −0.348426 | − | 0.937336i | \(-0.613284\pi\) | ||||
−0.348426 | + | 0.937336i | \(0.613284\pi\) | |||||||
\(524\) | 3.51172 | 0.153410 | ||||||||
\(525\) | −131.525 | −5.74021 | ||||||||
\(526\) | −9.41042 | −0.410314 | ||||||||
\(527\) | 2.84329 | 0.123855 | ||||||||
\(528\) | 23.4164 | 1.01907 | ||||||||
\(529\) | −21.7417 | −0.945292 | ||||||||
\(530\) | 42.3651 | 1.84022 | ||||||||
\(531\) | 1.30994 | 0.0568467 | ||||||||
\(532\) | −1.29236 | −0.0560310 | ||||||||
\(533\) | 40.1221 | 1.73788 | ||||||||
\(534\) | 38.2141 | 1.65368 | ||||||||
\(535\) | −54.9214 | −2.37446 | ||||||||
\(536\) | 21.6533 | 0.935282 | ||||||||
\(537\) | −17.8493 | −0.770254 | ||||||||
\(538\) | −7.73444 | −0.333456 | ||||||||
\(539\) | 53.2039 | 2.29166 | ||||||||
\(540\) | 11.6892 | 0.503024 | ||||||||
\(541\) | −2.14379 | −0.0921686 | −0.0460843 | − | 0.998938i | \(-0.514674\pi\) | ||||
−0.0460843 | + | 0.998938i | \(0.514674\pi\) | |||||||
\(542\) | 44.5567 | 1.91387 | ||||||||
\(543\) | 20.0797 | 0.861701 | ||||||||
\(544\) | −4.96161 | −0.212727 | ||||||||
\(545\) | 4.42213 | 0.189423 | ||||||||
\(546\) | 49.1506 | 2.10345 | ||||||||
\(547\) | −19.8007 | −0.846618 | −0.423309 | − | 0.905985i | \(-0.639132\pi\) | ||||
−0.423309 | + | 0.905985i | \(0.639132\pi\) | |||||||
\(548\) | −0.861810 | −0.0368147 | ||||||||
\(549\) | −0.791770 | −0.0337919 | ||||||||
\(550\) | −64.1947 | −2.73727 | ||||||||
\(551\) | 2.83566 | 0.120803 | ||||||||
\(552\) | 4.65734 | 0.198230 | ||||||||
\(553\) | 46.1157 | 1.96104 | ||||||||
\(554\) | 19.5143 | 0.829082 | ||||||||
\(555\) | 7.81429 | 0.331698 | ||||||||
\(556\) | 2.03771 | 0.0864184 | ||||||||
\(557\) | −3.59104 | −0.152157 | −0.0760786 | − | 0.997102i | \(-0.524240\pi\) | ||||
−0.0760786 | + | 0.997102i | \(0.524240\pi\) | |||||||
\(558\) | 0.320296 | 0.0135592 | ||||||||
\(559\) | −37.4938 | −1.58582 | ||||||||
\(560\) | −107.853 | −4.55762 | ||||||||
\(561\) | 8.48187 | 0.358105 | ||||||||
\(562\) | 16.3780 | 0.690863 | ||||||||
\(563\) | 21.2772 | 0.896728 | 0.448364 | − | 0.893851i | \(-0.352007\pi\) | ||||
0.448364 | + | 0.893851i | \(0.352007\pi\) | |||||||
\(564\) | −7.87987 | −0.331802 | ||||||||
\(565\) | 30.4439 | 1.28079 | ||||||||
\(566\) | 21.2141 | 0.891696 | ||||||||
\(567\) | −47.8267 | −2.00853 | ||||||||
\(568\) | −12.0814 | −0.506923 | ||||||||
\(569\) | −11.7051 | −0.490702 | −0.245351 | − | 0.969434i | \(-0.578903\pi\) | ||||
−0.245351 | + | 0.969434i | \(0.578903\pi\) | |||||||
\(570\) | −6.03028 | −0.252581 | ||||||||
\(571\) | −42.3921 | −1.77406 | −0.887028 | − | 0.461716i | \(-0.847234\pi\) | ||||
−0.887028 | + | 0.461716i | \(0.847234\pi\) | |||||||
\(572\) | 4.94923 | 0.206938 | ||||||||
\(573\) | −20.3676 | −0.850868 | ||||||||
\(574\) | −95.0498 | −3.96730 | ||||||||
\(575\) | −16.3271 | −0.680889 | ||||||||
\(576\) | 0.610535 | 0.0254390 | ||||||||
\(577\) | −2.68638 | −0.111835 | −0.0559177 | − | 0.998435i | \(-0.517808\pi\) | ||||
−0.0559177 | + | 0.998435i | \(0.517808\pi\) | |||||||
\(578\) | 22.2482 | 0.925403 | ||||||||
\(579\) | −34.0521 | −1.41516 | ||||||||
\(580\) | −13.4098 | −0.556812 | ||||||||
\(581\) | −21.4664 | −0.890577 | ||||||||
\(582\) | 11.6768 | 0.484018 | ||||||||
\(583\) | −16.7679 | −0.694454 | ||||||||
\(584\) | −15.3073 | −0.633419 | ||||||||
\(585\) | 1.85767 | 0.0768051 | ||||||||
\(586\) | 14.7854 | 0.610777 | ||||||||
\(587\) | −12.3327 | −0.509023 | −0.254512 | − | 0.967070i | \(-0.581915\pi\) | ||||
−0.254512 | + | 0.967070i | \(0.581915\pi\) | |||||||
\(588\) | −17.5917 | −0.725468 | ||||||||
\(589\) | 0.800086 | 0.0329670 | ||||||||
\(590\) | −75.0047 | −3.08789 | ||||||||
\(591\) | −22.5560 | −0.927828 | ||||||||
\(592\) | 4.76948 | 0.196024 | ||||||||
\(593\) | −46.8281 | −1.92300 | −0.961500 | − | 0.274803i | \(-0.911387\pi\) | ||||
−0.961500 | + | 0.274803i | \(0.911387\pi\) | |||||||
\(594\) | −22.4253 | −0.920121 | ||||||||
\(595\) | −39.0665 | −1.60157 | ||||||||
\(596\) | −10.7746 | −0.441344 | ||||||||
\(597\) | 15.0621 | 0.616451 | ||||||||
\(598\) | 6.10144 | 0.249506 | ||||||||
\(599\) | 26.1827 | 1.06980 | 0.534898 | − | 0.844916i | \(-0.320350\pi\) | ||||
0.534898 | + | 0.844916i | \(0.320350\pi\) | |||||||
\(600\) | −60.4319 | −2.46712 | ||||||||
\(601\) | −34.8891 | −1.42316 | −0.711579 | − | 0.702606i | \(-0.752020\pi\) | ||||
−0.711579 | + | 0.702606i | \(0.752020\pi\) | |||||||
\(602\) | 88.8232 | 3.62016 | ||||||||
\(603\) | 1.12985 | 0.0460111 | ||||||||
\(604\) | −1.59852 | −0.0650429 | ||||||||
\(605\) | −14.5074 | −0.589810 | ||||||||
\(606\) | −40.2259 | −1.63407 | ||||||||
\(607\) | −4.39048 | −0.178204 | −0.0891020 | − | 0.996023i | \(-0.528400\pi\) | ||||
−0.0891020 | + | 0.996023i | \(0.528400\pi\) | |||||||
\(608\) | −1.39617 | −0.0566222 | ||||||||
\(609\) | 52.7089 | 2.13587 | ||||||||
\(610\) | 45.3351 | 1.83556 | ||||||||
\(611\) | 29.3912 | 1.18904 | ||||||||
\(612\) | −0.110109 | −0.00445090 | ||||||||
\(613\) | 16.6726 | 0.673402 | 0.336701 | − | 0.941612i | \(-0.390689\pi\) | ||||
0.336701 | + | 0.941612i | \(0.390689\pi\) | |||||||
\(614\) | 32.9565 | 1.33002 | ||||||||
\(615\) | −91.5001 | −3.68964 | ||||||||
\(616\) | 33.3818 | 1.34499 | ||||||||
\(617\) | −7.24082 | −0.291505 | −0.145752 | − | 0.989321i | \(-0.546560\pi\) | ||||
−0.145752 | + | 0.989321i | \(0.546560\pi\) | |||||||
\(618\) | −18.4953 | −0.743991 | ||||||||
\(619\) | −37.5708 | −1.51010 | −0.755049 | − | 0.655669i | \(-0.772387\pi\) | ||||
−0.755049 | + | 0.655669i | \(0.772387\pi\) | |||||||
\(620\) | −3.78360 | −0.151953 | ||||||||
\(621\) | −5.70361 | −0.228878 | ||||||||
\(622\) | −31.2768 | −1.25408 | ||||||||
\(623\) | 69.6636 | 2.79101 | ||||||||
\(624\) | 28.8789 | 1.15608 | ||||||||
\(625\) | 114.079 | 4.56314 | ||||||||
\(626\) | 31.6835 | 1.26633 | ||||||||
\(627\) | 2.38675 | 0.0953177 | ||||||||
\(628\) | −0.270724 | −0.0108031 | ||||||||
\(629\) | 1.72760 | 0.0688839 | ||||||||
\(630\) | −4.40084 | −0.175334 | ||||||||
\(631\) | 27.7660 | 1.10535 | 0.552674 | − | 0.833398i | \(-0.313607\pi\) | ||||
0.552674 | + | 0.833398i | \(0.313607\pi\) | |||||||
\(632\) | 21.1889 | 0.842848 | ||||||||
\(633\) | −44.5921 | −1.77238 | ||||||||
\(634\) | 21.4707 | 0.852711 | ||||||||
\(635\) | −4.93574 | −0.195869 | ||||||||
\(636\) | 5.54422 | 0.219843 | ||||||||
\(637\) | 65.6152 | 2.59977 | ||||||||
\(638\) | 25.7262 | 1.01851 | ||||||||
\(639\) | −0.630394 | −0.0249380 | ||||||||
\(640\) | −60.3584 | −2.38588 | ||||||||
\(641\) | −28.1153 | −1.11049 | −0.555243 | − | 0.831688i | \(-0.687375\pi\) | ||||
−0.555243 | + | 0.831688i | \(0.687375\pi\) | |||||||
\(642\) | −34.8384 | −1.37496 | ||||||||
\(643\) | 5.94671 | 0.234515 | 0.117258 | − | 0.993102i | \(-0.462590\pi\) | ||||
0.117258 | + | 0.993102i | \(0.462590\pi\) | |||||||
\(644\) | −2.98206 | −0.117510 | ||||||||
\(645\) | 85.5060 | 3.36680 | ||||||||
\(646\) | −1.33319 | −0.0524535 | ||||||||
\(647\) | −7.30140 | −0.287048 | −0.143524 | − | 0.989647i | \(-0.545843\pi\) | ||||
−0.143524 | + | 0.989647i | \(0.545843\pi\) | |||||||
\(648\) | −21.9750 | −0.863259 | ||||||||
\(649\) | 29.6865 | 1.16530 | ||||||||
\(650\) | −79.1699 | −3.10530 | ||||||||
\(651\) | 14.8719 | 0.582875 | ||||||||
\(652\) | 3.79439 | 0.148600 | ||||||||
\(653\) | 6.35953 | 0.248868 | 0.124434 | − | 0.992228i | \(-0.460289\pi\) | ||||
0.124434 | + | 0.992228i | \(0.460289\pi\) | |||||||
\(654\) | 2.80509 | 0.109688 | ||||||||
\(655\) | 29.8714 | 1.16717 | ||||||||
\(656\) | −55.8474 | −2.18047 | ||||||||
\(657\) | −0.798718 | −0.0311610 | ||||||||
\(658\) | −69.6281 | −2.71439 | ||||||||
\(659\) | 20.5644 | 0.801074 | 0.400537 | − | 0.916281i | \(-0.368824\pi\) | ||||
0.400537 | + | 0.916281i | \(0.368824\pi\) | |||||||
\(660\) | −11.2869 | −0.439343 | ||||||||
\(661\) | −32.1941 | −1.25221 | −0.626103 | − | 0.779741i | \(-0.715351\pi\) | ||||
−0.626103 | + | 0.779741i | \(0.715351\pi\) | |||||||
\(662\) | −28.1950 | −1.09583 | ||||||||
\(663\) | 10.4605 | 0.406252 | ||||||||
\(664\) | −9.86321 | −0.382767 | ||||||||
\(665\) | −10.9931 | −0.426294 | ||||||||
\(666\) | 0.194614 | 0.00754114 | ||||||||
\(667\) | 6.54315 | 0.253352 | ||||||||
\(668\) | −5.29100 | −0.204715 | ||||||||
\(669\) | −38.3522 | −1.48278 | ||||||||
\(670\) | −64.6929 | −2.49931 | ||||||||
\(671\) | −17.9434 | −0.692697 | ||||||||
\(672\) | −25.9518 | −1.00111 | ||||||||
\(673\) | 25.4698 | 0.981789 | 0.490894 | − | 0.871219i | \(-0.336670\pi\) | ||||
0.490894 | + | 0.871219i | \(0.336670\pi\) | |||||||
\(674\) | −34.6070 | −1.33301 | ||||||||
\(675\) | 74.0078 | 2.84856 | ||||||||
\(676\) | −0.654542 | −0.0251747 | ||||||||
\(677\) | 33.6943 | 1.29498 | 0.647488 | − | 0.762076i | \(-0.275820\pi\) | ||||
0.647488 | + | 0.762076i | \(0.275820\pi\) | |||||||
\(678\) | 19.3115 | 0.741654 | ||||||||
\(679\) | 21.2866 | 0.816903 | ||||||||
\(680\) | −17.9499 | −0.688349 | ||||||||
\(681\) | 48.5256 | 1.85950 | ||||||||
\(682\) | 7.25868 | 0.277949 | ||||||||
\(683\) | 47.1946 | 1.80585 | 0.902926 | − | 0.429796i | \(-0.141415\pi\) | ||||
0.902926 | + | 0.429796i | \(0.141415\pi\) | |||||||
\(684\) | −0.0309841 | −0.00118471 | ||||||||
\(685\) | −7.33073 | −0.280093 | ||||||||
\(686\) | −98.6213 | −3.76538 | ||||||||
\(687\) | −24.5037 | −0.934873 | ||||||||
\(688\) | 52.1889 | 1.98968 | ||||||||
\(689\) | −20.6794 | −0.787824 | ||||||||
\(690\) | −13.9146 | −0.529719 | ||||||||
\(691\) | −29.5757 | −1.12511 | −0.562556 | − | 0.826759i | \(-0.690182\pi\) | ||||
−0.562556 | + | 0.826759i | \(0.690182\pi\) | |||||||
\(692\) | −10.3020 | −0.391624 | ||||||||
\(693\) | 1.74183 | 0.0661667 | ||||||||
\(694\) | −5.03245 | −0.191029 | ||||||||
\(695\) | 17.3332 | 0.657487 | ||||||||
\(696\) | 24.2182 | 0.917990 | ||||||||
\(697\) | −20.2290 | −0.766229 | ||||||||
\(698\) | 8.43251 | 0.319175 | ||||||||
\(699\) | −20.5962 | −0.779020 | ||||||||
\(700\) | 38.6941 | 1.46250 | ||||||||
\(701\) | −8.11350 | −0.306443 | −0.153221 | − | 0.988192i | \(-0.548965\pi\) | ||||
−0.153221 | + | 0.988192i | \(0.548965\pi\) | |||||||
\(702\) | −27.6566 | −1.04383 | ||||||||
\(703\) | 0.486137 | 0.0183350 | ||||||||
\(704\) | 13.8362 | 0.521471 | ||||||||
\(705\) | −67.0278 | −2.52441 | ||||||||
\(706\) | −17.6430 | −0.664003 | ||||||||
\(707\) | −73.3311 | −2.75790 | ||||||||
\(708\) | −9.81570 | −0.368897 | ||||||||
\(709\) | −39.4395 | −1.48118 | −0.740590 | − | 0.671957i | \(-0.765454\pi\) | ||||
−0.740590 | + | 0.671957i | \(0.765454\pi\) | |||||||
\(710\) | 36.0951 | 1.35462 | ||||||||
\(711\) | 1.10561 | 0.0414638 | ||||||||
\(712\) | 32.0084 | 1.19957 | ||||||||
\(713\) | 1.84616 | 0.0691392 | ||||||||
\(714\) | −24.7811 | −0.927408 | ||||||||
\(715\) | 42.0992 | 1.57442 | ||||||||
\(716\) | 5.25120 | 0.196246 | ||||||||
\(717\) | 23.6589 | 0.883558 | ||||||||
\(718\) | −10.4459 | −0.389837 | ||||||||
\(719\) | −8.24918 | −0.307642 | −0.153821 | − | 0.988099i | \(-0.549158\pi\) | ||||
−0.153821 | + | 0.988099i | \(0.549158\pi\) | |||||||
\(720\) | −2.58575 | −0.0963654 | ||||||||
\(721\) | −33.7167 | −1.25567 | ||||||||
\(722\) | 29.7856 | 1.10851 | ||||||||
\(723\) | 32.0007 | 1.19012 | ||||||||
\(724\) | −5.90737 | −0.219546 | ||||||||
\(725\) | −84.9014 | −3.15316 | ||||||||
\(726\) | −9.20250 | −0.341537 | ||||||||
\(727\) | −28.4855 | −1.05647 | −0.528235 | − | 0.849098i | \(-0.677146\pi\) | ||||
−0.528235 | + | 0.849098i | \(0.677146\pi\) | |||||||
\(728\) | 41.1690 | 1.52583 | ||||||||
\(729\) | 25.8083 | 0.955862 | ||||||||
\(730\) | 45.7329 | 1.69265 | ||||||||
\(731\) | 18.9038 | 0.699184 | ||||||||
\(732\) | 5.93291 | 0.219286 | ||||||||
\(733\) | 28.5200 | 1.05341 | 0.526706 | − | 0.850048i | \(-0.323427\pi\) | ||||
0.526706 | + | 0.850048i | \(0.323427\pi\) | |||||||
\(734\) | 3.04956 | 0.112561 | ||||||||
\(735\) | −149.638 | −5.51949 | ||||||||
\(736\) | −3.22160 | −0.118750 | ||||||||
\(737\) | 25.6051 | 0.943177 | ||||||||
\(738\) | −2.27880 | −0.0838838 | ||||||||
\(739\) | 2.71011 | 0.0996931 | 0.0498466 | − | 0.998757i | \(-0.484127\pi\) | ||||
0.0498466 | + | 0.998757i | \(0.484127\pi\) | |||||||
\(740\) | −2.29894 | −0.0845106 | ||||||||
\(741\) | 2.94353 | 0.108133 | ||||||||
\(742\) | 48.9899 | 1.79848 | ||||||||
\(743\) | −18.3544 | −0.673358 | −0.336679 | − | 0.941619i | \(-0.609304\pi\) | ||||
−0.336679 | + | 0.941619i | \(0.609304\pi\) | |||||||
\(744\) | 6.83321 | 0.250518 | ||||||||
\(745\) | −91.6508 | −3.35783 | ||||||||
\(746\) | −15.5561 | −0.569548 | ||||||||
\(747\) | −0.514653 | −0.0188302 | ||||||||
\(748\) | −2.49534 | −0.0912385 | ||||||||
\(749\) | −63.5098 | −2.32060 | ||||||||
\(750\) | 118.528 | 4.32802 | ||||||||
\(751\) | 24.5853 | 0.897131 | 0.448565 | − | 0.893750i | \(-0.351935\pi\) | ||||
0.448565 | + | 0.893750i | \(0.351935\pi\) | |||||||
\(752\) | −40.9106 | −1.49186 | ||||||||
\(753\) | −1.98008 | −0.0721583 | ||||||||
\(754\) | 31.7275 | 1.15545 | ||||||||
\(755\) | −13.5973 | −0.494858 | ||||||||
\(756\) | 13.5171 | 0.491613 | ||||||||
\(757\) | −2.34333 | −0.0851697 | −0.0425849 | − | 0.999093i | \(-0.513559\pi\) | ||||
−0.0425849 | + | 0.999093i | \(0.513559\pi\) | |||||||
\(758\) | −18.1572 | −0.659501 | ||||||||
\(759\) | 5.50732 | 0.199903 | ||||||||
\(760\) | −5.05102 | −0.183220 | ||||||||
\(761\) | 42.7488 | 1.54964 | 0.774821 | − | 0.632181i | \(-0.217840\pi\) | ||||
0.774821 | + | 0.632181i | \(0.217840\pi\) | |||||||
\(762\) | −3.13089 | −0.113420 | ||||||||
\(763\) | 5.11364 | 0.185126 | ||||||||
\(764\) | 5.99207 | 0.216786 | ||||||||
\(765\) | −0.936611 | −0.0338632 | ||||||||
\(766\) | −39.4500 | −1.42539 | ||||||||
\(767\) | 36.6117 | 1.32197 | ||||||||
\(768\) | −20.6872 | −0.746484 | ||||||||
\(769\) | 29.4532 | 1.06211 | 0.531054 | − | 0.847338i | \(-0.321796\pi\) | ||||
0.531054 | + | 0.847338i | \(0.321796\pi\) | |||||||
\(770\) | −99.7336 | −3.59415 | ||||||||
\(771\) | −33.7033 | −1.21379 | ||||||||
\(772\) | 10.0180 | 0.360556 | ||||||||
\(773\) | −20.9131 | −0.752193 | −0.376096 | − | 0.926581i | \(-0.622734\pi\) | ||||
−0.376096 | + | 0.926581i | \(0.622734\pi\) | |||||||
\(774\) | 2.12952 | 0.0765440 | ||||||||
\(775\) | −23.9550 | −0.860490 | ||||||||
\(776\) | 9.78057 | 0.351102 | ||||||||
\(777\) | 9.03625 | 0.324174 | ||||||||
\(778\) | −23.7991 | −0.853238 | ||||||||
\(779\) | −5.69234 | −0.203949 | ||||||||
\(780\) | −13.9199 | −0.498413 | ||||||||
\(781\) | −14.2862 | −0.511202 | ||||||||
\(782\) | −3.07626 | −0.110007 | ||||||||
\(783\) | −29.6588 | −1.05992 | ||||||||
\(784\) | −91.3322 | −3.26186 | ||||||||
\(785\) | −2.30284 | −0.0821917 | ||||||||
\(786\) | 18.9483 | 0.675865 | ||||||||
\(787\) | −42.4487 | −1.51313 | −0.756566 | − | 0.653917i | \(-0.773124\pi\) | ||||
−0.756566 | + | 0.653917i | \(0.773124\pi\) | |||||||
\(788\) | 6.63589 | 0.236394 | ||||||||
\(789\) | −10.4756 | −0.372940 | ||||||||
\(790\) | −63.3052 | −2.25230 | ||||||||
\(791\) | 35.2046 | 1.25173 | ||||||||
\(792\) | 0.800321 | 0.0284382 | ||||||||
\(793\) | −22.1292 | −0.785830 | ||||||||
\(794\) | 33.0256 | 1.17204 | ||||||||
\(795\) | 47.1603 | 1.67260 | ||||||||
\(796\) | −4.43122 | −0.157060 | ||||||||
\(797\) | 35.7010 | 1.26460 | 0.632298 | − | 0.774726i | \(-0.282112\pi\) | ||||
0.632298 | + | 0.774726i | \(0.282112\pi\) | |||||||
\(798\) | −6.97326 | −0.246851 | ||||||||
\(799\) | −14.8186 | −0.524246 | ||||||||
\(800\) | 41.8022 | 1.47793 | ||||||||
\(801\) | 1.67017 | 0.0590126 | ||||||||
\(802\) | 36.5122 | 1.28929 | ||||||||
\(803\) | −18.1009 | −0.638765 | ||||||||
\(804\) | −8.46623 | −0.298581 | ||||||||
\(805\) | −25.3660 | −0.894036 | ||||||||
\(806\) | 8.95197 | 0.315320 | ||||||||
\(807\) | −8.60990 | −0.303083 | ||||||||
\(808\) | −33.6936 | −1.18534 | ||||||||
\(809\) | −31.9045 | −1.12170 | −0.560852 | − | 0.827916i | \(-0.689526\pi\) | ||||
−0.560852 | + | 0.827916i | \(0.689526\pi\) | |||||||
\(810\) | 65.6539 | 2.30684 | ||||||||
\(811\) | 38.8036 | 1.36258 | 0.681289 | − | 0.732014i | \(-0.261420\pi\) | ||||
0.681289 | + | 0.732014i | \(0.261420\pi\) | |||||||
\(812\) | −15.5068 | −0.544181 | ||||||||
\(813\) | 49.6000 | 1.73955 | ||||||||
\(814\) | 4.41042 | 0.154585 | ||||||||
\(815\) | 32.2759 | 1.13057 | ||||||||
\(816\) | −14.5603 | −0.509714 | ||||||||
\(817\) | 5.31944 | 0.186104 | ||||||||
\(818\) | 45.5902 | 1.59402 | ||||||||
\(819\) | 2.14816 | 0.0750628 | ||||||||
\(820\) | 26.9190 | 0.940053 | ||||||||
\(821\) | −42.7537 | −1.49211 | −0.746057 | − | 0.665883i | \(-0.768055\pi\) | ||||
−0.746057 | + | 0.665883i | \(0.768055\pi\) | |||||||
\(822\) | −4.65011 | −0.162191 | ||||||||
\(823\) | 3.35599 | 0.116983 | 0.0584913 | − | 0.998288i | \(-0.481371\pi\) | ||||
0.0584913 | + | 0.998288i | \(0.481371\pi\) | |||||||
\(824\) | −15.4919 | −0.539684 | ||||||||
\(825\) | −71.4608 | −2.48795 | ||||||||
\(826\) | −86.7335 | −3.01784 | ||||||||
\(827\) | 34.0233 | 1.18311 | 0.591553 | − | 0.806266i | \(-0.298515\pi\) | ||||
0.591553 | + | 0.806266i | \(0.298515\pi\) | |||||||
\(828\) | −0.0714944 | −0.00248460 | ||||||||
\(829\) | 40.8090 | 1.41736 | 0.708678 | − | 0.705532i | \(-0.249292\pi\) | ||||
0.708678 | + | 0.705532i | \(0.249292\pi\) | |||||||
\(830\) | 29.4680 | 1.02285 | ||||||||
\(831\) | 21.7231 | 0.753565 | ||||||||
\(832\) | 17.0639 | 0.591583 | ||||||||
\(833\) | −33.0823 | −1.14623 | ||||||||
\(834\) | 10.9950 | 0.380726 | ||||||||
\(835\) | −45.0064 | −1.55751 | ||||||||
\(836\) | −0.702174 | −0.0242852 | ||||||||
\(837\) | −8.36828 | −0.289250 | ||||||||
\(838\) | −11.9255 | −0.411961 | ||||||||
\(839\) | 30.7121 | 1.06030 | 0.530149 | − | 0.847904i | \(-0.322136\pi\) | ||||
0.530149 | + | 0.847904i | \(0.322136\pi\) | |||||||
\(840\) | −93.8876 | −3.23943 | ||||||||
\(841\) | 5.02446 | 0.173257 | ||||||||
\(842\) | 1.00040 | 0.0344760 | ||||||||
\(843\) | 18.2318 | 0.627936 | ||||||||
\(844\) | 13.1188 | 0.451569 | ||||||||
\(845\) | −5.56767 | −0.191534 | ||||||||
\(846\) | −1.66932 | −0.0573924 | ||||||||
\(847\) | −16.7760 | −0.576430 | ||||||||
\(848\) | 28.7844 | 0.988462 | ||||||||
\(849\) | 23.6153 | 0.810476 | ||||||||
\(850\) | 39.9164 | 1.36912 | ||||||||
\(851\) | 1.12174 | 0.0384527 | ||||||||
\(852\) | 4.72369 | 0.161831 | ||||||||
\(853\) | 18.6869 | 0.639827 | 0.319914 | − | 0.947447i | \(-0.396346\pi\) | ||||
0.319914 | + | 0.947447i | \(0.396346\pi\) | |||||||
\(854\) | 52.4243 | 1.79392 | ||||||||
\(855\) | −0.263557 | −0.00901347 | ||||||||
\(856\) | −29.1809 | −0.997384 | ||||||||
\(857\) | −10.9252 | −0.373199 | −0.186599 | − | 0.982436i | \(-0.559747\pi\) | ||||
−0.186599 | + | 0.982436i | \(0.559747\pi\) | |||||||
\(858\) | 26.7048 | 0.911687 | ||||||||
\(859\) | 22.4774 | 0.766919 | 0.383460 | − | 0.923558i | \(-0.374733\pi\) | ||||
0.383460 | + | 0.923558i | \(0.374733\pi\) | |||||||
\(860\) | −25.1556 | −0.857798 | ||||||||
\(861\) | −105.808 | −3.60594 | ||||||||
\(862\) | −8.56457 | −0.291710 | ||||||||
\(863\) | 34.2217 | 1.16492 | 0.582460 | − | 0.812859i | \(-0.302090\pi\) | ||||
0.582460 | + | 0.812859i | \(0.302090\pi\) | |||||||
\(864\) | 14.6029 | 0.496800 | ||||||||
\(865\) | −87.6310 | −2.97954 | ||||||||
\(866\) | 27.2811 | 0.927048 | ||||||||
\(867\) | 24.7664 | 0.841113 | ||||||||
\(868\) | −4.37526 | −0.148506 | ||||||||
\(869\) | 25.0559 | 0.849962 | ||||||||
\(870\) | −72.3560 | −2.45310 | ||||||||
\(871\) | 31.5782 | 1.06999 | ||||||||
\(872\) | 2.34957 | 0.0795665 | ||||||||
\(873\) | 0.510341 | 0.0172724 | ||||||||
\(874\) | −0.865644 | −0.0292808 | ||||||||
\(875\) | 216.074 | 7.30464 | ||||||||
\(876\) | 5.98497 | 0.202213 | ||||||||
\(877\) | −14.8590 | −0.501752 | −0.250876 | − | 0.968019i | \(-0.580719\pi\) | ||||
−0.250876 | + | 0.968019i | \(0.580719\pi\) | |||||||
\(878\) | −37.3033 | −1.25892 | ||||||||
\(879\) | 16.4589 | 0.555145 | ||||||||
\(880\) | −58.5994 | −1.97538 | ||||||||
\(881\) | 6.96375 | 0.234615 | 0.117307 | − | 0.993096i | \(-0.462574\pi\) | ||||
0.117307 | + | 0.993096i | \(0.462574\pi\) | |||||||
\(882\) | −3.72672 | −0.125485 | ||||||||
\(883\) | 27.8071 | 0.935782 | 0.467891 | − | 0.883786i | \(-0.345014\pi\) | ||||
0.467891 | + | 0.883786i | \(0.345014\pi\) | |||||||
\(884\) | −3.07744 | −0.103506 | ||||||||
\(885\) | −83.4944 | −2.80663 | ||||||||
\(886\) | 15.5219 | 0.521470 | ||||||||
\(887\) | 34.7010 | 1.16514 | 0.582572 | − | 0.812779i | \(-0.302046\pi\) | ||||
0.582572 | + | 0.812779i | \(0.302046\pi\) | |||||||
\(888\) | 4.15190 | 0.139329 | ||||||||
\(889\) | −5.70757 | −0.191426 | ||||||||
\(890\) | −95.6305 | −3.20554 | ||||||||
\(891\) | −25.9855 | −0.870546 | ||||||||
\(892\) | 11.2831 | 0.377786 | ||||||||
\(893\) | −4.16988 | −0.139540 | ||||||||
\(894\) | −58.1369 | −1.94439 | ||||||||
\(895\) | 44.6678 | 1.49308 | ||||||||
\(896\) | −69.7970 | −2.33175 | ||||||||
\(897\) | 6.79205 | 0.226780 | ||||||||
\(898\) | −30.6157 | −1.02166 | ||||||||
\(899\) | 9.60005 | 0.320180 | ||||||||
\(900\) | 0.927683 | 0.0309228 | ||||||||
\(901\) | 10.4263 | 0.347350 | ||||||||
\(902\) | −51.6431 | −1.71953 | ||||||||
\(903\) | 98.8770 | 3.29042 | ||||||||
\(904\) | 16.1755 | 0.537989 | ||||||||
\(905\) | −50.2493 | −1.67034 | ||||||||
\(906\) | −8.62522 | −0.286554 | ||||||||
\(907\) | 12.1165 | 0.402322 | 0.201161 | − | 0.979558i | \(-0.435528\pi\) | ||||
0.201161 | + | 0.979558i | \(0.435528\pi\) | |||||||
\(908\) | −14.2761 | −0.473768 | ||||||||
\(909\) | −1.75810 | −0.0583125 | ||||||||
\(910\) | −122.999 | −4.07738 | ||||||||
\(911\) | 7.69811 | 0.255050 | 0.127525 | − | 0.991835i | \(-0.459297\pi\) | ||||
0.127525 | + | 0.991835i | \(0.459297\pi\) | |||||||
\(912\) | −4.09720 | −0.135672 | ||||||||
\(913\) | −11.6633 | −0.385998 | ||||||||
\(914\) | 37.2028 | 1.23056 | ||||||||
\(915\) | 50.4665 | 1.66837 | ||||||||
\(916\) | 7.20889 | 0.238189 | ||||||||
\(917\) | 34.5425 | 1.14070 | ||||||||
\(918\) | 13.9441 | 0.460224 | ||||||||
\(919\) | −28.3823 | −0.936247 | −0.468123 | − | 0.883663i | \(-0.655070\pi\) | ||||
−0.468123 | + | 0.883663i | \(0.655070\pi\) | |||||||
\(920\) | −11.6550 | −0.384253 | ||||||||
\(921\) | 36.6868 | 1.20887 | ||||||||
\(922\) | 49.4475 | 1.62847 | ||||||||
\(923\) | −17.6189 | −0.579933 | ||||||||
\(924\) | −13.0519 | −0.429377 | ||||||||
\(925\) | −14.5552 | −0.478573 | ||||||||
\(926\) | 10.3748 | 0.340937 | ||||||||
\(927\) | −0.808351 | −0.0265497 | ||||||||
\(928\) | −16.7523 | −0.549923 | ||||||||
\(929\) | 15.3153 | 0.502479 | 0.251240 | − | 0.967925i | \(-0.419162\pi\) | ||||
0.251240 | + | 0.967925i | \(0.419162\pi\) | |||||||
\(930\) | −20.4153 | −0.669445 | ||||||||
\(931\) | −9.30919 | −0.305096 | ||||||||
\(932\) | 6.05933 | 0.198480 | ||||||||
\(933\) | −34.8170 | −1.13986 | ||||||||
\(934\) | −65.7624 | −2.15181 | ||||||||
\(935\) | −21.2258 | −0.694159 | ||||||||
\(936\) | 0.987019 | 0.0322617 | ||||||||
\(937\) | 28.4763 | 0.930279 | 0.465139 | − | 0.885237i | \(-0.346004\pi\) | ||||
0.465139 | + | 0.885237i | \(0.346004\pi\) | |||||||
\(938\) | −74.8093 | −2.44261 | ||||||||
\(939\) | 35.2698 | 1.15098 | ||||||||
\(940\) | 19.7193 | 0.643174 | ||||||||
\(941\) | 37.0245 | 1.20696 | 0.603481 | − | 0.797377i | \(-0.293780\pi\) | ||||
0.603481 | + | 0.797377i | \(0.293780\pi\) | |||||||
\(942\) | −1.46076 | −0.0475941 | ||||||||
\(943\) | −13.1348 | −0.427728 | ||||||||
\(944\) | −50.9610 | −1.65864 | ||||||||
\(945\) | 114.979 | 3.74028 | ||||||||
\(946\) | 48.2600 | 1.56907 | ||||||||
\(947\) | 58.6024 | 1.90432 | 0.952161 | − | 0.305597i | \(-0.0988559\pi\) | ||||
0.952161 | + | 0.305597i | \(0.0988559\pi\) | |||||||
\(948\) | −8.28462 | −0.269072 | ||||||||
\(949\) | −22.3234 | −0.724648 | ||||||||
\(950\) | 11.2323 | 0.364422 | ||||||||
\(951\) | 23.9010 | 0.775042 | ||||||||
\(952\) | −20.7569 | −0.672734 | ||||||||
\(953\) | 56.8330 | 1.84100 | 0.920501 | − | 0.390741i | \(-0.127781\pi\) | ||||
0.920501 | + | 0.390741i | \(0.127781\pi\) | |||||||
\(954\) | 1.17452 | 0.0380266 | ||||||||
\(955\) | 50.9698 | 1.64934 | ||||||||
\(956\) | −6.96037 | −0.225114 | ||||||||
\(957\) | 28.6381 | 0.925739 | ||||||||
\(958\) | −13.5705 | −0.438442 | ||||||||
\(959\) | −8.47707 | −0.273739 | ||||||||
\(960\) | −38.9148 | −1.25597 | ||||||||
\(961\) | −28.2913 | −0.912624 | ||||||||
\(962\) | 5.43927 | 0.175369 | ||||||||
\(963\) | −1.52263 | −0.0490662 | ||||||||
\(964\) | −9.41449 | −0.303220 | ||||||||
\(965\) | 85.2152 | 2.74317 | ||||||||
\(966\) | −16.0905 | −0.517702 | ||||||||
\(967\) | 46.5744 | 1.49773 | 0.748866 | − | 0.662722i | \(-0.230599\pi\) | ||||
0.748866 | + | 0.662722i | \(0.230599\pi\) | |||||||
\(968\) | −7.70810 | −0.247748 | ||||||||
\(969\) | −1.48409 | −0.0476758 | ||||||||
\(970\) | −29.2211 | −0.938232 | ||||||||
\(971\) | −45.9141 | −1.47345 | −0.736727 | − | 0.676191i | \(-0.763630\pi\) | ||||
−0.736727 | + | 0.676191i | \(0.763630\pi\) | |||||||
\(972\) | 0.661948 | 0.0212320 | ||||||||
\(973\) | 20.0437 | 0.642571 | ||||||||
\(974\) | 6.48762 | 0.207877 | ||||||||
\(975\) | −88.1310 | −2.82245 | ||||||||
\(976\) | 30.8024 | 0.985960 | ||||||||
\(977\) | 22.8651 | 0.731519 | 0.365760 | − | 0.930709i | \(-0.380809\pi\) | ||||
0.365760 | + | 0.930709i | \(0.380809\pi\) | |||||||
\(978\) | 20.4736 | 0.654673 | ||||||||
\(979\) | 37.8501 | 1.20969 | ||||||||
\(980\) | 44.0230 | 1.40626 | ||||||||
\(981\) | 0.122598 | 0.00391427 | ||||||||
\(982\) | −6.22196 | −0.198551 | ||||||||
\(983\) | −55.7627 | −1.77855 | −0.889276 | − | 0.457370i | \(-0.848791\pi\) | ||||
−0.889276 | + | 0.457370i | \(0.848791\pi\) | |||||||
\(984\) | −48.6160 | −1.54982 | ||||||||
\(985\) | 56.4462 | 1.79853 | ||||||||
\(986\) | −15.9966 | −0.509435 | ||||||||
\(987\) | −77.5092 | −2.46715 | ||||||||
\(988\) | −0.865976 | −0.0275504 | ||||||||
\(989\) | 12.2743 | 0.390302 | ||||||||
\(990\) | −2.39109 | −0.0759939 | ||||||||
\(991\) | −16.9098 | −0.537156 | −0.268578 | − | 0.963258i | \(-0.586554\pi\) | ||||
−0.268578 | + | 0.963258i | \(0.586554\pi\) | |||||||
\(992\) | −4.72670 | −0.150073 | ||||||||
\(993\) | −31.3864 | −0.996017 | ||||||||
\(994\) | 41.7394 | 1.32389 | ||||||||
\(995\) | −37.6929 | −1.19494 | ||||||||
\(996\) | 3.85641 | 0.122195 | ||||||||
\(997\) | 9.24358 | 0.292747 | 0.146374 | − | 0.989229i | \(-0.453240\pi\) | ||||
0.146374 | + | 0.989229i | \(0.453240\pi\) | |||||||
\(998\) | 30.0818 | 0.952222 | ||||||||
\(999\) | −5.08462 | −0.160870 |
(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 | 4033.2.a.e.1.18 | ✓ | 82 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4033.2.a.e.1.18 | ✓ | 82 | 1.1 | even | 1 | trivial |