Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4002,2,Mod(1,4002)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4002, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("4002.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4002 = 2 \cdot 3 \cdot 23 \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4002.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: | \(31.9561308889\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{12})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 3 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(1.73205\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4002.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 3.00000 | 1.34164 | 0.670820 | − | 0.741620i | \(-0.265942\pi\) | ||||
0.670820 | + | 0.741620i | \(0.265942\pi\) | |||||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | 3.00000 | 1.13389 | 0.566947 | − | 0.823754i | \(-0.308125\pi\) | ||||
0.566947 | + | 0.823754i | \(0.308125\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 3.00000 | 0.948683 | ||||||||
\(11\) | −2.73205 | −0.823744 | −0.411872 | − | 0.911242i | \(-0.635125\pi\) | ||||
−0.411872 | + | 0.911242i | \(0.635125\pi\) | |||||||
\(12\) | 1.00000 | 0.288675 | ||||||||
\(13\) | 1.26795 | 0.351666 | 0.175833 | − | 0.984420i | \(-0.443738\pi\) | ||||
0.175833 | + | 0.984420i | \(0.443738\pi\) | |||||||
\(14\) | 3.00000 | 0.801784 | ||||||||
\(15\) | 3.00000 | 0.774597 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −6.46410 | −1.56777 | −0.783887 | − | 0.620903i | \(-0.786766\pi\) | ||||
−0.783887 | + | 0.620903i | \(0.786766\pi\) | |||||||
\(18\) | 1.00000 | 0.235702 | ||||||||
\(19\) | 2.46410 | 0.565304 | 0.282652 | − | 0.959223i | \(-0.408786\pi\) | ||||
0.282652 | + | 0.959223i | \(0.408786\pi\) | |||||||
\(20\) | 3.00000 | 0.670820 | ||||||||
\(21\) | 3.00000 | 0.654654 | ||||||||
\(22\) | −2.73205 | −0.582475 | ||||||||
\(23\) | 1.00000 | 0.208514 | ||||||||
\(24\) | 1.00000 | 0.204124 | ||||||||
\(25\) | 4.00000 | 0.800000 | ||||||||
\(26\) | 1.26795 | 0.248665 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 3.00000 | 0.566947 | ||||||||
\(29\) | −1.00000 | −0.185695 | ||||||||
\(30\) | 3.00000 | 0.547723 | ||||||||
\(31\) | 0.732051 | 0.131480 | 0.0657401 | − | 0.997837i | \(-0.479059\pi\) | ||||
0.0657401 | + | 0.997837i | \(0.479059\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | −2.73205 | −0.475589 | ||||||||
\(34\) | −6.46410 | −1.10858 | ||||||||
\(35\) | 9.00000 | 1.52128 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | −7.19615 | −1.18304 | −0.591520 | − | 0.806290i | \(-0.701472\pi\) | ||||
−0.591520 | + | 0.806290i | \(0.701472\pi\) | |||||||
\(38\) | 2.46410 | 0.399730 | ||||||||
\(39\) | 1.26795 | 0.203034 | ||||||||
\(40\) | 3.00000 | 0.474342 | ||||||||
\(41\) | 12.1244 | 1.89351 | 0.946753 | − | 0.321960i | \(-0.104342\pi\) | ||||
0.946753 | + | 0.321960i | \(0.104342\pi\) | |||||||
\(42\) | 3.00000 | 0.462910 | ||||||||
\(43\) | 1.92820 | 0.294048 | 0.147024 | − | 0.989133i | \(-0.453031\pi\) | ||||
0.147024 | + | 0.989133i | \(0.453031\pi\) | |||||||
\(44\) | −2.73205 | −0.411872 | ||||||||
\(45\) | 3.00000 | 0.447214 | ||||||||
\(46\) | 1.00000 | 0.147442 | ||||||||
\(47\) | 11.3923 | 1.66174 | 0.830869 | − | 0.556468i | \(-0.187844\pi\) | ||||
0.830869 | + | 0.556468i | \(0.187844\pi\) | |||||||
\(48\) | 1.00000 | 0.144338 | ||||||||
\(49\) | 2.00000 | 0.285714 | ||||||||
\(50\) | 4.00000 | 0.565685 | ||||||||
\(51\) | −6.46410 | −0.905155 | ||||||||
\(52\) | 1.26795 | 0.175833 | ||||||||
\(53\) | 9.46410 | 1.29999 | 0.649997 | − | 0.759937i | \(-0.274770\pi\) | ||||
0.649997 | + | 0.759937i | \(0.274770\pi\) | |||||||
\(54\) | 1.00000 | 0.136083 | ||||||||
\(55\) | −8.19615 | −1.10517 | ||||||||
\(56\) | 3.00000 | 0.400892 | ||||||||
\(57\) | 2.46410 | 0.326378 | ||||||||
\(58\) | −1.00000 | −0.131306 | ||||||||
\(59\) | 3.53590 | 0.460335 | 0.230167 | − | 0.973151i | \(-0.426073\pi\) | ||||
0.230167 | + | 0.973151i | \(0.426073\pi\) | |||||||
\(60\) | 3.00000 | 0.387298 | ||||||||
\(61\) | 6.39230 | 0.818451 | 0.409225 | − | 0.912433i | \(-0.365799\pi\) | ||||
0.409225 | + | 0.912433i | \(0.365799\pi\) | |||||||
\(62\) | 0.732051 | 0.0929705 | ||||||||
\(63\) | 3.00000 | 0.377964 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 3.80385 | 0.471809 | ||||||||
\(66\) | −2.73205 | −0.336292 | ||||||||
\(67\) | −9.46410 | −1.15622 | −0.578112 | − | 0.815957i | \(-0.696210\pi\) | ||||
−0.578112 | + | 0.815957i | \(0.696210\pi\) | |||||||
\(68\) | −6.46410 | −0.783887 | ||||||||
\(69\) | 1.00000 | 0.120386 | ||||||||
\(70\) | 9.00000 | 1.07571 | ||||||||
\(71\) | 5.66025 | 0.671749 | 0.335874 | − | 0.941907i | \(-0.390968\pi\) | ||||
0.335874 | + | 0.941907i | \(0.390968\pi\) | |||||||
\(72\) | 1.00000 | 0.117851 | ||||||||
\(73\) | −12.9282 | −1.51313 | −0.756566 | − | 0.653917i | \(-0.773124\pi\) | ||||
−0.756566 | + | 0.653917i | \(0.773124\pi\) | |||||||
\(74\) | −7.19615 | −0.836536 | ||||||||
\(75\) | 4.00000 | 0.461880 | ||||||||
\(76\) | 2.46410 | 0.282652 | ||||||||
\(77\) | −8.19615 | −0.934038 | ||||||||
\(78\) | 1.26795 | 0.143567 | ||||||||
\(79\) | −17.1244 | −1.92664 | −0.963320 | − | 0.268354i | \(-0.913520\pi\) | ||||
−0.963320 | + | 0.268354i | \(0.913520\pi\) | |||||||
\(80\) | 3.00000 | 0.335410 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 12.1244 | 1.33891 | ||||||||
\(83\) | −4.53590 | −0.497880 | −0.248940 | − | 0.968519i | \(-0.580082\pi\) | ||||
−0.248940 | + | 0.968519i | \(0.580082\pi\) | |||||||
\(84\) | 3.00000 | 0.327327 | ||||||||
\(85\) | −19.3923 | −2.10339 | ||||||||
\(86\) | 1.92820 | 0.207924 | ||||||||
\(87\) | −1.00000 | −0.107211 | ||||||||
\(88\) | −2.73205 | −0.291238 | ||||||||
\(89\) | −5.46410 | −0.579194 | −0.289597 | − | 0.957149i | \(-0.593521\pi\) | ||||
−0.289597 | + | 0.957149i | \(0.593521\pi\) | |||||||
\(90\) | 3.00000 | 0.316228 | ||||||||
\(91\) | 3.80385 | 0.398752 | ||||||||
\(92\) | 1.00000 | 0.104257 | ||||||||
\(93\) | 0.732051 | 0.0759101 | ||||||||
\(94\) | 11.3923 | 1.17503 | ||||||||
\(95\) | 7.39230 | 0.758434 | ||||||||
\(96\) | 1.00000 | 0.102062 | ||||||||
\(97\) | 4.00000 | 0.406138 | 0.203069 | − | 0.979164i | \(-0.434908\pi\) | ||||
0.203069 | + | 0.979164i | \(0.434908\pi\) | |||||||
\(98\) | 2.00000 | 0.202031 | ||||||||
\(99\) | −2.73205 | −0.274581 | ||||||||
\(100\) | 4.00000 | 0.400000 | ||||||||
\(101\) | 3.07180 | 0.305655 | 0.152828 | − | 0.988253i | \(-0.451162\pi\) | ||||
0.152828 | + | 0.988253i | \(0.451162\pi\) | |||||||
\(102\) | −6.46410 | −0.640041 | ||||||||
\(103\) | 14.8564 | 1.46385 | 0.731923 | − | 0.681388i | \(-0.238623\pi\) | ||||
0.731923 | + | 0.681388i | \(0.238623\pi\) | |||||||
\(104\) | 1.26795 | 0.124333 | ||||||||
\(105\) | 9.00000 | 0.878310 | ||||||||
\(106\) | 9.46410 | 0.919235 | ||||||||
\(107\) | −1.19615 | −0.115636 | −0.0578182 | − | 0.998327i | \(-0.518414\pi\) | ||||
−0.0578182 | + | 0.998327i | \(0.518414\pi\) | |||||||
\(108\) | 1.00000 | 0.0962250 | ||||||||
\(109\) | −8.00000 | −0.766261 | −0.383131 | − | 0.923694i | \(-0.625154\pi\) | ||||
−0.383131 | + | 0.923694i | \(0.625154\pi\) | |||||||
\(110\) | −8.19615 | −0.781472 | ||||||||
\(111\) | −7.19615 | −0.683029 | ||||||||
\(112\) | 3.00000 | 0.283473 | ||||||||
\(113\) | −9.39230 | −0.883554 | −0.441777 | − | 0.897125i | \(-0.645652\pi\) | ||||
−0.441777 | + | 0.897125i | \(0.645652\pi\) | |||||||
\(114\) | 2.46410 | 0.230784 | ||||||||
\(115\) | 3.00000 | 0.279751 | ||||||||
\(116\) | −1.00000 | −0.0928477 | ||||||||
\(117\) | 1.26795 | 0.117222 | ||||||||
\(118\) | 3.53590 | 0.325506 | ||||||||
\(119\) | −19.3923 | −1.77769 | ||||||||
\(120\) | 3.00000 | 0.273861 | ||||||||
\(121\) | −3.53590 | −0.321445 | ||||||||
\(122\) | 6.39230 | 0.578732 | ||||||||
\(123\) | 12.1244 | 1.09322 | ||||||||
\(124\) | 0.732051 | 0.0657401 | ||||||||
\(125\) | −3.00000 | −0.268328 | ||||||||
\(126\) | 3.00000 | 0.267261 | ||||||||
\(127\) | 4.53590 | 0.402496 | 0.201248 | − | 0.979540i | \(-0.435500\pi\) | ||||
0.201248 | + | 0.979540i | \(0.435500\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 1.92820 | 0.169769 | ||||||||
\(130\) | 3.80385 | 0.333620 | ||||||||
\(131\) | −7.80385 | −0.681825 | −0.340913 | − | 0.940095i | \(-0.610736\pi\) | ||||
−0.340913 | + | 0.940095i | \(0.610736\pi\) | |||||||
\(132\) | −2.73205 | −0.237795 | ||||||||
\(133\) | 7.39230 | 0.640994 | ||||||||
\(134\) | −9.46410 | −0.817574 | ||||||||
\(135\) | 3.00000 | 0.258199 | ||||||||
\(136\) | −6.46410 | −0.554292 | ||||||||
\(137\) | 0.928203 | 0.0793018 | 0.0396509 | − | 0.999214i | \(-0.487375\pi\) | ||||
0.0396509 | + | 0.999214i | \(0.487375\pi\) | |||||||
\(138\) | 1.00000 | 0.0851257 | ||||||||
\(139\) | 7.85641 | 0.666372 | 0.333186 | − | 0.942861i | \(-0.391876\pi\) | ||||
0.333186 | + | 0.942861i | \(0.391876\pi\) | |||||||
\(140\) | 9.00000 | 0.760639 | ||||||||
\(141\) | 11.3923 | 0.959405 | ||||||||
\(142\) | 5.66025 | 0.474998 | ||||||||
\(143\) | −3.46410 | −0.289683 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | −3.00000 | −0.249136 | ||||||||
\(146\) | −12.9282 | −1.06995 | ||||||||
\(147\) | 2.00000 | 0.164957 | ||||||||
\(148\) | −7.19615 | −0.591520 | ||||||||
\(149\) | 5.00000 | 0.409616 | 0.204808 | − | 0.978802i | \(-0.434343\pi\) | ||||
0.204808 | + | 0.978802i | \(0.434343\pi\) | |||||||
\(150\) | 4.00000 | 0.326599 | ||||||||
\(151\) | −10.1244 | −0.823908 | −0.411954 | − | 0.911205i | \(-0.635154\pi\) | ||||
−0.411954 | + | 0.911205i | \(0.635154\pi\) | |||||||
\(152\) | 2.46410 | 0.199865 | ||||||||
\(153\) | −6.46410 | −0.522592 | ||||||||
\(154\) | −8.19615 | −0.660465 | ||||||||
\(155\) | 2.19615 | 0.176399 | ||||||||
\(156\) | 1.26795 | 0.101517 | ||||||||
\(157\) | −3.73205 | −0.297850 | −0.148925 | − | 0.988848i | \(-0.547581\pi\) | ||||
−0.148925 | + | 0.988848i | \(0.547581\pi\) | |||||||
\(158\) | −17.1244 | −1.36234 | ||||||||
\(159\) | 9.46410 | 0.750552 | ||||||||
\(160\) | 3.00000 | 0.237171 | ||||||||
\(161\) | 3.00000 | 0.236433 | ||||||||
\(162\) | 1.00000 | 0.0785674 | ||||||||
\(163\) | −23.7321 | −1.85884 | −0.929419 | − | 0.369027i | \(-0.879691\pi\) | ||||
−0.929419 | + | 0.369027i | \(0.879691\pi\) | |||||||
\(164\) | 12.1244 | 0.946753 | ||||||||
\(165\) | −8.19615 | −0.638070 | ||||||||
\(166\) | −4.53590 | −0.352054 | ||||||||
\(167\) | −7.85641 | −0.607947 | −0.303973 | − | 0.952680i | \(-0.598313\pi\) | ||||
−0.303973 | + | 0.952680i | \(0.598313\pi\) | |||||||
\(168\) | 3.00000 | 0.231455 | ||||||||
\(169\) | −11.3923 | −0.876331 | ||||||||
\(170\) | −19.3923 | −1.48732 | ||||||||
\(171\) | 2.46410 | 0.188435 | ||||||||
\(172\) | 1.92820 | 0.147024 | ||||||||
\(173\) | 11.7321 | 0.891971 | 0.445986 | − | 0.895040i | \(-0.352853\pi\) | ||||
0.445986 | + | 0.895040i | \(0.352853\pi\) | |||||||
\(174\) | −1.00000 | −0.0758098 | ||||||||
\(175\) | 12.0000 | 0.907115 | ||||||||
\(176\) | −2.73205 | −0.205936 | ||||||||
\(177\) | 3.53590 | 0.265774 | ||||||||
\(178\) | −5.46410 | −0.409552 | ||||||||
\(179\) | −10.3923 | −0.776757 | −0.388379 | − | 0.921500i | \(-0.626965\pi\) | ||||
−0.388379 | + | 0.921500i | \(0.626965\pi\) | |||||||
\(180\) | 3.00000 | 0.223607 | ||||||||
\(181\) | −5.12436 | −0.380890 | −0.190445 | − | 0.981698i | \(-0.560993\pi\) | ||||
−0.190445 | + | 0.981698i | \(0.560993\pi\) | |||||||
\(182\) | 3.80385 | 0.281960 | ||||||||
\(183\) | 6.39230 | 0.472533 | ||||||||
\(184\) | 1.00000 | 0.0737210 | ||||||||
\(185\) | −21.5885 | −1.58721 | ||||||||
\(186\) | 0.732051 | 0.0536766 | ||||||||
\(187\) | 17.6603 | 1.29145 | ||||||||
\(188\) | 11.3923 | 0.830869 | ||||||||
\(189\) | 3.00000 | 0.218218 | ||||||||
\(190\) | 7.39230 | 0.536294 | ||||||||
\(191\) | −26.1244 | −1.89029 | −0.945146 | − | 0.326648i | \(-0.894081\pi\) | ||||
−0.945146 | + | 0.326648i | \(0.894081\pi\) | |||||||
\(192\) | 1.00000 | 0.0721688 | ||||||||
\(193\) | 2.53590 | 0.182538 | 0.0912690 | − | 0.995826i | \(-0.470908\pi\) | ||||
0.0912690 | + | 0.995826i | \(0.470908\pi\) | |||||||
\(194\) | 4.00000 | 0.287183 | ||||||||
\(195\) | 3.80385 | 0.272399 | ||||||||
\(196\) | 2.00000 | 0.142857 | ||||||||
\(197\) | 14.2679 | 1.01655 | 0.508275 | − | 0.861195i | \(-0.330283\pi\) | ||||
0.508275 | + | 0.861195i | \(0.330283\pi\) | |||||||
\(198\) | −2.73205 | −0.194158 | ||||||||
\(199\) | −17.3205 | −1.22782 | −0.613909 | − | 0.789377i | \(-0.710404\pi\) | ||||
−0.613909 | + | 0.789377i | \(0.710404\pi\) | |||||||
\(200\) | 4.00000 | 0.282843 | ||||||||
\(201\) | −9.46410 | −0.667546 | ||||||||
\(202\) | 3.07180 | 0.216131 | ||||||||
\(203\) | −3.00000 | −0.210559 | ||||||||
\(204\) | −6.46410 | −0.452578 | ||||||||
\(205\) | 36.3731 | 2.54041 | ||||||||
\(206\) | 14.8564 | 1.03509 | ||||||||
\(207\) | 1.00000 | 0.0695048 | ||||||||
\(208\) | 1.26795 | 0.0879165 | ||||||||
\(209\) | −6.73205 | −0.465666 | ||||||||
\(210\) | 9.00000 | 0.621059 | ||||||||
\(211\) | 0.803848 | 0.0553391 | 0.0276696 | − | 0.999617i | \(-0.491191\pi\) | ||||
0.0276696 | + | 0.999617i | \(0.491191\pi\) | |||||||
\(212\) | 9.46410 | 0.649997 | ||||||||
\(213\) | 5.66025 | 0.387834 | ||||||||
\(214\) | −1.19615 | −0.0817673 | ||||||||
\(215\) | 5.78461 | 0.394507 | ||||||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | 2.19615 | 0.149085 | ||||||||
\(218\) | −8.00000 | −0.541828 | ||||||||
\(219\) | −12.9282 | −0.873607 | ||||||||
\(220\) | −8.19615 | −0.552584 | ||||||||
\(221\) | −8.19615 | −0.551333 | ||||||||
\(222\) | −7.19615 | −0.482974 | ||||||||
\(223\) | 8.00000 | 0.535720 | 0.267860 | − | 0.963458i | \(-0.413684\pi\) | ||||
0.267860 | + | 0.963458i | \(0.413684\pi\) | |||||||
\(224\) | 3.00000 | 0.200446 | ||||||||
\(225\) | 4.00000 | 0.266667 | ||||||||
\(226\) | −9.39230 | −0.624767 | ||||||||
\(227\) | 5.58846 | 0.370919 | 0.185459 | − | 0.982652i | \(-0.440623\pi\) | ||||
0.185459 | + | 0.982652i | \(0.440623\pi\) | |||||||
\(228\) | 2.46410 | 0.163189 | ||||||||
\(229\) | 2.80385 | 0.185283 | 0.0926417 | − | 0.995700i | \(-0.470469\pi\) | ||||
0.0926417 | + | 0.995700i | \(0.470469\pi\) | |||||||
\(230\) | 3.00000 | 0.197814 | ||||||||
\(231\) | −8.19615 | −0.539267 | ||||||||
\(232\) | −1.00000 | −0.0656532 | ||||||||
\(233\) | −11.3205 | −0.741631 | −0.370816 | − | 0.928707i | \(-0.620922\pi\) | ||||
−0.370816 | + | 0.928707i | \(0.620922\pi\) | |||||||
\(234\) | 1.26795 | 0.0828884 | ||||||||
\(235\) | 34.1769 | 2.22946 | ||||||||
\(236\) | 3.53590 | 0.230167 | ||||||||
\(237\) | −17.1244 | −1.11235 | ||||||||
\(238\) | −19.3923 | −1.25702 | ||||||||
\(239\) | 19.8564 | 1.28440 | 0.642202 | − | 0.766535i | \(-0.278021\pi\) | ||||
0.642202 | + | 0.766535i | \(0.278021\pi\) | |||||||
\(240\) | 3.00000 | 0.193649 | ||||||||
\(241\) | 10.2679 | 0.661417 | 0.330708 | − | 0.943733i | \(-0.392712\pi\) | ||||
0.330708 | + | 0.943733i | \(0.392712\pi\) | |||||||
\(242\) | −3.53590 | −0.227296 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 6.39230 | 0.409225 | ||||||||
\(245\) | 6.00000 | 0.383326 | ||||||||
\(246\) | 12.1244 | 0.773021 | ||||||||
\(247\) | 3.12436 | 0.198798 | ||||||||
\(248\) | 0.732051 | 0.0464853 | ||||||||
\(249\) | −4.53590 | −0.287451 | ||||||||
\(250\) | −3.00000 | −0.189737 | ||||||||
\(251\) | −5.46410 | −0.344891 | −0.172446 | − | 0.985019i | \(-0.555167\pi\) | ||||
−0.172446 | + | 0.985019i | \(0.555167\pi\) | |||||||
\(252\) | 3.00000 | 0.188982 | ||||||||
\(253\) | −2.73205 | −0.171763 | ||||||||
\(254\) | 4.53590 | 0.284608 | ||||||||
\(255\) | −19.3923 | −1.21439 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −19.2679 | −1.20190 | −0.600951 | − | 0.799286i | \(-0.705211\pi\) | ||||
−0.600951 | + | 0.799286i | \(0.705211\pi\) | |||||||
\(258\) | 1.92820 | 0.120045 | ||||||||
\(259\) | −21.5885 | −1.34144 | ||||||||
\(260\) | 3.80385 | 0.235905 | ||||||||
\(261\) | −1.00000 | −0.0618984 | ||||||||
\(262\) | −7.80385 | −0.482123 | ||||||||
\(263\) | −9.05256 | −0.558205 | −0.279102 | − | 0.960261i | \(-0.590037\pi\) | ||||
−0.279102 | + | 0.960261i | \(0.590037\pi\) | |||||||
\(264\) | −2.73205 | −0.168146 | ||||||||
\(265\) | 28.3923 | 1.74413 | ||||||||
\(266\) | 7.39230 | 0.453251 | ||||||||
\(267\) | −5.46410 | −0.334398 | ||||||||
\(268\) | −9.46410 | −0.578112 | ||||||||
\(269\) | 5.66025 | 0.345112 | 0.172556 | − | 0.985000i | \(-0.444797\pi\) | ||||
0.172556 | + | 0.985000i | \(0.444797\pi\) | |||||||
\(270\) | 3.00000 | 0.182574 | ||||||||
\(271\) | −16.7846 | −1.01959 | −0.509796 | − | 0.860295i | \(-0.670279\pi\) | ||||
−0.509796 | + | 0.860295i | \(0.670279\pi\) | |||||||
\(272\) | −6.46410 | −0.391944 | ||||||||
\(273\) | 3.80385 | 0.230219 | ||||||||
\(274\) | 0.928203 | 0.0560748 | ||||||||
\(275\) | −10.9282 | −0.658995 | ||||||||
\(276\) | 1.00000 | 0.0601929 | ||||||||
\(277\) | −5.12436 | −0.307893 | −0.153946 | − | 0.988079i | \(-0.549198\pi\) | ||||
−0.153946 | + | 0.988079i | \(0.549198\pi\) | |||||||
\(278\) | 7.85641 | 0.471196 | ||||||||
\(279\) | 0.732051 | 0.0438267 | ||||||||
\(280\) | 9.00000 | 0.537853 | ||||||||
\(281\) | 20.5359 | 1.22507 | 0.612534 | − | 0.790444i | \(-0.290150\pi\) | ||||
0.612534 | + | 0.790444i | \(0.290150\pi\) | |||||||
\(282\) | 11.3923 | 0.678402 | ||||||||
\(283\) | −22.5885 | −1.34274 | −0.671372 | − | 0.741120i | \(-0.734295\pi\) | ||||
−0.671372 | + | 0.741120i | \(0.734295\pi\) | |||||||
\(284\) | 5.66025 | 0.335874 | ||||||||
\(285\) | 7.39230 | 0.437882 | ||||||||
\(286\) | −3.46410 | −0.204837 | ||||||||
\(287\) | 36.3731 | 2.14703 | ||||||||
\(288\) | 1.00000 | 0.0589256 | ||||||||
\(289\) | 24.7846 | 1.45792 | ||||||||
\(290\) | −3.00000 | −0.176166 | ||||||||
\(291\) | 4.00000 | 0.234484 | ||||||||
\(292\) | −12.9282 | −0.756566 | ||||||||
\(293\) | 6.00000 | 0.350524 | 0.175262 | − | 0.984522i | \(-0.443923\pi\) | ||||
0.175262 | + | 0.984522i | \(0.443923\pi\) | |||||||
\(294\) | 2.00000 | 0.116642 | ||||||||
\(295\) | 10.6077 | 0.617604 | ||||||||
\(296\) | −7.19615 | −0.418268 | ||||||||
\(297\) | −2.73205 | −0.158530 | ||||||||
\(298\) | 5.00000 | 0.289642 | ||||||||
\(299\) | 1.26795 | 0.0733274 | ||||||||
\(300\) | 4.00000 | 0.230940 | ||||||||
\(301\) | 5.78461 | 0.333419 | ||||||||
\(302\) | −10.1244 | −0.582591 | ||||||||
\(303\) | 3.07180 | 0.176470 | ||||||||
\(304\) | 2.46410 | 0.141326 | ||||||||
\(305\) | 19.1769 | 1.09807 | ||||||||
\(306\) | −6.46410 | −0.369528 | ||||||||
\(307\) | −22.9282 | −1.30858 | −0.654291 | − | 0.756243i | \(-0.727033\pi\) | ||||
−0.654291 | + | 0.756243i | \(0.727033\pi\) | |||||||
\(308\) | −8.19615 | −0.467019 | ||||||||
\(309\) | 14.8564 | 0.845151 | ||||||||
\(310\) | 2.19615 | 0.124733 | ||||||||
\(311\) | 28.3205 | 1.60591 | 0.802954 | − | 0.596041i | \(-0.203260\pi\) | ||||
0.802954 | + | 0.596041i | \(0.203260\pi\) | |||||||
\(312\) | 1.26795 | 0.0717835 | ||||||||
\(313\) | 4.12436 | 0.233122 | 0.116561 | − | 0.993184i | \(-0.462813\pi\) | ||||
0.116561 | + | 0.993184i | \(0.462813\pi\) | |||||||
\(314\) | −3.73205 | −0.210612 | ||||||||
\(315\) | 9.00000 | 0.507093 | ||||||||
\(316\) | −17.1244 | −0.963320 | ||||||||
\(317\) | 27.6603 | 1.55355 | 0.776777 | − | 0.629775i | \(-0.216853\pi\) | ||||
0.776777 | + | 0.629775i | \(0.216853\pi\) | |||||||
\(318\) | 9.46410 | 0.530720 | ||||||||
\(319\) | 2.73205 | 0.152965 | ||||||||
\(320\) | 3.00000 | 0.167705 | ||||||||
\(321\) | −1.19615 | −0.0667627 | ||||||||
\(322\) | 3.00000 | 0.167183 | ||||||||
\(323\) | −15.9282 | −0.886269 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 5.07180 | 0.281333 | ||||||||
\(326\) | −23.7321 | −1.31440 | ||||||||
\(327\) | −8.00000 | −0.442401 | ||||||||
\(328\) | 12.1244 | 0.669456 | ||||||||
\(329\) | 34.1769 | 1.88423 | ||||||||
\(330\) | −8.19615 | −0.451183 | ||||||||
\(331\) | −29.4449 | −1.61844 | −0.809218 | − | 0.587508i | \(-0.800109\pi\) | ||||
−0.809218 | + | 0.587508i | \(0.800109\pi\) | |||||||
\(332\) | −4.53590 | −0.248940 | ||||||||
\(333\) | −7.19615 | −0.394347 | ||||||||
\(334\) | −7.85641 | −0.429883 | ||||||||
\(335\) | −28.3923 | −1.55124 | ||||||||
\(336\) | 3.00000 | 0.163663 | ||||||||
\(337\) | −7.07180 | −0.385225 | −0.192613 | − | 0.981275i | \(-0.561696\pi\) | ||||
−0.192613 | + | 0.981275i | \(0.561696\pi\) | |||||||
\(338\) | −11.3923 | −0.619660 | ||||||||
\(339\) | −9.39230 | −0.510120 | ||||||||
\(340\) | −19.3923 | −1.05170 | ||||||||
\(341\) | −2.00000 | −0.108306 | ||||||||
\(342\) | 2.46410 | 0.133243 | ||||||||
\(343\) | −15.0000 | −0.809924 | ||||||||
\(344\) | 1.92820 | 0.103962 | ||||||||
\(345\) | 3.00000 | 0.161515 | ||||||||
\(346\) | 11.7321 | 0.630719 | ||||||||
\(347\) | −8.85641 | −0.475437 | −0.237718 | − | 0.971334i | \(-0.576400\pi\) | ||||
−0.237718 | + | 0.971334i | \(0.576400\pi\) | |||||||
\(348\) | −1.00000 | −0.0536056 | ||||||||
\(349\) | 14.3923 | 0.770402 | 0.385201 | − | 0.922833i | \(-0.374132\pi\) | ||||
0.385201 | + | 0.922833i | \(0.374132\pi\) | |||||||
\(350\) | 12.0000 | 0.641427 | ||||||||
\(351\) | 1.26795 | 0.0676781 | ||||||||
\(352\) | −2.73205 | −0.145619 | ||||||||
\(353\) | −4.53590 | −0.241422 | −0.120711 | − | 0.992688i | \(-0.538517\pi\) | ||||
−0.120711 | + | 0.992688i | \(0.538517\pi\) | |||||||
\(354\) | 3.53590 | 0.187931 | ||||||||
\(355\) | 16.9808 | 0.901245 | ||||||||
\(356\) | −5.46410 | −0.289597 | ||||||||
\(357\) | −19.3923 | −1.02635 | ||||||||
\(358\) | −10.3923 | −0.549250 | ||||||||
\(359\) | −7.73205 | −0.408082 | −0.204041 | − | 0.978962i | \(-0.565408\pi\) | ||||
−0.204041 | + | 0.978962i | \(0.565408\pi\) | |||||||
\(360\) | 3.00000 | 0.158114 | ||||||||
\(361\) | −12.9282 | −0.680432 | ||||||||
\(362\) | −5.12436 | −0.269330 | ||||||||
\(363\) | −3.53590 | −0.185587 | ||||||||
\(364\) | 3.80385 | 0.199376 | ||||||||
\(365\) | −38.7846 | −2.03008 | ||||||||
\(366\) | 6.39230 | 0.334131 | ||||||||
\(367\) | 31.6603 | 1.65265 | 0.826326 | − | 0.563192i | \(-0.190427\pi\) | ||||
0.826326 | + | 0.563192i | \(0.190427\pi\) | |||||||
\(368\) | 1.00000 | 0.0521286 | ||||||||
\(369\) | 12.1244 | 0.631169 | ||||||||
\(370\) | −21.5885 | −1.12233 | ||||||||
\(371\) | 28.3923 | 1.47406 | ||||||||
\(372\) | 0.732051 | 0.0379551 | ||||||||
\(373\) | 17.0718 | 0.883944 | 0.441972 | − | 0.897029i | \(-0.354279\pi\) | ||||
0.441972 | + | 0.897029i | \(0.354279\pi\) | |||||||
\(374\) | 17.6603 | 0.913190 | ||||||||
\(375\) | −3.00000 | −0.154919 | ||||||||
\(376\) | 11.3923 | 0.587513 | ||||||||
\(377\) | −1.26795 | −0.0653027 | ||||||||
\(378\) | 3.00000 | 0.154303 | ||||||||
\(379\) | −23.8564 | −1.22542 | −0.612711 | − | 0.790307i | \(-0.709921\pi\) | ||||
−0.612711 | + | 0.790307i | \(0.709921\pi\) | |||||||
\(380\) | 7.39230 | 0.379217 | ||||||||
\(381\) | 4.53590 | 0.232381 | ||||||||
\(382\) | −26.1244 | −1.33664 | ||||||||
\(383\) | 20.1962 | 1.03198 | 0.515988 | − | 0.856596i | \(-0.327425\pi\) | ||||
0.515988 | + | 0.856596i | \(0.327425\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | −24.5885 | −1.25314 | ||||||||
\(386\) | 2.53590 | 0.129074 | ||||||||
\(387\) | 1.92820 | 0.0980161 | ||||||||
\(388\) | 4.00000 | 0.203069 | ||||||||
\(389\) | −13.8564 | −0.702548 | −0.351274 | − | 0.936273i | \(-0.614251\pi\) | ||||
−0.351274 | + | 0.936273i | \(0.614251\pi\) | |||||||
\(390\) | 3.80385 | 0.192615 | ||||||||
\(391\) | −6.46410 | −0.326904 | ||||||||
\(392\) | 2.00000 | 0.101015 | ||||||||
\(393\) | −7.80385 | −0.393652 | ||||||||
\(394\) | 14.2679 | 0.718809 | ||||||||
\(395\) | −51.3731 | −2.58486 | ||||||||
\(396\) | −2.73205 | −0.137291 | ||||||||
\(397\) | 0.339746 | 0.0170514 | 0.00852568 | − | 0.999964i | \(-0.497286\pi\) | ||||
0.00852568 | + | 0.999964i | \(0.497286\pi\) | |||||||
\(398\) | −17.3205 | −0.868199 | ||||||||
\(399\) | 7.39230 | 0.370078 | ||||||||
\(400\) | 4.00000 | 0.200000 | ||||||||
\(401\) | −25.7128 | −1.28404 | −0.642018 | − | 0.766689i | \(-0.721903\pi\) | ||||
−0.642018 | + | 0.766689i | \(0.721903\pi\) | |||||||
\(402\) | −9.46410 | −0.472026 | ||||||||
\(403\) | 0.928203 | 0.0462371 | ||||||||
\(404\) | 3.07180 | 0.152828 | ||||||||
\(405\) | 3.00000 | 0.149071 | ||||||||
\(406\) | −3.00000 | −0.148888 | ||||||||
\(407\) | 19.6603 | 0.974523 | ||||||||
\(408\) | −6.46410 | −0.320021 | ||||||||
\(409\) | 19.1244 | 0.945639 | 0.472819 | − | 0.881159i | \(-0.343236\pi\) | ||||
0.472819 | + | 0.881159i | \(0.343236\pi\) | |||||||
\(410\) | 36.3731 | 1.79634 | ||||||||
\(411\) | 0.928203 | 0.0457849 | ||||||||
\(412\) | 14.8564 | 0.731923 | ||||||||
\(413\) | 10.6077 | 0.521971 | ||||||||
\(414\) | 1.00000 | 0.0491473 | ||||||||
\(415\) | −13.6077 | −0.667975 | ||||||||
\(416\) | 1.26795 | 0.0621663 | ||||||||
\(417\) | 7.85641 | 0.384730 | ||||||||
\(418\) | −6.73205 | −0.329275 | ||||||||
\(419\) | −9.58846 | −0.468427 | −0.234213 | − | 0.972185i | \(-0.575251\pi\) | ||||
−0.234213 | + | 0.972185i | \(0.575251\pi\) | |||||||
\(420\) | 9.00000 | 0.439155 | ||||||||
\(421\) | 30.3923 | 1.48123 | 0.740615 | − | 0.671929i | \(-0.234534\pi\) | ||||
0.740615 | + | 0.671929i | \(0.234534\pi\) | |||||||
\(422\) | 0.803848 | 0.0391307 | ||||||||
\(423\) | 11.3923 | 0.553913 | ||||||||
\(424\) | 9.46410 | 0.459617 | ||||||||
\(425\) | −25.8564 | −1.25422 | ||||||||
\(426\) | 5.66025 | 0.274240 | ||||||||
\(427\) | 19.1769 | 0.928036 | ||||||||
\(428\) | −1.19615 | −0.0578182 | ||||||||
\(429\) | −3.46410 | −0.167248 | ||||||||
\(430\) | 5.78461 | 0.278959 | ||||||||
\(431\) | 30.1962 | 1.45450 | 0.727249 | − | 0.686374i | \(-0.240799\pi\) | ||||
0.727249 | + | 0.686374i | \(0.240799\pi\) | |||||||
\(432\) | 1.00000 | 0.0481125 | ||||||||
\(433\) | 11.5167 | 0.553455 | 0.276728 | − | 0.960948i | \(-0.410750\pi\) | ||||
0.276728 | + | 0.960948i | \(0.410750\pi\) | |||||||
\(434\) | 2.19615 | 0.105419 | ||||||||
\(435\) | −3.00000 | −0.143839 | ||||||||
\(436\) | −8.00000 | −0.383131 | ||||||||
\(437\) | 2.46410 | 0.117874 | ||||||||
\(438\) | −12.9282 | −0.617733 | ||||||||
\(439\) | 21.1962 | 1.01164 | 0.505819 | − | 0.862640i | \(-0.331191\pi\) | ||||
0.505819 | + | 0.862640i | \(0.331191\pi\) | |||||||
\(440\) | −8.19615 | −0.390736 | ||||||||
\(441\) | 2.00000 | 0.0952381 | ||||||||
\(442\) | −8.19615 | −0.389851 | ||||||||
\(443\) | 25.1769 | 1.19619 | 0.598096 | − | 0.801425i | \(-0.295924\pi\) | ||||
0.598096 | + | 0.801425i | \(0.295924\pi\) | |||||||
\(444\) | −7.19615 | −0.341514 | ||||||||
\(445\) | −16.3923 | −0.777070 | ||||||||
\(446\) | 8.00000 | 0.378811 | ||||||||
\(447\) | 5.00000 | 0.236492 | ||||||||
\(448\) | 3.00000 | 0.141737 | ||||||||
\(449\) | 8.66025 | 0.408703 | 0.204351 | − | 0.978898i | \(-0.434492\pi\) | ||||
0.204351 | + | 0.978898i | \(0.434492\pi\) | |||||||
\(450\) | 4.00000 | 0.188562 | ||||||||
\(451\) | −33.1244 | −1.55976 | ||||||||
\(452\) | −9.39230 | −0.441777 | ||||||||
\(453\) | −10.1244 | −0.475684 | ||||||||
\(454\) | 5.58846 | 0.262279 | ||||||||
\(455\) | 11.4115 | 0.534981 | ||||||||
\(456\) | 2.46410 | 0.115392 | ||||||||
\(457\) | 30.9090 | 1.44586 | 0.722930 | − | 0.690921i | \(-0.242795\pi\) | ||||
0.722930 | + | 0.690921i | \(0.242795\pi\) | |||||||
\(458\) | 2.80385 | 0.131015 | ||||||||
\(459\) | −6.46410 | −0.301718 | ||||||||
\(460\) | 3.00000 | 0.139876 | ||||||||
\(461\) | −8.05256 | −0.375045 | −0.187523 | − | 0.982260i | \(-0.560046\pi\) | ||||
−0.187523 | + | 0.982260i | \(0.560046\pi\) | |||||||
\(462\) | −8.19615 | −0.381320 | ||||||||
\(463\) | −31.1769 | −1.44891 | −0.724457 | − | 0.689320i | \(-0.757909\pi\) | ||||
−0.724457 | + | 0.689320i | \(0.757909\pi\) | |||||||
\(464\) | −1.00000 | −0.0464238 | ||||||||
\(465\) | 2.19615 | 0.101844 | ||||||||
\(466\) | −11.3205 | −0.524412 | ||||||||
\(467\) | 22.1962 | 1.02712 | 0.513558 | − | 0.858055i | \(-0.328327\pi\) | ||||
0.513558 | + | 0.858055i | \(0.328327\pi\) | |||||||
\(468\) | 1.26795 | 0.0586110 | ||||||||
\(469\) | −28.3923 | −1.31103 | ||||||||
\(470\) | 34.1769 | 1.57646 | ||||||||
\(471\) | −3.73205 | −0.171964 | ||||||||
\(472\) | 3.53590 | 0.162753 | ||||||||
\(473\) | −5.26795 | −0.242221 | ||||||||
\(474\) | −17.1244 | −0.786548 | ||||||||
\(475\) | 9.85641 | 0.452243 | ||||||||
\(476\) | −19.3923 | −0.888845 | ||||||||
\(477\) | 9.46410 | 0.433331 | ||||||||
\(478\) | 19.8564 | 0.908211 | ||||||||
\(479\) | −1.85641 | −0.0848214 | −0.0424107 | − | 0.999100i | \(-0.513504\pi\) | ||||
−0.0424107 | + | 0.999100i | \(0.513504\pi\) | |||||||
\(480\) | 3.00000 | 0.136931 | ||||||||
\(481\) | −9.12436 | −0.416035 | ||||||||
\(482\) | 10.2679 | 0.467692 | ||||||||
\(483\) | 3.00000 | 0.136505 | ||||||||
\(484\) | −3.53590 | −0.160723 | ||||||||
\(485\) | 12.0000 | 0.544892 | ||||||||
\(486\) | 1.00000 | 0.0453609 | ||||||||
\(487\) | 12.5167 | 0.567184 | 0.283592 | − | 0.958945i | \(-0.408474\pi\) | ||||
0.283592 | + | 0.958945i | \(0.408474\pi\) | |||||||
\(488\) | 6.39230 | 0.289366 | ||||||||
\(489\) | −23.7321 | −1.07320 | ||||||||
\(490\) | 6.00000 | 0.271052 | ||||||||
\(491\) | −23.6603 | −1.06777 | −0.533886 | − | 0.845556i | \(-0.679269\pi\) | ||||
−0.533886 | + | 0.845556i | \(0.679269\pi\) | |||||||
\(492\) | 12.1244 | 0.546608 | ||||||||
\(493\) | 6.46410 | 0.291128 | ||||||||
\(494\) | 3.12436 | 0.140571 | ||||||||
\(495\) | −8.19615 | −0.368390 | ||||||||
\(496\) | 0.732051 | 0.0328701 | ||||||||
\(497\) | 16.9808 | 0.761691 | ||||||||
\(498\) | −4.53590 | −0.203258 | ||||||||
\(499\) | −18.0526 | −0.808144 | −0.404072 | − | 0.914727i | \(-0.632405\pi\) | ||||
−0.404072 | + | 0.914727i | \(0.632405\pi\) | |||||||
\(500\) | −3.00000 | −0.134164 | ||||||||
\(501\) | −7.85641 | −0.350998 | ||||||||
\(502\) | −5.46410 | −0.243875 | ||||||||
\(503\) | −8.66025 | −0.386142 | −0.193071 | − | 0.981185i | \(-0.561845\pi\) | ||||
−0.193071 | + | 0.981185i | \(0.561845\pi\) | |||||||
\(504\) | 3.00000 | 0.133631 | ||||||||
\(505\) | 9.21539 | 0.410079 | ||||||||
\(506\) | −2.73205 | −0.121454 | ||||||||
\(507\) | −11.3923 | −0.505950 | ||||||||
\(508\) | 4.53590 | 0.201248 | ||||||||
\(509\) | 14.1244 | 0.626051 | 0.313026 | − | 0.949745i | \(-0.398657\pi\) | ||||
0.313026 | + | 0.949745i | \(0.398657\pi\) | |||||||
\(510\) | −19.3923 | −0.858706 | ||||||||
\(511\) | −38.7846 | −1.71573 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 2.46410 | 0.108793 | ||||||||
\(514\) | −19.2679 | −0.849873 | ||||||||
\(515\) | 44.5692 | 1.96395 | ||||||||
\(516\) | 1.92820 | 0.0848844 | ||||||||
\(517\) | −31.1244 | −1.36885 | ||||||||
\(518\) | −21.5885 | −0.948542 | ||||||||
\(519\) | 11.7321 | 0.514980 | ||||||||
\(520\) | 3.80385 | 0.166810 | ||||||||
\(521\) | −5.51666 | −0.241689 | −0.120845 | − | 0.992671i | \(-0.538560\pi\) | ||||
−0.120845 | + | 0.992671i | \(0.538560\pi\) | |||||||
\(522\) | −1.00000 | −0.0437688 | ||||||||
\(523\) | 4.24871 | 0.185783 | 0.0928916 | − | 0.995676i | \(-0.470389\pi\) | ||||
0.0928916 | + | 0.995676i | \(0.470389\pi\) | |||||||
\(524\) | −7.80385 | −0.340913 | ||||||||
\(525\) | 12.0000 | 0.523723 | ||||||||
\(526\) | −9.05256 | −0.394710 | ||||||||
\(527\) | −4.73205 | −0.206131 | ||||||||
\(528\) | −2.73205 | −0.118897 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 28.3923 | 1.23328 | ||||||||
\(531\) | 3.53590 | 0.153445 | ||||||||
\(532\) | 7.39230 | 0.320497 | ||||||||
\(533\) | 15.3731 | 0.665881 | ||||||||
\(534\) | −5.46410 | −0.236455 | ||||||||
\(535\) | −3.58846 | −0.155143 | ||||||||
\(536\) | −9.46410 | −0.408787 | ||||||||
\(537\) | −10.3923 | −0.448461 | ||||||||
\(538\) | 5.66025 | 0.244031 | ||||||||
\(539\) | −5.46410 | −0.235356 | ||||||||
\(540\) | 3.00000 | 0.129099 | ||||||||
\(541\) | 28.3205 | 1.21759 | 0.608797 | − | 0.793326i | \(-0.291652\pi\) | ||||
0.608797 | + | 0.793326i | \(0.291652\pi\) | |||||||
\(542\) | −16.7846 | −0.720961 | ||||||||
\(543\) | −5.12436 | −0.219907 | ||||||||
\(544\) | −6.46410 | −0.277146 | ||||||||
\(545\) | −24.0000 | −1.02805 | ||||||||
\(546\) | 3.80385 | 0.162790 | ||||||||
\(547\) | 1.32051 | 0.0564608 | 0.0282304 | − | 0.999601i | \(-0.491013\pi\) | ||||
0.0282304 | + | 0.999601i | \(0.491013\pi\) | |||||||
\(548\) | 0.928203 | 0.0396509 | ||||||||
\(549\) | 6.39230 | 0.272817 | ||||||||
\(550\) | −10.9282 | −0.465980 | ||||||||
\(551\) | −2.46410 | −0.104974 | ||||||||
\(552\) | 1.00000 | 0.0425628 | ||||||||
\(553\) | −51.3731 | −2.18461 | ||||||||
\(554\) | −5.12436 | −0.217713 | ||||||||
\(555\) | −21.5885 | −0.916379 | ||||||||
\(556\) | 7.85641 | 0.333186 | ||||||||
\(557\) | 17.9282 | 0.759642 | 0.379821 | − | 0.925060i | \(-0.375986\pi\) | ||||
0.379821 | + | 0.925060i | \(0.375986\pi\) | |||||||
\(558\) | 0.732051 | 0.0309902 | ||||||||
\(559\) | 2.44486 | 0.103407 | ||||||||
\(560\) | 9.00000 | 0.380319 | ||||||||
\(561\) | 17.6603 | 0.745617 | ||||||||
\(562\) | 20.5359 | 0.866255 | ||||||||
\(563\) | 2.67949 | 0.112927 | 0.0564636 | − | 0.998405i | \(-0.482018\pi\) | ||||
0.0564636 | + | 0.998405i | \(0.482018\pi\) | |||||||
\(564\) | 11.3923 | 0.479703 | ||||||||
\(565\) | −28.1769 | −1.18541 | ||||||||
\(566\) | −22.5885 | −0.949464 | ||||||||
\(567\) | 3.00000 | 0.125988 | ||||||||
\(568\) | 5.66025 | 0.237499 | ||||||||
\(569\) | −31.3923 | −1.31603 | −0.658017 | − | 0.753003i | \(-0.728604\pi\) | ||||
−0.658017 | + | 0.753003i | \(0.728604\pi\) | |||||||
\(570\) | 7.39230 | 0.309630 | ||||||||
\(571\) | 41.9090 | 1.75384 | 0.876918 | − | 0.480640i | \(-0.159596\pi\) | ||||
0.876918 | + | 0.480640i | \(0.159596\pi\) | |||||||
\(572\) | −3.46410 | −0.144841 | ||||||||
\(573\) | −26.1244 | −1.09136 | ||||||||
\(574\) | 36.3731 | 1.51818 | ||||||||
\(575\) | 4.00000 | 0.166812 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | −34.4449 | −1.43396 | −0.716979 | − | 0.697095i | \(-0.754476\pi\) | ||||
−0.716979 | + | 0.697095i | \(0.754476\pi\) | |||||||
\(578\) | 24.7846 | 1.03090 | ||||||||
\(579\) | 2.53590 | 0.105388 | ||||||||
\(580\) | −3.00000 | −0.124568 | ||||||||
\(581\) | −13.6077 | −0.564542 | ||||||||
\(582\) | 4.00000 | 0.165805 | ||||||||
\(583\) | −25.8564 | −1.07086 | ||||||||
\(584\) | −12.9282 | −0.534973 | ||||||||
\(585\) | 3.80385 | 0.157270 | ||||||||
\(586\) | 6.00000 | 0.247858 | ||||||||
\(587\) | −34.1769 | −1.41063 | −0.705316 | − | 0.708893i | \(-0.749195\pi\) | ||||
−0.705316 | + | 0.708893i | \(0.749195\pi\) | |||||||
\(588\) | 2.00000 | 0.0824786 | ||||||||
\(589\) | 1.80385 | 0.0743262 | ||||||||
\(590\) | 10.6077 | 0.436712 | ||||||||
\(591\) | 14.2679 | 0.586905 | ||||||||
\(592\) | −7.19615 | −0.295760 | ||||||||
\(593\) | 26.5359 | 1.08970 | 0.544849 | − | 0.838534i | \(-0.316587\pi\) | ||||
0.544849 | + | 0.838534i | \(0.316587\pi\) | |||||||
\(594\) | −2.73205 | −0.112097 | ||||||||
\(595\) | −58.1769 | −2.38502 | ||||||||
\(596\) | 5.00000 | 0.204808 | ||||||||
\(597\) | −17.3205 | −0.708881 | ||||||||
\(598\) | 1.26795 | 0.0518503 | ||||||||
\(599\) | −21.6077 | −0.882866 | −0.441433 | − | 0.897294i | \(-0.645530\pi\) | ||||
−0.441433 | + | 0.897294i | \(0.645530\pi\) | |||||||
\(600\) | 4.00000 | 0.163299 | ||||||||
\(601\) | −20.7846 | −0.847822 | −0.423911 | − | 0.905704i | \(-0.639343\pi\) | ||||
−0.423911 | + | 0.905704i | \(0.639343\pi\) | |||||||
\(602\) | 5.78461 | 0.235763 | ||||||||
\(603\) | −9.46410 | −0.385408 | ||||||||
\(604\) | −10.1244 | −0.411954 | ||||||||
\(605\) | −10.6077 | −0.431264 | ||||||||
\(606\) | 3.07180 | 0.124783 | ||||||||
\(607\) | −17.1244 | −0.695056 | −0.347528 | − | 0.937670i | \(-0.612979\pi\) | ||||
−0.347528 | + | 0.937670i | \(0.612979\pi\) | |||||||
\(608\) | 2.46410 | 0.0999325 | ||||||||
\(609\) | −3.00000 | −0.121566 | ||||||||
\(610\) | 19.1769 | 0.776451 | ||||||||
\(611\) | 14.4449 | 0.584377 | ||||||||
\(612\) | −6.46410 | −0.261296 | ||||||||
\(613\) | −39.8564 | −1.60979 | −0.804893 | − | 0.593421i | \(-0.797777\pi\) | ||||
−0.804893 | + | 0.593421i | \(0.797777\pi\) | |||||||
\(614\) | −22.9282 | −0.925307 | ||||||||
\(615\) | 36.3731 | 1.46670 | ||||||||
\(616\) | −8.19615 | −0.330232 | ||||||||
\(617\) | −48.8564 | −1.96688 | −0.983442 | − | 0.181221i | \(-0.941995\pi\) | ||||
−0.983442 | + | 0.181221i | \(0.941995\pi\) | |||||||
\(618\) | 14.8564 | 0.597612 | ||||||||
\(619\) | −31.0000 | −1.24600 | −0.622998 | − | 0.782224i | \(-0.714085\pi\) | ||||
−0.622998 | + | 0.782224i | \(0.714085\pi\) | |||||||
\(620\) | 2.19615 | 0.0881996 | ||||||||
\(621\) | 1.00000 | 0.0401286 | ||||||||
\(622\) | 28.3205 | 1.13555 | ||||||||
\(623\) | −16.3923 | −0.656744 | ||||||||
\(624\) | 1.26795 | 0.0507586 | ||||||||
\(625\) | −29.0000 | −1.16000 | ||||||||
\(626\) | 4.12436 | 0.164842 | ||||||||
\(627\) | −6.73205 | −0.268852 | ||||||||
\(628\) | −3.73205 | −0.148925 | ||||||||
\(629\) | 46.5167 | 1.85474 | ||||||||
\(630\) | 9.00000 | 0.358569 | ||||||||
\(631\) | −17.0000 | −0.676759 | −0.338380 | − | 0.941010i | \(-0.609879\pi\) | ||||
−0.338380 | + | 0.941010i | \(0.609879\pi\) | |||||||
\(632\) | −17.1244 | −0.681170 | ||||||||
\(633\) | 0.803848 | 0.0319501 | ||||||||
\(634\) | 27.6603 | 1.09853 | ||||||||
\(635\) | 13.6077 | 0.540005 | ||||||||
\(636\) | 9.46410 | 0.375276 | ||||||||
\(637\) | 2.53590 | 0.100476 | ||||||||
\(638\) | 2.73205 | 0.108163 | ||||||||
\(639\) | 5.66025 | 0.223916 | ||||||||
\(640\) | 3.00000 | 0.118585 | ||||||||
\(641\) | 1.53590 | 0.0606643 | 0.0303322 | − | 0.999540i | \(-0.490343\pi\) | ||||
0.0303322 | + | 0.999540i | \(0.490343\pi\) | |||||||
\(642\) | −1.19615 | −0.0472084 | ||||||||
\(643\) | 35.9090 | 1.41611 | 0.708056 | − | 0.706157i | \(-0.249573\pi\) | ||||
0.708056 | + | 0.706157i | \(0.249573\pi\) | |||||||
\(644\) | 3.00000 | 0.118217 | ||||||||
\(645\) | 5.78461 | 0.227769 | ||||||||
\(646\) | −15.9282 | −0.626687 | ||||||||
\(647\) | 14.5885 | 0.573531 | 0.286766 | − | 0.958001i | \(-0.407420\pi\) | ||||
0.286766 | + | 0.958001i | \(0.407420\pi\) | |||||||
\(648\) | 1.00000 | 0.0392837 | ||||||||
\(649\) | −9.66025 | −0.379198 | ||||||||
\(650\) | 5.07180 | 0.198932 | ||||||||
\(651\) | 2.19615 | 0.0860740 | ||||||||
\(652\) | −23.7321 | −0.929419 | ||||||||
\(653\) | 38.3923 | 1.50241 | 0.751203 | − | 0.660071i | \(-0.229474\pi\) | ||||
0.751203 | + | 0.660071i | \(0.229474\pi\) | |||||||
\(654\) | −8.00000 | −0.312825 | ||||||||
\(655\) | −23.4115 | −0.914765 | ||||||||
\(656\) | 12.1244 | 0.473377 | ||||||||
\(657\) | −12.9282 | −0.504377 | ||||||||
\(658\) | 34.1769 | 1.33235 | ||||||||
\(659\) | 32.0000 | 1.24654 | 0.623272 | − | 0.782006i | \(-0.285803\pi\) | ||||
0.623272 | + | 0.782006i | \(0.285803\pi\) | |||||||
\(660\) | −8.19615 | −0.319035 | ||||||||
\(661\) | −16.0000 | −0.622328 | −0.311164 | − | 0.950356i | \(-0.600719\pi\) | ||||
−0.311164 | + | 0.950356i | \(0.600719\pi\) | |||||||
\(662\) | −29.4449 | −1.14441 | ||||||||
\(663\) | −8.19615 | −0.318312 | ||||||||
\(664\) | −4.53590 | −0.176027 | ||||||||
\(665\) | 22.1769 | 0.859984 | ||||||||
\(666\) | −7.19615 | −0.278845 | ||||||||
\(667\) | −1.00000 | −0.0387202 | ||||||||
\(668\) | −7.85641 | −0.303973 | ||||||||
\(669\) | 8.00000 | 0.309298 | ||||||||
\(670\) | −28.3923 | −1.09689 | ||||||||
\(671\) | −17.4641 | −0.674194 | ||||||||
\(672\) | 3.00000 | 0.115728 | ||||||||
\(673\) | 19.0000 | 0.732396 | 0.366198 | − | 0.930537i | \(-0.380659\pi\) | ||||
0.366198 | + | 0.930537i | \(0.380659\pi\) | |||||||
\(674\) | −7.07180 | −0.272395 | ||||||||
\(675\) | 4.00000 | 0.153960 | ||||||||
\(676\) | −11.3923 | −0.438166 | ||||||||
\(677\) | −34.7846 | −1.33688 | −0.668441 | − | 0.743766i | \(-0.733038\pi\) | ||||
−0.668441 | + | 0.743766i | \(0.733038\pi\) | |||||||
\(678\) | −9.39230 | −0.360709 | ||||||||
\(679\) | 12.0000 | 0.460518 | ||||||||
\(680\) | −19.3923 | −0.743661 | ||||||||
\(681\) | 5.58846 | 0.214150 | ||||||||
\(682\) | −2.00000 | −0.0765840 | ||||||||
\(683\) | −28.4641 | −1.08915 | −0.544574 | − | 0.838713i | \(-0.683309\pi\) | ||||
−0.544574 | + | 0.838713i | \(0.683309\pi\) | |||||||
\(684\) | 2.46410 | 0.0942173 | ||||||||
\(685\) | 2.78461 | 0.106394 | ||||||||
\(686\) | −15.0000 | −0.572703 | ||||||||
\(687\) | 2.80385 | 0.106973 | ||||||||
\(688\) | 1.92820 | 0.0735121 | ||||||||
\(689\) | 12.0000 | 0.457164 | ||||||||
\(690\) | 3.00000 | 0.114208 | ||||||||
\(691\) | 5.51666 | 0.209864 | 0.104932 | − | 0.994479i | \(-0.466538\pi\) | ||||
0.104932 | + | 0.994479i | \(0.466538\pi\) | |||||||
\(692\) | 11.7321 | 0.445986 | ||||||||
\(693\) | −8.19615 | −0.311346 | ||||||||
\(694\) | −8.85641 | −0.336185 | ||||||||
\(695\) | 23.5692 | 0.894031 | ||||||||
\(696\) | −1.00000 | −0.0379049 | ||||||||
\(697\) | −78.3731 | −2.96859 | ||||||||
\(698\) | 14.3923 | 0.544757 | ||||||||
\(699\) | −11.3205 | −0.428181 | ||||||||
\(700\) | 12.0000 | 0.453557 | ||||||||
\(701\) | 17.7846 | 0.671715 | 0.335858 | − | 0.941913i | \(-0.390974\pi\) | ||||
0.335858 | + | 0.941913i | \(0.390974\pi\) | |||||||
\(702\) | 1.26795 | 0.0478557 | ||||||||
\(703\) | −17.7321 | −0.668777 | ||||||||
\(704\) | −2.73205 | −0.102968 | ||||||||
\(705\) | 34.1769 | 1.28718 | ||||||||
\(706\) | −4.53590 | −0.170711 | ||||||||
\(707\) | 9.21539 | 0.346580 | ||||||||
\(708\) | 3.53590 | 0.132887 | ||||||||
\(709\) | 21.6603 | 0.813468 | 0.406734 | − | 0.913547i | \(-0.366668\pi\) | ||||
0.406734 | + | 0.913547i | \(0.366668\pi\) | |||||||
\(710\) | 16.9808 | 0.637277 | ||||||||
\(711\) | −17.1244 | −0.642214 | ||||||||
\(712\) | −5.46410 | −0.204776 | ||||||||
\(713\) | 0.732051 | 0.0274155 | ||||||||
\(714\) | −19.3923 | −0.725739 | ||||||||
\(715\) | −10.3923 | −0.388650 | ||||||||
\(716\) | −10.3923 | −0.388379 | ||||||||
\(717\) | 19.8564 | 0.741551 | ||||||||
\(718\) | −7.73205 | −0.288558 | ||||||||
\(719\) | 27.8038 | 1.03691 | 0.518454 | − | 0.855105i | \(-0.326508\pi\) | ||||
0.518454 | + | 0.855105i | \(0.326508\pi\) | |||||||
\(720\) | 3.00000 | 0.111803 | ||||||||
\(721\) | 44.5692 | 1.65984 | ||||||||
\(722\) | −12.9282 | −0.481138 | ||||||||
\(723\) | 10.2679 | 0.381869 | ||||||||
\(724\) | −5.12436 | −0.190445 | ||||||||
\(725\) | −4.00000 | −0.148556 | ||||||||
\(726\) | −3.53590 | −0.131229 | ||||||||
\(727\) | 28.2487 | 1.04769 | 0.523843 | − | 0.851815i | \(-0.324498\pi\) | ||||
0.523843 | + | 0.851815i | \(0.324498\pi\) | |||||||
\(728\) | 3.80385 | 0.140980 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −38.7846 | −1.43548 | ||||||||
\(731\) | −12.4641 | −0.461001 | ||||||||
\(732\) | 6.39230 | 0.236266 | ||||||||
\(733\) | 10.9282 | 0.403642 | 0.201821 | − | 0.979422i | \(-0.435314\pi\) | ||||
0.201821 | + | 0.979422i | \(0.435314\pi\) | |||||||
\(734\) | 31.6603 | 1.16860 | ||||||||
\(735\) | 6.00000 | 0.221313 | ||||||||
\(736\) | 1.00000 | 0.0368605 | ||||||||
\(737\) | 25.8564 | 0.952433 | ||||||||
\(738\) | 12.1244 | 0.446304 | ||||||||
\(739\) | −36.3923 | −1.33871 | −0.669356 | − | 0.742942i | \(-0.733430\pi\) | ||||
−0.669356 | + | 0.742942i | \(0.733430\pi\) | |||||||
\(740\) | −21.5885 | −0.793607 | ||||||||
\(741\) | 3.12436 | 0.114776 | ||||||||
\(742\) | 28.3923 | 1.04231 | ||||||||
\(743\) | 11.4449 | 0.419871 | 0.209936 | − | 0.977715i | \(-0.432675\pi\) | ||||
0.209936 | + | 0.977715i | \(0.432675\pi\) | |||||||
\(744\) | 0.732051 | 0.0268383 | ||||||||
\(745\) | 15.0000 | 0.549557 | ||||||||
\(746\) | 17.0718 | 0.625043 | ||||||||
\(747\) | −4.53590 | −0.165960 | ||||||||
\(748\) | 17.6603 | 0.645723 | ||||||||
\(749\) | −3.58846 | −0.131119 | ||||||||
\(750\) | −3.00000 | −0.109545 | ||||||||
\(751\) | 5.32051 | 0.194148 | 0.0970740 | − | 0.995277i | \(-0.469052\pi\) | ||||
0.0970740 | + | 0.995277i | \(0.469052\pi\) | |||||||
\(752\) | 11.3923 | 0.415435 | ||||||||
\(753\) | −5.46410 | −0.199123 | ||||||||
\(754\) | −1.26795 | −0.0461760 | ||||||||
\(755\) | −30.3731 | −1.10539 | ||||||||
\(756\) | 3.00000 | 0.109109 | ||||||||
\(757\) | 9.19615 | 0.334240 | 0.167120 | − | 0.985937i | \(-0.446553\pi\) | ||||
0.167120 | + | 0.985937i | \(0.446553\pi\) | |||||||
\(758\) | −23.8564 | −0.866504 | ||||||||
\(759\) | −2.73205 | −0.0991672 | ||||||||
\(760\) | 7.39230 | 0.268147 | ||||||||
\(761\) | 22.1962 | 0.804610 | 0.402305 | − | 0.915506i | \(-0.368209\pi\) | ||||
0.402305 | + | 0.915506i | \(0.368209\pi\) | |||||||
\(762\) | 4.53590 | 0.164318 | ||||||||
\(763\) | −24.0000 | −0.868858 | ||||||||
\(764\) | −26.1244 | −0.945146 | ||||||||
\(765\) | −19.3923 | −0.701130 | ||||||||
\(766\) | 20.1962 | 0.729717 | ||||||||
\(767\) | 4.48334 | 0.161884 | ||||||||
\(768\) | 1.00000 | 0.0360844 | ||||||||
\(769\) | 46.0526 | 1.66070 | 0.830349 | − | 0.557244i | \(-0.188141\pi\) | ||||
0.830349 | + | 0.557244i | \(0.188141\pi\) | |||||||
\(770\) | −24.5885 | −0.886106 | ||||||||
\(771\) | −19.2679 | −0.693918 | ||||||||
\(772\) | 2.53590 | 0.0912690 | ||||||||
\(773\) | −26.9808 | −0.970431 | −0.485215 | − | 0.874395i | \(-0.661259\pi\) | ||||
−0.485215 | + | 0.874395i | \(0.661259\pi\) | |||||||
\(774\) | 1.92820 | 0.0693078 | ||||||||
\(775\) | 2.92820 | 0.105184 | ||||||||
\(776\) | 4.00000 | 0.143592 | ||||||||
\(777\) | −21.5885 | −0.774482 | ||||||||
\(778\) | −13.8564 | −0.496776 | ||||||||
\(779\) | 29.8756 | 1.07041 | ||||||||
\(780\) | 3.80385 | 0.136200 | ||||||||
\(781\) | −15.4641 | −0.553349 | ||||||||
\(782\) | −6.46410 | −0.231156 | ||||||||
\(783\) | −1.00000 | −0.0357371 | ||||||||
\(784\) | 2.00000 | 0.0714286 | ||||||||
\(785\) | −11.1962 | −0.399608 | ||||||||
\(786\) | −7.80385 | −0.278354 | ||||||||
\(787\) | −16.1962 | −0.577330 | −0.288665 | − | 0.957430i | \(-0.593211\pi\) | ||||
−0.288665 | + | 0.957430i | \(0.593211\pi\) | |||||||
\(788\) | 14.2679 | 0.508275 | ||||||||
\(789\) | −9.05256 | −0.322280 | ||||||||
\(790\) | −51.3731 | −1.82777 | ||||||||
\(791\) | −28.1769 | −1.00186 | ||||||||
\(792\) | −2.73205 | −0.0970792 | ||||||||
\(793\) | 8.10512 | 0.287821 | ||||||||
\(794\) | 0.339746 | 0.0120571 | ||||||||
\(795\) | 28.3923 | 1.00697 | ||||||||
\(796\) | −17.3205 | −0.613909 | ||||||||
\(797\) | 47.2295 | 1.67295 | 0.836477 | − | 0.548002i | \(-0.184611\pi\) | ||||
0.836477 | + | 0.548002i | \(0.184611\pi\) | |||||||
\(798\) | 7.39230 | 0.261685 | ||||||||
\(799\) | −73.6410 | −2.60523 | ||||||||
\(800\) | 4.00000 | 0.141421 | ||||||||
\(801\) | −5.46410 | −0.193065 | ||||||||
\(802\) | −25.7128 | −0.907951 | ||||||||
\(803\) | 35.3205 | 1.24643 | ||||||||
\(804\) | −9.46410 | −0.333773 | ||||||||
\(805\) | 9.00000 | 0.317208 | ||||||||
\(806\) | 0.928203 | 0.0326946 | ||||||||
\(807\) | 5.66025 | 0.199250 | ||||||||
\(808\) | 3.07180 | 0.108065 | ||||||||
\(809\) | 6.00000 | 0.210949 | 0.105474 | − | 0.994422i | \(-0.466364\pi\) | ||||
0.105474 | + | 0.994422i | \(0.466364\pi\) | |||||||
\(810\) | 3.00000 | 0.105409 | ||||||||
\(811\) | 29.5692 | 1.03832 | 0.519158 | − | 0.854678i | \(-0.326246\pi\) | ||||
0.519158 | + | 0.854678i | \(0.326246\pi\) | |||||||
\(812\) | −3.00000 | −0.105279 | ||||||||
\(813\) | −16.7846 | −0.588662 | ||||||||
\(814\) | 19.6603 | 0.689092 | ||||||||
\(815\) | −71.1962 | −2.49389 | ||||||||
\(816\) | −6.46410 | −0.226289 | ||||||||
\(817\) | 4.75129 | 0.166227 | ||||||||
\(818\) | 19.1244 | 0.668667 | ||||||||
\(819\) | 3.80385 | 0.132917 | ||||||||
\(820\) | 36.3731 | 1.27020 | ||||||||
\(821\) | 0.535898 | 0.0187030 | 0.00935149 | − | 0.999956i | \(-0.497023\pi\) | ||||
0.00935149 | + | 0.999956i | \(0.497023\pi\) | |||||||
\(822\) | 0.928203 | 0.0323748 | ||||||||
\(823\) | −40.3013 | −1.40481 | −0.702407 | − | 0.711776i | \(-0.747891\pi\) | ||||
−0.702407 | + | 0.711776i | \(0.747891\pi\) | |||||||
\(824\) | 14.8564 | 0.517547 | ||||||||
\(825\) | −10.9282 | −0.380471 | ||||||||
\(826\) | 10.6077 | 0.369089 | ||||||||
\(827\) | −34.9282 | −1.21457 | −0.607286 | − | 0.794483i | \(-0.707742\pi\) | ||||
−0.607286 | + | 0.794483i | \(0.707742\pi\) | |||||||
\(828\) | 1.00000 | 0.0347524 | ||||||||
\(829\) | −35.3923 | −1.22923 | −0.614613 | − | 0.788829i | \(-0.710688\pi\) | ||||
−0.614613 | + | 0.788829i | \(0.710688\pi\) | |||||||
\(830\) | −13.6077 | −0.472330 | ||||||||
\(831\) | −5.12436 | −0.177762 | ||||||||
\(832\) | 1.26795 | 0.0439582 | ||||||||
\(833\) | −12.9282 | −0.447936 | ||||||||
\(834\) | 7.85641 | 0.272045 | ||||||||
\(835\) | −23.5692 | −0.815646 | ||||||||
\(836\) | −6.73205 | −0.232833 | ||||||||
\(837\) | 0.732051 | 0.0253034 | ||||||||
\(838\) | −9.58846 | −0.331228 | ||||||||
\(839\) | 23.7321 | 0.819321 | 0.409661 | − | 0.912238i | \(-0.365647\pi\) | ||||
0.409661 | + | 0.912238i | \(0.365647\pi\) | |||||||
\(840\) | 9.00000 | 0.310530 | ||||||||
\(841\) | 1.00000 | 0.0344828 | ||||||||
\(842\) | 30.3923 | 1.04739 | ||||||||
\(843\) | 20.5359 | 0.707294 | ||||||||
\(844\) | 0.803848 | 0.0276696 | ||||||||
\(845\) | −34.1769 | −1.17572 | ||||||||
\(846\) | 11.3923 | 0.391676 | ||||||||
\(847\) | −10.6077 | −0.364485 | ||||||||
\(848\) | 9.46410 | 0.324999 | ||||||||
\(849\) | −22.5885 | −0.775234 | ||||||||
\(850\) | −25.8564 | −0.886867 | ||||||||
\(851\) | −7.19615 | −0.246681 | ||||||||
\(852\) | 5.66025 | 0.193917 | ||||||||
\(853\) | 43.7846 | 1.49916 | 0.749578 | − | 0.661916i | \(-0.230256\pi\) | ||||
0.749578 | + | 0.661916i | \(0.230256\pi\) | |||||||
\(854\) | 19.1769 | 0.656221 | ||||||||
\(855\) | 7.39230 | 0.252811 | ||||||||
\(856\) | −1.19615 | −0.0408836 | ||||||||
\(857\) | −26.4449 | −0.903339 | −0.451670 | − | 0.892185i | \(-0.649171\pi\) | ||||
−0.451670 | + | 0.892185i | \(0.649171\pi\) | |||||||
\(858\) | −3.46410 | −0.118262 | ||||||||
\(859\) | −25.5885 | −0.873067 | −0.436533 | − | 0.899688i | \(-0.643794\pi\) | ||||
−0.436533 | + | 0.899688i | \(0.643794\pi\) | |||||||
\(860\) | 5.78461 | 0.197254 | ||||||||
\(861\) | 36.3731 | 1.23959 | ||||||||
\(862\) | 30.1962 | 1.02849 | ||||||||
\(863\) | 5.94744 | 0.202453 | 0.101227 | − | 0.994863i | \(-0.467723\pi\) | ||||
0.101227 | + | 0.994863i | \(0.467723\pi\) | |||||||
\(864\) | 1.00000 | 0.0340207 | ||||||||
\(865\) | 35.1962 | 1.19671 | ||||||||
\(866\) | 11.5167 | 0.391352 | ||||||||
\(867\) | 24.7846 | 0.841729 | ||||||||
\(868\) | 2.19615 | 0.0745423 | ||||||||
\(869\) | 46.7846 | 1.58706 | ||||||||
\(870\) | −3.00000 | −0.101710 | ||||||||
\(871\) | −12.0000 | −0.406604 | ||||||||
\(872\) | −8.00000 | −0.270914 | ||||||||
\(873\) | 4.00000 | 0.135379 | ||||||||
\(874\) | 2.46410 | 0.0833495 | ||||||||
\(875\) | −9.00000 | −0.304256 | ||||||||
\(876\) | −12.9282 | −0.436804 | ||||||||
\(877\) | 11.1244 | 0.375643 | 0.187821 | − | 0.982203i | \(-0.439857\pi\) | ||||
0.187821 | + | 0.982203i | \(0.439857\pi\) | |||||||
\(878\) | 21.1962 | 0.715335 | ||||||||
\(879\) | 6.00000 | 0.202375 | ||||||||
\(880\) | −8.19615 | −0.276292 | ||||||||
\(881\) | 1.07180 | 0.0361098 | 0.0180549 | − | 0.999837i | \(-0.494253\pi\) | ||||
0.0180549 | + | 0.999837i | \(0.494253\pi\) | |||||||
\(882\) | 2.00000 | 0.0673435 | ||||||||
\(883\) | 9.51666 | 0.320261 | 0.160131 | − | 0.987096i | \(-0.448808\pi\) | ||||
0.160131 | + | 0.987096i | \(0.448808\pi\) | |||||||
\(884\) | −8.19615 | −0.275666 | ||||||||
\(885\) | 10.6077 | 0.356574 | ||||||||
\(886\) | 25.1769 | 0.845835 | ||||||||
\(887\) | −15.4641 | −0.519234 | −0.259617 | − | 0.965712i | \(-0.583596\pi\) | ||||
−0.259617 | + | 0.965712i | \(0.583596\pi\) | |||||||
\(888\) | −7.19615 | −0.241487 | ||||||||
\(889\) | 13.6077 | 0.456387 | ||||||||
\(890\) | −16.3923 | −0.549471 | ||||||||
\(891\) | −2.73205 | −0.0915271 | ||||||||
\(892\) | 8.00000 | 0.267860 | ||||||||
\(893\) | 28.0718 | 0.939387 | ||||||||
\(894\) | 5.00000 | 0.167225 | ||||||||
\(895\) | −31.1769 | −1.04213 | ||||||||
\(896\) | 3.00000 | 0.100223 | ||||||||
\(897\) | 1.26795 | 0.0423356 | ||||||||
\(898\) | 8.66025 | 0.288996 | ||||||||
\(899\) | −0.732051 | −0.0244153 | ||||||||
\(900\) | 4.00000 | 0.133333 | ||||||||
\(901\) | −61.1769 | −2.03810 | ||||||||
\(902\) | −33.1244 | −1.10292 | ||||||||
\(903\) | 5.78461 | 0.192500 | ||||||||
\(904\) | −9.39230 | −0.312383 | ||||||||
\(905\) | −15.3731 | −0.511018 | ||||||||
\(906\) | −10.1244 | −0.336359 | ||||||||
\(907\) | −51.8564 | −1.72186 | −0.860932 | − | 0.508720i | \(-0.830119\pi\) | ||||
−0.860932 | + | 0.508720i | \(0.830119\pi\) | |||||||
\(908\) | 5.58846 | 0.185459 | ||||||||
\(909\) | 3.07180 | 0.101885 | ||||||||
\(910\) | 11.4115 | 0.378289 | ||||||||
\(911\) | −16.0000 | −0.530104 | −0.265052 | − | 0.964234i | \(-0.585389\pi\) | ||||
−0.265052 | + | 0.964234i | \(0.585389\pi\) | |||||||
\(912\) | 2.46410 | 0.0815946 | ||||||||
\(913\) | 12.3923 | 0.410125 | ||||||||
\(914\) | 30.9090 | 1.02238 | ||||||||
\(915\) | 19.1769 | 0.633969 | ||||||||
\(916\) | 2.80385 | 0.0926417 | ||||||||
\(917\) | −23.4115 | −0.773117 | ||||||||
\(918\) | −6.46410 | −0.213347 | ||||||||
\(919\) | 53.3923 | 1.76125 | 0.880625 | − | 0.473814i | \(-0.157123\pi\) | ||||
0.880625 | + | 0.473814i | \(0.157123\pi\) | |||||||
\(920\) | 3.00000 | 0.0989071 | ||||||||
\(921\) | −22.9282 | −0.755510 | ||||||||
\(922\) | −8.05256 | −0.265197 | ||||||||
\(923\) | 7.17691 | 0.236231 | ||||||||
\(924\) | −8.19615 | −0.269634 | ||||||||
\(925\) | −28.7846 | −0.946432 | ||||||||
\(926\) | −31.1769 | −1.02454 | ||||||||
\(927\) | 14.8564 | 0.487948 | ||||||||
\(928\) | −1.00000 | −0.0328266 | ||||||||
\(929\) | 42.0000 | 1.37798 | 0.688988 | − | 0.724773i | \(-0.258055\pi\) | ||||
0.688988 | + | 0.724773i | \(0.258055\pi\) | |||||||
\(930\) | 2.19615 | 0.0720147 | ||||||||
\(931\) | 4.92820 | 0.161515 | ||||||||
\(932\) | −11.3205 | −0.370816 | ||||||||
\(933\) | 28.3205 | 0.927172 | ||||||||
\(934\) | 22.1962 | 0.726280 | ||||||||
\(935\) | 52.9808 | 1.73266 | ||||||||
\(936\) | 1.26795 | 0.0414442 | ||||||||
\(937\) | −24.4115 | −0.797490 | −0.398745 | − | 0.917062i | \(-0.630554\pi\) | ||||
−0.398745 | + | 0.917062i | \(0.630554\pi\) | |||||||
\(938\) | −28.3923 | −0.927042 | ||||||||
\(939\) | 4.12436 | 0.134593 | ||||||||
\(940\) | 34.1769 | 1.11473 | ||||||||
\(941\) | 25.1769 | 0.820744 | 0.410372 | − | 0.911918i | \(-0.365399\pi\) | ||||
0.410372 | + | 0.911918i | \(0.365399\pi\) | |||||||
\(942\) | −3.73205 | −0.121597 | ||||||||
\(943\) | 12.1244 | 0.394823 | ||||||||
\(944\) | 3.53590 | 0.115084 | ||||||||
\(945\) | 9.00000 | 0.292770 | ||||||||
\(946\) | −5.26795 | −0.171276 | ||||||||
\(947\) | 10.0526 | 0.326664 | 0.163332 | − | 0.986571i | \(-0.447776\pi\) | ||||
0.163332 | + | 0.986571i | \(0.447776\pi\) | |||||||
\(948\) | −17.1244 | −0.556173 | ||||||||
\(949\) | −16.3923 | −0.532117 | ||||||||
\(950\) | 9.85641 | 0.319784 | ||||||||
\(951\) | 27.6603 | 0.896945 | ||||||||
\(952\) | −19.3923 | −0.628508 | ||||||||
\(953\) | −45.4641 | −1.47273 | −0.736363 | − | 0.676586i | \(-0.763459\pi\) | ||||
−0.736363 | + | 0.676586i | \(0.763459\pi\) | |||||||
\(954\) | 9.46410 | 0.306412 | ||||||||
\(955\) | −78.3731 | −2.53609 | ||||||||
\(956\) | 19.8564 | 0.642202 | ||||||||
\(957\) | 2.73205 | 0.0883147 | ||||||||
\(958\) | −1.85641 | −0.0599778 | ||||||||
\(959\) | 2.78461 | 0.0899197 | ||||||||
\(960\) | 3.00000 | 0.0968246 | ||||||||
\(961\) | −30.4641 | −0.982713 | ||||||||
\(962\) | −9.12436 | −0.294181 | ||||||||
\(963\) | −1.19615 | −0.0385455 | ||||||||
\(964\) | 10.2679 | 0.330708 | ||||||||
\(965\) | 7.60770 | 0.244900 | ||||||||
\(966\) | 3.00000 | 0.0965234 | ||||||||
\(967\) | −14.8756 | −0.478368 | −0.239184 | − | 0.970974i | \(-0.576880\pi\) | ||||
−0.239184 | + | 0.970974i | \(0.576880\pi\) | |||||||
\(968\) | −3.53590 | −0.113648 | ||||||||
\(969\) | −15.9282 | −0.511688 | ||||||||
\(970\) | 12.0000 | 0.385297 | ||||||||
\(971\) | −40.5885 | −1.30255 | −0.651273 | − | 0.758844i | \(-0.725765\pi\) | ||||
−0.651273 | + | 0.758844i | \(0.725765\pi\) | |||||||
\(972\) | 1.00000 | 0.0320750 | ||||||||
\(973\) | 23.5692 | 0.755594 | ||||||||
\(974\) | 12.5167 | 0.401060 | ||||||||
\(975\) | 5.07180 | 0.162427 | ||||||||
\(976\) | 6.39230 | 0.204613 | ||||||||
\(977\) | −32.9808 | −1.05515 | −0.527574 | − | 0.849509i | \(-0.676898\pi\) | ||||
−0.527574 | + | 0.849509i | \(0.676898\pi\) | |||||||
\(978\) | −23.7321 | −0.758867 | ||||||||
\(979\) | 14.9282 | 0.477107 | ||||||||
\(980\) | 6.00000 | 0.191663 | ||||||||
\(981\) | −8.00000 | −0.255420 | ||||||||
\(982\) | −23.6603 | −0.755029 | ||||||||
\(983\) | 50.1051 | 1.59811 | 0.799053 | − | 0.601261i | \(-0.205335\pi\) | ||||
0.799053 | + | 0.601261i | \(0.205335\pi\) | |||||||
\(984\) | 12.1244 | 0.386510 | ||||||||
\(985\) | 42.8038 | 1.36384 | ||||||||
\(986\) | 6.46410 | 0.205859 | ||||||||
\(987\) | 34.1769 | 1.08786 | ||||||||
\(988\) | 3.12436 | 0.0993990 | ||||||||
\(989\) | 1.92820 | 0.0613133 | ||||||||
\(990\) | −8.19615 | −0.260491 | ||||||||
\(991\) | 45.4449 | 1.44360 | 0.721802 | − | 0.692100i | \(-0.243314\pi\) | ||||
0.721802 | + | 0.692100i | \(0.243314\pi\) | |||||||
\(992\) | 0.732051 | 0.0232426 | ||||||||
\(993\) | −29.4449 | −0.934405 | ||||||||
\(994\) | 16.9808 | 0.538597 | ||||||||
\(995\) | −51.9615 | −1.64729 | ||||||||
\(996\) | −4.53590 | −0.143725 | ||||||||
\(997\) | 43.4974 | 1.37758 | 0.688789 | − | 0.724962i | \(-0.258143\pi\) | ||||
0.688789 | + | 0.724962i | \(0.258143\pi\) | |||||||
\(998\) | −18.0526 | −0.571444 | ||||||||
\(999\) | −7.19615 | −0.227676 |
(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 | 4002.2.a.w.1.1 | ✓ | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4002.2.a.w.1.1 | ✓ | 2 | 1.1 | even | 1 | trivial |