Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2850,2,Mod(1,2850)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2850, 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("2850.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2850 = 2 \cdot 3 \cdot 5^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2850.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: | \(22.7573645761\) |
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: | \(\Z[a_1, \ldots, a_{7}]\) |
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 | \(\chi\) | \(=\) | 2850.1 |
$q$-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 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 1.00000 | 0.408248 | ||||||||
\(7\) | −0.732051 | −0.276689 | −0.138345 | − | 0.990384i | \(-0.544178\pi\) | ||||
−0.138345 | + | 0.990384i | \(0.544178\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.73205 | 1.12526 | 0.562628 | − | 0.826710i | \(-0.309790\pi\) | ||||
0.562628 | + | 0.826710i | \(0.309790\pi\) | |||||||
\(12\) | 1.00000 | 0.288675 | ||||||||
\(13\) | 2.73205 | 0.757735 | 0.378867 | − | 0.925451i | \(-0.376314\pi\) | ||||
0.378867 | + | 0.925451i | \(0.376314\pi\) | |||||||
\(14\) | −0.732051 | −0.195649 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 6.19615 | 1.50279 | 0.751394 | − | 0.659854i | \(-0.229382\pi\) | ||||
0.751394 | + | 0.659854i | \(0.229382\pi\) | |||||||
\(18\) | 1.00000 | 0.235702 | ||||||||
\(19\) | −1.00000 | −0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.732051 | −0.159747 | ||||||||
\(22\) | 3.73205 | 0.795676 | ||||||||
\(23\) | −5.92820 | −1.23612 | −0.618058 | − | 0.786133i | \(-0.712080\pi\) | ||||
−0.618058 | + | 0.786133i | \(0.712080\pi\) | |||||||
\(24\) | 1.00000 | 0.204124 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 2.73205 | 0.535799 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | −0.732051 | −0.138345 | ||||||||
\(29\) | −1.73205 | −0.321634 | −0.160817 | − | 0.986984i | \(-0.551413\pi\) | ||||
−0.160817 | + | 0.986984i | \(0.551413\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.46410 | −0.442566 | −0.221283 | − | 0.975210i | \(-0.571024\pi\) | ||||
−0.221283 | + | 0.975210i | \(0.571024\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 3.73205 | 0.649667 | ||||||||
\(34\) | 6.19615 | 1.06263 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 2.00000 | 0.328798 | 0.164399 | − | 0.986394i | \(-0.447432\pi\) | ||||
0.164399 | + | 0.986394i | \(0.447432\pi\) | |||||||
\(38\) | −1.00000 | −0.162221 | ||||||||
\(39\) | 2.73205 | 0.437478 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2.92820 | −0.457309 | −0.228654 | − | 0.973508i | \(-0.573433\pi\) | ||||
−0.228654 | + | 0.973508i | \(0.573433\pi\) | |||||||
\(42\) | −0.732051 | −0.112958 | ||||||||
\(43\) | 8.19615 | 1.24990 | 0.624951 | − | 0.780664i | \(-0.285119\pi\) | ||||
0.624951 | + | 0.780664i | \(0.285119\pi\) | |||||||
\(44\) | 3.73205 | 0.562628 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −5.92820 | −0.874066 | ||||||||
\(47\) | −3.46410 | −0.505291 | −0.252646 | − | 0.967559i | \(-0.581301\pi\) | ||||
−0.252646 | + | 0.967559i | \(0.581301\pi\) | |||||||
\(48\) | 1.00000 | 0.144338 | ||||||||
\(49\) | −6.46410 | −0.923443 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 6.19615 | 0.867635 | ||||||||
\(52\) | 2.73205 | 0.378867 | ||||||||
\(53\) | 1.73205 | 0.237915 | 0.118958 | − | 0.992899i | \(-0.462045\pi\) | ||||
0.118958 | + | 0.992899i | \(0.462045\pi\) | |||||||
\(54\) | 1.00000 | 0.136083 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −0.732051 | −0.0978244 | ||||||||
\(57\) | −1.00000 | −0.132453 | ||||||||
\(58\) | −1.73205 | −0.227429 | ||||||||
\(59\) | −8.19615 | −1.06705 | −0.533524 | − | 0.845785i | \(-0.679133\pi\) | ||||
−0.533524 | + | 0.845785i | \(0.679133\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 10.6603 | 1.36491 | 0.682453 | − | 0.730930i | \(-0.260913\pi\) | ||||
0.682453 | + | 0.730930i | \(0.260913\pi\) | |||||||
\(62\) | −2.46410 | −0.312941 | ||||||||
\(63\) | −0.732051 | −0.0922297 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 3.73205 | 0.459384 | ||||||||
\(67\) | 0.267949 | 0.0327352 | 0.0163676 | − | 0.999866i | \(-0.494790\pi\) | ||||
0.0163676 | + | 0.999866i | \(0.494790\pi\) | |||||||
\(68\) | 6.19615 | 0.751394 | ||||||||
\(69\) | −5.92820 | −0.713672 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 12.1962 | 1.44742 | 0.723708 | − | 0.690106i | \(-0.242436\pi\) | ||||
0.723708 | + | 0.690106i | \(0.242436\pi\) | |||||||
\(72\) | 1.00000 | 0.117851 | ||||||||
\(73\) | 2.46410 | 0.288401 | 0.144201 | − | 0.989548i | \(-0.453939\pi\) | ||||
0.144201 | + | 0.989548i | \(0.453939\pi\) | |||||||
\(74\) | 2.00000 | 0.232495 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −1.00000 | −0.114708 | ||||||||
\(77\) | −2.73205 | −0.311346 | ||||||||
\(78\) | 2.73205 | 0.309344 | ||||||||
\(79\) | −5.53590 | −0.622837 | −0.311419 | − | 0.950273i | \(-0.600804\pi\) | ||||
−0.311419 | + | 0.950273i | \(0.600804\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −2.92820 | −0.323366 | ||||||||
\(83\) | −3.73205 | −0.409646 | −0.204823 | − | 0.978799i | \(-0.565662\pi\) | ||||
−0.204823 | + | 0.978799i | \(0.565662\pi\) | |||||||
\(84\) | −0.732051 | −0.0798733 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 8.19615 | 0.883814 | ||||||||
\(87\) | −1.73205 | −0.185695 | ||||||||
\(88\) | 3.73205 | 0.397838 | ||||||||
\(89\) | 10.8564 | 1.15078 | 0.575388 | − | 0.817880i | \(-0.304851\pi\) | ||||
0.575388 | + | 0.817880i | \(0.304851\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.00000 | −0.209657 | ||||||||
\(92\) | −5.92820 | −0.618058 | ||||||||
\(93\) | −2.46410 | −0.255515 | ||||||||
\(94\) | −3.46410 | −0.357295 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 1.00000 | 0.102062 | ||||||||
\(97\) | 15.1244 | 1.53565 | 0.767823 | − | 0.640662i | \(-0.221340\pi\) | ||||
0.767823 | + | 0.640662i | \(0.221340\pi\) | |||||||
\(98\) | −6.46410 | −0.652973 | ||||||||
\(99\) | 3.73205 | 0.375085 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 9.26795 | 0.922195 | 0.461098 | − | 0.887349i | \(-0.347456\pi\) | ||||
0.461098 | + | 0.887349i | \(0.347456\pi\) | |||||||
\(102\) | 6.19615 | 0.613511 | ||||||||
\(103\) | 3.53590 | 0.348402 | 0.174201 | − | 0.984710i | \(-0.444266\pi\) | ||||
0.174201 | + | 0.984710i | \(0.444266\pi\) | |||||||
\(104\) | 2.73205 | 0.267900 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1.73205 | 0.168232 | ||||||||
\(107\) | −2.19615 | −0.212310 | −0.106155 | − | 0.994350i | \(-0.533854\pi\) | ||||
−0.106155 | + | 0.994350i | \(0.533854\pi\) | |||||||
\(108\) | 1.00000 | 0.0962250 | ||||||||
\(109\) | 2.39230 | 0.229141 | 0.114571 | − | 0.993415i | \(-0.463451\pi\) | ||||
0.114571 | + | 0.993415i | \(0.463451\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 2.00000 | 0.189832 | ||||||||
\(112\) | −0.732051 | −0.0691723 | ||||||||
\(113\) | 13.3923 | 1.25984 | 0.629921 | − | 0.776659i | \(-0.283087\pi\) | ||||
0.629921 | + | 0.776659i | \(0.283087\pi\) | |||||||
\(114\) | −1.00000 | −0.0936586 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −1.73205 | −0.160817 | ||||||||
\(117\) | 2.73205 | 0.252578 | ||||||||
\(118\) | −8.19615 | −0.754517 | ||||||||
\(119\) | −4.53590 | −0.415805 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2.92820 | 0.266200 | ||||||||
\(122\) | 10.6603 | 0.965134 | ||||||||
\(123\) | −2.92820 | −0.264027 | ||||||||
\(124\) | −2.46410 | −0.221283 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −0.732051 | −0.0652163 | ||||||||
\(127\) | 5.00000 | 0.443678 | 0.221839 | − | 0.975083i | \(-0.428794\pi\) | ||||
0.221839 | + | 0.975083i | \(0.428794\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 8.19615 | 0.721631 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 10.2679 | 0.897115 | 0.448557 | − | 0.893754i | \(-0.351938\pi\) | ||||
0.448557 | + | 0.893754i | \(0.351938\pi\) | |||||||
\(132\) | 3.73205 | 0.324833 | ||||||||
\(133\) | 0.732051 | 0.0634769 | ||||||||
\(134\) | 0.267949 | 0.0231473 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 6.19615 | 0.531316 | ||||||||
\(137\) | 12.3923 | 1.05875 | 0.529373 | − | 0.848389i | \(-0.322427\pi\) | ||||
0.529373 | + | 0.848389i | \(0.322427\pi\) | |||||||
\(138\) | −5.92820 | −0.504642 | ||||||||
\(139\) | −21.1244 | −1.79174 | −0.895872 | − | 0.444312i | \(-0.853448\pi\) | ||||
−0.895872 | + | 0.444312i | \(0.853448\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −3.46410 | −0.291730 | ||||||||
\(142\) | 12.1962 | 1.02348 | ||||||||
\(143\) | 10.1962 | 0.852645 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 2.46410 | 0.203931 | ||||||||
\(147\) | −6.46410 | −0.533150 | ||||||||
\(148\) | 2.00000 | 0.164399 | ||||||||
\(149\) | −21.8564 | −1.79055 | −0.895273 | − | 0.445517i | \(-0.853020\pi\) | ||||
−0.895273 | + | 0.445517i | \(0.853020\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −11.4641 | −0.932935 | −0.466468 | − | 0.884538i | \(-0.654474\pi\) | ||||
−0.466468 | + | 0.884538i | \(0.654474\pi\) | |||||||
\(152\) | −1.00000 | −0.0811107 | ||||||||
\(153\) | 6.19615 | 0.500929 | ||||||||
\(154\) | −2.73205 | −0.220155 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 2.73205 | 0.218739 | ||||||||
\(157\) | −13.8564 | −1.10586 | −0.552931 | − | 0.833227i | \(-0.686491\pi\) | ||||
−0.552931 | + | 0.833227i | \(0.686491\pi\) | |||||||
\(158\) | −5.53590 | −0.440412 | ||||||||
\(159\) | 1.73205 | 0.137361 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 4.33975 | 0.342020 | ||||||||
\(162\) | 1.00000 | 0.0785674 | ||||||||
\(163\) | 2.00000 | 0.156652 | 0.0783260 | − | 0.996928i | \(-0.475042\pi\) | ||||
0.0783260 | + | 0.996928i | \(0.475042\pi\) | |||||||
\(164\) | −2.92820 | −0.228654 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −3.73205 | −0.289663 | ||||||||
\(167\) | 8.92820 | 0.690885 | 0.345443 | − | 0.938440i | \(-0.387729\pi\) | ||||
0.345443 | + | 0.938440i | \(0.387729\pi\) | |||||||
\(168\) | −0.732051 | −0.0564789 | ||||||||
\(169\) | −5.53590 | −0.425838 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.00000 | −0.0764719 | ||||||||
\(172\) | 8.19615 | 0.624951 | ||||||||
\(173\) | −13.5885 | −1.03311 | −0.516556 | − | 0.856254i | \(-0.672786\pi\) | ||||
−0.516556 | + | 0.856254i | \(0.672786\pi\) | |||||||
\(174\) | −1.73205 | −0.131306 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 3.73205 | 0.281314 | ||||||||
\(177\) | −8.19615 | −0.616061 | ||||||||
\(178\) | 10.8564 | 0.813722 | ||||||||
\(179\) | −12.0000 | −0.896922 | −0.448461 | − | 0.893802i | \(-0.648028\pi\) | ||||
−0.448461 | + | 0.893802i | \(0.648028\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −16.5885 | −1.23301 | −0.616505 | − | 0.787351i | \(-0.711452\pi\) | ||||
−0.616505 | + | 0.787351i | \(0.711452\pi\) | |||||||
\(182\) | −2.00000 | −0.148250 | ||||||||
\(183\) | 10.6603 | 0.788029 | ||||||||
\(184\) | −5.92820 | −0.437033 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −2.46410 | −0.180677 | ||||||||
\(187\) | 23.1244 | 1.69102 | ||||||||
\(188\) | −3.46410 | −0.252646 | ||||||||
\(189\) | −0.732051 | −0.0532489 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 3.00000 | 0.217072 | 0.108536 | − | 0.994092i | \(-0.465384\pi\) | ||||
0.108536 | + | 0.994092i | \(0.465384\pi\) | |||||||
\(192\) | 1.00000 | 0.0721688 | ||||||||
\(193\) | −22.0526 | −1.58738 | −0.793689 | − | 0.608324i | \(-0.791842\pi\) | ||||
−0.793689 | + | 0.608324i | \(0.791842\pi\) | |||||||
\(194\) | 15.1244 | 1.08587 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −6.46410 | −0.461722 | ||||||||
\(197\) | −24.5885 | −1.75186 | −0.875928 | − | 0.482443i | \(-0.839750\pi\) | ||||
−0.875928 | + | 0.482443i | \(0.839750\pi\) | |||||||
\(198\) | 3.73205 | 0.265225 | ||||||||
\(199\) | −14.0000 | −0.992434 | −0.496217 | − | 0.868199i | \(-0.665278\pi\) | ||||
−0.496217 | + | 0.868199i | \(0.665278\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0.267949 | 0.0188997 | ||||||||
\(202\) | 9.26795 | 0.652091 | ||||||||
\(203\) | 1.26795 | 0.0889926 | ||||||||
\(204\) | 6.19615 | 0.433817 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 3.53590 | 0.246358 | ||||||||
\(207\) | −5.92820 | −0.412039 | ||||||||
\(208\) | 2.73205 | 0.189434 | ||||||||
\(209\) | −3.73205 | −0.258151 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −10.2679 | −0.706875 | −0.353437 | − | 0.935458i | \(-0.614987\pi\) | ||||
−0.353437 | + | 0.935458i | \(0.614987\pi\) | |||||||
\(212\) | 1.73205 | 0.118958 | ||||||||
\(213\) | 12.1962 | 0.835667 | ||||||||
\(214\) | −2.19615 | −0.150126 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | 1.80385 | 0.122453 | ||||||||
\(218\) | 2.39230 | 0.162027 | ||||||||
\(219\) | 2.46410 | 0.166509 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 16.9282 | 1.13871 | ||||||||
\(222\) | 2.00000 | 0.134231 | ||||||||
\(223\) | 3.53590 | 0.236781 | 0.118391 | − | 0.992967i | \(-0.462226\pi\) | ||||
0.118391 | + | 0.992967i | \(0.462226\pi\) | |||||||
\(224\) | −0.732051 | −0.0489122 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 13.3923 | 0.890843 | ||||||||
\(227\) | 6.00000 | 0.398234 | 0.199117 | − | 0.979976i | \(-0.436193\pi\) | ||||
0.199117 | + | 0.979976i | \(0.436193\pi\) | |||||||
\(228\) | −1.00000 | −0.0662266 | ||||||||
\(229\) | −6.26795 | −0.414198 | −0.207099 | − | 0.978320i | \(-0.566402\pi\) | ||||
−0.207099 | + | 0.978320i | \(0.566402\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −2.73205 | −0.179756 | ||||||||
\(232\) | −1.73205 | −0.113715 | ||||||||
\(233\) | 21.1244 | 1.38390 | 0.691951 | − | 0.721944i | \(-0.256751\pi\) | ||||
0.691951 | + | 0.721944i | \(0.256751\pi\) | |||||||
\(234\) | 2.73205 | 0.178600 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −8.19615 | −0.533524 | ||||||||
\(237\) | −5.53590 | −0.359595 | ||||||||
\(238\) | −4.53590 | −0.294019 | ||||||||
\(239\) | −14.0000 | −0.905585 | −0.452792 | − | 0.891616i | \(-0.649572\pi\) | ||||
−0.452792 | + | 0.891616i | \(0.649572\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −30.1962 | −1.94511 | −0.972553 | − | 0.232683i | \(-0.925249\pi\) | ||||
−0.972553 | + | 0.232683i | \(0.925249\pi\) | |||||||
\(242\) | 2.92820 | 0.188232 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 10.6603 | 0.682453 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −2.92820 | −0.186695 | ||||||||
\(247\) | −2.73205 | −0.173836 | ||||||||
\(248\) | −2.46410 | −0.156471 | ||||||||
\(249\) | −3.73205 | −0.236509 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 11.4641 | 0.723608 | 0.361804 | − | 0.932254i | \(-0.382161\pi\) | ||||
0.361804 | + | 0.932254i | \(0.382161\pi\) | |||||||
\(252\) | −0.732051 | −0.0461149 | ||||||||
\(253\) | −22.1244 | −1.39095 | ||||||||
\(254\) | 5.00000 | 0.313728 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −9.00000 | −0.561405 | −0.280702 | − | 0.959795i | \(-0.590567\pi\) | ||||
−0.280702 | + | 0.959795i | \(0.590567\pi\) | |||||||
\(258\) | 8.19615 | 0.510270 | ||||||||
\(259\) | −1.46410 | −0.0909748 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.73205 | −0.107211 | ||||||||
\(262\) | 10.2679 | 0.634356 | ||||||||
\(263\) | −15.0000 | −0.924940 | −0.462470 | − | 0.886635i | \(-0.653037\pi\) | ||||
−0.462470 | + | 0.886635i | \(0.653037\pi\) | |||||||
\(264\) | 3.73205 | 0.229692 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0.732051 | 0.0448849 | ||||||||
\(267\) | 10.8564 | 0.664401 | ||||||||
\(268\) | 0.267949 | 0.0163676 | ||||||||
\(269\) | −20.5359 | −1.25210 | −0.626048 | − | 0.779785i | \(-0.715329\pi\) | ||||
−0.626048 | + | 0.779785i | \(0.715329\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −15.8038 | −0.960015 | −0.480008 | − | 0.877264i | \(-0.659366\pi\) | ||||
−0.480008 | + | 0.877264i | \(0.659366\pi\) | |||||||
\(272\) | 6.19615 | 0.375697 | ||||||||
\(273\) | −2.00000 | −0.121046 | ||||||||
\(274\) | 12.3923 | 0.748647 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −5.92820 | −0.356836 | ||||||||
\(277\) | −11.1962 | −0.672712 | −0.336356 | − | 0.941735i | \(-0.609194\pi\) | ||||
−0.336356 | + | 0.941735i | \(0.609194\pi\) | |||||||
\(278\) | −21.1244 | −1.26695 | ||||||||
\(279\) | −2.46410 | −0.147522 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 17.7846 | 1.06094 | 0.530470 | − | 0.847703i | \(-0.322015\pi\) | ||||
0.530470 | + | 0.847703i | \(0.322015\pi\) | |||||||
\(282\) | −3.46410 | −0.206284 | ||||||||
\(283\) | −4.00000 | −0.237775 | −0.118888 | − | 0.992908i | \(-0.537933\pi\) | ||||
−0.118888 | + | 0.992908i | \(0.537933\pi\) | |||||||
\(284\) | 12.1962 | 0.723708 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 10.1962 | 0.602911 | ||||||||
\(287\) | 2.14359 | 0.126532 | ||||||||
\(288\) | 1.00000 | 0.0589256 | ||||||||
\(289\) | 21.3923 | 1.25837 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 15.1244 | 0.886605 | ||||||||
\(292\) | 2.46410 | 0.144201 | ||||||||
\(293\) | 27.7321 | 1.62012 | 0.810062 | − | 0.586344i | \(-0.199433\pi\) | ||||
0.810062 | + | 0.586344i | \(0.199433\pi\) | |||||||
\(294\) | −6.46410 | −0.376994 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 2.00000 | 0.116248 | ||||||||
\(297\) | 3.73205 | 0.216556 | ||||||||
\(298\) | −21.8564 | −1.26611 | ||||||||
\(299\) | −16.1962 | −0.936648 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −6.00000 | −0.345834 | ||||||||
\(302\) | −11.4641 | −0.659685 | ||||||||
\(303\) | 9.26795 | 0.532430 | ||||||||
\(304\) | −1.00000 | −0.0573539 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 6.19615 | 0.354210 | ||||||||
\(307\) | 20.2679 | 1.15675 | 0.578376 | − | 0.815770i | \(-0.303686\pi\) | ||||
0.578376 | + | 0.815770i | \(0.303686\pi\) | |||||||
\(308\) | −2.73205 | −0.155673 | ||||||||
\(309\) | 3.53590 | 0.201150 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −29.3205 | −1.66261 | −0.831307 | − | 0.555814i | \(-0.812407\pi\) | ||||
−0.831307 | + | 0.555814i | \(0.812407\pi\) | |||||||
\(312\) | 2.73205 | 0.154672 | ||||||||
\(313\) | 3.92820 | 0.222035 | 0.111018 | − | 0.993818i | \(-0.464589\pi\) | ||||
0.111018 | + | 0.993818i | \(0.464589\pi\) | |||||||
\(314\) | −13.8564 | −0.781962 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −5.53590 | −0.311419 | ||||||||
\(317\) | 1.73205 | 0.0972817 | 0.0486408 | − | 0.998816i | \(-0.484511\pi\) | ||||
0.0486408 | + | 0.998816i | \(0.484511\pi\) | |||||||
\(318\) | 1.73205 | 0.0971286 | ||||||||
\(319\) | −6.46410 | −0.361920 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −2.19615 | −0.122577 | ||||||||
\(322\) | 4.33975 | 0.241845 | ||||||||
\(323\) | −6.19615 | −0.344763 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 2.00000 | 0.110770 | ||||||||
\(327\) | 2.39230 | 0.132295 | ||||||||
\(328\) | −2.92820 | −0.161683 | ||||||||
\(329\) | 2.53590 | 0.139809 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −22.2679 | −1.22396 | −0.611979 | − | 0.790874i | \(-0.709626\pi\) | ||||
−0.611979 | + | 0.790874i | \(0.709626\pi\) | |||||||
\(332\) | −3.73205 | −0.204823 | ||||||||
\(333\) | 2.00000 | 0.109599 | ||||||||
\(334\) | 8.92820 | 0.488530 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −0.732051 | −0.0399366 | ||||||||
\(337\) | −10.5359 | −0.573927 | −0.286963 | − | 0.957942i | \(-0.592646\pi\) | ||||
−0.286963 | + | 0.957942i | \(0.592646\pi\) | |||||||
\(338\) | −5.53590 | −0.301113 | ||||||||
\(339\) | 13.3923 | 0.727370 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −9.19615 | −0.498000 | ||||||||
\(342\) | −1.00000 | −0.0540738 | ||||||||
\(343\) | 9.85641 | 0.532196 | ||||||||
\(344\) | 8.19615 | 0.441907 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −13.5885 | −0.730520 | ||||||||
\(347\) | 20.7846 | 1.11578 | 0.557888 | − | 0.829916i | \(-0.311612\pi\) | ||||
0.557888 | + | 0.829916i | \(0.311612\pi\) | |||||||
\(348\) | −1.73205 | −0.0928477 | ||||||||
\(349\) | −17.0526 | −0.912803 | −0.456401 | − | 0.889774i | \(-0.650862\pi\) | ||||
−0.456401 | + | 0.889774i | \(0.650862\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2.73205 | 0.145826 | ||||||||
\(352\) | 3.73205 | 0.198919 | ||||||||
\(353\) | −16.0526 | −0.854391 | −0.427196 | − | 0.904159i | \(-0.640498\pi\) | ||||
−0.427196 | + | 0.904159i | \(0.640498\pi\) | |||||||
\(354\) | −8.19615 | −0.435621 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 10.8564 | 0.575388 | ||||||||
\(357\) | −4.53590 | −0.240065 | ||||||||
\(358\) | −12.0000 | −0.634220 | ||||||||
\(359\) | −16.9282 | −0.893436 | −0.446718 | − | 0.894675i | \(-0.647407\pi\) | ||||
−0.446718 | + | 0.894675i | \(0.647407\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | −16.5885 | −0.871870 | ||||||||
\(363\) | 2.92820 | 0.153691 | ||||||||
\(364\) | −2.00000 | −0.104828 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 10.6603 | 0.557220 | ||||||||
\(367\) | 13.2679 | 0.692581 | 0.346291 | − | 0.938127i | \(-0.387441\pi\) | ||||
0.346291 | + | 0.938127i | \(0.387441\pi\) | |||||||
\(368\) | −5.92820 | −0.309029 | ||||||||
\(369\) | −2.92820 | −0.152436 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1.26795 | −0.0658286 | ||||||||
\(372\) | −2.46410 | −0.127758 | ||||||||
\(373\) | 31.5167 | 1.63187 | 0.815935 | − | 0.578143i | \(-0.196222\pi\) | ||||
0.815935 | + | 0.578143i | \(0.196222\pi\) | |||||||
\(374\) | 23.1244 | 1.19573 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −3.46410 | −0.178647 | ||||||||
\(377\) | −4.73205 | −0.243713 | ||||||||
\(378\) | −0.732051 | −0.0376526 | ||||||||
\(379\) | −0.392305 | −0.0201513 | −0.0100757 | − | 0.999949i | \(-0.503207\pi\) | ||||
−0.0100757 | + | 0.999949i | \(0.503207\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 5.00000 | 0.256158 | ||||||||
\(382\) | 3.00000 | 0.153493 | ||||||||
\(383\) | 19.5167 | 0.997255 | 0.498627 | − | 0.866816i | \(-0.333838\pi\) | ||||
0.498627 | + | 0.866816i | \(0.333838\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −22.0526 | −1.12245 | ||||||||
\(387\) | 8.19615 | 0.416634 | ||||||||
\(388\) | 15.1244 | 0.767823 | ||||||||
\(389\) | 21.7128 | 1.10088 | 0.550442 | − | 0.834874i | \(-0.314459\pi\) | ||||
0.550442 | + | 0.834874i | \(0.314459\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −36.7321 | −1.85762 | ||||||||
\(392\) | −6.46410 | −0.326486 | ||||||||
\(393\) | 10.2679 | 0.517950 | ||||||||
\(394\) | −24.5885 | −1.23875 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 3.73205 | 0.187543 | ||||||||
\(397\) | −11.7321 | −0.588815 | −0.294407 | − | 0.955680i | \(-0.595122\pi\) | ||||
−0.294407 | + | 0.955680i | \(0.595122\pi\) | |||||||
\(398\) | −14.0000 | −0.701757 | ||||||||
\(399\) | 0.732051 | 0.0366484 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 16.8564 | 0.841769 | 0.420884 | − | 0.907114i | \(-0.361720\pi\) | ||||
0.420884 | + | 0.907114i | \(0.361720\pi\) | |||||||
\(402\) | 0.267949 | 0.0133641 | ||||||||
\(403\) | −6.73205 | −0.335347 | ||||||||
\(404\) | 9.26795 | 0.461098 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 1.26795 | 0.0629273 | ||||||||
\(407\) | 7.46410 | 0.369982 | ||||||||
\(408\) | 6.19615 | 0.306755 | ||||||||
\(409\) | 1.60770 | 0.0794954 | 0.0397477 | − | 0.999210i | \(-0.487345\pi\) | ||||
0.0397477 | + | 0.999210i | \(0.487345\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 12.3923 | 0.611267 | ||||||||
\(412\) | 3.53590 | 0.174201 | ||||||||
\(413\) | 6.00000 | 0.295241 | ||||||||
\(414\) | −5.92820 | −0.291355 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 2.73205 | 0.133950 | ||||||||
\(417\) | −21.1244 | −1.03446 | ||||||||
\(418\) | −3.73205 | −0.182541 | ||||||||
\(419\) | 13.8564 | 0.676930 | 0.338465 | − | 0.940979i | \(-0.390092\pi\) | ||||
0.338465 | + | 0.940979i | \(0.390092\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 6.78461 | 0.330662 | 0.165331 | − | 0.986238i | \(-0.447131\pi\) | ||||
0.165331 | + | 0.986238i | \(0.447131\pi\) | |||||||
\(422\) | −10.2679 | −0.499836 | ||||||||
\(423\) | −3.46410 | −0.168430 | ||||||||
\(424\) | 1.73205 | 0.0841158 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 12.1962 | 0.590906 | ||||||||
\(427\) | −7.80385 | −0.377655 | ||||||||
\(428\) | −2.19615 | −0.106155 | ||||||||
\(429\) | 10.1962 | 0.492275 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −29.3205 | −1.41232 | −0.706160 | − | 0.708053i | \(-0.749574\pi\) | ||||
−0.706160 | + | 0.708053i | \(0.749574\pi\) | |||||||
\(432\) | 1.00000 | 0.0481125 | ||||||||
\(433\) | −24.1962 | −1.16279 | −0.581396 | − | 0.813620i | \(-0.697493\pi\) | ||||
−0.581396 | + | 0.813620i | \(0.697493\pi\) | |||||||
\(434\) | 1.80385 | 0.0865875 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 2.39230 | 0.114571 | ||||||||
\(437\) | 5.92820 | 0.283584 | ||||||||
\(438\) | 2.46410 | 0.117739 | ||||||||
\(439\) | 25.7846 | 1.23063 | 0.615316 | − | 0.788280i | \(-0.289028\pi\) | ||||
0.615316 | + | 0.788280i | \(0.289028\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −6.46410 | −0.307814 | ||||||||
\(442\) | 16.9282 | 0.805193 | ||||||||
\(443\) | −3.33975 | −0.158676 | −0.0793381 | − | 0.996848i | \(-0.525281\pi\) | ||||
−0.0793381 | + | 0.996848i | \(0.525281\pi\) | |||||||
\(444\) | 2.00000 | 0.0949158 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 3.53590 | 0.167430 | ||||||||
\(447\) | −21.8564 | −1.03377 | ||||||||
\(448\) | −0.732051 | −0.0345861 | ||||||||
\(449\) | 24.4641 | 1.15453 | 0.577266 | − | 0.816556i | \(-0.304120\pi\) | ||||
0.577266 | + | 0.816556i | \(0.304120\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −10.9282 | −0.514589 | ||||||||
\(452\) | 13.3923 | 0.629921 | ||||||||
\(453\) | −11.4641 | −0.538630 | ||||||||
\(454\) | 6.00000 | 0.281594 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −1.00000 | −0.0468293 | ||||||||
\(457\) | −5.07180 | −0.237249 | −0.118624 | − | 0.992939i | \(-0.537848\pi\) | ||||
−0.118624 | + | 0.992939i | \(0.537848\pi\) | |||||||
\(458\) | −6.26795 | −0.292882 | ||||||||
\(459\) | 6.19615 | 0.289212 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −17.8564 | −0.831656 | −0.415828 | − | 0.909443i | \(-0.636508\pi\) | ||||
−0.415828 | + | 0.909443i | \(0.636508\pi\) | |||||||
\(462\) | −2.73205 | −0.127107 | ||||||||
\(463\) | −35.3205 | −1.64148 | −0.820742 | − | 0.571300i | \(-0.806439\pi\) | ||||
−0.820742 | + | 0.571300i | \(0.806439\pi\) | |||||||
\(464\) | −1.73205 | −0.0804084 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 21.1244 | 0.978567 | ||||||||
\(467\) | 7.19615 | 0.332998 | 0.166499 | − | 0.986042i | \(-0.446754\pi\) | ||||
0.166499 | + | 0.986042i | \(0.446754\pi\) | |||||||
\(468\) | 2.73205 | 0.126289 | ||||||||
\(469\) | −0.196152 | −0.00905748 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −13.8564 | −0.638470 | ||||||||
\(472\) | −8.19615 | −0.377258 | ||||||||
\(473\) | 30.5885 | 1.40646 | ||||||||
\(474\) | −5.53590 | −0.254272 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −4.53590 | −0.207903 | ||||||||
\(477\) | 1.73205 | 0.0793052 | ||||||||
\(478\) | −14.0000 | −0.640345 | ||||||||
\(479\) | 3.14359 | 0.143634 | 0.0718172 | − | 0.997418i | \(-0.477120\pi\) | ||||
0.0718172 | + | 0.997418i | \(0.477120\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 5.46410 | 0.249142 | ||||||||
\(482\) | −30.1962 | −1.37540 | ||||||||
\(483\) | 4.33975 | 0.197465 | ||||||||
\(484\) | 2.92820 | 0.133100 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 1.00000 | 0.0453609 | ||||||||
\(487\) | 2.14359 | 0.0971355 | 0.0485677 | − | 0.998820i | \(-0.484534\pi\) | ||||
0.0485677 | + | 0.998820i | \(0.484534\pi\) | |||||||
\(488\) | 10.6603 | 0.482567 | ||||||||
\(489\) | 2.00000 | 0.0904431 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −2.92820 | −0.132148 | −0.0660740 | − | 0.997815i | \(-0.521047\pi\) | ||||
−0.0660740 | + | 0.997815i | \(0.521047\pi\) | |||||||
\(492\) | −2.92820 | −0.132014 | ||||||||
\(493\) | −10.7321 | −0.483347 | ||||||||
\(494\) | −2.73205 | −0.122921 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −2.46410 | −0.110641 | ||||||||
\(497\) | −8.92820 | −0.400485 | ||||||||
\(498\) | −3.73205 | −0.167237 | ||||||||
\(499\) | 41.3731 | 1.85211 | 0.926056 | − | 0.377385i | \(-0.123177\pi\) | ||||
0.926056 | + | 0.377385i | \(0.123177\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 8.92820 | 0.398883 | ||||||||
\(502\) | 11.4641 | 0.511668 | ||||||||
\(503\) | −17.8564 | −0.796178 | −0.398089 | − | 0.917347i | \(-0.630326\pi\) | ||||
−0.398089 | + | 0.917347i | \(0.630326\pi\) | |||||||
\(504\) | −0.732051 | −0.0326081 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −22.1244 | −0.983548 | ||||||||
\(507\) | −5.53590 | −0.245858 | ||||||||
\(508\) | 5.00000 | 0.221839 | ||||||||
\(509\) | 13.8756 | 0.615027 | 0.307514 | − | 0.951544i | \(-0.400503\pi\) | ||||
0.307514 | + | 0.951544i | \(0.400503\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.80385 | −0.0797975 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −1.00000 | −0.0441511 | ||||||||
\(514\) | −9.00000 | −0.396973 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 8.19615 | 0.360815 | ||||||||
\(517\) | −12.9282 | −0.568582 | ||||||||
\(518\) | −1.46410 | −0.0643289 | ||||||||
\(519\) | −13.5885 | −0.596467 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 24.1769 | 1.05921 | 0.529605 | − | 0.848244i | \(-0.322340\pi\) | ||||
0.529605 | + | 0.848244i | \(0.322340\pi\) | |||||||
\(522\) | −1.73205 | −0.0758098 | ||||||||
\(523\) | 4.00000 | 0.174908 | 0.0874539 | − | 0.996169i | \(-0.472127\pi\) | ||||
0.0874539 | + | 0.996169i | \(0.472127\pi\) | |||||||
\(524\) | 10.2679 | 0.448557 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −15.0000 | −0.654031 | ||||||||
\(527\) | −15.2679 | −0.665082 | ||||||||
\(528\) | 3.73205 | 0.162417 | ||||||||
\(529\) | 12.1436 | 0.527982 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −8.19615 | −0.355683 | ||||||||
\(532\) | 0.732051 | 0.0317384 | ||||||||
\(533\) | −8.00000 | −0.346518 | ||||||||
\(534\) | 10.8564 | 0.469803 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0.267949 | 0.0115736 | ||||||||
\(537\) | −12.0000 | −0.517838 | ||||||||
\(538\) | −20.5359 | −0.885365 | ||||||||
\(539\) | −24.1244 | −1.03911 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 17.1962 | 0.739320 | 0.369660 | − | 0.929167i | \(-0.379474\pi\) | ||||
0.369660 | + | 0.929167i | \(0.379474\pi\) | |||||||
\(542\) | −15.8038 | −0.678833 | ||||||||
\(543\) | −16.5885 | −0.711879 | ||||||||
\(544\) | 6.19615 | 0.265658 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −2.00000 | −0.0855921 | ||||||||
\(547\) | −43.4449 | −1.85757 | −0.928784 | − | 0.370621i | \(-0.879145\pi\) | ||||
−0.928784 | + | 0.370621i | \(0.879145\pi\) | |||||||
\(548\) | 12.3923 | 0.529373 | ||||||||
\(549\) | 10.6603 | 0.454969 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.73205 | 0.0737878 | ||||||||
\(552\) | −5.92820 | −0.252321 | ||||||||
\(553\) | 4.05256 | 0.172332 | ||||||||
\(554\) | −11.1962 | −0.475679 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −21.1244 | −0.895872 | ||||||||
\(557\) | −3.80385 | −0.161174 | −0.0805871 | − | 0.996748i | \(-0.525680\pi\) | ||||
−0.0805871 | + | 0.996748i | \(0.525680\pi\) | |||||||
\(558\) | −2.46410 | −0.104314 | ||||||||
\(559\) | 22.3923 | 0.947094 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 23.1244 | 0.976311 | ||||||||
\(562\) | 17.7846 | 0.750198 | ||||||||
\(563\) | −7.66025 | −0.322841 | −0.161421 | − | 0.986886i | \(-0.551608\pi\) | ||||
−0.161421 | + | 0.986886i | \(0.551608\pi\) | |||||||
\(564\) | −3.46410 | −0.145865 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −4.00000 | −0.168133 | ||||||||
\(567\) | −0.732051 | −0.0307432 | ||||||||
\(568\) | 12.1962 | 0.511739 | ||||||||
\(569\) | 18.0000 | 0.754599 | 0.377300 | − | 0.926091i | \(-0.376853\pi\) | ||||
0.377300 | + | 0.926091i | \(0.376853\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −6.19615 | −0.259301 | −0.129650 | − | 0.991560i | \(-0.541386\pi\) | ||||
−0.129650 | + | 0.991560i | \(0.541386\pi\) | |||||||
\(572\) | 10.1962 | 0.426323 | ||||||||
\(573\) | 3.00000 | 0.125327 | ||||||||
\(574\) | 2.14359 | 0.0894719 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | 17.2487 | 0.718073 | 0.359037 | − | 0.933323i | \(-0.383105\pi\) | ||||
0.359037 | + | 0.933323i | \(0.383105\pi\) | |||||||
\(578\) | 21.3923 | 0.889803 | ||||||||
\(579\) | −22.0526 | −0.916473 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 2.73205 | 0.113345 | ||||||||
\(582\) | 15.1244 | 0.626925 | ||||||||
\(583\) | 6.46410 | 0.267716 | ||||||||
\(584\) | 2.46410 | 0.101965 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 27.7321 | 1.14560 | ||||||||
\(587\) | 12.2679 | 0.506352 | 0.253176 | − | 0.967420i | \(-0.418525\pi\) | ||||
0.253176 | + | 0.967420i | \(0.418525\pi\) | |||||||
\(588\) | −6.46410 | −0.266575 | ||||||||
\(589\) | 2.46410 | 0.101532 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −24.5885 | −1.01143 | ||||||||
\(592\) | 2.00000 | 0.0821995 | ||||||||
\(593\) | 27.6077 | 1.13371 | 0.566856 | − | 0.823817i | \(-0.308160\pi\) | ||||
0.566856 | + | 0.823817i | \(0.308160\pi\) | |||||||
\(594\) | 3.73205 | 0.153128 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −21.8564 | −0.895273 | ||||||||
\(597\) | −14.0000 | −0.572982 | ||||||||
\(598\) | −16.1962 | −0.662310 | ||||||||
\(599\) | −3.66025 | −0.149554 | −0.0747770 | − | 0.997200i | \(-0.523824\pi\) | ||||
−0.0747770 | + | 0.997200i | \(0.523824\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −10.0526 | −0.410052 | −0.205026 | − | 0.978756i | \(-0.565728\pi\) | ||||
−0.205026 | + | 0.978756i | \(0.565728\pi\) | |||||||
\(602\) | −6.00000 | −0.244542 | ||||||||
\(603\) | 0.267949 | 0.0109117 | ||||||||
\(604\) | −11.4641 | −0.466468 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 9.26795 | 0.376485 | ||||||||
\(607\) | 11.7846 | 0.478323 | 0.239161 | − | 0.970980i | \(-0.423128\pi\) | ||||
0.239161 | + | 0.970980i | \(0.423128\pi\) | |||||||
\(608\) | −1.00000 | −0.0405554 | ||||||||
\(609\) | 1.26795 | 0.0513799 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −9.46410 | −0.382877 | ||||||||
\(612\) | 6.19615 | 0.250465 | ||||||||
\(613\) | −38.7846 | −1.56650 | −0.783248 | − | 0.621710i | \(-0.786438\pi\) | ||||
−0.783248 | + | 0.621710i | \(0.786438\pi\) | |||||||
\(614\) | 20.2679 | 0.817948 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −2.73205 | −0.110077 | ||||||||
\(617\) | −46.3923 | −1.86768 | −0.933842 | − | 0.357686i | \(-0.883566\pi\) | ||||
−0.933842 | + | 0.357686i | \(0.883566\pi\) | |||||||
\(618\) | 3.53590 | 0.142235 | ||||||||
\(619\) | −0.196152 | −0.00788403 | −0.00394202 | − | 0.999992i | \(-0.501255\pi\) | ||||
−0.00394202 | + | 0.999992i | \(0.501255\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −5.92820 | −0.237891 | ||||||||
\(622\) | −29.3205 | −1.17565 | ||||||||
\(623\) | −7.94744 | −0.318408 | ||||||||
\(624\) | 2.73205 | 0.109370 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 3.92820 | 0.157003 | ||||||||
\(627\) | −3.73205 | −0.149044 | ||||||||
\(628\) | −13.8564 | −0.552931 | ||||||||
\(629\) | 12.3923 | 0.494114 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 2.92820 | 0.116570 | 0.0582850 | − | 0.998300i | \(-0.481437\pi\) | ||||
0.0582850 | + | 0.998300i | \(0.481437\pi\) | |||||||
\(632\) | −5.53590 | −0.220206 | ||||||||
\(633\) | −10.2679 | −0.408114 | ||||||||
\(634\) | 1.73205 | 0.0687885 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 1.73205 | 0.0686803 | ||||||||
\(637\) | −17.6603 | −0.699725 | ||||||||
\(638\) | −6.46410 | −0.255916 | ||||||||
\(639\) | 12.1962 | 0.482472 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 10.5359 | 0.416143 | 0.208071 | − | 0.978114i | \(-0.433281\pi\) | ||||
0.208071 | + | 0.978114i | \(0.433281\pi\) | |||||||
\(642\) | −2.19615 | −0.0866752 | ||||||||
\(643\) | −27.0718 | −1.06761 | −0.533804 | − | 0.845608i | \(-0.679238\pi\) | ||||
−0.533804 | + | 0.845608i | \(0.679238\pi\) | |||||||
\(644\) | 4.33975 | 0.171010 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −6.19615 | −0.243784 | ||||||||
\(647\) | −9.39230 | −0.369250 | −0.184625 | − | 0.982809i | \(-0.559107\pi\) | ||||
−0.184625 | + | 0.982809i | \(0.559107\pi\) | |||||||
\(648\) | 1.00000 | 0.0392837 | ||||||||
\(649\) | −30.5885 | −1.20070 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 1.80385 | 0.0706984 | ||||||||
\(652\) | 2.00000 | 0.0783260 | ||||||||
\(653\) | 17.4641 | 0.683423 | 0.341712 | − | 0.939805i | \(-0.388993\pi\) | ||||
0.341712 | + | 0.939805i | \(0.388993\pi\) | |||||||
\(654\) | 2.39230 | 0.0935465 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −2.92820 | −0.114327 | ||||||||
\(657\) | 2.46410 | 0.0961338 | ||||||||
\(658\) | 2.53590 | 0.0988596 | ||||||||
\(659\) | 7.41154 | 0.288713 | 0.144356 | − | 0.989526i | \(-0.453889\pi\) | ||||
0.144356 | + | 0.989526i | \(0.453889\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −22.6410 | −0.880633 | −0.440317 | − | 0.897843i | \(-0.645134\pi\) | ||||
−0.440317 | + | 0.897843i | \(0.645134\pi\) | |||||||
\(662\) | −22.2679 | −0.865468 | ||||||||
\(663\) | 16.9282 | 0.657437 | ||||||||
\(664\) | −3.73205 | −0.144832 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 2.00000 | 0.0774984 | ||||||||
\(667\) | 10.2679 | 0.397577 | ||||||||
\(668\) | 8.92820 | 0.345443 | ||||||||
\(669\) | 3.53590 | 0.136706 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 39.7846 | 1.53587 | ||||||||
\(672\) | −0.732051 | −0.0282395 | ||||||||
\(673\) | −6.98076 | −0.269089 | −0.134544 | − | 0.990908i | \(-0.542957\pi\) | ||||
−0.134544 | + | 0.990908i | \(0.542957\pi\) | |||||||
\(674\) | −10.5359 | −0.405828 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −5.53590 | −0.212919 | ||||||||
\(677\) | 8.66025 | 0.332841 | 0.166420 | − | 0.986055i | \(-0.446779\pi\) | ||||
0.166420 | + | 0.986055i | \(0.446779\pi\) | |||||||
\(678\) | 13.3923 | 0.514328 | ||||||||
\(679\) | −11.0718 | −0.424897 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 6.00000 | 0.229920 | ||||||||
\(682\) | −9.19615 | −0.352139 | ||||||||
\(683\) | −46.9808 | −1.79767 | −0.898834 | − | 0.438288i | \(-0.855585\pi\) | ||||
−0.898834 | + | 0.438288i | \(0.855585\pi\) | |||||||
\(684\) | −1.00000 | −0.0382360 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 9.85641 | 0.376319 | ||||||||
\(687\) | −6.26795 | −0.239137 | ||||||||
\(688\) | 8.19615 | 0.312475 | ||||||||
\(689\) | 4.73205 | 0.180277 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −22.1962 | −0.844381 | −0.422191 | − | 0.906507i | \(-0.638739\pi\) | ||||
−0.422191 | + | 0.906507i | \(0.638739\pi\) | |||||||
\(692\) | −13.5885 | −0.516556 | ||||||||
\(693\) | −2.73205 | −0.103782 | ||||||||
\(694\) | 20.7846 | 0.788973 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −1.73205 | −0.0656532 | ||||||||
\(697\) | −18.1436 | −0.687238 | ||||||||
\(698\) | −17.0526 | −0.645449 | ||||||||
\(699\) | 21.1244 | 0.798997 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 3.60770 | 0.136261 | 0.0681304 | − | 0.997676i | \(-0.478297\pi\) | ||||
0.0681304 | + | 0.997676i | \(0.478297\pi\) | |||||||
\(702\) | 2.73205 | 0.103115 | ||||||||
\(703\) | −2.00000 | −0.0754314 | ||||||||
\(704\) | 3.73205 | 0.140657 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −16.0526 | −0.604146 | ||||||||
\(707\) | −6.78461 | −0.255162 | ||||||||
\(708\) | −8.19615 | −0.308030 | ||||||||
\(709\) | 47.3013 | 1.77644 | 0.888218 | − | 0.459422i | \(-0.151943\pi\) | ||||
0.888218 | + | 0.459422i | \(0.151943\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −5.53590 | −0.207612 | ||||||||
\(712\) | 10.8564 | 0.406861 | ||||||||
\(713\) | 14.6077 | 0.547062 | ||||||||
\(714\) | −4.53590 | −0.169752 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −12.0000 | −0.448461 | ||||||||
\(717\) | −14.0000 | −0.522840 | ||||||||
\(718\) | −16.9282 | −0.631755 | ||||||||
\(719\) | 12.1769 | 0.454122 | 0.227061 | − | 0.973881i | \(-0.427088\pi\) | ||||
0.227061 | + | 0.973881i | \(0.427088\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −2.58846 | −0.0963992 | ||||||||
\(722\) | 1.00000 | 0.0372161 | ||||||||
\(723\) | −30.1962 | −1.12301 | ||||||||
\(724\) | −16.5885 | −0.616505 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 2.92820 | 0.108676 | ||||||||
\(727\) | 38.1051 | 1.41324 | 0.706620 | − | 0.707593i | \(-0.250219\pi\) | ||||
0.706620 | + | 0.707593i | \(0.250219\pi\) | |||||||
\(728\) | −2.00000 | −0.0741249 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 50.7846 | 1.87834 | ||||||||
\(732\) | 10.6603 | 0.394014 | ||||||||
\(733\) | 20.5167 | 0.757800 | 0.378900 | − | 0.925438i | \(-0.376302\pi\) | ||||
0.378900 | + | 0.925438i | \(0.376302\pi\) | |||||||
\(734\) | 13.2679 | 0.489729 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −5.92820 | −0.218516 | ||||||||
\(737\) | 1.00000 | 0.0368355 | ||||||||
\(738\) | −2.92820 | −0.107789 | ||||||||
\(739\) | −53.1769 | −1.95614 | −0.978072 | − | 0.208266i | \(-0.933218\pi\) | ||||
−0.978072 | + | 0.208266i | \(0.933218\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −2.73205 | −0.100364 | ||||||||
\(742\) | −1.26795 | −0.0465479 | ||||||||
\(743\) | 5.07180 | 0.186066 | 0.0930331 | − | 0.995663i | \(-0.470344\pi\) | ||||
0.0930331 | + | 0.995663i | \(0.470344\pi\) | |||||||
\(744\) | −2.46410 | −0.0903383 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 31.5167 | 1.15391 | ||||||||
\(747\) | −3.73205 | −0.136549 | ||||||||
\(748\) | 23.1244 | 0.845510 | ||||||||
\(749\) | 1.60770 | 0.0587439 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 7.46410 | 0.272369 | 0.136184 | − | 0.990683i | \(-0.456516\pi\) | ||||
0.136184 | + | 0.990683i | \(0.456516\pi\) | |||||||
\(752\) | −3.46410 | −0.126323 | ||||||||
\(753\) | 11.4641 | 0.417775 | ||||||||
\(754\) | −4.73205 | −0.172331 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −0.732051 | −0.0266244 | ||||||||
\(757\) | 13.5885 | 0.493881 | 0.246940 | − | 0.969031i | \(-0.420575\pi\) | ||||
0.246940 | + | 0.969031i | \(0.420575\pi\) | |||||||
\(758\) | −0.392305 | −0.0142492 | ||||||||
\(759\) | −22.1244 | −0.803063 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1.26795 | 0.0459631 | 0.0229816 | − | 0.999736i | \(-0.492684\pi\) | ||||
0.0229816 | + | 0.999736i | \(0.492684\pi\) | |||||||
\(762\) | 5.00000 | 0.181131 | ||||||||
\(763\) | −1.75129 | −0.0634009 | ||||||||
\(764\) | 3.00000 | 0.108536 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 19.5167 | 0.705166 | ||||||||
\(767\) | −22.3923 | −0.808539 | ||||||||
\(768\) | 1.00000 | 0.0360844 | ||||||||
\(769\) | −34.7128 | −1.25178 | −0.625888 | − | 0.779913i | \(-0.715263\pi\) | ||||
−0.625888 | + | 0.779913i | \(0.715263\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −9.00000 | −0.324127 | ||||||||
\(772\) | −22.0526 | −0.793689 | ||||||||
\(773\) | 45.3205 | 1.63007 | 0.815033 | − | 0.579415i | \(-0.196719\pi\) | ||||
0.815033 | + | 0.579415i | \(0.196719\pi\) | |||||||
\(774\) | 8.19615 | 0.294605 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 15.1244 | 0.542933 | ||||||||
\(777\) | −1.46410 | −0.0525244 | ||||||||
\(778\) | 21.7128 | 0.778442 | ||||||||
\(779\) | 2.92820 | 0.104914 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 45.5167 | 1.62871 | ||||||||
\(782\) | −36.7321 | −1.31354 | ||||||||
\(783\) | −1.73205 | −0.0618984 | ||||||||
\(784\) | −6.46410 | −0.230861 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 10.2679 | 0.366246 | ||||||||
\(787\) | −2.12436 | −0.0757251 | −0.0378626 | − | 0.999283i | \(-0.512055\pi\) | ||||
−0.0378626 | + | 0.999283i | \(0.512055\pi\) | |||||||
\(788\) | −24.5885 | −0.875928 | ||||||||
\(789\) | −15.0000 | −0.534014 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −9.80385 | −0.348585 | ||||||||
\(792\) | 3.73205 | 0.132613 | ||||||||
\(793\) | 29.1244 | 1.03424 | ||||||||
\(794\) | −11.7321 | −0.416355 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −14.0000 | −0.496217 | ||||||||
\(797\) | −20.0000 | −0.708436 | −0.354218 | − | 0.935163i | \(-0.615253\pi\) | ||||
−0.354218 | + | 0.935163i | \(0.615253\pi\) | |||||||
\(798\) | 0.732051 | 0.0259143 | ||||||||
\(799\) | −21.4641 | −0.759345 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 10.8564 | 0.383592 | ||||||||
\(802\) | 16.8564 | 0.595220 | ||||||||
\(803\) | 9.19615 | 0.324525 | ||||||||
\(804\) | 0.267949 | 0.00944984 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −6.73205 | −0.237126 | ||||||||
\(807\) | −20.5359 | −0.722898 | ||||||||
\(808\) | 9.26795 | 0.326045 | ||||||||
\(809\) | 37.5167 | 1.31902 | 0.659508 | − | 0.751698i | \(-0.270765\pi\) | ||||
0.659508 | + | 0.751698i | \(0.270765\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 18.3731 | 0.645166 | 0.322583 | − | 0.946541i | \(-0.395449\pi\) | ||||
0.322583 | + | 0.946541i | \(0.395449\pi\) | |||||||
\(812\) | 1.26795 | 0.0444963 | ||||||||
\(813\) | −15.8038 | −0.554265 | ||||||||
\(814\) | 7.46410 | 0.261617 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 6.19615 | 0.216909 | ||||||||
\(817\) | −8.19615 | −0.286747 | ||||||||
\(818\) | 1.60770 | 0.0562117 | ||||||||
\(819\) | −2.00000 | −0.0698857 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 2.48334 | 0.0866691 | 0.0433346 | − | 0.999061i | \(-0.486202\pi\) | ||||
0.0433346 | + | 0.999061i | \(0.486202\pi\) | |||||||
\(822\) | 12.3923 | 0.432231 | ||||||||
\(823\) | 6.78461 | 0.236497 | 0.118248 | − | 0.992984i | \(-0.462272\pi\) | ||||
0.118248 | + | 0.992984i | \(0.462272\pi\) | |||||||
\(824\) | 3.53590 | 0.123179 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 6.00000 | 0.208767 | ||||||||
\(827\) | −6.73205 | −0.234096 | −0.117048 | − | 0.993126i | \(-0.537343\pi\) | ||||
−0.117048 | + | 0.993126i | \(0.537343\pi\) | |||||||
\(828\) | −5.92820 | −0.206019 | ||||||||
\(829\) | 6.19615 | 0.215201 | 0.107601 | − | 0.994194i | \(-0.465683\pi\) | ||||
0.107601 | + | 0.994194i | \(0.465683\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −11.1962 | −0.388390 | ||||||||
\(832\) | 2.73205 | 0.0947168 | ||||||||
\(833\) | −40.0526 | −1.38774 | ||||||||
\(834\) | −21.1244 | −0.731477 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −3.73205 | −0.129076 | ||||||||
\(837\) | −2.46410 | −0.0851718 | ||||||||
\(838\) | 13.8564 | 0.478662 | ||||||||
\(839\) | −46.5885 | −1.60841 | −0.804206 | − | 0.594351i | \(-0.797409\pi\) | ||||
−0.804206 | + | 0.594351i | \(0.797409\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −26.0000 | −0.896552 | ||||||||
\(842\) | 6.78461 | 0.233813 | ||||||||
\(843\) | 17.7846 | 0.612534 | ||||||||
\(844\) | −10.2679 | −0.353437 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −3.46410 | −0.119098 | ||||||||
\(847\) | −2.14359 | −0.0736547 | ||||||||
\(848\) | 1.73205 | 0.0594789 | ||||||||
\(849\) | −4.00000 | −0.137280 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −11.8564 | −0.406432 | ||||||||
\(852\) | 12.1962 | 0.417833 | ||||||||
\(853\) | 4.53590 | 0.155306 | 0.0776531 | − | 0.996980i | \(-0.475257\pi\) | ||||
0.0776531 | + | 0.996980i | \(0.475257\pi\) | |||||||
\(854\) | −7.80385 | −0.267042 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −2.19615 | −0.0750629 | ||||||||
\(857\) | 42.9282 | 1.46640 | 0.733200 | − | 0.680013i | \(-0.238026\pi\) | ||||
0.733200 | + | 0.680013i | \(0.238026\pi\) | |||||||
\(858\) | 10.1962 | 0.348091 | ||||||||
\(859\) | 56.9282 | 1.94237 | 0.971183 | − | 0.238337i | \(-0.0766021\pi\) | ||||
0.971183 | + | 0.238337i | \(0.0766021\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 2.14359 | 0.0730535 | ||||||||
\(862\) | −29.3205 | −0.998660 | ||||||||
\(863\) | 55.3205 | 1.88313 | 0.941566 | − | 0.336829i | \(-0.109354\pi\) | ||||
0.941566 | + | 0.336829i | \(0.109354\pi\) | |||||||
\(864\) | 1.00000 | 0.0340207 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −24.1962 | −0.822219 | ||||||||
\(867\) | 21.3923 | 0.726521 | ||||||||
\(868\) | 1.80385 | 0.0612266 | ||||||||
\(869\) | −20.6603 | −0.700851 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0.732051 | 0.0248046 | ||||||||
\(872\) | 2.39230 | 0.0810137 | ||||||||
\(873\) | 15.1244 | 0.511882 | ||||||||
\(874\) | 5.92820 | 0.200524 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 2.46410 | 0.0832543 | ||||||||
\(877\) | −31.1769 | −1.05277 | −0.526385 | − | 0.850246i | \(-0.676453\pi\) | ||||
−0.526385 | + | 0.850246i | \(0.676453\pi\) | |||||||
\(878\) | 25.7846 | 0.870188 | ||||||||
\(879\) | 27.7321 | 0.935379 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −26.5359 | −0.894017 | −0.447009 | − | 0.894530i | \(-0.647511\pi\) | ||||
−0.447009 | + | 0.894530i | \(0.647511\pi\) | |||||||
\(882\) | −6.46410 | −0.217658 | ||||||||
\(883\) | −27.2679 | −0.917640 | −0.458820 | − | 0.888529i | \(-0.651728\pi\) | ||||
−0.458820 | + | 0.888529i | \(0.651728\pi\) | |||||||
\(884\) | 16.9282 | 0.569357 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −3.33975 | −0.112201 | ||||||||
\(887\) | 7.60770 | 0.255441 | 0.127721 | − | 0.991810i | \(-0.459234\pi\) | ||||
0.127721 | + | 0.991810i | \(0.459234\pi\) | |||||||
\(888\) | 2.00000 | 0.0671156 | ||||||||
\(889\) | −3.66025 | −0.122761 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 3.73205 | 0.125028 | ||||||||
\(892\) | 3.53590 | 0.118391 | ||||||||
\(893\) | 3.46410 | 0.115922 | ||||||||
\(894\) | −21.8564 | −0.730988 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −0.732051 | −0.0244561 | ||||||||
\(897\) | −16.1962 | −0.540774 | ||||||||
\(898\) | 24.4641 | 0.816378 | ||||||||
\(899\) | 4.26795 | 0.142344 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 10.7321 | 0.357536 | ||||||||
\(902\) | −10.9282 | −0.363869 | ||||||||
\(903\) | −6.00000 | −0.199667 | ||||||||
\(904\) | 13.3923 | 0.445421 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −11.4641 | −0.380869 | ||||||||
\(907\) | −49.3205 | −1.63766 | −0.818830 | − | 0.574036i | \(-0.805377\pi\) | ||||
−0.818830 | + | 0.574036i | \(0.805377\pi\) | |||||||
\(908\) | 6.00000 | 0.199117 | ||||||||
\(909\) | 9.26795 | 0.307398 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 34.1051 | 1.12995 | 0.564976 | − | 0.825107i | \(-0.308885\pi\) | ||||
0.564976 | + | 0.825107i | \(0.308885\pi\) | |||||||
\(912\) | −1.00000 | −0.0331133 | ||||||||
\(913\) | −13.9282 | −0.460956 | ||||||||
\(914\) | −5.07180 | −0.167760 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −6.26795 | −0.207099 | ||||||||
\(917\) | −7.51666 | −0.248222 | ||||||||
\(918\) | 6.19615 | 0.204504 | ||||||||
\(919\) | −4.48334 | −0.147892 | −0.0739459 | − | 0.997262i | \(-0.523559\pi\) | ||||
−0.0739459 | + | 0.997262i | \(0.523559\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 20.2679 | 0.667852 | ||||||||
\(922\) | −17.8564 | −0.588069 | ||||||||
\(923\) | 33.3205 | 1.09676 | ||||||||
\(924\) | −2.73205 | −0.0898779 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −35.3205 | −1.16070 | ||||||||
\(927\) | 3.53590 | 0.116134 | ||||||||
\(928\) | −1.73205 | −0.0568574 | ||||||||
\(929\) | 42.9282 | 1.40843 | 0.704214 | − | 0.709987i | \(-0.251299\pi\) | ||||
0.704214 | + | 0.709987i | \(0.251299\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 6.46410 | 0.211852 | ||||||||
\(932\) | 21.1244 | 0.691951 | ||||||||
\(933\) | −29.3205 | −0.959910 | ||||||||
\(934\) | 7.19615 | 0.235465 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 2.73205 | 0.0892999 | ||||||||
\(937\) | 13.2154 | 0.431728 | 0.215864 | − | 0.976423i | \(-0.430743\pi\) | ||||
0.215864 | + | 0.976423i | \(0.430743\pi\) | |||||||
\(938\) | −0.196152 | −0.00640460 | ||||||||
\(939\) | 3.92820 | 0.128192 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −12.2679 | −0.399924 | −0.199962 | − | 0.979804i | \(-0.564082\pi\) | ||||
−0.199962 | + | 0.979804i | \(0.564082\pi\) | |||||||
\(942\) | −13.8564 | −0.451466 | ||||||||
\(943\) | 17.3590 | 0.565286 | ||||||||
\(944\) | −8.19615 | −0.266762 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 30.5885 | 0.994517 | ||||||||
\(947\) | −5.85641 | −0.190308 | −0.0951538 | − | 0.995463i | \(-0.530334\pi\) | ||||
−0.0951538 | + | 0.995463i | \(0.530334\pi\) | |||||||
\(948\) | −5.53590 | −0.179798 | ||||||||
\(949\) | 6.73205 | 0.218532 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 1.73205 | 0.0561656 | ||||||||
\(952\) | −4.53590 | −0.147009 | ||||||||
\(953\) | −5.24871 | −0.170022 | −0.0850112 | − | 0.996380i | \(-0.527093\pi\) | ||||
−0.0850112 | + | 0.996380i | \(0.527093\pi\) | |||||||
\(954\) | 1.73205 | 0.0560772 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −14.0000 | −0.452792 | ||||||||
\(957\) | −6.46410 | −0.208955 | ||||||||
\(958\) | 3.14359 | 0.101565 | ||||||||
\(959\) | −9.07180 | −0.292944 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −24.9282 | −0.804136 | ||||||||
\(962\) | 5.46410 | 0.176170 | ||||||||
\(963\) | −2.19615 | −0.0707700 | ||||||||
\(964\) | −30.1962 | −0.972553 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 4.33975 | 0.139629 | ||||||||
\(967\) | 18.1051 | 0.582221 | 0.291111 | − | 0.956689i | \(-0.405975\pi\) | ||||
0.291111 | + | 0.956689i | \(0.405975\pi\) | |||||||
\(968\) | 2.92820 | 0.0941160 | ||||||||
\(969\) | −6.19615 | −0.199049 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −37.7654 | −1.21195 | −0.605974 | − | 0.795484i | \(-0.707217\pi\) | ||||
−0.605974 | + | 0.795484i | \(0.707217\pi\) | |||||||
\(972\) | 1.00000 | 0.0320750 | ||||||||
\(973\) | 15.4641 | 0.495756 | ||||||||
\(974\) | 2.14359 | 0.0686852 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 10.6603 | 0.341226 | ||||||||
\(977\) | −1.46410 | −0.0468408 | −0.0234204 | − | 0.999726i | \(-0.507456\pi\) | ||||
−0.0234204 | + | 0.999726i | \(0.507456\pi\) | |||||||
\(978\) | 2.00000 | 0.0639529 | ||||||||
\(979\) | 40.5167 | 1.29492 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 2.39230 | 0.0763804 | ||||||||
\(982\) | −2.92820 | −0.0934427 | ||||||||
\(983\) | −30.3397 | −0.967688 | −0.483844 | − | 0.875154i | \(-0.660760\pi\) | ||||
−0.483844 | + | 0.875154i | \(0.660760\pi\) | |||||||
\(984\) | −2.92820 | −0.0933477 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −10.7321 | −0.341778 | ||||||||
\(987\) | 2.53590 | 0.0807185 | ||||||||
\(988\) | −2.73205 | −0.0869181 | ||||||||
\(989\) | −48.5885 | −1.54502 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −40.3205 | −1.28082 | −0.640412 | − | 0.768032i | \(-0.721236\pi\) | ||||
−0.640412 | + | 0.768032i | \(0.721236\pi\) | |||||||
\(992\) | −2.46410 | −0.0782353 | ||||||||
\(993\) | −22.2679 | −0.706652 | ||||||||
\(994\) | −8.92820 | −0.283185 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −3.73205 | −0.118255 | ||||||||
\(997\) | −63.0526 | −1.99689 | −0.998447 | − | 0.0557047i | \(-0.982259\pi\) | ||||
−0.998447 | + | 0.0557047i | \(0.982259\pi\) | |||||||
\(998\) | 41.3731 | 1.30964 | ||||||||
\(999\) | 2.00000 | 0.0632772 |
(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 | 2850.2.a.bi.1.1 | yes | 2 | |
3.2 | odd | 2 | 8550.2.a.bs.1.1 | 2 | |||
5.2 | odd | 4 | 2850.2.d.x.799.3 | 4 | |||
5.3 | odd | 4 | 2850.2.d.x.799.2 | 4 | |||
5.4 | even | 2 | 2850.2.a.bd.1.2 | ✓ | 2 | ||
15.14 | odd | 2 | 8550.2.a.by.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2850.2.a.bd.1.2 | ✓ | 2 | 5.4 | even | 2 | ||
2850.2.a.bi.1.1 | yes | 2 | 1.1 | even | 1 | trivial | |
2850.2.d.x.799.2 | 4 | 5.3 | odd | 4 | |||
2850.2.d.x.799.3 | 4 | 5.2 | odd | 4 | |||
8550.2.a.bs.1.1 | 2 | 3.2 | odd | 2 | |||
8550.2.a.by.1.2 | 2 | 15.14 | odd | 2 |