Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [966,2,Mod(277,966)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(966, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 4, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("966.277");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 966.i (of order \(3\), degree \(2\), minimal) |
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: | no |
Analytic conductor: | \(7.71354883526\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 415.1 | ||
Root | \(0.500000 - 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 966.415 |
Dual form | 966.2.i.e.277.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/966\mathbb{Z}\right)^\times\).
\(n\) | \(323\) | \(829\) | \(925\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.500000 | − | 0.866025i | 0.353553 | − | 0.612372i | ||||
\(3\) | −0.500000 | − | 0.866025i | −0.288675 | − | 0.500000i | ||||
\(4\) | −0.500000 | − | 0.866025i | −0.250000 | − | 0.433013i | ||||
\(5\) | −1.50000 | + | 2.59808i | −0.670820 | + | 1.16190i | 0.306851 | + | 0.951757i | \(0.400725\pi\) |
−0.977672 | + | 0.210138i | \(0.932609\pi\) | |||||||
\(6\) | −1.00000 | −0.408248 | ||||||||
\(7\) | 0.500000 | − | 2.59808i | 0.188982 | − | 0.981981i | ||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | −0.500000 | + | 0.866025i | −0.166667 | + | 0.288675i | ||||
\(10\) | 1.50000 | + | 2.59808i | 0.474342 | + | 0.821584i | ||||
\(11\) | 2.50000 | + | 4.33013i | 0.753778 | + | 1.30558i | 0.945979 | + | 0.324227i | \(0.105104\pi\) |
−0.192201 | + | 0.981356i | \(0.561563\pi\) | |||||||
\(12\) | −0.500000 | + | 0.866025i | −0.144338 | + | 0.250000i | ||||
\(13\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(14\) | −2.00000 | − | 1.73205i | −0.534522 | − | 0.462910i | ||||
\(15\) | 3.00000 | 0.774597 | ||||||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | 2.00000 | + | 3.46410i | 0.485071 | + | 0.840168i | 0.999853 | − | 0.0171533i | \(-0.00546033\pi\) |
−0.514782 | + | 0.857321i | \(0.672127\pi\) | |||||||
\(18\) | 0.500000 | + | 0.866025i | 0.117851 | + | 0.204124i | ||||
\(19\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(20\) | 3.00000 | 0.670820 | ||||||||
\(21\) | −2.50000 | + | 0.866025i | −0.545545 | + | 0.188982i | ||||
\(22\) | 5.00000 | 1.06600 | ||||||||
\(23\) | −0.500000 | + | 0.866025i | −0.104257 | + | 0.180579i | ||||
\(24\) | 0.500000 | + | 0.866025i | 0.102062 | + | 0.176777i | ||||
\(25\) | −2.00000 | − | 3.46410i | −0.400000 | − | 0.692820i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | −2.50000 | + | 0.866025i | −0.472456 | + | 0.163663i | ||||
\(29\) | −3.00000 | −0.557086 | −0.278543 | − | 0.960424i | \(-0.589851\pi\) | ||||
−0.278543 | + | 0.960424i | \(0.589851\pi\) | |||||||
\(30\) | 1.50000 | − | 2.59808i | 0.273861 | − | 0.474342i | ||||
\(31\) | 4.50000 | + | 7.79423i | 0.808224 | + | 1.39988i | 0.914093 | + | 0.405505i | \(0.132904\pi\) |
−0.105869 | + | 0.994380i | \(0.533762\pi\) | |||||||
\(32\) | 0.500000 | + | 0.866025i | 0.0883883 | + | 0.153093i | ||||
\(33\) | 2.50000 | − | 4.33013i | 0.435194 | − | 0.753778i | ||||
\(34\) | 4.00000 | 0.685994 | ||||||||
\(35\) | 6.00000 | + | 5.19615i | 1.01419 | + | 0.878310i | ||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | 6.00000 | − | 10.3923i | 0.986394 | − | 1.70848i | 0.350823 | − | 0.936442i | \(-0.385902\pi\) |
0.635571 | − | 0.772043i | \(-0.280765\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1.50000 | − | 2.59808i | 0.237171 | − | 0.410792i | ||||
\(41\) | 12.0000 | 1.87409 | 0.937043 | − | 0.349215i | \(-0.113552\pi\) | ||||
0.937043 | + | 0.349215i | \(0.113552\pi\) | |||||||
\(42\) | −0.500000 | + | 2.59808i | −0.0771517 | + | 0.400892i | ||||
\(43\) | 6.00000 | 0.914991 | 0.457496 | − | 0.889212i | \(-0.348747\pi\) | ||||
0.457496 | + | 0.889212i | \(0.348747\pi\) | |||||||
\(44\) | 2.50000 | − | 4.33013i | 0.376889 | − | 0.652791i | ||||
\(45\) | −1.50000 | − | 2.59808i | −0.223607 | − | 0.387298i | ||||
\(46\) | 0.500000 | + | 0.866025i | 0.0737210 | + | 0.127688i | ||||
\(47\) | −1.00000 | + | 1.73205i | −0.145865 | + | 0.252646i | −0.929695 | − | 0.368329i | \(-0.879930\pi\) |
0.783830 | + | 0.620975i | \(0.213263\pi\) | |||||||
\(48\) | 1.00000 | 0.144338 | ||||||||
\(49\) | −6.50000 | − | 2.59808i | −0.928571 | − | 0.371154i | ||||
\(50\) | −4.00000 | −0.565685 | ||||||||
\(51\) | 2.00000 | − | 3.46410i | 0.280056 | − | 0.485071i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −2.50000 | − | 4.33013i | −0.343401 | − | 0.594789i | 0.641661 | − | 0.766989i | \(-0.278246\pi\) |
−0.985062 | + | 0.172200i | \(0.944912\pi\) | |||||||
\(54\) | 0.500000 | − | 0.866025i | 0.0680414 | − | 0.117851i | ||||
\(55\) | −15.0000 | −2.02260 | ||||||||
\(56\) | −0.500000 | + | 2.59808i | −0.0668153 | + | 0.347183i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −1.50000 | + | 2.59808i | −0.196960 | + | 0.341144i | ||||
\(59\) | 4.50000 | + | 7.79423i | 0.585850 | + | 1.01472i | 0.994769 | + | 0.102151i | \(0.0325726\pi\) |
−0.408919 | + | 0.912571i | \(0.634094\pi\) | |||||||
\(60\) | −1.50000 | − | 2.59808i | −0.193649 | − | 0.335410i | ||||
\(61\) | 1.00000 | − | 1.73205i | 0.128037 | − | 0.221766i | −0.794879 | − | 0.606768i | \(-0.792466\pi\) |
0.922916 | + | 0.385002i | \(0.125799\pi\) | |||||||
\(62\) | 9.00000 | 1.14300 | ||||||||
\(63\) | 2.00000 | + | 1.73205i | 0.251976 | + | 0.218218i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −2.50000 | − | 4.33013i | −0.307729 | − | 0.533002i | ||||
\(67\) | 1.00000 | + | 1.73205i | 0.122169 | + | 0.211604i | 0.920623 | − | 0.390453i | \(-0.127682\pi\) |
−0.798454 | + | 0.602056i | \(0.794348\pi\) | |||||||
\(68\) | 2.00000 | − | 3.46410i | 0.242536 | − | 0.420084i | ||||
\(69\) | 1.00000 | 0.120386 | ||||||||
\(70\) | 7.50000 | − | 2.59808i | 0.896421 | − | 0.310530i | ||||
\(71\) | 6.00000 | 0.712069 | 0.356034 | − | 0.934473i | \(-0.384129\pi\) | ||||
0.356034 | + | 0.934473i | \(0.384129\pi\) | |||||||
\(72\) | 0.500000 | − | 0.866025i | 0.0589256 | − | 0.102062i | ||||
\(73\) | 7.00000 | + | 12.1244i | 0.819288 | + | 1.41905i | 0.906208 | + | 0.422833i | \(0.138964\pi\) |
−0.0869195 | + | 0.996215i | \(0.527702\pi\) | |||||||
\(74\) | −6.00000 | − | 10.3923i | −0.697486 | − | 1.20808i | ||||
\(75\) | −2.00000 | + | 3.46410i | −0.230940 | + | 0.400000i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 12.5000 | − | 4.33013i | 1.42451 | − | 0.493464i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −5.50000 | + | 9.52628i | −0.618798 | + | 1.07179i | 0.370907 | + | 0.928670i | \(0.379047\pi\) |
−0.989705 | + | 0.143120i | \(0.954286\pi\) | |||||||
\(80\) | −1.50000 | − | 2.59808i | −0.167705 | − | 0.290474i | ||||
\(81\) | −0.500000 | − | 0.866025i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | 6.00000 | − | 10.3923i | 0.662589 | − | 1.14764i | ||||
\(83\) | −17.0000 | −1.86599 | −0.932996 | − | 0.359886i | \(-0.882816\pi\) | ||||
−0.932996 | + | 0.359886i | \(0.882816\pi\) | |||||||
\(84\) | 2.00000 | + | 1.73205i | 0.218218 | + | 0.188982i | ||||
\(85\) | −12.0000 | −1.30158 | ||||||||
\(86\) | 3.00000 | − | 5.19615i | 0.323498 | − | 0.560316i | ||||
\(87\) | 1.50000 | + | 2.59808i | 0.160817 | + | 0.278543i | ||||
\(88\) | −2.50000 | − | 4.33013i | −0.266501 | − | 0.461593i | ||||
\(89\) | −5.00000 | + | 8.66025i | −0.529999 | + | 0.917985i | 0.469389 | + | 0.882992i | \(0.344474\pi\) |
−0.999388 | + | 0.0349934i | \(0.988859\pi\) | |||||||
\(90\) | −3.00000 | −0.316228 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 1.00000 | 0.104257 | ||||||||
\(93\) | 4.50000 | − | 7.79423i | 0.466628 | − | 0.808224i | ||||
\(94\) | 1.00000 | + | 1.73205i | 0.103142 | + | 0.178647i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0.500000 | − | 0.866025i | 0.0510310 | − | 0.0883883i | ||||
\(97\) | −13.0000 | −1.31995 | −0.659975 | − | 0.751288i | \(-0.729433\pi\) | ||||
−0.659975 | + | 0.751288i | \(0.729433\pi\) | |||||||
\(98\) | −5.50000 | + | 4.33013i | −0.555584 | + | 0.437409i | ||||
\(99\) | −5.00000 | −0.502519 | ||||||||
\(100\) | −2.00000 | + | 3.46410i | −0.200000 | + | 0.346410i | ||||
\(101\) | 1.00000 | + | 1.73205i | 0.0995037 | + | 0.172345i | 0.911479 | − | 0.411346i | \(-0.134941\pi\) |
−0.811976 | + | 0.583691i | \(0.801608\pi\) | |||||||
\(102\) | −2.00000 | − | 3.46410i | −0.198030 | − | 0.342997i | ||||
\(103\) | −4.00000 | + | 6.92820i | −0.394132 | + | 0.682656i | −0.992990 | − | 0.118199i | \(-0.962288\pi\) |
0.598858 | + | 0.800855i | \(0.295621\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1.50000 | − | 7.79423i | 0.146385 | − | 0.760639i | ||||
\(106\) | −5.00000 | −0.485643 | ||||||||
\(107\) | 9.50000 | − | 16.4545i | 0.918400 | − | 1.59071i | 0.116553 | − | 0.993184i | \(-0.462815\pi\) |
0.801846 | − | 0.597530i | \(-0.203851\pi\) | |||||||
\(108\) | −0.500000 | − | 0.866025i | −0.0481125 | − | 0.0833333i | ||||
\(109\) | −3.00000 | − | 5.19615i | −0.287348 | − | 0.497701i | 0.685828 | − | 0.727764i | \(-0.259440\pi\) |
−0.973176 | + | 0.230063i | \(0.926107\pi\) | |||||||
\(110\) | −7.50000 | + | 12.9904i | −0.715097 | + | 1.23858i | ||||
\(111\) | −12.0000 | −1.13899 | ||||||||
\(112\) | 2.00000 | + | 1.73205i | 0.188982 | + | 0.163663i | ||||
\(113\) | 12.0000 | 1.12887 | 0.564433 | − | 0.825479i | \(-0.309095\pi\) | ||||
0.564433 | + | 0.825479i | \(0.309095\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.50000 | − | 2.59808i | −0.139876 | − | 0.242272i | ||||
\(116\) | 1.50000 | + | 2.59808i | 0.139272 | + | 0.241225i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 9.00000 | 0.828517 | ||||||||
\(119\) | 10.0000 | − | 3.46410i | 0.916698 | − | 0.317554i | ||||
\(120\) | −3.00000 | −0.273861 | ||||||||
\(121\) | −7.00000 | + | 12.1244i | −0.636364 | + | 1.10221i | ||||
\(122\) | −1.00000 | − | 1.73205i | −0.0905357 | − | 0.156813i | ||||
\(123\) | −6.00000 | − | 10.3923i | −0.541002 | − | 0.937043i | ||||
\(124\) | 4.50000 | − | 7.79423i | 0.404112 | − | 0.699942i | ||||
\(125\) | −3.00000 | −0.268328 | ||||||||
\(126\) | 2.50000 | − | 0.866025i | 0.222718 | − | 0.0771517i | ||||
\(127\) | −11.0000 | −0.976092 | −0.488046 | − | 0.872818i | \(-0.662290\pi\) | ||||
−0.488046 | + | 0.872818i | \(0.662290\pi\) | |||||||
\(128\) | 0.500000 | − | 0.866025i | 0.0441942 | − | 0.0765466i | ||||
\(129\) | −3.00000 | − | 5.19615i | −0.264135 | − | 0.457496i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1.50000 | + | 2.59808i | −0.131056 | + | 0.226995i | −0.924084 | − | 0.382190i | \(-0.875170\pi\) |
0.793028 | + | 0.609185i | \(0.208503\pi\) | |||||||
\(132\) | −5.00000 | −0.435194 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 2.00000 | 0.172774 | ||||||||
\(135\) | −1.50000 | + | 2.59808i | −0.129099 | + | 0.223607i | ||||
\(136\) | −2.00000 | − | 3.46410i | −0.171499 | − | 0.297044i | ||||
\(137\) | 3.00000 | + | 5.19615i | 0.256307 | + | 0.443937i | 0.965250 | − | 0.261329i | \(-0.0841608\pi\) |
−0.708942 | + | 0.705266i | \(0.750827\pi\) | |||||||
\(138\) | 0.500000 | − | 0.866025i | 0.0425628 | − | 0.0737210i | ||||
\(139\) | −6.00000 | −0.508913 | −0.254457 | − | 0.967084i | \(-0.581897\pi\) | ||||
−0.254457 | + | 0.967084i | \(0.581897\pi\) | |||||||
\(140\) | 1.50000 | − | 7.79423i | 0.126773 | − | 0.658733i | ||||
\(141\) | 2.00000 | 0.168430 | ||||||||
\(142\) | 3.00000 | − | 5.19615i | 0.251754 | − | 0.436051i | ||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −0.500000 | − | 0.866025i | −0.0416667 | − | 0.0721688i | ||||
\(145\) | 4.50000 | − | 7.79423i | 0.373705 | − | 0.647275i | ||||
\(146\) | 14.0000 | 1.15865 | ||||||||
\(147\) | 1.00000 | + | 6.92820i | 0.0824786 | + | 0.571429i | ||||
\(148\) | −12.0000 | −0.986394 | ||||||||
\(149\) | 7.00000 | − | 12.1244i | 0.573462 | − | 0.993266i | −0.422744 | − | 0.906249i | \(-0.638933\pi\) |
0.996207 | − | 0.0870170i | \(-0.0277334\pi\) | |||||||
\(150\) | 2.00000 | + | 3.46410i | 0.163299 | + | 0.282843i | ||||
\(151\) | 4.50000 | + | 7.79423i | 0.366205 | + | 0.634285i | 0.988969 | − | 0.148124i | \(-0.0473236\pi\) |
−0.622764 | + | 0.782410i | \(0.713990\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −4.00000 | −0.323381 | ||||||||
\(154\) | 2.50000 | − | 12.9904i | 0.201456 | − | 1.04679i | ||||
\(155\) | −27.0000 | −2.16869 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 4.00000 | + | 6.92820i | 0.319235 | + | 0.552931i | 0.980329 | − | 0.197372i | \(-0.0632408\pi\) |
−0.661094 | + | 0.750303i | \(0.729907\pi\) | |||||||
\(158\) | 5.50000 | + | 9.52628i | 0.437557 | + | 0.757870i | ||||
\(159\) | −2.50000 | + | 4.33013i | −0.198263 | + | 0.343401i | ||||
\(160\) | −3.00000 | −0.237171 | ||||||||
\(161\) | 2.00000 | + | 1.73205i | 0.157622 | + | 0.136505i | ||||
\(162\) | −1.00000 | −0.0785674 | ||||||||
\(163\) | 10.0000 | − | 17.3205i | 0.783260 | − | 1.35665i | −0.146772 | − | 0.989170i | \(-0.546888\pi\) |
0.930033 | − | 0.367477i | \(-0.119778\pi\) | |||||||
\(164\) | −6.00000 | − | 10.3923i | −0.468521 | − | 0.811503i | ||||
\(165\) | 7.50000 | + | 12.9904i | 0.583874 | + | 1.01130i | ||||
\(166\) | −8.50000 | + | 14.7224i | −0.659728 | + | 1.14268i | ||||
\(167\) | −2.00000 | −0.154765 | −0.0773823 | − | 0.997001i | \(-0.524656\pi\) | ||||
−0.0773823 | + | 0.997001i | \(0.524656\pi\) | |||||||
\(168\) | 2.50000 | − | 0.866025i | 0.192879 | − | 0.0668153i | ||||
\(169\) | −13.0000 | −1.00000 | ||||||||
\(170\) | −6.00000 | + | 10.3923i | −0.460179 | + | 0.797053i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −3.00000 | − | 5.19615i | −0.228748 | − | 0.396203i | ||||
\(173\) | 3.00000 | − | 5.19615i | 0.228086 | − | 0.395056i | −0.729155 | − | 0.684349i | \(-0.760087\pi\) |
0.957241 | + | 0.289292i | \(0.0934200\pi\) | |||||||
\(174\) | 3.00000 | 0.227429 | ||||||||
\(175\) | −10.0000 | + | 3.46410i | −0.755929 | + | 0.261861i | ||||
\(176\) | −5.00000 | −0.376889 | ||||||||
\(177\) | 4.50000 | − | 7.79423i | 0.338241 | − | 0.585850i | ||||
\(178\) | 5.00000 | + | 8.66025i | 0.374766 | + | 0.649113i | ||||
\(179\) | 10.0000 | + | 17.3205i | 0.747435 | + | 1.29460i | 0.949048 | + | 0.315130i | \(0.102048\pi\) |
−0.201613 | + | 0.979465i | \(0.564618\pi\) | |||||||
\(180\) | −1.50000 | + | 2.59808i | −0.111803 | + | 0.193649i | ||||
\(181\) | −8.00000 | −0.594635 | −0.297318 | − | 0.954779i | \(-0.596092\pi\) | ||||
−0.297318 | + | 0.954779i | \(0.596092\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −2.00000 | −0.147844 | ||||||||
\(184\) | 0.500000 | − | 0.866025i | 0.0368605 | − | 0.0638442i | ||||
\(185\) | 18.0000 | + | 31.1769i | 1.32339 | + | 2.29217i | ||||
\(186\) | −4.50000 | − | 7.79423i | −0.329956 | − | 0.571501i | ||||
\(187\) | −10.0000 | + | 17.3205i | −0.731272 | + | 1.26660i | ||||
\(188\) | 2.00000 | 0.145865 | ||||||||
\(189\) | 0.500000 | − | 2.59808i | 0.0363696 | − | 0.188982i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −6.00000 | + | 10.3923i | −0.434145 | + | 0.751961i | −0.997225 | − | 0.0744412i | \(-0.976283\pi\) |
0.563081 | + | 0.826402i | \(0.309616\pi\) | |||||||
\(192\) | −0.500000 | − | 0.866025i | −0.0360844 | − | 0.0625000i | ||||
\(193\) | −6.50000 | − | 11.2583i | −0.467880 | − | 0.810392i | 0.531446 | − | 0.847092i | \(-0.321649\pi\) |
−0.999326 | + | 0.0366998i | \(0.988315\pi\) | |||||||
\(194\) | −6.50000 | + | 11.2583i | −0.466673 | + | 0.808301i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.00000 | + | 6.92820i | 0.0714286 | + | 0.494872i | ||||
\(197\) | −2.00000 | −0.142494 | −0.0712470 | − | 0.997459i | \(-0.522698\pi\) | ||||
−0.0712470 | + | 0.997459i | \(0.522698\pi\) | |||||||
\(198\) | −2.50000 | + | 4.33013i | −0.177667 | + | 0.307729i | ||||
\(199\) | 10.0000 | + | 17.3205i | 0.708881 | + | 1.22782i | 0.965272 | + | 0.261245i | \(0.0841331\pi\) |
−0.256391 | + | 0.966573i | \(0.582534\pi\) | |||||||
\(200\) | 2.00000 | + | 3.46410i | 0.141421 | + | 0.244949i | ||||
\(201\) | 1.00000 | − | 1.73205i | 0.0705346 | − | 0.122169i | ||||
\(202\) | 2.00000 | 0.140720 | ||||||||
\(203\) | −1.50000 | + | 7.79423i | −0.105279 | + | 0.547048i | ||||
\(204\) | −4.00000 | −0.280056 | ||||||||
\(205\) | −18.0000 | + | 31.1769i | −1.25717 | + | 2.17749i | ||||
\(206\) | 4.00000 | + | 6.92820i | 0.278693 | + | 0.482711i | ||||
\(207\) | −0.500000 | − | 0.866025i | −0.0347524 | − | 0.0601929i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | −6.00000 | − | 5.19615i | −0.414039 | − | 0.358569i | ||||
\(211\) | 6.00000 | 0.413057 | 0.206529 | − | 0.978441i | \(-0.433783\pi\) | ||||
0.206529 | + | 0.978441i | \(0.433783\pi\) | |||||||
\(212\) | −2.50000 | + | 4.33013i | −0.171701 | + | 0.297394i | ||||
\(213\) | −3.00000 | − | 5.19615i | −0.205557 | − | 0.356034i | ||||
\(214\) | −9.50000 | − | 16.4545i | −0.649407 | − | 1.12481i | ||||
\(215\) | −9.00000 | + | 15.5885i | −0.613795 | + | 1.06312i | ||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | 22.5000 | − | 7.79423i | 1.52740 | − | 0.529107i | ||||
\(218\) | −6.00000 | −0.406371 | ||||||||
\(219\) | 7.00000 | − | 12.1244i | 0.473016 | − | 0.819288i | ||||
\(220\) | 7.50000 | + | 12.9904i | 0.505650 | + | 0.875811i | ||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −6.00000 | + | 10.3923i | −0.402694 | + | 0.697486i | ||||
\(223\) | 13.0000 | 0.870544 | 0.435272 | − | 0.900299i | \(-0.356652\pi\) | ||||
0.435272 | + | 0.900299i | \(0.356652\pi\) | |||||||
\(224\) | 2.50000 | − | 0.866025i | 0.167038 | − | 0.0578638i | ||||
\(225\) | 4.00000 | 0.266667 | ||||||||
\(226\) | 6.00000 | − | 10.3923i | 0.399114 | − | 0.691286i | ||||
\(227\) | −2.50000 | − | 4.33013i | −0.165931 | − | 0.287401i | 0.771055 | − | 0.636769i | \(-0.219730\pi\) |
−0.936985 | + | 0.349368i | \(0.886396\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 12.0000 | − | 20.7846i | 0.792982 | − | 1.37349i | −0.131130 | − | 0.991365i | \(-0.541861\pi\) |
0.924113 | − | 0.382121i | \(-0.124806\pi\) | |||||||
\(230\) | −3.00000 | −0.197814 | ||||||||
\(231\) | −10.0000 | − | 8.66025i | −0.657952 | − | 0.569803i | ||||
\(232\) | 3.00000 | 0.196960 | ||||||||
\(233\) | −10.0000 | + | 17.3205i | −0.655122 | + | 1.13470i | 0.326741 | + | 0.945114i | \(0.394049\pi\) |
−0.981863 | + | 0.189590i | \(0.939284\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −3.00000 | − | 5.19615i | −0.195698 | − | 0.338960i | ||||
\(236\) | 4.50000 | − | 7.79423i | 0.292925 | − | 0.507361i | ||||
\(237\) | 11.0000 | 0.714527 | ||||||||
\(238\) | 2.00000 | − | 10.3923i | 0.129641 | − | 0.673633i | ||||
\(239\) | −24.0000 | −1.55243 | −0.776215 | − | 0.630468i | \(-0.782863\pi\) | ||||
−0.776215 | + | 0.630468i | \(0.782863\pi\) | |||||||
\(240\) | −1.50000 | + | 2.59808i | −0.0968246 | + | 0.167705i | ||||
\(241\) | −9.50000 | − | 16.4545i | −0.611949 | − | 1.05993i | −0.990912 | − | 0.134515i | \(-0.957053\pi\) |
0.378963 | − | 0.925412i | \(-0.376281\pi\) | |||||||
\(242\) | 7.00000 | + | 12.1244i | 0.449977 | + | 0.779383i | ||||
\(243\) | −0.500000 | + | 0.866025i | −0.0320750 | + | 0.0555556i | ||||
\(244\) | −2.00000 | −0.128037 | ||||||||
\(245\) | 16.5000 | − | 12.9904i | 1.05415 | − | 0.829925i | ||||
\(246\) | −12.0000 | −0.765092 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −4.50000 | − | 7.79423i | −0.285750 | − | 0.494934i | ||||
\(249\) | 8.50000 | + | 14.7224i | 0.538666 | + | 0.932996i | ||||
\(250\) | −1.50000 | + | 2.59808i | −0.0948683 | + | 0.164317i | ||||
\(251\) | −5.00000 | −0.315597 | −0.157799 | − | 0.987471i | \(-0.550440\pi\) | ||||
−0.157799 | + | 0.987471i | \(0.550440\pi\) | |||||||
\(252\) | 0.500000 | − | 2.59808i | 0.0314970 | − | 0.163663i | ||||
\(253\) | −5.00000 | −0.314347 | ||||||||
\(254\) | −5.50000 | + | 9.52628i | −0.345101 | + | 0.597732i | ||||
\(255\) | 6.00000 | + | 10.3923i | 0.375735 | + | 0.650791i | ||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | −5.00000 | + | 8.66025i | −0.311891 | + | 0.540212i | −0.978772 | − | 0.204953i | \(-0.934296\pi\) |
0.666880 | + | 0.745165i | \(0.267629\pi\) | |||||||
\(258\) | −6.00000 | −0.373544 | ||||||||
\(259\) | −24.0000 | − | 20.7846i | −1.49129 | − | 1.29149i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.50000 | − | 2.59808i | 0.0928477 | − | 0.160817i | ||||
\(262\) | 1.50000 | + | 2.59808i | 0.0926703 | + | 0.160510i | ||||
\(263\) | −9.00000 | − | 15.5885i | −0.554964 | − | 0.961225i | −0.997906 | − | 0.0646755i | \(-0.979399\pi\) |
0.442943 | − | 0.896550i | \(-0.353935\pi\) | |||||||
\(264\) | −2.50000 | + | 4.33013i | −0.153864 | + | 0.266501i | ||||
\(265\) | 15.0000 | 0.921443 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 10.0000 | 0.611990 | ||||||||
\(268\) | 1.00000 | − | 1.73205i | 0.0610847 | − | 0.105802i | ||||
\(269\) | −4.50000 | − | 7.79423i | −0.274370 | − | 0.475223i | 0.695606 | − | 0.718423i | \(-0.255136\pi\) |
−0.969976 | + | 0.243201i | \(0.921803\pi\) | |||||||
\(270\) | 1.50000 | + | 2.59808i | 0.0912871 | + | 0.158114i | ||||
\(271\) | 6.50000 | − | 11.2583i | 0.394847 | − | 0.683895i | −0.598235 | − | 0.801321i | \(-0.704131\pi\) |
0.993082 | + | 0.117426i | \(0.0374643\pi\) | |||||||
\(272\) | −4.00000 | −0.242536 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 6.00000 | 0.362473 | ||||||||
\(275\) | 10.0000 | − | 17.3205i | 0.603023 | − | 1.04447i | ||||
\(276\) | −0.500000 | − | 0.866025i | −0.0300965 | − | 0.0521286i | ||||
\(277\) | −4.00000 | − | 6.92820i | −0.240337 | − | 0.416275i | 0.720473 | − | 0.693482i | \(-0.243925\pi\) |
−0.960810 | + | 0.277207i | \(0.910591\pi\) | |||||||
\(278\) | −3.00000 | + | 5.19615i | −0.179928 | + | 0.311645i | ||||
\(279\) | −9.00000 | −0.538816 | ||||||||
\(280\) | −6.00000 | − | 5.19615i | −0.358569 | − | 0.310530i | ||||
\(281\) | 2.00000 | 0.119310 | 0.0596550 | − | 0.998219i | \(-0.481000\pi\) | ||||
0.0596550 | + | 0.998219i | \(0.481000\pi\) | |||||||
\(282\) | 1.00000 | − | 1.73205i | 0.0595491 | − | 0.103142i | ||||
\(283\) | −3.00000 | − | 5.19615i | −0.178331 | − | 0.308879i | 0.762978 | − | 0.646425i | \(-0.223737\pi\) |
−0.941309 | + | 0.337546i | \(0.890403\pi\) | |||||||
\(284\) | −3.00000 | − | 5.19615i | −0.178017 | − | 0.308335i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 6.00000 | − | 31.1769i | 0.354169 | − | 1.84032i | ||||
\(288\) | −1.00000 | −0.0589256 | ||||||||
\(289\) | 0.500000 | − | 0.866025i | 0.0294118 | − | 0.0509427i | ||||
\(290\) | −4.50000 | − | 7.79423i | −0.264249 | − | 0.457693i | ||||
\(291\) | 6.50000 | + | 11.2583i | 0.381037 | + | 0.659975i | ||||
\(292\) | 7.00000 | − | 12.1244i | 0.409644 | − | 0.709524i | ||||
\(293\) | 33.0000 | 1.92788 | 0.963940 | − | 0.266119i | \(-0.0857413\pi\) | ||||
0.963940 | + | 0.266119i | \(0.0857413\pi\) | |||||||
\(294\) | 6.50000 | + | 2.59808i | 0.379088 | + | 0.151523i | ||||
\(295\) | −27.0000 | −1.57200 | ||||||||
\(296\) | −6.00000 | + | 10.3923i | −0.348743 | + | 0.604040i | ||||
\(297\) | 2.50000 | + | 4.33013i | 0.145065 | + | 0.251259i | ||||
\(298\) | −7.00000 | − | 12.1244i | −0.405499 | − | 0.702345i | ||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 4.00000 | 0.230940 | ||||||||
\(301\) | 3.00000 | − | 15.5885i | 0.172917 | − | 0.898504i | ||||
\(302\) | 9.00000 | 0.517892 | ||||||||
\(303\) | 1.00000 | − | 1.73205i | 0.0574485 | − | 0.0995037i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 3.00000 | + | 5.19615i | 0.171780 | + | 0.297531i | ||||
\(306\) | −2.00000 | + | 3.46410i | −0.114332 | + | 0.198030i | ||||
\(307\) | 12.0000 | 0.684876 | 0.342438 | − | 0.939540i | \(-0.388747\pi\) | ||||
0.342438 | + | 0.939540i | \(0.388747\pi\) | |||||||
\(308\) | −10.0000 | − | 8.66025i | −0.569803 | − | 0.493464i | ||||
\(309\) | 8.00000 | 0.455104 | ||||||||
\(310\) | −13.5000 | + | 23.3827i | −0.766748 | + | 1.32805i | ||||
\(311\) | −10.0000 | − | 17.3205i | −0.567048 | − | 0.982156i | −0.996856 | − | 0.0792356i | \(-0.974752\pi\) |
0.429808 | − | 0.902920i | \(-0.358581\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 5.50000 | − | 9.52628i | 0.310878 | − | 0.538457i | −0.667674 | − | 0.744453i | \(-0.732710\pi\) |
0.978553 | + | 0.205996i | \(0.0660435\pi\) | |||||||
\(314\) | 8.00000 | 0.451466 | ||||||||
\(315\) | −7.50000 | + | 2.59808i | −0.422577 | + | 0.146385i | ||||
\(316\) | 11.0000 | 0.618798 | ||||||||
\(317\) | −2.50000 | + | 4.33013i | −0.140414 | + | 0.243204i | −0.927653 | − | 0.373444i | \(-0.878177\pi\) |
0.787239 | + | 0.616649i | \(0.211510\pi\) | |||||||
\(318\) | 2.50000 | + | 4.33013i | 0.140193 | + | 0.242821i | ||||
\(319\) | −7.50000 | − | 12.9904i | −0.419919 | − | 0.727322i | ||||
\(320\) | −1.50000 | + | 2.59808i | −0.0838525 | + | 0.145237i | ||||
\(321\) | −19.0000 | −1.06048 | ||||||||
\(322\) | 2.50000 | − | 0.866025i | 0.139320 | − | 0.0482617i | ||||
\(323\) | 0 | 0 | ||||||||
\(324\) | −0.500000 | + | 0.866025i | −0.0277778 | + | 0.0481125i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −10.0000 | − | 17.3205i | −0.553849 | − | 0.959294i | ||||
\(327\) | −3.00000 | + | 5.19615i | −0.165900 | + | 0.287348i | ||||
\(328\) | −12.0000 | −0.662589 | ||||||||
\(329\) | 4.00000 | + | 3.46410i | 0.220527 | + | 0.190982i | ||||
\(330\) | 15.0000 | 0.825723 | ||||||||
\(331\) | 8.00000 | − | 13.8564i | 0.439720 | − | 0.761617i | −0.557948 | − | 0.829876i | \(-0.688411\pi\) |
0.997668 | + | 0.0682590i | \(0.0217444\pi\) | |||||||
\(332\) | 8.50000 | + | 14.7224i | 0.466498 | + | 0.807998i | ||||
\(333\) | 6.00000 | + | 10.3923i | 0.328798 | + | 0.569495i | ||||
\(334\) | −1.00000 | + | 1.73205i | −0.0547176 | + | 0.0947736i | ||||
\(335\) | −6.00000 | −0.327815 | ||||||||
\(336\) | 0.500000 | − | 2.59808i | 0.0272772 | − | 0.141737i | ||||
\(337\) | 21.0000 | 1.14394 | 0.571971 | − | 0.820274i | \(-0.306179\pi\) | ||||
0.571971 | + | 0.820274i | \(0.306179\pi\) | |||||||
\(338\) | −6.50000 | + | 11.2583i | −0.353553 | + | 0.612372i | ||||
\(339\) | −6.00000 | − | 10.3923i | −0.325875 | − | 0.564433i | ||||
\(340\) | 6.00000 | + | 10.3923i | 0.325396 | + | 0.563602i | ||||
\(341\) | −22.5000 | + | 38.9711i | −1.21844 | + | 2.11041i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −10.0000 | + | 15.5885i | −0.539949 | + | 0.841698i | ||||
\(344\) | −6.00000 | −0.323498 | ||||||||
\(345\) | −1.50000 | + | 2.59808i | −0.0807573 | + | 0.139876i | ||||
\(346\) | −3.00000 | − | 5.19615i | −0.161281 | − | 0.279347i | ||||
\(347\) | 2.00000 | + | 3.46410i | 0.107366 | + | 0.185963i | 0.914702 | − | 0.404128i | \(-0.132425\pi\) |
−0.807337 | + | 0.590091i | \(0.799092\pi\) | |||||||
\(348\) | 1.50000 | − | 2.59808i | 0.0804084 | − | 0.139272i | ||||
\(349\) | 22.0000 | 1.17763 | 0.588817 | − | 0.808267i | \(-0.299594\pi\) | ||||
0.588817 | + | 0.808267i | \(0.299594\pi\) | |||||||
\(350\) | −2.00000 | + | 10.3923i | −0.106904 | + | 0.555492i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −2.50000 | + | 4.33013i | −0.133250 | + | 0.230797i | ||||
\(353\) | −2.00000 | − | 3.46410i | −0.106449 | − | 0.184376i | 0.807880 | − | 0.589347i | \(-0.200615\pi\) |
−0.914329 | + | 0.404971i | \(0.867282\pi\) | |||||||
\(354\) | −4.50000 | − | 7.79423i | −0.239172 | − | 0.414259i | ||||
\(355\) | −9.00000 | + | 15.5885i | −0.477670 | + | 0.827349i | ||||
\(356\) | 10.0000 | 0.529999 | ||||||||
\(357\) | −8.00000 | − | 6.92820i | −0.423405 | − | 0.366679i | ||||
\(358\) | 20.0000 | 1.05703 | ||||||||
\(359\) | 5.00000 | − | 8.66025i | 0.263890 | − | 0.457071i | −0.703382 | − | 0.710812i | \(-0.748328\pi\) |
0.967272 | + | 0.253741i | \(0.0816611\pi\) | |||||||
\(360\) | 1.50000 | + | 2.59808i | 0.0790569 | + | 0.136931i | ||||
\(361\) | 9.50000 | + | 16.4545i | 0.500000 | + | 0.866025i | ||||
\(362\) | −4.00000 | + | 6.92820i | −0.210235 | + | 0.364138i | ||||
\(363\) | 14.0000 | 0.734809 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −42.0000 | −2.19838 | ||||||||
\(366\) | −1.00000 | + | 1.73205i | −0.0522708 | + | 0.0905357i | ||||
\(367\) | −12.5000 | − | 21.6506i | −0.652495 | − | 1.13015i | −0.982516 | − | 0.186180i | \(-0.940389\pi\) |
0.330021 | − | 0.943974i | \(-0.392944\pi\) | |||||||
\(368\) | −0.500000 | − | 0.866025i | −0.0260643 | − | 0.0451447i | ||||
\(369\) | −6.00000 | + | 10.3923i | −0.312348 | + | 0.541002i | ||||
\(370\) | 36.0000 | 1.87155 | ||||||||
\(371\) | −12.5000 | + | 4.33013i | −0.648968 | + | 0.224809i | ||||
\(372\) | −9.00000 | −0.466628 | ||||||||
\(373\) | 4.00000 | − | 6.92820i | 0.207112 | − | 0.358729i | −0.743691 | − | 0.668523i | \(-0.766927\pi\) |
0.950804 | + | 0.309794i | \(0.100260\pi\) | |||||||
\(374\) | 10.0000 | + | 17.3205i | 0.517088 | + | 0.895622i | ||||
\(375\) | 1.50000 | + | 2.59808i | 0.0774597 | + | 0.134164i | ||||
\(376\) | 1.00000 | − | 1.73205i | 0.0515711 | − | 0.0893237i | ||||
\(377\) | 0 | 0 | ||||||||
\(378\) | −2.00000 | − | 1.73205i | −0.102869 | − | 0.0890871i | ||||
\(379\) | −16.0000 | −0.821865 | −0.410932 | − | 0.911666i | \(-0.634797\pi\) | ||||
−0.410932 | + | 0.911666i | \(0.634797\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 5.50000 | + | 9.52628i | 0.281774 | + | 0.488046i | ||||
\(382\) | 6.00000 | + | 10.3923i | 0.306987 | + | 0.531717i | ||||
\(383\) | 9.00000 | − | 15.5885i | 0.459879 | − | 0.796533i | −0.539076 | − | 0.842257i | \(-0.681226\pi\) |
0.998954 | + | 0.0457244i | \(0.0145596\pi\) | |||||||
\(384\) | −1.00000 | −0.0510310 | ||||||||
\(385\) | −7.50000 | + | 38.9711i | −0.382235 | + | 1.98615i | ||||
\(386\) | −13.0000 | −0.661683 | ||||||||
\(387\) | −3.00000 | + | 5.19615i | −0.152499 | + | 0.264135i | ||||
\(388\) | 6.50000 | + | 11.2583i | 0.329988 | + | 0.571555i | ||||
\(389\) | −9.00000 | − | 15.5885i | −0.456318 | − | 0.790366i | 0.542445 | − | 0.840091i | \(-0.317499\pi\) |
−0.998763 | + | 0.0497253i | \(0.984165\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −4.00000 | −0.202289 | ||||||||
\(392\) | 6.50000 | + | 2.59808i | 0.328300 | + | 0.131223i | ||||
\(393\) | 3.00000 | 0.151330 | ||||||||
\(394\) | −1.00000 | + | 1.73205i | −0.0503793 | + | 0.0872595i | ||||
\(395\) | −16.5000 | − | 28.5788i | −0.830205 | − | 1.43796i | ||||
\(396\) | 2.50000 | + | 4.33013i | 0.125630 | + | 0.217597i | ||||
\(397\) | 4.00000 | − | 6.92820i | 0.200754 | − | 0.347717i | −0.748017 | − | 0.663679i | \(-0.768994\pi\) |
0.948772 | + | 0.315963i | \(0.102327\pi\) | |||||||
\(398\) | 20.0000 | 1.00251 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 4.00000 | 0.200000 | ||||||||
\(401\) | −16.0000 | + | 27.7128i | −0.799002 | + | 1.38391i | 0.121265 | + | 0.992620i | \(0.461305\pi\) |
−0.920267 | + | 0.391292i | \(0.872028\pi\) | |||||||
\(402\) | −1.00000 | − | 1.73205i | −0.0498755 | − | 0.0863868i | ||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 1.00000 | − | 1.73205i | 0.0497519 | − | 0.0861727i | ||||
\(405\) | 3.00000 | 0.149071 | ||||||||
\(406\) | 6.00000 | + | 5.19615i | 0.297775 | + | 0.257881i | ||||
\(407\) | 60.0000 | 2.97409 | ||||||||
\(408\) | −2.00000 | + | 3.46410i | −0.0990148 | + | 0.171499i | ||||
\(409\) | −3.50000 | − | 6.06218i | −0.173064 | − | 0.299755i | 0.766426 | − | 0.642333i | \(-0.222033\pi\) |
−0.939490 | + | 0.342578i | \(0.888700\pi\) | |||||||
\(410\) | 18.0000 | + | 31.1769i | 0.888957 | + | 1.53972i | ||||
\(411\) | 3.00000 | − | 5.19615i | 0.147979 | − | 0.256307i | ||||
\(412\) | 8.00000 | 0.394132 | ||||||||
\(413\) | 22.5000 | − | 7.79423i | 1.10715 | − | 0.383529i | ||||
\(414\) | −1.00000 | −0.0491473 | ||||||||
\(415\) | 25.5000 | − | 44.1673i | 1.25175 | − | 2.16809i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 3.00000 | + | 5.19615i | 0.146911 | + | 0.254457i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −16.0000 | −0.781651 | −0.390826 | − | 0.920465i | \(-0.627810\pi\) | ||||
−0.390826 | + | 0.920465i | \(0.627810\pi\) | |||||||
\(420\) | −7.50000 | + | 2.59808i | −0.365963 | + | 0.126773i | ||||
\(421\) | −6.00000 | −0.292422 | −0.146211 | − | 0.989253i | \(-0.546708\pi\) | ||||
−0.146211 | + | 0.989253i | \(0.546708\pi\) | |||||||
\(422\) | 3.00000 | − | 5.19615i | 0.146038 | − | 0.252945i | ||||
\(423\) | −1.00000 | − | 1.73205i | −0.0486217 | − | 0.0842152i | ||||
\(424\) | 2.50000 | + | 4.33013i | 0.121411 | + | 0.210290i | ||||
\(425\) | 8.00000 | − | 13.8564i | 0.388057 | − | 0.672134i | ||||
\(426\) | −6.00000 | −0.290701 | ||||||||
\(427\) | −4.00000 | − | 3.46410i | −0.193574 | − | 0.167640i | ||||
\(428\) | −19.0000 | −0.918400 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 9.00000 | + | 15.5885i | 0.434019 | + | 0.751742i | ||||
\(431\) | 6.00000 | + | 10.3923i | 0.289010 | + | 0.500580i | 0.973574 | − | 0.228373i | \(-0.0733406\pi\) |
−0.684564 | + | 0.728953i | \(0.740007\pi\) | |||||||
\(432\) | −0.500000 | + | 0.866025i | −0.0240563 | + | 0.0416667i | ||||
\(433\) | 14.0000 | 0.672797 | 0.336399 | − | 0.941720i | \(-0.390791\pi\) | ||||
0.336399 | + | 0.941720i | \(0.390791\pi\) | |||||||
\(434\) | 4.50000 | − | 23.3827i | 0.216007 | − | 1.12240i | ||||
\(435\) | −9.00000 | −0.431517 | ||||||||
\(436\) | −3.00000 | + | 5.19615i | −0.143674 | + | 0.248851i | ||||
\(437\) | 0 | 0 | ||||||||
\(438\) | −7.00000 | − | 12.1244i | −0.334473 | − | 0.579324i | ||||
\(439\) | 6.50000 | − | 11.2583i | 0.310228 | − | 0.537331i | −0.668184 | − | 0.743996i | \(-0.732928\pi\) |
0.978412 | + | 0.206666i | \(0.0662612\pi\) | |||||||
\(440\) | 15.0000 | 0.715097 | ||||||||
\(441\) | 5.50000 | − | 4.33013i | 0.261905 | − | 0.206197i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 14.5000 | − | 25.1147i | 0.688916 | − | 1.19324i | −0.283273 | − | 0.959039i | \(-0.591420\pi\) |
0.972189 | − | 0.234198i | \(-0.0752464\pi\) | |||||||
\(444\) | 6.00000 | + | 10.3923i | 0.284747 | + | 0.493197i | ||||
\(445\) | −15.0000 | − | 25.9808i | −0.711068 | − | 1.23161i | ||||
\(446\) | 6.50000 | − | 11.2583i | 0.307784 | − | 0.533097i | ||||
\(447\) | −14.0000 | −0.662177 | ||||||||
\(448\) | 0.500000 | − | 2.59808i | 0.0236228 | − | 0.122748i | ||||
\(449\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(450\) | 2.00000 | − | 3.46410i | 0.0942809 | − | 0.163299i | ||||
\(451\) | 30.0000 | + | 51.9615i | 1.41264 | + | 2.44677i | ||||
\(452\) | −6.00000 | − | 10.3923i | −0.282216 | − | 0.488813i | ||||
\(453\) | 4.50000 | − | 7.79423i | 0.211428 | − | 0.366205i | ||||
\(454\) | −5.00000 | −0.234662 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 10.5000 | − | 18.1865i | 0.491169 | − | 0.850730i | −0.508779 | − | 0.860897i | \(-0.669903\pi\) |
0.999948 | + | 0.0101670i | \(0.00323631\pi\) | |||||||
\(458\) | −12.0000 | − | 20.7846i | −0.560723 | − | 0.971201i | ||||
\(459\) | 2.00000 | + | 3.46410i | 0.0933520 | + | 0.161690i | ||||
\(460\) | −1.50000 | + | 2.59808i | −0.0699379 | + | 0.121136i | ||||
\(461\) | 14.0000 | 0.652045 | 0.326023 | − | 0.945362i | \(-0.394291\pi\) | ||||
0.326023 | + | 0.945362i | \(0.394291\pi\) | |||||||
\(462\) | −12.5000 | + | 4.33013i | −0.581553 | + | 0.201456i | ||||
\(463\) | −32.0000 | −1.48717 | −0.743583 | − | 0.668644i | \(-0.766875\pi\) | ||||
−0.743583 | + | 0.668644i | \(0.766875\pi\) | |||||||
\(464\) | 1.50000 | − | 2.59808i | 0.0696358 | − | 0.120613i | ||||
\(465\) | 13.5000 | + | 23.3827i | 0.626048 | + | 1.08435i | ||||
\(466\) | 10.0000 | + | 17.3205i | 0.463241 | + | 0.802357i | ||||
\(467\) | −14.0000 | + | 24.2487i | −0.647843 | + | 1.12210i | 0.335794 | + | 0.941935i | \(0.390995\pi\) |
−0.983637 | + | 0.180161i | \(0.942338\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 5.00000 | − | 1.73205i | 0.230879 | − | 0.0799787i | ||||
\(470\) | −6.00000 | −0.276759 | ||||||||
\(471\) | 4.00000 | − | 6.92820i | 0.184310 | − | 0.319235i | ||||
\(472\) | −4.50000 | − | 7.79423i | −0.207129 | − | 0.358758i | ||||
\(473\) | 15.0000 | + | 25.9808i | 0.689701 | + | 1.19460i | ||||
\(474\) | 5.50000 | − | 9.52628i | 0.252623 | − | 0.437557i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −8.00000 | − | 6.92820i | −0.366679 | − | 0.317554i | ||||
\(477\) | 5.00000 | 0.228934 | ||||||||
\(478\) | −12.0000 | + | 20.7846i | −0.548867 | + | 0.950666i | ||||
\(479\) | −9.00000 | − | 15.5885i | −0.411220 | − | 0.712255i | 0.583803 | − | 0.811895i | \(-0.301564\pi\) |
−0.995023 | + | 0.0996406i | \(0.968231\pi\) | |||||||
\(480\) | 1.50000 | + | 2.59808i | 0.0684653 | + | 0.118585i | ||||
\(481\) | 0 | 0 | ||||||||
\(482\) | −19.0000 | −0.865426 | ||||||||
\(483\) | 0.500000 | − | 2.59808i | 0.0227508 | − | 0.118217i | ||||
\(484\) | 14.0000 | 0.636364 | ||||||||
\(485\) | 19.5000 | − | 33.7750i | 0.885449 | − | 1.53364i | ||||
\(486\) | 0.500000 | + | 0.866025i | 0.0226805 | + | 0.0392837i | ||||
\(487\) | 11.5000 | + | 19.9186i | 0.521115 | + | 0.902597i | 0.999698 | + | 0.0245553i | \(0.00781698\pi\) |
−0.478584 | + | 0.878042i | \(0.658850\pi\) | |||||||
\(488\) | −1.00000 | + | 1.73205i | −0.0452679 | + | 0.0784063i | ||||
\(489\) | −20.0000 | −0.904431 | ||||||||
\(490\) | −3.00000 | − | 20.7846i | −0.135526 | − | 0.938953i | ||||
\(491\) | 27.0000 | 1.21849 | 0.609246 | − | 0.792981i | \(-0.291472\pi\) | ||||
0.609246 | + | 0.792981i | \(0.291472\pi\) | |||||||
\(492\) | −6.00000 | + | 10.3923i | −0.270501 | + | 0.468521i | ||||
\(493\) | −6.00000 | − | 10.3923i | −0.270226 | − | 0.468046i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 7.50000 | − | 12.9904i | 0.337100 | − | 0.583874i | ||||
\(496\) | −9.00000 | −0.404112 | ||||||||
\(497\) | 3.00000 | − | 15.5885i | 0.134568 | − | 0.699238i | ||||
\(498\) | 17.0000 | 0.761788 | ||||||||
\(499\) | −5.00000 | + | 8.66025i | −0.223831 | + | 0.387686i | −0.955968 | − | 0.293471i | \(-0.905190\pi\) |
0.732137 | + | 0.681157i | \(0.238523\pi\) | |||||||
\(500\) | 1.50000 | + | 2.59808i | 0.0670820 | + | 0.116190i | ||||
\(501\) | 1.00000 | + | 1.73205i | 0.0446767 | + | 0.0773823i | ||||
\(502\) | −2.50000 | + | 4.33013i | −0.111580 | + | 0.193263i | ||||
\(503\) | 12.0000 | 0.535054 | 0.267527 | − | 0.963550i | \(-0.413794\pi\) | ||||
0.267527 | + | 0.963550i | \(0.413794\pi\) | |||||||
\(504\) | −2.00000 | − | 1.73205i | −0.0890871 | − | 0.0771517i | ||||
\(505\) | −6.00000 | −0.266996 | ||||||||
\(506\) | −2.50000 | + | 4.33013i | −0.111139 | + | 0.192498i | ||||
\(507\) | 6.50000 | + | 11.2583i | 0.288675 | + | 0.500000i | ||||
\(508\) | 5.50000 | + | 9.52628i | 0.244023 | + | 0.422660i | ||||
\(509\) | 15.5000 | − | 26.8468i | 0.687025 | − | 1.18996i | −0.285770 | − | 0.958298i | \(-0.592249\pi\) |
0.972796 | − | 0.231665i | \(-0.0744172\pi\) | |||||||
\(510\) | 12.0000 | 0.531369 | ||||||||
\(511\) | 35.0000 | − | 12.1244i | 1.54831 | − | 0.536350i | ||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 5.00000 | + | 8.66025i | 0.220541 | + | 0.381987i | ||||
\(515\) | −12.0000 | − | 20.7846i | −0.528783 | − | 0.915879i | ||||
\(516\) | −3.00000 | + | 5.19615i | −0.132068 | + | 0.228748i | ||||
\(517\) | −10.0000 | −0.439799 | ||||||||
\(518\) | −30.0000 | + | 10.3923i | −1.31812 | + | 0.456612i | ||||
\(519\) | −6.00000 | −0.263371 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −15.0000 | − | 25.9808i | −0.657162 | − | 1.13824i | −0.981347 | − | 0.192244i | \(-0.938423\pi\) |
0.324185 | − | 0.945994i | \(-0.394910\pi\) | |||||||
\(522\) | −1.50000 | − | 2.59808i | −0.0656532 | − | 0.113715i | ||||
\(523\) | −18.0000 | + | 31.1769i | −0.787085 | + | 1.36327i | 0.140660 | + | 0.990058i | \(0.455077\pi\) |
−0.927746 | + | 0.373213i | \(0.878256\pi\) | |||||||
\(524\) | 3.00000 | 0.131056 | ||||||||
\(525\) | 8.00000 | + | 6.92820i | 0.349149 | + | 0.302372i | ||||
\(526\) | −18.0000 | −0.784837 | ||||||||
\(527\) | −18.0000 | + | 31.1769i | −0.784092 | + | 1.35809i | ||||
\(528\) | 2.50000 | + | 4.33013i | 0.108799 | + | 0.188445i | ||||
\(529\) | −0.500000 | − | 0.866025i | −0.0217391 | − | 0.0376533i | ||||
\(530\) | 7.50000 | − | 12.9904i | 0.325779 | − | 0.564266i | ||||
\(531\) | −9.00000 | −0.390567 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 5.00000 | − | 8.66025i | 0.216371 | − | 0.374766i | ||||
\(535\) | 28.5000 | + | 49.3634i | 1.23216 | + | 2.13417i | ||||
\(536\) | −1.00000 | − | 1.73205i | −0.0431934 | − | 0.0748132i | ||||
\(537\) | 10.0000 | − | 17.3205i | 0.431532 | − | 0.747435i | ||||
\(538\) | −9.00000 | −0.388018 | ||||||||
\(539\) | −5.00000 | − | 34.6410i | −0.215365 | − | 1.49209i | ||||
\(540\) | 3.00000 | 0.129099 | ||||||||
\(541\) | 17.0000 | − | 29.4449i | 0.730887 | − | 1.26593i | −0.225617 | − | 0.974216i | \(-0.572440\pi\) |
0.956504 | − | 0.291718i | \(-0.0942267\pi\) | |||||||
\(542\) | −6.50000 | − | 11.2583i | −0.279199 | − | 0.483587i | ||||
\(543\) | 4.00000 | + | 6.92820i | 0.171656 | + | 0.297318i | ||||
\(544\) | −2.00000 | + | 3.46410i | −0.0857493 | + | 0.148522i | ||||
\(545\) | 18.0000 | 0.771035 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −44.0000 | −1.88130 | −0.940652 | − | 0.339372i | \(-0.889785\pi\) | ||||
−0.940652 | + | 0.339372i | \(0.889785\pi\) | |||||||
\(548\) | 3.00000 | − | 5.19615i | 0.128154 | − | 0.221969i | ||||
\(549\) | 1.00000 | + | 1.73205i | 0.0426790 | + | 0.0739221i | ||||
\(550\) | −10.0000 | − | 17.3205i | −0.426401 | − | 0.738549i | ||||
\(551\) | 0 | 0 | ||||||||
\(552\) | −1.00000 | −0.0425628 | ||||||||
\(553\) | 22.0000 | + | 19.0526i | 0.935535 | + | 0.810197i | ||||
\(554\) | −8.00000 | −0.339887 | ||||||||
\(555\) | 18.0000 | − | 31.1769i | 0.764057 | − | 1.32339i | ||||
\(556\) | 3.00000 | + | 5.19615i | 0.127228 | + | 0.220366i | ||||
\(557\) | −1.50000 | − | 2.59808i | −0.0635570 | − | 0.110084i | 0.832496 | − | 0.554031i | \(-0.186911\pi\) |
−0.896053 | + | 0.443947i | \(0.853578\pi\) | |||||||
\(558\) | −4.50000 | + | 7.79423i | −0.190500 | + | 0.329956i | ||||
\(559\) | 0 | 0 | ||||||||
\(560\) | −7.50000 | + | 2.59808i | −0.316933 | + | 0.109789i | ||||
\(561\) | 20.0000 | 0.844401 | ||||||||
\(562\) | 1.00000 | − | 1.73205i | 0.0421825 | − | 0.0730622i | ||||
\(563\) | −19.5000 | − | 33.7750i | −0.821827 | − | 1.42345i | −0.904320 | − | 0.426855i | \(-0.859622\pi\) |
0.0824933 | − | 0.996592i | \(-0.473712\pi\) | |||||||
\(564\) | −1.00000 | − | 1.73205i | −0.0421076 | − | 0.0729325i | ||||
\(565\) | −18.0000 | + | 31.1769i | −0.757266 | + | 1.31162i | ||||
\(566\) | −6.00000 | −0.252199 | ||||||||
\(567\) | −2.50000 | + | 0.866025i | −0.104990 | + | 0.0363696i | ||||
\(568\) | −6.00000 | −0.251754 | ||||||||
\(569\) | −10.0000 | + | 17.3205i | −0.419222 | + | 0.726113i | −0.995861 | − | 0.0908852i | \(-0.971030\pi\) |
0.576640 | + | 0.816999i | \(0.304364\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −5.00000 | − | 8.66025i | −0.209243 | − | 0.362420i | 0.742233 | − | 0.670142i | \(-0.233767\pi\) |
−0.951476 | + | 0.307722i | \(0.900433\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 12.0000 | 0.501307 | ||||||||
\(574\) | −24.0000 | − | 20.7846i | −1.00174 | − | 0.867533i | ||||
\(575\) | 4.00000 | 0.166812 | ||||||||
\(576\) | −0.500000 | + | 0.866025i | −0.0208333 | + | 0.0360844i | ||||
\(577\) | −19.5000 | − | 33.7750i | −0.811796 | − | 1.40607i | −0.911606 | − | 0.411065i | \(-0.865157\pi\) |
0.0998105 | − | 0.995006i | \(-0.468176\pi\) | |||||||
\(578\) | −0.500000 | − | 0.866025i | −0.0207973 | − | 0.0360219i | ||||
\(579\) | −6.50000 | + | 11.2583i | −0.270131 | + | 0.467880i | ||||
\(580\) | −9.00000 | −0.373705 | ||||||||
\(581\) | −8.50000 | + | 44.1673i | −0.352639 | + | 1.83237i | ||||
\(582\) | 13.0000 | 0.538867 | ||||||||
\(583\) | 12.5000 | − | 21.6506i | 0.517697 | − | 0.896678i | ||||
\(584\) | −7.00000 | − | 12.1244i | −0.289662 | − | 0.501709i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 16.5000 | − | 28.5788i | 0.681609 | − | 1.18058i | ||||
\(587\) | −15.0000 | −0.619116 | −0.309558 | − | 0.950881i | \(-0.600181\pi\) | ||||
−0.309558 | + | 0.950881i | \(0.600181\pi\) | |||||||
\(588\) | 5.50000 | − | 4.33013i | 0.226816 | − | 0.178571i | ||||
\(589\) | 0 | 0 | ||||||||
\(590\) | −13.5000 | + | 23.3827i | −0.555786 | + | 0.962650i | ||||
\(591\) | 1.00000 | + | 1.73205i | 0.0411345 | + | 0.0712470i | ||||
\(592\) | 6.00000 | + | 10.3923i | 0.246598 | + | 0.427121i | ||||
\(593\) | −4.00000 | + | 6.92820i | −0.164260 | + | 0.284507i | −0.936392 | − | 0.350955i | \(-0.885857\pi\) |
0.772132 | + | 0.635462i | \(0.219190\pi\) | |||||||
\(594\) | 5.00000 | 0.205152 | ||||||||
\(595\) | −6.00000 | + | 31.1769i | −0.245976 | + | 1.27813i | ||||
\(596\) | −14.0000 | −0.573462 | ||||||||
\(597\) | 10.0000 | − | 17.3205i | 0.409273 | − | 0.708881i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 11.0000 | + | 19.0526i | 0.449448 | + | 0.778466i | 0.998350 | − | 0.0574201i | \(-0.0182874\pi\) |
−0.548902 | + | 0.835887i | \(0.684954\pi\) | |||||||
\(600\) | 2.00000 | − | 3.46410i | 0.0816497 | − | 0.141421i | ||||
\(601\) | 11.0000 | 0.448699 | 0.224350 | − | 0.974509i | \(-0.427974\pi\) | ||||
0.224350 | + | 0.974509i | \(0.427974\pi\) | |||||||
\(602\) | −12.0000 | − | 10.3923i | −0.489083 | − | 0.423559i | ||||
\(603\) | −2.00000 | −0.0814463 | ||||||||
\(604\) | 4.50000 | − | 7.79423i | 0.183102 | − | 0.317143i | ||||
\(605\) | −21.0000 | − | 36.3731i | −0.853771 | − | 1.47878i | ||||
\(606\) | −1.00000 | − | 1.73205i | −0.0406222 | − | 0.0703598i | ||||
\(607\) | 7.50000 | − | 12.9904i | 0.304416 | − | 0.527263i | −0.672715 | − | 0.739901i | \(-0.734872\pi\) |
0.977131 | + | 0.212638i | \(0.0682055\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 7.50000 | − | 2.59808i | 0.303915 | − | 0.105279i | ||||
\(610\) | 6.00000 | 0.242933 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 2.00000 | + | 3.46410i | 0.0808452 | + | 0.140028i | ||||
\(613\) | −8.00000 | − | 13.8564i | −0.323117 | − | 0.559655i | 0.658012 | − | 0.753007i | \(-0.271397\pi\) |
−0.981129 | + | 0.193352i | \(0.938064\pi\) | |||||||
\(614\) | 6.00000 | − | 10.3923i | 0.242140 | − | 0.419399i | ||||
\(615\) | 36.0000 | 1.45166 | ||||||||
\(616\) | −12.5000 | + | 4.33013i | −0.503639 | + | 0.174466i | ||||
\(617\) | 42.0000 | 1.69086 | 0.845428 | − | 0.534089i | \(-0.179345\pi\) | ||||
0.845428 | + | 0.534089i | \(0.179345\pi\) | |||||||
\(618\) | 4.00000 | − | 6.92820i | 0.160904 | − | 0.278693i | ||||
\(619\) | 23.0000 | + | 39.8372i | 0.924448 | + | 1.60119i | 0.792446 | + | 0.609941i | \(0.208807\pi\) |
0.132002 | + | 0.991250i | \(0.457860\pi\) | |||||||
\(620\) | 13.5000 | + | 23.3827i | 0.542173 | + | 0.939071i | ||||
\(621\) | −0.500000 | + | 0.866025i | −0.0200643 | + | 0.0347524i | ||||
\(622\) | −20.0000 | −0.801927 | ||||||||
\(623\) | 20.0000 | + | 17.3205i | 0.801283 | + | 0.693932i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 14.5000 | − | 25.1147i | 0.580000 | − | 1.00459i | ||||
\(626\) | −5.50000 | − | 9.52628i | −0.219824 | − | 0.380747i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 4.00000 | − | 6.92820i | 0.159617 | − | 0.276465i | ||||
\(629\) | 48.0000 | 1.91389 | ||||||||
\(630\) | −1.50000 | + | 7.79423i | −0.0597614 | + | 0.310530i | ||||
\(631\) | 37.0000 | 1.47295 | 0.736473 | − | 0.676467i | \(-0.236490\pi\) | ||||
0.736473 | + | 0.676467i | \(0.236490\pi\) | |||||||
\(632\) | 5.50000 | − | 9.52628i | 0.218778 | − | 0.378935i | ||||
\(633\) | −3.00000 | − | 5.19615i | −0.119239 | − | 0.206529i | ||||
\(634\) | 2.50000 | + | 4.33013i | 0.0992877 | + | 0.171971i | ||||
\(635\) | 16.5000 | − | 28.5788i | 0.654783 | − | 1.13412i | ||||
\(636\) | 5.00000 | 0.198263 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −15.0000 | −0.593856 | ||||||||
\(639\) | −3.00000 | + | 5.19615i | −0.118678 | + | 0.205557i | ||||
\(640\) | 1.50000 | + | 2.59808i | 0.0592927 | + | 0.102698i | ||||
\(641\) | −15.0000 | − | 25.9808i | −0.592464 | − | 1.02618i | −0.993899 | − | 0.110291i | \(-0.964822\pi\) |
0.401435 | − | 0.915888i | \(-0.368512\pi\) | |||||||
\(642\) | −9.50000 | + | 16.4545i | −0.374935 | + | 0.649407i | ||||
\(643\) | −14.0000 | −0.552106 | −0.276053 | − | 0.961142i | \(-0.589027\pi\) | ||||
−0.276053 | + | 0.961142i | \(0.589027\pi\) | |||||||
\(644\) | 0.500000 | − | 2.59808i | 0.0197028 | − | 0.102379i | ||||
\(645\) | 18.0000 | 0.708749 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 9.00000 | + | 15.5885i | 0.353827 | + | 0.612845i | 0.986916 | − | 0.161233i | \(-0.0515470\pi\) |
−0.633090 | + | 0.774078i | \(0.718214\pi\) | |||||||
\(648\) | 0.500000 | + | 0.866025i | 0.0196419 | + | 0.0340207i | ||||
\(649\) | −22.5000 | + | 38.9711i | −0.883202 | + | 1.52975i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −18.0000 | − | 15.5885i | −0.705476 | − | 0.610960i | ||||
\(652\) | −20.0000 | −0.783260 | ||||||||
\(653\) | 8.50000 | − | 14.7224i | 0.332631 | − | 0.576133i | −0.650396 | − | 0.759595i | \(-0.725397\pi\) |
0.983027 | + | 0.183462i | \(0.0587304\pi\) | |||||||
\(654\) | 3.00000 | + | 5.19615i | 0.117309 | + | 0.203186i | ||||
\(655\) | −4.50000 | − | 7.79423i | −0.175830 | − | 0.304546i | ||||
\(656\) | −6.00000 | + | 10.3923i | −0.234261 | + | 0.405751i | ||||
\(657\) | −14.0000 | −0.546192 | ||||||||
\(658\) | 5.00000 | − | 1.73205i | 0.194920 | − | 0.0675224i | ||||
\(659\) | −24.0000 | −0.934907 | −0.467454 | − | 0.884018i | \(-0.654829\pi\) | ||||
−0.467454 | + | 0.884018i | \(0.654829\pi\) | |||||||
\(660\) | 7.50000 | − | 12.9904i | 0.291937 | − | 0.505650i | ||||
\(661\) | −11.0000 | − | 19.0526i | −0.427850 | − | 0.741059i | 0.568831 | − | 0.822454i | \(-0.307396\pi\) |
−0.996682 | + | 0.0813955i | \(0.974062\pi\) | |||||||
\(662\) | −8.00000 | − | 13.8564i | −0.310929 | − | 0.538545i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 17.0000 | 0.659728 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 12.0000 | 0.464991 | ||||||||
\(667\) | 1.50000 | − | 2.59808i | 0.0580802 | − | 0.100598i | ||||
\(668\) | 1.00000 | + | 1.73205i | 0.0386912 | + | 0.0670151i | ||||
\(669\) | −6.50000 | − | 11.2583i | −0.251305 | − | 0.435272i | ||||
\(670\) | −3.00000 | + | 5.19615i | −0.115900 | + | 0.200745i | ||||
\(671\) | 10.0000 | 0.386046 | ||||||||
\(672\) | −2.00000 | − | 1.73205i | −0.0771517 | − | 0.0668153i | ||||
\(673\) | 13.0000 | 0.501113 | 0.250557 | − | 0.968102i | \(-0.419386\pi\) | ||||
0.250557 | + | 0.968102i | \(0.419386\pi\) | |||||||
\(674\) | 10.5000 | − | 18.1865i | 0.404445 | − | 0.700519i | ||||
\(675\) | −2.00000 | − | 3.46410i | −0.0769800 | − | 0.133333i | ||||
\(676\) | 6.50000 | + | 11.2583i | 0.250000 | + | 0.433013i | ||||
\(677\) | −15.5000 | + | 26.8468i | −0.595713 | + | 1.03181i | 0.397732 | + | 0.917501i | \(0.369797\pi\) |
−0.993446 | + | 0.114304i | \(0.963536\pi\) | |||||||
\(678\) | −12.0000 | −0.460857 | ||||||||
\(679\) | −6.50000 | + | 33.7750i | −0.249447 | + | 1.29617i | ||||
\(680\) | 12.0000 | 0.460179 | ||||||||
\(681\) | −2.50000 | + | 4.33013i | −0.0958002 | + | 0.165931i | ||||
\(682\) | 22.5000 | + | 38.9711i | 0.861570 | + | 1.49228i | ||||
\(683\) | 21.5000 | + | 37.2391i | 0.822675 | + | 1.42491i | 0.903684 | + | 0.428201i | \(0.140852\pi\) |
−0.0810089 | + | 0.996713i | \(0.525814\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −18.0000 | −0.687745 | ||||||||
\(686\) | 8.50000 | + | 16.4545i | 0.324532 | + | 0.628235i | ||||
\(687\) | −24.0000 | −0.915657 | ||||||||
\(688\) | −3.00000 | + | 5.19615i | −0.114374 | + | 0.198101i | ||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 1.50000 | + | 2.59808i | 0.0571040 | + | 0.0989071i | ||||
\(691\) | −14.0000 | + | 24.2487i | −0.532585 | + | 0.922464i | 0.466691 | + | 0.884420i | \(0.345446\pi\) |
−0.999276 | + | 0.0380440i | \(0.987887\pi\) | |||||||
\(692\) | −6.00000 | −0.228086 | ||||||||
\(693\) | −2.50000 | + | 12.9904i | −0.0949671 | + | 0.493464i | ||||
\(694\) | 4.00000 | 0.151838 | ||||||||
\(695\) | 9.00000 | − | 15.5885i | 0.341389 | − | 0.591304i | ||||
\(696\) | −1.50000 | − | 2.59808i | −0.0568574 | − | 0.0984798i | ||||
\(697\) | 24.0000 | + | 41.5692i | 0.909065 | + | 1.57455i | ||||
\(698\) | 11.0000 | − | 19.0526i | 0.416356 | − | 0.721150i | ||||
\(699\) | 20.0000 | 0.756469 | ||||||||
\(700\) | 8.00000 | + | 6.92820i | 0.302372 | + | 0.261861i | ||||
\(701\) | 9.00000 | 0.339925 | 0.169963 | − | 0.985451i | \(-0.445635\pi\) | ||||
0.169963 | + | 0.985451i | \(0.445635\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 2.50000 | + | 4.33013i | 0.0942223 | + | 0.163198i | ||||
\(705\) | −3.00000 | + | 5.19615i | −0.112987 | + | 0.195698i | ||||
\(706\) | −4.00000 | −0.150542 | ||||||||
\(707\) | 5.00000 | − | 1.73205i | 0.188044 | − | 0.0651405i | ||||
\(708\) | −9.00000 | −0.338241 | ||||||||
\(709\) | 11.0000 | − | 19.0526i | 0.413114 | − | 0.715534i | −0.582115 | − | 0.813107i | \(-0.697775\pi\) |
0.995228 | + | 0.0975728i | \(0.0311079\pi\) | |||||||
\(710\) | 9.00000 | + | 15.5885i | 0.337764 | + | 0.585024i | ||||
\(711\) | −5.50000 | − | 9.52628i | −0.206266 | − | 0.357263i | ||||
\(712\) | 5.00000 | − | 8.66025i | 0.187383 | − | 0.324557i | ||||
\(713\) | −9.00000 | −0.337053 | ||||||||
\(714\) | −10.0000 | + | 3.46410i | −0.374241 | + | 0.129641i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 10.0000 | − | 17.3205i | 0.373718 | − | 0.647298i | ||||
\(717\) | 12.0000 | + | 20.7846i | 0.448148 | + | 0.776215i | ||||
\(718\) | −5.00000 | − | 8.66025i | −0.186598 | − | 0.323198i | ||||
\(719\) | −7.00000 | + | 12.1244i | −0.261056 | + | 0.452162i | −0.966523 | − | 0.256581i | \(-0.917404\pi\) |
0.705467 | + | 0.708743i | \(0.250737\pi\) | |||||||
\(720\) | 3.00000 | 0.111803 | ||||||||
\(721\) | 16.0000 | + | 13.8564i | 0.595871 | + | 0.516040i | ||||
\(722\) | 19.0000 | 0.707107 | ||||||||
\(723\) | −9.50000 | + | 16.4545i | −0.353309 | + | 0.611949i | ||||
\(724\) | 4.00000 | + | 6.92820i | 0.148659 | + | 0.257485i | ||||
\(725\) | 6.00000 | + | 10.3923i | 0.222834 | + | 0.385961i | ||||
\(726\) | 7.00000 | − | 12.1244i | 0.259794 | − | 0.449977i | ||||
\(727\) | 7.00000 | 0.259616 | 0.129808 | − | 0.991539i | \(-0.458564\pi\) | ||||
0.129808 | + | 0.991539i | \(0.458564\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −21.0000 | + | 36.3731i | −0.777245 | + | 1.34623i | ||||
\(731\) | 12.0000 | + | 20.7846i | 0.443836 | + | 0.768747i | ||||
\(732\) | 1.00000 | + | 1.73205i | 0.0369611 | + | 0.0640184i | ||||
\(733\) | 23.0000 | − | 39.8372i | 0.849524 | − | 1.47142i | −0.0321090 | − | 0.999484i | \(-0.510222\pi\) |
0.881633 | − | 0.471935i | \(-0.156444\pi\) | |||||||
\(734\) | −25.0000 | −0.922767 | ||||||||
\(735\) | −19.5000 | − | 7.79423i | −0.719268 | − | 0.287494i | ||||
\(736\) | −1.00000 | −0.0368605 | ||||||||
\(737\) | −5.00000 | + | 8.66025i | −0.184177 | + | 0.319005i | ||||
\(738\) | 6.00000 | + | 10.3923i | 0.220863 | + | 0.382546i | ||||
\(739\) | −1.00000 | − | 1.73205i | −0.0367856 | − | 0.0637145i | 0.847046 | − | 0.531519i | \(-0.178379\pi\) |
−0.883832 | + | 0.467804i | \(0.845045\pi\) | |||||||
\(740\) | 18.0000 | − | 31.1769i | 0.661693 | − | 1.14609i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −2.50000 | + | 12.9904i | −0.0917779 | + | 0.476892i | ||||
\(743\) | −26.0000 | −0.953847 | −0.476924 | − | 0.878945i | \(-0.658248\pi\) | ||||
−0.476924 | + | 0.878945i | \(0.658248\pi\) | |||||||
\(744\) | −4.50000 | + | 7.79423i | −0.164978 | + | 0.285750i | ||||
\(745\) | 21.0000 | + | 36.3731i | 0.769380 | + | 1.33261i | ||||
\(746\) | −4.00000 | − | 6.92820i | −0.146450 | − | 0.253660i | ||||
\(747\) | 8.50000 | − | 14.7224i | 0.310999 | − | 0.538666i | ||||
\(748\) | 20.0000 | 0.731272 | ||||||||
\(749\) | −38.0000 | − | 32.9090i | −1.38849 | − | 1.20247i | ||||
\(750\) | 3.00000 | 0.109545 | ||||||||
\(751\) | −2.50000 | + | 4.33013i | −0.0912263 | + | 0.158009i | −0.908027 | − | 0.418911i | \(-0.862412\pi\) |
0.816801 | + | 0.576919i | \(0.195745\pi\) | |||||||
\(752\) | −1.00000 | − | 1.73205i | −0.0364662 | − | 0.0631614i | ||||
\(753\) | 2.50000 | + | 4.33013i | 0.0911051 | + | 0.157799i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −27.0000 | −0.982631 | ||||||||
\(756\) | −2.50000 | + | 0.866025i | −0.0909241 | + | 0.0314970i | ||||
\(757\) | −22.0000 | −0.799604 | −0.399802 | − | 0.916602i | \(-0.630921\pi\) | ||||
−0.399802 | + | 0.916602i | \(0.630921\pi\) | |||||||
\(758\) | −8.00000 | + | 13.8564i | −0.290573 | + | 0.503287i | ||||
\(759\) | 2.50000 | + | 4.33013i | 0.0907443 | + | 0.157174i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 0 | 0 | −0.866025 | − | 0.500000i | \(-0.833333\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(762\) | 11.0000 | 0.398488 | ||||||||
\(763\) | −15.0000 | + | 5.19615i | −0.543036 | + | 0.188113i | ||||
\(764\) | 12.0000 | 0.434145 | ||||||||
\(765\) | 6.00000 | − | 10.3923i | 0.216930 | − | 0.375735i | ||||
\(766\) | −9.00000 | − | 15.5885i | −0.325183 | − | 0.563234i | ||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −0.500000 | + | 0.866025i | −0.0180422 | + | 0.0312500i | ||||
\(769\) | −31.0000 | −1.11789 | −0.558944 | − | 0.829205i | \(-0.688793\pi\) | ||||
−0.558944 | + | 0.829205i | \(0.688793\pi\) | |||||||
\(770\) | 30.0000 | + | 25.9808i | 1.08112 | + | 0.936282i | ||||
\(771\) | 10.0000 | 0.360141 | ||||||||
\(772\) | −6.50000 | + | 11.2583i | −0.233940 | + | 0.405196i | ||||
\(773\) | −23.0000 | − | 39.8372i | −0.827253 | − | 1.43284i | −0.900186 | − | 0.435507i | \(-0.856569\pi\) |
0.0729331 | − | 0.997337i | \(-0.476764\pi\) | |||||||
\(774\) | 3.00000 | + | 5.19615i | 0.107833 | + | 0.186772i | ||||
\(775\) | 18.0000 | − | 31.1769i | 0.646579 | − | 1.11991i | ||||
\(776\) | 13.0000 | 0.466673 | ||||||||
\(777\) | −6.00000 | + | 31.1769i | −0.215249 | + | 1.11847i | ||||
\(778\) | −18.0000 | −0.645331 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 15.0000 | + | 25.9808i | 0.536742 | + | 0.929665i | ||||
\(782\) | −2.00000 | + | 3.46410i | −0.0715199 | + | 0.123876i | ||||
\(783\) | −3.00000 | −0.107211 | ||||||||
\(784\) | 5.50000 | − | 4.33013i | 0.196429 | − | 0.154647i | ||||
\(785\) | −24.0000 | −0.856597 | ||||||||
\(786\) | 1.50000 | − | 2.59808i | 0.0535032 | − | 0.0926703i | ||||
\(787\) | 11.0000 | + | 19.0526i | 0.392108 | + | 0.679150i | 0.992727 | − | 0.120384i | \(-0.0384127\pi\) |
−0.600620 | + | 0.799535i | \(0.705079\pi\) | |||||||
\(788\) | 1.00000 | + | 1.73205i | 0.0356235 | + | 0.0617018i | ||||
\(789\) | −9.00000 | + | 15.5885i | −0.320408 | + | 0.554964i | ||||
\(790\) | −33.0000 | −1.17409 | ||||||||
\(791\) | 6.00000 | − | 31.1769i | 0.213335 | − | 1.10852i | ||||
\(792\) | 5.00000 | 0.177667 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −4.00000 | − | 6.92820i | −0.141955 | − | 0.245873i | ||||
\(795\) | −7.50000 | − | 12.9904i | −0.265998 | − | 0.460721i | ||||
\(796\) | 10.0000 | − | 17.3205i | 0.354441 | − | 0.613909i | ||||
\(797\) | −49.0000 | −1.73567 | −0.867835 | − | 0.496853i | \(-0.834489\pi\) | ||||
−0.867835 | + | 0.496853i | \(0.834489\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −8.00000 | −0.283020 | ||||||||
\(800\) | 2.00000 | − | 3.46410i | 0.0707107 | − | 0.122474i | ||||
\(801\) | −5.00000 | − | 8.66025i | −0.176666 | − | 0.305995i | ||||
\(802\) | 16.0000 | + | 27.7128i | 0.564980 | + | 0.978573i | ||||
\(803\) | −35.0000 | + | 60.6218i | −1.23512 | + | 2.13930i | ||||
\(804\) | −2.00000 | −0.0705346 | ||||||||
\(805\) | −7.50000 | + | 2.59808i | −0.264340 | + | 0.0915702i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −4.50000 | + | 7.79423i | −0.158408 | + | 0.274370i | ||||
\(808\) | −1.00000 | − | 1.73205i | −0.0351799 | − | 0.0609333i | ||||
\(809\) | −22.0000 | − | 38.1051i | −0.773479 | − | 1.33970i | −0.935645 | − | 0.352941i | \(-0.885182\pi\) |
0.162167 | − | 0.986763i | \(-0.448152\pi\) | |||||||
\(810\) | 1.50000 | − | 2.59808i | 0.0527046 | − | 0.0912871i | ||||
\(811\) | 42.0000 | 1.47482 | 0.737410 | − | 0.675446i | \(-0.236049\pi\) | ||||
0.737410 | + | 0.675446i | \(0.236049\pi\) | |||||||
\(812\) | 7.50000 | − | 2.59808i | 0.263198 | − | 0.0911746i | ||||
\(813\) | −13.0000 | −0.455930 | ||||||||
\(814\) | 30.0000 | − | 51.9615i | 1.05150 | − | 1.82125i | ||||
\(815\) | 30.0000 | + | 51.9615i | 1.05085 | + | 1.82013i | ||||
\(816\) | 2.00000 | + | 3.46410i | 0.0700140 | + | 0.121268i | ||||
\(817\) | 0 | 0 | ||||||||
\(818\) | −7.00000 | −0.244749 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 36.0000 | 1.25717 | ||||||||
\(821\) | −28.5000 | + | 49.3634i | −0.994657 | + | 1.72280i | −0.407923 | + | 0.913016i | \(0.633747\pi\) |
−0.586734 | + | 0.809780i | \(0.699586\pi\) | |||||||
\(822\) | −3.00000 | − | 5.19615i | −0.104637 | − | 0.181237i | ||||
\(823\) | 4.00000 | + | 6.92820i | 0.139431 | + | 0.241502i | 0.927281 | − | 0.374365i | \(-0.122139\pi\) |
−0.787850 | + | 0.615867i | \(0.788806\pi\) | |||||||
\(824\) | 4.00000 | − | 6.92820i | 0.139347 | − | 0.241355i | ||||
\(825\) | −20.0000 | −0.696311 | ||||||||
\(826\) | 4.50000 | − | 23.3827i | 0.156575 | − | 0.813588i | ||||
\(827\) | −33.0000 | −1.14752 | −0.573761 | − | 0.819023i | \(-0.694516\pi\) | ||||
−0.573761 | + | 0.819023i | \(0.694516\pi\) | |||||||
\(828\) | −0.500000 | + | 0.866025i | −0.0173762 | + | 0.0300965i | ||||
\(829\) | −10.0000 | − | 17.3205i | −0.347314 | − | 0.601566i | 0.638457 | − | 0.769657i | \(-0.279573\pi\) |
−0.985771 | + | 0.168091i | \(0.946240\pi\) | |||||||
\(830\) | −25.5000 | − | 44.1673i | −0.885118 | − | 1.53307i | ||||
\(831\) | −4.00000 | + | 6.92820i | −0.138758 | + | 0.240337i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −4.00000 | − | 27.7128i | −0.138592 | − | 0.960192i | ||||
\(834\) | 6.00000 | 0.207763 | ||||||||
\(835\) | 3.00000 | − | 5.19615i | 0.103819 | − | 0.179820i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 4.50000 | + | 7.79423i | 0.155543 | + | 0.269408i | ||||
\(838\) | −8.00000 | + | 13.8564i | −0.276355 | + | 0.478662i | ||||
\(839\) | −12.0000 | −0.414286 | −0.207143 | − | 0.978311i | \(-0.566417\pi\) | ||||
−0.207143 | + | 0.978311i | \(0.566417\pi\) | |||||||
\(840\) | −1.50000 | + | 7.79423i | −0.0517549 | + | 0.268926i | ||||
\(841\) | −20.0000 | −0.689655 | ||||||||
\(842\) | −3.00000 | + | 5.19615i | −0.103387 | + | 0.179071i | ||||
\(843\) | −1.00000 | − | 1.73205i | −0.0344418 | − | 0.0596550i | ||||
\(844\) | −3.00000 | − | 5.19615i | −0.103264 | − | 0.178859i | ||||
\(845\) | 19.5000 | − | 33.7750i | 0.670820 | − | 1.16190i | ||||
\(846\) | −2.00000 | −0.0687614 | ||||||||
\(847\) | 28.0000 | + | 24.2487i | 0.962091 | + | 0.833196i | ||||
\(848\) | 5.00000 | 0.171701 | ||||||||
\(849\) | −3.00000 | + | 5.19615i | −0.102960 | + | 0.178331i | ||||
\(850\) | −8.00000 | − | 13.8564i | −0.274398 | − | 0.475271i | ||||
\(851\) | 6.00000 | + | 10.3923i | 0.205677 | + | 0.356244i | ||||
\(852\) | −3.00000 | + | 5.19615i | −0.102778 | + | 0.178017i | ||||
\(853\) | −26.0000 | −0.890223 | −0.445112 | − | 0.895475i | \(-0.646836\pi\) | ||||
−0.445112 | + | 0.895475i | \(0.646836\pi\) | |||||||
\(854\) | −5.00000 | + | 1.73205i | −0.171096 | + | 0.0592696i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −9.50000 | + | 16.4545i | −0.324703 | + | 0.562403i | ||||
\(857\) | 27.0000 | + | 46.7654i | 0.922302 | + | 1.59747i | 0.795843 | + | 0.605503i | \(0.207028\pi\) |
0.126459 | + | 0.991972i | \(0.459639\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −11.0000 | + | 19.0526i | −0.375315 | + | 0.650065i | −0.990374 | − | 0.138416i | \(-0.955799\pi\) |
0.615059 | + | 0.788481i | \(0.289132\pi\) | |||||||
\(860\) | 18.0000 | 0.613795 | ||||||||
\(861\) | −30.0000 | + | 10.3923i | −1.02240 | + | 0.354169i | ||||
\(862\) | 12.0000 | 0.408722 | ||||||||
\(863\) | 7.00000 | − | 12.1244i | 0.238283 | − | 0.412718i | −0.721939 | − | 0.691957i | \(-0.756749\pi\) |
0.960222 | + | 0.279239i | \(0.0900822\pi\) | |||||||
\(864\) | 0.500000 | + | 0.866025i | 0.0170103 | + | 0.0294628i | ||||
\(865\) | 9.00000 | + | 15.5885i | 0.306009 | + | 0.530023i | ||||
\(866\) | 7.00000 | − | 12.1244i | 0.237870 | − | 0.412002i | ||||
\(867\) | −1.00000 | −0.0339618 | ||||||||
\(868\) | −18.0000 | − | 15.5885i | −0.610960 | − | 0.529107i | ||||
\(869\) | −55.0000 | −1.86575 | ||||||||
\(870\) | −4.50000 | + | 7.79423i | −0.152564 | + | 0.264249i | ||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 3.00000 | + | 5.19615i | 0.101593 | + | 0.175964i | ||||
\(873\) | 6.50000 | − | 11.2583i | 0.219992 | − | 0.381037i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −1.50000 | + | 7.79423i | −0.0507093 | + | 0.263493i | ||||
\(876\) | −14.0000 | −0.473016 | ||||||||
\(877\) | 6.00000 | − | 10.3923i | 0.202606 | − | 0.350923i | −0.746762 | − | 0.665092i | \(-0.768392\pi\) |
0.949367 | + | 0.314169i | \(0.101726\pi\) | |||||||
\(878\) | −6.50000 | − | 11.2583i | −0.219364 | − | 0.379950i | ||||
\(879\) | −16.5000 | − | 28.5788i | −0.556531 | − | 0.963940i | ||||
\(880\) | 7.50000 | − | 12.9904i | 0.252825 | − | 0.437906i | ||||
\(881\) | −6.00000 | −0.202145 | −0.101073 | − | 0.994879i | \(-0.532227\pi\) | ||||
−0.101073 | + | 0.994879i | \(0.532227\pi\) | |||||||
\(882\) | −1.00000 | − | 6.92820i | −0.0336718 | − | 0.233285i | ||||
\(883\) | 36.0000 | 1.21150 | 0.605748 | − | 0.795656i | \(-0.292874\pi\) | ||||
0.605748 | + | 0.795656i | \(0.292874\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 13.5000 | + | 23.3827i | 0.453798 | + | 0.786000i | ||||
\(886\) | −14.5000 | − | 25.1147i | −0.487137 | − | 0.843746i | ||||
\(887\) | 12.0000 | − | 20.7846i | 0.402921 | − | 0.697879i | −0.591156 | − | 0.806557i | \(-0.701328\pi\) |
0.994077 | + | 0.108678i | \(0.0346618\pi\) | |||||||
\(888\) | 12.0000 | 0.402694 | ||||||||
\(889\) | −5.50000 | + | 28.5788i | −0.184464 | + | 0.958503i | ||||
\(890\) | −30.0000 | −1.00560 | ||||||||
\(891\) | 2.50000 | − | 4.33013i | 0.0837532 | − | 0.145065i | ||||
\(892\) | −6.50000 | − | 11.2583i | −0.217636 | − | 0.376957i | ||||
\(893\) | 0 | 0 | ||||||||
\(894\) | −7.00000 | + | 12.1244i | −0.234115 | + | 0.405499i | ||||
\(895\) | −60.0000 | −2.00558 | ||||||||
\(896\) | −2.00000 | − | 1.73205i | −0.0668153 | − | 0.0578638i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −13.5000 | − | 23.3827i | −0.450250 | − | 0.779856i | ||||
\(900\) | −2.00000 | − | 3.46410i | −0.0666667 | − | 0.115470i | ||||
\(901\) | 10.0000 | − | 17.3205i | 0.333148 | − | 0.577030i | ||||
\(902\) | 60.0000 | 1.99778 | ||||||||
\(903\) | −15.0000 | + | 5.19615i | −0.499169 | + | 0.172917i | ||||
\(904\) | −12.0000 | −0.399114 | ||||||||
\(905\) | 12.0000 | − | 20.7846i | 0.398893 | − | 0.690904i | ||||
\(906\) | −4.50000 | − | 7.79423i | −0.149502 | − | 0.258946i | ||||
\(907\) | 22.0000 | + | 38.1051i | 0.730498 | + | 1.26526i | 0.956671 | + | 0.291172i | \(0.0940453\pi\) |
−0.226173 | + | 0.974087i | \(0.572621\pi\) | |||||||
\(908\) | −2.50000 | + | 4.33013i | −0.0829654 | + | 0.143700i | ||||
\(909\) | −2.00000 | −0.0663358 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −10.0000 | −0.331315 | −0.165657 | − | 0.986183i | \(-0.552975\pi\) | ||||
−0.165657 | + | 0.986183i | \(0.552975\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −42.5000 | − | 73.6122i | −1.40654 | − | 2.43621i | ||||
\(914\) | −10.5000 | − | 18.1865i | −0.347309 | − | 0.601557i | ||||
\(915\) | 3.00000 | − | 5.19615i | 0.0991769 | − | 0.171780i | ||||
\(916\) | −24.0000 | −0.792982 | ||||||||
\(917\) | 6.00000 | + | 5.19615i | 0.198137 | + | 0.171592i | ||||
\(918\) | 4.00000 | 0.132020 | ||||||||
\(919\) | 12.0000 | − | 20.7846i | 0.395843 | − | 0.685621i | −0.597365 | − | 0.801970i | \(-0.703786\pi\) |
0.993208 | + | 0.116348i | \(0.0371189\pi\) | |||||||
\(920\) | 1.50000 | + | 2.59808i | 0.0494535 | + | 0.0856560i | ||||
\(921\) | −6.00000 | − | 10.3923i | −0.197707 | − | 0.342438i | ||||
\(922\) | 7.00000 | − | 12.1244i | 0.230533 | − | 0.399294i | ||||
\(923\) | 0 | 0 | ||||||||
\(924\) | −2.50000 | + | 12.9904i | −0.0822440 | + | 0.427352i | ||||
\(925\) | −48.0000 | −1.57823 | ||||||||
\(926\) | −16.0000 | + | 27.7128i | −0.525793 | + | 0.910700i | ||||
\(927\) | −4.00000 | − | 6.92820i | −0.131377 | − | 0.227552i | ||||
\(928\) | −1.50000 | − | 2.59808i | −0.0492399 | − | 0.0852860i | ||||
\(929\) | −3.00000 | + | 5.19615i | −0.0984268 | + | 0.170480i | −0.911034 | − | 0.412332i | \(-0.864714\pi\) |
0.812607 | + | 0.582812i | \(0.198048\pi\) | |||||||
\(930\) | 27.0000 | 0.885365 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 20.0000 | 0.655122 | ||||||||
\(933\) | −10.0000 | + | 17.3205i | −0.327385 | + | 0.567048i | ||||
\(934\) | 14.0000 | + | 24.2487i | 0.458094 | + | 0.793442i | ||||
\(935\) | −30.0000 | − | 51.9615i | −0.981105 | − | 1.69932i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 7.00000 | 0.228680 | 0.114340 | − | 0.993442i | \(-0.463525\pi\) | ||||
0.114340 | + | 0.993442i | \(0.463525\pi\) | |||||||
\(938\) | 1.00000 | − | 5.19615i | 0.0326512 | − | 0.169660i | ||||
\(939\) | −11.0000 | −0.358971 | ||||||||
\(940\) | −3.00000 | + | 5.19615i | −0.0978492 | + | 0.169480i | ||||
\(941\) | −7.50000 | − | 12.9904i | −0.244493 | − | 0.423474i | 0.717496 | − | 0.696563i | \(-0.245288\pi\) |
−0.961989 | + | 0.273088i | \(0.911955\pi\) | |||||||
\(942\) | −4.00000 | − | 6.92820i | −0.130327 | − | 0.225733i | ||||
\(943\) | −6.00000 | + | 10.3923i | −0.195387 | + | 0.338420i | ||||
\(944\) | −9.00000 | −0.292925 | ||||||||
\(945\) | 6.00000 | + | 5.19615i | 0.195180 | + | 0.169031i | ||||
\(946\) | 30.0000 | 0.975384 | ||||||||
\(947\) | −4.00000 | + | 6.92820i | −0.129983 | + | 0.225136i | −0.923670 | − | 0.383190i | \(-0.874825\pi\) |
0.793687 | + | 0.608326i | \(0.208159\pi\) | |||||||
\(948\) | −5.50000 | − | 9.52628i | −0.178632 | − | 0.309399i | ||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 5.00000 | 0.162136 | ||||||||
\(952\) | −10.0000 | + | 3.46410i | −0.324102 | + | 0.112272i | ||||
\(953\) | 34.0000 | 1.10137 | 0.550684 | − | 0.834714i | \(-0.314367\pi\) | ||||
0.550684 | + | 0.834714i | \(0.314367\pi\) | |||||||
\(954\) | 2.50000 | − | 4.33013i | 0.0809405 | − | 0.140193i | ||||
\(955\) | −18.0000 | − | 31.1769i | −0.582466 | − | 1.00886i | ||||
\(956\) | 12.0000 | + | 20.7846i | 0.388108 | + | 0.672222i | ||||
\(957\) | −7.50000 | + | 12.9904i | −0.242441 | + | 0.419919i | ||||
\(958\) | −18.0000 | −0.581554 | ||||||||
\(959\) | 15.0000 | − | 5.19615i | 0.484375 | − | 0.167793i | ||||
\(960\) | 3.00000 | 0.0968246 | ||||||||
\(961\) | −25.0000 | + | 43.3013i | −0.806452 | + | 1.39682i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 9.50000 | + | 16.4545i | 0.306133 | + | 0.530238i | ||||
\(964\) | −9.50000 | + | 16.4545i | −0.305974 | + | 0.529963i | ||||
\(965\) | 39.0000 | 1.25545 | ||||||||
\(966\) | −2.00000 | − | 1.73205i | −0.0643489 | − | 0.0557278i | ||||
\(967\) | 7.00000 | 0.225105 | 0.112552 | − | 0.993646i | \(-0.464097\pi\) | ||||
0.112552 | + | 0.993646i | \(0.464097\pi\) | |||||||
\(968\) | 7.00000 | − | 12.1244i | 0.224989 | − | 0.389692i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −19.5000 | − | 33.7750i | −0.626107 | − | 1.08445i | ||||
\(971\) | 7.50000 | − | 12.9904i | 0.240686 | − | 0.416881i | −0.720224 | − | 0.693742i | \(-0.755961\pi\) |
0.960910 | + | 0.276861i | \(0.0892941\pi\) | |||||||
\(972\) | 1.00000 | 0.0320750 | ||||||||
\(973\) | −3.00000 | + | 15.5885i | −0.0961756 | + | 0.499743i | ||||
\(974\) | 23.0000 | 0.736968 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 1.00000 | + | 1.73205i | 0.0320092 | + | 0.0554416i | ||||
\(977\) | 31.0000 | + | 53.6936i | 0.991778 | + | 1.71781i | 0.606715 | + | 0.794919i | \(0.292487\pi\) |
0.385063 | + | 0.922890i | \(0.374180\pi\) | |||||||
\(978\) | −10.0000 | + | 17.3205i | −0.319765 | + | 0.553849i | ||||
\(979\) | −50.0000 | −1.59801 | ||||||||
\(980\) | −19.5000 | − | 7.79423i | −0.622905 | − | 0.248978i | ||||
\(981\) | 6.00000 | 0.191565 | ||||||||
\(982\) | 13.5000 | − | 23.3827i | 0.430802 | − | 0.746171i | ||||
\(983\) | 0 | 0 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
−0.866025 | + | 0.500000i | \(0.833333\pi\) | |||||||
\(984\) | 6.00000 | + | 10.3923i | 0.191273 | + | 0.331295i | ||||
\(985\) | 3.00000 | − | 5.19615i | 0.0955879 | − | 0.165563i | ||||
\(986\) | −12.0000 | −0.382158 | ||||||||
\(987\) | 1.00000 | − | 5.19615i | 0.0318304 | − | 0.165395i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −3.00000 | + | 5.19615i | −0.0953945 | + | 0.165228i | ||||
\(990\) | −7.50000 | − | 12.9904i | −0.238366 | − | 0.412861i | ||||
\(991\) | −25.5000 | − | 44.1673i | −0.810034 | − | 1.40302i | −0.912839 | − | 0.408319i | \(-0.866115\pi\) |
0.102805 | − | 0.994702i | \(-0.467218\pi\) | |||||||
\(992\) | −4.50000 | + | 7.79423i | −0.142875 | + | 0.247467i | ||||
\(993\) | −16.0000 | −0.507745 | ||||||||
\(994\) | −12.0000 | − | 10.3923i | −0.380617 | − | 0.329624i | ||||
\(995\) | −60.0000 | −1.90213 | ||||||||
\(996\) | 8.50000 | − | 14.7224i | 0.269333 | − | 0.466498i | ||||
\(997\) | 11.0000 | + | 19.0526i | 0.348373 | + | 0.603401i | 0.985961 | − | 0.166978i | \(-0.0534008\pi\) |
−0.637587 | + | 0.770378i | \(0.720067\pi\) | |||||||
\(998\) | 5.00000 | + | 8.66025i | 0.158272 | + | 0.274136i | ||||
\(999\) | 6.00000 | − | 10.3923i | 0.189832 | − | 0.328798i |
(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 | 966.2.i.e.415.1 | yes | 2 | |
7.2 | even | 3 | 6762.2.a.t.1.1 | 1 | |||
7.4 | even | 3 | inner | 966.2.i.e.277.1 | ✓ | 2 | |
7.5 | odd | 6 | 6762.2.a.a.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
966.2.i.e.277.1 | ✓ | 2 | 7.4 | even | 3 | inner | |
966.2.i.e.415.1 | yes | 2 | 1.1 | even | 1 | trivial | |
6762.2.a.a.1.1 | 1 | 7.5 | odd | 6 | |||
6762.2.a.t.1.1 | 1 | 7.2 | even | 3 |