Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3450,2,Mod(1,3450)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3450, 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("3450.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3450 = 2 \cdot 3 \cdot 5^{2} \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3450.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: | \(27.5483886973\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{8})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 690) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(1.41421\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3450.1 |
$q$-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 | ||||||||
\(7\) | 2.00000 | 0.755929 | 0.377964 | − | 0.925820i | \(-0.376624\pi\) | ||||
0.377964 | + | 0.925820i | \(0.376624\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.24264 | 1.27920 | 0.639602 | − | 0.768706i | \(-0.279099\pi\) | ||||
0.639602 | + | 0.768706i | \(0.279099\pi\) | |||||||
\(12\) | −1.00000 | −0.288675 | ||||||||
\(13\) | −4.82843 | −1.33916 | −0.669582 | − | 0.742738i | \(-0.733527\pi\) | ||||
−0.669582 | + | 0.742738i | \(0.733527\pi\) | |||||||
\(14\) | −2.00000 | −0.534522 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −1.17157 | −0.284148 | −0.142074 | − | 0.989856i | \(-0.545377\pi\) | ||||
−0.142074 | + | 0.989856i | \(0.545377\pi\) | |||||||
\(18\) | −1.00000 | −0.235702 | ||||||||
\(19\) | −2.24264 | −0.514497 | −0.257249 | − | 0.966345i | \(-0.582816\pi\) | ||||
−0.257249 | + | 0.966345i | \(0.582816\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.00000 | −0.436436 | ||||||||
\(22\) | −4.24264 | −0.904534 | ||||||||
\(23\) | 1.00000 | 0.208514 | ||||||||
\(24\) | 1.00000 | 0.204124 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 4.82843 | 0.946932 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 2.00000 | 0.377964 | ||||||||
\(29\) | −7.65685 | −1.42184 | −0.710921 | − | 0.703272i | \(-0.751722\pi\) | ||||
−0.710921 | + | 0.703272i | \(0.751722\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.00000 | 1.07763 | 0.538816 | − | 0.842424i | \(-0.318872\pi\) | ||||
0.538816 | + | 0.842424i | \(0.318872\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −4.24264 | −0.738549 | ||||||||
\(34\) | 1.17157 | 0.200923 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | −3.41421 | −0.561293 | −0.280647 | − | 0.959811i | \(-0.590549\pi\) | ||||
−0.280647 | + | 0.959811i | \(0.590549\pi\) | |||||||
\(38\) | 2.24264 | 0.363804 | ||||||||
\(39\) | 4.82843 | 0.773167 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.17157 | −0.182969 | −0.0914845 | − | 0.995807i | \(-0.529161\pi\) | ||||
−0.0914845 | + | 0.995807i | \(0.529161\pi\) | |||||||
\(42\) | 2.00000 | 0.308607 | ||||||||
\(43\) | −1.75736 | −0.267995 | −0.133997 | − | 0.990982i | \(-0.542781\pi\) | ||||
−0.133997 | + | 0.990982i | \(0.542781\pi\) | |||||||
\(44\) | 4.24264 | 0.639602 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −1.00000 | −0.147442 | ||||||||
\(47\) | −4.82843 | −0.704298 | −0.352149 | − | 0.935944i | \(-0.614549\pi\) | ||||
−0.352149 | + | 0.935944i | \(0.614549\pi\) | |||||||
\(48\) | −1.00000 | −0.144338 | ||||||||
\(49\) | −3.00000 | −0.428571 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.17157 | 0.164053 | ||||||||
\(52\) | −4.82843 | −0.669582 | ||||||||
\(53\) | −13.4142 | −1.84258 | −0.921292 | − | 0.388872i | \(-0.872865\pi\) | ||||
−0.921292 | + | 0.388872i | \(0.872865\pi\) | |||||||
\(54\) | 1.00000 | 0.136083 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −2.00000 | −0.267261 | ||||||||
\(57\) | 2.24264 | 0.297045 | ||||||||
\(58\) | 7.65685 | 1.00539 | ||||||||
\(59\) | −8.48528 | −1.10469 | −0.552345 | − | 0.833616i | \(-0.686267\pi\) | ||||
−0.552345 | + | 0.833616i | \(0.686267\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.41421 | −0.437145 | −0.218573 | − | 0.975821i | \(-0.570140\pi\) | ||||
−0.218573 | + | 0.975821i | \(0.570140\pi\) | |||||||
\(62\) | −6.00000 | −0.762001 | ||||||||
\(63\) | 2.00000 | 0.251976 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 4.24264 | 0.522233 | ||||||||
\(67\) | 0.585786 | 0.0715652 | 0.0357826 | − | 0.999360i | \(-0.488608\pi\) | ||||
0.0357826 | + | 0.999360i | \(0.488608\pi\) | |||||||
\(68\) | −1.17157 | −0.142074 | ||||||||
\(69\) | −1.00000 | −0.120386 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 5.65685 | 0.671345 | 0.335673 | − | 0.941979i | \(-0.391036\pi\) | ||||
0.335673 | + | 0.941979i | \(0.391036\pi\) | |||||||
\(72\) | −1.00000 | −0.117851 | ||||||||
\(73\) | 3.65685 | 0.428002 | 0.214001 | − | 0.976833i | \(-0.431350\pi\) | ||||
0.214001 | + | 0.976833i | \(0.431350\pi\) | |||||||
\(74\) | 3.41421 | 0.396894 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −2.24264 | −0.257249 | ||||||||
\(77\) | 8.48528 | 0.966988 | ||||||||
\(78\) | −4.82843 | −0.546712 | ||||||||
\(79\) | 7.65685 | 0.861463 | 0.430732 | − | 0.902480i | \(-0.358256\pi\) | ||||
0.430732 | + | 0.902480i | \(0.358256\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 1.17157 | 0.129379 | ||||||||
\(83\) | 1.41421 | 0.155230 | 0.0776151 | − | 0.996983i | \(-0.475269\pi\) | ||||
0.0776151 | + | 0.996983i | \(0.475269\pi\) | |||||||
\(84\) | −2.00000 | −0.218218 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 1.75736 | 0.189501 | ||||||||
\(87\) | 7.65685 | 0.820901 | ||||||||
\(88\) | −4.24264 | −0.452267 | ||||||||
\(89\) | 14.8284 | 1.57181 | 0.785905 | − | 0.618347i | \(-0.212197\pi\) | ||||
0.785905 | + | 0.618347i | \(0.212197\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −9.65685 | −1.01231 | ||||||||
\(92\) | 1.00000 | 0.104257 | ||||||||
\(93\) | −6.00000 | −0.622171 | ||||||||
\(94\) | 4.82843 | 0.498014 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 1.00000 | 0.102062 | ||||||||
\(97\) | 6.00000 | 0.609208 | 0.304604 | − | 0.952479i | \(-0.401476\pi\) | ||||
0.304604 | + | 0.952479i | \(0.401476\pi\) | |||||||
\(98\) | 3.00000 | 0.303046 | ||||||||
\(99\) | 4.24264 | 0.426401 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −9.31371 | −0.926749 | −0.463374 | − | 0.886163i | \(-0.653361\pi\) | ||||
−0.463374 | + | 0.886163i | \(0.653361\pi\) | |||||||
\(102\) | −1.17157 | −0.116003 | ||||||||
\(103\) | 12.1421 | 1.19640 | 0.598200 | − | 0.801347i | \(-0.295883\pi\) | ||||
0.598200 | + | 0.801347i | \(0.295883\pi\) | |||||||
\(104\) | 4.82843 | 0.473466 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 13.4142 | 1.30290 | ||||||||
\(107\) | −15.0711 | −1.45698 | −0.728488 | − | 0.685059i | \(-0.759776\pi\) | ||||
−0.728488 | + | 0.685059i | \(0.759776\pi\) | |||||||
\(108\) | −1.00000 | −0.0962250 | ||||||||
\(109\) | 15.4142 | 1.47641 | 0.738207 | − | 0.674574i | \(-0.235673\pi\) | ||||
0.738207 | + | 0.674574i | \(0.235673\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 3.41421 | 0.324063 | ||||||||
\(112\) | 2.00000 | 0.188982 | ||||||||
\(113\) | −16.9706 | −1.59646 | −0.798228 | − | 0.602355i | \(-0.794229\pi\) | ||||
−0.798228 | + | 0.602355i | \(0.794229\pi\) | |||||||
\(114\) | −2.24264 | −0.210043 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −7.65685 | −0.710921 | ||||||||
\(117\) | −4.82843 | −0.446388 | ||||||||
\(118\) | 8.48528 | 0.781133 | ||||||||
\(119\) | −2.34315 | −0.214796 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 7.00000 | 0.636364 | ||||||||
\(122\) | 3.41421 | 0.309108 | ||||||||
\(123\) | 1.17157 | 0.105637 | ||||||||
\(124\) | 6.00000 | 0.538816 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −2.00000 | −0.178174 | ||||||||
\(127\) | 2.00000 | 0.177471 | 0.0887357 | − | 0.996055i | \(-0.471717\pi\) | ||||
0.0887357 | + | 0.996055i | \(0.471717\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 1.75736 | 0.154727 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −10.3431 | −0.903685 | −0.451842 | − | 0.892098i | \(-0.649233\pi\) | ||||
−0.451842 | + | 0.892098i | \(0.649233\pi\) | |||||||
\(132\) | −4.24264 | −0.369274 | ||||||||
\(133\) | −4.48528 | −0.388923 | ||||||||
\(134\) | −0.585786 | −0.0506042 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 1.17157 | 0.100462 | ||||||||
\(137\) | −8.48528 | −0.724947 | −0.362473 | − | 0.931994i | \(-0.618068\pi\) | ||||
−0.362473 | + | 0.931994i | \(0.618068\pi\) | |||||||
\(138\) | 1.00000 | 0.0851257 | ||||||||
\(139\) | 16.9706 | 1.43942 | 0.719712 | − | 0.694273i | \(-0.244274\pi\) | ||||
0.719712 | + | 0.694273i | \(0.244274\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 4.82843 | 0.406627 | ||||||||
\(142\) | −5.65685 | −0.474713 | ||||||||
\(143\) | −20.4853 | −1.71307 | ||||||||
\(144\) | 1.00000 | 0.0833333 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −3.65685 | −0.302643 | ||||||||
\(147\) | 3.00000 | 0.247436 | ||||||||
\(148\) | −3.41421 | −0.280647 | ||||||||
\(149\) | −12.7279 | −1.04271 | −0.521356 | − | 0.853339i | \(-0.674574\pi\) | ||||
−0.521356 | + | 0.853339i | \(0.674574\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −15.6569 | −1.27414 | −0.637068 | − | 0.770807i | \(-0.719853\pi\) | ||||
−0.637068 | + | 0.770807i | \(0.719853\pi\) | |||||||
\(152\) | 2.24264 | 0.181902 | ||||||||
\(153\) | −1.17157 | −0.0947161 | ||||||||
\(154\) | −8.48528 | −0.683763 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 4.82843 | 0.386584 | ||||||||
\(157\) | −6.92893 | −0.552989 | −0.276494 | − | 0.961016i | \(-0.589173\pi\) | ||||
−0.276494 | + | 0.961016i | \(0.589173\pi\) | |||||||
\(158\) | −7.65685 | −0.609147 | ||||||||
\(159\) | 13.4142 | 1.06382 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2.00000 | 0.157622 | ||||||||
\(162\) | −1.00000 | −0.0785674 | ||||||||
\(163\) | −1.17157 | −0.0917647 | −0.0458823 | − | 0.998947i | \(-0.514610\pi\) | ||||
−0.0458823 | + | 0.998947i | \(0.514610\pi\) | |||||||
\(164\) | −1.17157 | −0.0914845 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −1.41421 | −0.109764 | ||||||||
\(167\) | 8.82843 | 0.683164 | 0.341582 | − | 0.939852i | \(-0.389037\pi\) | ||||
0.341582 | + | 0.939852i | \(0.389037\pi\) | |||||||
\(168\) | 2.00000 | 0.154303 | ||||||||
\(169\) | 10.3137 | 0.793362 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −2.24264 | −0.171499 | ||||||||
\(172\) | −1.75736 | −0.133997 | ||||||||
\(173\) | −3.17157 | −0.241130 | −0.120565 | − | 0.992705i | \(-0.538471\pi\) | ||||
−0.120565 | + | 0.992705i | \(0.538471\pi\) | |||||||
\(174\) | −7.65685 | −0.580465 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 4.24264 | 0.319801 | ||||||||
\(177\) | 8.48528 | 0.637793 | ||||||||
\(178\) | −14.8284 | −1.11144 | ||||||||
\(179\) | −10.3431 | −0.773083 | −0.386542 | − | 0.922272i | \(-0.626330\pi\) | ||||
−0.386542 | + | 0.922272i | \(0.626330\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 16.3848 | 1.21787 | 0.608935 | − | 0.793220i | \(-0.291597\pi\) | ||||
0.608935 | + | 0.793220i | \(0.291597\pi\) | |||||||
\(182\) | 9.65685 | 0.715814 | ||||||||
\(183\) | 3.41421 | 0.252386 | ||||||||
\(184\) | −1.00000 | −0.0737210 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 6.00000 | 0.439941 | ||||||||
\(187\) | −4.97056 | −0.363484 | ||||||||
\(188\) | −4.82843 | −0.352149 | ||||||||
\(189\) | −2.00000 | −0.145479 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −5.17157 | −0.374202 | −0.187101 | − | 0.982341i | \(-0.559909\pi\) | ||||
−0.187101 | + | 0.982341i | \(0.559909\pi\) | |||||||
\(192\) | −1.00000 | −0.0721688 | ||||||||
\(193\) | −12.9706 | −0.933642 | −0.466821 | − | 0.884352i | \(-0.654601\pi\) | ||||
−0.466821 | + | 0.884352i | \(0.654601\pi\) | |||||||
\(194\) | −6.00000 | −0.430775 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −3.00000 | −0.214286 | ||||||||
\(197\) | 24.6274 | 1.75463 | 0.877315 | − | 0.479914i | \(-0.159332\pi\) | ||||
0.877315 | + | 0.479914i | \(0.159332\pi\) | |||||||
\(198\) | −4.24264 | −0.301511 | ||||||||
\(199\) | −14.0000 | −0.992434 | −0.496217 | − | 0.868199i | \(-0.665278\pi\) | ||||
−0.496217 | + | 0.868199i | \(0.665278\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −0.585786 | −0.0413182 | ||||||||
\(202\) | 9.31371 | 0.655310 | ||||||||
\(203\) | −15.3137 | −1.07481 | ||||||||
\(204\) | 1.17157 | 0.0820265 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −12.1421 | −0.845983 | ||||||||
\(207\) | 1.00000 | 0.0695048 | ||||||||
\(208\) | −4.82843 | −0.334791 | ||||||||
\(209\) | −9.51472 | −0.658147 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −20.4853 | −1.41026 | −0.705132 | − | 0.709076i | \(-0.749112\pi\) | ||||
−0.705132 | + | 0.709076i | \(0.749112\pi\) | |||||||
\(212\) | −13.4142 | −0.921292 | ||||||||
\(213\) | −5.65685 | −0.387601 | ||||||||
\(214\) | 15.0711 | 1.03024 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 1.00000 | 0.0680414 | ||||||||
\(217\) | 12.0000 | 0.814613 | ||||||||
\(218\) | −15.4142 | −1.04398 | ||||||||
\(219\) | −3.65685 | −0.247107 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 5.65685 | 0.380521 | ||||||||
\(222\) | −3.41421 | −0.229147 | ||||||||
\(223\) | −16.0000 | −1.07144 | −0.535720 | − | 0.844396i | \(-0.679960\pi\) | ||||
−0.535720 | + | 0.844396i | \(0.679960\pi\) | |||||||
\(224\) | −2.00000 | −0.133631 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 16.9706 | 1.12887 | ||||||||
\(227\) | −14.3848 | −0.954751 | −0.477376 | − | 0.878699i | \(-0.658412\pi\) | ||||
−0.477376 | + | 0.878699i | \(0.658412\pi\) | |||||||
\(228\) | 2.24264 | 0.148523 | ||||||||
\(229\) | 1.75736 | 0.116130 | 0.0580648 | − | 0.998313i | \(-0.481507\pi\) | ||||
0.0580648 | + | 0.998313i | \(0.481507\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −8.48528 | −0.558291 | ||||||||
\(232\) | 7.65685 | 0.502697 | ||||||||
\(233\) | 26.1421 | 1.71263 | 0.856314 | − | 0.516455i | \(-0.172749\pi\) | ||||
0.856314 | + | 0.516455i | \(0.172749\pi\) | |||||||
\(234\) | 4.82843 | 0.315644 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −8.48528 | −0.552345 | ||||||||
\(237\) | −7.65685 | −0.497366 | ||||||||
\(238\) | 2.34315 | 0.151884 | ||||||||
\(239\) | −11.1716 | −0.722629 | −0.361314 | − | 0.932444i | \(-0.617672\pi\) | ||||
−0.361314 | + | 0.932444i | \(0.617672\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −10.4853 | −0.675416 | −0.337708 | − | 0.941251i | \(-0.609652\pi\) | ||||
−0.337708 | + | 0.941251i | \(0.609652\pi\) | |||||||
\(242\) | −7.00000 | −0.449977 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −3.41421 | −0.218573 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −1.17157 | −0.0746968 | ||||||||
\(247\) | 10.8284 | 0.688996 | ||||||||
\(248\) | −6.00000 | −0.381000 | ||||||||
\(249\) | −1.41421 | −0.0896221 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −24.7279 | −1.56081 | −0.780406 | − | 0.625273i | \(-0.784988\pi\) | ||||
−0.780406 | + | 0.625273i | \(0.784988\pi\) | |||||||
\(252\) | 2.00000 | 0.125988 | ||||||||
\(253\) | 4.24264 | 0.266733 | ||||||||
\(254\) | −2.00000 | −0.125491 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −18.0000 | −1.12281 | −0.561405 | − | 0.827541i | \(-0.689739\pi\) | ||||
−0.561405 | + | 0.827541i | \(0.689739\pi\) | |||||||
\(258\) | −1.75736 | −0.109408 | ||||||||
\(259\) | −6.82843 | −0.424298 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −7.65685 | −0.473947 | ||||||||
\(262\) | 10.3431 | 0.639002 | ||||||||
\(263\) | 17.6569 | 1.08877 | 0.544384 | − | 0.838836i | \(-0.316763\pi\) | ||||
0.544384 | + | 0.838836i | \(0.316763\pi\) | |||||||
\(264\) | 4.24264 | 0.261116 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 4.48528 | 0.275010 | ||||||||
\(267\) | −14.8284 | −0.907485 | ||||||||
\(268\) | 0.585786 | 0.0357826 | ||||||||
\(269\) | −24.8284 | −1.51382 | −0.756908 | − | 0.653521i | \(-0.773291\pi\) | ||||
−0.756908 | + | 0.653521i | \(0.773291\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.65685 | −0.100647 | −0.0503234 | − | 0.998733i | \(-0.516025\pi\) | ||||
−0.0503234 | + | 0.998733i | \(0.516025\pi\) | |||||||
\(272\) | −1.17157 | −0.0710370 | ||||||||
\(273\) | 9.65685 | 0.584459 | ||||||||
\(274\) | 8.48528 | 0.512615 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −1.00000 | −0.0601929 | ||||||||
\(277\) | −30.4853 | −1.83168 | −0.915842 | − | 0.401540i | \(-0.868475\pi\) | ||||
−0.915842 | + | 0.401540i | \(0.868475\pi\) | |||||||
\(278\) | −16.9706 | −1.01783 | ||||||||
\(279\) | 6.00000 | 0.359211 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −30.1421 | −1.79813 | −0.899065 | − | 0.437816i | \(-0.855752\pi\) | ||||
−0.899065 | + | 0.437816i | \(0.855752\pi\) | |||||||
\(282\) | −4.82843 | −0.287529 | ||||||||
\(283\) | 27.2132 | 1.61766 | 0.808829 | − | 0.588045i | \(-0.200102\pi\) | ||||
0.808829 | + | 0.588045i | \(0.200102\pi\) | |||||||
\(284\) | 5.65685 | 0.335673 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 20.4853 | 1.21132 | ||||||||
\(287\) | −2.34315 | −0.138312 | ||||||||
\(288\) | −1.00000 | −0.0589256 | ||||||||
\(289\) | −15.6274 | −0.919260 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −6.00000 | −0.351726 | ||||||||
\(292\) | 3.65685 | 0.214001 | ||||||||
\(293\) | 28.0416 | 1.63821 | 0.819105 | − | 0.573644i | \(-0.194471\pi\) | ||||
0.819105 | + | 0.573644i | \(0.194471\pi\) | |||||||
\(294\) | −3.00000 | −0.174964 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 3.41421 | 0.198447 | ||||||||
\(297\) | −4.24264 | −0.246183 | ||||||||
\(298\) | 12.7279 | 0.737309 | ||||||||
\(299\) | −4.82843 | −0.279235 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −3.51472 | −0.202585 | ||||||||
\(302\) | 15.6569 | 0.900951 | ||||||||
\(303\) | 9.31371 | 0.535059 | ||||||||
\(304\) | −2.24264 | −0.128624 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 1.17157 | 0.0669744 | ||||||||
\(307\) | 25.4558 | 1.45284 | 0.726421 | − | 0.687250i | \(-0.241182\pi\) | ||||
0.726421 | + | 0.687250i | \(0.241182\pi\) | |||||||
\(308\) | 8.48528 | 0.483494 | ||||||||
\(309\) | −12.1421 | −0.690742 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 17.7990 | 1.00929 | 0.504644 | − | 0.863328i | \(-0.331624\pi\) | ||||
0.504644 | + | 0.863328i | \(0.331624\pi\) | |||||||
\(312\) | −4.82843 | −0.273356 | ||||||||
\(313\) | −18.0000 | −1.01742 | −0.508710 | − | 0.860938i | \(-0.669877\pi\) | ||||
−0.508710 | + | 0.860938i | \(0.669877\pi\) | |||||||
\(314\) | 6.92893 | 0.391022 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 7.65685 | 0.430732 | ||||||||
\(317\) | −2.48528 | −0.139587 | −0.0697937 | − | 0.997561i | \(-0.522234\pi\) | ||||
−0.0697937 | + | 0.997561i | \(0.522234\pi\) | |||||||
\(318\) | −13.4142 | −0.752232 | ||||||||
\(319\) | −32.4853 | −1.81883 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 15.0711 | 0.841185 | ||||||||
\(322\) | −2.00000 | −0.111456 | ||||||||
\(323\) | 2.62742 | 0.146193 | ||||||||
\(324\) | 1.00000 | 0.0555556 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 1.17157 | 0.0648874 | ||||||||
\(327\) | −15.4142 | −0.852408 | ||||||||
\(328\) | 1.17157 | 0.0646893 | ||||||||
\(329\) | −9.65685 | −0.532400 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3.51472 | −0.193186 | −0.0965932 | − | 0.995324i | \(-0.530795\pi\) | ||||
−0.0965932 | + | 0.995324i | \(0.530795\pi\) | |||||||
\(332\) | 1.41421 | 0.0776151 | ||||||||
\(333\) | −3.41421 | −0.187098 | ||||||||
\(334\) | −8.82843 | −0.483070 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −2.00000 | −0.109109 | ||||||||
\(337\) | 9.51472 | 0.518300 | 0.259150 | − | 0.965837i | \(-0.416558\pi\) | ||||
0.259150 | + | 0.965837i | \(0.416558\pi\) | |||||||
\(338\) | −10.3137 | −0.560992 | ||||||||
\(339\) | 16.9706 | 0.921714 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 25.4558 | 1.37851 | ||||||||
\(342\) | 2.24264 | 0.121268 | ||||||||
\(343\) | −20.0000 | −1.07990 | ||||||||
\(344\) | 1.75736 | 0.0947505 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 3.17157 | 0.170505 | ||||||||
\(347\) | −7.79899 | −0.418672 | −0.209336 | − | 0.977844i | \(-0.567130\pi\) | ||||
−0.209336 | + | 0.977844i | \(0.567130\pi\) | |||||||
\(348\) | 7.65685 | 0.410450 | ||||||||
\(349\) | 25.3137 | 1.35501 | 0.677506 | − | 0.735517i | \(-0.263061\pi\) | ||||
0.677506 | + | 0.735517i | \(0.263061\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 4.82843 | 0.257722 | ||||||||
\(352\) | −4.24264 | −0.226134 | ||||||||
\(353\) | 26.1421 | 1.39141 | 0.695703 | − | 0.718330i | \(-0.255093\pi\) | ||||
0.695703 | + | 0.718330i | \(0.255093\pi\) | |||||||
\(354\) | −8.48528 | −0.450988 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 14.8284 | 0.785905 | ||||||||
\(357\) | 2.34315 | 0.124012 | ||||||||
\(358\) | 10.3431 | 0.546652 | ||||||||
\(359\) | −19.7990 | −1.04495 | −0.522475 | − | 0.852654i | \(-0.674991\pi\) | ||||
−0.522475 | + | 0.852654i | \(0.674991\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −13.9706 | −0.735293 | ||||||||
\(362\) | −16.3848 | −0.861165 | ||||||||
\(363\) | −7.00000 | −0.367405 | ||||||||
\(364\) | −9.65685 | −0.506157 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −3.41421 | −0.178464 | ||||||||
\(367\) | −34.9706 | −1.82545 | −0.912724 | − | 0.408576i | \(-0.866025\pi\) | ||||
−0.912724 | + | 0.408576i | \(0.866025\pi\) | |||||||
\(368\) | 1.00000 | 0.0521286 | ||||||||
\(369\) | −1.17157 | −0.0609896 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −26.8284 | −1.39286 | ||||||||
\(372\) | −6.00000 | −0.311086 | ||||||||
\(373\) | −19.2132 | −0.994822 | −0.497411 | − | 0.867515i | \(-0.665716\pi\) | ||||
−0.497411 | + | 0.867515i | \(0.665716\pi\) | |||||||
\(374\) | 4.97056 | 0.257022 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 4.82843 | 0.249007 | ||||||||
\(377\) | 36.9706 | 1.90408 | ||||||||
\(378\) | 2.00000 | 0.102869 | ||||||||
\(379\) | −19.2132 | −0.986916 | −0.493458 | − | 0.869770i | \(-0.664267\pi\) | ||||
−0.493458 | + | 0.869770i | \(0.664267\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −2.00000 | −0.102463 | ||||||||
\(382\) | 5.17157 | 0.264601 | ||||||||
\(383\) | 18.6274 | 0.951817 | 0.475908 | − | 0.879495i | \(-0.342119\pi\) | ||||
0.475908 | + | 0.879495i | \(0.342119\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 12.9706 | 0.660184 | ||||||||
\(387\) | −1.75736 | −0.0893316 | ||||||||
\(388\) | 6.00000 | 0.304604 | ||||||||
\(389\) | 6.38478 | 0.323721 | 0.161861 | − | 0.986814i | \(-0.448251\pi\) | ||||
0.161861 | + | 0.986814i | \(0.448251\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.17157 | −0.0592490 | ||||||||
\(392\) | 3.00000 | 0.151523 | ||||||||
\(393\) | 10.3431 | 0.521743 | ||||||||
\(394\) | −24.6274 | −1.24071 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 4.24264 | 0.213201 | ||||||||
\(397\) | 8.34315 | 0.418730 | 0.209365 | − | 0.977838i | \(-0.432860\pi\) | ||||
0.209365 | + | 0.977838i | \(0.432860\pi\) | |||||||
\(398\) | 14.0000 | 0.701757 | ||||||||
\(399\) | 4.48528 | 0.224545 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −28.9706 | −1.44672 | −0.723360 | − | 0.690471i | \(-0.757403\pi\) | ||||
−0.723360 | + | 0.690471i | \(0.757403\pi\) | |||||||
\(402\) | 0.585786 | 0.0292164 | ||||||||
\(403\) | −28.9706 | −1.44313 | ||||||||
\(404\) | −9.31371 | −0.463374 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 15.3137 | 0.760007 | ||||||||
\(407\) | −14.4853 | −0.718009 | ||||||||
\(408\) | −1.17157 | −0.0580015 | ||||||||
\(409\) | 18.0000 | 0.890043 | 0.445021 | − | 0.895520i | \(-0.353196\pi\) | ||||
0.445021 | + | 0.895520i | \(0.353196\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 8.48528 | 0.418548 | ||||||||
\(412\) | 12.1421 | 0.598200 | ||||||||
\(413\) | −16.9706 | −0.835067 | ||||||||
\(414\) | −1.00000 | −0.0491473 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 4.82843 | 0.236733 | ||||||||
\(417\) | −16.9706 | −0.831052 | ||||||||
\(418\) | 9.51472 | 0.465380 | ||||||||
\(419\) | −24.9289 | −1.21786 | −0.608929 | − | 0.793225i | \(-0.708401\pi\) | ||||
−0.608929 | + | 0.793225i | \(0.708401\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 10.2426 | 0.499196 | 0.249598 | − | 0.968350i | \(-0.419702\pi\) | ||||
0.249598 | + | 0.968350i | \(0.419702\pi\) | |||||||
\(422\) | 20.4853 | 0.997208 | ||||||||
\(423\) | −4.82843 | −0.234766 | ||||||||
\(424\) | 13.4142 | 0.651452 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 5.65685 | 0.274075 | ||||||||
\(427\) | −6.82843 | −0.330451 | ||||||||
\(428\) | −15.0711 | −0.728488 | ||||||||
\(429\) | 20.4853 | 0.989039 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 8.48528 | 0.408722 | 0.204361 | − | 0.978896i | \(-0.434488\pi\) | ||||
0.204361 | + | 0.978896i | \(0.434488\pi\) | |||||||
\(432\) | −1.00000 | −0.0481125 | ||||||||
\(433\) | −26.9706 | −1.29612 | −0.648061 | − | 0.761588i | \(-0.724420\pi\) | ||||
−0.648061 | + | 0.761588i | \(0.724420\pi\) | |||||||
\(434\) | −12.0000 | −0.576018 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 15.4142 | 0.738207 | ||||||||
\(437\) | −2.24264 | −0.107280 | ||||||||
\(438\) | 3.65685 | 0.174731 | ||||||||
\(439\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −3.00000 | −0.142857 | ||||||||
\(442\) | −5.65685 | −0.269069 | ||||||||
\(443\) | 23.3137 | 1.10767 | 0.553834 | − | 0.832627i | \(-0.313164\pi\) | ||||
0.553834 | + | 0.832627i | \(0.313164\pi\) | |||||||
\(444\) | 3.41421 | 0.162031 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 16.0000 | 0.757622 | ||||||||
\(447\) | 12.7279 | 0.602010 | ||||||||
\(448\) | 2.00000 | 0.0944911 | ||||||||
\(449\) | −22.8284 | −1.07734 | −0.538670 | − | 0.842517i | \(-0.681073\pi\) | ||||
−0.538670 | + | 0.842517i | \(0.681073\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −4.97056 | −0.234055 | ||||||||
\(452\) | −16.9706 | −0.798228 | ||||||||
\(453\) | 15.6569 | 0.735623 | ||||||||
\(454\) | 14.3848 | 0.675111 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −2.24264 | −0.105021 | ||||||||
\(457\) | −1.02944 | −0.0481550 | −0.0240775 | − | 0.999710i | \(-0.507665\pi\) | ||||
−0.0240775 | + | 0.999710i | \(0.507665\pi\) | |||||||
\(458\) | −1.75736 | −0.0821160 | ||||||||
\(459\) | 1.17157 | 0.0546843 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −12.8284 | −0.597479 | −0.298740 | − | 0.954335i | \(-0.596566\pi\) | ||||
−0.298740 | + | 0.954335i | \(0.596566\pi\) | |||||||
\(462\) | 8.48528 | 0.394771 | ||||||||
\(463\) | −2.97056 | −0.138054 | −0.0690269 | − | 0.997615i | \(-0.521989\pi\) | ||||
−0.0690269 | + | 0.997615i | \(0.521989\pi\) | |||||||
\(464\) | −7.65685 | −0.355461 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −26.1421 | −1.21101 | ||||||||
\(467\) | −39.3553 | −1.82115 | −0.910574 | − | 0.413346i | \(-0.864360\pi\) | ||||
−0.910574 | + | 0.413346i | \(0.864360\pi\) | |||||||
\(468\) | −4.82843 | −0.223194 | ||||||||
\(469\) | 1.17157 | 0.0540982 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 6.92893 | 0.319268 | ||||||||
\(472\) | 8.48528 | 0.390567 | ||||||||
\(473\) | −7.45584 | −0.342820 | ||||||||
\(474\) | 7.65685 | 0.351691 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −2.34315 | −0.107398 | ||||||||
\(477\) | −13.4142 | −0.614195 | ||||||||
\(478\) | 11.1716 | 0.510976 | ||||||||
\(479\) | 4.68629 | 0.214122 | 0.107061 | − | 0.994252i | \(-0.465856\pi\) | ||||
0.107061 | + | 0.994252i | \(0.465856\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 16.4853 | 0.751664 | ||||||||
\(482\) | 10.4853 | 0.477591 | ||||||||
\(483\) | −2.00000 | −0.0910032 | ||||||||
\(484\) | 7.00000 | 0.318182 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 1.00000 | 0.0453609 | ||||||||
\(487\) | 27.9411 | 1.26613 | 0.633067 | − | 0.774097i | \(-0.281796\pi\) | ||||
0.633067 | + | 0.774097i | \(0.281796\pi\) | |||||||
\(488\) | 3.41421 | 0.154554 | ||||||||
\(489\) | 1.17157 | 0.0529804 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 26.6274 | 1.20168 | 0.600839 | − | 0.799370i | \(-0.294833\pi\) | ||||
0.600839 | + | 0.799370i | \(0.294833\pi\) | |||||||
\(492\) | 1.17157 | 0.0528186 | ||||||||
\(493\) | 8.97056 | 0.404014 | ||||||||
\(494\) | −10.8284 | −0.487194 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 6.00000 | 0.269408 | ||||||||
\(497\) | 11.3137 | 0.507489 | ||||||||
\(498\) | 1.41421 | 0.0633724 | ||||||||
\(499\) | 13.4558 | 0.602366 | 0.301183 | − | 0.953566i | \(-0.402618\pi\) | ||||
0.301183 | + | 0.953566i | \(0.402618\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −8.82843 | −0.394425 | ||||||||
\(502\) | 24.7279 | 1.10366 | ||||||||
\(503\) | −22.1421 | −0.987269 | −0.493635 | − | 0.869669i | \(-0.664332\pi\) | ||||
−0.493635 | + | 0.869669i | \(0.664332\pi\) | |||||||
\(504\) | −2.00000 | −0.0890871 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −4.24264 | −0.188608 | ||||||||
\(507\) | −10.3137 | −0.458048 | ||||||||
\(508\) | 2.00000 | 0.0887357 | ||||||||
\(509\) | 22.9706 | 1.01815 | 0.509076 | − | 0.860721i | \(-0.329987\pi\) | ||||
0.509076 | + | 0.860721i | \(0.329987\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 7.31371 | 0.323539 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 2.24264 | 0.0990150 | ||||||||
\(514\) | 18.0000 | 0.793946 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 1.75736 | 0.0773634 | ||||||||
\(517\) | −20.4853 | −0.900942 | ||||||||
\(518\) | 6.82843 | 0.300024 | ||||||||
\(519\) | 3.17157 | 0.139217 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −16.2843 | −0.713427 | −0.356713 | − | 0.934214i | \(-0.616103\pi\) | ||||
−0.356713 | + | 0.934214i | \(0.616103\pi\) | |||||||
\(522\) | 7.65685 | 0.335131 | ||||||||
\(523\) | 2.92893 | 0.128073 | 0.0640366 | − | 0.997948i | \(-0.479603\pi\) | ||||
0.0640366 | + | 0.997948i | \(0.479603\pi\) | |||||||
\(524\) | −10.3431 | −0.451842 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −17.6569 | −0.769875 | ||||||||
\(527\) | −7.02944 | −0.306207 | ||||||||
\(528\) | −4.24264 | −0.184637 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −8.48528 | −0.368230 | ||||||||
\(532\) | −4.48528 | −0.194462 | ||||||||
\(533\) | 5.65685 | 0.245026 | ||||||||
\(534\) | 14.8284 | 0.641689 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −0.585786 | −0.0253021 | ||||||||
\(537\) | 10.3431 | 0.446340 | ||||||||
\(538\) | 24.8284 | 1.07043 | ||||||||
\(539\) | −12.7279 | −0.548230 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 35.9411 | 1.54523 | 0.772615 | − | 0.634875i | \(-0.218948\pi\) | ||||
0.772615 | + | 0.634875i | \(0.218948\pi\) | |||||||
\(542\) | 1.65685 | 0.0711680 | ||||||||
\(543\) | −16.3848 | −0.703138 | ||||||||
\(544\) | 1.17157 | 0.0502308 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −9.65685 | −0.413275 | ||||||||
\(547\) | 4.48528 | 0.191777 | 0.0958884 | − | 0.995392i | \(-0.469431\pi\) | ||||
0.0958884 | + | 0.995392i | \(0.469431\pi\) | |||||||
\(548\) | −8.48528 | −0.362473 | ||||||||
\(549\) | −3.41421 | −0.145715 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 17.1716 | 0.731534 | ||||||||
\(552\) | 1.00000 | 0.0425628 | ||||||||
\(553\) | 15.3137 | 0.651205 | ||||||||
\(554\) | 30.4853 | 1.29520 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 16.9706 | 0.719712 | ||||||||
\(557\) | 14.8701 | 0.630065 | 0.315032 | − | 0.949081i | \(-0.397985\pi\) | ||||
0.315032 | + | 0.949081i | \(0.397985\pi\) | |||||||
\(558\) | −6.00000 | −0.254000 | ||||||||
\(559\) | 8.48528 | 0.358889 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 4.97056 | 0.209857 | ||||||||
\(562\) | 30.1421 | 1.27147 | ||||||||
\(563\) | 21.8995 | 0.922954 | 0.461477 | − | 0.887152i | \(-0.347320\pi\) | ||||
0.461477 | + | 0.887152i | \(0.347320\pi\) | |||||||
\(564\) | 4.82843 | 0.203313 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −27.2132 | −1.14386 | ||||||||
\(567\) | 2.00000 | 0.0839921 | ||||||||
\(568\) | −5.65685 | −0.237356 | ||||||||
\(569\) | 25.6569 | 1.07559 | 0.537796 | − | 0.843075i | \(-0.319257\pi\) | ||||
0.537796 | + | 0.843075i | \(0.319257\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −42.7279 | −1.78811 | −0.894054 | − | 0.447959i | \(-0.852151\pi\) | ||||
−0.894054 | + | 0.447959i | \(0.852151\pi\) | |||||||
\(572\) | −20.4853 | −0.856533 | ||||||||
\(573\) | 5.17157 | 0.216046 | ||||||||
\(574\) | 2.34315 | 0.0978010 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | 20.6274 | 0.858731 | 0.429365 | − | 0.903131i | \(-0.358737\pi\) | ||||
0.429365 | + | 0.903131i | \(0.358737\pi\) | |||||||
\(578\) | 15.6274 | 0.650015 | ||||||||
\(579\) | 12.9706 | 0.539038 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 2.82843 | 0.117343 | ||||||||
\(582\) | 6.00000 | 0.248708 | ||||||||
\(583\) | −56.9117 | −2.35704 | ||||||||
\(584\) | −3.65685 | −0.151322 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −28.0416 | −1.15839 | ||||||||
\(587\) | −26.8284 | −1.10733 | −0.553664 | − | 0.832740i | \(-0.686771\pi\) | ||||
−0.553664 | + | 0.832740i | \(0.686771\pi\) | |||||||
\(588\) | 3.00000 | 0.123718 | ||||||||
\(589\) | −13.4558 | −0.554438 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −24.6274 | −1.01304 | ||||||||
\(592\) | −3.41421 | −0.140323 | ||||||||
\(593\) | 12.3431 | 0.506872 | 0.253436 | − | 0.967352i | \(-0.418439\pi\) | ||||
0.253436 | + | 0.967352i | \(0.418439\pi\) | |||||||
\(594\) | 4.24264 | 0.174078 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −12.7279 | −0.521356 | ||||||||
\(597\) | 14.0000 | 0.572982 | ||||||||
\(598\) | 4.82843 | 0.197449 | ||||||||
\(599\) | −40.1421 | −1.64016 | −0.820082 | − | 0.572247i | \(-0.806072\pi\) | ||||
−0.820082 | + | 0.572247i | \(0.806072\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −20.9706 | −0.855407 | −0.427704 | − | 0.903919i | \(-0.640677\pi\) | ||||
−0.427704 | + | 0.903919i | \(0.640677\pi\) | |||||||
\(602\) | 3.51472 | 0.143249 | ||||||||
\(603\) | 0.585786 | 0.0238551 | ||||||||
\(604\) | −15.6569 | −0.637068 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −9.31371 | −0.378344 | ||||||||
\(607\) | 16.9706 | 0.688814 | 0.344407 | − | 0.938820i | \(-0.388080\pi\) | ||||
0.344407 | + | 0.938820i | \(0.388080\pi\) | |||||||
\(608\) | 2.24264 | 0.0909511 | ||||||||
\(609\) | 15.3137 | 0.620543 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 23.3137 | 0.943172 | ||||||||
\(612\) | −1.17157 | −0.0473580 | ||||||||
\(613\) | 14.2426 | 0.575255 | 0.287627 | − | 0.957742i | \(-0.407134\pi\) | ||||
0.287627 | + | 0.957742i | \(0.407134\pi\) | |||||||
\(614\) | −25.4558 | −1.02731 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −8.48528 | −0.341882 | ||||||||
\(617\) | 31.3137 | 1.26064 | 0.630321 | − | 0.776334i | \(-0.282923\pi\) | ||||
0.630321 | + | 0.776334i | \(0.282923\pi\) | |||||||
\(618\) | 12.1421 | 0.488428 | ||||||||
\(619\) | −19.2132 | −0.772244 | −0.386122 | − | 0.922448i | \(-0.626186\pi\) | ||||
−0.386122 | + | 0.922448i | \(0.626186\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.00000 | −0.0401286 | ||||||||
\(622\) | −17.7990 | −0.713674 | ||||||||
\(623\) | 29.6569 | 1.18818 | ||||||||
\(624\) | 4.82843 | 0.193292 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 18.0000 | 0.719425 | ||||||||
\(627\) | 9.51472 | 0.379981 | ||||||||
\(628\) | −6.92893 | −0.276494 | ||||||||
\(629\) | 4.00000 | 0.159490 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 35.1716 | 1.40016 | 0.700079 | − | 0.714065i | \(-0.253148\pi\) | ||||
0.700079 | + | 0.714065i | \(0.253148\pi\) | |||||||
\(632\) | −7.65685 | −0.304573 | ||||||||
\(633\) | 20.4853 | 0.814217 | ||||||||
\(634\) | 2.48528 | 0.0987031 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 13.4142 | 0.531908 | ||||||||
\(637\) | 14.4853 | 0.573928 | ||||||||
\(638\) | 32.4853 | 1.28610 | ||||||||
\(639\) | 5.65685 | 0.223782 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −8.28427 | −0.327209 | −0.163605 | − | 0.986526i | \(-0.552312\pi\) | ||||
−0.163605 | + | 0.986526i | \(0.552312\pi\) | |||||||
\(642\) | −15.0711 | −0.594808 | ||||||||
\(643\) | 32.3848 | 1.27713 | 0.638565 | − | 0.769568i | \(-0.279528\pi\) | ||||
0.638565 | + | 0.769568i | \(0.279528\pi\) | |||||||
\(644\) | 2.00000 | 0.0788110 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −2.62742 | −0.103374 | ||||||||
\(647\) | 29.6569 | 1.16593 | 0.582966 | − | 0.812497i | \(-0.301892\pi\) | ||||
0.582966 | + | 0.812497i | \(0.301892\pi\) | |||||||
\(648\) | −1.00000 | −0.0392837 | ||||||||
\(649\) | −36.0000 | −1.41312 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −12.0000 | −0.470317 | ||||||||
\(652\) | −1.17157 | −0.0458823 | ||||||||
\(653\) | −43.4558 | −1.70056 | −0.850279 | − | 0.526332i | \(-0.823567\pi\) | ||||
−0.850279 | + | 0.526332i | \(0.823567\pi\) | |||||||
\(654\) | 15.4142 | 0.602743 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −1.17157 | −0.0457422 | ||||||||
\(657\) | 3.65685 | 0.142667 | ||||||||
\(658\) | 9.65685 | 0.376463 | ||||||||
\(659\) | −26.1005 | −1.01673 | −0.508366 | − | 0.861141i | \(-0.669750\pi\) | ||||
−0.508366 | + | 0.861141i | \(0.669750\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 9.27208 | 0.360642 | 0.180321 | − | 0.983608i | \(-0.442286\pi\) | ||||
0.180321 | + | 0.983608i | \(0.442286\pi\) | |||||||
\(662\) | 3.51472 | 0.136603 | ||||||||
\(663\) | −5.65685 | −0.219694 | ||||||||
\(664\) | −1.41421 | −0.0548821 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 3.41421 | 0.132298 | ||||||||
\(667\) | −7.65685 | −0.296475 | ||||||||
\(668\) | 8.82843 | 0.341582 | ||||||||
\(669\) | 16.0000 | 0.618596 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −14.4853 | −0.559198 | ||||||||
\(672\) | 2.00000 | 0.0771517 | ||||||||
\(673\) | 39.9411 | 1.53962 | 0.769809 | − | 0.638275i | \(-0.220352\pi\) | ||||
0.769809 | + | 0.638275i | \(0.220352\pi\) | |||||||
\(674\) | −9.51472 | −0.366493 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 10.3137 | 0.396681 | ||||||||
\(677\) | −24.5269 | −0.942646 | −0.471323 | − | 0.881961i | \(-0.656223\pi\) | ||||
−0.471323 | + | 0.881961i | \(0.656223\pi\) | |||||||
\(678\) | −16.9706 | −0.651751 | ||||||||
\(679\) | 12.0000 | 0.460518 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 14.3848 | 0.551226 | ||||||||
\(682\) | −25.4558 | −0.974755 | ||||||||
\(683\) | −8.48528 | −0.324680 | −0.162340 | − | 0.986735i | \(-0.551904\pi\) | ||||
−0.162340 | + | 0.986735i | \(0.551904\pi\) | |||||||
\(684\) | −2.24264 | −0.0857495 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 20.0000 | 0.763604 | ||||||||
\(687\) | −1.75736 | −0.0670474 | ||||||||
\(688\) | −1.75736 | −0.0669987 | ||||||||
\(689\) | 64.7696 | 2.46752 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −18.8284 | −0.716267 | −0.358134 | − | 0.933670i | \(-0.616587\pi\) | ||||
−0.358134 | + | 0.933670i | \(0.616587\pi\) | |||||||
\(692\) | −3.17157 | −0.120565 | ||||||||
\(693\) | 8.48528 | 0.322329 | ||||||||
\(694\) | 7.79899 | 0.296046 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −7.65685 | −0.290232 | ||||||||
\(697\) | 1.37258 | 0.0519903 | ||||||||
\(698\) | −25.3137 | −0.958138 | ||||||||
\(699\) | −26.1421 | −0.988786 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 38.1838 | 1.44218 | 0.721090 | − | 0.692841i | \(-0.243641\pi\) | ||||
0.721090 | + | 0.692841i | \(0.243641\pi\) | |||||||
\(702\) | −4.82843 | −0.182237 | ||||||||
\(703\) | 7.65685 | 0.288784 | ||||||||
\(704\) | 4.24264 | 0.159901 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −26.1421 | −0.983872 | ||||||||
\(707\) | −18.6274 | −0.700556 | ||||||||
\(708\) | 8.48528 | 0.318896 | ||||||||
\(709\) | 35.4142 | 1.33001 | 0.665004 | − | 0.746839i | \(-0.268430\pi\) | ||||
0.665004 | + | 0.746839i | \(0.268430\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 7.65685 | 0.287154 | ||||||||
\(712\) | −14.8284 | −0.555719 | ||||||||
\(713\) | 6.00000 | 0.224702 | ||||||||
\(714\) | −2.34315 | −0.0876900 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −10.3431 | −0.386542 | ||||||||
\(717\) | 11.1716 | 0.417210 | ||||||||
\(718\) | 19.7990 | 0.738892 | ||||||||
\(719\) | 28.1421 | 1.04952 | 0.524762 | − | 0.851249i | \(-0.324154\pi\) | ||||
0.524762 | + | 0.851249i | \(0.324154\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 24.2843 | 0.904394 | ||||||||
\(722\) | 13.9706 | 0.519931 | ||||||||
\(723\) | 10.4853 | 0.389952 | ||||||||
\(724\) | 16.3848 | 0.608935 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 7.00000 | 0.259794 | ||||||||
\(727\) | 31.6569 | 1.17409 | 0.587044 | − | 0.809555i | \(-0.300292\pi\) | ||||
0.587044 | + | 0.809555i | \(0.300292\pi\) | |||||||
\(728\) | 9.65685 | 0.357907 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 2.05887 | 0.0761502 | ||||||||
\(732\) | 3.41421 | 0.126193 | ||||||||
\(733\) | −8.58579 | −0.317123 | −0.158562 | − | 0.987349i | \(-0.550686\pi\) | ||||
−0.158562 | + | 0.987349i | \(0.550686\pi\) | |||||||
\(734\) | 34.9706 | 1.29079 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −1.00000 | −0.0368605 | ||||||||
\(737\) | 2.48528 | 0.0915465 | ||||||||
\(738\) | 1.17157 | 0.0431262 | ||||||||
\(739\) | 42.6274 | 1.56807 | 0.784037 | − | 0.620714i | \(-0.213157\pi\) | ||||
0.784037 | + | 0.620714i | \(0.213157\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −10.8284 | −0.397792 | ||||||||
\(742\) | 26.8284 | 0.984903 | ||||||||
\(743\) | −2.34315 | −0.0859617 | −0.0429808 | − | 0.999076i | \(-0.513685\pi\) | ||||
−0.0429808 | + | 0.999076i | \(0.513685\pi\) | |||||||
\(744\) | 6.00000 | 0.219971 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 19.2132 | 0.703445 | ||||||||
\(747\) | 1.41421 | 0.0517434 | ||||||||
\(748\) | −4.97056 | −0.181742 | ||||||||
\(749\) | −30.1421 | −1.10137 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −48.8284 | −1.78177 | −0.890887 | − | 0.454224i | \(-0.849916\pi\) | ||||
−0.890887 | + | 0.454224i | \(0.849916\pi\) | |||||||
\(752\) | −4.82843 | −0.176075 | ||||||||
\(753\) | 24.7279 | 0.901136 | ||||||||
\(754\) | −36.9706 | −1.34639 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −2.00000 | −0.0727393 | ||||||||
\(757\) | −42.2426 | −1.53533 | −0.767667 | − | 0.640848i | \(-0.778583\pi\) | ||||
−0.767667 | + | 0.640848i | \(0.778583\pi\) | |||||||
\(758\) | 19.2132 | 0.697855 | ||||||||
\(759\) | −4.24264 | −0.153998 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −24.3431 | −0.882438 | −0.441219 | − | 0.897399i | \(-0.645454\pi\) | ||||
−0.441219 | + | 0.897399i | \(0.645454\pi\) | |||||||
\(762\) | 2.00000 | 0.0724524 | ||||||||
\(763\) | 30.8284 | 1.11606 | ||||||||
\(764\) | −5.17157 | −0.187101 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −18.6274 | −0.673036 | ||||||||
\(767\) | 40.9706 | 1.47936 | ||||||||
\(768\) | −1.00000 | −0.0360844 | ||||||||
\(769\) | 45.7990 | 1.65155 | 0.825777 | − | 0.563997i | \(-0.190737\pi\) | ||||
0.825777 | + | 0.563997i | \(0.190737\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 18.0000 | 0.648254 | ||||||||
\(772\) | −12.9706 | −0.466821 | ||||||||
\(773\) | 16.9289 | 0.608891 | 0.304446 | − | 0.952530i | \(-0.401529\pi\) | ||||
0.304446 | + | 0.952530i | \(0.401529\pi\) | |||||||
\(774\) | 1.75736 | 0.0631670 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −6.00000 | −0.215387 | ||||||||
\(777\) | 6.82843 | 0.244968 | ||||||||
\(778\) | −6.38478 | −0.228905 | ||||||||
\(779\) | 2.62742 | 0.0941370 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 24.0000 | 0.858788 | ||||||||
\(782\) | 1.17157 | 0.0418954 | ||||||||
\(783\) | 7.65685 | 0.273634 | ||||||||
\(784\) | −3.00000 | −0.107143 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −10.3431 | −0.368928 | ||||||||
\(787\) | −2.72792 | −0.0972399 | −0.0486200 | − | 0.998817i | \(-0.515482\pi\) | ||||
−0.0486200 | + | 0.998817i | \(0.515482\pi\) | |||||||
\(788\) | 24.6274 | 0.877315 | ||||||||
\(789\) | −17.6569 | −0.628601 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −33.9411 | −1.20681 | ||||||||
\(792\) | −4.24264 | −0.150756 | ||||||||
\(793\) | 16.4853 | 0.585410 | ||||||||
\(794\) | −8.34315 | −0.296087 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −14.0000 | −0.496217 | ||||||||
\(797\) | 21.4142 | 0.758530 | 0.379265 | − | 0.925288i | \(-0.376177\pi\) | ||||
0.379265 | + | 0.925288i | \(0.376177\pi\) | |||||||
\(798\) | −4.48528 | −0.158777 | ||||||||
\(799\) | 5.65685 | 0.200125 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 14.8284 | 0.523937 | ||||||||
\(802\) | 28.9706 | 1.02299 | ||||||||
\(803\) | 15.5147 | 0.547503 | ||||||||
\(804\) | −0.585786 | −0.0206591 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 28.9706 | 1.02044 | ||||||||
\(807\) | 24.8284 | 0.874002 | ||||||||
\(808\) | 9.31371 | 0.327655 | ||||||||
\(809\) | 13.3137 | 0.468085 | 0.234043 | − | 0.972226i | \(-0.424804\pi\) | ||||
0.234043 | + | 0.972226i | \(0.424804\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 6.82843 | 0.239779 | 0.119889 | − | 0.992787i | \(-0.461746\pi\) | ||||
0.119889 | + | 0.992787i | \(0.461746\pi\) | |||||||
\(812\) | −15.3137 | −0.537406 | ||||||||
\(813\) | 1.65685 | 0.0581084 | ||||||||
\(814\) | 14.4853 | 0.507709 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 1.17157 | 0.0410133 | ||||||||
\(817\) | 3.94113 | 0.137883 | ||||||||
\(818\) | −18.0000 | −0.629355 | ||||||||
\(819\) | −9.65685 | −0.337438 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −6.68629 | −0.233353 | −0.116677 | − | 0.993170i | \(-0.537224\pi\) | ||||
−0.116677 | + | 0.993170i | \(0.537224\pi\) | |||||||
\(822\) | −8.48528 | −0.295958 | ||||||||
\(823\) | −32.2843 | −1.12536 | −0.562679 | − | 0.826675i | \(-0.690229\pi\) | ||||
−0.562679 | + | 0.826675i | \(0.690229\pi\) | |||||||
\(824\) | −12.1421 | −0.422991 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 16.9706 | 0.590481 | ||||||||
\(827\) | −18.1005 | −0.629416 | −0.314708 | − | 0.949188i | \(-0.601907\pi\) | ||||
−0.314708 | + | 0.949188i | \(0.601907\pi\) | |||||||
\(828\) | 1.00000 | 0.0347524 | ||||||||
\(829\) | 50.2843 | 1.74644 | 0.873222 | − | 0.487322i | \(-0.162026\pi\) | ||||
0.873222 | + | 0.487322i | \(0.162026\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 30.4853 | 1.05752 | ||||||||
\(832\) | −4.82843 | −0.167396 | ||||||||
\(833\) | 3.51472 | 0.121778 | ||||||||
\(834\) | 16.9706 | 0.587643 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −9.51472 | −0.329073 | ||||||||
\(837\) | −6.00000 | −0.207390 | ||||||||
\(838\) | 24.9289 | 0.861156 | ||||||||
\(839\) | −33.9411 | −1.17178 | −0.585889 | − | 0.810391i | \(-0.699255\pi\) | ||||
−0.585889 | + | 0.810391i | \(0.699255\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 29.6274 | 1.02164 | ||||||||
\(842\) | −10.2426 | −0.352985 | ||||||||
\(843\) | 30.1421 | 1.03815 | ||||||||
\(844\) | −20.4853 | −0.705132 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 4.82843 | 0.166005 | ||||||||
\(847\) | 14.0000 | 0.481046 | ||||||||
\(848\) | −13.4142 | −0.460646 | ||||||||
\(849\) | −27.2132 | −0.933955 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −3.41421 | −0.117038 | ||||||||
\(852\) | −5.65685 | −0.193801 | ||||||||
\(853\) | −1.31371 | −0.0449805 | −0.0224903 | − | 0.999747i | \(-0.507159\pi\) | ||||
−0.0224903 | + | 0.999747i | \(0.507159\pi\) | |||||||
\(854\) | 6.82843 | 0.233664 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 15.0711 | 0.515118 | ||||||||
\(857\) | 45.1716 | 1.54303 | 0.771516 | − | 0.636210i | \(-0.219499\pi\) | ||||
0.771516 | + | 0.636210i | \(0.219499\pi\) | |||||||
\(858\) | −20.4853 | −0.699356 | ||||||||
\(859\) | −32.2843 | −1.10153 | −0.550763 | − | 0.834662i | \(-0.685663\pi\) | ||||
−0.550763 | + | 0.834662i | \(0.685663\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 2.34315 | 0.0798542 | ||||||||
\(862\) | −8.48528 | −0.289010 | ||||||||
\(863\) | −22.6274 | −0.770246 | −0.385123 | − | 0.922865i | \(-0.625841\pi\) | ||||
−0.385123 | + | 0.922865i | \(0.625841\pi\) | |||||||
\(864\) | 1.00000 | 0.0340207 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 26.9706 | 0.916497 | ||||||||
\(867\) | 15.6274 | 0.530735 | ||||||||
\(868\) | 12.0000 | 0.407307 | ||||||||
\(869\) | 32.4853 | 1.10199 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −2.82843 | −0.0958376 | ||||||||
\(872\) | −15.4142 | −0.521991 | ||||||||
\(873\) | 6.00000 | 0.203069 | ||||||||
\(874\) | 2.24264 | 0.0758585 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −3.65685 | −0.123554 | ||||||||
\(877\) | 11.1716 | 0.377237 | 0.188619 | − | 0.982050i | \(-0.439599\pi\) | ||||
0.188619 | + | 0.982050i | \(0.439599\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −28.0416 | −0.945821 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −2.14214 | −0.0721704 | −0.0360852 | − | 0.999349i | \(-0.511489\pi\) | ||||
−0.0360852 | + | 0.999349i | \(0.511489\pi\) | |||||||
\(882\) | 3.00000 | 0.101015 | ||||||||
\(883\) | −13.1716 | −0.443259 | −0.221629 | − | 0.975131i | \(-0.571138\pi\) | ||||
−0.221629 | + | 0.975131i | \(0.571138\pi\) | |||||||
\(884\) | 5.65685 | 0.190261 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −23.3137 | −0.783239 | ||||||||
\(887\) | 48.4264 | 1.62600 | 0.813000 | − | 0.582264i | \(-0.197833\pi\) | ||||
0.813000 | + | 0.582264i | \(0.197833\pi\) | |||||||
\(888\) | −3.41421 | −0.114574 | ||||||||
\(889\) | 4.00000 | 0.134156 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 4.24264 | 0.142134 | ||||||||
\(892\) | −16.0000 | −0.535720 | ||||||||
\(893\) | 10.8284 | 0.362359 | ||||||||
\(894\) | −12.7279 | −0.425685 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −2.00000 | −0.0668153 | ||||||||
\(897\) | 4.82843 | 0.161216 | ||||||||
\(898\) | 22.8284 | 0.761794 | ||||||||
\(899\) | −45.9411 | −1.53222 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 15.7157 | 0.523567 | ||||||||
\(902\) | 4.97056 | 0.165502 | ||||||||
\(903\) | 3.51472 | 0.116963 | ||||||||
\(904\) | 16.9706 | 0.564433 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −15.6569 | −0.520164 | ||||||||
\(907\) | −27.2132 | −0.903600 | −0.451800 | − | 0.892119i | \(-0.649218\pi\) | ||||
−0.451800 | + | 0.892119i | \(0.649218\pi\) | |||||||
\(908\) | −14.3848 | −0.477376 | ||||||||
\(909\) | −9.31371 | −0.308916 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −0.201010 | −0.00665976 | −0.00332988 | − | 0.999994i | \(-0.501060\pi\) | ||||
−0.00332988 | + | 0.999994i | \(0.501060\pi\) | |||||||
\(912\) | 2.24264 | 0.0742613 | ||||||||
\(913\) | 6.00000 | 0.198571 | ||||||||
\(914\) | 1.02944 | 0.0340508 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 1.75736 | 0.0580648 | ||||||||
\(917\) | −20.6863 | −0.683122 | ||||||||
\(918\) | −1.17157 | −0.0386677 | ||||||||
\(919\) | 5.02944 | 0.165906 | 0.0829529 | − | 0.996553i | \(-0.473565\pi\) | ||||
0.0829529 | + | 0.996553i | \(0.473565\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −25.4558 | −0.838799 | ||||||||
\(922\) | 12.8284 | 0.422482 | ||||||||
\(923\) | −27.3137 | −0.899042 | ||||||||
\(924\) | −8.48528 | −0.279145 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 2.97056 | 0.0976187 | ||||||||
\(927\) | 12.1421 | 0.398800 | ||||||||
\(928\) | 7.65685 | 0.251349 | ||||||||
\(929\) | 42.1421 | 1.38264 | 0.691319 | − | 0.722549i | \(-0.257030\pi\) | ||||
0.691319 | + | 0.722549i | \(0.257030\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 6.72792 | 0.220499 | ||||||||
\(932\) | 26.1421 | 0.856314 | ||||||||
\(933\) | −17.7990 | −0.582713 | ||||||||
\(934\) | 39.3553 | 1.28775 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 4.82843 | 0.157822 | ||||||||
\(937\) | −44.4264 | −1.45135 | −0.725674 | − | 0.688039i | \(-0.758472\pi\) | ||||
−0.725674 | + | 0.688039i | \(0.758472\pi\) | |||||||
\(938\) | −1.17157 | −0.0382532 | ||||||||
\(939\) | 18.0000 | 0.587408 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −31.5563 | −1.02871 | −0.514354 | − | 0.857578i | \(-0.671968\pi\) | ||||
−0.514354 | + | 0.857578i | \(0.671968\pi\) | |||||||
\(942\) | −6.92893 | −0.225757 | ||||||||
\(943\) | −1.17157 | −0.0381517 | ||||||||
\(944\) | −8.48528 | −0.276172 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 7.45584 | 0.242410 | ||||||||
\(947\) | −1.45584 | −0.0473086 | −0.0236543 | − | 0.999720i | \(-0.507530\pi\) | ||||
−0.0236543 | + | 0.999720i | \(0.507530\pi\) | |||||||
\(948\) | −7.65685 | −0.248683 | ||||||||
\(949\) | −17.6569 | −0.573166 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 2.48528 | 0.0805908 | ||||||||
\(952\) | 2.34315 | 0.0759418 | ||||||||
\(953\) | −40.0833 | −1.29842 | −0.649212 | − | 0.760607i | \(-0.724901\pi\) | ||||
−0.649212 | + | 0.760607i | \(0.724901\pi\) | |||||||
\(954\) | 13.4142 | 0.434301 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −11.1716 | −0.361314 | ||||||||
\(957\) | 32.4853 | 1.05010 | ||||||||
\(958\) | −4.68629 | −0.151407 | ||||||||
\(959\) | −16.9706 | −0.548008 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 5.00000 | 0.161290 | ||||||||
\(962\) | −16.4853 | −0.531507 | ||||||||
\(963\) | −15.0711 | −0.485658 | ||||||||
\(964\) | −10.4853 | −0.337708 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 2.00000 | 0.0643489 | ||||||||
\(967\) | −4.97056 | −0.159843 | −0.0799213 | − | 0.996801i | \(-0.525467\pi\) | ||||
−0.0799213 | + | 0.996801i | \(0.525467\pi\) | |||||||
\(968\) | −7.00000 | −0.224989 | ||||||||
\(969\) | −2.62742 | −0.0844048 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −17.6152 | −0.565299 | −0.282650 | − | 0.959223i | \(-0.591213\pi\) | ||||
−0.282650 | + | 0.959223i | \(0.591213\pi\) | |||||||
\(972\) | −1.00000 | −0.0320750 | ||||||||
\(973\) | 33.9411 | 1.08810 | ||||||||
\(974\) | −27.9411 | −0.895291 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −3.41421 | −0.109286 | ||||||||
\(977\) | −19.7990 | −0.633426 | −0.316713 | − | 0.948521i | \(-0.602579\pi\) | ||||
−0.316713 | + | 0.948521i | \(0.602579\pi\) | |||||||
\(978\) | −1.17157 | −0.0374628 | ||||||||
\(979\) | 62.9117 | 2.01067 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 15.4142 | 0.492138 | ||||||||
\(982\) | −26.6274 | −0.849715 | ||||||||
\(983\) | 20.4853 | 0.653379 | 0.326690 | − | 0.945132i | \(-0.394067\pi\) | ||||
0.326690 | + | 0.945132i | \(0.394067\pi\) | |||||||
\(984\) | −1.17157 | −0.0373484 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −8.97056 | −0.285681 | ||||||||
\(987\) | 9.65685 | 0.307381 | ||||||||
\(988\) | 10.8284 | 0.344498 | ||||||||
\(989\) | −1.75736 | −0.0558808 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 51.9411 | 1.64996 | 0.824982 | − | 0.565159i | \(-0.191185\pi\) | ||||
0.824982 | + | 0.565159i | \(0.191185\pi\) | |||||||
\(992\) | −6.00000 | −0.190500 | ||||||||
\(993\) | 3.51472 | 0.111536 | ||||||||
\(994\) | −11.3137 | −0.358849 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −1.41421 | −0.0448111 | ||||||||
\(997\) | 46.9706 | 1.48757 | 0.743786 | − | 0.668417i | \(-0.233028\pi\) | ||||
0.743786 | + | 0.668417i | \(0.233028\pi\) | |||||||
\(998\) | −13.4558 | −0.425937 | ||||||||
\(999\) | 3.41421 | 0.108021 |
(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 | 3450.2.a.bg.1.2 | 2 | ||
5.2 | odd | 4 | 690.2.d.b.139.2 | ✓ | 4 | ||
5.3 | odd | 4 | 690.2.d.b.139.4 | yes | 4 | ||
5.4 | even | 2 | 3450.2.a.bk.1.2 | 2 | |||
15.2 | even | 4 | 2070.2.d.a.829.3 | 4 | |||
15.8 | even | 4 | 2070.2.d.a.829.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
690.2.d.b.139.2 | ✓ | 4 | 5.2 | odd | 4 | ||
690.2.d.b.139.4 | yes | 4 | 5.3 | odd | 4 | ||
2070.2.d.a.829.1 | 4 | 15.8 | even | 4 | |||
2070.2.d.a.829.3 | 4 | 15.2 | even | 4 | |||
3450.2.a.bg.1.2 | 2 | 1.1 | even | 1 | trivial | ||
3450.2.a.bk.1.2 | 2 | 5.4 | even | 2 |