Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3150,2,Mod(251,3150)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3150, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3150.251");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3150 = 2 \cdot 3^{2} \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3150.b (of order \(2\), degree \(1\), 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: | \(25.1528766367\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.40960000.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 7x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{17}]\) |
Coefficient ring index: | \( 2^{6} \) |
Twist minimal: | no (minimal twist has level 630) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 251.6 | ||
Root | \(1.14412 + 1.14412i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3150.251 |
Dual form | 3150.2.b.b.251.1 |
$q$-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 \(\left(\mathbb{Z}/3150\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(451\) | \(2801\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000i | 0.707107i | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.41421 | + | 2.23607i | −0.534522 | + | 0.845154i | ||||
\(8\) | − | 1.00000i | − | 0.353553i | ||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 5.65685i | 1.70561i | 0.522233 | + | 0.852803i | \(0.325099\pi\) | ||||
−0.522233 | + | 0.852803i | \(0.674901\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.47214i | 1.24035i | 0.784465 | + | 0.620174i | \(0.212938\pi\) | ||||
−0.784465 | + | 0.620174i | \(0.787062\pi\) | |||||||
\(14\) | −2.23607 | − | 1.41421i | −0.597614 | − | 0.377964i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 3.16228 | 0.766965 | 0.383482 | − | 0.923548i | \(-0.374725\pi\) | ||||
0.383482 | + | 0.923548i | \(0.374725\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.16228i | 0.725476i | 0.931891 | + | 0.362738i | \(0.118158\pi\) | ||||
−0.931891 | + | 0.362738i | \(0.881842\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −5.65685 | −1.20605 | ||||||||
\(23\) | 4.00000i | 0.834058i | 0.908893 | + | 0.417029i | \(0.136929\pi\) | ||||
−0.908893 | + | 0.417029i | \(0.863071\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −4.47214 | −0.877058 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 1.41421 | − | 2.23607i | 0.267261 | − | 0.422577i | ||||
\(29\) | − | 2.82843i | − | 0.525226i | −0.964901 | − | 0.262613i | \(-0.915416\pi\) | ||
0.964901 | − | 0.262613i | \(-0.0845842\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 6.32456i | − | 1.13592i | −0.823055 | − | 0.567962i | \(-0.807732\pi\) | ||
0.823055 | − | 0.567962i | \(-0.192268\pi\) | |||||||
\(32\) | 1.00000i | 0.176777i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 3.16228i | 0.542326i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 9.89949 | 1.62747 | 0.813733 | − | 0.581238i | \(-0.197432\pi\) | ||||
0.813733 | + | 0.581238i | \(0.197432\pi\) | |||||||
\(38\) | −3.16228 | −0.512989 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 4.47214 | 0.698430 | 0.349215 | − | 0.937043i | \(-0.386448\pi\) | ||||
0.349215 | + | 0.937043i | \(0.386448\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.41421 | −0.215666 | −0.107833 | − | 0.994169i | \(-0.534391\pi\) | ||||
−0.107833 | + | 0.994169i | \(0.534391\pi\) | |||||||
\(44\) | − | 5.65685i | − | 0.852803i | ||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −4.00000 | −0.589768 | ||||||||
\(47\) | −9.48683 | −1.38380 | −0.691898 | − | 0.721995i | \(-0.743225\pi\) | ||||
−0.691898 | + | 0.721995i | \(0.743225\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −3.00000 | − | 6.32456i | −0.428571 | − | 0.903508i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | − | 4.47214i | − | 0.620174i | ||||||
\(53\) | 4.00000i | 0.549442i | 0.961524 | + | 0.274721i | \(0.0885855\pi\) | ||||
−0.961524 | + | 0.274721i | \(0.911414\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 2.23607 | + | 1.41421i | 0.298807 | + | 0.188982i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 2.82843 | 0.371391 | ||||||||
\(59\) | −4.47214 | −0.582223 | −0.291111 | − | 0.956689i | \(-0.594025\pi\) | ||||
−0.291111 | + | 0.956689i | \(0.594025\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 9.48683i | − | 1.21466i | −0.794448 | − | 0.607332i | \(-0.792240\pi\) | ||
0.794448 | − | 0.607332i | \(-0.207760\pi\) | |||||||
\(62\) | 6.32456 | 0.803219 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 7.07107 | 0.863868 | 0.431934 | − | 0.901905i | \(-0.357831\pi\) | ||||
0.431934 | + | 0.901905i | \(0.357831\pi\) | |||||||
\(68\) | −3.16228 | −0.383482 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.41421i | 0.167836i | 0.996473 | + | 0.0839181i | \(0.0267434\pi\) | ||||
−0.996473 | + | 0.0839181i | \(0.973257\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 13.4164i | 1.57027i | 0.619324 | + | 0.785136i | \(0.287407\pi\) | ||||
−0.619324 | + | 0.785136i | \(0.712593\pi\) | |||||||
\(74\) | 9.89949i | 1.15079i | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | − | 3.16228i | − | 0.362738i | ||||||
\(77\) | −12.6491 | − | 8.00000i | −1.44150 | − | 0.911685i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −6.00000 | −0.675053 | −0.337526 | − | 0.941316i | \(-0.609590\pi\) | ||||
−0.337526 | + | 0.941316i | \(0.609590\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 4.47214i | 0.493865i | ||||||||
\(83\) | −12.6491 | −1.38842 | −0.694210 | − | 0.719772i | \(-0.744246\pi\) | ||||
−0.694210 | + | 0.719772i | \(0.744246\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | − | 1.41421i | − | 0.152499i | ||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 5.65685 | 0.603023 | ||||||||
\(89\) | 4.47214 | 0.474045 | 0.237023 | − | 0.971504i | \(-0.423828\pi\) | ||||
0.237023 | + | 0.971504i | \(0.423828\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −10.0000 | − | 6.32456i | −1.04828 | − | 0.662994i | ||||
\(92\) | − | 4.00000i | − | 0.417029i | ||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | − | 9.48683i | − | 0.978492i | ||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(98\) | 6.32456 | − | 3.00000i | 0.638877 | − | 0.303046i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −17.8885 | −1.77998 | −0.889988 | − | 0.455983i | \(-0.849288\pi\) | ||||
−0.889988 | + | 0.455983i | \(0.849288\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 8.94427i | − | 0.881305i | −0.897678 | − | 0.440653i | \(-0.854747\pi\) | ||
0.897678 | − | 0.440653i | \(-0.145253\pi\) | |||||||
\(104\) | 4.47214 | 0.438529 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −4.00000 | −0.388514 | ||||||||
\(107\) | 18.0000i | 1.74013i | 0.492941 | + | 0.870063i | \(0.335922\pi\) | ||||
−0.492941 | + | 0.870063i | \(0.664078\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 10.0000 | 0.957826 | 0.478913 | − | 0.877862i | \(-0.341031\pi\) | ||||
0.478913 | + | 0.877862i | \(0.341031\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −1.41421 | + | 2.23607i | −0.133631 | + | 0.211289i | ||||
\(113\) | 6.00000i | 0.564433i | 0.959351 | + | 0.282216i | \(0.0910696\pi\) | ||||
−0.959351 | + | 0.282216i | \(0.908930\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 2.82843i | 0.262613i | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | − | 4.47214i | − | 0.411693i | ||||||
\(119\) | −4.47214 | + | 7.07107i | −0.409960 | + | 0.648204i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −21.0000 | −1.90909 | ||||||||
\(122\) | 9.48683 | 0.858898 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 6.32456i | 0.567962i | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −14.1421 | −1.25491 | −0.627456 | − | 0.778652i | \(-0.715904\pi\) | ||||
−0.627456 | + | 0.778652i | \(0.715904\pi\) | |||||||
\(128\) | − | 1.00000i | − | 0.0883883i | ||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −17.8885 | −1.56293 | −0.781465 | − | 0.623949i | \(-0.785527\pi\) | ||||
−0.781465 | + | 0.623949i | \(0.785527\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −7.07107 | − | 4.47214i | −0.613139 | − | 0.387783i | ||||
\(134\) | 7.07107i | 0.610847i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | − | 3.16228i | − | 0.271163i | ||||||
\(137\) | 2.00000i | 0.170872i | 0.996344 | + | 0.0854358i | \(0.0272282\pi\) | ||||
−0.996344 | + | 0.0854358i | \(0.972772\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 15.8114i | − | 1.34110i | −0.741862 | − | 0.670552i | \(-0.766057\pi\) | ||
0.741862 | − | 0.670552i | \(-0.233943\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −1.41421 | −0.118678 | ||||||||
\(143\) | −25.2982 | −2.11554 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −13.4164 | −1.11035 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −9.89949 | −0.813733 | ||||||||
\(149\) | 16.9706i | 1.39028i | 0.718873 | + | 0.695141i | \(0.244658\pi\) | ||||
−0.718873 | + | 0.695141i | \(0.755342\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 10.0000 | 0.813788 | 0.406894 | − | 0.913475i | \(-0.366612\pi\) | ||||
0.406894 | + | 0.913475i | \(0.366612\pi\) | |||||||
\(152\) | 3.16228 | 0.256495 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 8.00000 | − | 12.6491i | 0.644658 | − | 1.01929i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 4.47214i | − | 0.356915i | −0.983948 | − | 0.178458i | \(-0.942889\pi\) | ||
0.983948 | − | 0.178458i | \(-0.0571108\pi\) | |||||||
\(158\) | − | 6.00000i | − | 0.477334i | ||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −8.94427 | − | 5.65685i | −0.704907 | − | 0.445823i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 21.2132 | 1.66155 | 0.830773 | − | 0.556611i | \(-0.187899\pi\) | ||||
0.830773 | + | 0.556611i | \(0.187899\pi\) | |||||||
\(164\) | −4.47214 | −0.349215 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | − | 12.6491i | − | 0.981761i | ||||||
\(167\) | −9.48683 | −0.734113 | −0.367057 | − | 0.930199i | \(-0.619634\pi\) | ||||
−0.367057 | + | 0.930199i | \(0.619634\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −7.00000 | −0.538462 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 1.41421 | 0.107833 | ||||||||
\(173\) | 25.2982 | 1.92339 | 0.961694 | − | 0.274125i | \(-0.0883882\pi\) | ||||
0.961694 | + | 0.274125i | \(0.0883882\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 5.65685i | 0.426401i | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 4.47214i | 0.335201i | ||||||||
\(179\) | − | 2.82843i | − | 0.211407i | −0.994398 | − | 0.105703i | \(-0.966291\pi\) | ||
0.994398 | − | 0.105703i | \(-0.0337094\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3.16228i | 0.235050i | 0.993070 | + | 0.117525i | \(0.0374961\pi\) | ||||
−0.993070 | + | 0.117525i | \(0.962504\pi\) | |||||||
\(182\) | 6.32456 | − | 10.0000i | 0.468807 | − | 0.741249i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 4.00000 | 0.294884 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 17.8885i | 1.30814i | ||||||||
\(188\) | 9.48683 | 0.691898 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 1.41421i | − | 0.102329i | −0.998690 | − | 0.0511645i | \(-0.983707\pi\) | ||
0.998690 | − | 0.0511645i | \(-0.0162933\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 8.48528 | 0.610784 | 0.305392 | − | 0.952227i | \(-0.401213\pi\) | ||||
0.305392 | + | 0.952227i | \(0.401213\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 3.00000 | + | 6.32456i | 0.214286 | + | 0.451754i | ||||
\(197\) | 12.0000i | 0.854965i | 0.904024 | + | 0.427482i | \(0.140599\pi\) | ||||
−0.904024 | + | 0.427482i | \(0.859401\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | − | 17.8885i | − | 1.25863i | ||||||
\(203\) | 6.32456 | + | 4.00000i | 0.443897 | + | 0.280745i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 8.94427 | 0.623177 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 4.47214i | 0.310087i | ||||||||
\(209\) | −17.8885 | −1.23738 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −20.0000 | −1.37686 | −0.688428 | − | 0.725304i | \(-0.741699\pi\) | ||||
−0.688428 | + | 0.725304i | \(0.741699\pi\) | |||||||
\(212\) | − | 4.00000i | − | 0.274721i | ||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −18.0000 | −1.23045 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 14.1421 | + | 8.94427i | 0.960031 | + | 0.607177i | ||||
\(218\) | 10.0000i | 0.677285i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 14.1421i | 0.951303i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 8.94427i | 0.598953i | 0.954104 | + | 0.299476i | \(0.0968120\pi\) | ||||
−0.954104 | + | 0.299476i | \(0.903188\pi\) | |||||||
\(224\) | −2.23607 | − | 1.41421i | −0.149404 | − | 0.0944911i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −6.00000 | −0.399114 | ||||||||
\(227\) | 18.9737 | 1.25933 | 0.629663 | − | 0.776868i | \(-0.283193\pi\) | ||||
0.629663 | + | 0.776868i | \(0.283193\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 15.8114i | − | 1.04485i | −0.852686 | − | 0.522423i | \(-0.825028\pi\) | ||
0.852686 | − | 0.522423i | \(-0.174972\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −2.82843 | −0.185695 | ||||||||
\(233\) | − | 14.0000i | − | 0.917170i | −0.888650 | − | 0.458585i | \(-0.848356\pi\) | ||
0.888650 | − | 0.458585i | \(-0.151644\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 4.47214 | 0.291111 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −7.07107 | − | 4.47214i | −0.458349 | − | 0.289886i | ||||
\(239\) | − | 4.24264i | − | 0.274434i | −0.990541 | − | 0.137217i | \(-0.956184\pi\) | ||
0.990541 | − | 0.137217i | \(-0.0438157\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 25.2982i | − | 1.62960i | −0.579741 | − | 0.814801i | \(-0.696846\pi\) | ||
0.579741 | − | 0.814801i | \(-0.303154\pi\) | |||||||
\(242\) | − | 21.0000i | − | 1.34993i | ||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 9.48683i | 0.607332i | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −14.1421 | −0.899843 | ||||||||
\(248\) | −6.32456 | −0.401610 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −22.6274 | −1.42257 | ||||||||
\(254\) | − | 14.1421i | − | 0.887357i | ||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −15.8114 | −0.986287 | −0.493144 | − | 0.869948i | \(-0.664152\pi\) | ||||
−0.493144 | + | 0.869948i | \(0.664152\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −14.0000 | + | 22.1359i | −0.869918 | + | 1.37546i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | − | 17.8885i | − | 1.10516i | ||||||
\(263\) | − | 16.0000i | − | 0.986602i | −0.869859 | − | 0.493301i | \(-0.835790\pi\) | ||
0.869859 | − | 0.493301i | \(-0.164210\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 4.47214 | − | 7.07107i | 0.274204 | − | 0.433555i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −7.07107 | −0.431934 | ||||||||
\(269\) | 17.8885 | 1.09068 | 0.545342 | − | 0.838214i | \(-0.316400\pi\) | ||||
0.545342 | + | 0.838214i | \(0.316400\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 6.32456i | − | 0.384189i | −0.981376 | − | 0.192095i | \(-0.938472\pi\) | ||
0.981376 | − | 0.192095i | \(-0.0615281\pi\) | |||||||
\(272\) | 3.16228 | 0.191741 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −2.00000 | −0.120824 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 21.2132 | 1.27458 | 0.637289 | − | 0.770625i | \(-0.280056\pi\) | ||||
0.637289 | + | 0.770625i | \(0.280056\pi\) | |||||||
\(278\) | 15.8114 | 0.948304 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 12.7279i | 0.759284i | 0.925133 | + | 0.379642i | \(0.123953\pi\) | ||||
−0.925133 | + | 0.379642i | \(0.876047\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(284\) | − | 1.41421i | − | 0.0839181i | ||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | − | 25.2982i | − | 1.49592i | ||||||
\(287\) | −6.32456 | + | 10.0000i | −0.373327 | + | 0.590281i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −7.00000 | −0.411765 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | − | 13.4164i | − | 0.785136i | ||||||
\(293\) | 6.32456 | 0.369484 | 0.184742 | − | 0.982787i | \(-0.440855\pi\) | ||||
0.184742 | + | 0.982787i | \(0.440855\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | − | 9.89949i | − | 0.575396i | ||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −16.9706 | −0.983078 | ||||||||
\(299\) | −17.8885 | −1.03452 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.00000 | − | 3.16228i | 0.115278 | − | 0.182271i | ||||
\(302\) | 10.0000i | 0.575435i | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 3.16228i | 0.181369i | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 26.8328i | 1.53143i | 0.643180 | + | 0.765715i | \(0.277615\pi\) | ||||
−0.643180 | + | 0.765715i | \(0.722385\pi\) | |||||||
\(308\) | 12.6491 | + | 8.00000i | 0.720750 | + | 0.455842i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 8.94427 | 0.507183 | 0.253592 | − | 0.967311i | \(-0.418388\pi\) | ||||
0.253592 | + | 0.967311i | \(0.418388\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 13.4164i | − | 0.758340i | −0.925327 | − | 0.379170i | \(-0.876210\pi\) | ||
0.925327 | − | 0.379170i | \(-0.123790\pi\) | |||||||
\(314\) | 4.47214 | 0.252377 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 6.00000 | 0.337526 | ||||||||
\(317\) | − | 18.0000i | − | 1.01098i | −0.862832 | − | 0.505490i | \(-0.831312\pi\) | ||
0.862832 | − | 0.505490i | \(-0.168688\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 16.0000 | 0.895828 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 5.65685 | − | 8.94427i | 0.315244 | − | 0.498445i | ||||
\(323\) | 10.0000i | 0.556415i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 21.2132i | 1.17489i | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | − | 4.47214i | − | 0.246932i | ||||||
\(329\) | 13.4164 | − | 21.2132i | 0.739671 | − | 1.16952i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 20.0000 | 1.09930 | 0.549650 | − | 0.835395i | \(-0.314761\pi\) | ||||
0.549650 | + | 0.835395i | \(0.314761\pi\) | |||||||
\(332\) | 12.6491 | 0.694210 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | − | 9.48683i | − | 0.519096i | ||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −25.4558 | −1.38667 | −0.693334 | − | 0.720616i | \(-0.743859\pi\) | ||||
−0.693334 | + | 0.720616i | \(0.743859\pi\) | |||||||
\(338\) | − | 7.00000i | − | 0.380750i | ||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 35.7771 | 1.93744 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 18.3848 | + | 2.23607i | 0.992685 | + | 0.120736i | ||||
\(344\) | 1.41421i | 0.0762493i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 25.2982i | 1.36004i | ||||||||
\(347\) | − | 12.0000i | − | 0.644194i | −0.946707 | − | 0.322097i | \(-0.895612\pi\) | ||
0.946707 | − | 0.322097i | \(-0.104388\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 15.8114i | − | 0.846364i | −0.906045 | − | 0.423182i | \(-0.860913\pi\) | ||
0.906045 | − | 0.423182i | \(-0.139087\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −5.65685 | −0.301511 | ||||||||
\(353\) | −3.16228 | −0.168311 | −0.0841555 | − | 0.996453i | \(-0.526819\pi\) | ||||
−0.0841555 | + | 0.996453i | \(0.526819\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −4.47214 | −0.237023 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 2.82843 | 0.149487 | ||||||||
\(359\) | − | 18.3848i | − | 0.970311i | −0.874428 | − | 0.485156i | \(-0.838763\pi\) | ||
0.874428 | − | 0.485156i | \(-0.161237\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 9.00000 | 0.473684 | ||||||||
\(362\) | −3.16228 | −0.166206 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 10.0000 | + | 6.32456i | 0.524142 | + | 0.331497i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 13.4164i | − | 0.700331i | −0.936688 | − | 0.350165i | \(-0.886125\pi\) | ||
0.936688 | − | 0.350165i | \(-0.113875\pi\) | |||||||
\(368\) | 4.00000i | 0.208514i | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −8.94427 | − | 5.65685i | −0.464363 | − | 0.293689i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −21.2132 | −1.09838 | −0.549189 | − | 0.835698i | \(-0.685063\pi\) | ||||
−0.549189 | + | 0.835698i | \(0.685063\pi\) | |||||||
\(374\) | −17.8885 | −0.924995 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 9.48683i | 0.489246i | ||||||||
\(377\) | 12.6491 | 0.651462 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 1.41421 | 0.0723575 | ||||||||
\(383\) | −9.48683 | −0.484755 | −0.242377 | − | 0.970182i | \(-0.577927\pi\) | ||||
−0.242377 | + | 0.970182i | \(0.577927\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 8.48528i | 0.431889i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 16.9706i | 0.860442i | 0.902724 | + | 0.430221i | \(0.141564\pi\) | ||||
−0.902724 | + | 0.430221i | \(0.858436\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 12.6491i | 0.639693i | ||||||||
\(392\) | −6.32456 | + | 3.00000i | −0.319438 | + | 0.151523i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −12.0000 | −0.604551 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 4.47214i | 0.224450i | 0.993683 | + | 0.112225i | \(0.0357978\pi\) | ||||
−0.993683 | + | 0.112225i | \(0.964202\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 1.41421i | − | 0.0706225i | −0.999376 | − | 0.0353112i | \(-0.988758\pi\) | ||
0.999376 | − | 0.0353112i | \(-0.0112422\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 28.2843 | 1.40894 | ||||||||
\(404\) | 17.8885 | 0.889988 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −4.00000 | + | 6.32456i | −0.198517 | + | 0.313882i | ||||
\(407\) | 56.0000i | 2.77582i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 37.9473i | 1.87637i | 0.346128 | + | 0.938187i | \(0.387496\pi\) | ||||
−0.346128 | + | 0.938187i | \(0.612504\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 8.94427i | 0.440653i | ||||||||
\(413\) | 6.32456 | − | 10.0000i | 0.311211 | − | 0.492068i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −4.47214 | −0.219265 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | − | 17.8885i | − | 0.874957i | ||||||
\(419\) | −13.4164 | −0.655434 | −0.327717 | − | 0.944776i | \(-0.606279\pi\) | ||||
−0.327717 | + | 0.944776i | \(0.606279\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 38.0000 | 1.85201 | 0.926003 | − | 0.377515i | \(-0.123221\pi\) | ||||
0.926003 | + | 0.377515i | \(0.123221\pi\) | |||||||
\(422\) | − | 20.0000i | − | 0.973585i | ||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 4.00000 | 0.194257 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 21.2132 | + | 13.4164i | 1.02658 | + | 0.649265i | ||||
\(428\) | − | 18.0000i | − | 0.870063i | ||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 15.5563i | 0.749323i | 0.927162 | + | 0.374661i | \(0.122241\pi\) | ||||
−0.927162 | + | 0.374661i | \(0.877759\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 26.8328i | − | 1.28950i | −0.764392 | − | 0.644751i | \(-0.776961\pi\) | ||
0.764392 | − | 0.644751i | \(-0.223039\pi\) | |||||||
\(434\) | −8.94427 | + | 14.1421i | −0.429339 | + | 0.678844i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −10.0000 | −0.478913 | ||||||||
\(437\) | −12.6491 | −0.605089 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 6.32456i | 0.301855i | 0.988545 | + | 0.150927i | \(0.0482259\pi\) | ||||
−0.988545 | + | 0.150927i | \(0.951774\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −14.1421 | −0.672673 | ||||||||
\(443\) | − | 4.00000i | − | 0.190046i | −0.995475 | − | 0.0950229i | \(-0.969708\pi\) | ||
0.995475 | − | 0.0950229i | \(-0.0302924\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −8.94427 | −0.423524 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 1.41421 | − | 2.23607i | 0.0668153 | − | 0.105644i | ||||
\(449\) | − | 9.89949i | − | 0.467186i | −0.972334 | − | 0.233593i | \(-0.924952\pi\) | ||
0.972334 | − | 0.233593i | \(-0.0750483\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 25.2982i | 1.19125i | ||||||||
\(452\) | − | 6.00000i | − | 0.282216i | ||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 18.9737i | 0.890478i | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −16.9706 | −0.793849 | −0.396925 | − | 0.917851i | \(-0.629923\pi\) | ||||
−0.396925 | + | 0.917851i | \(0.629923\pi\) | |||||||
\(458\) | 15.8114 | 0.738818 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −8.94427 | −0.416576 | −0.208288 | − | 0.978068i | \(-0.566789\pi\) | ||||
−0.208288 | + | 0.978068i | \(0.566789\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(464\) | − | 2.82843i | − | 0.131306i | ||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 14.0000 | 0.648537 | ||||||||
\(467\) | −12.6491 | −0.585331 | −0.292666 | − | 0.956215i | \(-0.594542\pi\) | ||||
−0.292666 | + | 0.956215i | \(0.594542\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −10.0000 | + | 15.8114i | −0.461757 | + | 0.730102i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 4.47214i | 0.205847i | ||||||||
\(473\) | − | 8.00000i | − | 0.367840i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 4.47214 | − | 7.07107i | 0.204980 | − | 0.324102i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 4.24264 | 0.194054 | ||||||||
\(479\) | 17.8885 | 0.817348 | 0.408674 | − | 0.912680i | \(-0.365991\pi\) | ||||
0.408674 | + | 0.912680i | \(0.365991\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 44.2719i | 2.01862i | ||||||||
\(482\) | 25.2982 | 1.15230 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 21.0000 | 0.954545 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 25.4558 | 1.15351 | 0.576757 | − | 0.816916i | \(-0.304318\pi\) | ||||
0.576757 | + | 0.816916i | \(0.304318\pi\) | |||||||
\(488\) | −9.48683 | −0.429449 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 19.7990i | − | 0.893516i | −0.894655 | − | 0.446758i | \(-0.852579\pi\) | ||
0.894655 | − | 0.446758i | \(-0.147421\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 8.94427i | − | 0.402830i | ||||||
\(494\) | − | 14.1421i | − | 0.636285i | ||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | − | 6.32456i | − | 0.283981i | ||||||
\(497\) | −3.16228 | − | 2.00000i | −0.141848 | − | 0.0897123i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 20.0000 | 0.895323 | 0.447661 | − | 0.894203i | \(-0.352257\pi\) | ||||
0.447661 | + | 0.894203i | \(0.352257\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −9.48683 | −0.422997 | −0.211498 | − | 0.977378i | \(-0.567834\pi\) | ||||
−0.211498 | + | 0.977378i | \(0.567834\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | − | 22.6274i | − | 1.00591i | ||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 14.1421 | 0.627456 | ||||||||
\(509\) | −13.4164 | −0.594672 | −0.297336 | − | 0.954773i | \(-0.596098\pi\) | ||||
−0.297336 | + | 0.954773i | \(0.596098\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −30.0000 | − | 18.9737i | −1.32712 | − | 0.839346i | ||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | − | 15.8114i | − | 0.697410i | ||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 53.6656i | − | 2.36021i | ||||||
\(518\) | −22.1359 | − | 14.0000i | −0.972598 | − | 0.615125i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 13.4164 | 0.587784 | 0.293892 | − | 0.955839i | \(-0.405049\pi\) | ||||
0.293892 | + | 0.955839i | \(0.405049\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 17.8885i | 0.782211i | 0.920346 | + | 0.391106i | \(0.127907\pi\) | ||||
−0.920346 | + | 0.391106i | \(0.872093\pi\) | |||||||
\(524\) | 17.8885 | 0.781465 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 16.0000 | 0.697633 | ||||||||
\(527\) | − | 20.0000i | − | 0.871214i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 7.00000 | 0.304348 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 7.07107 | + | 4.47214i | 0.306570 | + | 0.193892i | ||||
\(533\) | 20.0000i | 0.866296i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | − | 7.07107i | − | 0.305424i | ||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 17.8885i | 0.771230i | ||||||||
\(539\) | 35.7771 | − | 16.9706i | 1.54103 | − | 0.730974i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −22.0000 | −0.945854 | −0.472927 | − | 0.881102i | \(-0.656803\pi\) | ||||
−0.472927 | + | 0.881102i | \(0.656803\pi\) | |||||||
\(542\) | 6.32456 | 0.271663 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 3.16228i | 0.135582i | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −21.2132 | −0.907011 | −0.453506 | − | 0.891253i | \(-0.649827\pi\) | ||||
−0.453506 | + | 0.891253i | \(0.649827\pi\) | |||||||
\(548\) | − | 2.00000i | − | 0.0854358i | ||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 8.94427 | 0.381039 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 8.48528 | − | 13.4164i | 0.360831 | − | 0.570524i | ||||
\(554\) | 21.2132i | 0.901263i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 15.8114i | 0.670552i | ||||||||
\(557\) | − | 38.0000i | − | 1.61011i | −0.593199 | − | 0.805056i | \(-0.702135\pi\) | ||
0.593199 | − | 0.805056i | \(-0.297865\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 6.32456i | − | 0.267500i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −12.7279 | −0.536895 | ||||||||
\(563\) | 18.9737 | 0.799645 | 0.399822 | − | 0.916593i | \(-0.369072\pi\) | ||||
0.399822 | + | 0.916593i | \(0.369072\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 1.41421 | 0.0593391 | ||||||||
\(569\) | 24.0416i | 1.00788i | 0.863739 | + | 0.503939i | \(0.168116\pi\) | ||||
−0.863739 | + | 0.503939i | \(0.831884\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 28.0000 | 1.17176 | 0.585882 | − | 0.810397i | \(-0.300748\pi\) | ||||
0.585882 | + | 0.810397i | \(0.300748\pi\) | |||||||
\(572\) | 25.2982 | 1.05777 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −10.0000 | − | 6.32456i | −0.417392 | − | 0.263982i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 22.3607i | 0.930887i | 0.885078 | + | 0.465444i | \(0.154105\pi\) | ||||
−0.885078 | + | 0.465444i | \(0.845895\pi\) | |||||||
\(578\) | − | 7.00000i | − | 0.291162i | ||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 17.8885 | − | 28.2843i | 0.742142 | − | 1.17343i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −22.6274 | −0.937132 | ||||||||
\(584\) | 13.4164 | 0.555175 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 6.32456i | 0.261265i | ||||||||
\(587\) | −31.6228 | −1.30521 | −0.652606 | − | 0.757698i | \(-0.726324\pi\) | ||||
−0.652606 | + | 0.757698i | \(0.726324\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 20.0000 | 0.824086 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 9.89949 | 0.406867 | ||||||||
\(593\) | −9.48683 | −0.389578 | −0.194789 | − | 0.980845i | \(-0.562402\pi\) | ||||
−0.194789 | + | 0.980845i | \(0.562402\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | − | 16.9706i | − | 0.695141i | ||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | − | 17.8885i | − | 0.731517i | ||||||
\(599\) | 32.5269i | 1.32901i | 0.747282 | + | 0.664507i | \(0.231358\pi\) | ||||
−0.747282 | + | 0.664507i | \(0.768642\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 25.2982i | 1.03194i | 0.856608 | + | 0.515968i | \(0.172568\pi\) | ||||
−0.856608 | + | 0.515968i | \(0.827432\pi\) | |||||||
\(602\) | 3.16228 | + | 2.00000i | 0.128885 | + | 0.0815139i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −10.0000 | −0.406894 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 8.94427i | − | 0.363037i | −0.983388 | − | 0.181518i | \(-0.941899\pi\) | ||
0.983388 | − | 0.181518i | \(-0.0581012\pi\) | |||||||
\(608\) | −3.16228 | −0.128247 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 42.4264i | − | 1.71639i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −35.3553 | −1.42799 | −0.713994 | − | 0.700151i | \(-0.753116\pi\) | ||||
−0.713994 | + | 0.700151i | \(0.753116\pi\) | |||||||
\(614\) | −26.8328 | −1.08288 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −8.00000 | + | 12.6491i | −0.322329 | + | 0.509647i | ||||
\(617\) | 38.0000i | 1.52982i | 0.644136 | + | 0.764911i | \(0.277217\pi\) | ||||
−0.644136 | + | 0.764911i | \(0.722783\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 28.4605i | − | 1.14392i | −0.820280 | − | 0.571962i | \(-0.806182\pi\) | ||
0.820280 | − | 0.571962i | \(-0.193818\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 8.94427i | 0.358633i | ||||||||
\(623\) | −6.32456 | + | 10.0000i | −0.253388 | + | 0.400642i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 13.4164 | 0.536228 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 4.47214i | 0.178458i | ||||||||
\(629\) | 31.3050 | 1.24821 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −8.00000 | −0.318475 | −0.159237 | − | 0.987240i | \(-0.550904\pi\) | ||||
−0.159237 | + | 0.987240i | \(0.550904\pi\) | |||||||
\(632\) | 6.00000i | 0.238667i | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 18.0000 | 0.714871 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 28.2843 | − | 13.4164i | 1.12066 | − | 0.531577i | ||||
\(638\) | 16.0000i | 0.633446i | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1.41421i | 0.0558581i | 0.999610 | + | 0.0279290i | \(0.00889125\pi\) | ||||
−0.999610 | + | 0.0279290i | \(0.991109\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 44.7214i | 1.76364i | 0.471588 | + | 0.881819i | \(0.343681\pi\) | ||||
−0.471588 | + | 0.881819i | \(0.656319\pi\) | |||||||
\(644\) | 8.94427 | + | 5.65685i | 0.352454 | + | 0.222911i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −10.0000 | −0.393445 | ||||||||
\(647\) | −34.7851 | −1.36754 | −0.683771 | − | 0.729697i | \(-0.739661\pi\) | ||||
−0.683771 | + | 0.729697i | \(0.739661\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 25.2982i | − | 0.993042i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −21.2132 | −0.830773 | ||||||||
\(653\) | 14.0000i | 0.547862i | 0.961749 | + | 0.273931i | \(0.0883240\pi\) | ||||
−0.961749 | + | 0.273931i | \(0.911676\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 4.47214 | 0.174608 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 21.2132 | + | 13.4164i | 0.826977 | + | 0.523026i | ||||
\(659\) | 16.9706i | 0.661079i | 0.943792 | + | 0.330540i | \(0.107231\pi\) | ||||
−0.943792 | + | 0.330540i | \(0.892769\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 3.16228i | − | 0.122998i | −0.998107 | − | 0.0614992i | \(-0.980412\pi\) | ||
0.998107 | − | 0.0614992i | \(-0.0195882\pi\) | |||||||
\(662\) | 20.0000i | 0.777322i | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 12.6491i | 0.490881i | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 11.3137 | 0.438069 | ||||||||
\(668\) | 9.48683 | 0.367057 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 53.6656 | 2.07174 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −19.7990 | −0.763195 | −0.381597 | − | 0.924329i | \(-0.624626\pi\) | ||||
−0.381597 | + | 0.924329i | \(0.624626\pi\) | |||||||
\(674\) | − | 25.4558i | − | 0.980522i | ||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 7.00000 | 0.269231 | ||||||||
\(677\) | 37.9473 | 1.45843 | 0.729217 | − | 0.684282i | \(-0.239884\pi\) | ||||
0.729217 | + | 0.684282i | \(0.239884\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 35.7771i | 1.36998i | ||||||||
\(683\) | 14.0000i | 0.535695i | 0.963461 | + | 0.267848i | \(0.0863124\pi\) | ||||
−0.963461 | + | 0.267848i | \(0.913688\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −2.23607 | + | 18.3848i | −0.0853735 | + | 0.701934i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −1.41421 | −0.0539164 | ||||||||
\(689\) | −17.8885 | −0.681499 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 28.4605i | 1.08269i | 0.840801 | + | 0.541344i | \(0.182084\pi\) | ||||
−0.840801 | + | 0.541344i | \(0.817916\pi\) | |||||||
\(692\) | −25.2982 | −0.961694 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 12.0000 | 0.455514 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 14.1421 | 0.535672 | ||||||||
\(698\) | 15.8114 | 0.598470 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 19.7990i | − | 0.747798i | −0.927470 | − | 0.373899i | \(-0.878021\pi\) | ||
0.927470 | − | 0.373899i | \(-0.121979\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 31.3050i | 1.18069i | ||||||||
\(704\) | − | 5.65685i | − | 0.213201i | ||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | − | 3.16228i | − | 0.119014i | ||||||
\(707\) | 25.2982 | − | 40.0000i | 0.951438 | − | 1.50435i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 30.0000 | 1.12667 | 0.563337 | − | 0.826227i | \(-0.309517\pi\) | ||||
0.563337 | + | 0.826227i | \(0.309517\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | − | 4.47214i | − | 0.167600i | ||||||
\(713\) | 25.2982 | 0.947426 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 2.82843i | 0.105703i | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 18.3848 | 0.686114 | ||||||||
\(719\) | 44.7214 | 1.66783 | 0.833913 | − | 0.551896i | \(-0.186096\pi\) | ||||
0.833913 | + | 0.551896i | \(0.186096\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 20.0000 | + | 12.6491i | 0.744839 | + | 0.471077i | ||||
\(722\) | 9.00000i | 0.334945i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | − | 3.16228i | − | 0.117525i | ||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 26.8328i | 0.995174i | 0.867414 | + | 0.497587i | \(0.165780\pi\) | ||||
−0.867414 | + | 0.497587i | \(0.834220\pi\) | |||||||
\(728\) | −6.32456 | + | 10.0000i | −0.234404 | + | 0.370625i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −4.47214 | −0.165408 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 40.2492i | 1.48664i | 0.668937 | + | 0.743319i | \(0.266750\pi\) | ||||
−0.668937 | + | 0.743319i | \(0.733250\pi\) | |||||||
\(734\) | 13.4164 | 0.495209 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −4.00000 | −0.147442 | ||||||||
\(737\) | 40.0000i | 1.47342i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −16.0000 | −0.588570 | −0.294285 | − | 0.955718i | \(-0.595081\pi\) | ||||
−0.294285 | + | 0.955718i | \(0.595081\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 5.65685 | − | 8.94427i | 0.207670 | − | 0.328355i | ||||
\(743\) | 36.0000i | 1.32071i | 0.750953 | + | 0.660356i | \(0.229595\pi\) | ||||
−0.750953 | + | 0.660356i | \(0.770405\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | − | 21.2132i | − | 0.776671i | ||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | − | 17.8885i | − | 0.654070i | ||||||
\(749\) | −40.2492 | − | 25.4558i | −1.47067 | − | 0.930136i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 40.0000 | 1.45962 | 0.729810 | − | 0.683650i | \(-0.239608\pi\) | ||||
0.729810 | + | 0.683650i | \(0.239608\pi\) | |||||||
\(752\) | −9.48683 | −0.345949 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 12.6491i | 0.460653i | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −32.5269 | −1.18221 | −0.591105 | − | 0.806594i | \(-0.701308\pi\) | ||||
−0.591105 | + | 0.806594i | \(0.701308\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −31.3050 | −1.13480 | −0.567402 | − | 0.823441i | \(-0.692051\pi\) | ||||
−0.567402 | + | 0.823441i | \(0.692051\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −14.1421 | + | 22.3607i | −0.511980 | + | 0.809511i | ||||
\(764\) | 1.41421i | 0.0511645i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | − | 9.48683i | − | 0.342773i | ||||||
\(767\) | − | 20.0000i | − | 0.722158i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 31.6228i | 1.14035i | 0.821524 | + | 0.570173i | \(0.193124\pi\) | ||||
−0.821524 | + | 0.570173i | \(0.806876\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −8.48528 | −0.305392 | ||||||||
\(773\) | 31.6228 | 1.13739 | 0.568696 | − | 0.822548i | \(-0.307448\pi\) | ||||
0.568696 | + | 0.822548i | \(0.307448\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −16.9706 | −0.608424 | ||||||||
\(779\) | 14.1421i | 0.506695i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −8.00000 | −0.286263 | ||||||||
\(782\) | −12.6491 | −0.452331 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −3.00000 | − | 6.32456i | −0.107143 | − | 0.225877i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 26.8328i | 0.956487i | 0.878227 | + | 0.478243i | \(0.158726\pi\) | ||||
−0.878227 | + | 0.478243i | \(0.841274\pi\) | |||||||
\(788\) | − | 12.0000i | − | 0.427482i | ||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −13.4164 | − | 8.48528i | −0.477033 | − | 0.301702i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 42.4264 | 1.50661 | ||||||||
\(794\) | −4.47214 | −0.158710 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 25.2982 | 0.896109 | 0.448054 | − | 0.894006i | \(-0.352117\pi\) | ||||
0.448054 | + | 0.894006i | \(0.352117\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −30.0000 | −1.06132 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 1.41421 | 0.0499376 | ||||||||
\(803\) | −75.8947 | −2.67826 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 28.2843i | 0.996271i | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 17.8885i | 0.629317i | ||||||||
\(809\) | − | 18.3848i | − | 0.646374i | −0.946335 | − | 0.323187i | \(-0.895246\pi\) | ||
0.946335 | − | 0.323187i | \(-0.104754\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 22.1359i | 0.777298i | 0.921386 | + | 0.388649i | \(0.127058\pi\) | ||||
−0.921386 | + | 0.388649i | \(0.872942\pi\) | |||||||
\(812\) | −6.32456 | − | 4.00000i | −0.221948 | − | 0.140372i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −56.0000 | −1.96280 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 4.47214i | − | 0.156460i | ||||||
\(818\) | −37.9473 | −1.32680 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 19.7990i | 0.690990i | 0.938421 | + | 0.345495i | \(0.112289\pi\) | ||||
−0.938421 | + | 0.345495i | \(0.887711\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 28.2843 | 0.985928 | 0.492964 | − | 0.870050i | \(-0.335913\pi\) | ||||
0.492964 | + | 0.870050i | \(0.335913\pi\) | |||||||
\(824\) | −8.94427 | −0.311588 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 10.0000 | + | 6.32456i | 0.347945 | + | 0.220059i | ||||
\(827\) | − | 12.0000i | − | 0.417281i | −0.977992 | − | 0.208640i | \(-0.933096\pi\) | ||
0.977992 | − | 0.208640i | \(-0.0669038\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 41.1096i | 1.42780i | 0.700250 | + | 0.713898i | \(0.253072\pi\) | ||||
−0.700250 | + | 0.713898i | \(0.746928\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | − | 4.47214i | − | 0.155043i | ||||||
\(833\) | −9.48683 | − | 20.0000i | −0.328699 | − | 0.692959i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 17.8885 | 0.618688 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | − | 13.4164i | − | 0.463462i | ||||||
\(839\) | −17.8885 | −0.617581 | −0.308791 | − | 0.951130i | \(-0.599924\pi\) | ||||
−0.308791 | + | 0.951130i | \(0.599924\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 21.0000 | 0.724138 | ||||||||
\(842\) | 38.0000i | 1.30957i | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 20.0000 | 0.688428 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 29.6985 | − | 46.9574i | 1.02045 | − | 1.61348i | ||||
\(848\) | 4.00000i | 0.137361i | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 39.5980i | 1.35740i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 49.1935i | − | 1.68435i | −0.539202 | − | 0.842177i | \(-0.681274\pi\) | ||
0.539202 | − | 0.842177i | \(-0.318726\pi\) | |||||||
\(854\) | −13.4164 | + | 21.2132i | −0.459100 | + | 0.725901i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 18.0000 | 0.615227 | ||||||||
\(857\) | −41.1096 | −1.40428 | −0.702139 | − | 0.712040i | \(-0.747771\pi\) | ||||
−0.702139 | + | 0.712040i | \(0.747771\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 34.7851i | 1.18685i | 0.804889 | + | 0.593425i | \(0.202225\pi\) | ||||
−0.804889 | + | 0.593425i | \(0.797775\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −15.5563 | −0.529851 | ||||||||
\(863\) | 36.0000i | 1.22545i | 0.790295 | + | 0.612727i | \(0.209928\pi\) | ||||
−0.790295 | + | 0.612727i | \(0.790072\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 26.8328 | 0.911816 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −14.1421 | − | 8.94427i | −0.480015 | − | 0.303588i | ||||
\(869\) | − | 33.9411i | − | 1.15137i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 31.6228i | 1.07150i | ||||||||
\(872\) | − | 10.0000i | − | 0.338643i | ||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | − | 12.6491i | − | 0.427863i | ||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −21.2132 | −0.716319 | −0.358159 | − | 0.933660i | \(-0.616596\pi\) | ||||
−0.358159 | + | 0.933660i | \(0.616596\pi\) | |||||||
\(878\) | −6.32456 | −0.213443 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 4.47214 | 0.150670 | 0.0753350 | − | 0.997158i | \(-0.475997\pi\) | ||||
0.0753350 | + | 0.997158i | \(0.475997\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −12.7279 | −0.428329 | −0.214164 | − | 0.976798i | \(-0.568703\pi\) | ||||
−0.214164 | + | 0.976798i | \(0.568703\pi\) | |||||||
\(884\) | − | 14.1421i | − | 0.475651i | ||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 4.00000 | 0.134383 | ||||||||
\(887\) | 9.48683 | 0.318537 | 0.159268 | − | 0.987235i | \(-0.449086\pi\) | ||||
0.159268 | + | 0.987235i | \(0.449086\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 20.0000 | − | 31.6228i | 0.670778 | − | 1.06059i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | − | 8.94427i | − | 0.299476i | ||||||
\(893\) | − | 30.0000i | − | 1.00391i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 2.23607 | + | 1.41421i | 0.0747018 | + | 0.0472456i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 9.89949 | 0.330350 | ||||||||
\(899\) | −17.8885 | −0.596616 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 12.6491i | 0.421403i | ||||||||
\(902\) | −25.2982 | −0.842339 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 6.00000 | 0.199557 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 46.6690 | 1.54962 | 0.774810 | − | 0.632194i | \(-0.217845\pi\) | ||||
0.774810 | + | 0.632194i | \(0.217845\pi\) | |||||||
\(908\) | −18.9737 | −0.629663 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 43.8406i | 1.45250i | 0.687428 | + | 0.726252i | \(0.258740\pi\) | ||||
−0.687428 | + | 0.726252i | \(0.741260\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 71.5542i | − | 2.36810i | ||||||
\(914\) | − | 16.9706i | − | 0.561336i | ||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 15.8114i | 0.522423i | ||||||||
\(917\) | 25.2982 | − | 40.0000i | 0.835421 | − | 1.32092i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 40.0000 | 1.31948 | 0.659739 | − | 0.751495i | \(-0.270667\pi\) | ||||
0.659739 | + | 0.751495i | \(0.270667\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | − | 8.94427i | − | 0.294564i | ||||||
\(923\) | −6.32456 | −0.208175 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 2.82843 | 0.0928477 | ||||||||
\(929\) | −22.3607 | −0.733630 | −0.366815 | − | 0.930294i | \(-0.619552\pi\) | ||||
−0.366815 | + | 0.930294i | \(0.619552\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 20.0000 | − | 9.48683i | 0.655474 | − | 0.310918i | ||||
\(932\) | 14.0000i | 0.458585i | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | − | 12.6491i | − | 0.413892i | ||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 53.6656i | 1.75318i | 0.481238 | + | 0.876590i | \(0.340187\pi\) | ||||
−0.481238 | + | 0.876590i | \(0.659813\pi\) | |||||||
\(938\) | −15.8114 | − | 10.0000i | −0.516260 | − | 0.326512i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −26.8328 | −0.874725 | −0.437362 | − | 0.899285i | \(-0.644087\pi\) | ||||
−0.437362 | + | 0.899285i | \(0.644087\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 17.8885i | 0.582531i | ||||||||
\(944\) | −4.47214 | −0.145556 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 8.00000 | 0.260102 | ||||||||
\(947\) | 42.0000i | 1.36482i | 0.730971 | + | 0.682408i | \(0.239067\pi\) | ||||
−0.730971 | + | 0.682408i | \(0.760933\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −60.0000 | −1.94768 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 7.07107 | + | 4.47214i | 0.229175 | + | 0.144943i | ||||
\(953\) | − | 54.0000i | − | 1.74923i | −0.484817 | − | 0.874616i | \(-0.661114\pi\) | ||
0.484817 | − | 0.874616i | \(-0.338886\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 4.24264i | 0.137217i | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 17.8885i | 0.577953i | ||||||||
\(959\) | −4.47214 | − | 2.82843i | −0.144413 | − | 0.0913347i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −9.00000 | −0.290323 | ||||||||
\(962\) | −44.2719 | −1.42738 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 25.2982i | 0.814801i | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −42.4264 | −1.36434 | −0.682171 | − | 0.731193i | \(-0.738964\pi\) | ||||
−0.682171 | + | 0.731193i | \(0.738964\pi\) | |||||||
\(968\) | 21.0000i | 0.674966i | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 35.7771 | 1.14814 | 0.574071 | − | 0.818806i | \(-0.305363\pi\) | ||||
0.574071 | + | 0.818806i | \(0.305363\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 35.3553 | + | 22.3607i | 1.13344 | + | 0.716850i | ||||
\(974\) | 25.4558i | 0.815658i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | − | 9.48683i | − | 0.303666i | ||||||
\(977\) | 18.0000i | 0.575871i | 0.957650 | + | 0.287936i | \(0.0929689\pi\) | ||||
−0.957650 | + | 0.287936i | \(0.907031\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 25.2982i | 0.808535i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 19.7990 | 0.631811 | ||||||||
\(983\) | −9.48683 | −0.302583 | −0.151291 | − | 0.988489i | \(-0.548343\pi\) | ||||
−0.151291 | + | 0.988489i | \(0.548343\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 8.94427 | 0.284844 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 14.1421 | 0.449921 | ||||||||
\(989\) | − | 5.65685i | − | 0.179878i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 40.0000 | 1.27064 | 0.635321 | − | 0.772248i | \(-0.280868\pi\) | ||||
0.635321 | + | 0.772248i | \(0.280868\pi\) | |||||||
\(992\) | 6.32456 | 0.200805 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 2.00000 | − | 3.16228i | 0.0634361 | − | 0.100301i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 13.4164i | − | 0.424902i | −0.977172 | − | 0.212451i | \(-0.931855\pi\) | ||
0.977172 | − | 0.212451i | \(-0.0681446\pi\) | |||||||
\(998\) | 20.0000i | 0.633089i | ||||||||
\(999\) | 0 | 0 |
(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 | 3150.2.b.b.251.6 | 8 | ||
3.2 | odd | 2 | inner | 3150.2.b.b.251.2 | 8 | ||
5.2 | odd | 4 | 630.2.d.b.629.3 | yes | 4 | ||
5.3 | odd | 4 | 630.2.d.c.629.4 | yes | 4 | ||
5.4 | even | 2 | inner | 3150.2.b.b.251.3 | 8 | ||
7.6 | odd | 2 | inner | 3150.2.b.b.251.5 | 8 | ||
15.2 | even | 4 | 630.2.d.c.629.1 | yes | 4 | ||
15.8 | even | 4 | 630.2.d.b.629.2 | yes | 4 | ||
15.14 | odd | 2 | inner | 3150.2.b.b.251.7 | 8 | ||
20.3 | even | 4 | 5040.2.k.c.1889.3 | 4 | |||
20.7 | even | 4 | 5040.2.k.b.1889.4 | 4 | |||
21.20 | even | 2 | inner | 3150.2.b.b.251.1 | 8 | ||
35.13 | even | 4 | 630.2.d.c.629.2 | yes | 4 | ||
35.27 | even | 4 | 630.2.d.b.629.1 | ✓ | 4 | ||
35.34 | odd | 2 | inner | 3150.2.b.b.251.4 | 8 | ||
60.23 | odd | 4 | 5040.2.k.b.1889.1 | 4 | |||
60.47 | odd | 4 | 5040.2.k.c.1889.2 | 4 | |||
105.62 | odd | 4 | 630.2.d.c.629.3 | yes | 4 | ||
105.83 | odd | 4 | 630.2.d.b.629.4 | yes | 4 | ||
105.104 | even | 2 | inner | 3150.2.b.b.251.8 | 8 | ||
140.27 | odd | 4 | 5040.2.k.b.1889.2 | 4 | |||
140.83 | odd | 4 | 5040.2.k.c.1889.1 | 4 | |||
420.83 | even | 4 | 5040.2.k.b.1889.3 | 4 | |||
420.167 | even | 4 | 5040.2.k.c.1889.4 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
630.2.d.b.629.1 | ✓ | 4 | 35.27 | even | 4 | ||
630.2.d.b.629.2 | yes | 4 | 15.8 | even | 4 | ||
630.2.d.b.629.3 | yes | 4 | 5.2 | odd | 4 | ||
630.2.d.b.629.4 | yes | 4 | 105.83 | odd | 4 | ||
630.2.d.c.629.1 | yes | 4 | 15.2 | even | 4 | ||
630.2.d.c.629.2 | yes | 4 | 35.13 | even | 4 | ||
630.2.d.c.629.3 | yes | 4 | 105.62 | odd | 4 | ||
630.2.d.c.629.4 | yes | 4 | 5.3 | odd | 4 | ||
3150.2.b.b.251.1 | 8 | 21.20 | even | 2 | inner | ||
3150.2.b.b.251.2 | 8 | 3.2 | odd | 2 | inner | ||
3150.2.b.b.251.3 | 8 | 5.4 | even | 2 | inner | ||
3150.2.b.b.251.4 | 8 | 35.34 | odd | 2 | inner | ||
3150.2.b.b.251.5 | 8 | 7.6 | odd | 2 | inner | ||
3150.2.b.b.251.6 | 8 | 1.1 | even | 1 | trivial | ||
3150.2.b.b.251.7 | 8 | 15.14 | odd | 2 | inner | ||
3150.2.b.b.251.8 | 8 | 105.104 | even | 2 | inner | ||
5040.2.k.b.1889.1 | 4 | 60.23 | odd | 4 | |||
5040.2.k.b.1889.2 | 4 | 140.27 | odd | 4 | |||
5040.2.k.b.1889.3 | 4 | 420.83 | even | 4 | |||
5040.2.k.b.1889.4 | 4 | 20.7 | even | 4 | |||
5040.2.k.c.1889.1 | 4 | 140.83 | odd | 4 | |||
5040.2.k.c.1889.2 | 4 | 60.47 | odd | 4 | |||
5040.2.k.c.1889.3 | 4 | 20.3 | even | 4 | |||
5040.2.k.c.1889.4 | 4 | 420.167 | even | 4 |