Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [630,2,Mod(629,630)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(630, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("630.629");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 630 = 2 \cdot 3^{2} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 630.d (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: | \(5.03057532734\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\sqrt{-2}, \sqrt{5})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 6x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 629.4 | ||
Root | \(-0.874032i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 630.629 |
Dual form | 630.2.d.b.629.3 |
$q$-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 \(\left(\mathbb{Z}/630\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(281\) | \(451\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 2.23607 | 1.00000 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.23607 | + | 1.41421i | −0.845154 | + | 0.534522i | ||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −2.23607 | −0.707107 | ||||||||
\(11\) | − | 5.65685i | − | 1.70561i | −0.522233 | − | 0.852803i | \(-0.674901\pi\) | ||
0.522233 | − | 0.852803i | \(-0.325099\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.47214 | 1.24035 | 0.620174 | − | 0.784465i | \(-0.287062\pi\) | ||||
0.620174 | + | 0.784465i | \(0.287062\pi\) | |||||||
\(14\) | 2.23607 | − | 1.41421i | 0.597614 | − | 0.377964i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | − | 3.16228i | − | 0.766965i | −0.923548 | − | 0.383482i | \(-0.874725\pi\) | ||
0.923548 | − | 0.383482i | \(-0.125275\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.16228i | 0.725476i | 0.931891 | + | 0.362738i | \(0.118158\pi\) | ||||
−0.931891 | + | 0.362738i | \(0.881842\pi\) | |||||||
\(20\) | 2.23607 | 0.500000 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 5.65685i | 1.20605i | ||||||||
\(23\) | 4.00000 | 0.834058 | 0.417029 | − | 0.908893i | \(-0.363071\pi\) | ||||
0.417029 | + | 0.908893i | \(0.363071\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 5.00000 | 1.00000 | ||||||||
\(26\) | −4.47214 | −0.877058 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −2.23607 | + | 1.41421i | −0.422577 | + | 0.267261i | ||||
\(29\) | − | 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 | \(0.192268\pi\) | ||||
−0.823055 | + | 0.567962i | \(0.807732\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 3.16228i | 0.542326i | ||||||||
\(35\) | −5.00000 | + | 3.16228i | −0.845154 | + | 0.534522i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 9.89949i | − | 1.62747i | −0.581238 | − | 0.813733i | \(-0.697432\pi\) | ||
0.581238 | − | 0.813733i | \(-0.302568\pi\) | |||||||
\(38\) | − | 3.16228i | − | 0.512989i | ||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −2.23607 | −0.353553 | ||||||||
\(41\) | 4.47214 | 0.698430 | 0.349215 | − | 0.937043i | \(-0.386448\pi\) | ||||
0.349215 | + | 0.937043i | \(0.386448\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 1.41421i | − | 0.215666i | −0.994169 | − | 0.107833i | \(-0.965609\pi\) | ||
0.994169 | − | 0.107833i | \(-0.0343911\pi\) | |||||||
\(44\) | − | 5.65685i | − | 0.852803i | ||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −4.00000 | −0.589768 | ||||||||
\(47\) | 9.48683i | 1.38380i | 0.721995 | + | 0.691898i | \(0.243225\pi\) | ||||
−0.721995 | + | 0.691898i | \(0.756775\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 3.00000 | − | 6.32456i | 0.428571 | − | 0.903508i | ||||
\(50\) | −5.00000 | −0.707107 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 4.47214 | 0.620174 | ||||||||
\(53\) | 4.00000 | 0.549442 | 0.274721 | − | 0.961524i | \(-0.411414\pi\) | ||||
0.274721 | + | 0.961524i | \(0.411414\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 12.6491i | − | 1.70561i | ||||||
\(56\) | 2.23607 | − | 1.41421i | 0.298807 | − | 0.188982i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 2.82843i | 0.371391i | ||||||||
\(59\) | 4.47214 | 0.582223 | 0.291111 | − | 0.956689i | \(-0.405975\pi\) | ||||
0.291111 | + | 0.956689i | \(0.405975\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 9.48683i | 1.21466i | 0.794448 | + | 0.607332i | \(0.207760\pi\) | ||||
−0.794448 | + | 0.607332i | \(0.792240\pi\) | |||||||
\(62\) | − | 6.32456i | − | 0.803219i | ||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 10.0000 | 1.24035 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 7.07107i | − | 0.863868i | −0.901905 | − | 0.431934i | \(-0.857831\pi\) | ||
0.901905 | − | 0.431934i | \(-0.142169\pi\) | |||||||
\(68\) | − | 3.16228i | − | 0.383482i | ||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 5.00000 | − | 3.16228i | 0.597614 | − | 0.377964i | ||||
\(71\) | − | 1.41421i | − | 0.167836i | −0.996473 | − | 0.0839181i | \(-0.973257\pi\) | ||
0.996473 | − | 0.0839181i | \(-0.0267434\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 13.4164 | 1.57027 | 0.785136 | − | 0.619324i | \(-0.212593\pi\) | ||||
0.785136 | + | 0.619324i | \(0.212593\pi\) | |||||||
\(74\) | 9.89949i | 1.15079i | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 3.16228i | 0.362738i | ||||||||
\(77\) | 8.00000 | + | 12.6491i | 0.911685 | + | 1.44150i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 6.00000 | 0.675053 | 0.337526 | − | 0.941316i | \(-0.390410\pi\) | ||||
0.337526 | + | 0.941316i | \(0.390410\pi\) | |||||||
\(80\) | 2.23607 | 0.250000 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −4.47214 | −0.493865 | ||||||||
\(83\) | − | 12.6491i | − | 1.38842i | −0.719772 | − | 0.694210i | \(-0.755754\pi\) | ||
0.719772 | − | 0.694210i | \(-0.244246\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − | 7.07107i | − | 0.766965i | ||||||
\(86\) | 1.41421i | 0.152499i | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 5.65685i | 0.603023i | ||||||||
\(89\) | −4.47214 | −0.474045 | −0.237023 | − | 0.971504i | \(-0.576172\pi\) | ||||
−0.237023 | + | 0.971504i | \(0.576172\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −10.0000 | + | 6.32456i | −1.04828 | + | 0.662994i | ||||
\(92\) | 4.00000 | 0.417029 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | − | 9.48683i | − | 0.978492i | ||||||
\(95\) | 7.07107i | 0.725476i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(98\) | −3.00000 | + | 6.32456i | −0.303046 | + | 0.638877i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 5.00000 | 0.500000 | ||||||||
\(101\) | −17.8885 | −1.77998 | −0.889988 | − | 0.455983i | \(-0.849288\pi\) | ||||
−0.889988 | + | 0.455983i | \(0.849288\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −8.94427 | −0.881305 | −0.440653 | − | 0.897678i | \(-0.645253\pi\) | ||||
−0.440653 | + | 0.897678i | \(0.645253\pi\) | |||||||
\(104\) | −4.47214 | −0.438529 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −4.00000 | −0.388514 | ||||||||
\(107\) | −18.0000 | −1.74013 | −0.870063 | − | 0.492941i | \(-0.835922\pi\) | ||||
−0.870063 | + | 0.492941i | \(0.835922\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −10.0000 | −0.957826 | −0.478913 | − | 0.877862i | \(-0.658969\pi\) | ||||
−0.478913 | + | 0.877862i | \(0.658969\pi\) | |||||||
\(110\) | 12.6491i | 1.20605i | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −2.23607 | + | 1.41421i | −0.211289 | + | 0.133631i | ||||
\(113\) | 6.00000 | 0.564433 | 0.282216 | − | 0.959351i | \(-0.408930\pi\) | ||||
0.282216 | + | 0.959351i | \(0.408930\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 8.94427 | 0.834058 | ||||||||
\(116\) | − | 2.82843i | − | 0.262613i | ||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −4.47214 | −0.411693 | ||||||||
\(119\) | 4.47214 | + | 7.07107i | 0.409960 | + | 0.648204i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −21.0000 | −1.90909 | ||||||||
\(122\) | − | 9.48683i | − | 0.858898i | ||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 6.32456i | 0.567962i | ||||||||
\(125\) | 11.1803 | 1.00000 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 14.1421i | 1.25491i | 0.778652 | + | 0.627456i | \(0.215904\pi\) | ||||
−0.778652 | + | 0.627456i | \(0.784096\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −10.0000 | −0.877058 | ||||||||
\(131\) | −17.8885 | −1.56293 | −0.781465 | − | 0.623949i | \(-0.785527\pi\) | ||||
−0.781465 | + | 0.623949i | \(0.785527\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −4.47214 | − | 7.07107i | −0.387783 | − | 0.613139i | ||||
\(134\) | 7.07107i | 0.610847i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 3.16228i | 0.271163i | ||||||||
\(137\) | −2.00000 | −0.170872 | −0.0854358 | − | 0.996344i | \(-0.527228\pi\) | ||||
−0.0854358 | + | 0.996344i | \(0.527228\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 15.8114i | − | 1.34110i | −0.741862 | − | 0.670552i | \(-0.766057\pi\) | ||
0.741862 | − | 0.670552i | \(-0.233943\pi\) | |||||||
\(140\) | −5.00000 | + | 3.16228i | −0.422577 | + | 0.267261i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 1.41421i | 0.118678i | ||||||||
\(143\) | − | 25.2982i | − | 2.11554i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 6.32456i | − | 0.525226i | ||||||
\(146\) | −13.4164 | −1.11035 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | − | 9.89949i | − | 0.813733i | ||||||
\(149\) | 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 | \(0.366612\pi\) | |||||||
\(152\) | − | 3.16228i | − | 0.256495i | ||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −8.00000 | − | 12.6491i | −0.644658 | − | 1.01929i | ||||
\(155\) | 14.1421i | 1.13592i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 4.47214 | 0.356915 | 0.178458 | − | 0.983948i | \(-0.442889\pi\) | ||||
0.178458 | + | 0.983948i | \(0.442889\pi\) | |||||||
\(158\) | −6.00000 | −0.477334 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −2.23607 | −0.176777 | ||||||||
\(161\) | −8.94427 | + | 5.65685i | −0.704907 | + | 0.445823i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 21.2132i | 1.66155i | 0.556611 | + | 0.830773i | \(0.312101\pi\) | ||||
−0.556611 | + | 0.830773i | \(0.687899\pi\) | |||||||
\(164\) | 4.47214 | 0.349215 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 12.6491i | 0.981761i | ||||||||
\(167\) | 9.48683i | 0.734113i | 0.930199 | + | 0.367057i | \(0.119634\pi\) | ||||
−0.930199 | + | 0.367057i | \(0.880366\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 7.00000 | 0.538462 | ||||||||
\(170\) | 7.07107i | 0.542326i | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | − | 1.41421i | − | 0.107833i | ||||||
\(173\) | 25.2982i | 1.92339i | 0.274125 | + | 0.961694i | \(0.411612\pi\) | ||||
−0.274125 | + | 0.961694i | \(0.588388\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −11.1803 | + | 7.07107i | −0.845154 | + | 0.534522i | ||||
\(176\) | − | 5.65685i | − | 0.426401i | ||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 4.47214 | 0.335201 | ||||||||
\(179\) | − | 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 | \(-0.962504\pi\) | ||
0.993070 | − | 0.117525i | \(-0.0374961\pi\) | |||||||
\(182\) | 10.0000 | − | 6.32456i | 0.741249 | − | 0.468807i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −4.00000 | −0.294884 | ||||||||
\(185\) | − | 22.1359i | − | 1.62747i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −17.8885 | −1.30814 | ||||||||
\(188\) | 9.48683i | 0.691898i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | − | 7.07107i | − | 0.512989i | ||||||
\(191\) | 1.41421i | 0.102329i | 0.998690 | + | 0.0511645i | \(0.0162933\pi\) | ||||
−0.998690 | + | 0.0511645i | \(0.983707\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 8.48528i | 0.610784i | 0.952227 | + | 0.305392i | \(0.0987875\pi\) | ||||
−0.952227 | + | 0.305392i | \(0.901213\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 3.00000 | − | 6.32456i | 0.214286 | − | 0.451754i | ||||
\(197\) | −12.0000 | −0.854965 | −0.427482 | − | 0.904024i | \(-0.640599\pi\) | ||||
−0.427482 | + | 0.904024i | \(0.640599\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(200\) | −5.00000 | −0.353553 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 17.8885 | 1.25863 | ||||||||
\(203\) | 4.00000 | + | 6.32456i | 0.280745 | + | 0.443897i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 10.0000 | 0.698430 | ||||||||
\(206\) | 8.94427 | 0.623177 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 4.47214 | 0.310087 | ||||||||
\(209\) | 17.8885 | 1.23738 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −20.0000 | −1.37686 | −0.688428 | − | 0.725304i | \(-0.741699\pi\) | ||||
−0.688428 | + | 0.725304i | \(0.741699\pi\) | |||||||
\(212\) | 4.00000 | 0.274721 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 18.0000 | 1.23045 | ||||||||
\(215\) | − | 3.16228i | − | 0.215666i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −8.94427 | − | 14.1421i | −0.607177 | − | 0.960031i | ||||
\(218\) | 10.0000 | 0.677285 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | − | 12.6491i | − | 0.852803i | ||||||
\(221\) | − | 14.1421i | − | 0.951303i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 8.94427 | 0.598953 | 0.299476 | − | 0.954104i | \(-0.403188\pi\) | ||||
0.299476 | + | 0.954104i | \(0.403188\pi\) | |||||||
\(224\) | 2.23607 | − | 1.41421i | 0.149404 | − | 0.0944911i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −6.00000 | −0.399114 | ||||||||
\(227\) | − | 18.9737i | − | 1.25933i | −0.776868 | − | 0.629663i | \(-0.783193\pi\) | ||
0.776868 | − | 0.629663i | \(-0.216807\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 15.8114i | − | 1.04485i | −0.852686 | − | 0.522423i | \(-0.825028\pi\) | ||
0.852686 | − | 0.522423i | \(-0.174972\pi\) | |||||||
\(230\) | −8.94427 | −0.589768 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 2.82843i | 0.185695i | ||||||||
\(233\) | −14.0000 | −0.917170 | −0.458585 | − | 0.888650i | \(-0.651644\pi\) | ||||
−0.458585 | + | 0.888650i | \(0.651644\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 21.2132i | 1.38380i | ||||||||
\(236\) | 4.47214 | 0.291111 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −4.47214 | − | 7.07107i | −0.289886 | − | 0.458349i | ||||
\(239\) | − | 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 | \(0.303154\pi\) | ||||
−0.579741 | + | 0.814801i | \(0.696846\pi\) | |||||||
\(242\) | 21.0000 | 1.34993 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 9.48683i | 0.607332i | ||||||||
\(245\) | 6.70820 | − | 14.1421i | 0.428571 | − | 0.903508i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 14.1421i | 0.899843i | ||||||||
\(248\) | − | 6.32456i | − | 0.401610i | ||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −11.1803 | −0.707107 | ||||||||
\(251\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 22.6274i | − | 1.42257i | ||||||
\(254\) | − | 14.1421i | − | 0.887357i | ||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 15.8114i | 0.986287i | 0.869948 | + | 0.493144i | \(0.164152\pi\) | ||||
−0.869948 | + | 0.493144i | \(0.835848\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 14.0000 | + | 22.1359i | 0.869918 | + | 1.37546i | ||||
\(260\) | 10.0000 | 0.620174 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 17.8885 | 1.10516 | ||||||||
\(263\) | −16.0000 | −0.986602 | −0.493301 | − | 0.869859i | \(-0.664210\pi\) | ||||
−0.493301 | + | 0.869859i | \(0.664210\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 8.94427 | 0.549442 | ||||||||
\(266\) | 4.47214 | + | 7.07107i | 0.274204 | + | 0.433555i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | − | 7.07107i | − | 0.431934i | ||||||
\(269\) | −17.8885 | −1.09068 | −0.545342 | − | 0.838214i | \(-0.683600\pi\) | ||||
−0.545342 | + | 0.838214i | \(0.683600\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 6.32456i | 0.384189i | 0.981376 | + | 0.192095i | \(0.0615281\pi\) | ||||
−0.981376 | + | 0.192095i | \(0.938472\pi\) | |||||||
\(272\) | − | 3.16228i | − | 0.191741i | ||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 2.00000 | 0.120824 | ||||||||
\(275\) | − | 28.2843i | − | 1.70561i | ||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 21.2132i | − | 1.27458i | −0.770625 | − | 0.637289i | \(-0.780056\pi\) | ||
0.770625 | − | 0.637289i | \(-0.219944\pi\) | |||||||
\(278\) | 15.8114i | 0.948304i | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 5.00000 | − | 3.16228i | 0.298807 | − | 0.188982i | ||||
\(281\) | − | 12.7279i | − | 0.759284i | −0.925133 | − | 0.379642i | \(-0.876047\pi\) | ||
0.925133 | − | 0.379642i | \(-0.123953\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(284\) | − | 1.41421i | − | 0.0839181i | ||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 25.2982i | 1.49592i | ||||||||
\(287\) | −10.0000 | + | 6.32456i | −0.590281 | + | 0.373327i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 7.00000 | 0.411765 | ||||||||
\(290\) | 6.32456i | 0.371391i | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 13.4164 | 0.785136 | ||||||||
\(293\) | 6.32456i | 0.369484i | 0.982787 | + | 0.184742i | \(0.0591450\pi\) | ||||
−0.982787 | + | 0.184742i | \(0.940855\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 10.0000 | 0.582223 | ||||||||
\(296\) | 9.89949i | 0.575396i | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | − | 16.9706i | − | 0.983078i | ||||||
\(299\) | 17.8885 | 1.03452 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.00000 | + | 3.16228i | 0.115278 | + | 0.182271i | ||||
\(302\) | −10.0000 | −0.575435 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 3.16228i | 0.181369i | ||||||||
\(305\) | 21.2132i | 1.21466i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −26.8328 | −1.53143 | −0.765715 | − | 0.643180i | \(-0.777615\pi\) | ||||
−0.765715 | + | 0.643180i | \(0.777615\pi\) | |||||||
\(308\) | 8.00000 | + | 12.6491i | 0.455842 | + | 0.720750i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | − | 14.1421i | − | 0.803219i | ||||||
\(311\) | 8.94427 | 0.507183 | 0.253592 | − | 0.967311i | \(-0.418388\pi\) | ||||
0.253592 | + | 0.967311i | \(0.418388\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −13.4164 | −0.758340 | −0.379170 | − | 0.925327i | \(-0.623790\pi\) | ||||
−0.379170 | + | 0.925327i | \(0.623790\pi\) | |||||||
\(314\) | −4.47214 | −0.252377 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 6.00000 | 0.337526 | ||||||||
\(317\) | 18.0000 | 1.01098 | 0.505490 | − | 0.862832i | \(-0.331312\pi\) | ||||
0.505490 | + | 0.862832i | \(0.331312\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −16.0000 | −0.895828 | ||||||||
\(320\) | 2.23607 | 0.125000 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 8.94427 | − | 5.65685i | 0.498445 | − | 0.315244i | ||||
\(323\) | 10.0000 | 0.556415 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 22.3607 | 1.24035 | ||||||||
\(326\) | − | 21.2132i | − | 1.17489i | ||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −4.47214 | −0.246932 | ||||||||
\(329\) | −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 | \(0.314761\pi\) | |||||||
\(332\) | − | 12.6491i | − | 0.694210i | ||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | − | 9.48683i | − | 0.519096i | ||||||
\(335\) | − | 15.8114i | − | 0.863868i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 25.4558i | 1.38667i | 0.720616 | + | 0.693334i | \(0.243859\pi\) | ||||
−0.720616 | + | 0.693334i | \(0.756141\pi\) | |||||||
\(338\) | −7.00000 | −0.380750 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | − | 7.07107i | − | 0.383482i | ||||||
\(341\) | 35.7771 | 1.93744 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 2.23607 | + | 18.3848i | 0.120736 | + | 0.992685i | ||||
\(344\) | 1.41421i | 0.0762493i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | − | 25.2982i | − | 1.36004i | ||||||
\(347\) | 12.0000 | 0.644194 | 0.322097 | − | 0.946707i | \(-0.395612\pi\) | ||||
0.322097 | + | 0.946707i | \(0.395612\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 15.8114i | − | 0.846364i | −0.906045 | − | 0.423182i | \(-0.860913\pi\) | ||
0.906045 | − | 0.423182i | \(-0.139087\pi\) | |||||||
\(350\) | 11.1803 | − | 7.07107i | 0.597614 | − | 0.377964i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 5.65685i | 0.301511i | ||||||||
\(353\) | − | 3.16228i | − | 0.168311i | −0.996453 | − | 0.0841555i | \(-0.973181\pi\) | ||
0.996453 | − | 0.0841555i | \(-0.0268193\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − | 3.16228i | − | 0.167836i | ||||||
\(356\) | −4.47214 | −0.237023 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 2.82843i | 0.149487i | ||||||||
\(359\) | − | 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 | ||||||||
\(362\) | 3.16228i | 0.166206i | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −10.0000 | + | 6.32456i | −0.524142 | + | 0.331497i | ||||
\(365\) | 30.0000 | 1.57027 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 13.4164 | 0.700331 | 0.350165 | − | 0.936688i | \(-0.386125\pi\) | ||||
0.350165 | + | 0.936688i | \(0.386125\pi\) | |||||||
\(368\) | 4.00000 | 0.208514 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 22.1359i | 1.15079i | ||||||||
\(371\) | −8.94427 | + | 5.65685i | −0.464363 | + | 0.293689i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 21.2132i | − | 1.09838i | −0.835698 | − | 0.549189i | \(-0.814937\pi\) | ||
0.835698 | − | 0.549189i | \(-0.185063\pi\) | |||||||
\(374\) | 17.8885 | 0.924995 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | − | 9.48683i | − | 0.489246i | ||||||
\(377\) | − | 12.6491i | − | 0.651462i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(380\) | 7.07107i | 0.362738i | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | − | 1.41421i | − | 0.0723575i | ||||||
\(383\) | − | 9.48683i | − | 0.484755i | −0.970182 | − | 0.242377i | \(-0.922073\pi\) | ||
0.970182 | − | 0.242377i | \(-0.0779272\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 17.8885 | + | 28.2843i | 0.911685 | + | 1.44150i | ||||
\(386\) | − | 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 | ||||||
\(392\) | −3.00000 | + | 6.32456i | −0.151523 | + | 0.319438i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 12.0000 | 0.604551 | ||||||||
\(395\) | 13.4164 | 0.675053 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −4.47214 | −0.224450 | −0.112225 | − | 0.993683i | \(-0.535798\pi\) | ||||
−0.112225 | + | 0.993683i | \(0.535798\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 5.00000 | 0.250000 | ||||||||
\(401\) | 1.41421i | 0.0706225i | 0.999376 | + | 0.0353112i | \(0.0112422\pi\) | ||||
−0.999376 | + | 0.0353112i | \(0.988758\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 28.2843i | 1.40894i | ||||||||
\(404\) | −17.8885 | −0.889988 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −4.00000 | − | 6.32456i | −0.198517 | − | 0.313882i | ||||
\(407\) | −56.0000 | −2.77582 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 37.9473i | 1.87637i | 0.346128 | + | 0.938187i | \(0.387496\pi\) | ||||
−0.346128 | + | 0.938187i | \(0.612504\pi\) | |||||||
\(410\) | −10.0000 | −0.493865 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −8.94427 | −0.440653 | ||||||||
\(413\) | −10.0000 | + | 6.32456i | −0.492068 | + | 0.311211i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 28.2843i | − | 1.38842i | ||||||
\(416\) | −4.47214 | −0.219265 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −17.8885 | −0.874957 | ||||||||
\(419\) | 13.4164 | 0.655434 | 0.327717 | − | 0.944776i | \(-0.393721\pi\) | ||||
0.327717 | + | 0.944776i | \(0.393721\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 38.0000 | 1.85201 | 0.926003 | − | 0.377515i | \(-0.123221\pi\) | ||||
0.926003 | + | 0.377515i | \(0.123221\pi\) | |||||||
\(422\) | 20.0000 | 0.973585 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −4.00000 | −0.194257 | ||||||||
\(425\) | − | 15.8114i | − | 0.766965i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −13.4164 | − | 21.2132i | −0.649265 | − | 1.02658i | ||||
\(428\) | −18.0000 | −0.870063 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 3.16228i | 0.152499i | ||||||||
\(431\) | − | 15.5563i | − | 0.749323i | −0.927162 | − | 0.374661i | \(-0.877759\pi\) | ||
0.927162 | − | 0.374661i | \(-0.122241\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −26.8328 | −1.28950 | −0.644751 | − | 0.764392i | \(-0.723039\pi\) | ||||
−0.644751 | + | 0.764392i | \(0.723039\pi\) | |||||||
\(434\) | 8.94427 | + | 14.1421i | 0.429339 | + | 0.678844i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −10.0000 | −0.478913 | ||||||||
\(437\) | 12.6491i | 0.605089i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 6.32456i | 0.301855i | 0.988545 | + | 0.150927i | \(0.0482259\pi\) | ||||
−0.988545 | + | 0.150927i | \(0.951774\pi\) | |||||||
\(440\) | 12.6491i | 0.603023i | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 14.1421i | 0.672673i | ||||||||
\(443\) | −4.00000 | −0.190046 | −0.0950229 | − | 0.995475i | \(-0.530292\pi\) | ||||
−0.0950229 | + | 0.995475i | \(0.530292\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −10.0000 | −0.474045 | ||||||||
\(446\) | −8.94427 | −0.423524 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −2.23607 | + | 1.41421i | −0.105644 | + | 0.0668153i | ||||
\(449\) | − | 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 | ||||||
\(452\) | 6.00000 | 0.282216 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 18.9737i | 0.890478i | ||||||||
\(455\) | −22.3607 | + | 14.1421i | −1.04828 | + | 0.662994i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 16.9706i | 0.793849i | 0.917851 | + | 0.396925i | \(0.129923\pi\) | ||||
−0.917851 | + | 0.396925i | \(0.870077\pi\) | |||||||
\(458\) | 15.8114i | 0.738818i | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 8.94427 | 0.417029 | ||||||||
\(461\) | −8.94427 | −0.416576 | −0.208288 | − | 0.978068i | \(-0.566789\pi\) | ||||
−0.208288 | + | 0.978068i | \(0.566789\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(464\) | − | 2.82843i | − | 0.131306i | ||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 14.0000 | 0.648537 | ||||||||
\(467\) | 12.6491i | 0.585331i | 0.956215 | + | 0.292666i | \(0.0945422\pi\) | ||||
−0.956215 | + | 0.292666i | \(0.905458\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 10.0000 | + | 15.8114i | 0.461757 | + | 0.730102i | ||||
\(470\) | − | 21.2132i | − | 0.978492i | ||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −4.47214 | −0.205847 | ||||||||
\(473\) | −8.00000 | −0.367840 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 15.8114i | 0.725476i | ||||||||
\(476\) | 4.47214 | + | 7.07107i | 0.204980 | + | 0.324102i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 4.24264i | 0.194054i | ||||||||
\(479\) | −17.8885 | −0.817348 | −0.408674 | − | 0.912680i | \(-0.634009\pi\) | ||||
−0.408674 | + | 0.912680i | \(0.634009\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − | 44.2719i | − | 2.01862i | ||||||
\(482\) | − | 25.2982i | − | 1.15230i | ||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −21.0000 | −0.954545 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 25.4558i | − | 1.15351i | −0.816916 | − | 0.576757i | \(-0.804318\pi\) | ||
0.816916 | − | 0.576757i | \(-0.195682\pi\) | |||||||
\(488\) | − | 9.48683i | − | 0.429449i | ||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −6.70820 | + | 14.1421i | −0.303046 | + | 0.638877i | ||||
\(491\) | 19.7990i | 0.893516i | 0.894655 | + | 0.446758i | \(0.147421\pi\) | ||||
−0.894655 | + | 0.446758i | \(0.852579\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −8.94427 | −0.402830 | ||||||||
\(494\) | − | 14.1421i | − | 0.636285i | ||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 6.32456i | 0.283981i | ||||||||
\(497\) | 2.00000 | + | 3.16228i | 0.0897123 | + | 0.141848i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −20.0000 | −0.895323 | −0.447661 | − | 0.894203i | \(-0.647743\pi\) | ||||
−0.447661 | + | 0.894203i | \(0.647743\pi\) | |||||||
\(500\) | 11.1803 | 0.500000 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 9.48683i | − | 0.422997i | −0.977378 | − | 0.211498i | \(-0.932166\pi\) | ||
0.977378 | − | 0.211498i | \(-0.0678343\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −40.0000 | −1.77998 | ||||||||
\(506\) | 22.6274i | 1.00591i | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 14.1421i | 0.627456i | ||||||||
\(509\) | 13.4164 | 0.594672 | 0.297336 | − | 0.954773i | \(-0.403902\pi\) | ||||
0.297336 | + | 0.954773i | \(0.403902\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −30.0000 | + | 18.9737i | −1.32712 | + | 0.839346i | ||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | − | 15.8114i | − | 0.697410i | ||||||
\(515\) | −20.0000 | −0.881305 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 53.6656 | 2.36021 | ||||||||
\(518\) | −14.0000 | − | 22.1359i | −0.615125 | − | 0.972598i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −10.0000 | −0.438529 | ||||||||
\(521\) | 13.4164 | 0.587784 | 0.293892 | − | 0.955839i | \(-0.405049\pi\) | ||||
0.293892 | + | 0.955839i | \(0.405049\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 17.8885 | 0.782211 | 0.391106 | − | 0.920346i | \(-0.372093\pi\) | ||||
0.391106 | + | 0.920346i | \(0.372093\pi\) | |||||||
\(524\) | −17.8885 | −0.781465 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 16.0000 | 0.697633 | ||||||||
\(527\) | 20.0000 | 0.871214 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −7.00000 | −0.304348 | ||||||||
\(530\) | −8.94427 | −0.388514 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −4.47214 | − | 7.07107i | −0.193892 | − | 0.306570i | ||||
\(533\) | 20.0000 | 0.866296 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −40.2492 | −1.74013 | ||||||||
\(536\) | 7.07107i | 0.305424i | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 17.8885 | 0.771230 | ||||||||
\(539\) | −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 | \(0.656803\pi\) | |||||||
\(542\) | − | 6.32456i | − | 0.271663i | ||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 3.16228i | 0.135582i | ||||||||
\(545\) | −22.3607 | −0.957826 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 21.2132i | 0.907011i | 0.891253 | + | 0.453506i | \(0.149827\pi\) | ||||
−0.891253 | + | 0.453506i | \(0.850173\pi\) | |||||||
\(548\) | −2.00000 | −0.0854358 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 28.2843i | 1.20605i | ||||||||
\(551\) | 8.94427 | 0.381039 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −13.4164 | + | 8.48528i | −0.570524 | + | 0.360831i | ||||
\(554\) | 21.2132i | 0.901263i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | − | 15.8114i | − | 0.670552i | ||||||
\(557\) | 38.0000 | 1.61011 | 0.805056 | − | 0.593199i | \(-0.202135\pi\) | ||||
0.805056 | + | 0.593199i | \(0.202135\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 6.32456i | − | 0.267500i | ||||||
\(560\) | −5.00000 | + | 3.16228i | −0.211289 | + | 0.133631i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 12.7279i | 0.536895i | ||||||||
\(563\) | 18.9737i | 0.799645i | 0.916593 | + | 0.399822i | \(0.130928\pi\) | ||||
−0.916593 | + | 0.399822i | \(0.869072\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 13.4164 | 0.564433 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 1.41421i | 0.0593391i | ||||||||
\(569\) | 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 | \(0.300748\pi\) | |||||||
\(572\) | − | 25.2982i | − | 1.05777i | ||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 10.0000 | − | 6.32456i | 0.417392 | − | 0.263982i | ||||
\(575\) | 20.0000 | 0.834058 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −22.3607 | −0.930887 | −0.465444 | − | 0.885078i | \(-0.654105\pi\) | ||||
−0.465444 | + | 0.885078i | \(0.654105\pi\) | |||||||
\(578\) | −7.00000 | −0.291162 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | − | 6.32456i | − | 0.262613i | ||||||
\(581\) | 17.8885 | + | 28.2843i | 0.742142 | + | 1.17343i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 22.6274i | − | 0.937132i | ||||||
\(584\) | −13.4164 | −0.555175 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | − | 6.32456i | − | 0.261265i | ||||||
\(587\) | 31.6228i | 1.30521i | 0.757698 | + | 0.652606i | \(0.226324\pi\) | ||||
−0.757698 | + | 0.652606i | \(0.773676\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −20.0000 | −0.824086 | ||||||||
\(590\) | −10.0000 | −0.411693 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | − | 9.89949i | − | 0.406867i | ||||||
\(593\) | − | 9.48683i | − | 0.389578i | −0.980845 | − | 0.194789i | \(-0.937598\pi\) | ||
0.980845 | − | 0.194789i | \(-0.0624021\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 10.0000 | + | 15.8114i | 0.409960 | + | 0.648204i | ||||
\(596\) | 16.9706i | 0.695141i | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −17.8885 | −0.731517 | ||||||||
\(599\) | 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 | \(-0.827432\pi\) | ||
0.856608 | − | 0.515968i | \(-0.172568\pi\) | |||||||
\(602\) | −2.00000 | − | 3.16228i | −0.0815139 | − | 0.128885i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 10.0000 | 0.406894 | ||||||||
\(605\) | −46.9574 | −1.90909 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 8.94427 | 0.363037 | 0.181518 | − | 0.983388i | \(-0.441899\pi\) | ||||
0.181518 | + | 0.983388i | \(0.441899\pi\) | |||||||
\(608\) | − | 3.16228i | − | 0.128247i | ||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | − | 21.2132i | − | 0.858898i | ||||||
\(611\) | 42.4264i | 1.71639i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 35.3553i | − | 1.42799i | −0.700151 | − | 0.713994i | \(-0.746884\pi\) | ||
0.700151 | − | 0.713994i | \(-0.253116\pi\) | |||||||
\(614\) | 26.8328 | 1.08288 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −8.00000 | − | 12.6491i | −0.322329 | − | 0.509647i | ||||
\(617\) | −38.0000 | −1.52982 | −0.764911 | − | 0.644136i | \(-0.777217\pi\) | ||||
−0.764911 | + | 0.644136i | \(0.777217\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 28.4605i | − | 1.14392i | −0.820280 | − | 0.571962i | \(-0.806182\pi\) | ||
0.820280 | − | 0.571962i | \(-0.193818\pi\) | |||||||
\(620\) | 14.1421i | 0.567962i | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −8.94427 | −0.358633 | ||||||||
\(623\) | 10.0000 | − | 6.32456i | 0.400642 | − | 0.253388i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 25.0000 | 1.00000 | ||||||||
\(626\) | 13.4164 | 0.536228 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 4.47214 | 0.178458 | ||||||||
\(629\) | −31.3050 | −1.24821 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −8.00000 | −0.318475 | −0.159237 | − | 0.987240i | \(-0.550904\pi\) | ||||
−0.159237 | + | 0.987240i | \(0.550904\pi\) | |||||||
\(632\) | −6.00000 | −0.238667 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −18.0000 | −0.714871 | ||||||||
\(635\) | 31.6228i | 1.25491i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 13.4164 | − | 28.2843i | 0.531577 | − | 1.12066i | ||||
\(638\) | 16.0000 | 0.633446 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −2.23607 | −0.0883883 | ||||||||
\(641\) | − | 1.41421i | − | 0.0558581i | −0.999610 | − | 0.0279290i | \(-0.991109\pi\) | ||
0.999610 | − | 0.0279290i | \(-0.00889125\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 44.7214 | 1.76364 | 0.881819 | − | 0.471588i | \(-0.156319\pi\) | ||||
0.881819 | + | 0.471588i | \(0.156319\pi\) | |||||||
\(644\) | −8.94427 | + | 5.65685i | −0.352454 | + | 0.222911i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −10.0000 | −0.393445 | ||||||||
\(647\) | 34.7851i | 1.36754i | 0.729697 | + | 0.683771i | \(0.239661\pi\) | ||||
−0.729697 | + | 0.683771i | \(0.760339\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 25.2982i | − | 0.993042i | ||||||
\(650\) | −22.3607 | −0.877058 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 21.2132i | 0.830773i | ||||||||
\(653\) | 14.0000 | 0.547862 | 0.273931 | − | 0.961749i | \(-0.411676\pi\) | ||||
0.273931 | + | 0.961749i | \(0.411676\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −40.0000 | −1.56293 | ||||||||
\(656\) | 4.47214 | 0.174608 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 13.4164 | + | 21.2132i | 0.523026 | + | 0.826977i | ||||
\(659\) | 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 | \(0.0195882\pi\) | ||||
−0.998107 | + | 0.0614992i | \(0.980412\pi\) | |||||||
\(662\) | −20.0000 | −0.777322 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 12.6491i | 0.490881i | ||||||||
\(665\) | −10.0000 | − | 15.8114i | −0.387783 | − | 0.613139i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 11.3137i | − | 0.438069i | ||||||
\(668\) | 9.48683i | 0.367057i | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 15.8114i | 0.610847i | ||||||||
\(671\) | 53.6656 | 2.07174 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 19.7990i | − | 0.763195i | −0.924329 | − | 0.381597i | \(-0.875374\pi\) | ||
0.924329 | − | 0.381597i | \(-0.124626\pi\) | |||||||
\(674\) | − | 25.4558i | − | 0.980522i | ||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 7.00000 | 0.269231 | ||||||||
\(677\) | − | 37.9473i | − | 1.45843i | −0.684282 | − | 0.729217i | \(-0.739884\pi\) | ||
0.684282 | − | 0.729217i | \(-0.260116\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 7.07107i | 0.271163i | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −35.7771 | −1.36998 | ||||||||
\(683\) | 14.0000 | 0.535695 | 0.267848 | − | 0.963461i | \(-0.413688\pi\) | ||||
0.267848 | + | 0.963461i | \(0.413688\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −4.47214 | −0.170872 | ||||||||
\(686\) | −2.23607 | − | 18.3848i | −0.0853735 | − | 0.701934i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | − | 1.41421i | − | 0.0539164i | ||||||
\(689\) | 17.8885 | 0.681499 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 28.4605i | − | 1.08269i | −0.840801 | − | 0.541344i | \(-0.817916\pi\) | ||
0.840801 | − | 0.541344i | \(-0.182084\pi\) | |||||||
\(692\) | 25.2982i | 0.961694i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −12.0000 | −0.455514 | ||||||||
\(695\) | − | 35.3553i | − | 1.34110i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 14.1421i | − | 0.535672i | ||||||
\(698\) | 15.8114i | 0.598470i | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −11.1803 | + | 7.07107i | −0.422577 | + | 0.267261i | ||||
\(701\) | 19.7990i | 0.747798i | 0.927470 | + | 0.373899i | \(0.121979\pi\) | ||||
−0.927470 | + | 0.373899i | \(0.878021\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 31.3050 | 1.18069 | ||||||||
\(704\) | − | 5.65685i | − | 0.213201i | ||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 3.16228i | 0.119014i | ||||||||
\(707\) | 40.0000 | − | 25.2982i | 1.50435 | − | 0.951438i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −30.0000 | −1.12667 | −0.563337 | − | 0.826227i | \(-0.690483\pi\) | ||||
−0.563337 | + | 0.826227i | \(0.690483\pi\) | |||||||
\(710\) | 3.16228i | 0.118678i | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 4.47214 | 0.167600 | ||||||||
\(713\) | 25.2982i | 0.947426i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 56.5685i | − | 2.11554i | ||||||
\(716\) | − | 2.82843i | − | 0.105703i | ||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 18.3848i | 0.686114i | ||||||||
\(719\) | −44.7214 | −1.66783 | −0.833913 | − | 0.551896i | \(-0.813904\pi\) | ||||
−0.833913 | + | 0.551896i | \(0.813904\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 20.0000 | − | 12.6491i | 0.744839 | − | 0.471077i | ||||
\(722\) | −9.00000 | −0.334945 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | − | 3.16228i | − | 0.117525i | ||||||
\(725\) | − | 14.1421i | − | 0.525226i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −26.8328 | −0.995174 | −0.497587 | − | 0.867414i | \(-0.665780\pi\) | ||||
−0.497587 | + | 0.867414i | \(0.665780\pi\) | |||||||
\(728\) | 10.0000 | − | 6.32456i | 0.370625 | − | 0.234404i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −30.0000 | −1.11035 | ||||||||
\(731\) | −4.47214 | −0.165408 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 40.2492 | 1.48664 | 0.743319 | − | 0.668937i | \(-0.233250\pi\) | ||||
0.743319 | + | 0.668937i | \(0.233250\pi\) | |||||||
\(734\) | −13.4164 | −0.495209 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −4.00000 | −0.147442 | ||||||||
\(737\) | −40.0000 | −1.47342 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 16.0000 | 0.588570 | 0.294285 | − | 0.955718i | \(-0.404919\pi\) | ||||
0.294285 | + | 0.955718i | \(0.404919\pi\) | |||||||
\(740\) | − | 22.1359i | − | 0.813733i | ||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 8.94427 | − | 5.65685i | 0.328355 | − | 0.207670i | ||||
\(743\) | 36.0000 | 1.32071 | 0.660356 | − | 0.750953i | \(-0.270405\pi\) | ||||
0.660356 | + | 0.750953i | \(0.270405\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 37.9473i | 1.39028i | ||||||||
\(746\) | 21.2132i | 0.776671i | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −17.8885 | −0.654070 | ||||||||
\(749\) | 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 | \(0.239608\pi\) | |||||||
\(752\) | 9.48683i | 0.345949i | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 12.6491i | 0.460653i | ||||||||
\(755\) | 22.3607 | 0.813788 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 32.5269i | 1.18221i | 0.806594 | + | 0.591105i | \(0.201308\pi\) | ||||
−0.806594 | + | 0.591105i | \(0.798692\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | − | 7.07107i | − | 0.256495i | ||||||
\(761\) | −31.3050 | −1.13480 | −0.567402 | − | 0.823441i | \(-0.692051\pi\) | ||||
−0.567402 | + | 0.823441i | \(0.692051\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 22.3607 | − | 14.1421i | 0.809511 | − | 0.511980i | ||||
\(764\) | 1.41421i | 0.0511645i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 9.48683i | 0.342773i | ||||||||
\(767\) | 20.0000 | 0.722158 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 31.6228i | 1.14035i | 0.821524 | + | 0.570173i | \(0.193124\pi\) | ||||
−0.821524 | + | 0.570173i | \(0.806876\pi\) | |||||||
\(770\) | −17.8885 | − | 28.2843i | −0.644658 | − | 1.01929i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 8.48528i | 0.305392i | ||||||||
\(773\) | 31.6228i | 1.13739i | 0.822548 | + | 0.568696i | \(0.192552\pi\) | ||||
−0.822548 | + | 0.568696i | \(0.807448\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 31.6228i | 1.13592i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | − | 16.9706i | − | 0.608424i | ||||||
\(779\) | 14.1421i | 0.506695i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −8.00000 | −0.286263 | ||||||||
\(782\) | 12.6491i | 0.452331i | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 3.00000 | − | 6.32456i | 0.107143 | − | 0.225877i | ||||
\(785\) | 10.0000 | 0.356915 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −26.8328 | −0.956487 | −0.478243 | − | 0.878227i | \(-0.658726\pi\) | ||||
−0.478243 | + | 0.878227i | \(0.658726\pi\) | |||||||
\(788\) | −12.0000 | −0.427482 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −13.4164 | −0.477334 | ||||||||
\(791\) | −13.4164 | + | 8.48528i | −0.477033 | + | 0.301702i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 42.4264i | 1.50661i | ||||||||
\(794\) | 4.47214 | 0.158710 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 25.2982i | − | 0.896109i | −0.894006 | − | 0.448054i | \(-0.852117\pi\) | ||
0.894006 | − | 0.448054i | \(-0.147883\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 30.0000 | 1.06132 | ||||||||
\(800\) | −5.00000 | −0.176777 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | − | 1.41421i | − | 0.0499376i | ||||||
\(803\) | − | 75.8947i | − | 2.67826i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −20.0000 | + | 12.6491i | −0.704907 | + | 0.445823i | ||||
\(806\) | − | 28.2843i | − | 0.996271i | ||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 17.8885 | 0.629317 | ||||||||
\(809\) | − | 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 | \(-0.872942\pi\) | ||
0.921386 | − | 0.388649i | \(-0.127058\pi\) | |||||||
\(812\) | 4.00000 | + | 6.32456i | 0.140372 | + | 0.221948i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 56.0000 | 1.96280 | ||||||||
\(815\) | 47.4342i | 1.66155i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 4.47214 | 0.156460 | ||||||||
\(818\) | − | 37.9473i | − | 1.32680i | ||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 10.0000 | 0.349215 | ||||||||
\(821\) | − | 19.7990i | − | 0.690990i | −0.938421 | − | 0.345495i | \(-0.887711\pi\) | ||
0.938421 | − | 0.345495i | \(-0.112289\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 28.2843i | 0.985928i | 0.870050 | + | 0.492964i | \(0.164087\pi\) | ||||
−0.870050 | + | 0.492964i | \(0.835913\pi\) | |||||||
\(824\) | 8.94427 | 0.311588 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 10.0000 | − | 6.32456i | 0.347945 | − | 0.220059i | ||||
\(827\) | 12.0000 | 0.417281 | 0.208640 | − | 0.977992i | \(-0.433096\pi\) | ||||
0.208640 | + | 0.977992i | \(0.433096\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 41.1096i | 1.42780i | 0.700250 | + | 0.713898i | \(0.253072\pi\) | ||||
−0.700250 | + | 0.713898i | \(0.746928\pi\) | |||||||
\(830\) | 28.2843i | 0.981761i | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 4.47214 | 0.155043 | ||||||||
\(833\) | −20.0000 | − | 9.48683i | −0.692959 | − | 0.328699i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 21.2132i | 0.734113i | ||||||||
\(836\) | 17.8885 | 0.618688 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −13.4164 | −0.463462 | ||||||||
\(839\) | 17.8885 | 0.617581 | 0.308791 | − | 0.951130i | \(-0.400076\pi\) | ||||
0.308791 | + | 0.951130i | \(0.400076\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 21.0000 | 0.724138 | ||||||||
\(842\) | −38.0000 | −1.30957 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −20.0000 | −0.688428 | ||||||||
\(845\) | 15.6525 | 0.538462 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 46.9574 | − | 29.6985i | 1.61348 | − | 1.02045i | ||||
\(848\) | 4.00000 | 0.137361 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 15.8114i | 0.542326i | ||||||||
\(851\) | − | 39.5980i | − | 1.35740i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −49.1935 | −1.68435 | −0.842177 | − | 0.539202i | \(-0.818726\pi\) | ||||
−0.842177 | + | 0.539202i | \(0.818726\pi\) | |||||||
\(854\) | 13.4164 | + | 21.2132i | 0.459100 | + | 0.725901i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 18.0000 | 0.615227 | ||||||||
\(857\) | 41.1096i | 1.40428i | 0.712040 | + | 0.702139i | \(0.247771\pi\) | ||||
−0.712040 | + | 0.702139i | \(0.752229\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 34.7851i | 1.18685i | 0.804889 | + | 0.593425i | \(0.202225\pi\) | ||||
−0.804889 | + | 0.593425i | \(0.797775\pi\) | |||||||
\(860\) | − | 3.16228i | − | 0.107833i | ||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 15.5563i | 0.529851i | ||||||||
\(863\) | 36.0000 | 1.22545 | 0.612727 | − | 0.790295i | \(-0.290072\pi\) | ||||
0.612727 | + | 0.790295i | \(0.290072\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 56.5685i | 1.92339i | ||||||||
\(866\) | 26.8328 | 0.911816 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −8.94427 | − | 14.1421i | −0.303588 | − | 0.480015i | ||||
\(869\) | − | 33.9411i | − | 1.15137i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 31.6228i | − | 1.07150i | ||||||
\(872\) | 10.0000 | 0.338643 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | − | 12.6491i | − | 0.427863i | ||||||
\(875\) | −25.0000 | + | 15.8114i | −0.845154 | + | 0.534522i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 21.2132i | 0.716319i | 0.933660 | + | 0.358159i | \(0.116596\pi\) | ||||
−0.933660 | + | 0.358159i | \(0.883404\pi\) | |||||||
\(878\) | − | 6.32456i | − | 0.213443i | ||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | − | 12.6491i | − | 0.426401i | ||||||
\(881\) | 4.47214 | 0.150670 | 0.0753350 | − | 0.997158i | \(-0.475997\pi\) | ||||
0.0753350 | + | 0.997158i | \(0.475997\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 12.7279i | − | 0.428329i | −0.976798 | − | 0.214164i | \(-0.931297\pi\) | ||
0.976798 | − | 0.214164i | \(-0.0687028\pi\) | |||||||
\(884\) | − | 14.1421i | − | 0.475651i | ||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 4.00000 | 0.134383 | ||||||||
\(887\) | − | 9.48683i | − | 0.318537i | −0.987235 | − | 0.159268i | \(-0.949086\pi\) | ||
0.987235 | − | 0.159268i | \(-0.0509135\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −20.0000 | − | 31.6228i | −0.670778 | − | 1.06059i | ||||
\(890\) | 10.0000 | 0.335201 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 8.94427 | 0.299476 | ||||||||
\(893\) | −30.0000 | −1.00391 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 6.32456i | − | 0.211407i | ||||||
\(896\) | 2.23607 | − | 1.41421i | 0.0747018 | − | 0.0472456i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 9.89949i | 0.330350i | ||||||||
\(899\) | 17.8885 | 0.596616 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 12.6491i | − | 0.421403i | ||||||
\(902\) | 25.2982i | 0.842339i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −6.00000 | −0.199557 | ||||||||
\(905\) | − | 7.07107i | − | 0.235050i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 46.6690i | − | 1.54962i | −0.632194 | − | 0.774810i | \(-0.717845\pi\) | ||
0.632194 | − | 0.774810i | \(-0.282155\pi\) | |||||||
\(908\) | − | 18.9737i | − | 0.629663i | ||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 22.3607 | − | 14.1421i | 0.741249 | − | 0.468807i | ||||
\(911\) | − | 43.8406i | − | 1.45250i | −0.687428 | − | 0.726252i | \(-0.741260\pi\) | ||
0.687428 | − | 0.726252i | \(-0.258740\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −71.5542 | −2.36810 | ||||||||
\(914\) | − | 16.9706i | − | 0.561336i | ||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | − | 15.8114i | − | 0.522423i | ||||||
\(917\) | 40.0000 | − | 25.2982i | 1.32092 | − | 0.835421i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −40.0000 | −1.31948 | −0.659739 | − | 0.751495i | \(-0.729333\pi\) | ||||
−0.659739 | + | 0.751495i | \(0.729333\pi\) | |||||||
\(920\) | −8.94427 | −0.294884 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 8.94427 | 0.294564 | ||||||||
\(923\) | − | 6.32456i | − | 0.208175i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − | 49.4975i | − | 1.62747i | ||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 2.82843i | 0.0928477i | ||||||||
\(929\) | 22.3607 | 0.733630 | 0.366815 | − | 0.930294i | \(-0.380448\pi\) | ||||
0.366815 | + | 0.930294i | \(0.380448\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 20.0000 | + | 9.48683i | 0.655474 | + | 0.310918i | ||||
\(932\) | −14.0000 | −0.458585 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | − | 12.6491i | − | 0.413892i | ||||||
\(935\) | −40.0000 | −1.30814 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −53.6656 | −1.75318 | −0.876590 | − | 0.481238i | \(-0.840187\pi\) | ||||
−0.876590 | + | 0.481238i | \(0.840187\pi\) | |||||||
\(938\) | −10.0000 | − | 15.8114i | −0.326512 | − | 0.516260i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 21.2132i | 0.691898i | ||||||||
\(941\) | −26.8328 | −0.874725 | −0.437362 | − | 0.899285i | \(-0.644087\pi\) | ||||
−0.437362 | + | 0.899285i | \(0.644087\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 17.8885 | 0.582531 | ||||||||
\(944\) | 4.47214 | 0.145556 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 8.00000 | 0.260102 | ||||||||
\(947\) | −42.0000 | −1.36482 | −0.682408 | − | 0.730971i | \(-0.739067\pi\) | ||||
−0.682408 | + | 0.730971i | \(0.739067\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 60.0000 | 1.94768 | ||||||||
\(950\) | − | 15.8114i | − | 0.512989i | ||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −4.47214 | − | 7.07107i | −0.144943 | − | 0.229175i | ||||
\(953\) | −54.0000 | −1.74923 | −0.874616 | − | 0.484817i | \(-0.838886\pi\) | ||||
−0.874616 | + | 0.484817i | \(0.838886\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 3.16228i | 0.102329i | ||||||||
\(956\) | − | 4.24264i | − | 0.137217i | ||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 17.8885 | 0.577953 | ||||||||
\(959\) | 4.47214 | − | 2.82843i | 0.144413 | − | 0.0913347i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −9.00000 | −0.290323 | ||||||||
\(962\) | 44.2719i | 1.42738i | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 25.2982i | 0.814801i | ||||||||
\(965\) | 18.9737i | 0.610784i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 42.4264i | 1.36434i | 0.731193 | + | 0.682171i | \(0.238964\pi\) | ||||
−0.731193 | + | 0.682171i | \(0.761036\pi\) | |||||||
\(968\) | 21.0000 | 0.674966 | ||||||||
\(969\) | 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 | ||||||||
\(973\) | 22.3607 | + | 35.3553i | 0.716850 | + | 1.13344i | ||||
\(974\) | 25.4558i | 0.815658i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 9.48683i | 0.303666i | ||||||||
\(977\) | −18.0000 | −0.575871 | −0.287936 | − | 0.957650i | \(-0.592969\pi\) | ||||
−0.287936 | + | 0.957650i | \(0.592969\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 25.2982i | 0.808535i | ||||||||
\(980\) | 6.70820 | − | 14.1421i | 0.214286 | − | 0.451754i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | − | 19.7990i | − | 0.631811i | ||||||
\(983\) | − | 9.48683i | − | 0.302583i | −0.988489 | − | 0.151291i | \(-0.951657\pi\) | ||
0.988489 | − | 0.151291i | \(-0.0483432\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −26.8328 | −0.854965 | ||||||||
\(986\) | 8.94427 | 0.284844 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 14.1421i | 0.449921i | ||||||||
\(989\) | − | 5.65685i | − | 0.179878i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 40.0000 | 1.27064 | 0.635321 | − | 0.772248i | \(-0.280868\pi\) | ||||
0.635321 | + | 0.772248i | \(0.280868\pi\) | |||||||
\(992\) | − | 6.32456i | − | 0.200805i | ||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −2.00000 | − | 3.16228i | −0.0634361 | − | 0.100301i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 13.4164 | 0.424902 | 0.212451 | − | 0.977172i | \(-0.431855\pi\) | ||||
0.212451 | + | 0.977172i | \(0.431855\pi\) | |||||||
\(998\) | 20.0000 | 0.633089 | ||||||||
\(999\) | 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 | 630.2.d.b.629.4 | yes | 4 | |
3.2 | odd | 2 | 630.2.d.c.629.2 | yes | 4 | ||
4.3 | odd | 2 | 5040.2.k.b.1889.3 | 4 | |||
5.2 | odd | 4 | 3150.2.b.b.251.1 | 8 | |||
5.3 | odd | 4 | 3150.2.b.b.251.8 | 8 | |||
5.4 | even | 2 | 630.2.d.c.629.3 | yes | 4 | ||
7.6 | odd | 2 | inner | 630.2.d.b.629.2 | yes | 4 | |
12.11 | even | 2 | 5040.2.k.c.1889.1 | 4 | |||
15.2 | even | 4 | 3150.2.b.b.251.5 | 8 | |||
15.8 | even | 4 | 3150.2.b.b.251.4 | 8 | |||
15.14 | odd | 2 | inner | 630.2.d.b.629.1 | ✓ | 4 | |
20.19 | odd | 2 | 5040.2.k.c.1889.4 | 4 | |||
21.20 | even | 2 | 630.2.d.c.629.4 | yes | 4 | ||
28.27 | even | 2 | 5040.2.k.b.1889.1 | 4 | |||
35.13 | even | 4 | 3150.2.b.b.251.7 | 8 | |||
35.27 | even | 4 | 3150.2.b.b.251.2 | 8 | |||
35.34 | odd | 2 | 630.2.d.c.629.1 | yes | 4 | ||
60.59 | even | 2 | 5040.2.k.b.1889.2 | 4 | |||
84.83 | odd | 2 | 5040.2.k.c.1889.3 | 4 | |||
105.62 | odd | 4 | 3150.2.b.b.251.6 | 8 | |||
105.83 | odd | 4 | 3150.2.b.b.251.3 | 8 | |||
105.104 | even | 2 | inner | 630.2.d.b.629.3 | yes | 4 | |
140.139 | even | 2 | 5040.2.k.c.1889.2 | 4 | |||
420.419 | odd | 2 | 5040.2.k.b.1889.4 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
630.2.d.b.629.1 | ✓ | 4 | 15.14 | odd | 2 | inner | |
630.2.d.b.629.2 | yes | 4 | 7.6 | odd | 2 | inner | |
630.2.d.b.629.3 | yes | 4 | 105.104 | even | 2 | inner | |
630.2.d.b.629.4 | yes | 4 | 1.1 | even | 1 | trivial | |
630.2.d.c.629.1 | yes | 4 | 35.34 | odd | 2 | ||
630.2.d.c.629.2 | yes | 4 | 3.2 | odd | 2 | ||
630.2.d.c.629.3 | yes | 4 | 5.4 | even | 2 | ||
630.2.d.c.629.4 | yes | 4 | 21.20 | even | 2 | ||
3150.2.b.b.251.1 | 8 | 5.2 | odd | 4 | |||
3150.2.b.b.251.2 | 8 | 35.27 | even | 4 | |||
3150.2.b.b.251.3 | 8 | 105.83 | odd | 4 | |||
3150.2.b.b.251.4 | 8 | 15.8 | even | 4 | |||
3150.2.b.b.251.5 | 8 | 15.2 | even | 4 | |||
3150.2.b.b.251.6 | 8 | 105.62 | odd | 4 | |||
3150.2.b.b.251.7 | 8 | 35.13 | even | 4 | |||
3150.2.b.b.251.8 | 8 | 5.3 | odd | 4 | |||
5040.2.k.b.1889.1 | 4 | 28.27 | even | 2 | |||
5040.2.k.b.1889.2 | 4 | 60.59 | even | 2 | |||
5040.2.k.b.1889.3 | 4 | 4.3 | odd | 2 | |||
5040.2.k.b.1889.4 | 4 | 420.419 | odd | 2 | |||
5040.2.k.c.1889.1 | 4 | 12.11 | even | 2 | |||
5040.2.k.c.1889.2 | 4 | 140.139 | even | 2 | |||
5040.2.k.c.1889.3 | 4 | 84.83 | odd | 2 | |||
5040.2.k.c.1889.4 | 4 | 20.19 | odd | 2 |