Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [315,2,Mod(8,315)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(315, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 3, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("315.8");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 315 = 3^{2} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 315.m (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(2.51528766367\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} + 18x^{10} + 107x^{8} + 240x^{6} + 151x^{4} + 30x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 197.6 | ||
Root | \(0.556948i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 315.197 |
Dual form | 315.2.m.b.8.6 |
$q$-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 \(\left(\mathbb{Z}/315\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(136\) | \(281\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.96418 | − | 1.96418i | 1.38888 | − | 1.38888i | 0.561214 | − | 0.827671i | \(-0.310334\pi\) |
0.827671 | − | 0.561214i | \(-0.189666\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | − | 5.71600i | − | 2.85800i | ||||||
\(5\) | 1.65089 | + | 1.50816i | 0.738303 | + | 0.674470i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.707107 | + | 0.707107i | 0.267261 | + | 0.267261i | ||||
\(8\) | −7.29890 | − | 7.29890i | −2.58055 | − | 2.58055i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 6.20495 | − | 0.280357i | 1.96218 | − | 0.0886565i | ||||
\(11\) | 0.248425i | 0.0749029i | 0.999298 | + | 0.0374515i | \(0.0119240\pi\) | ||||
−0.999298 | + | 0.0374515i | \(0.988076\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.37141 | + | 3.37141i | −0.935061 | + | 0.935061i | −0.998016 | − | 0.0629552i | \(-0.979947\pi\) |
0.0629552 | + | 0.998016i | \(0.479947\pi\) | |||||||
\(14\) | 2.77777 | 0.742390 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −17.2407 | −4.31017 | ||||||||
\(17\) | 1.75881 | − | 1.75881i | 0.426573 | − | 0.426573i | −0.460886 | − | 0.887459i | \(-0.652468\pi\) |
0.887459 | + | 0.460886i | \(0.152468\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.91639i | 0.898481i | 0.893411 | + | 0.449241i | \(0.148305\pi\) | ||||
−0.893411 | + | 0.449241i | \(0.851695\pi\) | |||||||
\(20\) | 8.62065 | − | 9.43652i | 1.92764 | − | 2.11007i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0.487951 | + | 0.487951i | 0.104032 | + | 0.104032i | ||||
\(23\) | −2.22082 | − | 2.22082i | −0.463073 | − | 0.463073i | 0.436588 | − | 0.899661i | \(-0.356187\pi\) |
−0.899661 | + | 0.436588i | \(0.856187\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.450907 | + | 4.97963i | 0.0901814 | + | 0.995925i | ||||
\(26\) | 13.2441i | 2.59738i | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 4.04182 | − | 4.04182i | 0.763833 | − | 0.763833i | ||||
\(29\) | 2.65164 | 0.492398 | 0.246199 | − | 0.969219i | \(-0.420818\pi\) | ||||
0.246199 | + | 0.969219i | \(0.420818\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.96443 | −0.532427 | −0.266213 | − | 0.963914i | \(-0.585773\pi\) | ||||
−0.266213 | + | 0.963914i | \(0.585773\pi\) | |||||||
\(32\) | −19.2660 | + | 19.2660i | −3.40578 | + | 3.40578i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | − | 6.90922i | − | 1.18492i | ||||||
\(35\) | 0.100929 | + | 2.23379i | 0.0170601 | + | 0.377579i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.76257 | + | 1.76257i | 0.289765 | + | 0.289765i | 0.836987 | − | 0.547222i | \(-0.184315\pi\) |
−0.547222 | + | 0.836987i | \(0.684315\pi\) | |||||||
\(38\) | 7.69249 | + | 7.69249i | 1.24789 | + | 1.24789i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −1.04181 | − | 23.0576i | −0.164724 | − | 3.64573i | ||||
\(41\) | − | 7.42003i | − | 1.15881i | −0.815038 | − | 0.579407i | \(-0.803284\pi\) | ||
0.815038 | − | 0.579407i | \(-0.196716\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.716003 | + | 0.716003i | −0.109189 | + | 0.109189i | −0.759591 | − | 0.650401i | \(-0.774601\pi\) |
0.650401 | + | 0.759591i | \(0.274601\pi\) | |||||||
\(44\) | 1.42000 | 0.214073 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −8.72418 | −1.28631 | ||||||||
\(47\) | 3.34257 | − | 3.34257i | 0.487564 | − | 0.487564i | −0.419972 | − | 0.907537i | \(-0.637960\pi\) |
0.907537 | + | 0.419972i | \(0.137960\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000i | 0.142857i | ||||||||
\(50\) | 10.6665 | + | 8.89522i | 1.50848 | + | 1.25797i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 19.2710 | + | 19.2710i | 2.67241 | + | 2.67241i | ||||
\(53\) | 4.25628 | + | 4.25628i | 0.584645 | + | 0.584645i | 0.936176 | − | 0.351531i | \(-0.114339\pi\) |
−0.351531 | + | 0.936176i | \(0.614339\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −0.374665 | + | 0.410123i | −0.0505198 | + | 0.0553010i | ||||
\(56\) | − | 10.3222i | − | 1.37936i | ||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 5.20830 | − | 5.20830i | 0.683884 | − | 0.683884i | ||||
\(59\) | 4.88610 | 0.636116 | 0.318058 | − | 0.948071i | \(-0.396969\pi\) | ||||
0.318058 | + | 0.948071i | \(0.396969\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 9.55025 | 1.22278 | 0.611392 | − | 0.791328i | \(-0.290610\pi\) | ||||
0.611392 | + | 0.791328i | \(0.290610\pi\) | |||||||
\(62\) | −5.82267 | + | 5.82267i | −0.739480 | + | 0.739480i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 41.2024i | 5.15030i | ||||||||
\(65\) | −10.6505 | + | 0.481217i | −1.32103 | + | 0.0596877i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −5.98889 | − | 5.98889i | −0.731660 | − | 0.731660i | 0.239289 | − | 0.970948i | \(-0.423086\pi\) |
−0.970948 | + | 0.239289i | \(0.923086\pi\) | |||||||
\(68\) | −10.0533 | − | 10.0533i | −1.21915 | − | 1.21915i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 4.58580 | + | 4.18932i | 0.548109 | + | 0.500720i | ||||
\(71\) | − | 6.31723i | − | 0.749717i | −0.927082 | − | 0.374858i | \(-0.877691\pi\) | ||
0.927082 | − | 0.374858i | \(-0.122309\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −10.3263 | + | 10.3263i | −1.20860 | + | 1.20860i | −0.237125 | + | 0.971479i | \(0.576205\pi\) |
−0.971479 | + | 0.237125i | \(0.923795\pi\) | |||||||
\(74\) | 6.92401 | 0.804900 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 22.3861 | 2.56786 | ||||||||
\(77\) | −0.175663 | + | 0.175663i | −0.0200187 | + | 0.0200187i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 11.2561i | − | 1.26641i | −0.773985 | − | 0.633204i | \(-0.781739\pi\) | ||
0.773985 | − | 0.633204i | \(-0.218261\pi\) | |||||||
\(80\) | −28.4626 | − | 26.0017i | −3.18221 | − | 2.90708i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −14.5743 | − | 14.5743i | −1.60946 | − | 1.60946i | ||||
\(83\) | −10.1710 | − | 10.1710i | −1.11641 | − | 1.11641i | −0.992264 | − | 0.124149i | \(-0.960380\pi\) |
−0.124149 | − | 0.992264i | \(-0.539620\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 5.55616 | − | 0.251043i | 0.602651 | − | 0.0272294i | ||||
\(86\) | 2.81272i | 0.303303i | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 1.81323 | − | 1.81323i | 0.193291 | − | 0.193291i | ||||
\(89\) | −1.91884 | −0.203396 | −0.101698 | − | 0.994815i | \(-0.532428\pi\) | ||||
−0.101698 | + | 0.994815i | \(0.532428\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −4.76790 | −0.499811 | ||||||||
\(92\) | −12.6942 | + | 12.6942i | −1.32346 | + | 1.32346i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | − | 13.1308i | − | 1.35434i | ||||||
\(95\) | −5.90654 | + | 6.46554i | −0.605998 | + | 0.663351i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.07023 | + | 1.07023i | 0.108666 | + | 0.108666i | 0.759349 | − | 0.650684i | \(-0.225518\pi\) |
−0.650684 | + | 0.759349i | \(0.725518\pi\) | |||||||
\(98\) | 1.96418 | + | 1.96418i | 0.198412 | + | 0.198412i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 28.4636 | − | 2.57738i | 2.84636 | − | 0.257738i | ||||
\(101\) | 8.86551i | 0.882151i | 0.897470 | + | 0.441076i | \(0.145403\pi\) | ||||
−0.897470 | + | 0.441076i | \(0.854597\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −12.8870 | + | 12.8870i | −1.26979 | + | 1.26979i | −0.323600 | + | 0.946194i | \(0.604893\pi\) |
−0.946194 | + | 0.323600i | \(0.895107\pi\) | |||||||
\(104\) | 49.2152 | 4.82594 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 16.7202 | 1.62401 | ||||||||
\(107\) | 0.890257 | − | 0.890257i | 0.0860644 | − | 0.0860644i | −0.662764 | − | 0.748828i | \(-0.730617\pi\) |
0.748828 | + | 0.662764i | \(0.230617\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 0.924031i | − | 0.0885061i | −0.999020 | − | 0.0442531i | \(-0.985909\pi\) | ||
0.999020 | − | 0.0442531i | \(-0.0140908\pi\) | |||||||
\(110\) | 0.0696476 | + | 1.54146i | 0.00664064 | + | 0.146973i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −12.1910 | − | 12.1910i | −1.15194 | − | 1.15194i | ||||
\(113\) | −4.32422 | − | 4.32422i | −0.406788 | − | 0.406788i | 0.473829 | − | 0.880617i | \(-0.342872\pi\) |
−0.880617 | + | 0.473829i | \(0.842872\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −0.316988 | − | 7.01570i | −0.0295593 | − | 0.654217i | ||||
\(116\) | − | 15.1568i | − | 1.40727i | ||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 9.59718 | − | 9.59718i | 0.883492 | − | 0.883492i | ||||
\(119\) | 2.48733 | 0.228013 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 10.9383 | 0.994390 | ||||||||
\(122\) | 18.7584 | − | 18.7584i | 1.69831 | − | 1.69831i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 16.9447i | 1.52168i | ||||||||
\(125\) | −6.76567 | + | 8.90088i | −0.605140 | + | 0.796119i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −9.90911 | − | 9.90911i | −0.879291 | − | 0.879291i | 0.114170 | − | 0.993461i | \(-0.463579\pi\) |
−0.993461 | + | 0.114170i | \(0.963579\pi\) | |||||||
\(128\) | 42.3969 | + | 42.3969i | 3.74740 | + | 3.74740i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −19.9742 | + | 21.8646i | −1.75186 | + | 1.91766i | ||||
\(131\) | 5.19668i | 0.454036i | 0.973891 | + | 0.227018i | \(0.0728977\pi\) | ||||
−0.973891 | + | 0.227018i | \(0.927102\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.76930 | + | 2.76930i | −0.240129 | + | 0.240129i | ||||
\(134\) | −23.5265 | −2.03238 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −25.6747 | −2.20159 | ||||||||
\(137\) | −4.28754 | + | 4.28754i | −0.366309 | + | 0.366309i | −0.866129 | − | 0.499820i | \(-0.833399\pi\) |
0.499820 | + | 0.866129i | \(0.333399\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 10.5755i | − | 0.897004i | −0.893782 | − | 0.448502i | \(-0.851958\pi\) | ||
0.893782 | − | 0.448502i | \(-0.148042\pi\) | |||||||
\(140\) | 12.7683 | − | 0.576909i | 1.07912 | − | 0.0487577i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −12.4082 | − | 12.4082i | −1.04127 | − | 1.04127i | ||||
\(143\) | −0.837543 | − | 0.837543i | −0.0700388 | − | 0.0700388i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 4.37758 | + | 3.99910i | 0.363539 | + | 0.332107i | ||||
\(146\) | 40.5655i | 3.35722i | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 10.0749 | − | 10.0749i | 0.828148 | − | 0.828148i | ||||
\(149\) | −23.2814 | −1.90728 | −0.953641 | − | 0.300945i | \(-0.902698\pi\) | ||||
−0.953641 | + | 0.300945i | \(0.902698\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 13.2865 | 1.08124 | 0.540619 | − | 0.841267i | \(-0.318190\pi\) | ||||
0.540619 | + | 0.841267i | \(0.318190\pi\) | |||||||
\(152\) | 28.5853 | − | 28.5853i | 2.31858 | − | 2.31858i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0.690067i | 0.0556072i | ||||||||
\(155\) | −4.89396 | − | 4.47083i | −0.393092 | − | 0.359106i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −4.82641 | − | 4.82641i | −0.385189 | − | 0.385189i | 0.487778 | − | 0.872968i | \(-0.337807\pi\) |
−0.872968 | + | 0.487778i | \(0.837807\pi\) | |||||||
\(158\) | −22.1090 | − | 22.1090i | −1.75890 | − | 1.75890i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −60.8624 | + | 2.74993i | −4.81159 | + | 0.217401i | ||||
\(161\) | − | 3.14072i | − | 0.247523i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 3.30623 | − | 3.30623i | 0.258964 | − | 0.258964i | −0.565669 | − | 0.824633i | \(-0.691382\pi\) |
0.824633 | + | 0.565669i | \(0.191382\pi\) | |||||||
\(164\) | −42.4129 | −3.31189 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −39.9553 | −3.10114 | ||||||||
\(167\) | −3.97778 | + | 3.97778i | −0.307810 | + | 0.307810i | −0.844060 | − | 0.536249i | \(-0.819841\pi\) |
0.536249 | + | 0.844060i | \(0.319841\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 9.73282i | − | 0.748679i | ||||||
\(170\) | 10.4202 | − | 11.4064i | 0.799194 | − | 0.874831i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 4.09268 | + | 4.09268i | 0.312064 | + | 0.312064i | ||||
\(173\) | 15.3803 | + | 15.3803i | 1.16934 | + | 1.16934i | 0.982364 | + | 0.186978i | \(0.0598692\pi\) |
0.186978 | + | 0.982364i | \(0.440131\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −3.20229 | + | 3.83997i | −0.242070 | + | 0.290274i | ||||
\(176\) | − | 4.28302i | − | 0.322845i | ||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −3.76894 | + | 3.76894i | −0.282494 | + | 0.282494i | ||||
\(179\) | 22.4863 | 1.68070 | 0.840352 | − | 0.542041i | \(-0.182348\pi\) | ||||
0.840352 | + | 0.542041i | \(0.182348\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 5.56307 | 0.413500 | 0.206750 | − | 0.978394i | \(-0.433711\pi\) | ||||
0.206750 | + | 0.978394i | \(0.433711\pi\) | |||||||
\(182\) | −9.36500 | + | 9.36500i | −0.694180 | + | 0.694180i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 32.4191i | 2.38997i | ||||||||
\(185\) | 0.251580 | + | 5.56806i | 0.0184965 | + | 0.409372i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.436931 | + | 0.436931i | 0.0319516 | + | 0.0319516i | ||||
\(188\) | −19.1062 | − | 19.1062i | −1.39346 | − | 1.39346i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 1.09799 | + | 24.3010i | 0.0796562 | + | 1.76298i | ||||
\(191\) | − | 10.0091i | − | 0.724230i | −0.932133 | − | 0.362115i | \(-0.882055\pi\) | ||
0.932133 | − | 0.362115i | \(-0.117945\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 5.10673 | − | 5.10673i | 0.367590 | − | 0.367590i | −0.499007 | − | 0.866598i | \(-0.666302\pi\) |
0.866598 | + | 0.499007i | \(0.166302\pi\) | |||||||
\(194\) | 4.20425 | 0.301848 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 5.71600 | 0.408286 | ||||||||
\(197\) | −4.32422 | + | 4.32422i | −0.308088 | + | 0.308088i | −0.844167 | − | 0.536080i | \(-0.819905\pi\) |
0.536080 | + | 0.844167i | \(0.319905\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 13.5542i | 0.960831i | 0.877041 | + | 0.480416i | \(0.159514\pi\) | ||||
−0.877041 | + | 0.480416i | \(0.840486\pi\) | |||||||
\(200\) | 33.0547 | − | 39.6369i | 2.33732 | − | 2.80275i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 17.4135 | + | 17.4135i | 1.22521 | + | 1.22521i | ||||
\(203\) | 1.87499 | + | 1.87499i | 0.131599 | + | 0.131599i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 11.1906 | − | 12.2497i | 0.781585 | − | 0.855556i | ||||
\(206\) | 50.6248i | 3.52720i | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 58.1254 | − | 58.1254i | 4.03027 | − | 4.03027i | ||||
\(209\) | −0.972929 | −0.0672989 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −16.9166 | −1.16459 | −0.582294 | − | 0.812978i | \(-0.697845\pi\) | ||||
−0.582294 | + | 0.812978i | \(0.697845\pi\) | |||||||
\(212\) | 24.3289 | − | 24.3289i | 1.67092 | − | 1.67092i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | − | 3.49725i | − | 0.239067i | ||||||
\(215\) | −2.26189 | + | 0.102198i | −0.154260 | + | 0.00696988i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2.09617 | − | 2.09617i | −0.142297 | − | 0.142297i | ||||
\(218\) | −1.81496 | − | 1.81496i | −0.122925 | − | 0.122925i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 2.34427 | + | 2.14158i | 0.158050 | + | 0.144386i | ||||
\(221\) | 11.8593i | 0.797744i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 7.46128 | − | 7.46128i | 0.499644 | − | 0.499644i | −0.411683 | − | 0.911327i | \(-0.635059\pi\) |
0.911327 | + | 0.411683i | \(0.135059\pi\) | |||||||
\(224\) | −27.2462 | −1.82047 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −16.9871 | −1.12996 | ||||||||
\(227\) | 7.75452 | − | 7.75452i | 0.514686 | − | 0.514686i | −0.401273 | − | 0.915959i | \(-0.631432\pi\) |
0.915959 | + | 0.401273i | \(0.131432\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 12.1905i | − | 0.805573i | −0.915294 | − | 0.402787i | \(-0.868042\pi\) | ||
0.915294 | − | 0.402787i | \(-0.131958\pi\) | |||||||
\(230\) | −14.4027 | − | 13.1575i | −0.949686 | − | 0.867577i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −19.3541 | − | 19.3541i | −1.27066 | − | 1.27066i | ||||
\(233\) | −17.0691 | − | 17.0691i | −1.11824 | − | 1.11824i | −0.992000 | − | 0.126235i | \(-0.959711\pi\) |
−0.126235 | − | 0.992000i | \(-0.540289\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 10.5594 | − | 0.477101i | 0.688817 | − | 0.0311226i | ||||
\(236\) | − | 27.9290i | − | 1.81802i | ||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 4.88556 | − | 4.88556i | 0.316684 | − | 0.316684i | ||||
\(239\) | 15.6083 | 1.00962 | 0.504808 | − | 0.863231i | \(-0.331563\pi\) | ||||
0.504808 | + | 0.863231i | \(0.331563\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 19.4210 | 1.25101 | 0.625507 | − | 0.780219i | \(-0.284892\pi\) | ||||
0.625507 | + | 0.780219i | \(0.284892\pi\) | |||||||
\(242\) | 21.4848 | − | 21.4848i | 1.38109 | − | 1.38109i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | − | 54.5893i | − | 3.49472i | ||||||
\(245\) | −1.50816 | + | 1.65089i | −0.0963528 | + | 0.105472i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −13.2038 | − | 13.2038i | −0.840135 | − | 0.840135i | ||||
\(248\) | 21.6371 | + | 21.6371i | 1.37395 | + | 1.37395i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 4.19393 | + | 30.7719i | 0.265247 | + | 1.94619i | ||||
\(251\) | − | 21.7281i | − | 1.37147i | −0.727853 | − | 0.685734i | \(-0.759482\pi\) | ||
0.727853 | − | 0.685734i | \(-0.240518\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0.551707 | − | 0.551707i | 0.0346855 | − | 0.0346855i | ||||
\(254\) | −38.9265 | −2.44247 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 84.1456 | 5.25910 | ||||||||
\(257\) | −1.95493 | + | 1.95493i | −0.121945 | + | 0.121945i | −0.765446 | − | 0.643500i | \(-0.777481\pi\) |
0.643500 | + | 0.765446i | \(0.277481\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2.49265i | 0.154886i | ||||||||
\(260\) | 2.75064 | + | 60.8781i | 0.170587 | + | 3.77550i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 10.2072 | + | 10.2072i | 0.630604 | + | 0.630604i | ||||
\(263\) | 5.40146 | + | 5.40146i | 0.333068 | + | 0.333068i | 0.853750 | − | 0.520682i | \(-0.174322\pi\) |
−0.520682 | + | 0.853750i | \(0.674322\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0.607519 | + | 13.4458i | 0.0373196 | + | 0.825970i | ||||
\(266\) | 10.8788i | 0.667023i | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −34.2325 | + | 34.2325i | −2.09108 | + | 2.09108i | ||||
\(269\) | 21.6690 | 1.32118 | 0.660590 | − | 0.750747i | \(-0.270306\pi\) | ||||
0.660590 | + | 0.750747i | \(0.270306\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 4.91623 | 0.298640 | 0.149320 | − | 0.988789i | \(-0.452292\pi\) | ||||
0.149320 | + | 0.988789i | \(0.452292\pi\) | |||||||
\(272\) | −30.3230 | + | 30.3230i | −1.83860 | + | 1.83860i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 16.8430i | 1.01752i | ||||||||
\(275\) | −1.23706 | + | 0.112016i | −0.0745977 | + | 0.00675485i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 17.4586 | + | 17.4586i | 1.04898 | + | 1.04898i | 0.998737 | + | 0.0502482i | \(0.0160012\pi\) |
0.0502482 | + | 0.998737i | \(0.483999\pi\) | |||||||
\(278\) | −20.7722 | − | 20.7722i | −1.24584 | − | 1.24584i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 15.5675 | − | 17.0409i | 0.930338 | − | 1.01839i | ||||
\(281\) | − | 14.4804i | − | 0.863830i | −0.901914 | − | 0.431915i | \(-0.857838\pi\) | ||
0.901914 | − | 0.431915i | \(-0.142162\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −18.5661 | + | 18.5661i | −1.10364 | + | 1.10364i | −0.109671 | + | 0.993968i | \(0.534980\pi\) |
−0.993968 | + | 0.109671i | \(0.965020\pi\) | |||||||
\(284\) | −36.1093 | −2.14269 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −3.29017 | −0.194552 | ||||||||
\(287\) | 5.24676 | − | 5.24676i | 0.309706 | − | 0.309706i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 10.8132i | 0.636071i | ||||||||
\(290\) | 16.4533 | − | 0.743406i | 0.966172 | − | 0.0436543i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 59.0253 | + | 59.0253i | 3.45419 | + | 3.45419i | ||||
\(293\) | 11.7184 | + | 11.7184i | 0.684596 | + | 0.684596i | 0.961032 | − | 0.276437i | \(-0.0891536\pi\) |
−0.276437 | + | 0.961032i | \(0.589154\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 8.06644 | + | 7.36903i | 0.469646 | + | 0.429041i | ||||
\(296\) | − | 25.7296i | − | 1.49551i | ||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −45.7288 | + | 45.7288i | −2.64900 | + | 2.64900i | ||||
\(299\) | 14.9746 | 0.866004 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.01258 | −0.0583642 | ||||||||
\(302\) | 26.0970 | − | 26.0970i | 1.50172 | − | 1.50172i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | − | 67.5212i | − | 3.87261i | ||||||
\(305\) | 15.7665 | + | 14.4033i | 0.902785 | + | 0.824731i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −20.9578 | − | 20.9578i | −1.19612 | − | 1.19612i | −0.975317 | − | 0.220807i | \(-0.929131\pi\) |
−0.220807 | − | 0.975317i | \(-0.570869\pi\) | |||||||
\(308\) | 1.00409 | + | 1.00409i | 0.0572133 | + | 0.0572133i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −18.3941 | + | 0.831097i | −1.04472 | + | 0.0472031i | ||||
\(311\) | 15.2031i | 0.862090i | 0.902330 | + | 0.431045i | \(0.141855\pi\) | ||||
−0.902330 | + | 0.431045i | \(0.858145\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 0.179190 | − | 0.179190i | 0.0101284 | − | 0.0101284i | −0.702024 | − | 0.712153i | \(-0.747720\pi\) |
0.712153 | + | 0.702024i | \(0.247720\pi\) | |||||||
\(314\) | −18.9599 | −1.06997 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −64.3398 | −3.61940 | ||||||||
\(317\) | 10.2500 | − | 10.2500i | 0.575697 | − | 0.575697i | −0.358018 | − | 0.933715i | \(-0.616547\pi\) |
0.933715 | + | 0.358018i | \(0.116547\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0.658734i | 0.0368820i | ||||||||
\(320\) | −62.1398 | + | 68.0209i | −3.47372 | + | 3.80248i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −6.16893 | − | 6.16893i | −0.343781 | − | 0.343781i | ||||
\(323\) | 6.88817 | + | 6.88817i | 0.383268 | + | 0.383268i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −18.3086 | − | 15.2682i | −1.01558 | − | 0.846926i | ||||
\(326\) | − | 12.9881i | − | 0.719342i | ||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −54.1581 | + | 54.1581i | −2.99038 | + | 2.99038i | ||||
\(329\) | 4.72711 | 0.260614 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 18.5908 | 1.02184 | 0.510920 | − | 0.859628i | \(-0.329305\pi\) | ||||
0.510920 | + | 0.859628i | \(0.329305\pi\) | |||||||
\(332\) | −58.1375 | + | 58.1375i | −3.19071 | + | 3.19071i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 15.6262i | 0.855025i | ||||||||
\(335\) | −0.854823 | − | 18.9192i | −0.0467040 | − | 1.03367i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 12.2286 | + | 12.2286i | 0.666132 | + | 0.666132i | 0.956818 | − | 0.290686i | \(-0.0938836\pi\) |
−0.290686 | + | 0.956818i | \(0.593884\pi\) | |||||||
\(338\) | −19.1170 | − | 19.1170i | −1.03983 | − | 1.03983i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −1.43496 | − | 31.7590i | −0.0778217 | − | 1.72238i | ||||
\(341\) | − | 0.736438i | − | 0.0398803i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −0.707107 | + | 0.707107i | −0.0381802 | + | 0.0381802i | ||||
\(344\) | 10.4521 | 0.563538 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 60.4193 | 3.24816 | ||||||||
\(347\) | −10.3260 | + | 10.3260i | −0.554327 | + | 0.554327i | −0.927687 | − | 0.373360i | \(-0.878206\pi\) |
0.373360 | + | 0.927687i | \(0.378206\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 2.62685i | 0.140612i | 0.997525 | + | 0.0703060i | \(0.0223976\pi\) | ||||
−0.997525 | + | 0.0703060i | \(0.977602\pi\) | |||||||
\(350\) | 1.25252 | + | 13.8323i | 0.0669497 | + | 0.739365i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −4.78616 | − | 4.78616i | −0.255103 | − | 0.255103i | ||||
\(353\) | −1.84420 | − | 1.84420i | −0.0981569 | − | 0.0981569i | 0.656323 | − | 0.754480i | \(-0.272111\pi\) |
−0.754480 | + | 0.656323i | \(0.772111\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 9.52739 | − | 10.4291i | 0.505661 | − | 0.553518i | ||||
\(356\) | 10.9681i | 0.581307i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 44.1671 | − | 44.1671i | 2.33430 | − | 2.33430i | ||||
\(359\) | 25.9440 | 1.36927 | 0.684637 | − | 0.728884i | \(-0.259961\pi\) | ||||
0.684637 | + | 0.728884i | \(0.259961\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 3.66191 | 0.192732 | ||||||||
\(362\) | 10.9269 | − | 10.9269i | 0.574303 | − | 0.574303i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 27.2533i | 1.42846i | ||||||||
\(365\) | −32.6214 | + | 1.47392i | −1.70748 | + | 0.0771487i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −13.5250 | − | 13.5250i | −0.706000 | − | 0.706000i | 0.259691 | − | 0.965692i | \(-0.416379\pi\) |
−0.965692 | + | 0.259691i | \(0.916379\pi\) | |||||||
\(368\) | 38.2885 | + | 38.2885i | 1.99592 | + | 1.99592i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 11.4308 | + | 10.4425i | 0.594260 | + | 0.542881i | ||||
\(371\) | 6.01929i | 0.312506i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 2.02011 | − | 2.02011i | 0.104597 | − | 0.104597i | −0.652871 | − | 0.757469i | \(-0.726436\pi\) |
0.757469 | + | 0.652871i | \(0.226436\pi\) | |||||||
\(374\) | 1.71642 | 0.0887541 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −48.7942 | −2.51637 | ||||||||
\(377\) | −8.93978 | + | 8.93978i | −0.460422 | + | 0.460422i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 4.11882i | 0.211570i | 0.994389 | + | 0.105785i | \(0.0337355\pi\) | ||||
−0.994389 | + | 0.105785i | \(0.966265\pi\) | |||||||
\(380\) | 36.9571 | + | 33.7618i | 1.89586 | + | 1.73194i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −19.6596 | − | 19.6596i | −1.00587 | − | 1.00587i | ||||
\(383\) | 18.0158 | + | 18.0158i | 0.920566 | + | 0.920566i | 0.997069 | − | 0.0765031i | \(-0.0243755\pi\) |
−0.0765031 | + | 0.997069i | \(0.524376\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −0.554929 | + | 0.0250732i | −0.0282818 | + | 0.00127785i | ||||
\(386\) | − | 20.0611i | − | 1.02108i | ||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 6.11745 | − | 6.11745i | 0.310566 | − | 0.310566i | ||||
\(389\) | 19.1306 | 0.969960 | 0.484980 | − | 0.874525i | \(-0.338827\pi\) | ||||
0.484980 | + | 0.874525i | \(0.338827\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −7.81199 | −0.395069 | ||||||||
\(392\) | 7.29890 | − | 7.29890i | 0.368650 | − | 0.368650i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 16.9871i | 0.855797i | ||||||||
\(395\) | 16.9760 | − | 18.5826i | 0.854154 | − | 0.934993i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 0.442442 | + | 0.442442i | 0.0222055 | + | 0.0222055i | 0.718122 | − | 0.695917i | \(-0.245002\pi\) |
−0.695917 | + | 0.718122i | \(0.745002\pi\) | |||||||
\(398\) | 26.6229 | + | 26.6229i | 1.33448 | + | 1.33448i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −7.77394 | − | 85.8522i | −0.388697 | − | 4.29261i | ||||
\(401\) | 14.9814i | 0.748137i | 0.927401 | + | 0.374068i | \(0.122037\pi\) | ||||
−0.927401 | + | 0.374068i | \(0.877963\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 9.99430 | − | 9.99430i | 0.497852 | − | 0.497852i | ||||
\(404\) | 50.6753 | 2.52119 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 7.36565 | 0.365551 | ||||||||
\(407\) | −0.437867 | + | 0.437867i | −0.0217042 | + | 0.0217042i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 33.1093i | 1.63715i | 0.574401 | + | 0.818574i | \(0.305235\pi\) | ||||
−0.574401 | + | 0.818574i | \(0.694765\pi\) | |||||||
\(410\) | −2.08026 | − | 46.0410i | −0.102737 | − | 2.27380i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 73.6621 | + | 73.6621i | 3.62907 | + | 3.62907i | ||||
\(413\) | 3.45500 | + | 3.45500i | 0.170009 | + | 0.170009i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1.45175 | − | 32.1307i | −0.0712638 | − | 1.57724i | ||||
\(416\) | − | 129.907i | − | 6.36923i | ||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −1.91101 | + | 1.91101i | −0.0934704 | + | 0.0934704i | ||||
\(419\) | 5.14936 | 0.251562 | 0.125781 | − | 0.992058i | \(-0.459856\pi\) | ||||
0.125781 | + | 0.992058i | \(0.459856\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2.85311 | −0.139052 | −0.0695261 | − | 0.997580i | \(-0.522149\pi\) | ||||
−0.0695261 | + | 0.997580i | \(0.522149\pi\) | |||||||
\(422\) | −33.2273 | + | 33.2273i | −1.61748 | + | 1.61748i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | − | 62.1323i | − | 3.01741i | ||||||
\(425\) | 9.55125 | + | 7.96514i | 0.463304 | + | 0.386366i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 6.75305 | + | 6.75305i | 0.326803 | + | 0.326803i | ||||
\(428\) | −5.08871 | − | 5.08871i | −0.245972 | − | 0.245972i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −4.24203 | + | 4.64350i | −0.204569 | + | 0.223929i | ||||
\(431\) | − | 22.0594i | − | 1.06256i | −0.847196 | − | 0.531281i | \(-0.821711\pi\) | ||
0.847196 | − | 0.531281i | \(-0.178289\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −10.9563 | + | 10.9563i | −0.526528 | + | 0.526528i | −0.919535 | − | 0.393007i | \(-0.871435\pi\) |
0.393007 | + | 0.919535i | \(0.371435\pi\) | |||||||
\(434\) | −8.23450 | −0.395269 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −5.28176 | −0.252951 | ||||||||
\(437\) | 8.69760 | − | 8.69760i | 0.416062 | − | 0.416062i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 7.45413i | 0.355766i | 0.984052 | + | 0.177883i | \(0.0569249\pi\) | ||||
−0.984052 | + | 0.177883i | \(0.943075\pi\) | |||||||
\(440\) | 5.72809 | − | 0.258811i | 0.273076 | − | 0.0123383i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 23.2938 | + | 23.2938i | 1.10797 | + | 1.10797i | ||||
\(443\) | 4.02408 | + | 4.02408i | 0.191190 | + | 0.191190i | 0.796210 | − | 0.605020i | \(-0.206835\pi\) |
−0.605020 | + | 0.796210i | \(0.706835\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −3.16780 | − | 2.89391i | −0.150168 | − | 0.137185i | ||||
\(446\) | − | 29.3106i | − | 1.38790i | ||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −29.1345 | + | 29.1345i | −1.37648 | + | 1.37648i | ||||
\(449\) | −22.8230 | −1.07708 | −0.538542 | − | 0.842599i | \(-0.681025\pi\) | ||||
−0.538542 | + | 0.842599i | \(0.681025\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.84332 | 0.0867986 | ||||||||
\(452\) | −24.7172 | + | 24.7172i | −1.16260 | + | 1.16260i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | − | 30.4625i | − | 1.42968i | ||||||
\(455\) | −7.87129 | − | 7.19075i | −0.369012 | − | 0.337107i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 21.3136 | + | 21.3136i | 0.997009 | + | 0.997009i | 0.999996 | − | 0.00298687i | \(-0.000950751\pi\) |
−0.00298687 | + | 0.999996i | \(0.500951\pi\) | |||||||
\(458\) | −23.9444 | − | 23.9444i | −1.11885 | − | 1.11885i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −40.1017 | + | 1.81191i | −1.86975 | + | 0.0844805i | ||||
\(461\) | − | 19.3297i | − | 0.900275i | −0.892959 | − | 0.450137i | \(-0.851375\pi\) | ||
0.892959 | − | 0.450137i | \(-0.148625\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 7.95996 | − | 7.95996i | 0.369931 | − | 0.369931i | −0.497521 | − | 0.867452i | \(-0.665756\pi\) |
0.867452 | + | 0.497521i | \(0.165756\pi\) | |||||||
\(464\) | −45.7161 | −2.12232 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −67.0536 | −3.10620 | ||||||||
\(467\) | −24.9349 | + | 24.9349i | −1.15385 | + | 1.15385i | −0.168076 | + | 0.985774i | \(0.553756\pi\) |
−0.985774 | + | 0.168076i | \(0.946244\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 8.46957i | − | 0.391088i | ||||||
\(470\) | 19.8034 | − | 21.6776i | 0.913462 | − | 0.999914i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −35.6632 | − | 35.6632i | −1.64153 | − | 1.64153i | ||||
\(473\) | −0.177873 | − | 0.177873i | −0.00817861 | − | 0.00817861i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −19.5022 | + | 1.76593i | −0.894820 | + | 0.0810262i | ||||
\(476\) | − | 14.2176i | − | 0.651661i | ||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 30.6575 | − | 30.6575i | 1.40224 | − | 1.40224i | ||||
\(479\) | −40.2495 | −1.83905 | −0.919524 | − | 0.393034i | \(-0.871426\pi\) | ||||
−0.919524 | + | 0.393034i | \(0.871426\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −11.8847 | −0.541896 | ||||||||
\(482\) | 38.1462 | − | 38.1462i | 1.73751 | − | 1.73751i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | − | 62.5233i | − | 2.84197i | ||||||
\(485\) | 0.152759 | + | 3.38092i | 0.00693644 | + | 0.153520i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 24.9159 | + | 24.9159i | 1.12905 | + | 1.12905i | 0.990332 | + | 0.138717i | \(0.0442978\pi\) |
0.138717 | + | 0.990332i | \(0.455702\pi\) | |||||||
\(488\) | −69.7063 | − | 69.7063i | −3.15546 | − | 3.15546i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0.280357 | + | 6.20495i | 0.0126652 | + | 0.280311i | ||||
\(491\) | 7.29487i | 0.329213i | 0.986359 | + | 0.164607i | \(0.0526354\pi\) | ||||
−0.986359 | + | 0.164607i | \(0.947365\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 4.66372 | − | 4.66372i | 0.210044 | − | 0.210044i | ||||
\(494\) | −51.8691 | −2.33370 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 51.1088 | 2.29485 | ||||||||
\(497\) | 4.46695 | − | 4.46695i | 0.200370 | − | 0.200370i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 8.99153i | 0.402516i | 0.979538 | + | 0.201258i | \(0.0645030\pi\) | ||||
−0.979538 | + | 0.201258i | \(0.935497\pi\) | |||||||
\(500\) | 50.8775 | + | 38.6726i | 2.27531 | + | 1.72949i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −42.6779 | − | 42.6779i | −1.90481 | − | 1.90481i | ||||
\(503\) | −14.4521 | − | 14.4521i | −0.644386 | − | 0.644386i | 0.307245 | − | 0.951631i | \(-0.400593\pi\) |
−0.951631 | + | 0.307245i | \(0.900593\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −13.3706 | + | 14.6360i | −0.594984 | + | 0.651294i | ||||
\(506\) | − | 2.16730i | − | 0.0963485i | ||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −56.6405 | + | 56.6405i | −2.51302 | + | 2.51302i | ||||
\(509\) | −20.2009 | −0.895391 | −0.447695 | − | 0.894186i | \(-0.647755\pi\) | ||||
−0.447695 | + | 0.894186i | \(0.647755\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −14.6036 | −0.646026 | ||||||||
\(512\) | 80.4832 | − | 80.4832i | 3.55689 | − | 3.55689i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 7.67967i | 0.338736i | ||||||||
\(515\) | −40.7107 | + | 1.83942i | −1.79393 | + | 0.0810546i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0.830379 | + | 0.830379i | 0.0365200 | + | 0.0365200i | ||||
\(518\) | 4.89601 | + | 4.89601i | 0.215119 | + | 0.215119i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 81.2491 | + | 74.2243i | 3.56301 | + | 3.25495i | ||||
\(521\) | − | 21.7026i | − | 0.950810i | −0.879767 | − | 0.475405i | \(-0.842302\pi\) | ||
0.879767 | − | 0.475405i | \(-0.157698\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 3.17763 | − | 3.17763i | 0.138948 | − | 0.138948i | −0.634211 | − | 0.773160i | \(-0.718675\pi\) |
0.773160 | + | 0.634211i | \(0.218675\pi\) | |||||||
\(524\) | 29.7043 | 1.29764 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 21.2189 | 0.925186 | ||||||||
\(527\) | −5.21385 | + | 5.21385i | −0.227119 | + | 0.227119i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | − | 13.1359i | − | 0.571126i | ||||||
\(530\) | 27.6033 | + | 25.2167i | 1.19901 | + | 1.09534i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 15.8294 | + | 15.8294i | 0.686289 | + | 0.686289i | ||||
\(533\) | 25.0160 | + | 25.0160i | 1.08356 | + | 1.08356i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 2.81237 | − | 0.127071i | 0.121589 | − | 0.00549374i | ||||
\(536\) | 87.4246i | 3.77617i | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 42.5617 | − | 42.5617i | 1.83497 | − | 1.83497i | ||||
\(539\) | −0.248425 | −0.0107004 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 17.9333 | 0.771012 | 0.385506 | − | 0.922705i | \(-0.374027\pi\) | ||||
0.385506 | + | 0.922705i | \(0.374027\pi\) | |||||||
\(542\) | 9.65636 | − | 9.65636i | 0.414776 | − | 0.414776i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 67.7703i | 2.90563i | ||||||||
\(545\) | 1.39359 | − | 1.52548i | 0.0596947 | − | 0.0653443i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 3.40977 | + | 3.40977i | 0.145791 | + | 0.145791i | 0.776235 | − | 0.630444i | \(-0.217127\pi\) |
−0.630444 | + | 0.776235i | \(0.717127\pi\) | |||||||
\(548\) | 24.5076 | + | 24.5076i | 1.04691 | + | 1.04691i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −2.20979 | + | 2.64984i | −0.0942260 | + | 0.112989i | ||||
\(551\) | 10.3849i | 0.442410i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 7.95925 | − | 7.95925i | 0.338462 | − | 0.338462i | ||||
\(554\) | 68.5836 | 2.91384 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −60.4497 | −2.56364 | ||||||||
\(557\) | 0.275161 | − | 0.275161i | 0.0116590 | − | 0.0116590i | −0.701253 | − | 0.712912i | \(-0.747376\pi\) |
0.712912 | + | 0.701253i | \(0.247376\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 4.82788i | − | 0.204198i | ||||||
\(560\) | −1.74008 | − | 38.5121i | −0.0735318 | − | 1.62743i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −28.4422 | − | 28.4422i | −1.19976 | − | 1.19976i | ||||
\(563\) | −25.1442 | − | 25.1442i | −1.05970 | − | 1.05970i | −0.998101 | − | 0.0616005i | \(-0.980380\pi\) |
−0.0616005 | − | 0.998101i | \(-0.519620\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −0.617216 | − | 13.6604i | −0.0259665 | − | 0.574699i | ||||
\(566\) | 72.9342i | 3.06565i | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −46.1088 | + | 46.1088i | −1.93468 | + | 1.93468i | ||||
\(569\) | −26.6023 | −1.11523 | −0.557614 | − | 0.830101i | \(-0.688283\pi\) | ||||
−0.557614 | + | 0.830101i | \(0.688283\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −33.9064 | −1.41894 | −0.709469 | − | 0.704736i | \(-0.751065\pi\) | ||||
−0.709469 | + | 0.704736i | \(0.751065\pi\) | |||||||
\(572\) | −4.78740 | + | 4.78740i | −0.200171 | + | 0.200171i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | − | 20.6111i | − | 0.860293i | ||||||
\(575\) | 10.0575 | − | 12.0602i | 0.419426 | − | 0.502947i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −16.6238 | − | 16.6238i | −0.692057 | − | 0.692057i | 0.270627 | − | 0.962684i | \(-0.412769\pi\) |
−0.962684 | + | 0.270627i | \(0.912769\pi\) | |||||||
\(578\) | 21.2391 | + | 21.2391i | 0.883429 | + | 0.883429i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 22.8589 | − | 25.0223i | 0.949163 | − | 1.03899i | ||||
\(581\) | − | 14.3840i | − | 0.596747i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.05737 | + | 1.05737i | −0.0437916 | + | 0.0437916i | ||||
\(584\) | 150.741 | 6.23773 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 46.0340 | 1.90165 | ||||||||
\(587\) | −4.60012 | + | 4.60012i | −0.189867 | + | 0.189867i | −0.795639 | − | 0.605772i | \(-0.792865\pi\) |
0.605772 | + | 0.795639i | \(0.292865\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 11.6098i | − | 0.478376i | ||||||
\(590\) | 30.3180 | − | 1.36985i | 1.24817 | − | 0.0563959i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −30.3879 | − | 30.3879i | −1.24894 | − | 1.24894i | ||||
\(593\) | −17.6196 | − | 17.6196i | −0.723551 | − | 0.723551i | 0.245775 | − | 0.969327i | \(-0.420957\pi\) |
−0.969327 | + | 0.245775i | \(0.920957\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 4.10631 | + | 3.75129i | 0.168342 | + | 0.153788i | ||||
\(596\) | 133.076i | 5.45102i | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 29.4128 | − | 29.4128i | 1.20278 | − | 1.20278i | ||||
\(599\) | −1.79409 | −0.0733046 | −0.0366523 | − | 0.999328i | \(-0.511669\pi\) | ||||
−0.0366523 | + | 0.999328i | \(0.511669\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −27.6926 | −1.12960 | −0.564802 | − | 0.825227i | \(-0.691047\pi\) | ||||
−0.564802 | + | 0.825227i | \(0.691047\pi\) | |||||||
\(602\) | −1.98889 | + | 1.98889i | −0.0810612 | + | 0.0810612i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | − | 75.9456i | − | 3.09018i | ||||||
\(605\) | 18.0580 | + | 16.4967i | 0.734160 | + | 0.670686i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −9.55102 | − | 9.55102i | −0.387664 | − | 0.387664i | 0.486189 | − | 0.873853i | \(-0.338387\pi\) |
−0.873853 | + | 0.486189i | \(0.838387\pi\) | |||||||
\(608\) | −75.4532 | − | 75.4532i | −3.06003 | − | 3.06003i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 59.2588 | − | 2.67748i | 2.39932 | − | 0.108408i | ||||
\(611\) | 22.5384i | 0.911805i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 32.8779 | − | 32.8779i | 1.32793 | − | 1.32793i | 0.420750 | − | 0.907177i | \(-0.361767\pi\) |
0.907177 | − | 0.420750i | \(-0.138233\pi\) | |||||||
\(614\) | −82.3298 | −3.32256 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 2.56429 | 0.103318 | ||||||||
\(617\) | −1.11112 | + | 1.11112i | −0.0447319 | + | 0.0447319i | −0.729119 | − | 0.684387i | \(-0.760070\pi\) |
0.684387 | + | 0.729119i | \(0.260070\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 28.3646i | 1.14007i | 0.821621 | + | 0.570035i | \(0.193070\pi\) | ||||
−0.821621 | + | 0.570035i | \(0.806930\pi\) | |||||||
\(620\) | −25.5553 | + | 27.9739i | −1.02633 | + | 1.12346i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 29.8617 | + | 29.8617i | 1.19734 | + | 1.19734i | ||||
\(623\) | −1.35682 | − | 1.35682i | −0.0543599 | − | 0.0543599i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −24.5934 | + | 4.49069i | −0.983735 | + | 0.179628i | ||||
\(626\) | − | 0.703922i | − | 0.0281344i | ||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −27.5878 | + | 27.5878i | −1.10087 | + | 1.10087i | ||||
\(629\) | 6.20004 | 0.247212 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −21.8241 | −0.868803 | −0.434401 | − | 0.900719i | \(-0.643040\pi\) | ||||
−0.434401 | + | 0.900719i | \(0.643040\pi\) | |||||||
\(632\) | −82.1570 | + | 82.1570i | −3.26803 | + | 3.26803i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | − | 40.2657i | − | 1.59915i | ||||||
\(635\) | −1.41437 | − | 31.3034i | −0.0561277 | − | 1.24224i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −3.37141 | − | 3.37141i | −0.133580 | − | 0.133580i | ||||
\(638\) | 1.29387 | + | 1.29387i | 0.0512249 | + | 0.0512249i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 6.05152 | + | 133.934i | 0.239207 | + | 5.29422i | ||||
\(641\) | 1.91757i | 0.0757395i | 0.999283 | + | 0.0378697i | \(0.0120572\pi\) | ||||
−0.999283 | + | 0.0378697i | \(0.987943\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 20.2152 | − | 20.2152i | 0.797209 | − | 0.797209i | −0.185446 | − | 0.982654i | \(-0.559373\pi\) |
0.982654 | + | 0.185446i | \(0.0593730\pi\) | |||||||
\(644\) | −17.9523 | −0.707421 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 27.0592 | 1.06463 | ||||||||
\(647\) | −24.4807 | + | 24.4807i | −0.962435 | + | 0.962435i | −0.999320 | − | 0.0368841i | \(-0.988257\pi\) |
0.0368841 | + | 0.999320i | \(0.488257\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.21383i | 0.0476470i | ||||||||
\(650\) | −65.9507 | + | 5.97186i | −2.58680 | + | 0.234236i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −18.8984 | − | 18.8984i | −0.740119 | − | 0.740119i | ||||
\(653\) | 17.3242 | + | 17.3242i | 0.677950 | + | 0.677950i | 0.959536 | − | 0.281586i | \(-0.0908605\pi\) |
−0.281586 | + | 0.959536i | \(0.590860\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −7.83743 | + | 8.57918i | −0.306234 | + | 0.335216i | ||||
\(656\) | 127.926i | 4.99469i | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 9.28490 | − | 9.28490i | 0.361963 | − | 0.361963i | ||||
\(659\) | −29.9820 | −1.16793 | −0.583967 | − | 0.811777i | \(-0.698500\pi\) | ||||
−0.583967 | + | 0.811777i | \(0.698500\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 36.5460 | 1.42147 | 0.710737 | − | 0.703458i | \(-0.248362\pi\) | ||||
0.710737 | + | 0.703458i | \(0.248362\pi\) | |||||||
\(662\) | 36.5156 | − | 36.5156i | 1.41922 | − | 1.41922i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 148.474i | 5.76192i | ||||||||
\(665\) | −8.74838 | + | 0.395276i | −0.339248 | + | 0.0153281i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −5.88882 | − | 5.88882i | −0.228016 | − | 0.228016i | ||||
\(668\) | 22.7370 | + | 22.7370i | 0.879722 | + | 0.879722i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −38.8398 | − | 35.4818i | −1.50051 | − | 1.37078i | ||||
\(671\) | 2.37252i | 0.0915902i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −27.4562 | + | 27.4562i | −1.05836 | + | 1.05836i | −0.0601718 | + | 0.998188i | \(0.519165\pi\) |
−0.998188 | + | 0.0601718i | \(0.980835\pi\) | |||||||
\(674\) | 48.0382 | 1.85036 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −55.6328 | −2.13972 | ||||||||
\(677\) | 18.4107 | − | 18.4107i | 0.707582 | − | 0.707582i | −0.258444 | − | 0.966026i | \(-0.583210\pi\) |
0.966026 | + | 0.258444i | \(0.0832098\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1.51354i | 0.0580842i | ||||||||
\(680\) | −42.3862 | − | 38.7215i | −1.62544 | − | 1.48490i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −1.44650 | − | 1.44650i | −0.0553892 | − | 0.0553892i | ||||
\(683\) | 6.18268 | + | 6.18268i | 0.236574 | + | 0.236574i | 0.815430 | − | 0.578856i | \(-0.196501\pi\) |
−0.578856 | + | 0.815430i | \(0.696501\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −13.5446 | + | 0.611981i | −0.517512 | + | 0.0233826i | ||||
\(686\) | 2.77777i | 0.106056i | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 12.3444 | − | 12.3444i | 0.470625 | − | 0.470625i | ||||
\(689\) | −28.6993 | −1.09336 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 39.0569 | 1.48579 | 0.742897 | − | 0.669406i | \(-0.233451\pi\) | ||||
0.742897 | + | 0.669406i | \(0.233451\pi\) | |||||||
\(692\) | 87.9138 | − | 87.9138i | 3.34198 | − | 3.34198i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 40.5641i | 1.53979i | ||||||||
\(695\) | 15.9496 | − | 17.4591i | 0.605002 | − | 0.662261i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −13.0504 | − | 13.0504i | −0.494319 | − | 0.494319i | ||||
\(698\) | 5.15960 | + | 5.15960i | 0.195294 | + | 0.195294i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 21.9493 | + | 18.3043i | 0.829604 | + | 0.691837i | ||||
\(701\) | − | 41.7309i | − | 1.57615i | −0.615577 | − | 0.788077i | \(-0.711077\pi\) | ||
0.615577 | − | 0.788077i | \(-0.288923\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −6.90291 | + | 6.90291i | −0.260348 | + | 0.260348i | ||||
\(704\) | −10.2357 | −0.385773 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −7.24468 | −0.272657 | ||||||||
\(707\) | −6.26886 | + | 6.26886i | −0.235765 | + | 0.235765i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 20.9505i | 0.786812i | 0.919365 | + | 0.393406i | \(0.128703\pi\) | ||||
−0.919365 | + | 0.393406i | \(0.871297\pi\) | |||||||
\(710\) | −1.77108 | − | 39.1981i | −0.0664673 | − | 1.47108i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 14.0054 | + | 14.0054i | 0.524874 | + | 0.524874i | ||||
\(713\) | 6.58346 | + | 6.58346i | 0.246553 | + | 0.246553i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −0.119546 | − | 2.64584i | −0.00447078 | − | 0.0989489i | ||||
\(716\) | − | 128.532i | − | 4.80346i | ||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 50.9587 | − | 50.9587i | 1.90176 | − | 1.90176i | ||||
\(719\) | −26.9899 | −1.00655 | −0.503277 | − | 0.864125i | \(-0.667872\pi\) | ||||
−0.503277 | + | 0.864125i | \(0.667872\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −18.2250 | −0.678734 | ||||||||
\(722\) | 7.19264 | − | 7.19264i | 0.267682 | − | 0.267682i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | − | 31.7985i | − | 1.18178i | ||||||
\(725\) | 1.19564 | + | 13.2042i | 0.0444051 | + | 0.490391i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 9.84200 | + | 9.84200i | 0.365020 | + | 0.365020i | 0.865657 | − | 0.500637i | \(-0.166901\pi\) |
−0.500637 | + | 0.865657i | \(0.666901\pi\) | |||||||
\(728\) | 34.8004 | + | 34.8004i | 1.28979 | + | 1.28979i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −61.1792 | + | 66.9693i | −2.26434 | + | 2.47865i | ||||
\(731\) | 2.51862i | 0.0931545i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 12.9130 | − | 12.9130i | 0.476951 | − | 0.476951i | −0.427204 | − | 0.904155i | \(-0.640501\pi\) |
0.904155 | + | 0.427204i | \(0.140501\pi\) | |||||||
\(734\) | −53.1311 | −1.96111 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 85.5727 | 3.15425 | ||||||||
\(737\) | 1.48779 | − | 1.48779i | 0.0548035 | − | 0.0548035i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 27.4269i | 1.00891i | 0.863437 | + | 0.504457i | \(0.168307\pi\) | ||||
−0.863437 | + | 0.504457i | \(0.831693\pi\) | |||||||
\(740\) | 31.8270 | − | 1.43803i | 1.16998 | − | 0.0528631i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 11.8230 | + | 11.8230i | 0.434035 | + | 0.434035i | ||||
\(743\) | 9.43704 | + | 9.43704i | 0.346212 | + | 0.346212i | 0.858696 | − | 0.512485i | \(-0.171275\pi\) |
−0.512485 | + | 0.858696i | \(0.671275\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −38.4351 | − | 35.1120i | −1.40815 | − | 1.28640i | ||||
\(746\) | − | 7.93572i | − | 0.290547i | ||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 2.49750 | − | 2.49750i | 0.0913177 | − | 0.0913177i | ||||
\(749\) | 1.25901 | 0.0460033 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −43.6512 | −1.59286 | −0.796428 | − | 0.604734i | \(-0.793279\pi\) | ||||
−0.796428 | + | 0.604734i | \(0.793279\pi\) | |||||||
\(752\) | −57.6282 | + | 57.6282i | −2.10149 | + | 2.10149i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 35.1187i | 1.27895i | ||||||||
\(755\) | 21.9346 | + | 20.0381i | 0.798281 | + | 0.729263i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 15.2034 | + | 15.2034i | 0.552579 | + | 0.552579i | 0.927184 | − | 0.374606i | \(-0.122222\pi\) |
−0.374606 | + | 0.927184i | \(0.622222\pi\) | |||||||
\(758\) | 8.09011 | + | 8.09011i | 0.293846 | + | 0.293846i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 90.3026 | − | 4.08012i | 3.27562 | − | 0.148001i | ||||
\(761\) | − | 6.27530i | − | 0.227479i | −0.993511 | − | 0.113740i | \(-0.963717\pi\) | ||
0.993511 | − | 0.113740i | \(-0.0362830\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0.653389 | − | 0.653389i | 0.0236543 | − | 0.0236543i | ||||
\(764\) | −57.2118 | −2.06985 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 70.7727 | 2.55712 | ||||||||
\(767\) | −16.4731 | + | 16.4731i | −0.594808 | + | 0.594808i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 36.5294i | 1.31728i | 0.752456 | + | 0.658642i | \(0.228869\pi\) | ||||
−0.752456 | + | 0.658642i | \(0.771131\pi\) | |||||||
\(770\) | −1.04073 | + | 1.13923i | −0.0375054 | + | 0.0410549i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −29.1901 | − | 29.1901i | −1.05057 | − | 1.05057i | ||||
\(773\) | −17.5844 | − | 17.5844i | −0.632468 | − | 0.632468i | 0.316219 | − | 0.948686i | \(-0.397587\pi\) |
−0.948686 | + | 0.316219i | \(0.897587\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1.33668 | − | 14.7617i | −0.0480150 | − | 0.530258i | ||||
\(776\) | − | 15.6230i | − | 0.560834i | ||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 37.5759 | − | 37.5759i | 1.34716 | − | 1.34716i | ||||
\(779\) | 29.0597 | 1.04117 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.56936 | 0.0561560 | ||||||||
\(782\) | −15.3441 | + | 15.3441i | −0.548705 | + | 0.548705i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | − | 17.2407i | − | 0.615739i | ||||||
\(785\) | −0.688896 | − | 15.2469i | −0.0245878 | − | 0.544185i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 16.9793 | + | 16.9793i | 0.605246 | + | 0.605246i | 0.941700 | − | 0.336454i | \(-0.109228\pi\) |
−0.336454 | + | 0.941700i | \(0.609228\pi\) | |||||||
\(788\) | 24.7172 | + | 24.7172i | 0.880516 | + | 0.880516i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −3.15572 | − | 69.8435i | −0.112275 | − | 2.48492i | ||||
\(791\) | − | 6.11537i | − | 0.217437i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −32.1978 | + | 32.1978i | −1.14338 | + | 1.14338i | ||||
\(794\) | 1.73807 | 0.0616818 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 77.4758 | 2.74606 | ||||||||
\(797\) | −19.7309 | + | 19.7309i | −0.698903 | + | 0.698903i | −0.964174 | − | 0.265271i | \(-0.914539\pi\) |
0.265271 | + | 0.964174i | \(0.414539\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 11.7579i | − | 0.415964i | ||||||
\(800\) | −104.625 | − | 87.2503i | −3.69904 | − | 3.08477i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 29.4262 | + | 29.4262i | 1.03908 | + | 1.03908i | ||||
\(803\) | −2.56531 | − | 2.56531i | −0.0905280 | − | 0.0905280i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 4.73670 | − | 5.18499i | 0.166947 | − | 0.182747i | ||||
\(806\) | − | 39.2612i | − | 1.38292i | ||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 64.7084 | − | 64.7084i | 2.27643 | − | 2.27643i | ||||
\(809\) | −31.7336 | −1.11569 | −0.557846 | − | 0.829944i | \(-0.688372\pi\) | ||||
−0.557846 | + | 0.829944i | \(0.688372\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −14.7328 | −0.517338 | −0.258669 | − | 0.965966i | \(-0.583284\pi\) | ||||
−0.258669 | + | 0.965966i | \(0.583284\pi\) | |||||||
\(812\) | 10.7175 | − | 10.7175i | 0.376110 | − | 0.376110i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 1.72010i | 0.0602894i | ||||||||
\(815\) | 10.4446 | − | 0.471914i | 0.365857 | − | 0.0165304i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −2.80415 | − | 2.80415i | −0.0981046 | − | 0.0981046i | ||||
\(818\) | 65.0326 | + | 65.0326i | 2.27381 | + | 2.27381i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −70.0193 | − | 63.9655i | −2.44518 | − | 2.23377i | ||||
\(821\) | 24.0674i | 0.839959i | 0.907534 | + | 0.419980i | \(0.137963\pi\) | ||||
−0.907534 | + | 0.419980i | \(0.862037\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 27.6196 | − | 27.6196i | 0.962759 | − | 0.962759i | −0.0365723 | − | 0.999331i | \(-0.511644\pi\) |
0.999331 | + | 0.0365723i | \(0.0116439\pi\) | |||||||
\(824\) | 188.122 | 6.55353 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 13.5725 | 0.472247 | ||||||||
\(827\) | 16.3828 | − | 16.3828i | 0.569687 | − | 0.569687i | −0.362354 | − | 0.932041i | \(-0.618027\pi\) |
0.932041 | + | 0.362354i | \(0.118027\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 30.5709i | − | 1.06177i | −0.847443 | − | 0.530886i | \(-0.821859\pi\) | ||
0.847443 | − | 0.530886i | \(-0.178141\pi\) | |||||||
\(830\) | −65.9621 | − | 60.2590i | −2.28958 | − | 2.09162i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −138.910 | − | 138.910i | −4.81585 | − | 4.81585i | ||||
\(833\) | 1.75881 | + | 1.75881i | 0.0609390 | + | 0.0609390i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −12.5660 | + | 0.567768i | −0.434865 | + | 0.0196484i | ||||
\(836\) | 5.56126i | 0.192340i | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 10.1143 | − | 10.1143i | 0.349391 | − | 0.349391i | ||||
\(839\) | 51.9468 | 1.79340 | 0.896701 | − | 0.442638i | \(-0.145957\pi\) | ||||
0.896701 | + | 0.442638i | \(0.145957\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −21.9688 | −0.757544 | ||||||||
\(842\) | −5.60403 | + | 5.60403i | −0.193128 | + | 0.193128i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 96.6955i | 3.32840i | ||||||||
\(845\) | 14.6787 | − | 16.0679i | 0.504961 | − | 0.552751i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 7.73454 | + | 7.73454i | 0.265762 | + | 0.265762i | ||||
\(848\) | −73.3812 | − | 73.3812i | −2.51992 | − | 2.51992i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 34.4053 | − | 3.11541i | 1.18009 | − | 0.106858i | ||||
\(851\) | − | 7.82871i | − | 0.268365i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −4.07950 | + | 4.07950i | −0.139679 | + | 0.139679i | −0.773489 | − | 0.633810i | \(-0.781490\pi\) |
0.633810 | + | 0.773489i | \(0.281490\pi\) | |||||||
\(854\) | 26.5284 | 0.907783 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −12.9958 | −0.444187 | ||||||||
\(857\) | 10.5745 | − | 10.5745i | 0.361217 | − | 0.361217i | −0.503044 | − | 0.864261i | \(-0.667786\pi\) |
0.864261 | + | 0.503044i | \(0.167786\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 33.2826i | 1.13559i | 0.823171 | + | 0.567794i | \(0.192203\pi\) | ||||
−0.823171 | + | 0.567794i | \(0.807797\pi\) | |||||||
\(860\) | 0.584167 | + | 12.9290i | 0.0199199 | + | 0.440875i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −43.3286 | − | 43.3286i | −1.47578 | − | 1.47578i | ||||
\(863\) | 11.6428 | + | 11.6428i | 0.396326 | + | 0.396326i | 0.876935 | − | 0.480609i | \(-0.159584\pi\) |
−0.480609 | + | 0.876935i | \(0.659584\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 2.19530 | + | 48.5872i | 0.0746425 | + | 1.65201i | ||||
\(866\) | 43.0405i | 1.46257i | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −11.9817 | + | 11.9817i | −0.406685 | + | 0.406685i | ||||
\(869\) | 2.79629 | 0.0948577 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 40.3820 | 1.36829 | ||||||||
\(872\) | −6.74441 | + | 6.74441i | −0.228394 | + | 0.228394i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | − | 34.1673i | − | 1.15573i | ||||||
\(875\) | −11.0779 | + | 1.50982i | −0.374502 | + | 0.0510412i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 16.0669 | + | 16.0669i | 0.542541 | + | 0.542541i | 0.924273 | − | 0.381732i | \(-0.124672\pi\) |
−0.381732 | + | 0.924273i | \(0.624672\pi\) | |||||||
\(878\) | 14.6412 | + | 14.6412i | 0.494118 | + | 0.494118i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 6.45947 | − | 7.07081i | 0.217749 | − | 0.238357i | ||||
\(881\) | − | 33.9802i | − | 1.14482i | −0.819967 | − | 0.572411i | \(-0.806008\pi\) | ||
0.819967 | − | 0.572411i | \(-0.193992\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 12.8883 | − | 12.8883i | 0.433726 | − | 0.433726i | −0.456168 | − | 0.889894i | \(-0.650778\pi\) |
0.889894 | + | 0.456168i | \(0.150778\pi\) | |||||||
\(884\) | 67.7879 | 2.27995 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 15.8080 | 0.531082 | ||||||||
\(887\) | 8.51813 | − | 8.51813i | 0.286011 | − | 0.286011i | −0.549490 | − | 0.835501i | \(-0.685178\pi\) |
0.835501 | + | 0.549490i | \(0.185178\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 14.0136i | − | 0.470001i | ||||||
\(890\) | −11.9063 | + | 0.537958i | −0.399100 | + | 0.0180324i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −42.6487 | − | 42.6487i | −1.42798 | − | 1.42798i | ||||
\(893\) | 13.0908 | + | 13.0908i | 0.438067 | + | 0.438067i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 37.1225 | + | 33.9129i | 1.24087 | + | 1.13358i | ||||
\(896\) | 59.9583i | 2.00307i | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −44.8285 | + | 44.8285i | −1.49595 | + | 1.49595i | ||||
\(899\) | −7.86060 | −0.262166 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 14.9719 | 0.498788 | ||||||||
\(902\) | 3.62062 | − | 3.62062i | 0.120553 | − | 0.120553i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 63.1241i | 2.09947i | ||||||||
\(905\) | 9.18404 | + | 8.39000i | 0.305288 | + | 0.278893i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1.99425 | + | 1.99425i | 0.0662179 | + | 0.0662179i | 0.739440 | − | 0.673222i | \(-0.235090\pi\) |
−0.673222 | + | 0.739440i | \(0.735090\pi\) | |||||||
\(908\) | −44.3249 | − | 44.3249i | −1.47097 | − | 1.47097i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −29.5846 | + | 1.33671i | −0.980718 | + | 0.0443115i | ||||
\(911\) | 5.34768i | 0.177176i | 0.996068 | + | 0.0885882i | \(0.0282355\pi\) | ||||
−0.996068 | + | 0.0885882i | \(0.971764\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 2.52673 | − | 2.52673i | 0.0836226 | − | 0.0836226i | ||||
\(914\) | 83.7275 | 2.76946 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −69.6812 | −2.30233 | ||||||||
\(917\) | −3.67461 | + | 3.67461i | −0.121346 | + | 0.121346i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 35.0647i | 1.15668i | 0.815796 | + | 0.578339i | \(0.196299\pi\) | ||||
−0.815796 | + | 0.578339i | \(0.803701\pi\) | |||||||
\(920\) | −48.8932 | + | 53.5205i | −1.61196 | + | 1.76452i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −37.9670 | − | 37.9670i | −1.25038 | − | 1.25038i | ||||
\(923\) | 21.2980 | + | 21.2980i | 0.701031 | + | 0.701031i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −7.98219 | + | 9.57170i | −0.262453 | + | 0.314716i | ||||
\(926\) | − | 31.2696i | − | 1.02758i | ||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −51.0866 | + | 51.0866i | −1.67700 | + | 1.67700i | ||||
\(929\) | −11.2129 | −0.367883 | −0.183941 | − | 0.982937i | \(-0.558886\pi\) | ||||
−0.183941 | + | 0.982937i | \(0.558886\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −3.91639 | −0.128354 | ||||||||
\(932\) | −97.5672 | + | 97.5672i | −3.19592 | + | 3.19592i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 97.9533i | 3.20513i | ||||||||
\(935\) | 0.0623653 | + | 1.38029i | 0.00203956 | + | 0.0451403i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1.24982 | + | 1.24982i | 0.0408298 | + | 0.0408298i | 0.727227 | − | 0.686397i | \(-0.240809\pi\) |
−0.686397 | + | 0.727227i | \(0.740809\pi\) | |||||||
\(938\) | −16.6358 | − | 16.6358i | −0.543177 | − | 0.543177i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −2.72711 | − | 60.3574i | −0.0889486 | − | 1.96864i | ||||
\(941\) | − | 2.58136i | − | 0.0841499i | −0.999114 | − | 0.0420750i | \(-0.986603\pi\) | ||
0.999114 | − | 0.0420750i | \(-0.0133968\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −16.4786 | + | 16.4786i | −0.536616 | + | 0.536616i | ||||
\(944\) | −84.2398 | −2.74177 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −0.698749 | −0.0227183 | ||||||||
\(947\) | 40.6372 | − | 40.6372i | 1.32053 | − | 1.32053i | 0.407184 | − | 0.913346i | \(-0.366511\pi\) |
0.913346 | − | 0.407184i | \(-0.133489\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 69.6285i | − | 2.26024i | ||||||
\(950\) | −34.8371 | + | 41.7743i | −1.13027 | + | 1.35534i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −18.1547 | − | 18.1547i | −0.588399 | − | 0.588399i | ||||
\(953\) | 31.8867 | + | 31.8867i | 1.03291 | + | 1.03291i | 0.999440 | + | 0.0334725i | \(0.0106566\pi\) |
0.0334725 | + | 0.999440i | \(0.489343\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 15.0953 | − | 16.5239i | 0.488471 | − | 0.534701i | ||||
\(956\) | − | 89.2171i | − | 2.88549i | ||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −79.0573 | + | 79.0573i | −2.55423 | + | 2.55423i | ||||
\(959\) | −6.06350 | −0.195801 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −22.2122 | −0.716522 | ||||||||
\(962\) | −23.3437 | + | 23.3437i | −0.752631 | + | 0.752631i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | − | 111.010i | − | 3.57540i | ||||||
\(965\) | 16.1324 | − | 0.728908i | 0.519321 | − | 0.0234644i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 41.0973 | + | 41.0973i | 1.32160 | + | 1.32160i | 0.912482 | + | 0.409118i | \(0.134163\pi\) |
0.409118 | + | 0.912482i | \(0.365837\pi\) | |||||||
\(968\) | −79.8374 | − | 79.8374i | −2.56607 | − | 2.56607i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 6.94078 | + | 6.34069i | 0.222855 | + | 0.203587i | ||||
\(971\) | 8.55398i | 0.274510i | 0.990536 | + | 0.137255i | \(0.0438280\pi\) | ||||
−0.990536 | + | 0.137255i | \(0.956172\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 7.47803 | − | 7.47803i | 0.239735 | − | 0.239735i | ||||
\(974\) | 97.8788 | 3.13624 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −164.653 | −5.27041 | ||||||||
\(977\) | 19.2987 | − | 19.2987i | 0.617420 | − | 0.617420i | −0.327449 | − | 0.944869i | \(-0.606189\pi\) |
0.944869 | + | 0.327449i | \(0.106189\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 0.476687i | − | 0.0152350i | ||||||
\(980\) | 9.43652 | + | 8.62065i | 0.301439 | + | 0.275376i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 14.3284 | + | 14.3284i | 0.457239 | + | 0.457239i | ||||
\(983\) | −11.4633 | − | 11.4633i | −0.365624 | − | 0.365624i | 0.500255 | − | 0.865878i | \(-0.333240\pi\) |
−0.865878 | + | 0.500255i | \(0.833240\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −13.6604 | + | 0.617216i | −0.435258 | + | 0.0196661i | ||||
\(986\) | − | 18.3208i | − | 0.583453i | ||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −75.4727 | + | 75.4727i | −2.40111 | + | 2.40111i | ||||
\(989\) | 3.18023 | 0.101125 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 42.4919 | 1.34980 | 0.674899 | − | 0.737910i | \(-0.264187\pi\) | ||||
0.674899 | + | 0.737910i | \(0.264187\pi\) | |||||||
\(992\) | 57.1127 | − | 57.1127i | 1.81333 | − | 1.81333i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | − | 17.5478i | − | 0.556582i | ||||||
\(995\) | −20.4419 | + | 22.3766i | −0.648052 | + | 0.709384i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −16.2954 | − | 16.2954i | −0.516082 | − | 0.516082i | 0.400302 | − | 0.916383i | \(-0.368905\pi\) |
−0.916383 | + | 0.400302i | \(0.868905\pi\) | |||||||
\(998\) | 17.6610 | + | 17.6610i | 0.559049 | + | 0.559049i | ||||
\(999\) | 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 | 315.2.m.b.197.6 | yes | 12 | |
3.2 | odd | 2 | 315.2.m.a.197.1 | yes | 12 | ||
5.2 | odd | 4 | 1575.2.m.c.1268.6 | 12 | |||
5.3 | odd | 4 | 315.2.m.a.8.1 | ✓ | 12 | ||
5.4 | even | 2 | 1575.2.m.d.1457.1 | 12 | |||
15.2 | even | 4 | 1575.2.m.d.1268.1 | 12 | |||
15.8 | even | 4 | inner | 315.2.m.b.8.6 | yes | 12 | |
15.14 | odd | 2 | 1575.2.m.c.1457.6 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
315.2.m.a.8.1 | ✓ | 12 | 5.3 | odd | 4 | ||
315.2.m.a.197.1 | yes | 12 | 3.2 | odd | 2 | ||
315.2.m.b.8.6 | yes | 12 | 15.8 | even | 4 | inner | |
315.2.m.b.197.6 | yes | 12 | 1.1 | even | 1 | trivial | |
1575.2.m.c.1268.6 | 12 | 5.2 | odd | 4 | |||
1575.2.m.c.1457.6 | 12 | 15.14 | odd | 2 | |||
1575.2.m.d.1268.1 | 12 | 15.2 | even | 4 | |||
1575.2.m.d.1457.1 | 12 | 5.4 | even | 2 |