Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2070,2,Mod(323,2070)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2070, 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("2070.323");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2070 = 2 \cdot 3^{2} \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2070.j (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: | \(16.5290332184\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Relative dimension: | \(10\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - 20 x^{18} + 187 x^{16} - 1012 x^{14} + 3533 x^{12} - 7896 x^{10} + 10837 x^{8} - 5668 x^{6} + \cdots + 3721 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{8} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 737.7 | ||
Root | \(1.39971 - 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2070.737 |
Dual form | 2070.2.j.j.323.7 |
$q$-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 \(\left(\mathbb{Z}/2070\mathbb{Z}\right)^\times\).
\(n\) | \(461\) | \(1657\) | \(1891\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{4}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.707107 | − | 0.707107i | 0.500000 | − | 0.500000i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | − | 1.00000i | − | 0.500000i | ||||||
\(5\) | −0.125717 | + | 2.23253i | −0.0562223 | + | 0.998418i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 3.50921 | + | 3.50921i | 1.32636 | + | 1.32636i | 0.908524 | + | 0.417832i | \(0.137210\pi\) |
0.417832 | + | 0.908524i | \(0.362790\pi\) | |||||||
\(8\) | −0.707107 | − | 0.707107i | −0.250000 | − | 0.250000i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 1.48974 | + | 1.66753i | 0.471098 | + | 0.527320i | ||||
\(11\) | − | 0.764834i | − | 0.230606i | −0.993330 | − | 0.115303i | \(-0.963216\pi\) | ||
0.993330 | − | 0.115303i | \(-0.0367839\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.69809 | + | 3.69809i | −1.02567 | + | 1.02567i | −0.0260052 | + | 0.999662i | \(0.508279\pi\) |
−0.999662 | + | 0.0260052i | \(0.991721\pi\) | |||||||
\(14\) | 4.96277 | 1.32636 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −1.00000 | −0.250000 | ||||||||
\(17\) | 0.764834 | − | 0.764834i | 0.185499 | − | 0.185499i | −0.608248 | − | 0.793747i | \(-0.708127\pi\) |
0.793747 | + | 0.608248i | \(0.208127\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 6.41670i | 1.47209i | 0.676931 | + | 0.736046i | \(0.263310\pi\) | ||||
−0.676931 | + | 0.736046i | \(0.736690\pi\) | |||||||
\(20\) | 2.23253 | + | 0.125717i | 0.499209 | + | 0.0281112i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −0.540819 | − | 0.540819i | −0.115303 | − | 0.115303i | ||||
\(23\) | 0.707107 | + | 0.707107i | 0.147442 | + | 0.147442i | ||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.96839 | − | 0.561334i | −0.993678 | − | 0.112267i | ||||
\(26\) | 5.22990i | 1.02567i | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 3.50921 | − | 3.50921i | 0.663178 | − | 0.663178i | ||||
\(29\) | 1.67897 | 0.311777 | 0.155888 | − | 0.987775i | \(-0.450176\pi\) | ||||
0.155888 | + | 0.987775i | \(0.450176\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −9.93678 | −1.78470 | −0.892349 | − | 0.451345i | \(-0.850944\pi\) | ||||
−0.892349 | + | 0.451345i | \(0.850944\pi\) | |||||||
\(32\) | −0.707107 | + | 0.707107i | −0.125000 | + | 0.125000i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | − | 1.08164i | − | 0.185499i | ||||||
\(35\) | −8.27559 | + | 7.39325i | −1.39883 | + | 1.24969i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −8.31090 | − | 8.31090i | −1.36630 | − | 1.36630i | −0.865644 | − | 0.500661i | \(-0.833090\pi\) |
−0.500661 | − | 0.865644i | \(-0.666910\pi\) | |||||||
\(38\) | 4.53730 | + | 4.53730i | 0.736046 | + | 0.736046i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1.66753 | − | 1.48974i | 0.263660 | − | 0.235549i | ||||
\(41\) | − | 10.5906i | − | 1.65398i | −0.562220 | − | 0.826988i | \(-0.690052\pi\) | ||
0.562220 | − | 0.826988i | \(-0.309948\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.96839 | − | 2.96839i | 0.452675 | − | 0.452675i | −0.443566 | − | 0.896242i | \(-0.646287\pi\) |
0.896242 | + | 0.443566i | \(0.146287\pi\) | |||||||
\(44\) | −0.764834 | −0.115303 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.00000 | 0.147442 | ||||||||
\(47\) | −2.54798 | + | 2.54798i | −0.371661 | + | 0.371661i | −0.868082 | − | 0.496421i | \(-0.834647\pi\) |
0.496421 | + | 0.868082i | \(0.334647\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 17.6291i | 2.51844i | ||||||||
\(50\) | −3.91011 | + | 3.11626i | −0.552972 | + | 0.440706i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 3.69809 | + | 3.69809i | 0.512833 | + | 0.512833i | ||||
\(53\) | 9.13318 | + | 9.13318i | 1.25454 | + | 1.25454i | 0.953664 | + | 0.300875i | \(0.0972787\pi\) |
0.300875 | + | 0.953664i | \(0.402721\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.70751 | + | 0.0961525i | 0.230241 | + | 0.0129652i | ||||
\(56\) | − | 4.96277i | − | 0.663178i | ||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 1.18721 | − | 1.18721i | 0.155888 | − | 0.155888i | ||||
\(59\) | 0.219632 | 0.0285936 | 0.0142968 | − | 0.999898i | \(-0.495449\pi\) | ||||
0.0142968 | + | 0.999898i | \(0.495449\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.82779 | −0.234024 | −0.117012 | − | 0.993130i | \(-0.537332\pi\) | ||||
−0.117012 | + | 0.993130i | \(0.537332\pi\) | |||||||
\(62\) | −7.02637 | + | 7.02637i | −0.892349 | + | 0.892349i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000i | 0.125000i | ||||||||
\(65\) | −7.79120 | − | 8.72102i | −0.966379 | − | 1.08171i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 5.38509 | + | 5.38509i | 0.657894 | + | 0.657894i | 0.954881 | − | 0.296987i | \(-0.0959819\pi\) |
−0.296987 | + | 0.954881i | \(0.595982\pi\) | |||||||
\(68\) | −0.764834 | − | 0.764834i | −0.0927497 | − | 0.0927497i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −0.623904 | + | 11.0795i | −0.0745708 | + | 1.32426i | ||||
\(71\) | 6.14124i | 0.728831i | 0.931236 | + | 0.364416i | \(0.118731\pi\) | ||||
−0.931236 | + | 0.364416i | \(0.881269\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1.36645 | + | 1.36645i | −0.159931 | + | 0.159931i | −0.782536 | − | 0.622605i | \(-0.786074\pi\) |
0.622605 | + | 0.782536i | \(0.286074\pi\) | |||||||
\(74\) | −11.7534 | −1.36630 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 6.41670 | 0.736046 | ||||||||
\(77\) | 2.68396 | − | 2.68396i | 0.305866 | − | 0.305866i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 4.66284i | − | 0.524610i | −0.964985 | − | 0.262305i | \(-0.915517\pi\) | ||
0.964985 | − | 0.262305i | \(-0.0844827\pi\) | |||||||
\(80\) | 0.125717 | − | 2.23253i | 0.0140556 | − | 0.249605i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −7.48869 | − | 7.48869i | −0.826988 | − | 0.826988i | ||||
\(83\) | 1.48645 | + | 1.48645i | 0.163159 | + | 0.163159i | 0.783964 | − | 0.620806i | \(-0.213194\pi\) |
−0.620806 | + | 0.783964i | \(0.713194\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.61136 | + | 1.80367i | 0.174777 | + | 0.195635i | ||||
\(86\) | − | 4.19794i | − | 0.452675i | ||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −0.540819 | + | 0.540819i | −0.0576515 | + | 0.0576515i | ||||
\(89\) | −1.81216 | −0.192089 | −0.0960443 | − | 0.995377i | \(-0.530619\pi\) | ||||
−0.0960443 | + | 0.995377i | \(0.530619\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −25.9548 | −2.72080 | ||||||||
\(92\) | 0.707107 | − | 0.707107i | 0.0737210 | − | 0.0737210i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 3.60339i | 0.371661i | ||||||||
\(95\) | −14.3255 | − | 0.806688i | −1.46976 | − | 0.0827645i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 8.54237 | + | 8.54237i | 0.867346 | + | 0.867346i | 0.992178 | − | 0.124832i | \(-0.0398391\pi\) |
−0.124832 | + | 0.992178i | \(0.539839\pi\) | |||||||
\(98\) | 12.4657 | + | 12.4657i | 1.25922 | + | 1.25922i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −0.561334 | + | 4.96839i | −0.0561334 | + | 0.496839i | ||||
\(101\) | − | 7.00584i | − | 0.697107i | −0.937289 | − | 0.348554i | \(-0.886673\pi\) | ||
0.937289 | − | 0.348554i | \(-0.113327\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0.839077 | − | 0.839077i | 0.0826767 | − | 0.0826767i | −0.664559 | − | 0.747236i | \(-0.731381\pi\) |
0.747236 | + | 0.664559i | \(0.231381\pi\) | |||||||
\(104\) | 5.22990 | 0.512833 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 12.9163 | 1.25454 | ||||||||
\(107\) | 7.70564 | − | 7.70564i | 0.744933 | − | 0.744933i | −0.228590 | − | 0.973523i | \(-0.573412\pi\) |
0.973523 | + | 0.228590i | \(0.0734115\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2.31665i | 0.221895i | 0.993826 | + | 0.110947i | \(0.0353885\pi\) | ||||
−0.993826 | + | 0.110947i | \(0.964612\pi\) | |||||||
\(110\) | 1.27539 | − | 1.13941i | 0.121603 | − | 0.108638i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −3.50921 | − | 3.50921i | −0.331589 | − | 0.331589i | ||||
\(113\) | 4.85580 | + | 4.85580i | 0.456796 | + | 0.456796i | 0.897602 | − | 0.440807i | \(-0.145308\pi\) |
−0.440807 | + | 0.897602i | \(0.645308\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.66753 | + | 1.48974i | −0.155498 | + | 0.138919i | ||||
\(116\) | − | 1.67897i | − | 0.155888i | ||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0.155303 | − | 0.155303i | 0.0142968 | − | 0.0142968i | ||||
\(119\) | 5.36792 | 0.492077 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 10.4150 | 0.946821 | ||||||||
\(122\) | −1.29244 | + | 1.29244i | −0.117012 | + | 0.117012i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 9.93678i | 0.892349i | ||||||||
\(125\) | 1.87781 | − | 11.0215i | 0.167956 | − | 0.985794i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 4.65707 | + | 4.65707i | 0.413248 | + | 0.413248i | 0.882868 | − | 0.469621i | \(-0.155609\pi\) |
−0.469621 | + | 0.882868i | \(0.655609\pi\) | |||||||
\(128\) | 0.707107 | + | 0.707107i | 0.0625000 | + | 0.0625000i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −11.6759 | − | 0.657486i | −1.02404 | − | 0.0576654i | ||||
\(131\) | 10.2612i | 0.896527i | 0.893901 | + | 0.448264i | \(0.147957\pi\) | ||||
−0.893901 | + | 0.448264i | \(0.852043\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −22.5176 | + | 22.5176i | −1.95252 | + | 1.95252i | ||||
\(134\) | 7.61567 | 0.657894 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −1.08164 | −0.0927497 | ||||||||
\(137\) | 11.2038 | − | 11.2038i | 0.957203 | − | 0.957203i | −0.0419178 | − | 0.999121i | \(-0.513347\pi\) |
0.999121 | + | 0.0419178i | \(0.0133468\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 11.6073i | 0.984521i | 0.870448 | + | 0.492261i | \(0.163829\pi\) | ||||
−0.870448 | + | 0.492261i | \(0.836171\pi\) | |||||||
\(140\) | 7.39325 | + | 8.27559i | 0.624844 | + | 0.699415i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 4.34251 | + | 4.34251i | 0.364416 | + | 0.364416i | ||||
\(143\) | 2.82843 | + | 2.82843i | 0.236525 | + | 0.236525i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −0.211075 | + | 3.74835i | −0.0175288 | + | 0.311284i | ||||
\(146\) | 1.93245i | 0.159931i | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −8.31090 | + | 8.31090i | −0.683152 | + | 0.683152i | ||||
\(149\) | 12.9190 | 1.05836 | 0.529181 | − | 0.848509i | \(-0.322499\pi\) | ||||
0.529181 | + | 0.848509i | \(0.322499\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 7.01447 | 0.570830 | 0.285415 | − | 0.958404i | \(-0.407869\pi\) | ||||
0.285415 | + | 0.958404i | \(0.407869\pi\) | |||||||
\(152\) | 4.53730 | − | 4.53730i | 0.368023 | − | 0.368023i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | − | 3.79569i | − | 0.305866i | ||||||
\(155\) | 1.24922 | − | 22.1842i | 0.100340 | − | 1.78188i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 4.68533 | + | 4.68533i | 0.373930 | + | 0.373930i | 0.868906 | − | 0.494977i | \(-0.164823\pi\) |
−0.494977 | + | 0.868906i | \(0.664823\pi\) | |||||||
\(158\) | −3.29712 | − | 3.29712i | −0.262305 | − | 0.262305i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −1.48974 | − | 1.66753i | −0.117774 | − | 0.131830i | ||||
\(161\) | 4.96277i | 0.391121i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2.89617 | − | 2.89617i | 0.226846 | − | 0.226846i | −0.584528 | − | 0.811374i | \(-0.698720\pi\) |
0.811374 | + | 0.584528i | \(0.198720\pi\) | |||||||
\(164\) | −10.5906 | −0.826988 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 2.10215 | 0.163159 | ||||||||
\(167\) | 1.29908 | − | 1.29908i | 0.100526 | − | 0.100526i | −0.655055 | − | 0.755581i | \(-0.727355\pi\) |
0.755581 | + | 0.655055i | \(0.227355\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 14.3518i | − | 1.10399i | ||||||
\(170\) | 2.41479 | + | 0.135980i | 0.185206 | + | 0.0104292i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −2.96839 | − | 2.96839i | −0.226338 | − | 0.226338i | ||||
\(173\) | 15.3651 | + | 15.3651i | 1.16819 | + | 1.16819i | 0.982634 | + | 0.185556i | \(0.0594085\pi\) |
0.185556 | + | 0.982634i | \(0.440591\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −15.4653 | − | 19.4050i | −1.16907 | − | 1.46688i | ||||
\(176\) | 0.764834i | 0.0576515i | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −1.28139 | + | 1.28139i | −0.0960443 | + | 0.0960443i | ||||
\(179\) | 5.04921 | 0.377396 | 0.188698 | − | 0.982035i | \(-0.439573\pi\) | ||||
0.188698 | + | 0.982035i | \(0.439573\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3.31623 | 0.246493 | 0.123247 | − | 0.992376i | \(-0.460669\pi\) | ||||
0.123247 | + | 0.992376i | \(0.460669\pi\) | |||||||
\(182\) | −18.3528 | + | 18.3528i | −1.36040 | + | 1.36040i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | − | 1.00000i | − | 0.0737210i | ||||||
\(185\) | 19.5992 | − | 17.5095i | 1.44096 | − | 1.28733i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −0.584970 | − | 0.584970i | −0.0427773 | − | 0.0427773i | ||||
\(188\) | 2.54798 | + | 2.54798i | 0.185831 | + | 0.185831i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −10.7001 | + | 9.55924i | −0.776264 | + | 0.693500i | ||||
\(191\) | − | 9.26011i | − | 0.670038i | −0.942211 | − | 0.335019i | \(-0.891257\pi\) | ||
0.942211 | − | 0.335019i | \(-0.108743\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 10.0816 | − | 10.0816i | 0.725692 | − | 0.725692i | −0.244066 | − | 0.969759i | \(-0.578481\pi\) |
0.969759 | + | 0.244066i | \(0.0784815\pi\) | |||||||
\(194\) | 12.0807 | 0.867346 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 17.6291 | 1.25922 | ||||||||
\(197\) | −19.7516 | + | 19.7516i | −1.40725 | + | 1.40725i | −0.633521 | + | 0.773726i | \(0.718391\pi\) |
−0.773726 | + | 0.633521i | \(0.781609\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 17.7223i | 1.25630i | 0.778092 | + | 0.628150i | \(0.216187\pi\) | ||||
−0.778092 | + | 0.628150i | \(0.783813\pi\) | |||||||
\(200\) | 3.11626 | + | 3.91011i | 0.220353 | + | 0.276486i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −4.95388 | − | 4.95388i | −0.348554 | − | 0.348554i | ||||
\(203\) | 5.89185 | + | 5.89185i | 0.413527 | + | 0.413527i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 23.6439 | + | 1.33142i | 1.65136 | + | 0.0929903i | ||||
\(206\) | − | 1.18663i | − | 0.0826767i | ||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 3.69809 | − | 3.69809i | 0.256417 | − | 0.256417i | ||||
\(209\) | 4.90771 | 0.339473 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 23.2846 | 1.60298 | 0.801491 | − | 0.598007i | \(-0.204041\pi\) | ||||
0.801491 | + | 0.598007i | \(0.204041\pi\) | |||||||
\(212\) | 9.13318 | − | 9.13318i | 0.627269 | − | 0.627269i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | − | 10.8974i | − | 0.744933i | ||||||
\(215\) | 6.25385 | + | 7.00020i | 0.426509 | + | 0.477410i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −34.8702 | − | 34.8702i | −2.36715 | − | 2.36715i | ||||
\(218\) | 1.63812 | + | 1.63812i | 0.110947 | + | 0.110947i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0.0961525 | − | 1.70751i | 0.00648260 | − | 0.115121i | ||||
\(221\) | 5.65685i | 0.380521i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 6.31235 | − | 6.31235i | 0.422706 | − | 0.422706i | −0.463428 | − | 0.886134i | \(-0.653381\pi\) |
0.886134 | + | 0.463428i | \(0.153381\pi\) | |||||||
\(224\) | −4.96277 | −0.331589 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 6.86714 | 0.456796 | ||||||||
\(227\) | 15.5235 | − | 15.5235i | 1.03033 | − | 1.03033i | 0.0308046 | − | 0.999525i | \(-0.490193\pi\) |
0.999525 | − | 0.0308046i | \(-0.00980695\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 26.6680i | 1.76227i | 0.472862 | + | 0.881137i | \(0.343221\pi\) | ||||
−0.472862 | + | 0.881137i | \(0.656779\pi\) | |||||||
\(230\) | −0.125717 | + | 2.23253i | −0.00828953 | + | 0.147209i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −1.18721 | − | 1.18721i | −0.0779442 | − | 0.0779442i | ||||
\(233\) | −14.3178 | − | 14.3178i | −0.937991 | − | 0.937991i | 0.0601958 | − | 0.998187i | \(-0.480827\pi\) |
−0.998187 | + | 0.0601958i | \(0.980827\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −5.36812 | − | 6.00877i | −0.350178 | − | 0.391969i | ||||
\(236\) | − | 0.219632i | − | 0.0142968i | ||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 3.79569 | − | 3.79569i | 0.246038 | − | 0.246038i | ||||
\(239\) | −8.13112 | −0.525958 | −0.262979 | − | 0.964801i | \(-0.584705\pi\) | ||||
−0.262979 | + | 0.964801i | \(0.584705\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.56965 | −0.101110 | −0.0505552 | − | 0.998721i | \(-0.516099\pi\) | ||||
−0.0505552 | + | 0.998721i | \(0.516099\pi\) | |||||||
\(242\) | 7.36454 | − | 7.36454i | 0.473410 | − | 0.473410i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 1.82779i | 0.117012i | ||||||||
\(245\) | −39.3575 | − | 2.21628i | −2.51446 | − | 0.141593i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −23.7296 | − | 23.7296i | −1.50988 | − | 1.50988i | ||||
\(248\) | 7.02637 | + | 7.02637i | 0.446175 | + | 0.446175i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −6.46558 | − | 9.12120i | −0.408919 | − | 0.576875i | ||||
\(251\) | 23.9786i | 1.51352i | 0.653695 | + | 0.756758i | \(0.273218\pi\) | ||||
−0.653695 | + | 0.756758i | \(0.726782\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0.540819 | − | 0.540819i | 0.0340010 | − | 0.0340010i | ||||
\(254\) | 6.58609 | 0.413248 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −12.5733 | + | 12.5733i | −0.784300 | + | 0.784300i | −0.980553 | − | 0.196253i | \(-0.937123\pi\) |
0.196253 | + | 0.980553i | \(0.437123\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 58.3294i | − | 3.62441i | ||||||
\(260\) | −8.72102 | + | 7.79120i | −0.540855 | + | 0.483190i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 7.25578 | + | 7.25578i | 0.448264 | + | 0.448264i | ||||
\(263\) | −6.07601 | − | 6.07601i | −0.374663 | − | 0.374663i | 0.494509 | − | 0.869172i | \(-0.335348\pi\) |
−0.869172 | + | 0.494509i | \(0.835348\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −21.5383 | + | 19.2419i | −1.32309 | + | 1.18202i | ||||
\(266\) | 31.8446i | 1.95252i | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 5.38509 | − | 5.38509i | 0.328947 | − | 0.328947i | ||||
\(269\) | −16.4382 | −1.00225 | −0.501127 | − | 0.865374i | \(-0.667081\pi\) | ||||
−0.501127 | + | 0.865374i | \(0.667081\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.91878 | 0.116558 | 0.0582789 | − | 0.998300i | \(-0.481439\pi\) | ||||
0.0582789 | + | 0.998300i | \(0.481439\pi\) | |||||||
\(272\) | −0.764834 | + | 0.764834i | −0.0463748 | + | 0.0463748i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | − | 15.8445i | − | 0.957203i | ||||||
\(275\) | −0.429327 | + | 3.79999i | −0.0258894 | + | 0.229148i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −11.4499 | − | 11.4499i | −0.687956 | − | 0.687956i | 0.273824 | − | 0.961780i | \(-0.411711\pi\) |
−0.961780 | + | 0.273824i | \(0.911711\pi\) | |||||||
\(278\) | 8.20762 | + | 8.20762i | 0.492261 | + | 0.492261i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 11.0795 | + | 0.623904i | 0.662129 | + | 0.0372854i | ||||
\(281\) | − | 12.0000i | − | 0.715859i | −0.933749 | − | 0.357930i | \(-0.883483\pi\) | ||
0.933749 | − | 0.357930i | \(-0.116517\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2.34054 | − | 2.34054i | 0.139131 | − | 0.139131i | −0.634111 | − | 0.773242i | \(-0.718634\pi\) |
0.773242 | + | 0.634111i | \(0.218634\pi\) | |||||||
\(284\) | 6.14124 | 0.364416 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 4.00000 | 0.236525 | ||||||||
\(287\) | 37.1647 | − | 37.1647i | 2.19376 | − | 2.19376i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 15.8301i | 0.931180i | ||||||||
\(290\) | 2.50123 | + | 2.79974i | 0.146877 | + | 0.164406i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 1.36645 | + | 1.36645i | 0.0799653 | + | 0.0799653i | ||||
\(293\) | −14.0431 | − | 14.0431i | −0.820406 | − | 0.820406i | 0.165760 | − | 0.986166i | \(-0.446992\pi\) |
−0.986166 | + | 0.165760i | \(0.946992\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −0.0276114 | + | 0.490335i | −0.00160760 | + | 0.0285484i | ||||
\(296\) | 11.7534i | 0.683152i | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 9.13509 | − | 9.13509i | 0.529181 | − | 0.529181i | ||||
\(299\) | −5.22990 | −0.302453 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 20.8334 | 1.20082 | ||||||||
\(302\) | 4.95998 | − | 4.95998i | 0.285415 | − | 0.285415i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | − | 6.41670i | − | 0.368023i | ||||||
\(305\) | 0.229784 | − | 4.08060i | 0.0131574 | − | 0.233654i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 5.27394 | + | 5.27394i | 0.301000 | + | 0.301000i | 0.841405 | − | 0.540405i | \(-0.181729\pi\) |
−0.540405 | + | 0.841405i | \(0.681729\pi\) | |||||||
\(308\) | −2.68396 | − | 2.68396i | −0.152933 | − | 0.152933i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −14.8032 | − | 16.5699i | −0.840768 | − | 0.941108i | ||||
\(311\) | − | 31.5861i | − | 1.79108i | −0.444977 | − | 0.895542i | \(-0.646788\pi\) | ||
0.444977 | − | 0.895542i | \(-0.353212\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −2.83163 | + | 2.83163i | −0.160053 | + | 0.160053i | −0.782590 | − | 0.622537i | \(-0.786102\pi\) |
0.622537 | + | 0.782590i | \(0.286102\pi\) | |||||||
\(314\) | 6.62605 | 0.373930 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −4.66284 | −0.262305 | ||||||||
\(317\) | 10.6011 | − | 10.6011i | 0.595420 | − | 0.595420i | −0.343671 | − | 0.939090i | \(-0.611670\pi\) |
0.939090 | + | 0.343671i | \(0.111670\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 1.28413i | − | 0.0718976i | ||||||
\(320\) | −2.23253 | − | 0.125717i | −0.124802 | − | 0.00702779i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 3.50921 | + | 3.50921i | 0.195561 | + | 0.195561i | ||||
\(323\) | 4.90771 | + | 4.90771i | 0.273072 | + | 0.273072i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 20.4494 | − | 16.2977i | 1.13433 | − | 0.904035i | ||||
\(326\) | − | 4.09581i | − | 0.226846i | ||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −7.48869 | + | 7.48869i | −0.413494 | + | 0.413494i | ||||
\(329\) | −17.8828 | −0.985911 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 7.81164 | 0.429367 | 0.214683 | − | 0.976684i | \(-0.431128\pi\) | ||||
0.214683 | + | 0.976684i | \(0.431128\pi\) | |||||||
\(332\) | 1.48645 | − | 1.48645i | 0.0815793 | − | 0.0815793i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | − | 1.83718i | − | 0.100526i | ||||||
\(335\) | −12.6994 | + | 11.3454i | −0.693842 | + | 0.619865i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −15.1462 | − | 15.1462i | −0.825065 | − | 0.825065i | 0.161764 | − | 0.986829i | \(-0.448282\pi\) |
−0.986829 | + | 0.161764i | \(0.948282\pi\) | |||||||
\(338\) | −10.1483 | − | 10.1483i | −0.551993 | − | 0.551993i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 1.80367 | − | 1.61136i | 0.0978176 | − | 0.0873884i | ||||
\(341\) | 7.59998i | 0.411562i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −37.2998 | + | 37.2998i | −2.01400 | + | 2.01400i | ||||
\(344\) | −4.19794 | −0.226338 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 21.7296 | 1.16819 | ||||||||
\(347\) | 25.3795 | − | 25.3795i | 1.36244 | − | 1.36244i | 0.491649 | − | 0.870794i | \(-0.336394\pi\) |
0.870794 | − | 0.491649i | \(-0.163606\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 23.9078i | 1.27975i | 0.768478 | + | 0.639876i | \(0.221014\pi\) | ||||
−0.768478 | + | 0.639876i | \(0.778986\pi\) | |||||||
\(350\) | −24.6570 | − | 2.78577i | −1.31797 | − | 0.148906i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0.540819 | + | 0.540819i | 0.0288258 | + | 0.0288258i | ||||
\(353\) | −16.3729 | − | 16.3729i | −0.871442 | − | 0.871442i | 0.121187 | − | 0.992630i | \(-0.461330\pi\) |
−0.992630 | + | 0.121187i | \(0.961330\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −13.7105 | − | 0.772058i | −0.727679 | − | 0.0409766i | ||||
\(356\) | 1.81216i | 0.0960443i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 3.57033 | − | 3.57033i | 0.188698 | − | 0.188698i | ||||
\(359\) | −29.2785 | −1.54526 | −0.772630 | − | 0.634857i | \(-0.781059\pi\) | ||||
−0.772630 | + | 0.634857i | \(0.781059\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −22.1741 | −1.16706 | ||||||||
\(362\) | 2.34493 | − | 2.34493i | 0.123247 | − | 0.123247i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 25.9548i | 1.36040i | ||||||||
\(365\) | −2.87885 | − | 3.22242i | −0.150686 | − | 0.168669i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −5.86479 | − | 5.86479i | −0.306140 | − | 0.306140i | 0.537270 | − | 0.843410i | \(-0.319455\pi\) |
−0.843410 | + | 0.537270i | \(0.819455\pi\) | |||||||
\(368\) | −0.707107 | − | 0.707107i | −0.0368605 | − | 0.0368605i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 1.47760 | − | 26.2398i | 0.0768168 | − | 1.36414i | ||||
\(371\) | 64.1005i | 3.32793i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −16.0815 | + | 16.0815i | −0.832669 | + | 0.832669i | −0.987881 | − | 0.155212i | \(-0.950394\pi\) |
0.155212 | + | 0.987881i | \(0.450394\pi\) | |||||||
\(374\) | −0.827273 | −0.0427773 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 3.60339 | 0.185831 | ||||||||
\(377\) | −6.20899 | + | 6.20899i | −0.319779 | + | 0.319779i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 3.82398i | 0.196425i | 0.995165 | + | 0.0982124i | \(0.0313125\pi\) | ||||
−0.995165 | + | 0.0982124i | \(0.968688\pi\) | |||||||
\(380\) | −0.806688 | + | 14.3255i | −0.0413822 | + | 0.734882i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −6.54789 | − | 6.54789i | −0.335019 | − | 0.335019i | ||||
\(383\) | −4.12422 | − | 4.12422i | −0.210738 | − | 0.210738i | 0.593843 | − | 0.804581i | \(-0.297610\pi\) |
−0.804581 | + | 0.593843i | \(0.797610\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 5.65461 | + | 6.32945i | 0.288186 | + | 0.322578i | ||||
\(386\) | − | 14.2576i | − | 0.725692i | ||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 8.54237 | − | 8.54237i | 0.433673 | − | 0.433673i | ||||
\(389\) | −34.1969 | −1.73385 | −0.866927 | − | 0.498435i | \(-0.833908\pi\) | ||||
−0.866927 | + | 0.498435i | \(0.833908\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.08164 | 0.0547008 | ||||||||
\(392\) | 12.4657 | − | 12.4657i | 0.629611 | − | 0.629611i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 27.9330i | 1.40725i | ||||||||
\(395\) | 10.4099 | + | 0.586197i | 0.523780 | + | 0.0294948i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 0.116895 | + | 0.116895i | 0.00586678 | + | 0.00586678i | 0.710034 | − | 0.704167i | \(-0.248680\pi\) |
−0.704167 | + | 0.710034i | \(0.748680\pi\) | |||||||
\(398\) | 12.5315 | + | 12.5315i | 0.628150 | + | 0.628150i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 4.96839 | + | 0.561334i | 0.248420 | + | 0.0280667i | ||||
\(401\) | − | 5.28905i | − | 0.264123i | −0.991242 | − | 0.132061i | \(-0.957840\pi\) | ||
0.991242 | − | 0.132061i | \(-0.0421596\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 36.7472 | − | 36.7472i | 1.83051 | − | 1.83051i | ||||
\(404\) | −7.00584 | −0.348554 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 8.33234 | 0.413527 | ||||||||
\(407\) | −6.35646 | + | 6.35646i | −0.315078 | + | 0.315078i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 2.72187i | − | 0.134588i | −0.997733 | − | 0.0672938i | \(-0.978564\pi\) | ||
0.997733 | − | 0.0672938i | \(-0.0214365\pi\) | |||||||
\(410\) | 17.6602 | − | 15.7773i | 0.872175 | − | 0.779185i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −0.839077 | − | 0.839077i | −0.0413384 | − | 0.0413384i | ||||
\(413\) | 0.770735 | + | 0.770735i | 0.0379254 | + | 0.0379254i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −3.50541 | + | 3.13167i | −0.172074 | + | 0.153727i | ||||
\(416\) | − | 5.22990i | − | 0.256417i | ||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 3.47028 | − | 3.47028i | 0.169737 | − | 0.169737i | ||||
\(419\) | −7.78582 | −0.380362 | −0.190181 | − | 0.981749i | \(-0.560908\pi\) | ||||
−0.190181 | + | 0.981749i | \(0.560908\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 31.1608 | 1.51868 | 0.759341 | − | 0.650693i | \(-0.225521\pi\) | ||||
0.759341 | + | 0.650693i | \(0.225521\pi\) | |||||||
\(422\) | 16.4647 | − | 16.4647i | 0.801491 | − | 0.801491i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | − | 12.9163i | − | 0.627269i | ||||||
\(425\) | −4.22932 | + | 3.37067i | −0.205152 | + | 0.163501i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −6.41409 | − | 6.41409i | −0.310400 | − | 0.310400i | ||||
\(428\) | −7.70564 | − | 7.70564i | −0.372466 | − | 0.372466i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 9.37203 | + | 0.527752i | 0.451959 | + | 0.0254504i | ||||
\(431\) | 12.6391i | 0.608805i | 0.952544 | + | 0.304402i | \(0.0984567\pi\) | ||||
−0.952544 | + | 0.304402i | \(0.901543\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 18.3279 | − | 18.3279i | 0.880782 | − | 0.880782i | −0.112833 | − | 0.993614i | \(-0.535992\pi\) |
0.993614 | + | 0.112833i | \(0.0359923\pi\) | |||||||
\(434\) | −49.3140 | −2.36715 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 2.31665 | 0.110947 | ||||||||
\(437\) | −4.53730 | + | 4.53730i | −0.217048 | + | 0.217048i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 29.6398i | 1.41463i | 0.706899 | + | 0.707315i | \(0.250094\pi\) | ||||
−0.706899 | + | 0.707315i | \(0.749906\pi\) | |||||||
\(440\) | −1.13941 | − | 1.27539i | −0.0543190 | − | 0.0608016i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 4.00000 | + | 4.00000i | 0.190261 | + | 0.190261i | ||||
\(443\) | −6.92423 | − | 6.92423i | −0.328980 | − | 0.328980i | 0.523218 | − | 0.852199i | \(-0.324731\pi\) |
−0.852199 | + | 0.523218i | \(0.824731\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0.227819 | − | 4.04570i | 0.0107997 | − | 0.191785i | ||||
\(446\) | − | 8.92701i | − | 0.422706i | ||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −3.50921 | + | 3.50921i | −0.165795 | + | 0.165795i | ||||
\(449\) | 15.6141 | 0.736877 | 0.368438 | − | 0.929652i | \(-0.379893\pi\) | ||||
0.368438 | + | 0.929652i | \(0.379893\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −8.10006 | −0.381417 | ||||||||
\(452\) | 4.85580 | − | 4.85580i | 0.228398 | − | 0.228398i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | − | 21.9535i | − | 1.03033i | ||||||
\(455\) | 3.26295 | − | 57.9449i | 0.152970 | − | 2.71650i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 23.0821 | + | 23.0821i | 1.07974 | + | 1.07974i | 0.996533 | + | 0.0832035i | \(0.0265151\pi\) |
0.0832035 | + | 0.996533i | \(0.473485\pi\) | |||||||
\(458\) | 18.8571 | + | 18.8571i | 0.881137 | + | 0.881137i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 1.48974 | + | 1.66753i | 0.0694596 | + | 0.0777491i | ||||
\(461\) | 21.5655i | 1.00441i | 0.864750 | + | 0.502203i | \(0.167477\pi\) | ||||
−0.864750 | + | 0.502203i | \(0.832523\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 11.0503 | − | 11.0503i | 0.513552 | − | 0.513552i | −0.402061 | − | 0.915613i | \(-0.631706\pi\) |
0.915613 | + | 0.402061i | \(0.131706\pi\) | |||||||
\(464\) | −1.67897 | −0.0779442 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −20.2484 | −0.937991 | ||||||||
\(467\) | 3.79664 | − | 3.79664i | 0.175687 | − | 0.175687i | −0.613785 | − | 0.789473i | \(-0.710354\pi\) |
0.789473 | + | 0.613785i | \(0.210354\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 37.7949i | 1.74520i | ||||||||
\(470\) | −8.04468 | − | 0.453007i | −0.371073 | − | 0.0208957i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −0.155303 | − | 0.155303i | −0.00714841 | − | 0.00714841i | ||||
\(473\) | −2.27032 | − | 2.27032i | −0.104390 | − | 0.104390i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 3.60191 | − | 31.8807i | 0.165267 | − | 1.46279i | ||||
\(476\) | − | 5.36792i | − | 0.246038i | ||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −5.74957 | + | 5.74957i | −0.262979 | + | 0.262979i | ||||
\(479\) | 30.3683 | 1.38756 | 0.693781 | − | 0.720186i | \(-0.255944\pi\) | ||||
0.693781 | + | 0.720186i | \(0.255944\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 61.4690 | 2.80275 | ||||||||
\(482\) | −1.10991 | + | 1.10991i | −0.0505552 | + | 0.0505552i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | − | 10.4150i | − | 0.473410i | ||||||
\(485\) | −20.1450 | + | 17.9972i | −0.914739 | + | 0.817210i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −18.5717 | − | 18.5717i | −0.841562 | − | 0.841562i | 0.147500 | − | 0.989062i | \(-0.452877\pi\) |
−0.989062 | + | 0.147500i | \(0.952877\pi\) | |||||||
\(488\) | 1.29244 | + | 1.29244i | 0.0585061 | + | 0.0585061i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −29.3971 | + | 26.2628i | −1.32803 | + | 1.18643i | ||||
\(491\) | − | 44.0696i | − | 1.98883i | −0.105520 | − | 0.994417i | \(-0.533651\pi\) | ||
0.105520 | − | 0.994417i | \(-0.466349\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1.28413 | − | 1.28413i | 0.0578344 | − | 0.0578344i | ||||
\(494\) | −33.5587 | −1.50988 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 9.93678 | 0.446175 | ||||||||
\(497\) | −21.5509 | + | 21.5509i | −0.966690 | + | 0.966690i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 8.79482i | − | 0.393710i | −0.980433 | − | 0.196855i | \(-0.936927\pi\) | ||
0.980433 | − | 0.196855i | \(-0.0630728\pi\) | |||||||
\(500\) | −11.0215 | − | 1.87781i | −0.492897 | − | 0.0839780i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 16.9554 | + | 16.9554i | 0.756758 | + | 0.756758i | ||||
\(503\) | −9.97229 | − | 9.97229i | −0.444643 | − | 0.444643i | 0.448926 | − | 0.893569i | \(-0.351807\pi\) |
−0.893569 | + | 0.448926i | \(0.851807\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 15.6408 | + | 0.880752i | 0.696004 | + | 0.0391930i | ||||
\(506\) | − | 0.764834i | − | 0.0340010i | ||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 4.65707 | − | 4.65707i | 0.206624 | − | 0.206624i | ||||
\(509\) | −12.7606 | −0.565603 | −0.282801 | − | 0.959178i | \(-0.591264\pi\) | ||||
−0.282801 | + | 0.959178i | \(0.591264\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −9.59031 | −0.424250 | ||||||||
\(512\) | 0.707107 | − | 0.707107i | 0.0312500 | − | 0.0312500i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 17.7813i | 0.784300i | ||||||||
\(515\) | 1.76778 | + | 1.97875i | 0.0778977 | + | 0.0871942i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.94878 | + | 1.94878i | 0.0857073 | + | 0.0857073i | ||||
\(518\) | −41.2451 | − | 41.2451i | −1.81221 | − | 1.81221i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −0.657486 | + | 11.6759i | −0.0288327 | + | 0.512022i | ||||
\(521\) | − | 5.51996i | − | 0.241834i | −0.992663 | − | 0.120917i | \(-0.961417\pi\) | ||
0.992663 | − | 0.120917i | \(-0.0385834\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 28.0942 | − | 28.0942i | 1.22847 | − | 1.22847i | 0.263930 | − | 0.964542i | \(-0.414981\pi\) |
0.964542 | − | 0.263930i | \(-0.0850188\pi\) | |||||||
\(524\) | 10.2612 | 0.448264 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −8.59278 | −0.374663 | ||||||||
\(527\) | −7.59998 | + | 7.59998i | −0.331060 | + | 0.331060i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.00000i | 0.0434783i | ||||||||
\(530\) | −1.62379 | + | 28.8360i | −0.0705331 | + | 1.25255i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 22.5176 | + | 22.5176i | 0.976260 | + | 0.976260i | ||||
\(533\) | 39.1651 | + | 39.1651i | 1.69643 | + | 1.69643i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 16.2344 | + | 18.1718i | 0.701873 | + | 0.785636i | ||||
\(536\) | − | 7.61567i | − | 0.328947i | ||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −11.6236 | + | 11.6236i | −0.501127 | + | 0.501127i | ||||
\(539\) | 13.4833 | 0.580768 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −27.4184 | −1.17881 | −0.589405 | − | 0.807837i | \(-0.700638\pi\) | ||||
−0.589405 | + | 0.807837i | \(0.700638\pi\) | |||||||
\(542\) | 1.35678 | − | 1.35678i | 0.0582789 | − | 0.0582789i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 1.08164i | 0.0463748i | ||||||||
\(545\) | −5.17199 | − | 0.291242i | −0.221544 | − | 0.0124754i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 9.37400 | + | 9.37400i | 0.400803 | + | 0.400803i | 0.878516 | − | 0.477713i | \(-0.158534\pi\) |
−0.477713 | + | 0.878516i | \(0.658534\pi\) | |||||||
\(548\) | −11.2038 | − | 11.2038i | −0.478602 | − | 0.478602i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 2.38342 | + | 2.99058i | 0.101629 | + | 0.127519i | ||||
\(551\) | 10.7734i | 0.458964i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 16.3629 | − | 16.3629i | 0.695820 | − | 0.695820i | ||||
\(554\) | −16.1926 | −0.687956 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 11.6073 | 0.492261 | ||||||||
\(557\) | −16.9474 | + | 16.9474i | −0.718085 | + | 0.718085i | −0.968213 | − | 0.250128i | \(-0.919527\pi\) |
0.250128 | + | 0.968213i | \(0.419527\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 21.9548i | 0.928588i | ||||||||
\(560\) | 8.27559 | − | 7.39325i | 0.349707 | − | 0.312422i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −8.48528 | − | 8.48528i | −0.357930 | − | 0.357930i | ||||
\(563\) | 18.3096 | + | 18.3096i | 0.771657 | + | 0.771657i | 0.978396 | − | 0.206739i | \(-0.0662852\pi\) |
−0.206739 | + | 0.978396i | \(0.566285\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −11.4512 | + | 10.2303i | −0.481755 | + | 0.430391i | ||||
\(566\) | − | 3.31003i | − | 0.139131i | ||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 4.34251 | − | 4.34251i | 0.182208 | − | 0.182208i | ||||
\(569\) | 21.2498 | 0.890837 | 0.445419 | − | 0.895322i | \(-0.353055\pi\) | ||||
0.445419 | + | 0.895322i | \(0.353055\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −10.4347 | −0.436679 | −0.218339 | − | 0.975873i | \(-0.570064\pi\) | ||||
−0.218339 | + | 0.975873i | \(0.570064\pi\) | |||||||
\(572\) | 2.82843 | − | 2.82843i | 0.118262 | − | 0.118262i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | − | 52.5588i | − | 2.19376i | ||||||
\(575\) | −3.11626 | − | 3.91011i | −0.129957 | − | 0.163063i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −2.81127 | − | 2.81127i | −0.117035 | − | 0.117035i | 0.646164 | − | 0.763199i | \(-0.276372\pi\) |
−0.763199 | + | 0.646164i | \(0.776372\pi\) | |||||||
\(578\) | 11.1935 | + | 11.1935i | 0.465590 | + | 0.465590i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 3.74835 | + | 0.211075i | 0.155642 | + | 0.00876440i | ||||
\(581\) | 10.4325i | 0.432813i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 6.98536 | − | 6.98536i | 0.289304 | − | 0.289304i | ||||
\(584\) | 1.93245 | 0.0799653 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −19.8599 | −0.820406 | ||||||||
\(587\) | 14.3854 | − | 14.3854i | 0.593751 | − | 0.593751i | −0.344892 | − | 0.938643i | \(-0.612084\pi\) |
0.938643 | + | 0.344892i | \(0.112084\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 63.7614i | − | 2.62724i | ||||||
\(590\) | 0.327195 | + | 0.366244i | 0.0134704 | + | 0.0150780i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 8.31090 | + | 8.31090i | 0.341576 | + | 0.341576i | ||||
\(593\) | −14.6106 | − | 14.6106i | −0.599984 | − | 0.599984i | 0.340324 | − | 0.940308i | \(-0.389463\pi\) |
−0.940308 | + | 0.340324i | \(0.889463\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −0.674839 | + | 11.9841i | −0.0276657 | + | 0.491298i | ||||
\(596\) | − | 12.9190i | − | 0.529181i | ||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −3.69809 | + | 3.69809i | −0.151226 | + | 0.151226i | ||||
\(599\) | 40.2853 | 1.64601 | 0.823007 | − | 0.568031i | \(-0.192295\pi\) | ||||
0.823007 | + | 0.568031i | \(0.192295\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −2.38537 | −0.0973013 | −0.0486507 | − | 0.998816i | \(-0.515492\pi\) | ||||
−0.0486507 | + | 0.998816i | \(0.515492\pi\) | |||||||
\(602\) | 14.7314 | − | 14.7314i | 0.600409 | − | 0.600409i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | − | 7.01447i | − | 0.285415i | ||||||
\(605\) | −1.30935 | + | 23.2519i | −0.0532324 | + | 0.945323i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −24.5540 | − | 24.5540i | −0.996614 | − | 0.996614i | 0.00338019 | − | 0.999994i | \(-0.498924\pi\) |
−0.999994 | + | 0.00338019i | \(0.998924\pi\) | |||||||
\(608\) | −4.53730 | − | 4.53730i | −0.184012 | − | 0.184012i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −2.72294 | − | 3.04790i | −0.110248 | − | 0.123406i | ||||
\(611\) | − | 18.8454i | − | 0.762401i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 15.5537 | − | 15.5537i | 0.628209 | − | 0.628209i | −0.319408 | − | 0.947617i | \(-0.603484\pi\) |
0.947617 | + | 0.319408i | \(0.103484\pi\) | |||||||
\(614\) | 7.45848 | 0.301000 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −3.79569 | −0.152933 | ||||||||
\(617\) | −6.57856 | + | 6.57856i | −0.264843 | + | 0.264843i | −0.827018 | − | 0.562175i | \(-0.809965\pi\) |
0.562175 | + | 0.827018i | \(0.309965\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 15.3899i | − | 0.618572i | −0.950969 | − | 0.309286i | \(-0.899910\pi\) | ||
0.950969 | − | 0.309286i | \(-0.100090\pi\) | |||||||
\(620\) | −22.1842 | − | 1.24922i | −0.890938 | − | 0.0501699i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −22.3347 | − | 22.3347i | −0.895542 | − | 0.895542i | ||||
\(623\) | −6.35925 | − | 6.35925i | −0.254778 | − | 0.254778i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 24.3698 | + | 5.57785i | 0.974792 | + | 0.223114i | ||||
\(626\) | 4.00453i | 0.160053i | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 4.68533 | − | 4.68533i | 0.186965 | − | 0.186965i | ||||
\(629\) | −12.7129 | −0.506897 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 31.5331 | 1.25531 | 0.627656 | − | 0.778491i | \(-0.284014\pi\) | ||||
0.627656 | + | 0.778491i | \(0.284014\pi\) | |||||||
\(632\) | −3.29712 | + | 3.29712i | −0.131153 | + | 0.131153i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | − | 14.9923i | − | 0.595420i | ||||||
\(635\) | −10.9825 | + | 9.81157i | −0.435828 | + | 0.389360i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −65.1941 | − | 65.1941i | −2.58308 | − | 2.58308i | ||||
\(638\) | −0.908018 | − | 0.908018i | −0.0359488 | − | 0.0359488i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −1.66753 | + | 1.48974i | −0.0659150 | + | 0.0588872i | ||||
\(641\) | 37.5286i | 1.48229i | 0.671345 | + | 0.741145i | \(0.265717\pi\) | ||||
−0.671345 | + | 0.741145i | \(0.734283\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −25.9099 | + | 25.9099i | −1.02179 | + | 1.02179i | −0.0220314 | + | 0.999757i | \(0.507013\pi\) |
−0.999757 | + | 0.0220314i | \(0.992987\pi\) | |||||||
\(644\) | 4.96277 | 0.195561 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 6.94055 | 0.273072 | ||||||||
\(647\) | −21.8642 | + | 21.8642i | −0.859570 | + | 0.859570i | −0.991287 | − | 0.131718i | \(-0.957951\pi\) |
0.131718 | + | 0.991287i | \(0.457951\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 0.167982i | − | 0.00659387i | ||||||
\(650\) | 2.93572 | − | 25.9842i | 0.115148 | − | 1.01918i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −2.89617 | − | 2.89617i | −0.113423 | − | 0.113423i | ||||
\(653\) | 27.6181 | + | 27.6181i | 1.08078 | + | 1.08078i | 0.996437 | + | 0.0843434i | \(0.0268793\pi\) |
0.0843434 | + | 0.996437i | \(0.473121\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −22.9085 | − | 1.29001i | −0.895109 | − | 0.0504048i | ||||
\(656\) | 10.5906i | 0.413494i | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −12.6450 | + | 12.6450i | −0.492955 | + | 0.492955i | ||||
\(659\) | 36.9228 | 1.43831 | 0.719154 | − | 0.694850i | \(-0.244529\pi\) | ||||
0.719154 | + | 0.694850i | \(0.244529\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 15.6368 | 0.608200 | 0.304100 | − | 0.952640i | \(-0.401644\pi\) | ||||
0.304100 | + | 0.952640i | \(0.401644\pi\) | |||||||
\(662\) | 5.52366 | − | 5.52366i | 0.214683 | − | 0.214683i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | − | 2.10215i | − | 0.0815793i | ||||||
\(665\) | −47.4403 | − | 53.1020i | −1.83966 | − | 2.05921i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.18721 | + | 1.18721i | 0.0459690 | + | 0.0459690i | ||||
\(668\) | −1.29908 | − | 1.29908i | −0.0502630 | − | 0.0502630i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −0.957419 | + | 17.0022i | −0.0369883 | + | 0.656853i | ||||
\(671\) | 1.39795i | 0.0539674i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −13.1080 | + | 13.1080i | −0.505277 | + | 0.505277i | −0.913073 | − | 0.407796i | \(-0.866298\pi\) |
0.407796 | + | 0.913073i | \(0.366298\pi\) | |||||||
\(674\) | −21.4199 | −0.825065 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −14.3518 | −0.551993 | ||||||||
\(677\) | −26.1392 | + | 26.1392i | −1.00461 | + | 1.00461i | −0.00462136 | + | 0.999989i | \(0.501471\pi\) |
−0.999989 | + | 0.00462136i | \(0.998529\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 59.9539i | 2.30082i | ||||||||
\(680\) | 0.135980 | − | 2.41479i | 0.00521460 | − | 0.0926030i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 5.37400 | + | 5.37400i | 0.205781 | + | 0.205781i | ||||
\(683\) | 17.3964 | + | 17.3964i | 0.665656 | + | 0.665656i | 0.956707 | − | 0.291051i | \(-0.0940051\pi\) |
−0.291051 | + | 0.956707i | \(0.594005\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 23.6043 | + | 26.4213i | 0.901873 | + | 1.00951i | ||||
\(686\) | 52.7498i | 2.01400i | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −2.96839 | + | 2.96839i | −0.113169 | + | 0.113169i | ||||
\(689\) | −67.5507 | −2.57348 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 35.7736 | 1.36089 | 0.680447 | − | 0.732798i | \(-0.261786\pi\) | ||||
0.680447 | + | 0.732798i | \(0.261786\pi\) | |||||||
\(692\) | 15.3651 | − | 15.3651i | 0.584095 | − | 0.584095i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | − | 35.8920i | − | 1.36244i | ||||||
\(695\) | −25.9137 | − | 1.45924i | −0.982964 | − | 0.0553521i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −8.10006 | − | 8.10006i | −0.306812 | − | 0.306812i | ||||
\(698\) | 16.9053 | + | 16.9053i | 0.639876 | + | 0.639876i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −19.4050 | + | 15.4653i | −0.733439 | + | 0.584533i | ||||
\(701\) | 13.9819i | 0.528088i | 0.964511 | + | 0.264044i | \(0.0850565\pi\) | ||||
−0.964511 | + | 0.264044i | \(0.914944\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 53.3286 | − | 53.3286i | 2.01133 | − | 2.01133i | ||||
\(704\) | 0.764834 | 0.0288258 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −23.1548 | −0.871442 | ||||||||
\(707\) | 24.5850 | − | 24.5850i | 0.924612 | − | 0.924612i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 28.3566i | − | 1.06495i | −0.846444 | − | 0.532477i | \(-0.821261\pi\) | ||
0.846444 | − | 0.532477i | \(-0.178739\pi\) | |||||||
\(710\) | −10.2407 | + | 9.14887i | −0.384328 | + | 0.343351i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 1.28139 | + | 1.28139i | 0.0480221 | + | 0.0480221i | ||||
\(713\) | −7.02637 | − | 7.02637i | −0.263139 | − | 0.263139i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −6.67013 | + | 5.95897i | −0.249449 | + | 0.222853i | ||||
\(716\) | − | 5.04921i | − | 0.188698i | ||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −20.7030 | + | 20.7030i | −0.772630 | + | 0.772630i | ||||
\(719\) | −2.41743 | −0.0901550 | −0.0450775 | − | 0.998983i | \(-0.514353\pi\) | ||||
−0.0450775 | + | 0.998983i | \(0.514353\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 5.88899 | 0.219318 | ||||||||
\(722\) | −15.6795 | + | 15.6795i | −0.583529 | + | 0.583529i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | − | 3.31623i | − | 0.123247i | ||||||
\(725\) | −8.34177 | − | 0.942462i | −0.309806 | − | 0.0350022i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −24.9673 | − | 24.9673i | −0.925987 | − | 0.925987i | 0.0714570 | − | 0.997444i | \(-0.477235\pi\) |
−0.997444 | + | 0.0714570i | \(0.977235\pi\) | |||||||
\(728\) | 18.3528 | + | 18.3528i | 0.680200 | + | 0.680200i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −4.31425 | − | 0.242942i | −0.159678 | − | 0.00899167i | ||||
\(731\) | − | 4.54065i | − | 0.167942i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 21.9350 | − | 21.9350i | 0.810187 | − | 0.810187i | −0.174475 | − | 0.984662i | \(-0.555823\pi\) |
0.984662 | + | 0.174475i | \(0.0558227\pi\) | |||||||
\(734\) | −8.29407 | −0.306140 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −1.00000 | −0.0368605 | ||||||||
\(737\) | 4.11870 | − | 4.11870i | 0.151714 | − | 0.151714i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 14.1633i | − | 0.521005i | −0.965473 | − | 0.260502i | \(-0.916112\pi\) | ||
0.965473 | − | 0.260502i | \(-0.0838881\pi\) | |||||||
\(740\) | −17.5095 | − | 19.5992i | −0.643663 | − | 0.720480i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 45.3259 | + | 45.3259i | 1.66397 | + | 1.66397i | ||||
\(743\) | −30.7853 | − | 30.7853i | −1.12940 | − | 1.12940i | −0.990274 | − | 0.139130i | \(-0.955569\pi\) |
−0.139130 | − | 0.990274i | \(-0.544431\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1.62413 | + | 28.8420i | −0.0595036 | + | 1.05669i | ||||
\(746\) | 22.7427i | 0.832669i | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −0.584970 | + | 0.584970i | −0.0213886 | + | 0.0213886i | ||||
\(749\) | 54.0814 | 1.97609 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −40.3869 | −1.47374 | −0.736869 | − | 0.676036i | \(-0.763697\pi\) | ||||
−0.736869 | + | 0.676036i | \(0.763697\pi\) | |||||||
\(752\) | 2.54798 | − | 2.54798i | 0.0929153 | − | 0.0929153i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 8.78083i | 0.319779i | ||||||||
\(755\) | −0.881838 | + | 15.6600i | −0.0320934 | + | 0.569927i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 17.1456 | + | 17.1456i | 0.623166 | + | 0.623166i | 0.946340 | − | 0.323174i | \(-0.104750\pi\) |
−0.323174 | + | 0.946340i | \(0.604750\pi\) | |||||||
\(758\) | 2.70397 | + | 2.70397i | 0.0982124 | + | 0.0982124i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 9.55924 | + | 10.7001i | 0.346750 | + | 0.388132i | ||||
\(761\) | − | 31.1739i | − | 1.13005i | −0.825073 | − | 0.565026i | \(-0.808866\pi\) | ||
0.825073 | − | 0.565026i | \(-0.191134\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −8.12960 | + | 8.12960i | −0.294311 | + | 0.294311i | ||||
\(764\) | −9.26011 | −0.335019 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −5.83253 | −0.210738 | ||||||||
\(767\) | −0.812220 | + | 0.812220i | −0.0293276 | + | 0.0293276i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 7.27059i | − | 0.262184i | −0.991370 | − | 0.131092i | \(-0.958152\pi\) | ||
0.991370 | − | 0.131092i | \(-0.0418484\pi\) | |||||||
\(770\) | 8.47401 | + | 0.477183i | 0.305382 | + | 0.0171965i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −10.0816 | − | 10.0816i | −0.362846 | − | 0.362846i | ||||
\(773\) | 8.06437 | + | 8.06437i | 0.290055 | + | 0.290055i | 0.837102 | − | 0.547047i | \(-0.184248\pi\) |
−0.547047 | + | 0.837102i | \(0.684248\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 49.3698 | + | 5.57785i | 1.77342 | + | 0.200362i | ||||
\(776\) | − | 12.0807i | − | 0.433673i | ||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −24.1809 | + | 24.1809i | −0.866927 | + | 0.866927i | ||||
\(779\) | 67.9568 | 2.43481 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 4.69703 | 0.168073 | ||||||||
\(782\) | 0.764834 | − | 0.764834i | 0.0273504 | − | 0.0273504i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | − | 17.6291i | − | 0.629611i | ||||||
\(785\) | −11.0492 | + | 9.87111i | −0.394361 | + | 0.352315i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −15.0672 | − | 15.0672i | −0.537087 | − | 0.537087i | 0.385585 | − | 0.922672i | \(-0.374000\pi\) |
−0.922672 | + | 0.385585i | \(0.874000\pi\) | |||||||
\(788\) | 19.7516 | + | 19.7516i | 0.703623 | + | 0.703623i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 7.77544 | − | 6.94643i | 0.276638 | − | 0.247143i | ||||
\(791\) | 34.0801i | 1.21175i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 6.75934 | − | 6.75934i | 0.240031 | − | 0.240031i | ||||
\(794\) | 0.165314 | 0.00586678 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 17.7223 | 0.628150 | ||||||||
\(797\) | 27.0095 | − | 27.0095i | 0.956727 | − | 0.956727i | −0.0423748 | − | 0.999102i | \(-0.513492\pi\) |
0.999102 | + | 0.0423748i | \(0.0134924\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 3.89756i | 0.137886i | ||||||||
\(800\) | 3.91011 | − | 3.11626i | 0.138243 | − | 0.110176i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −3.73992 | − | 3.73992i | −0.132061 | − | 0.132061i | ||||
\(803\) | 1.04511 | + | 1.04511i | 0.0368810 | + | 0.0368810i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −11.0795 | − | 0.623904i | −0.390503 | − | 0.0219897i | ||||
\(806\) | − | 51.9683i | − | 1.83051i | ||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −4.95388 | + | 4.95388i | −0.174277 | + | 0.174277i | ||||
\(809\) | −25.4136 | −0.893493 | −0.446746 | − | 0.894661i | \(-0.647417\pi\) | ||||
−0.446746 | + | 0.894661i | \(0.647417\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −15.7740 | −0.553899 | −0.276949 | − | 0.960885i | \(-0.589323\pi\) | ||||
−0.276949 | + | 0.960885i | \(0.589323\pi\) | |||||||
\(812\) | 5.89185 | − | 5.89185i | 0.206764 | − | 0.206764i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 8.98939i | 0.315078i | ||||||||
\(815\) | 6.10170 | + | 6.82989i | 0.213733 | + | 0.239241i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 19.0473 | + | 19.0473i | 0.666380 | + | 0.666380i | ||||
\(818\) | −1.92465 | − | 1.92465i | −0.0672938 | − | 0.0672938i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 1.33142 | − | 23.6439i | 0.0464952 | − | 0.825680i | ||||
\(821\) | 23.8083i | 0.830914i | 0.909613 | + | 0.415457i | \(0.136378\pi\) | ||||
−0.909613 | + | 0.415457i | \(0.863622\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 6.89778 | − | 6.89778i | 0.240441 | − | 0.240441i | −0.576591 | − | 0.817033i | \(-0.695617\pi\) |
0.817033 | + | 0.576591i | \(0.195617\pi\) | |||||||
\(824\) | −1.18663 | −0.0413384 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 1.08998 | 0.0379254 | ||||||||
\(827\) | −14.3996 | + | 14.3996i | −0.500724 | + | 0.500724i | −0.911663 | − | 0.410939i | \(-0.865201\pi\) |
0.410939 | + | 0.911663i | \(0.365201\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 34.6696i | 1.20412i | 0.798449 | + | 0.602062i | \(0.205654\pi\) | ||||
−0.798449 | + | 0.602062i | \(0.794346\pi\) | |||||||
\(830\) | −0.264276 | + | 4.69312i | −0.00917316 | + | 0.162901i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −3.69809 | − | 3.69809i | −0.128208 | − | 0.128208i | ||||
\(833\) | 13.4833 | + | 13.4833i | 0.467170 | + | 0.467170i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 2.73692 | + | 3.06356i | 0.0947152 | + | 0.106019i | ||||
\(836\) | − | 4.90771i | − | 0.169737i | ||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −5.50541 | + | 5.50541i | −0.190181 | + | 0.190181i | ||||
\(839\) | 15.3817 | 0.531035 | 0.265517 | − | 0.964106i | \(-0.414457\pi\) | ||||
0.265517 | + | 0.964106i | \(0.414457\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −26.1811 | −0.902795 | ||||||||
\(842\) | 22.0340 | − | 22.0340i | 0.759341 | − | 0.759341i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | − | 23.2846i | − | 0.801491i | ||||||
\(845\) | 32.0409 | + | 1.80426i | 1.10224 | + | 0.0620686i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 36.5485 | + | 36.5485i | 1.25582 | + | 1.25582i | ||||
\(848\) | −9.13318 | − | 9.13318i | −0.313635 | − | 0.313635i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −0.607160 | + | 5.37400i | −0.0208254 | + | 0.184327i | ||||
\(851\) | − | 11.7534i | − | 0.402901i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −24.5725 | + | 24.5725i | −0.841348 | + | 0.841348i | −0.989034 | − | 0.147687i | \(-0.952817\pi\) |
0.147687 | + | 0.989034i | \(0.452817\pi\) | |||||||
\(854\) | −9.07090 | −0.310400 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −10.8974 | −0.372466 | ||||||||
\(857\) | −1.01111 | + | 1.01111i | −0.0345388 | + | 0.0345388i | −0.724165 | − | 0.689626i | \(-0.757775\pi\) |
0.689626 | + | 0.724165i | \(0.257775\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 23.4672i | − | 0.800691i | −0.916364 | − | 0.400346i | \(-0.868890\pi\) | ||
0.916364 | − | 0.400346i | \(-0.131110\pi\) | |||||||
\(860\) | 7.00020 | − | 6.25385i | 0.238705 | − | 0.213254i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 8.93720 | + | 8.93720i | 0.304402 | + | 0.304402i | ||||
\(863\) | −16.8159 | − | 16.8159i | −0.572421 | − | 0.572421i | 0.360383 | − | 0.932804i | \(-0.382646\pi\) |
−0.932804 | + | 0.360383i | \(0.882646\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −36.2348 | + | 32.3715i | −1.23202 | + | 1.10066i | ||||
\(866\) | − | 25.9195i | − | 0.880782i | ||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −34.8702 | + | 34.8702i | −1.18357 | + | 1.18357i | ||||
\(869\) | −3.56630 | −0.120978 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −39.8292 | −1.34956 | ||||||||
\(872\) | 1.63812 | − | 1.63812i | 0.0554736 | − | 0.0554736i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 6.41670i | 0.217048i | ||||||||
\(875\) | 45.2664 | − | 32.0872i | 1.53028 | − | 1.08475i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 11.2750 | + | 11.2750i | 0.380731 | + | 0.380731i | 0.871366 | − | 0.490634i | \(-0.163235\pi\) |
−0.490634 | + | 0.871366i | \(0.663235\pi\) | |||||||
\(878\) | 20.9585 | + | 20.9585i | 0.707315 | + | 0.707315i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −1.70751 | − | 0.0961525i | −0.0575603 | − | 0.00324130i | ||||
\(881\) | − | 1.95840i | − | 0.0659801i | −0.999456 | − | 0.0329901i | \(-0.989497\pi\) | ||
0.999456 | − | 0.0329901i | \(-0.0105030\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 13.9971 | − | 13.9971i | 0.471040 | − | 0.471040i | −0.431211 | − | 0.902251i | \(-0.641914\pi\) |
0.902251 | + | 0.431211i | \(0.141914\pi\) | |||||||
\(884\) | 5.65685 | 0.190261 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −9.79234 | −0.328980 | ||||||||
\(887\) | 19.7538 | − | 19.7538i | 0.663269 | − | 0.663269i | −0.292880 | − | 0.956149i | \(-0.594614\pi\) |
0.956149 | + | 0.292880i | \(0.0946137\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 32.6852i | 1.09623i | ||||||||
\(890\) | −2.69965 | − | 3.02184i | −0.0904925 | − | 0.101292i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −6.31235 | − | 6.31235i | −0.211353 | − | 0.211353i | ||||
\(893\) | −16.3496 | − | 16.3496i | −0.547120 | − | 0.547120i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −0.634771 | + | 11.2725i | −0.0212181 | + | 0.376799i | ||||
\(896\) | 4.96277i | 0.165795i | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 11.0409 | − | 11.0409i | 0.368438 | − | 0.368438i | ||||
\(899\) | −16.6835 | −0.556428 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 13.9707 | 0.465432 | ||||||||
\(902\) | −5.72761 | + | 5.72761i | −0.190708 | + | 0.190708i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | − | 6.86714i | − | 0.228398i | ||||||
\(905\) | −0.416906 | + | 7.40358i | −0.0138584 | + | 0.246103i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 6.93556 | + | 6.93556i | 0.230291 | + | 0.230291i | 0.812814 | − | 0.582523i | \(-0.197934\pi\) |
−0.582523 | + | 0.812814i | \(0.697934\pi\) | |||||||
\(908\) | −15.5235 | − | 15.5235i | −0.515165 | − | 0.515165i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −38.6659 | − | 43.2805i | −1.28176 | − | 1.43473i | ||||
\(911\) | − | 12.0729i | − | 0.399994i | −0.979796 | − | 0.199997i | \(-0.935907\pi\) | ||
0.979796 | − | 0.199997i | \(-0.0640933\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1.13688 | − | 1.13688i | 0.0376254 | − | 0.0376254i | ||||
\(914\) | 32.6430 | 1.07974 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 26.6680 | 0.881137 | ||||||||
\(917\) | −36.0088 | + | 36.0088i | −1.18911 | + | 1.18911i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 46.3777i | 1.52986i | 0.644113 | + | 0.764930i | \(0.277227\pi\) | ||||
−0.644113 | + | 0.764930i | \(0.722773\pi\) | |||||||
\(920\) | 2.23253 | + | 0.125717i | 0.0736044 | + | 0.00414476i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 15.2491 | + | 15.2491i | 0.502203 | + | 0.502203i | ||||
\(923\) | −22.7109 | − | 22.7109i | −0.747538 | − | 0.747538i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 36.6266 | + | 45.9570i | 1.20428 | + | 1.51106i | ||||
\(926\) | − | 15.6275i | − | 0.513552i | ||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −1.18721 | + | 1.18721i | −0.0389721 | + | 0.0389721i | ||||
\(929\) | −16.9443 | −0.555924 | −0.277962 | − | 0.960592i | \(-0.589659\pi\) | ||||
−0.277962 | + | 0.960592i | \(0.589659\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −113.121 | −3.70738 | ||||||||
\(932\) | −14.3178 | + | 14.3178i | −0.468995 | + | 0.468995i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | − | 5.36926i | − | 0.175687i | ||||||
\(935\) | 1.37951 | − | 1.23242i | 0.0451146 | − | 0.0403046i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 11.8835 | + | 11.8835i | 0.388216 | + | 0.388216i | 0.874051 | − | 0.485835i | \(-0.161484\pi\) |
−0.485835 | + | 0.874051i | \(0.661484\pi\) | |||||||
\(938\) | 26.7250 | + | 26.7250i | 0.872602 | + | 0.872602i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −6.00877 | + | 5.36812i | −0.195985 | + | 0.175089i | ||||
\(941\) | 23.3437i | 0.760982i | 0.924785 | + | 0.380491i | \(0.124245\pi\) | ||||
−0.924785 | + | 0.380491i | \(0.875755\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 7.48869 | − | 7.48869i | 0.243865 | − | 0.243865i | ||||
\(944\) | −0.219632 | −0.00714841 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −3.21072 | −0.104390 | ||||||||
\(947\) | 36.3518 | − | 36.3518i | 1.18128 | − | 1.18128i | 0.201861 | − | 0.979414i | \(-0.435301\pi\) |
0.979414 | − | 0.201861i | \(-0.0646990\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 10.1065i | − | 0.328071i | ||||||
\(950\) | −19.9961 | − | 25.0900i | −0.648760 | − | 0.814027i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −3.79569 | − | 3.79569i | −0.123019 | − | 0.123019i | ||||
\(953\) | 11.3056 | + | 11.3056i | 0.366224 | + | 0.366224i | 0.866098 | − | 0.499874i | \(-0.166620\pi\) |
−0.499874 | + | 0.866098i | \(0.666620\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 20.6735 | + | 1.16415i | 0.668978 | + | 0.0376711i | ||||
\(956\) | 8.13112i | 0.262979i | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 21.4736 | − | 21.4736i | 0.693781 | − | 0.693781i | ||||
\(959\) | 78.6328 | 2.53919 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 67.7396 | 2.18515 | ||||||||
\(962\) | 43.4652 | − | 43.4652i | 1.40137 | − | 1.40137i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 1.56965i | 0.0505552i | ||||||||
\(965\) | 21.2401 | + | 23.7750i | 0.683744 | + | 0.765344i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −5.50134 | − | 5.50134i | −0.176911 | − | 0.176911i | 0.613097 | − | 0.790008i | \(-0.289924\pi\) |
−0.790008 | + | 0.613097i | \(0.789924\pi\) | |||||||
\(968\) | −7.36454 | − | 7.36454i | −0.236705 | − | 0.236705i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −1.51875 | + | 26.9706i | −0.0487642 | + | 0.865974i | ||||
\(971\) | 55.1034i | 1.76835i | 0.467154 | + | 0.884176i | \(0.345279\pi\) | ||||
−0.467154 | + | 0.884176i | \(0.654721\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −40.7326 | + | 40.7326i | −1.30583 | + | 1.30583i | ||||
\(974\) | −26.2643 | −0.841562 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 1.82779 | 0.0585061 | ||||||||
\(977\) | 24.2198 | − | 24.2198i | 0.774861 | − | 0.774861i | −0.204091 | − | 0.978952i | \(-0.565424\pi\) |
0.978952 | + | 0.204091i | \(0.0654239\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1.38600i | 0.0442968i | ||||||||
\(980\) | −2.21628 | + | 39.3575i | −0.0707963 | + | 1.25723i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −31.1619 | − | 31.1619i | −0.994417 | − | 0.994417i | ||||
\(983\) | −11.9012 | − | 11.9012i | −0.379591 | − | 0.379591i | 0.491364 | − | 0.870954i | \(-0.336499\pi\) |
−0.870954 | + | 0.491364i | \(0.836499\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −41.6130 | − | 46.5793i | −1.32590 | − | 1.48414i | ||||
\(986\) | − | 1.81604i | − | 0.0578344i | ||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −23.7296 | + | 23.7296i | −0.754939 | + | 0.754939i | ||||
\(989\) | 4.19794 | 0.133487 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 16.7779 | 0.532969 | 0.266484 | − | 0.963839i | \(-0.414138\pi\) | ||||
0.266484 | + | 0.963839i | \(0.414138\pi\) | |||||||
\(992\) | 7.02637 | − | 7.02637i | 0.223087 | − | 0.223087i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 30.4776i | 0.966690i | ||||||||
\(995\) | −39.5656 | − | 2.22799i | −1.25431 | − | 0.0706321i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −10.1977 | − | 10.1977i | −0.322963 | − | 0.322963i | 0.526940 | − | 0.849903i | \(-0.323339\pi\) |
−0.849903 | + | 0.526940i | \(0.823339\pi\) | |||||||
\(998\) | −6.21888 | − | 6.21888i | −0.196855 | − | 0.196855i | ||||
\(999\) | 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 | 2070.2.j.j.737.7 | yes | 20 | |
3.2 | odd | 2 | inner | 2070.2.j.j.737.4 | yes | 20 | |
5.3 | odd | 4 | inner | 2070.2.j.j.323.4 | ✓ | 20 | |
15.8 | even | 4 | inner | 2070.2.j.j.323.7 | yes | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2070.2.j.j.323.4 | ✓ | 20 | 5.3 | odd | 4 | inner | |
2070.2.j.j.323.7 | yes | 20 | 15.8 | even | 4 | inner | |
2070.2.j.j.737.4 | yes | 20 | 3.2 | odd | 2 | inner | |
2070.2.j.j.737.7 | yes | 20 | 1.1 | even | 1 | trivial |