Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [690,2,Mod(47,690)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(690, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("690.47");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 690.i (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: | \(5.50967773947\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(i)\) |
Coefficient field: | 8.0.40960000.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 7x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 323.2 | ||
Root | \(1.14412 - 1.14412i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 690.323 |
Dual form | 690.2.i.d.47.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/690\mathbb{Z}\right)^\times\).
\(n\) | \(277\) | \(461\) | \(511\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.707107 | − | 0.707107i | −0.500000 | − | 0.500000i | ||||
\(3\) | −1.70711 | − | 0.292893i | −0.985599 | − | 0.169102i | ||||
\(4\) | 1.00000i | 0.500000i | ||||||||
\(5\) | 2.23607i | 1.00000i | ||||||||
\(6\) | 1.00000 | + | 1.41421i | 0.408248 | + | 0.577350i | ||||
\(7\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(8\) | 0.707107 | − | 0.707107i | 0.250000 | − | 0.250000i | ||||
\(9\) | 2.82843 | + | 1.00000i | 0.942809 | + | 0.333333i | ||||
\(10\) | 1.58114 | − | 1.58114i | 0.500000 | − | 0.500000i | ||||
\(11\) | 2.82843i | 0.852803i | 0.904534 | + | 0.426401i | \(0.140219\pi\) | ||||
−0.904534 | + | 0.426401i | \(0.859781\pi\) | |||||||
\(12\) | 0.292893 | − | 1.70711i | 0.0845510 | − | 0.492799i | ||||
\(13\) | −2.16228 | − | 2.16228i | −0.599708 | − | 0.599708i | 0.340527 | − | 0.940235i | \(-0.389395\pi\) |
−0.940235 | + | 0.340527i | \(0.889395\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.654929 | − | 3.81721i | 0.169102 | − | 0.985599i | ||||
\(16\) | −1.00000 | −0.250000 | ||||||||
\(17\) | 0.821854 | + | 0.821854i | 0.199329 | + | 0.199329i | 0.799712 | − | 0.600383i | \(-0.204985\pi\) |
−0.600383 | + | 0.799712i | \(0.704985\pi\) | |||||||
\(18\) | −1.29289 | − | 2.70711i | −0.304738 | − | 0.638071i | ||||
\(19\) | − | 1.16228i | − | 0.266645i | −0.991073 | − | 0.133322i | \(-0.957435\pi\) | ||
0.991073 | − | 0.133322i | \(-0.0425646\pi\) | |||||||
\(20\) | −2.23607 | −0.500000 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 2.00000 | − | 2.00000i | 0.426401 | − | 0.426401i | ||||
\(23\) | 0.707107 | − | 0.707107i | 0.147442 | − | 0.147442i | ||||
\(24\) | −1.41421 | + | 1.00000i | −0.288675 | + | 0.204124i | ||||
\(25\) | −5.00000 | −1.00000 | ||||||||
\(26\) | 3.05792i | 0.599708i | ||||||||
\(27\) | −4.53553 | − | 2.53553i | −0.872864 | − | 0.487964i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −4.47214 | −0.830455 | −0.415227 | − | 0.909718i | \(-0.636298\pi\) | ||||
−0.415227 | + | 0.909718i | \(0.636298\pi\) | |||||||
\(30\) | −3.16228 | + | 2.23607i | −0.577350 | + | 0.408248i | ||||
\(31\) | −2.32456 | −0.417502 | −0.208751 | − | 0.977969i | \(-0.566940\pi\) | ||||
−0.208751 | + | 0.977969i | \(0.566940\pi\) | |||||||
\(32\) | 0.707107 | + | 0.707107i | 0.125000 | + | 0.125000i | ||||
\(33\) | 0.828427 | − | 4.82843i | 0.144211 | − | 0.840521i | ||||
\(34\) | − | 1.16228i | − | 0.199329i | ||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −1.00000 | + | 2.82843i | −0.166667 | + | 0.471405i | ||||
\(37\) | −1.16228 | + | 1.16228i | −0.191077 | + | 0.191077i | −0.796161 | − | 0.605084i | \(-0.793139\pi\) |
0.605084 | + | 0.796161i | \(0.293139\pi\) | |||||||
\(38\) | −0.821854 | + | 0.821854i | −0.133322 | + | 0.133322i | ||||
\(39\) | 3.05792 | + | 4.32456i | 0.489659 | + | 0.692483i | ||||
\(40\) | 1.58114 | + | 1.58114i | 0.250000 | + | 0.250000i | ||||
\(41\) | 11.7727i | 1.83859i | 0.393573 | + | 0.919293i | \(0.371239\pi\) | ||||
−0.393573 | + | 0.919293i | \(0.628761\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −9.16228 | − | 9.16228i | −1.39723 | − | 1.39723i | −0.807861 | − | 0.589374i | \(-0.799375\pi\) |
−0.589374 | − | 0.807861i | \(-0.700625\pi\) | |||||||
\(44\) | −2.82843 | −0.426401 | ||||||||
\(45\) | −2.23607 | + | 6.32456i | −0.333333 | + | 0.942809i | ||||
\(46\) | −1.00000 | −0.147442 | ||||||||
\(47\) | −0.229495 | − | 0.229495i | −0.0334753 | − | 0.0334753i | 0.690171 | − | 0.723646i | \(-0.257535\pi\) |
−0.723646 | + | 0.690171i | \(0.757535\pi\) | |||||||
\(48\) | 1.70711 | + | 0.292893i | 0.246400 | + | 0.0422755i | ||||
\(49\) | 7.00000i | 1.00000i | ||||||||
\(50\) | 3.53553 | + | 3.53553i | 0.500000 | + | 0.500000i | ||||
\(51\) | −1.16228 | − | 1.64371i | −0.162751 | − | 0.230165i | ||||
\(52\) | 2.16228 | − | 2.16228i | 0.299854 | − | 0.299854i | ||||
\(53\) | −6.70820 | + | 6.70820i | −0.921443 | + | 0.921443i | −0.997131 | − | 0.0756888i | \(-0.975884\pi\) |
0.0756888 | + | 0.997131i | \(0.475884\pi\) | |||||||
\(54\) | 1.41421 | + | 5.00000i | 0.192450 | + | 0.680414i | ||||
\(55\) | −6.32456 | −0.852803 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −0.340423 | + | 1.98413i | −0.0450902 | + | 0.262805i | ||||
\(58\) | 3.16228 | + | 3.16228i | 0.415227 | + | 0.415227i | ||||
\(59\) | −9.89949 | −1.28880 | −0.644402 | − | 0.764687i | \(-0.722894\pi\) | ||||
−0.644402 | + | 0.764687i | \(0.722894\pi\) | |||||||
\(60\) | 3.81721 | + | 0.654929i | 0.492799 | + | 0.0845510i | ||||
\(61\) | 8.00000 | 1.02430 | 0.512148 | − | 0.858898i | \(-0.328850\pi\) | ||||
0.512148 | + | 0.858898i | \(0.328850\pi\) | |||||||
\(62\) | 1.64371 | + | 1.64371i | 0.208751 | + | 0.208751i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | − | 1.00000i | − | 0.125000i | ||||||
\(65\) | 4.83500 | − | 4.83500i | 0.599708 | − | 0.599708i | ||||
\(66\) | −4.00000 | + | 2.82843i | −0.492366 | + | 0.348155i | ||||
\(67\) | −1.16228 | + | 1.16228i | −0.141995 | + | 0.141995i | −0.774531 | − | 0.632536i | \(-0.782014\pi\) |
0.632536 | + | 0.774531i | \(0.282014\pi\) | |||||||
\(68\) | −0.821854 | + | 0.821854i | −0.0996645 | + | 0.0996645i | ||||
\(69\) | −1.41421 | + | 1.00000i | −0.170251 | + | 0.120386i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 5.88635i | − | 0.698581i | −0.937014 | − | 0.349291i | \(-0.886423\pi\) | ||
0.937014 | − | 0.349291i | \(-0.113577\pi\) | |||||||
\(72\) | 2.70711 | − | 1.29289i | 0.319036 | − | 0.152369i | ||||
\(73\) | 5.32456 | + | 5.32456i | 0.623192 | + | 0.623192i | 0.946346 | − | 0.323154i | \(-0.104743\pi\) |
−0.323154 | + | 0.946346i | \(0.604743\pi\) | |||||||
\(74\) | 1.64371 | 0.191077 | ||||||||
\(75\) | 8.53553 | + | 1.46447i | 0.985599 | + | 0.169102i | ||||
\(76\) | 1.16228 | 0.133322 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0.895645 | − | 5.22020i | 0.101412 | − | 0.591071i | ||||
\(79\) | − | 3.16228i | − | 0.355784i | −0.984050 | − | 0.177892i | \(-0.943072\pi\) | ||
0.984050 | − | 0.177892i | \(-0.0569278\pi\) | |||||||
\(80\) | − | 2.23607i | − | 0.250000i | ||||||
\(81\) | 7.00000 | + | 5.65685i | 0.777778 | + | 0.628539i | ||||
\(82\) | 8.32456 | − | 8.32456i | 0.919293 | − | 0.919293i | ||||
\(83\) | −3.05792 | + | 3.05792i | −0.335651 | + | 0.335651i | −0.854728 | − | 0.519077i | \(-0.826276\pi\) |
0.519077 | + | 0.854728i | \(0.326276\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.83772 | + | 1.83772i | −0.199329 | + | 0.199329i | ||||
\(86\) | 12.9574i | 1.39723i | ||||||||
\(87\) | 7.63441 | + | 1.30986i | 0.818495 | + | 0.140432i | ||||
\(88\) | 2.00000 | + | 2.00000i | 0.213201 | + | 0.213201i | ||||
\(89\) | −17.4296 | −1.84753 | −0.923764 | − | 0.382961i | \(-0.874904\pi\) | ||||
−0.923764 | + | 0.382961i | \(0.874904\pi\) | |||||||
\(90\) | 6.05327 | − | 2.89100i | 0.638071 | − | 0.304738i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0.707107 | + | 0.707107i | 0.0737210 | + | 0.0737210i | ||||
\(93\) | 3.96826 | + | 0.680846i | 0.411490 | + | 0.0706005i | ||||
\(94\) | 0.324555i | 0.0334753i | ||||||||
\(95\) | 2.59893 | 0.266645 | ||||||||
\(96\) | −1.00000 | − | 1.41421i | −0.102062 | − | 0.144338i | ||||
\(97\) | −5.16228 | + | 5.16228i | −0.524150 | + | 0.524150i | −0.918822 | − | 0.394672i | \(-0.870858\pi\) |
0.394672 | + | 0.918822i | \(0.370858\pi\) | |||||||
\(98\) | 4.94975 | − | 4.94975i | 0.500000 | − | 0.500000i | ||||
\(99\) | −2.82843 | + | 8.00000i | −0.284268 | + | 0.804030i | ||||
\(100\) | − | 5.00000i | − | 0.500000i | ||||||
\(101\) | − | 7.30056i | − | 0.726433i | −0.931705 | − | 0.363217i | \(-0.881679\pi\) | ||
0.931705 | − | 0.363217i | \(-0.118321\pi\) | |||||||
\(102\) | −0.340423 | + | 1.98413i | −0.0337069 | + | 0.196458i | ||||
\(103\) | −4.83772 | − | 4.83772i | −0.476675 | − | 0.476675i | 0.427392 | − | 0.904067i | \(-0.359433\pi\) |
−0.904067 | + | 0.427392i | \(0.859433\pi\) | |||||||
\(104\) | −3.05792 | −0.299854 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 9.48683 | 0.921443 | ||||||||
\(107\) | −7.53006 | − | 7.53006i | −0.727958 | − | 0.727958i | 0.242255 | − | 0.970213i | \(-0.422113\pi\) |
−0.970213 | + | 0.242255i | \(0.922113\pi\) | |||||||
\(108\) | 2.53553 | − | 4.53553i | 0.243982 | − | 0.436432i | ||||
\(109\) | − | 1.67544i | − | 0.160478i | −0.996776 | − | 0.0802392i | \(-0.974432\pi\) | ||
0.996776 | − | 0.0802392i | \(-0.0255684\pi\) | |||||||
\(110\) | 4.47214 | + | 4.47214i | 0.426401 | + | 0.426401i | ||||
\(111\) | 2.32456 | − | 1.64371i | 0.220637 | − | 0.156014i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −0.362864 | + | 0.362864i | −0.0341354 | + | 0.0341354i | −0.723968 | − | 0.689833i | \(-0.757684\pi\) |
0.689833 | + | 0.723968i | \(0.257684\pi\) | |||||||
\(114\) | 1.64371 | − | 1.16228i | 0.153947 | − | 0.108857i | ||||
\(115\) | 1.58114 | + | 1.58114i | 0.147442 | + | 0.147442i | ||||
\(116\) | − | 4.47214i | − | 0.415227i | ||||||
\(117\) | −3.95357 | − | 8.27812i | −0.365507 | − | 0.765313i | ||||
\(118\) | 7.00000 | + | 7.00000i | 0.644402 | + | 0.644402i | ||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −2.23607 | − | 3.16228i | −0.204124 | − | 0.288675i | ||||
\(121\) | 3.00000 | 0.272727 | ||||||||
\(122\) | −5.65685 | − | 5.65685i | −0.512148 | − | 0.512148i | ||||
\(123\) | 3.44814 | − | 20.0973i | 0.310909 | − | 1.81211i | ||||
\(124\) | − | 2.32456i | − | 0.208751i | ||||||
\(125\) | − | 11.1803i | − | 1.00000i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.16228 | − | 1.16228i | 0.103135 | − | 0.103135i | −0.653656 | − | 0.756792i | \(-0.726766\pi\) |
0.756792 | + | 0.653656i | \(0.226766\pi\) | |||||||
\(128\) | −0.707107 | + | 0.707107i | −0.0625000 | + | 0.0625000i | ||||
\(129\) | 12.9574 | + | 18.3246i | 1.14084 | + | 1.61339i | ||||
\(130\) | −6.83772 | −0.599708 | ||||||||
\(131\) | − | 10.3585i | − | 0.905025i | −0.891758 | − | 0.452513i | \(-0.850528\pi\) | ||
0.891758 | − | 0.452513i | \(-0.149472\pi\) | |||||||
\(132\) | 4.82843 | + | 0.828427i | 0.420261 | + | 0.0721053i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 1.64371 | 0.141995 | ||||||||
\(135\) | 5.66963 | − | 10.1418i | 0.487964 | − | 0.872864i | ||||
\(136\) | 1.16228 | 0.0996645 | ||||||||
\(137\) | −0.821854 | − | 0.821854i | −0.0702158 | − | 0.0702158i | 0.671127 | − | 0.741343i | \(-0.265811\pi\) |
−0.741343 | + | 0.671127i | \(0.765811\pi\) | |||||||
\(138\) | 1.70711 | + | 0.292893i | 0.145319 | + | 0.0249327i | ||||
\(139\) | 10.3246i | 0.875717i | 0.899044 | + | 0.437859i | \(0.144263\pi\) | ||||
−0.899044 | + | 0.437859i | \(0.855737\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0.324555 | + | 0.458991i | 0.0273325 | + | 0.0386540i | ||||
\(142\) | −4.16228 | + | 4.16228i | −0.349291 | + | 0.349291i | ||||
\(143\) | 6.11584 | − | 6.11584i | 0.511433 | − | 0.511433i | ||||
\(144\) | −2.82843 | − | 1.00000i | −0.235702 | − | 0.0833333i | ||||
\(145\) | − | 10.0000i | − | 0.830455i | ||||||
\(146\) | − | 7.53006i | − | 0.623192i | ||||||
\(147\) | 2.05025 | − | 11.9497i | 0.169102 | − | 0.985599i | ||||
\(148\) | −1.16228 | − | 1.16228i | −0.0955386 | − | 0.0955386i | ||||
\(149\) | −7.75955 | −0.635687 | −0.317844 | − | 0.948143i | \(-0.602959\pi\) | ||||
−0.317844 | + | 0.948143i | \(0.602959\pi\) | |||||||
\(150\) | −5.00000 | − | 7.07107i | −0.408248 | − | 0.577350i | ||||
\(151\) | −10.3246 | −0.840200 | −0.420100 | − | 0.907478i | \(-0.638005\pi\) | ||||
−0.420100 | + | 0.907478i | \(0.638005\pi\) | |||||||
\(152\) | −0.821854 | − | 0.821854i | −0.0666612 | − | 0.0666612i | ||||
\(153\) | 1.50270 | + | 3.14641i | 0.121486 | + | 0.254372i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 5.19786i | − | 0.417502i | ||||||
\(156\) | −4.32456 | + | 3.05792i | −0.346242 | + | 0.244830i | ||||
\(157\) | 9.48683 | − | 9.48683i | 0.757132 | − | 0.757132i | −0.218668 | − | 0.975799i | \(-0.570171\pi\) |
0.975799 | + | 0.218668i | \(0.0701711\pi\) | |||||||
\(158\) | −2.23607 | + | 2.23607i | −0.177892 | + | 0.177892i | ||||
\(159\) | 13.4164 | − | 9.48683i | 1.06399 | − | 0.752355i | ||||
\(160\) | −1.58114 | + | 1.58114i | −0.125000 | + | 0.125000i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −0.949747 | − | 8.94975i | −0.0746192 | − | 0.703159i | ||||
\(163\) | −8.64911 | − | 8.64911i | −0.677451 | − | 0.677451i | 0.281972 | − | 0.959423i | \(-0.409011\pi\) |
−0.959423 | + | 0.281972i | \(0.909011\pi\) | |||||||
\(164\) | −11.7727 | −0.919293 | ||||||||
\(165\) | 10.7967 | + | 1.85242i | 0.840521 | + | 0.144211i | ||||
\(166\) | 4.32456 | 0.335651 | ||||||||
\(167\) | 14.6011 | + | 14.6011i | 1.12987 | + | 1.12987i | 0.990198 | + | 0.139671i | \(0.0446045\pi\) |
0.139671 | + | 0.990198i | \(0.455395\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 3.64911i | − | 0.280701i | ||||||
\(170\) | 2.59893 | 0.199329 | ||||||||
\(171\) | 1.16228 | − | 3.28742i | 0.0888816 | − | 0.251395i | ||||
\(172\) | 9.16228 | − | 9.16228i | 0.698617 | − | 0.698617i | ||||
\(173\) | −8.71478 | + | 8.71478i | −0.662572 | + | 0.662572i | −0.955986 | − | 0.293413i | \(-0.905209\pi\) |
0.293413 | + | 0.955986i | \(0.405209\pi\) | |||||||
\(174\) | −4.47214 | − | 6.32456i | −0.339032 | − | 0.479463i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | − | 2.82843i | − | 0.213201i | ||||||
\(177\) | 16.8995 | + | 2.89949i | 1.27024 | + | 0.217939i | ||||
\(178\) | 12.3246 | + | 12.3246i | 0.923764 | + | 0.923764i | ||||
\(179\) | 13.1869 | 0.985636 | 0.492818 | − | 0.870132i | \(-0.335967\pi\) | ||||
0.492818 | + | 0.870132i | \(0.335967\pi\) | |||||||
\(180\) | −6.32456 | − | 2.23607i | −0.471405 | − | 0.166667i | ||||
\(181\) | 22.3246 | 1.65937 | 0.829686 | − | 0.558231i | \(-0.188520\pi\) | ||||
0.829686 | + | 0.558231i | \(0.188520\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −13.6569 | − | 2.34315i | −1.00954 | − | 0.173210i | ||||
\(184\) | − | 1.00000i | − | 0.0737210i | ||||||
\(185\) | −2.59893 | − | 2.59893i | −0.191077 | − | 0.191077i | ||||
\(186\) | −2.32456 | − | 3.28742i | −0.170445 | − | 0.241045i | ||||
\(187\) | −2.32456 | + | 2.32456i | −0.169988 | + | 0.169988i | ||||
\(188\) | 0.229495 | − | 0.229495i | 0.0167377 | − | 0.0167377i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −1.83772 | − | 1.83772i | −0.133322 | − | 0.133322i | ||||
\(191\) | 17.4296i | 1.26116i | 0.776125 | + | 0.630579i | \(0.217183\pi\) | ||||
−0.776125 | + | 0.630579i | \(0.782817\pi\) | |||||||
\(192\) | −0.292893 | + | 1.70711i | −0.0211377 | + | 0.123200i | ||||
\(193\) | 3.00000 | + | 3.00000i | 0.215945 | + | 0.215945i | 0.806787 | − | 0.590842i | \(-0.201204\pi\) |
−0.590842 | + | 0.806787i | \(0.701204\pi\) | |||||||
\(194\) | 7.30056 | 0.524150 | ||||||||
\(195\) | −9.67000 | + | 6.83772i | −0.692483 | + | 0.489659i | ||||
\(196\) | −7.00000 | −0.500000 | ||||||||
\(197\) | 2.59893 | + | 2.59893i | 0.185166 | + | 0.185166i | 0.793603 | − | 0.608436i | \(-0.208203\pi\) |
−0.608436 | + | 0.793603i | \(0.708203\pi\) | |||||||
\(198\) | 7.65685 | − | 3.65685i | 0.544149 | − | 0.259881i | ||||
\(199\) | 15.1623i | 1.07483i | 0.843319 | + | 0.537413i | \(0.180598\pi\) | ||||
−0.843319 | + | 0.537413i | \(0.819402\pi\) | |||||||
\(200\) | −3.53553 | + | 3.53553i | −0.250000 | + | 0.250000i | ||||
\(201\) | 2.32456 | − | 1.64371i | 0.163961 | − | 0.115938i | ||||
\(202\) | −5.16228 | + | 5.16228i | −0.363217 | + | 0.363217i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 1.64371 | − | 1.16228i | 0.115083 | − | 0.0813757i | ||||
\(205\) | −26.3246 | −1.83859 | ||||||||
\(206\) | 6.84157i | 0.476675i | ||||||||
\(207\) | 2.70711 | − | 1.29289i | 0.188157 | − | 0.0898623i | ||||
\(208\) | 2.16228 | + | 2.16228i | 0.149927 | + | 0.149927i | ||||
\(209\) | 3.28742 | 0.227395 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.67544 | 0.115342 | 0.0576712 | − | 0.998336i | \(-0.481633\pi\) | ||||
0.0576712 | + | 0.998336i | \(0.481633\pi\) | |||||||
\(212\) | −6.70820 | − | 6.70820i | −0.460721 | − | 0.460721i | ||||
\(213\) | −1.72407 | + | 10.0486i | −0.118131 | + | 0.688521i | ||||
\(214\) | 10.6491i | 0.727958i | ||||||||
\(215\) | 20.4875 | − | 20.4875i | 1.39723 | − | 1.39723i | ||||
\(216\) | −5.00000 | + | 1.41421i | −0.340207 | + | 0.0962250i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −1.18472 | + | 1.18472i | −0.0802392 | + | 0.0802392i | ||||
\(219\) | −7.53006 | − | 10.6491i | −0.508834 | − | 0.719600i | ||||
\(220\) | − | 6.32456i | − | 0.426401i | ||||||
\(221\) | − | 3.55415i | − | 0.239078i | ||||||
\(222\) | −2.80599 | − | 0.481431i | −0.188325 | − | 0.0323115i | ||||
\(223\) | 6.83772 | + | 6.83772i | 0.457888 | + | 0.457888i | 0.897962 | − | 0.440074i | \(-0.145048\pi\) |
−0.440074 | + | 0.897962i | \(0.645048\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −14.1421 | − | 5.00000i | −0.942809 | − | 0.333333i | ||||
\(226\) | 0.513167 | 0.0341354 | ||||||||
\(227\) | 4.24264 | + | 4.24264i | 0.281594 | + | 0.281594i | 0.833744 | − | 0.552151i | \(-0.186193\pi\) |
−0.552151 | + | 0.833744i | \(0.686193\pi\) | |||||||
\(228\) | −1.98413 | − | 0.340423i | −0.131402 | − | 0.0225451i | ||||
\(229\) | 25.2982i | 1.67175i | 0.548917 | + | 0.835877i | \(0.315040\pi\) | ||||
−0.548917 | + | 0.835877i | \(0.684960\pi\) | |||||||
\(230\) | − | 2.23607i | − | 0.147442i | ||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −3.16228 | + | 3.16228i | −0.207614 | + | 0.207614i | ||||
\(233\) | −3.05792 | + | 3.05792i | −0.200331 | + | 0.200331i | −0.800142 | − | 0.599811i | \(-0.795243\pi\) |
0.599811 | + | 0.800142i | \(0.295243\pi\) | |||||||
\(234\) | −3.05792 | + | 8.64911i | −0.199903 | + | 0.565410i | ||||
\(235\) | 0.513167 | − | 0.513167i | 0.0334753 | − | 0.0334753i | ||||
\(236\) | − | 9.89949i | − | 0.644402i | ||||||
\(237\) | −0.926210 | + | 5.39835i | −0.0601638 | + | 0.350660i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 20.4875 | 1.32522 | 0.662612 | − | 0.748963i | \(-0.269448\pi\) | ||||
0.662612 | + | 0.748963i | \(0.269448\pi\) | |||||||
\(240\) | −0.654929 | + | 3.81721i | −0.0422755 | + | 0.246400i | ||||
\(241\) | −4.32456 | −0.278569 | −0.139285 | − | 0.990252i | \(-0.544480\pi\) | ||||
−0.139285 | + | 0.990252i | \(0.544480\pi\) | |||||||
\(242\) | −2.12132 | − | 2.12132i | −0.136364 | − | 0.136364i | ||||
\(243\) | −10.2929 | − | 11.7071i | −0.660289 | − | 0.751011i | ||||
\(244\) | 8.00000i | 0.512148i | ||||||||
\(245\) | −15.6525 | −1.00000 | ||||||||
\(246\) | −16.6491 | + | 11.7727i | −1.06151 | + | 0.750600i | ||||
\(247\) | −2.51317 | + | 2.51317i | −0.159909 | + | 0.159909i | ||||
\(248\) | −1.64371 | + | 1.64371i | −0.104376 | + | 0.104376i | ||||
\(249\) | 6.11584 | − | 4.32456i | 0.387576 | − | 0.274058i | ||||
\(250\) | −7.90569 | + | 7.90569i | −0.500000 | + | 0.500000i | ||||
\(251\) | − | 5.65685i | − | 0.357057i | −0.983935 | − | 0.178529i | \(-0.942866\pi\) | ||
0.983935 | − | 0.178529i | \(-0.0571337\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.00000 | + | 2.00000i | 0.125739 | + | 0.125739i | ||||
\(254\) | −1.64371 | −0.103135 | ||||||||
\(255\) | 3.67544 | − | 2.59893i | 0.230165 | − | 0.162751i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 19.3028 | + | 19.3028i | 1.20407 | + | 1.20407i | 0.972917 | + | 0.231156i | \(0.0742509\pi\) |
0.231156 | + | 0.972917i | \(0.425749\pi\) | |||||||
\(258\) | 3.79514 | − | 22.1197i | 0.236275 | − | 1.37711i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 4.83500 | + | 4.83500i | 0.299854 | + | 0.299854i | ||||
\(261\) | −12.6491 | − | 4.47214i | −0.782960 | − | 0.276818i | ||||
\(262\) | −7.32456 | + | 7.32456i | −0.452513 | + | 0.452513i | ||||
\(263\) | 0.458991 | − | 0.458991i | 0.0283026 | − | 0.0283026i | −0.692814 | − | 0.721116i | \(-0.743629\pi\) |
0.721116 | + | 0.692814i | \(0.243629\pi\) | |||||||
\(264\) | −2.82843 | − | 4.00000i | −0.174078 | − | 0.246183i | ||||
\(265\) | −15.0000 | − | 15.0000i | −0.921443 | − | 0.921443i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 29.7541 | + | 5.10500i | 1.82092 | + | 0.312421i | ||||
\(268\) | −1.16228 | − | 1.16228i | −0.0709974 | − | 0.0709974i | ||||
\(269\) | −9.67000 | −0.589590 | −0.294795 | − | 0.955560i | \(-0.595251\pi\) | ||||
−0.294795 | + | 0.955560i | \(0.595251\pi\) | |||||||
\(270\) | −11.1803 | + | 3.16228i | −0.680414 | + | 0.192450i | ||||
\(271\) | 30.9737 | 1.88152 | 0.940758 | − | 0.339078i | \(-0.110115\pi\) | ||||
0.940758 | + | 0.339078i | \(0.110115\pi\) | |||||||
\(272\) | −0.821854 | − | 0.821854i | −0.0498322 | − | 0.0498322i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 1.16228i | 0.0702158i | ||||||||
\(275\) | − | 14.1421i | − | 0.852803i | ||||||
\(276\) | −1.00000 | − | 1.41421i | −0.0601929 | − | 0.0851257i | ||||
\(277\) | −2.16228 | + | 2.16228i | −0.129919 | + | 0.129919i | −0.769076 | − | 0.639157i | \(-0.779283\pi\) |
0.639157 | + | 0.769076i | \(0.279283\pi\) | |||||||
\(278\) | 7.30056 | − | 7.30056i | 0.437859 | − | 0.437859i | ||||
\(279\) | −6.57484 | − | 2.32456i | −0.393625 | − | 0.139167i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 24.7301i | − | 1.47528i | −0.675197 | − | 0.737638i | \(-0.735941\pi\) | ||
0.675197 | − | 0.737638i | \(-0.264059\pi\) | |||||||
\(282\) | 0.0950601 | − | 0.554051i | 0.00566074 | − | 0.0329932i | ||||
\(283\) | 8.64911 | + | 8.64911i | 0.514136 | + | 0.514136i | 0.915791 | − | 0.401655i | \(-0.131565\pi\) |
−0.401655 | + | 0.915791i | \(0.631565\pi\) | |||||||
\(284\) | 5.88635 | 0.349291 | ||||||||
\(285\) | −4.43665 | − | 0.761210i | −0.262805 | − | 0.0450902i | ||||
\(286\) | −8.64911 | −0.511433 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 1.29289 | + | 2.70711i | 0.0761845 | + | 0.159518i | ||||
\(289\) | − | 15.6491i | − | 0.920536i | ||||||
\(290\) | −7.07107 | + | 7.07107i | −0.415227 | + | 0.415227i | ||||
\(291\) | 10.3246 | − | 7.30056i | 0.605236 | − | 0.427967i | ||||
\(292\) | −5.32456 | + | 5.32456i | −0.311596 | + | 0.311596i | ||||
\(293\) | −22.4940 | + | 22.4940i | −1.31412 | + | 1.31412i | −0.395764 | + | 0.918352i | \(0.629520\pi\) |
−0.918352 | + | 0.395764i | \(0.870480\pi\) | |||||||
\(294\) | −9.89949 | + | 7.00000i | −0.577350 | + | 0.408248i | ||||
\(295\) | − | 22.1359i | − | 1.28880i | ||||||
\(296\) | 1.64371i | 0.0955386i | ||||||||
\(297\) | 7.17157 | − | 12.8284i | 0.416137 | − | 0.744381i | ||||
\(298\) | 5.48683 | + | 5.48683i | 0.317844 | + | 0.317844i | ||||
\(299\) | −3.05792 | −0.176844 | ||||||||
\(300\) | −1.46447 | + | 8.53553i | −0.0845510 | + | 0.492799i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 7.30056 | + | 7.30056i | 0.420100 | + | 0.420100i | ||||
\(303\) | −2.13829 | + | 12.4628i | −0.122841 | + | 0.715971i | ||||
\(304\) | 1.16228i | 0.0666612i | ||||||||
\(305\) | 17.8885i | 1.02430i | ||||||||
\(306\) | 1.16228 | − | 3.28742i | 0.0664430 | − | 0.187929i | ||||
\(307\) | −10.3246 | + | 10.3246i | −0.589253 | + | 0.589253i | −0.937429 | − | 0.348176i | \(-0.886801\pi\) |
0.348176 | + | 0.937429i | \(0.386801\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 6.84157 | + | 9.67544i | 0.389203 | + | 0.550417i | ||||
\(310\) | −3.67544 | + | 3.67544i | −0.208751 | + | 0.208751i | ||||
\(311\) | 18.1180i | 1.02738i | 0.857976 | + | 0.513690i | \(0.171722\pi\) | ||||
−0.857976 | + | 0.513690i | \(0.828278\pi\) | |||||||
\(312\) | 5.22020 | + | 0.895645i | 0.295536 | + | 0.0507059i | ||||
\(313\) | −2.83772 | − | 2.83772i | −0.160398 | − | 0.160398i | 0.622345 | − | 0.782743i | \(-0.286180\pi\) |
−0.782743 | + | 0.622345i | \(0.786180\pi\) | |||||||
\(314\) | −13.4164 | −0.757132 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 3.16228 | 0.177892 | ||||||||
\(317\) | 11.5432 | + | 11.5432i | 0.648331 | + | 0.648331i | 0.952589 | − | 0.304259i | \(-0.0984087\pi\) |
−0.304259 | + | 0.952589i | \(0.598409\pi\) | |||||||
\(318\) | −16.1950 | − | 2.77863i | −0.908173 | − | 0.155818i | ||||
\(319\) | − | 12.6491i | − | 0.708214i | ||||||
\(320\) | 2.23607 | 0.125000 | ||||||||
\(321\) | 10.6491 | + | 15.0601i | 0.594375 | + | 0.840574i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0.955223 | − | 0.955223i | 0.0531500 | − | 0.0531500i | ||||
\(324\) | −5.65685 | + | 7.00000i | −0.314270 | + | 0.388889i | ||||
\(325\) | 10.8114 | + | 10.8114i | 0.599708 | + | 0.599708i | ||||
\(326\) | 12.2317i | 0.677451i | ||||||||
\(327\) | −0.490726 | + | 2.86016i | −0.0271372 | + | 0.158167i | ||||
\(328\) | 8.32456 | + | 8.32456i | 0.459647 | + | 0.459647i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −6.32456 | − | 8.94427i | −0.348155 | − | 0.492366i | ||||
\(331\) | −34.9737 | −1.92233 | −0.961163 | − | 0.275980i | \(-0.910998\pi\) | ||||
−0.961163 | + | 0.275980i | \(0.910998\pi\) | |||||||
\(332\) | −3.05792 | − | 3.05792i | −0.167825 | − | 0.167825i | ||||
\(333\) | −4.44970 | + | 2.12514i | −0.243842 | + | 0.116457i | ||||
\(334\) | − | 20.6491i | − | 1.12987i | ||||||
\(335\) | −2.59893 | − | 2.59893i | −0.141995 | − | 0.141995i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 9.48683 | − | 9.48683i | 0.516781 | − | 0.516781i | −0.399815 | − | 0.916596i | \(-0.630926\pi\) |
0.916596 | + | 0.399815i | \(0.130926\pi\) | |||||||
\(338\) | −2.58031 | + | 2.58031i | −0.140350 | + | 0.140350i | ||||
\(339\) | 0.725728 | − | 0.513167i | 0.0394161 | − | 0.0278714i | ||||
\(340\) | −1.83772 | − | 1.83772i | −0.0996645 | − | 0.0996645i | ||||
\(341\) | − | 6.57484i | − | 0.356047i | ||||||
\(342\) | −3.14641 | + | 1.50270i | −0.170138 | + | 0.0812568i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −12.9574 | −0.698617 | ||||||||
\(345\) | −2.23607 | − | 3.16228i | −0.120386 | − | 0.170251i | ||||
\(346\) | 12.3246 | 0.662572 | ||||||||
\(347\) | 18.8438 | + | 18.8438i | 1.01159 | + | 1.01159i | 0.999932 | + | 0.0116543i | \(0.00370977\pi\) |
0.0116543 | + | 0.999932i | \(0.496290\pi\) | |||||||
\(348\) | −1.30986 | + | 7.63441i | −0.0702158 | + | 0.409248i | ||||
\(349\) | − | 14.0000i | − | 0.749403i | −0.927146 | − | 0.374701i | \(-0.877745\pi\) | ||
0.927146 | − | 0.374701i | \(-0.122255\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 4.32456 | + | 15.2896i | 0.230828 | + | 0.816099i | ||||
\(352\) | −2.00000 | + | 2.00000i | −0.106600 | + | 0.106600i | ||||
\(353\) | 9.17377 | − | 9.17377i | 0.488270 | − | 0.488270i | −0.419490 | − | 0.907760i | \(-0.637791\pi\) |
0.907760 | + | 0.419490i | \(0.137791\pi\) | |||||||
\(354\) | −9.89949 | − | 14.0000i | −0.526152 | − | 0.744092i | ||||
\(355\) | 13.1623 | 0.698581 | ||||||||
\(356\) | − | 17.4296i | − | 0.923764i | ||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −9.32456 | − | 9.32456i | −0.492818 | − | 0.492818i | ||||
\(359\) | −19.7990 | −1.04495 | −0.522475 | − | 0.852654i | \(-0.674991\pi\) | ||||
−0.522475 | + | 0.852654i | \(0.674991\pi\) | |||||||
\(360\) | 2.89100 | + | 6.05327i | 0.152369 | + | 0.319036i | ||||
\(361\) | 17.6491 | 0.928901 | ||||||||
\(362\) | −15.7858 | − | 15.7858i | −0.829686 | − | 0.829686i | ||||
\(363\) | −5.12132 | − | 0.878680i | −0.268800 | − | 0.0461187i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −11.9061 | + | 11.9061i | −0.623192 | + | 0.623192i | ||||
\(366\) | 8.00000 | + | 11.3137i | 0.418167 | + | 0.591377i | ||||
\(367\) | −17.4868 | + | 17.4868i | −0.912805 | + | 0.912805i | −0.996492 | − | 0.0836869i | \(-0.973330\pi\) |
0.0836869 | + | 0.996492i | \(0.473330\pi\) | |||||||
\(368\) | −0.707107 | + | 0.707107i | −0.0368605 | + | 0.0368605i | ||||
\(369\) | −11.7727 | + | 33.2982i | −0.612862 | + | 1.73344i | ||||
\(370\) | 3.67544i | 0.191077i | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −0.680846 | + | 3.96826i | −0.0353002 | + | 0.205745i | ||||
\(373\) | −5.48683 | − | 5.48683i | −0.284097 | − | 0.284097i | 0.550643 | − | 0.834741i | \(-0.314382\pi\) |
−0.834741 | + | 0.550643i | \(0.814382\pi\) | |||||||
\(374\) | 3.28742 | 0.169988 | ||||||||
\(375\) | −3.27465 | + | 19.0860i | −0.169102 | + | 0.985599i | ||||
\(376\) | −0.324555 | −0.0167377 | ||||||||
\(377\) | 9.67000 | + | 9.67000i | 0.498030 | + | 0.498030i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 15.4868i | − | 0.795505i | −0.917493 | − | 0.397753i | \(-0.869790\pi\) | ||
0.917493 | − | 0.397753i | \(-0.130210\pi\) | |||||||
\(380\) | 2.59893i | 0.133322i | ||||||||
\(381\) | −2.32456 | + | 1.64371i | −0.119091 | + | 0.0842098i | ||||
\(382\) | 12.3246 | − | 12.3246i | 0.630579 | − | 0.630579i | ||||
\(383\) | −15.7858 | + | 15.7858i | −0.806619 | + | 0.806619i | −0.984121 | − | 0.177502i | \(-0.943199\pi\) |
0.177502 | + | 0.984121i | \(0.443199\pi\) | |||||||
\(384\) | 1.41421 | − | 1.00000i | 0.0721688 | − | 0.0510310i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | − | 4.24264i | − | 0.215945i | ||||||
\(387\) | −16.7526 | − | 35.0771i | −0.851580 | − | 1.78307i | ||||
\(388\) | −5.16228 | − | 5.16228i | −0.262075 | − | 0.262075i | ||||
\(389\) | 21.4427 | 1.08719 | 0.543594 | − | 0.839348i | \(-0.317063\pi\) | ||||
0.543594 | + | 0.839348i | \(0.317063\pi\) | |||||||
\(390\) | 11.6727 | + | 2.00272i | 0.591071 | + | 0.101412i | ||||
\(391\) | 1.16228 | 0.0587789 | ||||||||
\(392\) | 4.94975 | + | 4.94975i | 0.250000 | + | 0.250000i | ||||
\(393\) | −3.03393 | + | 17.6830i | −0.153042 | + | 0.891991i | ||||
\(394\) | − | 3.67544i | − | 0.185166i | ||||||
\(395\) | 7.07107 | 0.355784 | ||||||||
\(396\) | −8.00000 | − | 2.82843i | −0.402015 | − | 0.142134i | ||||
\(397\) | −24.8114 | + | 24.8114i | −1.24525 | + | 1.24525i | −0.287453 | + | 0.957795i | \(0.592809\pi\) |
−0.957795 | + | 0.287453i | \(0.907191\pi\) | |||||||
\(398\) | 10.7213 | − | 10.7213i | 0.537413 | − | 0.537413i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 5.00000 | 0.250000 | ||||||||
\(401\) | − | 19.7990i | − | 0.988714i | −0.869259 | − | 0.494357i | \(-0.835403\pi\) | ||
0.869259 | − | 0.494357i | \(-0.164597\pi\) | |||||||
\(402\) | −2.80599 | − | 0.481431i | −0.139950 | − | 0.0240116i | ||||
\(403\) | 5.02633 | + | 5.02633i | 0.250380 | + | 0.250380i | ||||
\(404\) | 7.30056 | 0.363217 | ||||||||
\(405\) | −12.6491 | + | 15.6525i | −0.628539 | + | 0.777778i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −3.28742 | − | 3.28742i | −0.162951 | − | 0.162951i | ||||
\(408\) | −1.98413 | − | 0.340423i | −0.0982292 | − | 0.0168535i | ||||
\(409\) | 20.0000i | 0.988936i | 0.869196 | + | 0.494468i | \(0.164637\pi\) | ||||
−0.869196 | + | 0.494468i | \(0.835363\pi\) | |||||||
\(410\) | 18.6143 | + | 18.6143i | 0.919293 | + | 0.919293i | ||||
\(411\) | 1.16228 | + | 1.64371i | 0.0573309 | + | 0.0810782i | ||||
\(412\) | 4.83772 | − | 4.83772i | 0.238337 | − | 0.238337i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −2.82843 | − | 1.00000i | −0.139010 | − | 0.0491473i | ||||
\(415\) | −6.83772 | − | 6.83772i | −0.335651 | − | 0.335651i | ||||
\(416\) | − | 3.05792i | − | 0.149927i | ||||||
\(417\) | 3.02399 | − | 17.6251i | 0.148086 | − | 0.863106i | ||||
\(418\) | −2.32456 | − | 2.32456i | −0.113698 | − | 0.113698i | ||||
\(419\) | 9.40326 | 0.459379 | 0.229690 | − | 0.973264i | \(-0.426229\pi\) | ||||
0.229690 | + | 0.973264i | \(0.426229\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 36.6491 | 1.78617 | 0.893084 | − | 0.449890i | \(-0.148537\pi\) | ||||
0.893084 | + | 0.449890i | \(0.148537\pi\) | |||||||
\(422\) | −1.18472 | − | 1.18472i | −0.0576712 | − | 0.0576712i | ||||
\(423\) | −0.419615 | − | 0.878606i | −0.0204024 | − | 0.0427193i | ||||
\(424\) | 9.48683i | 0.460721i | ||||||||
\(425\) | −4.10927 | − | 4.10927i | −0.199329 | − | 0.199329i | ||||
\(426\) | 8.32456 | − | 5.88635i | 0.403326 | − | 0.285195i | ||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 7.53006 | − | 7.53006i | 0.363979 | − | 0.363979i | ||||
\(429\) | −12.2317 | + | 8.64911i | −0.590552 | + | 0.417583i | ||||
\(430\) | −28.9737 | −1.39723 | ||||||||
\(431\) | 11.7727i | 0.567071i | 0.958962 | + | 0.283535i | \(0.0915074\pi\) | ||||
−0.958962 | + | 0.283535i | \(0.908493\pi\) | |||||||
\(432\) | 4.53553 | + | 2.53553i | 0.218216 | + | 0.121991i | ||||
\(433\) | −28.1359 | − | 28.1359i | −1.35213 | − | 1.35213i | −0.883279 | − | 0.468849i | \(-0.844669\pi\) |
−0.468849 | − | 0.883279i | \(-0.655331\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −2.92893 | + | 17.0711i | −0.140432 | + | 0.818495i | ||||
\(436\) | 1.67544 | 0.0802392 | ||||||||
\(437\) | −0.821854 | − | 0.821854i | −0.0393146 | − | 0.0393146i | ||||
\(438\) | −2.20550 | + | 12.8546i | −0.105383 | + | 0.614217i | ||||
\(439\) | − | 36.6491i | − | 1.74917i | −0.484875 | − | 0.874583i | \(-0.661135\pi\) | ||
0.484875 | − | 0.874583i | \(-0.338865\pi\) | |||||||
\(440\) | −4.47214 | + | 4.47214i | −0.213201 | + | 0.213201i | ||||
\(441\) | −7.00000 | + | 19.7990i | −0.333333 | + | 0.942809i | ||||
\(442\) | −2.51317 | + | 2.51317i | −0.119539 | + | 0.119539i | ||||
\(443\) | −11.3137 | + | 11.3137i | −0.537531 | + | 0.537531i | −0.922803 | − | 0.385272i | \(-0.874107\pi\) |
0.385272 | + | 0.922803i | \(0.374107\pi\) | |||||||
\(444\) | 1.64371 | + | 2.32456i | 0.0780070 | + | 0.110319i | ||||
\(445\) | − | 38.9737i | − | 1.84753i | ||||||
\(446\) | − | 9.67000i | − | 0.457888i | ||||||
\(447\) | 13.2464 | + | 2.27272i | 0.626533 | + | 0.107496i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 5.65685 | 0.266963 | 0.133482 | − | 0.991051i | \(-0.457384\pi\) | ||||
0.133482 | + | 0.991051i | \(0.457384\pi\) | |||||||
\(450\) | 6.46447 | + | 13.5355i | 0.304738 | + | 0.638071i | ||||
\(451\) | −33.2982 | −1.56795 | ||||||||
\(452\) | −0.362864 | − | 0.362864i | −0.0170677 | − | 0.0170677i | ||||
\(453\) | 17.6251 | + | 3.02399i | 0.828100 | + | 0.142080i | ||||
\(454\) | − | 6.00000i | − | 0.281594i | ||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 1.16228 | + | 1.64371i | 0.0544286 | + | 0.0769737i | ||||
\(457\) | −12.8377 | + | 12.8377i | −0.600523 | + | 0.600523i | −0.940451 | − | 0.339928i | \(-0.889597\pi\) |
0.339928 | + | 0.940451i | \(0.389597\pi\) | |||||||
\(458\) | 17.8885 | − | 17.8885i | 0.835877 | − | 0.835877i | ||||
\(459\) | −1.64371 | − | 5.81139i | −0.0767218 | − | 0.271252i | ||||
\(460\) | −1.58114 | + | 1.58114i | −0.0737210 | + | 0.0737210i | ||||
\(461\) | 12.9574i | 0.603487i | 0.953389 | + | 0.301744i | \(0.0975686\pi\) | ||||
−0.953389 | + | 0.301744i | \(0.902431\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 18.1359 | + | 18.1359i | 0.842849 | + | 0.842849i | 0.989228 | − | 0.146380i | \(-0.0467621\pi\) |
−0.146380 | + | 0.989228i | \(0.546762\pi\) | |||||||
\(464\) | 4.47214 | 0.207614 | ||||||||
\(465\) | −1.52242 | + | 8.87331i | −0.0706005 | + | 0.411490i | ||||
\(466\) | 4.32456 | 0.200331 | ||||||||
\(467\) | −13.1869 | − | 13.1869i | −0.610218 | − | 0.610218i | 0.332785 | − | 0.943003i | \(-0.392012\pi\) |
−0.943003 | + | 0.332785i | \(0.892012\pi\) | |||||||
\(468\) | 8.27812 | − | 3.95357i | 0.382656 | − | 0.182754i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −0.725728 | −0.0334753 | ||||||||
\(471\) | −18.9737 | + | 13.4164i | −0.874260 | + | 0.618195i | ||||
\(472\) | −7.00000 | + | 7.00000i | −0.322201 | + | 0.322201i | ||||
\(473\) | 25.9148 | − | 25.9148i | 1.19157 | − | 1.19157i | ||||
\(474\) | 4.47214 | − | 3.16228i | 0.205412 | − | 0.145248i | ||||
\(475\) | 5.81139i | 0.266645i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −25.6819 | + | 12.2655i | −1.17589 | + | 0.561597i | ||||
\(478\) | −14.4868 | − | 14.4868i | −0.662612 | − | 0.662612i | ||||
\(479\) | 28.2843 | 1.29234 | 0.646171 | − | 0.763193i | \(-0.276369\pi\) | ||||
0.646171 | + | 0.763193i | \(0.276369\pi\) | |||||||
\(480\) | 3.16228 | − | 2.23607i | 0.144338 | − | 0.102062i | ||||
\(481\) | 5.02633 | 0.229181 | ||||||||
\(482\) | 3.05792 | + | 3.05792i | 0.139285 | + | 0.139285i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 3.00000i | 0.136364i | ||||||||
\(485\) | −11.5432 | − | 11.5432i | −0.524150 | − | 0.524150i | ||||
\(486\) | −1.00000 | + | 15.5563i | −0.0453609 | + | 0.705650i | ||||
\(487\) | −16.8377 | + | 16.8377i | −0.762990 | + | 0.762990i | −0.976862 | − | 0.213872i | \(-0.931393\pi\) |
0.213872 | + | 0.976862i | \(0.431393\pi\) | |||||||
\(488\) | 5.65685 | − | 5.65685i | 0.256074 | − | 0.256074i | ||||
\(489\) | 12.2317 | + | 17.2982i | 0.553136 | + | 0.782253i | ||||
\(490\) | 11.0680 | + | 11.0680i | 0.500000 | + | 0.500000i | ||||
\(491\) | 9.89949i | 0.446758i | 0.974732 | + | 0.223379i | \(0.0717087\pi\) | ||||
−0.974732 | + | 0.223379i | \(0.928291\pi\) | |||||||
\(492\) | 20.0973 | + | 3.44814i | 0.906054 | + | 0.155454i | ||||
\(493\) | −3.67544 | − | 3.67544i | −0.165534 | − | 0.165534i | ||||
\(494\) | 3.55415 | 0.159909 | ||||||||
\(495\) | −17.8885 | − | 6.32456i | −0.804030 | − | 0.284268i | ||||
\(496\) | 2.32456 | 0.104376 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −7.38248 | − | 1.26663i | −0.330817 | − | 0.0567592i | ||||
\(499\) | − | 40.6491i | − | 1.81970i | −0.414933 | − | 0.909852i | \(-0.636195\pi\) | ||
0.414933 | − | 0.909852i | \(-0.363805\pi\) | |||||||
\(500\) | 11.1803 | 0.500000 | ||||||||
\(501\) | −20.6491 | − | 29.2023i | −0.922534 | − | 1.30466i | ||||
\(502\) | −4.00000 | + | 4.00000i | −0.178529 | + | 0.178529i | ||||
\(503\) | 6.84157 | − | 6.84157i | 0.305051 | − | 0.305051i | −0.537935 | − | 0.842986i | \(-0.680796\pi\) |
0.842986 | + | 0.537935i | \(0.180796\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 16.3246 | 0.726433 | ||||||||
\(506\) | − | 2.82843i | − | 0.125739i | ||||||
\(507\) | −1.06880 | + | 6.22942i | −0.0474671 | + | 0.276658i | ||||
\(508\) | 1.16228 | + | 1.16228i | 0.0515677 | + | 0.0515677i | ||||
\(509\) | −18.1553 | −0.804719 | −0.402359 | − | 0.915482i | \(-0.631810\pi\) | ||||
−0.402359 | + | 0.915482i | \(0.631810\pi\) | |||||||
\(510\) | −4.43665 | − | 0.761210i | −0.196458 | − | 0.0337069i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −0.707107 | − | 0.707107i | −0.0312500 | − | 0.0312500i | ||||
\(513\) | −2.94699 | + | 5.27155i | −0.130113 | + | 0.232745i | ||||
\(514\) | − | 27.2982i | − | 1.20407i | ||||||
\(515\) | 10.8175 | − | 10.8175i | 0.476675 | − | 0.476675i | ||||
\(516\) | −18.3246 | + | 12.9574i | −0.806694 | + | 0.570418i | ||||
\(517\) | 0.649111 | − | 0.649111i | 0.0285479 | − | 0.0285479i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 17.4296 | − | 12.3246i | 0.765072 | − | 0.540988i | ||||
\(520\) | − | 6.83772i | − | 0.299854i | ||||||
\(521\) | − | 26.3738i | − | 1.15546i | −0.816229 | − | 0.577729i | \(-0.803939\pi\) | ||
0.816229 | − | 0.577729i | \(-0.196061\pi\) | |||||||
\(522\) | 5.78199 | + | 12.1065i | 0.253071 | + | 0.529889i | ||||
\(523\) | 29.2982 | + | 29.2982i | 1.28112 | + | 1.28112i | 0.940030 | + | 0.341092i | \(0.110797\pi\) |
0.341092 | + | 0.940030i | \(0.389203\pi\) | |||||||
\(524\) | 10.3585 | 0.452513 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −0.649111 | −0.0283026 | ||||||||
\(527\) | −1.91045 | − | 1.91045i | −0.0832203 | − | 0.0832203i | ||||
\(528\) | −0.828427 | + | 4.82843i | −0.0360527 | + | 0.210130i | ||||
\(529\) | − | 1.00000i | − | 0.0434783i | ||||||
\(530\) | 21.2132i | 0.921443i | ||||||||
\(531\) | −28.0000 | − | 9.89949i | −1.21510 | − | 0.429601i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 25.4558 | − | 25.4558i | 1.10262 | − | 1.10262i | ||||
\(534\) | −17.4296 | − | 24.6491i | −0.754251 | − | 1.06667i | ||||
\(535\) | 16.8377 | − | 16.8377i | 0.727958 | − | 0.727958i | ||||
\(536\) | 1.64371i | 0.0709974i | ||||||||
\(537\) | −22.5115 | − | 3.86236i | −0.971442 | − | 0.166673i | ||||
\(538\) | 6.83772 | + | 6.83772i | 0.294795 | + | 0.294795i | ||||
\(539\) | −19.7990 | −0.852803 | ||||||||
\(540\) | 10.1418 | + | 5.66963i | 0.436432 | + | 0.243982i | ||||
\(541\) | 13.6754 | 0.587953 | 0.293977 | − | 0.955813i | \(-0.405021\pi\) | ||||
0.293977 | + | 0.955813i | \(0.405021\pi\) | |||||||
\(542\) | −21.9017 | − | 21.9017i | −0.940758 | − | 0.940758i | ||||
\(543\) | −38.1104 | − | 6.53871i | −1.63547 | − | 0.280603i | ||||
\(544\) | 1.16228i | 0.0498322i | ||||||||
\(545\) | 3.74641 | 0.160478 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −6.32456 | + | 6.32456i | −0.270418 | + | 0.270418i | −0.829269 | − | 0.558850i | \(-0.811243\pi\) |
0.558850 | + | 0.829269i | \(0.311243\pi\) | |||||||
\(548\) | 0.821854 | − | 0.821854i | 0.0351079 | − | 0.0351079i | ||||
\(549\) | 22.6274 | + | 8.00000i | 0.965715 | + | 0.341432i | ||||
\(550\) | −10.0000 | + | 10.0000i | −0.426401 | + | 0.426401i | ||||
\(551\) | 5.19786i | 0.221436i | ||||||||
\(552\) | −0.292893 | + | 1.70711i | −0.0124664 | + | 0.0726593i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 3.05792 | 0.129919 | ||||||||
\(555\) | 3.67544 | + | 5.19786i | 0.156014 | + | 0.220637i | ||||
\(556\) | −10.3246 | −0.437859 | ||||||||
\(557\) | 17.5629 | + | 17.5629i | 0.744165 | + | 0.744165i | 0.973377 | − | 0.229212i | \(-0.0736148\pi\) |
−0.229212 | + | 0.973377i | \(0.573615\pi\) | |||||||
\(558\) | 3.00540 | + | 6.29282i | 0.127229 | + | 0.266396i | ||||
\(559\) | 39.6228i | 1.67586i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 4.64911 | − | 3.28742i | 0.196286 | − | 0.138795i | ||||
\(562\) | −17.4868 | + | 17.4868i | −0.737638 | + | 0.737638i | ||||
\(563\) | 5.88635 | − | 5.88635i | 0.248080 | − | 0.248080i | −0.572102 | − | 0.820182i | \(-0.693872\pi\) |
0.820182 | + | 0.572102i | \(0.193872\pi\) | |||||||
\(564\) | −0.458991 | + | 0.324555i | −0.0193270 | + | 0.0136662i | ||||
\(565\) | −0.811388 | − | 0.811388i | −0.0341354 | − | 0.0341354i | ||||
\(566\) | − | 12.2317i | − | 0.514136i | ||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −4.16228 | − | 4.16228i | −0.174645 | − | 0.174645i | ||||
\(569\) | −10.1290 | −0.424629 | −0.212315 | − | 0.977201i | \(-0.568100\pi\) | ||||
−0.212315 | + | 0.977201i | \(0.568100\pi\) | |||||||
\(570\) | 2.59893 | + | 3.67544i | 0.108857 | + | 0.153947i | ||||
\(571\) | −10.8377 | −0.453545 | −0.226772 | − | 0.973948i | \(-0.572817\pi\) | ||||
−0.226772 | + | 0.973948i | \(0.572817\pi\) | |||||||
\(572\) | 6.11584 | + | 6.11584i | 0.255716 | + | 0.255716i | ||||
\(573\) | 5.10500 | − | 29.7541i | 0.213264 | − | 1.24300i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −3.53553 | + | 3.53553i | −0.147442 | + | 0.147442i | ||||
\(576\) | 1.00000 | − | 2.82843i | 0.0416667 | − | 0.117851i | ||||
\(577\) | −6.67544 | + | 6.67544i | −0.277902 | + | 0.277902i | −0.832271 | − | 0.554369i | \(-0.812960\pi\) |
0.554369 | + | 0.832271i | \(0.312960\pi\) | |||||||
\(578\) | −11.0656 | + | 11.0656i | −0.460268 | + | 0.460268i | ||||
\(579\) | −4.24264 | − | 6.00000i | −0.176318 | − | 0.249351i | ||||
\(580\) | 10.0000 | 0.415227 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −12.4628 | − | 2.13829i | −0.516601 | − | 0.0886348i | ||||
\(583\) | −18.9737 | − | 18.9737i | −0.785809 | − | 0.785809i | ||||
\(584\) | 7.53006 | 0.311596 | ||||||||
\(585\) | 18.5104 | − | 8.84044i | 0.765313 | − | 0.365507i | ||||
\(586\) | 31.8114 | 1.31412 | ||||||||
\(587\) | −7.07107 | − | 7.07107i | −0.291854 | − | 0.291854i | 0.545958 | − | 0.837812i | \(-0.316166\pi\) |
−0.837812 | + | 0.545958i | \(0.816166\pi\) | |||||||
\(588\) | 11.9497 | + | 2.05025i | 0.492799 | + | 0.0845510i | ||||
\(589\) | 2.70178i | 0.111325i | ||||||||
\(590\) | −15.6525 | + | 15.6525i | −0.644402 | + | 0.644402i | ||||
\(591\) | −3.67544 | − | 5.19786i | −0.151188 | − | 0.213812i | ||||
\(592\) | 1.16228 | − | 1.16228i | 0.0477693 | − | 0.0477693i | ||||
\(593\) | 27.7880 | − | 27.7880i | 1.14112 | − | 1.14112i | 0.152872 | − | 0.988246i | \(-0.451148\pi\) |
0.988246 | − | 0.152872i | \(-0.0488522\pi\) | |||||||
\(594\) | −14.1421 | + | 4.00000i | −0.580259 | + | 0.164122i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | − | 7.75955i | − | 0.317844i | ||||||
\(597\) | 4.44093 | − | 25.8836i | 0.181755 | − | 1.05935i | ||||
\(598\) | 2.16228 | + | 2.16228i | 0.0884221 | + | 0.0884221i | ||||
\(599\) | 17.2001 | 0.702775 | 0.351388 | − | 0.936230i | \(-0.385710\pi\) | ||||
0.351388 | + | 0.936230i | \(0.385710\pi\) | |||||||
\(600\) | 7.07107 | − | 5.00000i | 0.288675 | − | 0.204124i | ||||
\(601\) | −9.35089 | −0.381431 | −0.190715 | − | 0.981645i | \(-0.561081\pi\) | ||||
−0.190715 | + | 0.981645i | \(0.561081\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −4.44970 | + | 2.12514i | −0.181206 | + | 0.0865424i | ||||
\(604\) | − | 10.3246i | − | 0.420100i | ||||||
\(605\) | 6.70820i | 0.272727i | ||||||||
\(606\) | 10.3246 | − | 7.30056i | 0.419406 | − | 0.296565i | ||||
\(607\) | 7.16228 | − | 7.16228i | 0.290708 | − | 0.290708i | −0.546652 | − | 0.837360i | \(-0.684098\pi\) |
0.837360 | + | 0.546652i | \(0.184098\pi\) | |||||||
\(608\) | 0.821854 | − | 0.821854i | 0.0333306 | − | 0.0333306i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 12.6491 | − | 12.6491i | 0.512148 | − | 0.512148i | ||||
\(611\) | 0.992465i | 0.0401508i | ||||||||
\(612\) | −3.14641 | + | 1.50270i | −0.127186 | + | 0.0607431i | ||||
\(613\) | 30.4605 | + | 30.4605i | 1.23029 | + | 1.23029i | 0.963853 | + | 0.266435i | \(0.0858458\pi\) |
0.266435 | + | 0.963853i | \(0.414154\pi\) | |||||||
\(614\) | 14.6011 | 0.589253 | ||||||||
\(615\) | 44.9388 | + | 7.71028i | 1.81211 | + | 0.310909i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −12.1356 | − | 12.1356i | −0.488559 | − | 0.488559i | 0.419292 | − | 0.907851i | \(-0.362278\pi\) |
−0.907851 | + | 0.419292i | \(0.862278\pi\) | |||||||
\(618\) | 2.00385 | − | 11.6793i | 0.0806067 | − | 0.469810i | ||||
\(619\) | 38.4605i | 1.54586i | 0.634493 | + | 0.772929i | \(0.281209\pi\) | ||||
−0.634493 | + | 0.772929i | \(0.718791\pi\) | |||||||
\(620\) | 5.19786 | 0.208751 | ||||||||
\(621\) | −5.00000 | + | 1.41421i | −0.200643 | + | 0.0567504i | ||||
\(622\) | 12.8114 | − | 12.8114i | 0.513690 | − | 0.513690i | ||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −3.05792 | − | 4.32456i | −0.122415 | − | 0.173121i | ||||
\(625\) | 25.0000 | 1.00000 | ||||||||
\(626\) | 4.01315i | 0.160398i | ||||||||
\(627\) | −5.61197 | − | 0.962862i | −0.224121 | − | 0.0384530i | ||||
\(628\) | 9.48683 | + | 9.48683i | 0.378566 | + | 0.378566i | ||||
\(629\) | −1.91045 | −0.0761745 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 3.81139 | 0.151729 | 0.0758645 | − | 0.997118i | \(-0.475828\pi\) | ||||
0.0758645 | + | 0.997118i | \(0.475828\pi\) | |||||||
\(632\) | −2.23607 | − | 2.23607i | −0.0889460 | − | 0.0889460i | ||||
\(633\) | −2.86016 | − | 0.490726i | −0.113681 | − | 0.0195046i | ||||
\(634\) | − | 16.3246i | − | 0.648331i | ||||||
\(635\) | 2.59893 | + | 2.59893i | 0.103135 | + | 0.103135i | ||||
\(636\) | 9.48683 | + | 13.4164i | 0.376177 | + | 0.531995i | ||||
\(637\) | 15.1359 | − | 15.1359i | 0.599708 | − | 0.599708i | ||||
\(638\) | −8.94427 | + | 8.94427i | −0.354107 | + | 0.354107i | ||||
\(639\) | 5.88635 | − | 16.6491i | 0.232860 | − | 0.658629i | ||||
\(640\) | −1.58114 | − | 1.58114i | −0.0625000 | − | 0.0625000i | ||||
\(641\) | − | 28.7433i | − | 1.13529i | −0.823273 | − | 0.567645i | \(-0.807855\pi\) | ||
0.823273 | − | 0.567645i | \(-0.192145\pi\) | |||||||
\(642\) | 3.11905 | − | 18.1792i | 0.123099 | − | 0.717475i | ||||
\(643\) | 1.16228 | + | 1.16228i | 0.0458358 | + | 0.0458358i | 0.729653 | − | 0.683817i | \(-0.239682\pi\) |
−0.683817 | + | 0.729653i | \(0.739682\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −40.9750 | + | 28.9737i | −1.61339 | + | 1.14084i | ||||
\(646\) | −1.35089 | −0.0531500 | ||||||||
\(647\) | −28.5138 | − | 28.5138i | −1.12099 | − | 1.12099i | −0.991593 | − | 0.129399i | \(-0.958695\pi\) |
−0.129399 | − | 0.991593i | \(-0.541305\pi\) | |||||||
\(648\) | 8.94975 | − | 0.949747i | 0.351579 | − | 0.0373096i | ||||
\(649\) | − | 28.0000i | − | 1.09910i | ||||||
\(650\) | − | 15.2896i | − | 0.599708i | ||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 8.64911 | − | 8.64911i | 0.338725 | − | 0.338725i | ||||
\(653\) | 9.17377 | − | 9.17377i | 0.358997 | − | 0.358997i | −0.504446 | − | 0.863443i | \(-0.668303\pi\) |
0.863443 | + | 0.504446i | \(0.168303\pi\) | |||||||
\(654\) | 2.36944 | − | 1.67544i | 0.0926523 | − | 0.0655151i | ||||
\(655\) | 23.1623 | 0.905025 | ||||||||
\(656\) | − | 11.7727i | − | 0.459647i | ||||||
\(657\) | 9.73556 | + | 20.3847i | 0.379820 | + | 0.795282i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −8.94427 | −0.348419 | −0.174210 | − | 0.984709i | \(-0.555737\pi\) | ||||
−0.174210 | + | 0.984709i | \(0.555737\pi\) | |||||||
\(660\) | −1.85242 | + | 10.7967i | −0.0721053 | + | 0.420261i | ||||
\(661\) | −7.35089 | −0.285916 | −0.142958 | − | 0.989729i | \(-0.545661\pi\) | ||||
−0.142958 | + | 0.989729i | \(0.545661\pi\) | |||||||
\(662\) | 24.7301 | + | 24.7301i | 0.961163 | + | 0.961163i | ||||
\(663\) | −1.04099 | + | 6.06732i | −0.0404286 | + | 0.235635i | ||||
\(664\) | 4.32456i | 0.167825i | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 4.64911 | + | 1.64371i | 0.180149 | + | 0.0636924i | ||||
\(667\) | −3.16228 | + | 3.16228i | −0.122444 | + | 0.122444i | ||||
\(668\) | −14.6011 | + | 14.6011i | −0.564935 | + | 0.564935i | ||||
\(669\) | −9.67000 | − | 13.6754i | −0.373864 | − | 0.528723i | ||||
\(670\) | 3.67544i | 0.141995i | ||||||||
\(671\) | 22.6274i | 0.873522i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 18.6754 | + | 18.6754i | 0.719885 | + | 0.719885i | 0.968582 | − | 0.248696i | \(-0.0800020\pi\) |
−0.248696 | + | 0.968582i | \(0.580002\pi\) | |||||||
\(674\) | −13.4164 | −0.516781 | ||||||||
\(675\) | 22.6777 | + | 12.6777i | 0.872864 | + | 0.487964i | ||||
\(676\) | 3.64911 | 0.140350 | ||||||||
\(677\) | −14.4678 | − | 14.4678i | −0.556041 | − | 0.556041i | 0.372137 | − | 0.928178i | \(-0.378625\pi\) |
−0.928178 | + | 0.372137i | \(0.878625\pi\) | |||||||
\(678\) | −0.876031 | − | 0.150303i | −0.0336438 | − | 0.00577236i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 2.59893i | 0.0996645i | ||||||||
\(681\) | −6.00000 | − | 8.48528i | −0.229920 | − | 0.325157i | ||||
\(682\) | −4.64911 | + | 4.64911i | −0.178024 | + | 0.178024i | ||||
\(683\) | 22.5902 | − | 22.5902i | 0.864389 | − | 0.864389i | −0.127455 | − | 0.991844i | \(-0.540681\pi\) |
0.991844 | + | 0.127455i | \(0.0406809\pi\) | |||||||
\(684\) | 3.28742 | + | 1.16228i | 0.125698 | + | 0.0444408i | ||||
\(685\) | 1.83772 | − | 1.83772i | 0.0702158 | − | 0.0702158i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 7.40968 | − | 43.1868i | 0.282697 | − | 1.64768i | ||||
\(688\) | 9.16228 | + | 9.16228i | 0.349309 | + | 0.349309i | ||||
\(689\) | 29.0100 | 1.10519 | ||||||||
\(690\) | −0.654929 | + | 3.81721i | −0.0249327 | + | 0.145319i | ||||
\(691\) | 12.6491 | 0.481195 | 0.240597 | − | 0.970625i | \(-0.422657\pi\) | ||||
0.240597 | + | 0.970625i | \(0.422657\pi\) | |||||||
\(692\) | −8.71478 | − | 8.71478i | −0.331286 | − | 0.331286i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | − | 26.6491i | − | 1.01159i | ||||||
\(695\) | −23.0864 | −0.875717 | ||||||||
\(696\) | 6.32456 | − | 4.47214i | 0.239732 | − | 0.169516i | ||||
\(697\) | −9.67544 | + | 9.67544i | −0.366484 | + | 0.366484i | ||||
\(698\) | −9.89949 | + | 9.89949i | −0.374701 | + | 0.374701i | ||||
\(699\) | 6.11584 | − | 4.32456i | 0.231322 | − | 0.163570i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 8.02629i | − | 0.303149i | −0.988446 | − | 0.151574i | \(-0.951566\pi\) | ||
0.988446 | − | 0.151574i | \(-0.0484343\pi\) | |||||||
\(702\) | 7.75347 | − | 13.8693i | 0.292636 | − | 0.523463i | ||||
\(703\) | 1.35089 | + | 1.35089i | 0.0509498 | + | 0.0509498i | ||||
\(704\) | 2.82843 | 0.106600 | ||||||||
\(705\) | −1.02633 | + | 0.725728i | −0.0386540 | + | 0.0273325i | ||||
\(706\) | −12.9737 | −0.488270 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −2.89949 | + | 16.8995i | −0.108970 | + | 0.635122i | ||||
\(709\) | − | 49.9473i | − | 1.87581i | −0.346890 | − | 0.937906i | \(-0.612762\pi\) | ||
0.346890 | − | 0.937906i | \(-0.387238\pi\) | |||||||
\(710\) | −9.30714 | − | 9.30714i | −0.349291 | − | 0.349291i | ||||
\(711\) | 3.16228 | − | 8.94427i | 0.118595 | − | 0.335436i | ||||
\(712\) | −12.3246 | + | 12.3246i | −0.461882 | + | 0.461882i | ||||
\(713\) | −1.64371 | + | 1.64371i | −0.0615574 | + | 0.0615574i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 13.6754 | + | 13.6754i | 0.511433 | + | 0.511433i | ||||
\(716\) | 13.1869i | 0.492818i | ||||||||
\(717\) | −34.9743 | − | 6.00064i | −1.30614 | − | 0.224098i | ||||
\(718\) | 14.0000 | + | 14.0000i | 0.522475 | + | 0.522475i | ||||
\(719\) | −50.1487 | −1.87023 | −0.935116 | − | 0.354342i | \(-0.884705\pi\) | ||||
−0.935116 | + | 0.354342i | \(0.884705\pi\) | |||||||
\(720\) | 2.23607 | − | 6.32456i | 0.0833333 | − | 0.235702i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −12.4798 | − | 12.4798i | −0.464450 | − | 0.464450i | ||||
\(723\) | 7.38248 | + | 1.26663i | 0.274557 | + | 0.0471066i | ||||
\(724\) | 22.3246i | 0.829686i | ||||||||
\(725\) | 22.3607 | 0.830455 | ||||||||
\(726\) | 3.00000 | + | 4.24264i | 0.111340 | + | 0.157459i | ||||
\(727\) | 26.3246 | − | 26.3246i | 0.976324 | − | 0.976324i | −0.0234024 | − | 0.999726i | \(-0.507450\pi\) |
0.999726 | + | 0.0234024i | \(0.00744990\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 14.1421 | + | 23.0000i | 0.523783 | + | 0.851852i | ||||
\(730\) | 16.8377 | 0.623192 | ||||||||
\(731\) | − | 15.0601i | − | 0.557019i | ||||||
\(732\) | 2.34315 | − | 13.6569i | 0.0866052 | − | 0.504772i | ||||
\(733\) | −2.18861 | − | 2.18861i | −0.0808382 | − | 0.0808382i | 0.665532 | − | 0.746370i | \(-0.268205\pi\) |
−0.746370 | + | 0.665532i | \(0.768205\pi\) | |||||||
\(734\) | 24.7301 | 0.912805 | ||||||||
\(735\) | 26.7204 | + | 4.58450i | 0.985599 | + | 0.169102i | ||||
\(736\) | 1.00000 | 0.0368605 | ||||||||
\(737\) | −3.28742 | − | 3.28742i | −0.121094 | − | 0.121094i | ||||
\(738\) | 31.8700 | − | 15.2208i | 1.17315 | − | 0.560287i | ||||
\(739\) | 36.2719i | 1.33428i | 0.744931 | + | 0.667141i | \(0.232482\pi\) | ||||
−0.744931 | + | 0.667141i | \(0.767518\pi\) | |||||||
\(740\) | 2.59893 | − | 2.59893i | 0.0955386 | − | 0.0955386i | ||||
\(741\) | 5.02633 | − | 3.55415i | 0.184647 | − | 0.130565i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −10.5880 | + | 10.5880i | −0.388435 | + | 0.388435i | −0.874129 | − | 0.485694i | \(-0.838567\pi\) |
0.485694 | + | 0.874129i | \(0.338567\pi\) | |||||||
\(744\) | 3.28742 | − | 2.32456i | 0.120523 | − | 0.0852223i | ||||
\(745\) | − | 17.3509i | − | 0.635687i | ||||||
\(746\) | 7.75955i | 0.284097i | ||||||||
\(747\) | −11.7070 | + | 5.59119i | −0.428338 | + | 0.204571i | ||||
\(748\) | −2.32456 | − | 2.32456i | −0.0849942 | − | 0.0849942i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 15.8114 | − | 11.1803i | 0.577350 | − | 0.408248i | ||||
\(751\) | 28.4605 | 1.03854 | 0.519269 | − | 0.854611i | \(-0.326204\pi\) | ||||
0.519269 | + | 0.854611i | \(0.326204\pi\) | |||||||
\(752\) | 0.229495 | + | 0.229495i | 0.00836883 | + | 0.00836883i | ||||
\(753\) | −1.65685 | + | 9.65685i | −0.0603791 | + | 0.351915i | ||||
\(754\) | − | 13.6754i | − | 0.498030i | ||||||
\(755\) | − | 23.0864i | − | 0.840200i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −9.48683 | + | 9.48683i | −0.344805 | + | 0.344805i | −0.858170 | − | 0.513365i | \(-0.828399\pi\) |
0.513365 | + | 0.858170i | \(0.328399\pi\) | |||||||
\(758\) | −10.9508 | + | 10.9508i | −0.397753 | + | 0.397753i | ||||
\(759\) | −2.82843 | − | 4.00000i | −0.102665 | − | 0.145191i | ||||
\(760\) | 1.83772 | − | 1.83772i | 0.0666612 | − | 0.0666612i | ||||
\(761\) | 32.4897i | 1.17775i | 0.808224 | + | 0.588875i | \(0.200429\pi\) | ||||
−0.808224 | + | 0.588875i | \(0.799571\pi\) | |||||||
\(762\) | 2.80599 | + | 0.481431i | 0.101650 | + | 0.0174404i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −17.4296 | −0.630579 | ||||||||
\(765\) | −7.03559 | + | 3.36014i | −0.254372 | + | 0.121486i | ||||
\(766\) | 22.3246 | 0.806619 | ||||||||
\(767\) | 21.4055 | + | 21.4055i | 0.772906 | + | 0.772906i | ||||
\(768\) | −1.70711 | − | 0.292893i | −0.0615999 | − | 0.0105689i | ||||
\(769\) | − | 16.3246i | − | 0.588679i | −0.955701 | − | 0.294339i | \(-0.904900\pi\) | ||
0.955701 | − | 0.294339i | \(-0.0950996\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −27.2982 | − | 38.6055i | −0.983121 | − | 1.39034i | ||||
\(772\) | −3.00000 | + | 3.00000i | −0.107972 | + | 0.107972i | ||||
\(773\) | −22.0351 | + | 22.0351i | −0.792546 | + | 0.792546i | −0.981907 | − | 0.189361i | \(-0.939358\pi\) |
0.189361 | + | 0.981907i | \(0.439358\pi\) | |||||||
\(774\) | −12.9574 | + | 36.6491i | −0.465745 | + | 1.31733i | ||||
\(775\) | 11.6228 | 0.417502 | ||||||||
\(776\) | 7.30056i | 0.262075i | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −15.1623 | − | 15.1623i | −0.543594 | − | 0.543594i | ||||
\(779\) | 13.6831 | 0.490250 | ||||||||
\(780\) | −6.83772 | − | 9.67000i | −0.244830 | − | 0.346242i | ||||
\(781\) | 16.6491 | 0.595752 | ||||||||
\(782\) | −0.821854 | − | 0.821854i | −0.0293895 | − | 0.0293895i | ||||
\(783\) | 20.2835 | + | 11.3393i | 0.724874 | + | 0.405232i | ||||
\(784\) | − | 7.00000i | − | 0.250000i | ||||||
\(785\) | 21.2132 | + | 21.2132i | 0.757132 | + | 0.757132i | ||||
\(786\) | 14.6491 | − | 10.3585i | 0.522516 | − | 0.369475i | ||||
\(787\) | −36.1359 | + | 36.1359i | −1.28811 | + | 1.28811i | −0.352172 | + | 0.935935i | \(0.614557\pi\) |
−0.935935 | + | 0.352172i | \(0.885443\pi\) | |||||||
\(788\) | −2.59893 | + | 2.59893i | −0.0925831 | + | 0.0925831i | ||||
\(789\) | −0.917981 | + | 0.649111i | −0.0326810 | + | 0.0231090i | ||||
\(790\) | −5.00000 | − | 5.00000i | −0.177892 | − | 0.177892i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 3.65685 | + | 7.65685i | 0.129941 | + | 0.272074i | ||||
\(793\) | −17.2982 | − | 17.2982i | −0.614278 | − | 0.614278i | ||||
\(794\) | 35.0886 | 1.24525 | ||||||||
\(795\) | 21.2132 | + | 30.0000i | 0.752355 | + | 1.06399i | ||||
\(796\) | −15.1623 | −0.537413 | ||||||||
\(797\) | 16.3782 | + | 16.3782i | 0.580146 | + | 0.580146i | 0.934943 | − | 0.354797i | \(-0.115450\pi\) |
−0.354797 | + | 0.934943i | \(0.615450\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 0.377223i | − | 0.0133452i | ||||||
\(800\) | −3.53553 | − | 3.53553i | −0.125000 | − | 0.125000i | ||||
\(801\) | −49.2982 | − | 17.4296i | −1.74187 | − | 0.615843i | ||||
\(802\) | −14.0000 | + | 14.0000i | −0.494357 | + | 0.494357i | ||||
\(803\) | −15.0601 | + | 15.0601i | −0.531460 | + | 0.531460i | ||||
\(804\) | 1.64371 | + | 2.32456i | 0.0579691 | + | 0.0819807i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | − | 7.10831i | − | 0.250380i | ||||||
\(807\) | 16.5077 | + | 2.83228i | 0.581099 | + | 0.0997009i | ||||
\(808\) | −5.16228 | − | 5.16228i | −0.181608 | − | 0.181608i | ||||
\(809\) | −22.1684 | −0.779400 | −0.389700 | − | 0.920942i | \(-0.627421\pi\) | ||||
−0.389700 | + | 0.920942i | \(0.627421\pi\) | |||||||
\(810\) | 20.0122 | − | 2.12370i | 0.703159 | − | 0.0746192i | ||||
\(811\) | −52.6491 | −1.84876 | −0.924380 | − | 0.381473i | \(-0.875417\pi\) | ||||
−0.924380 | + | 0.381473i | \(0.875417\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −52.8754 | − | 9.07198i | −1.85442 | − | 0.318168i | ||||
\(814\) | 4.64911i | 0.162951i | ||||||||
\(815\) | 19.3400 | − | 19.3400i | 0.677451 | − | 0.677451i | ||||
\(816\) | 1.16228 | + | 1.64371i | 0.0406879 | + | 0.0575413i | ||||
\(817\) | −10.6491 | + | 10.6491i | −0.372565 | + | 0.372565i | ||||
\(818\) | 14.1421 | − | 14.1421i | 0.494468 | − | 0.494468i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | − | 26.3246i | − | 0.919293i | ||||||
\(821\) | − | 44.9881i | − | 1.57010i | −0.619435 | − | 0.785048i | \(-0.712638\pi\) | ||
0.619435 | − | 0.785048i | \(-0.287362\pi\) | |||||||
\(822\) | 0.340423 | − | 1.98413i | 0.0118736 | − | 0.0692046i | ||||
\(823\) | −0.188612 | − | 0.188612i | −0.00657459 | − | 0.00657459i | 0.703812 | − | 0.710386i | \(-0.251480\pi\) |
−0.710386 | + | 0.703812i | \(0.751480\pi\) | |||||||
\(824\) | −6.84157 | −0.238337 | ||||||||
\(825\) | −4.14214 | + | 24.1421i | −0.144211 | + | 0.840521i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −30.1575 | − | 30.1575i | −1.04868 | − | 1.04868i | −0.998753 | − | 0.0499252i | \(-0.984102\pi\) |
−0.0499252 | − | 0.998753i | \(-0.515898\pi\) | |||||||
\(828\) | 1.29289 | + | 2.70711i | 0.0449311 | + | 0.0940785i | ||||
\(829\) | 42.3246i | 1.46999i | 0.678071 | + | 0.734996i | \(0.262816\pi\) | ||||
−0.678071 | + | 0.734996i | \(0.737184\pi\) | |||||||
\(830\) | 9.67000i | 0.335651i | ||||||||
\(831\) | 4.32456 | − | 3.05792i | 0.150017 | − | 0.106078i | ||||
\(832\) | −2.16228 | + | 2.16228i | −0.0749635 | + | 0.0749635i | ||||
\(833\) | −5.75298 | + | 5.75298i | −0.199329 | + | 0.199329i | ||||
\(834\) | −14.6011 | + | 10.3246i | −0.505596 | + | 0.357510i | ||||
\(835\) | −32.6491 | + | 32.6491i | −1.12987 | + | 1.12987i | ||||
\(836\) | 3.28742i | 0.113698i | ||||||||
\(837\) | 10.5431 | + | 5.89399i | 0.364423 | + | 0.203726i | ||||
\(838\) | −6.64911 | − | 6.64911i | −0.229690 | − | 0.229690i | ||||
\(839\) | 20.7170 | 0.715229 | 0.357615 | − | 0.933869i | \(-0.383590\pi\) | ||||
0.357615 | + | 0.933869i | \(0.383590\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −9.00000 | −0.310345 | ||||||||
\(842\) | −25.9148 | − | 25.9148i | −0.893084 | − | 0.893084i | ||||
\(843\) | −7.24328 | + | 42.2169i | −0.249472 | + | 1.45403i | ||||
\(844\) | 1.67544i | 0.0576712i | ||||||||
\(845\) | 8.15966 | 0.280701 | ||||||||
\(846\) | −0.324555 | + | 0.917981i | −0.0111584 | + | 0.0315608i | ||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 6.70820 | − | 6.70820i | 0.230361 | − | 0.230361i | ||||
\(849\) | −12.2317 | − | 17.2982i | −0.419790 | − | 0.593673i | ||||
\(850\) | 5.81139i | 0.199329i | ||||||||
\(851\) | 1.64371i | 0.0563456i | ||||||||
\(852\) | −10.0486 | − | 1.72407i | −0.344260 | − | 0.0590657i | ||||
\(853\) | 24.1623 | + | 24.1623i | 0.827301 | + | 0.827301i | 0.987143 | − | 0.159842i | \(-0.0510985\pi\) |
−0.159842 | + | 0.987143i | \(0.551098\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 7.35089 | + | 2.59893i | 0.251395 | + | 0.0888816i | ||||
\(856\) | −10.6491 | −0.363979 | ||||||||
\(857\) | 7.07107 | + | 7.07107i | 0.241543 | + | 0.241543i | 0.817488 | − | 0.575945i | \(-0.195366\pi\) |
−0.575945 | + | 0.817488i | \(0.695366\pi\) | |||||||
\(858\) | 14.7650 | + | 2.53327i | 0.504067 | + | 0.0864843i | ||||
\(859\) | 30.3246i | 1.03466i | 0.855786 | + | 0.517330i | \(0.173074\pi\) | ||||
−0.855786 | + | 0.517330i | \(0.826926\pi\) | |||||||
\(860\) | 20.4875 | + | 20.4875i | 0.698617 | + | 0.698617i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 8.32456 | − | 8.32456i | 0.283535 | − | 0.283535i | ||||
\(863\) | 11.3137 | − | 11.3137i | 0.385123 | − | 0.385123i | −0.487821 | − | 0.872944i | \(-0.662208\pi\) |
0.872944 | + | 0.487821i | \(0.162208\pi\) | |||||||
\(864\) | −1.41421 | − | 5.00000i | −0.0481125 | − | 0.170103i | ||||
\(865\) | −19.4868 | − | 19.4868i | −0.662572 | − | 0.662572i | ||||
\(866\) | 39.7902i | 1.35213i | ||||||||
\(867\) | −4.58352 | + | 26.7147i | −0.155664 | + | 0.907279i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 8.94427 | 0.303414 | ||||||||
\(870\) | 14.1421 | − | 10.0000i | 0.479463 | − | 0.339032i | ||||
\(871\) | 5.02633 | 0.170311 | ||||||||
\(872\) | −1.18472 | − | 1.18472i | −0.0401196 | − | 0.0401196i | ||||
\(873\) | −19.7634 | + | 9.43885i | −0.668890 | + | 0.319457i | ||||
\(874\) | 1.16228i | 0.0393146i | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 10.6491 | − | 7.53006i | 0.359800 | − | 0.254417i | ||||
\(877\) | −0.811388 | + | 0.811388i | −0.0273986 | + | 0.0273986i | −0.720673 | − | 0.693275i | \(-0.756167\pi\) |
0.693275 | + | 0.720673i | \(0.256167\pi\) | |||||||
\(878\) | −25.9148 | + | 25.9148i | −0.874583 | + | 0.874583i | ||||
\(879\) | 44.9881 | − | 31.8114i | 1.51741 | − | 1.07297i | ||||
\(880\) | 6.32456 | 0.213201 | ||||||||
\(881\) | 45.9061i | 1.54662i | 0.634031 | + | 0.773308i | \(0.281399\pi\) | ||||
−0.634031 | + | 0.773308i | \(0.718601\pi\) | |||||||
\(882\) | 18.9497 | − | 9.05025i | 0.638071 | − | 0.304738i | ||||
\(883\) | −9.67544 | − | 9.67544i | −0.325605 | − | 0.325605i | 0.525308 | − | 0.850912i | \(-0.323950\pi\) |
−0.850912 | + | 0.525308i | \(0.823950\pi\) | |||||||
\(884\) | 3.55415 | 0.119539 | ||||||||
\(885\) | −6.48347 | + | 37.7884i | −0.217939 | + | 1.27024i | ||||
\(886\) | 16.0000 | 0.537531 | ||||||||
\(887\) | −31.5717 | − | 31.5717i | −1.06007 | − | 1.06007i | −0.998076 | − | 0.0619972i | \(-0.980253\pi\) |
−0.0619972 | − | 0.998076i | \(-0.519747\pi\) | |||||||
\(888\) | 0.481431 | − | 2.80599i | 0.0161558 | − | 0.0941627i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −27.5585 | + | 27.5585i | −0.923764 | + | 0.923764i | ||||
\(891\) | −16.0000 | + | 19.7990i | −0.536020 | + | 0.663291i | ||||
\(892\) | −6.83772 | + | 6.83772i | −0.228944 | + | 0.228944i | ||||
\(893\) | −0.266737 | + | 0.266737i | −0.00892602 | + | 0.00892602i | ||||
\(894\) | −7.75955 | − | 10.9737i | −0.259518 | − | 0.367014i | ||||
\(895\) | 29.4868i | 0.985636i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 5.22020 | + | 0.895645i | 0.174297 | + | 0.0299047i | ||||
\(898\) | −4.00000 | − | 4.00000i | −0.133482 | − | 0.133482i | ||||
\(899\) | 10.3957 | 0.346717 | ||||||||
\(900\) | 5.00000 | − | 14.1421i | 0.166667 | − | 0.471405i | ||||
\(901\) | −11.0263 | −0.367340 | ||||||||
\(902\) | 23.5454 | + | 23.5454i | 0.783976 | + | 0.783976i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0.513167i | 0.0170677i | ||||||||
\(905\) | 49.9192i | 1.65937i | ||||||||
\(906\) | −10.3246 | − | 14.6011i | −0.343010 | − | 0.485090i | ||||
\(907\) | 0 | 0 | −0.707107 | − | 0.707107i | \(-0.750000\pi\) | ||||
0.707107 | + | 0.707107i | \(0.250000\pi\) | |||||||
\(908\) | −4.24264 | + | 4.24264i | −0.140797 | + | 0.140797i | ||||
\(909\) | 7.30056 | − | 20.6491i | 0.242144 | − | 0.684888i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 14.6011i | − | 0.483757i | −0.970307 | − | 0.241878i | \(-0.922236\pi\) | ||
0.970307 | − | 0.241878i | \(-0.0777635\pi\) | |||||||
\(912\) | 0.340423 | − | 1.98413i | 0.0112725 | − | 0.0657012i | ||||
\(913\) | −8.64911 | − | 8.64911i | −0.286244 | − | 0.286244i | ||||
\(914\) | 18.1553 | 0.600523 | ||||||||
\(915\) | 5.23943 | − | 30.5377i | 0.173210 | − | 1.00954i | ||||
\(916\) | −25.2982 | −0.835877 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | −2.94699 | + | 5.27155i | −0.0972653 | + | 0.173987i | ||||
\(919\) | 26.1359i | 0.862145i | 0.902317 | + | 0.431073i | \(0.141865\pi\) | ||||
−0.902317 | + | 0.431073i | \(0.858135\pi\) | |||||||
\(920\) | 2.23607 | 0.0737210 | ||||||||
\(921\) | 20.6491 | − | 14.6011i | 0.680411 | − | 0.481123i | ||||
\(922\) | 9.16228 | − | 9.16228i | 0.301744 | − | 0.301744i | ||||
\(923\) | −12.7279 | + | 12.7279i | −0.418945 | + | 0.418945i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 5.81139 | − | 5.81139i | 0.191077 | − | 0.191077i | ||||
\(926\) | − | 25.6481i | − | 0.842849i | ||||||
\(927\) | −8.84542 | − | 18.5209i | −0.290522 | − | 0.608305i | ||||
\(928\) | −3.16228 | − | 3.16228i | −0.103807 | − | 0.103807i | ||||
\(929\) | 20.2580 | 0.664643 | 0.332321 | − | 0.943166i | \(-0.392168\pi\) | ||||
0.332321 | + | 0.943166i | \(0.392168\pi\) | |||||||
\(930\) | 7.35089 | − | 5.19786i | 0.241045 | − | 0.170445i | ||||
\(931\) | 8.13594 | 0.266645 | ||||||||
\(932\) | −3.05792 | − | 3.05792i | −0.100166 | − | 0.100166i | ||||
\(933\) | 5.30665 | − | 30.9294i | 0.173732 | − | 1.01258i | ||||
\(934\) | 18.6491i | 0.610218i | ||||||||
\(935\) | −5.19786 | − | 5.19786i | −0.169988 | − | 0.169988i | ||||
\(936\) | −8.64911 | − | 3.05792i | −0.282705 | − | 0.0999513i | ||||
\(937\) | −1.81139 | + | 1.81139i | −0.0591755 | + | 0.0591755i | −0.736075 | − | 0.676900i | \(-0.763323\pi\) |
0.676900 | + | 0.736075i | \(0.263323\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 4.01315 | + | 5.67544i | 0.130964 | + | 0.185211i | ||||
\(940\) | 0.513167 | + | 0.513167i | 0.0167377 | + | 0.0167377i | ||||
\(941\) | 56.3018i | 1.83539i | 0.397290 | + | 0.917693i | \(0.369951\pi\) | ||||
−0.397290 | + | 0.917693i | \(0.630049\pi\) | |||||||
\(942\) | 22.9032 | + | 3.92957i | 0.746228 | + | 0.128032i | ||||
\(943\) | 8.32456 | + | 8.32456i | 0.271085 | + | 0.271085i | ||||
\(944\) | 9.89949 | 0.322201 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −36.6491 | −1.19157 | ||||||||
\(947\) | −35.3181 | − | 35.3181i | −1.14768 | − | 1.14768i | −0.987007 | − | 0.160677i | \(-0.948632\pi\) |
−0.160677 | − | 0.987007i | \(-0.551368\pi\) | |||||||
\(948\) | −5.39835 | − | 0.926210i | −0.175330 | − | 0.0300819i | ||||
\(949\) | − | 23.0263i | − | 0.747466i | ||||||
\(950\) | 4.10927 | − | 4.10927i | 0.133322 | − | 0.133322i | ||||
\(951\) | −16.3246 | − | 23.0864i | −0.529360 | − | 0.748628i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −41.7968 | + | 41.7968i | −1.35393 | + | 1.35393i | −0.472717 | + | 0.881214i | \(0.656727\pi\) |
−0.881214 | + | 0.472717i | \(0.843273\pi\) | |||||||
\(954\) | 26.8328 | + | 9.48683i | 0.868744 | + | 0.307148i | ||||
\(955\) | −38.9737 | −1.26116 | ||||||||
\(956\) | 20.4875i | 0.662612i | ||||||||
\(957\) | −3.70484 | + | 21.5934i | −0.119760 | + | 0.698015i | ||||
\(958\) | −20.0000 | − | 20.0000i | −0.646171 | − | 0.646171i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −3.81721 | − | 0.654929i | −0.123200 | − | 0.0211377i | ||||
\(961\) | −25.5964 | −0.825692 | ||||||||
\(962\) | −3.55415 | − | 3.55415i | −0.114591 | − | 0.114591i | ||||
\(963\) | −13.7682 | − | 28.8283i | −0.443673 | − | 0.928978i | ||||
\(964\) | − | 4.32456i | − | 0.139285i | ||||||
\(965\) | −6.70820 | + | 6.70820i | −0.215945 | + | 0.215945i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 28.8377 | − | 28.8377i | 0.927359 | − | 0.927359i | −0.0701760 | − | 0.997535i | \(-0.522356\pi\) |
0.997535 | + | 0.0701760i | \(0.0223561\pi\) | |||||||
\(968\) | 2.12132 | − | 2.12132i | 0.0681818 | − | 0.0681818i | ||||
\(969\) | −1.91045 | + | 1.35089i | −0.0613724 | + | 0.0433968i | ||||
\(970\) | 16.3246i | 0.524150i | ||||||||
\(971\) | 7.03383i | 0.225726i | 0.993611 | + | 0.112863i | \(0.0360022\pi\) | ||||
−0.993611 | + | 0.112863i | \(0.963998\pi\) | |||||||
\(972\) | 11.7071 | − | 10.2929i | 0.375506 | − | 0.330145i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 23.8121 | 0.762990 | ||||||||
\(975\) | −15.2896 | − | 21.6228i | −0.489659 | − | 0.692483i | ||||
\(976\) | −8.00000 | −0.256074 | ||||||||
\(977\) | 8.58141 | + | 8.58141i | 0.274544 | + | 0.274544i | 0.830926 | − | 0.556383i | \(-0.187811\pi\) |
−0.556383 | + | 0.830926i | \(0.687811\pi\) | |||||||
\(978\) | 3.58258 | − | 20.8808i | 0.114558 | − | 0.667694i | ||||
\(979\) | − | 49.2982i | − | 1.57558i | ||||||
\(980\) | − | 15.6525i | − | 0.500000i | ||||||
\(981\) | 1.67544 | − | 4.73887i | 0.0534928 | − | 0.151301i | ||||
\(982\) | 7.00000 | − | 7.00000i | 0.223379 | − | 0.223379i | ||||
\(983\) | −14.1421 | + | 14.1421i | −0.451064 | + | 0.451064i | −0.895708 | − | 0.444644i | \(-0.853330\pi\) |
0.444644 | + | 0.895708i | \(0.353330\pi\) | |||||||
\(984\) | −11.7727 | − | 16.6491i | −0.375300 | − | 0.530754i | ||||
\(985\) | −5.81139 | + | 5.81139i | −0.185166 | + | 0.185166i | ||||
\(986\) | 5.19786i | 0.165534i | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −2.51317 | − | 2.51317i | −0.0799545 | − | 0.0799545i | ||||
\(989\) | −12.9574 | −0.412022 | ||||||||
\(990\) | 8.17697 | + | 17.1212i | 0.259881 | + | 0.544149i | ||||
\(991\) | −25.2982 | −0.803624 | −0.401812 | − | 0.915722i | \(-0.631620\pi\) | ||||
−0.401812 | + | 0.915722i | \(0.631620\pi\) | |||||||
\(992\) | −1.64371 | − | 1.64371i | −0.0521878 | − | 0.0521878i | ||||
\(993\) | 59.7038 | + | 10.2435i | 1.89464 | + | 0.325069i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −33.9039 | −1.07483 | ||||||||
\(996\) | 4.32456 | + | 6.11584i | 0.137029 | + | 0.193788i | ||||
\(997\) | 37.4605 | − | 37.4605i | 1.18639 | − | 1.18639i | 0.208327 | − | 0.978059i | \(-0.433198\pi\) |
0.978059 | − | 0.208327i | \(-0.0668017\pi\) | |||||||
\(998\) | −28.7433 | + | 28.7433i | −0.909852 | + | 0.909852i | ||||
\(999\) | 8.21854 | − | 2.32456i | 0.260023 | − | 0.0735457i |
(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 | 690.2.i.d.323.2 | yes | 8 | |
3.2 | odd | 2 | inner | 690.2.i.d.323.3 | yes | 8 | |
5.2 | odd | 4 | inner | 690.2.i.d.47.4 | yes | 8 | |
15.2 | even | 4 | inner | 690.2.i.d.47.1 | ✓ | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
690.2.i.d.47.1 | ✓ | 8 | 15.2 | even | 4 | inner | |
690.2.i.d.47.4 | yes | 8 | 5.2 | odd | 4 | inner | |
690.2.i.d.323.2 | yes | 8 | 1.1 | even | 1 | trivial | |
690.2.i.d.323.3 | yes | 8 | 3.2 | odd | 2 | inner |