Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [756,2,Mod(71,756)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(756, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 5, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("756.71");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 756 = 2^{2} \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 756.ba (of order \(6\), degree \(2\), not 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: | \(6.03669039281\) |
Analytic rank: | \(0\) |
Dimension: | \(72\) |
Relative dimension: | \(36\) over \(\Q(\zeta_{6})\) |
Twist minimal: | no (minimal twist has level 252) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 575.20 | ||
Character | \(\chi\) | \(=\) | 756.575 |
Dual form | 756.2.ba.a.71.20 |
$q$-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 \(\left(\mathbb{Z}/756\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(325\) | \(379\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.0405943 | + | 1.41363i | 0.0287045 | + | 0.999588i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.99670 | + | 0.114771i | −0.998352 | + | 0.0573853i | ||||
\(5\) | 2.16781 | − | 1.25159i | 0.969474 | − | 0.559726i | 0.0703980 | − | 0.997519i | \(-0.477573\pi\) |
0.899076 | + | 0.437793i | \(0.144240\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.866025 | + | 0.500000i | 0.327327 | + | 0.188982i | ||||
\(8\) | −0.243298 | − | 2.81794i | −0.0860189 | − | 0.996294i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 1.85728 | + | 3.01367i | 0.587324 | + | 0.953008i | ||||
\(11\) | 0.351433 | − | 0.608700i | 0.105961 | − | 0.183530i | −0.808169 | − | 0.588950i | \(-0.799541\pi\) |
0.914130 | + | 0.405420i | \(0.132875\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.55324 | + | 2.69030i | 0.430792 | + | 0.746154i | 0.996942 | − | 0.0781487i | \(-0.0249009\pi\) |
−0.566150 | + | 0.824302i | \(0.691568\pi\) | |||||||
\(14\) | −0.671660 | + | 1.24454i | −0.179509 | + | 0.332617i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 3.97366 | − | 0.458326i | 0.993414 | − | 0.114582i | ||||
\(17\) | − | 7.91554i | − | 1.91980i | −0.280343 | − | 0.959900i | \(-0.590448\pi\) | ||
0.280343 | − | 0.959900i | \(-0.409552\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 2.37413i | − | 0.544662i | −0.962204 | − | 0.272331i | \(-0.912205\pi\) | ||
0.962204 | − | 0.272331i | \(-0.0877945\pi\) | |||||||
\(20\) | −4.18483 | + | 2.74785i | −0.935756 | + | 0.614437i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0.874743 | + | 0.472087i | 0.186496 | + | 0.100649i | ||||
\(23\) | 0.346619 | + | 0.600362i | 0.0722751 | + | 0.125184i | 0.899898 | − | 0.436100i | \(-0.143641\pi\) |
−0.827623 | + | 0.561284i | \(0.810307\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.632931 | − | 1.09627i | 0.126586 | − | 0.219254i | ||||
\(26\) | −3.74003 | + | 2.30492i | −0.733481 | + | 0.452033i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −1.78658 | − | 0.898958i | −0.337632 | − | 0.169887i | ||||
\(29\) | 8.70126 | + | 5.02368i | 1.61578 | + | 0.932873i | 0.987994 | + | 0.154490i | \(0.0493735\pi\) |
0.627789 | + | 0.778383i | \(0.283960\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 7.34846 | − | 4.24264i | 1.31982 | − | 0.762000i | 0.336123 | − | 0.941818i | \(-0.390884\pi\) |
0.983700 | + | 0.179818i | \(0.0575509\pi\) | |||||||
\(32\) | 0.809212 | + | 5.59868i | 0.143050 | + | 0.989715i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 11.1896 | − | 0.321326i | 1.91901 | − | 0.0551069i | ||||
\(35\) | 2.50317 | 0.423113 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.85107 | 0.468712 | 0.234356 | − | 0.972151i | \(-0.424702\pi\) | ||||
0.234356 | + | 0.972151i | \(0.424702\pi\) | |||||||
\(38\) | 3.35614 | − | 0.0963760i | 0.544437 | − | 0.0156342i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −4.05432 | − | 5.80426i | −0.641044 | − | 0.917733i | ||||
\(41\) | −5.82034 | + | 3.36037i | −0.908984 | + | 0.524802i | −0.880104 | − | 0.474781i | \(-0.842527\pi\) |
−0.0288798 | + | 0.999583i | \(0.509194\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.17043 | + | 1.83045i | 0.483485 | + | 0.279140i | 0.721868 | − | 0.692031i | \(-0.243284\pi\) |
−0.238383 | + | 0.971171i | \(0.576617\pi\) | |||||||
\(44\) | −0.631847 | + | 1.25573i | −0.0952545 | + | 0.189308i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −0.834620 | + | 0.514363i | −0.123058 | + | 0.0758387i | ||||
\(47\) | −3.67787 | + | 6.37026i | −0.536473 | + | 0.929198i | 0.462618 | + | 0.886558i | \(0.346910\pi\) |
−0.999091 | + | 0.0426400i | \(0.986423\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0.500000 | + | 0.866025i | 0.0714286 | + | 0.123718i | ||||
\(50\) | 1.57541 | + | 0.850229i | 0.222797 | + | 0.120241i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −3.41013 | − | 5.19346i | −0.472900 | − | 0.720203i | ||||
\(53\) | − | 0.889576i | − | 0.122193i | −0.998132 | − | 0.0610964i | \(-0.980540\pi\) | ||
0.998132 | − | 0.0610964i | \(-0.0194597\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 1.75939i | − | 0.237237i | ||||||
\(56\) | 1.19827 | − | 2.56206i | 0.160125 | − | 0.342370i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −6.74840 | + | 12.5043i | −0.886109 | + | 1.64190i | ||||
\(59\) | −3.63052 | − | 6.28824i | −0.472653 | − | 0.818660i | 0.526857 | − | 0.849954i | \(-0.323370\pi\) |
−0.999510 | + | 0.0312945i | \(0.990037\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.39732 | + | 4.15228i | −0.306946 | + | 0.531645i | −0.977693 | − | 0.210041i | \(-0.932640\pi\) |
0.670747 | + | 0.741686i | \(0.265974\pi\) | |||||||
\(62\) | 6.29583 | + | 10.2158i | 0.799571 | + | 1.29741i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −7.88161 | + | 1.37120i | −0.985201 | + | 0.171400i | ||||
\(65\) | 6.73427 | + | 3.88803i | 0.835283 | + | 0.482251i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −7.40811 | + | 4.27707i | −0.905044 | + | 0.522528i | −0.878833 | − | 0.477129i | \(-0.841677\pi\) |
−0.0262109 | + | 0.999656i | \(0.508344\pi\) | |||||||
\(68\) | 0.908472 | + | 15.8050i | 0.110168 | + | 1.91664i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0.101614 | + | 3.53856i | 0.0121452 | + | 0.422939i | ||||
\(71\) | −6.34514 | −0.753030 | −0.376515 | − | 0.926411i | \(-0.622878\pi\) | ||||
−0.376515 | + | 0.926411i | \(0.622878\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 8.20222 | 0.959998 | 0.479999 | − | 0.877269i | \(-0.340637\pi\) | ||||
0.479999 | + | 0.877269i | \(0.340637\pi\) | |||||||
\(74\) | 0.115737 | + | 4.03035i | 0.0134542 | + | 0.468519i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0.272480 | + | 4.74043i | 0.0312556 | + | 0.543764i | ||||
\(77\) | 0.608700 | − | 0.351433i | 0.0693678 | − | 0.0400495i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.27268 | + | 1.31214i | 0.255697 | + | 0.147627i | 0.622370 | − | 0.782723i | \(-0.286170\pi\) |
−0.366673 | + | 0.930350i | \(0.619503\pi\) | |||||||
\(80\) | 8.04049 | − | 5.96693i | 0.898954 | − | 0.667123i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −4.98660 | − | 8.09139i | −0.550678 | − | 0.893545i | ||||
\(83\) | 6.50432 | − | 11.2658i | 0.713942 | − | 1.23658i | −0.249425 | − | 0.968394i | \(-0.580241\pi\) |
0.963366 | − | 0.268189i | \(-0.0864252\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −9.90697 | − | 17.1594i | −1.07456 | − | 1.86120i | ||||
\(86\) | −2.45887 | + | 4.55612i | −0.265147 | + | 0.491299i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −1.80079 | − | 0.842223i | −0.191964 | − | 0.0897813i | ||||
\(89\) | − | 1.71842i | − | 0.182152i | −0.995844 | − | 0.0910760i | \(-0.970969\pi\) | ||
0.995844 | − | 0.0910760i | \(-0.0290306\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.10649i | 0.325648i | ||||||||
\(92\) | −0.761000 | − | 1.15896i | −0.0793398 | − | 0.120830i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −9.15449 | − | 4.94056i | −0.944214 | − | 0.509579i | ||||
\(95\) | −2.97142 | − | 5.14665i | −0.304861 | − | 0.528035i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −6.81083 | + | 11.7967i | −0.691535 | + | 1.19777i | 0.279800 | + | 0.960058i | \(0.409732\pi\) |
−0.971335 | + | 0.237716i | \(0.923601\pi\) | |||||||
\(98\) | −1.20394 | + | 0.741971i | −0.121617 | + | 0.0749504i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −1.13796 | + | 2.26157i | −0.113796 | + | 0.226157i | ||||
\(101\) | −2.23784 | − | 1.29202i | −0.222673 | − | 0.128560i | 0.384514 | − | 0.923119i | \(-0.374369\pi\) |
−0.607187 | + | 0.794559i | \(0.707702\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 11.6579 | − | 6.73069i | 1.14869 | − | 0.663195i | 0.200120 | − | 0.979771i | \(-0.435867\pi\) |
0.948567 | + | 0.316576i | \(0.102533\pi\) | |||||||
\(104\) | 7.20320 | − | 5.03149i | 0.706332 | − | 0.493379i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1.25753 | − | 0.0361117i | 0.122142 | − | 0.00350748i | ||||
\(107\) | −17.0371 | −1.64703 | −0.823517 | − | 0.567291i | \(-0.807991\pi\) | ||||
−0.823517 | + | 0.567291i | \(0.807991\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −2.43459 | −0.233191 | −0.116596 | − | 0.993179i | \(-0.537198\pi\) | ||||
−0.116596 | + | 0.993179i | \(0.537198\pi\) | |||||||
\(110\) | 2.48713 | − | 0.0714214i | 0.237139 | − | 0.00680976i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 3.67045 | + | 1.58991i | 0.346825 | + | 0.150232i | ||||
\(113\) | 4.13789 | − | 2.38901i | 0.389260 | − | 0.224739i | −0.292580 | − | 0.956241i | \(-0.594514\pi\) |
0.681839 | + | 0.731502i | \(0.261180\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.50281 | + | 0.867647i | 0.140138 | + | 0.0809085i | ||||
\(116\) | −17.9504 | − | 9.03215i | −1.66665 | − | 0.838614i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 8.74188 | − | 5.38748i | 0.804755 | − | 0.495958i | ||||
\(119\) | 3.95777 | − | 6.85506i | 0.362808 | − | 0.628402i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.25299 | + | 9.09844i | 0.477544 | + | 0.827131i | ||||
\(122\) | −5.96711 | − | 3.22037i | −0.540237 | − | 0.291559i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −14.1858 | + | 9.31468i | −1.27392 | + | 0.836483i | ||||
\(125\) | 9.34718i | 0.836037i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 4.91393i | − | 0.436041i | −0.975944 | − | 0.218020i | \(-0.930040\pi\) | ||
0.975944 | − | 0.218020i | \(-0.0699599\pi\) | |||||||
\(128\) | −2.25832 | − | 11.0860i | −0.199609 | − | 0.979876i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −5.22287 | + | 9.67760i | −0.458076 | + | 0.848782i | ||||
\(131\) | 2.61968 | + | 4.53741i | 0.228882 | + | 0.396435i | 0.957477 | − | 0.288509i | \(-0.0931596\pi\) |
−0.728595 | + | 0.684945i | \(0.759826\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.18706 | − | 2.05605i | 0.102931 | − | 0.178282i | ||||
\(134\) | −6.34693 | − | 10.2987i | −0.548291 | − | 0.889672i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −22.3055 | + | 1.92584i | −1.91268 | + | 0.165139i | ||||
\(137\) | −9.03659 | − | 5.21728i | −0.772048 | − | 0.445742i | 0.0615566 | − | 0.998104i | \(-0.480394\pi\) |
−0.833605 | + | 0.552361i | \(0.813727\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 10.2848 | − | 5.93796i | 0.872349 | − | 0.503651i | 0.00422072 | − | 0.999991i | \(-0.498656\pi\) |
0.868128 | + | 0.496340i | \(0.165323\pi\) | |||||||
\(140\) | −4.99809 | + | 0.287291i | −0.422416 | + | 0.0242805i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −0.257577 | − | 8.96969i | −0.0216153 | − | 0.752719i | ||||
\(143\) | 2.18344 | 0.182589 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 25.1502 | 2.08861 | ||||||||
\(146\) | 0.332963 | + | 11.5949i | 0.0275563 | + | 0.959602i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −5.69273 | + | 0.327219i | −0.467940 | + | 0.0268972i | ||||
\(149\) | −15.3300 | + | 8.85079i | −1.25588 | + | 0.725085i | −0.972272 | − | 0.233854i | \(-0.924866\pi\) |
−0.283612 | + | 0.958939i | \(0.591533\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −18.1796 | − | 10.4960i | −1.47944 | − | 0.854152i | −0.479706 | − | 0.877429i | \(-0.659257\pi\) |
−0.999729 | + | 0.0232767i | \(0.992590\pi\) | |||||||
\(152\) | −6.69015 | + | 0.577621i | −0.542643 | + | 0.0468512i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0.521507 | + | 0.846211i | 0.0420242 | + | 0.0681896i | ||||
\(155\) | 10.6200 | − | 18.3945i | 0.853022 | − | 1.47748i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −0.841990 | − | 1.45837i | −0.0671981 | − | 0.116391i | 0.830469 | − | 0.557065i | \(-0.188073\pi\) |
−0.897667 | + | 0.440675i | \(0.854739\pi\) | |||||||
\(158\) | −1.76262 | + | 3.26600i | −0.140226 | + | 0.259829i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 8.76144 | + | 11.1241i | 0.692652 | + | 0.879435i | ||||
\(161\) | 0.693239i | 0.0546349i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 14.9299i | − | 1.16940i | −0.811249 | − | 0.584700i | \(-0.801212\pi\) | ||
0.811249 | − | 0.584700i | \(-0.198788\pi\) | |||||||
\(164\) | 11.2358 | − | 7.37767i | 0.877370 | − | 0.576100i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 16.1897 | + | 8.73738i | 1.25657 | + | 0.678152i | ||||
\(167\) | −1.17066 | − | 2.02764i | −0.0905885 | − | 0.156904i | 0.817170 | − | 0.576396i | \(-0.195541\pi\) |
−0.907759 | + | 0.419492i | \(0.862208\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.67487 | − | 2.90097i | 0.128836 | − | 0.223151i | ||||
\(170\) | 23.8549 | − | 14.7014i | 1.82958 | − | 1.12754i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −6.54048 | − | 3.29099i | −0.498707 | − | 0.250935i | ||||
\(173\) | −0.875908 | − | 0.505706i | −0.0665940 | − | 0.0384481i | 0.466333 | − | 0.884609i | \(-0.345575\pi\) |
−0.532927 | + | 0.846161i | \(0.678908\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.09627 | − | 0.632931i | 0.0828702 | − | 0.0478451i | ||||
\(176\) | 1.11749 | − | 2.57984i | 0.0842341 | − | 0.194462i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 2.42921 | − | 0.0697580i | 0.182077 | − | 0.00522858i | ||||
\(179\) | 11.8651 | 0.886837 | 0.443419 | − | 0.896315i | \(-0.353765\pi\) | ||||
0.443419 | + | 0.896315i | \(0.353765\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −11.7216 | −0.871262 | −0.435631 | − | 0.900125i | \(-0.643475\pi\) | ||||
−0.435631 | + | 0.900125i | \(0.643475\pi\) | |||||||
\(182\) | −4.39142 | + | 0.126106i | −0.325514 | + | 0.00934757i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 1.60746 | − | 1.12282i | 0.118503 | − | 0.0827754i | ||||
\(185\) | 6.18057 | − | 3.56835i | 0.454404 | − | 0.262350i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −4.81819 | − | 2.78178i | −0.352341 | − | 0.203424i | ||||
\(188\) | 6.61250 | − | 13.1416i | 0.482266 | − | 0.958452i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 7.15484 | − | 4.40942i | 0.519067 | − | 0.319893i | ||||
\(191\) | −3.38132 | + | 5.85662i | −0.244664 | + | 0.423770i | −0.962037 | − | 0.272919i | \(-0.912011\pi\) |
0.717373 | + | 0.696689i | \(0.245344\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1.38307 | − | 2.39554i | −0.0995553 | − | 0.172435i | 0.811945 | − | 0.583733i | \(-0.198409\pi\) |
−0.911501 | + | 0.411299i | \(0.865075\pi\) | |||||||
\(194\) | −16.9527 | − | 9.14912i | −1.21713 | − | 0.656869i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1.09775 | − | 1.67181i | −0.0784105 | − | 0.119415i | ||||
\(197\) | − | 17.2636i | − | 1.22998i | −0.788536 | − | 0.614989i | \(-0.789161\pi\) | ||
0.788536 | − | 0.614989i | \(-0.210839\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 14.4922i | 1.02732i | 0.857993 | + | 0.513662i | \(0.171711\pi\) | ||||
−0.857993 | + | 0.513662i | \(0.828289\pi\) | |||||||
\(200\) | −3.24322 | − | 1.51684i | −0.229330 | − | 0.107257i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 1.73559 | − | 3.21592i | 0.122116 | − | 0.226272i | ||||
\(203\) | 5.02368 | + | 8.70126i | 0.352593 | + | 0.610709i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −8.41159 | + | 14.5693i | −0.587491 | + | 1.01756i | ||||
\(206\) | 9.98796 | + | 16.2067i | 0.695894 | + | 1.12918i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 7.40509 | + | 9.97842i | 0.513450 | + | 0.691879i | ||||
\(209\) | −1.44513 | − | 0.834347i | −0.0999618 | − | 0.0577130i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −22.1795 | + | 12.8053i | −1.52690 | + | 0.881555i | −0.527407 | + | 0.849612i | \(0.676836\pi\) |
−0.999490 | + | 0.0319420i | \(0.989831\pi\) | |||||||
\(212\) | 0.102097 | + | 1.77622i | 0.00701207 | + | 0.121991i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −0.691607 | − | 24.0841i | −0.0472773 | − | 1.64636i | ||||
\(215\) | 9.16384 | 0.624968 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 8.48527 | 0.576018 | ||||||||
\(218\) | −0.0988305 | − | 3.44161i | −0.00669364 | − | 0.233095i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0.201927 | + | 3.51299i | 0.0136139 | + | 0.236846i | ||||
\(221\) | 21.2951 | − | 12.2948i | 1.43247 | − | 0.827035i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −13.2137 | − | 7.62891i | −0.884853 | − | 0.510870i | −0.0125973 | − | 0.999921i | \(-0.504010\pi\) |
−0.872255 | + | 0.489051i | \(0.837343\pi\) | |||||||
\(224\) | −2.09854 | + | 5.25320i | −0.140215 | + | 0.350994i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 3.54515 | + | 5.75247i | 0.235820 | + | 0.382648i | ||||
\(227\) | −3.88279 | + | 6.72519i | −0.257710 | + | 0.446367i | −0.965628 | − | 0.259928i | \(-0.916301\pi\) |
0.707918 | + | 0.706295i | \(0.249635\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −5.70048 | − | 9.87351i | −0.376698 | − | 0.652460i | 0.613882 | − | 0.789398i | \(-0.289607\pi\) |
−0.990580 | + | 0.136938i | \(0.956274\pi\) | |||||||
\(230\) | −1.16553 | + | 2.15964i | −0.0768526 | + | 0.142402i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 12.0394 | − | 25.7419i | 0.790428 | − | 1.69004i | ||||
\(233\) | 19.4113i | 1.27167i | 0.771824 | + | 0.635837i | \(0.219345\pi\) | ||||
−0.771824 | + | 0.635837i | \(0.780655\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 18.4127i | 1.20111i | ||||||||
\(236\) | 7.97078 | + | 12.1391i | 0.518853 | + | 0.790187i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 9.85118 | + | 5.31655i | 0.638557 | + | 0.344621i | ||||
\(239\) | 3.57434 | + | 6.19093i | 0.231205 | + | 0.400458i | 0.958163 | − | 0.286224i | \(-0.0924000\pi\) |
−0.726958 | + | 0.686682i | \(0.759067\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.19735 | + | 2.07386i | −0.0771279 | + | 0.133589i | −0.902010 | − | 0.431716i | \(-0.857908\pi\) |
0.824882 | + | 0.565305i | \(0.191242\pi\) | |||||||
\(242\) | −12.6486 | + | 7.79513i | −0.813083 | + | 0.501090i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 4.31018 | − | 8.56602i | 0.275931 | − | 0.548383i | ||||
\(245\) | 2.16781 | + | 1.25159i | 0.138496 | + | 0.0799609i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 6.38710 | − | 3.68759i | 0.406401 | − | 0.234636i | ||||
\(248\) | −13.7434 | − | 19.6753i | −0.872705 | − | 1.24938i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −13.2135 | + | 0.379442i | −0.835693 | + | 0.0239980i | ||||
\(251\) | 3.05973 | 0.193129 | 0.0965644 | − | 0.995327i | \(-0.469215\pi\) | ||||
0.0965644 | + | 0.995327i | \(0.469215\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0.487254 | 0.0306334 | ||||||||
\(254\) | 6.94648 | − | 0.199478i | 0.435861 | − | 0.0125163i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 15.5799 | − | 3.64246i | 0.973742 | − | 0.227654i | ||||
\(257\) | −17.1928 | + | 9.92624i | −1.07245 | + | 0.619182i | −0.928851 | − | 0.370453i | \(-0.879202\pi\) |
−0.143603 | + | 0.989635i | \(0.545869\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2.46909 | + | 1.42553i | 0.153422 | + | 0.0885783i | ||||
\(260\) | −13.8926 | − | 6.99035i | −0.861581 | − | 0.433523i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −6.30788 | + | 3.88745i | −0.389702 | + | 0.240167i | ||||
\(263\) | −9.51239 | + | 16.4759i | −0.586559 | + | 1.01595i | 0.408120 | + | 0.912928i | \(0.366184\pi\) |
−0.994679 | + | 0.103022i | \(0.967149\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1.11338 | − | 1.92843i | −0.0683944 | − | 0.118463i | ||||
\(266\) | 2.95469 | + | 1.59460i | 0.181164 | + | 0.0977715i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 14.3009 | − | 9.39028i | 0.873567 | − | 0.573603i | ||||
\(269\) | − | 27.0790i | − | 1.65103i | −0.564378 | − | 0.825517i | \(-0.690884\pi\) | ||
0.564378 | − | 0.825517i | \(-0.309116\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 29.1249i | 1.76921i | 0.466337 | + | 0.884607i | \(0.345573\pi\) | ||||
−0.466337 | + | 0.884607i | \(0.654427\pi\) | |||||||
\(272\) | −3.62790 | − | 31.4536i | −0.219974 | − | 1.90716i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 7.00847 | − | 12.9862i | 0.423397 | − | 0.784525i | ||||
\(275\) | −0.444866 | − | 0.770531i | −0.0268264 | − | 0.0464648i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 8.22279 | − | 14.2423i | 0.494060 | − | 0.855737i | −0.505917 | − | 0.862582i | \(-0.668846\pi\) |
0.999977 | + | 0.00684565i | \(0.00217905\pi\) | |||||||
\(278\) | 8.81158 | + | 14.2979i | 0.528484 | + | 0.857532i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −0.609017 | − | 7.05379i | −0.0363957 | − | 0.421545i | ||||
\(281\) | −5.47490 | − | 3.16093i | −0.326605 | − | 0.188566i | 0.327728 | − | 0.944772i | \(-0.393717\pi\) |
−0.654333 | + | 0.756207i | \(0.727050\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 7.14839 | − | 4.12712i | 0.424927 | − | 0.245332i | −0.272256 | − | 0.962225i | \(-0.587770\pi\) |
0.697183 | + | 0.716893i | \(0.254436\pi\) | |||||||
\(284\) | 12.6694 | − | 0.728236i | 0.751789 | − | 0.0432129i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0.0886354 | + | 3.08658i | 0.00524112 | + | 0.182514i | ||||
\(287\) | −6.72075 | −0.396713 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −45.6557 | −2.68563 | ||||||||
\(290\) | 1.02096 | + | 35.5531i | 0.0599526 | + | 2.08775i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −16.3774 | + | 0.941375i | −0.958416 | + | 0.0550898i | ||||
\(293\) | −6.70404 | + | 3.87058i | −0.391654 | + | 0.226122i | −0.682877 | − | 0.730534i | \(-0.739271\pi\) |
0.291222 | + | 0.956655i | \(0.405938\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −15.7405 | − | 9.08781i | −0.916450 | − | 0.529113i | ||||
\(296\) | −0.693659 | − | 8.03414i | −0.0403181 | − | 0.466975i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −13.1341 | − | 21.3117i | −0.760836 | − | 1.23455i | ||||
\(299\) | −1.07677 | + | 1.86502i | −0.0622711 | + | 0.107857i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.83045 | + | 3.17043i | 0.105505 | + | 0.182740i | ||||
\(302\) | 14.0995 | − | 26.1253i | 0.811334 | − | 1.50334i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −1.08812 | − | 9.43396i | −0.0624082 | − | 0.541075i | ||||
\(305\) | 12.0018i | 0.687222i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 14.7032i | 0.839154i | 0.907720 | + | 0.419577i | \(0.137822\pi\) | ||||
−0.907720 | + | 0.419577i | \(0.862178\pi\) | |||||||
\(308\) | −1.17506 | + | 0.771569i | −0.0669553 | + | 0.0439642i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 26.4341 | + | 14.2661i | 1.50135 | + | 0.810261i | ||||
\(311\) | 6.26710 | + | 10.8549i | 0.355375 | + | 0.615527i | 0.987182 | − | 0.159599i | \(-0.0510200\pi\) |
−0.631807 | + | 0.775125i | \(0.717687\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −11.6110 | + | 20.1108i | −0.656292 | + | 1.13673i | 0.325276 | + | 0.945619i | \(0.394543\pi\) |
−0.981568 | + | 0.191112i | \(0.938790\pi\) | |||||||
\(314\) | 2.02742 | − | 1.24946i | 0.114414 | − | 0.0705113i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −4.68847 | − | 2.35911i | −0.263747 | − | 0.132710i | ||||
\(317\) | −5.93134 | − | 3.42446i | −0.333137 | − | 0.192337i | 0.324096 | − | 0.946024i | \(-0.394940\pi\) |
−0.657233 | + | 0.753687i | \(0.728273\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 6.11582 | − | 3.53097i | 0.342420 | − | 0.197697i | ||||
\(320\) | −15.3697 | + | 12.8370i | −0.859190 | + | 0.717611i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −0.979983 | + | 0.0281415i | −0.0546123 | + | 0.00156827i | ||||
\(323\) | −18.7925 | −1.04564 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 3.93239 | 0.218129 | ||||||||
\(326\) | 21.1054 | − | 0.606069i | 1.16892 | − | 0.0335671i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 10.8854 | + | 15.5838i | 0.601047 | + | 0.860472i | ||||
\(329\) | −6.37026 | + | 3.67787i | −0.351204 | + | 0.202768i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −6.98234 | − | 4.03126i | −0.383784 | − | 0.221578i | 0.295679 | − | 0.955287i | \(-0.404454\pi\) |
−0.679463 | + | 0.733709i | \(0.737787\pi\) | |||||||
\(332\) | −11.6942 | + | 23.2410i | −0.641803 | + | 1.27552i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 2.81882 | − | 1.73719i | 0.154239 | − | 0.0950550i | ||||
\(335\) | −10.7062 | + | 18.5438i | −0.584944 | + | 1.01315i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −8.08375 | − | 14.0015i | −0.440350 | − | 0.762708i | 0.557365 | − | 0.830267i | \(-0.311812\pi\) |
−0.997715 | + | 0.0675590i | \(0.978479\pi\) | |||||||
\(338\) | 4.16888 | + | 2.24989i | 0.226757 | + | 0.122378i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 21.7507 | + | 33.1252i | 1.17960 | + | 1.79646i | ||||
\(341\) | − | 5.96401i | − | 0.322969i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000i | 0.0539949i | ||||||||
\(344\) | 4.38673 | − | 9.37942i | 0.236517 | − | 0.505705i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0.679324 | − | 1.25874i | 0.0365207 | − | 0.0676702i | ||||
\(347\) | 3.82900 | + | 6.63203i | 0.205552 | + | 0.356026i | 0.950308 | − | 0.311310i | \(-0.100768\pi\) |
−0.744757 | + | 0.667336i | \(0.767434\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 4.40927 | − | 7.63708i | 0.236023 | − | 0.408803i | −0.723547 | − | 0.690275i | \(-0.757489\pi\) |
0.959569 | + | 0.281472i | \(0.0908227\pi\) | |||||||
\(350\) | 0.939234 | + | 1.52403i | 0.0502042 | + | 0.0814627i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 3.69230 | + | 1.47499i | 0.196800 | + | 0.0786174i | ||||
\(353\) | 2.81435 | + | 1.62487i | 0.149793 | + | 0.0864830i | 0.573023 | − | 0.819539i | \(-0.305771\pi\) |
−0.423230 | + | 0.906022i | \(0.639104\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −13.7551 | + | 7.94149i | −0.730043 | + | 0.421490i | ||||
\(356\) | 0.197224 | + | 3.43117i | 0.0104529 | + | 0.181852i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0.481654 | + | 16.7728i | 0.0254562 | + | 0.886472i | ||||
\(359\) | 28.4033 | 1.49907 | 0.749533 | − | 0.661967i | \(-0.230278\pi\) | ||||
0.749533 | + | 0.661967i | \(0.230278\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 13.3635 | 0.703343 | ||||||||
\(362\) | −0.475831 | − | 16.5701i | −0.0250091 | − | 0.870903i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −0.356534 | − | 6.20273i | −0.0186874 | − | 0.325112i | ||||
\(365\) | 17.7809 | − | 10.2658i | 0.930692 | − | 0.537336i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 4.00164 | + | 2.31035i | 0.208884 | + | 0.120599i | 0.600793 | − | 0.799405i | \(-0.294852\pi\) |
−0.391909 | + | 0.920004i | \(0.628185\pi\) | |||||||
\(368\) | 1.65251 | + | 2.22677i | 0.0861429 | + | 0.116078i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 5.29523 | + | 8.59218i | 0.275286 | + | 0.446686i | ||||
\(371\) | 0.444788 | − | 0.770396i | 0.0230923 | − | 0.0399970i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −13.7859 | − | 23.8779i | −0.713808 | − | 1.23635i | −0.963417 | − | 0.268005i | \(-0.913636\pi\) |
0.249609 | − | 0.968347i | \(-0.419698\pi\) | |||||||
\(374\) | 3.73682 | − | 6.92406i | 0.193226 | − | 0.358035i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 18.8458 | + | 8.81416i | 0.971900 | + | 0.454556i | ||||
\(377\) | 31.2120i | 1.60750i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 20.5766i | 1.05695i | 0.848949 | + | 0.528475i | \(0.177236\pi\) | ||||
−0.848949 | + | 0.528475i | \(0.822764\pi\) | |||||||
\(380\) | 6.52373 | + | 9.93531i | 0.334660 | + | 0.509671i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −8.41636 | − | 4.54219i | −0.430618 | − | 0.232399i | ||||
\(383\) | 0.0457558 | + | 0.0792514i | 0.00233801 | + | 0.00404955i | 0.867192 | − | 0.497974i | \(-0.165922\pi\) |
−0.864854 | + | 0.502023i | \(0.832589\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0.879697 | − | 1.52368i | 0.0448335 | − | 0.0776539i | ||||
\(386\) | 3.33027 | − | 2.05239i | 0.169506 | − | 0.104464i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 12.2453 | − | 24.3362i | 0.621661 | − | 1.23548i | ||||
\(389\) | 1.65481 | + | 0.955404i | 0.0839021 | + | 0.0484409i | 0.541364 | − | 0.840788i | \(-0.317908\pi\) |
−0.457462 | + | 0.889229i | \(0.651241\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 4.75219 | − | 2.74368i | 0.240329 | − | 0.138754i | ||||
\(392\) | 2.31876 | − | 1.61967i | 0.117115 | − | 0.0818059i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 24.4043 | − | 0.700802i | 1.22947 | − | 0.0353059i | ||||
\(395\) | 6.56900 | 0.330522 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 30.4353 | 1.52750 | 0.763751 | − | 0.645511i | \(-0.223355\pi\) | ||||
0.763751 | + | 0.645511i | \(0.223355\pi\) | |||||||
\(398\) | −20.4866 | + | 0.588300i | −1.02690 | + | 0.0294888i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 2.01260 | − | 4.64629i | 0.100630 | − | 0.232314i | ||||
\(401\) | −18.9221 | + | 10.9247i | −0.944922 | + | 0.545551i | −0.891500 | − | 0.453021i | \(-0.850346\pi\) |
−0.0534223 | + | 0.998572i | \(0.517013\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 22.8279 | + | 13.1797i | 1.13714 | + | 0.656527i | ||||
\(404\) | 4.61658 | + | 2.32294i | 0.229684 | + | 0.115570i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −12.0964 | + | 7.45484i | −0.600336 | + | 0.369978i | ||||
\(407\) | 1.00196 | − | 1.73544i | 0.0496653 | − | 0.0860228i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 2.23786 | + | 3.87609i | 0.110655 | + | 0.191660i | 0.916035 | − | 0.401099i | \(-0.131372\pi\) |
−0.805379 | + | 0.592760i | \(0.798038\pi\) | |||||||
\(410\) | −20.9371 | − | 11.2994i | −1.03401 | − | 0.558040i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −22.5049 | + | 14.7772i | −1.10874 | + | 0.728020i | ||||
\(413\) | − | 7.26104i | − | 0.357292i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 32.5628i | − | 1.59845i | ||||||
\(416\) | −13.8052 | + | 10.8731i | −0.676855 | + | 0.533099i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 1.12079 | − | 2.07675i | 0.0548198 | − | 0.101577i | ||||
\(419\) | 11.4022 | + | 19.7492i | 0.557033 | + | 0.964809i | 0.997742 | + | 0.0671595i | \(0.0213936\pi\) |
−0.440709 | + | 0.897650i | \(0.645273\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −14.0510 | + | 24.3370i | −0.684803 | + | 1.18611i | 0.288696 | + | 0.957421i | \(0.406778\pi\) |
−0.973499 | + | 0.228693i | \(0.926555\pi\) | |||||||
\(422\) | −19.0024 | − | 30.8337i | −0.925020 | − | 1.50096i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −2.50678 | + | 0.216432i | −0.121740 | + | 0.0105109i | ||||
\(425\) | −8.67756 | − | 5.00999i | −0.420924 | − | 0.243020i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −4.15228 | + | 2.39732i | −0.200943 | + | 0.116015i | ||||
\(428\) | 34.0180 | − | 1.95535i | 1.64432 | − | 0.0945156i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0.371999 | + | 12.9543i | 0.0179394 | + | 0.624711i | ||||
\(431\) | 0.610755 | 0.0294190 | 0.0147095 | − | 0.999892i | \(-0.495318\pi\) | ||||
0.0147095 | + | 0.999892i | \(0.495318\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 10.5169 | 0.505410 | 0.252705 | − | 0.967543i | \(-0.418680\pi\) | ||||
0.252705 | + | 0.967543i | \(0.418680\pi\) | |||||||
\(434\) | 0.344454 | + | 11.9950i | 0.0165343 | + | 0.575781i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 4.86116 | − | 0.279420i | 0.232807 | − | 0.0133818i | ||||
\(437\) | 1.42534 | − | 0.822918i | 0.0681830 | − | 0.0393655i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 32.6334 | + | 18.8409i | 1.55751 | + | 0.899227i | 0.997495 | + | 0.0707423i | \(0.0225368\pi\) |
0.560012 | + | 0.828485i | \(0.310797\pi\) | |||||||
\(440\) | −4.95787 | + | 0.428057i | −0.236357 | + | 0.0204068i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 18.2447 | + | 29.6044i | 0.867812 | + | 1.40814i | ||||
\(443\) | −20.7455 | + | 35.9322i | −0.985647 | + | 1.70719i | −0.346622 | + | 0.938005i | \(0.612671\pi\) |
−0.639025 | + | 0.769186i | \(0.720662\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −2.15075 | − | 3.72520i | −0.101955 | − | 0.176592i | ||||
\(446\) | 10.2481 | − | 18.9889i | 0.485260 | − | 0.899152i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −7.51128 | − | 2.75331i | −0.354874 | − | 0.130082i | ||||
\(449\) | 31.9656i | 1.50855i | 0.656559 | + | 0.754275i | \(0.272011\pi\) | ||||
−0.656559 | + | 0.754275i | \(0.727989\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 4.72379i | 0.222434i | ||||||||
\(452\) | −7.98795 | + | 5.24506i | −0.375722 | + | 0.246707i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −9.66456 | − | 5.21583i | −0.453580 | − | 0.244791i | ||||
\(455\) | 3.88803 | + | 6.73427i | 0.182274 | + | 0.315707i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −14.8515 | + | 25.7236i | −0.694724 | + | 1.20330i | 0.275549 | + | 0.961287i | \(0.411140\pi\) |
−0.970274 | + | 0.242011i | \(0.922193\pi\) | |||||||
\(458\) | 13.7261 | − | 8.45918i | 0.641378 | − | 0.395271i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −3.10025 | − | 1.55996i | −0.144550 | − | 0.0727333i | ||||
\(461\) | 8.96753 | + | 5.17741i | 0.417659 | + | 0.241136i | 0.694075 | − | 0.719902i | \(-0.255813\pi\) |
−0.276416 | + | 0.961038i | \(0.589147\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 13.7219 | − | 7.92236i | 0.637712 | − | 0.368183i | −0.146021 | − | 0.989282i | \(-0.546647\pi\) |
0.783733 | + | 0.621098i | \(0.213313\pi\) | |||||||
\(464\) | 36.8783 | + | 15.9743i | 1.71203 | + | 0.741590i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −27.4403 | + | 0.787986i | −1.27115 | + | 0.0365028i | ||||
\(467\) | 27.9844 | 1.29496 | 0.647481 | − | 0.762081i | \(-0.275822\pi\) | ||||
0.647481 | + | 0.762081i | \(0.275822\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −8.55414 | −0.394994 | ||||||||
\(470\) | −26.0287 | + | 0.747450i | −1.20062 | + | 0.0344773i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −16.8366 | + | 11.7605i | −0.774968 | + | 0.541322i | ||||
\(473\) | 2.22839 | − | 1.28656i | 0.102461 | − | 0.0591560i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −2.60268 | − | 1.50266i | −0.119419 | − | 0.0689467i | ||||
\(476\) | −7.11573 | + | 14.1418i | −0.326149 | + | 0.648186i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −8.60659 | + | 5.30411i | −0.393656 | + | 0.242604i | ||||
\(479\) | −11.5844 | + | 20.0648i | −0.529306 | + | 0.916785i | 0.470110 | + | 0.882608i | \(0.344214\pi\) |
−0.999416 | + | 0.0341768i | \(0.989119\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 4.42840 | + | 7.67021i | 0.201918 | + | 0.349731i | ||||
\(482\) | −2.98028 | − | 1.60842i | −0.135748 | − | 0.0732615i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −11.5329 | − | 17.5640i | −0.524223 | − | 0.798364i | ||||
\(485\) | 34.0973i | 1.54828i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 13.8456i | 0.627406i | 0.949521 | + | 0.313703i | \(0.101570\pi\) | ||||
−0.949521 | + | 0.313703i | \(0.898430\pi\) | |||||||
\(488\) | 12.2842 | + | 5.74527i | 0.556078 | + | 0.260076i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −1.68128 | + | 3.11529i | −0.0759524 | + | 0.140734i | ||||
\(491\) | −1.97999 | − | 3.42944i | −0.0893557 | − | 0.154769i | 0.817883 | − | 0.575384i | \(-0.195147\pi\) |
−0.907239 | + | 0.420616i | \(0.861814\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 39.7651 | − | 68.8752i | 1.79093 | − | 3.10198i | ||||
\(494\) | 5.47218 | + | 8.87931i | 0.246205 | + | 0.399499i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 27.2557 | − | 20.2268i | 1.22382 | − | 0.908209i | ||||
\(497\) | −5.49505 | − | 3.17257i | −0.246487 | − | 0.142309i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −18.6834 | + | 10.7868i | −0.836382 | + | 0.482886i | −0.856033 | − | 0.516921i | \(-0.827078\pi\) |
0.0196506 | + | 0.999807i | \(0.493745\pi\) | |||||||
\(500\) | −1.07278 | − | 18.6636i | −0.0479763 | − | 0.834660i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0.124208 | + | 4.32534i | 0.00554366 | + | 0.193049i | ||||
\(503\) | −24.7621 | −1.10409 | −0.552044 | − | 0.833815i | \(-0.686152\pi\) | ||||
−0.552044 | + | 0.833815i | \(0.686152\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −6.46827 | −0.287834 | ||||||||
\(506\) | 0.0197797 | + | 0.688797i | 0.000879317 | + | 0.0306208i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0.563975 | + | 9.81166i | 0.0250224 | + | 0.435322i | ||||
\(509\) | 22.5133 | − | 12.9980i | 0.997882 | − | 0.576128i | 0.0902614 | − | 0.995918i | \(-0.471230\pi\) |
0.907621 | + | 0.419790i | \(0.137896\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 7.10333 | + | 4.10111i | 0.314233 | + | 0.181422i | ||||
\(512\) | 5.78155 | + | 21.8763i | 0.255511 | + | 0.966806i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −14.7300 | − | 23.9013i | −0.649711 | − | 1.05424i | ||||
\(515\) | 16.8481 | − | 29.1817i | 0.742415 | − | 1.28590i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2.58505 | + | 4.47744i | 0.113690 | + | 0.196918i | ||||
\(518\) | −1.91495 | + | 3.54826i | −0.0841379 | + | 0.155901i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 9.31782 | − | 19.9227i | 0.408613 | − | 0.873670i | ||||
\(521\) | − | 16.4772i | − | 0.721880i | −0.932589 | − | 0.360940i | \(-0.882456\pi\) | ||
0.932589 | − | 0.360940i | \(-0.117544\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 35.6352i | − | 1.55822i | −0.626888 | − | 0.779110i | \(-0.715671\pi\) | ||
0.626888 | − | 0.779110i | \(-0.284329\pi\) | |||||||
\(524\) | −5.75148 | − | 8.75921i | −0.251255 | − | 0.382648i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −23.6770 | − | 12.7782i | −1.03237 | − | 0.557155i | ||||
\(527\) | −33.5827 | − | 58.1670i | −1.46289 | − | 2.53380i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 11.2597 | − | 19.5024i | 0.489553 | − | 0.847930i | ||||
\(530\) | 2.68089 | − | 1.65219i | 0.116451 | − | 0.0717667i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −2.13424 | + | 4.24157i | −0.0925310 | + | 0.183895i | ||||
\(533\) | −18.0808 | − | 10.4390i | −0.783166 | − | 0.452161i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −36.9331 | + | 21.3233i | −1.59676 | + | 0.921888i | ||||
\(536\) | 13.8549 | + | 19.8350i | 0.598442 | + | 0.856742i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 38.2796 | − | 1.09925i | 1.65035 | − | 0.0473921i | ||||
\(539\) | 0.702866 | 0.0302746 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 16.0235 | 0.688903 | 0.344452 | − | 0.938804i | \(-0.388065\pi\) | ||||
0.344452 | + | 0.938804i | \(0.388065\pi\) | |||||||
\(542\) | −41.1719 | + | 1.18231i | −1.76849 | + | 0.0507844i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 44.3165 | − | 6.40535i | 1.90006 | − | 0.274627i | ||||
\(545\) | −5.27773 | + | 3.04710i | −0.226073 | + | 0.130523i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −9.75181 | − | 5.63021i | −0.416957 | − | 0.240730i | 0.276817 | − | 0.960923i | \(-0.410720\pi\) |
−0.693775 | + | 0.720192i | \(0.744054\pi\) | |||||||
\(548\) | 18.6422 | + | 9.38023i | 0.796355 | + | 0.400703i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 1.07119 | − | 0.660156i | 0.0456756 | − | 0.0281491i | ||||
\(551\) | 11.9268 | − | 20.6579i | 0.508100 | − | 0.880056i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1.31214 | + | 2.27268i | 0.0557977 | + | 0.0966444i | ||||
\(554\) | 20.4671 | + | 11.0458i | 0.869566 | + | 0.469293i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −19.8543 | + | 13.0367i | −0.842009 | + | 0.552881i | ||||
\(557\) | − | 25.2666i | − | 1.07058i | −0.844669 | − | 0.535289i | \(-0.820203\pi\) | ||
0.844669 | − | 0.535289i | \(-0.179797\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 11.3725i | 0.481006i | ||||||||
\(560\) | 9.94674 | − | 1.14727i | 0.420326 | − | 0.0484810i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 4.24614 | − | 7.86780i | 0.179113 | − | 0.331883i | ||||
\(563\) | −6.29010 | − | 10.8948i | −0.265096 | − | 0.459160i | 0.702493 | − | 0.711691i | \(-0.252070\pi\) |
−0.967589 | + | 0.252531i | \(0.918737\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 5.98010 | − | 10.3578i | 0.251585 | − | 0.435758i | ||||
\(566\) | 6.12441 | + | 9.93764i | 0.257428 | + | 0.417710i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 1.54376 | + | 17.8803i | 0.0647748 | + | 0.750239i | ||||
\(569\) | 9.64118 | + | 5.56634i | 0.404179 | + | 0.233353i | 0.688286 | − | 0.725440i | \(-0.258364\pi\) |
−0.284107 | + | 0.958793i | \(0.591697\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 38.6886 | − | 22.3369i | 1.61907 | − | 0.934769i | 0.631906 | − | 0.775045i | \(-0.282273\pi\) |
0.987162 | − | 0.159724i | \(-0.0510605\pi\) | |||||||
\(572\) | −4.35969 | + | 0.250595i | −0.182288 | + | 0.0104779i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −0.272824 | − | 9.50065i | −0.0113875 | − | 0.396550i | ||||
\(575\) | 0.877545 | 0.0365962 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 0.773772 | 0.0322125 | 0.0161063 | − | 0.999870i | \(-0.494873\pi\) | ||||
0.0161063 | + | 0.999870i | \(0.494873\pi\) | |||||||
\(578\) | −1.85336 | − | 64.5404i | −0.0770897 | − | 2.68452i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −50.2176 | + | 2.88651i | −2.08517 | + | 0.119856i | ||||
\(581\) | 11.2658 | − | 6.50432i | 0.467385 | − | 0.269845i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −0.541485 | − | 0.312627i | −0.0224260 | − | 0.0129477i | ||||
\(584\) | −1.99559 | − | 23.1134i | −0.0825779 | − | 0.956439i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −5.74372 | − | 9.31992i | −0.237271 | − | 0.385002i | ||||
\(587\) | 3.95356 | − | 6.84776i | 0.163181 | − | 0.282637i | −0.772827 | − | 0.634617i | \(-0.781158\pi\) |
0.936008 | + | 0.351979i | \(0.114491\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −10.0726 | − | 17.4462i | −0.415032 | − | 0.718857i | ||||
\(590\) | 12.2078 | − | 22.6202i | 0.502588 | − | 0.931260i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 11.3292 | − | 1.30672i | 0.465625 | − | 0.0537058i | ||||
\(593\) | − | 13.0459i | − | 0.535732i | −0.963456 | − | 0.267866i | \(-0.913682\pi\) | ||
0.963456 | − | 0.267866i | \(-0.0863184\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − | 19.8139i | − | 0.812292i | ||||||
\(596\) | 29.5937 | − | 19.4319i | 1.21221 | − | 0.795960i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −2.68016 | − | 1.44644i | −0.109600 | − | 0.0591495i | ||||
\(599\) | 5.35898 | + | 9.28202i | 0.218962 | + | 0.379253i | 0.954491 | − | 0.298240i | \(-0.0963996\pi\) |
−0.735529 | + | 0.677493i | \(0.763066\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −2.22698 | + | 3.85725i | −0.0908406 | + | 0.157341i | −0.907865 | − | 0.419262i | \(-0.862289\pi\) |
0.817024 | + | 0.576603i | \(0.195622\pi\) | |||||||
\(602\) | −4.40750 | + | 2.71628i | −0.179636 | + | 0.110707i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 37.5039 | + | 18.8709i | 1.52601 | + | 0.767847i | ||||
\(605\) | 22.7750 | + | 13.1491i | 0.925934 | + | 0.534588i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −29.7000 | + | 17.1473i | −1.20549 | + | 0.695988i | −0.961770 | − | 0.273858i | \(-0.911700\pi\) |
−0.243717 | + | 0.969846i | \(0.578367\pi\) | |||||||
\(608\) | 13.2920 | − | 1.92117i | 0.539060 | − | 0.0779138i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −16.9661 | + | 0.487205i | −0.686938 | + | 0.0197264i | ||||
\(611\) | −22.8505 | −0.924433 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −27.5606 | −1.11316 | −0.556581 | − | 0.830794i | \(-0.687887\pi\) | ||||
−0.556581 | + | 0.830794i | \(0.687887\pi\) | |||||||
\(614\) | −20.7849 | + | 0.596865i | −0.838808 | + | 0.0240875i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −1.13841 | − | 1.62978i | −0.0458680 | − | 0.0656657i | ||||
\(617\) | −21.8157 | + | 12.5953i | −0.878268 | + | 0.507068i | −0.870087 | − | 0.492899i | \(-0.835937\pi\) |
−0.00818075 | + | 0.999967i | \(0.502604\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −2.44808 | − | 1.41340i | −0.0983968 | − | 0.0568094i | 0.449994 | − | 0.893032i | \(-0.351426\pi\) |
−0.548391 | + | 0.836222i | \(0.684759\pi\) | |||||||
\(620\) | −19.0939 | + | 37.9472i | −0.766831 | + | 1.52399i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −15.0905 | + | 9.30001i | −0.605072 | + | 0.372897i | ||||
\(623\) | 0.859209 | − | 1.48819i | 0.0344235 | − | 0.0596232i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 14.8635 | + | 25.7443i | 0.594538 | + | 1.02977i | ||||
\(626\) | −28.9006 | − | 15.5973i | −1.15510 | − | 0.623393i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 1.84858 | + | 2.81530i | 0.0737665 | + | 0.112343i | ||||
\(629\) | − | 22.5677i | − | 0.899834i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 35.3279i | − | 1.40638i | −0.711002 | − | 0.703190i | \(-0.751758\pi\) | ||
0.711002 | − | 0.703190i | \(-0.248242\pi\) | |||||||
\(632\) | 3.14458 | − | 6.72354i | 0.125085 | − | 0.267448i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 4.60015 | − | 8.52374i | 0.182695 | − | 0.338521i | ||||
\(635\) | −6.15020 | − | 10.6525i | −0.244063 | − | 0.422730i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.55324 | + | 2.69030i | −0.0615417 | + | 0.106593i | ||||
\(638\) | 5.23976 | + | 8.50218i | 0.207444 | + | 0.336605i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −18.7707 | − | 21.2059i | −0.741978 | − | 0.838237i | ||||
\(641\) | −17.8094 | − | 10.2823i | −0.703431 | − | 0.406126i | 0.105193 | − | 0.994452i | \(-0.466454\pi\) |
−0.808624 | + | 0.588326i | \(0.799787\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 16.6218 | − | 9.59659i | 0.655499 | − | 0.378453i | −0.135061 | − | 0.990837i | \(-0.543123\pi\) |
0.790560 | + | 0.612385i | \(0.209790\pi\) | |||||||
\(644\) | −0.0795635 | − | 1.38419i | −0.00313524 | − | 0.0545448i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −0.762868 | − | 26.5656i | −0.0300146 | − | 1.04521i | ||||
\(647\) | 30.9160 | 1.21544 | 0.607718 | − | 0.794153i | \(-0.292085\pi\) | ||||
0.607718 | + | 0.794153i | \(0.292085\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −5.10354 | −0.200331 | ||||||||
\(650\) | 0.159632 | + | 5.55894i | 0.00626130 | + | 0.218040i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 1.71352 | + | 29.8106i | 0.0671064 | + | 1.16747i | ||||
\(653\) | 14.2740 | − | 8.24109i | 0.558584 | − | 0.322499i | −0.193993 | − | 0.981003i | \(-0.562144\pi\) |
0.752577 | + | 0.658504i | \(0.228810\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 11.3579 | + | 6.55749i | 0.443790 | + | 0.256222i | ||||
\(656\) | −21.5879 | + | 16.0206i | −0.842864 | + | 0.625498i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −5.45775 | − | 8.85589i | −0.212765 | − | 0.345239i | ||||
\(659\) | −13.7838 | + | 23.8743i | −0.536942 | + | 0.930010i | 0.462125 | + | 0.886815i | \(0.347087\pi\) |
−0.999067 | + | 0.0431955i | \(0.986246\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 5.86138 | + | 10.1522i | 0.227981 | + | 0.394875i | 0.957210 | − | 0.289395i | \(-0.0934542\pi\) |
−0.729229 | + | 0.684270i | \(0.760121\pi\) | |||||||
\(662\) | 5.41527 | − | 10.0341i | 0.210470 | − | 0.389986i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −33.3289 | − | 15.5879i | −1.29341 | − | 0.604926i | ||||
\(665\) | − | 5.94284i | − | 0.230454i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 6.96521i | 0.269694i | ||||||||
\(668\) | 2.57018 | + | 3.91425i | 0.0994432 | + | 0.151447i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −26.6486 | − | 14.3819i | −1.02953 | − | 0.555621i | ||||
\(671\) | 1.68500 | + | 2.91850i | 0.0650486 | + | 0.112667i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −3.04565 | + | 5.27522i | −0.117401 | + | 0.203345i | −0.918737 | − | 0.394870i | \(-0.870790\pi\) |
0.801336 | + | 0.598215i | \(0.204123\pi\) | |||||||
\(674\) | 19.4647 | − | 11.9958i | 0.749754 | − | 0.462062i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −3.01128 | + | 5.98460i | −0.115818 | + | 0.230177i | ||||
\(677\) | −25.8756 | − | 14.9393i | −0.994481 | − | 0.574164i | −0.0878702 | − | 0.996132i | \(-0.528006\pi\) |
−0.906611 | + | 0.421968i | \(0.861339\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −11.7967 | + | 6.81083i | −0.452716 | + | 0.261376i | ||||
\(680\) | −45.9438 | + | 32.0921i | −1.76186 | + | 1.23068i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 8.43091 | − | 0.242105i | 0.322836 | − | 0.00927068i | ||||
\(683\) | −5.57818 | −0.213443 | −0.106722 | − | 0.994289i | \(-0.534035\pi\) | ||||
−0.106722 | + | 0.994289i | \(0.534035\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −26.1195 | −0.997974 | ||||||||
\(686\) | −1.41363 | + | 0.0405943i | −0.0539727 | + | 0.00154990i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 13.4371 | + | 5.82047i | 0.512285 | + | 0.221903i | ||||
\(689\) | 2.39322 | − | 1.38173i | 0.0911745 | − | 0.0526396i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 6.59535 | + | 3.80783i | 0.250899 | + | 0.144857i | 0.620176 | − | 0.784463i | \(-0.287061\pi\) |
−0.369277 | + | 0.929319i | \(0.620395\pi\) | |||||||
\(692\) | 1.80697 | + | 0.909216i | 0.0686907 | + | 0.0345632i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −9.21981 | + | 5.68202i | −0.349979 | + | 0.215687i | ||||
\(695\) | 14.8637 | − | 25.7447i | 0.563813 | − | 0.976553i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 26.5992 | + | 46.0711i | 1.00751 | + | 1.74507i | ||||
\(698\) | 10.9750 | + | 5.92306i | 0.415410 | + | 0.224191i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −2.11628 | + | 1.38960i | −0.0799880 | + | 0.0525218i | ||||
\(701\) | 13.6591i | 0.515896i | 0.966159 | + | 0.257948i | \(0.0830463\pi\) | ||||
−0.966159 | + | 0.257948i | \(0.916954\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 6.76879i | − | 0.255290i | ||||||
\(704\) | −1.93521 | + | 5.27942i | −0.0729360 | + | 0.198976i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −2.18272 | + | 4.04442i | −0.0821476 | + | 0.152214i | ||||
\(707\) | −1.29202 | − | 2.23784i | −0.0485913 | − | 0.0841625i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −11.1244 | + | 19.2680i | −0.417784 | + | 0.723624i | −0.995716 | − | 0.0924613i | \(-0.970527\pi\) |
0.577932 | + | 0.816085i | \(0.303860\pi\) | |||||||
\(710\) | −11.7847 | − | 19.1222i | −0.442272 | − | 0.717643i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −4.84241 | + | 0.418088i | −0.181477 | + | 0.0156685i | ||||
\(713\) | 5.09424 | + | 2.94116i | 0.190781 | + | 0.110147i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 4.73329 | − | 2.73277i | 0.177015 | − | 0.102200i | ||||
\(716\) | −23.6910 | + | 1.36176i | −0.885376 | + | 0.0508915i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 1.15301 | + | 40.1517i | 0.0430299 | + | 1.49845i | ||||
\(719\) | 17.7827 | 0.663184 | 0.331592 | − | 0.943423i | \(-0.392414\pi\) | ||||
0.331592 | + | 0.943423i | \(0.392414\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 13.4614 | 0.501328 | ||||||||
\(722\) | 0.542483 | + | 18.8911i | 0.0201891 | + | 0.703054i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 23.4046 | − | 1.34530i | 0.869826 | − | 0.0499977i | ||||
\(725\) | 11.0146 | − | 6.35929i | 0.409072 | − | 0.236178i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −45.2123 | − | 26.1034i | −1.67683 | − | 0.968120i | −0.963660 | − | 0.267131i | \(-0.913924\pi\) |
−0.713173 | − | 0.700988i | \(-0.752742\pi\) | |||||||
\(728\) | 8.75390 | − | 0.755802i | 0.324441 | − | 0.0280119i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 15.2338 | + | 24.7188i | 0.563829 | + | 0.914885i | ||||
\(731\) | 14.4890 | − | 25.0956i | 0.535894 | − | 0.928195i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −5.30936 | − | 9.19609i | −0.196106 | − | 0.339665i | 0.751157 | − | 0.660124i | \(-0.229496\pi\) |
−0.947262 | + | 0.320459i | \(0.896163\pi\) | |||||||
\(734\) | −3.10354 | + | 5.75063i | −0.114554 | + | 0.212260i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −3.08075 | + | 2.42643i | −0.113558 | + | 0.0894394i | ||||
\(737\) | 6.01242i | 0.221470i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 25.7536i | − | 0.947362i | −0.880696 | − | 0.473681i | \(-0.842925\pi\) | ||
0.880696 | − | 0.473681i | \(-0.157075\pi\) | |||||||
\(740\) | −11.9312 | + | 7.83429i | −0.438600 | + | 0.287994i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 1.10711 | + | 0.597493i | 0.0406433 | + | 0.0219346i | ||||
\(743\) | −1.97016 | − | 3.41241i | −0.0722780 | − | 0.125189i | 0.827621 | − | 0.561287i | \(-0.189694\pi\) |
−0.899899 | + | 0.436098i | \(0.856360\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −22.1550 | + | 38.3737i | −0.811698 | + | 1.40590i | ||||
\(746\) | 33.1949 | − | 20.4575i | 1.21535 | − | 0.749003i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 9.93976 | + | 5.00141i | 0.363434 | + | 0.182870i | ||||
\(749\) | −14.7545 | − | 8.51853i | −0.539119 | − | 0.311260i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 10.3540 | − | 5.97786i | 0.377821 | − | 0.218135i | −0.299049 | − | 0.954238i | \(-0.596669\pi\) |
0.676870 | + | 0.736103i | \(0.263336\pi\) | |||||||
\(752\) | −11.6949 | + | 26.9989i | −0.426470 | + | 0.984548i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −44.1222 | + | 1.26703i | −1.60684 | + | 0.0461424i | ||||
\(755\) | −52.5466 | −1.91237 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1.73758 | 0.0631534 | 0.0315767 | − | 0.999501i | \(-0.489947\pi\) | ||||
0.0315767 | + | 0.999501i | \(0.489947\pi\) | |||||||
\(758\) | −29.0877 | + | 0.835293i | −1.05651 | + | 0.0303392i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −13.7800 | + | 9.62547i | −0.499854 | + | 0.349152i | ||||
\(761\) | 25.7786 | − | 14.8833i | 0.934473 | − | 0.539518i | 0.0462496 | − | 0.998930i | \(-0.485273\pi\) |
0.888223 | + | 0.459412i | \(0.151940\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −2.10842 | − | 1.21729i | −0.0763298 | − | 0.0440690i | ||||
\(764\) | 6.07933 | − | 12.0820i | 0.219942 | − | 0.437112i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −0.110175 | + | 0.0678989i | −0.00398077 | + | 0.00245329i | ||||
\(767\) | 11.2782 | − | 19.5343i | 0.407231 | − | 0.705344i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 11.5167 | + | 19.9475i | 0.415303 | + | 0.719327i | 0.995460 | − | 0.0951782i | \(-0.0303421\pi\) |
−0.580157 | + | 0.814505i | \(0.697009\pi\) | |||||||
\(770\) | 2.18963 | + | 1.18171i | 0.0789089 | + | 0.0425860i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 3.03651 | + | 4.62445i | 0.109287 | + | 0.166438i | ||||
\(773\) | − | 1.33102i | − | 0.0478734i | −0.999713 | − | 0.0239367i | \(-0.992380\pi\) | ||
0.999713 | − | 0.0239367i | \(-0.00762002\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 10.7412i | − | 0.385835i | ||||||
\(776\) | 34.8995 | + | 16.3224i | 1.25282 | + | 0.585941i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −1.28341 | + | 2.37807i | −0.0460126 | + | 0.0852580i | ||||
\(779\) | 7.97795 | + | 13.8182i | 0.285840 | + | 0.495089i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −2.22989 | + | 3.86229i | −0.0797919 | + | 0.138204i | ||||
\(782\) | 4.07146 | + | 6.60646i | 0.145595 | + | 0.236247i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 2.38375 | + | 3.21212i | 0.0851339 | + | 0.114719i | ||||
\(785\) | −3.65055 | − | 2.10764i | −0.130294 | − | 0.0752250i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1.23901 | − | 0.715343i | 0.0441659 | − | 0.0254992i | −0.477754 | − | 0.878493i | \(-0.658549\pi\) |
0.521920 | + | 0.852994i | \(0.325216\pi\) | |||||||
\(788\) | 1.98135 | + | 34.4702i | 0.0705827 | + | 1.22795i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0.266664 | + | 9.28614i | 0.00948747 | + | 0.330386i | ||||
\(791\) | 4.77802 | 0.169887 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −14.8945 | −0.528919 | ||||||||
\(794\) | 1.23550 | + | 43.0242i | 0.0438462 | + | 1.52687i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −1.66328 | − | 28.9366i | −0.0589533 | − | 1.02563i | ||||
\(797\) | 29.9747 | − | 17.3059i | 1.06176 | − | 0.613007i | 0.135841 | − | 0.990731i | \(-0.456627\pi\) |
0.925918 | + | 0.377724i | \(0.123293\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 50.4240 | + | 29.1123i | 1.78387 | + | 1.02992i | ||||
\(800\) | 6.64983 | + | 2.65646i | 0.235107 | + | 0.0939202i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −16.2116 | − | 26.3053i | −0.572450 | − | 0.928873i | ||||
\(803\) | 2.88253 | − | 4.99269i | 0.101722 | − | 0.176188i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0.867647 | + | 1.50281i | 0.0305805 | + | 0.0529671i | ||||
\(806\) | −17.7045 | + | 32.8052i | −0.623616 | + | 1.15552i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −3.09637 | + | 6.62044i | −0.108930 | + | 0.232906i | ||||
\(809\) | 21.7895i | 0.766078i | 0.923732 | + | 0.383039i | \(0.125122\pi\) | ||||
−0.923732 | + | 0.383039i | \(0.874878\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 14.6383i | − | 0.514020i | −0.966409 | − | 0.257010i | \(-0.917263\pi\) | ||
0.966409 | − | 0.257010i | \(-0.0827374\pi\) | |||||||
\(812\) | −11.0294 | − | 16.7973i | −0.387058 | − | 0.589469i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 2.49395 | + | 1.34595i | 0.0874129 | + | 0.0471756i | ||||
\(815\) | −18.6860 | − | 32.3652i | −0.654544 | − | 1.13370i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 4.34571 | − | 7.52699i | 0.152037 | − | 0.263336i | ||||
\(818\) | −5.38851 | + | 3.32086i | −0.188405 | + | 0.116111i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 15.1233 | − | 30.0560i | 0.528129 | − | 1.04960i | ||||
\(821\) | 15.6555 | + | 9.03872i | 0.546382 | + | 0.315454i | 0.747661 | − | 0.664080i | \(-0.231177\pi\) |
−0.201280 | + | 0.979534i | \(0.564510\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −10.4800 | + | 6.05062i | −0.365309 | + | 0.210911i | −0.671407 | − | 0.741089i | \(-0.734310\pi\) |
0.306098 | + | 0.952000i | \(0.400976\pi\) | |||||||
\(824\) | −21.8031 | − | 31.2138i | −0.759546 | − | 1.08738i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 10.2644 | − | 0.294757i | 0.357145 | − | 0.0102559i | ||||
\(827\) | −50.7180 | −1.76364 | −0.881819 | − | 0.471588i | \(-0.843681\pi\) | ||||
−0.881819 | + | 0.471588i | \(0.843681\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −14.5505 | −0.505359 | −0.252679 | − | 0.967550i | \(-0.581312\pi\) | ||||
−0.252679 | + | 0.967550i | \(0.581312\pi\) | |||||||
\(830\) | 46.0318 | − | 1.32187i | 1.59779 | − | 0.0458826i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −15.9310 | − | 19.0741i | −0.552308 | − | 0.661274i | ||||
\(833\) | 6.85506 | − | 3.95777i | 0.237514 | − | 0.137129i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −5.07554 | − | 2.93036i | −0.175646 | − | 0.101409i | ||||
\(836\) | 2.98126 | + | 1.50008i | 0.103109 | + | 0.0518815i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −27.4552 | + | 16.9202i | −0.948423 | + | 0.584498i | ||||
\(839\) | 7.34607 | − | 12.7238i | 0.253615 | − | 0.439273i | −0.710904 | − | 0.703289i | \(-0.751714\pi\) |
0.964518 | + | 0.264016i | \(0.0850472\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 35.9746 | + | 62.3099i | 1.24050 | + | 2.14862i | ||||
\(842\) | −34.9739 | − | 18.8750i | −1.20528 | − | 0.650474i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 42.8162 | − | 28.1140i | 1.47379 | − | 0.967723i | ||||
\(845\) | − | 8.38499i | − | 0.288452i | ||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 10.5060i | 0.360990i | ||||||||
\(848\) | −0.407716 | − | 3.53487i | −0.0140010 | − | 0.121388i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 6.73002 | − | 12.4702i | 0.230838 | − | 0.427726i | ||||
\(851\) | 0.988234 | + | 1.71167i | 0.0338762 | + | 0.0586754i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 0.885883 | − | 1.53439i | 0.0303321 | − | 0.0525367i | −0.850461 | − | 0.526038i | \(-0.823677\pi\) |
0.880793 | + | 0.473502i | \(0.157010\pi\) | |||||||
\(854\) | −3.55749 | − | 5.77248i | −0.121735 | − | 0.197530i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 4.14508 | + | 48.0095i | 0.141676 | + | 1.64093i | ||||
\(857\) | −0.277829 | − | 0.160404i | −0.00949045 | − | 0.00547931i | 0.495247 | − | 0.868752i | \(-0.335077\pi\) |
−0.504738 | + | 0.863273i | \(0.668411\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 27.9931 | − | 16.1618i | 0.955112 | − | 0.551434i | 0.0604467 | − | 0.998171i | \(-0.480747\pi\) |
0.894665 | + | 0.446737i | \(0.147414\pi\) | |||||||
\(860\) | −18.2975 | + | 1.05174i | −0.623939 | + | 0.0358640i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0.0247931 | + | 0.863381i | 0.000844458 | + | 0.0294069i | ||||
\(863\) | 18.8459 | 0.641522 | 0.320761 | − | 0.947160i | \(-0.396061\pi\) | ||||
0.320761 | + | 0.947160i | \(0.396061\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −2.53174 | −0.0860816 | ||||||||
\(866\) | 0.426926 | + | 14.8670i | 0.0145075 | + | 0.505202i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −16.9426 | + | 0.973861i | −0.575069 | + | 0.0330550i | ||||
\(869\) | 1.59739 | − | 0.922256i | 0.0541879 | − | 0.0312854i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −23.0132 | − | 13.2867i | −0.779772 | − | 0.450201i | ||||
\(872\) | 0.592331 | + | 6.86054i | 0.0200589 | + | 0.232327i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 1.22116 | + | 1.98149i | 0.0413064 | + | 0.0670250i | ||||
\(875\) | −4.67359 | + | 8.09490i | −0.157996 | + | 0.273657i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −20.0001 | − | 34.6412i | −0.675355 | − | 1.16975i | −0.976365 | − | 0.216129i | \(-0.930657\pi\) |
0.301010 | − | 0.953621i | \(-0.402676\pi\) | |||||||
\(878\) | −25.3093 | + | 46.8964i | −0.854149 | + | 1.58268i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −0.806377 | − | 6.99123i | −0.0271830 | − | 0.235674i | ||||
\(881\) | 4.11680i | 0.138699i | 0.997592 | + | 0.0693493i | \(0.0220923\pi\) | ||||
−0.997592 | + | 0.0693493i | \(0.977908\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 58.6257i | − | 1.97291i | −0.164027 | − | 0.986456i | \(-0.552449\pi\) | ||
0.164027 | − | 0.986456i | \(-0.447551\pi\) | |||||||
\(884\) | −41.1090 | + | 26.9930i | −1.38265 | + | 0.907874i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −51.6370 | − | 27.8678i | −1.73478 | − | 0.936237i | ||||
\(887\) | −14.3027 | − | 24.7730i | −0.480238 | − | 0.831797i | 0.519505 | − | 0.854468i | \(-0.326117\pi\) |
−0.999743 | + | 0.0226703i | \(0.992783\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 2.45696 | − | 4.25559i | 0.0824040 | − | 0.142728i | ||||
\(890\) | 5.17875 | − | 3.19158i | 0.173592 | − | 0.106982i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 27.2594 | + | 13.7161i | 0.912711 | + | 0.459250i | ||||
\(893\) | 15.1238 | + | 8.73173i | 0.506099 | + | 0.292196i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 25.7212 | − | 14.8502i | 0.859766 | − | 0.496386i | ||||
\(896\) | 3.58725 | − | 10.7299i | 0.119842 | − | 0.358462i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −45.1876 | + | 1.29762i | −1.50793 | + | 0.0433022i | ||||
\(899\) | 85.2545 | 2.84340 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −7.04147 | −0.234586 | ||||||||
\(902\) | −6.67769 | + | 0.191759i | −0.222343 | + | 0.00638487i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −7.73884 | − | 11.0791i | −0.257390 | − | 0.368485i | ||||
\(905\) | −25.4103 | + | 14.6706i | −0.844666 | + | 0.487668i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −9.05264 | − | 5.22654i | −0.300588 | − | 0.173545i | 0.342119 | − | 0.939657i | \(-0.388855\pi\) |
−0.642707 | + | 0.766112i | \(0.722189\pi\) | |||||||
\(908\) | 6.98093 | − | 13.8739i | 0.231670 | − | 0.460420i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −9.36194 | + | 5.76961i | −0.310345 | + | 0.191261i | ||||
\(911\) | 7.21831 | − | 12.5025i | 0.239153 | − | 0.414226i | −0.721318 | − | 0.692604i | \(-0.756463\pi\) |
0.960472 | + | 0.278378i | \(0.0897968\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −4.57167 | − | 7.91836i | −0.151300 | − | 0.262059i | ||||
\(914\) | −36.9665 | − | 19.9503i | −1.22274 | − | 0.659898i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 12.5154 | + | 19.0602i | 0.413519 | + | 0.629768i | ||||
\(917\) | 5.23935i | 0.173019i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 12.1505i | − | 0.400810i | −0.979713 | − | 0.200405i | \(-0.935774\pi\) | ||
0.979713 | − | 0.200405i | \(-0.0642257\pi\) | |||||||
\(920\) | 2.07935 | − | 4.44593i | 0.0685541 | − | 0.146578i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −6.95491 | + | 12.8869i | −0.229048 | + | 0.424409i | ||||
\(923\) | −9.85555 | − | 17.0703i | −0.324399 | − | 0.561876i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.80453 | − | 3.12554i | 0.0593325 | − | 0.102767i | ||||
\(926\) | 11.7563 | + | 19.0761i | 0.386337 | + | 0.626881i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −21.0848 | + | 52.7808i | −0.692142 | + | 1.73261i | ||||
\(929\) | 38.7325 | + | 22.3622i | 1.27077 | + | 0.733680i | 0.975133 | − | 0.221620i | \(-0.0711344\pi\) |
0.295638 | + | 0.955300i | \(0.404468\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.05605 | − | 1.18706i | 0.0673844 | − | 0.0389044i | ||||
\(932\) | −2.22784 | − | 38.7585i | −0.0729754 | − | 1.26958i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 1.13601 | + | 39.5596i | 0.0371713 | + | 1.29443i | ||||
\(935\) | −13.9266 | −0.455447 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −28.8712 | −0.943180 | −0.471590 | − | 0.881818i | \(-0.656320\pi\) | ||||
−0.471590 | + | 0.881818i | \(0.656320\pi\) | |||||||
\(938\) | −0.347249 | − | 12.0924i | −0.0113381 | − | 0.394831i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −2.11324 | − | 36.7647i | −0.0689261 | − | 1.19913i | ||||
\(941\) | −31.0674 | + | 17.9368i | −1.01277 | + | 0.584723i | −0.912001 | − | 0.410187i | \(-0.865463\pi\) |
−0.100768 | + | 0.994910i | \(0.532130\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −4.03488 | − | 2.32954i | −0.131394 | − | 0.0758603i | ||||
\(944\) | −17.3085 | − | 23.3233i | −0.563344 | − | 0.759110i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 1.90918 | + | 3.09789i | 0.0620728 | + | 0.100721i | ||||
\(947\) | 8.81974 | − | 15.2762i | 0.286603 | − | 0.496411i | −0.686394 | − | 0.727230i | \(-0.740807\pi\) |
0.972997 | + | 0.230819i | \(0.0741406\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 12.7400 | + | 22.0664i | 0.413559 | + | 0.716306i | ||||
\(950\) | 2.01855 | − | 3.74023i | 0.0654904 | − | 0.121349i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −20.2801 | − | 9.48495i | −0.657281 | − | 0.307409i | ||||
\(953\) | − | 9.66882i | − | 0.313204i | −0.987662 | − | 0.156602i | \(-0.949946\pi\) | ||
0.987662 | − | 0.156602i | \(-0.0500540\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 16.9280i | 0.547779i | ||||||||
\(956\) | −7.84743 | − | 11.9512i | −0.253804 | − | 0.386530i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −28.8345 | − | 15.5616i | −0.931600 | − | 0.502772i | ||||
\(959\) | −5.21728 | − | 9.03659i | −0.168475 | − | 0.291807i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 20.4999 | − | 35.5069i | 0.661288 | − | 1.14538i | ||||
\(962\) | −10.6631 | + | 6.57148i | −0.343791 | + | 0.211873i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 2.15273 | − | 4.27831i | 0.0693347 | − | 0.137795i | ||||
\(965\) | −5.99645 | − | 3.46205i | −0.193033 | − | 0.111447i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −2.67131 | + | 1.54228i | −0.0859036 | + | 0.0495964i | −0.542336 | − | 0.840161i | \(-0.682460\pi\) |
0.456433 | + | 0.889758i | \(0.349127\pi\) | |||||||
\(968\) | 24.3609 | − | 17.0163i | 0.782988 | − | 0.546923i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −48.2011 | + | 1.38416i | −1.54764 | + | 0.0444426i | ||||
\(971\) | −24.5223 | −0.786958 | −0.393479 | − | 0.919334i | \(-0.628729\pi\) | ||||
−0.393479 | + | 0.919334i | \(0.628729\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 11.8759 | 0.380724 | ||||||||
\(974\) | −19.5726 | + | 0.562054i | −0.627147 | + | 0.0180094i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −7.62303 | + | 17.5985i | −0.244007 | + | 0.563314i | ||||
\(977\) | −9.43845 | + | 5.44929i | −0.301963 | + | 0.174338i | −0.643324 | − | 0.765594i | \(-0.722445\pi\) |
0.341362 | + | 0.939932i | \(0.389112\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1.04600 | − | 0.603909i | −0.0334304 | − | 0.0193010i | ||||
\(980\) | −4.47212 | − | 2.25024i | −0.142857 | − | 0.0718814i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 4.76759 | − | 2.93819i | 0.152140 | − | 0.0937615i | ||||
\(983\) | −14.8209 | + | 25.6706i | −0.472715 | + | 0.818766i | −0.999512 | − | 0.0312247i | \(-0.990059\pi\) |
0.526798 | + | 0.849991i | \(0.323393\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −21.6068 | − | 37.4241i | −0.688450 | − | 1.19243i | ||||
\(986\) | 98.9783 | + | 53.4172i | 3.15211 | + | 1.70115i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −12.3299 | + | 8.09609i | −0.392267 | + | 0.257571i | ||||
\(989\) | 2.53787i | 0.0806996i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 20.5496i | 0.652779i | 0.945235 | + | 0.326390i | \(0.105832\pi\) | ||||
−0.945235 | + | 0.326390i | \(0.894168\pi\) | |||||||
\(992\) | 29.6996 | + | 37.7085i | 0.942964 | + | 1.19725i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 4.26178 | − | 7.89677i | 0.135175 | − | 0.250470i | ||||
\(995\) | 18.1382 | + | 31.4163i | 0.575020 | + | 0.995963i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 6.42074 | − | 11.1210i | 0.203347 | − | 0.352207i | −0.746258 | − | 0.665657i | \(-0.768151\pi\) |
0.949605 | + | 0.313450i | \(0.101485\pi\) | |||||||
\(998\) | −16.0071 | − | 25.9735i | −0.506695 | − | 0.822177i | ||||
\(999\) | 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 | 756.2.ba.a.575.20 | 72 | ||
3.2 | odd | 2 | 252.2.ba.a.155.17 | yes | 72 | ||
4.3 | odd | 2 | inner | 756.2.ba.a.575.31 | 72 | ||
9.4 | even | 3 | 252.2.ba.a.239.6 | yes | 72 | ||
9.5 | odd | 6 | inner | 756.2.ba.a.71.31 | 72 | ||
12.11 | even | 2 | 252.2.ba.a.155.6 | ✓ | 72 | ||
36.23 | even | 6 | inner | 756.2.ba.a.71.20 | 72 | ||
36.31 | odd | 6 | 252.2.ba.a.239.17 | yes | 72 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
252.2.ba.a.155.6 | ✓ | 72 | 12.11 | even | 2 | ||
252.2.ba.a.155.17 | yes | 72 | 3.2 | odd | 2 | ||
252.2.ba.a.239.6 | yes | 72 | 9.4 | even | 3 | ||
252.2.ba.a.239.17 | yes | 72 | 36.31 | odd | 6 | ||
756.2.ba.a.71.20 | 72 | 36.23 | even | 6 | inner | ||
756.2.ba.a.71.31 | 72 | 9.5 | odd | 6 | inner | ||
756.2.ba.a.575.20 | 72 | 1.1 | even | 1 | trivial | ||
756.2.ba.a.575.31 | 72 | 4.3 | odd | 2 | inner |