Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [570,2,Mod(77,570)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(570, 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("570.77");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 570.k (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: | \(4.55147291521\) |
Analytic rank: | \(0\) |
Dimension: | \(36\) |
Relative dimension: | \(18\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 533.6 | ||
Character | \(\chi\) | \(=\) | 570.533 |
Dual form | 570.2.k.b.77.6 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/570\mathbb{Z}\right)^\times\).
\(n\) | \(191\) | \(211\) | \(457\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(e\left(\frac{3}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.707107 | − | 0.707107i | −0.500000 | − | 0.500000i | ||||
\(3\) | 0.577604 | − | 1.63290i | 0.333480 | − | 0.942757i | ||||
\(4\) | 1.00000i | 0.500000i | ||||||||
\(5\) | 2.23603 | + | 0.0135681i | 0.999982 | + | 0.00606782i | ||||
\(6\) | −1.56306 | + | 0.746209i | −0.638119 | + | 0.304639i | ||||
\(7\) | 3.38538 | − | 3.38538i | 1.27955 | − | 1.27955i | 0.338638 | − | 0.940917i | \(-0.390034\pi\) |
0.940917 | − | 0.338638i | \(-0.109966\pi\) | |||||||
\(8\) | 0.707107 | − | 0.707107i | 0.250000 | − | 0.250000i | ||||
\(9\) | −2.33275 | − | 1.88634i | −0.777582 | − | 0.628781i | ||||
\(10\) | −1.57152 | − | 1.59070i | −0.496957 | − | 0.503025i | ||||
\(11\) | 1.22574i | 0.369575i | 0.982779 | + | 0.184787i | \(0.0591597\pi\) | ||||
−0.982779 | + | 0.184787i | \(0.940840\pi\) | |||||||
\(12\) | 1.63290 | + | 0.577604i | 0.471379 | + | 0.166740i | ||||
\(13\) | 3.51689 | + | 3.51689i | 0.975410 | + | 0.975410i | 0.999705 | − | 0.0242950i | \(-0.00773410\pi\) |
−0.0242950 | + | 0.999705i | \(0.507734\pi\) | |||||||
\(14\) | −4.78765 | −1.27955 | ||||||||
\(15\) | 1.31369 | − | 3.64338i | 0.339194 | − | 0.940716i | ||||
\(16\) | −1.00000 | −0.250000 | ||||||||
\(17\) | 0.826034 | + | 0.826034i | 0.200343 | + | 0.200343i | 0.800147 | − | 0.599804i | \(-0.204755\pi\) |
−0.599804 | + | 0.800147i | \(0.704755\pi\) | |||||||
\(18\) | 0.315656 | + | 2.98335i | 0.0744008 | + | 0.703182i | ||||
\(19\) | 1.00000i | 0.229416i | ||||||||
\(20\) | −0.0135681 | + | 2.23603i | −0.00303391 | + | 0.499991i | ||||
\(21\) | −3.57259 | − | 7.48341i | −0.779604 | − | 1.63301i | ||||
\(22\) | 0.866730 | − | 0.866730i | 0.184787 | − | 0.184787i | ||||
\(23\) | −1.04719 | + | 1.04719i | −0.218353 | + | 0.218353i | −0.807804 | − | 0.589451i | \(-0.799344\pi\) |
0.589451 | + | 0.807804i | \(0.299344\pi\) | |||||||
\(24\) | −0.746209 | − | 1.56306i | −0.152319 | − | 0.319059i | ||||
\(25\) | 4.99963 | + | 0.0606771i | 0.999926 | + | 0.0121354i | ||||
\(26\) | − | 4.97363i | − | 0.975410i | ||||||
\(27\) | −4.42762 | + | 2.71959i | −0.852096 | + | 0.523386i | ||||
\(28\) | 3.38538 | + | 3.38538i | 0.639777 | + | 0.639777i | ||||
\(29\) | −8.14348 | −1.51221 | −0.756103 | − | 0.654453i | \(-0.772899\pi\) | ||||
−0.756103 | + | 0.654453i | \(0.772899\pi\) | |||||||
\(30\) | −3.50518 | + | 1.64734i | −0.639955 | + | 0.300761i | ||||
\(31\) | 7.41990 | 1.33265 | 0.666327 | − | 0.745660i | \(-0.267866\pi\) | ||||
0.666327 | + | 0.745660i | \(0.267866\pi\) | |||||||
\(32\) | 0.707107 | + | 0.707107i | 0.125000 | + | 0.125000i | ||||
\(33\) | 2.00152 | + | 0.707993i | 0.348419 | + | 0.123246i | ||||
\(34\) | − | 1.16819i | − | 0.200343i | ||||||
\(35\) | 7.61574 | − | 7.52387i | 1.28730 | − | 1.27177i | ||||
\(36\) | 1.88634 | − | 2.33275i | 0.314390 | − | 0.388791i | ||||
\(37\) | −5.83375 | + | 5.83375i | −0.959063 | + | 0.959063i | −0.999194 | − | 0.0401316i | \(-0.987222\pi\) |
0.0401316 | + | 0.999194i | \(0.487222\pi\) | |||||||
\(38\) | 0.707107 | − | 0.707107i | 0.114708 | − | 0.114708i | ||||
\(39\) | 7.77411 | − | 3.71137i | 1.24485 | − | 0.594295i | ||||
\(40\) | 1.59070 | − | 1.57152i | 0.251512 | − | 0.248478i | ||||
\(41\) | 3.53572i | 0.552187i | 0.961131 | + | 0.276093i | \(0.0890399\pi\) | ||||
−0.961131 | + | 0.276093i | \(0.910960\pi\) | |||||||
\(42\) | −2.76537 | + | 7.81778i | −0.426706 | + | 1.20631i | ||||
\(43\) | −2.68748 | − | 2.68748i | −0.409836 | − | 0.409836i | 0.471845 | − | 0.881681i | \(-0.343588\pi\) |
−0.881681 | + | 0.471845i | \(0.843588\pi\) | |||||||
\(44\) | −1.22574 | −0.184787 | ||||||||
\(45\) | −5.19049 | − | 4.24956i | −0.773753 | − | 0.633488i | ||||
\(46\) | 1.48094 | 0.218353 | ||||||||
\(47\) | −6.84848 | − | 6.84848i | −0.998953 | − | 0.998953i | 0.00104620 | − | 0.999999i | \(-0.499667\pi\) |
−0.999999 | + | 0.00104620i | \(0.999667\pi\) | |||||||
\(48\) | −0.577604 | + | 1.63290i | −0.0833699 | + | 0.235689i | ||||
\(49\) | − | 15.9216i | − | 2.27452i | ||||||
\(50\) | −3.49237 | − | 3.57818i | −0.493895 | − | 0.506031i | ||||
\(51\) | 1.82595 | − | 0.871713i | 0.255685 | − | 0.122064i | ||||
\(52\) | −3.51689 | + | 3.51689i | −0.487705 | + | 0.487705i | ||||
\(53\) | −3.40629 | + | 3.40629i | −0.467890 | + | 0.467890i | −0.901230 | − | 0.433340i | \(-0.857335\pi\) |
0.433340 | + | 0.901230i | \(0.357335\pi\) | |||||||
\(54\) | 5.05384 | + | 1.20776i | 0.687741 | + | 0.164355i | ||||
\(55\) | −0.0166309 | + | 2.74079i | −0.00224251 | + | 0.369568i | ||||
\(56\) | − | 4.78765i | − | 0.639777i | ||||||
\(57\) | 1.63290 | + | 0.577604i | 0.216283 | + | 0.0765055i | ||||
\(58\) | 5.75831 | + | 5.75831i | 0.756103 | + | 0.756103i | ||||
\(59\) | −9.91906 | −1.29135 | −0.645676 | − | 0.763612i | \(-0.723424\pi\) | ||||
−0.645676 | + | 0.763612i | \(0.723424\pi\) | |||||||
\(60\) | 3.64338 | + | 1.31369i | 0.470358 | + | 0.169597i | ||||
\(61\) | −10.5422 | −1.34979 | −0.674894 | − | 0.737915i | \(-0.735811\pi\) | ||||
−0.674894 | + | 0.737915i | \(0.735811\pi\) | |||||||
\(62\) | −5.24666 | − | 5.24666i | −0.666327 | − | 0.666327i | ||||
\(63\) | −14.2832 | + | 1.51125i | −1.79952 | + | 0.190400i | ||||
\(64\) | − | 1.00000i | − | 0.125000i | ||||||
\(65\) | 7.81614 | + | 7.91158i | 0.969473 | + | 0.981310i | ||||
\(66\) | −0.914660 | − | 1.91591i | −0.112587 | − | 0.235833i | ||||
\(67\) | 6.00309 | − | 6.00309i | 0.733394 | − | 0.733394i | −0.237896 | − | 0.971291i | \(-0.576458\pi\) |
0.971291 | + | 0.237896i | \(0.0764579\pi\) | |||||||
\(68\) | −0.826034 | + | 0.826034i | −0.100171 | + | 0.100171i | ||||
\(69\) | 1.10509 | + | 2.31481i | 0.133038 | + | 0.278671i | ||||
\(70\) | −10.7053 | − | 0.0649592i | −1.27953 | − | 0.00776411i | ||||
\(71\) | 8.35839i | 0.991958i | 0.868334 | + | 0.495979i | \(0.165191\pi\) | ||||
−0.868334 | + | 0.495979i | \(0.834809\pi\) | |||||||
\(72\) | −2.98335 | + | 0.315656i | −0.351591 | + | 0.0372004i | ||||
\(73\) | −3.99393 | − | 3.99393i | −0.467454 | − | 0.467454i | 0.433635 | − | 0.901089i | \(-0.357231\pi\) |
−0.901089 | + | 0.433635i | \(0.857231\pi\) | |||||||
\(74\) | 8.25017 | 0.959063 | ||||||||
\(75\) | 2.98689 | − | 8.12887i | 0.344896 | − | 0.938641i | ||||
\(76\) | −1.00000 | −0.114708 | ||||||||
\(77\) | 4.14960 | + | 4.14960i | 0.472891 | + | 0.472891i | ||||
\(78\) | −8.12146 | − | 2.87279i | −0.919575 | − | 0.325279i | ||||
\(79\) | − | 6.75057i | − | 0.759498i | −0.925090 | − | 0.379749i | \(-0.876010\pi\) | ||
0.925090 | − | 0.379749i | \(-0.123990\pi\) | |||||||
\(80\) | −2.23603 | − | 0.0135681i | −0.249995 | − | 0.00151695i | ||||
\(81\) | 1.88342 | + | 8.80072i | 0.209269 | + | 0.977858i | ||||
\(82\) | 2.50013 | − | 2.50013i | 0.276093 | − | 0.276093i | ||||
\(83\) | 0.717790 | − | 0.717790i | 0.0787877 | − | 0.0787877i | −0.666615 | − | 0.745402i | \(-0.732257\pi\) |
0.745402 | + | 0.666615i | \(0.232257\pi\) | |||||||
\(84\) | 7.48341 | − | 3.57259i | 0.816507 | − | 0.389802i | ||||
\(85\) | 1.83583 | + | 1.85824i | 0.199123 | + | 0.201555i | ||||
\(86\) | 3.80067i | 0.409836i | ||||||||
\(87\) | −4.70370 | + | 13.2975i | −0.504290 | + | 1.42564i | ||||
\(88\) | 0.866730 | + | 0.866730i | 0.0923937 | + | 0.0923937i | ||||
\(89\) | −0.384471 | −0.0407539 | −0.0203769 | − | 0.999792i | \(-0.506487\pi\) | ||||
−0.0203769 | + | 0.999792i | \(0.506487\pi\) | |||||||
\(90\) | 0.665336 | + | 6.67513i | 0.0701326 | + | 0.703620i | ||||
\(91\) | 23.8120 | 2.49618 | ||||||||
\(92\) | −1.04719 | − | 1.04719i | −0.109177 | − | 0.109177i | ||||
\(93\) | 4.28576 | − | 12.1160i | 0.444413 | − | 1.25637i | ||||
\(94\) | 9.68521i | 0.998953i | ||||||||
\(95\) | −0.0135681 | + | 2.23603i | −0.00139205 | + | 0.229412i | ||||
\(96\) | 1.56306 | − | 0.746209i | 0.159530 | − | 0.0761597i | ||||
\(97\) | −12.5444 | + | 12.5444i | −1.27369 | + | 1.27369i | −0.329554 | + | 0.944137i | \(0.606899\pi\) |
−0.944137 | + | 0.329554i | \(0.893101\pi\) | |||||||
\(98\) | −11.2583 | + | 11.2583i | −1.13726 | + | 1.13726i | ||||
\(99\) | 2.31217 | − | 2.85934i | 0.232382 | − | 0.287375i | ||||
\(100\) | −0.0606771 | + | 4.99963i | −0.00606771 | + | 0.499963i | ||||
\(101\) | 1.19949i | 0.119354i | 0.998218 | + | 0.0596768i | \(0.0190070\pi\) | ||||
−0.998218 | + | 0.0596768i | \(0.980993\pi\) | |||||||
\(102\) | −1.90754 | − | 0.674750i | −0.188875 | − | 0.0668102i | ||||
\(103\) | 13.1711 | + | 13.1711i | 1.29778 | + | 1.29778i | 0.929853 | + | 0.367931i | \(0.119934\pi\) |
0.367931 | + | 0.929853i | \(0.380066\pi\) | |||||||
\(104\) | 4.97363 | 0.487705 | ||||||||
\(105\) | −7.88688 | − | 16.7816i | −0.769681 | − | 1.63772i | ||||
\(106\) | 4.81722 | 0.467890 | ||||||||
\(107\) | 9.98389 | + | 9.98389i | 0.965179 | + | 0.965179i | 0.999414 | − | 0.0342348i | \(-0.0108994\pi\) |
−0.0342348 | + | 0.999414i | \(0.510899\pi\) | |||||||
\(108\) | −2.71959 | − | 4.42762i | −0.261693 | − | 0.426048i | ||||
\(109\) | − | 8.95394i | − | 0.857632i | −0.903392 | − | 0.428816i | \(-0.858931\pi\) | ||
0.903392 | − | 0.428816i | \(-0.141069\pi\) | |||||||
\(110\) | 1.94979 | − | 1.92627i | 0.185905 | − | 0.183663i | ||||
\(111\) | 6.15635 | + | 12.8956i | 0.584335 | + | 1.22399i | ||||
\(112\) | −3.38538 | + | 3.38538i | −0.319889 | + | 0.319889i | ||||
\(113\) | 13.3747 | − | 13.3747i | 1.25818 | − | 1.25818i | 0.306225 | − | 0.951959i | \(-0.400934\pi\) |
0.951959 | − | 0.306225i | \(-0.0990661\pi\) | |||||||
\(114\) | −0.746209 | − | 1.56306i | −0.0698889 | − | 0.146394i | ||||
\(115\) | −2.35574 | + | 2.32733i | −0.219674 | + | 0.217024i | ||||
\(116\) | − | 8.14348i | − | 0.756103i | ||||||
\(117\) | −1.56996 | − | 14.8381i | −0.145142 | − | 1.37178i | ||||
\(118\) | 7.01383 | + | 7.01383i | 0.645676 | + | 0.645676i | ||||
\(119\) | 5.59288 | 0.512699 | ||||||||
\(120\) | −1.64734 | − | 3.50518i | −0.150381 | − | 0.319978i | ||||
\(121\) | 9.49756 | 0.863414 | ||||||||
\(122\) | 7.45445 | + | 7.45445i | 0.674894 | + | 0.674894i | ||||
\(123\) | 5.77349 | + | 2.04225i | 0.520578 | + | 0.184143i | ||||
\(124\) | 7.41990i | 0.666327i | ||||||||
\(125\) | 11.1785 | + | 0.203511i | 0.999834 | + | 0.0182026i | ||||
\(126\) | 11.1684 | + | 9.03116i | 0.994959 | + | 0.804560i | ||||
\(127\) | −6.46428 | + | 6.46428i | −0.573612 | + | 0.573612i | −0.933136 | − | 0.359524i | \(-0.882939\pi\) |
0.359524 | + | 0.933136i | \(0.382939\pi\) | |||||||
\(128\) | −0.707107 | + | 0.707107i | −0.0625000 | + | 0.0625000i | ||||
\(129\) | −5.94069 | + | 2.83609i | −0.523048 | + | 0.249704i | ||||
\(130\) | 0.0674826 | − | 11.1212i | 0.00591861 | − | 0.975392i | ||||
\(131\) | − | 4.64733i | − | 0.406039i | −0.979175 | − | 0.203020i | \(-0.934924\pi\) | ||
0.979175 | − | 0.203020i | \(-0.0650755\pi\) | |||||||
\(132\) | −0.707993 | + | 2.00152i | −0.0616229 | + | 0.174210i | ||||
\(133\) | 3.38538 | + | 3.38538i | 0.293550 | + | 0.293550i | ||||
\(134\) | −8.48965 | −0.733394 | ||||||||
\(135\) | −9.93718 | + | 6.02101i | −0.855256 | + | 0.518206i | ||||
\(136\) | 1.16819 | 0.100171 | ||||||||
\(137\) | −0.825480 | − | 0.825480i | −0.0705255 | − | 0.0705255i | 0.670964 | − | 0.741490i | \(-0.265880\pi\) |
−0.741490 | + | 0.670964i | \(0.765880\pi\) | |||||||
\(138\) | 0.855399 | − | 2.41824i | 0.0728164 | − | 0.205854i | ||||
\(139\) | 3.47441i | 0.294695i | 0.989085 | + | 0.147348i | \(0.0470736\pi\) | ||||
−0.989085 | + | 0.147348i | \(0.952926\pi\) | |||||||
\(140\) | 7.52387 | + | 7.61574i | 0.635883 | + | 0.643648i | ||||
\(141\) | −15.1386 | + | 7.22720i | −1.27490 | + | 0.608640i | ||||
\(142\) | 5.91027 | − | 5.91027i | 0.495979 | − | 0.495979i | ||||
\(143\) | −4.31080 | + | 4.31080i | −0.360487 | + | 0.360487i | ||||
\(144\) | 2.33275 | + | 1.88634i | 0.194396 | + | 0.157195i | ||||
\(145\) | −18.2090 | − | 0.110491i | −1.51218 | − | 0.00917579i | ||||
\(146\) | 5.64827i | 0.467454i | ||||||||
\(147\) | −25.9985 | − | 9.19640i | −2.14432 | − | 0.758506i | ||||
\(148\) | −5.83375 | − | 5.83375i | −0.479531 | − | 0.479531i | ||||
\(149\) | −1.10597 | −0.0906042 | −0.0453021 | − | 0.998973i | \(-0.514425\pi\) | ||||
−0.0453021 | + | 0.998973i | \(0.514425\pi\) | |||||||
\(150\) | −7.86003 | + | 3.63593i | −0.641768 | + | 0.296872i | ||||
\(151\) | 3.28699 | 0.267491 | 0.133746 | − | 0.991016i | \(-0.457299\pi\) | ||||
0.133746 | + | 0.991016i | \(0.457299\pi\) | |||||||
\(152\) | 0.707107 | + | 0.707107i | 0.0573539 | + | 0.0573539i | ||||
\(153\) | −0.368745 | − | 3.48511i | −0.0298113 | − | 0.281755i | ||||
\(154\) | − | 5.86842i | − | 0.472891i | ||||||
\(155\) | 16.5911 | + | 0.100674i | 1.33263 | + | 0.00808630i | ||||
\(156\) | 3.71137 | + | 7.77411i | 0.297148 | + | 0.622427i | ||||
\(157\) | −12.0134 | + | 12.0134i | −0.958773 | + | 0.958773i | −0.999183 | − | 0.0404098i | \(-0.987134\pi\) |
0.0404098 | + | 0.999183i | \(0.487134\pi\) | |||||||
\(158\) | −4.77337 | + | 4.77337i | −0.379749 | + | 0.379749i | ||||
\(159\) | 3.59466 | + | 7.52963i | 0.285075 | + | 0.597138i | ||||
\(160\) | 1.57152 | + | 1.59070i | 0.124239 | + | 0.125756i | ||||
\(161\) | 7.09025i | 0.558790i | ||||||||
\(162\) | 4.89127 | − | 7.55483i | 0.384295 | − | 0.593564i | ||||
\(163\) | 3.82552 | + | 3.82552i | 0.299638 | + | 0.299638i | 0.840872 | − | 0.541234i | \(-0.182043\pi\) |
−0.541234 | + | 0.840872i | \(0.682043\pi\) | |||||||
\(164\) | −3.53572 | −0.276093 | ||||||||
\(165\) | 4.46584 | + | 1.61025i | 0.347665 | + | 0.125358i | ||||
\(166\) | −1.01511 | −0.0787877 | ||||||||
\(167\) | 14.1056 | + | 14.1056i | 1.09152 | + | 1.09152i | 0.995366 | + | 0.0961553i | \(0.0306545\pi\) |
0.0961553 | + | 0.995366i | \(0.469345\pi\) | |||||||
\(168\) | −7.81778 | − | 2.76537i | −0.603155 | − | 0.213353i | ||||
\(169\) | 11.7370i | 0.902849i | ||||||||
\(170\) | 0.0158500 | − | 2.61210i | 0.00121564 | − | 0.200339i | ||||
\(171\) | 1.88634 | − | 2.33275i | 0.144252 | − | 0.178390i | ||||
\(172\) | 2.68748 | − | 2.68748i | 0.204918 | − | 0.204918i | ||||
\(173\) | 6.57463 | − | 6.57463i | 0.499860 | − | 0.499860i | −0.411535 | − | 0.911394i | \(-0.635007\pi\) |
0.911394 | + | 0.411535i | \(0.135007\pi\) | |||||||
\(174\) | 12.7288 | − | 6.07674i | 0.964966 | − | 0.460676i | ||||
\(175\) | 17.1311 | − | 16.7203i | 1.29499 | − | 1.26393i | ||||
\(176\) | − | 1.22574i | − | 0.0923937i | ||||||
\(177\) | −5.72929 | + | 16.1969i | −0.430639 | + | 1.21743i | ||||
\(178\) | 0.271862 | + | 0.271862i | 0.0203769 | + | 0.0203769i | ||||
\(179\) | −11.2885 | −0.843741 | −0.421870 | − | 0.906656i | \(-0.638626\pi\) | ||||
−0.421870 | + | 0.906656i | \(0.638626\pi\) | |||||||
\(180\) | 4.24956 | − | 5.19049i | 0.316744 | − | 0.386876i | ||||
\(181\) | −9.96083 | −0.740383 | −0.370191 | − | 0.928956i | \(-0.620708\pi\) | ||||
−0.370191 | + | 0.928956i | \(0.620708\pi\) | |||||||
\(182\) | −16.8377 | − | 16.8377i | −1.24809 | − | 1.24809i | ||||
\(183\) | −6.08920 | + | 17.2144i | −0.450127 | + | 1.27252i | ||||
\(184\) | 1.48094i | 0.109177i | ||||||||
\(185\) | −13.1236 | + | 12.9653i | −0.964865 | + | 0.953226i | ||||
\(186\) | −11.5978 | + | 5.53680i | −0.850391 | + | 0.405978i | ||||
\(187\) | −1.01250 | + | 1.01250i | −0.0740416 | + | 0.0740416i | ||||
\(188\) | 6.84848 | − | 6.84848i | 0.499477 | − | 0.499477i | ||||
\(189\) | −5.78233 | + | 24.1961i | −0.420602 | + | 1.76000i | ||||
\(190\) | 1.59070 | − | 1.57152i | 0.115402 | − | 0.114010i | ||||
\(191\) | − | 10.1454i | − | 0.734095i | −0.930202 | − | 0.367048i | \(-0.880369\pi\) | ||
0.930202 | − | 0.367048i | \(-0.119631\pi\) | |||||||
\(192\) | −1.63290 | − | 0.577604i | −0.117845 | − | 0.0416850i | ||||
\(193\) | 1.33016 | + | 1.33016i | 0.0957468 | + | 0.0957468i | 0.753358 | − | 0.657611i | \(-0.228433\pi\) |
−0.657611 | + | 0.753358i | \(0.728433\pi\) | |||||||
\(194\) | 17.7405 | 1.27369 | ||||||||
\(195\) | 17.4335 | − | 8.19325i | 1.24844 | − | 0.586731i | ||||
\(196\) | 15.9216 | 1.13726 | ||||||||
\(197\) | 3.67465 | + | 3.67465i | 0.261808 | + | 0.261808i | 0.825788 | − | 0.563980i | \(-0.190731\pi\) |
−0.563980 | + | 0.825788i | \(0.690731\pi\) | |||||||
\(198\) | −3.65681 | + | 0.386912i | −0.259878 | + | 0.0274966i | ||||
\(199\) | 0.894086i | 0.0633801i | 0.999498 | + | 0.0316900i | \(0.0100889\pi\) | ||||
−0.999498 | + | 0.0316900i | \(0.989911\pi\) | |||||||
\(200\) | 3.57818 | − | 3.49237i | 0.253015 | − | 0.246948i | ||||
\(201\) | −6.33506 | − | 13.2699i | −0.446841 | − | 0.935985i | ||||
\(202\) | 0.848167 | − | 0.848167i | 0.0596768 | − | 0.0596768i | ||||
\(203\) | −27.5688 | + | 27.5688i | −1.93495 | + | 1.93495i | ||||
\(204\) | 0.871713 | + | 1.82595i | 0.0610321 | + | 0.127842i | ||||
\(205\) | −0.0479729 | + | 7.90597i | −0.00335057 | + | 0.552177i | ||||
\(206\) | − | 18.6267i | − | 1.29778i | ||||||
\(207\) | 4.41817 | − | 0.467469i | 0.307084 | − | 0.0324913i | ||||
\(208\) | −3.51689 | − | 3.51689i | −0.243852 | − | 0.243852i | ||||
\(209\) | −1.22574 | −0.0847863 | ||||||||
\(210\) | −6.28951 | + | 17.4432i | −0.434017 | + | 1.20370i | ||||
\(211\) | −0.656325 | −0.0451833 | −0.0225916 | − | 0.999745i | \(-0.507192\pi\) | ||||
−0.0225916 | + | 0.999745i | \(0.507192\pi\) | |||||||
\(212\) | −3.40629 | − | 3.40629i | −0.233945 | − | 0.233945i | ||||
\(213\) | 13.6484 | + | 4.82784i | 0.935176 | + | 0.330798i | ||||
\(214\) | − | 14.1194i | − | 0.965179i | ||||||
\(215\) | −5.97281 | − | 6.04574i | −0.407342 | − | 0.412316i | ||||
\(216\) | −1.20776 | + | 5.05384i | −0.0821775 | + | 0.343870i | ||||
\(217\) | 25.1192 | − | 25.1192i | 1.70520 | − | 1.70520i | ||||
\(218\) | −6.33139 | + | 6.33139i | −0.428816 | + | 0.428816i | ||||
\(219\) | −8.82861 | + | 4.21479i | −0.596582 | + | 0.284809i | ||||
\(220\) | −2.74079 | − | 0.0166309i | −0.184784 | − | 0.00112126i | ||||
\(221\) | 5.81014i | 0.390832i | ||||||||
\(222\) | 4.76533 | − | 13.4717i | 0.319828 | − | 0.904163i | ||||
\(223\) | −5.81309 | − | 5.81309i | −0.389273 | − | 0.389273i | 0.485155 | − | 0.874428i | \(-0.338763\pi\) |
−0.874428 | + | 0.485155i | \(0.838763\pi\) | |||||||
\(224\) | 4.78765 | 0.319889 | ||||||||
\(225\) | −11.5484 | − | 9.57256i | −0.769895 | − | 0.638171i | ||||
\(226\) | −18.9147 | −1.25818 | ||||||||
\(227\) | −11.1211 | − | 11.1211i | −0.738133 | − | 0.738133i | 0.234083 | − | 0.972217i | \(-0.424791\pi\) |
−0.972217 | + | 0.234083i | \(0.924791\pi\) | |||||||
\(228\) | −0.577604 | + | 1.63290i | −0.0382528 | + | 0.108142i | ||||
\(229\) | − | 15.9766i | − | 1.05576i | −0.849318 | − | 0.527881i | \(-0.822987\pi\) | ||
0.849318 | − | 0.527881i | \(-0.177013\pi\) | |||||||
\(230\) | 3.31143 | + | 0.0200935i | 0.218349 | + | 0.00132493i | ||||
\(231\) | 9.17273 | − | 4.37907i | 0.603521 | − | 0.288122i | ||||
\(232\) | −5.75831 | + | 5.75831i | −0.378051 | + | 0.378051i | ||||
\(233\) | 10.3048 | − | 10.3048i | 0.675090 | − | 0.675090i | −0.283795 | − | 0.958885i | \(-0.591593\pi\) |
0.958885 | + | 0.283795i | \(0.0915935\pi\) | |||||||
\(234\) | −9.38198 | + | 11.6022i | −0.613319 | + | 0.758462i | ||||
\(235\) | −15.2205 | − | 15.4063i | −0.992873 | − | 1.00500i | ||||
\(236\) | − | 9.91906i | − | 0.645676i | ||||||
\(237\) | −11.0230 | − | 3.89915i | −0.716022 | − | 0.253277i | ||||
\(238\) | −3.95477 | − | 3.95477i | −0.256349 | − | 0.256349i | ||||
\(239\) | 16.1045 | 1.04172 | 0.520858 | − | 0.853644i | \(-0.325612\pi\) | ||||
0.520858 | + | 0.853644i | \(0.325612\pi\) | |||||||
\(240\) | −1.31369 | + | 3.64338i | −0.0847985 | + | 0.235179i | ||||
\(241\) | −19.9193 | −1.28312 | −0.641559 | − | 0.767074i | \(-0.721712\pi\) | ||||
−0.641559 | + | 0.767074i | \(0.721712\pi\) | |||||||
\(242\) | −6.71579 | − | 6.71579i | −0.431707 | − | 0.431707i | ||||
\(243\) | 15.4586 | + | 2.00789i | 0.991670 | + | 0.128806i | ||||
\(244\) | − | 10.5422i | − | 0.674894i | ||||||
\(245\) | 0.216026 | − | 35.6012i | 0.0138014 | − | 2.27448i | ||||
\(246\) | −2.63839 | − | 5.52656i | −0.168218 | − | 0.352361i | ||||
\(247\) | −3.51689 | + | 3.51689i | −0.223774 | + | 0.223774i | ||||
\(248\) | 5.24666 | − | 5.24666i | 0.333163 | − | 0.333163i | ||||
\(249\) | −0.757484 | − | 1.58668i | −0.0480036 | − | 0.100552i | ||||
\(250\) | −7.76048 | − | 8.04829i | −0.490816 | − | 0.509018i | ||||
\(251\) | − | 17.8998i | − | 1.12982i | −0.825151 | − | 0.564912i | \(-0.808910\pi\) | ||
0.825151 | − | 0.564912i | \(-0.191090\pi\) | |||||||
\(252\) | −1.51125 | − | 14.2832i | −0.0951998 | − | 0.899759i | ||||
\(253\) | −1.28358 | − | 1.28358i | −0.0806979 | − | 0.0806979i | ||||
\(254\) | 9.14187 | 0.573612 | ||||||||
\(255\) | 4.09471 | − | 1.92440i | 0.256421 | − | 0.120511i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 14.5464 | + | 14.5464i | 0.907378 | + | 0.907378i | 0.996060 | − | 0.0886822i | \(-0.0282655\pi\) |
−0.0886822 | + | 0.996060i | \(0.528266\pi\) | |||||||
\(258\) | 6.20612 | + | 2.19528i | 0.386376 | + | 0.136672i | ||||
\(259\) | 39.4990i | 2.45435i | ||||||||
\(260\) | −7.91158 | + | 7.81614i | −0.490655 | + | 0.484737i | ||||
\(261\) | 18.9967 | + | 15.3614i | 1.17586 | + | 0.950846i | ||||
\(262\) | −3.28616 | + | 3.28616i | −0.203020 | + | 0.203020i | ||||
\(263\) | −6.05674 | + | 6.05674i | −0.373475 | + | 0.373475i | −0.868741 | − | 0.495266i | \(-0.835070\pi\) |
0.495266 | + | 0.868741i | \(0.335070\pi\) | |||||||
\(264\) | 1.91591 | − | 0.914660i | 0.117916 | − | 0.0562934i | ||||
\(265\) | −7.66277 | + | 7.57034i | −0.470720 | + | 0.465042i | ||||
\(266\) | − | 4.78765i | − | 0.293550i | ||||||
\(267\) | −0.222072 | + | 0.627804i | −0.0135906 | + | 0.0384210i | ||||
\(268\) | 6.00309 | + | 6.00309i | 0.366697 | + | 0.366697i | ||||
\(269\) | 9.51326 | 0.580034 | 0.290017 | − | 0.957022i | \(-0.406339\pi\) | ||||
0.290017 | + | 0.957022i | \(0.406339\pi\) | |||||||
\(270\) | 11.2841 | + | 2.76915i | 0.686731 | + | 0.168525i | ||||
\(271\) | 0.405502 | 0.0246325 | 0.0123162 | − | 0.999924i | \(-0.496080\pi\) | ||||
0.0123162 | + | 0.999924i | \(0.496080\pi\) | |||||||
\(272\) | −0.826034 | − | 0.826034i | −0.0500857 | − | 0.0500857i | ||||
\(273\) | 13.7539 | − | 38.8828i | 0.832426 | − | 2.35329i | ||||
\(274\) | 1.16740i | 0.0705255i | ||||||||
\(275\) | −0.0743744 | + | 6.12825i | −0.00448494 | + | 0.369548i | ||||
\(276\) | −2.31481 | + | 1.10509i | −0.139335 | + | 0.0665189i | ||||
\(277\) | 3.15621 | − | 3.15621i | 0.189639 | − | 0.189639i | −0.605901 | − | 0.795540i | \(-0.707187\pi\) |
0.795540 | + | 0.605901i | \(0.207187\pi\) | |||||||
\(278\) | 2.45678 | − | 2.45678i | 0.147348 | − | 0.147348i | ||||
\(279\) | −17.3088 | − | 13.9965i | −1.03625 | − | 0.837947i | ||||
\(280\) | 0.0649592 | − | 10.7053i | 0.00388205 | − | 0.639765i | ||||
\(281\) | − | 11.9223i | − | 0.711227i | −0.934633 | − | 0.355613i | \(-0.884272\pi\) | ||
0.934633 | − | 0.355613i | \(-0.115728\pi\) | |||||||
\(282\) | 15.8150 | + | 5.59422i | 0.941770 | + | 0.333131i | ||||
\(283\) | 11.1386 | + | 11.1386i | 0.662120 | + | 0.662120i | 0.955879 | − | 0.293759i | \(-0.0949063\pi\) |
−0.293759 | + | 0.955879i | \(0.594906\pi\) | |||||||
\(284\) | −8.35839 | −0.495979 | ||||||||
\(285\) | 3.64338 | + | 1.31369i | 0.215815 | + | 0.0778165i | ||||
\(286\) | 6.09639 | 0.360487 | ||||||||
\(287\) | 11.9698 | + | 11.9698i | 0.706553 | + | 0.706553i | ||||
\(288\) | −0.315656 | − | 2.98335i | −0.0186002 | − | 0.175795i | ||||
\(289\) | − | 15.6353i | − | 0.919726i | ||||||
\(290\) | 12.7976 | + | 12.9539i | 0.751501 | + | 0.760677i | ||||
\(291\) | 13.2381 | + | 27.7295i | 0.776031 | + | 1.62553i | ||||
\(292\) | 3.99393 | − | 3.99393i | 0.233727 | − | 0.233727i | ||||
\(293\) | −3.32969 | + | 3.32969i | −0.194522 | + | 0.194522i | −0.797647 | − | 0.603125i | \(-0.793922\pi\) |
0.603125 | + | 0.797647i | \(0.293922\pi\) | |||||||
\(294\) | 11.8809 | + | 24.8866i | 0.692907 | + | 1.45141i | ||||
\(295\) | −22.1793 | − | 0.134582i | −1.29133 | − | 0.00783569i | ||||
\(296\) | 8.25017i | 0.479531i | ||||||||
\(297\) | −3.33352 | − | 5.42712i | −0.193430 | − | 0.314913i | ||||
\(298\) | 0.782036 | + | 0.782036i | 0.0453021 | + | 0.0453021i | ||||
\(299\) | −7.36568 | −0.425968 | ||||||||
\(300\) | 8.12887 | + | 2.98689i | 0.469320 | + | 0.172448i | ||||
\(301\) | −18.1963 | −1.04882 | ||||||||
\(302\) | −2.32425 | − | 2.32425i | −0.133746 | − | 0.133746i | ||||
\(303\) | 1.95865 | + | 0.692830i | 0.112522 | + | 0.0398020i | ||||
\(304\) | − | 1.00000i | − | 0.0573539i | ||||||
\(305\) | −23.5726 | − | 0.143037i | −1.34976 | − | 0.00819027i | ||||
\(306\) | −2.20360 | + | 2.72509i | −0.125972 | + | 0.155783i | ||||
\(307\) | −1.69015 | + | 1.69015i | −0.0964621 | + | 0.0964621i | −0.753691 | − | 0.657229i | \(-0.771728\pi\) |
0.657229 | + | 0.753691i | \(0.271728\pi\) | |||||||
\(308\) | −4.14960 | + | 4.14960i | −0.236446 | + | 0.236446i | ||||
\(309\) | 29.1147 | − | 13.8994i | 1.65628 | − | 0.790711i | ||||
\(310\) | −11.6605 | − | 11.8029i | −0.662271 | − | 0.670358i | ||||
\(311\) | − | 14.3337i | − | 0.812790i | −0.913697 | − | 0.406395i | \(-0.866786\pi\) | ||
0.913697 | − | 0.406395i | \(-0.133214\pi\) | |||||||
\(312\) | 2.87279 | − | 8.12146i | 0.162640 | − | 0.459787i | ||||
\(313\) | 1.56414 | + | 1.56414i | 0.0884102 | + | 0.0884102i | 0.749929 | − | 0.661519i | \(-0.230088\pi\) |
−0.661519 | + | 0.749929i | \(0.730088\pi\) | |||||||
\(314\) | 16.9895 | 0.958773 | ||||||||
\(315\) | −31.9582 | + | 3.18540i | −1.80064 | + | 0.179477i | ||||
\(316\) | 6.75057 | 0.379749 | ||||||||
\(317\) | −21.5987 | − | 21.5987i | −1.21311 | − | 1.21311i | −0.969999 | − | 0.243107i | \(-0.921833\pi\) |
−0.243107 | − | 0.969999i | \(-0.578167\pi\) | |||||||
\(318\) | 2.78245 | − | 7.86606i | 0.156032 | − | 0.441107i | ||||
\(319\) | − | 9.98179i | − | 0.558873i | ||||||
\(320\) | 0.0135681 | − | 2.23603i | 0.000758477 | − | 0.124998i | ||||
\(321\) | 22.0695 | − | 10.5360i | 1.23180 | − | 0.588062i | ||||
\(322\) | 5.01356 | − | 5.01356i | 0.279395 | − | 0.279395i | ||||
\(323\) | −0.826034 | + | 0.826034i | −0.0459618 | + | 0.0459618i | ||||
\(324\) | −8.80072 | + | 1.88342i | −0.488929 | + | 0.104635i | ||||
\(325\) | 17.3698 | + | 17.7966i | 0.963501 | + | 0.987175i | ||||
\(326\) | − | 5.41010i | − | 0.299638i | ||||||
\(327\) | −14.6209 | − | 5.17183i | −0.808538 | − | 0.286003i | ||||
\(328\) | 2.50013 | + | 2.50013i | 0.138047 | + | 0.138047i | ||||
\(329\) | −46.3694 | −2.55643 | ||||||||
\(330\) | −2.01921 | − | 4.29644i | −0.111154 | − | 0.236511i | ||||
\(331\) | −6.37126 | −0.350196 | −0.175098 | − | 0.984551i | \(-0.556024\pi\) | ||||
−0.175098 | + | 0.984551i | \(0.556024\pi\) | |||||||
\(332\) | 0.717790 | + | 0.717790i | 0.0393939 | + | 0.0393939i | ||||
\(333\) | 24.6131 | − | 2.60421i | 1.34879 | − | 0.142710i | ||||
\(334\) | − | 19.9483i | − | 1.09152i | ||||||
\(335\) | 13.5045 | − | 13.3416i | 0.737831 | − | 0.728931i | ||||
\(336\) | 3.57259 | + | 7.48341i | 0.194901 | + | 0.408254i | ||||
\(337\) | 1.13280 | − | 1.13280i | 0.0617073 | − | 0.0617073i | −0.675580 | − | 0.737287i | \(-0.736107\pi\) |
0.737287 | + | 0.675580i | \(0.236107\pi\) | |||||||
\(338\) | 8.29934 | − | 8.29934i | 0.451424 | − | 0.451424i | ||||
\(339\) | −14.1143 | − | 29.5648i | −0.766583 | − | 1.60574i | ||||
\(340\) | −1.85824 | + | 1.83583i | −0.100777 | + | 0.0995617i | ||||
\(341\) | 9.09487i | 0.492515i | ||||||||
\(342\) | −2.98335 | + | 0.315656i | −0.161321 | + | 0.0170687i | ||||
\(343\) | −30.2032 | − | 30.2032i | −1.63082 | − | 1.63082i | ||||
\(344\) | −3.80067 | −0.204918 | ||||||||
\(345\) | 2.43961 | + | 5.19098i | 0.131344 | + | 0.279473i | ||||
\(346\) | −9.29793 | −0.499860 | ||||||||
\(347\) | 22.1434 | + | 22.1434i | 1.18872 | + | 1.18872i | 0.977422 | + | 0.211296i | \(0.0677683\pi\) |
0.211296 | + | 0.977422i | \(0.432232\pi\) | |||||||
\(348\) | −13.2975 | − | 4.70370i | −0.712821 | − | 0.252145i | ||||
\(349\) | 19.6754i | 1.05320i | 0.850113 | + | 0.526600i | \(0.176533\pi\) | ||||
−0.850113 | + | 0.526600i | \(0.823467\pi\) | |||||||
\(350\) | −23.9365 | − | 0.290501i | −1.27946 | − | 0.0155279i | ||||
\(351\) | −25.1360 | − | 6.00695i | −1.34166 | − | 0.320627i | ||||
\(352\) | −0.866730 | + | 0.866730i | −0.0461969 | + | 0.0461969i | ||||
\(353\) | −24.9047 | + | 24.9047i | −1.32554 | + | 1.32554i | −0.416330 | + | 0.909214i | \(0.636684\pi\) |
−0.909214 | + | 0.416330i | \(0.863316\pi\) | |||||||
\(354\) | 15.5041 | − | 7.40169i | 0.824035 | − | 0.393396i | ||||
\(355\) | −0.113407 | + | 18.6896i | −0.00601902 | + | 0.991940i | ||||
\(356\) | − | 0.384471i | − | 0.0203769i | ||||||
\(357\) | 3.23047 | − | 9.13264i | 0.170975 | − | 0.483350i | ||||
\(358\) | 7.98216 | + | 7.98216i | 0.421870 | + | 0.421870i | ||||
\(359\) | 20.9304 | 1.10466 | 0.552331 | − | 0.833625i | \(-0.313739\pi\) | ||||
0.552331 | + | 0.833625i | \(0.313739\pi\) | |||||||
\(360\) | −6.67513 | + | 0.665336i | −0.351810 | + | 0.0350663i | ||||
\(361\) | −1.00000 | −0.0526316 | ||||||||
\(362\) | 7.04337 | + | 7.04337i | 0.370191 | + | 0.370191i | ||||
\(363\) | 5.48583 | − | 15.5086i | 0.287931 | − | 0.813990i | ||||
\(364\) | 23.8120i | 1.24809i | ||||||||
\(365\) | −8.87634 | − | 8.98472i | −0.464609 | − | 0.470282i | ||||
\(366\) | 16.4781 | − | 7.86667i | 0.861325 | − | 0.411198i | ||||
\(367\) | 26.3718 | − | 26.3718i | 1.37660 | − | 1.37660i | 0.526301 | − | 0.850298i | \(-0.323578\pi\) |
0.850298 | − | 0.526301i | \(-0.176422\pi\) | |||||||
\(368\) | 1.04719 | − | 1.04719i | 0.0545883 | − | 0.0545883i | ||||
\(369\) | 6.66958 | − | 8.24795i | 0.347205 | − | 0.429371i | ||||
\(370\) | 18.4476 | + | 0.111939i | 0.959045 | + | 0.00581942i | ||||
\(371\) | 23.0632i | 1.19738i | ||||||||
\(372\) | 12.1160 | + | 4.28576i | 0.628184 | + | 0.222206i | ||||
\(373\) | −6.66242 | − | 6.66242i | −0.344967 | − | 0.344967i | 0.513264 | − | 0.858231i | \(-0.328436\pi\) |
−0.858231 | + | 0.513264i | \(0.828436\pi\) | |||||||
\(374\) | 1.43190 | 0.0740416 | ||||||||
\(375\) | 6.78905 | − | 18.1358i | 0.350585 | − | 0.936531i | ||||
\(376\) | −9.68521 | −0.499477 | ||||||||
\(377\) | −28.6397 | − | 28.6397i | −1.47502 | − | 1.47502i | ||||
\(378\) | 21.1979 | − | 13.0205i | 1.09030 | − | 0.669701i | ||||
\(379\) | − | 0.205871i | − | 0.0105749i | −0.999986 | − | 0.00528745i | \(-0.998317\pi\) | ||
0.999986 | − | 0.00528745i | \(-0.00168305\pi\) | |||||||
\(380\) | −2.23603 | − | 0.0135681i | −0.114706 | − | 0.000696027i | ||||
\(381\) | 6.82175 | + | 14.2893i | 0.349489 | + | 0.732065i | ||||
\(382\) | −7.17388 | + | 7.17388i | −0.367048 | + | 0.367048i | ||||
\(383\) | 8.26926 | − | 8.26926i | 0.422539 | − | 0.422539i | −0.463538 | − | 0.886077i | \(-0.653420\pi\) |
0.886077 | + | 0.463538i | \(0.153420\pi\) | |||||||
\(384\) | 0.746209 | + | 1.56306i | 0.0380798 | + | 0.0797648i | ||||
\(385\) | 9.22232 | + | 9.33493i | 0.470013 | + | 0.475752i | ||||
\(386\) | − | 1.88113i | − | 0.0957468i | ||||||
\(387\) | 1.19970 | + | 11.3387i | 0.0609843 | + | 0.576379i | ||||
\(388\) | −12.5444 | − | 12.5444i | −0.636846 | − | 0.636846i | ||||
\(389\) | 25.3999 | 1.28782 | 0.643912 | − | 0.765099i | \(-0.277310\pi\) | ||||
0.643912 | + | 0.765099i | \(0.277310\pi\) | |||||||
\(390\) | −18.1208 | − | 6.53383i | −0.917584 | − | 0.330853i | ||||
\(391\) | −1.73002 | −0.0874910 | ||||||||
\(392\) | −11.2583 | − | 11.2583i | −0.568630 | − | 0.568630i | ||||
\(393\) | −7.58865 | − | 2.68432i | −0.382797 | − | 0.135406i | ||||
\(394\) | − | 5.19674i | − | 0.261808i | ||||||
\(395\) | 0.0915921 | − | 15.0944i | 0.00460850 | − | 0.759484i | ||||
\(396\) | 2.85934 | + | 2.31217i | 0.143687 | + | 0.116191i | ||||
\(397\) | 14.4297 | − | 14.4297i | 0.724206 | − | 0.724206i | −0.245253 | − | 0.969459i | \(-0.578871\pi\) |
0.969459 | + | 0.245253i | \(0.0788711\pi\) | |||||||
\(398\) | 0.632214 | − | 0.632214i | 0.0316900 | − | 0.0316900i | ||||
\(399\) | 7.48341 | − | 3.57259i | 0.374639 | − | 0.178853i | ||||
\(400\) | −4.99963 | − | 0.0606771i | −0.249982 | − | 0.00303385i | ||||
\(401\) | − | 8.03063i | − | 0.401030i | −0.979691 | − | 0.200515i | \(-0.935738\pi\) | ||
0.979691 | − | 0.200515i | \(-0.0642616\pi\) | |||||||
\(402\) | −4.90366 | + | 13.8628i | −0.244572 | + | 0.691413i | ||||
\(403\) | 26.0950 | + | 26.0950i | 1.29988 | + | 1.29988i | ||||
\(404\) | −1.19949 | −0.0596768 | ||||||||
\(405\) | 4.09197 | + | 19.7042i | 0.203332 | + | 0.979110i | ||||
\(406\) | 38.9882 | 1.93495 | ||||||||
\(407\) | −7.15067 | − | 7.15067i | −0.354445 | − | 0.354445i | ||||
\(408\) | 0.674750 | − | 1.90754i | 0.0334051 | − | 0.0944373i | ||||
\(409\) | 13.8653i | 0.685596i | 0.939409 | + | 0.342798i | \(0.111375\pi\) | ||||
−0.939409 | + | 0.342798i | \(0.888625\pi\) | |||||||
\(410\) | 5.62429 | − | 5.55644i | 0.277764 | − | 0.274413i | ||||
\(411\) | −1.82473 | + | 0.871129i | −0.0900073 | + | 0.0429696i | ||||
\(412\) | −13.1711 | + | 13.1711i | −0.648892 | + | 0.648892i | ||||
\(413\) | −33.5798 | + | 33.5798i | −1.65235 | + | 1.65235i | ||||
\(414\) | −3.45467 | − | 2.79357i | −0.169788 | − | 0.137296i | ||||
\(415\) | 1.61474 | − | 1.59526i | 0.0792643 | − | 0.0783082i | ||||
\(416\) | 4.97363i | 0.243852i | ||||||||
\(417\) | 5.67337 | + | 2.00683i | 0.277826 | + | 0.0982749i | ||||
\(418\) | 0.866730 | + | 0.866730i | 0.0423931 | + | 0.0423931i | ||||
\(419\) | −17.7272 | −0.866028 | −0.433014 | − | 0.901387i | \(-0.642550\pi\) | ||||
−0.433014 | + | 0.901387i | \(0.642550\pi\) | |||||||
\(420\) | 16.7816 | − | 7.88688i | 0.818858 | − | 0.384840i | ||||
\(421\) | 2.65269 | 0.129284 | 0.0646420 | − | 0.997909i | \(-0.479409\pi\) | ||||
0.0646420 | + | 0.997909i | \(0.479409\pi\) | |||||||
\(422\) | 0.464092 | + | 0.464092i | 0.0225916 | + | 0.0225916i | ||||
\(423\) | 3.05719 | + | 28.8943i | 0.148646 | + | 1.40489i | ||||
\(424\) | 4.81722i | 0.233945i | ||||||||
\(425\) | 4.07974 | + | 4.17999i | 0.197897 | + | 0.202759i | ||||
\(426\) | −6.23711 | − | 13.0647i | −0.302189 | − | 0.632987i | ||||
\(427\) | −35.6893 | + | 35.6893i | −1.72713 | + | 1.72713i | ||||
\(428\) | −9.98389 | + | 9.98389i | −0.482590 | + | 0.482590i | ||||
\(429\) | 4.54918 | + | 9.52905i | 0.219637 | + | 0.460067i | ||||
\(430\) | −0.0515677 | + | 8.49839i | −0.00248681 | + | 0.409829i | ||||
\(431\) | − | 17.0087i | − | 0.819280i | −0.912247 | − | 0.409640i | \(-0.865654\pi\) | ||
0.912247 | − | 0.409640i | \(-0.134346\pi\) | |||||||
\(432\) | 4.42762 | − | 2.71959i | 0.213024 | − | 0.130846i | ||||
\(433\) | 13.8732 | + | 13.8732i | 0.666705 | + | 0.666705i | 0.956952 | − | 0.290247i | \(-0.0937375\pi\) |
−0.290247 | + | 0.956952i | \(0.593738\pi\) | |||||||
\(434\) | −35.5239 | −1.70520 | ||||||||
\(435\) | −10.6980 | + | 29.6698i | −0.512931 | + | 1.42256i | ||||
\(436\) | 8.95394 | 0.428816 | ||||||||
\(437\) | −1.04719 | − | 1.04719i | −0.0500937 | − | 0.0500937i | ||||
\(438\) | 9.22308 | + | 3.26246i | 0.440696 | + | 0.155887i | ||||
\(439\) | − | 7.44257i | − | 0.355214i | −0.984101 | − | 0.177607i | \(-0.943164\pi\) | ||
0.984101 | − | 0.177607i | \(-0.0568357\pi\) | |||||||
\(440\) | 1.92627 | + | 1.94979i | 0.0918314 | + | 0.0929526i | ||||
\(441\) | −30.0337 | + | 37.1412i | −1.43017 | + | 1.76863i | ||||
\(442\) | 4.10839 | − | 4.10839i | 0.195416 | − | 0.195416i | ||||
\(443\) | 14.0091 | − | 14.0091i | 0.665593 | − | 0.665593i | −0.291100 | − | 0.956693i | \(-0.594021\pi\) |
0.956693 | + | 0.291100i | \(0.0940213\pi\) | |||||||
\(444\) | −12.8956 | + | 6.15635i | −0.611996 | + | 0.292168i | ||||
\(445\) | −0.859688 | − | 0.00521653i | −0.0407531 | − | 0.000247287i | ||||
\(446\) | 8.22095i | 0.389273i | ||||||||
\(447\) | −0.638810 | + | 1.80593i | −0.0302147 | + | 0.0854178i | ||||
\(448\) | −3.38538 | − | 3.38538i | −0.159944 | − | 0.159944i | ||||
\(449\) | −17.0757 | −0.805851 | −0.402926 | − | 0.915233i | \(-0.632007\pi\) | ||||
−0.402926 | + | 0.915233i | \(0.632007\pi\) | |||||||
\(450\) | 1.39714 | + | 14.9348i | 0.0658619 | + | 0.704033i | ||||
\(451\) | −4.33388 | −0.204074 | ||||||||
\(452\) | 13.3747 | + | 13.3747i | 0.629092 | + | 0.629092i | ||||
\(453\) | 1.89858 | − | 5.36734i | 0.0892030 | − | 0.252179i | ||||
\(454\) | 15.7276i | 0.738133i | ||||||||
\(455\) | 53.2444 | + | 0.323083i | 2.49613 | + | 0.0151464i | ||||
\(456\) | 1.56306 | − | 0.746209i | 0.0731972 | − | 0.0349445i | ||||
\(457\) | −4.57545 | + | 4.57545i | −0.214030 | + | 0.214030i | −0.805977 | − | 0.591947i | \(-0.798360\pi\) |
0.591947 | + | 0.805977i | \(0.298360\pi\) | |||||||
\(458\) | −11.2971 | + | 11.2971i | −0.527881 | + | 0.527881i | ||||
\(459\) | −5.90384 | − | 1.41089i | −0.275568 | − | 0.0658547i | ||||
\(460\) | −2.32733 | − | 2.35574i | −0.108512 | − | 0.109837i | ||||
\(461\) | − | 0.120191i | − | 0.00559787i | −0.999996 | − | 0.00279893i | \(-0.999109\pi\) | ||
0.999996 | − | 0.00279893i | \(-0.000890930\pi\) | |||||||
\(462\) | −9.58257 | − | 3.38963i | −0.445822 | − | 0.157700i | ||||
\(463\) | −5.82164 | − | 5.82164i | −0.270555 | − | 0.270555i | 0.558769 | − | 0.829323i | \(-0.311274\pi\) |
−0.829323 | + | 0.558769i | \(0.811274\pi\) | |||||||
\(464\) | 8.14348 | 0.378051 | ||||||||
\(465\) | 9.74747 | − | 27.0335i | 0.452028 | − | 1.25365i | ||||
\(466\) | −14.5732 | −0.675090 | ||||||||
\(467\) | 1.26700 | + | 1.26700i | 0.0586298 | + | 0.0586298i | 0.735814 | − | 0.677184i | \(-0.236800\pi\) |
−0.677184 | + | 0.735814i | \(0.736800\pi\) | |||||||
\(468\) | 14.8381 | − | 1.56996i | 0.685890 | − | 0.0725712i | ||||
\(469\) | − | 40.6455i | − | 1.87684i | ||||||
\(470\) | −0.131410 | + | 21.6564i | −0.00606147 | + | 0.998935i | ||||
\(471\) | 12.6777 | + | 26.5557i | 0.584159 | + | 1.22362i | ||||
\(472\) | −7.01383 | + | 7.01383i | −0.322838 | + | 0.322838i | ||||
\(473\) | 3.29415 | − | 3.29415i | 0.151465 | − | 0.151465i | ||||
\(474\) | 5.03734 | + | 10.5516i | 0.231373 | + | 0.484650i | ||||
\(475\) | −0.0606771 | + | 4.99963i | −0.00278406 | + | 0.229399i | ||||
\(476\) | 5.59288i | 0.256349i | ||||||||
\(477\) | 14.3714 | − | 1.52058i | 0.658023 | − | 0.0696227i | ||||
\(478\) | −11.3876 | − | 11.3876i | −0.520858 | − | 0.520858i | ||||
\(479\) | 4.76857 | 0.217881 | 0.108941 | − | 0.994048i | \(-0.465254\pi\) | ||||
0.108941 | + | 0.994048i | \(0.465254\pi\) | |||||||
\(480\) | 3.50518 | − | 1.64734i | 0.159989 | − | 0.0751903i | ||||
\(481\) | −41.0333 | −1.87096 | ||||||||
\(482\) | 14.0851 | + | 14.0851i | 0.641559 | + | 0.641559i | ||||
\(483\) | 11.5777 | + | 4.09536i | 0.526803 | + | 0.186345i | ||||
\(484\) | 9.49756i | 0.431707i | ||||||||
\(485\) | −28.2198 | + | 27.8794i | −1.28140 | + | 1.26594i | ||||
\(486\) | −9.51109 | − | 12.3507i | −0.431432 | − | 0.560238i | ||||
\(487\) | 18.6777 | − | 18.6777i | 0.846368 | − | 0.846368i | −0.143310 | − | 0.989678i | \(-0.545775\pi\) |
0.989678 | + | 0.143310i | \(0.0457747\pi\) | |||||||
\(488\) | −7.45445 | + | 7.45445i | −0.337447 | + | 0.337447i | ||||
\(489\) | 8.45634 | − | 4.03707i | 0.382409 | − | 0.182563i | ||||
\(490\) | −25.3266 | + | 25.0211i | −1.14414 | + | 1.13034i | ||||
\(491\) | 42.9796i | 1.93964i | 0.243814 | + | 0.969822i | \(0.421601\pi\) | ||||
−0.243814 | + | 0.969822i | \(0.578399\pi\) | |||||||
\(492\) | −2.04225 | + | 5.77349i | −0.0920716 | + | 0.260289i | ||||
\(493\) | −6.72679 | − | 6.72679i | −0.302959 | − | 0.302959i | ||||
\(494\) | 4.97363 | 0.223774 | ||||||||
\(495\) | 5.20886 | − | 6.36220i | 0.234121 | − | 0.285960i | ||||
\(496\) | −7.41990 | −0.333163 | ||||||||
\(497\) | 28.2963 | + | 28.2963i | 1.26926 | + | 1.26926i | ||||
\(498\) | −0.586331 | + | 1.65757i | −0.0262741 | + | 0.0742777i | ||||
\(499\) | − | 20.8455i | − | 0.933173i | −0.884475 | − | 0.466587i | \(-0.845484\pi\) | ||
0.884475 | − | 0.466587i | \(-0.154516\pi\) | |||||||
\(500\) | −0.203511 | + | 11.1785i | −0.00910128 | + | 0.499917i | ||||
\(501\) | 31.1805 | − | 14.8856i | 1.39304 | − | 0.665040i | ||||
\(502\) | −12.6570 | + | 12.6570i | −0.564912 | + | 0.564912i | ||||
\(503\) | 15.7847 | − | 15.7847i | 0.703804 | − | 0.703804i | −0.261421 | − | 0.965225i | \(-0.584191\pi\) |
0.965225 | + | 0.261421i | \(0.0841911\pi\) | |||||||
\(504\) | −9.03116 | + | 11.1684i | −0.402280 | + | 0.497480i | ||||
\(505\) | −0.0162747 | + | 2.68209i | −0.000724216 | + | 0.119351i | ||||
\(506\) | 1.81525i | 0.0806979i | ||||||||
\(507\) | 19.1654 | + | 6.77936i | 0.851167 | + | 0.301082i | ||||
\(508\) | −6.46428 | − | 6.46428i | −0.286806 | − | 0.286806i | ||||
\(509\) | −4.31039 | −0.191055 | −0.0955274 | − | 0.995427i | \(-0.530454\pi\) | ||||
−0.0955274 | + | 0.995427i | \(0.530454\pi\) | |||||||
\(510\) | −4.25615 | − | 1.53464i | −0.188466 | − | 0.0679551i | ||||
\(511\) | −27.0420 | −1.19627 | ||||||||
\(512\) | −0.707107 | − | 0.707107i | −0.0312500 | − | 0.0312500i | ||||
\(513\) | −2.71959 | − | 4.42762i | −0.120073 | − | 0.195484i | ||||
\(514\) | − | 20.5717i | − | 0.907378i | ||||||
\(515\) | 29.2722 | + | 29.6296i | 1.28989 | + | 1.30563i | ||||
\(516\) | −2.83609 | − | 5.94069i | −0.124852 | − | 0.261524i | ||||
\(517\) | 8.39446 | − | 8.39446i | 0.369188 | − | 0.369188i | ||||
\(518\) | 27.9300 | − | 27.9300i | 1.22717 | − | 1.22717i | ||||
\(519\) | −6.93820 | − | 14.5333i | −0.304553 | − | 0.637939i | ||||
\(520\) | 11.1212 | + | 0.0674826i | 0.487696 | + | 0.00295931i | ||||
\(521\) | − | 11.7874i | − | 0.516417i | −0.966089 | − | 0.258208i | \(-0.916868\pi\) | ||
0.966089 | − | 0.258208i | \(-0.0831321\pi\) | |||||||
\(522\) | −2.57053 | − | 24.2948i | −0.112509 | − | 1.06336i | ||||
\(523\) | −9.59018 | − | 9.59018i | −0.419349 | − | 0.419349i | 0.465630 | − | 0.884979i | \(-0.345828\pi\) |
−0.884979 | + | 0.465630i | \(0.845828\pi\) | |||||||
\(524\) | 4.64733 | 0.203020 | ||||||||
\(525\) | −17.4076 | − | 37.6311i | −0.759729 | − | 1.64236i | ||||
\(526\) | 8.56553 | 0.373475 | ||||||||
\(527\) | 6.12909 | + | 6.12909i | 0.266987 | + | 0.266987i | ||||
\(528\) | −2.00152 | − | 0.707993i | −0.0871048 | − | 0.0308114i | ||||
\(529\) | 20.8068i | 0.904644i | ||||||||
\(530\) | 10.7714 | + | 0.0653603i | 0.467881 | + | 0.00283907i | ||||
\(531\) | 23.1387 | + | 18.7107i | 1.00413 | + | 0.811977i | ||||
\(532\) | −3.38538 | + | 3.38538i | −0.146775 | + | 0.146775i | ||||
\(533\) | −12.4347 | + | 12.4347i | −0.538609 | + | 0.538609i | ||||
\(534\) | 0.600953 | − | 0.286896i | 0.0260058 | − | 0.0124152i | ||||
\(535\) | 22.1888 | + | 22.4597i | 0.959305 | + | 0.971018i | ||||
\(536\) | − | 8.48965i | − | 0.366697i | ||||||
\(537\) | −6.52027 | + | 18.4330i | −0.281370 | + | 0.795443i | ||||
\(538\) | −6.72689 | − | 6.72689i | −0.290017 | − | 0.290017i | ||||
\(539\) | 19.5158 | 0.840605 | ||||||||
\(540\) | −6.02101 | − | 9.93718i | −0.259103 | − | 0.427628i | ||||
\(541\) | −29.8151 | −1.28185 | −0.640925 | − | 0.767603i | \(-0.721449\pi\) | ||||
−0.640925 | + | 0.767603i | \(0.721449\pi\) | |||||||
\(542\) | −0.286733 | − | 0.286733i | −0.0123162 | − | 0.0123162i | ||||
\(543\) | −5.75341 | + | 16.2651i | −0.246903 | + | 0.698001i | ||||
\(544\) | 1.16819i | 0.0500857i | ||||||||
\(545\) | 0.121488 | − | 20.0212i | 0.00520395 | − | 0.857616i | ||||
\(546\) | −37.2198 | + | 17.7688i | −1.59286 | + | 0.760433i | ||||
\(547\) | −9.70052 | + | 9.70052i | −0.414764 | + | 0.414764i | −0.883395 | − | 0.468630i | \(-0.844748\pi\) |
0.468630 | + | 0.883395i | \(0.344748\pi\) | |||||||
\(548\) | 0.825480 | − | 0.825480i | 0.0352628 | − | 0.0352628i | ||||
\(549\) | 24.5922 | + | 19.8862i | 1.04957 | + | 0.848721i | ||||
\(550\) | 4.38592 | − | 4.28074i | 0.187016 | − | 0.182531i | ||||
\(551\) | − | 8.14348i | − | 0.346924i | ||||||
\(552\) | 2.41824 | + | 0.855399i | 0.102927 | + | 0.0364082i | ||||
\(553\) | −22.8533 | − | 22.8533i | −0.971819 | − | 0.971819i | ||||
\(554\) | −4.46356 | −0.189639 | ||||||||
\(555\) | 13.5908 | + | 28.9183i | 0.576898 | + | 1.22751i | ||||
\(556\) | −3.47441 | −0.147348 | ||||||||
\(557\) | 19.7758 | + | 19.7758i | 0.837928 | + | 0.837928i | 0.988586 | − | 0.150658i | \(-0.0481393\pi\) |
−0.150658 | + | 0.988586i | \(0.548139\pi\) | |||||||
\(558\) | 2.34213 | + | 22.1361i | 0.0991504 | + | 0.937097i | ||||
\(559\) | − | 18.9031i | − | 0.799517i | ||||||
\(560\) | −7.61574 | + | 7.52387i | −0.321824 | + | 0.317942i | ||||
\(561\) | 1.06849 | + | 2.23815i | 0.0451119 | + | 0.0944946i | ||||
\(562\) | −8.43036 | + | 8.43036i | −0.355613 | + | 0.355613i | ||||
\(563\) | 26.3822 | − | 26.3822i | 1.11188 | − | 1.11188i | 0.118981 | − | 0.992896i | \(-0.462037\pi\) |
0.992896 | − | 0.118981i | \(-0.0379629\pi\) | |||||||
\(564\) | −7.22720 | − | 15.1386i | −0.304320 | − | 0.637451i | ||||
\(565\) | 30.0876 | − | 29.7247i | 1.26580 | − | 1.25053i | ||||
\(566\) | − | 15.7523i | − | 0.662120i | ||||||
\(567\) | 36.1699 | + | 23.4177i | 1.51899 | + | 0.983452i | ||||
\(568\) | 5.91027 | + | 5.91027i | 0.247990 | + | 0.247990i | ||||
\(569\) | −21.7175 | −0.910445 | −0.455222 | − | 0.890378i | \(-0.650440\pi\) | ||||
−0.455222 | + | 0.890378i | \(0.650440\pi\) | |||||||
\(570\) | −1.64734 | − | 3.50518i | −0.0689993 | − | 0.146816i | ||||
\(571\) | −15.2769 | −0.639319 | −0.319660 | − | 0.947532i | \(-0.603569\pi\) | ||||
−0.319660 | + | 0.947532i | \(0.603569\pi\) | |||||||
\(572\) | −4.31080 | − | 4.31080i | −0.180243 | − | 0.180243i | ||||
\(573\) | −16.5665 | − | 5.86002i | −0.692073 | − | 0.244806i | ||||
\(574\) | − | 16.9278i | − | 0.706553i | ||||||
\(575\) | −5.29908 | + | 5.17200i | −0.220987 | + | 0.215687i | ||||
\(576\) | −1.88634 | + | 2.33275i | −0.0785976 | + | 0.0971978i | ||||
\(577\) | 7.00181 | − | 7.00181i | 0.291489 | − | 0.291489i | −0.546179 | − | 0.837668i | \(-0.683918\pi\) |
0.837668 | + | 0.546179i | \(0.183918\pi\) | |||||||
\(578\) | −11.0559 | + | 11.0559i | −0.459863 | + | 0.459863i | ||||
\(579\) | 2.94032 | − | 1.40371i | 0.122196 | − | 0.0583364i | ||||
\(580\) | 0.110491 | − | 18.2090i | 0.00458790 | − | 0.756089i | ||||
\(581\) | − | 4.85999i | − | 0.201626i | ||||||
\(582\) | 10.2470 | − | 28.9685i | 0.424750 | − | 1.20078i | ||||
\(583\) | −4.17523 | − | 4.17523i | −0.172920 | − | 0.172920i | ||||
\(584\) | −5.64827 | −0.233727 | ||||||||
\(585\) | −3.30914 | − | 33.1996i | −0.136816 | − | 1.37264i | ||||
\(586\) | 4.70889 | 0.194522 | ||||||||
\(587\) | −5.53868 | − | 5.53868i | −0.228606 | − | 0.228606i | 0.583504 | − | 0.812110i | \(-0.301681\pi\) |
−0.812110 | + | 0.583504i | \(0.801681\pi\) | |||||||
\(588\) | 9.19640 | − | 25.9985i | 0.379253 | − | 1.07216i | ||||
\(589\) | 7.41990i | 0.305732i | ||||||||
\(590\) | 15.5880 | + | 15.7783i | 0.641746 | + | 0.649582i | ||||
\(591\) | 8.12283 | − | 3.87785i | 0.334129 | − | 0.159514i | ||||
\(592\) | 5.83375 | − | 5.83375i | 0.239766 | − | 0.239766i | ||||
\(593\) | 31.4864 | − | 31.4864i | 1.29299 | − | 1.29299i | 0.360061 | − | 0.932929i | \(-0.382756\pi\) |
0.932929 | − | 0.360061i | \(-0.117244\pi\) | |||||||
\(594\) | −1.48040 | + | 6.19470i | −0.0607415 | + | 0.254172i | ||||
\(595\) | 12.5058 | + | 0.0758846i | 0.512689 | + | 0.00311096i | ||||
\(596\) | − | 1.10597i | − | 0.0453021i | ||||||
\(597\) | 1.45996 | + | 0.516428i | 0.0597520 | + | 0.0211360i | ||||
\(598\) | 5.20832 | + | 5.20832i | 0.212984 | + | 0.212984i | ||||
\(599\) | −31.3766 | −1.28201 | −0.641007 | − | 0.767535i | \(-0.721483\pi\) | ||||
−0.641007 | + | 0.767535i | \(0.721483\pi\) | |||||||
\(600\) | −3.63593 | − | 7.86003i | −0.148436 | − | 0.320884i | ||||
\(601\) | −36.3695 | −1.48354 | −0.741771 | − | 0.670654i | \(-0.766014\pi\) | ||||
−0.741771 | + | 0.670654i | \(0.766014\pi\) | |||||||
\(602\) | 12.8667 | + | 12.8667i | 0.524408 | + | 0.524408i | ||||
\(603\) | −25.3276 | + | 2.67981i | −1.03142 | + | 0.109130i | ||||
\(604\) | 3.28699i | 0.133746i | ||||||||
\(605\) | 21.2368 | + | 0.128863i | 0.863399 | + | 0.00523904i | ||||
\(606\) | −0.895070 | − | 1.87488i | −0.0363597 | − | 0.0761618i | ||||
\(607\) | 8.74748 | − | 8.74748i | 0.355049 | − | 0.355049i | −0.506935 | − | 0.861984i | \(-0.669222\pi\) |
0.861984 | + | 0.506935i | \(0.169222\pi\) | |||||||
\(608\) | −0.707107 | + | 0.707107i | −0.0286770 | + | 0.0286770i | ||||
\(609\) | 29.0933 | + | 60.9410i | 1.17892 | + | 2.46945i | ||||
\(610\) | 16.5672 | + | 16.7695i | 0.670786 | + | 0.678977i | ||||
\(611\) | − | 48.1707i | − | 1.94878i | ||||||
\(612\) | 3.48511 | − | 0.368745i | 0.140877 | − | 0.0149056i | ||||
\(613\) | −1.37399 | − | 1.37399i | −0.0554951 | − | 0.0554951i | 0.678815 | − | 0.734310i | \(-0.262494\pi\) |
−0.734310 | + | 0.678815i | \(0.762494\pi\) | |||||||
\(614\) | 2.39024 | 0.0964621 | ||||||||
\(615\) | 12.8820 | + | 4.64485i | 0.519451 | + | 0.187299i | ||||
\(616\) | 5.86842 | 0.236446 | ||||||||
\(617\) | 11.8837 | + | 11.8837i | 0.478419 | + | 0.478419i | 0.904626 | − | 0.426207i | \(-0.140150\pi\) |
−0.426207 | + | 0.904626i | \(0.640150\pi\) | |||||||
\(618\) | −30.4156 | − | 10.7589i | −1.22350 | − | 0.432785i | ||||
\(619\) | − | 4.06759i | − | 0.163490i | −0.996653 | − | 0.0817450i | \(-0.973951\pi\) | ||
0.996653 | − | 0.0817450i | \(-0.0260493\pi\) | |||||||
\(620\) | −0.100674 | + | 16.5911i | −0.00404315 | + | 0.666314i | ||||
\(621\) | 1.78862 | − | 7.48446i | 0.0717750 | − | 0.300341i | ||||
\(622\) | −10.1355 | + | 10.1355i | −0.406395 | + | 0.406395i | ||||
\(623\) | −1.30158 | + | 1.30158i | −0.0521468 | + | 0.0521468i | ||||
\(624\) | −7.77411 | + | 3.71137i | −0.311214 | + | 0.148574i | ||||
\(625\) | 24.9926 | + | 0.606726i | 0.999705 | + | 0.0242690i | ||||
\(626\) | − | 2.21202i | − | 0.0884102i | ||||||
\(627\) | −0.707993 | + | 2.00152i | −0.0282745 | + | 0.0799329i | ||||
\(628\) | −12.0134 | − | 12.0134i | −0.479387 | − | 0.479387i | ||||
\(629\) | −9.63775 | −0.384282 | ||||||||
\(630\) | 24.8503 | + | 20.3454i | 0.990059 | + | 0.810582i | ||||
\(631\) | −5.67496 | −0.225917 | −0.112958 | − | 0.993600i | \(-0.536033\pi\) | ||||
−0.112958 | + | 0.993600i | \(0.536033\pi\) | |||||||
\(632\) | −4.77337 | − | 4.77337i | −0.189875 | − | 0.189875i | ||||
\(633\) | −0.379096 | + | 1.07172i | −0.0150677 | + | 0.0425969i | ||||
\(634\) | 30.5452i | 1.21311i | ||||||||
\(635\) | −14.5420 | + | 14.3666i | −0.577082 | + | 0.570121i | ||||
\(636\) | −7.52963 | + | 3.59466i | −0.298569 | + | 0.142537i | ||||
\(637\) | 55.9947 | − | 55.9947i | 2.21859 | − | 2.21859i | ||||
\(638\) | −7.05819 | + | 7.05819i | −0.279437 | + | 0.279437i | ||||
\(639\) | 15.7668 | − | 19.4980i | 0.623724 | − | 0.771329i | ||||
\(640\) | −1.59070 | + | 1.57152i | −0.0628781 | + | 0.0621196i | ||||
\(641\) | − | 1.58825i | − | 0.0627323i | −0.999508 | − | 0.0313661i | \(-0.990014\pi\) | ||
0.999508 | − | 0.0313661i | \(-0.00998579\pi\) | |||||||
\(642\) | −23.0555 | − | 8.15539i | −0.909930 | − | 0.321868i | ||||
\(643\) | −8.25666 | − | 8.25666i | −0.325611 | − | 0.325611i | 0.525304 | − | 0.850915i | \(-0.323952\pi\) |
−0.850915 | + | 0.525304i | \(0.823952\pi\) | |||||||
\(644\) | −7.09025 | −0.279395 | ||||||||
\(645\) | −13.3220 | + | 6.26098i | −0.524554 | + | 0.246526i | ||||
\(646\) | 1.16819 | 0.0459618 | ||||||||
\(647\) | −12.9377 | − | 12.9377i | −0.508635 | − | 0.508635i | 0.405472 | − | 0.914107i | \(-0.367107\pi\) |
−0.914107 | + | 0.405472i | \(0.867107\pi\) | |||||||
\(648\) | 7.55483 | + | 4.89127i | 0.296782 | + | 0.192147i | ||||
\(649\) | − | 12.1582i | − | 0.477251i | ||||||
\(650\) | 0.301786 | − | 24.8663i | 0.0118370 | − | 0.975338i | ||||
\(651\) | −26.5083 | − | 55.5262i | −1.03894 | − | 2.17624i | ||||
\(652\) | −3.82552 | + | 3.82552i | −0.149819 | + | 0.149819i | ||||
\(653\) | 16.2867 | − | 16.2867i | 0.637350 | − | 0.637350i | −0.312551 | − | 0.949901i | \(-0.601184\pi\) |
0.949901 | + | 0.312551i | \(0.101184\pi\) | |||||||
\(654\) | 6.68151 | + | 13.9956i | 0.261268 | + | 0.547271i | ||||
\(655\) | 0.0630553 | − | 10.3916i | 0.00246377 | − | 0.406032i | ||||
\(656\) | − | 3.53572i | − | 0.138047i | ||||||
\(657\) | 1.78291 | + | 16.8508i | 0.0695579 | + | 0.657410i | ||||
\(658\) | 32.7882 | + | 32.7882i | 1.27822 | + | 1.27822i | ||||
\(659\) | −40.1270 | −1.56313 | −0.781563 | − | 0.623827i | \(-0.785577\pi\) | ||||
−0.781563 | + | 0.623827i | \(0.785577\pi\) | |||||||
\(660\) | −1.61025 | + | 4.46584i | −0.0626788 | + | 0.173833i | ||||
\(661\) | −17.8333 | −0.693634 | −0.346817 | − | 0.937933i | \(-0.612737\pi\) | ||||
−0.346817 | + | 0.937933i | \(0.612737\pi\) | |||||||
\(662\) | 4.50516 | + | 4.50516i | 0.175098 | + | 0.175098i | ||||
\(663\) | 9.48740 | + | 3.35596i | 0.368460 | + | 0.130335i | ||||
\(664\) | − | 1.01511i | − | 0.0393939i | ||||||
\(665\) | 7.52387 | + | 7.61574i | 0.291763 | + | 0.295326i | ||||
\(666\) | −19.2456 | − | 15.5626i | −0.745750 | − | 0.603040i | ||||
\(667\) | 8.52773 | − | 8.52773i | 0.330195 | − | 0.330195i | ||||
\(668\) | −14.1056 | + | 14.1056i | −0.545761 | + | 0.545761i | ||||
\(669\) | −12.8499 | + | 6.13455i | −0.496805 | + | 0.237176i | ||||
\(670\) | −18.9831 | − | 0.115188i | −0.733381 | − | 0.00445010i | ||||
\(671\) | − | 12.9220i | − | 0.498848i | ||||||
\(672\) | 2.76537 | − | 7.81778i | 0.106676 | − | 0.301577i | ||||
\(673\) | 15.7599 | + | 15.7599i | 0.607498 | + | 0.607498i | 0.942292 | − | 0.334793i | \(-0.108667\pi\) |
−0.334793 | + | 0.942292i | \(0.608667\pi\) | |||||||
\(674\) | −1.60201 | −0.0617073 | ||||||||
\(675\) | −22.3015 | + | 13.3283i | −0.858385 | + | 0.513007i | ||||
\(676\) | −11.7370 | −0.451424 | ||||||||
\(677\) | 28.0078 | + | 28.0078i | 1.07643 | + | 1.07643i | 0.996827 | + | 0.0795985i | \(0.0253638\pi\) |
0.0795985 | + | 0.996827i | \(0.474636\pi\) | |||||||
\(678\) | −10.9252 | + | 30.8858i | −0.419579 | + | 1.18616i | ||||
\(679\) | 84.9352i | 3.25951i | ||||||||
\(680\) | 2.61210 | + | 0.0158500i | 0.100169 | + | 0.000607822i | ||||
\(681\) | −24.5833 | + | 11.7361i | −0.942033 | + | 0.449728i | ||||
\(682\) | 6.43105 | − | 6.43105i | 0.246258 | − | 0.246258i | ||||
\(683\) | −11.0403 | + | 11.0403i | −0.422444 | + | 0.422444i | −0.886045 | − | 0.463600i | \(-0.846557\pi\) |
0.463600 | + | 0.886045i | \(0.346557\pi\) | |||||||
\(684\) | 2.33275 | + | 1.88634i | 0.0891948 | + | 0.0721261i | ||||
\(685\) | −1.83459 | − | 1.85700i | −0.0700963 | − | 0.0709521i | ||||
\(686\) | 42.7137i | 1.63082i | ||||||||
\(687\) | −26.0882 | − | 9.22813i | −0.995327 | − | 0.352075i | ||||
\(688\) | 2.68748 | + | 2.68748i | 0.102459 | + | 0.102459i | ||||
\(689\) | −23.9591 | −0.912769 | ||||||||
\(690\) | 1.94551 | − | 5.39564i | 0.0740642 | − | 0.205409i | ||||
\(691\) | −34.6717 | −1.31897 | −0.659486 | − | 0.751717i | \(-0.729226\pi\) | ||||
−0.659486 | + | 0.751717i | \(0.729226\pi\) | |||||||
\(692\) | 6.57463 | + | 6.57463i | 0.249930 | + | 0.249930i | ||||
\(693\) | −1.85240 | − | 17.5075i | −0.0703669 | − | 0.665057i | ||||
\(694\) | − | 31.3154i | − | 1.18872i | ||||||
\(695\) | −0.0471409 | + | 7.76887i | −0.00178816 | + | 0.294690i | ||||
\(696\) | 6.07674 | + | 12.7288i | 0.230338 | + | 0.482483i | ||||
\(697\) | −2.92063 | + | 2.92063i | −0.110627 | + | 0.110627i | ||||
\(698\) | 13.9126 | − | 13.9126i | 0.526600 | − | 0.526600i | ||||
\(699\) | −10.8747 | − | 22.7788i | −0.411317 | − | 0.861575i | ||||
\(700\) | 16.7203 | + | 17.1311i | 0.631966 | + | 0.647494i | ||||
\(701\) | 2.11730i | 0.0799692i | 0.999200 | + | 0.0399846i | \(0.0127309\pi\) | ||||
−0.999200 | + | 0.0399846i | \(0.987269\pi\) | |||||||
\(702\) | 13.5263 | + | 22.0214i | 0.510516 | + | 0.831143i | ||||
\(703\) | −5.83375 | − | 5.83375i | −0.220024 | − | 0.220024i | ||||
\(704\) | 1.22574 | 0.0461969 | ||||||||
\(705\) | −33.9484 | + | 15.9548i | −1.27857 | + | 0.600893i | ||||
\(706\) | 35.2206 | 1.32554 | ||||||||
\(707\) | 4.06073 | + | 4.06073i | 0.152719 | + | 0.152719i | ||||
\(708\) | −16.1969 | − | 5.72929i | −0.608715 | − | 0.215320i | ||||
\(709\) | 14.5305i | 0.545705i | 0.962056 | + | 0.272852i | \(0.0879670\pi\) | ||||
−0.962056 | + | 0.272852i | \(0.912033\pi\) | |||||||
\(710\) | 13.2957 | − | 13.1353i | 0.498979 | − | 0.492960i | ||||
\(711\) | −12.7339 | + | 15.7474i | −0.477558 | + | 0.590572i | ||||
\(712\) | −0.271862 | + | 0.271862i | −0.0101885 | + | 0.0101885i | ||||
\(713\) | −7.77001 | + | 7.77001i | −0.290989 | + | 0.290989i | ||||
\(714\) | −8.74204 | + | 4.17346i | −0.327163 | + | 0.156188i | ||||
\(715\) | −9.69755 | + | 9.58057i | −0.362668 | + | 0.358293i | ||||
\(716\) | − | 11.2885i | − | 0.421870i | ||||||
\(717\) | 9.30204 | − | 26.2971i | 0.347391 | − | 0.982085i | ||||
\(718\) | −14.8000 | − | 14.8000i | −0.552331 | − | 0.552331i | ||||
\(719\) | −2.51322 | −0.0937272 | −0.0468636 | − | 0.998901i | \(-0.514923\pi\) | ||||
−0.0468636 | + | 0.998901i | \(0.514923\pi\) | |||||||
\(720\) | 5.19049 | + | 4.24956i | 0.193438 | + | 0.158372i | ||||
\(721\) | 89.1782 | 3.32117 | ||||||||
\(722\) | 0.707107 | + | 0.707107i | 0.0263158 | + | 0.0263158i | ||||
\(723\) | −11.5055 | + | 32.5264i | −0.427894 | + | 1.20967i | ||||
\(724\) | − | 9.96083i | − | 0.370191i | ||||||
\(725\) | −40.7144 | − | 0.494122i | −1.51209 | − | 0.0183512i | ||||
\(726\) | −14.8453 | + | 7.08717i | −0.550961 | + | 0.263029i | ||||
\(727\) | −7.64794 | + | 7.64794i | −0.283646 | + | 0.283646i | −0.834561 | − | 0.550915i | \(-0.814279\pi\) |
0.550915 | + | 0.834561i | \(0.314279\pi\) | |||||||
\(728\) | 16.8377 | − | 16.8377i | 0.624045 | − | 0.624045i | ||||
\(729\) | 12.2076 | − | 24.0826i | 0.452135 | − | 0.891950i | ||||
\(730\) | −0.0766361 | + | 12.6297i | −0.00283643 | + | 0.467446i | ||||
\(731\) | − | 4.43990i | − | 0.164215i | ||||||
\(732\) | −17.2144 | − | 6.08920i | −0.636261 | − | 0.225063i | ||||
\(733\) | 24.3729 | + | 24.3729i | 0.900235 | + | 0.900235i | 0.995456 | − | 0.0952214i | \(-0.0303559\pi\) |
−0.0952214 | + | 0.995456i | \(0.530356\pi\) | |||||||
\(734\) | −37.2954 | −1.37660 | ||||||||
\(735\) | −58.0086 | − | 20.9161i | −2.13968 | − | 0.771504i | ||||
\(736\) | −1.48094 | −0.0545883 | ||||||||
\(737\) | 7.35823 | + | 7.35823i | 0.271044 | + | 0.271044i | ||||
\(738\) | −10.5483 | + | 1.11607i | −0.388288 | + | 0.0410831i | ||||
\(739\) | 30.8274i | 1.13401i | 0.823716 | + | 0.567003i | \(0.191897\pi\) | ||||
−0.823716 | + | 0.567003i | \(0.808103\pi\) | |||||||
\(740\) | −12.9653 | − | 13.1236i | −0.476613 | − | 0.482432i | ||||
\(741\) | 3.71137 | + | 7.77411i | 0.136341 | + | 0.285589i | ||||
\(742\) | 16.3081 | − | 16.3081i | 0.598691 | − | 0.598691i | ||||
\(743\) | −23.0214 | + | 23.0214i | −0.844574 | + | 0.844574i | −0.989450 | − | 0.144876i | \(-0.953722\pi\) |
0.144876 | + | 0.989450i | \(0.453722\pi\) | |||||||
\(744\) | −5.53680 | − | 11.5978i | −0.202989 | − | 0.425195i | ||||
\(745\) | −2.47297 | − | 0.0150058i | −0.0906026 | − | 0.000549770i | ||||
\(746\) | 9.42209i | 0.344967i | ||||||||
\(747\) | −3.02842 | + | 0.320425i | −0.110804 | + | 0.0117237i | ||||
\(748\) | −1.01250 | − | 1.01250i | −0.0370208 | − | 0.0370208i | ||||
\(749\) | 67.5986 | 2.47000 | ||||||||
\(750\) | −17.6246 | + | 8.02339i | −0.643558 | + | 0.292973i | ||||
\(751\) | 43.6630 | 1.59329 | 0.796643 | − | 0.604450i | \(-0.206607\pi\) | ||||
0.796643 | + | 0.604450i | \(0.206607\pi\) | |||||||
\(752\) | 6.84848 | + | 6.84848i | 0.249738 | + | 0.249738i | ||||
\(753\) | −29.2286 | − | 10.3390i | −1.06515 | − | 0.376773i | ||||
\(754\) | 40.5027i | 1.47502i | ||||||||
\(755\) | 7.34980 | + | 0.0445981i | 0.267486 | + | 0.00162309i | ||||
\(756\) | −24.1961 | − | 5.78233i | −0.880002 | − | 0.210301i | ||||
\(757\) | −8.25576 | + | 8.25576i | −0.300061 | + | 0.300061i | −0.841038 | − | 0.540977i | \(-0.818055\pi\) |
0.540977 | + | 0.841038i | \(0.318055\pi\) | |||||||
\(758\) | −0.145573 | + | 0.145573i | −0.00528745 | + | 0.00528745i | ||||
\(759\) | −2.83736 | + | 1.35456i | −0.102990 | + | 0.0491674i | ||||
\(760\) | 1.57152 | + | 1.59070i | 0.0570049 | + | 0.0577009i | ||||
\(761\) | − | 45.4398i | − | 1.64719i | −0.567176 | − | 0.823596i | \(-0.691964\pi\) | ||
0.567176 | − | 0.823596i | \(-0.308036\pi\) | |||||||
\(762\) | 5.28038 | − | 14.9278i | 0.191288 | − | 0.540777i | ||||
\(763\) | −30.3125 | − | 30.3125i | −1.09739 | − | 1.09739i | ||||
\(764\) | 10.1454 | 0.367048 | ||||||||
\(765\) | −0.777238 | − | 7.79781i | −0.0281011 | − | 0.281930i | ||||
\(766\) | −11.6945 | −0.422539 | ||||||||
\(767\) | −34.8842 | − | 34.8842i | −1.25960 | − | 1.25960i | ||||
\(768\) | 0.577604 | − | 1.63290i | 0.0208425 | − | 0.0589223i | ||||
\(769\) | 14.3253i | 0.516582i | 0.966067 | + | 0.258291i | \(0.0831593\pi\) | ||||
−0.966067 | + | 0.258291i | \(0.916841\pi\) | |||||||
\(770\) | 0.0796231 | − | 13.1220i | 0.00286942 | − | 0.472882i | ||||
\(771\) | 32.1549 | − | 15.3508i | 1.15803 | − | 0.552845i | ||||
\(772\) | −1.33016 | + | 1.33016i | −0.0478734 | + | 0.0478734i | ||||
\(773\) | −30.7793 | + | 30.7793i | −1.10706 | + | 1.10706i | −0.113520 | + | 0.993536i | \(0.536212\pi\) |
−0.993536 | + | 0.113520i | \(0.963788\pi\) | |||||||
\(774\) | 7.16936 | − | 8.86600i | 0.257697 | − | 0.318682i | ||||
\(775\) | 37.0968 | + | 0.450218i | 1.33256 | + | 0.0161723i | ||||
\(776\) | 17.7405i | 0.636846i | ||||||||
\(777\) | 64.4980 | + | 22.8148i | 2.31385 | + | 0.818475i | ||||
\(778\) | −17.9604 | − | 17.9604i | −0.643912 | − | 0.643912i | ||||
\(779\) | −3.53572 | −0.126680 | ||||||||
\(780\) | 8.19325 | + | 17.4335i | 0.293365 | + | 0.624219i | ||||
\(781\) | −10.2452 | −0.366603 | ||||||||
\(782\) | 1.22331 | + | 1.22331i | 0.0437455 | + | 0.0437455i | ||||
\(783\) | 36.0562 | − | 22.1469i | 1.28854 | − | 0.791467i | ||||
\(784\) | 15.9216i | 0.568630i | ||||||||
\(785\) | −27.0253 | + | 26.6993i | −0.964573 | + | 0.952938i | ||||
\(786\) | 3.46788 | + | 7.26408i | 0.123695 | + | 0.259101i | ||||
\(787\) | −4.68011 | + | 4.68011i | −0.166828 | + | 0.166828i | −0.785583 | − | 0.618756i | \(-0.787637\pi\) |
0.618756 | + | 0.785583i | \(0.287637\pi\) | |||||||
\(788\) | −3.67465 | + | 3.67465i | −0.130904 | + | 0.130904i | ||||
\(789\) | 6.39168 | + | 13.3885i | 0.227550 | + | 0.476642i | ||||
\(790\) | −10.7382 | + | 10.6086i | −0.382046 | + | 0.377438i | ||||
\(791\) | − | 90.5568i | − | 3.21983i | ||||||
\(792\) | −0.386912 | − | 3.65681i | −0.0137483 | − | 0.129939i | ||||
\(793\) | −37.0757 | − | 37.0757i | −1.31660 | − | 1.31660i | ||||
\(794\) | −20.4067 | −0.724206 | ||||||||
\(795\) | 7.93558 | + | 16.8852i | 0.281446 | + | 0.598857i | ||||
\(796\) | −0.894086 | −0.0316900 | ||||||||
\(797\) | −0.135863 | − | 0.135863i | −0.00481251 | − | 0.00481251i | 0.704696 | − | 0.709509i | \(-0.251083\pi\) |
−0.709509 | + | 0.704696i | \(0.751083\pi\) | |||||||
\(798\) | −7.81778 | − | 2.76537i | −0.276746 | − | 0.0978930i | ||||
\(799\) | − | 11.3142i | − | 0.400266i | ||||||
\(800\) | 3.49237 | + | 3.57818i | 0.123474 | + | 0.126508i | ||||
\(801\) | 0.896874 | + | 0.725245i | 0.0316895 | + | 0.0256253i | ||||
\(802\) | −5.67851 | + | 5.67851i | −0.200515 | + | 0.200515i | ||||
\(803\) | 4.89552 | − | 4.89552i | 0.172759 | − | 0.172759i | ||||
\(804\) | 13.2699 | − | 6.33506i | 0.467992 | − | 0.223420i | ||||
\(805\) | −0.0962009 | + | 15.8540i | −0.00339064 | + | 0.558780i | ||||
\(806\) | − | 36.9039i | − | 1.29988i | ||||||
\(807\) | 5.49490 | − | 15.5342i | 0.193430 | − | 0.546831i | ||||
\(808\) | 0.848167 | + | 0.848167i | 0.0298384 | + | 0.0298384i | ||||
\(809\) | −19.5668 | −0.687933 | −0.343967 | − | 0.938982i | \(-0.611771\pi\) | ||||
−0.343967 | + | 0.938982i | \(0.611771\pi\) | |||||||
\(810\) | 11.0395 | − | 16.8264i | 0.387889 | − | 0.591221i | ||||
\(811\) | 19.4917 | 0.684447 | 0.342223 | − | 0.939619i | \(-0.388820\pi\) | ||||
0.342223 | + | 0.939619i | \(0.388820\pi\) | |||||||
\(812\) | −27.5688 | − | 27.5688i | −0.967475 | − | 0.967475i | ||||
\(813\) | 0.234220 | − | 0.662146i | 0.00821444 | − | 0.0232225i | ||||
\(814\) | 10.1126i | 0.354445i | ||||||||
\(815\) | 8.50206 | + | 8.60587i | 0.297814 | + | 0.301451i | ||||
\(816\) | −1.82595 | + | 0.871713i | −0.0639212 | + | 0.0305161i | ||||
\(817\) | 2.68748 | − | 2.68748i | 0.0940229 | − | 0.0940229i | ||||
\(818\) | 9.80426 | − | 9.80426i | 0.342798 | − | 0.342798i | ||||
\(819\) | −55.5475 | − | 44.9177i | −1.94099 | − | 1.56955i | ||||
\(820\) | −7.90597 | − | 0.0479729i | −0.276088 | − | 0.00167529i | ||||
\(821\) | 1.40866i | 0.0491626i | 0.999698 | + | 0.0245813i | \(0.00782525\pi\) | ||||
−0.999698 | + | 0.0245813i | \(0.992175\pi\) | |||||||
\(822\) | 1.90626 | + | 0.674298i | 0.0664884 | + | 0.0235188i | ||||
\(823\) | −33.6212 | − | 33.6212i | −1.17196 | − | 1.17196i | −0.981741 | − | 0.190220i | \(-0.939080\pi\) |
−0.190220 | − | 0.981741i | \(-0.560920\pi\) | |||||||
\(824\) | 18.6267 | 0.648892 | ||||||||
\(825\) | 9.96389 | + | 3.66115i | 0.346898 | + | 0.127465i | ||||
\(826\) | 47.4890 | 1.65235 | ||||||||
\(827\) | −27.8950 | − | 27.8950i | −0.970006 | − | 0.970006i | 0.0295575 | − | 0.999563i | \(-0.490590\pi\) |
−0.999563 | + | 0.0295575i | \(0.990590\pi\) | |||||||
\(828\) | 0.467469 | + | 4.41817i | 0.0162457 | + | 0.153542i | ||||
\(829\) | − | 17.3145i | − | 0.601357i | −0.953725 | − | 0.300679i | \(-0.902787\pi\) | ||
0.953725 | − | 0.300679i | \(-0.0972132\pi\) | |||||||
\(830\) | −2.26981 | − | 0.0137731i | −0.0787863 | − | 0.000478070i | ||||
\(831\) | −3.33075 | − | 6.97684i | −0.115542 | − | 0.242024i | ||||
\(832\) | 3.51689 | − | 3.51689i | 0.121926 | − | 0.121926i | ||||
\(833\) | 13.1518 | − | 13.1518i | 0.455683 | − | 0.455683i | ||||
\(834\) | −2.59263 | − | 5.43072i | −0.0897756 | − | 0.188051i | ||||
\(835\) | 31.3490 | + | 31.7318i | 1.08488 | + | 1.09812i | ||||
\(836\) | − | 1.22574i | − | 0.0423931i | ||||||
\(837\) | −32.8525 | + | 20.1791i | −1.13555 | + | 0.697492i | ||||
\(838\) | 12.5350 | + | 12.5350i | 0.433014 | + | 0.433014i | ||||
\(839\) | 24.7985 | 0.856141 | 0.428070 | − | 0.903745i | \(-0.359194\pi\) | ||||
0.428070 | + | 0.903745i | \(0.359194\pi\) | |||||||
\(840\) | −17.4432 | − | 6.28951i | −0.601849 | − | 0.217009i | ||||
\(841\) | 37.3162 | 1.28677 | ||||||||
\(842\) | −1.87573 | − | 1.87573i | −0.0646420 | − | 0.0646420i | ||||
\(843\) | −19.4680 | − | 6.88639i | −0.670514 | − | 0.237180i | ||||
\(844\) | − | 0.656325i | − | 0.0225916i | ||||||
\(845\) | −0.159249 | + | 26.2443i | −0.00547832 | + | 0.902832i | ||||
\(846\) | 18.2696 | − | 22.5932i | 0.628123 | − | 0.776769i | ||||
\(847\) | 32.1529 | − | 32.1529i | 1.10479 | − | 1.10479i | ||||
\(848\) | 3.40629 | − | 3.40629i | 0.116972 | − | 0.116972i | ||||
\(849\) | 24.6219 | − | 11.7545i | 0.845023 | − | 0.403415i | ||||
\(850\) | 0.0708823 | − | 5.84051i | 0.00243124 | − | 0.200328i | ||||
\(851\) | − | 12.2180i | − | 0.418829i | ||||||
\(852\) | −4.82784 | + | 13.6484i | −0.165399 | + | 0.467588i | ||||
\(853\) | 26.5568 | + | 26.5568i | 0.909288 | + | 0.909288i | 0.996215 | − | 0.0869270i | \(-0.0277047\pi\) |
−0.0869270 | + | 0.996215i | \(0.527705\pi\) | |||||||
\(854\) | 50.4723 | 1.72713 | ||||||||
\(855\) | 4.24956 | − | 5.19049i | 0.145332 | − | 0.177511i | ||||
\(856\) | 14.1194 | 0.482590 | ||||||||
\(857\) | −29.8963 | − | 29.8963i | −1.02124 | − | 1.02124i | −0.999769 | − | 0.0214701i | \(-0.993165\pi\) |
−0.0214701 | − | 0.999769i | \(-0.506835\pi\) | |||||||
\(858\) | 3.52130 | − | 9.95481i | 0.120215 | − | 0.339852i | ||||
\(859\) | − | 54.0727i | − | 1.84494i | −0.386074 | − | 0.922468i | \(-0.626169\pi\) | ||
0.386074 | − | 0.922468i | \(-0.373831\pi\) | |||||||
\(860\) | 6.04574 | − | 5.97281i | 0.206158 | − | 0.203671i | ||||
\(861\) | 26.4593 | − | 12.6317i | 0.901730 | − | 0.430487i | ||||
\(862\) | −12.0270 | + | 12.0270i | −0.409640 | + | 0.409640i | ||||
\(863\) | 35.2140 | − | 35.2140i | 1.19870 | − | 1.19870i | 0.224142 | − | 0.974557i | \(-0.428042\pi\) |
0.974557 | − | 0.224142i | \(-0.0719579\pi\) | |||||||
\(864\) | −5.05384 | − | 1.20776i | −0.171935 | − | 0.0410888i | ||||
\(865\) | 14.7902 | − | 14.6118i | 0.502884 | − | 0.496817i | ||||
\(866\) | − | 19.6197i | − | 0.666705i | ||||||
\(867\) | −25.5310 | − | 9.03103i | −0.867078 | − | 0.306710i | ||||
\(868\) | 25.1192 | + | 25.1192i | 0.852601 | + | 0.852601i | ||||
\(869\) | 8.27445 | 0.280691 | ||||||||
\(870\) | 28.5443 | − | 13.4150i | 0.967744 | − | 0.454813i | ||||
\(871\) | 42.2244 | 1.43072 | ||||||||
\(872\) | −6.33139 | − | 6.33139i | −0.214408 | − | 0.214408i | ||||
\(873\) | 52.9260 | − | 5.59988i | 1.79127 | − | 0.189527i | ||||
\(874\) | 1.48094i | 0.0500937i | ||||||||
\(875\) | 38.5324 | − | 37.1545i | 1.30263 | − | 1.25605i | ||||
\(876\) | −4.21479 | − | 8.82861i | −0.142405 | − | 0.298291i | ||||
\(877\) | 6.50626 | − | 6.50626i | 0.219701 | − | 0.219701i | −0.588671 | − | 0.808372i | \(-0.700349\pi\) |
0.808372 | + | 0.588671i | \(0.200349\pi\) | |||||||
\(878\) | −5.26269 | + | 5.26269i | −0.177607 | + | 0.177607i | ||||
\(879\) | 3.51382 | + | 7.36030i | 0.118518 | + | 0.248257i | ||||
\(880\) | 0.0166309 | − | 2.74079i | 0.000560628 | − | 0.0923920i | ||||
\(881\) | 40.0528i | 1.34941i | 0.738087 | + | 0.674706i | \(0.235730\pi\) | ||||
−0.738087 | + | 0.674706i | \(0.764270\pi\) | |||||||
\(882\) | 47.4998 | − | 5.02576i | 1.59940 | − | 0.169226i | ||||
\(883\) | −14.6050 | − | 14.6050i | −0.491496 | − | 0.491496i | 0.417281 | − | 0.908777i | \(-0.362983\pi\) |
−0.908777 | + | 0.417281i | \(0.862983\pi\) | |||||||
\(884\) | −5.81014 | −0.195416 | ||||||||
\(885\) | −13.0306 | + | 36.1389i | −0.438019 | + | 1.21480i | ||||
\(886\) | −19.8119 | −0.665593 | ||||||||
\(887\) | 38.9555 | + | 38.9555i | 1.30800 | + | 1.30800i | 0.922857 | + | 0.385142i | \(0.125847\pi\) |
0.385142 | + | 0.922857i | \(0.374153\pi\) | |||||||
\(888\) | 13.4717 | + | 4.76533i | 0.452082 | + | 0.159914i | ||||
\(889\) | 43.7681i | 1.46794i | ||||||||
\(890\) | 0.604203 | + | 0.611580i | 0.0202529 | + | 0.0205002i | ||||
\(891\) | −10.7874 | + | 2.30859i | −0.361392 | + | 0.0773406i | ||||
\(892\) | 5.81309 | − | 5.81309i | 0.194637 | − | 0.194637i | ||||
\(893\) | 6.84848 | − | 6.84848i | 0.229176 | − | 0.229176i | ||||
\(894\) | 1.72870 | − | 0.825282i | 0.0578162 | − | 0.0276016i | ||||
\(895\) | −25.2413 | − | 0.153163i | −0.843725 | − | 0.00511967i | ||||
\(896\) | 4.78765i | 0.159944i | ||||||||
\(897\) | −4.25444 | + | 12.0274i | −0.142052 | + | 0.401584i | ||||
\(898\) | 12.0743 | + | 12.0743i | 0.402926 | + | 0.402926i | ||||
\(899\) | −60.4238 | −2.01525 | ||||||||
\(900\) | 9.57256 | − | 11.5484i | 0.319085 | − | 0.384947i | ||||
\(901\) | −5.62742 | −0.187477 | ||||||||
\(902\) | 3.06452 | + | 3.06452i | 0.102037 | + | 0.102037i | ||||
\(903\) | −10.5102 | + | 29.7128i | −0.349759 | + | 0.988779i | ||||
\(904\) | − | 18.9147i | − | 0.629092i | ||||||
\(905\) | −22.2727 | − | 0.135149i | −0.740369 | − | 0.00449251i | ||||
\(906\) | −5.13778 | + | 2.45278i | −0.170691 | + | 0.0814882i | ||||
\(907\) | 1.61743 | − | 1.61743i | 0.0537059 | − | 0.0537059i | −0.679744 | − | 0.733450i | \(-0.737909\pi\) |
0.733450 | + | 0.679744i | \(0.237909\pi\) | |||||||
\(908\) | 11.1211 | − | 11.1211i | 0.369067 | − | 0.369067i | ||||
\(909\) | 2.26265 | − | 2.79811i | 0.0750473 | − | 0.0928073i | ||||
\(910\) | −37.4210 | − | 37.8779i | −1.24049 | − | 1.25564i | ||||
\(911\) | − | 28.2902i | − | 0.937298i | −0.883385 | − | 0.468649i | \(-0.844741\pi\) | ||
0.883385 | − | 0.468649i | \(-0.155259\pi\) | |||||||
\(912\) | −1.63290 | − | 0.577604i | −0.0540708 | − | 0.0191264i | ||||
\(913\) | 0.879825 | + | 0.879825i | 0.0291180 | + | 0.0291180i | ||||
\(914\) | 6.47066 | 0.214030 | ||||||||
\(915\) | −13.8492 | + | 38.4092i | −0.457840 | + | 1.26977i | ||||
\(916\) | 15.9766 | 0.527881 | ||||||||
\(917\) | −15.7330 | − | 15.7330i | −0.519550 | − | 0.519550i | ||||
\(918\) | 3.17700 | + | 5.17229i | 0.104857 | + | 0.170711i | ||||
\(919\) | 32.0879i | 1.05848i | 0.848472 | + | 0.529241i | \(0.177523\pi\) | ||||
−0.848472 | + | 0.529241i | \(0.822477\pi\) | |||||||
\(920\) | −0.0200935 | + | 3.31143i | −0.000662464 | + | 0.109175i | ||||
\(921\) | 1.78362 | + | 3.73609i | 0.0587722 | + | 0.123109i | ||||
\(922\) | −0.0849881 | + | 0.0849881i | −0.00279893 | + | 0.00279893i | ||||
\(923\) | −29.3955 | + | 29.3955i | −0.967566 | + | 0.967566i | ||||
\(924\) | 4.37907 | + | 9.17273i | 0.144061 | + | 0.301761i | ||||
\(925\) | −29.5206 | + | 28.8126i | −0.970631 | + | 0.947354i | ||||
\(926\) | 8.23304i | 0.270555i | ||||||||
\(927\) | −5.87963 | − | 55.5699i | −0.193112 | − | 1.82516i | ||||
\(928\) | −5.75831 | − | 5.75831i | −0.189026 | − | 0.189026i | ||||
\(929\) | 46.3379 | 1.52030 | 0.760149 | − | 0.649749i | \(-0.225126\pi\) | ||||
0.760149 | + | 0.649749i | \(0.225126\pi\) | |||||||
\(930\) | −26.0081 | + | 12.2231i | −0.852838 | + | 0.400810i | ||||
\(931\) | 15.9216 | 0.521811 | ||||||||
\(932\) | 10.3048 | + | 10.3048i | 0.337545 | + | 0.337545i | ||||
\(933\) | −23.4056 | − | 8.27921i | −0.766264 | − | 0.271049i | ||||
\(934\) | − | 1.79181i | − | 0.0586298i | ||||||
\(935\) | −2.27772 | + | 2.25025i | −0.0744895 | + | 0.0735910i | ||||
\(936\) | −11.6022 | − | 9.38198i | −0.379231 | − | 0.306660i | ||||
\(937\) | −35.8203 | + | 35.8203i | −1.17020 | + | 1.17020i | −0.188037 | + | 0.982162i | \(0.560212\pi\) |
−0.982162 | + | 0.188037i | \(0.939788\pi\) | |||||||
\(938\) | −28.7407 | + | 28.7407i | −0.938418 | + | 0.938418i | ||||
\(939\) | 3.45754 | − | 1.65063i | 0.112832 | − | 0.0538664i | ||||
\(940\) | 15.4063 | − | 15.2205i | 0.502498 | − | 0.496437i | ||||
\(941\) | 36.8148i | 1.20013i | 0.799951 | + | 0.600065i | \(0.204859\pi\) | ||||
−0.799951 | + | 0.600065i | \(0.795141\pi\) | |||||||
\(942\) | 9.81321 | − | 27.7422i | 0.319732 | − | 0.903891i | ||||
\(943\) | −3.70256 | − | 3.70256i | −0.120572 | − | 0.120572i | ||||
\(944\) | 9.91906 | 0.322838 | ||||||||
\(945\) | −13.2577 | + | 54.0246i | −0.431274 | + | 1.75742i | ||||
\(946\) | −4.65863 | −0.151465 | ||||||||
\(947\) | −14.0227 | − | 14.0227i | −0.455676 | − | 0.455676i | 0.441557 | − | 0.897233i | \(-0.354426\pi\) |
−0.897233 | + | 0.441557i | \(0.854426\pi\) | |||||||
\(948\) | 3.89915 | − | 11.0230i | 0.126639 | − | 0.358011i | ||||
\(949\) | − | 28.0924i | − | 0.911919i | ||||||
\(950\) | 3.57818 | − | 3.49237i | 0.116091 | − | 0.113307i | ||||
\(951\) | −47.7442 | + | 22.7931i | −1.54821 | + | 0.739118i | ||||
\(952\) | 3.95477 | − | 3.95477i | 0.128175 | − | 0.128175i | ||||
\(953\) | −2.01500 | + | 2.01500i | −0.0652723 | + | 0.0652723i | −0.738989 | − | 0.673717i | \(-0.764697\pi\) |
0.673717 | + | 0.738989i | \(0.264697\pi\) | |||||||
\(954\) | −11.2374 | − | 9.08693i | −0.363823 | − | 0.294200i | ||||
\(955\) | 0.137653 | − | 22.6854i | 0.00445436 | − | 0.734082i | ||||
\(956\) | 16.1045i | 0.520858i | ||||||||
\(957\) | −16.2993 | − | 5.76552i | −0.526882 | − | 0.186373i | ||||
\(958\) | −3.37189 | − | 3.37189i | −0.108941 | − | 0.108941i | ||||
\(959\) | −5.58913 | −0.180482 | ||||||||
\(960\) | −3.64338 | − | 1.31369i | −0.117590 | − | 0.0423993i | ||||
\(961\) | 24.0549 | 0.775965 | ||||||||
\(962\) | 29.0149 | + | 29.0149i | 0.935479 | + | 0.935479i | ||||
\(963\) | −4.45685 | − | 42.1229i | −0.143620 | − | 1.35739i | ||||
\(964\) | − | 19.9193i | − | 0.641559i | ||||||
\(965\) | 2.95622 | + | 2.99231i | 0.0951640 | + | 0.0963260i | ||||
\(966\) | −5.29081 | − | 11.0825i | −0.170229 | − | 0.356574i | ||||
\(967\) | 3.86264 | − | 3.86264i | 0.124214 | − | 0.124214i | −0.642267 | − | 0.766481i | \(-0.722006\pi\) |
0.766481 | + | 0.642267i | \(0.222006\pi\) | |||||||
\(968\) | 6.71579 | − | 6.71579i | 0.215854 | − | 0.215854i | ||||
\(969\) | 0.871713 | + | 1.82595i | 0.0280035 | + | 0.0586581i | ||||
\(970\) | 39.6682 | + | 0.240704i | 1.27367 | + | 0.00772853i | ||||
\(971\) | 4.62291i | 0.148356i | 0.997245 | + | 0.0741781i | \(0.0236333\pi\) | ||||
−0.997245 | + | 0.0741781i | \(0.976367\pi\) | |||||||
\(972\) | −2.00789 | + | 15.4586i | −0.0644030 | + | 0.495835i | ||||
\(973\) | 11.7622 | + | 11.7622i | 0.377079 | + | 0.377079i | ||||
\(974\) | −26.4143 | −0.846368 | ||||||||
\(975\) | 39.0929 | − | 18.0838i | 1.25197 | − | 0.579145i | ||||
\(976\) | 10.5422 | 0.337447 | ||||||||
\(977\) | −40.0087 | − | 40.0087i | −1.27999 | − | 1.27999i | −0.940670 | − | 0.339323i | \(-0.889802\pi\) |
−0.339323 | − | 0.940670i | \(-0.610198\pi\) | |||||||
\(978\) | −8.83418 | − | 3.12490i | −0.282486 | − | 0.0999232i | ||||
\(979\) | − | 0.471262i | − | 0.0150616i | ||||||
\(980\) | 35.6012 | + | 0.216026i | 1.13724 | + | 0.00690069i | ||||
\(981\) | −16.8902 | + | 20.8873i | −0.539262 | + | 0.666879i | ||||
\(982\) | 30.3912 | − | 30.3912i | 0.969822 | − | 0.969822i | ||||
\(983\) | 12.9031 | − | 12.9031i | 0.411545 | − | 0.411545i | −0.470731 | − | 0.882277i | \(-0.656010\pi\) |
0.882277 | + | 0.470731i | \(0.156010\pi\) | |||||||
\(984\) | 5.52656 | − | 2.63839i | 0.176180 | − | 0.0841088i | ||||
\(985\) | 8.16675 | + | 8.26647i | 0.260214 | + | 0.263392i | ||||
\(986\) | 9.51312i | 0.302959i | ||||||||
\(987\) | −26.7832 | + | 75.7168i | −0.852518 | + | 2.41009i | ||||
\(988\) | −3.51689 | − | 3.51689i | −0.111887 | − | 0.111887i | ||||
\(989\) | 5.62858 | 0.178978 | ||||||||
\(990\) | −8.18198 | + | 0.815530i | −0.260040 | + | 0.0259192i | ||||
\(991\) | 16.7867 | 0.533248 | 0.266624 | − | 0.963801i | \(-0.414092\pi\) | ||||
0.266624 | + | 0.963801i | \(0.414092\pi\) | |||||||
\(992\) | 5.24666 | + | 5.24666i | 0.166582 | + | 0.166582i | ||||
\(993\) | −3.68006 | + | 10.4036i | −0.116783 | + | 0.330150i | ||||
\(994\) | − | 40.0171i | − | 1.26926i | ||||||
\(995\) | −0.0121310 | + | 1.99920i | −0.000384579 | + | 0.0633789i | ||||
\(996\) | 1.58668 | − | 0.757484i | 0.0502759 | − | 0.0240018i | ||||
\(997\) | 10.3397 | − | 10.3397i | 0.327460 | − | 0.327460i | −0.524160 | − | 0.851620i | \(-0.675620\pi\) |
0.851620 | + | 0.524160i | \(0.175620\pi\) | |||||||
\(998\) | −14.7400 | + | 14.7400i | −0.466587 | + | 0.466587i | ||||
\(999\) | 9.96421 | − | 41.6951i | 0.315254 | − | 1.31917i |
(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 | 570.2.k.b.533.6 | yes | 36 | |
3.2 | odd | 2 | inner | 570.2.k.b.533.11 | yes | 36 | |
5.2 | odd | 4 | inner | 570.2.k.b.77.11 | yes | 36 | |
15.2 | even | 4 | inner | 570.2.k.b.77.6 | ✓ | 36 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
570.2.k.b.77.6 | ✓ | 36 | 15.2 | even | 4 | inner | |
570.2.k.b.77.11 | yes | 36 | 5.2 | odd | 4 | inner | |
570.2.k.b.533.6 | yes | 36 | 1.1 | even | 1 | trivial | |
570.2.k.b.533.11 | yes | 36 | 3.2 | odd | 2 | inner |