Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [363,3,Mod(122,363)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(363, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("363.122");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 363 = 3 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 363.b (of order \(2\), degree \(1\), 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: | \(9.89103359628\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 29x^{6} + 282x^{4} + 1061x^{2} + 1331 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 33) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 122.3 | ||
Root | \(-2.00420i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 363.122 |
Dual form | 363.3.b.m.122.6 |
$q$-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 \(\left(\mathbb{Z}/363\mathbb{Z}\right)^\times\).
\(n\) | \(122\) | \(244\) |
\(\chi(n)\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 2.00420i | − | 1.00210i | −0.865419 | − | 0.501049i | \(-0.832948\pi\) | ||
0.865419 | − | 0.501049i | \(-0.167052\pi\) | |||||||
\(3\) | 2.80061 | + | 1.07544i | 0.933538 | + | 0.358479i | ||||
\(4\) | −0.0168066 | −0.00420164 | ||||||||
\(5\) | 5.48438i | 1.09688i | 0.836191 | + | 0.548438i | \(0.184777\pi\) | ||||
−0.836191 | + | 0.548438i | \(0.815223\pi\) | |||||||
\(6\) | 2.15539 | − | 5.61298i | 0.359231 | − | 0.935497i | ||||
\(7\) | 5.59084 | 0.798691 | 0.399346 | − | 0.916800i | \(-0.369237\pi\) | ||||
0.399346 | + | 0.916800i | \(0.369237\pi\) | |||||||
\(8\) | − | 7.98311i | − | 0.997888i | ||||||
\(9\) | 6.68687 | + | 6.02376i | 0.742986 | + | 0.669307i | ||||
\(10\) | 10.9918 | 1.09918 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | −0.0470687 | − | 0.0180744i | −0.00392239 | − | 0.00150620i | ||||
\(13\) | −9.71679 | −0.747446 | −0.373723 | − | 0.927540i | \(-0.621919\pi\) | ||||
−0.373723 | + | 0.927540i | \(0.621919\pi\) | |||||||
\(14\) | − | 11.2051i | − | 0.800368i | ||||||
\(15\) | −5.89810 | + | 15.3596i | −0.393207 | + | 1.02398i | ||||
\(16\) | −16.0669 | −1.00418 | ||||||||
\(17\) | 17.8716i | 1.05127i | 0.850710 | + | 0.525635i | \(0.176172\pi\) | ||||
−0.850710 | + | 0.525635i | \(0.823828\pi\) | |||||||
\(18\) | 12.0728 | − | 13.4018i | 0.670712 | − | 0.744545i | ||||
\(19\) | 18.6589 | 0.982047 | 0.491024 | − | 0.871146i | \(-0.336623\pi\) | ||||
0.491024 | + | 0.871146i | \(0.336623\pi\) | |||||||
\(20\) | − | 0.0921737i | − | 0.00460868i | ||||||
\(21\) | 15.6578 | + | 6.01259i | 0.745609 | + | 0.286314i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 12.3649i | − | 0.537603i | −0.963196 | − | 0.268801i | \(-0.913372\pi\) | ||
0.963196 | − | 0.268801i | \(-0.0866275\pi\) | |||||||
\(24\) | 8.58532 | − | 22.3576i | 0.357722 | − | 0.931566i | ||||
\(25\) | −5.07844 | −0.203138 | ||||||||
\(26\) | 19.4744i | 0.749014i | ||||||||
\(27\) | 12.2492 | + | 24.0615i | 0.453673 | + | 0.891168i | ||||
\(28\) | −0.0939629 | −0.00335582 | ||||||||
\(29\) | 2.47732i | 0.0854250i | 0.999087 | + | 0.0427125i | \(0.0135999\pi\) | ||||
−0.999087 | + | 0.0427125i | \(0.986400\pi\) | |||||||
\(30\) | 30.7837 | + | 11.8210i | 1.02612 | + | 0.394032i | ||||
\(31\) | 49.2308 | 1.58809 | 0.794046 | − | 0.607858i | \(-0.207971\pi\) | ||||
0.794046 | + | 0.607858i | \(0.207971\pi\) | |||||||
\(32\) | 0.268903i | 0.00840323i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 35.8182 | 1.05348 | ||||||||
\(35\) | 30.6623i | 0.876066i | ||||||||
\(36\) | −0.112383 | − | 0.101239i | −0.00312176 | − | 0.00281219i | ||||
\(37\) | −39.3307 | −1.06299 | −0.531496 | − | 0.847061i | \(-0.678370\pi\) | ||||
−0.531496 | + | 0.847061i | \(0.678370\pi\) | |||||||
\(38\) | − | 37.3961i | − | 0.984108i | ||||||
\(39\) | −27.2130 | − | 10.4498i | −0.697769 | − | 0.267943i | ||||
\(40\) | 43.7824 | 1.09456 | ||||||||
\(41\) | − | 56.5236i | − | 1.37862i | −0.724465 | − | 0.689312i | \(-0.757913\pi\) | ||
0.724465 | − | 0.689312i | \(-0.242087\pi\) | |||||||
\(42\) | 12.0504 | − | 31.3813i | 0.286915 | − | 0.747174i | ||||
\(43\) | −43.9060 | −1.02107 | −0.510534 | − | 0.859857i | \(-0.670552\pi\) | ||||
−0.510534 | + | 0.859857i | \(0.670552\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −33.0366 | + | 36.6734i | −0.734147 | + | 0.814964i | ||||
\(46\) | −24.7816 | −0.538731 | ||||||||
\(47\) | 57.7840i | 1.22945i | 0.788743 | + | 0.614723i | \(0.210732\pi\) | ||||
−0.788743 | + | 0.614723i | \(0.789268\pi\) | |||||||
\(48\) | −44.9973 | − | 17.2790i | −0.937444 | − | 0.359979i | ||||
\(49\) | −17.7425 | −0.362092 | ||||||||
\(50\) | 10.1782i | 0.203564i | ||||||||
\(51\) | −19.2197 | + | 50.0514i | −0.376858 | + | 0.981400i | ||||
\(52\) | 0.163306 | 0.00314050 | ||||||||
\(53\) | − | 43.1158i | − | 0.813506i | −0.913538 | − | 0.406753i | \(-0.866661\pi\) | ||
0.913538 | − | 0.406753i | \(-0.133339\pi\) | |||||||
\(54\) | 48.2241 | − | 24.5498i | 0.893038 | − | 0.454625i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | − | 44.6323i | − | 0.797005i | ||||||
\(57\) | 52.2564 | + | 20.0665i | 0.916778 | + | 0.352043i | ||||
\(58\) | 4.96505 | 0.0856042 | ||||||||
\(59\) | − | 90.0311i | − | 1.52595i | −0.646427 | − | 0.762976i | \(-0.723738\pi\) | ||
0.646427 | − | 0.762976i | \(-0.276262\pi\) | |||||||
\(60\) | 0.0991269 | − | 0.258143i | 0.00165211 | − | 0.00430238i | ||||
\(61\) | −30.8695 | −0.506058 | −0.253029 | − | 0.967459i | \(-0.581427\pi\) | ||||
−0.253029 | + | 0.967459i | \(0.581427\pi\) | |||||||
\(62\) | − | 98.6683i | − | 1.59142i | ||||||
\(63\) | 37.3852 | + | 33.6779i | 0.593417 | + | 0.534570i | ||||
\(64\) | −63.7288 | −0.995763 | ||||||||
\(65\) | − | 53.2906i | − | 0.819855i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 34.0775 | 0.508620 | 0.254310 | − | 0.967123i | \(-0.418152\pi\) | ||||
0.254310 | + | 0.967123i | \(0.418152\pi\) | |||||||
\(68\) | − | 0.300360i | − | 0.00441706i | ||||||
\(69\) | 13.2976 | − | 34.6292i | 0.192719 | − | 0.501872i | ||||
\(70\) | 61.4533 | 0.877904 | ||||||||
\(71\) | − | 37.5962i | − | 0.529524i | −0.964314 | − | 0.264762i | \(-0.914707\pi\) | ||
0.964314 | − | 0.264762i | \(-0.0852934\pi\) | |||||||
\(72\) | 48.0883 | − | 53.3820i | 0.667893 | − | 0.741417i | ||||
\(73\) | −12.1261 | −0.166111 | −0.0830554 | − | 0.996545i | \(-0.526468\pi\) | ||||
−0.0830554 | + | 0.996545i | \(0.526468\pi\) | |||||||
\(74\) | 78.8265i | 1.06522i | ||||||||
\(75\) | −14.2228 | − | 5.46154i | −0.189637 | − | 0.0728205i | ||||
\(76\) | −0.313592 | −0.00412621 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −20.9434 | + | 54.5402i | −0.268506 | + | 0.699233i | ||||
\(79\) | −63.1447 | −0.799300 | −0.399650 | − | 0.916668i | \(-0.630868\pi\) | ||||
−0.399650 | + | 0.916668i | \(0.630868\pi\) | |||||||
\(80\) | − | 88.1173i | − | 1.10147i | ||||||
\(81\) | 8.42858 | + | 80.5603i | 0.104056 | + | 0.994571i | ||||
\(82\) | −113.284 | −1.38152 | ||||||||
\(83\) | − | 9.70147i | − | 0.116885i | −0.998291 | − | 0.0584426i | \(-0.981387\pi\) | ||
0.998291 | − | 0.0584426i | \(-0.0186135\pi\) | |||||||
\(84\) | −0.263154 | − | 0.101051i | −0.00313278 | − | 0.00120299i | ||||
\(85\) | −98.0146 | −1.15311 | ||||||||
\(86\) | 87.9962i | 1.02321i | ||||||||
\(87\) | −2.66420 | + | 6.93803i | −0.0306230 | + | 0.0797474i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 34.1289i | − | 0.383471i | −0.981447 | − | 0.191735i | \(-0.938588\pi\) | ||
0.981447 | − | 0.191735i | \(-0.0614115\pi\) | |||||||
\(90\) | 73.5007 | + | 66.2119i | 0.816674 | + | 0.735688i | ||||
\(91\) | −54.3250 | −0.596978 | ||||||||
\(92\) | 0.207811i | 0.00225881i | ||||||||
\(93\) | 137.877 | + | 52.9446i | 1.48254 | + | 0.569297i | ||||
\(94\) | 115.811 | 1.23203 | ||||||||
\(95\) | 102.333i | 1.07718i | ||||||||
\(96\) | −0.289188 | + | 0.753095i | −0.00301238 | + | 0.00784473i | ||||
\(97\) | −37.8227 | −0.389925 | −0.194962 | − | 0.980811i | \(-0.562458\pi\) | ||||
−0.194962 | + | 0.980811i | \(0.562458\pi\) | |||||||
\(98\) | 35.5595i | 0.362852i | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0.0853512 | 0.000853512 | ||||||||
\(101\) | − | 46.9047i | − | 0.464403i | −0.972668 | − | 0.232202i | \(-0.925407\pi\) | ||
0.972668 | − | 0.232202i | \(-0.0745929\pi\) | |||||||
\(102\) | 100.313 | + | 38.5202i | 0.983460 | + | 0.377649i | ||||
\(103\) | 104.797 | 1.01744 | 0.508722 | − | 0.860931i | \(-0.330118\pi\) | ||||
0.508722 | + | 0.860931i | \(0.330118\pi\) | |||||||
\(104\) | 77.5702i | 0.745867i | ||||||||
\(105\) | −32.9753 | + | 85.8733i | −0.314051 | + | 0.817841i | ||||
\(106\) | −86.4126 | −0.815213 | ||||||||
\(107\) | − | 46.6302i | − | 0.435796i | −0.975972 | − | 0.217898i | \(-0.930080\pi\) | ||
0.975972 | − | 0.217898i | \(-0.0699200\pi\) | |||||||
\(108\) | −0.205867 | − | 0.404392i | −0.00190617 | − | 0.00374437i | ||||
\(109\) | −168.413 | −1.54507 | −0.772537 | − | 0.634969i | \(-0.781013\pi\) | ||||
−0.772537 | + | 0.634969i | \(0.781013\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −110.150 | − | 42.2977i | −0.992344 | − | 0.381060i | ||||
\(112\) | −89.8277 | −0.802033 | ||||||||
\(113\) | 46.3202i | 0.409913i | 0.978771 | + | 0.204957i | \(0.0657053\pi\) | ||||
−0.978771 | + | 0.204957i | \(0.934295\pi\) | |||||||
\(114\) | 40.2171 | − | 104.732i | 0.352782 | − | 0.918702i | ||||
\(115\) | 67.8136 | 0.589684 | ||||||||
\(116\) | − | 0.0416353i | − | 0.000358925i | ||||||
\(117\) | −64.9750 | − | 58.5317i | −0.555342 | − | 0.500271i | ||||
\(118\) | −180.440 | −1.52915 | ||||||||
\(119\) | 99.9172i | 0.839640i | ||||||||
\(120\) | 122.618 | + | 47.0852i | 1.02181 | + | 0.392376i | ||||
\(121\) | 0 | 0 | ||||||||
\(122\) | 61.8686i | 0.507120i | ||||||||
\(123\) | 60.7875 | − | 158.301i | 0.494207 | − | 1.28700i | ||||
\(124\) | −0.827402 | −0.00667260 | ||||||||
\(125\) | 109.257i | 0.874059i | ||||||||
\(126\) | 67.4971 | − | 74.9274i | 0.535692 | − | 0.594662i | ||||
\(127\) | −68.2888 | −0.537707 | −0.268854 | − | 0.963181i | \(-0.586645\pi\) | ||||
−0.268854 | + | 0.963181i | \(0.586645\pi\) | |||||||
\(128\) | 128.801i | 1.00626i | ||||||||
\(129\) | −122.964 | − | 47.2180i | −0.953206 | − | 0.366031i | ||||
\(130\) | −106.805 | −0.821576 | ||||||||
\(131\) | 162.272i | 1.23872i | 0.785109 | + | 0.619358i | \(0.212607\pi\) | ||||
−0.785109 | + | 0.619358i | \(0.787393\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 104.319 | 0.784353 | ||||||||
\(134\) | − | 68.2981i | − | 0.509687i | ||||||
\(135\) | −131.963 | + | 67.1792i | −0.977501 | + | 0.497624i | ||||
\(136\) | 142.671 | 1.04905 | ||||||||
\(137\) | − | 52.8671i | − | 0.385891i | −0.981209 | − | 0.192946i | \(-0.938196\pi\) | ||
0.981209 | − | 0.192946i | \(-0.0618041\pi\) | |||||||
\(138\) | −69.4037 | − | 26.6510i | −0.502926 | − | 0.193124i | ||||
\(139\) | −86.5357 | −0.622559 | −0.311279 | − | 0.950318i | \(-0.600758\pi\) | ||||
−0.311279 | + | 0.950318i | \(0.600758\pi\) | |||||||
\(140\) | − | 0.515328i | − | 0.00368092i | ||||||
\(141\) | −62.1430 | + | 161.831i | −0.440730 | + | 1.14773i | ||||
\(142\) | −75.3502 | −0.530635 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −107.438 | − | 96.7835i | −0.746095 | − | 0.672107i | ||||
\(145\) | −13.5866 | −0.0937006 | ||||||||
\(146\) | 24.3031i | 0.166459i | ||||||||
\(147\) | −49.6899 | − | 19.0809i | −0.338027 | − | 0.129802i | ||||
\(148\) | 0.661015 | 0.00446631 | ||||||||
\(149\) | − | 64.4499i | − | 0.432550i | −0.976332 | − | 0.216275i | \(-0.930609\pi\) | ||
0.976332 | − | 0.216275i | \(-0.0693908\pi\) | |||||||
\(150\) | −10.9460 | + | 28.5052i | −0.0729734 | + | 0.190035i | ||||
\(151\) | 44.6348 | 0.295595 | 0.147797 | − | 0.989018i | \(-0.452782\pi\) | ||||
0.147797 | + | 0.989018i | \(0.452782\pi\) | |||||||
\(152\) | − | 148.956i | − | 0.979973i | ||||||
\(153\) | −107.654 | + | 119.505i | −0.703622 | + | 0.781079i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 270.001i | 1.74194i | ||||||||
\(156\) | 0.457357 | + | 0.175625i | 0.00293178 | + | 0.00112580i | ||||
\(157\) | −141.066 | −0.898510 | −0.449255 | − | 0.893404i | \(-0.648311\pi\) | ||||
−0.449255 | + | 0.893404i | \(0.648311\pi\) | |||||||
\(158\) | 126.554i | 0.800978i | ||||||||
\(159\) | 46.3683 | − | 120.751i | 0.291625 | − | 0.759439i | ||||
\(160\) | −1.47477 | −0.00921731 | ||||||||
\(161\) | − | 69.1300i | − | 0.429379i | ||||||
\(162\) | 161.459 | − | 16.8925i | 0.996659 | − | 0.104275i | ||||
\(163\) | 120.965 | 0.742114 | 0.371057 | − | 0.928610i | \(-0.378995\pi\) | ||||
0.371057 | + | 0.928610i | \(0.378995\pi\) | |||||||
\(164\) | 0.949967i | 0.00579248i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −19.4437 | −0.117130 | ||||||||
\(167\) | 107.432i | 0.643304i | 0.946858 | + | 0.321652i | \(0.104238\pi\) | ||||
−0.946858 | + | 0.321652i | \(0.895762\pi\) | |||||||
\(168\) | 47.9992 | − | 124.998i | 0.285709 | − | 0.744034i | ||||
\(169\) | −74.5839 | −0.441325 | ||||||||
\(170\) | 196.441i | 1.15553i | ||||||||
\(171\) | 124.770 | + | 112.397i | 0.729647 | + | 0.657291i | ||||
\(172\) | 0.737909 | 0.00429017 | ||||||||
\(173\) | 328.814i | 1.90066i | 0.311246 | + | 0.950329i | \(0.399254\pi\) | ||||
−0.311246 | + | 0.950329i | \(0.600746\pi\) | |||||||
\(174\) | 13.9052 | + | 5.33959i | 0.0799148 | + | 0.0306873i | ||||
\(175\) | −28.3928 | −0.162244 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 96.8227 | − | 252.142i | 0.547021 | − | 1.42453i | ||||
\(178\) | −68.4011 | −0.384276 | ||||||||
\(179\) | − | 48.2985i | − | 0.269824i | −0.990858 | − | 0.134912i | \(-0.956925\pi\) | ||
0.990858 | − | 0.134912i | \(-0.0430752\pi\) | |||||||
\(180\) | 0.555232 | − | 0.616354i | 0.00308462 | − | 0.00342419i | ||||
\(181\) | 0.0665674 | 0.000367776 | 0.000183888 | − | 1.00000i | \(-0.499941\pi\) | ||||
0.000183888 | 1.00000i | \(0.499941\pi\) | ||||||||
\(182\) | 108.878i | 0.598231i | ||||||||
\(183\) | −86.4536 | − | 33.1982i | −0.472424 | − | 0.181411i | ||||
\(184\) | −98.7100 | −0.536467 | ||||||||
\(185\) | − | 215.705i | − | 1.16597i | ||||||
\(186\) | 106.111 | − | 276.332i | 0.570492 | − | 1.48566i | ||||
\(187\) | 0 | 0 | ||||||||
\(188\) | − | 0.971151i | − | 0.00516570i | ||||||
\(189\) | 68.4832 | + | 134.524i | 0.362345 | + | 0.711768i | ||||
\(190\) | 205.095 | 1.07944 | ||||||||
\(191\) | − | 197.414i | − | 1.03358i | −0.856112 | − | 0.516790i | \(-0.827127\pi\) | ||
0.856112 | − | 0.516790i | \(-0.172873\pi\) | |||||||
\(192\) | −178.480 | − | 68.5363i | −0.929583 | − | 0.356960i | ||||
\(193\) | 1.52366 | 0.00789462 | 0.00394731 | − | 0.999992i | \(-0.498744\pi\) | ||||
0.00394731 | + | 0.999992i | \(0.498744\pi\) | |||||||
\(194\) | 75.8042i | 0.390743i | ||||||||
\(195\) | 57.3106 | − | 149.246i | 0.293901 | − | 0.765366i | ||||
\(196\) | 0.298191 | 0.00152138 | ||||||||
\(197\) | − | 215.460i | − | 1.09370i | −0.837229 | − | 0.546852i | \(-0.815826\pi\) | ||
0.837229 | − | 0.546852i | \(-0.184174\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −106.663 | −0.535993 | −0.267997 | − | 0.963420i | \(-0.586362\pi\) | ||||
−0.267997 | + | 0.963420i | \(0.586362\pi\) | |||||||
\(200\) | 40.5417i | 0.202709i | ||||||||
\(201\) | 95.4380 | + | 36.6482i | 0.474816 | + | 0.182329i | ||||
\(202\) | −94.0063 | −0.465378 | ||||||||
\(203\) | 13.8503i | 0.0682282i | ||||||||
\(204\) | 0.323018 | − | 0.841193i | 0.00158342 | − | 0.00412349i | ||||
\(205\) | 309.997 | 1.51218 | ||||||||
\(206\) | − | 210.033i | − | 1.01958i | ||||||
\(207\) | 74.4830 | − | 82.6823i | 0.359821 | − | 0.399431i | ||||
\(208\) | 156.119 | 0.750573 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 172.107 | + | 66.0891i | 0.819557 | + | 0.314710i | ||||
\(211\) | 214.825 | 1.01813 | 0.509065 | − | 0.860728i | \(-0.329991\pi\) | ||||
0.509065 | + | 0.860728i | \(0.329991\pi\) | |||||||
\(212\) | 0.724629i | 0.00341806i | ||||||||
\(213\) | 40.4323 | − | 105.292i | 0.189823 | − | 0.494331i | ||||
\(214\) | −93.4561 | −0.436711 | ||||||||
\(215\) | − | 240.797i | − | 1.11999i | ||||||
\(216\) | 192.086 | − | 97.7865i | 0.889286 | − | 0.452715i | ||||
\(217\) | 275.242 | 1.26840 | ||||||||
\(218\) | 337.533i | 1.54832i | ||||||||
\(219\) | −33.9605 | − | 13.0408i | −0.155071 | − | 0.0595472i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 173.654i | − | 0.785767i | ||||||
\(222\) | −84.7729 | + | 220.763i | −0.381860 | + | 0.994426i | ||||
\(223\) | 44.7688 | 0.200757 | 0.100379 | − | 0.994949i | \(-0.467995\pi\) | ||||
0.100379 | + | 0.994949i | \(0.467995\pi\) | |||||||
\(224\) | 1.50340i | 0.00671159i | ||||||||
\(225\) | −33.9589 | − | 30.5913i | −0.150928 | − | 0.135961i | ||||
\(226\) | 92.8348 | 0.410773 | ||||||||
\(227\) | − | 224.504i | − | 0.989004i | −0.869177 | − | 0.494502i | \(-0.835351\pi\) | ||
0.869177 | − | 0.494502i | \(-0.164649\pi\) | |||||||
\(228\) | −0.878250 | − | 0.337248i | −0.00385197 | − | 0.00147916i | ||||
\(229\) | −104.101 | −0.454589 | −0.227294 | − | 0.973826i | \(-0.572988\pi\) | ||||
−0.227294 | + | 0.973826i | \(0.572988\pi\) | |||||||
\(230\) | − | 135.912i | − | 0.590921i | ||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 19.7767 | 0.0852446 | ||||||||
\(233\) | − | 61.5290i | − | 0.264073i | −0.991245 | − | 0.132036i | \(-0.957848\pi\) | ||
0.991245 | − | 0.132036i | \(-0.0421516\pi\) | |||||||
\(234\) | −117.309 | + | 130.223i | −0.501320 | + | 0.556507i | ||||
\(235\) | −316.909 | −1.34855 | ||||||||
\(236\) | 1.51311i | 0.00641150i | ||||||||
\(237\) | −176.844 | − | 67.9081i | −0.746177 | − | 0.286532i | ||||
\(238\) | 200.254 | 0.841402 | ||||||||
\(239\) | 149.260i | 0.624520i | 0.949997 | + | 0.312260i | \(0.101086\pi\) | ||||
−0.949997 | + | 0.312260i | \(0.898914\pi\) | |||||||
\(240\) | 94.7645 | − | 246.782i | 0.394852 | − | 1.02826i | ||||
\(241\) | 358.881 | 1.48913 | 0.744567 | − | 0.667548i | \(-0.232656\pi\) | ||||
0.744567 | + | 0.667548i | \(0.232656\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −63.0323 | + | 234.683i | −0.259392 | + | 0.965772i | ||||
\(244\) | 0.518811 | 0.00212627 | ||||||||
\(245\) | − | 97.3067i | − | 0.397170i | ||||||
\(246\) | −317.266 | − | 121.830i | −1.28970 | − | 0.495244i | ||||
\(247\) | −181.305 | −0.734027 | ||||||||
\(248\) | − | 393.015i | − | 1.58474i | ||||||
\(249\) | 10.4333 | − | 27.1701i | 0.0419008 | − | 0.109117i | ||||
\(250\) | 218.973 | 0.875894 | ||||||||
\(251\) | − | 357.022i | − | 1.42240i | −0.702990 | − | 0.711199i | \(-0.748152\pi\) | ||
0.702990 | − | 0.711199i | \(-0.251848\pi\) | |||||||
\(252\) | −0.628318 | − | 0.566010i | −0.00249332 | − | 0.00224607i | ||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 136.864i | 0.538836i | ||||||||
\(255\) | −274.501 | − | 105.408i | −1.07647 | − | 0.413366i | ||||
\(256\) | 3.22681 | 0.0126047 | ||||||||
\(257\) | 66.0935i | 0.257173i | 0.991698 | + | 0.128586i | \(0.0410440\pi\) | ||||
−0.991698 | + | 0.128586i | \(0.958956\pi\) | |||||||
\(258\) | −94.6343 | + | 246.443i | −0.366800 | + | 0.955207i | ||||
\(259\) | −219.892 | −0.849003 | ||||||||
\(260\) | 0.895632i | 0.00344474i | ||||||||
\(261\) | −14.9228 | + | 16.5656i | −0.0571755 | + | 0.0634696i | ||||
\(262\) | 325.224 | 1.24131 | ||||||||
\(263\) | − | 85.4194i | − | 0.324789i | −0.986726 | − | 0.162394i | \(-0.948078\pi\) | ||
0.986726 | − | 0.162394i | \(-0.0519216\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 236.464 | 0.892315 | ||||||||
\(266\) | − | 209.076i | − | 0.785999i | ||||||
\(267\) | 36.7035 | − | 95.5819i | 0.137466 | − | 0.357985i | ||||
\(268\) | −0.572726 | −0.00213704 | ||||||||
\(269\) | − | 161.784i | − | 0.601427i | −0.953715 | − | 0.300713i | \(-0.902775\pi\) | ||
0.953715 | − | 0.300713i | \(-0.0972248\pi\) | |||||||
\(270\) | 134.640 | + | 264.479i | 0.498668 | + | 0.979553i | ||||
\(271\) | −259.994 | −0.959386 | −0.479693 | − | 0.877436i | \(-0.659252\pi\) | ||||
−0.479693 | + | 0.877436i | \(0.659252\pi\) | |||||||
\(272\) | − | 287.142i | − | 1.05567i | ||||||
\(273\) | −152.143 | − | 58.4231i | −0.557302 | − | 0.214004i | ||||
\(274\) | −105.956 | −0.386701 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −0.223487 | + | 0.581998i | −0.000809737 | + | 0.00210869i | ||||
\(277\) | −86.7920 | −0.313329 | −0.156664 | − | 0.987652i | \(-0.550074\pi\) | ||||
−0.156664 | + | 0.987652i | \(0.550074\pi\) | |||||||
\(278\) | 173.435i | 0.623865i | ||||||||
\(279\) | 329.200 | + | 296.555i | 1.17993 | + | 1.06292i | ||||
\(280\) | 244.780 | 0.874216 | ||||||||
\(281\) | 484.715i | 1.72496i | 0.506087 | + | 0.862482i | \(0.331091\pi\) | ||||
−0.506087 | + | 0.862482i | \(0.668909\pi\) | |||||||
\(282\) | 324.340 | + | 124.547i | 1.15014 | + | 0.441655i | ||||
\(283\) | 432.072 | 1.52676 | 0.763379 | − | 0.645951i | \(-0.223539\pi\) | ||||
0.763379 | + | 0.645951i | \(0.223539\pi\) | |||||||
\(284\) | 0.631864i | 0.00222487i | ||||||||
\(285\) | −110.052 | + | 286.594i | −0.386148 | + | 1.00559i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 316.014i | − | 1.10109i | ||||||
\(288\) | −1.61981 | + | 1.79812i | −0.00562434 | + | 0.00624348i | ||||
\(289\) | −30.3935 | −0.105168 | ||||||||
\(290\) | 27.2302i | 0.0938973i | ||||||||
\(291\) | −105.927 | − | 40.6759i | −0.364010 | − | 0.139780i | ||||
\(292\) | 0.203798 | 0.000697939 | ||||||||
\(293\) | − | 5.52957i | − | 0.0188723i | −0.999955 | − | 0.00943613i | \(-0.996996\pi\) | ||
0.999955 | − | 0.00943613i | \(-0.00300366\pi\) | |||||||
\(294\) | −38.2419 | + | 99.5884i | −0.130075 | + | 0.338736i | ||||
\(295\) | 493.765 | 1.67378 | ||||||||
\(296\) | 313.981i | 1.06075i | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −129.170 | −0.433458 | ||||||||
\(299\) | 120.147i | 0.401829i | ||||||||
\(300\) | 0.239036 | + | 0.0917898i | 0.000796786 | + | 0.000305966i | ||||
\(301\) | −245.471 | −0.815519 | ||||||||
\(302\) | − | 89.4569i | − | 0.296215i | ||||||
\(303\) | 50.4430 | − | 131.362i | 0.166479 | − | 0.433538i | ||||
\(304\) | −299.791 | −0.986156 | ||||||||
\(305\) | − | 169.300i | − | 0.555083i | ||||||
\(306\) | 239.512 | + | 215.760i | 0.782718 | + | 0.705099i | ||||
\(307\) | 219.257 | 0.714191 | 0.357095 | − | 0.934068i | \(-0.383767\pi\) | ||||
0.357095 | + | 0.934068i | \(0.383767\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 293.495 | + | 112.702i | 0.949823 | + | 0.364732i | ||||
\(310\) | 541.135 | 1.74560 | ||||||||
\(311\) | − | 142.150i | − | 0.457075i | −0.973535 | − | 0.228537i | \(-0.926606\pi\) | ||
0.973535 | − | 0.228537i | \(-0.0733943\pi\) | |||||||
\(312\) | −83.4218 | + | 217.244i | −0.267377 | + | 0.696295i | ||||
\(313\) | 94.2857 | 0.301232 | 0.150616 | − | 0.988592i | \(-0.451874\pi\) | ||||
0.150616 | + | 0.988592i | \(0.451874\pi\) | |||||||
\(314\) | 282.724i | 0.900396i | ||||||||
\(315\) | −184.702 | + | 205.035i | −0.586357 | + | 0.650905i | ||||
\(316\) | 1.06125 | 0.00335838 | ||||||||
\(317\) | 501.215i | 1.58112i | 0.612385 | + | 0.790560i | \(0.290210\pi\) | ||||
−0.612385 | + | 0.790560i | \(0.709790\pi\) | |||||||
\(318\) | −242.008 | − | 92.9312i | −0.761032 | − | 0.292237i | ||||
\(319\) | 0 | 0 | ||||||||
\(320\) | − | 349.513i | − | 1.09223i | ||||||
\(321\) | 50.1478 | − | 130.593i | 0.156224 | − | 0.406832i | ||||
\(322\) | −138.550 | −0.430280 | ||||||||
\(323\) | 333.464i | 1.03240i | ||||||||
\(324\) | −0.141655 | − | 1.35394i | −0.000437208 | − | 0.00417883i | ||||
\(325\) | 49.3462 | 0.151834 | ||||||||
\(326\) | − | 242.437i | − | 0.743672i | ||||||
\(327\) | −471.660 | − | 181.118i | −1.44239 | − | 0.553876i | ||||
\(328\) | −451.234 | −1.37571 | ||||||||
\(329\) | 323.061i | 0.981948i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −653.489 | −1.97429 | −0.987143 | − | 0.159839i | \(-0.948903\pi\) | ||||
−0.987143 | + | 0.159839i | \(0.948903\pi\) | |||||||
\(332\) | 0.163048i | 0.000491110i | ||||||||
\(333\) | −263.000 | − | 236.919i | −0.789789 | − | 0.711468i | ||||
\(334\) | 215.314 | 0.644654 | ||||||||
\(335\) | 186.894i | 0.557893i | ||||||||
\(336\) | −251.573 | − | 96.6040i | −0.748728 | − | 0.287512i | ||||
\(337\) | 659.365 | 1.95657 | 0.978287 | − | 0.207256i | \(-0.0664532\pi\) | ||||
0.978287 | + | 0.207256i | \(0.0664532\pi\) | |||||||
\(338\) | 149.481i | 0.442251i | ||||||||
\(339\) | −49.8144 | + | 129.725i | −0.146945 | + | 0.382669i | ||||
\(340\) | 1.64729 | 0.00484497 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 225.265 | − | 250.063i | 0.658670 | − | 0.731179i | ||||
\(343\) | −373.147 | −1.08789 | ||||||||
\(344\) | 350.506i | 1.01891i | ||||||||
\(345\) | 189.920 | + | 72.9292i | 0.550492 | + | 0.211389i | ||||
\(346\) | 659.008 | 1.90465 | ||||||||
\(347\) | 277.880i | 0.800806i | 0.916339 | + | 0.400403i | \(0.131130\pi\) | ||||
−0.916339 | + | 0.400403i | \(0.868870\pi\) | |||||||
\(348\) | 0.0447761 | − | 0.116604i | 0.000128667 | − | 0.000335070i | ||||
\(349\) | −252.775 | −0.724284 | −0.362142 | − | 0.932123i | \(-0.617954\pi\) | ||||
−0.362142 | + | 0.932123i | \(0.617954\pi\) | |||||||
\(350\) | 56.9047i | 0.162585i | ||||||||
\(351\) | −119.023 | − | 233.801i | −0.339096 | − | 0.666100i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 560.803i | 1.58868i | 0.607476 | + | 0.794338i | \(0.292182\pi\) | ||||
−0.607476 | + | 0.794338i | \(0.707818\pi\) | |||||||
\(354\) | −505.343 | − | 194.052i | −1.42752 | − | 0.548169i | ||||
\(355\) | 206.192 | 0.580823 | ||||||||
\(356\) | 0.573590i | 0.00161121i | ||||||||
\(357\) | −107.455 | + | 279.829i | −0.300993 | + | 0.783836i | ||||
\(358\) | −96.7998 | −0.270390 | ||||||||
\(359\) | 296.063i | 0.824689i | 0.911028 | + | 0.412345i | \(0.135290\pi\) | ||||
−0.911028 | + | 0.412345i | \(0.864710\pi\) | |||||||
\(360\) | 292.767 | + | 263.735i | 0.813243 | + | 0.732597i | ||||
\(361\) | −12.8456 | −0.0355834 | ||||||||
\(362\) | − | 0.133414i | − | 0.000368547i | ||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0.913018 | 0.00250829 | ||||||||
\(365\) | − | 66.5041i | − | 0.182203i | ||||||
\(366\) | −66.5357 | + | 173.270i | −0.181792 | + | 0.473415i | ||||
\(367\) | 84.8579 | 0.231220 | 0.115610 | − | 0.993295i | \(-0.463118\pi\) | ||||
0.115610 | + | 0.993295i | \(0.463118\pi\) | |||||||
\(368\) | 198.666i | 0.539852i | ||||||||
\(369\) | 340.485 | − | 377.966i | 0.922722 | − | 1.02430i | ||||
\(370\) | −432.315 | −1.16842 | ||||||||
\(371\) | − | 241.054i | − | 0.649740i | ||||||
\(372\) | −2.31723 | − | 0.889818i | −0.00622912 | − | 0.00239198i | ||||
\(373\) | 316.098 | 0.847447 | 0.423724 | − | 0.905792i | \(-0.360723\pi\) | ||||
0.423724 | + | 0.905792i | \(0.360723\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −117.499 | + | 305.988i | −0.313332 | + | 0.815968i | ||||
\(376\) | 461.296 | 1.22685 | ||||||||
\(377\) | − | 24.0716i | − | 0.0638505i | ||||||
\(378\) | 269.613 | − | 137.254i | 0.713262 | − | 0.363105i | ||||
\(379\) | −108.737 | −0.286905 | −0.143453 | − | 0.989657i | \(-0.545820\pi\) | ||||
−0.143453 | + | 0.989657i | \(0.545820\pi\) | |||||||
\(380\) | − | 1.71986i | − | 0.00452594i | ||||||
\(381\) | −191.251 | − | 73.4403i | −0.501970 | − | 0.192757i | ||||
\(382\) | −395.656 | −1.03575 | ||||||||
\(383\) | − | 442.014i | − | 1.15408i | −0.816715 | − | 0.577041i | \(-0.804207\pi\) | ||
0.816715 | − | 0.577041i | \(-0.195793\pi\) | |||||||
\(384\) | −138.517 | + | 360.721i | −0.360721 | + | 0.939378i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | − | 3.05372i | − | 0.00791119i | ||||||
\(387\) | −293.594 | − | 264.479i | −0.758640 | − | 0.683408i | ||||
\(388\) | 0.635670 | 0.00163833 | ||||||||
\(389\) | − | 509.597i | − | 1.31002i | −0.755621 | − | 0.655009i | \(-0.772665\pi\) | ||
0.755621 | − | 0.655009i | \(-0.227335\pi\) | |||||||
\(390\) | −299.119 | − | 114.862i | −0.766972 | − | 0.294517i | ||||
\(391\) | 220.980 | 0.565165 | ||||||||
\(392\) | 141.640i | 0.361327i | ||||||||
\(393\) | −174.513 | + | 454.460i | −0.444053 | + | 1.15639i | ||||
\(394\) | −431.824 | −1.09600 | ||||||||
\(395\) | − | 346.310i | − | 0.876734i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 13.0481 | 0.0328668 | 0.0164334 | − | 0.999865i | \(-0.494769\pi\) | ||||
0.0164334 | + | 0.999865i | \(0.494769\pi\) | |||||||
\(398\) | 213.773i | 0.537118i | ||||||||
\(399\) | 292.157 | + | 112.188i | 0.732223 | + | 0.281174i | ||||
\(400\) | 81.5950 | 0.203988 | ||||||||
\(401\) | − | 549.606i | − | 1.37059i | −0.728267 | − | 0.685294i | \(-0.759674\pi\) | ||
0.728267 | − | 0.685294i | \(-0.240326\pi\) | |||||||
\(402\) | 73.4502 | − | 191.277i | 0.182712 | − | 0.475812i | ||||
\(403\) | −478.366 | −1.18701 | ||||||||
\(404\) | 0.788308i | 0.00195126i | ||||||||
\(405\) | −441.823 | + | 46.2255i | −1.09092 | + | 0.114137i | ||||
\(406\) | 27.7588 | 0.0683714 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 399.566 | + | 153.433i | 0.979327 | + | 0.376062i | ||||
\(409\) | 618.166 | 1.51141 | 0.755704 | − | 0.654913i | \(-0.227295\pi\) | ||||
0.755704 | + | 0.654913i | \(0.227295\pi\) | |||||||
\(410\) | − | 621.295i | − | 1.51535i | ||||||
\(411\) | 56.8552 | − | 148.060i | 0.138334 | − | 0.360244i | ||||
\(412\) | −1.76128 | −0.00427494 | ||||||||
\(413\) | − | 503.350i | − | 1.21876i | ||||||
\(414\) | −165.712 | − | 149.279i | −0.400270 | − | 0.360576i | ||||
\(415\) | 53.2066 | 0.128209 | ||||||||
\(416\) | − | 2.61288i | − | 0.00628096i | ||||||
\(417\) | −242.353 | − | 93.0636i | −0.581182 | − | 0.223174i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 440.342i | − | 1.05094i | −0.850814 | − | 0.525468i | \(-0.823890\pi\) | ||
0.850814 | − | 0.525468i | \(-0.176110\pi\) | |||||||
\(420\) | 0.554203 | − | 1.44324i | 0.00131953 | − | 0.00343627i | ||||
\(421\) | 574.230 | 1.36397 | 0.681983 | − | 0.731368i | \(-0.261118\pi\) | ||||
0.681983 | + | 0.731368i | \(0.261118\pi\) | |||||||
\(422\) | − | 430.552i | − | 1.02027i | ||||||
\(423\) | −348.077 | + | 386.394i | −0.822877 | + | 0.913462i | ||||
\(424\) | −344.198 | −0.811788 | ||||||||
\(425\) | − | 90.7598i | − | 0.213552i | ||||||
\(426\) | −211.027 | − | 81.0344i | −0.495368 | − | 0.190222i | ||||
\(427\) | −172.587 | −0.404184 | ||||||||
\(428\) | 0.783693i | 0.00183106i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −482.605 | −1.12234 | ||||||||
\(431\) | 661.481i | 1.53476i | 0.641193 | + | 0.767380i | \(0.278440\pi\) | ||||
−0.641193 | + | 0.767380i | \(0.721560\pi\) | |||||||
\(432\) | −196.807 | − | 386.595i | −0.455572 | − | 0.894897i | ||||
\(433\) | 212.781 | 0.491412 | 0.245706 | − | 0.969344i | \(-0.420980\pi\) | ||||
0.245706 | + | 0.969344i | \(0.420980\pi\) | |||||||
\(434\) | − | 551.639i | − | 1.27106i | ||||||
\(435\) | −38.0508 | − | 14.6115i | −0.0874731 | − | 0.0335897i | ||||
\(436\) | 2.83045 | 0.00649185 | ||||||||
\(437\) | − | 230.715i | − | 0.527951i | ||||||
\(438\) | −26.1364 | + | 68.0635i | −0.0596722 | + | 0.155396i | ||||
\(439\) | −103.815 | −0.236482 | −0.118241 | − | 0.992985i | \(-0.537725\pi\) | ||||
−0.118241 | + | 0.992985i | \(0.537725\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −118.642 | − | 106.877i | −0.269029 | − | 0.242351i | ||||
\(442\) | −348.038 | −0.787416 | ||||||||
\(443\) | 276.769i | 0.624760i | 0.949957 | + | 0.312380i | \(0.101126\pi\) | ||||
−0.949957 | + | 0.312380i | \(0.898874\pi\) | |||||||
\(444\) | 1.85125 | + | 0.710879i | 0.00416947 | + | 0.00160108i | ||||
\(445\) | 187.176 | 0.420620 | ||||||||
\(446\) | − | 89.7255i | − | 0.201178i | ||||||
\(447\) | 69.3118 | − | 180.499i | 0.155060 | − | 0.403802i | ||||
\(448\) | −356.298 | −0.795308 | ||||||||
\(449\) | 497.877i | 1.10886i | 0.832231 | + | 0.554428i | \(0.187063\pi\) | ||||
−0.832231 | + | 0.554428i | \(0.812937\pi\) | |||||||
\(450\) | −61.3111 | + | 68.0603i | −0.136247 | + | 0.151245i | ||||
\(451\) | 0 | 0 | ||||||||
\(452\) | − | 0.778483i | − | 0.00172231i | ||||||
\(453\) | 125.005 | + | 48.0018i | 0.275949 | + | 0.105964i | ||||
\(454\) | −449.950 | −0.991079 | ||||||||
\(455\) | − | 297.939i | − | 0.654812i | ||||||
\(456\) | 160.193 | − | 417.168i | 0.351300 | − | 0.914842i | ||||
\(457\) | 811.116 | 1.77487 | 0.887435 | − | 0.460932i | \(-0.152485\pi\) | ||||
0.887435 | + | 0.460932i | \(0.152485\pi\) | |||||||
\(458\) | 208.638i | 0.455543i | ||||||||
\(459\) | −430.018 | + | 218.912i | −0.936858 | + | 0.476933i | ||||
\(460\) | −1.13971 | −0.00247764 | ||||||||
\(461\) | − | 790.057i | − | 1.71379i | −0.515492 | − | 0.856894i | \(-0.672391\pi\) | ||
0.515492 | − | 0.856894i | \(-0.327609\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 540.381 | 1.16713 | 0.583565 | − | 0.812067i | \(-0.301658\pi\) | ||||
0.583565 | + | 0.812067i | \(0.301658\pi\) | |||||||
\(464\) | − | 39.8030i | − | 0.0857824i | ||||||
\(465\) | −290.369 | + | 756.168i | −0.624449 | + | 1.62617i | ||||
\(466\) | −123.316 | −0.264627 | ||||||||
\(467\) | 277.866i | 0.595003i | 0.954721 | + | 0.297501i | \(0.0961533\pi\) | ||||
−0.954721 | + | 0.297501i | \(0.903847\pi\) | |||||||
\(468\) | 1.09201 | + | 0.983716i | 0.00233335 | + | 0.00210196i | ||||
\(469\) | 190.522 | 0.406230 | ||||||||
\(470\) | 635.149i | 1.35138i | ||||||||
\(471\) | −395.072 | − | 151.708i | −0.838793 | − | 0.322097i | ||||
\(472\) | −718.728 | −1.52273 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | −136.101 | + | 354.430i | −0.287133 | + | 0.747743i | ||||
\(475\) | −94.7581 | −0.199491 | ||||||||
\(476\) | − | 1.67927i | − | 0.00352787i | ||||||
\(477\) | 259.719 | − | 288.310i | 0.544485 | − | 0.604423i | ||||
\(478\) | 299.147 | 0.625831 | ||||||||
\(479\) | 470.226i | 0.981683i | 0.871249 | + | 0.490841i | \(0.163311\pi\) | ||||
−0.871249 | + | 0.490841i | \(0.836689\pi\) | |||||||
\(480\) | −4.13026 | − | 1.58602i | −0.00860470 | − | 0.00330421i | ||||
\(481\) | 382.168 | 0.794529 | ||||||||
\(482\) | − | 719.269i | − | 1.49226i | ||||||
\(483\) | 74.3449 | − | 193.606i | 0.153923 | − | 0.400841i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − | 207.434i | − | 0.427699i | ||||||
\(486\) | 470.350 | + | 126.329i | 0.967799 | + | 0.259936i | ||||
\(487\) | 254.199 | 0.521969 | 0.260984 | − | 0.965343i | \(-0.415953\pi\) | ||||
0.260984 | + | 0.965343i | \(0.415953\pi\) | |||||||
\(488\) | 246.435i | 0.504989i | ||||||||
\(489\) | 338.775 | + | 130.090i | 0.692792 | + | 0.266032i | ||||
\(490\) | −195.022 | −0.398004 | ||||||||
\(491\) | 123.123i | 0.250760i | 0.992109 | + | 0.125380i | \(0.0400151\pi\) | ||||
−0.992109 | + | 0.125380i | \(0.959985\pi\) | |||||||
\(492\) | −1.02163 | + | 2.66049i | −0.00207648 | + | 0.00540750i | ||||
\(493\) | −44.2737 | −0.0898047 | ||||||||
\(494\) | 363.370i | 0.735567i | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −790.989 | −1.59474 | ||||||||
\(497\) | − | 210.194i | − | 0.422926i | ||||||
\(498\) | −54.4542 | − | 20.9104i | −0.109346 | − | 0.0419888i | ||||
\(499\) | 65.3282 | 0.130918 | 0.0654591 | − | 0.997855i | \(-0.479149\pi\) | ||||
0.0654591 | + | 0.997855i | \(0.479149\pi\) | |||||||
\(500\) | − | 1.83624i | − | 0.00367249i | ||||||
\(501\) | −115.536 | + | 300.875i | −0.230611 | + | 0.600549i | ||||
\(502\) | −715.543 | −1.42538 | ||||||||
\(503\) | 425.899i | 0.846718i | 0.905962 | + | 0.423359i | \(0.139149\pi\) | ||||
−0.905962 | + | 0.423359i | \(0.860851\pi\) | |||||||
\(504\) | 268.854 | − | 298.450i | 0.533441 | − | 0.592163i | ||||
\(505\) | 257.243 | 0.509393 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −208.881 | − | 80.2103i | −0.411994 | − | 0.158206i | ||||
\(508\) | 1.14770 | 0.00225925 | ||||||||
\(509\) | − | 69.8611i | − | 0.137252i | −0.997642 | − | 0.0686258i | \(-0.978139\pi\) | ||
0.997642 | − | 0.0686258i | \(-0.0218614\pi\) | |||||||
\(510\) | −211.259 | + | 550.154i | −0.414234 | + | 1.07873i | ||||
\(511\) | −67.7951 | −0.132671 | ||||||||
\(512\) | 508.736i | 0.993625i | ||||||||
\(513\) | 228.556 | + | 448.962i | 0.445529 | + | 0.875169i | ||||
\(514\) | 132.464 | 0.257713 | ||||||||
\(515\) | 574.746i | 1.11601i | ||||||||
\(516\) | 2.06660 | + | 0.793574i | 0.00400503 | + | 0.00153793i | ||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 440.706i | 0.850785i | ||||||||
\(519\) | −353.618 | + | 920.881i | −0.681346 | + | 1.77434i | ||||
\(520\) | −425.424 | −0.818124 | ||||||||
\(521\) | − | 100.640i | − | 0.193168i | −0.995325 | − | 0.0965839i | \(-0.969208\pi\) | ||
0.995325 | − | 0.0965839i | \(-0.0307916\pi\) | |||||||
\(522\) | 33.2006 | + | 29.9083i | 0.0636028 | + | 0.0572955i | ||||
\(523\) | −851.945 | −1.62896 | −0.814479 | − | 0.580193i | \(-0.802977\pi\) | ||||
−0.814479 | + | 0.580193i | \(0.802977\pi\) | |||||||
\(524\) | − | 2.72723i | − | 0.00520464i | ||||||
\(525\) | −79.5171 | − | 30.5346i | −0.151461 | − | 0.0581611i | ||||
\(526\) | −171.197 | −0.325470 | ||||||||
\(527\) | 879.833i | 1.66951i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 376.110 | 0.710983 | ||||||||
\(530\) | − | 473.920i | − | 0.894188i | ||||||
\(531\) | 542.326 | − | 602.027i | 1.02133 | − | 1.13376i | ||||
\(532\) | −1.75324 | −0.00329557 | ||||||||
\(533\) | 549.228i | 1.03045i | ||||||||
\(534\) | −191.565 | − | 73.5610i | −0.358736 | − | 0.137755i | ||||
\(535\) | 255.738 | 0.478014 | ||||||||
\(536\) | − | 272.044i | − | 0.507546i | ||||||
\(537\) | 51.9420 | − | 135.265i | 0.0967262 | − | 0.251891i | ||||
\(538\) | −324.247 | −0.602689 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 2.21784 | − | 1.12905i | 0.00410711 | − | 0.00209084i | ||||
\(541\) | 731.425 | 1.35199 | 0.675994 | − | 0.736907i | \(-0.263715\pi\) | ||||
0.675994 | + | 0.736907i | \(0.263715\pi\) | |||||||
\(542\) | 521.078i | 0.961399i | ||||||||
\(543\) | 0.186430 | + | 0.0715890i | 0.000343332 | + | 0.000131840i | ||||
\(544\) | −4.80573 | −0.00883406 | ||||||||
\(545\) | − | 923.642i | − | 1.69476i | ||||||
\(546\) | −117.091 | + | 304.925i | −0.214453 | + | 0.558472i | ||||
\(547\) | −123.279 | −0.225373 | −0.112686 | − | 0.993631i | \(-0.535946\pi\) | ||||
−0.112686 | + | 0.993631i | \(0.535946\pi\) | |||||||
\(548\) | 0.888514i | 0.00162138i | ||||||||
\(549\) | −206.421 | − | 185.951i | −0.375994 | − | 0.338708i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 46.2241i | 0.0838913i | ||||||||
\(552\) | −276.449 | − | 106.156i | −0.500813 | − | 0.192312i | ||||
\(553\) | −353.032 | −0.638394 | ||||||||
\(554\) | 173.948i | 0.313986i | ||||||||
\(555\) | 231.977 | − | 604.105i | 0.417976 | − | 1.08848i | ||||
\(556\) | 1.45437 | 0.00261577 | ||||||||
\(557\) | − | 201.775i | − | 0.362253i | −0.983460 | − | 0.181127i | \(-0.942026\pi\) | ||
0.983460 | − | 0.181127i | \(-0.0579744\pi\) | |||||||
\(558\) | 594.355 | − | 659.783i | 1.06515 | − | 1.18241i | ||||
\(559\) | 426.625 | 0.763193 | ||||||||
\(560\) | − | 492.649i | − | 0.879731i | ||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 971.465 | 1.72858 | ||||||||
\(563\) | − | 484.108i | − | 0.859871i | −0.902860 | − | 0.429936i | \(-0.858536\pi\) | ||
0.902860 | − | 0.429936i | \(-0.141464\pi\) | |||||||
\(564\) | 1.04441 | − | 2.71982i | 0.00185179 | − | 0.00482237i | ||||
\(565\) | −254.037 | −0.449624 | ||||||||
\(566\) | − | 865.958i | − | 1.52996i | ||||||
\(567\) | 47.1228 | + | 450.400i | 0.0831090 | + | 0.794356i | ||||
\(568\) | −300.135 | −0.528406 | ||||||||
\(569\) | − | 467.419i | − | 0.821474i | −0.911754 | − | 0.410737i | \(-0.865271\pi\) | ||
0.911754 | − | 0.410737i | \(-0.134729\pi\) | |||||||
\(570\) | 574.391 | + | 220.566i | 1.00770 | + | 0.386958i | ||||
\(571\) | 656.796 | 1.15026 | 0.575128 | − | 0.818064i | \(-0.304952\pi\) | ||||
0.575128 | + | 0.818064i | \(0.304952\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 212.306 | − | 552.879i | 0.370516 | − | 0.964885i | ||||
\(574\) | −633.355 | −1.10341 | ||||||||
\(575\) | 62.7942i | 0.109207i | ||||||||
\(576\) | −426.147 | − | 383.887i | −0.739838 | − | 0.666471i | ||||
\(577\) | −873.454 | −1.51378 | −0.756892 | − | 0.653540i | \(-0.773283\pi\) | ||||
−0.756892 | + | 0.653540i | \(0.773283\pi\) | |||||||
\(578\) | 60.9146i | 0.105389i | ||||||||
\(579\) | 4.26719 | + | 1.63860i | 0.00736993 | + | 0.00283005i | ||||
\(580\) | 0.228344 | 0.000393697 | ||||||||
\(581\) | − | 54.2394i | − | 0.0933552i | ||||||
\(582\) | −81.5225 | + | 212.298i | −0.140073 | + | 0.364774i | ||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 96.8039i | 0.165760i | ||||||||
\(585\) | 321.010 | − | 356.348i | 0.548735 | − | 0.609141i | ||||
\(586\) | −11.0824 | −0.0189119 | ||||||||
\(587\) | 790.603i | 1.34685i | 0.739254 | + | 0.673427i | \(0.235178\pi\) | ||||
−0.739254 | + | 0.673427i | \(0.764822\pi\) | |||||||
\(588\) | 0.835117 | + | 0.320685i | 0.00142027 | + | 0.000545383i | ||||
\(589\) | 918.593 | 1.55958 | ||||||||
\(590\) | − | 989.603i | − | 1.67729i | ||||||
\(591\) | 231.713 | − | 603.419i | 0.392069 | − | 1.02101i | ||||
\(592\) | 631.924 | 1.06744 | ||||||||
\(593\) | 928.634i | 1.56599i | 0.622026 | + | 0.782997i | \(0.286310\pi\) | ||||
−0.622026 | + | 0.782997i | \(0.713690\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −547.984 | −0.920981 | ||||||||
\(596\) | 1.08318i | 0.00181742i | ||||||||
\(597\) | −298.721 | − | 114.709i | −0.500370 | − | 0.192142i | ||||
\(598\) | 240.798 | 0.402672 | ||||||||
\(599\) | 917.368i | 1.53150i | 0.643139 | + | 0.765749i | \(0.277632\pi\) | ||||
−0.643139 | + | 0.765749i | \(0.722368\pi\) | |||||||
\(600\) | −43.6000 | + | 113.542i | −0.0726667 | + | 0.189236i | ||||
\(601\) | 955.662 | 1.59012 | 0.795060 | − | 0.606530i | \(-0.207439\pi\) | ||||
0.795060 | + | 0.606530i | \(0.207439\pi\) | |||||||
\(602\) | 491.973i | 0.817230i | ||||||||
\(603\) | 227.872 | + | 205.275i | 0.377897 | + | 0.340423i | ||||
\(604\) | −0.750158 | −0.00124198 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −263.275 | − | 101.098i | −0.434448 | − | 0.166828i | ||||
\(607\) | −781.619 | −1.28768 | −0.643838 | − | 0.765162i | \(-0.722659\pi\) | ||||
−0.643838 | + | 0.765162i | \(0.722659\pi\) | |||||||
\(608\) | 5.01744i | 0.00825237i | ||||||||
\(609\) | −14.8951 | + | 38.7894i | −0.0244584 | + | 0.0636936i | ||||
\(610\) | −339.311 | −0.556248 | ||||||||
\(611\) | − | 561.475i | − | 0.918944i | ||||||
\(612\) | 1.80930 | − | 2.00847i | 0.00295637 | − | 0.00328181i | ||||
\(613\) | 85.9782 | 0.140258 | 0.0701290 | − | 0.997538i | \(-0.477659\pi\) | ||||
0.0701290 | + | 0.997538i | \(0.477659\pi\) | |||||||
\(614\) | − | 439.433i | − | 0.715690i | ||||||
\(615\) | 868.181 | + | 333.382i | 1.41168 | + | 0.542084i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 7.47837i | − | 0.0121205i | −0.999982 | − | 0.00606027i | \(-0.998071\pi\) | ||
0.999982 | − | 0.00606027i | \(-0.00192905\pi\) | |||||||
\(618\) | 225.878 | − | 588.223i | 0.365498 | − | 0.951817i | ||||
\(619\) | 325.144 | 0.525273 | 0.262636 | − | 0.964895i | \(-0.415408\pi\) | ||||
0.262636 | + | 0.964895i | \(0.415408\pi\) | |||||||
\(620\) | − | 4.53779i | − | 0.00731901i | ||||||
\(621\) | 297.518 | − | 151.459i | 0.479094 | − | 0.243896i | ||||
\(622\) | −284.897 | −0.458034 | ||||||||
\(623\) | − | 190.809i | − | 0.306275i | ||||||
\(624\) | 437.229 | + | 167.896i | 0.700688 | + | 0.269064i | ||||
\(625\) | −726.170 | −1.16187 | ||||||||
\(626\) | − | 188.967i | − | 0.301864i | ||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 2.37084 | 0.00377522 | ||||||||
\(629\) | − | 702.902i | − | 1.11749i | ||||||
\(630\) | 410.931 | + | 370.180i | 0.652271 | + | 0.587587i | ||||
\(631\) | −685.538 | −1.08643 | −0.543216 | − | 0.839593i | \(-0.682793\pi\) | ||||
−0.543216 | + | 0.839593i | \(0.682793\pi\) | |||||||
\(632\) | 504.091i | 0.797612i | ||||||||
\(633\) | 601.643 | + | 231.031i | 0.950463 | + | 0.364978i | ||||
\(634\) | 1004.53 | 1.58444 | ||||||||
\(635\) | − | 374.522i | − | 0.589798i | ||||||
\(636\) | −0.779292 | + | 2.02941i | −0.00122530 | + | 0.00319089i | ||||
\(637\) | 172.400 | 0.270644 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 226.471 | − | 251.401i | 0.354414 | − | 0.393429i | ||||
\(640\) | −706.393 | −1.10374 | ||||||||
\(641\) | 273.299i | 0.426364i | 0.977013 | + | 0.213182i | \(0.0683826\pi\) | ||||
−0.977013 | + | 0.213182i | \(0.931617\pi\) | |||||||
\(642\) | −261.734 | − | 100.506i | −0.407686 | − | 0.156551i | ||||
\(643\) | 184.624 | 0.287129 | 0.143564 | − | 0.989641i | \(-0.454144\pi\) | ||||
0.143564 | + | 0.989641i | \(0.454144\pi\) | |||||||
\(644\) | 1.16184i | 0.00180410i | ||||||||
\(645\) | 258.962 | − | 674.379i | 0.401491 | − | 1.04555i | ||||
\(646\) | 668.328 | 1.03456 | ||||||||
\(647\) | 360.098i | 0.556565i | 0.960499 | + | 0.278283i | \(0.0897652\pi\) | ||||
−0.960499 | + | 0.278283i | \(0.910235\pi\) | |||||||
\(648\) | 643.121 | − | 67.2862i | 0.992471 | − | 0.103837i | ||||
\(649\) | 0 | 0 | ||||||||
\(650\) | − | 98.8995i | − | 0.152153i | ||||||
\(651\) | 770.846 | + | 296.005i | 1.18410 | + | 0.454693i | ||||
\(652\) | −2.03300 | −0.00311810 | ||||||||
\(653\) | 1030.37i | 1.57789i | 0.614461 | + | 0.788947i | \(0.289374\pi\) | ||||
−0.614461 | + | 0.788947i | \(0.710626\pi\) | |||||||
\(654\) | −362.995 | + | 945.300i | −0.555039 | + | 1.44541i | ||||
\(655\) | −889.960 | −1.35872 | ||||||||
\(656\) | 908.161i | 1.38439i | ||||||||
\(657\) | −81.0857 | − | 73.0447i | −0.123418 | − | 0.111179i | ||||
\(658\) | 647.478 | 0.984009 | ||||||||
\(659\) | − | 1071.63i | − | 1.62614i | −0.582166 | − | 0.813070i | \(-0.697795\pi\) | ||
0.582166 | − | 0.813070i | \(-0.302205\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 441.357 | 0.667712 | 0.333856 | − | 0.942624i | \(-0.391650\pi\) | ||||
0.333856 | + | 0.942624i | \(0.391650\pi\) | |||||||
\(662\) | 1309.72i | 1.97843i | ||||||||
\(663\) | 186.754 | − | 486.339i | 0.281681 | − | 0.733543i | ||||
\(664\) | −77.4479 | −0.116638 | ||||||||
\(665\) | 572.125i | 0.860338i | ||||||||
\(666\) | −474.832 | + | 527.103i | −0.712961 | + | 0.791446i | ||||
\(667\) | 30.6318 | 0.0459247 | ||||||||
\(668\) | − | 1.80556i | − | 0.00270293i | ||||||
\(669\) | 125.380 | + | 48.1460i | 0.187414 | + | 0.0719671i | ||||
\(670\) | 374.573 | 0.559064 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | −1.61681 | + | 4.21043i | −0.00240596 | + | 0.00626552i | ||||
\(673\) | −370.702 | −0.550820 | −0.275410 | − | 0.961327i | \(-0.588814\pi\) | ||||
−0.275410 | + | 0.961327i | \(0.588814\pi\) | |||||||
\(674\) | − | 1321.50i | − | 1.96068i | ||||||
\(675\) | −62.2068 | − | 122.195i | −0.0921582 | − | 0.181030i | ||||
\(676\) | 1.25350 | 0.00185429 | ||||||||
\(677\) | − | 75.2277i | − | 0.111119i | −0.998455 | − | 0.0555596i | \(-0.982306\pi\) | ||
0.998455 | − | 0.0555596i | \(-0.0176943\pi\) | |||||||
\(678\) | 259.994 | + | 99.8379i | 0.383472 | + | 0.147253i | ||||
\(679\) | −211.461 | −0.311430 | ||||||||
\(680\) | 782.461i | 1.15068i | ||||||||
\(681\) | 241.440 | − | 628.749i | 0.354537 | − | 0.923272i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 987.234i | 1.44544i | 0.691142 | + | 0.722719i | \(0.257108\pi\) | ||||
−0.691142 | + | 0.722719i | \(0.742892\pi\) | |||||||
\(684\) | −2.09695 | − | 1.88900i | −0.00306572 | − | 0.00276170i | ||||
\(685\) | 289.943 | 0.423275 | ||||||||
\(686\) | 747.860i | 1.09017i | ||||||||
\(687\) | −291.546 | − | 111.954i | −0.424376 | − | 0.162960i | ||||
\(688\) | 705.434 | 1.02534 | ||||||||
\(689\) | 418.947i | 0.608051i | ||||||||
\(690\) | 146.165 | − | 380.637i | 0.211833 | − | 0.551647i | ||||
\(691\) | 1026.80 | 1.48597 | 0.742983 | − | 0.669311i | \(-0.233411\pi\) | ||||
0.742983 | + | 0.669311i | \(0.233411\pi\) | |||||||
\(692\) | − | 5.52624i | − | 0.00798589i | ||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 556.925 | 0.802486 | ||||||||
\(695\) | − | 474.595i | − | 0.682870i | ||||||
\(696\) | 55.3870 | + | 21.2686i | 0.0795790 | + | 0.0305584i | ||||
\(697\) | 1010.17 | 1.44931 | ||||||||
\(698\) | 506.611i | 0.725804i | ||||||||
\(699\) | 66.1705 | − | 172.319i | 0.0946645 | − | 0.246522i | ||||
\(700\) | 0.477185 | 0.000681693 | ||||||||
\(701\) | 186.947i | 0.266687i | 0.991070 | + | 0.133343i | \(0.0425713\pi\) | ||||
−0.991070 | + | 0.133343i | \(0.957429\pi\) | |||||||
\(702\) | −468.583 | + | 238.545i | −0.667498 | + | 0.339808i | ||||
\(703\) | −733.868 | −1.04391 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −887.541 | − | 340.816i | −1.25892 | − | 0.483427i | ||||
\(706\) | 1123.96 | 1.59201 | ||||||||
\(707\) | − | 262.237i | − | 0.370915i | ||||||
\(708\) | −1.62726 | + | 4.23765i | −0.00229839 | + | 0.00598538i | ||||
\(709\) | −713.675 | −1.00659 | −0.503297 | − | 0.864114i | \(-0.667880\pi\) | ||||
−0.503297 | + | 0.864114i | \(0.667880\pi\) | |||||||
\(710\) | − | 413.249i | − | 0.582042i | ||||||
\(711\) | −422.241 | − | 380.369i | −0.593869 | − | 0.534977i | ||||
\(712\) | −272.455 | −0.382661 | ||||||||
\(713\) | − | 608.733i | − | 0.853762i | ||||||
\(714\) | 560.833 | + | 215.360i | 0.785481 | + | 0.301625i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0.811733i | 0.00113370i | ||||||||
\(717\) | −160.520 | + | 418.020i | −0.223877 | + | 0.583013i | ||||
\(718\) | 593.369 | 0.826420 | ||||||||
\(719\) | − | 498.723i | − | 0.693634i | −0.937933 | − | 0.346817i | \(-0.887262\pi\) | ||
0.937933 | − | 0.346817i | \(-0.112738\pi\) | |||||||
\(720\) | 530.797 | − | 589.229i | 0.737219 | − | 0.818374i | ||||
\(721\) | 585.902 | 0.812624 | ||||||||
\(722\) | 25.7452i | 0.0356581i | ||||||||
\(723\) | 1005.09 | + | 385.954i | 1.39016 | + | 0.533823i | ||||
\(724\) | −0.00111877 | −1.54526e−6 | ||||||||
\(725\) | − | 12.5809i | − | 0.0173530i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 427.838 | 0.588498 | 0.294249 | − | 0.955729i | \(-0.404930\pi\) | ||||
0.294249 | + | 0.955729i | \(0.404930\pi\) | |||||||
\(728\) | 433.683i | 0.595718i | ||||||||
\(729\) | −428.915 | + | 589.468i | −0.588361 | + | 0.808598i | ||||
\(730\) | −133.287 | −0.182585 | ||||||||
\(731\) | − | 784.669i | − | 1.07342i | ||||||
\(732\) | 1.45299 | + | 0.557948i | 0.00198496 | + | 0.000762224i | ||||
\(733\) | 957.424 | 1.30617 | 0.653086 | − | 0.757284i | \(-0.273474\pi\) | ||||
0.653086 | + | 0.757284i | \(0.273474\pi\) | |||||||
\(734\) | − | 170.072i | − | 0.231706i | ||||||
\(735\) | 104.647 | − | 272.518i | 0.142377 | − | 0.370773i | ||||
\(736\) | 3.32495 | 0.00451760 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | −757.518 | − | 682.398i | −1.02645 | − | 0.924659i | ||||
\(739\) | −1134.98 | −1.53584 | −0.767918 | − | 0.640549i | \(-0.778707\pi\) | ||||
−0.767918 | + | 0.640549i | \(0.778707\pi\) | |||||||
\(740\) | 3.62526i | 0.00489900i | ||||||||
\(741\) | −507.764 | − | 194.982i | −0.685242 | − | 0.263133i | ||||
\(742\) | −483.119 | −0.651104 | ||||||||
\(743\) | 866.886i | 1.16674i | 0.812207 | + | 0.583369i | \(0.198266\pi\) | ||||
−0.812207 | + | 0.583369i | \(0.801734\pi\) | |||||||
\(744\) | 422.663 | − | 1100.68i | 0.568095 | − | 1.47941i | ||||
\(745\) | 353.468 | 0.474454 | ||||||||
\(746\) | − | 633.522i | − | 0.849226i | ||||||
\(747\) | 58.4393 | − | 64.8725i | 0.0782321 | − | 0.0868441i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 260.702i | − | 0.348067i | ||||||
\(750\) | 613.260 | + | 235.492i | 0.817680 | + | 0.313989i | ||||
\(751\) | −1157.47 | −1.54124 | −0.770618 | − | 0.637297i | \(-0.780053\pi\) | ||||
−0.770618 | + | 0.637297i | \(0.780053\pi\) | |||||||
\(752\) | − | 928.412i | − | 1.23459i | ||||||
\(753\) | 383.954 | − | 999.881i | 0.509900 | − | 1.32786i | ||||
\(754\) | −48.2443 | −0.0639845 | ||||||||
\(755\) | 244.794i | 0.324231i | ||||||||
\(756\) | −1.15097 | − | 2.26089i | −0.00152244 | − | 0.00299060i | ||||
\(757\) | −410.295 | −0.542001 | −0.271001 | − | 0.962579i | \(-0.587355\pi\) | ||||
−0.271001 | + | 0.962579i | \(0.587355\pi\) | |||||||
\(758\) | 217.931i | 0.287508i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 816.931 | 1.07491 | ||||||||
\(761\) | − | 253.490i | − | 0.333101i | −0.986033 | − | 0.166550i | \(-0.946737\pi\) | ||
0.986033 | − | 0.166550i | \(-0.0532629\pi\) | |||||||
\(762\) | −147.189 | + | 383.304i | −0.193161 | + | 0.503024i | ||||
\(763\) | −941.571 | −1.23404 | ||||||||
\(764\) | 3.31785i | 0.00434273i | ||||||||
\(765\) | −655.411 | − | 590.417i | −0.856747 | − | 0.771786i | ||||
\(766\) | −885.883 | −1.15650 | ||||||||
\(767\) | 874.814i | 1.14057i | ||||||||
\(768\) | 9.03703 | + | 3.47022i | 0.0117670 | + | 0.00451852i | ||||
\(769\) | −788.887 | −1.02586 | −0.512931 | − | 0.858430i | \(-0.671440\pi\) | ||||
−0.512931 | + | 0.858430i | \(0.671440\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −71.0793 | + | 185.102i | −0.0921910 | + | 0.240081i | ||||
\(772\) | −0.0256075 | −3.31704e−5 | ||||||||
\(773\) | 343.352i | 0.444182i | 0.975026 | + | 0.222091i | \(0.0712881\pi\) | ||||
−0.975026 | + | 0.222091i | \(0.928712\pi\) | |||||||
\(774\) | −530.068 | + | 588.419i | −0.684843 | + | 0.760232i | ||||
\(775\) | −250.016 | −0.322601 | ||||||||
\(776\) | 301.943i | 0.389101i | ||||||||
\(777\) | −615.832 | − | 236.480i | −0.792576 | − | 0.304349i | ||||
\(778\) | −1021.33 | −1.31277 | ||||||||
\(779\) | − | 1054.67i | − | 1.35387i | ||||||
\(780\) | −0.963195 | + | 2.50832i | −0.00123487 | + | 0.00321580i | ||||
\(781\) | 0 | 0 | ||||||||
\(782\) | − | 442.887i | − | 0.566351i | ||||||
\(783\) | −59.6082 | + | 30.3452i | −0.0761280 | + | 0.0387550i | ||||
\(784\) | 285.068 | 0.363607 | ||||||||
\(785\) | − | 773.660i | − | 0.985554i | ||||||
\(786\) | 910.828 | + | 349.758i | 1.15881 | + | 0.444985i | ||||
\(787\) | −193.445 | −0.245800 | −0.122900 | − | 0.992419i | \(-0.539219\pi\) | ||||
−0.122900 | + | 0.992419i | \(0.539219\pi\) | |||||||
\(788\) | 3.62114i | 0.00459535i | ||||||||
\(789\) | 91.8631 | − | 239.227i | 0.116430 | − | 0.303202i | ||||
\(790\) | −694.073 | −0.878574 | ||||||||
\(791\) | 258.969i | 0.327394i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 299.953 | 0.378251 | ||||||||
\(794\) | − | 26.1510i | − | 0.0329358i | ||||||
\(795\) | 662.243 | + | 254.301i | 0.833010 | + | 0.319876i | ||||
\(796\) | 1.79263 | 0.00225205 | ||||||||
\(797\) | − | 531.926i | − | 0.667411i | −0.942677 | − | 0.333705i | \(-0.891701\pi\) | ||
0.942677 | − | 0.333705i | \(-0.108299\pi\) | |||||||
\(798\) | 224.848 | − | 585.540i | 0.281764 | − | 0.733760i | ||||
\(799\) | −1032.69 | −1.29248 | ||||||||
\(800\) | − | 1.36561i | − | 0.00170701i | ||||||
\(801\) | 205.584 | − | 228.216i | 0.256660 | − | 0.284913i | ||||
\(802\) | −1101.52 | −1.37346 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | −1.60399 | − | 0.615931i | −0.00199501 | − | 0.000766083i | ||||
\(805\) | 379.135 | 0.470975 | ||||||||
\(806\) | 958.740i | 1.18950i | ||||||||
\(807\) | 173.988 | − | 453.094i | 0.215599 | − | 0.561455i | ||||
\(808\) | −374.445 | −0.463423 | ||||||||
\(809\) | 290.427i | 0.358995i | 0.983758 | + | 0.179497i | \(0.0574471\pi\) | ||||
−0.983758 | + | 0.179497i | \(0.942553\pi\) | |||||||
\(810\) | 92.6451 | + | 885.501i | 0.114377 | + | 1.09321i | ||||
\(811\) | 384.552 | 0.474170 | 0.237085 | − | 0.971489i | \(-0.423808\pi\) | ||||
0.237085 | + | 0.971489i | \(0.423808\pi\) | |||||||
\(812\) | − | 0.232776i | − | 0.000286671i | ||||||
\(813\) | −728.142 | − | 279.607i | −0.895623 | − | 0.343919i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 663.416i | 0.814008i | ||||||||
\(816\) | 308.803 | − | 804.173i | 0.378435 | − | 0.985506i | ||||
\(817\) | −819.237 | −1.00274 | ||||||||
\(818\) | − | 1238.93i | − | 1.51458i | ||||||
\(819\) | −363.265 | − | 327.241i | −0.443547 | − | 0.399562i | ||||
\(820\) | −5.20998 | −0.00635364 | ||||||||
\(821\) | − | 621.724i | − | 0.757277i | −0.925545 | − | 0.378638i | \(-0.876392\pi\) | ||
0.925545 | − | 0.378638i | \(-0.123608\pi\) | |||||||
\(822\) | −296.742 | − | 113.949i | −0.361000 | − | 0.138624i | ||||
\(823\) | −286.383 | −0.347974 | −0.173987 | − | 0.984748i | \(-0.555665\pi\) | ||||
−0.173987 | + | 0.984748i | \(0.555665\pi\) | |||||||
\(824\) | − | 836.604i | − | 1.01530i | ||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −1008.81 | −1.22132 | ||||||||
\(827\) | 417.508i | 0.504847i | 0.967617 | + | 0.252423i | \(0.0812276\pi\) | ||||
−0.967617 | + | 0.252423i | \(0.918772\pi\) | |||||||
\(828\) | −1.25180 | + | 1.38961i | −0.00151184 | + | 0.00167827i | ||||
\(829\) | 370.857 | 0.447355 | 0.223677 | − | 0.974663i | \(-0.428194\pi\) | ||||
0.223677 | + | 0.974663i | \(0.428194\pi\) | |||||||
\(830\) | − | 106.636i | − | 0.128478i | ||||||
\(831\) | −243.071 | − | 93.3393i | −0.292504 | − | 0.112322i | ||||
\(832\) | 619.240 | 0.744279 | ||||||||
\(833\) | − | 317.087i | − | 0.380656i | ||||||
\(834\) | −186.518 | + | 485.723i | −0.223642 | + | 0.582402i | ||||
\(835\) | −589.197 | −0.705625 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 603.038 | + | 1184.57i | 0.720475 | + | 1.41526i | ||||
\(838\) | −882.532 | −1.05314 | ||||||||
\(839\) | − | 865.855i | − | 1.03201i | −0.856586 | − | 0.516004i | \(-0.827419\pi\) | ||
0.856586 | − | 0.516004i | \(-0.172581\pi\) | |||||||
\(840\) | 685.535 | + | 263.246i | 0.816113 | + | 0.313388i | ||||
\(841\) | 834.863 | 0.992703 | ||||||||
\(842\) | − | 1150.87i | − | 1.36683i | ||||||
\(843\) | −521.280 | + | 1357.50i | −0.618363 | + | 1.61032i | ||||
\(844\) | −3.61048 | −0.00427782 | ||||||||
\(845\) | − | 409.047i | − | 0.484079i | ||||||
\(846\) | 774.410 | + | 697.615i | 0.915379 | + | 0.824604i | ||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 692.739i | 0.816910i | ||||||||
\(849\) | 1210.07 | + | 464.666i | 1.42529 | + | 0.547310i | ||||
\(850\) | −181.901 | −0.214001 | ||||||||
\(851\) | 486.319i | 0.571468i | ||||||||
\(852\) | −0.679529 | + | 1.76961i | −0.000797569 | + | 0.00207700i | ||||
\(853\) | −1346.86 | −1.57897 | −0.789483 | − | 0.613772i | \(-0.789651\pi\) | ||||
−0.789483 | + | 0.613772i | \(0.789651\pi\) | |||||||
\(854\) | 345.897i | 0.405032i | ||||||||
\(855\) | −616.427 | + | 684.285i | −0.720967 | + | 0.800333i | ||||
\(856\) | −372.254 | −0.434876 | ||||||||
\(857\) | 770.599i | 0.899182i | 0.893235 | + | 0.449591i | \(0.148430\pi\) | ||||
−0.893235 | + | 0.449591i | \(0.851570\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −549.532 | −0.639735 | −0.319867 | − | 0.947462i | \(-0.603638\pi\) | ||||
−0.319867 | + | 0.947462i | \(0.603638\pi\) | |||||||
\(860\) | 4.04697i | 0.00470578i | ||||||||
\(861\) | 339.853 | − | 885.034i | 0.394719 | − | 1.02791i | ||||
\(862\) | 1325.74 | 1.53798 | ||||||||
\(863\) | − | 1095.93i | − | 1.26990i | −0.772552 | − | 0.634952i | \(-0.781020\pi\) | ||
0.772552 | − | 0.634952i | \(-0.218980\pi\) | |||||||
\(864\) | −6.47023 | + | 3.29385i | −0.00748869 | + | 0.00381232i | ||||
\(865\) | −1803.34 | −2.08479 | ||||||||
\(866\) | − | 426.456i | − | 0.492443i | ||||||
\(867\) | −85.1205 | − | 32.6863i | −0.0981782 | − | 0.0377004i | ||||
\(868\) | −4.62587 | −0.00532935 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | −29.2843 | + | 76.2613i | −0.0336602 | + | 0.0876567i | ||||
\(871\) | −331.124 | −0.380166 | ||||||||
\(872\) | 1344.46i | 1.54181i | ||||||||
\(873\) | −252.916 | − | 227.835i | −0.289709 | − | 0.260979i | ||||
\(874\) | −462.398 | −0.529059 | ||||||||
\(875\) | 610.841i | 0.698104i | ||||||||
\(876\) | 0.570760 | + | 0.219172i | 0.000651552 | + | 0.000250196i | ||||
\(877\) | −1443.15 | −1.64556 | −0.822778 | − | 0.568363i | \(-0.807577\pi\) | ||||
−0.822778 | + | 0.568363i | \(0.807577\pi\) | |||||||
\(878\) | 208.066i | 0.236978i | ||||||||
\(879\) | 5.94670 | − | 15.4862i | 0.00676531 | − | 0.0176180i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 162.080i | − | 0.183973i | −0.995760 | − | 0.0919866i | \(-0.970678\pi\) | ||
0.995760 | − | 0.0919866i | \(-0.0293217\pi\) | |||||||
\(882\) | −214.202 | + | 237.782i | −0.242859 | + | 0.269594i | ||||
\(883\) | −87.1163 | −0.0986595 | −0.0493297 | − | 0.998783i | \(-0.515709\pi\) | ||||
−0.0493297 | + | 0.998783i | \(0.515709\pi\) | |||||||
\(884\) | 2.91854i | 0.00330151i | ||||||||
\(885\) | 1382.85 | + | 531.013i | 1.56254 | + | 0.600015i | ||||
\(886\) | 554.699 | 0.626071 | ||||||||
\(887\) | 816.228i | 0.920212i | 0.887864 | + | 0.460106i | \(0.152189\pi\) | ||||
−0.887864 | + | 0.460106i | \(0.847811\pi\) | |||||||
\(888\) | −337.667 | + | 879.340i | −0.380255 | + | 0.990248i | ||||
\(889\) | −381.792 | −0.429462 | ||||||||
\(890\) | − | 375.137i | − | 0.421503i | ||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −0.752410 | −0.000843509 | ||||||||
\(893\) | 1078.19i | 1.20737i | ||||||||
\(894\) | −361.756 | − | 138.915i | −0.404649 | − | 0.155385i | ||||
\(895\) | 264.888 | 0.295964 | ||||||||
\(896\) | 720.105i | 0.803688i | ||||||||
\(897\) | −129.210 | + | 336.485i | −0.144047 | + | 0.375122i | ||||
\(898\) | 997.843 | 1.11118 | ||||||||
\(899\) | 121.961i | 0.135663i | ||||||||
\(900\) | 0.570733 | + | 0.514135i | 0.000634148 | + | 0.000571262i | ||||
\(901\) | 770.548 | 0.855214 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −687.470 | − | 263.989i | −0.761318 | − | 0.292346i | ||||
\(904\) | 369.779 | 0.409047 | ||||||||
\(905\) | 0.365081i | 0.000403404i | ||||||||
\(906\) | 96.2052 | − | 250.534i | 0.106187 | − | 0.276528i | ||||
\(907\) | 558.559 | 0.615832 | 0.307916 | − | 0.951414i | \(-0.400368\pi\) | ||||
0.307916 | + | 0.951414i | \(0.400368\pi\) | |||||||
\(908\) | 3.77314i | 0.00415544i | ||||||||
\(909\) | 282.543 | − | 313.646i | 0.310828 | − | 0.345045i | ||||
\(910\) | −597.129 | −0.656186 | ||||||||
\(911\) | 1627.04i | 1.78600i | 0.450058 | + | 0.892999i | \(0.351403\pi\) | ||||
−0.450058 | + | 0.892999i | \(0.648597\pi\) | |||||||
\(912\) | −839.600 | − | 322.407i | −0.920614 | − | 0.353516i | ||||
\(913\) | 0 | 0 | ||||||||
\(914\) | − | 1625.64i | − | 1.77860i | ||||||
\(915\) | 182.072 | − | 474.144i | 0.198985 | − | 0.518191i | ||||
\(916\) | 1.74958 | 0.00191002 | ||||||||
\(917\) | 907.235i | 0.989351i | ||||||||
\(918\) | 438.743 | + | 861.840i | 0.477934 | + | 0.938824i | ||||
\(919\) | 57.5879 | 0.0626637 | 0.0313319 | − | 0.999509i | \(-0.490025\pi\) | ||||
0.0313319 | + | 0.999509i | \(0.490025\pi\) | |||||||
\(920\) | − | 541.363i | − | 0.588438i | ||||||
\(921\) | 614.053 | + | 235.796i | 0.666724 | + | 0.256022i | ||||
\(922\) | −1583.43 | −1.71739 | ||||||||
\(923\) | 365.315i | 0.395791i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 199.739 | 0.215934 | ||||||||
\(926\) | − | 1083.03i | − | 1.16958i | ||||||
\(927\) | 700.763 | + | 631.271i | 0.755947 | + | 0.680983i | ||||
\(928\) | −0.666161 | −0.000717846 | ||||||||
\(929\) | 21.5006i | 0.0231438i | 0.999933 | + | 0.0115719i | \(0.00368353\pi\) | ||||
−0.999933 | + | 0.0115719i | \(0.996316\pi\) | |||||||
\(930\) | 1515.51 | + | 581.956i | 1.62958 | + | 0.625759i | ||||
\(931\) | −331.056 | −0.355591 | ||||||||
\(932\) | 1.03409i | 0.00110954i | ||||||||
\(933\) | 152.873 | − | 398.108i | 0.163852 | − | 0.426696i | ||||
\(934\) | 556.899 | 0.596251 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −467.264 | + | 518.702i | −0.499214 | + | 0.554169i | ||||
\(937\) | −228.958 | −0.244352 | −0.122176 | − | 0.992508i | \(-0.538987\pi\) | ||||
−0.122176 | + | 0.992508i | \(0.538987\pi\) | |||||||
\(938\) | − | 381.844i | − | 0.407083i | ||||||
\(939\) | 264.058 | + | 101.398i | 0.281212 | + | 0.107985i | ||||
\(940\) | 5.32616 | 0.00566613 | ||||||||
\(941\) | 863.164i | 0.917284i | 0.888621 | + | 0.458642i | \(0.151664\pi\) | ||||
−0.888621 | + | 0.458642i | \(0.848336\pi\) | |||||||
\(942\) | −304.052 | + | 791.801i | −0.322773 | + | 0.840553i | ||||
\(943\) | −698.906 | −0.741152 | ||||||||
\(944\) | 1446.53i | 1.53234i | ||||||||
\(945\) | −737.782 | + | 375.588i | −0.780722 | + | 0.397448i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 1155.70i | − | 1.22038i | −0.792253 | − | 0.610192i | \(-0.791092\pi\) | ||
0.792253 | − | 0.610192i | \(-0.208908\pi\) | |||||||
\(948\) | 2.97214 | + | 1.14130i | 0.00313517 | + | 0.00120391i | ||||
\(949\) | 117.827 | 0.124159 | ||||||||
\(950\) | 189.914i | 0.199909i | ||||||||
\(951\) | −539.025 | + | 1403.71i | −0.566798 | + | 1.47603i | ||||
\(952\) | 797.649 | 0.837867 | ||||||||
\(953\) | − | 1797.11i | − | 1.88574i | −0.333163 | − | 0.942869i | \(-0.608116\pi\) | ||
0.333163 | − | 0.942869i | \(-0.391884\pi\) | |||||||
\(954\) | −577.830 | − | 520.529i | −0.605692 | − | 0.545628i | ||||
\(955\) | 1082.69 | 1.13371 | ||||||||
\(956\) | − | 2.50855i | − | 0.00262401i | ||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 942.426 | 0.983743 | ||||||||
\(959\) | − | 295.571i | − | 0.308208i | ||||||
\(960\) | 375.879 | − | 978.852i | 0.391541 | − | 1.01964i | ||||
\(961\) | 1462.68 | 1.52204 | ||||||||
\(962\) | − | 765.941i | − | 0.796196i | ||||||
\(963\) | 280.889 | − | 311.810i | 0.291681 | − | 0.323790i | ||||
\(964\) | −6.03156 | −0.00625681 | ||||||||
\(965\) | 8.35634i | 0.00865942i | ||||||||
\(966\) | −388.025 | − | 149.002i | −0.401682 | − | 0.154246i | ||||
\(967\) | −1767.36 | −1.82767 | −0.913835 | − | 0.406085i | \(-0.866894\pi\) | ||||
−0.913835 | + | 0.406085i | \(0.866894\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −358.619 | + | 933.904i | −0.370092 | + | 0.963781i | ||||
\(970\) | −415.739 | −0.428597 | ||||||||
\(971\) | − | 508.729i | − | 0.523922i | −0.965078 | − | 0.261961i | \(-0.915631\pi\) | ||
0.965078 | − | 0.261961i | \(-0.0843692\pi\) | |||||||
\(972\) | 1.05936 | − | 3.94421i | 0.00108987 | − | 0.00405783i | ||||
\(973\) | −483.807 | −0.497233 | ||||||||
\(974\) | − | 509.465i | − | 0.523064i | ||||||
\(975\) | 138.200 | + | 53.0687i | 0.141743 | + | 0.0544294i | ||||
\(976\) | 495.979 | 0.508175 | ||||||||
\(977\) | 1414.51i | 1.44781i | 0.689902 | + | 0.723903i | \(0.257654\pi\) | ||||
−0.689902 | + | 0.723903i | \(0.742346\pi\) | |||||||
\(978\) | 260.726 | − | 678.972i | 0.266590 | − | 0.694246i | ||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 1.63539i | 0.00166877i | ||||||||
\(981\) | −1126.16 | − | 1014.48i | −1.14797 | − | 1.03413i | ||||
\(982\) | 246.764 | 0.251287 | ||||||||
\(983\) | − | 1.12205i | − | 0.00114145i | −1.00000 | 0.000570727i | \(-0.999818\pi\) | |||
1.00000 | 0.000570727i | \(-0.000181668\pi\) | ||||||||
\(984\) | −1263.73 | − | 485.273i | −1.28428 | − | 0.493164i | ||||
\(985\) | 1181.66 | 1.19966 | ||||||||
\(986\) | 88.7332i | 0.0899931i | ||||||||
\(987\) | −347.432 | + | 904.769i | −0.352008 | + | 0.916686i | ||||
\(988\) | 3.04711 | 0.00308412 | ||||||||
\(989\) | 542.891i | 0.548929i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1431.64 | −1.44464 | −0.722320 | − | 0.691559i | \(-0.756924\pi\) | ||||
−0.722320 | + | 0.691559i | \(0.756924\pi\) | |||||||
\(992\) | 13.2383i | 0.0133451i | ||||||||
\(993\) | −1830.17 | − | 702.785i | −1.84307 | − | 0.707740i | ||||
\(994\) | −421.271 | −0.423814 | ||||||||
\(995\) | − | 584.979i | − | 0.587918i | ||||||
\(996\) | −0.175348 | + | 0.456636i | −0.000176052 | + | 0.000458470i | ||||
\(997\) | −1166.36 | −1.16987 | −0.584937 | − | 0.811079i | \(-0.698881\pi\) | ||||
−0.584937 | + | 0.811079i | \(0.698881\pi\) | |||||||
\(998\) | − | 130.931i | − | 0.131193i | ||||||
\(999\) | −481.769 | − | 946.358i | −0.482251 | − | 0.947305i |
(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 | 363.3.b.m.122.3 | 8 | ||
3.2 | odd | 2 | inner | 363.3.b.m.122.6 | 8 | ||
11.2 | odd | 10 | 363.3.h.n.323.3 | 16 | |||
11.3 | even | 5 | 33.3.h.b.20.2 | yes | 16 | ||
11.4 | even | 5 | 33.3.h.b.5.3 | yes | 16 | ||
11.5 | even | 5 | 363.3.h.o.245.3 | 16 | |||
11.6 | odd | 10 | 363.3.h.n.245.2 | 16 | |||
11.7 | odd | 10 | 363.3.h.j.269.2 | 16 | |||
11.8 | odd | 10 | 363.3.h.j.251.3 | 16 | |||
11.9 | even | 5 | 363.3.h.o.323.2 | 16 | |||
11.10 | odd | 2 | 363.3.b.l.122.6 | 8 | |||
33.2 | even | 10 | 363.3.h.n.323.2 | 16 | |||
33.5 | odd | 10 | 363.3.h.o.245.2 | 16 | |||
33.8 | even | 10 | 363.3.h.j.251.2 | 16 | |||
33.14 | odd | 10 | 33.3.h.b.20.3 | yes | 16 | ||
33.17 | even | 10 | 363.3.h.n.245.3 | 16 | |||
33.20 | odd | 10 | 363.3.h.o.323.3 | 16 | |||
33.26 | odd | 10 | 33.3.h.b.5.2 | ✓ | 16 | ||
33.29 | even | 10 | 363.3.h.j.269.3 | 16 | |||
33.32 | even | 2 | 363.3.b.l.122.3 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
33.3.h.b.5.2 | ✓ | 16 | 33.26 | odd | 10 | ||
33.3.h.b.5.3 | yes | 16 | 11.4 | even | 5 | ||
33.3.h.b.20.2 | yes | 16 | 11.3 | even | 5 | ||
33.3.h.b.20.3 | yes | 16 | 33.14 | odd | 10 | ||
363.3.b.l.122.3 | 8 | 33.32 | even | 2 | |||
363.3.b.l.122.6 | 8 | 11.10 | odd | 2 | |||
363.3.b.m.122.3 | 8 | 1.1 | even | 1 | trivial | ||
363.3.b.m.122.6 | 8 | 3.2 | odd | 2 | inner | ||
363.3.h.j.251.2 | 16 | 33.8 | even | 10 | |||
363.3.h.j.251.3 | 16 | 11.8 | odd | 10 | |||
363.3.h.j.269.2 | 16 | 11.7 | odd | 10 | |||
363.3.h.j.269.3 | 16 | 33.29 | even | 10 | |||
363.3.h.n.245.2 | 16 | 11.6 | odd | 10 | |||
363.3.h.n.245.3 | 16 | 33.17 | even | 10 | |||
363.3.h.n.323.2 | 16 | 33.2 | even | 10 | |||
363.3.h.n.323.3 | 16 | 11.2 | odd | 10 | |||
363.3.h.o.245.2 | 16 | 33.5 | odd | 10 | |||
363.3.h.o.245.3 | 16 | 11.5 | even | 5 | |||
363.3.h.o.323.2 | 16 | 11.9 | even | 5 | |||
363.3.h.o.323.3 | 16 | 33.20 | odd | 10 |