Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [354,3,Mod(235,354)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(354, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("354.235");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 354 = 2 \cdot 3 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 354.d (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: | \(9.64580135835\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} - 300 x^{18} - 88 x^{17} + 37952 x^{16} + 27000 x^{15} - 2574056 x^{14} - 3295208 x^{13} + \cdots + 2455573689828 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{11}\cdot 3^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 235.10 | ||
Root | \(7.74549 + 1.41421i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 354.235 |
Dual form | 354.3.d.a.235.20 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/354\mathbb{Z}\right)^\times\).
\(n\) | \(61\) | \(119\) |
\(\chi(n)\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 1.41421i | − | 0.707107i | ||||||
\(3\) | 1.73205 | 0.577350 | ||||||||
\(4\) | −2.00000 | −0.500000 | ||||||||
\(5\) | 7.74549 | 1.54910 | 0.774549 | − | 0.632514i | \(-0.217977\pi\) | ||||
0.774549 | + | 0.632514i | \(0.217977\pi\) | |||||||
\(6\) | − | 2.44949i | − | 0.408248i | ||||||
\(7\) | 7.40466 | 1.05781 | 0.528904 | − | 0.848681i | \(-0.322603\pi\) | ||||
0.528904 | + | 0.848681i | \(0.322603\pi\) | |||||||
\(8\) | 2.82843i | 0.353553i | ||||||||
\(9\) | 3.00000 | 0.333333 | ||||||||
\(10\) | − | 10.9538i | − | 1.09538i | ||||||
\(11\) | 4.00447i | 0.364043i | 0.983295 | + | 0.182021i | \(0.0582640\pi\) | ||||
−0.983295 | + | 0.182021i | \(0.941736\pi\) | |||||||
\(12\) | −3.46410 | −0.288675 | ||||||||
\(13\) | 19.5586i | 1.50451i | 0.658872 | + | 0.752255i | \(0.271034\pi\) | ||||
−0.658872 | + | 0.752255i | \(0.728966\pi\) | |||||||
\(14\) | − | 10.4718i | − | 0.747984i | ||||||
\(15\) | 13.4156 | 0.894372 | ||||||||
\(16\) | 4.00000 | 0.250000 | ||||||||
\(17\) | 8.82813 | 0.519302 | 0.259651 | − | 0.965703i | \(-0.416393\pi\) | ||||
0.259651 | + | 0.965703i | \(0.416393\pi\) | |||||||
\(18\) | − | 4.24264i | − | 0.235702i | ||||||
\(19\) | −29.4750 | −1.55132 | −0.775659 | − | 0.631153i | \(-0.782582\pi\) | ||||
−0.775659 | + | 0.631153i | \(0.782582\pi\) | |||||||
\(20\) | −15.4910 | −0.774549 | ||||||||
\(21\) | 12.8252 | 0.610726 | ||||||||
\(22\) | 5.66318 | 0.257417 | ||||||||
\(23\) | 1.24447i | 0.0541072i | 0.999634 | + | 0.0270536i | \(0.00861249\pi\) | ||||
−0.999634 | + | 0.0270536i | \(0.991388\pi\) | |||||||
\(24\) | 4.89898i | 0.204124i | ||||||||
\(25\) | 34.9926 | 1.39970 | ||||||||
\(26\) | 27.6601 | 1.06385 | ||||||||
\(27\) | 5.19615 | 0.192450 | ||||||||
\(28\) | −14.8093 | −0.528904 | ||||||||
\(29\) | −25.5288 | −0.880303 | −0.440151 | − | 0.897924i | \(-0.645075\pi\) | ||||
−0.440151 | + | 0.897924i | \(0.645075\pi\) | |||||||
\(30\) | − | 18.9725i | − | 0.632416i | ||||||
\(31\) | 4.73284i | 0.152672i | 0.997082 | + | 0.0763362i | \(0.0243222\pi\) | ||||
−0.997082 | + | 0.0763362i | \(0.975678\pi\) | |||||||
\(32\) | − | 5.65685i | − | 0.176777i | ||||||
\(33\) | 6.93595i | 0.210180i | ||||||||
\(34\) | − | 12.4849i | − | 0.367202i | ||||||
\(35\) | 57.3527 | 1.63865 | ||||||||
\(36\) | −6.00000 | −0.166667 | ||||||||
\(37\) | − | 58.2356i | − | 1.57394i | −0.616994 | − | 0.786968i | \(-0.711650\pi\) | ||
0.616994 | − | 0.786968i | \(-0.288350\pi\) | |||||||
\(38\) | 41.6840i | 1.09695i | ||||||||
\(39\) | 33.8765i | 0.868629i | ||||||||
\(40\) | 21.9075i | 0.547689i | ||||||||
\(41\) | 31.1751 | 0.760368 | 0.380184 | − | 0.924911i | \(-0.375861\pi\) | ||||
0.380184 | + | 0.924911i | \(0.375861\pi\) | |||||||
\(42\) | − | 18.1376i | − | 0.431849i | ||||||
\(43\) | − | 80.6621i | − | 1.87586i | −0.346821 | − | 0.937931i | \(-0.612739\pi\) | ||
0.346821 | − | 0.937931i | \(-0.387261\pi\) | |||||||
\(44\) | − | 8.00894i | − | 0.182021i | ||||||
\(45\) | 23.2365 | 0.516366 | ||||||||
\(46\) | 1.75994 | 0.0382596 | ||||||||
\(47\) | − | 34.4873i | − | 0.733772i | −0.930266 | − | 0.366886i | \(-0.880424\pi\) | ||
0.930266 | − | 0.366886i | \(-0.119576\pi\) | |||||||
\(48\) | 6.92820 | 0.144338 | ||||||||
\(49\) | 5.82899 | 0.118959 | ||||||||
\(50\) | − | 49.4869i | − | 0.989739i | ||||||
\(51\) | 15.2908 | 0.299819 | ||||||||
\(52\) | − | 39.1172i | − | 0.752255i | ||||||
\(53\) | −44.0290 | −0.830737 | −0.415368 | − | 0.909653i | \(-0.636347\pi\) | ||||
−0.415368 | + | 0.909653i | \(0.636347\pi\) | |||||||
\(54\) | − | 7.34847i | − | 0.136083i | ||||||
\(55\) | 31.0166i | 0.563938i | ||||||||
\(56\) | 20.9435i | 0.373992i | ||||||||
\(57\) | −51.0522 | −0.895653 | ||||||||
\(58\) | 36.1031i | 0.622468i | ||||||||
\(59\) | −33.7393 | + | 48.4011i | −0.571852 | + | 0.820357i | ||||
\(60\) | −26.8312 | −0.447186 | ||||||||
\(61\) | − | 37.8344i | − | 0.620236i | −0.950698 | − | 0.310118i | \(-0.899631\pi\) | ||
0.950698 | − | 0.310118i | \(-0.100369\pi\) | |||||||
\(62\) | 6.69325 | 0.107956 | ||||||||
\(63\) | 22.2140 | 0.352603 | ||||||||
\(64\) | −8.00000 | −0.125000 | ||||||||
\(65\) | 151.491i | 2.33063i | ||||||||
\(66\) | 9.80891 | 0.148620 | ||||||||
\(67\) | − | 32.0552i | − | 0.478436i | −0.970966 | − | 0.239218i | \(-0.923109\pi\) | ||
0.970966 | − | 0.239218i | \(-0.0768911\pi\) | |||||||
\(68\) | −17.6563 | −0.259651 | ||||||||
\(69\) | 2.15548i | 0.0312388i | ||||||||
\(70\) | − | 81.1090i | − | 1.15870i | ||||||
\(71\) | −117.363 | −1.65300 | −0.826499 | − | 0.562938i | \(-0.809671\pi\) | ||||
−0.826499 | + | 0.562938i | \(0.809671\pi\) | |||||||
\(72\) | 8.48528i | 0.117851i | ||||||||
\(73\) | − | 24.0627i | − | 0.329626i | −0.986325 | − | 0.164813i | \(-0.947298\pi\) | ||
0.986325 | − | 0.164813i | \(-0.0527020\pi\) | |||||||
\(74\) | −82.3576 | −1.11294 | ||||||||
\(75\) | 60.6089 | 0.808118 | ||||||||
\(76\) | 58.9501 | 0.775659 | ||||||||
\(77\) | 29.6518i | 0.385088i | ||||||||
\(78\) | 47.9086 | 0.614213 | ||||||||
\(79\) | 112.119 | 1.41923 | 0.709614 | − | 0.704590i | \(-0.248869\pi\) | ||||
0.709614 | + | 0.704590i | \(0.248869\pi\) | |||||||
\(80\) | 30.9819 | 0.387274 | ||||||||
\(81\) | 9.00000 | 0.111111 | ||||||||
\(82\) | − | 44.0883i | − | 0.537662i | ||||||
\(83\) | − | 151.334i | − | 1.82330i | −0.410968 | − | 0.911650i | \(-0.634809\pi\) | ||
0.410968 | − | 0.911650i | \(-0.365191\pi\) | |||||||
\(84\) | −25.6505 | −0.305363 | ||||||||
\(85\) | 68.3782 | 0.804449 | ||||||||
\(86\) | −114.073 | −1.32644 | ||||||||
\(87\) | −44.2171 | −0.508243 | ||||||||
\(88\) | −11.3264 | −0.128709 | ||||||||
\(89\) | 66.5946i | 0.748253i | 0.927378 | + | 0.374127i | \(0.122058\pi\) | ||||
−0.927378 | + | 0.374127i | \(0.877942\pi\) | |||||||
\(90\) | − | 32.8613i | − | 0.365126i | ||||||
\(91\) | 144.825i | 1.59148i | ||||||||
\(92\) | − | 2.48893i | − | 0.0270536i | ||||||
\(93\) | 8.19753i | 0.0881455i | ||||||||
\(94\) | −48.7724 | −0.518855 | ||||||||
\(95\) | −228.298 | −2.40314 | ||||||||
\(96\) | − | 9.79796i | − | 0.102062i | ||||||
\(97\) | 97.4651i | 1.00479i | 0.864637 | + | 0.502397i | \(0.167548\pi\) | ||||
−0.864637 | + | 0.502397i | \(0.832452\pi\) | |||||||
\(98\) | − | 8.24343i | − | 0.0841167i | ||||||
\(99\) | 12.0134i | 0.121348i | ||||||||
\(100\) | −69.9851 | −0.699851 | ||||||||
\(101\) | 98.6578i | 0.976810i | 0.872617 | + | 0.488405i | \(0.162421\pi\) | ||||
−0.872617 | + | 0.488405i | \(0.837579\pi\) | |||||||
\(102\) | − | 21.6244i | − | 0.212004i | ||||||
\(103\) | − | 7.05381i | − | 0.0684836i | −0.999414 | − | 0.0342418i | \(-0.989098\pi\) | ||
0.999414 | − | 0.0342418i | \(-0.0109016\pi\) | |||||||
\(104\) | −55.3201 | −0.531924 | ||||||||
\(105\) | 99.3378 | 0.946074 | ||||||||
\(106\) | 62.2665i | 0.587419i | ||||||||
\(107\) | 57.4186 | 0.536622 | 0.268311 | − | 0.963332i | \(-0.413534\pi\) | ||||
0.268311 | + | 0.963332i | \(0.413534\pi\) | |||||||
\(108\) | −10.3923 | −0.0962250 | ||||||||
\(109\) | − | 138.622i | − | 1.27176i | −0.771788 | − | 0.635880i | \(-0.780637\pi\) | ||
0.771788 | − | 0.635880i | \(-0.219363\pi\) | |||||||
\(110\) | 43.8641 | 0.398764 | ||||||||
\(111\) | − | 100.867i | − | 0.908713i | ||||||
\(112\) | 29.6186 | 0.264452 | ||||||||
\(113\) | 209.920i | 1.85770i | 0.370462 | + | 0.928848i | \(0.379199\pi\) | ||||
−0.370462 | + | 0.928848i | \(0.620801\pi\) | |||||||
\(114\) | 72.1988i | 0.633323i | ||||||||
\(115\) | 9.63900i | 0.0838174i | ||||||||
\(116\) | 51.0576 | 0.440151 | ||||||||
\(117\) | 58.6759i | 0.501503i | ||||||||
\(118\) | 68.4494 | + | 47.7145i | 0.580080 | + | 0.404360i | ||||
\(119\) | 65.3693 | 0.549322 | ||||||||
\(120\) | 37.9450i | 0.316208i | ||||||||
\(121\) | 104.964 | 0.867473 | ||||||||
\(122\) | −53.5059 | −0.438573 | ||||||||
\(123\) | 53.9969 | 0.438999 | ||||||||
\(124\) | − | 9.46569i | − | 0.0763362i | ||||||
\(125\) | 77.3972 | 0.619177 | ||||||||
\(126\) | − | 31.4153i | − | 0.249328i | ||||||
\(127\) | −190.451 | −1.49961 | −0.749807 | − | 0.661657i | \(-0.769854\pi\) | ||||
−0.749807 | + | 0.661657i | \(0.769854\pi\) | |||||||
\(128\) | 11.3137i | 0.0883883i | ||||||||
\(129\) | − | 139.711i | − | 1.08303i | ||||||
\(130\) | 214.241 | 1.64801 | ||||||||
\(131\) | 235.226i | 1.79562i | 0.440383 | + | 0.897810i | \(0.354843\pi\) | ||||
−0.440383 | + | 0.897810i | \(0.645157\pi\) | |||||||
\(132\) | − | 13.8719i | − | 0.105090i | ||||||
\(133\) | −218.253 | −1.64100 | ||||||||
\(134\) | −45.3329 | −0.338305 | ||||||||
\(135\) | 40.2467 | 0.298124 | ||||||||
\(136\) | 24.9697i | 0.183601i | ||||||||
\(137\) | 2.22930 | 0.0162723 | 0.00813614 | − | 0.999967i | \(-0.497410\pi\) | ||||
0.00813614 | + | 0.999967i | \(0.497410\pi\) | |||||||
\(138\) | 3.04831 | 0.0220892 | ||||||||
\(139\) | −113.790 | −0.818631 | −0.409316 | − | 0.912393i | \(-0.634232\pi\) | ||||
−0.409316 | + | 0.912393i | \(0.634232\pi\) | |||||||
\(140\) | −114.705 | −0.819324 | ||||||||
\(141\) | − | 59.7337i | − | 0.423643i | ||||||
\(142\) | 165.976i | 1.16885i | ||||||||
\(143\) | −78.3220 | −0.547706 | ||||||||
\(144\) | 12.0000 | 0.0833333 | ||||||||
\(145\) | −197.733 | −1.36367 | ||||||||
\(146\) | −34.0297 | −0.233080 | ||||||||
\(147\) | 10.0961 | 0.0686810 | ||||||||
\(148\) | 116.471i | 0.786968i | ||||||||
\(149\) | 57.5687i | 0.386367i | 0.981163 | + | 0.193184i | \(0.0618813\pi\) | ||||
−0.981163 | + | 0.193184i | \(0.938119\pi\) | |||||||
\(150\) | − | 85.7139i | − | 0.571426i | ||||||
\(151\) | 24.9883i | 0.165485i | 0.996571 | + | 0.0827426i | \(0.0263679\pi\) | ||||
−0.996571 | + | 0.0827426i | \(0.973632\pi\) | |||||||
\(152\) | − | 83.3680i | − | 0.548473i | ||||||
\(153\) | 26.4844 | 0.173101 | ||||||||
\(154\) | 41.9339 | 0.272298 | ||||||||
\(155\) | 36.6582i | 0.236504i | ||||||||
\(156\) | − | 67.7531i | − | 0.434314i | ||||||
\(157\) | − | 114.433i | − | 0.728872i | −0.931228 | − | 0.364436i | \(-0.881262\pi\) | ||
0.931228 | − | 0.364436i | \(-0.118738\pi\) | |||||||
\(158\) | − | 158.560i | − | 1.00355i | ||||||
\(159\) | −76.2605 | −0.479626 | ||||||||
\(160\) | − | 43.8151i | − | 0.273844i | ||||||
\(161\) | 9.21485i | 0.0572351i | ||||||||
\(162\) | − | 12.7279i | − | 0.0785674i | ||||||
\(163\) | 115.726 | 0.709977 | 0.354989 | − | 0.934871i | \(-0.384485\pi\) | ||||
0.354989 | + | 0.934871i | \(0.384485\pi\) | |||||||
\(164\) | −62.3502 | −0.380184 | ||||||||
\(165\) | 53.7223i | 0.325590i | ||||||||
\(166\) | −214.018 | −1.28927 | ||||||||
\(167\) | 10.5436 | 0.0631356 | 0.0315678 | − | 0.999502i | \(-0.489950\pi\) | ||||
0.0315678 | + | 0.999502i | \(0.489950\pi\) | |||||||
\(168\) | 36.2753i | 0.215924i | ||||||||
\(169\) | −213.540 | −1.26355 | ||||||||
\(170\) | − | 96.7013i | − | 0.568831i | ||||||
\(171\) | −88.4251 | −0.517106 | ||||||||
\(172\) | 161.324i | 0.937931i | ||||||||
\(173\) | 68.9417i | 0.398507i | 0.979948 | + | 0.199253i | \(0.0638517\pi\) | ||||
−0.979948 | + | 0.199253i | \(0.936148\pi\) | |||||||
\(174\) | 62.5325i | 0.359382i | ||||||||
\(175\) | 259.108 | 1.48062 | ||||||||
\(176\) | 16.0179i | 0.0910107i | ||||||||
\(177\) | −58.4381 | + | 83.8331i | −0.330159 | + | 0.473633i | ||||
\(178\) | 94.1789 | 0.529095 | ||||||||
\(179\) | − | 152.087i | − | 0.849649i | −0.905276 | − | 0.424825i | \(-0.860336\pi\) | ||
0.905276 | − | 0.424825i | \(-0.139664\pi\) | |||||||
\(180\) | −46.4729 | −0.258183 | ||||||||
\(181\) | −81.1957 | −0.448595 | −0.224297 | − | 0.974521i | \(-0.572009\pi\) | ||||
−0.224297 | + | 0.974521i | \(0.572009\pi\) | |||||||
\(182\) | 204.813 | 1.12535 | ||||||||
\(183\) | − | 65.5311i | − | 0.358093i | ||||||
\(184\) | −3.51988 | −0.0191298 | ||||||||
\(185\) | − | 451.063i | − | 2.43818i | ||||||
\(186\) | 11.5931 | 0.0623283 | ||||||||
\(187\) | 35.3520i | 0.189048i | ||||||||
\(188\) | 68.9745i | 0.366886i | ||||||||
\(189\) | 38.4757 | 0.203575 | ||||||||
\(190\) | 322.863i | 1.69928i | ||||||||
\(191\) | − | 13.5994i | − | 0.0712012i | −0.999366 | − | 0.0356006i | \(-0.988666\pi\) | ||
0.999366 | − | 0.0356006i | \(-0.0113344\pi\) | |||||||
\(192\) | −13.8564 | −0.0721688 | ||||||||
\(193\) | 216.667 | 1.12263 | 0.561314 | − | 0.827603i | \(-0.310296\pi\) | ||||
0.561314 | + | 0.827603i | \(0.310296\pi\) | |||||||
\(194\) | 137.836 | 0.710497 | ||||||||
\(195\) | 262.390i | 1.34559i | ||||||||
\(196\) | −11.6580 | −0.0594795 | ||||||||
\(197\) | 265.328 | 1.34684 | 0.673422 | − | 0.739258i | \(-0.264824\pi\) | ||||
0.673422 | + | 0.739258i | \(0.264824\pi\) | |||||||
\(198\) | 16.9895 | 0.0858057 | ||||||||
\(199\) | −131.448 | −0.660544 | −0.330272 | − | 0.943886i | \(-0.607140\pi\) | ||||
−0.330272 | + | 0.943886i | \(0.607140\pi\) | |||||||
\(200\) | 98.9739i | 0.494869i | ||||||||
\(201\) | − | 55.5213i | − | 0.276225i | ||||||
\(202\) | 139.523 | 0.690709 | ||||||||
\(203\) | −189.032 | −0.931192 | ||||||||
\(204\) | −30.5815 | −0.149910 | ||||||||
\(205\) | 241.466 | 1.17788 | ||||||||
\(206\) | −9.97559 | −0.0484252 | ||||||||
\(207\) | 3.73340i | 0.0180357i | ||||||||
\(208\) | 78.2345i | 0.376127i | ||||||||
\(209\) | − | 118.032i | − | 0.564746i | ||||||
\(210\) | − | 140.485i | − | 0.668975i | ||||||
\(211\) | − | 362.962i | − | 1.72020i | −0.510124 | − | 0.860101i | \(-0.670401\pi\) | ||
0.510124 | − | 0.860101i | \(-0.329599\pi\) | |||||||
\(212\) | 88.0581 | 0.415368 | ||||||||
\(213\) | −203.278 | −0.954359 | ||||||||
\(214\) | − | 81.2022i | − | 0.379449i | ||||||
\(215\) | − | 624.767i | − | 2.90589i | ||||||
\(216\) | 14.6969i | 0.0680414i | ||||||||
\(217\) | 35.0451i | 0.161498i | ||||||||
\(218\) | −196.041 | −0.899270 | ||||||||
\(219\) | − | 41.6778i | − | 0.190309i | ||||||
\(220\) | − | 62.0332i | − | 0.281969i | ||||||
\(221\) | 172.666i | 0.781295i | ||||||||
\(222\) | −142.648 | −0.642557 | ||||||||
\(223\) | −69.0199 | −0.309506 | −0.154753 | − | 0.987953i | \(-0.549458\pi\) | ||||
−0.154753 | + | 0.987953i | \(0.549458\pi\) | |||||||
\(224\) | − | 41.8871i | − | 0.186996i | ||||||
\(225\) | 104.978 | 0.466567 | ||||||||
\(226\) | 296.871 | 1.31359 | ||||||||
\(227\) | 134.615i | 0.593020i | 0.955030 | + | 0.296510i | \(0.0958227\pi\) | ||||
−0.955030 | + | 0.296510i | \(0.904177\pi\) | |||||||
\(228\) | 102.104 | 0.447827 | ||||||||
\(229\) | 321.197i | 1.40261i | 0.712864 | + | 0.701303i | \(0.247398\pi\) | ||||
−0.712864 | + | 0.701303i | \(0.752602\pi\) | |||||||
\(230\) | 13.6316 | 0.0592678 | ||||||||
\(231\) | 51.3583i | 0.222330i | ||||||||
\(232\) | − | 72.2063i | − | 0.311234i | ||||||
\(233\) | − | 141.218i | − | 0.606085i | −0.952977 | − | 0.303042i | \(-0.901998\pi\) | ||
0.952977 | − | 0.303042i | \(-0.0980024\pi\) | |||||||
\(234\) | 82.9802 | 0.354616 | ||||||||
\(235\) | − | 267.121i | − | 1.13668i | ||||||
\(236\) | 67.4785 | − | 96.8021i | 0.285926 | − | 0.410178i | ||||
\(237\) | 194.196 | 0.819392 | ||||||||
\(238\) | − | 92.4462i | − | 0.388429i | ||||||
\(239\) | 42.8513 | 0.179294 | 0.0896471 | − | 0.995974i | \(-0.471426\pi\) | ||||
0.0896471 | + | 0.995974i | \(0.471426\pi\) | |||||||
\(240\) | 53.6623 | 0.223593 | ||||||||
\(241\) | 167.621 | 0.695523 | 0.347761 | − | 0.937583i | \(-0.386942\pi\) | ||||
0.347761 | + | 0.937583i | \(0.386942\pi\) | |||||||
\(242\) | − | 148.442i | − | 0.613396i | ||||||
\(243\) | 15.5885 | 0.0641500 | ||||||||
\(244\) | 75.6688i | 0.310118i | ||||||||
\(245\) | 45.1483 | 0.184279 | ||||||||
\(246\) | − | 76.3631i | − | 0.310419i | ||||||
\(247\) | − | 576.491i | − | 2.33397i | ||||||
\(248\) | −13.3865 | −0.0539778 | ||||||||
\(249\) | − | 262.118i | − | 1.05268i | ||||||
\(250\) | − | 109.456i | − | 0.437825i | ||||||
\(251\) | 80.1349 | 0.319263 | 0.159631 | − | 0.987177i | \(-0.448969\pi\) | ||||
0.159631 | + | 0.987177i | \(0.448969\pi\) | |||||||
\(252\) | −44.4280 | −0.176301 | ||||||||
\(253\) | −4.98343 | −0.0196974 | ||||||||
\(254\) | 269.338i | 1.06039i | ||||||||
\(255\) | 118.434 | 0.464449 | ||||||||
\(256\) | 16.0000 | 0.0625000 | ||||||||
\(257\) | 163.633 | 0.636704 | 0.318352 | − | 0.947973i | \(-0.396871\pi\) | ||||
0.318352 | + | 0.947973i | \(0.396871\pi\) | |||||||
\(258\) | −197.581 | −0.765818 | ||||||||
\(259\) | − | 431.215i | − | 1.66492i | ||||||
\(260\) | − | 302.982i | − | 1.16532i | ||||||
\(261\) | −76.5863 | −0.293434 | ||||||||
\(262\) | 332.660 | 1.26970 | ||||||||
\(263\) | 105.069 | 0.399502 | 0.199751 | − | 0.979847i | \(-0.435987\pi\) | ||||
0.199751 | + | 0.979847i | \(0.435987\pi\) | |||||||
\(264\) | −19.6178 | −0.0743099 | ||||||||
\(265\) | −341.026 | −1.28689 | ||||||||
\(266\) | 308.656i | 1.16036i | ||||||||
\(267\) | 115.345i | 0.432004i | ||||||||
\(268\) | 64.1104i | 0.239218i | ||||||||
\(269\) | 469.581i | 1.74565i | 0.488029 | + | 0.872827i | \(0.337716\pi\) | ||||
−0.488029 | + | 0.872827i | \(0.662284\pi\) | |||||||
\(270\) | − | 56.9175i | − | 0.210805i | ||||||
\(271\) | 185.388 | 0.684087 | 0.342044 | − | 0.939684i | \(-0.388881\pi\) | ||||
0.342044 | + | 0.939684i | \(0.388881\pi\) | |||||||
\(272\) | 35.3125 | 0.129825 | ||||||||
\(273\) | 250.844i | 0.918843i | ||||||||
\(274\) | − | 3.15271i | − | 0.0115062i | ||||||
\(275\) | 140.127i | 0.509552i | ||||||||
\(276\) | − | 4.31096i | − | 0.0156194i | ||||||
\(277\) | 470.537 | 1.69869 | 0.849345 | − | 0.527839i | \(-0.176997\pi\) | ||||
0.849345 | + | 0.527839i | \(0.176997\pi\) | |||||||
\(278\) | 160.923i | 0.578860i | ||||||||
\(279\) | 14.1985i | 0.0508908i | ||||||||
\(280\) | 162.218i | 0.579350i | ||||||||
\(281\) | −111.017 | −0.395077 | −0.197539 | − | 0.980295i | \(-0.563295\pi\) | ||||
−0.197539 | + | 0.980295i | \(0.563295\pi\) | |||||||
\(282\) | −84.4762 | −0.299561 | ||||||||
\(283\) | − | 81.8102i | − | 0.289082i | −0.989499 | − | 0.144541i | \(-0.953829\pi\) | ||
0.989499 | − | 0.144541i | \(-0.0461706\pi\) | |||||||
\(284\) | 234.726 | 0.826499 | ||||||||
\(285\) | −395.424 | −1.38745 | ||||||||
\(286\) | 110.764i | 0.387287i | ||||||||
\(287\) | 230.841 | 0.804324 | ||||||||
\(288\) | − | 16.9706i | − | 0.0589256i | ||||||
\(289\) | −211.064 | −0.730326 | ||||||||
\(290\) | 279.636i | 0.964263i | ||||||||
\(291\) | 168.814i | 0.580118i | ||||||||
\(292\) | 48.1253i | 0.164813i | ||||||||
\(293\) | −209.795 | −0.716026 | −0.358013 | − | 0.933717i | \(-0.616546\pi\) | ||||
−0.358013 | + | 0.933717i | \(0.616546\pi\) | |||||||
\(294\) | − | 14.2780i | − | 0.0485648i | ||||||
\(295\) | −261.327 | + | 374.890i | −0.885854 | + | 1.27081i | ||||
\(296\) | 164.715 | 0.556471 | ||||||||
\(297\) | 20.8078i | 0.0700601i | ||||||||
\(298\) | 81.4144 | 0.273203 | ||||||||
\(299\) | −24.3401 | −0.0814049 | ||||||||
\(300\) | −121.218 | −0.404059 | ||||||||
\(301\) | − | 597.275i | − | 1.98430i | ||||||
\(302\) | 35.3387 | 0.117016 | ||||||||
\(303\) | 170.880i | 0.563961i | ||||||||
\(304\) | −117.900 | −0.387829 | ||||||||
\(305\) | − | 293.046i | − | 0.960806i | ||||||
\(306\) | − | 37.4546i | − | 0.122401i | ||||||
\(307\) | −241.024 | −0.785094 | −0.392547 | − | 0.919732i | \(-0.628406\pi\) | ||||
−0.392547 | + | 0.919732i | \(0.628406\pi\) | |||||||
\(308\) | − | 59.3035i | − | 0.192544i | ||||||
\(309\) | − | 12.2176i | − | 0.0395390i | ||||||
\(310\) | 51.8425 | 0.167234 | ||||||||
\(311\) | −4.50483 | −0.0144850 | −0.00724249 | − | 0.999974i | \(-0.502305\pi\) | ||||
−0.00724249 | + | 0.999974i | \(0.502305\pi\) | |||||||
\(312\) | −95.8173 | −0.307107 | ||||||||
\(313\) | 489.847i | 1.56501i | 0.622647 | + | 0.782503i | \(0.286057\pi\) | ||||
−0.622647 | + | 0.782503i | \(0.713943\pi\) | |||||||
\(314\) | −161.833 | −0.515390 | ||||||||
\(315\) | 172.058 | 0.546216 | ||||||||
\(316\) | −224.238 | −0.709614 | ||||||||
\(317\) | 499.798 | 1.57665 | 0.788325 | − | 0.615259i | \(-0.210948\pi\) | ||||
0.788325 | + | 0.615259i | \(0.210948\pi\) | |||||||
\(318\) | 107.849i | 0.339147i | ||||||||
\(319\) | − | 102.229i | − | 0.320468i | ||||||
\(320\) | −61.9639 | −0.193637 | ||||||||
\(321\) | 99.4519 | 0.309819 | ||||||||
\(322\) | 13.0318 | 0.0404713 | ||||||||
\(323\) | −260.209 | −0.805602 | ||||||||
\(324\) | −18.0000 | −0.0555556 | ||||||||
\(325\) | 684.406i | 2.10587i | ||||||||
\(326\) | − | 163.662i | − | 0.502030i | ||||||
\(327\) | − | 240.100i | − | 0.734251i | ||||||
\(328\) | 88.1765i | 0.268831i | ||||||||
\(329\) | − | 255.366i | − | 0.776190i | ||||||
\(330\) | 75.9748 | 0.230227 | ||||||||
\(331\) | −375.117 | −1.13328 | −0.566641 | − | 0.823965i | \(-0.691758\pi\) | ||||
−0.566641 | + | 0.823965i | \(0.691758\pi\) | |||||||
\(332\) | 302.668i | 0.911650i | ||||||||
\(333\) | − | 174.707i | − | 0.524645i | ||||||
\(334\) | − | 14.9110i | − | 0.0446436i | ||||||
\(335\) | − | 248.283i | − | 0.741144i | ||||||
\(336\) | 51.3010 | 0.152682 | ||||||||
\(337\) | 381.288i | 1.13142i | 0.824605 | + | 0.565710i | \(0.191398\pi\) | ||||
−0.824605 | + | 0.565710i | \(0.808602\pi\) | |||||||
\(338\) | 301.991i | 0.893464i | ||||||||
\(339\) | 363.591i | 1.07254i | ||||||||
\(340\) | −136.756 | −0.402225 | ||||||||
\(341\) | −18.9525 | −0.0555793 | ||||||||
\(342\) | 125.052i | 0.365649i | ||||||||
\(343\) | −319.667 | −0.931973 | ||||||||
\(344\) | 228.147 | 0.663218 | ||||||||
\(345\) | 16.6952i | 0.0483920i | ||||||||
\(346\) | 97.4982 | 0.281787 | ||||||||
\(347\) | − | 355.001i | − | 1.02306i | −0.859266 | − | 0.511528i | \(-0.829080\pi\) | ||
0.859266 | − | 0.511528i | \(-0.170920\pi\) | |||||||
\(348\) | 88.4343 | 0.254122 | ||||||||
\(349\) | − | 5.79204i | − | 0.0165961i | −0.999966 | − | 0.00829805i | \(-0.997359\pi\) | ||
0.999966 | − | 0.00829805i | \(-0.00264138\pi\) | |||||||
\(350\) | − | 366.434i | − | 1.04695i | ||||||
\(351\) | 101.630i | 0.289543i | ||||||||
\(352\) | 22.6527 | 0.0643543 | ||||||||
\(353\) | 477.888i | 1.35379i | 0.736079 | + | 0.676895i | \(0.236675\pi\) | ||||
−0.736079 | + | 0.676895i | \(0.763325\pi\) | |||||||
\(354\) | 118.558 | + | 82.6440i | 0.334909 | + | 0.233458i | ||||
\(355\) | −909.032 | −2.56065 | ||||||||
\(356\) | − | 133.189i | − | 0.374127i | ||||||
\(357\) | 113.223 | 0.317151 | ||||||||
\(358\) | −215.084 | −0.600793 | ||||||||
\(359\) | −332.764 | −0.926919 | −0.463459 | − | 0.886118i | \(-0.653392\pi\) | ||||
−0.463459 | + | 0.886118i | \(0.653392\pi\) | |||||||
\(360\) | 65.7226i | 0.182563i | ||||||||
\(361\) | 507.777 | 1.40659 | ||||||||
\(362\) | 114.828i | 0.317205i | ||||||||
\(363\) | 181.803 | 0.500836 | ||||||||
\(364\) | − | 289.650i | − | 0.795742i | ||||||
\(365\) | − | 186.377i | − | 0.510622i | ||||||
\(366\) | −92.6749 | −0.253210 | ||||||||
\(367\) | 492.687i | 1.34247i | 0.741244 | + | 0.671235i | \(0.234236\pi\) | ||||
−0.741244 | + | 0.671235i | \(0.765764\pi\) | |||||||
\(368\) | 4.97787i | 0.0135268i | ||||||||
\(369\) | 93.5253 | 0.253456 | ||||||||
\(370\) | −637.900 | −1.72405 | ||||||||
\(371\) | −326.020 | −0.878760 | ||||||||
\(372\) | − | 16.3951i | − | 0.0440727i | ||||||
\(373\) | 367.073 | 0.984110 | 0.492055 | − | 0.870564i | \(-0.336246\pi\) | ||||
0.492055 | + | 0.870564i | \(0.336246\pi\) | |||||||
\(374\) | 49.9953 | 0.133677 | ||||||||
\(375\) | 134.056 | 0.357482 | ||||||||
\(376\) | 97.5447 | 0.259427 | ||||||||
\(377\) | − | 499.308i | − | 1.32442i | ||||||
\(378\) | − | 54.4129i | − | 0.143950i | ||||||
\(379\) | 347.845 | 0.917798 | 0.458899 | − | 0.888489i | \(-0.348244\pi\) | ||||
0.458899 | + | 0.888489i | \(0.348244\pi\) | |||||||
\(380\) | 456.597 | 1.20157 | ||||||||
\(381\) | −329.871 | −0.865802 | ||||||||
\(382\) | −19.2325 | −0.0503468 | ||||||||
\(383\) | 320.942 | 0.837969 | 0.418985 | − | 0.907993i | \(-0.362386\pi\) | ||||
0.418985 | + | 0.907993i | \(0.362386\pi\) | |||||||
\(384\) | 19.5959i | 0.0510310i | ||||||||
\(385\) | 229.667i | 0.596538i | ||||||||
\(386\) | − | 306.414i | − | 0.793817i | ||||||
\(387\) | − | 241.986i | − | 0.625288i | ||||||
\(388\) | − | 194.930i | − | 0.502397i | ||||||
\(389\) | 344.325 | 0.885154 | 0.442577 | − | 0.896731i | \(-0.354064\pi\) | ||||
0.442577 | + | 0.896731i | \(0.354064\pi\) | |||||||
\(390\) | 371.076 | 0.951476 | ||||||||
\(391\) | 10.9863i | 0.0280980i | ||||||||
\(392\) | 16.4869i | 0.0420583i | ||||||||
\(393\) | 407.424i | 1.03670i | ||||||||
\(394\) | − | 375.231i | − | 0.952363i | ||||||
\(395\) | 868.417 | 2.19852 | ||||||||
\(396\) | − | 24.0268i | − | 0.0606738i | ||||||
\(397\) | − | 339.996i | − | 0.856414i | −0.903681 | − | 0.428207i | \(-0.859145\pi\) | ||
0.903681 | − | 0.428207i | \(-0.140855\pi\) | |||||||
\(398\) | 185.896i | 0.467075i | ||||||||
\(399\) | −378.025 | −0.947430 | ||||||||
\(400\) | 139.970 | 0.349926 | ||||||||
\(401\) | 33.6512i | 0.0839183i | 0.999119 | + | 0.0419591i | \(0.0133599\pi\) | ||||
−0.999119 | + | 0.0419591i | \(0.986640\pi\) | |||||||
\(402\) | −78.5189 | −0.195321 | ||||||||
\(403\) | −92.5679 | −0.229697 | ||||||||
\(404\) | − | 197.316i | − | 0.488405i | ||||||
\(405\) | 69.7094 | 0.172122 | ||||||||
\(406\) | 267.332i | 0.658452i | ||||||||
\(407\) | 233.203 | 0.572980 | ||||||||
\(408\) | 43.2488i | 0.106002i | ||||||||
\(409\) | − | 37.6215i | − | 0.0919842i | −0.998942 | − | 0.0459921i | \(-0.985355\pi\) | ||
0.998942 | − | 0.0459921i | \(-0.0146449\pi\) | |||||||
\(410\) | − | 341.485i | − | 0.832890i | ||||||
\(411\) | 3.86126 | 0.00939480 | ||||||||
\(412\) | 14.1076i | 0.0342418i | ||||||||
\(413\) | −249.828 | + | 358.393i | −0.604910 | + | 0.867780i | ||||
\(414\) | 5.27983 | 0.0127532 | ||||||||
\(415\) | − | 1172.15i | − | 2.82447i | ||||||
\(416\) | 110.640 | 0.265962 | ||||||||
\(417\) | −197.090 | −0.472637 | ||||||||
\(418\) | −166.922 | −0.399336 | ||||||||
\(419\) | − | 408.607i | − | 0.975196i | −0.873068 | − | 0.487598i | \(-0.837873\pi\) | ||
0.873068 | − | 0.487598i | \(-0.162127\pi\) | |||||||
\(420\) | −198.676 | −0.473037 | ||||||||
\(421\) | 645.164i | 1.53246i | 0.642569 | + | 0.766228i | \(0.277869\pi\) | ||||
−0.642569 | + | 0.766228i | \(0.722131\pi\) | |||||||
\(422\) | −513.306 | −1.21637 | ||||||||
\(423\) | − | 103.462i | − | 0.244591i | ||||||
\(424\) | − | 124.533i | − | 0.293710i | ||||||
\(425\) | 308.919 | 0.726868 | ||||||||
\(426\) | 287.479i | 0.674834i | ||||||||
\(427\) | − | 280.151i | − | 0.656091i | ||||||
\(428\) | −114.837 | −0.268311 | ||||||||
\(429\) | −135.658 | −0.316218 | ||||||||
\(430\) | −883.554 | −2.05478 | ||||||||
\(431\) | 308.175i | 0.715023i | 0.933909 | + | 0.357512i | \(0.116375\pi\) | ||||
−0.933909 | + | 0.357512i | \(0.883625\pi\) | |||||||
\(432\) | 20.7846 | 0.0481125 | ||||||||
\(433\) | −784.573 | −1.81195 | −0.905973 | − | 0.423335i | \(-0.860859\pi\) | ||||
−0.905973 | + | 0.423335i | \(0.860859\pi\) | |||||||
\(434\) | 49.5613 | 0.114196 | ||||||||
\(435\) | −342.483 | −0.787318 | ||||||||
\(436\) | 277.244i | 0.635880i | ||||||||
\(437\) | − | 36.6807i | − | 0.0839375i | ||||||
\(438\) | −58.9413 | −0.134569 | ||||||||
\(439\) | −362.248 | −0.825167 | −0.412583 | − | 0.910920i | \(-0.635373\pi\) | ||||
−0.412583 | + | 0.910920i | \(0.635373\pi\) | |||||||
\(440\) | −87.7281 | −0.199382 | ||||||||
\(441\) | 17.4870 | 0.0396530 | ||||||||
\(442\) | 244.187 | 0.552459 | ||||||||
\(443\) | 49.2729i | 0.111226i | 0.998452 | + | 0.0556128i | \(0.0177112\pi\) | ||||
−0.998452 | + | 0.0556128i | \(0.982289\pi\) | |||||||
\(444\) | 201.734i | 0.454356i | ||||||||
\(445\) | 515.807i | 1.15912i | ||||||||
\(446\) | 97.6089i | 0.218854i | ||||||||
\(447\) | 99.7119i | 0.223069i | ||||||||
\(448\) | −59.2373 | −0.132226 | ||||||||
\(449\) | 384.700 | 0.856792 | 0.428396 | − | 0.903591i | \(-0.359079\pi\) | ||||
0.428396 | + | 0.903591i | \(0.359079\pi\) | |||||||
\(450\) | − | 148.461i | − | 0.329913i | ||||||
\(451\) | 124.840i | 0.276807i | ||||||||
\(452\) | − | 419.839i | − | 0.928848i | ||||||
\(453\) | 43.2809i | 0.0955429i | ||||||||
\(454\) | 190.375 | 0.419328 | ||||||||
\(455\) | 1121.74i | 2.46536i | ||||||||
\(456\) | − | 144.398i | − | 0.316661i | ||||||
\(457\) | 416.205i | 0.910733i | 0.890304 | + | 0.455366i | \(0.150492\pi\) | ||||
−0.890304 | + | 0.455366i | \(0.849508\pi\) | |||||||
\(458\) | 454.241 | 0.991792 | ||||||||
\(459\) | 45.8723 | 0.0999397 | ||||||||
\(460\) | − | 19.2780i | − | 0.0419087i | ||||||
\(461\) | −222.765 | −0.483222 | −0.241611 | − | 0.970373i | \(-0.577676\pi\) | ||||
−0.241611 | + | 0.970373i | \(0.577676\pi\) | |||||||
\(462\) | 72.6317 | 0.157211 | ||||||||
\(463\) | 145.299i | 0.313821i | 0.987613 | + | 0.156911i | \(0.0501535\pi\) | ||||
−0.987613 | + | 0.156911i | \(0.949847\pi\) | |||||||
\(464\) | −102.115 | −0.220076 | ||||||||
\(465\) | 63.4938i | 0.136546i | ||||||||
\(466\) | −199.712 | −0.428567 | ||||||||
\(467\) | − | 387.905i | − | 0.830631i | −0.909677 | − | 0.415315i | \(-0.863671\pi\) | ||
0.909677 | − | 0.415315i | \(-0.136329\pi\) | |||||||
\(468\) | − | 117.352i | − | 0.250752i | ||||||
\(469\) | − | 237.358i | − | 0.506094i | ||||||
\(470\) | −377.766 | −0.803757 | ||||||||
\(471\) | − | 198.204i | − | 0.420815i | ||||||
\(472\) | −136.899 | − | 95.4291i | −0.290040 | − | 0.202180i | ||||
\(473\) | 323.009 | 0.682894 | ||||||||
\(474\) | − | 274.634i | − | 0.579398i | ||||||
\(475\) | −1031.41 | −2.17138 | ||||||||
\(476\) | −130.739 | −0.274661 | ||||||||
\(477\) | −132.087 | −0.276912 | ||||||||
\(478\) | − | 60.6009i | − | 0.126780i | ||||||
\(479\) | −727.357 | −1.51849 | −0.759245 | − | 0.650805i | \(-0.774432\pi\) | ||||
−0.759245 | + | 0.650805i | \(0.774432\pi\) | |||||||
\(480\) | − | 75.8900i | − | 0.158104i | ||||||
\(481\) | 1139.01 | 2.36800 | ||||||||
\(482\) | − | 237.052i | − | 0.491809i | ||||||
\(483\) | 15.9606i | 0.0330447i | ||||||||
\(484\) | −209.928 | −0.433736 | ||||||||
\(485\) | 754.914i | 1.55652i | ||||||||
\(486\) | − | 22.0454i | − | 0.0453609i | ||||||
\(487\) | −491.586 | −1.00942 | −0.504709 | − | 0.863290i | \(-0.668400\pi\) | ||||
−0.504709 | + | 0.863290i | \(0.668400\pi\) | |||||||
\(488\) | 107.012 | 0.219287 | ||||||||
\(489\) | 200.444 | 0.409906 | ||||||||
\(490\) | − | 63.8494i | − | 0.130305i | ||||||
\(491\) | 726.370 | 1.47937 | 0.739684 | − | 0.672954i | \(-0.234975\pi\) | ||||
0.739684 | + | 0.672954i | \(0.234975\pi\) | |||||||
\(492\) | −107.994 | −0.219499 | ||||||||
\(493\) | −225.371 | −0.457143 | ||||||||
\(494\) | −815.281 | −1.65037 | ||||||||
\(495\) | 93.0497i | 0.187979i | ||||||||
\(496\) | 18.9314i | 0.0381681i | ||||||||
\(497\) | −869.032 | −1.74856 | ||||||||
\(498\) | −370.691 | −0.744359 | ||||||||
\(499\) | 621.595 | 1.24568 | 0.622840 | − | 0.782349i | \(-0.285979\pi\) | ||||
0.622840 | + | 0.782349i | \(0.285979\pi\) | |||||||
\(500\) | −154.794 | −0.309589 | ||||||||
\(501\) | 18.2621 | 0.0364514 | ||||||||
\(502\) | − | 113.328i | − | 0.225753i | ||||||
\(503\) | 878.744i | 1.74701i | 0.486818 | + | 0.873503i | \(0.338157\pi\) | ||||
−0.486818 | + | 0.873503i | \(0.661843\pi\) | |||||||
\(504\) | 62.8306i | 0.124664i | ||||||||
\(505\) | 764.153i | 1.51317i | ||||||||
\(506\) | 7.04764i | 0.0139281i | ||||||||
\(507\) | −369.862 | −0.729510 | ||||||||
\(508\) | 380.902 | 0.749807 | ||||||||
\(509\) | 182.390i | 0.358329i | 0.983819 | + | 0.179165i | \(0.0573395\pi\) | ||||
−0.983819 | + | 0.179165i | \(0.942661\pi\) | |||||||
\(510\) | − | 167.492i | − | 0.328415i | ||||||
\(511\) | − | 178.176i | − | 0.348681i | ||||||
\(512\) | − | 22.6274i | − | 0.0441942i | ||||||
\(513\) | −153.157 | −0.298551 | ||||||||
\(514\) | − | 231.412i | − | 0.450218i | ||||||
\(515\) | − | 54.6352i | − | 0.106088i | ||||||
\(516\) | 279.422i | 0.541515i | ||||||||
\(517\) | 138.103 | 0.267124 | ||||||||
\(518\) | −609.830 | −1.17728 | ||||||||
\(519\) | 119.410i | 0.230078i | ||||||||
\(520\) | −428.481 | −0.824003 | ||||||||
\(521\) | −980.540 | −1.88203 | −0.941017 | − | 0.338360i | \(-0.890128\pi\) | ||||
−0.941017 | + | 0.338360i | \(0.890128\pi\) | |||||||
\(522\) | 108.309i | 0.207489i | ||||||||
\(523\) | −536.582 | −1.02597 | −0.512985 | − | 0.858398i | \(-0.671460\pi\) | ||||
−0.512985 | + | 0.858398i | \(0.671460\pi\) | |||||||
\(524\) | − | 470.453i | − | 0.897810i | ||||||
\(525\) | 448.788 | 0.854835 | ||||||||
\(526\) | − | 148.590i | − | 0.282490i | ||||||
\(527\) | 41.7822i | 0.0792831i | ||||||||
\(528\) | 27.7438i | 0.0525451i | ||||||||
\(529\) | 527.451 | 0.997072 | ||||||||
\(530\) | 482.284i | 0.909970i | ||||||||
\(531\) | −101.218 | + | 145.203i | −0.190617 | + | 0.273452i | ||||
\(532\) | 436.505 | 0.820498 | ||||||||
\(533\) | 609.742i | 1.14398i | ||||||||
\(534\) | 163.123 | 0.305473 | ||||||||
\(535\) | 444.735 | 0.831280 | ||||||||
\(536\) | 90.6658 | 0.169153 | ||||||||
\(537\) | − | 263.423i | − | 0.490545i | ||||||
\(538\) | 664.088 | 1.23436 | ||||||||
\(539\) | 23.3420i | 0.0433062i | ||||||||
\(540\) | −80.4935 | −0.149062 | ||||||||
\(541\) | − | 513.326i | − | 0.948847i | −0.880297 | − | 0.474424i | \(-0.842656\pi\) | ||
0.880297 | − | 0.474424i | \(-0.157344\pi\) | |||||||
\(542\) | − | 262.178i | − | 0.483723i | ||||||
\(543\) | −140.635 | −0.258996 | ||||||||
\(544\) | − | 49.9395i | − | 0.0918005i | ||||||
\(545\) | − | 1073.69i | − | 1.97008i | ||||||
\(546\) | 354.747 | 0.649720 | ||||||||
\(547\) | −27.4285 | −0.0501435 | −0.0250718 | − | 0.999686i | \(-0.507981\pi\) | ||||
−0.0250718 | + | 0.999686i | \(0.507981\pi\) | |||||||
\(548\) | −4.45860 | −0.00813614 | ||||||||
\(549\) | − | 113.503i | − | 0.206745i | ||||||
\(550\) | 198.169 | 0.360307 | ||||||||
\(551\) | 752.461 | 1.36563 | ||||||||
\(552\) | −6.09662 | −0.0110446 | ||||||||
\(553\) | 830.204 | 1.50127 | ||||||||
\(554\) | − | 665.440i | − | 1.20115i | ||||||
\(555\) | − | 781.265i | − | 1.40768i | ||||||
\(556\) | 227.579 | 0.409316 | ||||||||
\(557\) | 24.2247 | 0.0434914 | 0.0217457 | − | 0.999764i | \(-0.493078\pi\) | ||||
0.0217457 | + | 0.999764i | \(0.493078\pi\) | |||||||
\(558\) | 20.0798 | 0.0359852 | ||||||||
\(559\) | 1577.64 | 2.82225 | ||||||||
\(560\) | 229.411 | 0.409662 | ||||||||
\(561\) | 61.2315i | 0.109147i | ||||||||
\(562\) | 157.001i | 0.279362i | ||||||||
\(563\) | 137.830i | 0.244814i | 0.992480 | + | 0.122407i | \(0.0390614\pi\) | ||||
−0.992480 | + | 0.122407i | \(0.960939\pi\) | |||||||
\(564\) | 119.467i | 0.211822i | ||||||||
\(565\) | 1625.93i | 2.87775i | ||||||||
\(566\) | −115.697 | −0.204412 | ||||||||
\(567\) | 66.6419 | 0.117534 | ||||||||
\(568\) | − | 331.952i | − | 0.584423i | ||||||
\(569\) | − | 691.407i | − | 1.21513i | −0.794271 | − | 0.607563i | \(-0.792147\pi\) | ||
0.794271 | − | 0.607563i | \(-0.207853\pi\) | |||||||
\(570\) | 559.215i | 0.981078i | ||||||||
\(571\) | − | 584.297i | − | 1.02329i | −0.859198 | − | 0.511644i | \(-0.829037\pi\) | ||
0.859198 | − | 0.511644i | \(-0.170963\pi\) | |||||||
\(572\) | 156.644 | 0.273853 | ||||||||
\(573\) | − | 23.5549i | − | 0.0411080i | ||||||
\(574\) | − | 326.459i | − | 0.568743i | ||||||
\(575\) | 43.5471i | 0.0757340i | ||||||||
\(576\) | −24.0000 | −0.0416667 | ||||||||
\(577\) | 339.647 | 0.588644 | 0.294322 | − | 0.955706i | \(-0.404906\pi\) | ||||
0.294322 | + | 0.955706i | \(0.404906\pi\) | |||||||
\(578\) | 298.490i | 0.516418i | ||||||||
\(579\) | 375.278 | 0.648149 | ||||||||
\(580\) | 395.466 | 0.681837 | ||||||||
\(581\) | − | 1120.58i | − | 1.92870i | ||||||
\(582\) | 238.740 | 0.410206 | ||||||||
\(583\) | − | 176.313i | − | 0.302424i | ||||||
\(584\) | 68.0595 | 0.116540 | ||||||||
\(585\) | 454.473i | 0.776877i | ||||||||
\(586\) | 296.696i | 0.506307i | ||||||||
\(587\) | 91.6472i | 0.156128i | 0.996948 | + | 0.0780641i | \(0.0248739\pi\) | ||||
−0.996948 | + | 0.0780641i | \(0.975126\pi\) | |||||||
\(588\) | −20.1922 | −0.0343405 | ||||||||
\(589\) | − | 139.501i | − | 0.236843i | ||||||
\(590\) | 530.174 | + | 369.572i | 0.898600 | + | 0.626394i | ||||
\(591\) | 459.562 | 0.777601 | ||||||||
\(592\) | − | 232.943i | − | 0.393484i | ||||||
\(593\) | −1151.07 | −1.94109 | −0.970547 | − | 0.240913i | \(-0.922553\pi\) | ||||
−0.970547 | + | 0.240913i | \(0.922553\pi\) | |||||||
\(594\) | 29.4267 | 0.0495400 | ||||||||
\(595\) | 506.317 | 0.850953 | ||||||||
\(596\) | − | 115.137i | − | 0.193184i | ||||||
\(597\) | −227.675 | −0.381365 | ||||||||
\(598\) | 34.4220i | 0.0575619i | ||||||||
\(599\) | 1042.38 | 1.74019 | 0.870096 | − | 0.492882i | \(-0.164057\pi\) | ||||
0.870096 | + | 0.492882i | \(0.164057\pi\) | |||||||
\(600\) | 171.428i | 0.285713i | ||||||||
\(601\) | − | 1054.03i | − | 1.75379i | −0.480685 | − | 0.876893i | \(-0.659612\pi\) | ||
0.480685 | − | 0.876893i | \(-0.340388\pi\) | |||||||
\(602\) | −844.675 | −1.40311 | ||||||||
\(603\) | − | 96.1657i | − | 0.159479i | ||||||
\(604\) | − | 49.9765i | − | 0.0827426i | ||||||
\(605\) | 812.999 | 1.34380 | ||||||||
\(606\) | 241.661 | 0.398781 | ||||||||
\(607\) | 369.407 | 0.608578 | 0.304289 | − | 0.952580i | \(-0.401581\pi\) | ||||
0.304289 | + | 0.952580i | \(0.401581\pi\) | |||||||
\(608\) | 166.736i | 0.274237i | ||||||||
\(609\) | −327.413 | −0.537624 | ||||||||
\(610\) | −414.429 | −0.679392 | ||||||||
\(611\) | 674.523 | 1.10397 | ||||||||
\(612\) | −52.9688 | −0.0865503 | ||||||||
\(613\) | − | 417.526i | − | 0.681120i | −0.940223 | − | 0.340560i | \(-0.889383\pi\) | ||
0.940223 | − | 0.340560i | \(-0.110617\pi\) | |||||||
\(614\) | 340.859i | 0.555145i | ||||||||
\(615\) | 418.232 | 0.680052 | ||||||||
\(616\) | −83.8678 | −0.136149 | ||||||||
\(617\) | −86.3926 | −0.140020 | −0.0700102 | − | 0.997546i | \(-0.522303\pi\) | ||||
−0.0700102 | + | 0.997546i | \(0.522303\pi\) | |||||||
\(618\) | −17.2782 | −0.0279583 | ||||||||
\(619\) | −390.327 | −0.630576 | −0.315288 | − | 0.948996i | \(-0.602101\pi\) | ||||
−0.315288 | + | 0.948996i | \(0.602101\pi\) | |||||||
\(620\) | − | 73.3164i | − | 0.118252i | ||||||
\(621\) | 6.46644i | 0.0104129i | ||||||||
\(622\) | 6.37079i | 0.0102424i | ||||||||
\(623\) | 493.110i | 0.791509i | ||||||||
\(624\) | 135.506i | 0.217157i | ||||||||
\(625\) | −275.335 | −0.440536 | ||||||||
\(626\) | 692.748 | 1.10663 | ||||||||
\(627\) | − | 204.437i | − | 0.326056i | ||||||
\(628\) | 228.866i | 0.364436i | ||||||||
\(629\) | − | 514.112i | − | 0.817348i | ||||||
\(630\) | − | 243.327i | − | 0.386233i | ||||||
\(631\) | −632.550 | −1.00246 | −0.501228 | − | 0.865315i | \(-0.667118\pi\) | ||||
−0.501228 | + | 0.865315i | \(0.667118\pi\) | |||||||
\(632\) | 317.121i | 0.501773i | ||||||||
\(633\) | − | 628.669i | − | 0.993159i | ||||||
\(634\) | − | 706.821i | − | 1.11486i | ||||||
\(635\) | −1475.14 | −2.32305 | ||||||||
\(636\) | 152.521 | 0.239813 | ||||||||
\(637\) | 114.007i | 0.178975i | ||||||||
\(638\) | −144.574 | −0.226605 | ||||||||
\(639\) | −352.089 | −0.550999 | ||||||||
\(640\) | 87.6302i | 0.136922i | ||||||||
\(641\) | −231.847 | −0.361696 | −0.180848 | − | 0.983511i | \(-0.557884\pi\) | ||||
−0.180848 | + | 0.983511i | \(0.557884\pi\) | |||||||
\(642\) | − | 140.646i | − | 0.219075i | ||||||
\(643\) | 987.623 | 1.53596 | 0.767981 | − | 0.640473i | \(-0.221262\pi\) | ||||
0.767981 | + | 0.640473i | \(0.221262\pi\) | |||||||
\(644\) | − | 18.4297i | − | 0.0286176i | ||||||
\(645\) | − | 1082.13i | − | 1.67772i | ||||||
\(646\) | 367.992i | 0.569647i | ||||||||
\(647\) | 796.971 | 1.23179 | 0.615897 | − | 0.787827i | \(-0.288794\pi\) | ||||
0.615897 | + | 0.787827i | \(0.288794\pi\) | |||||||
\(648\) | 25.4558i | 0.0392837i | ||||||||
\(649\) | −193.821 | − | 135.108i | −0.298645 | − | 0.208179i | ||||
\(650\) | 967.897 | 1.48907 | ||||||||
\(651\) | 60.6999i | 0.0932410i | ||||||||
\(652\) | −231.453 | −0.354989 | ||||||||
\(653\) | −151.955 | −0.232703 | −0.116352 | − | 0.993208i | \(-0.537120\pi\) | ||||
−0.116352 | + | 0.993208i | \(0.537120\pi\) | |||||||
\(654\) | −339.553 | −0.519194 | ||||||||
\(655\) | 1821.94i | 2.78159i | ||||||||
\(656\) | 124.700 | 0.190092 | ||||||||
\(657\) | − | 72.1880i | − | 0.109875i | ||||||
\(658\) | −361.143 | −0.548849 | ||||||||
\(659\) | 1159.62i | 1.75967i | 0.475282 | + | 0.879834i | \(0.342346\pi\) | ||||
−0.475282 | + | 0.879834i | \(0.657654\pi\) | |||||||
\(660\) | − | 107.445i | − | 0.162795i | ||||||
\(661\) | 801.056 | 1.21188 | 0.605942 | − | 0.795509i | \(-0.292796\pi\) | ||||
0.605942 | + | 0.795509i | \(0.292796\pi\) | |||||||
\(662\) | 530.495i | 0.801352i | ||||||||
\(663\) | 299.066i | 0.451081i | ||||||||
\(664\) | 428.037 | 0.644634 | ||||||||
\(665\) | −1690.47 | −2.54206 | ||||||||
\(666\) | −247.073 | −0.370980 | ||||||||
\(667\) | − | 31.7697i | − | 0.0476308i | ||||||
\(668\) | −21.0873 | −0.0315678 | ||||||||
\(669\) | −119.546 | −0.178694 | ||||||||
\(670\) | −351.126 | −0.524068 | ||||||||
\(671\) | 151.507 | 0.225792 | ||||||||
\(672\) | − | 72.5506i | − | 0.107962i | ||||||
\(673\) | − | 697.466i | − | 1.03635i | −0.855273 | − | 0.518177i | \(-0.826611\pi\) | ||
0.855273 | − | 0.518177i | \(-0.173389\pi\) | |||||||
\(674\) | 539.223 | 0.800034 | ||||||||
\(675\) | 181.827 | 0.269373 | ||||||||
\(676\) | 427.080 | 0.631774 | ||||||||
\(677\) | 626.963 | 0.926090 | 0.463045 | − | 0.886335i | \(-0.346757\pi\) | ||||
0.463045 | + | 0.886335i | \(0.346757\pi\) | |||||||
\(678\) | 514.196 | 0.758401 | ||||||||
\(679\) | 721.696i | 1.06288i | ||||||||
\(680\) | 193.403i | 0.284416i | ||||||||
\(681\) | 233.161i | 0.342380i | ||||||||
\(682\) | 26.8029i | 0.0393005i | ||||||||
\(683\) | − | 550.936i | − | 0.806641i | −0.915059 | − | 0.403321i | \(-0.867856\pi\) | ||
0.915059 | − | 0.403321i | \(-0.132144\pi\) | |||||||
\(684\) | 176.850 | 0.258553 | ||||||||
\(685\) | 17.2670 | 0.0252073 | ||||||||
\(686\) | 452.077i | 0.659004i | ||||||||
\(687\) | 556.329i | 0.809794i | ||||||||
\(688\) | − | 322.648i | − | 0.468966i | ||||||
\(689\) | − | 861.147i | − | 1.24985i | ||||||
\(690\) | 23.6106 | 0.0342183 | ||||||||
\(691\) | − | 1267.62i | − | 1.83448i | −0.398337 | − | 0.917239i | \(-0.630412\pi\) | ||
0.398337 | − | 0.917239i | \(-0.369588\pi\) | |||||||
\(692\) | − | 137.883i | − | 0.199253i | ||||||
\(693\) | 88.9553i | 0.128363i | ||||||||
\(694\) | −502.047 | −0.723410 | ||||||||
\(695\) | −881.357 | −1.26814 | ||||||||
\(696\) | − | 125.065i | − | 0.179691i | ||||||
\(697\) | 275.218 | 0.394861 | ||||||||
\(698\) | −8.19118 | −0.0117352 | ||||||||
\(699\) | − | 244.596i | − | 0.349923i | ||||||
\(700\) | −518.216 | −0.740308 | ||||||||
\(701\) | − | 1267.37i | − | 1.80794i | −0.427595 | − | 0.903970i | \(-0.640639\pi\) | ||
0.427595 | − | 0.903970i | \(-0.359361\pi\) | |||||||
\(702\) | 143.726 | 0.204738 | ||||||||
\(703\) | 1716.50i | 2.44167i | ||||||||
\(704\) | − | 32.0358i | − | 0.0455054i | ||||||
\(705\) | − | 462.666i | − | 0.656264i | ||||||
\(706\) | 675.836 | 0.957274 | ||||||||
\(707\) | 730.528i | 1.03328i | ||||||||
\(708\) | 116.876 | − | 167.666i | 0.165079 | − | 0.236817i | ||||
\(709\) | −501.357 | −0.707132 | −0.353566 | − | 0.935410i | \(-0.615031\pi\) | ||||
−0.353566 | + | 0.935410i | \(0.615031\pi\) | |||||||
\(710\) | 1285.57i | 1.81066i | ||||||||
\(711\) | 336.357 | 0.473076 | ||||||||
\(712\) | −188.358 | −0.264548 | ||||||||
\(713\) | −5.88987 | −0.00826068 | ||||||||
\(714\) | − | 160.121i | − | 0.224260i | ||||||
\(715\) | −606.642 | −0.848450 | ||||||||
\(716\) | 304.174i | 0.424825i | ||||||||
\(717\) | 74.2206 | 0.103516 | ||||||||
\(718\) | 470.599i | 0.655431i | ||||||||
\(719\) | 561.681i | 0.781198i | 0.920561 | + | 0.390599i | \(0.127732\pi\) | ||||
−0.920561 | + | 0.390599i | \(0.872268\pi\) | |||||||
\(720\) | 92.9458 | 0.129091 | ||||||||
\(721\) | − | 52.2310i | − | 0.0724425i | ||||||
\(722\) | − | 718.106i | − | 0.994606i | ||||||
\(723\) | 290.328 | 0.401560 | ||||||||
\(724\) | 162.391 | 0.224297 | ||||||||
\(725\) | −893.317 | −1.23216 | ||||||||
\(726\) | − | 257.109i | − | 0.354144i | ||||||
\(727\) | 1053.55 | 1.44918 | 0.724589 | − | 0.689181i | \(-0.242030\pi\) | ||||
0.724589 | + | 0.689181i | \(0.242030\pi\) | |||||||
\(728\) | −409.627 | −0.562674 | ||||||||
\(729\) | 27.0000 | 0.0370370 | ||||||||
\(730\) | −263.577 | −0.361064 | ||||||||
\(731\) | − | 712.096i | − | 0.974139i | ||||||
\(732\) | 131.062i | 0.179047i | ||||||||
\(733\) | −1122.48 | −1.53136 | −0.765678 | − | 0.643223i | \(-0.777597\pi\) | ||||
−0.765678 | + | 0.643223i | \(0.777597\pi\) | |||||||
\(734\) | 696.764 | 0.949270 | ||||||||
\(735\) | 78.1992 | 0.106394 | ||||||||
\(736\) | 7.03977 | 0.00956490 | ||||||||
\(737\) | 128.364 | 0.174171 | ||||||||
\(738\) | − | 132.265i | − | 0.179221i | ||||||
\(739\) | − | 140.089i | − | 0.189566i | −0.995498 | − | 0.0947831i | \(-0.969784\pi\) | ||
0.995498 | − | 0.0947831i | \(-0.0302158\pi\) | |||||||
\(740\) | 902.127i | 1.21909i | ||||||||
\(741\) | − | 998.512i | − | 1.34752i | ||||||
\(742\) | 461.062i | 0.621377i | ||||||||
\(743\) | 174.473 | 0.234822 | 0.117411 | − | 0.993083i | \(-0.462540\pi\) | ||||
0.117411 | + | 0.993083i | \(0.462540\pi\) | |||||||
\(744\) | −23.1861 | −0.0311641 | ||||||||
\(745\) | 445.898i | 0.598520i | ||||||||
\(746\) | − | 519.119i | − | 0.695871i | ||||||
\(747\) | − | 454.002i | − | 0.607767i | ||||||
\(748\) | − | 70.7040i | − | 0.0945241i | ||||||
\(749\) | 425.165 | 0.567644 | ||||||||
\(750\) | − | 189.584i | − | 0.252778i | ||||||
\(751\) | 391.697i | 0.521567i | 0.965397 | + | 0.260783i | \(0.0839809\pi\) | ||||
−0.965397 | + | 0.260783i | \(0.916019\pi\) | |||||||
\(752\) | − | 137.949i | − | 0.183443i | ||||||
\(753\) | 138.798 | 0.184326 | ||||||||
\(754\) | −706.128 | −0.936509 | ||||||||
\(755\) | 193.546i | 0.256353i | ||||||||
\(756\) | −76.9515 | −0.101788 | ||||||||
\(757\) | 382.403 | 0.505156 | 0.252578 | − | 0.967576i | \(-0.418722\pi\) | ||||
0.252578 | + | 0.967576i | \(0.418722\pi\) | |||||||
\(758\) | − | 491.928i | − | 0.648981i | ||||||
\(759\) | −8.63156 | −0.0113723 | ||||||||
\(760\) | − | 645.725i | − | 0.849639i | ||||||
\(761\) | −943.577 | −1.23992 | −0.619959 | − | 0.784634i | \(-0.712851\pi\) | ||||
−0.619959 | + | 0.784634i | \(0.712851\pi\) | |||||||
\(762\) | 466.508i | 0.612215i | ||||||||
\(763\) | − | 1026.45i | − | 1.34528i | ||||||
\(764\) | 27.1988i | 0.0356006i | ||||||||
\(765\) | 205.134 | 0.268150 | ||||||||
\(766\) | − | 453.881i | − | 0.592534i | ||||||
\(767\) | −946.658 | − | 659.894i | −1.23423 | − | 0.860357i | ||||
\(768\) | 27.7128 | 0.0360844 | ||||||||
\(769\) | − | 148.742i | − | 0.193423i | −0.995312 | − | 0.0967114i | \(-0.969168\pi\) | ||
0.995312 | − | 0.0967114i | \(-0.0308324\pi\) | |||||||
\(770\) | 324.798 | 0.421816 | ||||||||
\(771\) | 283.420 | 0.367601 | ||||||||
\(772\) | −433.334 | −0.561314 | ||||||||
\(773\) | 585.587i | 0.757551i | 0.925489 | + | 0.378776i | \(0.123655\pi\) | ||||
−0.925489 | + | 0.378776i | \(0.876345\pi\) | |||||||
\(774\) | −342.220 | −0.442145 | ||||||||
\(775\) | 165.614i | 0.213696i | ||||||||
\(776\) | −275.673 | −0.355248 | ||||||||
\(777\) | − | 746.887i | − | 0.961244i | ||||||
\(778\) | − | 486.949i | − | 0.625898i | ||||||
\(779\) | −918.887 | −1.17957 | ||||||||
\(780\) | − | 524.780i | − | 0.672795i | ||||||
\(781\) | − | 469.976i | − | 0.601762i | ||||||
\(782\) | 15.5370 | 0.0198683 | ||||||||
\(783\) | −132.651 | −0.169414 | ||||||||
\(784\) | 23.3160 | 0.0297397 | ||||||||
\(785\) | − | 886.339i | − | 1.12909i | ||||||
\(786\) | 576.184 | 0.733059 | ||||||||
\(787\) | 1136.37 | 1.44392 | 0.721962 | − | 0.691932i | \(-0.243240\pi\) | ||||
0.721962 | + | 0.691932i | \(0.243240\pi\) | |||||||
\(788\) | −530.657 | −0.673422 | ||||||||
\(789\) | 181.985 | 0.230652 | ||||||||
\(790\) | − | 1228.13i | − | 1.55459i | ||||||
\(791\) | 1554.38i | 1.96509i | ||||||||
\(792\) | −33.9791 | −0.0429029 | ||||||||
\(793\) | 739.989 | 0.933151 | ||||||||
\(794\) | −480.827 | −0.605576 | ||||||||
\(795\) | −590.675 | −0.742987 | ||||||||
\(796\) | 262.897 | 0.330272 | ||||||||
\(797\) | − | 394.545i | − | 0.495038i | −0.968883 | − | 0.247519i | \(-0.920385\pi\) | ||
0.968883 | − | 0.247519i | \(-0.0796152\pi\) | |||||||
\(798\) | 534.607i | 0.669934i | ||||||||
\(799\) | − | 304.458i | − | 0.381049i | ||||||
\(800\) | − | 197.948i | − | 0.247435i | ||||||
\(801\) | 199.784i | 0.249418i | ||||||||
\(802\) | 47.5900 | 0.0593392 | ||||||||
\(803\) | 96.3583 | 0.119998 | ||||||||
\(804\) | 111.043i | 0.138113i | ||||||||
\(805\) | 71.3735i | 0.0886627i | ||||||||
\(806\) | 130.911i | 0.162420i | ||||||||
\(807\) | 813.338i | 1.00785i | ||||||||
\(808\) | −279.046 | −0.345354 | ||||||||
\(809\) | − | 1246.53i | − | 1.54083i | −0.637545 | − | 0.770413i | \(-0.720050\pi\) | ||
0.637545 | − | 0.770413i | \(-0.279950\pi\) | |||||||
\(810\) | − | 98.5839i | − | 0.121709i | ||||||
\(811\) | − | 468.351i | − | 0.577499i | −0.957405 | − | 0.288749i | \(-0.906761\pi\) | ||
0.957405 | − | 0.288749i | \(-0.0932394\pi\) | |||||||
\(812\) | 378.064 | 0.465596 | ||||||||
\(813\) | 321.101 | 0.394958 | ||||||||
\(814\) | − | 329.799i | − | 0.405158i | ||||||
\(815\) | 896.356 | 1.09982 | ||||||||
\(816\) | 61.1631 | 0.0749548 | ||||||||
\(817\) | 2377.52i | 2.91006i | ||||||||
\(818\) | −53.2049 | −0.0650427 | ||||||||
\(819\) | 434.475i | 0.530494i | ||||||||
\(820\) | −482.933 | −0.588942 | ||||||||
\(821\) | 77.0645i | 0.0938666i | 0.998898 | + | 0.0469333i | \(0.0149448\pi\) | ||||
−0.998898 | + | 0.0469333i | \(0.985055\pi\) | |||||||
\(822\) | − | 5.46065i | − | 0.00664313i | ||||||
\(823\) | 332.546i | 0.404066i | 0.979379 | + | 0.202033i | \(0.0647548\pi\) | ||||
−0.979379 | + | 0.202033i | \(0.935245\pi\) | |||||||
\(824\) | 19.9512 | 0.0242126 | ||||||||
\(825\) | 242.707i | 0.294190i | ||||||||
\(826\) | 506.845 | + | 353.310i | 0.613613 | + | 0.427736i | ||||
\(827\) | −1240.44 | −1.49993 | −0.749964 | − | 0.661478i | \(-0.769929\pi\) | ||||
−0.749964 | + | 0.661478i | \(0.769929\pi\) | |||||||
\(828\) | − | 7.46680i | − | 0.00901787i | ||||||
\(829\) | 228.732 | 0.275913 | 0.137957 | − | 0.990438i | \(-0.455947\pi\) | ||||
0.137957 | + | 0.990438i | \(0.455947\pi\) | |||||||
\(830\) | −1657.68 | −1.99720 | ||||||||
\(831\) | 814.994 | 0.980739 | ||||||||
\(832\) | − | 156.469i | − | 0.188064i | ||||||
\(833\) | 51.4591 | 0.0617756 | ||||||||
\(834\) | 278.727i | 0.334205i | ||||||||
\(835\) | 81.6657 | 0.0978032 | ||||||||
\(836\) | 236.064i | 0.282373i | ||||||||
\(837\) | 24.5926i | 0.0293818i | ||||||||
\(838\) | −577.857 | −0.689567 | ||||||||
\(839\) | 752.073i | 0.896392i | 0.893935 | + | 0.448196i | \(0.147933\pi\) | ||||
−0.893935 | + | 0.448196i | \(0.852067\pi\) | |||||||
\(840\) | 280.970i | 0.334488i | ||||||||
\(841\) | −189.281 | −0.225067 | ||||||||
\(842\) | 912.400 | 1.08361 | ||||||||
\(843\) | −192.286 | −0.228098 | ||||||||
\(844\) | 725.925i | 0.860101i | ||||||||
\(845\) | −1653.97 | −1.95736 | ||||||||
\(846\) | −146.317 | −0.172952 | ||||||||
\(847\) | 777.224 | 0.917620 | ||||||||
\(848\) | −176.116 | −0.207684 | ||||||||
\(849\) | − | 141.699i | − | 0.166902i | ||||||
\(850\) | − | 436.877i | − | 0.513973i | ||||||
\(851\) | 72.4723 | 0.0851614 | ||||||||
\(852\) | 406.557 | 0.477179 | ||||||||
\(853\) | −713.731 | −0.836731 | −0.418365 | − | 0.908279i | \(-0.637397\pi\) | ||||
−0.418365 | + | 0.908279i | \(0.637397\pi\) | |||||||
\(854\) | −396.193 | −0.463926 | ||||||||
\(855\) | −684.895 | −0.801047 | ||||||||
\(856\) | 162.404i | 0.189725i | ||||||||
\(857\) | − | 572.158i | − | 0.667629i | −0.942639 | − | 0.333815i | \(-0.891664\pi\) | ||
0.942639 | − | 0.333815i | \(-0.108336\pi\) | |||||||
\(858\) | 191.849i | 0.223600i | ||||||||
\(859\) | − | 604.917i | − | 0.704211i | −0.935960 | − | 0.352105i | \(-0.885466\pi\) | ||
0.935960 | − | 0.352105i | \(-0.114534\pi\) | |||||||
\(860\) | 1249.53i | 1.45295i | ||||||||
\(861\) | 399.828 | 0.464377 | ||||||||
\(862\) | 435.825 | 0.505598 | ||||||||
\(863\) | 588.590i | 0.682028i | 0.940058 | + | 0.341014i | \(0.110770\pi\) | ||||
−0.940058 | + | 0.341014i | \(0.889230\pi\) | |||||||
\(864\) | − | 29.3939i | − | 0.0340207i | ||||||
\(865\) | 533.987i | 0.617326i | ||||||||
\(866\) | 1109.55i | 1.28124i | ||||||||
\(867\) | −365.574 | −0.421654 | ||||||||
\(868\) | − | 70.0902i | − | 0.0807491i | ||||||
\(869\) | 448.978i | 0.516660i | ||||||||
\(870\) | 484.344i | 0.556718i | ||||||||
\(871\) | 626.956 | 0.719812 | ||||||||
\(872\) | 392.082 | 0.449635 | ||||||||
\(873\) | 292.395i | 0.334931i | ||||||||
\(874\) | −51.8743 | −0.0593528 | ||||||||
\(875\) | 573.100 | 0.654971 | ||||||||
\(876\) | 83.3555i | 0.0951547i | ||||||||
\(877\) | −1654.43 | −1.88646 | −0.943232 | − | 0.332136i | \(-0.892231\pi\) | ||||
−0.943232 | + | 0.332136i | \(0.892231\pi\) | |||||||
\(878\) | 512.296i | 0.583481i | ||||||||
\(879\) | −363.376 | −0.413398 | ||||||||
\(880\) | 124.066i | 0.140984i | ||||||||
\(881\) | 82.6260i | 0.0937866i | 0.998900 | + | 0.0468933i | \(0.0149321\pi\) | ||||
−0.998900 | + | 0.0468933i | \(0.985068\pi\) | |||||||
\(882\) | − | 24.7303i | − | 0.0280389i | ||||||
\(883\) | −1094.98 | −1.24007 | −0.620035 | − | 0.784574i | \(-0.712882\pi\) | ||||
−0.620035 | + | 0.784574i | \(0.712882\pi\) | |||||||
\(884\) | − | 345.332i | − | 0.390647i | ||||||
\(885\) | −452.632 | + | 649.328i | −0.511448 | + | 0.733704i | ||||
\(886\) | 69.6825 | 0.0786484 | ||||||||
\(887\) | − | 91.1653i | − | 0.102779i | −0.998679 | − | 0.0513897i | \(-0.983635\pi\) | ||
0.998679 | − | 0.0513897i | \(-0.0163651\pi\) | |||||||
\(888\) | 285.295 | 0.321278 | ||||||||
\(889\) | −1410.22 | −1.58630 | ||||||||
\(890\) | 729.462 | 0.819620 | ||||||||
\(891\) | 36.0402i | 0.0404492i | ||||||||
\(892\) | 138.040 | 0.154753 | ||||||||
\(893\) | 1016.51i | 1.13831i | ||||||||
\(894\) | 141.014 | 0.157734 | ||||||||
\(895\) | − | 1177.99i | − | 1.31619i | ||||||
\(896\) | 83.7742i | 0.0934980i | ||||||||
\(897\) | −42.1582 | −0.0469991 | ||||||||
\(898\) | − | 544.047i | − | 0.605843i | ||||||
\(899\) | − | 120.824i | − | 0.134398i | ||||||
\(900\) | −209.955 | −0.233284 | ||||||||
\(901\) | −388.694 | −0.431403 | ||||||||
\(902\) | 176.550 | 0.195732 | ||||||||
\(903\) | − | 1034.51i | − | 1.14564i | ||||||
\(904\) | −593.742 | −0.656794 | ||||||||
\(905\) | −628.900 | −0.694917 | ||||||||
\(906\) | 61.2085 | 0.0675590 | ||||||||
\(907\) | −926.857 | −1.02189 | −0.510947 | − | 0.859612i | \(-0.670705\pi\) | ||||
−0.510947 | + | 0.859612i | \(0.670705\pi\) | |||||||
\(908\) | − | 269.231i | − | 0.296510i | ||||||
\(909\) | 295.973i | 0.325603i | ||||||||
\(910\) | 1586.38 | 1.74327 | ||||||||
\(911\) | 118.777 | 0.130380 | 0.0651902 | − | 0.997873i | \(-0.479235\pi\) | ||||
0.0651902 | + | 0.997873i | \(0.479235\pi\) | |||||||
\(912\) | −204.209 | −0.223913 | ||||||||
\(913\) | 606.012 | 0.663759 | ||||||||
\(914\) | 588.603 | 0.643985 | ||||||||
\(915\) | − | 507.570i | − | 0.554721i | ||||||
\(916\) | − | 642.393i | − | 0.701303i | ||||||
\(917\) | 1741.77i | 1.89942i | ||||||||
\(918\) | − | 64.8732i | − | 0.0706680i | ||||||
\(919\) | 1249.99i | 1.36016i | 0.733137 | + | 0.680081i | \(0.238056\pi\) | ||||
−0.733137 | + | 0.680081i | \(0.761944\pi\) | |||||||
\(920\) | −27.2632 | −0.0296339 | ||||||||
\(921\) | −417.465 | −0.453274 | ||||||||
\(922\) | 315.038i | 0.341689i | ||||||||
\(923\) | − | 2295.46i | − | 2.48695i | ||||||
\(924\) | − | 102.717i | − | 0.111165i | ||||||
\(925\) | − | 2037.81i | − | 2.20304i | ||||||
\(926\) | 205.484 | 0.221905 | ||||||||
\(927\) | − | 21.1614i | − | 0.0228279i | ||||||
\(928\) | 144.413i | 0.155617i | ||||||||
\(929\) | 1432.06i | 1.54151i | 0.637133 | + | 0.770754i | \(0.280120\pi\) | ||||
−0.637133 | + | 0.770754i | \(0.719880\pi\) | |||||||
\(930\) | 89.7938 | 0.0965525 | ||||||||
\(931\) | −171.810 | −0.184543 | ||||||||
\(932\) | 282.435i | 0.303042i | ||||||||
\(933\) | −7.80259 | −0.00836291 | ||||||||
\(934\) | −548.580 | −0.587345 | ||||||||
\(935\) | 273.818i | 0.292854i | ||||||||
\(936\) | −165.960 | −0.177308 | ||||||||
\(937\) | − | 331.956i | − | 0.354276i | −0.984186 | − | 0.177138i | \(-0.943316\pi\) | ||
0.984186 | − | 0.177138i | \(-0.0566838\pi\) | |||||||
\(938\) | −335.675 | −0.357862 | ||||||||
\(939\) | 848.440i | 0.903557i | ||||||||
\(940\) | 534.241i | 0.568342i | ||||||||
\(941\) | − | 1114.80i | − | 1.18470i | −0.805682 | − | 0.592349i | \(-0.798201\pi\) | ||
0.805682 | − | 0.592349i | \(-0.201799\pi\) | |||||||
\(942\) | −280.302 | −0.297561 | ||||||||
\(943\) | 38.7964i | 0.0411414i | ||||||||
\(944\) | −134.957 | + | 193.604i | −0.142963 | + | 0.205089i | ||||
\(945\) | 298.013 | 0.315358 | ||||||||
\(946\) | − | 456.804i | − | 0.482879i | ||||||
\(947\) | −1671.37 | −1.76491 | −0.882457 | − | 0.470393i | \(-0.844112\pi\) | ||||
−0.882457 | + | 0.470393i | \(0.844112\pi\) | |||||||
\(948\) | −388.392 | −0.409696 | ||||||||
\(949\) | 470.633 | 0.495925 | ||||||||
\(950\) | 1458.63i | 1.53540i | ||||||||
\(951\) | 865.676 | 0.910280 | ||||||||
\(952\) | 184.892i | 0.194215i | ||||||||
\(953\) | 212.089 | 0.222549 | 0.111275 | − | 0.993790i | \(-0.464507\pi\) | ||||
0.111275 | + | 0.993790i | \(0.464507\pi\) | |||||||
\(954\) | 186.799i | 0.195806i | ||||||||
\(955\) | − | 105.334i | − | 0.110298i | ||||||
\(956\) | −85.7026 | −0.0896471 | ||||||||
\(957\) | − | 177.066i | − | 0.185022i | ||||||
\(958\) | 1028.64i | 1.07374i | ||||||||
\(959\) | 16.5072 | 0.0172130 | ||||||||
\(960\) | −107.325 | −0.111796 | ||||||||
\(961\) | 938.600 | 0.976691 | ||||||||
\(962\) | − | 1610.80i | − | 1.67443i | ||||||
\(963\) | 172.256 | 0.178874 | ||||||||
\(964\) | −335.242 | −0.347761 | ||||||||
\(965\) | 1678.19 | 1.73906 | ||||||||
\(966\) | 22.5717 | 0.0233661 | ||||||||
\(967\) | − | 1471.95i | − | 1.52218i | −0.648648 | − | 0.761088i | \(-0.724665\pi\) | ||
0.648648 | − | 0.761088i | \(-0.275335\pi\) | |||||||
\(968\) | 296.884i | 0.306698i | ||||||||
\(969\) | −450.696 | −0.465114 | ||||||||
\(970\) | 1067.61 | 1.10063 | ||||||||
\(971\) | −594.572 | −0.612330 | −0.306165 | − | 0.951979i | \(-0.599046\pi\) | ||||
−0.306165 | + | 0.951979i | \(0.599046\pi\) | |||||||
\(972\) | −31.1769 | −0.0320750 | ||||||||
\(973\) | −842.574 | −0.865955 | ||||||||
\(974\) | 695.208i | 0.713766i | ||||||||
\(975\) | 1185.43i | 1.21582i | ||||||||
\(976\) | − | 151.338i | − | 0.155059i | ||||||
\(977\) | − | 370.295i | − | 0.379012i | −0.981880 | − | 0.189506i | \(-0.939311\pi\) | ||
0.981880 | − | 0.189506i | \(-0.0606887\pi\) | |||||||
\(978\) | − | 283.470i | − | 0.289847i | ||||||
\(979\) | −266.676 | −0.272396 | ||||||||
\(980\) | −90.2967 | −0.0921395 | ||||||||
\(981\) | − | 415.865i | − | 0.423920i | ||||||
\(982\) | − | 1027.24i | − | 1.04607i | ||||||
\(983\) | 632.522i | 0.643461i | 0.946831 | + | 0.321730i | \(0.104264\pi\) | ||||
−0.946831 | + | 0.321730i | \(0.895736\pi\) | |||||||
\(984\) | 152.726i | 0.155210i | ||||||||
\(985\) | 2055.10 | 2.08639 | ||||||||
\(986\) | 318.723i | 0.323249i | ||||||||
\(987\) | − | 442.308i | − | 0.448133i | ||||||
\(988\) | 1152.98i | 1.16699i | ||||||||
\(989\) | 100.381 | 0.101498 | ||||||||
\(990\) | 131.592 | 0.132921 | ||||||||
\(991\) | − | 897.086i | − | 0.905233i | −0.891705 | − | 0.452616i | \(-0.850491\pi\) | ||
0.891705 | − | 0.452616i | \(-0.149509\pi\) | |||||||
\(992\) | 26.7730 | 0.0269889 | ||||||||
\(993\) | −649.721 | −0.654301 | ||||||||
\(994\) | 1229.00i | 1.23642i | ||||||||
\(995\) | −1018.13 | −1.02325 | ||||||||
\(996\) | 524.236i | 0.526341i | ||||||||
\(997\) | −178.238 | −0.178774 | −0.0893871 | − | 0.995997i | \(-0.528491\pi\) | ||||
−0.0893871 | + | 0.995997i | \(0.528491\pi\) | |||||||
\(998\) | − | 879.068i | − | 0.880829i | ||||||
\(999\) | − | 302.601i | − | 0.302904i |
(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 | 354.3.d.a.235.10 | ✓ | 20 | |
3.2 | odd | 2 | 1062.3.d.f.235.11 | 20 | |||
59.58 | odd | 2 | inner | 354.3.d.a.235.20 | yes | 20 | |
177.176 | even | 2 | 1062.3.d.f.235.1 | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
354.3.d.a.235.10 | ✓ | 20 | 1.1 | even | 1 | trivial | |
354.3.d.a.235.20 | yes | 20 | 59.58 | odd | 2 | inner | |
1062.3.d.f.235.1 | 20 | 177.176 | even | 2 | |||
1062.3.d.f.235.11 | 20 | 3.2 | odd | 2 |