Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [950,3,Mod(949,950)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(950, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("950.949");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 950 = 2 \cdot 5^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 950.d (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(25.8856251142\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 949.6 | ||
Character | \(\chi\) | \(=\) | 950.949 |
Dual form | 950.3.d.b.949.7 |
$q$-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 \(\left(\mathbb{Z}/950\mathbb{Z}\right)^\times\).
\(n\) | \(77\) | \(401\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.41421 | −0.707107 | ||||||||
\(3\) | 1.89288 | 0.630961 | 0.315481 | − | 0.948932i | \(-0.397834\pi\) | ||||
0.315481 | + | 0.948932i | \(0.397834\pi\) | |||||||
\(4\) | 2.00000 | 0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −2.67694 | −0.446157 | ||||||||
\(7\) | 1.68650i | 0.240928i | 0.992718 | + | 0.120464i | \(0.0384382\pi\) | ||||
−0.992718 | + | 0.120464i | \(0.961562\pi\) | |||||||
\(8\) | −2.82843 | −0.353553 | ||||||||
\(9\) | −5.41699 | −0.601888 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.04411 | 0.0949193 | 0.0474596 | − | 0.998873i | \(-0.484887\pi\) | ||||
0.0474596 | + | 0.998873i | \(0.484887\pi\) | |||||||
\(12\) | 3.78577 | 0.315481 | ||||||||
\(13\) | −6.02294 | −0.463303 | −0.231652 | − | 0.972799i | \(-0.574413\pi\) | ||||
−0.231652 | + | 0.972799i | \(0.574413\pi\) | |||||||
\(14\) | − | 2.38506i | − | 0.170362i | ||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 4.00000 | 0.250000 | ||||||||
\(17\) | − | 21.6652i | − | 1.27442i | −0.770689 | − | 0.637212i | \(-0.780088\pi\) | ||
0.770689 | − | 0.637212i | \(-0.219912\pi\) | |||||||
\(18\) | 7.66078 | 0.425599 | ||||||||
\(19\) | 17.3019 | + | 7.85143i | 0.910625 | + | 0.413233i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 3.19234i | 0.152016i | ||||||||
\(22\) | −1.47660 | −0.0671181 | ||||||||
\(23\) | 39.8186i | 1.73124i | 0.500698 | + | 0.865622i | \(0.333077\pi\) | ||||
−0.500698 | + | 0.865622i | \(0.666923\pi\) | |||||||
\(24\) | −5.35389 | −0.223079 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 8.51772 | 0.327605 | ||||||||
\(27\) | −27.2897 | −1.01073 | ||||||||
\(28\) | 3.37299i | 0.120464i | ||||||||
\(29\) | 0.278403i | 0.00960011i | 0.999988 | + | 0.00480006i | \(0.00152791\pi\) | ||||
−0.999988 | + | 0.00480006i | \(0.998472\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 19.8410i | 0.640034i | 0.947412 | + | 0.320017i | \(0.103689\pi\) | ||||
−0.947412 | + | 0.320017i | \(0.896311\pi\) | |||||||
\(32\) | −5.65685 | −0.176777 | ||||||||
\(33\) | 1.97638 | 0.0598904 | ||||||||
\(34\) | 30.6392i | 0.901154i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −10.8340 | −0.300944 | ||||||||
\(37\) | −68.3424 | −1.84709 | −0.923546 | − | 0.383488i | \(-0.874723\pi\) | ||||
−0.923546 | + | 0.383488i | \(0.874723\pi\) | |||||||
\(38\) | −24.4686 | − | 11.1036i | −0.643909 | − | 0.292200i | ||||
\(39\) | −11.4007 | −0.292326 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.84932i | 0.0938858i | 0.998898 | + | 0.0469429i | \(0.0149479\pi\) | ||||
−0.998898 | + | 0.0469429i | \(0.985052\pi\) | |||||||
\(42\) | − | 4.51465i | − | 0.107492i | ||||||
\(43\) | 65.0642i | 1.51312i | 0.653924 | + | 0.756561i | \(0.273122\pi\) | ||||
−0.653924 | + | 0.756561i | \(0.726878\pi\) | |||||||
\(44\) | 2.08822 | 0.0474596 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | − | 56.3120i | − | 1.22417i | ||||||
\(47\) | − | 9.61045i | − | 0.204478i | −0.994760 | − | 0.102239i | \(-0.967399\pi\) | ||
0.994760 | − | 0.102239i | \(-0.0326006\pi\) | |||||||
\(48\) | 7.57154 | 0.157740 | ||||||||
\(49\) | 46.1557 | 0.941954 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | − | 41.0097i | − | 0.804112i | ||||||
\(52\) | −12.0459 | −0.231652 | ||||||||
\(53\) | −62.0602 | −1.17095 | −0.585474 | − | 0.810691i | \(-0.699091\pi\) | ||||
−0.585474 | + | 0.810691i | \(0.699091\pi\) | |||||||
\(54\) | 38.5935 | 0.714694 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | − | 4.77013i | − | 0.0851809i | ||||||
\(57\) | 32.7505 | + | 14.8618i | 0.574569 | + | 0.260734i | ||||
\(58\) | − | 0.393722i | − | 0.00678830i | ||||||
\(59\) | 94.0807i | 1.59459i | 0.603591 | + | 0.797294i | \(0.293736\pi\) | ||||
−0.603591 | + | 0.797294i | \(0.706264\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −19.4070 | −0.318148 | −0.159074 | − | 0.987267i | \(-0.550851\pi\) | ||||
−0.159074 | + | 0.987267i | \(0.550851\pi\) | |||||||
\(62\) | − | 28.0595i | − | 0.452572i | ||||||
\(63\) | − | 9.13572i | − | 0.145012i | ||||||
\(64\) | 8.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −2.79503 | −0.0423489 | ||||||||
\(67\) | −62.2388 | −0.928937 | −0.464469 | − | 0.885590i | \(-0.653755\pi\) | ||||
−0.464469 | + | 0.885590i | \(0.653755\pi\) | |||||||
\(68\) | − | 43.3304i | − | 0.637212i | ||||||
\(69\) | 75.3720i | 1.09235i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 41.4101i | − | 0.583241i | −0.956534 | − | 0.291621i | \(-0.905805\pi\) | ||
0.956534 | − | 0.291621i | \(-0.0941945\pi\) | |||||||
\(72\) | 15.3216 | 0.212799 | ||||||||
\(73\) | − | 3.25235i | − | 0.0445527i | −0.999752 | − | 0.0222763i | \(-0.992909\pi\) | ||
0.999752 | − | 0.0222763i | \(-0.00709137\pi\) | |||||||
\(74\) | 96.6507 | 1.30609 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 34.6038 | + | 15.7029i | 0.455313 | + | 0.206617i | ||||
\(77\) | 1.76089i | 0.0228687i | ||||||||
\(78\) | 16.1231 | 0.206706 | ||||||||
\(79\) | 84.1379i | 1.06504i | 0.846418 | + | 0.532519i | \(0.178754\pi\) | ||||
−0.846418 | + | 0.532519i | \(0.821246\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −2.90334 | −0.0358437 | ||||||||
\(82\) | − | 5.44376i | − | 0.0663873i | ||||||
\(83\) | 5.58177i | 0.0672503i | 0.999435 | + | 0.0336251i | \(0.0107052\pi\) | ||||
−0.999435 | + | 0.0336251i | \(0.989295\pi\) | |||||||
\(84\) | 6.38468i | 0.0760081i | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | − | 92.0147i | − | 1.06994i | ||||||
\(87\) | 0.526985i | 0.00605730i | ||||||||
\(88\) | −2.95319 | −0.0335590 | ||||||||
\(89\) | − | 84.3407i | − | 0.947648i | −0.880619 | − | 0.473824i | \(-0.842873\pi\) | ||
0.880619 | − | 0.473824i | \(-0.157127\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 10.1577i | − | 0.111623i | ||||||
\(92\) | 79.6372i | 0.865622i | ||||||||
\(93\) | 37.5568i | 0.403837i | ||||||||
\(94\) | 13.5912i | 0.144588i | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −10.7078 | −0.111539 | ||||||||
\(97\) | 1.89498 | 0.0195359 | 0.00976795 | − | 0.999952i | \(-0.496891\pi\) | ||||
0.00976795 | + | 0.999952i | \(0.496891\pi\) | |||||||
\(98\) | −65.2741 | −0.666062 | ||||||||
\(99\) | −5.65594 | −0.0571307 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 15.0979 | 0.149484 | 0.0747418 | − | 0.997203i | \(-0.476187\pi\) | ||||
0.0747418 | + | 0.997203i | \(0.476187\pi\) | |||||||
\(102\) | 57.9965i | 0.568593i | ||||||||
\(103\) | −143.352 | −1.39177 | −0.695883 | − | 0.718155i | \(-0.744987\pi\) | ||||
−0.695883 | + | 0.718155i | \(0.744987\pi\) | |||||||
\(104\) | 17.0354 | 0.163802 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 87.7664 | 0.827985 | ||||||||
\(107\) | −118.658 | −1.10895 | −0.554475 | − | 0.832200i | \(-0.687081\pi\) | ||||
−0.554475 | + | 0.832200i | \(0.687081\pi\) | |||||||
\(108\) | −54.5794 | −0.505365 | ||||||||
\(109\) | 62.2344i | 0.570957i | 0.958385 | + | 0.285479i | \(0.0921526\pi\) | ||||
−0.958385 | + | 0.285479i | \(0.907847\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −129.364 | −1.16544 | ||||||||
\(112\) | 6.74598i | 0.0602320i | ||||||||
\(113\) | 88.8122 | 0.785949 | 0.392974 | − | 0.919549i | \(-0.371446\pi\) | ||||
0.392974 | + | 0.919549i | \(0.371446\pi\) | |||||||
\(114\) | −46.3161 | − | 21.0178i | −0.406282 | − | 0.184367i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0.556806i | 0.00480006i | ||||||||
\(117\) | 32.6262 | 0.278856 | ||||||||
\(118\) | − | 133.050i | − | 1.12754i | ||||||
\(119\) | 36.5383 | 0.307044 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −119.910 | −0.990990 | ||||||||
\(122\) | 27.4456 | 0.224964 | ||||||||
\(123\) | 7.28632i | 0.0592383i | ||||||||
\(124\) | 39.6821i | 0.320017i | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 12.9199i | 0.102539i | ||||||||
\(127\) | −9.31099 | −0.0733149 | −0.0366574 | − | 0.999328i | \(-0.511671\pi\) | ||||
−0.0366574 | + | 0.999328i | \(0.511671\pi\) | |||||||
\(128\) | −11.3137 | −0.0883883 | ||||||||
\(129\) | 123.159i | 0.954721i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 147.708 | 1.12754 | 0.563769 | − | 0.825932i | \(-0.309351\pi\) | ||||
0.563769 | + | 0.825932i | \(0.309351\pi\) | |||||||
\(132\) | 3.95277 | 0.0299452 | ||||||||
\(133\) | −13.2414 | + | 29.1795i | −0.0995594 | + | 0.219395i | ||||
\(134\) | 88.0189 | 0.656858 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 61.2785i | 0.450577i | ||||||||
\(137\) | 147.080i | 1.07358i | 0.843716 | + | 0.536789i | \(0.180363\pi\) | ||||
−0.843716 | + | 0.536789i | \(0.819637\pi\) | |||||||
\(138\) | − | 106.592i | − | 0.772407i | ||||||
\(139\) | 78.4626 | 0.564479 | 0.282240 | − | 0.959344i | \(-0.408923\pi\) | ||||
0.282240 | + | 0.959344i | \(0.408923\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − | 18.1915i | − | 0.129018i | ||||||
\(142\) | 58.5628i | 0.412414i | ||||||||
\(143\) | −6.28862 | −0.0439764 | ||||||||
\(144\) | −21.6680 | −0.150472 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 4.59951i | 0.0315035i | ||||||||
\(147\) | 87.3675 | 0.594337 | ||||||||
\(148\) | −136.685 | −0.923546 | ||||||||
\(149\) | −135.184 | −0.907273 | −0.453637 | − | 0.891187i | \(-0.649874\pi\) | ||||
−0.453637 | + | 0.891187i | \(0.649874\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 168.771i | 1.11769i | 0.829272 | + | 0.558846i | \(0.188756\pi\) | ||||
−0.829272 | + | 0.558846i | \(0.811244\pi\) | |||||||
\(152\) | −48.9371 | − | 22.2072i | −0.321955 | − | 0.146100i | ||||
\(153\) | 117.360i | 0.767060i | ||||||||
\(154\) | − | 2.49027i | − | 0.0161706i | ||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −22.8015 | −0.146163 | ||||||||
\(157\) | 4.58432i | 0.0291995i | 0.999893 | + | 0.0145998i | \(0.00464741\pi\) | ||||
−0.999893 | + | 0.0145998i | \(0.995353\pi\) | |||||||
\(158\) | − | 118.989i | − | 0.753095i | ||||||
\(159\) | −117.473 | −0.738823 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −67.1539 | −0.417105 | ||||||||
\(162\) | 4.10594 | 0.0253453 | ||||||||
\(163\) | 187.644i | 1.15119i | 0.817734 | + | 0.575596i | \(0.195230\pi\) | ||||
−0.817734 | + | 0.575596i | \(0.804770\pi\) | |||||||
\(164\) | 7.69864i | 0.0469429i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | − | 7.89382i | − | 0.0475531i | ||||||
\(167\) | −108.235 | −0.648112 | −0.324056 | − | 0.946038i | \(-0.605047\pi\) | ||||
−0.324056 | + | 0.946038i | \(0.605047\pi\) | |||||||
\(168\) | − | 9.02930i | − | 0.0537458i | ||||||
\(169\) | −132.724 | −0.785350 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −93.7241 | − | 42.5311i | −0.548094 | − | 0.248720i | ||||
\(172\) | 130.128i | 0.756561i | ||||||||
\(173\) | 102.097 | 0.590155 | 0.295078 | − | 0.955473i | \(-0.404655\pi\) | ||||
0.295078 | + | 0.955473i | \(0.404655\pi\) | |||||||
\(174\) | − | 0.745270i | − | 0.00428316i | ||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 4.17645 | 0.0237298 | ||||||||
\(177\) | 178.084i | 1.00612i | ||||||||
\(178\) | 119.276i | 0.670089i | ||||||||
\(179\) | 121.752i | 0.680181i | 0.940393 | + | 0.340090i | \(0.110458\pi\) | ||||
−0.940393 | + | 0.340090i | \(0.889542\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 40.3187i | 0.222755i | 0.993778 | + | 0.111378i | \(0.0355263\pi\) | ||||
−0.993778 | + | 0.111378i | \(0.964474\pi\) | |||||||
\(182\) | 14.3651i | 0.0789291i | ||||||||
\(183\) | −36.7352 | −0.200739 | ||||||||
\(184\) | − | 112.624i | − | 0.612087i | ||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | − | 53.1133i | − | 0.285556i | ||||||
\(187\) | − | 22.6209i | − | 0.120967i | ||||||
\(188\) | − | 19.2209i | − | 0.102239i | ||||||
\(189\) | − | 46.0239i | − | 0.243513i | ||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −226.244 | −1.18452 | −0.592261 | − | 0.805746i | \(-0.701765\pi\) | ||||
−0.592261 | + | 0.805746i | \(0.701765\pi\) | |||||||
\(192\) | 15.1431 | 0.0788702 | ||||||||
\(193\) | 6.91887 | 0.0358491 | 0.0179245 | − | 0.999839i | \(-0.494294\pi\) | ||||
0.0179245 | + | 0.999839i | \(0.494294\pi\) | |||||||
\(194\) | −2.67991 | −0.0138140 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 92.3115 | 0.470977 | ||||||||
\(197\) | − | 235.124i | − | 1.19352i | −0.802419 | − | 0.596762i | \(-0.796454\pi\) | ||
0.802419 | − | 0.596762i | \(-0.203546\pi\) | |||||||
\(198\) | 7.99871 | 0.0403975 | ||||||||
\(199\) | −39.9542 | −0.200775 | −0.100388 | − | 0.994948i | \(-0.532008\pi\) | ||||
−0.100388 | + | 0.994948i | \(0.532008\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −117.811 | −0.586124 | ||||||||
\(202\) | −21.3516 | −0.105701 | ||||||||
\(203\) | −0.469526 | −0.00231293 | ||||||||
\(204\) | − | 82.0195i | − | 0.402056i | ||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 202.730 | 0.984128 | ||||||||
\(207\) | − | 215.697i | − | 1.04201i | ||||||
\(208\) | −24.0918 | −0.115826 | ||||||||
\(209\) | 18.0651 | + | 8.19777i | 0.0864359 | + | 0.0392238i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 244.243i | − | 1.15755i | −0.815487 | − | 0.578776i | \(-0.803531\pi\) | ||
0.815487 | − | 0.578776i | \(-0.196469\pi\) | |||||||
\(212\) | −124.120 | −0.585474 | ||||||||
\(213\) | − | 78.3846i | − | 0.368003i | ||||||
\(214\) | 167.807 | 0.784146 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 77.1869 | 0.357347 | ||||||||
\(217\) | −33.4618 | −0.154202 | ||||||||
\(218\) | − | 88.0127i | − | 0.403728i | ||||||
\(219\) | − | 6.15632i | − | 0.0281110i | ||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 130.488i | 0.590444i | ||||||||
\(222\) | 182.949 | 0.824093 | ||||||||
\(223\) | 336.370 | 1.50839 | 0.754193 | − | 0.656653i | \(-0.228028\pi\) | ||||
0.754193 | + | 0.656653i | \(0.228028\pi\) | |||||||
\(224\) | − | 9.54026i | − | 0.0425904i | ||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −125.599 | −0.555750 | ||||||||
\(227\) | 288.533 | 1.27107 | 0.635536 | − | 0.772071i | \(-0.280779\pi\) | ||||
0.635536 | + | 0.772071i | \(0.280779\pi\) | |||||||
\(228\) | 65.5009 | + | 29.7237i | 0.287285 | + | 0.130367i | ||||
\(229\) | −412.489 | −1.80126 | −0.900632 | − | 0.434583i | \(-0.856896\pi\) | ||||
−0.900632 | + | 0.434583i | \(0.856896\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 3.33316i | 0.0144293i | ||||||||
\(232\) | − | 0.787443i | − | 0.00339415i | ||||||
\(233\) | 33.7493i | 0.144847i | 0.997374 | + | 0.0724234i | \(0.0230733\pi\) | ||||
−0.997374 | + | 0.0724234i | \(0.976927\pi\) | |||||||
\(234\) | −46.1404 | −0.197181 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 188.161i | 0.797294i | ||||||||
\(237\) | 159.263i | 0.671998i | ||||||||
\(238\) | −51.6729 | −0.217113 | ||||||||
\(239\) | 197.741 | 0.827368 | 0.413684 | − | 0.910421i | \(-0.364242\pi\) | ||||
0.413684 | + | 0.910421i | \(0.364242\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 348.779i | 1.44722i | 0.690211 | + | 0.723608i | \(0.257518\pi\) | ||||
−0.690211 | + | 0.723608i | \(0.742482\pi\) | |||||||
\(242\) | 169.578 | 0.700736 | ||||||||
\(243\) | 240.112 | 0.988113 | ||||||||
\(244\) | −38.8140 | −0.159074 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | − | 10.3044i | − | 0.0418878i | ||||||
\(247\) | −104.208 | − | 47.2887i | −0.421895 | − | 0.191452i | ||||
\(248\) | − | 56.1189i | − | 0.226286i | ||||||
\(249\) | 10.5657i | 0.0424323i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 70.8555 | 0.282293 | 0.141146 | − | 0.989989i | \(-0.454921\pi\) | ||||
0.141146 | + | 0.989989i | \(0.454921\pi\) | |||||||
\(252\) | − | 18.2714i | − | 0.0725058i | ||||||
\(253\) | 41.5751i | 0.164328i | ||||||||
\(254\) | 13.1677 | 0.0518414 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 16.0000 | 0.0625000 | ||||||||
\(257\) | 513.143 | 1.99667 | 0.998333 | − | 0.0577124i | \(-0.0183806\pi\) | ||||
0.998333 | + | 0.0577124i | \(0.0183806\pi\) | |||||||
\(258\) | − | 174.173i | − | 0.675090i | ||||||
\(259\) | − | 115.259i | − | 0.445016i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | − | 1.50811i | − | 0.00577819i | ||||||
\(262\) | −208.890 | −0.797290 | ||||||||
\(263\) | 39.7483i | 0.151134i | 0.997141 | + | 0.0755670i | \(0.0240767\pi\) | ||||
−0.997141 | + | 0.0755670i | \(0.975923\pi\) | |||||||
\(264\) | −5.59006 | −0.0211745 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 18.7262 | − | 41.2661i | 0.0703991 | − | 0.155136i | ||||
\(267\) | − | 159.647i | − | 0.597930i | ||||||
\(268\) | −124.478 | −0.464469 | ||||||||
\(269\) | − | 516.941i | − | 1.92172i | −0.277043 | − | 0.960858i | \(-0.589354\pi\) | ||
0.277043 | − | 0.960858i | \(-0.410646\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 147.956 | 0.545963 | 0.272982 | − | 0.962019i | \(-0.411990\pi\) | ||||
0.272982 | + | 0.962019i | \(0.411990\pi\) | |||||||
\(272\) | − | 86.6608i | − | 0.318606i | ||||||
\(273\) | − | 19.2273i | − | 0.0704296i | ||||||
\(274\) | − | 208.003i | − | 0.759135i | ||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 150.744i | 0.546174i | ||||||||
\(277\) | − | 400.546i | − | 1.44601i | −0.690840 | − | 0.723007i | \(-0.742759\pi\) | ||
0.690840 | − | 0.723007i | \(-0.257241\pi\) | |||||||
\(278\) | −110.963 | −0.399147 | ||||||||
\(279\) | − | 107.479i | − | 0.385228i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 251.143i | − | 0.893748i | −0.894597 | − | 0.446874i | \(-0.852537\pi\) | ||
0.894597 | − | 0.446874i | \(-0.147463\pi\) | |||||||
\(282\) | 25.7266i | 0.0912292i | ||||||||
\(283\) | 420.587i | 1.48617i | 0.669195 | + | 0.743087i | \(0.266639\pi\) | ||||
−0.669195 | + | 0.743087i | \(0.733361\pi\) | |||||||
\(284\) | − | 82.8203i | − | 0.291621i | ||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 8.89346 | 0.0310960 | ||||||||
\(287\) | −6.49186 | −0.0226197 | ||||||||
\(288\) | 30.6431 | 0.106400 | ||||||||
\(289\) | −180.381 | −0.624156 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 3.58698 | 0.0123264 | ||||||||
\(292\) | − | 6.50469i | − | 0.0222763i | ||||||
\(293\) | 335.367 | 1.14460 | 0.572299 | − | 0.820045i | \(-0.306052\pi\) | ||||
0.572299 | + | 0.820045i | \(0.306052\pi\) | |||||||
\(294\) | −123.556 | −0.420259 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 193.301 | 0.653046 | ||||||||
\(297\) | −28.4935 | −0.0959377 | ||||||||
\(298\) | 191.179 | 0.641539 | ||||||||
\(299\) | − | 239.825i | − | 0.802091i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −109.730 | −0.364553 | ||||||||
\(302\) | − | 238.679i | − | 0.790327i | ||||||
\(303\) | 28.5785 | 0.0943185 | ||||||||
\(304\) | 69.2075 | + | 31.4057i | 0.227656 | + | 0.103308i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | − | 165.972i | − | 0.542393i | ||||||
\(307\) | −311.594 | −1.01497 | −0.507483 | − | 0.861662i | \(-0.669424\pi\) | ||||
−0.507483 | + | 0.861662i | \(0.669424\pi\) | |||||||
\(308\) | 3.52178i | 0.0114343i | ||||||||
\(309\) | −271.349 | −0.878151 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 288.128 | 0.926457 | 0.463228 | − | 0.886239i | \(-0.346691\pi\) | ||||
0.463228 | + | 0.886239i | \(0.346691\pi\) | |||||||
\(312\) | 32.2461 | 0.103353 | ||||||||
\(313\) | − | 137.897i | − | 0.440567i | −0.975436 | − | 0.220284i | \(-0.929302\pi\) | ||
0.975436 | − | 0.220284i | \(-0.0706983\pi\) | |||||||
\(314\) | − | 6.48321i | − | 0.0206472i | ||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 168.276i | 0.532519i | ||||||||
\(317\) | 288.819 | 0.911101 | 0.455551 | − | 0.890210i | \(-0.349442\pi\) | ||||
0.455551 | + | 0.890210i | \(0.349442\pi\) | |||||||
\(318\) | 166.132 | 0.522426 | ||||||||
\(319\) | 0.290684i | 0.000911236i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −224.605 | −0.699705 | ||||||||
\(322\) | 94.9700 | 0.294938 | ||||||||
\(323\) | 170.103 | − | 374.849i | 0.526634 | − | 1.16052i | ||||
\(324\) | −5.80668 | −0.0179218 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | − | 265.369i | − | 0.814016i | ||||||
\(327\) | 117.802i | 0.360252i | ||||||||
\(328\) | − | 10.8875i | − | 0.0331937i | ||||||
\(329\) | 16.2080 | 0.0492644 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 114.877i | 0.347060i | 0.984829 | + | 0.173530i | \(0.0555173\pi\) | ||||
−0.984829 | + | 0.173530i | \(0.944483\pi\) | |||||||
\(332\) | 11.1635i | 0.0336251i | ||||||||
\(333\) | 370.210 | 1.11174 | ||||||||
\(334\) | 153.067 | 0.458284 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 12.7694i | 0.0380041i | ||||||||
\(337\) | −11.1235 | −0.0330075 | −0.0165038 | − | 0.999864i | \(-0.505254\pi\) | ||||
−0.0165038 | + | 0.999864i | \(0.505254\pi\) | |||||||
\(338\) | 187.700 | 0.555327 | ||||||||
\(339\) | 168.111 | 0.495903 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 20.7163i | 0.0607515i | ||||||||
\(342\) | 132.546 | + | 60.1481i | 0.387561 | + | 0.175872i | ||||
\(343\) | 160.480i | 0.467871i | ||||||||
\(344\) | − | 184.029i | − | 0.534969i | ||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −144.387 | −0.417303 | ||||||||
\(347\) | − | 258.149i | − | 0.743944i | −0.928244 | − | 0.371972i | \(-0.878682\pi\) | ||
0.928244 | − | 0.371972i | \(-0.121318\pi\) | |||||||
\(348\) | 1.05397i | 0.00302865i | ||||||||
\(349\) | 465.062 | 1.33256 | 0.666278 | − | 0.745703i | \(-0.267886\pi\) | ||||
0.666278 | + | 0.745703i | \(0.267886\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 164.364 | 0.468274 | ||||||||
\(352\) | −5.90639 | −0.0167795 | ||||||||
\(353\) | − | 506.379i | − | 1.43450i | −0.696815 | − | 0.717251i | \(-0.745400\pi\) | ||
0.696815 | − | 0.717251i | \(-0.254600\pi\) | |||||||
\(354\) | − | 251.849i | − | 0.711437i | ||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | − | 168.681i | − | 0.473824i | ||||||
\(357\) | 69.1627 | 0.193733 | ||||||||
\(358\) | − | 172.184i | − | 0.480960i | ||||||
\(359\) | 2.91049 | 0.00810722 | 0.00405361 | − | 0.999992i | \(-0.498710\pi\) | ||||
0.00405361 | + | 0.999992i | \(0.498710\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 237.710 | + | 271.689i | 0.658477 | + | 0.752601i | ||||
\(362\) | − | 57.0192i | − | 0.157512i | ||||||
\(363\) | −226.975 | −0.625277 | ||||||||
\(364\) | − | 20.3153i | − | 0.0558113i | ||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 51.9514 | 0.141944 | ||||||||
\(367\) | − | 382.586i | − | 1.04247i | −0.853414 | − | 0.521234i | \(-0.825472\pi\) | ||
0.853414 | − | 0.521234i | \(-0.174528\pi\) | |||||||
\(368\) | 159.274i | 0.432811i | ||||||||
\(369\) | − | 20.8517i | − | 0.0565087i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 104.664i | − | 0.282114i | ||||||
\(372\) | 75.1136i | 0.201918i | ||||||||
\(373\) | −394.786 | −1.05841 | −0.529204 | − | 0.848495i | \(-0.677509\pi\) | ||||
−0.529204 | + | 0.848495i | \(0.677509\pi\) | |||||||
\(374\) | 31.9908i | 0.0855368i | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 27.1825i | 0.0722938i | ||||||||
\(377\) | − | 1.67681i | − | 0.00444776i | ||||||
\(378\) | 65.0877i | 0.172190i | ||||||||
\(379\) | − | 614.957i | − | 1.62258i | −0.584645 | − | 0.811289i | \(-0.698766\pi\) | ||
0.584645 | − | 0.811289i | \(-0.301234\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −17.6246 | −0.0462589 | ||||||||
\(382\) | 319.957 | 0.837584 | ||||||||
\(383\) | −445.383 | −1.16288 | −0.581440 | − | 0.813589i | \(-0.697511\pi\) | ||||
−0.581440 | + | 0.813589i | \(0.697511\pi\) | |||||||
\(384\) | −21.4155 | −0.0557696 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −9.78477 | −0.0253491 | ||||||||
\(387\) | − | 352.452i | − | 0.910729i | ||||||
\(388\) | 3.78996 | 0.00976795 | ||||||||
\(389\) | −116.462 | −0.299387 | −0.149694 | − | 0.988732i | \(-0.547829\pi\) | ||||
−0.149694 | + | 0.988732i | \(0.547829\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 862.679 | 2.20634 | ||||||||
\(392\) | −130.548 | −0.333031 | ||||||||
\(393\) | 279.593 | 0.711433 | ||||||||
\(394\) | 332.516i | 0.843948i | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −11.3119 | −0.0285654 | ||||||||
\(397\) | 310.718i | 0.782665i | 0.920249 | + | 0.391332i | \(0.127986\pi\) | ||||
−0.920249 | + | 0.391332i | \(0.872014\pi\) | |||||||
\(398\) | 56.5038 | 0.141969 | ||||||||
\(399\) | −25.0644 | + | 55.2335i | −0.0628181 | + | 0.138430i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 462.347i | − | 1.15299i | −0.817102 | − | 0.576493i | \(-0.804421\pi\) | ||
0.817102 | − | 0.576493i | \(-0.195579\pi\) | |||||||
\(402\) | 166.610 | 0.414452 | ||||||||
\(403\) | − | 119.501i | − | 0.296530i | ||||||
\(404\) | 30.1957 | 0.0747418 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0.664010 | 0.00163549 | ||||||||
\(407\) | −71.3571 | −0.175325 | ||||||||
\(408\) | 115.993i | 0.284297i | ||||||||
\(409\) | − | 552.392i | − | 1.35059i | −0.737547 | − | 0.675296i | \(-0.764016\pi\) | ||
0.737547 | − | 0.675296i | \(-0.235984\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 278.406i | 0.677387i | ||||||||
\(412\) | −286.704 | −0.695883 | ||||||||
\(413\) | −158.667 | −0.384181 | ||||||||
\(414\) | 305.042i | 0.736816i | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 34.0709 | 0.0819012 | ||||||||
\(417\) | 148.521 | 0.356165 | ||||||||
\(418\) | −25.5479 | − | 11.5934i | −0.0611194 | − | 0.0277354i | ||||
\(419\) | 35.7864 | 0.0854090 | 0.0427045 | − | 0.999088i | \(-0.486403\pi\) | ||||
0.0427045 | + | 0.999088i | \(0.486403\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 669.640i | 1.59059i | 0.606221 | + | 0.795297i | \(0.292685\pi\) | ||||
−0.606221 | + | 0.795297i | \(0.707315\pi\) | |||||||
\(422\) | 345.412i | 0.818513i | ||||||||
\(423\) | 52.0597i | 0.123073i | ||||||||
\(424\) | 175.533 | 0.413992 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 110.853i | 0.260217i | ||||||||
\(427\) | − | 32.7298i | − | 0.0766506i | ||||||
\(428\) | −237.315 | −0.554475 | ||||||||
\(429\) | −11.9036 | −0.0277474 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 174.646i | − | 0.405212i | −0.979260 | − | 0.202606i | \(-0.935059\pi\) | ||
0.979260 | − | 0.202606i | \(-0.0649411\pi\) | |||||||
\(432\) | −109.159 | −0.252682 | ||||||||
\(433\) | −111.608 | −0.257755 | −0.128877 | − | 0.991661i | \(-0.541137\pi\) | ||||
−0.128877 | + | 0.991661i | \(0.541137\pi\) | |||||||
\(434\) | 47.3222 | 0.109037 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 124.469i | 0.285479i | ||||||||
\(437\) | −312.633 | + | 688.937i | −0.715408 | + | 1.57651i | ||||
\(438\) | 8.70634i | 0.0198775i | ||||||||
\(439\) | 93.1300i | 0.212141i | 0.994359 | + | 0.106071i | \(0.0338270\pi\) | ||||
−0.994359 | + | 0.106071i | \(0.966173\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −250.025 | −0.566950 | ||||||||
\(442\) | − | 184.538i | − | 0.417507i | ||||||
\(443\) | − | 796.123i | − | 1.79712i | −0.438854 | − | 0.898558i | \(-0.644616\pi\) | ||
0.438854 | − | 0.898558i | \(-0.355384\pi\) | |||||||
\(444\) | −258.729 | −0.582722 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −475.699 | −1.06659 | ||||||||
\(447\) | −255.887 | −0.572454 | ||||||||
\(448\) | 13.4920i | 0.0301160i | ||||||||
\(449\) | − | 186.109i | − | 0.414496i | −0.978288 | − | 0.207248i | \(-0.933549\pi\) | ||
0.978288 | − | 0.207248i | \(-0.0664508\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 4.01912i | 0.00891157i | ||||||||
\(452\) | 177.624 | 0.392974 | ||||||||
\(453\) | 319.465i | 0.705220i | ||||||||
\(454\) | −408.048 | −0.898784 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −92.6323 | − | 42.0357i | −0.203141 | − | 0.0921834i | ||||
\(457\) | 576.986i | 1.26255i | 0.775558 | + | 0.631276i | \(0.217468\pi\) | ||||
−0.775558 | + | 0.631276i | \(0.782532\pi\) | |||||||
\(458\) | 583.348 | 1.27369 | ||||||||
\(459\) | 591.237i | 1.28810i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 223.865 | 0.485608 | 0.242804 | − | 0.970075i | \(-0.421933\pi\) | ||||
0.242804 | + | 0.970075i | \(0.421933\pi\) | |||||||
\(462\) | − | 4.71380i | − | 0.0102030i | ||||||
\(463\) | 452.579i | 0.977492i | 0.872426 | + | 0.488746i | \(0.162545\pi\) | ||||
−0.872426 | + | 0.488746i | \(0.837455\pi\) | |||||||
\(464\) | 1.11361i | 0.00240003i | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | − | 47.7287i | − | 0.102422i | ||||||
\(467\) | 69.9506i | 0.149787i | 0.997192 | + | 0.0748936i | \(0.0238617\pi\) | ||||
−0.997192 | + | 0.0748936i | \(0.976138\pi\) | |||||||
\(468\) | 65.2524 | 0.139428 | ||||||||
\(469\) | − | 104.965i | − | 0.223807i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 8.67760i | 0.0184238i | ||||||||
\(472\) | − | 266.100i | − | 0.563772i | ||||||
\(473\) | 67.9343i | 0.143624i | ||||||||
\(474\) | − | 225.232i | − | 0.475174i | ||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 73.0765 | 0.153522 | ||||||||
\(477\) | 336.179 | 0.704779 | ||||||||
\(478\) | −279.648 | −0.585037 | ||||||||
\(479\) | 137.500 | 0.287055 | 0.143528 | − | 0.989646i | \(-0.454155\pi\) | ||||
0.143528 | + | 0.989646i | \(0.454155\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 411.622 | 0.855763 | ||||||||
\(482\) | − | 493.248i | − | 1.02334i | ||||||
\(483\) | −127.115 | −0.263177 | ||||||||
\(484\) | −239.820 | −0.495495 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −339.569 | −0.698702 | ||||||||
\(487\) | −329.190 | −0.675954 | −0.337977 | − | 0.941154i | \(-0.609743\pi\) | ||||
−0.337977 | + | 0.941154i | \(0.609743\pi\) | |||||||
\(488\) | 54.8913 | 0.112482 | ||||||||
\(489\) | 355.189i | 0.726358i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −438.255 | −0.892576 | −0.446288 | − | 0.894889i | \(-0.647254\pi\) | ||||
−0.446288 | + | 0.894889i | \(0.647254\pi\) | |||||||
\(492\) | 14.5726i | 0.0296192i | ||||||||
\(493\) | 6.03166 | 0.0122346 | ||||||||
\(494\) | 147.373 | + | 66.8763i | 0.298325 | + | 0.135377i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 79.3642i | 0.160008i | ||||||||
\(497\) | 69.8380 | 0.140519 | ||||||||
\(498\) | − | 14.9421i | − | 0.0300042i | ||||||
\(499\) | 695.692 | 1.39417 | 0.697086 | − | 0.716988i | \(-0.254480\pi\) | ||||
0.697086 | + | 0.716988i | \(0.254480\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −204.876 | −0.408934 | ||||||||
\(502\) | −100.205 | −0.199611 | ||||||||
\(503\) | 34.2415i | 0.0680746i | 0.999421 | + | 0.0340373i | \(0.0108365\pi\) | ||||
−0.999421 | + | 0.0340373i | \(0.989163\pi\) | |||||||
\(504\) | 25.8397i | 0.0512693i | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | − | 58.7961i | − | 0.116198i | ||||||
\(507\) | −251.232 | −0.495526 | ||||||||
\(508\) | −18.6220 | −0.0366574 | ||||||||
\(509\) | 391.055i | 0.768281i | 0.923275 | + | 0.384140i | \(0.125502\pi\) | ||||
−0.923275 | + | 0.384140i | \(0.874498\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 5.48507 | 0.0107340 | ||||||||
\(512\) | −22.6274 | −0.0441942 | ||||||||
\(513\) | −472.163 | − | 214.263i | −0.920396 | − | 0.417667i | ||||
\(514\) | −725.694 | −1.41186 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 246.318i | 0.477361i | ||||||||
\(517\) | − | 10.0344i | − | 0.0194089i | ||||||
\(518\) | 163.001i | 0.314674i | ||||||||
\(519\) | 193.258 | 0.372365 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 423.418i | 0.812702i | 0.913717 | + | 0.406351i | \(0.133199\pi\) | ||||
−0.913717 | + | 0.406351i | \(0.866801\pi\) | |||||||
\(522\) | 2.13279i | 0.00408580i | ||||||||
\(523\) | 277.177 | 0.529976 | 0.264988 | − | 0.964252i | \(-0.414632\pi\) | ||||
0.264988 | + | 0.964252i | \(0.414632\pi\) | |||||||
\(524\) | 295.415 | 0.563769 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | − | 56.2125i | − | 0.106868i | ||||||
\(527\) | 429.860 | 0.815674 | ||||||||
\(528\) | 7.90553 | 0.0149726 | ||||||||
\(529\) | −1056.52 | −1.99721 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 509.634i | − | 0.959762i | ||||||
\(532\) | −26.4828 | + | 58.3591i | −0.0497797 | + | 0.109698i | ||||
\(533\) | − | 23.1842i | − | 0.0434976i | ||||||
\(534\) | 225.775i | 0.422800i | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 176.038 | 0.328429 | ||||||||
\(537\) | 230.463i | 0.429168i | ||||||||
\(538\) | 731.066i | 1.35886i | ||||||||
\(539\) | 48.1918 | 0.0894096 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −562.342 | −1.03945 | −0.519725 | − | 0.854334i | \(-0.673965\pi\) | ||||
−0.519725 | + | 0.854334i | \(0.673965\pi\) | |||||||
\(542\) | −209.241 | −0.386054 | ||||||||
\(543\) | 76.3186i | 0.140550i | ||||||||
\(544\) | 122.557i | 0.225288i | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 27.1915i | 0.0498012i | ||||||||
\(547\) | 727.214 | 1.32946 | 0.664729 | − | 0.747084i | \(-0.268547\pi\) | ||||
0.664729 | + | 0.747084i | \(0.268547\pi\) | |||||||
\(548\) | 294.161i | 0.536789i | ||||||||
\(549\) | 105.128 | 0.191489 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −2.18586 | + | 4.81690i | −0.00396708 | + | 0.00874210i | ||||
\(552\) | − | 213.184i | − | 0.386204i | ||||||
\(553\) | −141.898 | −0.256597 | ||||||||
\(554\) | 566.458i | 1.02249i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 156.925 | 0.282240 | ||||||||
\(557\) | 692.987i | 1.24414i | 0.782961 | + | 0.622071i | \(0.213709\pi\) | ||||
−0.782961 | + | 0.622071i | \(0.786291\pi\) | |||||||
\(558\) | 151.998i | 0.272398i | ||||||||
\(559\) | − | 391.878i | − | 0.701034i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | − | 42.8187i | − | 0.0763257i | ||||||
\(562\) | 355.170i | 0.631975i | ||||||||
\(563\) | −285.285 | −0.506723 | −0.253362 | − | 0.967372i | \(-0.581536\pi\) | ||||
−0.253362 | + | 0.967372i | \(0.581536\pi\) | |||||||
\(564\) | − | 36.3829i | − | 0.0645088i | ||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | − | 594.800i | − | 1.05088i | ||||||
\(567\) | − | 4.89647i | − | 0.00863574i | ||||||
\(568\) | 117.126i | 0.206207i | ||||||||
\(569\) | 843.131i | 1.48178i | 0.671628 | + | 0.740888i | \(0.265595\pi\) | ||||
−0.671628 | + | 0.740888i | \(0.734405\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −798.131 | −1.39778 | −0.698889 | − | 0.715230i | \(-0.746322\pi\) | ||||
−0.698889 | + | 0.715230i | \(0.746322\pi\) | |||||||
\(572\) | −12.5772 | −0.0219882 | ||||||||
\(573\) | −428.253 | −0.747388 | ||||||||
\(574\) | 9.18087 | 0.0159946 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −43.3359 | −0.0752360 | ||||||||
\(577\) | 28.4942i | 0.0493834i | 0.999695 | + | 0.0246917i | \(0.00786041\pi\) | ||||
−0.999695 | + | 0.0246917i | \(0.992140\pi\) | |||||||
\(578\) | 255.097 | 0.441345 | ||||||||
\(579\) | 13.0966 | 0.0226194 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −9.41364 | −0.0162025 | ||||||||
\(582\) | −5.07276 | −0.00871608 | ||||||||
\(583\) | −64.7978 | −0.111145 | ||||||||
\(584\) | 9.19902i | 0.0157518i | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −474.281 | −0.809352 | ||||||||
\(587\) | − | 546.088i | − | 0.930303i | −0.885231 | − | 0.465151i | \(-0.846000\pi\) | ||
0.885231 | − | 0.465151i | \(-0.154000\pi\) | |||||||
\(588\) | 174.735 | 0.297168 | ||||||||
\(589\) | −155.781 | + | 343.287i | −0.264483 | + | 0.582831i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − | 445.063i | − | 0.753067i | ||||||
\(592\) | −273.370 | −0.461773 | ||||||||
\(593\) | − | 1058.29i | − | 1.78464i | −0.451407 | − | 0.892318i | \(-0.649078\pi\) | ||
0.451407 | − | 0.892318i | \(-0.350922\pi\) | |||||||
\(594\) | 40.2959 | 0.0678382 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −270.367 | −0.453637 | ||||||||
\(597\) | −75.6288 | −0.126681 | ||||||||
\(598\) | 339.164i | 0.567164i | ||||||||
\(599\) | − | 554.840i | − | 0.926278i | −0.886286 | − | 0.463139i | \(-0.846723\pi\) | ||
0.886286 | − | 0.463139i | \(-0.153277\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 662.009i | 1.10151i | 0.834666 | + | 0.550756i | \(0.185661\pi\) | ||||
−0.834666 | + | 0.550756i | \(0.814339\pi\) | |||||||
\(602\) | 155.182 | 0.257778 | ||||||||
\(603\) | 337.147 | 0.559116 | ||||||||
\(604\) | 337.543i | 0.558846i | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −40.4161 | −0.0666932 | ||||||||
\(607\) | −895.503 | −1.47529 | −0.737646 | − | 0.675187i | \(-0.764063\pi\) | ||||
−0.737646 | + | 0.675187i | \(0.764063\pi\) | |||||||
\(608\) | −97.8742 | − | 44.4144i | −0.160977 | − | 0.0730500i | ||||
\(609\) | −0.888758 | −0.00145937 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 57.8832i | 0.0947351i | ||||||||
\(612\) | 234.720i | 0.383530i | ||||||||
\(613\) | − | 548.725i | − | 0.895146i | −0.894247 | − | 0.447573i | \(-0.852288\pi\) | ||
0.894247 | − | 0.447573i | \(-0.147712\pi\) | |||||||
\(614\) | 440.661 | 0.717689 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | − | 4.98055i | − | 0.00808531i | ||||||
\(617\) | 763.924i | 1.23813i | 0.785341 | + | 0.619063i | \(0.212487\pi\) | ||||
−0.785341 | + | 0.619063i | \(0.787513\pi\) | |||||||
\(618\) | 383.745 | 0.620947 | ||||||||
\(619\) | 508.039 | 0.820741 | 0.410370 | − | 0.911919i | \(-0.365399\pi\) | ||||
0.410370 | + | 0.911919i | \(0.365399\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | − | 1086.64i | − | 1.74982i | ||||||
\(622\) | −407.475 | −0.655104 | ||||||||
\(623\) | 142.240 | 0.228315 | ||||||||
\(624\) | −45.6029 | −0.0730816 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 195.016i | 0.311528i | ||||||||
\(627\) | 34.1951 | + | 15.5174i | 0.0545377 | + | 0.0247487i | ||||
\(628\) | 9.16865i | 0.0145998i | ||||||||
\(629\) | 1480.65i | 2.35398i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 673.489 | 1.06734 | 0.533668 | − | 0.845694i | \(-0.320813\pi\) | ||||
0.533668 | + | 0.845694i | \(0.320813\pi\) | |||||||
\(632\) | − | 237.978i | − | 0.376548i | ||||||
\(633\) | − | 462.325i | − | 0.730371i | ||||||
\(634\) | −408.452 | −0.644246 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −234.946 | −0.369411 | ||||||||
\(637\) | −277.993 | −0.436410 | ||||||||
\(638\) | − | 0.411089i | − | 0.000644341i | ||||||
\(639\) | 224.318i | 0.351046i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 1084.01i | − | 1.69112i | −0.533878 | − | 0.845562i | \(-0.679266\pi\) | ||
0.533878 | − | 0.845562i | \(-0.320734\pi\) | |||||||
\(642\) | 317.640 | 0.494766 | ||||||||
\(643\) | 579.940i | 0.901929i | 0.892542 | + | 0.450964i | \(0.148920\pi\) | ||||
−0.892542 | + | 0.450964i | \(0.851080\pi\) | |||||||
\(644\) | −134.308 | −0.208553 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −240.562 | + | 530.116i | −0.372387 | + | 0.820613i | ||||
\(647\) | 585.847i | 0.905482i | 0.891642 | + | 0.452741i | \(0.149554\pi\) | ||||
−0.891642 | + | 0.452741i | \(0.850446\pi\) | |||||||
\(648\) | 8.21188 | 0.0126727 | ||||||||
\(649\) | 98.2307i | 0.151357i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −63.3394 | −0.0972955 | ||||||||
\(652\) | 375.289i | 0.575596i | ||||||||
\(653\) | 715.361i | 1.09550i | 0.836642 | + | 0.547749i | \(0.184515\pi\) | ||||
−0.836642 | + | 0.547749i | \(0.815485\pi\) | |||||||
\(654\) | − | 166.598i | − | 0.254737i | ||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 15.3973i | 0.0234715i | ||||||||
\(657\) | 17.6179i | 0.0268157i | ||||||||
\(658\) | −22.9215 | −0.0348352 | ||||||||
\(659\) | 669.081i | 1.01530i | 0.861564 | + | 0.507649i | \(0.169485\pi\) | ||||
−0.861564 | + | 0.507649i | \(0.830515\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 291.273i | − | 0.440655i | −0.975426 | − | 0.220327i | \(-0.929287\pi\) | ||
0.975426 | − | 0.220327i | \(-0.0707126\pi\) | |||||||
\(662\) | − | 162.460i | − | 0.245408i | ||||||
\(663\) | 246.999i | 0.372548i | ||||||||
\(664\) | − | 15.7876i | − | 0.0237766i | ||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −523.556 | −0.786120 | ||||||||
\(667\) | −11.0856 | −0.0166201 | ||||||||
\(668\) | −216.469 | −0.324056 | ||||||||
\(669\) | 636.710 | 0.951734 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −20.2631 | −0.0301983 | ||||||||
\(672\) | − | 18.0586i | − | 0.0268729i | ||||||
\(673\) | −1212.39 | −1.80147 | −0.900734 | − | 0.434372i | \(-0.856970\pi\) | ||||
−0.900734 | + | 0.434372i | \(0.856970\pi\) | |||||||
\(674\) | 15.7311 | 0.0233398 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −265.448 | −0.392675 | ||||||||
\(677\) | −158.703 | −0.234421 | −0.117211 | − | 0.993107i | \(-0.537395\pi\) | ||||
−0.117211 | + | 0.993107i | \(0.537395\pi\) | |||||||
\(678\) | −237.745 | −0.350657 | ||||||||
\(679\) | 3.19588i | 0.00470674i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 546.160 | 0.801998 | ||||||||
\(682\) | − | 29.2972i | − | 0.0429578i | ||||||
\(683\) | 109.346 | 0.160097 | 0.0800483 | − | 0.996791i | \(-0.474493\pi\) | ||||
0.0800483 | + | 0.996791i | \(0.474493\pi\) | |||||||
\(684\) | −187.448 | − | 85.0622i | −0.274047 | − | 0.124360i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | − | 226.953i | − | 0.330835i | ||||||
\(687\) | −780.795 | −1.13653 | ||||||||
\(688\) | 260.257i | 0.378280i | ||||||||
\(689\) | 373.785 | 0.542503 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 487.341 | 0.705269 | 0.352634 | − | 0.935761i | \(-0.385286\pi\) | ||||
0.352634 | + | 0.935761i | \(0.385286\pi\) | |||||||
\(692\) | 204.194 | 0.295078 | ||||||||
\(693\) | − | 9.53872i | − | 0.0137644i | ||||||
\(694\) | 365.077i | 0.526048i | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | − | 1.49054i | − | 0.00214158i | ||||||
\(697\) | 83.3963 | 0.119650 | ||||||||
\(698\) | −657.697 | −0.942259 | ||||||||
\(699\) | 63.8835i | 0.0913927i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −925.556 | −1.32034 | −0.660168 | − | 0.751118i | \(-0.729515\pi\) | ||||
−0.660168 | + | 0.751118i | \(0.729515\pi\) | |||||||
\(702\) | −232.446 | −0.331120 | ||||||||
\(703\) | −1182.45 | − | 536.585i | −1.68201 | − | 0.763279i | ||||
\(704\) | 8.35290 | 0.0118649 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 716.128i | 1.01435i | ||||||||
\(707\) | 25.4625i | 0.0360148i | ||||||||
\(708\) | 356.168i | 0.503062i | ||||||||
\(709\) | 181.394 | 0.255845 | 0.127923 | − | 0.991784i | \(-0.459169\pi\) | ||||
0.127923 | + | 0.991784i | \(0.459169\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − | 455.774i | − | 0.641033i | ||||||
\(712\) | 238.552i | 0.335044i | ||||||||
\(713\) | −790.043 | −1.10805 | ||||||||
\(714\) | −97.8108 | −0.136990 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 243.505i | 0.340090i | ||||||||
\(717\) | 374.301 | 0.522037 | ||||||||
\(718\) | −4.11606 | −0.00573267 | ||||||||
\(719\) | 783.075 | 1.08912 | 0.544559 | − | 0.838723i | \(-0.316697\pi\) | ||||
0.544559 | + | 0.838723i | \(0.316697\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 241.762i | − | 0.335315i | ||||||
\(722\) | −336.173 | − | 384.226i | −0.465613 | − | 0.532169i | ||||
\(723\) | 660.199i | 0.913138i | ||||||||
\(724\) | 80.6374i | 0.111378i | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 320.992 | 0.442137 | ||||||||
\(727\) | − | 790.679i | − | 1.08759i | −0.839217 | − | 0.543796i | \(-0.816987\pi\) | ||
0.839217 | − | 0.543796i | \(-0.183013\pi\) | |||||||
\(728\) | 28.7302i | 0.0394646i | ||||||||
\(729\) | 480.633 | 0.659305 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1409.63 | 1.92836 | ||||||||
\(732\) | −73.4704 | −0.100369 | ||||||||
\(733\) | − | 820.219i | − | 1.11899i | −0.828834 | − | 0.559494i | \(-0.810995\pi\) | ||
0.828834 | − | 0.559494i | \(-0.189005\pi\) | |||||||
\(734\) | 541.058i | 0.737136i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | − | 225.248i | − | 0.306044i | ||||||
\(737\) | −64.9843 | −0.0881740 | ||||||||
\(738\) | 29.4888i | 0.0399577i | ||||||||
\(739\) | −19.5055 | −0.0263944 | −0.0131972 | − | 0.999913i | \(-0.504201\pi\) | ||||
−0.0131972 | + | 0.999913i | \(0.504201\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −197.254 | − | 89.5120i | −0.266200 | − | 0.120799i | ||||
\(742\) | 148.018i | 0.199485i | ||||||||
\(743\) | 1204.63 | 1.62131 | 0.810653 | − | 0.585527i | \(-0.199113\pi\) | ||||
0.810653 | + | 0.585527i | \(0.199113\pi\) | |||||||
\(744\) | − | 106.227i | − | 0.142778i | ||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 558.312 | 0.748407 | ||||||||
\(747\) | − | 30.2364i | − | 0.0404771i | ||||||
\(748\) | − | 45.2418i | − | 0.0604837i | ||||||
\(749\) | − | 200.116i | − | 0.267177i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1442.98i | 1.92141i | 0.277575 | + | 0.960704i | \(0.410469\pi\) | ||||
−0.277575 | + | 0.960704i | \(0.589531\pi\) | |||||||
\(752\) | − | 38.4418i | − | 0.0511194i | ||||||
\(753\) | 134.121 | 0.178116 | ||||||||
\(754\) | 2.37136i | 0.00314504i | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | − | 92.0479i | − | 0.121756i | ||||||
\(757\) | 947.346i | 1.25145i | 0.780044 | + | 0.625724i | \(0.215196\pi\) | ||||
−0.780044 | + | 0.625724i | \(0.784804\pi\) | |||||||
\(758\) | 869.681i | 1.14734i | ||||||||
\(759\) | 78.6969i | 0.103685i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −892.677 | −1.17303 | −0.586516 | − | 0.809938i | \(-0.699501\pi\) | ||||
−0.586516 | + | 0.809938i | \(0.699501\pi\) | |||||||
\(762\) | 24.9250 | 0.0327099 | ||||||||
\(763\) | −104.958 | −0.137560 | ||||||||
\(764\) | −452.487 | −0.592261 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 629.867 | 0.822281 | ||||||||
\(767\) | − | 566.642i | − | 0.738777i | ||||||
\(768\) | 30.2862 | 0.0394351 | ||||||||
\(769\) | 629.290 | 0.818322 | 0.409161 | − | 0.912462i | \(-0.365821\pi\) | ||||
0.409161 | + | 0.912462i | \(0.365821\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 971.321 | 1.25982 | ||||||||
\(772\) | 13.8377 | 0.0179245 | ||||||||
\(773\) | −291.337 | −0.376892 | −0.188446 | − | 0.982084i | \(-0.560345\pi\) | ||||
−0.188446 | + | 0.982084i | \(0.560345\pi\) | |||||||
\(774\) | 498.442i | 0.643983i | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −5.35982 | −0.00690698 | ||||||||
\(777\) | − | 218.172i | − | 0.280788i | ||||||
\(778\) | 164.702 | 0.211699 | ||||||||
\(779\) | −30.2227 | + | 66.6005i | −0.0387967 | + | 0.0854948i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 43.2368i | − | 0.0553609i | ||||||
\(782\) | −1220.01 | −1.56012 | ||||||||
\(783\) | − | 7.59754i | − | 0.00970311i | ||||||
\(784\) | 184.623 | 0.235488 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −395.405 | −0.503059 | ||||||||
\(787\) | −889.115 | −1.12975 | −0.564876 | − | 0.825176i | \(-0.691076\pi\) | ||||
−0.564876 | + | 0.825176i | \(0.691076\pi\) | |||||||
\(788\) | − | 470.248i | − | 0.596762i | ||||||
\(789\) | 75.2388i | 0.0953598i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 149.781i | 0.189357i | ||||||||
\(792\) | 15.9974 | 0.0201988 | ||||||||
\(793\) | 116.887 | 0.147399 | ||||||||
\(794\) | − | 439.421i | − | 0.553427i | ||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −79.9085 | −0.100388 | ||||||||
\(797\) | 800.716 | 1.00466 | 0.502331 | − | 0.864675i | \(-0.332476\pi\) | ||||
0.502331 | + | 0.864675i | \(0.332476\pi\) | |||||||
\(798\) | 35.4465 | − | 78.1120i | 0.0444191 | − | 0.0978847i | ||||
\(799\) | −208.212 | −0.260591 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 456.873i | 0.570378i | ||||||||
\(802\) | 653.858i | 0.815284i | ||||||||
\(803\) | − | 3.39581i | − | 0.00422891i | ||||||
\(804\) | −235.622 | −0.293062 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 169.000i | 0.209678i | ||||||||
\(807\) | − | 978.510i | − | 1.21253i | ||||||
\(808\) | −42.7032 | −0.0528505 | ||||||||
\(809\) | 327.560 | 0.404894 | 0.202447 | − | 0.979293i | \(-0.435111\pi\) | ||||
0.202447 | + | 0.979293i | \(0.435111\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 414.555i | − | 0.511166i | −0.966787 | − | 0.255583i | \(-0.917733\pi\) | ||
0.966787 | − | 0.255583i | \(-0.0822673\pi\) | |||||||
\(812\) | −0.939051 | −0.00115647 | ||||||||
\(813\) | 280.064 | 0.344482 | ||||||||
\(814\) | 100.914 | 0.123973 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | − | 164.039i | − | 0.201028i | ||||||
\(817\) | −510.847 | + | 1125.73i | −0.625272 | + | 1.37789i | ||||
\(818\) | 781.201i | 0.955013i | ||||||||
\(819\) | 55.0239i | 0.0671843i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −594.805 | −0.724489 | −0.362244 | − | 0.932083i | \(-0.617989\pi\) | ||||
−0.362244 | + | 0.932083i | \(0.617989\pi\) | |||||||
\(822\) | − | 393.726i | − | 0.478985i | ||||||
\(823\) | − | 704.177i | − | 0.855622i | −0.903868 | − | 0.427811i | \(-0.859285\pi\) | ||
0.903868 | − | 0.427811i | \(-0.140715\pi\) | |||||||
\(824\) | 405.461 | 0.492064 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 224.388 | 0.271657 | ||||||||
\(827\) | 829.642 | 1.00319 | 0.501597 | − | 0.865101i | \(-0.332746\pi\) | ||||
0.501597 | + | 0.865101i | \(0.332746\pi\) | |||||||
\(828\) | − | 431.394i | − | 0.521007i | ||||||
\(829\) | − | 693.036i | − | 0.835990i | −0.908449 | − | 0.417995i | \(-0.862733\pi\) | ||
0.908449 | − | 0.417995i | \(-0.137267\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | − | 758.188i | − | 0.912380i | ||||||
\(832\) | −48.1835 | −0.0579129 | ||||||||
\(833\) | − | 999.973i | − | 1.20045i | ||||||
\(834\) | −210.040 | −0.251846 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 36.1302 | + | 16.3955i | 0.0432179 | + | 0.0196119i | ||||
\(837\) | − | 541.456i | − | 0.646901i | ||||||
\(838\) | −50.6096 | −0.0603933 | ||||||||
\(839\) | − | 1482.55i | − | 1.76704i | −0.468391 | − | 0.883521i | \(-0.655166\pi\) | ||
0.468391 | − | 0.883521i | \(-0.344834\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 840.922 | 0.999908 | ||||||||
\(842\) | − | 947.014i | − | 1.12472i | ||||||
\(843\) | − | 475.385i | − | 0.563921i | ||||||
\(844\) | − | 488.487i | − | 0.578776i | ||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | − | 73.6235i | − | 0.0870254i | ||||||
\(847\) | − | 202.227i | − | 0.238757i | ||||||
\(848\) | −248.241 | −0.292737 | ||||||||
\(849\) | 796.123i | 0.937718i | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 2721.30i | − | 3.19777i | ||||||
\(852\) | − | 156.769i | − | 0.184001i | ||||||
\(853\) | 1327.68i | 1.55648i | 0.627966 | + | 0.778240i | \(0.283888\pi\) | ||||
−0.627966 | + | 0.778240i | \(0.716112\pi\) | |||||||
\(854\) | 46.2870i | 0.0542002i | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 335.615 | 0.392073 | ||||||||
\(857\) | −274.944 | −0.320822 | −0.160411 | − | 0.987050i | \(-0.551282\pi\) | ||||
−0.160411 | + | 0.987050i | \(0.551282\pi\) | |||||||
\(858\) | 16.8343 | 0.0196204 | ||||||||
\(859\) | 182.211 | 0.212120 | 0.106060 | − | 0.994360i | \(-0.466176\pi\) | ||||
0.106060 | + | 0.994360i | \(0.466176\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −12.2883 | −0.0142722 | ||||||||
\(862\) | 246.987i | 0.286528i | ||||||||
\(863\) | −173.434 | −0.200966 | −0.100483 | − | 0.994939i | \(-0.532039\pi\) | ||||
−0.100483 | + | 0.994939i | \(0.532039\pi\) | |||||||
\(864\) | 154.374 | 0.178673 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 157.837 | 0.182260 | ||||||||
\(867\) | −341.441 | −0.393818 | ||||||||
\(868\) | −66.9236 | −0.0771010 | ||||||||
\(869\) | 87.8494i | 0.101093i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 374.860 | 0.430379 | ||||||||
\(872\) | − | 176.025i | − | 0.201864i | ||||||
\(873\) | −10.2651 | −0.0117584 | ||||||||
\(874\) | 442.130 | − | 974.304i | 0.505869 | − | 1.11476i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | − | 12.3126i | − | 0.0140555i | ||||||
\(877\) | −708.930 | −0.808358 | −0.404179 | − | 0.914680i | \(-0.632443\pi\) | ||||
−0.404179 | + | 0.914680i | \(0.632443\pi\) | |||||||
\(878\) | − | 131.706i | − | 0.150006i | ||||||
\(879\) | 634.811 | 0.722197 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −188.482 | −0.213941 | −0.106970 | − | 0.994262i | \(-0.534115\pi\) | ||||
−0.106970 | + | 0.994262i | \(0.534115\pi\) | |||||||
\(882\) | 353.589 | 0.400894 | ||||||||
\(883\) | 227.812i | 0.257998i | 0.991645 | + | 0.128999i | \(0.0411764\pi\) | ||||
−0.991645 | + | 0.128999i | \(0.958824\pi\) | |||||||
\(884\) | 260.976i | 0.295222i | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 1125.89i | 1.27075i | ||||||||
\(887\) | 799.124 | 0.900928 | 0.450464 | − | 0.892794i | \(-0.351258\pi\) | ||||
0.450464 | + | 0.892794i | \(0.351258\pi\) | |||||||
\(888\) | 365.897 | 0.412047 | ||||||||
\(889\) | − | 15.7029i | − | 0.0176636i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −3.03141 | −0.00340226 | ||||||||
\(892\) | 672.740 | 0.754193 | ||||||||
\(893\) | 75.4558 | − | 166.279i | 0.0844969 | − | 0.186203i | ||||
\(894\) | 361.879 | 0.404786 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | − | 19.0805i | − | 0.0212952i | ||||||
\(897\) | − | 453.961i | − | 0.506088i | ||||||
\(898\) | 263.198i | 0.293093i | ||||||||
\(899\) | −5.52381 | −0.00614439 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1344.55i | 1.49228i | ||||||||
\(902\) | − | 5.68389i | − | 0.00630143i | ||||||
\(903\) | −207.707 | −0.230019 | ||||||||
\(904\) | −251.199 | −0.277875 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | − | 451.791i | − | 0.498666i | ||||||
\(907\) | 182.629 | 0.201355 | 0.100677 | − | 0.994919i | \(-0.467899\pi\) | ||||
0.100677 | + | 0.994919i | \(0.467899\pi\) | |||||||
\(908\) | 577.067 | 0.635536 | ||||||||
\(909\) | −81.7849 | −0.0899724 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1124.39i | 1.23423i | 0.786872 | + | 0.617116i | \(0.211699\pi\) | ||||
−0.786872 | + | 0.617116i | \(0.788301\pi\) | |||||||
\(912\) | 131.002 | + | 59.4474i | 0.143642 | + | 0.0651835i | ||||
\(913\) | 5.82800i | 0.00638335i | ||||||||
\(914\) | − | 815.982i | − | 0.892759i | ||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −824.979 | −0.900632 | ||||||||
\(917\) | 249.108i | 0.271656i | ||||||||
\(918\) | − | 836.135i | − | 0.910823i | ||||||
\(919\) | −985.231 | −1.07207 | −0.536034 | − | 0.844196i | \(-0.680078\pi\) | ||||
−0.536034 | + | 0.844196i | \(0.680078\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −589.812 | −0.640404 | ||||||||
\(922\) | −316.593 | −0.343377 | ||||||||
\(923\) | 249.411i | 0.270218i | ||||||||
\(924\) | 6.66632i | 0.00721463i | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | − | 640.043i | − | 0.691191i | ||||||
\(927\) | 776.536 | 0.837687 | ||||||||
\(928\) | − | 1.57489i | − | 0.00169708i | ||||||
\(929\) | −842.513 | −0.906903 | −0.453452 | − | 0.891281i | \(-0.649807\pi\) | ||||
−0.453452 | + | 0.891281i | \(0.649807\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 798.581 | + | 362.388i | 0.857767 | + | 0.389246i | ||||
\(932\) | 67.4986i | 0.0724234i | ||||||||
\(933\) | 545.393 | 0.584559 | ||||||||
\(934\) | − | 98.9251i | − | 0.105916i | ||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −92.2808 | −0.0985906 | ||||||||
\(937\) | 612.166i | 0.653326i | 0.945141 | + | 0.326663i | \(0.105924\pi\) | ||||
−0.945141 | + | 0.326663i | \(0.894076\pi\) | |||||||
\(938\) | 148.444i | 0.158255i | ||||||||
\(939\) | − | 261.024i | − | 0.277981i | ||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 760.768i | 0.808467i | 0.914656 | + | 0.404234i | \(0.132462\pi\) | ||||
−0.914656 | + | 0.404234i | \(0.867538\pi\) | |||||||
\(942\) | − | 12.2720i | − | 0.0130276i | ||||||
\(943\) | −153.275 | −0.162539 | ||||||||
\(944\) | 376.323i | 0.398647i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | − | 96.0736i | − | 0.101558i | ||||||
\(947\) | − | 23.9008i | − | 0.0252384i | −0.999920 | − | 0.0126192i | \(-0.995983\pi\) | ||
0.999920 | − | 0.0126192i | \(-0.00401693\pi\) | |||||||
\(948\) | 318.527i | 0.335999i | ||||||||
\(949\) | 19.5887i | 0.0206414i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 546.701 | 0.574870 | ||||||||
\(952\) | −103.346 | −0.108557 | ||||||||
\(953\) | 52.0625 | 0.0546301 | 0.0273150 | − | 0.999627i | \(-0.491304\pi\) | ||||
0.0273150 | + | 0.999627i | \(0.491304\pi\) | |||||||
\(954\) | −475.429 | −0.498354 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 395.482 | 0.413684 | ||||||||
\(957\) | 0.550231i | 0.000574955i | ||||||||
\(958\) | −194.454 | −0.202979 | ||||||||
\(959\) | −248.050 | −0.258655 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 567.333 | 0.590357 | ||||||||
\(962\) | −582.122 | −0.605116 | ||||||||
\(963\) | 642.767 | 0.667463 | ||||||||
\(964\) | 697.558i | 0.723608i | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 179.767 | 0.186094 | ||||||||
\(967\) | − | 987.119i | − | 1.02081i | −0.859935 | − | 0.510403i | \(-0.829496\pi\) | ||
0.859935 | − | 0.510403i | \(-0.170504\pi\) | |||||||
\(968\) | 339.156 | 0.350368 | ||||||||
\(969\) | 321.985 | − | 709.545i | 0.332286 | − | 0.732245i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 1204.48i | − | 1.24045i | −0.784422 | − | 0.620227i | \(-0.787040\pi\) | ||
0.784422 | − | 0.620227i | \(-0.212960\pi\) | |||||||
\(972\) | 480.223 | 0.494057 | ||||||||
\(973\) | 132.327i | 0.135999i | ||||||||
\(974\) | 465.544 | 0.477972 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −77.6280 | −0.0795369 | ||||||||
\(977\) | 556.615 | 0.569719 | 0.284859 | − | 0.958569i | \(-0.408053\pi\) | ||||
0.284859 | + | 0.958569i | \(0.408053\pi\) | |||||||
\(978\) | − | 502.313i | − | 0.513613i | ||||||
\(979\) | − | 88.0611i | − | 0.0899501i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − | 337.123i | − | 0.343652i | ||||||
\(982\) | 619.786 | 0.631146 | ||||||||
\(983\) | 462.624 | 0.470625 | 0.235312 | − | 0.971920i | \(-0.424389\pi\) | ||||
0.235312 | + | 0.971920i | \(0.424389\pi\) | |||||||
\(984\) | − | 20.6088i | − | 0.0209439i | ||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −8.53006 | −0.00865118 | ||||||||
\(987\) | 30.6798 | 0.0310839 | ||||||||
\(988\) | −208.416 | − | 94.5774i | −0.210948 | − | 0.0957261i | ||||
\(989\) | −2590.77 | −2.61958 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1691.69i | 1.70706i | 0.521046 | + | 0.853528i | \(0.325542\pi\) | ||||
−0.521046 | + | 0.853528i | \(0.674458\pi\) | |||||||
\(992\) | − | 112.238i | − | 0.113143i | ||||||
\(993\) | 217.448i | 0.218981i | ||||||||
\(994\) | −98.7659 | −0.0993620 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 21.1313i | 0.0212162i | ||||||||
\(997\) | − | 742.809i | − | 0.745044i | −0.928023 | − | 0.372522i | \(-0.878493\pi\) | ||
0.928023 | − | 0.372522i | \(-0.121507\pi\) | |||||||
\(998\) | −983.857 | −0.985828 | ||||||||
\(999\) | 1865.04 | 1.86691 |
(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 | 950.3.d.b.949.6 | 24 | ||
5.2 | odd | 4 | 950.3.c.c.151.3 | yes | 12 | ||
5.3 | odd | 4 | 950.3.c.b.151.10 | yes | 12 | ||
5.4 | even | 2 | inner | 950.3.d.b.949.19 | 24 | ||
19.18 | odd | 2 | inner | 950.3.d.b.949.18 | 24 | ||
95.18 | even | 4 | 950.3.c.b.151.3 | ✓ | 12 | ||
95.37 | even | 4 | 950.3.c.c.151.10 | yes | 12 | ||
95.94 | odd | 2 | inner | 950.3.d.b.949.7 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
950.3.c.b.151.3 | ✓ | 12 | 95.18 | even | 4 | ||
950.3.c.b.151.10 | yes | 12 | 5.3 | odd | 4 | ||
950.3.c.c.151.3 | yes | 12 | 5.2 | odd | 4 | ||
950.3.c.c.151.10 | yes | 12 | 95.37 | even | 4 | ||
950.3.d.b.949.6 | 24 | 1.1 | even | 1 | trivial | ||
950.3.d.b.949.7 | 24 | 95.94 | odd | 2 | inner | ||
950.3.d.b.949.18 | 24 | 19.18 | odd | 2 | inner | ||
950.3.d.b.949.19 | 24 | 5.4 | even | 2 | inner |