Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [147,4,Mod(146,147)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(147, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("147.146");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 147 = 3 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 147.c (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: | \(8.67328077084\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 146.13 | ||
Character | \(\chi\) | \(=\) | 147.146 |
Dual form | 147.4.c.b.146.11 |
$q$-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 \(\left(\mathbb{Z}/147\mathbb{Z}\right)^\times\).
\(n\) | \(50\) | \(52\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.222948i | 0.0788240i | 0.999223 | + | 0.0394120i | \(0.0125485\pi\) | ||||
−0.999223 | + | 0.0394120i | \(0.987452\pi\) | |||||||
\(3\) | −3.69409 | − | 3.65427i | −0.710928 | − | 0.703265i | ||||
\(4\) | 7.95029 | 0.993787 | ||||||||
\(5\) | 18.7021 | 1.67277 | 0.836385 | − | 0.548143i | \(-0.184665\pi\) | ||||
0.836385 | + | 0.548143i | \(0.184665\pi\) | |||||||
\(6\) | 0.814713 | − | 0.823589i | 0.0554342 | − | 0.0560382i | ||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 3.55609i | 0.157158i | ||||||||
\(9\) | 0.292585 | + | 26.9984i | 0.0108365 | + | 0.999941i | ||||
\(10\) | 4.16960i | 0.131854i | ||||||||
\(11\) | 45.8073i | 1.25558i | 0.778382 | + | 0.627792i | \(0.216041\pi\) | ||||
−0.778382 | + | 0.627792i | \(0.783959\pi\) | |||||||
\(12\) | −29.3691 | − | 29.0525i | −0.706511 | − | 0.698896i | ||||
\(13\) | − | 59.3740i | − | 1.26672i | −0.773857 | − | 0.633361i | \(-0.781675\pi\) | ||
0.773857 | − | 0.633361i | \(-0.218325\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −69.0873 | − | 68.3427i | −1.18922 | − | 1.17640i | ||||
\(16\) | 62.8095 | 0.981399 | ||||||||
\(17\) | 28.9343 | 0.412799 | 0.206400 | − | 0.978468i | \(-0.433825\pi\) | ||||
0.206400 | + | 0.978468i | \(0.433825\pi\) | |||||||
\(18\) | −6.01924 | + | 0.0652311i | −0.0788194 | + | 0.000854173i | ||||
\(19\) | 38.9416i | 0.470201i | 0.971971 | + | 0.235100i | \(0.0755419\pi\) | ||||
−0.971971 | + | 0.235100i | \(0.924458\pi\) | |||||||
\(20\) | 148.687 | 1.66238 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −10.2126 | −0.0989701 | ||||||||
\(23\) | − | 1.79304i | − | 0.0162554i | −0.999967 | − | 0.00812772i | \(-0.997413\pi\) | ||
0.999967 | − | 0.00812772i | \(-0.00258716\pi\) | |||||||
\(24\) | 12.9949 | − | 13.1365i | 0.110524 | − | 0.111728i | ||||
\(25\) | 224.770 | 1.79816 | ||||||||
\(26\) | 13.2373 | 0.0998480 | ||||||||
\(27\) | 97.5787 | − | 100.804i | 0.695520 | − | 0.718507i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 148.759i | − | 0.952545i | −0.879298 | − | 0.476272i | \(-0.841988\pi\) | ||
0.879298 | − | 0.476272i | \(-0.158012\pi\) | |||||||
\(30\) | 15.2369 | − | 15.4029i | 0.0927286 | − | 0.0937389i | ||||
\(31\) | − | 104.052i | − | 0.602848i | −0.953490 | − | 0.301424i | \(-0.902538\pi\) | ||
0.953490 | − | 0.301424i | \(-0.0974620\pi\) | |||||||
\(32\) | 42.4519i | 0.234516i | ||||||||
\(33\) | 167.392 | − | 169.216i | 0.883008 | − | 0.892629i | ||||
\(34\) | 6.45083i | 0.0325385i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 2.32613 | + | 214.645i | 0.0107691 | + | 0.993728i | ||||
\(37\) | −24.1630 | −0.107361 | −0.0536806 | − | 0.998558i | \(-0.517095\pi\) | ||||
−0.0536806 | + | 0.998558i | \(0.517095\pi\) | |||||||
\(38\) | −8.68195 | −0.0370631 | ||||||||
\(39\) | −216.969 | + | 219.333i | −0.890841 | + | 0.900547i | ||||
\(40\) | 66.5064i | 0.262890i | ||||||||
\(41\) | −254.946 | −0.971118 | −0.485559 | − | 0.874204i | \(-0.661384\pi\) | ||||
−0.485559 | + | 0.874204i | \(0.661384\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −59.6604 | −0.211584 | −0.105792 | − | 0.994388i | \(-0.533738\pi\) | ||||
−0.105792 | + | 0.994388i | \(0.533738\pi\) | |||||||
\(44\) | 364.181i | 1.24778i | ||||||||
\(45\) | 5.47195 | + | 504.928i | 0.0181269 | + | 1.67267i | ||||
\(46\) | 0.399755 | 0.00128132 | ||||||||
\(47\) | −262.649 | −0.815135 | −0.407567 | − | 0.913175i | \(-0.633623\pi\) | ||||
−0.407567 | + | 0.913175i | \(0.633623\pi\) | |||||||
\(48\) | −232.024 | − | 229.523i | −0.697704 | − | 0.690184i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 50.1119i | 0.141738i | ||||||||
\(51\) | −106.886 | − | 105.734i | −0.293470 | − | 0.290307i | ||||
\(52\) | − | 472.040i | − | 1.25885i | ||||||
\(53\) | − | 381.628i | − | 0.989069i | −0.869158 | − | 0.494534i | \(-0.835339\pi\) | ||
0.869158 | − | 0.494534i | \(-0.164661\pi\) | |||||||
\(54\) | 22.4740 | + | 21.7550i | 0.0566356 | + | 0.0548237i | ||||
\(55\) | 856.694i | 2.10030i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 142.303 | − | 143.854i | 0.330676 | − | 0.334279i | ||||
\(58\) | 33.1654 | 0.0750834 | ||||||||
\(59\) | −371.060 | −0.818779 | −0.409389 | − | 0.912360i | \(-0.634258\pi\) | ||||
−0.409389 | + | 0.912360i | \(0.634258\pi\) | |||||||
\(60\) | −549.265 | − | 543.344i | −1.18183 | − | 1.16909i | ||||
\(61\) | 696.288i | 1.46148i | 0.682654 | + | 0.730742i | \(0.260826\pi\) | ||||
−0.682654 | + | 0.730742i | \(0.739174\pi\) | |||||||
\(62\) | 23.1982 | 0.0475189 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 493.012 | 0.962913 | ||||||||
\(65\) | − | 1110.42i | − | 2.11893i | ||||||
\(66\) | 37.7264 | + | 37.3198i | 0.0703606 | + | 0.0696022i | ||||
\(67\) | 434.164 | 0.791665 | 0.395833 | − | 0.918323i | \(-0.370456\pi\) | ||||
0.395833 | + | 0.918323i | \(0.370456\pi\) | |||||||
\(68\) | 230.036 | 0.410235 | ||||||||
\(69\) | −6.55227 | + | 6.62366i | −0.0114319 | + | 0.0115564i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 824.756i | 1.37860i | 0.724476 | + | 0.689300i | \(0.242082\pi\) | ||||
−0.724476 | + | 0.689300i | \(0.757918\pi\) | |||||||
\(72\) | −96.0087 | + | 1.04046i | −0.157149 | + | 0.00170304i | ||||
\(73\) | 0.395276i | 0.000633747i | 1.00000 | 0.000316873i | \(0.000100864\pi\) | |||||
−1.00000 | 0.000316873i | \(0.999899\pi\) | ||||||||
\(74\) | − | 5.38708i | − | 0.00846264i | ||||||
\(75\) | −830.319 | − | 821.370i | −1.27836 | − | 1.26458i | ||||
\(76\) | 309.597i | 0.467279i | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −48.8998 | − | 48.3727i | −0.0709847 | − | 0.0702196i | ||||
\(79\) | −731.265 | −1.04144 | −0.520720 | − | 0.853728i | \(-0.674336\pi\) | ||||
−0.520720 | + | 0.853728i | \(0.674336\pi\) | |||||||
\(80\) | 1174.67 | 1.64165 | ||||||||
\(81\) | −728.829 | + | 15.7986i | −0.999765 | + | 0.0216717i | ||||
\(82\) | − | 56.8397i | − | 0.0765474i | ||||||
\(83\) | −586.330 | −0.775399 | −0.387700 | − | 0.921786i | \(-0.626730\pi\) | ||||
−0.387700 | + | 0.921786i | \(0.626730\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 541.132 | 0.690518 | ||||||||
\(86\) | − | 13.3012i | − | 0.0166779i | ||||||
\(87\) | −543.605 | + | 549.528i | −0.669891 | + | 0.677190i | ||||
\(88\) | −162.895 | −0.197325 | ||||||||
\(89\) | 440.284 | 0.524382 | 0.262191 | − | 0.965016i | \(-0.415555\pi\) | ||||
0.262191 | + | 0.965016i | \(0.415555\pi\) | |||||||
\(90\) | −112.573 | + | 1.21996i | −0.131847 | + | 0.00142884i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | − | 14.2552i | − | 0.0161544i | ||||||
\(93\) | −380.234 | + | 384.377i | −0.423962 | + | 0.428581i | ||||
\(94\) | − | 58.5571i | − | 0.0642522i | ||||||
\(95\) | 728.291i | 0.786538i | ||||||||
\(96\) | 155.131 | − | 156.821i | 0.164927 | − | 0.166724i | ||||
\(97\) | − | 634.224i | − | 0.663873i | −0.943302 | − | 0.331937i | \(-0.892298\pi\) | ||
0.943302 | − | 0.331937i | \(-0.107702\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1236.72 | + | 13.4025i | −1.25551 | + | 0.0136061i | ||||
\(100\) | 1786.99 | 1.78699 | ||||||||
\(101\) | −1533.91 | −1.51119 | −0.755593 | − | 0.655042i | \(-0.772651\pi\) | ||||
−0.755593 | + | 0.655042i | \(0.772651\pi\) | |||||||
\(102\) | 23.5731 | − | 23.8300i | 0.0228832 | − | 0.0231325i | ||||
\(103\) | 1214.17i | 1.16151i | 0.814079 | + | 0.580754i | \(0.197242\pi\) | ||||
−0.814079 | + | 0.580754i | \(0.802758\pi\) | |||||||
\(104\) | 211.139 | 0.199076 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 85.0832 | 0.0779624 | ||||||||
\(107\) | 1794.55i | 1.62136i | 0.585487 | + | 0.810682i | \(0.300903\pi\) | ||||
−0.585487 | + | 0.810682i | \(0.699097\pi\) | |||||||
\(108\) | 775.780 | − | 801.419i | 0.691198 | − | 0.714043i | ||||
\(109\) | 1483.26 | 1.30340 | 0.651700 | − | 0.758477i | \(-0.274056\pi\) | ||||
0.651700 | + | 0.758477i | \(0.274056\pi\) | |||||||
\(110\) | −190.998 | −0.165554 | ||||||||
\(111\) | 89.2601 | + | 88.2980i | 0.0763261 | + | 0.0755034i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 1665.23i | − | 1.38630i | −0.720794 | − | 0.693150i | \(-0.756222\pi\) | ||
0.720794 | − | 0.693150i | \(-0.243778\pi\) | |||||||
\(114\) | 32.0719 | + | 31.7262i | 0.0263492 | + | 0.0260652i | ||||
\(115\) | − | 33.5337i | − | 0.0271916i | ||||||
\(116\) | − | 1182.68i | − | 0.946626i | ||||||
\(117\) | 1603.00 | − | 17.3719i | 1.26665 | − | 0.0137268i | ||||
\(118\) | − | 82.7271i | − | 0.0645394i | ||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 243.032 | − | 245.680i | 0.184881 | − | 0.186895i | ||||
\(121\) | −767.307 | −0.576489 | ||||||||
\(122\) | −155.236 | −0.115200 | ||||||||
\(123\) | 941.793 | + | 931.642i | 0.690395 | + | 0.682954i | ||||
\(124\) | − | 827.244i | − | 0.599102i | ||||||
\(125\) | 1865.91 | 1.33513 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1784.43 | −1.24679 | −0.623395 | − | 0.781907i | \(-0.714247\pi\) | ||||
−0.623395 | + | 0.781907i | \(0.714247\pi\) | |||||||
\(128\) | 449.531i | 0.310417i | ||||||||
\(129\) | 220.391 | + | 218.015i | 0.150421 | + | 0.148800i | ||||
\(130\) | 247.566 | 0.167023 | ||||||||
\(131\) | −1103.06 | −0.735686 | −0.367843 | − | 0.929888i | \(-0.619904\pi\) | ||||
−0.367843 | + | 0.929888i | \(0.619904\pi\) | |||||||
\(132\) | 1330.82 | − | 1345.32i | 0.877521 | − | 0.887083i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 96.7960i | 0.0624022i | ||||||||
\(135\) | 1824.93 | − | 1885.24i | 1.16344 | − | 1.20190i | ||||
\(136\) | 102.893i | 0.0648748i | ||||||||
\(137\) | 2168.96i | 1.35260i | 0.736625 | + | 0.676302i | \(0.236418\pi\) | ||||
−0.736625 | + | 0.676302i | \(0.763582\pi\) | |||||||
\(138\) | −1.47673 | − | 1.46081i | −0.000910925 | − | 0.000901107i | ||||
\(139\) | − | 2246.90i | − | 1.37107i | −0.728038 | − | 0.685537i | \(-0.759568\pi\) | ||
0.728038 | − | 0.685537i | \(-0.240432\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 970.250 | + | 959.792i | 0.579502 | + | 0.573256i | ||||
\(142\) | −183.878 | −0.108667 | ||||||||
\(143\) | 2719.76 | 1.59047 | ||||||||
\(144\) | 18.3771 | + | 1695.76i | 0.0106349 | + | 0.981341i | ||||
\(145\) | − | 2782.10i | − | 1.59339i | ||||||
\(146\) | −0.0881259 | −4.99545e−5 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −192.103 | −0.106694 | ||||||||
\(149\) | − | 1554.26i | − | 0.854563i | −0.904119 | − | 0.427281i | \(-0.859471\pi\) | ||
0.904119 | − | 0.427281i | \(-0.140529\pi\) | |||||||
\(150\) | 183.123 | − | 185.118i | 0.0996794 | − | 0.100765i | ||||
\(151\) | −1878.53 | −1.01240 | −0.506201 | − | 0.862416i | \(-0.668950\pi\) | ||||
−0.506201 | + | 0.862416i | \(0.668950\pi\) | |||||||
\(152\) | −138.480 | −0.0738960 | ||||||||
\(153\) | 8.46572 | + | 781.179i | 0.00447328 | + | 0.412775i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 1945.99i | − | 1.00843i | ||||||
\(156\) | −1724.96 | + | 1743.76i | −0.885306 | + | 0.894952i | ||||
\(157\) | − | 45.7355i | − | 0.0232490i | −0.999932 | − | 0.0116245i | \(-0.996300\pi\) | ||
0.999932 | − | 0.0116245i | \(-0.00370028\pi\) | |||||||
\(158\) | − | 163.034i | − | 0.0820905i | ||||||
\(159\) | −1394.57 | + | 1409.77i | −0.695578 | + | 0.703157i | ||||
\(160\) | 793.942i | 0.392291i | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −3.52227 | − | 162.491i | −0.00170825 | − | 0.0788055i | ||||
\(163\) | 664.899 | 0.319503 | 0.159751 | − | 0.987157i | \(-0.448931\pi\) | ||||
0.159751 | + | 0.987157i | \(0.448931\pi\) | |||||||
\(164\) | −2026.89 | −0.965085 | ||||||||
\(165\) | 3130.59 | − | 3164.70i | 1.47707 | − | 1.49316i | ||||
\(166\) | − | 130.721i | − | 0.0611201i | ||||||
\(167\) | −88.2591 | −0.0408964 | −0.0204482 | − | 0.999791i | \(-0.506509\pi\) | ||||
−0.0204482 | + | 0.999791i | \(0.506509\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1328.27 | −0.604582 | ||||||||
\(170\) | 120.644i | 0.0544294i | ||||||||
\(171\) | −1051.36 | + | 11.3937i | −0.470173 | + | 0.00509531i | ||||
\(172\) | −474.318 | −0.210270 | ||||||||
\(173\) | 2730.30 | 1.19989 | 0.599945 | − | 0.800041i | \(-0.295189\pi\) | ||||
0.599945 | + | 0.800041i | \(0.295189\pi\) | |||||||
\(174\) | −122.516 | − | 121.196i | −0.0533789 | − | 0.0528035i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 2877.13i | 1.23223i | ||||||||
\(177\) | 1370.73 | + | 1355.96i | 0.582092 | + | 0.575818i | ||||
\(178\) | 98.1603i | 0.0413339i | ||||||||
\(179\) | − | 1620.70i | − | 0.676741i | −0.941013 | − | 0.338371i | \(-0.890124\pi\) | ||
0.941013 | − | 0.338371i | \(-0.109876\pi\) | |||||||
\(180\) | 43.5036 | + | 4014.33i | 0.0180143 | + | 1.66228i | ||||
\(181\) | 1433.62i | 0.588728i | 0.955693 | + | 0.294364i | \(0.0951078\pi\) | ||||
−0.955693 | + | 0.294364i | \(0.904892\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 2544.43 | − | 2572.15i | 1.02781 | − | 1.03901i | ||||
\(184\) | 6.37621 | 0.00255468 | ||||||||
\(185\) | −451.899 | −0.179591 | ||||||||
\(186\) | −85.6961 | − | 84.7725i | −0.0337825 | − | 0.0334184i | ||||
\(187\) | 1325.40i | 0.518304i | ||||||||
\(188\) | −2088.14 | −0.810070 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −162.371 | −0.0619980 | ||||||||
\(191\) | 541.389i | 0.205097i | 0.994728 | + | 0.102549i | \(0.0326997\pi\) | ||||
−0.994728 | + | 0.102549i | \(0.967300\pi\) | |||||||
\(192\) | −1821.23 | − | 1801.60i | −0.684562 | − | 0.677183i | ||||
\(193\) | −4950.31 | −1.84627 | −0.923137 | − | 0.384470i | \(-0.874384\pi\) | ||||
−0.923137 | + | 0.384470i | \(0.874384\pi\) | |||||||
\(194\) | 141.399 | 0.0523291 | ||||||||
\(195\) | −4057.78 | + | 4101.99i | −1.49017 | + | 1.50641i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 3674.51i | 1.32892i | 0.747322 | + | 0.664462i | \(0.231339\pi\) | ||||
−0.747322 | + | 0.664462i | \(0.768661\pi\) | |||||||
\(198\) | −2.98806 | − | 275.725i | −0.00107249 | − | 0.0989643i | ||||
\(199\) | 2322.22i | 0.827227i | 0.910453 | + | 0.413613i | \(0.135733\pi\) | ||||
−0.910453 | + | 0.413613i | \(0.864267\pi\) | |||||||
\(200\) | 799.300i | 0.282595i | ||||||||
\(201\) | −1603.84 | − | 1586.55i | −0.562817 | − | 0.556750i | ||||
\(202\) | − | 341.982i | − | 0.119118i | ||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −849.773 | − | 840.614i | −0.291647 | − | 0.288504i | ||||
\(205\) | −4768.03 | −1.62446 | ||||||||
\(206\) | −270.696 | −0.0915548 | ||||||||
\(207\) | 48.4093 | − | 0.524617i | 0.0162545 | − | 0.000176152i | ||||
\(208\) | − | 3729.25i | − | 1.24316i | ||||||
\(209\) | −1783.81 | −0.590376 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4047.51 | 1.32058 | 0.660289 | − | 0.751012i | \(-0.270434\pi\) | ||||
0.660289 | + | 0.751012i | \(0.270434\pi\) | |||||||
\(212\) | − | 3034.06i | − | 0.982924i | ||||||
\(213\) | 3013.88 | − | 3046.72i | 0.969521 | − | 0.980084i | ||||
\(214\) | −400.092 | −0.127802 | ||||||||
\(215\) | −1115.78 | −0.353932 | ||||||||
\(216\) | 358.467 | + | 346.998i | 0.112919 | + | 0.109307i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 330.690i | 0.102739i | ||||||||
\(219\) | 1.44444 | − | 1.46018i | 0.000445692 | − | 0.000450548i | ||||
\(220\) | 6810.97i | 2.08725i | ||||||||
\(221\) | − | 1717.94i | − | 0.522902i | ||||||
\(222\) | −19.6859 | + | 19.9004i | −0.00595148 | + | 0.00601633i | ||||
\(223\) | − | 3387.56i | − | 1.01725i | −0.860987 | − | 0.508627i | \(-0.830153\pi\) | ||
0.860987 | − | 0.508627i | \(-0.169847\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 65.7641 | + | 6068.43i | 0.0194857 | + | 1.79805i | ||||
\(226\) | 371.260 | 0.109274 | ||||||||
\(227\) | 2323.62 | 0.679402 | 0.339701 | − | 0.940533i | \(-0.389674\pi\) | ||||
0.339701 | + | 0.940533i | \(0.389674\pi\) | |||||||
\(228\) | 1131.35 | − | 1143.68i | 0.328621 | − | 0.332202i | ||||
\(229\) | 280.878i | 0.0810521i | 0.999178 | + | 0.0405261i | \(0.0129034\pi\) | ||||
−0.999178 | + | 0.0405261i | \(0.987097\pi\) | |||||||
\(230\) | 7.47627 | 0.00214335 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 528.999 | 0.149700 | ||||||||
\(233\) | − | 1559.78i | − | 0.438562i | −0.975662 | − | 0.219281i | \(-0.929629\pi\) | ||
0.975662 | − | 0.219281i | \(-0.0703711\pi\) | |||||||
\(234\) | 3.87303 | + | 357.386i | 0.00108200 | + | 0.0998422i | ||||
\(235\) | −4912.10 | −1.36353 | ||||||||
\(236\) | −2950.04 | −0.813691 | ||||||||
\(237\) | 2701.36 | + | 2672.24i | 0.740389 | + | 0.732408i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 1346.90i | − | 0.364534i | −0.983249 | − | 0.182267i | \(-0.941656\pi\) | ||
0.983249 | − | 0.182267i | \(-0.0583436\pi\) | |||||||
\(240\) | −4339.34 | − | 4292.57i | −1.16710 | − | 1.15452i | ||||
\(241\) | − | 4034.73i | − | 1.07842i | −0.842171 | − | 0.539211i | \(-0.818723\pi\) | ||
0.842171 | − | 0.539211i | \(-0.181277\pi\) | |||||||
\(242\) | − | 171.069i | − | 0.0454412i | ||||||
\(243\) | 2750.09 | + | 2604.98i | 0.726002 | + | 0.687693i | ||||
\(244\) | 5535.69i | 1.45240i | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −207.708 | + | 209.971i | −0.0538331 | + | 0.0544197i | ||||
\(247\) | 2312.12 | 0.595613 | ||||||||
\(248\) | 370.018 | 0.0947425 | ||||||||
\(249\) | 2165.96 | + | 2142.61i | 0.551253 | + | 0.545311i | ||||
\(250\) | 416.000i | 0.105241i | ||||||||
\(251\) | 585.826 | 0.147319 | 0.0736593 | − | 0.997283i | \(-0.476532\pi\) | ||||
0.0736593 | + | 0.997283i | \(0.476532\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 82.1344 | 0.0204101 | ||||||||
\(254\) | − | 397.834i | − | 0.0982770i | ||||||
\(255\) | −1998.99 | − | 1977.44i | −0.490908 | − | 0.485617i | ||||
\(256\) | 3843.87 | 0.938445 | ||||||||
\(257\) | −1768.90 | −0.429342 | −0.214671 | − | 0.976686i | \(-0.568868\pi\) | ||||
−0.214671 | + | 0.976686i | \(0.568868\pi\) | |||||||
\(258\) | −48.6061 | + | 49.1357i | −0.0117290 | + | 0.0118568i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | − | 8828.16i | − | 2.10577i | ||||||
\(261\) | 4016.25 | − | 43.5245i | 0.952489 | − | 0.0103222i | ||||
\(262\) | − | 245.925i | − | 0.0579897i | ||||||
\(263\) | − | 7837.35i | − | 1.83754i | −0.394799 | − | 0.918768i | \(-0.629186\pi\) | ||
0.394799 | − | 0.918768i | \(-0.370814\pi\) | |||||||
\(264\) | 601.747 | + | 595.261i | 0.140284 | + | 0.138772i | ||||
\(265\) | − | 7137.26i | − | 1.65448i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −1626.45 | − | 1608.92i | −0.372797 | − | 0.368779i | ||||
\(268\) | 3451.73 | 0.786746 | ||||||||
\(269\) | −4786.13 | −1.08482 | −0.542408 | − | 0.840115i | \(-0.682487\pi\) | ||||
−0.542408 | + | 0.840115i | \(0.682487\pi\) | |||||||
\(270\) | 420.311 | + | 406.864i | 0.0947383 | + | 0.0917073i | ||||
\(271\) | 2088.95i | 0.468246i | 0.972207 | + | 0.234123i | \(0.0752219\pi\) | ||||
−0.972207 | + | 0.234123i | \(0.924778\pi\) | |||||||
\(272\) | 1817.35 | 0.405121 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −483.565 | −0.106618 | ||||||||
\(275\) | 10296.1i | 2.25774i | ||||||||
\(276\) | −52.0925 | + | 52.6600i | −0.0113609 | + | 0.0114846i | ||||
\(277\) | 1577.27 | 0.342126 | 0.171063 | − | 0.985260i | \(-0.445280\pi\) | ||||
0.171063 | + | 0.985260i | \(0.445280\pi\) | |||||||
\(278\) | 500.941 | 0.108073 | ||||||||
\(279\) | 2809.24 | − | 30.4440i | 0.602813 | − | 0.00653274i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 4744.03i | 1.00714i | 0.863956 | + | 0.503568i | \(0.167980\pi\) | ||||
−0.863956 | + | 0.503568i | \(0.832020\pi\) | |||||||
\(282\) | −213.984 | + | 216.315i | −0.0451863 | + | 0.0456787i | ||||
\(283\) | 39.7652i | 0.00835264i | 0.999991 | + | 0.00417632i | \(0.00132937\pi\) | ||||
−0.999991 | + | 0.00417632i | \(0.998671\pi\) | |||||||
\(284\) | 6557.05i | 1.37003i | ||||||||
\(285\) | 2661.37 | − | 2690.37i | 0.553144 | − | 0.559171i | ||||
\(286\) | 606.365i | 0.125367i | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −1146.14 | + | 12.4208i | −0.234502 | + | 0.00254132i | ||||
\(289\) | −4075.81 | −0.829597 | ||||||||
\(290\) | 620.264 | 0.125597 | ||||||||
\(291\) | −2317.63 | + | 2342.88i | −0.466879 | + | 0.471966i | ||||
\(292\) | 3.14256i | 0.000629809i | ||||||||
\(293\) | 67.9150 | 0.0135414 | 0.00677071 | − | 0.999977i | \(-0.497845\pi\) | ||||
0.00677071 | + | 0.999977i | \(0.497845\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −6939.62 | −1.36963 | ||||||||
\(296\) | − | 85.9255i | − | 0.0168727i | ||||||
\(297\) | 4617.54 | + | 4469.82i | 0.902145 | + | 0.873283i | ||||
\(298\) | 346.519 | 0.0673601 | ||||||||
\(299\) | −106.460 | −0.0205911 | ||||||||
\(300\) | −6601.28 | − | 6530.13i | −1.27042 | − | 1.25672i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | − | 418.814i | − | 0.0798015i | ||||||
\(303\) | 5666.40 | + | 5605.33i | 1.07434 | + | 1.06276i | ||||
\(304\) | 2445.90i | 0.461455i | ||||||||
\(305\) | 13022.1i | 2.44473i | ||||||||
\(306\) | −174.162 | + | 1.88741i | −0.0325366 | + | 0.000352602i | ||||
\(307\) | − | 846.145i | − | 0.157303i | −0.996902 | − | 0.0786516i | \(-0.974939\pi\) | ||
0.996902 | − | 0.0786516i | \(-0.0250615\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 4436.90 | − | 4485.24i | 0.816848 | − | 0.825749i | ||||
\(310\) | 433.855 | 0.0794881 | ||||||||
\(311\) | 3327.42 | 0.606690 | 0.303345 | − | 0.952881i | \(-0.401896\pi\) | ||||
0.303345 | + | 0.952881i | \(0.401896\pi\) | |||||||
\(312\) | −779.966 | − | 771.559i | −0.141528 | − | 0.140003i | ||||
\(313\) | − | 7816.49i | − | 1.41155i | −0.708438 | − | 0.705773i | \(-0.750600\pi\) | ||
0.708438 | − | 0.705773i | \(-0.249400\pi\) | |||||||
\(314\) | 10.1966 | 0.00183258 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −5813.77 | −1.03497 | ||||||||
\(317\) | − | 2263.17i | − | 0.400984i | −0.979695 | − | 0.200492i | \(-0.935746\pi\) | ||
0.979695 | − | 0.200492i | \(-0.0642541\pi\) | |||||||
\(318\) | −314.305 | − | 310.917i | −0.0554256 | − | 0.0548282i | ||||
\(319\) | 6814.23 | 1.19600 | ||||||||
\(320\) | 9220.37 | 1.61073 | ||||||||
\(321\) | 6557.78 | − | 6629.23i | 1.14025 | − | 1.15267i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1126.75i | 0.194099i | ||||||||
\(324\) | −5794.40 | + | 125.604i | −0.993553 | + | 0.0215370i | ||||
\(325\) | − | 13345.5i | − | 2.27776i | ||||||
\(326\) | 148.238i | 0.0251845i | ||||||||
\(327\) | −5479.29 | − | 5420.24i | −0.926623 | − | 0.916635i | ||||
\(328\) | − | 906.609i | − | 0.152619i | ||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 705.564 | + | 697.959i | 0.117697 | + | 0.116428i | ||||
\(331\) | 5712.25 | 0.948562 | 0.474281 | − | 0.880374i | \(-0.342708\pi\) | ||||
0.474281 | + | 0.880374i | \(0.342708\pi\) | |||||||
\(332\) | −4661.50 | −0.770581 | ||||||||
\(333\) | −7.06971 | − | 652.362i | −0.00116342 | − | 0.107355i | ||||
\(334\) | − | 19.6772i | − | 0.00322362i | ||||||
\(335\) | 8119.79 | 1.32427 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 9067.99 | 1.46577 | 0.732886 | − | 0.680352i | \(-0.238173\pi\) | ||||
0.732886 | + | 0.680352i | \(0.238173\pi\) | |||||||
\(338\) | − | 296.134i | − | 0.0476556i | ||||||
\(339\) | −6085.21 | + | 6151.52i | −0.974936 | + | 0.985559i | ||||
\(340\) | 4302.16 | 0.686228 | ||||||||
\(341\) | 4766.34 | 0.756926 | ||||||||
\(342\) | −2.54020 | − | 234.399i | −0.000401633 | − | 0.0370609i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | − | 212.157i | − | 0.0332522i | ||||||
\(345\) | −122.541 | + | 123.877i | −0.0191229 | + | 0.0193313i | ||||
\(346\) | 608.715i | 0.0945801i | ||||||||
\(347\) | − | 8616.41i | − | 1.33301i | −0.745502 | − | 0.666503i | \(-0.767790\pi\) | ||
0.745502 | − | 0.666503i | \(-0.232210\pi\) | |||||||
\(348\) | −4321.82 | + | 4368.91i | −0.665729 | + | 0.672983i | ||||
\(349\) | 7966.10i | 1.22182i | 0.791700 | + | 0.610911i | \(0.209197\pi\) | ||||
−0.791700 | + | 0.610911i | \(0.790803\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −5985.12 | − | 5793.64i | −0.910148 | − | 0.881030i | ||||
\(352\) | −1944.61 | −0.294454 | ||||||||
\(353\) | 12274.8 | 1.85077 | 0.925385 | − | 0.379028i | \(-0.123741\pi\) | ||||
0.925385 | + | 0.379028i | \(0.123741\pi\) | |||||||
\(354\) | −302.308 | + | 305.601i | −0.0453883 | + | 0.0458829i | ||||
\(355\) | 15424.7i | 2.30608i | ||||||||
\(356\) | 3500.38 | 0.521124 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 361.331 | 0.0533434 | ||||||||
\(359\) | − | 11637.0i | − | 1.71080i | −0.517966 | − | 0.855401i | \(-0.673311\pi\) | ||
0.517966 | − | 0.855401i | \(-0.326689\pi\) | |||||||
\(360\) | −1795.57 | + | 19.4587i | −0.262874 | + | 0.00284879i | ||||
\(361\) | 5342.55 | 0.778911 | ||||||||
\(362\) | −319.622 | −0.0464059 | ||||||||
\(363\) | 2834.50 | + | 2803.95i | 0.409842 | + | 0.405425i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 7.39250i | 0.00106011i | ||||||||
\(366\) | 573.455 | + | 567.274i | 0.0818989 | + | 0.0810161i | ||||
\(367\) | − | 2435.83i | − | 0.346455i | −0.984882 | − | 0.173228i | \(-0.944580\pi\) | ||
0.984882 | − | 0.173228i | \(-0.0554197\pi\) | |||||||
\(368\) | − | 112.620i | − | 0.0159531i | ||||||
\(369\) | −74.5932 | − | 6883.13i | −0.0105235 | − | 0.971061i | ||||
\(370\) | − | 100.750i | − | 0.0141560i | ||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −3022.97 | + | 3055.91i | −0.421328 | + | 0.425918i | ||||
\(373\) | 2398.17 | 0.332902 | 0.166451 | − | 0.986050i | \(-0.446769\pi\) | ||||
0.166451 | + | 0.986050i | \(0.446769\pi\) | |||||||
\(374\) | −295.495 | −0.0408548 | ||||||||
\(375\) | −6892.82 | − | 6818.53i | −0.949183 | − | 0.938953i | ||||
\(376\) | − | 934.003i | − | 0.128105i | ||||||
\(377\) | −8832.39 | −1.20661 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −7291.15 | −0.988183 | −0.494091 | − | 0.869410i | \(-0.664499\pi\) | ||||
−0.494091 | + | 0.869410i | \(0.664499\pi\) | |||||||
\(380\) | 5790.13i | 0.781651i | ||||||||
\(381\) | 6591.83 | + | 6520.78i | 0.886377 | + | 0.876824i | ||||
\(382\) | −120.702 | −0.0161666 | ||||||||
\(383\) | −9402.66 | −1.25445 | −0.627224 | − | 0.778839i | \(-0.715809\pi\) | ||||
−0.627224 | + | 0.778839i | \(0.715809\pi\) | |||||||
\(384\) | 1642.71 | − | 1660.61i | 0.218305 | − | 0.220684i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | − | 1103.66i | − | 0.145531i | ||||||
\(387\) | −17.4557 | − | 1610.74i | −0.00229283 | − | 0.211572i | ||||
\(388\) | − | 5042.27i | − | 0.659748i | ||||||
\(389\) | − | 292.651i | − | 0.0381439i | −0.999818 | − | 0.0190720i | \(-0.993929\pi\) | ||
0.999818 | − | 0.0190720i | \(-0.00607116\pi\) | |||||||
\(390\) | −914.530 | − | 904.673i | −0.118741 | − | 0.117461i | ||||
\(391\) | − | 51.8804i | − | 0.00671024i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 4074.80 | + | 4030.88i | 0.523019 | + | 0.517382i | ||||
\(394\) | −819.224 | −0.104751 | ||||||||
\(395\) | −13676.2 | −1.74209 | ||||||||
\(396\) | −9832.32 | + | 106.554i | −1.24771 | + | 0.0135215i | ||||
\(397\) | 6673.62i | 0.843676i | 0.906671 | + | 0.421838i | \(0.138615\pi\) | ||||
−0.906671 | + | 0.421838i | \(0.861385\pi\) | |||||||
\(398\) | −517.735 | −0.0652053 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 14117.7 | 1.76471 | ||||||||
\(401\) | 2274.67i | 0.283270i | 0.989919 | + | 0.141635i | \(0.0452360\pi\) | ||||
−0.989919 | + | 0.141635i | \(0.954764\pi\) | |||||||
\(402\) | 353.719 | − | 357.573i | 0.0438853 | − | 0.0443635i | ||||
\(403\) | −6177.98 | −0.763640 | ||||||||
\(404\) | −12195.0 | −1.50180 | ||||||||
\(405\) | −13630.7 | + | 295.468i | −1.67238 | + | 0.0362517i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 1106.84i | − | 0.134801i | ||||||
\(408\) | 375.998 | − | 380.095i | 0.0456242 | − | 0.0461213i | ||||
\(409\) | 14591.8i | 1.76411i | 0.471151 | + | 0.882053i | \(0.343839\pi\) | ||||
−0.471151 | + | 0.882053i | \(0.656161\pi\) | |||||||
\(410\) | − | 1063.02i | − | 0.128046i | ||||||
\(411\) | 7925.97 | − | 8012.33i | 0.951239 | − | 0.961603i | ||||
\(412\) | 9652.98i | 1.15429i | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0.116962 | + | 10.7928i | 1.38850e−5 | + | 0.00128124i | ||||
\(415\) | −10965.6 | −1.29706 | ||||||||
\(416\) | 2520.54 | 0.297066 | ||||||||
\(417\) | −8210.77 | + | 8300.23i | −0.964228 | + | 0.974734i | ||||
\(418\) | − | 397.697i | − | 0.0465358i | ||||||
\(419\) | −12090.7 | −1.40971 | −0.704855 | − | 0.709351i | \(-0.748988\pi\) | ||||
−0.704855 | + | 0.709351i | \(0.748988\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 7230.48 | 0.837036 | 0.418518 | − | 0.908209i | \(-0.362550\pi\) | ||||
0.418518 | + | 0.908209i | \(0.362550\pi\) | |||||||
\(422\) | 902.384i | 0.104093i | ||||||||
\(423\) | −76.8471 | − | 7091.11i | −0.00883318 | − | 0.815087i | ||||
\(424\) | 1357.10 | 0.155440 | ||||||||
\(425\) | 6503.54 | 0.742278 | ||||||||
\(426\) | 679.261 | + | 671.939i | 0.0772542 | + | 0.0764215i | ||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 14267.2i | 1.61129i | ||||||||
\(429\) | −10047.0 | − | 9938.74i | −1.13071 | − | 1.11852i | ||||
\(430\) | − | 248.760i | − | 0.0278983i | ||||||
\(431\) | − | 1901.11i | − | 0.212467i | −0.994341 | − | 0.106233i | \(-0.966121\pi\) | ||
0.994341 | − | 0.106233i | \(-0.0338791\pi\) | |||||||
\(432\) | 6128.87 | − | 6331.43i | 0.682582 | − | 0.705142i | ||||
\(433\) | 1867.06i | 0.207218i | 0.994618 | + | 0.103609i | \(0.0330391\pi\) | ||||
−0.994618 | + | 0.103609i | \(0.966961\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −10166.6 | + | 10277.3i | −1.12057 | + | 1.13278i | ||||
\(436\) | 11792.4 | 1.29530 | ||||||||
\(437\) | 69.8240 | 0.00764333 | ||||||||
\(438\) | 0.325545 | + | 0.322036i | 3.55140e−5 | + | 3.51312e-5i | ||||
\(439\) | 7249.39i | 0.788142i | 0.919080 | + | 0.394071i | \(0.128934\pi\) | ||||
−0.919080 | + | 0.394071i | \(0.871066\pi\) | |||||||
\(440\) | −3046.48 | −0.330080 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 383.012 | 0.0412172 | ||||||||
\(443\) | 10213.3i | 1.09537i | 0.836684 | + | 0.547685i | \(0.184491\pi\) | ||||
−0.836684 | + | 0.547685i | \(0.815509\pi\) | |||||||
\(444\) | 709.644 | + | 701.995i | 0.0758518 | + | 0.0750343i | ||||
\(445\) | 8234.24 | 0.877170 | ||||||||
\(446\) | 755.249 | 0.0801841 | ||||||||
\(447\) | −5679.69 | + | 5741.57i | −0.600984 | + | 0.607532i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 5515.44i | − | 0.579710i | −0.957071 | − | 0.289855i | \(-0.906393\pi\) | ||
0.957071 | − | 0.289855i | \(-0.0936071\pi\) | |||||||
\(450\) | −1352.94 | + | 14.6620i | −0.141730 | + | 0.00153594i | ||||
\(451\) | − | 11678.4i | − | 1.21932i | ||||||
\(452\) | − | 13239.1i | − | 1.37769i | ||||||
\(453\) | 6939.46 | + | 6864.66i | 0.719744 | + | 0.711986i | ||||
\(454\) | 518.047i | 0.0535532i | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 511.556 | + | 506.042i | 0.0525347 | + | 0.0519684i | ||||
\(457\) | −7867.61 | −0.805320 | −0.402660 | − | 0.915350i | \(-0.631914\pi\) | ||||
−0.402660 | + | 0.915350i | \(0.631914\pi\) | |||||||
\(458\) | −62.6212 | −0.00638885 | ||||||||
\(459\) | 2823.37 | − | 2916.68i | 0.287110 | − | 0.296599i | ||||
\(460\) | − | 266.603i | − | 0.0270227i | ||||||
\(461\) | −1034.73 | −0.104538 | −0.0522691 | − | 0.998633i | \(-0.516645\pi\) | ||||
−0.0522691 | + | 0.998633i | \(0.516645\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 17777.7 | 1.78445 | 0.892226 | − | 0.451590i | \(-0.149143\pi\) | ||||
0.892226 | + | 0.451590i | \(0.149143\pi\) | |||||||
\(464\) | − | 9343.46i | − | 0.934826i | ||||||
\(465\) | −7111.19 | + | 7188.67i | −0.709191 | + | 0.716918i | ||||
\(466\) | 347.751 | 0.0345692 | ||||||||
\(467\) | 1792.39 | 0.177606 | 0.0888029 | − | 0.996049i | \(-0.471696\pi\) | ||||
0.0888029 | + | 0.996049i | \(0.471696\pi\) | |||||||
\(468\) | 12744.3 | − | 138.112i | 1.25878 | − | 0.0136415i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | − | 1095.14i | − | 0.107479i | ||||||
\(471\) | −167.130 | + | 168.951i | −0.0163502 | + | 0.0165284i | ||||
\(472\) | − | 1319.52i | − | 0.128678i | ||||||
\(473\) | − | 2732.88i | − | 0.265662i | ||||||
\(474\) | −595.771 | + | 602.262i | −0.0577314 | + | 0.0583604i | ||||
\(475\) | 8752.89i | 0.845495i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 10303.4 | − | 111.658i | 0.989011 | − | 0.0107180i | ||||
\(478\) | 300.288 | 0.0287340 | ||||||||
\(479\) | −12548.4 | −1.19697 | −0.598487 | − | 0.801133i | \(-0.704231\pi\) | ||||
−0.598487 | + | 0.801133i | \(0.704231\pi\) | |||||||
\(480\) | 2901.28 | − | 2932.89i | 0.275885 | − | 0.278891i | ||||
\(481\) | 1434.65i | 0.135997i | ||||||||
\(482\) | 899.534 | 0.0850055 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −6100.31 | −0.572907 | ||||||||
\(485\) | − | 11861.3i | − | 1.11051i | ||||||
\(486\) | −580.774 | + | 613.127i | −0.0542067 | + | 0.0572264i | ||||
\(487\) | −4480.51 | −0.416902 | −0.208451 | − | 0.978033i | \(-0.566842\pi\) | ||||
−0.208451 | + | 0.978033i | \(0.566842\pi\) | |||||||
\(488\) | −2476.06 | −0.229684 | ||||||||
\(489\) | −2456.20 | − | 2429.72i | −0.227143 | − | 0.224695i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 14924.2i | − | 1.37173i | −0.727729 | − | 0.685865i | \(-0.759424\pi\) | ||
0.727729 | − | 0.685865i | \(-0.240576\pi\) | |||||||
\(492\) | 7487.53 | + | 7406.83i | 0.686105 | + | 0.678710i | ||||
\(493\) | − | 4304.22i | − | 0.393210i | ||||||
\(494\) | 515.482i | 0.0469486i | ||||||||
\(495\) | −23129.4 | + | 250.655i | −2.10018 | + | 0.0227598i | ||||
\(496\) | − | 6535.46i | − | 0.591634i | ||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −477.691 | + | 482.896i | −0.0429836 | + | 0.0434519i | ||||
\(499\) | 4653.18 | 0.417445 | 0.208722 | − | 0.977975i | \(-0.433069\pi\) | ||||
0.208722 | + | 0.977975i | \(0.433069\pi\) | |||||||
\(500\) | 14834.5 | 1.32684 | ||||||||
\(501\) | 326.037 | + | 322.523i | 0.0290744 | + | 0.0287610i | ||||
\(502\) | 130.609i | 0.0116122i | ||||||||
\(503\) | 14993.7 | 1.32910 | 0.664548 | − | 0.747246i | \(-0.268624\pi\) | ||||
0.664548 | + | 0.747246i | \(0.268624\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −28687.4 | −2.52787 | ||||||||
\(506\) | 18.3117i | 0.00160880i | ||||||||
\(507\) | 4906.74 | + | 4853.85i | 0.429814 | + | 0.425182i | ||||
\(508\) | −14186.7 | −1.23904 | ||||||||
\(509\) | −2997.18 | −0.260998 | −0.130499 | − | 0.991448i | \(-0.541658\pi\) | ||||
−0.130499 | + | 0.991448i | \(0.541658\pi\) | |||||||
\(510\) | 440.867 | − | 445.671i | 0.0382783 | − | 0.0386954i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 4453.23i | 0.384389i | ||||||||
\(513\) | 3925.46 | + | 3799.87i | 0.337843 | + | 0.327034i | ||||
\(514\) | − | 394.372i | − | 0.0338425i | ||||||
\(515\) | 22707.5i | 1.94294i | ||||||||
\(516\) | 1752.17 | + | 1733.29i | 0.149487 | + | 0.147875i | ||||
\(517\) | − | 12031.2i | − | 1.02347i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −10086.0 | − | 9977.27i | −0.853035 | − | 0.843841i | ||||
\(520\) | 3948.75 | 0.333008 | ||||||||
\(521\) | 15844.1 | 1.33233 | 0.666164 | − | 0.745806i | \(-0.267935\pi\) | ||||
0.666164 | + | 0.745806i | \(0.267935\pi\) | |||||||
\(522\) | 9.70369 | + | 895.414i | 0.000813638 | + | 0.0750790i | ||||
\(523\) | − | 12833.2i | − | 1.07296i | −0.843913 | − | 0.536480i | \(-0.819754\pi\) | ||
0.843913 | − | 0.536480i | \(-0.180246\pi\) | |||||||
\(524\) | −8769.65 | −0.731115 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 1747.32 | 0.144842 | ||||||||
\(527\) | − | 3010.67i | − | 0.248855i | ||||||
\(528\) | 10513.8 | − | 10628.4i | 0.866583 | − | 0.876025i | ||||
\(529\) | 12163.8 | 0.999736 | ||||||||
\(530\) | 1591.24 | 0.130413 | ||||||||
\(531\) | −108.567 | − | 10018.0i | −0.00887267 | − | 0.818731i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 15137.1i | 1.23014i | ||||||||
\(534\) | 358.705 | − | 362.613i | 0.0290687 | − | 0.0293854i | ||||
\(535\) | 33561.9i | 2.71217i | ||||||||
\(536\) | 1543.92i | 0.124417i | ||||||||
\(537\) | −5922.47 | + | 5987.00i | −0.475928 | + | 0.481114i | ||||
\(538\) | − | 1067.06i | − | 0.0855095i | ||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 14508.7 | − | 14988.2i | 1.15622 | − | 1.19443i | ||||
\(541\) | −8704.63 | −0.691759 | −0.345879 | − | 0.938279i | \(-0.612419\pi\) | ||||
−0.345879 | + | 0.938279i | \(0.612419\pi\) | |||||||
\(542\) | −465.727 | −0.0369090 | ||||||||
\(543\) | 5238.82 | − | 5295.90i | 0.414032 | − | 0.418543i | ||||
\(544\) | 1228.32i | 0.0968081i | ||||||||
\(545\) | 27740.1 | 2.18029 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −12998.5 | −1.01604 | −0.508020 | − | 0.861345i | \(-0.669623\pi\) | ||||
−0.508020 | + | 0.861345i | \(0.669623\pi\) | |||||||
\(548\) | 17243.9i | 1.34420i | ||||||||
\(549\) | −18798.7 | + | 203.723i | −1.46140 | + | 0.0158373i | ||||
\(550\) | −2295.49 | −0.177964 | ||||||||
\(551\) | 5792.90 | 0.447887 | ||||||||
\(552\) | −23.5543 | − | 23.3004i | −0.00181619 | − | 0.00179662i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 351.649i | 0.0269678i | ||||||||
\(555\) | 1669.35 | + | 1651.36i | 0.127676 | + | 0.126300i | ||||
\(556\) | − | 17863.5i | − | 1.36255i | ||||||
\(557\) | 4992.42i | 0.379777i | 0.981806 | + | 0.189888i | \(0.0608126\pi\) | ||||
−0.981806 | + | 0.189888i | \(0.939187\pi\) | |||||||
\(558\) | 6.78743 | + | 626.314i | 0.000514937 | + | 0.0475161i | ||||
\(559\) | 3542.27i | 0.268018i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 4843.37 | − | 4896.14i | 0.364505 | − | 0.368477i | ||||
\(562\) | −1057.67 | −0.0793865 | ||||||||
\(563\) | −13270.9 | −0.993431 | −0.496715 | − | 0.867914i | \(-0.665461\pi\) | ||||
−0.496715 | + | 0.867914i | \(0.665461\pi\) | |||||||
\(564\) | 7713.77 | + | 7630.63i | 0.575901 | + | 0.569694i | ||||
\(565\) | − | 31143.4i | − | 2.31896i | ||||||
\(566\) | −8.86558 | −0.000658389 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −2932.90 | −0.216658 | ||||||||
\(569\) | − | 3130.67i | − | 0.230658i | −0.993327 | − | 0.115329i | \(-0.963208\pi\) | ||
0.993327 | − | 0.115329i | \(-0.0367923\pi\) | |||||||
\(570\) | 599.813 | + | 593.348i | 0.0440761 | + | 0.0436011i | ||||
\(571\) | 10740.6 | 0.787184 | 0.393592 | − | 0.919285i | \(-0.371232\pi\) | ||||
0.393592 | + | 0.919285i | \(0.371232\pi\) | |||||||
\(572\) | 21622.9 | 1.58059 | ||||||||
\(573\) | 1978.38 | − | 1999.94i | 0.144238 | − | 0.145809i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 403.022i | − | 0.0292299i | ||||||
\(576\) | 144.248 | + | 13310.5i | 0.0104346 | + | 0.962857i | ||||
\(577\) | − | 19326.6i | − | 1.39441i | −0.716870 | − | 0.697207i | \(-0.754426\pi\) | ||
0.716870 | − | 0.697207i | \(-0.245574\pi\) | |||||||
\(578\) | − | 908.693i | − | 0.0653921i | ||||||
\(579\) | 18286.9 | + | 18089.8i | 1.31257 | + | 1.29842i | ||||
\(580\) | − | 22118.5i | − | 1.58349i | ||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −522.340 | − | 516.710i | −0.0372022 | − | 0.0368013i | ||||
\(583\) | 17481.3 | 1.24186 | ||||||||
\(584\) | −1.40563 | −9.95985e−5 | ||||||||
\(585\) | 29979.6 | − | 324.892i | 2.11881 | − | 0.0229617i | ||||
\(586\) | 15.1415i | 0.00106739i | ||||||||
\(587\) | −9837.78 | −0.691736 | −0.345868 | − | 0.938283i | \(-0.612415\pi\) | ||||
−0.345868 | + | 0.938283i | \(0.612415\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 4051.95 | 0.283460 | ||||||||
\(590\) | − | 1547.17i | − | 0.107960i | ||||||
\(591\) | 13427.7 | − | 13574.0i | 0.934585 | − | 0.944768i | ||||
\(592\) | −1517.66 | −0.105364 | ||||||||
\(593\) | 9153.70 | 0.633891 | 0.316946 | − | 0.948444i | \(-0.397343\pi\) | ||||
0.316946 | + | 0.948444i | \(0.397343\pi\) | |||||||
\(594\) | −996.536 | + | 1029.47i | −0.0688357 | + | 0.0711107i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | − | 12356.8i | − | 0.849253i | ||||||
\(597\) | 8486.04 | − | 8578.50i | 0.581760 | − | 0.588098i | ||||
\(598\) | − | 23.7351i | − | 0.00162307i | ||||||
\(599\) | 19675.1i | 1.34208i | 0.741422 | + | 0.671039i | \(0.234152\pi\) | ||||
−0.741422 | + | 0.671039i | \(0.765848\pi\) | |||||||
\(600\) | 2920.86 | − | 2952.69i | 0.198739 | − | 0.200905i | ||||
\(601\) | 688.430i | 0.0467249i | 0.999727 | + | 0.0233624i | \(0.00743717\pi\) | ||||
−0.999727 | + | 0.0233624i | \(0.992563\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 127.030 | + | 11721.7i | 0.00857885 | + | 0.791619i | ||||
\(604\) | −14934.9 | −1.00611 | ||||||||
\(605\) | −14350.3 | −0.964333 | ||||||||
\(606\) | −1249.70 | + | 1263.31i | −0.0837713 | + | 0.0846841i | ||||
\(607\) | 12261.9i | 0.819926i | 0.912102 | + | 0.409963i | \(0.134458\pi\) | ||||
−0.912102 | + | 0.409963i | \(0.865542\pi\) | |||||||
\(608\) | −1653.15 | −0.110270 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −2903.24 | −0.192703 | ||||||||
\(611\) | 15594.5i | 1.03255i | ||||||||
\(612\) | 67.3049 | + | 6210.60i | 0.00444549 | + | 0.410210i | ||||
\(613\) | −24768.2 | −1.63194 | −0.815969 | − | 0.578095i | \(-0.803796\pi\) | ||||
−0.815969 | + | 0.578095i | \(0.803796\pi\) | |||||||
\(614\) | 188.646 | 0.0123993 | ||||||||
\(615\) | 17613.5 | + | 17423.7i | 1.15487 | + | 1.14242i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 11630.7i | − | 0.758891i | −0.925214 | − | 0.379445i | \(-0.876115\pi\) | ||
0.925214 | − | 0.379445i | \(-0.123885\pi\) | |||||||
\(618\) | 999.975 | + | 989.197i | 0.0650888 | + | 0.0643873i | ||||
\(619\) | 28222.2i | 1.83255i | 0.400555 | + | 0.916273i | \(0.368817\pi\) | ||||
−0.400555 | + | 0.916273i | \(0.631183\pi\) | |||||||
\(620\) | − | 15471.2i | − | 1.00216i | ||||||
\(621\) | −180.745 | − | 174.963i | −0.0116797 | − | 0.0113060i | ||||
\(622\) | 741.842i | 0.0478218i | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −13627.7 | + | 13776.2i | −0.874270 | + | 0.883796i | ||||
\(625\) | 6800.20 | 0.435213 | ||||||||
\(626\) | 1742.67 | 0.111264 | ||||||||
\(627\) | 6589.55 | + | 6518.52i | 0.419715 | + | 0.415191i | ||||
\(628\) | − | 363.611i | − | 0.0231045i | ||||||
\(629\) | −699.137 | −0.0443186 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 5143.24 | 0.324483 | 0.162242 | − | 0.986751i | \(-0.448128\pi\) | ||||
0.162242 | + | 0.986751i | \(0.448128\pi\) | |||||||
\(632\) | − | 2600.44i | − | 0.163671i | ||||||
\(633\) | −14951.9 | − | 14790.7i | −0.938836 | − | 0.928716i | ||||
\(634\) | 504.568 | 0.0316072 | ||||||||
\(635\) | −33372.6 | −2.08559 | ||||||||
\(636\) | −11087.3 | + | 11208.1i | −0.691256 | + | 0.698788i | ||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 1519.22i | 0.0942734i | ||||||||
\(639\) | −22267.1 | + | 241.311i | −1.37852 | + | 0.0149391i | ||||
\(640\) | 8407.20i | 0.519256i | ||||||||
\(641\) | − | 14609.4i | − | 0.900212i | −0.892975 | − | 0.450106i | \(-0.851386\pi\) | ||
0.892975 | − | 0.450106i | \(-0.148614\pi\) | |||||||
\(642\) | 1477.97 | + | 1462.04i | 0.0908582 | + | 0.0898789i | ||||
\(643\) | − | 28909.8i | − | 1.77308i | −0.462653 | − | 0.886539i | \(-0.653102\pi\) | ||
0.462653 | − | 0.886539i | \(-0.346898\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 4121.78 | + | 4077.35i | 0.251620 | + | 0.248908i | ||||
\(646\) | −251.206 | −0.0152996 | ||||||||
\(647\) | 27280.4 | 1.65765 | 0.828827 | − | 0.559504i | \(-0.189008\pi\) | ||||
0.828827 | + | 0.559504i | \(0.189008\pi\) | |||||||
\(648\) | −56.1813 | − | 2591.78i | −0.00340588 | − | 0.157121i | ||||
\(649\) | − | 16997.3i | − | 1.02804i | ||||||
\(650\) | 2975.34 | 0.179542 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 5286.14 | 0.317517 | ||||||||
\(653\) | 13193.1i | 0.790635i | 0.918545 | + | 0.395317i | \(0.129365\pi\) | ||||
−0.918545 | + | 0.395317i | \(0.870635\pi\) | |||||||
\(654\) | 1208.43 | − | 1221.60i | 0.0722529 | − | 0.0730401i | ||||
\(655\) | −20629.6 | −1.23063 | ||||||||
\(656\) | −16013.0 | −0.953055 | ||||||||
\(657\) | −10.6718 | + | 0.115652i | −0.000633710 | + | 6.86757e-6i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 17560.9i | − | 1.03805i | −0.854759 | − | 0.519026i | \(-0.826295\pi\) | ||
0.854759 | − | 0.519026i | \(-0.173705\pi\) | |||||||
\(660\) | 24889.1 | − | 25160.3i | 1.46789 | − | 1.48388i | ||||
\(661\) | 21645.5i | 1.27369i | 0.770991 | + | 0.636846i | \(0.219761\pi\) | ||||
−0.770991 | + | 0.636846i | \(0.780239\pi\) | |||||||
\(662\) | 1273.54i | 0.0747694i | ||||||||
\(663\) | −6277.83 | + | 6346.23i | −0.367738 | + | 0.371745i | ||||
\(664\) | − | 2085.04i | − | 0.121860i | ||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 145.443 | − | 1.57618i | 0.00846214 | − | 9.17051e-5i | ||||
\(667\) | −266.731 | −0.0154840 | ||||||||
\(668\) | −701.686 | −0.0406423 | ||||||||
\(669\) | −12379.1 | + | 12513.9i | −0.715400 | + | 0.723194i | ||||
\(670\) | 1810.29i | 0.104385i | ||||||||
\(671\) | −31895.0 | −1.83501 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −14429.9 | −0.826498 | −0.413249 | − | 0.910618i | \(-0.635606\pi\) | ||||
−0.413249 | + | 0.910618i | \(0.635606\pi\) | |||||||
\(674\) | 2021.69i | 0.115538i | ||||||||
\(675\) | 21932.7 | − | 22657.6i | 1.25065 | − | 1.29199i | ||||
\(676\) | −10560.1 | −0.600826 | ||||||||
\(677\) | −16185.5 | −0.918849 | −0.459424 | − | 0.888217i | \(-0.651944\pi\) | ||||
−0.459424 | + | 0.888217i | \(0.651944\pi\) | |||||||
\(678\) | −1371.47 | − | 1356.69i | −0.0776857 | − | 0.0768484i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 1924.31i | 0.108521i | ||||||||
\(681\) | −8583.67 | − | 8491.16i | −0.483006 | − | 0.477800i | ||||
\(682\) | 1062.65i | 0.0596639i | ||||||||
\(683\) | − | 25233.4i | − | 1.41366i | −0.707385 | − | 0.706828i | \(-0.750125\pi\) | ||
0.707385 | − | 0.706828i | \(-0.249875\pi\) | |||||||
\(684\) | −8358.63 | + | 90.5834i | −0.467252 | + | 0.00506366i | ||||
\(685\) | 40564.2i | 2.26259i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 1026.40 | − | 1037.59i | 0.0570011 | − | 0.0576222i | ||||
\(688\) | −3747.24 | −0.207649 | ||||||||
\(689\) | −22658.8 | −1.25287 | ||||||||
\(690\) | −27.6180 | − | 27.3203i | −0.00152377 | − | 0.00150734i | ||||
\(691\) | 2028.23i | 0.111661i | 0.998440 | + | 0.0558304i | \(0.0177806\pi\) | ||||
−0.998440 | + | 0.0558304i | \(0.982219\pi\) | |||||||
\(692\) | 21706.7 | 1.19243 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 1921.01 | 0.105073 | ||||||||
\(695\) | − | 42021.7i | − | 2.29349i | ||||||
\(696\) | −1954.17 | − | 1933.10i | −0.106426 | − | 0.105279i | ||||
\(697\) | −7376.67 | −0.400877 | ||||||||
\(698\) | −1776.03 | −0.0963088 | ||||||||
\(699\) | −5699.88 | + | 5761.98i | −0.308425 | + | 0.311786i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 33881.6i | 1.82552i | 0.408497 | + | 0.912760i | \(0.366053\pi\) | ||||
−0.408497 | + | 0.912760i | \(0.633947\pi\) | |||||||
\(702\) | 1291.68 | − | 1334.37i | 0.0694463 | − | 0.0717415i | ||||
\(703\) | − | 940.944i | − | 0.0504813i | ||||||
\(704\) | 22583.5i | 1.20902i | ||||||||
\(705\) | 18145.7 | + | 17950.2i | 0.969373 | + | 0.958925i | ||||
\(706\) | 2736.64i | 0.145885i | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 10897.7 | + | 10780.2i | 0.578476 | + | 0.572241i | ||||
\(709\) | −17416.8 | −0.922570 | −0.461285 | − | 0.887252i | \(-0.652611\pi\) | ||||
−0.461285 | + | 0.887252i | \(0.652611\pi\) | |||||||
\(710\) | −3438.90 | −0.181774 | ||||||||
\(711\) | −213.957 | − | 19743.0i | −0.0112855 | − | 1.04138i | ||||
\(712\) | 1565.69i | 0.0824109i | ||||||||
\(713\) | −186.570 | −0.00979956 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 50865.3 | 2.66050 | ||||||||
\(716\) | − | 12885.0i | − | 0.672536i | ||||||
\(717\) | −4921.94 | + | 4975.57i | −0.256364 | + | 0.259157i | ||||
\(718\) | 2594.45 | 0.134852 | ||||||||
\(719\) | 31681.3 | 1.64327 | 0.821637 | − | 0.570010i | \(-0.193061\pi\) | ||||
0.821637 | + | 0.570010i | \(0.193061\pi\) | |||||||
\(720\) | 343.691 | + | 31714.3i | 0.0177897 | + | 1.64156i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 1191.11i | 0.0613969i | ||||||||
\(723\) | −14744.0 | + | 14904.6i | −0.758416 | + | 0.766680i | ||||
\(724\) | 11397.7i | 0.585070i | ||||||||
\(725\) | − | 33436.4i | − | 1.71283i | ||||||
\(726\) | −625.134 | + | 631.946i | −0.0319572 | + | 0.0323054i | ||||
\(727\) | − | 19420.1i | − | 0.990719i | −0.868688 | − | 0.495360i | \(-0.835036\pi\) | ||
0.868688 | − | 0.495360i | \(-0.164964\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −639.782 | − | 19672.6i | −0.0325043 | − | 0.999472i | ||||
\(730\) | −1.64814 | −8.35623e−5 | ||||||||
\(731\) | −1726.23 | −0.0873419 | ||||||||
\(732\) | 20228.9 | − | 20449.3i | 1.02142 | − | 1.03255i | ||||
\(733\) | 13762.9i | 0.693513i | 0.937955 | + | 0.346756i | \(0.112717\pi\) | ||||
−0.937955 | + | 0.346756i | \(0.887283\pi\) | |||||||
\(734\) | 543.063 | 0.0273090 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 76.1181 | 0.00381216 | ||||||||
\(737\) | 19887.9i | 0.994001i | ||||||||
\(738\) | 1534.58 | − | 16.6304i | 0.0765429 | − | 0.000829503i | ||||
\(739\) | 14792.1 | 0.736316 | 0.368158 | − | 0.929763i | \(-0.379988\pi\) | ||||
0.368158 | + | 0.929763i | \(0.379988\pi\) | |||||||
\(740\) | −3592.73 | −0.178475 | ||||||||
\(741\) | −8541.17 | − | 8449.11i | −0.423438 | − | 0.418874i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 24521.7i | 1.21078i | 0.795928 | + | 0.605392i | \(0.206984\pi\) | ||||
−0.795928 | + | 0.605392i | \(0.793016\pi\) | |||||||
\(744\) | −1366.88 | − | 1352.15i | −0.0673551 | − | 0.0666291i | ||||
\(745\) | − | 29068.0i | − | 1.42949i | ||||||
\(746\) | 534.667i | 0.0262407i | ||||||||
\(747\) | −171.551 | − | 15830.0i | −0.00840258 | − | 0.775354i | ||||
\(748\) | 10537.3i | 0.515084i | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 1520.18 | − | 1536.74i | 0.0740120 | − | 0.0748184i | ||||
\(751\) | 8398.16 | 0.408060 | 0.204030 | − | 0.978965i | \(-0.434596\pi\) | ||||
0.204030 | + | 0.978965i | \(0.434596\pi\) | |||||||
\(752\) | −16496.9 | −0.799972 | ||||||||
\(753\) | −2164.09 | − | 2140.77i | −0.104733 | − | 0.103604i | ||||
\(754\) | − | 1969.16i | − | 0.0951097i | ||||||
\(755\) | −35132.5 | −1.69351 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −18400.3 | −0.883446 | −0.441723 | − | 0.897151i | \(-0.645633\pi\) | ||||
−0.441723 | + | 0.897151i | \(0.645633\pi\) | |||||||
\(758\) | − | 1625.55i | − | 0.0778925i | ||||||
\(759\) | −303.412 | − | 300.142i | −0.0145101 | − | 0.0143537i | ||||
\(760\) | −2589.86 | −0.123611 | ||||||||
\(761\) | 31893.4 | 1.51923 | 0.759616 | − | 0.650372i | \(-0.225387\pi\) | ||||
0.759616 | + | 0.650372i | \(0.225387\pi\) | |||||||
\(762\) | −1453.80 | + | 1469.64i | −0.0691147 | + | 0.0698678i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 4304.20i | 0.203823i | ||||||||
\(765\) | 158.327 | + | 14609.7i | 0.00748277 | + | 0.690478i | ||||
\(766\) | − | 2096.30i | − | 0.0988806i | ||||||
\(767\) | 22031.3i | 1.03716i | ||||||||
\(768\) | −14199.6 | − | 14046.6i | −0.667167 | − | 0.659976i | ||||
\(769\) | 21058.0i | 0.987478i | 0.869610 | + | 0.493739i | \(0.164370\pi\) | ||||
−0.869610 | + | 0.493739i | \(0.835630\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 6534.47 | + | 6464.04i | 0.305231 | + | 0.301941i | ||||
\(772\) | −39356.4 | −1.83480 | ||||||||
\(773\) | 37818.8 | 1.75970 | 0.879849 | − | 0.475254i | \(-0.157644\pi\) | ||||
0.879849 | + | 0.475254i | \(0.157644\pi\) | |||||||
\(774\) | 359.110 | − | 3.89171i | 0.0166769 | − | 0.000180730i | ||||
\(775\) | − | 23387.7i | − | 1.08402i | ||||||
\(776\) | 2255.35 | 0.104333 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 65.2459 | 0.00300666 | ||||||||
\(779\) | − | 9928.00i | − | 0.456621i | ||||||
\(780\) | −32260.5 | + | 32612.0i | −1.48091 | + | 1.49705i | ||||
\(781\) | −37779.8 | −1.73095 | ||||||||
\(782\) | 11.5666 | 0.000528928 | ||||||||
\(783\) | −14995.4 | − | 14515.7i | −0.684410 | − | 0.662514i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 855.352i | − | 0.0388902i | ||||||
\(786\) | −898.677 | + | 908.469i | −0.0407821 | + | 0.0412265i | ||||
\(787\) | − | 1973.27i | − | 0.0893766i | −0.999001 | − | 0.0446883i | \(-0.985771\pi\) | ||
0.999001 | − | 0.0446883i | \(-0.0142295\pi\) | |||||||
\(788\) | 29213.4i | 1.32067i | ||||||||
\(789\) | −28639.8 | + | 28951.9i | −1.29227 | + | 1.30635i | ||||
\(790\) | − | 3049.08i | − | 0.137318i | ||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −47.6604 | − | 4397.90i | −0.00213831 | − | 0.197314i | ||||
\(793\) | 41341.4 | 1.85129 | ||||||||
\(794\) | −1487.87 | −0.0665019 | ||||||||
\(795\) | −26081.5 | + | 26365.7i | −1.16354 | + | 1.17622i | ||||
\(796\) | 18462.4i | 0.822087i | ||||||||
\(797\) | −7865.72 | −0.349583 | −0.174792 | − | 0.984605i | \(-0.555925\pi\) | ||||
−0.174792 | + | 0.984605i | \(0.555925\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −7599.56 | −0.336487 | ||||||||
\(800\) | 9541.91i | 0.421697i | ||||||||
\(801\) | 128.820 | + | 11887.0i | 0.00568244 | + | 0.524351i | ||||
\(802\) | −507.132 | −0.0223285 | ||||||||
\(803\) | −18.1065 | −0.000795722 | ||||||||
\(804\) | −12751.0 | − | 12613.6i | −0.559320 | − | 0.553291i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | − | 1377.37i | − | 0.0601932i | ||||||
\(807\) | 17680.4 | + | 17489.8i | 0.771225 | + | 0.762913i | ||||
\(808\) | − | 5454.71i | − | 0.237495i | ||||||
\(809\) | − | 13314.4i | − | 0.578628i | −0.957234 | − | 0.289314i | \(-0.906573\pi\) | ||
0.957234 | − | 0.289314i | \(-0.0934272\pi\) | |||||||
\(810\) | −65.8740 | − | 3038.93i | −0.00285750 | − | 0.131823i | ||||
\(811\) | 17376.6i | 0.752374i | 0.926544 | + | 0.376187i | \(0.122765\pi\) | ||||
−0.926544 | + | 0.376187i | \(0.877235\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 7633.59 | − | 7716.77i | 0.329301 | − | 0.332889i | ||||
\(814\) | 246.768 | 0.0106255 | ||||||||
\(815\) | 12435.0 | 0.534454 | ||||||||
\(816\) | −6713.44 | − | 6641.08i | −0.288012 | − | 0.284907i | ||||
\(817\) | − | 2323.27i | − | 0.0994871i | ||||||
\(818\) | −3253.22 | −0.139054 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −37907.2 | −1.61436 | ||||||||
\(821\) | 5793.64i | 0.246284i | 0.992389 | + | 0.123142i | \(0.0392971\pi\) | ||||
−0.992389 | + | 0.123142i | \(0.960703\pi\) | |||||||
\(822\) | 1786.33 | + | 1767.08i | 0.0757974 | + | 0.0749804i | ||||
\(823\) | 26470.7 | 1.12115 | 0.560577 | − | 0.828103i | \(-0.310580\pi\) | ||||
0.560577 | + | 0.828103i | \(0.310580\pi\) | |||||||
\(824\) | −4317.68 | −0.182541 | ||||||||
\(825\) | 37624.7 | − | 38034.7i | 1.58779 | − | 1.60509i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 8572.60i | − | 0.360458i | −0.983625 | − | 0.180229i | \(-0.942316\pi\) | ||
0.983625 | − | 0.180229i | \(-0.0576838\pi\) | |||||||
\(828\) | 384.868 | − | 4.17086i | 0.0161535 | − | 0.000175057i | ||||
\(829\) | 3151.37i | 0.132028i | 0.997819 | + | 0.0660141i | \(0.0210282\pi\) | ||||
−0.997819 | + | 0.0660141i | \(0.978972\pi\) | |||||||
\(830\) | − | 2444.76i | − | 0.102240i | ||||||
\(831\) | −5826.58 | − | 5763.78i | −0.243227 | − | 0.240606i | ||||
\(832\) | − | 29272.1i | − | 1.21974i | ||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −1850.52 | − | 1830.57i | −0.0768324 | − | 0.0760043i | ||||
\(835\) | −1650.63 | −0.0684102 | ||||||||
\(836\) | −14181.8 | −0.586708 | ||||||||
\(837\) | −10488.8 | − | 10153.3i | −0.433150 | − | 0.419293i | ||||
\(838\) | − | 2695.59i | − | 0.111119i | ||||||
\(839\) | 47134.1 | 1.93951 | 0.969755 | − | 0.244082i | \(-0.0784865\pi\) | ||||
0.969755 | + | 0.244082i | \(0.0784865\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 2259.85 | 0.0926587 | ||||||||
\(842\) | 1612.02i | 0.0659785i | ||||||||
\(843\) | 17336.0 | − | 17524.9i | 0.708283 | − | 0.716001i | ||||
\(844\) | 32178.9 | 1.31237 | ||||||||
\(845\) | −24841.4 | −1.01133 | ||||||||
\(846\) | 1580.95 | − | 17.1329i | 0.0642484 | − | 0.000696266i | ||||
\(847\) | 0 | 0 | ||||||||
\(848\) | − | 23969.9i | − | 0.970671i | ||||||
\(849\) | 145.313 | − | 146.896i | 0.00587412 | − | 0.00593813i | ||||
\(850\) | 1449.95i | 0.0585093i | ||||||||
\(851\) | 43.3252i | 0.00174520i | ||||||||
\(852\) | 23961.3 | − | 24222.3i | 0.963497 | − | 0.973995i | ||||
\(853\) | 24635.1i | 0.988849i | 0.869221 | + | 0.494424i | \(0.164621\pi\) | ||||
−0.869221 | + | 0.494424i | \(0.835379\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −19662.7 | + | 213.087i | −0.786492 | + | 0.00852329i | ||||
\(856\) | −6381.58 | −0.254811 | ||||||||
\(857\) | −115.941 | −0.00462133 | −0.00231067 | − | 0.999997i | \(-0.500736\pi\) | ||||
−0.00231067 | + | 0.999997i | \(0.500736\pi\) | |||||||
\(858\) | 2215.82 | − | 2239.97i | 0.0881666 | − | 0.0891272i | ||||
\(859\) | − | 3735.89i | − | 0.148390i | −0.997244 | − | 0.0741950i | \(-0.976361\pi\) | ||
0.997244 | − | 0.0741950i | \(-0.0236387\pi\) | |||||||
\(860\) | −8870.75 | −0.351733 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 423.849 | 0.0167475 | ||||||||
\(863\) | − | 9534.46i | − | 0.376080i | −0.982161 | − | 0.188040i | \(-0.939787\pi\) | ||
0.982161 | − | 0.188040i | \(-0.0602134\pi\) | |||||||
\(864\) | 4279.31 | + | 4142.41i | 0.168501 | + | 0.163111i | ||||
\(865\) | 51062.5 | 2.00714 | ||||||||
\(866\) | −416.258 | −0.0163338 | ||||||||
\(867\) | 15056.4 | + | 14894.1i | 0.589783 | + | 0.583426i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 33497.3i | − | 1.30761i | ||||||
\(870\) | −2291.31 | − | 2266.62i | −0.0892905 | − | 0.0883281i | ||||
\(871\) | − | 25778.0i | − | 1.00282i | ||||||
\(872\) | 5274.60i | 0.204840i | ||||||||
\(873\) | 17123.0 | − | 185.564i | 0.663834 | − | 0.00719404i | ||||
\(874\) | 15.5671i | 0.000602478i | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 11.4838 | − | 11.6089i | 0.000442923 | − | 0.000447749i | ||||
\(877\) | 18980.7 | 0.730825 | 0.365412 | − | 0.930846i | \(-0.380928\pi\) | ||||
0.365412 | + | 0.930846i | \(0.380928\pi\) | |||||||
\(878\) | −1616.24 | −0.0621245 | ||||||||
\(879\) | −250.884 | − | 248.180i | −0.00962697 | − | 0.00952320i | ||||
\(880\) | 53808.5i | 2.06123i | ||||||||
\(881\) | 46006.5 | 1.75936 | 0.879682 | − | 0.475563i | \(-0.157756\pi\) | ||||
0.879682 | + | 0.475563i | \(0.157756\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 17460.6 | 0.665455 | 0.332728 | − | 0.943023i | \(-0.392031\pi\) | ||||
0.332728 | + | 0.943023i | \(0.392031\pi\) | |||||||
\(884\) | − | 13658.1i | − | 0.519653i | ||||||
\(885\) | 25635.6 | + | 25359.3i | 0.973707 | + | 0.963212i | ||||
\(886\) | −2277.04 | −0.0863415 | ||||||||
\(887\) | −4844.77 | −0.183395 | −0.0916975 | − | 0.995787i | \(-0.529229\pi\) | ||||
−0.0916975 | + | 0.995787i | \(0.529229\pi\) | |||||||
\(888\) | −313.995 | + | 317.417i | −0.0118660 | + | 0.0119953i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 1835.81i | 0.0691420i | ||||||||
\(891\) | −723.692 | − | 33385.7i | −0.0272106 | − | 1.25529i | ||||
\(892\) | − | 26932.1i | − | 1.01093i | ||||||
\(893\) | − | 10228.0i | − | 0.383277i | ||||||
\(894\) | −1280.07 | − | 1266.27i | −0.0478881 | − | 0.0473720i | ||||
\(895\) | − | 30310.5i | − | 1.13203i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 393.273 | + | 389.034i | 0.0146388 | + | 0.0144810i | ||||
\(898\) | 1229.66 | 0.0456951 | ||||||||
\(899\) | −15478.6 | −0.574240 | ||||||||
\(900\) | 522.844 | + | 48245.8i | 0.0193646 | + | 1.78688i | ||||
\(901\) | − | 11042.1i | − | 0.408287i | ||||||
\(902\) | 2603.67 | 0.0961117 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 5921.71 | 0.217868 | ||||||||
\(905\) | 26811.7i | 0.984806i | ||||||||
\(906\) | −1530.46 | + | 1547.14i | −0.0561216 | + | 0.0567331i | ||||
\(907\) | 24674.0 | 0.903294 | 0.451647 | − | 0.892197i | \(-0.350837\pi\) | ||||
0.451647 | + | 0.892197i | \(0.350837\pi\) | |||||||
\(908\) | 18473.5 | 0.675181 | ||||||||
\(909\) | −448.798 | − | 41413.1i | −0.0163759 | − | 1.51110i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 27995.1i | 1.01813i | 0.860727 | + | 0.509067i | \(0.170010\pi\) | ||||
−0.860727 | + | 0.509067i | \(0.829990\pi\) | |||||||
\(912\) | 8938.00 | − | 9035.39i | 0.324525 | − | 0.328061i | ||||
\(913\) | − | 26858.2i | − | 0.973578i | ||||||
\(914\) | − | 1754.07i | − | 0.0634786i | ||||||
\(915\) | 47586.2 | − | 48104.7i | 1.71929 | − | 1.73802i | ||||
\(916\) | 2233.06i | 0.0805485i | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 650.268 | + | 629.464i | 0.0233791 | + | 0.0226312i | ||||
\(919\) | 43522.2 | 1.56220 | 0.781102 | − | 0.624403i | \(-0.214658\pi\) | ||||
0.781102 | + | 0.624403i | \(0.214658\pi\) | |||||||
\(920\) | 119.249 | 0.00427339 | ||||||||
\(921\) | −3092.05 | + | 3125.74i | −0.110626 | + | 0.111831i | ||||
\(922\) | − | 230.690i | − | 0.00824011i | ||||||
\(923\) | 48969.0 | 1.74630 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −5431.10 | −0.193052 | ||||||||
\(926\) | 3963.51i | 0.140658i | ||||||||
\(927\) | −32780.6 | + | 355.246i | −1.16144 | + | 0.0125866i | ||||
\(928\) | 6315.09 | 0.223387 | ||||||||
\(929\) | −21771.5 | −0.768892 | −0.384446 | − | 0.923148i | \(-0.625607\pi\) | ||||
−0.384446 | + | 0.923148i | \(0.625607\pi\) | |||||||
\(930\) | −1602.70 | − | 1585.43i | −0.0565103 | − | 0.0559012i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | − | 12400.7i | − | 0.435837i | ||||||
\(933\) | −12291.8 | − | 12159.3i | −0.431313 | − | 0.426664i | ||||
\(934\) | 399.610i | 0.0139996i | ||||||||
\(935\) | 24787.8i | 0.867003i | ||||||||
\(936\) | 61.7760 | + | 5700.41i | 0.00215728 | + | 0.199064i | ||||
\(937\) | − | 18715.6i | − | 0.652521i | −0.945280 | − | 0.326260i | \(-0.894211\pi\) | ||
0.945280 | − | 0.326260i | \(-0.105789\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −28563.6 | + | 28874.8i | −0.992691 | + | 1.00351i | ||||
\(940\) | −39052.6 | −1.35506 | ||||||||
\(941\) | 16024.4 | 0.555133 | 0.277567 | − | 0.960706i | \(-0.410472\pi\) | ||||
0.277567 | + | 0.960706i | \(0.410472\pi\) | |||||||
\(942\) | −37.6673 | − | 37.2613i | −0.00130283 | − | 0.00128879i | ||||
\(943\) | 457.129i | 0.0157860i | ||||||||
\(944\) | −23306.1 | −0.803549 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 609.290 | 0.0209405 | ||||||||
\(947\) | 50339.0i | 1.72735i | 0.504053 | + | 0.863673i | \(0.331842\pi\) | ||||
−0.504053 | + | 0.863673i | \(0.668158\pi\) | |||||||
\(948\) | 21476.6 | + | 21245.1i | 0.735788 | + | 0.727858i | ||||
\(949\) | 23.4691 | 0.000802780 | ||||||||
\(950\) | −1951.44 | −0.0666453 | ||||||||
\(951\) | −8270.22 | + | 8360.33i | −0.281998 | + | 0.285071i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 46401.8i | − | 1.57723i | −0.614887 | − | 0.788615i | \(-0.710798\pi\) | ||
0.614887 | − | 0.788615i | \(-0.289202\pi\) | |||||||
\(954\) | 24.8940 | + | 2297.11i | 0.000844836 | + | 0.0779578i | ||||
\(955\) | 10125.1i | 0.343080i | ||||||||
\(956\) | − | 10708.2i | − | 0.362269i | ||||||
\(957\) | −25172.4 | − | 24901.1i | −0.850269 | − | 0.841104i | ||||
\(958\) | − | 2797.64i | − | 0.0943503i | ||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −34060.9 | − | 33693.7i | −1.14511 | − | 1.13277i | ||||
\(961\) | 18964.2 | 0.636574 | ||||||||
\(962\) | −319.852 | −0.0107198 | ||||||||
\(963\) | −48450.1 | + | 525.058i | −1.62127 | + | 0.0175698i | ||||
\(964\) | − | 32077.3i | − | 1.07172i | ||||||
\(965\) | −92581.3 | −3.08839 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 27821.0 | 0.925195 | 0.462597 | − | 0.886569i | \(-0.346918\pi\) | ||||
0.462597 | + | 0.886569i | \(0.346918\pi\) | |||||||
\(968\) | − | 2728.61i | − | 0.0906000i | ||||||
\(969\) | 4117.44 | − | 4162.30i | 0.136503 | − | 0.137990i | ||||
\(970\) | 2644.46 | 0.0875346 | ||||||||
\(971\) | −7488.77 | −0.247504 | −0.123752 | − | 0.992313i | \(-0.539493\pi\) | ||||
−0.123752 | + | 0.992313i | \(0.539493\pi\) | |||||||
\(972\) | 21864.0 | + | 20710.3i | 0.721491 | + | 0.683420i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | − | 998.920i | − | 0.0328619i | ||||||
\(975\) | −48768.0 | + | 49299.3i | −1.60187 | + | 1.61933i | ||||
\(976\) | 43733.5i | 1.43430i | ||||||||
\(977\) | 37379.7i | 1.22404i | 0.790844 | + | 0.612018i | \(0.209642\pi\) | ||||
−0.790844 | + | 0.612018i | \(0.790358\pi\) | |||||||
\(978\) | 541.702 | − | 547.604i | 0.0177114 | − | 0.0179043i | ||||
\(979\) | 20168.2i | 0.658405i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 433.979 | + | 40045.7i | 0.0141242 | + | 1.30332i | ||||
\(982\) | 3327.32 | 0.108125 | ||||||||
\(983\) | 13675.3 | 0.443718 | 0.221859 | − | 0.975079i | \(-0.428788\pi\) | ||||
0.221859 | + | 0.975079i | \(0.428788\pi\) | |||||||
\(984\) | −3313.00 | + | 3349.09i | −0.107332 | + | 0.108501i | ||||
\(985\) | 68721.1i | 2.22298i | ||||||||
\(986\) | 959.618 | 0.0309944 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 18382.0 | 0.591913 | ||||||||
\(989\) | 106.974i | 0.00343940i | ||||||||
\(990\) | −55.8831 | − | 5156.65i | −0.00179402 | − | 0.165544i | ||||
\(991\) | 7130.49 | 0.228565 | 0.114282 | − | 0.993448i | \(-0.463543\pi\) | ||||
0.114282 | + | 0.993448i | \(0.463543\pi\) | |||||||
\(992\) | 4417.21 | 0.141378 | ||||||||
\(993\) | −21101.6 | − | 20874.1i | −0.674359 | − | 0.667090i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 43430.5i | 1.38376i | ||||||||
\(996\) | 17220.0 | + | 17034.4i | 0.547828 | + | 0.541923i | ||||
\(997\) | 10629.0i | 0.337638i | 0.985647 | + | 0.168819i | \(0.0539953\pi\) | ||||
−0.985647 | + | 0.168819i | \(0.946005\pi\) | |||||||
\(998\) | 1037.42i | 0.0329047i | ||||||||
\(999\) | −2357.79 | + | 2435.72i | −0.0746719 | + | 0.0771398i |
(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 | 147.4.c.b.146.13 | yes | 24 | |
3.2 | odd | 2 | inner | 147.4.c.b.146.12 | yes | 24 | |
7.2 | even | 3 | 147.4.g.e.80.14 | 48 | |||
7.3 | odd | 6 | 147.4.g.e.68.12 | 48 | |||
7.4 | even | 3 | 147.4.g.e.68.11 | 48 | |||
7.5 | odd | 6 | 147.4.g.e.80.13 | 48 | |||
7.6 | odd | 2 | inner | 147.4.c.b.146.14 | yes | 24 | |
21.2 | odd | 6 | 147.4.g.e.80.12 | 48 | |||
21.5 | even | 6 | 147.4.g.e.80.11 | 48 | |||
21.11 | odd | 6 | 147.4.g.e.68.13 | 48 | |||
21.17 | even | 6 | 147.4.g.e.68.14 | 48 | |||
21.20 | even | 2 | inner | 147.4.c.b.146.11 | ✓ | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
147.4.c.b.146.11 | ✓ | 24 | 21.20 | even | 2 | inner | |
147.4.c.b.146.12 | yes | 24 | 3.2 | odd | 2 | inner | |
147.4.c.b.146.13 | yes | 24 | 1.1 | even | 1 | trivial | |
147.4.c.b.146.14 | yes | 24 | 7.6 | odd | 2 | inner | |
147.4.g.e.68.11 | 48 | 7.4 | even | 3 | |||
147.4.g.e.68.12 | 48 | 7.3 | odd | 6 | |||
147.4.g.e.68.13 | 48 | 21.11 | odd | 6 | |||
147.4.g.e.68.14 | 48 | 21.17 | even | 6 | |||
147.4.g.e.80.11 | 48 | 21.5 | even | 6 | |||
147.4.g.e.80.12 | 48 | 21.2 | odd | 6 | |||
147.4.g.e.80.13 | 48 | 7.5 | odd | 6 | |||
147.4.g.e.80.14 | 48 | 7.2 | even | 3 |