Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [570,4,Mod(121,570)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(570, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 2]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("570.121");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 570 = 2 \cdot 3 \cdot 5 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 570.i (of order \(3\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(33.6310887033\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\Q(\sqrt{-3}, \sqrt{385})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} + 97x^{2} + 96x + 9216 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 391.2 | ||
Root | \(-4.65535 - 8.06331i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 570.391 |
Dual form | 570.4.i.h.121.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/570\mathbb{Z}\right)^\times\).
\(n\) | \(191\) | \(211\) | \(457\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | + | 1.73205i | −0.353553 | + | 0.612372i | ||||
\(3\) | 1.50000 | − | 2.59808i | 0.288675 | − | 0.500000i | ||||
\(4\) | −2.00000 | − | 3.46410i | −0.250000 | − | 0.433013i | ||||
\(5\) | 2.50000 | − | 4.33013i | 0.223607 | − | 0.387298i | ||||
\(6\) | 3.00000 | + | 5.19615i | 0.204124 | + | 0.353553i | ||||
\(7\) | 28.6214 | 1.54541 | 0.772706 | − | 0.634765i | \(-0.218903\pi\) | ||||
0.772706 | + | 0.634765i | \(0.218903\pi\) | |||||||
\(8\) | 8.00000 | 0.353553 | ||||||||
\(9\) | −4.50000 | − | 7.79423i | −0.166667 | − | 0.288675i | ||||
\(10\) | 5.00000 | + | 8.66025i | 0.158114 | + | 0.273861i | ||||
\(11\) | 4.31071 | 0.118157 | 0.0590785 | − | 0.998253i | \(-0.481184\pi\) | ||||
0.0590785 | + | 0.998253i | \(0.481184\pi\) | |||||||
\(12\) | −12.0000 | −0.288675 | ||||||||
\(13\) | 23.0000 | + | 39.8372i | 0.490696 | + | 0.849911i | 0.999943 | − | 0.0107098i | \(-0.00340911\pi\) |
−0.509246 | + | 0.860621i | \(0.670076\pi\) | |||||||
\(14\) | −28.6214 | + | 49.5737i | −0.546385 | + | 0.946367i | ||||
\(15\) | −7.50000 | − | 12.9904i | −0.129099 | − | 0.223607i | ||||
\(16\) | −8.00000 | + | 13.8564i | −0.125000 | + | 0.216506i | ||||
\(17\) | −40.9661 | + | 70.9553i | −0.584455 | + | 1.01231i | 0.410488 | + | 0.911866i | \(0.365358\pi\) |
−0.994943 | + | 0.100439i | \(0.967975\pi\) | |||||||
\(18\) | 18.0000 | 0.235702 | ||||||||
\(19\) | 63.4321 | + | 53.2482i | 0.765912 | + | 0.642945i | ||||
\(20\) | −20.0000 | −0.223607 | ||||||||
\(21\) | 42.9321 | − | 74.3606i | 0.446122 | − | 0.772706i | ||||
\(22\) | −4.31071 | + | 7.46637i | −0.0417748 | + | 0.0723561i | ||||
\(23\) | 64.4857 | + | 111.692i | 0.584617 | + | 1.01259i | 0.994923 | + | 0.100638i | \(0.0320885\pi\) |
−0.410306 | + | 0.911948i | \(0.634578\pi\) | |||||||
\(24\) | 12.0000 | − | 20.7846i | 0.102062 | − | 0.176777i | ||||
\(25\) | −12.5000 | − | 21.6506i | −0.100000 | − | 0.173205i | ||||
\(26\) | −92.0000 | −0.693949 | ||||||||
\(27\) | −27.0000 | −0.192450 | ||||||||
\(28\) | −57.2428 | − | 99.1475i | −0.386353 | − | 0.669183i | ||||
\(29\) | −35.3303 | − | 61.1939i | −0.226230 | − | 0.391842i | 0.730458 | − | 0.682958i | \(-0.239307\pi\) |
−0.956688 | + | 0.291116i | \(0.905973\pi\) | |||||||
\(30\) | 30.0000 | 0.182574 | ||||||||
\(31\) | 189.486 | 1.09783 | 0.548913 | − | 0.835879i | \(-0.315042\pi\) | ||||
0.548913 | + | 0.835879i | \(0.315042\pi\) | |||||||
\(32\) | −16.0000 | − | 27.7128i | −0.0883883 | − | 0.153093i | ||||
\(33\) | 6.46606 | − | 11.1995i | 0.0341090 | − | 0.0590785i | ||||
\(34\) | −81.9321 | − | 141.911i | −0.413272 | − | 0.715808i | ||||
\(35\) | 71.5535 | − | 123.934i | 0.345564 | − | 0.598535i | ||||
\(36\) | −18.0000 | + | 31.1769i | −0.0833333 | + | 0.144338i | ||||
\(37\) | −271.379 | −1.20579 | −0.602897 | − | 0.797819i | \(-0.705987\pi\) | ||||
−0.602897 | + | 0.797819i | \(0.705987\pi\) | |||||||
\(38\) | −155.661 | + | 56.6195i | −0.664513 | + | 0.241708i | ||||
\(39\) | 138.000 | 0.566607 | ||||||||
\(40\) | 20.0000 | − | 34.6410i | 0.0790569 | − | 0.136931i | ||||
\(41\) | 60.7285 | − | 105.185i | 0.231322 | − | 0.400661i | −0.726875 | − | 0.686769i | \(-0.759028\pi\) |
0.958197 | + | 0.286108i | \(0.0923616\pi\) | |||||||
\(42\) | 85.8643 | + | 148.721i | 0.315456 | + | 0.546385i | ||||
\(43\) | −13.7572 | + | 23.8281i | −0.0487895 | + | 0.0845059i | −0.889389 | − | 0.457152i | \(-0.848870\pi\) |
0.840599 | + | 0.541657i | \(0.182203\pi\) | |||||||
\(44\) | −8.62142 | − | 14.9327i | −0.0295393 | − | 0.0511635i | ||||
\(45\) | −45.0000 | −0.149071 | ||||||||
\(46\) | −257.943 | −0.826773 | ||||||||
\(47\) | −24.1018 | − | 41.7456i | −0.0748002 | − | 0.129558i | 0.826199 | − | 0.563378i | \(-0.190499\pi\) |
−0.900999 | + | 0.433820i | \(0.857165\pi\) | |||||||
\(48\) | 24.0000 | + | 41.5692i | 0.0721688 | + | 0.125000i | ||||
\(49\) | 476.186 | 1.38830 | ||||||||
\(50\) | 50.0000 | 0.141421 | ||||||||
\(51\) | 122.898 | + | 212.866i | 0.337435 | + | 0.584455i | ||||
\(52\) | 92.0000 | − | 159.349i | 0.245348 | − | 0.424955i | ||||
\(53\) | −77.3160 | − | 133.915i | −0.200381 | − | 0.347069i | 0.748271 | − | 0.663394i | \(-0.230885\pi\) |
−0.948651 | + | 0.316324i | \(0.897551\pi\) | |||||||
\(54\) | 27.0000 | − | 46.7654i | 0.0680414 | − | 0.117851i | ||||
\(55\) | 10.7768 | − | 18.6659i | 0.0264207 | − | 0.0457620i | ||||
\(56\) | 228.971 | 0.546385 | ||||||||
\(57\) | 233.491 | − | 84.9293i | 0.542572 | − | 0.197354i | ||||
\(58\) | 141.321 | 0.319938 | ||||||||
\(59\) | 39.6697 | − | 68.7099i | 0.0875348 | − | 0.151615i | −0.818934 | − | 0.573888i | \(-0.805434\pi\) |
0.906469 | + | 0.422273i | \(0.138768\pi\) | |||||||
\(60\) | −30.0000 | + | 51.9615i | −0.0645497 | + | 0.111803i | ||||
\(61\) | 256.505 | + | 444.280i | 0.538396 | + | 0.932529i | 0.998991 | + | 0.0449182i | \(0.0143027\pi\) |
−0.460595 | + | 0.887610i | \(0.652364\pi\) | |||||||
\(62\) | −189.486 | + | 328.199i | −0.388140 | + | 0.672279i | ||||
\(63\) | −128.796 | − | 223.082i | −0.257569 | − | 0.446122i | ||||
\(64\) | 64.0000 | 0.125000 | ||||||||
\(65\) | 230.000 | 0.438892 | ||||||||
\(66\) | 12.9321 | + | 22.3991i | 0.0241187 | + | 0.0417748i | ||||
\(67\) | 451.243 | + | 781.576i | 0.822807 | + | 1.42514i | 0.903584 | + | 0.428412i | \(0.140927\pi\) |
−0.0807764 | + | 0.996732i | \(0.525740\pi\) | |||||||
\(68\) | 327.729 | 0.584455 | ||||||||
\(69\) | 386.914 | 0.675058 | ||||||||
\(70\) | 143.107 | + | 247.869i | 0.244351 | + | 0.423228i | ||||
\(71\) | −89.0091 | + | 154.168i | −0.148781 | + | 0.257696i | −0.930777 | − | 0.365587i | \(-0.880868\pi\) |
0.781996 | + | 0.623283i | \(0.214202\pi\) | |||||||
\(72\) | −36.0000 | − | 62.3538i | −0.0589256 | − | 0.102062i | ||||
\(73\) | 280.186 | − | 485.296i | 0.449222 | − | 0.778076i | −0.549113 | − | 0.835748i | \(-0.685034\pi\) |
0.998336 | + | 0.0576720i | \(0.0183678\pi\) | |||||||
\(74\) | 271.379 | − | 470.041i | 0.426312 | − | 0.738395i | ||||
\(75\) | −75.0000 | −0.115470 | ||||||||
\(76\) | 57.5928 | − | 326.232i | 0.0869255 | − | 0.492386i | ||||
\(77\) | 123.379 | 0.182601 | ||||||||
\(78\) | −138.000 | + | 239.023i | −0.200326 | + | 0.346975i | ||||
\(79\) | 472.069 | − | 817.648i | 0.672303 | − | 1.16446i | −0.304946 | − | 0.952370i | \(-0.598638\pi\) |
0.977249 | − | 0.212094i | \(-0.0680282\pi\) | |||||||
\(80\) | 40.0000 | + | 69.2820i | 0.0559017 | + | 0.0968246i | ||||
\(81\) | −40.5000 | + | 70.1481i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | 121.457 | + | 210.370i | 0.163569 | + | 0.283310i | ||||
\(83\) | 107.446 | 0.142094 | 0.0710469 | − | 0.997473i | \(-0.477366\pi\) | ||||
0.0710469 | + | 0.997473i | \(0.477366\pi\) | |||||||
\(84\) | −343.457 | −0.446122 | ||||||||
\(85\) | 204.830 | + | 354.777i | 0.261376 | + | 0.452717i | ||||
\(86\) | −27.5143 | − | 47.6562i | −0.0344994 | − | 0.0597547i | ||||
\(87\) | −211.982 | −0.261228 | ||||||||
\(88\) | 34.4857 | 0.0417748 | ||||||||
\(89\) | −297.612 | − | 515.480i | −0.354459 | − | 0.613941i | 0.632566 | − | 0.774506i | \(-0.282002\pi\) |
−0.987025 | + | 0.160565i | \(0.948668\pi\) | |||||||
\(90\) | 45.0000 | − | 77.9423i | 0.0527046 | − | 0.0912871i | ||||
\(91\) | 658.293 | + | 1140.20i | 0.758328 | + | 1.31346i | ||||
\(92\) | 257.943 | − | 446.770i | 0.292309 | − | 0.506293i | ||||
\(93\) | 284.229 | − | 492.298i | 0.316915 | − | 0.548913i | ||||
\(94\) | 96.4072 | 0.105783 | ||||||||
\(95\) | 389.152 | − | 141.549i | 0.420275 | − | 0.152869i | ||||
\(96\) | −96.0000 | −0.102062 | ||||||||
\(97\) | −331.175 | + | 573.612i | −0.346657 | + | 0.600427i | −0.985653 | − | 0.168782i | \(-0.946017\pi\) |
0.638996 | + | 0.769210i | \(0.279350\pi\) | |||||||
\(98\) | −476.186 | + | 824.777i | −0.490837 | + | 0.850154i | ||||
\(99\) | −19.3982 | − | 33.5986i | −0.0196928 | − | 0.0341090i | ||||
\(100\) | −50.0000 | + | 86.6025i | −0.0500000 | + | 0.0866025i | ||||
\(101\) | 390.730 | + | 676.764i | 0.384941 | + | 0.666738i | 0.991761 | − | 0.128101i | \(-0.0408883\pi\) |
−0.606820 | + | 0.794840i | \(0.707555\pi\) | |||||||
\(102\) | −491.593 | −0.477205 | ||||||||
\(103\) | 852.314 | 0.815349 | 0.407675 | − | 0.913127i | \(-0.366340\pi\) | ||||
0.407675 | + | 0.913127i | \(0.366340\pi\) | |||||||
\(104\) | 184.000 | + | 318.697i | 0.173487 | + | 0.300489i | ||||
\(105\) | −214.661 | − | 371.803i | −0.199512 | − | 0.345564i | ||||
\(106\) | 309.264 | 0.283381 | ||||||||
\(107\) | 792.903 | 0.716382 | 0.358191 | − | 0.933648i | \(-0.383394\pi\) | ||||
0.358191 | + | 0.933648i | \(0.383394\pi\) | |||||||
\(108\) | 54.0000 | + | 93.5307i | 0.0481125 | + | 0.0833333i | ||||
\(109\) | 290.918 | − | 503.884i | 0.255641 | − | 0.442783i | −0.709428 | − | 0.704778i | \(-0.751047\pi\) |
0.965069 | + | 0.261994i | \(0.0843802\pi\) | |||||||
\(110\) | 21.5535 | + | 37.3318i | 0.0186823 | + | 0.0323586i | ||||
\(111\) | −407.068 | + | 705.062i | −0.348083 | + | 0.602897i | ||||
\(112\) | −228.971 | + | 396.590i | −0.193176 | + | 0.334591i | ||||
\(113\) | −682.747 | −0.568384 | −0.284192 | − | 0.958767i | \(-0.591725\pi\) | ||||
−0.284192 | + | 0.958767i | \(0.591725\pi\) | |||||||
\(114\) | −86.3891 | + | 489.347i | −0.0709744 | + | 0.402031i | ||||
\(115\) | 644.857 | 0.522897 | ||||||||
\(116\) | −141.321 | + | 244.776i | −0.113115 | + | 0.195921i | ||||
\(117\) | 207.000 | − | 358.535i | 0.163565 | − | 0.283304i | ||||
\(118\) | 79.3394 | + | 137.420i | 0.0618965 | + | 0.107208i | ||||
\(119\) | −1172.51 | + | 2030.84i | −0.903223 | + | 1.56443i | ||||
\(120\) | −60.0000 | − | 103.923i | −0.0456435 | − | 0.0790569i | ||||
\(121\) | −1312.42 | −0.986039 | ||||||||
\(122\) | −1026.02 | −0.761406 | ||||||||
\(123\) | −182.186 | − | 315.555i | −0.133554 | − | 0.231322i | ||||
\(124\) | −378.971 | − | 656.398i | −0.274457 | − | 0.475373i | ||||
\(125\) | −125.000 | −0.0894427 | ||||||||
\(126\) | 515.186 | 0.364257 | ||||||||
\(127\) | 866.293 | + | 1500.46i | 0.605284 | + | 1.04838i | 0.992007 | + | 0.126186i | \(0.0402737\pi\) |
−0.386723 | + | 0.922196i | \(0.626393\pi\) | |||||||
\(128\) | −64.0000 | + | 110.851i | −0.0441942 | + | 0.0765466i | ||||
\(129\) | 41.2715 | + | 71.4843i | 0.0281686 | + | 0.0487895i | ||||
\(130\) | −230.000 | + | 398.372i | −0.155172 | + | 0.268765i | ||||
\(131\) | 906.350 | − | 1569.84i | 0.604490 | − | 1.04701i | −0.387642 | − | 0.921810i | \(-0.626710\pi\) |
0.992132 | − | 0.125197i | \(-0.0399563\pi\) | |||||||
\(132\) | −51.7285 | −0.0341090 | ||||||||
\(133\) | 1815.52 | + | 1524.04i | 1.18365 | + | 0.993615i | ||||
\(134\) | −1804.97 | −1.16363 | ||||||||
\(135\) | −67.5000 | + | 116.913i | −0.0430331 | + | 0.0745356i | ||||
\(136\) | −327.729 | + | 567.642i | −0.206636 | + | 0.357904i | ||||
\(137\) | −971.577 | − | 1682.82i | −0.605894 | − | 1.04944i | −0.991910 | − | 0.126946i | \(-0.959482\pi\) |
0.386016 | − | 0.922492i | \(-0.373851\pi\) | |||||||
\(138\) | −386.914 | + | 670.155i | −0.238669 | + | 0.413387i | ||||
\(139\) | −1003.92 | − | 1738.84i | −0.612599 | − | 1.06105i | −0.990801 | − | 0.135330i | \(-0.956791\pi\) |
0.378201 | − | 0.925723i | \(-0.376543\pi\) | |||||||
\(140\) | −572.428 | −0.345564 | ||||||||
\(141\) | −144.611 | −0.0863719 | ||||||||
\(142\) | −178.018 | − | 308.336i | −0.105204 | − | 0.182218i | ||||
\(143\) | 99.1463 | + | 171.726i | 0.0579792 | + | 0.100423i | ||||
\(144\) | 144.000 | 0.0833333 | ||||||||
\(145\) | −353.303 | −0.202346 | ||||||||
\(146\) | 560.371 | + | 970.591i | 0.317648 | + | 0.550183i | ||||
\(147\) | 714.278 | − | 1237.17i | 0.400767 | − | 0.694148i | ||||
\(148\) | 542.757 | + | 940.083i | 0.301448 | + | 0.522124i | ||||
\(149\) | −1150.17 | + | 1992.15i | −0.632386 | + | 1.09532i | 0.354677 | + | 0.934989i | \(0.384591\pi\) |
−0.987063 | + | 0.160336i | \(0.948742\pi\) | |||||||
\(150\) | 75.0000 | − | 129.904i | 0.0408248 | − | 0.0707107i | ||||
\(151\) | 637.507 | 0.343573 | 0.171787 | − | 0.985134i | \(-0.445046\pi\) | ||||
0.171787 | + | 0.985134i | \(0.445046\pi\) | |||||||
\(152\) | 507.457 | + | 425.985i | 0.270791 | + | 0.227316i | ||||
\(153\) | 737.389 | 0.389636 | ||||||||
\(154\) | −123.379 | + | 213.698i | −0.0645593 | + | 0.111820i | ||||
\(155\) | 473.714 | − | 820.497i | 0.245482 | − | 0.425186i | ||||
\(156\) | −276.000 | − | 478.046i | −0.141652 | − | 0.245348i | ||||
\(157\) | −527.979 | + | 914.486i | −0.268390 | + | 0.464866i | −0.968446 | − | 0.249222i | \(-0.919825\pi\) |
0.700056 | + | 0.714088i | \(0.253158\pi\) | |||||||
\(158\) | 944.139 | + | 1635.30i | 0.475390 | + | 0.823400i | ||||
\(159\) | −463.896 | −0.231379 | ||||||||
\(160\) | −160.000 | −0.0790569 | ||||||||
\(161\) | 1845.67 | + | 3196.80i | 0.903474 | + | 1.56486i | ||||
\(162\) | −81.0000 | − | 140.296i | −0.0392837 | − | 0.0680414i | ||||
\(163\) | 3251.73 | 1.56255 | 0.781275 | − | 0.624188i | \(-0.214570\pi\) | ||||
0.781275 | + | 0.624188i | \(0.214570\pi\) | |||||||
\(164\) | −485.828 | −0.231322 | ||||||||
\(165\) | −32.3303 | − | 55.9977i | −0.0152540 | − | 0.0264207i | ||||
\(166\) | −107.446 | + | 186.103i | −0.0502377 | + | 0.0870143i | ||||
\(167\) | 820.501 | + | 1421.15i | 0.380193 | + | 0.658514i | 0.991090 | − | 0.133196i | \(-0.0425241\pi\) |
−0.610896 | + | 0.791711i | \(0.709191\pi\) | |||||||
\(168\) | 343.457 | − | 594.885i | 0.157728 | − | 0.273193i | ||||
\(169\) | 40.5000 | − | 70.1481i | 0.0184342 | − | 0.0319290i | ||||
\(170\) | −819.321 | −0.369642 | ||||||||
\(171\) | 129.584 | − | 734.021i | 0.0579504 | − | 0.328257i | ||||
\(172\) | 110.057 | 0.0487895 | ||||||||
\(173\) | 1897.55 | − | 3286.65i | 0.833919 | − | 1.44439i | −0.0609887 | − | 0.998138i | \(-0.519425\pi\) |
0.894908 | − | 0.446251i | \(-0.147241\pi\) | |||||||
\(174\) | 211.982 | − | 367.163i | 0.0923581 | − | 0.159969i | ||||
\(175\) | −357.768 | − | 619.672i | −0.154541 | − | 0.267673i | ||||
\(176\) | −34.4857 | + | 59.7309i | −0.0147696 | + | 0.0255818i | ||||
\(177\) | −119.009 | − | 206.130i | −0.0505382 | − | 0.0875348i | ||||
\(178\) | 1190.45 | 0.501281 | ||||||||
\(179\) | −1668.07 | −0.696520 | −0.348260 | − | 0.937398i | \(-0.613227\pi\) | ||||
−0.348260 | + | 0.937398i | \(0.613227\pi\) | |||||||
\(180\) | 90.0000 | + | 155.885i | 0.0372678 | + | 0.0645497i | ||||
\(181\) | 576.966 | + | 999.335i | 0.236937 | + | 0.410386i | 0.959834 | − | 0.280569i | \(-0.0905233\pi\) |
−0.722897 | + | 0.690956i | \(0.757190\pi\) | |||||||
\(182\) | −2633.17 | −1.07244 | ||||||||
\(183\) | 1539.03 | 0.621686 | ||||||||
\(184\) | 515.885 | + | 893.540i | 0.206693 | + | 0.358003i | ||||
\(185\) | −678.446 | + | 1175.10i | −0.269624 | + | 0.467002i | ||||
\(186\) | 568.457 | + | 984.596i | 0.224093 | + | 0.388140i | ||||
\(187\) | −176.593 | + | 305.868i | −0.0690574 | + | 0.119611i | ||||
\(188\) | −96.4072 | + | 166.982i | −0.0374001 | + | 0.0647789i | ||||
\(189\) | −772.778 | −0.297415 | ||||||||
\(190\) | −143.982 | + | 815.579i | −0.0549765 | + | 0.311412i | ||||
\(191\) | −2740.14 | −1.03806 | −0.519031 | − | 0.854755i | \(-0.673707\pi\) | ||||
−0.519031 | + | 0.854755i | \(0.673707\pi\) | |||||||
\(192\) | 96.0000 | − | 166.277i | 0.0360844 | − | 0.0625000i | ||||
\(193\) | 2578.97 | − | 4466.91i | 0.961858 | − | 1.66599i | 0.244029 | − | 0.969768i | \(-0.421531\pi\) |
0.717829 | − | 0.696219i | \(-0.245136\pi\) | |||||||
\(194\) | −662.350 | − | 1147.22i | −0.245123 | − | 0.424566i | ||||
\(195\) | 345.000 | − | 597.558i | 0.126697 | − | 0.219446i | ||||
\(196\) | −952.371 | − | 1649.55i | −0.347074 | − | 0.601150i | ||||
\(197\) | −3205.90 | −1.15945 | −0.579723 | − | 0.814813i | \(-0.696839\pi\) | ||||
−0.579723 | + | 0.814813i | \(0.696839\pi\) | |||||||
\(198\) | 77.5928 | 0.0278499 | ||||||||
\(199\) | −409.988 | − | 710.120i | −0.146047 | − | 0.252960i | 0.783716 | − | 0.621119i | \(-0.213322\pi\) |
−0.929763 | + | 0.368159i | \(0.879988\pi\) | |||||||
\(200\) | −100.000 | − | 173.205i | −0.0353553 | − | 0.0612372i | ||||
\(201\) | 2707.46 | 0.950096 | ||||||||
\(202\) | −1562.92 | −0.544389 | ||||||||
\(203\) | −1011.20 | − | 1751.46i | −0.349619 | − | 0.605557i | ||||
\(204\) | 491.593 | − | 851.464i | 0.168718 | − | 0.292227i | ||||
\(205\) | −303.643 | − | 525.924i | −0.103450 | − | 0.179181i | ||||
\(206\) | −852.314 | + | 1476.25i | −0.288269 | + | 0.499297i | ||||
\(207\) | 580.371 | − | 1005.23i | 0.194872 | − | 0.337529i | ||||
\(208\) | −736.000 | −0.245348 | ||||||||
\(209\) | 273.437 | + | 229.537i | 0.0904979 | + | 0.0759685i | ||||
\(210\) | 858.643 | 0.282152 | ||||||||
\(211\) | 1263.76 | − | 2188.90i | 0.412327 | − | 0.714172i | −0.582816 | − | 0.812604i | \(-0.698049\pi\) |
0.995144 | + | 0.0984318i | \(0.0313826\pi\) | |||||||
\(212\) | −309.264 | + | 535.661i | −0.100190 | + | 0.173535i | ||||
\(213\) | 267.027 | + | 462.505i | 0.0858986 | + | 0.148781i | ||||
\(214\) | −792.903 | + | 1373.35i | −0.253279 | + | 0.438693i | ||||
\(215\) | 68.7858 | + | 119.141i | 0.0218193 | + | 0.0377922i | ||||
\(216\) | −216.000 | −0.0680414 | ||||||||
\(217\) | 5423.35 | 1.69659 | ||||||||
\(218\) | 581.836 | + | 1007.77i | 0.180765 | + | 0.313095i | ||||
\(219\) | −840.557 | − | 1455.89i | −0.259359 | − | 0.449222i | ||||
\(220\) | −86.2142 | −0.0264207 | ||||||||
\(221\) | −3768.88 | −1.14716 | ||||||||
\(222\) | −814.136 | − | 1410.12i | −0.246132 | − | 0.426312i | ||||
\(223\) | 975.431 | − | 1689.50i | 0.292914 | − | 0.507341i | −0.681584 | − | 0.731740i | \(-0.738709\pi\) |
0.974497 | + | 0.224399i | \(0.0720419\pi\) | |||||||
\(224\) | −457.943 | − | 793.180i | −0.136596 | − | 0.236592i | ||||
\(225\) | −112.500 | + | 194.856i | −0.0333333 | + | 0.0577350i | ||||
\(226\) | 682.747 | − | 1182.55i | 0.200954 | − | 0.348063i | ||||
\(227\) | −3629.36 | −1.06119 | −0.530593 | − | 0.847627i | \(-0.678031\pi\) | ||||
−0.530593 | + | 0.847627i | \(0.678031\pi\) | |||||||
\(228\) | −761.186 | − | 638.978i | −0.221100 | − | 0.185602i | ||||
\(229\) | −145.350 | −0.0419432 | −0.0209716 | − | 0.999780i | \(-0.506676\pi\) | ||||
−0.0209716 | + | 0.999780i | \(0.506676\pi\) | |||||||
\(230\) | −644.857 | + | 1116.92i | −0.184872 | + | 0.320208i | ||||
\(231\) | 185.068 | − | 320.547i | 0.0527124 | − | 0.0913006i | ||||
\(232\) | −282.643 | − | 489.551i | −0.0799844 | − | 0.138537i | ||||
\(233\) | −2093.44 | + | 3625.94i | −0.588609 | + | 1.01950i | 0.405806 | + | 0.913959i | \(0.366991\pi\) |
−0.994415 | + | 0.105541i | \(0.966343\pi\) | |||||||
\(234\) | 414.000 | + | 717.069i | 0.115658 | + | 0.200326i | ||||
\(235\) | −241.018 | −0.0669034 | ||||||||
\(236\) | −317.357 | −0.0875348 | ||||||||
\(237\) | −1416.21 | − | 2452.94i | −0.388154 | − | 0.672303i | ||||
\(238\) | −2345.01 | − | 4061.68i | −0.638675 | − | 1.10622i | ||||
\(239\) | −5470.20 | −1.48049 | −0.740247 | − | 0.672335i | \(-0.765291\pi\) | ||||
−0.740247 | + | 0.672335i | \(0.765291\pi\) | |||||||
\(240\) | 240.000 | 0.0645497 | ||||||||
\(241\) | −2905.25 | − | 5032.05i | −0.776530 | − | 1.34499i | −0.933930 | − | 0.357455i | \(-0.883645\pi\) |
0.157400 | − | 0.987535i | \(-0.449689\pi\) | |||||||
\(242\) | 1312.42 | − | 2273.17i | 0.348617 | − | 0.603823i | ||||
\(243\) | 121.500 | + | 210.444i | 0.0320750 | + | 0.0555556i | ||||
\(244\) | 1026.02 | − | 1777.12i | 0.269198 | − | 0.466264i | ||||
\(245\) | 1190.46 | − | 2061.94i | 0.310432 | − | 0.537685i | ||||
\(246\) | 728.742 | 0.188874 | ||||||||
\(247\) | −662.317 | + | 3751.66i | −0.170616 | + | 0.966448i | ||||
\(248\) | 1515.89 | 0.388140 | ||||||||
\(249\) | 161.170 | − | 279.154i | 0.0410189 | − | 0.0710469i | ||||
\(250\) | 125.000 | − | 216.506i | 0.0316228 | − | 0.0547723i | ||||
\(251\) | −1298.77 | − | 2249.53i | −0.326604 | − | 0.565695i | 0.655232 | − | 0.755428i | \(-0.272571\pi\) |
−0.981836 | + | 0.189733i | \(0.939238\pi\) | |||||||
\(252\) | −515.186 | + | 892.327i | −0.128784 | + | 0.223061i | ||||
\(253\) | 277.979 | + | 481.474i | 0.0690766 | + | 0.119644i | ||||
\(254\) | −3465.17 | −0.856000 | ||||||||
\(255\) | 1228.98 | 0.301811 | ||||||||
\(256\) | −128.000 | − | 221.703i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | −2230.58 | − | 3863.47i | −0.541399 | − | 0.937731i | −0.998824 | − | 0.0484827i | \(-0.984561\pi\) |
0.457425 | − | 0.889248i | \(-0.348772\pi\) | |||||||
\(258\) | −165.086 | −0.0398365 | ||||||||
\(259\) | −7767.24 | −1.86345 | ||||||||
\(260\) | −460.000 | − | 796.743i | −0.109723 | − | 0.190046i | ||||
\(261\) | −317.973 | + | 550.745i | −0.0754101 | + | 0.130614i | ||||
\(262\) | 1812.70 | + | 3139.69i | 0.427439 | + | 0.740346i | ||||
\(263\) | −2707.67 | + | 4689.83i | −0.634838 | + | 1.09957i | 0.351712 | + | 0.936108i | \(0.385600\pi\) |
−0.986550 | + | 0.163463i | \(0.947734\pi\) | |||||||
\(264\) | 51.7285 | − | 89.5964i | 0.0120594 | − | 0.0208874i | ||||
\(265\) | −773.160 | −0.179226 | ||||||||
\(266\) | −4455.23 | + | 1620.53i | −1.02695 | + | 0.373538i | ||||
\(267\) | −1785.67 | −0.409294 | ||||||||
\(268\) | 1804.97 | − | 3126.30i | 0.411404 | − | 0.712572i | ||||
\(269\) | 3613.08 | − | 6258.04i | 0.818934 | − | 1.41844i | −0.0875335 | − | 0.996162i | \(-0.527898\pi\) |
0.906468 | − | 0.422275i | \(-0.138768\pi\) | |||||||
\(270\) | −135.000 | − | 233.827i | −0.0304290 | − | 0.0527046i | ||||
\(271\) | 417.557 | − | 723.231i | 0.0935971 | − | 0.162115i | −0.815425 | − | 0.578863i | \(-0.803497\pi\) |
0.909022 | + | 0.416748i | \(0.136830\pi\) | |||||||
\(272\) | −655.457 | − | 1135.28i | −0.146114 | − | 0.253076i | ||||
\(273\) | 3949.76 | 0.875641 | ||||||||
\(274\) | 3886.31 | 0.856863 | ||||||||
\(275\) | −53.8839 | − | 93.3296i | −0.0118157 | − | 0.0204654i | ||||
\(276\) | −773.828 | − | 1340.31i | −0.168764 | − | 0.292309i | ||||
\(277\) | −209.858 | −0.0455204 | −0.0227602 | − | 0.999741i | \(-0.507245\pi\) | ||||
−0.0227602 | + | 0.999741i | \(0.507245\pi\) | |||||||
\(278\) | 4015.68 | 0.866346 | ||||||||
\(279\) | −852.686 | − | 1476.89i | −0.182971 | − | 0.316915i | ||||
\(280\) | 572.428 | − | 991.475i | 0.122175 | − | 0.211614i | ||||
\(281\) | 859.842 | + | 1489.29i | 0.182540 | + | 0.316169i | 0.942745 | − | 0.333515i | \(-0.108235\pi\) |
−0.760205 | + | 0.649684i | \(0.774901\pi\) | |||||||
\(282\) | 144.611 | − | 250.473i | 0.0305371 | − | 0.0528917i | ||||
\(283\) | −147.157 | + | 254.883i | −0.0309101 | + | 0.0535379i | −0.881067 | − | 0.472992i | \(-0.843174\pi\) |
0.850157 | + | 0.526530i | \(0.176507\pi\) | |||||||
\(284\) | 712.072 | 0.148781 | ||||||||
\(285\) | 215.973 | − | 1223.37i | 0.0448882 | − | 0.254267i | ||||
\(286\) | −396.585 | −0.0819950 | ||||||||
\(287\) | 1738.14 | − | 3010.54i | 0.357487 | − | 0.619186i | ||||
\(288\) | −144.000 | + | 249.415i | −0.0294628 | + | 0.0510310i | ||||
\(289\) | −899.937 | − | 1558.74i | −0.183175 | − | 0.317268i | ||||
\(290\) | 353.303 | − | 611.939i | 0.0715403 | − | 0.123911i | ||||
\(291\) | 993.525 | + | 1720.84i | 0.200142 | + | 0.346657i | ||||
\(292\) | −2241.48 | −0.449222 | ||||||||
\(293\) | 6457.02 | 1.28745 | 0.643725 | − | 0.765257i | \(-0.277388\pi\) | ||||
0.643725 | + | 0.765257i | \(0.277388\pi\) | |||||||
\(294\) | 1428.56 | + | 2474.33i | 0.283385 | + | 0.490837i | ||||
\(295\) | −198.348 | − | 343.550i | −0.0391468 | − | 0.0678042i | ||||
\(296\) | −2171.03 | −0.426312 | ||||||||
\(297\) | −116.389 | −0.0227393 | ||||||||
\(298\) | −2300.34 | − | 3984.30i | −0.447164 | − | 0.774511i | ||||
\(299\) | −2966.34 | + | 5137.85i | −0.573739 | + | 0.993745i | ||||
\(300\) | 150.000 | + | 259.808i | 0.0288675 | + | 0.0500000i | ||||
\(301\) | −393.750 | + | 681.994i | −0.0753998 | + | 0.130596i | ||||
\(302\) | −637.507 | + | 1104.19i | −0.121471 | + | 0.210395i | ||||
\(303\) | 2344.38 | 0.444492 | ||||||||
\(304\) | −1245.29 | + | 452.956i | −0.234941 | + | 0.0854566i | ||||
\(305\) | 2565.05 | 0.481556 | ||||||||
\(306\) | −737.389 | + | 1277.20i | −0.137757 | + | 0.238603i | ||||
\(307\) | 1926.96 | − | 3337.59i | 0.358232 | − | 0.620476i | −0.629434 | − | 0.777054i | \(-0.716713\pi\) |
0.987666 | + | 0.156578i | \(0.0500464\pi\) | |||||||
\(308\) | −246.757 | − | 427.396i | −0.0456503 | − | 0.0790687i | ||||
\(309\) | 1278.47 | − | 2214.38i | 0.235371 | − | 0.407675i | ||||
\(310\) | 947.428 | + | 1640.99i | 0.173582 | + | 0.300652i | ||||
\(311\) | −8358.72 | −1.52405 | −0.762025 | − | 0.647548i | \(-0.775795\pi\) | ||||
−0.762025 | + | 0.647548i | \(0.775795\pi\) | |||||||
\(312\) | 1104.00 | 0.200326 | ||||||||
\(313\) | −1925.35 | − | 3334.80i | −0.347690 | − | 0.602218i | 0.638148 | − | 0.769913i | \(-0.279701\pi\) |
−0.985839 | + | 0.167696i | \(0.946367\pi\) | |||||||
\(314\) | −1055.96 | − | 1828.97i | −0.189781 | − | 0.328710i | ||||
\(315\) | −1287.96 | −0.230376 | ||||||||
\(316\) | −3776.55 | −0.672303 | ||||||||
\(317\) | 3892.71 | + | 6742.37i | 0.689704 | + | 1.19460i | 0.971933 | + | 0.235256i | \(0.0755928\pi\) |
−0.282229 | + | 0.959347i | \(0.591074\pi\) | |||||||
\(318\) | 463.896 | − | 803.491i | 0.0818050 | − | 0.141690i | ||||
\(319\) | −152.299 | − | 263.789i | −0.0267307 | − | 0.0462989i | ||||
\(320\) | 160.000 | − | 277.128i | 0.0279508 | − | 0.0484123i | ||||
\(321\) | 1189.36 | − | 2060.02i | 0.206802 | − | 0.358191i | ||||
\(322\) | −7382.68 | −1.27770 | ||||||||
\(323\) | −6376.80 | + | 2319.48i | −1.09850 | + | 0.399564i | ||||
\(324\) | 324.000 | 0.0555556 | ||||||||
\(325\) | 575.000 | − | 995.929i | 0.0981393 | − | 0.169982i | ||||
\(326\) | −3251.73 | + | 5632.17i | −0.552445 | + | 0.956862i | ||||
\(327\) | −872.753 | − | 1511.65i | −0.147594 | − | 0.255641i | ||||
\(328\) | 485.828 | − | 841.479i | 0.0817846 | − | 0.141655i | ||||
\(329\) | −689.828 | − | 1194.82i | −0.115597 | − | 0.200220i | ||||
\(330\) | 129.321 | 0.0215724 | ||||||||
\(331\) | −3570.70 | −0.592940 | −0.296470 | − | 0.955042i | \(-0.595810\pi\) | ||||
−0.296470 | + | 0.955042i | \(0.595810\pi\) | |||||||
\(332\) | −214.893 | − | 372.205i | −0.0355234 | − | 0.0615284i | ||||
\(333\) | 1221.20 | + | 2115.19i | 0.200966 | + | 0.348083i | ||||
\(334\) | −3282.01 | −0.537675 | ||||||||
\(335\) | 4512.43 | 0.735941 | ||||||||
\(336\) | 686.914 | + | 1189.77i | 0.111530 | + | 0.193176i | ||||
\(337\) | −1633.33 | + | 2829.01i | −0.264015 | + | 0.457287i | −0.967305 | − | 0.253616i | \(-0.918380\pi\) |
0.703290 | + | 0.710903i | \(0.251713\pi\) | |||||||
\(338\) | 81.0000 | + | 140.296i | 0.0130350 | + | 0.0225772i | ||||
\(339\) | −1024.12 | + | 1773.83i | −0.164078 | + | 0.284192i | ||||
\(340\) | 819.321 | − | 1419.11i | 0.130688 | − | 0.226358i | ||||
\(341\) | 816.817 | 0.129716 | ||||||||
\(342\) | 1141.78 | + | 958.467i | 0.180527 | + | 0.151544i | ||||
\(343\) | 3811.96 | 0.600077 | ||||||||
\(344\) | −110.057 | + | 190.625i | −0.0172497 | + | 0.0298773i | ||||
\(345\) | 967.285 | − | 1675.39i | 0.150947 | − | 0.261449i | ||||
\(346\) | 3795.10 | + | 6573.30i | 0.589670 | + | 1.02134i | ||||
\(347\) | 2745.92 | − | 4756.07i | 0.424808 | − | 0.735790i | −0.571594 | − | 0.820537i | \(-0.693675\pi\) |
0.996403 | + | 0.0847468i | \(0.0270081\pi\) | |||||||
\(348\) | 423.964 | + | 734.327i | 0.0653070 | + | 0.113115i | ||||
\(349\) | 4375.75 | 0.671142 | 0.335571 | − | 0.942015i | \(-0.391071\pi\) | ||||
0.335571 | + | 0.942015i | \(0.391071\pi\) | |||||||
\(350\) | 1431.07 | 0.218554 | ||||||||
\(351\) | −621.000 | − | 1075.60i | −0.0944346 | − | 0.163565i | ||||
\(352\) | −68.9713 | − | 119.462i | −0.0104437 | − | 0.0180890i | ||||
\(353\) | 9525.41 | 1.43622 | 0.718111 | − | 0.695929i | \(-0.245007\pi\) | ||||
0.718111 | + | 0.695929i | \(0.245007\pi\) | |||||||
\(354\) | 476.036 | 0.0714719 | ||||||||
\(355\) | 445.045 | + | 770.841i | 0.0665368 | + | 0.115245i | ||||
\(356\) | −1190.45 | + | 2061.92i | −0.177229 | + | 0.306970i | ||||
\(357\) | 3517.52 | + | 6092.52i | 0.521476 | + | 0.903223i | ||||
\(358\) | 1668.07 | − | 2889.18i | 0.246257 | − | 0.426530i | ||||
\(359\) | 627.576 | − | 1086.99i | 0.0922624 | − | 0.159803i | −0.816200 | − | 0.577769i | \(-0.803923\pi\) |
0.908463 | + | 0.417966i | \(0.137257\pi\) | |||||||
\(360\) | −360.000 | −0.0527046 | ||||||||
\(361\) | 1188.27 | + | 6755.29i | 0.173242 | + | 0.984879i | ||||
\(362\) | −2307.86 | −0.335079 | ||||||||
\(363\) | −1968.63 | + | 3409.76i | −0.284645 | + | 0.493019i | ||||
\(364\) | 2633.17 | − | 4560.78i | 0.379164 | − | 0.656731i | ||||
\(365\) | −1400.93 | − | 2426.48i | −0.200898 | − | 0.347966i | ||||
\(366\) | −1539.03 | + | 2665.68i | −0.219799 | + | 0.380703i | ||||
\(367\) | −5243.43 | − | 9081.88i | −0.745789 | − | 1.29174i | −0.949825 | − | 0.312781i | \(-0.898739\pi\) |
0.204036 | − | 0.978963i | \(-0.434594\pi\) | |||||||
\(368\) | −2063.54 | −0.292309 | ||||||||
\(369\) | −1093.11 | −0.154215 | ||||||||
\(370\) | −1356.89 | − | 2350.21i | −0.190653 | − | 0.330220i | ||||
\(371\) | −2212.89 | − | 3832.84i | −0.309670 | − | 0.536365i | ||||
\(372\) | −2273.83 | −0.316915 | ||||||||
\(373\) | −7848.84 | −1.08954 | −0.544769 | − | 0.838586i | \(-0.683383\pi\) | ||||
−0.544769 | + | 0.838586i | \(0.683383\pi\) | |||||||
\(374\) | −353.186 | − | 611.735i | −0.0488310 | − | 0.0845777i | ||||
\(375\) | −187.500 | + | 324.760i | −0.0258199 | + | 0.0447214i | ||||
\(376\) | −192.814 | − | 333.965i | −0.0264459 | − | 0.0458056i | ||||
\(377\) | 1625.19 | − | 2814.92i | 0.222021 | − | 0.384551i | ||||
\(378\) | 772.778 | − | 1338.49i | 0.105152 | − | 0.182128i | ||||
\(379\) | 4137.48 | 0.560760 | 0.280380 | − | 0.959889i | \(-0.409540\pi\) | ||||
0.280380 | + | 0.959889i | \(0.409540\pi\) | |||||||
\(380\) | −1268.64 | − | 1064.96i | −0.171263 | − | 0.143767i | ||||
\(381\) | 5197.76 | 0.698921 | ||||||||
\(382\) | 2740.14 | − | 4746.07i | 0.367010 | − | 0.635681i | ||||
\(383\) | −39.5605 | + | 68.5207i | −0.00527792 | + | 0.00914163i | −0.868652 | − | 0.495422i | \(-0.835013\pi\) |
0.863374 | + | 0.504564i | \(0.168347\pi\) | |||||||
\(384\) | 192.000 | + | 332.554i | 0.0255155 | + | 0.0441942i | ||||
\(385\) | 308.446 | − | 534.245i | 0.0408309 | − | 0.0707212i | ||||
\(386\) | 5157.95 | + | 8933.83i | 0.680136 | + | 1.17803i | ||||
\(387\) | 247.629 | 0.0325263 | ||||||||
\(388\) | 2649.40 | 0.346657 | ||||||||
\(389\) | 3676.32 | + | 6367.58i | 0.479170 | + | 0.829946i | 0.999715 | − | 0.0238880i | \(-0.00760450\pi\) |
−0.520545 | + | 0.853834i | \(0.674271\pi\) | |||||||
\(390\) | 690.000 | + | 1195.12i | 0.0895885 | + | 0.155172i | ||||
\(391\) | −10566.9 | −1.36673 | ||||||||
\(392\) | 3809.48 | 0.490837 | ||||||||
\(393\) | −2719.05 | − | 4709.53i | −0.349002 | − | 0.604490i | ||||
\(394\) | 3205.90 | − | 5552.78i | 0.409926 | − | 0.710013i | ||||
\(395\) | −2360.35 | − | 4088.24i | −0.300663 | − | 0.520764i | ||||
\(396\) | −77.5928 | + | 134.395i | −0.00984642 | + | 0.0170545i | ||||
\(397\) | −5491.24 | + | 9511.11i | −0.694201 | + | 1.20239i | 0.276249 | + | 0.961086i | \(0.410909\pi\) |
−0.970449 | + | 0.241305i | \(0.922425\pi\) | |||||||
\(398\) | 1639.95 | 0.206541 | ||||||||
\(399\) | 6682.84 | − | 2430.80i | 0.838498 | − | 0.304993i | ||||
\(400\) | 400.000 | 0.0500000 | ||||||||
\(401\) | −1035.41 | + | 1793.39i | −0.128943 | + | 0.223335i | −0.923267 | − | 0.384158i | \(-0.874492\pi\) |
0.794325 | + | 0.607494i | \(0.207825\pi\) | |||||||
\(402\) | −2707.46 | + | 4689.45i | −0.335910 | + | 0.581813i | ||||
\(403\) | 4358.17 | + | 7548.57i | 0.538700 | + | 0.933055i | ||||
\(404\) | 1562.92 | − | 2707.06i | 0.192471 | − | 0.333369i | ||||
\(405\) | 202.500 | + | 350.740i | 0.0248452 | + | 0.0430331i | ||||
\(406\) | 4044.81 | 0.494435 | ||||||||
\(407\) | −1169.83 | −0.142473 | ||||||||
\(408\) | 983.186 | + | 1702.93i | 0.119301 | + | 0.206636i | ||||
\(409\) | 4531.55 | + | 7848.87i | 0.547850 | + | 0.948904i | 0.998422 | + | 0.0561638i | \(0.0178869\pi\) |
−0.450572 | + | 0.892740i | \(0.648780\pi\) | |||||||
\(410\) | 1214.57 | 0.146301 | ||||||||
\(411\) | −5829.46 | −0.699626 | ||||||||
\(412\) | −1704.63 | − | 2952.50i | −0.203837 | − | 0.353057i | ||||
\(413\) | 1135.40 | − | 1966.58i | 0.135277 | − | 0.234307i | ||||
\(414\) | 1160.74 | + | 2010.46i | 0.137796 | + | 0.238669i | ||||
\(415\) | 268.616 | − | 465.257i | 0.0317731 | − | 0.0550327i | ||||
\(416\) | 736.000 | − | 1274.79i | 0.0867437 | − | 0.150244i | ||||
\(417\) | −6023.52 | −0.707369 | ||||||||
\(418\) | −671.008 | + | 244.070i | −0.0785169 | + | 0.0285595i | ||||
\(419\) | −1690.59 | −0.197113 | −0.0985567 | − | 0.995131i | \(-0.531423\pi\) | ||||
−0.0985567 | + | 0.995131i | \(0.531423\pi\) | |||||||
\(420\) | −858.643 | + | 1487.21i | −0.0997559 | + | 0.172782i | ||||
\(421\) | −7501.22 | + | 12992.5i | −0.868378 | + | 1.50407i | −0.00472430 | + | 0.999989i | \(0.501504\pi\) |
−0.863654 | + | 0.504086i | \(0.831830\pi\) | |||||||
\(422\) | 2527.53 | + | 4377.81i | 0.291560 | + | 0.504996i | ||||
\(423\) | −216.916 | + | 375.710i | −0.0249334 | + | 0.0431859i | ||||
\(424\) | −618.528 | − | 1071.32i | −0.0708452 | − | 0.122707i | ||||
\(425\) | 2048.30 | 0.233782 | ||||||||
\(426\) | −1068.11 | −0.121479 | ||||||||
\(427\) | 7341.54 | + | 12715.9i | 0.832043 | + | 1.44114i | ||||
\(428\) | −1585.81 | − | 2746.70i | −0.179095 | − | 0.310202i | ||||
\(429\) | 594.878 | 0.0669486 | ||||||||
\(430\) | −275.143 | −0.0308572 | ||||||||
\(431\) | −6820.70 | − | 11813.8i | −0.762277 | − | 1.32030i | −0.941674 | − | 0.336526i | \(-0.890748\pi\) |
0.179397 | − | 0.983777i | \(-0.442585\pi\) | |||||||
\(432\) | 216.000 | − | 374.123i | 0.0240563 | − | 0.0416667i | ||||
\(433\) | 5415.71 | + | 9380.29i | 0.601068 | + | 1.04108i | 0.992660 | + | 0.120942i | \(0.0385914\pi\) |
−0.391591 | + | 0.920139i | \(0.628075\pi\) | |||||||
\(434\) | −5423.35 | + | 9393.51i | −0.599837 | + | 1.03895i | ||||
\(435\) | −529.955 | + | 917.908i | −0.0584124 | + | 0.101173i | ||||
\(436\) | −2327.34 | −0.255641 | ||||||||
\(437\) | −1856.95 | + | 10518.6i | −0.203273 | + | 1.15143i | ||||
\(438\) | 3362.23 | 0.366789 | ||||||||
\(439\) | −6346.96 | + | 10993.3i | −0.690032 | + | 1.19517i | 0.281795 | + | 0.959475i | \(0.409070\pi\) |
−0.971827 | + | 0.235695i | \(0.924263\pi\) | |||||||
\(440\) | 86.2142 | − | 149.327i | 0.00934113 | − | 0.0161793i | ||||
\(441\) | −2142.83 | − | 3711.50i | −0.231383 | − | 0.400767i | ||||
\(442\) | 3768.88 | − | 6527.89i | 0.405582 | − | 0.702489i | ||||
\(443\) | −1450.82 | − | 2512.89i | −0.155599 | − | 0.269505i | 0.777678 | − | 0.628663i | \(-0.216397\pi\) |
−0.933277 | + | 0.359157i | \(0.883064\pi\) | |||||||
\(444\) | 3256.54 | 0.348083 | ||||||||
\(445\) | −2976.12 | −0.317038 | ||||||||
\(446\) | 1950.86 | + | 3378.99i | 0.207121 | + | 0.358744i | ||||
\(447\) | 3450.51 | + | 5976.45i | 0.365108 | + | 0.632386i | ||||
\(448\) | 1831.77 | 0.193176 | ||||||||
\(449\) | −50.5038 | −0.00530829 | −0.00265414 | − | 0.999996i | \(-0.500845\pi\) | ||||
−0.00265414 | + | 0.999996i | \(0.500845\pi\) | |||||||
\(450\) | −225.000 | − | 389.711i | −0.0235702 | − | 0.0408248i | ||||
\(451\) | 261.783 | − | 453.421i | 0.0273323 | − | 0.0473410i | ||||
\(452\) | 1365.49 | + | 2365.10i | 0.142096 | + | 0.246118i | ||||
\(453\) | 956.260 | − | 1656.29i | 0.0991811 | − | 0.171787i | ||||
\(454\) | 3629.36 | − | 6286.24i | 0.375186 | − | 0.649841i | ||||
\(455\) | 6582.93 | 0.678269 | ||||||||
\(456\) | 1867.93 | − | 679.434i | 0.191828 | − | 0.0697750i | ||||
\(457\) | −10840.4 | −1.10961 | −0.554804 | − | 0.831981i | \(-0.687207\pi\) | ||||
−0.554804 | + | 0.831981i | \(0.687207\pi\) | |||||||
\(458\) | 145.350 | − | 251.753i | 0.0148292 | − | 0.0256849i | ||||
\(459\) | 1106.08 | − | 1915.79i | 0.112478 | − | 0.194818i | ||||
\(460\) | −1289.71 | − | 2233.85i | −0.130724 | − | 0.226421i | ||||
\(461\) | −1804.67 | + | 3125.77i | −0.182325 | + | 0.315795i | −0.942672 | − | 0.333721i | \(-0.891695\pi\) |
0.760347 | + | 0.649517i | \(0.225029\pi\) | |||||||
\(462\) | 370.136 | + | 641.094i | 0.0372733 | + | 0.0645593i | ||||
\(463\) | 9096.20 | 0.913038 | 0.456519 | − | 0.889714i | \(-0.349096\pi\) | ||||
0.456519 | + | 0.889714i | \(0.349096\pi\) | |||||||
\(464\) | 1130.57 | 0.113115 | ||||||||
\(465\) | −1421.14 | − | 2461.49i | −0.141729 | − | 0.245482i | ||||
\(466\) | −4186.88 | − | 7251.89i | −0.416209 | − | 0.720895i | ||||
\(467\) | 1927.45 | 0.190989 | 0.0954943 | − | 0.995430i | \(-0.469557\pi\) | ||||
0.0954943 | + | 0.995430i | \(0.469557\pi\) | |||||||
\(468\) | −1656.00 | −0.163565 | ||||||||
\(469\) | 12915.2 | + | 22369.8i | 1.27158 | + | 2.20243i | ||||
\(470\) | 241.018 | − | 417.456i | 0.0236539 | − | 0.0409698i | ||||
\(471\) | 1583.94 | + | 2743.46i | 0.154955 | + | 0.268390i | ||||
\(472\) | 317.357 | − | 549.679i | 0.0309482 | − | 0.0536039i | ||||
\(473\) | −59.3031 | + | 102.716i | −0.00576482 | + | 0.00998497i | ||||
\(474\) | 5664.83 | 0.548933 | ||||||||
\(475\) | 359.955 | − | 2038.95i | 0.0347702 | − | 0.196954i | ||||
\(476\) | 9380.05 | 0.903223 | ||||||||
\(477\) | −695.844 | + | 1205.24i | −0.0667935 | + | 0.115690i | ||||
\(478\) | 5470.20 | − | 9474.67i | 0.523434 | − | 0.906613i | ||||
\(479\) | 9349.27 | + | 16193.4i | 0.891814 | + | 1.54467i | 0.837699 | + | 0.546132i | \(0.183900\pi\) |
0.0541151 | + | 0.998535i | \(0.482766\pi\) | |||||||
\(480\) | −240.000 | + | 415.692i | −0.0228218 | + | 0.0395285i | ||||
\(481\) | −6241.71 | − | 10811.0i | −0.591679 | − | 1.02482i | ||||
\(482\) | 11621.0 | 1.09818 | ||||||||
\(483\) | 11074.0 | 1.04324 | ||||||||
\(484\) | 2624.84 | + | 4546.35i | 0.246510 | + | 0.426967i | ||||
\(485\) | 1655.87 | + | 2868.06i | 0.155030 | + | 0.268519i | ||||
\(486\) | −486.000 | −0.0453609 | ||||||||
\(487\) | 9370.36 | 0.871892 | 0.435946 | − | 0.899973i | \(-0.356414\pi\) | ||||
0.435946 | + | 0.899973i | \(0.356414\pi\) | |||||||
\(488\) | 2052.04 | + | 3554.24i | 0.190352 | + | 0.329699i | ||||
\(489\) | 4877.60 | − | 8448.25i | 0.451069 | − | 0.781275i | ||||
\(490\) | 2380.93 | + | 4123.89i | 0.219509 | + | 0.380200i | ||||
\(491\) | −8801.87 | + | 15245.3i | −0.809008 | + | 1.40124i | 0.104544 | + | 0.994520i | \(0.466662\pi\) |
−0.913552 | + | 0.406723i | \(0.866671\pi\) | |||||||
\(492\) | −728.742 | + | 1262.22i | −0.0667769 | + | 0.115661i | ||||
\(493\) | 5789.38 | 0.528885 | ||||||||
\(494\) | −5835.76 | − | 4898.83i | −0.531504 | − | 0.446172i | ||||
\(495\) | −193.982 | −0.0176138 | ||||||||
\(496\) | −1515.89 | + | 2625.59i | −0.137228 | + | 0.237686i | ||||
\(497\) | −2547.57 | + | 4412.51i | −0.229927 | + | 0.398246i | ||||
\(498\) | 322.339 | + | 558.308i | 0.0290048 | + | 0.0502377i | ||||
\(499\) | −9161.02 | + | 15867.3i | −0.821851 | + | 1.42349i | 0.0824520 | + | 0.996595i | \(0.473725\pi\) |
−0.904303 | + | 0.426892i | \(0.859608\pi\) | |||||||
\(500\) | 250.000 | + | 433.013i | 0.0223607 | + | 0.0387298i | ||||
\(501\) | 4923.01 | 0.439010 | ||||||||
\(502\) | 5195.08 | 0.461888 | ||||||||
\(503\) | −5635.20 | − | 9760.45i | −0.499525 | − | 0.865203i | 0.500475 | − | 0.865751i | \(-0.333159\pi\) |
−1.00000 | 0.000548122i | \(0.999826\pi\) | ||||||||
\(504\) | −1030.37 | − | 1784.65i | −0.0910642 | − | 0.157728i | ||||
\(505\) | 3907.30 | 0.344302 | ||||||||
\(506\) | −1111.92 | −0.0976891 | ||||||||
\(507\) | −121.500 | − | 210.444i | −0.0106430 | − | 0.0184342i | ||||
\(508\) | 3465.17 | − | 6001.85i | 0.302642 | − | 0.524191i | ||||
\(509\) | −2067.88 | − | 3581.68i | −0.180073 | − | 0.311896i | 0.761832 | − | 0.647775i | \(-0.224300\pi\) |
−0.941905 | + | 0.335878i | \(0.890967\pi\) | |||||||
\(510\) | −1228.98 | + | 2128.66i | −0.106706 | + | 0.184821i | ||||
\(511\) | 8019.31 | − | 13889.8i | 0.694233 | − | 1.20245i | ||||
\(512\) | 512.000 | 0.0441942 | ||||||||
\(513\) | −1712.67 | − | 1437.70i | −0.147400 | − | 0.123735i | ||||
\(514\) | 8922.31 | 0.765654 | ||||||||
\(515\) | 2130.78 | − | 3690.63i | 0.182318 | − | 0.315783i | ||||
\(516\) | 165.086 | − | 285.937i | 0.0140843 | − | 0.0243947i | ||||
\(517\) | −103.896 | − | 179.953i | −0.00883817 | − | 0.0153082i | ||||
\(518\) | 7767.24 | − | 13453.3i | 0.658828 | − | 1.14112i | ||||
\(519\) | −5692.65 | − | 9859.95i | −0.481463 | − | 0.833919i | ||||
\(520\) | 1840.00 | 0.155172 | ||||||||
\(521\) | −5893.76 | −0.495606 | −0.247803 | − | 0.968810i | \(-0.579709\pi\) | ||||
−0.247803 | + | 0.968810i | \(0.579709\pi\) | |||||||
\(522\) | −635.946 | − | 1101.49i | −0.0533230 | − | 0.0923581i | ||||
\(523\) | −2513.85 | − | 4354.11i | −0.210178 | − | 0.364038i | 0.741592 | − | 0.670851i | \(-0.234071\pi\) |
−0.951770 | + | 0.306812i | \(0.900738\pi\) | |||||||
\(524\) | −7250.80 | −0.604490 | ||||||||
\(525\) | −2146.61 | −0.178449 | ||||||||
\(526\) | −5415.35 | − | 9379.66i | −0.448898 | − | 0.777514i | ||||
\(527\) | −7762.48 | + | 13445.0i | −0.641630 | + | 1.11134i | ||||
\(528\) | 103.457 | + | 179.193i | 0.00852725 | + | 0.0147696i | ||||
\(529\) | −2233.30 | + | 3868.19i | −0.183554 | + | 0.317925i | ||||
\(530\) | 773.160 | − | 1339.15i | 0.0633659 | − | 0.109753i | ||||
\(531\) | −714.054 | −0.0583565 | ||||||||
\(532\) | 1648.39 | − | 9337.21i | 0.134336 | − | 0.760939i | ||||
\(533\) | 5587.02 | 0.454035 | ||||||||
\(534\) | 1785.67 | − | 3092.88i | 0.144707 | − | 0.250640i | ||||
\(535\) | 1982.26 | − | 3433.37i | 0.160188 | − | 0.277454i | ||||
\(536\) | 3609.94 | + | 6252.60i | 0.290906 | + | 0.503864i | ||||
\(537\) | −2502.10 | + | 4333.76i | −0.201068 | + | 0.348260i | ||||
\(538\) | 7226.16 | + | 12516.1i | 0.579074 | + | 1.00299i | ||||
\(539\) | 2052.70 | 0.164037 | ||||||||
\(540\) | 540.000 | 0.0430331 | ||||||||
\(541\) | −7786.73 | − | 13487.0i | −0.618813 | − | 1.07181i | −0.989703 | − | 0.143138i | \(-0.954281\pi\) |
0.370890 | − | 0.928677i | \(-0.379053\pi\) | |||||||
\(542\) | 835.115 | + | 1446.46i | 0.0661831 | + | 0.114633i | ||||
\(543\) | 3461.80 | 0.273591 | ||||||||
\(544\) | 2621.83 | 0.206636 | ||||||||
\(545\) | −1454.59 | − | 2519.42i | −0.114326 | − | 0.198019i | ||||
\(546\) | −3949.76 | + | 6841.18i | −0.309586 | + | 0.536219i | ||||
\(547\) | −3746.10 | − | 6488.44i | −0.292819 | − | 0.507177i | 0.681656 | − | 0.731672i | \(-0.261260\pi\) |
−0.974475 | + | 0.224496i | \(0.927927\pi\) | |||||||
\(548\) | −3886.31 | + | 6731.28i | −0.302947 | + | 0.524719i | ||||
\(549\) | 2308.55 | − | 3998.52i | 0.179465 | − | 0.310843i | ||||
\(550\) | 215.535 | 0.0167099 | ||||||||
\(551\) | 1017.38 | − | 5762.93i | 0.0786607 | − | 0.445570i | ||||
\(552\) | 3095.31 | 0.238669 | ||||||||
\(553\) | 13511.3 | − | 23402.2i | 1.03898 | − | 1.79957i | ||||
\(554\) | 209.858 | − | 363.485i | 0.0160939 | − | 0.0278755i | ||||
\(555\) | 2035.34 | + | 3525.31i | 0.155667 | + | 0.269624i | ||||
\(556\) | −4015.68 | + | 6955.36i | −0.306300 | + | 0.530527i | ||||
\(557\) | 2062.15 | + | 3571.75i | 0.156869 | + | 0.271705i | 0.933738 | − | 0.357957i | \(-0.116527\pi\) |
−0.776869 | + | 0.629662i | \(0.783193\pi\) | |||||||
\(558\) | 3410.74 | 0.258760 | ||||||||
\(559\) | −1265.66 | −0.0957633 | ||||||||
\(560\) | 1144.86 | + | 1982.95i | 0.0863911 | + | 0.149634i | ||||
\(561\) | 529.778 | + | 917.603i | 0.0398703 | + | 0.0690574i | ||||
\(562\) | −3439.37 | −0.258151 | ||||||||
\(563\) | 7596.95 | 0.568691 | 0.284346 | − | 0.958722i | \(-0.408224\pi\) | ||||
0.284346 | + | 0.958722i | \(0.408224\pi\) | |||||||
\(564\) | 289.222 | + | 500.947i | 0.0215930 | + | 0.0374001i | ||||
\(565\) | −1706.87 | + | 2956.38i | −0.127095 | + | 0.220134i | ||||
\(566\) | −294.314 | − | 509.766i | −0.0218568 | − | 0.0378570i | ||||
\(567\) | −1159.17 | + | 2007.74i | −0.0858562 | + | 0.148707i | ||||
\(568\) | −712.072 | + | 1233.35i | −0.0526019 | + | 0.0911092i | ||||
\(569\) | −25780.6 | −1.89943 | −0.949717 | − | 0.313108i | \(-0.898630\pi\) | ||||
−0.949717 | + | 0.313108i | \(0.898630\pi\) | |||||||
\(570\) | 1902.96 | + | 1597.44i | 0.139836 | + | 0.117385i | ||||
\(571\) | −16636.4 | −1.21928 | −0.609642 | − | 0.792677i | \(-0.708687\pi\) | ||||
−0.609642 | + | 0.792677i | \(0.708687\pi\) | |||||||
\(572\) | 396.585 | − | 686.906i | 0.0289896 | − | 0.0502115i | ||||
\(573\) | −4110.22 | + | 7119.10i | −0.299663 | + | 0.519031i | ||||
\(574\) | 3476.27 | + | 6021.08i | 0.252782 | + | 0.437831i | ||||
\(575\) | 1612.14 | − | 2792.31i | 0.116923 | − | 0.202517i | ||||
\(576\) | −288.000 | − | 498.831i | −0.0208333 | − | 0.0360844i | ||||
\(577\) | 1857.95 | 0.134051 | 0.0670254 | − | 0.997751i | \(-0.478649\pi\) | ||||
0.0670254 | + | 0.997751i | \(0.478649\pi\) | |||||||
\(578\) | 3599.75 | 0.259048 | ||||||||
\(579\) | −7736.92 | − | 13400.7i | −0.555329 | − | 0.961858i | ||||
\(580\) | 706.606 | + | 1223.88i | 0.0505866 | + | 0.0876186i | ||||
\(581\) | 3075.27 | 0.219593 | ||||||||
\(582\) | −3974.10 | −0.283044 | ||||||||
\(583\) | −333.287 | − | 577.269i | −0.0236764 | − | 0.0410087i | ||||
\(584\) | 2241.48 | − | 3882.36i | 0.158824 | − | 0.275091i | ||||
\(585\) | −1035.00 | − | 1792.67i | −0.0731487 | − | 0.126697i | ||||
\(586\) | −6457.02 | + | 11183.9i | −0.455183 | + | 0.788399i | ||||
\(587\) | 12908.6 | − | 22358.4i | 0.907658 | − | 1.57211i | 0.0903484 | − | 0.995910i | \(-0.471202\pi\) |
0.817309 | − | 0.576199i | \(-0.195465\pi\) | |||||||
\(588\) | −5714.23 | −0.400767 | ||||||||
\(589\) | 12019.5 | + | 10089.8i | 0.840839 | + | 0.705843i | ||||
\(590\) | 793.394 | 0.0553619 | ||||||||
\(591\) | −4808.85 | + | 8329.18i | −0.334704 | + | 0.579723i | ||||
\(592\) | 2171.03 | − | 3760.33i | 0.150724 | − | 0.261062i | ||||
\(593\) | −241.613 | − | 418.486i | −0.0167316 | − | 0.0289801i | 0.857538 | − | 0.514420i | \(-0.171993\pi\) |
−0.874270 | + | 0.485440i | \(0.838659\pi\) | |||||||
\(594\) | 116.389 | − | 201.592i | 0.00803957 | − | 0.0139249i | ||||
\(595\) | 5862.53 | + | 10154.2i | 0.403934 | + | 0.699633i | ||||
\(596\) | 9201.35 | 0.632386 | ||||||||
\(597\) | −2459.93 | −0.168640 | ||||||||
\(598\) | −5932.68 | − | 10275.7i | −0.405695 | − | 0.702684i | ||||
\(599\) | −3337.55 | − | 5780.80i | −0.227660 | − | 0.394319i | 0.729454 | − | 0.684030i | \(-0.239774\pi\) |
−0.957114 | + | 0.289711i | \(0.906441\pi\) | |||||||
\(600\) | −600.000 | −0.0408248 | ||||||||
\(601\) | −1767.06 | −0.119933 | −0.0599665 | − | 0.998200i | \(-0.519099\pi\) | ||||
−0.0599665 | + | 0.998200i | \(0.519099\pi\) | |||||||
\(602\) | −787.499 | − | 1363.99i | −0.0533157 | − | 0.0923456i | ||||
\(603\) | 4061.19 | − | 7034.18i | 0.274269 | − | 0.475048i | ||||
\(604\) | −1275.01 | − | 2208.39i | −0.0858933 | − | 0.148772i | ||||
\(605\) | −3281.04 | + | 5682.94i | −0.220485 | + | 0.381891i | ||||
\(606\) | −2344.38 | + | 4060.59i | −0.157152 | + | 0.272195i | ||||
\(607\) | −25376.2 | −1.69685 | −0.848426 | − | 0.529314i | \(-0.822449\pi\) | ||||
−0.848426 | + | 0.529314i | \(0.822449\pi\) | |||||||
\(608\) | 460.742 | − | 2609.85i | 0.0307328 | − | 0.174085i | ||||
\(609\) | −6067.22 | −0.403705 | ||||||||
\(610\) | −2565.05 | + | 4442.80i | −0.170256 | + | 0.294891i | ||||
\(611\) | 1108.68 | − | 1920.30i | 0.0734084 | − | 0.127147i | ||||
\(612\) | −1474.78 | − | 2554.39i | −0.0974091 | − | 0.168718i | ||||
\(613\) | 10802.8 | − | 18711.0i | 0.711780 | − | 1.23284i | −0.252409 | − | 0.967621i | \(-0.581223\pi\) |
0.964189 | − | 0.265218i | \(-0.0854438\pi\) | |||||||
\(614\) | 3853.91 | + | 6675.17i | 0.253308 | + | 0.438743i | ||||
\(615\) | −1821.86 | −0.119454 | ||||||||
\(616\) | 987.029 | 0.0645593 | ||||||||
\(617\) | 6471.86 | + | 11209.6i | 0.422281 | + | 0.731412i | 0.996162 | − | 0.0875266i | \(-0.0278963\pi\) |
−0.573881 | + | 0.818938i | \(0.694563\pi\) | |||||||
\(618\) | 2556.94 | + | 4428.75i | 0.166432 | + | 0.288269i | ||||
\(619\) | −10134.0 | −0.658030 | −0.329015 | − | 0.944325i | \(-0.606717\pi\) | ||||
−0.329015 | + | 0.944325i | \(0.606717\pi\) | |||||||
\(620\) | −3789.71 | −0.245482 | ||||||||
\(621\) | −1741.11 | − | 3015.70i | −0.112510 | − | 0.194872i | ||||
\(622\) | 8358.72 | − | 14477.7i | 0.538833 | − | 0.933286i | ||||
\(623\) | −8518.09 | − | 14753.8i | −0.547785 | − | 0.948791i | ||||
\(624\) | −1104.00 | + | 1912.18i | −0.0708259 | + | 0.122674i | ||||
\(625\) | −312.500 | + | 541.266i | −0.0200000 | + | 0.0346410i | ||||
\(626\) | 7701.39 | 0.491709 | ||||||||
\(627\) | 1006.51 | − | 366.105i | 0.0641088 | − | 0.0233187i | ||||
\(628\) | 4223.83 | 0.268390 | ||||||||
\(629\) | 11117.3 | − | 19255.7i | 0.704732 | − | 1.22063i | ||||
\(630\) | 1287.96 | − | 2230.82i | 0.0814503 | − | 0.141076i | ||||
\(631\) | 3914.47 | + | 6780.07i | 0.246962 | + | 0.427750i | 0.962681 | − | 0.270638i | \(-0.0872345\pi\) |
−0.715720 | + | 0.698388i | \(0.753901\pi\) | |||||||
\(632\) | 3776.55 | − | 6541.18i | 0.237695 | − | 0.411700i | ||||
\(633\) | −3791.29 | − | 6566.71i | −0.238057 | − | 0.412327i | ||||
\(634\) | −15570.8 | −0.975389 | ||||||||
\(635\) | 8662.93 | 0.541382 | ||||||||
\(636\) | 927.792 | + | 1606.98i | 0.0578449 | + | 0.100190i | ||||
\(637\) | 10952.3 | + | 18969.9i | 0.681232 | + | 1.17993i | ||||
\(638\) | 609.195 | 0.0378029 | ||||||||
\(639\) | 1602.16 | 0.0991872 | ||||||||
\(640\) | 320.000 | + | 554.256i | 0.0197642 | + | 0.0342327i | ||||
\(641\) | −2251.98 | + | 3900.55i | −0.138764 | + | 0.240347i | −0.927029 | − | 0.374989i | \(-0.877646\pi\) |
0.788265 | + | 0.615336i | \(0.210980\pi\) | |||||||
\(642\) | 2378.71 | + | 4120.05i | 0.146231 | + | 0.253279i | ||||
\(643\) | −8593.07 | + | 14883.6i | −0.527026 | + | 0.912836i | 0.472478 | + | 0.881342i | \(0.343360\pi\) |
−0.999504 | + | 0.0314933i | \(0.989974\pi\) | |||||||
\(644\) | 7382.68 | − | 12787.2i | 0.451737 | − | 0.782431i | ||||
\(645\) | 412.715 | 0.0251948 | ||||||||
\(646\) | 2359.35 | − | 13364.4i | 0.143696 | − | 0.813957i | ||||
\(647\) | −8654.23 | −0.525862 | −0.262931 | − | 0.964815i | \(-0.584689\pi\) | ||||
−0.262931 | + | 0.964815i | \(0.584689\pi\) | |||||||
\(648\) | −324.000 | + | 561.184i | −0.0196419 | + | 0.0340207i | ||||
\(649\) | 171.004 | − | 296.188i | 0.0103429 | − | 0.0179143i | ||||
\(650\) | 1150.00 | + | 1991.86i | 0.0693949 | + | 0.120196i | ||||
\(651\) | 8135.02 | − | 14090.3i | 0.489764 | − | 0.848297i | ||||
\(652\) | −6503.47 | − | 11264.3i | −0.390637 | − | 0.676604i | ||||
\(653\) | −3442.22 | −0.206286 | −0.103143 | − | 0.994667i | \(-0.532890\pi\) | ||||
−0.103143 | + | 0.994667i | \(0.532890\pi\) | |||||||
\(654\) | 3491.01 | 0.208730 | ||||||||
\(655\) | −4531.75 | − | 7849.22i | −0.270336 | − | 0.468236i | ||||
\(656\) | 971.656 | + | 1682.96i | 0.0578305 | + | 0.100165i | ||||
\(657\) | −5043.34 | −0.299482 | ||||||||
\(658\) | 2759.31 | 0.163479 | ||||||||
\(659\) | 607.674 | + | 1052.52i | 0.0359205 | + | 0.0622162i | 0.883427 | − | 0.468569i | \(-0.155230\pi\) |
−0.847506 | + | 0.530785i | \(0.821897\pi\) | |||||||
\(660\) | −129.321 | + | 223.991i | −0.00762700 | + | 0.0132104i | ||||
\(661\) | 9794.68 | + | 16964.9i | 0.576352 | + | 0.998271i | 0.995893 | + | 0.0905351i | \(0.0288577\pi\) |
−0.419541 | + | 0.907736i | \(0.637809\pi\) | |||||||
\(662\) | 3570.70 | − | 6184.63i | 0.209636 | − | 0.363100i | ||||
\(663\) | −5653.32 | + | 9791.83i | −0.331156 | + | 0.573580i | ||||
\(664\) | 859.572 | 0.0502377 | ||||||||
\(665\) | 11138.1 | − | 4051.33i | 0.649497 | − | 0.236246i | ||||
\(666\) | −4884.81 | −0.284208 | ||||||||
\(667\) | 4556.60 | − | 7892.26i | 0.264516 | − | 0.458155i | ||||
\(668\) | 3282.01 | − | 5684.60i | 0.190097 | − | 0.329257i | ||||
\(669\) | −2926.29 | − | 5068.49i | −0.169114 | − | 0.292914i | ||||
\(670\) | −4512.43 | + | 7815.76i | −0.260195 | + | 0.450670i | ||||
\(671\) | 1105.72 | + | 1915.16i | 0.0636152 | + | 0.110185i | ||||
\(672\) | −2747.66 | −0.157728 | ||||||||
\(673\) | 17853.2 | 1.02257 | 0.511284 | − | 0.859412i | \(-0.329170\pi\) | ||||
0.511284 | + | 0.859412i | \(0.329170\pi\) | |||||||
\(674\) | −3266.65 | − | 5658.01i | −0.186687 | − | 0.323351i | ||||
\(675\) | 337.500 | + | 584.567i | 0.0192450 | + | 0.0333333i | ||||
\(676\) | −324.000 | −0.0184342 | ||||||||
\(677\) | 20443.0 | 1.16054 | 0.580271 | − | 0.814423i | \(-0.302947\pi\) | ||||
0.580271 | + | 0.814423i | \(0.302947\pi\) | |||||||
\(678\) | −2048.24 | − | 3547.66i | −0.116021 | − | 0.200954i | ||||
\(679\) | −9478.70 | + | 16417.6i | −0.535728 | + | 0.927907i | ||||
\(680\) | 1638.64 | + | 2838.21i | 0.0924104 | + | 0.160060i | ||||
\(681\) | −5444.05 | + | 9429.36i | −0.306338 | + | 0.530593i | ||||
\(682\) | −816.817 | + | 1414.77i | −0.0458615 | + | 0.0794345i | ||||
\(683\) | −3882.95 | −0.217536 | −0.108768 | − | 0.994067i | \(-0.534691\pi\) | ||||
−0.108768 | + | 0.994067i | \(0.534691\pi\) | |||||||
\(684\) | −2801.89 | + | 1019.15i | −0.156627 | + | 0.0569711i | ||||
\(685\) | −9715.77 | −0.541928 | ||||||||
\(686\) | −3811.96 | + | 6602.50i | −0.212159 | + | 0.367471i | ||||
\(687\) | −218.025 | + | 377.630i | −0.0121080 | + | 0.0209716i | ||||
\(688\) | −220.115 | − | 381.250i | −0.0121974 | − | 0.0211265i | ||||
\(689\) | 3556.54 | − | 6160.10i | 0.196652 | − | 0.340611i | ||||
\(690\) | 1934.57 | + | 3350.77i | 0.106736 | + | 0.184872i | ||||
\(691\) | 12415.2 | 0.683496 | 0.341748 | − | 0.939792i | \(-0.388981\pi\) | ||||
0.341748 | + | 0.939792i | \(0.388981\pi\) | |||||||
\(692\) | −15180.4 | −0.833919 | ||||||||
\(693\) | −555.204 | − | 961.641i | −0.0304335 | − | 0.0527124i | ||||
\(694\) | 5491.83 | + | 9512.13i | 0.300385 | + | 0.520282i | ||||
\(695\) | −10039.2 | −0.547926 | ||||||||
\(696\) | −1695.86 | −0.0923581 | ||||||||
\(697\) | 4975.62 | + | 8618.02i | 0.270394 | + | 0.468337i | ||||
\(698\) | −4375.75 | + | 7579.02i | −0.237285 | + | 0.410989i | ||||
\(699\) | 6280.32 | + | 10877.8i | 0.339833 | + | 0.588609i | ||||
\(700\) | −1431.07 | + | 2478.69i | −0.0772706 | + | 0.133837i | ||||
\(701\) | 18484.8 | − | 32016.6i | 0.995950 | − | 1.72504i | 0.420111 | − | 0.907473i | \(-0.361991\pi\) |
0.575839 | − | 0.817563i | \(-0.304676\pi\) | |||||||
\(702\) | 2484.00 | 0.133551 | ||||||||
\(703\) | −17214.1 | − | 14450.4i | −0.923532 | − | 0.775260i | ||||
\(704\) | 275.885 | 0.0147696 | ||||||||
\(705\) | −361.527 | + | 626.183i | −0.0193133 | + | 0.0334517i | ||||
\(706\) | −9525.41 | + | 16498.5i | −0.507781 | + | 0.879503i | ||||
\(707\) | 11183.2 | + | 19369.9i | 0.594893 | + | 1.03038i | ||||
\(708\) | −476.036 | + | 824.519i | −0.0252691 | + | 0.0437674i | ||||
\(709\) | −1299.50 | − | 2250.80i | −0.0688346 | − | 0.119225i | 0.829554 | − | 0.558427i | \(-0.188595\pi\) |
−0.898389 | + | 0.439201i | \(0.855261\pi\) | |||||||
\(710\) | −1780.18 | −0.0940972 | ||||||||
\(711\) | −8497.25 | −0.448202 | ||||||||
\(712\) | −2380.90 | − | 4123.84i | −0.125320 | − | 0.217061i | ||||
\(713\) | 12219.1 | + | 21164.1i | 0.641808 | + | 1.11164i | ||||
\(714\) | −14070.1 | −0.737478 | ||||||||
\(715\) | 991.463 | 0.0518582 | ||||||||
\(716\) | 3336.13 | + | 5778.35i | 0.174130 | + | 0.301602i | ||||
\(717\) | −8205.30 | + | 14212.0i | −0.427382 | + | 0.740247i | ||||
\(718\) | 1255.15 | + | 2173.99i | 0.0652394 | + | 0.112998i | ||||
\(719\) | 1928.66 | − | 3340.54i | 0.100037 | − | 0.173270i | −0.811662 | − | 0.584127i | \(-0.801437\pi\) |
0.911700 | + | 0.410857i | \(0.134770\pi\) | |||||||
\(720\) | 360.000 | − | 623.538i | 0.0186339 | − | 0.0322749i | ||||
\(721\) | 24394.4 | 1.26005 | ||||||||
\(722\) | −12888.8 | − | 4697.14i | −0.664363 | − | 0.242119i | ||||
\(723\) | −17431.5 | −0.896660 | ||||||||
\(724\) | 2307.86 | − | 3997.34i | 0.118468 | − | 0.205193i | ||||
\(725\) | −883.258 | + | 1529.85i | −0.0452460 | + | 0.0783684i | ||||
\(726\) | −3937.25 | − | 6819.52i | −0.201274 | − | 0.348617i | ||||
\(727\) | −6751.68 | + | 11694.2i | −0.344437 | + | 0.596583i | −0.985251 | − | 0.171113i | \(-0.945264\pi\) |
0.640814 | + | 0.767696i | \(0.278597\pi\) | |||||||
\(728\) | 5266.34 | + | 9121.57i | 0.268109 | + | 0.464379i | ||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 5603.71 | 0.284113 | ||||||||
\(731\) | −1127.15 | − | 1952.29i | −0.0570305 | − | 0.0987797i | ||||
\(732\) | −3078.06 | − | 5331.36i | −0.155421 | − | 0.269198i | ||||
\(733\) | −39035.0 | −1.96697 | −0.983485 | − | 0.180987i | \(-0.942071\pi\) | ||||
−0.983485 | + | 0.180987i | \(0.942071\pi\) | |||||||
\(734\) | 20973.7 | 1.05470 | ||||||||
\(735\) | −3571.39 | − | 6185.83i | −0.179228 | − | 0.310432i | ||||
\(736\) | 2063.54 | − | 3574.16i | 0.103347 | − | 0.179002i | ||||
\(737\) | 1945.18 | + | 3369.14i | 0.0972205 | + | 0.168391i | ||||
\(738\) | 1093.11 | − | 1893.33i | 0.0545231 | − | 0.0944368i | ||||
\(739\) | −4629.94 | + | 8019.30i | −0.230467 | + | 0.399181i | −0.957946 | − | 0.286950i | \(-0.907359\pi\) |
0.727479 | + | 0.686130i | \(0.240692\pi\) | |||||||
\(740\) | 5427.57 | 0.269624 | ||||||||
\(741\) | 8753.63 | + | 7348.24i | 0.433971 | + | 0.364298i | ||||
\(742\) | 8851.57 | 0.437940 | ||||||||
\(743\) | 14970.9 | − | 25930.4i | 0.739205 | − | 1.28034i | −0.213648 | − | 0.976911i | \(-0.568535\pi\) |
0.952854 | − | 0.303430i | \(-0.0981320\pi\) | |||||||
\(744\) | 2273.83 | − | 3938.39i | 0.112046 | − | 0.194070i | ||||
\(745\) | 5750.84 | + | 9960.75i | 0.282812 | + | 0.489844i | ||||
\(746\) | 7848.84 | − | 13594.6i | 0.385210 | − | 0.667203i | ||||
\(747\) | −483.509 | − | 837.462i | −0.0236823 | − | 0.0410189i | ||||
\(748\) | 1412.74 | 0.0690574 | ||||||||
\(749\) | 22694.0 | 1.10710 | ||||||||
\(750\) | −375.000 | − | 649.519i | −0.0182574 | − | 0.0316228i | ||||
\(751\) | −14364.7 | − | 24880.5i | −0.697972 | − | 1.20892i | −0.969168 | − | 0.246399i | \(-0.920753\pi\) |
0.271196 | − | 0.962524i | \(-0.412581\pi\) | |||||||
\(752\) | 771.258 | 0.0374001 | ||||||||
\(753\) | −7792.62 | −0.377130 | ||||||||
\(754\) | 3250.39 | + | 5629.84i | 0.156992 | + | 0.271919i | ||||
\(755\) | 1593.77 | − | 2760.49i | 0.0768253 | − | 0.133065i | ||||
\(756\) | 1545.56 | + | 2676.98i | 0.0743536 | + | 0.128784i | ||||
\(757\) | −16105.9 | + | 27896.2i | −0.773286 | + | 1.33937i | 0.162468 | + | 0.986714i | \(0.448055\pi\) |
−0.935753 | + | 0.352656i | \(0.885279\pi\) | |||||||
\(758\) | −4137.48 | + | 7166.32i | −0.198259 | + | 0.343394i | ||||
\(759\) | 1667.87 | 0.0797628 | ||||||||
\(760\) | 3113.21 | − | 1132.39i | 0.148590 | − | 0.0540475i | ||||
\(761\) | −26848.7 | −1.27893 | −0.639465 | − | 0.768820i | \(-0.720844\pi\) | ||||
−0.639465 | + | 0.768820i | \(0.720844\pi\) | |||||||
\(762\) | −5197.76 | + | 9002.78i | −0.247106 | + | 0.428000i | ||||
\(763\) | 8326.48 | − | 14421.9i | 0.395071 | − | 0.684282i | ||||
\(764\) | 5480.29 | + | 9492.14i | 0.259516 | + | 0.449494i | ||||
\(765\) | 1843.47 | − | 3192.99i | 0.0871254 | − | 0.150906i | ||||
\(766\) | −79.1209 | − | 137.041i | −0.00373206 | − | 0.00646411i | ||||
\(767\) | 3649.61 | 0.171812 | ||||||||
\(768\) | −768.000 | −0.0360844 | ||||||||
\(769\) | −752.838 | − | 1303.95i | −0.0353030 | − | 0.0611467i | 0.847834 | − | 0.530262i | \(-0.177906\pi\) |
−0.883137 | + | 0.469115i | \(0.844573\pi\) | |||||||
\(770\) | 616.893 | + | 1068.49i | 0.0288718 | + | 0.0500074i | ||||
\(771\) | −13383.5 | −0.625154 | ||||||||
\(772\) | −20631.8 | −0.961858 | ||||||||
\(773\) | −2065.25 | − | 3577.12i | −0.0960957 | − | 0.166443i | 0.813970 | − | 0.580907i | \(-0.197302\pi\) |
−0.910065 | + | 0.414465i | \(0.863969\pi\) | |||||||
\(774\) | −247.629 | + | 428.906i | −0.0114998 | + | 0.0199182i | ||||
\(775\) | −2368.57 | − | 4102.49i | −0.109783 | − | 0.190149i | ||||
\(776\) | −2649.40 | + | 4588.89i | −0.122562 | + | 0.212283i | ||||
\(777\) | −11650.9 | + | 20179.9i | −0.537931 | + | 0.931724i | ||||
\(778\) | −14705.3 | −0.677648 | ||||||||
\(779\) | 9453.04 | − | 3438.42i | 0.434776 | − | 0.158144i | ||||
\(780\) | −2760.00 | −0.126697 | ||||||||
\(781\) | −383.692 | + | 664.574i | −0.0175795 | + | 0.0304486i | ||||
\(782\) | 10566.9 | − | 18302.4i | 0.483212 | − | 0.836947i | ||||
\(783\) | 953.918 | + | 1652.24i | 0.0435380 | + | 0.0754101i | ||||
\(784\) | −3809.48 | + | 6598.22i | −0.173537 | + | 0.300575i | ||||
\(785\) | 2639.89 | + | 4572.43i | 0.120028 | + | 0.207894i | ||||
\(786\) | 10876.2 | 0.493564 | ||||||||
\(787\) | −40000.2 | −1.81176 | −0.905878 | − | 0.423540i | \(-0.860787\pi\) | ||||
−0.905878 | + | 0.423540i | \(0.860787\pi\) | |||||||
\(788\) | 6411.80 | + | 11105.6i | 0.289862 | + | 0.502055i | ||||
\(789\) | 8123.02 | + | 14069.5i | 0.366524 | + | 0.634838i | ||||
\(790\) | 9441.39 | 0.425202 | ||||||||
\(791\) | −19541.2 | −0.878387 | ||||||||
\(792\) | −155.186 | − | 268.789i | −0.00696247 | − | 0.0120594i | ||||
\(793\) | −11799.2 | + | 20436.9i | −0.528378 | + | 0.915177i | ||||
\(794\) | −10982.5 | − | 19022.2i | −0.490874 | − | 0.850219i | ||||
\(795\) | −1159.74 | + | 2008.73i | −0.0517380 | + | 0.0896129i | ||||
\(796\) | −1639.95 | + | 2840.48i | −0.0730233 | + | 0.126480i | ||||
\(797\) | −37984.2 | −1.68817 | −0.844085 | − | 0.536210i | \(-0.819856\pi\) | ||||
−0.844085 | + | 0.536210i | \(0.819856\pi\) | |||||||
\(798\) | −2472.58 | + | 14005.8i | −0.109685 | + | 0.621304i | ||||
\(799\) | 3949.43 | 0.174869 | ||||||||
\(800\) | −400.000 | + | 692.820i | −0.0176777 | + | 0.0306186i | ||||
\(801\) | −2678.51 | + | 4639.32i | −0.118153 | + | 0.204647i | ||||
\(802\) | −2070.82 | − | 3586.77i | −0.0911762 | − | 0.157922i | ||||
\(803\) | 1207.80 | − | 2091.97i | 0.0530788 | − | 0.0919352i | ||||
\(804\) | −5414.91 | − | 9378.91i | −0.237524 | − | 0.411404i | ||||
\(805\) | 18456.7 | 0.808091 | ||||||||
\(806\) | −17432.7 | −0.761836 | ||||||||
\(807\) | −10839.2 | − | 18774.1i | −0.472812 | − | 0.818934i | ||||
\(808\) | 3125.84 | + | 5414.11i | 0.136097 | + | 0.235728i | ||||
\(809\) | −2726.35 | −0.118484 | −0.0592418 | − | 0.998244i | \(-0.518868\pi\) | ||||
−0.0592418 | + | 0.998244i | \(0.518868\pi\) | |||||||
\(810\) | −810.000 | −0.0351364 | ||||||||
\(811\) | −8725.27 | − | 15112.6i | −0.377787 | − | 0.654347i | 0.612953 | − | 0.790120i | \(-0.289982\pi\) |
−0.990740 | + | 0.135773i | \(0.956648\pi\) | |||||||
\(812\) | −4044.81 | + | 7005.82i | −0.174809 | + | 0.302779i | ||||
\(813\) | −1252.67 | − | 2169.69i | −0.0540383 | − | 0.0935971i | ||||
\(814\) | 1169.83 | − | 2026.21i | 0.0503718 | − | 0.0872465i | ||||
\(815\) | 8129.34 | − | 14080.4i | 0.349397 | − | 0.605173i | ||||
\(816\) | −3932.74 | −0.168718 | ||||||||
\(817\) | −2141.45 | + | 778.924i | −0.0917011 | + | 0.0333551i | ||||
\(818\) | −18126.2 | −0.774777 | ||||||||
\(819\) | 5924.63 | − | 10261.8i | 0.252776 | − | 0.437821i | ||||
\(820\) | −1214.57 | + | 2103.70i | −0.0517252 | + | 0.0895906i | ||||
\(821\) | 7041.11 | + | 12195.6i | 0.299313 | + | 0.518426i | 0.975979 | − | 0.217864i | \(-0.0699090\pi\) |
−0.676666 | + | 0.736290i | \(0.736576\pi\) | |||||||
\(822\) | 5829.46 | − | 10096.9i | 0.247355 | − | 0.428431i | ||||
\(823\) | −18673.4 | − | 32343.3i | −0.790905 | − | 1.36989i | −0.925407 | − | 0.378974i | \(-0.876277\pi\) |
0.134503 | − | 0.990913i | \(-0.457056\pi\) | |||||||
\(824\) | 6818.51 | 0.288269 | ||||||||
\(825\) | −323.303 | −0.0136436 | ||||||||
\(826\) | 2270.81 | + | 3933.15i | 0.0956555 | + | 0.165680i | ||||
\(827\) | −2252.06 | − | 3900.68i | −0.0946939 | − | 0.164015i | 0.814787 | − | 0.579761i | \(-0.196854\pi\) |
−0.909481 | + | 0.415746i | \(0.863521\pi\) | |||||||
\(828\) | −4642.97 | −0.194872 | ||||||||
\(829\) | 34842.9 | 1.45976 | 0.729881 | − | 0.683574i | \(-0.239575\pi\) | ||||
0.729881 | + | 0.683574i | \(0.239575\pi\) | |||||||
\(830\) | 537.232 | + | 930.514i | 0.0224670 | + | 0.0389140i | ||||
\(831\) | −314.787 | + | 545.228i | −0.0131406 | + | 0.0227602i | ||||
\(832\) | 1472.00 | + | 2549.58i | 0.0613370 | + | 0.106239i | ||||
\(833\) | −19507.4 | + | 33787.9i | −0.811396 | + | 1.40538i | ||||
\(834\) | 6023.52 | − | 10433.0i | 0.250093 | − | 0.433173i | ||||
\(835\) | 8205.01 | 0.340055 | ||||||||
\(836\) | 248.266 | − | 1406.29i | 0.0102709 | − | 0.0581789i | ||||
\(837\) | −5116.11 | −0.211277 | ||||||||
\(838\) | 1690.59 | − | 2928.18i | 0.0696901 | − | 0.120707i | ||||
\(839\) | −180.915 | + | 313.355i | −0.00744445 | + | 0.0128942i | −0.869724 | − | 0.493539i | \(-0.835703\pi\) |
0.862279 | + | 0.506433i | \(0.169036\pi\) | |||||||
\(840\) | −1717.29 | − | 2974.42i | −0.0705381 | − | 0.122175i | ||||
\(841\) | 9698.04 | − | 16797.5i | 0.397640 | − | 0.688732i | ||||
\(842\) | −15002.4 | − | 25985.0i | −0.614036 | − | 1.06354i | ||||
\(843\) | 5159.05 | 0.210779 | ||||||||
\(844\) | −10110.1 | −0.412327 | ||||||||
\(845\) | −202.500 | − | 350.740i | −0.00824404 | − | 0.0142791i | ||||
\(846\) | −433.833 | − | 751.420i | −0.0176306 | − | 0.0305371i | ||||
\(847\) | −37563.3 | −1.52384 | ||||||||
\(848\) | 2474.11 | 0.100190 | ||||||||
\(849\) | 441.471 | + | 764.649i | 0.0178460 | + | 0.0309101i | ||||
\(850\) | −2048.30 | + | 3547.77i | −0.0826544 | + | 0.143162i | ||||
\(851\) | −17500.0 | − | 30310.9i | −0.704927 | − | 1.22097i | ||||
\(852\) | 1068.11 | − | 1850.02i | 0.0429493 | − | 0.0743904i | ||||
\(853\) | −7499.86 | + | 12990.1i | −0.301044 | + | 0.521423i | −0.976373 | − | 0.216094i | \(-0.930668\pi\) |
0.675329 | + | 0.737517i | \(0.264002\pi\) | |||||||
\(854\) | −29366.2 | −1.17669 | ||||||||
\(855\) | −2854.45 | − | 2396.17i | −0.114175 | − | 0.0958446i | ||||
\(856\) | 6343.23 | 0.253279 | ||||||||
\(857\) | 18382.3 | − | 31839.1i | 0.732705 | − | 1.26908i | −0.223018 | − | 0.974814i | \(-0.571591\pi\) |
0.955723 | − | 0.294268i | \(-0.0950758\pi\) | |||||||
\(858\) | −594.878 | + | 1030.36i | −0.0236699 | + | 0.0409975i | ||||
\(859\) | 12909.2 | + | 22359.4i | 0.512754 | + | 0.888116i | 0.999891 | + | 0.0147901i | \(0.00470802\pi\) |
−0.487137 | + | 0.873326i | \(0.661959\pi\) | |||||||
\(860\) | 275.143 | − | 476.562i | 0.0109097 | − | 0.0188961i | ||||
\(861\) | −5214.41 | − | 9031.62i | −0.206395 | − | 0.357487i | ||||
\(862\) | 27282.8 | 1.07802 | ||||||||
\(863\) | 24106.5 | 0.950863 | 0.475431 | − | 0.879753i | \(-0.342292\pi\) | ||||
0.475431 | + | 0.879753i | \(0.342292\pi\) | |||||||
\(864\) | 432.000 | + | 748.246i | 0.0170103 | + | 0.0294628i | ||||
\(865\) | −9487.74 | − | 16433.3i | −0.372940 | − | 0.645951i | ||||
\(866\) | −21662.9 | −0.850039 | ||||||||
\(867\) | −5399.62 | −0.211512 | ||||||||
\(868\) | −10846.7 | − | 18787.0i | −0.424148 | − | 0.734647i | ||||
\(869\) | 2034.95 | − | 3524.64i | 0.0794374 | − | 0.137590i | ||||
\(870\) | −1059.91 | − | 1835.82i | −0.0413038 | − | 0.0715403i | ||||
\(871\) | −20757.2 | + | 35952.5i | −0.807497 | + | 1.39863i | ||||
\(872\) | 2327.34 | − | 4031.08i | 0.0903827 | − | 0.156548i | ||||
\(873\) | 5961.15 | 0.231105 | ||||||||
\(874\) | −16361.9 | − | 13735.0i | −0.633236 | − | 0.531570i | ||||
\(875\) | −3577.68 | −0.138226 | ||||||||
\(876\) | −3362.23 | + | 5823.55i | −0.129679 | + | 0.224611i | ||||
\(877\) | 21466.0 | − | 37180.2i | 0.826517 | − | 1.43157i | −0.0742374 | − | 0.997241i | \(-0.523652\pi\) |
0.900754 | − | 0.434329i | \(-0.143014\pi\) | |||||||
\(878\) | −12693.9 | − | 21986.5i | −0.487926 | − | 0.845113i | ||||
\(879\) | 9685.53 | − | 16775.8i | 0.371655 | − | 0.643725i | ||||
\(880\) | 172.428 | + | 298.655i | 0.00660518 | + | 0.0114405i | ||||
\(881\) | 24231.9 | 0.926667 | 0.463334 | − | 0.886184i | \(-0.346653\pi\) | ||||
0.463334 | + | 0.886184i | \(0.346653\pi\) | |||||||
\(882\) | 8571.34 | 0.327224 | ||||||||
\(883\) | 2388.34 | + | 4136.72i | 0.0910237 | + | 0.157658i | 0.907942 | − | 0.419095i | \(-0.137653\pi\) |
−0.816918 | + | 0.576753i | \(0.804319\pi\) | |||||||
\(884\) | 7537.76 | + | 13055.8i | 0.286790 | + | 0.496734i | ||||
\(885\) | −1190.09 | −0.0452028 | ||||||||
\(886\) | 5803.27 | 0.220050 | ||||||||
\(887\) | 12767.7 | + | 22114.3i | 0.483311 | + | 0.837120i | 0.999816 | − | 0.0191644i | \(-0.00610058\pi\) |
−0.516505 | + | 0.856284i | \(0.672767\pi\) | |||||||
\(888\) | −3256.54 | + | 5640.50i | −0.123066 | + | 0.213156i | ||||
\(889\) | 24794.5 | + | 42945.4i | 0.935412 | + | 1.62018i | ||||
\(890\) | 2976.12 | − | 5154.80i | 0.112090 | − | 0.194145i | ||||
\(891\) | −174.584 | + | 302.388i | −0.00656428 | + | 0.0113697i | ||||
\(892\) | −7803.45 | −0.292914 | ||||||||
\(893\) | 694.045 | − | 3931.39i | 0.0260082 | − | 0.147322i | ||||
\(894\) | −13802.0 | −0.516341 | ||||||||
\(895\) | −4170.17 | + | 7222.94i | −0.155747 | + | 0.269761i | ||||
\(896\) | −1831.77 | + | 3172.72i | −0.0682982 | + | 0.118296i | ||||
\(897\) | 8899.02 | + | 15413.6i | 0.331248 | + | 0.573739i | ||||
\(898\) | 50.5038 | − | 87.4751i | 0.00187676 | − | 0.00325065i | ||||
\(899\) | −6694.59 | − | 11595.4i | −0.248362 | − | 0.430175i | ||||
\(900\) | 900.000 | 0.0333333 | ||||||||
\(901\) | 12669.3 | 0.468453 | ||||||||
\(902\) | 523.566 | + | 906.842i | 0.0193269 | + | 0.0334751i | ||||
\(903\) | 1181.25 | + | 2045.98i | 0.0435321 | + | 0.0753998i | ||||
\(904\) | −5461.97 | −0.200954 | ||||||||
\(905\) | 5769.66 | 0.211923 | ||||||||
\(906\) | 1912.52 | + | 3312.58i | 0.0701316 | + | 0.121471i | ||||
\(907\) | 8162.61 | − | 14138.1i | 0.298826 | − | 0.517582i | −0.677042 | − | 0.735945i | \(-0.736738\pi\) |
0.975868 | + | 0.218363i | \(0.0700717\pi\) | |||||||
\(908\) | 7258.73 | + | 12572.5i | 0.265297 | + | 0.459507i | ||||
\(909\) | 3516.57 | − | 6090.88i | 0.128314 | − | 0.222246i | ||||
\(910\) | −6582.93 | + | 11402.0i | −0.239804 | + | 0.415353i | ||||
\(911\) | 8345.82 | 0.303523 | 0.151761 | − | 0.988417i | \(-0.451505\pi\) | ||||
0.151761 | + | 0.988417i | \(0.451505\pi\) | |||||||
\(912\) | −691.113 | + | 3914.78i | −0.0250932 | + | 0.142140i | ||||
\(913\) | 463.170 | 0.0167894 | ||||||||
\(914\) | 10840.4 | − | 18776.0i | 0.392305 | − | 0.679493i | ||||
\(915\) | 3847.58 | − | 6664.20i | 0.139013 | − | 0.240778i | ||||
\(916\) | 290.700 | + | 503.507i | 0.0104858 | + | 0.0181619i | ||||
\(917\) | 25941.0 | − | 44931.2i | 0.934185 | − | 1.61806i | ||||
\(918\) | 2212.17 | + | 3831.59i | 0.0795342 | + | 0.137757i | ||||
\(919\) | −43563.2 | −1.56367 | −0.781837 | − | 0.623483i | \(-0.785717\pi\) | ||||
−0.781837 | + | 0.623483i | \(0.785717\pi\) | |||||||
\(920\) | 5158.85 | 0.184872 | ||||||||
\(921\) | −5780.87 | − | 10012.8i | −0.206825 | − | 0.358232i | ||||
\(922\) | −3609.33 | − | 6251.54i | −0.128923 | − | 0.223301i | ||||
\(923\) | −8188.83 | −0.292025 | ||||||||
\(924\) | −1480.54 | −0.0527124 | ||||||||
\(925\) | 3392.23 | + | 5875.52i | 0.120579 | + | 0.208850i | ||||
\(926\) | −9096.20 | + | 15755.1i | −0.322808 | + | 0.559119i | ||||
\(927\) | −3835.41 | − | 6643.13i | −0.135892 | − | 0.235371i | ||||
\(928\) | −1130.57 | + | 1958.20i | −0.0399922 | + | 0.0692686i | ||||
\(929\) | −13485.0 | + | 23356.7i | −0.476241 | + | 0.824874i | −0.999629 | − | 0.0272201i | \(-0.991335\pi\) |
0.523388 | + | 0.852094i | \(0.324668\pi\) | |||||||
\(930\) | 5684.57 | 0.200435 | ||||||||
\(931\) | 30205.5 | + | 25356.0i | 1.06331 | + | 0.892599i | ||||
\(932\) | 16747.5 | 0.588609 | ||||||||
\(933\) | −12538.1 | + | 21716.6i | −0.439955 | + | 0.762025i | ||||
\(934\) | −1927.45 | + | 3338.44i | −0.0675247 | + | 0.116956i | ||||
\(935\) | 882.964 | + | 1529.34i | 0.0308834 | + | 0.0534917i | ||||
\(936\) | 1656.00 | − | 2868.28i | 0.0578291 | − | 0.100163i | ||||
\(937\) | 1035.57 | + | 1793.67i | 0.0361054 | + | 0.0625364i | 0.883513 | − | 0.468406i | \(-0.155171\pi\) |
−0.847408 | + | 0.530942i | \(0.821838\pi\) | |||||||
\(938\) | −51660.8 | −1.79828 | ||||||||
\(939\) | −11552.1 | −0.401478 | ||||||||
\(940\) | 482.036 | + | 834.911i | 0.0167258 | + | 0.0289700i | ||||
\(941\) | 11248.2 | + | 19482.4i | 0.389670 | + | 0.674928i | 0.992405 | − | 0.123013i | \(-0.0392558\pi\) |
−0.602735 | + | 0.797941i | \(0.705922\pi\) | |||||||
\(942\) | −6335.75 | −0.219140 | ||||||||
\(943\) | 15664.5 | 0.540939 | ||||||||
\(944\) | 634.715 | + | 1099.36i | 0.0218837 | + | 0.0379037i | ||||
\(945\) | −1931.95 | + | 3346.23i | −0.0665039 | + | 0.115188i | ||||
\(946\) | −118.606 | − | 205.432i | −0.00407634 | − | 0.00706044i | ||||
\(947\) | 13834.8 | − | 23962.6i | 0.474732 | − | 0.822261i | −0.524849 | − | 0.851195i | \(-0.675878\pi\) |
0.999581 | + | 0.0289347i | \(0.00921150\pi\) | |||||||
\(948\) | −5664.83 | + | 9811.78i | −0.194077 | + | 0.336152i | ||||
\(949\) | 25777.1 | 0.881727 | ||||||||
\(950\) | 3171.61 | + | 2662.41i | 0.108316 | + | 0.0909262i | ||||
\(951\) | 23356.2 | 0.796402 | ||||||||
\(952\) | −9380.05 | + | 16246.7i | −0.319337 | + | 0.553109i | ||||
\(953\) | −12059.6 | + | 20887.8i | −0.409914 | + | 0.709991i | −0.994880 | − | 0.101067i | \(-0.967775\pi\) |
0.584966 | + | 0.811058i | \(0.301108\pi\) | |||||||
\(954\) | −1391.69 | − | 2410.47i | −0.0472301 | − | 0.0818050i | ||||
\(955\) | −6850.36 | + | 11865.2i | −0.232118 | + | 0.402040i | ||||
\(956\) | 10940.4 | + | 18949.3i | 0.370123 | + | 0.641073i | ||||
\(957\) | −913.792 | −0.0308659 | ||||||||
\(958\) | −37397.1 | −1.26122 | ||||||||
\(959\) | −27807.9 | − | 48164.7i | −0.936355 | − | 1.62181i | ||||
\(960\) | −480.000 | − | 831.384i | −0.0161374 | − | 0.0279508i | ||||
\(961\) | 6113.82 | 0.205224 | ||||||||
\(962\) | 24966.8 | 0.836760 | ||||||||
\(963\) | −3568.07 | − | 6180.07i | −0.119397 | − | 0.206802i | ||||
\(964\) | −11621.0 | + | 20128.2i | −0.388265 | + | 0.672495i | ||||
\(965\) | −12894.9 | − | 22334.6i | −0.430156 | − | 0.745052i | ||||
\(966\) | −11074.0 | + | 19180.8i | −0.368842 | + | 0.638852i | ||||
\(967\) | −24174.6 | + | 41871.6i | −0.803931 | + | 1.39245i | 0.113079 | + | 0.993586i | \(0.463929\pi\) |
−0.917010 | + | 0.398864i | \(0.869405\pi\) | |||||||
\(968\) | −10499.3 | −0.348617 | ||||||||
\(969\) | −3539.02 | + | 20046.6i | −0.117327 | + | 0.664593i | ||||
\(970\) | −6623.50 | −0.219245 | ||||||||
\(971\) | 18108.4 | − | 31364.7i | 0.598484 | − | 1.03660i | −0.394561 | − | 0.918870i | \(-0.629103\pi\) |
0.993045 | − | 0.117735i | \(-0.0375632\pi\) | |||||||
\(972\) | 486.000 | − | 841.777i | 0.0160375 | − | 0.0277778i | ||||
\(973\) | −28733.6 | − | 49768.0i | −0.946718 | − | 1.63976i | ||||
\(974\) | −9370.36 | + | 16229.9i | −0.308260 | + | 0.533923i | ||||
\(975\) | −1725.00 | − | 2987.79i | −0.0566607 | − | 0.0981393i | ||||
\(976\) | −8208.17 | −0.269198 | ||||||||
\(977\) | 6145.65 | 0.201245 | 0.100623 | − | 0.994925i | \(-0.467917\pi\) | ||||
0.100623 | + | 0.994925i | \(0.467917\pi\) | |||||||
\(978\) | 9755.20 | + | 16896.5i | 0.318954 | + | 0.552445i | ||||
\(979\) | −1282.92 | − | 2222.08i | −0.0418818 | − | 0.0725414i | ||||
\(980\) | −9523.71 | −0.310432 | ||||||||
\(981\) | −5236.52 | −0.170427 | ||||||||
\(982\) | −17603.7 | − | 30490.6i | −0.572055 | − | 0.990828i | ||||
\(983\) | 13123.1 | − | 22729.9i | 0.425801 | − | 0.737510i | −0.570693 | − | 0.821163i | \(-0.693326\pi\) |
0.996495 | + | 0.0836535i | \(0.0266589\pi\) | |||||||
\(984\) | −1457.48 | − | 2524.44i | −0.0472184 | − | 0.0817846i | ||||
\(985\) | −8014.75 | + | 13882.0i | −0.259260 | + | 0.449052i | ||||
\(986\) | −5789.38 | + | 10027.5i | −0.186989 | + | 0.323875i | ||||
\(987\) | −4138.97 | −0.133480 | ||||||||
\(988\) | 14320.8 | − | 5209.00i | 0.461138 | − | 0.167733i | ||||
\(989\) | −3548.56 | −0.114093 | ||||||||
\(990\) | 193.982 | − | 335.986i | 0.00622742 | − | 0.0107862i | ||||
\(991\) | 16444.3 | − | 28482.4i | 0.527116 | − | 0.912991i | −0.472385 | − | 0.881392i | \(-0.656607\pi\) |
0.999501 | − | 0.0315988i | \(-0.0100599\pi\) | |||||||
\(992\) | −3031.77 | − | 5251.18i | −0.0970351 | − | 0.168070i | ||||
\(993\) | −5356.04 | + | 9276.94i | −0.171167 | + | 0.296470i | ||||
\(994\) | −5095.13 | − | 8825.03i | −0.162583 | − | 0.281602i | ||||
\(995\) | −4099.88 | −0.130628 | ||||||||
\(996\) | −1289.36 | −0.0410189 | ||||||||
\(997\) | 7911.13 | + | 13702.5i | 0.251302 | + | 0.435268i | 0.963885 | − | 0.266320i | \(-0.0858079\pi\) |
−0.712583 | + | 0.701588i | \(0.752475\pi\) | |||||||
\(998\) | −18322.0 | − | 31734.7i | −0.581136 | − | 1.00656i | ||||
\(999\) | 7327.22 | 0.232055 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 570.4.i.h.391.2 | yes | 4 | |
19.7 | even | 3 | inner | 570.4.i.h.121.2 | ✓ | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
570.4.i.h.121.2 | ✓ | 4 | 19.7 | even | 3 | inner | |
570.4.i.h.391.2 | yes | 4 | 1.1 | even | 1 | trivial |