Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [105,4,Mod(16,105)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(105, 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("105.16");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 105 = 3 \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 105.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: | \(6.19520055060\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Relative dimension: | \(5\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - 2 x^{9} + 34 x^{8} + 16 x^{7} + 791 x^{6} - 132 x^{5} + 4906 x^{4} - 1674 x^{3} + 25257 x^{2} - 12852 x + 7056 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 46.1 | ||
Root | \(-2.05285 - 3.55565i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 105.46 |
Dual form | 105.4.i.d.16.1 |
$q$-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 \(\left(\mathbb{Z}/105\mathbb{Z}\right)^\times\).
\(n\) | \(22\) | \(31\) | \(71\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.55285 | − | 4.42167i | −0.902570 | − | 1.56330i | −0.824146 | − | 0.566377i | \(-0.808345\pi\) |
−0.0784237 | − | 0.996920i | \(-0.524989\pi\) | |||||||
\(3\) | −1.50000 | + | 2.59808i | −0.288675 | + | 0.500000i | ||||
\(4\) | −9.03412 | + | 15.6476i | −1.12927 | + | 1.95594i | ||||
\(5\) | −2.50000 | − | 4.33013i | −0.223607 | − | 0.387298i | ||||
\(6\) | 15.3171 | 1.04220 | ||||||||
\(7\) | −2.74187 | + | 18.3162i | −0.148047 | + | 0.988980i | ||||
\(8\) | 51.4055 | 2.27182 | ||||||||
\(9\) | −4.50000 | − | 7.79423i | −0.166667 | − | 0.288675i | ||||
\(10\) | −12.7643 | + | 22.1084i | −0.403642 | + | 0.699128i | ||||
\(11\) | 20.3677 | − | 35.2779i | 0.558281 | − | 0.966972i | −0.439359 | − | 0.898312i | \(-0.644794\pi\) |
0.997640 | − | 0.0686601i | \(-0.0218724\pi\) | |||||||
\(12\) | −27.1024 | − | 46.9427i | −0.651982 | − | 1.12927i | ||||
\(13\) | 70.9263 | 1.51319 | 0.756593 | − | 0.653887i | \(-0.226863\pi\) | ||||
0.756593 | + | 0.653887i | \(0.226863\pi\) | |||||||
\(14\) | 87.9877 | − | 34.6349i | 1.67969 | − | 0.661183i | ||||
\(15\) | 15.0000 | 0.258199 | ||||||||
\(16\) | −58.9577 | − | 102.118i | −0.921215 | − | 1.59559i | ||||
\(17\) | −11.3350 | + | 19.6329i | −0.161715 | + | 0.280098i | −0.935484 | − | 0.353370i | \(-0.885036\pi\) |
0.773769 | + | 0.633468i | \(0.218369\pi\) | |||||||
\(18\) | −22.9757 | + | 39.7950i | −0.300857 | + | 0.521099i | ||||
\(19\) | −38.8294 | − | 67.2545i | −0.468846 | − | 0.812065i | 0.530520 | − | 0.847672i | \(-0.321997\pi\) |
−0.999366 | + | 0.0356075i | \(0.988663\pi\) | |||||||
\(20\) | 90.3412 | 1.01005 | ||||||||
\(21\) | −43.4740 | − | 34.5978i | −0.451753 | − | 0.359517i | ||||
\(22\) | −207.983 | −2.01555 | ||||||||
\(23\) | 45.0311 | + | 77.9962i | 0.408245 | + | 0.707101i | 0.994693 | − | 0.102886i | \(-0.0328076\pi\) |
−0.586448 | + | 0.809987i | \(0.699474\pi\) | |||||||
\(24\) | −77.1083 | + | 133.555i | −0.655819 | + | 1.13591i | ||||
\(25\) | −12.5000 | + | 21.6506i | −0.100000 | + | 0.173205i | ||||
\(26\) | −181.064 | − | 313.613i | −1.36576 | − | 2.36556i | ||||
\(27\) | 27.0000 | 0.192450 | ||||||||
\(28\) | −261.833 | − | 208.374i | −1.76721 | − | 1.40639i | ||||
\(29\) | 213.332 | 1.36603 | 0.683013 | − | 0.730406i | \(-0.260669\pi\) | ||||
0.683013 | + | 0.730406i | \(0.260669\pi\) | |||||||
\(30\) | −38.2928 | − | 66.3251i | −0.233043 | − | 0.403642i | ||||
\(31\) | 87.8644 | − | 152.186i | 0.509062 | − | 0.881721i | −0.490883 | − | 0.871225i | \(-0.663326\pi\) |
0.999945 | − | 0.0104956i | \(-0.00334091\pi\) | |||||||
\(32\) | −95.3990 | + | 165.236i | −0.527010 | + | 0.912808i | ||||
\(33\) | 61.1031 | + | 105.834i | 0.322324 | + | 0.558281i | ||||
\(34\) | 115.747 | 0.583836 | ||||||||
\(35\) | 86.1660 | − | 33.9178i | 0.416135 | − | 0.163804i | ||||
\(36\) | 162.614 | 0.752844 | ||||||||
\(37\) | 177.466 | + | 307.381i | 0.788521 | + | 1.36576i | 0.926873 | + | 0.375376i | \(0.122486\pi\) |
−0.138351 | + | 0.990383i | \(0.544180\pi\) | |||||||
\(38\) | −198.251 | + | 343.382i | −0.846333 | + | 1.46589i | ||||
\(39\) | −106.389 | + | 184.272i | −0.436819 | + | 0.756593i | ||||
\(40\) | −128.514 | − | 222.592i | −0.507995 | − | 0.879874i | ||||
\(41\) | 249.001 | 0.948475 | 0.474238 | − | 0.880397i | \(-0.342724\pi\) | ||||
0.474238 | + | 0.880397i | \(0.342724\pi\) | |||||||
\(42\) | −41.9975 | + | 280.551i | −0.154294 | + | 1.03071i | ||||
\(43\) | 297.920 | 1.05657 | 0.528284 | − | 0.849068i | \(-0.322836\pi\) | ||||
0.528284 | + | 0.849068i | \(0.322836\pi\) | |||||||
\(44\) | 368.009 | + | 637.410i | 1.26090 | + | 2.18394i | ||||
\(45\) | −22.5000 | + | 38.9711i | −0.0745356 | + | 0.129099i | ||||
\(46\) | 229.916 | − | 398.226i | 0.736939 | − | 1.27642i | ||||
\(47\) | −84.3854 | − | 146.160i | −0.261891 | − | 0.453608i | 0.704853 | − | 0.709353i | \(-0.251013\pi\) |
−0.966744 | + | 0.255745i | \(0.917679\pi\) | |||||||
\(48\) | 353.746 | 1.06373 | ||||||||
\(49\) | −327.964 | − | 100.441i | −0.956164 | − | 0.292831i | ||||
\(50\) | 127.643 | 0.361028 | ||||||||
\(51\) | −34.0051 | − | 58.8986i | −0.0933661 | − | 0.161715i | ||||
\(52\) | −640.757 | + | 1109.82i | −1.70879 | + | 2.95971i | ||||
\(53\) | 51.2366 | − | 88.7444i | 0.132790 | − | 0.230000i | −0.791961 | − | 0.610572i | \(-0.790940\pi\) |
0.924751 | + | 0.380572i | \(0.124273\pi\) | |||||||
\(54\) | −68.9270 | − | 119.385i | −0.173700 | − | 0.300857i | ||||
\(55\) | −203.677 | −0.499342 | ||||||||
\(56\) | −140.947 | + | 941.552i | −0.336336 | + | 2.24679i | ||||
\(57\) | 232.976 | 0.541377 | ||||||||
\(58\) | −544.605 | − | 943.284i | −1.23293 | − | 2.13551i | ||||
\(59\) | 11.7399 | − | 20.3340i | 0.0259051 | − | 0.0448689i | −0.852782 | − | 0.522267i | \(-0.825087\pi\) |
0.878687 | + | 0.477398i | \(0.158420\pi\) | |||||||
\(60\) | −135.512 | + | 234.713i | −0.291575 | + | 0.505023i | ||||
\(61\) | 437.314 | + | 757.450i | 0.917907 | + | 1.58986i | 0.802589 | + | 0.596533i | \(0.203455\pi\) |
0.115318 | + | 0.993329i | \(0.463211\pi\) | |||||||
\(62\) | −897.220 | −1.83786 | ||||||||
\(63\) | 155.099 | − | 61.0521i | 0.310169 | − | 0.122093i | ||||
\(64\) | 30.8343 | 0.0602232 | ||||||||
\(65\) | −177.316 | − | 307.120i | −0.338358 | − | 0.586054i | ||||
\(66\) | 311.975 | − | 540.356i | 0.581840 | − | 1.00778i | ||||
\(67\) | 405.386 | − | 702.149i | 0.739190 | − | 1.28032i | −0.213670 | − | 0.976906i | \(-0.568542\pi\) |
0.952860 | − | 0.303409i | \(-0.0981249\pi\) | |||||||
\(68\) | −204.804 | − | 354.731i | −0.365238 | − | 0.632610i | ||||
\(69\) | −270.187 | −0.471401 | ||||||||
\(70\) | −369.943 | − | 294.411i | −0.631666 | − | 0.502697i | ||||
\(71\) | −632.487 | −1.05722 | −0.528608 | − | 0.848866i | \(-0.677286\pi\) | ||||
−0.528608 | + | 0.848866i | \(0.677286\pi\) | |||||||
\(72\) | −231.325 | − | 400.666i | −0.378637 | − | 0.655819i | ||||
\(73\) | −457.436 | + | 792.302i | −0.733409 | + | 1.27030i | 0.222010 | + | 0.975045i | \(0.428738\pi\) |
−0.955418 | + | 0.295256i | \(0.904595\pi\) | |||||||
\(74\) | 906.091 | − | 1569.40i | 1.42339 | − | 2.46539i | ||||
\(75\) | −37.5000 | − | 64.9519i | −0.0577350 | − | 0.100000i | ||||
\(76\) | 1403.16 | 2.11781 | ||||||||
\(77\) | 590.311 | + | 469.786i | 0.873664 | + | 0.695286i | ||||
\(78\) | 1086.39 | 1.57704 | ||||||||
\(79\) | 260.443 | + | 451.101i | 0.370913 | + | 0.642441i | 0.989706 | − | 0.143113i | \(-0.0457114\pi\) |
−0.618793 | + | 0.785554i | \(0.712378\pi\) | |||||||
\(80\) | −294.789 | + | 510.589i | −0.411980 | + | 0.713570i | ||||
\(81\) | −40.5000 | + | 70.1481i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | −635.664 | − | 1101.00i | −0.856065 | − | 1.48275i | ||||
\(83\) | −1027.67 | −1.35905 | −0.679527 | − | 0.733651i | \(-0.737815\pi\) | ||||
−0.679527 | + | 0.733651i | \(0.737815\pi\) | |||||||
\(84\) | 934.121 | − | 367.701i | 1.21334 | − | 0.477613i | ||||
\(85\) | 113.350 | 0.144642 | ||||||||
\(86\) | −760.546 | − | 1317.30i | −0.953626 | − | 1.65173i | ||||
\(87\) | −319.998 | + | 554.253i | −0.394338 | + | 0.683013i | ||||
\(88\) | 1047.01 | − | 1813.48i | 1.26832 | − | 2.19679i | ||||
\(89\) | −501.875 | − | 869.273i | −0.597738 | − | 1.03531i | −0.993154 | − | 0.116810i | \(-0.962733\pi\) |
0.395416 | − | 0.918502i | \(-0.370600\pi\) | |||||||
\(90\) | 229.757 | 0.269094 | ||||||||
\(91\) | −194.470 | + | 1299.10i | −0.224022 | + | 1.49651i | ||||
\(92\) | −1627.27 | −1.84407 | ||||||||
\(93\) | 263.593 | + | 456.557i | 0.293907 | + | 0.509062i | ||||
\(94\) | −430.847 | + | 746.249i | −0.472750 | + | 0.818827i | ||||
\(95\) | −194.147 | + | 336.272i | −0.209674 | + | 0.363166i | ||||
\(96\) | −286.197 | − | 495.708i | −0.304269 | − | 0.527010i | ||||
\(97\) | −639.620 | −0.669522 | −0.334761 | − | 0.942303i | \(-0.608656\pi\) | ||||
−0.334761 | + | 0.942303i | \(0.608656\pi\) | |||||||
\(98\) | 393.128 | + | 1706.56i | 0.405224 | + | 1.75907i | ||||
\(99\) | −366.619 | −0.372188 | ||||||||
\(100\) | −225.853 | − | 391.189i | −0.225853 | − | 0.391189i | ||||
\(101\) | 316.935 | − | 548.947i | 0.312239 | − | 0.540814i | −0.666608 | − | 0.745409i | \(-0.732254\pi\) |
0.978847 | + | 0.204595i | \(0.0655876\pi\) | |||||||
\(102\) | −173.620 | + | 300.719i | −0.168539 | + | 0.291918i | ||||
\(103\) | 193.789 | + | 335.653i | 0.185385 | + | 0.321096i | 0.943706 | − | 0.330785i | \(-0.107314\pi\) |
−0.758321 | + | 0.651881i | \(0.773980\pi\) | |||||||
\(104\) | 3646.00 | 3.43769 | ||||||||
\(105\) | −41.1280 | + | 274.743i | −0.0382255 | + | 0.255354i | ||||
\(106\) | −523.198 | −0.479410 | ||||||||
\(107\) | −69.3650 | − | 120.144i | −0.0626707 | − | 0.108549i | 0.832988 | − | 0.553292i | \(-0.186628\pi\) |
−0.895658 | + | 0.444743i | \(0.853295\pi\) | |||||||
\(108\) | −243.921 | + | 422.484i | −0.217327 | + | 0.376422i | ||||
\(109\) | 856.485 | − | 1483.48i | 0.752628 | − | 1.30359i | −0.193918 | − | 0.981018i | \(-0.562119\pi\) |
0.946545 | − | 0.322571i | \(-0.104547\pi\) | |||||||
\(110\) | 519.958 | + | 900.593i | 0.450691 | + | 0.780620i | ||||
\(111\) | −1064.80 | −0.910506 | ||||||||
\(112\) | 2032.06 | − | 799.887i | 1.71439 | − | 0.674841i | ||||
\(113\) | 2083.35 | 1.73438 | 0.867192 | − | 0.497975i | \(-0.165923\pi\) | ||||
0.867192 | + | 0.497975i | \(0.165923\pi\) | |||||||
\(114\) | −594.754 | − | 1030.14i | −0.488630 | − | 0.846333i | ||||
\(115\) | 225.156 | − | 389.981i | 0.182573 | − | 0.316225i | ||||
\(116\) | −1927.27 | + | 3338.13i | −1.54261 | + | 2.67187i | ||||
\(117\) | −319.168 | − | 552.816i | −0.252198 | − | 0.436819i | ||||
\(118\) | −119.881 | −0.0935246 | ||||||||
\(119\) | −328.520 | − | 261.445i | −0.253070 | − | 0.201400i | ||||
\(120\) | 771.083 | 0.586582 | ||||||||
\(121\) | −164.187 | − | 284.381i | −0.123356 | − | 0.213660i | ||||
\(122\) | 2232.80 | − | 3867.32i | 1.65695 | − | 2.86992i | ||||
\(123\) | −373.502 | + | 646.925i | −0.273801 | + | 0.474238i | ||||
\(124\) | 1587.56 | + | 2749.73i | 1.14973 | + | 1.99139i | ||||
\(125\) | 125.000 | 0.0894427 | ||||||||
\(126\) | −665.897 | − | 529.939i | −0.470816 | − | 0.374688i | ||||
\(127\) | 432.085 | 0.301900 | 0.150950 | − | 0.988541i | \(-0.451767\pi\) | ||||
0.150950 | + | 0.988541i | \(0.451767\pi\) | |||||||
\(128\) | 684.476 | + | 1185.55i | 0.472654 | + | 0.818661i | ||||
\(129\) | −446.880 | + | 774.019i | −0.305005 | + | 0.528284i | ||||
\(130\) | −905.322 | + | 1568.06i | −0.610784 | + | 1.05791i | ||||
\(131\) | 328.750 | + | 569.411i | 0.219259 | + | 0.379769i | 0.954582 | − | 0.297949i | \(-0.0963025\pi\) |
−0.735322 | + | 0.677718i | \(0.762969\pi\) | |||||||
\(132\) | −2208.05 | −1.45596 | ||||||||
\(133\) | 1338.31 | − | 526.803i | 0.872527 | − | 0.343456i | ||||
\(134\) | −4139.56 | −2.66868 | ||||||||
\(135\) | −67.5000 | − | 116.913i | −0.0430331 | − | 0.0745356i | ||||
\(136\) | −582.683 | + | 1009.24i | −0.367387 | + | 0.636334i | ||||
\(137\) | −146.258 | + | 253.326i | −0.0912090 | + | 0.157979i | −0.908020 | − | 0.418927i | \(-0.862406\pi\) |
0.816811 | + | 0.576905i | \(0.195740\pi\) | |||||||
\(138\) | 689.747 | + | 1194.68i | 0.425472 | + | 0.736939i | ||||
\(139\) | −1673.02 | −1.02089 | −0.510445 | − | 0.859910i | \(-0.670519\pi\) | ||||
−0.510445 | + | 0.859910i | \(0.670519\pi\) | |||||||
\(140\) | −247.703 | + | 1654.71i | −0.149534 | + | 0.998915i | ||||
\(141\) | 506.312 | 0.302406 | ||||||||
\(142\) | 1614.65 | + | 2796.65i | 0.954212 | + | 1.65274i | ||||
\(143\) | 1444.61 | − | 2502.13i | 0.844783 | − | 1.46321i | ||||
\(144\) | −530.620 | + | 919.060i | −0.307072 | + | 0.531864i | ||||
\(145\) | −533.330 | − | 923.755i | −0.305453 | − | 0.529060i | ||||
\(146\) | 4671.07 | 2.64781 | ||||||||
\(147\) | 752.900 | − | 701.415i | 0.422436 | − | 0.393549i | ||||
\(148\) | −6413.01 | −3.56180 | ||||||||
\(149\) | −1260.50 | − | 2183.26i | −0.693050 | − | 1.20040i | −0.970834 | − | 0.239754i | \(-0.922933\pi\) |
0.277784 | − | 0.960644i | \(-0.410400\pi\) | |||||||
\(150\) | −191.464 | + | 331.625i | −0.104220 | + | 0.180514i | ||||
\(151\) | −689.660 | + | 1194.53i | −0.371680 | + | 0.643769i | −0.989824 | − | 0.142296i | \(-0.954552\pi\) |
0.618144 | + | 0.786065i | \(0.287885\pi\) | |||||||
\(152\) | −1996.04 | − | 3457.25i | −1.06514 | − | 1.84487i | ||||
\(153\) | 204.031 | 0.107810 | ||||||||
\(154\) | 570.262 | − | 3809.45i | 0.298396 | − | 1.99334i | ||||
\(155\) | −878.644 | −0.455319 | ||||||||
\(156\) | −1922.27 | − | 3329.47i | −0.986569 | − | 1.70879i | ||||
\(157\) | −996.365 | + | 1725.76i | −0.506488 | + | 0.877263i | 0.493484 | + | 0.869755i | \(0.335723\pi\) |
−0.999972 | + | 0.00750789i | \(0.997610\pi\) | |||||||
\(158\) | 1329.75 | − | 2303.19i | 0.669550 | − | 1.15970i | ||||
\(159\) | 153.710 | + | 266.233i | 0.0766666 | + | 0.132790i | ||||
\(160\) | 953.990 | 0.471372 | ||||||||
\(161\) | −1552.06 | + | 610.943i | −0.759749 | + | 0.299062i | ||||
\(162\) | 413.562 | 0.200571 | ||||||||
\(163\) | −951.472 | − | 1648.00i | −0.457209 | − | 0.791909i | 0.541603 | − | 0.840634i | \(-0.317817\pi\) |
−0.998812 | + | 0.0487253i | \(0.984484\pi\) | |||||||
\(164\) | −2249.51 | + | 3896.26i | −1.07108 | + | 1.85516i | ||||
\(165\) | 305.516 | − | 529.169i | 0.144148 | − | 0.249671i | ||||
\(166\) | 2623.49 | + | 4544.02i | 1.22664 | + | 2.12460i | ||||
\(167\) | −378.184 | −0.175238 | −0.0876189 | − | 0.996154i | \(-0.527926\pi\) | ||||
−0.0876189 | + | 0.996154i | \(0.527926\pi\) | |||||||
\(168\) | −2234.80 | − | 1778.52i | −1.02630 | − | 0.816760i | ||||
\(169\) | 2833.54 | 1.28973 | ||||||||
\(170\) | −289.367 | − | 501.198i | −0.130550 | − | 0.226119i | ||||
\(171\) | −349.464 | + | 605.290i | −0.156282 | + | 0.270688i | ||||
\(172\) | −2691.45 | + | 4661.72i | −1.19314 | + | 2.06659i | ||||
\(173\) | 332.018 | + | 575.073i | 0.145913 | + | 0.252728i | 0.929713 | − | 0.368285i | \(-0.120055\pi\) |
−0.783800 | + | 0.621013i | \(0.786722\pi\) | |||||||
\(174\) | 3267.63 | 1.42367 | ||||||||
\(175\) | −362.283 | − | 288.315i | −0.156492 | − | 0.124540i | ||||
\(176\) | −4803.34 | −2.05719 | ||||||||
\(177\) | 35.2196 | + | 61.0021i | 0.0149563 | + | 0.0259051i | ||||
\(178\) | −2562.43 | + | 4438.26i | −1.07900 | + | 1.86888i | ||||
\(179\) | 167.500 | − | 290.118i | 0.0699414 | − | 0.121142i | −0.828934 | − | 0.559347i | \(-0.811052\pi\) |
0.898875 | + | 0.438204i | \(0.144385\pi\) | |||||||
\(180\) | −406.535 | − | 704.140i | −0.168341 | − | 0.291575i | ||||
\(181\) | 1225.58 | 0.503298 | 0.251649 | − | 0.967819i | \(-0.419027\pi\) | ||||
0.251649 | + | 0.967819i | \(0.419027\pi\) | |||||||
\(182\) | 6240.64 | − | 2456.52i | 2.54169 | − | 1.00049i | ||||
\(183\) | −2623.88 | −1.05991 | ||||||||
\(184\) | 2314.85 | + | 4009.43i | 0.927461 | + | 1.60641i | ||||
\(185\) | 887.332 | − | 1536.90i | 0.352637 | − | 0.610786i | ||||
\(186\) | 1345.83 | − | 2331.05i | 0.530543 | − | 0.918928i | ||||
\(187\) | 461.738 | + | 799.753i | 0.180565 | + | 0.312747i | ||||
\(188\) | 3049.39 | 1.18298 | ||||||||
\(189\) | −74.0304 | + | 494.537i | −0.0284916 | + | 0.190329i | ||||
\(190\) | 1982.51 | 0.756983 | ||||||||
\(191\) | 790.698 | + | 1369.53i | 0.299544 | + | 0.518826i | 0.976032 | − | 0.217628i | \(-0.0698321\pi\) |
−0.676488 | + | 0.736454i | \(0.736499\pi\) | |||||||
\(192\) | −46.2515 | + | 80.1099i | −0.0173850 | + | 0.0301116i | ||||
\(193\) | 1947.31 | − | 3372.85i | 0.726273 | − | 1.25794i | −0.232175 | − | 0.972674i | \(-0.574584\pi\) |
0.958448 | − | 0.285268i | \(-0.0920825\pi\) | |||||||
\(194\) | 1632.86 | + | 2828.19i | 0.604290 | + | 1.04666i | ||||
\(195\) | 1063.89 | 0.390703 | ||||||||
\(196\) | 4534.53 | − | 4224.45i | 1.65252 | − | 1.53952i | ||||
\(197\) | 993.858 | 0.359439 | 0.179719 | − | 0.983718i | \(-0.442481\pi\) | ||||
0.179719 | + | 0.983718i | \(0.442481\pi\) | |||||||
\(198\) | 935.924 | + | 1621.07i | 0.335925 | + | 0.581840i | ||||
\(199\) | 1539.94 | − | 2667.26i | 0.548560 | − | 0.950134i | −0.449813 | − | 0.893123i | \(-0.648509\pi\) |
0.998374 | − | 0.0570118i | \(-0.0181572\pi\) | |||||||
\(200\) | −642.569 | + | 1112.96i | −0.227182 | + | 0.393491i | ||||
\(201\) | 1216.16 | + | 2106.45i | 0.426772 | + | 0.739190i | ||||
\(202\) | −3236.35 | −1.12727 | ||||||||
\(203\) | −584.928 | + | 3907.43i | −0.202236 | + | 1.35097i | ||||
\(204\) | 1228.83 | 0.421740 | ||||||||
\(205\) | −622.503 | − | 1078.21i | −0.212085 | − | 0.367343i | ||||
\(206\) | 989.431 | − | 1713.74i | 0.334645 | − | 0.579622i | ||||
\(207\) | 405.280 | − | 701.966i | 0.136082 | − | 0.235700i | ||||
\(208\) | −4181.65 | − | 7242.83i | −1.39397 | − | 2.41442i | ||||
\(209\) | −3163.46 | −1.04699 | ||||||||
\(210\) | 1319.82 | − | 519.523i | 0.433695 | − | 0.170717i | ||||
\(211\) | 2114.72 | 0.689968 | 0.344984 | − | 0.938609i | \(-0.387884\pi\) | ||||
0.344984 | + | 0.938609i | \(0.387884\pi\) | |||||||
\(212\) | 925.756 | + | 1603.46i | 0.299911 | + | 0.519461i | ||||
\(213\) | 948.730 | − | 1643.25i | 0.305192 | − | 0.528608i | ||||
\(214\) | −354.157 | + | 613.419i | −0.113129 | + | 0.195946i | ||||
\(215\) | −744.800 | − | 1290.03i | −0.236256 | − | 0.409207i | ||||
\(216\) | 1387.95 | 0.437213 | ||||||||
\(217\) | 2546.55 | + | 2026.61i | 0.796640 | + | 0.633988i | ||||
\(218\) | −8745.92 | −2.71720 | ||||||||
\(219\) | −1372.31 | − | 2376.91i | −0.423434 | − | 0.733409i | ||||
\(220\) | 1840.04 | − | 3187.05i | 0.563890 | − | 0.976686i | ||||
\(221\) | −803.952 | + | 1392.49i | −0.244704 | + | 0.423840i | ||||
\(222\) | 2718.27 | + | 4708.19i | 0.821795 | + | 1.42339i | ||||
\(223\) | 2578.44 | 0.774282 | 0.387141 | − | 0.922021i | \(-0.373463\pi\) | ||||
0.387141 | + | 0.922021i | \(0.373463\pi\) | |||||||
\(224\) | −2764.92 | − | 2200.40i | −0.824727 | − | 0.656341i | ||||
\(225\) | 225.000 | 0.0666667 | ||||||||
\(226\) | −5318.49 | − | 9211.90i | −1.56540 | − | 2.71136i | ||||
\(227\) | −1462.96 | + | 2533.93i | −0.427754 | + | 0.740892i | −0.996673 | − | 0.0815014i | \(-0.974028\pi\) |
0.568919 | + | 0.822394i | \(0.307362\pi\) | |||||||
\(228\) | −2104.74 | + | 3645.51i | −0.611358 | + | 1.05890i | ||||
\(229\) | 523.938 | + | 907.488i | 0.151191 | + | 0.261871i | 0.931666 | − | 0.363317i | \(-0.118356\pi\) |
−0.780474 | + | 0.625188i | \(0.785022\pi\) | |||||||
\(230\) | −2299.16 | −0.659139 | ||||||||
\(231\) | −2106.01 | + | 828.994i | −0.599848 | + | 0.236120i | ||||
\(232\) | 10966.4 | 3.10337 | ||||||||
\(233\) | 1934.99 | + | 3351.51i | 0.544058 | + | 0.942337i | 0.998666 | + | 0.0516447i | \(0.0164463\pi\) |
−0.454607 | + | 0.890692i | \(0.650220\pi\) | |||||||
\(234\) | −1629.58 | + | 2822.51i | −0.455252 | + | 0.788519i | ||||
\(235\) | −421.927 | + | 730.799i | −0.117121 | + | 0.202860i | ||||
\(236\) | 212.119 | + | 367.400i | 0.0585074 | + | 0.101338i | ||||
\(237\) | −1562.66 | −0.428294 | ||||||||
\(238\) | −317.362 | + | 2120.04i | −0.0864350 | + | 0.577402i | ||||
\(239\) | −6060.77 | −1.64033 | −0.820164 | − | 0.572128i | \(-0.806118\pi\) | ||||
−0.820164 | + | 0.572128i | \(0.806118\pi\) | |||||||
\(240\) | −884.366 | − | 1531.77i | −0.237857 | − | 0.411980i | ||||
\(241\) | 2092.06 | − | 3623.55i | 0.559176 | − | 0.968521i | −0.438390 | − | 0.898785i | \(-0.644451\pi\) |
0.997565 | − | 0.0697357i | \(-0.0222156\pi\) | |||||||
\(242\) | −838.292 | + | 1451.97i | −0.222676 | + | 0.385685i | ||||
\(243\) | −121.500 | − | 210.444i | −0.0320750 | − | 0.0555556i | ||||
\(244\) | −15803.0 | −4.14624 | ||||||||
\(245\) | 384.989 | + | 1671.23i | 0.100392 | + | 0.435800i | ||||
\(246\) | 3813.98 | 0.988499 | ||||||||
\(247\) | −2754.02 | − | 4770.11i | −0.709451 | − | 1.22880i | ||||
\(248\) | 4516.72 | − | 7823.18i | 1.15650 | − | 2.00311i | ||||
\(249\) | 1541.50 | − | 2669.96i | 0.392325 | − | 0.679527i | ||||
\(250\) | −319.107 | − | 552.709i | −0.0807283 | − | 0.139826i | ||||
\(251\) | −2631.65 | −0.661786 | −0.330893 | − | 0.943668i | \(-0.607350\pi\) | ||||
−0.330893 | + | 0.943668i | \(0.607350\pi\) | |||||||
\(252\) | −445.866 | + | 2978.47i | −0.111456 | + | 0.744547i | ||||
\(253\) | 3668.72 | 0.911663 | ||||||||
\(254\) | −1103.05 | − | 1910.54i | −0.272486 | − | 0.471959i | ||||
\(255\) | −170.026 | + | 294.493i | −0.0417546 | + | 0.0723210i | ||||
\(256\) | 3618.07 | − | 6266.68i | 0.883318 | − | 1.52995i | ||||
\(257\) | −1644.38 | − | 2848.15i | −0.399120 | − | 0.691296i | 0.594498 | − | 0.804097i | \(-0.297351\pi\) |
−0.993618 | + | 0.112802i | \(0.964018\pi\) | |||||||
\(258\) | 4563.28 | 1.10115 | ||||||||
\(259\) | −6116.63 | + | 2407.71i | −1.46745 | + | 0.577636i | ||||
\(260\) | 6407.57 | 1.52839 | ||||||||
\(261\) | −959.994 | − | 1662.76i | −0.227671 | − | 0.394338i | ||||
\(262\) | 1678.50 | − | 2907.25i | 0.395794 | − | 0.685535i | ||||
\(263\) | 2704.45 | − | 4684.24i | 0.634081 | − | 1.09826i | −0.352627 | − | 0.935764i | \(-0.614712\pi\) |
0.986709 | − | 0.162498i | \(-0.0519550\pi\) | |||||||
\(264\) | 3141.04 | + | 5440.44i | 0.732263 | + | 1.26832i | ||||
\(265\) | −512.366 | −0.118771 | ||||||||
\(266\) | −5745.86 | − | 4572.71i | −1.32444 | − | 1.05403i | ||||
\(267\) | 3011.25 | 0.690208 | ||||||||
\(268\) | 7324.61 | + | 12686.6i | 1.66948 | + | 2.89163i | ||||
\(269\) | −269.894 | + | 467.470i | −0.0611738 | + | 0.105956i | −0.894990 | − | 0.446086i | \(-0.852818\pi\) |
0.833817 | + | 0.552042i | \(0.186151\pi\) | |||||||
\(270\) | −344.635 | + | 596.926i | −0.0776809 | + | 0.134547i | ||||
\(271\) | −2045.57 | − | 3543.03i | −0.458522 | − | 0.794184i | 0.540361 | − | 0.841433i | \(-0.318288\pi\) |
−0.998883 | + | 0.0472494i | \(0.984954\pi\) | |||||||
\(272\) | 2673.15 | 0.595896 | ||||||||
\(273\) | −3083.45 | − | 2453.90i | −0.683586 | − | 0.544016i | ||||
\(274\) | 1493.50 | 0.329290 | ||||||||
\(275\) | 509.193 | + | 881.948i | 0.111656 | + | 0.193394i | ||||
\(276\) | 2440.90 | − | 4227.76i | 0.532336 | − | 0.922034i | ||||
\(277\) | −1545.67 | + | 2677.18i | −0.335271 | + | 0.580707i | −0.983537 | − | 0.180707i | \(-0.942161\pi\) |
0.648265 | + | 0.761414i | \(0.275495\pi\) | |||||||
\(278\) | 4270.97 | + | 7397.55i | 0.921425 | + | 1.59595i | ||||
\(279\) | −1581.56 | −0.339375 | ||||||||
\(280\) | 4429.41 | − | 1743.56i | 0.945385 | − | 0.372135i | ||||
\(281\) | 7215.73 | 1.53187 | 0.765933 | − | 0.642920i | \(-0.222277\pi\) | ||||
0.765933 | + | 0.642920i | \(0.222277\pi\) | |||||||
\(282\) | −1292.54 | − | 2238.75i | −0.272942 | − | 0.472750i | ||||
\(283\) | −1482.36 | + | 2567.52i | −0.311368 | + | 0.539305i | −0.978659 | − | 0.205492i | \(-0.934120\pi\) |
0.667291 | + | 0.744797i | \(0.267454\pi\) | |||||||
\(284\) | 5713.96 | − | 9896.87i | 1.19388 | − | 2.06786i | ||||
\(285\) | −582.441 | − | 1008.82i | −0.121055 | − | 0.209674i | ||||
\(286\) | −14751.5 | −3.04990 | ||||||||
\(287\) | −682.728 | + | 4560.75i | −0.140419 | + | 0.938023i | ||||
\(288\) | 1717.18 | 0.351340 | ||||||||
\(289\) | 2199.53 | + | 3809.70i | 0.447697 | + | 0.775433i | ||||
\(290\) | −2723.03 | + | 4716.42i | −0.551385 | + | 0.955027i | ||||
\(291\) | 959.430 | − | 1661.78i | 0.193274 | − | 0.334761i | ||||
\(292\) | −8265.06 | − | 14315.5i | −1.65643 | − | 2.86901i | ||||
\(293\) | −7924.10 | −1.57997 | −0.789984 | − | 0.613127i | \(-0.789911\pi\) | ||||
−0.789984 | + | 0.613127i | \(0.789911\pi\) | |||||||
\(294\) | −5023.47 | − | 1538.47i | −0.996513 | − | 0.305188i | ||||
\(295\) | −117.399 | −0.0231702 | ||||||||
\(296\) | 9122.75 | + | 15801.1i | 1.79138 | + | 3.10276i | ||||
\(297\) | 549.928 | − | 952.504i | 0.107441 | − | 0.186094i | ||||
\(298\) | −6435.76 | + | 11147.1i | −1.25105 | + | 2.16689i | ||||
\(299\) | 3193.89 | + | 5531.98i | 0.617750 | + | 1.06997i | ||||
\(300\) | 1355.12 | 0.260793 | ||||||||
\(301\) | −816.857 | + | 5456.76i | −0.156421 | + | 1.04492i | ||||
\(302\) | 7042.41 | 1.34187 | ||||||||
\(303\) | 950.804 | + | 1646.84i | 0.180271 | + | 0.312239i | ||||
\(304\) | −4578.59 | + | 7930.34i | −0.863816 | + | 1.49617i | ||||
\(305\) | 2186.57 | − | 3787.25i | 0.410500 | − | 0.711008i | ||||
\(306\) | −520.861 | − | 902.157i | −0.0973059 | − | 0.168539i | ||||
\(307\) | −4067.00 | −0.756079 | −0.378039 | − | 0.925790i | \(-0.623402\pi\) | ||||
−0.378039 | + | 0.925790i | \(0.623402\pi\) | |||||||
\(308\) | −12683.9 | + | 4992.82i | −2.34654 | + | 0.923676i | ||||
\(309\) | −1162.73 | −0.214064 | ||||||||
\(310\) | 2243.05 | + | 3885.08i | 0.410957 | + | 0.711799i | ||||
\(311\) | −3826.29 | + | 6627.33i | −0.697650 | + | 1.20836i | 0.271630 | + | 0.962402i | \(0.412437\pi\) |
−0.969279 | + | 0.245963i | \(0.920896\pi\) | |||||||
\(312\) | −5469.00 | + | 9472.59i | −0.992376 | + | 1.71884i | ||||
\(313\) | −911.061 | − | 1578.00i | −0.164525 | − | 0.284965i | 0.771962 | − | 0.635669i | \(-0.219276\pi\) |
−0.936486 | + | 0.350704i | \(0.885942\pi\) | |||||||
\(314\) | 10174.3 | 1.82856 | ||||||||
\(315\) | −652.110 | − | 518.968i | −0.116642 | − | 0.0928270i | ||||
\(316\) | −9411.50 | −1.67544 | ||||||||
\(317\) | −1574.43 | − | 2726.99i | −0.278955 | − | 0.483164i | 0.692170 | − | 0.721734i | \(-0.256655\pi\) |
−0.971125 | + | 0.238570i | \(0.923321\pi\) | |||||||
\(318\) | 784.797 | − | 1359.31i | 0.138394 | − | 0.239705i | ||||
\(319\) | 4345.09 | − | 7525.91i | 0.762627 | − | 1.32091i | ||||
\(320\) | −77.0858 | − | 133.516i | −0.0134663 | − | 0.0233244i | ||||
\(321\) | 416.190 | 0.0723659 | ||||||||
\(322\) | 6663.57 | + | 5303.06i | 1.15325 | + | 0.917788i | ||||
\(323\) | 1760.53 | 0.303277 | ||||||||
\(324\) | −731.764 | − | 1267.45i | −0.125474 | − | 0.217327i | ||||
\(325\) | −886.578 | + | 1535.60i | −0.151319 | + | 0.262091i | ||||
\(326\) | −4857.94 | + | 8414.19i | −0.825326 | + | 1.42951i | ||||
\(327\) | 2569.46 | + | 4450.43i | 0.434530 | + | 0.752628i | ||||
\(328\) | 12800.0 | 2.15477 | ||||||||
\(329\) | 2908.46 | − | 1144.87i | 0.487382 | − | 0.191850i | ||||
\(330\) | −3119.75 | −0.520413 | ||||||||
\(331\) | 2928.06 | + | 5071.55i | 0.486226 | + | 0.842168i | 0.999875 | − | 0.0158326i | \(-0.00503989\pi\) |
−0.513649 | + | 0.858001i | \(0.671707\pi\) | |||||||
\(332\) | 9284.10 | − | 16080.5i | 1.53473 | − | 2.65823i | ||||
\(333\) | 1597.20 | − | 2766.43i | 0.262840 | − | 0.455253i | ||||
\(334\) | 965.447 | + | 1672.20i | 0.158164 | + | 0.273949i | ||||
\(335\) | −4053.86 | −0.661152 | ||||||||
\(336\) | −969.925 | + | 6479.28i | −0.157481 | + | 1.05201i | ||||
\(337\) | −7065.69 | −1.14212 | −0.571058 | − | 0.820910i | \(-0.693467\pi\) | ||||
−0.571058 | + | 0.820910i | \(0.693467\pi\) | |||||||
\(338\) | −7233.60 | − | 12529.0i | −1.16407 | − | 2.01623i | ||||
\(339\) | −3125.03 | + | 5412.71i | −0.500673 | + | 0.867192i | ||||
\(340\) | −1024.02 | + | 1773.66i | −0.163339 | + | 0.282912i | ||||
\(341\) | −3579.20 | − | 6199.35i | −0.568400 | − | 0.984497i | ||||
\(342\) | 3568.53 | 0.564222 | ||||||||
\(343\) | 2738.93 | − | 5731.66i | 0.431161 | − | 0.902275i | ||||
\(344\) | 15314.7 | 2.40033 | ||||||||
\(345\) | 675.467 | + | 1169.94i | 0.105408 | + | 0.182573i | ||||
\(346\) | 1695.19 | − | 2936.15i | 0.263393 | − | 0.456210i | ||||
\(347\) | −4948.72 | + | 8571.44i | −0.765595 | + | 1.32605i | 0.174337 | + | 0.984686i | \(0.444222\pi\) |
−0.939932 | + | 0.341363i | \(0.889111\pi\) | |||||||
\(348\) | −5781.80 | − | 10014.4i | −0.890624 | − | 1.54261i | ||||
\(349\) | 11832.6 | 1.81486 | 0.907431 | − | 0.420201i | \(-0.138040\pi\) | ||||
0.907431 | + | 0.420201i | \(0.138040\pi\) | |||||||
\(350\) | −349.979 | + | 2337.93i | −0.0534490 | + | 0.357050i | ||||
\(351\) | 1915.01 | 0.291213 | ||||||||
\(352\) | 3886.12 | + | 6730.95i | 0.588440 | + | 1.01921i | ||||
\(353\) | −3503.69 | + | 6068.57i | −0.528279 | + | 0.915007i | 0.471177 | + | 0.882039i | \(0.343829\pi\) |
−0.999456 | + | 0.0329681i | \(0.989504\pi\) | |||||||
\(354\) | 179.821 | − | 311.459i | 0.0269982 | − | 0.0467623i | ||||
\(355\) | 1581.22 | + | 2738.75i | 0.236401 | + | 0.409458i | ||||
\(356\) | 18136.0 | 2.70002 | ||||||||
\(357\) | 1172.03 | − | 461.352i | 0.173755 | − | 0.0683959i | ||||
\(358\) | −1710.41 | −0.252508 | ||||||||
\(359\) | −1407.19 | − | 2437.33i | −0.206877 | − | 0.358322i | 0.743852 | − | 0.668344i | \(-0.232997\pi\) |
−0.950729 | + | 0.310023i | \(0.899663\pi\) | |||||||
\(360\) | −1156.62 | + | 2003.33i | −0.169332 | + | 0.293291i | ||||
\(361\) | 414.057 | − | 717.169i | 0.0603670 | − | 0.104559i | ||||
\(362\) | −3128.73 | − | 5419.13i | −0.454261 | − | 0.786804i | ||||
\(363\) | 985.124 | 0.142440 | ||||||||
\(364\) | −18570.8 | − | 14779.2i | −2.67411 | − | 2.12813i | ||||
\(365\) | 4574.36 | 0.655981 | ||||||||
\(366\) | 6698.39 | + | 11602.0i | 0.956641 | + | 1.65695i | ||||
\(367\) | −1174.93 | + | 2035.03i | −0.167114 | + | 0.289449i | −0.937404 | − | 0.348244i | \(-0.886778\pi\) |
0.770290 | + | 0.637694i | \(0.220111\pi\) | |||||||
\(368\) | 5309.87 | − | 9196.96i | 0.752163 | − | 1.30278i | ||||
\(369\) | −1120.51 | − | 1940.77i | −0.158079 | − | 0.273801i | ||||
\(370\) | −9060.91 | −1.27312 | ||||||||
\(371\) | 1484.97 | + | 1181.78i | 0.207806 | + | 0.165378i | ||||
\(372\) | −9525.34 | −1.32760 | ||||||||
\(373\) | 829.650 | + | 1437.00i | 0.115168 | + | 0.199477i | 0.917847 | − | 0.396935i | \(-0.129926\pi\) |
−0.802679 | + | 0.596411i | \(0.796593\pi\) | |||||||
\(374\) | 2357.50 | − | 4083.31i | 0.325945 | − | 0.564553i | ||||
\(375\) | −187.500 | + | 324.760i | −0.0258199 | + | 0.0447214i | ||||
\(376\) | −4337.87 | − | 7513.42i | −0.594970 | − | 1.03052i | ||||
\(377\) | 15130.8 | 2.06705 | ||||||||
\(378\) | 2375.67 | − | 935.142i | 0.323257 | − | 0.127245i | ||||
\(379\) | 5327.80 | 0.722087 | 0.361043 | − | 0.932549i | \(-0.382421\pi\) | ||||
0.361043 | + | 0.932549i | \(0.382421\pi\) | |||||||
\(380\) | −3507.89 | − | 6075.85i | −0.473556 | − | 0.820223i | ||||
\(381\) | −648.127 | + | 1122.59i | −0.0871510 | + | 0.150950i | ||||
\(382\) | 4037.07 | − | 6992.42i | 0.540719 | − | 0.936553i | ||||
\(383\) | −3119.88 | − | 5403.78i | −0.416235 | − | 0.720941i | 0.579322 | − | 0.815099i | \(-0.303317\pi\) |
−0.995557 | + | 0.0941580i | \(0.969984\pi\) | |||||||
\(384\) | −4106.86 | −0.545774 | ||||||||
\(385\) | 558.455 | − | 3730.59i | 0.0739260 | − | 0.493840i | ||||
\(386\) | −19884.8 | −2.62205 | ||||||||
\(387\) | −1340.64 | − | 2322.06i | −0.176095 | − | 0.305005i | ||||
\(388\) | 5778.41 | − | 10008.5i | 0.756067 | − | 1.30955i | ||||
\(389\) | −4742.61 | + | 8214.43i | −0.618148 | + | 1.07066i | 0.371675 | + | 0.928363i | \(0.378784\pi\) |
−0.989823 | + | 0.142301i | \(0.954550\pi\) | |||||||
\(390\) | −2715.97 | − | 4704.19i | −0.352637 | − | 0.610784i | ||||
\(391\) | −2041.72 | −0.264077 | ||||||||
\(392\) | −16859.2 | − | 5163.22i | −2.17224 | − | 0.665260i | ||||
\(393\) | −1972.50 | −0.253179 | ||||||||
\(394\) | −2537.17 | − | 4394.51i | −0.324419 | − | 0.561910i | ||||
\(395\) | 1302.22 | − | 2255.50i | 0.165877 | − | 0.287308i | ||||
\(396\) | 3312.08 | − | 5736.69i | 0.420299 | − | 0.727978i | ||||
\(397\) | −3946.37 | − | 6835.31i | −0.498898 | − | 0.864117i | 0.501101 | − | 0.865389i | \(-0.332928\pi\) |
−0.999999 | + | 0.00127185i | \(0.999595\pi\) | |||||||
\(398\) | −15725.0 | −1.98046 | ||||||||
\(399\) | −638.790 | + | 4267.23i | −0.0801491 | + | 0.535411i | ||||
\(400\) | 2947.89 | 0.368486 | ||||||||
\(401\) | 6229.83 | + | 10790.4i | 0.775817 | + | 1.34375i | 0.934334 | + | 0.356398i | \(0.115995\pi\) |
−0.158517 | + | 0.987356i | \(0.550671\pi\) | |||||||
\(402\) | 6209.34 | − | 10754.9i | 0.770383 | − | 1.33434i | ||||
\(403\) | 6231.90 | − | 10794.0i | 0.770305 | − | 1.33421i | ||||
\(404\) | 5726.45 | + | 9918.50i | 0.705202 | + | 1.22145i | ||||
\(405\) | 405.000 | 0.0496904 | ||||||||
\(406\) | 18770.6 | − | 7388.73i | 2.29450 | − | 0.903193i | ||||
\(407\) | 14458.3 | 1.76087 | ||||||||
\(408\) | −1748.05 | − | 3027.71i | −0.212111 | − | 0.367387i | ||||
\(409\) | −1701.81 | + | 2947.62i | −0.205744 | + | 0.356358i | −0.950369 | − | 0.311124i | \(-0.899295\pi\) |
0.744626 | + | 0.667482i | \(0.232628\pi\) | |||||||
\(410\) | −3178.32 | + | 5505.01i | −0.382844 | + | 0.663105i | ||||
\(411\) | −438.773 | − | 759.977i | −0.0526595 | − | 0.0912090i | ||||
\(412\) | −7002.86 | −0.837393 | ||||||||
\(413\) | 340.253 | + | 270.783i | 0.0405393 | + | 0.0322623i | ||||
\(414\) | −4138.48 | −0.491293 | ||||||||
\(415\) | 2569.17 | + | 4449.94i | 0.303894 | + | 0.526359i | ||||
\(416\) | −6766.29 | + | 11719.6i | −0.797463 | + | 1.38125i | ||||
\(417\) | 2509.53 | − | 4346.63i | 0.294706 | − | 0.510445i | ||||
\(418\) | 8075.86 | + | 13987.8i | 0.944983 | + | 1.63676i | ||||
\(419\) | −1376.83 | −0.160532 | −0.0802658 | − | 0.996773i | \(-0.525577\pi\) | ||||
−0.0802658 | + | 0.996773i | \(0.525577\pi\) | |||||||
\(420\) | −3927.50 | − | 3125.61i | −0.456291 | − | 0.363129i | ||||
\(421\) | −15757.3 | −1.82414 | −0.912069 | − | 0.410036i | \(-0.865516\pi\) | ||||
−0.912069 | + | 0.410036i | \(0.865516\pi\) | |||||||
\(422\) | −5398.57 | − | 9350.60i | −0.622745 | − | 1.07863i | ||||
\(423\) | −759.469 | + | 1315.44i | −0.0872970 | + | 0.151203i | ||||
\(424\) | 2633.84 | − | 4561.95i | 0.301676 | − | 0.522519i | ||||
\(425\) | −283.376 | − | 490.822i | −0.0323430 | − | 0.0560196i | ||||
\(426\) | −9687.88 | −1.10183 | ||||||||
\(427\) | −15072.6 | + | 5933.09i | −1.70823 | + | 0.672418i | ||||
\(428\) | 2506.61 | 0.283088 | ||||||||
\(429\) | 4333.82 | + | 7506.39i | 0.487736 | + | 0.844783i | ||||
\(430\) | −3802.73 | + | 6586.52i | −0.426474 | + | 0.738675i | ||||
\(431\) | −2541.85 | + | 4402.62i | −0.284076 | + | 0.492034i | −0.972385 | − | 0.233384i | \(-0.925020\pi\) |
0.688309 | + | 0.725418i | \(0.258353\pi\) | |||||||
\(432\) | −1591.86 | − | 2757.18i | −0.177288 | − | 0.307072i | ||||
\(433\) | 4631.44 | 0.514025 | 0.257013 | − | 0.966408i | \(-0.417262\pi\) | ||||
0.257013 | + | 0.966408i | \(0.417262\pi\) | |||||||
\(434\) | 2460.06 | − | 16433.6i | 0.272089 | − | 1.81760i | ||||
\(435\) | 3199.98 | 0.352706 | ||||||||
\(436\) | 15475.2 | + | 26803.8i | 1.69983 | + | 2.94420i | ||||
\(437\) | 3497.06 | − | 6057.09i | 0.382808 | − | 0.663043i | ||||
\(438\) | −7006.60 | + | 12135.8i | −0.764357 | + | 1.32391i | ||||
\(439\) | 1169.44 | + | 2025.52i | 0.127139 | + | 0.220212i | 0.922567 | − | 0.385837i | \(-0.126087\pi\) |
−0.795428 | + | 0.606048i | \(0.792754\pi\) | |||||||
\(440\) | −10470.1 | −1.13442 | ||||||||
\(441\) | 692.980 | + | 3008.21i | 0.0748277 | + | 0.324826i | ||||
\(442\) | 8209.49 | 0.883451 | ||||||||
\(443\) | −5905.74 | − | 10229.0i | −0.633387 | − | 1.09706i | −0.986854 | − | 0.161612i | \(-0.948331\pi\) |
0.353468 | − | 0.935447i | \(-0.385002\pi\) | |||||||
\(444\) | 9619.52 | − | 16661.5i | 1.02820 | − | 1.78090i | ||||
\(445\) | −2509.38 | + | 4346.37i | −0.267316 | + | 0.463006i | ||||
\(446\) | −6582.37 | − | 11401.0i | −0.698844 | − | 1.21043i | ||||
\(447\) | 7563.02 | 0.800265 | ||||||||
\(448\) | −84.5435 | + | 564.766i | −0.00891586 | + | 0.0595596i | ||||
\(449\) | 9582.29 | 1.00716 | 0.503582 | − | 0.863948i | \(-0.332015\pi\) | ||||
0.503582 | + | 0.863948i | \(0.332015\pi\) | |||||||
\(450\) | −574.392 | − | 994.876i | −0.0601713 | − | 0.104220i | ||||
\(451\) | 5071.59 | − | 8784.25i | 0.529516 | − | 0.917149i | ||||
\(452\) | −18821.3 | + | 32599.4i | −1.95858 | + | 3.39236i | ||||
\(453\) | −2068.98 | − | 3583.58i | −0.214590 | − | 0.371680i | ||||
\(454\) | 14938.9 | 1.54431 | ||||||||
\(455\) | 6111.43 | − | 2405.66i | 0.629689 | − | 0.247866i | ||||
\(456\) | 11976.3 | 1.22991 | ||||||||
\(457\) | 3285.97 | + | 5691.47i | 0.336349 | + | 0.582573i | 0.983743 | − | 0.179582i | \(-0.0574746\pi\) |
−0.647394 | + | 0.762155i | \(0.724141\pi\) | |||||||
\(458\) | 2675.08 | − | 4633.37i | 0.272922 | − | 0.472714i | ||||
\(459\) | −306.046 | + | 530.087i | −0.0311220 | + | 0.0539049i | ||||
\(460\) | 4068.17 | + | 7046.27i | 0.412346 | + | 0.714204i | ||||
\(461\) | −4197.59 | −0.424081 | −0.212041 | − | 0.977261i | \(-0.568011\pi\) | ||||
−0.212041 | + | 0.977261i | \(0.568011\pi\) | |||||||
\(462\) | 9041.86 | + | 7195.77i | 0.910531 | + | 0.724626i | ||||
\(463\) | −6125.75 | −0.614876 | −0.307438 | − | 0.951568i | \(-0.599472\pi\) | ||||
−0.307438 | + | 0.951568i | \(0.599472\pi\) | |||||||
\(464\) | −12577.6 | − | 21785.0i | −1.25840 | − | 2.17962i | ||||
\(465\) | 1317.97 | − | 2282.79i | 0.131439 | − | 0.227659i | ||||
\(466\) | 9879.51 | − | 17111.8i | 0.982101 | − | 1.70105i | ||||
\(467\) | −1614.04 | − | 2795.60i | −0.159934 | − | 0.277013i | 0.774911 | − | 0.632070i | \(-0.217795\pi\) |
−0.934845 | + | 0.355057i | \(0.884461\pi\) | |||||||
\(468\) | 11533.6 | 1.13919 | ||||||||
\(469\) | 11749.2 | + | 9350.31i | 1.15677 | + | 0.920591i | ||||
\(470\) | 4308.47 | 0.422840 | ||||||||
\(471\) | −2989.10 | − | 5177.27i | −0.292421 | − | 0.506488i | ||||
\(472\) | 603.494 | − | 1045.28i | 0.0588518 | − | 0.101934i | ||||
\(473\) | 6067.95 | − | 10510.0i | 0.589862 | − | 1.02167i | ||||
\(474\) | 3989.24 | + | 6909.57i | 0.386565 | + | 0.669550i | ||||
\(475\) | 1941.47 | 0.187538 | ||||||||
\(476\) | 7058.87 | − | 2778.60i | 0.679711 | − | 0.267557i | ||||
\(477\) | −922.259 | −0.0885269 | ||||||||
\(478\) | 15472.3 | + | 26798.7i | 1.48051 | + | 2.56432i | ||||
\(479\) | −1563.15 | + | 2707.46i | −0.149107 | + | 0.258261i | −0.930898 | − | 0.365280i | \(-0.880973\pi\) |
0.781791 | + | 0.623541i | \(0.214307\pi\) | |||||||
\(480\) | −1430.98 | + | 2478.54i | −0.136073 | + | 0.235686i | ||||
\(481\) | 12587.0 | + | 21801.4i | 1.19318 | + | 2.06665i | ||||
\(482\) | −21362.9 | −2.01878 | ||||||||
\(483\) | 740.815 | − | 4948.79i | 0.0697894 | − | 0.466206i | ||||
\(484\) | 5933.15 | 0.557208 | ||||||||
\(485\) | 1599.05 | + | 2769.64i | 0.149710 | + | 0.259305i | ||||
\(486\) | −620.343 | + | 1074.47i | −0.0578999 | + | 0.100286i | ||||
\(487\) | 434.519 | − | 752.609i | 0.0404311 | − | 0.0700286i | −0.845102 | − | 0.534605i | \(-0.820460\pi\) |
0.885533 | + | 0.464577i | \(0.153794\pi\) | |||||||
\(488\) | 22480.3 | + | 38937.1i | 2.08532 | + | 3.61188i | ||||
\(489\) | 5708.83 | 0.527939 | ||||||||
\(490\) | 6406.81 | − | 5968.70i | 0.590674 | − | 0.550282i | ||||
\(491\) | 6617.71 | 0.608254 | 0.304127 | − | 0.952631i | \(-0.401635\pi\) | ||||
0.304127 | + | 0.952631i | \(0.401635\pi\) | |||||||
\(492\) | −6748.53 | − | 11688.8i | −0.618388 | − | 1.07108i | ||||
\(493\) | −2418.13 | + | 4188.32i | −0.220907 | + | 0.382622i | ||||
\(494\) | −14061.2 | + | 24354.8i | −1.28066 | + | 2.21816i | ||||
\(495\) | 916.547 | + | 1587.51i | 0.0832237 | + | 0.144148i | ||||
\(496\) | −20721.2 | −1.87582 | ||||||||
\(497\) | 1734.19 | − | 11584.7i | 0.156518 | − | 1.04557i | ||||
\(498\) | −15740.9 | −1.41640 | ||||||||
\(499\) | 444.077 | + | 769.164i | 0.0398389 | + | 0.0690030i | 0.885257 | − | 0.465102i | \(-0.153982\pi\) |
−0.845418 | + | 0.534105i | \(0.820649\pi\) | |||||||
\(500\) | −1129.27 | + | 1955.94i | −0.101005 | + | 0.174945i | ||||
\(501\) | 567.275 | − | 982.550i | 0.0505868 | − | 0.0876189i | ||||
\(502\) | 6718.21 | + | 11636.3i | 0.597308 | + | 1.03457i | ||||
\(503\) | −10757.4 | −0.953572 | −0.476786 | − | 0.879019i | \(-0.658198\pi\) | ||||
−0.476786 | + | 0.879019i | \(0.658198\pi\) | |||||||
\(504\) | 7972.93 | − | 3138.41i | 0.704648 | − | 0.277373i | ||||
\(505\) | −3169.35 | −0.279275 | ||||||||
\(506\) | −9365.71 | − | 16221.9i | −0.822839 | − | 1.42520i | ||||
\(507\) | −4250.30 | + | 7361.74i | −0.372313 | + | 0.644865i | ||||
\(508\) | −3903.50 | + | 6761.07i | −0.340925 | + | 0.590500i | ||||
\(509\) | −4430.01 | − | 7673.01i | −0.385770 | − | 0.668173i | 0.606106 | − | 0.795384i | \(-0.292731\pi\) |
−0.991876 | + | 0.127211i | \(0.959397\pi\) | |||||||
\(510\) | 1736.20 | 0.150746 | ||||||||
\(511\) | −13257.7 | − | 10550.9i | −1.14772 | − | 0.913391i | ||||
\(512\) | −25994.0 | −2.24372 | ||||||||
\(513\) | −1048.39 | − | 1815.87i | −0.0902294 | − | 0.156282i | ||||
\(514\) | −8395.74 | + | 14541.8i | −0.720467 | + | 1.24789i | ||||
\(515\) | 968.946 | − | 1678.26i | 0.0829065 | − | 0.143598i | ||||
\(516\) | −8074.34 | − | 13985.2i | −0.688862 | − | 1.19314i | ||||
\(517\) | −6874.95 | −0.584835 | ||||||||
\(518\) | 26261.0 | + | 20899.2i | 2.22749 | + | 1.77270i | ||||
\(519\) | −1992.11 | −0.168485 | ||||||||
\(520\) | −9115.00 | − | 15787.6i | −0.768691 | − | 1.33141i | ||||
\(521\) | 37.6937 | − | 65.2875i | 0.00316966 | − | 0.00549001i | −0.864436 | − | 0.502742i | \(-0.832324\pi\) |
0.867606 | + | 0.497252i | \(0.165658\pi\) | |||||||
\(522\) | −4901.45 | + | 8489.56i | −0.410978 | + | 0.711835i | ||||
\(523\) | −4333.30 | − | 7505.49i | −0.362298 | − | 0.627518i | 0.626041 | − | 0.779790i | \(-0.284674\pi\) |
−0.988339 | + | 0.152272i | \(0.951341\pi\) | |||||||
\(524\) | −11879.9 | −0.990408 | ||||||||
\(525\) | 1292.49 | − | 508.767i | 0.107446 | − | 0.0422941i | ||||
\(526\) | −27616.2 | −2.28921 | ||||||||
\(527\) | 1991.89 | + | 3450.06i | 0.164646 | + | 0.285175i | ||||
\(528\) | 7205.01 | − | 12479.4i | 0.593859 | − | 1.02859i | ||||
\(529\) | 2027.90 | − | 3512.42i | 0.166672 | − | 0.288684i | ||||
\(530\) | 1308.00 | + | 2265.51i | 0.107199 | + | 0.185675i | ||||
\(531\) | −211.318 | −0.0172701 | ||||||||
\(532\) | −3847.27 | + | 25700.5i | −0.313534 | + | 2.09447i | ||||
\(533\) | 17660.7 | 1.43522 | ||||||||
\(534\) | −7687.28 | − | 13314.8i | −0.622961 | − | 1.07900i | ||||
\(535\) | −346.825 | + | 600.719i | −0.0280272 | + | 0.0485445i | ||||
\(536\) | 20839.1 | − | 36094.3i | 1.67931 | − | 2.90865i | ||||
\(537\) | 502.499 | + | 870.354i | 0.0403807 | + | 0.0699414i | ||||
\(538\) | 2756.00 | 0.220854 | ||||||||
\(539\) | −10223.2 | + | 9524.14i | −0.816968 | + | 0.761102i | ||||
\(540\) | 2439.21 | 0.194383 | ||||||||
\(541\) | −6142.38 | − | 10638.9i | −0.488136 | − | 0.845477i | 0.511771 | − | 0.859122i | \(-0.328990\pi\) |
−0.999907 | + | 0.0136455i | \(0.995656\pi\) | |||||||
\(542\) | −10444.1 | + | 18089.7i | −0.827697 | + | 1.43361i | ||||
\(543\) | −1838.37 | + | 3184.16i | −0.145290 | + | 0.251649i | ||||
\(544\) | −2162.70 | − | 3745.91i | −0.170451 | − | 0.295229i | ||||
\(545\) | −8564.85 | −0.673171 | ||||||||
\(546\) | −2978.72 | + | 19898.4i | −0.233476 | + | 1.55966i | ||||
\(547\) | −2906.85 | −0.227218 | −0.113609 | − | 0.993526i | \(-0.536241\pi\) | ||||
−0.113609 | + | 0.993526i | \(0.536241\pi\) | |||||||
\(548\) | −2642.62 | − | 4577.15i | −0.205998 | − | 0.356800i | ||||
\(549\) | 3935.83 | − | 6817.05i | 0.305969 | − | 0.529954i | ||||
\(550\) | 2599.79 | − | 4502.97i | 0.201555 | − | 0.349104i | ||||
\(551\) | −8283.55 | − | 14347.5i | −0.640456 | − | 1.10930i | ||||
\(552\) | −13889.1 | −1.07094 | ||||||||
\(553\) | −8976.54 | + | 3533.46i | −0.690274 | + | 0.271715i | ||||
\(554\) | 15783.5 | 1.21042 | ||||||||
\(555\) | 2662.00 | + | 4610.71i | 0.203595 | + | 0.352637i | ||||
\(556\) | 15114.3 | − | 26178.7i | 1.15286 | − | 1.99680i | ||||
\(557\) | −1936.91 | + | 3354.83i | −0.147342 | + | 0.255204i | −0.930244 | − | 0.366941i | \(-0.880405\pi\) |
0.782902 | + | 0.622145i | \(0.213738\pi\) | |||||||
\(558\) | 4037.49 | + | 6993.14i | 0.306309 | + | 0.530543i | ||||
\(559\) | 21130.4 | 1.59878 | ||||||||
\(560\) | −8543.77 | − | 6799.37i | −0.644714 | − | 0.513082i | ||||
\(561\) | −2770.43 | −0.208498 | ||||||||
\(562\) | −18420.7 | − | 31905.6i | −1.38262 | − | 2.39476i | ||||
\(563\) | 2730.54 | − | 4729.44i | 0.204403 | − | 0.354036i | −0.745540 | − | 0.666461i | \(-0.767808\pi\) |
0.949942 | + | 0.312426i | \(0.101141\pi\) | |||||||
\(564\) | −4574.09 | + | 7922.55i | −0.341496 | + | 0.591489i | ||||
\(565\) | −5208.38 | − | 9021.18i | −0.387820 | − | 0.671724i | ||||
\(566\) | 15137.0 | 1.12412 | ||||||||
\(567\) | −1173.80 | − | 934.142i | −0.0869399 | − | 0.0691892i | ||||
\(568\) | −32513.3 | −2.40181 | ||||||||
\(569\) | −6552.48 | − | 11349.2i | −0.482767 | − | 0.836177i | 0.517037 | − | 0.855963i | \(-0.327035\pi\) |
−0.999804 | + | 0.0197860i | \(0.993701\pi\) | |||||||
\(570\) | −2973.77 | + | 5150.72i | −0.218522 | + | 0.378491i | ||||
\(571\) | −1719.63 | + | 2978.49i | −0.126032 | + | 0.218294i | −0.922136 | − | 0.386866i | \(-0.873558\pi\) |
0.796104 | + | 0.605160i | \(0.206891\pi\) | |||||||
\(572\) | 26101.5 | + | 45209.1i | 1.90797 | + | 3.30470i | ||||
\(573\) | −4744.19 | −0.345884 | ||||||||
\(574\) | 21909.1 | − | 8624.13i | 1.59315 | − | 0.627115i | ||||
\(575\) | −2251.56 | −0.163298 | ||||||||
\(576\) | −138.754 | − | 240.330i | −0.0100372 | − | 0.0173850i | ||||
\(577\) | −8896.09 | + | 15408.5i | −0.641853 | + | 1.11172i | 0.343166 | + | 0.939275i | \(0.388501\pi\) |
−0.985019 | + | 0.172447i | \(0.944833\pi\) | |||||||
\(578\) | 11230.2 | − | 19451.2i | 0.808155 | − | 1.39977i | ||||
\(579\) | 5841.94 | + | 10118.5i | 0.419314 | + | 0.726273i | ||||
\(580\) | 19272.7 | 1.37975 | ||||||||
\(581\) | 2817.73 | − | 18823.0i | 0.201204 | − | 1.34408i | ||||
\(582\) | −9797.14 | −0.697774 | ||||||||
\(583\) | −2087.15 | − | 3615.04i | −0.148269 | − | 0.256809i | ||||
\(584\) | −23514.7 | + | 40728.7i | −1.66617 | + | 2.88590i | ||||
\(585\) | −1595.84 | + | 2764.08i | −0.112786 | + | 0.195351i | ||||
\(586\) | 20229.1 | + | 35037.8i | 1.42603 | + | 2.46996i | ||||
\(587\) | 14416.6 | 1.01369 | 0.506846 | − | 0.862037i | \(-0.330811\pi\) | ||||
0.506846 | + | 0.862037i | \(0.330811\pi\) | |||||||
\(588\) | 4173.64 | + | 18117.7i | 0.292718 | + | 1.27068i | ||||
\(589\) | −13646.9 | −0.954686 | ||||||||
\(590\) | 299.702 | + | 519.098i | 0.0209127 | + | 0.0362219i | ||||
\(591\) | −1490.79 | + | 2582.12i | −0.103761 | + | 0.179719i | ||||
\(592\) | 20926.0 | − | 36245.0i | 1.45280 | − | 2.51631i | ||||
\(593\) | −4086.02 | − | 7077.19i | −0.282955 | − | 0.490093i | 0.689156 | − | 0.724613i | \(-0.257982\pi\) |
−0.972111 | + | 0.234520i | \(0.924648\pi\) | |||||||
\(594\) | −5615.54 | −0.387893 | ||||||||
\(595\) | −310.792 | + | 2076.15i | −0.0214138 | + | 0.143048i | ||||
\(596\) | 45550.2 | 3.13055 | ||||||||
\(597\) | 4619.82 | + | 8001.77i | 0.316711 | + | 0.548560i | ||||
\(598\) | 16307.1 | − | 28244.7i | 1.11513 | − | 1.93145i | ||||
\(599\) | 1246.09 | − | 2158.29i | 0.0849980 | − | 0.147221i | −0.820392 | − | 0.571801i | \(-0.806245\pi\) |
0.905390 | + | 0.424580i | \(0.139578\pi\) | |||||||
\(600\) | −1927.71 | − | 3338.89i | −0.131164 | − | 0.227182i | ||||
\(601\) | −13835.4 | −0.939031 | −0.469516 | − | 0.882924i | \(-0.655571\pi\) | ||||
−0.469516 | + | 0.882924i | \(0.655571\pi\) | |||||||
\(602\) | 26213.3 | − | 10318.4i | 1.77471 | − | 0.698584i | ||||
\(603\) | −7296.94 | −0.492794 | ||||||||
\(604\) | −12460.9 | − | 21583.0i | −0.839452 | − | 1.45397i | ||||
\(605\) | −820.937 | + | 1421.90i | −0.0551666 | + | 0.0955514i | ||||
\(606\) | 4854.52 | − | 8408.28i | 0.325415 | − | 0.563636i | ||||
\(607\) | −3667.95 | − | 6353.08i | −0.245268 | − | 0.424816i | 0.716939 | − | 0.697136i | \(-0.245543\pi\) |
−0.962207 | + | 0.272320i | \(0.912209\pi\) | |||||||
\(608\) | 14817.1 | 0.988345 | ||||||||
\(609\) | −9274.40 | − | 7380.83i | −0.617106 | − | 0.491110i | ||||
\(610\) | −22328.0 | −1.48202 | ||||||||
\(611\) | −5985.14 | − | 10366.6i | −0.396289 | − | 0.686394i | ||||
\(612\) | −1843.24 | + | 3192.58i | −0.121746 | + | 0.210870i | ||||
\(613\) | −3006.02 | + | 5206.58i | −0.198062 | + | 0.343054i | −0.947900 | − | 0.318568i | \(-0.896798\pi\) |
0.749838 | + | 0.661622i | \(0.230131\pi\) | |||||||
\(614\) | 10382.5 | + | 17983.0i | 0.682414 | + | 1.18198i | ||||
\(615\) | 3735.02 | 0.244895 | ||||||||
\(616\) | 30345.2 | + | 24149.6i | 1.98481 | + | 1.57957i | ||||
\(617\) | −22927.4 | −1.49598 | −0.747991 | − | 0.663708i | \(-0.768982\pi\) | ||||
−0.747991 | + | 0.663708i | \(0.768982\pi\) | |||||||
\(618\) | 2968.29 | + | 5141.23i | 0.193207 | + | 0.334645i | ||||
\(619\) | −8960.76 | + | 15520.5i | −0.581847 | + | 1.00779i | 0.413413 | + | 0.910543i | \(0.364336\pi\) |
−0.995260 | + | 0.0972452i | \(0.968997\pi\) | |||||||
\(620\) | 7937.78 | − | 13748.6i | 0.514176 | − | 0.890578i | ||||
\(621\) | 1215.84 | + | 2105.90i | 0.0785668 | + | 0.136082i | ||||
\(622\) | 39071.8 | 2.51871 | ||||||||
\(623\) | 17297.8 | − | 6809.00i | 1.11240 | − | 0.437876i | ||||
\(624\) | 25089.9 | 1.60962 | ||||||||
\(625\) | −312.500 | − | 541.266i | −0.0200000 | − | 0.0346410i | ||||
\(626\) | −4651.61 | + | 8056.82i | −0.296990 | + | 0.514402i | ||||
\(627\) | 4745.19 | − | 8218.92i | 0.302241 | − | 0.523496i | ||||
\(628\) | −18002.6 | − | 31181.4i | −1.14392 | − | 1.98132i | ||||
\(629\) | −8046.35 | −0.510062 | ||||||||
\(630\) | −629.962 | + | 4208.27i | −0.0398386 | + | 0.266129i | ||||
\(631\) | 19270.7 | 1.21578 | 0.607888 | − | 0.794023i | \(-0.292017\pi\) | ||||
0.607888 | + | 0.794023i | \(0.292017\pi\) | |||||||
\(632\) | 13388.2 | + | 23189.1i | 0.842650 | + | 1.45951i | ||||
\(633\) | −3172.08 | + | 5494.20i | −0.199177 | + | 0.344984i | ||||
\(634\) | −8038.57 | + | 13923.2i | −0.503553 | + | 0.872179i | ||||
\(635\) | −1080.21 | − | 1870.98i | −0.0675069 | − | 0.116925i | ||||
\(636\) | −5554.53 | −0.346308 | ||||||||
\(637\) | −23261.3 | − | 7123.90i | −1.44685 | − | 0.443107i | ||||
\(638\) | −44369.5 | −2.75330 | ||||||||
\(639\) | 2846.19 | + | 4929.75i | 0.176203 | + | 0.305192i | ||||
\(640\) | 3422.38 | − | 5927.74i | 0.211377 | − | 0.366116i | ||||
\(641\) | −14119.3 | + | 24455.3i | −0.870013 | + | 1.50691i | −0.00803063 | + | 0.999968i | \(0.502556\pi\) |
−0.861982 | + | 0.506939i | \(0.830777\pi\) | |||||||
\(642\) | −1062.47 | − | 1840.26i | −0.0653153 | − | 0.113129i | ||||
\(643\) | −19055.3 | −1.16869 | −0.584346 | − | 0.811505i | \(-0.698649\pi\) | ||||
−0.584346 | + | 0.811505i | \(0.698649\pi\) | |||||||
\(644\) | 4461.74 | − | 29805.3i | 0.273008 | − | 1.82375i | ||||
\(645\) | 4468.80 | 0.272804 | ||||||||
\(646\) | −4494.38 | − | 7784.49i | −0.273729 | − | 0.474112i | ||||
\(647\) | 8105.65 | − | 14039.4i | 0.492529 | − | 0.853084i | −0.507434 | − | 0.861690i | \(-0.669406\pi\) |
0.999963 | + | 0.00860593i | \(0.00273939\pi\) | |||||||
\(648\) | −2081.92 | + | 3606.00i | −0.126212 | + | 0.218606i | ||||
\(649\) | −478.228 | − | 828.316i | −0.0289247 | − | 0.0500990i | ||||
\(650\) | 9053.22 | 0.546302 | ||||||||
\(651\) | −9085.11 | + | 3576.20i | −0.546964 | + | 0.215303i | ||||
\(652\) | 34382.9 | 2.06524 | ||||||||
\(653\) | 13266.0 | + | 22977.4i | 0.795007 | + | 1.37699i | 0.922834 | + | 0.385197i | \(0.125866\pi\) |
−0.127827 | + | 0.991796i | \(0.540800\pi\) | |||||||
\(654\) | 13118.9 | − | 22722.6i | 0.784387 | − | 1.35860i | ||||
\(655\) | 1643.75 | − | 2847.06i | 0.0980558 | − | 0.169838i | ||||
\(656\) | −14680.6 | − | 25427.5i | −0.873749 | − | 1.51338i | ||||
\(657\) | 8233.85 | 0.488939 | ||||||||
\(658\) | −12487.1 | − | 9937.58i | −0.739814 | − | 0.588765i | ||||
\(659\) | 1883.19 | 0.111318 | 0.0556592 | − | 0.998450i | \(-0.482274\pi\) | ||||
0.0556592 | + | 0.998450i | \(0.482274\pi\) | |||||||
\(660\) | 5520.13 | + | 9561.15i | 0.325562 | + | 0.563890i | ||||
\(661\) | −2337.13 | + | 4048.03i | −0.137525 | + | 0.238200i | −0.926559 | − | 0.376149i | \(-0.877248\pi\) |
0.789034 | + | 0.614349i | \(0.210581\pi\) | |||||||
\(662\) | 14949.8 | − | 25893.8i | 0.877706 | − | 1.52023i | ||||
\(663\) | −2411.86 | − | 4177.46i | −0.141280 | − | 0.244704i | ||||
\(664\) | −52827.9 | −3.08753 | ||||||||
\(665\) | −5626.90 | − | 4478.04i | −0.328123 | − | 0.261129i | ||||
\(666\) | −16309.6 | −0.948928 | ||||||||
\(667\) | 9606.58 | + | 16639.1i | 0.557673 | + | 0.965919i | ||||
\(668\) | 3416.56 | − | 5917.65i | 0.197890 | − | 0.342756i | ||||
\(669\) | −3867.65 | + | 6698.97i | −0.223516 | + | 0.387141i | ||||
\(670\) | 10348.9 | + | 17924.8i | 0.596736 | + | 1.03358i | ||||
\(671\) | 35628.3 | 2.04980 | ||||||||
\(672\) | 9864.18 | − | 3882.87i | 0.566248 | − | 0.222894i | ||||
\(673\) | −23344.3 | −1.33709 | −0.668543 | − | 0.743674i | \(-0.733082\pi\) | ||||
−0.668543 | + | 0.743674i | \(0.733082\pi\) | |||||||
\(674\) | 18037.7 | + | 31242.2i | 1.03084 | + | 1.78547i | ||||
\(675\) | −337.500 | + | 584.567i | −0.0192450 | + | 0.0333333i | ||||
\(676\) | −25598.5 | + | 44337.9i | −1.45645 | + | 2.52264i | ||||
\(677\) | −699.747 | − | 1212.00i | −0.0397245 | − | 0.0688048i | 0.845480 | − | 0.534008i | \(-0.179315\pi\) |
−0.885204 | + | 0.465203i | \(0.845981\pi\) | |||||||
\(678\) | 31911.0 | 1.80757 | ||||||||
\(679\) | 1753.75 | − | 11715.4i | 0.0991205 | − | 0.662144i | ||||
\(680\) | 5826.83 | 0.328601 | ||||||||
\(681\) | −4388.89 | − | 7601.78i | −0.246964 | − | 0.427754i | ||||
\(682\) | −18274.3 | + | 31652.1i | −1.02604 | + | 1.77716i | ||||
\(683\) | −16510.3 | + | 28596.8i | −0.924964 | + | 1.60209i | −0.133346 | + | 0.991070i | \(0.542572\pi\) |
−0.791618 | + | 0.611016i | \(0.790761\pi\) | |||||||
\(684\) | −6314.21 | − | 10936.5i | −0.352968 | − | 0.611358i | ||||
\(685\) | 1462.58 | 0.0815798 | ||||||||
\(686\) | −32335.6 | + | 2521.44i | −1.79968 | + | 0.140334i | ||||
\(687\) | −3143.63 | −0.174581 | ||||||||
\(688\) | −17564.7 | − | 30422.9i | −0.973325 | − | 1.68585i | ||||
\(689\) | 3634.02 | − | 6294.31i | 0.200936 | − | 0.348032i | ||||
\(690\) | 3448.73 | − | 5973.38i | 0.190277 | − | 0.329569i | ||||
\(691\) | −360.088 | − | 623.691i | −0.0198240 | − | 0.0343362i | 0.855943 | − | 0.517070i | \(-0.172977\pi\) |
−0.875767 | + | 0.482734i | \(0.839644\pi\) | |||||||
\(692\) | −11998.0 | −0.659096 | ||||||||
\(693\) | 1005.22 | − | 6715.05i | 0.0551012 | − | 0.368086i | ||||
\(694\) | 50533.5 | 2.76401 | ||||||||
\(695\) | 4182.55 | + | 7244.39i | 0.228278 | + | 0.395389i | ||||
\(696\) | −16449.7 | + | 28491.6i | −0.895866 | + | 1.55169i | ||||
\(697\) | −2822.44 | + | 4888.61i | −0.153382 | + | 0.265666i | ||||
\(698\) | −30207.0 | − | 52320.1i | −1.63804 | − | 2.83717i | ||||
\(699\) | −11610.0 | −0.628224 | ||||||||
\(700\) | 7784.34 | − | 3064.18i | 0.420315 | − | 0.165450i | ||||
\(701\) | 11675.1 | 0.629048 | 0.314524 | − | 0.949249i | \(-0.398155\pi\) | ||||
0.314524 | + | 0.949249i | \(0.398155\pi\) | |||||||
\(702\) | −4888.74 | − | 8467.54i | −0.262840 | − | 0.455252i | ||||
\(703\) | 13781.8 | − | 23870.8i | 0.739390 | − | 1.28066i | ||||
\(704\) | 628.024 | − | 1087.77i | 0.0336215 | − | 0.0582342i | ||||
\(705\) | −1265.78 | − | 2192.40i | −0.0676200 | − | 0.117121i | ||||
\(706\) | 35777.6 | 1.90724 | ||||||||
\(707\) | 9185.61 | + | 7310.17i | 0.488629 | + | 0.388864i | ||||
\(708\) | −1272.71 | −0.0675586 | ||||||||
\(709\) | 13385.9 | + | 23185.0i | 0.709050 | + | 1.22811i | 0.965210 | + | 0.261477i | \(0.0842095\pi\) |
−0.256159 | + | 0.966635i | \(0.582457\pi\) | |||||||
\(710\) | 8073.23 | − | 13983.2i | 0.426736 | − | 0.739129i | ||||
\(711\) | 2343.99 | − | 4059.91i | 0.123638 | − | 0.214147i | ||||
\(712\) | −25799.1 | − | 44685.4i | −1.35796 | − | 2.35205i | ||||
\(713\) | 15826.5 | 0.831288 | ||||||||
\(714\) | −5031.98 | − | 4004.59i | −0.263749 | − | 0.209899i | ||||
\(715\) | −14446.1 | −0.755597 | ||||||||
\(716\) | 3026.43 | + | 5241.92i | 0.157965 | + | 0.273603i | ||||
\(717\) | 9091.15 | − | 15746.3i | 0.473522 | − | 0.820164i | ||||
\(718\) | −7184.72 | + | 12444.3i | −0.373442 | + | 0.646821i | ||||
\(719\) | −17391.7 | − | 30123.4i | −0.902089 | − | 1.56246i | −0.824778 | − | 0.565457i | \(-0.808700\pi\) |
−0.0773114 | − | 0.997007i | \(-0.524634\pi\) | |||||||
\(720\) | 5306.20 | 0.274653 | ||||||||
\(721\) | −6679.22 | + | 2629.16i | −0.345003 | + | 0.135805i | ||||
\(722\) | −4228.11 | −0.217942 | ||||||||
\(723\) | 6276.18 | + | 10870.7i | 0.322840 | + | 0.559176i | ||||
\(724\) | −11072.1 | + | 19177.4i | −0.568357 | + | 0.984422i | ||||
\(725\) | −2666.65 | + | 4618.77i | −0.136603 | + | 0.236603i | ||||
\(726\) | −2514.88 | − | 4355.90i | −0.128562 | − | 0.222676i | ||||
\(727\) | 25368.1 | 1.29415 | 0.647077 | − | 0.762425i | \(-0.275991\pi\) | ||||
0.647077 | + | 0.762425i | \(0.275991\pi\) | |||||||
\(728\) | −9996.84 | + | 66780.8i | −0.508939 | + | 3.39981i | ||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | −11677.7 | − | 20226.3i | −0.592068 | − | 1.02549i | ||||
\(731\) | −3376.94 | + | 5849.02i | −0.170863 | + | 0.295943i | ||||
\(732\) | 23704.5 | − | 41057.4i | 1.19692 | − | 2.07312i | ||||
\(733\) | −15845.8 | − | 27445.7i | −0.798468 | − | 1.38299i | −0.920614 | − | 0.390474i | \(-0.872311\pi\) |
0.122146 | − | 0.992512i | \(-0.461022\pi\) | |||||||
\(734\) | 11997.7 | 0.603327 | ||||||||
\(735\) | −4919.47 | − | 1506.61i | −0.246881 | − | 0.0756086i | ||||
\(736\) | −17183.7 | −0.860596 | ||||||||
\(737\) | −16513.6 | − | 28602.3i | −0.825352 | − | 1.42955i | ||||
\(738\) | −5720.98 | + | 9909.02i | −0.285355 | + | 0.494249i | ||||
\(739\) | 6597.98 | − | 11428.0i | 0.328431 | − | 0.568860i | −0.653770 | − | 0.756694i | \(-0.726813\pi\) |
0.982201 | + | 0.187834i | \(0.0601467\pi\) | |||||||
\(740\) | 16032.5 | + | 27769.2i | 0.796443 | + | 1.37948i | ||||
\(741\) | 16524.1 | 0.819203 | ||||||||
\(742\) | 1434.54 | − | 9582.99i | 0.0709752 | − | 0.474128i | ||||
\(743\) | 8244.34 | 0.407073 | 0.203537 | − | 0.979067i | \(-0.434756\pi\) | ||||
0.203537 | + | 0.979067i | \(0.434756\pi\) | |||||||
\(744\) | 13550.1 | + | 23469.5i | 0.667705 | + | 1.15650i | ||||
\(745\) | −6302.52 | + | 10916.3i | −0.309941 | + | 0.536834i | ||||
\(746\) | 4235.95 | − | 7336.88i | 0.207894 | − | 0.360083i | ||||
\(747\) | 4624.51 | + | 8009.89i | 0.226509 | + | 0.392325i | ||||
\(748\) | −16685.6 | −0.815622 | ||||||||
\(749\) | 2390.76 | − | 941.084i | 0.116631 | − | 0.0459098i | ||||
\(750\) | 1914.64 | 0.0932170 | ||||||||
\(751\) | −15884.9 | − | 27513.4i | −0.771834 | − | 1.33686i | −0.936557 | − | 0.350516i | \(-0.886006\pi\) |
0.164722 | − | 0.986340i | \(-0.447327\pi\) | |||||||
\(752\) | −9950.35 | + | 17234.5i | −0.482516 | + | 0.835742i | ||||
\(753\) | 3947.47 | − | 6837.22i | 0.191041 | − | 0.330893i | ||||
\(754\) | −38626.8 | − | 66903.6i | −1.86566 | − | 3.23141i | ||||
\(755\) | 6896.60 | 0.332441 | ||||||||
\(756\) | −7069.49 | − | 5626.10i | −0.340099 | − | 0.270660i | ||||
\(757\) | −3019.09 | −0.144954 | −0.0724772 | − | 0.997370i | \(-0.523090\pi\) | ||||
−0.0724772 | + | 0.997370i | \(0.523090\pi\) | |||||||
\(758\) | −13601.1 | − | 23557.8i | −0.651734 | − | 1.12884i | ||||
\(759\) | −5503.08 | + | 9531.62i | −0.263174 | + | 0.455831i | ||||
\(760\) | −9980.22 | + | 17286.2i | −0.476343 | + | 0.825050i | ||||
\(761\) | −12048.2 | − | 20868.0i | −0.573910 | − | 0.994041i | −0.996159 | − | 0.0875612i | \(-0.972093\pi\) |
0.422249 | − | 0.906480i | \(-0.361241\pi\) | |||||||
\(762\) | 6618.29 | 0.314640 | ||||||||
\(763\) | 24823.2 | + | 19755.0i | 1.17780 | + | 0.937326i | ||||
\(764\) | −28573.1 | −1.35306 | ||||||||
\(765\) | −510.077 | − | 883.479i | −0.0241070 | − | 0.0417546i | ||||
\(766\) | −15929.2 | + | 27590.1i | −0.751363 | + | 1.30140i | ||||
\(767\) | 832.665 | − | 1442.22i | 0.0391992 | − | 0.0678950i | ||||
\(768\) | 10854.2 | + | 18800.1i | 0.509984 | + | 0.883318i | ||||
\(769\) | 7954.16 | 0.372996 | 0.186498 | − | 0.982455i | \(-0.440286\pi\) | ||||
0.186498 | + | 0.982455i | \(0.440286\pi\) | |||||||
\(770\) | −17921.1 | + | 7054.33i | −0.838741 | + | 0.330156i | ||||
\(771\) | 9866.30 | 0.460864 | ||||||||
\(772\) | 35184.5 | + | 60941.4i | 1.64031 | + | 2.84110i | ||||
\(773\) | −18119.7 | + | 31384.2i | −0.843105 | + | 1.46030i | 0.0441523 | + | 0.999025i | \(0.485941\pi\) |
−0.887257 | + | 0.461275i | \(0.847392\pi\) | |||||||
\(774\) | −6844.92 | + | 11855.7i | −0.317875 | + | 0.550576i | ||||
\(775\) | 2196.61 | + | 3804.64i | 0.101812 | + | 0.176344i | ||||
\(776\) | −32880.0 | −1.52104 | ||||||||
\(777\) | 2919.53 | − | 19503.0i | 0.134798 | − | 0.900473i | ||||
\(778\) | 48428.7 | 2.23169 | ||||||||
\(779\) | −9668.57 | − | 16746.5i | −0.444689 | − | 0.770223i | ||||
\(780\) | −9611.35 | + | 16647.3i | −0.441207 | + | 0.764193i | ||||
\(781\) | −12882.3 | + | 22312.8i | −0.590224 | + | 1.02230i | ||||
\(782\) | 5212.21 | + | 9027.81i | 0.238348 | + | 0.412831i | ||||
\(783\) | 5759.96 | 0.262892 | ||||||||
\(784\) | 9079.23 | + | 39412.8i | 0.413595 | + | 1.79541i | ||||
\(785\) | 9963.65 | 0.453017 | ||||||||
\(786\) | 5035.50 | + | 8721.74i | 0.228512 | + | 0.395794i | ||||
\(787\) | 4842.06 | − | 8386.70i | 0.219315 | − | 0.379865i | −0.735284 | − | 0.677759i | \(-0.762951\pi\) |
0.954599 | + | 0.297895i | \(0.0962844\pi\) | |||||||
\(788\) | −8978.63 | + | 15551.4i | −0.405902 | + | 0.703042i | ||||
\(789\) | 8113.34 | + | 14052.7i | 0.366087 | + | 0.634081i | ||||
\(790\) | −13297.5 | −0.598864 | ||||||||
\(791\) | −5712.27 | + | 38159.0i | −0.256770 | + | 1.71527i | ||||
\(792\) | −18846.2 | −0.845545 | ||||||||
\(793\) | 31017.0 | + | 53723.1i | 1.38896 | + | 2.40575i | ||||
\(794\) | −20149.0 | + | 34899.1i | −0.900581 | + | 1.55985i | ||||
\(795\) | 768.549 | − | 1331.17i | 0.0342863 | − | 0.0593857i | ||||
\(796\) | 27824.0 | + | 48192.6i | 1.23894 | + | 2.14591i | ||||
\(797\) | 6717.98 | 0.298573 | 0.149287 | − | 0.988794i | \(-0.452302\pi\) | ||||
0.149287 | + | 0.988794i | \(0.452302\pi\) | |||||||
\(798\) | 20499.0 | − | 8069.11i | 0.909346 | − | 0.357949i | ||||
\(799\) | 3826.05 | 0.169407 | ||||||||
\(800\) | −2384.97 | − | 4130.90i | −0.105402 | − | 0.182562i | ||||
\(801\) | −4516.88 | + | 7823.46i | −0.199246 | + | 0.345104i | ||||
\(802\) | 31807.7 | − | 55092.5i | 1.40046 | − | 2.42567i | ||||
\(803\) | 18633.8 | + | 32274.8i | 0.818897 | + | 1.41837i | ||||
\(804\) | −43947.7 | −1.92775 | ||||||||
\(805\) | 6525.61 | + | 5193.26i | 0.285711 | + | 0.227377i | ||||
\(806\) | −63636.5 | −2.78102 | ||||||||
\(807\) | −809.683 | − | 1402.41i | −0.0353187 | − | 0.0611738i | ||||
\(808\) | 16292.2 | − | 28218.9i | 0.709353 | − | 1.22863i | ||||
\(809\) | 605.364 | − | 1048.52i | 0.0263083 | − | 0.0455674i | −0.852571 | − | 0.522611i | \(-0.824958\pi\) |
0.878880 | + | 0.477043i | \(0.158291\pi\) | |||||||
\(810\) | −1033.91 | − | 1790.78i | −0.0448491 | − | 0.0776809i | ||||
\(811\) | 34825.1 | 1.50786 | 0.753930 | − | 0.656955i | \(-0.228156\pi\) | ||||
0.753930 | + | 0.656955i | \(0.228156\pi\) | |||||||
\(812\) | −55857.4 | − | 44452.9i | −2.41405 | − | 1.92117i | ||||
\(813\) | 12273.4 | 0.529456 | ||||||||
\(814\) | −36910.0 | − | 63930.0i | −1.58931 | − | 2.75276i | ||||
\(815\) | −4757.36 | + | 8239.99i | −0.204470 | + | 0.354152i | ||||
\(816\) | −4009.73 | + | 6945.06i | −0.172020 | + | 0.297948i | ||||
\(817\) | −11568.1 | − | 20036.5i | −0.495367 | − | 0.858001i | ||||
\(818\) | 17377.9 | 0.742792 | ||||||||
\(819\) | 11000.6 | − | 4330.19i | 0.469342 | − | 0.184749i | ||||
\(820\) | 22495.1 | 0.958003 | ||||||||
\(821\) | −15084.8 | − | 26127.7i | −0.641247 | − | 1.11067i | −0.985155 | − | 0.171669i | \(-0.945084\pi\) |
0.343908 | − | 0.939003i | \(-0.388249\pi\) | |||||||
\(822\) | −2240.25 | + | 3880.22i | −0.0950579 | + | 0.164645i | ||||
\(823\) | 13008.2 | − | 22530.8i | 0.550956 | − | 0.954284i | −0.447250 | − | 0.894409i | \(-0.647597\pi\) |
0.998206 | − | 0.0598746i | \(-0.0190701\pi\) | |||||||
\(824\) | 9961.83 | + | 17254.4i | 0.421161 | + | 0.729472i | ||||
\(825\) | −3055.16 | −0.128930 | ||||||||
\(826\) | 328.696 | − | 2195.75i | 0.0138460 | − | 0.0924940i | ||||
\(827\) | 15602.4 | 0.656045 | 0.328022 | − | 0.944670i | \(-0.393618\pi\) | ||||
0.328022 | + | 0.944670i | \(0.393618\pi\) | |||||||
\(828\) | 7322.70 | + | 12683.3i | 0.307345 | + | 0.532336i | ||||
\(829\) | 9753.00 | − | 16892.7i | 0.408607 | − | 0.707729i | −0.586126 | − | 0.810220i | \(-0.699348\pi\) |
0.994734 | + | 0.102491i | \(0.0326812\pi\) | |||||||
\(830\) | 13117.5 | − | 22720.1i | 0.548570 | − | 0.950152i | ||||
\(831\) | −4637.00 | − | 8031.53i | −0.193569 | − | 0.335271i | ||||
\(832\) | 2186.96 | 0.0911289 | ||||||||
\(833\) | 5689.43 | − | 5300.38i | 0.236647 | − | 0.220465i | ||||
\(834\) | −25625.8 | −1.06397 | ||||||||
\(835\) | 945.459 | + | 1637.58i | 0.0391844 | + | 0.0678693i | ||||
\(836\) | 28579.1 | − | 49500.5i | 1.18233 | − | 2.04786i | ||||
\(837\) | 2372.34 | − | 4109.01i | 0.0979690 | − | 0.169687i | ||||
\(838\) | 3514.86 | + | 6087.91i | 0.144891 | + | 0.250959i | ||||
\(839\) | −12231.2 | −0.503300 | −0.251650 | − | 0.967818i | \(-0.580973\pi\) | ||||
−0.251650 | + | 0.967818i | \(0.580973\pi\) | |||||||
\(840\) | −2114.20 | + | 14123.3i | −0.0868417 | + | 0.580118i | ||||
\(841\) | 21121.6 | 0.866028 | ||||||||
\(842\) | 40226.0 | + | 69673.5i | 1.64641 | + | 2.85167i | ||||
\(843\) | −10823.6 | + | 18747.0i | −0.442212 | + | 0.765933i | ||||
\(844\) | −19104.6 | + | 33090.2i | −0.779157 | + | 1.34954i | ||||
\(845\) | −7083.84 | − | 12269.6i | −0.288392 | − | 0.499510i | ||||
\(846\) | 7755.25 | 0.315167 | ||||||||
\(847\) | 5658.95 | − | 2227.55i | 0.229568 | − | 0.0903654i | ||||
\(848\) | −12083.2 | −0.489314 | ||||||||
\(849\) | −4447.07 | − | 7702.56i | −0.179768 | − | 0.311368i | ||||
\(850\) | −1446.83 | + | 2505.99i | −0.0583836 | + | 0.101123i | ||||
\(851\) | −15983.0 | + | 27683.4i | −0.643820 | + | 1.11513i | ||||
\(852\) | 17141.9 | + | 29690.6i | 0.689286 | + | 1.19388i | ||||
\(853\) | 1234.83 | 0.0495660 | 0.0247830 | − | 0.999693i | \(-0.492111\pi\) | ||||
0.0247830 | + | 0.999693i | \(0.492111\pi\) | |||||||
\(854\) | 64712.4 | + | 51500.0i | 2.59299 | + | 2.06357i | ||||
\(855\) | 3494.64 | 0.139783 | ||||||||
\(856\) | −3565.74 | − | 6176.05i | −0.142377 | − | 0.246604i | ||||
\(857\) | −12050.7 | + | 20872.4i | −0.480331 | + | 0.831958i | −0.999745 | − | 0.0225648i | \(-0.992817\pi\) |
0.519414 | + | 0.854523i | \(0.326150\pi\) | |||||||
\(858\) | 22127.2 | − | 38325.4i | 0.880431 | − | 1.52495i | ||||
\(859\) | −6681.47 | − | 11572.6i | −0.265389 | − | 0.459666i | 0.702277 | − | 0.711904i | \(-0.252167\pi\) |
−0.967665 | + | 0.252238i | \(0.918834\pi\) | |||||||
\(860\) | 26914.5 | 1.06718 | ||||||||
\(861\) | −10825.1 | − | 8614.91i | −0.428476 | − | 0.340993i | ||||
\(862\) | 25955.9 | 1.02559 | ||||||||
\(863\) | 10967.0 | + | 18995.5i | 0.432587 | + | 0.749262i | 0.997095 | − | 0.0761649i | \(-0.0242675\pi\) |
−0.564508 | + | 0.825427i | \(0.690934\pi\) | |||||||
\(864\) | −2575.77 | + | 4461.37i | −0.101423 | + | 0.175670i | ||||
\(865\) | 1660.09 | − | 2875.36i | 0.0652541 | − | 0.113023i | ||||
\(866\) | −11823.4 | − | 20478.7i | −0.463944 | − | 0.803574i | ||||
\(867\) | −13197.2 | −0.516956 | ||||||||
\(868\) | −54717.4 | + | 21538.6i | −2.13966 | + | 0.842243i | ||||
\(869\) | 21218.5 | 0.828296 | ||||||||
\(870\) | −8169.08 | − | 14149.3i | −0.318342 | − | 0.551385i | ||||
\(871\) | 28752.5 | − | 49800.8i | 1.11853 | − | 1.93735i | ||||
\(872\) | 44028.1 | − | 76258.8i | 1.70984 | − | 2.96152i | ||||
\(873\) | 2878.29 | + | 4985.35i | 0.111587 | + | 0.193274i | ||||
\(874\) | −35709.9 | −1.38204 | ||||||||
\(875\) | −342.733 | + | 2289.52i | −0.0132417 | + | 0.0884571i | ||||
\(876\) | 49590.4 | 1.91268 | ||||||||
\(877\) | 385.159 | + | 667.115i | 0.0148300 | + | 0.0256863i | 0.873345 | − | 0.487102i | \(-0.161946\pi\) |
−0.858515 | + | 0.512788i | \(0.828613\pi\) | |||||||
\(878\) | 5970.80 | − | 10341.7i | 0.229504 | − | 0.397513i | ||||
\(879\) | 11886.1 | − | 20587.4i | 0.456097 | − | 0.789984i | ||||
\(880\) | 12008.3 | + | 20799.1i | 0.460001 | + | 0.796746i | ||||
\(881\) | 17887.9 | 0.684064 | 0.342032 | − | 0.939688i | \(-0.388885\pi\) | ||||
0.342032 | + | 0.939688i | \(0.388885\pi\) | |||||||
\(882\) | 11532.3 | − | 10743.7i | 0.440262 | − | 0.410156i | ||||
\(883\) | 583.389 | 0.0222340 | 0.0111170 | − | 0.999938i | \(-0.496461\pi\) | ||||
0.0111170 | + | 0.999938i | \(0.496461\pi\) | |||||||
\(884\) | −14526.0 | − | 25159.8i | −0.552672 | − | 0.957257i | ||||
\(885\) | 176.098 | − | 305.011i | 0.00668866 | − | 0.0115851i | ||||
\(886\) | −30153.0 | + | 52226.5i | −1.14335 | + | 1.98034i | ||||
\(887\) | 21221.9 | + | 36757.4i | 0.803340 | + | 1.39143i | 0.917406 | + | 0.397952i | \(0.130279\pi\) |
−0.114067 | + | 0.993473i | \(0.536388\pi\) | |||||||
\(888\) | −54736.5 | −2.06851 | ||||||||
\(889\) | −1184.72 | + | 7914.14i | −0.0446953 | + | 0.298573i | ||||
\(890\) | 25624.3 | 0.965087 | ||||||||
\(891\) | 1649.78 | + | 2857.51i | 0.0620313 | + | 0.107441i | ||||
\(892\) | −23293.9 | + | 40346.2i | −0.874370 | + | 1.51445i | ||||
\(893\) | −6553.27 | + | 11350.6i | −0.245573 | + | 0.425345i | ||||
\(894\) | −19307.3 | − | 33441.2i | −0.722295 | − | 1.25105i | ||||
\(895\) | −1675.00 | −0.0625575 | ||||||||
\(896\) | −23591.4 | + | 9286.37i | −0.879614 | + | 0.346245i | ||||
\(897\) | −19163.3 | −0.713317 | ||||||||
\(898\) | −24462.2 | − | 42369.8i | −0.909036 | − | 1.57450i | ||||
\(899\) | 18744.3 | − | 32466.1i | 0.695392 | − | 1.20445i | ||||
\(900\) | −2032.68 | + | 3520.70i | −0.0752844 | + | 0.130396i | ||||
\(901\) | 1161.54 | + | 2011.84i | 0.0429483 | + | 0.0743887i | ||||
\(902\) | −51788.1 | −1.91170 | ||||||||
\(903\) | −12951.8 | − | 10307.4i | −0.477307 | − | 0.379854i | ||||
\(904\) | 107096. | 3.94021 | ||||||||
\(905\) | −3063.96 | − | 5306.93i | −0.112541 | − | 0.194926i | ||||
\(906\) | −10563.6 | + | 18296.7i | −0.387365 | + | 0.670935i | ||||
\(907\) | 13858.9 | − | 24004.3i | 0.507362 | − | 0.878777i | −0.492602 | − | 0.870255i | \(-0.663954\pi\) |
0.999964 | − | 0.00852197i | \(-0.00271266\pi\) | |||||||
\(908\) | −26433.2 | − | 45783.6i | −0.966096 | − | 1.67333i | ||||
\(909\) | −5704.82 | −0.208160 | ||||||||
\(910\) | −26238.6 | − | 20881.4i | −0.955827 | − | 0.760674i | ||||
\(911\) | 20446.7 | 0.743609 | 0.371805 | − | 0.928311i | \(-0.378739\pi\) | ||||
0.371805 | + | 0.928311i | \(0.378739\pi\) | |||||||
\(912\) | −13735.8 | − | 23791.0i | −0.498724 | − | 0.863816i | ||||
\(913\) | −20931.3 | + | 36254.0i | −0.758734 | + | 1.31417i | ||||
\(914\) | 16777.2 | − | 29059.0i | 0.607156 | − | 1.05163i | ||||
\(915\) | 6559.71 | + | 11361.8i | 0.237003 | + | 0.410500i | ||||
\(916\) | −18933.3 | −0.682941 | ||||||||
\(917\) | −11330.8 | + | 4460.19i | −0.408044 | + | 0.160620i | ||||
\(918\) | 3125.16 | 0.112359 | ||||||||
\(919\) | −8727.76 | − | 15116.9i | −0.313278 | − | 0.542613i | 0.665792 | − | 0.746137i | \(-0.268094\pi\) |
−0.979070 | + | 0.203524i | \(0.934760\pi\) | |||||||
\(920\) | 11574.2 | − | 20047.2i | 0.414773 | − | 0.718408i | ||||
\(921\) | 6100.50 | − | 10566.4i | 0.218261 | − | 0.378039i | ||||
\(922\) | 10715.8 | + | 18560.4i | 0.382763 | + | 0.662965i | ||||
\(923\) | −44859.9 | −1.59976 | ||||||||
\(924\) | 6054.18 | − | 40443.1i | 0.215550 | − | 1.43991i | ||||
\(925\) | −8873.32 | −0.315409 | ||||||||
\(926\) | 15638.1 | + | 27086.0i | 0.554969 | + | 0.961234i | ||||
\(927\) | 1744.10 | − | 3020.87i | 0.0617949 | − | 0.107032i | ||||
\(928\) | −20351.7 | + | 35250.1i | −0.719909 | + | 1.24692i | ||||
\(929\) | −10374.4 | − | 17969.0i | −0.366387 | − | 0.634600i | 0.622611 | − | 0.782531i | \(-0.286072\pi\) |
−0.988998 | + | 0.147931i | \(0.952739\pi\) | |||||||
\(930\) | −13458.3 | −0.474532 | ||||||||
\(931\) | 5979.55 | + | 25957.1i | 0.210496 | + | 0.913760i | ||||
\(932\) | −69923.8 | −2.45754 | ||||||||
\(933\) | −11478.9 | − | 19882.0i | −0.402788 | − | 0.697650i | ||||
\(934\) | −8240.83 | + | 14273.5i | −0.288702 | + | 0.500047i | ||||
\(935\) | 2308.69 | − | 3998.77i | 0.0807510 | − | 0.139865i | ||||
\(936\) | −16407.0 | − | 28417.8i | −0.572948 | − | 0.992376i | ||||
\(937\) | 12135.5 | 0.423106 | 0.211553 | − | 0.977366i | \(-0.432148\pi\) | ||||
0.211553 | + | 0.977366i | \(0.432148\pi\) | |||||||
\(938\) | 11350.1 | − | 75820.9i | 0.395090 | − | 2.63928i | ||||
\(939\) | 5466.36 | 0.189977 | ||||||||
\(940\) | −7623.48 | − | 13204.3i | −0.264522 | − | 0.458165i | ||||
\(941\) | 12633.0 | − | 21881.0i | 0.437646 | − | 0.758025i | −0.559862 | − | 0.828586i | \(-0.689146\pi\) |
0.997507 | + | 0.0705612i | \(0.0224790\pi\) | |||||||
\(942\) | −15261.4 | + | 26433.6i | −0.527861 | + | 0.914282i | ||||
\(943\) | 11212.8 | + | 19421.2i | 0.387210 | + | 0.670668i | ||||
\(944\) | −2768.62 | −0.0954566 | ||||||||
\(945\) | 2326.48 | − | 915.781i | 0.0800852 | − | 0.0315242i | ||||
\(946\) | −61962.3 | −2.12957 | ||||||||
\(947\) | 21384.4 | + | 37038.8i | 0.733789 | + | 1.27096i | 0.955253 | + | 0.295791i | \(0.0955832\pi\) |
−0.221464 | + | 0.975169i | \(0.571083\pi\) | |||||||
\(948\) | 14117.3 | − | 24451.8i | 0.483657 | − | 0.837719i | ||||
\(949\) | −32444.2 | + | 56195.0i | −1.10978 | + | 1.92220i | ||||
\(950\) | −4956.29 | − | 8584.54i | −0.169267 | − | 0.293178i | ||||
\(951\) | 9446.57 | 0.322110 | ||||||||
\(952\) | −16887.7 | − | 13439.7i | −0.574931 | − | 0.457546i | ||||
\(953\) | −25855.5 | −0.878846 | −0.439423 | − | 0.898280i | \(-0.644817\pi\) | ||||
−0.439423 | + | 0.898280i | \(0.644817\pi\) | |||||||
\(954\) | 2354.39 | + | 4077.93i | 0.0799017 | + | 0.138394i | ||||
\(955\) | 3953.49 | − | 6847.65i | 0.133960 | − | 0.232026i | ||||
\(956\) | 54753.7 | − | 94836.2i | 1.85237 | − | 3.20839i | ||||
\(957\) | 13035.3 | + | 22577.7i | 0.440303 | + | 0.762627i | ||||
\(958\) | 15962.0 | 0.538318 | ||||||||
\(959\) | −4238.94 | − | 3373.47i | −0.142735 | − | 0.113592i | ||||
\(960\) | 462.515 | 0.0155496 | ||||||||
\(961\) | −544.820 | − | 943.655i | −0.0182881 | − | 0.0316758i | ||||
\(962\) | 64265.7 | − | 111311.i | 2.15385 | − | 3.73059i | ||||
\(963\) | −624.285 | + | 1081.29i | −0.0208902 | + | 0.0361830i | ||||
\(964\) | 37799.8 | + | 65471.2i | 1.26292 | + | 2.18743i | ||||
\(965\) | −19473.1 | −0.649598 | ||||||||
\(966\) | −23773.1 | + | 9357.88i | −0.791808 | + | 0.311682i | ||||
\(967\) | −20336.0 | −0.676278 | −0.338139 | − | 0.941096i | \(-0.609797\pi\) | ||||
−0.338139 | + | 0.941096i | \(0.609797\pi\) | |||||||
\(968\) | −8440.13 | − | 14618.7i | −0.280244 | − | 0.485397i | ||||
\(969\) | −2640.80 | + | 4573.99i | −0.0875486 | + | 0.151639i | ||||
\(970\) | 8164.28 | − | 14141.0i | 0.270247 | − | 0.468081i | ||||
\(971\) | 15561.9 | + | 26953.9i | 0.514319 | + | 0.890827i | 0.999862 | + | 0.0166139i | \(0.00528862\pi\) |
−0.485543 | + | 0.874213i | \(0.661378\pi\) | |||||||
\(972\) | 4390.58 | 0.144885 | ||||||||
\(973\) | 4587.20 | − | 30643.3i | 0.151140 | − | 1.00964i | ||||
\(974\) | −4437.05 | −0.145967 | ||||||||
\(975\) | −2659.73 | − | 4606.80i | −0.0873638 | − | 0.151319i | ||||
\(976\) | 51566.1 | − | 89315.1i | 1.69118 | − | 2.92921i | ||||
\(977\) | −15658.7 | + | 27121.6i | −0.512758 | + | 0.888123i | 0.487132 | + | 0.873328i | \(0.338043\pi\) |
−0.999891 | + | 0.0147951i | \(0.995290\pi\) | |||||||
\(978\) | −14573.8 | − | 25242.6i | −0.476502 | − | 0.825326i | ||||
\(979\) | −40888.2 | −1.33482 | ||||||||
\(980\) | −29628.7 | − | 9073.96i | −0.965769 | − | 0.295772i | ||||
\(981\) | −15416.7 | −0.501752 | ||||||||
\(982\) | −16894.0 | − | 29261.3i | −0.548992 | − | 0.950882i | ||||
\(983\) | 2001.06 | − | 3465.94i | 0.0649277 | − | 0.112458i | −0.831734 | − | 0.555174i | \(-0.812652\pi\) |
0.896662 | + | 0.442716i | \(0.145985\pi\) | |||||||
\(984\) | −19200.1 | + | 33255.5i | −0.622028 | + | 1.07738i | ||||
\(985\) | −2484.64 | − | 4303.53i | −0.0803729 | − | 0.139210i | ||||
\(986\) | 24692.5 | 0.797535 | ||||||||
\(987\) | −1388.24 | + | 9273.70i | −0.0447702 | + | 0.299073i | ||||
\(988\) | 99520.7 | 3.20463 | ||||||||
\(989\) | 13415.7 | + | 23236.6i | 0.431338 | + | 0.747100i | ||||
\(990\) | 4679.62 | − | 8105.34i | 0.150230 | − | 0.260207i | ||||
\(991\) | −5021.23 | + | 8697.02i | −0.160953 | + | 0.278779i | −0.935211 | − | 0.354091i | \(-0.884790\pi\) |
0.774258 | + | 0.632871i | \(0.218123\pi\) | |||||||
\(992\) | 16764.4 | + | 29036.7i | 0.536561 | + | 0.929351i | ||||
\(993\) | −17568.4 | −0.561445 | ||||||||
\(994\) | −55651.0 | + | 21906.1i | −1.77580 | + | 0.699013i | ||||
\(995\) | −15399.4 | −0.490647 | ||||||||
\(996\) | 27852.3 | + | 48241.6i | 0.886078 | + | 1.53473i | ||||
\(997\) | 4703.72 | − | 8147.08i | 0.149417 | − | 0.258797i | −0.781595 | − | 0.623786i | \(-0.785594\pi\) |
0.931012 | + | 0.364989i | \(0.118927\pi\) | |||||||
\(998\) | 2267.33 | − | 3927.13i | 0.0719148 | − | 0.124560i | ||||
\(999\) | 4791.59 | + | 8299.28i | 0.151751 | + | 0.262840i |
(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 | 105.4.i.d.46.1 | yes | 10 | |
3.2 | odd | 2 | 315.4.j.h.46.5 | 10 | |||
7.2 | even | 3 | inner | 105.4.i.d.16.1 | ✓ | 10 | |
7.3 | odd | 6 | 735.4.a.z.1.5 | 5 | |||
7.4 | even | 3 | 735.4.a.ba.1.5 | 5 | |||
21.2 | odd | 6 | 315.4.j.h.226.5 | 10 | |||
21.11 | odd | 6 | 2205.4.a.br.1.1 | 5 | |||
21.17 | even | 6 | 2205.4.a.bs.1.1 | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
105.4.i.d.16.1 | ✓ | 10 | 7.2 | even | 3 | inner | |
105.4.i.d.46.1 | yes | 10 | 1.1 | even | 1 | trivial | |
315.4.j.h.46.5 | 10 | 3.2 | odd | 2 | |||
315.4.j.h.226.5 | 10 | 21.2 | odd | 6 | |||
735.4.a.z.1.5 | 5 | 7.3 | odd | 6 | |||
735.4.a.ba.1.5 | 5 | 7.4 | even | 3 | |||
2205.4.a.br.1.1 | 5 | 21.11 | odd | 6 | |||
2205.4.a.bs.1.1 | 5 | 21.17 | even | 6 |