Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [177,4,Mod(176,177)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(177, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("177.176");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 177 = 3 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 177.d (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(10.4433380710\) |
Analytic rank: | \(0\) |
Dimension: | \(52\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 176.15 | ||
Character | \(\chi\) | \(=\) | 177.176 |
Dual form | 177.4.d.c.176.16 |
$q$-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 \(\left(\mathbb{Z}/177\mathbb{Z}\right)^\times\).
\(n\) | \(61\) | \(119\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.68371 | −0.948833 | −0.474417 | − | 0.880300i | \(-0.657341\pi\) | ||||
−0.474417 | + | 0.880300i | \(0.657341\pi\) | |||||||
\(3\) | −3.19645 | − | 4.09667i | −0.615157 | − | 0.788405i | ||||
\(4\) | −0.797724 | −0.0997154 | ||||||||
\(5\) | − | 15.8157i | − | 1.41460i | −0.706915 | − | 0.707298i | \(-0.749914\pi\) | ||
0.706915 | − | 0.707298i | \(-0.250086\pi\) | |||||||
\(6\) | 8.57832 | + | 10.9943i | 0.583681 | + | 0.748065i | ||||
\(7\) | 25.4256 | 1.37285 | 0.686427 | − | 0.727198i | \(-0.259178\pi\) | ||||
0.686427 | + | 0.727198i | \(0.259178\pi\) | |||||||
\(8\) | 23.6105 | 1.04345 | ||||||||
\(9\) | −6.56545 | + | 26.1896i | −0.243165 | + | 0.969985i | ||||
\(10\) | 42.4446i | 1.34222i | ||||||||
\(11\) | 64.0388 | 1.75531 | 0.877656 | − | 0.479291i | \(-0.159106\pi\) | ||||
0.877656 | + | 0.479291i | \(0.159106\pi\) | |||||||
\(12\) | 2.54988 | + | 3.26801i | 0.0613406 | + | 0.0786162i | ||||
\(13\) | − | 26.7287i | − | 0.570247i | −0.958491 | − | 0.285124i | \(-0.907965\pi\) | ||
0.958491 | − | 0.285124i | \(-0.0920346\pi\) | |||||||
\(14\) | −68.2349 | −1.30261 | ||||||||
\(15\) | −64.7916 | + | 50.5539i | −1.11527 | + | 0.870198i | ||||
\(16\) | −56.9818 | −0.890341 | ||||||||
\(17\) | − | 54.3878i | − | 0.775940i | −0.921672 | − | 0.387970i | \(-0.873176\pi\) | ||
0.921672 | − | 0.387970i | \(-0.126824\pi\) | |||||||
\(18\) | 17.6197 | − | 70.2852i | 0.230723 | − | 0.920354i | ||||
\(19\) | 47.4395 | 0.572809 | 0.286405 | − | 0.958109i | \(-0.407540\pi\) | ||||
0.286405 | + | 0.958109i | \(0.407540\pi\) | |||||||
\(20\) | 12.6165i | 0.141057i | ||||||||
\(21\) | −81.2717 | − | 104.160i | −0.844521 | − | 1.08237i | ||||
\(22\) | −171.861 | −1.66550 | ||||||||
\(23\) | 174.401 | 1.58109 | 0.790546 | − | 0.612402i | \(-0.209797\pi\) | ||||
0.790546 | + | 0.612402i | \(0.209797\pi\) | |||||||
\(24\) | −75.4697 | − | 96.7245i | −0.641883 | − | 0.822659i | ||||
\(25\) | −125.135 | −1.00108 | ||||||||
\(26\) | 71.7320i | 0.541069i | ||||||||
\(27\) | 128.276 | − | 56.8171i | 0.914325 | − | 0.404980i | ||||
\(28\) | −20.2826 | −0.136895 | ||||||||
\(29\) | − | 169.829i | − | 1.08746i | −0.839259 | − | 0.543732i | \(-0.817011\pi\) | ||
0.839259 | − | 0.543732i | \(-0.182989\pi\) | |||||||
\(30\) | 173.882 | − | 135.672i | 1.05821 | − | 0.825673i | ||||
\(31\) | 217.458i | 1.25989i | 0.776639 | + | 0.629945i | \(0.216923\pi\) | ||||
−0.776639 | + | 0.629945i | \(0.783077\pi\) | |||||||
\(32\) | −35.9615 | −0.198661 | ||||||||
\(33\) | −204.697 | − | 262.346i | −1.07979 | − | 1.38390i | ||||
\(34\) | 145.961i | 0.736238i | ||||||||
\(35\) | − | 402.123i | − | 1.94204i | ||||||
\(36\) | 5.23742 | − | 20.8921i | 0.0242473 | − | 0.0967225i | ||||
\(37\) | − | 122.447i | − | 0.544057i | −0.962289 | − | 0.272028i | \(-0.912306\pi\) | ||
0.962289 | − | 0.272028i | \(-0.0876944\pi\) | |||||||
\(38\) | −127.314 | −0.543500 | ||||||||
\(39\) | −109.499 | + | 85.4369i | −0.449586 | + | 0.350791i | ||||
\(40\) | − | 373.416i | − | 1.47606i | ||||||
\(41\) | 368.046i | 1.40193i | 0.713195 | + | 0.700966i | \(0.247247\pi\) | ||||
−0.713195 | + | 0.700966i | \(0.752753\pi\) | |||||||
\(42\) | 218.109 | + | 279.536i | 0.801309 | + | 1.02698i | ||||
\(43\) | 3.01728i | 0.0107007i | 0.999986 | + | 0.00535035i | \(0.00170308\pi\) | ||||
−0.999986 | + | 0.00535035i | \(0.998297\pi\) | |||||||
\(44\) | −51.0853 | −0.175032 | ||||||||
\(45\) | 414.206 | + | 103.837i | 1.37214 | + | 0.343980i | ||||
\(46\) | −468.041 | −1.50019 | ||||||||
\(47\) | −314.192 | −0.975098 | −0.487549 | − | 0.873096i | \(-0.662109\pi\) | ||||
−0.487549 | + | 0.873096i | \(0.662109\pi\) | |||||||
\(48\) | 182.139 | + | 233.436i | 0.547699 | + | 0.701950i | ||||
\(49\) | 303.463 | 0.884731 | ||||||||
\(50\) | 335.826 | 0.949860 | ||||||||
\(51\) | −222.809 | + | 173.848i | −0.611755 | + | 0.477325i | ||||
\(52\) | 21.3221i | 0.0568624i | ||||||||
\(53\) | − | 468.533i | − | 1.21430i | −0.794587 | − | 0.607150i | \(-0.792313\pi\) | ||
0.794587 | − | 0.607150i | \(-0.207687\pi\) | |||||||
\(54\) | −344.256 | + | 152.480i | −0.867542 | + | 0.384259i | ||||
\(55\) | − | 1012.82i | − | 2.48306i | ||||||
\(56\) | 600.312 | 1.43250 | ||||||||
\(57\) | −151.638 | − | 194.344i | −0.352367 | − | 0.451606i | ||||
\(58\) | 455.771i | 1.03182i | ||||||||
\(59\) | −224.948 | − | 393.417i | −0.496369 | − | 0.868112i | ||||
\(60\) | 51.6858 | − | 40.3281i | 0.111210 | − | 0.0867722i | ||||
\(61\) | 558.899i | 1.17311i | 0.809910 | + | 0.586554i | \(0.199516\pi\) | ||||
−0.809910 | + | 0.586554i | \(0.800484\pi\) | |||||||
\(62\) | − | 583.593i | − | 1.19543i | ||||||
\(63\) | −166.931 | + | 665.887i | −0.333830 | + | 1.33165i | ||||
\(64\) | 552.365 | 1.07884 | ||||||||
\(65\) | −422.733 | −0.806669 | ||||||||
\(66\) | 549.346 | + | 704.060i | 1.02454 | + | 1.31309i | ||||
\(67\) | 284.086i | 0.518009i | 0.965876 | + | 0.259004i | \(0.0833944\pi\) | ||||
−0.965876 | + | 0.259004i | \(0.916606\pi\) | |||||||
\(68\) | 43.3865i | 0.0773732i | ||||||||
\(69\) | −557.464 | − | 714.464i | −0.972619 | − | 1.24654i | ||||
\(70\) | 1079.18i | 1.84267i | ||||||||
\(71\) | 279.692i | 0.467512i | 0.972295 | + | 0.233756i | \(0.0751017\pi\) | ||||
−0.972295 | + | 0.233756i | \(0.924898\pi\) | |||||||
\(72\) | −155.014 | + | 618.349i | −0.253730 | + | 1.01213i | ||||
\(73\) | 877.906i | 1.40755i | 0.710423 | + | 0.703775i | \(0.248504\pi\) | ||||
−0.710423 | + | 0.703775i | \(0.751496\pi\) | |||||||
\(74\) | 328.611i | 0.516219i | ||||||||
\(75\) | 399.988 | + | 512.638i | 0.615822 | + | 0.789258i | ||||
\(76\) | −37.8436 | −0.0571179 | ||||||||
\(77\) | 1628.23 | 2.40979 | ||||||||
\(78\) | 293.863 | − | 229.288i | 0.426582 | − | 0.332842i | ||||
\(79\) | −63.0858 | −0.0898445 | −0.0449222 | − | 0.998990i | \(-0.514304\pi\) | ||||
−0.0449222 | + | 0.998990i | \(0.514304\pi\) | |||||||
\(80\) | 901.206i | 1.25947i | ||||||||
\(81\) | −642.790 | − | 343.893i | −0.881742 | − | 0.471733i | ||||
\(82\) | − | 987.728i | − | 1.33020i | ||||||
\(83\) | 941.269 | 1.24479 | 0.622396 | − | 0.782703i | \(-0.286159\pi\) | ||||
0.622396 | + | 0.782703i | \(0.286159\pi\) | |||||||
\(84\) | 64.8323 | + | 83.0913i | 0.0842118 | + | 0.107929i | ||||
\(85\) | −860.180 | −1.09764 | ||||||||
\(86\) | − | 8.09748i | − | 0.0101532i | ||||||
\(87\) | −695.733 | + | 542.849i | −0.857361 | + | 0.668960i | ||||
\(88\) | 1511.99 | 1.83157 | ||||||||
\(89\) | −199.336 | −0.237411 | −0.118706 | − | 0.992930i | \(-0.537874\pi\) | ||||
−0.118706 | + | 0.992930i | \(0.537874\pi\) | |||||||
\(90\) | −1111.61 | − | 278.668i | −1.30193 | − | 0.326380i | ||||
\(91\) | − | 679.594i | − | 0.782867i | ||||||
\(92\) | −139.124 | −0.157659 | ||||||||
\(93\) | 890.854 | − | 695.093i | 0.993304 | − | 0.775030i | ||||
\(94\) | 843.199 | 0.925206 | ||||||||
\(95\) | − | 750.288i | − | 0.810294i | ||||||
\(96\) | 114.949 | + | 147.322i | 0.122208 | + | 0.156625i | ||||
\(97\) | − | 432.568i | − | 0.452790i | −0.974036 | − | 0.226395i | \(-0.927306\pi\) | ||
0.974036 | − | 0.226395i | \(-0.0726939\pi\) | |||||||
\(98\) | −814.404 | −0.839462 | ||||||||
\(99\) | −420.444 | + | 1677.15i | −0.426830 | + | 1.70263i | ||||
\(100\) | 99.8234 | 0.0998234 | ||||||||
\(101\) | −1768.19 | −1.74200 | −0.870999 | − | 0.491285i | \(-0.836528\pi\) | ||||
−0.870999 | + | 0.491285i | \(0.836528\pi\) | |||||||
\(102\) | 597.954 | − | 466.556i | 0.580454 | − | 0.452902i | ||||
\(103\) | 947.121i | 0.906044i | 0.891499 | + | 0.453022i | \(0.149654\pi\) | ||||
−0.891499 | + | 0.453022i | \(0.850346\pi\) | |||||||
\(104\) | − | 631.078i | − | 0.595022i | ||||||
\(105\) | −1647.37 | + | 1285.37i | −1.53111 | + | 1.19466i | ||||
\(106\) | 1257.40i | 1.15217i | ||||||||
\(107\) | − | 1078.46i | − | 0.974379i | −0.873296 | − | 0.487190i | \(-0.838022\pi\) | ||
0.873296 | − | 0.487190i | \(-0.161978\pi\) | |||||||
\(108\) | −102.329 | + | 45.3244i | −0.0911724 | + | 0.0403828i | ||||
\(109\) | − | 1042.51i | − | 0.916096i | −0.888927 | − | 0.458048i | \(-0.848549\pi\) | ||
0.888927 | − | 0.458048i | \(-0.151451\pi\) | |||||||
\(110\) | 2718.10i | 2.35601i | ||||||||
\(111\) | −501.624 | + | 391.394i | −0.428937 | + | 0.334680i | ||||
\(112\) | −1448.80 | −1.22231 | ||||||||
\(113\) | 733.402 | 0.610555 | 0.305277 | − | 0.952263i | \(-0.401251\pi\) | ||||
0.305277 | + | 0.952263i | \(0.401251\pi\) | |||||||
\(114\) | 406.952 | + | 521.563i | 0.334338 | + | 0.428498i | ||||
\(115\) | − | 2758.27i | − | 2.23661i | ||||||
\(116\) | 135.476i | 0.108437i | ||||||||
\(117\) | 700.014 | + | 175.486i | 0.553131 | + | 0.138664i | ||||
\(118\) | 603.695 | + | 1055.82i | 0.470972 | + | 0.823693i | ||||
\(119\) | − | 1382.84i | − | 1.06525i | ||||||
\(120\) | −1529.76 | + | 1193.60i | −1.16373 | + | 0.908005i | ||||
\(121\) | 2769.97 | 2.08112 | ||||||||
\(122\) | − | 1499.92i | − | 1.11308i | ||||||
\(123\) | 1507.77 | − | 1176.44i | 1.10529 | − | 0.862407i | ||||
\(124\) | − | 173.471i | − | 0.125631i | ||||||
\(125\) | 2.14016i | 0.00153137i | ||||||||
\(126\) | 447.993 | − | 1787.04i | 0.316749 | − | 1.26351i | ||||
\(127\) | −365.016 | −0.255039 | −0.127520 | − | 0.991836i | \(-0.540702\pi\) | ||||
−0.127520 | + | 0.991836i | \(0.540702\pi\) | |||||||
\(128\) | −1194.69 | −0.824976 | ||||||||
\(129\) | 12.3608 | − | 9.64457i | 0.00843649 | − | 0.00658261i | ||||
\(130\) | 1134.49 | 0.765395 | ||||||||
\(131\) | 263.810 | 0.175948 | 0.0879741 | − | 0.996123i | \(-0.471961\pi\) | ||||
0.0879741 | + | 0.996123i | \(0.471961\pi\) | |||||||
\(132\) | 163.291 | + | 209.280i | 0.107672 | + | 0.137996i | ||||
\(133\) | 1206.18 | 0.786384 | ||||||||
\(134\) | − | 762.403i | − | 0.491504i | ||||||
\(135\) | −898.601 | − | 2028.78i | −0.572883 | − | 1.29340i | ||||
\(136\) | − | 1284.12i | − | 0.809652i | ||||||
\(137\) | 1218.37i | 0.759799i | 0.925028 | + | 0.379900i | \(0.124041\pi\) | ||||
−0.925028 | + | 0.379900i | \(0.875959\pi\) | |||||||
\(138\) | 1496.07 | + | 1917.41i | 0.922854 | + | 1.18276i | ||||
\(139\) | −1137.74 | −0.694256 | −0.347128 | − | 0.937818i | \(-0.612843\pi\) | ||||
−0.347128 | + | 0.937818i | \(0.612843\pi\) | |||||||
\(140\) | 320.783i | 0.193651i | ||||||||
\(141\) | 1004.30 | + | 1287.14i | 0.599838 | + | 0.768772i | ||||
\(142\) | − | 750.612i | − | 0.443591i | ||||||
\(143\) | − | 1711.68i | − | 1.00096i | ||||||
\(144\) | 374.112 | − | 1492.33i | 0.216500 | − | 0.863618i | ||||
\(145\) | −2685.96 | −1.53832 | ||||||||
\(146\) | − | 2356.04i | − | 1.33553i | ||||||
\(147\) | −970.002 | − | 1243.19i | −0.544248 | − | 0.697526i | ||||
\(148\) | 97.6785i | 0.0542509i | ||||||||
\(149\) | −991.213 | −0.544989 | −0.272494 | − | 0.962157i | \(-0.587849\pi\) | ||||
−0.272494 | + | 0.962157i | \(0.587849\pi\) | |||||||
\(150\) | −1073.45 | − | 1375.77i | −0.584313 | − | 0.748875i | ||||
\(151\) | − | 3527.16i | − | 1.90090i | −0.310874 | − | 0.950451i | \(-0.600622\pi\) | ||
0.310874 | − | 0.950451i | \(-0.399378\pi\) | |||||||
\(152\) | 1120.07 | 0.597696 | ||||||||
\(153\) | 1424.40 | + | 357.081i | 0.752650 | + | 0.188681i | ||||
\(154\) | −4369.68 | −2.28649 | ||||||||
\(155\) | 3439.24 | 1.78224 | ||||||||
\(156\) | 87.3498 | − | 68.1551i | 0.0448306 | − | 0.0349793i | ||||
\(157\) | 1442.44i | 0.733241i | 0.930371 | + | 0.366621i | \(0.119485\pi\) | ||||
−0.930371 | + | 0.366621i | \(0.880515\pi\) | |||||||
\(158\) | 169.304 | 0.0852474 | ||||||||
\(159\) | −1919.43 | + | 1497.64i | −0.957361 | + | 0.746985i | ||||
\(160\) | 568.755i | 0.281025i | ||||||||
\(161\) | 4434.26 | 2.17061 | ||||||||
\(162\) | 1725.06 | + | 922.908i | 0.836626 | + | 0.447596i | ||||
\(163\) | −2181.89 | −1.04846 | −0.524229 | − | 0.851577i | \(-0.675646\pi\) | ||||
−0.524229 | + | 0.851577i | \(0.675646\pi\) | |||||||
\(164\) | − | 293.599i | − | 0.139794i | ||||||
\(165\) | −4149.18 | + | 3237.41i | −1.95766 | + | 1.52747i | ||||
\(166\) | −2526.09 | −1.18110 | ||||||||
\(167\) | 2121.08i | 0.982840i | 0.870923 | + | 0.491420i | \(0.163522\pi\) | ||||
−0.870923 | + | 0.491420i | \(0.836478\pi\) | |||||||
\(168\) | −1918.86 | − | 2459.28i | −0.881212 | − | 1.12939i | ||||
\(169\) | 1482.58 | 0.674818 | ||||||||
\(170\) | 2308.47 | 1.04148 | ||||||||
\(171\) | −311.462 | + | 1242.42i | −0.139287 | + | 0.555616i | ||||
\(172\) | − | 2.40695i | − | 0.00106703i | ||||||
\(173\) | −3125.58 | −1.37360 | −0.686801 | − | 0.726845i | \(-0.740986\pi\) | ||||
−0.686801 | + | 0.726845i | \(0.740986\pi\) | |||||||
\(174\) | 1867.14 | − | 1456.85i | 0.813493 | − | 0.634732i | ||||
\(175\) | −3181.64 | −1.37434 | ||||||||
\(176\) | −3649.05 | −1.56283 | ||||||||
\(177\) | −892.667 | + | 2179.08i | −0.379079 | + | 0.925364i | ||||
\(178\) | 534.959 | 0.225263 | ||||||||
\(179\) | −509.207 | −0.212625 | −0.106313 | − | 0.994333i | \(-0.533904\pi\) | ||||
−0.106313 | + | 0.994333i | \(0.533904\pi\) | |||||||
\(180\) | −330.422 | − | 82.8332i | −0.136823 | − | 0.0343001i | ||||
\(181\) | 454.608 | 0.186689 | 0.0933445 | − | 0.995634i | \(-0.470244\pi\) | ||||
0.0933445 | + | 0.995634i | \(0.470244\pi\) | |||||||
\(182\) | 1823.83i | 0.742810i | ||||||||
\(183\) | 2289.62 | − | 1786.49i | 0.924885 | − | 0.721645i | ||||
\(184\) | 4117.70 | 1.64979 | ||||||||
\(185\) | −1936.57 | −0.769621 | ||||||||
\(186\) | −2390.79 | + | 1865.43i | −0.942480 | + | 0.735374i | ||||
\(187\) | − | 3482.93i | − | 1.36202i | ||||||
\(188\) | 250.638 | 0.0972324 | ||||||||
\(189\) | 3261.51 | − | 1444.61i | 1.25524 | − | 0.555979i | ||||
\(190\) | 2013.55i | 0.768833i | ||||||||
\(191\) | 162.666 | 0.0616234 | 0.0308117 | − | 0.999525i | \(-0.490191\pi\) | ||||
0.0308117 | + | 0.999525i | \(0.490191\pi\) | |||||||
\(192\) | −1765.61 | − | 2262.86i | −0.663654 | − | 0.850561i | ||||
\(193\) | −2139.02 | −0.797773 | −0.398887 | − | 0.917000i | \(-0.630603\pi\) | ||||
−0.398887 | + | 0.917000i | \(0.630603\pi\) | |||||||
\(194\) | 1160.88i | 0.429622i | ||||||||
\(195\) | 1351.24 | + | 1731.80i | 0.496228 | + | 0.635982i | ||||
\(196\) | −242.079 | −0.0882213 | ||||||||
\(197\) | 5343.19i | 1.93242i | 0.257755 | + | 0.966210i | \(0.417017\pi\) | ||||
−0.257755 | + | 0.966210i | \(0.582983\pi\) | |||||||
\(198\) | 1128.35 | − | 4500.98i | 0.404991 | − | 1.61551i | ||||
\(199\) | −3654.95 | −1.30197 | −0.650987 | − | 0.759089i | \(-0.725645\pi\) | ||||
−0.650987 | + | 0.759089i | \(0.725645\pi\) | |||||||
\(200\) | −2954.51 | −1.04458 | ||||||||
\(201\) | 1163.81 | − | 908.065i | 0.408401 | − | 0.318657i | ||||
\(202\) | 4745.31 | 1.65287 | ||||||||
\(203\) | − | 4318.01i | − | 1.49293i | ||||||
\(204\) | 177.740 | − | 138.682i | 0.0610014 | − | 0.0475967i | ||||
\(205\) | 5820.90 | 1.98317 | ||||||||
\(206\) | − | 2541.79i | − | 0.859685i | ||||||
\(207\) | −1145.02 | + | 4567.49i | −0.384466 | + | 1.53364i | ||||
\(208\) | 1523.05i | 0.507715i | ||||||||
\(209\) | 3037.97 | 1.00546 | ||||||||
\(210\) | 4421.05 | − | 3449.54i | 1.45277 | − | 1.13353i | ||||
\(211\) | 3655.96i | 1.19283i | 0.802677 | + | 0.596415i | \(0.203409\pi\) | ||||
−0.802677 | + | 0.596415i | \(0.796591\pi\) | |||||||
\(212\) | 373.760i | 0.121085i | ||||||||
\(213\) | 1145.81 | − | 894.022i | 0.368589 | − | 0.287593i | ||||
\(214\) | 2894.27i | 0.924524i | ||||||||
\(215\) | 47.7202 | 0.0151372 | ||||||||
\(216\) | 3028.67 | − | 1341.48i | 0.954050 | − | 0.422575i | ||||
\(217\) | 5529.01i | 1.72965i | ||||||||
\(218\) | 2797.79i | 0.869222i | ||||||||
\(219\) | 3596.49 | − | 2806.18i | 1.10972 | − | 0.865864i | ||||
\(220\) | 807.948i | 0.247599i | ||||||||
\(221\) | −1453.72 | −0.442478 | ||||||||
\(222\) | 1346.21 | − | 1050.39i | 0.406990 | − | 0.317556i | ||||
\(223\) | 111.332 | 0.0334319 | 0.0167160 | − | 0.999860i | \(-0.494679\pi\) | ||||
0.0167160 | + | 0.999860i | \(0.494679\pi\) | |||||||
\(224\) | −914.344 | −0.272733 | ||||||||
\(225\) | 821.570 | − | 3277.24i | 0.243428 | − | 0.971035i | ||||
\(226\) | −1968.24 | −0.579315 | ||||||||
\(227\) | 1122.58 | 0.328229 | 0.164115 | − | 0.986441i | \(-0.447523\pi\) | ||||
0.164115 | + | 0.986441i | \(0.447523\pi\) | |||||||
\(228\) | 120.965 | + | 155.033i | 0.0351365 | + | 0.0450320i | ||||
\(229\) | 113.487i | 0.0327485i | 0.999866 | + | 0.0163743i | \(0.00521232\pi\) | ||||
−0.999866 | + | 0.0163743i | \(0.994788\pi\) | |||||||
\(230\) | 7402.38i | 2.12217i | ||||||||
\(231\) | −5204.54 | − | 6670.31i | −1.48240 | − | 1.89989i | ||||
\(232\) | − | 4009.74i | − | 1.13471i | ||||||
\(233\) | 704.563 | 0.198101 | 0.0990503 | − | 0.995082i | \(-0.468420\pi\) | ||||
0.0990503 | + | 0.995082i | \(0.468420\pi\) | |||||||
\(234\) | −1878.63 | − | 470.953i | −0.524829 | − | 0.131569i | ||||
\(235\) | 4969.16i | 1.37937i | ||||||||
\(236\) | 179.447 | + | 313.838i | 0.0494957 | + | 0.0865641i | ||||
\(237\) | 201.651 | + | 258.442i | 0.0552684 | + | 0.0708338i | ||||
\(238\) | 3711.15i | 1.01075i | ||||||||
\(239\) | 5082.40i | 1.37554i | 0.725930 | + | 0.687768i | \(0.241409\pi\) | ||||
−0.725930 | + | 0.687768i | \(0.758591\pi\) | |||||||
\(240\) | 3691.95 | − | 2880.66i | 0.992975 | − | 0.774773i | ||||
\(241\) | 3832.06 | 1.02425 | 0.512126 | − | 0.858910i | \(-0.328858\pi\) | ||||
0.512126 | + | 0.858910i | \(0.328858\pi\) | |||||||
\(242\) | −7433.79 | −1.97464 | ||||||||
\(243\) | 645.826 | + | 3732.53i | 0.170493 | + | 0.985359i | ||||
\(244\) | − | 445.847i | − | 0.116977i | ||||||
\(245\) | − | 4799.46i | − | 1.25154i | ||||||
\(246\) | −4046.40 | + | 3157.22i | −1.04874 | + | 0.818281i | ||||
\(247\) | − | 1268.00i | − | 0.326643i | ||||||
\(248\) | 5134.29i | 1.31463i | ||||||||
\(249\) | −3008.72 | − | 3856.07i | −0.765742 | − | 0.981400i | ||||
\(250\) | − | 5.74355i | − | 0.00145302i | ||||||
\(251\) | − | 2141.56i | − | 0.538542i | −0.963064 | − | 0.269271i | \(-0.913217\pi\) | ||
0.963064 | − | 0.269271i | \(-0.0867828\pi\) | |||||||
\(252\) | 133.165 | − | 531.194i | 0.0332880 | − | 0.132786i | ||||
\(253\) | 11168.4 | 2.77531 | ||||||||
\(254\) | 979.596 | 0.241990 | ||||||||
\(255\) | 2749.52 | + | 3523.87i | 0.675222 | + | 0.865387i | ||||
\(256\) | −1212.72 | −0.296073 | ||||||||
\(257\) | − | 2229.18i | − | 0.541059i | −0.962712 | − | 0.270530i | \(-0.912801\pi\) | ||
0.962712 | − | 0.270530i | \(-0.0871988\pi\) | |||||||
\(258\) | −33.1727 | + | 25.8832i | −0.00800482 | + | 0.00624580i | ||||
\(259\) | − | 3113.28i | − | 0.746911i | ||||||
\(260\) | 337.224 | 0.0804374 | ||||||||
\(261\) | 4447.75 | + | 1115.00i | 1.05482 | + | 0.264433i | ||||
\(262\) | −707.989 | −0.166945 | ||||||||
\(263\) | 2699.89i | 0.633013i | 0.948590 | + | 0.316506i | \(0.102510\pi\) | ||||
−0.948590 | + | 0.316506i | \(0.897490\pi\) | |||||||
\(264\) | −4832.99 | − | 6194.12i | −1.12670 | − | 1.44402i | ||||
\(265\) | −7410.16 | −1.71775 | ||||||||
\(266\) | −3237.03 | −0.746147 | ||||||||
\(267\) | 637.167 | + | 816.615i | 0.146045 | + | 0.187176i | ||||
\(268\) | − | 226.622i | − | 0.0516535i | ||||||
\(269\) | −6427.83 | −1.45692 | −0.728460 | − | 0.685088i | \(-0.759764\pi\) | ||||
−0.728460 | + | 0.685088i | \(0.759764\pi\) | |||||||
\(270\) | 2411.58 | + | 5444.64i | 0.543571 | + | 1.22722i | ||||
\(271\) | −2588.09 | −0.580130 | −0.290065 | − | 0.957007i | \(-0.593677\pi\) | ||||
−0.290065 | + | 0.957007i | \(0.593677\pi\) | |||||||
\(272\) | 3099.12i | 0.690852i | ||||||||
\(273\) | −2784.08 | + | 2172.29i | −0.617216 | + | 0.481585i | ||||
\(274\) | − | 3269.75i | − | 0.720923i | ||||||
\(275\) | −8013.52 | −1.75721 | ||||||||
\(276\) | 444.702 | + | 569.945i | 0.0969852 | + | 0.124299i | ||||
\(277\) | 7307.96 | 1.58517 | 0.792586 | − | 0.609760i | \(-0.208734\pi\) | ||||
0.792586 | + | 0.609760i | \(0.208734\pi\) | |||||||
\(278\) | 3053.35 | 0.658733 | ||||||||
\(279\) | −5695.14 | − | 1427.71i | −1.22208 | − | 0.306361i | ||||
\(280\) | − | 9494.33i | − | 2.02641i | ||||||
\(281\) | − | 4020.21i | − | 0.853472i | −0.904376 | − | 0.426736i | \(-0.859663\pi\) | ||
0.904376 | − | 0.426736i | \(-0.140337\pi\) | |||||||
\(282\) | −2695.24 | − | 3454.31i | −0.569146 | − | 0.729437i | ||||
\(283\) | 246.102i | 0.0516934i | 0.999666 | + | 0.0258467i | \(0.00822817\pi\) | ||||
−0.999666 | + | 0.0258467i | \(0.991772\pi\) | |||||||
\(284\) | − | 223.117i | − | 0.0466182i | ||||||
\(285\) | −3073.68 | + | 2398.25i | −0.638839 | + | 0.498457i | ||||
\(286\) | 4593.63i | 0.949746i | ||||||||
\(287\) | 9357.81i | 1.92465i | ||||||||
\(288\) | 236.103 | − | 941.817i | 0.0483074 | − | 0.192698i | ||||
\(289\) | 1954.96 | 0.397917 | ||||||||
\(290\) | 7208.32 | 1.45961 | ||||||||
\(291\) | −1772.09 | + | 1382.68i | −0.356982 | + | 0.278536i | ||||
\(292\) | − | 700.326i | − | 0.140354i | ||||||
\(293\) | 3404.05i | 0.678726i | 0.940656 | + | 0.339363i | \(0.110211\pi\) | ||||
−0.940656 | + | 0.339363i | \(0.889789\pi\) | |||||||
\(294\) | 2603.20 | + | 3336.35i | 0.516400 | + | 0.661836i | ||||
\(295\) | −6222.16 | + | 3557.71i | −1.22803 | + | 0.702162i | ||||
\(296\) | − | 2891.03i | − | 0.567694i | ||||||
\(297\) | 8214.66 | − | 3638.50i | 1.60493 | − | 0.710866i | ||||
\(298\) | 2660.12 | 0.517103 | ||||||||
\(299\) | − | 4661.52i | − | 0.901614i | ||||||
\(300\) | −319.080 | − | 408.944i | −0.0614070 | − | 0.0787013i | ||||
\(301\) | 76.7162i | 0.0146905i | ||||||||
\(302\) | 9465.86i | 1.80364i | ||||||||
\(303\) | 5651.94 | + | 7243.71i | 1.07160 | + | 1.37340i | ||||
\(304\) | −2703.19 | −0.509996 | ||||||||
\(305\) | 8839.35 | 1.65948 | ||||||||
\(306\) | −3822.66 | − | 958.300i | −0.714140 | − | 0.179027i | ||||
\(307\) | 4099.88 | 0.762190 | 0.381095 | − | 0.924536i | \(-0.375547\pi\) | ||||
0.381095 | + | 0.924536i | \(0.375547\pi\) | |||||||
\(308\) | −1298.88 | −0.240293 | ||||||||
\(309\) | 3880.04 | − | 3027.42i | 0.714330 | − | 0.557359i | ||||
\(310\) | −9229.92 | −1.69105 | ||||||||
\(311\) | − | 1445.91i | − | 0.263633i | −0.991274 | − | 0.131817i | \(-0.957919\pi\) | ||
0.991274 | − | 0.131817i | \(-0.0420810\pi\) | |||||||
\(312\) | −2585.32 | + | 2017.21i | −0.469119 | + | 0.366032i | ||||
\(313\) | − | 1949.24i | − | 0.352005i | −0.984390 | − | 0.176002i | \(-0.943683\pi\) | ||
0.984390 | − | 0.176002i | \(-0.0563166\pi\) | |||||||
\(314\) | − | 3871.07i | − | 0.695724i | ||||||
\(315\) | 10531.4 | + | 2640.12i | 1.88375 | + | 0.472235i | ||||
\(316\) | 50.3251 | 0.00895888 | ||||||||
\(317\) | − | 8787.37i | − | 1.55693i | −0.627686 | − | 0.778466i | \(-0.715998\pi\) | ||
0.627686 | − | 0.778466i | \(-0.284002\pi\) | |||||||
\(318\) | 5151.17 | − | 4019.23i | 0.908376 | − | 0.708764i | ||||
\(319\) | − | 10875.6i | − | 1.90884i | ||||||
\(320\) | − | 8736.02i | − | 1.52612i | ||||||
\(321\) | −4418.09 | + | 3447.24i | −0.768206 | + | 0.599396i | ||||
\(322\) | −11900.2 | −2.05955 | ||||||||
\(323\) | − | 2580.13i | − | 0.444466i | ||||||
\(324\) | 512.768 | + | 274.332i | 0.0879233 | + | 0.0470390i | ||||
\(325\) | 3344.71i | 0.570864i | ||||||||
\(326\) | 5855.54 | 0.994811 | ||||||||
\(327\) | −4270.83 | + | 3332.33i | −0.722255 | + | 0.563542i | ||||
\(328\) | 8689.76i | 1.46284i | ||||||||
\(329\) | −7988.53 | −1.33867 | ||||||||
\(330\) | 11135.2 | − | 8688.27i | 1.85749 | − | 1.44931i | ||||
\(331\) | −2972.50 | −0.493606 | −0.246803 | − | 0.969066i | \(-0.579380\pi\) | ||||
−0.246803 | + | 0.969066i | \(0.579380\pi\) | |||||||
\(332\) | −750.873 | −0.124125 | ||||||||
\(333\) | 3206.83 | + | 803.917i | 0.527727 | + | 0.132295i | ||||
\(334\) | − | 5692.36i | − | 0.932552i | ||||||
\(335\) | 4493.01 | 0.732773 | ||||||||
\(336\) | 4631.01 | + | 5935.26i | 0.751912 | + | 0.963675i | ||||
\(337\) | 4402.05i | 0.711558i | 0.934570 | + | 0.355779i | \(0.115784\pi\) | ||||
−0.934570 | + | 0.355779i | \(0.884216\pi\) | |||||||
\(338\) | −3978.80 | −0.640290 | ||||||||
\(339\) | −2344.28 | − | 3004.51i | −0.375587 | − | 0.481364i | ||||
\(340\) | 686.186 | 0.109452 | ||||||||
\(341\) | 13925.8i | 2.21150i | ||||||||
\(342\) | 835.872 | − | 3334.29i | 0.132160 | − | 0.527187i | ||||
\(343\) | −1005.26 | −0.158248 | ||||||||
\(344\) | 71.2394i | 0.0111656i | ||||||||
\(345\) | −11299.7 | + | 8816.66i | −1.76335 | + | 1.37586i | ||||
\(346\) | 8388.13 | 1.30332 | ||||||||
\(347\) | 4806.25 | 0.743554 | 0.371777 | − | 0.928322i | \(-0.378749\pi\) | ||||
0.371777 | + | 0.928322i | \(0.378749\pi\) | |||||||
\(348\) | 555.003 | − | 433.043i | 0.0854922 | − | 0.0667056i | ||||
\(349\) | 9011.33i | 1.38214i | 0.722790 | + | 0.691068i | \(0.242859\pi\) | ||||
−0.722790 | + | 0.691068i | \(0.757141\pi\) | |||||||
\(350\) | 8538.60 | 1.30402 | ||||||||
\(351\) | −1518.65 | − | 3428.66i | −0.230939 | − | 0.521391i | ||||
\(352\) | −2302.93 | −0.348712 | ||||||||
\(353\) | −11298.7 | −1.70359 | −0.851797 | − | 0.523872i | \(-0.824487\pi\) | ||||
−0.851797 | + | 0.523872i | \(0.824487\pi\) | |||||||
\(354\) | 2395.66 | − | 5848.00i | 0.359683 | − | 0.878017i | ||||
\(355\) | 4423.52 | 0.661341 | ||||||||
\(356\) | 159.015 | 0.0236735 | ||||||||
\(357\) | −5665.06 | + | 4420.19i | −0.839851 | + | 0.655298i | ||||
\(358\) | 1366.56 | 0.201746 | ||||||||
\(359\) | − | 7880.94i | − | 1.15861i | −0.815112 | − | 0.579304i | \(-0.803324\pi\) | ||
0.815112 | − | 0.579304i | \(-0.196676\pi\) | |||||||
\(360\) | 9779.61 | + | 2451.64i | 1.43175 | + | 0.358925i | ||||
\(361\) | −4608.49 | −0.671890 | ||||||||
\(362\) | −1220.03 | −0.177137 | ||||||||
\(363\) | −8854.06 | − | 11347.7i | −1.28021 | − | 1.64077i | ||||
\(364\) | 542.129i | 0.0780639i | ||||||||
\(365\) | 13884.7 | 1.99111 | ||||||||
\(366\) | −6144.68 | + | 4794.41i | −0.877561 | + | 0.684721i | ||||
\(367\) | 4266.06i | 0.606775i | 0.952867 | + | 0.303388i | \(0.0981177\pi\) | ||||
−0.952867 | + | 0.303388i | \(0.901882\pi\) | |||||||
\(368\) | −9937.69 | −1.40771 | ||||||||
\(369\) | −9638.99 | − | 2416.39i | −1.35985 | − | 0.340901i | ||||
\(370\) | 5197.20 | 0.730242 | ||||||||
\(371\) | − | 11912.7i | − | 1.66706i | ||||||
\(372\) | −710.656 | + | 554.492i | −0.0990478 | + | 0.0772825i | ||||
\(373\) | 5386.56 | 0.747736 | 0.373868 | − | 0.927482i | \(-0.378031\pi\) | ||||
0.373868 | + | 0.927482i | \(0.378031\pi\) | |||||||
\(374\) | 9347.17i | 1.29233i | ||||||||
\(375\) | 8.76751 | − | 6.84089i | 0.00120734 | − | 0.000942032i | ||||
\(376\) | −7418.23 | −1.01746 | ||||||||
\(377\) | −4539.31 | −0.620123 | ||||||||
\(378\) | −8752.92 | + | 3876.91i | −1.19101 | + | 0.527531i | ||||
\(379\) | −2251.27 | −0.305119 | −0.152560 | − | 0.988294i | \(-0.548752\pi\) | ||||
−0.152560 | + | 0.988294i | \(0.548752\pi\) | |||||||
\(380\) | 598.522i | 0.0807988i | ||||||||
\(381\) | 1166.76 | + | 1495.35i | 0.156889 | + | 0.201074i | ||||
\(382\) | −436.547 | −0.0584703 | ||||||||
\(383\) | 7169.18i | 0.956470i | 0.878232 | + | 0.478235i | \(0.158723\pi\) | ||||
−0.878232 | + | 0.478235i | \(0.841277\pi\) | |||||||
\(384\) | 3818.77 | + | 4894.27i | 0.507489 | + | 0.650415i | ||||
\(385\) | − | 25751.5i | − | 3.40888i | ||||||
\(386\) | 5740.51 | 0.756954 | ||||||||
\(387\) | −79.0213 | − | 19.8098i | −0.0103795 | − | 0.00260204i | ||||
\(388\) | 345.069i | 0.0451501i | ||||||||
\(389\) | 2424.33i | 0.315986i | 0.987440 | + | 0.157993i | \(0.0505024\pi\) | ||||
−0.987440 | + | 0.157993i | \(0.949498\pi\) | |||||||
\(390\) | −3626.34 | − | 4647.63i | −0.470838 | − | 0.603441i | ||||
\(391\) | − | 9485.29i | − | 1.22683i | ||||||
\(392\) | 7164.90 | 0.923169 | ||||||||
\(393\) | −843.255 | − | 1080.74i | −0.108236 | − | 0.138718i | ||||
\(394\) | − | 14339.6i | − | 1.83354i | ||||||
\(395\) | 997.745i | 0.127094i | ||||||||
\(396\) | 335.398 | − | 1337.90i | 0.0425616 | − | 0.169778i | ||||
\(397\) | 14687.4i | 1.85677i | 0.371615 | + | 0.928387i | \(0.378804\pi\) | ||||
−0.371615 | + | 0.928387i | \(0.621196\pi\) | |||||||
\(398\) | 9808.82 | 1.23536 | ||||||||
\(399\) | −3855.49 | − | 4941.32i | −0.483749 | − | 0.619989i | ||||
\(400\) | 7130.44 | 0.891305 | ||||||||
\(401\) | 9413.70 | 1.17231 | 0.586157 | − | 0.810198i | \(-0.300640\pi\) | ||||
0.586157 | + | 0.810198i | \(0.300640\pi\) | |||||||
\(402\) | −3123.31 | + | 2436.98i | −0.387504 | + | 0.302352i | ||||
\(403\) | 5812.37 | 0.718449 | ||||||||
\(404\) | 1410.53 | 0.173704 | ||||||||
\(405\) | −5438.90 | + | 10166.1i | −0.667311 | + | 1.24731i | ||||
\(406\) | 11588.3i | 1.41654i | ||||||||
\(407\) | − | 7841.34i | − | 0.954989i | ||||||
\(408\) | −5260.64 | + | 4104.63i | −0.638334 | + | 0.498063i | ||||
\(409\) | − | 7052.63i | − | 0.852641i | −0.904572 | − | 0.426321i | \(-0.859810\pi\) | ||
0.904572 | − | 0.426321i | \(-0.140190\pi\) | |||||||
\(410\) | −15621.6 | −1.88169 | ||||||||
\(411\) | 4991.27 | − | 3894.46i | 0.599029 | − | 0.467395i | ||||
\(412\) | − | 755.540i | − | 0.0903466i | ||||||
\(413\) | −5719.45 | − | 10002.9i | −0.681443 | − | 1.19179i | ||||
\(414\) | 3072.90 | − | 12257.8i | 0.364794 | − | 1.45516i | ||||
\(415\) | − | 14886.8i | − | 1.76088i | ||||||
\(416\) | 961.205i | 0.113286i | ||||||||
\(417\) | 3636.72 | + | 4660.94i | 0.427076 | + | 0.547355i | ||||
\(418\) | −8153.02 | −0.954012 | ||||||||
\(419\) | 8388.86 | 0.978097 | 0.489048 | − | 0.872257i | \(-0.337344\pi\) | ||||
0.489048 | + | 0.872257i | \(0.337344\pi\) | |||||||
\(420\) | 1314.14 | − | 1025.37i | 0.152675 | − | 0.119126i | ||||
\(421\) | − | 8187.26i | − | 0.947797i | −0.880580 | − | 0.473898i | \(-0.842846\pi\) | ||
0.880580 | − | 0.473898i | \(-0.157154\pi\) | |||||||
\(422\) | − | 9811.53i | − | 1.13180i | ||||||
\(423\) | 2062.81 | − | 8228.56i | 0.237110 | − | 0.945831i | ||||
\(424\) | − | 11062.3i | − | 1.26706i | ||||||
\(425\) | 6805.84i | 0.776780i | ||||||||
\(426\) | −3075.01 | + | 2399.29i | −0.349730 | + | 0.272878i | ||||
\(427\) | 14210.3i | 1.61051i | ||||||||
\(428\) | 860.312i | 0.0971607i | ||||||||
\(429\) | −7012.17 | + | 5471.28i | −0.789163 | + | 0.615748i | ||||
\(430\) | −128.067 | −0.0143627 | ||||||||
\(431\) | −12633.2 | −1.41188 | −0.705941 | − | 0.708271i | \(-0.749476\pi\) | ||||
−0.705941 | + | 0.708271i | \(0.749476\pi\) | |||||||
\(432\) | −7309.42 | + | 3237.55i | −0.814062 | + | 0.360571i | ||||
\(433\) | 6515.64 | 0.723145 | 0.361572 | − | 0.932344i | \(-0.382240\pi\) | ||||
0.361572 | + | 0.932344i | \(0.382240\pi\) | |||||||
\(434\) | − | 14838.2i | − | 1.64115i | ||||||
\(435\) | 8585.52 | + | 11003.5i | 0.946308 | + | 1.21282i | ||||
\(436\) | 831.636i | 0.0913489i | ||||||||
\(437\) | 8273.50 | 0.905664 | ||||||||
\(438\) | −9651.93 | + | 7530.96i | −1.05294 | + | 0.821560i | ||||
\(439\) | −196.698 | −0.0213848 | −0.0106924 | − | 0.999943i | \(-0.503404\pi\) | ||||
−0.0106924 | + | 0.999943i | \(0.503404\pi\) | |||||||
\(440\) | − | 23913.1i | − | 2.59094i | ||||||
\(441\) | −1992.37 | + | 7947.56i | −0.215135 | + | 0.858175i | ||||
\(442\) | 3901.35 | 0.419838 | ||||||||
\(443\) | −1592.00 | −0.170741 | −0.0853705 | − | 0.996349i | \(-0.527207\pi\) | ||||
−0.0853705 | + | 0.996349i | \(0.527207\pi\) | |||||||
\(444\) | 400.157 | − | 312.224i | 0.0427716 | − | 0.0333728i | ||||
\(445\) | 3152.63i | 0.335841i | ||||||||
\(446\) | −298.781 | −0.0317213 | ||||||||
\(447\) | 3168.36 | + | 4060.67i | 0.335253 | + | 0.429672i | ||||
\(448\) | 14044.2 | 1.48109 | ||||||||
\(449\) | − | 13078.6i | − | 1.37464i | −0.726352 | − | 0.687322i | \(-0.758786\pi\) | ||
0.726352 | − | 0.687322i | \(-0.241214\pi\) | |||||||
\(450\) | −2204.85 | + | 8795.16i | −0.230973 | + | 0.921350i | ||||
\(451\) | 23569.3i | 2.46083i | ||||||||
\(452\) | −585.052 | −0.0608817 | ||||||||
\(453\) | −14449.6 | + | 11274.4i | −1.49868 | + | 1.16935i | ||||
\(454\) | −3012.66 | −0.311435 | ||||||||
\(455\) | −10748.2 | −1.10744 | ||||||||
\(456\) | −3580.25 | − | 4588.56i | −0.367676 | − | 0.471226i | ||||
\(457\) | − | 10222.0i | − | 1.04632i | −0.852236 | − | 0.523158i | \(-0.824754\pi\) | ||
0.852236 | − | 0.523158i | \(-0.175246\pi\) | |||||||
\(458\) | − | 304.565i | − | 0.0310729i | ||||||
\(459\) | −3090.16 | − | 6976.67i | −0.314240 | − | 0.709462i | ||||
\(460\) | 2200.34i | 0.223024i | ||||||||
\(461\) | 18372.6i | 1.85618i | 0.372354 | + | 0.928091i | \(0.378551\pi\) | ||||
−0.372354 | + | 0.928091i | \(0.621449\pi\) | |||||||
\(462\) | 13967.5 | + | 17901.2i | 1.40655 | + | 1.80268i | ||||
\(463\) | 3624.32i | 0.363794i | 0.983318 | + | 0.181897i | \(0.0582237\pi\) | ||||
−0.983318 | + | 0.181897i | \(0.941776\pi\) | |||||||
\(464\) | 9677.16i | 0.968213i | ||||||||
\(465\) | −10993.4 | − | 14089.5i | −1.09635 | − | 1.40512i | ||||
\(466\) | −1890.84 | −0.187964 | ||||||||
\(467\) | 16332.5 | 1.61837 | 0.809184 | − | 0.587556i | \(-0.199910\pi\) | ||||
0.809184 | + | 0.587556i | \(0.199910\pi\) | |||||||
\(468\) | −558.418 | − | 139.989i | −0.0551557 | − | 0.0138270i | ||||
\(469\) | 7223.06i | 0.711151i | ||||||||
\(470\) | − | 13335.8i | − | 1.30879i | ||||||
\(471\) | 5909.19 | − | 4610.67i | 0.578091 | − | 0.451058i | ||||
\(472\) | −5311.14 | − | 9288.78i | −0.517935 | − | 0.905828i | ||||
\(473\) | 193.223i | 0.0187831i | ||||||||
\(474\) | −541.171 | − | 693.582i | −0.0524405 | − | 0.0672095i | ||||
\(475\) | −5936.36 | −0.573429 | ||||||||
\(476\) | 1103.13i | 0.106222i | ||||||||
\(477\) | 12270.7 | + | 3076.13i | 1.17785 | + | 0.295275i | ||||
\(478\) | − | 13639.7i | − | 1.30515i | ||||||
\(479\) | − | 2919.57i | − | 0.278494i | −0.990258 | − | 0.139247i | \(-0.955532\pi\) | ||
0.990258 | − | 0.139247i | \(-0.0444682\pi\) | |||||||
\(480\) | 2330.00 | − | 1818.00i | 0.221562 | − | 0.172874i | ||||
\(481\) | −3272.84 | −0.310247 | ||||||||
\(482\) | −10284.1 | −0.971845 | ||||||||
\(483\) | −14173.9 | − | 18165.7i | −1.33527 | − | 1.71132i | ||||
\(484\) | −2209.67 | −0.207520 | ||||||||
\(485\) | −6841.34 | −0.640514 | ||||||||
\(486\) | −1733.21 | − | 10017.0i | −0.161769 | − | 0.934941i | ||||
\(487\) | 10408.9 | 0.968524 | 0.484262 | − | 0.874923i | \(-0.339088\pi\) | ||||
0.484262 | + | 0.874923i | \(0.339088\pi\) | |||||||
\(488\) | 13195.9i | 1.22408i | ||||||||
\(489\) | 6974.29 | + | 8938.48i | 0.644965 | + | 0.826609i | ||||
\(490\) | 12880.3i | 1.18750i | ||||||||
\(491\) | 4360.92i | 0.400826i | 0.979712 | + | 0.200413i | \(0.0642284\pi\) | ||||
−0.979712 | + | 0.200413i | \(0.935772\pi\) | |||||||
\(492\) | −1202.78 | + | 938.475i | −0.110214 | + | 0.0859953i | ||||
\(493\) | −9236.62 | −0.843806 | ||||||||
\(494\) | 3402.93i | 0.309929i | ||||||||
\(495\) | 26525.3 | + | 6649.60i | 2.40853 | + | 0.603793i | ||||
\(496\) | − | 12391.2i | − | 1.12173i | ||||||
\(497\) | 7111.35i | 0.641827i | ||||||||
\(498\) | 8074.51 | + | 10348.6i | 0.726561 | + | 0.931185i | ||||
\(499\) | 984.722 | 0.0883411 | 0.0441705 | − | 0.999024i | \(-0.485936\pi\) | ||||
0.0441705 | + | 0.999024i | \(0.485936\pi\) | |||||||
\(500\) | − | 1.70725i | − | 0.000152701i | ||||||
\(501\) | 8689.38 | − | 6779.93i | 0.774876 | − | 0.604601i | ||||
\(502\) | 5747.32i | 0.510987i | ||||||||
\(503\) | 11292.6 | 1.00102 | 0.500510 | − | 0.865731i | \(-0.333146\pi\) | ||||
0.500510 | + | 0.865731i | \(0.333146\pi\) | |||||||
\(504\) | −3941.32 | + | 15721.9i | −0.348334 | + | 1.38950i | ||||
\(505\) | 27965.2i | 2.46422i | ||||||||
\(506\) | −29972.8 | −2.63331 | ||||||||
\(507\) | −4738.97 | − | 6073.63i | −0.415119 | − | 0.532030i | ||||
\(508\) | 291.182 | 0.0254313 | ||||||||
\(509\) | −1779.89 | −0.154994 | −0.0774971 | − | 0.996993i | \(-0.524693\pi\) | ||||
−0.0774971 | + | 0.996993i | \(0.524693\pi\) | |||||||
\(510\) | −7378.90 | − | 9457.04i | −0.640673 | − | 0.821108i | ||||
\(511\) | 22321.3i | 1.93236i | ||||||||
\(512\) | 12812.1 | 1.10590 | ||||||||
\(513\) | 6085.37 | − | 2695.38i | 0.523734 | − | 0.231976i | ||||
\(514\) | 5982.46i | 0.513375i | ||||||||
\(515\) | 14979.3 | 1.28169 | ||||||||
\(516\) | −9.86050 | + | 7.69370i | −0.000841248 | + | 0.000656388i | ||||
\(517\) | −20120.5 | −1.71160 | ||||||||
\(518\) | 8355.13i | 0.708694i | ||||||||
\(519\) | 9990.74 | + | 12804.5i | 0.844981 | + | 1.08296i | ||||
\(520\) | −9980.93 | −0.841716 | ||||||||
\(521\) | − | 10556.1i | − | 0.887662i | −0.896110 | − | 0.443831i | \(-0.853619\pi\) | ||
0.896110 | − | 0.443831i | \(-0.146381\pi\) | |||||||
\(522\) | −11936.4 | − | 2992.34i | −1.00085 | − | 0.250903i | ||||
\(523\) | −1374.67 | −0.114934 | −0.0574668 | − | 0.998347i | \(-0.518302\pi\) | ||||
−0.0574668 | + | 0.998347i | \(0.518302\pi\) | |||||||
\(524\) | −210.448 | −0.0175447 | ||||||||
\(525\) | 10170.0 | + | 13034.2i | 0.845435 | + | 1.08354i | ||||
\(526\) | − | 7245.71i | − | 0.600623i | ||||||
\(527\) | 11827.1 | 0.977600 | ||||||||
\(528\) | 11664.0 | + | 14949.0i | 0.961383 | + | 1.23214i | ||||
\(529\) | 18248.7 | 1.49985 | ||||||||
\(530\) | 19886.7 | 1.62985 | ||||||||
\(531\) | 11780.3 | − | 3308.34i | 0.962755 | − | 0.270376i | ||||
\(532\) | −962.198 | −0.0784146 | ||||||||
\(533\) | 9837.41 | 0.799447 | ||||||||
\(534\) | −1709.97 | − | 2191.55i | −0.138572 | − | 0.177599i | ||||
\(535\) | −17056.6 | −1.37835 | ||||||||
\(536\) | 6707.41i | 0.540515i | ||||||||
\(537\) | 1627.65 | + | 2086.06i | 0.130798 | + | 0.167635i | ||||
\(538\) | 17250.4 | 1.38237 | ||||||||
\(539\) | 19433.4 | 1.55298 | ||||||||
\(540\) | 716.835 | + | 1618.40i | 0.0571253 | + | 0.128972i | ||||
\(541\) | 10311.3i | 0.819443i | 0.912211 | + | 0.409722i | \(0.134374\pi\) | ||||
−0.912211 | + | 0.409722i | \(0.865626\pi\) | |||||||
\(542\) | 6945.67 | 0.550446 | ||||||||
\(543\) | −1453.13 | − | 1862.38i | −0.114843 | − | 0.147187i | ||||
\(544\) | 1955.87i | 0.154149i | ||||||||
\(545\) | −16488.0 | −1.29591 | ||||||||
\(546\) | 7471.64 | − | 5829.78i | 0.585635 | − | 0.456944i | ||||
\(547\) | 24725.9 | 1.93273 | 0.966367 | − | 0.257168i | \(-0.0827895\pi\) | ||||
0.966367 | + | 0.257168i | \(0.0827895\pi\) | |||||||
\(548\) | − | 971.923i | − | 0.0757637i | ||||||
\(549\) | −14637.3 | − | 3669.42i | −1.13790 | − | 0.285259i | ||||
\(550\) | 21505.9 | 1.66730 | ||||||||
\(551\) | − | 8056.60i | − | 0.622909i | ||||||
\(552\) | −13162.0 | − | 16868.9i | −1.01488 | − | 1.30070i | ||||
\(553\) | −1604.00 | −0.123343 | ||||||||
\(554\) | −19612.4 | −1.50406 | ||||||||
\(555\) | 6190.16 | + | 7933.51i | 0.473437 | + | 0.606773i | ||||
\(556\) | 907.600 | 0.0692281 | ||||||||
\(557\) | − | 8023.94i | − | 0.610387i | −0.952290 | − | 0.305193i | \(-0.901279\pi\) | ||
0.952290 | − | 0.305193i | \(-0.0987211\pi\) | |||||||
\(558\) | 15284.1 | + | 3831.55i | 1.15955 | + | 0.290686i | ||||
\(559\) | 80.6479 | 0.00610205 | ||||||||
\(560\) | 22913.7i | 1.72907i | ||||||||
\(561\) | −14268.4 | + | 11133.0i | −1.07382 | + | 0.837854i | ||||
\(562\) | 10789.1i | 0.809803i | ||||||||
\(563\) | −25776.6 | −1.92958 | −0.964791 | − | 0.263017i | \(-0.915283\pi\) | ||||
−0.964791 | + | 0.263017i | \(0.915283\pi\) | |||||||
\(564\) | −801.152 | − | 1026.78i | −0.0598131 | − | 0.0766585i | ||||
\(565\) | − | 11599.2i | − | 0.863689i | ||||||
\(566\) | − | 660.464i | − | 0.0490484i | ||||||
\(567\) | −16343.3 | − | 8743.70i | −1.21050 | − | 0.647620i | ||||
\(568\) | 6603.68i | 0.487824i | ||||||||
\(569\) | 5461.25 | 0.402368 | 0.201184 | − | 0.979553i | \(-0.435521\pi\) | ||||
0.201184 | + | 0.979553i | \(0.435521\pi\) | |||||||
\(570\) | 8248.86 | − | 6436.21i | 0.606152 | − | 0.472953i | ||||
\(571\) | 6208.29i | 0.455007i | 0.973777 | + | 0.227503i | \(0.0730562\pi\) | ||||
−0.973777 | + | 0.227503i | \(0.926944\pi\) | |||||||
\(572\) | 1365.44i | 0.0998113i | ||||||||
\(573\) | −519.952 | − | 666.388i | −0.0379080 | − | 0.0485842i | ||||
\(574\) | − | 25113.6i | − | 1.82617i | ||||||
\(575\) | −21823.7 | −1.58280 | ||||||||
\(576\) | −3626.53 | + | 14466.2i | −0.262335 | + | 1.04646i | ||||
\(577\) | −4213.28 | −0.303988 | −0.151994 | − | 0.988381i | \(-0.548569\pi\) | ||||
−0.151994 | + | 0.988381i | \(0.548569\pi\) | |||||||
\(578\) | −5246.55 | −0.377556 | ||||||||
\(579\) | 6837.27 | + | 8762.87i | 0.490755 | + | 0.628968i | ||||
\(580\) | 2142.65 | 0.153394 | ||||||||
\(581\) | 23932.4 | 1.70892 | ||||||||
\(582\) | 4755.76 | − | 3710.70i | 0.338716 | − | 0.264285i | ||||
\(583\) | − | 30004.3i | − | 2.13148i | ||||||
\(584\) | 20727.8i | 1.46870i | ||||||||
\(585\) | 2775.43 | − | 11071.2i | 0.196154 | − | 0.782457i | ||||
\(586\) | − | 9135.46i | − | 0.643997i | ||||||
\(587\) | −3713.24 | −0.261093 | −0.130547 | − | 0.991442i | \(-0.541673\pi\) | ||||
−0.130547 | + | 0.991442i | \(0.541673\pi\) | |||||||
\(588\) | 773.794 | + | 991.719i | 0.0542699 | + | 0.0695541i | ||||
\(589\) | 10316.1i | 0.721677i | ||||||||
\(590\) | 16698.4 | − | 9547.84i | 1.16519 | − | 0.666235i | ||||
\(591\) | 21889.3 | − | 17079.2i | 1.52353 | − | 1.18874i | ||||
\(592\) | 6977.23i | 0.484396i | ||||||||
\(593\) | 13741.9i | 0.951621i | 0.879548 | + | 0.475811i | \(0.157845\pi\) | ||||
−0.879548 | + | 0.475811i | \(0.842155\pi\) | |||||||
\(594\) | −22045.7 | + | 9764.67i | −1.52281 | + | 0.674494i | ||||
\(595\) | −21870.6 | −1.50690 | ||||||||
\(596\) | 790.714 | 0.0543438 | ||||||||
\(597\) | 11682.9 | + | 14973.2i | 0.800918 | + | 1.02648i | ||||
\(598\) | 12510.1i | 0.855481i | ||||||||
\(599\) | − | 13344.3i | − | 0.910242i | −0.890430 | − | 0.455121i | \(-0.849596\pi\) | ||
0.890430 | − | 0.455121i | \(-0.150404\pi\) | |||||||
\(600\) | 9443.93 | + | 12103.7i | 0.642578 | + | 0.823549i | ||||
\(601\) | 11246.9i | 0.763348i | 0.924297 | + | 0.381674i | \(0.124652\pi\) | ||||
−0.924297 | + | 0.381674i | \(0.875348\pi\) | |||||||
\(602\) | − | 205.884i | − | 0.0139389i | ||||||
\(603\) | −7440.09 | − | 1865.15i | −0.502461 | − | 0.125962i | ||||
\(604\) | 2813.70i | 0.189549i | ||||||||
\(605\) | − | 43808.9i | − | 2.94394i | ||||||
\(606\) | −15168.1 | − | 19440.0i | −1.01677 | − | 1.30313i | ||||
\(607\) | −25098.2 | −1.67826 | −0.839129 | − | 0.543932i | \(-0.816935\pi\) | ||||
−0.839129 | + | 0.543932i | \(0.816935\pi\) | |||||||
\(608\) | −1706.00 | −0.113795 | ||||||||
\(609\) | −17689.5 | + | 13802.3i | −1.17703 | + | 0.918385i | ||||
\(610\) | −23722.2 | −1.57457 | ||||||||
\(611\) | 8397.95i | 0.556047i | ||||||||
\(612\) | −1136.27 | − | 284.852i | −0.0750509 | − | 0.0188145i | ||||
\(613\) | − | 25146.8i | − | 1.65688i | −0.560074 | − | 0.828442i | \(-0.689227\pi\) | ||
0.560074 | − | 0.828442i | \(-0.310773\pi\) | |||||||
\(614\) | −11002.9 | −0.723192 | ||||||||
\(615\) | −18606.2 | − | 23846.3i | −1.21996 | − | 1.56354i | ||||
\(616\) | 38443.3 | 2.51449 | ||||||||
\(617\) | 10367.6i | 0.676476i | 0.941061 | + | 0.338238i | \(0.109831\pi\) | ||||
−0.941061 | + | 0.338238i | \(0.890169\pi\) | |||||||
\(618\) | −10412.9 | + | 8124.71i | −0.677780 | + | 0.528841i | ||||
\(619\) | −19220.6 | −1.24804 | −0.624022 | − | 0.781407i | \(-0.714502\pi\) | ||||
−0.624022 | + | 0.781407i | \(0.714502\pi\) | |||||||
\(620\) | −2743.57 | −0.177717 | ||||||||
\(621\) | 22371.5 | − | 9908.97i | 1.44563 | − | 0.640311i | ||||
\(622\) | 3880.39i | 0.250144i | ||||||||
\(623\) | −5068.25 | −0.325931 | ||||||||
\(624\) | 6239.44 | − | 4868.35i | 0.400285 | − | 0.312324i | ||||
\(625\) | −15608.1 | −0.998916 | ||||||||
\(626\) | 5231.18i | 0.333994i | ||||||||
\(627\) | −9710.71 | − | 12445.6i | −0.618514 | − | 0.792709i | ||||
\(628\) | − | 1150.66i | − | 0.0731155i | ||||||
\(629\) | −6659.60 | −0.422156 | ||||||||
\(630\) | −28263.3 | − | 7085.31i | −1.78736 | − | 0.448072i | ||||
\(631\) | 5697.06 | 0.359424 | 0.179712 | − | 0.983719i | \(-0.442483\pi\) | ||||
0.179712 | + | 0.983719i | \(0.442483\pi\) | |||||||
\(632\) | −1489.49 | −0.0937479 | ||||||||
\(633\) | 14977.3 | − | 11686.1i | 0.940432 | − | 0.733777i | ||||
\(634\) | 23582.7i | 1.47727i | ||||||||
\(635\) | 5772.98i | 0.360777i | ||||||||
\(636\) | 1531.17 | − | 1194.70i | 0.0954637 | − | 0.0744859i | ||||
\(637\) | − | 8111.17i | − | 0.504515i | ||||||
\(638\) | 29187.0i | 1.81117i | ||||||||
\(639\) | −7325.03 | − | 1836.31i | −0.453480 | − | 0.113683i | ||||
\(640\) | 18894.9i | 1.16701i | ||||||||
\(641\) | 14951.6i | 0.921296i | 0.887583 | + | 0.460648i | \(0.152383\pi\) | ||||
−0.887583 | + | 0.460648i | \(0.847617\pi\) | |||||||
\(642\) | 11856.9 | − | 9251.37i | 0.728899 | − | 0.568727i | ||||
\(643\) | −10278.6 | −0.630401 | −0.315201 | − | 0.949025i | \(-0.602072\pi\) | ||||
−0.315201 | + | 0.949025i | \(0.602072\pi\) | |||||||
\(644\) | −3537.31 | −0.216443 | ||||||||
\(645\) | −152.535 | − | 195.494i | −0.00931173 | − | 0.0119342i | ||||
\(646\) | 6924.32i | 0.421724i | ||||||||
\(647\) | − | 30130.8i | − | 1.83086i | −0.402483 | − | 0.915428i | \(-0.631853\pi\) | ||
0.402483 | − | 0.915428i | \(-0.368147\pi\) | |||||||
\(648\) | −15176.6 | − | 8119.49i | −0.920050 | − | 0.492228i | ||||
\(649\) | −14405.4 | − | 25194.0i | −0.871283 | − | 1.52381i | ||||
\(650\) | − | 8976.21i | − | 0.541655i | ||||||
\(651\) | 22650.5 | − | 17673.2i | 1.36366 | − | 1.06400i | ||||
\(652\) | 1740.54 | 0.104547 | ||||||||
\(653\) | − | 19130.6i | − | 1.14646i | −0.819394 | − | 0.573231i | \(-0.805690\pi\) | ||
0.819394 | − | 0.573231i | \(-0.194310\pi\) | |||||||
\(654\) | 11461.6 | − | 8943.00i | 0.685299 | − | 0.534708i | ||||
\(655\) | − | 4172.33i | − | 0.248896i | ||||||
\(656\) | − | 20972.0i | − | 1.24820i | ||||||
\(657\) | −22992.0 | − | 5763.85i | −1.36530 | − | 0.342267i | ||||
\(658\) | 21438.9 | 1.27017 | ||||||||
\(659\) | −3783.93 | −0.223674 | −0.111837 | − | 0.993727i | \(-0.535673\pi\) | ||||
−0.111837 | + | 0.993727i | \(0.535673\pi\) | |||||||
\(660\) | 3309.90 | − | 2582.56i | 0.195208 | − | 0.152312i | ||||
\(661\) | 14846.5 | 0.873619 | 0.436809 | − | 0.899554i | \(-0.356108\pi\) | ||||
0.436809 | + | 0.899554i | \(0.356108\pi\) | |||||||
\(662\) | 7977.32 | 0.468350 | ||||||||
\(663\) | 4646.73 | + | 5955.40i | 0.272193 | + | 0.348852i | ||||
\(664\) | 22223.8 | 1.29887 | ||||||||
\(665\) | − | 19076.5i | − | 1.11242i | ||||||
\(666\) | −8606.18 | − | 2157.48i | −0.500725 | − | 0.125526i | ||||
\(667\) | − | 29618.3i | − | 1.71938i | ||||||
\(668\) | − | 1692.04i | − | 0.0980044i | ||||||
\(669\) | −355.866 | − | 456.089i | −0.0205659 | − | 0.0263579i | ||||
\(670\) | −12057.9 | −0.695280 | ||||||||
\(671\) | 35791.2i | 2.05917i | ||||||||
\(672\) | 2922.65 | + | 3745.77i | 0.167773 | + | 0.215024i | ||||
\(673\) | 25796.1i | 1.47752i | 0.673971 | + | 0.738758i | \(0.264587\pi\) | ||||
−0.673971 | + | 0.738758i | \(0.735413\pi\) | |||||||
\(674\) | − | 11813.8i | − | 0.675150i | ||||||
\(675\) | −16051.9 | + | 7109.83i | −0.915315 | + | 0.405419i | ||||
\(676\) | −1182.69 | −0.0672898 | ||||||||
\(677\) | − | 19445.2i | − | 1.10390i | −0.833878 | − | 0.551949i | \(-0.813884\pi\) | ||
0.833878 | − | 0.551949i | \(-0.186116\pi\) | |||||||
\(678\) | 6291.36 | + | 8063.22i | 0.356369 | + | 0.456735i | ||||
\(679\) | − | 10998.3i | − | 0.621614i | ||||||
\(680\) | −20309.3 | −1.14533 | ||||||||
\(681\) | −3588.26 | − | 4598.83i | −0.201912 | − | 0.258778i | ||||
\(682\) | − | 37372.6i | − | 2.09835i | ||||||
\(683\) | 16732.4 | 0.937404 | 0.468702 | − | 0.883356i | \(-0.344722\pi\) | ||||
0.468702 | + | 0.883356i | \(0.344722\pi\) | |||||||
\(684\) | 248.461 | − | 991.109i | 0.0138891 | − | 0.0554035i | ||||
\(685\) | 19269.4 | 1.07481 | ||||||||
\(686\) | 2697.83 | 0.150151 | ||||||||
\(687\) | 464.918 | − | 362.754i | 0.0258191 | − | 0.0201455i | ||||
\(688\) | − | 171.930i | − | 0.00952728i | ||||||
\(689\) | −12523.3 | −0.692451 | ||||||||
\(690\) | 30325.1 | − | 23661.3i | 1.67313 | − | 1.30547i | ||||
\(691\) | 16776.9i | 0.923620i | 0.886979 | + | 0.461810i | \(0.152800\pi\) | ||||
−0.886979 | + | 0.461810i | \(0.847200\pi\) | |||||||
\(692\) | 2493.35 | 0.136969 | ||||||||
\(693\) | −10690.0 | + | 42642.6i | −0.585976 | + | 2.33746i | ||||
\(694\) | −12898.6 | −0.705509 | ||||||||
\(695\) | 17994.1i | 0.982092i | ||||||||
\(696\) | −16426.6 | + | 12816.9i | −0.894611 | + | 0.698024i | ||||
\(697\) | 20017.2 | 1.08782 | ||||||||
\(698\) | − | 24183.7i | − | 1.31142i | ||||||
\(699\) | −2252.10 | − | 2886.36i | −0.121863 | − | 0.156183i | ||||
\(700\) | 2538.07 | 0.137043 | ||||||||
\(701\) | 27374.7 | 1.47493 | 0.737466 | − | 0.675385i | \(-0.236022\pi\) | ||||
0.737466 | + | 0.675385i | \(0.236022\pi\) | |||||||
\(702\) | 4075.61 | + | 9201.52i | 0.219122 | + | 0.494714i | ||||
\(703\) | − | 5808.81i | − | 0.311641i | ||||||
\(704\) | 35372.8 | 1.89370 | ||||||||
\(705\) | 20357.0 | − | 15883.6i | 1.08750 | − | 0.848529i | ||||
\(706\) | 30322.4 | 1.61643 | ||||||||
\(707\) | −44957.4 | −2.39151 | ||||||||
\(708\) | 712.101 | − | 1738.30i | 0.0378000 | − | 0.0922731i | ||||
\(709\) | −32178.8 | −1.70452 | −0.852258 | − | 0.523122i | \(-0.824767\pi\) | ||||
−0.852258 | + | 0.523122i | \(0.824767\pi\) | |||||||
\(710\) | −11871.4 | −0.627503 | ||||||||
\(711\) | 414.187 | − | 1652.19i | 0.0218470 | − | 0.0871478i | ||||
\(712\) | −4706.42 | −0.247726 | ||||||||
\(713\) | 37924.9i | 1.99200i | ||||||||
\(714\) | 15203.4 | − | 11862.5i | 0.796879 | − | 0.621768i | ||||
\(715\) | −27071.3 | −1.41596 | ||||||||
\(716\) | 406.207 | 0.0212020 | ||||||||
\(717\) | 20820.9 | − | 16245.6i | 1.08448 | − | 0.846170i | ||||
\(718\) | 21150.1i | 1.09933i | ||||||||
\(719\) | 24046.9 | 1.24728 | 0.623641 | − | 0.781711i | \(-0.285653\pi\) | ||||
0.623641 | + | 0.781711i | \(0.285653\pi\) | |||||||
\(720\) | −23602.2 | − | 5916.82i | −1.22167 | − | 0.306260i | ||||
\(721\) | 24081.1i | 1.24387i | ||||||||
\(722\) | 12367.8 | 0.637511 | ||||||||
\(723\) | −12249.0 | − | 15698.7i | −0.630075 | − | 0.807526i | ||||
\(724\) | −362.651 | −0.0186158 | ||||||||
\(725\) | 21251.6i | 1.08864i | ||||||||
\(726\) | 23761.7 | + | 30453.8i | 1.21471 | + | 1.55681i | ||||
\(727\) | 22341.6 | 1.13976 | 0.569878 | − | 0.821729i | \(-0.306990\pi\) | ||||
0.569878 | + | 0.821729i | \(0.306990\pi\) | |||||||
\(728\) | − | 16045.6i | − | 0.816879i | ||||||
\(729\) | 13226.6 | − | 14576.6i | 0.671982 | − | 0.740567i | ||||
\(730\) | −37262.4 | −1.88924 | ||||||||
\(731\) | 164.103 | 0.00830311 | ||||||||
\(732\) | −1826.49 | + | 1425.12i | −0.0922253 | + | 0.0719592i | ||||
\(733\) | 7788.17 | 0.392445 | 0.196223 | − | 0.980559i | \(-0.437132\pi\) | ||||
0.196223 | + | 0.980559i | \(0.437132\pi\) | |||||||
\(734\) | − | 11448.8i | − | 0.575728i | ||||||
\(735\) | −19661.8 | + | 15341.2i | −0.986718 | + | 0.769891i | ||||
\(736\) | −6271.72 | −0.314102 | ||||||||
\(737\) | 18192.5i | 0.909267i | ||||||||
\(738\) | 25868.2 | + | 6484.88i | 1.29027 | + | 0.323458i | ||||
\(739\) | − | 11705.7i | − | 0.582680i | −0.956620 | − | 0.291340i | \(-0.905899\pi\) | ||
0.956620 | − | 0.291340i | \(-0.0941011\pi\) | |||||||
\(740\) | 1544.85 | 0.0767431 | ||||||||
\(741\) | −5194.57 | + | 4053.09i | −0.257527 | + | 0.200936i | ||||
\(742\) | 31970.3i | 1.58176i | ||||||||
\(743\) | 3213.88i | 0.158689i | 0.996847 | + | 0.0793443i | \(0.0252827\pi\) | ||||
−0.996847 | + | 0.0793443i | \(0.974717\pi\) | |||||||
\(744\) | 21033.5 | − | 16411.5i | 1.03646 | − | 0.808703i | ||||
\(745\) | 15676.7i | 0.770939i | ||||||||
\(746\) | −14455.9 | −0.709477 | ||||||||
\(747\) | −6179.86 | + | 24651.5i | −0.302690 | + | 1.20743i | ||||
\(748\) | 2778.42i | 0.135814i | ||||||||
\(749\) | − | 27420.5i | − | 1.33768i | ||||||
\(750\) | −23.5294 | + | 18.3589i | −0.00114556 | + | 0.000893832i | ||||
\(751\) | − | 30502.5i | − | 1.48209i | −0.671453 | − | 0.741047i | \(-0.734329\pi\) | ||
0.671453 | − | 0.741047i | \(-0.265671\pi\) | |||||||
\(752\) | 17903.2 | 0.868170 | ||||||||
\(753\) | −8773.27 | + | 6845.39i | −0.424589 | + | 0.331288i | ||||
\(754\) | 12182.2 | 0.588393 | ||||||||
\(755\) | −55784.4 | −2.68901 | ||||||||
\(756\) | −2601.78 | + | 1152.40i | −0.125166 | + | 0.0554397i | ||||
\(757\) | −12073.7 | −0.579689 | −0.289845 | − | 0.957074i | \(-0.593604\pi\) | ||||
−0.289845 | + | 0.957074i | \(0.593604\pi\) | |||||||
\(758\) | 6041.76 | 0.289507 | ||||||||
\(759\) | −35699.3 | − | 45753.4i | −1.70725 | − | 2.18807i | ||||
\(760\) | − | 17714.7i | − | 0.845498i | ||||||
\(761\) | − | 1492.69i | − | 0.0711040i | −0.999368 | − | 0.0355520i | \(-0.988681\pi\) | ||
0.999368 | − | 0.0355520i | \(-0.0113189\pi\) | |||||||
\(762\) | −3131.23 | − | 4013.09i | −0.148861 | − | 0.190786i | ||||
\(763\) | − | 26506.5i | − | 1.25767i | ||||||
\(764\) | −129.762 | −0.00614480 | ||||||||
\(765\) | 5647.47 | − | 22527.8i | 0.266908 | − | 1.06470i | ||||
\(766\) | − | 19240.0i | − | 0.907530i | ||||||
\(767\) | −10515.5 | + | 6012.58i | −0.495038 | + | 0.283053i | ||||
\(768\) | 3876.38 | + | 4968.10i | 0.182131 | + | 0.233425i | ||||
\(769\) | − | 15205.3i | − | 0.713026i | −0.934290 | − | 0.356513i | \(-0.883965\pi\) | ||
0.934290 | − | 0.356513i | \(-0.116035\pi\) | |||||||
\(770\) | 69109.4i | 3.23446i | ||||||||
\(771\) | −9132.21 | + | 7125.45i | −0.426574 | + | 0.332836i | ||||
\(772\) | 1706.35 | 0.0795503 | ||||||||
\(773\) | 19916.9 | 0.926727 | 0.463364 | − | 0.886168i | \(-0.346642\pi\) | ||||
0.463364 | + | 0.886168i | \(0.346642\pi\) | |||||||
\(774\) | 212.070 | + | 53.1636i | 0.00984844 | + | 0.00246890i | ||||
\(775\) | − | 27211.7i | − | 1.26125i | ||||||
\(776\) | − | 10213.1i | − | 0.472462i | ||||||
\(777\) | −12754.1 | + | 9951.44i | −0.588868 | + | 0.459467i | ||||
\(778\) | − | 6506.20i | − | 0.299818i | ||||||
\(779\) | 17459.9i | 0.803039i | ||||||||
\(780\) | −1077.92 | − | 1381.50i | −0.0494816 | − | 0.0634173i | ||||
\(781\) | 17911.2i | 0.820630i | ||||||||
\(782\) | 25455.7i | 1.16406i | ||||||||
\(783\) | −9649.19 | − | 21785.0i | −0.440401 | − | 0.994295i | ||||
\(784\) | −17291.9 | −0.787712 | ||||||||
\(785\) | 22813.1 | 1.03724 | ||||||||
\(786\) | 2263.05 | + | 2900.40i | 0.102698 | + | 0.131621i | ||||
\(787\) | 34472.2 | 1.56138 | 0.780688 | − | 0.624921i | \(-0.214869\pi\) | ||||
0.780688 | + | 0.624921i | \(0.214869\pi\) | |||||||
\(788\) | − | 4262.39i | − | 0.192692i | ||||||
\(789\) | 11060.6 | − | 8630.05i | 0.499070 | − | 0.389402i | ||||
\(790\) | − | 2677.65i | − | 0.120591i | ||||||
\(791\) | 18647.2 | 0.838203 | ||||||||
\(792\) | −9926.89 | + | 39598.4i | −0.445375 | + | 1.77660i | ||||
\(793\) | 14938.6 | 0.668962 | ||||||||
\(794\) | − | 39416.6i | − | 1.76177i | ||||||
\(795\) | 23686.2 | + | 30357.0i | 1.05668 | + | 1.35428i | ||||
\(796\) | 2915.64 | 0.129827 | ||||||||
\(797\) | −23026.6 | −1.02339 | −0.511697 | − | 0.859166i | \(-0.670983\pi\) | ||||
−0.511697 | + | 0.859166i | \(0.670983\pi\) | |||||||
\(798\) | 10347.0 | + | 13261.1i | 0.458997 | + | 0.588266i | ||||
\(799\) | 17088.2i | 0.756618i | ||||||||
\(800\) | 4500.05 | 0.198876 | ||||||||
\(801\) | 1308.73 | − | 5220.53i | 0.0577300 | − | 0.230285i | ||||
\(802\) | −25263.6 | −1.11233 | ||||||||
\(803\) | 56220.1i | 2.47069i | ||||||||
\(804\) | −928.396 | + | 724.385i | −0.0407239 | + | 0.0317750i | ||||
\(805\) | − | 70130.7i | − | 3.07054i | ||||||
\(806\) | −15598.7 | −0.681688 | ||||||||
\(807\) | 20546.2 | + | 26332.7i | 0.896234 | + | 1.14864i | ||||
\(808\) | −41747.9 | −1.81768 | ||||||||
\(809\) | −15062.8 | −0.654611 | −0.327305 | − | 0.944919i | \(-0.606141\pi\) | ||||
−0.327305 | + | 0.944919i | \(0.606141\pi\) | |||||||
\(810\) | 14596.4 | − | 27282.9i | 0.633167 | − | 1.18349i | ||||
\(811\) | 17099.9i | 0.740394i | 0.928953 | + | 0.370197i | \(0.120710\pi\) | ||||
−0.928953 | + | 0.370197i | \(0.879290\pi\) | |||||||
\(812\) | 3444.57i | 0.148868i | ||||||||
\(813\) | 8272.69 | + | 10602.6i | 0.356871 | + | 0.457377i | ||||
\(814\) | 21043.8i | 0.906125i | ||||||||
\(815\) | 34508.0i | 1.48314i | ||||||||
\(816\) | 12696.1 | − | 9906.17i | 0.544671 | − | 0.424982i | ||||
\(817\) | 143.138i | 0.00612946i | ||||||||
\(818\) | 18927.2i | 0.809014i | ||||||||
\(819\) | 17798.3 | + | 4461.85i | 0.759369 | + | 0.190366i | ||||
\(820\) | −4643.47 | −0.197752 | ||||||||
\(821\) | −28651.4 | −1.21795 | −0.608977 | − | 0.793188i | \(-0.708420\pi\) | ||||
−0.608977 | + | 0.793188i | \(0.708420\pi\) | |||||||
\(822\) | −13395.1 | + | 10451.6i | −0.568379 | + | 0.443480i | ||||
\(823\) | − | 3501.54i | − | 0.148306i | −0.997247 | − | 0.0741530i | \(-0.976375\pi\) | ||
0.997247 | − | 0.0741530i | \(-0.0236253\pi\) | |||||||
\(824\) | 22362.0i | 0.945409i | ||||||||
\(825\) | 25614.8 | + | 32828.8i | 1.08096 | + | 1.38539i | ||||
\(826\) | 15349.3 | + | 26844.8i | 0.646576 | + | 1.13081i | ||||
\(827\) | − | 17211.6i | − | 0.723708i | −0.932235 | − | 0.361854i | \(-0.882144\pi\) | ||
0.932235 | − | 0.361854i | \(-0.117856\pi\) | |||||||
\(828\) | 913.411 | − | 3643.60i | 0.0383372 | − | 0.152927i | ||||
\(829\) | −22678.7 | −0.950139 | −0.475069 | − | 0.879948i | \(-0.657577\pi\) | ||||
−0.475069 | + | 0.879948i | \(0.657577\pi\) | |||||||
\(830\) | 39951.8i | 1.67078i | ||||||||
\(831\) | −23359.5 | − | 29938.3i | −0.975129 | − | 1.24976i | ||||
\(832\) | − | 14764.0i | − | 0.615204i | ||||||
\(833\) | − | 16504.7i | − | 0.686498i | ||||||
\(834\) | −9759.88 | − | 12508.6i | −0.405224 | − | 0.519349i | ||||
\(835\) | 33546.3 | 1.39032 | ||||||||
\(836\) | −2423.46 | −0.100260 | ||||||||
\(837\) | 12355.3 | + | 27894.7i | 0.510231 | + | 1.15195i | ||||
\(838\) | −22513.2 | −0.928051 | ||||||||
\(839\) | 2844.91 | 0.117065 | 0.0585324 | − | 0.998286i | \(-0.481358\pi\) | ||||
0.0585324 | + | 0.998286i | \(0.481358\pi\) | |||||||
\(840\) | −38895.2 | + | 30348.1i | −1.59763 | + | 1.24656i | ||||
\(841\) | −4452.85 | −0.182576 | ||||||||
\(842\) | 21972.2i | 0.899301i | ||||||||
\(843\) | −16469.5 | + | 12850.4i | −0.672882 | + | 0.525019i | ||||
\(844\) | − | 2916.45i | − | 0.118943i | ||||||
\(845\) | − | 23447.9i | − | 0.954595i | ||||||
\(846\) | −5535.98 | + | 22083.0i | −0.224978 | + | 0.897436i | ||||
\(847\) | 70428.2 | 2.85708 | ||||||||
\(848\) | 26697.9i | 1.08114i | ||||||||
\(849\) | 1008.20 | − | 786.651i | 0.0407553 | − | 0.0317995i | ||||
\(850\) | − | 18264.9i | − | 0.737035i | ||||||
\(851\) | − | 21354.8i | − | 0.860204i | ||||||
\(852\) | −914.038 | + | 713.182i | −0.0367540 | + | 0.0286775i | ||||
\(853\) | 8819.84 | 0.354028 | 0.177014 | − | 0.984208i | \(-0.443356\pi\) | ||||
0.177014 | + | 0.984208i | \(0.443356\pi\) | |||||||
\(854\) | − | 38136.4i | − | 1.52810i | ||||||
\(855\) | 19649.7 | + | 4925.98i | 0.785973 | + | 0.197035i | ||||
\(856\) | − | 25463.0i | − | 1.01671i | ||||||
\(857\) | −10291.3 | −0.410203 | −0.205102 | − | 0.978741i | \(-0.565753\pi\) | ||||
−0.205102 | + | 0.978741i | \(0.565753\pi\) | |||||||
\(858\) | 18818.6 | − | 14683.3i | 0.748784 | − | 0.584242i | ||||
\(859\) | 33874.6i | 1.34550i | 0.739868 | + | 0.672752i | \(0.234888\pi\) | ||||
−0.739868 | + | 0.672752i | \(0.765112\pi\) | |||||||
\(860\) | −38.0676 | −0.00150941 | ||||||||
\(861\) | 38335.9 | − | 29911.7i | 1.51740 | − | 1.18396i | ||||
\(862\) | 33903.9 | 1.33964 | ||||||||
\(863\) | −10238.2 | −0.403837 | −0.201918 | − | 0.979402i | \(-0.564718\pi\) | ||||
−0.201918 | + | 0.979402i | \(0.564718\pi\) | |||||||
\(864\) | −4613.01 | + | 2043.23i | −0.181641 | + | 0.0804538i | ||||
\(865\) | 49433.1i | 1.94309i | ||||||||
\(866\) | −17486.1 | −0.686144 | ||||||||
\(867\) | −6248.94 | − | 8008.85i | −0.244781 | − | 0.313719i | ||||
\(868\) | − | 4410.62i | − | 0.172473i | ||||||
\(869\) | −4039.94 | −0.157705 | ||||||||
\(870\) | −23041.0 | − | 29530.1i | −0.897889 | − | 1.15076i | ||||
\(871\) | 7593.25 | 0.295393 | ||||||||
\(872\) | − | 24614.2i | − | 0.955897i | ||||||
\(873\) | 11328.8 | + | 2840.00i | 0.439199 | + | 0.110103i | ||||
\(874\) | −22203.6 | −0.859324 | ||||||||
\(875\) | 54.4148i | 0.00210235i | ||||||||
\(876\) | −2869.01 | + | 2238.56i | −0.110656 | + | 0.0863400i | ||||
\(877\) | −10811.8 | −0.416293 | −0.208147 | − | 0.978098i | \(-0.566743\pi\) | ||||
−0.208147 | + | 0.978098i | \(0.566743\pi\) | |||||||
\(878\) | 527.881 | 0.0202906 | ||||||||
\(879\) | 13945.3 | − | 10880.9i | 0.535111 | − | 0.417522i | ||||
\(880\) | 57712.2i | 2.21077i | ||||||||
\(881\) | 25219.0 | 0.964415 | 0.482208 | − | 0.876057i | \(-0.339835\pi\) | ||||
0.482208 | + | 0.876057i | \(0.339835\pi\) | |||||||
\(882\) | 5346.93 | − | 21328.9i | 0.204128 | − | 0.814265i | ||||
\(883\) | 4824.16 | 0.183857 | 0.0919287 | − | 0.995766i | \(-0.470697\pi\) | ||||
0.0919287 | + | 0.995766i | \(0.470697\pi\) | |||||||
\(884\) | 1159.66 | 0.0441219 | ||||||||
\(885\) | 34463.6 | + | 14118.1i | 1.30902 | + | 0.536243i | ||||
\(886\) | 4272.46 | 0.162005 | ||||||||
\(887\) | −18780.5 | −0.710921 | −0.355461 | − | 0.934691i | \(-0.615676\pi\) | ||||
−0.355461 | + | 0.934691i | \(0.615676\pi\) | |||||||
\(888\) | −11843.6 | + | 9241.01i | −0.447573 | + | 0.349221i | ||||
\(889\) | −9280.77 | −0.350132 | ||||||||
\(890\) | − | 8460.74i | − | 0.318657i | ||||||
\(891\) | −41163.5 | − | 22022.5i | −1.54773 | − | 0.828038i | ||||
\(892\) | −88.8119 | −0.00333368 | ||||||||
\(893\) | −14905.1 | −0.558545 | ||||||||
\(894\) | −8502.94 | − | 10897.7i | −0.318100 | − | 0.407687i | ||||
\(895\) | 8053.45i | 0.300779i | ||||||||
\(896\) | −30375.8 | −1.13257 | ||||||||
\(897\) | −19096.7 | + | 14900.3i | −0.710837 | + | 0.554633i | ||||
\(898\) | 35099.0i | 1.30431i | ||||||||
\(899\) | 36930.7 | 1.37008 | ||||||||
\(900\) | −655.386 | + | 2614.33i | −0.0242735 | + | 0.0968272i | ||||
\(901\) | −25482.5 | −0.942225 | ||||||||
\(902\) | − | 63253.0i | − | 2.33491i | ||||||
\(903\) | 314.281 | − | 245.219i | 0.0115821 | − | 0.00903697i | ||||
\(904\) | 17316.0 | 0.637081 | ||||||||
\(905\) | − | 7189.92i | − | 0.264090i | ||||||
\(906\) | 38778.5 | − | 30257.1i | 1.42200 | − | 1.10952i | ||||
\(907\) | 20867.1 | 0.763925 | 0.381962 | − | 0.924178i | \(-0.375248\pi\) | ||||
0.381962 | + | 0.924178i | \(0.375248\pi\) | |||||||
\(908\) | −895.506 | −0.0327295 | ||||||||
\(909\) | 11609.0 | − | 46308.3i | 0.423593 | − | 1.68971i | ||||
\(910\) | 28845.1 | 1.05078 | ||||||||
\(911\) | 25871.7i | 0.940909i | 0.882424 | + | 0.470454i | \(0.155910\pi\) | ||||
−0.882424 | + | 0.470454i | \(0.844090\pi\) | |||||||
\(912\) | 8640.61 | + | 11074.1i | 0.313727 | + | 0.402083i | ||||
\(913\) | 60277.8 | 2.18500 | ||||||||
\(914\) | 27432.9i | 0.992780i | ||||||||
\(915\) | −28254.5 | − | 36211.9i | −1.02084 | − | 1.30834i | ||||
\(916\) | − | 90.5310i | − | 0.00326553i | ||||||
\(917\) | 6707.54 | 0.241551 | ||||||||
\(918\) | 8293.08 | + | 18723.3i | 0.298162 | + | 0.673161i | ||||
\(919\) | − | 12942.5i | − | 0.464562i | −0.972649 | − | 0.232281i | \(-0.925381\pi\) | ||
0.972649 | − | 0.232281i | \(-0.0746189\pi\) | |||||||
\(920\) | − | 65124.1i | − | 2.33378i | ||||||
\(921\) | −13105.0 | − | 16795.9i | −0.468866 | − | 0.600915i | ||||
\(922\) | − | 49306.8i | − | 1.76121i | ||||||
\(923\) | 7475.82 | 0.266598 | ||||||||
\(924\) | 4151.79 | + | 5321.07i | 0.147818 | + | 0.189448i | ||||
\(925\) | 15322.4i | 0.544646i | ||||||||
\(926\) | − | 9726.62i | − | 0.345180i | ||||||
\(927\) | −24804.7 | − | 6218.28i | −0.878849 | − | 0.220318i | ||||
\(928\) | 6107.30i | 0.216037i | ||||||||
\(929\) | 37529.0 | 1.32539 | 0.662694 | − | 0.748890i | \(-0.269413\pi\) | ||||
0.662694 | + | 0.748890i | \(0.269413\pi\) | |||||||
\(930\) | 29502.9 | + | 37812.0i | 1.04026 | + | 1.33323i | ||||
\(931\) | 14396.1 | 0.506782 | ||||||||
\(932\) | −562.046 | −0.0197537 | ||||||||
\(933\) | −5923.41 | + | 4621.77i | −0.207850 | + | 0.162176i | ||||
\(934\) | −43831.6 | −1.53556 | ||||||||
\(935\) | −55084.9 | −1.92670 | ||||||||
\(936\) | 16527.7 | + | 4143.32i | 0.577163 | + | 0.144689i | ||||
\(937\) | − | 26577.3i | − | 0.926619i | −0.886197 | − | 0.463309i | \(-0.846662\pi\) | ||
0.886197 | − | 0.463309i | \(-0.153338\pi\) | |||||||
\(938\) | − | 19384.6i | − | 0.674764i | ||||||
\(939\) | −7985.39 | + | 6230.64i | −0.277522 | + | 0.216538i | ||||
\(940\) | − | 3964.01i | − | 0.137545i | ||||||
\(941\) | −11505.9 | −0.398598 | −0.199299 | − | 0.979939i | \(-0.563867\pi\) | ||||
−0.199299 | + | 0.979939i | \(0.563867\pi\) | |||||||
\(942\) | −15858.5 | + | 12373.7i | −0.548512 | + | 0.427979i | ||||
\(943\) | 64187.7i | 2.21658i | ||||||||
\(944\) | 12818.0 | + | 22417.7i | 0.441938 | + | 0.772916i | ||||
\(945\) | −22847.5 | − | 51582.9i | −0.786486 | − | 1.77565i | ||||
\(946\) | − | 518.553i | − | 0.0178220i | ||||||
\(947\) | 3123.78i | 0.107190i | 0.998563 | + | 0.0535952i | \(0.0170680\pi\) | ||||
−0.998563 | + | 0.0535952i | \(0.982932\pi\) | |||||||
\(948\) | −160.861 | − | 206.165i | −0.00551111 | − | 0.00706323i | ||||
\(949\) | 23465.3 | 0.802651 | ||||||||
\(950\) | 15931.4 | 0.544089 | ||||||||
\(951\) | −35999.0 | + | 28088.4i | −1.22749 | + | 0.957757i | ||||
\(952\) | − | 32649.7i | − | 1.11154i | ||||||
\(953\) | 6989.12i | 0.237565i | 0.992920 | + | 0.118783i | \(0.0378992\pi\) | ||||
−0.992920 | + | 0.118783i | \(0.962101\pi\) | |||||||
\(954\) | −32930.9 | − | 8255.43i | −1.11759 | − | 0.280167i | ||||
\(955\) | − | 2572.66i | − | 0.0871722i | ||||||
\(956\) | − | 4054.35i | − | 0.137162i | ||||||
\(957\) | −44553.9 | + | 34763.4i | −1.50494 | + | 1.17423i | ||||
\(958\) | 7835.27i | 0.264244i | ||||||||
\(959\) | 30977.9i | 1.04309i | ||||||||
\(960\) | −35788.6 | + | 27924.2i | −1.20320 | + | 0.938802i | ||||
\(961\) | −17497.0 | −0.587325 | ||||||||
\(962\) | 8783.34 | 0.294372 | ||||||||
\(963\) | 28244.4 | + | 7080.57i | 0.945133 | + | 0.236935i | ||||
\(964\) | −3056.93 | −0.102134 | ||||||||
\(965\) | 33830.1i | 1.12853i | ||||||||
\(966\) | 38038.5 | + | 48751.4i | 1.26694 | + | 1.62376i | ||||
\(967\) | 37950.7i | 1.26206i | 0.775758 | + | 0.631031i | \(0.217368\pi\) | ||||
−0.775758 | + | 0.631031i | \(0.782632\pi\) | |||||||
\(968\) | 65400.4 | 2.17154 | ||||||||
\(969\) | −10570.0 | + | 8247.26i | −0.350419 | + | 0.273416i | ||||
\(970\) | 18360.2 | 0.607741 | ||||||||
\(971\) | 35858.0i | 1.18511i | 0.805532 | + | 0.592553i | \(0.201880\pi\) | ||||
−0.805532 | + | 0.592553i | \(0.798120\pi\) | |||||||
\(972\) | −515.190 | − | 2977.53i | −0.0170008 | − | 0.0982555i | ||||
\(973\) | −28927.7 | −0.953113 | ||||||||
\(974\) | −27934.4 | −0.918968 | ||||||||
\(975\) | 13702.2 | − | 10691.2i | 0.450072 | − | 0.351171i | ||||
\(976\) | − | 31847.1i | − | 1.04447i | ||||||
\(977\) | 2537.66 | 0.0830983 | 0.0415492 | − | 0.999136i | \(-0.486771\pi\) | ||||
0.0415492 | + | 0.999136i | \(0.486771\pi\) | |||||||
\(978\) | −18716.9 | − | 23988.2i | −0.611965 | − | 0.784314i | ||||
\(979\) | −12765.2 | −0.416730 | ||||||||
\(980\) | 3828.64i | 0.124798i | ||||||||
\(981\) | 27302.9 | + | 6844.56i | 0.888599 | + | 0.222762i | ||||
\(982\) | − | 11703.4i | − | 0.380317i | ||||||
\(983\) | −15668.4 | −0.508389 | −0.254194 | − | 0.967153i | \(-0.581810\pi\) | ||||
−0.254194 | + | 0.967153i | \(0.581810\pi\) | |||||||
\(984\) | 35599.1 | − | 27776.4i | 1.15331 | − | 0.899876i | ||||
\(985\) | 84506.2 | 2.73359 | ||||||||
\(986\) | 24788.4 | 0.800632 | ||||||||
\(987\) | 25534.9 | + | 32726.4i | 0.823491 | + | 1.05541i | ||||
\(988\) | 1011.51i | 0.0325713i | ||||||||
\(989\) | 526.216i | 0.0169188i | ||||||||
\(990\) | −71186.0 | − | 17845.6i | −2.28529 | − | 0.572898i | ||||
\(991\) | 29443.1i | 0.943784i | 0.881656 | + | 0.471892i | \(0.156429\pi\) | ||||
−0.881656 | + | 0.471892i | \(0.843571\pi\) | |||||||
\(992\) | − | 7820.12i | − | 0.250291i | ||||||
\(993\) | 9501.45 | + | 12177.4i | 0.303645 | + | 0.389161i | ||||
\(994\) | − | 19084.8i | − | 0.608986i | ||||||
\(995\) | 57805.5i | 1.84177i | ||||||||
\(996\) | 2400.12 | + | 3076.08i | 0.0763563 | + | 0.0978607i | ||||
\(997\) | −4185.23 | −0.132946 | −0.0664732 | − | 0.997788i | \(-0.521175\pi\) | ||||
−0.0664732 | + | 0.997788i | \(0.521175\pi\) | |||||||
\(998\) | −2642.70 | −0.0838209 | ||||||||
\(999\) | −6957.07 | − | 15707.0i | −0.220332 | − | 0.497445i |
(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 | 177.4.d.c.176.15 | ✓ | 52 | |
3.2 | odd | 2 | inner | 177.4.d.c.176.38 | yes | 52 | |
59.58 | odd | 2 | inner | 177.4.d.c.176.37 | yes | 52 | |
177.176 | even | 2 | inner | 177.4.d.c.176.16 | yes | 52 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
177.4.d.c.176.15 | ✓ | 52 | 1.1 | even | 1 | trivial | |
177.4.d.c.176.16 | yes | 52 | 177.176 | even | 2 | inner | |
177.4.d.c.176.37 | yes | 52 | 59.58 | odd | 2 | inner | |
177.4.d.c.176.38 | yes | 52 | 3.2 | odd | 2 | inner |