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 | 176.13 | ||
Character | \(\chi\) | \(=\) | 177.176 |
Dual form | 177.4.d.c.176.14 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −3.37014 | −1.19152 | −0.595762 | − | 0.803161i | \(-0.703150\pi\) | ||||
−0.595762 | + | 0.803161i | \(0.703150\pi\) | |||||||
\(3\) | 1.51919 | − | 4.96911i | 0.292368 | − | 0.956306i | ||||
\(4\) | 3.35783 | 0.419729 | ||||||||
\(5\) | − | 10.3951i | − | 0.929764i | −0.885373 | − | 0.464882i | \(-0.846097\pi\) | ||
0.885373 | − | 0.464882i | \(-0.153903\pi\) | |||||||
\(6\) | −5.11987 | + | 16.7466i | −0.348363 | + | 1.13946i | ||||
\(7\) | −22.3857 | −1.20871 | −0.604357 | − | 0.796713i | \(-0.706570\pi\) | ||||
−0.604357 | + | 0.796713i | \(0.706570\pi\) | |||||||
\(8\) | 15.6447 | 0.691407 | ||||||||
\(9\) | −22.3841 | − | 15.0980i | −0.829042 | − | 0.559186i | ||||
\(10\) | 35.0329i | 1.10784i | ||||||||
\(11\) | −29.3191 | −0.803641 | −0.401820 | − | 0.915719i | \(-0.631622\pi\) | ||||
−0.401820 | + | 0.915719i | \(0.631622\pi\) | |||||||
\(12\) | 5.10117 | − | 16.6854i | 0.122715 | − | 0.401389i | ||||
\(13\) | − | 2.60330i | − | 0.0555405i | −0.999614 | − | 0.0277702i | \(-0.991159\pi\) | ||
0.999614 | − | 0.0277702i | \(-0.00884068\pi\) | |||||||
\(14\) | 75.4429 | 1.44021 | ||||||||
\(15\) | −51.6543 | − | 15.7921i | −0.889139 | − | 0.271833i | ||||
\(16\) | −79.5876 | −1.24356 | ||||||||
\(17\) | − | 37.1200i | − | 0.529584i | −0.964306 | − | 0.264792i | \(-0.914697\pi\) | ||
0.964306 | − | 0.264792i | \(-0.0853032\pi\) | |||||||
\(18\) | 75.4377 | + | 50.8824i | 0.987824 | + | 0.666283i | ||||
\(19\) | 116.745 | 1.40964 | 0.704818 | − | 0.709389i | \(-0.251029\pi\) | ||||
0.704818 | + | 0.709389i | \(0.251029\pi\) | |||||||
\(20\) | − | 34.9049i | − | 0.390249i | ||||||
\(21\) | −34.0081 | + | 111.237i | −0.353389 | + | 1.15590i | ||||
\(22\) | 98.8095 | 0.957557 | ||||||||
\(23\) | −70.3128 | −0.637445 | −0.318723 | − | 0.947848i | \(-0.603254\pi\) | ||||
−0.318723 | + | 0.947848i | \(0.603254\pi\) | |||||||
\(24\) | 23.7673 | − | 77.7405i | 0.202145 | − | 0.661196i | ||||
\(25\) | 16.9423 | 0.135539 | ||||||||
\(26\) | 8.77349i | 0.0661778i | ||||||||
\(27\) | −109.029 | + | 88.2926i | −0.777138 | + | 0.629330i | ||||
\(28\) | −75.1674 | −0.507333 | ||||||||
\(29\) | − | 82.7478i | − | 0.529858i | −0.964268 | − | 0.264929i | \(-0.914651\pi\) | ||
0.964268 | − | 0.264929i | \(-0.0853485\pi\) | |||||||
\(30\) | 174.082 | + | 53.2214i | 1.05943 | + | 0.323895i | ||||
\(31\) | 269.641i | 1.56222i | 0.624392 | + | 0.781112i | \(0.285347\pi\) | ||||
−0.624392 | + | 0.781112i | \(0.714653\pi\) | |||||||
\(32\) | 143.063 | 0.790321 | ||||||||
\(33\) | −44.5412 | + | 145.690i | −0.234959 | + | 0.768526i | ||||
\(34\) | 125.099i | 0.631011i | ||||||||
\(35\) | 232.701i | 1.12382i | ||||||||
\(36\) | −75.1622 | − | 50.6966i | −0.347973 | − | 0.234706i | ||||
\(37\) | 248.510i | 1.10418i | 0.833783 | + | 0.552092i | \(0.186170\pi\) | ||||
−0.833783 | + | 0.552092i | \(0.813830\pi\) | |||||||
\(38\) | −393.446 | −1.67961 | ||||||||
\(39\) | −12.9361 | − | 3.95490i | −0.0531137 | − | 0.0162382i | ||||
\(40\) | − | 162.628i | − | 0.642845i | ||||||
\(41\) | 129.586i | 0.493608i | 0.969065 | + | 0.246804i | \(0.0793803\pi\) | ||||
−0.969065 | + | 0.246804i | \(0.920620\pi\) | |||||||
\(42\) | 114.612 | − | 374.884i | 0.421071 | − | 1.37728i | ||||
\(43\) | 161.471i | 0.572654i | 0.958132 | + | 0.286327i | \(0.0924343\pi\) | ||||
−0.958132 | + | 0.286327i | \(0.907566\pi\) | |||||||
\(44\) | −98.4487 | −0.337311 | ||||||||
\(45\) | −156.945 | + | 232.685i | −0.519911 | + | 0.770814i | ||||
\(46\) | 236.964 | 0.759531 | ||||||||
\(47\) | −349.870 | −1.08583 | −0.542913 | − | 0.839789i | \(-0.682678\pi\) | ||||
−0.542913 | + | 0.839789i | \(0.682678\pi\) | |||||||
\(48\) | −120.908 | + | 395.480i | −0.363576 | + | 1.18922i | ||||
\(49\) | 158.120 | 0.460991 | ||||||||
\(50\) | −57.0980 | −0.161497 | ||||||||
\(51\) | −184.453 | − | 56.3922i | −0.506444 | − | 0.154833i | ||||
\(52\) | − | 8.74145i | − | 0.0233119i | ||||||
\(53\) | 264.779i | 0.686230i | 0.939293 | + | 0.343115i | \(0.111482\pi\) | ||||
−0.939293 | + | 0.343115i | \(0.888518\pi\) | |||||||
\(54\) | 367.444 | − | 297.558i | 0.925978 | − | 0.749862i | ||||
\(55\) | 304.775i | 0.747196i | ||||||||
\(56\) | −350.219 | −0.835713 | ||||||||
\(57\) | 177.357 | − | 580.117i | 0.412132 | − | 1.34804i | ||||
\(58\) | 278.872i | 0.631339i | ||||||||
\(59\) | 404.169 | − | 205.003i | 0.891836 | − | 0.452358i | ||||
\(60\) | −173.447 | − | 53.0271i | −0.373197 | − | 0.114096i | ||||
\(61\) | − | 623.548i | − | 1.30881i | −0.756146 | − | 0.654403i | \(-0.772920\pi\) | ||
0.756146 | − | 0.654403i | \(-0.227080\pi\) | |||||||
\(62\) | − | 908.727i | − | 1.86143i | ||||||
\(63\) | 501.085 | + | 337.980i | 1.00208 | + | 0.675896i | ||||
\(64\) | 154.558 | 0.301871 | ||||||||
\(65\) | −27.0615 | −0.0516395 | ||||||||
\(66\) | 150.110 | − | 490.995i | 0.279959 | − | 0.915718i | ||||
\(67\) | 11.5921i | 0.0211373i | 0.999944 | + | 0.0105687i | \(0.00336417\pi\) | ||||
−0.999944 | + | 0.0105687i | \(0.996636\pi\) | |||||||
\(68\) | − | 124.643i | − | 0.222282i | ||||||
\(69\) | −106.818 | + | 349.392i | −0.186368 | + | 0.609593i | ||||
\(70\) | − | 784.235i | − | 1.33906i | ||||||
\(71\) | 97.1804i | 0.162439i | 0.996696 | + | 0.0812196i | \(0.0258815\pi\) | ||||
−0.996696 | + | 0.0812196i | \(0.974118\pi\) | |||||||
\(72\) | −350.194 | − | 236.205i | −0.573205 | − | 0.386625i | ||||
\(73\) | − | 562.273i | − | 0.901495i | −0.892652 | − | 0.450747i | \(-0.851157\pi\) | ||
0.892652 | − | 0.450747i | \(-0.148843\pi\) | |||||||
\(74\) | − | 837.513i | − | 1.31566i | ||||||
\(75\) | 25.7386 | − | 84.1883i | 0.0396271 | − | 0.129616i | ||||
\(76\) | 392.009 | 0.591665 | ||||||||
\(77\) | 656.329 | 0.971372 | ||||||||
\(78\) | 43.5964 | + | 13.3286i | 0.0632862 | + | 0.0193482i | ||||
\(79\) | −599.822 | −0.854244 | −0.427122 | − | 0.904194i | \(-0.640472\pi\) | ||||
−0.427122 | + | 0.904194i | \(0.640472\pi\) | |||||||
\(80\) | 827.320i | 1.15621i | ||||||||
\(81\) | 273.100 | + | 675.912i | 0.374623 | + | 0.927177i | ||||
\(82\) | − | 436.722i | − | 0.588145i | ||||||
\(83\) | −499.474 | −0.660534 | −0.330267 | − | 0.943887i | \(-0.607139\pi\) | ||||
−0.330267 | + | 0.943887i | \(0.607139\pi\) | |||||||
\(84\) | −114.193 | + | 373.515i | −0.148328 | + | 0.485165i | ||||
\(85\) | −385.865 | −0.492388 | ||||||||
\(86\) | − | 544.180i | − | 0.682331i | ||||||
\(87\) | −411.183 | − | 125.709i | −0.506707 | − | 0.154913i | ||||
\(88\) | −458.690 | −0.555643 | ||||||||
\(89\) | −530.960 | −0.632378 | −0.316189 | − | 0.948696i | \(-0.602403\pi\) | ||||
−0.316189 | + | 0.948696i | \(0.602403\pi\) | |||||||
\(90\) | 528.927 | − | 784.180i | 0.619486 | − | 0.918443i | ||||
\(91\) | 58.2768i | 0.0671326i | ||||||||
\(92\) | −236.099 | −0.267554 | ||||||||
\(93\) | 1339.88 | + | 409.635i | 1.49396 | + | 0.456743i | ||||
\(94\) | 1179.11 | 1.29379 | ||||||||
\(95\) | − | 1213.57i | − | 1.31063i | ||||||
\(96\) | 217.340 | − | 710.898i | 0.231064 | − | 0.755788i | ||||
\(97\) | − | 1527.88i | − | 1.59930i | −0.600464 | − | 0.799652i | \(-0.705017\pi\) | ||
0.600464 | − | 0.799652i | \(-0.294983\pi\) | |||||||
\(98\) | −532.886 | −0.549282 | ||||||||
\(99\) | 656.283 | + | 442.661i | 0.666252 | + | 0.449384i | ||||
\(100\) | 56.8895 | 0.0568895 | ||||||||
\(101\) | −257.690 | −0.253872 | −0.126936 | − | 0.991911i | \(-0.540514\pi\) | ||||
−0.126936 | + | 0.991911i | \(0.540514\pi\) | |||||||
\(102\) | 621.633 | + | 190.049i | 0.603440 | + | 0.184487i | ||||
\(103\) | − | 1232.61i | − | 1.17916i | −0.807712 | − | 0.589578i | \(-0.799294\pi\) | ||
0.807712 | − | 0.589578i | \(-0.200706\pi\) | |||||||
\(104\) | − | 40.7280i | − | 0.0384011i | ||||||
\(105\) | 1156.32 | + | 353.517i | 1.07472 | + | 0.328568i | ||||
\(106\) | − | 892.342i | − | 0.817660i | ||||||
\(107\) | 1418.59i | 1.28168i | 0.767673 | + | 0.640842i | \(0.221414\pi\) | ||||
−0.767673 | + | 0.640842i | \(0.778586\pi\) | |||||||
\(108\) | −366.102 | + | 296.472i | −0.326187 | + | 0.264148i | ||||
\(109\) | 2213.07i | 1.94471i | 0.233498 | + | 0.972357i | \(0.424983\pi\) | ||||
−0.233498 | + | 0.972357i | \(0.575017\pi\) | |||||||
\(110\) | − | 1027.13i | − | 0.890302i | ||||||
\(111\) | 1234.87 | + | 377.533i | 1.05594 | + | 0.322828i | ||||
\(112\) | 1781.63 | 1.50310 | ||||||||
\(113\) | −2305.55 | −1.91936 | −0.959682 | − | 0.281088i | \(-0.909305\pi\) | ||||
−0.959682 | + | 0.281088i | \(0.909305\pi\) | |||||||
\(114\) | −597.717 | + | 1955.08i | −0.491065 | + | 1.60622i | ||||
\(115\) | 730.907i | 0.592674i | ||||||||
\(116\) | − | 277.853i | − | 0.222397i | ||||||
\(117\) | −39.3047 | + | 58.2727i | −0.0310574 | + | 0.0460454i | ||||
\(118\) | −1362.11 | + | 690.889i | −1.06264 | + | 0.538996i | ||||
\(119\) | 830.957i | 0.640115i | ||||||||
\(120\) | −808.119 | − | 247.063i | −0.614757 | − | 0.187947i | ||||
\(121\) | −471.389 | −0.354162 | ||||||||
\(122\) | 2101.44i | 1.55947i | ||||||||
\(123\) | 643.927 | + | 196.865i | 0.472040 | + | 0.144315i | ||||
\(124\) | 905.408i | 0.655710i | ||||||||
\(125\) | − | 1475.50i | − | 1.05578i | ||||||
\(126\) | −1688.73 | − | 1139.04i | −1.19400 | − | 0.805346i | ||||
\(127\) | −587.658 | −0.410600 | −0.205300 | − | 0.978699i | \(-0.565817\pi\) | ||||
−0.205300 | + | 0.978699i | \(0.565817\pi\) | |||||||
\(128\) | −1665.39 | −1.15001 | ||||||||
\(129\) | 802.368 | + | 245.305i | 0.547632 | + | 0.167425i | ||||
\(130\) | 91.2011 | 0.0615297 | ||||||||
\(131\) | 830.179 | 0.553688 | 0.276844 | − | 0.960915i | \(-0.410711\pi\) | ||||
0.276844 | + | 0.960915i | \(0.410711\pi\) | |||||||
\(132\) | −149.562 | + | 489.203i | −0.0986189 | + | 0.322573i | ||||
\(133\) | −2613.41 | −1.70385 | ||||||||
\(134\) | − | 39.0670i | − | 0.0251856i | ||||||
\(135\) | 917.809 | + | 1133.37i | 0.585129 | + | 0.722555i | ||||
\(136\) | − | 580.733i | − | 0.366158i | ||||||
\(137\) | − | 513.844i | − | 0.320443i | −0.987081 | − | 0.160221i | \(-0.948779\pi\) | ||
0.987081 | − | 0.160221i | \(-0.0512208\pi\) | |||||||
\(138\) | 359.992 | − | 1177.50i | 0.222062 | − | 0.726344i | ||||
\(139\) | −1894.55 | −1.15607 | −0.578033 | − | 0.816013i | \(-0.696180\pi\) | ||||
−0.578033 | + | 0.816013i | \(0.696180\pi\) | |||||||
\(140\) | 781.372i | 0.471700i | ||||||||
\(141\) | −531.518 | + | 1738.54i | −0.317460 | + | 1.03838i | ||||
\(142\) | − | 327.511i | − | 0.193550i | ||||||
\(143\) | 76.3265i | 0.0446346i | ||||||||
\(144\) | 1781.50 | + | 1201.62i | 1.03096 | + | 0.695379i | ||||
\(145\) | −860.170 | −0.492643 | ||||||||
\(146\) | 1894.94i | 1.07415i | ||||||||
\(147\) | 240.214 | − | 785.715i | 0.134779 | − | 0.440848i | ||||
\(148\) | 834.455i | 0.463458i | ||||||||
\(149\) | −2830.23 | −1.55612 | −0.778058 | − | 0.628193i | \(-0.783795\pi\) | ||||
−0.778058 | + | 0.628193i | \(0.783795\pi\) | |||||||
\(150\) | −86.7425 | + | 283.726i | −0.0472166 | + | 0.154441i | ||||
\(151\) | 2008.00i | 1.08218i | 0.840965 | + | 0.541089i | \(0.181988\pi\) | ||||
−0.840965 | + | 0.541089i | \(0.818012\pi\) | |||||||
\(152\) | 1826.44 | 0.974631 | ||||||||
\(153\) | −560.438 | + | 830.899i | −0.296136 | + | 0.439047i | ||||
\(154\) | −2211.92 | −1.15741 | ||||||||
\(155\) | 2802.94 | 1.45250 | ||||||||
\(156\) | −43.4373 | − | 13.2799i | −0.0222934 | − | 0.00681566i | ||||
\(157\) | 1331.26i | 0.676726i | 0.941016 | + | 0.338363i | \(0.109873\pi\) | ||||
−0.941016 | + | 0.338363i | \(0.890127\pi\) | |||||||
\(158\) | 2021.48 | 1.01785 | ||||||||
\(159\) | 1315.72 | + | 402.249i | 0.656246 | + | 0.200631i | ||||
\(160\) | − | 1487.15i | − | 0.734812i | ||||||
\(161\) | 1574.00 | 0.770489 | ||||||||
\(162\) | −920.384 | − | 2277.92i | −0.446372 | − | 1.10475i | ||||
\(163\) | 462.931 | 0.222451 | 0.111226 | − | 0.993795i | \(-0.464522\pi\) | ||||
0.111226 | + | 0.993795i | \(0.464522\pi\) | |||||||
\(164\) | 435.127i | 0.207181i | ||||||||
\(165\) | 1514.46 | + | 463.009i | 0.714548 | + | 0.218456i | ||||
\(166\) | 1683.30 | 0.787042 | ||||||||
\(167\) | − | 3421.98i | − | 1.58563i | −0.609460 | − | 0.792817i | \(-0.708614\pi\) | ||
0.609460 | − | 0.792817i | \(-0.291386\pi\) | |||||||
\(168\) | −532.048 | + | 1740.28i | −0.244335 | + | 0.799198i | ||||
\(169\) | 2190.22 | 0.996915 | ||||||||
\(170\) | 1300.42 | 0.586692 | ||||||||
\(171\) | −2613.23 | − | 1762.61i | −1.16865 | − | 0.788248i | ||||
\(172\) | 542.193i | 0.240359i | ||||||||
\(173\) | −1531.18 | −0.672910 | −0.336455 | − | 0.941699i | \(-0.609228\pi\) | ||||
−0.336455 | + | 0.941699i | \(0.609228\pi\) | |||||||
\(174\) | 1385.74 | + | 423.658i | 0.603753 | + | 0.184583i | ||||
\(175\) | −379.266 | −0.163828 | ||||||||
\(176\) | 2333.44 | 0.999373 | ||||||||
\(177\) | −404.675 | − | 2319.80i | −0.171849 | − | 0.985123i | ||||
\(178\) | 1789.41 | 0.753494 | ||||||||
\(179\) | 2200.21 | 0.918723 | 0.459362 | − | 0.888249i | \(-0.348078\pi\) | ||||
0.459362 | + | 0.888249i | \(0.348078\pi\) | |||||||
\(180\) | −526.995 | + | 781.317i | −0.218222 | + | 0.323533i | ||||
\(181\) | −2254.70 | −0.925913 | −0.462956 | − | 0.886381i | \(-0.653211\pi\) | ||||
−0.462956 | + | 0.886381i | \(0.653211\pi\) | |||||||
\(182\) | − | 196.401i | − | 0.0799901i | ||||||
\(183\) | −3098.48 | − | 947.285i | −1.25162 | − | 0.382652i | ||||
\(184\) | −1100.03 | −0.440734 | ||||||||
\(185\) | 2583.28 | 1.02663 | ||||||||
\(186\) | −4515.56 | − | 1380.53i | −1.78009 | − | 0.544221i | ||||
\(187\) | 1088.33i | 0.425595i | ||||||||
\(188\) | −1174.80 | −0.455752 | ||||||||
\(189\) | 2440.70 | − | 1976.49i | 0.939338 | − | 0.760681i | ||||
\(190\) | 4089.90i | 1.56164i | ||||||||
\(191\) | 2228.16 | 0.844104 | 0.422052 | − | 0.906572i | \(-0.361310\pi\) | ||||
0.422052 | + | 0.906572i | \(0.361310\pi\) | |||||||
\(192\) | 234.802 | − | 768.015i | 0.0882572 | − | 0.288681i | ||||
\(193\) | 2575.61 | 0.960603 | 0.480301 | − | 0.877104i | \(-0.340527\pi\) | ||||
0.480301 | + | 0.877104i | \(0.340527\pi\) | |||||||
\(194\) | 5149.16i | 1.90561i | ||||||||
\(195\) | −41.1115 | + | 134.472i | −0.0150977 | + | 0.0493832i | ||||
\(196\) | 530.940 | 0.193491 | ||||||||
\(197\) | − | 4723.13i | − | 1.70817i | −0.520136 | − | 0.854083i | \(-0.674119\pi\) | ||
0.520136 | − | 0.854083i | \(-0.325881\pi\) | |||||||
\(198\) | −2211.77 | − | 1491.83i | −0.793855 | − | 0.535452i | ||||
\(199\) | 425.662 | 0.151630 | 0.0758151 | − | 0.997122i | \(-0.475844\pi\) | ||||
0.0758151 | + | 0.997122i | \(0.475844\pi\) | |||||||
\(200\) | 265.058 | 0.0937123 | ||||||||
\(201\) | 57.6025 | + | 17.6106i | 0.0202138 | + | 0.00617987i | ||||
\(202\) | 868.450 | 0.302495 | ||||||||
\(203\) | 1852.37i | 0.640447i | ||||||||
\(204\) | −619.363 | − | 189.355i | −0.212569 | − | 0.0649879i | ||||
\(205\) | 1347.06 | 0.458939 | ||||||||
\(206\) | 4154.08i | 1.40499i | ||||||||
\(207\) | 1573.89 | + | 1061.58i | 0.528469 | + | 0.356450i | ||||
\(208\) | 207.191i | 0.0690677i | ||||||||
\(209\) | −3422.85 | −1.13284 | ||||||||
\(210\) | −3896.95 | − | 1191.40i | −1.28055 | − | 0.391497i | ||||
\(211\) | 436.103i | 0.142287i | 0.997466 | + | 0.0711435i | \(0.0226648\pi\) | ||||
−0.997466 | + | 0.0711435i | \(0.977335\pi\) | |||||||
\(212\) | 889.084i | 0.288031i | ||||||||
\(213\) | 482.900 | + | 147.635i | 0.155342 | + | 0.0474920i | ||||
\(214\) | − | 4780.84i | − | 1.52716i | ||||||
\(215\) | 1678.50 | 0.532433 | ||||||||
\(216\) | −1705.74 | + | 1381.32i | −0.537318 | + | 0.435123i | ||||
\(217\) | − | 6036.10i | − | 1.88828i | ||||||
\(218\) | − | 7458.36i | − | 2.31717i | ||||||
\(219\) | −2794.00 | − | 854.198i | −0.862105 | − | 0.263568i | ||||
\(220\) | 1023.38i | 0.313620i | ||||||||
\(221\) | −96.6345 | −0.0294133 | ||||||||
\(222\) | −4161.70 | − | 1272.34i | −1.25817 | − | 0.384657i | ||||
\(223\) | −3186.19 | −0.956785 | −0.478392 | − | 0.878146i | \(-0.658780\pi\) | ||||
−0.478392 | + | 0.878146i | \(0.658780\pi\) | |||||||
\(224\) | −3202.57 | −0.955272 | ||||||||
\(225\) | −379.240 | − | 255.796i | −0.112367 | − | 0.0757913i | ||||
\(226\) | 7770.03 | 2.28697 | ||||||||
\(227\) | −2499.16 | −0.730727 | −0.365364 | − | 0.930865i | \(-0.619055\pi\) | ||||
−0.365364 | + | 0.930865i | \(0.619055\pi\) | |||||||
\(228\) | 595.535 | − | 1947.94i | 0.172984 | − | 0.565813i | ||||
\(229\) | − | 1010.52i | − | 0.291602i | −0.989314 | − | 0.145801i | \(-0.953424\pi\) | ||
0.989314 | − | 0.145801i | \(-0.0465759\pi\) | |||||||
\(230\) | − | 2463.26i | − | 0.706185i | ||||||
\(231\) | 997.087 | − | 3261.37i | 0.283998 | − | 0.928929i | ||||
\(232\) | − | 1294.57i | − | 0.366347i | ||||||
\(233\) | −5588.38 | −1.57128 | −0.785638 | − | 0.618687i | \(-0.787665\pi\) | ||||
−0.785638 | + | 0.618687i | \(0.787665\pi\) | |||||||
\(234\) | 132.462 | − | 196.387i | 0.0370057 | − | 0.0548642i | ||||
\(235\) | 3636.93i | 1.00956i | ||||||||
\(236\) | 1357.13 | − | 688.366i | 0.374330 | − | 0.189868i | ||||
\(237\) | −911.242 | + | 2980.58i | −0.249753 | + | 0.816918i | ||||
\(238\) | − | 2800.44i | − | 0.762713i | ||||||
\(239\) | 6666.77i | 1.80434i | 0.431379 | + | 0.902171i | \(0.358027\pi\) | ||||
−0.431379 | + | 0.902171i | \(0.641973\pi\) | |||||||
\(240\) | 4111.04 | + | 1256.85i | 1.10569 | + | 0.338040i | ||||
\(241\) | −3807.75 | −1.01775 | −0.508877 | − | 0.860839i | \(-0.669939\pi\) | ||||
−0.508877 | + | 0.860839i | \(0.669939\pi\) | |||||||
\(242\) | 1588.65 | 0.421992 | ||||||||
\(243\) | 3773.57 | − | 330.227i | 0.996193 | − | 0.0871772i | ||||
\(244\) | − | 2093.77i | − | 0.549344i | ||||||
\(245\) | − | 1643.67i | − | 0.428613i | ||||||
\(246\) | −2170.12 | − | 663.462i | −0.562447 | − | 0.171955i | ||||
\(247\) | − | 303.922i | − | 0.0782918i | ||||||
\(248\) | 4218.46i | 1.08013i | ||||||||
\(249\) | −758.794 | + | 2481.94i | −0.193119 | + | 0.631673i | ||||
\(250\) | 4972.64i | 1.25799i | ||||||||
\(251\) | 2293.16i | 0.576666i | 0.957530 | + | 0.288333i | \(0.0931009\pi\) | ||||
−0.957530 | + | 0.288333i | \(0.906899\pi\) | |||||||
\(252\) | 1682.56 | + | 1134.88i | 0.420600 | + | 0.283693i | ||||
\(253\) | 2061.51 | 0.512277 | ||||||||
\(254\) | 1980.49 | 0.489240 | ||||||||
\(255\) | −586.201 | + | 1917.41i | −0.143958 | + | 0.470873i | ||||
\(256\) | 4376.12 | 1.06839 | ||||||||
\(257\) | − | 4853.05i | − | 1.17792i | −0.808163 | − | 0.588959i | \(-0.799538\pi\) | ||
0.808163 | − | 0.588959i | \(-0.200462\pi\) | |||||||
\(258\) | −2704.09 | − | 826.711i | −0.652517 | − | 0.199491i | ||||
\(259\) | − | 5563.07i | − | 1.33464i | ||||||
\(260\) | −90.8681 | −0.0216746 | ||||||||
\(261\) | −1249.33 | + | 1852.24i | −0.296289 | + | 0.439275i | ||||
\(262\) | −2797.82 | −0.659732 | ||||||||
\(263\) | 1427.79i | 0.334759i | 0.985893 | + | 0.167379i | \(0.0535305\pi\) | ||||
−0.985893 | + | 0.167379i | \(0.946470\pi\) | |||||||
\(264\) | −696.836 | + | 2279.28i | −0.162452 | + | 0.531364i | ||||
\(265\) | 2752.40 | 0.638032 | ||||||||
\(266\) | 8807.56 | 2.03017 | ||||||||
\(267\) | −806.628 | + | 2638.40i | −0.184887 | + | 0.604747i | ||||
\(268\) | 38.9243i | 0.00887195i | ||||||||
\(269\) | −1987.25 | −0.450426 | −0.225213 | − | 0.974310i | \(-0.572308\pi\) | ||||
−0.225213 | + | 0.974310i | \(0.572308\pi\) | |||||||
\(270\) | −3093.14 | − | 3819.61i | −0.697195 | − | 0.860941i | ||||
\(271\) | 6430.82 | 1.44149 | 0.720746 | − | 0.693199i | \(-0.243799\pi\) | ||||
0.720746 | + | 0.693199i | \(0.243799\pi\) | |||||||
\(272\) | 2954.29i | 0.658567i | ||||||||
\(273\) | 289.584 | + | 88.5333i | 0.0641993 | + | 0.0196274i | ||||
\(274\) | 1731.73i | 0.381815i | ||||||||
\(275\) | −496.734 | −0.108924 | ||||||||
\(276\) | −358.678 | + | 1173.20i | −0.0782242 | + | 0.255864i | ||||
\(277\) | 2442.33 | 0.529766 | 0.264883 | − | 0.964281i | \(-0.414667\pi\) | ||||
0.264883 | + | 0.964281i | \(0.414667\pi\) | |||||||
\(278\) | 6384.88 | 1.37748 | ||||||||
\(279\) | 4071.04 | − | 6035.68i | 0.873573 | − | 1.29515i | ||||
\(280\) | 3640.55i | 0.777016i | ||||||||
\(281\) | 8202.30i | 1.74131i | 0.491894 | + | 0.870655i | \(0.336305\pi\) | ||||
−0.491894 | + | 0.870655i | \(0.663695\pi\) | |||||||
\(282\) | 1791.29 | − | 5859.13i | 0.378261 | − | 1.23726i | ||||
\(283\) | 4649.58i | 0.976639i | 0.872665 | + | 0.488320i | \(0.162390\pi\) | ||||
−0.872665 | + | 0.488320i | \(0.837610\pi\) | |||||||
\(284\) | 326.315i | 0.0681805i | ||||||||
\(285\) | −6030.37 | − | 1843.64i | −1.25336 | − | 0.383185i | ||||
\(286\) | − | 257.231i | − | 0.0531832i | ||||||
\(287\) | − | 2900.87i | − | 0.596631i | ||||||
\(288\) | −3202.35 | − | 2159.97i | −0.655209 | − | 0.441936i | ||||
\(289\) | 3535.11 | 0.719541 | ||||||||
\(290\) | 2898.89 | 0.586996 | ||||||||
\(291\) | −7592.20 | − | 2321.13i | −1.52942 | − | 0.467585i | ||||
\(292\) | − | 1888.02i | − | 0.378384i | ||||||
\(293\) | 3469.71i | 0.691817i | 0.938268 | + | 0.345909i | \(0.112429\pi\) | ||||
−0.938268 | + | 0.345909i | \(0.887571\pi\) | |||||||
\(294\) | −809.553 | + | 2647.97i | −0.160592 | + | 0.525281i | ||||
\(295\) | −2131.02 | − | 4201.37i | −0.420587 | − | 0.829197i | ||||
\(296\) | 3887.88i | 0.763440i | ||||||||
\(297\) | 3196.65 | − | 2588.66i | 0.624540 | − | 0.505756i | ||||
\(298\) | 9538.26 | 1.85415 | ||||||||
\(299\) | 183.046i | 0.0354040i | ||||||||
\(300\) | 86.4258 | − | 282.690i | 0.0166326 | − | 0.0544038i | ||||
\(301\) | − | 3614.64i | − | 0.692175i | ||||||
\(302\) | − | 6767.24i | − | 1.28944i | ||||||
\(303\) | −391.479 | + | 1280.49i | −0.0742240 | + | 0.242780i | ||||
\(304\) | −9291.43 | −1.75296 | ||||||||
\(305\) | −6481.83 | −1.21688 | ||||||||
\(306\) | 1888.75 | − | 2800.25i | 0.352853 | − | 0.523135i | ||||
\(307\) | 307.080 | 0.0570879 | 0.0285439 | − | 0.999593i | \(-0.490913\pi\) | ||||
0.0285439 | + | 0.999593i | \(0.490913\pi\) | |||||||
\(308\) | 2203.84 | 0.407713 | ||||||||
\(309\) | −6125.00 | − | 1872.57i | −1.12763 | − | 0.344747i | ||||
\(310\) | −9446.29 | −1.73069 | ||||||||
\(311\) | 3479.56i | 0.634430i | 0.948354 | + | 0.317215i | \(0.102748\pi\) | ||||
−0.948354 | + | 0.317215i | \(0.897252\pi\) | |||||||
\(312\) | −202.382 | − | 61.8734i | −0.0367232 | − | 0.0112272i | ||||
\(313\) | − | 7489.91i | − | 1.35257i | −0.736640 | − | 0.676285i | \(-0.763589\pi\) | ||
0.736640 | − | 0.676285i | \(-0.236411\pi\) | |||||||
\(314\) | − | 4486.52i | − | 0.806335i | ||||||
\(315\) | 3513.33 | − | 5208.82i | 0.628424 | − | 0.931694i | ||||
\(316\) | −2014.10 | −0.358551 | ||||||||
\(317\) | − | 1313.10i | − | 0.232654i | −0.993211 | − | 0.116327i | \(-0.962888\pi\) | ||
0.993211 | − | 0.116327i | \(-0.0371120\pi\) | |||||||
\(318\) | −4434.15 | − | 1355.63i | −0.781933 | − | 0.239057i | ||||
\(319\) | 2426.09i | 0.425816i | ||||||||
\(320\) | − | 1606.64i | − | 0.280669i | ||||||
\(321\) | 7049.12 | + | 2155.10i | 1.22568 | + | 0.374723i | ||||
\(322\) | −5304.60 | −0.918056 | ||||||||
\(323\) | − | 4333.56i | − | 0.746520i | ||||||
\(324\) | 917.023 | + | 2269.60i | 0.157240 | + | 0.389163i | ||||
\(325\) | − | 44.1060i | − | 0.00752788i | ||||||
\(326\) | −1560.14 | −0.265056 | ||||||||
\(327\) | 10997.0 | + | 3362.07i | 1.85974 | + | 0.568571i | ||||
\(328\) | 2027.34i | 0.341284i | ||||||||
\(329\) | 7832.09 | 1.31245 | ||||||||
\(330\) | −5103.94 | − | 1560.41i | −0.851401 | − | 0.260296i | ||||
\(331\) | −9986.34 | −1.65830 | −0.829152 | − | 0.559023i | \(-0.811176\pi\) | ||||
−0.829152 | + | 0.559023i | \(0.811176\pi\) | |||||||
\(332\) | −1677.15 | −0.277245 | ||||||||
\(333\) | 3752.01 | − | 5562.68i | 0.617444 | − | 0.915415i | ||||
\(334\) | 11532.6i | 1.88932i | ||||||||
\(335\) | 120.501 | 0.0196527 | ||||||||
\(336\) | 2706.62 | − | 8853.09i | 0.439459 | − | 1.43743i | ||||
\(337\) | 3454.99i | 0.558473i | 0.960222 | + | 0.279236i | \(0.0900813\pi\) | ||||
−0.960222 | + | 0.279236i | \(0.909919\pi\) | |||||||
\(338\) | −7381.35 | −1.18785 | ||||||||
\(339\) | −3502.56 | + | 11456.5i | −0.561160 | + | 1.83550i | ||||
\(340\) | −1295.67 | −0.206669 | ||||||||
\(341\) | − | 7905.63i | − | 1.25547i | ||||||
\(342\) | 8806.95 | + | 5940.25i | 1.39247 | + | 0.939216i | ||||
\(343\) | 4138.67 | 0.651508 | ||||||||
\(344\) | 2526.17i | 0.395937i | ||||||||
\(345\) | 3631.96 | + | 1110.38i | 0.566777 | + | 0.173279i | ||||
\(346\) | 5160.29 | 0.801789 | ||||||||
\(347\) | −3191.72 | −0.493776 | −0.246888 | − | 0.969044i | \(-0.579408\pi\) | ||||
−0.246888 | + | 0.969044i | \(0.579408\pi\) | |||||||
\(348\) | −1380.68 | − | 422.111i | −0.212679 | − | 0.0650216i | ||||
\(349\) | − | 285.854i | − | 0.0438435i | −0.999760 | − | 0.0219218i | \(-0.993022\pi\) | ||
0.999760 | − | 0.0219218i | \(-0.00697848\pi\) | |||||||
\(350\) | 1278.18 | 0.195204 | ||||||||
\(351\) | 229.852 | + | 283.837i | 0.0349533 | + | 0.0431626i | ||||
\(352\) | −4194.49 | −0.635134 | ||||||||
\(353\) | 1417.10 | 0.213668 | 0.106834 | − | 0.994277i | \(-0.465929\pi\) | ||||
0.106834 | + | 0.994277i | \(0.465929\pi\) | |||||||
\(354\) | 1363.81 | + | 7818.05i | 0.204762 | + | 1.17380i | ||||
\(355\) | 1010.20 | 0.151030 | ||||||||
\(356\) | −1782.88 | −0.265428 | ||||||||
\(357\) | 4129.12 | + | 1262.38i | 0.612146 | + | 0.187149i | ||||
\(358\) | −7415.01 | −1.09468 | ||||||||
\(359\) | 1416.48i | 0.208242i | 0.994565 | + | 0.104121i | \(0.0332029\pi\) | ||||
−0.994565 | + | 0.104121i | \(0.966797\pi\) | |||||||
\(360\) | −2455.37 | + | 3640.30i | −0.359470 | + | 0.532946i | ||||
\(361\) | 6770.32 | 0.987071 | ||||||||
\(362\) | 7598.64 | 1.10325 | ||||||||
\(363\) | −716.128 | + | 2342.38i | −0.103545 | + | 0.338687i | ||||
\(364\) | 195.684i | 0.0281775i | ||||||||
\(365\) | −5844.88 | −0.838178 | ||||||||
\(366\) | 10442.3 | + | 3192.48i | 1.49133 | + | 0.455939i | ||||
\(367\) | 12370.0i | 1.75943i | 0.475503 | + | 0.879714i | \(0.342266\pi\) | ||||
−0.475503 | + | 0.879714i | \(0.657734\pi\) | |||||||
\(368\) | 5596.03 | 0.792699 | ||||||||
\(369\) | 1956.49 | − | 2900.67i | 0.276018 | − | 0.409222i | ||||
\(370\) | −8706.02 | −1.22325 | ||||||||
\(371\) | − | 5927.27i | − | 0.829456i | ||||||
\(372\) | 4499.08 | + | 1375.48i | 0.627060 | + | 0.191708i | ||||
\(373\) | 7175.24 | 0.996031 | 0.498016 | − | 0.867168i | \(-0.334062\pi\) | ||||
0.498016 | + | 0.867168i | \(0.334062\pi\) | |||||||
\(374\) | − | 3667.81i | − | 0.507106i | ||||||
\(375\) | −7331.93 | − | 2241.56i | −1.00965 | − | 0.308677i | ||||
\(376\) | −5473.63 | −0.750747 | ||||||||
\(377\) | −215.418 | −0.0294286 | ||||||||
\(378\) | −8225.50 | + | 6661.05i | −1.11924 | + | 0.906369i | ||||
\(379\) | −7996.12 | −1.08373 | −0.541864 | − | 0.840466i | \(-0.682281\pi\) | ||||
−0.541864 | + | 0.840466i | \(0.682281\pi\) | |||||||
\(380\) | − | 4074.97i | − | 0.550109i | ||||||
\(381\) | −892.762 | + | 2920.14i | −0.120046 | + | 0.392660i | ||||
\(382\) | −7509.20 | −1.00577 | ||||||||
\(383\) | − | 4584.32i | − | 0.611613i | −0.952094 | − | 0.305807i | \(-0.901074\pi\) | ||
0.952094 | − | 0.305807i | \(-0.0989261\pi\) | |||||||
\(384\) | −2530.03 | + | 8275.50i | −0.336225 | + | 1.09976i | ||||
\(385\) | − | 6822.59i | − | 0.903147i | ||||||
\(386\) | −8680.15 | −1.14458 | ||||||||
\(387\) | 2437.89 | − | 3614.39i | 0.320220 | − | 0.474754i | ||||
\(388\) | − | 5130.36i | − | 0.671274i | ||||||
\(389\) | 10782.3i | 1.40536i | 0.711504 | + | 0.702682i | \(0.248014\pi\) | ||||
−0.711504 | + | 0.702682i | \(0.751986\pi\) | |||||||
\(390\) | 138.551 | − | 453.188i | 0.0179893 | − | 0.0588413i | ||||
\(391\) | 2610.01i | 0.337580i | ||||||||
\(392\) | 2473.75 | 0.318732 | ||||||||
\(393\) | 1261.20 | − | 4125.25i | 0.161880 | − | 0.529495i | ||||
\(394\) | 15917.6i | 2.03532i | ||||||||
\(395\) | 6235.20i | 0.794245i | ||||||||
\(396\) | 2203.69 | + | 1486.38i | 0.279645 | + | 0.188620i | ||||
\(397\) | − | 14023.6i | − | 1.77285i | −0.462869 | − | 0.886426i | \(-0.653180\pi\) | ||
0.462869 | − | 0.886426i | \(-0.346820\pi\) | |||||||
\(398\) | −1434.54 | −0.180671 | ||||||||
\(399\) | −3970.26 | + | 12986.3i | −0.498149 | + | 1.62940i | ||||
\(400\) | −1348.40 | −0.168550 | ||||||||
\(401\) | 11372.8 | 1.41629 | 0.708143 | − | 0.706069i | \(-0.249533\pi\) | ||||
0.708143 | + | 0.706069i | \(0.249533\pi\) | |||||||
\(402\) | −194.128 | − | 59.3501i | −0.0240852 | − | 0.00736346i | ||||
\(403\) | 701.956 | 0.0867666 | ||||||||
\(404\) | −865.279 | −0.106558 | ||||||||
\(405\) | 7026.16 | − | 2838.89i | 0.862056 | − | 0.348311i | ||||
\(406\) | − | 6242.74i | − | 0.763108i | ||||||
\(407\) | − | 7286.10i | − | 0.887367i | ||||||
\(408\) | −2885.73 | − | 882.242i | −0.350159 | − | 0.107053i | ||||
\(409\) | − | 12028.5i | − | 1.45421i | −0.686527 | − | 0.727104i | \(-0.740866\pi\) | ||
0.686527 | − | 0.727104i | \(-0.259134\pi\) | |||||||
\(410\) | −4539.76 | −0.546836 | ||||||||
\(411\) | −2553.35 | − | 780.625i | −0.306441 | − | 0.0936871i | ||||
\(412\) | − | 4138.91i | − | 0.494926i | ||||||
\(413\) | −9047.61 | + | 4589.14i | −1.07798 | + | 0.546772i | ||||
\(414\) | −5304.23 | − | 3577.69i | −0.629683 | − | 0.424719i | ||||
\(415\) | 5192.07i | 0.614141i | ||||||||
\(416\) | − | 372.437i | − | 0.0438948i | ||||||
\(417\) | −2878.17 | + | 9414.21i | −0.337996 | + | 1.10555i | ||||
\(418\) | 11535.5 | 1.34981 | ||||||||
\(419\) | 6467.36 | 0.754060 | 0.377030 | − | 0.926201i | \(-0.376945\pi\) | ||||
0.377030 | + | 0.926201i | \(0.376945\pi\) | |||||||
\(420\) | 3882.72 | + | 1187.05i | 0.451089 | + | 0.137910i | ||||
\(421\) | − | 11696.5i | − | 1.35404i | −0.735964 | − | 0.677021i | \(-0.763271\pi\) | ||
0.735964 | − | 0.677021i | \(-0.236729\pi\) | |||||||
\(422\) | − | 1469.73i | − | 0.169538i | ||||||
\(423\) | 7831.54 | + | 5282.34i | 0.900195 | + | 0.607178i | ||||
\(424\) | 4142.40i | 0.474464i | ||||||||
\(425\) | − | 628.899i | − | 0.0717790i | ||||||
\(426\) | −1627.44 | − | 497.551i | −0.185093 | − | 0.0565878i | ||||
\(427\) | 13958.6i | 1.58197i | ||||||||
\(428\) | 4763.38i | 0.537960i | ||||||||
\(429\) | 379.275 | + | 115.954i | 0.0426843 | + | 0.0130497i | ||||
\(430\) | −5656.79 | −0.634407 | ||||||||
\(431\) | −15276.2 | −1.70726 | −0.853630 | − | 0.520880i | \(-0.825604\pi\) | ||||
−0.853630 | + | 0.520880i | \(0.825604\pi\) | |||||||
\(432\) | 8677.39 | − | 7027.00i | 0.966415 | − | 0.782608i | ||||
\(433\) | 8311.84 | 0.922497 | 0.461249 | − | 0.887271i | \(-0.347402\pi\) | ||||
0.461249 | + | 0.887271i | \(0.347402\pi\) | |||||||
\(434\) | 20342.5i | 2.24993i | ||||||||
\(435\) | −1306.76 | + | 4274.28i | −0.144033 | + | 0.471118i | ||||
\(436\) | 7431.12i | 0.816253i | ||||||||
\(437\) | −8208.65 | −0.898565 | ||||||||
\(438\) | 9416.17 | + | 2878.77i | 1.02722 | + | 0.314047i | ||||
\(439\) | −11860.1 | −1.28941 | −0.644705 | − | 0.764431i | \(-0.723020\pi\) | ||||
−0.644705 | + | 0.764431i | \(0.723020\pi\) | |||||||
\(440\) | 4768.12i | 0.516617i | ||||||||
\(441\) | −3539.38 | − | 2387.30i | −0.382181 | − | 0.257779i | ||||
\(442\) | 325.672 | 0.0350467 | ||||||||
\(443\) | −4519.87 | −0.484753 | −0.242376 | − | 0.970182i | \(-0.577927\pi\) | ||||
−0.242376 | + | 0.970182i | \(0.577927\pi\) | |||||||
\(444\) | 4146.50 | + | 1267.69i | 0.443208 | + | 0.135500i | ||||
\(445\) | 5519.37i | 0.587963i | ||||||||
\(446\) | 10737.9 | 1.14003 | ||||||||
\(447\) | −4299.64 | + | 14063.7i | −0.454958 | + | 1.48812i | ||||
\(448\) | −3459.89 | −0.364876 | ||||||||
\(449\) | − | 7370.48i | − | 0.774687i | −0.921935 | − | 0.387344i | \(-0.873393\pi\) | ||
0.921935 | − | 0.387344i | \(-0.126607\pi\) | |||||||
\(450\) | 1278.09 | + | 862.066i | 0.133888 | + | 0.0903071i | ||||
\(451\) | − | 3799.34i | − | 0.396683i | ||||||
\(452\) | −7741.66 | −0.805613 | ||||||||
\(453\) | 9977.99 | + | 3050.53i | 1.03489 | + | 0.316394i | ||||
\(454\) | 8422.52 | 0.870679 | ||||||||
\(455\) | 605.792 | 0.0624175 | ||||||||
\(456\) | 2774.70 | − | 9075.79i | 0.284951 | − | 0.932046i | ||||
\(457\) | − | 8543.74i | − | 0.874528i | −0.899333 | − | 0.437264i | \(-0.855948\pi\) | ||
0.899333 | − | 0.437264i | \(-0.144052\pi\) | |||||||
\(458\) | 3405.58i | 0.347451i | ||||||||
\(459\) | 3277.42 | + | 4047.17i | 0.333283 | + | 0.411559i | ||||
\(460\) | 2454.26i | 0.248762i | ||||||||
\(461\) | 2030.35i | 0.205125i | 0.994727 | + | 0.102563i | \(0.0327042\pi\) | ||||
−0.994727 | + | 0.102563i | \(0.967296\pi\) | |||||||
\(462\) | −3360.32 | + | 10991.3i | −0.338390 | + | 1.10684i | ||||
\(463\) | 6633.07i | 0.665799i | 0.942962 | + | 0.332899i | \(0.108027\pi\) | ||||
−0.942962 | + | 0.332899i | \(0.891973\pi\) | |||||||
\(464\) | 6585.70i | 0.658909i | ||||||||
\(465\) | 4258.18 | − | 13928.1i | 0.424664 | − | 1.38903i | ||||
\(466\) | 18833.6 | 1.87221 | ||||||||
\(467\) | 477.556 | 0.0473204 | 0.0236602 | − | 0.999720i | \(-0.492468\pi\) | ||||
0.0236602 | + | 0.999720i | \(0.492468\pi\) | |||||||
\(468\) | −131.979 | + | 195.670i | −0.0130357 | + | 0.0193266i | ||||
\(469\) | − | 259.497i | − | 0.0255490i | ||||||
\(470\) | − | 12256.9i | − | 1.20292i | ||||||
\(471\) | 6615.17 | + | 2022.43i | 0.647157 | + | 0.197853i | ||||
\(472\) | 6323.12 | − | 3207.22i | 0.616622 | − | 0.312764i | ||||
\(473\) | − | 4734.19i | − | 0.460208i | ||||||
\(474\) | 3071.01 | − | 10045.0i | 0.297587 | − | 0.973378i | ||||
\(475\) | 1977.93 | 0.191060 | ||||||||
\(476\) | 2790.21i | 0.268675i | ||||||||
\(477\) | 3997.64 | − | 5926.85i | 0.383730 | − | 0.568914i | ||||
\(478\) | − | 22467.9i | − | 2.14992i | ||||||
\(479\) | − | 4268.57i | − | 0.407173i | −0.979057 | − | 0.203587i | \(-0.934740\pi\) | ||
0.979057 | − | 0.203587i | \(-0.0652599\pi\) | |||||||
\(480\) | −7389.84 | − | 2259.26i | −0.702705 | − | 0.214835i | ||||
\(481\) | 646.947 | 0.0613269 | ||||||||
\(482\) | 12832.7 | 1.21268 | ||||||||
\(483\) | 2391.20 | − | 7821.39i | 0.225266 | − | 0.736823i | ||||
\(484\) | −1582.85 | −0.148652 | ||||||||
\(485\) | −15882.4 | −1.48698 | ||||||||
\(486\) | −12717.5 | + | 1112.91i | −1.18699 | + | 0.103874i | ||||
\(487\) | −8039.94 | −0.748100 | −0.374050 | − | 0.927409i | \(-0.622031\pi\) | ||||
−0.374050 | + | 0.927409i | \(0.622031\pi\) | |||||||
\(488\) | − | 9755.25i | − | 0.904917i | ||||||
\(489\) | 703.279 | − | 2300.36i | 0.0650376 | − | 0.212732i | ||||
\(490\) | 5539.39i | 0.510702i | ||||||||
\(491\) | − | 13575.7i | − | 1.24778i | −0.781511 | − | 0.623892i | \(-0.785551\pi\) | ||
0.781511 | − | 0.623892i | \(-0.214449\pi\) | |||||||
\(492\) | 2162.20 | + | 661.040i | 0.198129 | + | 0.0605731i | ||||
\(493\) | −3071.60 | −0.280604 | ||||||||
\(494\) | 1024.26i | 0.0932865i | ||||||||
\(495\) | 4601.49 | − | 6822.12i | 0.417822 | − | 0.619457i | ||||
\(496\) | − | 21460.1i | − | 1.94271i | ||||||
\(497\) | − | 2175.45i | − | 0.196343i | ||||||
\(498\) | 2557.24 | − | 8364.48i | 0.230106 | − | 0.752653i | ||||
\(499\) | 2461.10 | 0.220789 | 0.110395 | − | 0.993888i | \(-0.464788\pi\) | ||||
0.110395 | + | 0.993888i | \(0.464788\pi\) | |||||||
\(500\) | − | 4954.49i | − | 0.443143i | ||||||
\(501\) | −17004.2 | − | 5198.63i | −1.51635 | − | 0.463588i | ||||
\(502\) | − | 7728.27i | − | 0.687111i | ||||||
\(503\) | −10940.9 | −0.969841 | −0.484920 | − | 0.874558i | \(-0.661151\pi\) | ||||
−0.484920 | + | 0.874558i | \(0.661151\pi\) | |||||||
\(504\) | 7839.35 | + | 5287.61i | 0.692842 | + | 0.467319i | ||||
\(505\) | 2678.71i | 0.236041i | ||||||||
\(506\) | −6947.57 | −0.610390 | ||||||||
\(507\) | 3327.36 | − | 10883.5i | 0.291466 | − | 0.953356i | ||||
\(508\) | −1973.26 | −0.172341 | ||||||||
\(509\) | 6598.10 | 0.574569 | 0.287284 | − | 0.957845i | \(-0.407248\pi\) | ||||
0.287284 | + | 0.957845i | \(0.407248\pi\) | |||||||
\(510\) | 1975.58 | − | 6461.93i | 0.171530 | − | 0.561057i | ||||
\(511\) | 12586.9i | 1.08965i | ||||||||
\(512\) | −1425.04 | −0.123005 | ||||||||
\(513\) | −12728.6 | + | 10307.7i | −1.09548 | + | 0.887126i | ||||
\(514\) | 16355.5i | 1.40352i | ||||||||
\(515\) | −12813.1 | −1.09634 | ||||||||
\(516\) | 2694.22 | + | 823.692i | 0.229857 | + | 0.0702733i | ||||
\(517\) | 10257.9 | 0.872613 | ||||||||
\(518\) | 18748.3i | 1.59026i | ||||||||
\(519\) | −2326.15 | + | 7608.61i | −0.196737 | + | 0.643508i | ||||
\(520\) | −423.371 | −0.0357039 | ||||||||
\(521\) | − | 14069.4i | − | 1.18310i | −0.806270 | − | 0.591548i | \(-0.798517\pi\) | ||
0.806270 | − | 0.591548i | \(-0.201483\pi\) | |||||||
\(522\) | 4210.41 | − | 6242.30i | 0.353036 | − | 0.523406i | ||||
\(523\) | 8391.38 | 0.701586 | 0.350793 | − | 0.936453i | \(-0.385912\pi\) | ||||
0.350793 | + | 0.936453i | \(0.385912\pi\) | |||||||
\(524\) | 2787.60 | 0.232399 | ||||||||
\(525\) | −576.176 | + | 1884.62i | −0.0478979 | + | 0.156669i | ||||
\(526\) | − | 4811.87i | − | 0.398873i | ||||||
\(527\) | 10009.1 | 0.827328 | ||||||||
\(528\) | 3544.93 | − | 11595.1i | 0.292184 | − | 0.955706i | ||||
\(529\) | −7223.11 | −0.593664 | ||||||||
\(530\) | −9275.97 | −0.760231 | ||||||||
\(531\) | −12142.1 | − | 1513.33i | −0.992322 | − | 0.123678i | ||||
\(532\) | −8775.40 | −0.715154 | ||||||||
\(533\) | 337.351 | 0.0274152 | ||||||||
\(534\) | 2718.45 | − | 8891.77i | 0.220297 | − | 0.720571i | ||||
\(535\) | 14746.3 | 1.19166 | ||||||||
\(536\) | 181.356i | 0.0146145i | ||||||||
\(537\) | 3342.53 | − | 10933.1i | 0.268605 | − | 0.878581i | ||||
\(538\) | 6697.29 | 0.536693 | ||||||||
\(539\) | −4635.94 | −0.370471 | ||||||||
\(540\) | 3081.85 | + | 3805.66i | 0.245596 | + | 0.303277i | ||||
\(541\) | 22826.0i | 1.81398i | 0.421150 | + | 0.906991i | \(0.361627\pi\) | ||||
−0.421150 | + | 0.906991i | \(0.638373\pi\) | |||||||
\(542\) | −21672.7 | −1.71757 | ||||||||
\(543\) | −3425.30 | + | 11203.8i | −0.270707 | + | 0.885456i | ||||
\(544\) | − | 5310.51i | − | 0.418541i | ||||||
\(545\) | 23005.1 | 1.80813 | ||||||||
\(546\) | −975.937 | − | 298.369i | −0.0764950 | − | 0.0233865i | ||||
\(547\) | −12977.5 | −1.01440 | −0.507201 | − | 0.861828i | \(-0.669320\pi\) | ||||
−0.507201 | + | 0.861828i | \(0.669320\pi\) | |||||||
\(548\) | − | 1725.40i | − | 0.134499i | ||||||
\(549\) | −9414.33 | + | 13957.6i | −0.731865 | + | 1.08505i | ||||
\(550\) | 1674.06 | 0.129786 | ||||||||
\(551\) | − | 9660.37i | − | 0.746907i | ||||||
\(552\) | −1671.15 | + | 5466.15i | −0.128856 | + | 0.421476i | ||||
\(553\) | 13427.4 | 1.03254 | ||||||||
\(554\) | −8230.97 | −0.631228 | ||||||||
\(555\) | 3924.49 | − | 12836.6i | 0.300153 | − | 0.981773i | ||||
\(556\) | −6361.57 | −0.485235 | ||||||||
\(557\) | − | 22118.7i | − | 1.68258i | −0.540582 | − | 0.841291i | \(-0.681796\pi\) | ||
0.540582 | − | 0.841291i | \(-0.318204\pi\) | |||||||
\(558\) | −13720.0 | + | 20341.1i | −1.04088 | + | 1.54320i | ||||
\(559\) | 420.358 | 0.0318055 | ||||||||
\(560\) | − | 18520.1i | − | 1.39753i | ||||||
\(561\) | 5408.01 | + | 1653.37i | 0.406999 | + | 0.124430i | ||||
\(562\) | − | 27642.9i | − | 2.07481i | ||||||
\(563\) | 1124.63 | 0.0841877 | 0.0420939 | − | 0.999114i | \(-0.486597\pi\) | ||||
0.0420939 | + | 0.999114i | \(0.486597\pi\) | |||||||
\(564\) | −1784.75 | + | 5837.74i | −0.133247 | + | 0.435839i | ||||
\(565\) | 23966.4i | 1.78456i | ||||||||
\(566\) | − | 15669.7i | − | 1.16369i | ||||||
\(567\) | −6113.53 | − | 15130.8i | −0.452812 | − | 1.12069i | ||||
\(568\) | 1520.36i | 0.112312i | ||||||||
\(569\) | −5453.65 | −0.401808 | −0.200904 | − | 0.979611i | \(-0.564388\pi\) | ||||
−0.200904 | + | 0.979611i | \(0.564388\pi\) | |||||||
\(570\) | 20323.2 | + | 6213.32i | 1.49341 | + | 0.456574i | ||||
\(571\) | − | 1714.66i | − | 0.125668i | −0.998024 | − | 0.0628340i | \(-0.979986\pi\) | ||
0.998024 | − | 0.0628340i | \(-0.0200139\pi\) | |||||||
\(572\) | 256.292i | 0.0187344i | ||||||||
\(573\) | 3384.99 | − | 11072.0i | 0.246789 | − | 0.807222i | ||||
\(574\) | 9776.33i | 0.710900i | ||||||||
\(575\) | −1191.26 | −0.0863984 | ||||||||
\(576\) | −3459.65 | − | 2333.52i | −0.250264 | − | 0.168802i | ||||
\(577\) | 6334.02 | 0.456999 | 0.228500 | − | 0.973544i | \(-0.426618\pi\) | ||||
0.228500 | + | 0.973544i | \(0.426618\pi\) | |||||||
\(578\) | −11913.8 | −0.857351 | ||||||||
\(579\) | 3912.83 | − | 12798.5i | 0.280849 | − | 0.918630i | ||||
\(580\) | −2888.31 | −0.206777 | ||||||||
\(581\) | 11181.1 | 0.798397 | ||||||||
\(582\) | 25586.7 | + | 7822.53i | 1.82235 | + | 0.557138i | ||||
\(583\) | − | 7763.09i | − | 0.551482i | ||||||
\(584\) | − | 8796.63i | − | 0.623300i | ||||||
\(585\) | 605.749 | + | 408.575i | 0.0428114 | + | 0.0288761i | ||||
\(586\) | − | 11693.4i | − | 0.824316i | ||||||
\(587\) | −303.276 | −0.0213246 | −0.0106623 | − | 0.999943i | \(-0.503394\pi\) | ||||
−0.0106623 | + | 0.999943i | \(0.503394\pi\) | |||||||
\(588\) | 806.597 | − | 2638.30i | 0.0565706 | − | 0.185037i | ||||
\(589\) | 31479.1i | 2.20216i | ||||||||
\(590\) | 7181.85 | + | 14159.2i | 0.501139 | + | 0.988008i | ||||
\(591\) | −23469.7 | − | 7175.31i | −1.63353 | − | 0.499413i | ||||
\(592\) | − | 19778.3i | − | 1.37311i | ||||||
\(593\) | − | 607.929i | − | 0.0420989i | −0.999778 | − | 0.0210495i | \(-0.993299\pi\) | ||
0.999778 | − | 0.0210495i | \(-0.00670075\pi\) | |||||||
\(594\) | −10773.1 | + | 8724.15i | −0.744154 | + | 0.602620i | ||||
\(595\) | 8637.87 | 0.595156 | ||||||||
\(596\) | −9503.43 | −0.653147 | ||||||||
\(597\) | 646.661 | − | 2115.16i | 0.0443318 | − | 0.145005i | ||||
\(598\) | − | 616.889i | − | 0.0421847i | ||||||
\(599\) | 24611.8i | 1.67882i | 0.543499 | + | 0.839410i | \(0.317099\pi\) | ||||
−0.543499 | + | 0.839410i | \(0.682901\pi\) | |||||||
\(600\) | 402.673 | − | 1317.11i | 0.0273984 | − | 0.0896176i | ||||
\(601\) | − | 11034.3i | − | 0.748915i | −0.927244 | − | 0.374458i | \(-0.877829\pi\) | ||
0.927244 | − | 0.374458i | \(-0.122171\pi\) | |||||||
\(602\) | 12181.9i | 0.824743i | ||||||||
\(603\) | 175.018 | − | 259.479i | 0.0118197 | − | 0.0175237i | ||||
\(604\) | 6742.53i | 0.454222i | ||||||||
\(605\) | 4900.13i | 0.329287i | ||||||||
\(606\) | 1319.34 | − | 4315.43i | 0.0884397 | − | 0.289278i | ||||
\(607\) | −25937.9 | −1.73441 | −0.867204 | − | 0.497953i | \(-0.834085\pi\) | ||||
−0.867204 | + | 0.497953i | \(0.834085\pi\) | |||||||
\(608\) | 16701.9 | 1.11406 | ||||||||
\(609\) | 9204.63 | + | 2814.09i | 0.612464 | + | 0.187246i | ||||
\(610\) | 21844.7 | 1.44994 | ||||||||
\(611\) | 910.817i | 0.0603072i | ||||||||
\(612\) | −1881.86 | + | 2790.02i | −0.124297 | + | 0.184281i | ||||
\(613\) | − | 25833.1i | − | 1.70211i | −0.525081 | − | 0.851053i | \(-0.675965\pi\) | ||
0.525081 | − | 0.851053i | \(-0.324035\pi\) | |||||||
\(614\) | −1034.90 | −0.0680216 | ||||||||
\(615\) | 2046.43 | − | 6693.67i | 0.134179 | − | 0.438886i | ||||
\(616\) | 10268.1 | 0.671613 | ||||||||
\(617\) | 2140.04i | 0.139635i | 0.997560 | + | 0.0698174i | \(0.0222417\pi\) | ||||
−0.997560 | + | 0.0698174i | \(0.977758\pi\) | |||||||
\(618\) | 20642.1 | + | 6310.82i | 1.34360 | + | 0.410774i | ||||
\(619\) | 24476.2 | 1.58931 | 0.794655 | − | 0.607061i | \(-0.207652\pi\) | ||||
0.794655 | + | 0.607061i | \(0.207652\pi\) | |||||||
\(620\) | 9411.79 | 0.609656 | ||||||||
\(621\) | 7666.17 | − | 6208.10i | 0.495383 | − | 0.401164i | ||||
\(622\) | − | 11726.6i | − | 0.755938i | ||||||
\(623\) | 11885.9 | 0.764365 | ||||||||
\(624\) | 1029.55 | + | 314.761i | 0.0660499 | + | 0.0201932i | ||||
\(625\) | −13220.2 | −0.846091 | ||||||||
\(626\) | 25242.0i | 1.61162i | ||||||||
\(627\) | −5199.95 | + | 17008.5i | −0.331206 | + | 1.08334i | ||||
\(628\) | 4470.14i | 0.284041i | ||||||||
\(629\) | 9224.69 | 0.584757 | ||||||||
\(630\) | −11840.4 | + | 17554.4i | −0.748782 | + | 1.11014i | ||||
\(631\) | 24399.6 | 1.53936 | 0.769678 | − | 0.638432i | \(-0.220417\pi\) | ||||
0.769678 | + | 0.638432i | \(0.220417\pi\) | |||||||
\(632\) | −9384.07 | −0.590630 | ||||||||
\(633\) | 2167.04 | + | 662.521i | 0.136070 | + | 0.0416001i | ||||
\(634\) | 4425.34i | 0.277212i | ||||||||
\(635\) | 6108.75i | 0.381761i | ||||||||
\(636\) | 4417.96 | + | 1350.68i | 0.275445 | + | 0.0842108i | ||||
\(637\) | − | 411.634i | − | 0.0256036i | ||||||
\(638\) | − | 8176.27i | − | 0.507369i | ||||||
\(639\) | 1467.23 | − | 2175.30i | 0.0908337 | − | 0.134669i | ||||
\(640\) | 17311.8i | 1.06924i | ||||||||
\(641\) | 30992.3i | 1.90971i | 0.297075 | + | 0.954854i | \(0.403989\pi\) | ||||
−0.297075 | + | 0.954854i | \(0.596011\pi\) | |||||||
\(642\) | −23756.5 | − | 7262.99i | −1.46043 | − | 0.446491i | ||||
\(643\) | −12100.0 | −0.742111 | −0.371056 | − | 0.928611i | \(-0.621004\pi\) | ||||
−0.371056 | + | 0.928611i | \(0.621004\pi\) | |||||||
\(644\) | 5285.23 | 0.323397 | ||||||||
\(645\) | 2549.96 | − | 8340.68i | 0.155666 | − | 0.509169i | ||||
\(646\) | 14604.7i | 0.889496i | ||||||||
\(647\) | 7277.03i | 0.442179i | 0.975254 | + | 0.221089i | \(0.0709612\pi\) | ||||
−0.975254 | + | 0.221089i | \(0.929039\pi\) | |||||||
\(648\) | 4272.58 | + | 10574.5i | 0.259017 | + | 0.641057i | ||||
\(649\) | −11849.9 | + | 6010.51i | −0.716716 | + | 0.363534i | ||||
\(650\) | 148.643i | 0.00896965i | ||||||||
\(651\) | −29994.1 | − | 9169.96i | −1.80578 | − | 0.552072i | ||||
\(652\) | 1554.45 | 0.0933693 | ||||||||
\(653\) | 22976.1i | 1.37691i | 0.725277 | + | 0.688457i | \(0.241712\pi\) | ||||
−0.725277 | + | 0.688457i | \(0.758288\pi\) | |||||||
\(654\) | −37061.4 | − | 11330.6i | −2.21593 | − | 0.677466i | ||||
\(655\) | − | 8629.78i | − | 0.514799i | ||||||
\(656\) | − | 10313.4i | − | 0.613829i | ||||||
\(657\) | −8489.21 | + | 12586.0i | −0.504103 | + | 0.747377i | ||||
\(658\) | −26395.2 | −1.56382 | ||||||||
\(659\) | 28281.7 | 1.67177 | 0.835886 | − | 0.548904i | \(-0.184955\pi\) | ||||
0.835886 | + | 0.548904i | \(0.184955\pi\) | |||||||
\(660\) | 5085.30 | + | 1554.71i | 0.299917 | + | 0.0916923i | ||||
\(661\) | −4139.77 | −0.243598 | −0.121799 | − | 0.992555i | \(-0.538866\pi\) | ||||
−0.121799 | + | 0.992555i | \(0.538866\pi\) | |||||||
\(662\) | 33655.3 | 1.97591 | ||||||||
\(663\) | −146.806 | + | 480.188i | −0.00859950 | + | 0.0281281i | ||||
\(664\) | −7814.14 | −0.456698 | ||||||||
\(665\) | 27166.6i | 1.58418i | ||||||||
\(666\) | −12644.8 | + | 18747.0i | −0.735699 | + | 1.09074i | ||||
\(667\) | 5818.23i | 0.337755i | ||||||||
\(668\) | − | 11490.4i | − | 0.665537i | ||||||
\(669\) | −4840.41 | + | 15832.5i | −0.279733 | + | 0.914979i | ||||
\(670\) | −406.105 | −0.0234167 | ||||||||
\(671\) | 18281.9i | 1.05181i | ||||||||
\(672\) | −4865.31 | + | 15913.9i | −0.279291 | + | 0.913532i | ||||
\(673\) | − | 20873.4i | − | 1.19556i | −0.801662 | − | 0.597778i | \(-0.796050\pi\) | ||
0.801662 | − | 0.597778i | \(-0.203950\pi\) | |||||||
\(674\) | − | 11643.8i | − | 0.665433i | ||||||
\(675\) | −1847.21 | + | 1495.88i | −0.105332 | + | 0.0852986i | ||||
\(676\) | 7354.40 | 0.418434 | ||||||||
\(677\) | − | 16752.5i | − | 0.951035i | −0.879706 | − | 0.475518i | \(-0.842261\pi\) | ||
0.879706 | − | 0.475518i | \(-0.157739\pi\) | |||||||
\(678\) | 11804.1 | − | 38610.2i | 0.668635 | − | 2.18704i | ||||
\(679\) | 34202.6i | 1.93310i | ||||||||
\(680\) | −6036.76 | −0.340440 | ||||||||
\(681\) | −3796.69 | + | 12418.6i | −0.213641 | + | 0.698799i | ||||
\(682\) | 26643.1i | 1.49592i | ||||||||
\(683\) | 2366.97 | 0.132605 | 0.0663027 | − | 0.997800i | \(-0.478880\pi\) | ||||
0.0663027 | + | 0.997800i | \(0.478880\pi\) | |||||||
\(684\) | −8774.79 | − | 5918.56i | −0.490515 | − | 0.330851i | ||||
\(685\) | −5341.45 | −0.297936 | ||||||||
\(686\) | −13947.9 | −0.776288 | ||||||||
\(687\) | −5021.37 | − | 1535.16i | −0.278861 | − | 0.0852549i | ||||
\(688\) | − | 12851.1i | − | 0.712127i | ||||||
\(689\) | 689.300 | 0.0381135 | ||||||||
\(690\) | −12240.2 | − | 3742.15i | −0.675329 | − | 0.206466i | ||||
\(691\) | 1808.80i | 0.0995804i | 0.998760 | + | 0.0497902i | \(0.0158553\pi\) | ||||
−0.998760 | + | 0.0497902i | \(0.984145\pi\) | |||||||
\(692\) | −5141.45 | −0.282440 | ||||||||
\(693\) | −14691.4 | − | 9909.27i | −0.805309 | − | 0.543178i | ||||
\(694\) | 10756.5 | 0.588346 | ||||||||
\(695\) | 19693.9i | 1.07487i | ||||||||
\(696\) | −6432.86 | − | 1966.69i | −0.350340 | − | 0.107108i | ||||
\(697\) | 4810.22 | 0.261406 | ||||||||
\(698\) | 963.366i | 0.0522406i | ||||||||
\(699\) | −8489.80 | + | 27769.3i | −0.459390 | + | 1.50262i | ||||
\(700\) | −1273.51 | −0.0687632 | ||||||||
\(701\) | −28316.6 | −1.52568 | −0.762841 | − | 0.646587i | \(-0.776196\pi\) | ||||
−0.762841 | + | 0.646587i | \(0.776196\pi\) | |||||||
\(702\) | −774.634 | − | 956.568i | −0.0416477 | − | 0.0514293i | ||||
\(703\) | 29012.2i | 1.55650i | ||||||||
\(704\) | −4531.50 | −0.242596 | ||||||||
\(705\) | 18072.3 | + | 5525.17i | 0.965449 | + | 0.295163i | ||||
\(706\) | −4775.83 | −0.254590 | ||||||||
\(707\) | 5768.57 | 0.306859 | ||||||||
\(708\) | −1358.83 | − | 7789.50i | −0.0721300 | − | 0.413485i | ||||
\(709\) | −12039.6 | −0.637737 | −0.318869 | − | 0.947799i | \(-0.603303\pi\) | ||||
−0.318869 | + | 0.947799i | \(0.603303\pi\) | |||||||
\(710\) | −3404.51 | −0.179956 | ||||||||
\(711\) | 13426.5 | + | 9056.12i | 0.708204 | + | 0.477681i | ||||
\(712\) | −8306.74 | −0.437231 | ||||||||
\(713\) | − | 18959.2i | − | 0.995831i | ||||||
\(714\) | −13915.7 | − | 4254.39i | −0.729387 | − | 0.222992i | ||||
\(715\) | 793.420 | 0.0414996 | ||||||||
\(716\) | 7387.94 | 0.385615 | ||||||||
\(717\) | 33127.9 | + | 10128.1i | 1.72550 | + | 0.527531i | ||||
\(718\) | − | 4773.73i | − | 0.248125i | ||||||
\(719\) | 19566.3 | 1.01488 | 0.507442 | − | 0.861686i | \(-0.330591\pi\) | ||||
0.507442 | + | 0.861686i | \(0.330591\pi\) | |||||||
\(720\) | 12490.9 | − | 18518.8i | 0.646539 | − | 0.958551i | ||||
\(721\) | 27592.9i | 1.42526i | ||||||||
\(722\) | −22816.9 | −1.17612 | ||||||||
\(723\) | −5784.69 | + | 18921.1i | −0.297559 | + | 0.973285i | ||||
\(724\) | −7570.89 | −0.388632 | ||||||||
\(725\) | − | 1401.94i | − | 0.0718162i | ||||||
\(726\) | 2413.45 | − | 7894.16i | 0.123377 | − | 0.403553i | ||||
\(727\) | −12878.8 | −0.657014 | −0.328507 | − | 0.944502i | \(-0.606545\pi\) | ||||
−0.328507 | + | 0.944502i | \(0.606545\pi\) | |||||||
\(728\) | 911.725i | 0.0464159i | ||||||||
\(729\) | 4091.83 | − | 19253.0i | 0.207886 | − | 0.978153i | ||||
\(730\) | 19698.0 | 0.998709 | ||||||||
\(731\) | 5993.81 | 0.303268 | ||||||||
\(732\) | −10404.2 | − | 3180.83i | −0.525340 | − | 0.160610i | ||||
\(733\) | −31693.2 | −1.59702 | −0.798509 | − | 0.601983i | \(-0.794377\pi\) | ||||
−0.798509 | + | 0.601983i | \(0.794377\pi\) | |||||||
\(734\) | − | 41688.7i | − | 2.09640i | ||||||
\(735\) | −8167.57 | − | 2497.04i | −0.409885 | − | 0.125312i | ||||
\(736\) | −10059.2 | −0.503786 | ||||||||
\(737\) | − | 339.870i | − | 0.0169868i | ||||||
\(738\) | −6593.64 | + | 9775.65i | −0.328882 | + | 0.487597i | ||||
\(739\) | − | 22257.6i | − | 1.10793i | −0.832541 | − | 0.553963i | \(-0.813115\pi\) | ||
0.832541 | − | 0.553963i | \(-0.186885\pi\) | |||||||
\(740\) | 8674.23 | 0.430907 | ||||||||
\(741\) | −1510.22 | − | 461.714i | −0.0748709 | − | 0.0228900i | ||||
\(742\) | 19975.7i | 0.988317i | ||||||||
\(743\) | − | 18899.0i | − | 0.933158i | −0.884480 | − | 0.466579i | \(-0.845486\pi\) | ||
0.884480 | − | 0.466579i | \(-0.154514\pi\) | |||||||
\(744\) | 20962.0 | + | 6408.63i | 1.03294 | + | 0.315795i | ||||
\(745\) | 29420.4i | 1.44682i | ||||||||
\(746\) | −24181.5 | −1.18680 | ||||||||
\(747\) | 11180.3 | + | 7541.06i | 0.547611 | + | 0.369361i | ||||
\(748\) | 3654.41i | 0.178635i | ||||||||
\(749\) | − | 31756.1i | − | 1.54919i | ||||||
\(750\) | 24709.6 | + | 7554.38i | 1.20302 | + | 0.367796i | ||||
\(751\) | − | 11556.3i | − | 0.561514i | −0.959779 | − | 0.280757i | \(-0.909415\pi\) | ||
0.959779 | − | 0.280757i | \(-0.0905855\pi\) | |||||||
\(752\) | 27845.3 | 1.35028 | ||||||||
\(753\) | 11395.0 | + | 3483.74i | 0.551469 | + | 0.168598i | ||||
\(754\) | 725.987 | 0.0350648 | ||||||||
\(755\) | 20873.3 | 1.00617 | ||||||||
\(756\) | 8195.46 | − | 6636.73i | 0.394267 | − | 0.319280i | ||||
\(757\) | −3877.16 | −0.186153 | −0.0930766 | − | 0.995659i | \(-0.529670\pi\) | ||||
−0.0930766 | + | 0.995659i | \(0.529670\pi\) | |||||||
\(758\) | 26948.0 | 1.29129 | ||||||||
\(759\) | 3131.82 | − | 10243.9i | 0.149773 | − | 0.489893i | ||||
\(760\) | − | 18986.0i | − | 0.906177i | ||||||
\(761\) | 12811.7i | 0.610280i | 0.952307 | + | 0.305140i | \(0.0987033\pi\) | ||||
−0.952307 | + | 0.305140i | \(0.901297\pi\) | |||||||
\(762\) | 3008.73 | − | 9841.27i | 0.143038 | − | 0.467863i | ||||
\(763\) | − | 49541.2i | − | 2.35060i | ||||||
\(764\) | 7481.78 | 0.354295 | ||||||||
\(765\) | 8637.26 | + | 5825.80i | 0.408210 | + | 0.275336i | ||||
\(766\) | 15449.8i | 0.728752i | ||||||||
\(767\) | −533.685 | − | 1052.17i | −0.0251242 | − | 0.0495330i | ||||
\(768\) | 6648.15 | − | 21745.5i | 0.312363 | − | 1.02171i | ||||
\(769\) | − | 26411.6i | − | 1.23853i | −0.785183 | − | 0.619264i | \(-0.787431\pi\) | ||
0.785183 | − | 0.619264i | \(-0.212569\pi\) | |||||||
\(770\) | 22993.1i | 1.07612i | ||||||||
\(771\) | −24115.4 | − | 7372.69i | −1.12645 | − | 0.344385i | ||||
\(772\) | 8648.46 | 0.403193 | ||||||||
\(773\) | −3435.09 | −0.159834 | −0.0799170 | − | 0.996802i | \(-0.525466\pi\) | ||||
−0.0799170 | + | 0.996802i | \(0.525466\pi\) | |||||||
\(774\) | −8216.04 | + | 12181.0i | −0.381550 | + | 0.565681i | ||||
\(775\) | 4568.34i | 0.211742i | ||||||||
\(776\) | − | 23903.3i | − | 1.10577i | ||||||
\(777\) | −27643.5 | − | 8451.34i | −1.27633 | − | 0.390206i | ||||
\(778\) | − | 36338.0i | − | 1.67452i | ||||||
\(779\) | 15128.5i | 0.695806i | ||||||||
\(780\) | −138.046 | + | 451.534i | −0.00633695 | + | 0.0207276i | ||||
\(781\) | − | 2849.24i | − | 0.130543i | ||||||
\(782\) | − | 8796.10i | − | 0.402235i | ||||||
\(783\) | 7306.02 | + | 9021.95i | 0.333456 | + | 0.411773i | ||||
\(784\) | −12584.4 | −0.573268 | ||||||||
\(785\) | 13838.5 | 0.629195 | ||||||||
\(786\) | −4250.41 | + | 13902.7i | −0.192884 | + | 0.630906i | ||||
\(787\) | 2711.20 | 0.122800 | 0.0614002 | − | 0.998113i | \(-0.480443\pi\) | ||||
0.0614002 | + | 0.998113i | \(0.480443\pi\) | |||||||
\(788\) | − | 15859.5i | − | 0.716967i | ||||||
\(789\) | 7094.87 | + | 2169.09i | 0.320132 | + | 0.0978726i | ||||
\(790\) | − | 21013.5i | − | 0.946362i | ||||||
\(791\) | 51611.4 | 2.31996 | ||||||||
\(792\) | 10267.4 | + | 6925.31i | 0.460651 | + | 0.310707i | ||||
\(793\) | −1623.28 | −0.0726917 | ||||||||
\(794\) | 47261.4i | 2.11240i | ||||||||
\(795\) | 4181.41 | − | 13677.0i | 0.186540 | − | 0.610154i | ||||
\(796\) | 1429.30 | 0.0636436 | ||||||||
\(797\) | −23051.3 | −1.02449 | −0.512246 | − | 0.858839i | \(-0.671186\pi\) | ||||
−0.512246 | + | 0.858839i | \(0.671186\pi\) | |||||||
\(798\) | 13380.3 | − | 43765.8i | 0.593557 | − | 1.94147i | ||||
\(799\) | 12987.2i | 0.575035i | ||||||||
\(800\) | 2423.83 | 0.107119 | ||||||||
\(801\) | 11885.1 | + | 8016.44i | 0.524268 | + | 0.353617i | ||||
\(802\) | −38327.9 | −1.68754 | ||||||||
\(803\) | 16485.4i | 0.724478i | ||||||||
\(804\) | 193.419 | + | 59.1333i | 0.00848430 | + | 0.00259387i | ||||
\(805\) | − | 16361.9i | − | 0.716373i | ||||||
\(806\) | −2365.69 | −0.103384 | ||||||||
\(807\) | −3019.00 | + | 9874.84i | −0.131690 | + | 0.430745i | ||||
\(808\) | −4031.49 | −0.175529 | ||||||||
\(809\) | −39643.2 | −1.72285 | −0.861423 | − | 0.507888i | \(-0.830426\pi\) | ||||
−0.861423 | + | 0.507888i | \(0.830426\pi\) | |||||||
\(810\) | −23679.1 | + | 9567.47i | −1.02716 | + | 0.415020i | ||||
\(811\) | − | 23867.9i | − | 1.03343i | −0.856156 | − | 0.516717i | \(-0.827154\pi\) | ||
0.856156 | − | 0.516717i | \(-0.172846\pi\) | |||||||
\(812\) | 6219.94i | 0.268814i | ||||||||
\(813\) | 9769.61 | − | 31955.5i | 0.421446 | − | 1.37851i | ||||
\(814\) | 24555.2i | 1.05732i | ||||||||
\(815\) | − | 4812.21i | − | 0.206827i | ||||||
\(816\) | 14680.2 | + | 4488.12i | 0.629792 | + | 0.192544i | ||||
\(817\) | 18850.9i | 0.807233i | ||||||||
\(818\) | 40537.7i | 1.73272i | ||||||||
\(819\) | 879.863 | − | 1304.48i | 0.0375396 | − | 0.0556557i | ||||
\(820\) | 4523.18 | 0.192630 | ||||||||
\(821\) | −3723.73 | −0.158293 | −0.0791467 | − | 0.996863i | \(-0.525220\pi\) | ||||
−0.0791467 | + | 0.996863i | \(0.525220\pi\) | |||||||
\(822\) | 8605.14 | + | 2630.81i | 0.365132 | + | 0.111630i | ||||
\(823\) | − | 19924.4i | − | 0.843890i | −0.906621 | − | 0.421945i | \(-0.861347\pi\) | ||
0.906621 | − | 0.421945i | \(-0.138653\pi\) | |||||||
\(824\) | − | 19283.9i | − | 0.815276i | ||||||
\(825\) | −754.632 | + | 2468.33i | −0.0318460 | + | 0.104165i | ||||
\(826\) | 30491.7 | − | 15466.0i | 1.28443 | − | 0.651492i | ||||
\(827\) | 12021.1i | 0.505459i | 0.967537 | + | 0.252730i | \(0.0813283\pi\) | ||||
−0.967537 | + | 0.252730i | \(0.918672\pi\) | |||||||
\(828\) | 5284.87 | + | 3564.62i | 0.221814 | + | 0.149612i | ||||
\(829\) | −26391.6 | −1.10569 | −0.552845 | − | 0.833284i | \(-0.686458\pi\) | ||||
−0.552845 | + | 0.833284i | \(0.686458\pi\) | |||||||
\(830\) | − | 17498.0i | − | 0.731764i | ||||||
\(831\) | 3710.35 | − | 12136.2i | 0.154886 | − | 0.506618i | ||||
\(832\) | − | 402.361i | − | 0.0167660i | ||||||
\(833\) | − | 5869.41i | − | 0.244133i | ||||||
\(834\) | 9699.82 | − | 31727.2i | 0.402731 | − | 1.31729i | ||||
\(835\) | −35571.8 | −1.47427 | ||||||||
\(836\) | −11493.4 | −0.475486 | ||||||||
\(837\) | −23807.3 | − | 29398.8i | −0.983155 | − | 1.21406i | ||||
\(838\) | −21795.9 | −0.898480 | ||||||||
\(839\) | 42586.7 | 1.75239 | 0.876195 | − | 0.481958i | \(-0.160074\pi\) | ||||
0.876195 | + | 0.481958i | \(0.160074\pi\) | |||||||
\(840\) | 18090.3 | + | 5530.68i | 0.743065 | + | 0.227174i | ||||
\(841\) | 17541.8 | 0.719250 | ||||||||
\(842\) | 39418.8i | 1.61337i | ||||||||
\(843\) | 40758.2 | + | 12460.8i | 1.66523 | + | 0.509103i | ||||
\(844\) | 1464.36i | 0.0597219i | ||||||||
\(845\) | − | 22767.5i | − | 0.926896i | ||||||
\(846\) | −26393.4 | − | 17802.2i | −1.07260 | − | 0.723467i | ||||
\(847\) | 10552.4 | 0.428080 | ||||||||
\(848\) | − | 21073.1i | − | 0.853366i | ||||||
\(849\) | 23104.3 | + | 7063.58i | 0.933966 | + | 0.285538i | ||||
\(850\) | 2119.48i | 0.0855264i | ||||||||
\(851\) | − | 17473.4i | − | 0.703856i | ||||||
\(852\) | 1621.50 | + | 495.734i | 0.0652014 | + | 0.0199338i | ||||
\(853\) | 35092.1 | 1.40859 | 0.704297 | − | 0.709906i | \(-0.251262\pi\) | ||||
0.704297 | + | 0.709906i | \(0.251262\pi\) | |||||||
\(854\) | − | 47042.3i | − | 1.88496i | ||||||
\(855\) | −18322.5 | + | 27164.7i | −0.732885 | + | 1.08657i | ||||
\(856\) | 22193.5i | 0.886164i | ||||||||
\(857\) | −17666.5 | −0.704174 | −0.352087 | − | 0.935967i | \(-0.614528\pi\) | ||||
−0.352087 | + | 0.935967i | \(0.614528\pi\) | |||||||
\(858\) | −1278.21 | − | 390.782i | −0.0508594 | − | 0.0155490i | ||||
\(859\) | − | 9939.85i | − | 0.394812i | −0.980322 | − | 0.197406i | \(-0.936748\pi\) | ||
0.980322 | − | 0.197406i | \(-0.0632517\pi\) | |||||||
\(860\) | 5636.14 | 0.223478 | ||||||||
\(861\) | −14414.8 | − | 4406.96i | −0.570561 | − | 0.174435i | ||||
\(862\) | 51482.9 | 2.03424 | ||||||||
\(863\) | −23853.5 | −0.940885 | −0.470442 | − | 0.882431i | \(-0.655906\pi\) | ||||
−0.470442 | + | 0.882431i | \(0.655906\pi\) | |||||||
\(864\) | −15598.1 | + | 12631.4i | −0.614188 | + | 0.497373i | ||||
\(865\) | 15916.7i | 0.625648i | ||||||||
\(866\) | −28012.0 | −1.09918 | ||||||||
\(867\) | 5370.49 | − | 17566.3i | 0.210371 | − | 0.688102i | ||||
\(868\) | − | 20268.2i | − | 0.792567i | ||||||
\(869\) | 17586.3 | 0.686505 | ||||||||
\(870\) | 4403.96 | − | 14404.9i | 0.171619 | − | 0.561348i | ||||
\(871\) | 30.1778 | 0.00117398 | ||||||||
\(872\) | 34623.0i | 1.34459i | ||||||||
\(873\) | −23067.9 | + | 34200.2i | −0.894308 | + | 1.32589i | ||||
\(874\) | 27664.3 | 1.07066 | ||||||||
\(875\) | 33030.1i | 1.27614i | ||||||||
\(876\) | −9381.78 | − | 2868.25i | −0.361850 | − | 0.110627i | ||||
\(877\) | −27678.4 | −1.06571 | −0.532857 | − | 0.846205i | \(-0.678882\pi\) | ||||
−0.532857 | + | 0.846205i | \(0.678882\pi\) | |||||||
\(878\) | 39970.2 | 1.53636 | ||||||||
\(879\) | 17241.4 | + | 5271.13i | 0.661589 | + | 0.202265i | ||||
\(880\) | − | 24256.3i | − | 0.929181i | ||||||
\(881\) | −29424.9 | −1.12526 | −0.562628 | − | 0.826710i | \(-0.690210\pi\) | ||||
−0.562628 | + | 0.826710i | \(0.690210\pi\) | |||||||
\(882\) | 11928.2 | + | 8045.52i | 0.455378 | + | 0.307150i | ||||
\(883\) | 18910.6 | 0.720718 | 0.360359 | − | 0.932814i | \(-0.382654\pi\) | ||||
0.360359 | + | 0.932814i | \(0.382654\pi\) | |||||||
\(884\) | −324.483 | −0.0123456 | ||||||||
\(885\) | −24114.5 | + | 4206.63i | −0.915932 | + | 0.159779i | ||||
\(886\) | 15232.6 | 0.577594 | ||||||||
\(887\) | −30185.3 | −1.14264 | −0.571322 | − | 0.820726i | \(-0.693569\pi\) | ||||
−0.571322 | + | 0.820726i | \(0.693569\pi\) | |||||||
\(888\) | 19319.3 | + | 5906.41i | 0.730082 | + | 0.223205i | ||||
\(889\) | 13155.1 | 0.496299 | ||||||||
\(890\) | − | 18601.1i | − | 0.700571i | ||||||
\(891\) | −8007.05 | − | 19817.2i | −0.301062 | − | 0.745118i | ||||
\(892\) | −10698.7 | −0.401590 | ||||||||
\(893\) | −40845.5 | −1.53062 | ||||||||
\(894\) | 14490.4 | − | 47396.7i | 0.542093 | − | 1.77313i | ||||
\(895\) | − | 22871.4i | − | 0.854196i | ||||||
\(896\) | 37280.9 | 1.39003 | ||||||||
\(897\) | 909.574 | + | 278.080i | 0.0338571 | + | 0.0103510i | ||||
\(898\) | 24839.5i | 0.923058i | ||||||||
\(899\) | 22312.2 | 0.827757 | ||||||||
\(900\) | −1273.42 | − | 858.918i | −0.0471638 | − | 0.0318118i | ||||
\(901\) | 9828.59 | 0.363416 | ||||||||
\(902\) | 12804.3i | 0.472657i | ||||||||
\(903\) | −17961.6 | − | 5491.32i | −0.661931 | − | 0.202370i | ||||
\(904\) | −36069.8 | −1.32706 | ||||||||
\(905\) | 23437.7i | 0.860880i | ||||||||
\(906\) | −33627.2 | − | 10280.7i | −1.23310 | − | 0.376991i | ||||
\(907\) | 18102.7 | 0.662724 | 0.331362 | − | 0.943504i | \(-0.392492\pi\) | ||||
0.331362 | + | 0.943504i | \(0.392492\pi\) | |||||||
\(908\) | −8391.76 | −0.306707 | ||||||||
\(909\) | 5768.17 | + | 3890.61i | 0.210471 | + | 0.141962i | ||||
\(910\) | −2041.60 | −0.0743719 | ||||||||
\(911\) | − | 15175.8i | − | 0.551916i | −0.961170 | − | 0.275958i | \(-0.911005\pi\) | ||
0.961170 | − | 0.275958i | \(-0.0889951\pi\) | |||||||
\(912\) | −14115.4 | + | 46170.2i | −0.512509 | + | 1.67637i | ||||
\(913\) | 14644.1 | 0.530832 | ||||||||
\(914\) | 28793.6i | 1.04202i | ||||||||
\(915\) | −9847.11 | + | 32208.9i | −0.355776 | + | 1.16371i | ||||
\(916\) | − | 3393.15i | − | 0.122394i | ||||||
\(917\) | −18584.2 | −0.669251 | ||||||||
\(918\) | −11045.4 | − | 13639.5i | −0.397115 | − | 0.490383i | ||||
\(919\) | 9982.42i | 0.358313i | 0.983821 | + | 0.179157i | \(0.0573369\pi\) | ||||
−0.983821 | + | 0.179157i | \(0.942663\pi\) | |||||||
\(920\) | 11434.9i | 0.409778i | ||||||||
\(921\) | 466.512 | − | 1525.91i | 0.0166906 | − | 0.0545935i | ||||
\(922\) | − | 6842.56i | − | 0.244412i | ||||||
\(923\) | 252.990 | 0.00902195 | ||||||||
\(924\) | 3348.05 | − | 10951.1i | 0.119202 | − | 0.389899i | ||||
\(925\) | 4210.34i | 0.149660i | ||||||||
\(926\) | − | 22354.4i | − | 0.793315i | ||||||
\(927\) | −18610.0 | + | 27591.0i | −0.659367 | + | 0.977570i | ||||
\(928\) | − | 11838.2i | − | 0.418758i | ||||||
\(929\) | 44241.8 | 1.56246 | 0.781231 | − | 0.624242i | \(-0.214592\pi\) | ||||
0.781231 | + | 0.624242i | \(0.214592\pi\) | |||||||
\(930\) | −14350.7 | + | 46939.7i | −0.505997 | + | 1.65507i | ||||
\(931\) | 18459.7 | 0.649829 | ||||||||
\(932\) | −18764.9 | −0.659510 | ||||||||
\(933\) | 17290.3 | + | 5286.10i | 0.606709 | + | 0.185487i | ||||
\(934\) | −1609.43 | −0.0563834 | ||||||||
\(935\) | 11313.2 | 0.395703 | ||||||||
\(936\) | −614.912 | + | 911.662i | −0.0214733 | + | 0.0318361i | ||||
\(937\) | − | 55172.0i | − | 1.92358i | −0.273795 | − | 0.961788i | \(-0.588279\pi\) | ||
0.273795 | − | 0.961788i | \(-0.411721\pi\) | |||||||
\(938\) | 874.542i | 0.0304422i | ||||||||
\(939\) | −37218.2 | − | 11378.6i | −1.29347 | − | 0.395448i | ||||
\(940\) | 12212.2i | 0.423742i | ||||||||
\(941\) | −9582.77 | −0.331976 | −0.165988 | − | 0.986128i | \(-0.553081\pi\) | ||||
−0.165988 | + | 0.986128i | \(0.553081\pi\) | |||||||
\(942\) | −22294.0 | − | 6815.87i | −0.771103 | − | 0.235746i | ||||
\(943\) | − | 9111.55i | − | 0.314648i | ||||||
\(944\) | −32166.9 | + | 16315.7i | −1.10905 | + | 0.562533i | ||||
\(945\) | −20545.8 | − | 25371.3i | −0.707254 | − | 0.873363i | ||||
\(946\) | 15954.9i | 0.548349i | ||||||||
\(947\) | 17371.2i | 0.596080i | 0.954553 | + | 0.298040i | \(0.0963329\pi\) | ||||
−0.954553 | + | 0.298040i | \(0.903667\pi\) | |||||||
\(948\) | −3059.80 | + | 10008.3i | −0.104829 | + | 0.342884i | ||||
\(949\) | −1463.77 | −0.0500695 | ||||||||
\(950\) | −6665.89 | −0.227653 | ||||||||
\(951\) | −6524.96 | − | 1994.85i | −0.222488 | − | 0.0680204i | ||||
\(952\) | 13000.1i | 0.442580i | ||||||||
\(953\) | − | 1947.46i | − | 0.0661957i | −0.999452 | − | 0.0330978i | \(-0.989463\pi\) | ||
0.999452 | − | 0.0330978i | \(-0.0105373\pi\) | |||||||
\(954\) | −13472.6 | + | 19974.3i | −0.457224 | + | 0.677874i | ||||
\(955\) | − | 23161.9i | − | 0.784818i | ||||||
\(956\) | 22385.9i | 0.757334i | ||||||||
\(957\) | 12055.5 | + | 3685.69i | 0.407210 | + | 0.124495i | ||||
\(958\) | 14385.7i | 0.485157i | ||||||||
\(959\) | 11502.8i | 0.387324i | ||||||||
\(960\) | −7983.58 | − | 2440.79i | −0.268405 | − | 0.0820584i | ||||
\(961\) | −42915.2 | −1.44054 | ||||||||
\(962\) | −2180.30 | −0.0730724 | ||||||||
\(963\) | 21417.9 | − | 31753.9i | 0.716699 | − | 1.06257i | ||||
\(964\) | −12785.8 | −0.427181 | ||||||||
\(965\) | − | 26773.6i | − | 0.893134i | ||||||
\(966\) | −8058.68 | + | 26359.2i | −0.268410 | + | 0.877943i | ||||
\(967\) | − | 11825.1i | − | 0.393245i | −0.980479 | − | 0.196623i | \(-0.937003\pi\) | ||
0.980479 | − | 0.196623i | \(-0.0629974\pi\) | |||||||
\(968\) | −7374.76 | −0.244870 | ||||||||
\(969\) | −21534.0 | − | 6583.49i | −0.713901 | − | 0.218258i | ||||
\(970\) | 53525.9 | 1.77177 | ||||||||
\(971\) | − | 45906.7i | − | 1.51722i | −0.651547 | − | 0.758608i | \(-0.725880\pi\) | ||
0.651547 | − | 0.758608i | \(-0.274120\pi\) | |||||||
\(972\) | 12671.0 | − | 1108.85i | 0.418131 | − | 0.0365908i | ||||
\(973\) | 42410.7 | 1.39735 | ||||||||
\(974\) | 27095.7 | 0.891378 | ||||||||
\(975\) | −219.168 | − | 67.0052i | −0.00719896 | − | 0.00220091i | ||||
\(976\) | 49626.7i | 1.62757i | ||||||||
\(977\) | 1579.81 | 0.0517325 | 0.0258663 | − | 0.999665i | \(-0.491766\pi\) | ||||
0.0258663 | + | 0.999665i | \(0.491766\pi\) | |||||||
\(978\) | −2370.15 | + | 7752.52i | −0.0774938 | + | 0.253475i | ||||
\(979\) | 15567.3 | 0.508205 | ||||||||
\(980\) | − | 5519.16i | − | 0.179901i | ||||||
\(981\) | 33413.0 | − | 49537.7i | 1.08746 | − | 1.61225i | ||||
\(982\) | 45751.9i | 1.48676i | ||||||||
\(983\) | −11769.9 | −0.381894 | −0.190947 | − | 0.981600i | \(-0.561156\pi\) | ||||
−0.190947 | + | 0.981600i | \(0.561156\pi\) | |||||||
\(984\) | 10074.1 | + | 3079.90i | 0.326372 | + | 0.0997802i | ||||
\(985\) | −49097.3 | −1.58819 | ||||||||
\(986\) | 10351.7 | 0.334346 | ||||||||
\(987\) | 11898.4 | − | 38918.5i | 0.383719 | − | 1.25511i | ||||
\(988\) | − | 1020.52i | − | 0.0328613i | ||||||
\(989\) | − | 11353.5i | − | 0.365035i | ||||||
\(990\) | −15507.7 | + | 22991.5i | −0.497844 | + | 0.738098i | ||||
\(991\) | 33297.2i | 1.06733i | 0.845697 | + | 0.533664i | \(0.179185\pi\) | ||||
−0.845697 | + | 0.533664i | \(0.820815\pi\) | |||||||
\(992\) | 38575.7i | 1.23466i | ||||||||
\(993\) | −15171.1 | + | 49623.2i | −0.484834 | + | 1.58585i | ||||
\(994\) | 7331.57i | 0.233947i | ||||||||
\(995\) | − | 4424.79i | − | 0.140980i | ||||||
\(996\) | −2547.90 | + | 8333.94i | −0.0810576 | + | 0.265131i | ||||
\(997\) | 33097.6 | 1.05137 | 0.525683 | − | 0.850680i | \(-0.323810\pi\) | ||||
0.525683 | + | 0.850680i | \(0.323810\pi\) | |||||||
\(998\) | −8294.25 | −0.263076 | ||||||||
\(999\) | −21941.6 | − | 27094.9i | −0.694896 | − | 0.858103i |
(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.176.13 | ✓ | 52 | |
3.2 | odd | 2 | inner | 177.4.d.c.176.40 | yes | 52 | |
59.58 | odd | 2 | inner | 177.4.d.c.176.39 | yes | 52 | |
177.176 | even | 2 | inner | 177.4.d.c.176.14 | yes | 52 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
177.4.d.c.176.13 | ✓ | 52 | 1.1 | even | 1 | trivial | |
177.4.d.c.176.14 | yes | 52 | 177.176 | even | 2 | inner | |
177.4.d.c.176.39 | yes | 52 | 59.58 | odd | 2 | inner | |
177.4.d.c.176.40 | yes | 52 | 3.2 | odd | 2 | inner |