Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [690,3,Mod(599,690)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(690, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("690.599");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 690.b (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: | \(18.8011382409\) |
Analytic rank: | \(0\) |
Dimension: | \(88\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 599.17 | ||
Character | \(\chi\) | \(=\) | 690.599 |
Dual form | 690.3.b.a.599.18 |
$q$-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 \(\left(\mathbb{Z}/690\mathbb{Z}\right)^\times\).
\(n\) | \(277\) | \(461\) | \(511\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.41421 | −0.707107 | ||||||||
\(3\) | −1.23483 | − | 2.73408i | −0.411609 | − | 0.911360i | ||||
\(4\) | 2.00000 | 0.500000 | ||||||||
\(5\) | 4.77075 | − | 1.49664i | 0.954151 | − | 0.299327i | ||||
\(6\) | 1.74631 | + | 3.86657i | 0.291052 | + | 0.644429i | ||||
\(7\) | 2.54772i | 0.363960i | 0.983302 | + | 0.181980i | \(0.0582506\pi\) | ||||
−0.983302 | + | 0.181980i | \(0.941749\pi\) | |||||||
\(8\) | −2.82843 | −0.353553 | ||||||||
\(9\) | −5.95040 | + | 6.75224i | −0.661156 | + | 0.750249i | ||||
\(10\) | −6.74686 | + | 2.11656i | −0.674686 | + | 0.211656i | ||||
\(11\) | − | 15.8694i | − | 1.44268i | −0.692583 | − | 0.721338i | \(-0.743527\pi\) | ||
0.692583 | − | 0.721338i | \(-0.256473\pi\) | |||||||
\(12\) | −2.46966 | − | 5.46816i | −0.205805 | − | 0.455680i | ||||
\(13\) | 23.6018i | 1.81552i | 0.419486 | + | 0.907762i | \(0.362210\pi\) | ||||
−0.419486 | + | 0.907762i | \(0.637790\pi\) | |||||||
\(14\) | − | 3.60302i | − | 0.257358i | ||||||
\(15\) | −9.98298 | − | 11.1955i | −0.665532 | − | 0.746369i | ||||
\(16\) | 4.00000 | 0.250000 | ||||||||
\(17\) | 32.3944 | 1.90555 | 0.952776 | − | 0.303673i | \(-0.0982131\pi\) | ||||
0.952776 | + | 0.303673i | \(0.0982131\pi\) | |||||||
\(18\) | 8.41514 | − | 9.54911i | 0.467508 | − | 0.530506i | ||||
\(19\) | 2.70349 | 0.142289 | 0.0711444 | − | 0.997466i | \(-0.477335\pi\) | ||||
0.0711444 | + | 0.997466i | \(0.477335\pi\) | |||||||
\(20\) | 9.54151 | − | 2.99327i | 0.477075 | − | 0.149664i | ||||
\(21\) | 6.96567 | − | 3.14599i | 0.331699 | − | 0.149809i | ||||
\(22\) | 22.4428i | 1.02013i | ||||||||
\(23\) | −4.79583 | −0.208514 | ||||||||
\(24\) | 3.49262 | + | 7.73315i | 0.145526 | + | 0.322215i | ||||
\(25\) | 20.5202 | − | 14.2802i | 0.820806 | − | 0.571206i | ||||
\(26\) | − | 33.3780i | − | 1.28377i | ||||||
\(27\) | 25.8089 | + | 7.93103i | 0.955885 | + | 0.293742i | ||||
\(28\) | 5.09544i | 0.181980i | ||||||||
\(29\) | − | 13.8764i | − | 0.478495i | −0.970959 | − | 0.239248i | \(-0.923099\pi\) | ||
0.970959 | − | 0.239248i | \(-0.0769008\pi\) | |||||||
\(30\) | 14.1181 | + | 15.8329i | 0.470602 | + | 0.527763i | ||||
\(31\) | 16.4061 | 0.529230 | 0.264615 | − | 0.964354i | \(-0.414755\pi\) | ||||
0.264615 | + | 0.964354i | \(0.414755\pi\) | |||||||
\(32\) | −5.65685 | −0.176777 | ||||||||
\(33\) | −43.3883 | + | 19.5960i | −1.31480 | + | 0.593819i | ||||
\(34\) | −45.8126 | −1.34743 | ||||||||
\(35\) | 3.81301 | + | 12.1545i | 0.108943 | + | 0.347272i | ||||
\(36\) | −11.9008 | + | 13.5045i | −0.330578 | + | 0.375124i | ||||
\(37\) | 8.63454i | 0.233366i | 0.993169 | + | 0.116683i | \(0.0372261\pi\) | ||||
−0.993169 | + | 0.116683i | \(0.962774\pi\) | |||||||
\(38\) | −3.82331 | −0.100613 | ||||||||
\(39\) | 64.5293 | − | 29.1442i | 1.65460 | − | 0.747286i | ||||
\(40\) | −13.4937 | + | 4.23313i | −0.337343 | + | 0.105828i | ||||
\(41\) | 59.3900i | 1.44854i | 0.689518 | + | 0.724269i | \(0.257822\pi\) | ||||
−0.689518 | + | 0.724269i | \(0.742178\pi\) | |||||||
\(42\) | −9.85095 | + | 4.44911i | −0.234546 | + | 0.105931i | ||||
\(43\) | 51.2988i | 1.19300i | 0.802615 | + | 0.596498i | \(0.203442\pi\) | ||||
−0.802615 | + | 0.596498i | \(0.796558\pi\) | |||||||
\(44\) | − | 31.7389i | − | 0.721338i | ||||||
\(45\) | −18.2822 | + | 41.1188i | −0.406272 | + | 0.913752i | ||||
\(46\) | 6.78233 | 0.147442 | ||||||||
\(47\) | −38.9126 | −0.827928 | −0.413964 | − | 0.910293i | \(-0.635856\pi\) | ||||
−0.413964 | + | 0.910293i | \(0.635856\pi\) | |||||||
\(48\) | −4.93931 | − | 10.9363i | −0.102902 | − | 0.227840i | ||||
\(49\) | 42.5091 | 0.867533 | ||||||||
\(50\) | −29.0199 | + | 20.1952i | −0.580398 | + | 0.403904i | ||||
\(51\) | −40.0015 | − | 88.5689i | −0.784343 | − | 1.73665i | ||||
\(52\) | 47.2036i | 0.907762i | ||||||||
\(53\) | 85.0310 | 1.60436 | 0.802180 | − | 0.597083i | \(-0.203674\pi\) | ||||
0.802180 | + | 0.597083i | \(0.203674\pi\) | |||||||
\(54\) | −36.4993 | − | 11.2162i | −0.675913 | − | 0.207707i | ||||
\(55\) | −23.7508 | − | 75.7091i | −0.431832 | − | 1.37653i | ||||
\(56\) | − | 7.20604i | − | 0.128679i | ||||||
\(57\) | −3.33834 | − | 7.39155i | −0.0585674 | − | 0.129676i | ||||
\(58\) | 19.6241i | 0.338347i | ||||||||
\(59\) | − | 78.7364i | − | 1.33452i | −0.744827 | − | 0.667258i | \(-0.767468\pi\) | ||
0.744827 | − | 0.667258i | \(-0.232532\pi\) | |||||||
\(60\) | −19.9660 | − | 22.3911i | −0.332766 | − | 0.373185i | ||||
\(61\) | −68.8771 | −1.12913 | −0.564567 | − | 0.825387i | \(-0.690957\pi\) | ||||
−0.564567 | + | 0.825387i | \(0.690957\pi\) | |||||||
\(62\) | −23.2018 | −0.374222 | ||||||||
\(63\) | −17.2028 | − | 15.1600i | −0.273060 | − | 0.240634i | ||||
\(64\) | 8.00000 | 0.125000 | ||||||||
\(65\) | 35.3233 | + | 112.598i | 0.543436 | + | 1.73228i | ||||
\(66\) | 61.3604 | − | 27.7130i | 0.929702 | − | 0.419893i | ||||
\(67\) | − | 66.3843i | − | 0.990810i | −0.868662 | − | 0.495405i | \(-0.835020\pi\) | ||
0.868662 | − | 0.495405i | \(-0.164980\pi\) | |||||||
\(68\) | 64.7888 | 0.952776 | ||||||||
\(69\) | 5.92203 | + | 13.1122i | 0.0858265 | + | 0.190032i | ||||
\(70\) | −5.39241 | − | 17.1891i | −0.0770344 | − | 0.245559i | ||||
\(71\) | − | 88.6614i | − | 1.24875i | −0.781124 | − | 0.624376i | \(-0.785353\pi\) | ||
0.781124 | − | 0.624376i | \(-0.214647\pi\) | |||||||
\(72\) | 16.8303 | − | 19.0982i | 0.233754 | − | 0.265253i | ||||
\(73\) | − | 37.1977i | − | 0.509557i | −0.966999 | − | 0.254778i | \(-0.917997\pi\) | ||
0.966999 | − | 0.254778i | \(-0.0820025\pi\) | |||||||
\(74\) | − | 12.2111i | − | 0.165015i | ||||||
\(75\) | −64.3820 | − | 38.4702i | −0.858426 | − | 0.512937i | ||||
\(76\) | 5.40697 | 0.0711444 | ||||||||
\(77\) | 40.4309 | 0.525076 | ||||||||
\(78\) | −91.2581 | + | 41.2161i | −1.16998 | + | 0.528411i | ||||
\(79\) | 104.696 | 1.32526 | 0.662631 | − | 0.748946i | \(-0.269440\pi\) | ||||
0.662631 | + | 0.748946i | \(0.269440\pi\) | |||||||
\(80\) | 19.0830 | − | 5.98654i | 0.238538 | − | 0.0748318i | ||||
\(81\) | −10.1854 | − | 80.3571i | −0.125746 | − | 0.992062i | ||||
\(82\) | − | 83.9902i | − | 1.02427i | ||||||
\(83\) | 76.6784 | 0.923836 | 0.461918 | − | 0.886923i | \(-0.347161\pi\) | ||||
0.461918 | + | 0.886923i | \(0.347161\pi\) | |||||||
\(84\) | 13.9313 | − | 6.29199i | 0.165849 | − | 0.0749046i | ||||
\(85\) | 154.546 | − | 48.4826i | 1.81818 | − | 0.570384i | ||||
\(86\) | − | 72.5475i | − | 0.843575i | ||||||
\(87\) | −37.9391 | + | 17.1349i | −0.436082 | + | 0.196953i | ||||
\(88\) | 44.8855i | 0.510063i | ||||||||
\(89\) | − | 76.2385i | − | 0.856612i | −0.903634 | − | 0.428306i | \(-0.859111\pi\) | ||
0.903634 | − | 0.428306i | \(-0.140889\pi\) | |||||||
\(90\) | 25.8550 | − | 58.1508i | 0.287278 | − | 0.646120i | ||||
\(91\) | −60.1308 | −0.660778 | ||||||||
\(92\) | −9.59166 | −0.104257 | ||||||||
\(93\) | −20.2588 | − | 44.8557i | −0.217836 | − | 0.482320i | ||||
\(94\) | 55.0308 | 0.585434 | ||||||||
\(95\) | 12.8977 | − | 4.04613i | 0.135765 | − | 0.0425909i | ||||
\(96\) | 6.98524 | + | 15.4663i | 0.0727629 | + | 0.161107i | ||||
\(97\) | − | 73.6041i | − | 0.758805i | −0.925232 | − | 0.379403i | \(-0.876130\pi\) | ||
0.925232 | − | 0.379403i | \(-0.123870\pi\) | |||||||
\(98\) | −60.1170 | −0.613439 | ||||||||
\(99\) | 107.154 | + | 94.4295i | 1.08237 | + | 0.953833i | ||||
\(100\) | 41.0403 | − | 28.5603i | 0.410403 | − | 0.285603i | ||||
\(101\) | − | 4.51645i | − | 0.0447173i | −0.999750 | − | 0.0223587i | \(-0.992882\pi\) | ||
0.999750 | − | 0.0223587i | \(-0.00711758\pi\) | |||||||
\(102\) | 56.5707 | + | 125.255i | 0.554614 | + | 1.22799i | ||||
\(103\) | − | 45.2000i | − | 0.438835i | −0.975631 | − | 0.219417i | \(-0.929584\pi\) | ||
0.975631 | − | 0.219417i | \(-0.0704156\pi\) | |||||||
\(104\) | − | 66.7560i | − | 0.641884i | ||||||
\(105\) | 28.5231 | − | 25.4338i | 0.271648 | − | 0.242227i | ||||
\(106\) | −120.252 | −1.13445 | ||||||||
\(107\) | 25.9543 | 0.242563 | 0.121282 | − | 0.992618i | \(-0.461300\pi\) | ||||
0.121282 | + | 0.992618i | \(0.461300\pi\) | |||||||
\(108\) | 51.6178 | + | 15.8621i | 0.477942 | + | 0.146871i | ||||
\(109\) | 53.8738 | 0.494255 | 0.247128 | − | 0.968983i | \(-0.420513\pi\) | ||||
0.247128 | + | 0.968983i | \(0.420513\pi\) | |||||||
\(110\) | 33.5887 | + | 107.069i | 0.305351 | + | 0.973354i | ||||
\(111\) | 23.6075 | − | 10.6622i | 0.212680 | − | 0.0960556i | ||||
\(112\) | 10.1909i | 0.0909900i | ||||||||
\(113\) | −82.8476 | −0.733165 | −0.366582 | − | 0.930386i | \(-0.619472\pi\) | ||||
−0.366582 | + | 0.930386i | \(0.619472\pi\) | |||||||
\(114\) | 4.72112 | + | 10.4532i | 0.0414134 | + | 0.0916950i | ||||
\(115\) | −22.8797 | + | 7.17762i | −0.198954 | + | 0.0624140i | ||||
\(116\) | − | 27.7527i | − | 0.239248i | ||||||
\(117\) | −159.365 | − | 140.440i | −1.36209 | − | 1.20034i | ||||
\(118\) | 111.350i | 0.943645i | ||||||||
\(119\) | 82.5318i | 0.693545i | ||||||||
\(120\) | 28.2361 | + | 31.6658i | 0.235301 | + | 0.263881i | ||||
\(121\) | −130.839 | −1.08131 | ||||||||
\(122\) | 97.4070 | 0.798418 | ||||||||
\(123\) | 162.377 | − | 73.3365i | 1.32014 | − | 0.596231i | ||||
\(124\) | 32.8123 | 0.264615 | ||||||||
\(125\) | 76.5244 | − | 98.8383i | 0.612195 | − | 0.790707i | ||||
\(126\) | 24.3284 | + | 21.4394i | 0.193083 | + | 0.170154i | ||||
\(127\) | 90.0823i | 0.709310i | 0.934997 | + | 0.354655i | \(0.115402\pi\) | ||||
−0.934997 | + | 0.354655i | \(0.884598\pi\) | |||||||
\(128\) | −11.3137 | −0.0883883 | ||||||||
\(129\) | 140.255 | − | 63.3452i | 1.08725 | − | 0.491048i | ||||
\(130\) | −49.9547 | − | 159.238i | −0.384267 | − | 1.22491i | ||||
\(131\) | 135.317i | 1.03296i | 0.856300 | + | 0.516478i | \(0.172757\pi\) | ||||
−0.856300 | + | 0.516478i | \(0.827243\pi\) | |||||||
\(132\) | −86.7767 | + | 39.1920i | −0.657399 | + | 0.296909i | ||||
\(133\) | 6.88772i | 0.0517874i | ||||||||
\(134\) | 93.8815i | 0.700609i | ||||||||
\(135\) | 134.998 | − | 0.789532i | 0.999983 | − | 0.00584839i | ||||
\(136\) | −91.6252 | −0.673715 | ||||||||
\(137\) | 117.874 | 0.860392 | 0.430196 | − | 0.902736i | \(-0.358444\pi\) | ||||
0.430196 | + | 0.902736i | \(0.358444\pi\) | |||||||
\(138\) | −8.37501 | − | 18.5434i | −0.0606885 | − | 0.134373i | ||||
\(139\) | −183.405 | −1.31946 | −0.659729 | − | 0.751504i | \(-0.729329\pi\) | ||||
−0.659729 | + | 0.751504i | \(0.729329\pi\) | |||||||
\(140\) | 7.62602 | + | 24.3091i | 0.0544715 | + | 0.173636i | ||||
\(141\) | 48.0504 | + | 106.390i | 0.340783 | + | 0.754541i | ||||
\(142\) | 125.386i | 0.883001i | ||||||||
\(143\) | 374.547 | 2.61921 | ||||||||
\(144\) | −23.8016 | + | 27.0090i | −0.165289 | + | 0.187562i | ||||
\(145\) | −20.7679 | − | 66.2007i | −0.143227 | − | 0.456556i | ||||
\(146\) | 52.6054i | 0.360311i | ||||||||
\(147\) | −52.4914 | − | 116.223i | −0.357085 | − | 0.790635i | ||||
\(148\) | 17.2691i | 0.116683i | ||||||||
\(149\) | − | 24.5997i | − | 0.165099i | −0.996587 | − | 0.0825493i | \(-0.973694\pi\) | ||
0.996587 | − | 0.0825493i | \(-0.0263062\pi\) | |||||||
\(150\) | 91.0499 | + | 54.4051i | 0.606999 | + | 0.362701i | ||||
\(151\) | −32.5412 | −0.215505 | −0.107752 | − | 0.994178i | \(-0.534365\pi\) | ||||
−0.107752 | + | 0.994178i | \(0.534365\pi\) | |||||||
\(152\) | −7.64661 | −0.0503067 | ||||||||
\(153\) | −192.760 | + | 218.735i | −1.25987 | + | 1.42964i | ||||
\(154\) | −57.1779 | −0.371285 | ||||||||
\(155\) | 78.2696 | − | 24.5540i | 0.504965 | − | 0.158413i | ||||
\(156\) | 129.059 | − | 58.2883i | 0.827298 | − | 0.373643i | ||||
\(157\) | − | 3.81607i | − | 0.0243062i | −0.999926 | − | 0.0121531i | \(-0.996131\pi\) | ||
0.999926 | − | 0.0121531i | \(-0.00386855\pi\) | |||||||
\(158\) | −148.062 | −0.937101 | ||||||||
\(159\) | −104.999 | − | 232.482i | −0.660369 | − | 1.46215i | ||||
\(160\) | −26.9875 | + | 8.46625i | −0.168672 | + | 0.0529141i | ||||
\(161\) | − | 12.2184i | − | 0.0758909i | ||||||
\(162\) | 14.4044 | + | 113.642i | 0.0889160 | + | 0.701494i | ||||
\(163\) | 176.476i | 1.08268i | 0.840805 | + | 0.541338i | \(0.182082\pi\) | ||||
−0.840805 | + | 0.541338i | \(0.817918\pi\) | |||||||
\(164\) | 118.780i | 0.724269i | ||||||||
\(165\) | −177.667 | + | 158.424i | −1.07677 | + | 0.960147i | ||||
\(166\) | −108.440 | −0.653251 | ||||||||
\(167\) | −157.350 | −0.942215 | −0.471107 | − | 0.882076i | \(-0.656146\pi\) | ||||
−0.471107 | + | 0.882076i | \(0.656146\pi\) | |||||||
\(168\) | −19.7019 | + | 8.89821i | −0.117273 | + | 0.0529656i | ||||
\(169\) | −388.045 | −2.29613 | ||||||||
\(170\) | −218.561 | + | 68.5648i | −1.28565 | + | 0.403322i | ||||
\(171\) | −16.0868 | + | 18.2546i | −0.0940750 | + | 0.106752i | ||||
\(172\) | 102.598i | 0.596498i | ||||||||
\(173\) | −248.801 | −1.43815 | −0.719077 | − | 0.694930i | \(-0.755435\pi\) | ||||
−0.719077 | + | 0.694930i | \(0.755435\pi\) | |||||||
\(174\) | 53.6540 | − | 24.2324i | 0.308356 | − | 0.139267i | ||||
\(175\) | 36.3818 | + | 52.2796i | 0.207896 | + | 0.298741i | ||||
\(176\) | − | 63.4777i | − | 0.360669i | ||||||
\(177\) | −215.272 | + | 97.2259i | −1.21622 | + | 0.549299i | ||||
\(178\) | 107.817i | 0.605716i | ||||||||
\(179\) | − | 111.059i | − | 0.620442i | −0.950664 | − | 0.310221i | \(-0.899597\pi\) | ||
0.950664 | − | 0.310221i | \(-0.100403\pi\) | |||||||
\(180\) | −36.5645 | + | 82.2377i | −0.203136 | + | 0.456876i | ||||
\(181\) | 219.405 | 1.21218 | 0.606092 | − | 0.795395i | \(-0.292736\pi\) | ||||
0.606092 | + | 0.795395i | \(0.292736\pi\) | |||||||
\(182\) | 85.0377 | 0.467240 | ||||||||
\(183\) | 85.0514 | + | 188.316i | 0.464762 | + | 1.02905i | ||||
\(184\) | 13.5647 | 0.0737210 | ||||||||
\(185\) | 12.9228 | + | 41.1933i | 0.0698528 | + | 0.222666i | ||||
\(186\) | 28.6502 | + | 63.4356i | 0.154033 | + | 0.341051i | ||||
\(187\) | − | 514.081i | − | 2.74909i | ||||||
\(188\) | −77.8252 | −0.413964 | ||||||||
\(189\) | −20.2060 | + | 65.7538i | −0.106910 | + | 0.347904i | ||||
\(190\) | −18.2400 | + | 5.72210i | −0.0960003 | + | 0.0301163i | ||||
\(191\) | 23.6963i | 0.124065i | 0.998074 | + | 0.0620323i | \(0.0197582\pi\) | ||||
−0.998074 | + | 0.0620323i | \(0.980242\pi\) | |||||||
\(192\) | −9.87862 | − | 21.8727i | −0.0514512 | − | 0.113920i | ||||
\(193\) | − | 98.0811i | − | 0.508192i | −0.967179 | − | 0.254096i | \(-0.918222\pi\) | ||
0.967179 | − | 0.254096i | \(-0.0817780\pi\) | |||||||
\(194\) | 104.092i | 0.536556i | ||||||||
\(195\) | 264.235 | − | 235.616i | 1.35505 | − | 1.20829i | ||||
\(196\) | 85.0183 | 0.433767 | ||||||||
\(197\) | 316.042 | 1.60428 | 0.802138 | − | 0.597139i | \(-0.203696\pi\) | ||||
0.802138 | + | 0.597139i | \(0.203696\pi\) | |||||||
\(198\) | −151.539 | − | 133.543i | −0.765348 | − | 0.674462i | ||||
\(199\) | 168.719 | 0.847835 | 0.423918 | − | 0.905701i | \(-0.360655\pi\) | ||||
0.423918 | + | 0.905701i | \(0.360655\pi\) | |||||||
\(200\) | −58.0398 | + | 40.3904i | −0.290199 | + | 0.201952i | ||||
\(201\) | −181.500 | + | 81.9731i | −0.902985 | + | 0.407827i | ||||
\(202\) | 6.38723i | 0.0316199i | ||||||||
\(203\) | 35.3531 | 0.174153 | ||||||||
\(204\) | −80.0030 | − | 177.138i | −0.392171 | − | 0.868323i | ||||
\(205\) | 88.8853 | + | 283.335i | 0.433587 | + | 1.38212i | ||||
\(206\) | 63.9224i | 0.310303i | ||||||||
\(207\) | 28.5371 | − | 32.3826i | 0.137860 | − | 0.156438i | ||||
\(208\) | 94.4072i | 0.453881i | ||||||||
\(209\) | − | 42.9028i | − | 0.205277i | ||||||
\(210\) | −40.3377 | + | 35.9689i | −0.192084 | + | 0.171280i | ||||
\(211\) | 168.980 | 0.800852 | 0.400426 | − | 0.916329i | \(-0.368862\pi\) | ||||
0.400426 | + | 0.916329i | \(0.368862\pi\) | |||||||
\(212\) | 170.062 | 0.802180 | ||||||||
\(213\) | −242.408 | + | 109.482i | −1.13806 | + | 0.513998i | ||||
\(214\) | −36.7049 | −0.171518 | ||||||||
\(215\) | 76.7756 | + | 244.734i | 0.357096 | + | 1.13830i | ||||
\(216\) | −72.9986 | − | 22.4323i | −0.337956 | − | 0.103853i | ||||
\(217\) | 41.7982i | 0.192619i | ||||||||
\(218\) | −76.1891 | −0.349491 | ||||||||
\(219\) | −101.701 | + | 45.9327i | −0.464390 | + | 0.209738i | ||||
\(220\) | −47.5015 | − | 151.418i | −0.215916 | − | 0.688265i | ||||
\(221\) | 764.566i | 3.45958i | ||||||||
\(222\) | −33.3861 | + | 15.0786i | −0.150388 | + | 0.0679215i | ||||
\(223\) | − | 256.517i | − | 1.15030i | −0.818048 | − | 0.575151i | \(-0.804943\pi\) | ||
0.818048 | − | 0.575151i | \(-0.195057\pi\) | |||||||
\(224\) | − | 14.4121i | − | 0.0643396i | ||||||
\(225\) | −25.6801 | + | 223.530i | −0.114134 | + | 0.993465i | ||||
\(226\) | 117.164 | 0.518426 | ||||||||
\(227\) | 319.013 | 1.40534 | 0.702672 | − | 0.711514i | \(-0.251990\pi\) | ||||
0.702672 | + | 0.711514i | \(0.251990\pi\) | |||||||
\(228\) | −6.67668 | − | 14.7831i | −0.0292837 | − | 0.0648382i | ||||
\(229\) | 88.2037 | 0.385169 | 0.192584 | − | 0.981280i | \(-0.438313\pi\) | ||||
0.192584 | + | 0.981280i | \(0.438313\pi\) | |||||||
\(230\) | 32.3568 | − | 10.1507i | 0.140682 | − | 0.0441334i | ||||
\(231\) | −49.9251 | − | 110.541i | −0.216126 | − | 0.478534i | ||||
\(232\) | 39.2483i | 0.169174i | ||||||||
\(233\) | −442.366 | −1.89857 | −0.949283 | − | 0.314423i | \(-0.898189\pi\) | ||||
−0.949283 | + | 0.314423i | \(0.898189\pi\) | |||||||
\(234\) | 225.376 | + | 198.612i | 0.963146 | + | 0.848771i | ||||
\(235\) | −185.642 | + | 58.2380i | −0.789968 | + | 0.247821i | ||||
\(236\) | − | 157.473i | − | 0.667258i | ||||||
\(237\) | −129.281 | − | 286.246i | −0.545490 | − | 1.20779i | ||||
\(238\) | − | 116.718i | − | 0.490410i | ||||||
\(239\) | 69.6082i | 0.291248i | 0.989340 | + | 0.145624i | \(0.0465189\pi\) | ||||
−0.989340 | + | 0.145624i | \(0.953481\pi\) | |||||||
\(240\) | −39.9319 | − | 44.7822i | −0.166383 | − | 0.186592i | ||||
\(241\) | −37.8588 | −0.157090 | −0.0785452 | − | 0.996911i | \(-0.525028\pi\) | ||||
−0.0785452 | + | 0.996911i | \(0.525028\pi\) | |||||||
\(242\) | 185.034 | 0.764604 | ||||||||
\(243\) | −207.125 | + | 127.075i | −0.852368 | + | 0.522942i | ||||
\(244\) | −137.754 | −0.564567 | ||||||||
\(245\) | 202.801 | − | 63.6207i | 0.827757 | − | 0.259676i | ||||
\(246\) | −229.636 | + | 103.713i | −0.933480 | + | 0.421599i | ||||
\(247\) | 63.8071i | 0.258329i | ||||||||
\(248\) | −46.4036 | −0.187111 | ||||||||
\(249\) | −94.6846 | − | 209.645i | −0.380260 | − | 0.841948i | ||||
\(250\) | −108.222 | + | 139.779i | −0.432887 | + | 0.559114i | ||||
\(251\) | 38.2880i | 0.152542i | 0.997087 | + | 0.0762709i | \(0.0243014\pi\) | ||||
−0.997087 | + | 0.0762709i | \(0.975699\pi\) | |||||||
\(252\) | −34.4056 | − | 30.3199i | −0.136530 | − | 0.120317i | ||||
\(253\) | 76.1071i | 0.300819i | ||||||||
\(254\) | − | 127.396i | − | 0.501558i | ||||||
\(255\) | −323.393 | − | 362.673i | −1.26821 | − | 1.42225i | ||||
\(256\) | 16.0000 | 0.0625000 | ||||||||
\(257\) | −5.46616 | −0.0212691 | −0.0106346 | − | 0.999943i | \(-0.503385\pi\) | ||||
−0.0106346 | + | 0.999943i | \(0.503385\pi\) | |||||||
\(258\) | −198.351 | + | 89.5836i | −0.768801 | + | 0.347223i | ||||
\(259\) | −21.9984 | −0.0849358 | ||||||||
\(260\) | 70.6466 | + | 225.197i | 0.271718 | + | 0.866141i | ||||
\(261\) | 93.6965 | + | 82.5699i | 0.358990 | + | 0.316360i | ||||
\(262\) | − | 191.368i | − | 0.730411i | ||||||
\(263\) | −485.162 | −1.84472 | −0.922361 | − | 0.386329i | \(-0.873743\pi\) | ||||
−0.922361 | + | 0.386329i | \(0.873743\pi\) | |||||||
\(264\) | 122.721 | − | 55.4259i | 0.464851 | − | 0.209947i | ||||
\(265\) | 405.662 | − | 127.261i | 1.53080 | − | 0.480228i | ||||
\(266\) | − | 9.74071i | − | 0.0366192i | ||||||
\(267\) | −208.442 | + | 94.1414i | −0.780682 | + | 0.352589i | ||||
\(268\) | − | 132.769i | − | 0.495405i | ||||||
\(269\) | 268.151i | 0.996844i | 0.866935 | + | 0.498422i | \(0.166087\pi\) | ||||
−0.866935 | + | 0.498422i | \(0.833913\pi\) | |||||||
\(270\) | −190.916 | + | 1.11657i | −0.707095 | + | 0.00413544i | ||||
\(271\) | 129.334 | 0.477246 | 0.238623 | − | 0.971112i | \(-0.423304\pi\) | ||||
0.238623 | + | 0.971112i | \(0.423304\pi\) | |||||||
\(272\) | 129.578 | 0.476388 | ||||||||
\(273\) | 74.2511 | + | 164.402i | 0.271982 | + | 0.602207i | ||||
\(274\) | −166.699 | −0.608389 | ||||||||
\(275\) | −226.618 | − | 325.643i | −0.824066 | − | 1.18416i | ||||
\(276\) | 11.8441 | + | 26.2244i | 0.0429132 | + | 0.0950159i | ||||
\(277\) | 403.297i | 1.45595i | 0.685605 | + | 0.727974i | \(0.259538\pi\) | ||||
−0.685605 | + | 0.727974i | \(0.740462\pi\) | |||||||
\(278\) | 259.373 | 0.932997 | ||||||||
\(279\) | −97.6231 | + | 110.778i | −0.349904 | + | 0.397054i | ||||
\(280\) | −10.7848 | − | 34.3782i | −0.0385172 | − | 0.122779i | ||||
\(281\) | − | 128.348i | − | 0.456755i | −0.973573 | − | 0.228378i | \(-0.926658\pi\) | ||
0.973573 | − | 0.228378i | \(-0.0733421\pi\) | |||||||
\(282\) | −67.9535 | − | 150.459i | −0.240970 | − | 0.533541i | ||||
\(283\) | 351.650i | 1.24258i | 0.783581 | + | 0.621289i | \(0.213391\pi\) | ||||
−0.783581 | + | 0.621289i | \(0.786609\pi\) | |||||||
\(284\) | − | 177.323i | − | 0.624376i | ||||||
\(285\) | −26.9889 | − | 30.2670i | −0.0946977 | − | 0.106200i | ||||
\(286\) | −529.690 | −1.85206 | ||||||||
\(287\) | −151.309 | −0.527209 | ||||||||
\(288\) | 33.6606 | − | 38.1964i | 0.116877 | − | 0.132626i | ||||
\(289\) | 760.397 | 2.63113 | ||||||||
\(290\) | 29.3702 | + | 93.6219i | 0.101277 | + | 0.322834i | ||||
\(291\) | −201.240 | + | 90.8884i | −0.691545 | + | 0.312331i | ||||
\(292\) | − | 74.3953i | − | 0.254778i | ||||||
\(293\) | 246.993 | 0.842979 | 0.421489 | − | 0.906833i | \(-0.361507\pi\) | ||||
0.421489 | + | 0.906833i | \(0.361507\pi\) | |||||||
\(294\) | 74.2341 | + | 164.365i | 0.252497 | + | 0.559064i | ||||
\(295\) | −117.840 | − | 375.632i | −0.399457 | − | 1.27333i | ||||
\(296\) | − | 24.4222i | − | 0.0825073i | ||||||
\(297\) | 125.861 | − | 409.572i | 0.423774 | − | 1.37903i | ||||
\(298\) | 34.7892i | 0.116742i | ||||||||
\(299\) | − | 113.190i | − | 0.378563i | ||||||
\(300\) | −128.764 | − | 76.9405i | −0.429213 | − | 0.256468i | ||||
\(301\) | −130.695 | −0.434202 | ||||||||
\(302\) | 46.0202 | 0.152385 | ||||||||
\(303\) | −12.3483 | + | 5.57704i | −0.0407536 | + | 0.0184061i | ||||
\(304\) | 10.8139 | 0.0355722 | ||||||||
\(305\) | −328.596 | + | 103.084i | −1.07736 | + | 0.337980i | ||||
\(306\) | 272.603 | − | 309.338i | 0.890860 | − | 1.01091i | ||||
\(307\) | − | 322.299i | − | 1.04983i | −0.851154 | − | 0.524917i | \(-0.824097\pi\) | ||
0.851154 | − | 0.524917i | \(-0.175903\pi\) | |||||||
\(308\) | 80.8617 | 0.262538 | ||||||||
\(309\) | −123.580 | + | 55.8142i | −0.399936 | + | 0.180628i | ||||
\(310\) | −110.690 | + | 34.7246i | −0.357064 | + | 0.112015i | ||||
\(311\) | 197.270i | 0.634308i | 0.948374 | + | 0.317154i | \(0.102727\pi\) | ||||
−0.948374 | + | 0.317154i | \(0.897273\pi\) | |||||||
\(312\) | −182.516 | + | 82.4321i | −0.584988 | + | 0.264206i | ||||
\(313\) | 542.137i | 1.73207i | 0.499987 | + | 0.866033i | \(0.333338\pi\) | ||||
−0.499987 | + | 0.866033i | \(0.666662\pi\) | |||||||
\(314\) | 5.39674i | 0.0171871i | ||||||||
\(315\) | −104.759 | − | 46.5780i | −0.332569 | − | 0.147867i | ||||
\(316\) | 209.391 | 0.662631 | ||||||||
\(317\) | −96.0108 | −0.302873 | −0.151437 | − | 0.988467i | \(-0.548390\pi\) | ||||
−0.151437 | + | 0.988467i | \(0.548390\pi\) | |||||||
\(318\) | 148.491 | + | 328.779i | 0.466951 | + | 1.03390i | ||||
\(319\) | −220.210 | −0.690314 | ||||||||
\(320\) | 38.1660 | − | 11.9731i | 0.119269 | − | 0.0374159i | ||||
\(321\) | −32.0490 | − | 70.9611i | −0.0998413 | − | 0.221063i | ||||
\(322\) | 17.2795i | 0.0536630i | ||||||||
\(323\) | 87.5778 | 0.271139 | ||||||||
\(324\) | −20.3709 | − | 160.714i | −0.0628731 | − | 0.496031i | ||||
\(325\) | 337.038 | + | 484.313i | 1.03704 | + | 1.49019i | ||||
\(326\) | − | 249.575i | − | 0.765567i | ||||||
\(327\) | −66.5249 | − | 147.295i | −0.203440 | − | 0.450444i | ||||
\(328\) | − | 167.980i | − | 0.512135i | ||||||
\(329\) | − | 99.1384i | − | 0.301333i | ||||||
\(330\) | 251.259 | − | 224.046i | 0.761391 | − | 0.678927i | ||||
\(331\) | 246.600 | 0.745016 | 0.372508 | − | 0.928029i | \(-0.378498\pi\) | ||||
0.372508 | + | 0.928029i | \(0.378498\pi\) | |||||||
\(332\) | 153.357 | 0.461918 | ||||||||
\(333\) | −58.3025 | − | 51.3790i | −0.175083 | − | 0.154291i | ||||
\(334\) | 222.526 | 0.666246 | ||||||||
\(335\) | −99.3531 | − | 316.703i | −0.296576 | − | 0.945382i | ||||
\(336\) | 27.8627 | − | 12.5840i | 0.0829247 | − | 0.0374523i | ||||
\(337\) | 136.820i | 0.405994i | 0.979179 | + | 0.202997i | \(0.0650682\pi\) | ||||
−0.979179 | + | 0.202997i | \(0.934932\pi\) | |||||||
\(338\) | 548.779 | 1.62361 | ||||||||
\(339\) | 102.303 | + | 226.512i | 0.301777 | + | 0.668177i | ||||
\(340\) | 309.091 | − | 96.9652i | 0.909092 | − | 0.285192i | ||||
\(341\) | − | 260.356i | − | 0.763508i | ||||||
\(342\) | 22.7502 | − | 25.8159i | 0.0665211 | − | 0.0754850i | ||||
\(343\) | 233.140i | 0.679707i | ||||||||
\(344\) | − | 145.095i | − | 0.421788i | ||||||
\(345\) | 47.8767 | + | 53.6919i | 0.138773 | + | 0.155629i | ||||
\(346\) | 351.857 | 1.01693 | ||||||||
\(347\) | 351.266 | 1.01229 | 0.506147 | − | 0.862447i | \(-0.331069\pi\) | ||||
0.506147 | + | 0.862447i | \(0.331069\pi\) | |||||||
\(348\) | −75.8782 | + | 34.2698i | −0.218041 | + | 0.0984765i | ||||
\(349\) | −210.440 | −0.602979 | −0.301489 | − | 0.953470i | \(-0.597484\pi\) | ||||
−0.301489 | + | 0.953470i | \(0.597484\pi\) | |||||||
\(350\) | −51.4517 | − | 73.9345i | −0.147005 | − | 0.211241i | ||||
\(351\) | −187.187 | + | 609.136i | −0.533295 | + | 1.73543i | ||||
\(352\) | 89.7711i | 0.255031i | ||||||||
\(353\) | −479.609 | −1.35867 | −0.679333 | − | 0.733830i | \(-0.737731\pi\) | ||||
−0.679333 | + | 0.733830i | \(0.737731\pi\) | |||||||
\(354\) | 304.440 | − | 137.498i | 0.860001 | − | 0.388413i | ||||
\(355\) | −132.694 | − | 422.982i | −0.373786 | − | 1.19150i | ||||
\(356\) | − | 152.477i | − | 0.428306i | ||||||
\(357\) | 225.649 | − | 101.913i | 0.632069 | − | 0.285469i | ||||
\(358\) | 157.061i | 0.438719i | ||||||||
\(359\) | 666.963i | 1.85783i | 0.370288 | + | 0.928917i | \(0.379259\pi\) | ||||
−0.370288 | + | 0.928917i | \(0.620741\pi\) | |||||||
\(360\) | 51.7100 | − | 116.302i | 0.143639 | − | 0.323060i | ||||
\(361\) | −353.691 | −0.979754 | ||||||||
\(362\) | −310.286 | −0.857143 | ||||||||
\(363\) | 161.564 | + | 357.724i | 0.445079 | + | 0.985467i | ||||
\(364\) | −120.262 | −0.330389 | ||||||||
\(365\) | −55.6714 | − | 177.461i | −0.152524 | − | 0.486194i | ||||
\(366\) | −120.281 | − | 266.319i | −0.328636 | − | 0.727647i | ||||
\(367\) | − | 503.975i | − | 1.37323i | −0.727022 | − | 0.686614i | \(-0.759096\pi\) | ||
0.727022 | − | 0.686614i | \(-0.240904\pi\) | |||||||
\(368\) | −19.1833 | −0.0521286 | ||||||||
\(369\) | −401.016 | − | 353.395i | −1.08676 | − | 0.957709i | ||||
\(370\) | −18.2756 | − | 58.2561i | −0.0493934 | − | 0.157449i | ||||
\(371\) | 216.635i | 0.583922i | ||||||||
\(372\) | −40.5175 | − | 89.7114i | −0.108918 | − | 0.241160i | ||||
\(373\) | 632.077i | 1.69458i | 0.531133 | + | 0.847288i | \(0.321766\pi\) | ||||
−0.531133 | + | 0.847288i | \(0.678234\pi\) | |||||||
\(374\) | 727.020i | 1.94390i | ||||||||
\(375\) | −364.726 | − | 87.1756i | −0.972604 | − | 0.232468i | ||||
\(376\) | 110.062 | 0.292717 | ||||||||
\(377\) | 327.507 | 0.868719 | ||||||||
\(378\) | 28.5757 | − | 92.9899i | 0.0755970 | − | 0.246005i | ||||
\(379\) | 567.452 | 1.49724 | 0.748618 | − | 0.663002i | \(-0.230718\pi\) | ||||
0.748618 | + | 0.663002i | \(0.230718\pi\) | |||||||
\(380\) | 25.7953 | − | 8.09227i | 0.0678824 | − | 0.0212954i | ||||
\(381\) | 246.292 | − | 111.236i | 0.646437 | − | 0.291958i | ||||
\(382\) | − | 33.5117i | − | 0.0877269i | ||||||
\(383\) | −75.9370 | −0.198269 | −0.0991345 | − | 0.995074i | \(-0.531607\pi\) | ||||
−0.0991345 | + | 0.995074i | \(0.531607\pi\) | |||||||
\(384\) | 13.9705 | + | 30.9326i | 0.0363815 | + | 0.0805536i | ||||
\(385\) | 192.886 | − | 60.5103i | 0.501002 | − | 0.157170i | ||||
\(386\) | 138.708i | 0.359346i | ||||||||
\(387\) | −346.382 | − | 305.248i | −0.895043 | − | 0.788756i | ||||
\(388\) | − | 147.208i | − | 0.379403i | ||||||
\(389\) | 216.366i | 0.556210i | 0.960551 | + | 0.278105i | \(0.0897063\pi\) | ||||
−0.960551 | + | 0.278105i | \(0.910294\pi\) | |||||||
\(390\) | −373.685 | + | 333.212i | −0.958166 | + | 0.854390i | ||||
\(391\) | −155.358 | −0.397335 | ||||||||
\(392\) | −120.234 | −0.306719 | ||||||||
\(393\) | 369.969 | − | 167.094i | 0.941396 | − | 0.425175i | ||||
\(394\) | −446.951 | −1.13439 | ||||||||
\(395\) | 499.477 | − | 156.691i | 1.26450 | − | 0.396687i | ||||
\(396\) | 214.308 | + | 188.859i | 0.541183 | + | 0.476917i | ||||
\(397\) | 723.583i | 1.82263i | 0.411712 | + | 0.911314i | \(0.364931\pi\) | ||||
−0.411712 | + | 0.911314i | \(0.635069\pi\) | |||||||
\(398\) | −238.605 | −0.599510 | ||||||||
\(399\) | 18.8316 | − | 8.50515i | 0.0471970 | − | 0.0213162i | ||||
\(400\) | 82.0806 | − | 57.1206i | 0.205202 | − | 0.142802i | ||||
\(401\) | − | 258.627i | − | 0.644955i | −0.946577 | − | 0.322478i | \(-0.895484\pi\) | ||
0.946577 | − | 0.322478i | \(-0.104516\pi\) | |||||||
\(402\) | 256.680 | − | 115.928i | 0.638507 | − | 0.288377i | ||||
\(403\) | 387.215i | 0.960830i | ||||||||
\(404\) | − | 9.03290i | − | 0.0223587i | ||||||
\(405\) | −168.858 | − | 368.120i | −0.416932 | − | 0.908938i | ||||
\(406\) | −49.9968 | −0.123145 | ||||||||
\(407\) | 137.025 | 0.336671 | ||||||||
\(408\) | 113.141 | + | 250.511i | 0.277307 | + | 0.613997i | ||||
\(409\) | −399.257 | −0.976178 | −0.488089 | − | 0.872794i | \(-0.662306\pi\) | ||||
−0.488089 | + | 0.872794i | \(0.662306\pi\) | |||||||
\(410\) | −125.703 | − | 400.696i | −0.306592 | − | 0.977308i | ||||
\(411\) | −145.554 | − | 322.276i | −0.354145 | − | 0.784127i | ||||
\(412\) | − | 90.3999i | − | 0.219417i | ||||||
\(413\) | 200.598 | 0.485710 | ||||||||
\(414\) | −40.3576 | + | 45.7959i | −0.0974821 | + | 0.110618i | ||||
\(415\) | 365.814 | − | 114.760i | 0.881479 | − | 0.276529i | ||||
\(416\) | − | 133.512i | − | 0.320942i | ||||||
\(417\) | 226.473 | + | 501.443i | 0.543101 | + | 1.20250i | ||||
\(418\) | 60.6737i | 0.145152i | ||||||||
\(419\) | − | 447.017i | − | 1.06687i | −0.845842 | − | 0.533434i | \(-0.820901\pi\) | ||
0.845842 | − | 0.533434i | \(-0.179099\pi\) | |||||||
\(420\) | 57.0462 | − | 50.8677i | 0.135824 | − | 0.121113i | ||||
\(421\) | 272.776 | 0.647923 | 0.323962 | − | 0.946070i | \(-0.394985\pi\) | ||||
0.323962 | + | 0.946070i | \(0.394985\pi\) | |||||||
\(422\) | −238.973 | −0.566288 | ||||||||
\(423\) | 231.546 | − | 262.747i | 0.547389 | − | 0.621152i | ||||
\(424\) | −240.504 | −0.567227 | ||||||||
\(425\) | 664.738 | − | 462.597i | 1.56409 | − | 1.08846i | ||||
\(426\) | 342.816 | − | 154.830i | 0.804732 | − | 0.363451i | ||||
\(427\) | − | 175.480i | − | 0.410959i | ||||||
\(428\) | 51.9085 | 0.121282 | ||||||||
\(429\) | −462.501 | − | 1024.04i | −1.07809 | − | 2.38705i | ||||
\(430\) | −108.577 | − | 346.106i | −0.252505 | − | 0.804898i | ||||
\(431\) | 436.879i | 1.01364i | 0.862052 | + | 0.506820i | \(0.169179\pi\) | ||||
−0.862052 | + | 0.506820i | \(0.830821\pi\) | |||||||
\(432\) | 103.236 | + | 31.7241i | 0.238971 | + | 0.0734355i | ||||
\(433\) | 81.5626i | 0.188366i | 0.995555 | + | 0.0941832i | \(0.0300239\pi\) | ||||
−0.995555 | + | 0.0941832i | \(0.969976\pi\) | |||||||
\(434\) | − | 59.1116i | − | 0.136202i | ||||||
\(435\) | −155.353 | + | 138.527i | −0.357134 | + | 0.318454i | ||||
\(436\) | 107.748 | 0.247128 | ||||||||
\(437\) | −12.9655 | −0.0296693 | ||||||||
\(438\) | 143.828 | − | 64.9586i | 0.328373 | − | 0.148307i | ||||
\(439\) | −459.523 | −1.04675 | −0.523375 | − | 0.852103i | \(-0.675327\pi\) | ||||
−0.523375 | + | 0.852103i | \(0.675327\pi\) | |||||||
\(440\) | 67.1773 | + | 214.138i | 0.152676 | + | 0.486677i | ||||
\(441\) | −252.946 | + | 287.032i | −0.573575 | + | 0.650866i | ||||
\(442\) | − | 1081.26i | − | 2.44629i | ||||||
\(443\) | 341.453 | 0.770773 | 0.385387 | − | 0.922755i | \(-0.374068\pi\) | ||||
0.385387 | + | 0.922755i | \(0.374068\pi\) | |||||||
\(444\) | 47.2151 | − | 21.3243i | 0.106340 | − | 0.0480278i | ||||
\(445\) | −114.101 | − | 363.715i | −0.256407 | − | 0.817337i | ||||
\(446\) | 362.770i | 0.813386i | ||||||||
\(447\) | −67.2575 | + | 30.3764i | −0.150464 | + | 0.0679561i | ||||
\(448\) | 20.3818i | 0.0454950i | ||||||||
\(449\) | − | 51.7486i | − | 0.115253i | −0.998338 | − | 0.0576264i | \(-0.981647\pi\) | ||
0.998338 | − | 0.0576264i | \(-0.0183532\pi\) | |||||||
\(450\) | 36.3172 | − | 316.119i | 0.0807049 | − | 0.702486i | ||||
\(451\) | 942.486 | 2.08977 | ||||||||
\(452\) | −165.695 | −0.366582 | ||||||||
\(453\) | 40.1828 | + | 88.9703i | 0.0887037 | + | 0.196402i | ||||
\(454\) | −451.152 | −0.993728 | ||||||||
\(455\) | −286.869 | + | 89.9939i | −0.630481 | + | 0.197789i | ||||
\(456\) | 9.44225 | + | 20.9065i | 0.0207067 | + | 0.0458475i | ||||
\(457\) | − | 408.775i | − | 0.894474i | −0.894416 | − | 0.447237i | \(-0.852408\pi\) | ||
0.894416 | − | 0.447237i | \(-0.147592\pi\) | |||||||
\(458\) | −124.739 | −0.272356 | ||||||||
\(459\) | 836.063 | + | 256.921i | 1.82149 | + | 0.559741i | ||||
\(460\) | −45.7595 | + | 14.3552i | −0.0994771 | + | 0.0312070i | ||||
\(461\) | 274.701i | 0.595882i | 0.954584 | + | 0.297941i | \(0.0962998\pi\) | ||||
−0.954584 | + | 0.297941i | \(0.903700\pi\) | |||||||
\(462\) | 70.6048 | + | 156.329i | 0.152824 | + | 0.338374i | ||||
\(463\) | 25.3001i | 0.0546439i | 0.999627 | + | 0.0273219i | \(0.00869793\pi\) | ||||
−0.999627 | + | 0.0273219i | \(0.991302\pi\) | |||||||
\(464\) | − | 55.5054i | − | 0.119624i | ||||||
\(465\) | −163.782 | − | 183.676i | −0.352220 | − | 0.395001i | ||||
\(466\) | 625.600 | 1.34249 | ||||||||
\(467\) | −745.058 | −1.59541 | −0.797706 | − | 0.603046i | \(-0.793953\pi\) | ||||
−0.797706 | + | 0.603046i | \(0.793953\pi\) | |||||||
\(468\) | −318.730 | − | 280.880i | −0.681047 | − | 0.600172i | ||||
\(469\) | 169.128 | 0.360615 | ||||||||
\(470\) | 262.538 | − | 82.3610i | 0.558592 | − | 0.175236i | ||||
\(471\) | −10.4335 | + | 4.71219i | −0.0221517 | + | 0.0100047i | ||||
\(472\) | 222.700i | 0.471822i | ||||||||
\(473\) | 814.083 | 1.72111 | ||||||||
\(474\) | 182.831 | + | 404.814i | 0.385720 | + | 0.854037i | ||||
\(475\) | 55.4760 | − | 38.6062i | 0.116791 | − | 0.0812762i | ||||
\(476\) | 165.064i | 0.346772i | ||||||||
\(477\) | −505.969 | + | 574.150i | −1.06073 | + | 1.20367i | ||||
\(478\) | − | 98.4409i | − | 0.205943i | ||||||
\(479\) | − | 168.038i | − | 0.350810i | −0.984496 | − | 0.175405i | \(-0.943876\pi\) | ||
0.984496 | − | 0.175405i | \(-0.0561235\pi\) | |||||||
\(480\) | 56.4723 | + | 63.3315i | 0.117651 | + | 0.131941i | ||||
\(481\) | −203.791 | −0.423681 | ||||||||
\(482\) | 53.5404 | 0.111080 | ||||||||
\(483\) | −33.4062 | + | 15.0877i | −0.0691639 | + | 0.0312374i | ||||
\(484\) | −261.678 | −0.540657 | ||||||||
\(485\) | −110.159 | − | 351.147i | −0.227131 | − | 0.724014i | ||||
\(486\) | 292.920 | − | 179.711i | 0.602715 | − | 0.369776i | ||||
\(487\) | 256.289i | 0.526261i | 0.964760 | + | 0.263131i | \(0.0847550\pi\) | ||||
−0.964760 | + | 0.263131i | \(0.915245\pi\) | |||||||
\(488\) | 194.814 | 0.399209 | ||||||||
\(489\) | 482.500 | − | 217.918i | 0.986707 | − | 0.445639i | ||||
\(490\) | −286.803 | + | 89.9733i | −0.585313 | + | 0.183619i | ||||
\(491\) | − | 631.851i | − | 1.28686i | −0.765503 | − | 0.643432i | \(-0.777510\pi\) | ||
0.765503 | − | 0.643432i | \(-0.222490\pi\) | |||||||
\(492\) | 324.754 | − | 146.673i | 0.660070 | − | 0.298116i | ||||
\(493\) | − | 449.516i | − | 0.911798i | ||||||
\(494\) | − | 90.2369i | − | 0.182666i | ||||||
\(495\) | 652.533 | + | 290.129i | 1.31825 | + | 0.586119i | ||||
\(496\) | 65.6246 | 0.132308 | ||||||||
\(497\) | 225.884 | 0.454496 | ||||||||
\(498\) | 133.904 | + | 296.483i | 0.268884 | + | 0.595347i | ||||
\(499\) | 539.468 | 1.08110 | 0.540550 | − | 0.841312i | \(-0.318216\pi\) | ||||
0.540550 | + | 0.841312i | \(0.318216\pi\) | |||||||
\(500\) | 153.049 | − | 197.677i | 0.306098 | − | 0.395353i | ||||
\(501\) | 194.300 | + | 430.207i | 0.387824 | + | 0.858697i | ||||
\(502\) | − | 54.1474i | − | 0.107863i | ||||||
\(503\) | −294.962 | −0.586406 | −0.293203 | − | 0.956050i | \(-0.594721\pi\) | ||||
−0.293203 | + | 0.956050i | \(0.594721\pi\) | |||||||
\(504\) | 48.6569 | + | 42.8788i | 0.0965414 | + | 0.0850770i | ||||
\(505\) | −6.75949 | − | 21.5469i | −0.0133851 | − | 0.0426671i | ||||
\(506\) | − | 107.632i | − | 0.212711i | ||||||
\(507\) | 479.169 | + | 1060.95i | 0.945106 | + | 2.09260i | ||||
\(508\) | 180.165i | 0.354655i | ||||||||
\(509\) | − | 145.947i | − | 0.286733i | −0.989670 | − | 0.143367i | \(-0.954207\pi\) | ||
0.989670 | − | 0.143367i | \(-0.0457928\pi\) | |||||||
\(510\) | 457.346 | + | 512.897i | 0.896757 | + | 1.00568i | ||||
\(511\) | 94.7692 | 0.185458 | ||||||||
\(512\) | −22.6274 | −0.0441942 | ||||||||
\(513\) | 69.7740 | + | 21.4414i | 0.136012 | + | 0.0417962i | ||||
\(514\) | 7.73032 | 0.0150395 | ||||||||
\(515\) | −67.6479 | − | 215.638i | −0.131355 | − | 0.418714i | ||||
\(516\) | 280.510 | − | 126.690i | 0.543624 | − | 0.245524i | ||||
\(517\) | 617.521i | 1.19443i | ||||||||
\(518\) | 31.1104 | 0.0600587 | ||||||||
\(519\) | 307.226 | + | 680.241i | 0.591958 | + | 1.31068i | ||||
\(520\) | −99.9094 | − | 318.476i | −0.192134 | − | 0.612454i | ||||
\(521\) | − | 699.345i | − | 1.34231i | −0.741316 | − | 0.671156i | \(-0.765798\pi\) | ||
0.741316 | − | 0.671156i | \(-0.234202\pi\) | |||||||
\(522\) | −132.507 | − | 116.772i | −0.253845 | − | 0.223700i | ||||
\(523\) | 807.343i | 1.54368i | 0.635819 | + | 0.771839i | \(0.280663\pi\) | ||||
−0.635819 | + | 0.771839i | \(0.719337\pi\) | |||||||
\(524\) | 270.635i | 0.516478i | ||||||||
\(525\) | 98.0114 | − | 164.027i | 0.186688 | − | 0.312433i | ||||
\(526\) | 686.123 | 1.30442 | ||||||||
\(527\) | 531.467 | 1.00848 | ||||||||
\(528\) | −173.553 | + | 78.3841i | −0.328699 | + | 0.148455i | ||||
\(529\) | 23.0000 | 0.0434783 | ||||||||
\(530\) | −573.693 | + | 179.974i | −1.08244 | + | 0.339573i | ||||
\(531\) | 531.647 | + | 468.513i | 1.00122 | + | 0.882323i | ||||
\(532\) | 13.7754i | 0.0258937i | ||||||||
\(533\) | −1401.71 | −2.62985 | ||||||||
\(534\) | 294.782 | − | 133.136i | 0.552026 | − | 0.249318i | ||||
\(535\) | 123.821 | − | 38.8441i | 0.231442 | − | 0.0726058i | ||||
\(536\) | 187.763i | 0.350304i | ||||||||
\(537\) | −303.645 | + | 137.139i | −0.565446 | + | 0.255380i | ||||
\(538\) | − | 379.223i | − | 0.704875i | ||||||
\(539\) | − | 674.596i | − | 1.25157i | ||||||
\(540\) | 269.995 | − | 1.57906i | 0.499991 | − | 0.00292419i | ||||
\(541\) | −91.7399 | −0.169575 | −0.0847873 | − | 0.996399i | \(-0.527021\pi\) | ||||
−0.0847873 | + | 0.996399i | \(0.527021\pi\) | |||||||
\(542\) | −182.906 | −0.337464 | ||||||||
\(543\) | −270.928 | − | 599.872i | −0.498946 | − | 1.10474i | ||||
\(544\) | −183.250 | −0.336857 | ||||||||
\(545\) | 257.019 | − | 80.6295i | 0.471594 | − | 0.147944i | ||||
\(546\) | −105.007 | − | 232.500i | −0.192320 | − | 0.425824i | ||||
\(547\) | − | 865.481i | − | 1.58223i | −0.611666 | − | 0.791116i | \(-0.709500\pi\) | ||
0.611666 | − | 0.791116i | \(-0.290500\pi\) | |||||||
\(548\) | 235.747 | 0.430196 | ||||||||
\(549\) | 409.847 | − | 465.075i | 0.746533 | − | 0.847131i | ||||
\(550\) | 320.486 | + | 460.529i | 0.582703 | + | 0.837326i | ||||
\(551\) | − | 37.5145i | − | 0.0680845i | ||||||
\(552\) | −16.7500 | − | 37.0869i | −0.0303442 | − | 0.0671864i | ||||
\(553\) | 266.735i | 0.482342i | ||||||||
\(554\) | − | 570.349i | − | 1.02951i | ||||||
\(555\) | 96.6683 | − | 86.1985i | 0.174177 | − | 0.155313i | ||||
\(556\) | −366.809 | −0.659729 | ||||||||
\(557\) | −399.268 | −0.716819 | −0.358410 | − | 0.933564i | \(-0.616681\pi\) | ||||
−0.358410 | + | 0.933564i | \(0.616681\pi\) | |||||||
\(558\) | 138.060 | − | 156.664i | 0.247419 | − | 0.280760i | ||||
\(559\) | −1210.74 | −2.16591 | ||||||||
\(560\) | 15.2520 | + | 48.6181i | 0.0272358 | + | 0.0868181i | ||||
\(561\) | −1405.54 | + | 634.801i | −2.50542 | + | 1.13155i | ||||
\(562\) | 181.512i | 0.322975i | ||||||||
\(563\) | −766.176 | −1.36088 | −0.680440 | − | 0.732804i | \(-0.738211\pi\) | ||||
−0.680440 | + | 0.732804i | \(0.738211\pi\) | |||||||
\(564\) | 96.1008 | + | 212.781i | 0.170391 | + | 0.377270i | ||||
\(565\) | −395.246 | + | 123.993i | −0.699550 | + | 0.219456i | ||||
\(566\) | − | 497.308i | − | 0.878636i | ||||||
\(567\) | 204.727 | − | 25.9497i | 0.361071 | − | 0.0457666i | ||||
\(568\) | 250.772i | 0.441501i | ||||||||
\(569\) | − | 783.307i | − | 1.37664i | −0.725408 | − | 0.688319i | \(-0.758349\pi\) | ||
0.725408 | − | 0.688319i | \(-0.241651\pi\) | |||||||
\(570\) | 38.1680 | + | 42.8040i | 0.0669614 | + | 0.0750947i | ||||
\(571\) | 88.9855 | 0.155841 | 0.0779207 | − | 0.996960i | \(-0.475172\pi\) | ||||
0.0779207 | + | 0.996960i | \(0.475172\pi\) | |||||||
\(572\) | 749.095 | 1.30961 | ||||||||
\(573\) | 64.7877 | − | 29.2609i | 0.113068 | − | 0.0510661i | ||||
\(574\) | 213.983 | 0.372793 | ||||||||
\(575\) | −98.4112 | + | 68.4853i | −0.171150 | + | 0.119105i | ||||
\(576\) | −47.6032 | + | 54.0179i | −0.0826445 | + | 0.0937811i | ||||
\(577\) | − | 459.789i | − | 0.796861i | −0.917199 | − | 0.398431i | \(-0.869555\pi\) | ||
0.917199 | − | 0.398431i | \(-0.130445\pi\) | |||||||
\(578\) | −1075.36 | −1.86049 | ||||||||
\(579\) | −268.162 | + | 121.113i | −0.463147 | + | 0.209177i | ||||
\(580\) | −41.5357 | − | 132.401i | −0.0716133 | − | 0.228278i | ||||
\(581\) | 195.355i | 0.336239i | ||||||||
\(582\) | 284.596 | − | 128.536i | 0.488996 | − | 0.220852i | ||||
\(583\) | − | 1349.39i | − | 2.31457i | ||||||
\(584\) | 105.211i | 0.180156i | ||||||||
\(585\) | −970.479 | − | 431.494i | −1.65894 | − | 0.737597i | ||||
\(586\) | −349.301 | −0.596076 | ||||||||
\(587\) | 294.716 | 0.502072 | 0.251036 | − | 0.967978i | \(-0.419229\pi\) | ||||
0.251036 | + | 0.967978i | \(0.419229\pi\) | |||||||
\(588\) | −104.983 | − | 232.447i | −0.178542 | − | 0.395318i | ||||
\(589\) | 44.3538 | 0.0753035 | ||||||||
\(590\) | 166.651 | + | 531.224i | 0.282459 | + | 0.900379i | ||||
\(591\) | −390.258 | − | 864.085i | −0.660334 | − | 1.46207i | ||||
\(592\) | 34.5382i | 0.0583415i | ||||||||
\(593\) | −882.001 | −1.48735 | −0.743677 | − | 0.668539i | \(-0.766920\pi\) | ||||
−0.743677 | + | 0.668539i | \(0.766920\pi\) | |||||||
\(594\) | −177.994 | + | 579.223i | −0.299654 | + | 0.975123i | ||||
\(595\) | 123.520 | + | 393.739i | 0.207597 | + | 0.661746i | ||||
\(596\) | − | 49.1994i | − | 0.0825493i | ||||||
\(597\) | −208.339 | − | 461.292i | −0.348977 | − | 0.772683i | ||||
\(598\) | 160.075i | 0.267684i | ||||||||
\(599\) | − | 615.514i | − | 1.02757i | −0.857919 | − | 0.513785i | \(-0.828243\pi\) | ||
0.857919 | − | 0.513785i | \(-0.171757\pi\) | |||||||
\(600\) | 182.100 | + | 108.810i | 0.303500 | + | 0.181350i | ||||
\(601\) | −16.1189 | −0.0268201 | −0.0134101 | − | 0.999910i | \(-0.504269\pi\) | ||||
−0.0134101 | + | 0.999910i | \(0.504269\pi\) | |||||||
\(602\) | 184.831 | 0.307027 | ||||||||
\(603\) | 448.242 | + | 395.013i | 0.743354 | + | 0.655080i | ||||
\(604\) | −65.0824 | −0.107752 | ||||||||
\(605\) | −624.200 | + | 195.818i | −1.03174 | + | 0.323667i | ||||
\(606\) | 17.4632 | − | 7.88712i | 0.0288172 | − | 0.0130151i | ||||
\(607\) | − | 189.949i | − | 0.312931i | −0.987683 | − | 0.156465i | \(-0.949990\pi\) | ||
0.987683 | − | 0.156465i | \(-0.0500100\pi\) | |||||||
\(608\) | −15.2932 | −0.0251533 | ||||||||
\(609\) | −43.6549 | − | 96.6582i | −0.0716830 | − | 0.158716i | ||||
\(610\) | 464.705 | − | 145.783i | 0.761811 | − | 0.238988i | ||||
\(611\) | − | 918.408i | − | 1.50312i | ||||||
\(612\) | −385.519 | + | 437.469i | −0.629933 | + | 0.714819i | ||||
\(613\) | 448.071i | 0.730947i | 0.930822 | + | 0.365474i | \(0.119093\pi\) | ||||
−0.930822 | + | 0.365474i | \(0.880907\pi\) | |||||||
\(614\) | 455.799i | 0.742344i | ||||||||
\(615\) | 664.903 | − | 592.890i | 1.08114 | − | 0.964048i | ||||
\(616\) | −114.356 | −0.185642 | ||||||||
\(617\) | −884.688 | −1.43385 | −0.716927 | − | 0.697148i | \(-0.754452\pi\) | ||||
−0.716927 | + | 0.697148i | \(0.754452\pi\) | |||||||
\(618\) | 174.769 | − | 78.9331i | 0.282798 | − | 0.127724i | ||||
\(619\) | −869.748 | −1.40509 | −0.702543 | − | 0.711641i | \(-0.747952\pi\) | ||||
−0.702543 | + | 0.711641i | \(0.747952\pi\) | |||||||
\(620\) | 156.539 | − | 49.1080i | 0.252483 | − | 0.0792065i | ||||
\(621\) | −123.775 | − | 38.0359i | −0.199316 | − | 0.0612494i | ||||
\(622\) | − | 278.981i | − | 0.448523i | ||||||
\(623\) | 194.234 | 0.311772 | ||||||||
\(624\) | 258.117 | − | 116.577i | 0.413649 | − | 0.186822i | ||||
\(625\) | 217.154 | − | 586.062i | 0.347446 | − | 0.937700i | ||||
\(626\) | − | 766.697i | − | 1.22476i | ||||||
\(627\) | −117.300 | + | 52.9776i | −0.187081 | + | 0.0844937i | ||||
\(628\) | − | 7.63215i | − | 0.0121531i | ||||||
\(629\) | 279.711i | 0.444691i | ||||||||
\(630\) | 148.152 | + | 65.8713i | 0.235162 | + | 0.104558i | ||||
\(631\) | 326.782 | 0.517880 | 0.258940 | − | 0.965893i | \(-0.416627\pi\) | ||||
0.258940 | + | 0.965893i | \(0.416627\pi\) | |||||||
\(632\) | −296.124 | −0.468551 | ||||||||
\(633\) | −208.661 | − | 462.004i | −0.329638 | − | 0.729865i | ||||
\(634\) | 135.780 | 0.214164 | ||||||||
\(635\) | 134.820 | + | 429.761i | 0.212316 | + | 0.676788i | ||||
\(636\) | −209.997 | − | 464.964i | −0.330185 | − | 0.731075i | ||||
\(637\) | 1003.29i | 1.57503i | ||||||||
\(638\) | 311.424 | 0.488125 | ||||||||
\(639\) | 598.663 | + | 527.571i | 0.936875 | + | 0.825620i | ||||
\(640\) | −53.9749 | + | 16.9325i | −0.0843358 | + | 0.0264570i | ||||
\(641\) | − | 219.166i | − | 0.341913i | −0.985279 | − | 0.170957i | \(-0.945314\pi\) | ||
0.985279 | − | 0.170957i | \(-0.0546858\pi\) | |||||||
\(642\) | 45.3242 | + | 100.354i | 0.0705984 | + | 0.156315i | ||||
\(643\) | 707.067i | 1.09964i | 0.835284 | + | 0.549819i | \(0.185303\pi\) | ||||
−0.835284 | + | 0.549819i | \(0.814697\pi\) | |||||||
\(644\) | − | 24.4369i | − | 0.0379454i | ||||||
\(645\) | 574.318 | − | 512.115i | 0.890415 | − | 0.793977i | ||||
\(646\) | −123.854 | −0.191724 | ||||||||
\(647\) | 127.046 | 0.196361 | 0.0981807 | − | 0.995169i | \(-0.468698\pi\) | ||||
0.0981807 | + | 0.995169i | \(0.468698\pi\) | |||||||
\(648\) | 28.8088 | + | 227.284i | 0.0444580 | + | 0.350747i | ||||
\(649\) | −1249.50 | −1.92527 | ||||||||
\(650\) | −476.643 | − | 684.922i | −0.733297 | − | 1.05373i | ||||
\(651\) | 114.280 | − | 51.6136i | 0.175545 | − | 0.0792836i | ||||
\(652\) | 352.952i | 0.541338i | ||||||||
\(653\) | 35.8607 | 0.0549169 | 0.0274585 | − | 0.999623i | \(-0.491259\pi\) | ||||
0.0274585 | + | 0.999623i | \(0.491259\pi\) | |||||||
\(654\) | 94.0804 | + | 208.307i | 0.143854 | + | 0.318512i | ||||
\(655\) | 202.521 | + | 645.566i | 0.309192 | + | 0.985596i | ||||
\(656\) | 237.560i | 0.362134i | ||||||||
\(657\) | 251.167 | + | 221.341i | 0.382294 | + | 0.336896i | ||||
\(658\) | 140.203i | 0.213074i | ||||||||
\(659\) | 152.748i | 0.231788i | 0.993262 | + | 0.115894i | \(0.0369733\pi\) | ||||
−0.993262 | + | 0.115894i | \(0.963027\pi\) | |||||||
\(660\) | −355.334 | + | 316.849i | −0.538384 | + | 0.480074i | ||||
\(661\) | −96.2217 | −0.145570 | −0.0727850 | − | 0.997348i | \(-0.523189\pi\) | ||||
−0.0727850 | + | 0.997348i | \(0.523189\pi\) | |||||||
\(662\) | −348.746 | −0.526806 | ||||||||
\(663\) | 2090.39 | − | 944.107i | 3.15292 | − | 1.42399i | ||||
\(664\) | −216.879 | −0.326625 | ||||||||
\(665\) | 10.3084 | + | 32.8596i | 0.0155014 | + | 0.0494130i | ||||
\(666\) | 82.4521 | + | 72.6609i | 0.123802 | + | 0.109100i | ||||
\(667\) | 66.5487i | 0.0997732i | ||||||||
\(668\) | −314.700 | −0.471107 | ||||||||
\(669\) | −701.339 | + | 316.755i | −1.04834 | + | 0.473475i | ||||
\(670\) | 140.507 | + | 447.886i | 0.209711 | + | 0.668486i | ||||
\(671\) | 1093.04i | 1.62897i | ||||||||
\(672\) | −39.4038 | + | 17.7964i | −0.0586366 | + | 0.0264828i | ||||
\(673\) | 1060.82i | 1.57626i | 0.615508 | + | 0.788130i | \(0.288951\pi\) | ||||
−0.615508 | + | 0.788130i | \(0.711049\pi\) | |||||||
\(674\) | − | 193.493i | − | 0.287081i | ||||||
\(675\) | 642.859 | − | 205.809i | 0.952384 | − | 0.304902i | ||||
\(676\) | −776.090 | −1.14806 | ||||||||
\(677\) | 1107.81 | 1.63634 | 0.818172 | − | 0.574973i | \(-0.194987\pi\) | ||||
0.818172 | + | 0.574973i | \(0.194987\pi\) | |||||||
\(678\) | −144.678 | − | 320.337i | −0.213389 | − | 0.472473i | ||||
\(679\) | 187.523 | 0.276175 | ||||||||
\(680\) | −437.121 | + | 137.130i | −0.642825 | + | 0.201661i | ||||
\(681\) | −393.926 | − | 872.207i | −0.578452 | − | 1.28077i | ||||
\(682\) | 368.199i | 0.539882i | ||||||||
\(683\) | −637.718 | −0.933701 | −0.466850 | − | 0.884336i | \(-0.654611\pi\) | ||||
−0.466850 | + | 0.884336i | \(0.654611\pi\) | |||||||
\(684\) | −32.1737 | + | 36.5092i | −0.0470375 | + | 0.0533760i | ||||
\(685\) | 562.346 | − | 176.414i | 0.820943 | − | 0.257539i | ||||
\(686\) | − | 329.709i | − | 0.480626i | ||||||
\(687\) | −108.916 | − | 241.156i | −0.158539 | − | 0.351028i | ||||
\(688\) | 205.195i | 0.298249i | ||||||||
\(689\) | 2006.89i | 2.91275i | ||||||||
\(690\) | −67.7079 | − | 75.9318i | −0.0981274 | − | 0.110046i | ||||
\(691\) | −1182.13 | −1.71075 | −0.855376 | − | 0.518008i | \(-0.826674\pi\) | ||||
−0.855376 | + | 0.518008i | \(0.826674\pi\) | |||||||
\(692\) | −497.601 | −0.719077 | ||||||||
\(693\) | −240.580 | + | 272.999i | −0.347157 | + | 0.393938i | ||||
\(694\) | −496.765 | −0.715800 | ||||||||
\(695\) | −874.978 | + | 274.490i | −1.25896 | + | 0.394950i | ||||
\(696\) | 107.308 | − | 48.4649i | 0.154178 | − | 0.0696334i | ||||
\(697\) | 1923.90i | 2.76026i | ||||||||
\(698\) | 297.607 | 0.426370 | ||||||||
\(699\) | 546.246 | + | 1209.46i | 0.781467 | + | 1.73028i | ||||
\(700\) | 72.7637 | + | 104.559i | 0.103948 | + | 0.149370i | ||||
\(701\) | 245.292i | 0.349917i | 0.984576 | + | 0.174958i | \(0.0559791\pi\) | ||||
−0.984576 | + | 0.174958i | \(0.944021\pi\) | |||||||
\(702\) | 264.722 | − | 861.449i | 0.377097 | − | 1.22714i | ||||
\(703\) | 23.3434i | 0.0332053i | ||||||||
\(704\) | − | 126.955i | − | 0.180334i | ||||||
\(705\) | 388.464 | + | 435.648i | 0.551013 | + | 0.617940i | ||||
\(706\) | 678.269 | 0.960721 | ||||||||
\(707\) | 11.5066 | 0.0162753 | ||||||||
\(708\) | −430.544 | + | 194.452i | −0.608112 | + | 0.274649i | ||||
\(709\) | 1079.15 | 1.52207 | 0.761034 | − | 0.648712i | \(-0.224692\pi\) | ||||
0.761034 | + | 0.648712i | \(0.224692\pi\) | |||||||
\(710\) | 187.657 | + | 598.186i | 0.264306 | + | 0.842516i | ||||
\(711\) | −622.981 | + | 706.930i | −0.876204 | + | 0.994276i | ||||
\(712\) | 215.635i | 0.302858i | ||||||||
\(713\) | −78.6811 | −0.110352 | ||||||||
\(714\) | −319.115 | + | 144.126i | −0.446940 | + | 0.201857i | ||||
\(715\) | 1786.87 | − | 560.561i | 2.49912 | − | 0.784002i | ||||
\(716\) | − | 222.118i | − | 0.310221i | ||||||
\(717\) | 190.315 | − | 85.9542i | 0.265432 | − | 0.119880i | ||||
\(718\) | − | 943.227i | − | 1.31369i | ||||||
\(719\) | 111.651i | 0.155287i | 0.996981 | + | 0.0776433i | \(0.0247395\pi\) | ||||
−0.996981 | + | 0.0776433i | \(0.975260\pi\) | |||||||
\(720\) | −73.1290 | + | 164.475i | −0.101568 | + | 0.228438i | ||||
\(721\) | 115.157 | 0.159718 | ||||||||
\(722\) | 500.195 | 0.692791 | ||||||||
\(723\) | 46.7491 | + | 103.509i | 0.0646599 | + | 0.143166i | ||||
\(724\) | 438.810 | 0.606092 | ||||||||
\(725\) | −198.157 | − | 284.745i | −0.273320 | − | 0.392752i | ||||
\(726\) | −228.485 | − | 505.899i | −0.314718 | − | 0.696830i | ||||
\(727\) | − | 699.812i | − | 0.962602i | −0.876555 | − | 0.481301i | \(-0.840164\pi\) | ||
0.876555 | − | 0.481301i | \(-0.159836\pi\) | |||||||
\(728\) | 170.075 | 0.233620 | ||||||||
\(729\) | 603.198 | + | 409.382i | 0.827431 | + | 0.561567i | ||||
\(730\) | 78.7312 | + | 250.967i | 0.107851 | + | 0.343791i | ||||
\(731\) | 1661.79i | 2.27332i | ||||||||
\(732\) | 170.103 | + | 376.631i | 0.232381 | + | 0.514524i | ||||
\(733\) | − | 1137.24i | − | 1.55148i | −0.631052 | − | 0.775740i | \(-0.717377\pi\) | ||
0.631052 | − | 0.775740i | \(-0.282623\pi\) | |||||||
\(734\) | 712.728i | 0.971019i | ||||||||
\(735\) | −424.368 | − | 475.913i | −0.577371 | − | 0.647500i | ||||
\(736\) | 27.1293 | 0.0368605 | ||||||||
\(737\) | −1053.48 | −1.42942 | ||||||||
\(738\) | 567.122 | + | 499.775i | 0.768458 | + | 0.677202i | ||||
\(739\) | −143.147 | −0.193704 | −0.0968519 | − | 0.995299i | \(-0.530877\pi\) | ||||
−0.0968519 | + | 0.995299i | \(0.530877\pi\) | |||||||
\(740\) | 25.8455 | + | 82.3865i | 0.0349264 | + | 0.111333i | ||||
\(741\) | 174.454 | − | 78.7908i | 0.235430 | − | 0.106330i | ||||
\(742\) | − | 306.368i | − | 0.412895i | ||||||
\(743\) | −516.019 | −0.694508 | −0.347254 | − | 0.937771i | \(-0.612886\pi\) | ||||
−0.347254 | + | 0.937771i | \(0.612886\pi\) | |||||||
\(744\) | 57.3004 | + | 126.871i | 0.0770167 | + | 0.170526i | ||||
\(745\) | −36.8168 | − | 117.359i | −0.0494185 | − | 0.157529i | ||||
\(746\) | − | 893.892i | − | 1.19825i | ||||||
\(747\) | −456.267 | + | 517.751i | −0.610800 | + | 0.693107i | ||||
\(748\) | − | 1028.16i | − | 1.37455i | ||||||
\(749\) | 66.1242i | 0.0882833i | ||||||||
\(750\) | 515.801 | + | 123.285i | 0.687735 | + | 0.164380i | ||||
\(751\) | 456.997 | 0.608518 | 0.304259 | − | 0.952589i | \(-0.401591\pi\) | ||||
0.304259 | + | 0.952589i | \(0.401591\pi\) | |||||||
\(752\) | −155.650 | −0.206982 | ||||||||
\(753\) | 104.683 | − | 47.2791i | 0.139021 | − | 0.0627876i | ||||
\(754\) | −463.165 | −0.614277 | ||||||||
\(755\) | −155.246 | + | 48.7024i | −0.205624 | + | 0.0645064i | ||||
\(756\) | −40.4121 | + | 131.508i | −0.0534551 | + | 0.173952i | ||||
\(757\) | − | 1156.06i | − | 1.52716i | −0.645711 | − | 0.763582i | \(-0.723439\pi\) | ||
0.645711 | − | 0.763582i | \(-0.276561\pi\) | |||||||
\(758\) | −802.499 | −1.05871 | ||||||||
\(759\) | 208.083 | − | 93.9792i | 0.274154 | − | 0.123820i | ||||
\(760\) | −36.4801 | + | 11.4442i | −0.0480001 | + | 0.0150582i | ||||
\(761\) | 146.174i | 0.192081i | 0.995377 | + | 0.0960405i | \(0.0306178\pi\) | ||||
−0.995377 | + | 0.0960405i | \(0.969382\pi\) | |||||||
\(762\) | −348.310 | + | 157.312i | −0.457100 | + | 0.206446i | ||||
\(763\) | 137.255i | 0.179889i | ||||||||
\(764\) | 47.3927i | 0.0620323i | ||||||||
\(765\) | −592.242 | + | 1332.02i | −0.774173 | + | 1.74120i | ||||
\(766\) | 107.391 | 0.140197 | ||||||||
\(767\) | 1858.32 | 2.42284 | ||||||||
\(768\) | −19.7572 | − | 43.7453i | −0.0257256 | − | 0.0569600i | ||||
\(769\) | 292.979 | 0.380986 | 0.190493 | − | 0.981689i | \(-0.438991\pi\) | ||||
0.190493 | + | 0.981689i | \(0.438991\pi\) | |||||||
\(770\) | −272.781 | + | 85.5745i | −0.354262 | + | 0.111136i | ||||
\(771\) | 6.74977 | + | 14.9449i | 0.00875457 | + | 0.0193838i | ||||
\(772\) | − | 196.162i | − | 0.254096i | ||||||
\(773\) | 43.2864 | 0.0559979 | 0.0279990 | − | 0.999608i | \(-0.491086\pi\) | ||||
0.0279990 | + | 0.999608i | \(0.491086\pi\) | |||||||
\(774\) | 489.858 | + | 431.687i | 0.632891 | + | 0.557735i | ||||
\(775\) | 336.657 | − | 234.282i | 0.434396 | − | 0.302300i | ||||
\(776\) | 208.184i | 0.268278i | ||||||||
\(777\) | 27.1642 | + | 60.1454i | 0.0349604 | + | 0.0774072i | ||||
\(778\) | − | 305.987i | − | 0.393300i | ||||||
\(779\) | 160.560i | 0.206111i | ||||||||
\(780\) | 528.470 | − | 471.233i | 0.677525 | − | 0.604145i | ||||
\(781\) | −1407.01 | −1.80154 | ||||||||
\(782\) | 219.709 | 0.280958 | ||||||||
\(783\) | 110.054 | − | 358.133i | 0.140554 | − | 0.457386i | ||||
\(784\) | 170.037 | 0.216883 | ||||||||
\(785\) | −5.71127 | − | 18.2055i | −0.00727551 | − | 0.0231918i | ||||
\(786\) | −523.215 | + | 236.306i | −0.665668 | + | 0.300644i | ||||
\(787\) | − | 117.711i | − | 0.149569i | −0.997200 | − | 0.0747845i | \(-0.976173\pi\) | ||
0.997200 | − | 0.0747845i | \(-0.0238269\pi\) | |||||||
\(788\) | 632.084 | 0.802138 | ||||||||
\(789\) | 599.091 | + | 1326.47i | 0.759305 | + | 1.68121i | ||||
\(790\) | −706.367 | + | 221.595i | −0.894136 | + | 0.280500i | ||||
\(791\) | − | 211.072i | − | 0.266843i | ||||||
\(792\) | −303.078 | − | 267.087i | −0.382674 | − | 0.337231i | ||||
\(793\) | − | 1625.63i | − | 2.04997i | ||||||
\(794\) | − | 1023.30i | − | 1.28879i | ||||||
\(795\) | −848.863 | − | 951.968i | −1.06775 | − | 1.19744i | ||||
\(796\) | 337.438 | 0.423918 | ||||||||
\(797\) | −257.448 | −0.323022 | −0.161511 | − | 0.986871i | \(-0.551637\pi\) | ||||
−0.161511 | + | 0.986871i | \(0.551637\pi\) | |||||||
\(798\) | −26.6319 | + | 12.0281i | −0.0333733 | + | 0.0150728i | ||||
\(799\) | −1260.55 | −1.57766 | ||||||||
\(800\) | −116.080 | + | 80.7808i | −0.145099 | + | 0.100976i | ||||
\(801\) | 514.780 | + | 453.650i | 0.642672 | + | 0.566354i | ||||
\(802\) | 365.754i | 0.456052i | ||||||||
\(803\) | −590.306 | −0.735126 | ||||||||
\(804\) | −363.000 | + | 163.946i | −0.451493 | + | 0.203913i | ||||
\(805\) | −18.2865 | − | 58.2911i | −0.0227162 | − | 0.0724113i | ||||
\(806\) | − | 547.604i | − | 0.679409i | ||||||
\(807\) | 733.146 | − | 331.120i | 0.908484 | − | 0.410310i | ||||
\(808\) | 12.7745i | 0.0158100i | ||||||||
\(809\) | 454.140i | 0.561360i | 0.959801 | + | 0.280680i | \(0.0905600\pi\) | ||||
−0.959801 | + | 0.280680i | \(0.909440\pi\) | |||||||
\(810\) | 238.801 | + | 520.600i | 0.294816 | + | 0.642716i | ||||
\(811\) | −1201.93 | −1.48204 | −0.741018 | − | 0.671486i | \(-0.765657\pi\) | ||||
−0.741018 | + | 0.671486i | \(0.765657\pi\) | |||||||
\(812\) | 70.7061 | 0.0870765 | ||||||||
\(813\) | −159.705 | − | 353.609i | −0.196439 | − | 0.434943i | ||||
\(814\) | −193.783 | −0.238063 | ||||||||
\(815\) | 264.120 | + | 841.924i | 0.324074 | + | 1.03304i | ||||
\(816\) | −160.006 | − | 354.276i | −0.196086 | − | 0.434161i | ||||
\(817\) | 138.686i | 0.169750i | ||||||||
\(818\) | 564.634 | 0.690262 | ||||||||
\(819\) | 357.802 | − | 406.017i | 0.436877 | − | 0.495748i | ||||
\(820\) | 177.771 | + | 566.670i | 0.216793 | + | 0.691061i | ||||
\(821\) | 8.09816i | 0.00986378i | 0.999988 | + | 0.00493189i | \(0.00156988\pi\) | ||||
−0.999988 | + | 0.00493189i | \(0.998430\pi\) | |||||||
\(822\) | 205.844 | + | 455.767i | 0.250418 | + | 0.554461i | ||||
\(823\) | − | 98.7169i | − | 0.119948i | −0.998200 | − | 0.0599738i | \(-0.980898\pi\) | ||
0.998200 | − | 0.0599738i | \(-0.0191017\pi\) | |||||||
\(824\) | 127.845i | 0.155151i | ||||||||
\(825\) | −610.501 | + | 1021.71i | −0.740001 | + | 1.23843i | ||||
\(826\) | −283.689 | −0.343449 | ||||||||
\(827\) | −768.746 | −0.929559 | −0.464780 | − | 0.885426i | \(-0.653866\pi\) | ||||
−0.464780 | + | 0.885426i | \(0.653866\pi\) | |||||||
\(828\) | 57.0742 | − | 64.7652i | 0.0689302 | − | 0.0782188i | ||||
\(829\) | −292.269 | −0.352556 | −0.176278 | − | 0.984340i | \(-0.556406\pi\) | ||||
−0.176278 | + | 0.984340i | \(0.556406\pi\) | |||||||
\(830\) | −517.339 | + | 162.295i | −0.623300 | + | 0.195536i | ||||
\(831\) | 1102.65 | − | 498.003i | 1.32689 | − | 0.599281i | ||||
\(832\) | 188.814i | 0.226940i | ||||||||
\(833\) | 1377.06 | 1.65313 | ||||||||
\(834\) | −320.281 | − | 709.148i | −0.384030 | − | 0.850297i | ||||
\(835\) | −750.677 | + | 235.495i | −0.899015 | + | 0.282031i | ||||
\(836\) | − | 85.8056i | − | 0.102638i | ||||||
\(837\) | 423.424 | + | 130.118i | 0.505883 | + | 0.155457i | ||||
\(838\) | 632.178i | 0.754389i | ||||||||
\(839\) | 721.813i | 0.860325i | 0.902751 | + | 0.430163i | \(0.141544\pi\) | ||||
−0.902751 | + | 0.430163i | \(0.858456\pi\) | |||||||
\(840\) | −80.6755 | + | 71.9377i | −0.0960422 | + | 0.0856402i | ||||
\(841\) | 648.447 | 0.771042 | ||||||||
\(842\) | −385.763 | −0.458151 | ||||||||
\(843\) | −350.914 | + | 158.488i | −0.416268 | + | 0.188005i | ||||
\(844\) | 337.959 | 0.400426 | ||||||||
\(845\) | −1851.27 | + | 580.762i | −2.19085 | + | 0.687293i | ||||
\(846\) | −327.455 | + | 371.581i | −0.387063 | + | 0.439221i | ||||
\(847\) | − | 333.341i | − | 0.393555i | ||||||
\(848\) | 340.124 | 0.401090 | ||||||||
\(849\) | 961.439 | − | 434.227i | 1.13244 | − | 0.511457i | ||||
\(850\) | −940.082 | + | 654.211i | −1.10598 | + | 0.769660i | ||||
\(851\) | − | 41.4098i | − | 0.0486602i | ||||||
\(852\) | −484.815 | + | 218.963i | −0.569032 | + | 0.256999i | ||||
\(853\) | 57.1658i | 0.0670174i | 0.999438 | + | 0.0335087i | \(0.0106681\pi\) | ||||
−0.999438 | + | 0.0335087i | \(0.989332\pi\) | |||||||
\(854\) | 248.166i | 0.290592i | ||||||||
\(855\) | −49.4258 | + | 111.164i | −0.0578080 | + | 0.130017i | ||||
\(856\) | −73.4097 | −0.0857590 | ||||||||
\(857\) | 35.9851 | 0.0419896 | 0.0209948 | − | 0.999780i | \(-0.493317\pi\) | ||||
0.0209948 | + | 0.999780i | \(0.493317\pi\) | |||||||
\(858\) | 654.076 | + | 1448.22i | 0.762326 | + | 1.68790i | ||||
\(859\) | −1394.03 | −1.62286 | −0.811428 | − | 0.584453i | \(-0.801309\pi\) | ||||
−0.811428 | + | 0.584453i | \(0.801309\pi\) | |||||||
\(860\) | 153.551 | + | 489.468i | 0.178548 | + | 0.569149i | ||||
\(861\) | 186.841 | + | 413.691i | 0.217004 | + | 0.480478i | ||||
\(862\) | − | 617.840i | − | 0.716752i | ||||||
\(863\) | 188.479 | 0.218400 | 0.109200 | − | 0.994020i | \(-0.465171\pi\) | ||||
0.109200 | + | 0.994020i | \(0.465171\pi\) | |||||||
\(864\) | −145.997 | − | 44.8647i | −0.168978 | − | 0.0519267i | ||||
\(865\) | −1186.97 | + | 372.364i | −1.37222 | + | 0.430479i | ||||
\(866\) | − | 115.347i | − | 0.133195i | ||||||
\(867\) | −938.959 | − | 2078.99i | −1.08300 | − | 2.39791i | ||||
\(868\) | 83.5965i | 0.0963093i | ||||||||
\(869\) | − | 1661.46i | − | 1.91192i | ||||||
\(870\) | 219.703 | − | 195.907i | 0.252532 | − | 0.225181i | ||||
\(871\) | 1566.79 | 1.79884 | ||||||||
\(872\) | −152.378 | −0.174746 | ||||||||
\(873\) | 496.993 | + | 437.974i | 0.569293 | + | 0.501688i | ||||
\(874\) | 18.3359 | 0.0209793 | ||||||||
\(875\) | 251.812 | + | 194.963i | 0.287785 | + | 0.222814i | ||||
\(876\) | −203.403 | + | 91.8654i | −0.232195 | + | 0.104869i | ||||
\(877\) | 1178.69i | 1.34400i | 0.740550 | + | 0.672001i | \(0.234565\pi\) | ||||
−0.740550 | + | 0.672001i | \(0.765435\pi\) | |||||||
\(878\) | 649.864 | 0.740164 | ||||||||
\(879\) | −304.994 | − | 675.298i | −0.346978 | − | 0.768258i | ||||
\(880\) | −95.0031 | − | 302.837i | −0.107958 | − | 0.344132i | ||||
\(881\) | − | 231.820i | − | 0.263133i | −0.991307 | − | 0.131567i | \(-0.957999\pi\) | ||
0.991307 | − | 0.131567i | \(-0.0420007\pi\) | |||||||
\(882\) | 357.720 | − | 405.924i | 0.405578 | − | 0.460232i | ||||
\(883\) | 52.4255i | 0.0593721i | 0.999559 | + | 0.0296860i | \(0.00945075\pi\) | ||||
−0.999559 | + | 0.0296860i | \(0.990549\pi\) | |||||||
\(884\) | 1529.13i | 1.72979i | ||||||||
\(885\) | −881.496 | + | 786.024i | −0.996041 | + | 0.888163i | ||||
\(886\) | −482.887 | −0.545019 | ||||||||
\(887\) | 1387.44 | 1.56420 | 0.782098 | − | 0.623155i | \(-0.214150\pi\) | ||||
0.782098 | + | 0.623155i | \(0.214150\pi\) | |||||||
\(888\) | −66.7722 | + | 30.1572i | −0.0751939 | + | 0.0339608i | ||||
\(889\) | −229.504 | −0.258160 | ||||||||
\(890\) | 161.364 | + | 514.371i | 0.181307 | + | 0.577944i | ||||
\(891\) | −1275.22 | + | 161.637i | −1.43122 | + | 0.181411i | ||||
\(892\) | − | 513.034i | − | 0.575151i | ||||||
\(893\) | −105.200 | −0.117805 | ||||||||
\(894\) | 95.1165 | − | 42.9587i | 0.106394 | − | 0.0480522i | ||||
\(895\) | −166.215 | − | 529.836i | −0.185715 | − | 0.591995i | ||||
\(896\) | − | 28.8241i | − | 0.0321698i | ||||||
\(897\) | −309.471 | + | 139.770i | −0.345007 | + | 0.155820i | ||||
\(898\) | 73.1835i | 0.0814961i | ||||||||
\(899\) | − | 227.658i | − | 0.253234i | ||||||
\(900\) | −51.3603 | + | 447.059i | −0.0570670 | + | 0.496733i | ||||
\(901\) | 2754.53 | 3.05719 | ||||||||
\(902\) | −1332.88 | −1.47769 | ||||||||
\(903\) | 161.386 | + | 357.331i | 0.178722 | + | 0.395715i | ||||
\(904\) | 234.328 | 0.259213 | ||||||||
\(905\) | 1046.73 | − | 328.370i | 1.15661 | − | 0.362840i | ||||
\(906\) | −56.8270 | − | 125.823i | −0.0627230 | − | 0.138878i | ||||
\(907\) | 456.201i | 0.502978i | 0.967860 | + | 0.251489i | \(0.0809203\pi\) | ||||
−0.967860 | + | 0.251489i | \(0.919080\pi\) | |||||||
\(908\) | 638.026 | 0.702672 | ||||||||
\(909\) | 30.4962 | + | 26.8747i | 0.0335491 | + | 0.0295651i | ||||
\(910\) | 405.694 | − | 127.271i | 0.445818 | − | 0.139858i | ||||
\(911\) | 583.845i | 0.640883i | 0.947268 | + | 0.320442i | \(0.103831\pi\) | ||||
−0.947268 | + | 0.320442i | \(0.896169\pi\) | |||||||
\(912\) | −13.3534 | − | 29.5662i | −0.0146418 | − | 0.0324191i | ||||
\(913\) | − | 1216.84i | − | 1.33280i | ||||||
\(914\) | 578.095i | 0.632489i | ||||||||
\(915\) | 687.599 | + | 771.117i | 0.751475 | + | 0.842751i | ||||
\(916\) | 176.407 | 0.192584 | ||||||||
\(917\) | −344.751 | −0.375955 | ||||||||
\(918\) | −1182.37 | − | 363.341i | −1.28799 | − | 0.395796i | ||||
\(919\) | 87.9255 | 0.0956752 | 0.0478376 | − | 0.998855i | \(-0.484767\pi\) | ||||
0.0478376 | + | 0.998855i | \(0.484767\pi\) | |||||||
\(920\) | 64.7136 | − | 20.3014i | 0.0703409 | − | 0.0220667i | ||||
\(921\) | −881.191 | + | 397.983i | −0.956776 | + | 0.432121i | ||||
\(922\) | − | 388.486i | − | 0.421352i | ||||||
\(923\) | 2092.57 | 2.26714 | ||||||||
\(924\) | −99.8503 | − | 221.083i | −0.108063 | − | 0.239267i | ||||
\(925\) | 123.303 | + | 177.182i | 0.133300 | + | 0.191548i | ||||
\(926\) | − | 35.7798i | − | 0.0386391i | ||||||
\(927\) | 305.201 | + | 268.958i | 0.329235 | + | 0.290138i | ||||
\(928\) | 78.4966i | 0.0845868i | ||||||||
\(929\) | − | 1379.83i | − | 1.48529i | −0.669685 | − | 0.742645i | \(-0.733571\pi\) | ||
0.669685 | − | 0.742645i | \(-0.266429\pi\) | |||||||
\(930\) | 231.623 | + | 259.756i | 0.249057 | + | 0.279308i | ||||
\(931\) | 114.923 | 0.123440 | ||||||||
\(932\) | −884.732 | −0.949283 | ||||||||
\(933\) | 539.351 | − | 243.594i | 0.578083 | − | 0.261087i | ||||
\(934\) | 1053.67 | 1.12813 | ||||||||
\(935\) | −769.392 | − | 2452.55i | −0.822879 | − | 2.62305i | ||||
\(936\) | 450.752 | + | 397.225i | 0.481573 | + | 0.424386i | ||||
\(937\) | − | 718.493i | − | 0.766801i | −0.923582 | − | 0.383400i | \(-0.874753\pi\) | ||
0.923582 | − | 0.383400i | \(-0.125247\pi\) | |||||||
\(938\) | −239.184 | −0.254993 | ||||||||
\(939\) | 1482.25 | − | 669.445i | 1.57854 | − | 0.712934i | ||||
\(940\) | −371.285 | + | 116.476i | −0.394984 | + | 0.123911i | ||||
\(941\) | 451.724i | 0.480047i | 0.970767 | + | 0.240023i | \(0.0771551\pi\) | ||||
−0.970767 | + | 0.240023i | \(0.922845\pi\) | |||||||
\(942\) | 14.7551 | − | 6.66405i | 0.0156636 | − | 0.00707436i | ||||
\(943\) | − | 284.825i | − | 0.302041i | ||||||
\(944\) | − | 314.946i | − | 0.333629i | ||||||
\(945\) | 2.01151 | + | 343.936i | 0.00212858 | + | 0.363954i | ||||
\(946\) | −1151.29 | −1.21701 | ||||||||
\(947\) | −1844.99 | −1.94825 | −0.974126 | − | 0.226008i | \(-0.927433\pi\) | ||||
−0.974126 | + | 0.226008i | \(0.927433\pi\) | |||||||
\(948\) | −258.562 | − | 572.493i | −0.272745 | − | 0.603895i | ||||
\(949\) | 877.932 | 0.925113 | ||||||||
\(950\) | −78.4549 | + | 54.5974i | −0.0825841 | + | 0.0574710i | ||||
\(951\) | 118.557 | + | 262.501i | 0.124665 | + | 0.276027i | ||||
\(952\) | − | 233.435i | − | 0.245205i | ||||||
\(953\) | 16.3417 | 0.0171477 | 0.00857384 | − | 0.999963i | \(-0.497271\pi\) | ||||
0.00857384 | + | 0.999963i | \(0.497271\pi\) | |||||||
\(954\) | 715.548 | − | 811.970i | 0.750050 | − | 0.851122i | ||||
\(955\) | 35.4648 | + | 113.049i | 0.0371359 | + | 0.118376i | ||||
\(956\) | 139.216i | 0.145624i | ||||||||
\(957\) | 271.921 | + | 602.072i | 0.284139 | + | 0.629124i | ||||
\(958\) | 237.642i | 0.248060i | ||||||||
\(959\) | 300.309i | 0.313148i | ||||||||
\(960\) | −79.8639 | − | 89.5643i | −0.0831915 | − | 0.0932961i | ||||
\(961\) | −691.839 | −0.719915 | ||||||||
\(962\) | 288.204 | 0.299588 | ||||||||
\(963\) | −154.438 | + | 175.249i | −0.160372 | + | 0.181983i | ||||
\(964\) | −75.7176 | −0.0785452 | ||||||||
\(965\) | −146.792 | − | 467.921i | −0.152116 | − | 0.484892i | ||||
\(966\) | 47.2435 | − | 21.3372i | 0.0489063 | − | 0.0220882i | ||||
\(967\) | 489.265i | 0.505961i | 0.967471 | + | 0.252981i | \(0.0814109\pi\) | ||||
−0.967471 | + | 0.252981i | \(0.918589\pi\) | |||||||
\(968\) | 370.069 | 0.382302 | ||||||||
\(969\) | −108.143 | − | 239.445i | −0.111603 | − | 0.247105i | ||||
\(970\) | 155.788 | + | 496.597i | 0.160606 | + | 0.511956i | ||||
\(971\) | 409.567i | 0.421799i | 0.977508 | + | 0.210900i | \(0.0676393\pi\) | ||||
−0.977508 | + | 0.210900i | \(0.932361\pi\) | |||||||
\(972\) | −414.251 | + | 254.150i | −0.426184 | + | 0.261471i | ||||
\(973\) | − | 467.263i | − | 0.480230i | ||||||
\(974\) | − | 362.448i | − | 0.372123i | ||||||
\(975\) | 907.967 | − | 1519.53i | 0.931248 | − | 1.55849i | ||||
\(976\) | −275.509 | −0.282283 | ||||||||
\(977\) | 1697.21 | 1.73717 | 0.868584 | − | 0.495542i | \(-0.165030\pi\) | ||||
0.868584 | + | 0.495542i | \(0.165030\pi\) | |||||||
\(978\) | −682.358 | + | 308.182i | −0.697708 | + | 0.315114i | ||||
\(979\) | −1209.86 | −1.23581 | ||||||||
\(980\) | 405.601 | − | 127.241i | 0.413879 | − | 0.129838i | ||||
\(981\) | −320.571 | + | 363.769i | −0.326780 | + | 0.370814i | ||||
\(982\) | 893.572i | 0.909951i | ||||||||
\(983\) | −122.701 | −0.124823 | −0.0624116 | − | 0.998050i | \(-0.519879\pi\) | ||||
−0.0624116 | + | 0.998050i | \(0.519879\pi\) | |||||||
\(984\) | −459.272 | + | 207.427i | −0.466740 | + | 0.210800i | ||||
\(985\) | 1507.76 | − | 473.000i | 1.53072 | − | 0.480203i | ||||
\(986\) | 635.712i | 0.644738i | ||||||||
\(987\) | −271.053 | + | 122.419i | −0.274623 | + | 0.124031i | ||||
\(988\) | 127.614i | 0.129164i | ||||||||
\(989\) | − | 246.020i | − | 0.248757i | ||||||
\(990\) | −922.821 | − | 410.304i | −0.932142 | − | 0.414449i | ||||
\(991\) | −303.360 | −0.306115 | −0.153057 | − | 0.988217i | \(-0.548912\pi\) | ||||
−0.153057 | + | 0.988217i | \(0.548912\pi\) | |||||||
\(992\) | −92.8071 | −0.0935556 | ||||||||
\(993\) | −304.509 | − | 674.226i | −0.306656 | − | 0.678978i | ||||
\(994\) | −319.449 | −0.321377 | ||||||||
\(995\) | 804.918 | − | 252.511i | 0.808962 | − | 0.253780i | ||||
\(996\) | −189.369 | − | 419.290i | −0.190130 | − | 0.420974i | ||||
\(997\) | − | 718.407i | − | 0.720569i | −0.932843 | − | 0.360284i | \(-0.882680\pi\) | ||
0.932843 | − | 0.360284i | \(-0.117320\pi\) | |||||||
\(998\) | −762.924 | −0.764453 | ||||||||
\(999\) | −68.4808 | + | 222.848i | −0.0685494 | + | 0.223071i |
(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 | 690.3.b.a.599.17 | ✓ | 88 | |
3.2 | odd | 2 | inner | 690.3.b.a.599.71 | yes | 88 | |
5.4 | even | 2 | inner | 690.3.b.a.599.72 | yes | 88 | |
15.14 | odd | 2 | inner | 690.3.b.a.599.18 | yes | 88 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
690.3.b.a.599.17 | ✓ | 88 | 1.1 | even | 1 | trivial | |
690.3.b.a.599.18 | yes | 88 | 15.14 | odd | 2 | inner | |
690.3.b.a.599.71 | yes | 88 | 3.2 | odd | 2 | inner | |
690.3.b.a.599.72 | yes | 88 | 5.4 | even | 2 | inner |