Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [690,3,Mod(277,690)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(690, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 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("690.277");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 690.k (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(18.8011382409\) |
Analytic rank: | \(0\) |
Dimension: | \(48\) |
Relative dimension: | \(24\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 277.1 | ||
Character | \(\chi\) | \(=\) | 690.277 |
Dual form | 690.3.k.b.553.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/690\mathbb{Z}\right)^\times\).
\(n\) | \(277\) | \(461\) | \(511\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | − | 1.00000i | −0.500000 | − | 0.500000i | ||||
\(3\) | −1.22474 | + | 1.22474i | −0.408248 | + | 0.408248i | ||||
\(4\) | 2.00000i | 0.500000i | ||||||||
\(5\) | 4.77937 | − | 1.46889i | 0.955874 | − | 0.293778i | ||||
\(6\) | 2.44949 | 0.408248 | ||||||||
\(7\) | 8.57539 | + | 8.57539i | 1.22506 | + | 1.22506i | 0.965812 | + | 0.259243i | \(0.0834732\pi\) |
0.259243 | + | 0.965812i | \(0.416527\pi\) | |||||||
\(8\) | 2.00000 | − | 2.00000i | 0.250000 | − | 0.250000i | ||||
\(9\) | − | 3.00000i | − | 0.333333i | ||||||
\(10\) | −6.24826 | − | 3.31048i | −0.624826 | − | 0.331048i | ||||
\(11\) | 5.33526 | 0.485024 | 0.242512 | − | 0.970148i | \(-0.422029\pi\) | ||||
0.242512 | + | 0.970148i | \(0.422029\pi\) | |||||||
\(12\) | −2.44949 | − | 2.44949i | −0.204124 | − | 0.204124i | ||||
\(13\) | 9.44105 | − | 9.44105i | 0.726235 | − | 0.726235i | −0.243633 | − | 0.969868i | \(-0.578339\pi\) |
0.969868 | + | 0.243633i | \(0.0783391\pi\) | |||||||
\(14\) | − | 17.1508i | − | 1.22506i | ||||||
\(15\) | −4.05449 | + | 7.65252i | −0.270299 | + | 0.510168i | ||||
\(16\) | −4.00000 | −0.250000 | ||||||||
\(17\) | 15.8456 | + | 15.8456i | 0.932097 | + | 0.932097i | 0.997837 | − | 0.0657401i | \(-0.0209408\pi\) |
−0.0657401 | + | 0.997837i | \(0.520941\pi\) | |||||||
\(18\) | −3.00000 | + | 3.00000i | −0.166667 | + | 0.166667i | ||||
\(19\) | − | 27.9154i | − | 1.46923i | −0.678482 | − | 0.734617i | \(-0.737362\pi\) | ||
0.678482 | − | 0.734617i | \(-0.262638\pi\) | |||||||
\(20\) | 2.93778 | + | 9.55874i | 0.146889 | + | 0.477937i | ||||
\(21\) | −21.0053 | −1.00025 | ||||||||
\(22\) | −5.33526 | − | 5.33526i | −0.242512 | − | 0.242512i | ||||
\(23\) | 3.39116 | − | 3.39116i | 0.147442 | − | 0.147442i | ||||
\(24\) | 4.89898i | 0.204124i | ||||||||
\(25\) | 20.6847 | − | 14.0407i | 0.827389 | − | 0.561630i | ||||
\(26\) | −18.8821 | −0.726235 | ||||||||
\(27\) | 3.67423 | + | 3.67423i | 0.136083 | + | 0.136083i | ||||
\(28\) | −17.1508 | + | 17.1508i | −0.612528 | + | 0.612528i | ||||
\(29\) | 43.2329i | 1.49079i | 0.666623 | + | 0.745395i | \(0.267739\pi\) | ||||
−0.666623 | + | 0.745395i | \(0.732261\pi\) | |||||||
\(30\) | 11.7070 | − | 3.59803i | 0.390234 | − | 0.119934i | ||||
\(31\) | −45.6018 | −1.47103 | −0.735513 | − | 0.677511i | \(-0.763059\pi\) | ||||
−0.735513 | + | 0.677511i | \(0.763059\pi\) | |||||||
\(32\) | 4.00000 | + | 4.00000i | 0.125000 | + | 0.125000i | ||||
\(33\) | −6.53434 | + | 6.53434i | −0.198010 | + | 0.198010i | ||||
\(34\) | − | 31.6913i | − | 0.932097i | ||||||
\(35\) | 53.5812 | + | 28.3886i | 1.53089 | + | 0.811103i | ||||
\(36\) | 6.00000 | 0.166667 | ||||||||
\(37\) | −22.6647 | − | 22.6647i | −0.612559 | − | 0.612559i | 0.331053 | − | 0.943612i | \(-0.392596\pi\) |
−0.943612 | + | 0.331053i | \(0.892596\pi\) | |||||||
\(38\) | −27.9154 | + | 27.9154i | −0.734617 | + | 0.734617i | ||||
\(39\) | 23.1258i | 0.592968i | ||||||||
\(40\) | 6.62095 | − | 12.4965i | 0.165524 | − | 0.312413i | ||||
\(41\) | 27.4529 | 0.669584 | 0.334792 | − | 0.942292i | \(-0.391334\pi\) | ||||
0.334792 | + | 0.942292i | \(0.391334\pi\) | |||||||
\(42\) | 21.0053 | + | 21.0053i | 0.500127 | + | 0.500127i | ||||
\(43\) | −2.61316 | + | 2.61316i | −0.0607711 | + | 0.0607711i | −0.736839 | − | 0.676068i | \(-0.763683\pi\) |
0.676068 | + | 0.736839i | \(0.263683\pi\) | |||||||
\(44\) | 10.6705i | 0.242512i | ||||||||
\(45\) | −4.40667 | − | 14.3381i | −0.0979261 | − | 0.318625i | ||||
\(46\) | −6.78233 | −0.147442 | ||||||||
\(47\) | −60.8180 | − | 60.8180i | −1.29400 | − | 1.29400i | −0.932291 | − | 0.361709i | \(-0.882194\pi\) |
−0.361709 | − | 0.932291i | \(-0.617806\pi\) | |||||||
\(48\) | 4.89898 | − | 4.89898i | 0.102062 | − | 0.102062i | ||||
\(49\) | 98.0746i | 2.00152i | ||||||||
\(50\) | −34.7255 | − | 6.64397i | −0.694509 | − | 0.132879i | ||||
\(51\) | −38.8137 | −0.761054 | ||||||||
\(52\) | 18.8821 | + | 18.8821i | 0.363117 | + | 0.363117i | ||||
\(53\) | 9.28016 | − | 9.28016i | 0.175097 | − | 0.175097i | −0.614117 | − | 0.789215i | \(-0.710488\pi\) |
0.789215 | + | 0.614117i | \(0.210488\pi\) | |||||||
\(54\) | − | 7.34847i | − | 0.136083i | ||||||
\(55\) | 25.4992 | − | 7.83692i | 0.463621 | − | 0.142489i | ||||
\(56\) | 34.3016 | 0.612528 | ||||||||
\(57\) | 34.1893 | + | 34.1893i | 0.599812 | + | 0.599812i | ||||
\(58\) | 43.2329 | − | 43.2329i | 0.745395 | − | 0.745395i | ||||
\(59\) | 62.7885i | 1.06421i | 0.846678 | + | 0.532106i | \(0.178599\pi\) | ||||
−0.846678 | + | 0.532106i | \(0.821401\pi\) | |||||||
\(60\) | −15.3050 | − | 8.10898i | −0.255084 | − | 0.135150i | ||||
\(61\) | 100.410 | 1.64607 | 0.823036 | − | 0.567990i | \(-0.192279\pi\) | ||||
0.823036 | + | 0.567990i | \(0.192279\pi\) | |||||||
\(62\) | 45.6018 | + | 45.6018i | 0.735513 | + | 0.735513i | ||||
\(63\) | 25.7262 | − | 25.7262i | 0.408352 | − | 0.408352i | ||||
\(64\) | − | 8.00000i | − | 0.125000i | ||||||
\(65\) | 31.2544 | − | 58.9901i | 0.480837 | − | 0.907541i | ||||
\(66\) | 13.0687 | 0.198010 | ||||||||
\(67\) | −23.2724 | − | 23.2724i | −0.347349 | − | 0.347349i | 0.511772 | − | 0.859121i | \(-0.328989\pi\) |
−0.859121 | + | 0.511772i | \(0.828989\pi\) | |||||||
\(68\) | −31.6913 | + | 31.6913i | −0.466048 | + | 0.466048i | ||||
\(69\) | 8.30662i | 0.120386i | ||||||||
\(70\) | −25.1926 | − | 81.9699i | −0.359895 | − | 1.17100i | ||||
\(71\) | 73.4573 | 1.03461 | 0.517305 | − | 0.855801i | \(-0.326935\pi\) | ||||
0.517305 | + | 0.855801i | \(0.326935\pi\) | |||||||
\(72\) | −6.00000 | − | 6.00000i | −0.0833333 | − | 0.0833333i | ||||
\(73\) | 74.1463 | − | 74.1463i | 1.01570 | − | 1.01570i | 0.0158275 | − | 0.999875i | \(-0.494962\pi\) |
0.999875 | − | 0.0158275i | \(-0.00503825\pi\) | |||||||
\(74\) | 45.3294i | 0.612559i | ||||||||
\(75\) | −8.13717 | + | 42.5298i | −0.108496 | + | 0.567064i | ||||
\(76\) | 55.8309 | 0.734617 | ||||||||
\(77\) | 45.7519 | + | 45.7519i | 0.594181 | + | 0.594181i | ||||
\(78\) | 23.1258 | − | 23.1258i | 0.296484 | − | 0.296484i | ||||
\(79\) | − | 42.9315i | − | 0.543437i | −0.962377 | − | 0.271718i | \(-0.912408\pi\) | ||
0.962377 | − | 0.271718i | \(-0.0875920\pi\) | |||||||
\(80\) | −19.1175 | + | 5.87557i | −0.238968 | + | 0.0734446i | ||||
\(81\) | −9.00000 | −0.111111 | ||||||||
\(82\) | −27.4529 | − | 27.4529i | −0.334792 | − | 0.334792i | ||||
\(83\) | 30.3118 | − | 30.3118i | 0.365202 | − | 0.365202i | −0.500522 | − | 0.865724i | \(-0.666858\pi\) |
0.865724 | + | 0.500522i | \(0.166858\pi\) | |||||||
\(84\) | − | 42.0106i | − | 0.500127i | ||||||
\(85\) | 99.0077 | + | 52.4566i | 1.16480 | + | 0.617137i | ||||
\(86\) | 5.22632 | 0.0607711 | ||||||||
\(87\) | −52.9493 | − | 52.9493i | −0.608613 | − | 0.608613i | ||||
\(88\) | 10.6705 | − | 10.6705i | 0.121256 | − | 0.121256i | ||||
\(89\) | 115.921i | 1.30249i | 0.758868 | + | 0.651244i | \(0.225753\pi\) | ||||
−0.758868 | + | 0.651244i | \(0.774247\pi\) | |||||||
\(90\) | −9.93143 | + | 18.7448i | −0.110349 | + | 0.208275i | ||||
\(91\) | 161.921 | 1.77936 | ||||||||
\(92\) | 6.78233 | + | 6.78233i | 0.0737210 | + | 0.0737210i | ||||
\(93\) | 55.8506 | − | 55.8506i | 0.600544 | − | 0.600544i | ||||
\(94\) | 121.636i | 1.29400i | ||||||||
\(95\) | −41.0047 | − | 133.418i | −0.431629 | − | 1.40440i | ||||
\(96\) | −9.79796 | −0.102062 | ||||||||
\(97\) | 131.149 | + | 131.149i | 1.35205 | + | 1.35205i | 0.883367 | + | 0.468682i | \(0.155271\pi\) |
0.468682 | + | 0.883367i | \(0.344729\pi\) | |||||||
\(98\) | 98.0746 | − | 98.0746i | 1.00076 | − | 1.00076i | ||||
\(99\) | − | 16.0058i | − | 0.161675i | ||||||
\(100\) | 28.0815 | + | 41.3694i | 0.280815 | + | 0.413694i | ||||
\(101\) | 23.7421 | 0.235071 | 0.117535 | − | 0.993069i | \(-0.462501\pi\) | ||||
0.117535 | + | 0.993069i | \(0.462501\pi\) | |||||||
\(102\) | 38.8137 | + | 38.8137i | 0.380527 | + | 0.380527i | ||||
\(103\) | −114.195 | + | 114.195i | −1.10869 | + | 1.10869i | −0.115368 | + | 0.993323i | \(0.536805\pi\) |
−0.993323 | + | 0.115368i | \(0.963195\pi\) | |||||||
\(104\) | − | 37.7642i | − | 0.363117i | ||||||
\(105\) | −100.392 | + | 30.8545i | −0.956116 | + | 0.293853i | ||||
\(106\) | −18.5603 | −0.175097 | ||||||||
\(107\) | 24.2252 | + | 24.2252i | 0.226404 | + | 0.226404i | 0.811189 | − | 0.584785i | \(-0.198821\pi\) |
−0.584785 | + | 0.811189i | \(0.698821\pi\) | |||||||
\(108\) | −7.34847 | + | 7.34847i | −0.0680414 | + | 0.0680414i | ||||
\(109\) | − | 33.7671i | − | 0.309790i | −0.987931 | − | 0.154895i | \(-0.950496\pi\) | ||
0.987931 | − | 0.154895i | \(-0.0495039\pi\) | |||||||
\(110\) | −33.3361 | − | 17.6623i | −0.303055 | − | 0.160566i | ||||
\(111\) | 55.5169 | 0.500153 | ||||||||
\(112\) | −34.3016 | − | 34.3016i | −0.306264 | − | 0.306264i | ||||
\(113\) | −109.556 | + | 109.556i | −0.969518 | + | 0.969518i | −0.999549 | − | 0.0300307i | \(-0.990439\pi\) |
0.0300307 | + | 0.999549i | \(0.490439\pi\) | |||||||
\(114\) | − | 68.3786i | − | 0.599812i | ||||||
\(115\) | 11.2264 | − | 21.1889i | 0.0976206 | − | 0.184251i | ||||
\(116\) | −86.4659 | −0.745395 | ||||||||
\(117\) | −28.3232 | − | 28.3232i | −0.242078 | − | 0.242078i | ||||
\(118\) | 62.7885 | − | 62.7885i | 0.532106 | − | 0.532106i | ||||
\(119\) | 271.765i | 2.28374i | ||||||||
\(120\) | 7.19607 | + | 23.4140i | 0.0599672 | + | 0.195117i | ||||
\(121\) | −92.5350 | −0.764752 | ||||||||
\(122\) | −100.410 | − | 100.410i | −0.823036 | − | 0.823036i | ||||
\(123\) | −33.6228 | + | 33.6228i | −0.273356 | + | 0.273356i | ||||
\(124\) | − | 91.2036i | − | 0.735513i | ||||||
\(125\) | 78.2355 | − | 97.4895i | 0.625884 | − | 0.779916i | ||||
\(126\) | −51.4523 | −0.408352 | ||||||||
\(127\) | −55.5449 | − | 55.5449i | −0.437362 | − | 0.437362i | 0.453762 | − | 0.891123i | \(-0.350082\pi\) |
−0.891123 | + | 0.453762i | \(0.850082\pi\) | |||||||
\(128\) | −8.00000 | + | 8.00000i | −0.0625000 | + | 0.0625000i | ||||
\(129\) | − | 6.40091i | − | 0.0496194i | ||||||
\(130\) | −90.2445 | + | 27.7358i | −0.694189 | + | 0.213352i | ||||
\(131\) | 20.3671 | 0.155474 | 0.0777370 | − | 0.996974i | \(-0.475231\pi\) | ||||
0.0777370 | + | 0.996974i | \(0.475231\pi\) | |||||||
\(132\) | −13.0687 | − | 13.0687i | −0.0990051 | − | 0.0990051i | ||||
\(133\) | 239.386 | − | 239.386i | 1.79989 | − | 1.79989i | ||||
\(134\) | 46.5448i | 0.347349i | ||||||||
\(135\) | 22.9576 | + | 12.1635i | 0.170056 | + | 0.0900998i | ||||
\(136\) | 63.3826 | 0.466048 | ||||||||
\(137\) | −109.723 | − | 109.723i | −0.800894 | − | 0.800894i | 0.182341 | − | 0.983235i | \(-0.441633\pi\) |
−0.983235 | + | 0.182341i | \(0.941633\pi\) | |||||||
\(138\) | 8.30662 | − | 8.30662i | 0.0601929 | − | 0.0601929i | ||||
\(139\) | − | 239.354i | − | 1.72197i | −0.508627 | − | 0.860987i | \(-0.669847\pi\) | ||
0.508627 | − | 0.860987i | \(-0.330153\pi\) | |||||||
\(140\) | −56.7772 | + | 107.162i | −0.405552 | + | 0.765446i | ||||
\(141\) | 148.973 | 1.05655 | ||||||||
\(142\) | −73.4573 | − | 73.4573i | −0.517305 | − | 0.517305i | ||||
\(143\) | 50.3705 | − | 50.3705i | 0.352241 | − | 0.352241i | ||||
\(144\) | 12.0000i | 0.0833333i | ||||||||
\(145\) | 63.5045 | + | 206.626i | 0.437962 | + | 1.42501i | ||||
\(146\) | −148.293 | −1.01570 | ||||||||
\(147\) | −120.116 | − | 120.116i | −0.817118 | − | 0.817118i | ||||
\(148\) | 45.3294 | − | 45.3294i | 0.306280 | − | 0.306280i | ||||
\(149\) | 187.064i | 1.25546i | 0.778430 | + | 0.627731i | \(0.216016\pi\) | ||||
−0.778430 | + | 0.627731i | \(0.783984\pi\) | |||||||
\(150\) | 50.6670 | − | 34.3927i | 0.337780 | − | 0.229284i | ||||
\(151\) | −156.167 | −1.03422 | −0.517109 | − | 0.855919i | \(-0.672992\pi\) | ||||
−0.517109 | + | 0.855919i | \(0.672992\pi\) | |||||||
\(152\) | −55.8309 | − | 55.8309i | −0.367308 | − | 0.367308i | ||||
\(153\) | 47.5369 | − | 47.5369i | 0.310699 | − | 0.310699i | ||||
\(154\) | − | 91.5039i | − | 0.594181i | ||||||
\(155\) | −217.948 | + | 66.9841i | −1.40612 | + | 0.432156i | ||||
\(156\) | −46.2515 | −0.296484 | ||||||||
\(157\) | −60.0337 | − | 60.0337i | −0.382380 | − | 0.382380i | 0.489579 | − | 0.871959i | \(-0.337151\pi\) |
−0.871959 | + | 0.489579i | \(0.837151\pi\) | |||||||
\(158\) | −42.9315 | + | 42.9315i | −0.271718 | + | 0.271718i | ||||
\(159\) | 22.7317i | 0.142966i | ||||||||
\(160\) | 24.9930 | + | 13.2419i | 0.156206 | + | 0.0827619i | ||||
\(161\) | 58.1611 | 0.361249 | ||||||||
\(162\) | 9.00000 | + | 9.00000i | 0.0555556 | + | 0.0555556i | ||||
\(163\) | 59.5443 | − | 59.5443i | 0.365303 | − | 0.365303i | −0.500458 | − | 0.865761i | \(-0.666835\pi\) |
0.865761 | + | 0.500458i | \(0.166835\pi\) | |||||||
\(164\) | 54.9059i | 0.334792i | ||||||||
\(165\) | −21.6318 | + | 40.8282i | −0.131102 | + | 0.247444i | ||||
\(166\) | −60.6236 | −0.365202 | ||||||||
\(167\) | 153.528 | + | 153.528i | 0.919327 | + | 0.919327i | 0.996980 | − | 0.0776536i | \(-0.0247428\pi\) |
−0.0776536 | + | 0.996980i | \(0.524743\pi\) | |||||||
\(168\) | −42.0106 | + | 42.0106i | −0.250063 | + | 0.250063i | ||||
\(169\) | − | 9.26698i | − | 0.0548342i | ||||||
\(170\) | −46.5511 | − | 151.464i | −0.273830 | − | 0.890967i | ||||
\(171\) | −83.7463 | −0.489744 | ||||||||
\(172\) | −5.22632 | − | 5.22632i | −0.0303856 | − | 0.0303856i | ||||
\(173\) | 89.1455 | − | 89.1455i | 0.515292 | − | 0.515292i | −0.400851 | − | 0.916143i | \(-0.631286\pi\) |
0.916143 | + | 0.400851i | \(0.131286\pi\) | |||||||
\(174\) | 105.899i | 0.608613i | ||||||||
\(175\) | 297.784 | + | 56.9746i | 1.70162 | + | 0.325569i | ||||
\(176\) | −21.3410 | −0.121256 | ||||||||
\(177\) | −76.8998 | − | 76.8998i | −0.434462 | − | 0.434462i | ||||
\(178\) | 115.921 | − | 115.921i | 0.651244 | − | 0.651244i | ||||
\(179\) | 297.612i | 1.66264i | 0.555797 | + | 0.831318i | \(0.312413\pi\) | ||||
−0.555797 | + | 0.831318i | \(0.687587\pi\) | |||||||
\(180\) | 28.6762 | − | 8.81335i | 0.159312 | − | 0.0489630i | ||||
\(181\) | −147.512 | −0.814981 | −0.407490 | − | 0.913209i | \(-0.633596\pi\) | ||||
−0.407490 | + | 0.913209i | \(0.633596\pi\) | |||||||
\(182\) | −161.921 | − | 161.921i | −0.889678 | − | 0.889678i | ||||
\(183\) | −122.977 | + | 122.977i | −0.672006 | + | 0.672006i | ||||
\(184\) | − | 13.5647i | − | 0.0737210i | ||||||
\(185\) | −141.615 | − | 75.0310i | −0.765486 | − | 0.405573i | ||||
\(186\) | −111.701 | −0.600544 | ||||||||
\(187\) | 84.5407 | + | 84.5407i | 0.452089 | + | 0.452089i | ||||
\(188\) | 121.636 | − | 121.636i | 0.647000 | − | 0.647000i | ||||
\(189\) | 63.0160i | 0.333418i | ||||||||
\(190\) | −92.4134 | + | 174.423i | −0.486386 | + | 0.918015i | ||||
\(191\) | −131.722 | −0.689643 | −0.344821 | − | 0.938668i | \(-0.612061\pi\) | ||||
−0.344821 | + | 0.938668i | \(0.612061\pi\) | |||||||
\(192\) | 9.79796 | + | 9.79796i | 0.0510310 | + | 0.0510310i | ||||
\(193\) | 207.885 | − | 207.885i | 1.07713 | − | 1.07713i | 0.0803601 | − | 0.996766i | \(-0.474393\pi\) |
0.996766 | − | 0.0803601i | \(-0.0256070\pi\) | |||||||
\(194\) | − | 262.298i | − | 1.35205i | ||||||
\(195\) | 33.9692 | + | 110.527i | 0.174201 | + | 0.566803i | ||||
\(196\) | −196.149 | −1.00076 | ||||||||
\(197\) | −241.609 | − | 241.609i | −1.22644 | − | 1.22644i | −0.965300 | − | 0.261142i | \(-0.915901\pi\) |
−0.261142 | − | 0.965300i | \(-0.584099\pi\) | |||||||
\(198\) | −16.0058 | + | 16.0058i | −0.0808373 | + | 0.0808373i | ||||
\(199\) | 217.535i | 1.09314i | 0.837413 | + | 0.546570i | \(0.184067\pi\) | ||||
−0.837413 | + | 0.546570i | \(0.815933\pi\) | |||||||
\(200\) | 13.2879 | − | 69.4509i | 0.0664397 | − | 0.347255i | ||||
\(201\) | 57.0055 | 0.283610 | ||||||||
\(202\) | −23.7421 | − | 23.7421i | −0.117535 | − | 0.117535i | ||||
\(203\) | −370.739 | + | 370.739i | −1.82630 | + | 1.82630i | ||||
\(204\) | − | 77.6275i | − | 0.380527i | ||||||
\(205\) | 131.208 | − | 40.3254i | 0.640037 | − | 0.196709i | ||||
\(206\) | 228.390 | 1.10869 | ||||||||
\(207\) | −10.1735 | − | 10.1735i | −0.0491473 | − | 0.0491473i | ||||
\(208\) | −37.7642 | + | 37.7642i | −0.181559 | + | 0.181559i | ||||
\(209\) | − | 148.936i | − | 0.712613i | ||||||
\(210\) | 131.247 | + | 69.5376i | 0.624984 | + | 0.331132i | ||||
\(211\) | 190.204 | 0.901440 | 0.450720 | − | 0.892665i | \(-0.351167\pi\) | ||||
0.450720 | + | 0.892665i | \(0.351167\pi\) | |||||||
\(212\) | 18.5603 | + | 18.5603i | 0.0875487 | + | 0.0875487i | ||||
\(213\) | −89.9664 | + | 89.9664i | −0.422378 | + | 0.422378i | ||||
\(214\) | − | 48.4505i | − | 0.226404i | ||||||
\(215\) | −8.65080 | + | 16.3277i | −0.0402363 | + | 0.0759428i | ||||
\(216\) | 14.6969 | 0.0680414 | ||||||||
\(217\) | −391.053 | − | 391.053i | −1.80209 | − | 1.80209i | ||||
\(218\) | −33.7671 | + | 33.7671i | −0.154895 | + | 0.154895i | ||||
\(219\) | 181.621i | 0.829317i | ||||||||
\(220\) | 15.6738 | + | 50.9984i | 0.0712447 | + | 0.231811i | ||||
\(221\) | 299.199 | 1.35384 | ||||||||
\(222\) | −55.5169 | − | 55.5169i | −0.250076 | − | 0.250076i | ||||
\(223\) | −148.820 | + | 148.820i | −0.667356 | + | 0.667356i | −0.957103 | − | 0.289747i | \(-0.906429\pi\) |
0.289747 | + | 0.957103i | \(0.406429\pi\) | |||||||
\(224\) | 68.6031i | 0.306264i | ||||||||
\(225\) | −42.1222 | − | 62.0542i | −0.187210 | − | 0.275796i | ||||
\(226\) | 219.111 | 0.969518 | ||||||||
\(227\) | 92.8831 | + | 92.8831i | 0.409177 | + | 0.409177i | 0.881451 | − | 0.472275i | \(-0.156567\pi\) |
−0.472275 | + | 0.881451i | \(0.656567\pi\) | |||||||
\(228\) | −68.3786 | + | 68.3786i | −0.299906 | + | 0.299906i | ||||
\(229\) | 292.034i | 1.27526i | 0.770344 | + | 0.637629i | \(0.220085\pi\) | ||||
−0.770344 | + | 0.637629i | \(0.779915\pi\) | |||||||
\(230\) | −32.4153 | + | 9.96251i | −0.140936 | + | 0.0433152i | ||||
\(231\) | −112.069 | −0.485147 | ||||||||
\(232\) | 86.4659 | + | 86.4659i | 0.372698 | + | 0.372698i | ||||
\(233\) | −41.9538 | + | 41.9538i | −0.180059 | + | 0.180059i | −0.791382 | − | 0.611323i | \(-0.790638\pi\) |
0.611323 | + | 0.791382i | \(0.290638\pi\) | |||||||
\(234\) | 56.6463i | 0.242078i | ||||||||
\(235\) | −380.007 | − | 201.337i | −1.61705 | − | 0.856751i | ||||
\(236\) | −125.577 | −0.532106 | ||||||||
\(237\) | 52.5802 | + | 52.5802i | 0.221857 | + | 0.221857i | ||||
\(238\) | 271.765 | − | 271.765i | 1.14187 | − | 1.14187i | ||||
\(239\) | 165.558i | 0.692713i | 0.938103 | + | 0.346357i | \(0.112581\pi\) | ||||
−0.938103 | + | 0.346357i | \(0.887419\pi\) | |||||||
\(240\) | 16.2180 | − | 30.6101i | 0.0675748 | − | 0.127542i | ||||
\(241\) | −376.816 | −1.56355 | −0.781777 | − | 0.623559i | \(-0.785686\pi\) | ||||
−0.781777 | + | 0.623559i | \(0.785686\pi\) | |||||||
\(242\) | 92.5350 | + | 92.5350i | 0.382376 | + | 0.382376i | ||||
\(243\) | 11.0227 | − | 11.0227i | 0.0453609 | − | 0.0453609i | ||||
\(244\) | 200.821i | 0.823036i | ||||||||
\(245\) | 144.061 | + | 468.734i | 0.588004 | + | 1.91320i | ||||
\(246\) | 67.2457 | 0.273356 | ||||||||
\(247\) | −263.551 | − | 263.551i | −1.06701 | − | 1.06701i | ||||
\(248\) | −91.2036 | + | 91.2036i | −0.367757 | + | 0.367757i | ||||
\(249\) | 74.2484i | 0.298186i | ||||||||
\(250\) | −175.725 | + | 19.2539i | −0.702900 | + | 0.0770157i | ||||
\(251\) | −149.704 | −0.596431 | −0.298216 | − | 0.954499i | \(-0.596391\pi\) | ||||
−0.298216 | + | 0.954499i | \(0.596391\pi\) | |||||||
\(252\) | 51.4523 | + | 51.4523i | 0.204176 | + | 0.204176i | ||||
\(253\) | 18.0928 | − | 18.0928i | 0.0715129 | − | 0.0715129i | ||||
\(254\) | 111.090i | 0.437362i | ||||||||
\(255\) | −185.505 | + | 57.0132i | −0.727471 | + | 0.223581i | ||||
\(256\) | 16.0000 | 0.0625000 | ||||||||
\(257\) | −268.353 | − | 268.353i | −1.04418 | − | 1.04418i | −0.998978 | − | 0.0451978i | \(-0.985608\pi\) |
−0.0451978 | − | 0.998978i | \(-0.514392\pi\) | |||||||
\(258\) | −6.40091 | + | 6.40091i | −0.0248097 | + | 0.0248097i | ||||
\(259\) | − | 388.717i | − | 1.50084i | ||||||
\(260\) | 117.980 | + | 62.5088i | 0.453770 | + | 0.240418i | ||||
\(261\) | 129.699 | 0.496930 | ||||||||
\(262\) | −20.3671 | − | 20.3671i | −0.0777370 | − | 0.0777370i | ||||
\(263\) | −80.7650 | + | 80.7650i | −0.307091 | + | 0.307091i | −0.843780 | − | 0.536689i | \(-0.819675\pi\) |
0.536689 | + | 0.843780i | \(0.319675\pi\) | |||||||
\(264\) | 26.1373i | 0.0990051i | ||||||||
\(265\) | 30.7218 | − | 57.9849i | 0.115931 | − | 0.218811i | ||||
\(266\) | −478.771 | −1.79989 | ||||||||
\(267\) | −141.974 | − | 141.974i | −0.531739 | − | 0.531739i | ||||
\(268\) | 46.5448 | − | 46.5448i | 0.173675 | − | 0.173675i | ||||
\(269\) | − | 51.5840i | − | 0.191762i | −0.995393 | − | 0.0958811i | \(-0.969433\pi\) | ||
0.995393 | − | 0.0958811i | \(-0.0305669\pi\) | |||||||
\(270\) | −10.7941 | − | 35.1210i | −0.0399782 | − | 0.130078i | ||||
\(271\) | 35.9992 | 0.132839 | 0.0664193 | − | 0.997792i | \(-0.478843\pi\) | ||||
0.0664193 | + | 0.997792i | \(0.478843\pi\) | |||||||
\(272\) | −63.3826 | − | 63.3826i | −0.233024 | − | 0.233024i | ||||
\(273\) | −198.312 | + | 198.312i | −0.726419 | + | 0.726419i | ||||
\(274\) | 219.445i | 0.800894i | ||||||||
\(275\) | 110.358 | − | 74.9111i | 0.401303 | − | 0.272404i | ||||
\(276\) | −16.6132 | −0.0601929 | ||||||||
\(277\) | 262.283 | + | 262.283i | 0.946870 | + | 0.946870i | 0.998658 | − | 0.0517881i | \(-0.0164920\pi\) |
−0.0517881 | + | 0.998658i | \(0.516492\pi\) | |||||||
\(278\) | −239.354 | + | 239.354i | −0.860987 | + | 0.860987i | ||||
\(279\) | 136.805i | 0.490342i | ||||||||
\(280\) | 163.940 | − | 50.3852i | 0.585499 | − | 0.179947i | ||||
\(281\) | −79.4049 | −0.282580 | −0.141290 | − | 0.989968i | \(-0.545125\pi\) | ||||
−0.141290 | + | 0.989968i | \(0.545125\pi\) | |||||||
\(282\) | −148.973 | − | 148.973i | −0.528273 | − | 0.528273i | ||||
\(283\) | −77.4320 | + | 77.4320i | −0.273611 | + | 0.273611i | −0.830552 | − | 0.556941i | \(-0.811975\pi\) |
0.556941 | + | 0.830552i | \(0.311975\pi\) | |||||||
\(284\) | 146.915i | 0.517305i | ||||||||
\(285\) | 213.624 | + | 113.183i | 0.749556 | + | 0.397133i | ||||
\(286\) | −100.741 | −0.352241 | ||||||||
\(287\) | 235.420 | + | 235.420i | 0.820277 | + | 0.820277i | ||||
\(288\) | 12.0000 | − | 12.0000i | 0.0416667 | − | 0.0416667i | ||||
\(289\) | 213.169i | 0.737609i | ||||||||
\(290\) | 143.122 | − | 270.131i | 0.493523 | − | 0.931485i | ||||
\(291\) | −321.248 | −1.10394 | ||||||||
\(292\) | 148.293 | + | 148.293i | 0.507851 | + | 0.507851i | ||||
\(293\) | 175.421 | − | 175.421i | 0.598707 | − | 0.598707i | −0.341262 | − | 0.939968i | \(-0.610854\pi\) |
0.939968 | + | 0.341262i | \(0.110854\pi\) | |||||||
\(294\) | 240.233i | 0.817118i | ||||||||
\(295\) | 92.2294 | + | 300.089i | 0.312642 | + | 1.01725i | ||||
\(296\) | −90.6588 | −0.306280 | ||||||||
\(297\) | 19.6030 | + | 19.6030i | 0.0660034 | + | 0.0660034i | ||||
\(298\) | 187.064 | − | 187.064i | 0.627731 | − | 0.627731i | ||||
\(299\) | − | 64.0323i | − | 0.214155i | ||||||
\(300\) | −85.0597 | − | 16.2743i | −0.283532 | − | 0.0542478i | ||||
\(301\) | −44.8177 | −0.148896 | ||||||||
\(302\) | 156.167 | + | 156.167i | 0.517109 | + | 0.517109i | ||||
\(303\) | −29.0781 | + | 29.0781i | −0.0959672 | + | 0.0959672i | ||||
\(304\) | 111.662i | 0.367308i | ||||||||
\(305\) | 479.898 | − | 147.492i | 1.57344 | − | 0.483580i | ||||
\(306\) | −95.0739 | −0.310699 | ||||||||
\(307\) | −230.973 | − | 230.973i | −0.752354 | − | 0.752354i | 0.222564 | − | 0.974918i | \(-0.428557\pi\) |
−0.974918 | + | 0.222564i | \(0.928557\pi\) | |||||||
\(308\) | −91.5039 | + | 91.5039i | −0.297091 | + | 0.297091i | ||||
\(309\) | − | 279.720i | − | 0.905242i | ||||||
\(310\) | 284.932 | + | 150.964i | 0.919135 | + | 0.486980i | ||||
\(311\) | 202.569 | 0.651347 | 0.325674 | − | 0.945482i | \(-0.394409\pi\) | ||||
0.325674 | + | 0.945482i | \(0.394409\pi\) | |||||||
\(312\) | 46.2515 | + | 46.2515i | 0.148242 | + | 0.148242i | ||||
\(313\) | 288.074 | − | 288.074i | 0.920366 | − | 0.920366i | −0.0766893 | − | 0.997055i | \(-0.524435\pi\) |
0.997055 | + | 0.0766893i | \(0.0244349\pi\) | |||||||
\(314\) | 120.067i | 0.382380i | ||||||||
\(315\) | 85.1659 | − | 160.744i | 0.270368 | − | 0.510298i | ||||
\(316\) | 85.8630 | 0.271718 | ||||||||
\(317\) | −17.6959 | − | 17.6959i | −0.0558232 | − | 0.0558232i | 0.678644 | − | 0.734467i | \(-0.262568\pi\) |
−0.734467 | + | 0.678644i | \(0.762568\pi\) | |||||||
\(318\) | 22.7317 | − | 22.7317i | 0.0714832 | − | 0.0714832i | ||||
\(319\) | 230.659i | 0.723069i | ||||||||
\(320\) | −11.7511 | − | 38.2349i | −0.0367223 | − | 0.119484i | ||||
\(321\) | −59.3394 | −0.184858 | ||||||||
\(322\) | −58.1611 | − | 58.1611i | −0.180625 | − | 0.180625i | ||||
\(323\) | 442.338 | − | 442.338i | 1.36947 | − | 1.36947i | ||||
\(324\) | − | 18.0000i | − | 0.0555556i | ||||||
\(325\) | 62.7261 | − | 327.845i | 0.193003 | − | 1.00875i | ||||
\(326\) | −119.089 | −0.365303 | ||||||||
\(327\) | 41.3561 | + | 41.3561i | 0.126471 | + | 0.126471i | ||||
\(328\) | 54.9059 | − | 54.9059i | 0.167396 | − | 0.167396i | ||||
\(329\) | − | 1043.08i | − | 3.17044i | ||||||
\(330\) | 62.4600 | − | 19.1965i | 0.189273 | − | 0.0581711i | ||||
\(331\) | −318.113 | −0.961067 | −0.480533 | − | 0.876976i | \(-0.659557\pi\) | ||||
−0.480533 | + | 0.876976i | \(0.659557\pi\) | |||||||
\(332\) | 60.6236 | + | 60.6236i | 0.182601 | + | 0.182601i | ||||
\(333\) | −67.9941 | + | 67.9941i | −0.204186 | + | 0.204186i | ||||
\(334\) | − | 307.055i | − | 0.919327i | ||||||
\(335\) | −145.412 | − | 77.0428i | −0.434066 | − | 0.229978i | ||||
\(336\) | 84.0213 | 0.250063 | ||||||||
\(337\) | 183.892 | + | 183.892i | 0.545675 | + | 0.545675i | 0.925187 | − | 0.379512i | \(-0.123908\pi\) |
−0.379512 | + | 0.925187i | \(0.623908\pi\) | |||||||
\(338\) | −9.26698 | + | 9.26698i | −0.0274171 | + | 0.0274171i | ||||
\(339\) | − | 268.355i | − | 0.791608i | ||||||
\(340\) | −104.913 | + | 198.015i | −0.308568 | + | 0.582398i | ||||
\(341\) | −243.298 | −0.713483 | ||||||||
\(342\) | 83.7463 | + | 83.7463i | 0.244872 | + | 0.244872i | ||||
\(343\) | −420.833 | + | 420.833i | −1.22692 | + | 1.22692i | ||||
\(344\) | 10.4526i | 0.0303856i | ||||||||
\(345\) | 12.2015 | + | 39.7004i | 0.0353667 | + | 0.115074i | ||||
\(346\) | −178.291 | −0.515292 | ||||||||
\(347\) | −27.3732 | − | 27.3732i | −0.0788854 | − | 0.0788854i | 0.666563 | − | 0.745449i | \(-0.267765\pi\) |
−0.745449 | + | 0.666563i | \(0.767765\pi\) | |||||||
\(348\) | 105.899 | − | 105.899i | 0.304306 | − | 0.304306i | ||||
\(349\) | − | 285.470i | − | 0.817965i | −0.912542 | − | 0.408982i | \(-0.865884\pi\) | ||
0.912542 | − | 0.408982i | \(-0.134116\pi\) | |||||||
\(350\) | −240.810 | − | 354.759i | −0.688028 | − | 1.01360i | ||||
\(351\) | 69.3773 | 0.197656 | ||||||||
\(352\) | 21.3410 | + | 21.3410i | 0.0606280 | + | 0.0606280i | ||||
\(353\) | 65.7593 | − | 65.7593i | 0.186287 | − | 0.186287i | −0.607802 | − | 0.794089i | \(-0.707948\pi\) |
0.794089 | + | 0.607802i | \(0.207948\pi\) | |||||||
\(354\) | 153.800i | 0.434462i | ||||||||
\(355\) | 351.079 | − | 107.901i | 0.988956 | − | 0.303946i | ||||
\(356\) | −231.843 | −0.651244 | ||||||||
\(357\) | −332.843 | − | 332.843i | −0.932333 | − | 0.932333i | ||||
\(358\) | 297.612 | − | 297.612i | 0.831318 | − | 0.831318i | ||||
\(359\) | − | 685.981i | − | 1.91081i | −0.295298 | − | 0.955405i | \(-0.595419\pi\) | ||
0.295298 | − | 0.955405i | \(-0.404581\pi\) | |||||||
\(360\) | −37.4896 | − | 19.8629i | −0.104138 | − | 0.0551746i | ||||
\(361\) | −418.272 | −1.15865 | ||||||||
\(362\) | 147.512 | + | 147.512i | 0.407490 | + | 0.407490i | ||||
\(363\) | 113.332 | − | 113.332i | 0.312209 | − | 0.312209i | ||||
\(364\) | 323.843i | 0.889678i | ||||||||
\(365\) | 245.459 | − | 463.285i | 0.672492 | − | 1.26927i | ||||
\(366\) | 245.954 | 0.672006 | ||||||||
\(367\) | −286.652 | − | 286.652i | −0.781069 | − | 0.781069i | 0.198943 | − | 0.980011i | \(-0.436249\pi\) |
−0.980011 | + | 0.198943i | \(0.936249\pi\) | |||||||
\(368\) | −13.5647 | + | 13.5647i | −0.0368605 | + | 0.0368605i | ||||
\(369\) | − | 82.3588i | − | 0.223195i | ||||||
\(370\) | 66.5840 | + | 216.646i | 0.179957 | + | 0.585529i | ||||
\(371\) | 159.162 | 0.429008 | ||||||||
\(372\) | 111.701 | + | 111.701i | 0.300272 | + | 0.300272i | ||||
\(373\) | −307.918 | + | 307.918i | −0.825516 | + | 0.825516i | −0.986893 | − | 0.161376i | \(-0.948407\pi\) |
0.161376 | + | 0.986893i | \(0.448407\pi\) | |||||||
\(374\) | − | 169.081i | − | 0.452089i | ||||||
\(375\) | 23.5812 | + | 215.218i | 0.0628831 | + | 0.573916i | ||||
\(376\) | −243.272 | −0.647000 | ||||||||
\(377\) | 408.164 | + | 408.164i | 1.08266 | + | 1.08266i | ||||
\(378\) | 63.0160 | − | 63.0160i | 0.166709 | − | 0.166709i | ||||
\(379\) | 86.8843i | 0.229246i | 0.993409 | + | 0.114623i | \(0.0365660\pi\) | ||||
−0.993409 | + | 0.114623i | \(0.963434\pi\) | |||||||
\(380\) | 266.836 | − | 82.0095i | 0.702201 | − | 0.215814i | ||||
\(381\) | 136.057 | 0.357104 | ||||||||
\(382\) | 131.722 | + | 131.722i | 0.344821 | + | 0.344821i | ||||
\(383\) | 159.134 | − | 159.134i | 0.415492 | − | 0.415492i | −0.468154 | − | 0.883647i | \(-0.655081\pi\) |
0.883647 | + | 0.468154i | \(0.155081\pi\) | |||||||
\(384\) | − | 19.5959i | − | 0.0510310i | ||||||
\(385\) | 285.870 | + | 151.461i | 0.742519 | + | 0.393405i | ||||
\(386\) | −415.771 | −1.07713 | ||||||||
\(387\) | 7.83948 | + | 7.83948i | 0.0202570 | + | 0.0202570i | ||||
\(388\) | −262.298 | + | 262.298i | −0.676025 | + | 0.676025i | ||||
\(389\) | − | 70.6535i | − | 0.181628i | −0.995868 | − | 0.0908142i | \(-0.971053\pi\) | ||
0.995868 | − | 0.0908142i | \(-0.0289469\pi\) | |||||||
\(390\) | 76.5573 | − | 144.496i | 0.196301 | − | 0.370502i | ||||
\(391\) | 107.470 | 0.274860 | ||||||||
\(392\) | 196.149 | + | 196.149i | 0.500380 | + | 0.500380i | ||||
\(393\) | −24.9445 | + | 24.9445i | −0.0634720 | + | 0.0634720i | ||||
\(394\) | 483.218i | 1.22644i | ||||||||
\(395\) | −63.0617 | − | 205.186i | −0.159650 | − | 0.519457i | ||||
\(396\) | 32.0116 | 0.0808373 | ||||||||
\(397\) | −7.66108 | − | 7.66108i | −0.0192974 | − | 0.0192974i | 0.697392 | − | 0.716690i | \(-0.254344\pi\) |
−0.716690 | + | 0.697392i | \(0.754344\pi\) | |||||||
\(398\) | 217.535 | − | 217.535i | 0.546570 | − | 0.546570i | ||||
\(399\) | 586.373i | 1.46961i | ||||||||
\(400\) | −82.7389 | + | 56.1630i | −0.206847 | + | 0.140407i | ||||
\(401\) | −436.861 | −1.08943 | −0.544715 | − | 0.838621i | \(-0.683362\pi\) | ||||
−0.544715 | + | 0.838621i | \(0.683362\pi\) | |||||||
\(402\) | −57.0055 | − | 57.0055i | −0.141805 | − | 0.141805i | ||||
\(403\) | −430.529 | + | 430.529i | −1.06831 | + | 1.06831i | ||||
\(404\) | 47.4843i | 0.117535i | ||||||||
\(405\) | −43.0143 | + | 13.2200i | −0.106208 | + | 0.0326420i | ||||
\(406\) | 741.478 | 1.82630 | ||||||||
\(407\) | −120.922 | − | 120.922i | −0.297106 | − | 0.297106i | ||||
\(408\) | −77.6275 | + | 77.6275i | −0.190263 | + | 0.190263i | ||||
\(409\) | − | 397.297i | − | 0.971385i | −0.874130 | − | 0.485693i | \(-0.838567\pi\) | ||
0.874130 | − | 0.485693i | \(-0.161433\pi\) | |||||||
\(410\) | −171.533 | − | 90.8823i | −0.418373 | − | 0.221664i | ||||
\(411\) | 268.764 | 0.653928 | ||||||||
\(412\) | −228.390 | − | 228.390i | −0.554346 | − | 0.554346i | ||||
\(413\) | −538.435 | + | 538.435i | −1.30372 | + | 1.30372i | ||||
\(414\) | 20.3470i | 0.0491473i | ||||||||
\(415\) | 100.346 | − | 189.396i | 0.241799 | − | 0.456376i | ||||
\(416\) | 75.5284 | 0.181559 | ||||||||
\(417\) | 293.148 | + | 293.148i | 0.702993 | + | 0.702993i | ||||
\(418\) | −148.936 | + | 148.936i | −0.356307 | + | 0.356307i | ||||
\(419\) | 188.910i | 0.450859i | 0.974260 | + | 0.225429i | \(0.0723785\pi\) | ||||
−0.974260 | + | 0.225429i | \(0.927622\pi\) | |||||||
\(420\) | −61.7091 | − | 200.784i | −0.146926 | − | 0.478058i | ||||
\(421\) | 92.6040 | 0.219962 | 0.109981 | − | 0.993934i | \(-0.464921\pi\) | ||||
0.109981 | + | 0.993934i | \(0.464921\pi\) | |||||||
\(422\) | −190.204 | − | 190.204i | −0.450720 | − | 0.450720i | ||||
\(423\) | −182.454 | + | 182.454i | −0.431333 | + | 0.431333i | ||||
\(424\) | − | 37.1207i | − | 0.0875487i | ||||||
\(425\) | 550.247 | + | 105.278i | 1.29470 | + | 0.247713i | ||||
\(426\) | 179.933 | 0.422378 | ||||||||
\(427\) | 861.058 | + | 861.058i | 2.01653 | + | 2.01653i | ||||
\(428\) | −48.4505 | + | 48.4505i | −0.113202 | + | 0.113202i | ||||
\(429\) | 123.382i | 0.287604i | ||||||||
\(430\) | 24.9785 | − | 7.67689i | 0.0580895 | − | 0.0178532i | ||||
\(431\) | 111.346 | 0.258344 | 0.129172 | − | 0.991622i | \(-0.458768\pi\) | ||||
0.129172 | + | 0.991622i | \(0.458768\pi\) | |||||||
\(432\) | −14.6969 | − | 14.6969i | −0.0340207 | − | 0.0340207i | ||||
\(433\) | 157.449 | − | 157.449i | 0.363623 | − | 0.363623i | −0.501522 | − | 0.865145i | \(-0.667226\pi\) |
0.865145 | + | 0.501522i | \(0.167226\pi\) | |||||||
\(434\) | 782.106i | 1.80209i | ||||||||
\(435\) | −330.841 | − | 175.287i | −0.760554 | − | 0.402960i | ||||
\(436\) | 67.5342 | 0.154895 | ||||||||
\(437\) | −94.6658 | − | 94.6658i | −0.216627 | − | 0.216627i | ||||
\(438\) | 181.621 | − | 181.621i | 0.414659 | − | 0.414659i | ||||
\(439\) | 108.313i | 0.246726i | 0.992362 | + | 0.123363i | \(0.0393680\pi\) | ||||
−0.992362 | + | 0.123363i | \(0.960632\pi\) | |||||||
\(440\) | 35.3245 | − | 66.6722i | 0.0802830 | − | 0.151528i | ||||
\(441\) | 294.224 | 0.667174 | ||||||||
\(442\) | −299.199 | − | 299.199i | −0.676921 | − | 0.676921i | ||||
\(443\) | 179.232 | − | 179.232i | 0.404586 | − | 0.404586i | −0.475260 | − | 0.879846i | \(-0.657646\pi\) |
0.879846 | + | 0.475260i | \(0.157646\pi\) | |||||||
\(444\) | 111.034i | 0.250076i | ||||||||
\(445\) | 170.276 | + | 554.031i | 0.382643 | + | 1.24501i | ||||
\(446\) | 297.641 | 0.667356 | ||||||||
\(447\) | −229.106 | − | 229.106i | −0.512540 | − | 0.512540i | ||||
\(448\) | 68.6031 | − | 68.6031i | 0.153132 | − | 0.153132i | ||||
\(449\) | 672.236i | 1.49719i | 0.663030 | + | 0.748593i | \(0.269270\pi\) | ||||
−0.663030 | + | 0.748593i | \(0.730730\pi\) | |||||||
\(450\) | −19.9319 | + | 104.176i | −0.0442932 | + | 0.231503i | ||||
\(451\) | 146.469 | 0.324764 | ||||||||
\(452\) | −219.111 | − | 219.111i | −0.484759 | − | 0.484759i | ||||
\(453\) | 191.265 | − | 191.265i | 0.422218 | − | 0.422218i | ||||
\(454\) | − | 185.766i | − | 0.409177i | ||||||
\(455\) | 773.882 | − | 237.845i | 1.70084 | − | 0.522736i | ||||
\(456\) | 136.757 | 0.299906 | ||||||||
\(457\) | −353.101 | − | 353.101i | −0.772649 | − | 0.772649i | 0.205920 | − | 0.978569i | \(-0.433981\pi\) |
−0.978569 | + | 0.205920i | \(0.933981\pi\) | |||||||
\(458\) | 292.034 | − | 292.034i | 0.637629 | − | 0.637629i | ||||
\(459\) | 116.441i | 0.253685i | ||||||||
\(460\) | 42.3778 | + | 22.4527i | 0.0921256 | + | 0.0488103i | ||||
\(461\) | 61.4442 | 0.133285 | 0.0666423 | − | 0.997777i | \(-0.478771\pi\) | ||||
0.0666423 | + | 0.997777i | \(0.478771\pi\) | |||||||
\(462\) | 112.069 | + | 112.069i | 0.242573 | + | 0.242573i | ||||
\(463\) | 593.423 | − | 593.423i | 1.28169 | − | 1.28169i | 0.341987 | − | 0.939705i | \(-0.388900\pi\) |
0.939705 | − | 0.341987i | \(-0.111100\pi\) | |||||||
\(464\) | − | 172.932i | − | 0.372698i | ||||||
\(465\) | 184.892 | − | 348.969i | 0.397617 | − | 0.750471i | ||||
\(466\) | 83.9075 | 0.180059 | ||||||||
\(467\) | −62.1024 | − | 62.1024i | −0.132982 | − | 0.132982i | 0.637483 | − | 0.770464i | \(-0.279976\pi\) |
−0.770464 | + | 0.637483i | \(0.779976\pi\) | |||||||
\(468\) | 56.6463 | − | 56.6463i | 0.121039 | − | 0.121039i | ||||
\(469\) | − | 399.140i | − | 0.851044i | ||||||
\(470\) | 178.670 | + | 581.343i | 0.380149 | + | 1.23690i | ||||
\(471\) | 147.052 | 0.312212 | ||||||||
\(472\) | 125.577 | + | 125.577i | 0.266053 | + | 0.266053i | ||||
\(473\) | −13.9419 | + | 13.9419i | −0.0294754 | + | 0.0294754i | ||||
\(474\) | − | 105.160i | − | 0.221857i | ||||||
\(475\) | −391.953 | − | 577.423i | −0.825165 | − | 1.21563i | ||||
\(476\) | −543.530 | −1.14187 | ||||||||
\(477\) | −27.8405 | − | 27.8405i | −0.0583658 | − | 0.0583658i | ||||
\(478\) | 165.558 | − | 165.558i | 0.346357 | − | 0.346357i | ||||
\(479\) | − | 188.974i | − | 0.394518i | −0.980351 | − | 0.197259i | \(-0.936796\pi\) | ||
0.980351 | − | 0.197259i | \(-0.0632040\pi\) | |||||||
\(480\) | −46.8281 | + | 14.3921i | −0.0975584 | + | 0.0299836i | ||||
\(481\) | −427.957 | −0.889724 | ||||||||
\(482\) | 376.816 | + | 376.816i | 0.781777 | + | 0.781777i | ||||
\(483\) | −71.2325 | + | 71.2325i | −0.147479 | + | 0.147479i | ||||
\(484\) | − | 185.070i | − | 0.382376i | ||||||
\(485\) | 819.451 | + | 434.165i | 1.68959 | + | 0.895185i | ||||
\(486\) | −22.0454 | −0.0453609 | ||||||||
\(487\) | −406.039 | − | 406.039i | −0.833756 | − | 0.833756i | 0.154272 | − | 0.988028i | \(-0.450697\pi\) |
−0.988028 | + | 0.154272i | \(0.950697\pi\) | |||||||
\(488\) | 200.821 | − | 200.821i | 0.411518 | − | 0.411518i | ||||
\(489\) | 145.853i | 0.298268i | ||||||||
\(490\) | 324.674 | − | 612.795i | 0.662599 | − | 1.25060i | ||||
\(491\) | −388.154 | −0.790538 | −0.395269 | − | 0.918565i | \(-0.629349\pi\) | ||||
−0.395269 | + | 0.918565i | \(0.629349\pi\) | |||||||
\(492\) | −67.2457 | − | 67.2457i | −0.136678 | − | 0.136678i | ||||
\(493\) | −685.054 | + | 685.054i | −1.38956 | + | 1.38956i | ||||
\(494\) | 527.102i | 1.06701i | ||||||||
\(495\) | −23.5108 | − | 76.4975i | −0.0474965 | − | 0.154540i | ||||
\(496\) | 182.407 | 0.367757 | ||||||||
\(497\) | 629.925 | + | 629.925i | 1.26745 | + | 1.26745i | ||||
\(498\) | 74.2484 | − | 74.2484i | 0.149093 | − | 0.149093i | ||||
\(499\) | − | 536.161i | − | 1.07447i | −0.843433 | − | 0.537235i | \(-0.819469\pi\) | ||
0.843433 | − | 0.537235i | \(-0.180531\pi\) | |||||||
\(500\) | 194.979 | + | 156.471i | 0.389958 | + | 0.312942i | ||||
\(501\) | −376.064 | −0.750627 | ||||||||
\(502\) | 149.704 | + | 149.704i | 0.298216 | + | 0.298216i | ||||
\(503\) | 135.474 | − | 135.474i | 0.269333 | − | 0.269333i | −0.559499 | − | 0.828831i | \(-0.689006\pi\) |
0.828831 | + | 0.559499i | \(0.189006\pi\) | |||||||
\(504\) | − | 102.905i | − | 0.204176i | ||||||
\(505\) | 113.472 | − | 34.8746i | 0.224698 | − | 0.0690587i | ||||
\(506\) | −36.1855 | −0.0715129 | ||||||||
\(507\) | 11.3497 | + | 11.3497i | 0.0223860 | + | 0.0223860i | ||||
\(508\) | 111.090 | − | 111.090i | 0.218681 | − | 0.218681i | ||||
\(509\) | − | 544.024i | − | 1.06881i | −0.845229 | − | 0.534405i | \(-0.820536\pi\) | ||
0.845229 | − | 0.534405i | \(-0.179464\pi\) | |||||||
\(510\) | 242.518 | + | 128.492i | 0.475526 | + | 0.251945i | ||||
\(511\) | 1271.67 | 2.48858 | ||||||||
\(512\) | −16.0000 | − | 16.0000i | −0.0312500 | − | 0.0312500i | ||||
\(513\) | 102.568 | − | 102.568i | 0.199937 | − | 0.199937i | ||||
\(514\) | 536.706i | 1.04418i | ||||||||
\(515\) | −378.040 | + | 713.521i | −0.734059 | + | 1.38548i | ||||
\(516\) | 12.8018 | 0.0248097 | ||||||||
\(517\) | −324.480 | − | 324.480i | −0.627621 | − | 0.627621i | ||||
\(518\) | −388.717 | + | 388.717i | −0.750419 | + | 0.750419i | ||||
\(519\) | 218.361i | 0.420734i | ||||||||
\(520\) | −55.4715 | − | 180.489i | −0.106676 | − | 0.347094i | ||||
\(521\) | −537.878 | −1.03240 | −0.516198 | − | 0.856469i | \(-0.672653\pi\) | ||||
−0.516198 | + | 0.856469i | \(0.672653\pi\) | |||||||
\(522\) | −129.699 | − | 129.699i | −0.248465 | − | 0.248465i | ||||
\(523\) | −417.463 | + | 417.463i | −0.798209 | + | 0.798209i | −0.982813 | − | 0.184604i | \(-0.940900\pi\) |
0.184604 | + | 0.982813i | \(0.440900\pi\) | |||||||
\(524\) | 40.7342i | 0.0777370i | ||||||||
\(525\) | −434.489 | + | 294.930i | −0.827598 | + | 0.561772i | ||||
\(526\) | 161.530 | 0.307091 | ||||||||
\(527\) | −722.590 | − | 722.590i | −1.37114 | − | 1.37114i | ||||
\(528\) | 26.1373 | − | 26.1373i | 0.0495025 | − | 0.0495025i | ||||
\(529\) | − | 23.0000i | − | 0.0434783i | ||||||
\(530\) | −88.7066 | + | 27.2631i | −0.167371 | + | 0.0514398i | ||||
\(531\) | 188.365 | 0.354737 | ||||||||
\(532\) | 478.771 | + | 478.771i | 0.899946 | + | 0.899946i | ||||
\(533\) | 259.185 | − | 259.185i | 0.486275 | − | 0.486275i | ||||
\(534\) | 283.949i | 0.531739i | ||||||||
\(535\) | 151.365 | + | 80.1970i | 0.282926 | + | 0.149901i | ||||
\(536\) | −93.0896 | −0.173675 | ||||||||
\(537\) | −364.499 | − | 364.499i | −0.678768 | − | 0.678768i | ||||
\(538\) | −51.5840 | + | 51.5840i | −0.0958811 | + | 0.0958811i | ||||
\(539\) | 523.253i | 0.970786i | ||||||||
\(540\) | −24.3269 | + | 45.9151i | −0.0450499 | + | 0.0850280i | ||||
\(541\) | 659.210 | 1.21850 | 0.609252 | − | 0.792977i | \(-0.291470\pi\) | ||||
0.609252 | + | 0.792977i | \(0.291470\pi\) | |||||||
\(542\) | −35.9992 | − | 35.9992i | −0.0664193 | − | 0.0664193i | ||||
\(543\) | 180.664 | − | 180.664i | 0.332715 | − | 0.332715i | ||||
\(544\) | 126.765i | 0.233024i | ||||||||
\(545\) | −49.6002 | − | 161.385i | −0.0910095 | − | 0.296120i | ||||
\(546\) | 396.625 | 0.726419 | ||||||||
\(547\) | −181.796 | − | 181.796i | −0.332350 | − | 0.332350i | 0.521128 | − | 0.853479i | \(-0.325511\pi\) |
−0.853479 | + | 0.521128i | \(0.825511\pi\) | |||||||
\(548\) | 219.445 | − | 219.445i | 0.400447 | − | 0.400447i | ||||
\(549\) | − | 301.231i | − | 0.548690i | ||||||
\(550\) | −185.269 | − | 35.4473i | −0.336854 | − | 0.0644497i | ||||
\(551\) | 1206.87 | 2.19032 | ||||||||
\(552\) | 16.6132 | + | 16.6132i | 0.0300965 | + | 0.0300965i | ||||
\(553\) | 368.154 | − | 368.154i | 0.665740 | − | 0.665740i | ||||
\(554\) | − | 524.566i | − | 0.946870i | ||||||
\(555\) | 265.336 | − | 81.5484i | 0.478083 | − | 0.146934i | ||||
\(556\) | 478.709 | 0.860987 | ||||||||
\(557\) | 114.798 | + | 114.798i | 0.206100 | + | 0.206100i | 0.802607 | − | 0.596508i | \(-0.203445\pi\) |
−0.596508 | + | 0.802607i | \(0.703445\pi\) | |||||||
\(558\) | 136.805 | − | 136.805i | 0.245171 | − | 0.245171i | ||||
\(559\) | 49.3419i | 0.0882682i | ||||||||
\(560\) | −214.325 | − | 113.554i | −0.382723 | − | 0.202776i | ||||
\(561\) | −207.081 | −0.369129 | ||||||||
\(562\) | 79.4049 | + | 79.4049i | 0.141290 | + | 0.141290i | ||||
\(563\) | −271.045 | + | 271.045i | −0.481430 | + | 0.481430i | −0.905588 | − | 0.424158i | \(-0.860570\pi\) |
0.424158 | + | 0.905588i | \(0.360570\pi\) | |||||||
\(564\) | 297.946i | 0.528273i | ||||||||
\(565\) | −362.681 | + | 684.532i | −0.641914 | + | 1.21156i | ||||
\(566\) | 154.864 | 0.273611 | ||||||||
\(567\) | −77.1785 | − | 77.1785i | −0.136117 | − | 0.136117i | ||||
\(568\) | 146.915 | − | 146.915i | 0.258652 | − | 0.258652i | ||||
\(569\) | 215.559i | 0.378837i | 0.981896 | + | 0.189419i | \(0.0606604\pi\) | ||||
−0.981896 | + | 0.189419i | \(0.939340\pi\) | |||||||
\(570\) | −100.441 | − | 326.806i | −0.176212 | − | 0.573344i | ||||
\(571\) | −622.372 | −1.08997 | −0.544984 | − | 0.838446i | \(-0.683464\pi\) | ||||
−0.544984 | + | 0.838446i | \(0.683464\pi\) | |||||||
\(572\) | 100.741 | + | 100.741i | 0.176121 | + | 0.176121i | ||||
\(573\) | 161.326 | − | 161.326i | 0.281546 | − | 0.281546i | ||||
\(574\) | − | 470.839i | − | 0.820277i | ||||||
\(575\) | 22.5308 | − | 117.760i | 0.0391840 | − | 0.204800i | ||||
\(576\) | −24.0000 | −0.0416667 | ||||||||
\(577\) | −454.606 | − | 454.606i | −0.787879 | − | 0.787879i | 0.193268 | − | 0.981146i | \(-0.438091\pi\) |
−0.981146 | + | 0.193268i | \(0.938091\pi\) | |||||||
\(578\) | 213.169 | − | 213.169i | 0.368804 | − | 0.368804i | ||||
\(579\) | 509.213i | 0.879470i | ||||||||
\(580\) | −413.252 | + | 127.009i | −0.712504 | + | 0.218981i | ||||
\(581\) | 519.871 | 0.894786 | ||||||||
\(582\) | 321.248 | + | 321.248i | 0.551972 | + | 0.551972i | ||||
\(583\) | 49.5121 | − | 49.5121i | 0.0849264 | − | 0.0849264i | ||||
\(584\) | − | 296.585i | − | 0.507851i | ||||||
\(585\) | −176.970 | − | 93.7632i | −0.302514 | − | 0.160279i | ||||
\(586\) | −350.842 | −0.598707 | ||||||||
\(587\) | 246.656 | + | 246.656i | 0.420197 | + | 0.420197i | 0.885272 | − | 0.465074i | \(-0.153972\pi\) |
−0.465074 | + | 0.885272i | \(0.653972\pi\) | |||||||
\(588\) | 240.233 | − | 240.233i | 0.408559 | − | 0.408559i | ||||
\(589\) | 1272.99i | 2.16128i | ||||||||
\(590\) | 207.860 | − | 392.319i | 0.352305 | − | 0.664947i | ||||
\(591\) | 591.819 | 1.00139 | ||||||||
\(592\) | 90.6588 | + | 90.6588i | 0.153140 | + | 0.153140i | ||||
\(593\) | −188.339 | + | 188.339i | −0.317603 | + | 0.317603i | −0.847846 | − | 0.530243i | \(-0.822101\pi\) |
0.530243 | + | 0.847846i | \(0.322101\pi\) | |||||||
\(594\) | − | 39.2060i | − | 0.0660034i | ||||||
\(595\) | 399.193 | + | 1298.87i | 0.670913 | + | 2.18297i | ||||
\(596\) | −374.128 | −0.627731 | ||||||||
\(597\) | −266.425 | − | 266.425i | −0.446273 | − | 0.446273i | ||||
\(598\) | −64.0323 | + | 64.0323i | −0.107077 | + | 0.107077i | ||||
\(599\) | 353.101i | 0.589485i | 0.955577 | + | 0.294742i | \(0.0952338\pi\) | ||||
−0.955577 | + | 0.294742i | \(0.904766\pi\) | |||||||
\(600\) | 68.7853 | + | 101.334i | 0.114642 | + | 0.168890i | ||||
\(601\) | −285.740 | −0.475441 | −0.237721 | − | 0.971334i | \(-0.576400\pi\) | ||||
−0.237721 | + | 0.971334i | \(0.576400\pi\) | |||||||
\(602\) | 44.8177 | + | 44.8177i | 0.0744480 | + | 0.0744480i | ||||
\(603\) | −69.8172 | + | 69.8172i | −0.115783 | + | 0.115783i | ||||
\(604\) | − | 312.334i | − | 0.517109i | ||||||
\(605\) | −442.259 | + | 135.924i | −0.731006 | + | 0.224667i | ||||
\(606\) | 58.1561 | 0.0959672 | ||||||||
\(607\) | −416.723 | − | 416.723i | −0.686529 | − | 0.686529i | 0.274934 | − | 0.961463i | \(-0.411344\pi\) |
−0.961463 | + | 0.274934i | \(0.911344\pi\) | |||||||
\(608\) | 111.662 | − | 111.662i | 0.183654 | − | 0.183654i | ||||
\(609\) | − | 908.122i | − | 1.49117i | ||||||
\(610\) | −627.390 | − | 332.406i | −1.02851 | − | 0.544928i | ||||
\(611\) | −1148.37 | −1.87950 | ||||||||
\(612\) | 95.0739 | + | 95.0739i | 0.155349 | + | 0.155349i | ||||
\(613\) | 362.012 | − | 362.012i | 0.590559 | − | 0.590559i | −0.347224 | − | 0.937782i | \(-0.612876\pi\) |
0.937782 | + | 0.347224i | \(0.112876\pi\) | |||||||
\(614\) | 461.945i | 0.752354i | ||||||||
\(615\) | −111.308 | + | 210.084i | −0.180988 | + | 0.341600i | ||||
\(616\) | 183.008 | 0.297091 | ||||||||
\(617\) | 163.519 | + | 163.519i | 0.265023 | + | 0.265023i | 0.827091 | − | 0.562068i | \(-0.189994\pi\) |
−0.562068 | + | 0.827091i | \(0.689994\pi\) | |||||||
\(618\) | −279.720 | + | 279.720i | −0.452621 | + | 0.452621i | ||||
\(619\) | − | 46.8175i | − | 0.0756341i | −0.999285 | − | 0.0378171i | \(-0.987960\pi\) | ||
0.999285 | − | 0.0378171i | \(-0.0120404\pi\) | |||||||
\(620\) | −133.968 | − | 435.896i | −0.216078 | − | 0.703058i | ||||
\(621\) | 24.9199 | 0.0401286 | ||||||||
\(622\) | −202.569 | − | 202.569i | −0.325674 | − | 0.325674i | ||||
\(623\) | −994.072 | + | 994.072i | −1.59562 | + | 1.59562i | ||||
\(624\) | − | 92.5031i | − | 0.148242i | ||||||
\(625\) | 230.715 | − | 580.858i | 0.369144 | − | 0.929372i | ||||
\(626\) | −576.149 | −0.920366 | ||||||||
\(627\) | 182.409 | + | 182.409i | 0.290923 | + | 0.290923i | ||||
\(628\) | 120.067 | − | 120.067i | 0.191190 | − | 0.191190i | ||||
\(629\) | − | 718.273i | − | 1.14193i | ||||||
\(630\) | −245.910 | + | 75.5779i | −0.390333 | + | 0.119965i | ||||
\(631\) | −984.554 | −1.56031 | −0.780154 | − | 0.625588i | \(-0.784859\pi\) | ||||
−0.780154 | + | 0.625588i | \(0.784859\pi\) | |||||||
\(632\) | −85.8630 | − | 85.8630i | −0.135859 | − | 0.135859i | ||||
\(633\) | −232.951 | + | 232.951i | −0.368011 | + | 0.368011i | ||||
\(634\) | 35.3919i | 0.0558232i | ||||||||
\(635\) | −347.059 | − | 183.880i | −0.546550 | − | 0.289575i | ||||
\(636\) | −45.4633 | −0.0714832 | ||||||||
\(637\) | 925.927 | + | 925.927i | 1.45357 | + | 1.45357i | ||||
\(638\) | 230.659 | − | 230.659i | 0.361534 | − | 0.361534i | ||||
\(639\) | − | 220.372i | − | 0.344870i | ||||||
\(640\) | −26.4838 | + | 49.9861i | −0.0413810 | + | 0.0781032i | ||||
\(641\) | −83.9542 | −0.130974 | −0.0654869 | − | 0.997853i | \(-0.520860\pi\) | ||||
−0.0654869 | + | 0.997853i | \(0.520860\pi\) | |||||||
\(642\) | 59.3394 | + | 59.3394i | 0.0924290 | + | 0.0924290i | ||||
\(643\) | 87.3495 | − | 87.3495i | 0.135847 | − | 0.135847i | −0.635914 | − | 0.771760i | \(-0.719377\pi\) |
0.771760 | + | 0.635914i | \(0.219377\pi\) | |||||||
\(644\) | 116.322i | 0.180625i | ||||||||
\(645\) | −9.40223 | − | 30.5923i | −0.0145771 | − | 0.0474299i | ||||
\(646\) | −884.676 | −1.36947 | ||||||||
\(647\) | −447.854 | − | 447.854i | −0.692202 | − | 0.692202i | 0.270514 | − | 0.962716i | \(-0.412806\pi\) |
−0.962716 | + | 0.270514i | \(0.912806\pi\) | |||||||
\(648\) | −18.0000 | + | 18.0000i | −0.0277778 | + | 0.0277778i | ||||
\(649\) | 334.993i | 0.516168i | ||||||||
\(650\) | −390.571 | + | 265.119i | −0.600879 | + | 0.407875i | ||||
\(651\) | 957.881 | 1.47140 | ||||||||
\(652\) | 119.089 | + | 119.089i | 0.182651 | + | 0.182651i | ||||
\(653\) | 525.679 | − | 525.679i | 0.805022 | − | 0.805022i | −0.178854 | − | 0.983876i | \(-0.557239\pi\) |
0.983876 | + | 0.178854i | \(0.0572388\pi\) | |||||||
\(654\) | − | 82.7121i | − | 0.126471i | ||||||
\(655\) | 97.3418 | − | 29.9170i | 0.148613 | − | 0.0456749i | ||||
\(656\) | −109.812 | −0.167396 | ||||||||
\(657\) | −222.439 | − | 222.439i | −0.338567 | − | 0.338567i | ||||
\(658\) | −1043.08 | + | 1043.08i | −1.58522 | + | 1.58522i | ||||
\(659\) | 279.050i | 0.423445i | 0.977330 | + | 0.211723i | \(0.0679073\pi\) | ||||
−0.977330 | + | 0.211723i | \(0.932093\pi\) | |||||||
\(660\) | −81.6564 | − | 43.2635i | −0.123722 | − | 0.0655508i | ||||
\(661\) | 210.642 | 0.318672 | 0.159336 | − | 0.987224i | \(-0.449065\pi\) | ||||
0.159336 | + | 0.987224i | \(0.449065\pi\) | |||||||
\(662\) | 318.113 | + | 318.113i | 0.480533 | + | 0.480533i | ||||
\(663\) | −366.443 | + | 366.443i | −0.552704 | + | 0.552704i | ||||
\(664\) | − | 121.247i | − | 0.182601i | ||||||
\(665\) | 792.481 | − | 1495.74i | 1.19170 | − | 2.24924i | ||||
\(666\) | 135.988 | 0.204186 | ||||||||
\(667\) | 146.610 | + | 146.610i | 0.219805 | + | 0.219805i | ||||
\(668\) | −307.055 | + | 307.055i | −0.459663 | + | 0.459663i | ||||
\(669\) | − | 364.534i | − | 0.544894i | ||||||
\(670\) | 68.3693 | + | 222.455i | 0.102044 | + | 0.332022i | ||||
\(671\) | 535.715 | 0.798384 | ||||||||
\(672\) | −84.0213 | − | 84.0213i | −0.125032 | − | 0.125032i | ||||
\(673\) | 440.741 | − | 440.741i | 0.654890 | − | 0.654890i | −0.299276 | − | 0.954166i | \(-0.596745\pi\) |
0.954166 | + | 0.299276i | \(0.0967453\pi\) | |||||||
\(674\) | − | 367.785i | − | 0.545675i | ||||||
\(675\) | 127.589 | + | 24.4115i | 0.189021 | + | 0.0361652i | ||||
\(676\) | 18.5340 | 0.0274171 | ||||||||
\(677\) | 707.522 | + | 707.522i | 1.04508 | + | 1.04508i | 0.998935 | + | 0.0461495i | \(0.0146951\pi\) |
0.0461495 | + | 0.998935i | \(0.485305\pi\) | |||||||
\(678\) | −268.355 | + | 268.355i | −0.395804 | + | 0.395804i | ||||
\(679\) | 2249.30i | 3.31267i | ||||||||
\(680\) | 302.929 | − | 93.1021i | 0.445483 | − | 0.136915i | ||||
\(681\) | −227.516 | −0.334091 | ||||||||
\(682\) | 243.298 | + | 243.298i | 0.356741 | + | 0.356741i | ||||
\(683\) | −346.952 | + | 346.952i | −0.507982 | + | 0.507982i | −0.913906 | − | 0.405925i | \(-0.866949\pi\) |
0.405925 | + | 0.913906i | \(0.366949\pi\) | |||||||
\(684\) | − | 167.493i | − | 0.244872i | ||||||
\(685\) | −685.575 | − | 363.234i | −1.00084 | − | 0.530268i | ||||
\(686\) | 841.667 | 1.22692 | ||||||||
\(687\) | −357.667 | − | 357.667i | −0.520622 | − | 0.520622i | ||||
\(688\) | 10.4526 | − | 10.4526i | 0.0151928 | − | 0.0151928i | ||||
\(689\) | − | 175.229i | − | 0.254324i | ||||||
\(690\) | 27.4989 | − | 51.9019i | 0.0398535 | − | 0.0752202i | ||||
\(691\) | −438.734 | −0.634926 | −0.317463 | − | 0.948271i | \(-0.602831\pi\) | ||||
−0.317463 | + | 0.948271i | \(0.602831\pi\) | |||||||
\(692\) | 178.291 | + | 178.291i | 0.257646 | + | 0.257646i | ||||
\(693\) | 137.256 | − | 137.256i | 0.198060 | − | 0.198060i | ||||
\(694\) | 54.7465i | 0.0788854i | ||||||||
\(695\) | −351.586 | − | 1143.96i | −0.505879 | − | 1.64599i | ||||
\(696\) | −211.797 | −0.304306 | ||||||||
\(697\) | 435.009 | + | 435.009i | 0.624117 | + | 0.624117i | ||||
\(698\) | −285.470 | + | 285.470i | −0.408982 | + | 0.408982i | ||||
\(699\) | − | 102.765i | − | 0.147018i | ||||||
\(700\) | −113.949 | + | 595.569i | −0.162785 | + | 0.850812i | ||||
\(701\) | −405.008 | −0.577758 | −0.288879 | − | 0.957366i | \(-0.593283\pi\) | ||||
−0.288879 | + | 0.957366i | \(0.593283\pi\) | |||||||
\(702\) | −69.3773 | − | 69.3773i | −0.0988280 | − | 0.0988280i | ||||
\(703\) | −632.695 | + | 632.695i | −0.899993 | + | 0.899993i | ||||
\(704\) | − | 42.6821i | − | 0.0606280i | ||||||
\(705\) | 711.997 | − | 218.825i | 1.00992 | − | 0.310390i | ||||
\(706\) | −131.519 | −0.186287 | ||||||||
\(707\) | 203.598 | + | 203.598i | 0.287975 | + | 0.287975i | ||||
\(708\) | 153.800 | − | 153.800i | 0.217231 | − | 0.217231i | ||||
\(709\) | − | 216.541i | − | 0.305417i | −0.988271 | − | 0.152708i | \(-0.951200\pi\) | ||
0.988271 | − | 0.152708i | \(-0.0487996\pi\) | |||||||
\(710\) | −458.980 | − | 243.179i | −0.646451 | − | 0.342505i | ||||
\(711\) | −128.795 | −0.181146 | ||||||||
\(712\) | 231.843 | + | 231.843i | 0.325622 | + | 0.325622i | ||||
\(713\) | −154.643 | + | 154.643i | −0.216891 | + | 0.216891i | ||||
\(714\) | 665.686i | 0.932333i | ||||||||
\(715\) | 166.750 | − | 314.728i | 0.233217 | − | 0.440179i | ||||
\(716\) | −595.224 | −0.831318 | ||||||||
\(717\) | −202.767 | − | 202.767i | −0.282799 | − | 0.282799i | ||||
\(718\) | −685.981 | + | 685.981i | −0.955405 | + | 0.955405i | ||||
\(719\) | − | 715.794i | − | 0.995541i | −0.867309 | − | 0.497771i | \(-0.834152\pi\) | ||
0.867309 | − | 0.497771i | \(-0.165848\pi\) | |||||||
\(720\) | 17.6267 | + | 57.3524i | 0.0244815 | + | 0.0796561i | ||||
\(721\) | −1958.54 | −2.71642 | ||||||||
\(722\) | 418.272 | + | 418.272i | 0.579323 | + | 0.579323i | ||||
\(723\) | 461.504 | − | 461.504i | 0.638318 | − | 0.638318i | ||||
\(724\) | − | 295.023i | − | 0.407490i | ||||||
\(725\) | 607.022 | + | 894.261i | 0.837272 | + | 1.23346i | ||||
\(726\) | −226.663 | −0.312209 | ||||||||
\(727\) | −518.797 | − | 518.797i | −0.713614 | − | 0.713614i | 0.253675 | − | 0.967289i | \(-0.418361\pi\) |
−0.967289 | + | 0.253675i | \(0.918361\pi\) | |||||||
\(728\) | 323.843 | − | 323.843i | 0.444839 | − | 0.444839i | ||||
\(729\) | 27.0000i | 0.0370370i | ||||||||
\(730\) | −708.745 | + | 217.826i | −0.970883 | + | 0.298391i | ||||
\(731\) | −82.8144 | −0.113289 | ||||||||
\(732\) | −245.954 | − | 245.954i | −0.336003 | − | 0.336003i | ||||
\(733\) | 229.564 | − | 229.564i | 0.313184 | − | 0.313184i | −0.532958 | − | 0.846142i | \(-0.678920\pi\) |
0.846142 | + | 0.532958i | \(0.178920\pi\) | |||||||
\(734\) | 573.304i | 0.781069i | ||||||||
\(735\) | −750.518 | − | 397.642i | −1.02111 | − | 0.541010i | ||||
\(736\) | 27.1293 | 0.0368605 | ||||||||
\(737\) | −124.164 | − | 124.164i | −0.168473 | − | 0.168473i | ||||
\(738\) | −82.3588 | + | 82.3588i | −0.111597 | + | 0.111597i | ||||
\(739\) | 585.332i | 0.792060i | 0.918238 | + | 0.396030i | \(0.129612\pi\) | ||||
−0.918238 | + | 0.396030i | \(0.870388\pi\) | |||||||
\(740\) | 150.062 | − | 283.230i | 0.202786 | − | 0.382743i | ||||
\(741\) | 645.566 | 0.871209 | ||||||||
\(742\) | −159.162 | − | 159.162i | −0.214504 | − | 0.214504i | ||||
\(743\) | 660.093 | − | 660.093i | 0.888416 | − | 0.888416i | −0.105955 | − | 0.994371i | \(-0.533790\pi\) |
0.994371 | + | 0.105955i | \(0.0337898\pi\) | |||||||
\(744\) | − | 223.402i | − | 0.300272i | ||||||
\(745\) | 274.777 | + | 894.047i | 0.368828 | + | 1.20006i | ||||
\(746\) | 615.835 | 0.825516 | ||||||||
\(747\) | −90.9353 | − | 90.9353i | −0.121734 | − | 0.121734i | ||||
\(748\) | −169.081 | + | 169.081i | −0.226045 | + | 0.226045i | ||||
\(749\) | 415.481i | 0.554715i | ||||||||
\(750\) | 191.637 | − | 238.799i | 0.255516 | − | 0.318399i | ||||
\(751\) | −778.164 | −1.03617 | −0.518085 | − | 0.855329i | \(-0.673355\pi\) | ||||
−0.518085 | + | 0.855329i | \(0.673355\pi\) | |||||||
\(752\) | 243.272 | + | 243.272i | 0.323500 | + | 0.323500i | ||||
\(753\) | 183.350 | − | 183.350i | 0.243492 | − | 0.243492i | ||||
\(754\) | − | 816.329i | − | 1.08266i | ||||||
\(755\) | −746.380 | + | 229.392i | −0.988582 | + | 0.303831i | ||||
\(756\) | −126.032 | −0.166709 | ||||||||
\(757\) | −788.525 | − | 788.525i | −1.04165 | − | 1.04165i | −0.999094 | − | 0.0425507i | \(-0.986452\pi\) |
−0.0425507 | − | 0.999094i | \(-0.513548\pi\) | |||||||
\(758\) | 86.8843 | − | 86.8843i | 0.114623 | − | 0.114623i | ||||
\(759\) | 44.3180i | 0.0583900i | ||||||||
\(760\) | −348.846 | − | 184.827i | −0.459008 | − | 0.243193i | ||||
\(761\) | 1511.09 | 1.98566 | 0.992830 | − | 0.119531i | \(-0.0381390\pi\) | ||||
0.992830 | + | 0.119531i | \(0.0381390\pi\) | |||||||
\(762\) | −136.057 | − | 136.057i | −0.178552 | − | 0.178552i | ||||
\(763\) | 289.566 | − | 289.566i | 0.379510 | − | 0.379510i | ||||
\(764\) | − | 263.444i | − | 0.344821i | ||||||
\(765\) | 157.370 | − | 297.023i | 0.205712 | − | 0.388265i | ||||
\(766\) | −318.267 | −0.415492 | ||||||||
\(767\) | 592.789 | + | 592.789i | 0.772867 | + | 0.772867i | ||||
\(768\) | −19.5959 | + | 19.5959i | −0.0255155 | + | 0.0255155i | ||||
\(769\) | 359.692i | 0.467740i | 0.972268 | + | 0.233870i | \(0.0751391\pi\) | ||||
−0.972268 | + | 0.233870i | \(0.924861\pi\) | |||||||
\(770\) | −134.409 | − | 437.331i | −0.174557 | − | 0.567962i | ||||
\(771\) | 657.328 | 0.852566 | ||||||||
\(772\) | 415.771 | + | 415.771i | 0.538563 | + | 0.538563i | ||||
\(773\) | −872.985 | + | 872.985i | −1.12935 | + | 1.12935i | −0.139063 | + | 0.990284i | \(0.544409\pi\) |
−0.990284 | + | 0.139063i | \(0.955591\pi\) | |||||||
\(774\) | − | 15.6790i | − | 0.0202570i | ||||||
\(775\) | −943.261 | + | 640.283i | −1.21711 | + | 0.826172i | ||||
\(776\) | 524.595 | 0.676025 | ||||||||
\(777\) | 476.079 | + | 476.079i | 0.612715 | + | 0.612715i | ||||
\(778\) | −70.6535 | + | 70.6535i | −0.0908142 | + | 0.0908142i | ||||
\(779\) | − | 766.361i | − | 0.983775i | ||||||
\(780\) | −221.053 | + | 67.9385i | −0.283401 | + | 0.0871006i | ||||
\(781\) | 391.914 | 0.501810 | ||||||||
\(782\) | −107.470 | − | 107.470i | −0.137430 | − | 0.137430i | ||||
\(783\) | −158.848 | + | 158.848i | −0.202871 | + | 0.202871i | ||||
\(784\) | − | 392.298i | − | 0.500380i | ||||||
\(785\) | −375.106 | − | 198.740i | −0.477842 | − | 0.253172i | ||||
\(786\) | 49.8890 | 0.0634720 | ||||||||
\(787\) | 133.713 | + | 133.713i | 0.169902 | + | 0.169902i | 0.786936 | − | 0.617034i | \(-0.211666\pi\) |
−0.617034 | + | 0.786936i | \(0.711666\pi\) | |||||||
\(788\) | 483.218 | − | 483.218i | 0.613221 | − | 0.613221i | ||||
\(789\) | − | 197.833i | − | 0.250739i | ||||||
\(790\) | −142.124 | + | 268.247i | −0.179904 | + | 0.339553i | ||||
\(791\) | −1878.96 | −2.37543 | ||||||||
\(792\) | −32.0116 | − | 32.0116i | −0.0404187 | − | 0.0404187i | ||||
\(793\) | 947.979 | − | 947.979i | 1.19543 | − | 1.19543i | ||||
\(794\) | 15.3222i | 0.0192974i | ||||||||
\(795\) | 33.3903 | + | 108.643i | 0.0420004 | + | 0.136658i | ||||
\(796\) | −435.070 | −0.546570 | ||||||||
\(797\) | 1004.81 | + | 1004.81i | 1.26074 | + | 1.26074i | 0.950735 | + | 0.310005i | \(0.100331\pi\) |
0.310005 | + | 0.950735i | \(0.399669\pi\) | |||||||
\(798\) | 586.373 | − | 586.373i | 0.734803 | − | 0.734803i | ||||
\(799\) | − | 1927.40i | − | 2.41227i | ||||||
\(800\) | 138.902 | + | 26.5759i | 0.173627 | + | 0.0332199i | ||||
\(801\) | 347.764 | 0.434163 | ||||||||
\(802\) | 436.861 | + | 436.861i | 0.544715 | + | 0.544715i | ||||
\(803\) | 395.590 | − | 395.590i | 0.492640 | − | 0.492640i | ||||
\(804\) | 114.011i | 0.141805i | ||||||||
\(805\) | 277.973 | − | 85.4323i | 0.345309 | − | 0.106127i | ||||
\(806\) | 861.058 | 1.06831 | ||||||||
\(807\) | 63.1773 | + | 63.1773i | 0.0782866 | + | 0.0782866i | ||||
\(808\) | 47.4843 | − | 47.4843i | 0.0587677 | − | 0.0587677i | ||||
\(809\) | − | 605.728i | − | 0.748737i | −0.927280 | − | 0.374369i | \(-0.877859\pi\) | ||
0.927280 | − | 0.374369i | \(-0.122141\pi\) | |||||||
\(810\) | 56.2343 | + | 29.7943i | 0.0694251 | + | 0.0367831i | ||||
\(811\) | −48.8085 | −0.0601831 | −0.0300915 | − | 0.999547i | \(-0.509580\pi\) | ||||
−0.0300915 | + | 0.999547i | \(0.509580\pi\) | |||||||
\(812\) | −741.478 | − | 741.478i | −0.913151 | − | 0.913151i | ||||
\(813\) | −44.0899 | + | 44.0899i | −0.0542311 | + | 0.0542311i | ||||
\(814\) | 241.844i | 0.297106i | ||||||||
\(815\) | 197.120 | − | 372.048i | 0.241865 | − | 0.456501i | ||||
\(816\) | 155.255 | 0.190263 | ||||||||
\(817\) | 72.9475 | + | 72.9475i | 0.0892870 | + | 0.0892870i | ||||
\(818\) | −397.297 | + | 397.297i | −0.485693 | + | 0.485693i | ||||
\(819\) | − | 485.764i | − | 0.593119i | ||||||
\(820\) | 80.6508 | + | 262.415i | 0.0983546 | + | 0.320019i | ||||
\(821\) | −200.603 | −0.244340 | −0.122170 | − | 0.992509i | \(-0.538985\pi\) | ||||
−0.122170 | + | 0.992509i | \(0.538985\pi\) | |||||||
\(822\) | −268.764 | − | 268.764i | −0.326964 | − | 0.326964i | ||||
\(823\) | −635.884 | + | 635.884i | −0.772642 | + | 0.772642i | −0.978568 | − | 0.205926i | \(-0.933980\pi\) |
0.205926 | + | 0.978568i | \(0.433980\pi\) | |||||||
\(824\) | 456.781i | 0.554346i | ||||||||
\(825\) | −43.4139 | + | 226.908i | −0.0526230 | + | 0.275040i | ||||
\(826\) | 1076.87 | 1.30372 | ||||||||
\(827\) | −349.120 | − | 349.120i | −0.422153 | − | 0.422153i | 0.463792 | − | 0.885944i | \(-0.346489\pi\) |
−0.885944 | + | 0.463792i | \(0.846489\pi\) | |||||||
\(828\) | 20.3470 | − | 20.3470i | 0.0245737 | − | 0.0245737i | ||||
\(829\) | − | 906.776i | − | 1.09382i | −0.837192 | − | 0.546909i | \(-0.815804\pi\) | ||
0.837192 | − | 0.546909i | \(-0.184196\pi\) | |||||||
\(830\) | −289.742 | + | 89.0494i | −0.349087 | + | 0.107288i | ||||
\(831\) | −642.459 | −0.773116 | ||||||||
\(832\) | −75.5284 | − | 75.5284i | −0.0907794 | − | 0.0907794i | ||||
\(833\) | −1554.05 | + | 1554.05i | −1.86561 | + | 1.86561i | ||||
\(834\) | − | 586.296i | − | 0.702993i | ||||||
\(835\) | 959.280 | + | 508.249i | 1.14884 | + | 0.608682i | ||||
\(836\) | 297.872 | 0.356307 | ||||||||
\(837\) | −167.552 | − | 167.552i | −0.200181 | − | 0.200181i | ||||
\(838\) | 188.910 | − | 188.910i | 0.225429 | − | 0.225429i | ||||
\(839\) | − | 527.100i | − | 0.628248i | −0.949382 | − | 0.314124i | \(-0.898289\pi\) | ||
0.949382 | − | 0.314124i | \(-0.101711\pi\) | |||||||
\(840\) | −139.075 | + | 262.493i | −0.165566 | + | 0.312492i | ||||
\(841\) | −1028.09 | −1.22246 | ||||||||
\(842\) | −92.6040 | − | 92.6040i | −0.109981 | − | 0.109981i | ||||
\(843\) | 97.2508 | − | 97.2508i | 0.115363 | − | 0.115363i | ||||
\(844\) | 380.408i | 0.450720i | ||||||||
\(845\) | −13.6122 | − | 44.2903i | −0.0161091 | − | 0.0524146i | ||||
\(846\) | 364.908 | 0.431333 | ||||||||
\(847\) | −793.523 | − | 793.523i | −0.936863 | − | 0.936863i | ||||
\(848\) | −37.1207 | + | 37.1207i | −0.0437744 | + | 0.0437744i | ||||
\(849\) | − | 189.669i | − | 0.223403i | ||||||
\(850\) | −444.969 | − | 655.525i | −0.523493 | − | 0.771206i | ||||
\(851\) | −153.719 | −0.180634 | ||||||||
\(852\) | −179.933 | − | 179.933i | −0.211189 | − | 0.211189i | ||||
\(853\) | −513.700 | + | 513.700i | −0.602228 | + | 0.602228i | −0.940903 | − | 0.338676i | \(-0.890021\pi\) |
0.338676 | + | 0.940903i | \(0.390021\pi\) | |||||||
\(854\) | − | 1722.12i | − | 2.01653i | ||||||
\(855\) | −400.254 | + | 123.014i | −0.468134 | + | 0.143876i | ||||
\(856\) | 96.9009 | 0.113202 | ||||||||
\(857\) | 626.346 | + | 626.346i | 0.730859 | + | 0.730859i | 0.970790 | − | 0.239931i | \(-0.0771249\pi\) |
−0.239931 | + | 0.970790i | \(0.577125\pi\) | |||||||
\(858\) | 123.382 | − | 123.382i | 0.143802 | − | 0.143802i | ||||
\(859\) | 249.366i | 0.290298i | 0.989410 | + | 0.145149i | \(0.0463661\pi\) | ||||
−0.989410 | + | 0.145149i | \(0.953634\pi\) | |||||||
\(860\) | −32.6554 | − | 17.3016i | −0.0379714 | − | 0.0201181i | ||||
\(861\) | −576.658 | −0.669754 | ||||||||
\(862\) | −111.346 | − | 111.346i | −0.129172 | − | 0.129172i | ||||
\(863\) | −987.163 | + | 987.163i | −1.14387 | + | 1.14387i | −0.156139 | + | 0.987735i | \(0.549905\pi\) |
−0.987735 | + | 0.156139i | \(0.950095\pi\) | |||||||
\(864\) | 29.3939i | 0.0340207i | ||||||||
\(865\) | 295.114 | − | 557.004i | 0.341172 | − | 0.643936i | ||||
\(866\) | −314.897 | −0.363623 | ||||||||
\(867\) | −261.077 | − | 261.077i | −0.301127 | − | 0.301127i | ||||
\(868\) | 782.106 | − | 782.106i | 0.901044 | − | 0.901044i | ||||
\(869\) | − | 229.051i | − | 0.263580i | ||||||
\(870\) | 155.554 | + | 506.128i | 0.178797 | + | 0.581757i | ||||
\(871\) | −439.432 | −0.504514 | ||||||||
\(872\) | −67.5342 | − | 67.5342i | −0.0774475 | − | 0.0774475i | ||||
\(873\) | 393.446 | − | 393.446i | 0.450683 | − | 0.450683i | ||||
\(874\) | 189.332i | 0.216627i | ||||||||
\(875\) | 1506.91 | − | 165.110i | 1.72218 | − | 0.188697i | ||||
\(876\) | −363.241 | −0.414659 | ||||||||
\(877\) | −557.202 | − | 557.202i | −0.635350 | − | 0.635350i | 0.314055 | − | 0.949405i | \(-0.398312\pi\) |
−0.949405 | + | 0.314055i | \(0.898312\pi\) | |||||||
\(878\) | 108.313 | − | 108.313i | 0.123363 | − | 0.123363i | ||||
\(879\) | 429.692i | 0.488842i | ||||||||
\(880\) | −101.997 | + | 31.3477i | −0.115905 | + | 0.0356224i | ||||
\(881\) | −169.442 | −0.192329 | −0.0961647 | − | 0.995365i | \(-0.530658\pi\) | ||||
−0.0961647 | + | 0.995365i | \(0.530658\pi\) | |||||||
\(882\) | −294.224 | − | 294.224i | −0.333587 | − | 0.333587i | ||||
\(883\) | −444.971 | + | 444.971i | −0.503931 | + | 0.503931i | −0.912657 | − | 0.408726i | \(-0.865973\pi\) |
0.408726 | + | 0.912657i | \(0.365973\pi\) | |||||||
\(884\) | 598.398i | 0.676921i | ||||||||
\(885\) | −480.490 | − | 254.575i | −0.542927 | − | 0.287656i | ||||
\(886\) | −358.463 | −0.404586 | ||||||||
\(887\) | 745.158 | + | 745.158i | 0.840087 | + | 0.840087i | 0.988870 | − | 0.148782i | \(-0.0475354\pi\) |
−0.148782 | + | 0.988870i | \(0.547535\pi\) | |||||||
\(888\) | 111.034 | − | 111.034i | 0.125038 | − | 0.125038i | ||||
\(889\) | − | 952.638i | − | 1.07158i | ||||||
\(890\) | 383.755 | − | 724.308i | 0.431186 | − | 0.813829i | ||||
\(891\) | −48.0174 | −0.0538915 | ||||||||
\(892\) | −297.641 | − | 297.641i | −0.333678 | − | 0.333678i | ||||
\(893\) | −1697.76 | + | 1697.76i | −1.90119 | + | 1.90119i | ||||
\(894\) | 458.211i | 0.512540i | ||||||||
\(895\) | 437.159 | + | 1422.40i | 0.488446 | + | 1.58927i | ||||
\(896\) | −137.206 | −0.153132 | ||||||||
\(897\) | 78.4233 | + | 78.4233i | 0.0874284 | + | 0.0874284i | ||||
\(898\) | 672.236 | − | 672.236i | 0.748593 | − | 0.748593i | ||||
\(899\) | − | 1971.50i | − | 2.19299i | ||||||
\(900\) | 124.108 | − | 84.2445i | 0.137898 | − | 0.0936050i | ||||
\(901\) | 294.100 | 0.326415 | ||||||||
\(902\) | −146.469 | − | 146.469i | −0.162382 | − | 0.162382i | ||||
\(903\) | 54.8902 | − | 54.8902i | 0.0607865 | − | 0.0607865i | ||||
\(904\) | 438.222i | 0.484759i | ||||||||
\(905\) | −705.012 | + | 216.678i | −0.779019 | + | 0.239424i | ||||
\(906\) | −382.530 | −0.422218 | ||||||||
\(907\) | 1079.06 | + | 1079.06i | 1.18971 | + | 1.18971i | 0.977149 | + | 0.212556i | \(0.0681789\pi\) |
0.212556 | + | 0.977149i | \(0.431821\pi\) | |||||||
\(908\) | −185.766 | + | 185.766i | −0.204588 | + | 0.204588i | ||||
\(909\) | − | 71.2264i | − | 0.0783569i | ||||||
\(910\) | −1011.73 | − | 536.037i | −1.11179 | − | 0.589052i | ||||
\(911\) | 527.825 | 0.579391 | 0.289696 | − | 0.957119i | \(-0.406446\pi\) | ||||
0.289696 | + | 0.957119i | \(0.406446\pi\) | |||||||
\(912\) | −136.757 | − | 136.757i | −0.149953 | − | 0.149953i | ||||
\(913\) | 161.721 | − | 161.721i | 0.177132 | − | 0.177132i | ||||
\(914\) | 706.201i | 0.772649i | ||||||||
\(915\) | −407.113 | + | 768.392i | −0.444932 | + | 0.839773i | ||||
\(916\) | −584.068 | −0.637629 | ||||||||
\(917\) | 174.656 | + | 174.656i | 0.190464 | + | 0.190464i | ||||
\(918\) | 116.441 | − | 116.441i | 0.126842 | − | 0.126842i | ||||
\(919\) | 1023.45i | 1.11366i | 0.830627 | + | 0.556830i | \(0.187982\pi\) | ||||
−0.830627 | + | 0.556830i | \(0.812018\pi\) | |||||||
\(920\) | −19.9250 | − | 64.8305i | −0.0216576 | − | 0.0704679i | ||||
\(921\) | 565.765 | 0.614295 | ||||||||
\(922\) | −61.4442 | − | 61.4442i | −0.0666423 | − | 0.0666423i | ||||
\(923\) | 693.514 | − | 693.514i | 0.751369 | − | 0.751369i | ||||
\(924\) | − | 224.138i | − | 0.242573i | ||||||
\(925\) | −787.042 | − | 150.584i | −0.850856 | − | 0.162793i | ||||
\(926\) | −1186.85 | −1.28169 | ||||||||
\(927\) | 342.586 | + | 342.586i | 0.369564 | + | 0.369564i | ||||
\(928\) | −172.932 | + | 172.932i | −0.186349 | + | 0.186349i | ||||
\(929\) | 89.6244i | 0.0964740i | 0.998836 | + | 0.0482370i | \(0.0153603\pi\) | ||||
−0.998836 | + | 0.0482370i | \(0.984640\pi\) | |||||||
\(930\) | −533.861 | + | 164.077i | −0.574044 | + | 0.176427i | ||||
\(931\) | 2737.79 | 2.94070 | ||||||||
\(932\) | −83.9075 | − | 83.9075i | −0.0900295 | − | 0.0900295i | ||||
\(933\) | −248.095 | + | 248.095i | −0.265911 | + | 0.265911i | ||||
\(934\) | 124.205i | 0.132982i | ||||||||
\(935\) | 528.232 | + | 279.870i | 0.564954 | + | 0.299326i | ||||
\(936\) | −113.293 | −0.121039 | ||||||||
\(937\) | −182.011 | − | 182.011i | −0.194248 | − | 0.194248i | 0.603281 | − | 0.797529i | \(-0.293860\pi\) |
−0.797529 | + | 0.603281i | \(0.793860\pi\) | |||||||
\(938\) | −399.140 | + | 399.140i | −0.425522 | + | 0.425522i | ||||
\(939\) | 705.635i | 0.751475i | ||||||||
\(940\) | 402.673 | − | 760.013i | 0.428376 | − | 0.808525i | ||||
\(941\) | −481.347 | −0.511527 | −0.255764 | − | 0.966739i | \(-0.582327\pi\) | ||||
−0.255764 | + | 0.966739i | \(0.582327\pi\) | |||||||
\(942\) | −147.052 | − | 147.052i | −0.156106 | − | 0.156106i | ||||
\(943\) | 93.0974 | − | 93.0974i | 0.0987247 | − | 0.0987247i | ||||
\(944\) | − | 251.154i | − | 0.266053i | ||||||
\(945\) | 92.5636 | + | 301.177i | 0.0979509 | + | 0.318705i | ||||
\(946\) | 27.8838 | 0.0294754 | ||||||||
\(947\) | 362.690 | + | 362.690i | 0.382989 | + | 0.382989i | 0.872178 | − | 0.489189i | \(-0.162707\pi\) |
−0.489189 | + | 0.872178i | \(0.662707\pi\) | |||||||
\(948\) | −105.160 | + | 105.160i | −0.110929 | + | 0.110929i | ||||
\(949\) | − | 1400.04i | − | 1.47528i | ||||||
\(950\) | −185.469 | + | 969.376i | −0.195231 | + | 1.02040i | ||||
\(951\) | 43.3460 | 0.0455794 | ||||||||
\(952\) | 543.530 | + | 543.530i | 0.570935 | + | 0.570935i | ||||
\(953\) | 261.038 | − | 261.038i | 0.273912 | − | 0.273912i | −0.556761 | − | 0.830673i | \(-0.687956\pi\) |
0.830673 | + | 0.556761i | \(0.187956\pi\) | |||||||
\(954\) | 55.6810i | 0.0583658i | ||||||||
\(955\) | −629.547 | + | 193.485i | −0.659211 | + | 0.202602i | ||||
\(956\) | −331.117 | −0.346357 | ||||||||
\(957\) | −282.498 | − | 282.498i | −0.295192 | − | 0.295192i | ||||
\(958\) | −188.974 | + | 188.974i | −0.197259 | + | 0.197259i | ||||
\(959\) | − | 1881.83i | − | 1.96228i | ||||||
\(960\) | 61.2202 | + | 32.4359i | 0.0637710 | + | 0.0337874i | ||||
\(961\) | 1118.53 | 1.16392 | ||||||||
\(962\) | 427.957 | + | 427.957i | 0.444862 | + | 0.444862i | ||||
\(963\) | 72.6757 | − | 72.6757i | 0.0754680 | − | 0.0754680i | ||||
\(964\) | − | 753.633i | − | 0.781777i | ||||||
\(965\) | 688.200 | − | 1298.92i | 0.713160 | − | 1.34603i | ||||
\(966\) | 142.465 | 0.147479 | ||||||||
\(967\) | 6.96638 | + | 6.96638i | 0.00720412 | + | 0.00720412i | 0.710700 | − | 0.703496i | \(-0.248378\pi\) |
−0.703496 | + | 0.710700i | \(0.748378\pi\) | |||||||
\(968\) | −185.070 | + | 185.070i | −0.191188 | + | 0.191188i | ||||
\(969\) | 1083.50i | 1.11817i | ||||||||
\(970\) | −385.287 | − | 1253.62i | −0.397203 | − | 1.29239i | ||||
\(971\) | −717.031 | −0.738445 | −0.369223 | − | 0.929341i | \(-0.620376\pi\) | ||||
−0.369223 | + | 0.929341i | \(0.620376\pi\) | |||||||
\(972\) | 22.0454 | + | 22.0454i | 0.0226805 | + | 0.0226805i | ||||
\(973\) | 2052.56 | − | 2052.56i | 2.10951 | − | 2.10951i | ||||
\(974\) | 812.079i | 0.833756i | ||||||||
\(975\) | 324.703 | + | 478.350i | 0.333029 | + | 0.490615i | ||||
\(976\) | −401.641 | −0.411518 | ||||||||
\(977\) | −286.202 | − | 286.202i | −0.292939 | − | 0.292939i | 0.545301 | − | 0.838240i | \(-0.316415\pi\) |
−0.838240 | + | 0.545301i | \(0.816415\pi\) | |||||||
\(978\) | 145.853 | − | 145.853i | 0.149134 | − | 0.149134i | ||||
\(979\) | 618.472i | 0.631738i | ||||||||
\(980\) | −937.469 | + | 288.122i | −0.956601 | + | 0.294002i | ||||
\(981\) | −101.301 | −0.103263 | ||||||||
\(982\) | 388.154 | + | 388.154i | 0.395269 | + | 0.395269i | ||||
\(983\) | 797.147 | − | 797.147i | 0.810933 | − | 0.810933i | −0.173841 | − | 0.984774i | \(-0.555618\pi\) |
0.984774 | + | 0.173841i | \(0.0556178\pi\) | |||||||
\(984\) | 134.491i | 0.136678i | ||||||||
\(985\) | −1509.64 | − | 799.842i | −1.53263 | − | 0.812022i | ||||
\(986\) | 1370.11 | 1.38956 | ||||||||
\(987\) | 1277.50 | + | 1277.50i | 1.29433 | + | 1.29433i | ||||
\(988\) | 527.102 | − | 527.102i | 0.533504 | − | 0.533504i | ||||
\(989\) | 17.7233i | 0.0179204i | ||||||||
\(990\) | −52.9868 | + | 100.008i | −0.0535220 | + | 0.101018i | ||||
\(991\) | −1155.41 | −1.16590 | −0.582949 | − | 0.812509i | \(-0.698101\pi\) | ||||
−0.582949 | + | 0.812509i | \(0.698101\pi\) | |||||||
\(992\) | −182.407 | − | 182.407i | −0.183878 | − | 0.183878i | ||||
\(993\) | 389.607 | − | 389.607i | 0.392354 | − | 0.392354i | ||||
\(994\) | − | 1259.85i | − | 1.26745i | ||||||
\(995\) | 319.535 | + | 1039.68i | 0.321141 | + | 1.04490i | ||||
\(996\) | −148.497 | −0.149093 | ||||||||
\(997\) | −264.992 | − | 264.992i | −0.265789 | − | 0.265789i | 0.561612 | − | 0.827401i | \(-0.310181\pi\) |
−0.827401 | + | 0.561612i | \(0.810181\pi\) | |||||||
\(998\) | −536.161 | + | 536.161i | −0.537235 | + | 0.537235i | ||||
\(999\) | − | 166.551i | − | 0.166718i |
(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.k.b.277.1 | ✓ | 48 | |
5.3 | odd | 4 | inner | 690.3.k.b.553.1 | yes | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
690.3.k.b.277.1 | ✓ | 48 | 1.1 | even | 1 | trivial | |
690.3.k.b.553.1 | yes | 48 | 5.3 | odd | 4 | inner |