Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [177,3,Mod(119,177)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(177, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("177.119");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 177 = 3 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 177.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: | \(4.82290067918\) |
Analytic rank: | \(0\) |
Dimension: | \(38\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 119.31 | ||
Character | \(\chi\) | \(=\) | 177.119 |
Dual form | 177.3.b.a.119.8 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/177\mathbb{Z}\right)^\times\).
\(n\) | \(61\) | \(119\) |
\(\chi(n)\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.79604i | 1.39802i | 0.715112 | + | 0.699010i | \(0.246376\pi\) | ||||
−0.715112 | + | 0.699010i | \(0.753624\pi\) | |||||||
\(3\) | 0.651071 | + | 2.92850i | 0.217024 | + | 0.976166i | ||||
\(4\) | −3.81783 | −0.954458 | ||||||||
\(5\) | 4.04341i | 0.808683i | 0.914608 | + | 0.404341i | \(0.132499\pi\) | ||||
−0.914608 | + | 0.404341i | \(0.867501\pi\) | |||||||
\(6\) | −8.18820 | + | 1.82042i | −1.36470 | + | 0.303403i | ||||
\(7\) | 6.95609 | 0.993727 | 0.496864 | − | 0.867829i | \(-0.334485\pi\) | ||||
0.496864 | + | 0.867829i | \(0.334485\pi\) | |||||||
\(8\) | 0.509352i | 0.0636690i | ||||||||
\(9\) | −8.15221 | + | 3.81332i | −0.905801 | + | 0.423703i | ||||
\(10\) | −11.3055 | −1.13055 | ||||||||
\(11\) | − | 3.60723i | − | 0.327930i | −0.986466 | − | 0.163965i | \(-0.947572\pi\) | ||
0.986466 | − | 0.163965i | \(-0.0524284\pi\) | |||||||
\(12\) | −2.48568 | − | 11.1805i | −0.207140 | − | 0.931709i | ||||
\(13\) | 6.03188 | 0.463990 | 0.231995 | − | 0.972717i | \(-0.425475\pi\) | ||||
0.231995 | + | 0.972717i | \(0.425475\pi\) | |||||||
\(14\) | 19.4495i | 1.38925i | ||||||||
\(15\) | −11.8411 | + | 2.63255i | −0.789409 | + | 0.175503i | ||||
\(16\) | −16.6955 | −1.04347 | ||||||||
\(17\) | − | 27.5797i | − | 1.62234i | −0.584813 | − | 0.811168i | \(-0.698832\pi\) | ||
0.584813 | − | 0.811168i | \(-0.301168\pi\) | |||||||
\(18\) | −10.6622 | − | 22.7939i | −0.592344 | − | 1.26633i | ||||
\(19\) | 11.5320 | 0.606948 | 0.303474 | − | 0.952840i | \(-0.401854\pi\) | ||||
0.303474 | + | 0.952840i | \(0.401854\pi\) | |||||||
\(20\) | − | 15.4371i | − | 0.771854i | ||||||
\(21\) | 4.52891 | + | 20.3709i | 0.215662 | + | 0.970043i | ||||
\(22\) | 10.0859 | 0.458452 | ||||||||
\(23\) | 6.63792i | 0.288605i | 0.989534 | + | 0.144303i | \(0.0460939\pi\) | ||||
−0.989534 | + | 0.144303i | \(0.953906\pi\) | |||||||
\(24\) | −1.49164 | + | 0.331625i | −0.0621515 | + | 0.0138177i | ||||
\(25\) | 8.65080 | 0.346032 | ||||||||
\(26\) | 16.8654i | 0.648667i | ||||||||
\(27\) | −16.4750 | − | 21.3910i | −0.610185 | − | 0.792259i | ||||
\(28\) | −26.5572 | −0.948470 | ||||||||
\(29\) | − | 7.59974i | − | 0.262060i | −0.991378 | − | 0.131030i | \(-0.958172\pi\) | ||
0.991378 | − | 0.131030i | \(-0.0418284\pi\) | |||||||
\(30\) | −7.36072 | − | 33.1083i | −0.245357 | − | 1.10361i | ||||
\(31\) | 40.0199 | 1.29096 | 0.645482 | − | 0.763776i | \(-0.276657\pi\) | ||||
0.645482 | + | 0.763776i | \(0.276657\pi\) | |||||||
\(32\) | − | 44.6438i | − | 1.39512i | ||||||
\(33\) | 10.5638 | − | 2.34856i | 0.320114 | − | 0.0711685i | ||||
\(34\) | 77.1139 | 2.26806 | ||||||||
\(35\) | 28.1264i | 0.803610i | ||||||||
\(36\) | 31.1238 | − | 14.5586i | 0.864549 | − | 0.404406i | ||||
\(37\) | −53.5956 | −1.44853 | −0.724264 | − | 0.689522i | \(-0.757820\pi\) | ||||
−0.724264 | + | 0.689522i | \(0.757820\pi\) | |||||||
\(38\) | 32.2439i | 0.848524i | ||||||||
\(39\) | 3.92718 | + | 17.6643i | 0.100697 | + | 0.452932i | ||||
\(40\) | −2.05952 | −0.0514880 | ||||||||
\(41\) | 33.0823i | 0.806885i | 0.915005 | + | 0.403442i | \(0.132186\pi\) | ||||
−0.915005 | + | 0.403442i | \(0.867814\pi\) | |||||||
\(42\) | −56.9578 | + | 12.6630i | −1.35614 | + | 0.301500i | ||||
\(43\) | −19.3543 | −0.450099 | −0.225049 | − | 0.974347i | \(-0.572254\pi\) | ||||
−0.225049 | + | 0.974347i | \(0.572254\pi\) | |||||||
\(44\) | 13.7718i | 0.312995i | ||||||||
\(45\) | −15.4188 | − | 32.9628i | −0.342641 | − | 0.732506i | ||||
\(46\) | −18.5599 | −0.403476 | ||||||||
\(47\) | 51.4877i | 1.09548i | 0.836647 | + | 0.547742i | \(0.184512\pi\) | ||||
−0.836647 | + | 0.547742i | \(0.815488\pi\) | |||||||
\(48\) | −10.8700 | − | 48.8927i | −0.226457 | − | 1.01860i | ||||
\(49\) | −0.612818 | −0.0125065 | ||||||||
\(50\) | 24.1880i | 0.483759i | ||||||||
\(51\) | 80.7671 | − | 17.9564i | 1.58367 | − | 0.352085i | ||||
\(52\) | −23.0287 | −0.442859 | ||||||||
\(53\) | 40.9324i | 0.772309i | 0.922434 | + | 0.386155i | \(0.126197\pi\) | ||||
−0.922434 | + | 0.386155i | \(0.873803\pi\) | |||||||
\(54\) | 59.8101 | − | 46.0647i | 1.10759 | − | 0.853050i | ||||
\(55\) | 14.5855 | 0.265191 | ||||||||
\(56\) | 3.54310i | 0.0632696i | ||||||||
\(57\) | 7.50816 | + | 33.7715i | 0.131722 | + | 0.592482i | ||||
\(58\) | 21.2492 | 0.366365 | ||||||||
\(59\) | − | 7.68115i | − | 0.130189i | ||||||
\(60\) | 45.2075 | − | 10.0506i | 0.753458 | − | 0.167511i | ||||
\(61\) | 48.9309 | 0.802146 | 0.401073 | − | 0.916046i | \(-0.368637\pi\) | ||||
0.401073 | + | 0.916046i | \(0.368637\pi\) | |||||||
\(62\) | 111.897i | 1.80479i | ||||||||
\(63\) | −56.7075 | + | 26.5258i | −0.900119 | + | 0.421045i | ||||
\(64\) | 58.0439 | 0.906936 | ||||||||
\(65\) | 24.3894i | 0.375221i | ||||||||
\(66\) | 6.56667 | + | 29.5367i | 0.0994950 | + | 0.447525i | ||||
\(67\) | 85.3697 | 1.27417 | 0.637087 | − | 0.770792i | \(-0.280139\pi\) | ||||
0.637087 | + | 0.770792i | \(0.280139\pi\) | |||||||
\(68\) | 105.295i | 1.54845i | ||||||||
\(69\) | −19.4391 | + | 4.32176i | −0.281727 | + | 0.0626342i | ||||
\(70\) | −78.6424 | −1.12346 | ||||||||
\(71\) | 32.2458i | 0.454166i | 0.973875 | + | 0.227083i | \(0.0729188\pi\) | ||||
−0.973875 | + | 0.227083i | \(0.927081\pi\) | |||||||
\(72\) | −1.94232 | − | 4.15235i | −0.0269767 | − | 0.0576715i | ||||
\(73\) | 71.6167 | 0.981050 | 0.490525 | − | 0.871427i | \(-0.336805\pi\) | ||||
0.490525 | + | 0.871427i | \(0.336805\pi\) | |||||||
\(74\) | − | 149.855i | − | 2.02507i | ||||||
\(75\) | 5.63229 | + | 25.3339i | 0.0750972 | + | 0.337785i | ||||
\(76\) | −44.0272 | −0.579306 | ||||||||
\(77\) | − | 25.0922i | − | 0.325873i | ||||||
\(78\) | −49.3902 | + | 10.9806i | −0.633207 | + | 0.140776i | ||||
\(79\) | −85.8602 | −1.08684 | −0.543419 | − | 0.839462i | \(-0.682871\pi\) | ||||
−0.543419 | + | 0.839462i | \(0.682871\pi\) | |||||||
\(80\) | − | 67.5068i | − | 0.843835i | ||||||
\(81\) | 51.9171 | − | 62.1741i | 0.640952 | − | 0.767581i | ||||
\(82\) | −92.4993 | −1.12804 | ||||||||
\(83\) | − | 131.770i | − | 1.58759i | −0.608185 | − | 0.793795i | \(-0.708102\pi\) | ||
0.608185 | − | 0.793795i | \(-0.291898\pi\) | |||||||
\(84\) | −17.2906 | − | 77.7727i | −0.205841 | − | 0.925865i | ||||
\(85\) | 111.516 | 1.31196 | ||||||||
\(86\) | − | 54.1152i | − | 0.629247i | ||||||
\(87\) | 22.2558 | − | 4.94797i | 0.255814 | − | 0.0568732i | ||||
\(88\) | 1.83735 | 0.0208790 | ||||||||
\(89\) | 96.1523i | 1.08036i | 0.841549 | + | 0.540182i | \(0.181644\pi\) | ||||
−0.841549 | + | 0.540182i | \(0.818356\pi\) | |||||||
\(90\) | 92.1652 | − | 43.1117i | 1.02406 | − | 0.479019i | ||||
\(91\) | 41.9583 | 0.461080 | ||||||||
\(92\) | − | 25.3425i | − | 0.275462i | ||||||
\(93\) | 26.0558 | + | 117.198i | 0.280170 | + | 1.26019i | ||||
\(94\) | −143.962 | −1.53151 | ||||||||
\(95\) | 46.6287i | 0.490828i | ||||||||
\(96\) | 130.739 | − | 29.0663i | 1.36187 | − | 0.302774i | ||||
\(97\) | −80.8331 | −0.833331 | −0.416665 | − | 0.909060i | \(-0.636801\pi\) | ||||
−0.416665 | + | 0.909060i | \(0.636801\pi\) | |||||||
\(98\) | − | 1.71346i | − | 0.0174843i | ||||||
\(99\) | 13.7555 | + | 29.4069i | 0.138945 | + | 0.297039i | ||||
\(100\) | −33.0273 | −0.330273 | ||||||||
\(101\) | − | 106.431i | − | 1.05378i | −0.849935 | − | 0.526888i | \(-0.823359\pi\) | ||
0.849935 | − | 0.526888i | \(-0.176641\pi\) | |||||||
\(102\) | 50.2067 | + | 225.828i | 0.492222 | + | 2.21400i | ||||
\(103\) | −98.8938 | −0.960134 | −0.480067 | − | 0.877232i | \(-0.659388\pi\) | ||||
−0.480067 | + | 0.877232i | \(0.659388\pi\) | |||||||
\(104\) | 3.07235i | 0.0295418i | ||||||||
\(105\) | −82.3680 | + | 18.3123i | −0.784457 | + | 0.174403i | ||||
\(106\) | −114.449 | −1.07970 | ||||||||
\(107\) | − | 170.612i | − | 1.59451i | −0.603645 | − | 0.797253i | \(-0.706286\pi\) | ||
0.603645 | − | 0.797253i | \(-0.293714\pi\) | |||||||
\(108\) | 62.8987 | + | 81.6672i | 0.582396 | + | 0.756178i | ||||
\(109\) | 158.872 | 1.45754 | 0.728769 | − | 0.684760i | \(-0.240093\pi\) | ||||
0.728769 | + | 0.684760i | \(0.240093\pi\) | |||||||
\(110\) | 40.7817i | 0.370742i | ||||||||
\(111\) | −34.8945 | − | 156.955i | −0.314365 | − | 1.41400i | ||||
\(112\) | −116.135 | −1.03692 | ||||||||
\(113\) | − | 122.753i | − | 1.08631i | −0.839632 | − | 0.543156i | \(-0.817229\pi\) | ||
0.839632 | − | 0.543156i | \(-0.182771\pi\) | |||||||
\(114\) | −94.4263 | + | 20.9931i | −0.828301 | + | 0.184150i | ||||
\(115\) | −26.8399 | −0.233390 | ||||||||
\(116\) | 29.0145i | 0.250125i | ||||||||
\(117\) | −49.1731 | + | 23.0015i | −0.420283 | + | 0.196594i | ||||
\(118\) | 21.4768 | 0.182007 | ||||||||
\(119\) | − | 191.847i | − | 1.61216i | ||||||
\(120\) | −1.34090 | − | 6.03131i | −0.0111741 | − | 0.0502609i | ||||
\(121\) | 107.988 | 0.892462 | ||||||||
\(122\) | 136.813i | 1.12142i | ||||||||
\(123\) | −96.8814 | + | 21.5389i | −0.787654 | + | 0.175113i | ||||
\(124\) | −152.789 | −1.23217 | ||||||||
\(125\) | 136.064i | 1.08851i | ||||||||
\(126\) | −74.1672 | − | 158.556i | −0.588629 | − | 1.25838i | ||||
\(127\) | −158.076 | −1.24469 | −0.622347 | − | 0.782742i | \(-0.713821\pi\) | ||||
−0.622347 | + | 0.782742i | \(0.713821\pi\) | |||||||
\(128\) | − | 16.2824i | − | 0.127206i | ||||||
\(129\) | −12.6010 | − | 56.6789i | −0.0976822 | − | 0.439371i | ||||
\(130\) | −68.1936 | −0.524566 | ||||||||
\(131\) | − | 164.456i | − | 1.25539i | −0.778459 | − | 0.627696i | \(-0.783998\pi\) | ||
0.778459 | − | 0.627696i | \(-0.216002\pi\) | |||||||
\(132\) | −40.3306 | + | 8.96641i | −0.305535 | + | 0.0679274i | ||||
\(133\) | 80.2176 | 0.603140 | ||||||||
\(134\) | 238.697i | 1.78132i | ||||||||
\(135\) | 86.4927 | − | 66.6152i | 0.640686 | − | 0.493446i | ||||
\(136\) | 14.0478 | 0.103292 | ||||||||
\(137\) | 215.202i | 1.57082i | 0.618977 | + | 0.785409i | \(0.287547\pi\) | ||||
−0.618977 | + | 0.785409i | \(0.712453\pi\) | |||||||
\(138\) | −12.0838 | − | 54.3526i | −0.0875638 | − | 0.393859i | ||||
\(139\) | −74.2004 | −0.533816 | −0.266908 | − | 0.963722i | \(-0.586002\pi\) | ||||
−0.266908 | + | 0.963722i | \(0.586002\pi\) | |||||||
\(140\) | − | 107.382i | − | 0.767012i | ||||||
\(141\) | −150.782 | + | 33.5222i | −1.06937 | + | 0.237746i | ||||
\(142\) | −90.1604 | −0.634932 | ||||||||
\(143\) | − | 21.7583i | − | 0.152156i | ||||||
\(144\) | 136.105 | − | 63.6653i | 0.945175 | − | 0.442120i | ||||
\(145\) | 30.7289 | 0.211923 | ||||||||
\(146\) | 200.243i | 1.37153i | ||||||||
\(147\) | −0.398988 | − | 1.79464i | −0.00271420 | − | 0.0122084i | ||||
\(148\) | 204.619 | 1.38256 | ||||||||
\(149\) | − | 241.103i | − | 1.61814i | −0.587711 | − | 0.809071i | \(-0.699971\pi\) | ||
0.587711 | − | 0.809071i | \(-0.300029\pi\) | |||||||
\(150\) | −70.8344 | + | 15.7481i | −0.472230 | + | 0.104987i | ||||
\(151\) | 30.4950 | 0.201954 | 0.100977 | − | 0.994889i | \(-0.467803\pi\) | ||||
0.100977 | + | 0.994889i | \(0.467803\pi\) | |||||||
\(152\) | 5.87385i | 0.0386437i | ||||||||
\(153\) | 105.170 | + | 224.836i | 0.687388 | + | 1.46951i | ||||
\(154\) | 70.1587 | 0.455576 | ||||||||
\(155\) | 161.817i | 1.04398i | ||||||||
\(156\) | −14.9933 | − | 67.4395i | −0.0961110 | − | 0.432304i | ||||
\(157\) | 65.8024 | 0.419124 | 0.209562 | − | 0.977795i | \(-0.432796\pi\) | ||||
0.209562 | + | 0.977795i | \(0.432796\pi\) | |||||||
\(158\) | − | 240.068i | − | 1.51942i | ||||||
\(159\) | −119.870 | + | 26.6499i | −0.753902 | + | 0.167609i | ||||
\(160\) | 180.513 | 1.12821 | ||||||||
\(161\) | 46.1740i | 0.286795i | ||||||||
\(162\) | 173.841 | + | 145.162i | 1.07309 | + | 0.896063i | ||||
\(163\) | −71.4607 | −0.438409 | −0.219205 | − | 0.975679i | \(-0.570346\pi\) | ||||
−0.219205 | + | 0.975679i | \(0.570346\pi\) | |||||||
\(164\) | − | 126.303i | − | 0.770137i | ||||||
\(165\) | 9.49621 | + | 42.7137i | 0.0575528 | + | 0.258871i | ||||
\(166\) | 368.434 | 2.21948 | ||||||||
\(167\) | − | 94.7545i | − | 0.567392i | −0.958914 | − | 0.283696i | \(-0.908439\pi\) | ||
0.958914 | − | 0.283696i | \(-0.0915607\pi\) | |||||||
\(168\) | −10.3760 | + | 2.30681i | −0.0617617 | + | 0.0137310i | ||||
\(169\) | −132.616 | −0.784713 | ||||||||
\(170\) | 311.804i | 1.83414i | ||||||||
\(171\) | −94.0113 | + | 43.9753i | −0.549774 | + | 0.257165i | ||||
\(172\) | 73.8913 | 0.429600 | ||||||||
\(173\) | − | 92.2355i | − | 0.533153i | −0.963814 | − | 0.266576i | \(-0.914108\pi\) | ||
0.963814 | − | 0.266576i | \(-0.0858925\pi\) | |||||||
\(174\) | 13.8347 | + | 62.2281i | 0.0795099 | + | 0.357633i | ||||
\(175\) | 60.1757 | 0.343861 | ||||||||
\(176\) | 60.2244i | 0.342184i | ||||||||
\(177\) | 22.4942 | − | 5.00097i | 0.127086 | − | 0.0282541i | ||||
\(178\) | −268.846 | −1.51037 | ||||||||
\(179\) | 48.5009i | 0.270955i | 0.990780 | + | 0.135477i | \(0.0432568\pi\) | ||||
−0.990780 | + | 0.135477i | \(0.956743\pi\) | |||||||
\(180\) | 58.8666 | + | 125.846i | 0.327036 | + | 0.699146i | ||||
\(181\) | 177.194 | 0.978975 | 0.489487 | − | 0.872010i | \(-0.337184\pi\) | ||||
0.489487 | + | 0.872010i | \(0.337184\pi\) | |||||||
\(182\) | 117.317i | 0.644598i | ||||||||
\(183\) | 31.8575 | + | 143.294i | 0.174085 | + | 0.783028i | ||||
\(184\) | −3.38104 | −0.0183752 | ||||||||
\(185\) | − | 216.709i | − | 1.17140i | ||||||
\(186\) | −327.690 | + | 72.8530i | −1.76178 | + | 0.391683i | ||||
\(187\) | −99.4863 | −0.532012 | ||||||||
\(188\) | − | 196.572i | − | 1.04559i | ||||||
\(189\) | −114.601 | − | 148.798i | −0.606357 | − | 0.787289i | ||||
\(190\) | −130.376 | −0.686187 | ||||||||
\(191\) | 137.245i | 0.718559i | 0.933230 | + | 0.359279i | \(0.116977\pi\) | ||||
−0.933230 | + | 0.359279i | \(0.883023\pi\) | |||||||
\(192\) | 37.7907 | + | 169.981i | 0.196827 | + | 0.885320i | ||||
\(193\) | 363.765 | 1.88479 | 0.942396 | − | 0.334499i | \(-0.108567\pi\) | ||||
0.942396 | + | 0.334499i | \(0.108567\pi\) | |||||||
\(194\) | − | 226.012i | − | 1.16501i | ||||||
\(195\) | −71.4242 | + | 15.8792i | −0.366278 | + | 0.0814319i | ||||
\(196\) | 2.33963 | 0.0119369 | ||||||||
\(197\) | 117.106i | 0.594445i | 0.954808 | + | 0.297223i | \(0.0960603\pi\) | ||||
−0.954808 | + | 0.297223i | \(0.903940\pi\) | |||||||
\(198\) | −82.2228 | + | 38.4610i | −0.415266 | + | 0.194247i | ||||
\(199\) | −176.062 | −0.884732 | −0.442366 | − | 0.896835i | \(-0.645861\pi\) | ||||
−0.442366 | + | 0.896835i | \(0.645861\pi\) | |||||||
\(200\) | 4.40630i | 0.0220315i | ||||||||
\(201\) | 55.5818 | + | 250.005i | 0.276526 | + | 1.24381i | ||||
\(202\) | 297.586 | 1.47320 | ||||||||
\(203\) | − | 52.8645i | − | 0.260416i | ||||||
\(204\) | −308.355 | + | 68.5543i | −1.51155 | + | 0.336051i | ||||
\(205\) | −133.765 | −0.652514 | ||||||||
\(206\) | − | 276.511i | − | 1.34229i | ||||||
\(207\) | −25.3125 | − | 54.1137i | −0.122283 | − | 0.261419i | ||||
\(208\) | −100.705 | −0.484159 | ||||||||
\(209\) | − | 41.5985i | − | 0.199036i | ||||||
\(210\) | −51.2018 | − | 230.304i | −0.243818 | − | 1.09669i | ||||
\(211\) | 9.09339 | 0.0430966 | 0.0215483 | − | 0.999768i | \(-0.493140\pi\) | ||||
0.0215483 | + | 0.999768i | \(0.493140\pi\) | |||||||
\(212\) | − | 156.273i | − | 0.737136i | ||||||
\(213\) | −94.4317 | + | 20.9943i | −0.443341 | + | 0.0985648i | ||||
\(214\) | 477.038 | 2.22915 | ||||||||
\(215\) | − | 78.2573i | − | 0.363987i | ||||||
\(216\) | 10.8955 | − | 8.39157i | 0.0504423 | − | 0.0388498i | ||||
\(217\) | 278.382 | 1.28287 | ||||||||
\(218\) | 444.211i | 2.03767i | ||||||||
\(219\) | 46.6276 | + | 209.729i | 0.212911 | + | 0.957668i | ||||
\(220\) | −55.6850 | −0.253114 | ||||||||
\(221\) | − | 166.357i | − | 0.752748i | ||||||
\(222\) | 438.851 | − | 97.5665i | 1.97681 | − | 0.439489i | ||||
\(223\) | 244.350 | 1.09574 | 0.547869 | − | 0.836564i | \(-0.315439\pi\) | ||||
0.547869 | + | 0.836564i | \(0.315439\pi\) | |||||||
\(224\) | − | 310.546i | − | 1.38637i | ||||||
\(225\) | −70.5232 | + | 32.9883i | −0.313436 | + | 0.146615i | ||||
\(226\) | 343.223 | 1.51868 | ||||||||
\(227\) | − | 46.8646i | − | 0.206452i | −0.994658 | − | 0.103226i | \(-0.967084\pi\) | ||
0.994658 | − | 0.103226i | \(-0.0329165\pi\) | |||||||
\(228\) | −28.6649 | − | 128.934i | −0.125723 | − | 0.565499i | ||||
\(229\) | −142.421 | −0.621925 | −0.310963 | − | 0.950422i | \(-0.600651\pi\) | ||||
−0.310963 | + | 0.950422i | \(0.600651\pi\) | |||||||
\(230\) | − | 75.0453i | − | 0.326284i | ||||||
\(231\) | 73.4825 | − | 16.3368i | 0.318106 | − | 0.0707221i | ||||
\(232\) | 3.87094 | 0.0166851 | ||||||||
\(233\) | 226.548i | 0.972308i | 0.873873 | + | 0.486154i | \(0.161601\pi\) | ||||
−0.873873 | + | 0.486154i | \(0.838399\pi\) | |||||||
\(234\) | −64.3131 | − | 137.490i | −0.274842 | − | 0.587564i | ||||
\(235\) | −208.186 | −0.885899 | ||||||||
\(236\) | 29.3253i | 0.124260i | ||||||||
\(237\) | −55.9011 | − | 251.442i | −0.235870 | − | 1.06093i | ||||
\(238\) | 536.411 | 2.25383 | ||||||||
\(239\) | − | 50.3598i | − | 0.210711i | −0.994435 | − | 0.105355i | \(-0.966402\pi\) | ||
0.994435 | − | 0.105355i | \(-0.0335980\pi\) | |||||||
\(240\) | 197.694 | − | 43.9517i | 0.823723 | − | 0.183132i | ||||
\(241\) | −252.513 | −1.04777 | −0.523887 | − | 0.851788i | \(-0.675519\pi\) | ||||
−0.523887 | + | 0.851788i | \(0.675519\pi\) | |||||||
\(242\) | 301.938i | 1.24768i | ||||||||
\(243\) | 215.878 | + | 111.559i | 0.888388 | + | 0.459093i | ||||
\(244\) | −186.810 | −0.765614 | ||||||||
\(245\) | − | 2.47788i | − | 0.0101138i | ||||||
\(246\) | −60.2237 | − | 270.884i | −0.244812 | − | 1.10116i | ||||
\(247\) | 69.5596 | 0.281618 | ||||||||
\(248\) | 20.3842i | 0.0821943i | ||||||||
\(249\) | 385.888 | − | 85.7917i | 1.54975 | − | 0.344545i | ||||
\(250\) | −380.441 | −1.52176 | ||||||||
\(251\) | 115.362i | 0.459610i | 0.973237 | + | 0.229805i | \(0.0738088\pi\) | ||||
−0.973237 | + | 0.229805i | \(0.926191\pi\) | |||||||
\(252\) | 216.500 | − | 101.271i | 0.859126 | − | 0.401869i | ||||
\(253\) | 23.9445 | 0.0946422 | ||||||||
\(254\) | − | 441.987i | − | 1.74011i | ||||||
\(255\) | 72.6050 | + | 326.575i | 0.284726 | + | 1.28069i | ||||
\(256\) | 277.702 | 1.08477 | ||||||||
\(257\) | − | 67.7037i | − | 0.263439i | −0.991287 | − | 0.131719i | \(-0.957950\pi\) | ||
0.991287 | − | 0.131719i | \(-0.0420498\pi\) | |||||||
\(258\) | 158.476 | − | 35.2329i | 0.614250 | − | 0.136562i | ||||
\(259\) | −372.816 | −1.43944 | ||||||||
\(260\) | − | 93.1145i | − | 0.358133i | ||||||
\(261\) | 28.9803 | + | 61.9547i | 0.111035 | + | 0.237374i | ||||
\(262\) | 459.826 | 1.75506 | ||||||||
\(263\) | − | 295.997i | − | 1.12546i | −0.826639 | − | 0.562732i | \(-0.809750\pi\) | ||
0.826639 | − | 0.562732i | \(-0.190250\pi\) | |||||||
\(264\) | 1.19624 | + | 5.38067i | 0.00453123 | + | 0.0203813i | ||||
\(265\) | −165.507 | −0.624553 | ||||||||
\(266\) | 224.292i | 0.843202i | ||||||||
\(267\) | −281.582 | + | 62.6020i | −1.05461 | + | 0.234465i | ||||
\(268\) | −325.927 | −1.21615 | ||||||||
\(269\) | − | 446.809i | − | 1.66100i | −0.557019 | − | 0.830500i | \(-0.688055\pi\) | ||
0.557019 | − | 0.830500i | \(-0.311945\pi\) | |||||||
\(270\) | 186.259 | + | 241.837i | 0.689847 | + | 0.895692i | ||||
\(271\) | 111.864 | 0.412781 | 0.206391 | − | 0.978470i | \(-0.433828\pi\) | ||||
0.206391 | + | 0.978470i | \(0.433828\pi\) | |||||||
\(272\) | 460.457i | 1.69286i | ||||||||
\(273\) | 27.3178 | + | 122.875i | 0.100065 | + | 0.450091i | ||||
\(274\) | −601.713 | −2.19603 | ||||||||
\(275\) | − | 31.2054i | − | 0.113474i | ||||||
\(276\) | 74.2154 | − | 16.4998i | 0.268896 | − | 0.0597817i | ||||
\(277\) | −245.137 | −0.884970 | −0.442485 | − | 0.896776i | \(-0.645903\pi\) | ||||
−0.442485 | + | 0.896776i | \(0.645903\pi\) | |||||||
\(278\) | − | 207.467i | − | 0.746285i | ||||||
\(279\) | −326.250 | + | 152.609i | −1.16936 | + | 0.546985i | ||||
\(280\) | −14.3262 | −0.0511650 | ||||||||
\(281\) | 197.586i | 0.703153i | 0.936159 | + | 0.351576i | \(0.114354\pi\) | ||||
−0.936159 | + | 0.351576i | \(0.885646\pi\) | |||||||
\(282\) | −93.7294 | − | 421.592i | −0.332374 | − | 1.49501i | ||||
\(283\) | −355.505 | −1.25620 | −0.628101 | − | 0.778132i | \(-0.716168\pi\) | ||||
−0.628101 | + | 0.778132i | \(0.716168\pi\) | |||||||
\(284\) | − | 123.109i | − | 0.433482i | ||||||
\(285\) | −136.552 | + | 30.3586i | −0.479130 | + | 0.106521i | ||||
\(286\) | 60.8372 | 0.212717 | ||||||||
\(287\) | 230.123i | 0.801823i | ||||||||
\(288\) | 170.241 | + | 363.946i | 0.591116 | + | 1.26370i | ||||
\(289\) | −471.640 | −1.63197 | ||||||||
\(290\) | 85.9192i | 0.296273i | ||||||||
\(291\) | −52.6281 | − | 236.720i | −0.180853 | − | 0.813469i | ||||
\(292\) | −273.420 | −0.936371 | ||||||||
\(293\) | 438.814i | 1.49766i | 0.662762 | + | 0.748830i | \(0.269384\pi\) | ||||
−0.662762 | + | 0.748830i | \(0.730616\pi\) | |||||||
\(294\) | 5.01787 | − | 1.11559i | 0.0170676 | − | 0.00379451i | ||||
\(295\) | 31.0581 | 0.105282 | ||||||||
\(296\) | − | 27.2990i | − | 0.0922264i | ||||||
\(297\) | −77.1622 | + | 59.4290i | −0.259805 | + | 0.200098i | ||||
\(298\) | 674.134 | 2.26219 | ||||||||
\(299\) | 40.0391i | 0.133910i | ||||||||
\(300\) | −21.5031 | − | 96.7204i | −0.0716771 | − | 0.322401i | ||||
\(301\) | −134.630 | −0.447276 | ||||||||
\(302\) | 85.2652i | 0.282335i | ||||||||
\(303\) | 311.684 | − | 69.2944i | 1.02866 | − | 0.228694i | ||||
\(304\) | −192.532 | −0.633330 | ||||||||
\(305\) | 197.848i | 0.648682i | ||||||||
\(306\) | −628.649 | + | 294.060i | −2.05441 | + | 0.960982i | ||||
\(307\) | −519.064 | −1.69076 | −0.845381 | − | 0.534163i | \(-0.820627\pi\) | ||||
−0.845381 | + | 0.534163i | \(0.820627\pi\) | |||||||
\(308\) | 95.7977i | 0.311032i | ||||||||
\(309\) | −64.3869 | − | 289.610i | −0.208372 | − | 0.937250i | ||||
\(310\) | −452.446 | −1.45950 | ||||||||
\(311\) | 327.149i | 1.05193i | 0.850507 | + | 0.525963i | \(0.176295\pi\) | ||||
−0.850507 | + | 0.525963i | \(0.823705\pi\) | |||||||
\(312\) | −8.99737 | + | 2.00032i | −0.0288377 | + | 0.00641127i | ||||
\(313\) | −309.990 | −0.990383 | −0.495191 | − | 0.868784i | \(-0.664902\pi\) | ||||
−0.495191 | + | 0.868784i | \(0.664902\pi\) | |||||||
\(314\) | 183.986i | 0.585943i | ||||||||
\(315\) | −107.255 | − | 229.292i | −0.340492 | − | 0.727911i | ||||
\(316\) | 327.800 | 1.03734 | ||||||||
\(317\) | 335.223i | 1.05749i | 0.848782 | + | 0.528743i | \(0.177336\pi\) | ||||
−0.848782 | + | 0.528743i | \(0.822664\pi\) | |||||||
\(318\) | −74.5142 | − | 335.162i | −0.234321 | − | 1.05397i | ||||
\(319\) | −27.4140 | −0.0859372 | ||||||||
\(320\) | 234.696i | 0.733423i | ||||||||
\(321\) | 499.637 | − | 111.081i | 1.55650 | − | 0.346046i | ||||
\(322\) | −129.104 | −0.400945 | ||||||||
\(323\) | − | 318.049i | − | 0.984673i | ||||||
\(324\) | −198.211 | + | 237.370i | −0.611762 | + | 0.732623i | ||||
\(325\) | 52.1805 | 0.160556 | ||||||||
\(326\) | − | 199.807i | − | 0.612904i | ||||||
\(327\) | 103.437 | + | 465.255i | 0.316320 | + | 1.42280i | ||||
\(328\) | −16.8505 | −0.0513735 | ||||||||
\(329\) | 358.153i | 1.08861i | ||||||||
\(330\) | −119.429 | + | 26.5518i | −0.361906 | + | 0.0804599i | ||||
\(331\) | 379.087 | 1.14528 | 0.572639 | − | 0.819808i | \(-0.305920\pi\) | ||||
0.572639 | + | 0.819808i | \(0.305920\pi\) | |||||||
\(332\) | 503.076i | 1.51529i | ||||||||
\(333\) | 436.922 | − | 204.377i | 1.31208 | − | 0.613745i | ||||
\(334\) | 264.937 | 0.793225 | ||||||||
\(335\) | 345.185i | 1.03040i | ||||||||
\(336\) | −75.6124 | − | 340.102i | −0.225037 | − | 1.01221i | ||||
\(337\) | 308.875 | 0.916542 | 0.458271 | − | 0.888813i | \(-0.348469\pi\) | ||||
0.458271 | + | 0.888813i | \(0.348469\pi\) | |||||||
\(338\) | − | 370.801i | − | 1.09704i | ||||||
\(339\) | 359.483 | − | 79.9211i | 1.06042 | − | 0.235756i | ||||
\(340\) | −425.750 | −1.25221 | ||||||||
\(341\) | − | 144.361i | − | 0.423345i | ||||||
\(342\) | −122.957 | − | 262.859i | −0.359522 | − | 0.768594i | ||||
\(343\) | −345.111 | −1.00616 | ||||||||
\(344\) | − | 9.85813i | − | 0.0286573i | ||||||
\(345\) | −17.4747 | − | 78.6005i | −0.0506512 | − | 0.227828i | ||||
\(346\) | 257.894 | 0.745358 | ||||||||
\(347\) | − | 515.591i | − | 1.48585i | −0.669373 | − | 0.742926i | \(-0.733437\pi\) | ||
0.669373 | − | 0.742926i | \(-0.266563\pi\) | |||||||
\(348\) | −84.9690 | + | 18.8905i | −0.244164 | + | 0.0542831i | ||||
\(349\) | 540.605 | 1.54901 | 0.774506 | − | 0.632567i | \(-0.217999\pi\) | ||||
0.774506 | + | 0.632567i | \(0.217999\pi\) | |||||||
\(350\) | 168.254i | 0.480725i | ||||||||
\(351\) | −99.3751 | − | 129.028i | −0.283120 | − | 0.367601i | ||||
\(352\) | −161.040 | −0.457501 | ||||||||
\(353\) | 34.9577i | 0.0990304i | 0.998773 | + | 0.0495152i | \(0.0157676\pi\) | ||||
−0.998773 | + | 0.0495152i | \(0.984232\pi\) | |||||||
\(354\) | 13.9829 | + | 62.8947i | 0.0394998 | + | 0.177669i | ||||
\(355\) | −130.383 | −0.367276 | ||||||||
\(356\) | − | 367.093i | − | 1.03116i | ||||||
\(357\) | 561.823 | − | 124.906i | 1.57374 | − | 0.349877i | ||||
\(358\) | −135.610 | −0.378800 | ||||||||
\(359\) | − | 474.613i | − | 1.32204i | −0.750368 | − | 0.661021i | \(-0.770124\pi\) | ||
0.750368 | − | 0.661021i | \(-0.229876\pi\) | |||||||
\(360\) | 16.7897 | − | 7.85362i | 0.0466379 | − | 0.0218156i | ||||
\(361\) | −228.013 | −0.631615 | ||||||||
\(362\) | 495.442i | 1.36863i | ||||||||
\(363\) | 70.3078 | + | 316.242i | 0.193686 | + | 0.871191i | ||||
\(364\) | −160.190 | −0.440081 | ||||||||
\(365\) | 289.576i | 0.793359i | ||||||||
\(366\) | −400.656 | + | 89.0748i | −1.09469 | + | 0.243374i | ||||
\(367\) | −573.939 | −1.56387 | −0.781934 | − | 0.623362i | \(-0.785767\pi\) | ||||
−0.781934 | + | 0.623362i | \(0.785767\pi\) | |||||||
\(368\) | − | 110.823i | − | 0.301150i | ||||||
\(369\) | −126.153 | − | 269.694i | −0.341879 | − | 0.730877i | ||||
\(370\) | 605.927 | 1.63764 | ||||||||
\(371\) | 284.729i | 0.767465i | ||||||||
\(372\) | −99.4766 | − | 447.443i | −0.267410 | − | 1.20280i | ||||
\(373\) | 485.686 | 1.30211 | 0.651053 | − | 0.759032i | \(-0.274327\pi\) | ||||
0.651053 | + | 0.759032i | \(0.274327\pi\) | |||||||
\(374\) | − | 278.167i | − | 0.743763i | ||||||
\(375\) | −398.464 | + | 88.5875i | −1.06257 | + | 0.236233i | ||||
\(376\) | −26.2254 | −0.0697484 | ||||||||
\(377\) | − | 45.8407i | − | 0.121593i | ||||||
\(378\) | 416.044 | − | 320.430i | 1.10065 | − | 0.847699i | ||||
\(379\) | −599.727 | −1.58239 | −0.791196 | − | 0.611562i | \(-0.790541\pi\) | ||||
−0.791196 | + | 0.611562i | \(0.790541\pi\) | |||||||
\(380\) | − | 178.020i | − | 0.468475i | ||||||
\(381\) | −102.919 | − | 462.926i | −0.270128 | − | 1.21503i | ||||
\(382\) | −383.742 | −1.00456 | ||||||||
\(383\) | 51.7725i | 0.135176i | 0.997713 | + | 0.0675881i | \(0.0215304\pi\) | ||||
−0.997713 | + | 0.0675881i | \(0.978470\pi\) | |||||||
\(384\) | 47.6829 | − | 10.6010i | 0.124174 | − | 0.0276067i | ||||
\(385\) | 101.458 | 0.263528 | ||||||||
\(386\) | 1017.10i | 2.63498i | ||||||||
\(387\) | 157.780 | − | 73.8040i | 0.407700 | − | 0.190708i | ||||
\(388\) | 308.607 | 0.795379 | ||||||||
\(389\) | − | 505.152i | − | 1.29859i | −0.760536 | − | 0.649296i | \(-0.775064\pi\) | ||
0.760536 | − | 0.649296i | \(-0.224936\pi\) | |||||||
\(390\) | −44.3989 | − | 199.705i | −0.113843 | − | 0.512064i | ||||
\(391\) | 183.072 | 0.468215 | ||||||||
\(392\) | − | 0.312140i | − | 0.000796275i | ||||||
\(393\) | 481.610 | − | 107.073i | 1.22547 | − | 0.272450i | ||||
\(394\) | −327.432 | −0.831046 | ||||||||
\(395\) | − | 347.168i | − | 0.878908i | ||||||
\(396\) | −52.5163 | − | 112.270i | −0.132617 | − | 0.283511i | ||||
\(397\) | 372.570 | 0.938465 | 0.469232 | − | 0.883075i | \(-0.344531\pi\) | ||||
0.469232 | + | 0.883075i | \(0.344531\pi\) | |||||||
\(398\) | − | 492.275i | − | 1.23687i | ||||||
\(399\) | 52.2274 | + | 234.917i | 0.130896 | + | 0.588765i | ||||
\(400\) | −144.429 | −0.361073 | ||||||||
\(401\) | − | 420.779i | − | 1.04933i | −0.851310 | − | 0.524663i | \(-0.824191\pi\) | ||
0.851310 | − | 0.524663i | \(-0.175809\pi\) | |||||||
\(402\) | −699.024 | + | 155.409i | −1.73887 | + | 0.386589i | ||||
\(403\) | 241.395 | 0.598995 | ||||||||
\(404\) | 406.337i | 1.00578i | ||||||||
\(405\) | 251.395 | + | 209.922i | 0.620730 | + | 0.518327i | ||||
\(406\) | 147.811 | 0.364067 | ||||||||
\(407\) | 193.331i | 0.475016i | ||||||||
\(408\) | 9.14611 | + | 41.1389i | 0.0224169 | + | 0.100831i | ||||
\(409\) | 392.844 | 0.960500 | 0.480250 | − | 0.877132i | \(-0.340546\pi\) | ||||
0.480250 | + | 0.877132i | \(0.340546\pi\) | |||||||
\(410\) | − | 374.013i | − | 0.912227i | ||||||
\(411\) | −630.219 | + | 140.112i | −1.53338 | + | 0.340905i | ||||
\(412\) | 377.560 | 0.916407 | ||||||||
\(413\) | − | 53.4307i | − | 0.129372i | ||||||
\(414\) | 151.304 | − | 70.7748i | 0.365469 | − | 0.170954i | ||||
\(415\) | 532.801 | 1.28386 | ||||||||
\(416\) | − | 269.286i | − | 0.647322i | ||||||
\(417\) | −48.3098 | − | 217.296i | −0.115851 | − | 0.521093i | ||||
\(418\) | 116.311 | 0.278256 | ||||||||
\(419\) | − | 286.270i | − | 0.683223i | −0.939841 | − | 0.341612i | \(-0.889027\pi\) | ||
0.939841 | − | 0.341612i | \(-0.110973\pi\) | |||||||
\(420\) | 314.467 | − | 69.9131i | 0.748731 | − | 0.166460i | ||||
\(421\) | 629.689 | 1.49570 | 0.747849 | − | 0.663869i | \(-0.231087\pi\) | ||||
0.747849 | + | 0.663869i | \(0.231087\pi\) | |||||||
\(422\) | 25.4255i | 0.0602499i | ||||||||
\(423\) | −196.339 | − | 419.739i | −0.464159 | − | 0.992291i | ||||
\(424\) | −20.8490 | −0.0491721 | ||||||||
\(425\) | − | 238.587i | − | 0.561380i | ||||||
\(426\) | −58.7009 | − | 264.035i | −0.137795 | − | 0.619800i | ||||
\(427\) | 340.368 | 0.797114 | ||||||||
\(428\) | 651.368i | 1.52189i | ||||||||
\(429\) | 63.7193 | − | 14.1662i | 0.148530 | − | 0.0330215i | ||||
\(430\) | 218.810 | 0.508861 | ||||||||
\(431\) | 125.145i | 0.290359i | 0.989405 | + | 0.145179i | \(0.0463759\pi\) | ||||
−0.989405 | + | 0.145179i | \(0.953624\pi\) | |||||||
\(432\) | 275.058 | + | 357.133i | 0.636708 | + | 0.826697i | ||||
\(433\) | −336.848 | −0.777941 | −0.388970 | − | 0.921250i | \(-0.627169\pi\) | ||||
−0.388970 | + | 0.921250i | \(0.627169\pi\) | |||||||
\(434\) | 778.366i | 1.79347i | ||||||||
\(435\) | 20.0067 | + | 89.9895i | 0.0459924 | + | 0.206872i | ||||
\(436\) | −606.545 | −1.39116 | ||||||||
\(437\) | 76.5485i | 0.175168i | ||||||||
\(438\) | −586.411 | + | 130.372i | −1.33884 | + | 0.297654i | ||||
\(439\) | 204.185 | 0.465115 | 0.232557 | − | 0.972583i | \(-0.425291\pi\) | ||||
0.232557 | + | 0.972583i | \(0.425291\pi\) | |||||||
\(440\) | 7.42916i | 0.0168845i | ||||||||
\(441\) | 4.99582 | − | 2.33687i | 0.0113284 | − | 0.00529903i | ||||
\(442\) | 465.142 | 1.05236 | ||||||||
\(443\) | − | 367.998i | − | 0.830695i | −0.909663 | − | 0.415348i | \(-0.863660\pi\) | ||
0.909663 | − | 0.415348i | \(-0.136340\pi\) | |||||||
\(444\) | 133.221 | + | 599.226i | 0.300048 | + | 1.34961i | ||||
\(445\) | −388.784 | −0.873671 | ||||||||
\(446\) | 683.211i | 1.53186i | ||||||||
\(447\) | 706.070 | − | 156.975i | 1.57958 | − | 0.351175i | ||||
\(448\) | 403.758 | 0.901247 | ||||||||
\(449\) | − | 42.2232i | − | 0.0940384i | −0.998894 | − | 0.0470192i | \(-0.985028\pi\) | ||
0.998894 | − | 0.0470192i | \(-0.0149722\pi\) | |||||||
\(450\) | −92.2366 | − | 197.185i | −0.204970 | − | 0.438190i | ||||
\(451\) | 119.335 | 0.264601 | ||||||||
\(452\) | 468.651i | 1.03684i | ||||||||
\(453\) | 19.8544 | + | 89.3046i | 0.0438288 | + | 0.197140i | ||||
\(454\) | 131.035 | 0.288624 | ||||||||
\(455\) | 169.655i | 0.372867i | ||||||||
\(456\) | −17.2016 | + | 3.82429i | −0.0377227 | + | 0.00838661i | ||||
\(457\) | −454.706 | −0.994981 | −0.497491 | − | 0.867469i | \(-0.665745\pi\) | ||||
−0.497491 | + | 0.867469i | \(0.665745\pi\) | |||||||
\(458\) | − | 398.214i | − | 0.869464i | ||||||
\(459\) | −589.957 | + | 454.375i | −1.28531 | + | 0.989925i | ||||
\(460\) | 102.470 | 0.222761 | ||||||||
\(461\) | − | 101.873i | − | 0.220984i | −0.993877 | − | 0.110492i | \(-0.964757\pi\) | ||
0.993877 | − | 0.110492i | \(-0.0352426\pi\) | |||||||
\(462\) | 45.6783 | + | 205.460i | 0.0988709 | + | 0.444718i | ||||
\(463\) | 835.368 | 1.80425 | 0.902125 | − | 0.431475i | \(-0.142007\pi\) | ||||
0.902125 | + | 0.431475i | \(0.142007\pi\) | |||||||
\(464\) | 126.881i | 0.273451i | ||||||||
\(465\) | −473.881 | + | 105.354i | −1.01910 | + | 0.226568i | ||||
\(466\) | −633.436 | −1.35931 | ||||||||
\(467\) | − | 5.68550i | − | 0.0121745i | −0.999981 | − | 0.00608726i | \(-0.998062\pi\) | ||
0.999981 | − | 0.00608726i | \(-0.00193765\pi\) | |||||||
\(468\) | 187.735 | − | 87.8158i | 0.401142 | − | 0.187641i | ||||
\(469\) | 593.839 | 1.26618 | ||||||||
\(470\) | − | 582.097i | − | 1.23850i | ||||||
\(471\) | 42.8421 | + | 192.702i | 0.0909598 | + | 0.409134i | ||||
\(472\) | 3.91241 | 0.00828900 | ||||||||
\(473\) | 69.8152i | 0.147601i | ||||||||
\(474\) | 703.040 | − | 156.302i | 1.48321 | − | 0.329751i | ||||
\(475\) | 99.7610 | 0.210023 | ||||||||
\(476\) | 732.439i | 1.53874i | ||||||||
\(477\) | −156.088 | − | 333.689i | −0.327229 | − | 0.699559i | ||||
\(478\) | 140.808 | 0.294577 | ||||||||
\(479\) | 565.886i | 1.18139i | 0.806895 | + | 0.590695i | \(0.201147\pi\) | ||||
−0.806895 | + | 0.590695i | \(0.798853\pi\) | |||||||
\(480\) | 117.527 | + | 528.634i | 0.244848 | + | 1.10132i | ||||
\(481\) | −323.282 | −0.672103 | ||||||||
\(482\) | − | 706.037i | − | 1.46481i | ||||||
\(483\) | −135.220 | + | 30.0626i | −0.279959 | + | 0.0622413i | ||||
\(484\) | −412.280 | −0.851817 | ||||||||
\(485\) | − | 326.842i | − | 0.673900i | ||||||
\(486\) | −311.925 | + | 603.604i | −0.641820 | + | 1.24198i | ||||
\(487\) | −576.100 | −1.18296 | −0.591478 | − | 0.806321i | \(-0.701455\pi\) | ||||
−0.591478 | + | 0.806321i | \(0.701455\pi\) | |||||||
\(488\) | 24.9230i | 0.0510718i | ||||||||
\(489\) | −46.5260 | − | 209.273i | −0.0951452 | − | 0.427960i | ||||
\(490\) | 6.92824 | 0.0141393 | ||||||||
\(491\) | − | 475.446i | − | 0.968321i | −0.874979 | − | 0.484161i | \(-0.839125\pi\) | ||
0.874979 | − | 0.484161i | \(-0.160875\pi\) | |||||||
\(492\) | 369.877 | − | 82.2320i | 0.751782 | − | 0.167138i | ||||
\(493\) | −209.599 | −0.425149 | ||||||||
\(494\) | 194.491i | 0.393707i | ||||||||
\(495\) | −118.904 | + | 55.6193i | −0.240210 | + | 0.112362i | ||||
\(496\) | −668.151 | −1.34708 | ||||||||
\(497\) | 224.304i | 0.451317i | ||||||||
\(498\) | 239.877 | + | 1078.96i | 0.481681 | + | 2.16658i | ||||
\(499\) | 61.4468 | 0.123140 | 0.0615699 | − | 0.998103i | \(-0.480389\pi\) | ||||
0.0615699 | + | 0.998103i | \(0.480389\pi\) | |||||||
\(500\) | − | 519.470i | − | 1.03894i | ||||||
\(501\) | 277.488 | − | 61.6919i | 0.553869 | − | 0.123138i | ||||
\(502\) | −322.557 | −0.642543 | ||||||||
\(503\) | 838.880i | 1.66775i | 0.551951 | + | 0.833876i | \(0.313883\pi\) | ||||
−0.551951 | + | 0.833876i | \(0.686117\pi\) | |||||||
\(504\) | −13.5110 | − | 28.8841i | −0.0268075 | − | 0.0573097i | ||||
\(505\) | 430.346 | 0.852171 | ||||||||
\(506\) | 66.9497i | 0.132312i | ||||||||
\(507\) | −86.3428 | − | 388.367i | −0.170301 | − | 0.766010i | ||||
\(508\) | 603.508 | 1.18801 | ||||||||
\(509\) | 877.915i | 1.72478i | 0.506242 | + | 0.862391i | \(0.331034\pi\) | ||||
−0.506242 | + | 0.862391i | \(0.668966\pi\) | |||||||
\(510\) | −913.116 | + | 203.006i | −1.79042 | + | 0.398052i | ||||
\(511\) | 498.172 | 0.974896 | ||||||||
\(512\) | 711.335i | 1.38933i | ||||||||
\(513\) | −189.990 | − | 246.681i | −0.370350 | − | 0.480860i | ||||
\(514\) | 189.302 | 0.368292 | ||||||||
\(515\) | − | 399.869i | − | 0.776444i | ||||||
\(516\) | 48.1085 | + | 216.391i | 0.0932335 | + | 0.419361i | ||||
\(517\) | 185.728 | 0.359242 | ||||||||
\(518\) | − | 1042.41i | − | 2.01237i | ||||||
\(519\) | 270.111 | − | 60.0519i | 0.520446 | − | 0.115707i | ||||
\(520\) | −12.4228 | −0.0238899 | ||||||||
\(521\) | 868.672i | 1.66732i | 0.552281 | + | 0.833658i | \(0.313758\pi\) | ||||
−0.552281 | + | 0.833658i | \(0.686242\pi\) | |||||||
\(522\) | −173.228 | + | 81.0299i | −0.331854 | + | 0.155230i | ||||
\(523\) | −971.738 | −1.85801 | −0.929004 | − | 0.370070i | \(-0.879334\pi\) | ||||
−0.929004 | + | 0.370070i | \(0.879334\pi\) | |||||||
\(524\) | 627.866i | 1.19822i | ||||||||
\(525\) | 39.1787 | + | 176.225i | 0.0746261 | + | 0.335666i | ||||
\(526\) | 827.619 | 1.57342 | ||||||||
\(527\) | − | 1103.74i | − | 2.09438i | ||||||
\(528\) | −176.367 | + | 39.2104i | −0.334029 | + | 0.0742621i | ||||
\(529\) | 484.938 | 0.916707 | ||||||||
\(530\) | − | 462.763i | − | 0.873137i | ||||||
\(531\) | 29.2907 | + | 62.6183i | 0.0551614 | + | 0.117925i | ||||
\(532\) | −306.257 | −0.575672 | ||||||||
\(533\) | 199.548i | 0.374387i | ||||||||
\(534\) | −175.038 | − | 787.314i | −0.327786 | − | 1.47437i | ||||
\(535\) | 689.856 | 1.28945 | ||||||||
\(536\) | 43.4832i | 0.0811254i | ||||||||
\(537\) | −142.035 | + | 31.5775i | −0.264497 | + | 0.0588036i | ||||
\(538\) | 1249.29 | 2.32211 | ||||||||
\(539\) | 2.21057i | 0.00410125i | ||||||||
\(540\) | −330.214 | + | 254.326i | −0.611508 | + | 0.470973i | ||||
\(541\) | 349.329 | 0.645710 | 0.322855 | − | 0.946448i | \(-0.395357\pi\) | ||||
0.322855 | + | 0.946448i | \(0.395357\pi\) | |||||||
\(542\) | 312.775i | 0.577076i | ||||||||
\(543\) | 115.366 | + | 518.914i | 0.212461 | + | 0.955642i | ||||
\(544\) | −1231.26 | −2.26335 | ||||||||
\(545\) | 642.384i | 1.17869i | ||||||||
\(546\) | −343.562 | + | 76.3817i | −0.629235 | + | 0.139893i | ||||
\(547\) | −97.0056 | −0.177341 | −0.0886706 | − | 0.996061i | \(-0.528262\pi\) | ||||
−0.0886706 | + | 0.996061i | \(0.528262\pi\) | |||||||
\(548\) | − | 821.605i | − | 1.49928i | ||||||
\(549\) | −398.895 | + | 186.589i | −0.726585 | + | 0.339871i | ||||
\(550\) | 87.2515 | 0.158639 | ||||||||
\(551\) | − | 87.6402i | − | 0.159057i | ||||||
\(552\) | −2.20130 | − | 9.90137i | −0.00398786 | − | 0.0179373i | ||||
\(553\) | −597.251 | −1.08002 | ||||||||
\(554\) | − | 685.412i | − | 1.23721i | ||||||
\(555\) | 634.632 | − | 141.093i | 1.14348 | − | 0.254222i | ||||
\(556\) | 283.285 | 0.509505 | ||||||||
\(557\) | − | 670.323i | − | 1.20345i | −0.798703 | − | 0.601726i | \(-0.794480\pi\) | ||
0.798703 | − | 0.601726i | \(-0.205520\pi\) | |||||||
\(558\) | −426.700 | − | 912.209i | −0.764695 | − | 1.63478i | ||||
\(559\) | −116.742 | −0.208842 | ||||||||
\(560\) | − | 469.583i | − | 0.838542i | ||||||
\(561\) | −64.7727 | − | 291.345i | −0.115459 | − | 0.519332i | ||||
\(562\) | −552.458 | −0.983021 | ||||||||
\(563\) | 354.081i | 0.628919i | 0.949271 | + | 0.314459i | \(0.101823\pi\) | ||||
−0.949271 | + | 0.314459i | \(0.898177\pi\) | |||||||
\(564\) | 575.659 | − | 127.982i | 1.02067 | − | 0.226919i | ||||
\(565\) | 496.342 | 0.878482 | ||||||||
\(566\) | − | 994.006i | − | 1.75620i | ||||||
\(567\) | 361.140 | − | 432.488i | 0.636931 | − | 0.762766i | ||||
\(568\) | −16.4244 | −0.0289163 | ||||||||
\(569\) | 923.710i | 1.62339i | 0.584080 | + | 0.811696i | \(0.301455\pi\) | ||||
−0.584080 | + | 0.811696i | \(0.698545\pi\) | |||||||
\(570\) | −84.8838 | − | 381.805i | −0.148919 | − | 0.669833i | ||||
\(571\) | −95.5951 | −0.167417 | −0.0837085 | − | 0.996490i | \(-0.526676\pi\) | ||||
−0.0837085 | + | 0.996490i | \(0.526676\pi\) | |||||||
\(572\) | 83.0697i | 0.145227i | ||||||||
\(573\) | −401.921 | + | 89.3561i | −0.701433 | + | 0.155944i | ||||
\(574\) | −643.434 | −1.12096 | ||||||||
\(575\) | 57.4233i | 0.0998666i | ||||||||
\(576\) | −473.186 | + | 221.340i | −0.821504 | + | 0.384271i | ||||
\(577\) | −709.681 | −1.22995 | −0.614975 | − | 0.788546i | \(-0.710834\pi\) | ||||
−0.614975 | + | 0.788546i | \(0.710834\pi\) | |||||||
\(578\) | − | 1318.72i | − | 2.28153i | ||||||
\(579\) | 236.837 | + | 1065.29i | 0.409045 | + | 1.83987i | ||||
\(580\) | −117.318 | −0.202272 | ||||||||
\(581\) | − | 916.604i | − | 1.57763i | ||||||
\(582\) | 661.877 | − | 147.150i | 1.13725 | − | 0.252835i | ||||
\(583\) | 147.652 | 0.253263 | ||||||||
\(584\) | 36.4781i | 0.0624625i | ||||||||
\(585\) | −93.0046 | − | 198.827i | −0.158982 | − | 0.339876i | ||||
\(586\) | −1226.94 | −2.09376 | ||||||||
\(587\) | − | 305.912i | − | 0.521144i | −0.965454 | − | 0.260572i | \(-0.916089\pi\) | ||
0.965454 | − | 0.260572i | \(-0.0839112\pi\) | |||||||
\(588\) | 1.52327 | + | 6.85162i | 0.00259059 | + | 0.0116524i | ||||
\(589\) | 461.509 | 0.783547 | ||||||||
\(590\) | 86.8395i | 0.147186i | ||||||||
\(591\) | −342.944 | + | 76.2442i | −0.580277 | + | 0.129009i | ||||
\(592\) | 894.804 | 1.51149 | ||||||||
\(593\) | 485.726i | 0.819100i | 0.912288 | + | 0.409550i | \(0.134314\pi\) | ||||
−0.912288 | + | 0.409550i | \(0.865686\pi\) | |||||||
\(594\) | −166.166 | − | 215.748i | −0.279740 | − | 0.363213i | ||||
\(595\) | 775.717 | 1.30373 | ||||||||
\(596\) | 920.491i | 1.54445i | ||||||||
\(597\) | −114.629 | − | 515.596i | −0.192008 | − | 0.863646i | ||||
\(598\) | −111.951 | −0.187209 | ||||||||
\(599\) | − | 1115.58i | − | 1.86240i | −0.364513 | − | 0.931198i | \(-0.618765\pi\) | ||
0.364513 | − | 0.931198i | \(-0.381235\pi\) | |||||||
\(600\) | −12.9038 | + | 2.86882i | −0.0215064 | + | 0.00478136i | ||||
\(601\) | −447.398 | −0.744423 | −0.372212 | − | 0.928148i | \(-0.621400\pi\) | ||||
−0.372212 | + | 0.928148i | \(0.621400\pi\) | |||||||
\(602\) | − | 376.430i | − | 0.625300i | ||||||
\(603\) | −695.952 | + | 325.542i | −1.15415 | + | 0.539871i | ||||
\(604\) | −116.425 | −0.192756 | ||||||||
\(605\) | 436.640i | 0.721719i | ||||||||
\(606\) | 193.750 | + | 871.481i | 0.319719 | + | 1.43809i | ||||
\(607\) | 717.432 | 1.18193 | 0.590965 | − | 0.806697i | \(-0.298747\pi\) | ||||
0.590965 | + | 0.806697i | \(0.298747\pi\) | |||||||
\(608\) | − | 514.833i | − | 0.846764i | ||||||
\(609\) | 154.814 | − | 34.4185i | 0.254209 | − | 0.0565165i | ||||
\(610\) | −553.190 | −0.906869 | ||||||||
\(611\) | 310.568i | 0.508294i | ||||||||
\(612\) | −401.523 | − | 858.384i | −0.656083 | − | 1.40259i | ||||
\(613\) | −1101.82 | −1.79743 | −0.898715 | − | 0.438534i | \(-0.855498\pi\) | ||||
−0.898715 | + | 0.438534i | \(0.855498\pi\) | |||||||
\(614\) | − | 1451.32i | − | 2.36372i | ||||||
\(615\) | −87.0908 | − | 391.732i | −0.141611 | − | 0.636962i | ||||
\(616\) | 12.7808 | 0.0207480 | ||||||||
\(617\) | 150.603i | 0.244089i | 0.992525 | + | 0.122044i | \(0.0389450\pi\) | ||||
−0.992525 | + | 0.122044i | \(0.961055\pi\) | |||||||
\(618\) | 809.762 | − | 180.028i | 1.31029 | − | 0.291308i | ||||
\(619\) | −621.716 | −1.00439 | −0.502193 | − | 0.864755i | \(-0.667473\pi\) | ||||
−0.502193 | + | 0.864755i | \(0.667473\pi\) | |||||||
\(620\) | − | 617.789i | − | 0.996435i | ||||||
\(621\) | 141.992 | − | 109.360i | 0.228650 | − | 0.176103i | ||||
\(622\) | −914.722 | −1.47061 | ||||||||
\(623\) | 668.844i | 1.07359i | ||||||||
\(624\) | −65.5662 | − | 294.915i | −0.105074 | − | 0.472620i | ||||
\(625\) | −333.894 | −0.534230 | ||||||||
\(626\) | − | 866.743i | − | 1.38457i | ||||||
\(627\) | 121.821 | − | 27.0836i | 0.194292 | − | 0.0431956i | ||||
\(628\) | −251.222 | −0.400036 | ||||||||
\(629\) | 1478.15i | 2.35000i | ||||||||
\(630\) | 641.109 | − | 299.889i | 1.01763 | − | 0.476014i | ||||
\(631\) | 310.615 | 0.492259 | 0.246129 | − | 0.969237i | \(-0.420841\pi\) | ||||
0.246129 | + | 0.969237i | \(0.420841\pi\) | |||||||
\(632\) | − | 43.7331i | − | 0.0691979i | ||||||
\(633\) | 5.92044 | + | 26.6300i | 0.00935299 | + | 0.0420695i | ||||
\(634\) | −937.296 | −1.47838 | ||||||||
\(635\) | − | 639.167i | − | 1.00656i | ||||||
\(636\) | 457.645 | − | 101.745i | 0.719568 | − | 0.159976i | ||||
\(637\) | −3.69644 | −0.00580289 | ||||||||
\(638\) | − | 76.6505i | − | 0.120142i | ||||||
\(639\) | −122.964 | − | 262.874i | −0.192431 | − | 0.411384i | ||||
\(640\) | 65.8363 | 0.102869 | ||||||||
\(641\) | − | 184.355i | − | 0.287606i | −0.989606 | − | 0.143803i | \(-0.954067\pi\) | ||
0.989606 | − | 0.143803i | \(-0.0459331\pi\) | |||||||
\(642\) | 310.586 | + | 1397.01i | 0.483779 | + | 2.17602i | ||||
\(643\) | −428.215 | −0.665964 | −0.332982 | − | 0.942933i | \(-0.608055\pi\) | ||||
−0.332982 | + | 0.942933i | \(0.608055\pi\) | |||||||
\(644\) | − | 176.284i | − | 0.273734i | ||||||
\(645\) | 229.176 | − | 50.9511i | 0.355312 | − | 0.0789939i | ||||
\(646\) | 889.278 | 1.37659 | ||||||||
\(647\) | − | 516.078i | − | 0.797648i | −0.917028 | − | 0.398824i | \(-0.869419\pi\) | ||
0.917028 | − | 0.398824i | \(-0.130581\pi\) | |||||||
\(648\) | 31.6685 | + | 26.4441i | 0.0488711 | + | 0.0408088i | ||||
\(649\) | −27.7076 | −0.0426928 | ||||||||
\(650\) | 145.899i | 0.224460i | ||||||||
\(651\) | 181.246 | + | 815.241i | 0.278412 | + | 1.25229i | ||||
\(652\) | 272.825 | 0.418443 | ||||||||
\(653\) | 983.392i | 1.50596i | 0.658044 | + | 0.752980i | \(0.271384\pi\) | ||||
−0.658044 | + | 0.752980i | \(0.728616\pi\) | |||||||
\(654\) | −1300.87 | + | 289.213i | −1.98910 | + | 0.442222i | ||||
\(655\) | 664.965 | 1.01521 | ||||||||
\(656\) | − | 552.325i | − | 0.841959i | ||||||
\(657\) | −583.834 | + | 273.098i | −0.888637 | + | 0.415674i | ||||
\(658\) | −1001.41 | −1.52190 | ||||||||
\(659\) | 152.558i | 0.231499i | 0.993278 | + | 0.115749i | \(0.0369270\pi\) | ||||
−0.993278 | + | 0.115749i | \(0.963073\pi\) | |||||||
\(660\) | −36.2549 | − | 163.074i | −0.0549317 | − | 0.247081i | ||||
\(661\) | −585.844 | −0.886300 | −0.443150 | − | 0.896447i | \(-0.646139\pi\) | ||||
−0.443150 | + | 0.896447i | \(0.646139\pi\) | |||||||
\(662\) | 1059.94i | 1.60112i | ||||||||
\(663\) | 487.177 | − | 108.311i | 0.734807 | − | 0.163364i | ||||
\(664\) | 67.1173 | 0.101080 | ||||||||
\(665\) | 324.353i | 0.487749i | ||||||||
\(666\) | 571.447 | + | 1221.65i | 0.858028 | + | 1.83431i | ||||
\(667\) | 50.4465 | 0.0756319 | ||||||||
\(668\) | 361.757i | 0.541552i | ||||||||
\(669\) | 159.089 | + | 715.577i | 0.237801 | + | 1.06962i | ||||
\(670\) | −965.151 | −1.44052 | ||||||||
\(671\) | − | 176.505i | − | 0.263047i | ||||||
\(672\) | 909.435 | − | 202.188i | 1.35333 | − | 0.300875i | ||||
\(673\) | 742.833 | 1.10376 | 0.551882 | − | 0.833922i | \(-0.313910\pi\) | ||||
0.551882 | + | 0.833922i | \(0.313910\pi\) | |||||||
\(674\) | 863.625i | 1.28134i | ||||||||
\(675\) | −142.522 | − | 185.049i | −0.211143 | − | 0.274147i | ||||
\(676\) | 506.307 | 0.748975 | ||||||||
\(677\) | 514.809i | 0.760427i | 0.924899 | + | 0.380213i | \(0.124149\pi\) | ||||
−0.924899 | + | 0.380213i | \(0.875851\pi\) | |||||||
\(678\) | 223.463 | + | 1005.13i | 0.329591 | + | 1.48249i | ||||
\(679\) | −562.282 | −0.828103 | ||||||||
\(680\) | 56.8010i | 0.0835309i | ||||||||
\(681\) | 137.243 | − | 30.5122i | 0.201531 | − | 0.0448050i | ||||
\(682\) | 403.638 | 0.591845 | ||||||||
\(683\) | 387.873i | 0.567896i | 0.958840 | + | 0.283948i | \(0.0916444\pi\) | ||||
−0.958840 | + | 0.283948i | \(0.908356\pi\) | |||||||
\(684\) | 358.919 | − | 167.890i | 0.524736 | − | 0.245453i | ||||
\(685\) | −870.151 | −1.27029 | ||||||||
\(686\) | − | 964.944i | − | 1.40662i | ||||||
\(687\) | −92.7262 | − | 417.080i | −0.134973 | − | 0.607103i | ||||
\(688\) | 323.129 | 0.469664 | ||||||||
\(689\) | 246.899i | 0.358344i | ||||||||
\(690\) | 219.770 | − | 48.8598i | 0.318507 | − | 0.0708114i | ||||
\(691\) | 1208.04 | 1.74826 | 0.874128 | − | 0.485696i | \(-0.161434\pi\) | ||||
0.874128 | + | 0.485696i | \(0.161434\pi\) | |||||||
\(692\) | 352.139i | 0.508872i | ||||||||
\(693\) | 95.6847 | + | 204.557i | 0.138073 | + | 0.295176i | ||||
\(694\) | 1441.61 | 2.07725 | ||||||||
\(695\) | − | 300.023i | − | 0.431688i | ||||||
\(696\) | 2.52026 | + | 11.3360i | 0.00362106 | + | 0.0162874i | ||||
\(697\) | 912.399 | 1.30904 | ||||||||
\(698\) | 1511.55i | 2.16555i | ||||||||
\(699\) | −663.445 | + | 147.499i | −0.949134 | + | 0.211014i | ||||
\(700\) | −229.741 | −0.328201 | ||||||||
\(701\) | − | 370.498i | − | 0.528527i | −0.964451 | − | 0.264264i | \(-0.914871\pi\) | ||
0.964451 | − | 0.264264i | \(-0.0851289\pi\) | |||||||
\(702\) | 360.767 | − | 277.857i | 0.513913 | − | 0.395807i | ||||
\(703\) | −618.064 | −0.879181 | ||||||||
\(704\) | − | 209.377i | − | 0.297411i | ||||||
\(705\) | −135.544 | − | 609.673i | −0.192261 | − | 0.864785i | ||||
\(706\) | −97.7432 | −0.138446 | ||||||||
\(707\) | − | 740.346i | − | 1.04717i | ||||||
\(708\) | −85.8792 | + | 19.0929i | −0.121298 | + | 0.0269673i | ||||
\(709\) | −1040.67 | −1.46779 | −0.733897 | − | 0.679260i | \(-0.762301\pi\) | ||||
−0.733897 | + | 0.679260i | \(0.762301\pi\) | |||||||
\(710\) | − | 364.556i | − | 0.513459i | ||||||
\(711\) | 699.951 | − | 327.413i | 0.984460 | − | 0.460496i | ||||
\(712\) | −48.9754 | −0.0687856 | ||||||||
\(713\) | 265.649i | 0.372579i | ||||||||
\(714\) | 349.242 | + | 1570.88i | 0.489135 | + | 2.20011i | ||||
\(715\) | 87.9780 | 0.123046 | ||||||||
\(716\) | − | 185.168i | − | 0.258615i | ||||||
\(717\) | 147.479 | − | 32.7878i | 0.205689 | − | 0.0457292i | ||||
\(718\) | 1327.04 | 1.84824 | ||||||||
\(719\) | 760.116i | 1.05719i | 0.848876 | + | 0.528593i | \(0.177280\pi\) | ||||
−0.848876 | + | 0.528593i | \(0.822720\pi\) | |||||||
\(720\) | 257.425 | + | 550.330i | 0.357535 | + | 0.764347i | ||||
\(721\) | −687.914 | −0.954111 | ||||||||
\(722\) | − | 637.533i | − | 0.883009i | ||||||
\(723\) | −164.404 | − | 739.485i | −0.227392 | − | 1.02280i | ||||
\(724\) | −676.498 | −0.934390 | ||||||||
\(725\) | − | 65.7438i | − | 0.0906811i | ||||||
\(726\) | −884.226 | + | 196.583i | −1.21794 | + | 0.270776i | ||||
\(727\) | −683.054 | −0.939552 | −0.469776 | − | 0.882786i | \(-0.655665\pi\) | ||||
−0.469776 | + | 0.882786i | \(0.655665\pi\) | |||||||
\(728\) | 21.3715i | 0.0293565i | ||||||||
\(729\) | −186.150 | + | 704.833i | −0.255349 | + | 0.966849i | ||||
\(730\) | −809.665 | −1.10913 | ||||||||
\(731\) | 533.785i | 0.730212i | ||||||||
\(732\) | −121.627 | − | 547.072i | −0.166157 | − | 0.747367i | ||||
\(733\) | −1050.25 | −1.43282 | −0.716408 | − | 0.697681i | \(-0.754215\pi\) | ||||
−0.716408 | + | 0.697681i | \(0.754215\pi\) | |||||||
\(734\) | − | 1604.76i | − | 2.18632i | ||||||
\(735\) | 7.25646 | − | 1.61327i | 0.00987273 | − | 0.00219493i | ||||
\(736\) | 296.342 | 0.402639 | ||||||||
\(737\) | − | 307.948i | − | 0.417840i | ||||||
\(738\) | 754.074 | − | 352.730i | 1.02178 | − | 0.477954i | ||||
\(739\) | −863.855 | −1.16895 | −0.584476 | − | 0.811411i | \(-0.698700\pi\) | ||||
−0.584476 | + | 0.811411i | \(0.698700\pi\) | |||||||
\(740\) | 827.359i | 1.11805i | ||||||||
\(741\) | 45.2883 | + | 203.705i | 0.0611178 | + | 0.274906i | ||||
\(742\) | −796.114 | −1.07293 | ||||||||
\(743\) | 604.163i | 0.813140i | 0.913620 | + | 0.406570i | \(0.133275\pi\) | ||||
−0.913620 | + | 0.406570i | \(0.866725\pi\) | |||||||
\(744\) | −59.6951 | + | 13.2716i | −0.0802353 | + | 0.0178381i | ||||
\(745\) | 974.880 | 1.30856 | ||||||||
\(746\) | 1358.00i | 1.82037i | ||||||||
\(747\) | 502.482 | + | 1074.22i | 0.672667 | + | 1.43804i | ||||
\(748\) | 379.822 | 0.507783 | ||||||||
\(749\) | − | 1186.79i | − | 1.58450i | ||||||
\(750\) | −247.694 | − | 1114.12i | −0.330259 | − | 1.48549i | ||||
\(751\) | 7.84121 | 0.0104410 | 0.00522051 | − | 0.999986i | \(-0.498338\pi\) | ||||
0.00522051 | + | 0.999986i | \(0.498338\pi\) | |||||||
\(752\) | − | 859.613i | − | 1.14310i | ||||||
\(753\) | −337.838 | + | 75.1089i | −0.448656 | + | 0.0997463i | ||||
\(754\) | 128.172 | 0.169990 | ||||||||
\(755\) | 123.304i | 0.163317i | ||||||||
\(756\) | 437.529 | + | 568.084i | 0.578742 | + | 0.751434i | ||||
\(757\) | 483.558 | 0.638782 | 0.319391 | − | 0.947623i | \(-0.396522\pi\) | ||||
0.319391 | + | 0.947623i | \(0.396522\pi\) | |||||||
\(758\) | − | 1676.86i | − | 2.21222i | ||||||
\(759\) | 15.5896 | + | 70.1214i | 0.0205396 | + | 0.0923866i | ||||
\(760\) | −23.7504 | −0.0312505 | ||||||||
\(761\) | − | 951.213i | − | 1.24995i | −0.780644 | − | 0.624976i | \(-0.785109\pi\) | ||
0.780644 | − | 0.624976i | \(-0.214891\pi\) | |||||||
\(762\) | 1294.36 | − | 287.765i | 1.69863 | − | 0.377644i | ||||
\(763\) | 1105.12 | 1.44839 | ||||||||
\(764\) | − | 523.977i | − | 0.685834i | ||||||
\(765\) | −909.104 | + | 425.247i | −1.18837 | + | 0.555879i | ||||
\(766\) | −144.758 | −0.188979 | ||||||||
\(767\) | − | 46.3317i | − | 0.0604064i | ||||||
\(768\) | 180.804 | + | 813.249i | 0.235421 | + | 1.05892i | ||||
\(769\) | −650.550 | −0.845969 | −0.422985 | − | 0.906137i | \(-0.639018\pi\) | ||||
−0.422985 | + | 0.906137i | \(0.639018\pi\) | |||||||
\(770\) | 283.681i | 0.368417i | ||||||||
\(771\) | 198.270 | − | 44.0800i | 0.257160 | − | 0.0571725i | ||||
\(772\) | −1388.79 | −1.79895 | ||||||||
\(773\) | − | 992.020i | − | 1.28334i | −0.766982 | − | 0.641669i | \(-0.778242\pi\) | ||
0.766982 | − | 0.641669i | \(-0.221758\pi\) | |||||||
\(774\) | 206.359 | + | 441.159i | 0.266614 | + | 0.569973i | ||||
\(775\) | 346.204 | 0.446715 | ||||||||
\(776\) | − | 41.1725i | − | 0.0530573i | ||||||
\(777\) | −242.730 | − | 1091.79i | −0.312393 | − | 1.40513i | ||||
\(778\) | 1412.42 | 1.81546 | ||||||||
\(779\) | 381.505i | 0.489737i | ||||||||
\(780\) | 272.686 | − | 60.6242i | 0.349597 | − | 0.0777233i | ||||
\(781\) | 116.318 | 0.148934 | ||||||||
\(782\) | 511.876i | 0.654573i | ||||||||
\(783\) | −162.566 | + | 125.206i | −0.207619 | + | 0.159905i | ||||
\(784\) | 10.2313 | 0.0130501 | ||||||||
\(785\) | 266.066i | 0.338938i | ||||||||
\(786\) | 299.380 | + | 1346.60i | 0.380890 | + | 1.71323i | ||||
\(787\) | −1242.88 | −1.57926 | −0.789630 | − | 0.613583i | \(-0.789728\pi\) | ||||
−0.789630 | + | 0.613583i | \(0.789728\pi\) | |||||||
\(788\) | − | 447.090i | − | 0.567373i | ||||||
\(789\) | 866.827 | − | 192.715i | 1.09864 | − | 0.244253i | ||||
\(790\) | 970.696 | 1.22873 | ||||||||
\(791\) | − | 853.882i | − | 1.07950i | ||||||
\(792\) | −14.9784 | + | 7.00640i | −0.0189122 | + | 0.00884647i | ||||
\(793\) | 295.145 | 0.372188 | ||||||||
\(794\) | 1041.72i | 1.31199i | ||||||||
\(795\) | −107.757 | − | 484.686i | −0.135543 | − | 0.609668i | ||||
\(796\) | 672.174 | 0.844439 | ||||||||
\(797\) | 572.779i | 0.718669i | 0.933209 | + | 0.359335i | \(0.116996\pi\) | ||||
−0.933209 | + | 0.359335i | \(0.883004\pi\) | |||||||
\(798\) | −656.838 | + | 146.030i | −0.823105 | + | 0.182995i | ||||
\(799\) | 1420.02 | 1.77724 | ||||||||
\(800\) | − | 386.205i | − | 0.482756i | ||||||
\(801\) | −366.660 | − | 783.854i | −0.457753 | − | 0.978594i | ||||
\(802\) | 1176.52 | 1.46698 | ||||||||
\(803\) | − | 258.338i | − | 0.321716i | ||||||
\(804\) | −212.202 | − | 954.477i | −0.263933 | − | 1.18716i | ||||
\(805\) | −186.701 | −0.231926 | ||||||||
\(806\) | 674.949i | 0.837406i | ||||||||
\(807\) | 1308.48 | − | 290.904i | 1.62141 | − | 0.360476i | ||||
\(808\) | 54.2110 | 0.0670929 | ||||||||
\(809\) | − | 534.139i | − | 0.660246i | −0.943938 | − | 0.330123i | \(-0.892910\pi\) | ||
0.943938 | − | 0.330123i | \(-0.107090\pi\) | |||||||
\(810\) | −586.951 | + | 702.911i | −0.724631 | + | 0.867792i | ||||
\(811\) | 1153.16 | 1.42190 | 0.710948 | − | 0.703244i | \(-0.248266\pi\) | ||||
0.710948 | + | 0.703244i | \(0.248266\pi\) | |||||||
\(812\) | 201.828i | 0.248556i | ||||||||
\(813\) | 72.8313 | + | 327.593i | 0.0895834 | + | 0.402943i | ||||
\(814\) | −540.562 | −0.664081 | ||||||||
\(815\) | − | 288.945i | − | 0.354534i | ||||||
\(816\) | −1348.45 | + | 299.790i | −1.65251 | + | 0.367390i | ||||
\(817\) | −223.193 | −0.273186 | ||||||||
\(818\) | 1098.41i | 1.34280i | ||||||||
\(819\) | −342.053 | + | 160.000i | −0.417647 | + | 0.195361i | ||||
\(820\) | 510.693 | 0.622797 | ||||||||
\(821\) | 238.118i | 0.290034i | 0.989429 | + | 0.145017i | \(0.0463238\pi\) | ||||
−0.989429 | + | 0.145017i | \(0.953676\pi\) | |||||||
\(822\) | −391.758 | − | 1762.12i | −0.476592 | − | 2.14369i | ||||
\(823\) | 1325.63 | 1.61073 | 0.805365 | − | 0.592779i | \(-0.201969\pi\) | ||||
0.805365 | + | 0.592779i | \(0.201969\pi\) | |||||||
\(824\) | − | 50.3717i | − | 0.0611308i | ||||||
\(825\) | 91.3850 | − | 20.3169i | 0.110770 | − | 0.0246266i | ||||
\(826\) | 149.394 | 0.180865 | ||||||||
\(827\) | 933.439i | 1.12870i | 0.825534 | + | 0.564352i | \(0.190874\pi\) | ||||
−0.825534 | + | 0.564352i | \(0.809126\pi\) | |||||||
\(828\) | 96.6390 | + | 206.597i | 0.116714 | + | 0.249513i | ||||
\(829\) | −234.018 | −0.282289 | −0.141144 | − | 0.989989i | \(-0.545078\pi\) | ||||
−0.141144 | + | 0.989989i | \(0.545078\pi\) | |||||||
\(830\) | 1489.73i | 1.79486i | ||||||||
\(831\) | −159.602 | − | 717.883i | −0.192060 | − | 0.863878i | ||||
\(832\) | 350.114 | 0.420809 | ||||||||
\(833\) | 16.9013i | 0.0202897i | ||||||||
\(834\) | 607.567 | − | 135.076i | 0.728498 | − | 0.161962i | ||||
\(835\) | 383.132 | 0.458840 | ||||||||
\(836\) | 158.816i | 0.189972i | ||||||||
\(837\) | −659.327 | − | 856.065i | −0.787726 | − | 1.02278i | ||||
\(838\) | 800.423 | 0.955159 | ||||||||
\(839\) | − | 646.303i | − | 0.770325i | −0.922849 | − | 0.385162i | \(-0.874145\pi\) | ||
0.922849 | − | 0.385162i | \(-0.125855\pi\) | |||||||
\(840\) | −9.32739 | − | 41.9543i | −0.0111040 | − | 0.0499456i | ||||
\(841\) | 783.244 | 0.931325 | ||||||||
\(842\) | 1760.63i | 2.09101i | ||||||||
\(843\) | −578.630 | + | 128.643i | −0.686394 | + | 0.152601i | ||||
\(844\) | −34.7170 | −0.0411339 | ||||||||
\(845\) | − | 536.223i | − | 0.634584i | ||||||
\(846\) | 1173.61 | − | 548.973i | 1.38724 | − | 0.648904i | ||||
\(847\) | 751.174 | 0.886864 | ||||||||
\(848\) | − | 683.386i | − | 0.805880i | ||||||
\(849\) | −231.459 | − | 1041.10i | −0.272626 | − | 1.22626i | ||||
\(850\) | 667.097 | 0.784820 | ||||||||
\(851\) | − | 355.763i | − | 0.418053i | ||||||
\(852\) | 360.524 | − | 80.1527i | 0.423150 | − | 0.0940759i | ||||
\(853\) | −24.1394 | −0.0282994 | −0.0141497 | − | 0.999900i | \(-0.504504\pi\) | ||||
−0.0141497 | + | 0.999900i | \(0.504504\pi\) | |||||||
\(854\) | 951.681i | 1.11438i | ||||||||
\(855\) | −177.810 | − | 380.127i | −0.207965 | − | 0.444593i | ||||
\(856\) | 86.9016 | 0.101521 | ||||||||
\(857\) | − | 135.299i | − | 0.157875i | −0.996880 | − | 0.0789373i | \(-0.974847\pi\) | ||
0.996880 | − | 0.0789373i | \(-0.0251527\pi\) | |||||||
\(858\) | 39.6093 | + | 178.162i | 0.0461647 | + | 0.207647i | ||||
\(859\) | −491.575 | −0.572264 | −0.286132 | − | 0.958190i | \(-0.592370\pi\) | ||||
−0.286132 | + | 0.958190i | \(0.592370\pi\) | |||||||
\(860\) | 298.773i | 0.347411i | ||||||||
\(861\) | −673.916 | + | 149.827i | −0.782713 | + | 0.174015i | ||||
\(862\) | −349.909 | −0.405927 | ||||||||
\(863\) | 51.2585i | 0.0593957i | 0.999559 | + | 0.0296979i | \(0.00945452\pi\) | ||||
−0.999559 | + | 0.0296979i | \(0.990545\pi\) | |||||||
\(864\) | −954.976 | + | 735.506i | −1.10530 | + | 0.851281i | ||||
\(865\) | 372.946 | 0.431152 | ||||||||
\(866\) | − | 941.841i | − | 1.08758i | ||||||
\(867\) | −307.072 | − | 1381.20i | −0.354177 | − | 1.59308i | ||||
\(868\) | −1062.81 | −1.22444 | ||||||||
\(869\) | 309.717i | 0.356407i | ||||||||
\(870\) | −251.614 | + | 55.9395i | −0.289212 | + | 0.0642983i | ||||
\(871\) | 514.939 | 0.591205 | ||||||||
\(872\) | 80.9215i | 0.0927999i | ||||||||
\(873\) | 658.968 | − | 308.243i | 0.754832 | − | 0.353084i | ||||
\(874\) | −214.033 | −0.244889 | ||||||||
\(875\) | 946.474i | 1.08168i | ||||||||
\(876\) | −178.016 | − | 800.711i | −0.203215 | − | 0.914054i | ||||
\(877\) | −1387.61 | −1.58222 | −0.791110 | − | 0.611674i | \(-0.790496\pi\) | ||||
−0.791110 | + | 0.611674i | \(0.790496\pi\) | |||||||
\(878\) | 570.910i | 0.650240i | ||||||||
\(879\) | −1285.07 | + | 285.700i | −1.46197 | + | 0.325028i | ||||
\(880\) | −243.512 | −0.276718 | ||||||||
\(881\) | 698.452i | 0.792795i | 0.918079 | + | 0.396398i | \(0.129740\pi\) | ||||
−0.918079 | + | 0.396398i | \(0.870260\pi\) | |||||||
\(882\) | 6.53399 | + | 13.9685i | 0.00740815 | + | 0.0158373i | ||||
\(883\) | −1111.31 | −1.25856 | −0.629279 | − | 0.777179i | \(-0.716650\pi\) | ||||
−0.629279 | + | 0.777179i | \(0.716650\pi\) | |||||||
\(884\) | 635.124i | 0.718466i | ||||||||
\(885\) | 20.2210 | + | 90.9535i | 0.0228486 | + | 0.102772i | ||||
\(886\) | 1028.94 | 1.16133 | ||||||||
\(887\) | − | 771.311i | − | 0.869573i | −0.900534 | − | 0.434787i | \(-0.856824\pi\) | ||
0.900534 | − | 0.434787i | \(-0.143176\pi\) | |||||||
\(888\) | 79.9451 | − | 17.7736i | 0.0900283 | − | 0.0200153i | ||||
\(889\) | −1099.59 | −1.23689 | ||||||||
\(890\) | − | 1087.05i | − | 1.22141i | ||||||
\(891\) | −224.276 | − | 187.277i | −0.251713 | − | 0.210187i | ||||
\(892\) | −932.885 | −1.04584 | ||||||||
\(893\) | 593.757i | 0.664901i | ||||||||
\(894\) | 438.909 | + | 1974.20i | 0.490950 | + | 2.20828i | ||||
\(895\) | −196.109 | −0.219116 | ||||||||
\(896\) | − | 113.262i | − | 0.126408i | ||||||
\(897\) | −117.254 | + | 26.0683i | −0.130718 | + | 0.0290617i | ||||
\(898\) | 118.058 | 0.131467 | ||||||||
\(899\) | − | 304.140i | − | 0.338310i | ||||||
\(900\) | 269.245 | − | 125.944i | 0.299162 | − | 0.139938i | ||||
\(901\) | 1128.90 | 1.25294 | ||||||||
\(902\) | 333.666i | 0.369918i | ||||||||
\(903\) | −87.6537 | − | 394.264i | −0.0970694 | − | 0.436615i | ||||
\(904\) | 62.5246 | 0.0691644 | ||||||||
\(905\) | 716.470i | 0.791680i | ||||||||
\(906\) | −249.699 | + | 55.5138i | −0.275606 | + | 0.0612735i | ||||
\(907\) | 924.774 | 1.01960 | 0.509798 | − | 0.860294i | \(-0.329720\pi\) | ||||
0.509798 | + | 0.860294i | \(0.329720\pi\) | |||||||
\(908\) | 178.921i | 0.197050i | ||||||||
\(909\) | 405.857 | + | 867.651i | 0.446488 | + | 0.954512i | ||||
\(910\) | −474.361 | −0.521276 | ||||||||
\(911\) | − | 884.822i | − | 0.971265i | −0.874163 | − | 0.485632i | \(-0.838589\pi\) | ||
0.874163 | − | 0.485632i | \(-0.161411\pi\) | |||||||
\(912\) | −125.352 | − | 563.831i | −0.137448 | − | 0.618236i | ||||
\(913\) | −475.324 | −0.520618 | ||||||||
\(914\) | − | 1271.38i | − | 1.39100i | ||||||
\(915\) | −579.397 | + | 128.813i | −0.633221 | + | 0.140779i | ||||
\(916\) | 543.739 | 0.593602 | ||||||||
\(917\) | − | 1143.97i | − | 1.24752i | ||||||
\(918\) | −1270.45 | − | 1649.54i | −1.38393 | − | 1.79689i | ||||
\(919\) | −624.037 | −0.679039 | −0.339520 | − | 0.940599i | \(-0.610265\pi\) | ||||
−0.339520 | + | 0.940599i | \(0.610265\pi\) | |||||||
\(920\) | − | 13.6709i | − | 0.0148597i | ||||||
\(921\) | −337.948 | − | 1520.08i | −0.366936 | − | 1.65047i | ||||
\(922\) | 284.842 | 0.308939 | ||||||||
\(923\) | 194.502i | 0.210728i | ||||||||
\(924\) | −280.544 | + | 62.3712i | −0.303619 | + | 0.0675013i | ||||
\(925\) | −463.644 | −0.501237 | ||||||||
\(926\) | 2335.72i | 2.52238i | ||||||||
\(927\) | 806.203 | − | 377.114i | 0.869691 | − | 0.406811i | ||||
\(928\) | −339.281 | −0.365605 | ||||||||
\(929\) | − | 584.667i | − | 0.629351i | −0.949199 | − | 0.314675i | \(-0.898104\pi\) | ||
0.949199 | − | 0.314675i | \(-0.101896\pi\) | |||||||
\(930\) | −294.575 | − | 1324.99i | −0.316747 | − | 1.42472i | ||||
\(931\) | −7.06702 | −0.00759078 | ||||||||
\(932\) | − | 864.921i | − | 0.928027i | ||||||
\(933\) | −958.056 | + | 212.997i | −1.02686 | + | 0.228293i | ||||
\(934\) | 15.8969 | 0.0170202 | ||||||||
\(935\) | − | 402.264i | − | 0.430229i | ||||||
\(936\) | −11.7159 | − | 25.0464i | −0.0125169 | − | 0.0267590i | ||||
\(937\) | −980.559 | −1.04649 | −0.523244 | − | 0.852183i | \(-0.675278\pi\) | ||||
−0.523244 | + | 0.852183i | \(0.675278\pi\) | |||||||
\(938\) | 1660.40i | 1.77015i | ||||||||
\(939\) | −201.825 | − | 907.805i | −0.214937 | − | 0.966778i | ||||
\(940\) | 794.820 | 0.845553 | ||||||||
\(941\) | − | 186.524i | − | 0.198219i | −0.995077 | − | 0.0991095i | \(-0.968401\pi\) | ||
0.995077 | − | 0.0991095i | \(-0.0315994\pi\) | |||||||
\(942\) | −538.803 | + | 119.788i | −0.571978 | + | 0.127164i | ||||
\(943\) | −219.598 | −0.232871 | ||||||||
\(944\) | 128.240i | 0.135848i | ||||||||
\(945\) | 601.651 | − | 463.381i | 0.636667 | − | 0.490351i | ||||
\(946\) | −195.206 | −0.206349 | ||||||||
\(947\) | 787.251i | 0.831311i | 0.909522 | + | 0.415655i | \(0.136448\pi\) | ||||
−0.909522 | + | 0.415655i | \(0.863552\pi\) | |||||||
\(948\) | 213.421 | + | 959.961i | 0.225128 | + | 1.01262i | ||||
\(949\) | 431.983 | 0.455198 | ||||||||
\(950\) | 278.936i | 0.293617i | ||||||||
\(951\) | −981.700 | + | 218.254i | −1.03228 | + | 0.229500i | ||||
\(952\) | 97.7176 | 0.102645 | ||||||||
\(953\) | 542.842i | 0.569613i | 0.958585 | + | 0.284807i | \(0.0919294\pi\) | ||||
−0.958585 | + | 0.284807i | \(0.908071\pi\) | |||||||
\(954\) | 933.009 | − | 436.429i | 0.977996 | − | 0.457473i | ||||
\(955\) | −554.937 | −0.581086 | ||||||||
\(956\) | 192.265i | 0.201114i | ||||||||
\(957\) | −17.8485 | − | 80.2818i | −0.0186504 | − | 0.0838890i | ||||
\(958\) | −1582.24 | −1.65161 | ||||||||
\(959\) | 1496.96i | 1.56096i | ||||||||
\(960\) | −687.306 | + | 152.804i | −0.715943 | + | 0.159170i | ||||
\(961\) | 640.589 | 0.666586 | ||||||||
\(962\) | − | 903.908i | − | 0.939613i | ||||||
\(963\) | 650.599 | + | 1390.87i | 0.675596 | + | 1.44431i | ||||
\(964\) | 964.054 | 1.00006 | ||||||||
\(965\) | 1470.85i | 1.52420i | ||||||||
\(966\) | −84.0561 | − | 378.082i | −0.0870146 | − | 0.391389i | ||||
\(967\) | 468.018 | 0.483989 | 0.241995 | − | 0.970278i | \(-0.422198\pi\) | ||||
0.241995 | + | 0.970278i | \(0.422198\pi\) | |||||||
\(968\) | 55.0039i | 0.0568222i | ||||||||
\(969\) | 931.407 | − | 207.073i | 0.961204 | − | 0.213697i | ||||
\(970\) | 913.862 | 0.942126 | ||||||||
\(971\) | 828.213i | 0.852949i | 0.904500 | + | 0.426474i | \(0.140245\pi\) | ||||
−0.904500 | + | 0.426474i | \(0.859755\pi\) | |||||||
\(972\) | −824.187 | − | 425.915i | −0.847929 | − | 0.438184i | ||||
\(973\) | −516.145 | −0.530467 | ||||||||
\(974\) | − | 1610.80i | − | 1.65380i | ||||||
\(975\) | 33.9733 | + | 152.811i | 0.0348444 | + | 0.156729i | ||||
\(976\) | −816.925 | −0.837014 | ||||||||
\(977\) | 5.87085i | 0.00600906i | 0.999995 | + | 0.00300453i | \(0.000956373\pi\) | ||||
−0.999995 | + | 0.00300453i | \(0.999044\pi\) | |||||||
\(978\) | 585.134 | − | 130.089i | 0.598297 | − | 0.133015i | ||||
\(979\) | 346.843 | 0.354283 | ||||||||
\(980\) | 9.46011i | 0.00965317i | ||||||||
\(981\) | −1295.15 | + | 605.829i | −1.32024 | + | 0.617562i | ||||
\(982\) | 1329.36 | 1.35373 | ||||||||
\(983\) | 687.595i | 0.699486i | 0.936846 | + | 0.349743i | \(0.113731\pi\) | ||||
−0.936846 | + | 0.349743i | \(0.886269\pi\) | |||||||
\(984\) | −10.9709 | − | 49.3467i | −0.0111493 | − | 0.0501491i | ||||
\(985\) | −473.507 | −0.480718 | ||||||||
\(986\) | − | 586.046i | − | 0.594367i | ||||||
\(987\) | −1048.85 | + | 233.183i | −1.06267 | + | 0.236255i | ||||
\(988\) | −265.567 | −0.268792 | ||||||||
\(989\) | − | 128.472i | − | 0.129901i | ||||||
\(990\) | −155.514 | − | 332.461i | −0.157084 | − | 0.335819i | ||||
\(991\) | 184.476 | 0.186151 | 0.0930755 | − | 0.995659i | \(-0.470330\pi\) | ||||
0.0930755 | + | 0.995659i | \(0.470330\pi\) | |||||||
\(992\) | − | 1786.64i | − | 1.80105i | ||||||
\(993\) | 246.813 | + | 1110.16i | 0.248553 | + | 1.11798i | ||||
\(994\) | −627.164 | −0.630949 | ||||||||
\(995\) | − | 711.890i | − | 0.715468i | ||||||
\(996\) | −1473.26 | + | 327.538i | −1.47917 | + | 0.328854i | ||||
\(997\) | 294.205 | 0.295091 | 0.147545 | − | 0.989055i | \(-0.452863\pi\) | ||||
0.147545 | + | 0.989055i | \(0.452863\pi\) | |||||||
\(998\) | 171.808i | 0.172152i | ||||||||
\(999\) | 882.986 | + | 1146.46i | 0.883870 | + | 1.14761i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 177.3.b.a.119.31 | yes | 38 | |
3.2 | odd | 2 | inner | 177.3.b.a.119.8 | ✓ | 38 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
177.3.b.a.119.8 | ✓ | 38 | 3.2 | odd | 2 | inner | |
177.3.b.a.119.31 | yes | 38 | 1.1 | even | 1 | trivial |