Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [74,3,Mod(23,74)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(74, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([5]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("74.23");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 74 = 2 \cdot 37 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 74.g (of order \(12\), degree \(4\), 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: | \(2.01635395627\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(3\) over \(\Q(\zeta_{12})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} + 82x^{10} + 2505x^{8} + 34456x^{6} + 196096x^{4} + 262464x^{2} + 69696 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 23.3 | ||
Root | \(5.23421i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 74.23 |
Dual form | 74.3.g.b.29.3 |
$q$-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 \(\left(\mathbb{Z}/74\mathbb{Z}\right)^\times\).
\(n\) | \(39\) |
\(\chi(n)\) | \(e\left(\frac{5}{12}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.366025 | + | 1.36603i | 0.183013 | + | 0.683013i | ||||
\(3\) | 4.53296 | − | 2.61711i | 1.51099 | − | 0.872369i | 0.511070 | − | 0.859539i | \(-0.329249\pi\) |
0.999918 | − | 0.0128300i | \(-0.00408404\pi\) | |||||||
\(4\) | −1.73205 | + | 1.00000i | −0.433013 | + | 0.250000i | ||||
\(5\) | −0.866025 | + | 3.23205i | −0.173205 | + | 0.646410i | 0.823645 | + | 0.567105i | \(0.191937\pi\) |
−0.996850 | + | 0.0793049i | \(0.974730\pi\) | |||||||
\(6\) | 5.23421 | + | 5.23421i | 0.872369 | + | 0.872369i | ||||
\(7\) | −0.548432 | − | 0.949912i | −0.0783474 | − | 0.135702i | 0.824190 | − | 0.566314i | \(-0.191631\pi\) |
−0.902537 | + | 0.430612i | \(0.858298\pi\) | |||||||
\(8\) | −2.00000 | − | 2.00000i | −0.250000 | − | 0.250000i | ||||
\(9\) | 9.19850 | − | 15.9323i | 1.02206 | − | 1.77025i | ||||
\(10\) | −4.73205 | −0.473205 | ||||||||
\(11\) | − | 7.96906i | − | 0.724460i | −0.932089 | − | 0.362230i | \(-0.882015\pi\) | ||
0.932089 | − | 0.362230i | \(-0.117985\pi\) | |||||||
\(12\) | −5.23421 | + | 9.06593i | −0.436185 | + | 0.755494i | ||||
\(13\) | −5.69692 | + | 21.2612i | −0.438224 | + | 1.63548i | 0.295006 | + | 0.955496i | \(0.404678\pi\) |
−0.733230 | + | 0.679981i | \(0.761988\pi\) | |||||||
\(14\) | 1.09686 | − | 1.09686i | 0.0783474 | − | 0.0783474i | ||||
\(15\) | 4.53296 | + | 16.9172i | 0.302198 | + | 1.12782i | ||||
\(16\) | 2.00000 | − | 3.46410i | 0.125000 | − | 0.216506i | ||||
\(17\) | −27.3687 | + | 7.33343i | −1.60993 | + | 0.431378i | −0.948021 | − | 0.318209i | \(-0.896919\pi\) |
−0.661905 | + | 0.749587i | \(0.730252\pi\) | |||||||
\(18\) | 25.1308 | + | 6.73377i | 1.39615 | + | 0.374098i | ||||
\(19\) | 5.66649 | − | 21.1476i | 0.298237 | − | 1.11303i | −0.640376 | − | 0.768061i | \(-0.721222\pi\) |
0.938613 | − | 0.344973i | \(-0.112112\pi\) | |||||||
\(20\) | −1.73205 | − | 6.46410i | −0.0866025 | − | 0.323205i | ||||
\(21\) | −4.97204 | − | 2.87061i | −0.236764 | − | 0.136696i | ||||
\(22\) | 10.8859 | − | 2.91688i | 0.494816 | − | 0.132585i | ||||
\(23\) | −11.3461 | − | 11.3461i | −0.493308 | − | 0.493308i | 0.416039 | − | 0.909347i | \(-0.363418\pi\) |
−0.909347 | + | 0.416039i | \(0.863418\pi\) | |||||||
\(24\) | −14.3001 | − | 3.83171i | −0.595839 | − | 0.159655i | ||||
\(25\) | 11.9545 | + | 6.90192i | 0.478179 | + | 0.276077i | ||||
\(26\) | −31.1285 | −1.19725 | ||||||||
\(27\) | − | 49.1859i | − | 1.82170i | ||||||
\(28\) | 1.89982 | + | 1.09686i | 0.0678509 | + | 0.0391737i | ||||
\(29\) | 6.59322 | − | 6.59322i | 0.227352 | − | 0.227352i | −0.584233 | − | 0.811586i | \(-0.698605\pi\) |
0.811586 | + | 0.584233i | \(0.198605\pi\) | |||||||
\(30\) | −21.4502 | + | 12.3843i | −0.715007 | + | 0.412810i | ||||
\(31\) | −17.7384 | + | 17.7384i | −0.572206 | + | 0.572206i | −0.932744 | − | 0.360538i | \(-0.882593\pi\) |
0.360538 | + | 0.932744i | \(0.382593\pi\) | |||||||
\(32\) | 5.46410 | + | 1.46410i | 0.170753 | + | 0.0457532i | ||||
\(33\) | −20.8559 | − | 36.1235i | −0.631997 | − | 1.09465i | ||||
\(34\) | −20.0353 | − | 34.7022i | −0.589274 | − | 1.02065i | ||||
\(35\) | 3.54512 | − | 0.949912i | 0.101289 | − | 0.0271403i | ||||
\(36\) | 36.7940i | 1.02206i | ||||||||
\(37\) | −5.38912 | − | 36.6054i | −0.145652 | − | 0.989336i | ||||
\(38\) | 30.9623 | 0.814797 | ||||||||
\(39\) | 29.8189 | + | 111.286i | 0.764587 | + | 2.85348i | ||||
\(40\) | 8.19615 | − | 4.73205i | 0.204904 | − | 0.118301i | ||||
\(41\) | −10.5120 | + | 6.06911i | −0.256391 | + | 0.148027i | −0.622687 | − | 0.782471i | \(-0.713959\pi\) |
0.366296 | + | 0.930498i | \(0.380626\pi\) | |||||||
\(42\) | 2.10143 | − | 7.84266i | 0.0500341 | − | 0.186730i | ||||
\(43\) | 49.1668 | + | 49.1668i | 1.14341 | + | 1.14341i | 0.987821 | + | 0.155594i | \(0.0497291\pi\) |
0.155594 | + | 0.987821i | \(0.450271\pi\) | |||||||
\(44\) | 7.96906 | + | 13.8028i | 0.181115 | + | 0.313700i | ||||
\(45\) | 43.5278 | + | 43.5278i | 0.967284 | + | 0.967284i | ||||
\(46\) | 11.3461 | − | 19.6520i | 0.246654 | − | 0.427217i | ||||
\(47\) | 37.1317 | 0.790036 | 0.395018 | − | 0.918673i | \(-0.370738\pi\) | ||||
0.395018 | + | 0.918673i | \(0.370738\pi\) | |||||||
\(48\) | − | 20.9369i | − | 0.436185i | ||||||
\(49\) | 23.8984 | − | 41.3933i | 0.487723 | − | 0.844762i | ||||
\(50\) | −5.05256 | + | 18.8564i | −0.101051 | + | 0.377128i | ||||
\(51\) | −104.869 | + | 104.869i | −2.05626 | + | 2.05626i | ||||
\(52\) | −11.3938 | − | 42.5224i | −0.219112 | − | 0.817738i | ||||
\(53\) | −6.36524 | + | 11.0249i | −0.120099 | + | 0.208017i | −0.919806 | − | 0.392372i | \(-0.871654\pi\) |
0.799708 | + | 0.600390i | \(0.204988\pi\) | |||||||
\(54\) | 67.1892 | − | 18.0033i | 1.24425 | − | 0.333395i | ||||
\(55\) | 25.7564 | + | 6.90141i | 0.468298 | + | 0.125480i | ||||
\(56\) | −0.802960 | + | 2.99669i | −0.0143386 | + | 0.0535123i | ||||
\(57\) | −29.6596 | − | 110.691i | −0.520345 | − | 1.94195i | ||||
\(58\) | 11.4198 | + | 6.59322i | 0.196893 | + | 0.113676i | ||||
\(59\) | −50.8363 | + | 13.6216i | −0.861633 | + | 0.230874i | −0.662466 | − | 0.749092i | \(-0.730490\pi\) |
−0.199167 | + | 0.979966i | \(0.563823\pi\) | |||||||
\(60\) | −24.7686 | − | 24.7686i | −0.412810 | − | 0.412810i | ||||
\(61\) | 105.650 | + | 28.3088i | 1.73196 | + | 0.464078i | 0.980634 | − | 0.195849i | \(-0.0627462\pi\) |
0.751330 | + | 0.659927i | \(0.229413\pi\) | |||||||
\(62\) | −30.7238 | − | 17.7384i | −0.495545 | − | 0.286103i | ||||
\(63\) | −20.1790 | −0.320302 | ||||||||
\(64\) | 8.00000i | 0.125000i | ||||||||
\(65\) | −63.7836 | − | 36.8255i | −0.981286 | − | 0.566546i | ||||
\(66\) | 41.7118 | − | 41.7118i | 0.631997 | − | 0.631997i | ||||
\(67\) | 51.2985 | − | 29.6172i | 0.765649 | − | 0.442048i | −0.0656711 | − | 0.997841i | \(-0.520919\pi\) |
0.831320 | + | 0.555793i | \(0.187585\pi\) | |||||||
\(68\) | 40.0706 | − | 40.0706i | 0.589274 | − | 0.589274i | ||||
\(69\) | −81.1253 | − | 21.7375i | −1.17573 | − | 0.315036i | ||||
\(70\) | 2.59521 | + | 4.49503i | 0.0370744 | + | 0.0642148i | ||||
\(71\) | 27.3533 | + | 47.3773i | 0.385258 | + | 0.667286i | 0.991805 | − | 0.127762i | \(-0.0407792\pi\) |
−0.606547 | + | 0.795048i | \(0.707446\pi\) | |||||||
\(72\) | −50.2616 | + | 13.4675i | −0.698077 | + | 0.187049i | ||||
\(73\) | 61.1000i | 0.836986i | 0.908220 | + | 0.418493i | \(0.137442\pi\) | ||||
−0.908220 | + | 0.418493i | \(0.862558\pi\) | |||||||
\(74\) | 48.0314 | − | 20.7602i | 0.649073 | − | 0.280543i | ||||
\(75\) | 72.2523 | 0.963364 | ||||||||
\(76\) | 11.3330 | + | 42.2953i | 0.149118 | + | 0.556517i | ||||
\(77\) | −7.56991 | + | 4.37049i | −0.0983105 | + | 0.0567596i | ||||
\(78\) | −141.105 | + | 81.4667i | −1.80903 | + | 1.04445i | ||||
\(79\) | 28.3909 | − | 105.956i | 0.359378 | − | 1.34122i | −0.515507 | − | 0.856885i | \(-0.672396\pi\) |
0.874885 | − | 0.484331i | \(-0.160937\pi\) | |||||||
\(80\) | 9.46410 | + | 9.46410i | 0.118301 | + | 0.118301i | ||||
\(81\) | −45.9384 | − | 79.5676i | −0.567140 | − | 0.982316i | ||||
\(82\) | −12.1382 | − | 12.1382i | −0.148027 | − | 0.148027i | ||||
\(83\) | −54.2776 | + | 94.0115i | −0.653947 | + | 1.13267i | 0.328210 | + | 0.944605i | \(0.393555\pi\) |
−0.982157 | + | 0.188064i | \(0.939779\pi\) | |||||||
\(84\) | 11.4824 | 0.136696 | ||||||||
\(85\) | − | 94.8081i | − | 1.11539i | ||||||
\(86\) | −49.1668 | + | 85.1595i | −0.571707 | + | 0.990226i | ||||
\(87\) | 12.6317 | − | 47.1420i | 0.145191 | − | 0.541862i | ||||
\(88\) | −15.9381 | + | 15.9381i | −0.181115 | + | 0.181115i | ||||
\(89\) | 6.28409 | + | 23.4525i | 0.0706077 | + | 0.263512i | 0.992202 | − | 0.124644i | \(-0.0397789\pi\) |
−0.921594 | + | 0.388156i | \(0.873112\pi\) | |||||||
\(90\) | −43.5278 | + | 75.3923i | −0.483642 | + | 0.837693i | ||||
\(91\) | 23.3206 | − | 6.24875i | 0.256271 | − | 0.0686675i | ||||
\(92\) | 30.9981 | + | 8.30591i | 0.336936 | + | 0.0902817i | ||||
\(93\) | −33.9842 | + | 126.831i | −0.365421 | + | 1.36377i | ||||
\(94\) | 13.5911 | + | 50.7228i | 0.144587 | + | 0.539605i | ||||
\(95\) | 63.4429 | + | 36.6288i | 0.667820 | + | 0.385566i | ||||
\(96\) | 28.6003 | − | 7.66342i | 0.297920 | − | 0.0798273i | ||||
\(97\) | −41.9263 | − | 41.9263i | −0.432230 | − | 0.432230i | 0.457156 | − | 0.889386i | \(-0.348868\pi\) |
−0.889386 | + | 0.457156i | \(0.848868\pi\) | |||||||
\(98\) | 65.2918 | + | 17.4949i | 0.666242 | + | 0.178519i | ||||
\(99\) | −126.965 | − | 73.3034i | −1.28248 | − | 0.740439i | ||||
\(100\) | −27.6077 | −0.276077 | ||||||||
\(101\) | − | 115.721i | − | 1.14575i | −0.819642 | − | 0.572876i | \(-0.805827\pi\) | ||
0.819642 | − | 0.572876i | \(-0.194173\pi\) | |||||||
\(102\) | −181.639 | − | 104.869i | −1.78077 | − | 1.02813i | ||||
\(103\) | 23.0389 | − | 23.0389i | 0.223678 | − | 0.223678i | −0.586367 | − | 0.810046i | \(-0.699442\pi\) |
0.810046 | + | 0.586367i | \(0.199442\pi\) | |||||||
\(104\) | 53.9162 | − | 31.1285i | 0.518425 | − | 0.299313i | ||||
\(105\) | 13.5839 | − | 13.5839i | 0.129370 | − | 0.129370i | ||||
\(106\) | −17.3901 | − | 4.65968i | −0.164058 | − | 0.0439592i | ||||
\(107\) | −5.43971 | − | 9.42185i | −0.0508384 | − | 0.0880547i | 0.839486 | − | 0.543381i | \(-0.182856\pi\) |
−0.890325 | + | 0.455326i | \(0.849523\pi\) | |||||||
\(108\) | 49.1859 | + | 85.1926i | 0.455425 | + | 0.788820i | ||||
\(109\) | −125.675 | + | 33.6745i | −1.15298 | + | 0.308941i | −0.784160 | − | 0.620559i | \(-0.786906\pi\) |
−0.368823 | + | 0.929500i | \(0.620239\pi\) | |||||||
\(110\) | 37.7100i | 0.342818i | ||||||||
\(111\) | −120.229 | − | 151.827i | −1.08314 | − | 1.36781i | ||||
\(112\) | −4.38746 | −0.0391737 | ||||||||
\(113\) | −55.7117 | − | 207.919i | −0.493024 | − | 1.83999i | −0.540830 | − | 0.841132i | \(-0.681890\pi\) |
0.0478062 | − | 0.998857i | \(-0.484777\pi\) | |||||||
\(114\) | 140.351 | − | 81.0317i | 1.23115 | − | 0.710804i | ||||
\(115\) | 46.4971 | − | 26.8451i | 0.404323 | − | 0.233436i | ||||
\(116\) | −4.82657 | + | 18.0130i | −0.0416084 | + | 0.155285i | ||||
\(117\) | 286.336 | + | 286.336i | 2.44732 | + | 2.44732i | ||||
\(118\) | −37.2148 | − | 64.4579i | −0.315379 | − | 0.546253i | ||||
\(119\) | 21.9760 | + | 21.9760i | 0.184672 | + | 0.184672i | ||||
\(120\) | 24.7686 | − | 42.9004i | 0.206405 | − | 0.357504i | ||||
\(121\) | 57.4941 | 0.475157 | ||||||||
\(122\) | 154.682i | 1.26789i | ||||||||
\(123\) | −31.7670 | + | 55.0221i | −0.258269 | + | 0.447334i | ||||
\(124\) | 12.9854 | − | 48.4622i | 0.104721 | − | 0.390824i | ||||
\(125\) | −91.8109 | + | 91.8109i | −0.734487 | + | 0.734487i | ||||
\(126\) | −7.38603 | − | 27.5650i | −0.0586193 | − | 0.218770i | ||||
\(127\) | −85.3177 | + | 147.775i | −0.671793 | + | 1.16358i | 0.305603 | + | 0.952159i | \(0.401142\pi\) |
−0.977395 | + | 0.211420i | \(0.932191\pi\) | |||||||
\(128\) | −10.9282 | + | 2.92820i | −0.0853766 | + | 0.0228766i | ||||
\(129\) | 351.546 | + | 94.1966i | 2.72517 | + | 0.730206i | ||||
\(130\) | 26.9581 | − | 100.609i | 0.207370 | − | 0.773916i | ||||
\(131\) | −29.5996 | − | 110.467i | −0.225951 | − | 0.843260i | −0.982021 | − | 0.188770i | \(-0.939550\pi\) |
0.756070 | − | 0.654490i | \(-0.227117\pi\) | |||||||
\(132\) | 72.2469 | + | 41.7118i | 0.547325 | + | 0.315998i | ||||
\(133\) | −23.1961 | + | 6.21537i | −0.174407 | + | 0.0467321i | ||||
\(134\) | 59.2344 | + | 59.2344i | 0.442048 | + | 0.442048i | ||||
\(135\) | 158.971 | + | 42.5963i | 1.17757 | + | 0.315528i | ||||
\(136\) | 69.4043 | + | 40.0706i | 0.510326 | + | 0.294637i | ||||
\(137\) | 7.64504 | 0.0558032 | 0.0279016 | − | 0.999611i | \(-0.491117\pi\) | ||||
0.0279016 | + | 0.999611i | \(0.491117\pi\) | |||||||
\(138\) | − | 118.776i | − | 0.860694i | ||||||
\(139\) | 8.95727 | + | 5.17148i | 0.0644408 | + | 0.0372049i | 0.531874 | − | 0.846823i | \(-0.321488\pi\) |
−0.467433 | + | 0.884028i | \(0.654821\pi\) | |||||||
\(140\) | −5.19042 | + | 5.19042i | −0.0370744 | + | 0.0370744i | ||||
\(141\) | 168.317 | − | 97.1776i | 1.19373 | − | 0.689203i | ||||
\(142\) | −54.7066 | + | 54.7066i | −0.385258 | + | 0.385258i | ||||
\(143\) | 169.432 | + | 45.3991i | 1.18484 | + | 0.317476i | ||||
\(144\) | −36.7940 | − | 63.7291i | −0.255514 | − | 0.442563i | ||||
\(145\) | 15.5997 | + | 27.0195i | 0.107584 | + | 0.186341i | ||||
\(146\) | −83.4642 | + | 22.3642i | −0.571672 | + | 0.153179i | ||||
\(147\) | − | 250.179i | − | 1.70190i | ||||||
\(148\) | 45.9397 | + | 58.0133i | 0.310403 | + | 0.391982i | ||||
\(149\) | −219.043 | −1.47009 | −0.735045 | − | 0.678018i | \(-0.762839\pi\) | ||||
−0.735045 | + | 0.678018i | \(0.762839\pi\) | |||||||
\(150\) | 26.4462 | + | 98.6985i | 0.176308 | + | 0.657990i | ||||
\(151\) | −117.627 | + | 67.9122i | −0.778989 | + | 0.449750i | −0.836072 | − | 0.548620i | \(-0.815153\pi\) |
0.0570827 | + | 0.998369i | \(0.481820\pi\) | |||||||
\(152\) | −53.6283 | + | 30.9623i | −0.352818 | + | 0.203699i | ||||
\(153\) | −134.913 | + | 503.503i | −0.881785 | + | 3.29087i | ||||
\(154\) | −8.74098 | − | 8.74098i | −0.0567596 | − | 0.0567596i | ||||
\(155\) | −41.9695 | − | 72.6933i | −0.270771 | − | 0.468989i | ||||
\(156\) | −162.933 | − | 162.933i | −1.04445 | − | 1.04445i | ||||
\(157\) | −33.6256 | + | 58.2413i | −0.214176 | + | 0.370964i | −0.953017 | − | 0.302916i | \(-0.902040\pi\) |
0.738841 | + | 0.673879i | \(0.235373\pi\) | |||||||
\(158\) | 155.131 | 0.981839 | ||||||||
\(159\) | 66.6340i | 0.419082i | ||||||||
\(160\) | −9.46410 | + | 16.3923i | −0.0591506 | + | 0.102452i | ||||
\(161\) | −4.55523 | + | 17.0003i | −0.0282933 | + | 0.105592i | ||||
\(162\) | 91.8767 | − | 91.8767i | 0.567140 | − | 0.567140i | ||||
\(163\) | −49.7651 | − | 185.726i | −0.305307 | − | 1.13942i | −0.932681 | − | 0.360703i | \(-0.882537\pi\) |
0.627373 | − | 0.778719i | \(-0.284130\pi\) | |||||||
\(164\) | 12.1382 | − | 21.0240i | 0.0740136 | − | 0.128195i | ||||
\(165\) | 134.815 | − | 36.1235i | 0.817058 | − | 0.218930i | ||||
\(166\) | −148.289 | − | 39.7339i | −0.893308 | − | 0.239361i | ||||
\(167\) | 7.67484 | − | 28.6429i | 0.0459571 | − | 0.171514i | −0.939133 | − | 0.343554i | \(-0.888369\pi\) |
0.985090 | + | 0.172040i | \(0.0550358\pi\) | |||||||
\(168\) | 4.20287 | + | 15.6853i | 0.0250171 | + | 0.0933649i | ||||
\(169\) | −273.225 | − | 157.747i | −1.61672 | − | 0.933411i | ||||
\(170\) | 129.510 | − | 34.7022i | 0.761825 | − | 0.204130i | ||||
\(171\) | −284.807 | − | 284.807i | −1.66554 | − | 1.66554i | ||||
\(172\) | −134.326 | − | 35.9926i | −0.780967 | − | 0.209259i | ||||
\(173\) | −79.5962 | − | 45.9549i | −0.460094 | − | 0.265635i | 0.251990 | − | 0.967730i | \(-0.418915\pi\) |
−0.712084 | + | 0.702095i | \(0.752248\pi\) | |||||||
\(174\) | 69.0206 | 0.396670 | ||||||||
\(175\) | − | 15.1409i | − | 0.0865197i | ||||||
\(176\) | −27.6056 | − | 15.9381i | −0.156850 | − | 0.0905575i | ||||
\(177\) | −194.790 | + | 194.790i | −1.10051 | + | 1.10051i | ||||
\(178\) | −29.7366 | + | 17.1684i | −0.167060 | + | 0.0964520i | ||||
\(179\) | 61.4177 | − | 61.4177i | 0.343116 | − | 0.343116i | −0.514422 | − | 0.857537i | \(-0.671993\pi\) |
0.857537 | + | 0.514422i | \(0.171993\pi\) | |||||||
\(180\) | −118.920 | − | 31.8645i | −0.660667 | − | 0.177025i | ||||
\(181\) | 21.8239 | + | 37.8001i | 0.120574 | + | 0.208841i | 0.919994 | − | 0.391932i | \(-0.128193\pi\) |
−0.799420 | + | 0.600772i | \(0.794860\pi\) | |||||||
\(182\) | 17.0719 | + | 29.5694i | 0.0938016 | + | 0.162469i | ||||
\(183\) | 552.994 | − | 148.174i | 3.02182 | − | 0.809695i | ||||
\(184\) | 45.3843i | 0.246654i | ||||||||
\(185\) | 122.978 | + | 14.2833i | 0.664744 | + | 0.0772071i | ||||
\(186\) | −185.693 | −0.998350 | ||||||||
\(187\) | 58.4406 | + | 218.103i | 0.312516 | + | 1.16633i | ||||
\(188\) | −64.3140 | + | 37.1317i | −0.342096 | + | 0.197509i | ||||
\(189\) | −46.7223 | + | 26.9751i | −0.247208 | + | 0.142726i | ||||
\(190\) | −26.8141 | + | 100.072i | −0.141127 | + | 0.526693i | ||||
\(191\) | 61.8580 | + | 61.8580i | 0.323864 | + | 0.323864i | 0.850247 | − | 0.526383i | \(-0.176452\pi\) |
−0.526383 | + | 0.850247i | \(0.676452\pi\) | |||||||
\(192\) | 20.9369 | + | 36.2637i | 0.109046 | + | 0.188873i | ||||
\(193\) | 265.059 | + | 265.059i | 1.37336 | + | 1.37336i | 0.855406 | + | 0.517957i | \(0.173307\pi\) |
0.517957 | + | 0.855406i | \(0.326693\pi\) | |||||||
\(194\) | 41.9263 | − | 72.6186i | 0.216115 | − | 0.374322i | ||||
\(195\) | −385.505 | −1.97695 | ||||||||
\(196\) | 95.5938i | 0.487723i | ||||||||
\(197\) | −57.3963 | + | 99.4133i | −0.291352 | + | 0.504636i | −0.974130 | − | 0.225990i | \(-0.927438\pi\) |
0.682778 | + | 0.730626i | \(0.260772\pi\) | |||||||
\(198\) | 53.6618 | − | 200.269i | 0.271019 | − | 1.01146i | ||||
\(199\) | −72.0011 | + | 72.0011i | −0.361815 | + | 0.361815i | −0.864481 | − | 0.502666i | \(-0.832353\pi\) |
0.502666 | + | 0.864481i | \(0.332353\pi\) | |||||||
\(200\) | −10.1051 | − | 37.7128i | −0.0505256 | − | 0.188564i | ||||
\(201\) | 155.023 | − | 268.507i | 0.771258 | − | 1.33586i | ||||
\(202\) | 158.078 | − | 42.3568i | 0.782564 | − | 0.209687i | ||||
\(203\) | −9.87891 | − | 2.64705i | −0.0486646 | − | 0.0130396i | ||||
\(204\) | 76.7695 | − | 286.508i | 0.376321 | − | 1.40445i | ||||
\(205\) | −10.5120 | − | 39.2314i | −0.0512781 | − | 0.191373i | ||||
\(206\) | 39.9045 | + | 23.0389i | 0.193711 | + | 0.111839i | ||||
\(207\) | −285.136 | + | 76.4020i | −1.37747 | + | 0.369092i | ||||
\(208\) | 62.2571 | + | 62.2571i | 0.299313 | + | 0.299313i | ||||
\(209\) | −168.527 | − | 45.1566i | −0.806349 | − | 0.216060i | ||||
\(210\) | 23.5280 | + | 13.5839i | 0.112038 | + | 0.0646851i | ||||
\(211\) | −244.211 | −1.15740 | −0.578700 | − | 0.815541i | \(-0.696440\pi\) | ||||
−0.578700 | + | 0.815541i | \(0.696440\pi\) | |||||||
\(212\) | − | 25.4609i | − | 0.120099i | ||||||
\(213\) | 247.983 | + | 143.173i | 1.16424 | + | 0.672174i | ||||
\(214\) | 10.8794 | − | 10.8794i | 0.0508384 | − | 0.0508384i | ||||
\(215\) | −201.489 | + | 116.330i | −0.937160 | + | 0.541070i | ||||
\(216\) | −98.3719 | + | 98.3719i | −0.455425 | + | 0.455425i | ||||
\(217\) | 26.5782 | + | 7.12161i | 0.122480 | + | 0.0328185i | ||||
\(218\) | −92.0006 | − | 159.350i | −0.422021 | − | 0.730962i | ||||
\(219\) | 159.905 | + | 276.964i | 0.730161 | + | 1.26468i | ||||
\(220\) | −51.5128 | + | 13.8028i | −0.234149 | + | 0.0627401i | ||||
\(221\) | − | 623.670i | − | 2.82204i | ||||||
\(222\) | 163.393 | − | 219.808i | 0.736004 | − | 0.990128i | ||||
\(223\) | −59.6793 | −0.267620 | −0.133810 | − | 0.991007i | \(-0.542721\pi\) | ||||
−0.133810 | + | 0.991007i | \(0.542721\pi\) | |||||||
\(224\) | −1.60592 | − | 5.99338i | −0.00716929 | − | 0.0267561i | ||||
\(225\) | 219.927 | − | 126.975i | 0.977452 | − | 0.564332i | ||||
\(226\) | 263.630 | − | 152.207i | 1.16651 | − | 0.673483i | ||||
\(227\) | 9.06348 | − | 33.8254i | 0.0399272 | − | 0.149010i | −0.943084 | − | 0.332553i | \(-0.892090\pi\) |
0.983012 | + | 0.183543i | \(0.0587566\pi\) | |||||||
\(228\) | 162.063 | + | 162.063i | 0.710804 | + | 0.710804i | ||||
\(229\) | 31.4476 | + | 54.4688i | 0.137326 | + | 0.237855i | 0.926483 | − | 0.376335i | \(-0.122816\pi\) |
−0.789158 | + | 0.614191i | \(0.789483\pi\) | |||||||
\(230\) | 53.6903 | + | 53.6903i | 0.233436 | + | 0.233436i | ||||
\(231\) | −22.8761 | + | 39.6225i | −0.0990306 | + | 0.171526i | ||||
\(232\) | −26.3729 | −0.113676 | ||||||||
\(233\) | 224.895i | 0.965216i | 0.875836 | + | 0.482608i | \(0.160310\pi\) | ||||
−0.875836 | + | 0.482608i | \(0.839690\pi\) | |||||||
\(234\) | −286.336 | + | 495.948i | −1.22366 | + | 2.11944i | ||||
\(235\) | −32.1570 | + | 120.012i | −0.136838 | + | 0.510687i | ||||
\(236\) | 74.4295 | − | 74.4295i | 0.315379 | − | 0.315379i | ||||
\(237\) | −148.604 | − | 554.597i | −0.627020 | − | 2.34007i | ||||
\(238\) | −21.9760 | + | 38.0636i | −0.0923362 | + | 0.159931i | ||||
\(239\) | 106.846 | − | 28.6292i | 0.447053 | − | 0.119788i | −0.0282670 | − | 0.999600i | \(-0.508999\pi\) |
0.475320 | + | 0.879813i | \(0.342332\pi\) | |||||||
\(240\) | 67.6690 | + | 18.1319i | 0.281954 | + | 0.0755494i | ||||
\(241\) | −0.837357 | + | 3.12506i | −0.00347451 | + | 0.0129671i | −0.967641 | − | 0.252330i | \(-0.918803\pi\) |
0.964167 | + | 0.265297i | \(0.0854699\pi\) | |||||||
\(242\) | 21.0443 | + | 78.5383i | 0.0869598 | + | 0.324539i | ||||
\(243\) | −33.1074 | − | 19.1146i | −0.136244 | − | 0.0786608i | ||||
\(244\) | −211.300 | + | 56.6175i | −0.865982 | + | 0.232039i | ||||
\(245\) | 113.089 | + | 113.089i | 0.461586 | + | 0.461586i | ||||
\(246\) | −86.7892 | − | 23.2551i | −0.352802 | − | 0.0945329i | ||||
\(247\) | 417.342 | + | 240.953i | 1.68965 | + | 0.975517i | ||||
\(248\) | 70.9536 | 0.286103 | ||||||||
\(249\) | 568.201i | 2.28193i | ||||||||
\(250\) | −159.021 | − | 91.8109i | −0.636084 | − | 0.367244i | ||||
\(251\) | 246.179 | − | 246.179i | 0.980791 | − | 0.980791i | −0.0190278 | − | 0.999819i | \(-0.506057\pi\) |
0.999819 | + | 0.0190278i | \(0.00605711\pi\) | |||||||
\(252\) | 34.9511 | − | 20.1790i | 0.138695 | − | 0.0800755i | ||||
\(253\) | −90.4177 | + | 90.4177i | −0.357382 | + | 0.357382i | ||||
\(254\) | −233.092 | − | 62.4569i | −0.917686 | − | 0.245893i | ||||
\(255\) | −248.123 | − | 429.762i | −0.973031 | − | 1.68534i | ||||
\(256\) | −8.00000 | − | 13.8564i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | 15.9581 | − | 4.27595i | 0.0620936 | − | 0.0166379i | −0.227639 | − | 0.973746i | \(-0.573100\pi\) |
0.289732 | + | 0.957108i | \(0.406434\pi\) | |||||||
\(258\) | 514.700i | 1.99496i | ||||||||
\(259\) | −31.8164 | + | 25.1948i | −0.122843 | + | 0.0972771i | ||||
\(260\) | 147.302 | 0.566546 | ||||||||
\(261\) | −44.3972 | − | 165.693i | −0.170104 | − | 0.634838i | ||||
\(262\) | 140.067 | − | 80.8675i | 0.534605 | − | 0.308655i | ||||
\(263\) | 424.963 | − | 245.352i | 1.61583 | − | 0.932899i | 0.627845 | − | 0.778338i | \(-0.283937\pi\) |
0.987983 | − | 0.154561i | \(-0.0493963\pi\) | |||||||
\(264\) | −30.5351 | + | 113.959i | −0.115663 | + | 0.431662i | ||||
\(265\) | −30.1206 | − | 30.1206i | −0.113663 | − | 0.113663i | ||||
\(266\) | −16.9807 | − | 29.4115i | −0.0638373 | − | 0.110569i | ||||
\(267\) | 89.8633 | + | 89.8633i | 0.336567 | + | 0.336567i | ||||
\(268\) | −59.2344 | + | 102.597i | −0.221024 | + | 0.382825i | ||||
\(269\) | −307.691 | −1.14383 | −0.571917 | − | 0.820311i | \(-0.693800\pi\) | ||||
−0.571917 | + | 0.820311i | \(0.693800\pi\) | |||||||
\(270\) | 232.750i | 0.862038i | ||||||||
\(271\) | −52.1193 | + | 90.2733i | −0.192322 | + | 0.333112i | −0.946019 | − | 0.324110i | \(-0.894935\pi\) |
0.753697 | + | 0.657222i | \(0.228269\pi\) | |||||||
\(272\) | −29.3337 | + | 109.475i | −0.107845 | + | 0.402481i | ||||
\(273\) | 89.3579 | − | 89.3579i | 0.327318 | − | 0.327318i | ||||
\(274\) | 2.79828 | + | 10.4433i | 0.0102127 | + | 0.0381143i | ||||
\(275\) | 55.0019 | − | 95.2660i | 0.200007 | − | 0.346422i | ||||
\(276\) | 162.251 | − | 43.4749i | 0.587865 | − | 0.157518i | ||||
\(277\) | −111.247 | − | 29.8086i | −0.401614 | − | 0.107612i | 0.0523574 | − | 0.998628i | \(-0.483327\pi\) |
−0.453971 | + | 0.891016i | \(0.649993\pi\) | |||||||
\(278\) | −3.78579 | + | 14.1287i | −0.0136179 | + | 0.0508228i | ||||
\(279\) | 119.446 | + | 445.780i | 0.428123 | + | 1.59778i | ||||
\(280\) | −8.99007 | − | 5.19042i | −0.0321074 | − | 0.0185372i | ||||
\(281\) | 290.413 | − | 77.8160i | 1.03350 | − | 0.276925i | 0.298082 | − | 0.954540i | \(-0.403653\pi\) |
0.735417 | + | 0.677615i | \(0.236986\pi\) | |||||||
\(282\) | 194.355 | + | 194.355i | 0.689203 | + | 0.689203i | ||||
\(283\) | −110.565 | − | 29.6257i | −0.390688 | − | 0.104685i | 0.0581270 | − | 0.998309i | \(-0.481487\pi\) |
−0.448815 | + | 0.893625i | \(0.648154\pi\) | |||||||
\(284\) | −94.7546 | − | 54.7066i | −0.333643 | − | 0.192629i | ||||
\(285\) | 383.446 | 1.34542 | ||||||||
\(286\) | 248.065i | 0.867361i | ||||||||
\(287\) | 11.5302 | + | 6.65699i | 0.0401751 | + | 0.0231951i | ||||
\(288\) | 73.5880 | − | 73.5880i | 0.255514 | − | 0.255514i | ||||
\(289\) | 444.987 | − | 256.914i | 1.53975 | − | 0.888974i | ||||
\(290\) | −31.1994 | + | 31.1994i | −0.107584 | + | 0.107584i | ||||
\(291\) | −299.776 | − | 80.3248i | −1.03016 | − | 0.276030i | ||||
\(292\) | −61.1000 | − | 105.828i | −0.209247 | − | 0.362426i | ||||
\(293\) | 56.1445 | + | 97.2451i | 0.191619 | + | 0.331894i | 0.945787 | − | 0.324787i | \(-0.105293\pi\) |
−0.754168 | + | 0.656682i | \(0.771959\pi\) | |||||||
\(294\) | 341.751 | − | 91.5719i | 1.16242 | − | 0.311469i | ||||
\(295\) | − | 176.102i | − | 0.596957i | ||||||
\(296\) | −62.4326 | + | 83.9891i | −0.210921 | + | 0.283747i | ||||
\(297\) | −391.966 | −1.31975 | ||||||||
\(298\) | −80.1755 | − | 299.219i | −0.269045 | − | 1.00409i | ||||
\(299\) | 305.869 | − | 176.594i | 1.02297 | − | 0.590614i | ||||
\(300\) | −125.145 | + | 72.2523i | −0.417149 | + | 0.240841i | ||||
\(301\) | 19.7395 | − | 73.6688i | 0.0655798 | − | 0.244747i | ||||
\(302\) | −135.824 | − | 135.824i | −0.449750 | − | 0.449750i | ||||
\(303\) | −302.854 | − | 524.559i | −0.999519 | − | 1.73122i | ||||
\(304\) | −61.9246 | − | 61.9246i | −0.203699 | − | 0.203699i | ||||
\(305\) | −182.991 | + | 316.949i | −0.599970 | + | 1.03918i | ||||
\(306\) | −737.179 | −2.40908 | ||||||||
\(307\) | − | 170.779i | − | 0.556285i | −0.960540 | − | 0.278142i | \(-0.910281\pi\) | ||
0.960540 | − | 0.278142i | \(-0.0897187\pi\) | |||||||
\(308\) | 8.74098 | − | 15.1398i | 0.0283798 | − | 0.0491553i | ||||
\(309\) | 44.1392 | − | 164.730i | 0.142845 | − | 0.533106i | ||||
\(310\) | 83.9390 | − | 83.9390i | 0.270771 | − | 0.270771i | ||||
\(311\) | 24.7120 | + | 92.2264i | 0.0794598 | + | 0.296548i | 0.994208 | − | 0.107477i | \(-0.0342774\pi\) |
−0.914748 | + | 0.404026i | \(0.867611\pi\) | |||||||
\(312\) | 162.933 | − | 282.209i | 0.522223 | − | 0.904516i | ||||
\(313\) | −190.739 | + | 51.1084i | −0.609390 | + | 0.163286i | −0.550300 | − | 0.834967i | \(-0.685487\pi\) |
−0.0590900 | + | 0.998253i | \(0.518820\pi\) | |||||||
\(314\) | −91.8669 | − | 24.6157i | −0.292570 | − | 0.0783938i | ||||
\(315\) | 17.4755 | − | 65.2196i | 0.0554779 | − | 0.207046i | ||||
\(316\) | 56.7817 | + | 211.912i | 0.179689 | + | 0.670608i | ||||
\(317\) | −189.409 | − | 109.355i | −0.597504 | − | 0.344969i | 0.170555 | − | 0.985348i | \(-0.445444\pi\) |
−0.768059 | + | 0.640379i | \(0.778777\pi\) | |||||||
\(318\) | −91.0238 | + | 24.3897i | −0.286238 | + | 0.0766973i | ||||
\(319\) | −52.5418 | − | 52.5418i | −0.164708 | − | 0.164708i | ||||
\(320\) | −25.8564 | − | 6.92820i | −0.0808013 | − | 0.0216506i | ||||
\(321\) | −49.3160 | − | 28.4726i | −0.153632 | − | 0.0886997i | ||||
\(322\) | −24.8902 | −0.0772989 | ||||||||
\(323\) | 620.339i | 1.92055i | ||||||||
\(324\) | 159.135 | + | 91.8767i | 0.491158 | + | 0.283570i | ||||
\(325\) | −214.847 | + | 214.847i | −0.661067 | + | 0.661067i | ||||
\(326\) | 235.491 | − | 135.961i | 0.722365 | − | 0.417057i | ||||
\(327\) | −481.551 | + | 481.551i | −1.47263 | + | 1.47263i | ||||
\(328\) | 33.1623 | + | 8.88580i | 0.101104 | + | 0.0270909i | ||||
\(329\) | −20.3642 | − | 35.2719i | −0.0618973 | − | 0.107209i | ||||
\(330\) | 98.6911 | + | 170.938i | 0.299064 | + | 0.517994i | ||||
\(331\) | 43.2300 | − | 11.5834i | 0.130604 | − | 0.0349953i | −0.192925 | − | 0.981214i | \(-0.561797\pi\) |
0.323529 | + | 0.946218i | \(0.395131\pi\) | |||||||
\(332\) | − | 217.110i | − | 0.653947i | ||||||
\(333\) | −632.780 | − | 250.854i | −1.90024 | − | 0.753316i | ||||
\(334\) | 41.9361 | 0.125557 | ||||||||
\(335\) | 51.2985 | + | 191.449i | 0.153130 | + | 0.571488i | ||||
\(336\) | −19.8882 | + | 11.4824i | −0.0591910 | + | 0.0341739i | ||||
\(337\) | −11.1262 | + | 6.42373i | −0.0330155 | + | 0.0190615i | −0.516417 | − | 0.856337i | \(-0.672735\pi\) |
0.483401 | + | 0.875399i | \(0.339401\pi\) | |||||||
\(338\) | 115.478 | − | 430.971i | 0.341652 | − | 1.27506i | ||||
\(339\) | −796.685 | − | 796.685i | −2.35010 | − | 2.35010i | ||||
\(340\) | 94.8081 | + | 164.212i | 0.278847 | + | 0.482978i | ||||
\(341\) | 141.358 | + | 141.358i | 0.414541 | + | 0.414541i | ||||
\(342\) | 284.807 | − | 493.300i | 0.832768 | − | 1.44240i | ||||
\(343\) | −106.173 | −0.309542 | ||||||||
\(344\) | − | 196.667i | − | 0.571707i | ||||||
\(345\) | 140.513 | − | 243.376i | 0.407285 | − | 0.705438i | ||||
\(346\) | 33.6413 | − | 125.551i | 0.0972292 | − | 0.362864i | ||||
\(347\) | −404.610 | + | 404.610i | −1.16602 | + | 1.16602i | −0.182890 | + | 0.983133i | \(0.558545\pi\) |
−0.983133 | + | 0.182890i | \(0.941455\pi\) | |||||||
\(348\) | 25.2633 | + | 94.2839i | 0.0725957 | + | 0.270931i | ||||
\(349\) | −8.11863 | + | 14.0619i | −0.0232625 | + | 0.0402919i | −0.877422 | − | 0.479719i | \(-0.840739\pi\) |
0.854160 | + | 0.520011i | \(0.174072\pi\) | |||||||
\(350\) | 20.6829 | − | 5.54197i | 0.0590940 | − | 0.0158342i | ||||
\(351\) | 1045.75 | + | 280.208i | 2.97935 | + | 0.798314i | ||||
\(352\) | 11.6675 | − | 43.5438i | 0.0331464 | − | 0.123704i | ||||
\(353\) | 173.137 | + | 646.154i | 0.490472 | + | 1.83047i | 0.554042 | + | 0.832489i | \(0.313085\pi\) |
−0.0635704 | + | 0.997977i | \(0.520249\pi\) | |||||||
\(354\) | −337.386 | − | 194.790i | −0.953069 | − | 0.550255i | ||||
\(355\) | −176.815 | + | 47.3773i | −0.498069 | + | 0.133457i | ||||
\(356\) | −34.3369 | − | 34.3369i | −0.0964520 | − | 0.0964520i | ||||
\(357\) | 157.130 | + | 42.1029i | 0.440140 | + | 0.117935i | ||||
\(358\) | 106.379 | + | 61.4177i | 0.297147 | + | 0.171558i | ||||
\(359\) | 197.067 | 0.548934 | 0.274467 | − | 0.961597i | \(-0.411499\pi\) | ||||
0.274467 | + | 0.961597i | \(0.411499\pi\) | |||||||
\(360\) | − | 174.111i | − | 0.483642i | ||||||
\(361\) | −102.478 | − | 59.1660i | −0.283874 | − | 0.163895i | ||||
\(362\) | −43.6478 | + | 43.6478i | −0.120574 | + | 0.120574i | ||||
\(363\) | 260.618 | − | 150.468i | 0.717957 | − | 0.414513i | ||||
\(364\) | −34.1438 | + | 34.1438i | −0.0938016 | + | 0.0938016i | ||||
\(365\) | −197.478 | − | 52.9142i | −0.541037 | − | 0.144970i | ||||
\(366\) | 404.819 | + | 701.168i | 1.10606 | + | 1.91576i | ||||
\(367\) | 18.2293 | + | 31.5741i | 0.0496711 | + | 0.0860329i | 0.889792 | − | 0.456366i | \(-0.150849\pi\) |
−0.840121 | + | 0.542399i | \(0.817516\pi\) | |||||||
\(368\) | −61.9962 | + | 16.6118i | −0.168468 | + | 0.0451408i | ||||
\(369\) | 223.307i | 0.605168i | ||||||||
\(370\) | 25.5016 | + | 173.219i | 0.0689232 | + | 0.468159i | ||||
\(371\) | 13.9636 | 0.0376377 | ||||||||
\(372\) | −67.9684 | − | 253.661i | −0.182711 | − | 0.681886i | ||||
\(373\) | 302.762 | − | 174.800i | 0.811695 | − | 0.468632i | −0.0358490 | − | 0.999357i | \(-0.511414\pi\) |
0.847544 | + | 0.530725i | \(0.178080\pi\) | |||||||
\(374\) | −276.544 | + | 159.663i | −0.739422 | + | 0.426905i | ||||
\(375\) | −175.896 | + | 656.454i | −0.469057 | + | 1.75054i | ||||
\(376\) | −74.2634 | − | 74.2634i | −0.197509 | − | 0.197509i | ||||
\(377\) | 102.619 | + | 177.741i | 0.272198 | + | 0.471461i | ||||
\(378\) | −53.9503 | − | 53.9503i | −0.142726 | − | 0.142726i | ||||
\(379\) | −121.998 | + | 211.307i | −0.321894 | + | 0.557537i | −0.980879 | − | 0.194619i | \(-0.937653\pi\) |
0.658985 | + | 0.752156i | \(0.270986\pi\) | |||||||
\(380\) | −146.515 | −0.385566 | ||||||||
\(381\) | 893.142i | 2.34420i | ||||||||
\(382\) | −61.8580 | + | 107.141i | −0.161932 | + | 0.280474i | ||||
\(383\) | 90.8995 | − | 339.241i | 0.237335 | − | 0.885748i | −0.739747 | − | 0.672885i | \(-0.765055\pi\) |
0.977082 | − | 0.212862i | \(-0.0682786\pi\) | |||||||
\(384\) | −41.8737 | + | 41.8737i | −0.109046 | + | 0.109046i | ||||
\(385\) | −7.56991 | − | 28.2513i | −0.0196621 | − | 0.0733800i | ||||
\(386\) | −265.059 | + | 459.096i | −0.686682 | + | 1.18937i | ||||
\(387\) | 1235.60 | − | 331.078i | 3.19277 | − | 0.855499i | ||||
\(388\) | 114.545 | + | 30.6922i | 0.295219 | + | 0.0791036i | ||||
\(389\) | 79.0227 | − | 294.917i | 0.203143 | − | 0.758141i | −0.786864 | − | 0.617126i | \(-0.788297\pi\) |
0.990007 | − | 0.141015i | \(-0.0450365\pi\) | |||||||
\(390\) | −141.105 | − | 526.609i | −0.361806 | − | 1.35028i | ||||
\(391\) | 393.734 | + | 227.322i | 1.00699 | + | 0.581387i | ||||
\(392\) | −130.584 | + | 34.9898i | −0.333121 | + | 0.0892596i | ||||
\(393\) | −423.278 | − | 423.278i | −1.07704 | − | 1.07704i | ||||
\(394\) | −156.810 | − | 42.0170i | −0.397994 | − | 0.106642i | ||||
\(395\) | 317.868 | + | 183.521i | 0.804730 | + | 0.464611i | ||||
\(396\) | 293.214 | 0.740439 | ||||||||
\(397\) | − | 331.348i | − | 0.834631i | −0.908762 | − | 0.417315i | \(-0.862971\pi\) | ||
0.908762 | − | 0.417315i | \(-0.137029\pi\) | |||||||
\(398\) | −124.710 | − | 72.0011i | −0.313341 | − | 0.180907i | ||||
\(399\) | −88.8807 | + | 88.8807i | −0.222759 | + | 0.222759i | ||||
\(400\) | 47.8179 | − | 27.6077i | 0.119545 | − | 0.0690192i | ||||
\(401\) | −27.1067 | + | 27.1067i | −0.0675979 | + | 0.0675979i | −0.740097 | − | 0.672500i | \(-0.765221\pi\) |
0.672500 | + | 0.740097i | \(0.265221\pi\) | |||||||
\(402\) | 423.530 | + | 113.485i | 1.05356 | + | 0.282300i | ||||
\(403\) | −276.085 | − | 478.193i | −0.685075 | − | 1.18658i | ||||
\(404\) | 115.721 | + | 200.435i | 0.286438 | + | 0.496126i | ||||
\(405\) | 296.950 | − | 79.5676i | 0.733211 | − | 0.196463i | ||||
\(406\) | − | 14.4637i | − | 0.0356249i | ||||||
\(407\) | −291.711 | + | 42.9462i | −0.716734 | + | 0.105519i | ||||
\(408\) | 419.476 | 1.02813 | ||||||||
\(409\) | −9.14751 | − | 34.1390i | −0.0223655 | − | 0.0834693i | 0.953841 | − | 0.300312i | \(-0.0970908\pi\) |
−0.976207 | + | 0.216843i | \(0.930424\pi\) | |||||||
\(410\) | 49.7434 | − | 28.7194i | 0.121325 | − | 0.0700472i | ||||
\(411\) | 34.6547 | − | 20.0079i | 0.0843179 | − | 0.0486810i | ||||
\(412\) | −16.8656 | + | 62.9434i | −0.0409360 | + | 0.152775i | ||||
\(413\) | 40.8195 | + | 40.8195i | 0.0988367 | + | 0.0988367i | ||||
\(414\) | −208.734 | − | 361.538i | −0.504188 | − | 0.873280i | ||||
\(415\) | −256.844 | − | 256.844i | −0.618902 | − | 0.618902i | ||||
\(416\) | −62.2571 | + | 107.832i | −0.149656 | + | 0.259213i | ||||
\(417\) | 54.1373 | 0.129826 | ||||||||
\(418\) | − | 246.740i | − | 0.590288i | ||||||
\(419\) | 2.98377 | − | 5.16805i | 0.00712118 | − | 0.0123342i | −0.862443 | − | 0.506154i | \(-0.831067\pi\) |
0.869564 | + | 0.493820i | \(0.164400\pi\) | |||||||
\(420\) | −9.94409 | + | 37.1118i | −0.0236764 | + | 0.0883615i | ||||
\(421\) | −44.7646 | + | 44.7646i | −0.106329 | + | 0.106329i | −0.758270 | − | 0.651941i | \(-0.773955\pi\) |
0.651941 | + | 0.758270i | \(0.273955\pi\) | |||||||
\(422\) | −89.3875 | − | 333.599i | −0.211819 | − | 0.790518i | ||||
\(423\) | 341.556 | − | 591.592i | 0.807461 | − | 1.39856i | ||||
\(424\) | 34.7803 | − | 9.31935i | 0.0820290 | − | 0.0219796i | ||||
\(425\) | −377.794 | − | 101.230i | −0.888927 | − | 0.238187i | ||||
\(426\) | −104.810 | + | 391.156i | −0.246033 | + | 0.918207i | ||||
\(427\) | −31.0509 | − | 115.883i | −0.0727187 | − | 0.271390i | ||||
\(428\) | 18.8437 | + | 10.8794i | 0.0440273 | + | 0.0254192i | ||||
\(429\) | 886.842 | − | 237.629i | 2.06723 | − | 0.553913i | ||||
\(430\) | −232.660 | − | 232.660i | −0.541070 | − | 0.541070i | ||||
\(431\) | −43.6534 | − | 11.6969i | −0.101284 | − | 0.0271389i | 0.207821 | − | 0.978167i | \(-0.433363\pi\) |
−0.309105 | + | 0.951028i | \(0.600029\pi\) | |||||||
\(432\) | −170.385 | − | 98.3719i | −0.394410 | − | 0.227713i | ||||
\(433\) | 308.294 | 0.711995 | 0.355997 | − | 0.934487i | \(-0.384141\pi\) | ||||
0.355997 | + | 0.934487i | \(0.384141\pi\) | |||||||
\(434\) | 38.9132i | 0.0896618i | ||||||||
\(435\) | 141.426 | + | 81.6523i | 0.325117 | + | 0.187706i | ||||
\(436\) | 184.001 | − | 184.001i | 0.422021 | − | 0.422021i | ||||
\(437\) | −304.236 | + | 175.650i | −0.696191 | + | 0.401946i | ||||
\(438\) | −319.811 | + | 319.811i | −0.730161 | + | 0.730161i | ||||
\(439\) | 519.254 | + | 139.134i | 1.18281 | + | 0.316933i | 0.796041 | − | 0.605243i | \(-0.206924\pi\) |
0.386770 | + | 0.922176i | \(0.373591\pi\) | |||||||
\(440\) | −37.7100 | − | 65.3156i | −0.0857046 | − | 0.148445i | ||||
\(441\) | −439.660 | − | 761.513i | −0.996961 | − | 1.72679i | ||||
\(442\) | 851.949 | − | 228.279i | 1.92749 | − | 0.516468i | ||||
\(443\) | 563.760i | 1.27260i | 0.771443 | + | 0.636298i | \(0.219535\pi\) | ||||
−0.771443 | + | 0.636298i | \(0.780465\pi\) | |||||||
\(444\) | 360.070 | + | 142.743i | 0.810968 | + | 0.321494i | ||||
\(445\) | −81.2420 | −0.182566 | ||||||||
\(446\) | −21.8441 | − | 81.5234i | −0.0489779 | − | 0.182788i | ||||
\(447\) | −992.916 | + | 573.260i | −2.22129 | + | 1.28246i | ||||
\(448\) | 7.59930 | − | 4.38746i | 0.0169627 | − | 0.00979343i | ||||
\(449\) | 34.5830 | − | 129.066i | 0.0770224 | − | 0.287451i | −0.916662 | − | 0.399664i | \(-0.869127\pi\) |
0.993684 | + | 0.112212i | \(0.0357936\pi\) | |||||||
\(450\) | 253.949 | + | 253.949i | 0.564332 | + | 0.564332i | ||||
\(451\) | 48.3651 | + | 83.7709i | 0.107240 | + | 0.185745i | ||||
\(452\) | 304.414 | + | 304.414i | 0.673483 | + | 0.673483i | ||||
\(453\) | −355.467 | + | 615.687i | −0.784695 | + | 1.35913i | ||||
\(454\) | 49.5238 | 0.109083 | ||||||||
\(455\) | 80.7850i | 0.177550i | ||||||||
\(456\) | −162.063 | + | 280.702i | −0.355402 | + | 0.615574i | ||||
\(457\) | 107.541 | − | 401.347i | 0.235319 | − | 0.878222i | −0.742686 | − | 0.669640i | \(-0.766448\pi\) |
0.978005 | − | 0.208582i | \(-0.0668848\pi\) | |||||||
\(458\) | −62.8952 | + | 62.8952i | −0.137326 | + | 0.137326i | ||||
\(459\) | 360.702 | + | 1346.16i | 0.785843 | + | 2.93280i | ||||
\(460\) | −53.6903 | + | 92.9943i | −0.116718 | + | 0.202161i | ||||
\(461\) | −802.672 | + | 215.075i | −1.74115 | + | 0.466541i | −0.982703 | − | 0.185188i | \(-0.940710\pi\) |
−0.758452 | + | 0.651729i | \(0.774044\pi\) | |||||||
\(462\) | −62.4986 | − | 16.7465i | −0.135278 | − | 0.0362477i | ||||
\(463\) | 46.7162 | − | 174.347i | 0.100899 | − | 0.376560i | −0.896949 | − | 0.442135i | \(-0.854221\pi\) |
0.997848 | + | 0.0655746i | \(0.0208880\pi\) | |||||||
\(464\) | −9.65314 | − | 36.0260i | −0.0208042 | − | 0.0776423i | ||||
\(465\) | −380.492 | − | 219.677i | −0.818263 | − | 0.472424i | ||||
\(466\) | −307.213 | + | 82.3174i | −0.659255 | + | 0.176647i | ||||
\(467\) | −111.727 | − | 111.727i | −0.239245 | − | 0.239245i | 0.577292 | − | 0.816537i | \(-0.304109\pi\) |
−0.816537 | + | 0.577292i | \(0.804109\pi\) | |||||||
\(468\) | −782.284 | − | 209.612i | −1.67155 | − | 0.447890i | ||||
\(469\) | −56.2675 | − | 32.4860i | −0.119973 | − | 0.0692666i | ||||
\(470\) | −175.709 | −0.373849 | ||||||||
\(471\) | 352.007i | 0.747362i | ||||||||
\(472\) | 128.916 | + | 74.4295i | 0.273127 | + | 0.157690i | ||||
\(473\) | 391.814 | − | 391.814i | 0.828359 | − | 0.828359i | ||||
\(474\) | 703.201 | − | 405.993i | 1.48355 | − | 0.856526i | ||||
\(475\) | 213.699 | − | 213.699i | 0.449894 | − | 0.449894i | ||||
\(476\) | −60.0396 | − | 16.0876i | −0.126134 | − | 0.0337974i | ||||
\(477\) | 117.101 | + | 202.825i | 0.245495 | + | 0.425210i | ||||
\(478\) | 78.2165 | + | 135.475i | 0.163633 | + | 0.283420i | ||||
\(479\) | −514.363 | + | 137.823i | −1.07383 | + | 0.287731i | −0.752065 | − | 0.659089i | \(-0.770942\pi\) |
−0.321763 | + | 0.946820i | \(0.604275\pi\) | |||||||
\(480\) | 99.0743i | 0.206405i | ||||||||
\(481\) | 808.976 | + | 93.9590i | 1.68186 | + | 0.195341i | ||||
\(482\) | −4.57540 | −0.00949254 | ||||||||
\(483\) | 23.8430 | + | 88.9834i | 0.0493645 | + | 0.184231i | ||||
\(484\) | −99.5826 | + | 57.4941i | −0.205749 | + | 0.118789i | ||||
\(485\) | 171.817 | − | 99.1988i | 0.354263 | − | 0.204534i | ||||
\(486\) | 13.9928 | − | 52.2220i | 0.0287918 | − | 0.107453i | ||||
\(487\) | −10.3553 | − | 10.3553i | −0.0212634 | − | 0.0212634i | 0.696395 | − | 0.717659i | \(-0.254786\pi\) |
−0.717659 | + | 0.696395i | \(0.754786\pi\) | |||||||
\(488\) | −154.682 | − | 267.917i | −0.316971 | − | 0.549010i | ||||
\(489\) | −711.648 | − | 711.648i | −1.45531 | − | 1.45531i | ||||
\(490\) | −113.089 | + | 195.875i | −0.230793 | + | 0.399745i | ||||
\(491\) | 816.251 | 1.66243 | 0.831213 | − | 0.555954i | \(-0.187647\pi\) | ||||
0.831213 | + | 0.555954i | \(0.187647\pi\) | |||||||
\(492\) | − | 127.068i | − | 0.258269i | ||||||
\(493\) | −132.097 | + | 228.799i | −0.267945 | + | 0.464095i | ||||
\(494\) | −176.390 | + | 658.295i | −0.357064 | + | 1.33258i | ||||
\(495\) | 346.876 | − | 346.876i | 0.700759 | − | 0.700759i | ||||
\(496\) | 25.9708 | + | 96.9244i | 0.0523605 | + | 0.195412i | ||||
\(497\) | 30.0029 | − | 51.9665i | 0.0603679 | − | 0.104560i | ||||
\(498\) | −776.177 | + | 207.976i | −1.55859 | + | 0.417622i | ||||
\(499\) | −868.763 | − | 232.784i | −1.74101 | − | 0.466502i | −0.758337 | − | 0.651863i | \(-0.773988\pi\) |
−0.982670 | + | 0.185361i | \(0.940654\pi\) | |||||||
\(500\) | 67.2102 | − | 250.832i | 0.134420 | − | 0.501664i | ||||
\(501\) | −40.1718 | − | 149.923i | −0.0801832 | − | 0.299248i | ||||
\(502\) | 426.394 | + | 246.179i | 0.849390 | + | 0.490396i | ||||
\(503\) | 487.086 | − | 130.514i | 0.968362 | − | 0.259472i | 0.260226 | − | 0.965548i | \(-0.416203\pi\) |
0.708136 | + | 0.706076i | \(0.249536\pi\) | |||||||
\(504\) | 40.3580 | + | 40.3580i | 0.0800755 | + | 0.0800755i | ||||
\(505\) | 374.016 | + | 100.217i | 0.740626 | + | 0.198450i | ||||
\(506\) | −156.608 | − | 90.4177i | −0.309502 | − | 0.178691i | ||||
\(507\) | −1651.36 | −3.25712 | ||||||||
\(508\) | − | 341.271i | − | 0.671793i | ||||||
\(509\) | −168.180 | − | 97.0988i | −0.330413 | − | 0.190764i | 0.325612 | − | 0.945504i | \(-0.394430\pi\) |
−0.656024 | + | 0.754740i | \(0.727763\pi\) | |||||||
\(510\) | 496.246 | − | 496.246i | 0.973031 | − | 0.973031i | ||||
\(511\) | 58.0396 | − | 33.5092i | 0.113581 | − | 0.0655757i | ||||
\(512\) | 16.0000 | − | 16.0000i | 0.0312500 | − | 0.0312500i | ||||
\(513\) | −1040.17 | − | 278.712i | −2.02762 | − | 0.543298i | ||||
\(514\) | 11.6821 | + | 20.2340i | 0.0227278 | + | 0.0393658i | ||||
\(515\) | 54.5106 | + | 94.4151i | 0.105846 | + | 0.183330i | ||||
\(516\) | −703.093 | + | 188.393i | −1.36258 | + | 0.365103i | ||||
\(517\) | − | 295.905i | − | 0.572350i | ||||||
\(518\) | −46.0623 | − | 34.2400i | −0.0889234 | − | 0.0661005i | ||||
\(519\) | −481.075 | −0.926928 | ||||||||
\(520\) | 53.9162 | + | 201.218i | 0.103685 | + | 0.386958i | ||||
\(521\) | 315.017 | − | 181.875i | 0.604638 | − | 0.349088i | −0.166226 | − | 0.986088i | \(-0.553158\pi\) |
0.770864 | + | 0.637000i | \(0.219825\pi\) | |||||||
\(522\) | 210.090 | − | 121.295i | 0.402471 | − | 0.232367i | ||||
\(523\) | 137.443 | − | 512.944i | 0.262797 | − | 0.980772i | −0.700788 | − | 0.713370i | \(-0.747168\pi\) |
0.963585 | − | 0.267402i | \(-0.0861653\pi\) | |||||||
\(524\) | 161.735 | + | 161.735i | 0.308655 | + | 0.308655i | ||||
\(525\) | −39.6255 | − | 68.6333i | −0.0754771 | − | 0.130730i | ||||
\(526\) | 490.705 | + | 490.705i | 0.932899 | + | 0.932899i | ||||
\(527\) | 355.394 | − | 615.561i | 0.674372 | − | 1.16805i | ||||
\(528\) | −166.847 | −0.315998 | ||||||||
\(529\) | − | 271.533i | − | 0.513294i | ||||||
\(530\) | 30.1206 | − | 52.1704i | 0.0568314 | − | 0.0984348i | ||||
\(531\) | −250.596 | + | 935.236i | −0.471932 | + | 1.76127i | ||||
\(532\) | 33.9614 | − | 33.9614i | 0.0638373 | − | 0.0638373i | ||||
\(533\) | −69.1505 | − | 258.073i | −0.129738 | − | 0.484190i | ||||
\(534\) | −89.8633 | + | 155.648i | −0.168283 | + | 0.291475i | ||||
\(535\) | 35.1628 | − | 9.42185i | 0.0657249 | − | 0.0176109i | ||||
\(536\) | −161.831 | − | 43.3626i | −0.301924 | − | 0.0809004i | ||||
\(537\) | 117.667 | − | 439.141i | 0.219120 | − | 0.817767i | ||||
\(538\) | −112.623 | − | 420.314i | −0.209336 | − | 0.781253i | ||||
\(539\) | −329.866 | − | 190.448i | −0.611996 | − | 0.353336i | ||||
\(540\) | −317.943 | + | 85.1926i | −0.588783 | + | 0.157764i | ||||
\(541\) | −350.399 | − | 350.399i | −0.647687 | − | 0.647687i | 0.304747 | − | 0.952433i | \(-0.401428\pi\) |
−0.952433 | + | 0.304747i | \(0.901428\pi\) | |||||||
\(542\) | −142.393 | − | 38.1540i | −0.262717 | − | 0.0703948i | ||||
\(543\) | 197.854 | + | 114.231i | 0.364372 | + | 0.210370i | ||||
\(544\) | −160.282 | −0.294637 | ||||||||
\(545\) | − | 435.351i | − | 0.798810i | ||||||
\(546\) | 154.772 | + | 89.3579i | 0.283466 | + | 0.163659i | ||||
\(547\) | −221.802 | + | 221.802i | −0.405487 | + | 0.405487i | −0.880162 | − | 0.474674i | \(-0.842566\pi\) |
0.474674 | + | 0.880162i | \(0.342566\pi\) | |||||||
\(548\) | −13.2416 | + | 7.64504i | −0.0241635 | + | 0.0139508i | ||||
\(549\) | 1422.84 | − | 1422.84i | 2.59170 | − | 2.59170i | ||||
\(550\) | 150.268 | + | 40.2642i | 0.273214 | + | 0.0732076i | ||||
\(551\) | −102.071 | − | 176.791i | −0.185246 | − | 0.320856i | ||||
\(552\) | 118.776 | + | 205.726i | 0.215173 | + | 0.372691i | ||||
\(553\) | −116.219 | + | 31.1409i | −0.210162 | + | 0.0563127i | ||||
\(554\) | − | 162.877i | − | 0.294002i | ||||||
\(555\) | 594.834 | − | 257.100i | 1.07177 | − | 0.463244i | ||||
\(556\) | −20.6859 | −0.0372049 | ||||||||
\(557\) | 274.119 | + | 1023.02i | 0.492134 | + | 1.83667i | 0.545523 | + | 0.838096i | \(0.316331\pi\) |
−0.0533893 | + | 0.998574i | \(0.517002\pi\) | |||||||
\(558\) | −565.226 | + | 326.333i | −1.01295 | + | 0.584827i | ||||
\(559\) | −1325.44 | + | 765.246i | −2.37110 | + | 1.36896i | ||||
\(560\) | 3.79965 | − | 14.1805i | 0.00678509 | − | 0.0253223i | ||||
\(561\) | 835.708 | + | 835.708i | 1.48968 | + | 1.48968i | ||||
\(562\) | 212.597 | + | 368.229i | 0.378287 | + | 0.655212i | ||||
\(563\) | 377.677 | + | 377.677i | 0.670829 | + | 0.670829i | 0.957907 | − | 0.287078i | \(-0.0926838\pi\) |
−0.287078 | + | 0.957907i | \(0.592684\pi\) | |||||||
\(564\) | −194.355 | + | 336.633i | −0.344602 | + | 0.596867i | ||||
\(565\) | 720.252 | 1.27478 | ||||||||
\(566\) | − | 161.878i | − | 0.286004i | ||||||
\(567\) | −50.3882 | + | 87.2748i | −0.0888680 | + | 0.153924i | ||||
\(568\) | 40.0480 | − | 149.461i | 0.0705071 | − | 0.263136i | ||||
\(569\) | −52.7742 | + | 52.7742i | −0.0927490 | + | 0.0927490i | −0.751959 | − | 0.659210i | \(-0.770891\pi\) |
0.659210 | + | 0.751959i | \(0.270891\pi\) | |||||||
\(570\) | 140.351 | + | 523.797i | 0.246230 | + | 0.918942i | ||||
\(571\) | 356.707 | − | 617.834i | 0.624705 | − | 1.08202i | −0.363893 | − | 0.931441i | \(-0.618553\pi\) |
0.988598 | − | 0.150580i | \(-0.0481142\pi\) | |||||||
\(572\) | −338.863 | + | 90.7982i | −0.592419 | + | 0.158738i | ||||
\(573\) | 442.289 | + | 118.511i | 0.771883 | + | 0.206825i | ||||
\(574\) | −4.87326 | + | 18.1872i | −0.00848999 | + | 0.0316851i | ||||
\(575\) | −57.3268 | − | 213.946i | −0.0996987 | − | 0.372081i | ||||
\(576\) | 127.458 | + | 73.5880i | 0.221282 | + | 0.127757i | ||||
\(577\) | 589.411 | − | 157.932i | 1.02151 | − | 0.273712i | 0.291078 | − | 0.956699i | \(-0.405986\pi\) |
0.730431 | + | 0.682987i | \(0.239319\pi\) | |||||||
\(578\) | 513.827 | + | 513.827i | 0.888974 | + | 0.888974i | ||||
\(579\) | 1895.19 | + | 507.815i | 3.27322 | + | 0.877056i | ||||
\(580\) | −54.0390 | − | 31.1994i | −0.0931707 | − | 0.0537921i | ||||
\(581\) | 119.070 | 0.204940 | ||||||||
\(582\) | − | 438.903i | − | 0.754129i | ||||||
\(583\) | 87.8582 | + | 50.7250i | 0.150700 | + | 0.0870068i | ||||
\(584\) | 122.200 | − | 122.200i | 0.209247 | − | 0.209247i | ||||
\(585\) | −1173.43 | + | 677.478i | −2.00586 | + | 1.15808i | ||||
\(586\) | −112.289 | + | 112.289i | −0.191619 | + | 0.191619i | ||||
\(587\) | 452.570 | + | 121.266i | 0.770988 | + | 0.206586i | 0.622808 | − | 0.782375i | \(-0.285992\pi\) |
0.148180 | + | 0.988960i | \(0.452659\pi\) | |||||||
\(588\) | 250.179 | + | 433.323i | 0.425475 | + | 0.736944i | ||||
\(589\) | 274.611 | + | 475.640i | 0.466232 | + | 0.807538i | ||||
\(590\) | 240.560 | − | 64.4579i | 0.407729 | − | 0.109251i | ||||
\(591\) | 600.849i | 1.01667i | ||||||||
\(592\) | −137.583 | − | 54.5424i | −0.232404 | − | 0.0921324i | ||||
\(593\) | −329.159 | −0.555074 | −0.277537 | − | 0.960715i | \(-0.589518\pi\) | ||||
−0.277537 | + | 0.960715i | \(0.589518\pi\) | |||||||
\(594\) | −143.469 | − | 535.435i | −0.241531 | − | 0.901406i | ||||
\(595\) | −90.0594 | + | 51.9958i | −0.151360 | + | 0.0873879i | ||||
\(596\) | 379.394 | − | 219.043i | 0.636568 | − | 0.367523i | ||||
\(597\) | −137.944 | + | 514.813i | −0.231061 | + | 0.862333i | ||||
\(598\) | 353.187 | + | 353.187i | 0.590614 | + | 0.590614i | ||||
\(599\) | −386.007 | − | 668.584i | −0.644419 | − | 1.11617i | −0.984435 | − | 0.175747i | \(-0.943766\pi\) |
0.340016 | − | 0.940420i | \(-0.389567\pi\) | |||||||
\(600\) | −144.505 | − | 144.505i | −0.240841 | − | 0.240841i | ||||
\(601\) | −307.381 | + | 532.400i | −0.511450 | + | 0.885857i | 0.488462 | + | 0.872585i | \(0.337558\pi\) |
−0.999912 | + | 0.0132720i | \(0.995775\pi\) | |||||||
\(602\) | 107.859 | 0.179167 | ||||||||
\(603\) | − | 1089.74i | − | 1.80719i | ||||||
\(604\) | 135.824 | − | 235.255i | 0.224875 | − | 0.389495i | ||||
\(605\) | −49.7913 | + | 185.824i | −0.0822997 | + | 0.307147i | ||||
\(606\) | 605.709 | − | 605.709i | 0.999519 | − | 0.999519i | ||||
\(607\) | −11.7934 | − | 44.0136i | −0.0194290 | − | 0.0725100i | 0.955531 | − | 0.294892i | \(-0.0952836\pi\) |
−0.974960 | + | 0.222382i | \(0.928617\pi\) | |||||||
\(608\) | 61.9246 | − | 107.257i | 0.101850 | − | 0.176409i | ||||
\(609\) | −51.7083 | + | 13.8552i | −0.0849069 | + | 0.0227507i | ||||
\(610\) | −499.940 | − | 133.959i | −0.819574 | − | 0.219604i | ||||
\(611\) | −211.536 | + | 789.464i | −0.346213 | + | 1.29209i | ||||
\(612\) | −269.826 | − | 1007.01i | −0.440893 | − | 1.64543i | ||||
\(613\) | 373.812 | + | 215.821i | 0.609808 | + | 0.352073i | 0.772890 | − | 0.634540i | \(-0.218810\pi\) |
−0.163082 | + | 0.986612i | \(0.552144\pi\) | |||||||
\(614\) | 233.289 | − | 62.5096i | 0.379950 | − | 0.101807i | ||||
\(615\) | −150.323 | − | 150.323i | −0.244428 | − | 0.244428i | ||||
\(616\) | 23.8808 | + | 6.39884i | 0.0387675 | + | 0.0103877i | ||||
\(617\) | −460.862 | − | 266.079i | −0.746940 | − | 0.431246i | 0.0776469 | − | 0.996981i | \(-0.475259\pi\) |
−0.824587 | + | 0.565735i | \(0.808593\pi\) | |||||||
\(618\) | 241.181 | 0.390260 | ||||||||
\(619\) | − | 729.925i | − | 1.17920i | −0.807695 | − | 0.589600i | \(-0.799285\pi\) | ||
0.807695 | − | 0.589600i | \(-0.200715\pi\) | |||||||
\(620\) | 145.387 | + | 83.9390i | 0.234494 | + | 0.135385i | ||||
\(621\) | −558.068 | + | 558.068i | −0.898660 | + | 0.898660i | ||||
\(622\) | −116.938 | + | 67.5144i | −0.188004 | + | 0.108544i | ||||
\(623\) | 18.8315 | − | 18.8315i | 0.0302271 | − | 0.0302271i | ||||
\(624\) | 445.143 | + | 119.276i | 0.713369 | + | 0.191147i | ||||
\(625\) | −44.6788 | − | 77.3860i | −0.0714861 | − | 0.123818i | ||||
\(626\) | −139.631 | − | 241.847i | −0.223052 | − | 0.386338i | ||||
\(627\) | −882.106 | + | 236.360i | −1.40687 | + | 0.376969i | ||||
\(628\) | − | 134.502i | − | 0.214176i | ||||||
\(629\) | 415.937 | + | 962.324i | 0.661267 | + | 1.52993i | ||||
\(630\) | 95.4881 | 0.151568 | ||||||||
\(631\) | −139.954 | − | 522.316i | −0.221797 | − | 0.827758i | −0.983662 | − | 0.180023i | \(-0.942383\pi\) |
0.761865 | − | 0.647736i | \(-0.224284\pi\) | |||||||
\(632\) | −268.694 | + | 155.131i | −0.425149 | + | 0.245460i | ||||
\(633\) | −1107.00 | + | 639.127i | −1.74882 | + | 1.00968i | ||||
\(634\) | 80.0536 | − | 298.764i | 0.126268 | − | 0.471237i | ||||
\(635\) | −403.727 | − | 403.727i | −0.635791 | − | 0.635791i | ||||
\(636\) | −66.6340 | − | 115.414i | −0.104770 | − | 0.181468i | ||||
\(637\) | 743.924 | + | 743.924i | 1.16786 | + | 1.16786i | ||||
\(638\) | 52.5418 | − | 91.0050i | 0.0823538 | − | 0.142641i | ||||
\(639\) | 1006.44 | 1.57502 | ||||||||
\(640\) | − | 37.8564i | − | 0.0591506i | ||||||
\(641\) | 221.255 | − | 383.225i | 0.345172 | − | 0.597855i | −0.640213 | − | 0.768197i | \(-0.721154\pi\) |
0.985385 | + | 0.170342i | \(0.0544874\pi\) | |||||||
\(642\) | 20.8434 | − | 77.7886i | 0.0324663 | − | 0.121166i | ||||
\(643\) | −628.036 | + | 628.036i | −0.976728 | + | 0.976728i | −0.999735 | − | 0.0230073i | \(-0.992676\pi\) |
0.0230073 | + | 0.999735i | \(0.492676\pi\) | |||||||
\(644\) | −9.11046 | − | 34.0007i | −0.0141467 | − | 0.0527961i | ||||
\(645\) | −608.896 | + | 1054.64i | −0.944025 | + | 1.63510i | ||||
\(646\) | −847.399 | + | 227.060i | −1.31176 | + | 0.351486i | ||||
\(647\) | 925.141 | + | 247.891i | 1.42989 | + | 0.383139i | 0.888983 | − | 0.457941i | \(-0.151413\pi\) |
0.540911 | + | 0.841080i | \(0.318080\pi\) | |||||||
\(648\) | −67.2584 | + | 251.012i | −0.103794 | + | 0.387364i | ||||
\(649\) | 108.551 | + | 405.118i | 0.167259 | + | 0.624219i | ||||
\(650\) | −372.126 | − | 214.847i | −0.572501 | − | 0.330534i | ||||
\(651\) | 139.116 | − | 37.2760i | 0.213696 | − | 0.0572597i | ||||
\(652\) | 271.921 | + | 271.921i | 0.417057 | + | 0.417057i | ||||
\(653\) | −879.488 | − | 235.658i | −1.34684 | − | 0.360886i | −0.487874 | − | 0.872914i | \(-0.662228\pi\) |
−0.858969 | + | 0.512028i | \(0.828894\pi\) | |||||||
\(654\) | −834.070 | − | 481.551i | −1.27534 | − | 0.736316i | ||||
\(655\) | 382.669 | 0.584228 | ||||||||
\(656\) | 48.5529i | 0.0740136i | ||||||||
\(657\) | 973.462 | + | 562.029i | 1.48168 | + | 0.855447i | ||||
\(658\) | 40.7284 | − | 40.7284i | 0.0618973 | − | 0.0618973i | ||||
\(659\) | 752.287 | − | 434.333i | 1.14156 | − | 0.659079i | 0.194742 | − | 0.980855i | \(-0.437613\pi\) |
0.946816 | + | 0.321776i | \(0.104280\pi\) | |||||||
\(660\) | −197.382 | + | 197.382i | −0.299064 | + | 0.299064i | ||||
\(661\) | −763.709 | − | 204.635i | −1.15538 | − | 0.309584i | −0.370263 | − | 0.928927i | \(-0.620733\pi\) |
−0.785121 | + | 0.619343i | \(0.787399\pi\) | |||||||
\(662\) | 31.6465 | + | 54.8134i | 0.0478044 | + | 0.0827997i | ||||
\(663\) | −1632.21 | − | 2827.07i | −2.46186 | − | 4.26406i | ||||
\(664\) | 296.578 | − | 79.4679i | 0.446654 | − | 0.119681i | ||||
\(665\) | − | 80.3536i | − | 0.120833i | ||||||
\(666\) | 111.060 | − | 956.212i | 0.166756 | − | 1.43575i | ||||
\(667\) | −149.614 | −0.224309 | ||||||||
\(668\) | 15.3497 | + | 57.2858i | 0.0229786 | + | 0.0857572i | ||||
\(669\) | −270.524 | + | 156.187i | −0.404371 | + | 0.233464i | ||||
\(670\) | −242.747 | + | 140.150i | −0.362309 | + | 0.209179i | ||||
\(671\) | 225.594 | − | 841.930i | 0.336206 | − | 1.25474i | ||||
\(672\) | −22.9649 | − | 22.9649i | −0.0341739 | − | 0.0341739i | ||||
\(673\) | 408.357 | + | 707.295i | 0.606771 | + | 1.05096i | 0.991769 | + | 0.128041i | \(0.0408689\pi\) |
−0.384998 | + | 0.922918i | \(0.625798\pi\) | |||||||
\(674\) | −12.8475 | − | 12.8475i | −0.0190615 | − | 0.0190615i | ||||
\(675\) | 339.478 | − | 587.992i | 0.502930 | − | 0.871100i | ||||
\(676\) | 630.986 | 0.933411 | ||||||||
\(677\) | 673.536i | 0.994884i | 0.867497 | + | 0.497442i | \(0.165727\pi\) | ||||
−0.867497 | + | 0.497442i | \(0.834273\pi\) | |||||||
\(678\) | 796.685 | − | 1379.90i | 1.17505 | − | 2.03525i | ||||
\(679\) | −16.8326 | + | 62.8201i | −0.0247903 | + | 0.0925185i | ||||
\(680\) | −189.616 | + | 189.616i | −0.278847 | + | 0.278847i | ||||
\(681\) | −47.4402 | − | 177.049i | −0.0696626 | − | 0.259984i | ||||
\(682\) | −141.358 | + | 244.840i | −0.207270 | + | 0.359003i | ||||
\(683\) | −266.637 | + | 71.4452i | −0.390391 | + | 0.104605i | −0.448675 | − | 0.893695i | \(-0.648104\pi\) |
0.0582838 | + | 0.998300i | \(0.481437\pi\) | |||||||
\(684\) | 778.107 | + | 208.493i | 1.13758 | + | 0.304814i | ||||
\(685\) | −6.62080 | + | 24.7092i | −0.00966540 | + | 0.0360718i | ||||
\(686\) | −38.8620 | − | 145.035i | −0.0566502 | − | 0.211421i | ||||
\(687\) | 285.101 | + | 164.603i | 0.414995 | + | 0.239597i | ||||
\(688\) | 268.653 | − | 71.9852i | 0.390483 | − | 0.104630i | ||||
\(689\) | −198.141 | − | 198.141i | −0.287577 | − | 0.287577i | ||||
\(690\) | 383.889 | + | 102.863i | 0.556361 | + | 0.149076i | ||||
\(691\) | 952.431 | + | 549.886i | 1.37834 | + | 0.795783i | 0.991959 | − | 0.126558i | \(-0.0403929\pi\) |
0.386377 | + | 0.922341i | \(0.373726\pi\) | |||||||
\(692\) | 183.820 | 0.265635 | ||||||||
\(693\) | 160.808i | 0.232046i | ||||||||
\(694\) | −700.805 | − | 404.610i | −1.00981 | − | 0.583012i | ||||
\(695\) | −24.4717 | + | 24.4717i | −0.0352111 | + | 0.0352111i | ||||
\(696\) | −119.547 | + | 69.0206i | −0.171763 | + | 0.0991676i | ||||
\(697\) | 243.193 | − | 243.193i | 0.348914 | − | 0.348914i | ||||
\(698\) | −22.1805 | − | 5.94325i | −0.0317772 | − | 0.00851468i | ||||
\(699\) | 588.575 | + | 1019.44i | 0.842025 | + | 1.45843i | ||||
\(700\) | 15.1409 | + | 26.2249i | 0.0216299 | + | 0.0374641i | ||||
\(701\) | −153.209 | + | 41.0521i | −0.218557 | + | 0.0585622i | −0.366436 | − | 0.930443i | \(-0.619422\pi\) |
0.147879 | + | 0.989005i | \(0.452755\pi\) | |||||||
\(702\) | 1531.09i | 2.18104i | ||||||||
\(703\) | −804.656 | − | 93.4572i | −1.14460 | − | 0.132941i | ||||
\(704\) | 63.7525 | 0.0905575 | ||||||||
\(705\) | 168.317 | + | 628.166i | 0.238747 | + | 0.891016i | ||||
\(706\) | −819.291 | + | 473.018i | −1.16047 | + | 0.669997i | ||||
\(707\) | −109.925 | + | 63.4651i | −0.155481 | + | 0.0897668i | ||||
\(708\) | 142.596 | − | 532.176i | 0.201407 | − | 0.751662i | ||||
\(709\) | −638.923 | − | 638.923i | −0.901160 | − | 0.901160i | 0.0943763 | − | 0.995537i | \(-0.469914\pi\) |
−0.995537 | + | 0.0943763i | \(0.969914\pi\) | |||||||
\(710\) | −129.437 | − | 224.192i | −0.182306 | − | 0.315763i | ||||
\(711\) | −1426.97 | − | 1426.97i | −2.00699 | − | 2.00699i | ||||
\(712\) | 34.3369 | − | 59.4733i | 0.0482260 | − | 0.0835298i | ||||
\(713\) | 402.523 | 0.564548 | ||||||||
\(714\) | 230.054i | 0.322205i | ||||||||
\(715\) | −293.464 | + | 508.295i | −0.410440 | + | 0.710902i | ||||
\(716\) | −44.9609 | + | 167.796i | −0.0627945 | + | 0.234352i | ||||
\(717\) | 409.402 | − | 409.402i | 0.570993 | − | 0.570993i | ||||
\(718\) | 72.1316 | + | 269.199i | 0.100462 | + | 0.374929i | ||||
\(719\) | −635.609 | + | 1100.91i | −0.884018 | + | 1.53116i | −0.0371834 | + | 0.999308i | \(0.511839\pi\) |
−0.846835 | + | 0.531856i | \(0.821495\pi\) | |||||||
\(720\) | 237.840 | − | 63.7291i | 0.330334 | − | 0.0885126i | ||||
\(721\) | −34.5202 | − | 9.24965i | −0.0478782 | − | 0.0128289i | ||||
\(722\) | 43.3125 | − | 161.644i | 0.0599896 | − | 0.223884i | ||||
\(723\) | 4.38291 | + | 16.3572i | 0.00606211 | + | 0.0226241i | ||||
\(724\) | −75.6003 | − | 43.6478i | −0.104420 | − | 0.0602871i | ||||
\(725\) | 124.324 | − | 33.3126i | 0.171482 | − | 0.0459484i | ||||
\(726\) | 300.936 | + | 300.936i | 0.414513 | + | 0.414513i | ||||
\(727\) | −235.524 | − | 63.1084i | −0.323967 | − | 0.0868066i | 0.0931704 | − | 0.995650i | \(-0.470300\pi\) |
−0.417137 | + | 0.908844i | \(0.636967\pi\) | |||||||
\(728\) | −59.1388 | − | 34.1438i | −0.0812346 | − | 0.0469008i | ||||
\(729\) | 626.791 | 0.859796 | ||||||||
\(730\) | − | 289.128i | − | 0.396066i | ||||||
\(731\) | −1706.20 | − | 985.073i | −2.33406 | − | 1.34757i | ||||
\(732\) | −809.639 | + | 809.639i | −1.10606 | + | 1.10606i | ||||
\(733\) | −843.518 | + | 487.006i | −1.15078 | + | 0.664400i | −0.949076 | − | 0.315047i | \(-0.897980\pi\) |
−0.201699 | + | 0.979447i | \(0.564646\pi\) | |||||||
\(734\) | −36.4586 | + | 36.4586i | −0.0496711 | + | 0.0496711i | ||||
\(735\) | 808.592 | + | 216.662i | 1.10012 | + | 0.294778i | ||||
\(736\) | −45.3843 | − | 78.6080i | −0.0616635 | − | 0.106804i | ||||
\(737\) | −236.021 | − | 408.801i | −0.320246 | − | 0.554682i | ||||
\(738\) | −305.043 | + | 81.7360i | −0.413337 | + | 0.110753i | ||||
\(739\) | − | 574.895i | − | 0.777937i | −0.921251 | − | 0.388969i | \(-0.872831\pi\) | ||
0.921251 | − | 0.388969i | \(-0.127169\pi\) | |||||||
\(740\) | −227.287 | + | 98.2383i | −0.307145 | + | 0.132754i | ||||
\(741\) | 2522.40 | 3.40405 | ||||||||
\(742\) | 5.11103 | + | 19.0746i | 0.00688818 | + | 0.0257070i | ||||
\(743\) | 331.399 | − | 191.333i | 0.446029 | − | 0.257515i | −0.260123 | − | 0.965576i | \(-0.583763\pi\) |
0.706151 | + | 0.708061i | \(0.250430\pi\) | |||||||
\(744\) | 321.630 | − | 185.693i | 0.432298 | − | 0.249588i | ||||
\(745\) | 189.697 | − | 707.960i | 0.254627 | − | 0.950281i | ||||
\(746\) | 349.600 | + | 349.600i | 0.468632 | + | 0.468632i | ||||
\(747\) | 998.545 | + | 1729.53i | 1.33674 | + | 2.31530i | ||||
\(748\) | −319.325 | − | 319.325i | −0.426905 | − | 0.426905i | ||||
\(749\) | −5.96662 | + | 10.3345i | −0.00796611 | + | 0.0137977i | ||||
\(750\) | −961.116 | −1.28149 | ||||||||
\(751\) | − | 1233.34i | − | 1.64227i | −0.570735 | − | 0.821134i | \(-0.693342\pi\) | ||
0.570735 | − | 0.821134i | \(-0.306658\pi\) | |||||||
\(752\) | 74.2634 | − | 128.628i | 0.0987545 | − | 0.171048i | ||||
\(753\) | 471.643 | − | 1760.19i | 0.626351 | − | 2.33758i | ||||
\(754\) | −205.237 | + | 205.237i | −0.272198 | + | 0.272198i | ||||
\(755\) | −117.627 | − | 438.991i | −0.155798 | − | 0.581445i | ||||
\(756\) | 53.9503 | − | 93.4446i | 0.0713628 | − | 0.123604i | ||||
\(757\) | −391.060 | + | 104.784i | −0.516592 | + | 0.138420i | −0.507690 | − | 0.861540i | \(-0.669500\pi\) |
−0.00890207 | + | 0.999960i | \(0.502834\pi\) | |||||||
\(758\) | −333.305 | − | 89.3087i | −0.439716 | − | 0.117821i | ||||
\(759\) | −173.227 | + | 646.493i | −0.228231 | + | 0.851769i | ||||
\(760\) | −53.6283 | − | 200.143i | −0.0705635 | − | 0.263347i | ||||
\(761\) | 598.566 | + | 345.582i | 0.786552 | + | 0.454116i | 0.838747 | − | 0.544521i | \(-0.183288\pi\) |
−0.0521953 | + | 0.998637i | \(0.516622\pi\) | |||||||
\(762\) | −1220.05 | + | 326.913i | −1.60112 | + | 0.429019i | ||||
\(763\) | 100.912 | + | 100.912i | 0.132257 | + | 0.132257i | ||||
\(764\) | −168.999 | − | 45.2832i | −0.221203 | − | 0.0592712i | ||||
\(765\) | −1510.51 | − | 872.092i | −1.97452 | − | 1.13999i | ||||
\(766\) | 496.684 | 0.648412 | ||||||||
\(767\) | − | 1158.44i | − | 1.51035i | ||||||
\(768\) | −72.5274 | − | 41.8737i | −0.0944367 | − | 0.0545231i | ||||
\(769\) | −815.124 | + | 815.124i | −1.05998 | + | 1.05998i | −0.0618968 | + | 0.998083i | \(0.519715\pi\) |
−0.998083 | + | 0.0618968i | \(0.980285\pi\) | |||||||
\(770\) | 35.8212 | − | 20.6814i | 0.0465210 | − | 0.0268589i | ||||
\(771\) | 61.1467 | − | 61.1467i | 0.0793082 | − | 0.0793082i | ||||
\(772\) | −724.155 | − | 194.037i | −0.938025 | − | 0.251343i | ||||
\(773\) | −25.7966 | − | 44.6811i | −0.0333721 | − | 0.0578022i | 0.848857 | − | 0.528623i | \(-0.177291\pi\) |
−0.882229 | + | 0.470820i | \(0.843958\pi\) | |||||||
\(774\) | 904.523 | + | 1566.68i | 1.16863 | + | 2.02413i | ||||
\(775\) | −334.482 | + | 89.6243i | −0.431590 | + | 0.115644i | ||||
\(776\) | 167.705i | 0.216115i | ||||||||
\(777\) | −78.2850 | + | 197.474i | −0.100753 | + | 0.254149i | ||||
\(778\) | 431.788 | 0.554998 | ||||||||
\(779\) | 68.7812 | + | 256.695i | 0.0882942 | + | 0.329518i | ||||
\(780\) | 667.714 | − | 385.505i | 0.856043 | − | 0.494237i | ||||
\(781\) | 377.553 | − | 217.980i | 0.483422 | − | 0.279104i | ||||
\(782\) | −166.412 | + | 621.056i | −0.212802 | + | 0.794189i | ||||
\(783\) | −324.294 | − | 324.294i | −0.414168 | − | 0.414168i | ||||
\(784\) | −95.5938 | − | 165.573i | −0.121931 | − | 0.211190i | ||||
\(785\) | −159.118 | − | 159.118i | −0.202698 | − | 0.202698i | ||||
\(786\) | 423.278 | − | 733.139i | 0.538522 | − | 0.932747i | ||||
\(787\) | 583.361 | 0.741246 | 0.370623 | − | 0.928783i | \(-0.379144\pi\) | ||||
0.370623 | + | 0.928783i | \(0.379144\pi\) | |||||||
\(788\) | − | 229.585i | − | 0.291352i | ||||||
\(789\) | 1284.23 | − | 2224.35i | 1.62766 | − | 2.81920i | ||||
\(790\) | −134.347 | + | 501.390i | −0.170059 | + | 0.634671i | ||||
\(791\) | −166.950 | + | 166.950i | −0.211063 | + | 0.211063i | ||||
\(792\) | 107.324 | + | 400.537i | 0.135510 | + | 0.505729i | ||||
\(793\) | −1203.76 | + | 2084.97i | −1.51798 | + | 2.62921i | ||||
\(794\) | 452.630 | − | 121.282i | 0.570063 | − | 0.152748i | ||||
\(795\) | −215.365 | − | 57.7068i | −0.270899 | − | 0.0725871i | ||||
\(796\) | 52.7085 | − | 196.711i | 0.0662167 | − | 0.247124i | ||||
\(797\) | 137.023 | + | 511.376i | 0.171923 | + | 0.641626i | 0.997055 | + | 0.0766860i | \(0.0244339\pi\) |
−0.825132 | + | 0.564940i | \(0.808899\pi\) | |||||||
\(798\) | −153.946 | − | 88.8807i | −0.192915 | − | 0.111379i | ||||
\(799\) | −1016.25 | + | 272.303i | −1.27190 | + | 0.340804i | ||||
\(800\) | 55.2154 | + | 55.2154i | 0.0690192 | + | 0.0690192i | ||||
\(801\) | 431.456 | + | 115.608i | 0.538647 | + | 0.144330i | ||||
\(802\) | −46.9503 | − | 27.1067i | −0.0585415 | − | 0.0337989i | ||||
\(803\) | 486.910 | 0.606363 | ||||||||
\(804\) | 620.091i | 0.771258i | ||||||||
\(805\) | −51.0010 | − | 29.4455i | −0.0633553 | − | 0.0365782i | ||||
\(806\) | 552.170 | − | 552.170i | 0.685075 | − | 0.685075i | ||||
\(807\) | −1394.75 | + | 805.261i | −1.72832 | + | 0.997846i | ||||
\(808\) | −231.442 | + | 231.442i | −0.286438 | + | 0.286438i | ||||
\(809\) | 270.117 | + | 72.3776i | 0.333890 | + | 0.0894655i | 0.421869 | − | 0.906657i | \(-0.361374\pi\) |
−0.0879791 | + | 0.996122i | \(0.528041\pi\) | |||||||
\(810\) | 217.383 | + | 376.518i | 0.268374 | + | 0.464837i | ||||
\(811\) | 679.349 | + | 1176.67i | 0.837668 | + | 1.45088i | 0.891840 | + | 0.452352i | \(0.149415\pi\) |
−0.0541715 | + | 0.998532i | \(0.517252\pi\) | |||||||
\(812\) | 19.7578 | − | 5.29409i | 0.0243323 | − | 0.00651982i | ||||
\(813\) | 545.607i | 0.671104i | ||||||||
\(814\) | −165.439 | − | 382.765i | −0.203242 | − | 0.470227i | ||||
\(815\) | 643.373 | 0.789415 | ||||||||
\(816\) | 153.539 | + | 573.015i | 0.188161 | + | 0.702225i | ||||
\(817\) | 1318.37 | − | 761.159i | 1.61367 | − | 0.931651i | ||||
\(818\) | 43.2865 | − | 24.9914i | 0.0529174 | − | 0.0305519i | ||||
\(819\) | 114.958 | − | 429.030i | 0.140364 | − | 0.523846i | ||||
\(820\) | 57.4387 | + | 57.4387i | 0.0700472 | + | 0.0700472i | ||||
\(821\) | −615.011 | − | 1065.23i | −0.749100 | − | 1.29748i | −0.948255 | − | 0.317511i | \(-0.897153\pi\) |
0.199155 | − | 0.979968i | \(-0.436180\pi\) | |||||||
\(822\) | 40.0158 | + | 40.0158i | 0.0486810 | + | 0.0486810i | ||||
\(823\) | −10.0892 | + | 17.4751i | −0.0122591 | + | 0.0212334i | −0.872090 | − | 0.489346i | \(-0.837236\pi\) |
0.859831 | + | 0.510579i | \(0.170569\pi\) | |||||||
\(824\) | −92.1555 | −0.111839 | ||||||||
\(825\) | − | 575.783i | − | 0.697919i | ||||||
\(826\) | −40.8195 | + | 70.7015i | −0.0494183 | + | 0.0855951i | ||||
\(827\) | −196.114 | + | 731.909i | −0.237140 | + | 0.885017i | 0.740033 | + | 0.672570i | \(0.234810\pi\) |
−0.977173 | + | 0.212446i | \(0.931857\pi\) | |||||||
\(828\) | 417.468 | − | 417.468i | 0.504188 | − | 0.504188i | ||||
\(829\) | 180.645 | + | 674.176i | 0.217907 | + | 0.813240i | 0.985123 | + | 0.171851i | \(0.0549748\pi\) |
−0.767216 | + | 0.641389i | \(0.778359\pi\) | |||||||
\(830\) | 256.844 | − | 444.867i | 0.309451 | − | 0.535985i | ||||
\(831\) | −582.291 | + | 156.024i | −0.700711 | + | 0.187755i | ||||
\(832\) | −170.090 | − | 45.5753i | −0.204435 | − | 0.0547781i | ||||
\(833\) | −350.515 | + | 1308.14i | −0.420787 | + | 1.57040i | ||||
\(834\) | 19.8156 | + | 73.9529i | 0.0237597 | + | 0.0886726i | ||||
\(835\) | 85.9287 | + | 49.6110i | 0.102909 | + | 0.0594143i | ||||
\(836\) | 337.054 | − | 90.3133i | 0.403174 | − | 0.108030i | ||||
\(837\) | 872.480 | + | 872.480i | 1.04239 | + | 1.04239i | ||||
\(838\) | 8.15182 | + | 2.18427i | 0.00972771 | + | 0.00260653i | ||||
\(839\) | 1076.40 | + | 621.463i | 1.28296 | + | 0.740718i | 0.977389 | − | 0.211450i | \(-0.0678187\pi\) |
0.305573 | + | 0.952169i | \(0.401152\pi\) | |||||||
\(840\) | −54.3355 | −0.0646851 | ||||||||
\(841\) | 754.059i | 0.896622i | ||||||||
\(842\) | −77.5345 | − | 44.7646i | −0.0920838 | − | 0.0531646i | ||||
\(843\) | 1112.78 | − | 1112.78i | 1.32002 | − | 1.32002i | ||||
\(844\) | 422.986 | − | 244.211i | 0.501169 | − | 0.289350i | ||||
\(845\) | 746.464 | − | 746.464i | 0.883390 | − | 0.883390i | ||||
\(846\) | 933.148 | + | 250.036i | 1.10301 | + | 0.295551i | ||||
\(847\) | −31.5316 | − | 54.6143i | −0.0372274 | − | 0.0644797i | ||||
\(848\) | 25.4609 | + | 44.0997i | 0.0300247 | + | 0.0520043i | ||||
\(849\) | −578.720 | + | 155.067i | −0.681649 | + | 0.182647i | ||||
\(850\) | − | 553.129i | − | 0.650740i | ||||||
\(851\) | −354.183 | + | 476.474i | −0.416196 | + | 0.559899i | ||||
\(852\) | −572.692 | −0.672174 | ||||||||
\(853\) | −147.550 | − | 550.663i | −0.172977 | − | 0.645560i | −0.996887 | − | 0.0788394i | \(-0.974879\pi\) |
0.823910 | − | 0.566721i | \(-0.191788\pi\) | |||||||
\(854\) | 146.934 | − | 84.8326i | 0.172054 | − | 0.0993356i | ||||
\(855\) | 1167.16 | − | 673.860i | 1.36510 | − | 0.788140i | ||||
\(856\) | −7.96428 | + | 29.7231i | −0.00930407 | + | 0.0347233i | ||||
\(857\) | 492.222 | + | 492.222i | 0.574355 | + | 0.574355i | 0.933342 | − | 0.358987i | \(-0.116878\pi\) |
−0.358987 | + | 0.933342i | \(0.616878\pi\) | |||||||
\(858\) | 649.213 | + | 1124.47i | 0.756659 | + | 1.31057i | ||||
\(859\) | −181.096 | − | 181.096i | −0.210822 | − | 0.210822i | 0.593795 | − | 0.804617i | \(-0.297629\pi\) |
−0.804617 | + | 0.593795i | \(0.797629\pi\) | |||||||
\(860\) | 232.660 | − | 402.979i | 0.270535 | − | 0.468580i | ||||
\(861\) | 69.6883 | 0.0809387 | ||||||||
\(862\) | − | 63.9129i | − | 0.0741450i | ||||||
\(863\) | −497.794 | + | 862.205i | −0.576819 | + | 0.999079i | 0.419023 | + | 0.907976i | \(0.362373\pi\) |
−0.995841 | + | 0.0911034i | \(0.970961\pi\) | |||||||
\(864\) | 72.0132 | − | 268.757i | 0.0833486 | − | 0.311061i | ||||
\(865\) | 217.461 | − | 217.461i | 0.251400 | − | 0.251400i | ||||
\(866\) | 112.843 | + | 421.137i | 0.130304 | + | 0.486302i | ||||
\(867\) | 1344.74 | − | 2329.16i | 1.55103 | − | 2.68646i | ||||
\(868\) | −53.1564 | + | 14.2432i | −0.0612401 | + | 0.0164092i | ||||
\(869\) | −844.371 | − | 226.248i | −0.971658 | − | 0.260355i | ||||
\(870\) | −59.7736 | + | 223.078i | −0.0687053 | + | 0.256412i | ||||
\(871\) | 337.454 | + | 1259.39i | 0.387432 | + | 1.44592i | ||||
\(872\) | 318.699 | + | 184.001i | 0.365481 | + | 0.211010i | ||||
\(873\) | −1053.64 | + | 282.322i | −1.20692 | + | 0.323393i | ||||
\(874\) | −351.301 | − | 351.301i | −0.401946 | − | 0.401946i | ||||
\(875\) | 137.564 | + | 36.8602i | 0.157216 | + | 0.0421260i | ||||
\(876\) | −553.928 | − | 319.811i | −0.632338 | − | 0.365081i | ||||
\(877\) | −1053.75 | −1.20153 | −0.600767 | − | 0.799424i | \(-0.705138\pi\) | ||||
−0.600767 | + | 0.799424i | \(0.705138\pi\) | |||||||
\(878\) | 760.241i | 0.865878i | ||||||||
\(879\) | 509.002 | + | 293.872i | 0.579069 | + | 0.334326i | ||||
\(880\) | 75.4200 | − | 75.4200i | 0.0857046 | − | 0.0857046i | ||||
\(881\) | −467.452 | + | 269.884i | −0.530593 | + | 0.306338i | −0.741258 | − | 0.671220i | \(-0.765770\pi\) |
0.210665 | + | 0.977558i | \(0.432437\pi\) | |||||||
\(882\) | 879.320 | − | 879.320i | 0.996961 | − | 0.996961i | ||||
\(883\) | 375.206 | + | 100.536i | 0.424922 | + | 0.113858i | 0.464942 | − | 0.885341i | \(-0.346075\pi\) |
−0.0400195 | + | 0.999199i | \(0.512742\pi\) | |||||||
\(884\) | 623.670 | + | 1080.23i | 0.705509 | + | 1.22198i | ||||
\(885\) | −460.878 | − | 798.265i | −0.520766 | − | 0.901994i | ||||
\(886\) | −770.111 | + | 206.351i | −0.869200 | + | 0.232901i | ||||
\(887\) | − | 1012.84i | − | 1.14188i | −0.820993 | − | 0.570938i | \(-0.806580\pi\) | ||
0.820993 | − | 0.570938i | \(-0.193420\pi\) | |||||||
\(888\) | −63.1962 | + | 544.112i | −0.0711669 | + | 0.612739i | ||||
\(889\) | 187.164 | 0.210533 | ||||||||
\(890\) | −29.7366 | − | 110.979i | −0.0334119 | − | 0.124695i | ||||
\(891\) | −634.079 | + | 366.086i | −0.711649 | + | 0.410871i | ||||
\(892\) | 103.368 | − | 59.6793i | 0.115883 | − | 0.0669050i | ||||
\(893\) | 210.407 | − | 785.248i | 0.235618 | − | 0.879337i | ||||
\(894\) | −1146.52 | − | 1146.52i | −1.28246 | − | 1.28246i | ||||
\(895\) | 145.316 | + | 251.694i | 0.162364 | + | 0.281223i | ||||
\(896\) | 8.77491 | + | 8.77491i | 0.00979343 | + | 0.00979343i | ||||
\(897\) | 924.329 | − | 1600.98i | 1.03047 | − | 1.78482i | ||||
\(898\) | 188.965 | 0.210429 | ||||||||
\(899\) | 233.906i | 0.260185i | ||||||||
\(900\) | −253.949 | + | 439.853i | −0.282166 | + | 0.488726i | ||||
\(901\) | 93.3581 | − | 348.417i | 0.103616 | − | 0.386700i | ||||
\(902\) | −96.7303 | + | 96.7303i | −0.107240 | + | 0.107240i | ||||
\(903\) | −103.321 | − | 385.599i | −0.114420 | − | 0.427019i | ||||
\(904\) | −304.414 | + | 527.261i | −0.336741 | + | 0.583253i | ||||
\(905\) | −141.072 | + | 37.8001i | −0.155881 | + | 0.0417681i | ||||
\(906\) | −971.154 | − | 260.220i | −1.07191 | − | 0.287218i | ||||
\(907\) | 354.112 | − | 1321.56i | 0.390421 | − | 1.45707i | −0.439020 | − | 0.898478i | \(-0.644674\pi\) |
0.829441 | − | 0.558595i | \(-0.188659\pi\) | |||||||
\(908\) | 18.1270 | + | 67.6508i | 0.0199636 | + | 0.0745052i | ||||
\(909\) | −1843.70 | − | 1064.46i | −2.02827 | − | 1.17102i | ||||
\(910\) | −110.354 | + | 29.5694i | −0.121269 | + | 0.0324938i | ||||
\(911\) | 882.939 | + | 882.939i | 0.969197 | + | 0.969197i | 0.999540 | − | 0.0303421i | \(-0.00965968\pi\) |
−0.0303421 | + | 0.999540i | \(0.509660\pi\) | |||||||
\(912\) | −442.765 | − | 118.639i | −0.485488 | − | 0.130086i | ||||
\(913\) | 749.184 | + | 432.541i | 0.820574 | + | 0.473758i | ||||
\(914\) | 587.613 | 0.642903 | ||||||||
\(915\) | 1915.63i | 2.09358i | ||||||||
\(916\) | −108.938 | − | 62.8952i | −0.118928 | − | 0.0686629i | ||||
\(917\) | −88.7007 | + | 88.7007i | −0.0967292 | + | 0.0967292i | ||||
\(918\) | −1706.86 | + | 985.455i | −1.85932 | + | 1.07348i | ||||
\(919\) | −1243.71 | + | 1243.71i | −1.35333 | + | 1.35333i | −0.471427 | + | 0.881905i | \(0.656261\pi\) |
−0.881905 | + | 0.471427i | \(0.843739\pi\) | |||||||
\(920\) | −146.685 | − | 39.3040i | −0.159440 | − | 0.0427217i | ||||
\(921\) | −446.948 | − | 774.137i | −0.485286 | − | 0.840539i | ||||
\(922\) | −587.597 | − | 1017.75i | −0.637307 | − | 1.10385i | ||||
\(923\) | −1163.13 | + | 311.659i | −1.26016 | + | 0.337659i | ||||
\(924\) | − | 91.5043i | − | 0.0990306i | ||||||
\(925\) | 188.224 | − | 474.794i | 0.203485 | − | 0.513291i | ||||
\(926\) | 255.262 | 0.275661 | ||||||||
\(927\) | −155.139 | − | 578.985i | −0.167356 | − | 0.624579i | ||||
\(928\) | 45.6791 | − | 26.3729i | 0.0492232 | − | 0.0284190i | ||||
\(929\) | 808.546 | − | 466.814i | 0.870340 | − | 0.502491i | 0.00287910 | − | 0.999996i | \(-0.499084\pi\) |
0.867461 | + | 0.497505i | \(0.165750\pi\) | |||||||
\(930\) | 160.815 | − | 600.170i | 0.172919 | − | 0.645344i | ||||
\(931\) | −739.951 | − | 739.951i | −0.794791 | − | 0.794791i | ||||
\(932\) | −224.895 | − | 389.530i | −0.241304 | − | 0.417951i | ||||
\(933\) | 353.385 | + | 353.385i | 0.378762 | + | 0.378762i | ||||
\(934\) | 111.727 | − | 193.518i | 0.119622 | − | 0.207192i | ||||
\(935\) | −755.532 | −0.808055 | ||||||||
\(936\) | − | 1145.34i | − | 1.22366i | ||||||
\(937\) | 590.350 | − | 1022.52i | 0.630042 | − | 1.09127i | −0.357500 | − | 0.933913i | \(-0.616371\pi\) |
0.987543 | − | 0.157352i | \(-0.0502958\pi\) | |||||||
\(938\) | 23.7814 | − | 88.7535i | 0.0253533 | − | 0.0946200i | ||||
\(939\) | −730.857 | + | 730.857i | −0.778335 | + | 0.778335i | ||||
\(940\) | −64.3140 | − | 240.023i | −0.0684191 | − | 0.255344i | ||||
\(941\) | 840.243 | − | 1455.34i | 0.892925 | − | 1.54659i | 0.0565734 | − | 0.998398i | \(-0.481982\pi\) |
0.836352 | − | 0.548193i | \(-0.184684\pi\) | |||||||
\(942\) | −480.851 | + | 128.844i | −0.510458 | + | 0.136777i | ||||
\(943\) | 188.131 | + | 50.4095i | 0.199503 | + | 0.0534565i | ||||
\(944\) | −54.4862 | + | 203.345i | −0.0577184 | + | 0.215408i | ||||
\(945\) | −46.7223 | − | 174.370i | −0.0494416 | − | 0.184519i | ||||
\(946\) | 678.641 | + | 391.814i | 0.717380 | + | 0.414179i | ||||
\(947\) | 659.754 | − | 176.781i | 0.696678 | − | 0.186674i | 0.106936 | − | 0.994266i | \(-0.465896\pi\) |
0.589742 | + | 0.807592i | \(0.299229\pi\) | |||||||
\(948\) | 811.986 | + | 811.986i | 0.856526 | + | 0.856526i | ||||
\(949\) | −1299.06 | − | 348.082i | −1.36887 | − | 0.366788i | ||||
\(950\) | 370.138 | + | 213.699i | 0.389619 | + | 0.224947i | ||||
\(951\) | −1144.78 | −1.20376 | ||||||||
\(952\) | − | 87.9040i | − | 0.0923362i | ||||||
\(953\) | 674.715 | + | 389.547i | 0.707990 | + | 0.408758i | 0.810316 | − | 0.585993i | \(-0.199295\pi\) |
−0.102326 | + | 0.994751i | \(0.532629\pi\) | |||||||
\(954\) | −234.203 | + | 234.203i | −0.245495 | + | 0.245495i | ||||
\(955\) | −253.499 | + | 146.358i | −0.265444 | + | 0.153254i | ||||
\(956\) | −156.433 | + | 156.433i | −0.163633 | + | 0.163633i | ||||
\(957\) | −375.677 | − | 100.662i | −0.392557 | − | 0.105185i | ||||
\(958\) | −376.540 | − | 652.187i | −0.393048 | − | 0.680780i | ||||
\(959\) | −4.19278 | − | 7.26211i | −0.00437204 | − | 0.00757259i | ||||
\(960\) | −135.338 | + | 36.2637i | −0.140977 | + | 0.0377747i | ||||
\(961\) | 331.699i | 0.345160i | ||||||||
\(962\) | 167.755 | + | 1139.47i | 0.174382 | + | 1.18448i | ||||
\(963\) | −200.149 | −0.207839 | ||||||||
\(964\) | −1.67471 | − | 6.25012i | −0.00173726 | − | 0.00648353i | ||||
\(965\) | −1086.23 | + | 627.137i | −1.12563 | + | 0.649883i | ||||
\(966\) | −112.826 | + | 65.1404i | −0.116798 | + | 0.0674331i | ||||
\(967\) | −121.165 | + | 452.194i | −0.125300 | + | 0.467626i | −0.999850 | − | 0.0173092i | \(-0.994490\pi\) |
0.874550 | + | 0.484935i | \(0.161157\pi\) | |||||||
\(968\) | −114.988 | − | 114.988i | −0.118789 | − | 0.118789i | ||||
\(969\) | 1623.49 | + | 2811.97i | 1.67543 | + | 2.90193i | ||||
\(970\) | 198.398 | + | 198.398i | 0.204534 | + | 0.204534i | ||||
\(971\) | −105.007 | + | 181.877i | −0.108143 | + | 0.187309i | −0.915018 | − | 0.403413i | \(-0.867824\pi\) |
0.806875 | + | 0.590722i | \(0.201157\pi\) | |||||||
\(972\) | 76.4583 | 0.0786608 | ||||||||
\(973\) | − | 11.3448i | − | 0.0116596i | ||||||
\(974\) | 10.3553 | − | 17.9359i | 0.0106317 | − | 0.0184147i | ||||
\(975\) | −411.615 | + | 1536.17i | −0.422170 | + | 1.57556i | ||||
\(976\) | 309.364 | − | 309.364i | 0.316971 | − | 0.316971i | ||||
\(977\) | −134.375 | − | 501.494i | −0.137538 | − | 0.513300i | −0.999975 | − | 0.00713434i | \(-0.997729\pi\) |
0.862436 | − | 0.506166i | \(-0.168938\pi\) | |||||||
\(978\) | 711.648 | − | 1232.61i | 0.727656 | − | 1.26034i | ||||
\(979\) | 186.895 | − | 50.0783i | 0.190904 | − | 0.0511525i | ||||
\(980\) | −308.964 | − | 82.7866i | −0.315269 | − | 0.0844762i | ||||
\(981\) | −619.511 | + | 2312.05i | −0.631509 | + | 2.35683i | ||||
\(982\) | 298.769 | + | 1115.02i | 0.304245 | + | 1.13546i | ||||
\(983\) | 1522.82 | + | 879.202i | 1.54916 | + | 0.894407i | 0.998206 | + | 0.0598706i | \(0.0190688\pi\) |
0.550953 | + | 0.834537i | \(0.314265\pi\) | |||||||
\(984\) | 173.578 | − | 46.5102i | 0.176401 | − | 0.0472664i | ||||
\(985\) | −271.602 | − | 271.602i | −0.275738 | − | 0.275738i | ||||
\(986\) | −360.896 | − | 96.7018i | −0.366020 | − | 0.0980749i | ||||
\(987\) | −184.620 | − | 106.591i | −0.187052 | − | 0.107995i | ||||
\(988\) | −963.811 | −0.975517 | ||||||||
\(989\) | − | 1115.70i | − | 1.12811i | ||||||
\(990\) | 600.806 | + | 346.876i | 0.606875 | + | 0.350379i | ||||
\(991\) | −620.013 | + | 620.013i | −0.625643 | + | 0.625643i | −0.946969 | − | 0.321325i | \(-0.895872\pi\) |
0.321325 | + | 0.946969i | \(0.395872\pi\) | |||||||
\(992\) | −122.895 | + | 70.9536i | −0.123886 | + | 0.0715258i | ||||
\(993\) | 165.645 | − | 165.645i | 0.166812 | − | 0.166812i | ||||
\(994\) | 81.9693 | + | 21.9636i | 0.0824641 | + | 0.0220962i | ||||
\(995\) | −170.356 | − | 295.066i | −0.171212 | − | 0.296549i | ||||
\(996\) | −568.201 | − | 984.153i | −0.570483 | − | 0.988105i | ||||
\(997\) | 1551.59 | − | 415.747i | 1.55626 | − | 0.416998i | 0.624782 | − | 0.780799i | \(-0.285188\pi\) |
0.931477 | + | 0.363800i | \(0.118521\pi\) | |||||||
\(998\) | − | 1271.96i | − | 1.27451i | ||||||
\(999\) | −1800.47 | + | 265.069i | −1.80227 | + | 0.265334i |
(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 | 74.3.g.b.23.3 | ✓ | 12 | |
37.29 | odd | 12 | inner | 74.3.g.b.29.3 | yes | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
74.3.g.b.23.3 | ✓ | 12 | 1.1 | even | 1 | trivial | |
74.3.g.b.29.3 | yes | 12 | 37.29 | odd | 12 | inner |