Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [315,3,Mod(191,315)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(315, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([1, 0, 2]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("315.191");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 315 = 3^{2} \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 315.bd (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(8.58312832735\) |
Analytic rank: | \(0\) |
Dimension: | \(128\) |
Relative dimension: | \(64\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 191.4 | ||
Character | \(\chi\) | \(=\) | 315.191 |
Dual form | 315.3.bd.a.221.4 |
$q$-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 \(\left(\mathbb{Z}/315\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(136\) | \(281\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{1}{6}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −3.13136 | + | 1.80789i | −1.56568 | + | 0.903947i | −0.569018 | + | 0.822325i | \(0.692677\pi\) |
−0.996663 | + | 0.0816216i | \(0.973990\pi\) | |||||||
\(3\) | −2.12443 | − | 2.11820i | −0.708144 | − | 0.706068i | ||||
\(4\) | 4.53696 | − | 7.85824i | 1.13424 | − | 1.96456i | ||||
\(5\) | − | 2.23607i | − | 0.447214i | ||||||
\(6\) | 10.4819 | + | 2.79212i | 1.74698 | + | 0.465353i | ||||
\(7\) | 6.87314 | − | 1.32662i | 0.981877 | − | 0.189517i | ||||
\(8\) | 18.3462i | 2.29327i | ||||||||
\(9\) | 0.0264256 | + | 8.99996i | 0.00293617 | + | 0.999996i | ||||
\(10\) | 4.04257 | + | 7.00194i | 0.404257 | + | 0.700194i | ||||
\(11\) | − | 10.6206i | − | 0.965512i | −0.875755 | − | 0.482756i | \(-0.839636\pi\) | ||
0.875755 | − | 0.482756i | \(-0.160364\pi\) | |||||||
\(12\) | −26.2838 | + | 7.08410i | −2.19032 | + | 0.590341i | ||||
\(13\) | 10.3447 | + | 17.9175i | 0.795743 | + | 1.37827i | 0.922366 | + | 0.386317i | \(0.126253\pi\) |
−0.126623 | + | 0.991951i | \(0.540414\pi\) | |||||||
\(14\) | −19.1239 | + | 16.5800i | −1.36599 | + | 1.18429i | ||||
\(15\) | −4.73645 | + | 4.75038i | −0.315763 | + | 0.316692i | ||||
\(16\) | −15.0201 | − | 26.0156i | −0.938757 | − | 1.62597i | ||||
\(17\) | −12.3742 | + | 7.14424i | −0.727893 | + | 0.420249i | −0.817651 | − | 0.575714i | \(-0.804724\pi\) |
0.0897577 | + | 0.995964i | \(0.471391\pi\) | |||||||
\(18\) | −16.3537 | − | 28.1344i | −0.908540 | − | 1.56302i | ||||
\(19\) | 14.2108 | − | 24.6137i | 0.747934 | − | 1.29546i | −0.200877 | − | 0.979616i | \(-0.564379\pi\) |
0.948811 | − | 0.315844i | \(-0.102287\pi\) | |||||||
\(20\) | −17.5716 | − | 10.1449i | −0.878578 | − | 0.507247i | ||||
\(21\) | −17.4116 | − | 11.7404i | −0.829123 | − | 0.559067i | ||||
\(22\) | 19.2010 | + | 33.2571i | 0.872772 | + | 1.51168i | ||||
\(23\) | 14.7477i | 0.641203i | 0.947214 | + | 0.320601i | \(0.103885\pi\) | ||||
−0.947214 | + | 0.320601i | \(0.896115\pi\) | |||||||
\(24\) | 38.8609 | − | 38.9752i | 1.61921 | − | 1.62397i | ||||
\(25\) | −5.00000 | −0.200000 | ||||||||
\(26\) | −64.7858 | − | 37.4041i | −2.49176 | − | 1.43862i | ||||
\(27\) | 19.0076 | − | 19.1758i | 0.703986 | − | 0.710214i | ||||
\(28\) | 20.7582 | − | 60.0296i | 0.741365 | − | 2.14391i | ||||
\(29\) | 29.3278 | + | 16.9324i | 1.01130 | + | 0.583875i | 0.911573 | − | 0.411139i | \(-0.134869\pi\) |
0.0997292 | + | 0.995015i | \(0.468202\pi\) | |||||||
\(30\) | 6.24337 | − | 23.4381i | 0.208112 | − | 0.781271i | ||||
\(31\) | 5.14174 | − | 8.90575i | 0.165862 | − | 0.287282i | −0.771099 | − | 0.636716i | \(-0.780293\pi\) |
0.936961 | + | 0.349433i | \(0.113626\pi\) | |||||||
\(32\) | 30.5138 | + | 17.6172i | 0.953556 | + | 0.550536i | ||||
\(33\) | −22.4967 | + | 22.5628i | −0.681717 | + | 0.683722i | ||||
\(34\) | 25.8320 | − | 44.7424i | 0.759766 | − | 1.31595i | ||||
\(35\) | −2.96642 | − | 15.3688i | −0.0847547 | − | 0.439109i | ||||
\(36\) | 70.8437 | + | 40.6248i | 1.96788 | + | 1.12847i | ||||
\(37\) | 3.55169 | − | 6.15171i | 0.0959916 | − | 0.166262i | −0.814030 | − | 0.580822i | \(-0.802731\pi\) |
0.910022 | + | 0.414560i | \(0.136064\pi\) | |||||||
\(38\) | 102.766i | 2.70437i | ||||||||
\(39\) | 15.9763 | − | 59.9766i | 0.409650 | − | 1.53786i | ||||
\(40\) | 41.0233 | 1.02558 | ||||||||
\(41\) | −3.48373 | + | 2.01133i | −0.0849691 | + | 0.0490569i | −0.541883 | − | 0.840454i | \(-0.682288\pi\) |
0.456913 | + | 0.889511i | \(0.348955\pi\) | |||||||
\(42\) | 75.7474 | + | 5.28517i | 1.80351 | + | 0.125837i | ||||
\(43\) | −23.5499 | + | 40.7896i | −0.547671 | + | 0.948594i | 0.450762 | + | 0.892644i | \(0.351152\pi\) |
−0.998434 | + | 0.0559504i | \(0.982181\pi\) | |||||||
\(44\) | −83.4595 | − | 48.1854i | −1.89681 | − | 1.09512i | ||||
\(45\) | 20.1245 | − | 0.0590894i | 0.447212 | − | 0.00131310i | ||||
\(46\) | −26.6622 | − | 46.1803i | −0.579613 | − | 1.00392i | ||||
\(47\) | 62.2276 | − | 35.9271i | 1.32399 | − | 0.764407i | 0.339629 | − | 0.940560i | \(-0.389699\pi\) |
0.984363 | + | 0.176153i | \(0.0563652\pi\) | |||||||
\(48\) | −23.1971 | + | 87.0840i | −0.483273 | + | 1.81425i | ||||
\(49\) | 45.4802 | − | 18.2361i | 0.928166 | − | 0.372166i | ||||
\(50\) | 15.6568 | − | 9.03947i | 0.313136 | − | 0.180789i | ||||
\(51\) | 41.4211 | + | 11.0336i | 0.812178 | + | 0.216345i | ||||
\(52\) | 187.733 | 3.61025 | ||||||||
\(53\) | 38.7353 | − | 22.3638i | 0.730854 | − | 0.421959i | −0.0878804 | − | 0.996131i | \(-0.528009\pi\) |
0.818735 | + | 0.574172i | \(0.194676\pi\) | |||||||
\(54\) | −24.8520 | + | 94.4101i | −0.460222 | + | 1.74833i | ||||
\(55\) | −23.7485 | −0.431790 | ||||||||
\(56\) | 24.3384 | + | 126.096i | 0.434615 | + | 2.25171i | ||||
\(57\) | −82.3267 | + | 22.1890i | −1.44433 | + | 0.389280i | ||||
\(58\) | −122.448 | −2.11117 | ||||||||
\(59\) | 40.2140 | + | 23.2175i | 0.681593 | + | 0.393518i | 0.800455 | − | 0.599393i | \(-0.204591\pi\) |
−0.118862 | + | 0.992911i | \(0.537925\pi\) | |||||||
\(60\) | 15.8405 | + | 58.7724i | 0.264009 | + | 0.979540i | ||||
\(61\) | −4.34832 | − | 7.53152i | −0.0712840 | − | 0.123467i | 0.828180 | − | 0.560462i | \(-0.189376\pi\) |
−0.899464 | + | 0.436994i | \(0.856043\pi\) | |||||||
\(62\) | 37.1828i | 0.599723i | ||||||||
\(63\) | 12.1212 | + | 61.8230i | 0.192400 | + | 0.981317i | ||||
\(64\) | −7.23884 | −0.113107 | ||||||||
\(65\) | 40.0647 | − | 23.1314i | 0.616380 | − | 0.355867i | ||||
\(66\) | 29.6541 | − | 111.324i | 0.449304 | − | 1.68673i | ||||
\(67\) | 12.4817 | − | 21.6190i | 0.186295 | − | 0.322672i | −0.757717 | − | 0.652583i | \(-0.773685\pi\) |
0.944012 | + | 0.329911i | \(0.107019\pi\) | |||||||
\(68\) | 129.652i | 1.90665i | ||||||||
\(69\) | 31.2386 | − | 31.3304i | 0.452733 | − | 0.454064i | ||||
\(70\) | 37.0741 | + | 42.7624i | 0.529630 | + | 0.610891i | ||||
\(71\) | − | 134.088i | − | 1.88856i | −0.329137 | − | 0.944282i | \(-0.606758\pi\) | ||
0.329137 | − | 0.944282i | \(-0.393242\pi\) | |||||||
\(72\) | −165.115 | + | 0.484808i | −2.29326 | + | 0.00673345i | ||||
\(73\) | −68.0045 | − | 117.787i | −0.931568 | − | 1.61352i | −0.780642 | − | 0.624979i | \(-0.785108\pi\) |
−0.150927 | − | 0.988545i | \(-0.548226\pi\) | |||||||
\(74\) | 25.6843i | 0.347085i | ||||||||
\(75\) | 10.6222 | + | 10.5910i | 0.141629 | + | 0.141214i | ||||
\(76\) | −128.947 | − | 223.343i | −1.69667 | − | 2.93872i | ||||
\(77\) | −14.0896 | − | 72.9971i | −0.182981 | − | 0.948015i | ||||
\(78\) | 58.4035 | + | 216.692i | 0.748763 | + | 2.77810i | ||||
\(79\) | −36.7050 | − | 63.5749i | −0.464620 | − | 0.804746i | 0.534564 | − | 0.845128i | \(-0.320476\pi\) |
−0.999184 | + | 0.0403820i | \(0.987143\pi\) | |||||||
\(80\) | −58.1726 | + | 33.5860i | −0.727158 | + | 0.419825i | ||||
\(81\) | −80.9986 | + | 0.475658i | −0.999983 | + | 0.00587232i | ||||
\(82\) | 7.27255 | − | 12.5964i | 0.0886897 | − | 0.153615i | ||||
\(83\) | −47.7133 | − | 27.5473i | −0.574859 | − | 0.331895i | 0.184229 | − | 0.982883i | \(-0.441021\pi\) |
−0.759088 | + | 0.650988i | \(0.774355\pi\) | |||||||
\(84\) | −171.254 | + | 83.5587i | −2.03874 | + | 0.994746i | ||||
\(85\) | 15.9750 | + | 27.6695i | 0.187941 | + | 0.325524i | ||||
\(86\) | − | 170.303i | − | 1.98026i | ||||||
\(87\) | −26.4386 | − | 98.0939i | −0.303892 | − | 1.12752i | ||||
\(88\) | 194.848 | 2.21418 | ||||||||
\(89\) | −8.61288 | − | 4.97265i | −0.0967739 | − | 0.0558724i | 0.450832 | − | 0.892609i | \(-0.351127\pi\) |
−0.547606 | + | 0.836736i | \(0.684461\pi\) | |||||||
\(90\) | −62.9104 | + | 36.5680i | −0.699004 | + | 0.406311i | ||||
\(91\) | 94.8700 | + | 109.426i | 1.04253 | + | 1.20248i | ||||
\(92\) | 115.891 | + | 66.9095i | 1.25968 | + | 0.727277i | ||||
\(93\) | −29.7875 | + | 8.02841i | −0.320295 | + | 0.0863270i | ||||
\(94\) | −129.905 | + | 225.002i | −1.38197 | + | 2.39364i | ||||
\(95\) | −55.0380 | − | 31.7762i | −0.579347 | − | 0.334486i | ||||
\(96\) | −27.5078 | − | 102.061i | −0.286540 | − | 1.06313i | ||||
\(97\) | 12.7390 | − | 22.0646i | 0.131330 | − | 0.227471i | −0.792859 | − | 0.609405i | \(-0.791409\pi\) |
0.924190 | + | 0.381934i | \(0.124742\pi\) | |||||||
\(98\) | −109.446 | + | 139.327i | −1.11679 | + | 1.42171i | ||||
\(99\) | 95.5853 | − | 0.280656i | 0.965508 | − | 0.00283491i | ||||
\(100\) | −22.6848 | + | 39.2912i | −0.226848 | + | 0.392912i | ||||
\(101\) | 19.1544i | 0.189647i | 0.995494 | + | 0.0948236i | \(0.0302287\pi\) | ||||
−0.995494 | + | 0.0948236i | \(0.969771\pi\) | |||||||
\(102\) | −149.652 | + | 40.3347i | −1.46718 | + | 0.395438i | ||||
\(103\) | 188.476 | 1.82986 | 0.914932 | − | 0.403609i | \(-0.132244\pi\) | ||||
0.914932 | + | 0.403609i | \(0.132244\pi\) | |||||||
\(104\) | −328.717 | + | 189.785i | −3.16074 | + | 1.82486i | ||||
\(105\) | −26.2523 | + | 38.9335i | −0.250022 | + | 0.370795i | ||||
\(106\) | −80.8628 | + | 140.058i | −0.762857 | + | 1.32131i | ||||
\(107\) | −80.6947 | − | 46.5891i | −0.754156 | − | 0.435412i | 0.0730376 | − | 0.997329i | \(-0.476731\pi\) |
−0.827194 | + | 0.561917i | \(0.810064\pi\) | |||||||
\(108\) | −64.4512 | − | 236.366i | −0.596770 | − | 2.18857i | ||||
\(109\) | −13.5892 | − | 23.5372i | −0.124671 | − | 0.215937i | 0.796933 | − | 0.604068i | \(-0.206454\pi\) |
−0.921604 | + | 0.388130i | \(0.873121\pi\) | |||||||
\(110\) | 74.3651 | − | 42.9347i | 0.676046 | − | 0.390315i | ||||
\(111\) | −20.5759 | + | 5.54568i | −0.185368 | + | 0.0499611i | ||||
\(112\) | −137.748 | − | 158.883i | −1.22989 | − | 1.41860i | ||||
\(113\) | 81.4191 | − | 47.0074i | 0.720523 | − | 0.415994i | −0.0944220 | − | 0.995532i | \(-0.530100\pi\) |
0.814945 | + | 0.579538i | \(0.196767\pi\) | |||||||
\(114\) | 217.679 | − | 218.320i | 1.90947 | − | 1.91508i | ||||
\(115\) | 32.9768 | 0.286755 | ||||||||
\(116\) | 266.117 | − | 153.643i | 2.29412 | − | 1.32451i | ||||
\(117\) | −160.983 | + | 93.5750i | −1.37593 | + | 0.799787i | ||||
\(118\) | −167.899 | −1.42288 | ||||||||
\(119\) | −75.5718 | + | 65.5192i | −0.635057 | + | 0.550582i | ||||
\(120\) | −87.1512 | − | 86.8957i | −0.726260 | − | 0.724131i | ||||
\(121\) | 8.20211 | 0.0677860 | ||||||||
\(122\) | 27.2324 | + | 15.7226i | 0.223216 | + | 0.128874i | ||||
\(123\) | 11.6614 | + | 3.10631i | 0.0948079 | + | 0.0252546i | ||||
\(124\) | −46.6557 | − | 80.8100i | −0.376255 | − | 0.651693i | ||||
\(125\) | 11.1803i | 0.0894427i | ||||||||
\(126\) | −149.725 | − | 171.676i | −1.18829 | − | 1.36251i | ||||
\(127\) | −212.116 | −1.67021 | −0.835103 | − | 0.550094i | \(-0.814592\pi\) | ||||
−0.835103 | + | 0.550094i | \(0.814592\pi\) | |||||||
\(128\) | −99.3878 | + | 57.3816i | −0.776467 | + | 0.448293i | ||||
\(129\) | 136.431 | − | 36.7712i | 1.05760 | − | 0.285048i | ||||
\(130\) | −83.6381 | + | 144.865i | −0.643370 | + | 1.11435i | ||||
\(131\) | 218.924i | 1.67118i | 0.549356 | + | 0.835589i | \(0.314873\pi\) | ||||
−0.549356 | + | 0.835589i | \(0.685127\pi\) | |||||||
\(132\) | 75.2376 | + | 279.151i | 0.569982 | + | 2.11478i | ||||
\(133\) | 65.0194 | − | 188.026i | 0.488868 | − | 1.41373i | ||||
\(134\) | 90.2626i | 0.673601i | ||||||||
\(135\) | −42.8784 | − | 42.5023i | −0.317617 | − | 0.314832i | ||||
\(136\) | −131.069 | − | 227.019i | −0.963746 | − | 1.66926i | ||||
\(137\) | − | 96.8735i | − | 0.707106i | −0.935414 | − | 0.353553i | \(-0.884973\pi\) | ||
0.935414 | − | 0.353553i | \(-0.115027\pi\) | |||||||
\(138\) | −41.1772 | + | 154.583i | −0.298386 | + | 1.12017i | ||||
\(139\) | 85.5085 | + | 148.105i | 0.615169 | + | 1.06550i | 0.990355 | + | 0.138554i | \(0.0442456\pi\) |
−0.375186 | + | 0.926950i | \(0.622421\pi\) | |||||||
\(140\) | −134.230 | − | 46.4168i | −0.958788 | − | 0.331549i | ||||
\(141\) | −208.299 | − | 55.4860i | −1.47730 | − | 0.393518i | ||||
\(142\) | 242.417 | + | 419.878i | 1.70716 | + | 2.95689i | ||||
\(143\) | 190.295 | − | 109.867i | 1.33073 | − | 0.768300i | ||||
\(144\) | 233.742 | − | 135.868i | 1.62321 | − | 0.943527i | ||||
\(145\) | 37.8620 | − | 65.5788i | 0.261117 | − | 0.452268i | ||||
\(146\) | 425.894 | + | 245.890i | 2.91708 | + | 1.68418i | ||||
\(147\) | −135.247 | − | 57.5948i | −0.920050 | − | 0.391802i | ||||
\(148\) | −32.2277 | − | 55.8200i | −0.217755 | − | 0.377162i | ||||
\(149\) | − | 6.94173i | − | 0.0465888i | −0.999729 | − | 0.0232944i | \(-0.992584\pi\) | ||
0.999729 | − | 0.0232944i | \(-0.00741550\pi\) | |||||||
\(150\) | −52.4093 | − | 13.9606i | −0.349395 | − | 0.0930706i | ||||
\(151\) | −134.675 | −0.891885 | −0.445942 | − | 0.895062i | \(-0.647131\pi\) | ||||
−0.445942 | + | 0.895062i | \(0.647131\pi\) | |||||||
\(152\) | 451.568 | + | 260.713i | 2.97084 | + | 1.71522i | ||||
\(153\) | −64.6249 | − | 111.178i | −0.422385 | − | 0.726656i | ||||
\(154\) | 176.091 | + | 203.108i | 1.14345 | + | 1.31888i | ||||
\(155\) | −19.9139 | − | 11.4973i | −0.128477 | − | 0.0741759i | ||||
\(156\) | −398.826 | − | 397.657i | −2.55658 | − | 2.54908i | ||||
\(157\) | −30.2252 | + | 52.3516i | −0.192517 | + | 0.333450i | −0.946084 | − | 0.323922i | \(-0.894999\pi\) |
0.753566 | + | 0.657372i | \(0.228332\pi\) | |||||||
\(158\) | 229.873 | + | 132.717i | 1.45489 | + | 0.839984i | ||||
\(159\) | −129.662 | − | 34.5388i | −0.815482 | − | 0.217225i | ||||
\(160\) | 39.3932 | − | 68.2309i | 0.246207 | − | 0.426443i | ||||
\(161\) | 19.5646 | + | 101.363i | 0.121519 | + | 0.629583i | ||||
\(162\) | 252.776 | − | 147.926i | 1.56035 | − | 0.913125i | ||||
\(163\) | −48.2453 | + | 83.5633i | −0.295983 | + | 0.512658i | −0.975213 | − | 0.221267i | \(-0.928981\pi\) |
0.679230 | + | 0.733926i | \(0.262314\pi\) | |||||||
\(164\) | 36.5013i | 0.222569i | ||||||||
\(165\) | 50.4520 | + | 50.3041i | 0.305770 | + | 0.304873i | ||||
\(166\) | 199.210 | 1.20006 | ||||||||
\(167\) | 123.674 | − | 71.4030i | 0.740561 | − | 0.427563i | −0.0817125 | − | 0.996656i | \(-0.526039\pi\) |
0.822273 | + | 0.569093i | \(0.192706\pi\) | |||||||
\(168\) | 215.391 | − | 319.436i | 1.28209 | − | 1.90140i | ||||
\(169\) | −129.524 | + | 224.342i | −0.766414 | + | 1.32747i | ||||
\(170\) | −100.047 | − | 57.7622i | −0.588512 | − | 0.339778i | ||||
\(171\) | 221.898 | + | 127.246i | 1.29765 | + | 0.744127i | ||||
\(172\) | 213.689 | + | 370.121i | 1.24238 | + | 2.15187i | ||||
\(173\) | 209.276 | − | 120.825i | 1.20969 | − | 0.698413i | 0.246996 | − | 0.969017i | \(-0.420557\pi\) |
0.962691 | + | 0.270604i | \(0.0872234\pi\) | |||||||
\(174\) | 260.132 | + | 259.369i | 1.49501 | + | 1.49063i | ||||
\(175\) | −34.3657 | + | 6.63311i | −0.196375 | + | 0.0379035i | ||||
\(176\) | −276.302 | + | 159.523i | −1.56990 | + | 0.906381i | ||||
\(177\) | −36.2524 | − | 134.505i | −0.204816 | − | 0.759918i | ||||
\(178\) | 35.9601 | 0.202023 | ||||||||
\(179\) | −52.7013 | + | 30.4271i | −0.294421 | + | 0.169984i | −0.639934 | − | 0.768430i | \(-0.721038\pi\) |
0.345513 | + | 0.938414i | \(0.387705\pi\) | |||||||
\(180\) | 90.8397 | − | 158.411i | 0.504665 | − | 0.880063i | ||||
\(181\) | 275.246 | 1.52069 | 0.760347 | − | 0.649517i | \(-0.225029\pi\) | ||||
0.760347 | + | 0.649517i | \(0.225029\pi\) | |||||||
\(182\) | −494.903 | − | 171.137i | −2.71925 | − | 0.940315i | ||||
\(183\) | −6.71557 | + | 25.2108i | −0.0366971 | + | 0.137764i | ||||
\(184\) | −270.563 | −1.47045 | ||||||||
\(185\) | −13.7556 | − | 7.94182i | −0.0743548 | − | 0.0429288i | ||||
\(186\) | 78.7608 | − | 78.9924i | 0.423445 | − | 0.424690i | ||||
\(187\) | 75.8764 | + | 131.422i | 0.405756 | + | 0.702790i | ||||
\(188\) | − | 651.999i | − | 3.46808i | ||||||
\(189\) | 105.203 | − | 157.014i | 0.556630 | − | 0.830761i | ||||
\(190\) | 229.792 | 1.20943 | ||||||||
\(191\) | 175.463 | − | 101.304i | 0.918657 | − | 0.530387i | 0.0354507 | − | 0.999371i | \(-0.488713\pi\) |
0.883206 | + | 0.468985i | \(0.155380\pi\) | |||||||
\(192\) | 15.3784 | + | 15.3333i | 0.0800960 | + | 0.0798611i | ||||
\(193\) | −81.5246 | + | 141.205i | −0.422407 | + | 0.731631i | −0.996174 | − | 0.0873877i | \(-0.972148\pi\) |
0.573767 | + | 0.819018i | \(0.305481\pi\) | |||||||
\(194\) | 92.1232i | 0.474862i | ||||||||
\(195\) | −134.112 | − | 35.7242i | −0.687752 | − | 0.183201i | ||||
\(196\) | 63.0377 | − | 440.130i | 0.321621 | − | 2.24556i | ||||
\(197\) | 42.5258i | 0.215867i | 0.994158 | + | 0.107933i | \(0.0344234\pi\) | ||||
−0.994158 | + | 0.107933i | \(0.965577\pi\) | |||||||
\(198\) | −298.805 | + | 173.687i | −1.50912 | + | 0.877206i | ||||
\(199\) | 178.784 | + | 309.662i | 0.898410 | + | 1.55609i | 0.829527 | + | 0.558467i | \(0.188610\pi\) |
0.0688829 | + | 0.997625i | \(0.478057\pi\) | |||||||
\(200\) | − | 91.7309i | − | 0.458654i | ||||||
\(201\) | −72.3101 | + | 19.4892i | −0.359752 | + | 0.0969614i | ||||
\(202\) | −34.6290 | − | 59.9793i | −0.171431 | − | 0.296927i | ||||
\(203\) | 224.037 | + | 77.4719i | 1.10363 | + | 0.381635i | ||||
\(204\) | 274.630 | − | 275.438i | 1.34623 | − | 1.35018i | ||||
\(205\) | 4.49748 | + | 7.78986i | 0.0219389 | + | 0.0379993i | ||||
\(206\) | −590.186 | + | 340.744i | −2.86498 | + | 1.65410i | ||||
\(207\) | −132.728 | + | 0.389715i | −0.641200 | + | 0.00188268i | ||||
\(208\) | 310.756 | − | 538.245i | 1.49402 | − | 2.58772i | ||||
\(209\) | −261.414 | − | 150.927i | −1.25078 | − | 0.722140i | ||||
\(210\) | 11.8180 | − | 169.376i | 0.0562762 | − | 0.806554i | ||||
\(211\) | −156.451 | − | 270.982i | −0.741476 | − | 1.28427i | −0.951823 | − | 0.306647i | \(-0.900793\pi\) |
0.210348 | − | 0.977627i | \(-0.432540\pi\) | |||||||
\(212\) | − | 405.855i | − | 1.91441i | ||||||
\(213\) | −284.026 | + | 284.861i | −1.33345 | + | 1.33738i | ||||
\(214\) | 336.912 | 1.57436 | ||||||||
\(215\) | 91.2082 | + | 52.6591i | 0.424224 | + | 0.244926i | ||||
\(216\) | 351.802 | + | 348.717i | 1.62871 | + | 1.61443i | ||||
\(217\) | 23.5253 | − | 68.0316i | 0.108412 | − | 0.313510i | ||||
\(218\) | 85.1054 | + | 49.1356i | 0.390392 | + | 0.225393i | ||||
\(219\) | −105.026 | + | 394.278i | −0.479573 | + | 1.80036i | ||||
\(220\) | −107.746 | + | 186.621i | −0.489753 | + | 0.848278i | ||||
\(221\) | −256.013 | − | 147.809i | −1.15843 | − | 0.668821i | ||||
\(222\) | 54.4046 | − | 54.5646i | 0.245066 | − | 0.245786i | ||||
\(223\) | −22.8277 | + | 39.5387i | −0.102366 | + | 0.177304i | −0.912659 | − | 0.408722i | \(-0.865975\pi\) |
0.810293 | + | 0.586025i | \(0.199308\pi\) | |||||||
\(224\) | 233.097 | + | 80.6049i | 1.04061 | + | 0.359843i | ||||
\(225\) | −0.132128 | − | 44.9998i | −0.000587235 | − | 0.199999i | ||||
\(226\) | −169.969 | + | 294.394i | −0.752073 | + | 1.30263i | ||||
\(227\) | − | 60.3635i | − | 0.265918i | −0.991122 | − | 0.132959i | \(-0.957552\pi\) | ||
0.991122 | − | 0.132959i | \(-0.0424479\pi\) | |||||||
\(228\) | −199.146 | + | 747.613i | −0.873449 | + | 3.27900i | ||||
\(229\) | −245.883 | −1.07372 | −0.536862 | − | 0.843670i | \(-0.680391\pi\) | ||||
−0.536862 | + | 0.843670i | \(0.680391\pi\) | |||||||
\(230\) | −103.262 | + | 59.6185i | −0.448966 | + | 0.259211i | ||||
\(231\) | −124.690 | + | 184.922i | −0.539786 | + | 0.800528i | ||||
\(232\) | −310.645 | + | 538.052i | −1.33899 | + | 2.31919i | ||||
\(233\) | −205.098 | − | 118.414i | −0.880250 | − | 0.508212i | −0.00950904 | − | 0.999955i | \(-0.503027\pi\) |
−0.870741 | + | 0.491742i | \(0.836360\pi\) | |||||||
\(234\) | 334.923 | − | 584.058i | 1.43130 | − | 2.49597i | ||||
\(235\) | −80.3355 | − | 139.145i | −0.341853 | − | 0.592107i | ||||
\(236\) | 364.898 | − | 210.674i | 1.54618 | − | 0.892686i | ||||
\(237\) | −56.6874 | + | 212.809i | −0.239187 | + | 0.897930i | ||||
\(238\) | 118.191 | − | 341.790i | 0.496601 | − | 1.43609i | ||||
\(239\) | 233.917 | − | 135.052i | 0.978732 | − | 0.565071i | 0.0768447 | − | 0.997043i | \(-0.475515\pi\) |
0.901887 | + | 0.431972i | \(0.142182\pi\) | |||||||
\(240\) | 194.726 | + | 51.8703i | 0.811358 | + | 0.216126i | ||||
\(241\) | −116.349 | −0.482774 | −0.241387 | − | 0.970429i | \(-0.577602\pi\) | ||||
−0.241387 | + | 0.970429i | \(0.577602\pi\) | |||||||
\(242\) | −25.6838 | + | 14.8285i | −0.106131 | + | 0.0612749i | ||||
\(243\) | 173.084 | + | 170.561i | 0.712278 | + | 0.701897i | ||||
\(244\) | −78.9126 | −0.323412 | ||||||||
\(245\) | −40.7772 | − | 101.697i | −0.166438 | − | 0.415089i | ||||
\(246\) | −42.1319 | + | 11.3555i | −0.171268 | + | 0.0461606i | ||||
\(247\) | 588.022 | 2.38065 | ||||||||
\(248\) | 163.386 | + | 94.3312i | 0.658816 | + | 0.380368i | ||||
\(249\) | 43.0129 | + | 159.589i | 0.172743 | + | 0.640919i | ||||
\(250\) | −20.2129 | − | 35.0097i | −0.0808514 | − | 0.140039i | ||||
\(251\) | − | 204.044i | − | 0.812923i | −0.913668 | − | 0.406462i | \(-0.866762\pi\) | ||
0.913668 | − | 0.406462i | \(-0.133238\pi\) | |||||||
\(252\) | 540.813 | + | 185.237i | 2.14608 | + | 0.735067i | ||||
\(253\) | 156.630 | 0.619089 | ||||||||
\(254\) | 664.212 | − | 383.483i | 2.61501 | − | 1.50978i | ||||
\(255\) | 24.6719 | − | 92.6203i | 0.0967524 | − | 0.363217i | ||||
\(256\) | 221.957 | − | 384.441i | 0.867020 | − | 1.50172i | ||||
\(257\) | 336.811i | 1.31055i | 0.755391 | + | 0.655274i | \(0.227447\pi\) | ||||
−0.755391 | + | 0.655274i | \(0.772553\pi\) | |||||||
\(258\) | −360.735 | + | 361.796i | −1.39820 | + | 1.40231i | ||||
\(259\) | 16.2503 | − | 46.9933i | 0.0627424 | − | 0.181441i | ||||
\(260\) | − | 419.784i | − | 1.61455i | ||||||
\(261\) | −151.616 | + | 264.396i | −0.580903 | + | 1.01301i | ||||
\(262\) | −395.792 | − | 685.531i | −1.51065 | − | 2.61653i | ||||
\(263\) | 198.941i | 0.756428i | 0.925718 | + | 0.378214i | \(0.123462\pi\) | ||||
−0.925718 | + | 0.378214i | \(0.876538\pi\) | |||||||
\(264\) | −413.942 | − | 412.728i | −1.56796 | − | 1.56336i | ||||
\(265\) | −50.0070 | − | 86.6147i | −0.188706 | − | 0.326848i | ||||
\(266\) | 136.332 | + | 706.326i | 0.512525 | + | 2.65536i | ||||
\(267\) | 7.76440 | + | 28.8079i | 0.0290801 | + | 0.107895i | ||||
\(268\) | −113.258 | − | 196.169i | −0.422605 | − | 0.731974i | ||||
\(269\) | −28.1552 | + | 16.2554i | −0.104666 | + | 0.0604291i | −0.551419 | − | 0.834228i | \(-0.685914\pi\) |
0.446753 | + | 0.894657i | \(0.352580\pi\) | |||||||
\(270\) | 211.107 | + | 55.5707i | 0.781879 | + | 0.205817i | ||||
\(271\) | 110.968 | − | 192.202i | 0.409475 | − | 0.709231i | −0.585356 | − | 0.810776i | \(-0.699045\pi\) |
0.994831 | + | 0.101545i | \(0.0323787\pi\) | |||||||
\(272\) | 371.723 | + | 214.615i | 1.36663 | + | 0.789024i | ||||
\(273\) | 30.2414 | − | 433.422i | 0.110774 | − | 1.58763i | ||||
\(274\) | 175.137 | + | 303.346i | 0.639186 | + | 1.10710i | ||||
\(275\) | 53.1032i | 0.193102i | ||||||||
\(276\) | −104.474 | − | 387.625i | −0.378529 | − | 1.40444i | ||||
\(277\) | −466.523 | −1.68420 | −0.842100 | − | 0.539322i | \(-0.818681\pi\) | ||||
−0.842100 | + | 0.539322i | \(0.818681\pi\) | |||||||
\(278\) | −535.516 | − | 309.180i | −1.92632 | − | 1.11216i | ||||
\(279\) | 80.2873 | + | 46.0401i | 0.287768 | + | 0.165018i | ||||
\(280\) | 281.959 | − | 54.4224i | 1.00700 | − | 0.194366i | ||||
\(281\) | 118.558 | + | 68.4496i | 0.421916 | + | 0.243593i | 0.695897 | − | 0.718142i | \(-0.255007\pi\) |
−0.273981 | + | 0.961735i | \(0.588341\pi\) | |||||||
\(282\) | 752.573 | − | 202.836i | 2.66870 | − | 0.719277i | ||||
\(283\) | −31.8418 | + | 55.1517i | −0.112515 | + | 0.194882i | −0.916784 | − | 0.399384i | \(-0.869224\pi\) |
0.804268 | + | 0.594266i | \(0.202557\pi\) | |||||||
\(284\) | −1053.70 | − | 608.352i | −3.71020 | − | 2.14208i | ||||
\(285\) | 49.6160 | + | 184.088i | 0.174091 | + | 0.645923i | ||||
\(286\) | −397.255 | + | 688.066i | −1.38900 | + | 2.40583i | ||||
\(287\) | −21.2759 | + | 18.4458i | −0.0741321 | + | 0.0642710i | ||||
\(288\) | −157.747 | + | 275.089i | −0.547734 | + | 0.955169i | ||||
\(289\) | −42.4197 | + | 73.4731i | −0.146781 | + | 0.254232i | ||||
\(290\) | 273.802i | 0.944143i | ||||||||
\(291\) | −73.8006 | + | 19.8910i | −0.253610 | + | 0.0683539i | ||||
\(292\) | −1234.13 | −4.22648 | ||||||||
\(293\) | 142.523 | − | 82.2856i | 0.486426 | − | 0.280838i | −0.236665 | − | 0.971591i | \(-0.576054\pi\) |
0.723091 | + | 0.690753i | \(0.242721\pi\) | |||||||
\(294\) | 527.634 | − | 64.1624i | 1.79467 | − | 0.218239i | ||||
\(295\) | 51.9160 | − | 89.9212i | 0.175986 | − | 0.304818i | ||||
\(296\) | 112.860 | + | 65.1599i | 0.381285 | + | 0.220135i | ||||
\(297\) | −203.659 | − | 201.873i | −0.685721 | − | 0.679707i | ||||
\(298\) | 12.5499 | + | 21.7371i | 0.0421138 | + | 0.0729432i | ||||
\(299\) | −264.241 | + | 152.560i | −0.883749 | + | 0.510233i | ||||
\(300\) | 131.419 | − | 35.4205i | 0.438063 | − | 0.118068i | ||||
\(301\) | −107.749 | + | 311.594i | −0.357971 | + | 1.03520i | ||||
\(302\) | 421.715 | − | 243.477i | 1.39641 | − | 0.806216i | ||||
\(303\) | 40.5728 | − | 40.6921i | 0.133904 | − | 0.134298i | ||||
\(304\) | −853.788 | −2.80851 | ||||||||
\(305\) | −16.8410 | + | 9.72315i | −0.0552163 | + | 0.0318792i | ||||
\(306\) | 403.363 | + | 231.305i | 1.31818 | + | 0.755899i | ||||
\(307\) | 143.740 | 0.468207 | 0.234104 | − | 0.972212i | \(-0.424784\pi\) | ||||
0.234104 | + | 0.972212i | \(0.424784\pi\) | |||||||
\(308\) | −637.553 | − | 220.466i | −2.06998 | − | 0.715797i | ||||
\(309\) | −400.404 | − | 399.230i | −1.29581 | − | 1.29201i | ||||
\(310\) | 83.1434 | 0.268204 | ||||||||
\(311\) | 394.698 | + | 227.879i | 1.26913 | + | 0.732731i | 0.974823 | − | 0.222981i | \(-0.0715788\pi\) |
0.294304 | + | 0.955712i | \(0.404912\pi\) | |||||||
\(312\) | 1100.34 | + | 293.105i | 3.52673 | + | 0.939438i | ||||
\(313\) | −2.02961 | − | 3.51539i | −0.00648439 | − | 0.0112313i | 0.862765 | − | 0.505605i | \(-0.168731\pi\) |
−0.869249 | + | 0.494374i | \(0.835397\pi\) | |||||||
\(314\) | − | 218.576i | − | 0.696102i | ||||||
\(315\) | 138.240 | − | 27.1038i | 0.438858 | − | 0.0860437i | ||||
\(316\) | −666.116 | −2.10796 | ||||||||
\(317\) | −364.252 | + | 210.301i | −1.14906 | + | 0.663410i | −0.948658 | − | 0.316303i | \(-0.897558\pi\) |
−0.200402 | + | 0.979714i | \(0.564225\pi\) | |||||||
\(318\) | 468.460 | − | 126.261i | 1.47314 | − | 0.397047i | ||||
\(319\) | 179.833 | − | 311.479i | 0.563739 | − | 0.976424i | ||||
\(320\) | 16.1865i | 0.0505829i | ||||||||
\(321\) | 72.7452 | + | 269.903i | 0.226621 | + | 0.840820i | ||||
\(322\) | −244.517 | − | 282.033i | −0.759369 | − | 0.875879i | ||||
\(323\) | 406.100i | 1.25728i | ||||||||
\(324\) | −363.749 | + | 638.664i | −1.12268 | + | 1.97119i | ||||
\(325\) | −51.7233 | − | 89.5874i | −0.159149 | − | 0.275654i | ||||
\(326\) | − | 348.889i | − | 1.07021i | ||||||
\(327\) | −20.9872 | + | 78.7878i | −0.0641810 | + | 0.240941i | ||||
\(328\) | −36.9003 | − | 63.9132i | −0.112501 | − | 0.194857i | ||||
\(329\) | 380.037 | − | 329.485i | 1.15513 | − | 1.00147i | ||||
\(330\) | −248.928 | − | 66.3085i | −0.754327 | − | 0.200935i | ||||
\(331\) | 7.38456 | + | 12.7904i | 0.0223099 | + | 0.0386418i | 0.876965 | − | 0.480555i | \(-0.159565\pi\) |
−0.854655 | + | 0.519196i | \(0.826231\pi\) | |||||||
\(332\) | −432.946 | + | 249.962i | −1.30406 | + | 0.752897i | ||||
\(333\) | 55.4590 | + | 31.8025i | 0.166543 | + | 0.0955030i | ||||
\(334\) | −258.178 | + | 447.177i | −0.772988 | + | 1.33885i | ||||
\(335\) | −48.3416 | − | 27.9100i | −0.144303 | − | 0.0833135i | ||||
\(336\) | −43.9096 | + | 629.315i | −0.130683 | + | 1.87296i | ||||
\(337\) | −151.755 | − | 262.847i | −0.450311 | − | 0.779962i | 0.548094 | − | 0.836417i | \(-0.315354\pi\) |
−0.998405 | + | 0.0564551i | \(0.982020\pi\) | |||||||
\(338\) | − | 936.662i | − | 2.77119i | ||||||
\(339\) | −272.541 | − | 72.5984i | −0.803954 | − | 0.214154i | ||||
\(340\) | 289.912 | 0.852681 | ||||||||
\(341\) | −94.5847 | − | 54.6085i | −0.277375 | − | 0.160142i | ||||
\(342\) | −924.891 | + | 2.71565i | −2.70436 | + | 0.00794050i | ||||
\(343\) | 288.399 | − | 185.674i | 0.840814 | − | 0.541325i | ||||
\(344\) | −748.333 | − | 432.050i | −2.17539 | − | 1.25596i | ||||
\(345\) | −70.0570 | − | 69.8516i | −0.203064 | − | 0.202468i | ||||
\(346\) | −436.879 | + | 756.696i | −1.26266 | + | 2.18698i | ||||
\(347\) | −149.035 | − | 86.0453i | −0.429495 | − | 0.247969i | 0.269636 | − | 0.962962i | \(-0.413096\pi\) |
−0.699131 | + | 0.714993i | \(0.746430\pi\) | |||||||
\(348\) | −890.796 | − | 237.287i | −2.55976 | − | 0.681859i | ||||
\(349\) | −2.11669 | + | 3.66621i | −0.00606500 | + | 0.0105049i | −0.869042 | − | 0.494738i | \(-0.835264\pi\) |
0.862977 | + | 0.505243i | \(0.168597\pi\) | |||||||
\(350\) | 95.6196 | − | 82.9002i | 0.273199 | − | 0.236858i | ||||
\(351\) | 540.209 | + | 142.202i | 1.53906 | + | 0.405132i | ||||
\(352\) | 187.105 | − | 324.076i | 0.531549 | − | 0.920670i | ||||
\(353\) | 244.380i | 0.692295i | 0.938180 | + | 0.346148i | \(0.112510\pi\) | ||||
−0.938180 | + | 0.346148i | \(0.887490\pi\) | |||||||
\(354\) | 356.691 | + | 355.645i | 1.00760 | + | 1.00465i | ||||
\(355\) | −299.830 | −0.844592 | ||||||||
\(356\) | −78.1525 | + | 45.1214i | −0.219529 | + | 0.126745i | ||||
\(357\) | 299.330 | + | 20.8854i | 0.838460 | + | 0.0585024i | ||||
\(358\) | 110.018 | − | 190.557i | 0.307313 | − | 0.532281i | ||||
\(359\) | 620.567 | + | 358.285i | 1.72860 | + | 0.998008i | 0.895847 | + | 0.444362i | \(0.146570\pi\) |
0.832752 | + | 0.553645i | \(0.186764\pi\) | |||||||
\(360\) | 1.08406 | + | 369.208i | 0.00301129 | + | 1.02558i | ||||
\(361\) | −223.391 | − | 386.924i | −0.618811 | − | 1.07181i | ||||
\(362\) | −861.894 | + | 497.615i | −2.38092 | + | 1.37463i | ||||
\(363\) | −17.4248 | − | 17.3737i | −0.0480023 | − | 0.0478615i | ||||
\(364\) | 1290.32 | − | 249.051i | 3.54482 | − | 0.684205i | ||||
\(365\) | −263.380 | + | 152.063i | −0.721590 | + | 0.416610i | ||||
\(366\) | −24.5496 | − | 91.0853i | −0.0670754 | − | 0.248867i | ||||
\(367\) | 98.6442 | 0.268785 | 0.134393 | − | 0.990928i | \(-0.457092\pi\) | ||||
0.134393 | + | 0.990928i | \(0.457092\pi\) | |||||||
\(368\) | 383.669 | − | 221.512i | 1.04258 | − | 0.601934i | ||||
\(369\) | −18.1940 | − | 31.3003i | −0.0493062 | − | 0.0848247i | ||||
\(370\) | 57.4319 | 0.155221 | ||||||||
\(371\) | 236.565 | − | 205.097i | 0.637641 | − | 0.552821i | ||||
\(372\) | −72.0552 | + | 270.502i | −0.193697 | + | 0.727155i | ||||
\(373\) | 439.041 | 1.17705 | 0.588527 | − | 0.808478i | \(-0.299708\pi\) | ||||
0.588527 | + | 0.808478i | \(0.299708\pi\) | |||||||
\(374\) | −475.193 | − | 274.353i | −1.27057 | − | 0.733563i | ||||
\(375\) | 23.6822 | − | 23.7519i | 0.0631526 | − | 0.0633383i | ||||
\(376\) | 659.125 | + | 1141.64i | 1.75299 | + | 3.03627i | ||||
\(377\) | 700.639i | 1.85846i | ||||||||
\(378\) | −45.5646 | + | 681.863i | −0.120541 | + | 1.80387i | ||||
\(379\) | 380.732 | 1.00457 | 0.502285 | − | 0.864702i | \(-0.332493\pi\) | ||||
0.502285 | + | 0.864702i | \(0.332493\pi\) | |||||||
\(380\) | −499.410 | + | 288.334i | −1.31424 | + | 0.758775i | ||||
\(381\) | 450.626 | + | 449.305i | 1.18275 | + | 1.17928i | ||||
\(382\) | −366.293 | + | 634.439i | −0.958883 | + | 1.66083i | ||||
\(383\) | − | 121.152i | − | 0.316323i | −0.987413 | − | 0.158161i | \(-0.949443\pi\) | ||
0.987413 | − | 0.158161i | \(-0.0505566\pi\) | |||||||
\(384\) | 332.688 | + | 88.6203i | 0.866376 | + | 0.230782i | ||||
\(385\) | −163.227 | + | 31.5052i | −0.423965 | + | 0.0818317i | ||||
\(386\) | − | 589.551i | − | 1.52733i | ||||||
\(387\) | −367.727 | − | 210.870i | −0.950198 | − | 0.544884i | ||||
\(388\) | −115.593 | − | 200.213i | −0.297920 | − | 0.516012i | ||||
\(389\) | 138.472i | 0.355970i | 0.984033 | + | 0.177985i | \(0.0569579\pi\) | ||||
−0.984033 | + | 0.177985i | \(0.943042\pi\) | |||||||
\(390\) | 484.538 | − | 130.594i | 1.24240 | − | 0.334857i | ||||
\(391\) | −105.361 | − | 182.490i | −0.269465 | − | 0.466727i | ||||
\(392\) | 334.563 | + | 834.387i | 0.853477 | + | 2.12854i | ||||
\(393\) | 463.726 | − | 465.090i | 1.17996 | − | 1.18343i | ||||
\(394\) | −76.8821 | − | 133.164i | −0.195132 | − | 0.337979i | ||||
\(395\) | −142.158 | + | 82.0749i | −0.359893 | + | 0.207785i | ||||
\(396\) | 431.461 | − | 752.405i | 1.08955 | − | 1.90001i | ||||
\(397\) | 360.644 | − | 624.654i | 0.908423 | − | 1.57344i | 0.0921681 | − | 0.995743i | \(-0.470620\pi\) |
0.816255 | − | 0.577692i | \(-0.196046\pi\) | |||||||
\(398\) | −1119.67 | − | 646.443i | −2.81325 | − | 1.62423i | ||||
\(399\) | −536.407 | + | 261.724i | −1.34438 | + | 0.655951i | ||||
\(400\) | 75.1006 | + | 130.078i | 0.187751 | + | 0.325195i | ||||
\(401\) | − | 281.052i | − | 0.700878i | −0.936586 | − | 0.350439i | \(-0.886032\pi\) | ||
0.936586 | − | 0.350439i | \(-0.113968\pi\) | |||||||
\(402\) | 191.195 | − | 191.757i | 0.475608 | − | 0.477007i | ||||
\(403\) | 212.758 | 0.527936 | ||||||||
\(404\) | 150.520 | + | 86.9025i | 0.372573 | + | 0.215105i | ||||
\(405\) | 1.06360 | + | 181.118i | 0.00262618 | + | 0.447206i | ||||
\(406\) | −841.601 | + | 162.442i | −2.07291 | + | 0.400103i | ||||
\(407\) | −65.3350 | − | 37.7212i | −0.160528 | − | 0.0926811i | ||||
\(408\) | −202.424 | + | 759.918i | −0.496138 | + | 1.86255i | ||||
\(409\) | −193.746 | + | 335.578i | −0.473707 | + | 0.820484i | −0.999547 | − | 0.0300995i | \(-0.990418\pi\) |
0.525840 | + | 0.850583i | \(0.323751\pi\) | |||||||
\(410\) | −28.1665 | − | 16.2619i | −0.0686987 | − | 0.0396632i | ||||
\(411\) | −205.198 | + | 205.801i | −0.499265 | + | 0.500733i | ||||
\(412\) | 855.107 | − | 1481.09i | 2.07550 | − | 3.59488i | ||||
\(413\) | 307.197 | + | 106.229i | 0.743819 | + | 0.257212i | ||||
\(414\) | 414.916 | − | 241.179i | 1.00221 | − | 0.582558i | ||||
\(415\) | −61.5976 | + | 106.690i | −0.148428 | + | 0.257085i | ||||
\(416\) | 728.974i | 1.75234i | ||||||||
\(417\) | 132.060 | − | 495.764i | 0.316690 | − | 1.18888i | ||||
\(418\) | 1091.44 | 2.61110 | ||||||||
\(419\) | −500.723 | + | 289.092i | −1.19504 | + | 0.689958i | −0.959446 | − | 0.281893i | \(-0.909038\pi\) |
−0.235597 | + | 0.971851i | \(0.575704\pi\) | |||||||
\(420\) | 186.843 | + | 382.936i | 0.444864 | + | 0.911753i | ||||
\(421\) | 74.8792 | − | 129.695i | 0.177860 | − | 0.308063i | −0.763287 | − | 0.646059i | \(-0.776416\pi\) |
0.941147 | + | 0.337996i | \(0.109749\pi\) | |||||||
\(422\) | 979.812 | + | 565.695i | 2.32183 | + | 1.34051i | ||||
\(423\) | 324.987 | + | 559.097i | 0.768291 | + | 1.32174i | ||||
\(424\) | 410.291 | + | 710.644i | 0.967667 | + | 1.67605i | ||||
\(425\) | 61.8709 | − | 35.7212i | 0.145579 | − | 0.0840499i | ||||
\(426\) | 374.390 | − | 1405.49i | 0.878849 | − | 3.29928i | ||||
\(427\) | −39.8781 | − | 45.9966i | −0.0933914 | − | 0.107720i | ||||
\(428\) | −732.216 | + | 422.745i | −1.71079 | + | 0.987723i | ||||
\(429\) | −636.989 | − | 169.679i | −1.48482 | − | 0.395522i | ||||
\(430\) | −380.808 | −0.885600 | ||||||||
\(431\) | 94.2168 | − | 54.3961i | 0.218600 | − | 0.126209i | −0.386702 | − | 0.922205i | \(-0.626386\pi\) |
0.605302 | + | 0.795996i | \(0.293052\pi\) | |||||||
\(432\) | −784.366 | − | 206.472i | −1.81566 | − | 0.477944i | ||||
\(433\) | −108.154 | −0.249779 | −0.124889 | − | 0.992171i | \(-0.539858\pi\) | ||||
−0.124889 | + | 0.992171i | \(0.539858\pi\) | |||||||
\(434\) | 49.3276 | + | 255.563i | 0.113658 | + | 0.588855i | ||||
\(435\) | −219.345 | + | 59.1185i | −0.504240 | + | 0.135905i | ||||
\(436\) | −246.614 | −0.565629 | ||||||||
\(437\) | 362.995 | + | 209.575i | 0.830653 | + | 0.479578i | ||||
\(438\) | −383.937 | − | 1424.51i | −0.876569 | − | 3.25230i | ||||
\(439\) | 234.021 | + | 405.336i | 0.533077 | + | 0.923316i | 0.999254 | + | 0.0386245i | \(0.0122976\pi\) |
−0.466177 | + | 0.884691i | \(0.654369\pi\) | |||||||
\(440\) | − | 435.694i | − | 0.990213i | ||||||
\(441\) | 165.326 | + | 408.838i | 0.374889 | + | 0.927070i | ||||
\(442\) | 1068.89 | 2.41831 | ||||||||
\(443\) | 375.426 | − | 216.752i | 0.847463 | − | 0.489283i | −0.0123309 | − | 0.999924i | \(-0.503925\pi\) |
0.859794 | + | 0.510641i | \(0.170592\pi\) | |||||||
\(444\) | −49.7726 | + | 186.851i | −0.112101 | + | 0.420835i | ||||
\(445\) | −11.1192 | + | 19.2590i | −0.0249869 | + | 0.0432786i | ||||
\(446\) | − | 165.080i | − | 0.370135i | ||||||
\(447\) | −14.7040 | + | 14.7472i | −0.0328948 | + | 0.0329916i | ||||
\(448\) | −49.7536 | + | 9.60320i | −0.111057 | + | 0.0214357i | ||||
\(449\) | 116.178i | 0.258749i | 0.991596 | + | 0.129374i | \(0.0412969\pi\) | ||||
−0.991596 | + | 0.129374i | \(0.958703\pi\) | |||||||
\(450\) | 81.7686 | + | 140.672i | 0.181708 | + | 0.312604i | ||||
\(451\) | 21.3616 | + | 36.9995i | 0.0473651 | + | 0.0820387i | ||||
\(452\) | − | 853.081i | − | 1.88735i | ||||||
\(453\) | 286.107 | + | 285.268i | 0.631583 | + | 0.629731i | ||||
\(454\) | 109.131 | + | 189.020i | 0.240376 | + | 0.416344i | ||||
\(455\) | 244.684 | − | 212.136i | 0.537767 | − | 0.466233i | ||||
\(456\) | −407.083 | − | 1510.38i | −0.892725 | − | 3.31224i | ||||
\(457\) | 149.571 | + | 259.065i | 0.327289 | + | 0.566881i | 0.981973 | − | 0.189021i | \(-0.0605316\pi\) |
−0.654684 | + | 0.755903i | \(0.727198\pi\) | |||||||
\(458\) | 769.949 | − | 444.530i | 1.68111 | − | 0.970590i | ||||
\(459\) | −98.2073 | + | 373.080i | −0.213959 | + | 0.812810i | ||||
\(460\) | 149.614 | − | 259.139i | 0.325248 | − | 0.563347i | ||||
\(461\) | −21.1254 | − | 12.1967i | −0.0458251 | − | 0.0264571i | 0.476912 | − | 0.878951i | \(-0.341756\pi\) |
−0.522738 | + | 0.852494i | \(0.675089\pi\) | |||||||
\(462\) | 56.1318 | − | 804.485i | 0.121497 | − | 1.74131i | ||||
\(463\) | −0.140082 | − | 0.242629i | −0.000302553 | − | 0.000524037i | 0.865874 | − | 0.500262i | \(-0.166763\pi\) |
−0.866177 | + | 0.499738i | \(0.833430\pi\) | |||||||
\(464\) | − | 1017.31i | − | 2.19247i | ||||||
\(465\) | 17.9521 | + | 66.6068i | 0.0386066 | + | 0.143240i | ||||
\(466\) | 856.316 | 1.83759 | ||||||||
\(467\) | −554.637 | − | 320.220i | −1.18766 | − | 0.685696i | −0.229886 | − | 0.973217i | \(-0.573835\pi\) |
−0.957774 | + | 0.287521i | \(0.907169\pi\) | |||||||
\(468\) | 4.96095 | + | 1689.59i | 0.0106003 | + | 3.61024i | ||||
\(469\) | 57.1085 | − | 165.149i | 0.121767 | − | 0.352130i | ||||
\(470\) | 503.119 | + | 290.476i | 1.07047 | + | 0.618034i | ||||
\(471\) | 175.103 | − | 47.1943i | 0.371768 | − | 0.100200i | ||||
\(472\) | −425.953 | + | 737.773i | −0.902443 | + | 1.56308i | ||||
\(473\) | 433.211 | + | 250.114i | 0.915880 | + | 0.528783i | ||||
\(474\) | −207.228 | − | 768.868i | −0.437190 | − | 1.62208i | ||||
\(475\) | −71.0538 | + | 123.069i | −0.149587 | + | 0.259092i | ||||
\(476\) | 172.000 | + | 891.119i | 0.361344 | + | 1.87210i | ||||
\(477\) | 202.297 | + | 348.025i | 0.424103 | + | 0.729612i | ||||
\(478\) | −488.319 | + | 845.793i | −1.02159 | + | 1.76944i | ||||
\(479\) | − | 654.059i | − | 1.36547i | −0.730667 | − | 0.682734i | \(-0.760791\pi\) | ||
0.730667 | − | 0.682734i | \(-0.239209\pi\) | |||||||
\(480\) | −228.215 | + | 61.5093i | −0.475448 | + | 0.128144i | ||||
\(481\) | 146.964 | 0.305539 | ||||||||
\(482\) | 364.330 | − | 210.346i | 0.755871 | − | 0.436402i | ||||
\(483\) | 173.143 | − | 256.780i | 0.358475 | − | 0.531636i | ||||
\(484\) | 37.2126 | − | 64.4541i | 0.0768855 | − | 0.133170i | ||||
\(485\) | −49.3380 | − | 28.4853i | −0.101728 | − | 0.0587326i | ||||
\(486\) | −850.344 | − | 221.172i | −1.74968 | − | 0.455086i | ||||
\(487\) | −282.093 | − | 488.600i | −0.579247 | − | 1.00329i | −0.995566 | − | 0.0940671i | \(-0.970013\pi\) |
0.416318 | − | 0.909219i | \(-0.363320\pi\) | |||||||
\(488\) | 138.175 | − | 79.7751i | 0.283145 | − | 0.163474i | ||||
\(489\) | 279.498 | − | 75.3312i | 0.571570 | − | 0.154052i | ||||
\(490\) | 311.545 | + | 244.728i | 0.635806 | + | 0.499446i | ||||
\(491\) | 69.6197 | − | 40.1949i | 0.141792 | − | 0.0818634i | −0.427426 | − | 0.904050i | \(-0.640580\pi\) |
0.569218 | + | 0.822187i | \(0.307246\pi\) | |||||||
\(492\) | 77.3173 | − | 77.5446i | 0.157149 | − | 0.157611i | ||||
\(493\) | −483.876 | −0.981493 | ||||||||
\(494\) | −1841.31 | + | 1063.08i | −3.72735 | + | 2.15198i | ||||
\(495\) | −0.627567 | − | 213.735i | −0.00126781 | − | 0.431788i | ||||
\(496\) | −308.918 | −0.622818 | ||||||||
\(497\) | −177.884 | − | 921.606i | −0.357916 | − | 1.85434i | ||||
\(498\) | −423.209 | − | 421.968i | −0.849817 | − | 0.847325i | ||||
\(499\) | −238.156 | −0.477266 | −0.238633 | − | 0.971110i | \(-0.576699\pi\) | ||||
−0.238633 | + | 0.971110i | \(0.576699\pi\) | |||||||
\(500\) | 87.8578 | + | 50.7247i | 0.175716 | + | 0.101449i | ||||
\(501\) | −413.982 | − | 110.275i | −0.826312 | − | 0.220110i | ||||
\(502\) | 368.889 | + | 638.935i | 0.734839 | + | 1.27278i | ||||
\(503\) | 942.622i | 1.87400i | 0.349330 | + | 0.937000i | \(0.386409\pi\) | ||||
−0.349330 | + | 0.937000i | \(0.613591\pi\) | |||||||
\(504\) | −1134.21 | + | 222.377i | −2.25043 | + | 0.441225i | ||||
\(505\) | 42.8305 | 0.0848128 | ||||||||
\(506\) | −490.464 | + | 283.170i | −0.969297 | + | 0.559624i | ||||
\(507\) | 750.367 | − | 202.241i | 1.48001 | − | 0.398898i | ||||
\(508\) | −962.361 | + | 1666.86i | −1.89441 | + | 3.28122i | ||||
\(509\) | 514.259i | 1.01033i | 0.863022 | + | 0.505166i | \(0.168569\pi\) | ||||
−0.863022 | + | 0.505166i | \(0.831431\pi\) | |||||||
\(510\) | 90.1911 | + | 334.632i | 0.176845 | + | 0.656141i | ||||
\(511\) | −623.664 | − | 719.352i | −1.22048 | − | 1.40773i | ||||
\(512\) | 1146.05i | 2.23837i | ||||||||
\(513\) | −201.875 | − | 740.351i | −0.393519 | − | 1.44318i | ||||
\(514\) | −608.918 | − | 1054.68i | −1.18467 | − | 2.05190i | ||||
\(515\) | − | 421.445i | − | 0.818340i | ||||||
\(516\) | 330.023 | − | 1238.93i | 0.639579 | − | 2.40104i | ||||
\(517\) | −381.569 | − | 660.897i | −0.738044 | − | 1.27833i | ||||
\(518\) | 34.0734 | + | 176.532i | 0.0657787 | + | 0.340795i | ||||
\(519\) | −700.525 | − | 186.603i | −1.34976 | − | 0.359544i | ||||
\(520\) | 424.372 | + | 735.034i | 0.816100 | + | 1.41353i | ||||
\(521\) | 271.046 | − | 156.488i | 0.520241 | − | 0.300361i | −0.216792 | − | 0.976218i | \(-0.569559\pi\) |
0.737033 | + | 0.675856i | \(0.236226\pi\) | |||||||
\(522\) | −3.23575 | − | 1102.03i | −0.00619876 | − | 2.11116i | ||||
\(523\) | −208.151 | + | 360.529i | −0.397995 | + | 0.689347i | −0.993478 | − | 0.114020i | \(-0.963627\pi\) |
0.595484 | + | 0.803367i | \(0.296960\pi\) | |||||||
\(524\) | 1720.36 | + | 993.249i | 3.28313 | + | 1.89551i | ||||
\(525\) | 87.0579 | + | 58.7020i | 0.165825 | + | 0.111813i | ||||
\(526\) | −359.663 | − | 622.955i | −0.683771 | − | 1.18433i | ||||
\(527\) | 146.935i | 0.278814i | ||||||||
\(528\) | 924.888 | + | 246.368i | 1.75168 | + | 0.466606i | ||||
\(529\) | 311.506 | 0.588859 | ||||||||
\(530\) | 313.180 | + | 180.815i | 0.590906 | + | 0.341160i | ||||
\(531\) | −207.894 | + | 362.538i | −0.391515 | + | 0.682745i | ||||
\(532\) | −1182.56 | − | 1364.00i | −2.22286 | − | 2.56392i | ||||
\(533\) | −72.0761 | − | 41.6131i | −0.135227 | − | 0.0780734i | ||||
\(534\) | −76.3947 | − | 76.1707i | −0.143061 | − | 0.142642i | ||||
\(535\) | −104.176 | + | 180.439i | −0.194722 | + | 0.337269i | ||||
\(536\) | 396.626 | + | 228.992i | 0.739974 | + | 0.427224i | ||||
\(537\) | 176.411 | + | 46.9918i | 0.328513 | + | 0.0875080i | ||||
\(538\) | 58.7762 | − | 101.803i | 0.109249 | − | 0.189225i | ||||
\(539\) | −193.679 | − | 483.028i | −0.359330 | − | 0.896156i | ||||
\(540\) | −528.530 | + | 144.117i | −0.978760 | + | 0.266884i | ||||
\(541\) | 48.7493 | − | 84.4363i | 0.0901096 | − | 0.156074i | −0.817447 | − | 0.576003i | \(-0.804612\pi\) |
0.907557 | + | 0.419929i | \(0.137945\pi\) | |||||||
\(542\) | 802.471i | 1.48057i | ||||||||
\(543\) | −584.741 | − | 583.027i | −1.07687 | − | 1.07371i | ||||
\(544\) | −503.445 | −0.925450 | ||||||||
\(545\) | −52.6307 | + | 30.3863i | −0.0965701 | + | 0.0557548i | ||||
\(546\) | 688.884 | + | 1411.87i | 1.26169 | + | 2.58585i | ||||
\(547\) | −172.803 | + | 299.304i | −0.315911 | + | 0.547174i | −0.979631 | − | 0.200807i | \(-0.935643\pi\) |
0.663720 | + | 0.747981i | \(0.268977\pi\) | |||||||
\(548\) | −761.255 | − | 439.511i | −1.38915 | − | 0.802027i | ||||
\(549\) | 67.6685 | − | 39.3338i | 0.123258 | − | 0.0716462i | ||||
\(550\) | −96.0049 | − | 166.285i | −0.174554 | − | 0.302337i | ||||
\(551\) | 833.539 | − | 481.244i | 1.51277 | − | 0.873401i | ||||
\(552\) | 574.794 | + | 573.108i | 1.04129 | + | 1.03824i | ||||
\(553\) | −336.619 | − | 388.266i | −0.608714 | − | 0.702108i | ||||
\(554\) | 1460.85 | − | 843.424i | 2.63692 | − | 1.52243i | ||||
\(555\) | 12.4005 | + | 46.0091i | 0.0223433 | + | 0.0828993i | ||||
\(556\) | 1551.79 | 2.79099 | ||||||||
\(557\) | −308.087 | + | 177.874i | −0.553119 | + | 0.319343i | −0.750379 | − | 0.661008i | \(-0.770129\pi\) |
0.197260 | + | 0.980351i | \(0.436796\pi\) | |||||||
\(558\) | −334.644 | + | 0.982578i | −0.599721 | + | 0.00176089i | ||||
\(559\) | −974.461 | −1.74322 | ||||||||
\(560\) | −355.273 | + | 308.014i | −0.634416 | + | 0.550026i | ||||
\(561\) | 117.184 | − | 439.918i | 0.208884 | − | 0.784168i | ||||
\(562\) | −494.999 | −0.880780 | ||||||||
\(563\) | −94.7108 | − | 54.6813i | −0.168225 | − | 0.0971249i | 0.413523 | − | 0.910493i | \(-0.364298\pi\) |
−0.581749 | + | 0.813369i | \(0.697631\pi\) | |||||||
\(564\) | −1381.07 | + | 1385.13i | −2.44870 | + | 2.45590i | ||||
\(565\) | −105.112 | − | 182.059i | −0.186038 | − | 0.322228i | ||||
\(566\) | − | 230.267i | − | 0.406831i | ||||||
\(567\) | −556.084 | + | 110.724i | −0.980748 | + | 0.195280i | ||||
\(568\) | 2460.00 | 4.33099 | ||||||||
\(569\) | −355.519 | + | 205.259i | −0.624814 | + | 0.360736i | −0.778741 | − | 0.627346i | \(-0.784141\pi\) |
0.153927 | + | 0.988082i | \(0.450808\pi\) | |||||||
\(570\) | −488.177 | − | 486.746i | −0.856452 | − | 0.853941i | ||||
\(571\) | −418.371 | + | 724.639i | −0.732698 | + | 1.26907i | 0.223028 | + | 0.974812i | \(0.428406\pi\) |
−0.955726 | + | 0.294258i | \(0.904927\pi\) | |||||||
\(572\) | − | 1993.84i | − | 3.48574i | ||||||
\(573\) | −587.343 | − | 156.454i | −1.02503 | − | 0.273044i | ||||
\(574\) | 33.2746 | − | 96.2250i | 0.0579697 | − | 0.167639i | ||||
\(575\) | − | 73.7383i | − | 0.128241i | ||||||
\(576\) | −0.191290 | − | 65.1493i | −0.000332101 | − | 0.113106i | ||||
\(577\) | 179.987 | + | 311.746i | 0.311935 | + | 0.540288i | 0.978781 | − | 0.204908i | \(-0.0656895\pi\) |
−0.666846 | + | 0.745196i | \(0.732356\pi\) | |||||||
\(578\) | − | 306.761i | − | 0.530729i | ||||||
\(579\) | 472.294 | − | 127.294i | 0.815706 | − | 0.219852i | ||||
\(580\) | −343.556 | − | 595.057i | −0.592338 | − | 1.02596i | ||||
\(581\) | −364.485 | − | 126.039i | −0.627341 | − | 0.216935i | ||||
\(582\) | 195.136 | − | 195.709i | 0.335285 | − | 0.336271i | ||||
\(583\) | −237.518 | − | 411.393i | −0.407406 | − | 0.705649i | ||||
\(584\) | 2160.95 | − | 1247.62i | 3.70025 | − | 2.13634i | ||||
\(585\) | 209.240 | + | 359.969i | 0.357675 | + | 0.615332i | ||||
\(586\) | −297.527 | + | 515.332i | −0.507726 | + | 0.879406i | ||||
\(587\) | 335.306 | + | 193.589i | 0.571220 | + | 0.329794i | 0.757636 | − | 0.652677i | \(-0.226354\pi\) |
−0.186416 | + | 0.982471i | \(0.559687\pi\) | |||||||
\(588\) | −1066.20 | + | 801.500i | −1.81327 | + | 1.36310i | ||||
\(589\) | −146.136 | − | 253.115i | −0.248108 | − | 0.429736i | ||||
\(590\) | 375.434i | 0.636329i | ||||||||
\(591\) | 90.0783 | − | 90.3432i | 0.152417 | − | 0.152865i | ||||
\(592\) | −213.387 | −0.360451 | ||||||||
\(593\) | −346.084 | − | 199.812i | −0.583616 | − | 0.336951i | 0.178953 | − | 0.983858i | \(-0.442729\pi\) |
−0.762569 | + | 0.646907i | \(0.776062\pi\) | |||||||
\(594\) | 1002.69 | + | 263.944i | 1.68804 | + | 0.444350i | ||||
\(595\) | 146.505 | + | 168.984i | 0.246228 | + | 0.284006i | ||||
\(596\) | −54.5497 | − | 31.4943i | −0.0915264 | − | 0.0528428i | ||||
\(597\) | 276.114 | − | 1036.56i | 0.462503 | − | 1.73628i | ||||
\(598\) | 551.623 | − | 955.439i | 0.922447 | − | 1.59772i | ||||
\(599\) | 691.915 | + | 399.477i | 1.15512 | + | 0.666907i | 0.950129 | − | 0.311858i | \(-0.100951\pi\) |
0.204988 | + | 0.978765i | \(0.434285\pi\) | |||||||
\(600\) | −194.305 | + | 194.876i | −0.323841 | + | 0.324793i | ||||
\(601\) | 349.867 | − | 605.987i | 0.582141 | − | 1.00830i | −0.413084 | − | 0.910693i | \(-0.635548\pi\) |
0.995225 | − | 0.0976052i | \(-0.0311182\pi\) | |||||||
\(602\) | −225.927 | − | 1170.51i | −0.375294 | − | 1.94437i | ||||
\(603\) | 194.900 | + | 111.764i | 0.323217 | + | 0.185346i | ||||
\(604\) | −611.013 | + | 1058.30i | −1.01161 | + | 1.75216i | ||||
\(605\) | − | 18.3405i | − | 0.0303148i | ||||||
\(606\) | −53.4812 | + | 200.773i | −0.0882529 | + | 0.331309i | ||||
\(607\) | −470.532 | −0.775176 | −0.387588 | − | 0.921833i | \(-0.626692\pi\) | ||||
−0.387588 | + | 0.921833i | \(0.626692\pi\) | |||||||
\(608\) | 867.248 | − | 500.706i | 1.42639 | − | 0.823529i | ||||
\(609\) | −311.850 | − | 639.139i | −0.512068 | − | 1.04949i | ||||
\(610\) | 35.1568 | − | 60.8934i | 0.0576341 | − | 0.0998252i | ||||
\(611\) | 1287.45 | + | 743.308i | 2.10711 | + | 1.21654i | ||||
\(612\) | −1166.87 | + | 3.42614i | −1.90664 | + | 0.00559826i | ||||
\(613\) | 490.272 | + | 849.176i | 0.799791 | + | 1.38528i | 0.919752 | + | 0.392500i | \(0.128390\pi\) |
−0.119961 | + | 0.992779i | \(0.538277\pi\) | |||||||
\(614\) | −450.101 | + | 259.866i | −0.733063 | + | 0.423234i | ||||
\(615\) | 6.94593 | − | 26.0756i | 0.0112942 | − | 0.0423994i | ||||
\(616\) | 1339.22 | − | 258.490i | 2.17406 | − | 0.419626i | ||||
\(617\) | −432.401 | + | 249.647i | −0.700812 | + | 0.404614i | −0.807650 | − | 0.589662i | \(-0.799261\pi\) |
0.106838 | + | 0.994276i | \(0.465927\pi\) | |||||||
\(618\) | 1975.58 | + | 526.247i | 3.19673 | + | 0.851532i | ||||
\(619\) | 533.451 | 0.861795 | 0.430897 | − | 0.902401i | \(-0.358197\pi\) | ||||
0.430897 | + | 0.902401i | \(0.358197\pi\) | |||||||
\(620\) | −180.697 | + | 104.325i | −0.291446 | + | 0.168266i | ||||
\(621\) | 282.798 | + | 280.318i | 0.455391 | + | 0.451398i | ||||
\(622\) | −1647.93 | −2.64940 | ||||||||
\(623\) | −65.7943 | − | 22.7517i | −0.105609 | − | 0.0365195i | ||||
\(624\) | −1800.29 | + | 485.221i | −2.88508 | + | 0.777597i | ||||
\(625\) | 25.0000 | 0.0400000 | ||||||||
\(626\) | 12.7109 | + | 7.33865i | 0.0203050 | + | 0.0117231i | ||||
\(627\) | 235.661 | + | 874.362i | 0.375855 | + | 1.39452i | ||||
\(628\) | 274.261 | + | 475.034i | 0.436722 | + | 0.756424i | ||||
\(629\) | 101.496i | 0.161362i | ||||||||
\(630\) | −383.880 | + | 334.795i | −0.609333 | + | 0.531421i | ||||
\(631\) | −1007.58 | −1.59680 | −0.798398 | − | 0.602130i | \(-0.794319\pi\) | ||||
−0.798398 | + | 0.602130i | \(0.794319\pi\) | |||||||
\(632\) | 1166.36 | − | 673.397i | 1.84550 | − | 1.06550i | ||||
\(633\) | −241.624 | + | 907.078i | −0.381713 | + | 1.43298i | ||||
\(634\) | 760.404 | − | 1317.06i | 1.19938 | − | 2.07738i | ||||
\(635\) | 474.306i | 0.746939i | ||||||||
\(636\) | −859.683 | + | 862.211i | −1.35170 | + | 1.35568i | ||||
\(637\) | 797.222 | + | 626.243i | 1.25153 | + | 0.983113i | ||||
\(638\) | 1300.47i | 2.03836i | ||||||||
\(639\) | 1206.79 | − | 3.54335i | 1.88856 | − | 0.00554515i | ||||
\(640\) | 128.309 | + | 222.238i | 0.200483 | + | 0.347247i | ||||
\(641\) | − | 33.9626i | − | 0.0529838i | −0.999649 | − | 0.0264919i | \(-0.991566\pi\) | ||
0.999649 | − | 0.0264919i | \(-0.00843361\pi\) | |||||||
\(642\) | −715.748 | − | 713.649i | −1.11487 | − | 1.11160i | ||||
\(643\) | 179.675 | + | 311.206i | 0.279433 | + | 0.483991i | 0.971244 | − | 0.238087i | \(-0.0765203\pi\) |
−0.691811 | + | 0.722078i | \(0.743187\pi\) | |||||||
\(644\) | 885.297 | + | 306.136i | 1.37468 | + | 0.475366i | ||||
\(645\) | −82.2230 | − | 305.068i | −0.127478 | − | 0.472974i | ||||
\(646\) | −734.185 | − | 1271.65i | −1.13651 | − | 1.96849i | ||||
\(647\) | −316.062 | + | 182.478i | −0.488504 | + | 0.282038i | −0.723954 | − | 0.689849i | \(-0.757677\pi\) |
0.235450 | + | 0.971887i | \(0.424344\pi\) | |||||||
\(648\) | −8.72651 | − | 1486.01i | −0.0134668 | − | 2.29323i | ||||
\(649\) | 246.585 | − | 427.098i | 0.379946 | − | 0.658086i | ||||
\(650\) | 323.929 | + | 187.020i | 0.498352 | + | 0.287724i | ||||
\(651\) | −194.083 | + | 94.6971i | −0.298130 | + | 0.145464i | ||||
\(652\) | 437.774 | + | 758.246i | 0.671432 | + | 1.16295i | ||||
\(653\) | − | 149.800i | − | 0.229403i | −0.993400 | − | 0.114701i | \(-0.963409\pi\) | ||
0.993400 | − | 0.114701i | \(-0.0365912\pi\) | |||||||
\(654\) | −76.7214 | − | 284.656i | −0.117311 | − | 0.435253i | ||||
\(655\) | 489.529 | 0.747373 | ||||||||
\(656\) | 104.652 | + | 60.4209i | 0.159531 | + | 0.0921051i | ||||
\(657\) | 1058.28 | − | 615.150i | 1.61078 | − | 0.936302i | ||||
\(658\) | −594.362 | + | 1718.80i | −0.903286 | + | 2.61216i | ||||
\(659\) | 149.933 | + | 86.5638i | 0.227516 | + | 0.131356i | 0.609425 | − | 0.792843i | \(-0.291400\pi\) |
−0.381910 | + | 0.924200i | \(0.624733\pi\) | |||||||
\(660\) | 624.200 | − | 168.236i | 0.945757 | − | 0.254904i | ||||
\(661\) | −257.977 | + | 446.829i | −0.390283 | + | 0.675990i | −0.992487 | − | 0.122353i | \(-0.960956\pi\) |
0.602204 | + | 0.798342i | \(0.294289\pi\) | |||||||
\(662\) | −46.2475 | − | 26.7010i | −0.0698603 | − | 0.0403338i | ||||
\(663\) | 230.793 | + | 856.300i | 0.348104 | + | 1.29155i | ||||
\(664\) | 505.388 | − | 875.357i | 0.761126 | − | 1.31831i | ||||
\(665\) | −420.439 | − | 145.388i | −0.632239 | − | 0.218628i | ||||
\(666\) | −231.158 | + | 0.678722i | −0.347084 | + | 0.00101910i | ||||
\(667\) | −249.713 | + | 432.516i | −0.374383 | + | 0.648450i | ||||
\(668\) | − | 1295.81i | − | 1.93983i | ||||||
\(669\) | 132.247 | − | 35.6436i | 0.197679 | − | 0.0532790i | ||||
\(670\) | 201.833 | 0.301244 | ||||||||
\(671\) | −79.9895 | + | 46.1820i | −0.119209 | + | 0.0688256i | ||||
\(672\) | −324.461 | − | 664.987i | −0.482829 | − | 0.989563i | ||||
\(673\) | 84.5076 | − | 146.371i | 0.125569 | − | 0.217491i | −0.796387 | − | 0.604788i | \(-0.793258\pi\) |
0.921955 | + | 0.387297i | \(0.126591\pi\) | |||||||
\(674\) | 950.399 | + | 548.713i | 1.41009 | + | 0.814114i | ||||
\(675\) | −95.0381 | + | 95.8789i | −0.140797 | + | 0.142043i | ||||
\(676\) | 1175.29 | + | 2035.66i | 1.73859 | + | 3.01133i | ||||
\(677\) | −935.827 | + | 540.300i | −1.38232 | + | 0.798080i | −0.992433 | − | 0.122785i | \(-0.960818\pi\) |
−0.389882 | + | 0.920865i | \(0.627484\pi\) | |||||||
\(678\) | 984.673 | − | 265.392i | 1.45232 | − | 0.391434i | ||||
\(679\) | 58.2857 | − | 168.553i | 0.0858405 | − | 0.248237i | ||||
\(680\) | −507.630 | + | 293.080i | −0.746515 | + | 0.431000i | ||||
\(681\) | −127.862 | + | 128.238i | −0.187757 | + | 0.188309i | ||||
\(682\) | 394.905 | 0.579040 | ||||||||
\(683\) | −743.007 | + | 428.975i | −1.08786 | + | 0.628075i | −0.933005 | − | 0.359862i | \(-0.882824\pi\) |
−0.154853 | + | 0.987938i | \(0.549490\pi\) | |||||||
\(684\) | 2006.67 | − | 1166.42i | 2.93373 | − | 1.70529i | ||||
\(685\) | −216.616 | −0.316227 | ||||||||
\(686\) | −567.403 | + | 1102.81i | −0.827118 | + | 1.60759i | ||||
\(687\) | 522.362 | + | 520.830i | 0.760352 | + | 0.758123i | ||||
\(688\) | 1414.89 | 2.05652 | ||||||||
\(689\) | 801.407 | + | 462.692i | 1.16314 | + | 0.671542i | ||||
\(690\) | 345.658 | + | 92.0751i | 0.500953 | + | 0.133442i | ||||
\(691\) | 74.4040 | + | 128.871i | 0.107676 | + | 0.186500i | 0.914828 | − | 0.403843i | \(-0.132326\pi\) |
−0.807152 | + | 0.590343i | \(0.798992\pi\) | |||||||
\(692\) | − | 2192.72i | − | 3.16867i | ||||||
\(693\) | 656.599 | − | 128.735i | 0.947473 | − | 0.185764i | ||||
\(694\) | 622.243 | 0.896603 | ||||||||
\(695\) | 331.173 | − | 191.203i | 0.476508 | − | 0.275112i | ||||
\(696\) | 1799.65 | − | 485.047i | 2.58570 | − | 0.696907i | ||||
\(697\) | 28.7389 | − | 49.7772i | 0.0412323 | − | 0.0714164i | ||||
\(698\) | − | 15.3070i | − | 0.0219298i | ||||||
\(699\) | 184.893 | + | 686.001i | 0.264511 | + | 0.981404i | ||||
\(700\) | −103.791 | + | 300.148i | −0.148273 | + | 0.428783i | ||||
\(701\) | 1313.93i | 1.87437i | 0.348836 | + | 0.937184i | \(0.386577\pi\) | ||||
−0.348836 | + | 0.937184i | \(0.613423\pi\) | |||||||
\(702\) | −1948.68 | + | 531.356i | −2.77589 | + | 0.756917i | ||||
\(703\) | −100.944 | − | 174.841i | −0.143591 | − | 0.248707i | ||||
\(704\) | 76.8811i | 0.109206i | ||||||||
\(705\) | −124.070 | + | 465.771i | −0.175986 | + | 0.660669i | ||||
\(706\) | −441.813 | − | 765.243i | −0.625798 | − | 1.08391i | ||||
\(707\) | 25.4106 | + | 131.651i | 0.0359414 | + | 0.186210i | ||||
\(708\) | −1221.45 | − | 325.366i | −1.72521 | − | 0.459556i | ||||
\(709\) | −383.702 | − | 664.592i | −0.541188 | − | 0.937365i | −0.998836 | − | 0.0482314i | \(-0.984642\pi\) |
0.457648 | − | 0.889133i | \(-0.348692\pi\) | |||||||
\(710\) | 938.877 | − | 542.061i | 1.32236 | − | 0.763466i | ||||
\(711\) | 571.202 | − | 332.024i | 0.803378 | − | 0.466981i | ||||
\(712\) | 91.2291 | − | 158.013i | 0.128131 | − | 0.221929i | ||||
\(713\) | 131.339 | + | 75.8286i | 0.184206 | + | 0.106352i | ||||
\(714\) | −975.070 | + | 475.758i | −1.36564 | + | 0.666327i | ||||
\(715\) | −245.670 | − | 425.513i | −0.343594 | − | 0.595122i | ||||
\(716\) | 552.186i | 0.771210i | ||||||||
\(717\) | −783.008 | − | 208.575i | −1.09206 | − | 0.290899i | ||||
\(718\) | −2590.96 | −3.60858 | ||||||||
\(719\) | −481.999 | − | 278.282i | −0.670375 | − | 0.387041i | 0.125844 | − | 0.992050i | \(-0.459836\pi\) |
−0.796219 | + | 0.605009i | \(0.793169\pi\) | |||||||
\(720\) | −303.810 | − | 522.664i | −0.421958 | − | 0.725922i | ||||
\(721\) | 1295.42 | − | 250.036i | 1.79670 | − | 0.346791i | ||||
\(722\) | 1399.04 | + | 807.734i | 1.93772 | + | 1.11874i | ||||
\(723\) | 247.175 | + | 246.450i | 0.341874 | + | 0.340871i | ||||
\(724\) | 1248.78 | − | 2162.95i | 1.72483 | − | 2.98749i | ||||
\(725\) | −146.639 | − | 84.6619i | −0.202260 | − | 0.116775i | ||||
\(726\) | 85.9733 | + | 22.9013i | 0.118421 | + | 0.0315444i | ||||
\(727\) | −61.6082 | + | 106.709i | −0.0847431 | + | 0.146779i | −0.905282 | − | 0.424812i | \(-0.860340\pi\) |
0.820539 | + | 0.571591i | \(0.193674\pi\) | |||||||
\(728\) | −2007.55 | + | 1740.50i | −2.75762 | + | 2.39080i | ||||
\(729\) | −6.42134 | − | 728.972i | −0.00880842 | − | 0.999961i | ||||
\(730\) | 549.826 | − | 952.327i | 0.753187 | − | 1.30456i | ||||
\(731\) | − | 672.983i | − | 0.920634i | ||||||
\(732\) | 167.644 | + | 167.153i | 0.229023 | + | 0.228351i | ||||
\(733\) | 420.219 | 0.573287 | 0.286643 | − | 0.958037i | \(-0.407461\pi\) | ||||
0.286643 | + | 0.958037i | \(0.407461\pi\) | |||||||
\(734\) | −308.891 | + | 178.338i | −0.420832 | + | 0.242967i | ||||
\(735\) | −128.786 | + | 302.422i | −0.175219 | + | 0.411459i | ||||
\(736\) | −259.812 | + | 450.007i | −0.353005 | + | 0.611423i | ||||
\(737\) | −229.608 | − | 132.564i | −0.311543 | − | 0.179870i | ||||
\(738\) | 113.560 | + | 65.1198i | 0.153875 | + | 0.0882383i | ||||
\(739\) | −107.703 | − | 186.548i | −0.145742 | − | 0.252432i | 0.783908 | − | 0.620878i | \(-0.213224\pi\) |
−0.929650 | + | 0.368445i | \(0.879890\pi\) | |||||||
\(740\) | −124.817 | + | 72.0634i | −0.168672 | + | 0.0973829i | ||||
\(741\) | −1249.21 | − | 1245.55i | −1.68585 | − | 1.68090i | ||||
\(742\) | −369.977 | + | 1069.92i | −0.498621 | + | 1.44194i | ||||
\(743\) | −899.741 | + | 519.466i | −1.21096 | + | 0.699146i | −0.962968 | − | 0.269617i | \(-0.913103\pi\) |
−0.247989 | + | 0.968763i | \(0.579770\pi\) | |||||||
\(744\) | −147.291 | − | 546.486i | −0.197971 | − | 0.734524i | ||||
\(745\) | −15.5222 | −0.0208351 | ||||||||
\(746\) | −1374.80 | + | 793.740i | −1.84289 | + | 1.06399i | ||||
\(747\) | 246.664 | − | 430.146i | 0.330206 | − | 0.575831i | ||||
\(748\) | 1376.99 | 1.84090 | ||||||||
\(749\) | −616.432 | − | 213.162i | −0.823007 | − | 0.284596i | ||||
\(750\) | −31.2168 | + | 117.191i | −0.0416224 | + | 0.156254i | ||||
\(751\) | −1214.27 | −1.61688 | −0.808439 | − | 0.588580i | \(-0.799687\pi\) | ||||
−0.808439 | + | 0.588580i | \(0.799687\pi\) | |||||||
\(752\) | −1869.33 | − | 1079.26i | −2.48581 | − | 1.43518i | ||||
\(753\) | −432.206 | + | 433.477i | −0.573979 | + | 0.575667i | ||||
\(754\) | −1266.68 | − | 2193.96i | −1.67995 | − | 2.90975i | ||||
\(755\) | 301.142i | 0.398863i | ||||||||
\(756\) | −756.550 | − | 1539.07i | −1.00073 | − | 2.03581i | ||||
\(757\) | 586.216 | 0.774393 | 0.387197 | − | 0.921997i | \(-0.373443\pi\) | ||||
0.387197 | + | 0.921997i | \(0.373443\pi\) | |||||||
\(758\) | −1192.21 | + | 688.323i | −1.57284 | + | 0.908078i | ||||
\(759\) | −332.749 | − | 331.773i | −0.438404 | − | 0.437119i | ||||
\(760\) | 582.972 | − | 1009.74i | 0.767068 | − | 1.32860i | ||||
\(761\) | − | 710.225i | − | 0.933278i | −0.884448 | − | 0.466639i | \(-0.845465\pi\) | ||
0.884448 | − | 0.466639i | \(-0.154535\pi\) | |||||||
\(762\) | −2223.37 | − | 592.253i | −2.91781 | − | 0.777235i | ||||
\(763\) | −124.625 | − | 143.747i | −0.163336 | − | 0.188397i | ||||
\(764\) | − | 1838.45i | − | 2.40634i | ||||||
\(765\) | −248.602 | + | 144.506i | −0.324971 | + | 0.188896i | ||||
\(766\) | 219.029 | + | 379.369i | 0.285939 | + | 0.495260i | ||||
\(767\) | 960.710i | 1.25256i | ||||||||
\(768\) | −1285.86 | + | 346.569i | −1.67429 | + | 0.451261i | ||||
\(769\) | −65.6078 | − | 113.636i | −0.0853158 | − | 0.147771i | 0.820210 | − | 0.572063i | \(-0.193857\pi\) |
−0.905526 | + | 0.424291i | \(0.860523\pi\) | |||||||
\(770\) | 454.163 | − | 393.750i | 0.589823 | − | 0.511364i | ||||
\(771\) | 713.434 | − | 715.532i | 0.925336 | − | 0.928057i | ||||
\(772\) | 739.747 | + | 1281.28i | 0.958221 | + | 1.65969i | ||||
\(773\) | 724.418 | − | 418.243i | 0.937152 | − | 0.541065i | 0.0480856 | − | 0.998843i | \(-0.484688\pi\) |
0.889066 | + | 0.457778i | \(0.151355\pi\) | |||||||
\(774\) | 1532.72 | − | 4.50034i | 1.98025 | − | 0.00581439i | ||||
\(775\) | −25.7087 | + | 44.5287i | −0.0331725 | + | 0.0574564i | ||||
\(776\) | 404.802 | + | 233.712i | 0.521652 | + | 0.301176i | ||||
\(777\) | −134.064 | + | 65.4127i | −0.172541 | + | 0.0841862i | ||||
\(778\) | −250.343 | − | 433.607i | −0.321778 | − | 0.557336i | ||||
\(779\) | 114.330i | 0.146765i | ||||||||
\(780\) | −889.188 | + | 891.802i | −1.13998 | + | 1.14334i | ||||
\(781\) | −1424.10 | −1.82343 | ||||||||
\(782\) | 659.846 | + | 380.962i | 0.843793 | + | 0.487164i | ||||
\(783\) | 882.142 | − | 240.538i | 1.12662 | − | 0.307201i | ||||
\(784\) | −1157.54 | − | 909.285i | −1.47645 | − | 1.15980i | ||||
\(785\) | 117.062 | + | 67.5857i | 0.149123 | + | 0.0860964i | ||||
\(786\) | −611.262 | + | 2294.73i | −0.777687 | + | 2.91951i | ||||
\(787\) | 626.263 | − | 1084.72i | 0.795760 | − | 1.37830i | −0.126596 | − | 0.991954i | \(-0.540405\pi\) |
0.922356 | − | 0.386342i | \(-0.126262\pi\) | |||||||
\(788\) | 334.178 | + | 192.938i | 0.424084 | + | 0.244845i | ||||
\(789\) | 421.397 | − | 422.636i | 0.534090 | − | 0.535660i | ||||
\(790\) | 296.765 | − | 514.013i | 0.375652 | − | 0.650649i | ||||
\(791\) | 497.244 | − | 431.101i | 0.628627 | − | 0.545007i | ||||
\(792\) | 5.14897 | + | 1753.63i | 0.00650123 | + | 2.21417i | ||||
\(793\) | 89.9639 | − | 155.822i | 0.113447 | − | 0.196497i | ||||
\(794\) | 2608.02i | 3.28466i | ||||||||
\(795\) | −77.2311 | + | 289.932i | −0.0971460 | + | 0.364695i | ||||
\(796\) | 3244.53 | 4.07605 | ||||||||
\(797\) | −608.051 | + | 351.059i | −0.762925 | + | 0.440475i | −0.830345 | − | 0.557250i | \(-0.811857\pi\) |
0.0674200 | + | 0.997725i | \(0.478523\pi\) | |||||||
\(798\) | 1206.51 | − | 1789.32i | 1.51192 | − | 2.24226i | ||||
\(799\) | −513.344 | + | 889.138i | −0.642483 | + | 1.11281i | ||||
\(800\) | −152.569 | − | 88.0858i | −0.190711 | − | 0.110107i | ||||
\(801\) | 44.5260 | − | 77.6470i | 0.0555881 | − | 0.0969375i | ||||
\(802\) | 508.112 | + | 880.076i | 0.633556 | + | 1.09735i | ||||
\(803\) | −1250.98 | + | 722.251i | −1.55788 | + | 0.899441i | ||||
\(804\) | −174.916 | + | 656.652i | −0.217558 | + | 0.816731i | ||||
\(805\) | 226.654 | − | 43.7477i | 0.281558 | − | 0.0543450i | ||||
\(806\) | −666.223 | + | 384.644i | −0.826579 | + | 0.477226i | ||||
\(807\) | 94.2462 | + | 25.1050i | 0.116786 | + | 0.0311090i | ||||
\(808\) | −351.409 | −0.434913 | ||||||||
\(809\) | −479.399 | + | 276.781i | −0.592583 | + | 0.342128i | −0.766118 | − | 0.642700i | \(-0.777814\pi\) |
0.173535 | + | 0.984828i | \(0.444481\pi\) | |||||||
\(810\) | −330.773 | − | 565.225i | −0.408362 | − | 0.697808i | ||||
\(811\) | 603.549 | 0.744203 | 0.372102 | − | 0.928192i | \(-0.378637\pi\) | ||||
0.372102 | + | 0.928192i | \(0.378637\pi\) | |||||||
\(812\) | 1625.24 | − | 1409.05i | 2.00152 | − | 1.73528i | ||||
\(813\) | −642.865 | + | 173.267i | −0.790732 | + | 0.213121i | ||||
\(814\) | 272.784 | 0.335115 | ||||||||
\(815\) | 186.853 | + | 107.880i | 0.229268 | + | 0.132368i | ||||
\(816\) | −335.104 | − | 1243.32i | −0.410666 | − | 1.52368i | ||||
\(817\) | 669.322 | + | 1159.30i | 0.819244 | + | 1.41897i | ||||
\(818\) | − | 1401.09i | − | 1.71282i | ||||||
\(819\) | −982.322 | + | 856.718i | −1.19942 | + | 1.04605i | ||||
\(820\) | 81.6195 | 0.0995359 | ||||||||
\(821\) | −830.740 | + | 479.628i | −1.01186 | + | 0.584200i | −0.911737 | − | 0.410775i | \(-0.865258\pi\) |
−0.100127 | + | 0.994975i | \(0.531925\pi\) | |||||||
\(822\) | 270.482 | − | 1015.41i | 0.329054 | − | 1.23530i | ||||
\(823\) | 229.849 | − | 398.110i | 0.279282 | − | 0.483730i | −0.691925 | − | 0.721970i | \(-0.743237\pi\) |
0.971206 | + | 0.238239i | \(0.0765703\pi\) | |||||||
\(824\) | 3457.81i | 4.19637i | ||||||||
\(825\) | 112.483 | − | 112.814i | 0.136343 | − | 0.136744i | ||||
\(826\) | −1154.00 | + | 222.739i | −1.39709 | + | 0.269660i | ||||
\(827\) | − | 662.111i | − | 0.800618i | −0.916380 | − | 0.400309i | \(-0.868903\pi\) | ||
0.916380 | − | 0.400309i | \(-0.131097\pi\) | |||||||
\(828\) | −599.121 | + | 1044.78i | −0.723576 | + | 1.26181i | ||||
\(829\) | 403.713 | + | 699.252i | 0.486988 | + | 0.843488i | 0.999888 | − | 0.0149602i | \(-0.00476215\pi\) |
−0.512900 | + | 0.858448i | \(0.671429\pi\) | |||||||
\(830\) | − | 445.448i | − | 0.536684i | ||||||
\(831\) | 991.097 | + | 988.191i | 1.19266 | + | 1.18916i | ||||
\(832\) | −74.8834 | − | 129.702i | −0.0900040 | − | 0.155892i | ||||
\(833\) | −432.497 | + | 550.578i | −0.519204 | + | 0.660958i | ||||
\(834\) | 482.761 | + | 1791.17i | 0.578850 | + | 2.14768i | ||||
\(835\) | −159.662 | − | 276.543i | −0.191212 | − | 0.331189i | ||||
\(836\) | −2372.04 | + | 1369.50i | −2.83737 | + | 1.63816i | ||||
\(837\) | −73.0426 | − | 267.874i | −0.0872671 | − | 0.320040i | ||||
\(838\) | 1045.30 | − | 1810.51i | 1.24737 | − | 2.16051i | ||||
\(839\) | 421.663 | + | 243.447i | 0.502578 | + | 0.290163i | 0.729777 | − | 0.683685i | \(-0.239624\pi\) |
−0.227200 | + | 0.973848i | \(0.572957\pi\) | |||||||
\(840\) | −714.281 | − | 481.630i | −0.850334 | − | 0.573369i | ||||
\(841\) | 152.911 | + | 264.850i | 0.181821 | + | 0.314923i | ||||
\(842\) | 541.494i | 0.643105i | ||||||||
\(843\) | −106.879 | − | 396.547i | −0.126784 | − | 0.470400i | ||||
\(844\) | −2839.25 | −3.36404 | ||||||||
\(845\) | 501.644 | + | 289.624i | 0.593662 | + | 0.342751i | ||||
\(846\) | −2028.44 | − | 1163.19i | −2.39768 | − | 1.37493i | ||||
\(847\) | 56.3742 | − | 10.8811i | 0.0665576 | − | 0.0128466i | ||||
\(848\) | −1163.62 | − | 671.814i | −1.37219 | − | 0.792234i | ||||
\(849\) | 184.468 | − | 49.7185i | 0.217277 | − | 0.0585613i | ||||
\(850\) | −129.160 | + | 223.712i | −0.151953 | + | 0.263191i | ||||
\(851\) | 90.7233 | + | 52.3791i | 0.106608 | + | 0.0615501i | ||||
\(852\) | 949.893 | + | 3524.34i | 1.11490 | + | 4.13655i | ||||
\(853\) | −104.121 | + | 180.343i | −0.122064 | + | 0.211422i | −0.920582 | − | 0.390550i | \(-0.872285\pi\) |
0.798517 | + | 0.601972i | \(0.205618\pi\) | |||||||
\(854\) | 208.030 | + | 71.9367i | 0.243595 | + | 0.0842350i | ||||
\(855\) | 284.530 | − | 496.180i | 0.332784 | − | 0.580327i | ||||
\(856\) | 854.732 | − | 1480.44i | 0.998519 | − | 1.72949i | ||||
\(857\) | − | 127.117i | − | 0.148328i | −0.997246 | − | 0.0741638i | \(-0.976371\pi\) | ||
0.997246 | − | 0.0741638i | \(-0.0236288\pi\) | |||||||
\(858\) | 2301.41 | − | 620.282i | 2.68229 | − | 0.722940i | ||||
\(859\) | −1123.84 | −1.30831 | −0.654156 | − | 0.756360i | \(-0.726976\pi\) | ||||
−0.654156 | + | 0.756360i | \(0.726976\pi\) | |||||||
\(860\) | 827.615 | − | 477.824i | 0.962343 | − | 0.555609i | ||||
\(861\) | 84.2712 | + | 5.87990i | 0.0978759 | + | 0.00682916i | ||||
\(862\) | −196.685 | + | 340.668i | −0.228172 | + | 0.395206i | ||||
\(863\) | −1001.84 | − | 578.412i | −1.16088 | − | 0.670235i | −0.209366 | − | 0.977837i | \(-0.567140\pi\) |
−0.951515 | + | 0.307603i | \(0.900473\pi\) | |||||||
\(864\) | 917.817 | − | 250.266i | 1.06229 | − | 0.289660i | ||||
\(865\) | −270.174 | − | 467.955i | −0.312340 | − | 0.540988i | ||||
\(866\) | 338.670 | − | 195.531i | 0.391074 | − | 0.225787i | ||||
\(867\) | 245.749 | − | 66.2350i | 0.283447 | − | 0.0763956i | ||||
\(868\) | −427.875 | − | 493.524i | −0.492944 | − | 0.568576i | ||||
\(869\) | −675.206 | + | 389.830i | −0.776992 | + | 0.448597i | ||||
\(870\) | 579.967 | − | 581.673i | 0.666629 | − | 0.668589i | ||||
\(871\) | 516.477 | 0.592971 | ||||||||
\(872\) | 431.817 | − | 249.310i | 0.495203 | − | 0.285906i | ||||
\(873\) | 198.918 | + | 114.068i | 0.227855 | + | 0.130662i | ||||
\(874\) | −1515.56 | −1.73405 | ||||||||
\(875\) | 14.8321 | + | 76.8441i | 0.0169509 | + | 0.0878218i | ||||
\(876\) | 2621.83 | + | 2614.15i | 2.99296 | + | 2.98419i | ||||
\(877\) | 1045.13 | 1.19171 | 0.595855 | − | 0.803092i | \(-0.296813\pi\) | ||||
0.595855 | + | 0.803092i | \(0.296813\pi\) | |||||||
\(878\) | −1465.61 | − | 846.169i | −1.66926 | − | 0.963746i | ||||
\(879\) | −477.078 | − | 127.082i | −0.542751 | − | 0.144576i | ||||
\(880\) | 356.705 | + | 617.830i | 0.405346 | + | 0.702080i | ||||
\(881\) | − | 444.324i | − | 0.504341i | −0.967683 | − | 0.252170i | \(-0.918856\pi\) | ||
0.967683 | − | 0.252170i | \(-0.0811443\pi\) | |||||||
\(882\) | −1256.83 | − | 981.327i | −1.42498 | − | 1.11262i | ||||
\(883\) | −1387.57 | −1.57142 | −0.785712 | − | 0.618592i | \(-0.787703\pi\) | ||||
−0.785712 | + | 0.618592i | \(0.787703\pi\) | |||||||
\(884\) | −2323.04 | + | 1341.21i | −2.62788 | + | 1.51721i | ||||
\(885\) | −300.763 | + | 81.0627i | −0.339846 | + | 0.0915963i | ||||
\(886\) | −783.730 | + | 1357.46i | −0.884572 | + | 1.53212i | ||||
\(887\) | − | 482.327i | − | 0.543774i | −0.962329 | − | 0.271887i | \(-0.912352\pi\) | ||
0.962329 | − | 0.271887i | \(-0.0876476\pi\) | |||||||
\(888\) | −101.742 | − | 377.489i | −0.114574 | − | 0.425100i | ||||
\(889\) | −1457.90 | + | 281.398i | −1.63994 | + | 0.316533i | ||||
\(890\) | − | 80.4091i | − | 0.0903473i | ||||||
\(891\) | 5.05179 | + | 860.257i | 0.00566980 | + | 0.965496i | ||||
\(892\) | 207.136 | + | 358.771i | 0.232216 | + | 0.402210i | ||||
\(893\) | − | 2042.21i | − | 2.28690i | ||||||
\(894\) | 19.3821 | − | 72.7622i | 0.0216802 | − | 0.0813895i | ||||
\(895\) | 68.0371 | + | 117.844i | 0.0760191 | + | 0.131669i | ||||
\(896\) | −606.983 | + | 526.242i | −0.677436 | + | 0.587323i | ||||
\(897\) | 884.515 | + | 235.614i | 0.986081 | + | 0.262669i | ||||
\(898\) | −210.038 | − | 363.796i | −0.233895 | − | 0.405118i | ||||
\(899\) | 301.591 | − | 174.124i | 0.335474 | − | 0.193686i | ||||
\(900\) | −354.219 | − | 203.124i | −0.393576 | − | 0.225693i | ||||
\(901\) | −319.545 | + | 553.468i | −0.354656 | + | 0.614282i | ||||
\(902\) | −133.782 | − | 77.2392i | −0.148317 | − | 0.0856310i | ||||
\(903\) | 888.926 | − | 433.726i | 0.984414 | − | 0.480317i | ||||
\(904\) | 862.405 | + | 1493.73i | 0.953988 | + | 1.65236i | ||||
\(905\) | − | 615.468i | − | 0.680075i | ||||||
\(906\) | −1411.64 | − | 376.027i | −1.55810 | − | 0.415041i | ||||
\(907\) | 1752.27 | 1.93194 | 0.965968 | − | 0.258660i | \(-0.0832808\pi\) | ||||
0.965968 | + | 0.258660i | \(0.0832808\pi\) | |||||||
\(908\) | −474.351 | − | 273.867i | −0.522413 | − | 0.301615i | ||||
\(909\) | −172.389 | + | 0.506165i | −0.189646 | + | 0.000556837i | ||||
\(910\) | −382.675 | + | 1106.64i | −0.420522 | + | 1.21608i | ||||
\(911\) | −393.060 | − | 226.934i | −0.431460 | − | 0.249104i | 0.268508 | − | 0.963277i | \(-0.413469\pi\) |
−0.699969 | + | 0.714174i | \(0.746803\pi\) | |||||||
\(912\) | 1813.82 | + | 1808.50i | 1.98883 | + | 1.98300i | ||||
\(913\) | −292.570 | + | 506.746i | −0.320449 | + | 0.555034i | ||||
\(914\) | −936.723 | − | 540.817i | −1.02486 | − | 0.591704i | ||||
\(915\) | 56.3731 | + | 15.0165i | 0.0616100 | + | 0.0164114i | ||||
\(916\) | −1115.56 | + | 1932.21i | −1.21786 | + | 2.10940i | ||||
\(917\) | 290.430 | + | 1504.70i | 0.316717 | + | 1.64089i | ||||
\(918\) | −366.965 | − | 1345.80i | −0.399744 | − | 1.46601i | ||||
\(919\) | 136.575 | − | 236.554i | 0.148612 | − | 0.257404i | −0.782102 | − | 0.623150i | \(-0.785853\pi\) |
0.930715 | + | 0.365746i | \(0.119186\pi\) | |||||||
\(920\) | 604.998i | 0.657607i | ||||||||
\(921\) | −305.365 | − | 304.470i | −0.331558 | − | 0.330586i | ||||
\(922\) | 88.2017 | 0.0956634 | ||||||||
\(923\) | 2402.52 | − | 1387.10i | 2.60295 | − | 1.50281i | ||||
\(924\) | 887.446 | + | 1818.83i | 0.960440 | + | 1.96843i | ||||
\(925\) | −17.7584 | + | 30.7585i | −0.0191983 | + | 0.0332525i | ||||
\(926\) | 0.877295 | + | 0.506506i | 0.000947403 | + | 0.000546983i | ||||
\(927\) | 4.98058 | + | 1696.28i | 0.00537280 | + | 1.82986i | ||||
\(928\) | 596.601 | + | 1033.34i | 0.642889 | + | 1.11352i | ||||
\(929\) | −127.864 | + | 73.8225i | −0.137636 | + | 0.0794644i | −0.567237 | − | 0.823555i | \(-0.691988\pi\) |
0.429601 | + | 0.903019i | \(0.358654\pi\) | |||||||
\(930\) | −176.632 | − | 176.115i | −0.189927 | − | 0.189371i | ||||
\(931\) | 197.448 | − | 1378.59i | 0.212082 | − | 1.48076i | ||||
\(932\) | −1861.04 | + | 1074.47i | −1.99683 | + | 1.15287i | ||||
\(933\) | −355.815 | − | 1320.17i | −0.381367 | − | 1.41497i | ||||
\(934\) | 2315.69 | 2.47933 | ||||||||
\(935\) | 293.868 | − | 169.665i | 0.314297 | − | 0.181460i | ||||
\(936\) | −1716.74 | − | 2953.43i | −1.83413 | − | 3.15537i | ||||
\(937\) | 1035.23 | 1.10483 | 0.552415 | − | 0.833569i | \(-0.313706\pi\) | ||||
0.552415 | + | 0.833569i | \(0.313706\pi\) | |||||||
\(938\) | 119.744 | + | 620.388i | 0.127659 | + | 0.661394i | ||||
\(939\) | −3.13454 | + | 11.7674i | −0.00333817 | + | 0.0125318i | ||||
\(940\) | −1457.91 | −1.55097 | ||||||||
\(941\) | −869.438 | − | 501.970i | −0.923951 | − | 0.533443i | −0.0390575 | − | 0.999237i | \(-0.512436\pi\) |
−0.884893 | + | 0.465794i | \(0.845769\pi\) | |||||||
\(942\) | −462.989 | + | 464.350i | −0.491495 | + | 0.492940i | ||||
\(943\) | −29.6625 | − | 51.3769i | −0.0314554 | − | 0.0544824i | ||||
\(944\) | − | 1394.92i | − | 1.47767i | ||||||
\(945\) | −351.093 | − | 235.241i | −0.371528 | − | 0.248932i | ||||
\(946\) | −1808.72 | −1.91197 | ||||||||
\(947\) | 179.487 | − | 103.627i | 0.189532 | − | 0.109426i | −0.402232 | − | 0.915538i | \(-0.631765\pi\) |
0.591763 | + | 0.806112i | \(0.298432\pi\) | |||||||
\(948\) | 1415.12 | + | 1410.97i | 1.49274 | + | 1.48836i | ||||
\(949\) | 1406.97 | − | 2436.94i | 1.48258 | − | 2.56790i | ||||
\(950\) | − | 513.830i | − | 0.540874i | ||||||
\(951\) | 1219.29 | + | 324.790i | 1.28211 | + | 0.341525i | ||||
\(952\) | −1202.03 | − | 1386.45i | −1.26263 | − | 1.45636i | ||||
\(953\) | 419.973i | 0.440685i | 0.975423 | + | 0.220342i | \(0.0707175\pi\) | ||||
−0.975423 | + | 0.220342i | \(0.929283\pi\) | |||||||
\(954\) | −1262.66 | − | 724.061i | −1.32354 | − | 0.758974i | ||||
\(955\) | −226.522 | − | 392.348i | −0.237196 | − | 0.410836i | ||||
\(956\) | − | 2450.90i | − | 2.56370i | ||||||
\(957\) | −1041.82 | + | 280.795i | −1.08863 | + | 0.293411i | ||||
\(958\) | 1182.47 | + | 2048.10i | 1.23431 | + | 2.13789i | ||||
\(959\) | −128.515 | − | 665.826i | −0.134009 | − | 0.694291i | ||||
\(960\) | 34.2864 | − | 34.3872i | 0.0357150 | − | 0.0358200i | ||||
\(961\) | 427.625 | + | 740.668i | 0.444979 | + | 0.770727i | ||||
\(962\) | −460.198 | + | 265.695i | −0.478376 | + | 0.276191i | ||||
\(963\) | 417.168 | − | 727.480i | 0.433196 | − | 0.755431i | ||||
\(964\) | −527.868 | + | 914.295i | −0.547581 | + | 0.948438i | ||||
\(965\) | 315.743 | + | 182.295i | 0.327195 | + | 0.188906i | ||||
\(966\) | −77.9439 | + | 1117.10i | −0.0806873 | + | 1.15641i | ||||
\(967\) | −621.933 | − | 1077.22i | −0.643157 | − | 1.11398i | −0.984724 | − | 0.174123i | \(-0.944291\pi\) |
0.341567 | − | 0.939857i | \(-0.389042\pi\) | |||||||
\(968\) | 150.477i | 0.155452i | ||||||||
\(969\) | 860.202 | − | 862.732i | 0.887722 | − | 0.890332i | ||||
\(970\) | 205.994 | 0.212365 | ||||||||
\(971\) | −340.282 | − | 196.462i | −0.350445 | − | 0.202330i | 0.314436 | − | 0.949279i | \(-0.398185\pi\) |
−0.664881 | + | 0.746949i | \(0.731518\pi\) | |||||||
\(972\) | 2125.58 | − | 586.304i | 2.18681 | − | 0.603194i | ||||
\(973\) | 784.191 | + | 904.510i | 0.805952 | + | 0.929609i | ||||
\(974\) | 1766.67 | + | 1019.99i | 1.81383 | + | 1.04722i | ||||
\(975\) | −79.8817 | + | 299.883i | −0.0819299 | + | 0.307572i | ||||
\(976\) | −130.625 | + | 226.248i | −0.133837 | + | 0.231812i | ||||
\(977\) | 338.231 | + | 195.278i | 0.346193 | + | 0.199875i | 0.663007 | − | 0.748613i | \(-0.269280\pi\) |
−0.316814 | + | 0.948488i | \(0.602613\pi\) | |||||||
\(978\) | −739.019 | + | 741.192i | −0.755643 | + | 0.757865i | ||||
\(979\) | −52.8127 | + | 91.4742i | −0.0539455 | + | 0.0934364i | ||||
\(980\) | −984.161 | − | 140.957i | −1.00425 | − | 0.143833i | ||||
\(981\) | 211.474 | − | 122.924i | 0.215570 | − | 0.125305i | ||||
\(982\) | −145.336 | + | 251.730i | −0.148000 | + | 0.256344i | ||||
\(983\) | − | 1501.14i | − | 1.52710i | −0.645747 | − | 0.763552i | \(-0.723454\pi\) | ||
0.645747 | − | 0.763552i | \(-0.276546\pi\) | |||||||
\(984\) | −56.9890 | + | 213.942i | −0.0579156 | + | 0.217420i | ||||
\(985\) | 95.0906 | 0.0965386 | ||||||||
\(986\) | 1515.19 | − | 874.796i | 1.53671 | − | 0.887217i | ||||
\(987\) | −1505.28 | − | 105.029i | −1.52511 | − | 0.106412i | ||||
\(988\) | 2667.83 | − | 4620.81i | 2.70023 | − | 4.67694i | ||||
\(989\) | −601.551 | − | 347.306i | −0.608242 | − | 0.351168i | ||||
\(990\) | 388.376 | + | 668.148i | 0.392299 | + | 0.674897i | ||||
\(991\) | −315.675 | − | 546.764i | −0.318542 | − | 0.551730i | 0.661642 | − | 0.749819i | \(-0.269860\pi\) |
−0.980184 | + | 0.198089i | \(0.936526\pi\) | |||||||
\(992\) | 313.788 | − | 181.166i | 0.316318 | − | 0.182627i | ||||
\(993\) | 11.4048 | − | 42.8144i | 0.0114851 | − | 0.0431163i | ||||
\(994\) | 2223.19 | + | 2564.29i | 2.23661 | + | 2.57977i | ||||
\(995\) | 692.426 | − | 399.772i | 0.695905 | − | 0.401781i | ||||
\(996\) | 1449.24 | + | 386.042i | 1.45506 | + | 0.387592i | ||||
\(997\) | 1188.97 | 1.19255 | 0.596276 | − | 0.802780i | \(-0.296647\pi\) | ||||
0.596276 | + | 0.802780i | \(0.296647\pi\) | |||||||
\(998\) | 745.752 | − | 430.560i | 0.747246 | − | 0.431423i | ||||
\(999\) | −50.4547 | − | 185.036i | −0.0505052 | − | 0.185221i |
(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 | 315.3.bd.a.191.4 | yes | 128 | |
7.4 | even | 3 | 315.3.s.a.11.4 | ✓ | 128 | ||
9.5 | odd | 6 | 315.3.s.a.86.61 | yes | 128 | ||
63.32 | odd | 6 | inner | 315.3.bd.a.221.4 | yes | 128 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
315.3.s.a.11.4 | ✓ | 128 | 7.4 | even | 3 | ||
315.3.s.a.86.61 | yes | 128 | 9.5 | odd | 6 | ||
315.3.bd.a.191.4 | yes | 128 | 1.1 | even | 1 | trivial | |
315.3.bd.a.221.4 | yes | 128 | 63.32 | odd | 6 | inner |