Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [60,4,Mod(11,60)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(60, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("60.11");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 60 = 2^{2} \cdot 3 \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 60.e (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(3.54011460034\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 11.8 | ||
Character | \(\chi\) | \(=\) | 60.11 |
Dual form | 60.4.e.a.11.7 |
$q$-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 \(\left(\mathbb{Z}/60\mathbb{Z}\right)^\times\).
\(n\) | \(31\) | \(37\) | \(41\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.91554 | + | 2.08103i | −0.677247 | + | 0.735755i | ||||
\(3\) | −2.09257 | − | 4.75617i | −0.402716 | − | 0.915325i | ||||
\(4\) | −0.661378 | − | 7.97261i | −0.0826723 | − | 0.996577i | ||||
\(5\) | 5.00000i | 0.447214i | ||||||||
\(6\) | 13.9062 | + | 4.75594i | 0.946194 | + | 0.323601i | ||||
\(7\) | 32.2690i | 1.74236i | 0.490964 | + | 0.871180i | \(0.336645\pi\) | ||||
−0.490964 | + | 0.871180i | \(0.663355\pi\) | |||||||
\(8\) | 17.8582 | + | 13.8955i | 0.789226 | + | 0.614102i | ||||
\(9\) | −18.2423 | + | 19.9053i | −0.675639 | + | 0.737232i | ||||
\(10\) | −10.4052 | − | 9.57772i | −0.329040 | − | 0.302874i | ||||
\(11\) | −32.4750 | −0.890144 | −0.445072 | − | 0.895495i | \(-0.646822\pi\) | ||||
−0.445072 | + | 0.895495i | \(0.646822\pi\) | |||||||
\(12\) | −36.5351 | + | 19.8289i | −0.878898 | + | 0.477010i | ||||
\(13\) | 44.9257 | 0.958473 | 0.479237 | − | 0.877686i | \(-0.340914\pi\) | ||||
0.479237 | + | 0.877686i | \(0.340914\pi\) | |||||||
\(14\) | −67.1527 | − | 61.8126i | −1.28195 | − | 1.18001i | ||||
\(15\) | 23.7808 | − | 10.4629i | 0.409346 | − | 0.180100i | ||||
\(16\) | −63.1252 | + | 10.5458i | −0.986331 | + | 0.164779i | ||||
\(17\) | 79.2204i | 1.13022i | 0.825015 | + | 0.565111i | \(0.191167\pi\) | ||||
−0.825015 | + | 0.565111i | \(0.808833\pi\) | |||||||
\(18\) | −6.47961 | − | 76.0921i | −0.0848478 | − | 0.996394i | ||||
\(19\) | 69.0323i | 0.833531i | 0.909014 | + | 0.416765i | \(0.136836\pi\) | ||||
−0.909014 | + | 0.416765i | \(0.863164\pi\) | |||||||
\(20\) | 39.8631 | − | 3.30689i | 0.445683 | − | 0.0369722i | ||||
\(21\) | 153.477 | − | 67.5252i | 1.59483 | − | 0.701676i | ||||
\(22\) | 62.2073 | − | 67.5815i | 0.602847 | − | 0.654928i | ||||
\(23\) | −72.8705 | −0.660632 | −0.330316 | − | 0.943870i | \(-0.607155\pi\) | ||||
−0.330316 | + | 0.943870i | \(0.607155\pi\) | |||||||
\(24\) | 28.7200 | − | 114.014i | 0.244269 | − | 0.969708i | ||||
\(25\) | −25.0000 | −0.200000 | ||||||||
\(26\) | −86.0572 | + | 93.4918i | −0.649123 | + | 0.705202i | ||||
\(27\) | 132.846 | + | 45.1100i | 0.946898 | + | 0.321534i | ||||
\(28\) | 257.268 | − | 21.3420i | 1.73640 | − | 0.144045i | ||||
\(29\) | − | 219.925i | − | 1.40824i | −0.710079 | − | 0.704122i | \(-0.751341\pi\) | ||
0.710079 | − | 0.704122i | \(-0.248659\pi\) | |||||||
\(30\) | −23.7797 | + | 69.5308i | −0.144719 | + | 0.423151i | ||||
\(31\) | 28.4726i | 0.164962i | 0.996593 | + | 0.0824812i | \(0.0262844\pi\) | ||||
−0.996593 | + | 0.0824812i | \(0.973716\pi\) | |||||||
\(32\) | 98.9729 | − | 151.566i | 0.546753 | − | 0.837294i | ||||
\(33\) | 67.9564 | + | 154.457i | 0.358475 | + | 0.814771i | ||||
\(34\) | −164.860 | − | 151.750i | −0.831566 | − | 0.765439i | ||||
\(35\) | −161.345 | −0.779207 | ||||||||
\(36\) | 170.762 | + | 132.274i | 0.790565 | + | 0.612378i | ||||
\(37\) | −152.826 | −0.679039 | −0.339520 | − | 0.940599i | \(-0.610265\pi\) | ||||
−0.339520 | + | 0.940599i | \(0.610265\pi\) | |||||||
\(38\) | −143.658 | − | 132.234i | −0.613275 | − | 0.564506i | ||||
\(39\) | −94.0104 | − | 213.674i | −0.385993 | − | 0.877314i | ||||
\(40\) | −69.4777 | + | 89.2908i | −0.274635 | + | 0.352953i | ||||
\(41\) | − | 104.817i | − | 0.399259i | −0.979871 | − | 0.199629i | \(-0.936026\pi\) | ||
0.979871 | − | 0.199629i | \(-0.0639738\pi\) | |||||||
\(42\) | −153.469 | + | 448.737i | −0.563829 | + | 1.64861i | ||||
\(43\) | 96.6054i | 0.342609i | 0.985218 | + | 0.171305i | \(0.0547982\pi\) | ||||
−0.985218 | + | 0.171305i | \(0.945202\pi\) | |||||||
\(44\) | 21.4783 | + | 258.911i | 0.0735902 | + | 0.887097i | ||||
\(45\) | −99.5264 | − | 91.2113i | −0.329700 | − | 0.302155i | ||||
\(46\) | 139.587 | − | 151.646i | 0.447411 | − | 0.486064i | ||||
\(47\) | 103.880 | 0.322391 | 0.161196 | − | 0.986922i | \(-0.448465\pi\) | ||||
0.161196 | + | 0.986922i | \(0.448465\pi\) | |||||||
\(48\) | 182.252 | + | 278.166i | 0.548037 | + | 0.836454i | ||||
\(49\) | −698.285 | −2.03582 | ||||||||
\(50\) | 47.8886 | − | 52.0258i | 0.135449 | − | 0.147151i | ||||
\(51\) | 376.785 | − | 165.775i | 1.03452 | − | 0.455158i | ||||
\(52\) | −29.7129 | − | 358.175i | −0.0792391 | − | 0.955192i | ||||
\(53\) | 544.398i | 1.41092i | 0.708750 | + | 0.705460i | \(0.249260\pi\) | ||||
−0.708750 | + | 0.705460i | \(0.750740\pi\) | |||||||
\(54\) | −348.348 | + | 190.047i | −0.877855 | + | 0.478927i | ||||
\(55\) | − | 162.375i | − | 0.398084i | ||||||
\(56\) | −448.395 | + | 576.264i | −1.06999 | + | 1.37512i | ||||
\(57\) | 328.329 | − | 144.455i | 0.762952 | − | 0.335676i | ||||
\(58\) | 457.671 | + | 421.276i | 1.03612 | + | 0.953729i | ||||
\(59\) | 431.052 | 0.951156 | 0.475578 | − | 0.879674i | \(-0.342239\pi\) | ||||
0.475578 | + | 0.879674i | \(0.342239\pi\) | |||||||
\(60\) | −99.1446 | − | 182.676i | −0.213325 | − | 0.393055i | ||||
\(61\) | 183.375 | 0.384898 | 0.192449 | − | 0.981307i | \(-0.438357\pi\) | ||||
0.192449 | + | 0.981307i | \(0.438357\pi\) | |||||||
\(62\) | −59.2524 | − | 54.5406i | −0.121372 | − | 0.111720i | ||||
\(63\) | −642.322 | − | 588.659i | −1.28452 | − | 1.17721i | ||||
\(64\) | 125.827 | + | 496.298i | 0.245757 | + | 0.969332i | ||||
\(65\) | 224.629i | 0.428642i | ||||||||
\(66\) | −451.602 | − | 154.449i | −0.842248 | − | 0.288051i | ||||
\(67\) | − | 290.222i | − | 0.529198i | −0.964359 | − | 0.264599i | \(-0.914760\pi\) | ||
0.964359 | − | 0.264599i | \(-0.0852395\pi\) | |||||||
\(68\) | 631.593 | − | 52.3946i | 1.12635 | − | 0.0934379i | ||||
\(69\) | 152.487 | + | 346.584i | 0.266047 | + | 0.604693i | ||||
\(70\) | 309.063 | − | 335.763i | 0.527716 | − | 0.573306i | ||||
\(71\) | 489.128 | 0.817589 | 0.408794 | − | 0.912627i | \(-0.365949\pi\) | ||||
0.408794 | + | 0.912627i | \(0.365949\pi\) | |||||||
\(72\) | −602.368 | + | 101.985i | −0.985969 | + | 0.166931i | ||||
\(73\) | −292.966 | −0.469713 | −0.234856 | − | 0.972030i | \(-0.575462\pi\) | ||||
−0.234856 | + | 0.972030i | \(0.575462\pi\) | |||||||
\(74\) | 292.745 | − | 318.036i | 0.459878 | − | 0.499607i | ||||
\(75\) | 52.3144 | + | 118.904i | 0.0805432 | + | 0.183065i | ||||
\(76\) | 550.368 | − | 45.6564i | 0.830677 | − | 0.0689099i | ||||
\(77\) | − | 1047.93i | − | 1.55095i | ||||||
\(78\) | 624.744 | + | 213.664i | 0.906901 | + | 0.310163i | ||||
\(79\) | 656.389i | 0.934805i | 0.884045 | + | 0.467402i | \(0.154810\pi\) | ||||
−0.884045 | + | 0.467402i | \(0.845190\pi\) | |||||||
\(80\) | −52.7291 | − | 315.626i | −0.0736912 | − | 0.441100i | ||||
\(81\) | −63.4397 | − | 726.234i | −0.0870228 | − | 0.996206i | ||||
\(82\) | 218.127 | + | 200.781i | 0.293757 | + | 0.270397i | ||||
\(83\) | −392.339 | −0.518853 | −0.259426 | − | 0.965763i | \(-0.583533\pi\) | ||||
−0.259426 | + | 0.965763i | \(0.583533\pi\) | |||||||
\(84\) | −639.858 | − | 1178.95i | −0.831122 | − | 1.53136i | ||||
\(85\) | −396.102 | −0.505450 | ||||||||
\(86\) | −201.039 | − | 185.052i | −0.252076 | − | 0.232031i | ||||
\(87\) | −1046.00 | + | 460.210i | −1.28900 | + | 0.567122i | ||||
\(88\) | −579.944 | − | 451.258i | −0.702525 | − | 0.546639i | ||||
\(89\) | − | 336.343i | − | 0.400588i | −0.979736 | − | 0.200294i | \(-0.935810\pi\) | ||
0.979736 | − | 0.200294i | \(-0.0641897\pi\) | |||||||
\(90\) | 380.461 | − | 32.3981i | 0.445601 | − | 0.0379451i | ||||
\(91\) | 1449.71i | 1.67000i | ||||||||
\(92\) | 48.1949 | + | 580.968i | 0.0546160 | + | 0.658371i | ||||
\(93\) | 135.421 | − | 59.5811i | 0.150994 | − | 0.0664330i | ||||
\(94\) | −198.986 | + | 216.177i | −0.218339 | + | 0.237201i | ||||
\(95\) | −345.161 | −0.372766 | ||||||||
\(96\) | −927.983 | − | 153.568i | −0.986582 | − | 0.163265i | ||||
\(97\) | 1039.74 | 1.08834 | 0.544171 | − | 0.838974i | \(-0.316844\pi\) | ||||
0.544171 | + | 0.838974i | \(0.316844\pi\) | |||||||
\(98\) | 1337.60 | − | 1453.15i | 1.37875 | − | 1.49786i | ||||
\(99\) | 592.417 | − | 646.424i | 0.601416 | − | 0.656243i | ||||
\(100\) | 16.5345 | + | 199.315i | 0.0165345 | + | 0.199315i | ||||
\(101\) | 308.323i | 0.303755i | 0.988399 | + | 0.151877i | \(0.0485319\pi\) | ||||
−0.988399 | + | 0.151877i | \(0.951468\pi\) | |||||||
\(102\) | −376.767 | + | 1101.65i | −0.365740 | + | 1.06941i | ||||
\(103\) | − | 264.352i | − | 0.252887i | −0.991974 | − | 0.126443i | \(-0.959644\pi\) | ||
0.991974 | − | 0.126443i | \(-0.0403562\pi\) | |||||||
\(104\) | 802.290 | + | 624.267i | 0.756452 | + | 0.588601i | ||||
\(105\) | 337.626 | + | 767.383i | 0.313799 | + | 0.713228i | ||||
\(106\) | −1132.91 | − | 1042.82i | −1.03809 | − | 0.955542i | ||||
\(107\) | 1561.77 | 1.41104 | 0.705522 | − | 0.708688i | \(-0.250713\pi\) | ||||
0.705522 | + | 0.708688i | \(0.250713\pi\) | |||||||
\(108\) | 271.783 | − | 1088.97i | 0.242151 | − | 0.970238i | ||||
\(109\) | 2178.35 | 1.91420 | 0.957100 | − | 0.289757i | \(-0.0935744\pi\) | ||||
0.957100 | + | 0.289757i | \(0.0935744\pi\) | |||||||
\(110\) | 337.907 | + | 311.037i | 0.292893 | + | 0.269602i | ||||
\(111\) | 319.800 | + | 726.867i | 0.273460 | + | 0.621542i | ||||
\(112\) | −340.303 | − | 2036.98i | −0.287103 | − | 1.71854i | ||||
\(113\) | 1715.85i | 1.42844i | 0.699920 | + | 0.714221i | \(0.253219\pi\) | ||||
−0.699920 | + | 0.714221i | \(0.746781\pi\) | |||||||
\(114\) | −328.313 | + | 959.973i | −0.269731 | + | 0.788682i | ||||
\(115\) | − | 364.352i | − | 0.295444i | ||||||
\(116\) | −1753.38 | + | 145.454i | −1.40342 | + | 0.116423i | ||||
\(117\) | −819.547 | + | 894.258i | −0.647582 | + | 0.706617i | ||||
\(118\) | −825.699 | + | 897.033i | −0.644168 | + | 0.699818i | ||||
\(119\) | −2556.36 | −1.96925 | ||||||||
\(120\) | 570.069 | + | 143.600i | 0.433666 | + | 0.109240i | ||||
\(121\) | −276.374 | −0.207644 | ||||||||
\(122\) | −351.263 | + | 381.610i | −0.260671 | + | 0.283191i | ||||
\(123\) | −498.525 | + | 219.337i | −0.365451 | + | 0.160788i | ||||
\(124\) | 227.001 | − | 18.8312i | 0.164398 | − | 0.0136378i | ||||
\(125\) | − | 125.000i | − | 0.0894427i | ||||||
\(126\) | 2455.41 | − | 209.090i | 1.73608 | − | 0.147835i | ||||
\(127\) | − | 1396.37i | − | 0.975652i | −0.872941 | − | 0.487826i | \(-0.837790\pi\) | ||
0.872941 | − | 0.487826i | \(-0.162210\pi\) | |||||||
\(128\) | −1273.84 | − | 688.830i | −0.879629 | − | 0.475660i | ||||
\(129\) | 459.472 | − | 202.154i | 0.313599 | − | 0.137974i | ||||
\(130\) | −467.459 | − | 430.286i | −0.315376 | − | 0.290297i | ||||
\(131\) | 1510.54 | 1.00745 | 0.503727 | − | 0.863863i | \(-0.331962\pi\) | ||||
0.503727 | + | 0.863863i | \(0.331962\pi\) | |||||||
\(132\) | 1186.48 | − | 643.944i | 0.782346 | − | 0.424607i | ||||
\(133\) | −2227.60 | −1.45231 | ||||||||
\(134\) | 603.961 | + | 555.933i | 0.389360 | + | 0.358398i | ||||
\(135\) | −225.550 | + | 664.231i | −0.143794 | + | 0.423466i | ||||
\(136\) | −1100.81 | + | 1414.73i | −0.694071 | + | 0.892000i | ||||
\(137\) | 541.789i | 0.337870i | 0.985627 | + | 0.168935i | \(0.0540327\pi\) | ||||
−0.985627 | + | 0.168935i | \(0.945967\pi\) | |||||||
\(138\) | −1013.35 | − | 346.567i | −0.625086 | − | 0.213781i | ||||
\(139\) | 713.800i | 0.435566i | 0.975997 | + | 0.217783i | \(0.0698825\pi\) | ||||
−0.975997 | + | 0.217783i | \(0.930117\pi\) | |||||||
\(140\) | 106.710 | + | 1286.34i | 0.0644188 | + | 0.776540i | ||||
\(141\) | −217.376 | − | 494.069i | −0.129832 | − | 0.295093i | ||||
\(142\) | −936.946 | + | 1017.89i | −0.553710 | + | 0.601545i | ||||
\(143\) | −1458.96 | −0.853179 | ||||||||
\(144\) | 941.628 | − | 1448.90i | 0.544924 | − | 0.838486i | ||||
\(145\) | 1099.63 | 0.629786 | ||||||||
\(146\) | 561.189 | − | 609.671i | 0.318112 | − | 0.345594i | ||||
\(147\) | 1461.21 | + | 3321.16i | 0.819857 | + | 1.86343i | ||||
\(148\) | 101.076 | + | 1218.42i | 0.0561377 | + | 0.676715i | ||||
\(149\) | − | 109.018i | − | 0.0599405i | −0.999551 | − | 0.0299702i | \(-0.990459\pi\) | ||
0.999551 | − | 0.0299702i | \(-0.00954126\pi\) | |||||||
\(150\) | −347.654 | − | 118.898i | −0.189239 | − | 0.0647201i | ||||
\(151\) | − | 3186.38i | − | 1.71725i | −0.512607 | − | 0.858623i | \(-0.671320\pi\) | ||
0.512607 | − | 0.858623i | \(-0.328680\pi\) | |||||||
\(152\) | −959.241 | + | 1232.79i | −0.511873 | + | 0.657845i | ||||
\(153\) | −1576.90 | − | 1445.16i | −0.833236 | − | 0.763622i | ||||
\(154\) | 2180.78 | + | 2007.36i | 1.14112 | + | 1.05038i | ||||
\(155\) | −142.363 | −0.0737734 | ||||||||
\(156\) | −1641.37 | + | 890.828i | −0.842400 | + | 0.457201i | ||||
\(157\) | −1029.37 | −0.523266 | −0.261633 | − | 0.965167i | \(-0.584261\pi\) | ||||
−0.261633 | + | 0.965167i | \(0.584261\pi\) | |||||||
\(158\) | −1365.97 | − | 1257.34i | −0.687788 | − | 0.633094i | ||||
\(159\) | 2589.25 | − | 1139.19i | 1.29145 | − | 0.568200i | ||||
\(160\) | 757.832 | + | 494.864i | 0.374449 | + | 0.244515i | ||||
\(161\) | − | 2351.45i | − | 1.15106i | ||||||
\(162\) | 1632.84 | + | 1259.11i | 0.791900 | + | 0.610650i | ||||
\(163\) | − | 224.555i | − | 0.107905i | −0.998544 | − | 0.0539524i | \(-0.982818\pi\) | ||
0.998544 | − | 0.0539524i | \(-0.0171819\pi\) | |||||||
\(164\) | −835.662 | + | 69.3234i | −0.397892 | + | 0.0330076i | ||||
\(165\) | −772.283 | + | 339.782i | −0.364377 | + | 0.160315i | ||||
\(166\) | 751.542 | − | 816.469i | 0.351392 | − | 0.381749i | ||||
\(167\) | −959.236 | −0.444479 | −0.222239 | − | 0.974992i | \(-0.571337\pi\) | ||||
−0.222239 | + | 0.974992i | \(0.571337\pi\) | |||||||
\(168\) | 3679.11 | + | 926.766i | 1.68958 | + | 0.425604i | ||||
\(169\) | −178.681 | −0.0813294 | ||||||||
\(170\) | 758.751 | − | 824.300i | 0.342315 | − | 0.371888i | ||||
\(171\) | −1374.11 | − | 1259.30i | −0.614506 | − | 0.563166i | ||||
\(172\) | 770.198 | − | 63.8927i | 0.341436 | − | 0.0283243i | ||||
\(173\) | − | 1819.46i | − | 0.799600i | −0.916602 | − | 0.399800i | \(-0.869080\pi\) | ||
0.916602 | − | 0.399800i | \(-0.130920\pi\) | |||||||
\(174\) | 1045.95 | − | 3058.31i | 0.455709 | − | 1.33247i | ||||
\(175\) | − | 806.724i | − | 0.348472i | ||||||
\(176\) | 2049.99 | − | 342.476i | 0.877976 | − | 0.146677i | ||||
\(177\) | −902.008 | − | 2050.16i | −0.383046 | − | 0.870617i | ||||
\(178\) | 699.941 | + | 644.280i | 0.294735 | + | 0.271297i | ||||
\(179\) | 797.802 | 0.333131 | 0.166566 | − | 0.986030i | \(-0.446732\pi\) | ||||
0.166566 | + | 0.986030i | \(0.446732\pi\) | |||||||
\(180\) | −661.368 | + | 853.810i | −0.273864 | + | 0.353552i | ||||
\(181\) | 1893.23 | 0.777472 | 0.388736 | − | 0.921349i | \(-0.372912\pi\) | ||||
0.388736 | + | 0.921349i | \(0.372912\pi\) | |||||||
\(182\) | −3016.88 | − | 2776.98i | −1.22872 | − | 1.13101i | ||||
\(183\) | −383.726 | − | 872.164i | −0.155005 | − | 0.352307i | ||||
\(184\) | −1301.33 | − | 1012.58i | −0.521388 | − | 0.405696i | ||||
\(185\) | − | 764.131i | − | 0.303676i | ||||||
\(186\) | −135.414 | + | 395.945i | −0.0533820 | + | 0.156086i | ||||
\(187\) | − | 2572.68i | − | 1.00606i | ||||||
\(188\) | −68.7037 | − | 828.192i | −0.0266528 | − | 0.321288i | ||||
\(189\) | −1455.65 | + | 4286.80i | −0.560228 | + | 1.64984i | ||||
\(190\) | 661.172 | − | 718.291i | 0.252455 | − | 0.274265i | ||||
\(191\) | −2169.17 | −0.821759 | −0.410879 | − | 0.911690i | \(-0.634778\pi\) | ||||
−0.410879 | + | 0.911690i | \(0.634778\pi\) | |||||||
\(192\) | 2097.17 | − | 1637.00i | 0.788283 | − | 0.615313i | ||||
\(193\) | 4329.69 | 1.61481 | 0.807405 | − | 0.589998i | \(-0.200872\pi\) | ||||
0.807405 | + | 0.589998i | \(0.200872\pi\) | |||||||
\(194\) | −1991.66 | + | 2163.72i | −0.737077 | + | 0.800754i | ||||
\(195\) | 1068.37 | − | 470.052i | 0.392347 | − | 0.172621i | ||||
\(196\) | 461.831 | + | 5567.16i | 0.168306 | + | 2.02885i | ||||
\(197\) | 2110.47i | 0.763274i | 0.924312 | + | 0.381637i | \(0.124640\pi\) | ||||
−0.924312 | + | 0.381637i | \(0.875360\pi\) | |||||||
\(198\) | 210.425 | + | 2471.09i | 0.0755267 | + | 0.886934i | ||||
\(199\) | 1465.10i | 0.521899i | 0.965352 | + | 0.260950i | \(0.0840357\pi\) | ||||
−0.965352 | + | 0.260950i | \(0.915964\pi\) | |||||||
\(200\) | −446.454 | − | 347.389i | −0.157845 | − | 0.122820i | ||||
\(201\) | −1380.34 | + | 607.311i | −0.484388 | + | 0.213116i | ||||
\(202\) | −641.629 | − | 590.606i | −0.223489 | − | 0.205717i | ||||
\(203\) | 7096.75 | 2.45367 | ||||||||
\(204\) | −1570.85 | − | 2894.32i | −0.539126 | − | 0.993349i | ||||
\(205\) | 524.083 | 0.178554 | ||||||||
\(206\) | 550.124 | + | 506.377i | 0.186063 | + | 0.171267i | ||||
\(207\) | 1329.32 | − | 1450.51i | 0.446349 | − | 0.487039i | ||||
\(208\) | −2835.94 | + | 473.779i | −0.945371 | + | 0.157936i | ||||
\(209\) | − | 2241.82i | − | 0.741962i | ||||||
\(210\) | −2243.68 | − | 767.346i | −0.737281 | − | 0.252152i | ||||
\(211\) | 2400.96i | 0.783361i | 0.920101 | + | 0.391681i | \(0.128106\pi\) | ||||
−0.920101 | + | 0.391681i | \(0.871894\pi\) | |||||||
\(212\) | 4340.27 | − | 360.053i | 1.40609 | − | 0.116644i | ||||
\(213\) | −1023.54 | − | 2326.37i | −0.329256 | − | 0.748359i | ||||
\(214\) | −2991.63 | + | 3250.08i | −0.955625 | + | 1.03818i | ||||
\(215\) | −483.027 | −0.153219 | ||||||||
\(216\) | 1745.56 | + | 2651.55i | 0.549862 | + | 0.835256i | ||||
\(217\) | −918.782 | −0.287424 | ||||||||
\(218\) | −4172.72 | + | 4533.21i | −1.29639 | + | 1.40838i | ||||
\(219\) | 613.052 | + | 1393.39i | 0.189161 | + | 0.429940i | ||||
\(220\) | −1294.55 | + | 107.391i | −0.396722 | + | 0.0329105i | ||||
\(221\) | 3559.03i | 1.08329i | ||||||||
\(222\) | −2125.22 | − | 726.832i | −0.642503 | − | 0.219738i | ||||
\(223\) | 1227.21i | 0.368521i | 0.982877 | + | 0.184260i | \(0.0589890\pi\) | ||||
−0.982877 | + | 0.184260i | \(0.941011\pi\) | |||||||
\(224\) | 4890.89 | + | 3193.75i | 1.45887 | + | 0.952640i | ||||
\(225\) | 456.057 | − | 497.632i | 0.135128 | − | 0.147446i | ||||
\(226\) | −3570.74 | − | 3286.79i | −1.05098 | − | 0.967408i | ||||
\(227\) | −6004.46 | −1.75564 | −0.877820 | − | 0.478991i | \(-0.841003\pi\) | ||||
−0.877820 | + | 0.478991i | \(0.841003\pi\) | |||||||
\(228\) | −1368.83 | − | 2522.10i | −0.397602 | − | 0.732589i | ||||
\(229\) | −3410.62 | −0.984192 | −0.492096 | − | 0.870541i | \(-0.663769\pi\) | ||||
−0.492096 | + | 0.870541i | \(0.663769\pi\) | |||||||
\(230\) | 758.228 | + | 697.933i | 0.217374 | + | 0.200088i | ||||
\(231\) | −4984.15 | + | 2192.88i | −1.41962 | + | 0.624593i | ||||
\(232\) | 3055.98 | − | 3927.46i | 0.864806 | − | 1.11142i | ||||
\(233\) | 6319.33i | 1.77679i | 0.459076 | + | 0.888397i | \(0.348181\pi\) | ||||
−0.459076 | + | 0.888397i | \(0.651819\pi\) | |||||||
\(234\) | −291.101 | − | 3418.49i | −0.0813243 | − | 0.955017i | ||||
\(235\) | 519.398i | 0.144178i | ||||||||
\(236\) | −285.088 | − | 3436.61i | −0.0786342 | − | 0.947900i | ||||
\(237\) | 3121.90 | − | 1373.54i | 0.855650 | − | 0.376461i | ||||
\(238\) | 4896.82 | − | 5319.86i | 1.33367 | − | 1.44889i | ||||
\(239\) | −3563.80 | −0.964533 | −0.482266 | − | 0.876025i | \(-0.660186\pi\) | ||||
−0.482266 | + | 0.876025i | \(0.660186\pi\) | |||||||
\(240\) | −1390.83 | + | 911.259i | −0.374074 | + | 0.245090i | ||||
\(241\) | −2833.81 | −0.757435 | −0.378718 | − | 0.925512i | \(-0.623635\pi\) | ||||
−0.378718 | + | 0.925512i | \(0.623635\pi\) | |||||||
\(242\) | 529.408 | − | 575.144i | 0.140626 | − | 0.152775i | ||||
\(243\) | −3321.34 | + | 1821.43i | −0.876807 | + | 0.480843i | ||||
\(244\) | −121.280 | − | 1461.98i | −0.0318204 | − | 0.383581i | ||||
\(245\) | − | 3491.43i | − | 0.910445i | ||||||
\(246\) | 498.501 | − | 1457.60i | 0.129200 | − | 0.377776i | ||||
\(247\) | 3101.32i | 0.798917i | ||||||||
\(248\) | −395.643 | + | 508.469i | −0.101304 | + | 0.130193i | ||||
\(249\) | 820.998 | + | 1866.03i | 0.208950 | + | 0.474919i | ||||
\(250\) | 260.129 | + | 239.443i | 0.0658080 | + | 0.0605748i | ||||
\(251\) | 3865.84 | 0.972149 | 0.486075 | − | 0.873917i | \(-0.338428\pi\) | ||||
0.486075 | + | 0.873917i | \(0.338428\pi\) | |||||||
\(252\) | −4268.33 | + | 5510.31i | −1.06698 | + | 1.37745i | ||||
\(253\) | 2366.47 | 0.588058 | ||||||||
\(254\) | 2905.89 | + | 2674.81i | 0.717841 | + | 0.660757i | ||||
\(255\) | 828.873 | + | 1883.93i | 0.203553 | + | 0.462651i | ||||
\(256\) | 3873.57 | − | 1331.41i | 0.945696 | − | 0.325052i | ||||
\(257\) | 2960.51i | 0.718566i | 0.933229 | + | 0.359283i | \(0.116979\pi\) | ||||
−0.933229 | + | 0.359283i | \(0.883021\pi\) | |||||||
\(258\) | −459.449 | + | 1343.41i | −0.110869 | + | 0.324174i | ||||
\(259\) | − | 4931.54i | − | 1.18313i | ||||||
\(260\) | 1790.88 | − | 148.564i | 0.427175 | − | 0.0354368i | ||||
\(261\) | 4377.67 | + | 4011.93i | 1.03820 | + | 0.951465i | ||||
\(262\) | −2893.50 | + | 3143.48i | −0.682295 | + | 0.741239i | ||||
\(263\) | 6555.46 | 1.53699 | 0.768493 | − | 0.639859i | \(-0.221007\pi\) | ||||
0.768493 | + | 0.639859i | \(0.221007\pi\) | |||||||
\(264\) | −932.683 | + | 3702.60i | −0.217434 | + | 0.863179i | ||||
\(265\) | −2721.99 | −0.630983 | ||||||||
\(266\) | 4267.06 | − | 4635.70i | 0.983573 | − | 1.06855i | ||||
\(267\) | −1599.70 | + | 703.823i | −0.366668 | + | 0.161323i | ||||
\(268\) | −2313.83 | + | 191.946i | −0.527386 | + | 0.0437500i | ||||
\(269\) | − | 8701.31i | − | 1.97222i | −0.166083 | − | 0.986112i | \(-0.553112\pi\) | ||
0.166083 | − | 0.986112i | \(-0.446888\pi\) | |||||||
\(270\) | −950.233 | − | 1741.74i | −0.214183 | − | 0.392589i | ||||
\(271\) | − | 2026.32i | − | 0.454207i | −0.973871 | − | 0.227104i | \(-0.927074\pi\) | ||
0.973871 | − | 0.227104i | \(-0.0729256\pi\) | |||||||
\(272\) | −835.444 | − | 5000.80i | −0.186236 | − | 1.11477i | ||||
\(273\) | 6895.04 | − | 3033.62i | 1.52860 | − | 0.672538i | ||||
\(274\) | −1127.48 | − | 1037.82i | −0.248589 | − | 0.228821i | ||||
\(275\) | 811.875 | 0.178029 | ||||||||
\(276\) | 2662.33 | − | 1444.94i | 0.580628 | − | 0.315128i | ||||
\(277\) | 6200.10 | 1.34487 | 0.672433 | − | 0.740158i | \(-0.265249\pi\) | ||||
0.672433 | + | 0.740158i | \(0.265249\pi\) | |||||||
\(278\) | −1485.44 | − | 1367.31i | −0.320470 | − | 0.294986i | ||||
\(279\) | −566.755 | − | 519.405i | −0.121616 | − | 0.111455i | ||||
\(280\) | −2881.32 | − | 2241.97i | −0.614971 | − | 0.478513i | ||||
\(281\) | 8199.53i | 1.74072i | 0.492413 | + | 0.870361i | \(0.336115\pi\) | ||||
−0.492413 | + | 0.870361i | \(0.663885\pi\) | |||||||
\(282\) | 1444.57 | + | 494.045i | 0.305045 | + | 0.104326i | ||||
\(283\) | 7615.89i | 1.59971i | 0.600194 | + | 0.799854i | \(0.295090\pi\) | ||||
−0.600194 | + | 0.799854i | \(0.704910\pi\) | |||||||
\(284\) | −323.498 | − | 3899.63i | −0.0675919 | − | 0.814790i | ||||
\(285\) | 722.276 | + | 1641.64i | 0.150119 | + | 0.341202i | ||||
\(286\) | 2794.71 | − | 3036.15i | 0.577813 | − | 0.627731i | ||||
\(287\) | 3382.32 | 0.695652 | ||||||||
\(288\) | 1211.48 | + | 4735.00i | 0.247872 | + | 0.968793i | ||||
\(289\) | −1362.87 | −0.277400 | ||||||||
\(290\) | −2106.38 | + | 2288.35i | −0.426521 | + | 0.463368i | ||||
\(291\) | −2175.72 | − | 4945.16i | −0.438293 | − | 0.996186i | ||||
\(292\) | 193.761 | + | 2335.70i | 0.0388322 | + | 0.468105i | ||||
\(293\) | − | 9294.47i | − | 1.85320i | −0.376044 | − | 0.926602i | \(-0.622716\pi\) | ||
0.376044 | − | 0.926602i | \(-0.377284\pi\) | |||||||
\(294\) | −9710.46 | − | 3321.00i | −1.92628 | − | 0.658792i | ||||
\(295\) | 2155.26i | 0.425370i | ||||||||
\(296\) | −2729.19 | − | 2123.60i | −0.535916 | − | 0.417000i | ||||
\(297\) | −4314.18 | − | 1464.95i | −0.842875 | − | 0.286212i | ||||
\(298\) | 226.871 | + | 208.830i | 0.0441016 | + | 0.0405945i | ||||
\(299\) | −3273.76 | −0.633198 | ||||||||
\(300\) | 913.378 | − | 495.723i | 0.175780 | − | 0.0954019i | ||||
\(301\) | −3117.36 | −0.596948 | ||||||||
\(302\) | 6630.96 | + | 6103.66i | 1.26347 | + | 1.16300i | ||||
\(303\) | 1466.43 | − | 645.188i | 0.278034 | − | 0.122327i | ||||
\(304\) | −728.002 | − | 4357.67i | −0.137348 | − | 0.822137i | ||||
\(305\) | 916.876i | 0.172132i | ||||||||
\(306\) | 6028.05 | − | 513.317i | 1.12615 | − | 0.0958967i | ||||
\(307\) | − | 1982.97i | − | 0.368646i | −0.982866 | − | 0.184323i | \(-0.940991\pi\) | ||
0.982866 | − | 0.184323i | \(-0.0590092\pi\) | |||||||
\(308\) | −8354.78 | + | 693.081i | −1.54564 | + | 0.128221i | ||||
\(309\) | −1257.30 | + | 553.176i | −0.231474 | + | 0.101842i | ||||
\(310\) | 272.703 | − | 296.262i | 0.0499629 | − | 0.0542792i | ||||
\(311\) | 326.148 | 0.0594668 | 0.0297334 | − | 0.999558i | \(-0.490534\pi\) | ||||
0.0297334 | + | 0.999558i | \(0.490534\pi\) | |||||||
\(312\) | 1290.27 | − | 5122.15i | 0.234125 | − | 0.929439i | ||||
\(313\) | 1059.90 | 0.191403 | 0.0957014 | − | 0.995410i | \(-0.469491\pi\) | ||||
0.0957014 | + | 0.995410i | \(0.469491\pi\) | |||||||
\(314\) | 1971.80 | − | 2142.15i | 0.354380 | − | 0.384996i | ||||
\(315\) | 2943.29 | − | 3211.61i | 0.526463 | − | 0.574457i | ||||
\(316\) | 5233.14 | − | 434.122i | 0.931605 | − | 0.0772824i | ||||
\(317\) | 1007.99i | 0.178595i | 0.996005 | + | 0.0892974i | \(0.0284621\pi\) | ||||
−0.996005 | + | 0.0892974i | \(0.971538\pi\) | |||||||
\(318\) | −2589.12 | + | 7570.48i | −0.456575 | + | 1.33500i | ||||
\(319\) | 7142.07i | 1.25354i | ||||||||
\(320\) | −2481.49 | + | 629.137i | −0.433498 | + | 0.109906i | ||||
\(321\) | −3268.11 | − | 7428.02i | −0.568250 | − | 1.29156i | ||||
\(322\) | 4893.45 | + | 4504.31i | 0.846898 | + | 0.779552i | ||||
\(323\) | −5468.76 | −0.942074 | ||||||||
\(324\) | −5748.03 | + | 986.095i | −0.985602 | + | 0.169084i | ||||
\(325\) | −1123.14 | −0.191695 | ||||||||
\(326\) | 467.305 | + | 430.145i | 0.0793916 | + | 0.0730783i | ||||
\(327\) | −4558.35 | − | 10360.6i | −0.770880 | − | 1.75212i | ||||
\(328\) | 1456.48 | − | 1871.83i | 0.245186 | − | 0.315105i | ||||
\(329\) | 3352.09i | 0.561722i | ||||||||
\(330\) | 772.246 | − | 2258.01i | 0.128820 | − | 0.376665i | ||||
\(331\) | 3283.67i | 0.545278i | 0.962116 | + | 0.272639i | \(0.0878965\pi\) | ||||
−0.962116 | + | 0.272639i | \(0.912104\pi\) | |||||||
\(332\) | 259.484 | + | 3127.97i | 0.0428947 | + | 0.517077i | ||||
\(333\) | 2787.89 | − | 3042.05i | 0.458786 | − | 0.500610i | ||||
\(334\) | 1837.46 | − | 1996.20i | 0.301022 | − | 0.327028i | ||||
\(335\) | 1451.11 | 0.236664 | ||||||||
\(336\) | −8976.12 | + | 5881.08i | −1.45740 | + | 0.954878i | ||||
\(337\) | −10806.5 | −1.74678 | −0.873391 | − | 0.487019i | \(-0.838084\pi\) | ||||
−0.873391 | + | 0.487019i | \(0.838084\pi\) | |||||||
\(338\) | 342.271 | − | 371.840i | 0.0550801 | − | 0.0598385i | ||||
\(339\) | 8160.89 | − | 3590.55i | 1.30749 | − | 0.575257i | ||||
\(340\) | 261.973 | + | 3157.97i | 0.0417867 | + | 0.503720i | ||||
\(341\) | − | 924.649i | − | 0.146840i | ||||||
\(342\) | 5252.81 | − | 447.302i | 0.830525 | − | 0.0707232i | ||||
\(343\) | − | 11464.7i | − | 1.80477i | ||||||
\(344\) | −1342.39 | + | 1725.19i | −0.210397 | + | 0.270396i | ||||
\(345\) | −1732.92 | + | 762.434i | −0.270427 | + | 0.118980i | ||||
\(346\) | 3786.35 | + | 3485.25i | 0.588310 | + | 0.541527i | ||||
\(347\) | 4257.61 | 0.658676 | 0.329338 | − | 0.944212i | \(-0.393174\pi\) | ||||
0.329338 | + | 0.944212i | \(0.393174\pi\) | |||||||
\(348\) | 4360.88 | + | 8034.99i | 0.671746 | + | 1.23770i | ||||
\(349\) | −1701.82 | −0.261022 | −0.130511 | − | 0.991447i | \(-0.541662\pi\) | ||||
−0.130511 | + | 0.991447i | \(0.541662\pi\) | |||||||
\(350\) | 1678.82 | + | 1545.32i | 0.256390 | + | 0.236002i | ||||
\(351\) | 5968.21 | + | 2026.60i | 0.907576 | + | 0.308182i | ||||
\(352\) | −3214.14 | + | 4922.12i | −0.486689 | + | 0.745312i | ||||
\(353\) | 3808.94i | 0.574305i | 0.957885 | + | 0.287152i | \(0.0927086\pi\) | ||||
−0.957885 | + | 0.287152i | \(0.907291\pi\) | |||||||
\(354\) | 5994.27 | + | 2050.06i | 0.899978 | + | 0.307795i | ||||
\(355\) | 2445.64i | 0.365637i | ||||||||
\(356\) | −2681.53 | + | 222.450i | −0.399216 | + | 0.0331175i | ||||
\(357\) | 5349.37 | + | 12158.5i | 0.793050 | + | 1.80251i | ||||
\(358\) | −1528.22 | + | 1660.25i | −0.225612 | + | 0.245103i | ||||
\(359\) | −3187.87 | −0.468660 | −0.234330 | − | 0.972157i | \(-0.575290\pi\) | ||||
−0.234330 | + | 0.972157i | \(0.575290\pi\) | |||||||
\(360\) | −509.926 | − | 3011.84i | −0.0746540 | − | 0.440939i | ||||
\(361\) | 2093.55 | 0.305226 | ||||||||
\(362\) | −3626.56 | + | 3939.86i | −0.526541 | + | 0.572029i | ||||
\(363\) | 578.334 | + | 1314.48i | 0.0836217 | + | 0.190062i | ||||
\(364\) | 11557.9 | − | 958.804i | 1.66429 | − | 0.138063i | ||||
\(365\) | − | 1464.83i | − | 0.210062i | ||||||
\(366\) | 2550.04 | + | 872.122i | 0.364188 | + | 0.124553i | ||||
\(367\) | 10714.8i | 1.52400i | 0.647576 | + | 0.762001i | \(0.275783\pi\) | ||||
−0.647576 | + | 0.762001i | \(0.724217\pi\) | |||||||
\(368\) | 4599.96 | − | 768.479i | 0.651602 | − | 0.108858i | ||||
\(369\) | 2086.40 | + | 1912.09i | 0.294346 | + | 0.269755i | ||||
\(370\) | 1590.18 | + | 1463.73i | 0.223431 | + | 0.205664i | ||||
\(371\) | −17567.1 | −2.45833 | ||||||||
\(372\) | −564.581 | − | 1040.25i | −0.0786887 | − | 0.144985i | ||||
\(373\) | −13485.1 | −1.87194 | −0.935969 | − | 0.352082i | \(-0.885474\pi\) | ||||
−0.935969 | + | 0.352082i | \(0.885474\pi\) | |||||||
\(374\) | 5353.83 | + | 4928.09i | 0.740214 | + | 0.681351i | ||||
\(375\) | −594.521 | + | 261.572i | −0.0818691 | + | 0.0360200i | ||||
\(376\) | 1855.10 | + | 1443.46i | 0.254440 | + | 0.197981i | ||||
\(377\) | − | 9880.29i | − | 1.34976i | ||||||
\(378\) | −6132.61 | − | 11240.8i | −0.834464 | − | 1.52954i | ||||
\(379\) | − | 14560.5i | − | 1.97341i | −0.162534 | − | 0.986703i | \(-0.551967\pi\) | ||
0.162534 | − | 0.986703i | \(-0.448033\pi\) | |||||||
\(380\) | 228.282 | + | 2751.84i | 0.0308174 | + | 0.371490i | ||||
\(381\) | −6641.37 | + | 2922.01i | −0.893038 | + | 0.392911i | ||||
\(382\) | 4155.15 | − | 4514.12i | 0.556534 | − | 0.604614i | ||||
\(383\) | 12768.6 | 1.70352 | 0.851759 | − | 0.523934i | \(-0.175536\pi\) | ||||
0.851759 | + | 0.523934i | \(0.175536\pi\) | |||||||
\(384\) | −610.587 | + | 7500.02i | −0.0811429 | + | 0.996702i | ||||
\(385\) | 5239.67 | 0.693606 | ||||||||
\(386\) | −8293.72 | + | 9010.23i | −1.09363 | + | 1.18810i | ||||
\(387\) | −1922.96 | − | 1762.30i | −0.252582 | − | 0.231480i | ||||
\(388\) | −687.658 | − | 8289.41i | −0.0899757 | − | 1.08462i | ||||
\(389\) | − | 1614.55i | − | 0.210439i | −0.994449 | − | 0.105220i | \(-0.966445\pi\) | ||
0.994449 | − | 0.105220i | \(-0.0335545\pi\) | |||||||
\(390\) | −1068.32 | + | 3123.72i | −0.138709 | + | 0.405579i | ||||
\(391\) | − | 5772.82i | − | 0.746660i | ||||||
\(392\) | −12470.1 | − | 9703.06i | −1.60672 | − | 1.25020i | ||||
\(393\) | −3160.92 | − | 7184.38i | −0.405718 | − | 0.922147i | ||||
\(394\) | −4391.96 | − | 4042.70i | −0.561583 | − | 0.516925i | ||||
\(395\) | −3281.95 | −0.418057 | ||||||||
\(396\) | −5545.50 | − | 4295.59i | −0.703717 | − | 0.545104i | ||||
\(397\) | −3366.61 | −0.425605 | −0.212803 | − | 0.977095i | \(-0.568259\pi\) | ||||
−0.212803 | + | 0.977095i | \(0.568259\pi\) | |||||||
\(398\) | −3048.91 | − | 2806.46i | −0.383990 | − | 0.353455i | ||||
\(399\) | 4661.42 | + | 10594.8i | 0.584869 | + | 1.32934i | ||||
\(400\) | 1578.13 | − | 263.646i | 0.197266 | − | 0.0329557i | ||||
\(401\) | 2084.43i | 0.259580i | 0.991542 | + | 0.129790i | \(0.0414303\pi\) | ||||
−0.991542 | + | 0.129790i | \(0.958570\pi\) | |||||||
\(402\) | 1380.28 | − | 4035.87i | 0.171249 | − | 0.500724i | ||||
\(403\) | 1279.15i | 0.158112i | ||||||||
\(404\) | 2458.14 | − | 203.918i | 0.302715 | − | 0.0251121i | ||||
\(405\) | 3631.17 | − | 317.198i | 0.445517 | − | 0.0389178i | ||||
\(406\) | −13594.1 | + | 14768.6i | −1.66174 | + | 1.80530i | ||||
\(407\) | 4963.03 | 0.604443 | ||||||||
\(408\) | 9032.22 | + | 2275.21i | 1.09598 | + | 0.276078i | ||||
\(409\) | 9008.16 | 1.08906 | 0.544529 | − | 0.838742i | \(-0.316708\pi\) | ||||
0.544529 | + | 0.838742i | \(0.316708\pi\) | |||||||
\(410\) | −1003.90 | + | 1090.63i | −0.120925 | + | 0.131372i | ||||
\(411\) | 2576.84 | − | 1133.73i | 0.309260 | − | 0.136066i | ||||
\(412\) | −2107.57 | + | 174.836i | −0.252021 | + | 0.0209067i | ||||
\(413\) | 13909.6i | 1.65726i | ||||||||
\(414\) | 472.172 | + | 5544.87i | 0.0560532 | + | 0.658250i | ||||
\(415\) | − | 1961.69i | − | 0.232038i | ||||||
\(416\) | 4446.43 | − | 6809.23i | 0.524048 | − | 0.802524i | ||||
\(417\) | 3394.95 | − | 1493.68i | 0.398685 | − | 0.175410i | ||||
\(418\) | 4665.30 | + | 4294.31i | 0.545903 | + | 0.502492i | ||||
\(419\) | −8794.29 | −1.02537 | −0.512684 | − | 0.858577i | \(-0.671349\pi\) | ||||
−0.512684 | + | 0.858577i | \(0.671349\pi\) | |||||||
\(420\) | 5894.75 | − | 3199.29i | 0.684844 | − | 0.371689i | ||||
\(421\) | 4897.05 | 0.566906 | 0.283453 | − | 0.958986i | \(-0.408520\pi\) | ||||
0.283453 | + | 0.958986i | \(0.408520\pi\) | |||||||
\(422\) | −4996.48 | − | 4599.15i | −0.576362 | − | 0.530529i | ||||
\(423\) | −1895.00 | + | 2067.75i | −0.217820 | + | 0.237677i | ||||
\(424\) | −7564.71 | + | 9721.94i | −0.866449 | + | 1.11354i | ||||
\(425\) | − | 1980.51i | − | 0.226044i | ||||||
\(426\) | 6801.88 | + | 2326.26i | 0.773597 | + | 0.264572i | ||||
\(427\) | 5917.33i | 0.670631i | ||||||||
\(428\) | −1032.92 | − | 12451.4i | −0.116654 | − | 1.40621i | ||||
\(429\) | 3052.99 | + | 6939.07i | 0.343589 | + | 0.780936i | ||||
\(430\) | 925.260 | − | 1005.19i | 0.103767 | − | 0.112732i | ||||
\(431\) | 11897.9 | 1.32970 | 0.664848 | − | 0.746978i | \(-0.268496\pi\) | ||||
0.664848 | + | 0.746978i | \(0.268496\pi\) | |||||||
\(432\) | −8861.65 | − | 1446.60i | −0.986936 | − | 0.161111i | ||||
\(433\) | 1169.38 | 0.129785 | 0.0648925 | − | 0.997892i | \(-0.479330\pi\) | ||||
0.0648925 | + | 0.997892i | \(0.479330\pi\) | |||||||
\(434\) | 1759.97 | − | 1912.01i | 0.194657 | − | 0.211474i | ||||
\(435\) | −2301.05 | − | 5230.00i | −0.253625 | − | 0.576459i | ||||
\(436\) | −1440.71 | − | 17367.1i | −0.158251 | − | 1.90765i | ||||
\(437\) | − | 5030.41i | − | 0.550657i | ||||||
\(438\) | −4074.02 | − | 1393.33i | −0.444439 | − | 0.151999i | ||||
\(439\) | 6786.60i | 0.737829i | 0.929463 | + | 0.368915i | \(0.120270\pi\) | ||||
−0.929463 | + | 0.368915i | \(0.879730\pi\) | |||||||
\(440\) | 2256.29 | − | 2899.72i | 0.244465 | − | 0.314179i | ||||
\(441\) | 12738.3 | − | 13899.6i | 1.37548 | − | 1.50087i | ||||
\(442\) | −7406.45 | − | 6817.48i | −0.797034 | − | 0.733653i | ||||
\(443\) | −9083.87 | −0.974238 | −0.487119 | − | 0.873336i | \(-0.661952\pi\) | ||||
−0.487119 | + | 0.873336i | \(0.661952\pi\) | |||||||
\(444\) | 5583.52 | − | 3030.38i | 0.596806 | − | 0.323908i | ||||
\(445\) | 1681.72 | 0.179148 | ||||||||
\(446\) | −2553.86 | − | 2350.78i | −0.271141 | − | 0.249580i | ||||
\(447\) | −518.510 | + | 228.129i | −0.0548650 | + | 0.0241390i | ||||
\(448\) | −16015.0 | + | 4060.32i | −1.68892 | + | 0.428196i | ||||
\(449\) | 3214.97i | 0.337914i | 0.985623 | + | 0.168957i | \(0.0540400\pi\) | ||||
−0.985623 | + | 0.168957i | \(0.945960\pi\) | |||||||
\(450\) | 161.990 | + | 1902.30i | 0.0169696 | + | 0.199279i | ||||
\(451\) | 3403.92i | 0.355398i | ||||||||
\(452\) | 13679.8 | − | 1134.83i | 1.42355 | − | 0.118093i | ||||
\(453\) | −15155.0 | + | 6667.75i | −1.57184 | + | 0.691563i | ||||
\(454\) | 11501.8 | − | 12495.5i | 1.18900 | − | 1.29172i | ||||
\(455\) | −7248.53 | −0.746849 | ||||||||
\(456\) | 7870.63 | + | 1982.61i | 0.808281 | + | 0.203606i | ||||
\(457\) | 12339.4 | 1.26304 | 0.631522 | − | 0.775358i | \(-0.282431\pi\) | ||||
0.631522 | + | 0.775358i | \(0.282431\pi\) | |||||||
\(458\) | 6533.19 | − | 7097.60i | 0.666541 | − | 0.724125i | ||||
\(459\) | −3573.63 | + | 10524.1i | −0.363405 | + | 1.07020i | ||||
\(460\) | −2904.84 | + | 240.975i | −0.294432 | + | 0.0244250i | ||||
\(461\) | − | 12038.7i | − | 1.21626i | −0.793837 | − | 0.608130i | \(-0.791920\pi\) | ||
0.793837 | − | 0.608130i | \(-0.208080\pi\) | |||||||
\(462\) | 4983.91 | − | 14572.7i | 0.501889 | − | 1.46750i | ||||
\(463\) | 2481.97i | 0.249130i | 0.992211 | + | 0.124565i | \(0.0397535\pi\) | ||||
−0.992211 | + | 0.124565i | \(0.960247\pi\) | |||||||
\(464\) | 2319.29 | + | 13882.8i | 0.232048 | + | 1.38899i | ||||
\(465\) | 297.905 | + | 677.103i | 0.0297098 | + | 0.0675267i | ||||
\(466\) | −13150.7 | − | 12105.0i | −1.30729 | − | 1.20333i | ||||
\(467\) | −1596.67 | −0.158212 | −0.0791060 | − | 0.996866i | \(-0.525207\pi\) | ||||
−0.0791060 | + | 0.996866i | \(0.525207\pi\) | |||||||
\(468\) | 7671.61 | + | 5942.49i | 0.757735 | + | 0.586948i | ||||
\(469\) | 9365.16 | 0.922053 | ||||||||
\(470\) | −1080.88 | − | 994.930i | −0.106080 | − | 0.0976440i | ||||
\(471\) | 2154.03 | + | 4895.86i | 0.210728 | + | 0.478958i | ||||
\(472\) | 7697.79 | + | 5989.70i | 0.750677 | + | 0.584107i | ||||
\(473\) | − | 3137.26i | − | 0.304971i | ||||||
\(474\) | −3121.75 | + | 9127.85i | −0.302503 | + | 0.884506i | ||||
\(475\) | − | 1725.81i | − | 0.166706i | ||||||
\(476\) | 1690.72 | + | 20380.9i | 0.162803 | + | 1.96251i | ||||
\(477\) | −10836.4 | − | 9931.05i | −1.04018 | − | 0.953273i | ||||
\(478\) | 6826.63 | − | 7416.39i | 0.653227 | − | 0.709660i | ||||
\(479\) | 13673.9 | 1.30433 | 0.652166 | − | 0.758076i | \(-0.273861\pi\) | ||||
0.652166 | + | 0.758076i | \(0.273861\pi\) | |||||||
\(480\) | 767.838 | − | 4639.92i | 0.0730143 | − | 0.441213i | ||||
\(481\) | −6865.82 | −0.650841 | ||||||||
\(482\) | 5428.29 | − | 5897.25i | 0.512971 | − | 0.557287i | ||||
\(483\) | −11183.9 | + | 4920.59i | −1.05359 | + | 0.463550i | ||||
\(484\) | 182.788 | + | 2203.43i | 0.0171664 | + | 0.206933i | ||||
\(485\) | 5198.68i | 0.486721i | ||||||||
\(486\) | 2571.73 | − | 10400.8i | 0.240033 | − | 0.970765i | ||||
\(487\) | 2712.51i | 0.252393i | 0.992005 | + | 0.126197i | \(0.0402770\pi\) | ||||
−0.992005 | + | 0.126197i | \(0.959723\pi\) | |||||||
\(488\) | 3274.74 | + | 2548.10i | 0.303772 | + | 0.236367i | ||||
\(489\) | −1068.02 | + | 469.898i | −0.0987680 | + | 0.0434550i | ||||
\(490\) | 7265.77 | + | 6687.98i | 0.669865 | + | 0.616597i | ||||
\(491\) | 7797.19 | 0.716664 | 0.358332 | − | 0.933594i | \(-0.383346\pi\) | ||||
0.358332 | + | 0.933594i | \(0.383346\pi\) | |||||||
\(492\) | 2078.40 | + | 3829.49i | 0.190450 | + | 0.350908i | ||||
\(493\) | 17422.5 | 1.59163 | ||||||||
\(494\) | −6453.95 | − | 5940.72i | −0.587807 | − | 0.541064i | ||||
\(495\) | 3232.12 | + | 2962.09i | 0.293481 | + | 0.268961i | ||||
\(496\) | −300.267 | − | 1797.34i | −0.0271823 | − | 0.162707i | ||||
\(497\) | 15783.6i | 1.42453i | ||||||||
\(498\) | −5455.92 | − | 1865.94i | −0.490935 | − | 0.167901i | ||||
\(499\) | − | 10440.3i | − | 0.936617i | −0.883565 | − | 0.468309i | \(-0.844864\pi\) | ||
0.883565 | − | 0.468309i | \(-0.155136\pi\) | |||||||
\(500\) | −996.577 | + | 82.6723i | −0.0891365 | + | 0.00739443i | ||||
\(501\) | 2007.27 | + | 4562.29i | 0.178999 | + | 0.406842i | ||||
\(502\) | −7405.18 | + | 8044.93i | −0.658386 | + | 0.715264i | ||||
\(503\) | −14638.9 | −1.29764 | −0.648822 | − | 0.760940i | \(-0.724738\pi\) | ||||
−0.648822 | + | 0.760940i | \(0.724738\pi\) | |||||||
\(504\) | −3290.95 | − | 19437.8i | −0.290855 | − | 1.71791i | ||||
\(505\) | −1541.61 | −0.135843 | ||||||||
\(506\) | −4533.07 | + | 4924.69i | −0.398260 | + | 0.432667i | ||||
\(507\) | 373.903 | + | 849.835i | 0.0327527 | + | 0.0744428i | ||||
\(508\) | −11132.7 | + | 923.528i | −0.972312 | + | 0.0806593i | ||||
\(509\) | 1254.81i | 0.109270i | 0.998506 | + | 0.0546351i | \(0.0173996\pi\) | ||||
−0.998506 | + | 0.0546351i | \(0.982600\pi\) | |||||||
\(510\) | −5508.25 | − | 1883.84i | −0.478254 | − | 0.163564i | ||||
\(511\) | − | 9453.70i | − | 0.818409i | ||||||
\(512\) | −4649.28 | + | 10611.4i | −0.401311 | + | 0.915942i | ||||
\(513\) | −3114.05 | + | 9170.67i | −0.268009 | + | 0.789269i | ||||
\(514\) | −6160.91 | − | 5670.99i | −0.528689 | − | 0.486647i | ||||
\(515\) | 1321.76 | 0.113094 | ||||||||
\(516\) | −1915.58 | − | 3529.49i | −0.163428 | − | 0.301118i | ||||
\(517\) | −3373.49 | −0.286975 | ||||||||
\(518\) | 10262.7 | + | 9446.58i | 0.870495 | + | 0.801272i | ||||
\(519\) | −8653.65 | + | 3807.35i | −0.731894 | + | 0.322012i | ||||
\(520\) | −3121.34 | + | 4011.45i | −0.263230 | + | 0.338296i | ||||
\(521\) | 2219.01i | 0.186596i | 0.995638 | + | 0.0932980i | \(0.0297409\pi\) | ||||
−0.995638 | + | 0.0932980i | \(0.970259\pi\) | |||||||
\(522\) | −16734.6 | + | 1425.03i | −1.40317 | + | 0.119486i | ||||
\(523\) | − | 11035.2i | − | 0.922633i | −0.887236 | − | 0.461317i | \(-0.847377\pi\) | ||
0.887236 | − | 0.461317i | \(-0.152623\pi\) | |||||||
\(524\) | −999.037 | − | 12042.9i | −0.0832885 | − | 1.00400i | ||||
\(525\) | −3836.91 | + | 1688.13i | −0.318965 | + | 0.140335i | ||||
\(526\) | −12557.3 | + | 13642.1i | −1.04092 | + | 1.13085i | ||||
\(527\) | −2255.61 | −0.186444 | ||||||||
\(528\) | −5918.63 | − | 9033.44i | −0.487832 | − | 0.744564i | ||||
\(529\) | −6856.90 | −0.563565 | ||||||||
\(530\) | 5214.09 | − | 5664.54i | 0.427331 | − | 0.464249i | ||||
\(531\) | −7863.36 | + | 8580.21i | −0.642638 | + | 0.701223i | ||||
\(532\) | 1473.29 | + | 17759.8i | 0.120066 | + | 1.44734i | ||||
\(533\) | − | 4708.96i | − | 0.382679i | ||||||
\(534\) | 1599.63 | − | 4677.24i | 0.129630 | − | 0.379034i | ||||
\(535\) | 7808.83i | 0.631038i | ||||||||
\(536\) | 4032.79 | − | 5182.83i | 0.324982 | − | 0.417657i | ||||
\(537\) | −1669.46 | − | 3794.48i | −0.134157 | − | 0.304923i | ||||
\(538\) | 18107.7 | + | 16667.7i | 1.45107 | + | 1.33568i | ||||
\(539\) | 22676.8 | 1.81217 | ||||||||
\(540\) | 5444.83 | + | 1358.92i | 0.433904 | + | 0.108293i | ||||
\(541\) | 4389.37 | 0.348824 | 0.174412 | − | 0.984673i | \(-0.444198\pi\) | ||||
0.174412 | + | 0.984673i | \(0.444198\pi\) | |||||||
\(542\) | 4216.83 | + | 3881.50i | 0.334185 | + | 0.307611i | ||||
\(543\) | −3961.72 | − | 9004.50i | −0.313101 | − | 0.711640i | ||||
\(544\) | 12007.1 | + | 7840.67i | 0.946327 | + | 0.617952i | ||||
\(545\) | 10891.7i | 0.856057i | ||||||||
\(546\) | −6894.71 | + | 20159.8i | −0.540415 | + | 1.58015i | ||||
\(547\) | − | 11409.4i | − | 0.891826i | −0.895076 | − | 0.445913i | \(-0.852879\pi\) | ||
0.895076 | − | 0.445913i | \(-0.147121\pi\) | |||||||
\(548\) | 4319.47 | − | 358.327i | 0.336713 | − | 0.0279324i | ||||
\(549\) | −3345.18 | + | 3650.13i | −0.260052 | + | 0.283759i | ||||
\(550\) | −1555.18 | + | 1689.54i | −0.120569 | + | 0.130986i | ||||
\(551\) | 15181.9 | 1.17381 | ||||||||
\(552\) | −2092.84 | + | 8308.24i | −0.161372 | + | 0.640620i | ||||
\(553\) | −21181.0 | −1.62877 | ||||||||
\(554\) | −11876.6 | + | 12902.6i | −0.910806 | + | 0.989492i | ||||
\(555\) | −3634.33 | + | 1599.00i | −0.277962 | + | 0.122295i | ||||
\(556\) | 5690.85 | − | 472.091i | 0.434075 | − | 0.0360092i | ||||
\(557\) | − | 9758.39i | − | 0.742327i | −0.928567 | − | 0.371164i | \(-0.878959\pi\) | ||
0.928567 | − | 0.371164i | \(-0.121041\pi\) | |||||||
\(558\) | 2166.54 | − | 184.492i | 0.164368 | − | 0.0139967i | ||||
\(559\) | 4340.07i | 0.328382i | ||||||||
\(560\) | 10184.9 | − | 1701.51i | 0.768556 | − | 0.128397i | ||||
\(561\) | −12236.1 | + | 5383.53i | −0.920871 | + | 0.405156i | ||||
\(562\) | −17063.5 | − | 15706.6i | −1.28075 | − | 1.17890i | ||||
\(563\) | −7722.59 | −0.578097 | −0.289048 | − | 0.957315i | \(-0.593339\pi\) | ||||
−0.289048 | + | 0.957315i | \(0.593339\pi\) | |||||||
\(564\) | −3795.25 | + | 2059.82i | −0.283349 | + | 0.153784i | ||||
\(565\) | −8579.27 | −0.638818 | ||||||||
\(566\) | −15848.9 | − | 14588.6i | −1.17699 | − | 1.08340i | ||||
\(567\) | 23434.8 | − | 2047.13i | 1.73575 | − | 0.151625i | ||||
\(568\) | 8734.92 | + | 6796.70i | 0.645262 | + | 0.502083i | ||||
\(569\) | − | 10040.4i | − | 0.739744i | −0.929083 | − | 0.369872i | \(-0.879402\pi\) | ||
0.929083 | − | 0.369872i | \(-0.120598\pi\) | |||||||
\(570\) | −4799.87 | − | 1641.57i | −0.352709 | − | 0.120627i | ||||
\(571\) | 18510.6i | 1.35664i | 0.734764 | + | 0.678322i | \(0.237293\pi\) | ||||
−0.734764 | + | 0.678322i | \(0.762707\pi\) | |||||||
\(572\) | 964.926 | + | 11631.7i | 0.0705342 | + | 0.850258i | ||||
\(573\) | 4539.16 | + | 10317.0i | 0.330936 | + | 0.752176i | ||||
\(574\) | −6478.99 | + | 7038.72i | −0.471129 | + | 0.511830i | ||||
\(575\) | 1821.76 | 0.132126 | ||||||||
\(576\) | −12174.3 | − | 6548.97i | −0.880665 | − | 0.473739i | ||||
\(577\) | 21556.9 | 1.55533 | 0.777664 | − | 0.628680i | \(-0.216404\pi\) | ||||
0.777664 | + | 0.628680i | \(0.216404\pi\) | |||||||
\(578\) | 2610.63 | − | 2836.16i | 0.187868 | − | 0.204098i | ||||
\(579\) | −9060.21 | − | 20592.7i | −0.650310 | − | 1.47807i | ||||
\(580\) | −727.268 | − | 8766.89i | −0.0520658 | − | 0.627630i | ||||
\(581\) | − | 12660.4i | − | 0.904028i | ||||||
\(582\) | 14458.7 | + | 4944.92i | 1.02978 | + | 0.352188i | ||||
\(583\) | − | 17679.3i | − | 1.25592i | ||||||
\(584\) | −5231.83 | − | 4070.92i | −0.370710 | − | 0.288452i | ||||
\(585\) | −4471.29 | − | 4097.73i | −0.316009 | − | 0.289608i | ||||
\(586\) | 19342.1 | + | 17804.0i | 1.36350 | + | 1.25508i | ||||
\(587\) | 7143.54 | 0.502292 | 0.251146 | − | 0.967949i | \(-0.419193\pi\) | ||||
0.251146 | + | 0.967949i | \(0.419193\pi\) | |||||||
\(588\) | 25511.9 | − | 13846.2i | 1.78928 | − | 0.971104i | ||||
\(589\) | −1965.53 | −0.137501 | ||||||||
\(590\) | −4485.16 | − | 4128.50i | −0.312968 | − | 0.288081i | ||||
\(591\) | 10037.8 | − | 4416.32i | 0.698643 | − | 0.307383i | ||||
\(592\) | 9647.17 | − | 1611.68i | 0.669757 | − | 0.111891i | ||||
\(593\) | 8287.65i | 0.573918i | 0.957943 | + | 0.286959i | \(0.0926443\pi\) | ||||
−0.957943 | + | 0.286959i | \(0.907356\pi\) | |||||||
\(594\) | 11312.6 | − | 6171.76i | 0.781417 | − | 0.426314i | ||||
\(595\) | − | 12781.8i | − | 0.880676i | ||||||
\(596\) | −869.162 | + | 72.1024i | −0.0597353 | + | 0.00495542i | ||||
\(597\) | 6968.25 | − | 3065.82i | 0.477707 | − | 0.210177i | ||||
\(598\) | 6271.03 | − | 6812.79i | 0.428832 | − | 0.465879i | ||||
\(599\) | −26207.7 | −1.78767 | −0.893837 | − | 0.448393i | \(-0.851997\pi\) | ||||
−0.893837 | + | 0.448393i | \(0.851997\pi\) | |||||||
\(600\) | −718.001 | + | 2850.35i | −0.0488538 | + | 0.193942i | ||||
\(601\) | 13315.0 | 0.903711 | 0.451855 | − | 0.892091i | \(-0.350762\pi\) | ||||
0.451855 | + | 0.892091i | \(0.350762\pi\) | |||||||
\(602\) | 5971.43 | − | 6487.31i | 0.404282 | − | 0.439208i | ||||
\(603\) | 5776.95 | + | 5294.30i | 0.390142 | + | 0.357547i | ||||
\(604\) | −25403.8 | + | 2107.40i | −1.71137 | + | 0.141969i | ||||
\(605\) | − | 1381.87i | − | 0.0928613i | ||||||
\(606\) | −1466.36 | + | 4287.58i | −0.0982953 | + | 0.287411i | ||||
\(607\) | − | 4763.81i | − | 0.318546i | −0.987235 | − | 0.159273i | \(-0.949085\pi\) | ||
0.987235 | − | 0.159273i | \(-0.0509149\pi\) | |||||||
\(608\) | 10463.0 | + | 6832.32i | 0.697910 | + | 0.455735i | ||||
\(609\) | −14850.5 | − | 33753.3i | −0.988131 | − | 2.24590i | ||||
\(610\) | −1908.05 | − | 1756.32i | −0.126647 | − | 0.116576i | ||||
\(611\) | 4666.86 | 0.309003 | ||||||||
\(612\) | −10478.8 | + | 13527.8i | −0.692122 | + | 0.893514i | ||||
\(613\) | 20511.4 | 1.35146 | 0.675731 | − | 0.737148i | \(-0.263828\pi\) | ||||
0.675731 | + | 0.737148i | \(0.263828\pi\) | |||||||
\(614\) | 4126.63 | + | 3798.47i | 0.271233 | + | 0.249664i | ||||
\(615\) | −1096.68 | − | 2492.63i | −0.0719065 | − | 0.163435i | ||||
\(616\) | 14561.6 | − | 18714.2i | 0.952442 | − | 1.22405i | ||||
\(617\) | 8679.39i | 0.566320i | 0.959073 | + | 0.283160i | \(0.0913827\pi\) | ||||
−0.959073 | + | 0.283160i | \(0.908617\pi\) | |||||||
\(618\) | 1257.24 | − | 3676.11i | 0.0818343 | − | 0.239280i | ||||
\(619\) | − | 20896.1i | − | 1.35684i | −0.734674 | − | 0.678420i | \(-0.762665\pi\) | ||
0.734674 | − | 0.678420i | \(-0.237335\pi\) | |||||||
\(620\) | 94.1559 | + | 1135.01i | 0.00609902 | + | 0.0735209i | ||||
\(621\) | −9680.56 | − | 3287.19i | −0.625551 | − | 0.212416i | ||||
\(622\) | −624.752 | + | 678.725i | −0.0402737 | + | 0.0437530i | ||||
\(623\) | 10853.4 | 0.697968 | ||||||||
\(624\) | 8187.79 | + | 12496.8i | 0.525279 | + | 0.801719i | ||||
\(625\) | 625.000 | 0.0400000 | ||||||||
\(626\) | −2030.29 | + | 2205.68i | −0.129627 | + | 0.140826i | ||||
\(627\) | −10662.5 | + | 4691.18i | −0.679136 | + | 0.298800i | ||||
\(628\) | 680.803 | + | 8206.77i | 0.0432596 | + | 0.521474i | ||||
\(629\) | − | 12106.9i | − | 0.767465i | ||||||
\(630\) | 1045.45 | + | 12277.1i | 0.0661140 | + | 0.776397i | ||||
\(631\) | 5444.29i | 0.343477i | 0.985143 | + | 0.171738i | \(0.0549384\pi\) | ||||
−0.985143 | + | 0.171738i | \(0.945062\pi\) | |||||||
\(632\) | −9120.89 | + | 11721.9i | −0.574066 | + | 0.737773i | ||||
\(633\) | 11419.4 | − | 5024.20i | 0.717030 | − | 0.315472i | ||||
\(634\) | −2097.66 | − | 1930.86i | −0.131402 | − | 0.120953i | ||||
\(635\) | 6981.85 | 0.436325 | ||||||||
\(636\) | −10794.8 | − | 19889.6i | −0.673023 | − | 1.24006i | ||||
\(637\) | −31371.0 | −1.95128 | ||||||||
\(638\) | −14862.9 | − | 13680.9i | −0.922298 | − | 0.848956i | ||||
\(639\) | −8922.80 | + | 9736.22i | −0.552395 | + | 0.602753i | ||||
\(640\) | 3444.15 | − | 6369.19i | 0.212722 | − | 0.393382i | ||||
\(641\) | − | 2664.42i | − | 0.164178i | −0.996625 | − | 0.0820890i | \(-0.973841\pi\) | ||
0.996625 | − | 0.0820890i | \(-0.0261592\pi\) | |||||||
\(642\) | 21718.2 | + | 7427.66i | 1.33512 | + | 0.456615i | ||||
\(643\) | 17860.6i | 1.09542i | 0.836668 | + | 0.547710i | \(0.184500\pi\) | ||||
−0.836668 | + | 0.547710i | \(0.815500\pi\) | |||||||
\(644\) | −18747.2 | + | 1555.20i | −1.14712 | + | 0.0951607i | ||||
\(645\) | 1010.77 | + | 2297.36i | 0.0617039 | + | 0.140246i | ||||
\(646\) | 10475.7 | − | 11380.7i | 0.638017 | − | 0.693136i | ||||
\(647\) | −21691.5 | −1.31805 | −0.659026 | − | 0.752120i | \(-0.729031\pi\) | ||||
−0.659026 | + | 0.752120i | \(0.729031\pi\) | |||||||
\(648\) | 8958.51 | − | 13850.7i | 0.543092 | − | 0.839673i | ||||
\(649\) | −13998.4 | −0.846665 | ||||||||
\(650\) | 2151.43 | − | 2337.29i | 0.129825 | − | 0.141040i | ||||
\(651\) | 1922.62 | + | 4369.88i | 0.115750 | + | 0.263086i | ||||
\(652\) | −1790.29 | + | 148.516i | −0.107535 | + | 0.00892074i | ||||
\(653\) | 5849.05i | 0.350522i | 0.984522 | + | 0.175261i | \(0.0560769\pi\) | ||||
−0.984522 | + | 0.175261i | \(0.943923\pi\) | |||||||
\(654\) | 30292.4 | + | 10360.1i | 1.81120 | + | 0.619437i | ||||
\(655\) | 7552.69i | 0.450547i | ||||||||
\(656\) | 1105.38 | + | 6616.56i | 0.0657892 | + | 0.393801i | ||||
\(657\) | 5344.36 | − | 5831.56i | 0.317356 | − | 0.346287i | ||||
\(658\) | −6975.79 | − | 6421.07i | −0.413290 | − | 0.380425i | ||||
\(659\) | 8922.46 | 0.527420 | 0.263710 | − | 0.964602i | \(-0.415054\pi\) | ||||
0.263710 | + | 0.964602i | \(0.415054\pi\) | |||||||
\(660\) | 3219.72 | + | 5932.39i | 0.189890 | + | 0.349876i | ||||
\(661\) | −2789.76 | −0.164159 | −0.0820796 | − | 0.996626i | \(-0.526156\pi\) | ||||
−0.0820796 | + | 0.996626i | \(0.526156\pi\) | |||||||
\(662\) | −6833.43 | − | 6290.02i | −0.401191 | − | 0.369288i | ||||
\(663\) | 16927.3 | − | 7447.54i | 0.991559 | − | 0.436257i | ||||
\(664\) | −7006.45 | − | 5451.76i | −0.409492 | − | 0.318629i | ||||
\(665\) | − | 11138.0i | − | 0.649493i | ||||||
\(666\) | 990.254 | + | 11628.9i | 0.0576150 | + | 0.676591i | ||||
\(667\) | 16026.0i | 0.930331i | ||||||||
\(668\) | 634.418 | + | 7647.62i | 0.0367460 | + | 0.442957i | ||||
\(669\) | 5836.82 | − | 2568.03i | 0.337316 | − | 0.148409i | ||||
\(670\) | −2779.66 | + | 3019.80i | −0.160280 | + | 0.174127i | ||||
\(671\) | −5955.11 | −0.342615 | ||||||||
\(672\) | 4955.46 | − | 29945.1i | 0.284466 | − | 1.71898i | ||||
\(673\) | −18308.8 | −1.04867 | −0.524334 | − | 0.851513i | \(-0.675686\pi\) | ||||
−0.524334 | + | 0.851513i | \(0.675686\pi\) | |||||||
\(674\) | 20700.3 | − | 22488.6i | 1.18300 | − | 1.28520i | ||||
\(675\) | −3321.15 | − | 1127.75i | −0.189380 | − | 0.0643068i | ||||
\(676\) | 118.175 | + | 1424.55i | 0.00672368 | + | 0.0810510i | ||||
\(677\) | − | 10293.0i | − | 0.584330i | −0.956368 | − | 0.292165i | \(-0.905624\pi\) | ||
0.956368 | − | 0.292165i | \(-0.0943756\pi\) | |||||||
\(678\) | −8160.49 | + | 23860.9i | −0.462245 | + | 1.35158i | ||||
\(679\) | 33551.2i | 1.89628i | ||||||||
\(680\) | −7073.65 | − | 5504.05i | −0.398915 | − | 0.310398i | ||||
\(681\) | 12564.8 | + | 28558.2i | 0.707025 | + | 1.60698i | ||||
\(682\) | 1924.22 | + | 1771.21i | 0.108039 | + | 0.0994472i | ||||
\(683\) | −21101.1 | −1.18215 | −0.591077 | − | 0.806615i | \(-0.701297\pi\) | ||||
−0.591077 | + | 0.806615i | \(0.701297\pi\) | |||||||
\(684\) | −9131.15 | + | 11788.1i | −0.510436 | + | 0.658960i | ||||
\(685\) | −2708.94 | −0.151100 | ||||||||
\(686\) | 23858.4 | + | 21961.1i | 1.32787 | + | 1.22227i | ||||
\(687\) | 7136.97 | + | 16221.5i | 0.396350 | + | 0.900856i | ||||
\(688\) | −1018.78 | − | 6098.23i | −0.0564546 | − | 0.337926i | ||||
\(689\) | 24457.5i | 1.35233i | ||||||||
\(690\) | 1732.84 | − | 5066.74i | 0.0956058 | − | 0.279547i | ||||
\(691\) | − | 17707.2i | − | 0.974841i | −0.873167 | − | 0.487420i | \(-0.837938\pi\) | ||
0.873167 | − | 0.487420i | \(-0.162062\pi\) | |||||||
\(692\) | −14505.8 | + | 1203.35i | −0.796863 | + | 0.0661048i | ||||
\(693\) | 20859.4 | + | 19116.7i | 1.14341 | + | 1.04788i | ||||
\(694\) | −8155.64 | + | 8860.22i | −0.446086 | + | 0.484624i | ||||
\(695\) | −3569.00 | −0.194791 | ||||||||
\(696\) | −25074.5 | − | 6316.26i | −1.36558 | − | 0.343990i | ||||
\(697\) | 8303.61 | 0.451251 | ||||||||
\(698\) | 3259.92 | − | 3541.55i | 0.176776 | − | 0.192048i | ||||
\(699\) | 30055.8 | − | 13223.7i | 1.62634 | − | 0.715544i | ||||
\(700\) | −6431.70 | + | 533.550i | −0.347279 | + | 0.0288090i | ||||
\(701\) | 390.697i | 0.0210505i | 0.999945 | + | 0.0105253i | \(0.00335035\pi\) | ||||
−0.999945 | + | 0.0105253i | \(0.996650\pi\) | |||||||
\(702\) | −15649.8 | + | 8537.98i | −0.841400 | + | 0.459039i | ||||
\(703\) | − | 10549.9i | − | 0.566000i | ||||||
\(704\) | −4086.24 | − | 16117.3i | −0.218759 | − | 0.862844i | ||||
\(705\) | 2470.34 | − | 1086.88i | 0.131970 | − | 0.0580627i | ||||
\(706\) | −7926.53 | − | 7296.20i | −0.422548 | − | 0.388946i | ||||
\(707\) | −9949.25 | −0.529250 | ||||||||
\(708\) | −15748.5 | + | 8547.29i | −0.835969 | + | 0.453710i | ||||
\(709\) | 3068.89 | 0.162559 | 0.0812797 | − | 0.996691i | \(-0.474099\pi\) | ||||
0.0812797 | + | 0.996691i | \(0.474099\pi\) | |||||||
\(710\) | −5089.45 | − | 4684.73i | −0.269019 | − | 0.247626i | ||||
\(711\) | −13065.6 | − | 11974.0i | −0.689168 | − | 0.631591i | ||||
\(712\) | 4673.67 | − | 6006.47i | 0.246002 | − | 0.316154i | ||||
\(713\) | − | 2074.81i | − | 0.108979i | ||||||
\(714\) | −35549.1 | − | 12157.9i | −1.86329 | − | 0.637251i | ||||
\(715\) | − | 7294.81i | − | 0.381553i | ||||||
\(716\) | −527.649 | − | 6360.57i | −0.0275407 | − | 0.331991i | ||||
\(717\) | 7457.53 | + | 16950.1i | 0.388433 | + | 0.882861i | ||||
\(718\) | 6106.50 | − | 6634.05i | 0.317399 | − | 0.344819i | ||||
\(719\) | 4167.04 | 0.216139 | 0.108070 | − | 0.994143i | \(-0.465533\pi\) | ||||
0.108070 | + | 0.994143i | \(0.465533\pi\) | |||||||
\(720\) | 7244.52 | + | 4708.14i | 0.374982 | + | 0.243697i | ||||
\(721\) | 8530.35 | 0.440620 | ||||||||
\(722\) | −4010.28 | + | 4356.74i | −0.206714 | + | 0.224572i | ||||
\(723\) | 5929.96 | + | 13478.1i | 0.305031 | + | 0.693299i | ||||
\(724\) | −1252.14 | − | 15094.0i | −0.0642754 | − | 0.774811i | ||||
\(725\) | 5498.13i | 0.281649i | ||||||||
\(726\) | −3843.30 | − | 1314.42i | −0.196472 | − | 0.0671938i | ||||
\(727\) | − | 36845.2i | − | 1.87966i | −0.341640 | − | 0.939831i | \(-0.610982\pi\) | ||
0.341640 | − | 0.939831i | \(-0.389018\pi\) | |||||||
\(728\) | −20144.5 | + | 25889.1i | −1.02555 | + | 1.31801i | ||||
\(729\) | 15613.2 | + | 11985.4i | 0.793232 | + | 0.608920i | ||||
\(730\) | 3048.35 | + | 2805.94i | 0.154554 | + | 0.142264i | ||||
\(731\) | −7653.12 | −0.387224 | ||||||||
\(732\) | −6699.64 | + | 3636.13i | −0.338286 | + | 0.183600i | ||||
\(733\) | 8332.32 | 0.419865 | 0.209933 | − | 0.977716i | \(-0.432676\pi\) | ||||
0.209933 | + | 0.977716i | \(0.432676\pi\) | |||||||
\(734\) | −22297.8 | − | 20524.7i | −1.12129 | − | 1.03213i | ||||
\(735\) | −16605.8 | + | 7306.07i | −0.833353 | + | 0.366651i | ||||
\(736\) | −7212.20 | + | 11044.7i | −0.361203 | + | 0.553143i | ||||
\(737\) | 9424.96i | 0.471062i | ||||||||
\(738\) | −7975.72 | + | 679.171i | −0.397819 | + | 0.0338762i | ||||
\(739\) | 29386.0i | 1.46276i | 0.681970 | + | 0.731381i | \(0.261124\pi\) | ||||
−0.681970 | + | 0.731381i | \(0.738876\pi\) | |||||||
\(740\) | −6092.12 | + | 505.379i | −0.302636 | + | 0.0251056i | ||||
\(741\) | 14750.4 | − | 6489.75i | 0.731269 | − | 0.321737i | ||||
\(742\) | 33650.6 | − | 36557.8i | 1.66490 | − | 1.80873i | ||||
\(743\) | −15195.8 | −0.750311 | −0.375155 | − | 0.926962i | \(-0.622411\pi\) | ||||
−0.375155 | + | 0.926962i | \(0.622411\pi\) | |||||||
\(744\) | 3246.27 | + | 817.735i | 0.159965 | + | 0.0402952i | ||||
\(745\) | 545.092 | 0.0268062 | ||||||||
\(746\) | 25831.3 | − | 28062.9i | 1.26777 | − | 1.37729i | ||||
\(747\) | 7157.15 | − | 7809.61i | 0.350557 | − | 0.382515i | ||||
\(748\) | −20511.0 | + | 1701.52i | −1.00262 | + | 0.0831732i | ||||
\(749\) | 50396.6i | 2.45854i | ||||||||
\(750\) | 594.492 | − | 1738.27i | 0.0289437 | − | 0.0846301i | ||||
\(751\) | 4230.63i | 0.205563i | 0.994704 | + | 0.102782i | \(0.0327742\pi\) | ||||
−0.994704 | + | 0.102782i | \(0.967226\pi\) | |||||||
\(752\) | −6557.42 | + | 1095.50i | −0.317984 | + | 0.0531232i | ||||
\(753\) | −8089.55 | − | 18386.6i | −0.391500 | − | 0.889833i | ||||
\(754\) | 20561.2 | + | 18926.1i | 0.993096 | + | 0.914124i | ||||
\(755\) | 15931.9 | 0.767976 | ||||||||
\(756\) | 35139.8 | + | 8770.16i | 1.69050 | + | 0.421915i | ||||
\(757\) | 15946.8 | 0.765649 | 0.382825 | − | 0.923821i | \(-0.374951\pi\) | ||||
0.382825 | + | 0.923821i | \(0.374951\pi\) | |||||||
\(758\) | 30300.8 | + | 27891.2i | 1.45194 | + | 1.33648i | ||||
\(759\) | −4952.01 | − | 11255.3i | −0.236820 | − | 0.538264i | ||||
\(760\) | −6163.94 | − | 4796.21i | −0.294197 | − | 0.228917i | ||||
\(761\) | − | 6461.80i | − | 0.307806i | −0.988086 | − | 0.153903i | \(-0.950816\pi\) | ||
0.988086 | − | 0.153903i | \(-0.0491843\pi\) | |||||||
\(762\) | 6641.05 | − | 19418.1i | 0.315722 | − | 0.923156i | ||||
\(763\) | 70293.0i | 3.33523i | ||||||||
\(764\) | 1434.64 | + | 17294.0i | 0.0679367 | + | 0.818946i | ||||
\(765\) | 7225.79 | − | 7884.51i | 0.341502 | − | 0.372634i | ||||
\(766\) | −24458.9 | + | 26571.9i | −1.15370 | + | 1.25337i | ||||
\(767\) | 19365.3 | 0.911657 | ||||||||
\(768\) | −14438.2 | − | 15637.3i | −0.678375 | − | 0.734715i | ||||
\(769\) | −28578.2 | −1.34013 | −0.670064 | − | 0.742304i | \(-0.733733\pi\) | ||||
−0.670064 | + | 0.742304i | \(0.733733\pi\) | |||||||
\(770\) | −10036.8 | + | 10903.9i | −0.469743 | + | 0.510325i | ||||
\(771\) | 14080.7 | − | 6195.09i | 0.657722 | − | 0.289378i | ||||
\(772\) | −2863.56 | − | 34519.0i | −0.133500 | − | 1.60928i | ||||
\(773\) | − | 31061.7i | − | 1.44530i | −0.691216 | − | 0.722648i | \(-0.742925\pi\) | ||
0.691216 | − | 0.722648i | \(-0.257075\pi\) | |||||||
\(774\) | 7350.91 | − | 625.966i | 0.341374 | − | 0.0290696i | ||||
\(775\) | − | 711.816i | − | 0.0329925i | ||||||
\(776\) | 18567.8 | + | 14447.7i | 0.858948 | + | 0.668353i | ||||
\(777\) | −23455.2 | + | 10319.6i | −1.08295 | + | 0.476466i | ||||
\(778\) | 3359.92 | + | 3092.74i | 0.154832 | + | 0.142519i | ||||
\(779\) | 7235.73 | 0.332794 | ||||||||
\(780\) | −4454.14 | − | 8206.83i | −0.204466 | − | 0.376733i | ||||
\(781\) | −15884.4 | −0.727771 | ||||||||
\(782\) | 12013.4 | + | 11058.1i | 0.549360 | + | 0.505674i | ||||
\(783\) | 9920.82 | − | 29216.2i | 0.452799 | − | 1.33346i | ||||
\(784\) | 44079.4 | − | 7364.00i | 2.00799 | − | 0.335459i | ||||
\(785\) | − | 5146.85i | − | 0.234011i | ||||||
\(786\) | 21005.8 | + | 7184.03i | 0.953246 | + | 0.326013i | ||||
\(787\) | 14851.0i | 0.672657i | 0.941745 | + | 0.336328i | \(0.109185\pi\) | ||||
−0.941745 | + | 0.336328i | \(0.890815\pi\) | |||||||
\(788\) | 16826.0 | − | 1395.82i | 0.760661 | − | 0.0631016i | ||||
\(789\) | −13717.8 | − | 31178.9i | −0.618969 | − | 1.40684i | ||||
\(790\) | 6286.71 | − | 6829.83i | 0.283128 | − | 0.307588i | ||||
\(791\) | −55368.8 | −2.48886 | ||||||||
\(792\) | 19561.9 | − | 3311.97i | 0.877654 | − | 0.148593i | ||||
\(793\) | 8238.26 | 0.368915 | ||||||||
\(794\) | 6448.89 | − | 7006.02i | 0.288240 | − | 0.313141i | ||||
\(795\) | 5695.96 | + | 12946.2i | 0.254107 | + | 0.577554i | ||||
\(796\) | 11680.7 | − | 968.983i | 0.520113 | − | 0.0431466i | ||||
\(797\) | − | 19580.3i | − | 0.870226i | −0.900376 | − | 0.435113i | \(-0.856708\pi\) | ||
0.900376 | − | 0.435113i | \(-0.143292\pi\) | |||||||
\(798\) | −30977.3 | − | 10594.3i | −1.37417 | − | 0.469969i | ||||
\(799\) | 8229.38i | 0.364374i | ||||||||
\(800\) | −2474.32 | + | 3789.16i | −0.109351 | + | 0.167459i | ||||
\(801\) | 6695.00 | + | 6135.66i | 0.295326 | + | 0.270653i | ||||
\(802\) | −4337.76 | − | 3992.82i | −0.190987 | − | 0.175800i | ||||
\(803\) | 9514.06 | 0.418112 | ||||||||
\(804\) | 5754.79 | + | 10603.3i | 0.252432 | + | 0.465111i | ||||
\(805\) | 11757.3 | 0.514769 | ||||||||
\(806\) | −2661.96 | − | 2450.27i | −0.116332 | − | 0.107081i | ||||
\(807\) | −41384.9 | + | 18208.1i | −1.80523 | + | 0.794246i | ||||
\(808\) | −4284.31 | + | 5506.07i | −0.186537 | + | 0.239731i | ||||
\(809\) | 22199.3i | 0.964754i | 0.875964 | + | 0.482377i | \(0.160226\pi\) | ||||
−0.875964 | + | 0.482377i | \(0.839774\pi\) | |||||||
\(810\) | −6295.57 | + | 8164.19i | −0.273091 | + | 0.354149i | ||||
\(811\) | 16803.2i | 0.727547i | 0.931488 | + | 0.363773i | \(0.118512\pi\) | ||||
−0.931488 | + | 0.363773i | \(0.881488\pi\) | |||||||
\(812\) | −4693.64 | − | 56579.7i | −0.202850 | − | 2.44527i | ||||
\(813\) | −9637.51 | + | 4240.22i | −0.415747 | + | 0.182917i | ||||
\(814\) | −9506.90 | + | 10328.2i | −0.409357 | + | 0.444722i | ||||
\(815\) | 1122.77 | 0.0482565 | ||||||||
\(816\) | −22036.4 | + | 14438.1i | −0.945378 | + | 0.619403i | ||||
\(817\) | −6668.89 | −0.285575 | ||||||||
\(818\) | −17255.5 | + | 18746.3i | −0.737562 | + | 0.801280i | ||||
\(819\) | −28856.8 | − | 26445.9i | −1.23118 | − | 1.12832i | ||||
\(820\) | −346.617 | − | 4178.31i | −0.0147615 | − | 0.177943i | ||||
\(821\) | − | 3573.41i | − | 0.151904i | −0.997111 | − | 0.0759519i | \(-0.975800\pi\) | ||
0.997111 | − | 0.0759519i | \(-0.0241995\pi\) | |||||||
\(822\) | −2576.71 | + | 7534.19i | −0.109335 | + | 0.319690i | ||||
\(823\) | − | 9176.02i | − | 0.388646i | −0.980938 | − | 0.194323i | \(-0.937749\pi\) | ||
0.980938 | − | 0.194323i | \(-0.0622510\pi\) | |||||||
\(824\) | 3673.31 | − | 4720.83i | 0.155298 | − | 0.199585i | ||||
\(825\) | −1698.91 | − | 3861.41i | −0.0716951 | − | 0.162954i | ||||
\(826\) | −28946.3 | − | 26644.5i | −1.21933 | − | 1.12237i | ||||
\(827\) | 14278.9 | 0.600394 | 0.300197 | − | 0.953877i | \(-0.402948\pi\) | ||||
0.300197 | + | 0.953877i | \(0.402948\pi\) | |||||||
\(828\) | −12443.5 | − | 9638.84i | −0.522273 | − | 0.404557i | ||||
\(829\) | 20720.7 | 0.868105 | 0.434052 | − | 0.900888i | \(-0.357083\pi\) | ||||
0.434052 | + | 0.900888i | \(0.357083\pi\) | |||||||
\(830\) | 4082.35 | + | 3757.71i | 0.170723 | + | 0.157147i | ||||
\(831\) | −12974.2 | − | 29488.7i | −0.541599 | − | 1.23099i | ||||
\(832\) | 5652.89 | + | 22296.5i | 0.235551 | + | 0.929078i | ||||
\(833\) | − | 55318.4i | − | 2.30092i | ||||||
\(834\) | −3394.79 | + | 9926.21i | −0.140949 | + | 0.412130i | ||||
\(835\) | − | 4796.18i | − | 0.198777i | ||||||
\(836\) | −17873.2 | + | 1482.69i | −0.739422 | + | 0.0613397i | ||||
\(837\) | −1284.40 | + | 3782.48i | −0.0530411 | + | 0.156203i | ||||
\(838\) | 16845.9 | − | 18301.2i | 0.694428 | − | 0.754420i | ||||
\(839\) | 26785.4 | 1.10219 | 0.551094 | − | 0.834443i | \(-0.314211\pi\) | ||||
0.551094 | + | 0.834443i | \(0.314211\pi\) | |||||||
\(840\) | −4633.83 | + | 18395.5i | −0.190336 | + | 0.755603i | ||||
\(841\) | −23978.1 | −0.983150 | ||||||||
\(842\) | −9380.51 | + | 10190.9i | −0.383935 | + | 0.417104i | ||||
\(843\) | 38998.4 | − | 17158.1i | 1.59333 | − | 0.701017i | ||||
\(844\) | 19142.0 | − | 1587.95i | 0.780680 | − | 0.0647622i | ||||
\(845\) | − | 893.403i | − | 0.0363716i | ||||||
\(846\) | −673.100 | − | 7904.42i | −0.0273542 | − | 0.321229i | ||||
\(847\) | − | 8918.31i | − | 0.361791i | ||||||
\(848\) | −5741.12 | − | 34365.2i | −0.232489 | − | 1.39163i | ||||
\(849\) | 36222.4 | − | 15936.8i | 1.46425 | − | 0.644229i | ||||
\(850\) | 4121.50 | + | 3793.75i | 0.166313 | + | 0.153088i | ||||
\(851\) | 11136.5 | 0.448595 | ||||||||
\(852\) | −17870.3 | + | 9698.87i | −0.718577 | + | 0.389998i | ||||
\(853\) | −20065.4 | −0.805425 | −0.402713 | − | 0.915326i | \(-0.631933\pi\) | ||||
−0.402713 | + | 0.915326i | \(0.631933\pi\) | |||||||
\(854\) | −12314.1 | − | 11334.9i | −0.493421 | − | 0.454183i | ||||
\(855\) | 6296.52 | − | 6870.53i | 0.251856 | − | 0.274815i | ||||
\(856\) | 27890.3 | + | 21701.6i | 1.11363 | + | 0.866525i | ||||
\(857\) | − | 1780.43i | − | 0.0709664i | −0.999370 | − | 0.0354832i | \(-0.988703\pi\) | ||
0.999370 | − | 0.0354832i | \(-0.0112970\pi\) | |||||||
\(858\) | −20288.6 | − | 6938.74i | −0.807272 | − | 0.276089i | ||||
\(859\) | − | 27394.4i | − | 1.08811i | −0.839050 | − | 0.544054i | \(-0.816889\pi\) | ||
0.839050 | − | 0.544054i | \(-0.183111\pi\) | |||||||
\(860\) | 319.464 | + | 3850.99i | 0.0126670 | + | 0.152695i | ||||
\(861\) | −7077.76 | − | 16086.9i | −0.280150 | − | 0.636748i | ||||
\(862\) | −22790.9 | + | 24759.8i | −0.900534 | + | 0.978332i | ||||
\(863\) | 39367.0 | 1.55280 | 0.776400 | − | 0.630240i | \(-0.217043\pi\) | ||||
0.776400 | + | 0.630240i | \(0.217043\pi\) | |||||||
\(864\) | 19985.3 | − | 15670.3i | 0.786938 | − | 0.617032i | ||||
\(865\) | 9097.29 | 0.357592 | ||||||||
\(866\) | −2240.00 | + | 2433.52i | −0.0878965 | + | 0.0954900i | ||||
\(867\) | 2851.90 | + | 6482.02i | 0.111713 | + | 0.253911i | ||||
\(868\) | 607.662 | + | 7325.09i | 0.0237620 | + | 0.286440i | ||||
\(869\) | − | 21316.2i | − | 0.832110i | ||||||
\(870\) | 15291.6 | + | 5229.75i | 0.595899 | + | 0.203799i | ||||
\(871\) | − | 13038.4i | − | 0.507222i | ||||||
\(872\) | 38901.3 | + | 30269.3i | 1.51074 | + | 1.17552i | ||||
\(873\) | −18967.1 | + | 20696.2i | −0.735327 | + | 0.802361i | ||||
\(874\) | 10468.4 | + | 9635.98i | 0.405149 | + | 0.372931i | ||||
\(875\) | 4033.62 | 0.155841 | ||||||||
\(876\) | 10703.5 | − | 5809.19i | 0.412830 | − | 0.224058i | ||||
\(877\) | −32232.4 | −1.24106 | −0.620530 | − | 0.784183i | \(-0.713082\pi\) | ||||
−0.620530 | + | 0.784183i | \(0.713082\pi\) | |||||||
\(878\) | −14123.1 | − | 13000.0i | −0.542862 | − | 0.499693i | ||||
\(879\) | −44206.0 | + | 19449.4i | −1.69628 | + | 0.746315i | ||||
\(880\) | 1712.38 | + | 10249.9i | 0.0655958 | + | 0.392643i | ||||
\(881\) | 35922.0i | 1.37372i | 0.726791 | + | 0.686858i | \(0.241011\pi\) | ||||
−0.726791 | + | 0.686858i | \(0.758989\pi\) | |||||||
\(882\) | 4524.62 | + | 53134.0i | 0.172735 | + | 2.02848i | ||||
\(883\) | − | 33930.5i | − | 1.29315i | −0.762851 | − | 0.646575i | \(-0.776201\pi\) | ||
0.762851 | − | 0.646575i | \(-0.223799\pi\) | |||||||
\(884\) | 28374.8 | − | 2353.87i | 1.07958 | − | 0.0895578i | ||||
\(885\) | 10250.8 | − | 4510.04i | 0.389352 | − | 0.171303i | ||||
\(886\) | 17400.5 | − | 18903.8i | 0.659800 | − | 0.716801i | ||||
\(887\) | −6145.77 | −0.232643 | −0.116322 | − | 0.993212i | \(-0.537110\pi\) | ||||
−0.116322 | + | 0.993212i | \(0.537110\pi\) | |||||||
\(888\) | −4389.17 | + | 17424.3i | −0.165868 | + | 0.658470i | ||||
\(889\) | 45059.4 | 1.69994 | ||||||||
\(890\) | −3221.40 | + | 3499.70i | −0.121328 | + | 0.131809i | ||||
\(891\) | 2060.20 | + | 23584.5i | 0.0774628 | + | 0.886767i | ||||
\(892\) | 9784.08 | − | 811.651i | 0.367259 | − | 0.0304665i | ||||
\(893\) | 7171.04i | 0.268723i | ||||||||
\(894\) | 518.485 | − | 1516.03i | 0.0193968 | − | 0.0567153i | ||||
\(895\) | 3989.01i | 0.148981i | ||||||||
\(896\) | 22227.8 | − | 41105.4i | 0.828771 | − | 1.53263i | ||||
\(897\) | 6850.58 | + | 15570.5i | 0.254999 | + | 0.579582i | ||||
\(898\) | −6690.44 | − | 6158.41i | −0.248622 | − | 0.228852i | ||||
\(899\) | 6261.85 | 0.232307 | ||||||||
\(900\) | −4269.05 | − | 3306.84i | −0.158113 | − | 0.122476i | ||||
\(901\) | −43127.4 | −1.59465 | ||||||||
\(902\) | −7083.66 | − | 6520.36i | −0.261486 | − | 0.240692i | ||||
\(903\) | 6523.30 | + | 14826.7i | 0.240401 | + | 0.546402i | ||||
\(904\) | −23842.7 | + | 30642.0i | −0.877209 | + | 1.12736i | ||||
\(905\) | 9466.13i | 0.347696i | ||||||||
\(906\) | 15154.2 | − | 44310.3i | 0.555702 | − | 1.62485i | ||||
\(907\) | − | 16054.2i | − | 0.587731i | −0.955847 | − | 0.293866i | \(-0.905058\pi\) | ||
0.955847 | − | 0.293866i | \(-0.0949418\pi\) | |||||||
\(908\) | 3971.22 | + | 47871.3i | 0.145143 | + | 1.74963i | ||||
\(909\) | −6137.24 | − | 5624.50i | −0.223938 | − | 0.205229i | ||||
\(910\) | 13884.9 | − | 15084.4i | 0.505801 | − | 0.549498i | ||||
\(911\) | 5066.28 | 0.184252 | 0.0921259 | − | 0.995747i | \(-0.470634\pi\) | ||||
0.0921259 | + | 0.995747i | \(0.470634\pi\) | |||||||
\(912\) | −19202.4 | + | 12581.3i | −0.697210 | + | 0.456806i | ||||
\(913\) | 12741.2 | 0.461853 | ||||||||
\(914\) | −23636.6 | + | 25678.6i | −0.855393 | + | 0.929291i | ||||
\(915\) | 4360.82 | − | 1918.63i | 0.157556 | − | 0.0693202i | ||||
\(916\) | 2255.71 | + | 27191.5i | 0.0813654 | + | 0.980823i | ||||
\(917\) | 48743.5i | 1.75535i | ||||||||
\(918\) | −15055.6 | − | 27596.2i | −0.541294 | − | 0.992170i | ||||
\(919\) | 3167.51i | 0.113696i | 0.998383 | + | 0.0568480i | \(0.0181050\pi\) | ||||
−0.998383 | + | 0.0568480i | \(0.981895\pi\) | |||||||
\(920\) | 5062.88 | − | 6506.66i | 0.181433 | − | 0.233172i | ||||
\(921\) | −9431.36 | + | 4149.52i | −0.337431 | + | 0.148460i | ||||
\(922\) | 25052.8 | + | 23060.6i | 0.894871 | + | 0.823709i | ||||
\(923\) | 21974.4 | 0.783637 | ||||||||
\(924\) | 20779.4 | + | 38286.4i | 0.739818 | + | 1.36313i | ||||
\(925\) | 3820.65 | 0.135808 | ||||||||
\(926\) | −5165.06 | − | 4754.33i | −0.183299 | − | 0.168722i | ||||
\(927\) | 5261.99 | + | 4822.37i | 0.186436 | + | 0.170860i | ||||
\(928\) | −33333.3 | − | 21766.6i | −1.17911 | − | 0.769961i | ||||
\(929\) | − | 11889.1i | − | 0.419880i | −0.977714 | − | 0.209940i | \(-0.932673\pi\) | ||
0.977714 | − | 0.209940i | \(-0.0673269\pi\) | |||||||
\(930\) | −1979.72 | − | 677.070i | −0.0698040 | − | 0.0238731i | ||||
\(931\) | − | 48204.2i | − | 1.69692i | ||||||
\(932\) | 50381.6 | − | 4179.47i | 1.77071 | − | 0.146892i | ||||
\(933\) | −682.490 | − | 1551.22i | −0.0239482 | − | 0.0544315i | ||||
\(934\) | 3058.49 | − | 3322.72i | 0.107149 | − | 0.116405i | ||||
\(935\) | 12863.4 | 0.449923 | ||||||||
\(936\) | −27061.8 | + | 4581.75i | −0.945024 | + | 0.159999i | ||||
\(937\) | −34124.2 | −1.18974 | −0.594871 | − | 0.803822i | \(-0.702797\pi\) | ||||
−0.594871 | + | 0.803822i | \(0.702797\pi\) | |||||||
\(938\) | −17939.4 | + | 19489.2i | −0.624458 | + | 0.678405i | ||||
\(939\) | −2217.92 | − | 5041.06i | −0.0770810 | − | 0.175196i | ||||
\(940\) | 4140.96 | − | 343.518i | 0.143684 | − | 0.0119195i | ||||
\(941\) | 35775.5i | 1.23937i | 0.784851 | + | 0.619685i | \(0.212740\pi\) | ||||
−0.784851 | + | 0.619685i | \(0.787260\pi\) | |||||||
\(942\) | −14314.6 | − | 4895.62i | −0.495111 | − | 0.169329i | ||||
\(943\) | 7638.03i | 0.263763i | ||||||||
\(944\) | −27210.2 | + | 4545.80i | −0.938154 | + | 0.156730i | ||||
\(945\) | −21434.0 | − | 7278.26i | −0.737830 | − | 0.250542i | ||||
\(946\) | 6528.74 | + | 6009.56i | 0.224384 | + | 0.206541i | ||||
\(947\) | −1532.43 | −0.0525841 | −0.0262921 | − | 0.999654i | \(-0.508370\pi\) | ||||
−0.0262921 | + | 0.999654i | \(0.508370\pi\) | |||||||
\(948\) | −13015.5 | − | 23981.3i | −0.445911 | − | 0.821598i | ||||
\(949\) | −13161.7 | −0.450207 | ||||||||
\(950\) | 3591.46 | + | 3305.86i | 0.122655 | + | 0.112901i | ||||
\(951\) | 4794.18 | − | 2109.30i | 0.163472 | − | 0.0719230i | ||||
\(952\) | −45651.8 | − | 35522.0i | −1.55419 | − | 1.20932i | ||||
\(953\) | − | 50714.5i | − | 1.72382i | −0.507060 | − | 0.861911i | \(-0.669268\pi\) | ||
0.507060 | − | 0.861911i | \(-0.330732\pi\) | |||||||
\(954\) | 41424.4 | − | 3527.49i | 1.40583 | − | 0.119713i | ||||
\(955\) | − | 10845.9i | − | 0.367502i | ||||||
\(956\) | 2357.02 | + | 28412.8i | 0.0797401 | + | 0.961231i | ||||
\(957\) | 33968.9 | − | 14945.3i | 1.14740 | − | 0.504821i | ||||
\(958\) | −26192.9 | + | 28455.7i | −0.883355 | + | 0.959669i | ||||
\(959\) | −17483.0 | −0.588690 | ||||||||
\(960\) | 8184.98 | + | 10485.9i | 0.275176 | + | 0.352531i | ||||
\(961\) | 28980.3 | 0.972787 | ||||||||
\(962\) | 13151.8 | − | 14288.0i | 0.440780 | − | 0.478860i | ||||
\(963\) | −28490.1 | + | 31087.4i | −0.953356 | + | 1.04027i | ||||
\(964\) | 1874.22 | + | 22592.9i | 0.0626189 | + | 0.754842i | ||||
\(965\) | 21648.5i | 0.722165i | ||||||||
\(966\) | 11183.4 | − | 32699.7i | 0.372483 | − | 1.08912i | ||||
\(967\) | − | 45357.2i | − | 1.50837i | −0.656664 | − | 0.754183i | \(-0.728033\pi\) | ||
0.656664 | − | 0.754183i | \(-0.271967\pi\) | |||||||
\(968\) | −4935.54 | − | 3840.37i | −0.163878 | − | 0.127515i | ||||
\(969\) | 11443.8 | + | 26010.3i | 0.379388 | + | 0.862304i | ||||
\(970\) | −10818.6 | − | 9958.30i | −0.358108 | − | 0.329631i | ||||
\(971\) | −33985.9 | −1.12323 | −0.561616 | − | 0.827398i | \(-0.689820\pi\) | ||||
−0.561616 | + | 0.827398i | \(0.689820\pi\) | |||||||
\(972\) | 16718.2 | + | 25275.1i | 0.551684 | + | 0.834053i | ||||
\(973\) | −23033.6 | −0.758913 | ||||||||
\(974\) | −5644.82 | − | 5195.93i | −0.185700 | − | 0.170933i | ||||
\(975\) | 2350.26 | + | 5341.86i | 0.0771985 | + | 0.175463i | ||||
\(976\) | −11575.6 | + | 1933.84i | −0.379637 | + | 0.0634230i | ||||
\(977\) | − | 24747.5i | − | 0.810382i | −0.914232 | − | 0.405191i | \(-0.867205\pi\) | ||
0.914232 | − | 0.405191i | \(-0.132795\pi\) | |||||||
\(978\) | 1067.97 | − | 3122.69i | 0.0349181 | − | 0.102099i | ||||
\(979\) | 10922.7i | 0.356581i | ||||||||
\(980\) | −27835.8 | + | 2309.15i | −0.907329 | + | 0.0752686i | ||||
\(981\) | −39738.0 | + | 43360.6i | −1.29331 | + | 1.41121i | ||||
\(982\) | −14935.9 | + | 16226.2i | −0.485359 | + | 0.527290i | ||||
\(983\) | −37535.3 | −1.21789 | −0.608947 | − | 0.793211i | \(-0.708408\pi\) | ||||
−0.608947 | + | 0.793211i | \(0.708408\pi\) | |||||||
\(984\) | −11950.5 | − | 3010.34i | −0.387164 | − | 0.0975265i | ||||
\(985\) | −10552.4 | −0.341346 | ||||||||
\(986\) | −33373.7 | + | 36256.9i | −1.07792 | + | 1.17105i | ||||
\(987\) | 15943.1 | − | 7014.49i | 0.514158 | − | 0.226214i | ||||
\(988\) | 24725.7 | − | 2051.15i | 0.796182 | − | 0.0660483i | ||||
\(989\) | − | 7039.68i | − | 0.226339i | ||||||
\(990\) | −12355.5 | + | 1052.13i | −0.396649 | + | 0.0337766i | ||||
\(991\) | 41257.7i | 1.32250i | 0.750167 | + | 0.661248i | \(0.229973\pi\) | ||||
−0.750167 | + | 0.661248i | \(0.770027\pi\) | |||||||
\(992\) | 4315.49 | + | 2818.02i | 0.138122 | + | 0.0901937i | ||||
\(993\) | 15617.7 | − | 6871.33i | 0.499107 | − | 0.219592i | ||||
\(994\) | −32846.2 | − | 30234.3i | −1.04811 | − | 0.964761i | ||||
\(995\) | −7325.48 | −0.233400 | ||||||||
\(996\) | 14334.1 | − | 7779.65i | 0.456019 | − | 0.247498i | ||||
\(997\) | 27189.9 | 0.863704 | 0.431852 | − | 0.901945i | \(-0.357860\pi\) | ||||
0.431852 | + | 0.901945i | \(0.357860\pi\) | |||||||
\(998\) | 21726.6 | + | 19998.9i | 0.689121 | + | 0.634321i | ||||
\(999\) | −20302.4 | − | 6893.99i | −0.642981 | − | 0.218334i |
(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 | 60.4.e.a.11.8 | yes | 24 | |
3.2 | odd | 2 | inner | 60.4.e.a.11.17 | yes | 24 | |
4.3 | odd | 2 | inner | 60.4.e.a.11.18 | yes | 24 | |
8.3 | odd | 2 | 960.4.h.d.191.7 | 24 | |||
8.5 | even | 2 | 960.4.h.d.191.18 | 24 | |||
12.11 | even | 2 | inner | 60.4.e.a.11.7 | ✓ | 24 | |
24.5 | odd | 2 | 960.4.h.d.191.8 | 24 | |||
24.11 | even | 2 | 960.4.h.d.191.17 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
60.4.e.a.11.7 | ✓ | 24 | 12.11 | even | 2 | inner | |
60.4.e.a.11.8 | yes | 24 | 1.1 | even | 1 | trivial | |
60.4.e.a.11.17 | yes | 24 | 3.2 | odd | 2 | inner | |
60.4.e.a.11.18 | yes | 24 | 4.3 | odd | 2 | inner | |
960.4.h.d.191.7 | 24 | 8.3 | odd | 2 | |||
960.4.h.d.191.8 | 24 | 24.5 | odd | 2 | |||
960.4.h.d.191.17 | 24 | 24.11 | even | 2 | |||
960.4.h.d.191.18 | 24 | 8.5 | even | 2 |