Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [105,4,Mod(16,105)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(105, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 2]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("105.16");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 105 = 3 \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 105.i (of order \(3\), 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: | \(6.19520055060\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\Q(\sqrt{2}, \sqrt{-3})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 2x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 16.2 | ||
Root | \(0.707107 + 1.22474i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 105.16 |
Dual form | 105.4.i.b.46.2 |
$q$-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 \(\left(\mathbb{Z}/105\mathbb{Z}\right)^\times\).
\(n\) | \(22\) | \(31\) | \(71\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.70711 | − | 2.95680i | 0.603553 | − | 1.04539i | −0.388725 | − | 0.921354i | \(-0.627084\pi\) |
0.992278 | − | 0.124031i | \(-0.0395823\pi\) | |||||||
\(3\) | 1.50000 | + | 2.59808i | 0.288675 | + | 0.500000i | ||||
\(4\) | −1.82843 | − | 3.16693i | −0.228553 | − | 0.395866i | ||||
\(5\) | 2.50000 | − | 4.33013i | 0.223607 | − | 0.387298i | ||||
\(6\) | 10.2426 | 0.696923 | ||||||||
\(7\) | 16.7426 | + | 7.91732i | 0.904018 | + | 0.427495i | ||||
\(8\) | 14.8284 | 0.655330 | ||||||||
\(9\) | −4.50000 | + | 7.79423i | −0.166667 | + | 0.288675i | ||||
\(10\) | −8.53553 | − | 14.7840i | −0.269917 | − | 0.467510i | ||||
\(11\) | −18.8701 | − | 32.6839i | −0.517231 | − | 0.895870i | −0.999800 | − | 0.0200118i | \(-0.993630\pi\) |
0.482569 | − | 0.875858i | \(-0.339704\pi\) | |||||||
\(12\) | 5.48528 | − | 9.50079i | 0.131955 | − | 0.228553i | ||||
\(13\) | 43.7696 | 0.933807 | 0.466903 | − | 0.884308i | \(-0.345370\pi\) | ||||
0.466903 | + | 0.884308i | \(0.345370\pi\) | |||||||
\(14\) | 51.9914 | − | 35.9889i | 0.992520 | − | 0.687030i | ||||
\(15\) | 15.0000 | 0.258199 | ||||||||
\(16\) | 39.9411 | − | 69.1801i | 0.624080 | − | 1.08094i | ||||
\(17\) | −19.0416 | − | 32.9811i | −0.271663 | − | 0.470534i | 0.697625 | − | 0.716463i | \(-0.254240\pi\) |
−0.969288 | + | 0.245929i | \(0.920907\pi\) | |||||||
\(18\) | 15.3640 | + | 26.6112i | 0.201184 | + | 0.348462i | ||||
\(19\) | −49.7548 | + | 86.1779i | −0.600765 | + | 1.04056i | 0.391940 | + | 0.919991i | \(0.371804\pi\) |
−0.992705 | + | 0.120565i | \(0.961529\pi\) | |||||||
\(20\) | −18.2843 | −0.204424 | ||||||||
\(21\) | 4.54416 | + | 55.3746i | 0.0472198 | + | 0.575416i | ||||
\(22\) | −128.853 | −1.24871 | ||||||||
\(23\) | −1.38478 | + | 2.39850i | −0.0125542 | + | 0.0217445i | −0.872234 | − | 0.489088i | \(-0.837330\pi\) |
0.859680 | + | 0.510833i | \(0.170663\pi\) | |||||||
\(24\) | 22.2426 | + | 38.5254i | 0.189178 | + | 0.327665i | ||||
\(25\) | −12.5000 | − | 21.6506i | −0.100000 | − | 0.173205i | ||||
\(26\) | 74.7193 | − | 129.418i | 0.563602 | − | 0.976188i | ||||
\(27\) | −27.0000 | −0.192450 | ||||||||
\(28\) | −5.53911 | − | 67.4990i | −0.0373854 | − | 0.455575i | ||||
\(29\) | −174.485 | −1.11728 | −0.558640 | − | 0.829410i | \(-0.688677\pi\) | ||||
−0.558640 | + | 0.829410i | \(0.688677\pi\) | |||||||
\(30\) | 25.6066 | − | 44.3519i | 0.155837 | − | 0.269917i | ||||
\(31\) | 8.95584 | + | 15.5120i | 0.0518876 | + | 0.0898720i | 0.890803 | − | 0.454390i | \(-0.150143\pi\) |
−0.838915 | + | 0.544262i | \(0.816810\pi\) | |||||||
\(32\) | −77.0538 | − | 133.461i | −0.425666 | − | 0.737276i | ||||
\(33\) | 56.6102 | − | 98.0517i | 0.298623 | − | 0.517231i | ||||
\(34\) | −130.024 | −0.655853 | ||||||||
\(35\) | 76.1396 | − | 52.7045i | 0.367713 | − | 0.254534i | ||||
\(36\) | 32.9117 | 0.152369 | ||||||||
\(37\) | −161.478 | + | 279.688i | −0.717480 | + | 1.24271i | 0.244515 | + | 0.969646i | \(0.421371\pi\) |
−0.961995 | + | 0.273067i | \(0.911962\pi\) | |||||||
\(38\) | 169.874 | + | 294.230i | 0.725188 | + | 1.25606i | ||||
\(39\) | 65.6543 | + | 113.717i | 0.269567 | + | 0.466903i | ||||
\(40\) | 37.0711 | − | 64.2090i | 0.146536 | − | 0.253808i | ||||
\(41\) | 248.534 | 0.946695 | 0.473348 | − | 0.880876i | \(-0.343045\pi\) | ||||
0.473348 | + | 0.880876i | \(0.343045\pi\) | |||||||
\(42\) | 171.489 | + | 81.0943i | 0.630031 | + | 0.297931i | ||||
\(43\) | −474.740 | −1.68366 | −0.841828 | − | 0.539746i | \(-0.818520\pi\) | ||||
−0.841828 | + | 0.539746i | \(0.818520\pi\) | |||||||
\(44\) | −69.0051 | + | 119.520i | −0.236430 | + | 0.409508i | ||||
\(45\) | 22.5000 | + | 38.9711i | 0.0745356 | + | 0.129099i | ||||
\(46\) | 4.72792 | + | 8.18900i | 0.0151542 | + | 0.0262479i | ||||
\(47\) | −31.8528 | + | 55.1707i | −0.0988555 | + | 0.171223i | −0.911211 | − | 0.411939i | \(-0.864852\pi\) |
0.812356 | + | 0.583162i | \(0.198185\pi\) | |||||||
\(48\) | 239.647 | 0.720626 | ||||||||
\(49\) | 217.632 | + | 265.114i | 0.634496 | + | 0.772926i | ||||
\(50\) | −85.3553 | −0.241421 | ||||||||
\(51\) | 57.1249 | − | 98.9432i | 0.156845 | − | 0.271663i | ||||
\(52\) | −80.0294 | − | 138.615i | −0.213425 | − | 0.369662i | ||||
\(53\) | 131.598 | + | 227.934i | 0.341064 | + | 0.590740i | 0.984631 | − | 0.174650i | \(-0.0558795\pi\) |
−0.643567 | + | 0.765390i | \(0.722546\pi\) | |||||||
\(54\) | −46.0919 | + | 79.8335i | −0.116154 | + | 0.201184i | ||||
\(55\) | −188.701 | −0.462625 | ||||||||
\(56\) | 248.267 | + | 117.401i | 0.592430 | + | 0.280150i | ||||
\(57\) | −298.529 | −0.693704 | ||||||||
\(58\) | −297.865 | + | 515.917i | −0.674338 | + | 1.16799i | ||||
\(59\) | 166.522 | + | 288.424i | 0.367446 | + | 0.636435i | 0.989165 | − | 0.146805i | \(-0.0468990\pi\) |
−0.621720 | + | 0.783240i | \(0.713566\pi\) | |||||||
\(60\) | −27.4264 | − | 47.5039i | −0.0590122 | − | 0.102212i | ||||
\(61\) | 140.574 | − | 243.481i | 0.295059 | − | 0.511057i | −0.679940 | − | 0.733268i | \(-0.737994\pi\) |
0.974999 | + | 0.222211i | \(0.0713273\pi\) | |||||||
\(62\) | 61.1543 | 0.125268 | ||||||||
\(63\) | −137.051 | + | 94.8680i | −0.274077 | + | 0.189718i | ||||
\(64\) | 112.902 | 0.220511 | ||||||||
\(65\) | 109.424 | − | 189.528i | 0.208806 | − | 0.361662i | ||||
\(66\) | −193.279 | − | 334.769i | −0.360470 | − | 0.624353i | ||||
\(67\) | −443.277 | − | 767.778i | −0.808282 | − | 1.39998i | −0.914053 | − | 0.405594i | \(-0.867065\pi\) |
0.105772 | − | 0.994390i | \(-0.466269\pi\) | |||||||
\(68\) | −69.6325 | + | 120.607i | −0.124179 | + | 0.215084i | ||||
\(69\) | −8.30866 | −0.0144963 | ||||||||
\(70\) | −25.8579 | − | 315.101i | −0.0441515 | − | 0.538026i | ||||
\(71\) | −951.897 | −1.59112 | −0.795559 | − | 0.605877i | \(-0.792823\pi\) | ||||
−0.795559 | + | 0.605877i | \(0.792823\pi\) | |||||||
\(72\) | −66.7279 | + | 115.576i | −0.109222 | + | 0.189178i | ||||
\(73\) | −406.429 | − | 703.956i | −0.651629 | − | 1.12865i | −0.982728 | − | 0.185058i | \(-0.940753\pi\) |
0.331099 | − | 0.943596i | \(-0.392581\pi\) | |||||||
\(74\) | 551.319 | + | 954.913i | 0.866075 | + | 1.50009i | ||||
\(75\) | 37.5000 | − | 64.9519i | 0.0577350 | − | 0.100000i | ||||
\(76\) | 363.892 | 0.549228 | ||||||||
\(77\) | −57.1657 | − | 696.615i | −0.0846056 | − | 1.03100i | ||||
\(78\) | 448.316 | 0.650792 | ||||||||
\(79\) | −260.873 | + | 451.845i | −0.371525 | + | 0.643500i | −0.989800 | − | 0.142462i | \(-0.954498\pi\) |
0.618276 | + | 0.785961i | \(0.287832\pi\) | |||||||
\(80\) | −199.706 | − | 345.900i | −0.279097 | − | 0.483410i | ||||
\(81\) | −40.5000 | − | 70.1481i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | 424.274 | − | 734.864i | 0.571381 | − | 0.989661i | ||||
\(83\) | 339.750 | 0.449306 | 0.224653 | − | 0.974439i | \(-0.427875\pi\) | ||||
0.224653 | + | 0.974439i | \(0.427875\pi\) | |||||||
\(84\) | 167.059 | − | 115.640i | 0.216995 | − | 0.150206i | ||||
\(85\) | −190.416 | −0.242983 | ||||||||
\(86\) | −810.432 | + | 1403.71i | −1.01618 | + | 1.76007i | ||||
\(87\) | −261.728 | − | 453.326i | −0.322531 | − | 0.558640i | ||||
\(88\) | −279.813 | − | 484.651i | −0.338957 | − | 0.587090i | ||||
\(89\) | 688.634 | − | 1192.75i | 0.820169 | − | 1.42057i | −0.0853874 | − | 0.996348i | \(-0.527213\pi\) |
0.905556 | − | 0.424226i | \(-0.139454\pi\) | |||||||
\(90\) | 153.640 | 0.179945 | ||||||||
\(91\) | 732.818 | + | 346.538i | 0.844178 | + | 0.399198i | ||||
\(92\) | 10.1279 | 0.0114772 | ||||||||
\(93\) | −26.8675 | + | 46.5359i | −0.0299573 | + | 0.0518876i | ||||
\(94\) | 108.752 | + | 188.365i | 0.119329 | + | 0.206684i | ||||
\(95\) | 248.774 | + | 430.890i | 0.268670 | + | 0.465351i | ||||
\(96\) | 231.161 | − | 400.383i | 0.245759 | − | 0.425666i | ||||
\(97\) | −194.861 | −0.203971 | −0.101985 | − | 0.994786i | \(-0.532519\pi\) | ||||
−0.101985 | + | 0.994786i | \(0.532519\pi\) | |||||||
\(98\) | 1155.41 | − | 190.916i | 1.19096 | − | 0.196790i | ||||
\(99\) | 339.661 | 0.344820 | ||||||||
\(100\) | −45.7107 | + | 79.1732i | −0.0457107 | + | 0.0791732i | ||||
\(101\) | −267.591 | − | 463.481i | −0.263627 | − | 0.456615i | 0.703576 | − | 0.710620i | \(-0.251585\pi\) |
−0.967203 | + | 0.254005i | \(0.918252\pi\) | |||||||
\(102\) | −195.037 | − | 337.813i | −0.189328 | − | 0.327926i | ||||
\(103\) | −619.497 | + | 1073.00i | −0.592630 | + | 1.02646i | 0.401247 | + | 0.915970i | \(0.368577\pi\) |
−0.993877 | + | 0.110495i | \(0.964756\pi\) | |||||||
\(104\) | 649.034 | 0.611952 | ||||||||
\(105\) | 251.140 | + | 118.760i | 0.233416 | + | 0.110379i | ||||
\(106\) | 898.607 | 0.823400 | ||||||||
\(107\) | 687.257 | − | 1190.36i | 0.620931 | − | 1.07548i | −0.368382 | − | 0.929675i | \(-0.620088\pi\) |
0.989313 | − | 0.145810i | \(-0.0465787\pi\) | |||||||
\(108\) | 49.3675 | + | 85.5071i | 0.0439851 | + | 0.0761845i | ||||
\(109\) | 448.221 | + | 776.341i | 0.393869 | + | 0.682202i | 0.992956 | − | 0.118482i | \(-0.0378029\pi\) |
−0.599087 | + | 0.800684i | \(0.704470\pi\) | |||||||
\(110\) | −322.132 | + | 557.949i | −0.279219 | + | 0.483621i | ||||
\(111\) | −968.866 | −0.828475 | ||||||||
\(112\) | 1216.44 | − | 842.030i | 1.02628 | − | 0.710396i | ||||
\(113\) | −252.794 | −0.210450 | −0.105225 | − | 0.994448i | \(-0.533556\pi\) | ||||
−0.105225 | + | 0.994448i | \(0.533556\pi\) | |||||||
\(114\) | −509.621 | + | 882.689i | −0.418687 | + | 0.725188i | ||||
\(115\) | 6.92388 | + | 11.9925i | 0.00561439 | + | 0.00972442i | ||||
\(116\) | 319.034 | + | 552.582i | 0.255358 | + | 0.442293i | ||||
\(117\) | −196.963 | + | 341.150i | −0.155634 | + | 0.269567i | ||||
\(118\) | 1137.08 | 0.887093 | ||||||||
\(119\) | −57.6854 | − | 702.949i | −0.0444371 | − | 0.541506i | ||||
\(120\) | 222.426 | 0.169206 | ||||||||
\(121\) | −46.6582 | + | 80.8143i | −0.0350550 | + | 0.0607170i | ||||
\(122\) | −479.948 | − | 831.295i | −0.356168 | − | 0.616901i | ||||
\(123\) | 372.801 | + | 645.710i | 0.273287 | + | 0.473348i | ||||
\(124\) | 32.7502 | − | 56.7250i | 0.0237182 | − | 0.0410811i | ||||
\(125\) | −125.000 | −0.0894427 | ||||||||
\(126\) | 46.5442 | + | 567.183i | 0.0329086 | + | 0.401021i | ||||
\(127\) | 2289.44 | 1.59965 | 0.799824 | − | 0.600235i | \(-0.204926\pi\) | ||||
0.799824 | + | 0.600235i | \(0.204926\pi\) | |||||||
\(128\) | 809.166 | − | 1401.52i | 0.558756 | − | 0.967794i | ||||
\(129\) | −712.110 | − | 1233.41i | −0.486029 | − | 0.841828i | ||||
\(130\) | −373.597 | − | 647.088i | −0.252051 | − | 0.436564i | ||||
\(131\) | −1458.83 | + | 2526.77i | −0.972967 | + | 1.68523i | −0.286481 | + | 0.958086i | \(0.592486\pi\) |
−0.686486 | + | 0.727143i | \(0.740848\pi\) | |||||||
\(132\) | −414.030 | −0.273005 | ||||||||
\(133\) | −1515.33 | + | 1048.92i | −0.987935 | + | 0.683857i | ||||
\(134\) | −3026.88 | −1.95136 | ||||||||
\(135\) | −67.5000 | + | 116.913i | −0.0430331 | + | 0.0745356i | ||||
\(136\) | −282.357 | − | 489.057i | −0.178029 | − | 0.308355i | ||||
\(137\) | −1320.80 | − | 2287.70i | −0.823678 | − | 1.42665i | −0.902925 | − | 0.429798i | \(-0.858585\pi\) |
0.0792468 | − | 0.996855i | \(-0.474748\pi\) | |||||||
\(138\) | −14.1838 | + | 24.5670i | −0.00874929 | + | 0.0151542i | ||||
\(139\) | 2946.18 | 1.79778 | 0.898892 | − | 0.438171i | \(-0.144373\pi\) | ||||
0.898892 | + | 0.438171i | \(0.144373\pi\) | |||||||
\(140\) | −306.127 | − | 144.762i | −0.184803 | − | 0.0873904i | ||||
\(141\) | −191.117 | −0.114149 | ||||||||
\(142\) | −1624.99 | + | 2814.56i | −0.960324 | + | 1.66333i | ||||
\(143\) | −825.934 | − | 1430.56i | −0.482993 | − | 0.836569i | ||||
\(144\) | 359.470 | + | 622.621i | 0.208027 | + | 0.360313i | ||||
\(145\) | −436.213 | + | 755.543i | −0.249831 | + | 0.432720i | ||||
\(146\) | −2775.27 | −1.57317 | ||||||||
\(147\) | −362.338 | + | 963.095i | −0.203300 | + | 0.540372i | ||||
\(148\) | 1181.00 | 0.655930 | ||||||||
\(149\) | 303.437 | − | 525.569i | 0.166836 | − | 0.288968i | −0.770470 | − | 0.637477i | \(-0.779978\pi\) |
0.937306 | + | 0.348508i | \(0.113312\pi\) | |||||||
\(150\) | −128.033 | − | 221.760i | −0.0696923 | − | 0.120711i | ||||
\(151\) | 797.034 | + | 1380.50i | 0.429548 | + | 0.743998i | 0.996833 | − | 0.0795231i | \(-0.0253397\pi\) |
−0.567286 | + | 0.823521i | \(0.692006\pi\) | |||||||
\(152\) | −737.786 | + | 1277.88i | −0.393700 | + | 0.681908i | ||||
\(153\) | 342.749 | 0.181109 | ||||||||
\(154\) | −2157.34 | − | 1020.17i | −1.12885 | − | 0.533815i | ||||
\(155\) | 89.5584 | 0.0464097 | ||||||||
\(156\) | 240.088 | − | 415.845i | 0.123221 | − | 0.213425i | ||||
\(157\) | 224.377 | + | 388.632i | 0.114059 | + | 0.197555i | 0.917403 | − | 0.397959i | \(-0.130281\pi\) |
−0.803344 | + | 0.595515i | \(0.796948\pi\) | |||||||
\(158\) | 890.675 | + | 1542.69i | 0.448470 | + | 0.776773i | ||||
\(159\) | −394.794 | + | 683.803i | −0.196913 | + | 0.341064i | ||||
\(160\) | −770.538 | −0.380727 | ||||||||
\(161\) | −42.1745 | + | 29.1936i | −0.0206448 | + | 0.0142905i | ||||
\(162\) | −276.551 | −0.134123 | ||||||||
\(163\) | −872.079 | + | 1510.49i | −0.419058 | + | 0.725830i | −0.995845 | − | 0.0910645i | \(-0.970973\pi\) |
0.576787 | + | 0.816895i | \(0.304306\pi\) | |||||||
\(164\) | −454.426 | − | 787.090i | −0.216370 | − | 0.374764i | ||||
\(165\) | −283.051 | − | 490.258i | −0.133548 | − | 0.231313i | ||||
\(166\) | 579.990 | − | 1004.57i | 0.271180 | − | 0.469698i | ||||
\(167\) | 2514.33 | 1.16506 | 0.582528 | − | 0.812811i | \(-0.302064\pi\) | ||||
0.582528 | + | 0.812811i | \(0.302064\pi\) | |||||||
\(168\) | 67.3827 | + | 821.119i | 0.0309446 | + | 0.377087i | ||||
\(169\) | −281.226 | −0.128005 | ||||||||
\(170\) | −325.061 | + | 563.022i | −0.146653 | + | 0.254011i | ||||
\(171\) | −447.794 | − | 775.601i | −0.200255 | − | 0.346852i | ||||
\(172\) | 868.028 | + | 1503.47i | 0.384805 | + | 0.666502i | ||||
\(173\) | −933.622 | + | 1617.08i | −0.410301 | + | 0.710661i | −0.994922 | − | 0.100644i | \(-0.967910\pi\) |
0.584622 | + | 0.811306i | \(0.301243\pi\) | |||||||
\(174\) | −1787.19 | −0.778658 | ||||||||
\(175\) | −37.8680 | − | 461.455i | −0.0163574 | − | 0.199330i | ||||
\(176\) | −3014.77 | −1.29117 | ||||||||
\(177\) | −499.566 | + | 865.273i | −0.212145 | + | 0.367446i | ||||
\(178\) | −2351.14 | − | 4072.30i | −0.990031 | − | 1.71478i | ||||
\(179\) | 1202.87 | + | 2083.43i | 0.502271 | + | 0.869960i | 0.999997 | + | 0.00262473i | \(0.000835477\pi\) |
−0.497725 | + | 0.867335i | \(0.665831\pi\) | |||||||
\(180\) | 82.2792 | − | 142.512i | 0.0340707 | − | 0.0590122i | ||||
\(181\) | 4565.55 | 1.87489 | 0.937443 | − | 0.348138i | \(-0.113186\pi\) | ||||
0.937443 | + | 0.348138i | \(0.113186\pi\) | |||||||
\(182\) | 2275.64 | − | 1575.22i | 0.926822 | − | 0.641554i | ||||
\(183\) | 843.442 | 0.340705 | ||||||||
\(184\) | −20.5341 | + | 35.5660i | −0.00822712 | + | 0.0142498i | ||||
\(185\) | 807.389 | + | 1398.44i | 0.320867 | + | 0.555758i | ||||
\(186\) | 91.7315 | + | 158.884i | 0.0361617 | + | 0.0626339i | ||||
\(187\) | −718.633 | + | 1244.71i | −0.281025 | + | 0.486750i | ||||
\(188\) | 232.962 | 0.0903751 | ||||||||
\(189\) | −452.051 | − | 213.768i | −0.173978 | − | 0.0822715i | ||||
\(190\) | 1698.74 | 0.648628 | ||||||||
\(191\) | 1970.27 | − | 3412.60i | 0.746406 | − | 1.29281i | −0.203129 | − | 0.979152i | \(-0.565111\pi\) |
0.949535 | − | 0.313661i | \(-0.101556\pi\) | |||||||
\(192\) | 169.352 | + | 293.327i | 0.0636560 | + | 0.110255i | ||||
\(193\) | 568.066 | + | 983.918i | 0.211867 | + | 0.366964i | 0.952299 | − | 0.305167i | \(-0.0987124\pi\) |
−0.740432 | + | 0.672131i | \(0.765379\pi\) | |||||||
\(194\) | −332.649 | + | 576.165i | −0.123107 | + | 0.213228i | ||||
\(195\) | 656.543 | 0.241108 | ||||||||
\(196\) | 441.672 | − | 1173.97i | 0.160959 | − | 0.427830i | ||||
\(197\) | 1302.42 | 0.471032 | 0.235516 | − | 0.971870i | \(-0.424322\pi\) | ||||
0.235516 | + | 0.971870i | \(0.424322\pi\) | |||||||
\(198\) | 579.838 | − | 1004.31i | 0.208118 | − | 0.360470i | ||||
\(199\) | 521.025 | + | 902.442i | 0.185601 | + | 0.321470i | 0.943779 | − | 0.330578i | \(-0.107244\pi\) |
−0.758178 | + | 0.652047i | \(0.773910\pi\) | |||||||
\(200\) | −185.355 | − | 321.045i | −0.0655330 | − | 0.113507i | ||||
\(201\) | 1329.83 | − | 2303.33i | 0.466662 | − | 0.808282i | ||||
\(202\) | −1827.22 | −0.636451 | ||||||||
\(203\) | −2921.34 | − | 1381.46i | −1.01004 | − | 0.477632i | ||||
\(204\) | −417.795 | −0.143390 | ||||||||
\(205\) | 621.335 | − | 1076.18i | 0.211687 | − | 0.366653i | ||||
\(206\) | 2115.10 | + | 3663.45i | 0.715367 | + | 1.23905i | ||||
\(207\) | −12.4630 | − | 21.5865i | −0.00418472 | − | 0.00724815i | ||||
\(208\) | 1748.21 | − | 3027.98i | 0.582770 | − | 1.00939i | ||||
\(209\) | 3755.51 | 1.24294 | ||||||||
\(210\) | 779.871 | − | 539.833i | 0.256268 | − | 0.177390i | ||||
\(211\) | 2098.50 | 0.684677 | 0.342338 | − | 0.939577i | \(-0.388781\pi\) | ||||
0.342338 | + | 0.939577i | \(0.388781\pi\) | |||||||
\(212\) | 481.235 | − | 833.523i | 0.155903 | − | 0.270031i | ||||
\(213\) | −1427.84 | − | 2473.10i | −0.459316 | − | 0.795559i | ||||
\(214\) | −2346.44 | − | 4064.16i | −0.749530 | − | 1.29822i | ||||
\(215\) | −1186.85 | + | 2055.69i | −0.376477 | + | 0.652077i | ||||
\(216\) | −400.368 | −0.126118 | ||||||||
\(217\) | 27.1312 | + | 330.618i | 0.00848748 | + | 0.103428i | ||||
\(218\) | 3060.64 | 0.950885 | ||||||||
\(219\) | 1219.29 | − | 2111.87i | 0.376218 | − | 0.651629i | ||||
\(220\) | 345.025 | + | 597.601i | 0.105735 | + | 0.183138i | ||||
\(221\) | −833.444 | − | 1443.57i | −0.253681 | − | 0.439388i | ||||
\(222\) | −1653.96 | + | 2864.74i | −0.500029 | + | 0.866075i | ||||
\(223\) | −122.225 | −0.0367032 | −0.0183516 | − | 0.999832i | \(-0.505842\pi\) | ||||
−0.0183516 | + | 0.999832i | \(0.505842\pi\) | |||||||
\(224\) | −233.430 | − | 2844.55i | −0.0696280 | − | 0.848480i | ||||
\(225\) | 225.000 | 0.0666667 | ||||||||
\(226\) | −431.546 | + | 747.460i | −0.127018 | + | 0.220001i | ||||
\(227\) | 2539.21 | + | 4398.05i | 0.742438 | + | 1.28594i | 0.951382 | + | 0.308013i | \(0.0996641\pi\) |
−0.208944 | + | 0.977928i | \(0.567003\pi\) | |||||||
\(228\) | 545.839 | + | 945.420i | 0.158548 | + | 0.274614i | ||||
\(229\) | 1245.22 | − | 2156.78i | 0.359328 | − | 0.622375i | −0.628521 | − | 0.777793i | \(-0.716339\pi\) |
0.987849 | + | 0.155418i | \(0.0496725\pi\) | |||||||
\(230\) | 47.2792 | 0.0135543 | ||||||||
\(231\) | 1724.11 | − | 1193.44i | 0.491074 | − | 0.339926i | ||||
\(232\) | −2587.34 | −0.732187 | ||||||||
\(233\) | −825.610 | + | 1430.00i | −0.232135 | + | 0.402070i | −0.958436 | − | 0.285307i | \(-0.907904\pi\) |
0.726301 | + | 0.687377i | \(0.241238\pi\) | |||||||
\(234\) | 672.474 | + | 1164.76i | 0.187867 | + | 0.325396i | ||||
\(235\) | 159.264 | + | 275.853i | 0.0442095 | + | 0.0765732i | ||||
\(236\) | 608.946 | − | 1054.73i | 0.167962 | − | 0.290919i | ||||
\(237\) | −1565.24 | −0.429000 | ||||||||
\(238\) | −2176.95 | − | 1029.44i | −0.592903 | − | 0.280374i | ||||
\(239\) | −2773.60 | −0.750666 | −0.375333 | − | 0.926890i | \(-0.622472\pi\) | ||||
−0.375333 | + | 0.926890i | \(0.622472\pi\) | |||||||
\(240\) | 599.117 | − | 1037.70i | 0.161137 | − | 0.279097i | ||||
\(241\) | −2441.07 | − | 4228.05i | −0.652460 | − | 1.13009i | −0.982524 | − | 0.186135i | \(-0.940404\pi\) |
0.330064 | − | 0.943959i | \(-0.392930\pi\) | |||||||
\(242\) | 159.301 | + | 275.917i | 0.0423151 | + | 0.0732919i | ||||
\(243\) | 121.500 | − | 210.444i | 0.0320750 | − | 0.0555556i | ||||
\(244\) | −1028.11 | −0.269747 | ||||||||
\(245\) | 1692.06 | − | 279.590i | 0.441231 | − | 0.0729075i | ||||
\(246\) | 2545.65 | 0.659774 | ||||||||
\(247\) | −2177.75 | + | 3771.97i | −0.560999 | + | 0.971678i | ||||
\(248\) | 132.801 | + | 230.018i | 0.0340035 | + | 0.0588959i | ||||
\(249\) | 509.625 | + | 882.697i | 0.129704 | + | 0.224653i | ||||
\(250\) | −213.388 | + | 369.599i | −0.0539835 | + | 0.0935021i | ||||
\(251\) | 24.7358 | 0.00622035 | 0.00311018 | − | 0.999995i | \(-0.499010\pi\) | ||||
0.00311018 | + | 0.999995i | \(0.499010\pi\) | |||||||
\(252\) | 551.029 | + | 260.572i | 0.137744 | + | 0.0651370i | ||||
\(253\) | 104.523 | 0.0259736 | ||||||||
\(254\) | 3908.32 | − | 6769.42i | 0.965473 | − | 1.67225i | ||||
\(255\) | −285.624 | − | 494.716i | −0.0701431 | − | 0.121491i | ||||
\(256\) | −2311.06 | − | 4002.87i | −0.564223 | − | 0.977263i | ||||
\(257\) | −2362.06 | + | 4091.20i | −0.573311 | + | 0.993004i | 0.422912 | + | 0.906171i | \(0.361008\pi\) |
−0.996223 | + | 0.0868333i | \(0.972325\pi\) | |||||||
\(258\) | −4862.59 | −1.17338 | ||||||||
\(259\) | −4917.94 | + | 3404.24i | −1.17987 | + | 0.816714i | ||||
\(260\) | −800.294 | −0.190893 | ||||||||
\(261\) | 785.184 | − | 1359.98i | 0.186213 | − | 0.322531i | ||||
\(262\) | 4980.76 | + | 8626.93i | 1.17448 | + | 2.03425i | ||||
\(263\) | 328.136 | + | 568.349i | 0.0769344 | + | 0.133254i | 0.901926 | − | 0.431891i | \(-0.142153\pi\) |
−0.824991 | + | 0.565145i | \(0.808820\pi\) | |||||||
\(264\) | 839.440 | − | 1453.95i | 0.195697 | − | 0.338957i | ||||
\(265\) | 1315.98 | 0.305057 | ||||||||
\(266\) | 514.621 | + | 6271.13i | 0.118622 | + | 1.44552i | ||||
\(267\) | 4131.80 | 0.947049 | ||||||||
\(268\) | −1621.00 | + | 2807.65i | −0.369471 | + | 0.639943i | ||||
\(269\) | −1540.70 | − | 2668.57i | −0.349213 | − | 0.604854i | 0.636897 | − | 0.770949i | \(-0.280218\pi\) |
−0.986110 | + | 0.166094i | \(0.946884\pi\) | |||||||
\(270\) | 230.459 | + | 399.167i | 0.0519456 | + | 0.0899724i | ||||
\(271\) | 2031.57 | − | 3518.79i | 0.455385 | − | 0.788749i | −0.543326 | − | 0.839522i | \(-0.682835\pi\) |
0.998710 | + | 0.0507729i | \(0.0161685\pi\) | |||||||
\(272\) | −3042.18 | −0.678158 | ||||||||
\(273\) | 198.896 | + | 2423.72i | 0.0440942 | + | 0.537327i | ||||
\(274\) | −9019.02 | −1.98854 | ||||||||
\(275\) | −471.751 | + | 817.097i | −0.103446 | + | 0.179174i | ||||
\(276\) | 15.1918 | + | 26.3129i | 0.00331318 | + | 0.00573859i | ||||
\(277\) | −4176.56 | − | 7234.02i | −0.905939 | − | 1.56913i | −0.819651 | − | 0.572863i | \(-0.805833\pi\) |
−0.0862883 | − | 0.996270i | \(-0.527501\pi\) | |||||||
\(278\) | 5029.45 | − | 8711.26i | 1.08506 | − | 1.87938i | ||||
\(279\) | −161.205 | −0.0345918 | ||||||||
\(280\) | 1129.03 | − | 781.524i | 0.240973 | − | 0.166804i | ||||
\(281\) | −3215.56 | −0.682649 | −0.341325 | − | 0.939946i | \(-0.610876\pi\) | ||||
−0.341325 | + | 0.939946i | \(0.610876\pi\) | |||||||
\(282\) | −326.257 | + | 565.094i | −0.0688947 | + | 0.119329i | ||||
\(283\) | 2227.93 | + | 3858.89i | 0.467974 | + | 0.810555i | 0.999330 | − | 0.0365937i | \(-0.0116507\pi\) |
−0.531356 | + | 0.847148i | \(0.678317\pi\) | |||||||
\(284\) | 1740.47 | + | 3014.59i | 0.363655 | + | 0.629869i | ||||
\(285\) | −746.323 | + | 1292.67i | −0.155117 | + | 0.268670i | ||||
\(286\) | −5639.83 | −1.16605 | ||||||||
\(287\) | 4161.12 | + | 1967.72i | 0.855829 | + | 0.404708i | ||||
\(288\) | 1386.97 | 0.283778 | ||||||||
\(289\) | 1731.33 | − | 2998.76i | 0.352398 | − | 0.610372i | ||||
\(290\) | 1489.33 | + | 2579.59i | 0.301573 | + | 0.522340i | ||||
\(291\) | −292.292 | − | 506.264i | −0.0588813 | − | 0.101985i | ||||
\(292\) | −1486.25 | + | 2574.26i | −0.297864 | + | 0.515916i | ||||
\(293\) | −8088.97 | −1.61284 | −0.806421 | − | 0.591342i | \(-0.798598\pi\) | ||||
−0.806421 | + | 0.591342i | \(0.798598\pi\) | |||||||
\(294\) | 2229.13 | + | 2715.46i | 0.442195 | + | 0.538670i | ||||
\(295\) | 1665.22 | 0.328653 | ||||||||
\(296\) | −2394.46 | + | 4147.33i | −0.470186 | + | 0.814387i | ||||
\(297\) | 509.492 | + | 882.465i | 0.0995411 | + | 0.172410i | ||||
\(298\) | −1036.00 | − | 1794.40i | −0.201389 | − | 0.348816i | ||||
\(299\) | −60.6110 | + | 104.981i | −0.0117232 | + | 0.0203051i | ||||
\(300\) | −274.264 | −0.0527821 | ||||||||
\(301\) | −7948.40 | − | 3758.67i | −1.52205 | − | 0.719755i | ||||
\(302\) | 5442.49 | 1.03702 | ||||||||
\(303\) | 802.773 | − | 1390.44i | 0.152205 | − | 0.263627i | ||||
\(304\) | 3974.53 | + | 6884.08i | 0.749851 | + | 1.29878i | ||||
\(305\) | −702.868 | − | 1217.40i | −0.131954 | − | 0.228552i | ||||
\(306\) | 585.110 | − | 1013.44i | 0.109309 | − | 0.189328i | ||||
\(307\) | −2025.28 | −0.376511 | −0.188255 | − | 0.982120i | \(-0.560283\pi\) | ||||
−0.188255 | + | 0.982120i | \(0.560283\pi\) | |||||||
\(308\) | −2101.61 | + | 1454.75i | −0.388799 | + | 0.269130i | ||||
\(309\) | −3716.98 | −0.684310 | ||||||||
\(310\) | 152.886 | − | 264.806i | 0.0280107 | − | 0.0485160i | ||||
\(311\) | 828.235 | + | 1434.55i | 0.151013 | + | 0.261561i | 0.931600 | − | 0.363485i | \(-0.118413\pi\) |
−0.780587 | + | 0.625047i | \(0.785080\pi\) | |||||||
\(312\) | 973.550 | + | 1686.24i | 0.176655 | + | 0.305976i | ||||
\(313\) | 883.292 | − | 1529.91i | 0.159510 | − | 0.276279i | −0.775182 | − | 0.631738i | \(-0.782342\pi\) |
0.934692 | + | 0.355459i | \(0.115675\pi\) | |||||||
\(314\) | 1532.14 | 0.275362 | ||||||||
\(315\) | 68.1623 | + | 830.620i | 0.0121921 | + | 0.148572i | ||||
\(316\) | 1907.95 | 0.339653 | ||||||||
\(317\) | 3060.95 | − | 5301.73i | 0.542335 | − | 0.939352i | −0.456434 | − | 0.889757i | \(-0.650874\pi\) |
0.998769 | − | 0.0495948i | \(-0.0157930\pi\) | |||||||
\(318\) | 1347.91 | + | 2334.65i | 0.237695 | + | 0.411700i | ||||
\(319\) | 3292.55 | + | 5702.86i | 0.577891 | + | 1.00094i | ||||
\(320\) | 282.254 | − | 488.878i | 0.0493077 | − | 0.0854035i | ||||
\(321\) | 4123.54 | 0.716990 | ||||||||
\(322\) | 14.3229 | + | 174.538i | 0.00247884 | + | 0.0302069i | ||||
\(323\) | 3789.65 | 0.652823 | ||||||||
\(324\) | −148.103 | + | 256.521i | −0.0253948 | + | 0.0439851i | ||||
\(325\) | −547.119 | − | 947.639i | −0.0933807 | − | 0.161740i | ||||
\(326\) | 2977.46 | + | 5157.12i | 0.505848 | + | 0.876155i | ||||
\(327\) | −1344.66 | + | 2329.02i | −0.227401 | + | 0.393869i | ||||
\(328\) | 3685.37 | 0.620398 | ||||||||
\(329\) | −970.104 | + | 671.514i | −0.162564 | + | 0.112528i | ||||
\(330\) | −1932.79 | −0.322414 | ||||||||
\(331\) | −3430.41 | + | 5941.64i | −0.569644 | + | 0.986653i | 0.426957 | + | 0.904272i | \(0.359586\pi\) |
−0.996601 | + | 0.0823805i | \(0.973748\pi\) | |||||||
\(332\) | −621.209 | − | 1075.96i | −0.102691 | − | 0.177865i | ||||
\(333\) | −1453.30 | − | 2517.19i | −0.239160 | − | 0.414237i | ||||
\(334\) | 4292.22 | − | 7434.35i | 0.703173 | − | 1.21793i | ||||
\(335\) | −4432.77 | −0.722949 | ||||||||
\(336\) | 4012.32 | + | 1897.36i | 0.651458 | + | 0.308064i | ||||
\(337\) | 4191.48 | 0.677520 | 0.338760 | − | 0.940873i | \(-0.389993\pi\) | ||||
0.338760 | + | 0.940873i | \(0.389993\pi\) | |||||||
\(338\) | −480.083 | + | 831.529i | −0.0772577 | + | 0.133814i | ||||
\(339\) | −379.191 | − | 656.778i | −0.0607517 | − | 0.105225i | ||||
\(340\) | 348.162 | + | 603.035i | 0.0555346 | + | 0.0961887i | ||||
\(341\) | 337.995 | − | 585.424i | 0.0536758 | − | 0.0929691i | ||||
\(342\) | −3057.73 | −0.483459 | ||||||||
\(343\) | 1544.74 | + | 6161.77i | 0.243173 | + | 0.969983i | ||||
\(344\) | −7039.65 | −1.10335 | ||||||||
\(345\) | −20.7716 | + | 35.9775i | −0.00324147 | + | 0.00561439i | ||||
\(346\) | 3187.59 | + | 5521.06i | 0.495277 | + | 0.857844i | ||||
\(347\) | −4369.87 | − | 7568.84i | −0.676044 | − | 1.17094i | −0.976163 | − | 0.217040i | \(-0.930360\pi\) |
0.300119 | − | 0.953902i | \(-0.402974\pi\) | |||||||
\(348\) | −957.101 | + | 1657.75i | −0.147431 | + | 0.255358i | ||||
\(349\) | 237.613 | 0.0364445 | 0.0182223 | − | 0.999834i | \(-0.494199\pi\) | ||||
0.0182223 | + | 0.999834i | \(0.494199\pi\) | |||||||
\(350\) | −1429.07 | − | 675.786i | −0.218249 | − | 0.103206i | ||||
\(351\) | −1181.78 | −0.179711 | ||||||||
\(352\) | −2908.02 | + | 5036.84i | −0.440335 | + | 0.762683i | ||||
\(353\) | −2561.68 | − | 4436.96i | −0.386245 | − | 0.668995i | 0.605696 | − | 0.795696i | \(-0.292895\pi\) |
−0.991941 | + | 0.126700i | \(0.959561\pi\) | |||||||
\(354\) | 1705.62 | + | 2954.23i | 0.256082 | + | 0.443546i | ||||
\(355\) | −2379.74 | + | 4121.83i | −0.355785 | + | 0.616237i | ||||
\(356\) | −5036.47 | −0.749809 | ||||||||
\(357\) | 1739.79 | − | 1204.29i | 0.257925 | − | 0.178538i | ||||
\(358\) | 8213.70 | 1.21259 | ||||||||
\(359\) | 4802.62 | − | 8318.39i | 0.706052 | − | 1.22292i | −0.260258 | − | 0.965539i | \(-0.583808\pi\) |
0.966311 | − | 0.257379i | \(-0.0828589\pi\) | |||||||
\(360\) | 333.640 | + | 577.881i | 0.0488454 | + | 0.0846028i | ||||
\(361\) | −1521.59 | − | 2635.47i | −0.221838 | − | 0.384235i | ||||
\(362\) | 7793.88 | − | 13499.4i | 1.13159 | − | 1.95998i | ||||
\(363\) | −279.949 | −0.0404780 | ||||||||
\(364\) | −242.444 | − | 2954.40i | −0.0349108 | − | 0.425419i | ||||
\(365\) | −4064.29 | −0.582835 | ||||||||
\(366\) | 1439.84 | − | 2493.88i | 0.205634 | − | 0.356168i | ||||
\(367\) | −2635.34 | − | 4564.54i | −0.374833 | − | 0.649230i | 0.615469 | − | 0.788161i | \(-0.288967\pi\) |
−0.990302 | + | 0.138931i | \(0.955633\pi\) | |||||||
\(368\) | 110.619 | + | 191.598i | 0.0156696 | + | 0.0271406i | ||||
\(369\) | −1118.40 | + | 1937.13i | −0.157783 | + | 0.273287i | ||||
\(370\) | 5513.19 | 0.774641 | ||||||||
\(371\) | 398.668 | + | 4858.13i | 0.0557892 | + | 0.679842i | ||||
\(372\) | 196.501 | 0.0273874 | ||||||||
\(373\) | 123.193 | − | 213.377i | 0.0171011 | − | 0.0296200i | −0.857348 | − | 0.514737i | \(-0.827890\pi\) |
0.874449 | + | 0.485117i | \(0.161223\pi\) | |||||||
\(374\) | 2453.57 | + | 4249.70i | 0.339227 | + | 0.587559i | ||||
\(375\) | −187.500 | − | 324.760i | −0.0258199 | − | 0.0447214i | ||||
\(376\) | −472.327 | + | 818.095i | −0.0647830 | + | 0.112207i | ||||
\(377\) | −7637.14 | −1.04332 | ||||||||
\(378\) | −1403.77 | + | 971.699i | −0.191011 | + | 0.132219i | ||||
\(379\) | −10120.5 | −1.37165 | −0.685826 | − | 0.727766i | \(-0.740559\pi\) | ||||
−0.685826 | + | 0.727766i | \(0.740559\pi\) | |||||||
\(380\) | 909.731 | − | 1575.70i | 0.122811 | − | 0.212715i | ||||
\(381\) | 3434.16 | + | 5948.15i | 0.461778 | + | 0.799824i | ||||
\(382\) | −6726.91 | − | 11651.4i | −0.900992 | − | 1.56056i | ||||
\(383\) | −1706.78 | + | 2956.23i | −0.227709 | + | 0.394403i | −0.957129 | − | 0.289663i | \(-0.906457\pi\) |
0.729420 | + | 0.684066i | \(0.239790\pi\) | |||||||
\(384\) | 4854.99 | 0.645196 | ||||||||
\(385\) | −3159.35 | − | 1494.00i | −0.418221 | − | 0.197770i | ||||
\(386\) | 3878.99 | 0.511491 | ||||||||
\(387\) | 2136.33 | − | 3700.23i | 0.280609 | − | 0.486029i | ||||
\(388\) | 356.289 | + | 617.111i | 0.0466182 | + | 0.0807451i | ||||
\(389\) | −2450.91 | − | 4245.10i | −0.319450 | − | 0.553303i | 0.660924 | − | 0.750453i | \(-0.270165\pi\) |
−0.980373 | + | 0.197150i | \(0.936831\pi\) | |||||||
\(390\) | 1120.79 | − | 1941.26i | 0.145521 | − | 0.252051i | ||||
\(391\) | 105.474 | 0.0136420 | ||||||||
\(392\) | 3227.14 | + | 3931.22i | 0.415804 | + | 0.506522i | ||||
\(393\) | −8752.99 | −1.12349 | ||||||||
\(394\) | 2223.36 | − | 3850.98i | 0.284293 | − | 0.492410i | ||||
\(395\) | 1304.36 | + | 2259.22i | 0.166151 | + | 0.287782i | ||||
\(396\) | −621.045 | − | 1075.68i | −0.0788099 | − | 0.136503i | ||||
\(397\) | 2205.15 | − | 3819.43i | 0.278774 | − | 0.482851i | −0.692306 | − | 0.721604i | \(-0.743405\pi\) |
0.971080 | + | 0.238753i | \(0.0767385\pi\) | |||||||
\(398\) | 3557.78 | 0.448079 | ||||||||
\(399\) | −4998.16 | − | 2363.55i | −0.627121 | − | 0.296555i | ||||
\(400\) | −1997.06 | −0.249632 | ||||||||
\(401\) | −3113.69 | + | 5393.08i | −0.387757 | + | 0.671614i | −0.992147 | − | 0.125074i | \(-0.960083\pi\) |
0.604391 | + | 0.796688i | \(0.293417\pi\) | |||||||
\(402\) | −4540.32 | − | 7864.07i | −0.563310 | − | 0.975682i | ||||
\(403\) | 391.993 | + | 678.952i | 0.0484530 | + | 0.0839231i | ||||
\(404\) | −978.541 | + | 1694.88i | −0.120505 | + | 0.208722i | ||||
\(405\) | −405.000 | −0.0496904 | ||||||||
\(406\) | −9071.73 | + | 6279.53i | −1.10892 | + | 0.767605i | ||||
\(407\) | 12188.4 | 1.48441 | ||||||||
\(408\) | 847.072 | − | 1467.17i | 0.102785 | − | 0.178029i | ||||
\(409\) | 4360.55 | + | 7552.69i | 0.527177 | + | 0.913097i | 0.999498 | + | 0.0316707i | \(0.0100828\pi\) |
−0.472322 | + | 0.881426i | \(0.656584\pi\) | |||||||
\(410\) | −2121.37 | − | 3674.32i | −0.255529 | − | 0.442590i | ||||
\(411\) | 3962.41 | − | 6863.10i | 0.475551 | − | 0.823678i | ||||
\(412\) | 4530.82 | 0.541790 | ||||||||
\(413\) | 504.468 | + | 6147.39i | 0.0601047 | + | 0.732430i | ||||
\(414\) | −85.1026 | −0.0101028 | ||||||||
\(415\) | 849.376 | − | 1471.16i | 0.100468 | − | 0.174016i | ||||
\(416\) | −3372.61 | − | 5841.53i | −0.397490 | − | 0.688473i | ||||
\(417\) | 4419.27 | + | 7654.41i | 0.518975 | + | 0.898892i | ||||
\(418\) | 6411.05 | − | 11104.3i | 0.750179 | − | 1.29935i | ||||
\(419\) | −4007.88 | −0.467298 | −0.233649 | − | 0.972321i | \(-0.575067\pi\) | ||||
−0.233649 | + | 0.972321i | \(0.575067\pi\) | |||||||
\(420\) | −83.0866 | − | 1012.48i | −0.00965288 | − | 0.117629i | ||||
\(421\) | 13518.9 | 1.56501 | 0.782504 | − | 0.622645i | \(-0.213942\pi\) | ||||
0.782504 | + | 0.622645i | \(0.213942\pi\) | |||||||
\(422\) | 3582.37 | − | 6204.84i | 0.413239 | − | 0.715751i | ||||
\(423\) | −286.675 | − | 496.536i | −0.0329518 | − | 0.0570743i | ||||
\(424\) | 1951.39 | + | 3379.91i | 0.223509 | + | 0.387129i | ||||
\(425\) | −476.041 | + | 824.527i | −0.0543326 | + | 0.0941069i | ||||
\(426\) | −9749.93 | −1.10889 | ||||||||
\(427\) | 4281.29 | − | 2963.54i | 0.485213 | − | 0.335868i | ||||
\(428\) | −5026.40 | −0.567664 | ||||||||
\(429\) | 2477.80 | − | 4291.68i | 0.278856 | − | 0.482993i | ||||
\(430\) | 4052.16 | + | 7018.55i | 0.454448 | + | 0.787127i | ||||
\(431\) | −1225.85 | − | 2123.24i | −0.137001 | − | 0.237292i | 0.789359 | − | 0.613932i | \(-0.210413\pi\) |
−0.926360 | + | 0.376639i | \(0.877080\pi\) | |||||||
\(432\) | −1078.41 | + | 1867.86i | −0.120104 | + | 0.208027i | ||||
\(433\) | 9390.37 | 1.04220 | 0.521100 | − | 0.853496i | \(-0.325522\pi\) | ||||
0.521100 | + | 0.853496i | \(0.325522\pi\) | |||||||
\(434\) | 1023.88 | + | 484.178i | 0.113244 | + | 0.0535514i | ||||
\(435\) | −2617.28 | −0.288480 | ||||||||
\(436\) | 1639.08 | − | 2838.97i | 0.180040 | − | 0.311839i | ||||
\(437\) | −137.799 | − | 238.674i | −0.0150842 | − | 0.0261266i | ||||
\(438\) | −4162.91 | − | 7210.36i | −0.454135 | − | 0.786586i | ||||
\(439\) | −2954.86 | + | 5117.96i | −0.321247 | + | 0.556417i | −0.980746 | − | 0.195289i | \(-0.937435\pi\) |
0.659498 | + | 0.751706i | \(0.270769\pi\) | |||||||
\(440\) | −2798.13 | −0.303172 | ||||||||
\(441\) | −3045.70 | + | 503.262i | −0.328874 | + | 0.0543421i | ||||
\(442\) | −5691.11 | −0.612440 | ||||||||
\(443\) | −866.692 | + | 1501.15i | −0.0929521 | + | 0.160998i | −0.908752 | − | 0.417336i | \(-0.862964\pi\) |
0.815800 | + | 0.578334i | \(0.196297\pi\) | |||||||
\(444\) | 1771.50 | + | 3068.33i | 0.189351 | + | 0.327965i | ||||
\(445\) | −3443.17 | − | 5963.74i | −0.366791 | − | 0.635300i | ||||
\(446\) | −208.652 | + | 361.396i | −0.0221524 | + | 0.0383690i | ||||
\(447\) | 1820.62 | 0.192646 | ||||||||
\(448\) | 1890.27 | + | 893.878i | 0.199346 | + | 0.0942674i | ||||
\(449\) | 15810.3 | 1.66177 | 0.830883 | − | 0.556447i | \(-0.187836\pi\) | ||||
0.830883 | + | 0.556447i | \(0.187836\pi\) | |||||||
\(450\) | 384.099 | − | 665.279i | 0.0402369 | − | 0.0696923i | ||||
\(451\) | −4689.85 | − | 8123.06i | −0.489660 | − | 0.848115i | ||||
\(452\) | 462.215 | + | 800.580i | 0.0480991 | + | 0.0833100i | ||||
\(453\) | −2391.10 | + | 4141.51i | −0.247999 | + | 0.429548i | ||||
\(454\) | 17338.8 | 1.79240 | ||||||||
\(455\) | 3332.60 | − | 2306.85i | 0.343373 | − | 0.237685i | ||||
\(456\) | −4426.72 | −0.454605 | ||||||||
\(457\) | 3537.54 | − | 6127.20i | 0.362099 | − | 0.627174i | −0.626207 | − | 0.779657i | \(-0.715394\pi\) |
0.988306 | + | 0.152483i | \(0.0487269\pi\) | |||||||
\(458\) | −4251.43 | − | 7363.70i | −0.433748 | − | 0.751273i | ||||
\(459\) | 514.124 | + | 890.489i | 0.0522816 | + | 0.0905544i | ||||
\(460\) | 25.3196 | − | 43.8549i | 0.00256638 | − | 0.00444510i | ||||
\(461\) | 7778.66 | 0.785875 | 0.392938 | − | 0.919565i | \(-0.371459\pi\) | ||||
0.392938 | + | 0.919565i | \(0.371459\pi\) | |||||||
\(462\) | −585.527 | − | 7135.18i | −0.0589636 | − | 0.718525i | ||||
\(463\) | 11287.4 | 1.13298 | 0.566489 | − | 0.824069i | \(-0.308301\pi\) | ||||
0.566489 | + | 0.824069i | \(0.308301\pi\) | |||||||
\(464\) | −6969.14 | + | 12070.9i | −0.697272 | + | 1.20771i | ||||
\(465\) | 134.338 | + | 232.680i | 0.0133973 | + | 0.0232049i | ||||
\(466\) | 2818.81 | + | 4882.32i | 0.280212 | + | 0.485341i | ||||
\(467\) | −9332.61 | + | 16164.5i | −0.924757 | + | 1.60173i | −0.132806 | + | 0.991142i | \(0.542399\pi\) |
−0.791951 | + | 0.610584i | \(0.790935\pi\) | |||||||
\(468\) | 1440.53 | 0.142283 | ||||||||
\(469\) | −1342.88 | − | 16364.2i | −0.132214 | − | 1.61115i | ||||
\(470\) | 1087.52 | 0.106731 | ||||||||
\(471\) | −673.130 | + | 1165.90i | −0.0658518 | + | 0.114059i | ||||
\(472\) | 2469.26 | + | 4276.88i | 0.240798 | + | 0.417075i | ||||
\(473\) | 8958.37 | + | 15516.4i | 0.870838 | + | 1.50834i | ||||
\(474\) | −2672.02 | + | 4628.08i | −0.258924 | + | 0.448470i | ||||
\(475\) | 2487.74 | 0.240306 | ||||||||
\(476\) | −2120.72 | + | 1467.98i | −0.204208 | + | 0.141354i | ||||
\(477\) | −2368.76 | −0.227376 | ||||||||
\(478\) | −4734.83 | + | 8200.96i | −0.453067 | + | 0.784735i | ||||
\(479\) | 3140.65 | + | 5439.77i | 0.299583 | + | 0.518893i | 0.976041 | − | 0.217589i | \(-0.0698192\pi\) |
−0.676458 | + | 0.736481i | \(0.736486\pi\) | |||||||
\(480\) | −1155.81 | − | 2001.92i | −0.109907 | − | 0.190364i | ||||
\(481\) | −7067.81 | + | 12241.8i | −0.669988 | + | 1.16045i | ||||
\(482\) | −16668.6 | −1.57518 | ||||||||
\(483\) | −139.109 | − | 65.7823i | −0.0131049 | − | 0.00619710i | ||||
\(484\) | 341.244 | 0.0320477 | ||||||||
\(485\) | −487.153 | + | 843.774i | −0.0456092 | + | 0.0789975i | ||||
\(486\) | −414.827 | − | 718.501i | −0.0387180 | − | 0.0670615i | ||||
\(487\) | −3382.23 | − | 5858.19i | −0.314709 | − | 0.545092i | 0.664666 | − | 0.747140i | \(-0.268574\pi\) |
−0.979376 | + | 0.202048i | \(0.935240\pi\) | |||||||
\(488\) | 2084.49 | − | 3610.43i | 0.193361 | − | 0.334911i | ||||
\(489\) | −5232.47 | −0.483887 | ||||||||
\(490\) | 2061.83 | − | 5480.35i | 0.190090 | − | 0.505260i | ||||
\(491\) | 13331.6 | 1.22535 | 0.612676 | − | 0.790334i | \(-0.290093\pi\) | ||||
0.612676 | + | 0.790334i | \(0.290093\pi\) | |||||||
\(492\) | 1363.28 | − | 2361.27i | 0.124921 | − | 0.216370i | ||||
\(493\) | 3322.48 | + | 5754.71i | 0.303524 | + | 0.525718i | ||||
\(494\) | 7435.29 | + | 12878.3i | 0.677185 | + | 1.17292i | ||||
\(495\) | 849.153 | − | 1470.78i | 0.0771042 | − | 0.133548i | ||||
\(496\) | 1430.83 | 0.129528 | ||||||||
\(497\) | −15937.3 | − | 7536.47i | −1.43840 | − | 0.680195i | ||||
\(498\) | 3479.94 | 0.313132 | ||||||||
\(499\) | −5870.49 | + | 10168.0i | −0.526651 | + | 0.912187i | 0.472866 | + | 0.881134i | \(0.343219\pi\) |
−0.999518 | + | 0.0310529i | \(0.990114\pi\) | |||||||
\(500\) | 228.553 | + | 395.866i | 0.0204424 | + | 0.0354073i | ||||
\(501\) | 3771.49 | + | 6532.41i | 0.336323 | + | 0.582528i | ||||
\(502\) | 42.2266 | − | 73.1387i | 0.00375432 | − | 0.00650267i | ||||
\(503\) | −20470.6 | −1.81459 | −0.907293 | − | 0.420498i | \(-0.861855\pi\) | ||||
−0.907293 | + | 0.420498i | \(0.861855\pi\) | |||||||
\(504\) | −2032.26 | + | 1406.74i | −0.179611 | + | 0.124328i | ||||
\(505\) | −2675.91 | −0.235795 | ||||||||
\(506\) | 178.432 | − | 309.054i | 0.0156765 | − | 0.0271524i | ||||
\(507\) | −421.839 | − | 730.647i | −0.0369518 | − | 0.0640023i | ||||
\(508\) | −4186.08 | − | 7250.50i | −0.365605 | − | 0.633246i | ||||
\(509\) | −8428.34 | + | 14598.3i | −0.733948 | + | 1.27124i | 0.221235 | + | 0.975221i | \(0.428991\pi\) |
−0.955183 | + | 0.296015i | \(0.904342\pi\) | |||||||
\(510\) | −1950.37 | −0.169340 | ||||||||
\(511\) | −1231.25 | − | 15003.9i | −0.106590 | − | 1.29889i | ||||
\(512\) | −2834.24 | −0.244642 | ||||||||
\(513\) | 1343.38 | − | 2326.80i | 0.115617 | − | 0.200255i | ||||
\(514\) | 8064.56 | + | 13968.2i | 0.692048 | + | 1.19866i | ||||
\(515\) | 3097.49 | + | 5365.00i | 0.265032 | + | 0.459049i | ||||
\(516\) | −2604.08 | + | 4510.40i | −0.222167 | + | 0.384805i | ||||
\(517\) | 2404.26 | 0.204524 | ||||||||
\(518\) | 1670.19 | + | 20352.7i | 0.141668 | + | 1.72635i | ||||
\(519\) | −5601.73 | −0.473774 | ||||||||
\(520\) | 1622.58 | − | 2810.40i | 0.136837 | − | 0.237008i | ||||
\(521\) | −7933.98 | − | 13742.1i | −0.667167 | − | 1.15557i | −0.978693 | − | 0.205329i | \(-0.934174\pi\) |
0.311526 | − | 0.950238i | \(-0.399160\pi\) | |||||||
\(522\) | −2680.79 | − | 4643.26i | −0.224779 | − | 0.389329i | ||||
\(523\) | −5326.58 | + | 9225.91i | −0.445344 | + | 0.771359i | −0.998076 | − | 0.0620000i | \(-0.980252\pi\) |
0.552732 | + | 0.833359i | \(0.313585\pi\) | |||||||
\(524\) | 10669.5 | 0.889500 | ||||||||
\(525\) | 1142.09 | − | 790.567i | 0.0949430 | − | 0.0657203i | ||||
\(526\) | 2240.65 | 0.185736 | ||||||||
\(527\) | 341.068 | − | 590.747i | 0.0281919 | − | 0.0488298i | ||||
\(528\) | −4522.15 | − | 7832.59i | −0.372730 | − | 0.645587i | ||||
\(529\) | 6079.66 | + | 10530.3i | 0.499685 | + | 0.865479i | ||||
\(530\) | 2246.52 | − | 3891.08i | 0.184118 | − | 0.318902i | ||||
\(531\) | −2997.39 | −0.244964 | ||||||||
\(532\) | 6092.52 | + | 2881.05i | 0.496512 | + | 0.234792i | ||||
\(533\) | 10878.2 | 0.884030 | ||||||||
\(534\) | 7053.43 | − | 12216.9i | 0.571595 | − | 0.990031i | ||||
\(535\) | −3436.28 | − | 5951.82i | −0.277689 | − | 0.480971i | ||||
\(536\) | −6573.10 | − | 11384.9i | −0.529691 | − | 0.917452i | ||||
\(537\) | −3608.60 | + | 6250.29i | −0.289987 | + | 0.502271i | ||||
\(538\) | −10520.6 | −0.843075 | ||||||||
\(539\) | 4558.22 | − | 12115.8i | 0.364261 | − | 0.968207i | ||||
\(540\) | 493.675 | 0.0393415 | ||||||||
\(541\) | 1020.16 | − | 1766.96i | 0.0810720 | − | 0.140421i | −0.822639 | − | 0.568565i | \(-0.807499\pi\) |
0.903711 | + | 0.428144i | \(0.140832\pi\) | |||||||
\(542\) | −6936.22 | − | 12013.9i | −0.549698 | − | 0.952104i | ||||
\(543\) | 6848.32 | + | 11861.6i | 0.541233 | + | 0.937443i | ||||
\(544\) | −2934.46 | + | 5082.64i | −0.231276 | + | 0.400581i | ||||
\(545\) | 4482.21 | 0.352287 | ||||||||
\(546\) | 7505.99 | + | 3549.46i | 0.588327 | + | 0.278210i | ||||
\(547\) | −19582.0 | −1.53065 | −0.765325 | − | 0.643644i | \(-0.777422\pi\) | ||||
−0.765325 | + | 0.643644i | \(0.777422\pi\) | |||||||
\(548\) | −4829.99 | + | 8365.79i | −0.376509 | + | 0.652133i | ||||
\(549\) | 1265.16 | + | 2191.33i | 0.0983530 | + | 0.170352i | ||||
\(550\) | 1610.66 | + | 2789.75i | 0.124871 | + | 0.216282i | ||||
\(551\) | 8681.49 | − | 15036.8i | 0.671223 | − | 1.16259i | ||||
\(552\) | −123.204 | −0.00949986 | ||||||||
\(553\) | −7945.09 | + | 5499.66i | −0.610958 | + | 0.422910i | ||||
\(554\) | −28519.3 | −2.18713 | ||||||||
\(555\) | −2422.17 | + | 4195.31i | −0.185253 | + | 0.320867i | ||||
\(556\) | −5386.88 | − | 9330.35i | −0.410890 | − | 0.711682i | ||||
\(557\) | 1606.58 | + | 2782.67i | 0.122213 | + | 0.211680i | 0.920640 | − | 0.390412i | \(-0.127667\pi\) |
−0.798427 | + | 0.602092i | \(0.794334\pi\) | |||||||
\(558\) | −275.194 | + | 476.651i | −0.0208780 | + | 0.0361617i | ||||
\(559\) | −20779.2 | −1.57221 | ||||||||
\(560\) | −604.996 | − | 7372.42i | −0.0456531 | − | 0.556324i | ||||
\(561\) | −4311.80 | −0.324500 | ||||||||
\(562\) | −5489.31 | + | 9507.76i | −0.412015 | + | 0.713631i | ||||
\(563\) | −10134.5 | − | 17553.5i | −0.758650 | − | 1.31402i | −0.943539 | − | 0.331261i | \(-0.892526\pi\) |
0.184889 | − | 0.982759i | \(-0.440807\pi\) | |||||||
\(564\) | 349.443 | + | 605.254i | 0.0260890 | + | 0.0451875i | ||||
\(565\) | −631.985 | + | 1094.63i | −0.0470581 | + | 0.0815069i | ||||
\(566\) | 15213.3 | 1.12979 | ||||||||
\(567\) | −122.692 | − | 1495.12i | −0.00908746 | − | 0.110739i | ||||
\(568\) | −14115.1 | −1.04271 | ||||||||
\(569\) | −1078.55 | + | 1868.10i | −0.0794642 | + | 0.137636i | −0.903019 | − | 0.429601i | \(-0.858654\pi\) |
0.823555 | + | 0.567237i | \(0.191988\pi\) | |||||||
\(570\) | 2548.10 | + | 4413.45i | 0.187243 | + | 0.324314i | ||||
\(571\) | 6634.49 | + | 11491.3i | 0.486243 | + | 0.842197i | 0.999875 | − | 0.0158132i | \(-0.00503372\pi\) |
−0.513632 | + | 0.858011i | \(0.671700\pi\) | |||||||
\(572\) | −3020.32 | + | 5231.35i | −0.220780 | + | 0.382401i | ||||
\(573\) | 11821.6 | 0.861875 | ||||||||
\(574\) | 12921.6 | − | 8944.46i | 0.939614 | − | 0.650408i | ||||
\(575\) | 69.2388 | 0.00502167 | ||||||||
\(576\) | −508.057 | + | 879.981i | −0.0367518 | + | 0.0636560i | ||||
\(577\) | −6850.77 | − | 11865.9i | −0.494283 | − | 0.856123i | 0.505695 | − | 0.862712i | \(-0.331236\pi\) |
−0.999978 | + | 0.00658894i | \(0.997903\pi\) | |||||||
\(578\) | −5911.14 | − | 10238.4i | −0.425382 | − | 0.736784i | ||||
\(579\) | −1704.20 | + | 2951.76i | −0.122321 | + | 0.211867i | ||||
\(580\) | 3190.34 | 0.228399 | ||||||||
\(581\) | 5688.32 | + | 2689.91i | 0.406181 | + | 0.192076i | ||||
\(582\) | −1995.89 | −0.142152 | ||||||||
\(583\) | 4966.52 | − | 8602.27i | 0.352817 | − | 0.611097i | ||||
\(584\) | −6026.70 | − | 10438.6i | −0.427032 | − | 0.739641i | ||||
\(585\) | 984.815 | + | 1705.75i | 0.0696019 | + | 0.120554i | ||||
\(586\) | −13808.7 | + | 23917.4i | −0.973436 | + | 1.68604i | ||||
\(587\) | 18697.5 | 1.31470 | 0.657351 | − | 0.753585i | \(-0.271677\pi\) | ||||
0.657351 | + | 0.753585i | \(0.271677\pi\) | |||||||
\(588\) | 3712.56 | − | 613.452i | 0.260380 | − | 0.0430244i | ||||
\(589\) | −1782.39 | −0.124689 | ||||||||
\(590\) | 2842.71 | − | 4923.71i | 0.198360 | − | 0.343569i | ||||
\(591\) | 1953.62 | + | 3383.78i | 0.135975 | + | 0.235516i | ||||
\(592\) | 12899.2 | + | 22342.1i | 0.895530 | + | 1.55110i | ||||
\(593\) | 7143.52 | − | 12372.9i | 0.494686 | − | 0.856822i | −0.505295 | − | 0.862947i | \(-0.668616\pi\) |
0.999981 | + | 0.00612480i | \(0.00194960\pi\) | |||||||
\(594\) | 3479.03 | 0.240313 | ||||||||
\(595\) | −3188.07 | − | 1507.59i | −0.219661 | − | 0.103874i | ||||
\(596\) | −2219.25 | −0.152524 | ||||||||
\(597\) | −1563.08 | + | 2707.33i | −0.107157 | + | 0.185601i | ||||
\(598\) | 206.939 | + | 358.429i | 0.0141511 | + | 0.0245104i | ||||
\(599\) | 2210.28 | + | 3828.31i | 0.150767 | + | 0.261136i | 0.931510 | − | 0.363717i | \(-0.118492\pi\) |
−0.780743 | + | 0.624853i | \(0.785159\pi\) | |||||||
\(600\) | 556.066 | − | 963.135i | 0.0378355 | − | 0.0655330i | ||||
\(601\) | 25208.4 | 1.71093 | 0.855467 | − | 0.517857i | \(-0.173270\pi\) | ||||
0.855467 | + | 0.517857i | \(0.173270\pi\) | |||||||
\(602\) | −24682.4 | + | 17085.4i | −1.67106 | + | 1.15672i | ||||
\(603\) | 7978.98 | 0.538854 | ||||||||
\(604\) | 2914.64 | − | 5048.30i | 0.196349 | − | 0.340087i | ||||
\(605\) | 233.291 | + | 404.071i | 0.0156771 | + | 0.0271535i | ||||
\(606\) | −2740.84 | − | 4747.27i | −0.183728 | − | 0.318225i | ||||
\(607\) | 11194.3 | − | 19389.0i | 0.748536 | − | 1.29650i | −0.199989 | − | 0.979798i | \(-0.564091\pi\) |
0.948524 | − | 0.316704i | \(-0.102576\pi\) | |||||||
\(608\) | 15335.2 | 1.02290 | ||||||||
\(609\) | −792.888 | − | 9662.06i | −0.0527577 | − | 0.642901i | ||||
\(610\) | −4799.48 | −0.318566 | ||||||||
\(611\) | −1394.18 | + | 2414.80i | −0.0923120 | + | 0.159889i | ||||
\(612\) | −626.692 | − | 1085.46i | −0.0413930 | − | 0.0716948i | ||||
\(613\) | −2322.41 | − | 4022.53i | −0.153020 | − | 0.265038i | 0.779316 | − | 0.626631i | \(-0.215567\pi\) |
−0.932336 | + | 0.361592i | \(0.882233\pi\) | |||||||
\(614\) | −3457.37 | + | 5988.34i | −0.227244 | + | 0.393599i | ||||
\(615\) | 3728.01 | 0.244436 | ||||||||
\(616\) | −847.677 | − | 10329.7i | −0.0554446 | − | 0.675642i | ||||
\(617\) | 17799.0 | 1.16137 | 0.580683 | − | 0.814130i | \(-0.302786\pi\) | ||||
0.580683 | + | 0.814130i | \(0.302786\pi\) | |||||||
\(618\) | −6345.29 | + | 10990.4i | −0.413018 | + | 0.715367i | ||||
\(619\) | 91.0870 | + | 157.767i | 0.00591453 | + | 0.0102443i | 0.868968 | − | 0.494869i | \(-0.164784\pi\) |
−0.863053 | + | 0.505113i | \(0.831451\pi\) | |||||||
\(620\) | −163.751 | − | 283.625i | −0.0106071 | − | 0.0183720i | ||||
\(621\) | 37.3890 | − | 64.7596i | 0.00241605 | − | 0.00418472i | ||||
\(622\) | 5655.54 | 0.364577 | ||||||||
\(623\) | 20972.9 | − | 14517.6i | 1.34874 | − | 0.933606i | ||||
\(624\) | 10489.2 | 0.672925 | ||||||||
\(625\) | −312.500 | + | 541.266i | −0.0200000 | + | 0.0346410i | ||||
\(626\) | −3015.75 | − | 5223.43i | −0.192546 | − | 0.333499i | ||||
\(627\) | 5633.26 | + | 9757.09i | 0.358805 | + | 0.621468i | ||||
\(628\) | 820.513 | − | 1421.17i | 0.0521370 | − | 0.0903039i | ||||
\(629\) | 12299.2 | 0.779652 | ||||||||
\(630\) | 2572.33 | + | 1216.41i | 0.162673 | + | 0.0769256i | ||||
\(631\) | 24442.1 | 1.54203 | 0.771017 | − | 0.636814i | \(-0.219748\pi\) | ||||
0.771017 | + | 0.636814i | \(0.219748\pi\) | |||||||
\(632\) | −3868.33 | + | 6700.14i | −0.243471 | + | 0.421705i | ||||
\(633\) | 3147.75 | + | 5452.07i | 0.197649 | + | 0.342338i | ||||
\(634\) | −10450.7 | − | 18101.2i | −0.654656 | − | 1.13390i | ||||
\(635\) | 5723.61 | − | 9913.58i | 0.357692 | − | 0.619541i | ||||
\(636\) | 2887.41 | 0.180021 | ||||||||
\(637\) | 9525.66 | + | 11603.9i | 0.592496 | + | 0.721764i | ||||
\(638\) | 22482.9 | 1.39515 | ||||||||
\(639\) | 4283.53 | − | 7419.30i | 0.265186 | − | 0.459316i | ||||
\(640\) | −4045.83 | − | 7007.58i | −0.249883 | − | 0.432811i | ||||
\(641\) | −8190.86 | − | 14187.0i | −0.504711 | − | 0.874184i | −0.999985 | − | 0.00544791i | \(-0.998266\pi\) |
0.495275 | − | 0.868737i | \(-0.335067\pi\) | |||||||
\(642\) | 7039.33 | − | 12192.5i | 0.432741 | − | 0.749530i | ||||
\(643\) | −22374.1 | −1.37223 | −0.686117 | − | 0.727491i | \(-0.740686\pi\) | ||||
−0.686117 | + | 0.727491i | \(0.740686\pi\) | |||||||
\(644\) | 169.567 | + | 80.1854i | 0.0103756 | + | 0.00490644i | ||||
\(645\) | −7121.10 | −0.434718 | ||||||||
\(646\) | 6469.34 | − | 11205.2i | 0.394014 | − | 0.682452i | ||||
\(647\) | −543.166 | − | 940.791i | −0.0330047 | − | 0.0571659i | 0.849051 | − | 0.528311i | \(-0.177174\pi\) |
−0.882056 | + | 0.471145i | \(0.843841\pi\) | |||||||
\(648\) | −600.551 | − | 1040.19i | −0.0364072 | − | 0.0630592i | ||||
\(649\) | 6284.55 | − | 10885.2i | 0.380108 | − | 0.658367i | ||||
\(650\) | −3735.97 | −0.225441 | ||||||||
\(651\) | −818.273 | + | 566.415i | −0.0492637 | + | 0.0341007i | ||||
\(652\) | 6378.13 | 0.383109 | ||||||||
\(653\) | −9381.49 | + | 16249.2i | −0.562215 | + | 0.973785i | 0.435088 | + | 0.900388i | \(0.356717\pi\) |
−0.997303 | + | 0.0733966i | \(0.976616\pi\) | |||||||
\(654\) | 4590.96 | + | 7951.78i | 0.274497 | + | 0.475442i | ||||
\(655\) | 7294.16 | + | 12633.9i | 0.435124 | + | 0.753657i | ||||
\(656\) | 9926.73 | − | 17193.6i | 0.590814 | − | 1.02332i | ||||
\(657\) | 7315.72 | 0.434419 | ||||||||
\(658\) | 329.458 | + | 4014.75i | 0.0195192 | + | 0.237859i | ||||
\(659\) | −13722.2 | −0.811138 | −0.405569 | − | 0.914064i | \(-0.632927\pi\) | ||||
−0.405569 | + | 0.914064i | \(0.632927\pi\) | |||||||
\(660\) | −1035.08 | + | 1792.80i | −0.0610459 | + | 0.105735i | ||||
\(661\) | −5289.08 | − | 9160.95i | −0.311227 | − | 0.539062i | 0.667401 | − | 0.744699i | \(-0.267407\pi\) |
−0.978628 | + | 0.205637i | \(0.934073\pi\) | |||||||
\(662\) | 11712.1 | + | 20286.0i | 0.687621 | + | 1.19099i | ||||
\(663\) | 2500.33 | − | 4330.70i | 0.146463 | − | 0.253681i | ||||
\(664\) | 5037.96 | 0.294444 | ||||||||
\(665\) | 753.646 | + | 9183.85i | 0.0439476 | + | 0.535541i | ||||
\(666\) | −9923.75 | −0.577384 | ||||||||
\(667\) | 241.623 | − | 418.503i | 0.0140265 | − | 0.0242946i | ||||
\(668\) | −4597.26 | − | 7962.69i | −0.266277 | − | 0.461206i | ||||
\(669\) | −183.338 | − | 317.551i | −0.0105953 | − | 0.0183516i | ||||
\(670\) | −7567.21 | + | 13106.8i | −0.436338 | + | 0.755760i | ||||
\(671\) | −10610.5 | −0.610454 | ||||||||
\(672\) | 7040.22 | − | 4873.30i | 0.404140 | − | 0.279749i | ||||
\(673\) | 10959.9 | 0.627748 | 0.313874 | − | 0.949465i | \(-0.398373\pi\) | ||||
0.313874 | + | 0.949465i | \(0.398373\pi\) | |||||||
\(674\) | 7155.30 | − | 12393.3i | 0.408920 | − | 0.708270i | ||||
\(675\) | 337.500 | + | 584.567i | 0.0192450 | + | 0.0333333i | ||||
\(676\) | 514.202 | + | 890.624i | 0.0292559 | + | 0.0506727i | ||||
\(677\) | −11387.5 | + | 19723.7i | −0.646466 | + | 1.11971i | 0.337495 | + | 0.941327i | \(0.390420\pi\) |
−0.983961 | + | 0.178384i | \(0.942913\pi\) | |||||||
\(678\) | −2589.28 | −0.146668 | ||||||||
\(679\) | −3262.49 | − | 1542.78i | −0.184393 | − | 0.0871965i | ||||
\(680\) | −2823.57 | −0.159234 | ||||||||
\(681\) | −7617.64 | + | 13194.1i | −0.428647 | + | 0.742438i | ||||
\(682\) | −1153.99 | − | 1998.76i | −0.0647924 | − | 0.112224i | ||||
\(683\) | −10081.1 | − | 17461.0i | −0.564776 | − | 0.978222i | −0.997070 | − | 0.0764888i | \(-0.975629\pi\) |
0.432294 | − | 0.901733i | \(-0.357704\pi\) | |||||||
\(684\) | −1637.52 | + | 2836.26i | −0.0915380 | + | 0.158548i | ||||
\(685\) | −13208.0 | −0.736720 | ||||||||
\(686\) | 20856.1 | + | 5951.30i | 1.16077 | + | 0.331227i | ||||
\(687\) | 7471.29 | 0.414917 | ||||||||
\(688\) | −18961.7 | + | 32842.5i | −1.05074 | + | 1.81993i | ||||
\(689\) | 5759.98 | + | 9976.59i | 0.318488 | + | 0.551637i | ||||
\(690\) | 70.9188 | + | 122.835i | 0.00391280 | + | 0.00677717i | ||||
\(691\) | −8150.10 | + | 14116.4i | −0.448689 | + | 0.777153i | −0.998301 | − | 0.0582676i | \(-0.981442\pi\) |
0.549612 | + | 0.835420i | \(0.314776\pi\) | |||||||
\(692\) | 6828.24 | 0.375102 | ||||||||
\(693\) | 5686.82 | + | 2689.21i | 0.311724 | + | 0.147409i | ||||
\(694\) | −29839.4 | −1.63211 | ||||||||
\(695\) | 7365.46 | − | 12757.3i | 0.401997 | − | 0.696279i | ||||
\(696\) | −3881.01 | − | 6722.11i | −0.211364 | − | 0.366093i | ||||
\(697\) | −4732.49 | − | 8196.92i | −0.257182 | − | 0.445453i | ||||
\(698\) | 405.631 | − | 702.574i | 0.0219962 | − | 0.0380986i | ||||
\(699\) | −4953.66 | −0.268047 | ||||||||
\(700\) | −1392.16 | + | 963.663i | −0.0751694 | + | 0.0520329i | ||||
\(701\) | −5644.95 | −0.304147 | −0.152073 | − | 0.988369i | \(-0.548595\pi\) | ||||
−0.152073 | + | 0.988369i | \(0.548595\pi\) | |||||||
\(702\) | −2017.42 | + | 3494.28i | −0.108465 | + | 0.187867i | ||||
\(703\) | −16068.6 | − | 27831.6i | −0.862075 | − | 1.49316i | ||||
\(704\) | −2130.46 | − | 3690.06i | −0.114055 | − | 0.197549i | ||||
\(705\) | −477.792 | + | 827.560i | −0.0255244 | + | 0.0442095i | ||||
\(706\) | −17492.2 | −0.932477 | ||||||||
\(707\) | −810.650 | − | 9878.50i | −0.0431225 | − | 0.525487i | ||||
\(708\) | 3653.68 | 0.193946 | ||||||||
\(709\) | 3373.06 | − | 5842.31i | 0.178671 | − | 0.309468i | −0.762754 | − | 0.646688i | \(-0.776153\pi\) |
0.941426 | + | 0.337221i | \(0.109487\pi\) | |||||||
\(710\) | 8124.95 | + | 14072.8i | 0.429470 | + | 0.743864i | ||||
\(711\) | −2347.85 | − | 4066.60i | −0.123842 | − | 0.214500i | ||||
\(712\) | 10211.4 | − | 17686.6i | 0.537481 | − | 0.930945i | ||||
\(713\) | −49.6074 | −0.00260562 | ||||||||
\(714\) | −590.851 | − | 7200.05i | −0.0309693 | − | 0.377388i | ||||
\(715\) | −8259.34 | −0.432003 | ||||||||
\(716\) | 4398.71 | − | 7618.79i | 0.229592 | − | 0.397664i | ||||
\(717\) | −4160.40 | − | 7206.02i | −0.216699 | − | 0.375333i | ||||
\(718\) | −16397.2 | − | 28400.7i | −0.852280 | − | 1.47619i | ||||
\(719\) | 4387.54 | − | 7599.45i | 0.227577 | − | 0.394175i | −0.729513 | − | 0.683967i | \(-0.760253\pi\) |
0.957089 | + | 0.289793i | \(0.0935864\pi\) | |||||||
\(720\) | 3594.70 | 0.186065 | ||||||||
\(721\) | −18867.3 | + | 13060.1i | −0.974556 | + | 0.674596i | ||||
\(722\) | −10390.0 | −0.535564 | ||||||||
\(723\) | 7323.20 | − | 12684.1i | 0.376698 | − | 0.652460i | ||||
\(724\) | −8347.77 | − | 14458.8i | −0.428512 | − | 0.742204i | ||||
\(725\) | 2181.07 | + | 3777.72i | 0.111728 | + | 0.193518i | ||||
\(726\) | −477.903 | + | 827.752i | −0.0244306 | + | 0.0423151i | ||||
\(727\) | 11113.0 | 0.566931 | 0.283466 | − | 0.958982i | \(-0.408516\pi\) | ||||
0.283466 | + | 0.958982i | \(0.408516\pi\) | |||||||
\(728\) | 10866.5 | + | 5138.61i | 0.553215 | + | 0.261606i | ||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | −6938.18 | + | 12017.3i | −0.351772 | + | 0.609287i | ||||
\(731\) | 9039.83 | + | 15657.4i | 0.457387 | + | 0.792218i | ||||
\(732\) | −1542.17 | − | 2671.12i | −0.0778693 | − | 0.134874i | ||||
\(733\) | 14359.9 | − | 24872.2i | 0.723597 | − | 1.25331i | −0.235951 | − | 0.971765i | \(-0.575821\pi\) |
0.959549 | − | 0.281542i | \(-0.0908460\pi\) | |||||||
\(734\) | −17995.2 | −0.904927 | ||||||||
\(735\) | 3264.48 | + | 3976.71i | 0.163826 | + | 0.199569i | ||||
\(736\) | 426.809 | 0.0213755 | ||||||||
\(737\) | −16729.3 | + | 28976.0i | −0.836136 | + | 1.44823i | ||||
\(738\) | 3818.47 | + | 6613.78i | 0.190460 | + | 0.329887i | ||||
\(739\) | −10312.0 | − | 17860.9i | −0.513304 | − | 0.889069i | −0.999881 | − | 0.0154313i | \(-0.995088\pi\) |
0.486577 | − | 0.873638i | \(-0.338245\pi\) | |||||||
\(740\) | 2952.50 | − | 5113.88i | 0.146670 | − | 0.254041i | ||||
\(741\) | −13066.5 | −0.647786 | ||||||||
\(742\) | 15045.1 | + | 7114.56i | 0.744369 | + | 0.352000i | ||||
\(743\) | −1217.72 | −0.0601265 | −0.0300633 | − | 0.999548i | \(-0.509571\pi\) | ||||
−0.0300633 | + | 0.999548i | \(0.509571\pi\) | |||||||
\(744\) | −398.403 | + | 690.055i | −0.0196320 | + | 0.0340035i | ||||
\(745\) | −1517.19 | − | 2627.84i | −0.0746113 | − | 0.129231i | ||||
\(746\) | −420.608 | − | 728.515i | −0.0206428 | − | 0.0357545i | ||||
\(747\) | −1528.88 | + | 2648.09i | −0.0748844 | + | 0.129704i | ||||
\(748\) | 5255.87 | 0.256917 | ||||||||
\(749\) | 20931.0 | − | 14488.6i | 1.02110 | − | 0.706812i | ||||
\(750\) | −1280.33 | −0.0623347 | ||||||||
\(751\) | −12483.9 | + | 21622.7i | −0.606582 | + | 1.05063i | 0.385217 | + | 0.922826i | \(0.374127\pi\) |
−0.991799 | + | 0.127805i | \(0.959207\pi\) | |||||||
\(752\) | 2544.47 | + | 4407.16i | 0.123388 | + | 0.213714i | ||||
\(753\) | 37.1037 | + | 64.2654i | 0.00179566 | + | 0.00311018i | ||||
\(754\) | −13037.4 | + | 22581.5i | −0.629701 | + | 1.09067i | ||||
\(755\) | 7970.34 | 0.384199 | ||||||||
\(756\) | 149.556 | + | 1822.47i | 0.00719483 | + | 0.0876755i | ||||
\(757\) | −32766.2 | −1.57319 | −0.786596 | − | 0.617468i | \(-0.788158\pi\) | ||||
−0.786596 | + | 0.617468i | \(0.788158\pi\) | |||||||
\(758\) | −17276.8 | + | 29924.3i | −0.827865 | + | 1.43390i | ||||
\(759\) | 156.785 | + | 271.559i | 0.00749793 | + | 0.0129868i | ||||
\(760\) | 3688.93 | + | 6389.41i | 0.176068 | + | 0.304958i | ||||
\(761\) | −9123.13 | + | 15801.7i | −0.434577 | + | 0.752710i | −0.997261 | − | 0.0739624i | \(-0.976436\pi\) |
0.562684 | + | 0.826672i | \(0.309769\pi\) | |||||||
\(762\) | 23449.9 | 1.11483 | ||||||||
\(763\) | 1357.86 | + | 16546.7i | 0.0644269 | + | 0.785100i | ||||
\(764\) | −14410.0 | −0.682374 | ||||||||
\(765\) | 856.873 | − | 1484.15i | 0.0404972 | − | 0.0701431i | ||||
\(766\) | 5827.32 | + | 10093.2i | 0.274869 | + | 0.476087i | ||||
\(767\) | 7288.59 | + | 12624.2i | 0.343123 | + | 0.594307i | ||||
\(768\) | 6933.17 | − | 12008.6i | 0.325754 | − | 0.564223i | ||||
\(769\) | 15150.4 | 0.710451 | 0.355225 | − | 0.934781i | \(-0.384404\pi\) | ||||
0.355225 | + | 0.934781i | \(0.384404\pi\) | |||||||
\(770\) | −9810.80 | + | 6791.12i | −0.459165 | + | 0.317838i | ||||
\(771\) | −14172.3 | −0.662003 | ||||||||
\(772\) | 2077.33 | − | 3598.05i | 0.0968457 | − | 0.167742i | ||||
\(773\) | 6365.80 | + | 11025.9i | 0.296199 | + | 0.513032i | 0.975263 | − | 0.221047i | \(-0.0709475\pi\) |
−0.679064 | + | 0.734079i | \(0.737614\pi\) | |||||||
\(774\) | −7293.89 | − | 12633.4i | −0.338725 | − | 0.586689i | ||||
\(775\) | 223.896 | − | 387.799i | 0.0103775 | − | 0.0179744i | ||||
\(776\) | −2889.48 | −0.133668 | ||||||||
\(777\) | −16221.4 | − | 7670.83i | −0.748956 | − | 0.354169i | ||||
\(778\) | −16735.8 | −0.771220 | ||||||||
\(779\) | −12365.8 | + | 21418.1i | −0.568742 | + | 0.985089i | ||||
\(780\) | −1200.44 | − | 2079.23i | −0.0551060 | − | 0.0954464i | ||||
\(781\) | 17962.3 | + | 31111.7i | 0.822975 | + | 1.42543i | ||||
\(782\) | 180.055 | − | 311.864i | 0.00823369 | − | 0.0142612i | ||||
\(783\) | 4711.10 | 0.215021 | ||||||||
\(784\) | 27033.1 | − | 4466.86i | 1.23146 | − | 0.203483i | ||||
\(785\) | 2243.77 | 0.102017 | ||||||||
\(786\) | −14942.3 | + | 25880.8i | −0.678084 | + | 1.17448i | ||||
\(787\) | 16020.6 | + | 27748.4i | 0.725631 | + | 1.25683i | 0.958714 | + | 0.284373i | \(0.0917853\pi\) |
−0.233083 | + | 0.972457i | \(0.574881\pi\) | |||||||
\(788\) | −2381.37 | − | 4124.66i | −0.107656 | − | 0.186466i | ||||
\(789\) | −984.409 | + | 1705.05i | −0.0444181 | + | 0.0769344i | ||||
\(790\) | 8906.75 | 0.401124 | ||||||||
\(791\) | −4232.44 | − | 2001.45i | −0.190251 | − | 0.0899664i | ||||
\(792\) | 5036.64 | 0.225971 | ||||||||
\(793\) | 6152.84 | − | 10657.0i | 0.275528 | − | 0.477229i | ||||
\(794\) | −7528.86 | − | 13040.4i | −0.336510 | − | 0.582853i | ||||
\(795\) | 1973.97 | + | 3419.02i | 0.0880623 | + | 0.152528i | ||||
\(796\) | 1905.31 | − | 3300.10i | 0.0848393 | − | 0.146946i | ||||
\(797\) | 1301.58 | 0.0578472 | 0.0289236 | − | 0.999582i | \(-0.490792\pi\) | ||||
0.0289236 | + | 0.999582i | \(0.490792\pi\) | |||||||
\(798\) | −15520.9 | + | 10743.7i | −0.688515 | + | 0.476596i | ||||
\(799\) | 2426.12 | 0.107422 | ||||||||
\(800\) | −1926.35 | + | 3336.53i | −0.0851333 | + | 0.147455i | ||||
\(801\) | 6197.70 | + | 10734.7i | 0.273390 | + | 0.473525i | ||||
\(802\) | 10630.8 | + | 18413.1i | 0.468064 | + | 0.810710i | ||||
\(803\) | −15338.7 | + | 26567.4i | −0.674085 | + | 1.16755i | ||||
\(804\) | −9725.99 | −0.426628 | ||||||||
\(805\) | 20.9755 | + | 255.605i | 0.000918370 | + | 0.0111912i | ||||
\(806\) | 2676.70 | 0.116976 | ||||||||
\(807\) | 4622.11 | − | 8005.72i | 0.201618 | − | 0.349213i | ||||
\(808\) | −3967.95 | − | 6872.69i | −0.172762 | − | 0.299233i | ||||
\(809\) | −7892.44 | − | 13670.1i | −0.342996 | − | 0.594086i | 0.641992 | − | 0.766711i | \(-0.278108\pi\) |
−0.984988 | + | 0.172626i | \(0.944775\pi\) | |||||||
\(810\) | −691.378 | + | 1197.50i | −0.0299908 | + | 0.0519456i | ||||
\(811\) | −27422.7 | −1.18735 | −0.593676 | − | 0.804704i | \(-0.702324\pi\) | ||||
−0.593676 | + | 0.804704i | \(0.702324\pi\) | |||||||
\(812\) | 966.492 | + | 11777.6i | 0.0417700 | + | 0.509005i | ||||
\(813\) | 12189.4 | 0.525833 | ||||||||
\(814\) | 20806.9 | − | 36038.5i | 0.895921 | − | 1.55178i | ||||
\(815\) | 4360.40 | + | 7552.43i | 0.187409 | + | 0.324601i | ||||
\(816\) | −4563.26 | − | 7903.81i | −0.195767 | − | 0.339079i | ||||
\(817\) | 23620.6 | − | 40912.1i | 1.01148 | − | 1.75194i | ||||
\(818\) | 29775.7 | 1.27272 | ||||||||
\(819\) | −5998.67 | + | 4152.33i | −0.255935 | + | 0.177160i | ||||
\(820\) | −4544.26 | −0.193528 | ||||||||
\(821\) | −2775.25 | + | 4806.87i | −0.117974 | + | 0.204337i | −0.918965 | − | 0.394340i | \(-0.870973\pi\) |
0.800991 | + | 0.598677i | \(0.204307\pi\) | |||||||
\(822\) | −13528.5 | − | 23432.1i | −0.574041 | − | 0.994268i | ||||
\(823\) | 7413.14 | + | 12839.9i | 0.313980 | + | 0.543830i | 0.979220 | − | 0.202800i | \(-0.0650041\pi\) |
−0.665240 | + | 0.746630i | \(0.731671\pi\) | |||||||
\(824\) | −9186.17 | + | 15910.9i | −0.388368 | + | 0.672673i | ||||
\(825\) | −2830.51 | −0.119449 | ||||||||
\(826\) | 19037.8 | + | 9002.65i | 0.801947 | + | 0.379228i | ||||
\(827\) | −25067.8 | −1.05404 | −0.527021 | − | 0.849852i | \(-0.676691\pi\) | ||||
−0.527021 | + | 0.849852i | \(0.676691\pi\) | |||||||
\(828\) | −45.5753 | + | 78.9388i | −0.00191286 | + | 0.00331318i | ||||
\(829\) | 9308.74 | + | 16123.2i | 0.389995 | + | 0.675491i | 0.992448 | − | 0.122663i | \(-0.0391434\pi\) |
−0.602453 | + | 0.798154i | \(0.705810\pi\) | |||||||
\(830\) | −2899.95 | − | 5022.86i | −0.121276 | − | 0.210055i | ||||
\(831\) | 12529.7 | − | 21702.0i | 0.523044 | − | 0.905939i | ||||
\(832\) | 4941.65 | 0.205915 | ||||||||
\(833\) | 4599.67 | − | 12225.9i | 0.191319 | − | 0.508528i | ||||
\(834\) | 30176.7 | 1.25292 | ||||||||
\(835\) | 6285.81 | − | 10887.3i | 0.260514 | − | 0.451224i | ||||
\(836\) | −6866.67 | − | 11893.4i | −0.284077 | − | 0.492037i | ||||
\(837\) | −241.808 | − | 418.823i | −0.00998578 | − | 0.0172959i | ||||
\(838\) | −6841.88 | + | 11850.5i | −0.282039 | + | 0.488506i | ||||
\(839\) | 9100.36 | 0.374469 | 0.187234 | − | 0.982315i | \(-0.440048\pi\) | ||||
0.187234 | + | 0.982315i | \(0.440048\pi\) | |||||||
\(840\) | 3724.01 | + | 1761.02i | 0.152965 | + | 0.0723345i | ||||
\(841\) | 6056.11 | 0.248313 | ||||||||
\(842\) | 23078.1 | − | 39972.5i | 0.944566 | − | 1.63604i | ||||
\(843\) | −4823.34 | − | 8354.28i | −0.197064 | − | 0.341325i | ||||
\(844\) | −3836.96 | − | 6645.80i | −0.156485 | − | 0.271040i | ||||
\(845\) | −703.066 | + | 1217.75i | −0.0286227 | + | 0.0495760i | ||||
\(846\) | −1957.54 | −0.0795528 | ||||||||
\(847\) | −1421.01 | + | 983.637i | −0.0576465 | + | 0.0399034i | ||||
\(848\) | 21024.7 | 0.851404 | ||||||||
\(849\) | −6683.79 | + | 11576.7i | −0.270185 | + | 0.467974i | ||||
\(850\) | 1625.30 | + | 2815.11i | 0.0655853 | + | 0.113597i | ||||
\(851\) | −447.221 | − | 774.609i | −0.0180147 | − | 0.0312024i | ||||
\(852\) | −5221.42 | + | 9043.77i | −0.209956 | + | 0.363655i | ||||
\(853\) | −43589.1 | −1.74966 | −0.874831 | − | 0.484429i | \(-0.839027\pi\) | ||||
−0.874831 | + | 0.484429i | \(0.839027\pi\) | |||||||
\(854\) | −1453.97 | − | 17718.0i | −0.0582599 | − | 0.709949i | ||||
\(855\) | −4477.94 | −0.179114 | ||||||||
\(856\) | 10190.9 | − | 17651.2i | 0.406915 | − | 0.704797i | ||||
\(857\) | 17632.4 | + | 30540.1i | 0.702812 | + | 1.21731i | 0.967475 | + | 0.252965i | \(0.0814057\pi\) |
−0.264664 | + | 0.964341i | \(0.585261\pi\) | |||||||
\(858\) | −8459.75 | − | 14652.7i | −0.336609 | − | 0.583025i | ||||
\(859\) | 7677.48 | − | 13297.8i | 0.304950 | − | 0.528189i | −0.672300 | − | 0.740279i | \(-0.734694\pi\) |
0.977250 | + | 0.212090i | \(0.0680269\pi\) | |||||||
\(860\) | 8680.28 | 0.344180 | ||||||||
\(861\) | 1129.38 | + | 13762.5i | 0.0447028 | + | 0.544744i | ||||
\(862\) | −8370.65 | −0.330749 | ||||||||
\(863\) | 4275.81 | − | 7405.93i | 0.168656 | − | 0.292121i | −0.769291 | − | 0.638898i | \(-0.779391\pi\) |
0.937948 | + | 0.346777i | \(0.112724\pi\) | |||||||
\(864\) | 2080.45 | + | 3603.45i | 0.0819195 | + | 0.141889i | ||||
\(865\) | 4668.11 | + | 8085.41i | 0.183492 | + | 0.317817i | ||||
\(866\) | 16030.4 | − | 27765.4i | 0.629023 | − | 1.08950i | ||||
\(867\) | 10388.0 | 0.406914 | ||||||||
\(868\) | 997.435 | − | 690.433i | 0.0390036 | − | 0.0269986i | ||||
\(869\) | 19690.7 | 0.768656 | ||||||||
\(870\) | −4467.98 | + | 7738.76i | −0.174113 | + | 0.301573i | ||||
\(871\) | −19402.0 | − | 33605.3i | −0.754779 | − | 1.30732i | ||||
\(872\) | 6646.41 | + | 11511.9i | 0.258114 | + | 0.447067i | ||||
\(873\) | 876.875 | − | 1518.79i | 0.0339951 | − | 0.0588813i | ||||
\(874\) | −940.948 | −0.0364165 | ||||||||
\(875\) | −2092.83 | − | 989.665i | −0.0808578 | − | 0.0382363i | ||||
\(876\) | −8917.51 | −0.343944 | ||||||||
\(877\) | −24431.5 | + | 42316.5i | −0.940697 | + | 1.62934i | −0.176552 | + | 0.984291i | \(0.556494\pi\) |
−0.764145 | + | 0.645044i | \(0.776839\pi\) | |||||||
\(878\) | 10088.5 | + | 17473.8i | 0.387780 | + | 0.671654i | ||||
\(879\) | −12133.5 | − | 21015.8i | −0.465587 | − | 0.806421i | ||||
\(880\) | −7536.91 | + | 13054.3i | −0.288715 | + | 0.500069i | ||||
\(881\) | −23123.4 | −0.884278 | −0.442139 | − | 0.896947i | \(-0.645780\pi\) | ||||
−0.442139 | + | 0.896947i | \(0.645780\pi\) | |||||||
\(882\) | −3711.29 | + | 9864.64i | −0.141685 | + | 0.376598i | ||||
\(883\) | 16904.0 | 0.644243 | 0.322121 | − | 0.946698i | \(-0.395604\pi\) | ||||
0.322121 | + | 0.946698i | \(0.395604\pi\) | |||||||
\(884\) | −3047.78 | + | 5278.91i | −0.115959 | + | 0.200847i | ||||
\(885\) | 2497.83 | + | 4326.36i | 0.0948741 | + | 0.164327i | ||||
\(886\) | 2959.07 | + | 5125.26i | 0.112203 | + | 0.194342i | ||||
\(887\) | 21809.1 | − | 37774.5i | 0.825567 | − | 1.42992i | −0.0759175 | − | 0.997114i | \(-0.524189\pi\) |
0.901485 | − | 0.432811i | \(-0.142478\pi\) | |||||||
\(888\) | −14366.8 | −0.542925 | ||||||||
\(889\) | 38331.3 | + | 18126.3i | 1.44611 | + | 0.683842i | ||||
\(890\) | −23511.4 | −0.885511 | ||||||||
\(891\) | −1528.47 | + | 2647.40i | −0.0574701 | + | 0.0995411i | ||||
\(892\) | 223.480 | + | 387.079i | 0.00838865 | + | 0.0145296i | ||||
\(893\) | −3169.66 | − | 5490.02i | −0.118778 | − | 0.205729i | ||||
\(894\) | 3108.00 | − | 5383.21i | 0.116272 | − | 0.201389i | ||||
\(895\) | 12028.7 | 0.449245 | ||||||||
\(896\) | 24643.8 | − | 17058.7i | 0.918853 | − | 0.636038i | ||||
\(897\) | −363.666 | −0.0135367 | ||||||||
\(898\) | 26989.8 | − | 46747.8i | 1.00296 | − | 1.73719i | ||||
\(899\) | −1562.66 | − | 2706.61i | −0.0579730 | − | 0.100412i | ||||
\(900\) | −411.396 | − | 712.559i | −0.0152369 | − | 0.0263911i | ||||
\(901\) | 5011.68 | − | 8680.48i | 0.185309 | − | 0.320964i | ||||
\(902\) | −32024.3 | −1.18214 | ||||||||
\(903\) | −2157.29 | − | 26288.6i | −0.0795019 | − | 0.968802i | ||||
\(904\) | −3748.54 | −0.137914 | ||||||||
\(905\) | 11413.9 | − | 19769.4i | 0.419237 | − | 0.726141i | ||||
\(906\) | 8163.73 | + | 14140.0i | 0.299362 | + | 0.518510i | ||||
\(907\) | 19793.2 | + | 34282.8i | 0.724612 | + | 1.25506i | 0.959134 | + | 0.282953i | \(0.0913141\pi\) |
−0.234522 | + | 0.972111i | \(0.575353\pi\) | |||||||
\(908\) | 9285.53 | − | 16083.0i | 0.339374 | − | 0.587812i | ||||
\(909\) | 4816.64 | 0.175751 | ||||||||
\(910\) | −1131.79 | − | 13791.8i | −0.0412290 | − | 0.502412i | ||||
\(911\) | −36388.3 | −1.32338 | −0.661690 | − | 0.749778i | \(-0.730160\pi\) | ||||
−0.661690 | + | 0.749778i | \(0.730160\pi\) | |||||||
\(912\) | −11923.6 | + | 20652.3i | −0.432927 | + | 0.749851i | ||||
\(913\) | −6411.11 | − | 11104.4i | −0.232395 | − | 0.402520i | ||||
\(914\) | −12077.9 | − | 20919.6i | −0.437092 | − | 0.757066i | ||||
\(915\) | 2108.60 | − | 3652.21i | 0.0761839 | − | 0.131954i | ||||
\(916\) | −9107.14 | −0.328503 | ||||||||
\(917\) | −44430.0 | + | 30754.8i | −1.60001 | + | 1.10754i | ||||
\(918\) | 3510.66 | 0.126219 | ||||||||
\(919\) | −2473.44 | + | 4284.12i | −0.0887826 | + | 0.153776i | −0.906997 | − | 0.421138i | \(-0.861631\pi\) |
0.818214 | + | 0.574914i | \(0.194964\pi\) | |||||||
\(920\) | 102.670 | + | 177.830i | 0.00367928 | + | 0.00637270i | ||||
\(921\) | −3037.92 | − | 5261.83i | −0.108689 | − | 0.188255i | ||||
\(922\) | 13279.0 | − | 22999.9i | 0.474318 | − | 0.821542i | ||||
\(923\) | −41664.1 | −1.48580 | ||||||||
\(924\) | −6931.96 | − | 3278.01i | −0.246802 | − | 0.116708i | ||||
\(925\) | 8073.89 | 0.286992 | ||||||||
\(926\) | 19268.8 | − | 33374.5i | 0.683813 | − | 1.18440i | ||||
\(927\) | −5575.47 | − | 9657.00i | −0.197543 | − | 0.342155i | ||||
\(928\) | 13444.8 | + | 23287.0i | 0.475588 | + | 0.823743i | ||||
\(929\) | −26728.8 | + | 46295.7i | −0.943966 | + | 1.63500i | −0.186157 | + | 0.982520i | \(0.559603\pi\) |
−0.757809 | + | 0.652477i | \(0.773730\pi\) | |||||||
\(930\) | 917.315 | 0.0323440 | ||||||||
\(931\) | −33675.2 | + | 5564.38i | −1.18546 | + | 0.195881i | ||||
\(932\) | 6038.27 | 0.212221 | ||||||||
\(933\) | −2484.70 | + | 4303.64i | −0.0871871 | + | 0.151013i | ||||
\(934\) | 31863.5 | + | 55189.2i | 1.11628 | + | 1.93345i | ||||
\(935\) | 3593.17 | + | 6223.55i | 0.125678 | + | 0.217681i | ||||
\(936\) | −2920.65 | + | 5058.72i | −0.101992 | + | 0.176655i | ||||
\(937\) | 1214.58 | 0.0423464 | 0.0211732 | − | 0.999776i | \(-0.493260\pi\) | ||||
0.0211732 | + | 0.999776i | \(0.493260\pi\) | |||||||
\(938\) | −50678.0 | − | 23964.8i | −1.76407 | − | 0.834199i | ||||
\(939\) | 5299.75 | 0.184186 | ||||||||
\(940\) | 582.405 | − | 1008.76i | 0.0202085 | − | 0.0350021i | ||||
\(941\) | 6117.84 | + | 10596.4i | 0.211940 | + | 0.367091i | 0.952322 | − | 0.305096i | \(-0.0986884\pi\) |
−0.740381 | + | 0.672187i | \(0.765355\pi\) | |||||||
\(942\) | 2298.21 | + | 3980.62i | 0.0794902 | + | 0.137681i | ||||
\(943\) | −344.164 | + | 596.110i | −0.0118850 | + | 0.0205854i | ||||
\(944\) | 26604.3 | 0.917262 | ||||||||
\(945\) | −2055.77 | + | 1423.02i | −0.0707663 | + | 0.0489850i | ||||
\(946\) | 61171.6 | 2.10239 | ||||||||
\(947\) | 15020.0 | − | 26015.4i | 0.515400 | − | 0.892699i | −0.484440 | − | 0.874824i | \(-0.660977\pi\) |
0.999840 | − | 0.0178744i | \(-0.00568990\pi\) | |||||||
\(948\) | 2861.92 | + | 4956.99i | 0.0980494 | + | 0.169827i | ||||
\(949\) | −17789.2 | − | 30811.8i | −0.608496 | − | 1.05395i | ||||
\(950\) | 4246.84 | − | 7355.74i | 0.145038 | − | 0.251212i | ||||
\(951\) | 18365.7 | 0.626235 | ||||||||
\(952\) | −855.384 | − | 10423.6i | −0.0291210 | − | 0.354865i | ||||
\(953\) | −58329.9 | −1.98268 | −0.991339 | − | 0.131327i | \(-0.958076\pi\) | ||||
−0.991339 | + | 0.131327i | \(0.958076\pi\) | |||||||
\(954\) | −4043.73 | + | 7003.95i | −0.137233 | + | 0.237695i | ||||
\(955\) | −9851.34 | − | 17063.0i | −0.333803 | − | 0.578164i | ||||
\(956\) | 5071.32 | + | 8783.79i | 0.171567 | + | 0.297163i | ||||
\(957\) | −9877.64 | + | 17108.6i | −0.333646 | + | 0.577891i | ||||
\(958\) | 21445.7 | 0.723257 | ||||||||
\(959\) | −4001.29 | − | 48759.4i | −0.134733 | − | 1.64184i | ||||
\(960\) | 1693.52 | 0.0569357 | ||||||||
\(961\) | 14735.1 | − | 25521.9i | 0.494615 | − | 0.856699i | ||||
\(962\) | 24131.0 | + | 41796.1i | 0.808747 | + | 1.40079i | ||||
\(963\) | 6185.31 | + | 10713.3i | 0.206977 | + | 0.358495i | ||||
\(964\) | −8926.62 | + | 15461.4i | −0.298244 | + | 0.516574i | ||||
\(965\) | 5680.66 | 0.189499 | ||||||||
\(966\) | −431.979 | + | 299.019i | −0.0143879 | + | 0.00995940i | ||||
\(967\) | 33211.1 | 1.10444 | 0.552222 | − | 0.833697i | \(-0.313780\pi\) | ||||
0.552222 | + | 0.833697i | \(0.313780\pi\) | |||||||
\(968\) | −691.867 | + | 1198.35i | −0.0229726 | + | 0.0397897i | ||||
\(969\) | 5684.48 | + | 9845.81i | 0.188454 | + | 0.326412i | ||||
\(970\) | 1663.24 | + | 2880.82i | 0.0550552 | + | 0.0953584i | ||||
\(971\) | 16715.4 | − | 28951.9i | 0.552443 | − | 0.956860i | −0.445654 | − | 0.895205i | \(-0.647029\pi\) |
0.998098 | − | 0.0616546i | \(-0.0196377\pi\) | |||||||
\(972\) | −888.616 | −0.0293234 | ||||||||
\(973\) | 49326.9 | + | 23325.9i | 1.62523 | + | 0.768544i | ||||
\(974\) | −23095.3 | −0.759775 | ||||||||
\(975\) | 1641.36 | − | 2842.92i | 0.0539134 | − | 0.0933807i | ||||
\(976\) | −11229.3 | − | 19449.8i | −0.368281 | − | 0.637881i | ||||
\(977\) | −24700.4 | − | 42782.3i | −0.808839 | − | 1.40095i | −0.913669 | − | 0.406460i | \(-0.866763\pi\) |
0.104830 | − | 0.994490i | \(-0.466570\pi\) | |||||||
\(978\) | −8932.39 | + | 15471.4i | −0.292052 | + | 0.505848i | ||||
\(979\) | −51978.2 | −1.69687 | ||||||||
\(980\) | −3979.24 | − | 4847.41i | −0.129706 | − | 0.158005i | ||||
\(981\) | −8067.97 | −0.262580 | ||||||||
\(982\) | 22758.5 | − | 39418.9i | 0.739565 | − | 1.28096i | ||||
\(983\) | −5762.56 | − | 9981.05i | −0.186976 | − | 0.323852i | 0.757265 | − | 0.653108i | \(-0.226535\pi\) |
−0.944241 | + | 0.329256i | \(0.893202\pi\) | |||||||
\(984\) | 5528.05 | + | 9574.87i | 0.179093 | + | 0.310199i | ||||
\(985\) | 3256.04 | − | 5639.63i | 0.105326 | − | 0.182430i | ||||
\(986\) | 22687.3 | 0.732771 | ||||||||
\(987\) | −3199.80 | − | 1513.13i | −0.103192 | − | 0.0487980i | ||||
\(988\) | 15927.4 | 0.512873 | ||||||||
\(989\) | 657.409 | − | 1138.67i | 0.0211369 | − | 0.0366102i | ||||
\(990\) | −2899.19 | − | 5021.54i | −0.0930730 | − | 0.161207i | ||||
\(991\) | −426.143 | − | 738.101i | −0.0136598 | − | 0.0236595i | 0.859115 | − | 0.511783i | \(-0.171015\pi\) |
−0.872775 | + | 0.488124i | \(0.837682\pi\) | |||||||
\(992\) | 1380.16 | − | 2390.51i | 0.0441736 | − | 0.0765110i | ||||
\(993\) | −20582.4 | −0.657768 | ||||||||
\(994\) | −49490.4 | + | 34257.7i | −1.57922 | + | 1.09315i | ||||
\(995\) | 5210.25 | 0.166006 | ||||||||
\(996\) | 1863.63 | − | 3227.89i | 0.0592884 | − | 0.102691i | ||||
\(997\) | −22412.8 | − | 38820.1i | −0.711957 | − | 1.23315i | −0.964121 | − | 0.265461i | \(-0.914476\pi\) |
0.252164 | − | 0.967684i | \(-0.418858\pi\) | |||||||
\(998\) | 20043.1 | + | 34715.7i | 0.635725 | + | 1.10111i | ||||
\(999\) | 4359.90 | − | 7551.56i | 0.138079 | − | 0.239160i |
(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 | 105.4.i.b.16.2 | ✓ | 4 | |
3.2 | odd | 2 | 315.4.j.d.226.1 | 4 | |||
7.2 | even | 3 | 735.4.a.l.1.1 | 2 | |||
7.4 | even | 3 | inner | 105.4.i.b.46.2 | yes | 4 | |
7.5 | odd | 6 | 735.4.a.n.1.1 | 2 | |||
21.2 | odd | 6 | 2205.4.a.bd.1.2 | 2 | |||
21.5 | even | 6 | 2205.4.a.bc.1.2 | 2 | |||
21.11 | odd | 6 | 315.4.j.d.46.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
105.4.i.b.16.2 | ✓ | 4 | 1.1 | even | 1 | trivial | |
105.4.i.b.46.2 | yes | 4 | 7.4 | even | 3 | inner | |
315.4.j.d.46.1 | 4 | 21.11 | odd | 6 | |||
315.4.j.d.226.1 | 4 | 3.2 | odd | 2 | |||
735.4.a.l.1.1 | 2 | 7.2 | even | 3 | |||
735.4.a.n.1.1 | 2 | 7.5 | odd | 6 | |||
2205.4.a.bc.1.2 | 2 | 21.5 | even | 6 | |||
2205.4.a.bd.1.2 | 2 | 21.2 | odd | 6 |