Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [525,3,Mod(349,525)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(525, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("525.349");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 525 = 3 \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 525.e (of order \(2\), degree \(1\), not 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: | \(14.3052138789\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | no (minimal twist has level 105) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 349.11 | ||
Character | \(\chi\) | \(=\) | 525.349 |
Dual form | 525.3.e.c.349.12 |
$q$-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 \(\left(\mathbb{Z}/525\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(176\) | \(451\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 3.80460i | − | 1.90230i | −0.308728 | − | 0.951150i | \(-0.599903\pi\) | ||
0.308728 | − | 0.951150i | \(-0.400097\pi\) | |||||||
\(3\) | −1.73205 | −0.577350 | ||||||||
\(4\) | −10.4750 | −2.61875 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 6.58976i | 1.09829i | ||||||||
\(7\) | −6.55866 | + | 2.44621i | −0.936952 | + | 0.349458i | ||||
\(8\) | 24.6348i | 3.07935i | ||||||||
\(9\) | 3.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 14.4489 | 1.31354 | 0.656768 | − | 0.754092i | \(-0.271923\pi\) | ||||
0.656768 | + | 0.754092i | \(0.271923\pi\) | |||||||
\(12\) | 18.1432 | 1.51193 | ||||||||
\(13\) | −16.9427 | −1.30329 | −0.651643 | − | 0.758526i | \(-0.725920\pi\) | ||||
−0.651643 | + | 0.758526i | \(0.725920\pi\) | |||||||
\(14\) | 9.30684 | + | 24.9531i | 0.664774 | + | 1.78236i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 51.8255 | 3.23909 | ||||||||
\(17\) | 13.0093 | 0.765251 | 0.382625 | − | 0.923904i | \(-0.375020\pi\) | ||||
0.382625 | + | 0.923904i | \(0.375020\pi\) | |||||||
\(18\) | − | 11.4138i | − | 0.634100i | ||||||
\(19\) | 18.6908i | 0.983729i | 0.870672 | + | 0.491864i | \(0.163684\pi\) | ||||
−0.870672 | + | 0.491864i | \(0.836316\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 11.3599 | − | 4.23695i | 0.540950 | − | 0.201760i | ||||
\(22\) | − | 54.9723i | − | 2.49874i | ||||||
\(23\) | − | 10.3861i | − | 0.451570i | −0.974177 | − | 0.225785i | \(-0.927505\pi\) | ||
0.974177 | − | 0.225785i | \(-0.0724948\pi\) | |||||||
\(24\) | − | 42.6687i | − | 1.77786i | ||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 64.4602i | 2.47924i | ||||||||
\(27\) | −5.19615 | −0.192450 | ||||||||
\(28\) | 68.7020 | − | 25.6240i | 2.45364 | − | 0.915142i | ||||
\(29\) | 13.7269 | 0.473341 | 0.236671 | − | 0.971590i | \(-0.423944\pi\) | ||||
0.236671 | + | 0.971590i | \(0.423944\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 42.4383i | − | 1.36898i | −0.729024 | − | 0.684488i | \(-0.760026\pi\) | ||
0.729024 | − | 0.684488i | \(-0.239974\pi\) | |||||||
\(32\) | − | 98.6363i | − | 3.08238i | ||||||
\(33\) | −25.0262 | −0.758371 | ||||||||
\(34\) | − | 49.4951i | − | 1.45574i | ||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −31.4250 | −0.872916 | ||||||||
\(37\) | 28.7434i | 0.776850i | 0.921480 | + | 0.388425i | \(0.126981\pi\) | ||||
−0.921480 | + | 0.388425i | \(0.873019\pi\) | |||||||
\(38\) | 71.1112 | 1.87135 | ||||||||
\(39\) | 29.3456 | 0.752452 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 28.8060i | 0.702585i | 0.936266 | + | 0.351293i | \(0.114258\pi\) | ||||
−0.936266 | + | 0.351293i | \(0.885742\pi\) | |||||||
\(42\) | −16.1199 | − | 43.2200i | −0.383807 | − | 1.02905i | ||||
\(43\) | 5.84593i | 0.135952i | 0.997687 | + | 0.0679759i | \(0.0216541\pi\) | ||||
−0.997687 | + | 0.0679759i | \(0.978346\pi\) | |||||||
\(44\) | −151.352 | −3.43982 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −39.5151 | −0.859023 | ||||||||
\(47\) | 10.5013 | 0.223432 | 0.111716 | − | 0.993740i | \(-0.464365\pi\) | ||||
0.111716 | + | 0.993740i | \(0.464365\pi\) | |||||||
\(48\) | −89.7644 | −1.87009 | ||||||||
\(49\) | 37.0322 | − | 32.0877i | 0.755758 | − | 0.654851i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −22.5327 | −0.441818 | ||||||||
\(52\) | 177.475 | 3.41298 | ||||||||
\(53\) | − | 81.9074i | − | 1.54542i | −0.634757 | − | 0.772712i | \(-0.718900\pi\) | ||
0.634757 | − | 0.772712i | \(-0.281100\pi\) | |||||||
\(54\) | 19.7693i | 0.366098i | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −60.2617 | − | 161.571i | −1.07610 | − | 2.88520i | ||||
\(57\) | − | 32.3735i | − | 0.567956i | ||||||
\(58\) | − | 52.2254i | − | 0.900438i | ||||||
\(59\) | 35.1680i | 0.596067i | 0.954555 | + | 0.298033i | \(0.0963307\pi\) | ||||
−0.954555 | + | 0.298033i | \(0.903669\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 68.4826i | 1.12267i | 0.827590 | + | 0.561333i | \(0.189711\pi\) | ||||
−0.827590 | + | 0.561333i | \(0.810289\pi\) | |||||||
\(62\) | −161.461 | −2.60421 | ||||||||
\(63\) | −19.6760 | + | 7.33862i | −0.312317 | + | 0.116486i | ||||
\(64\) | −167.970 | −2.62453 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 95.2149i | 1.44265i | ||||||||
\(67\) | 47.4637i | 0.708414i | 0.935167 | + | 0.354207i | \(0.115249\pi\) | ||||
−0.935167 | + | 0.354207i | \(0.884751\pi\) | |||||||
\(68\) | −136.272 | −2.00400 | ||||||||
\(69\) | 17.9893i | 0.260714i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 47.6548 | 0.671194 | 0.335597 | − | 0.942006i | \(-0.391062\pi\) | ||||
0.335597 | + | 0.942006i | \(0.391062\pi\) | |||||||
\(72\) | 73.9043i | 1.02645i | ||||||||
\(73\) | 125.967 | 1.72557 | 0.862786 | − | 0.505569i | \(-0.168717\pi\) | ||||
0.862786 | + | 0.505569i | \(0.168717\pi\) | |||||||
\(74\) | 109.357 | 1.47780 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | − | 195.786i | − | 2.57614i | ||||||
\(77\) | −94.7655 | + | 35.3450i | −1.23072 | + | 0.459026i | ||||
\(78\) | − | 111.648i | − | 1.43139i | ||||||
\(79\) | 129.527 | 1.63958 | 0.819790 | − | 0.572665i | \(-0.194090\pi\) | ||||
0.819790 | + | 0.572665i | \(0.194090\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 9.00000 | 0.111111 | ||||||||
\(82\) | 109.595 | 1.33653 | ||||||||
\(83\) | 42.6906 | 0.514345 | 0.257173 | − | 0.966365i | \(-0.417209\pi\) | ||||
0.257173 | + | 0.966365i | \(0.417209\pi\) | |||||||
\(84\) | −118.995 | + | 44.3820i | −1.41661 | + | 0.528358i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 22.2414 | 0.258621 | ||||||||
\(87\) | −23.7757 | −0.273284 | ||||||||
\(88\) | 355.945i | 4.04483i | ||||||||
\(89\) | 25.5329i | 0.286886i | 0.989659 | + | 0.143443i | \(0.0458174\pi\) | ||||
−0.989659 | + | 0.143443i | \(0.954183\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 111.122 | − | 41.4453i | 1.22112 | − | 0.455443i | ||||
\(92\) | 108.795i | 1.18255i | ||||||||
\(93\) | 73.5053i | 0.790379i | ||||||||
\(94\) | − | 39.9533i | − | 0.425035i | ||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 170.843i | 1.77961i | ||||||||
\(97\) | 28.7310 | 0.296196 | 0.148098 | − | 0.988973i | \(-0.452685\pi\) | ||||
0.148098 | + | 0.988973i | \(0.452685\pi\) | |||||||
\(98\) | −122.081 | − | 140.893i | −1.24572 | − | 1.43768i | ||||
\(99\) | 43.3467 | 0.437846 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 12.4609i | 0.123375i | 0.998096 | + | 0.0616875i | \(0.0196482\pi\) | ||||
−0.998096 | + | 0.0616875i | \(0.980352\pi\) | |||||||
\(102\) | 85.7280i | 0.840470i | ||||||||
\(103\) | 38.4795 | 0.373587 | 0.186794 | − | 0.982399i | \(-0.440190\pi\) | ||||
0.186794 | + | 0.982399i | \(0.440190\pi\) | |||||||
\(104\) | − | 417.380i | − | 4.01326i | ||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −311.625 | −2.93986 | ||||||||
\(107\) | − | 87.7985i | − | 0.820547i | −0.911963 | − | 0.410273i | \(-0.865433\pi\) | ||
0.911963 | − | 0.410273i | \(-0.134567\pi\) | |||||||
\(108\) | 54.4297 | 0.503978 | ||||||||
\(109\) | −130.012 | −1.19277 | −0.596386 | − | 0.802698i | \(-0.703397\pi\) | ||||
−0.596386 | + | 0.802698i | \(0.703397\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − | 49.7851i | − | 0.448515i | ||||||
\(112\) | −339.906 | + | 126.776i | −3.03487 | + | 1.13193i | ||||
\(113\) | 158.597i | 1.40351i | 0.712417 | + | 0.701757i | \(0.247601\pi\) | ||||
−0.712417 | + | 0.701757i | \(0.752399\pi\) | |||||||
\(114\) | −123.168 | −1.08042 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −143.789 | −1.23956 | ||||||||
\(117\) | −50.8281 | −0.434428 | ||||||||
\(118\) | 133.800 | 1.13390 | ||||||||
\(119\) | −85.3234 | + | 31.8233i | −0.717003 | + | 0.267423i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 87.7709 | 0.725379 | ||||||||
\(122\) | 260.549 | 2.13565 | ||||||||
\(123\) | − | 49.8934i | − | 0.405638i | ||||||
\(124\) | 444.541i | 3.58501i | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 27.9205 | + | 74.8593i | 0.221591 | + | 0.594122i | ||||
\(127\) | 43.0643i | 0.339089i | 0.985523 | + | 0.169545i | \(0.0542297\pi\) | ||||
−0.985523 | + | 0.169545i | \(0.945770\pi\) | |||||||
\(128\) | 244.513i | 1.91026i | ||||||||
\(129\) | − | 10.1254i | − | 0.0784919i | ||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0.686731i | 0.00524222i | 0.999997 | + | 0.00262111i | \(0.000834326\pi\) | ||||
−0.999997 | + | 0.00262111i | \(0.999166\pi\) | |||||||
\(132\) | 262.150 | 1.98598 | ||||||||
\(133\) | −45.7216 | − | 122.587i | −0.343772 | − | 0.921707i | ||||
\(134\) | 180.581 | 1.34762 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 320.480i | 2.35647i | ||||||||
\(137\) | 76.2084i | 0.556266i | 0.960543 | + | 0.278133i | \(0.0897155\pi\) | ||||
−0.960543 | + | 0.278133i | \(0.910284\pi\) | |||||||
\(138\) | 68.4421 | 0.495957 | ||||||||
\(139\) | − | 49.0445i | − | 0.352838i | −0.984315 | − | 0.176419i | \(-0.943549\pi\) | ||
0.984315 | − | 0.176419i | \(-0.0564514\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −18.1888 | −0.128998 | ||||||||
\(142\) | − | 181.307i | − | 1.27681i | ||||||
\(143\) | −244.804 | −1.71191 | ||||||||
\(144\) | 155.476 | 1.07970 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | − | 479.253i | − | 3.28256i | ||||||
\(147\) | −64.1416 | + | 55.5775i | −0.436337 | + | 0.378078i | ||||
\(148\) | − | 301.087i | − | 2.03437i | ||||||
\(149\) | 242.344 | 1.62647 | 0.813236 | − | 0.581934i | \(-0.197704\pi\) | ||||
0.813236 | + | 0.581934i | \(0.197704\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 107.704 | 0.713271 | 0.356636 | − | 0.934244i | \(-0.383924\pi\) | ||||
0.356636 | + | 0.934244i | \(0.383924\pi\) | |||||||
\(152\) | −460.445 | −3.02924 | ||||||||
\(153\) | 39.0278 | 0.255084 | ||||||||
\(154\) | 134.474 | + | 360.545i | 0.873205 | + | 2.34120i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −307.395 | −1.97048 | ||||||||
\(157\) | 76.1684 | 0.485149 | 0.242575 | − | 0.970133i | \(-0.422008\pi\) | ||||
0.242575 | + | 0.970133i | \(0.422008\pi\) | |||||||
\(158\) | − | 492.798i | − | 3.11897i | ||||||
\(159\) | 141.868i | 0.892250i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 25.4066 | + | 68.1191i | 0.157805 | + | 0.423100i | ||||
\(162\) | − | 34.2414i | − | 0.211367i | ||||||
\(163\) | − | 10.4287i | − | 0.0639800i | −0.999488 | − | 0.0319900i | \(-0.989816\pi\) | ||
0.999488 | − | 0.0319900i | \(-0.0101845\pi\) | |||||||
\(164\) | − | 301.743i | − | 1.83989i | ||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | − | 162.421i | − | 0.978439i | ||||||
\(167\) | 75.7598 | 0.453652 | 0.226826 | − | 0.973935i | \(-0.427165\pi\) | ||||
0.226826 | + | 0.973935i | \(0.427165\pi\) | |||||||
\(168\) | 104.376 | + | 279.849i | 0.621287 | + | 1.66577i | ||||
\(169\) | 118.055 | 0.698552 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 56.0725i | 0.327910i | ||||||||
\(172\) | − | 61.2361i | − | 0.356024i | ||||||
\(173\) | 325.843 | 1.88349 | 0.941743 | − | 0.336333i | \(-0.109187\pi\) | ||||
0.941743 | + | 0.336333i | \(0.109187\pi\) | |||||||
\(174\) | 90.4570i | 0.519868i | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 748.822 | 4.25467 | ||||||||
\(177\) | − | 60.9127i | − | 0.344139i | ||||||
\(178\) | 97.1424 | 0.545744 | ||||||||
\(179\) | 30.9215 | 0.172746 | 0.0863728 | − | 0.996263i | \(-0.472472\pi\) | ||||
0.0863728 | + | 0.996263i | \(0.472472\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 211.403i | 1.16797i | 0.811764 | + | 0.583985i | \(0.198507\pi\) | ||||
−0.811764 | + | 0.583985i | \(0.801493\pi\) | |||||||
\(182\) | −157.683 | − | 422.773i | −0.866390 | − | 2.32293i | ||||
\(183\) | − | 118.615i | − | 0.648171i | ||||||
\(184\) | 255.860 | 1.39054 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 279.658 | 1.50354 | ||||||||
\(187\) | 187.970 | 1.00519 | ||||||||
\(188\) | −110.001 | −0.585112 | ||||||||
\(189\) | 34.0798 | − | 12.7109i | 0.180317 | − | 0.0672532i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 112.093 | 0.586874 | 0.293437 | − | 0.955978i | \(-0.405201\pi\) | ||||
0.293437 | + | 0.955978i | \(0.405201\pi\) | |||||||
\(192\) | 290.932 | 1.51527 | ||||||||
\(193\) | 293.541i | 1.52094i | 0.649373 | + | 0.760470i | \(0.275031\pi\) | ||||
−0.649373 | + | 0.760470i | \(0.724969\pi\) | |||||||
\(194\) | − | 109.310i | − | 0.563453i | ||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −387.912 | + | 336.118i | −1.97914 | + | 1.71489i | ||||
\(197\) | − | 90.7583i | − | 0.460702i | −0.973108 | − | 0.230351i | \(-0.926013\pi\) | ||
0.973108 | − | 0.230351i | \(-0.0739874\pi\) | |||||||
\(198\) | − | 164.917i | − | 0.832914i | ||||||
\(199\) | − | 389.421i | − | 1.95689i | −0.206505 | − | 0.978445i | \(-0.566209\pi\) | ||
0.206505 | − | 0.978445i | \(-0.433791\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | − | 82.2096i | − | 0.409003i | ||||||
\(202\) | 47.4086 | 0.234696 | ||||||||
\(203\) | −90.0301 | + | 33.5788i | −0.443498 | + | 0.165413i | ||||
\(204\) | 236.030 | 1.15701 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | − | 146.399i | − | 0.710676i | ||||||
\(207\) | − | 31.1584i | − | 0.150523i | ||||||
\(208\) | −878.064 | −4.22146 | ||||||||
\(209\) | 270.062i | 1.29216i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −21.1049 | −0.100023 | −0.0500115 | − | 0.998749i | \(-0.515926\pi\) | ||||
−0.0500115 | + | 0.998749i | \(0.515926\pi\) | |||||||
\(212\) | 857.980i | 4.04707i | ||||||||
\(213\) | −82.5405 | −0.387514 | ||||||||
\(214\) | −334.038 | −1.56093 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | − | 128.006i | − | 0.592620i | ||||||
\(217\) | 103.813 | + | 278.338i | 0.478400 | + | 1.28267i | ||||
\(218\) | 494.645i | 2.26901i | ||||||||
\(219\) | −218.181 | −0.996259 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −220.412 | −0.997340 | ||||||||
\(222\) | −189.413 | −0.853209 | ||||||||
\(223\) | −293.039 | −1.31408 | −0.657039 | − | 0.753857i | \(-0.728191\pi\) | ||||
−0.657039 | + | 0.753857i | \(0.728191\pi\) | |||||||
\(224\) | 241.285 | + | 646.922i | 1.07716 | + | 2.88805i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 603.398 | 2.66990 | ||||||||
\(227\) | 73.9333 | 0.325697 | 0.162849 | − | 0.986651i | \(-0.447932\pi\) | ||||
0.162849 | + | 0.986651i | \(0.447932\pi\) | |||||||
\(228\) | 339.112i | 1.48733i | ||||||||
\(229\) | − | 233.516i | − | 1.01972i | −0.860257 | − | 0.509860i | \(-0.829697\pi\) | ||
0.860257 | − | 0.509860i | \(-0.170303\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 164.139 | − | 61.2193i | 0.710557 | − | 0.265019i | ||||
\(232\) | 338.159i | 1.45758i | ||||||||
\(233\) | 385.429i | 1.65420i | 0.562054 | + | 0.827101i | \(0.310011\pi\) | ||||
−0.562054 | + | 0.827101i | \(0.689989\pi\) | |||||||
\(234\) | 193.381i | 0.826413i | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | − | 368.384i | − | 1.56095i | ||||||
\(237\) | −224.347 | −0.946611 | ||||||||
\(238\) | 121.075 | + | 324.621i | 0.508719 | + | 1.36396i | ||||
\(239\) | −407.373 | −1.70449 | −0.852244 | − | 0.523144i | \(-0.824759\pi\) | ||||
−0.852244 | + | 0.523144i | \(0.824759\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 271.816i | 1.12787i | 0.825820 | + | 0.563934i | \(0.190713\pi\) | ||||
−0.825820 | + | 0.563934i | \(0.809287\pi\) | |||||||
\(242\) | − | 333.933i | − | 1.37989i | ||||||
\(243\) | −15.5885 | −0.0641500 | ||||||||
\(244\) | − | 717.355i | − | 2.93998i | ||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −189.825 | −0.771645 | ||||||||
\(247\) | − | 316.673i | − | 1.28208i | ||||||
\(248\) | 1045.46 | 4.21555 | ||||||||
\(249\) | −73.9424 | −0.296957 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 442.250i | 1.76195i | 0.473162 | + | 0.880976i | \(0.343113\pi\) | ||||
−0.473162 | + | 0.880976i | \(0.656887\pi\) | |||||||
\(252\) | 206.106 | − | 76.8719i | 0.817880 | − | 0.305047i | ||||
\(253\) | − | 150.068i | − | 0.593154i | ||||||
\(254\) | 163.843 | 0.645049 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 258.395 | 1.00935 | ||||||||
\(257\) | −390.436 | −1.51921 | −0.759604 | − | 0.650386i | \(-0.774607\pi\) | ||||
−0.759604 | + | 0.650386i | \(0.774607\pi\) | |||||||
\(258\) | −38.5233 | −0.149315 | ||||||||
\(259\) | −70.3124 | − | 188.519i | −0.271476 | − | 0.727871i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 41.1807 | 0.157780 | ||||||||
\(262\) | 2.61274 | 0.00997228 | ||||||||
\(263\) | 1.63279i | 0.00620832i | 0.999995 | + | 0.00310416i | \(0.000988086\pi\) | ||||
−0.999995 | + | 0.00310416i | \(0.999012\pi\) | |||||||
\(264\) | − | 616.515i | − | 2.33529i | ||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −466.395 | + | 173.953i | −1.75336 | + | 0.653957i | ||||
\(267\) | − | 44.2242i | − | 0.165634i | ||||||
\(268\) | − | 497.182i | − | 1.85516i | ||||||
\(269\) | 410.340i | 1.52543i | 0.646737 | + | 0.762713i | \(0.276133\pi\) | ||||
−0.646737 | + | 0.762713i | \(0.723867\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 470.030i | − | 1.73443i | −0.497937 | − | 0.867213i | \(-0.665909\pi\) | ||
0.497937 | − | 0.867213i | \(-0.334091\pi\) | |||||||
\(272\) | 674.211 | 2.47872 | ||||||||
\(273\) | −192.468 | + | 71.7854i | −0.705011 | + | 0.262950i | ||||
\(274\) | 289.943 | 1.05818 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | − | 188.438i | − | 0.682745i | ||||||
\(277\) | 366.582i | 1.32340i | 0.749768 | + | 0.661701i | \(0.230165\pi\) | ||||
−0.749768 | + | 0.661701i | \(0.769835\pi\) | |||||||
\(278\) | −186.595 | −0.671204 | ||||||||
\(279\) | − | 127.315i | − | 0.456326i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 10.1164 | 0.0360015 | 0.0180008 | − | 0.999838i | \(-0.494270\pi\) | ||||
0.0180008 | + | 0.999838i | \(0.494270\pi\) | |||||||
\(282\) | 69.2011i | 0.245394i | ||||||||
\(283\) | 121.896 | 0.430729 | 0.215364 | − | 0.976534i | \(-0.430906\pi\) | ||||
0.215364 | + | 0.976534i | \(0.430906\pi\) | |||||||
\(284\) | −499.183 | −1.75769 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 931.380i | 3.25657i | ||||||||
\(287\) | −70.4654 | − | 188.929i | −0.245524 | − | 0.658289i | ||||
\(288\) | − | 295.909i | − | 1.02746i | ||||||
\(289\) | −119.759 | −0.414391 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −49.7635 | −0.171009 | ||||||||
\(292\) | −1319.50 | −4.51884 | ||||||||
\(293\) | −292.803 | −0.999327 | −0.499663 | − | 0.866220i | \(-0.666543\pi\) | ||||
−0.499663 | + | 0.866220i | \(0.666543\pi\) | |||||||
\(294\) | 211.450 | + | 244.033i | 0.719218 | + | 0.830045i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −708.088 | −2.39219 | ||||||||
\(297\) | −75.0787 | −0.252790 | ||||||||
\(298\) | − | 922.023i | − | 3.09404i | ||||||
\(299\) | 175.969i | 0.588525i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −14.3003 | − | 38.3415i | −0.0475095 | − | 0.127380i | ||||
\(302\) | − | 409.771i | − | 1.35686i | ||||||
\(303\) | − | 21.5829i | − | 0.0712306i | ||||||
\(304\) | 968.662i | 3.18639i | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | − | 148.485i | − | 0.485246i | ||||||
\(307\) | 167.855 | 0.546758 | 0.273379 | − | 0.961906i | \(-0.411859\pi\) | ||||
0.273379 | + | 0.961906i | \(0.411859\pi\) | |||||||
\(308\) | 992.668 | − | 370.238i | 3.22295 | − | 1.20207i | ||||
\(309\) | −66.6485 | −0.215691 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 303.739i | − | 0.976652i | −0.872661 | − | 0.488326i | \(-0.837608\pi\) | ||
0.872661 | − | 0.488326i | \(-0.162392\pi\) | |||||||
\(312\) | 722.923i | 2.31706i | ||||||||
\(313\) | −17.2151 | −0.0550004 | −0.0275002 | − | 0.999622i | \(-0.508755\pi\) | ||||
−0.0275002 | + | 0.999622i | \(0.508755\pi\) | |||||||
\(314\) | − | 289.790i | − | 0.922899i | ||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1356.79 | −4.29364 | ||||||||
\(317\) | 82.8657i | 0.261406i | 0.991422 | + | 0.130703i | \(0.0417234\pi\) | ||||
−0.991422 | + | 0.130703i | \(0.958277\pi\) | |||||||
\(318\) | 539.750 | 1.69733 | ||||||||
\(319\) | 198.339 | 0.621751 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 152.071i | 0.473743i | ||||||||
\(322\) | 259.166 | − | 96.6619i | 0.804863 | − | 0.300192i | ||||
\(323\) | 243.154i | 0.752799i | ||||||||
\(324\) | −94.2749 | −0.290972 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −39.6772 | −0.121709 | ||||||||
\(327\) | 225.188 | 0.688647 | ||||||||
\(328\) | −709.629 | −2.16350 | ||||||||
\(329\) | −68.8745 | + | 25.6883i | −0.209345 | + | 0.0780800i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −451.490 | −1.36402 | −0.682009 | − | 0.731343i | \(-0.738894\pi\) | ||||
−0.682009 | + | 0.731343i | \(0.738894\pi\) | |||||||
\(332\) | −447.184 | −1.34694 | ||||||||
\(333\) | 86.2303i | 0.258950i | ||||||||
\(334\) | − | 288.236i | − | 0.862982i | ||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 588.734 | − | 219.582i | 1.75219 | − | 0.653518i | ||||
\(337\) | 204.157i | 0.605808i | 0.953021 | + | 0.302904i | \(0.0979561\pi\) | ||||
−0.953021 | + | 0.302904i | \(0.902044\pi\) | |||||||
\(338\) | − | 449.153i | − | 1.32886i | ||||||
\(339\) | − | 274.698i | − | 0.810319i | ||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 613.187i | − | 1.79820i | ||||||
\(342\) | 213.334 | 0.623783 | ||||||||
\(343\) | −164.388 | + | 301.041i | −0.479267 | + | 0.877669i | ||||
\(344\) | −144.013 | −0.418643 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | − | 1239.70i | − | 3.58296i | ||||||
\(347\) | 146.593i | 0.422458i | 0.977437 | + | 0.211229i | \(0.0677465\pi\) | ||||
−0.977437 | + | 0.211229i | \(0.932253\pi\) | |||||||
\(348\) | 249.050 | 0.715661 | ||||||||
\(349\) | − | 11.4454i | − | 0.0327947i | −0.999866 | − | 0.0163974i | \(-0.994780\pi\) | ||
0.999866 | − | 0.0163974i | \(-0.00521968\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 88.0369 | 0.250817 | ||||||||
\(352\) | − | 1425.19i | − | 4.04882i | ||||||
\(353\) | 177.817 | 0.503730 | 0.251865 | − | 0.967762i | \(-0.418956\pi\) | ||||
0.251865 | + | 0.967762i | \(0.418956\pi\) | |||||||
\(354\) | −231.748 | −0.654657 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | − | 267.457i | − | 0.751283i | ||||||
\(357\) | 147.784 | − | 55.1196i | 0.413962 | − | 0.154397i | ||||
\(358\) | − | 117.644i | − | 0.328614i | ||||||
\(359\) | −653.079 | −1.81916 | −0.909581 | − | 0.415526i | \(-0.863598\pi\) | ||||
−0.909581 | + | 0.415526i | \(0.863598\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 11.6523 | 0.0322780 | ||||||||
\(362\) | 804.303 | 2.22183 | ||||||||
\(363\) | −152.024 | −0.418798 | ||||||||
\(364\) | −1164.00 | + | 434.140i | −3.19779 | + | 1.19269i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −451.284 | −1.23302 | ||||||||
\(367\) | 466.632 | 1.27148 | 0.635738 | − | 0.771905i | \(-0.280696\pi\) | ||||
0.635738 | + | 0.771905i | \(0.280696\pi\) | |||||||
\(368\) | − | 538.266i | − | 1.46268i | ||||||
\(369\) | 86.4180i | 0.234195i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 200.362 | + | 537.203i | 0.540060 | + | 1.44799i | ||||
\(372\) | − | 769.967i | − | 2.06980i | ||||||
\(373\) | 452.082i | 1.21202i | 0.795459 | + | 0.606008i | \(0.207230\pi\) | ||||
−0.795459 | + | 0.606008i | \(0.792770\pi\) | |||||||
\(374\) | − | 715.149i | − | 1.91216i | ||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 258.697i | 0.688024i | ||||||||
\(377\) | −232.571 | −0.616899 | ||||||||
\(378\) | −48.3597 | − | 129.660i | −0.127936 | − | 0.343016i | ||||
\(379\) | −326.478 | −0.861420 | −0.430710 | − | 0.902490i | \(-0.641737\pi\) | ||||
−0.430710 | + | 0.902490i | \(0.641737\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | − | 74.5896i | − | 0.195773i | ||||||
\(382\) | − | 426.469i | − | 1.11641i | ||||||
\(383\) | 381.262 | 0.995462 | 0.497731 | − | 0.867331i | \(-0.334167\pi\) | ||||
0.497731 | + | 0.867331i | \(0.334167\pi\) | |||||||
\(384\) | − | 423.509i | − | 1.10289i | ||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 1116.81 | 2.89329 | ||||||||
\(387\) | 17.5378i | 0.0453173i | ||||||||
\(388\) | −300.957 | −0.775662 | ||||||||
\(389\) | 68.8443 | 0.176978 | 0.0884888 | − | 0.996077i | \(-0.471796\pi\) | ||||
0.0884888 | + | 0.996077i | \(0.471796\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 135.116i | − | 0.345565i | ||||||
\(392\) | 790.472 | + | 912.278i | 2.01651 | + | 2.32724i | ||||
\(393\) | − | 1.18945i | − | 0.00302660i | ||||||
\(394\) | −345.299 | −0.876394 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −454.056 | −1.14661 | ||||||||
\(397\) | 370.531 | 0.933328 | 0.466664 | − | 0.884435i | \(-0.345456\pi\) | ||||
0.466664 | + | 0.884435i | \(0.345456\pi\) | |||||||
\(398\) | −1481.59 | −3.72259 | ||||||||
\(399\) | 79.1922 | + | 212.327i | 0.198477 | + | 0.532148i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 8.95073 | 0.0223210 | 0.0111605 | − | 0.999938i | \(-0.496447\pi\) | ||||
0.0111605 | + | 0.999938i | \(0.496447\pi\) | |||||||
\(402\) | −312.775 | −0.778047 | ||||||||
\(403\) | 719.019i | 1.78417i | ||||||||
\(404\) | − | 130.528i | − | 0.323088i | ||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 127.754 | + | 342.529i | 0.314665 | + | 0.843667i | ||||
\(407\) | 415.311i | 1.02042i | ||||||||
\(408\) | − | 555.088i | − | 1.36051i | ||||||
\(409\) | − | 63.1330i | − | 0.154359i | −0.997017 | − | 0.0771797i | \(-0.975408\pi\) | ||
0.997017 | − | 0.0771797i | \(-0.0245915\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − | 131.997i | − | 0.321160i | ||||||
\(412\) | −403.072 | −0.978331 | ||||||||
\(413\) | −86.0280 | − | 230.655i | −0.208300 | − | 0.558486i | ||||
\(414\) | −118.545 | −0.286341 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 1671.17i | 4.01722i | ||||||||
\(417\) | 84.9475i | 0.203711i | ||||||||
\(418\) | 1027.48 | 2.45808 | ||||||||
\(419\) | − | 3.58774i | − | 0.00856263i | −0.999991 | − | 0.00428131i | \(-0.998637\pi\) | ||
0.999991 | − | 0.00428131i | \(-0.00136279\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 119.594 | 0.284071 | 0.142035 | − | 0.989862i | \(-0.454635\pi\) | ||||
0.142035 | + | 0.989862i | \(0.454635\pi\) | |||||||
\(422\) | 80.2956i | 0.190274i | ||||||||
\(423\) | 31.5039 | 0.0744773 | ||||||||
\(424\) | 2017.77 | 4.75889 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 314.034i | 0.737168i | ||||||||
\(427\) | −167.523 | − | 449.154i | −0.392324 | − | 1.05188i | ||||
\(428\) | 919.689i | 2.14881i | ||||||||
\(429\) | 424.012 | 0.988373 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −404.488 | −0.938488 | −0.469244 | − | 0.883069i | \(-0.655473\pi\) | ||||
−0.469244 | + | 0.883069i | \(0.655473\pi\) | |||||||
\(432\) | −269.293 | −0.623364 | ||||||||
\(433\) | 116.085 | 0.268094 | 0.134047 | − | 0.990975i | \(-0.457203\pi\) | ||||
0.134047 | + | 0.990975i | \(0.457203\pi\) | |||||||
\(434\) | 1058.97 | − | 394.966i | 2.44002 | − | 0.910060i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 1361.88 | 3.12357 | ||||||||
\(437\) | 194.125 | 0.444223 | ||||||||
\(438\) | 830.091i | 1.89519i | ||||||||
\(439\) | − | 58.4183i | − | 0.133071i | −0.997784 | − | 0.0665357i | \(-0.978805\pi\) | ||
0.997784 | − | 0.0665357i | \(-0.0211946\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 111.096 | − | 96.2630i | 0.251919 | − | 0.218284i | ||||
\(442\) | 838.580i | 1.89724i | ||||||||
\(443\) | − | 267.301i | − | 0.603388i | −0.953405 | − | 0.301694i | \(-0.902448\pi\) | ||
0.953405 | − | 0.301694i | \(-0.0975520\pi\) | |||||||
\(444\) | 521.499i | 1.17455i | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 1114.90i | 2.49977i | ||||||||
\(447\) | −419.753 | −0.939044 | ||||||||
\(448\) | 1101.66 | − | 410.888i | 2.45906 | − | 0.917162i | ||||
\(449\) | −296.478 | −0.660307 | −0.330154 | − | 0.943927i | \(-0.607101\pi\) | ||||
−0.330154 | + | 0.943927i | \(0.607101\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 416.215i | 0.922872i | ||||||||
\(452\) | − | 1661.30i | − | 3.67545i | ||||||
\(453\) | −186.549 | −0.411807 | ||||||||
\(454\) | − | 281.287i | − | 0.619574i | ||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 797.513 | 1.74893 | ||||||||
\(457\) | 12.1251i | 0.0265320i | 0.999912 | + | 0.0132660i | \(0.00422282\pi\) | ||||
−0.999912 | + | 0.0132660i | \(0.995777\pi\) | |||||||
\(458\) | −888.435 | −1.93981 | ||||||||
\(459\) | −67.5981 | −0.147273 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 103.948i | − | 0.225483i | −0.993624 | − | 0.112741i | \(-0.964037\pi\) | ||
0.993624 | − | 0.112741i | \(-0.0359632\pi\) | |||||||
\(462\) | −232.915 | − | 624.482i | −0.504145 | − | 1.35169i | ||||
\(463\) | − | 498.831i | − | 1.07739i | −0.842501 | − | 0.538694i | \(-0.818918\pi\) | ||
0.842501 | − | 0.538694i | \(-0.181082\pi\) | |||||||
\(464\) | 711.403 | 1.53320 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 1466.40 | 3.14679 | ||||||||
\(467\) | −597.683 | −1.27983 | −0.639917 | − | 0.768444i | \(-0.721031\pi\) | ||||
−0.639917 | + | 0.768444i | \(0.721031\pi\) | |||||||
\(468\) | 532.424 | 1.13766 | ||||||||
\(469\) | −116.106 | − | 311.299i | −0.247561 | − | 0.663750i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −131.928 | −0.280101 | ||||||||
\(472\) | −866.354 | −1.83550 | ||||||||
\(473\) | 84.4673i | 0.178578i | ||||||||
\(474\) | 853.551i | 1.80074i | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 893.762 | − | 333.349i | 1.87765 | − | 0.700313i | ||||
\(477\) | − | 245.722i | − | 0.515141i | ||||||
\(478\) | 1549.89i | 3.24245i | ||||||||
\(479\) | 276.703i | 0.577669i | 0.957379 | + | 0.288834i | \(0.0932677\pi\) | ||||
−0.957379 | + | 0.288834i | \(0.906732\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − | 486.992i | − | 1.01246i | ||||||
\(482\) | 1034.15 | 2.14554 | ||||||||
\(483\) | −44.0055 | − | 117.986i | −0.0911087 | − | 0.244277i | ||||
\(484\) | −919.399 | −1.89958 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 59.3079i | 0.122033i | ||||||||
\(487\) | − | 542.653i | − | 1.11428i | −0.830420 | − | 0.557138i | \(-0.811899\pi\) | ||
0.830420 | − | 0.557138i | \(-0.188101\pi\) | |||||||
\(488\) | −1687.05 | −3.45708 | ||||||||
\(489\) | 18.0631i | 0.0369389i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 574.817 | 1.17071 | 0.585353 | − | 0.810778i | \(-0.300956\pi\) | ||||
0.585353 | + | 0.810778i | \(0.300956\pi\) | |||||||
\(492\) | 522.633i | 1.06226i | ||||||||
\(493\) | 178.577 | 0.362225 | ||||||||
\(494\) | −1204.82 | −2.43890 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | − | 2199.38i | − | 4.43424i | ||||||
\(497\) | −312.552 | + | 116.573i | −0.628877 | + | 0.234554i | ||||
\(498\) | 281.321i | 0.564902i | ||||||||
\(499\) | 549.967 | 1.10214 | 0.551070 | − | 0.834459i | \(-0.314220\pi\) | ||||
0.551070 | + | 0.834459i | \(0.314220\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −131.220 | −0.261916 | ||||||||
\(502\) | 1682.58 | 3.35176 | ||||||||
\(503\) | 397.053 | 0.789369 | 0.394685 | − | 0.918817i | \(-0.370854\pi\) | ||||
0.394685 | + | 0.918817i | \(0.370854\pi\) | |||||||
\(504\) | −180.785 | − | 484.713i | −0.358701 | − | 0.961733i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −570.949 | −1.12836 | ||||||||
\(507\) | −204.478 | −0.403309 | ||||||||
\(508\) | − | 451.098i | − | 0.887989i | ||||||
\(509\) | − | 557.813i | − | 1.09590i | −0.836511 | − | 0.547950i | \(-0.815408\pi\) | ||
0.836511 | − | 0.547950i | \(-0.184592\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −826.174 | + | 308.141i | −1.61678 | + | 0.603015i | ||||
\(512\) | − | 5.03806i | − | 0.00983995i | ||||||
\(513\) | − | 97.1205i | − | 0.189319i | ||||||
\(514\) | 1485.45i | 2.88999i | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 106.064i | 0.205550i | ||||||||
\(517\) | 151.732 | 0.293486 | ||||||||
\(518\) | −717.238 | + | 267.511i | −1.38463 | + | 0.516430i | ||||
\(519\) | −564.377 | −1.08743 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 287.300i | − | 0.551439i | −0.961238 | − | 0.275719i | \(-0.911084\pi\) | ||
0.961238 | − | 0.275719i | \(-0.0889161\pi\) | |||||||
\(522\) | − | 156.676i | − | 0.300146i | ||||||
\(523\) | 1012.28 | 1.93553 | 0.967766 | − | 0.251853i | \(-0.0810399\pi\) | ||||
0.967766 | + | 0.251853i | \(0.0810399\pi\) | |||||||
\(524\) | − | 7.19350i | − | 0.0137281i | ||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 6.21211 | 0.0118101 | ||||||||
\(527\) | − | 552.091i | − | 1.04761i | ||||||
\(528\) | −1297.00 | −2.45643 | ||||||||
\(529\) | 421.128 | 0.796084 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 105.504i | 0.198689i | ||||||||
\(532\) | 478.934 | + | 1284.10i | 0.900252 | + | 2.41372i | ||||
\(533\) | − | 488.051i | − | 0.915669i | ||||||
\(534\) | −168.256 | −0.315085 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −1169.26 | −2.18145 | ||||||||
\(537\) | −53.5575 | −0.0997347 | ||||||||
\(538\) | 1561.18 | 2.90182 | ||||||||
\(539\) | 535.074 | − | 463.632i | 0.992716 | − | 0.860170i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 526.853 | 0.973851 | 0.486925 | − | 0.873444i | \(-0.338118\pi\) | ||||
0.486925 | + | 0.873444i | \(0.338118\pi\) | |||||||
\(542\) | −1788.28 | −3.29940 | ||||||||
\(543\) | − | 366.160i | − | 0.674328i | ||||||
\(544\) | − | 1283.19i | − | 2.35880i | ||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 273.115 | + | 732.265i | 0.500211 | + | 1.34114i | ||||
\(547\) | − | 250.549i | − | 0.458042i | −0.973421 | − | 0.229021i | \(-0.926447\pi\) | ||
0.973421 | − | 0.229021i | \(-0.0735525\pi\) | |||||||
\(548\) | − | 798.282i | − | 1.45672i | ||||||
\(549\) | 205.448i | 0.374222i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 256.567i | 0.465640i | ||||||||
\(552\) | −443.162 | −0.802829 | ||||||||
\(553\) | −849.522 | + | 316.849i | −1.53621 | + | 0.572964i | ||||
\(554\) | 1394.70 | 2.51751 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 513.741i | 0.923994i | ||||||||
\(557\) | − | 64.1496i | − | 0.115170i | −0.998341 | − | 0.0575849i | \(-0.981660\pi\) | ||
0.998341 | − | 0.0575849i | \(-0.0183400\pi\) | |||||||
\(558\) | −484.382 | −0.868069 | ||||||||
\(559\) | − | 99.0459i | − | 0.177184i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −325.573 | −0.580344 | ||||||||
\(562\) | − | 38.4890i | − | 0.0684857i | ||||||
\(563\) | −17.3869 | −0.0308826 | −0.0154413 | − | 0.999881i | \(-0.504915\pi\) | ||||
−0.0154413 | + | 0.999881i | \(0.504915\pi\) | |||||||
\(564\) | 190.527 | 0.337814 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | − | 463.767i | − | 0.819376i | ||||||
\(567\) | −59.0280 | + | 22.0158i | −0.104106 | + | 0.0388287i | ||||
\(568\) | 1173.96i | 2.06684i | ||||||||
\(569\) | −174.914 | −0.307405 | −0.153703 | − | 0.988117i | \(-0.549120\pi\) | ||||
−0.153703 | + | 0.988117i | \(0.549120\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −376.637 | −0.659609 | −0.329805 | − | 0.944049i | \(-0.606983\pi\) | ||||
−0.329805 | + | 0.944049i | \(0.606983\pi\) | |||||||
\(572\) | 2564.32 | 4.48307 | ||||||||
\(573\) | −194.151 | −0.338832 | ||||||||
\(574\) | −718.799 | + | 268.093i | −1.25226 | + | 0.467060i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −503.909 | −0.874842 | ||||||||
\(577\) | −448.775 | −0.777773 | −0.388886 | − | 0.921286i | \(-0.627140\pi\) | ||||
−0.388886 | + | 0.921286i | \(0.627140\pi\) | |||||||
\(578\) | 455.636i | 0.788297i | ||||||||
\(579\) | − | 508.429i | − | 0.878115i | ||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −279.994 | + | 104.430i | −0.481917 | + | 0.179742i | ||||
\(582\) | 189.330i | 0.325310i | ||||||||
\(583\) | − | 1183.47i | − | 2.02997i | ||||||
\(584\) | 3103.16i | 5.31363i | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 1114.00i | 1.90102i | ||||||||
\(587\) | −275.916 | −0.470044 | −0.235022 | − | 0.971990i | \(-0.575516\pi\) | ||||
−0.235022 | + | 0.971990i | \(0.575516\pi\) | |||||||
\(588\) | 671.883 | − | 582.174i | 1.14266 | − | 0.990091i | ||||
\(589\) | 793.207 | 1.34670 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 157.198i | 0.265986i | ||||||||
\(592\) | 1489.64i | 2.51629i | ||||||||
\(593\) | 893.938 | 1.50748 | 0.753742 | − | 0.657171i | \(-0.228247\pi\) | ||||
0.753742 | + | 0.657171i | \(0.228247\pi\) | |||||||
\(594\) | 285.645i | 0.480883i | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −2538.55 | −4.25932 | ||||||||
\(597\) | 674.497i | 1.12981i | ||||||||
\(598\) | 669.492 | 1.11955 | ||||||||
\(599\) | 122.407 | 0.204352 | 0.102176 | − | 0.994766i | \(-0.467419\pi\) | ||||
0.102176 | + | 0.994766i | \(0.467419\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 594.921i | − | 0.989885i | −0.868926 | − | 0.494943i | \(-0.835189\pi\) | ||
0.868926 | − | 0.494943i | \(-0.164811\pi\) | |||||||
\(602\) | −145.874 | + | 54.4071i | −0.242316 | + | 0.0903773i | ||||
\(603\) | 142.391i | 0.236138i | ||||||||
\(604\) | −1128.20 | −1.86788 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −82.1142 | −0.135502 | ||||||||
\(607\) | 539.772 | 0.889246 | 0.444623 | − | 0.895718i | \(-0.353338\pi\) | ||||
0.444623 | + | 0.895718i | \(0.353338\pi\) | |||||||
\(608\) | 1843.60 | 3.03223 | ||||||||
\(609\) | 155.937 | − | 58.1602i | 0.256054 | − | 0.0955012i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −177.920 | −0.291195 | ||||||||
\(612\) | −408.816 | −0.668000 | ||||||||
\(613\) | − | 1180.07i | − | 1.92508i | −0.271140 | − | 0.962540i | \(-0.587401\pi\) | ||
0.271140 | − | 0.962540i | \(-0.412599\pi\) | |||||||
\(614\) | − | 638.620i | − | 1.04010i | ||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −870.715 | − | 2334.53i | −1.41350 | − | 3.78982i | ||||
\(617\) | − | 777.688i | − | 1.26043i | −0.776419 | − | 0.630217i | \(-0.782966\pi\) | ||
0.776419 | − | 0.630217i | \(-0.217034\pi\) | |||||||
\(618\) | 253.571i | 0.410309i | ||||||||
\(619\) | − | 285.107i | − | 0.460592i | −0.973121 | − | 0.230296i | \(-0.926030\pi\) | ||
0.973121 | − | 0.230296i | \(-0.0739695\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 53.9679i | 0.0869048i | ||||||||
\(622\) | −1155.60 | −1.85789 | ||||||||
\(623\) | −62.4586 | − | 167.462i | −0.100255 | − | 0.268799i | ||||
\(624\) | 1520.85 | 2.43726 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 65.4967i | 0.104627i | ||||||||
\(627\) | − | 467.762i | − | 0.746031i | ||||||
\(628\) | −797.863 | −1.27048 | ||||||||
\(629\) | 373.931i | 0.594485i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 506.946 | 0.803401 | 0.401700 | − | 0.915771i | \(-0.368419\pi\) | ||||
0.401700 | + | 0.915771i | \(0.368419\pi\) | |||||||
\(632\) | 3190.86i | 5.04883i | ||||||||
\(633\) | 36.5547 | 0.0577483 | ||||||||
\(634\) | 315.271 | 0.497273 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | − | 1486.06i | − | 2.33658i | ||||||
\(637\) | −627.425 | + | 543.652i | −0.984969 | + | 0.853457i | ||||
\(638\) | − | 754.600i | − | 1.18276i | ||||||
\(639\) | 142.964 | 0.223731 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 537.896 | 0.839152 | 0.419576 | − | 0.907720i | \(-0.362179\pi\) | ||||
0.419576 | + | 0.907720i | \(0.362179\pi\) | |||||||
\(642\) | 578.571 | 0.901202 | ||||||||
\(643\) | −673.330 | −1.04717 | −0.523585 | − | 0.851973i | \(-0.675406\pi\) | ||||
−0.523585 | + | 0.851973i | \(0.675406\pi\) | |||||||
\(644\) | −266.134 | − | 713.547i | −0.413251 | − | 1.10799i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 925.104 | 1.43205 | ||||||||
\(647\) | 1082.21 | 1.67266 | 0.836332 | − | 0.548224i | \(-0.184696\pi\) | ||||
0.836332 | + | 0.548224i | \(0.184696\pi\) | |||||||
\(648\) | 221.713i | 0.342149i | ||||||||
\(649\) | 508.138i | 0.782956i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −179.809 | − | 482.096i | −0.276204 | − | 0.740547i | ||||
\(652\) | 109.241i | 0.167547i | ||||||||
\(653\) | 491.429i | 0.752571i | 0.926504 | + | 0.376285i | \(0.122799\pi\) | ||||
−0.926504 | + | 0.376285i | \(0.877201\pi\) | |||||||
\(654\) | − | 856.749i | − | 1.31001i | ||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 1492.88i | 2.27574i | ||||||||
\(657\) | 377.900 | 0.575191 | ||||||||
\(658\) | 97.7339 | + | 262.040i | 0.148532 | + | 0.398237i | ||||
\(659\) | −248.373 | −0.376893 | −0.188447 | − | 0.982083i | \(-0.560345\pi\) | ||||
−0.188447 | + | 0.982083i | \(0.560345\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 681.545i | 1.03108i | 0.856865 | + | 0.515541i | \(0.172409\pi\) | ||||
−0.856865 | + | 0.515541i | \(0.827591\pi\) | |||||||
\(662\) | 1717.74i | 2.59477i | ||||||||
\(663\) | 381.765 | 0.575814 | ||||||||
\(664\) | 1051.67i | 1.58385i | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 328.072 | 0.492601 | ||||||||
\(667\) | − | 142.569i | − | 0.213747i | ||||||
\(668\) | −793.584 | −1.18800 | ||||||||
\(669\) | 507.559 | 0.758683 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 989.499i | 1.47466i | ||||||||
\(672\) | −417.917 | − | 1120.50i | −0.621900 | − | 1.66741i | ||||
\(673\) | − | 86.1498i | − | 0.128009i | −0.997950 | − | 0.0640043i | \(-0.979613\pi\) | ||
0.997950 | − | 0.0640043i | \(-0.0203871\pi\) | |||||||
\(674\) | 776.737 | 1.15243 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −1236.63 | −1.82933 | ||||||||
\(677\) | 793.846 | 1.17259 | 0.586297 | − | 0.810096i | \(-0.300585\pi\) | ||||
0.586297 | + | 0.810096i | \(0.300585\pi\) | |||||||
\(678\) | −1045.12 | −1.54147 | ||||||||
\(679\) | −188.437 | + | 70.2819i | −0.277521 | + | 0.103508i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −128.056 | −0.188041 | ||||||||
\(682\) | −2332.93 | −3.42072 | ||||||||
\(683\) | 186.736i | 0.273406i | 0.990612 | + | 0.136703i | \(0.0436506\pi\) | ||||
−0.990612 | + | 0.136703i | \(0.956349\pi\) | |||||||
\(684\) | − | 587.359i | − | 0.858712i | ||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 1145.34 | + | 625.433i | 1.66959 | + | 0.911709i | ||||
\(687\) | 404.461i | 0.588736i | ||||||||
\(688\) | 302.968i | 0.440361i | ||||||||
\(689\) | 1387.73i | 2.01413i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 1030.46i | − | 1.49126i | −0.666361 | − | 0.745630i | \(-0.732149\pi\) | ||
0.666361 | − | 0.745630i | \(-0.267851\pi\) | |||||||
\(692\) | −3413.20 | −4.93238 | ||||||||
\(693\) | −284.297 | + | 106.035i | −0.410240 | + | 0.153009i | ||||
\(694\) | 557.727 | 0.803642 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | − | 585.709i | − | 0.841535i | ||||||
\(697\) | 374.745i | 0.537654i | ||||||||
\(698\) | −43.5450 | −0.0623854 | ||||||||
\(699\) | − | 667.582i | − | 0.955054i | ||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −1143.88 | −1.63179 | −0.815893 | − | 0.578203i | \(-0.803754\pi\) | ||||
−0.815893 | + | 0.578203i | \(0.803754\pi\) | |||||||
\(702\) | − | 334.945i | − | 0.477130i | ||||||
\(703\) | −537.239 | −0.764210 | ||||||||
\(704\) | −2426.98 | −3.44741 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | − | 676.521i | − | 0.958246i | ||||||
\(707\) | −30.4818 | − | 81.7267i | −0.0431143 | − | 0.115596i | ||||
\(708\) | 638.060i | 0.901214i | ||||||||
\(709\) | 316.757 | 0.446766 | 0.223383 | − | 0.974731i | \(-0.428290\pi\) | ||||
0.223383 | + | 0.974731i | \(0.428290\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 388.580 | 0.546526 | ||||||||
\(712\) | −628.996 | −0.883422 | ||||||||
\(713\) | −440.769 | −0.618190 | ||||||||
\(714\) | −209.708 | − | 562.261i | −0.293709 | − | 0.787480i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −323.902 | −0.452377 | ||||||||
\(717\) | 705.590 | 0.984087 | ||||||||
\(718\) | 2484.71i | 3.46059i | ||||||||
\(719\) | 1145.95i | 1.59381i | 0.604104 | + | 0.796906i | \(0.293531\pi\) | ||||
−0.604104 | + | 0.796906i | \(0.706469\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −252.374 | + | 94.1288i | −0.350034 | + | 0.130553i | ||||
\(722\) | − | 44.3325i | − | 0.0614024i | ||||||
\(723\) | − | 470.799i | − | 0.651174i | ||||||
\(724\) | − | 2214.44i | − | 3.05862i | ||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 578.389i | 0.796679i | ||||||||
\(727\) | 149.829 | 0.206093 | 0.103046 | − | 0.994677i | \(-0.467141\pi\) | ||||
0.103046 | + | 0.994677i | \(0.467141\pi\) | |||||||
\(728\) | 1021.00 | + | 2737.45i | 1.40247 | + | 3.76024i | ||||
\(729\) | 27.0000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 76.0512i | 0.104037i | ||||||||
\(732\) | 1242.49i | 1.69740i | ||||||||
\(733\) | −70.3231 | −0.0959388 | −0.0479694 | − | 0.998849i | \(-0.515275\pi\) | ||||
−0.0479694 | + | 0.998849i | \(0.515275\pi\) | |||||||
\(734\) | − | 1775.35i | − | 2.41873i | ||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −1024.45 | −1.39191 | ||||||||
\(737\) | 685.799i | 0.930528i | ||||||||
\(738\) | 328.786 | 0.445509 | ||||||||
\(739\) | −774.145 | −1.04756 | −0.523779 | − | 0.851854i | \(-0.675478\pi\) | ||||
−0.523779 | + | 0.851854i | \(0.675478\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 548.495i | 0.740209i | ||||||||
\(742\) | 2043.84 | − | 762.299i | 2.75451 | − | 1.02736i | ||||
\(743\) | − | 1071.79i | − | 1.44252i | −0.692665 | − | 0.721260i | \(-0.743563\pi\) | ||
0.692665 | − | 0.721260i | \(-0.256437\pi\) | |||||||
\(744\) | −1810.78 | −2.43385 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 1719.99 | 2.30562 | ||||||||
\(747\) | 128.072 | 0.171448 | ||||||||
\(748\) | −1968.98 | −2.63233 | ||||||||
\(749\) | 214.773 | + | 575.841i | 0.286747 | + | 0.768813i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 361.789 | 0.481742 | 0.240871 | − | 0.970557i | \(-0.422567\pi\) | ||||
0.240871 | + | 0.970557i | \(0.422567\pi\) | |||||||
\(752\) | 544.235 | 0.723717 | ||||||||
\(753\) | − | 765.999i | − | 1.01726i | ||||||
\(754\) | 884.839i | 1.17353i | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −356.986 | + | 133.146i | −0.472203 | + | 0.176119i | ||||
\(757\) | 812.552i | 1.07338i | 0.843778 | + | 0.536692i | \(0.180326\pi\) | ||||
−0.843778 | + | 0.536692i | \(0.819674\pi\) | |||||||
\(758\) | 1242.12i | 1.63868i | ||||||||
\(759\) | 259.926i | 0.342458i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 728.812i | − | 0.957703i | −0.877896 | − | 0.478851i | \(-0.841053\pi\) | ||
0.877896 | − | 0.478851i | \(-0.158947\pi\) | |||||||
\(762\) | −283.784 | −0.372419 | ||||||||
\(763\) | 852.706 | − | 318.036i | 1.11757 | − | 0.416824i | ||||
\(764\) | −1174.17 | −1.53688 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | − | 1450.55i | − | 1.89367i | ||||||
\(767\) | − | 595.840i | − | 0.776845i | ||||||
\(768\) | −447.553 | −0.582751 | ||||||||
\(769\) | 624.378i | 0.811935i | 0.913888 | + | 0.405967i | \(0.133065\pi\) | ||||
−0.913888 | + | 0.405967i | \(0.866935\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 676.255 | 0.877115 | ||||||||
\(772\) | − | 3074.84i | − | 3.98296i | ||||||
\(773\) | 34.6106 | 0.0447744 | 0.0223872 | − | 0.999749i | \(-0.492873\pi\) | ||||
0.0223872 | + | 0.999749i | \(0.492873\pi\) | |||||||
\(774\) | 66.7243 | 0.0862071 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 707.781i | 0.912089i | ||||||||
\(777\) | 121.785 | + | 326.524i | 0.156737 | + | 0.420237i | ||||
\(778\) | − | 261.925i | − | 0.336665i | ||||||
\(779\) | −538.408 | −0.691153 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 688.559 | 0.881638 | ||||||||
\(782\) | −514.062 | −0.657368 | ||||||||
\(783\) | −71.3271 | −0.0910946 | ||||||||
\(784\) | 1919.21 | − | 1662.96i | 2.44797 | − | 2.12112i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −4.52539 | −0.00575750 | ||||||||
\(787\) | −563.953 | −0.716586 | −0.358293 | − | 0.933609i | \(-0.616641\pi\) | ||||
−0.358293 | + | 0.933609i | \(0.616641\pi\) | |||||||
\(788\) | 950.692i | 1.20646i | ||||||||
\(789\) | − | 2.82807i | − | 0.00358437i | ||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −387.961 | − | 1040.18i | −0.490469 | − | 1.31502i | ||||
\(792\) | 1067.84i | 1.34828i | ||||||||
\(793\) | − | 1160.28i | − | 1.46315i | ||||||
\(794\) | − | 1409.72i | − | 1.77547i | ||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 4079.18i | 5.12460i | ||||||||
\(797\) | −887.777 | −1.11390 | −0.556949 | − | 0.830546i | \(-0.688028\pi\) | ||||
−0.556949 | + | 0.830546i | \(0.688028\pi\) | |||||||
\(798\) | 807.819 | − | 301.295i | 1.01230 | − | 0.377562i | ||||
\(799\) | 136.614 | 0.170981 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 76.5986i | 0.0956287i | ||||||||
\(802\) | − | 34.0540i | − | 0.0424613i | ||||||
\(803\) | 1820.08 | 2.26660 | ||||||||
\(804\) | 861.145i | 1.07108i | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 2735.58 | 3.39402 | ||||||||
\(807\) | − | 710.729i | − | 0.880706i | ||||||
\(808\) | −306.971 | −0.379914 | ||||||||
\(809\) | 1338.15 | 1.65408 | 0.827041 | − | 0.562142i | \(-0.190023\pi\) | ||||
0.827041 | + | 0.562142i | \(0.190023\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1002.03i | 1.23555i | 0.786353 | + | 0.617777i | \(0.211967\pi\) | ||||
−0.786353 | + | 0.617777i | \(0.788033\pi\) | |||||||
\(812\) | 943.065 | − | 351.738i | 1.16141 | − | 0.433175i | ||||
\(813\) | 814.115i | 1.00137i | ||||||||
\(814\) | 1580.09 | 1.94115 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −1167.77 | −1.43109 | ||||||||
\(817\) | −109.265 | −0.133740 | ||||||||
\(818\) | −240.196 | −0.293638 | ||||||||
\(819\) | 333.365 | − | 124.336i | 0.407039 | − | 0.151814i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −519.980 | −0.633349 | −0.316675 | − | 0.948534i | \(-0.602566\pi\) | ||||
−0.316675 | + | 0.948534i | \(0.602566\pi\) | |||||||
\(822\) | −502.195 | −0.610943 | ||||||||
\(823\) | 35.2676i | 0.0428524i | 0.999770 | + | 0.0214262i | \(0.00682070\pi\) | ||||
−0.999770 | + | 0.0214262i | \(0.993179\pi\) | |||||||
\(824\) | 947.933i | 1.15040i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −877.550 | + | 327.302i | −1.06241 | + | 0.396250i | ||||
\(827\) | − | 1047.83i | − | 1.26703i | −0.773731 | − | 0.633514i | \(-0.781612\pi\) | ||
0.773731 | − | 0.633514i | \(-0.218388\pi\) | |||||||
\(828\) | 326.384i | 0.394183i | ||||||||
\(829\) | 125.947i | 0.151926i | 0.997111 | + | 0.0759632i | \(0.0242031\pi\) | ||||
−0.997111 | + | 0.0759632i | \(0.975797\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | − | 634.939i | − | 0.764067i | ||||||
\(832\) | 2845.86 | 3.42051 | ||||||||
\(833\) | 481.761 | − | 417.437i | 0.578345 | − | 0.501125i | ||||
\(834\) | 323.192 | 0.387520 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | − | 2828.90i | − | 3.38385i | ||||||
\(837\) | 220.516i | 0.263460i | ||||||||
\(838\) | −13.6499 | −0.0162887 | ||||||||
\(839\) | 456.709i | 0.544349i | 0.962248 | + | 0.272174i | \(0.0877427\pi\) | ||||
−0.962248 | + | 0.272174i | \(0.912257\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −652.572 | −0.775948 | ||||||||
\(842\) | − | 455.007i | − | 0.540388i | ||||||
\(843\) | −17.5222 | −0.0207855 | ||||||||
\(844\) | 221.073 | 0.261935 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | − | 119.860i | − | 0.141678i | ||||||
\(847\) | −575.660 | + | 214.706i | −0.679645 | + | 0.253489i | ||||
\(848\) | − | 4244.89i | − | 5.00577i | ||||||
\(849\) | −211.131 | −0.248681 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 298.533 | 0.350802 | ||||||||
\(852\) | 864.611 | 1.01480 | ||||||||
\(853\) | −815.418 | −0.955941 | −0.477971 | − | 0.878376i | \(-0.658627\pi\) | ||||
−0.477971 | + | 0.878376i | \(0.658627\pi\) | |||||||
\(854\) | −1708.85 | + | 637.356i | −2.00100 | + | 0.746319i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 2162.90 | 2.52675 | ||||||||
\(857\) | 609.807 | 0.711560 | 0.355780 | − | 0.934570i | \(-0.384215\pi\) | ||||
0.355780 | + | 0.934570i | \(0.384215\pi\) | |||||||
\(858\) | − | 1613.20i | − | 1.88018i | ||||||
\(859\) | − | 136.971i | − | 0.159454i | −0.996817 | − | 0.0797272i | \(-0.974595\pi\) | ||
0.996817 | − | 0.0797272i | \(-0.0254049\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 122.050 | + | 327.234i | 0.141753 | + | 0.380063i | ||||
\(862\) | 1538.92i | 1.78529i | ||||||||
\(863\) | − | 305.240i | − | 0.353696i | −0.984238 | − | 0.176848i | \(-0.943410\pi\) | ||
0.984238 | − | 0.176848i | \(-0.0565902\pi\) | |||||||
\(864\) | 512.529i | 0.593205i | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | − | 441.657i | − | 0.509996i | ||||||
\(867\) | 207.429 | 0.239249 | ||||||||
\(868\) | −1087.44 | − | 2915.59i | −1.25281 | − | 3.35898i | ||||
\(869\) | 1871.52 | 2.15365 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 804.164i | − | 0.923266i | ||||||
\(872\) | − | 3202.82i | − | 3.67296i | ||||||
\(873\) | 86.1929 | 0.0987319 | ||||||||
\(874\) | − | 738.570i | − | 0.845045i | ||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 2285.44 | 2.60895 | ||||||||
\(877\) | 621.320i | 0.708461i | 0.935158 | + | 0.354231i | \(0.115257\pi\) | ||||
−0.935158 | + | 0.354231i | \(0.884743\pi\) | |||||||
\(878\) | −222.258 | −0.253142 | ||||||||
\(879\) | 507.149 | 0.576962 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 739.549i | 0.839443i | 0.907653 | + | 0.419721i | \(0.137872\pi\) | ||||
−0.907653 | + | 0.419721i | \(0.862128\pi\) | |||||||
\(882\) | −366.242 | − | 422.678i | −0.415241 | − | 0.479227i | ||||
\(883\) | − | 643.821i | − | 0.729129i | −0.931178 | − | 0.364564i | \(-0.881218\pi\) | ||
0.931178 | − | 0.364564i | \(-0.118782\pi\) | |||||||
\(884\) | 2308.82 | 2.61178 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −1016.97 | −1.14782 | ||||||||
\(887\) | 926.753 | 1.04482 | 0.522409 | − | 0.852695i | \(-0.325034\pi\) | ||||
0.522409 | + | 0.852695i | \(0.325034\pi\) | |||||||
\(888\) | 1226.44 | 1.38113 | ||||||||
\(889\) | −105.344 | − | 282.444i | −0.118497 | − | 0.317710i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 130.040 | 0.145949 | ||||||||
\(892\) | 3069.58 | 3.44124 | ||||||||
\(893\) | 196.278i | 0.219796i | ||||||||
\(894\) | 1596.99i | 1.78634i | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −598.128 | − | 1603.68i | −0.667554 | − | 1.78982i | ||||
\(897\) | − | 304.787i | − | 0.339785i | ||||||
\(898\) | 1127.98i | 1.25610i | ||||||||
\(899\) | − | 582.546i | − | 0.647994i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 1065.56i | − | 1.18264i | ||||||
\(902\) | 1583.53 | 1.75558 | ||||||||
\(903\) | 24.7689 | + | 66.4094i | 0.0274296 | + | 0.0735431i | ||||
\(904\) | −3907.00 | −4.32190 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 709.744i | 0.783382i | ||||||||
\(907\) | − | 1540.97i | − | 1.69898i | −0.527607 | − | 0.849489i | \(-0.676910\pi\) | ||
0.527607 | − | 0.849489i | \(-0.323090\pi\) | |||||||
\(908\) | −774.450 | −0.852919 | ||||||||
\(909\) | 37.3826i | 0.0411250i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −1187.49 | −1.30350 | −0.651748 | − | 0.758435i | \(-0.725964\pi\) | ||||
−0.651748 | + | 0.758435i | \(0.725964\pi\) | |||||||
\(912\) | − | 1677.77i | − | 1.83966i | ||||||
\(913\) | 616.833 | 0.675611 | ||||||||
\(914\) | 46.1312 | 0.0504718 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 2446.08i | 2.67039i | ||||||||
\(917\) | −1.67988 | − | 4.50404i | −0.00183194 | − | 0.00491171i | ||||
\(918\) | 257.184i | 0.280157i | ||||||||
\(919\) | −223.009 | −0.242665 | −0.121333 | − | 0.992612i | \(-0.538717\pi\) | ||||
−0.121333 | + | 0.992612i | \(0.538717\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −290.733 | −0.315671 | ||||||||
\(922\) | −395.479 | −0.428936 | ||||||||
\(923\) | −807.401 | −0.874757 | ||||||||
\(924\) | −1719.35 | + | 641.272i | −1.86077 | + | 0.694017i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −1897.85 | −2.04952 | ||||||||
\(927\) | 115.439 | 0.124529 | ||||||||
\(928\) | − | 1353.97i | − | 1.45902i | ||||||
\(929\) | − | 1482.17i | − | 1.59545i | −0.603024 | − | 0.797723i | \(-0.706038\pi\) | ||
0.603024 | − | 0.797723i | \(-0.293962\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 599.746 | + | 692.162i | 0.644195 | + | 0.743461i | ||||
\(932\) | − | 4037.36i | − | 4.33194i | ||||||
\(933\) | 526.091i | 0.563870i | ||||||||
\(934\) | 2273.95i | 2.43463i | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | − | 1252.14i | − | 1.33775i | ||||||
\(937\) | −836.508 | −0.892751 | −0.446376 | − | 0.894846i | \(-0.647285\pi\) | ||||
−0.446376 | + | 0.894846i | \(0.647285\pi\) | |||||||
\(938\) | −1184.37 | + | 441.737i | −1.26265 | + | 0.470935i | ||||
\(939\) | 29.8175 | 0.0317545 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 1637.85i | 1.74055i | 0.492569 | + | 0.870273i | \(0.336058\pi\) | ||||
−0.492569 | + | 0.870273i | \(0.663942\pi\) | |||||||
\(942\) | 501.932i | 0.532836i | ||||||||
\(943\) | 299.183 | 0.317267 | ||||||||
\(944\) | 1822.60i | 1.93072i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 321.364 | 0.339709 | ||||||||
\(947\) | 748.381i | 0.790265i | 0.918624 | + | 0.395133i | \(0.129301\pi\) | ||||
−0.918624 | + | 0.395133i | \(0.870699\pi\) | |||||||
\(948\) | 2350.03 | 2.47894 | ||||||||
\(949\) | −2134.22 | −2.24891 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 143.528i | − | 0.150923i | ||||||
\(952\) | −783.960 | − | 2101.92i | −0.823487 | − | 2.20790i | ||||
\(953\) | 942.124i | 0.988588i | 0.869295 | + | 0.494294i | \(0.164573\pi\) | ||||
−0.869295 | + | 0.494294i | \(0.835427\pi\) | |||||||
\(954\) | −934.875 | −0.979953 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 4267.23 | 4.46362 | ||||||||
\(957\) | −343.533 | −0.358968 | ||||||||
\(958\) | 1052.75 | 1.09890 | ||||||||
\(959\) | −186.421 | − | 499.825i | −0.194391 | − | 0.521194i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −840.008 | −0.874098 | ||||||||
\(962\) | −1852.81 | −1.92600 | ||||||||
\(963\) | − | 263.396i | − | 0.273516i | ||||||
\(964\) | − | 2847.27i | − | 2.95360i | ||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −448.889 | + | 167.423i | −0.464688 | + | 0.173316i | ||||
\(967\) | − | 1654.90i | − | 1.71138i | −0.517489 | − | 0.855690i | \(-0.673133\pi\) | ||
0.517489 | − | 0.855690i | \(-0.326867\pi\) | |||||||
\(968\) | 2162.21i | 2.23369i | ||||||||
\(969\) | − | 421.155i | − | 0.434629i | ||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 354.436i | − | 0.365022i | −0.983204 | − | 0.182511i | \(-0.941578\pi\) | ||
0.983204 | − | 0.182511i | \(-0.0584224\pi\) | |||||||
\(972\) | 163.289 | 0.167993 | ||||||||
\(973\) | 119.973 | + | 321.666i | 0.123302 | + | 0.330592i | ||||
\(974\) | −2064.58 | −2.11969 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 3549.14i | 3.63642i | ||||||||
\(977\) | 1726.63i | 1.76727i | 0.468173 | + | 0.883637i | \(0.344912\pi\) | ||||
−0.468173 | + | 0.883637i | \(0.655088\pi\) | |||||||
\(978\) | 68.7229 | 0.0702688 | ||||||||
\(979\) | 368.922i | 0.376836i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −390.037 | −0.397591 | ||||||||
\(982\) | − | 2186.95i | − | 2.22704i | ||||||
\(983\) | 1635.34 | 1.66362 | 0.831809 | − | 0.555062i | \(-0.187306\pi\) | ||||
0.831809 | + | 0.555062i | \(0.187306\pi\) | |||||||
\(984\) | 1229.11 | 1.24910 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | − | 679.414i | − | 0.689061i | ||||||
\(987\) | 119.294 | − | 44.4935i | 0.120865 | − | 0.0450795i | ||||
\(988\) | 3317.15i | 3.35744i | ||||||||
\(989\) | 60.7165 | 0.0613919 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −313.579 | −0.316427 | −0.158213 | − | 0.987405i | \(-0.550573\pi\) | ||||
−0.158213 | + | 0.987405i | \(0.550573\pi\) | |||||||
\(992\) | −4185.95 | −4.21971 | ||||||||
\(993\) | 782.004 | 0.787517 | ||||||||
\(994\) | 443.515 | + | 1189.13i | 0.446192 | + | 1.19631i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 774.546 | 0.777656 | ||||||||
\(997\) | −17.3708 | −0.0174231 | −0.00871155 | − | 0.999962i | \(-0.502773\pi\) | ||||
−0.00871155 | + | 0.999962i | \(0.502773\pi\) | |||||||
\(998\) | − | 2092.41i | − | 2.09660i | ||||||
\(999\) | − | 149.355i | − | 0.149505i |
(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 | 525.3.e.c.349.11 | 24 | ||
5.2 | odd | 4 | 525.3.h.d.76.12 | 12 | |||
5.3 | odd | 4 | 105.3.h.a.76.1 | ✓ | 12 | ||
5.4 | even | 2 | inner | 525.3.e.c.349.4 | 24 | ||
7.6 | odd | 2 | inner | 525.3.e.c.349.3 | 24 | ||
15.8 | even | 4 | 315.3.h.d.181.12 | 12 | |||
20.3 | even | 4 | 1680.3.s.c.1441.8 | 12 | |||
35.13 | even | 4 | 105.3.h.a.76.2 | yes | 12 | ||
35.27 | even | 4 | 525.3.h.d.76.11 | 12 | |||
35.34 | odd | 2 | inner | 525.3.e.c.349.12 | 24 | ||
105.83 | odd | 4 | 315.3.h.d.181.11 | 12 | |||
140.83 | odd | 4 | 1680.3.s.c.1441.5 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
105.3.h.a.76.1 | ✓ | 12 | 5.3 | odd | 4 | ||
105.3.h.a.76.2 | yes | 12 | 35.13 | even | 4 | ||
315.3.h.d.181.11 | 12 | 105.83 | odd | 4 | |||
315.3.h.d.181.12 | 12 | 15.8 | even | 4 | |||
525.3.e.c.349.3 | 24 | 7.6 | odd | 2 | inner | ||
525.3.e.c.349.4 | 24 | 5.4 | even | 2 | inner | ||
525.3.e.c.349.11 | 24 | 1.1 | even | 1 | trivial | ||
525.3.e.c.349.12 | 24 | 35.34 | odd | 2 | inner | ||
525.3.h.d.76.11 | 12 | 35.27 | even | 4 | |||
525.3.h.d.76.12 | 12 | 5.2 | odd | 4 | |||
1680.3.s.c.1441.5 | 12 | 140.83 | odd | 4 | |||
1680.3.s.c.1441.8 | 12 | 20.3 | even | 4 |