Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [225,4,Mod(76,225)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(225, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([2, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("225.76");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 225 = 3^{2} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 225.e (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: | \(13.2754297513\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(12\) over \(\Q(\zeta_{3})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 76.4 | ||
Character | \(\chi\) | \(=\) | 225.76 |
Dual form | 225.4.e.f.151.4 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/225\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(127\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.832171 | − | 1.44136i | −0.294217 | − | 0.509599i | 0.680586 | − | 0.732669i | \(-0.261725\pi\) |
−0.974802 | + | 0.223070i | \(0.928392\pi\) | |||||||
\(3\) | −4.88113 | + | 1.78172i | −0.939375 | + | 0.342893i | ||||
\(4\) | 2.61498 | − | 4.52928i | 0.326873 | − | 0.566160i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 6.63004 | + | 5.55278i | 0.451117 | + | 0.377819i | ||||
\(7\) | 5.28358 | + | 9.15142i | 0.285286 | + | 0.494130i | 0.972679 | − | 0.232156i | \(-0.0745780\pi\) |
−0.687392 | + | 0.726286i | \(0.741245\pi\) | |||||||
\(8\) | −22.0192 | −0.973120 | ||||||||
\(9\) | 20.6509 | − | 17.3936i | 0.764849 | − | 0.644209i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −14.5398 | − | 25.1837i | −0.398539 | − | 0.690289i | 0.595007 | − | 0.803720i | \(-0.297149\pi\) |
−0.993546 | + | 0.113431i | \(0.963816\pi\) | |||||||
\(12\) | −4.69416 | + | 26.7672i | −0.112924 | + | 0.643919i | ||||
\(13\) | 11.7510 | − | 20.3533i | 0.250703 | − | 0.434230i | −0.713017 | − | 0.701147i | \(-0.752672\pi\) |
0.963719 | + | 0.266917i | \(0.0860050\pi\) | |||||||
\(14\) | 8.79368 | − | 15.2311i | 0.167872 | − | 0.290763i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −2.59614 | − | 4.49664i | −0.0405646 | − | 0.0702600i | ||||
\(17\) | −35.6583 | −0.508731 | −0.254365 | − | 0.967108i | \(-0.581867\pi\) | ||||
−0.254365 | + | 0.967108i | \(0.581867\pi\) | |||||||
\(18\) | −42.2557 | − | 15.2910i | −0.553320 | − | 0.200229i | ||||
\(19\) | 23.7670 | 0.286975 | 0.143488 | − | 0.989652i | \(-0.454168\pi\) | ||||
0.143488 | + | 0.989652i | \(0.454168\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −42.0951 | − | 35.2555i | −0.437424 | − | 0.366351i | ||||
\(22\) | −24.1993 | + | 41.9143i | −0.234514 | + | 0.406190i | ||||
\(23\) | −39.4733 | + | 68.3697i | −0.357858 | + | 0.619829i | −0.987603 | − | 0.156974i | \(-0.949826\pi\) |
0.629744 | + | 0.776802i | \(0.283160\pi\) | |||||||
\(24\) | 107.479 | − | 39.2321i | 0.914124 | − | 0.333676i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −39.1153 | −0.295044 | ||||||||
\(27\) | −69.8093 | + | 121.695i | −0.497585 | + | 0.867415i | ||||
\(28\) | 55.2658 | 0.373009 | ||||||||
\(29\) | −74.0997 | − | 128.344i | −0.474481 | − | 0.821826i | 0.525092 | − | 0.851046i | \(-0.324031\pi\) |
−0.999573 | + | 0.0292198i | \(0.990698\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −170.912 | + | 296.028i | −0.990217 | + | 1.71511i | −0.374265 | + | 0.927322i | \(0.622105\pi\) |
−0.615951 | + | 0.787784i | \(0.711228\pi\) | |||||||
\(32\) | −92.3976 | + | 160.037i | −0.510429 | + | 0.884090i | ||||
\(33\) | 115.841 | + | 97.0192i | 0.611072 | + | 0.511784i | ||||
\(34\) | 29.6738 | + | 51.3966i | 0.149677 | + | 0.259248i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −24.7789 | − | 139.018i | −0.114717 | − | 0.643602i | ||||
\(37\) | −337.627 | −1.50015 | −0.750074 | − | 0.661354i | \(-0.769982\pi\) | ||||
−0.750074 | + | 0.661354i | \(0.769982\pi\) | |||||||
\(38\) | −19.7782 | − | 34.2569i | −0.0844329 | − | 0.146242i | ||||
\(39\) | −21.0942 | + | 120.284i | −0.0866095 | + | 0.493868i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −177.023 | + | 306.613i | −0.674301 | + | 1.16792i | 0.302372 | + | 0.953190i | \(0.402222\pi\) |
−0.976673 | + | 0.214733i | \(0.931112\pi\) | |||||||
\(42\) | −15.7855 | + | 90.0129i | −0.0579943 | + | 0.330697i | ||||
\(43\) | −9.76327 | − | 16.9105i | −0.0346252 | − | 0.0599727i | 0.848193 | − | 0.529687i | \(-0.177690\pi\) |
−0.882819 | + | 0.469714i | \(0.844357\pi\) | |||||||
\(44\) | −152.086 | −0.521086 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 131.394 | 0.421152 | ||||||||
\(47\) | −56.0915 | − | 97.1533i | −0.174080 | − | 0.301516i | 0.765762 | − | 0.643124i | \(-0.222362\pi\) |
−0.939843 | + | 0.341608i | \(0.889029\pi\) | |||||||
\(48\) | 20.6839 | + | 17.3231i | 0.0621970 | + | 0.0520912i | ||||
\(49\) | 115.668 | − | 200.342i | 0.337223 | − | 0.584088i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 174.053 | − | 63.5333i | 0.477889 | − | 0.174440i | ||||
\(52\) | −61.4572 | − | 106.447i | −0.163896 | − | 0.283876i | ||||
\(53\) | −699.829 | −1.81375 | −0.906876 | − | 0.421398i | \(-0.861540\pi\) | ||||
−0.906876 | + | 0.421398i | \(0.861540\pi\) | |||||||
\(54\) | 233.500 | − | 0.650493i | 0.588431 | − | 0.00163927i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −116.340 | − | 201.507i | −0.277618 | − | 0.480848i | ||||
\(57\) | −116.010 | + | 42.3462i | −0.269577 | + | 0.0984017i | ||||
\(58\) | −123.327 | + | 213.609i | −0.279201 | + | 0.483590i | ||||
\(59\) | −13.7297 | + | 23.7805i | −0.0302958 | + | 0.0524739i | −0.880776 | − | 0.473534i | \(-0.842978\pi\) |
0.850480 | + | 0.526007i | \(0.176312\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 412.663 | + | 714.754i | 0.866166 | + | 1.50024i | 0.865885 | + | 0.500243i | \(0.166756\pi\) |
0.000280785 | 1.00000i | \(0.499911\pi\) | ||||||||
\(62\) | 568.912 | 1.16535 | ||||||||
\(63\) | 268.287 | + | 97.0847i | 0.536524 | + | 0.194151i | ||||
\(64\) | 266.024 | 0.519579 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 43.4401 | − | 247.706i | 0.0810168 | − | 0.461977i | ||||
\(67\) | 412.657 | − | 714.743i | 0.752449 | − | 1.30328i | −0.194183 | − | 0.980965i | \(-0.562206\pi\) |
0.946633 | − | 0.322315i | \(-0.104461\pi\) | |||||||
\(68\) | −93.2460 | + | 161.507i | −0.166290 | + | 0.288023i | ||||
\(69\) | 70.8584 | − | 404.052i | 0.123628 | − | 0.704958i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −337.616 | −0.564332 | −0.282166 | − | 0.959366i | \(-0.591053\pi\) | ||||
−0.282166 | + | 0.959366i | \(0.591053\pi\) | |||||||
\(72\) | −454.717 | + | 382.994i | −0.744290 | + | 0.626893i | ||||
\(73\) | 717.566 | 1.15048 | 0.575238 | − | 0.817986i | \(-0.304909\pi\) | ||||
0.575238 | + | 0.817986i | \(0.304909\pi\) | |||||||
\(74\) | 280.963 | + | 486.642i | 0.441369 | + | 0.764473i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 62.1504 | − | 107.648i | 0.0938044 | − | 0.162474i | ||||
\(77\) | 153.645 | − | 266.120i | 0.227395 | − | 0.393860i | ||||
\(78\) | 190.927 | − | 69.6926i | 0.277157 | − | 0.101168i | ||||
\(79\) | 155.091 | + | 268.625i | 0.220875 | + | 0.382566i | 0.955074 | − | 0.296368i | \(-0.0957755\pi\) |
−0.734199 | + | 0.678934i | \(0.762442\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 123.922 | − | 718.390i | 0.169989 | − | 0.985446i | ||||
\(82\) | 589.253 | 0.793563 | ||||||||
\(83\) | −276.069 | − | 478.166i | −0.365091 | − | 0.632356i | 0.623700 | − | 0.781664i | \(-0.285629\pi\) |
−0.988791 | + | 0.149308i | \(0.952295\pi\) | |||||||
\(84\) | −269.760 | + | 98.4684i | −0.350396 | + | 0.127902i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −16.2494 | + | 28.1448i | −0.0203747 | + | 0.0352899i | ||||
\(87\) | 590.364 | + | 494.441i | 0.727514 | + | 0.609306i | ||||
\(88\) | 320.155 | + | 554.525i | 0.387826 | + | 0.671734i | ||||
\(89\) | −1085.33 | −1.29264 | −0.646319 | − | 0.763067i | \(-0.723692\pi\) | ||||
−0.646319 | + | 0.763067i | \(0.723692\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 248.349 | 0.286088 | ||||||||
\(92\) | 206.444 | + | 357.571i | 0.233948 | + | 0.405210i | ||||
\(93\) | 306.804 | − | 1749.47i | 0.342087 | − | 1.95066i | ||||
\(94\) | −93.3554 | + | 161.696i | −0.102435 | + | 0.177422i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 165.863 | − | 945.791i | 0.176337 | − | 1.00551i | ||||
\(97\) | −583.915 | − | 1011.37i | −0.611212 | − | 1.05865i | −0.991037 | − | 0.133591i | \(-0.957349\pi\) |
0.379825 | − | 0.925058i | \(-0.375984\pi\) | |||||||
\(98\) | −385.021 | −0.396867 | ||||||||
\(99\) | −738.298 | − | 267.167i | −0.749513 | − | 0.271225i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −640.039 | − | 1108.58i | −0.630557 | − | 1.09216i | −0.987438 | − | 0.158006i | \(-0.949493\pi\) |
0.356881 | − | 0.934150i | \(-0.383840\pi\) | |||||||
\(102\) | −236.416 | − | 198.003i | −0.229497 | − | 0.192208i | ||||
\(103\) | −62.4748 | + | 108.210i | −0.0597653 | + | 0.103517i | −0.894360 | − | 0.447348i | \(-0.852369\pi\) |
0.834595 | + | 0.550865i | \(0.185702\pi\) | |||||||
\(104\) | −258.747 | + | 448.163i | −0.243964 | + | 0.422558i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 582.377 | + | 1008.71i | 0.533636 | + | 0.924285i | ||||
\(107\) | 1350.01 | 1.21973 | 0.609863 | − | 0.792507i | \(-0.291225\pi\) | ||||
0.609863 | + | 0.792507i | \(0.291225\pi\) | |||||||
\(108\) | 368.641 | + | 634.416i | 0.328449 | + | 0.565248i | ||||
\(109\) | −1143.61 | −1.00494 | −0.502468 | − | 0.864596i | \(-0.667574\pi\) | ||||
−0.502468 | + | 0.864596i | \(0.667574\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1648.00 | − | 601.557i | 1.40920 | − | 0.514390i | ||||
\(112\) | 27.4338 | − | 47.5167i | 0.0231451 | − | 0.0400884i | ||||
\(113\) | 329.517 | − | 570.740i | 0.274322 | − | 0.475139i | −0.695642 | − | 0.718389i | \(-0.744880\pi\) |
0.969964 | + | 0.243249i | \(0.0782133\pi\) | |||||||
\(114\) | 157.576 | + | 131.973i | 0.129460 | + | 0.108425i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −775.077 | −0.620380 | ||||||||
\(117\) | −111.349 | − | 624.707i | −0.0879850 | − | 0.493625i | ||||
\(118\) | 45.7018 | 0.0356542 | ||||||||
\(119\) | −188.404 | − | 326.325i | −0.145134 | − | 0.251379i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 242.686 | − | 420.345i | 0.182334 | − | 0.315811i | ||||
\(122\) | 686.813 | − | 1189.59i | 0.509681 | − | 0.882794i | ||||
\(123\) | 317.774 | − | 1812.02i | 0.232949 | − | 1.32833i | ||||
\(124\) | 893.865 | + | 1548.22i | 0.647350 | + | 1.12124i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −83.3267 | − | 467.490i | −0.0589153 | − | 0.330535i | ||||
\(127\) | −1564.04 | −1.09281 | −0.546403 | − | 0.837522i | \(-0.684003\pi\) | ||||
−0.546403 | + | 0.837522i | \(0.684003\pi\) | |||||||
\(128\) | 517.803 | + | 896.861i | 0.357561 | + | 0.619313i | ||||
\(129\) | 77.7856 | + | 65.1469i | 0.0530903 | + | 0.0444641i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1089.75 | + | 1887.50i | −0.726807 | + | 1.25887i | 0.231419 | + | 0.972854i | \(0.425663\pi\) |
−0.958226 | + | 0.286012i | \(0.907670\pi\) | |||||||
\(132\) | 742.351 | − | 270.974i | 0.489495 | − | 0.178677i | ||||
\(133\) | 125.575 | + | 217.502i | 0.0818701 | + | 0.141803i | ||||
\(134\) | −1373.60 | −0.885533 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 785.168 | 0.495056 | ||||||||
\(137\) | 526.947 | + | 912.698i | 0.328614 | + | 0.569176i | 0.982237 | − | 0.187644i | \(-0.0600852\pi\) |
−0.653623 | + | 0.756820i | \(0.726752\pi\) | |||||||
\(138\) | −641.352 | + | 234.108i | −0.395619 | + | 0.144410i | ||||
\(139\) | −243.303 | + | 421.413i | −0.148465 | + | 0.257150i | −0.930660 | − | 0.365884i | \(-0.880767\pi\) |
0.782195 | + | 0.623034i | \(0.214100\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 446.890 | + | 374.279i | 0.266914 | + | 0.223546i | ||||
\(142\) | 280.954 | + | 486.626i | 0.166036 | + | 0.287583i | ||||
\(143\) | −683.429 | −0.399659 | ||||||||
\(144\) | −131.826 | − | 47.7035i | −0.0762880 | − | 0.0276062i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −597.138 | − | 1034.27i | −0.338489 | − | 0.586281i | ||||
\(147\) | −207.635 | + | 1183.98i | −0.116500 | + | 0.664309i | ||||
\(148\) | −882.888 | + | 1529.21i | −0.490358 | + | 0.849324i | ||||
\(149\) | 1623.33 | − | 2811.69i | 0.892540 | − | 1.54592i | 0.0557190 | − | 0.998446i | \(-0.482255\pi\) |
0.836821 | − | 0.547477i | \(-0.184412\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 764.874 | + | 1324.80i | 0.412216 | + | 0.713978i | 0.995132 | − | 0.0985540i | \(-0.0314217\pi\) |
−0.582916 | + | 0.812532i | \(0.698088\pi\) | |||||||
\(152\) | −523.331 | −0.279261 | ||||||||
\(153\) | −736.378 | + | 620.229i | −0.389102 | + | 0.327729i | ||||
\(154\) | −511.435 | −0.267614 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 489.640 | + | 410.082i | 0.251298 | + | 0.210467i | ||||
\(157\) | 365.776 | − | 633.543i | 0.185937 | − | 0.322052i | −0.757955 | − | 0.652307i | \(-0.773801\pi\) |
0.943892 | + | 0.330255i | \(0.107135\pi\) | |||||||
\(158\) | 258.124 | − | 447.084i | 0.129970 | − | 0.225115i | ||||
\(159\) | 3415.96 | − | 1246.90i | 1.70379 | − | 0.621922i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −834.240 | −0.408368 | ||||||||
\(162\) | −1138.58 | + | 419.207i | −0.552195 | + | 0.203309i | ||||
\(163\) | −132.833 | −0.0638298 | −0.0319149 | − | 0.999491i | \(-0.510161\pi\) | ||||
−0.0319149 | + | 0.999491i | \(0.510161\pi\) | |||||||
\(164\) | 925.824 | + | 1603.57i | 0.440821 | + | 0.763525i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −459.474 | + | 795.832i | −0.214832 | + | 0.372099i | ||||
\(167\) | 684.073 | − | 1184.85i | 0.316977 | − | 0.549021i | −0.662879 | − | 0.748727i | \(-0.730665\pi\) |
0.979856 | + | 0.199706i | \(0.0639988\pi\) | |||||||
\(168\) | 926.901 | + | 776.296i | 0.425666 | + | 0.356503i | ||||
\(169\) | 822.329 | + | 1424.32i | 0.374296 | + | 0.648300i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 490.811 | − | 413.395i | 0.219493 | − | 0.184872i | ||||
\(172\) | −102.123 | −0.0452722 | ||||||||
\(173\) | 1058.70 | + | 1833.72i | 0.465268 | + | 0.805867i | 0.999214 | − | 0.0396515i | \(-0.0126248\pi\) |
−0.533946 | + | 0.845519i | \(0.679291\pi\) | |||||||
\(174\) | 221.385 | − | 1262.39i | 0.0964547 | − | 0.550008i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −75.4948 | + | 130.761i | −0.0323332 | + | 0.0560027i | ||||
\(177\) | 24.6462 | − | 140.538i | 0.0104662 | − | 0.0596809i | ||||
\(178\) | 903.180 | + | 1564.35i | 0.380316 | + | 0.658726i | ||||
\(179\) | 2224.74 | 0.928966 | 0.464483 | − | 0.885582i | \(-0.346240\pi\) | ||||
0.464483 | + | 0.885582i | \(0.346240\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −723.066 | −0.296934 | −0.148467 | − | 0.988917i | \(-0.547434\pi\) | ||||
−0.148467 | + | 0.988917i | \(0.547434\pi\) | |||||||
\(182\) | −206.669 | − | 357.961i | −0.0841720 | − | 0.145790i | ||||
\(183\) | −3287.76 | − | 2753.56i | −1.32808 | − | 1.11229i | ||||
\(184\) | 869.169 | − | 1505.44i | 0.348239 | − | 0.603168i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −2776.94 | + | 1013.64i | −1.09470 | + | 0.399591i | ||||
\(187\) | 518.467 | + | 898.010i | 0.202749 | + | 0.351171i | ||||
\(188\) | −586.713 | −0.227609 | ||||||||
\(189\) | −1482.52 | + | 4.13007i | −0.570570 | + | 0.00158952i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 125.680 | + | 217.685i | 0.0476121 | + | 0.0824666i | 0.888849 | − | 0.458200i | \(-0.151506\pi\) |
−0.841237 | + | 0.540666i | \(0.818172\pi\) | |||||||
\(192\) | −1298.50 | + | 473.981i | −0.488079 | + | 0.178160i | ||||
\(193\) | −190.385 | + | 329.756i | −0.0710061 | + | 0.122986i | −0.899343 | − | 0.437245i | \(-0.855954\pi\) |
0.828336 | + | 0.560231i | \(0.189288\pi\) | |||||||
\(194\) | −971.833 | + | 1683.26i | −0.359658 | + | 0.622945i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −604.938 | − | 1047.78i | −0.220458 | − | 0.381845i | ||||
\(197\) | −4369.98 | −1.58045 | −0.790225 | − | 0.612817i | \(-0.790036\pi\) | ||||
−0.790225 | + | 0.612817i | \(0.790036\pi\) | |||||||
\(198\) | 229.306 | + | 1286.48i | 0.0823034 | + | 0.461750i | ||||
\(199\) | −985.541 | −0.351071 | −0.175536 | − | 0.984473i | \(-0.556166\pi\) | ||||
−0.175536 | + | 0.984473i | \(0.556166\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −740.761 | + | 4224.00i | −0.259946 | + | 1.48228i | ||||
\(202\) | −1065.24 | + | 1845.06i | −0.371041 | + | 0.642661i | ||||
\(203\) | 783.022 | − | 1356.23i | 0.270726 | − | 0.468911i | ||||
\(204\) | 167.386 | − | 954.474i | 0.0574478 | − | 0.327581i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 207.959 | 0.0703358 | ||||||||
\(207\) | 374.039 | + | 2098.48i | 0.125592 | + | 0.704611i | ||||
\(208\) | −122.029 | −0.0406787 | ||||||||
\(209\) | −345.569 | − | 598.542i | −0.114371 | − | 0.198096i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −480.664 | + | 832.535i | −0.156826 | + | 0.271631i | −0.933722 | − | 0.357998i | \(-0.883460\pi\) |
0.776896 | + | 0.629628i | \(0.216793\pi\) | |||||||
\(212\) | −1830.04 | + | 3169.72i | −0.592866 | + | 1.02687i | ||||
\(213\) | 1647.95 | − | 601.537i | 0.530120 | − | 0.193505i | ||||
\(214\) | −1123.44 | − | 1945.86i | −0.358864 | − | 0.621570i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 1537.14 | − | 2679.62i | 0.484210 | − | 0.844099i | ||||
\(217\) | −3612.11 | −1.12998 | ||||||||
\(218\) | 951.679 | + | 1648.36i | 0.295669 | + | 0.512114i | ||||
\(219\) | −3502.54 | + | 1278.50i | −1.08073 | + | 0.394490i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −419.020 | + | 725.765i | −0.127540 | + | 0.220906i | ||||
\(222\) | −2238.48 | − | 1874.77i | −0.676743 | − | 0.566784i | ||||
\(223\) | −2396.87 | − | 4151.50i | −0.719758 | − | 1.24666i | −0.961095 | − | 0.276217i | \(-0.910919\pi\) |
0.241337 | − | 0.970441i | \(-0.422414\pi\) | |||||||
\(224\) | −1952.76 | −0.582474 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −1096.86 | −0.322840 | ||||||||
\(227\) | 2115.92 | + | 3664.89i | 0.618673 | + | 1.07157i | 0.989728 | + | 0.142962i | \(0.0456628\pi\) |
−0.371055 | + | 0.928611i | \(0.621004\pi\) | |||||||
\(228\) | −111.566 | + | 636.177i | −0.0324063 | + | 0.184789i | ||||
\(229\) | 801.351 | − | 1387.98i | 0.231243 | − | 0.400525i | −0.726931 | − | 0.686711i | \(-0.759054\pi\) |
0.958174 | + | 0.286185i | \(0.0923873\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −275.808 | + | 1572.72i | −0.0785576 | + | 0.447954i | ||||
\(232\) | 1631.61 | + | 2826.04i | 0.461727 | + | 0.799735i | ||||
\(233\) | −6094.84 | −1.71368 | −0.856838 | − | 0.515586i | \(-0.827574\pi\) | ||||
−0.856838 | + | 0.515586i | \(0.827574\pi\) | |||||||
\(234\) | −807.767 | + | 680.358i | −0.225664 | + | 0.190070i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 71.8058 | + | 124.371i | 0.0198058 | + | 0.0343046i | ||||
\(237\) | −1235.64 | − | 1034.87i | −0.338663 | − | 0.283637i | ||||
\(238\) | −313.568 | + | 543.116i | −0.0854017 | + | 0.147920i | ||||
\(239\) | 1939.22 | − | 3358.83i | 0.524844 | − | 0.909057i | −0.474737 | − | 0.880128i | \(-0.657457\pi\) |
0.999581 | − | 0.0289294i | \(-0.00920978\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −3253.39 | − | 5635.04i | −0.869583 | − | 1.50616i | −0.862424 | − | 0.506187i | \(-0.831055\pi\) |
−0.00715909 | − | 0.999974i | \(-0.502279\pi\) | |||||||
\(242\) | −807.826 | −0.214583 | ||||||||
\(243\) | 675.092 | + | 3727.35i | 0.178219 | + | 0.983991i | ||||
\(244\) | 4316.43 | 1.13250 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −2876.22 | + | 1049.89i | −0.745453 | + | 0.272107i | ||||
\(247\) | 279.286 | − | 483.737i | 0.0719455 | − | 0.124613i | ||||
\(248\) | 3763.35 | − | 6518.31i | 0.963600 | − | 1.66900i | ||||
\(249\) | 2199.49 | + | 1842.11i | 0.559787 | + | 0.468832i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 7716.46 | 1.94047 | 0.970236 | − | 0.242161i | \(-0.0778562\pi\) | ||||
0.970236 | + | 0.242161i | \(0.0778562\pi\) | |||||||
\(252\) | 1141.29 | − | 961.275i | 0.285296 | − | 0.240296i | ||||
\(253\) | 2295.74 | 0.570482 | ||||||||
\(254\) | 1301.55 | + | 2254.35i | 0.321522 | + | 0.556892i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1925.90 | − | 3335.75i | 0.470190 | − | 0.814393i | ||||
\(257\) | 1268.87 | − | 2197.75i | 0.307977 | − | 0.533432i | −0.669942 | − | 0.742413i | \(-0.733681\pi\) |
0.977920 | + | 0.208981i | \(0.0670146\pi\) | |||||||
\(258\) | 29.1693 | − | 166.331i | 0.00703878 | − | 0.0401368i | ||||
\(259\) | −1783.88 | − | 3089.76i | −0.427972 | − | 0.741268i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −3762.60 | − | 1361.57i | −0.892335 | − | 0.322908i | ||||
\(262\) | 3627.43 | 0.855356 | ||||||||
\(263\) | 3100.17 | + | 5369.65i | 0.726861 | + | 1.25896i | 0.958203 | + | 0.286088i | \(0.0923550\pi\) |
−0.231342 | + | 0.972872i | \(0.574312\pi\) | |||||||
\(264\) | −2550.73 | − | 2136.28i | −0.594646 | − | 0.498027i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 209.000 | − | 361.998i | 0.0481751 | − | 0.0834418i | ||||
\(267\) | 5297.64 | − | 1933.76i | 1.21427 | − | 0.443236i | ||||
\(268\) | −2158.18 | − | 3738.08i | −0.491910 | − | 0.852014i | ||||
\(269\) | 1737.04 | 0.393715 | 0.196858 | − | 0.980432i | \(-0.436926\pi\) | ||||
0.196858 | + | 0.980432i | \(0.436926\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2510.25 | −0.562683 | −0.281341 | − | 0.959608i | \(-0.590779\pi\) | ||||
−0.281341 | + | 0.959608i | \(0.590779\pi\) | |||||||
\(272\) | 92.5739 | + | 160.343i | 0.0206365 | + | 0.0357434i | ||||
\(273\) | −1212.22 | + | 442.488i | −0.268744 | + | 0.0980975i | ||||
\(274\) | 877.019 | − | 1519.04i | 0.193367 | − | 0.334922i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −1644.77 | − | 1377.53i | −0.358709 | − | 0.300425i | ||||
\(277\) | −489.727 | − | 848.232i | −0.106227 | − | 0.183990i | 0.808012 | − | 0.589166i | \(-0.200544\pi\) |
−0.914239 | + | 0.405176i | \(0.867210\pi\) | |||||||
\(278\) | 809.879 | 0.174724 | ||||||||
\(279\) | 1619.52 | + | 9086.05i | 0.347520 | + | 1.94970i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 841.453 | + | 1457.44i | 0.178636 | + | 0.309407i | 0.941414 | − | 0.337254i | \(-0.109498\pi\) |
−0.762777 | + | 0.646661i | \(0.776165\pi\) | |||||||
\(282\) | 167.582 | − | 955.594i | 0.0353879 | − | 0.201790i | ||||
\(283\) | 1209.16 | − | 2094.33i | 0.253984 | − | 0.439913i | −0.710635 | − | 0.703561i | \(-0.751592\pi\) |
0.964619 | + | 0.263648i | \(0.0849257\pi\) | |||||||
\(284\) | −882.859 | + | 1529.16i | −0.184465 | + | 0.319503i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 568.730 | + | 985.069i | 0.117586 | + | 0.203666i | ||||
\(287\) | −3741.26 | −0.769475 | ||||||||
\(288\) | 875.537 | + | 4912.05i | 0.179137 | + | 1.00502i | ||||
\(289\) | −3641.48 | −0.741193 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 4652.14 | + | 3896.26i | 0.937160 | + | 0.784889i | ||||
\(292\) | 1876.42 | − | 3250.06i | 0.376059 | − | 0.651354i | ||||
\(293\) | 899.642 | − | 1558.23i | 0.179378 | − | 0.310691i | −0.762290 | − | 0.647236i | \(-0.775925\pi\) |
0.941668 | + | 0.336545i | \(0.109258\pi\) | |||||||
\(294\) | 1879.34 | − | 686.001i | 0.372807 | − | 0.136083i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 7434.26 | 1.45982 | ||||||||
\(297\) | 4079.75 | − | 11.3655i | 0.797074 | − | 0.00222052i | ||||
\(298\) | −5403.55 | −1.05040 | ||||||||
\(299\) | 927.699 | + | 1606.82i | 0.179432 | + | 0.310785i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 103.170 | − | 178.696i | 0.0197562 | − | 0.0342188i | ||||
\(302\) | 1273.01 | − | 2204.92i | 0.242562 | − | 0.420129i | ||||
\(303\) | 5099.29 | + | 4270.75i | 0.966821 | + | 0.809731i | ||||
\(304\) | −61.7024 | − | 106.872i | −0.0116410 | − | 0.0201629i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 1506.77 | + | 545.251i | 0.281491 | + | 0.101863i | ||||
\(307\) | 7372.67 | 1.37062 | 0.685311 | − | 0.728251i | \(-0.259666\pi\) | ||||
0.685311 | + | 0.728251i | \(0.259666\pi\) | |||||||
\(308\) | −803.556 | − | 1391.80i | −0.148659 | − | 0.257484i | ||||
\(309\) | 112.149 | − | 639.498i | 0.0206470 | − | 0.117734i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 2854.02 | − | 4943.30i | 0.520374 | − | 0.901315i | −0.479345 | − | 0.877627i | \(-0.659126\pi\) |
0.999719 | − | 0.0236884i | \(-0.00754096\pi\) | |||||||
\(312\) | 464.477 | − | 2648.56i | 0.0842815 | − | 0.480593i | ||||
\(313\) | 355.174 | + | 615.180i | 0.0641394 | + | 0.111093i | 0.896312 | − | 0.443424i | \(-0.146236\pi\) |
−0.832173 | + | 0.554517i | \(0.812903\pi\) | |||||||
\(314\) | −1217.55 | −0.218823 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 1622.24 | 0.288792 | ||||||||
\(317\) | −4149.33 | − | 7186.85i | −0.735172 | − | 1.27336i | −0.954648 | − | 0.297737i | \(-0.903768\pi\) |
0.219476 | − | 0.975618i | \(-0.429565\pi\) | |||||||
\(318\) | −4639.90 | − | 3886.00i | −0.818215 | − | 0.685270i | ||||
\(319\) | −2154.79 | + | 3732.21i | −0.378198 | + | 0.655059i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −6589.59 | + | 2405.35i | −1.14578 | + | 0.418235i | ||||
\(322\) | 694.230 | + | 1202.44i | 0.120149 | + | 0.208104i | ||||
\(323\) | −847.493 | −0.145993 | ||||||||
\(324\) | −2929.74 | − | 2439.86i | −0.502356 | − | 0.418357i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 110.540 | + | 191.460i | 0.0187798 | + | 0.0325276i | ||||
\(327\) | 5582.11 | − | 2037.60i | 0.944011 | − | 0.344585i | ||||
\(328\) | 3897.90 | − | 6751.36i | 0.656176 | − | 1.13653i | ||||
\(329\) | 592.727 | − | 1026.63i | 0.0993255 | − | 0.172037i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2168.95 | − | 3756.74i | −0.360171 | − | 0.623834i | 0.627818 | − | 0.778360i | \(-0.283948\pi\) |
−0.987989 | + | 0.154526i | \(0.950615\pi\) | |||||||
\(332\) | −2887.67 | −0.477353 | ||||||||
\(333\) | −6972.30 | + | 5872.56i | −1.14739 | + | 0.966409i | ||||
\(334\) | −2277.06 | −0.373040 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −49.2464 | + | 280.815i | −0.00799586 | + | 0.0455943i | ||||
\(337\) | −2537.40 | + | 4394.90i | −0.410151 | + | 0.710402i | −0.994906 | − | 0.100808i | \(-0.967857\pi\) |
0.584755 | + | 0.811210i | \(0.301191\pi\) | |||||||
\(338\) | 1368.64 | − | 2370.55i | 0.220249 | − | 0.381482i | ||||
\(339\) | −591.516 | + | 3372.97i | −0.0947692 | + | 0.540397i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 9940.14 | 1.57856 | ||||||||
\(342\) | −1004.29 | − | 363.421i | −0.158789 | − | 0.0574607i | ||||
\(343\) | 6069.09 | 0.955394 | ||||||||
\(344\) | 214.979 | + | 372.355i | 0.0336945 | + | 0.0583606i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 1762.03 | − | 3051.93i | 0.273779 | − | 0.474199i | ||||
\(347\) | 2267.51 | − | 3927.45i | 0.350797 | − | 0.607598i | −0.635592 | − | 0.772025i | \(-0.719244\pi\) |
0.986389 | + | 0.164427i | \(0.0525774\pi\) | |||||||
\(348\) | 3783.26 | − | 1380.97i | 0.582770 | − | 0.212724i | ||||
\(349\) | −1041.87 | − | 1804.56i | −0.159799 | − | 0.276780i | 0.774997 | − | 0.631965i | \(-0.217751\pi\) |
−0.934796 | + | 0.355185i | \(0.884418\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1656.56 | + | 2850.88i | 0.251911 | + | 0.433530i | ||||
\(352\) | 5373.78 | 0.813704 | ||||||||
\(353\) | 4211.89 | + | 7295.21i | 0.635060 | + | 1.09996i | 0.986502 | + | 0.163747i | \(0.0523581\pi\) |
−0.351442 | + | 0.936210i | \(0.614309\pi\) | |||||||
\(354\) | −223.077 | + | 81.4279i | −0.0334926 | + | 0.0122256i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −2838.12 | + | 4915.77i | −0.422528 | + | 0.731841i | ||||
\(357\) | 1501.04 | + | 1257.15i | 0.222531 | + | 0.186374i | ||||
\(358\) | −1851.36 | − | 3206.66i | −0.273317 | − | 0.473400i | ||||
\(359\) | −9286.16 | −1.36519 | −0.682597 | − | 0.730795i | \(-0.739150\pi\) | ||||
−0.682597 | + | 0.730795i | \(0.739150\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6294.13 | −0.917645 | ||||||||
\(362\) | 601.714 | + | 1042.20i | 0.0873630 | + | 0.151317i | ||||
\(363\) | −435.646 | + | 2484.16i | −0.0629903 | + | 0.359186i | ||||
\(364\) | 649.428 | − | 1124.84i | 0.0935145 | − | 0.161972i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −1232.90 | + | 7030.28i | −0.176078 | + | 1.00404i | ||||
\(367\) | 76.2330 | + | 132.039i | 0.0108429 | + | 0.0187804i | 0.871396 | − | 0.490580i | \(-0.163215\pi\) |
−0.860553 | + | 0.509361i | \(0.829882\pi\) | |||||||
\(368\) | 409.912 | 0.0580656 | ||||||||
\(369\) | 1677.43 | + | 9410.91i | 0.236648 | + | 1.32768i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −3697.60 | − | 6404.43i | −0.517439 | − | 0.896230i | ||||
\(372\) | −7121.57 | − | 5964.44i | −0.992570 | − | 0.831296i | ||||
\(373\) | 3414.46 | − | 5914.03i | 0.473979 | − | 0.820956i | −0.525577 | − | 0.850746i | \(-0.676150\pi\) |
0.999556 | + | 0.0297898i | \(0.00948381\pi\) | |||||||
\(374\) | 862.906 | − | 1494.60i | 0.119304 | − | 0.206641i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 1235.09 | + | 2139.24i | 0.169401 | + | 0.293411i | ||||
\(377\) | −3482.97 | −0.475815 | ||||||||
\(378\) | 1239.67 | + | 2133.42i | 0.168681 | + | 0.290294i | ||||
\(379\) | −6963.21 | −0.943736 | −0.471868 | − | 0.881669i | \(-0.656420\pi\) | ||||
−0.471868 | + | 0.881669i | \(0.656420\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 7634.30 | − | 2786.69i | 1.02655 | − | 0.374715i | ||||
\(382\) | 209.175 | − | 362.302i | 0.0280166 | − | 0.0485261i | ||||
\(383\) | 183.927 | − | 318.571i | 0.0245385 | − | 0.0425018i | −0.853495 | − | 0.521100i | \(-0.825522\pi\) |
0.878034 | + | 0.478599i | \(0.158855\pi\) | |||||||
\(384\) | −4125.42 | − | 3455.12i | −0.548241 | − | 0.459162i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 633.730 | 0.0835648 | ||||||||
\(387\) | −495.756 | − | 179.398i | −0.0651180 | − | 0.0235642i | ||||
\(388\) | −6107.71 | −0.799154 | ||||||||
\(389\) | 2765.15 | + | 4789.39i | 0.360408 | + | 0.624246i | 0.988028 | − | 0.154274i | \(-0.0493040\pi\) |
−0.627620 | + | 0.778520i | \(0.715971\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1407.55 | − | 2437.95i | 0.182053 | − | 0.315326i | ||||
\(392\) | −2546.91 | + | 4411.37i | −0.328159 | + | 0.568388i | ||||
\(393\) | 1956.21 | − | 11154.8i | 0.251088 | − | 1.43176i | ||||
\(394\) | 3636.57 | + | 6298.73i | 0.464995 | + | 0.805395i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −3140.71 | + | 2645.33i | −0.398552 | + | 0.335688i | ||||
\(397\) | −9871.38 | −1.24794 | −0.623968 | − | 0.781450i | \(-0.714480\pi\) | ||||
−0.623968 | + | 0.781450i | \(0.714480\pi\) | |||||||
\(398\) | 820.139 | + | 1420.52i | 0.103291 | + | 0.178905i | ||||
\(399\) | −1000.48 | − | 837.917i | −0.125530 | − | 0.105134i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 950.974 | − | 1647.14i | 0.118427 | − | 0.205122i | −0.800717 | − | 0.599042i | \(-0.795548\pi\) |
0.919145 | + | 0.393920i | \(0.128881\pi\) | |||||||
\(402\) | 6704.75 | − | 2447.38i | 0.831847 | − | 0.303643i | ||||
\(403\) | 4016.77 | + | 6957.25i | 0.496500 | + | 0.859963i | ||||
\(404\) | −6694.76 | −0.824447 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −2606.43 | −0.318609 | ||||||||
\(407\) | 4909.03 | + | 8502.70i | 0.597867 | + | 1.03554i | ||||
\(408\) | −3832.51 | + | 1398.95i | −0.465043 | + | 0.169751i | ||||
\(409\) | −2105.94 | + | 3647.59i | −0.254601 | + | 0.440982i | −0.964787 | − | 0.263032i | \(-0.915278\pi\) |
0.710186 | + | 0.704014i | \(0.248611\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −4198.27 | − | 3516.13i | −0.503858 | − | 0.421990i | ||||
\(412\) | 326.741 | + | 565.932i | 0.0390713 | + | 0.0676735i | ||||
\(413\) | −290.168 | −0.0345719 | ||||||||
\(414\) | 2713.41 | − | 2285.42i | 0.322118 | − | 0.271310i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 2171.52 | + | 3761.19i | 0.255932 | + | 0.443287i | ||||
\(417\) | 436.753 | − | 2490.47i | 0.0512899 | − | 0.292468i | ||||
\(418\) | −575.144 | + | 996.179i | −0.0672996 | + | 0.116566i | ||||
\(419\) | 8364.24 | − | 14487.3i | 0.975226 | − | 1.68914i | 0.296038 | − | 0.955176i | \(-0.404334\pi\) |
0.679188 | − | 0.733965i | \(-0.262332\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −6570.41 | − | 11380.3i | −0.760623 | − | 1.31744i | −0.942530 | − | 0.334122i | \(-0.891560\pi\) |
0.181907 | − | 0.983316i | \(-0.441773\pi\) | |||||||
\(422\) | 1599.98 | 0.184563 | ||||||||
\(423\) | −2848.19 | − | 1030.67i | −0.327385 | − | 0.118470i | ||||
\(424\) | 15409.7 | 1.76500 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −2238.41 | − | 1874.71i | −0.254580 | − | 0.213216i | ||||
\(427\) | −4360.68 | + | 7552.91i | −0.494210 | + | 0.855998i | ||||
\(428\) | 3530.26 | − | 6114.59i | 0.398695 | − | 0.690560i | ||||
\(429\) | 3335.91 | − | 1217.68i | 0.375429 | − | 0.137040i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −5801.99 | −0.648426 | −0.324213 | − | 0.945984i | \(-0.605100\pi\) | ||||
−0.324213 | + | 0.945984i | \(0.605100\pi\) | |||||||
\(432\) | 728.453 | − | 2.02935i | 0.0811290 | − | 0.000226012i | ||||
\(433\) | −9599.49 | −1.06541 | −0.532705 | − | 0.846301i | \(-0.678824\pi\) | ||||
−0.532705 | + | 0.846301i | \(0.678824\pi\) | |||||||
\(434\) | 3005.89 | + | 5206.36i | 0.332460 | + | 0.575837i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −2990.52 | + | 5179.74i | −0.328486 | + | 0.568955i | ||||
\(437\) | −938.162 | + | 1624.94i | −0.102696 | + | 0.177876i | ||||
\(438\) | 4757.49 | + | 3984.49i | 0.519000 | + | 0.434672i | ||||
\(439\) | −7018.70 | − | 12156.7i | −0.763062 | − | 1.32166i | −0.941265 | − | 0.337669i | \(-0.890362\pi\) |
0.178202 | − | 0.983994i | \(-0.442972\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1096.04 | − | 6149.14i | −0.118350 | − | 0.663982i | ||||
\(442\) | 1394.79 | 0.150098 | ||||||||
\(443\) | 3565.25 | + | 6175.19i | 0.382370 | + | 0.662285i | 0.991401 | − | 0.130862i | \(-0.0417745\pi\) |
−0.609030 | + | 0.793147i | \(0.708441\pi\) | |||||||
\(444\) | 1584.87 | − | 9037.32i | 0.169402 | − | 0.965974i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −3989.21 | + | 6909.51i | −0.423530 | + | 0.733575i | ||||
\(447\) | −2914.04 | + | 16616.6i | −0.308343 | + | 1.75825i | ||||
\(448\) | 1405.56 | + | 2434.50i | 0.148229 | + | 0.256740i | ||||
\(449\) | 15299.1 | 1.60804 | 0.804019 | − | 0.594604i | \(-0.202691\pi\) | ||||
0.804019 | + | 0.594604i | \(0.202691\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 10295.5 | 1.07494 | ||||||||
\(452\) | −1723.36 | − | 2984.95i | −0.179337 | − | 0.310620i | ||||
\(453\) | −6093.88 | − | 5103.74i | −0.632043 | − | 0.529347i | ||||
\(454\) | 3521.62 | − | 6099.63i | 0.364048 | − | 0.630550i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 2554.45 | − | 932.430i | 0.262331 | − | 0.0957566i | ||||
\(457\) | 960.083 | + | 1662.91i | 0.0982731 | + | 0.170214i | 0.910970 | − | 0.412473i | \(-0.135335\pi\) |
−0.812697 | + | 0.582687i | \(0.802001\pi\) | |||||||
\(458\) | −2667.44 | −0.272143 | ||||||||
\(459\) | 2489.28 | − | 4339.44i | 0.253137 | − | 0.441280i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −3344.76 | − | 5793.30i | −0.337920 | − | 0.585295i | 0.646121 | − | 0.763235i | \(-0.276390\pi\) |
−0.984041 | + | 0.177940i | \(0.943057\pi\) | |||||||
\(462\) | 2496.38 | − | 911.234i | 0.251390 | − | 0.0917629i | ||||
\(463\) | −7723.08 | + | 13376.8i | −0.775209 | + | 1.34270i | 0.159468 | + | 0.987203i | \(0.449022\pi\) |
−0.934677 | + | 0.355498i | \(0.884311\pi\) | |||||||
\(464\) | −384.746 | + | 666.399i | −0.0384943 | + | 0.0666741i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 5071.95 | + | 8784.88i | 0.504192 | + | 0.873287i | ||||
\(467\) | 6054.68 | 0.599951 | 0.299976 | − | 0.953947i | \(-0.403021\pi\) | ||||
0.299976 | + | 0.953947i | \(0.403021\pi\) | |||||||
\(468\) | −3120.65 | − | 1129.26i | −0.308231 | − | 0.111539i | ||||
\(469\) | 8721.22 | 0.858654 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −656.605 | + | 3744.12i | −0.0642351 | + | 0.366284i | ||||
\(472\) | 302.317 | − | 523.628i | 0.0294815 | − | 0.0510634i | ||||
\(473\) | −283.913 | + | 491.751i | −0.0275990 | + | 0.0478029i | ||||
\(474\) | −463.359 | + | 2642.18i | −0.0449004 | + | 0.256033i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −1970.69 | −0.189761 | ||||||||
\(477\) | −14452.1 | + | 12172.6i | −1.38725 | + | 1.16844i | ||||
\(478\) | −6455.05 | −0.617672 | ||||||||
\(479\) | −1528.14 | − | 2646.81i | −0.145767 | − | 0.252476i | 0.783892 | − | 0.620897i | \(-0.213232\pi\) |
−0.929659 | + | 0.368421i | \(0.879898\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3967.44 | + | 6871.81i | −0.376091 | + | 0.651409i | ||||
\(482\) | −5414.76 | + | 9378.64i | −0.511692 | + | 0.886276i | ||||
\(483\) | 4072.04 | − | 1486.38i | 0.383611 | − | 0.140026i | ||||
\(484\) | −1269.24 | − | 2198.39i | −0.119200 | − | 0.206460i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 4810.67 | − | 4074.85i | 0.449005 | − | 0.380327i | ||||
\(487\) | −2335.83 | −0.217344 | −0.108672 | − | 0.994078i | \(-0.534660\pi\) | ||||
−0.108672 | + | 0.994078i | \(0.534660\pi\) | |||||||
\(488\) | −9086.51 | − | 15738.3i | −0.842883 | − | 1.45992i | ||||
\(489\) | 648.374 | − | 236.671i | 0.0599601 | − | 0.0218868i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −2748.50 | + | 4760.54i | −0.252624 | + | 0.437557i | −0.964247 | − | 0.265004i | \(-0.914627\pi\) |
0.711624 | + | 0.702561i | \(0.247960\pi\) | |||||||
\(492\) | −7376.19 | − | 6177.70i | −0.675903 | − | 0.566082i | ||||
\(493\) | 2642.27 | + | 4576.55i | 0.241383 | + | 0.418088i | ||||
\(494\) | −929.654 | −0.0846703 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 1774.84 | 0.160671 | ||||||||
\(497\) | −1783.82 | − | 3089.66i | −0.160996 | − | 0.278854i | ||||
\(498\) | 824.801 | − | 4703.22i | 0.0742173 | − | 0.423205i | ||||
\(499\) | −8741.68 | + | 15141.0i | −0.784231 | + | 1.35833i | 0.145226 | + | 0.989399i | \(0.453609\pi\) |
−0.929457 | + | 0.368930i | \(0.879724\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1227.98 | + | 7002.24i | −0.109505 | + | 0.624425i | ||||
\(502\) | −6421.41 | − | 11122.2i | −0.570920 | − | 0.988862i | ||||
\(503\) | −6699.56 | −0.593874 | −0.296937 | − | 0.954897i | \(-0.595965\pi\) | ||||
−0.296937 | + | 0.954897i | \(0.595965\pi\) | |||||||
\(504\) | −5907.47 | − | 2137.73i | −0.522102 | − | 0.188932i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −1910.45 | − | 3308.99i | −0.167845 | − | 0.290717i | ||||
\(507\) | −6551.63 | − | 5487.11i | −0.573902 | − | 0.480653i | ||||
\(508\) | −4089.95 | + | 7083.99i | −0.357209 | + | 0.618703i | ||||
\(509\) | −1316.44 | + | 2280.13i | −0.114637 | + | 0.198556i | −0.917634 | − | 0.397426i | \(-0.869904\pi\) |
0.802998 | + | 0.595982i | \(0.203237\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 3791.31 | + | 6566.75i | 0.328215 | + | 0.568485i | ||||
\(512\) | 1874.14 | 0.161770 | ||||||||
\(513\) | −1659.16 | + | 2892.33i | −0.142795 | + | 0.248927i | ||||
\(514\) | −4223.68 | −0.362448 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 498.477 | − | 181.955i | 0.0425276 | − | 0.0155235i | ||||
\(517\) | −1631.12 | + | 2825.18i | −0.138756 | + | 0.240332i | ||||
\(518\) | −2968.98 | + | 5142.42i | −0.251833 | + | 0.436187i | ||||
\(519\) | −8434.82 | − | 7064.32i | −0.713386 | − | 0.597474i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −18292.5 | −1.53821 | −0.769105 | − | 0.639122i | \(-0.779298\pi\) | ||||
−0.769105 | + | 0.639122i | \(0.779298\pi\) | |||||||
\(522\) | 1168.62 | + | 6556.33i | 0.0979866 | + | 0.549737i | ||||
\(523\) | 16446.5 | 1.37506 | 0.687530 | − | 0.726156i | \(-0.258695\pi\) | ||||
0.687530 | + | 0.726156i | \(0.258695\pi\) | |||||||
\(524\) | 5699.34 | + | 9871.55i | 0.475147 | + | 0.822979i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 5159.74 | − | 8936.93i | 0.427710 | − | 0.740815i | ||||
\(527\) | 6094.44 | − | 10555.9i | 0.503754 | − | 0.872527i | ||||
\(528\) | 135.521 | − | 772.772i | 0.0111700 | − | 0.0636943i | ||||
\(529\) | 2967.22 | + | 5139.38i | 0.243875 | + | 0.422404i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 130.099 | + | 729.899i | 0.0106324 | + | 0.0596515i | ||||
\(532\) | 1313.50 | 0.107044 | ||||||||
\(533\) | 4160.38 | + | 7206.00i | 0.338098 | + | 0.585603i | ||||
\(534\) | −7195.79 | − | 6026.61i | −0.583132 | − | 0.488383i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −9086.37 | + | 15738.1i | −0.732223 | + | 1.26825i | ||||
\(537\) | −10859.3 | + | 3963.87i | −0.872647 | + | 0.318535i | ||||
\(538\) | −1445.52 | − | 2503.71i | −0.115838 | − | 0.200637i | ||||
\(539\) | −6727.15 | −0.537586 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 13884.4 | 1.10340 | 0.551698 | − | 0.834044i | \(-0.313980\pi\) | ||||
0.551698 | + | 0.834044i | \(0.313980\pi\) | |||||||
\(542\) | 2088.96 | + | 3618.19i | 0.165551 | + | 0.286742i | ||||
\(543\) | 3529.38 | − | 1288.30i | 0.278932 | − | 0.101816i | ||||
\(544\) | 3294.75 | − | 5706.67i | 0.259671 | − | 0.449763i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 1646.56 | + | 1379.03i | 0.129059 | + | 0.108090i | ||||
\(547\) | −3391.55 | − | 5874.33i | −0.265104 | − | 0.459174i | 0.702487 | − | 0.711697i | \(-0.252073\pi\) |
−0.967591 | + | 0.252523i | \(0.918740\pi\) | |||||||
\(548\) | 5511.83 | 0.429660 | ||||||||
\(549\) | 20954.1 | + | 7582.61i | 1.62896 | + | 0.589468i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1761.13 | − | 3050.36i | −0.136164 | − | 0.235844i | ||||
\(552\) | −1560.25 | + | 8896.89i | −0.120305 | + | 0.686009i | ||||
\(553\) | −1638.87 | + | 2838.61i | −0.126025 | + | 0.218282i | ||||
\(554\) | −815.074 | + | 1411.75i | −0.0625075 | + | 0.108266i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 1272.47 | + | 2203.98i | 0.0970586 | + | 0.168110i | ||||
\(557\) | 8088.38 | 0.615288 | 0.307644 | − | 0.951501i | \(-0.400459\pi\) | ||||
0.307644 | + | 0.951501i | \(0.400459\pi\) | |||||||
\(558\) | 11748.6 | − | 9895.46i | 0.891320 | − | 0.750732i | ||||
\(559\) | −458.912 | −0.0347226 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −4130.71 | − | 3459.55i | −0.310871 | − | 0.260360i | ||||
\(562\) | 1400.46 | − | 2425.68i | 0.105116 | − | 0.182066i | ||||
\(563\) | −83.7997 | + | 145.145i | −0.00627307 | + | 0.0108653i | −0.869145 | − | 0.494558i | \(-0.835330\pi\) |
0.862872 | + | 0.505423i | \(0.168663\pi\) | |||||||
\(564\) | 2863.82 | − | 1045.36i | 0.213810 | − | 0.0780453i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −4024.93 | −0.298905 | ||||||||
\(567\) | 7229.04 | − | 2661.61i | 0.535434 | − | 0.197138i | ||||
\(568\) | 7434.02 | 0.549163 | ||||||||
\(569\) | −3653.15 | − | 6327.45i | −0.269153 | − | 0.466187i | 0.699490 | − | 0.714642i | \(-0.253410\pi\) |
−0.968643 | + | 0.248455i | \(0.920077\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −11611.2 | + | 20111.1i | −0.850985 | + | 1.47395i | 0.0293354 | + | 0.999570i | \(0.490661\pi\) |
−0.880320 | + | 0.474380i | \(0.842672\pi\) | |||||||
\(572\) | −1787.16 | + | 3095.44i | −0.130638 | + | 0.226271i | ||||
\(573\) | −1001.32 | − | 838.621i | −0.0730028 | − | 0.0611412i | ||||
\(574\) | 3113.36 | + | 5392.51i | 0.226393 | + | 0.392123i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 5493.65 | − | 4627.13i | 0.397399 | − | 0.334717i | ||||
\(577\) | −5447.52 | −0.393038 | −0.196519 | − | 0.980500i | \(-0.562964\pi\) | ||||
−0.196519 | + | 0.980500i | \(0.562964\pi\) | |||||||
\(578\) | 3030.34 | + | 5248.70i | 0.218072 | + | 0.377711i | ||||
\(579\) | 341.759 | − | 1948.79i | 0.0245303 | − | 0.139878i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 2917.27 | − | 5052.85i | 0.208311 | − | 0.360805i | ||||
\(582\) | 1744.54 | − | 9947.78i | 0.124250 | − | 0.708503i | ||||
\(583\) | 10175.4 | + | 17624.3i | 0.722850 | + | 1.25201i | ||||
\(584\) | −15800.2 | −1.11955 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −2994.62 | −0.211104 | ||||||||
\(587\) | 6436.20 | + | 11147.8i | 0.452556 | + | 0.783850i | 0.998544 | − | 0.0539429i | \(-0.0171789\pi\) |
−0.545988 | + | 0.837793i | \(0.683846\pi\) | |||||||
\(588\) | 4819.64 | + | 4036.54i | 0.338025 | + | 0.283102i | ||||
\(589\) | −4062.07 | + | 7035.72i | −0.284168 | + | 0.492193i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 21330.5 | − | 7786.10i | 1.48463 | − | 0.541924i | ||||
\(592\) | 876.525 | + | 1518.19i | 0.0608529 | + | 0.105400i | ||||
\(593\) | −16563.3 | −1.14700 | −0.573501 | − | 0.819205i | \(-0.694415\pi\) | ||||
−0.573501 | + | 0.819205i | \(0.694415\pi\) | |||||||
\(594\) | −3411.43 | − | 5870.94i | −0.235644 | − | 0.405535i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −8489.96 | − | 14705.0i | −0.583494 | − | 1.01064i | ||||
\(597\) | 4810.56 | − | 1755.96i | 0.329787 | − | 0.120380i | ||||
\(598\) | 1544.01 | − | 2674.30i | 0.105584 | − | 0.182877i | ||||
\(599\) | −7881.18 | + | 13650.6i | −0.537590 | + | 0.931133i | 0.461444 | + | 0.887170i | \(0.347332\pi\) |
−0.999033 | + | 0.0439629i | \(0.986002\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 6317.51 | + | 10942.3i | 0.428780 | + | 0.742668i | 0.996765 | − | 0.0803703i | \(-0.0256103\pi\) |
−0.567985 | + | 0.823039i | \(0.692277\pi\) | |||||||
\(602\) | −343.420 | −0.0232504 | ||||||||
\(603\) | −3910.24 | − | 21937.7i | −0.264075 | − | 1.48155i | ||||
\(604\) | 8000.53 | 0.538968 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 1912.22 | − | 10903.9i | 0.128182 | − | 0.730927i | ||||
\(607\) | 9672.84 | − | 16753.8i | 0.646801 | − | 1.12029i | −0.337081 | − | 0.941476i | \(-0.609440\pi\) |
0.983882 | − | 0.178817i | \(-0.0572271\pi\) | |||||||
\(608\) | −2196.02 | + | 3803.61i | −0.146481 | + | 0.253712i | ||||
\(609\) | −1405.60 | + | 8015.09i | −0.0935270 | + | 0.533313i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −2636.52 | −0.174570 | ||||||||
\(612\) | 883.576 | + | 4957.15i | 0.0583602 | + | 0.327420i | ||||
\(613\) | 4801.16 | 0.316341 | 0.158170 | − | 0.987412i | \(-0.449440\pi\) | ||||
0.158170 | + | 0.987412i | \(0.449440\pi\) | |||||||
\(614\) | −6135.33 | − | 10626.7i | −0.403260 | − | 0.698467i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −3383.13 | + | 5859.75i | −0.221283 | + | 0.383273i | ||||
\(617\) | 11018.4 | − | 19084.5i | 0.718939 | − | 1.24524i | −0.242481 | − | 0.970156i | \(-0.577961\pi\) |
0.961420 | − | 0.275083i | \(-0.0887055\pi\) | |||||||
\(618\) | −1015.08 | + | 370.525i | −0.0660717 | + | 0.0241176i | ||||
\(619\) | 727.050 | + | 1259.29i | 0.0472094 | + | 0.0817690i | 0.888664 | − | 0.458558i | \(-0.151634\pi\) |
−0.841455 | + | 0.540327i | \(0.818301\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −5564.64 | − | 9576.54i | −0.359584 | − | 0.618829i | ||||
\(622\) | −9500.12 | −0.612412 | ||||||||
\(623\) | −5734.43 | − | 9932.32i | −0.368772 | − | 0.638732i | ||||
\(624\) | 595.638 | − | 217.421i | 0.0382125 | − | 0.0139484i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 591.131 | − | 1023.87i | 0.0377418 | − | 0.0653707i | ||||
\(627\) | 2753.20 | + | 2305.86i | 0.175363 | + | 0.146869i | ||||
\(628\) | −1913.00 | − | 3313.41i | −0.121555 | − | 0.210540i | ||||
\(629\) | 12039.2 | 0.763171 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 2680.50 | 0.169111 | 0.0845554 | − | 0.996419i | \(-0.473053\pi\) | ||||
0.0845554 | + | 0.996419i | \(0.473053\pi\) | |||||||
\(632\) | −3414.98 | − | 5914.91i | −0.214937 | − | 0.372283i | ||||
\(633\) | 862.840 | − | 4920.12i | 0.0541782 | − | 0.308937i | ||||
\(634\) | −6905.90 | + | 11961.4i | −0.432600 | + | 0.749285i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 3285.11 | − | 18732.5i | 0.204816 | − | 1.16791i | ||||
\(637\) | −2718.42 | − | 4708.43i | −0.169086 | − | 0.292865i | ||||
\(638\) | 7172.63 | 0.445089 | ||||||||
\(639\) | −6972.08 | + | 5872.37i | −0.431629 | + | 0.363548i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 11176.6 | + | 19358.5i | 0.688690 | + | 1.19285i | 0.972262 | + | 0.233895i | \(0.0751472\pi\) |
−0.283572 | + | 0.958951i | \(0.591519\pi\) | |||||||
\(642\) | 8950.64 | + | 7496.33i | 0.550240 | + | 0.460836i | ||||
\(643\) | 6558.35 | − | 11359.4i | 0.402233 | − | 0.696688i | −0.591762 | − | 0.806113i | \(-0.701567\pi\) |
0.993995 | + | 0.109424i | \(0.0349008\pi\) | |||||||
\(644\) | −2181.52 | + | 3778.51i | −0.133485 | + | 0.231202i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 705.259 | + | 1221.54i | 0.0429536 | + | 0.0743979i | ||||
\(647\) | 21272.7 | 1.29261 | 0.646303 | − | 0.763081i | \(-0.276314\pi\) | ||||
0.646303 | + | 0.763081i | \(0.276314\pi\) | |||||||
\(648\) | −2728.66 | + | 15818.4i | −0.165420 | + | 0.958957i | ||||
\(649\) | 798.510 | 0.0482962 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 17631.2 | − | 6435.77i | 1.06148 | − | 0.387462i | ||||
\(652\) | −347.355 | + | 601.637i | −0.0208642 | + | 0.0361379i | ||||
\(653\) | −6489.93 | + | 11240.9i | −0.388929 | + | 0.673644i | −0.992306 | − | 0.123812i | \(-0.960488\pi\) |
0.603377 | + | 0.797456i | \(0.293821\pi\) | |||||||
\(654\) | −7582.19 | − | 6350.22i | −0.453344 | − | 0.379684i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 1838.30 | 0.109411 | ||||||||
\(657\) | 14818.4 | − | 12481.1i | 0.879941 | − | 0.741147i | ||||
\(658\) | −1973.00 | −0.116893 | ||||||||
\(659\) | −14864.1 | − | 25745.4i | −0.878640 | − | 1.52185i | −0.852834 | − | 0.522183i | \(-0.825118\pi\) |
−0.0258068 | − | 0.999667i | \(-0.508215\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 3469.44 | − | 6009.24i | 0.204153 | − | 0.353604i | −0.745709 | − | 0.666272i | \(-0.767889\pi\) |
0.949863 | + | 0.312667i | \(0.101223\pi\) | |||||||
\(662\) | −3609.88 | + | 6252.50i | −0.211937 | + | 0.367085i | ||||
\(663\) | 752.184 | − | 4289.13i | 0.0440609 | − | 0.251246i | ||||
\(664\) | 6078.82 | + | 10528.8i | 0.355277 | + | 0.615358i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 14266.6 | + | 5162.64i | 0.830061 | + | 0.300373i | ||||
\(667\) | 11699.8 | 0.679188 | ||||||||
\(668\) | −3577.68 | − | 6196.73i | −0.207223 | − | 0.358920i | ||||
\(669\) | 19096.2 | + | 15993.5i | 1.10359 | + | 0.924279i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 12000.1 | − | 20784.8i | 0.690401 | − | 1.19581i | ||||
\(672\) | 9531.68 | − | 3479.27i | 0.547161 | − | 0.199726i | ||||
\(673\) | −6886.81 | − | 11928.3i | −0.394453 | − | 0.683213i | 0.598578 | − | 0.801065i | \(-0.295733\pi\) |
−0.993031 | + | 0.117851i | \(0.962399\pi\) | |||||||
\(674\) | 8446.19 | 0.482693 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 8601.51 | 0.489389 | ||||||||
\(677\) | −6080.24 | − | 10531.3i | −0.345174 | − | 0.597859i | 0.640211 | − | 0.768199i | \(-0.278847\pi\) |
−0.985385 | + | 0.170340i | \(0.945513\pi\) | |||||||
\(678\) | 5353.91 | − | 1954.30i | 0.303268 | − | 0.110700i | ||||
\(679\) | 6170.31 | − | 10687.3i | 0.348741 | − | 0.604037i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −16857.9 | − | 14118.8i | −0.948600 | − | 0.794470i | ||||
\(682\) | −8271.89 | − | 14327.3i | −0.464439 | − | 0.804431i | ||||
\(683\) | −7397.68 | −0.414443 | −0.207221 | − | 0.978294i | \(-0.566442\pi\) | ||||
−0.207221 | + | 0.978294i | \(0.566442\pi\) | |||||||
\(684\) | −588.921 | − | 3304.04i | −0.0329210 | − | 0.184698i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −5050.52 | − | 8747.76i | −0.281093 | − | 0.486867i | ||||
\(687\) | −1438.51 | + | 8202.70i | −0.0798870 | + | 0.455535i | ||||
\(688\) | −50.6936 | + | 87.8039i | −0.00280912 | + | 0.00486554i | ||||
\(689\) | −8223.67 | + | 14243.8i | −0.454712 | + | 0.787585i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 11338.7 | + | 19639.3i | 0.624235 | + | 1.08121i | 0.988688 | + | 0.149985i | \(0.0479225\pi\) |
−0.364453 | + | 0.931222i | \(0.618744\pi\) | |||||||
\(692\) | 11073.9 | 0.608333 | ||||||||
\(693\) | −1455.90 | − | 8168.08i | −0.0798052 | − | 0.447734i | ||||
\(694\) | −7547.84 | −0.412842 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −12999.3 | − | 10887.2i | −0.707958 | − | 0.592928i | ||||
\(697\) | 6312.34 | − | 10933.3i | 0.343037 | − | 0.594158i | ||||
\(698\) | −1734.02 | + | 3003.41i | −0.0940310 | + | 0.162866i | ||||
\(699\) | 29749.7 | − | 10859.3i | 1.60978 | − | 0.587607i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −18577.8 | −1.00096 | −0.500479 | − | 0.865748i | \(-0.666843\pi\) | ||||
−0.500479 | + | 0.865748i | \(0.666843\pi\) | |||||||
\(702\) | 2730.61 | − | 4760.13i | 0.146810 | − | 0.255925i | ||||
\(703\) | −8024.38 | −0.430505 | ||||||||
\(704\) | −3867.95 | − | 6699.48i | −0.207072 | − | 0.358660i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 7010.03 | − | 12141.7i | 0.373691 | − | 0.647252i | ||||
\(707\) | 6763.39 | − | 11714.5i | 0.359778 | − | 0.623154i | ||||
\(708\) | −572.089 | − | 479.135i | −0.0303678 | − | 0.0254336i | ||||
\(709\) | −4891.93 | − | 8473.07i | −0.259126 | − | 0.448819i | 0.706882 | − | 0.707331i | \(-0.250101\pi\) |
−0.966008 | + | 0.258512i | \(0.916768\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 7875.15 | + | 2849.77i | 0.415388 | + | 0.150316i | ||||
\(712\) | 23898.1 | 1.25789 | ||||||||
\(713\) | −13492.9 | − | 23370.4i | −0.708715 | − | 1.22753i | ||||
\(714\) | 562.886 | − | 3209.71i | 0.0295035 | − | 0.168236i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 5817.66 | − | 10076.5i | 0.303654 | − | 0.525944i | ||||
\(717\) | −3481.10 | + | 19850.0i | −0.181316 | + | 1.03391i | ||||
\(718\) | 7727.68 | + | 13384.7i | 0.401663 | + | 0.695701i | ||||
\(719\) | −15405.6 | −0.799073 | −0.399537 | − | 0.916717i | \(-0.630829\pi\) | ||||
−0.399537 | + | 0.916717i | \(0.630829\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1320.36 | −0.0682009 | ||||||||
\(722\) | 5237.79 | + | 9072.12i | 0.269987 | + | 0.467631i | ||||
\(723\) | 25920.3 | + | 21708.7i | 1.33332 | + | 1.11668i | ||||
\(724\) | −1890.80 | + | 3274.97i | −0.0970597 | + | 0.168112i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 3943.11 | − | 1439.32i | 0.201574 | − | 0.0735788i | ||||
\(727\) | 7374.44 | + | 12772.9i | 0.376207 | + | 0.651610i | 0.990507 | − | 0.137463i | \(-0.0438947\pi\) |
−0.614300 | + | 0.789073i | \(0.710561\pi\) | |||||||
\(728\) | −5468.44 | −0.278398 | ||||||||
\(729\) | −9936.32 | − | 16990.9i | −0.504817 | − | 0.863226i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 348.142 | + | 603.000i | 0.0176149 | + | 0.0305099i | ||||
\(732\) | −21069.1 | + | 7690.68i | −1.06385 | + | 0.388327i | ||||
\(733\) | 11399.6 | − | 19744.7i | 0.574425 | − | 0.994933i | −0.421679 | − | 0.906745i | \(-0.638559\pi\) |
0.996104 | − | 0.0881879i | \(-0.0281076\pi\) | |||||||
\(734\) | 126.878 | − | 219.759i | 0.00638030 | − | 0.0110510i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −7294.47 | − | 12634.4i | −0.365323 | − | 0.632758i | ||||
\(737\) | −23999.9 | −1.19952 | ||||||||
\(738\) | 12168.6 | − | 10249.3i | 0.606956 | − | 0.511220i | ||||
\(739\) | −23076.7 | −1.14870 | −0.574350 | − | 0.818610i | \(-0.694745\pi\) | ||||
−0.574350 | + | 0.818610i | \(0.694745\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −501.346 | + | 2858.80i | −0.0248548 | + | 0.141728i | ||||
\(742\) | −6154.07 | + | 10659.2i | −0.304478 | + | 0.527372i | ||||
\(743\) | 3949.16 | − | 6840.14i | 0.194994 | − | 0.337740i | −0.751905 | − | 0.659272i | \(-0.770865\pi\) |
0.946899 | + | 0.321532i | \(0.104198\pi\) | |||||||
\(744\) | −6755.58 | + | 38522.0i | −0.332892 | + | 1.89823i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −11365.7 | −0.557811 | ||||||||
\(747\) | −14018.1 | − | 5072.72i | −0.686609 | − | 0.248462i | ||||
\(748\) | 5423.12 | 0.265092 | ||||||||
\(749\) | 7132.89 | + | 12354.5i | 0.347971 | + | 0.602704i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1487.18 | + | 2575.86i | −0.0722607 | + | 0.125159i | −0.899892 | − | 0.436113i | \(-0.856355\pi\) |
0.827631 | + | 0.561273i | \(0.189688\pi\) | |||||||
\(752\) | −291.242 | + | 504.446i | −0.0141230 | + | 0.0244618i | ||||
\(753\) | −37665.1 | + | 13748.6i | −1.82283 | + | 0.665374i | ||||
\(754\) | 2898.43 | + | 5020.23i | 0.139993 | + | 0.242475i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −3858.07 | + | 6725.57i | −0.185604 | + | 0.323554i | ||||
\(757\) | −24466.0 | −1.17468 | −0.587340 | − | 0.809340i | \(-0.699825\pi\) | ||||
−0.587340 | + | 0.809340i | \(0.699825\pi\) | |||||||
\(758\) | 5794.58 | + | 10036.5i | 0.277663 | + | 0.480927i | ||||
\(759\) | −11205.8 | + | 4090.37i | −0.535896 | + | 0.195614i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −8145.43 | + | 14108.3i | −0.388005 | + | 0.672044i | −0.992181 | − | 0.124807i | \(-0.960169\pi\) |
0.604176 | + | 0.796851i | \(0.293502\pi\) | |||||||
\(762\) | −10369.7 | − | 8684.79i | −0.492984 | − | 0.412883i | ||||
\(763\) | −6042.35 | − | 10465.7i | −0.286694 | − | 0.496569i | ||||
\(764\) | 1314.61 | 0.0622524 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −612.235 | −0.0288785 | ||||||||
\(767\) | 322.675 | + | 558.889i | 0.0151905 | + | 0.0263107i | ||||
\(768\) | −3457.18 | + | 19713.7i | −0.162435 | + | 0.926245i | ||||
\(769\) | 12453.0 | − | 21569.2i | 0.583962 | − | 1.01145i | −0.411042 | − | 0.911616i | \(-0.634835\pi\) |
0.995004 | − | 0.0998355i | \(-0.0318317\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −2277.76 | + | 12988.3i | −0.106396 | + | 0.606696i | ||||
\(772\) | 995.705 | + | 1724.61i | 0.0464200 | + | 0.0804017i | ||||
\(773\) | 21955.7 | 1.02160 | 0.510798 | − | 0.859701i | \(-0.329350\pi\) | ||||
0.510798 | + | 0.859701i | \(0.329350\pi\) | |||||||
\(774\) | 153.976 | + | 863.854i | 0.00715056 | + | 0.0401170i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 12857.3 | + | 22269.5i | 0.594782 | + | 1.03019i | ||||
\(777\) | 14212.4 | + | 11903.2i | 0.656201 | + | 0.549581i | ||||
\(778\) | 4602.16 | − | 7971.18i | 0.212076 | − | 0.367327i | ||||
\(779\) | −4207.31 | + | 7287.27i | −0.193508 | + | 0.335165i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 4908.88 | + | 8502.42i | 0.224908 | + | 0.389553i | ||||
\(782\) | −4685.29 | −0.214253 | ||||||||
\(783\) | 20791.7 | − | 57.9223i | 0.948959 | − | 0.00264365i | ||||
\(784\) | −1201.16 | −0.0547174 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −17706.0 | + | 6463.07i | −0.803499 | + | 0.293295i | ||||
\(787\) | 1691.08 | − | 2929.04i | 0.0765955 | − | 0.132667i | −0.825183 | − | 0.564865i | \(-0.808928\pi\) |
0.901779 | + | 0.432197i | \(0.142262\pi\) | |||||||
\(788\) | −11427.4 | + | 19792.9i | −0.516606 | + | 0.894788i | ||||
\(789\) | −24699.5 | − | 20686.3i | −1.11448 | − | 0.933400i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 6964.12 | 0.313041 | ||||||||
\(792\) | 16256.7 | + | 5882.80i | 0.729366 | + | 0.263934i | ||||
\(793\) | 19396.8 | 0.868600 | ||||||||
\(794\) | 8214.68 | + | 14228.2i | 0.367164 | + | 0.635946i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −2577.17 | + | 4463.79i | −0.114756 | + | 0.198763i | ||||
\(797\) | −9008.39 | + | 15603.0i | −0.400368 | + | 0.693458i | −0.993770 | − | 0.111448i | \(-0.964451\pi\) |
0.593402 | + | 0.804906i | \(0.297784\pi\) | |||||||
\(798\) | −375.175 | + | 2139.34i | −0.0166429 | + | 0.0949020i | ||||
\(799\) | 2000.13 | + | 3464.32i | 0.0885600 | + | 0.153390i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −22413.1 | + | 18877.9i | −0.988673 | + | 0.832729i | ||||
\(802\) | −3165.49 | −0.139373 | ||||||||
\(803\) | −10433.3 | − | 18071.0i | −0.458509 | − | 0.794161i | ||||
\(804\) | 17194.6 | + | 14400.8i | 0.754237 | + | 0.631688i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 6685.28 | − | 11579.2i | 0.292157 | − | 0.506031i | ||||
\(807\) | −8478.74 | + | 3094.93i | −0.369846 | + | 0.135002i | ||||
\(808\) | 14093.1 | + | 24410.0i | 0.613607 | + | 1.06280i | ||||
\(809\) | 18030.0 | 0.783559 | 0.391780 | − | 0.920059i | \(-0.371860\pi\) | ||||
0.391780 | + | 0.920059i | \(0.371860\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −35444.8 | −1.53469 | −0.767347 | − | 0.641233i | \(-0.778423\pi\) | ||||
−0.767347 | + | 0.641233i | \(0.778423\pi\) | |||||||
\(812\) | −4095.18 | − | 7093.06i | −0.176986 | − | 0.306549i | ||||
\(813\) | 12252.9 | − | 4472.58i | 0.528570 | − | 0.192940i | ||||
\(814\) | 8170.31 | − | 14151.4i | 0.351805 | − | 0.609344i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −737.552 | − | 617.713i | −0.0316415 | − | 0.0265004i | ||||
\(817\) | −232.044 | − | 401.912i | −0.00993659 | − | 0.0172107i | ||||
\(818\) | 7010.00 | 0.299632 | ||||||||
\(819\) | 5128.63 | − | 4319.69i | 0.218814 | − | 0.184301i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 11304.9 | + | 19580.6i | 0.480563 | + | 0.832360i | 0.999751 | − | 0.0222999i | \(-0.00709887\pi\) |
−0.519188 | + | 0.854660i | \(0.673766\pi\) | |||||||
\(822\) | −1574.34 | + | 8977.25i | −0.0668021 | + | 0.380922i | ||||
\(823\) | −16926.0 | + | 29316.8i | −0.716895 | + | 1.24170i | 0.245329 | + | 0.969440i | \(0.421104\pi\) |
−0.962224 | + | 0.272259i | \(0.912229\pi\) | |||||||
\(824\) | 1375.64 | − | 2382.69i | 0.0581588 | − | 0.100734i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 241.469 | + | 418.237i | 0.0101716 | + | 0.0176178i | ||||
\(827\) | −29173.2 | −1.22667 | −0.613333 | − | 0.789824i | \(-0.710172\pi\) | ||||
−0.613333 | + | 0.789824i | \(0.710172\pi\) | |||||||
\(828\) | 10482.7 | + | 3793.37i | 0.439976 | + | 0.159213i | ||||
\(829\) | 20552.8 | 0.861073 | 0.430537 | − | 0.902573i | \(-0.358324\pi\) | ||||
0.430537 | + | 0.902573i | \(0.358324\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 3901.74 | + | 3267.78i | 0.162876 | + | 0.136412i | ||||
\(832\) | 3126.04 | − | 5414.47i | 0.130260 | − | 0.225616i | ||||
\(833\) | −4124.52 | + | 7143.87i | −0.171556 | + | 0.297143i | ||||
\(834\) | −3953.13 | + | 1442.98i | −0.164131 | + | 0.0599116i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −3614.62 | −0.149539 | ||||||||
\(837\) | −24093.9 | − | 41464.7i | −0.994991 | − | 1.71234i | ||||
\(838\) | −27841.9 | −1.14771 | ||||||||
\(839\) | −6923.52 | − | 11991.9i | −0.284895 | − | 0.493452i | 0.687689 | − | 0.726005i | \(-0.258625\pi\) |
−0.972584 | + | 0.232553i | \(0.925292\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1212.98 | − | 2100.95i | 0.0497348 | − | 0.0861432i | ||||
\(842\) | −10935.4 | + | 18940.7i | −0.447576 | + | 0.775225i | ||||
\(843\) | −6703.99 | − | 5614.72i | −0.273900 | − | 0.229396i | ||||
\(844\) | 2513.86 | + | 4354.13i | 0.102524 | + | 0.177577i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 884.612 | + | 4962.97i | 0.0359499 | + | 0.201691i | ||||
\(847\) | 5129.01 | 0.208069 | ||||||||
\(848\) | 1816.85 | + | 3146.88i | 0.0735742 | + | 0.127434i | ||||
\(849\) | −2170.57 | + | 12377.1i | −0.0877430 | + | 0.500332i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 13327.2 | − | 23083.4i | 0.536840 | − | 0.929835i | ||||
\(852\) | 1584.82 | − | 9037.03i | 0.0637266 | − | 0.363384i | ||||
\(853\) | −18976.1 | − | 32867.6i | −0.761701 | − | 1.31930i | −0.941973 | − | 0.335688i | \(-0.891031\pi\) |
0.180272 | − | 0.983617i | \(-0.442302\pi\) | |||||||
\(854\) | 14515.3 | 0.581620 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −29726.2 | −1.18694 | ||||||||
\(857\) | 2960.12 | + | 5127.08i | 0.117988 | + | 0.204361i | 0.918970 | − | 0.394327i | \(-0.129022\pi\) |
−0.800982 | + | 0.598688i | \(0.795689\pi\) | |||||||
\(858\) | −4531.17 | − | 3794.94i | −0.180293 | − | 0.150999i | ||||
\(859\) | 10240.2 | − | 17736.5i | 0.406740 | − | 0.704494i | −0.587782 | − | 0.809019i | \(-0.699999\pi\) |
0.994522 | + | 0.104525i | \(0.0333322\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 18261.6 | − | 6665.88i | 0.722825 | − | 0.263847i | ||||
\(862\) | 4828.24 | + | 8362.76i | 0.190778 | + | 0.330437i | ||||
\(863\) | 21117.9 | 0.832980 | 0.416490 | − | 0.909140i | \(-0.363260\pi\) | ||||
0.416490 | + | 0.909140i | \(0.363260\pi\) | |||||||
\(864\) | −13025.5 | − | 22416.4i | −0.512890 | − | 0.882664i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 7988.42 | + | 13836.3i | 0.313461 | + | 0.542931i | ||||
\(867\) | 17774.6 | − | 6488.11i | 0.696258 | − | 0.254150i | ||||
\(868\) | −9445.60 | + | 16360.3i | −0.369360 | + | 0.639751i | ||||
\(869\) | 4509.99 | − | 7811.54i | 0.176054 | − | 0.304935i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −9698.25 | − | 16797.9i | −0.377282 | − | 0.653472i | ||||
\(872\) | 25181.4 | 0.977923 | ||||||||
\(873\) | −29649.8 | − | 10729.3i | −1.14948 | − | 0.415959i | ||||
\(874\) | 3122.84 | 0.120860 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −3368.37 | + | 19207.2i | −0.129916 | + | 0.740813i | ||||
\(877\) | −14201.6 | + | 24597.9i | −0.546812 | + | 0.947107i | 0.451678 | + | 0.892181i | \(0.350826\pi\) |
−0.998490 | + | 0.0549258i | \(0.982508\pi\) | |||||||
\(878\) | −11681.5 | + | 20233.0i | −0.449012 | + | 0.777711i | ||||
\(879\) | −1614.95 | + | 9208.82i | −0.0619691 | + | 0.353363i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 14925.4 | 0.570772 | 0.285386 | − | 0.958413i | \(-0.407878\pi\) | ||||
0.285386 | + | 0.958413i | \(0.407878\pi\) | |||||||
\(882\) | −7951.04 | + | 6696.92i | −0.303544 | + | 0.255666i | ||||
\(883\) | −10817.4 | −0.412271 | −0.206136 | − | 0.978523i | \(-0.566089\pi\) | ||||
−0.206136 | + | 0.978523i | \(0.566089\pi\) | |||||||
\(884\) | 2191.46 | + | 3795.72i | 0.0833788 | + | 0.144416i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 5933.79 | − | 10277.6i | 0.225000 | − | 0.389711i | ||||
\(887\) | −7105.65 | + | 12307.3i | −0.268979 | + | 0.465885i | −0.968598 | − | 0.248630i | \(-0.920020\pi\) |
0.699619 | + | 0.714516i | \(0.253353\pi\) | |||||||
\(888\) | −36287.6 | + | 13245.8i | −1.37132 | + | 0.500563i | ||||
\(889\) | −8263.74 | − | 14313.2i | −0.311763 | − | 0.539989i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −19893.6 | + | 7324.46i | −0.747990 | + | 0.275397i | ||||
\(892\) | −25071.1 | −0.941078 | ||||||||
\(893\) | −1333.13 | − | 2309.04i | −0.0499568 | − | 0.0865277i | ||||
\(894\) | 26375.5 | − | 9627.63i | 0.986720 | − | 0.360175i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −5471.71 | + | 9477.27i | −0.204014 | + | 0.353363i | ||||
\(897\) | −7391.13 | − | 6190.21i | −0.275120 | − | 0.230418i | ||||
\(898\) | −12731.5 | − | 22051.5i | −0.473112 | − | 0.819454i | ||||
\(899\) | 50658.1 | 1.87936 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 24954.7 | 0.922711 | ||||||||
\(902\) | −8567.65 | − | 14839.6i | −0.316265 | − | 0.547788i | ||||
\(903\) | −185.200 | + | 1056.06i | −0.00682512 | + | 0.0389185i | ||||
\(904\) | −7255.70 | + | 12567.2i | −0.266948 | + | 0.462367i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −2285.18 | + | 13030.7i | −0.0837971 | + | 0.477831i | ||||
\(907\) | 14121.3 | + | 24458.7i | 0.516967 | + | 0.895412i | 0.999806 | + | 0.0197034i | \(0.00627220\pi\) |
−0.482839 | + | 0.875709i | \(0.660394\pi\) | |||||||
\(908\) | 22132.4 | 0.808910 | ||||||||
\(909\) | −32499.6 | − | 11760.6i | −1.18586 | − | 0.429124i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 15380.3 | + | 26639.5i | 0.559355 | + | 0.968832i | 0.997550 | + | 0.0699518i | \(0.0222846\pi\) |
−0.438195 | + | 0.898880i | \(0.644382\pi\) | |||||||
\(912\) | 491.594 | + | 411.719i | 0.0178490 | + | 0.0149489i | ||||
\(913\) | −8028.00 | + | 13904.9i | −0.291006 | + | 0.504037i | ||||
\(914\) | 1597.91 | − | 2767.66i | 0.0578272 | − | 0.100160i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −4191.04 | − | 7259.09i | −0.151174 | − | 0.261842i | ||||
\(917\) | −23031.1 | −0.829392 | ||||||||
\(918\) | −8326.22 | + | 23.1955i | −0.299353 | + | 0.000833949i | ||||
\(919\) | 9067.61 | 0.325476 | 0.162738 | − | 0.986669i | \(-0.447967\pi\) | ||||
0.162738 | + | 0.986669i | \(0.447967\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −35987.0 | + | 13136.1i | −1.28753 | + | 0.469976i | ||||
\(922\) | −5566.83 | + | 9642.03i | −0.198844 | + | 0.344407i | ||||
\(923\) | −3967.31 | + | 6871.59i | −0.141480 | + | 0.245050i | ||||
\(924\) | 6402.07 | + | 5361.85i | 0.227936 | + | 0.190900i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 25707.7 | 0.912318 | ||||||||
\(927\) | 591.996 | + | 3321.29i | 0.0209749 | + | 0.117676i | ||||
\(928\) | 27386.5 | 0.968757 | ||||||||
\(929\) | −13529.2 | − | 23433.2i | −0.477802 | − | 0.827578i | 0.521874 | − | 0.853023i | \(-0.325233\pi\) |
−0.999676 | + | 0.0254448i | \(0.991900\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2749.08 | − | 4761.54i | 0.0967748 | − | 0.167619i | ||||
\(932\) | −15937.9 | + | 27605.3i | −0.560154 | + | 0.970215i | ||||
\(933\) | −5123.25 | + | 29214.0i | −0.179772 | + | 1.02510i | ||||
\(934\) | −5038.53 | − | 8726.99i | −0.176516 | − | 0.305734i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 2451.82 | + | 13755.5i | 0.0856200 | + | 0.480357i | ||||
\(937\) | 3320.73 | 0.115778 | 0.0578888 | − | 0.998323i | \(-0.481563\pi\) | ||||
0.0578888 | + | 0.998323i | \(0.481563\pi\) | |||||||
\(938\) | −7257.55 | − | 12570.4i | −0.252630 | − | 0.437569i | ||||
\(939\) | −2829.73 | − | 2369.95i | −0.0983438 | − | 0.0823647i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 6934.00 | − | 12010.0i | 0.240215 | − | 0.416064i | −0.720561 | − | 0.693392i | \(-0.756115\pi\) |
0.960775 | + | 0.277328i | \(0.0894488\pi\) | |||||||
\(942\) | 5943.04 | − | 2169.34i | 0.205557 | − | 0.0750328i | ||||
\(943\) | −13975.3 | − | 24206.0i | −0.482608 | − | 0.835902i | ||||
\(944\) | 142.577 | 0.00491576 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 945.056 | 0.0324804 | ||||||||
\(947\) | 15184.1 | + | 26299.6i | 0.521032 | + | 0.902454i | 0.999701 | + | 0.0244583i | \(0.00778609\pi\) |
−0.478669 | + | 0.877995i | \(0.658881\pi\) | |||||||
\(948\) | −7918.37 | + | 2890.38i | −0.271284 | + | 0.0990245i | ||||
\(949\) | 8432.10 | − | 14604.8i | 0.288427 | − | 0.499571i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 33058.4 | + | 27687.0i | 1.12723 | + | 0.944073i | ||||
\(952\) | 4148.49 | + | 7185.40i | 0.141233 | + | 0.244622i | ||||
\(953\) | 55107.7 | 1.87315 | 0.936576 | − | 0.350464i | \(-0.113976\pi\) | ||||
0.936576 | + | 0.350464i | \(0.113976\pi\) | |||||||
\(954\) | 29571.7 | + | 10701.1i | 1.00358 | + | 0.363166i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −10142.1 | − | 17566.6i | −0.343115 | − | 0.594292i | ||||
\(957\) | 3868.07 | − | 22056.7i | 0.130655 | − | 0.745027i | ||||
\(958\) | −2543.34 | + | 4405.20i | −0.0857743 | + | 0.148565i | ||||
\(959\) | −5568.33 | + | 9644.62i | −0.187498 | + | 0.324756i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −43526.4 | − | 75389.9i | −1.46106 | − | 2.53063i | ||||
\(962\) | 13206.4 | 0.442609 | ||||||||
\(963\) | 27879.0 | − | 23481.6i | 0.932906 | − | 0.785759i | ||||
\(964\) | −34030.3 | −1.13697 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −5531.05 | − | 4632.35i | −0.184222 | − | 0.154289i | ||||
\(967\) | 1366.23 | − | 2366.37i | 0.0454342 | − | 0.0786943i | −0.842414 | − | 0.538831i | \(-0.818866\pi\) |
0.887848 | + | 0.460137i | \(0.152200\pi\) | |||||||
\(968\) | −5343.75 | + | 9255.65i | −0.177433 | + | 0.307322i | ||||
\(969\) | 4136.73 | − | 1510.00i | 0.137142 | − | 0.0500599i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −52740.8 | −1.74308 | −0.871542 | − | 0.490321i | \(-0.836880\pi\) | ||||
−0.871542 | + | 0.490321i | \(0.836880\pi\) | |||||||
\(972\) | 18647.6 | + | 6689.28i | 0.615352 | + | 0.220739i | ||||
\(973\) | −5142.04 | −0.169421 | ||||||||
\(974\) | 1943.81 | + | 3366.78i | 0.0639464 | + | 0.110758i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 2142.66 | − | 3711.20i | 0.0702714 | − | 0.121714i | ||||
\(977\) | 12493.6 | − | 21639.6i | 0.409116 | − | 0.708611i | −0.585674 | − | 0.810546i | \(-0.699170\pi\) |
0.994791 | + | 0.101936i | \(0.0325036\pi\) | |||||||
\(978\) | −880.687 | − | 737.592i | −0.0287948 | − | 0.0241161i | ||||
\(979\) | 15780.5 | + | 27332.7i | 0.515166 | + | 0.892294i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −23616.6 | + | 19891.6i | −0.768624 | + | 0.647389i | ||||
\(982\) | 9148.89 | 0.297304 | ||||||||
\(983\) | −5551.41 | − | 9615.32i | −0.180125 | − | 0.311985i | 0.761798 | − | 0.647814i | \(-0.224317\pi\) |
−0.941923 | + | 0.335829i | \(0.890983\pi\) | |||||||
\(984\) | −6997.12 | + | 39899.3i | −0.226687 | + | 1.29262i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 4397.64 | − | 7616.94i | 0.142038 | − | 0.246017i | ||||
\(987\) | −1064.00 | + | 6067.21i | −0.0343137 | + | 0.195665i | ||||
\(988\) | −1460.65 | − | 2529.93i | −0.0470340 | − | 0.0814653i | ||||
\(989\) | 1541.55 | 0.0495637 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 4790.04 | 0.153543 | 0.0767713 | − | 0.997049i | \(-0.475539\pi\) | ||||
0.0767713 | + | 0.997049i | \(0.475539\pi\) | |||||||
\(992\) | −31583.7 | − | 54704.6i | −1.01087 | − | 1.75088i | ||||
\(993\) | 17280.4 | + | 14472.7i | 0.552243 | + | 0.462514i | ||||
\(994\) | −2968.88 | + | 5142.26i | −0.0947357 | + | 0.164087i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 14095.1 | − | 5145.02i | 0.448413 | − | 0.163681i | ||||
\(997\) | 18138.0 | + | 31415.9i | 0.576164 | + | 0.997945i | 0.995914 | + | 0.0903053i | \(0.0287843\pi\) |
−0.419750 | + | 0.907640i | \(0.637882\pi\) | |||||||
\(998\) | 29098.3 | 0.922936 | ||||||||
\(999\) | 23569.5 | − | 41087.4i | 0.746452 | − | 1.30125i |
(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 | 225.4.e.f.76.4 | yes | 24 | |
5.2 | odd | 4 | 225.4.k.e.49.16 | 48 | |||
5.3 | odd | 4 | 225.4.k.e.49.9 | 48 | |||
5.4 | even | 2 | 225.4.e.e.76.9 | ✓ | 24 | ||
9.4 | even | 3 | 2025.4.a.bf.1.9 | 12 | |||
9.5 | odd | 6 | 2025.4.a.bj.1.4 | 12 | |||
9.7 | even | 3 | inner | 225.4.e.f.151.4 | yes | 24 | |
45.4 | even | 6 | 2025.4.a.bi.1.4 | 12 | |||
45.7 | odd | 12 | 225.4.k.e.124.9 | 48 | |||
45.14 | odd | 6 | 2025.4.a.be.1.9 | 12 | |||
45.34 | even | 6 | 225.4.e.e.151.9 | yes | 24 | ||
45.43 | odd | 12 | 225.4.k.e.124.16 | 48 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
225.4.e.e.76.9 | ✓ | 24 | 5.4 | even | 2 | ||
225.4.e.e.151.9 | yes | 24 | 45.34 | even | 6 | ||
225.4.e.f.76.4 | yes | 24 | 1.1 | even | 1 | trivial | |
225.4.e.f.151.4 | yes | 24 | 9.7 | even | 3 | inner | |
225.4.k.e.49.9 | 48 | 5.3 | odd | 4 | |||
225.4.k.e.49.16 | 48 | 5.2 | odd | 4 | |||
225.4.k.e.124.9 | 48 | 45.7 | odd | 12 | |||
225.4.k.e.124.16 | 48 | 45.43 | odd | 12 | |||
2025.4.a.be.1.9 | 12 | 45.14 | odd | 6 | |||
2025.4.a.bf.1.9 | 12 | 9.4 | even | 3 | |||
2025.4.a.bi.1.4 | 12 | 45.4 | even | 6 | |||
2025.4.a.bj.1.4 | 12 | 9.5 | odd | 6 |