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 | 151.2 | ||
Character | \(\chi\) | \(=\) | 225.151 |
Dual form | 225.4.e.f.76.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/225\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(127\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.16773 | + | 3.75461i | −0.766407 | + | 1.32746i | 0.173093 | + | 0.984906i | \(0.444624\pi\) |
−0.939500 | + | 0.342550i | \(0.888709\pi\) | |||||||
\(3\) | −0.193913 | − | 5.19253i | −0.0373185 | − | 0.999303i | ||||
\(4\) | −5.39807 | − | 9.34974i | −0.674759 | − | 1.16872i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 19.9163 | + | 10.5279i | 1.35513 | + | 0.716334i | ||||
\(7\) | −6.50075 | + | 11.2596i | −0.351007 | + | 0.607963i | −0.986426 | − | 0.164205i | \(-0.947494\pi\) |
0.635419 | + | 0.772168i | \(0.280827\pi\) | |||||||
\(8\) | 12.1226 | 0.535747 | ||||||||
\(9\) | −26.9248 | + | 2.01380i | −0.997215 | + | 0.0745850i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 17.2761 | − | 29.9230i | 0.473539 | − | 0.820194i | −0.526002 | − | 0.850483i | \(-0.676310\pi\) |
0.999541 | + | 0.0302897i | \(0.00964297\pi\) | |||||||
\(12\) | −47.5021 | + | 29.8427i | −1.14272 | + | 0.717904i | ||||
\(13\) | 3.77884 | + | 6.54514i | 0.0806200 | + | 0.139638i | 0.903516 | − | 0.428553i | \(-0.140977\pi\) |
−0.822896 | + | 0.568191i | \(0.807643\pi\) | |||||||
\(14\) | −28.1837 | − | 48.8156i | −0.538029 | − | 0.931894i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 16.9062 | − | 29.2824i | 0.264159 | − | 0.457537i | ||||
\(17\) | −82.0901 | −1.17116 | −0.585581 | − | 0.810614i | \(-0.699134\pi\) | ||||
−0.585581 | + | 0.810614i | \(0.699134\pi\) | |||||||
\(18\) | 50.8046 | − | 105.458i | 0.665264 | − | 1.38092i | ||||
\(19\) | 146.406 | 1.76778 | 0.883890 | − | 0.467696i | \(-0.154916\pi\) | ||||
0.883890 | + | 0.467696i | \(0.154916\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 59.7265 | + | 31.5720i | 0.620638 | + | 0.328075i | ||||
\(22\) | 74.8995 | + | 129.730i | 0.725847 | + | 1.25720i | ||||
\(23\) | 93.9451 | + | 162.718i | 0.851691 | + | 1.47517i | 0.879681 | + | 0.475565i | \(0.157756\pi\) |
−0.0279894 | + | 0.999608i | \(0.508910\pi\) | |||||||
\(24\) | −2.35072 | − | 62.9468i | −0.0199933 | − | 0.535374i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −32.7659 | −0.247151 | ||||||||
\(27\) | 15.6778 | + | 139.417i | 0.111748 | + | 0.993737i | ||||
\(28\) | 140.366 | 0.947382 | ||||||||
\(29\) | −21.8589 | + | 37.8607i | −0.139969 | + | 0.242433i | −0.927485 | − | 0.373861i | \(-0.878034\pi\) |
0.787516 | + | 0.616295i | \(0.211367\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 29.3391 | + | 50.8168i | 0.169982 | + | 0.294418i | 0.938413 | − | 0.345514i | \(-0.112296\pi\) |
−0.768431 | + | 0.639933i | \(0.778962\pi\) | |||||||
\(32\) | 121.786 | + | 210.940i | 0.672780 | + | 1.16529i | ||||
\(33\) | −158.726 | − | 83.9041i | −0.837294 | − | 0.442601i | ||||
\(34\) | 177.949 | − | 308.216i | 0.897587 | − | 1.55467i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 164.171 | + | 240.869i | 0.760049 | + | 1.11514i | ||||
\(37\) | 329.358 | 1.46341 | 0.731705 | − | 0.681621i | \(-0.238725\pi\) | ||||
0.731705 | + | 0.681621i | \(0.238725\pi\) | |||||||
\(38\) | −317.368 | + | 549.697i | −1.35484 | + | 2.34665i | ||||
\(39\) | 33.2531 | − | 20.8909i | 0.136532 | − | 0.0857750i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 86.4845 | + | 149.796i | 0.329429 | + | 0.570588i | 0.982399 | − | 0.186796i | \(-0.0598103\pi\) |
−0.652969 | + | 0.757384i | \(0.726477\pi\) | |||||||
\(42\) | −248.011 | + | 155.811i | −0.911166 | + | 0.572431i | ||||
\(43\) | 78.3437 | − | 135.695i | 0.277844 | − | 0.481240i | −0.693004 | − | 0.720933i | \(-0.743713\pi\) |
0.970849 | + | 0.239693i | \(0.0770467\pi\) | |||||||
\(44\) | −373.030 | −1.27810 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −814.589 | −2.61097 | ||||||||
\(47\) | 84.6230 | − | 146.571i | 0.262628 | − | 0.454886i | −0.704311 | − | 0.709891i | \(-0.748744\pi\) |
0.966940 | + | 0.255006i | \(0.0820774\pi\) | |||||||
\(48\) | −155.328 | − | 82.1077i | −0.467076 | − | 0.246900i | ||||
\(49\) | 86.9806 | + | 150.655i | 0.253588 | + | 0.439227i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 15.9183 | + | 426.255i | 0.0437061 | + | 1.17035i | ||||
\(52\) | 40.7969 | − | 70.6623i | 0.108798 | − | 0.188444i | ||||
\(53\) | −609.837 | −1.58052 | −0.790259 | − | 0.612772i | \(-0.790054\pi\) | ||||
−0.790259 | + | 0.612772i | \(0.790054\pi\) | |||||||
\(54\) | −557.443 | − | 243.355i | −1.40479 | − | 0.613267i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −78.8058 | + | 136.496i | −0.188051 | + | 0.325714i | ||||
\(57\) | −28.3899 | − | 760.217i | −0.0659709 | − | 1.76655i | ||||
\(58\) | −94.7682 | − | 164.143i | −0.214546 | − | 0.371605i | ||||
\(59\) | 297.215 | + | 514.792i | 0.655833 | + | 1.13594i | 0.981684 | + | 0.190514i | \(0.0610156\pi\) |
−0.325852 | + | 0.945421i | \(0.605651\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −162.538 | + | 281.525i | −0.341163 | + | 0.590911i | −0.984649 | − | 0.174547i | \(-0.944154\pi\) |
0.643486 | + | 0.765458i | \(0.277487\pi\) | |||||||
\(62\) | −254.396 | −0.521103 | ||||||||
\(63\) | 152.357 | − | 316.254i | 0.304685 | − | 0.632449i | ||||
\(64\) | −785.498 | −1.53418 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 659.102 | − | 414.075i | 1.22924 | − | 0.772258i | ||||
\(67\) | 344.191 | + | 596.156i | 0.627606 | + | 1.08705i | 0.988031 | + | 0.154257i | \(0.0492985\pi\) |
−0.360425 | + | 0.932788i | \(0.617368\pi\) | |||||||
\(68\) | 443.128 | + | 767.521i | 0.790253 | + | 1.36876i | ||||
\(69\) | 826.700 | − | 519.366i | 1.44236 | − | 0.906149i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −515.170 | −0.861119 | −0.430560 | − | 0.902562i | \(-0.641684\pi\) | ||||
−0.430560 | + | 0.902562i | \(0.641684\pi\) | |||||||
\(72\) | −326.398 | + | 24.4124i | −0.534255 | + | 0.0399587i | ||||
\(73\) | 1088.37 | 1.74499 | 0.872497 | − | 0.488619i | \(-0.162499\pi\) | ||||
0.872497 | + | 0.488619i | \(0.162499\pi\) | |||||||
\(74\) | −713.959 | + | 1236.61i | −1.12157 | + | 1.94261i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −790.310 | − | 1368.86i | −1.19283 | − | 2.06603i | ||||
\(77\) | 224.615 | + | 389.044i | 0.332431 | + | 0.575788i | ||||
\(78\) | 6.35373 | + | 170.138i | 0.00922331 | + | 0.246979i | ||||
\(79\) | 262.896 | − | 455.349i | 0.374406 | − | 0.648491i | −0.615832 | − | 0.787878i | \(-0.711180\pi\) |
0.990238 | + | 0.139387i | \(0.0445131\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 720.889 | − | 108.442i | 0.988874 | − | 0.148755i | ||||
\(82\) | −749.899 | −1.00991 | ||||||||
\(83\) | 179.006 | − | 310.048i | 0.236729 | − | 0.410027i | −0.723045 | − | 0.690801i | \(-0.757258\pi\) |
0.959774 | + | 0.280775i | \(0.0905913\pi\) | |||||||
\(84\) | −27.2188 | − | 728.855i | −0.0353549 | − | 0.946722i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 339.655 | + | 588.300i | 0.425884 | + | 0.737652i | ||||
\(87\) | 200.832 | + | 106.161i | 0.247488 | + | 0.130824i | ||||
\(88\) | 209.430 | − | 362.744i | 0.253697 | − | 0.439416i | ||||
\(89\) | 1517.67 | 1.80756 | 0.903779 | − | 0.427999i | \(-0.140781\pi\) | ||||
0.903779 | + | 0.427999i | \(0.140781\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −98.2610 | −0.113193 | ||||||||
\(92\) | 1014.25 | − | 1756.72i | 1.14937 | − | 1.99077i | ||||
\(93\) | 258.179 | − | 162.198i | 0.287870 | − | 0.180851i | ||||
\(94\) | 366.879 | + | 635.453i | 0.402560 | + | 0.697255i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 1071.70 | − | 673.283i | 1.13937 | − | 0.715798i | ||||
\(97\) | 197.680 | − | 342.393i | 0.206922 | − | 0.358399i | −0.743822 | − | 0.668378i | \(-0.766989\pi\) |
0.950743 | + | 0.309979i | \(0.100322\pi\) | |||||||
\(98\) | −754.200 | −0.777405 | ||||||||
\(99\) | −404.896 | + | 840.462i | −0.411046 | + | 0.853228i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −166.629 | + | 288.610i | −0.164160 | + | 0.284334i | −0.936357 | − | 0.351050i | \(-0.885825\pi\) |
0.772197 | + | 0.635384i | \(0.219158\pi\) | |||||||
\(102\) | −1634.93 | − | 864.238i | −1.58708 | − | 0.838944i | ||||
\(103\) | −815.444 | − | 1412.39i | −0.780078 | − | 1.35114i | −0.931896 | − | 0.362727i | \(-0.881846\pi\) |
0.151817 | − | 0.988409i | \(-0.451487\pi\) | |||||||
\(104\) | 45.8092 | + | 79.3439i | 0.0431919 | + | 0.0748106i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1321.96 | − | 2289.70i | 1.21132 | − | 2.09807i | ||||
\(107\) | −688.472 | −0.622029 | −0.311015 | − | 0.950405i | \(-0.600669\pi\) | ||||
−0.311015 | + | 0.950405i | \(0.600669\pi\) | |||||||
\(108\) | 1218.89 | − | 899.168i | 1.08599 | − | 0.801134i | ||||
\(109\) | −1188.95 | −1.04478 | −0.522390 | − | 0.852707i | \(-0.674959\pi\) | ||||
−0.522390 | + | 0.852707i | \(0.674959\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −63.8668 | − | 1710.20i | −0.0546123 | − | 1.46239i | ||||
\(112\) | 219.806 | + | 380.715i | 0.185444 | + | 0.321198i | ||||
\(113\) | −134.208 | − | 232.455i | −0.111727 | − | 0.193518i | 0.804739 | − | 0.593628i | \(-0.202305\pi\) |
−0.916467 | + | 0.400111i | \(0.868972\pi\) | |||||||
\(114\) | 2915.86 | + | 1541.35i | 2.39557 | + | 1.26632i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 471.984 | 0.377781 | ||||||||
\(117\) | −114.925 | − | 168.617i | −0.0908104 | − | 0.133236i | ||||
\(118\) | −2577.12 | −2.01054 | ||||||||
\(119\) | 533.647 | − | 924.303i | 0.411087 | − | 0.712023i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 68.5754 | + | 118.776i | 0.0515217 | + | 0.0892382i | ||||
\(122\) | −704.678 | − | 1220.54i | −0.522939 | − | 0.905756i | ||||
\(123\) | 761.048 | − | 478.121i | 0.557897 | − | 0.350493i | ||||
\(124\) | 316.749 | − | 548.625i | 0.229394 | − | 0.397323i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 857.144 | + | 1257.59i | 0.606036 | + | 0.889169i | ||||
\(127\) | −145.302 | −0.101523 | −0.0507616 | − | 0.998711i | \(-0.516165\pi\) | ||||
−0.0507616 | + | 0.998711i | \(0.516165\pi\) | |||||||
\(128\) | 728.455 | − | 1261.72i | 0.503023 | − | 0.871261i | ||||
\(129\) | −719.794 | − | 380.489i | −0.491274 | − | 0.259692i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 134.659 | + | 233.237i | 0.0898110 | + | 0.155557i | 0.907431 | − | 0.420201i | \(-0.138040\pi\) |
−0.817620 | + | 0.575758i | \(0.804707\pi\) | |||||||
\(132\) | 72.3352 | + | 1936.97i | 0.0476968 | + | 1.27721i | ||||
\(133\) | −951.747 | + | 1648.47i | −0.620504 | + | 1.07474i | ||||
\(134\) | −2984.45 | −1.92401 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −995.143 | −0.627447 | ||||||||
\(137\) | 413.688 | − | 716.528i | 0.257984 | − | 0.446841i | −0.707718 | − | 0.706495i | \(-0.750275\pi\) |
0.965702 | + | 0.259654i | \(0.0836086\pi\) | |||||||
\(138\) | 157.959 | + | 4229.78i | 0.0974375 | + | 2.60915i | ||||
\(139\) | 84.9350 | + | 147.112i | 0.0518280 | + | 0.0897687i | 0.890775 | − | 0.454444i | \(-0.150162\pi\) |
−0.838947 | + | 0.544212i | \(0.816829\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −777.486 | − | 410.986i | −0.464370 | − | 0.245470i | ||||
\(142\) | 1116.75 | − | 1934.26i | 0.659968 | − | 1.14310i | ||||
\(143\) | 261.134 | 0.152707 | ||||||||
\(144\) | −396.227 | + | 822.467i | −0.229298 | + | 0.475965i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −2359.30 | + | 4086.42i | −1.33738 | + | 2.31640i | ||||
\(147\) | 765.413 | − | 480.863i | 0.429457 | − | 0.269802i | ||||
\(148\) | −1777.90 | − | 3079.41i | −0.987450 | − | 1.71031i | ||||
\(149\) | −873.174 | − | 1512.38i | −0.480089 | − | 0.831538i | 0.519650 | − | 0.854379i | \(-0.326062\pi\) |
−0.999739 | + | 0.0228410i | \(0.992729\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −171.419 | + | 296.906i | −0.0923832 | + | 0.160012i | −0.908513 | − | 0.417856i | \(-0.862782\pi\) |
0.816130 | + | 0.577868i | \(0.196115\pi\) | |||||||
\(152\) | 1774.82 | 0.947082 | ||||||||
\(153\) | 2210.26 | − | 165.313i | 1.16790 | − | 0.0873512i | ||||
\(154\) | −1947.61 | −1.01911 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −374.827 | − | 198.137i | −0.192373 | − | 0.101690i | ||||
\(157\) | 1747.85 | + | 3027.36i | 0.888494 | + | 1.53892i | 0.841656 | + | 0.540014i | \(0.181581\pi\) |
0.0468373 | + | 0.998903i | \(0.485086\pi\) | |||||||
\(158\) | 1139.77 | + | 1974.15i | 0.573895 | + | 0.994016i | ||||
\(159\) | 118.255 | + | 3166.60i | 0.0589826 | + | 1.57942i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −2442.85 | −1.19580 | ||||||||
\(162\) | −1155.53 | + | 2941.73i | −0.560415 | + | 1.42669i | ||||
\(163\) | 663.542 | 0.318851 | 0.159425 | − | 0.987210i | \(-0.449036\pi\) | ||||
0.159425 | + | 0.987210i | \(0.449036\pi\) | |||||||
\(164\) | 933.699 | − | 1617.21i | 0.444571 | − | 0.770020i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 776.074 | + | 1344.20i | 0.362862 | + | 0.628495i | ||||
\(167\) | −1229.82 | − | 2130.11i | −0.569858 | − | 0.987023i | −0.996579 | − | 0.0826401i | \(-0.973665\pi\) |
0.426721 | − | 0.904383i | \(-0.359669\pi\) | |||||||
\(168\) | 724.039 | + | 382.733i | 0.332505 | + | 0.175765i | ||||
\(169\) | 1069.94 | − | 1853.19i | 0.487001 | − | 0.843510i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −3941.95 | + | 294.831i | −1.76286 | + | 0.131850i | ||||
\(172\) | −1691.62 | −0.749912 | ||||||||
\(173\) | 763.873 | − | 1323.07i | 0.335701 | − | 0.581451i | −0.647918 | − | 0.761710i | \(-0.724360\pi\) |
0.983619 | + | 0.180259i | \(0.0576936\pi\) | |||||||
\(174\) | −833.943 | + | 523.917i | −0.363339 | + | 0.228264i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −584.144 | − | 1011.77i | −0.250179 | − | 0.433323i | ||||
\(177\) | 2615.44 | − | 1643.12i | 1.11067 | − | 0.697767i | ||||
\(178\) | −3289.89 | + | 5698.26i | −1.38533 | + | 2.39945i | ||||
\(179\) | 1006.17 | 0.420137 | 0.210069 | − | 0.977687i | \(-0.432631\pi\) | ||||
0.210069 | + | 0.977687i | \(0.432631\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 591.861 | 0.243053 | 0.121527 | − | 0.992588i | \(-0.461221\pi\) | ||||
0.121527 | + | 0.992588i | \(0.461221\pi\) | |||||||
\(182\) | 213.003 | − | 368.932i | 0.0867518 | − | 0.150259i | ||||
\(183\) | 1493.35 | + | 789.395i | 0.603231 | + | 0.318873i | ||||
\(184\) | 1138.86 | + | 1972.56i | 0.456291 | + | 0.790319i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 49.3307 | + | 1320.96i | 0.0194468 | + | 0.520740i | ||||
\(187\) | −1418.19 | + | 2456.38i | −0.554591 | + | 0.960580i | ||||
\(188\) | −1827.20 | −0.708843 | ||||||||
\(189\) | −1671.70 | − | 729.792i | −0.643379 | − | 0.280870i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1822.29 | + | 3156.29i | −0.690345 | + | 1.19571i | 0.281379 | + | 0.959597i | \(0.409208\pi\) |
−0.971725 | + | 0.236117i | \(0.924125\pi\) | |||||||
\(192\) | 152.318 | + | 4078.72i | 0.0572531 | + | 1.53311i | ||||
\(193\) | −6.70078 | − | 11.6061i | −0.00249913 | − | 0.00432862i | 0.864773 | − | 0.502163i | \(-0.167462\pi\) |
−0.867272 | + | 0.497834i | \(0.834129\pi\) | |||||||
\(194\) | 857.034 | + | 1484.43i | 0.317173 | + | 0.549359i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 939.055 | − | 1626.49i | 0.342221 | − | 0.592745i | ||||
\(197\) | −63.1983 | −0.0228563 | −0.0114281 | − | 0.999935i | \(-0.503638\pi\) | ||||
−0.0114281 | + | 0.999935i | \(0.503638\pi\) | |||||||
\(198\) | −2277.90 | − | 3342.12i | −0.817594 | − | 1.19957i | ||||
\(199\) | −4902.79 | −1.74648 | −0.873240 | − | 0.487291i | \(-0.837985\pi\) | ||||
−0.873240 | + | 0.487291i | \(0.837985\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 3028.82 | − | 1902.82i | 1.06287 | − | 0.667736i | ||||
\(202\) | −722.411 | − | 1251.25i | −0.251627 | − | 0.435831i | ||||
\(203\) | −284.198 | − | 492.246i | −0.0982602 | − | 0.170192i | ||||
\(204\) | 3899.45 | − | 2449.79i | 1.33831 | − | 0.840783i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 7070.64 | 2.39143 | ||||||||
\(207\) | −2857.13 | − | 4191.95i | −0.959345 | − | 1.40754i | ||||
\(208\) | 255.543 | 0.0851861 | ||||||||
\(209\) | 2529.32 | − | 4380.90i | 0.837112 | − | 1.44992i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1556.11 | + | 2695.26i | 0.507711 | + | 0.879381i | 0.999960 | + | 0.00892670i | \(0.00284149\pi\) |
−0.492249 | + | 0.870454i | \(0.663825\pi\) | |||||||
\(212\) | 3291.94 | + | 5701.81i | 1.06647 | + | 1.84718i | ||||
\(213\) | 99.8980 | + | 2675.04i | 0.0321357 | + | 0.860519i | ||||
\(214\) | 1492.42 | − | 2584.95i | 0.476728 | − | 0.825717i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 190.055 | + | 1690.10i | 0.0598685 | + | 0.532391i | ||||
\(217\) | −762.904 | −0.238660 | ||||||||
\(218\) | 2577.32 | − | 4464.06i | 0.800727 | − | 1.38690i | ||||
\(219\) | −211.050 | − | 5651.42i | −0.0651206 | − | 1.74378i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −310.205 | − | 537.291i | −0.0944192 | − | 0.163539i | ||||
\(222\) | 6559.60 | + | 3467.46i | 1.98311 | + | 1.04829i | ||||
\(223\) | 2434.71 | − | 4217.05i | 0.731123 | − | 1.26634i | −0.225281 | − | 0.974294i | \(-0.572330\pi\) |
0.956404 | − | 0.292048i | \(-0.0943368\pi\) | |||||||
\(224\) | −3166.81 | −0.944603 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 1163.70 | 0.342515 | ||||||||
\(227\) | −3293.59 | + | 5704.67i | −0.963011 | + | 1.66798i | −0.248144 | + | 0.968723i | \(0.579820\pi\) |
−0.714867 | + | 0.699260i | \(0.753513\pi\) | |||||||
\(228\) | −6954.58 | + | 4369.15i | −2.02008 | + | 1.26910i | ||||
\(229\) | −8.21503 | − | 14.2288i | −0.00237059 | − | 0.00410598i | 0.864838 | − | 0.502052i | \(-0.167421\pi\) |
−0.867208 | + | 0.497946i | \(0.834088\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1976.57 | − | 1241.76i | 0.562981 | − | 0.353687i | ||||
\(232\) | −264.986 | + | 458.969i | −0.0749879 | + | 0.129883i | ||||
\(233\) | −707.542 | −0.198938 | −0.0994692 | − | 0.995041i | \(-0.531714\pi\) | ||||
−0.0994692 | + | 0.995041i | \(0.531714\pi\) | |||||||
\(234\) | 882.216 | − | 65.9839i | 0.246463 | − | 0.0184338i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 3208.78 | − | 5557.77i | 0.885058 | − | 1.53297i | ||||
\(237\) | −2415.39 | − | 1276.80i | −0.662012 | − | 0.349945i | ||||
\(238\) | 2313.60 | + | 4007.27i | 0.630120 | + | 1.09140i | ||||
\(239\) | 3056.02 | + | 5293.18i | 0.827102 | + | 1.43258i | 0.900302 | + | 0.435266i | \(0.143346\pi\) |
−0.0731999 | + | 0.997317i | \(0.523321\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1544.12 | + | 2674.49i | −0.412719 | + | 0.714850i | −0.995186 | − | 0.0980044i | \(-0.968754\pi\) |
0.582467 | + | 0.812854i | \(0.302087\pi\) | |||||||
\(242\) | −594.611 | −0.157946 | ||||||||
\(243\) | −702.879 | − | 3722.21i | −0.185554 | − | 0.982634i | ||||
\(244\) | 3509.58 | 0.920810 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 145.415 | + | 3893.87i | 0.0376883 | + | 1.00920i | ||||
\(247\) | 553.244 | + | 958.246i | 0.142518 | + | 0.246849i | ||||
\(248\) | 355.665 | + | 616.030i | 0.0910676 | + | 0.157734i | ||||
\(249\) | −1644.65 | − | 869.375i | −0.418575 | − | 0.221263i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 2743.28 | 0.689859 | 0.344929 | − | 0.938629i | \(-0.387903\pi\) | ||||
0.344929 | + | 0.938629i | \(0.387903\pi\) | |||||||
\(252\) | −3779.33 | + | 282.669i | −0.944743 | + | 0.0706605i | ||||
\(253\) | 6492.00 | 1.61324 | ||||||||
\(254\) | 314.974 | − | 545.552i | 0.0778081 | − | 0.134768i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 16.1888 | + | 28.0399i | 0.00395235 | + | 0.00684568i | ||||
\(257\) | 360.023 | + | 623.578i | 0.0873838 | + | 0.151353i | 0.906404 | − | 0.422411i | \(-0.138816\pi\) |
−0.819021 | + | 0.573764i | \(0.805483\pi\) | |||||||
\(258\) | 2988.91 | − | 1877.75i | 0.721245 | − | 0.453115i | ||||
\(259\) | −2141.08 | + | 3708.45i | −0.513668 | + | 0.889699i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 512.303 | − | 1063.41i | 0.121497 | − | 0.252197i | ||||
\(262\) | −1167.62 | −0.275327 | ||||||||
\(263\) | −2614.08 | + | 4527.72i | −0.612894 | + | 1.06156i | 0.377857 | + | 0.925864i | \(0.376661\pi\) |
−0.990750 | + | 0.135699i | \(0.956672\pi\) | |||||||
\(264\) | −1924.17 | − | 1017.13i | −0.448578 | − | 0.237122i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −4126.26 | − | 7146.88i | −0.951116 | − | 1.64738i | ||||
\(267\) | −294.295 | − | 7880.55i | −0.0674554 | − | 1.80630i | ||||
\(268\) | 3715.94 | − | 6436.19i | 0.846966 | − | 1.46699i | ||||
\(269\) | 320.400 | 0.0726213 | 0.0363107 | − | 0.999341i | \(-0.488439\pi\) | ||||
0.0363107 | + | 0.999341i | \(0.488439\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1044.06 | −0.234029 | −0.117014 | − | 0.993130i | \(-0.537332\pi\) | ||||
−0.117014 | + | 0.993130i | \(0.537332\pi\) | |||||||
\(272\) | −1387.83 | + | 2403.79i | −0.309373 | + | 0.535850i | ||||
\(273\) | 19.0541 | + | 510.224i | 0.00422419 | + | 0.113114i | ||||
\(274\) | 1793.52 | + | 3106.48i | 0.395441 | + | 0.684923i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −9318.52 | − | 4925.85i | −2.03228 | − | 1.07428i | ||||
\(277\) | 1665.66 | − | 2885.01i | 0.361299 | − | 0.625789i | −0.626876 | − | 0.779119i | \(-0.715667\pi\) |
0.988175 | + | 0.153330i | \(0.0489999\pi\) | |||||||
\(278\) | −736.463 | −0.158885 | ||||||||
\(279\) | −892.283 | − | 1309.15i | −0.191468 | − | 0.280920i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2800.64 | − | 4850.86i | 0.594563 | − | 1.02981i | −0.399045 | − | 0.916931i | \(-0.630658\pi\) |
0.993608 | − | 0.112883i | \(-0.0360084\pi\) | |||||||
\(282\) | 3228.47 | − | 2028.25i | 0.681746 | − | 0.428300i | ||||
\(283\) | 3133.92 | + | 5428.11i | 0.658277 | + | 1.14017i | 0.981062 | + | 0.193696i | \(0.0620476\pi\) |
−0.322785 | + | 0.946472i | \(0.604619\pi\) | |||||||
\(284\) | 2780.93 | + | 4816.71i | 0.581048 | + | 1.00640i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −566.066 | + | 980.455i | −0.117036 | + | 0.202712i | ||||
\(287\) | −2248.85 | −0.462529 | ||||||||
\(288\) | −3703.86 | − | 5434.26i | −0.757819 | − | 1.11186i | ||||
\(289\) | 1825.78 | 0.371622 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1816.22 | − | 960.068i | −0.365871 | − | 0.193403i | ||||
\(292\) | −5875.12 | − | 10176.0i | −1.17745 | − | 2.03940i | ||||
\(293\) | 1051.43 | + | 1821.13i | 0.209642 | + | 0.363111i | 0.951602 | − | 0.307334i | \(-0.0994368\pi\) |
−0.741960 | + | 0.670445i | \(0.766103\pi\) | |||||||
\(294\) | 146.249 | + | 3916.21i | 0.0290116 | + | 0.776864i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 3992.67 | 0.784018 | ||||||||
\(297\) | 4442.64 | + | 1939.46i | 0.867973 | + | 0.378918i | ||||
\(298\) | 7571.21 | 1.47177 | ||||||||
\(299\) | −710.006 | + | 1229.77i | −0.137327 | + | 0.237857i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1018.59 | + | 1764.24i | 0.195051 | + | 0.337838i | ||||
\(302\) | −743.178 | − | 1287.22i | −0.141606 | − | 0.245269i | ||||
\(303\) | 1530.93 | + | 809.260i | 0.290262 | + | 0.153435i | ||||
\(304\) | 2475.16 | − | 4287.11i | 0.466975 | − | 0.808824i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −4170.55 | + | 8657.02i | −0.779132 | + | 1.61728i | ||||
\(307\) | −2020.07 | −0.375543 | −0.187771 | − | 0.982213i | \(-0.560126\pi\) | ||||
−0.187771 | + | 0.982213i | \(0.560126\pi\) | |||||||
\(308\) | 2424.97 | − | 4200.18i | 0.448622 | − | 0.777037i | ||||
\(309\) | −7175.76 | + | 4508.10i | −1.32108 | + | 0.829957i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −2696.66 | − | 4670.75i | −0.491684 | − | 0.851621i | 0.508270 | − | 0.861198i | \(-0.330285\pi\) |
−0.999954 | + | 0.00957637i | \(0.996952\pi\) | |||||||
\(312\) | 403.113 | − | 253.252i | 0.0731467 | − | 0.0459537i | ||||
\(313\) | −1555.89 | + | 2694.87i | −0.280971 | + | 0.486656i | −0.971624 | − | 0.236530i | \(-0.923990\pi\) |
0.690653 | + | 0.723186i | \(0.257323\pi\) | |||||||
\(314\) | −15155.4 | −2.72379 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −5676.53 | −1.01054 | ||||||||
\(317\) | 2466.79 | − | 4272.60i | 0.437062 | − | 0.757013i | −0.560399 | − | 0.828222i | \(-0.689352\pi\) |
0.997461 | + | 0.0712090i | \(0.0226857\pi\) | |||||||
\(318\) | −12145.7 | − | 6420.31i | −2.14181 | − | 1.13218i | ||||
\(319\) | 755.271 | + | 1308.17i | 0.132561 | + | 0.229603i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 133.504 | + | 3574.92i | 0.0232132 | + | 0.621596i | ||||
\(322\) | 5295.44 | − | 9171.96i | 0.916469 | − | 1.58737i | ||||
\(323\) | −12018.5 | −2.07036 | ||||||||
\(324\) | −4905.32 | − | 6154.75i | −0.841104 | − | 1.05534i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −1438.38 | + | 2491.34i | −0.244369 | + | 0.423260i | ||||
\(327\) | 230.553 | + | 6173.68i | 0.0389896 | + | 1.04405i | ||||
\(328\) | 1048.41 | + | 1815.91i | 0.176491 | + | 0.305691i | ||||
\(329\) | 1100.23 | + | 1905.65i | 0.184369 | + | 0.319336i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −4386.39 | + | 7597.45i | −0.728392 | + | 1.26161i | 0.229171 | + | 0.973386i | \(0.426399\pi\) |
−0.957563 | + | 0.288226i | \(0.906935\pi\) | |||||||
\(332\) | −3865.16 | −0.638940 | ||||||||
\(333\) | −8867.91 | + | 663.260i | −1.45933 | + | 0.109148i | ||||
\(334\) | 10663.7 | 1.74697 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 1934.25 | − | 1215.17i | 0.314053 | − | 0.197301i | ||||
\(337\) | 5171.06 | + | 8956.54i | 0.835863 | + | 1.44776i | 0.893326 | + | 0.449409i | \(0.148365\pi\) |
−0.0574635 | + | 0.998348i | \(0.518301\pi\) | |||||||
\(338\) | 4638.68 | + | 8034.43i | 0.746482 | + | 1.29294i | ||||
\(339\) | −1181.00 | + | 741.954i | −0.189213 | + | 0.118871i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2027.46 | 0.321973 | ||||||||
\(342\) | 7438.09 | − | 15439.6i | 1.17604 | − | 2.44116i | ||||
\(343\) | −6721.27 | −1.05806 | ||||||||
\(344\) | 949.727 | − | 1644.98i | 0.148854 | − | 0.257823i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 3311.74 | + | 5736.10i | 0.514567 | + | 0.891256i | ||||
\(347\) | −669.161 | − | 1159.02i | −0.103523 | − | 0.179307i | 0.809611 | − | 0.586967i | \(-0.199678\pi\) |
−0.913134 | + | 0.407660i | \(0.866345\pi\) | |||||||
\(348\) | −91.5236 | − | 2450.79i | −0.0140982 | − | 0.377518i | ||||
\(349\) | −5056.17 | + | 8757.55i | −0.775503 | + | 1.34321i | 0.159008 | + | 0.987277i | \(0.449170\pi\) |
−0.934511 | + | 0.355934i | \(0.884163\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −853.262 | + | 629.448i | −0.129754 | + | 0.0957193i | ||||
\(352\) | 8415.95 | 1.27435 | ||||||||
\(353\) | −822.140 | + | 1423.99i | −0.123961 | + | 0.214706i | −0.921326 | − | 0.388791i | \(-0.872893\pi\) |
0.797366 | + | 0.603497i | \(0.206226\pi\) | |||||||
\(354\) | 499.737 | + | 13381.8i | 0.0750303 | + | 2.00914i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −8192.50 | − | 14189.8i | −1.21967 | − | 2.11253i | ||||
\(357\) | −4902.96 | − | 2591.74i | −0.726868 | − | 0.384229i | ||||
\(358\) | −2181.10 | + | 3777.77i | −0.321996 | + | 0.557714i | ||||
\(359\) | 11283.0 | 1.65876 | 0.829379 | − | 0.558686i | \(-0.188694\pi\) | ||||
0.829379 | + | 0.558686i | \(0.188694\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 14575.7 | 2.12504 | ||||||||
\(362\) | −1282.99 | + | 2222.21i | −0.186278 | + | 0.322643i | ||||
\(363\) | 603.451 | − | 379.112i | 0.0872533 | − | 0.0548160i | ||||
\(364\) | 530.420 | + | 918.715i | 0.0763780 | + | 0.132291i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −6201.04 | + | 3895.74i | −0.885610 | + | 0.556376i | ||||
\(367\) | 139.011 | − | 240.774i | 0.0197720 | − | 0.0342461i | −0.855970 | − | 0.517025i | \(-0.827039\pi\) |
0.875742 | + | 0.482779i | \(0.160373\pi\) | |||||||
\(368\) | 6353.01 | 0.899928 | ||||||||
\(369\) | −2630.23 | − | 3859.05i | −0.371069 | − | 0.544429i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 3964.39 | − | 6866.53i | 0.554774 | − | 0.960896i | ||||
\(372\) | −2910.18 | − | 1538.34i | −0.405607 | − | 0.214407i | ||||
\(373\) | −4916.70 | − | 8515.98i | −0.682513 | − | 1.18215i | −0.974212 | − | 0.225637i | \(-0.927554\pi\) |
0.291699 | − | 0.956510i | \(-0.405780\pi\) | |||||||
\(374\) | −6148.51 | − | 10649.5i | −0.850085 | − | 1.47239i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 1025.85 | − | 1776.82i | 0.140702 | − | 0.243704i | ||||
\(377\) | −330.405 | −0.0451372 | ||||||||
\(378\) | 6363.88 | − | 4694.61i | 0.865933 | − | 0.638796i | ||||
\(379\) | 13511.9 | 1.83129 | 0.915644 | − | 0.401990i | \(-0.131681\pi\) | ||||
0.915644 | + | 0.401990i | \(0.131681\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 28.1758 | + | 754.484i | 0.00378869 | + | 0.101452i | ||||
\(382\) | −7900.43 | − | 13683.9i | −1.05817 | − | 1.83281i | ||||
\(383\) | 694.822 | + | 1203.47i | 0.0926991 | + | 0.160559i | 0.908646 | − | 0.417567i | \(-0.137117\pi\) |
−0.815947 | + | 0.578127i | \(0.803784\pi\) | |||||||
\(384\) | −6692.78 | − | 3537.86i | −0.889426 | − | 0.470158i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 58.1018 | 0.00766141 | ||||||||
\(387\) | −1836.13 | + | 3811.34i | −0.241177 | + | 0.500623i | ||||
\(388\) | −4268.38 | −0.558490 | ||||||||
\(389\) | 453.369 | − | 785.258i | 0.0590918 | − | 0.102350i | −0.834966 | − | 0.550301i | \(-0.814513\pi\) |
0.894058 | + | 0.447951i | \(0.147846\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −7711.96 | − | 13357.5i | −0.997469 | − | 1.72767i | ||||
\(392\) | 1054.43 | + | 1826.32i | 0.135859 | + | 0.235314i | ||||
\(393\) | 1184.98 | − | 744.450i | 0.152097 | − | 0.0955536i | ||||
\(394\) | 136.997 | − | 237.285i | 0.0175172 | − | 0.0303407i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 10043.8 | − | 751.206i | 1.27454 | − | 0.0953271i | ||||
\(397\) | 1904.52 | 0.240769 | 0.120384 | − | 0.992727i | \(-0.461587\pi\) | ||||
0.120384 | + | 0.992727i | \(0.461587\pi\) | |||||||
\(398\) | 10627.9 | − | 18408.1i | 1.33851 | − | 2.31837i | ||||
\(399\) | 8744.32 | + | 4622.32i | 1.09715 | + | 0.579963i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 5206.91 | + | 9018.64i | 0.648431 | + | 1.12312i | 0.983498 | + | 0.180921i | \(0.0579078\pi\) |
−0.335067 | + | 0.942194i | \(0.608759\pi\) | |||||||
\(402\) | 578.722 | + | 15496.8i | 0.0718011 | + | 1.92267i | ||||
\(403\) | −221.735 | + | 384.057i | −0.0274080 | + | 0.0474720i | ||||
\(404\) | 3597.90 | 0.443075 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 2464.26 | 0.301229 | ||||||||
\(407\) | 5690.02 | − | 9855.40i | 0.692982 | − | 1.20028i | ||||
\(408\) | 192.971 | + | 5167.31i | 0.0234154 | + | 0.627010i | ||||
\(409\) | −3124.74 | − | 5412.21i | −0.377771 | − | 0.654319i | 0.612966 | − | 0.790109i | \(-0.289976\pi\) |
−0.990738 | + | 0.135790i | \(0.956643\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −3800.82 | − | 2009.14i | −0.456157 | − | 0.241128i | ||||
\(412\) | −8803.65 | + | 15248.4i | −1.05273 | + | 1.82338i | ||||
\(413\) | −7728.48 | −0.920808 | ||||||||
\(414\) | 21932.6 | − | 1640.42i | 2.60370 | − | 0.194739i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −920.420 | + | 1594.21i | −0.108479 | + | 0.187891i | ||||
\(417\) | 747.413 | − | 469.555i | 0.0877721 | − | 0.0551419i | ||||
\(418\) | 10965.7 | + | 18993.2i | 1.28314 | + | 2.22246i | ||||
\(419\) | −1495.14 | − | 2589.65i | −0.174325 | − | 0.301940i | 0.765602 | − | 0.643314i | \(-0.222441\pi\) |
−0.939927 | + | 0.341374i | \(0.889108\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 2346.32 | − | 4063.95i | 0.271622 | − | 0.470463i | −0.697656 | − | 0.716433i | \(-0.745773\pi\) |
0.969277 | + | 0.245971i | \(0.0791067\pi\) | |||||||
\(422\) | −13492.9 | −1.55645 | ||||||||
\(423\) | −1983.29 | + | 4116.82i | −0.227969 | + | 0.473207i | ||||
\(424\) | −7392.79 | −0.846758 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −10260.3 | − | 5423.67i | −1.16693 | − | 0.616849i | ||||
\(427\) | −2113.24 | − | 3660.24i | −0.239501 | − | 0.414828i | ||||
\(428\) | 3716.43 | + | 6437.04i | 0.419720 | + | 0.726977i | ||||
\(429\) | −50.6371 | − | 1355.94i | −0.00569879 | − | 0.152601i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 817.709 | 0.0913866 | 0.0456933 | − | 0.998956i | \(-0.485450\pi\) | ||||
0.0456933 | + | 0.998956i | \(0.485450\pi\) | |||||||
\(432\) | 4347.52 | + | 1897.93i | 0.484190 | + | 0.211376i | ||||
\(433\) | 5547.29 | 0.615671 | 0.307836 | − | 0.951440i | \(-0.400395\pi\) | ||||
0.307836 | + | 0.951440i | \(0.400395\pi\) | |||||||
\(434\) | 1653.77 | − | 2864.41i | 0.182911 | − | 0.316811i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 6418.06 | + | 11116.4i | 0.704975 | + | 1.22105i | ||||
\(437\) | 13754.1 | + | 23822.8i | 1.50560 | + | 2.60778i | ||||
\(438\) | 21676.4 | + | 11458.3i | 2.36470 | + | 1.25000i | ||||
\(439\) | −6690.82 | + | 11588.8i | −0.727416 | + | 1.25992i | 0.230556 | + | 0.973059i | \(0.425946\pi\) |
−0.957972 | + | 0.286862i | \(0.907388\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2645.32 | − | 3881.19i | −0.285641 | − | 0.419089i | ||||
\(442\) | 2689.76 | 0.289454 | ||||||||
\(443\) | 5418.44 | − | 9385.00i | 0.581123 | − | 1.00654i | −0.414223 | − | 0.910175i | \(-0.635947\pi\) |
0.995347 | − | 0.0963598i | \(-0.0307199\pi\) | |||||||
\(444\) | −15645.2 | + | 9828.95i | −1.67227 | + | 1.05059i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 10555.6 | + | 18282.8i | 1.12068 | + | 1.94107i | ||||
\(447\) | −7683.77 | + | 4827.26i | −0.813043 | + | 0.510786i | ||||
\(448\) | 5106.32 | − | 8844.41i | 0.538507 | − | 0.932721i | ||||
\(449\) | 2970.62 | 0.312232 | 0.156116 | − | 0.987739i | \(-0.450103\pi\) | ||||
0.156116 | + | 0.987739i | \(0.450103\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 5976.44 | 0.623991 | ||||||||
\(452\) | −1448.93 | + | 2509.61i | −0.150778 | + | 0.261155i | ||||
\(453\) | 1574.94 | + | 832.524i | 0.163349 | + | 0.0863475i | ||||
\(454\) | −14279.2 | − | 24732.3i | −1.47612 | − | 2.55671i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −344.159 | − | 9215.79i | −0.0353437 | − | 0.946423i | ||||
\(457\) | −8088.16 | + | 14009.1i | −0.827896 | + | 1.43396i | 0.0717901 | + | 0.997420i | \(0.477129\pi\) |
−0.899686 | + | 0.436538i | \(0.856204\pi\) | |||||||
\(458\) | 71.2317 | 0.00726733 | ||||||||
\(459\) | −1286.99 | − | 11444.8i | −0.130875 | − | 1.16383i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −2865.91 | + | 4963.90i | −0.289541 | + | 0.501500i | −0.973700 | − | 0.227833i | \(-0.926836\pi\) |
0.684159 | + | 0.729333i | \(0.260169\pi\) | |||||||
\(462\) | 377.667 | + | 10113.0i | 0.0380317 | + | 1.01840i | ||||
\(463\) | −7020.03 | − | 12159.1i | −0.704641 | − | 1.22047i | −0.966821 | − | 0.255454i | \(-0.917775\pi\) |
0.262181 | − | 0.965019i | \(-0.415558\pi\) | |||||||
\(464\) | 739.101 | + | 1280.16i | 0.0739481 | + | 0.128082i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 1533.76 | − | 2656.55i | 0.152468 | − | 0.264082i | ||||
\(467\) | 3.48921 | 0.000345742 | 0.000172871 | − | 1.00000i | \(-0.499945\pi\) | ||||
0.000172871 | 1.00000i | \(0.499945\pi\) | ||||||||
\(468\) | −956.148 | + | 1984.72i | −0.0944401 | + | 0.196034i | ||||
\(469\) | −8949.99 | −0.881177 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 15380.7 | − | 9662.80i | 1.50469 | − | 0.945305i | ||||
\(472\) | 3603.01 | + | 6240.60i | 0.351360 | + | 0.608574i | ||||
\(473\) | −2706.94 | − | 4688.56i | −0.263140 | − | 0.455772i | ||||
\(474\) | 10029.8 | − | 6301.12i | 0.971907 | − | 0.610591i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −11522.7 | −1.10954 | ||||||||
\(477\) | 16419.7 | − | 1228.09i | 1.57612 | − | 0.117883i | ||||
\(478\) | −26498.4 | −2.53559 | ||||||||
\(479\) | 1825.54 | − | 3161.93i | 0.174136 | − | 0.301612i | −0.765726 | − | 0.643167i | \(-0.777620\pi\) |
0.939862 | + | 0.341555i | \(0.110954\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1244.59 | + | 2155.69i | 0.117980 | + | 0.204348i | ||||
\(482\) | −6694.44 | − | 11595.1i | −0.632621 | − | 1.09573i | ||||
\(483\) | 473.700 | + | 12684.6i | 0.0446255 | + | 1.19497i | ||||
\(484\) | 740.350 | − | 1282.32i | 0.0695295 | − | 0.120429i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 15499.1 | + | 5429.70i | 1.44661 | + | 0.506782i | ||||
\(487\) | −13646.8 | −1.26981 | −0.634903 | − | 0.772592i | \(-0.718960\pi\) | ||||
−0.634903 | + | 0.772592i | \(0.718960\pi\) | |||||||
\(488\) | −1970.38 | + | 3412.80i | −0.182777 | + | 0.316579i | ||||
\(489\) | −128.669 | − | 3445.46i | −0.0118990 | − | 0.318628i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −20.8492 | − | 36.1118i | −0.00191631 | − | 0.00331915i | 0.865066 | − | 0.501659i | \(-0.167277\pi\) |
−0.866982 | + | 0.498340i | \(0.833943\pi\) | |||||||
\(492\) | −8578.50 | − | 4534.67i | −0.786074 | − | 0.415525i | ||||
\(493\) | 1794.40 | − | 3107.99i | 0.163926 | − | 0.283929i | ||||
\(494\) | −4797.12 | −0.436908 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 1984.05 | 0.179610 | ||||||||
\(497\) | 3348.99 | − | 5800.62i | 0.302259 | − | 0.523528i | ||||
\(498\) | 6829.31 | − | 4290.45i | 0.614515 | − | 0.386063i | ||||
\(499\) | 1196.47 | + | 2072.34i | 0.107337 | + | 0.185913i | 0.914691 | − | 0.404155i | \(-0.132434\pi\) |
−0.807354 | + | 0.590068i | \(0.799101\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −10822.2 | + | 6798.94i | −0.965070 | + | 0.606295i | ||||
\(502\) | −5946.69 | + | 10300.0i | −0.528713 | + | 0.915757i | ||||
\(503\) | −1254.89 | −0.111238 | −0.0556190 | − | 0.998452i | \(-0.517713\pi\) | ||||
−0.0556190 | + | 0.998452i | \(0.517713\pi\) | |||||||
\(504\) | 1846.95 | − | 3833.81i | 0.163234 | − | 0.338833i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −14072.9 | + | 24375.0i | −1.23640 | + | 2.14150i | ||||
\(507\) | −9830.23 | − | 5196.35i | −0.861097 | − | 0.455183i | ||||
\(508\) | 784.349 | + | 1358.53i | 0.0685037 | + | 0.118652i | ||||
\(509\) | −273.965 | − | 474.521i | −0.0238571 | − | 0.0413217i | 0.853850 | − | 0.520519i | \(-0.174261\pi\) |
−0.877707 | + | 0.479197i | \(0.840928\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −7075.25 | + | 12254.7i | −0.612506 | + | 1.06089i | ||||
\(512\) | 11514.9 | 0.993929 | ||||||||
\(513\) | 2295.32 | + | 20411.5i | 0.197545 | + | 1.75671i | ||||
\(514\) | −3121.73 | −0.267886 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 328.027 | + | 8783.80i | 0.0279856 | + | 0.749390i | ||||
\(517\) | −2923.90 | − | 5064.35i | −0.248729 | − | 0.430812i | ||||
\(518\) | −9282.53 | − | 16077.8i | −0.787357 | − | 1.36374i | ||||
\(519\) | −7018.20 | − | 3709.88i | −0.593573 | − | 0.313768i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 12151.4 | 1.02181 | 0.510903 | − | 0.859638i | \(-0.329311\pi\) | ||||
0.510903 | + | 0.859638i | \(0.329311\pi\) | |||||||
\(522\) | 2882.17 | + | 4228.68i | 0.241665 | + | 0.354568i | ||||
\(523\) | −18913.8 | −1.58134 | −0.790672 | − | 0.612241i | \(-0.790268\pi\) | ||||
−0.790672 | + | 0.612241i | \(0.790268\pi\) | |||||||
\(524\) | 1453.80 | − | 2518.06i | 0.121202 | − | 0.209927i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −11333.2 | − | 19629.7i | −0.939452 | − | 1.62718i | ||||
\(527\) | −2408.45 | − | 4171.55i | −0.199077 | − | 0.344812i | ||||
\(528\) | −5140.37 | + | 3229.38i | −0.423685 | + | 0.266176i | ||||
\(529\) | −11567.9 | + | 20036.1i | −0.950757 | + | 1.64676i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −9039.14 | − | 13262.1i | −0.738730 | − | 1.08386i | ||||
\(532\) | 20550.4 | 1.67476 | ||||||||
\(533\) | −653.621 | + | 1132.11i | −0.0531172 | + | 0.0920017i | ||||
\(534\) | 30226.4 | + | 15977.9i | 2.44948 | + | 1.29482i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 4172.48 | + | 7226.94i | 0.336238 | + | 0.582381i | ||||
\(537\) | −195.109 | − | 5224.56i | −0.0156789 | − | 0.419845i | ||||
\(538\) | −694.540 | + | 1202.98i | −0.0556575 | + | 0.0964016i | ||||
\(539\) | 6010.73 | 0.480335 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −9936.16 | −0.789628 | −0.394814 | − | 0.918761i | \(-0.629191\pi\) | ||||
−0.394814 | + | 0.918761i | \(0.629191\pi\) | |||||||
\(542\) | 2263.23 | − | 3920.02i | 0.179361 | − | 0.310663i | ||||
\(543\) | −114.769 | − | 3073.26i | −0.00907039 | − | 0.242884i | ||||
\(544\) | −9997.44 | − | 17316.1i | −0.787935 | − | 1.36474i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −1957.00 | − | 1034.48i | −0.153391 | − | 0.0810840i | ||||
\(547\) | 6359.84 | − | 11015.6i | 0.497125 | − | 0.861045i | −0.502870 | − | 0.864362i | \(-0.667722\pi\) |
0.999994 | + | 0.00331677i | \(0.00105576\pi\) | |||||||
\(548\) | −8932.47 | −0.696307 | ||||||||
\(549\) | 3809.38 | − | 7907.32i | 0.296139 | − | 0.614711i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −3200.27 | + | 5543.03i | −0.247434 | + | 0.428568i | ||||
\(552\) | 10021.7 | − | 6296.05i | 0.772741 | − | 0.485467i | ||||
\(553\) | 3418.04 | + | 5920.22i | 0.262839 | + | 0.455250i | ||||
\(554\) | 7221.40 | + | 12507.8i | 0.553805 | + | 0.959218i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 916.971 | − | 1588.24i | 0.0699429 | − | 0.121145i | ||||
\(557\) | 16006.5 | 1.21763 | 0.608813 | − | 0.793314i | \(-0.291646\pi\) | ||||
0.608813 | + | 0.793314i | \(0.291646\pi\) | |||||||
\(558\) | 6849.57 | − | 512.302i | 0.519651 | − | 0.0388665i | ||||
\(559\) | 1184.19 | 0.0895993 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 13029.9 | + | 6887.69i | 0.980608 | + | 0.518358i | ||||
\(562\) | 12142.1 | + | 21030.7i | 0.911355 | + | 1.57851i | ||||
\(563\) | 2313.29 | + | 4006.74i | 0.173168 | + | 0.299936i | 0.939526 | − | 0.342478i | \(-0.111266\pi\) |
−0.766358 | + | 0.642414i | \(0.777933\pi\) | |||||||
\(564\) | 354.318 | + | 9487.82i | 0.0264530 | + | 0.708350i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −27173.9 | −2.01803 | ||||||||
\(567\) | −3465.30 | + | 8821.90i | −0.256665 | + | 0.653412i | ||||
\(568\) | −6245.19 | −0.461342 | ||||||||
\(569\) | −8429.52 | + | 14600.4i | −0.621061 | + | 1.07571i | 0.368227 | + | 0.929736i | \(0.379965\pi\) |
−0.989288 | + | 0.145974i | \(0.953369\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −8074.57 | − | 13985.6i | −0.591787 | − | 1.02501i | −0.993992 | − | 0.109455i | \(-0.965089\pi\) |
0.402205 | − | 0.915550i | \(-0.368244\pi\) | |||||||
\(572\) | −1409.62 | − | 2441.53i | −0.103040 | − | 0.178471i | ||||
\(573\) | 16742.5 | + | 8850.23i | 1.22064 | + | 0.645242i | ||||
\(574\) | 4874.90 | − | 8443.58i | 0.354485 | − | 0.613986i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 21149.4 | − | 1581.83i | 1.52990 | − | 0.114427i | ||||
\(577\) | −7430.10 | −0.536082 | −0.268041 | − | 0.963408i | \(-0.586376\pi\) | ||||
−0.268041 | + | 0.963408i | \(0.586376\pi\) | |||||||
\(578\) | −3957.79 | + | 6855.10i | −0.284814 | + | 0.493312i | ||||
\(579\) | −58.9656 | + | 37.0446i | −0.00423234 | + | 0.00265893i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 2327.35 | + | 4031.09i | 0.166187 | + | 0.287845i | ||||
\(582\) | 7541.75 | − | 4738.03i | 0.537140 | − | 0.337453i | ||||
\(583\) | −10535.6 | + | 18248.2i | −0.748437 | + | 1.29633i | ||||
\(584\) | 13193.9 | 0.934875 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −9116.84 | −0.642685 | ||||||||
\(587\) | 8576.06 | − | 14854.2i | 0.603019 | − | 1.04446i | −0.389343 | − | 0.921093i | \(-0.627298\pi\) |
0.992361 | − | 0.123366i | \(-0.0393689\pi\) | |||||||
\(588\) | −8627.70 | − | 4560.68i | −0.605103 | − | 0.319863i | ||||
\(589\) | 4295.41 | + | 7439.87i | 0.300491 | + | 0.520466i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 12.2549 | + | 328.159i | 0.000852963 | + | 0.0228404i | ||||
\(592\) | 5568.19 | − | 9644.39i | 0.386573 | − | 0.669564i | ||||
\(593\) | 15477.7 | 1.07183 | 0.535913 | − | 0.844273i | \(-0.319967\pi\) | ||||
0.535913 | + | 0.844273i | \(0.319967\pi\) | |||||||
\(594\) | −16912.3 | + | 12476.2i | −1.16822 | + | 0.861790i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −9426.92 | + | 16327.9i | −0.647889 | + | 1.12218i | ||||
\(597\) | 950.713 | + | 25457.9i | 0.0651760 | + | 1.74526i | ||||
\(598\) | −3078.20 | − | 5331.59i | −0.210496 | − | 0.364590i | ||||
\(599\) | −9479.61 | − | 16419.2i | −0.646622 | − | 1.11998i | −0.983924 | − | 0.178586i | \(-0.942848\pi\) |
0.337302 | − | 0.941396i | \(-0.390486\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1046.80 | − | 1813.12i | 0.0710482 | − | 0.123059i | −0.828313 | − | 0.560266i | \(-0.810699\pi\) |
0.899361 | + | 0.437207i | \(0.144032\pi\) | |||||||
\(602\) | −8832.06 | −0.597953 | ||||||||
\(603\) | −10467.8 | − | 15358.3i | −0.706935 | − | 1.03721i | ||||
\(604\) | 3701.33 | 0.249346 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −6357.09 | + | 3993.78i | −0.426137 | + | 0.267716i | ||||
\(607\) | −3067.63 | − | 5313.28i | −0.205125 | − | 0.355288i | 0.745047 | − | 0.667012i | \(-0.232427\pi\) |
−0.950173 | + | 0.311724i | \(0.899094\pi\) | |||||||
\(608\) | 17830.2 | + | 30882.8i | 1.18933 | + | 2.05997i | ||||
\(609\) | −2500.89 | + | 1571.16i | −0.166406 | + | 0.104543i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1279.11 | 0.0846924 | ||||||||
\(612\) | −13476.8 | − | 19773.0i | −0.890141 | − | 1.30600i | ||||
\(613\) | 12762.8 | 0.840922 | 0.420461 | − | 0.907311i | \(-0.361868\pi\) | ||||
0.420461 | + | 0.907311i | \(0.361868\pi\) | |||||||
\(614\) | 4378.96 | − | 7584.59i | 0.287819 | − | 0.498516i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 2722.91 | + | 4716.21i | 0.178099 | + | 0.308477i | ||||
\(617\) | 367.040 | + | 635.732i | 0.0239489 | + | 0.0414807i | 0.877751 | − | 0.479116i | \(-0.159043\pi\) |
−0.853803 | + | 0.520597i | \(0.825709\pi\) | |||||||
\(618\) | −1371.09 | − | 36714.5i | −0.0892446 | − | 2.38976i | ||||
\(619\) | 5324.85 | − | 9222.91i | 0.345757 | − | 0.598869i | −0.639734 | − | 0.768597i | \(-0.720955\pi\) |
0.985491 | + | 0.169727i | \(0.0542887\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −21212.8 | + | 15648.6i | −1.37076 | + | 1.01120i | ||||
\(622\) | 23382.5 | 1.50732 | ||||||||
\(623\) | −9865.99 | + | 17088.4i | −0.634466 | + | 1.09893i | ||||
\(624\) | −49.5530 | − | 1326.91i | −0.00317902 | − | 0.0851267i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −6745.47 | − | 11683.5i | −0.430676 | − | 0.745952i | ||||
\(627\) | −23238.5 | − | 12284.0i | −1.48015 | − | 0.782420i | ||||
\(628\) | 18870.0 | − | 32683.9i | 1.19904 | − | 2.07680i | ||||
\(629\) | −27037.1 | −1.71389 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −3465.43 | −0.218632 | −0.109316 | − | 0.994007i | \(-0.534866\pi\) | ||||
−0.109316 | + | 0.994007i | \(0.534866\pi\) | |||||||
\(632\) | 3186.98 | − | 5520.00i | 0.200587 | − | 0.347427i | ||||
\(633\) | 13693.5 | − | 8602.79i | 0.859821 | − | 0.540174i | ||||
\(634\) | 10694.6 | + | 18523.7i | 0.669935 | + | 1.16036i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 28968.5 | − | 18199.2i | 1.80609 | − | 1.13466i | ||||
\(637\) | −657.371 | + | 1138.60i | −0.0408885 | + | 0.0708209i | ||||
\(638\) | −6548.89 | −0.406384 | ||||||||
\(639\) | 13870.9 | − | 1037.45i | 0.858721 | − | 0.0642266i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 14605.0 | − | 25296.7i | 0.899945 | − | 1.55875i | 0.0723819 | − | 0.997377i | \(-0.476940\pi\) |
0.827563 | − | 0.561373i | \(-0.189727\pi\) | |||||||
\(642\) | −13711.8 | − | 7248.19i | −0.842932 | − | 0.445581i | ||||
\(643\) | −8512.87 | − | 14744.7i | −0.522107 | − | 0.904316i | −0.999669 | − | 0.0257183i | \(-0.991813\pi\) |
0.477562 | − | 0.878598i | \(-0.341521\pi\) | |||||||
\(644\) | 13186.7 | + | 22840.0i | 0.806877 | + | 1.39755i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 26052.7 | − | 45124.7i | 1.58674 | − | 2.74831i | ||||
\(647\) | −8673.26 | −0.527019 | −0.263509 | − | 0.964657i | \(-0.584880\pi\) | ||||
−0.263509 | + | 0.964657i | \(0.584880\pi\) | |||||||
\(648\) | 8739.03 | − | 1314.60i | 0.529786 | − | 0.0796948i | ||||
\(649\) | 20538.8 | 1.24225 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 147.937 | + | 3961.40i | 0.00890645 | + | 0.238494i | ||||
\(652\) | −3581.85 | − | 6203.95i | −0.215147 | − | 0.372646i | ||||
\(653\) | −540.335 | − | 935.888i | −0.0323812 | − | 0.0560859i | 0.849381 | − | 0.527781i | \(-0.176976\pi\) |
−0.881762 | + | 0.471695i | \(0.843642\pi\) | |||||||
\(654\) | −23679.5 | − | 12517.2i | −1.41582 | − | 0.748412i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 5848.49 | 0.348087 | ||||||||
\(657\) | −29304.3 | + | 2191.76i | −1.74013 | + | 0.130150i | ||||
\(658\) | −9539.95 | −0.565206 | ||||||||
\(659\) | −3484.81 | + | 6035.86i | −0.205992 | + | 0.356789i | −0.950448 | − | 0.310882i | \(-0.899375\pi\) |
0.744456 | + | 0.667671i | \(0.232709\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −5448.66 | − | 9437.36i | −0.320618 | − | 0.555326i | 0.659998 | − | 0.751267i | \(-0.270557\pi\) |
−0.980616 | + | 0.195941i | \(0.937224\pi\) | |||||||
\(662\) | −19017.0 | − | 32938.4i | −1.11649 | − | 1.93382i | ||||
\(663\) | −2729.75 | + | 1714.94i | −0.159901 | + | 0.100456i | ||||
\(664\) | 2170.02 | − | 3758.58i | 0.126827 | − | 0.219671i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 16732.9 | − | 34733.3i | 0.973554 | − | 2.02085i | ||||
\(667\) | −8214.14 | −0.476841 | ||||||||
\(668\) | −13277.3 | + | 22997.0i | −0.769034 | + | 1.33201i | ||||
\(669\) | −22369.3 | − | 11824.6i | −1.29274 | − | 0.683356i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 5616.05 | + | 9727.28i | 0.323108 | + | 0.559639i | ||||
\(672\) | 614.084 | + | 16443.7i | 0.0352512 | + | 0.943945i | ||||
\(673\) | 14803.9 | − | 25641.2i | 0.847919 | − | 1.46864i | −0.0351426 | − | 0.999382i | \(-0.511189\pi\) |
0.883062 | − | 0.469257i | \(-0.155478\pi\) | |||||||
\(674\) | −44837.8 | −2.56244 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −23102.5 | −1.31443 | ||||||||
\(677\) | 3193.71 | − | 5531.66i | 0.181306 | − | 0.314031i | −0.761020 | − | 0.648729i | \(-0.775301\pi\) |
0.942326 | + | 0.334698i | \(0.108634\pi\) | |||||||
\(678\) | −225.657 | − | 6042.56i | −0.0127821 | − | 0.342276i | ||||
\(679\) | 2570.14 | + | 4451.62i | 0.145262 | + | 0.251601i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 30260.4 | + | 15995.9i | 1.70276 | + | 0.900093i | ||||
\(682\) | −4394.97 | + | 7612.31i | −0.246762 | + | 0.427405i | ||||
\(683\) | 19929.2 | 1.11650 | 0.558251 | − | 0.829672i | \(-0.311473\pi\) | ||||
0.558251 | + | 0.829672i | \(0.311473\pi\) | |||||||
\(684\) | 24035.5 | + | 35264.7i | 1.34360 | + | 1.97131i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 14569.9 | − | 25235.8i | 0.810904 | − | 1.40453i | ||||
\(687\) | −72.2907 | + | 45.4159i | −0.00401465 | + | 0.00252216i | ||||
\(688\) | −2648.99 | − | 4588.18i | −0.146790 | − | 0.254248i | ||||
\(689\) | −2304.47 | − | 3991.46i | −0.127421 | − | 0.220700i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −6473.59 | + | 11212.6i | −0.356392 | + | 0.617289i | −0.987355 | − | 0.158524i | \(-0.949327\pi\) |
0.630963 | + | 0.775813i | \(0.282660\pi\) | |||||||
\(692\) | −16493.8 | −0.906069 | ||||||||
\(693\) | −6831.16 | − | 10022.6i | −0.374451 | − | 0.549390i | ||||
\(694\) | 5802.23 | 0.317362 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 2434.60 | + | 1286.95i | 0.132591 | + | 0.0700886i | ||||
\(697\) | −7099.52 | − | 12296.7i | −0.385815 | − | 0.668252i | ||||
\(698\) | −21920.8 | − | 37967.9i | −1.18870 | − | 2.05889i | ||||
\(699\) | 137.201 | + | 3673.94i | 0.00742408 | + | 0.198800i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −10692.9 | −0.576125 | −0.288063 | − | 0.957612i | \(-0.593011\pi\) | ||||
−0.288063 | + | 0.957612i | \(0.593011\pi\) | |||||||
\(702\) | −513.696 | − | 4568.14i | −0.0276185 | − | 0.245603i | ||||
\(703\) | 48220.0 | 2.58699 | ||||||||
\(704\) | −13570.3 | + | 23504.5i | −0.726492 | + | 1.25832i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −3564.35 | − | 6173.63i | −0.190009 | − | 0.329104i | ||||
\(707\) | −2166.42 | − | 3752.35i | −0.115243 | − | 0.199607i | ||||
\(708\) | −29481.1 | − | 15584.0i | −1.56493 | − | 0.827234i | ||||
\(709\) | 11786.7 | − | 20415.2i | 0.624343 | − | 1.08139i | −0.364325 | − | 0.931272i | \(-0.618700\pi\) |
0.988668 | − | 0.150122i | \(-0.0479665\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −6161.44 | + | 12789.6i | −0.324996 | + | 0.674610i | ||||
\(712\) | 18398.1 | 0.968394 | ||||||||
\(713\) | −5512.52 | + | 9547.97i | −0.289545 | + | 0.501507i | ||||
\(714\) | 20359.3 | − | 12790.5i | 1.06712 | − | 0.670410i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −5431.37 | − | 9407.41i | −0.283492 | − | 0.491022i | ||||
\(717\) | 26892.4 | − | 16894.9i | 1.40072 | − | 0.879988i | ||||
\(718\) | −24458.5 | + | 42363.3i | −1.27128 | + | 2.20193i | ||||
\(719\) | 27013.2 | 1.40114 | 0.700572 | − | 0.713581i | \(-0.252928\pi\) | ||||
0.700572 | + | 0.713581i | \(0.252928\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 21204.0 | 1.09525 | ||||||||
\(722\) | −31596.1 | + | 54726.0i | −1.62865 | + | 2.82090i | ||||
\(723\) | 14186.8 | + | 7499.25i | 0.729754 | + | 0.385754i | ||||
\(724\) | −3194.91 | − | 5533.74i | −0.164003 | − | 0.284061i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 115.303 | + | 3087.54i | 0.00589432 | + | 0.157836i | ||||
\(727\) | 8927.02 | − | 15462.1i | 0.455412 | − | 0.788797i | −0.543299 | − | 0.839539i | \(-0.682825\pi\) |
0.998712 | + | 0.0507416i | \(0.0161585\pi\) | |||||||
\(728\) | −1191.18 | −0.0606428 | ||||||||
\(729\) | −19191.4 | + | 4371.50i | −0.975025 | + | 0.222095i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −6431.24 | + | 11139.2i | −0.325401 | + | 0.563611i | ||||
\(732\) | −680.552 | − | 18223.6i | −0.0343633 | − | 0.920169i | ||||
\(733\) | −4795.40 | − | 8305.88i | −0.241640 | − | 0.418533i | 0.719541 | − | 0.694449i | \(-0.244352\pi\) |
−0.961182 | + | 0.275916i | \(0.911019\pi\) | |||||||
\(734\) | 602.676 | + | 1043.87i | 0.0303068 | + | 0.0524929i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −22882.4 | + | 39633.5i | −1.14600 | + | 1.98493i | ||||
\(737\) | 23785.1 | 1.18878 | ||||||||
\(738\) | 20190.9 | − | 1510.14i | 1.00710 | − | 0.0753240i | ||||
\(739\) | −6237.43 | −0.310484 | −0.155242 | − | 0.987876i | \(-0.549616\pi\) | ||||
−0.155242 | + | 0.987876i | \(0.549616\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 4868.44 | − | 3058.55i | 0.241359 | − | 0.151631i | ||||
\(742\) | 17187.4 | + | 29769.5i | 0.850365 | + | 1.47288i | ||||
\(743\) | 8567.24 | + | 14838.9i | 0.423017 | + | 0.732687i | 0.996233 | − | 0.0867173i | \(-0.0276377\pi\) |
−0.573216 | + | 0.819404i | \(0.694304\pi\) | |||||||
\(744\) | 3129.79 | − | 1966.26i | 0.154225 | − | 0.0968905i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 42632.3 | 2.09233 | ||||||||
\(747\) | −4195.34 | + | 8708.47i | −0.205488 | + | 0.426541i | ||||
\(748\) | 30622.1 | 1.49686 | ||||||||
\(749\) | 4475.59 | − | 7751.94i | 0.218337 | − | 0.378171i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −19570.8 | − | 33897.7i | −0.950932 | − | 1.64706i | −0.743414 | − | 0.668831i | \(-0.766795\pi\) |
−0.207518 | − | 0.978231i | \(-0.566538\pi\) | |||||||
\(752\) | −2861.30 | − | 4955.92i | −0.138751 | − | 0.240324i | ||||
\(753\) | −531.958 | − | 14244.6i | −0.0257445 | − | 0.689378i | ||||
\(754\) | 716.227 | − | 1240.54i | 0.0345934 | − | 0.0599176i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 2200.63 | + | 19569.5i | 0.105868 | + | 0.941448i | ||||
\(757\) | 3774.26 | 0.181212 | 0.0906062 | − | 0.995887i | \(-0.471120\pi\) | ||||
0.0906062 | + | 0.995887i | \(0.471120\pi\) | |||||||
\(758\) | −29290.0 | + | 50731.8i | −1.40351 | + | 2.43095i | ||||
\(759\) | −1258.88 | − | 33709.9i | −0.0602036 | − | 1.61211i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −12998.9 | − | 22514.8i | −0.619200 | − | 1.07249i | −0.989632 | − | 0.143627i | \(-0.954124\pi\) |
0.370432 | − | 0.928860i | \(-0.379210\pi\) | |||||||
\(762\) | −2893.87 | − | 1529.73i | −0.137577 | − | 0.0727245i | ||||
\(763\) | 7729.08 | − | 13387.2i | 0.366725 | − | 0.635187i | ||||
\(764\) | 39347.3 | 1.86327 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −6024.73 | −0.284181 | ||||||||
\(767\) | −2246.25 | + | 3890.63i | −0.105746 | + | 0.183158i | ||||
\(768\) | 142.459 | − | 89.4984i | 0.00669341 | − | 0.00420507i | ||||
\(769\) | −7817.68 | − | 13540.6i | −0.366597 | − | 0.634964i | 0.622434 | − | 0.782672i | \(-0.286144\pi\) |
−0.989031 | + | 0.147708i | \(0.952810\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 3168.14 | − | 1990.35i | 0.147987 | − | 0.0929712i | ||||
\(772\) | −72.3426 | + | 125.301i | −0.00337262 | + | 0.00584156i | ||||
\(773\) | −5936.28 | −0.276213 | −0.138107 | − | 0.990417i | \(-0.544102\pi\) | ||||
−0.138107 | + | 0.990417i | \(0.544102\pi\) | |||||||
\(774\) | −10329.9 | − | 15155.9i | −0.479715 | − | 0.703833i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 2396.40 | − | 4150.68i | 0.110858 | − | 0.192011i | ||||
\(777\) | 19671.4 | + | 10398.5i | 0.908248 | + | 0.480108i | ||||
\(778\) | 1965.56 | + | 3404.45i | 0.0905767 | + | 0.156883i | ||||
\(779\) | 12661.8 | + | 21930.9i | 0.582358 | + | 1.00867i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −8900.11 | + | 15415.4i | −0.407773 | + | 0.706284i | ||||
\(782\) | 66869.7 | 3.05787 | ||||||||
\(783\) | −5621.14 | − | 2453.94i | −0.256556 | − | 0.112001i | ||||
\(784\) | 5882.04 | 0.267950 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 226.416 | + | 6062.89i | 0.0102748 | + | 0.275135i | ||||
\(787\) | 5193.86 | + | 8996.04i | 0.235249 | + | 0.407464i | 0.959345 | − | 0.282236i | \(-0.0910760\pi\) |
−0.724096 | + | 0.689699i | \(0.757743\pi\) | |||||||
\(788\) | 341.149 | + | 590.887i | 0.0154225 | + | 0.0267126i | ||||
\(789\) | 24017.2 | + | 12695.7i | 1.08370 | + | 0.572851i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 3489.80 | 0.156869 | ||||||||
\(792\) | −4908.38 | + | 10188.6i | −0.220217 | + | 0.457114i | ||||
\(793\) | −2456.82 | −0.110018 | ||||||||
\(794\) | −4128.48 | + | 7150.73i | −0.184527 | + | 0.319610i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 26465.6 | + | 45839.8i | 1.17845 | + | 2.04114i | ||||
\(797\) | 697.430 | + | 1207.98i | 0.0309966 | + | 0.0536876i | 0.881108 | − | 0.472916i | \(-0.156799\pi\) |
−0.850111 | + | 0.526604i | \(0.823465\pi\) | |||||||
\(798\) | −36310.3 | + | 22811.6i | −1.61074 | + | 1.01193i | ||||
\(799\) | −6946.71 | + | 12032.0i | −0.307580 | + | 0.532745i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −40863.0 | + | 3056.28i | −1.80252 | + | 0.134817i | ||||
\(802\) | −45148.6 | −1.98785 | ||||||||
\(803\) | 18802.8 | − | 32567.4i | 0.826323 | − | 1.43123i | ||||
\(804\) | −34140.7 | − | 18047.1i | −1.49757 | − | 0.791630i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −961.322 | − | 1665.06i | −0.0420113 | − | 0.0727658i | ||||
\(807\) | −62.1296 | − | 1663.69i | −0.00271012 | − | 0.0725708i | ||||
\(808\) | −2019.97 | + | 3498.69i | −0.0879483 | + | 0.152331i | ||||
\(809\) | −7633.11 | −0.331726 | −0.165863 | − | 0.986149i | \(-0.553041\pi\) | ||||
−0.165863 | + | 0.986149i | \(0.553041\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −38117.1 | −1.65040 | −0.825199 | − | 0.564842i | \(-0.808937\pi\) | ||||
−0.825199 | + | 0.564842i | \(0.808937\pi\) | |||||||
\(812\) | −3068.25 | + | 5314.36i | −0.132604 | + | 0.229677i | ||||
\(813\) | 202.456 | + | 5421.29i | 0.00873361 | + | 0.233866i | ||||
\(814\) | 24668.8 | + | 42727.6i | 1.06221 | + | 1.83981i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 12750.9 | + | 6740.23i | 0.547022 | + | 0.289161i | ||||
\(817\) | 11470.0 | − | 19866.6i | 0.491167 | − | 0.850727i | ||||
\(818\) | 27094.3 | 1.15811 | ||||||||
\(819\) | 2645.66 | − | 197.878i | 0.112878 | − | 0.00844250i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −1965.53 | + | 3404.41i | −0.0835537 | + | 0.144719i | −0.904774 | − | 0.425892i | \(-0.859960\pi\) |
0.821220 | + | 0.570611i | \(0.193294\pi\) | |||||||
\(822\) | 15782.7 | − | 9915.32i | 0.669689 | − | 0.420726i | ||||
\(823\) | 10749.1 | + | 18618.0i | 0.455274 | + | 0.788558i | 0.998704 | − | 0.0508966i | \(-0.0162079\pi\) |
−0.543430 | + | 0.839455i | \(0.682875\pi\) | |||||||
\(824\) | −9885.27 | − | 17121.8i | −0.417925 | − | 0.723867i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 16753.2 | − | 29017.5i | 0.705714 | − | 1.22233i | ||||
\(827\) | −5272.26 | −0.221686 | −0.110843 | − | 0.993838i | \(-0.535355\pi\) | ||||
−0.110843 | + | 0.993838i | \(0.535355\pi\) | |||||||
\(828\) | −23770.7 | + | 49341.9i | −0.997690 | + | 2.07095i | ||||
\(829\) | −13595.1 | −0.569573 | −0.284786 | − | 0.958591i | \(-0.591923\pi\) | ||||
−0.284786 | + | 0.958591i | \(0.591923\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −15303.5 | − | 8089.57i | −0.638836 | − | 0.337694i | ||||
\(832\) | −2968.27 | − | 5141.19i | −0.123685 | − | 0.214229i | ||||
\(833\) | −7140.24 | − | 12367.3i | −0.296992 | − | 0.514406i | ||||
\(834\) | 142.810 | + | 3824.11i | 0.00592937 | + | 0.158775i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −54613.8 | −2.25940 | ||||||||
\(837\) | −6624.77 | + | 4887.07i | −0.273579 | + | 0.201818i | ||||
\(838\) | 12964.2 | 0.534416 | ||||||||
\(839\) | −7738.30 | + | 13403.1i | −0.318422 | + | 0.551522i | −0.980159 | − | 0.198213i | \(-0.936486\pi\) |
0.661737 | + | 0.749736i | \(0.269819\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 11238.9 | + | 19466.3i | 0.460817 | + | 0.798159i | ||||
\(842\) | 10172.4 | + | 17619.1i | 0.416346 | + | 0.721132i | ||||
\(843\) | −25731.3 | − | 13601.8i | −1.05128 | − | 0.555718i | ||||
\(844\) | 16800.0 | − | 29098.4i | 0.685165 | − | 1.18674i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −11157.8 | − | 16370.6i | −0.453444 | − | 0.665288i | ||||
\(847\) | −1783.16 | −0.0723380 | ||||||||
\(848\) | −10310.0 | + | 17857.5i | −0.417508 | + | 0.723146i | ||||
\(849\) | 27577.9 | − | 17325.6i | 1.11481 | − | 0.700367i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 30941.6 | + | 53592.4i | 1.24637 | + | 2.15878i | ||||
\(852\) | 24471.7 | − | 15374.1i | 0.984020 | − | 0.618201i | ||||
\(853\) | −15155.0 | + | 26249.2i | −0.608320 | + | 1.05364i | 0.383198 | + | 0.923666i | \(0.374823\pi\) |
−0.991517 | + | 0.129974i | \(0.958511\pi\) | |||||||
\(854\) | 18323.7 | 0.734221 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −8346.06 | −0.333250 | ||||||||
\(857\) | −15576.6 | + | 26979.5i | −0.620872 | + | 1.07538i | 0.368452 | + | 0.929647i | \(0.379888\pi\) |
−0.989324 | + | 0.145734i | \(0.953446\pi\) | |||||||
\(858\) | 5200.81 | + | 2749.19i | 0.206938 | + | 0.109389i | ||||
\(859\) | 8955.94 | + | 15512.1i | 0.355731 | + | 0.616144i | 0.987243 | − | 0.159222i | \(-0.0508987\pi\) |
−0.631512 | + | 0.775366i | \(0.717565\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 436.081 | + | 11677.3i | 0.0172609 | + | 0.462206i | ||||
\(862\) | −1772.57 | + | 3070.18i | −0.0700394 | + | 0.121312i | ||||
\(863\) | −34410.6 | −1.35730 | −0.678649 | − | 0.734462i | \(-0.737434\pi\) | ||||
−0.678649 | + | 0.734462i | \(0.737434\pi\) | |||||||
\(864\) | −27499.4 | + | 20286.2i | −1.08281 | + | 0.798785i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −12025.0 | + | 20827.9i | −0.471855 | + | 0.817276i | ||||
\(867\) | −354.042 | − | 9480.43i | −0.0138684 | − | 0.371364i | ||||
\(868\) | 4118.21 | + | 7132.95i | 0.161038 | + | 0.278926i | ||||
\(869\) | −9083.62 | − | 15733.3i | −0.354592 | − | 0.614172i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −2601.28 | + | 4505.55i | −0.101195 | + | 0.175275i | ||||
\(872\) | −14413.2 | −0.559738 | ||||||||
\(873\) | −4633.00 | + | 9616.94i | −0.179614 | + | 0.372834i | ||||
\(874\) | −119261. | −4.61562 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −51700.0 | + | 32480.0i | −1.99404 | + | 1.25274i | ||||
\(877\) | 14114.7 | + | 24447.3i | 0.543464 | + | 0.941308i | 0.998702 | + | 0.0509378i | \(0.0162210\pi\) |
−0.455237 | + | 0.890370i | \(0.650446\pi\) | |||||||
\(878\) | −29007.7 | − | 50242.9i | −1.11499 | − | 1.93122i | ||||
\(879\) | 9252.39 | − | 5812.72i | 0.355034 | − | 0.223047i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −20204.7 | −0.772661 | −0.386331 | − | 0.922360i | \(-0.626258\pi\) | ||||
−0.386331 | + | 0.922360i | \(0.626258\pi\) | |||||||
\(882\) | 20306.7 | − | 1518.81i | 0.775240 | − | 0.0579828i | ||||
\(883\) | −19916.7 | −0.759061 | −0.379530 | − | 0.925179i | \(-0.623914\pi\) | ||||
−0.379530 | + | 0.925179i | \(0.623914\pi\) | |||||||
\(884\) | −3349.02 | + | 5800.67i | −0.127420 | + | 0.220699i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 23491.4 | + | 40688.2i | 0.890754 | + | 1.54283i | ||||
\(887\) | 3513.60 | + | 6085.74i | 0.133005 | + | 0.230371i | 0.924834 | − | 0.380372i | \(-0.124204\pi\) |
−0.791829 | + | 0.610743i | \(0.790871\pi\) | |||||||
\(888\) | −774.229 | − | 20732.1i | −0.0292584 | − | 0.783471i | ||||
\(889\) | 944.570 | − | 1636.04i | 0.0356354 | − | 0.0617223i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 9209.21 | − | 23444.6i | 0.346263 | − | 0.881509i | ||||
\(892\) | −52571.0 | −1.97333 | ||||||||
\(893\) | 12389.3 | − | 21458.9i | 0.464269 | − | 0.804137i | ||||
\(894\) | −1468.15 | − | 39313.8i | −0.0549244 | − | 1.47075i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 9471.00 | + | 16404.3i | 0.353129 | + | 0.611638i | ||||
\(897\) | 6523.28 | + | 3448.26i | 0.242816 | + | 0.128355i | ||||
\(898\) | −6439.49 | + | 11153.5i | −0.239297 | + | 0.414474i | ||||
\(899\) | −2565.28 | −0.0951689 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 50061.5 | 1.85104 | ||||||||
\(902\) | −12955.3 | + | 22439.2i | −0.478231 | + | 0.828320i | ||||
\(903\) | 8963.37 | − | 5631.15i | 0.330324 | − | 0.207523i | ||||
\(904\) | −1626.94 | − | 2817.95i | −0.0598576 | − | 0.103676i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −6539.83 | + | 4108.59i | −0.239814 | + | 0.150661i | ||||
\(907\) | −3186.11 | + | 5518.50i | −0.116641 | + | 0.202027i | −0.918434 | − | 0.395573i | \(-0.870546\pi\) |
0.801794 | + | 0.597601i | \(0.203879\pi\) | |||||||
\(908\) | 71116.2 | 2.59920 | ||||||||
\(909\) | 3905.25 | − | 8106.31i | 0.142496 | − | 0.295786i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 17448.0 | − | 30220.8i | 0.634553 | − | 1.09908i | −0.352057 | − | 0.935979i | \(-0.614518\pi\) |
0.986610 | − | 0.163099i | \(-0.0521491\pi\) | |||||||
\(912\) | −22740.9 | − | 12021.0i | −0.825688 | − | 0.436466i | ||||
\(913\) | −6185.05 | − | 10712.8i | −0.224201 | − | 0.388327i | ||||
\(914\) | −35065.9 | − | 60735.8i | −1.26901 | − | 2.19799i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −88.6906 | + | 153.617i | −0.00319915 | + | 0.00554109i | ||||
\(917\) | −3501.54 | −0.126097 | ||||||||
\(918\) | 45760.6 | + | 19977.0i | 1.64523 | + | 0.718235i | ||||
\(919\) | −702.234 | −0.0252063 | −0.0126031 | − | 0.999921i | \(-0.504012\pi\) | ||||
−0.0126031 | + | 0.999921i | \(0.504012\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 391.718 | + | 10489.3i | 0.0140147 | + | 0.375281i | ||||
\(922\) | −12425.0 | − | 21520.7i | −0.443813 | − | 0.768707i | ||||
\(923\) | −1946.74 | − | 3371.86i | −0.0694235 | − | 0.120245i | ||||
\(924\) | −22279.8 | − | 11777.3i | −0.793237 | − | 0.419312i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 60870.0 | 2.16017 | ||||||||
\(927\) | 24799.9 | + | 36386.2i | 0.878680 | + | 1.28919i | ||||
\(928\) | −10648.5 | −0.376673 | ||||||||
\(929\) | 15286.7 | − | 26477.3i | 0.539871 | − | 0.935084i | −0.459039 | − | 0.888416i | \(-0.651806\pi\) |
0.998910 | − | 0.0466681i | \(-0.0148603\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 12734.5 | + | 22056.7i | 0.448287 | + | 0.776456i | ||||
\(932\) | 3819.37 | + | 6615.33i | 0.134235 | + | 0.232503i | ||||
\(933\) | −23730.1 | + | 14908.2i | −0.832679 | + | 0.523122i | ||||
\(934\) | −7.56366 | + | 13.1006i | −0.000264979 | + | 0.000458957i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −1393.19 | − | 2044.07i | −0.0486514 | − | 0.0713808i | ||||
\(937\) | −13601.7 | −0.474224 | −0.237112 | − | 0.971482i | \(-0.576201\pi\) | ||||
−0.237112 | + | 0.971482i | \(0.576201\pi\) | |||||||
\(938\) | 19401.1 | − | 33603.7i | 0.675341 | − | 1.16972i | ||||
\(939\) | 14294.9 | + | 7556.42i | 0.496802 | + | 0.262614i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −23803.1 | − | 41228.2i | −0.824611 | − | 1.42827i | −0.902216 | − | 0.431284i | \(-0.858061\pi\) |
0.0776049 | − | 0.996984i | \(-0.475273\pi\) | |||||||
\(942\) | 2938.83 | + | 78695.1i | 0.101648 | + | 2.72189i | ||||
\(943\) | −16249.6 | + | 28145.1i | −0.561144 | + | 0.971931i | ||||
\(944\) | 20099.1 | 0.692976 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 23471.6 | 0.806690 | ||||||||
\(947\) | 24267.1 | − | 42031.9i | 0.832710 | − | 1.44230i | −0.0631720 | − | 0.998003i | \(-0.520122\pi\) |
0.895882 | − | 0.444293i | \(-0.146545\pi\) | |||||||
\(948\) | 1100.75 | + | 29475.6i | 0.0377117 | + | 1.00983i | ||||
\(949\) | 4112.79 | + | 7123.56i | 0.140681 | + | 0.243667i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −22664.0 | − | 11980.4i | −0.772797 | − | 0.408507i | ||||
\(952\) | 6469.17 | − | 11204.9i | 0.220238 | − | 0.381464i | ||||
\(953\) | 30379.5 | 1.03262 | 0.516312 | − | 0.856401i | \(-0.327305\pi\) | ||||
0.516312 | + | 0.856401i | \(0.327305\pi\) | |||||||
\(954\) | −30982.5 | + | 64311.9i | −1.05146 | + | 2.18257i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 32993.2 | − | 57146.0i | 1.11619 | − | 1.93330i | ||||
\(957\) | 6646.25 | − | 4175.44i | 0.224496 | − | 0.141037i | ||||
\(958\) | 7914.54 | + | 13708.4i | 0.266918 | + | 0.462315i | ||||
\(959\) | 5378.56 | + | 9315.94i | 0.181108 | + | 0.313689i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 13173.9 | − | 22817.9i | 0.442212 | − | 0.765934i | ||||
\(962\) | −10791.7 | −0.361683 | ||||||||
\(963\) | 18537.0 | − | 1386.44i | 0.620297 | − | 0.0463941i | ||||
\(964\) | 33341.0 | 1.11394 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −48652.6 | − | 25718.2i | −1.62047 | − | 0.856593i | ||||
\(967\) | 16161.9 | + | 27993.3i | 0.537470 | + | 0.930925i | 0.999039 | + | 0.0438207i | \(0.0139530\pi\) |
−0.461570 | + | 0.887104i | \(0.652714\pi\) | |||||||
\(968\) | 831.310 | + | 1439.87i | 0.0276026 | + | 0.0478091i | ||||
\(969\) | 2330.53 | + | 62406.3i | 0.0772627 | + | 2.06892i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −27461.7 | −0.907609 | −0.453805 | − | 0.891101i | \(-0.649934\pi\) | ||||
−0.453805 | + | 0.891101i | \(0.649934\pi\) | |||||||
\(972\) | −31007.5 | + | 26664.5i | −1.02322 | + | 0.879902i | ||||
\(973\) | −2208.56 | −0.0727681 | ||||||||
\(974\) | 29582.5 | − | 51238.4i | 0.973188 | − | 1.68561i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 5495.81 | + | 9519.02i | 0.180242 | + | 0.312189i | ||||
\(977\) | 21771.9 | + | 37710.1i | 0.712943 | + | 1.23485i | 0.963747 | + | 0.266816i | \(0.0859716\pi\) |
−0.250804 | + | 0.968038i | \(0.580695\pi\) | |||||||
\(978\) | 13215.3 | + | 6985.72i | 0.432085 | + | 0.228404i | ||||
\(979\) | 26219.4 | − | 45413.3i | 0.855949 | − | 1.48255i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 32012.3 | − | 2394.31i | 1.04187 | − | 0.0779249i | ||||
\(982\) | 180.781 | 0.00587470 | ||||||||
\(983\) | 17184.5 | − | 29764.4i | 0.557579 | − | 0.965756i | −0.440118 | − | 0.897940i | \(-0.645064\pi\) |
0.997698 | − | 0.0678161i | \(-0.0216031\pi\) | |||||||
\(984\) | 9225.85 | − | 5796.05i | 0.298892 | − | 0.187776i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 7779.53 | + | 13474.5i | 0.251268 | + | 0.435210i | ||||
\(987\) | 9681.78 | − | 6082.48i | 0.312234 | − | 0.196158i | ||||
\(988\) | 5972.90 | − | 10345.4i | 0.192331 | − | 0.333128i | ||||
\(989\) | 29440.0 | 0.946550 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 4360.89 | 0.139786 | 0.0698931 | − | 0.997554i | \(-0.477734\pi\) | ||||
0.0698931 | + | 0.997554i | \(0.477734\pi\) | |||||||
\(992\) | −7146.19 | + | 12377.6i | −0.228722 | + | 0.396157i | ||||
\(993\) | 40300.6 | + | 21303.2i | 1.28792 | + | 0.680803i | ||||
\(994\) | 14519.4 | + | 25148.3i | 0.463307 | + | 0.802471i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 749.504 | + | 20070.0i | 0.0238443 | + | 0.638495i | ||||
\(997\) | 14677.3 | − | 25421.9i | 0.466235 | − | 0.807543i | −0.533021 | − | 0.846102i | \(-0.678943\pi\) |
0.999256 | + | 0.0385591i | \(0.0122768\pi\) | |||||||
\(998\) | −10374.4 | −0.329056 | ||||||||
\(999\) | 5163.60 | + | 45918.3i | 0.163533 | + | 1.45424i |
(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.151.2 | yes | 24 | |
5.2 | odd | 4 | 225.4.k.e.124.4 | 48 | |||
5.3 | odd | 4 | 225.4.k.e.124.21 | 48 | |||
5.4 | even | 2 | 225.4.e.e.151.11 | yes | 24 | ||
9.2 | odd | 6 | 2025.4.a.bj.1.2 | 12 | |||
9.4 | even | 3 | inner | 225.4.e.f.76.2 | yes | 24 | |
9.7 | even | 3 | 2025.4.a.bf.1.11 | 12 | |||
45.4 | even | 6 | 225.4.e.e.76.11 | ✓ | 24 | ||
45.13 | odd | 12 | 225.4.k.e.49.4 | 48 | |||
45.22 | odd | 12 | 225.4.k.e.49.21 | 48 | |||
45.29 | odd | 6 | 2025.4.a.be.1.11 | 12 | |||
45.34 | even | 6 | 2025.4.a.bi.1.2 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
225.4.e.e.76.11 | ✓ | 24 | 45.4 | even | 6 | ||
225.4.e.e.151.11 | yes | 24 | 5.4 | even | 2 | ||
225.4.e.f.76.2 | yes | 24 | 9.4 | even | 3 | inner | |
225.4.e.f.151.2 | yes | 24 | 1.1 | even | 1 | trivial | |
225.4.k.e.49.4 | 48 | 45.13 | odd | 12 | |||
225.4.k.e.49.21 | 48 | 45.22 | odd | 12 | |||
225.4.k.e.124.4 | 48 | 5.2 | odd | 4 | |||
225.4.k.e.124.21 | 48 | 5.3 | odd | 4 | |||
2025.4.a.be.1.11 | 12 | 45.29 | odd | 6 | |||
2025.4.a.bf.1.11 | 12 | 9.7 | even | 3 | |||
2025.4.a.bi.1.2 | 12 | 45.34 | even | 6 | |||
2025.4.a.bj.1.2 | 12 | 9.2 | odd | 6 |