Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [63,4,Mod(22,63)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(63, 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("63.22");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 63 = 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 63.f (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: | \(3.71712033036\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 3 x^{15} + 58 x^{14} - 129 x^{13} + 2107 x^{12} - 4455 x^{11} + 42901 x^{10} - 76404 x^{9} + \cdots + 21307456 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{4}]\) |
Coefficient ring index: | \( 2^{2}\cdot 3^{7} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 43.7 | ||
Root | \(-1.96709 + 3.40709i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 63.43 |
Dual form | 63.4.f.b.22.7 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/63\mathbb{Z}\right)^\times\).
\(n\) | \(10\) | \(29\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.96709 | − | 3.40709i | 0.695470 | − | 1.20459i | −0.274552 | − | 0.961572i | \(-0.588530\pi\) |
0.970022 | − | 0.243017i | \(-0.0781371\pi\) | |||||||
\(3\) | 1.35403 | − | 5.01663i | 0.260583 | − | 0.965452i | ||||
\(4\) | −3.73885 | − | 6.47588i | −0.467357 | − | 0.809485i | ||||
\(5\) | 1.21571 | + | 2.10567i | 0.108736 | + | 0.188337i | 0.915259 | − | 0.402867i | \(-0.131986\pi\) |
−0.806522 | + | 0.591204i | \(0.798653\pi\) | |||||||
\(6\) | −14.4286 | − | 14.4814i | −0.981745 | − | 0.985337i | ||||
\(7\) | 3.50000 | − | 6.06218i | 0.188982 | − | 0.327327i | ||||
\(8\) | 2.05480 | 0.0908100 | ||||||||
\(9\) | −23.3332 | − | 13.5853i | −0.864193 | − | 0.503160i | ||||
\(10\) | 9.56561 | 0.302491 | ||||||||
\(11\) | −21.0862 | + | 36.5223i | −0.577975 | + | 1.00108i | 0.417737 | + | 0.908568i | \(0.362823\pi\) |
−0.995711 | + | 0.0925133i | \(0.970510\pi\) | |||||||
\(12\) | −37.5496 | + | 9.98793i | −0.903304 | + | 0.240272i | ||||
\(13\) | 19.7866 | + | 34.2714i | 0.422139 | + | 0.731166i | 0.996148 | − | 0.0876824i | \(-0.0279460\pi\) |
−0.574009 | + | 0.818849i | \(0.694613\pi\) | |||||||
\(14\) | −13.7696 | − | 23.8496i | −0.262863 | − | 0.455292i | ||||
\(15\) | 12.2095 | − | 3.24763i | 0.210165 | − | 0.0559023i | ||||
\(16\) | 33.9528 | − | 58.8079i | 0.530512 | − | 0.918874i | ||||
\(17\) | −2.07697 | −0.0296317 | −0.0148158 | − | 0.999890i | \(-0.504716\pi\) | ||||
−0.0148158 | + | 0.999890i | \(0.504716\pi\) | |||||||
\(18\) | −92.1849 | + | 52.7750i | −1.20712 | + | 0.691066i | ||||
\(19\) | 96.1013 | 1.16038 | 0.580188 | − | 0.814483i | \(-0.302979\pi\) | ||||
0.580188 | + | 0.814483i | \(0.302979\pi\) | |||||||
\(20\) | 9.09070 | − | 15.7456i | 0.101637 | − | 0.176041i | ||||
\(21\) | −25.6726 | − | 25.7666i | −0.266773 | − | 0.267749i | ||||
\(22\) | 82.9566 | + | 143.685i | 0.803928 | + | 1.39244i | ||||
\(23\) | −36.8754 | − | 63.8701i | −0.334307 | − | 0.579036i | 0.649045 | − | 0.760750i | \(-0.275169\pi\) |
−0.983351 | + | 0.181714i | \(0.941836\pi\) | |||||||
\(24\) | 2.78225 | − | 10.3082i | 0.0236635 | − | 0.0876727i | ||||
\(25\) | 59.5441 | − | 103.133i | 0.476353 | − | 0.825067i | ||||
\(26\) | 155.688 | 1.17434 | ||||||||
\(27\) | −99.7463 | + | 98.6594i | −0.710970 | + | 0.703222i | ||||
\(28\) | −52.3439 | −0.353288 | ||||||||
\(29\) | −9.60379 | + | 16.6342i | −0.0614958 | + | 0.106514i | −0.895134 | − | 0.445797i | \(-0.852920\pi\) |
0.833638 | + | 0.552311i | \(0.186254\pi\) | |||||||
\(30\) | 12.9521 | − | 47.9871i | 0.0788239 | − | 0.292040i | ||||
\(31\) | 119.748 | + | 207.410i | 0.693788 | + | 1.20168i | 0.970587 | + | 0.240749i | \(0.0773930\pi\) |
−0.276799 | + | 0.960928i | \(0.589274\pi\) | |||||||
\(32\) | −125.357 | − | 217.124i | −0.692505 | − | 1.19945i | ||||
\(33\) | 154.668 | + | 155.234i | 0.815885 | + | 0.818871i | ||||
\(34\) | −4.08557 | + | 7.07642i | −0.0206079 | + | 0.0356940i | ||||
\(35\) | 17.0199 | 0.0821968 | ||||||||
\(36\) | −0.737407 | + | 201.897i | −0.00341392 | + | 0.934707i | ||||
\(37\) | −144.310 | −0.641202 | −0.320601 | − | 0.947214i | \(-0.603885\pi\) | ||||
−0.320601 | + | 0.947214i | \(0.603885\pi\) | |||||||
\(38\) | 189.039 | − | 327.426i | 0.807007 | − | 1.39778i | ||||
\(39\) | 198.718 | − | 52.8577i | 0.815908 | − | 0.217026i | ||||
\(40\) | 2.49803 | + | 4.32672i | 0.00987434 | + | 0.0171029i | ||||
\(41\) | 36.1409 | + | 62.5979i | 0.137665 | + | 0.238443i | 0.926612 | − | 0.376018i | \(-0.122707\pi\) |
−0.788947 | + | 0.614461i | \(0.789374\pi\) | |||||||
\(42\) | −138.289 | + | 36.7840i | −0.508060 | + | 0.135140i | ||||
\(43\) | −240.274 | + | 416.167i | −0.852128 | + | 1.47593i | 0.0271568 | + | 0.999631i | \(0.491355\pi\) |
−0.879284 | + | 0.476297i | \(0.841979\pi\) | |||||||
\(44\) | 315.352 | 1.08048 | ||||||||
\(45\) | 0.239772 | − | 65.6478i | 0.000794291 | − | 0.217471i | ||||
\(46\) | −290.148 | −0.930001 | ||||||||
\(47\) | −147.354 | + | 255.224i | −0.457313 | + | 0.792090i | −0.998818 | − | 0.0486079i | \(-0.984522\pi\) |
0.541505 | + | 0.840698i | \(0.317855\pi\) | |||||||
\(48\) | −249.045 | − | 249.956i | −0.748886 | − | 0.751626i | ||||
\(49\) | −24.5000 | − | 42.4352i | −0.0714286 | − | 0.123718i | ||||
\(50\) | −234.257 | − | 405.745i | −0.662578 | − | 1.14762i | ||||
\(51\) | −2.81227 | + | 10.4194i | −0.00772150 | + | 0.0286079i | ||||
\(52\) | 147.958 | − | 256.271i | 0.394579 | − | 0.683431i | ||||
\(53\) | −627.210 | −1.62555 | −0.812773 | − | 0.582580i | \(-0.802043\pi\) | ||||
−0.812773 | + | 0.582580i | \(0.802043\pi\) | |||||||
\(54\) | 139.932 | + | 533.916i | 0.352636 | + | 1.34550i | ||||
\(55\) | −102.538 | −0.251387 | ||||||||
\(56\) | 7.19179 | − | 12.4565i | 0.0171615 | − | 0.0297246i | ||||
\(57\) | 130.124 | − | 482.105i | 0.302374 | − | 1.12029i | ||||
\(58\) | 37.7829 | + | 65.4420i | 0.0855370 | + | 0.148154i | ||||
\(59\) | −74.8093 | − | 129.573i | −0.165074 | − | 0.285916i | 0.771608 | − | 0.636098i | \(-0.219453\pi\) |
−0.936681 | + | 0.350183i | \(0.886119\pi\) | |||||||
\(60\) | −66.6807 | − | 66.9246i | −0.143474 | − | 0.143999i | ||||
\(61\) | 315.358 | − | 546.216i | 0.661926 | − | 1.14649i | −0.318183 | − | 0.948029i | \(-0.603073\pi\) |
0.980109 | − | 0.198460i | \(-0.0635939\pi\) | |||||||
\(62\) | 942.221 | 1.93004 | ||||||||
\(63\) | −164.023 | + | 93.9016i | −0.328015 | + | 0.187785i | ||||
\(64\) | −443.106 | −0.865442 | ||||||||
\(65\) | −48.1094 | + | 83.3279i | −0.0918036 | + | 0.159009i | ||||
\(66\) | 833.141 | − | 221.610i | 1.55383 | − | 0.413307i | ||||
\(67\) | −2.02124 | − | 3.50089i | −0.00368558 | − | 0.00638361i | 0.864177 | − | 0.503188i | \(-0.167840\pi\) |
−0.867862 | + | 0.496805i | \(0.834506\pi\) | |||||||
\(68\) | 7.76547 | + | 13.4502i | 0.0138486 | + | 0.0239864i | ||||
\(69\) | −370.343 | + | 98.5087i | −0.646146 | + | 0.171870i | ||||
\(70\) | 33.4796 | − | 57.9884i | 0.0571654 | − | 0.0990134i | ||||
\(71\) | −798.373 | −1.33450 | −0.667249 | − | 0.744835i | \(-0.732528\pi\) | ||||
−0.667249 | + | 0.744835i | \(0.732528\pi\) | |||||||
\(72\) | −47.9450 | − | 27.9150i | −0.0784774 | − | 0.0456919i | ||||
\(73\) | 444.022 | 0.711902 | 0.355951 | − | 0.934505i | \(-0.384157\pi\) | ||||
0.355951 | + | 0.934505i | \(0.384157\pi\) | |||||||
\(74\) | −283.871 | + | 491.679i | −0.445937 | + | 0.772386i | ||||
\(75\) | −436.758 | − | 438.356i | −0.672433 | − | 0.674894i | ||||
\(76\) | −359.309 | − | 622.341i | −0.542309 | − | 0.939308i | ||||
\(77\) | 147.603 | + | 255.656i | 0.218454 | + | 0.378373i | ||||
\(78\) | 210.805 | − | 781.027i | 0.306013 | − | 1.13377i | ||||
\(79\) | 287.769 | − | 498.431i | 0.409830 | − | 0.709847i | −0.585040 | − | 0.811004i | \(-0.698921\pi\) |
0.994870 | + | 0.101158i | \(0.0322547\pi\) | |||||||
\(80\) | 165.107 | 0.230744 | ||||||||
\(81\) | 359.879 | + | 633.978i | 0.493661 | + | 0.869655i | ||||
\(82\) | 284.369 | 0.382967 | ||||||||
\(83\) | −645.117 | + | 1117.38i | −0.853143 | + | 1.47769i | 0.0252150 | + | 0.999682i | \(0.491973\pi\) |
−0.878358 | + | 0.478004i | \(0.841360\pi\) | |||||||
\(84\) | −70.8751 | + | 262.590i | −0.0920608 | + | 0.341083i | ||||
\(85\) | −2.52498 | − | 4.37340i | −0.00322204 | − | 0.00558073i | ||||
\(86\) | 945.280 | + | 1637.27i | 1.18526 | + | 2.05293i | ||||
\(87\) | 70.4441 | + | 70.7019i | 0.0868092 | + | 0.0871269i | ||||
\(88\) | −43.3278 | + | 75.0459i | −0.0524859 | + | 0.0909082i | ||||
\(89\) | 750.701 | 0.894091 | 0.447046 | − | 0.894511i | \(-0.352476\pi\) | ||||
0.447046 | + | 0.894511i | \(0.352476\pi\) | |||||||
\(90\) | −223.196 | − | 129.952i | −0.261411 | − | 0.152201i | ||||
\(91\) | 277.012 | 0.319107 | ||||||||
\(92\) | −275.744 | + | 477.602i | −0.312481 | + | 0.541233i | ||||
\(93\) | 1202.64 | − | 319.895i | 1.34095 | − | 0.356683i | ||||
\(94\) | 579.714 | + | 1004.09i | 0.636095 | + | 1.10175i | ||||
\(95\) | 116.831 | + | 202.357i | 0.126175 | + | 0.218541i | ||||
\(96\) | −1258.97 | + | 334.877i | −1.33847 | + | 0.356024i | ||||
\(97\) | −209.774 | + | 363.339i | −0.219581 | + | 0.380325i | −0.954680 | − | 0.297635i | \(-0.903802\pi\) |
0.735099 | + | 0.677960i | \(0.237136\pi\) | |||||||
\(98\) | −192.774 | −0.198706 | ||||||||
\(99\) | 988.175 | − | 565.721i | 1.00319 | − | 0.574314i | ||||
\(100\) | −890.507 | −0.890507 | ||||||||
\(101\) | −452.812 | + | 784.293i | −0.446103 | + | 0.772674i | −0.998128 | − | 0.0611539i | \(-0.980522\pi\) |
0.552025 | + | 0.833828i | \(0.313855\pi\) | |||||||
\(102\) | 29.9678 | + | 30.0775i | 0.0290907 | + | 0.0291972i | ||||
\(103\) | −1033.87 | − | 1790.71i | −0.989030 | − | 1.71305i | −0.622439 | − | 0.782668i | \(-0.713858\pi\) |
−0.366591 | − | 0.930382i | \(-0.619475\pi\) | |||||||
\(104\) | 40.6574 | + | 70.4206i | 0.0383345 | + | 0.0663972i | ||||
\(105\) | 23.0454 | − | 85.3826i | 0.0214191 | − | 0.0793571i | ||||
\(106\) | −1233.78 | + | 2136.96i | −1.13052 | + | 1.95812i | ||||
\(107\) | 1728.25 | 1.56146 | 0.780730 | − | 0.624869i | \(-0.214848\pi\) | ||||
0.780730 | + | 0.624869i | \(0.214848\pi\) | |||||||
\(108\) | 1011.84 | + | 277.073i | 0.901525 | + | 0.246864i | ||||
\(109\) | 925.211 | 0.813020 | 0.406510 | − | 0.913646i | \(-0.366746\pi\) | ||||
0.406510 | + | 0.913646i | \(0.366746\pi\) | |||||||
\(110\) | −201.702 | + | 349.358i | −0.174832 | + | 0.302818i | ||||
\(111\) | −195.400 | + | 723.953i | −0.167086 | + | 0.619050i | ||||
\(112\) | −237.669 | − | 411.656i | −0.200515 | − | 0.347302i | ||||
\(113\) | −1093.61 | − | 1894.18i | −0.910424 | − | 1.57690i | −0.813467 | − | 0.581612i | \(-0.802422\pi\) |
−0.0969571 | − | 0.995289i | \(-0.530911\pi\) | |||||||
\(114\) | −1386.61 | − | 1391.69i | −1.13919 | − | 1.14336i | ||||
\(115\) | 89.6595 | − | 155.295i | 0.0727025 | − | 0.125924i | ||||
\(116\) | 143.629 | 0.114962 | ||||||||
\(117\) | 3.90247 | − | 1068.47i | 0.00308362 | − | 0.844273i | ||||
\(118\) | −588.625 | −0.459215 | ||||||||
\(119\) | −7.26938 | + | 12.5909i | −0.00559986 | + | 0.00969924i | ||||
\(120\) | 25.0880 | − | 6.67322i | 0.0190851 | − | 0.00507649i | ||||
\(121\) | −223.753 | − | 387.552i | −0.168109 | − | 0.291174i | ||||
\(122\) | −1240.67 | − | 2148.91i | −0.920699 | − | 1.59470i | ||||
\(123\) | 362.967 | − | 96.5465i | 0.266078 | − | 0.0707748i | ||||
\(124\) | 895.443 | − | 1550.95i | 0.648493 | − | 1.12322i | ||||
\(125\) | 593.480 | 0.424660 | ||||||||
\(126\) | −2.71575 | + | 743.553i | −0.00192015 | + | 0.525722i | ||||
\(127\) | 898.130 | 0.627529 | 0.313764 | − | 0.949501i | \(-0.398410\pi\) | ||||
0.313764 | + | 0.949501i | \(0.398410\pi\) | |||||||
\(128\) | 131.227 | − | 227.291i | 0.0906165 | − | 0.156952i | ||||
\(129\) | 1762.42 | + | 1768.87i | 1.20289 | + | 1.20729i | ||||
\(130\) | 189.271 | + | 327.826i | 0.127693 | + | 0.221171i | ||||
\(131\) | −1067.26 | − | 1848.56i | −0.711812 | − | 1.23289i | −0.964176 | − | 0.265262i | \(-0.914541\pi\) |
0.252364 | − | 0.967632i | \(-0.418792\pi\) | |||||||
\(132\) | 426.996 | − | 1582.01i | 0.281554 | − | 1.04315i | ||||
\(133\) | 336.355 | − | 582.583i | 0.219290 | − | 0.379822i | ||||
\(134\) | −15.9038 | −0.0102528 | ||||||||
\(135\) | −329.006 | − | 90.0917i | −0.209751 | − | 0.0574360i | ||||
\(136\) | −4.26774 | −0.00269085 | ||||||||
\(137\) | 1080.63 | − | 1871.71i | 0.673901 | − | 1.16723i | −0.302888 | − | 0.953026i | \(-0.597951\pi\) |
0.976789 | − | 0.214205i | \(-0.0687160\pi\) | |||||||
\(138\) | −392.869 | + | 1455.57i | −0.242342 | + | 0.897871i | ||||
\(139\) | −1150.08 | − | 1992.00i | −0.701789 | − | 1.21553i | −0.967838 | − | 0.251575i | \(-0.919052\pi\) |
0.266049 | − | 0.963960i | \(-0.414282\pi\) | |||||||
\(140\) | −63.6349 | − | 110.219i | −0.0384152 | − | 0.0665371i | ||||
\(141\) | 1080.84 | + | 1084.80i | 0.645557 | + | 0.647919i | ||||
\(142\) | −1570.47 | + | 2720.13i | −0.928103 | + | 1.60752i | ||||
\(143\) | −1668.89 | −0.975943 | ||||||||
\(144\) | −1591.15 | + | 910.920i | −0.920806 | + | 0.527153i | ||||
\(145\) | −46.7016 | −0.0267473 | ||||||||
\(146\) | 873.430 | − | 1512.82i | 0.495107 | − | 0.857550i | ||||
\(147\) | −246.056 | + | 65.4491i | −0.138057 | + | 0.0367221i | ||||
\(148\) | 539.556 | + | 934.538i | 0.299670 | + | 0.519044i | ||||
\(149\) | 591.768 | + | 1024.97i | 0.325366 | + | 0.563551i | 0.981586 | − | 0.191019i | \(-0.0611791\pi\) |
−0.656220 | + | 0.754569i | \(0.727846\pi\) | |||||||
\(150\) | −2352.66 | + | 625.791i | −1.28063 | + | 0.340638i | ||||
\(151\) | −1718.81 | + | 2977.06i | −0.926322 | + | 1.60444i | −0.136901 | + | 0.990585i | \(0.543714\pi\) |
−0.789421 | + | 0.613852i | \(0.789619\pi\) | |||||||
\(152\) | 197.469 | 0.105374 | ||||||||
\(153\) | 48.4623 | + | 28.2162i | 0.0256075 | + | 0.0149095i | ||||
\(154\) | 1161.39 | 0.607712 | ||||||||
\(155\) | −291.158 | + | 504.300i | −0.150880 | + | 0.261331i | ||||
\(156\) | −1085.28 | − | 1089.25i | −0.556999 | − | 0.559037i | ||||
\(157\) | 10.4307 | + | 18.0665i | 0.00530229 | + | 0.00918383i | 0.868664 | − | 0.495401i | \(-0.164979\pi\) |
−0.863362 | + | 0.504585i | \(0.831646\pi\) | |||||||
\(158\) | −1132.13 | − | 1960.91i | −0.570049 | − | 0.987354i | ||||
\(159\) | −849.260 | + | 3146.49i | −0.423589 | + | 1.56939i | ||||
\(160\) | 304.795 | − | 527.920i | 0.150601 | − | 0.260848i | ||||
\(161\) | −516.256 | −0.252712 | ||||||||
\(162\) | 2867.93 | + | 20.9500i | 1.39090 | + | 0.0101604i | ||||
\(163\) | −1654.46 | −0.795015 | −0.397507 | − | 0.917599i | \(-0.630125\pi\) | ||||
−0.397507 | + | 0.917599i | \(0.630125\pi\) | |||||||
\(164\) | 270.251 | − | 468.089i | 0.128677 | − | 0.222876i | ||||
\(165\) | −138.840 | + | 514.398i | −0.0655071 | + | 0.242702i | ||||
\(166\) | 2538.00 | + | 4395.95i | 1.18667 | + | 2.05537i | ||||
\(167\) | 980.611 | + | 1698.47i | 0.454383 | + | 0.787014i | 0.998652 | − | 0.0518963i | \(-0.0165265\pi\) |
−0.544270 | + | 0.838910i | \(0.683193\pi\) | |||||||
\(168\) | −52.7520 | − | 52.9450i | −0.0242256 | − | 0.0243143i | ||||
\(169\) | 315.483 | − | 546.433i | 0.143597 | − | 0.248718i | ||||
\(170\) | −19.8674 | −0.00896331 | ||||||||
\(171\) | −2242.35 | − | 1305.57i | −1.00279 | − | 0.583855i | ||||
\(172\) | 3593.40 | 1.59299 | ||||||||
\(173\) | 13.6713 | − | 23.6794i | 0.00600816 | − | 0.0104064i | −0.863006 | − | 0.505194i | \(-0.831421\pi\) |
0.869014 | + | 0.494788i | \(0.164754\pi\) | |||||||
\(174\) | 379.458 | − | 100.933i | 0.165325 | − | 0.0439754i | ||||
\(175\) | −416.809 | − | 721.934i | −0.180044 | − | 0.311846i | ||||
\(176\) | 1431.87 | + | 2480.07i | 0.613245 | + | 1.06217i | ||||
\(177\) | −751.316 | + | 199.845i | −0.319053 | + | 0.0848658i | ||||
\(178\) | 1476.69 | − | 2557.71i | 0.621813 | − | 1.07701i | ||||
\(179\) | 130.832 | 0.0546302 | 0.0273151 | − | 0.999627i | \(-0.491304\pi\) | ||||
0.0273151 | + | 0.999627i | \(0.491304\pi\) | |||||||
\(180\) | −426.024 | + | 243.895i | −0.176411 | + | 0.100994i | ||||
\(181\) | 2460.11 | 1.01027 | 0.505134 | − | 0.863041i | \(-0.331443\pi\) | ||||
0.505134 | + | 0.863041i | \(0.331443\pi\) | |||||||
\(182\) | 544.906 | − | 943.806i | 0.221929 | − | 0.384393i | ||||
\(183\) | −2313.16 | − | 2321.63i | −0.934393 | − | 0.937812i | ||||
\(184\) | −75.7715 | − | 131.240i | −0.0303584 | − | 0.0525823i | ||||
\(185\) | −175.439 | − | 303.870i | −0.0697219 | − | 0.120762i | ||||
\(186\) | 1275.79 | − | 4726.78i | 0.502934 | − | 1.86336i | ||||
\(187\) | 43.7953 | − | 75.8556i | 0.0171264 | − | 0.0296637i | ||||
\(188\) | 2203.73 | 0.854914 | ||||||||
\(189\) | 248.978 | + | 949.988i | 0.0958228 | + | 0.365616i | ||||
\(190\) | 919.267 | 0.351003 | ||||||||
\(191\) | 654.703 | − | 1133.98i | 0.248024 | − | 0.429591i | −0.714953 | − | 0.699172i | \(-0.753552\pi\) |
0.962978 | + | 0.269581i | \(0.0868853\pi\) | |||||||
\(192\) | −599.978 | + | 2222.90i | −0.225519 | + | 0.835543i | ||||
\(193\) | −431.867 | − | 748.016i | −0.161070 | − | 0.278981i | 0.774183 | − | 0.632962i | \(-0.218161\pi\) |
−0.935253 | + | 0.353981i | \(0.884828\pi\) | |||||||
\(194\) | 825.287 | + | 1429.44i | 0.305424 | + | 0.529009i | ||||
\(195\) | 352.884 | + | 354.175i | 0.129593 | + | 0.130067i | ||||
\(196\) | −183.204 | + | 317.318i | −0.0667652 | + | 0.115641i | ||||
\(197\) | 2958.90 | 1.07012 | 0.535058 | − | 0.844815i | \(-0.320290\pi\) | ||||
0.535058 | + | 0.844815i | \(0.320290\pi\) | |||||||
\(198\) | 16.3614 | − | 4479.63i | 0.00587249 | − | 1.60784i | ||||
\(199\) | −1559.83 | −0.555646 | −0.277823 | − | 0.960632i | \(-0.589613\pi\) | ||||
−0.277823 | + | 0.960632i | \(0.589613\pi\) | |||||||
\(200\) | 122.351 | − | 211.918i | 0.0432576 | − | 0.0749244i | ||||
\(201\) | −20.2995 | + | 5.39952i | −0.00712346 | + | 0.00189479i | ||||
\(202\) | 1781.44 | + | 3085.54i | 0.620503 | + | 1.07474i | ||||
\(203\) | 67.2265 | + | 116.440i | 0.0232432 | + | 0.0402585i | ||||
\(204\) | 77.9893 | − | 20.7446i | 0.0267664 | − | 0.00711967i | ||||
\(205\) | −87.8736 | + | 152.202i | −0.0299383 | + | 0.0518547i | ||||
\(206\) | −8134.83 | −2.75136 | ||||||||
\(207\) | −7.27288 | + | 1991.26i | −0.00244203 | + | 0.668609i | ||||
\(208\) | 2687.24 | 0.895800 | ||||||||
\(209\) | −2026.41 | + | 3509.84i | −0.670668 | + | 1.16163i | ||||
\(210\) | −245.574 | − | 246.473i | −0.0806964 | − | 0.0809916i | ||||
\(211\) | −1253.20 | − | 2170.60i | −0.408880 | − | 0.708201i | 0.585885 | − | 0.810394i | \(-0.300747\pi\) |
−0.994765 | + | 0.102194i | \(0.967414\pi\) | |||||||
\(212\) | 2345.05 | + | 4061.74i | 0.759710 | + | 1.31586i | ||||
\(213\) | −1081.02 | + | 4005.14i | −0.347747 | + | 1.28839i | ||||
\(214\) | 3399.61 | − | 5888.31i | 1.08595 | − | 1.88092i | ||||
\(215\) | −1168.41 | −0.370628 | ||||||||
\(216\) | −204.958 | + | 202.725i | −0.0645632 | + | 0.0638596i | ||||
\(217\) | 1676.48 | 0.524455 | ||||||||
\(218\) | 1819.97 | − | 3152.28i | 0.565431 | − | 0.979355i | ||||
\(219\) | 601.218 | − | 2227.50i | 0.185509 | − | 0.687307i | ||||
\(220\) | 383.376 | + | 664.027i | 0.117487 | + | 0.203494i | ||||
\(221\) | −41.0961 | − | 71.1805i | −0.0125087 | − | 0.0216657i | ||||
\(222\) | 2082.20 | + | 2089.82i | 0.629497 | + | 0.631801i | ||||
\(223\) | −2024.21 | + | 3506.03i | −0.607851 | + | 1.05283i | 0.383743 | + | 0.923440i | \(0.374635\pi\) |
−0.991594 | + | 0.129389i | \(0.958698\pi\) | |||||||
\(224\) | −1755.00 | −0.523485 | ||||||||
\(225\) | −2790.46 | + | 1597.51i | −0.826802 | + | 0.473336i | ||||
\(226\) | −8604.87 | −2.53269 | ||||||||
\(227\) | 313.734 | − | 543.404i | 0.0917325 | − | 0.158885i | −0.816508 | − | 0.577335i | \(-0.804093\pi\) |
0.908240 | + | 0.418449i | \(0.137426\pi\) | |||||||
\(228\) | −3608.57 | + | 959.853i | −1.04817 | + | 0.278806i | ||||
\(229\) | 494.563 | + | 856.608i | 0.142715 | + | 0.247189i | 0.928518 | − | 0.371288i | \(-0.121084\pi\) |
−0.785803 | + | 0.618476i | \(0.787750\pi\) | |||||||
\(230\) | −352.736 | − | 610.956i | −0.101125 | − | 0.175153i | ||||
\(231\) | 1482.39 | − | 394.306i | 0.422226 | − | 0.112309i | ||||
\(232\) | −19.7338 | + | 34.1800i | −0.00558444 | + | 0.00967253i | ||||
\(233\) | −3125.53 | −0.878799 | −0.439399 | − | 0.898292i | \(-0.644809\pi\) | ||||
−0.439399 | + | 0.898292i | \(0.644809\pi\) | |||||||
\(234\) | −3632.69 | − | 2115.06i | −1.01486 | − | 0.590881i | ||||
\(235\) | −716.555 | −0.198906 | ||||||||
\(236\) | −559.402 | + | 968.912i | −0.154296 | + | 0.267249i | ||||
\(237\) | −2110.80 | − | 2118.52i | −0.578528 | − | 0.580645i | ||||
\(238\) | 28.5990 | + | 49.5349i | 0.00778907 | + | 0.0134911i | ||||
\(239\) | 1512.51 | + | 2619.75i | 0.409357 | + | 0.709027i | 0.994818 | − | 0.101674i | \(-0.0324197\pi\) |
−0.585461 | + | 0.810701i | \(0.699086\pi\) | |||||||
\(240\) | 223.559 | − | 828.279i | 0.0601277 | − | 0.222772i | ||||
\(241\) | 2799.43 | − | 4848.75i | 0.748245 | − | 1.29600i | −0.200419 | − | 0.979710i | \(-0.564230\pi\) |
0.948663 | − | 0.316288i | \(-0.102436\pi\) | |||||||
\(242\) | −1760.57 | −0.467659 | ||||||||
\(243\) | 3667.72 | − | 946.955i | 0.968249 | − | 0.249989i | ||||
\(244\) | −4716.31 | −1.23742 | ||||||||
\(245\) | 59.5697 | − | 103.178i | 0.0155337 | − | 0.0269052i | ||||
\(246\) | 385.043 | − | 1426.58i | 0.0997946 | − | 0.369736i | ||||
\(247\) | 1901.52 | + | 3293.52i | 0.489840 | + | 0.848428i | ||||
\(248\) | 246.058 | + | 426.186i | 0.0630029 | + | 0.109124i | ||||
\(249\) | 4731.96 | + | 4749.27i | 1.20432 | + | 1.20873i | ||||
\(250\) | 1167.43 | − | 2022.04i | 0.295338 | − | 0.511540i | ||||
\(251\) | 2960.32 | 0.744438 | 0.372219 | − | 0.928145i | \(-0.378597\pi\) | ||||
0.372219 | + | 0.928145i | \(0.378597\pi\) | |||||||
\(252\) | 1221.35 | + | 711.109i | 0.305310 | + | 0.177760i | ||||
\(253\) | 3110.25 | 0.772883 | ||||||||
\(254\) | 1766.70 | − | 3060.01i | 0.436427 | − | 0.755915i | ||||
\(255\) | −25.3586 | + | 6.74522i | −0.00622753 | + | 0.00165648i | ||||
\(256\) | −2288.69 | − | 3964.13i | −0.558763 | − | 0.967806i | ||||
\(257\) | −2997.84 | − | 5192.41i | −0.727627 | − | 1.26029i | −0.957884 | − | 0.287157i | \(-0.907290\pi\) |
0.230256 | − | 0.973130i | \(-0.426044\pi\) | |||||||
\(258\) | 9493.54 | − | 2525.21i | 2.29086 | − | 0.609352i | ||||
\(259\) | −505.087 | + | 874.836i | −0.121176 | + | 0.209883i | ||||
\(260\) | 719.496 | 0.171620 | ||||||||
\(261\) | 450.069 | − | 257.660i | 0.106738 | − | 0.0611064i | ||||
\(262\) | −8397.61 | −1.98017 | ||||||||
\(263\) | −891.843 | + | 1544.72i | −0.209100 | + | 0.362172i | −0.951431 | − | 0.307861i | \(-0.900387\pi\) |
0.742331 | + | 0.670033i | \(0.233720\pi\) | |||||||
\(264\) | 317.811 | + | 318.974i | 0.0740906 | + | 0.0743617i | ||||
\(265\) | −762.505 | − | 1320.70i | −0.176756 | − | 0.306150i | ||||
\(266\) | −1323.28 | − | 2291.98i | −0.305020 | − | 0.528310i | ||||
\(267\) | 1016.47 | − | 3765.99i | 0.232985 | − | 0.863202i | ||||
\(268\) | −15.1142 | + | 26.1786i | −0.00344496 | + | 0.00596684i | ||||
\(269\) | 6348.32 | 1.43890 | 0.719450 | − | 0.694545i | \(-0.244394\pi\) | ||||
0.719450 | + | 0.694545i | \(0.244394\pi\) | |||||||
\(270\) | −954.134 | + | 943.736i | −0.215062 | + | 0.212718i | ||||
\(271\) | −6712.35 | −1.50460 | −0.752299 | − | 0.658822i | \(-0.771055\pi\) | ||||
−0.752299 | + | 0.658822i | \(0.771055\pi\) | |||||||
\(272\) | −70.5188 | + | 122.142i | −0.0157200 | + | 0.0272278i | ||||
\(273\) | 375.082 | − | 1389.67i | 0.0831538 | − | 0.308083i | ||||
\(274\) | −4251.38 | − | 7363.61i | −0.937356 | − | 1.62355i | ||||
\(275\) | 2511.11 | + | 4349.38i | 0.550640 | + | 0.953736i | ||||
\(276\) | 2022.59 | + | 2029.99i | 0.441107 | + | 0.442721i | ||||
\(277\) | −1138.28 | + | 1971.56i | −0.246905 | + | 0.427653i | −0.962666 | − | 0.270693i | \(-0.912747\pi\) |
0.715760 | + | 0.698346i | \(0.246080\pi\) | |||||||
\(278\) | −9049.24 | −1.95229 | ||||||||
\(279\) | 23.6178 | − | 6466.37i | 0.00506795 | − | 1.38757i | ||||
\(280\) | 34.9724 | 0.00746430 | ||||||||
\(281\) | 742.994 | − | 1286.90i | 0.157734 | − | 0.273203i | −0.776317 | − | 0.630343i | \(-0.782914\pi\) |
0.934051 | + | 0.357139i | \(0.116248\pi\) | |||||||
\(282\) | 5822.12 | − | 1548.64i | 1.22944 | − | 0.327022i | ||||
\(283\) | 4505.10 | + | 7803.06i | 0.946291 | + | 1.63902i | 0.753146 | + | 0.657853i | \(0.228535\pi\) |
0.193144 | + | 0.981170i | \(0.438132\pi\) | |||||||
\(284\) | 2985.00 | + | 5170.17i | 0.623687 | + | 1.08026i | ||||
\(285\) | 1173.35 | − | 312.101i | 0.243870 | − | 0.0648677i | ||||
\(286\) | −3282.85 | + | 5686.07i | −0.678739 | + | 1.17561i | ||||
\(287\) | 505.973 | 0.104065 | ||||||||
\(288\) | −24.7239 | + | 6769.23i | −0.00505858 | + | 1.38500i | ||||
\(289\) | −4908.69 | −0.999122 | ||||||||
\(290\) | −91.8660 | + | 159.117i | −0.0186019 | + | 0.0322195i | ||||
\(291\) | 1538.70 | + | 1544.33i | 0.309966 | + | 0.311101i | ||||
\(292\) | −1660.13 | − | 2875.44i | −0.332712 | − | 0.576274i | ||||
\(293\) | −3767.56 | − | 6525.60i | −0.751205 | − | 1.30113i | −0.947239 | − | 0.320528i | \(-0.896140\pi\) |
0.196034 | − | 0.980597i | \(-0.437194\pi\) | |||||||
\(294\) | −261.022 | + | 967.079i | −0.0517792 | + | 0.191841i | ||||
\(295\) | 181.892 | − | 315.047i | 0.0358989 | − | 0.0621788i | ||||
\(296\) | −296.529 | −0.0582276 | ||||||||
\(297\) | −1500.00 | − | 5723.32i | −0.293060 | − | 1.11818i | ||||
\(298\) | 4656.24 | 0.905129 | ||||||||
\(299\) | 1459.28 | − | 2527.54i | 0.282248 | − | 0.488868i | ||||
\(300\) | −1205.77 | + | 4467.35i | −0.232051 | + | 0.859741i | ||||
\(301\) | 1681.92 | + | 2913.17i | 0.322074 | + | 0.557848i | ||||
\(302\) | 6762.09 | + | 11712.3i | 1.28846 | + | 2.23167i | ||||
\(303\) | 3321.39 | + | 3333.54i | 0.629732 | + | 0.632036i | ||||
\(304\) | 3262.91 | − | 5651.52i | 0.615594 | − | 1.06624i | ||||
\(305\) | 1533.53 | 0.287901 | ||||||||
\(306\) | 191.465 | − | 109.612i | 0.0357690 | − | 0.0204774i | ||||
\(307\) | 2765.48 | 0.514119 | 0.257059 | − | 0.966396i | \(-0.417246\pi\) | ||||
0.257059 | + | 0.966396i | \(0.417246\pi\) | |||||||
\(308\) | 1103.73 | − | 1911.72i | 0.204192 | − | 0.353670i | ||||
\(309\) | −10383.2 | + | 2761.87i | −1.91159 | + | 0.508470i | ||||
\(310\) | 1145.47 | + | 1984.00i | 0.209865 | + | 0.363496i | ||||
\(311\) | 1507.11 | + | 2610.39i | 0.274792 | + | 0.475953i | 0.970083 | − | 0.242775i | \(-0.0780578\pi\) |
−0.695291 | + | 0.718728i | \(0.744724\pi\) | |||||||
\(312\) | 408.326 | − | 108.612i | 0.0740926 | − | 0.0197081i | ||||
\(313\) | −1374.07 | + | 2379.96i | −0.248138 | + | 0.429787i | −0.963009 | − | 0.269469i | \(-0.913152\pi\) |
0.714871 | + | 0.699256i | \(0.246485\pi\) | |||||||
\(314\) | 82.0722 | 0.0147503 | ||||||||
\(315\) | −397.129 | − | 231.221i | −0.0710340 | − | 0.0413581i | ||||
\(316\) | −4303.71 | −0.766147 | ||||||||
\(317\) | −1966.70 | + | 3406.42i | −0.348457 | + | 0.603545i | −0.985976 | − | 0.166890i | \(-0.946627\pi\) |
0.637519 | + | 0.770435i | \(0.279961\pi\) | |||||||
\(318\) | 9049.80 | + | 9082.91i | 1.59587 | + | 1.60171i | ||||
\(319\) | −405.014 | − | 701.505i | −0.0710860 | − | 0.123125i | ||||
\(320\) | −538.688 | − | 933.035i | −0.0941049 | − | 0.162994i | ||||
\(321\) | 2340.10 | − | 8669.99i | 0.406889 | − | 1.50751i | ||||
\(322\) | −1015.52 | + | 1758.93i | −0.175754 | + | 0.304414i | ||||
\(323\) | −199.599 | −0.0343839 | ||||||||
\(324\) | 2760.04 | − | 4700.88i | 0.473257 | − | 0.806050i | ||||
\(325\) | 4712.70 | 0.804349 | ||||||||
\(326\) | −3254.47 | + | 5636.90i | −0.552909 | + | 0.957666i | ||||
\(327\) | 1252.76 | − | 4641.45i | 0.211859 | − | 0.784931i | ||||
\(328\) | 74.2622 | + | 128.626i | 0.0125014 | + | 0.0216530i | ||||
\(329\) | 1031.47 | + | 1786.57i | 0.172848 | + | 0.299382i | ||||
\(330\) | 1479.49 | + | 1484.91i | 0.246798 | + | 0.247701i | ||||
\(331\) | −2302.21 | + | 3987.55i | −0.382299 | + | 0.662161i | −0.991390 | − | 0.130939i | \(-0.958201\pi\) |
0.609092 | + | 0.793100i | \(0.291534\pi\) | |||||||
\(332\) | 9648.00 | 1.59489 | ||||||||
\(333\) | 3367.23 | + | 1960.50i | 0.554123 | + | 0.322627i | ||||
\(334\) | 7715.78 | 1.26404 | ||||||||
\(335\) | 4.91447 | − | 8.51211i | 0.000801511 | − | 0.00138826i | ||||
\(336\) | −2386.94 | + | 634.908i | −0.387554 | + | 0.103087i | ||||
\(337\) | −1386.37 | − | 2401.26i | −0.224096 | − | 0.388146i | 0.731952 | − | 0.681356i | \(-0.238610\pi\) |
−0.956048 | + | 0.293211i | \(0.905276\pi\) | |||||||
\(338\) | −1241.16 | − | 2149.76i | −0.199735 | − | 0.345951i | ||||
\(339\) | −10983.2 | + | 2921.45i | −1.75966 | + | 0.468057i | ||||
\(340\) | −18.8811 | + | 32.7030i | −0.00301168 | + | 0.00521638i | ||||
\(341\) | −10100.1 | −1.60397 | ||||||||
\(342\) | −8859.08 | + | 5071.74i | −1.40071 | + | 0.801896i | ||||
\(343\) | −343.000 | −0.0539949 | ||||||||
\(344\) | −493.715 | + | 855.139i | −0.0773817 | + | 0.134029i | ||||
\(345\) | −657.656 | − | 660.062i | −0.102629 | − | 0.103004i | ||||
\(346\) | −53.7854 | − | 93.1590i | −0.00835699 | − | 0.0144747i | ||||
\(347\) | −4211.45 | − | 7294.44i | −0.651534 | − | 1.12849i | −0.982751 | − | 0.184935i | \(-0.940792\pi\) |
0.331217 | − | 0.943555i | \(-0.392541\pi\) | |||||||
\(348\) | 194.477 | − | 720.532i | 0.0299571 | − | 0.110990i | ||||
\(349\) | 1939.99 | − | 3360.15i | 0.297550 | − | 0.515372i | −0.678025 | − | 0.735039i | \(-0.737164\pi\) |
0.975575 | + | 0.219667i | \(0.0704971\pi\) | |||||||
\(350\) | −3279.59 | −0.500862 | ||||||||
\(351\) | −5354.83 | − | 1466.31i | −0.814301 | − | 0.222980i | ||||
\(352\) | 10573.2 | 1.60100 | ||||||||
\(353\) | −1962.36 | + | 3398.91i | −0.295881 | + | 0.512481i | −0.975190 | − | 0.221372i | \(-0.928947\pi\) |
0.679308 | + | 0.733853i | \(0.262280\pi\) | |||||||
\(354\) | −797.014 | + | 2952.92i | −0.119663 | + | 0.443349i | ||||
\(355\) | −970.588 | − | 1681.11i | −0.145108 | − | 0.251335i | ||||
\(356\) | −2806.76 | − | 4861.45i | −0.417859 | − | 0.723754i | ||||
\(357\) | 53.3212 | + | 53.5163i | 0.00790492 | + | 0.00793385i | ||||
\(358\) | 257.357 | − | 445.755i | 0.0379937 | − | 0.0658069i | ||||
\(359\) | 6623.52 | 0.973749 | 0.486874 | − | 0.873472i | \(-0.338137\pi\) | ||||
0.486874 | + | 0.873472i | \(0.338137\pi\) | |||||||
\(360\) | 0.492682 | − | 134.893i | 7.21296e−5 | − | 0.0197485i | ||||
\(361\) | 2376.46 | 0.346473 | ||||||||
\(362\) | 4839.24 | − | 8381.82i | 0.702611 | − | 1.21696i | ||||
\(363\) | −2247.17 | + | 597.732i | −0.324920 | + | 0.0864265i | ||||
\(364\) | −1035.71 | − | 1793.90i | −0.149137 | − | 0.258313i | ||||
\(365\) | 539.801 | + | 934.963i | 0.0774095 | + | 0.134077i | ||||
\(366\) | −12460.2 | + | 3314.32i | −1.77952 | + | 0.473340i | ||||
\(367\) | 4605.97 | − | 7977.77i | 0.655122 | − | 1.13470i | −0.326742 | − | 0.945114i | \(-0.605951\pi\) |
0.981863 | − | 0.189590i | \(-0.0607159\pi\) | |||||||
\(368\) | −5008.09 | −0.709415 | ||||||||
\(369\) | 7.12801 | − | 1951.60i | 0.00100561 | − | 0.275328i | ||||
\(370\) | −1380.42 | −0.193958 | ||||||||
\(371\) | −2195.24 | + | 3802.26i | −0.307199 | + | 0.532085i | ||||
\(372\) | −6568.11 | − | 6592.14i | −0.915431 | − | 0.918781i | ||||
\(373\) | 3763.16 | + | 6517.99i | 0.522384 | + | 0.904796i | 0.999661 | + | 0.0260427i | \(0.00829058\pi\) |
−0.477277 | + | 0.878753i | \(0.658376\pi\) | |||||||
\(374\) | −172.298 | − | 298.429i | −0.0238217 | − | 0.0412604i | ||||
\(375\) | 803.588 | − | 2977.27i | 0.110659 | − | 0.409988i | ||||
\(376\) | −302.781 | + | 524.433i | −0.0415286 | + | 0.0719297i | ||||
\(377\) | −760.104 | −0.103839 | ||||||||
\(378\) | 3726.46 | + | 1020.42i | 0.507059 | + | 0.138848i | ||||
\(379\) | 9542.86 | 1.29336 | 0.646681 | − | 0.762761i | \(-0.276157\pi\) | ||||
0.646681 | + | 0.762761i | \(0.276157\pi\) | |||||||
\(380\) | 873.628 | − | 1513.17i | 0.117937 | − | 0.204273i | ||||
\(381\) | 1216.09 | − | 4505.59i | 0.163523 | − | 0.605849i | ||||
\(382\) | −2575.71 | − | 4461.27i | −0.344987 | − | 0.597535i | ||||
\(383\) | 1896.64 | + | 3285.08i | 0.253039 | + | 0.438276i | 0.964361 | − | 0.264590i | \(-0.0852366\pi\) |
−0.711322 | + | 0.702866i | \(0.751903\pi\) | |||||||
\(384\) | −962.553 | − | 966.075i | −0.127917 | − | 0.128385i | ||||
\(385\) | −358.885 | + | 621.607i | −0.0475077 | + | 0.0822857i | ||||
\(386\) | −3398.08 | −0.448077 | ||||||||
\(387\) | 11260.1 | − | 6446.32i | 1.47903 | − | 0.846731i | ||||
\(388\) | 3137.26 | 0.410490 | ||||||||
\(389\) | 3089.58 | − | 5351.31i | 0.402694 | − | 0.697486i | −0.591356 | − | 0.806411i | \(-0.701407\pi\) |
0.994050 | + | 0.108924i | \(0.0347406\pi\) | |||||||
\(390\) | 1900.86 | − | 505.616i | 0.246805 | − | 0.0656483i | ||||
\(391\) | 76.5890 | + | 132.656i | 0.00990607 | + | 0.0171578i | ||||
\(392\) | −50.3425 | − | 87.1958i | −0.00648643 | − | 0.0112348i | ||||
\(393\) | −10718.6 | + | 2851.08i | −1.37579 | + | 0.365949i | ||||
\(394\) | 5820.41 | − | 10081.2i | 0.744233 | − | 1.28905i | ||||
\(395\) | 1399.37 | 0.178253 | ||||||||
\(396\) | −7358.19 | − | 4284.16i | −0.933744 | − | 0.543654i | ||||
\(397\) | 179.912 | 0.0227444 | 0.0113722 | − | 0.999935i | \(-0.496380\pi\) | ||||
0.0113722 | + | 0.999935i | \(0.496380\pi\) | |||||||
\(398\) | −3068.32 | + | 5314.49i | −0.386435 | + | 0.669325i | ||||
\(399\) | −2467.17 | − | 2476.20i | −0.309557 | − | 0.310689i | ||||
\(400\) | −4043.38 | − | 7003.33i | −0.505422 | − | 0.875417i | ||||
\(401\) | −3651.73 | − | 6324.98i | −0.454760 | − | 0.787667i | 0.543915 | − | 0.839140i | \(-0.316941\pi\) |
−0.998674 | + | 0.0514737i | \(0.983608\pi\) | |||||||
\(402\) | −21.5342 | + | 79.7835i | −0.00267171 | + | 0.00989861i | ||||
\(403\) | −4738.82 | + | 8207.87i | −0.585750 | + | 1.01455i | ||||
\(404\) | 6771.98 | 0.833957 | ||||||||
\(405\) | −897.440 | + | 1528.52i | −0.110109 | + | 0.187537i | ||||
\(406\) | 528.961 | 0.0646599 | ||||||||
\(407\) | 3042.95 | − | 5270.55i | 0.370599 | − | 0.641896i | ||||
\(408\) | −5.77864 | + | 21.4097i | −0.000701189 | + | 0.00259789i | ||||
\(409\) | 1055.98 | + | 1829.01i | 0.127664 | + | 0.221121i | 0.922771 | − | 0.385348i | \(-0.125919\pi\) |
−0.795107 | + | 0.606469i | \(0.792585\pi\) | |||||||
\(410\) | 345.710 | + | 598.787i | 0.0416424 | + | 0.0721268i | ||||
\(411\) | −7926.46 | − | 7955.47i | −0.951298 | − | 0.954779i | ||||
\(412\) | −7730.96 | + | 13390.4i | −0.924459 | + | 1.60121i | ||||
\(413\) | −1047.33 | −0.124784 | ||||||||
\(414\) | 6770.10 | + | 3941.76i | 0.803701 | + | 0.467939i | ||||
\(415\) | −3137.10 | −0.371070 | ||||||||
\(416\) | 4960.77 | − | 8592.30i | 0.584667 | − | 1.01267i | ||||
\(417\) | −11550.4 | + | 3072.32i | −1.35641 | + | 0.360796i | ||||
\(418\) | 7972.24 | + | 13808.3i | 0.932859 | + | 1.61576i | ||||
\(419\) | 2862.87 | + | 4958.63i | 0.333795 | + | 0.578151i | 0.983253 | − | 0.182247i | \(-0.0583372\pi\) |
−0.649457 | + | 0.760398i | \(0.725004\pi\) | |||||||
\(420\) | −639.091 | + | 169.994i | −0.0742487 | + | 0.0197496i | ||||
\(421\) | −2633.26 | + | 4560.94i | −0.304839 | + | 0.527997i | −0.977225 | − | 0.212204i | \(-0.931936\pi\) |
0.672386 | + | 0.740200i | \(0.265269\pi\) | |||||||
\(422\) | −9860.59 | −1.13745 | ||||||||
\(423\) | 6905.53 | − | 3953.35i | 0.793755 | − | 0.454417i | ||||
\(424\) | −1288.79 | −0.147616 | ||||||||
\(425\) | −123.671 | + | 214.205i | −0.0141151 | + | 0.0244481i | ||||
\(426\) | 11519.4 | + | 11561.6i | 1.31014 | + | 1.31493i | ||||
\(427\) | −2207.51 | − | 3823.51i | −0.250184 | − | 0.433332i | ||||
\(428\) | −6461.67 | − | 11191.9i | −0.729758 | − | 1.26398i | ||||
\(429\) | −2259.73 | + | 8372.22i | −0.254314 | + | 0.942225i | ||||
\(430\) | −2298.37 | + | 3980.89i | −0.257761 | + | 0.446455i | ||||
\(431\) | 15827.4 | 1.76886 | 0.884430 | − | 0.466672i | \(-0.154547\pi\) | ||||
0.884430 | + | 0.466672i | \(0.154547\pi\) | |||||||
\(432\) | 2415.29 | + | 9215.64i | 0.268994 | + | 1.02636i | ||||
\(433\) | 4537.27 | 0.503574 | 0.251787 | − | 0.967783i | \(-0.418982\pi\) | ||||
0.251787 | + | 0.967783i | \(0.418982\pi\) | |||||||
\(434\) | 3297.77 | − | 5711.91i | 0.364742 | − | 0.631752i | ||||
\(435\) | −63.2352 | + | 234.285i | −0.00696988 | + | 0.0258232i | ||||
\(436\) | −3459.23 | − | 5991.56i | −0.379970 | − | 0.658128i | ||||
\(437\) | −3543.78 | − | 6138.00i | −0.387922 | − | 0.671900i | ||||
\(438\) | −6406.64 | − | 6430.08i | −0.698907 | − | 0.701464i | ||||
\(439\) | −4463.41 | + | 7730.85i | −0.485255 | + | 0.840486i | −0.999856 | − | 0.0169432i | \(-0.994607\pi\) |
0.514601 | + | 0.857429i | \(0.327940\pi\) | |||||||
\(440\) | −210.696 | −0.0228285 | ||||||||
\(441\) | −4.83209 | + | 1322.99i | −0.000521768 | + | 0.142856i | ||||
\(442\) | −323.358 | −0.0347977 | ||||||||
\(443\) | 3222.48 | − | 5581.50i | 0.345609 | − | 0.598612i | −0.639856 | − | 0.768495i | \(-0.721006\pi\) |
0.985464 | + | 0.169884i | \(0.0543392\pi\) | |||||||
\(444\) | 5418.81 | − | 1441.36i | 0.579201 | − | 0.154063i | ||||
\(445\) | 912.632 | + | 1580.73i | 0.0972201 | + | 0.168390i | ||||
\(446\) | 7963.57 | + | 13793.3i | 0.845484 | + | 1.46442i | ||||
\(447\) | 5943.18 | − | 1580.84i | 0.628866 | − | 0.167274i | ||||
\(448\) | −1550.87 | + | 2686.19i | −0.163553 | + | 0.283282i | ||||
\(449\) | −6202.27 | −0.651901 | −0.325950 | − | 0.945387i | \(-0.605684\pi\) | ||||
−0.325950 | + | 0.945387i | \(0.605684\pi\) | |||||||
\(450\) | −46.2021 | + | 12649.8i | −0.00483997 | + | 1.32515i | ||||
\(451\) | −3048.29 | −0.318267 | ||||||||
\(452\) | −8177.67 | + | 14164.1i | −0.850985 | + | 1.47395i | ||||
\(453\) | 12607.5 | + | 12653.7i | 1.30762 | + | 1.31241i | ||||
\(454\) | −1234.28 | − | 2137.84i | −0.127594 | − | 0.221000i | ||||
\(455\) | 336.766 | + | 583.295i | 0.0346985 | + | 0.0600996i | ||||
\(456\) | 267.378 | − | 990.627i | 0.0274586 | − | 0.101733i | ||||
\(457\) | 1550.46 | − | 2685.48i | 0.158704 | − | 0.274883i | −0.775698 | − | 0.631105i | \(-0.782602\pi\) |
0.934402 | + | 0.356222i | \(0.115935\pi\) | |||||||
\(458\) | 3891.39 | 0.397015 | ||||||||
\(459\) | 207.170 | − | 204.912i | 0.0210672 | − | 0.0208376i | ||||
\(460\) | −1340.89 | −0.135912 | ||||||||
\(461\) | −2174.51 | + | 3766.36i | −0.219690 | + | 0.380514i | −0.954713 | − | 0.297528i | \(-0.903838\pi\) |
0.735023 | + | 0.678042i | \(0.237171\pi\) | |||||||
\(462\) | 1572.56 | − | 5826.28i | 0.158359 | − | 0.586717i | ||||
\(463\) | 3722.76 | + | 6448.00i | 0.373674 | + | 0.647223i | 0.990128 | − | 0.140169i | \(-0.0447645\pi\) |
−0.616453 | + | 0.787391i | \(0.711431\pi\) | |||||||
\(464\) | 652.151 | + | 1129.56i | 0.0652486 | + | 0.113014i | ||||
\(465\) | 2135.65 | + | 2143.47i | 0.212986 | + | 0.213766i | ||||
\(466\) | −6148.18 | + | 10649.0i | −0.611178 | + | 1.05859i | ||||
\(467\) | 15424.1 | 1.52836 | 0.764178 | − | 0.645006i | \(-0.223145\pi\) | ||||
0.764178 | + | 0.645006i | \(0.223145\pi\) | |||||||
\(468\) | −6933.86 | + | 3969.57i | −0.684867 | + | 0.392080i | ||||
\(469\) | −28.2973 | −0.00278603 | ||||||||
\(470\) | −1409.53 | + | 2441.37i | −0.138333 | + | 0.239600i | ||||
\(471\) | 104.756 | − | 27.8644i | 0.0102482 | − | 0.00272596i | ||||
\(472\) | −153.718 | − | 266.247i | −0.0149903 | − | 0.0259640i | ||||
\(473\) | −10132.9 | − | 17550.8i | −0.985016 | − | 1.70610i | ||||
\(474\) | −11370.1 | + | 3024.37i | −1.10179 | + | 0.293067i | ||||
\(475\) | 5722.27 | − | 9911.25i | 0.552749 | − | 0.957389i | ||||
\(476\) | 108.717 | 0.0104685 | ||||||||
\(477\) | 14634.8 | + | 8520.85i | 1.40479 | + | 0.817910i | ||||
\(478\) | 11901.0 | 1.13878 | ||||||||
\(479\) | −4325.21 | + | 7491.49i | −0.412576 | + | 0.714603i | −0.995171 | − | 0.0981602i | \(-0.968704\pi\) |
0.582595 | + | 0.812763i | \(0.302038\pi\) | |||||||
\(480\) | −2235.68 | − | 2243.86i | −0.212592 | − | 0.213370i | ||||
\(481\) | −2855.41 | − | 4945.71i | −0.270677 | − | 0.468826i | ||||
\(482\) | −11013.4 | − | 19075.8i | −1.04076 | − | 1.80265i | ||||
\(483\) | −699.024 | + | 2589.87i | −0.0658524 | + | 0.243981i | ||||
\(484\) | −1673.16 | + | 2898.00i | −0.157134 | + | 0.272164i | ||||
\(485\) | −1020.10 | −0.0955055 | ||||||||
\(486\) | 3988.36 | − | 14359.0i | 0.372254 | − | 1.34020i | ||||
\(487\) | −13668.2 | −1.27179 | −0.635897 | − | 0.771774i | \(-0.719370\pi\) | ||||
−0.635897 | + | 0.771774i | \(0.719370\pi\) | |||||||
\(488\) | 647.997 | − | 1122.36i | 0.0601095 | − | 0.104113i | ||||
\(489\) | −2240.18 | + | 8299.83i | −0.207167 | + | 0.767548i | ||||
\(490\) | −234.357 | − | 405.919i | −0.0216065 | − | 0.0374236i | ||||
\(491\) | 589.304 | + | 1020.70i | 0.0541648 | + | 0.0938162i | 0.891836 | − | 0.452358i | \(-0.149417\pi\) |
−0.837672 | + | 0.546174i | \(0.816084\pi\) | |||||||
\(492\) | −1982.30 | − | 1989.56i | −0.181644 | − | 0.182309i | ||||
\(493\) | 19.9467 | − | 34.5488i | 0.00182222 | − | 0.00315618i | ||||
\(494\) | 14961.8 | 1.36268 | ||||||||
\(495\) | 2392.55 | + | 1393.02i | 0.217247 | + | 0.126488i | ||||
\(496\) | 16263.2 | 1.47225 | ||||||||
\(497\) | −2794.30 | + | 4839.88i | −0.252196 | + | 0.436817i | ||||
\(498\) | 25489.4 | − | 6780.00i | 2.29359 | − | 0.610078i | ||||
\(499\) | 19.2536 | + | 33.3482i | 0.00172727 | + | 0.00299173i | 0.866888 | − | 0.498503i | \(-0.166117\pi\) |
−0.865160 | + | 0.501495i | \(0.832784\pi\) | |||||||
\(500\) | −2218.93 | − | 3843.31i | −0.198467 | − | 0.343756i | ||||
\(501\) | 9848.36 | − | 2619.59i | 0.878228 | − | 0.233602i | ||||
\(502\) | 5823.21 | − | 10086.1i | 0.517734 | − | 0.896742i | ||||
\(503\) | 4489.37 | 0.397954 | 0.198977 | − | 0.980004i | \(-0.436238\pi\) | ||||
0.198977 | + | 0.980004i | \(0.436238\pi\) | |||||||
\(504\) | −337.033 | + | 192.949i | −0.0297870 | + | 0.0170528i | ||||
\(505\) | −2201.95 | −0.194030 | ||||||||
\(506\) | 6118.12 | − | 10596.9i | 0.537517 | − | 0.931007i | ||||
\(507\) | −2314.08 | − | 2322.55i | −0.202706 | − | 0.203448i | ||||
\(508\) | −3357.98 | − | 5816.19i | −0.293280 | − | 0.507976i | ||||
\(509\) | 6578.27 | + | 11393.9i | 0.572842 | + | 0.992192i | 0.996272 | + | 0.0862632i | \(0.0274926\pi\) |
−0.423430 | + | 0.905929i | \(0.639174\pi\) | |||||||
\(510\) | −26.9010 | + | 99.6677i | −0.00233568 | + | 0.00865365i | ||||
\(511\) | 1554.08 | − | 2691.74i | 0.134537 | − | 0.233025i | ||||
\(512\) | −15908.6 | −1.37318 | ||||||||
\(513\) | −9585.75 | + | 9481.29i | −0.824993 | + | 0.816002i | ||||
\(514\) | −23588.0 | −2.02417 | ||||||||
\(515\) | 2513.76 | − | 4353.97i | 0.215087 | − | 0.372541i | ||||
\(516\) | 4865.56 | − | 18026.8i | 0.415105 | − | 1.53795i | ||||
\(517\) | −6214.24 | − | 10763.4i | −0.528631 | − | 0.915616i | ||||
\(518\) | 1987.10 | + | 3441.75i | 0.168548 | + | 0.291934i | ||||
\(519\) | −100.280 | − | 100.647i | −0.00848130 | − | 0.00851233i | ||||
\(520\) | −98.8550 | + | 171.222i | −0.00833669 | + | 0.0144396i | ||||
\(521\) | 2198.40 | 0.184863 | 0.0924317 | − | 0.995719i | \(-0.470536\pi\) | ||||
0.0924317 | + | 0.995719i | \(0.470536\pi\) | |||||||
\(522\) | 7.45187 | − | 2040.27i | 0.000624826 | − | 0.171073i | ||||
\(523\) | −7784.24 | −0.650824 | −0.325412 | − | 0.945572i | \(-0.605503\pi\) | ||||
−0.325412 | + | 0.945572i | \(0.605503\pi\) | |||||||
\(524\) | −7980.69 | + | 13823.0i | −0.665340 | + | 1.15240i | ||||
\(525\) | −4186.05 | + | 1113.46i | −0.347989 | + | 0.0925625i | ||||
\(526\) | 3508.66 | + | 6077.18i | 0.290846 | + | 0.503760i | ||||
\(527\) | −248.713 | − | 430.784i | −0.0205581 | − | 0.0356077i | ||||
\(528\) | 14380.4 | − | 3825.08i | 1.18528 | − | 0.315275i | ||||
\(529\) | 3363.91 | − | 5826.46i | 0.276478 | − | 0.478874i | ||||
\(530\) | −5999.65 | −0.491713 | ||||||||
\(531\) | −14.7545 | + | 4039.67i | −0.00120582 | + | 0.330145i | ||||
\(532\) | −5030.32 | −0.409947 | ||||||||
\(533\) | −1430.21 | + | 2477.20i | −0.116228 | + | 0.201312i | ||||
\(534\) | −10831.6 | − | 10871.2i | −0.877769 | − | 0.880981i | ||||
\(535\) | 2101.05 | + | 3639.12i | 0.169787 | + | 0.294080i | ||||
\(536\) | −4.15323 | − | 7.19361i | −0.000334687 | − | 0.000579695i | ||||
\(537\) | 177.149 | − | 656.334i | 0.0142357 | − | 0.0527428i | ||||
\(538\) | 12487.7 | − | 21629.3i | 1.00071 | − | 1.73328i | ||||
\(539\) | 2066.44 | 0.165136 | ||||||||
\(540\) | 646.682 | + | 2467.45i | 0.0515348 | + | 0.196633i | ||||
\(541\) | −8493.26 | −0.674961 | −0.337480 | − | 0.941333i | \(-0.609575\pi\) | ||||
−0.337480 | + | 0.941333i | \(0.609575\pi\) | |||||||
\(542\) | −13203.8 | + | 22869.6i | −1.04640 | + | 1.81242i | ||||
\(543\) | 3331.05 | − | 12341.5i | 0.263258 | − | 0.975364i | ||||
\(544\) | 260.362 | + | 450.960i | 0.0205201 | + | 0.0355418i | ||||
\(545\) | 1124.79 | + | 1948.19i | 0.0884047 | + | 0.153121i | ||||
\(546\) | −3996.91 | − | 4011.53i | −0.313282 | − | 0.314428i | ||||
\(547\) | −3663.38 | + | 6345.16i | −0.286352 | + | 0.495977i | −0.972936 | − | 0.231074i | \(-0.925776\pi\) |
0.686584 | + | 0.727051i | \(0.259109\pi\) | |||||||
\(548\) | −16161.3 | −1.25981 | ||||||||
\(549\) | −14778.8 | + | 8460.75i | −1.14890 | + | 0.657734i | ||||
\(550\) | 19758.3 | 1.53181 | ||||||||
\(551\) | −922.936 | + | 1598.57i | −0.0713583 | + | 0.123596i | ||||
\(552\) | −760.980 | + | 202.415i | −0.0586765 | + | 0.0156075i | ||||
\(553\) | −2014.39 | − | 3489.02i | −0.154901 | − | 0.268297i | ||||
\(554\) | 4478.20 | + | 7756.47i | 0.343431 | + | 0.594839i | ||||
\(555\) | −1761.95 | + | 468.667i | −0.134758 | + | 0.0358447i | ||||
\(556\) | −8599.97 | + | 14895.6i | −0.655971 | + | 1.13618i | ||||
\(557\) | 7394.34 | 0.562492 | 0.281246 | − | 0.959636i | \(-0.409252\pi\) | ||||
0.281246 | + | 0.959636i | \(0.409252\pi\) | |||||||
\(558\) | −21985.1 | − | 12800.4i | −1.66792 | − | 0.971116i | ||||
\(559\) | −19016.8 | −1.43887 | ||||||||
\(560\) | 577.873 | − | 1000.91i | 0.0436064 | − | 0.0755286i | ||||
\(561\) | −321.240 | − | 322.415i | −0.0241760 | − | 0.0242645i | ||||
\(562\) | −2923.06 | − | 5062.90i | −0.219399 | − | 0.380010i | ||||
\(563\) | 1437.18 | + | 2489.27i | 0.107584 | + | 0.186341i | 0.914791 | − | 0.403927i | \(-0.132355\pi\) |
−0.807207 | + | 0.590269i | \(0.799022\pi\) | |||||||
\(564\) | 2983.91 | − | 11055.3i | 0.222776 | − | 0.825378i | ||||
\(565\) | 2659.01 | − | 4605.55i | 0.197992 | − | 0.342932i | ||||
\(566\) | 35447.6 | 2.63247 | ||||||||
\(567\) | 5102.86 | + | 37.2759i | 0.377954 | + | 0.00276092i | ||||
\(568\) | −1640.49 | −0.121186 | ||||||||
\(569\) | −7864.92 | + | 13622.4i | −0.579463 | + | 1.00366i | 0.416078 | + | 0.909329i | \(0.363404\pi\) |
−0.995541 | + | 0.0943307i | \(0.969929\pi\) | |||||||
\(570\) | 1244.71 | − | 4611.63i | 0.0914654 | − | 0.338877i | ||||
\(571\) | 5659.53 | + | 9802.59i | 0.414788 | + | 0.718434i | 0.995406 | − | 0.0957422i | \(-0.0305224\pi\) |
−0.580618 | + | 0.814176i | \(0.697189\pi\) | |||||||
\(572\) | 6239.74 | + | 10807.6i | 0.456113 | + | 0.790011i | ||||
\(573\) | −4802.27 | − | 4819.84i | −0.350118 | − | 0.351399i | ||||
\(574\) | 995.292 | − | 1723.90i | 0.0723740 | − | 0.125355i | ||||
\(575\) | −8782.86 | −0.636992 | ||||||||
\(576\) | 10339.1 | + | 6019.74i | 0.747910 | + | 0.435456i | ||||
\(577\) | 1090.45 | 0.0786758 | 0.0393379 | − | 0.999226i | \(-0.487475\pi\) | ||||
0.0393379 | + | 0.999226i | \(0.487475\pi\) | |||||||
\(578\) | −9655.81 | + | 16724.3i | −0.694859 | + | 1.20353i | ||||
\(579\) | −4337.28 | + | 1153.69i | −0.311315 | + | 0.0828076i | ||||
\(580\) | 174.610 | + | 302.434i | 0.0125005 | + | 0.0216515i | ||||
\(581\) | 4515.82 | + | 7821.63i | 0.322458 | + | 0.558513i | ||||
\(582\) | 8288.43 | − | 2204.66i | 0.590321 | − | 0.157021i | ||||
\(583\) | 13225.5 | − | 22907.2i | 0.939525 | − | 1.62730i | ||||
\(584\) | 912.375 | 0.0646478 | ||||||||
\(585\) | 2254.58 | − | 1290.73i | 0.159343 | − | 0.0912222i | ||||
\(586\) | −29644.4 | −2.08976 | ||||||||
\(587\) | −13048.0 | + | 22599.8i | −0.917458 | + | 1.58908i | −0.114197 | + | 0.993458i | \(0.536429\pi\) |
−0.803262 | + | 0.595626i | \(0.796904\pi\) | |||||||
\(588\) | 1343.81 | + | 1348.72i | 0.0942477 | + | 0.0945926i | ||||
\(589\) | 11508.0 | + | 19932.4i | 0.805055 | + | 1.39440i | ||||
\(590\) | −715.596 | − | 1239.45i | −0.0499333 | − | 0.0864869i | ||||
\(591\) | 4006.43 | − | 14843.7i | 0.278853 | − | 1.03314i | ||||
\(592\) | −4899.74 | + | 8486.60i | −0.340166 | + | 0.589184i | ||||
\(593\) | −2675.40 | −0.185271 | −0.0926354 | − | 0.995700i | \(-0.529529\pi\) | ||||
−0.0926354 | + | 0.995700i | \(0.529529\pi\) | |||||||
\(594\) | −22450.5 | − | 6147.61i | −1.55077 | − | 0.424646i | ||||
\(595\) | −35.3498 | −0.00243563 | ||||||||
\(596\) | 4425.07 | − | 7664.45i | 0.304124 | − | 0.526758i | ||||
\(597\) | −2112.05 | + | 7825.10i | −0.144792 | + | 0.536449i | ||||
\(598\) | −5741.04 | − | 9943.78i | −0.392590 | − | 0.679986i | ||||
\(599\) | 2483.86 | + | 4302.18i | 0.169429 | + | 0.293459i | 0.938219 | − | 0.346042i | \(-0.112474\pi\) |
−0.768790 | + | 0.639501i | \(0.779141\pi\) | |||||||
\(600\) | −897.449 | − | 900.733i | −0.0610637 | − | 0.0612871i | ||||
\(601\) | 9440.30 | − | 16351.1i | 0.640728 | − | 1.10977i | −0.344542 | − | 0.938771i | \(-0.611966\pi\) |
0.985270 | − | 0.171003i | \(-0.0547009\pi\) | |||||||
\(602\) | 13233.9 | 0.895971 | ||||||||
\(603\) | −0.398645 | + | 109.146i | −2.69222e−5 | + | 0.00737110i | ||||
\(604\) | 25705.5 | 1.73169 | ||||||||
\(605\) | 544.037 | − | 942.300i | 0.0365591 | − | 0.0633222i | ||||
\(606\) | 17891.1 | − | 4758.92i | 1.19930 | − | 0.319006i | ||||
\(607\) | −11401.1 | − | 19747.2i | −0.762364 | − | 1.32045i | −0.941629 | − | 0.336653i | \(-0.890705\pi\) |
0.179265 | − | 0.983801i | \(-0.442628\pi\) | |||||||
\(608\) | −12047.0 | − | 20865.9i | −0.803567 | − | 1.39182i | ||||
\(609\) | 675.162 | − | 179.588i | 0.0449244 | − | 0.0119496i | ||||
\(610\) | 3016.59 | − | 5224.89i | 0.200227 | − | 0.346803i | ||||
\(611\) | −11662.5 | −0.772199 | ||||||||
\(612\) | 1.53157 | − | 419.333i | 0.000101160 | − | 0.0276969i | ||||
\(613\) | −16589.5 | −1.09306 | −0.546529 | − | 0.837440i | \(-0.684051\pi\) | ||||
−0.546529 | + | 0.837440i | \(0.684051\pi\) | |||||||
\(614\) | 5439.94 | − | 9422.26i | 0.357554 | − | 0.619302i | ||||
\(615\) | 644.556 | + | 646.914i | 0.0422618 | + | 0.0424164i | ||||
\(616\) | 303.294 | + | 525.321i | 0.0198378 | + | 0.0343601i | ||||
\(617\) | −12595.3 | − | 21815.7i | −0.821827 | − | 1.42345i | −0.904320 | − | 0.426855i | \(-0.859622\pi\) |
0.0824929 | − | 0.996592i | \(-0.473712\pi\) | |||||||
\(618\) | −11014.8 | + | 40809.5i | −0.716957 | + | 2.65631i | ||||
\(619\) | −6076.11 | + | 10524.1i | −0.394538 | + | 0.683361i | −0.993042 | − | 0.117759i | \(-0.962429\pi\) |
0.598504 | + | 0.801120i | \(0.295762\pi\) | |||||||
\(620\) | 4354.39 | 0.282059 | ||||||||
\(621\) | 9979.57 | + | 2732.70i | 0.644873 | + | 0.176586i | ||||
\(622\) | 11858.4 | 0.764437 | ||||||||
\(623\) | 2627.45 | − | 4550.88i | 0.168967 | − | 0.292660i | ||||
\(624\) | 3638.59 | − | 13480.9i | 0.233430 | − | 0.864851i | ||||
\(625\) | −6721.52 | − | 11642.0i | −0.430177 | − | 0.745088i | ||||
\(626\) | 5405.83 | + | 9363.17i | 0.345144 | + | 0.597808i | ||||
\(627\) | 14863.8 | + | 14918.2i | 0.946734 | + | 0.950198i | ||||
\(628\) | 77.9976 | − | 135.096i | 0.00495612 | − | 0.00858425i | ||||
\(629\) | 299.728 | 0.0189999 | ||||||||
\(630\) | −1568.98 | + | 898.225i | −0.0992216 | + | 0.0568034i | ||||
\(631\) | 13761.8 | 0.868224 | 0.434112 | − | 0.900859i | \(-0.357062\pi\) | ||||
0.434112 | + | 0.900859i | \(0.357062\pi\) | |||||||
\(632\) | 591.307 | − | 1024.17i | 0.0372167 | − | 0.0644612i | ||||
\(633\) | −12586.0 | + | 3347.78i | −0.790281 | + | 0.210209i | ||||
\(634\) | 7737.33 | + | 13401.4i | 0.484682 | + | 0.839494i | ||||
\(635\) | 1091.86 | + | 1891.16i | 0.0682351 | + | 0.118187i | ||||
\(636\) | 23551.5 | − | 6264.54i | 1.46836 | − | 0.390574i | ||||
\(637\) | 969.542 | − | 1679.30i | 0.0603056 | − | 0.104452i | ||||
\(638\) | −3186.79 | −0.197753 | ||||||||
\(639\) | 18628.6 | + | 10846.1i | 1.15326 | + | 0.671466i | ||||
\(640\) | 638.133 | 0.0394132 | ||||||||
\(641\) | 191.189 | − | 331.149i | 0.0117808 | − | 0.0204050i | −0.860075 | − | 0.510168i | \(-0.829583\pi\) |
0.871856 | + | 0.489763i | \(0.162917\pi\) | |||||||
\(642\) | −24936.3 | − | 25027.5i | −1.53296 | − | 1.53856i | ||||
\(643\) | 4008.98 | + | 6943.76i | 0.245877 | + | 0.425871i | 0.962378 | − | 0.271715i | \(-0.0875908\pi\) |
−0.716501 | + | 0.697586i | \(0.754257\pi\) | |||||||
\(644\) | 1930.20 | + | 3343.21i | 0.118107 | + | 0.204567i | ||||
\(645\) | −1582.06 | + | 5861.50i | −0.0965793 | + | 0.357824i | ||||
\(646\) | −392.629 | + | 680.053i | −0.0239130 | + | 0.0414185i | ||||
\(647\) | −548.646 | −0.0333377 | −0.0166689 | − | 0.999861i | \(-0.505306\pi\) | ||||
−0.0166689 | + | 0.999861i | \(0.505306\pi\) | |||||||
\(648\) | 739.477 | + | 1302.70i | 0.0448293 | + | 0.0789733i | ||||
\(649\) | 6309.76 | 0.381633 | ||||||||
\(650\) | 9270.28 | − | 16056.6i | 0.559400 | − | 0.968910i | ||||
\(651\) | 2269.99 | − | 8410.27i | 0.136664 | − | 0.506336i | ||||
\(652\) | 6185.79 | + | 10714.1i | 0.371555 | + | 0.643553i | ||||
\(653\) | −3408.56 | − | 5903.80i | −0.204268 | − | 0.353803i | 0.745631 | − | 0.666359i | \(-0.232148\pi\) |
−0.949899 | + | 0.312556i | \(0.898815\pi\) | |||||||
\(654\) | −13349.5 | − | 13398.4i | −0.798178 | − | 0.801099i | ||||
\(655\) | 2594.96 | − | 4494.61i | 0.154799 | − | 0.268121i | ||||
\(656\) | 4908.34 | 0.292132 | ||||||||
\(657\) | −10360.5 | − | 6032.18i | −0.615221 | − | 0.358201i | ||||
\(658\) | 8116.00 | 0.480843 | ||||||||
\(659\) | 15876.6 | − | 27499.0i | 0.938487 | − | 1.62551i | 0.170193 | − | 0.985411i | \(-0.445561\pi\) |
0.768294 | − | 0.640097i | \(-0.221106\pi\) | |||||||
\(660\) | 3850.28 | − | 1024.15i | 0.227079 | − | 0.0604014i | ||||
\(661\) | 9540.80 | + | 16525.1i | 0.561413 | + | 0.972396i | 0.997374 | + | 0.0724299i | \(0.0230754\pi\) |
−0.435961 | + | 0.899966i | \(0.643591\pi\) | |||||||
\(662\) | 9057.29 | + | 15687.7i | 0.531755 | + | 0.921026i | ||||
\(663\) | −412.731 | + | 109.784i | −0.0241767 | + | 0.00643083i | ||||
\(664\) | −1325.58 | + | 2295.98i | −0.0774739 | + | 0.134189i | ||||
\(665\) | 1635.64 | 0.0953793 | ||||||||
\(666\) | 13303.2 | − | 7615.98i | 0.774009 | − | 0.443113i | ||||
\(667\) | 1416.58 | 0.0822339 | ||||||||
\(668\) | 7332.72 | − | 12700.6i | 0.424718 | − | 0.735632i | ||||
\(669\) | 14847.6 | + | 14902.0i | 0.858060 | + | 0.861200i | ||||
\(670\) | −19.3344 | − | 33.4881i | −0.00111485 | − | 0.00193098i | ||||
\(671\) | 13299.4 | + | 23035.2i | 0.765152 | + | 1.32528i | ||||
\(672\) | −2376.31 | + | 8804.17i | −0.136411 | + | 0.505399i | ||||
\(673\) | 6635.90 | − | 11493.7i | 0.380082 | − | 0.658321i | −0.610992 | − | 0.791637i | \(-0.709229\pi\) |
0.991074 | + | 0.133316i | \(0.0425625\pi\) | |||||||
\(674\) | −10908.4 | −0.623408 | ||||||||
\(675\) | 4235.77 | + | 16161.8i | 0.241533 | + | 0.921580i | ||||
\(676\) | −4718.18 | −0.268444 | ||||||||
\(677\) | −2667.73 | + | 4620.64i | −0.151446 | + | 0.262312i | −0.931759 | − | 0.363077i | \(-0.881726\pi\) |
0.780313 | + | 0.625389i | \(0.215060\pi\) | |||||||
\(678\) | −11651.2 | + | 43167.5i | −0.659975 | + | 2.44519i | ||||
\(679\) | 1468.42 | + | 2543.38i | 0.0829937 | + | 0.143749i | ||||
\(680\) | −5.18833 | − | 8.98645i | −0.000292593 | − | 0.000506786i | ||||
\(681\) | −2301.25 | − | 2309.67i | −0.129492 | − | 0.129966i | ||||
\(682\) | −19867.8 | + | 34412.1i | −1.11551 | + | 1.93212i | ||||
\(683\) | −26921.0 | −1.50820 | −0.754101 | − | 0.656758i | \(-0.771927\pi\) | ||||
−0.754101 | + | 0.656758i | \(0.771927\pi\) | |||||||
\(684\) | −70.8658 | + | 19402.5i | −0.00396144 | + | 1.08461i | ||||
\(685\) | 5254.92 | 0.293110 | ||||||||
\(686\) | −674.710 | + | 1168.63i | −0.0375518 | + | 0.0650417i | ||||
\(687\) | 4966.94 | − | 1321.17i | 0.275838 | − | 0.0733709i | ||||
\(688\) | 16316.0 | + | 28260.1i | 0.904128 | + | 1.56600i | ||||
\(689\) | −12410.3 | − | 21495.4i | −0.686207 | − | 1.18855i | ||||
\(690\) | −3542.56 | + | 942.295i | −0.195453 | + | 0.0519892i | ||||
\(691\) | −2308.65 | + | 3998.69i | −0.127099 | + | 0.220141i | −0.922551 | − | 0.385875i | \(-0.873900\pi\) |
0.795453 | + | 0.606016i | \(0.207233\pi\) | |||||||
\(692\) | −204.460 | −0.0112318 | ||||||||
\(693\) | 29.1115 | − | 7970.52i | 0.00159575 | − | 0.436905i | ||||
\(694\) | −33137.1 | −1.81249 | ||||||||
\(695\) | 2796.33 | − | 4843.38i | 0.152620 | − | 0.264345i | ||||
\(696\) | 144.748 | + | 145.278i | 0.00788315 | + | 0.00791199i | ||||
\(697\) | −75.0635 | − | 130.014i | −0.00407924 | − | 0.00706546i | ||||
\(698\) | −7632.24 | − | 13219.4i | −0.413874 | − | 0.716852i | ||||
\(699\) | −4232.05 | + | 15679.6i | −0.229000 | + | 0.848438i | ||||
\(700\) | −3116.77 | + | 5398.41i | −0.168290 | + | 0.291487i | ||||
\(701\) | −15895.3 | −0.856430 | −0.428215 | − | 0.903677i | \(-0.640857\pi\) | ||||
−0.428215 | + | 0.903677i | \(0.640857\pi\) | |||||||
\(702\) | −15529.3 | + | 15360.0i | −0.834921 | + | 0.825822i | ||||
\(703\) | −13868.4 | −0.744036 | ||||||||
\(704\) | 9343.42 | − | 16183.3i | 0.500204 | − | 0.866378i | ||||
\(705\) | −970.235 | + | 3594.70i | −0.0518315 | + | 0.192034i | ||||
\(706\) | 7720.27 | + | 13371.9i | 0.411553 | + | 0.712831i | ||||
\(707\) | 3169.68 | + | 5490.05i | 0.168611 | + | 0.292043i | ||||
\(708\) | 4103.23 | + | 4118.25i | 0.217809 | + | 0.218606i | ||||
\(709\) | 1794.91 | − | 3108.88i | 0.0950766 | − | 0.164677i | −0.814564 | − | 0.580074i | \(-0.803024\pi\) |
0.909641 | + | 0.415396i | \(0.136357\pi\) | |||||||
\(710\) | −7636.92 | −0.403674 | ||||||||
\(711\) | −13485.9 | + | 7720.57i | −0.711339 | + | 0.407235i | ||||
\(712\) | 1542.54 | 0.0811924 | ||||||||
\(713\) | 8831.54 | − | 15296.7i | 0.463876 | − | 0.803457i | ||||
\(714\) | 287.222 | − | 76.3991i | 0.0150547 | − | 0.00400443i | ||||
\(715\) | −2028.89 | − | 3514.13i | −0.106120 | − | 0.183806i | ||||
\(716\) | −489.160 | − | 847.250i | −0.0255318 | − | 0.0442223i | ||||
\(717\) | 15190.3 | − | 4040.51i | 0.791203 | − | 0.210454i | ||||
\(718\) | 13029.0 | − | 22566.9i | 0.677213 | − | 1.17297i | ||||
\(719\) | 3759.41 | 0.194996 | 0.0974981 | − | 0.995236i | \(-0.468916\pi\) | ||||
0.0974981 | + | 0.995236i | \(0.468916\pi\) | |||||||
\(720\) | −3852.47 | − | 2243.03i | −0.199407 | − | 0.116101i | ||||
\(721\) | −14474.2 | −0.747636 | ||||||||
\(722\) | 4674.70 | − | 8096.81i | 0.240961 | − | 0.417358i | ||||
\(723\) | −20533.9 | − | 20609.0i | −1.05624 | − | 1.06011i | ||||
\(724\) | −9197.98 | − | 15931.4i | −0.472155 | − | 0.817797i | ||||
\(725\) | 1143.70 | + | 1980.94i | 0.0585874 | + | 0.101476i | ||||
\(726\) | −2383.86 | + | 8832.12i | −0.121864 | + | 0.451503i | ||||
\(727\) | −12693.7 | + | 21986.2i | −0.647572 | + | 1.12163i | 0.336129 | + | 0.941816i | \(0.390882\pi\) |
−0.983701 | + | 0.179811i | \(0.942451\pi\) | |||||||
\(728\) | 569.203 | 0.0289781 | ||||||||
\(729\) | 215.665 | − | 19681.8i | 0.0109569 | − | 0.999940i | ||||
\(730\) | 4247.34 | 0.215344 | ||||||||
\(731\) | 499.042 | − | 864.366i | 0.0252500 | − | 0.0437342i | ||||
\(732\) | −6386.01 | + | 23660.0i | −0.322450 | + | 1.19467i | ||||
\(733\) | −10097.6 | − | 17489.5i | −0.508815 | − | 0.881294i | −0.999948 | − | 0.0102093i | \(-0.996750\pi\) |
0.491132 | − | 0.871085i | \(-0.336583\pi\) | |||||||
\(734\) | −18120.7 | − | 31385.9i | −0.911235 | − | 1.57830i | ||||
\(735\) | −436.946 | − | 438.545i | −0.0219279 | − | 0.0220081i | ||||
\(736\) | −9245.18 | + | 16013.1i | −0.463019 | + | 0.801972i | ||||
\(737\) | 170.481 | 0.00852068 | ||||||||
\(738\) | −6635.25 | − | 3863.24i | −0.330958 | − | 0.192694i | ||||
\(739\) | −2153.33 | −0.107187 | −0.0535936 | − | 0.998563i | \(-0.517068\pi\) | ||||
−0.0535936 | + | 0.998563i | \(0.517068\pi\) | |||||||
\(740\) | −1311.88 | + | 2272.25i | −0.0651700 | + | 0.112878i | ||||
\(741\) | 19097.1 | − | 5079.69i | 0.946760 | − | 0.251831i | ||||
\(742\) | 8636.44 | + | 14958.7i | 0.427296 | + | 0.740098i | ||||
\(743\) | −494.183 | − | 855.949i | −0.0244008 | − | 0.0422634i | 0.853567 | − | 0.520983i | \(-0.174434\pi\) |
−0.877968 | + | 0.478719i | \(0.841101\pi\) | |||||||
\(744\) | 2471.19 | − | 657.318i | 0.121772 | − | 0.0323904i | ||||
\(745\) | −1438.83 | + | 2492.14i | −0.0707582 | + | 0.122557i | ||||
\(746\) | 29609.9 | 1.45321 | ||||||||
\(747\) | 30232.6 | − | 17307.9i | 1.48079 | − | 0.847740i | ||||
\(748\) | −654.976 | −0.0320165 | ||||||||
\(749\) | 6048.87 | − | 10477.0i | 0.295088 | − | 0.511108i | ||||
\(750\) | −8563.11 | − | 8594.44i | −0.416908 | − | 0.418433i | ||||
\(751\) | −8964.88 | − | 15527.6i | −0.435597 | − | 0.754476i | 0.561747 | − | 0.827309i | \(-0.310129\pi\) |
−0.997344 | + | 0.0728330i | \(0.976796\pi\) | |||||||
\(752\) | 10006.1 | + | 17331.1i | 0.485221 | + | 0.840427i | ||||
\(753\) | 4008.36 | − | 14850.9i | 0.193988 | − | 0.718719i | ||||
\(754\) | −1495.19 | + | 2589.75i | −0.0722170 | + | 0.125084i | ||||
\(755\) | −8358.27 | −0.402899 | ||||||||
\(756\) | 5221.12 | − | 5164.22i | 0.251177 | − | 0.248440i | ||||
\(757\) | 34271.4 | 1.64546 | 0.822732 | − | 0.568429i | \(-0.192449\pi\) | ||||
0.822732 | + | 0.568429i | \(0.192449\pi\) | |||||||
\(758\) | 18771.6 | − | 32513.4i | 0.899494 | − | 1.55797i | ||||
\(759\) | 4211.36 | − | 15603.0i | 0.201400 | − | 0.746182i | ||||
\(760\) | 240.064 | + | 415.803i | 0.0114579 | + | 0.0198457i | ||||
\(761\) | 8679.95 | + | 15034.1i | 0.413466 | + | 0.716145i | 0.995266 | − | 0.0971873i | \(-0.0309846\pi\) |
−0.581800 | + | 0.813332i | \(0.697651\pi\) | |||||||
\(762\) | −12958.8 | − | 13006.2i | −0.616073 | − | 0.618328i | ||||
\(763\) | 3238.24 | − | 5608.80i | 0.153646 | − | 0.266123i | ||||
\(764\) | −9791.36 | −0.463663 | ||||||||
\(765\) | −0.497998 | + | 136.348i | −2.35362e−5 | + | 0.00644403i | ||||
\(766\) | 14923.4 | 0.703923 | ||||||||
\(767\) | 2960.44 | − | 5127.63i | 0.139368 | − | 0.241392i | ||||
\(768\) | −22985.6 | + | 6114.00i | −1.07997 | + | 0.287265i | ||||
\(769\) | 2411.70 | + | 4177.19i | 0.113093 | + | 0.195882i | 0.917016 | − | 0.398851i | \(-0.130591\pi\) |
−0.803923 | + | 0.594733i | \(0.797258\pi\) | |||||||
\(770\) | 1411.91 | + | 2445.51i | 0.0660803 | + | 0.114454i | ||||
\(771\) | −30107.6 | + | 8008.40i | −1.40635 | + | 0.374080i | ||||
\(772\) | −3229.38 | + | 5593.45i | −0.150554 | + | 0.260768i | ||||
\(773\) | 4103.77 | 0.190947 | 0.0954736 | − | 0.995432i | \(-0.469563\pi\) | ||||
0.0954736 | + | 0.995432i | \(0.469563\pi\) | |||||||
\(774\) | 186.436 | − | 51044.8i | 0.00865801 | − | 2.37050i | ||||
\(775\) | 28521.2 | 1.32195 | ||||||||
\(776\) | −431.043 | + | 746.588i | −0.0199401 | + | 0.0345373i | ||||
\(777\) | 3704.83 | + | 3718.39i | 0.171055 | + | 0.171681i | ||||
\(778\) | −12154.9 | − | 21053.0i | −0.560123 | − | 0.970162i | ||||
\(779\) | 3473.19 | + | 6015.74i | 0.159743 | + | 0.276683i | ||||
\(780\) | 974.216 | − | 3609.45i | 0.0447212 | − | 0.165691i | ||||
\(781\) | 16834.6 | − | 29158.4i | 0.771306 | − | 1.33594i | ||||
\(782\) | 602.629 | 0.0275575 | ||||||||
\(783\) | −683.181 | − | 2606.71i | −0.0311812 | − | 0.118973i | ||||
\(784\) | −3327.37 | −0.151575 | ||||||||
\(785\) | −25.3613 | + | 43.9271i | −0.00115310 | + | 0.00199723i | ||||
\(786\) | −11370.6 | + | 42127.7i | −0.515999 | + | 1.91176i | ||||
\(787\) | −12340.2 | − | 21373.9i | −0.558934 | − | 0.968102i | −0.997586 | − | 0.0694447i | \(-0.977877\pi\) |
0.438652 | − | 0.898657i | \(-0.355456\pi\) | |||||||
\(788\) | −11062.9 | − | 19161.5i | −0.500126 | − | 0.866243i | ||||
\(789\) | 6541.70 | + | 6565.64i | 0.295172 | + | 0.296252i | ||||
\(790\) | 2752.69 | − | 4767.79i | 0.123970 | − | 0.214722i | ||||
\(791\) | −15310.5 | −0.688216 | ||||||||
\(792\) | 2030.50 | − | 1162.44i | 0.0910993 | − | 0.0521535i | ||||
\(793\) | 24959.4 | 1.11770 | ||||||||
\(794\) | 353.902 | − | 612.976i | 0.0158180 | − | 0.0273976i | ||||
\(795\) | −7657.90 | + | 2036.95i | −0.341632 | + | 0.0908718i | ||||
\(796\) | 5831.98 | + | 10101.3i | 0.259685 | + | 0.449787i | ||||
\(797\) | −5069.67 | − | 8780.93i | −0.225316 | − | 0.390259i | 0.731098 | − | 0.682272i | \(-0.239008\pi\) |
−0.956414 | + | 0.292013i | \(0.905675\pi\) | |||||||
\(798\) | −13289.8 | + | 3534.99i | −0.589540 | + | 0.156814i | ||||
\(799\) | 306.048 | − | 530.091i | 0.0135510 | − | 0.0234709i | ||||
\(800\) | −29857.1 | −1.31951 | ||||||||
\(801\) | −17516.3 | − | 10198.5i | −0.772668 | − | 0.449871i | ||||
\(802\) | −28733.1 | −1.26509 | ||||||||
\(803\) | −9362.73 | + | 16216.7i | −0.411461 | + | 0.712672i | ||||
\(804\) | 110.863 | + | 111.269i | 0.00486300 | + | 0.00488079i | ||||
\(805\) | −627.616 | − | 1087.06i | −0.0274790 | − | 0.0475950i | ||||
\(806\) | 18643.3 | + | 32291.2i | 0.814743 | + | 1.41118i | ||||
\(807\) | 8595.79 | − | 31847.2i | 0.374952 | − | 1.38919i | ||||
\(808\) | −930.435 | + | 1611.56i | −0.0405106 | + | 0.0701665i | ||||
\(809\) | −25446.0 | −1.10585 | −0.552926 | − | 0.833230i | \(-0.686489\pi\) | ||||
−0.552926 | + | 0.833230i | \(0.686489\pi\) | |||||||
\(810\) | 3442.46 | + | 6064.39i | 0.149328 | + | 0.263063i | ||||
\(811\) | 22279.3 | 0.964652 | 0.482326 | − | 0.875992i | \(-0.339792\pi\) | ||||
0.482326 | + | 0.875992i | \(0.339792\pi\) | |||||||
\(812\) | 502.700 | − | 870.702i | 0.0217258 | − | 0.0376301i | ||||
\(813\) | −9088.70 | + | 33673.4i | −0.392072 | + | 1.45262i | ||||
\(814\) | −11971.5 | − | 20735.3i | −0.515480 | − | 0.892838i | ||||
\(815\) | −2011.34 | − | 3483.75i | −0.0864469 | − | 0.149730i | ||||
\(816\) | 517.258 | + | 519.151i | 0.0221907 | + | 0.0222719i | ||||
\(817\) | −23090.7 | + | 39994.2i | −0.988789 | + | 1.71263i | ||||
\(818\) | 8308.80 | 0.355147 | ||||||||
\(819\) | −6463.58 | − | 3763.29i | −0.275770 | − | 0.160562i | ||||
\(820\) | 1314.19 | 0.0559675 | ||||||||
\(821\) | −4403.40 | + | 7626.91i | −0.187186 | + | 0.324216i | −0.944311 | − | 0.329054i | \(-0.893270\pi\) |
0.757125 | + | 0.653270i | \(0.226603\pi\) | |||||||
\(822\) | −42697.0 | + | 11357.1i | −1.81172 | + | 0.481903i | ||||
\(823\) | 5036.16 | + | 8722.89i | 0.213304 | + | 0.369454i | 0.952747 | − | 0.303766i | \(-0.0982441\pi\) |
−0.739442 | + | 0.673220i | \(0.764911\pi\) | |||||||
\(824\) | −2124.39 | − | 3679.55i | −0.0898138 | − | 0.155562i | ||||
\(825\) | 25219.4 | − | 6708.17i | 1.06427 | − | 0.283089i | ||||
\(826\) | −2060.19 | + | 3568.35i | −0.0867834 | + | 0.150313i | ||||
\(827\) | 24609.0 | 1.03475 | 0.517375 | − | 0.855759i | \(-0.326909\pi\) | ||||
0.517375 | + | 0.855759i | \(0.326909\pi\) | |||||||
\(828\) | 12922.4 | − | 7397.93i | 0.542371 | − | 0.310502i | ||||
\(829\) | 40946.1 | 1.71546 | 0.857730 | − | 0.514101i | \(-0.171874\pi\) | ||||
0.857730 | + | 0.514101i | \(0.171874\pi\) | |||||||
\(830\) | −6170.94 | + | 10688.4i | −0.258068 | + | 0.446987i | ||||
\(831\) | 8349.35 | + | 8379.90i | 0.348539 | + | 0.349814i | ||||
\(832\) | −8767.56 | − | 15185.9i | −0.365337 | − | 0.632782i | ||||
\(833\) | 50.8857 | + | 88.1366i | 0.00211655 | + | 0.00366597i | ||||
\(834\) | −12252.9 | + | 45396.7i | −0.508733 | + | 1.88484i | ||||
\(835\) | −2384.27 | + | 4129.68i | −0.0988157 | + | 0.171154i | ||||
\(836\) | 30305.8 | 1.25376 | ||||||||
\(837\) | −32407.4 | − | 8874.12i | −1.33831 | − | 0.366469i | ||||
\(838\) | 22526.0 | 0.928579 | ||||||||
\(839\) | −20439.4 | + | 35402.2i | −0.841058 | + | 1.45676i | 0.0479423 | + | 0.998850i | \(0.484734\pi\) |
−0.889001 | + | 0.457906i | \(0.848600\pi\) | |||||||
\(840\) | 47.3536 | − | 175.444i | 0.00194507 | − | 0.00720642i | ||||
\(841\) | 12010.0 | + | 20802.0i | 0.492437 | + | 0.852925i | ||||
\(842\) | 10359.7 | + | 17943.5i | 0.424013 | + | 0.734412i | ||||
\(843\) | −5449.89 | − | 5469.83i | −0.222662 | − | 0.223477i | ||||
\(844\) | −9371.04 | + | 16231.1i | −0.382185 | + | 0.661965i | ||||
\(845\) | 1534.14 | 0.0624568 | ||||||||
\(846\) | 114.336 | − | 31304.4i | 0.00464652 | − | 1.27218i | ||||
\(847\) | −3132.55 | −0.127079 | ||||||||
\(848\) | −21295.5 | + | 36885.0i | −0.862372 | + | 1.49367i | ||||
\(849\) | 45245.1 | − | 12034.9i | 1.82898 | − | 0.486497i | ||||
\(850\) | 486.543 | + | 842.718i | 0.0196333 | + | 0.0340059i | ||||
\(851\) | 5321.51 | + | 9217.12i | 0.214358 | + | 0.371280i | ||||
\(852\) | 29978.6 | − | 7974.09i | 1.20546 | − | 0.320643i | ||||
\(853\) | 1184.06 | − | 2050.85i | 0.0475279 | − | 0.0823208i | −0.841283 | − | 0.540595i | \(-0.818199\pi\) |
0.888811 | + | 0.458275i | \(0.151532\pi\) | |||||||
\(854\) | −17369.4 | −0.695983 | ||||||||
\(855\) | 23.0424 | − | 6308.84i | 0.000921676 | − | 0.252348i | ||||
\(856\) | 3551.20 | 0.141796 | ||||||||
\(857\) | 6095.19 | − | 10557.2i | 0.242949 | − | 0.420801i | −0.718604 | − | 0.695420i | \(-0.755218\pi\) |
0.961553 | + | 0.274619i | \(0.0885517\pi\) | |||||||
\(858\) | 24079.9 | + | 24168.0i | 0.958127 | + | 0.961633i | ||||
\(859\) | 9118.19 | + | 15793.2i | 0.362175 | + | 0.627306i | 0.988319 | − | 0.152402i | \(-0.0487008\pi\) |
−0.626143 | + | 0.779708i | \(0.715367\pi\) | |||||||
\(860\) | 4368.53 | + | 7566.51i | 0.173216 | + | 0.300018i | ||||
\(861\) | 685.101 | − | 2538.28i | 0.0271175 | − | 0.100470i | ||||
\(862\) | 31133.8 | − | 53925.4i | 1.23019 | − | 2.13075i | ||||
\(863\) | −35518.1 | −1.40099 | −0.700493 | − | 0.713659i | \(-0.747036\pi\) | ||||
−0.700493 | + | 0.713659i | \(0.747036\pi\) | |||||||
\(864\) | 33925.3 | + | 9289.75i | 1.33583 | + | 0.365791i | ||||
\(865\) | 66.4814 | 0.00261322 | ||||||||
\(866\) | 8925.20 | − | 15458.9i | 0.350220 | − | 0.606599i | ||||
\(867\) | −6646.49 | + | 24625.1i | −0.260354 | + | 0.964604i | ||||
\(868\) | −6268.10 | − | 10856.7i | −0.245107 | − | 0.424538i | ||||
\(869\) | 12135.9 | + | 21020.0i | 0.473743 | + | 0.820546i | ||||
\(870\) | 673.841 | + | 676.307i | 0.0262590 | + | 0.0263551i | ||||
\(871\) | 79.9868 | − | 138.541i | 0.00311165 | − | 0.00538954i | ||||
\(872\) | 1901.12 | 0.0738303 | ||||||||
\(873\) | 9830.78 | − | 5628.03i | 0.381124 | − | 0.218190i | ||||
\(874\) | −27883.6 | −1.07915 | ||||||||
\(875\) | 2077.18 | − | 3597.78i | 0.0802531 | − | 0.139002i | ||||
\(876\) | −16672.9 | + | 4434.86i | −0.643064 | + | 0.171050i | ||||
\(877\) | −92.2388 | − | 159.762i | −0.00355152 | − | 0.00615141i | 0.864244 | − | 0.503073i | \(-0.167797\pi\) |
−0.867796 | + | 0.496921i | \(0.834464\pi\) | |||||||
\(878\) | 17559.8 | + | 30414.5i | 0.674960 | + | 1.16907i | ||||
\(879\) | −37837.9 | + | 10064.6i | −1.45192 | + | 0.386201i | ||||
\(880\) | −3481.47 | + | 6030.08i | −0.133364 | + | 0.230993i | ||||
\(881\) | 16067.4 | 0.614444 | 0.307222 | − | 0.951638i | \(-0.400601\pi\) | ||||
0.307222 | + | 0.951638i | \(0.400601\pi\) | |||||||
\(882\) | 4498.05 | + | 2618.90i | 0.171720 | + | 0.0999807i | ||||
\(883\) | −591.975 | −0.0225612 | −0.0112806 | − | 0.999936i | \(-0.503591\pi\) | ||||
−0.0112806 | + | 0.999936i | \(0.503591\pi\) | |||||||
\(884\) | −307.304 | + | 532.266i | −0.0116920 | + | 0.0202512i | ||||
\(885\) | −1334.19 | − | 1339.07i | −0.0506760 | − | 0.0508614i | ||||
\(886\) | −12677.8 | − | 21958.6i | −0.480721 | − | 0.832633i | ||||
\(887\) | 8427.50 | + | 14596.9i | 0.319017 | + | 0.552553i | 0.980283 | − | 0.197598i | \(-0.0633140\pi\) |
−0.661266 | + | 0.750151i | \(0.729981\pi\) | |||||||
\(888\) | −401.508 | + | 1487.57i | −0.0151731 | + | 0.0562159i | ||||
\(889\) | 3143.46 | − | 5444.63i | 0.118592 | − | 0.205407i | ||||
\(890\) | 7180.91 | 0.270454 | ||||||||
\(891\) | −30742.8 | − | 224.573i | −1.15592 | − | 0.00844386i | ||||
\(892\) | 30272.8 | 1.13633 | ||||||||
\(893\) | −14160.9 | + | 24527.3i | −0.530655 | + | 0.919122i | ||||
\(894\) | 6304.67 | − | 23358.6i | 0.235861 | − | 0.873859i | ||||
\(895\) | 159.053 | + | 275.488i | 0.00594028 | + | 0.0102889i | ||||
\(896\) | −918.587 | − | 1591.04i | −0.0342498 | − | 0.0593224i | ||||
\(897\) | −10703.8 | − | 10743.0i | −0.398429 | − | 0.399887i | ||||
\(898\) | −12200.4 | + | 21131.7i | −0.453377 | + | 0.785273i | ||||
\(899\) | −4600.15 | −0.170660 | ||||||||
\(900\) | 20778.4 | + | 12097.8i | 0.769570 | + | 0.448067i | ||||
\(901\) | 1302.70 | 0.0481677 | ||||||||
\(902\) | −5996.26 | + | 10385.8i | −0.221345 | + | 0.383381i | ||||
\(903\) | 16891.7 | − | 4493.06i | 0.622503 | − | 0.165581i | ||||
\(904\) | −2247.14 | − | 3892.16i | −0.0826756 | − | 0.143198i | ||||
\(905\) | 2990.77 | + | 5180.17i | 0.109853 | + | 0.190270i | ||||
\(906\) | 67912.2 | − | 18064.2i | 2.49032 | − | 0.662408i | ||||
\(907\) | −19344.8 | + | 33506.2i | −0.708195 | + | 1.22663i | 0.257331 | + | 0.966323i | \(0.417157\pi\) |
−0.965526 | + | 0.260307i | \(0.916176\pi\) | |||||||
\(908\) | −4692.03 | −0.171487 | ||||||||
\(909\) | 21220.4 | − | 12148.5i | 0.774298 | − | 0.443278i | ||||
\(910\) | 2649.79 | 0.0965270 | ||||||||
\(911\) | 11808.0 | − | 20452.0i | 0.429436 | − | 0.743804i | −0.567388 | − | 0.823451i | \(-0.692046\pi\) |
0.996823 | + | 0.0796467i | \(0.0253792\pi\) | |||||||
\(912\) | −23933.5 | − | 24021.1i | −0.868990 | − | 0.872169i | ||||
\(913\) | −27206.1 | − | 47122.4i | −0.986189 | − | 1.70813i | ||||
\(914\) | −6099.79 | − | 10565.2i | −0.220747 | − | 0.382346i | ||||
\(915\) | 2076.44 | − | 7693.17i | 0.0750220 | − | 0.277955i | ||||
\(916\) | 3698.20 | − | 6405.46i | 0.133397 | − | 0.231051i | ||||
\(917\) | −14941.7 | −0.538079 | ||||||||
\(918\) | −290.634 | − | 1108.93i | −0.0104492 | − | 0.0398693i | ||||
\(919\) | −30560.7 | −1.09696 | −0.548478 | − | 0.836165i | \(-0.684793\pi\) | ||||
−0.548478 | + | 0.836165i | \(0.684793\pi\) | |||||||
\(920\) | 184.232 | − | 319.099i | 0.00660212 | − | 0.0114352i | ||||
\(921\) | 3744.54 | − | 13873.4i | 0.133970 | − | 0.496357i | ||||
\(922\) | 8554.89 | + | 14817.5i | 0.305575 | + | 0.529272i | ||||
\(923\) | −15797.1 | − | 27361.3i | −0.563344 | − | 0.975740i | ||||
\(924\) | −8095.92 | − | 8125.55i | −0.288243 | − | 0.289298i | ||||
\(925\) | −8592.84 | + | 14883.2i | −0.305439 | + | 0.529035i | ||||
\(926\) | 29291.9 | 1.03952 | ||||||||
\(927\) | −203.908 | + | 55828.5i | −0.00722462 | + | 1.97805i | ||||
\(928\) | 4815.60 | 0.170345 | ||||||||
\(929\) | −5842.24 | + | 10119.1i | −0.206327 | + | 0.357369i | −0.950555 | − | 0.310557i | \(-0.899484\pi\) |
0.744228 | + | 0.667926i | \(0.232818\pi\) | |||||||
\(930\) | 11504.0 | − | 3059.98i | 0.405625 | − | 0.107893i | ||||
\(931\) | −2354.48 | − | 4078.08i | −0.0828840 | − | 0.143559i | ||||
\(932\) | 11685.9 | + | 20240.6i | 0.410712 | + | 0.711375i | ||||
\(933\) | 15136.0 | − | 4026.07i | 0.531116 | − | 0.141273i | ||||
\(934\) | 30340.5 | − | 52551.3i | 1.06293 | − | 1.84104i | ||||
\(935\) | 212.969 | 0.00744902 | ||||||||
\(936\) | 8.01878 | − | 2195.48i | 0.000280024 | − | 0.0766684i | ||||
\(937\) | −49115.3 | −1.71241 | −0.856204 | − | 0.516638i | \(-0.827183\pi\) | ||||
−0.856204 | + | 0.516638i | \(0.827183\pi\) | |||||||
\(938\) | −55.6633 | + | 96.4117i | −0.00193760 | + | 0.00335603i | ||||
\(939\) | 10078.9 | + | 10115.7i | 0.350278 | + | 0.351560i | ||||
\(940\) | 2679.10 | + | 4640.33i | 0.0929601 | + | 0.161012i | ||||
\(941\) | 11827.1 | + | 20485.1i | 0.409725 | + | 0.709665i | 0.994859 | − | 0.101272i | \(-0.0322912\pi\) |
−0.585133 | + | 0.810937i | \(0.698958\pi\) | |||||||
\(942\) | 111.128 | − | 411.726i | 0.00384368 | − | 0.0142407i | ||||
\(943\) | 2665.42 | − | 4616.65i | 0.0920447 | − | 0.159426i | ||||
\(944\) | −10159.9 | −0.350294 | ||||||||
\(945\) | −1697.67 | + | 1679.17i | −0.0584395 | + | 0.0578027i | ||||
\(946\) | −79729.4 | −2.74020 | ||||||||
\(947\) | 22791.8 | − | 39476.6i | 0.782086 | − | 1.35461i | −0.148639 | − | 0.988892i | \(-0.547489\pi\) |
0.930725 | − | 0.365721i | \(-0.119177\pi\) | |||||||
\(948\) | −5827.34 | + | 21590.1i | −0.199645 | + | 0.739678i | ||||
\(949\) | 8785.68 | + | 15217.2i | 0.300522 | + | 0.520519i | ||||
\(950\) | −22512.4 | − | 38992.6i | −0.768840 | − | 1.33167i | ||||
\(951\) | 14425.8 | + | 14478.6i | 0.491891 | + | 0.493691i | ||||
\(952\) | −14.9371 | + | 25.8718i | −0.000508523 | + | 0.000880788i | ||||
\(953\) | 44104.9 | 1.49916 | 0.749579 | − | 0.661915i | \(-0.230256\pi\) | ||||
0.749579 | + | 0.661915i | \(0.230256\pi\) | |||||||
\(954\) | 57819.3 | − | 33101.0i | 1.96223 | − | 1.12336i | ||||
\(955\) | 3183.71 | 0.107877 | ||||||||
\(956\) | 11310.1 | − | 19589.7i | 0.382631 | − | 0.662737i | ||||
\(957\) | −4067.59 | + | 1081.95i | −0.137395 | + | 0.0365460i | ||||
\(958\) | 17016.1 | + | 29472.8i | 0.573868 | + | 0.993969i | ||||
\(959\) | −7564.41 | − | 13101.9i | −0.254711 | − | 0.441172i | ||||
\(960\) | −5410.09 | + | 1439.05i | −0.181885 | + | 0.0483802i | ||||
\(961\) | −13783.8 | + | 23874.3i | −0.462684 | + | 0.801393i | ||||
\(962\) | −22467.3 | −0.752990 | ||||||||
\(963\) | −40325.6 | − | 23478.8i | −1.34940 | − | 0.785664i | ||||
\(964\) | −41866.6 | −1.39879 | ||||||||
\(965\) | 1050.05 | − | 1818.74i | 0.0350283 | − | 0.0606707i | ||||
\(966\) | 7448.87 | + | 7476.13i | 0.248099 | + | 0.249007i | ||||
\(967\) | −20951.9 | − | 36289.7i | −0.696760 | − | 1.20682i | −0.969584 | − | 0.244760i | \(-0.921291\pi\) |
0.272824 | − | 0.962064i | \(-0.412042\pi\) | |||||||
\(968\) | −459.767 | − | 796.340i | −0.0152660 | − | 0.0264415i | ||||
\(969\) | −270.263 | + | 1001.32i | −0.00895984 | + | 0.0331960i | ||||
\(970\) | −2006.62 | + | 3475.56i | −0.0664212 | + | 0.115045i | ||||
\(971\) | −21924.5 | −0.724606 | −0.362303 | − | 0.932060i | \(-0.618009\pi\) | ||||
−0.362303 | + | 0.932060i | \(0.618009\pi\) | |||||||
\(972\) | −19845.4 | − | 20211.2i | −0.654880 | − | 0.666949i | ||||
\(973\) | −16101.1 | −0.530503 | ||||||||
\(974\) | −26886.5 | + | 46568.7i | −0.884495 | + | 1.53199i | ||||
\(975\) | 6381.12 | − | 23641.9i | 0.209599 | − | 0.776560i | ||||
\(976\) | −21414.6 | − | 37091.1i | −0.702319 | − | 1.21645i | ||||
\(977\) | 6888.95 | + | 11932.0i | 0.225586 | + | 0.390726i | 0.956495 | − | 0.291749i | \(-0.0942372\pi\) |
−0.730909 | + | 0.682474i | \(0.760904\pi\) | |||||||
\(978\) | 23871.6 | + | 23959.0i | 0.780502 | + | 0.783358i | ||||
\(979\) | −15829.4 | + | 27417.3i | −0.516762 | + | 0.895058i | ||||
\(980\) | −890.889 | −0.0290392 | ||||||||
\(981\) | −21588.2 | − | 12569.3i | −0.702606 | − | 0.409079i | ||||
\(982\) | 4636.85 | 0.150680 | ||||||||
\(983\) | 6554.20 | − | 11352.2i | 0.212662 | − | 0.368341i | −0.739885 | − | 0.672733i | \(-0.765120\pi\) |
0.952547 | + | 0.304393i | \(0.0984534\pi\) | |||||||
\(984\) | 745.822 | − | 198.383i | 0.0241625 | − | 0.00642706i | ||||
\(985\) | 3597.16 | + | 6230.46i | 0.116360 | + | 0.201542i | ||||
\(986\) | −78.4739 | − | 135.921i | −0.00253460 | − | 0.00439006i | ||||
\(987\) | 10359.2 | − | 2755.47i | 0.334080 | − | 0.0888629i | ||||
\(988\) | 14219.0 | − | 24628.0i | 0.457860 | − | 0.793037i | ||||
\(989\) | 35440.9 | 1.13949 | ||||||||
\(990\) | 9452.50 | − | 5411.47i | 0.303455 | − | 0.173725i | ||||
\(991\) | −12950.1 | −0.415109 | −0.207555 | − | 0.978223i | \(-0.566550\pi\) | ||||
−0.207555 | + | 0.978223i | \(0.566550\pi\) | |||||||
\(992\) | 30022.6 | − | 52000.6i | 0.960904 | − | 1.66434i | ||||
\(993\) | 16886.8 | + | 16948.6i | 0.539664 | + | 0.541639i | ||||
\(994\) | 10993.3 | + | 19040.9i | 0.350790 | + | 0.607586i | ||||
\(995\) | −1896.30 | − | 3284.49i | −0.0604188 | − | 0.104648i | ||||
\(996\) | 13063.6 | − | 48400.5i | 0.415600 | − | 1.53979i | ||||
\(997\) | −18059.8 | + | 31280.5i | −0.573682 | + | 0.993646i | 0.422502 | + | 0.906362i | \(0.361152\pi\) |
−0.996184 | + | 0.0872835i | \(0.972181\pi\) | |||||||
\(998\) | 151.494 | 0.00480507 | ||||||||
\(999\) | 14394.4 | − | 14237.6i | 0.455876 | − | 0.450908i |
(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 | 63.4.f.b.43.7 | yes | 16 | |
3.2 | odd | 2 | 189.4.f.b.127.2 | 16 | |||
9.2 | odd | 6 | 567.4.a.g.1.7 | 8 | |||
9.4 | even | 3 | inner | 63.4.f.b.22.7 | ✓ | 16 | |
9.5 | odd | 6 | 189.4.f.b.64.2 | 16 | |||
9.7 | even | 3 | 567.4.a.i.1.2 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
63.4.f.b.22.7 | ✓ | 16 | 9.4 | even | 3 | inner | |
63.4.f.b.43.7 | yes | 16 | 1.1 | even | 1 | trivial | |
189.4.f.b.64.2 | 16 | 9.5 | odd | 6 | |||
189.4.f.b.127.2 | 16 | 3.2 | odd | 2 | |||
567.4.a.g.1.7 | 8 | 9.2 | odd | 6 | |||
567.4.a.i.1.2 | 8 | 9.7 | even | 3 |