Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [75,4,Mod(32,75)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(75, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("75.32");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 75 = 3 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 75.e (of order \(4\), 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: | \(4.42514325043\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 36x^{14} + 562x^{12} - 3672x^{10} + 16413x^{8} - 6588x^{6} + 43024x^{4} + 499896x^{2} + 532900 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{6}\cdot 3^{8}\cdot 5^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 68.3 | ||
Root | \(0.0852547 - 1.22474i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 75.68 |
Dual form | 75.4.e.d.32.3 |
$q$-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 \(\left(\mathbb{Z}/75\mathbb{Z}\right)^\times\).
\(n\) | \(26\) | \(52\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{3}{4}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.39558 | − | 1.39558i | −0.493414 | − | 0.493414i | 0.415966 | − | 0.909380i | \(-0.363443\pi\) |
−0.909380 | + | 0.415966i | \(0.863443\pi\) | |||||||
\(3\) | −4.93508 | + | 1.62635i | −0.949756 | + | 0.312992i | ||||
\(4\) | − | 4.10469i | − | 0.513086i | ||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 9.15703 | + | 4.61761i | 0.623057 | + | 0.314188i | ||||
\(7\) | −3.80245 | + | 3.80245i | −0.205313 | + | 0.205313i | −0.802272 | − | 0.596959i | \(-0.796376\pi\) |
0.596959 | + | 0.802272i | \(0.296376\pi\) | |||||||
\(8\) | −16.8931 | + | 16.8931i | −0.746577 | + | 0.746577i | ||||
\(9\) | 21.7100 | − | 16.0523i | 0.804073 | − | 0.594531i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 61.8903i | 1.69642i | 0.529659 | + | 0.848211i | \(0.322320\pi\) | ||||
−0.529659 | + | 0.848211i | \(0.677680\pi\) | |||||||
\(12\) | 6.67567 | + | 20.2569i | 0.160592 | + | 0.487306i | ||||
\(13\) | 48.1497 | + | 48.1497i | 1.02726 | + | 1.02726i | 0.999618 | + | 0.0276375i | \(0.00879842\pi\) |
0.0276375 | + | 0.999618i | \(0.491202\pi\) | |||||||
\(14\) | 10.6133 | 0.202608 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 14.3141 | 0.223657 | ||||||||
\(17\) | −47.5960 | − | 47.5960i | −0.679042 | − | 0.679042i | 0.280741 | − | 0.959784i | \(-0.409420\pi\) |
−0.959784 | + | 0.280741i | \(0.909420\pi\) | |||||||
\(18\) | −52.7005 | − | 7.89568i | −0.690090 | − | 0.103391i | ||||
\(19\) | 93.4187i | 1.12799i | 0.825780 | + | 0.563993i | \(0.190735\pi\) | ||||
−0.825780 | + | 0.563993i | \(0.809265\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 12.5813 | − | 24.9495i | 0.130736 | − | 0.259258i | ||||
\(22\) | 86.3732 | − | 86.3732i | 0.837038 | − | 0.837038i | ||||
\(23\) | 33.7862 | − | 33.7862i | 0.306301 | − | 0.306301i | −0.537172 | − | 0.843473i | \(-0.680507\pi\) |
0.843473 | + | 0.537172i | \(0.180507\pi\) | |||||||
\(24\) | 55.8947 | − | 110.843i | 0.475394 | − | 0.942739i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | − | 134.394i | − | 1.01372i | ||||||
\(27\) | −81.0335 | + | 114.528i | −0.577589 | + | 0.816327i | ||||
\(28\) | 15.6079 | + | 15.6079i | 0.105343 | + | 0.105343i | ||||
\(29\) | −179.192 | −1.14742 | −0.573709 | − | 0.819059i | \(-0.694496\pi\) | ||||
−0.573709 | + | 0.819059i | \(0.694496\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −123.523 | −0.715660 | −0.357830 | − | 0.933787i | \(-0.616483\pi\) | ||||
−0.357830 | + | 0.933787i | \(0.616483\pi\) | |||||||
\(32\) | 115.168 | + | 115.168i | 0.636222 | + | 0.636222i | ||||
\(33\) | −100.655 | − | 305.434i | −0.530966 | − | 1.61119i | ||||
\(34\) | 132.848i | 0.670098i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −65.8898 | − | 89.1126i | −0.305046 | − | 0.412558i | ||||
\(37\) | −10.5672 | + | 10.5672i | −0.0469525 | + | 0.0469525i | −0.730193 | − | 0.683241i | \(-0.760570\pi\) |
0.683241 | + | 0.730193i | \(0.260570\pi\) | |||||||
\(38\) | 130.374 | − | 130.374i | 0.556564 | − | 0.556564i | ||||
\(39\) | −315.931 | − | 159.314i | −1.29716 | − | 0.654120i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 61.8903i | − | 0.235747i | −0.993029 | − | 0.117874i | \(-0.962392\pi\) | ||
0.993029 | − | 0.117874i | \(-0.0376078\pi\) | |||||||
\(42\) | −52.3773 | + | 17.2609i | −0.192429 | + | 0.0634147i | ||||
\(43\) | 133.882 | + | 133.882i | 0.474809 | + | 0.474809i | 0.903467 | − | 0.428658i | \(-0.141013\pi\) |
−0.428658 | + | 0.903467i | \(0.641013\pi\) | |||||||
\(44\) | 254.040 | 0.870410 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −94.3031 | −0.302266 | ||||||||
\(47\) | −56.9922 | − | 56.9922i | −0.176876 | − | 0.176876i | 0.613117 | − | 0.789992i | \(-0.289916\pi\) |
−0.789992 | + | 0.613117i | \(0.789916\pi\) | |||||||
\(48\) | −70.6410 | + | 23.2797i | −0.212420 | + | 0.0700028i | ||||
\(49\) | 314.083i | 0.915693i | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 312.298 | + | 157.482i | 0.857459 | + | 0.432390i | ||||
\(52\) | 197.639 | − | 197.639i | 0.527070 | − | 0.527070i | ||||
\(53\) | −234.750 | + | 234.750i | −0.608405 | + | 0.608405i | −0.942529 | − | 0.334124i | \(-0.891559\pi\) |
0.334124 | + | 0.942529i | \(0.391559\pi\) | |||||||
\(54\) | 272.922 | − | 46.7438i | 0.687778 | − | 0.117797i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | − | 128.470i | − | 0.306564i | ||||||
\(57\) | −151.932 | − | 461.029i | −0.353050 | − | 1.07131i | ||||
\(58\) | 250.078 | + | 250.078i | 0.566152 | + | 0.566152i | ||||
\(59\) | 260.519 | 0.574860 | 0.287430 | − | 0.957802i | \(-0.407199\pi\) | ||||
0.287430 | + | 0.957802i | \(0.407199\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 240.664 | 0.505145 | 0.252573 | − | 0.967578i | \(-0.418723\pi\) | ||||
0.252573 | + | 0.967578i | \(0.418723\pi\) | |||||||
\(62\) | 172.387 | + | 172.387i | 0.353117 | + | 0.353117i | ||||
\(63\) | −21.5128 | + | 143.589i | −0.0430215 | + | 0.287151i | ||||
\(64\) | − | 435.967i | − | 0.851498i | ||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −285.785 | + | 566.732i | −0.532996 | + | 1.05697i | ||||
\(67\) | −320.313 | + | 320.313i | −0.584066 | + | 0.584066i | −0.936018 | − | 0.351952i | \(-0.885518\pi\) |
0.351952 | + | 0.936018i | \(0.385518\pi\) | |||||||
\(68\) | −195.367 | + | 195.367i | −0.348407 | + | 0.348407i | ||||
\(69\) | −111.789 | + | 221.686i | −0.195041 | + | 0.386780i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1084.53i | 1.81282i | 0.422400 | + | 0.906410i | \(0.361188\pi\) | ||||
−0.422400 | + | 0.906410i | \(0.638812\pi\) | |||||||
\(72\) | −95.5747 | + | 637.923i | −0.156439 | + | 1.04417i | ||||
\(73\) | −208.052 | − | 208.052i | −0.333570 | − | 0.333570i | 0.520371 | − | 0.853940i | \(-0.325794\pi\) |
−0.853940 | + | 0.520371i | \(0.825794\pi\) | |||||||
\(74\) | 29.4950 | 0.0463341 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 383.455 | 0.578753 | ||||||||
\(77\) | −235.335 | − | 235.335i | −0.348297 | − | 0.348297i | ||||
\(78\) | 218.572 | + | 663.244i | 0.317287 | + | 0.962790i | ||||
\(79\) | − | 676.816i | − | 0.963895i | −0.876200 | − | 0.481947i | \(-0.839930\pi\) | ||
0.876200 | − | 0.481947i | \(-0.160070\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 213.645 | − | 696.991i | 0.293065 | − | 0.956092i | ||||
\(82\) | −86.3732 | + | 86.3732i | −0.116321 | + | 0.116321i | ||||
\(83\) | −71.3863 | + | 71.3863i | −0.0944056 | + | 0.0944056i | −0.752732 | − | 0.658327i | \(-0.771265\pi\) |
0.658327 | + | 0.752732i | \(0.271265\pi\) | |||||||
\(84\) | −102.410 | − | 51.6421i | −0.133022 | − | 0.0670788i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | − | 373.687i | − | 0.468555i | ||||||
\(87\) | 884.326 | − | 291.429i | 1.08977 | − | 0.359132i | ||||
\(88\) | −1045.52 | − | 1045.52i | −1.26651 | − | 1.26651i | ||||
\(89\) | −228.124 | −0.271698 | −0.135849 | − | 0.990730i | \(-0.543376\pi\) | ||||
−0.135849 | + | 0.990730i | \(0.543376\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −366.173 | −0.421818 | ||||||||
\(92\) | −138.682 | − | 138.682i | −0.157159 | − | 0.157159i | ||||
\(93\) | 609.598 | − | 200.893i | 0.679702 | − | 0.223996i | ||||
\(94\) | 159.075i | 0.174546i | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −755.670 | − | 381.061i | −0.803387 | − | 0.405123i | ||||
\(97\) | −89.5346 | + | 89.5346i | −0.0937202 | + | 0.0937202i | −0.752412 | − | 0.658692i | \(-0.771110\pi\) |
0.658692 | + | 0.752412i | \(0.271110\pi\) | |||||||
\(98\) | 438.329 | − | 438.329i | 0.451816 | − | 0.451816i | ||||
\(99\) | 993.485 | + | 1343.64i | 1.00858 | + | 1.36405i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 1514.86i | − | 1.49242i | −0.665710 | − | 0.746210i | \(-0.731871\pi\) | ||
0.665710 | − | 0.746210i | \(-0.268129\pi\) | |||||||
\(102\) | −216.058 | − | 655.617i | −0.209735 | − | 0.636429i | ||||
\(103\) | 71.0084 | + | 71.0084i | 0.0679288 | + | 0.0679288i | 0.740255 | − | 0.672326i | \(-0.234705\pi\) |
−0.672326 | + | 0.740255i | \(0.734705\pi\) | |||||||
\(104\) | −1626.80 | −1.53385 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 655.228 | 0.600391 | ||||||||
\(107\) | −28.8036 | − | 28.8036i | −0.0260238 | − | 0.0260238i | 0.693975 | − | 0.719999i | \(-0.255858\pi\) |
−0.719999 | + | 0.693975i | \(0.755858\pi\) | |||||||
\(108\) | 470.100 | + | 332.617i | 0.418846 | + | 0.296353i | ||||
\(109\) | − | 600.245i | − | 0.527459i | −0.964597 | − | 0.263730i | \(-0.915047\pi\) | ||
0.964597 | − | 0.263730i | \(-0.0849527\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 34.9641 | − | 69.3362i | 0.0298977 | − | 0.0592892i | ||||
\(112\) | −54.4285 | + | 54.4285i | −0.0459197 | + | 0.0459197i | ||||
\(113\) | 1149.62 | − | 1149.62i | 0.957058 | − | 0.957058i | −0.0420576 | − | 0.999115i | \(-0.513391\pi\) |
0.999115 | + | 0.0420576i | \(0.0133913\pi\) | |||||||
\(114\) | −431.371 | + | 855.438i | −0.354400 | + | 0.702799i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 735.527i | 0.588724i | ||||||||
\(117\) | 1818.24 | + | 272.412i | 1.43672 | + | 0.215252i | ||||
\(118\) | −363.577 | − | 363.577i | −0.283644 | − | 0.283644i | ||||
\(119\) | 361.963 | 0.278832 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −2499.41 | −1.87785 | ||||||||
\(122\) | −335.867 | − | 335.867i | −0.249246 | − | 0.249246i | ||||
\(123\) | 100.655 | + | 305.434i | 0.0737870 | + | 0.223903i | ||||
\(124\) | 507.025i | 0.367195i | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 230.414 | − | 170.368i | 0.162912 | − | 0.120457i | ||||
\(127\) | −1327.45 | + | 1327.45i | −0.927501 | + | 0.927501i | −0.997544 | − | 0.0700433i | \(-0.977686\pi\) |
0.0700433 | + | 0.997544i | \(0.477686\pi\) | |||||||
\(128\) | 312.918 | − | 312.918i | 0.216081 | − | 0.216081i | ||||
\(129\) | −878.456 | − | 442.978i | −0.599564 | − | 0.302341i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 88.4849i | 0.0590150i | 0.999565 | + | 0.0295075i | \(0.00939389\pi\) | ||||
−0.999565 | + | 0.0295075i | \(0.990606\pi\) | |||||||
\(132\) | −1253.71 | + | 413.159i | −0.826677 | + | 0.272431i | ||||
\(133\) | −355.220 | − | 355.220i | −0.231590 | − | 0.231590i | ||||
\(134\) | 894.048 | 0.576373 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 1608.09 | 1.01392 | ||||||||
\(137\) | 1491.02 | + | 1491.02i | 0.929830 | + | 0.929830i | 0.997695 | − | 0.0678646i | \(-0.0216186\pi\) |
−0.0678646 | + | 0.997695i | \(0.521619\pi\) | |||||||
\(138\) | 465.393 | − | 153.370i | 0.287079 | − | 0.0946067i | ||||
\(139\) | − | 2123.04i | − | 1.29550i | −0.761854 | − | 0.647748i | \(-0.775711\pi\) | ||
0.761854 | − | 0.647748i | \(-0.224289\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 373.950 | + | 188.571i | 0.223350 | + | 0.112628i | ||||
\(142\) | 1513.56 | − | 1513.56i | 0.894470 | − | 0.894470i | ||||
\(143\) | −2980.00 | + | 2980.00i | −1.74266 | + | 1.74266i | ||||
\(144\) | 310.758 | − | 229.774i | 0.179837 | − | 0.132971i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 580.707i | 0.329176i | ||||||||
\(147\) | −510.809 | − | 1550.02i | −0.286604 | − | 0.869685i | ||||
\(148\) | 43.3752 | + | 43.3752i | 0.0240907 | + | 0.0240907i | ||||
\(149\) | 1237.81 | 0.680571 | 0.340286 | − | 0.940322i | \(-0.389476\pi\) | ||||
0.340286 | + | 0.940322i | \(0.389476\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2364.27 | 1.27418 | 0.637092 | − | 0.770788i | \(-0.280137\pi\) | ||||
0.637092 | + | 0.770788i | \(0.280137\pi\) | |||||||
\(152\) | −1578.13 | − | 1578.13i | −0.842129 | − | 0.842129i | ||||
\(153\) | −1797.33 | − | 269.280i | −0.949711 | − | 0.142287i | ||||
\(154\) | 656.859i | 0.343709i | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −653.934 | + | 1296.80i | −0.335619 | + | 0.665557i | ||||
\(157\) | −709.026 | + | 709.026i | −0.360423 | + | 0.360423i | −0.863969 | − | 0.503546i | \(-0.832029\pi\) |
0.503546 | + | 0.863969i | \(0.332029\pi\) | |||||||
\(158\) | −944.553 | + | 944.553i | −0.475599 | + | 0.475599i | ||||
\(159\) | 776.724 | − | 1540.30i | 0.387410 | − | 0.768262i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 256.941i | 0.125775i | ||||||||
\(162\) | −1270.87 | + | 674.551i | −0.616352 | + | 0.327147i | ||||
\(163\) | 1909.69 | + | 1909.69i | 0.917662 | + | 0.917662i | 0.996859 | − | 0.0791974i | \(-0.0252357\pi\) |
−0.0791974 | + | 0.996859i | \(0.525236\pi\) | |||||||
\(164\) | −254.040 | −0.120959 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 199.251 | 0.0931621 | ||||||||
\(167\) | 1002.75 | + | 1002.75i | 0.464639 | + | 0.464639i | 0.900173 | − | 0.435533i | \(-0.143440\pi\) |
−0.435533 | + | 0.900173i | \(0.643440\pi\) | |||||||
\(168\) | 208.938 | + | 634.011i | 0.0959519 | + | 0.291161i | ||||
\(169\) | 2439.79i | 1.11051i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1499.59 | + | 2028.12i | 0.670623 | + | 0.906982i | ||||
\(172\) | 549.543 | − | 549.543i | 0.243618 | − | 0.243618i | ||||
\(173\) | 2360.68 | − | 2360.68i | 1.03745 | − | 1.03745i | 0.0381828 | − | 0.999271i | \(-0.487843\pi\) |
0.999271 | − | 0.0381828i | \(-0.0121569\pi\) | |||||||
\(174\) | −1640.87 | − | 827.438i | −0.714906 | − | 0.360505i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 885.902i | 0.379417i | ||||||||
\(177\) | −1285.68 | + | 423.696i | −0.545977 | + | 0.179926i | ||||
\(178\) | 318.367 | + | 318.367i | 0.134059 | + | 0.134059i | ||||
\(179\) | 2605.87 | 1.08811 | 0.544056 | − | 0.839049i | \(-0.316888\pi\) | ||||
0.544056 | + | 0.839049i | \(0.316888\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −3682.37 | −1.51220 | −0.756100 | − | 0.654456i | \(-0.772898\pi\) | ||||
−0.756100 | + | 0.654456i | \(0.772898\pi\) | |||||||
\(182\) | 511.026 | + | 511.026i | 0.208131 | + | 0.208131i | ||||
\(183\) | −1187.70 | + | 391.404i | −0.479765 | + | 0.158106i | ||||
\(184\) | 1141.51i | 0.457354i | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −1131.11 | − | 570.382i | −0.445897 | − | 0.224852i | ||||
\(187\) | 2945.73 | − | 2945.73i | 1.15194 | − | 1.15194i | ||||
\(188\) | −233.935 | + | 233.935i | −0.0907525 | + | 0.0907525i | ||||
\(189\) | −127.359 | − | 743.611i | −0.0490160 | − | 0.286189i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 842.771i | − | 0.319271i | −0.987176 | − | 0.159635i | \(-0.948968\pi\) | ||
0.987176 | − | 0.159635i | \(-0.0510319\pi\) | |||||||
\(192\) | 709.036 | + | 2151.53i | 0.266512 | + | 0.808716i | ||||
\(193\) | 2343.62 | + | 2343.62i | 0.874079 | + | 0.874079i | 0.992914 | − | 0.118835i | \(-0.0379158\pi\) |
−0.118835 | + | 0.992914i | \(0.537916\pi\) | |||||||
\(194\) | 249.906 | 0.0924857 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1289.21 | 0.469829 | ||||||||
\(197\) | −309.658 | − | 309.658i | −0.111991 | − | 0.111991i | 0.648891 | − | 0.760882i | \(-0.275233\pi\) |
−0.760882 | + | 0.648891i | \(0.775233\pi\) | |||||||
\(198\) | 488.666 | − | 3261.65i | 0.175394 | − | 1.17068i | ||||
\(199\) | 1759.07i | 0.626618i | 0.949651 | + | 0.313309i | \(0.101438\pi\) | ||||
−0.949651 | + | 0.313309i | \(0.898562\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1059.83 | − | 2101.71i | 0.371913 | − | 0.737528i | ||||
\(202\) | −2114.12 | + | 2114.12i | −0.736381 | + | 0.736381i | ||||
\(203\) | 681.368 | − | 681.368i | 0.235580 | − | 0.235580i | ||||
\(204\) | 646.414 | − | 1281.88i | 0.221853 | − | 0.439950i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | − | 198.196i | − | 0.0670340i | ||||||
\(207\) | 191.149 | − | 1275.85i | 0.0641826 | − | 0.428393i | ||||
\(208\) | 689.218 | + | 689.218i | 0.229753 | + | 0.229753i | ||||
\(209\) | −5781.72 | −1.91354 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1344.63 | −0.438710 | −0.219355 | − | 0.975645i | \(-0.570395\pi\) | ||||
−0.219355 | + | 0.975645i | \(0.570395\pi\) | |||||||
\(212\) | 963.577 | + | 963.577i | 0.312164 | + | 0.312164i | ||||
\(213\) | −1763.83 | − | 5352.24i | −0.567397 | − | 1.72174i | ||||
\(214\) | 80.3957i | 0.0256810i | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −565.819 | − | 3303.64i | −0.178236 | − | 1.04067i | ||||
\(217\) | 469.692 | − | 469.692i | 0.146934 | − | 0.146934i | ||||
\(218\) | −837.693 | + | 837.693i | −0.260256 | + | 0.260256i | ||||
\(219\) | 1365.12 | + | 688.385i | 0.421214 | + | 0.212405i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 4583.46i | − | 1.39510i | ||||||
\(222\) | −145.560 | + | 47.9692i | −0.0440060 | + | 0.0145022i | ||||
\(223\) | −3146.44 | − | 3146.44i | −0.944850 | − | 0.944850i | 0.0537070 | − | 0.998557i | \(-0.482896\pi\) |
−0.998557 | + | 0.0537070i | \(0.982896\pi\) | |||||||
\(224\) | −875.844 | −0.261249 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −3208.79 | −0.944451 | ||||||||
\(227\) | −4427.84 | − | 4427.84i | −1.29465 | − | 1.29465i | −0.931876 | − | 0.362776i | \(-0.881829\pi\) |
−0.362776 | − | 0.931876i | \(-0.618171\pi\) | |||||||
\(228\) | −1892.38 | + | 623.632i | −0.549675 | + | 0.181145i | ||||
\(229\) | 2059.29i | 0.594242i | 0.954840 | + | 0.297121i | \(0.0960265\pi\) | ||||
−0.954840 | + | 0.297121i | \(0.903973\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1544.13 | + | 778.658i | 0.439812 | + | 0.221783i | ||||
\(232\) | 3027.11 | − | 3027.11i | 0.856636 | − | 0.856636i | ||||
\(233\) | 2302.49 | − | 2302.49i | 0.647387 | − | 0.647387i | −0.304973 | − | 0.952361i | \(-0.598648\pi\) |
0.952361 | + | 0.304973i | \(0.0986476\pi\) | |||||||
\(234\) | −2157.34 | − | 2917.69i | −0.602691 | − | 0.815108i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | − | 1069.35i | − | 0.294953i | ||||||
\(237\) | 1100.74 | + | 3340.14i | 0.301691 | + | 0.915465i | ||||
\(238\) | −505.149 | − | 505.149i | −0.137580 | − | 0.137580i | ||||
\(239\) | −2459.08 | −0.665542 | −0.332771 | − | 0.943008i | \(-0.607984\pi\) | ||||
−0.332771 | + | 0.943008i | \(0.607984\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 4461.08 | 1.19238 | 0.596189 | − | 0.802844i | \(-0.296681\pi\) | ||||
0.596189 | + | 0.802844i | \(0.296681\pi\) | |||||||
\(242\) | 3488.14 | + | 3488.14i | 0.926555 | + | 0.926555i | ||||
\(243\) | 79.2012 | + | 3787.17i | 0.0209085 | + | 0.999781i | ||||
\(244\) | − | 987.850i | − | 0.259183i | ||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 285.785 | − | 566.732i | 0.0740691 | − | 0.146884i | ||||
\(247\) | −4498.08 | + | 4498.08i | −1.15873 | + | 1.15873i | ||||
\(248\) | 2086.70 | − | 2086.70i | 0.534296 | − | 0.534296i | ||||
\(249\) | 236.198 | − | 468.396i | 0.0601141 | − | 0.119210i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 5602.53i | 1.40888i | 0.709765 | + | 0.704439i | \(0.248801\pi\) | ||||
−0.709765 | + | 0.704439i | \(0.751199\pi\) | |||||||
\(252\) | 589.389 | + | 88.3033i | 0.147333 | + | 0.0220737i | ||||
\(253\) | 2091.04 | + | 2091.04i | 0.519615 | + | 0.519615i | ||||
\(254\) | 3705.15 | 0.915283 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −4361.15 | −1.06473 | ||||||||
\(257\) | −980.647 | − | 980.647i | −0.238020 | − | 0.238020i | 0.578010 | − | 0.816030i | \(-0.303829\pi\) |
−0.816030 | + | 0.578010i | \(0.803829\pi\) | |||||||
\(258\) | 607.746 | + | 1844.17i | 0.146654 | + | 0.445012i | ||||
\(259\) | − | 80.3628i | − | 0.0192799i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −3890.25 | + | 2876.45i | −0.922607 | + | 0.682176i | ||||
\(262\) | 123.488 | − | 123.488i | 0.0291188 | − | 0.0291188i | ||||
\(263\) | −1277.16 | + | 1277.16i | −0.299440 | + | 0.299440i | −0.840795 | − | 0.541354i | \(-0.817912\pi\) |
0.541354 | + | 0.840795i | \(0.317912\pi\) | |||||||
\(264\) | 6860.11 | + | 3459.34i | 1.59928 | + | 0.806468i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 991.479i | 0.228539i | ||||||||
\(267\) | 1125.81 | − | 371.010i | 0.258047 | − | 0.0850391i | ||||
\(268\) | 1314.78 | + | 1314.78i | 0.299676 | + | 0.299676i | ||||
\(269\) | −1742.31 | −0.394909 | −0.197454 | − | 0.980312i | \(-0.563267\pi\) | ||||
−0.197454 | + | 0.980312i | \(0.563267\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2262.36 | 0.507116 | 0.253558 | − | 0.967320i | \(-0.418399\pi\) | ||||
0.253558 | + | 0.967320i | \(0.418399\pi\) | |||||||
\(272\) | −681.292 | − | 681.292i | −0.151873 | − | 0.151873i | ||||
\(273\) | 1807.09 | − | 595.527i | 0.400624 | − | 0.132025i | ||||
\(274\) | − | 4161.70i | − | 0.917582i | ||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 909.951 | + | 458.860i | 0.198452 | + | 0.100073i | ||||
\(277\) | 3801.88 | − | 3801.88i | 0.824668 | − | 0.824668i | −0.162106 | − | 0.986773i | \(-0.551829\pi\) |
0.986773 | + | 0.162106i | \(0.0518286\pi\) | |||||||
\(278\) | −2962.89 | + | 2962.89i | −0.639216 | + | 0.639216i | ||||
\(279\) | −2681.69 | + | 1982.84i | −0.575443 | + | 0.425482i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 3737.11i | 0.793372i | 0.917954 | + | 0.396686i | \(0.129840\pi\) | ||||
−0.917954 | + | 0.396686i | \(0.870160\pi\) | |||||||
\(282\) | −258.712 | − | 785.046i | −0.0546314 | − | 0.165776i | ||||
\(283\) | −549.478 | − | 549.478i | −0.115417 | − | 0.115417i | 0.647039 | − | 0.762457i | \(-0.276007\pi\) |
−0.762457 | + | 0.647039i | \(0.776007\pi\) | |||||||
\(284\) | 4451.66 | 0.930132 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 8317.69 | 1.71970 | ||||||||
\(287\) | 235.335 | + | 235.335i | 0.0484020 | + | 0.0484020i | ||||
\(288\) | 4349.03 | + | 651.579i | 0.889822 | + | 0.133315i | ||||
\(289\) | − | 382.245i | − | 0.0778028i | ||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 296.245 | − | 587.475i | 0.0596777 | − | 0.118345i | ||||
\(292\) | −853.986 | + | 853.986i | −0.171150 | + | 0.171150i | ||||
\(293\) | −5554.60 | + | 5554.60i | −1.10752 | + | 1.10752i | −0.114043 | + | 0.993476i | \(0.536380\pi\) |
−0.993476 | + | 0.114043i | \(0.963620\pi\) | |||||||
\(294\) | −1450.31 | + | 2876.07i | −0.287700 | + | 0.570529i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | − | 357.027i | − | 0.0701074i | ||||||
\(297\) | −7088.15 | − | 5015.19i | −1.38484 | − | 0.979835i | ||||
\(298\) | −1727.46 | − | 1727.46i | −0.335803 | − | 0.335803i | ||||
\(299\) | 3253.59 | 0.629298 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1018.16 | −0.194969 | ||||||||
\(302\) | −3299.54 | − | 3299.54i | −0.628700 | − | 0.628700i | ||||
\(303\) | 2463.70 | + | 7475.96i | 0.467115 | + | 1.41744i | ||||
\(304\) | 1337.20i | 0.252282i | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 2132.53 | + | 2884.13i | 0.398394 | + | 0.538807i | ||||
\(307\) | −5210.62 | + | 5210.62i | −0.968684 | + | 0.968684i | −0.999524 | − | 0.0308404i | \(-0.990182\pi\) |
0.0308404 | + | 0.999524i | \(0.490182\pi\) | |||||||
\(308\) | −965.976 | + | 965.976i | −0.178706 | + | 0.178706i | ||||
\(309\) | −465.916 | − | 234.947i | −0.0857769 | − | 0.0432546i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 2717.37i | 0.495460i | 0.968829 | + | 0.247730i | \(0.0796846\pi\) | ||||
−0.968829 | + | 0.247730i | \(0.920315\pi\) | |||||||
\(312\) | 8028.37 | − | 2645.74i | 1.45678 | − | 0.480083i | ||||
\(313\) | −6206.89 | − | 6206.89i | −1.12088 | − | 1.12088i | −0.991610 | − | 0.129266i | \(-0.958738\pi\) |
−0.129266 | − | 0.991610i | \(-0.541262\pi\) | |||||||
\(314\) | 1979.01 | 0.355675 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −2778.12 | −0.494561 | ||||||||
\(317\) | 3909.79 | + | 3909.79i | 0.692731 | + | 0.692731i | 0.962832 | − | 0.270101i | \(-0.0870571\pi\) |
−0.270101 | + | 0.962832i | \(0.587057\pi\) | |||||||
\(318\) | −3233.60 | + | 1065.63i | −0.570224 | + | 0.187917i | ||||
\(319\) | − | 11090.2i | − | 1.94650i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 188.993 | + | 95.3031i | 0.0328615 | + | 0.0165710i | ||||
\(322\) | 358.583 | − | 358.583i | 0.0620591 | − | 0.0620591i | ||||
\(323\) | 4446.36 | − | 4446.36i | 0.765950 | − | 0.765950i | ||||
\(324\) | −2860.93 | − | 876.944i | −0.490557 | − | 0.150368i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | − | 5330.28i | − | 0.905574i | ||||||
\(327\) | 976.210 | + | 2962.26i | 0.165090 | + | 0.500958i | ||||
\(328\) | 1045.52 | + | 1045.52i | 0.176004 | + | 0.176004i | ||||
\(329\) | 433.420 | 0.0726298 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 3332.16 | 0.553330 | 0.276665 | − | 0.960966i | \(-0.410771\pi\) | ||||
0.276665 | + | 0.960966i | \(0.410771\pi\) | |||||||
\(332\) | 293.018 | + | 293.018i | 0.0484382 | + | 0.0484382i | ||||
\(333\) | −59.7854 | + | 399.043i | −0.00983850 | + | 0.0656680i | ||||
\(334\) | − | 2798.83i | − | 0.458519i | ||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 180.089 | − | 357.129i | 0.0292400 | − | 0.0579850i | ||||
\(337\) | −2214.55 | + | 2214.55i | −0.357965 | + | 0.357965i | −0.863063 | − | 0.505097i | \(-0.831457\pi\) |
0.505097 | + | 0.863063i | \(0.331457\pi\) | |||||||
\(338\) | 3404.93 | − | 3404.93i | 0.547940 | − | 0.547940i | ||||
\(339\) | −3803.79 | + | 7543.17i | −0.609420 | + | 1.20852i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 7644.91i | − | 1.21406i | ||||||
\(342\) | 737.605 | − | 4923.21i | 0.116623 | − | 0.778412i | ||||
\(343\) | −2498.52 | − | 2498.52i | −0.393317 | − | 0.393317i | ||||
\(344\) | −4523.36 | −0.708963 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −6589.07 | −1.02379 | ||||||||
\(347\) | 5447.38 | + | 5447.38i | 0.842740 | + | 0.842740i | 0.989214 | − | 0.146475i | \(-0.0467927\pi\) |
−0.146475 | + | 0.989214i | \(0.546793\pi\) | |||||||
\(348\) | −1196.23 | − | 3629.88i | −0.184266 | − | 0.559144i | ||||
\(349\) | 2153.29i | 0.330267i | 0.986271 | + | 0.165134i | \(0.0528055\pi\) | ||||
−0.986271 | + | 0.165134i | \(0.947194\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −9416.21 | + | 1612.73i | −1.43191 | + | 0.245245i | ||||
\(352\) | −7127.81 | + | 7127.81i | −1.07930 | + | 1.07930i | ||||
\(353\) | 723.013 | − | 723.013i | 0.109014 | − | 0.109014i | −0.650496 | − | 0.759510i | \(-0.725439\pi\) |
0.759510 | + | 0.650496i | \(0.225439\pi\) | |||||||
\(354\) | 2385.58 | + | 1202.98i | 0.358171 | + | 0.180614i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 936.378i | 0.139404i | ||||||||
\(357\) | −1786.31 | + | 588.679i | −0.264823 | + | 0.0872722i | ||||
\(358\) | −3636.72 | − | 3636.72i | −0.536890 | − | 0.536890i | ||||
\(359\) | −2816.10 | −0.414006 | −0.207003 | − | 0.978340i | \(-0.566371\pi\) | ||||
−0.207003 | + | 0.978340i | \(0.566371\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1868.06 | −0.272352 | ||||||||
\(362\) | 5139.06 | + | 5139.06i | 0.746140 | + | 0.746140i | ||||
\(363\) | 12334.8 | − | 4064.93i | 1.78350 | − | 0.587750i | ||||
\(364\) | 1503.03i | 0.216429i | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 2203.77 | + | 1111.29i | 0.314734 | + | 0.158711i | ||||
\(367\) | 7080.66 | − | 7080.66i | 1.00710 | − | 1.00710i | 0.00712974 | − | 0.999975i | \(-0.497731\pi\) |
0.999975 | − | 0.00712974i | \(-0.00226949\pi\) | |||||||
\(368\) | 483.618 | − | 483.618i | 0.0685064 | − | 0.0685064i | ||||
\(369\) | −993.485 | − | 1343.64i | −0.140159 | − | 0.189558i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 1785.25i | − | 0.249827i | ||||||
\(372\) | −824.601 | − | 2502.21i | −0.114929 | − | 0.348746i | ||||
\(373\) | 3207.86 | + | 3207.86i | 0.445299 | + | 0.445299i | 0.893788 | − | 0.448489i | \(-0.148038\pi\) |
−0.448489 | + | 0.893788i | \(0.648038\pi\) | |||||||
\(374\) | −8222.04 | −1.13677 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 1925.55 | 0.264103 | ||||||||
\(377\) | −8628.04 | − | 8628.04i | −1.17869 | − | 1.17869i | ||||
\(378\) | −860.032 | + | 1215.51i | −0.117024 | + | 0.165395i | ||||
\(379\) | 2987.72i | 0.404930i | 0.979289 | + | 0.202465i | \(0.0648953\pi\) | ||||
−0.979289 | + | 0.202465i | \(0.935105\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 4392.18 | − | 8710.00i | 0.590599 | − | 1.17120i | ||||
\(382\) | −1176.16 | + | 1176.16i | −0.157533 | + | 0.157533i | ||||
\(383\) | 993.565 | − | 993.565i | 0.132556 | − | 0.132556i | −0.637716 | − | 0.770272i | \(-0.720121\pi\) |
0.770272 | + | 0.637716i | \(0.220121\pi\) | |||||||
\(384\) | −1035.36 | + | 2053.19i | −0.137593 | + | 0.272856i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | − | 6541.44i | − | 0.862566i | ||||||
\(387\) | 5055.69 | + | 757.452i | 0.664070 | + | 0.0994921i | ||||
\(388\) | 367.511 | + | 367.511i | 0.0480865 | + | 0.0480865i | ||||
\(389\) | 12754.3 | 1.66239 | 0.831197 | − | 0.555979i | \(-0.187656\pi\) | ||||
0.831197 | + | 0.555979i | \(0.187656\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −3216.18 | −0.415982 | ||||||||
\(392\) | −5305.84 | − | 5305.84i | −0.683636 | − | 0.683636i | ||||
\(393\) | −143.908 | − | 436.680i | −0.0184712 | − | 0.0560498i | ||||
\(394\) | 864.309i | 0.110516i | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 5515.21 | − | 4077.94i | 0.699873 | − | 0.517486i | ||||
\(397\) | 8826.34 | − | 8826.34i | 1.11582 | − | 1.11582i | 0.123474 | − | 0.992348i | \(-0.460596\pi\) |
0.992348 | − | 0.123474i | \(-0.0394036\pi\) | |||||||
\(398\) | 2454.93 | − | 2454.93i | 0.309182 | − | 0.309182i | ||||
\(399\) | 2330.75 | + | 1175.33i | 0.292440 | + | 0.147468i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 4022.87i | 0.500979i | 0.968119 | + | 0.250490i | \(0.0805916\pi\) | ||||
−0.968119 | + | 0.250490i | \(0.919408\pi\) | |||||||
\(402\) | −4412.19 | + | 1454.04i | −0.547413 | + | 0.180400i | ||||
\(403\) | −5947.62 | − | 5947.62i | −0.735166 | − | 0.735166i | ||||
\(404\) | −6218.04 | −0.765740 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −1901.81 | −0.232476 | ||||||||
\(407\) | −654.010 | − | 654.010i | −0.0796513 | − | 0.0796513i | ||||
\(408\) | −7936.04 | + | 2615.32i | −0.962972 | + | 0.317347i | ||||
\(409\) | 12309.0i | 1.48812i | 0.668110 | + | 0.744062i | \(0.267103\pi\) | ||||
−0.668110 | + | 0.744062i | \(0.732897\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −9783.24 | − | 4933.38i | −1.17414 | − | 0.592082i | ||||
\(412\) | 291.467 | − | 291.467i | 0.0348533 | − | 0.0348533i | ||||
\(413\) | −990.612 | + | 990.612i | −0.118026 | + | 0.118026i | ||||
\(414\) | −2047.32 | + | 1513.79i | −0.243044 | + | 0.179707i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 11090.7i | 1.30712i | ||||||||
\(417\) | 3452.81 | + | 10477.4i | 0.405480 | + | 1.23041i | ||||
\(418\) | 8068.88 | + | 8068.88i | 0.944167 | + | 0.944167i | ||||
\(419\) | 3075.95 | 0.358639 | 0.179320 | − | 0.983791i | \(-0.442610\pi\) | ||||
0.179320 | + | 0.983791i | \(0.442610\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 12055.0 | 1.39554 | 0.697770 | − | 0.716322i | \(-0.254176\pi\) | ||||
0.697770 | + | 0.716322i | \(0.254176\pi\) | |||||||
\(422\) | 1876.54 | + | 1876.54i | 0.216466 | + | 0.216466i | ||||
\(423\) | −2152.16 | − | 322.440i | −0.247379 | − | 0.0370628i | ||||
\(424\) | − | 7931.33i | − | 0.908442i | ||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −5007.94 | + | 9931.08i | −0.569566 | + | 1.12949i | ||||
\(427\) | −915.113 | + | 915.113i | −0.103713 | + | 0.103713i | ||||
\(428\) | −118.230 | + | 118.230i | −0.0133524 | + | 0.0133524i | ||||
\(429\) | 9860.00 | − | 19553.1i | 1.10966 | − | 2.20054i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 6265.92i | − | 0.700275i | −0.936698 | − | 0.350138i | \(-0.886135\pi\) | ||
0.936698 | − | 0.350138i | \(-0.113865\pi\) | |||||||
\(432\) | −1159.92 | + | 1639.35i | −0.129182 | + | 0.182577i | ||||
\(433\) | 8190.21 | + | 8190.21i | 0.908998 | + | 0.908998i | 0.996191 | − | 0.0871933i | \(-0.0277898\pi\) |
−0.0871933 | + | 0.996191i | \(0.527790\pi\) | |||||||
\(434\) | −1310.99 | −0.144999 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −2463.82 | −0.270632 | ||||||||
\(437\) | 3156.27 | + | 3156.27i | 0.345503 | + | 0.345503i | ||||
\(438\) | −944.434 | − | 2865.83i | −0.103029 | − | 0.312637i | ||||
\(439\) | − | 8494.79i | − | 0.923541i | −0.887000 | − | 0.461770i | \(-0.847214\pi\) | ||
0.887000 | − | 0.461770i | \(-0.152786\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 5041.76 | + | 6818.72i | 0.544408 | + | 0.736284i | ||||
\(442\) | −6396.61 | + | 6396.61i | −0.688362 | + | 0.688362i | ||||
\(443\) | −9078.70 | + | 9078.70i | −0.973684 | + | 0.973684i | −0.999663 | − | 0.0259785i | \(-0.991730\pi\) |
0.0259785 | + | 0.999663i | \(0.491730\pi\) | |||||||
\(444\) | −284.603 | − | 143.517i | −0.0304204 | − | 0.0153401i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 8782.26i | 0.932404i | ||||||||
\(447\) | −6108.67 | + | 2013.11i | −0.646376 | + | 0.213013i | ||||
\(448\) | 1657.74 | + | 1657.74i | 0.174824 | + | 0.174824i | ||||
\(449\) | −4883.04 | −0.513241 | −0.256620 | − | 0.966512i | \(-0.582609\pi\) | ||||
−0.256620 | + | 0.966512i | \(0.582609\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 3830.41 | 0.399927 | ||||||||
\(452\) | −4718.84 | − | 4718.84i | −0.491053 | − | 0.491053i | ||||
\(453\) | −11667.9 | + | 3845.14i | −1.21016 | + | 0.398809i | ||||
\(454\) | 12358.9i | 1.27760i | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 10354.8 | + | 5221.61i | 1.06340 | + | 0.536237i | ||||
\(457\) | 5081.87 | − | 5081.87i | 0.520175 | − | 0.520175i | −0.397449 | − | 0.917624i | \(-0.630104\pi\) |
0.917624 | + | 0.397449i | \(0.130104\pi\) | |||||||
\(458\) | 2873.91 | − | 2873.91i | 0.293207 | − | 0.293207i | ||||
\(459\) | 9307.92 | − | 1594.18i | 0.946529 | − | 0.162113i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 17258.2i | 1.74359i | 0.489871 | + | 0.871795i | \(0.337044\pi\) | ||||
−0.489871 | + | 0.871795i | \(0.662956\pi\) | |||||||
\(462\) | −1068.28 | − | 3241.65i | −0.107578 | − | 0.326440i | ||||
\(463\) | −2519.17 | − | 2519.17i | −0.252864 | − | 0.252864i | 0.569280 | − | 0.822144i | \(-0.307222\pi\) |
−0.822144 | + | 0.569280i | \(0.807222\pi\) | |||||||
\(464\) | −2564.96 | −0.256628 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −6426.65 | −0.638860 | ||||||||
\(467\) | 4169.76 | + | 4169.76i | 0.413177 | + | 0.413177i | 0.882844 | − | 0.469667i | \(-0.155626\pi\) |
−0.469667 | + | 0.882844i | \(0.655626\pi\) | |||||||
\(468\) | 1118.17 | − | 7463.32i | 0.110443 | − | 0.737162i | ||||
\(469\) | − | 2435.95i | − | 0.239833i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 2345.97 | − | 4652.22i | 0.229505 | − | 0.455123i | ||||
\(472\) | −4400.99 | + | 4400.99i | −0.429178 | + | 0.429178i | ||||
\(473\) | −8285.99 | + | 8285.99i | −0.805476 | + | 0.805476i | ||||
\(474\) | 3125.27 | − | 6197.62i | 0.302844 | − | 0.600561i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | − | 1485.74i | − | 0.143065i | ||||||
\(477\) | −1328.13 | + | 8864.72i | −0.127486 | + | 0.850917i | ||||
\(478\) | 3431.85 | + | 3431.85i | 0.328387 | + | 0.328387i | ||||
\(479\) | −4040.09 | −0.385378 | −0.192689 | − | 0.981260i | \(-0.561721\pi\) | ||||
−0.192689 | + | 0.981260i | \(0.561721\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1017.62 | −0.0964645 | ||||||||
\(482\) | −6225.81 | − | 6225.81i | −0.588336 | − | 0.588336i | ||||
\(483\) | −417.876 | − | 1268.02i | −0.0393665 | − | 0.119456i | ||||
\(484\) | 10259.3i | 0.963496i | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 5174.78 | − | 5395.84i | 0.482989 | − | 0.503622i | ||||
\(487\) | 5543.45 | − | 5543.45i | 0.515806 | − | 0.515806i | −0.400493 | − | 0.916300i | \(-0.631161\pi\) |
0.916300 | + | 0.400493i | \(0.131161\pi\) | |||||||
\(488\) | −4065.57 | + | 4065.57i | −0.377130 | + | 0.377130i | ||||
\(489\) | −12530.3 | − | 6318.65i | −1.15877 | − | 0.584334i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 9978.85i | − | 0.917187i | −0.888646 | − | 0.458594i | \(-0.848353\pi\) | ||
0.888646 | − | 0.458594i | \(-0.151647\pi\) | |||||||
\(492\) | 1253.71 | − | 413.159i | 0.114881 | − | 0.0378591i | ||||
\(493\) | 8528.82 | + | 8528.82i | 0.779145 | + | 0.779145i | ||||
\(494\) | 12554.9 | 1.14347 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −1768.12 | −0.160063 | ||||||||
\(497\) | −4123.87 | − | 4123.87i | −0.372195 | − | 0.372195i | ||||
\(498\) | −983.321 | + | 324.053i | −0.0884812 | + | 0.0291589i | ||||
\(499\) | 1383.97i | 0.124159i | 0.998071 | + | 0.0620793i | \(0.0197732\pi\) | ||||
−0.998071 | + | 0.0620793i | \(0.980227\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −6579.44 | − | 3317.81i | −0.586722 | − | 0.295866i | ||||
\(502\) | 7818.80 | − | 7818.80i | 0.695160 | − | 0.695160i | ||||
\(503\) | 11241.0 | − | 11241.0i | 0.996447 | − | 0.996447i | −0.00354658 | − | 0.999994i | \(-0.501129\pi\) |
0.999994 | + | 0.00354658i | \(0.00112892\pi\) | |||||||
\(504\) | −2062.25 | − | 2789.09i | −0.182262 | − | 0.246500i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | − | 5836.45i | − | 0.512771i | ||||||
\(507\) | −3967.95 | − | 12040.5i | −0.347580 | − | 1.05471i | ||||
\(508\) | 5448.79 | + | 5448.79i | 0.475887 | + | 0.475887i | ||||
\(509\) | 20619.5 | 1.79557 | 0.897785 | − | 0.440434i | \(-0.145175\pi\) | ||||
0.897785 | + | 0.440434i | \(0.145175\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1582.21 | 0.136972 | ||||||||
\(512\) | 3583.00 | + | 3583.00i | 0.309273 | + | 0.309273i | ||||
\(513\) | −10699.0 | − | 7570.05i | −0.920806 | − | 0.651513i | ||||
\(514\) | 2737.15i | 0.234884i | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −1818.29 | + | 3605.79i | −0.155127 | + | 0.307628i | ||||
\(517\) | 3527.27 | − | 3527.27i | 0.300056 | − | 0.300056i | ||||
\(518\) | −112.153 | + | 112.153i | −0.00951298 | + | 0.00951298i | ||||
\(519\) | −7810.85 | + | 15489.5i | −0.660613 | + | 1.31004i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 3009.42i | 0.253062i | 0.991963 | + | 0.126531i | \(0.0403843\pi\) | ||||
−0.991963 | + | 0.126531i | \(0.959616\pi\) | |||||||
\(522\) | 9443.50 | + | 1414.84i | 0.791822 | + | 0.118632i | ||||
\(523\) | −3916.11 | − | 3916.11i | −0.327418 | − | 0.327418i | 0.524186 | − | 0.851604i | \(-0.324370\pi\) |
−0.851604 | + | 0.524186i | \(0.824370\pi\) | |||||||
\(524\) | 363.203 | 0.0302797 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 3564.76 | 0.295496 | ||||||||
\(527\) | 5879.22 | + | 5879.22i | 0.485964 | + | 0.485964i | ||||
\(528\) | −1440.79 | − | 4371.99i | −0.118754 | − | 0.360353i | ||||
\(529\) | 9883.98i | 0.812360i | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 5655.87 | − | 4181.95i | 0.462229 | − | 0.341772i | ||||
\(532\) | −1458.07 | + | 1458.07i | −0.118826 | + | 0.118826i | ||||
\(533\) | 2980.00 | − | 2980.00i | 0.242173 | − | 0.242173i | ||||
\(534\) | −2088.94 | − | 1053.39i | −0.169283 | − | 0.0853643i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | − | 10822.2i | − | 0.872101i | ||||||
\(537\) | −12860.2 | + | 4238.07i | −1.03344 | + | 0.340570i | ||||
\(538\) | 2431.54 | + | 2431.54i | 0.194853 | + | 0.194853i | ||||
\(539\) | −19438.7 | −1.55340 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −13166.8 | −1.04637 | −0.523184 | − | 0.852220i | \(-0.675256\pi\) | ||||
−0.523184 | + | 0.852220i | \(0.675256\pi\) | |||||||
\(542\) | −3157.31 | − | 3157.31i | −0.250218 | − | 0.250218i | ||||
\(543\) | 18172.8 | − | 5988.83i | 1.43622 | − | 0.473306i | ||||
\(544\) | − | 10963.1i | − | 0.864043i | ||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −3353.06 | − | 1690.84i | −0.262816 | − | 0.132530i | ||||
\(547\) | −8856.30 | + | 8856.30i | −0.692263 | + | 0.692263i | −0.962729 | − | 0.270466i | \(-0.912822\pi\) |
0.270466 | + | 0.962729i | \(0.412822\pi\) | |||||||
\(548\) | 6120.18 | − | 6120.18i | 0.477083 | − | 0.477083i | ||||
\(549\) | 5224.81 | − | 3863.22i | 0.406174 | − | 0.300325i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 16739.9i | − | 1.29427i | ||||||
\(552\) | −1856.50 | − | 5633.44i | −0.143148 | − | 0.434375i | ||||
\(553\) | 2573.56 | + | 2573.56i | 0.197900 | + | 0.197900i | ||||
\(554\) | −10611.7 | −0.813805 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −8714.42 | −0.664701 | ||||||||
\(557\) | 14446.6 | + | 14446.6i | 1.09896 | + | 1.09896i | 0.994532 | + | 0.104431i | \(0.0333020\pi\) |
0.104431 | + | 0.994532i | \(0.466698\pi\) | |||||||
\(558\) | 6509.75 | + | 975.302i | 0.493870 | + | 0.0739925i | ||||
\(559\) | 12892.7i | 0.975500i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −9746.61 | + | 19328.2i | −0.733516 | + | 1.45461i | ||||
\(562\) | 5215.46 | − | 5215.46i | 0.391461 | − | 0.391461i | ||||
\(563\) | 8100.71 | − | 8100.71i | 0.606402 | − | 0.606402i | −0.335602 | − | 0.942004i | \(-0.608940\pi\) |
0.942004 | + | 0.335602i | \(0.108940\pi\) | |||||||
\(564\) | 774.027 | − | 1534.95i | 0.0577879 | − | 0.114597i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 1533.69i | 0.113897i | ||||||||
\(567\) | 1837.90 | + | 3462.65i | 0.136128 | + | 0.256468i | ||||
\(568\) | −18321.1 | − | 18321.1i | −1.35341 | − | 1.35341i | ||||
\(569\) | −11158.8 | −0.822149 | −0.411074 | − | 0.911602i | \(-0.634846\pi\) | ||||
−0.411074 | + | 0.911602i | \(0.634846\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −7508.76 | −0.550318 | −0.275159 | − | 0.961399i | \(-0.588731\pi\) | ||||
−0.275159 | + | 0.961399i | \(0.588731\pi\) | |||||||
\(572\) | 12232.0 | + | 12232.0i | 0.894133 | + | 0.894133i | ||||
\(573\) | 1370.64 | + | 4159.14i | 0.0999291 | + | 0.303229i | ||||
\(574\) | − | 656.859i | − | 0.0477644i | ||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −6998.29 | − | 9464.83i | −0.506242 | − | 0.684666i | ||||
\(577\) | −5375.41 | + | 5375.41i | −0.387836 | + | 0.387836i | −0.873915 | − | 0.486079i | \(-0.838427\pi\) |
0.486079 | + | 0.873915i | \(0.338427\pi\) | |||||||
\(578\) | −533.456 | + | 533.456i | −0.0383890 | + | 0.0383890i | ||||
\(579\) | −15377.5 | − | 7754.39i | −1.10374 | − | 0.556583i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − | 542.886i | − | 0.0387654i | ||||||
\(582\) | −1233.31 | + | 406.435i | −0.0878388 | + | 0.0289472i | ||||
\(583\) | −14528.8 | − | 14528.8i | −1.03211 | − | 1.03211i | ||||
\(584\) | 7029.28 | 0.498071 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 15503.8 | 1.09293 | ||||||||
\(587\) | −13341.5 | − | 13341.5i | −0.938094 | − | 0.938094i | 0.0600982 | − | 0.998192i | \(-0.480859\pi\) |
−0.998192 | + | 0.0600982i | \(0.980859\pi\) | |||||||
\(588\) | −6362.36 | + | 2096.71i | −0.446223 | + | 0.147053i | ||||
\(589\) | − | 11539.4i | − | 0.807254i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 2031.80 | + | 1024.57i | 0.141416 | + | 0.0713119i | ||||
\(592\) | −151.260 | + | 151.260i | −0.0105013 | + | 0.0105013i | ||||
\(593\) | −1787.90 | + | 1787.90i | −0.123812 | + | 0.123812i | −0.766298 | − | 0.642486i | \(-0.777903\pi\) |
0.642486 | + | 0.766298i | \(0.277903\pi\) | |||||||
\(594\) | 2892.99 | + | 16891.2i | 0.199833 | + | 1.16676i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | − | 5080.81i | − | 0.349191i | ||||||
\(597\) | −2860.86 | − | 8681.13i | −0.196126 | − | 0.595134i | ||||
\(598\) | −4540.67 | − | 4540.67i | −0.310504 | − | 0.310504i | ||||
\(599\) | 12112.1 | 0.826190 | 0.413095 | − | 0.910688i | \(-0.364448\pi\) | ||||
0.413095 | + | 0.910688i | \(0.364448\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 16891.6 | 1.14646 | 0.573230 | − | 0.819394i | \(-0.305690\pi\) | ||||
0.573230 | + | 0.819394i | \(0.305690\pi\) | |||||||
\(602\) | 1420.93 | + | 1420.93i | 0.0962003 | + | 0.0962003i | ||||
\(603\) | −1812.21 | + | 12095.8i | −0.122386 | + | 0.816877i | ||||
\(604\) | − | 9704.60i | − | 0.653766i | ||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 6995.04 | − | 13871.6i | 0.468901 | − | 0.929863i | ||||
\(607\) | −910.639 | + | 910.639i | −0.0608924 | + | 0.0608924i | −0.736897 | − | 0.676005i | \(-0.763710\pi\) |
0.676005 | + | 0.736897i | \(0.263710\pi\) | |||||||
\(608\) | −10758.9 | + | 10758.9i | −0.717649 | + | 0.717649i | ||||
\(609\) | −2254.46 | + | 4470.75i | −0.150009 | + | 0.297478i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 5488.31i | − | 0.363393i | ||||||
\(612\) | −1105.31 | + | 7377.49i | −0.0730057 | + | 0.487283i | ||||
\(613\) | 12990.7 | + | 12990.7i | 0.855934 | + | 0.855934i | 0.990856 | − | 0.134922i | \(-0.0430785\pi\) |
−0.134922 | + | 0.990856i | \(0.543079\pi\) | |||||||
\(614\) | 14543.7 | 0.955924 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 7951.08 | 0.520062 | ||||||||
\(617\) | −15676.0 | − | 15676.0i | −1.02284 | − | 1.02284i | −0.999733 | − | 0.0231063i | \(-0.992644\pi\) |
−0.0231063 | − | 0.999733i | \(-0.507356\pi\) | |||||||
\(618\) | 322.337 | + | 978.114i | 0.0209811 | + | 0.0636659i | ||||
\(619\) | − | 22193.5i | − | 1.44109i | −0.693411 | − | 0.720543i | \(-0.743893\pi\) | ||
0.693411 | − | 0.720543i | \(-0.256107\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1131.64 | + | 6607.27i | 0.0731257 | + | 0.426958i | ||||
\(622\) | 3792.33 | − | 3792.33i | 0.244467 | − | 0.244467i | ||||
\(623\) | 867.430 | − | 867.430i | 0.0557831 | − | 0.0557831i | ||||
\(624\) | −4522.25 | − | 2280.43i | −0.290120 | − | 0.146299i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 17324.5i | 1.10611i | ||||||||
\(627\) | 28533.2 | − | 9403.11i | 1.81740 | − | 0.598922i | ||||
\(628\) | 2910.33 | + | 2910.33i | 0.184928 | + | 0.184928i | ||||
\(629\) | 1005.92 | 0.0637655 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −3000.41 | −0.189294 | −0.0946470 | − | 0.995511i | \(-0.530172\pi\) | ||||
−0.0946470 | + | 0.995511i | \(0.530172\pi\) | |||||||
\(632\) | 11433.5 | + | 11433.5i | 0.719622 | + | 0.719622i | ||||
\(633\) | 6635.83 | − | 2186.83i | 0.416667 | − | 0.137313i | ||||
\(634\) | − | 10912.9i | − | 0.683606i | ||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −6322.44 | − | 3188.21i | −0.394184 | − | 0.198775i | ||||
\(637\) | −15123.0 | + | 15123.0i | −0.940651 | + | 0.940651i | ||||
\(638\) | −15477.4 | + | 15477.4i | −0.960432 | + | 0.960432i | ||||
\(639\) | 17409.3 | + | 23545.1i | 1.07778 | + | 1.45764i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 26111.9i | 1.60898i | 0.593963 | + | 0.804492i | \(0.297562\pi\) | ||||
−0.593963 | + | 0.804492i | \(0.702438\pi\) | |||||||
\(642\) | −130.752 | − | 396.759i | −0.00803794 | − | 0.0243907i | ||||
\(643\) | −15717.3 | − | 15717.3i | −0.963964 | − | 0.963964i | 0.0354091 | − | 0.999373i | \(-0.488727\pi\) |
−0.999373 | + | 0.0354091i | \(0.988727\pi\) | |||||||
\(644\) | 1054.66 | 0.0645334 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −12410.5 | −0.755861 | ||||||||
\(647\) | −16612.6 | − | 16612.6i | −1.00944 | − | 1.00944i | −0.999955 | − | 0.00948360i | \(-0.996981\pi\) |
−0.00948360 | − | 0.999955i | \(-0.503019\pi\) | |||||||
\(648\) | 8165.23 | + | 15383.5i | 0.495001 | + | 0.932593i | ||||
\(649\) | 16123.6i | 0.975205i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1554.08 | + | 3081.85i | −0.0935625 | + | 0.185541i | ||||
\(652\) | 7838.70 | − | 7838.70i | 0.470839 | − | 0.470839i | ||||
\(653\) | 592.526 | − | 592.526i | 0.0355090 | − | 0.0355090i | −0.689129 | − | 0.724638i | \(-0.742007\pi\) |
0.724638 | + | 0.689129i | \(0.242007\pi\) | |||||||
\(654\) | 2771.70 | − | 5496.46i | 0.165722 | − | 0.328637i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | − | 885.902i | − | 0.0527266i | ||||||
\(657\) | −7856.51 | − | 1177.08i | −0.466532 | − | 0.0698966i | ||||
\(658\) | −604.874 | − | 604.874i | −0.0358365 | − | 0.0358365i | ||||
\(659\) | −16623.0 | −0.982608 | −0.491304 | − | 0.870988i | \(-0.663480\pi\) | ||||
−0.491304 | + | 0.870988i | \(0.663480\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 10421.2 | 0.613217 | 0.306609 | − | 0.951836i | \(-0.400806\pi\) | ||||
0.306609 | + | 0.951836i | \(0.400806\pi\) | |||||||
\(662\) | −4650.32 | − | 4650.32i | −0.273021 | − | 0.273021i | ||||
\(663\) | 7454.33 | + | 22619.7i | 0.436655 | + | 1.32500i | ||||
\(664\) | − | 2411.87i | − | 0.140962i | ||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 640.335 | − | 473.463i | 0.0372559 | − | 0.0275470i | ||||
\(667\) | −6054.22 | + | 6054.22i | −0.351455 | + | 0.351455i | ||||
\(668\) | 4115.95 | − | 4115.95i | 0.238400 | − | 0.238400i | ||||
\(669\) | 20645.2 | + | 10410.7i | 1.19311 | + | 0.601647i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 14894.8i | 0.856940i | ||||||||
\(672\) | 4322.36 | − | 1424.43i | 0.248123 | − | 0.0817688i | ||||
\(673\) | 11678.9 | + | 11678.9i | 0.668930 | + | 0.668930i | 0.957468 | − | 0.288539i | \(-0.0931694\pi\) |
−0.288539 | + | 0.957468i | \(0.593169\pi\) | |||||||
\(674\) | 6181.19 | 0.353250 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 10014.6 | 0.569786 | ||||||||
\(677\) | 15362.2 | + | 15362.2i | 0.872111 | + | 0.872111i | 0.992702 | − | 0.120591i | \(-0.0384791\pi\) |
−0.120591 | + | 0.992702i | \(0.538479\pi\) | |||||||
\(678\) | 15835.6 | − | 5218.63i | 0.896998 | − | 0.295605i | ||||
\(679\) | − | 680.901i | − | 0.0384839i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 29053.0 | + | 14650.5i | 1.63482 | + | 0.824389i | ||||
\(682\) | −10669.1 | + | 10669.1i | −0.599035 | + | 0.599035i | ||||
\(683\) | −494.598 | + | 494.598i | −0.0277090 | + | 0.0277090i | −0.720826 | − | 0.693117i | \(-0.756237\pi\) |
0.693117 | + | 0.720826i | \(0.256237\pi\) | |||||||
\(684\) | 8324.78 | − | 6155.35i | 0.465360 | − | 0.344087i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 6973.80i | 0.388136i | ||||||||
\(687\) | −3349.12 | − | 10162.7i | −0.185993 | − | 0.564385i | ||||
\(688\) | 1916.39 | + | 1916.39i | 0.106194 | + | 0.106194i | ||||
\(689\) | −22606.3 | −1.24997 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −16751.9 | −0.922247 | −0.461124 | − | 0.887336i | \(-0.652554\pi\) | ||||
−0.461124 | + | 0.887336i | \(0.652554\pi\) | |||||||
\(692\) | −9689.87 | − | 9689.87i | −0.532303 | − | 0.532303i | ||||
\(693\) | −8886.78 | − | 1331.43i | −0.487130 | − | 0.0729827i | ||||
\(694\) | − | 15204.6i | − | 0.831639i | ||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −10015.9 | + | 19862.2i | −0.545475 | + | 1.08171i | ||||
\(697\) | −2945.73 | + | 2945.73i | −0.160083 | + | 0.160083i | ||||
\(698\) | 3005.10 | − | 3005.10i | 0.162958 | − | 0.162958i | ||||
\(699\) | −7618.31 | + | 15107.6i | −0.412233 | + | 0.817487i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 3170.42i | 0.170820i | 0.996346 | + | 0.0854102i | \(0.0272201\pi\) | ||||
−0.996346 | + | 0.0854102i | \(0.972780\pi\) | |||||||
\(702\) | 15391.8 | + | 10890.4i | 0.827531 | + | 0.585516i | ||||
\(703\) | −987.179 | − | 987.179i | −0.0529618 | − | 0.0529618i | ||||
\(704\) | 26982.2 | 1.44450 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −2018.05 | −0.107578 | ||||||||
\(707\) | 5760.19 | + | 5760.19i | 0.306413 | + | 0.306413i | ||||
\(708\) | 1739.14 | + | 5277.33i | 0.0923177 | + | 0.280133i | ||||
\(709\) | − | 17069.4i | − | 0.904166i | −0.891976 | − | 0.452083i | \(-0.850681\pi\) | ||
0.891976 | − | 0.452083i | \(-0.149319\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −10864.5 | − | 14693.6i | −0.573066 | − | 0.775041i | ||||
\(712\) | 3853.73 | − | 3853.73i | 0.202843 | − | 0.202843i | ||||
\(713\) | −4173.39 | + | 4173.39i | −0.219207 | + | 0.219207i | ||||
\(714\) | 3314.50 | + | 1671.40i | 0.173728 | + | 0.0876059i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | − | 10696.3i | − | 0.558295i | ||||||
\(717\) | 12135.7 | − | 3999.32i | 0.632102 | − | 0.208309i | ||||
\(718\) | 3930.11 | + | 3930.11i | 0.204276 | + | 0.204276i | ||||
\(719\) | −1123.41 | −0.0582698 | −0.0291349 | − | 0.999575i | \(-0.509275\pi\) | ||||
−0.0291349 | + | 0.999575i | \(0.509275\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −540.011 | −0.0278933 | ||||||||
\(722\) | 2607.04 | + | 2607.04i | 0.134382 | + | 0.134382i | ||||
\(723\) | −22015.8 | + | 7255.28i | −1.13247 | + | 0.373205i | ||||
\(724\) | 15115.0i | 0.775888i | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −22887.2 | − | 11541.3i | −1.17001 | − | 0.589997i | ||||
\(727\) | −8990.29 | + | 8990.29i | −0.458640 | + | 0.458640i | −0.898209 | − | 0.439569i | \(-0.855131\pi\) |
0.439569 | + | 0.898209i | \(0.355131\pi\) | |||||||
\(728\) | 6185.81 | − | 6185.81i | 0.314920 | − | 0.314920i | ||||
\(729\) | −6550.13 | − | 18561.1i | −0.332781 | − | 0.943004i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 12744.5i | − | 0.644831i | ||||||
\(732\) | 1606.59 | + | 4875.12i | 0.0811221 | + | 0.246161i | ||||
\(733\) | −20609.7 | − | 20609.7i | −1.03852 | − | 1.03852i | −0.999228 | − | 0.0392966i | \(-0.987488\pi\) |
−0.0392966 | − | 0.999228i | \(-0.512512\pi\) | |||||||
\(734\) | −19763.3 | −0.993838 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 7782.22 | 0.389750 | ||||||||
\(737\) | −19824.3 | − | 19824.3i | −0.990823 | − | 0.990823i | ||||
\(738\) | −488.666 | + | 3261.65i | −0.0243741 | + | 0.162687i | ||||
\(739\) | − | 14256.7i | − | 0.709664i | −0.934930 | − | 0.354832i | \(-0.884538\pi\) | ||
0.934930 | − | 0.354832i | \(-0.115462\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 14882.9 | − | 29513.9i | 0.737838 | − | 1.46318i | ||||
\(742\) | −2491.47 | + | 2491.47i | −0.123268 | + | 0.123268i | ||||
\(743\) | 14523.7 | − | 14523.7i | 0.717123 | − | 0.717123i | −0.250892 | − | 0.968015i | \(-0.580724\pi\) |
0.968015 | + | 0.250892i | \(0.0807240\pi\) | |||||||
\(744\) | −6904.30 | + | 13691.7i | −0.340220 | + | 0.674680i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | − | 8953.67i | − | 0.439433i | ||||||
\(747\) | −403.876 | + | 2695.71i | −0.0197819 | + | 0.132036i | ||||
\(748\) | −12091.3 | − | 12091.3i | −0.591045 | − | 0.591045i | ||||
\(749\) | 219.048 | 0.0106860 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 32325.6 | 1.57068 | 0.785339 | − | 0.619066i | \(-0.212489\pi\) | ||||
0.785339 | + | 0.619066i | \(0.212489\pi\) | |||||||
\(752\) | −815.789 | − | 815.789i | −0.0395595 | − | 0.0395595i | ||||
\(753\) | −9111.68 | − | 27648.9i | −0.440967 | − | 1.33809i | ||||
\(754\) | 24082.3i | 1.16316i | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −3052.29 | + | 522.770i | −0.146840 | + | 0.0251494i | ||||
\(757\) | 26700.7 | − | 26700.7i | 1.28197 | − | 1.28197i | 0.342430 | − | 0.939544i | \(-0.388750\pi\) |
0.939544 | − | 0.342430i | \(-0.111250\pi\) | |||||||
\(758\) | 4169.61 | − | 4169.61i | 0.199798 | − | 0.199798i | ||||
\(759\) | −13720.2 | − | 6918.68i | −0.656143 | − | 0.330872i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 29296.8i | − | 1.39554i | −0.716319 | − | 0.697772i | \(-0.754175\pi\) | ||
0.716319 | − | 0.697772i | \(-0.245825\pi\) | |||||||
\(762\) | −18285.2 | + | 6025.88i | −0.869295 | + | 0.286476i | ||||
\(763\) | 2282.40 | + | 2282.40i | 0.108294 | + | 0.108294i | ||||
\(764\) | −3459.31 | −0.163813 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −2773.21 | −0.130809 | ||||||||
\(767\) | 12543.9 | + | 12543.9i | 0.590528 | + | 0.590528i | ||||
\(768\) | 21522.6 | − | 7092.76i | 1.01124 | − | 0.333252i | ||||
\(769\) | 3977.36i | 0.186511i | 0.995642 | + | 0.0932556i | \(0.0297274\pi\) | ||||
−0.995642 | + | 0.0932556i | \(0.970273\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 6434.44 | + | 3244.69i | 0.300559 | + | 0.151562i | ||||
\(772\) | 9619.82 | − | 9619.82i | 0.448478 | − | 0.448478i | ||||
\(773\) | −21519.4 | + | 21519.4i | −1.00129 | + | 1.00129i | −0.00129452 | + | 0.999999i | \(0.500412\pi\) |
−0.999999 | + | 0.00129452i | \(0.999588\pi\) | |||||||
\(774\) | −5998.55 | − | 8112.73i | −0.278570 | − | 0.376752i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | − | 3025.04i | − | 0.139939i | ||||||
\(777\) | 130.698 | + | 396.597i | 0.00603446 | + | 0.0183112i | ||||
\(778\) | −17799.8 | − | 17799.8i | −0.820248 | − | 0.820248i | ||||
\(779\) | 5781.72 | 0.265920 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −67122.0 | −3.07531 | ||||||||
\(782\) | 4488.45 | + | 4488.45i | 0.205251 | + | 0.205251i | ||||
\(783\) | 14520.6 | − | 20522.4i | 0.662736 | − | 0.936668i | ||||
\(784\) | 4495.80i | 0.204801i | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −408.588 | + | 810.259i | −0.0185418 | + | 0.0367697i | ||||
\(787\) | −11206.4 | + | 11206.4i | −0.507578 | + | 0.507578i | −0.913782 | − | 0.406204i | \(-0.866852\pi\) |
0.406204 | + | 0.913782i | \(0.366852\pi\) | |||||||
\(788\) | −1271.05 | + | 1271.05i | −0.0574610 | + | 0.0574610i | ||||
\(789\) | 4225.76 | − | 8379.97i | 0.190673 | − | 0.378118i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 8742.77i | 0.392993i | ||||||||
\(792\) | −39481.3 | − | 5915.15i | −1.77135 | − | 0.265386i | ||||
\(793\) | 11587.9 | + | 11587.9i | 0.518913 | + | 0.518913i | ||||
\(794\) | −24635.8 | −1.10112 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 7220.42 | 0.321509 | ||||||||
\(797\) | 16231.3 | + | 16231.3i | 0.721382 | + | 0.721382i | 0.968887 | − | 0.247504i | \(-0.0796104\pi\) |
−0.247504 | + | 0.968887i | \(0.579610\pi\) | |||||||
\(798\) | −1612.49 | − | 4893.03i | −0.0715309 | − | 0.217057i | ||||
\(799\) | 5425.20i | 0.240212i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −4952.57 | + | 3661.93i | −0.218465 | + | 0.161533i | ||||
\(802\) | 5614.26 | − | 5614.26i | 0.247190 | − | 0.247190i | ||||
\(803\) | 12876.4 | − | 12876.4i | 0.565875 | − | 0.565875i | ||||
\(804\) | −8626.86 | − | 4350.26i | −0.378415 | − | 0.190823i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 16600.8i | 0.725482i | ||||||||
\(807\) | 8598.43 | − | 2833.61i | 0.375067 | − | 0.123603i | ||||
\(808\) | 25590.8 | + | 25590.8i | 1.11421 | + | 1.11421i | ||||
\(809\) | 10404.2 | 0.452155 | 0.226078 | − | 0.974109i | \(-0.427410\pi\) | ||||
0.226078 | + | 0.974109i | \(0.427410\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 6213.04 | 0.269013 | 0.134506 | − | 0.990913i | \(-0.457055\pi\) | ||||
0.134506 | + | 0.990913i | \(0.457055\pi\) | |||||||
\(812\) | −2796.80 | − | 2796.80i | −0.120873 | − | 0.120873i | ||||
\(813\) | −11164.9 | + | 3679.39i | −0.481637 | + | 0.158723i | ||||
\(814\) | 1825.45i | 0.0786021i | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 4470.25 | + | 2254.21i | 0.191777 | + | 0.0967071i | ||||
\(817\) | −12507.1 | + | 12507.1i | −0.535578 | + | 0.535578i | ||||
\(818\) | 17178.3 | − | 17178.3i | 0.734261 | − | 0.734261i | ||||
\(819\) | −7949.61 | + | 5877.94i | −0.339172 | + | 0.250784i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 46193.4i | − | 1.96365i | −0.189776 | − | 0.981827i | \(-0.560776\pi\) | ||
0.189776 | − | 0.981827i | \(-0.439224\pi\) | |||||||
\(822\) | 6768.39 | + | 20538.3i | 0.287195 | + | 0.871479i | ||||
\(823\) | 24122.0 | + | 24122.0i | 1.02168 | + | 1.02168i | 0.999760 | + | 0.0219179i | \(0.00697724\pi\) |
0.0219179 | + | 0.999760i | \(0.493023\pi\) | |||||||
\(824\) | −2399.10 | −0.101428 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 2764.97 | 0.116472 | ||||||||
\(827\) | 25996.5 | + | 25996.5i | 1.09309 | + | 1.09309i | 0.995197 | + | 0.0978962i | \(0.0312113\pi\) |
0.0978962 | + | 0.995197i | \(0.468789\pi\) | |||||||
\(828\) | −5236.95 | − | 784.609i | −0.219803 | − | 0.0329312i | ||||
\(829\) | 45991.6i | 1.92684i | 0.267988 | + | 0.963422i | \(0.413641\pi\) | ||||
−0.267988 | + | 0.963422i | \(0.586359\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −12579.4 | + | 24945.8i | −0.525119 | + | 1.04135i | ||||
\(832\) | 20991.7 | − | 20991.7i | 0.874706 | − | 0.874706i | ||||
\(833\) | 14949.1 | − | 14949.1i | 0.621795 | − | 0.621795i | ||||
\(834\) | 9803.37 | − | 19440.8i | 0.407030 | − | 0.807168i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 23732.1i | 0.981810i | ||||||||
\(837\) | 10009.5 | − | 14146.8i | 0.413358 | − | 0.584213i | ||||
\(838\) | −4292.74 | − | 4292.74i | −0.176957 | − | 0.176957i | ||||
\(839\) | 29393.2 | 1.20949 | 0.604747 | − | 0.796418i | \(-0.293274\pi\) | ||||
0.604747 | + | 0.796418i | \(0.293274\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 7720.75 | 0.316567 | ||||||||
\(842\) | −16823.7 | − | 16823.7i | −0.688579 | − | 0.688579i | ||||
\(843\) | −6077.86 | − | 18442.9i | −0.248319 | − | 0.753510i | ||||
\(844\) | 5519.26i | 0.225096i | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 2553.52 | + | 3453.51i | 0.103773 | + | 0.140348i | ||||
\(847\) | 9503.89 | − | 9503.89i | 0.385546 | − | 0.385546i | ||||
\(848\) | −3360.23 | + | 3360.23i | −0.136074 | + | 0.136074i | ||||
\(849\) | 3605.36 | + | 1818.07i | 0.145743 | + | 0.0734936i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 714.055i | 0.0287632i | ||||||||
\(852\) | −21969.3 | + | 7239.97i | −0.883398 | + | 0.291123i | ||||
\(853\) | 12249.5 | + | 12249.5i | 0.491693 | + | 0.491693i | 0.908839 | − | 0.417146i | \(-0.136970\pi\) |
−0.417146 | + | 0.908839i | \(0.636970\pi\) | |||||||
\(854\) | 2554.23 | 0.102347 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 973.164 | 0.0388576 | ||||||||
\(857\) | −18196.1 | − | 18196.1i | −0.725282 | − | 0.725282i | 0.244394 | − | 0.969676i | \(-0.421411\pi\) |
−0.969676 | + | 0.244394i | \(0.921411\pi\) | |||||||
\(858\) | −41048.4 | + | 13527.5i | −1.63330 | + | 0.538253i | ||||
\(859\) | − | 7995.99i | − | 0.317602i | −0.987311 | − | 0.158801i | \(-0.949237\pi\) | ||
0.987311 | − | 0.158801i | \(-0.0507628\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −1544.13 | − | 778.658i | −0.0611195 | − | 0.0308207i | ||||
\(862\) | −8744.62 | + | 8744.62i | −0.345525 | + | 0.345525i | ||||
\(863\) | −23615.8 | + | 23615.8i | −0.931509 | + | 0.931509i | −0.997800 | − | 0.0662917i | \(-0.978883\pi\) |
0.0662917 | + | 0.997800i | \(0.478883\pi\) | |||||||
\(864\) | −22522.5 | + | 3857.46i | −0.886840 | + | 0.151890i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | − | 22860.3i | − | 0.897024i | ||||||
\(867\) | 621.665 | + | 1886.41i | 0.0243516 | + | 0.0738937i | ||||
\(868\) | −1927.94 | − | 1927.94i | −0.0753899 | − | 0.0753899i | ||||
\(869\) | 41888.3 | 1.63517 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −30845.9 | −1.19997 | ||||||||
\(872\) | 10140.0 | + | 10140.0i | 0.393789 | + | 0.393789i | ||||
\(873\) | −506.552 | + | 3381.03i | −0.0196383 | + | 0.131077i | ||||
\(874\) | − | 8809.68i | − | 0.340952i | ||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 2825.61 | − | 5603.37i | 0.108982 | − | 0.216119i | ||||
\(877\) | 27239.2 | − | 27239.2i | 1.04880 | − | 1.04880i | 0.0500573 | − | 0.998746i | \(-0.484060\pi\) |
0.998746 | − | 0.0500573i | \(-0.0159404\pi\) | |||||||
\(878\) | −11855.2 | + | 11855.2i | −0.455688 | + | 0.455688i | ||||
\(879\) | 18378.6 | − | 36446.1i | 0.705228 | − | 1.39852i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 43322.3i | 1.65671i | 0.560202 | + | 0.828356i | \(0.310724\pi\) | ||||
−0.560202 | + | 0.828356i | \(0.689276\pi\) | |||||||
\(882\) | 2479.90 | − | 16552.3i | 0.0946740 | − | 0.631911i | ||||
\(883\) | 27549.3 | + | 27549.3i | 1.04995 | + | 1.04995i | 0.998685 | + | 0.0512690i | \(0.0163266\pi\) |
0.0512690 | + | 0.998685i | \(0.483673\pi\) | |||||||
\(884\) | −18813.7 | −0.715806 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 25340.2 | 0.960858 | ||||||||
\(887\) | −5088.76 | − | 5088.76i | −0.192631 | − | 0.192631i | 0.604201 | − | 0.796832i | \(-0.293492\pi\) |
−0.796832 | + | 0.604201i | \(0.793492\pi\) | |||||||
\(888\) | 580.652 | + | 1761.96i | 0.0219430 | + | 0.0665849i | ||||
\(889\) | − | 10095.2i | − | 0.380856i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 43137.0 | + | 13222.5i | 1.62194 | + | 0.497162i | ||||
\(892\) | −12915.2 | + | 12915.2i | −0.484789 | + | 0.484789i | ||||
\(893\) | 5324.14 | − | 5324.14i | 0.199513 | − | 0.199513i | ||||
\(894\) | 11334.6 | + | 5715.70i | 0.424034 | + | 0.213827i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 2379.71i | 0.0887284i | ||||||||
\(897\) | −16056.7 | + | 5291.49i | −0.597680 | + | 0.196965i | ||||
\(898\) | 6814.70 | + | 6814.70i | 0.253240 | + | 0.253240i | ||||
\(899\) | 22134.4 | 0.821161 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 22346.4 | 0.826265 | ||||||||
\(902\) | −5345.67 | − | 5345.67i | −0.197330 | − | 0.197330i | ||||
\(903\) | 5024.69 | − | 1655.88i | 0.185173 | − | 0.0610236i | ||||
\(904\) | 38841.5i | 1.42903i | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 21649.7 | + | 10917.3i | 0.793889 | + | 0.400334i | ||||
\(907\) | −38018.9 | + | 38018.9i | −1.39184 | + | 1.39184i | −0.570627 | + | 0.821210i | \(0.693300\pi\) |
−0.821210 | + | 0.570627i | \(0.806700\pi\) | |||||||
\(908\) | −18174.9 | + | 18174.9i | −0.664268 | + | 0.664268i | ||||
\(909\) | −24317.1 | − | 32887.6i | −0.887291 | − | 1.20001i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 31712.0i | 1.15331i | 0.816987 | + | 0.576656i | \(0.195643\pi\) | ||||
−0.816987 | + | 0.576656i | \(0.804357\pi\) | |||||||
\(912\) | −2174.76 | − | 6599.19i | −0.0789622 | − | 0.239606i | ||||
\(913\) | −4418.12 | − | 4418.12i | −0.160152 | − | 0.160152i | ||||
\(914\) | −14184.4 | −0.513323 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 8452.72 | 0.304897 | ||||||||
\(917\) | −336.459 | − | 336.459i | −0.0121165 | − | 0.0121165i | ||||
\(918\) | −15214.8 | − | 10765.2i | −0.547019 | − | 0.387041i | ||||
\(919\) | − | 3339.87i | − | 0.119883i | −0.998202 | − | 0.0599413i | \(-0.980909\pi\) | ||
0.998202 | − | 0.0599413i | \(-0.0190913\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 17240.5 | − | 34189.1i | 0.616823 | − | 1.22320i | ||||
\(922\) | 24085.3 | − | 24085.3i | 0.860311 | − | 0.860311i | ||||
\(923\) | −52219.8 | + | 52219.8i | −1.86223 | + | 1.86223i | ||||
\(924\) | 3196.15 | − | 6338.18i | 0.113794 | − | 0.225661i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 7031.44i | 0.249533i | ||||||||
\(927\) | 2681.44 | + | 401.738i | 0.0950054 | + | 0.0142339i | ||||
\(928\) | −20637.3 | − | 20637.3i | −0.730012 | − | 0.730012i | ||||
\(929\) | −27741.7 | −0.979736 | −0.489868 | − | 0.871797i | \(-0.662955\pi\) | ||||
−0.489868 | + | 0.871797i | \(0.662955\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −29341.2 | −1.03289 | ||||||||
\(932\) | −9451.01 | − | 9451.01i | −0.332165 | − | 0.332165i | ||||
\(933\) | −4419.41 | − | 13410.4i | −0.155075 | − | 0.470566i | ||||
\(934\) | − | 11638.5i | − | 0.407734i | ||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −35317.7 | + | 26113.9i | −1.23333 | + | 0.911923i | ||||
\(937\) | 1426.31 | − | 1426.31i | 0.0497284 | − | 0.0497284i | −0.681805 | − | 0.731534i | \(-0.738805\pi\) |
0.731534 | + | 0.681805i | \(0.238805\pi\) | |||||||
\(938\) | −3399.57 | + | 3399.57i | −0.118337 | + | 0.118337i | ||||
\(939\) | 40726.1 | + | 20536.9i | 1.41538 | + | 0.713734i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 16728.8i | − | 0.579535i | −0.957097 | − | 0.289768i | \(-0.906422\pi\) | ||
0.957097 | − | 0.289768i | \(-0.0935780\pi\) | |||||||
\(942\) | −9766.57 | + | 3218.57i | −0.337805 | + | 0.111323i | ||||
\(943\) | −2091.04 | − | 2091.04i | −0.0722096 | − | 0.0722096i | ||||
\(944\) | 3729.09 | 0.128572 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 23127.6 | 0.794866 | ||||||||
\(947\) | 173.759 | + | 173.759i | 0.00596243 | + | 0.00596243i | 0.710082 | − | 0.704119i | \(-0.248658\pi\) |
−0.704119 | + | 0.710082i | \(0.748658\pi\) | |||||||
\(948\) | 13710.2 | − | 4518.19i | 0.469712 | − | 0.154793i | ||||
\(949\) | − | 20035.2i | − | 0.685323i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −25653.8 | − | 12936.4i | −0.874744 | − | 0.441106i | ||||
\(952\) | −6114.68 | + | 6114.68i | −0.208170 | + | 0.208170i | ||||
\(953\) | 20457.0 | − | 20457.0i | 0.695350 | − | 0.695350i | −0.268054 | − | 0.963404i | \(-0.586380\pi\) |
0.963404 | + | 0.268054i | \(0.0863805\pi\) | |||||||
\(954\) | 14225.0 | − | 10517.9i | 0.482758 | − | 0.356951i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 10093.7i | 0.341480i | ||||||||
\(957\) | 18036.6 | + | 54731.2i | 0.609239 | + | 1.84870i | ||||
\(958\) | 5638.28 | + | 5638.28i | 0.190151 | + | 0.190151i | ||||
\(959\) | −11339.1 | −0.381812 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −14533.0 | −0.487831 | ||||||||
\(962\) | 1420.17 | + | 1420.17i | 0.0475969 | + | 0.0475969i | ||||
\(963\) | −1087.69 | − | 162.960i | −0.0363970 | − | 0.00545306i | ||||
\(964\) | − | 18311.3i | − | 0.611793i | ||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −1186.45 | + | 2352.81i | −0.0395170 | + | 0.0783650i | ||||
\(967\) | 22650.2 | − | 22650.2i | 0.753237 | − | 0.753237i | −0.221845 | − | 0.975082i | \(-0.571208\pi\) |
0.975082 | + | 0.221845i | \(0.0712080\pi\) | |||||||
\(968\) | 42222.9 | − | 42222.9i | 1.40196 | − | 1.40196i | ||||
\(969\) | −14711.8 | + | 29174.5i | −0.487730 | + | 0.967202i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 41716.5i | 1.37873i | 0.724415 | + | 0.689365i | \(0.242110\pi\) | ||||
−0.724415 | + | 0.689365i | \(0.757890\pi\) | |||||||
\(972\) | 15545.1 | − | 325.096i | 0.512974 | − | 0.0107278i | ||||
\(973\) | 8072.76 | + | 8072.76i | 0.265982 | + | 0.265982i | ||||
\(974\) | −15472.7 | −0.509012 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 3444.88 | 0.112979 | ||||||||
\(977\) | 29670.6 | + | 29670.6i | 0.971595 | + | 0.971595i | 0.999608 | − | 0.0280129i | \(-0.00891795\pi\) |
−0.0280129 | + | 0.999608i | \(0.508918\pi\) | |||||||
\(978\) | 8668.91 | + | 26305.3i | 0.283437 | + | 0.860074i | ||||
\(979\) | − | 14118.7i | − | 0.460914i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −9635.34 | − | 13031.3i | −0.313591 | − | 0.424116i | ||||
\(982\) | −13926.3 | + | 13926.3i | −0.452553 | + | 0.452553i | ||||
\(983\) | 14537.3 | − | 14537.3i | 0.471686 | − | 0.471686i | −0.430774 | − | 0.902460i | \(-0.641759\pi\) |
0.902460 | + | 0.430774i | \(0.141759\pi\) | |||||||
\(984\) | −6860.11 | − | 3459.34i | −0.222248 | − | 0.112073i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | − | 23805.4i | − | 0.768882i | ||||||
\(987\) | −2138.96 | + | 704.893i | −0.0689806 | + | 0.0227325i | ||||
\(988\) | 18463.2 | + | 18463.2i | 0.594528 | + | 0.594528i | ||||
\(989\) | 9046.73 | 0.290869 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 2344.55 | 0.0751536 | 0.0375768 | − | 0.999294i | \(-0.488036\pi\) | ||||
0.0375768 | + | 0.999294i | \(0.488036\pi\) | |||||||
\(992\) | −14226.0 | − | 14226.0i | −0.455319 | − | 0.455319i | ||||
\(993\) | −16444.5 | + | 5419.27i | −0.525529 | + | 0.173188i | ||||
\(994\) | 11510.4i | 0.367292i | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −1922.62 | − | 969.517i | −0.0611652 | − | 0.0308437i | ||||
\(997\) | −24252.2 | + | 24252.2i | −0.770385 | + | 0.770385i | −0.978174 | − | 0.207789i | \(-0.933373\pi\) |
0.207789 | + | 0.978174i | \(0.433373\pi\) | |||||||
\(998\) | 1931.45 | − | 1931.45i | 0.0612615 | − | 0.0612615i | ||||
\(999\) | −353.940 | − | 2066.54i | −0.0112094 | − | 0.0654479i |
(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 | 75.4.e.d.68.3 | yes | 16 | |
3.2 | odd | 2 | inner | 75.4.e.d.68.5 | yes | 16 | |
5.2 | odd | 4 | inner | 75.4.e.d.32.5 | yes | 16 | |
5.3 | odd | 4 | inner | 75.4.e.d.32.4 | yes | 16 | |
5.4 | even | 2 | inner | 75.4.e.d.68.6 | yes | 16 | |
15.2 | even | 4 | inner | 75.4.e.d.32.3 | ✓ | 16 | |
15.8 | even | 4 | inner | 75.4.e.d.32.6 | yes | 16 | |
15.14 | odd | 2 | inner | 75.4.e.d.68.4 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
75.4.e.d.32.3 | ✓ | 16 | 15.2 | even | 4 | inner | |
75.4.e.d.32.4 | yes | 16 | 5.3 | odd | 4 | inner | |
75.4.e.d.32.5 | yes | 16 | 5.2 | odd | 4 | inner | |
75.4.e.d.32.6 | yes | 16 | 15.8 | even | 4 | inner | |
75.4.e.d.68.3 | yes | 16 | 1.1 | even | 1 | trivial | |
75.4.e.d.68.4 | yes | 16 | 15.14 | odd | 2 | inner | |
75.4.e.d.68.5 | yes | 16 | 3.2 | odd | 2 | inner | |
75.4.e.d.68.6 | yes | 16 | 5.4 | even | 2 | inner |