Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [225,4,Mod(49,225)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(225, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([2, 3]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("225.49");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 225 = 3^{2} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 225.k (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(13.2754297513\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 23x^{10} + 198x^{8} - 719x^{6} + 886x^{4} + 585x^{2} + 81 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{6}\cdot 3^{2} \) |
Twist minimal: | no (minimal twist has level 45) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 49.1 | ||
Root | \(-2.88506 - 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 225.49 |
Dual form | 225.4.k.c.124.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/225\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(127\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −3.96084 | + | 2.28679i | −1.40037 | + | 0.808502i | −0.994430 | − | 0.105398i | \(-0.966388\pi\) |
−0.405937 | + | 0.913901i | \(0.633055\pi\) | |||||||
\(3\) | −3.96084 | − | 3.36330i | −0.762263 | − | 0.647267i | ||||
\(4\) | 6.45882 | − | 11.1870i | 0.807352 | − | 1.39838i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 23.3794 | + | 4.26387i | 1.59077 | + | 0.290120i | ||||
\(7\) | −17.4197 | + | 10.0573i | −0.940575 | + | 0.543041i | −0.890141 | − | 0.455686i | \(-0.849394\pi\) |
−0.0504348 | + | 0.998727i | \(0.516061\pi\) | |||||||
\(8\) | 22.4912i | 0.993981i | ||||||||
\(9\) | 4.37646 | + | 26.6429i | 0.162091 | + | 0.986776i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −33.1708 | − | 57.4535i | −0.909215 | − | 1.57481i | −0.815157 | − | 0.579240i | \(-0.803349\pi\) |
−0.0940582 | − | 0.995567i | \(-0.529984\pi\) | |||||||
\(12\) | −63.2076 | + | 22.5870i | −1.52054 | + | 0.543358i | ||||
\(13\) | −40.5305 | − | 23.4003i | −0.864703 | − | 0.499237i | 0.000881222 | − | 1.00000i | \(-0.499719\pi\) |
−0.865584 | + | 0.500763i | \(0.833053\pi\) | |||||||
\(14\) | 45.9977 | − | 79.6704i | 0.878101 | − | 1.52092i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0.237854 | + | 0.411975i | 0.00371647 | + | 0.00643711i | ||||
\(17\) | − | 47.6233i | − | 0.679432i | −0.940528 | − | 0.339716i | \(-0.889669\pi\) | ||
0.940528 | − | 0.339716i | \(-0.110331\pi\) | |||||||
\(18\) | −78.2613 | − | 95.5203i | −1.02480 | − | 1.25080i | ||||
\(19\) | 9.95276 | 0.120175 | 0.0600874 | − | 0.998193i | \(-0.480862\pi\) | ||||
0.0600874 | + | 0.998193i | \(0.480862\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 102.822 | + | 18.7524i | 1.06846 | + | 0.194863i | ||||
\(22\) | 262.768 | + | 151.709i | 2.54647 | + | 1.47021i | ||||
\(23\) | 8.30695 | + | 4.79602i | 0.0753095 | + | 0.0434800i | 0.537182 | − | 0.843466i | \(-0.319489\pi\) |
−0.461872 | + | 0.886946i | \(0.652822\pi\) | |||||||
\(24\) | 75.6447 | − | 89.0841i | 0.643371 | − | 0.757675i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 214.046 | 1.61454 | ||||||||
\(27\) | 72.2737 | − | 120.248i | 0.515151 | − | 0.857099i | ||||
\(28\) | 259.832i | 1.75370i | ||||||||
\(29\) | −89.3675 | − | 154.789i | −0.572246 | − | 0.991158i | −0.996335 | − | 0.0855380i | \(-0.972739\pi\) |
0.424089 | − | 0.905620i | \(-0.360594\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −77.0186 | + | 133.400i | −0.446224 | + | 0.772883i | −0.998137 | − | 0.0610190i | \(-0.980565\pi\) |
0.551912 | + | 0.833902i | \(0.313898\pi\) | |||||||
\(32\) | −157.708 | − | 91.0527i | −0.871222 | − | 0.503000i | ||||
\(33\) | −61.8491 | + | 339.127i | −0.326259 | + | 1.78892i | ||||
\(34\) | 108.905 | + | 188.628i | 0.549323 | + | 0.951455i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 326.322 | + | 123.123i | 1.51075 | + | 0.570012i | ||||
\(37\) | 248.864i | 1.10576i | 0.833262 | + | 0.552878i | \(0.186471\pi\) | ||||
−0.833262 | + | 0.552878i | \(0.813529\pi\) | |||||||
\(38\) | −39.4213 | + | 22.7599i | −0.168289 | + | 0.0971616i | ||||
\(39\) | 81.8326 | + | 229.001i | 0.335992 | + | 0.940244i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −124.832 | + | 216.216i | −0.475500 | + | 0.823590i | −0.999606 | − | 0.0280628i | \(-0.991066\pi\) |
0.524106 | + | 0.851653i | \(0.324400\pi\) | |||||||
\(42\) | −450.145 | + | 160.857i | −1.65378 | + | 0.590972i | ||||
\(43\) | 183.809 | − | 106.122i | 0.651876 | − | 0.376361i | −0.137299 | − | 0.990530i | \(-0.543842\pi\) |
0.789175 | + | 0.614169i | \(0.210509\pi\) | |||||||
\(44\) | −856.976 | −2.93623 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −43.8700 | −0.140615 | ||||||||
\(47\) | 411.963 | − | 237.847i | 1.27853 | − | 0.738160i | 0.301953 | − | 0.953323i | \(-0.402362\pi\) |
0.976578 | + | 0.215163i | \(0.0690282\pi\) | |||||||
\(48\) | 0.443494 | − | 2.43174i | 0.00133360 | − | 0.00731232i | ||||
\(49\) | 30.7973 | − | 53.3425i | 0.0897880 | − | 0.155517i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −160.171 | + | 188.628i | −0.439774 | + | 0.517906i | ||||
\(52\) | −523.559 | + | 302.277i | −1.39624 | + | 0.806120i | ||||
\(53\) | 546.314i | 1.41589i | 0.706269 | + | 0.707944i | \(0.250377\pi\) | ||||
−0.706269 | + | 0.707944i | \(0.749623\pi\) | |||||||
\(54\) | −11.2831 | + | 641.556i | −0.0284341 | + | 1.61675i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −226.200 | − | 391.790i | −0.539773 | − | 0.934914i | ||||
\(57\) | −39.4213 | − | 33.4741i | −0.0916048 | − | 0.0777851i | ||||
\(58\) | 707.940 | + | 408.729i | 1.60271 | + | 0.925324i | ||||
\(59\) | −209.648 | + | 363.121i | −0.462608 | + | 0.801261i | −0.999090 | − | 0.0426512i | \(-0.986420\pi\) |
0.536482 | + | 0.843912i | \(0.319753\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 272.605 | + | 472.165i | 0.572188 | + | 0.991059i | 0.996341 | + | 0.0854682i | \(0.0272386\pi\) |
−0.424153 | + | 0.905591i | \(0.639428\pi\) | |||||||
\(62\) | − | 704.502i | − | 1.44309i | ||||||
\(63\) | −344.192 | − | 420.097i | −0.688319 | − | 0.840115i | ||||
\(64\) | 829.068 | 1.61927 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −530.538 | − | 1484.66i | −0.989466 | − | 2.76893i | ||||
\(67\) | 387.872 | + | 223.938i | 0.707256 | + | 0.408335i | 0.810044 | − | 0.586369i | \(-0.199443\pi\) |
−0.102788 | + | 0.994703i | \(0.532776\pi\) | |||||||
\(68\) | −532.762 | − | 307.590i | −0.950102 | − | 0.548541i | ||||
\(69\) | −16.7720 | − | 46.9350i | −0.0292625 | − | 0.0818885i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 409.542 | 0.684559 | 0.342279 | − | 0.939598i | \(-0.388801\pi\) | ||||
0.342279 | + | 0.939598i | \(0.388801\pi\) | |||||||
\(72\) | −599.232 | + | 98.4319i | −0.980836 | + | 0.161115i | ||||
\(73\) | 358.548i | 0.574861i | 0.957801 | + | 0.287431i | \(0.0928011\pi\) | ||||
−0.957801 | + | 0.287431i | \(0.907199\pi\) | |||||||
\(74\) | −569.100 | − | 985.710i | −0.894007 | − | 1.54847i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 64.2831 | − | 111.342i | 0.0970234 | − | 0.168049i | ||||
\(77\) | 1155.65 | + | 667.215i | 1.71037 | + | 0.987483i | ||||
\(78\) | −847.803 | − | 719.902i | −1.23070 | − | 1.04504i | ||||
\(79\) | −325.776 | − | 564.260i | −0.463958 | − | 0.803598i | 0.535196 | − | 0.844728i | \(-0.320238\pi\) |
−0.999154 | + | 0.0411297i | \(0.986904\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −690.693 | + | 233.204i | −0.947453 | + | 0.319895i | ||||
\(82\) | − | 1141.86i | − | 1.53777i | ||||||
\(83\) | 704.202 | − | 406.571i | 0.931280 | − | 0.537675i | 0.0440636 | − | 0.999029i | \(-0.485970\pi\) |
0.887216 | + | 0.461354i | \(0.152636\pi\) | |||||||
\(84\) | 873.893 | − | 1029.15i | 1.13511 | − | 1.33678i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −485.359 | + | 840.667i | −0.608577 | + | 1.05409i | ||||
\(87\) | −166.631 | + | 913.663i | −0.205342 | + | 1.12592i | ||||
\(88\) | 1292.20 | − | 746.051i | 1.56533 | − | 0.903743i | ||||
\(89\) | 201.000 | 0.239393 | 0.119696 | − | 0.992811i | \(-0.461808\pi\) | ||||
0.119696 | + | 0.992811i | \(0.461808\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 941.373 | 1.08442 | ||||||||
\(92\) | 107.306 | − | 61.9532i | 0.121603 | − | 0.0702073i | ||||
\(93\) | 753.723 | − | 269.340i | 0.840402 | − | 0.300314i | ||||
\(94\) | −1087.81 | + | 1884.14i | −1.19361 | + | 2.06739i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 318.418 | + | 891.064i | 0.338525 | + | 0.947331i | ||||
\(97\) | 218.367 | − | 126.074i | 0.228576 | − | 0.131968i | −0.381339 | − | 0.924435i | \(-0.624537\pi\) |
0.609915 | + | 0.792467i | \(0.291204\pi\) | |||||||
\(98\) | 281.708i | 0.290375i | ||||||||
\(99\) | 1385.56 | − | 1135.21i | 1.40661 | − | 1.15245i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −21.8013 | − | 37.7610i | −0.0214783 | − | 0.0372016i | 0.855086 | − | 0.518485i | \(-0.173504\pi\) |
−0.876565 | + | 0.481284i | \(0.840171\pi\) | |||||||
\(102\) | 203.060 | − | 1113.40i | 0.197117 | − | 1.08082i | ||||
\(103\) | −1247.38 | − | 720.176i | −1.19328 | − | 0.688942i | −0.234233 | − | 0.972180i | \(-0.575258\pi\) |
−0.959050 | + | 0.283238i | \(0.908591\pi\) | |||||||
\(104\) | 526.301 | − | 911.581i | 0.496232 | − | 0.859498i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1249.31 | − | 2163.86i | −1.14475 | − | 1.98276i | ||||
\(107\) | 355.755i | 0.321422i | 0.987002 | + | 0.160711i | \(0.0513786\pi\) | ||||
−0.987002 | + | 0.160711i | \(0.948621\pi\) | |||||||
\(108\) | −878.409 | − | 1585.18i | −0.782638 | − | 1.41236i | ||||
\(109\) | 1522.51 | 1.33789 | 0.668946 | − | 0.743311i | \(-0.266746\pi\) | ||||
0.668946 | + | 0.743311i | \(0.266746\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 837.004 | − | 985.710i | 0.715720 | − | 0.842878i | ||||
\(112\) | −8.28669 | − | 4.78432i | −0.00699124 | − | 0.00403639i | ||||
\(113\) | −704.077 | − | 406.499i | −0.586142 | − | 0.338409i | 0.177429 | − | 0.984134i | \(-0.443222\pi\) |
−0.763570 | + | 0.645725i | \(0.776555\pi\) | |||||||
\(114\) | 232.689 | + | 42.4373i | 0.191170 | + | 0.0348650i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −2308.83 | −1.84802 | ||||||||
\(117\) | 446.073 | − | 1182.26i | 0.352474 | − | 0.934190i | ||||
\(118\) | − | 1917.69i | − | 1.49608i | ||||||
\(119\) | 478.960 | + | 829.584i | 0.368960 | + | 0.639057i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1535.10 | + | 2658.87i | −1.15334 | + | 1.99765i | ||||
\(122\) | −2159.49 | − | 1246.78i | −1.60255 | − | 0.925231i | ||||
\(123\) | 1221.64 | − | 436.547i | 0.895539 | − | 0.320017i | ||||
\(124\) | 994.899 | + | 1723.22i | 0.720521 | + | 1.24798i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 2323.96 | + | 876.841i | 1.64313 | + | 0.619962i | ||||
\(127\) | − | 864.662i | − | 0.604144i | −0.953285 | − | 0.302072i | \(-0.902322\pi\) | ||
0.953285 | − | 0.302072i | \(-0.0976784\pi\) | |||||||
\(128\) | −2022.14 | + | 1167.48i | −1.39636 | + | 0.806187i | ||||
\(129\) | −1084.96 | − | 197.872i | −0.740507 | − | 0.135052i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1089.26 | − | 1886.65i | 0.726482 | − | 1.25830i | −0.231879 | − | 0.972745i | \(-0.574487\pi\) |
0.958361 | − | 0.285559i | \(-0.0921792\pi\) | |||||||
\(132\) | 3394.34 | + | 2882.27i | 2.23818 | + | 1.90052i | ||||
\(133\) | −173.374 | + | 100.098i | −0.113033 | + | 0.0652599i | ||||
\(134\) | −2048.40 | −1.32056 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 1071.11 | 0.675343 | ||||||||
\(137\) | −1991.13 | + | 1149.58i | −1.24171 | + | 0.716900i | −0.969442 | − | 0.245322i | \(-0.921106\pi\) |
−0.272266 | + | 0.962222i | \(0.587773\pi\) | |||||||
\(138\) | 173.762 | + | 147.548i | 0.107185 | + | 0.0910152i | ||||
\(139\) | −1066.98 | + | 1848.06i | −0.651077 | + | 1.12770i | 0.331785 | + | 0.943355i | \(0.392349\pi\) |
−0.982862 | + | 0.184343i | \(0.940984\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −2431.67 | − | 443.481i | −1.45236 | − | 0.264878i | ||||
\(142\) | −1622.13 | + | 936.536i | −0.958634 | + | 0.553467i | ||||
\(143\) | 3104.83i | 1.81565i | ||||||||
\(144\) | −9.93528 | + | 8.14012i | −0.00574958 | + | 0.00471072i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −819.924 | − | 1420.15i | −0.464777 | − | 0.805017i | ||||
\(147\) | −301.390 | + | 107.700i | −0.169103 | + | 0.0604284i | ||||
\(148\) | 2784.04 | + | 1607.37i | 1.54626 | + | 0.892735i | ||||
\(149\) | 875.309 | − | 1516.08i | 0.481263 | − | 0.833572i | −0.518506 | − | 0.855074i | \(-0.673512\pi\) |
0.999769 | + | 0.0215024i | \(0.00684497\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −437.977 | − | 758.598i | −0.236040 | − | 0.408833i | 0.723534 | − | 0.690288i | \(-0.242516\pi\) |
−0.959574 | + | 0.281455i | \(0.909183\pi\) | |||||||
\(152\) | 223.850i | 0.119451i | ||||||||
\(153\) | 1268.83 | − | 208.421i | 0.670447 | − | 0.110130i | ||||
\(154\) | −6103.12 | −3.19353 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 3090.38 | + | 563.615i | 1.58608 | + | 0.289265i | ||||
\(157\) | 224.642 | + | 129.697i | 0.114194 | + | 0.0659298i | 0.556009 | − | 0.831176i | \(-0.312332\pi\) |
−0.441815 | + | 0.897106i | \(0.645665\pi\) | |||||||
\(158\) | 2580.69 | + | 1489.96i | 1.29942 | + | 0.750222i | ||||
\(159\) | 1837.42 | − | 2163.86i | 0.916457 | − | 1.07928i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −192.939 | −0.0944457 | ||||||||
\(162\) | 2202.44 | − | 2503.15i | 1.06815 | − | 1.21399i | ||||
\(163\) | 1201.80i | 0.577498i | 0.957405 | + | 0.288749i | \(0.0932393\pi\) | ||||
−0.957405 | + | 0.288749i | \(0.906761\pi\) | |||||||
\(164\) | 1612.54 | + | 2792.99i | 0.767792 | + | 1.32986i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −1859.49 | + | 3220.72i | −0.869422 | + | 1.50588i | ||||
\(167\) | 1453.97 | + | 839.452i | 0.673724 | + | 0.388975i | 0.797486 | − | 0.603337i | \(-0.206163\pi\) |
−0.123762 | + | 0.992312i | \(0.539496\pi\) | |||||||
\(168\) | −421.765 | + | 2312.60i | −0.193690 | + | 1.06203i | ||||
\(169\) | −3.35162 | − | 5.80518i | −0.00152554 | − | 0.00264232i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 43.5578 | + | 265.171i | 0.0194792 | + | 0.118586i | ||||
\(172\) | − | 2741.70i | − | 1.21542i | ||||||
\(173\) | −806.961 | + | 465.899i | −0.354636 | + | 0.204749i | −0.666725 | − | 0.745303i | \(-0.732305\pi\) |
0.312089 | + | 0.950053i | \(0.398971\pi\) | |||||||
\(174\) | −1429.36 | − | 3999.92i | −0.622754 | − | 1.74272i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 15.7796 | − | 27.3311i | 0.00675814 | − | 0.0117054i | ||||
\(177\) | 2051.67 | − | 733.155i | 0.871259 | − | 0.311341i | ||||
\(178\) | −796.127 | + | 459.644i | −0.335237 | + | 0.193549i | ||||
\(179\) | −1023.40 | −0.427333 | −0.213667 | − | 0.976907i | \(-0.568541\pi\) | ||||
−0.213667 | + | 0.976907i | \(0.568541\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2639.93 | 1.08411 | 0.542056 | − | 0.840342i | \(-0.317646\pi\) | ||||
0.542056 | + | 0.840342i | \(0.317646\pi\) | |||||||
\(182\) | −3728.62 | + | 2152.72i | −1.51859 | + | 0.876760i | ||||
\(183\) | 508.289 | − | 2787.02i | 0.205322 | − | 1.12581i | ||||
\(184\) | −107.868 | + | 186.833i | −0.0432182 | + | 0.0748562i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −2369.45 | + | 2790.42i | −0.934067 | + | 1.10002i | ||||
\(187\) | −2736.13 | + | 1579.70i | −1.06997 | + | 0.617750i | ||||
\(188\) | − | 6144.84i | − | 2.38382i | ||||||
\(189\) | −49.6230 | + | 2821.56i | −0.0190981 | + | 1.08591i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 406.640 | + | 704.322i | 0.154050 | + | 0.266822i | 0.932713 | − | 0.360621i | \(-0.117435\pi\) |
−0.778663 | + | 0.627442i | \(0.784102\pi\) | |||||||
\(192\) | −3283.80 | − | 2788.40i | −1.23431 | − | 1.04810i | ||||
\(193\) | −705.154 | − | 407.121i | −0.262995 | − | 0.151840i | 0.362705 | − | 0.931904i | \(-0.381853\pi\) |
−0.625700 | + | 0.780064i | \(0.715187\pi\) | |||||||
\(194\) | −576.612 | + | 998.720i | −0.213393 | + | 0.369608i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −397.828 | − | 689.059i | −0.144981 | − | 0.251115i | ||||
\(197\) | 4078.41i | 1.47500i | 0.675348 | + | 0.737499i | \(0.263994\pi\) | ||||
−0.675348 | + | 0.737499i | \(0.736006\pi\) | |||||||
\(198\) | −2891.99 | + | 7664.87i | −1.03800 | + | 2.75110i | ||||
\(199\) | 1342.49 | 0.478224 | 0.239112 | − | 0.970992i | \(-0.423144\pi\) | ||||
0.239112 | + | 0.970992i | \(0.423144\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −783.129 | − | 2191.51i | −0.274814 | − | 0.769042i | ||||
\(202\) | 172.703 | + | 99.7101i | 0.0601551 | + | 0.0347306i | ||||
\(203\) | 3113.51 | + | 1797.58i | 1.07648 | + | 0.621506i | ||||
\(204\) | 1075.67 | + | 3010.15i | 0.369175 | + | 1.03310i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 6587.56 | 2.22805 | ||||||||
\(207\) | −91.4250 | + | 242.311i | −0.0306980 | + | 0.0813613i | ||||
\(208\) | − | 22.2634i | − | 0.00742159i | ||||||
\(209\) | −330.141 | − | 571.821i | −0.109265 | − | 0.189252i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1477.49 | − | 2559.08i | 0.482059 | − | 0.834950i | −0.517729 | − | 0.855545i | \(-0.673222\pi\) |
0.999788 | + | 0.0205943i | \(0.00655583\pi\) | |||||||
\(212\) | 6111.62 | + | 3528.55i | 1.97994 | + | 1.14312i | ||||
\(213\) | −1622.13 | − | 1377.41i | −0.521814 | − | 0.443092i | ||||
\(214\) | −813.536 | − | 1409.09i | −0.259870 | − | 0.450108i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 2704.52 | + | 1625.52i | 0.851940 | + | 0.512050i | ||||
\(217\) | − | 3098.39i | − | 0.969273i | ||||||
\(218\) | −6030.42 | + | 3481.66i | −1.87354 | + | 1.08169i | ||||
\(219\) | 1205.90 | − | 1420.15i | 0.372089 | − | 0.438196i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1114.40 | + | 1930.20i | −0.339198 | + | 0.587507i | ||||
\(222\) | −1061.12 | + | 5818.29i | −0.320802 | + | 1.75900i | ||||
\(223\) | −3037.03 | + | 1753.43i | −0.911993 | + | 0.526539i | −0.881072 | − | 0.472982i | \(-0.843177\pi\) |
−0.0309212 | + | 0.999522i | \(0.509844\pi\) | |||||||
\(224\) | 3662.97 | 1.09260 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 3718.31 | 1.09442 | ||||||||
\(227\) | 565.364 | − | 326.413i | 0.165306 | − | 0.0954396i | −0.415064 | − | 0.909792i | \(-0.636241\pi\) |
0.580371 | + | 0.814352i | \(0.302908\pi\) | |||||||
\(228\) | −629.090 | + | 224.803i | −0.182730 | + | 0.0652979i | ||||
\(229\) | 2291.78 | − | 3969.47i | 0.661331 | − | 1.14546i | −0.318935 | − | 0.947776i | \(-0.603325\pi\) |
0.980266 | − | 0.197682i | \(-0.0633414\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −2333.30 | − | 6529.52i | −0.664588 | − | 1.85979i | ||||
\(232\) | 3481.39 | − | 2009.98i | 0.985192 | − | 0.568801i | ||||
\(233\) | − | 317.527i | − | 0.0892785i | −0.999003 | − | 0.0446392i | \(-0.985786\pi\) | ||
0.999003 | − | 0.0446392i | \(-0.0142138\pi\) | |||||||
\(234\) | 936.765 | + | 5702.83i | 0.261702 | + | 1.59319i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 2708.16 | + | 4690.67i | 0.746975 | + | 1.29380i | ||||
\(237\) | −607.430 | + | 3330.62i | −0.166485 | + | 0.912858i | ||||
\(238\) | −3794.17 | − | 2190.56i | −1.03336 | − | 0.596610i | ||||
\(239\) | 928.835 | − | 1608.79i | 0.251386 | − | 0.435414i | −0.712521 | − | 0.701650i | \(-0.752447\pi\) |
0.963908 | + | 0.266236i | \(0.0857802\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1633.47 | + | 2829.25i | 0.436602 | + | 0.756217i | 0.997425 | − | 0.0717190i | \(-0.0228485\pi\) |
−0.560823 | + | 0.827936i | \(0.689515\pi\) | |||||||
\(242\) | − | 14041.8i | − | 3.72993i | ||||||
\(243\) | 3520.06 | + | 1399.33i | 0.929266 | + | 0.369411i | ||||
\(244\) | 7042.82 | 1.84783 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −3840.41 | + | 4522.72i | −0.995349 | + | 1.17219i | ||||
\(247\) | −403.390 | − | 232.898i | −0.103915 | − | 0.0599956i | ||||
\(248\) | −3000.33 | − | 1732.24i | −0.768231 | − | 0.443538i | ||||
\(249\) | −4156.65 | − | 758.079i | −1.05790 | − | 0.192937i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −5641.37 | −1.41865 | −0.709323 | − | 0.704884i | \(-0.750999\pi\) | ||||
−0.709323 | + | 0.704884i | \(0.750999\pi\) | |||||||
\(252\) | −6922.70 | + | 1137.15i | −1.73051 | + | 0.284260i | ||||
\(253\) | − | 636.351i | − | 0.158131i | ||||||
\(254\) | 1977.30 | + | 3424.78i | 0.488452 | + | 0.846024i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 2023.31 | − | 3504.47i | 0.493971 | − | 0.855584i | ||||
\(257\) | 1016.25 | + | 586.731i | 0.246661 | + | 0.142410i | 0.618234 | − | 0.785994i | \(-0.287848\pi\) |
−0.371574 | + | 0.928404i | \(0.621182\pi\) | |||||||
\(258\) | 4749.84 | − | 1697.34i | 1.14617 | − | 0.409580i | ||||
\(259\) | −2502.89 | − | 4335.14i | −0.600472 | − | 1.04005i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 3732.92 | − | 3058.44i | 0.885295 | − | 0.725336i | ||||
\(262\) | 9963.64i | 2.34945i | ||||||||
\(263\) | 2509.71 | − | 1448.98i | 0.588423 | − | 0.339726i | −0.176051 | − | 0.984381i | \(-0.556332\pi\) |
0.764474 | + | 0.644655i | \(0.222999\pi\) | |||||||
\(264\) | −7627.38 | − | 1391.06i | −1.77815 | − | 0.324295i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 457.804 | − | 792.940i | 0.105526 | − | 0.182776i | ||||
\(267\) | −796.127 | − | 676.022i | −0.182480 | − | 0.154951i | ||||
\(268\) | 5010.40 | − | 2892.75i | 1.14201 | − | 0.659340i | ||||
\(269\) | −2930.13 | −0.664138 | −0.332069 | − | 0.943255i | \(-0.607747\pi\) | ||||
−0.332069 | + | 0.943255i | \(0.607747\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −668.881 | −0.149932 | −0.0749661 | − | 0.997186i | \(-0.523885\pi\) | ||||
−0.0749661 | + | 0.997186i | \(0.523885\pi\) | |||||||
\(272\) | 19.6196 | − | 11.3274i | 0.00437358 | − | 0.00252509i | ||||
\(273\) | −3728.62 | − | 3166.12i | −0.826617 | − | 0.701912i | ||||
\(274\) | 5257.70 | − | 9106.60i | 1.15923 | − | 2.00785i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −633.389 | − | 115.516i | −0.138136 | − | 0.0251929i | ||||
\(277\) | −547.874 | + | 316.315i | −0.118840 | + | 0.0686121i | −0.558241 | − | 0.829679i | \(-0.688524\pi\) |
0.439402 | + | 0.898291i | \(0.355190\pi\) | |||||||
\(278\) | − | 9759.80i | − | 2.10559i | ||||||
\(279\) | −3891.24 | − | 1468.18i | −0.834991 | − | 0.315046i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1797.65 | + | 3113.62i | 0.381633 | + | 0.661007i | 0.991296 | − | 0.131653i | \(-0.0420286\pi\) |
−0.609663 | + | 0.792661i | \(0.708695\pi\) | |||||||
\(282\) | 10645.6 | − | 3804.16i | 2.24800 | − | 0.803313i | ||||
\(283\) | 436.796 | + | 252.184i | 0.0917485 | + | 0.0529710i | 0.545172 | − | 0.838324i | \(-0.316464\pi\) |
−0.453424 | + | 0.891295i | \(0.649798\pi\) | |||||||
\(284\) | 2645.16 | − | 4581.55i | 0.552680 | − | 0.957270i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −7100.08 | − | 12297.7i | −1.46796 | − | 2.54258i | ||||
\(287\) | − | 5021.88i | − | 1.03286i | ||||||
\(288\) | 1735.71 | − | 4600.29i | 0.355131 | − | 0.941232i | ||||
\(289\) | 2645.02 | 0.538372 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1288.94 | − | 235.074i | −0.259654 | − | 0.0473549i | ||||
\(292\) | 4011.08 | + | 2315.80i | 0.803872 | + | 0.464116i | ||||
\(293\) | 5368.06 | + | 3099.25i | 1.07033 | + | 0.617953i | 0.928270 | − | 0.371906i | \(-0.121296\pi\) |
0.142055 | + | 0.989859i | \(0.454629\pi\) | |||||||
\(294\) | 947.467 | − | 1115.80i | 0.187950 | − | 0.221343i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −5597.26 | −1.09910 | ||||||||
\(297\) | −9306.02 | − | 163.666i | −1.81815 | − | 0.0319760i | ||||
\(298\) | 8006.60i | 1.55641i | ||||||||
\(299\) | −224.457 | − | 388.770i | −0.0434136 | − | 0.0751945i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2134.60 | + | 3697.24i | −0.408759 | + | 0.707991i | ||||
\(302\) | 3469.51 | + | 2003.12i | 0.661086 | + | 0.381678i | ||||
\(303\) | −40.6500 | + | 222.889i | −0.00770719 | + | 0.0422596i | ||||
\(304\) | 2.36730 | + | 4.10029i | 0.000446626 | + | 0.000773578i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −4548.99 | + | 3727.06i | −0.849832 | + | 0.696281i | ||||
\(307\) | − | 1966.79i | − | 0.365636i | −0.983147 | − | 0.182818i | \(-0.941478\pi\) | ||
0.983147 | − | 0.182818i | \(-0.0585220\pi\) | |||||||
\(308\) | 14928.3 | − | 8618.84i | 2.76174 | − | 1.59449i | ||||
\(309\) | 2518.51 | + | 7047.81i | 0.463666 | + | 1.29753i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1153.05 | − | 1997.15i | 0.210237 | − | 0.364141i | −0.741552 | − | 0.670896i | \(-0.765910\pi\) |
0.951789 | + | 0.306755i | \(0.0992431\pi\) | |||||||
\(312\) | −5150.51 | + | 1840.51i | −0.934584 | + | 0.333970i | ||||
\(313\) | −8922.14 | + | 5151.20i | −1.61121 | + | 0.930234i | −0.622122 | + | 0.782920i | \(0.713729\pi\) |
−0.989090 | + | 0.147314i | \(0.952937\pi\) | |||||||
\(314\) | −1186.36 | −0.213218 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −8416.51 | −1.49831 | ||||||||
\(317\) | −1473.83 | + | 850.916i | −0.261131 | + | 0.150764i | −0.624850 | − | 0.780745i | \(-0.714840\pi\) |
0.363719 | + | 0.931509i | \(0.381507\pi\) | |||||||
\(318\) | −2329.41 | + | 12772.5i | −0.410777 | + | 2.25235i | ||||
\(319\) | −5928.78 | + | 10268.9i | −1.04059 | + | 1.80235i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1196.51 | − | 1409.09i | 0.208046 | − | 0.245008i | ||||
\(322\) | 764.201 | − | 441.212i | 0.132259 | − | 0.0763596i | ||||
\(323\) | − | 473.983i | − | 0.0816506i | ||||||
\(324\) | −1852.21 | + | 9233.01i | −0.317595 | + | 1.58316i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −2748.26 | − | 4760.13i | −0.466908 | − | 0.808709i | ||||
\(327\) | −6030.42 | − | 5120.66i | −1.01983 | − | 0.865973i | ||||
\(328\) | −4862.95 | − | 2807.63i | −0.818633 | − | 0.472638i | ||||
\(329\) | −4784.18 | + | 8286.44i | −0.801703 | + | 1.38859i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4175.74 | + | 7232.60i | 0.693413 | + | 1.20103i | 0.970713 | + | 0.240243i | \(0.0772271\pi\) |
−0.277300 | + | 0.960783i | \(0.589440\pi\) | |||||||
\(332\) | − | 10503.9i | − | 1.73637i | ||||||
\(333\) | −6630.47 | + | 1089.14i | −1.09113 | + | 0.179233i | ||||
\(334\) | −7678.61 | −1.25795 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 16.7311 | + | 46.8205i | 0.00271654 | + | 0.00760199i | ||||
\(337\) | 6804.73 | + | 3928.71i | 1.09993 | + | 0.635046i | 0.936203 | − | 0.351459i | \(-0.114314\pi\) |
0.163729 | + | 0.986505i | \(0.447648\pi\) | |||||||
\(338\) | 26.5504 | + | 15.3289i | 0.00427264 | + | 0.00246681i | ||||
\(339\) | 1421.56 | + | 3978.10i | 0.227753 | + | 0.637347i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 10219.1 | 1.62286 | ||||||||
\(342\) | −778.916 | − | 950.691i | −0.123155 | − | 0.150314i | ||||
\(343\) | − | 5660.34i | − | 0.891048i | ||||||
\(344\) | 2386.82 | + | 4134.10i | 0.374095 | + | 0.647952i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 2130.83 | − | 3690.70i | 0.331081 | − | 0.573449i | ||||
\(347\) | −1049.78 | − | 606.088i | −0.162406 | − | 0.0937652i | 0.416594 | − | 0.909093i | \(-0.363224\pi\) |
−0.579000 | + | 0.815327i | \(0.696557\pi\) | |||||||
\(348\) | 9144.91 | + | 7765.29i | 1.40867 | + | 1.19616i | ||||
\(349\) | 699.332 | + | 1211.28i | 0.107262 | + | 0.185783i | 0.914660 | − | 0.404224i | \(-0.132458\pi\) |
−0.807398 | + | 0.590007i | \(0.799125\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −5743.12 | + | 3182.47i | −0.873348 | + | 0.483954i | ||||
\(352\) | 12081.2i | 1.82934i | ||||||||
\(353\) | −2276.28 | + | 1314.21i | −0.343214 | + | 0.198154i | −0.661692 | − | 0.749776i | \(-0.730161\pi\) |
0.318479 | + | 0.947930i | \(0.396828\pi\) | |||||||
\(354\) | −6449.75 | + | 7595.64i | −0.968362 | + | 1.14041i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 1298.22 | − | 2248.59i | 0.193274 | − | 0.334761i | ||||
\(357\) | 893.053 | − | 4896.73i | 0.132396 | − | 0.725946i | ||||
\(358\) | 4053.53 | − | 2340.31i | 0.598424 | − | 0.345500i | ||||
\(359\) | −3677.48 | −0.540640 | −0.270320 | − | 0.962770i | \(-0.587130\pi\) | ||||
−0.270320 | + | 0.962770i | \(0.587130\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6759.94 | −0.985558 | ||||||||
\(362\) | −10456.3 | + | 6036.96i | −1.51815 | + | 0.876507i | ||||
\(363\) | 15022.9 | − | 5368.36i | 2.17217 | − | 0.776215i | ||||
\(364\) | 6080.16 | − | 10531.1i | 0.875513 | − | 1.51643i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 4360.08 | + | 12201.3i | 0.622692 | + | 1.74255i | ||||
\(367\) | 9898.47 | − | 5714.88i | 1.40789 | − | 0.812846i | 0.412706 | − | 0.910864i | \(-0.364584\pi\) |
0.995185 | + | 0.0980185i | \(0.0312504\pi\) | |||||||
\(368\) | 4.56301i | 0.000646368i | ||||||||
\(369\) | −6306.94 | − | 2379.64i | −0.889773 | − | 0.335715i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −5494.43 | − | 9516.63i | −0.768886 | − | 1.33175i | ||||
\(372\) | 1855.05 | − | 10171.5i | 0.258549 | − | 1.41766i | ||||
\(373\) | 1957.13 | + | 1129.95i | 0.271679 | + | 0.156854i | 0.629650 | − | 0.776879i | \(-0.283198\pi\) |
−0.357971 | + | 0.933733i | \(0.616531\pi\) | |||||||
\(374\) | 7224.90 | − | 12513.9i | 0.998905 | − | 1.73015i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 5349.47 | + | 9265.55i | 0.733717 | + | 1.27084i | ||||
\(377\) | 8364.90i | 1.14274i | ||||||||
\(378\) | −6255.76 | − | 11289.2i | −0.851221 | − | 1.53612i | ||||
\(379\) | 11815.8 | 1.60142 | 0.800709 | − | 0.599053i | \(-0.204456\pi\) | ||||
0.800709 | + | 0.599053i | \(0.204456\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −2908.12 | + | 3424.78i | −0.391043 | + | 0.460517i | ||||
\(382\) | −3221.27 | − | 1859.80i | −0.431452 | − | 0.249099i | ||||
\(383\) | −6997.68 | − | 4040.11i | −0.933589 | − | 0.539008i | −0.0456440 | − | 0.998958i | \(-0.514534\pi\) |
−0.887945 | + | 0.459950i | \(0.847867\pi\) | |||||||
\(384\) | 11936.0 | + | 2176.85i | 1.58621 | + | 0.289289i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 3724.00 | 0.491054 | ||||||||
\(387\) | 3631.85 | + | 4432.78i | 0.477047 | + | 0.582251i | ||||
\(388\) | − | 3257.17i | − | 0.426180i | ||||||
\(389\) | 1550.22 | + | 2685.05i | 0.202054 | + | 0.349968i | 0.949190 | − | 0.314703i | \(-0.101905\pi\) |
−0.747136 | + | 0.664671i | \(0.768572\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 228.402 | − | 395.604i | 0.0295417 | − | 0.0511677i | ||||
\(392\) | 1199.74 | + | 692.669i | 0.154581 | + | 0.0892476i | ||||
\(393\) | −10659.8 | + | 3809.22i | −1.36823 | + | 0.488931i | ||||
\(394\) | −9326.47 | − | 16153.9i | −1.19254 | − | 2.06554i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −3750.52 | − | 22832.4i | −0.475936 | − | 2.89740i | ||||
\(397\) | − | 11990.1i | − | 1.51578i | −0.652382 | − | 0.757890i | \(-0.726230\pi\) | ||
0.652382 | − | 0.757890i | \(-0.273770\pi\) | |||||||
\(398\) | −5317.38 | + | 3069.99i | −0.669689 | + | 0.386645i | ||||
\(399\) | 1023.36 | + | 186.638i | 0.128402 | + | 0.0234176i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −6426.63 | + | 11131.3i | −0.800326 | + | 1.38620i | 0.119076 | + | 0.992885i | \(0.462007\pi\) |
−0.919402 | + | 0.393320i | \(0.871327\pi\) | |||||||
\(402\) | 8113.38 | + | 6889.38i | 1.00661 | + | 0.854753i | ||||
\(403\) | 6243.21 | − | 3604.52i | 0.771703 | − | 0.445543i | ||||
\(404\) | −563.243 | −0.0693623 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −16442.8 | −2.00996 | ||||||||
\(407\) | 14298.1 | − | 8255.02i | 1.74135 | − | 1.00537i | ||||
\(408\) | −4242.48 | − | 3602.45i | −0.514789 | − | 0.437127i | ||||
\(409\) | 1112.54 | − | 1926.98i | 0.134503 | − | 0.232966i | −0.790904 | − | 0.611940i | \(-0.790390\pi\) |
0.925408 | + | 0.378974i | \(0.123723\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 11752.9 | + | 2143.47i | 1.41053 | + | 0.257249i | ||||
\(412\) | −16113.2 | + | 9302.97i | −1.92680 | + | 1.11244i | ||||
\(413\) | − | 8433.95i | − | 1.00486i | ||||||
\(414\) | −191.995 | − | 1168.82i | −0.0227924 | − | 0.138755i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 4261.32 | + | 7380.83i | 0.502232 | + | 0.869891i | ||||
\(417\) | 10441.7 | − | 3731.29i | 1.22621 | − | 0.438183i | ||||
\(418\) | 2615.27 | + | 1509.93i | 0.306021 | + | 0.176682i | ||||
\(419\) | 4838.33 | − | 8380.23i | 0.564123 | − | 0.977090i | −0.433007 | − | 0.901390i | \(-0.642548\pi\) |
0.997131 | − | 0.0756998i | \(-0.0241191\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 4981.30 | + | 8627.87i | 0.576660 | + | 0.998804i | 0.995859 | + | 0.0909098i | \(0.0289775\pi\) |
−0.419199 | + | 0.907894i | \(0.637689\pi\) | |||||||
\(422\) | 13514.8i | 1.55898i | ||||||||
\(423\) | 8139.88 | + | 9934.98i | 0.935637 | + | 1.14197i | ||||
\(424\) | −12287.3 | −1.40737 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 9574.84 | + | 1746.23i | 1.08897 | + | 0.198604i | ||||
\(427\) | −9497.39 | − | 5483.32i | −1.07637 | − | 0.621444i | ||||
\(428\) | 3979.83 | + | 2297.76i | 0.449468 | + | 0.259500i | ||||
\(429\) | 10442.5 | − | 12297.7i | 1.17521 | − | 1.38401i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −2461.47 | −0.275092 | −0.137546 | − | 0.990495i | \(-0.543922\pi\) | ||||
−0.137546 | + | 0.990495i | \(0.543922\pi\) | |||||||
\(432\) | 66.7297 | + | 1.17358i | 0.00743179 | + | 0.000130704i | ||||
\(433\) | − | 7818.49i | − | 0.867743i | −0.900975 | − | 0.433871i | \(-0.857147\pi\) | ||
0.900975 | − | 0.433871i | \(-0.142853\pi\) | |||||||
\(434\) | 7085.36 | + | 12272.2i | 0.783660 | + | 1.35734i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 9833.63 | − | 17032.3i | 1.08015 | − | 1.87087i | ||||
\(437\) | 82.6770 | + | 47.7336i | 0.00905030 | + | 0.00522519i | ||||
\(438\) | −1528.80 | + | 8382.64i | −0.166779 | + | 0.914470i | ||||
\(439\) | 3105.91 | + | 5379.60i | 0.337670 | + | 0.584862i | 0.983994 | − | 0.178201i | \(-0.0570278\pi\) |
−0.646324 | + | 0.763063i | \(0.723694\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1555.98 | + | 587.080i | 0.168015 | + | 0.0633927i | ||||
\(442\) | − | 10193.6i | − | 1.09697i | ||||||
\(443\) | −2584.52 | + | 1492.17i | −0.277188 | + | 0.160034i | −0.632150 | − | 0.774846i | \(-0.717827\pi\) |
0.354962 | + | 0.934881i | \(0.384494\pi\) | |||||||
\(444\) | −5621.08 | − | 15730.1i | −0.600822 | − | 1.68134i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 8019.45 | − | 13890.1i | 0.851417 | − | 1.47470i | ||||
\(447\) | −8565.99 | + | 3061.02i | −0.906392 | + | 0.323896i | ||||
\(448\) | −14442.1 | + | 8338.16i | −1.52305 | + | 0.879333i | ||||
\(449\) | 810.476 | 0.0851865 | 0.0425932 | − | 0.999092i | \(-0.486438\pi\) | ||||
0.0425932 | + | 0.999092i | \(0.486438\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 16563.1 | 1.72933 | ||||||||
\(452\) | −9095.01 | + | 5251.01i | −0.946446 | + | 0.546431i | ||||
\(453\) | −816.637 | + | 4477.73i | −0.0846996 | + | 0.464420i | ||||
\(454\) | −1492.88 | + | 2585.74i | −0.154326 | + | 0.267301i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 752.873 | − | 886.632i | 0.0773169 | − | 0.0910534i | ||||
\(457\) | 1361.20 | − | 785.887i | 0.139331 | − | 0.0804425i | −0.428714 | − | 0.903440i | \(-0.641033\pi\) |
0.568045 | + | 0.822998i | \(0.307700\pi\) | |||||||
\(458\) | 20963.2i | 2.13875i | ||||||||
\(459\) | −5726.59 | − | 3441.91i | −0.582341 | − | 0.350010i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −1031.35 | − | 1786.34i | −0.104196 | − | 0.180474i | 0.809213 | − | 0.587515i | \(-0.199894\pi\) |
−0.913410 | + | 0.407042i | \(0.866560\pi\) | |||||||
\(462\) | 24173.5 | + | 20526.6i | 2.43431 | + | 2.06707i | ||||
\(463\) | 2410.35 | + | 1391.62i | 0.241940 | + | 0.139684i | 0.616068 | − | 0.787693i | \(-0.288725\pi\) |
−0.374128 | + | 0.927377i | \(0.622058\pi\) | |||||||
\(464\) | 42.5128 | − | 73.6344i | 0.00425347 | − | 0.00736722i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 726.118 | + | 1257.67i | 0.0721819 | + | 0.125023i | ||||
\(467\) | 10939.7i | 1.08400i | 0.840379 | + | 0.541999i | \(0.182332\pi\) | ||||
−0.840379 | + | 0.541999i | \(0.817668\pi\) | |||||||
\(468\) | −10344.9 | − | 12626.2i | −1.02178 | − | 1.24711i | ||||
\(469\) | −9008.83 | −0.886970 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −453.561 | − | 1269.25i | −0.0443716 | − | 0.124170i | ||||
\(472\) | −8167.04 | − | 4715.24i | −0.796438 | − | 0.459823i | ||||
\(473\) | −12194.2 | − | 7040.33i | −1.18539 | − | 0.684386i | ||||
\(474\) | −5210.51 | − | 14581.1i | −0.504908 | − | 1.41294i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 12374.1 | 1.19152 | ||||||||
\(477\) | −14555.4 | + | 2390.92i | −1.39716 | + | 0.229503i | ||||
\(478\) | 8496.21i | 0.812986i | ||||||||
\(479\) | 7311.85 | + | 12664.5i | 0.697467 | + | 1.20805i | 0.969342 | + | 0.245716i | \(0.0790230\pi\) |
−0.271875 | + | 0.962333i | \(0.587644\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 5823.49 | − | 10086.6i | 0.552034 | − | 0.956151i | ||||
\(482\) | −12939.8 | − | 7470.81i | −1.22281 | − | 0.705987i | ||||
\(483\) | 764.201 | + | 648.913i | 0.0719925 | + | 0.0611316i | ||||
\(484\) | 19829.9 | + | 34346.4i | 1.86231 | + | 3.22562i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −17142.3 | + | 2507.13i | −1.59998 | + | 0.234003i | ||||
\(487\) | 16473.6i | 1.53284i | 0.642341 | + | 0.766419i | \(0.277963\pi\) | ||||
−0.642341 | + | 0.766419i | \(0.722037\pi\) | |||||||
\(488\) | −10619.6 | + | 6131.22i | −0.985093 | + | 0.568744i | ||||
\(489\) | 4042.01 | − | 4760.13i | 0.373795 | − | 0.440206i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −10264.6 | + | 17778.8i | −0.943450 | + | 1.63410i | −0.184626 | + | 0.982809i | \(0.559107\pi\) |
−0.758825 | + | 0.651295i | \(0.774226\pi\) | |||||||
\(492\) | 3006.68 | − | 16486.0i | 0.275511 | − | 1.51067i | ||||
\(493\) | −7371.56 | + | 4255.97i | −0.673425 | + | 0.388802i | ||||
\(494\) | 2130.35 | 0.194026 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −73.2768 | −0.00663352 | ||||||||
\(497\) | −7134.10 | + | 4118.87i | −0.643879 | + | 0.371744i | ||||
\(498\) | 18197.4 | − | 6502.76i | 1.63744 | − | 0.585132i | ||||
\(499\) | −7202.31 | + | 12474.8i | −0.646131 | + | 1.11913i | 0.337908 | + | 0.941179i | \(0.390281\pi\) |
−0.984039 | + | 0.177953i | \(0.943053\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −2935.63 | − | 8215.08i | −0.261785 | − | 0.732580i | ||||
\(502\) | 22344.5 | − | 12900.6i | 1.98663 | − | 1.14698i | ||||
\(503\) | 2953.63i | 0.261821i | 0.991394 | + | 0.130910i | \(0.0417901\pi\) | ||||
−0.991394 | + | 0.130910i | \(0.958210\pi\) | |||||||
\(504\) | 9448.49 | − | 7741.30i | 0.835058 | − | 0.684176i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 1455.20 | + | 2520.48i | 0.127849 | + | 0.221441i | ||||
\(507\) | −6.24932 | + | 34.2659i | −0.000547420 | + | 0.00300158i | ||||
\(508\) | −9672.98 | − | 5584.69i | −0.844821 | − | 0.487757i | ||||
\(509\) | −8684.44 | + | 15041.9i | −0.756250 | + | 1.30986i | 0.188500 | + | 0.982073i | \(0.439637\pi\) |
−0.944750 | + | 0.327790i | \(0.893696\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3606.02 | − | 6245.80i | −0.312174 | − | 0.540701i | ||||
\(512\) | − | 172.223i | − | 0.0148657i | ||||||
\(513\) | 719.323 | − | 1196.80i | 0.0619082 | − | 0.103002i | ||||
\(514\) | −5366.92 | −0.460554 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −9221.16 | + | 10859.4i | −0.786703 | + | 0.926473i | ||||
\(517\) | −27330.3 | − | 15779.1i | −2.32492 | − | 1.34229i | ||||
\(518\) | 19827.1 | + | 11447.2i | 1.68176 | + | 0.970966i | ||||
\(519\) | 4763.20 | + | 868.699i | 0.402854 | + | 0.0734714i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −6146.30 | −0.516841 | −0.258421 | − | 0.966033i | \(-0.583202\pi\) | ||||
−0.258421 | + | 0.966033i | \(0.583202\pi\) | |||||||
\(522\) | −7791.48 | + | 20650.4i | −0.653303 | + | 1.73150i | ||||
\(523\) | 4554.68i | 0.380807i | 0.981706 | + | 0.190404i | \(0.0609797\pi\) | ||||
−0.981706 | + | 0.190404i | \(0.939020\pi\) | |||||||
\(524\) | −14070.7 | − | 24371.1i | −1.17305 | − | 2.03179i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −6627.03 | + | 11478.4i | −0.549339 | + | 0.951483i | ||||
\(527\) | 6352.96 | + | 3667.88i | 0.525122 | + | 0.303179i | ||||
\(528\) | −154.423 | + | 55.1824i | −0.0127280 | + | 0.00454831i | ||||
\(529\) | −6037.50 | − | 10457.3i | −0.496219 | − | 0.859476i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −10592.1 | − | 3996.46i | −0.865649 | − | 0.326613i | ||||
\(532\) | 2586.05i | 0.210751i | ||||||||
\(533\) | 10119.0 | − | 5842.22i | 0.822333 | − | 0.474774i | ||||
\(534\) | 4699.25 | + | 857.037i | 0.380817 | + | 0.0694525i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −5036.64 | + | 8723.72i | −0.405877 | + | 0.702999i | ||||
\(537\) | 4053.53 | + | 3442.01i | 0.325741 | + | 0.276599i | ||||
\(538\) | 11605.8 | − | 6700.59i | 0.930037 | − | 0.536957i | ||||
\(539\) | −4086.28 | −0.326547 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 18091.8 | 1.43776 | 0.718879 | − | 0.695135i | \(-0.244655\pi\) | ||||
0.718879 | + | 0.695135i | \(0.244655\pi\) | |||||||
\(542\) | 2649.33 | − | 1529.59i | 0.209960 | − | 0.121221i | ||||
\(543\) | −10456.3 | − | 8878.86i | −0.826379 | − | 0.701710i | ||||
\(544\) | −4336.23 | + | 7510.58i | −0.341754 | + | 0.591936i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 22008.7 | + | 4013.89i | 1.72507 | + | 0.314613i | ||||
\(547\) | 13667.1 | − | 7890.69i | 1.06830 | − | 0.616786i | 0.140586 | − | 0.990068i | \(-0.455101\pi\) |
0.927718 | + | 0.373283i | \(0.121768\pi\) | |||||||
\(548\) | 29699.7i | 2.31516i | ||||||||
\(549\) | −11386.8 | + | 9329.41i | −0.885206 | + | 0.725263i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −889.453 | − | 1540.58i | −0.0687694 | − | 0.119112i | ||||
\(552\) | 1055.62 | − | 377.223i | 0.0813956 | − | 0.0290864i | ||||
\(553\) | 11349.8 | + | 6552.83i | 0.872774 | + | 0.503896i | ||||
\(554\) | 1446.69 | − | 2505.75i | 0.110946 | − | 0.192164i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 13782.8 | + | 23872.5i | 1.05130 | + | 1.82090i | ||||
\(557\) | − | 13954.5i | − | 1.06153i | −0.847519 | − | 0.530766i | \(-0.821904\pi\) | ||
0.847519 | − | 0.530766i | \(-0.178096\pi\) | |||||||
\(558\) | 18770.0 | − | 3083.22i | 1.42401 | − | 0.233913i | ||||
\(559\) | −9933.18 | −0.751572 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 16150.4 | + | 2945.46i | 1.21545 | + | 0.221671i | ||||
\(562\) | −14240.4 | − | 8221.69i | −1.06885 | − | 0.617102i | ||||
\(563\) | −11781.4 | − | 6801.97i | −0.881927 | − | 0.509181i | −0.0106339 | − | 0.999943i | \(-0.503385\pi\) |
−0.871293 | + | 0.490762i | \(0.836718\pi\) | |||||||
\(564\) | −20666.9 | + | 24338.7i | −1.54297 | + | 1.81710i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −2306.77 | −0.171309 | ||||||||
\(567\) | 9686.28 | − | 11008.8i | 0.717435 | − | 0.815392i | ||||
\(568\) | 9211.10i | 0.680438i | ||||||||
\(569\) | −6229.30 | − | 10789.5i | −0.458956 | − | 0.794935i | 0.539950 | − | 0.841697i | \(-0.318443\pi\) |
−0.998906 | + | 0.0467619i | \(0.985110\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 6728.56 | − | 11654.2i | 0.493137 | − | 0.854139i | −0.506831 | − | 0.862045i | \(-0.669183\pi\) |
0.999969 | + | 0.00790629i | \(0.00251668\pi\) | |||||||
\(572\) | 34733.7 | + | 20053.5i | 2.53897 | + | 1.46587i | ||||
\(573\) | 758.207 | − | 4157.36i | 0.0552785 | − | 0.303100i | ||||
\(574\) | 11484.0 | + | 19890.8i | 0.835074 | + | 1.44639i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 3628.38 | + | 22088.8i | 0.262470 | + | 1.59786i | ||||
\(577\) | 3722.70i | 0.268592i | 0.990941 | + | 0.134296i | \(0.0428774\pi\) | ||||
−0.990941 | + | 0.134296i | \(0.957123\pi\) | |||||||
\(578\) | −10476.5 | + | 6048.61i | −0.753918 | + | 0.435275i | ||||
\(579\) | 1423.73 | + | 3984.18i | 0.102190 | + | 0.285971i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −8177.99 | + | 14164.7i | −0.583959 | + | 1.01145i | ||||
\(582\) | 5642.86 | − | 2016.45i | 0.401897 | − | 0.143616i | ||||
\(583\) | 31387.7 | − | 18121.7i | 2.22975 | − | 1.28735i | ||||
\(584\) | −8064.19 | −0.571401 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −28349.3 | −1.99847 | ||||||||
\(587\) | −15190.4 | + | 8770.16i | −1.06810 | + | 0.616667i | −0.927661 | − | 0.373423i | \(-0.878184\pi\) |
−0.140437 | + | 0.990090i | \(0.544851\pi\) | |||||||
\(588\) | −741.777 | + | 4067.27i | −0.0520244 | + | 0.285257i | ||||
\(589\) | −766.548 | + | 1327.70i | −0.0536249 | + | 0.0928810i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 13716.9 | − | 16153.9i | 0.954718 | − | 1.12434i | ||||
\(592\) | −102.526 | + | 59.1933i | −0.00711788 | + | 0.00410951i | ||||
\(593\) | 22350.6i | 1.54777i | 0.633325 | + | 0.773886i | \(0.281690\pi\) | ||||
−0.633325 | + | 0.773886i | \(0.718310\pi\) | |||||||
\(594\) | 37233.9 | − | 20632.7i | 2.57193 | − | 1.42520i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −11306.9 | − | 19584.2i | −0.777097 | − | 1.34597i | ||||
\(597\) | −5317.38 | − | 4515.19i | −0.364533 | − | 0.309539i | ||||
\(598\) | 1778.07 | + | 1026.57i | 0.121590 | + | 0.0702000i | ||||
\(599\) | −1280.81 | + | 2218.43i | −0.0873665 | + | 0.151323i | −0.906397 | − | 0.422427i | \(-0.861178\pi\) |
0.819031 | + | 0.573750i | \(0.194512\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −6692.51 | − | 11591.8i | −0.454232 | − | 0.786752i | 0.544412 | − | 0.838818i | \(-0.316753\pi\) |
−0.998644 | + | 0.0520656i | \(0.983420\pi\) | |||||||
\(602\) | − | 19525.6i | − | 1.32193i | ||||||
\(603\) | −4268.87 | + | 11314.1i | −0.288295 | + | 0.764091i | ||||
\(604\) | −11315.3 | −0.762270 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −348.693 | − | 975.786i | −0.0233741 | − | 0.0654103i | ||||
\(607\) | 24793.1 | + | 14314.3i | 1.65786 | + | 0.957166i | 0.973700 | + | 0.227835i | \(0.0731646\pi\) |
0.684161 | + | 0.729331i | \(0.260169\pi\) | |||||||
\(608\) | −1569.63 | − | 906.226i | −0.104699 | − | 0.0604479i | ||||
\(609\) | −6286.29 | − | 17591.6i | −0.418281 | − | 1.17052i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −22262.8 | −1.47407 | ||||||||
\(612\) | 5863.50 | − | 15540.5i | 0.387284 | − | 1.02645i | ||||
\(613\) | − | 7188.12i | − | 0.473614i | −0.971557 | − | 0.236807i | \(-0.923899\pi\) | ||
0.971557 | − | 0.236807i | \(-0.0761010\pi\) | |||||||
\(614\) | 4497.63 | + | 7790.12i | 0.295618 | + | 0.512025i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −15006.5 | + | 25992.0i | −0.981539 | + | 1.70008i | ||||
\(617\) | −13452.6 | − | 7766.88i | −0.877767 | − | 0.506779i | −0.00784559 | − | 0.999969i | \(-0.502497\pi\) |
−0.869922 | + | 0.493190i | \(0.835831\pi\) | |||||||
\(618\) | −26092.3 | − | 22155.9i | −1.69836 | − | 1.44214i | ||||
\(619\) | −11079.9 | − | 19191.0i | −0.719450 | − | 1.24612i | −0.961218 | − | 0.275789i | \(-0.911061\pi\) |
0.241769 | − | 0.970334i | \(-0.422272\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1177.08 | − | 652.265i | 0.0760624 | − | 0.0421490i | ||||
\(622\) | 10547.2i | 0.679908i | ||||||||
\(623\) | −3501.36 | + | 2021.51i | −0.225167 | + | 0.130000i | ||||
\(624\) | −74.8785 | + | 88.1818i | −0.00480375 | + | 0.00565721i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 23559.4 | − | 40806.1i | 1.50419 | − | 2.60534i | ||||
\(627\) | −615.569 | + | 3375.25i | −0.0392081 | + | 0.214983i | ||||
\(628\) | 2901.85 | − | 1675.38i | 0.184389 | − | 0.106457i | ||||
\(629\) | 11851.7 | 0.751287 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −25582.8 | −1.61400 | −0.807002 | − | 0.590549i | \(-0.798911\pi\) | ||||
−0.807002 | + | 0.590549i | \(0.798911\pi\) | |||||||
\(632\) | 12690.9 | − | 7327.10i | 0.798761 | − | 0.461165i | ||||
\(633\) | −14459.0 | + | 5166.88i | −0.907891 | + | 0.324431i | ||||
\(634\) | 3891.73 | − | 6740.68i | 0.243786 | − | 0.422250i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −12339.6 | − | 34531.2i | −0.769334 | − | 2.15291i | ||||
\(637\) | −2496.46 | + | 1441.33i | −0.155280 | + | 0.0896510i | ||||
\(638\) | − | 54231.5i | − | 3.36527i | ||||||
\(639\) | 1792.34 | + | 10911.4i | 0.110961 | + | 0.675506i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −1905.34 | − | 3300.14i | −0.117405 | − | 0.203351i | 0.801334 | − | 0.598217i | \(-0.204124\pi\) |
−0.918738 | + | 0.394867i | \(0.870791\pi\) | |||||||
\(642\) | −1516.89 | + | 8317.33i | −0.0932507 | + | 0.511306i | ||||
\(643\) | 23140.3 | + | 13360.0i | 1.41923 | + | 0.819391i | 0.996231 | − | 0.0867402i | \(-0.0276450\pi\) |
0.422996 | + | 0.906131i | \(0.360978\pi\) | |||||||
\(644\) | −1246.16 | + | 2158.41i | −0.0762509 | + | 0.132071i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 1083.90 | + | 1877.37i | 0.0660147 | + | 0.114341i | ||||
\(647\) | 5114.23i | 0.310759i | 0.987855 | + | 0.155380i | \(0.0496601\pi\) | ||||
−0.987855 | + | 0.155380i | \(0.950340\pi\) | |||||||
\(648\) | −5245.03 | − | 15534.5i | −0.317970 | − | 0.941750i | ||||
\(649\) | 27816.8 | 1.68244 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −10420.8 | + | 12272.2i | −0.627378 | + | 0.738842i | ||||
\(652\) | 13444.5 | + | 7762.20i | 0.807559 | + | 0.466244i | ||||
\(653\) | −7682.56 | − | 4435.53i | −0.460401 | − | 0.265813i | 0.251812 | − | 0.967776i | \(-0.418974\pi\) |
−0.712213 | + | 0.701964i | \(0.752307\pi\) | |||||||
\(654\) | 35595.4 | + | 6491.79i | 2.12827 | + | 0.388148i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −118.767 | −0.00706872 | ||||||||
\(657\) | −9552.78 | + | 1569.17i | −0.567259 | + | 0.0931799i | ||||
\(658\) | − | 43761.7i | − | 2.59272i | ||||||
\(659\) | −12102.2 | − | 20961.7i | −0.715382 | − | 1.23908i | −0.962812 | − | 0.270172i | \(-0.912920\pi\) |
0.247430 | − | 0.968906i | \(-0.420414\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −10689.8 | + | 18515.2i | −0.629023 | + | 1.08950i | 0.358726 | + | 0.933443i | \(0.383211\pi\) |
−0.987748 | + | 0.156056i | \(0.950122\pi\) | |||||||
\(662\) | −33078.9 | − | 19098.1i | −1.94207 | − | 1.12125i | ||||
\(663\) | 10905.8 | − | 3897.14i | 0.638832 | − | 0.228284i | ||||
\(664\) | 9144.28 | + | 15838.4i | 0.534438 | + | 0.925674i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 23771.6 | − | 19476.4i | 1.38308 | − | 1.13318i | ||||
\(667\) | − | 1714.43i | − | 0.0995248i | ||||||
\(668\) | 18781.9 | − | 10843.7i | 1.08787 | − | 0.628079i | ||||
\(669\) | 17926.5 | + | 3269.38i | 1.03599 | + | 0.188941i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 18085.0 | − | 31324.2i | 1.04048 | − | 1.80217i | ||||
\(672\) | −14508.4 | − | 12319.6i | −0.832849 | − | 0.707203i | ||||
\(673\) | −25722.1 | + | 14850.7i | −1.47328 | + | 0.850597i | −0.999548 | − | 0.0300732i | \(-0.990426\pi\) |
−0.473730 | + | 0.880670i | \(0.657093\pi\) | |||||||
\(674\) | −35936.6 | −2.05375 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −86.5900 | −0.00492661 | ||||||||
\(677\) | 2304.91 | − | 1330.74i | 0.130849 | − | 0.0755459i | −0.433147 | − | 0.901324i | \(-0.642597\pi\) |
0.563996 | + | 0.825778i | \(0.309263\pi\) | |||||||
\(678\) | −14727.6 | − | 12505.8i | −0.834235 | − | 0.708381i | ||||
\(679\) | −2535.93 | + | 4392.36i | −0.143328 | + | 0.248252i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −3337.14 | − | 608.618i | −0.187782 | − | 0.0342471i | ||||
\(682\) | −40476.1 | + | 23368.9i | −2.27259 | + | 1.31208i | ||||
\(683\) | − | 28698.1i | − | 1.60776i | −0.594789 | − | 0.803882i | \(-0.702765\pi\) | ||
0.594789 | − | 0.803882i | \(-0.297235\pi\) | |||||||
\(684\) | 3247.80 | + | 1225.41i | 0.181554 | + | 0.0685010i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 12944.0 | + | 22419.7i | 0.720415 | + | 1.24780i | ||||
\(687\) | −22427.9 | + | 8014.51i | −1.24553 | + | 0.445084i | ||||
\(688\) | 87.4396 | + | 50.4833i | 0.00484535 | + | 0.00279747i | ||||
\(689\) | 12783.9 | − | 22142.4i | 0.706863 | − | 1.22432i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −8412.62 | − | 14571.1i | −0.463142 | − | 0.802186i | 0.535973 | − | 0.844235i | \(-0.319945\pi\) |
−0.999116 | + | 0.0420492i | \(0.986611\pi\) | |||||||
\(692\) | 12036.6i | 0.661220i | ||||||||
\(693\) | −12718.9 | + | 33710.0i | −0.697189 | + | 1.84781i | ||||
\(694\) | 5543.99 | 0.303238 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −20549.4 | − | 3747.74i | −1.11914 | − | 0.204106i | ||||
\(697\) | 10296.9 | + | 5944.92i | 0.559574 | + | 0.323070i | ||||
\(698\) | −5539.88 | − | 3198.45i | −0.300412 | − | 0.173443i | ||||
\(699\) | −1067.94 | + | 1257.67i | −0.0577870 | + | 0.0680537i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −998.795 | −0.0538145 | −0.0269073 | − | 0.999638i | \(-0.508566\pi\) | ||||
−0.0269073 | + | 0.999638i | \(0.508566\pi\) | |||||||
\(702\) | 15469.9 | − | 25738.6i | 0.831730 | − | 1.38382i | ||||
\(703\) | 2476.88i | 0.132884i | ||||||||
\(704\) | −27500.8 | − | 47632.9i | −1.47227 | − | 2.55004i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 6010.66 | − | 10410.8i | 0.320417 | − | 0.554978i | ||||
\(707\) | 759.545 | + | 438.523i | 0.0404040 | + | 0.0233272i | ||||
\(708\) | 5049.54 | − | 27687.3i | 0.268041 | − | 1.46971i | ||||
\(709\) | 16626.9 | + | 28798.6i | 0.880727 | + | 1.52546i | 0.850534 | + | 0.525921i | \(0.176279\pi\) |
0.0301937 | + | 0.999544i | \(0.490388\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 13607.8 | − | 11149.1i | 0.717768 | − | 0.588078i | ||||
\(712\) | 4520.73i | 0.237952i | ||||||||
\(713\) | −1279.58 | + | 738.765i | −0.0672099 | + | 0.0388036i | ||||
\(714\) | 7660.56 | + | 21437.4i | 0.401526 | + | 1.12363i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −6609.97 | + | 11448.8i | −0.345009 | + | 0.597573i | ||||
\(717\) | −9089.81 | + | 3248.21i | −0.473452 | + | 0.169186i | ||||
\(718\) | 14565.9 | − | 8409.62i | 0.757095 | − | 0.437109i | ||||
\(719\) | −1178.94 | −0.0611503 | −0.0305752 | − | 0.999532i | \(-0.509734\pi\) | ||||
−0.0305752 | + | 0.999532i | \(0.509734\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 28972.0 | 1.49650 | ||||||||
\(722\) | 26775.0 | − | 15458.6i | 1.38014 | − | 0.796826i | ||||
\(723\) | 3045.71 | − | 16700.1i | 0.156668 | − | 0.859034i | ||||
\(724\) | 17050.8 | − | 29532.9i | 0.875260 | − | 1.51600i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −47226.8 | + | 55617.4i | −2.41426 | + | 2.84319i | ||||
\(727\) | 10978.3 | − | 6338.35i | 0.560061 | − | 0.323351i | −0.193109 | − | 0.981177i | \(-0.561857\pi\) |
0.753170 | + | 0.657826i | \(0.228524\pi\) | |||||||
\(728\) | 21172.6i | 1.07790i | ||||||||
\(729\) | −9236.02 | − | 17381.5i | −0.469238 | − | 0.883072i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −5053.90 | − | 8753.61i | −0.255712 | − | 0.442906i | ||||
\(732\) | −27895.5 | − | 23687.1i | −1.40853 | − | 1.19604i | ||||
\(733\) | 8492.98 | + | 4903.42i | 0.427961 | + | 0.247083i | 0.698478 | − | 0.715632i | \(-0.253861\pi\) |
−0.270517 | + | 0.962715i | \(0.587195\pi\) | |||||||
\(734\) | −26137.5 | + | 45271.4i | −1.31438 | + | 2.27657i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −873.381 | − | 1512.74i | −0.0437408 | − | 0.0757613i | ||||
\(737\) | − | 29712.8i | − | 1.48506i | ||||||
\(738\) | 30422.5 | − | 4997.30i | 1.51744 | − | 0.249259i | ||||
\(739\) | 29970.4 | 1.49185 | 0.745927 | − | 0.666028i | \(-0.232007\pi\) | ||||
0.745927 | + | 0.666028i | \(0.232007\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 814.460 | + | 2279.19i | 0.0403778 | + | 0.112994i | ||||
\(742\) | 43525.1 | + | 25129.2i | 2.15345 | + | 1.24329i | ||||
\(743\) | 18790.6 | + | 10848.8i | 0.927808 | + | 0.535670i | 0.886118 | − | 0.463460i | \(-0.153392\pi\) |
0.0416904 | + | 0.999131i | \(0.486726\pi\) | |||||||
\(744\) | 6057.78 | + | 16952.1i | 0.298507 | + | 0.835344i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −10335.8 | −0.507267 | ||||||||
\(747\) | 13914.2 | + | 16982.7i | 0.681516 | + | 0.831812i | ||||
\(748\) | 40812.1i | 1.99497i | ||||||||
\(749\) | −3577.92 | − | 6197.14i | −0.174545 | − | 0.302321i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −8512.10 | + | 14743.4i | −0.413596 | + | 0.716370i | −0.995280 | − | 0.0970452i | \(-0.969061\pi\) |
0.581684 | + | 0.813415i | \(0.302394\pi\) | |||||||
\(752\) | 195.974 | + | 113.146i | 0.00950324 | + | 0.00548670i | ||||
\(753\) | 22344.5 | + | 18973.6i | 1.08138 | + | 0.918243i | ||||
\(754\) | −19128.8 | − | 33132.0i | −0.923911 | − | 1.60026i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 31244.2 | + | 18779.0i | 1.50310 | + | 0.903422i | ||||
\(757\) | 30745.2i | 1.47616i | 0.674714 | + | 0.738080i | \(0.264267\pi\) | ||||
−0.674714 | + | 0.738080i | \(0.735733\pi\) | |||||||
\(758\) | −46800.5 | + | 27020.3i | −2.24257 | + | 1.29475i | ||||
\(759\) | −2140.24 | + | 2520.48i | −0.102353 | + | 0.120537i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −10748.3 | + | 18616.6i | −0.511992 | + | 0.886797i | 0.487911 | + | 0.872893i | \(0.337759\pi\) |
−0.999903 | + | 0.0139035i | \(0.995574\pi\) | |||||||
\(762\) | 3686.81 | − | 20215.3i | 0.175274 | − | 0.961052i | ||||
\(763\) | −26521.7 | + | 15312.3i | −1.25839 | + | 0.726530i | ||||
\(764\) | 10505.7 | 0.497489 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 36955.5 | 1.74316 | ||||||||
\(767\) | 16994.3 | − | 9811.66i | 0.800037 | − | 0.461902i | ||||
\(768\) | −19800.6 | + | 7075.65i | −0.930327 | + | 0.332449i | ||||
\(769\) | 11028.7 | − | 19102.4i | 0.517174 | − | 0.895772i | −0.482627 | − | 0.875826i | \(-0.660317\pi\) |
0.999801 | − | 0.0199457i | \(-0.00634935\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −2051.84 | − | 5741.89i | −0.0958434 | − | 0.268209i | ||||
\(772\) | −9108.93 | + | 5259.04i | −0.424660 | + | 0.245178i | ||||
\(773\) | − | 30155.8i | − | 1.40314i | −0.712601 | − | 0.701570i | \(-0.752483\pi\) | ||
0.712601 | − | 0.701570i | \(-0.247517\pi\) | |||||||
\(774\) | −24522.0 | − | 9252.26i | −1.13879 | − | 0.429671i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 2835.57 | + | 4911.35i | 0.131174 | + | 0.227200i | ||||
\(777\) | −4666.81 | + | 25588.7i | −0.215471 | + | 1.18146i | ||||
\(778\) | −12280.3 | − | 7090.04i | −0.565900 | − | 0.326723i | ||||
\(779\) | −1242.42 | + | 2151.94i | −0.0571431 | + | 0.0989747i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −13584.8 | − | 23529.6i | −0.622411 | − | 1.07805i | ||||
\(782\) | 2089.23i | 0.0955381i | ||||||||
\(783\) | −25071.9 | − | 440.943i | −1.14431 | − | 0.0201252i | ||||
\(784\) | 29.3010 | 0.00133478 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 33510.7 | − | 39464.4i | 1.52072 | − | 1.79090i | ||||
\(787\) | 2813.47 | + | 1624.36i | 0.127433 | + | 0.0735733i | 0.562361 | − | 0.826892i | \(-0.309893\pi\) |
−0.434929 | + | 0.900465i | \(0.643226\pi\) | |||||||
\(788\) | 45625.2 | + | 26341.7i | 2.06260 | + | 1.19084i | ||||
\(789\) | −14813.9 | − | 2701.72i | −0.668427 | − | 0.121906i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 16353.1 | 0.735081 | ||||||||
\(792\) | 25532.3 | + | 31162.9i | 1.14552 | + | 1.39814i | ||||
\(793\) | − | 25516.1i | − | 1.14263i | ||||||
\(794\) | 27418.8 | + | 47490.8i | 1.22551 | + | 2.12265i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 8670.90 | − | 15018.4i | 0.386095 | − | 0.668737i | ||||
\(797\) | 23997.7 | + | 13855.1i | 1.06655 | + | 0.615775i | 0.927238 | − | 0.374473i | \(-0.122176\pi\) |
0.139316 | + | 0.990248i | \(0.455510\pi\) | |||||||
\(798\) | −4480.18 | + | 1600.98i | −0.198743 | + | 0.0710199i | ||||
\(799\) | −11327.1 | − | 19619.0i | −0.501530 | − | 0.868675i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 879.667 | + | 5355.23i | 0.0388034 | + | 0.236227i | ||||
\(802\) | − | 58785.4i | − | 2.58826i | ||||||
\(803\) | 20599.8 | − | 11893.3i | 0.905296 | − | 0.522673i | ||||
\(804\) | −29574.6 | − | 5393.73i | −1.29728 | − | 0.236595i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −16485.6 | + | 28553.8i | −0.720445 | + | 1.24785i | ||||
\(807\) | 11605.8 | + | 9854.90i | 0.506248 | + | 0.429875i | ||||
\(808\) | 849.290 | − | 490.338i | 0.0369776 | − | 0.0213491i | ||||
\(809\) | 2244.10 | 0.0975259 | 0.0487630 | − | 0.998810i | \(-0.484472\pi\) | ||||
0.0487630 | + | 0.998810i | \(0.484472\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −2739.73 | −0.118625 | −0.0593126 | − | 0.998239i | \(-0.518891\pi\) | ||||
−0.0593126 | + | 0.998239i | \(0.518891\pi\) | |||||||
\(812\) | 40219.2 | − | 23220.6i | 1.73820 | − | 1.00355i | ||||
\(813\) | 2649.33 | + | 2249.65i | 0.114288 | + | 0.0970462i | ||||
\(814\) | −37755.0 | + | 65393.5i | −1.62569 | + | 2.81578i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −115.808 | − | 21.1207i | −0.00496823 | − | 0.000906092i | ||||
\(817\) | 1829.41 | − | 1056.21i | 0.0783390 | − | 0.0452290i | ||||
\(818\) | 10176.6i | 0.434984i | ||||||||
\(819\) | 4119.88 | + | 25080.9i | 0.175776 | + | 1.07008i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 8616.06 | + | 14923.5i | 0.366264 | + | 0.634388i | 0.988978 | − | 0.148062i | \(-0.0473034\pi\) |
−0.622714 | + | 0.782449i | \(0.713970\pi\) | |||||||
\(822\) | −51453.1 | + | 18386.6i | −2.18325 | + | 0.780177i | ||||
\(823\) | 16702.1 | + | 9642.94i | 0.707409 | + | 0.408422i | 0.810101 | − | 0.586291i | \(-0.199412\pi\) |
−0.102692 | + | 0.994713i | \(0.532746\pi\) | |||||||
\(824\) | 16197.6 | − | 28055.1i | 0.684795 | − | 1.18610i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 19286.7 | + | 33405.5i | 0.812433 | + | 1.40717i | ||||
\(827\) | 26379.4i | 1.10919i | 0.832120 | + | 0.554595i | \(0.187127\pi\) | ||||
−0.832120 | + | 0.554595i | \(0.812873\pi\) | |||||||
\(828\) | 2120.24 | + | 2587.82i | 0.0889896 | + | 0.108615i | ||||
\(829\) | 8718.15 | 0.365252 | 0.182626 | − | 0.983182i | \(-0.441540\pi\) | ||||
0.182626 | + | 0.983182i | \(0.441540\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 3233.90 | + | 589.790i | 0.134997 | + | 0.0246205i | ||||
\(832\) | −33602.6 | − | 19400.4i | −1.40019 | − | 0.808401i | ||||
\(833\) | −2540.35 | − | 1466.67i | −0.105664 | − | 0.0610049i | ||||
\(834\) | −32825.1 | + | 38657.0i | −1.36288 | + | 1.60501i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −8529.28 | −0.352860 | ||||||||
\(837\) | 10474.6 | + | 18902.6i | 0.432565 | + | 0.780610i | ||||
\(838\) | 44256.9i | 1.82438i | ||||||||
\(839\) | −6738.10 | − | 11670.7i | −0.277265 | − | 0.480236i | 0.693439 | − | 0.720515i | \(-0.256095\pi\) |
−0.970704 | + | 0.240279i | \(0.922761\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −3778.58 | + | 6544.70i | −0.154930 | + | 0.268346i | ||||
\(842\) | −39460.2 | − | 22782.4i | −1.61507 | − | 0.932462i | ||||
\(843\) | 3351.83 | − | 18378.6i | 0.136943 | − | 0.750880i | ||||
\(844\) | −19085.6 | − | 33057.3i | −0.778383 | − | 1.34820i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −54959.9 | − | 20736.6i | −2.23352 | − | 0.842718i | ||||
\(847\) | − | 61755.7i | − | 2.50526i | ||||||
\(848\) | −225.068 | + | 129.943i | −0.00911423 | + | 0.00526210i | ||||
\(849\) | −881.907 | − | 2467.93i | −0.0356501 | − | 0.0997636i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1193.56 | + | 2067.30i | −0.0480783 | + | 0.0832740i | ||||
\(852\) | −25886.1 | + | 9250.31i | −1.04090 | + | 0.371960i | ||||
\(853\) | 24453.6 | − | 14118.3i | 0.981567 | − | 0.566708i | 0.0788242 | − | 0.996889i | \(-0.474883\pi\) |
0.902743 | + | 0.430181i | \(0.141550\pi\) | |||||||
\(854\) | 50156.8 | 2.00975 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −8001.36 | −0.319487 | ||||||||
\(857\) | 7324.98 | − | 4229.08i | 0.291968 | − | 0.168568i | −0.346861 | − | 0.937917i | \(-0.612752\pi\) |
0.638829 | + | 0.769349i | \(0.279419\pi\) | |||||||
\(858\) | −13238.6 | + | 72588.9i | −0.526757 | + | 2.88828i | ||||
\(859\) | −11527.2 | + | 19965.6i | −0.457860 | + | 0.793036i | −0.998848 | − | 0.0479940i | \(-0.984717\pi\) |
0.540988 | + | 0.841030i | \(0.318050\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −16890.1 | + | 19890.8i | −0.668539 | + | 0.787315i | ||||
\(862\) | 9749.48 | − | 5628.86i | 0.385230 | − | 0.222413i | ||||
\(863\) | 42314.4i | 1.66906i | 0.550963 | + | 0.834529i | \(0.314260\pi\) | ||||
−0.550963 | + | 0.834529i | \(0.685740\pi\) | |||||||
\(864\) | −22347.0 | + | 12383.3i | −0.879932 | + | 0.487602i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 17879.2 | + | 30967.8i | 0.701572 | + | 1.21516i | ||||
\(867\) | −10476.5 | − | 8895.99i | −0.410381 | − | 0.348470i | ||||
\(868\) | −34661.7 | − | 20011.9i | −1.35541 | − | 0.782545i | ||||
\(869\) | −21612.5 | + | 37433.9i | −0.843674 | + | 1.46129i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −10480.4 | − | 18152.7i | −0.407711 | − | 0.706176i | ||||
\(872\) | 34243.1i | 1.32984i | ||||||||
\(873\) | 4314.67 | + | 5266.19i | 0.167273 | + | 0.204162i | ||||
\(874\) | −436.627 | −0.0168983 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −8098.51 | − | 22663.0i | −0.312356 | − | 0.874098i | ||||
\(877\) | 8816.15 | + | 5090.00i | 0.339453 | + | 0.195983i | 0.660030 | − | 0.751239i | \(-0.270544\pi\) |
−0.320577 | + | 0.947222i | \(0.603877\pi\) | |||||||
\(878\) | −24604.0 | − | 14205.2i | −0.945725 | − | 0.546014i | ||||
\(879\) | −10838.3 | − | 30330.0i | −0.415890 | − | 1.16383i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 6030.64 | 0.230621 | 0.115311 | − | 0.993329i | \(-0.463214\pi\) | ||||
0.115311 | + | 0.993329i | \(0.463214\pi\) | |||||||
\(882\) | −7505.53 | + | 1232.88i | −0.286535 | + | 0.0470673i | ||||
\(883\) | 30238.0i | 1.15242i | 0.817301 | + | 0.576211i | \(0.195469\pi\) | ||||
−0.817301 | + | 0.576211i | \(0.804531\pi\) | |||||||
\(884\) | 14395.4 | + | 24933.6i | 0.547704 | + | 0.948651i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 6824.57 | − | 11820.5i | 0.258776 | − | 0.448214i | ||||
\(887\) | −16260.7 | − | 9388.09i | −0.615535 | − | 0.355379i | 0.159594 | − | 0.987183i | \(-0.448982\pi\) |
−0.775129 | + | 0.631804i | \(0.782315\pi\) | |||||||
\(888\) | 22169.8 | + | 18825.2i | 0.837805 | + | 0.711412i | ||||
\(889\) | 8696.14 | + | 15062.1i | 0.328075 | + | 0.568243i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 36309.2 | + | 31947.2i | 1.36521 | + | 1.20120i | ||||
\(892\) | 45300.3i | 1.70041i | ||||||||
\(893\) | 4100.17 | − | 2367.23i | 0.153647 | − | 0.0887082i | ||||
\(894\) | 26928.6 | − | 31712.8i | 1.00741 | − | 1.18639i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 23483.4 | − | 40674.4i | 0.875586 | − | 1.51656i | ||||
\(897\) | −418.514 | + | 2294.77i | −0.0155783 | + | 0.0854182i | ||||
\(898\) | −3210.16 | + | 1853.39i | −0.119292 | + | 0.0688735i | ||||
\(899\) | 27531.8 | 1.02140 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 26017.3 | 0.962000 | ||||||||
\(902\) | −65603.8 | + | 37876.4i | −2.42169 | + | 1.39817i | ||||
\(903\) | 20889.7 | − | 7464.86i | 0.769841 | − | 0.275100i | ||||
\(904\) | 9142.66 | − | 15835.6i | 0.336372 | − | 0.582614i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −7005.07 | − | 19603.0i | −0.256874 | − | 0.718838i | ||||
\(907\) | −32608.1 | + | 18826.3i | −1.19375 | + | 0.689213i | −0.959155 | − | 0.282880i | \(-0.908710\pi\) |
−0.234597 | + | 0.972093i | \(0.575377\pi\) | |||||||
\(908\) | − | 8432.97i | − | 0.308214i | ||||||
\(909\) | 910.651 | − | 746.111i | 0.0332282 | − | 0.0272243i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 23793.1 | + | 41210.8i | 0.865312 | + | 1.49877i | 0.866737 | + | 0.498766i | \(0.166213\pi\) |
−0.00142411 | + | 0.999999i | \(0.500453\pi\) | |||||||
\(912\) | 4.41399 | − | 24.2025i | 0.000160265 | − | 0.000878756i | ||||
\(913\) | −46717.9 | − | 26972.6i | −1.69347 | − | 0.977724i | ||||
\(914\) | −3594.32 | + | 6225.54i | −0.130076 | + | 0.225298i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −29604.3 | − | 51276.2i | −1.06785 | − | 1.84958i | ||||
\(917\) | 43819.9i | 1.57804i | ||||||||
\(918\) | 30553.0 | + | 537.340i | 1.09848 | + | 0.0193190i | ||||
\(919\) | −32177.3 | −1.15499 | −0.577493 | − | 0.816396i | \(-0.695969\pi\) | ||||
−0.577493 | + | 0.816396i | \(0.695969\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −6614.88 | + | 7790.12i | −0.236664 | + | 0.278711i | ||||
\(922\) | 8169.99 | + | 4716.94i | 0.291827 | + | 0.168486i | ||||
\(923\) | −16598.9 | − | 9583.40i | −0.591940 | − | 0.341757i | ||||
\(924\) | −88116.2 | − | 16070.4i | −3.13724 | − | 0.572161i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −12729.3 | −0.451741 | ||||||||
\(927\) | 13728.5 | − | 36385.7i | 0.486411 | − | 1.28917i | ||||
\(928\) | 32548.6i | 1.15136i | ||||||||
\(929\) | 20321.8 | + | 35198.4i | 0.717694 | + | 1.24308i | 0.961911 | + | 0.273362i | \(0.0881355\pi\) |
−0.244218 | + | 0.969720i | \(0.578531\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 306.518 | − | 530.905i | 0.0107903 | − | 0.0186893i | ||||
\(932\) | −3552.18 | − | 2050.85i | −0.124845 | − | 0.0720792i | ||||
\(933\) | −11284.1 | + | 4032.31i | −0.395952 | + | 0.141492i | ||||
\(934\) | −25016.7 | − | 43330.2i | −0.876415 | − | 1.51799i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 26590.5 | + | 10032.7i | 0.928567 | + | 0.350352i | ||||
\(937\) | 6077.87i | 0.211905i | 0.994371 | + | 0.105953i | \(0.0337892\pi\) | ||||
−0.994371 | + | 0.105953i | \(0.966211\pi\) | |||||||
\(938\) | 35682.5 | − | 20601.3i | 1.24208 | − | 0.717118i | ||||
\(939\) | 52664.2 | + | 9604.75i | 1.83028 | + | 0.333801i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −732.293 | + | 1268.37i | −0.0253688 | + | 0.0439401i | −0.878431 | − | 0.477869i | \(-0.841409\pi\) |
0.853062 | + | 0.521809i | \(0.174743\pi\) | |||||||
\(942\) | 4698.99 | + | 3990.09i | 0.162528 | + | 0.138009i | ||||
\(943\) | −2073.95 | + | 1197.39i | −0.0716193 | + | 0.0413494i | ||||
\(944\) | −199.463 | −0.00687707 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 64399.0 | 2.21331 | ||||||||
\(947\) | −9187.43 | + | 5304.36i | −0.315260 | + | 0.182015i | −0.649278 | − | 0.760551i | \(-0.724929\pi\) |
0.334018 | + | 0.942567i | \(0.391595\pi\) | |||||||
\(948\) | 33336.4 | + | 28307.2i | 1.14211 | + | 0.969806i | ||||
\(949\) | 8390.14 | − | 14532.1i | 0.286992 | − | 0.497085i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 8699.48 | + | 1586.59i | 0.296635 | + | 0.0540995i | ||||
\(952\) | −18658.4 | + | 10772.4i | −0.635211 | + | 0.366739i | ||||
\(953\) | 43623.4i | 1.48279i | 0.671068 | + | 0.741396i | \(0.265836\pi\) | ||||
−0.671068 | + | 0.741396i | \(0.734164\pi\) | |||||||
\(954\) | 52184.1 | − | 42755.3i | 1.77099 | − | 1.45100i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −11998.4 | − | 20781.8i | −0.405915 | − | 0.703065i | ||||
\(957\) | 58020.4 | − | 20733.4i | 1.95981 | − | 0.700329i | ||||
\(958\) | −57922.1 | − | 33441.3i | −1.95342 | − | 1.12781i | ||||
\(959\) | 23123.3 | − | 40050.7i | 0.778613 | − | 1.34860i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 3031.76 | + | 5251.17i | 0.101768 | + | 0.176267i | ||||
\(962\) | 53268.4i | 1.78528i | ||||||||
\(963\) | −9478.35 | + | 1556.95i | −0.317171 | + | 0.0520996i | ||||
\(964\) | 42201.2 | 1.40997 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −4510.80 | − | 822.668i | −0.150241 | − | 0.0274005i | ||||
\(967\) | −4399.73 | − | 2540.19i | −0.146314 | − | 0.0844745i | 0.425056 | − | 0.905167i | \(-0.360254\pi\) |
−0.571370 | + | 0.820693i | \(0.693588\pi\) | |||||||
\(968\) | −59801.3 | − | 34526.3i | −1.98563 | − | 1.14640i | ||||
\(969\) | −1594.15 | + | 1877.37i | −0.0528497 | + | 0.0622393i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 9875.60 | 0.326388 | 0.163194 | − | 0.986594i | \(-0.447820\pi\) | ||||
0.163194 | + | 0.986594i | \(0.447820\pi\) | |||||||
\(972\) | 38389.7 | − | 30340.9i | 1.26682 | − | 1.00122i | ||||
\(973\) | − | 42923.4i | − | 1.41425i | ||||||
\(974\) | −37671.8 | − | 65249.4i | −1.23930 | − | 2.14654i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −129.680 | + | 224.613i | −0.00425304 | + | 0.00736648i | ||||
\(977\) | −21287.6 | − | 12290.4i | −0.697084 | − | 0.402461i | 0.109177 | − | 0.994022i | \(-0.465179\pi\) |
−0.806260 | + | 0.591561i | \(0.798512\pi\) | |||||||
\(978\) | −5124.31 | + | 28097.3i | −0.167543 | + | 0.918664i | ||||
\(979\) | −6667.32 | − | 11548.1i | −0.217659 | − | 0.376997i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 6663.21 | + | 40564.2i | 0.216860 | + | 1.32020i | ||||
\(982\) | − | 93891.8i | − | 3.05113i | ||||||
\(983\) | 27592.1 | − | 15930.3i | 0.895270 | − | 0.516885i | 0.0196076 | − | 0.999808i | \(-0.493758\pi\) |
0.875663 | + | 0.482923i | \(0.160425\pi\) | |||||||
\(984\) | 9818.48 | + | 27476.1i | 0.318091 | + | 0.890149i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 19465.0 | − | 33714.4i | 0.628695 | − | 1.08893i | ||||
\(987\) | 46819.1 | − | 16730.6i | 1.50990 | − | 0.539556i | ||||
\(988\) | −5210.85 | + | 3008.49i | −0.167793 | + | 0.0968752i | ||||
\(989\) | 2035.86 | 0.0654566 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −36921.3 | −1.18350 | −0.591748 | − | 0.806123i | \(-0.701562\pi\) | ||||
−0.591748 | + | 0.806123i | \(0.701562\pi\) | |||||||
\(992\) | 24292.9 | − | 14025.5i | 0.777520 | − | 0.448902i | ||||
\(993\) | 7785.95 | − | 42691.4i | 0.248821 | − | 1.36432i | ||||
\(994\) | 18838.0 | − | 32628.4i | 0.601112 | − | 1.04116i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −35327.7 | + | 41604.2i | −1.12390 | + | 1.32357i | ||||
\(997\) | −3233.84 | + | 1867.06i | −0.102725 | + | 0.0593083i | −0.550482 | − | 0.834847i | \(-0.685556\pi\) |
0.447757 | + | 0.894155i | \(0.352223\pi\) | |||||||
\(998\) | − | 65880.7i | − | 2.08959i | ||||||
\(999\) | 29925.3 | + | 17986.3i | 0.947743 | + | 0.569632i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 225.4.k.c.49.1 | 12 | ||
5.2 | odd | 4 | 225.4.e.c.76.1 | 6 | |||
5.3 | odd | 4 | 45.4.e.b.31.3 | yes | 6 | ||
5.4 | even | 2 | inner | 225.4.k.c.49.6 | 12 | ||
9.7 | even | 3 | inner | 225.4.k.c.124.6 | 12 | ||
15.8 | even | 4 | 135.4.e.b.91.1 | 6 | |||
45.7 | odd | 12 | 225.4.e.c.151.1 | 6 | |||
45.13 | odd | 12 | 405.4.a.h.1.1 | 3 | |||
45.22 | odd | 12 | 2025.4.a.s.1.3 | 3 | |||
45.23 | even | 12 | 405.4.a.j.1.3 | 3 | |||
45.32 | even | 12 | 2025.4.a.q.1.1 | 3 | |||
45.34 | even | 6 | inner | 225.4.k.c.124.1 | 12 | ||
45.38 | even | 12 | 135.4.e.b.46.1 | 6 | |||
45.43 | odd | 12 | 45.4.e.b.16.3 | ✓ | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
45.4.e.b.16.3 | ✓ | 6 | 45.43 | odd | 12 | ||
45.4.e.b.31.3 | yes | 6 | 5.3 | odd | 4 | ||
135.4.e.b.46.1 | 6 | 45.38 | even | 12 | |||
135.4.e.b.91.1 | 6 | 15.8 | even | 4 | |||
225.4.e.c.76.1 | 6 | 5.2 | odd | 4 | |||
225.4.e.c.151.1 | 6 | 45.7 | odd | 12 | |||
225.4.k.c.49.1 | 12 | 1.1 | even | 1 | trivial | ||
225.4.k.c.49.6 | 12 | 5.4 | even | 2 | inner | ||
225.4.k.c.124.1 | 12 | 45.34 | even | 6 | inner | ||
225.4.k.c.124.6 | 12 | 9.7 | even | 3 | inner | ||
405.4.a.h.1.1 | 3 | 45.13 | odd | 12 | |||
405.4.a.j.1.3 | 3 | 45.23 | even | 12 | |||
2025.4.a.q.1.1 | 3 | 45.32 | even | 12 | |||
2025.4.a.s.1.3 | 3 | 45.22 | odd | 12 |