Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4001,2,Mod(1,4001)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4001, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4001.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4001 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4001.a (trivial) |
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: | yes |
Analytic conductor: | \(31.9481458487\) |
Analytic rank: | \(0\) |
Dimension: | \(184\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.14 | ||
Character | \(\chi\) | \(=\) | 4001.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.61059 | −1.84597 | −0.922983 | − | 0.384841i | \(-0.874256\pi\) | ||||
−0.922983 | + | 0.384841i | \(0.874256\pi\) | |||||||
\(3\) | −0.259768 | −0.149977 | −0.0749885 | − | 0.997184i | \(-0.523892\pi\) | ||||
−0.0749885 | + | 0.997184i | \(0.523892\pi\) | |||||||
\(4\) | 4.81518 | 2.40759 | ||||||||
\(5\) | −4.09316 | −1.83052 | −0.915259 | − | 0.402865i | \(-0.868014\pi\) | ||||
−0.915259 | + | 0.402865i | \(0.868014\pi\) | |||||||
\(6\) | 0.678147 | 0.276852 | ||||||||
\(7\) | 2.08780 | 0.789113 | 0.394556 | − | 0.918872i | \(-0.370898\pi\) | ||||
0.394556 | + | 0.918872i | \(0.370898\pi\) | |||||||
\(8\) | −7.34928 | −2.59836 | ||||||||
\(9\) | −2.93252 | −0.977507 | ||||||||
\(10\) | 10.6856 | 3.37907 | ||||||||
\(11\) | −4.54556 | −1.37054 | −0.685269 | − | 0.728290i | \(-0.740315\pi\) | ||||
−0.685269 | + | 0.728290i | \(0.740315\pi\) | |||||||
\(12\) | −1.25083 | −0.361083 | ||||||||
\(13\) | −2.98042 | −0.826619 | −0.413309 | − | 0.910591i | \(-0.635627\pi\) | ||||
−0.413309 | + | 0.910591i | \(0.635627\pi\) | |||||||
\(14\) | −5.45038 | −1.45668 | ||||||||
\(15\) | 1.06327 | 0.274536 | ||||||||
\(16\) | 9.55560 | 2.38890 | ||||||||
\(17\) | 4.39920 | 1.06696 | 0.533482 | − | 0.845812i | \(-0.320883\pi\) | ||||
0.533482 | + | 0.845812i | \(0.320883\pi\) | |||||||
\(18\) | 7.65561 | 1.80444 | ||||||||
\(19\) | −0.751344 | −0.172370 | −0.0861851 | − | 0.996279i | \(-0.527468\pi\) | ||||
−0.0861851 | + | 0.996279i | \(0.527468\pi\) | |||||||
\(20\) | −19.7093 | −4.40714 | ||||||||
\(21\) | −0.542342 | −0.118349 | ||||||||
\(22\) | 11.8666 | 2.52997 | ||||||||
\(23\) | −0.781648 | −0.162985 | −0.0814925 | − | 0.996674i | \(-0.525969\pi\) | ||||
−0.0814925 | + | 0.996674i | \(0.525969\pi\) | |||||||
\(24\) | 1.90911 | 0.389695 | ||||||||
\(25\) | 11.7540 | 2.35080 | ||||||||
\(26\) | 7.78065 | 1.52591 | ||||||||
\(27\) | 1.54108 | 0.296580 | ||||||||
\(28\) | 10.0531 | 1.89986 | ||||||||
\(29\) | −4.78053 | −0.887723 | −0.443861 | − | 0.896095i | \(-0.646392\pi\) | ||||
−0.443861 | + | 0.896095i | \(0.646392\pi\) | |||||||
\(30\) | −2.77577 | −0.506783 | ||||||||
\(31\) | −3.90479 | −0.701322 | −0.350661 | − | 0.936502i | \(-0.614043\pi\) | ||||
−0.350661 | + | 0.936502i | \(0.614043\pi\) | |||||||
\(32\) | −10.2472 | −1.81146 | ||||||||
\(33\) | 1.18079 | 0.205549 | ||||||||
\(34\) | −11.4845 | −1.96958 | ||||||||
\(35\) | −8.54569 | −1.44449 | ||||||||
\(36\) | −14.1206 | −2.35344 | ||||||||
\(37\) | −6.77693 | −1.11412 | −0.557060 | − | 0.830472i | \(-0.688071\pi\) | ||||
−0.557060 | + | 0.830472i | \(0.688071\pi\) | |||||||
\(38\) | 1.96145 | 0.318190 | ||||||||
\(39\) | 0.774216 | 0.123974 | ||||||||
\(40\) | 30.0818 | 4.75635 | ||||||||
\(41\) | −11.6528 | −1.81987 | −0.909934 | − | 0.414753i | \(-0.863868\pi\) | ||||
−0.909934 | + | 0.414753i | \(0.863868\pi\) | |||||||
\(42\) | 1.41583 | 0.218468 | ||||||||
\(43\) | 0.552335 | 0.0842303 | 0.0421152 | − | 0.999113i | \(-0.486590\pi\) | ||||
0.0421152 | + | 0.999113i | \(0.486590\pi\) | |||||||
\(44\) | −21.8877 | −3.29969 | ||||||||
\(45\) | 12.0033 | 1.78934 | ||||||||
\(46\) | 2.04056 | 0.300865 | ||||||||
\(47\) | −1.35892 | −0.198218 | −0.0991091 | − | 0.995077i | \(-0.531599\pi\) | ||||
−0.0991091 | + | 0.995077i | \(0.531599\pi\) | |||||||
\(48\) | −2.48224 | −0.358280 | ||||||||
\(49\) | −2.64111 | −0.377301 | ||||||||
\(50\) | −30.6848 | −4.33949 | ||||||||
\(51\) | −1.14277 | −0.160020 | ||||||||
\(52\) | −14.3512 | −1.99016 | ||||||||
\(53\) | −8.71995 | −1.19778 | −0.598888 | − | 0.800833i | \(-0.704391\pi\) | ||||
−0.598888 | + | 0.800833i | \(0.704391\pi\) | |||||||
\(54\) | −4.02312 | −0.547477 | ||||||||
\(55\) | 18.6057 | 2.50879 | ||||||||
\(56\) | −15.3438 | −2.05040 | ||||||||
\(57\) | 0.195175 | 0.0258516 | ||||||||
\(58\) | 12.4800 | 1.63871 | ||||||||
\(59\) | −11.9100 | −1.55055 | −0.775275 | − | 0.631624i | \(-0.782389\pi\) | ||||
−0.775275 | + | 0.631624i | \(0.782389\pi\) | |||||||
\(60\) | 5.11984 | 0.660969 | ||||||||
\(61\) | −0.470997 | −0.0603050 | −0.0301525 | − | 0.999545i | \(-0.509599\pi\) | ||||
−0.0301525 | + | 0.999545i | \(0.509599\pi\) | |||||||
\(62\) | 10.1938 | 1.29462 | ||||||||
\(63\) | −6.12251 | −0.771363 | ||||||||
\(64\) | 7.64001 | 0.955001 | ||||||||
\(65\) | 12.1993 | 1.51314 | ||||||||
\(66\) | −3.08256 | −0.379436 | ||||||||
\(67\) | −8.34431 | −1.01942 | −0.509710 | − | 0.860346i | \(-0.670247\pi\) | ||||
−0.509710 | + | 0.860346i | \(0.670247\pi\) | |||||||
\(68\) | 21.1830 | 2.56881 | ||||||||
\(69\) | 0.203047 | 0.0244440 | ||||||||
\(70\) | 22.3093 | 2.66647 | ||||||||
\(71\) | 10.0343 | 1.19085 | 0.595423 | − | 0.803412i | \(-0.296984\pi\) | ||||
0.595423 | + | 0.803412i | \(0.296984\pi\) | |||||||
\(72\) | 21.5519 | 2.53992 | ||||||||
\(73\) | 7.49575 | 0.877311 | 0.438656 | − | 0.898655i | \(-0.355455\pi\) | ||||
0.438656 | + | 0.898655i | \(0.355455\pi\) | |||||||
\(74\) | 17.6918 | 2.05663 | ||||||||
\(75\) | −3.05331 | −0.352565 | ||||||||
\(76\) | −3.61786 | −0.414997 | ||||||||
\(77\) | −9.49020 | −1.08151 | ||||||||
\(78\) | −2.02116 | −0.228851 | ||||||||
\(79\) | −10.3980 | −1.16987 | −0.584936 | − | 0.811080i | \(-0.698880\pi\) | ||||
−0.584936 | + | 0.811080i | \(0.698880\pi\) | |||||||
\(80\) | −39.1126 | −4.37293 | ||||||||
\(81\) | 8.39724 | 0.933027 | ||||||||
\(82\) | 30.4208 | 3.35941 | ||||||||
\(83\) | −13.4273 | −1.47384 | −0.736920 | − | 0.675980i | \(-0.763721\pi\) | ||||
−0.736920 | + | 0.675980i | \(0.763721\pi\) | |||||||
\(84\) | −2.61147 | −0.284935 | ||||||||
\(85\) | −18.0067 | −1.95310 | ||||||||
\(86\) | −1.44192 | −0.155486 | ||||||||
\(87\) | 1.24183 | 0.133138 | ||||||||
\(88\) | 33.4066 | 3.56115 | ||||||||
\(89\) | 11.9262 | 1.26418 | 0.632088 | − | 0.774897i | \(-0.282198\pi\) | ||||
0.632088 | + | 0.774897i | \(0.282198\pi\) | |||||||
\(90\) | −31.3357 | −3.30307 | ||||||||
\(91\) | −6.22250 | −0.652295 | ||||||||
\(92\) | −3.76378 | −0.392401 | ||||||||
\(93\) | 1.01434 | 0.105182 | ||||||||
\(94\) | 3.54757 | 0.365904 | ||||||||
\(95\) | 3.07538 | 0.315527 | ||||||||
\(96\) | 2.66189 | 0.271678 | ||||||||
\(97\) | −18.5687 | −1.88537 | −0.942683 | − | 0.333689i | \(-0.891706\pi\) | ||||
−0.942683 | + | 0.333689i | \(0.891706\pi\) | |||||||
\(98\) | 6.89485 | 0.696485 | ||||||||
\(99\) | 13.3299 | 1.33971 | ||||||||
\(100\) | 56.5976 | 5.65976 | ||||||||
\(101\) | −11.1905 | −1.11350 | −0.556749 | − | 0.830681i | \(-0.687951\pi\) | ||||
−0.556749 | + | 0.830681i | \(0.687951\pi\) | |||||||
\(102\) | 2.98331 | 0.295391 | ||||||||
\(103\) | 10.2361 | 1.00859 | 0.504296 | − | 0.863531i | \(-0.331752\pi\) | ||||
0.504296 | + | 0.863531i | \(0.331752\pi\) | |||||||
\(104\) | 21.9039 | 2.14786 | ||||||||
\(105\) | 2.21989 | 0.216639 | ||||||||
\(106\) | 22.7642 | 2.21105 | ||||||||
\(107\) | 3.78086 | 0.365509 | 0.182755 | − | 0.983159i | \(-0.441499\pi\) | ||||
0.182755 | + | 0.983159i | \(0.441499\pi\) | |||||||
\(108\) | 7.42056 | 0.714044 | ||||||||
\(109\) | −9.49382 | −0.909343 | −0.454671 | − | 0.890659i | \(-0.650243\pi\) | ||||
−0.454671 | + | 0.890659i | \(0.650243\pi\) | |||||||
\(110\) | −48.5719 | −4.63115 | ||||||||
\(111\) | 1.76043 | 0.167092 | ||||||||
\(112\) | 19.9501 | 1.88511 | ||||||||
\(113\) | −5.83525 | −0.548934 | −0.274467 | − | 0.961597i | \(-0.588501\pi\) | ||||
−0.274467 | + | 0.961597i | \(0.588501\pi\) | |||||||
\(114\) | −0.509522 | −0.0477211 | ||||||||
\(115\) | 3.19942 | 0.298347 | ||||||||
\(116\) | −23.0191 | −2.13727 | ||||||||
\(117\) | 8.74013 | 0.808026 | ||||||||
\(118\) | 31.0921 | 2.86226 | ||||||||
\(119\) | 9.18464 | 0.841955 | ||||||||
\(120\) | −7.81428 | −0.713343 | ||||||||
\(121\) | 9.66210 | 0.878373 | ||||||||
\(122\) | 1.22958 | 0.111321 | ||||||||
\(123\) | 3.02703 | 0.272938 | ||||||||
\(124\) | −18.8023 | −1.68850 | ||||||||
\(125\) | −27.6452 | −2.47266 | ||||||||
\(126\) | 15.9834 | 1.42391 | ||||||||
\(127\) | −8.99415 | −0.798102 | −0.399051 | − | 0.916929i | \(-0.630660\pi\) | ||||
−0.399051 | + | 0.916929i | \(0.630660\pi\) | |||||||
\(128\) | 0.549442 | 0.0485643 | ||||||||
\(129\) | −0.143479 | −0.0126326 | ||||||||
\(130\) | −31.8475 | −2.79321 | ||||||||
\(131\) | 7.48803 | 0.654233 | 0.327116 | − | 0.944984i | \(-0.393923\pi\) | ||||
0.327116 | + | 0.944984i | \(0.393923\pi\) | |||||||
\(132\) | 5.68571 | 0.494878 | ||||||||
\(133\) | −1.56865 | −0.136020 | ||||||||
\(134\) | 21.7836 | 1.88181 | ||||||||
\(135\) | −6.30788 | −0.542896 | ||||||||
\(136\) | −32.3310 | −2.77236 | ||||||||
\(137\) | 1.45083 | 0.123953 | 0.0619764 | − | 0.998078i | \(-0.480260\pi\) | ||||
0.0619764 | + | 0.998078i | \(0.480260\pi\) | |||||||
\(138\) | −0.530072 | −0.0451228 | ||||||||
\(139\) | −12.7844 | −1.08436 | −0.542179 | − | 0.840263i | \(-0.682401\pi\) | ||||
−0.542179 | + | 0.840263i | \(0.682401\pi\) | |||||||
\(140\) | −41.1490 | −3.47773 | ||||||||
\(141\) | 0.353002 | 0.0297282 | ||||||||
\(142\) | −26.1953 | −2.19826 | ||||||||
\(143\) | 13.5477 | 1.13291 | ||||||||
\(144\) | −28.0220 | −2.33517 | ||||||||
\(145\) | 19.5675 | 1.62499 | ||||||||
\(146\) | −19.5683 | −1.61949 | ||||||||
\(147\) | 0.686074 | 0.0565865 | ||||||||
\(148\) | −32.6321 | −2.68235 | ||||||||
\(149\) | −0.904473 | −0.0740973 | −0.0370487 | − | 0.999313i | \(-0.511796\pi\) | ||||
−0.0370487 | + | 0.999313i | \(0.511796\pi\) | |||||||
\(150\) | 7.97093 | 0.650824 | ||||||||
\(151\) | 16.4418 | 1.33801 | 0.669007 | − | 0.743256i | \(-0.266720\pi\) | ||||
0.669007 | + | 0.743256i | \(0.266720\pi\) | |||||||
\(152\) | 5.52184 | 0.447880 | ||||||||
\(153\) | −12.9008 | −1.04296 | ||||||||
\(154\) | 24.7750 | 1.99643 | ||||||||
\(155\) | 15.9830 | 1.28378 | ||||||||
\(156\) | 3.72799 | 0.298478 | ||||||||
\(157\) | −23.7994 | −1.89940 | −0.949701 | − | 0.313159i | \(-0.898613\pi\) | ||||
−0.949701 | + | 0.313159i | \(0.898613\pi\) | |||||||
\(158\) | 27.1450 | 2.15954 | ||||||||
\(159\) | 2.26516 | 0.179639 | ||||||||
\(160\) | 41.9434 | 3.31592 | ||||||||
\(161\) | −1.63192 | −0.128614 | ||||||||
\(162\) | −21.9218 | −1.72234 | ||||||||
\(163\) | −19.3108 | −1.51254 | −0.756271 | − | 0.654259i | \(-0.772981\pi\) | ||||
−0.756271 | + | 0.654259i | \(0.772981\pi\) | |||||||
\(164\) | −56.1105 | −4.38150 | ||||||||
\(165\) | −4.83316 | −0.376261 | ||||||||
\(166\) | 35.0532 | 2.72066 | ||||||||
\(167\) | 4.19358 | 0.324509 | 0.162254 | − | 0.986749i | \(-0.448123\pi\) | ||||
0.162254 | + | 0.986749i | \(0.448123\pi\) | |||||||
\(168\) | 3.98582 | 0.307513 | ||||||||
\(169\) | −4.11712 | −0.316701 | ||||||||
\(170\) | 47.0080 | 3.60535 | ||||||||
\(171\) | 2.20333 | 0.168493 | ||||||||
\(172\) | 2.65959 | 0.202792 | ||||||||
\(173\) | 11.4519 | 0.870673 | 0.435336 | − | 0.900268i | \(-0.356629\pi\) | ||||
0.435336 | + | 0.900268i | \(0.356629\pi\) | |||||||
\(174\) | −3.24190 | −0.245768 | ||||||||
\(175\) | 24.5399 | 1.85504 | ||||||||
\(176\) | −43.4355 | −3.27408 | ||||||||
\(177\) | 3.09383 | 0.232547 | ||||||||
\(178\) | −31.1344 | −2.33362 | ||||||||
\(179\) | 4.80326 | 0.359013 | 0.179506 | − | 0.983757i | \(-0.442550\pi\) | ||||
0.179506 | + | 0.983757i | \(0.442550\pi\) | |||||||
\(180\) | 57.7980 | 4.30801 | ||||||||
\(181\) | 20.4628 | 1.52098 | 0.760492 | − | 0.649347i | \(-0.224958\pi\) | ||||
0.760492 | + | 0.649347i | \(0.224958\pi\) | |||||||
\(182\) | 16.2444 | 1.20412 | ||||||||
\(183\) | 0.122350 | 0.00904435 | ||||||||
\(184\) | 5.74455 | 0.423494 | ||||||||
\(185\) | 27.7391 | 2.03942 | ||||||||
\(186\) | −2.64802 | −0.194163 | ||||||||
\(187\) | −19.9968 | −1.46231 | ||||||||
\(188\) | −6.54342 | −0.477228 | ||||||||
\(189\) | 3.21745 | 0.234035 | ||||||||
\(190\) | −8.02855 | −0.582452 | ||||||||
\(191\) | −6.12788 | −0.443398 | −0.221699 | − | 0.975115i | \(-0.571160\pi\) | ||||
−0.221699 | + | 0.975115i | \(0.571160\pi\) | |||||||
\(192\) | −1.98463 | −0.143228 | ||||||||
\(193\) | −1.47115 | −0.105896 | −0.0529480 | − | 0.998597i | \(-0.516862\pi\) | ||||
−0.0529480 | + | 0.998597i | \(0.516862\pi\) | |||||||
\(194\) | 48.4753 | 3.48032 | ||||||||
\(195\) | −3.16899 | −0.226936 | ||||||||
\(196\) | −12.7174 | −0.908386 | ||||||||
\(197\) | −0.514119 | −0.0366295 | −0.0183147 | − | 0.999832i | \(-0.505830\pi\) | ||||
−0.0183147 | + | 0.999832i | \(0.505830\pi\) | |||||||
\(198\) | −34.7990 | −2.47306 | ||||||||
\(199\) | 20.6196 | 1.46169 | 0.730844 | − | 0.682545i | \(-0.239127\pi\) | ||||
0.730844 | + | 0.682545i | \(0.239127\pi\) | |||||||
\(200\) | −86.3834 | −6.10823 | ||||||||
\(201\) | 2.16758 | 0.152889 | ||||||||
\(202\) | 29.2138 | 2.05548 | ||||||||
\(203\) | −9.98078 | −0.700513 | ||||||||
\(204\) | −5.50265 | −0.385262 | ||||||||
\(205\) | 47.6970 | 3.33130 | ||||||||
\(206\) | −26.7223 | −1.86183 | ||||||||
\(207\) | 2.29220 | 0.159319 | ||||||||
\(208\) | −28.4797 | −1.97471 | ||||||||
\(209\) | 3.41528 | 0.236240 | ||||||||
\(210\) | −5.79523 | −0.399909 | ||||||||
\(211\) | −0.169116 | −0.0116424 | −0.00582122 | − | 0.999983i | \(-0.501853\pi\) | ||||
−0.00582122 | + | 0.999983i | \(0.501853\pi\) | |||||||
\(212\) | −41.9881 | −2.88376 | ||||||||
\(213\) | −2.60657 | −0.178600 | ||||||||
\(214\) | −9.87027 | −0.674718 | ||||||||
\(215\) | −2.26080 | −0.154185 | ||||||||
\(216\) | −11.3258 | −0.770624 | ||||||||
\(217\) | −8.15242 | −0.553422 | ||||||||
\(218\) | 24.7845 | 1.67862 | ||||||||
\(219\) | −1.94715 | −0.131576 | ||||||||
\(220\) | 89.5899 | 6.04015 | ||||||||
\(221\) | −13.1115 | −0.881972 | ||||||||
\(222\) | −4.59575 | −0.308447 | ||||||||
\(223\) | −3.78724 | −0.253613 | −0.126806 | − | 0.991928i | \(-0.540473\pi\) | ||||
−0.126806 | + | 0.991928i | \(0.540473\pi\) | |||||||
\(224\) | −21.3940 | −1.42945 | ||||||||
\(225\) | −34.4688 | −2.29792 | ||||||||
\(226\) | 15.2334 | 1.01331 | ||||||||
\(227\) | −14.0626 | −0.933368 | −0.466684 | − | 0.884424i | \(-0.654552\pi\) | ||||
−0.466684 | + | 0.884424i | \(0.654552\pi\) | |||||||
\(228\) | 0.939803 | 0.0622400 | ||||||||
\(229\) | −6.47850 | −0.428111 | −0.214056 | − | 0.976821i | \(-0.568667\pi\) | ||||
−0.214056 | + | 0.976821i | \(0.568667\pi\) | |||||||
\(230\) | −8.35236 | −0.550738 | ||||||||
\(231\) | 2.46525 | 0.162201 | ||||||||
\(232\) | 35.1335 | 2.30663 | ||||||||
\(233\) | 8.11537 | 0.531655 | 0.265828 | − | 0.964021i | \(-0.414355\pi\) | ||||
0.265828 | + | 0.964021i | \(0.414355\pi\) | |||||||
\(234\) | −22.8169 | −1.49159 | ||||||||
\(235\) | 5.56227 | 0.362842 | ||||||||
\(236\) | −57.3488 | −3.73309 | ||||||||
\(237\) | 2.70108 | 0.175454 | ||||||||
\(238\) | −23.9773 | −1.55422 | ||||||||
\(239\) | −24.2326 | −1.56748 | −0.783739 | − | 0.621091i | \(-0.786690\pi\) | ||||
−0.783739 | + | 0.621091i | \(0.786690\pi\) | |||||||
\(240\) | 10.1602 | 0.655838 | ||||||||
\(241\) | 12.3097 | 0.792937 | 0.396469 | − | 0.918048i | \(-0.370236\pi\) | ||||
0.396469 | + | 0.918048i | \(0.370236\pi\) | |||||||
\(242\) | −25.2238 | −1.62145 | ||||||||
\(243\) | −6.80456 | −0.436513 | ||||||||
\(244\) | −2.26793 | −0.145190 | ||||||||
\(245\) | 10.8105 | 0.690657 | ||||||||
\(246\) | −7.90234 | −0.503835 | ||||||||
\(247\) | 2.23932 | 0.142484 | ||||||||
\(248\) | 28.6974 | 1.82229 | ||||||||
\(249\) | 3.48798 | 0.221042 | ||||||||
\(250\) | 72.1703 | 4.56445 | ||||||||
\(251\) | −15.5663 | −0.982537 | −0.491269 | − | 0.871008i | \(-0.663467\pi\) | ||||
−0.491269 | + | 0.871008i | \(0.663467\pi\) | |||||||
\(252\) | −29.4810 | −1.85713 | ||||||||
\(253\) | 3.55303 | 0.223377 | ||||||||
\(254\) | 23.4800 | 1.47327 | ||||||||
\(255\) | 4.67755 | 0.292919 | ||||||||
\(256\) | −16.7144 | −1.04465 | ||||||||
\(257\) | 12.3264 | 0.768901 | 0.384450 | − | 0.923146i | \(-0.374391\pi\) | ||||
0.384450 | + | 0.923146i | \(0.374391\pi\) | |||||||
\(258\) | 0.374564 | 0.0233194 | ||||||||
\(259\) | −14.1488 | −0.879167 | ||||||||
\(260\) | 58.7420 | 3.64302 | ||||||||
\(261\) | 14.0190 | 0.867755 | ||||||||
\(262\) | −19.5482 | −1.20769 | ||||||||
\(263\) | −5.57478 | −0.343756 | −0.171878 | − | 0.985118i | \(-0.554983\pi\) | ||||
−0.171878 | + | 0.985118i | \(0.554983\pi\) | |||||||
\(264\) | −8.67795 | −0.534091 | ||||||||
\(265\) | 35.6922 | 2.19255 | ||||||||
\(266\) | 4.09511 | 0.251087 | ||||||||
\(267\) | −3.09804 | −0.189597 | ||||||||
\(268\) | −40.1794 | −2.45434 | ||||||||
\(269\) | 24.8679 | 1.51622 | 0.758111 | − | 0.652126i | \(-0.226123\pi\) | ||||
0.758111 | + | 0.652126i | \(0.226123\pi\) | |||||||
\(270\) | 16.4673 | 1.00217 | ||||||||
\(271\) | −14.2423 | −0.865161 | −0.432580 | − | 0.901595i | \(-0.642397\pi\) | ||||
−0.432580 | + | 0.901595i | \(0.642397\pi\) | |||||||
\(272\) | 42.0370 | 2.54887 | ||||||||
\(273\) | 1.61640 | 0.0978293 | ||||||||
\(274\) | −3.78752 | −0.228813 | ||||||||
\(275\) | −53.4285 | −3.22186 | ||||||||
\(276\) | 0.977708 | 0.0588511 | ||||||||
\(277\) | 32.3841 | 1.94577 | 0.972887 | − | 0.231282i | \(-0.0742921\pi\) | ||||
0.972887 | + | 0.231282i | \(0.0742921\pi\) | |||||||
\(278\) | 33.3748 | 2.00169 | ||||||||
\(279\) | 11.4509 | 0.685547 | ||||||||
\(280\) | 62.8047 | 3.75330 | ||||||||
\(281\) | −5.35320 | −0.319345 | −0.159673 | − | 0.987170i | \(-0.551044\pi\) | ||||
−0.159673 | + | 0.987170i | \(0.551044\pi\) | |||||||
\(282\) | −0.921545 | −0.0548772 | ||||||||
\(283\) | −4.26767 | −0.253687 | −0.126843 | − | 0.991923i | \(-0.540485\pi\) | ||||
−0.126843 | + | 0.991923i | \(0.540485\pi\) | |||||||
\(284\) | 48.3167 | 2.86707 | ||||||||
\(285\) | −0.798883 | −0.0473218 | ||||||||
\(286\) | −35.3674 | −2.09132 | ||||||||
\(287\) | −24.3288 | −1.43608 | ||||||||
\(288\) | 30.0501 | 1.77072 | ||||||||
\(289\) | 2.35299 | 0.138411 | ||||||||
\(290\) | −51.0827 | −2.99968 | ||||||||
\(291\) | 4.82355 | 0.282761 | ||||||||
\(292\) | 36.0934 | 2.11221 | ||||||||
\(293\) | 7.60370 | 0.444213 | 0.222107 | − | 0.975022i | \(-0.428707\pi\) | ||||
0.222107 | + | 0.975022i | \(0.428707\pi\) | |||||||
\(294\) | −1.79106 | −0.104457 | ||||||||
\(295\) | 48.7496 | 2.83831 | ||||||||
\(296\) | 49.8056 | 2.89489 | ||||||||
\(297\) | −7.00506 | −0.406475 | ||||||||
\(298\) | 2.36121 | 0.136781 | ||||||||
\(299\) | 2.32964 | 0.134726 | ||||||||
\(300\) | −14.7022 | −0.848833 | ||||||||
\(301\) | 1.15316 | 0.0664672 | ||||||||
\(302\) | −42.9228 | −2.46993 | ||||||||
\(303\) | 2.90693 | 0.166999 | ||||||||
\(304\) | −7.17955 | −0.411775 | ||||||||
\(305\) | 1.92787 | 0.110389 | ||||||||
\(306\) | 33.6786 | 1.92528 | ||||||||
\(307\) | 6.82587 | 0.389573 | 0.194786 | − | 0.980846i | \(-0.437599\pi\) | ||||
0.194786 | + | 0.980846i | \(0.437599\pi\) | |||||||
\(308\) | −45.6970 | −2.60383 | ||||||||
\(309\) | −2.65901 | −0.151266 | ||||||||
\(310\) | −41.7250 | −2.36982 | ||||||||
\(311\) | −22.8574 | −1.29612 | −0.648061 | − | 0.761588i | \(-0.724420\pi\) | ||||
−0.648061 | + | 0.761588i | \(0.724420\pi\) | |||||||
\(312\) | −5.68993 | −0.322129 | ||||||||
\(313\) | −1.85118 | −0.104635 | −0.0523175 | − | 0.998631i | \(-0.516661\pi\) | ||||
−0.0523175 | + | 0.998631i | \(0.516661\pi\) | |||||||
\(314\) | 62.1306 | 3.50623 | ||||||||
\(315\) | 25.0604 | 1.41199 | ||||||||
\(316\) | −50.0685 | −2.81657 | ||||||||
\(317\) | −20.6041 | −1.15724 | −0.578621 | − | 0.815597i | \(-0.696409\pi\) | ||||
−0.578621 | + | 0.815597i | \(0.696409\pi\) | |||||||
\(318\) | −5.91340 | −0.331607 | ||||||||
\(319\) | 21.7302 | 1.21666 | ||||||||
\(320\) | −31.2718 | −1.74815 | ||||||||
\(321\) | −0.982145 | −0.0548180 | ||||||||
\(322\) | 4.26028 | 0.237416 | ||||||||
\(323\) | −3.30532 | −0.183913 | ||||||||
\(324\) | 40.4342 | 2.24635 | ||||||||
\(325\) | −35.0318 | −1.94321 | ||||||||
\(326\) | 50.4127 | 2.79210 | ||||||||
\(327\) | 2.46619 | 0.136380 | ||||||||
\(328\) | 85.6400 | 4.72868 | ||||||||
\(329\) | −2.83714 | −0.156417 | ||||||||
\(330\) | 12.6174 | 0.694565 | ||||||||
\(331\) | −6.35867 | −0.349504 | −0.174752 | − | 0.984612i | \(-0.555912\pi\) | ||||
−0.174752 | + | 0.984612i | \(0.555912\pi\) | |||||||
\(332\) | −64.6550 | −3.54840 | ||||||||
\(333\) | 19.8735 | 1.08906 | ||||||||
\(334\) | −10.9477 | −0.599032 | ||||||||
\(335\) | 34.1546 | 1.86607 | ||||||||
\(336\) | −5.18240 | −0.282723 | ||||||||
\(337\) | 7.40140 | 0.403180 | 0.201590 | − | 0.979470i | \(-0.435389\pi\) | ||||
0.201590 | + | 0.979470i | \(0.435389\pi\) | |||||||
\(338\) | 10.7481 | 0.584620 | ||||||||
\(339\) | 1.51581 | 0.0823274 | ||||||||
\(340\) | −86.7053 | −4.70226 | ||||||||
\(341\) | 17.7495 | 0.961188 | ||||||||
\(342\) | −5.75200 | −0.311033 | ||||||||
\(343\) | −20.1287 | −1.08685 | ||||||||
\(344\) | −4.05927 | −0.218861 | ||||||||
\(345\) | −0.831105 | −0.0447452 | ||||||||
\(346\) | −29.8962 | −1.60723 | ||||||||
\(347\) | 2.97440 | 0.159674 | 0.0798371 | − | 0.996808i | \(-0.474560\pi\) | ||||
0.0798371 | + | 0.996808i | \(0.474560\pi\) | |||||||
\(348\) | 5.97963 | 0.320542 | ||||||||
\(349\) | −0.315419 | −0.0168840 | −0.00844199 | − | 0.999964i | \(-0.502687\pi\) | ||||
−0.00844199 | + | 0.999964i | \(0.502687\pi\) | |||||||
\(350\) | −64.0637 | −3.42435 | ||||||||
\(351\) | −4.59305 | −0.245159 | ||||||||
\(352\) | 46.5792 | 2.48268 | ||||||||
\(353\) | −23.4323 | −1.24717 | −0.623587 | − | 0.781754i | \(-0.714325\pi\) | ||||
−0.623587 | + | 0.781754i | \(0.714325\pi\) | |||||||
\(354\) | −8.07673 | −0.429273 | ||||||||
\(355\) | −41.0718 | −2.17987 | ||||||||
\(356\) | 57.4268 | 3.04362 | ||||||||
\(357\) | −2.38587 | −0.126274 | ||||||||
\(358\) | −12.5394 | −0.662725 | ||||||||
\(359\) | 20.2783 | 1.07025 | 0.535124 | − | 0.844774i | \(-0.320265\pi\) | ||||
0.535124 | + | 0.844774i | \(0.320265\pi\) | |||||||
\(360\) | −88.2155 | −4.64937 | ||||||||
\(361\) | −18.4355 | −0.970289 | ||||||||
\(362\) | −53.4199 | −2.80769 | ||||||||
\(363\) | −2.50990 | −0.131736 | ||||||||
\(364\) | −29.9625 | −1.57046 | ||||||||
\(365\) | −30.6813 | −1.60593 | ||||||||
\(366\) | −0.319405 | −0.0166956 | ||||||||
\(367\) | −36.3136 | −1.89555 | −0.947776 | − | 0.318936i | \(-0.896675\pi\) | ||||
−0.947776 | + | 0.318936i | \(0.896675\pi\) | |||||||
\(368\) | −7.46912 | −0.389355 | ||||||||
\(369\) | 34.1722 | 1.77893 | ||||||||
\(370\) | −72.4154 | −3.76470 | ||||||||
\(371\) | −18.2055 | −0.945181 | ||||||||
\(372\) | 4.88423 | 0.253235 | ||||||||
\(373\) | 3.70281 | 0.191724 | 0.0958620 | − | 0.995395i | \(-0.469439\pi\) | ||||
0.0958620 | + | 0.995395i | \(0.469439\pi\) | |||||||
\(374\) | 52.2035 | 2.69938 | ||||||||
\(375\) | 7.18133 | 0.370842 | ||||||||
\(376\) | 9.98705 | 0.515043 | ||||||||
\(377\) | 14.2480 | 0.733808 | ||||||||
\(378\) | −8.39945 | −0.432021 | ||||||||
\(379\) | 27.7795 | 1.42694 | 0.713468 | − | 0.700687i | \(-0.247123\pi\) | ||||
0.713468 | + | 0.700687i | \(0.247123\pi\) | |||||||
\(380\) | 14.8085 | 0.759659 | ||||||||
\(381\) | 2.33639 | 0.119697 | ||||||||
\(382\) | 15.9974 | 0.818497 | ||||||||
\(383\) | 31.5241 | 1.61081 | 0.805404 | − | 0.592726i | \(-0.201948\pi\) | ||||
0.805404 | + | 0.592726i | \(0.201948\pi\) | |||||||
\(384\) | −0.142727 | −0.00728352 | ||||||||
\(385\) | 38.8449 | 1.97972 | ||||||||
\(386\) | 3.84058 | 0.195480 | ||||||||
\(387\) | −1.61973 | −0.0823357 | ||||||||
\(388\) | −89.4117 | −4.53919 | ||||||||
\(389\) | 23.2436 | 1.17850 | 0.589250 | − | 0.807951i | \(-0.299423\pi\) | ||||
0.589250 | + | 0.807951i | \(0.299423\pi\) | |||||||
\(390\) | 8.27294 | 0.418917 | ||||||||
\(391\) | −3.43863 | −0.173899 | ||||||||
\(392\) | 19.4102 | 0.980365 | ||||||||
\(393\) | −1.94515 | −0.0981198 | ||||||||
\(394\) | 1.34215 | 0.0676168 | ||||||||
\(395\) | 42.5609 | 2.14147 | ||||||||
\(396\) | 64.1861 | 3.22547 | ||||||||
\(397\) | −33.6923 | −1.69097 | −0.845484 | − | 0.534001i | \(-0.820688\pi\) | ||||
−0.845484 | + | 0.534001i | \(0.820688\pi\) | |||||||
\(398\) | −53.8294 | −2.69823 | ||||||||
\(399\) | 0.407486 | 0.0203998 | ||||||||
\(400\) | 112.316 | 5.61582 | ||||||||
\(401\) | −19.3137 | −0.964480 | −0.482240 | − | 0.876039i | \(-0.660177\pi\) | ||||
−0.482240 | + | 0.876039i | \(0.660177\pi\) | |||||||
\(402\) | −5.65867 | −0.282229 | ||||||||
\(403\) | 11.6379 | 0.579726 | ||||||||
\(404\) | −53.8843 | −2.68085 | ||||||||
\(405\) | −34.3713 | −1.70792 | ||||||||
\(406\) | 26.0557 | 1.29312 | ||||||||
\(407\) | 30.8049 | 1.52694 | ||||||||
\(408\) | 8.39854 | 0.415790 | ||||||||
\(409\) | 34.4975 | 1.70579 | 0.852896 | − | 0.522080i | \(-0.174844\pi\) | ||||
0.852896 | + | 0.522080i | \(0.174844\pi\) | |||||||
\(410\) | −124.517 | −6.14947 | ||||||||
\(411\) | −0.376879 | −0.0185901 | ||||||||
\(412\) | 49.2886 | 2.42828 | ||||||||
\(413\) | −24.8656 | −1.22356 | ||||||||
\(414\) | −5.98400 | −0.294097 | ||||||||
\(415\) | 54.9602 | 2.69789 | ||||||||
\(416\) | 30.5409 | 1.49739 | ||||||||
\(417\) | 3.32097 | 0.162629 | ||||||||
\(418\) | −8.91590 | −0.436091 | ||||||||
\(419\) | 15.4010 | 0.752389 | 0.376194 | − | 0.926541i | \(-0.377232\pi\) | ||||
0.376194 | + | 0.926541i | \(0.377232\pi\) | |||||||
\(420\) | 10.6892 | 0.521579 | ||||||||
\(421\) | 40.2951 | 1.96386 | 0.981931 | − | 0.189241i | \(-0.0606027\pi\) | ||||
0.981931 | + | 0.189241i | \(0.0606027\pi\) | |||||||
\(422\) | 0.441493 | 0.0214916 | ||||||||
\(423\) | 3.98505 | 0.193760 | ||||||||
\(424\) | 64.0853 | 3.11226 | ||||||||
\(425\) | 51.7082 | 2.50822 | ||||||||
\(426\) | 6.80470 | 0.329689 | ||||||||
\(427\) | −0.983345 | −0.0475874 | ||||||||
\(428\) | 18.2055 | 0.879997 | ||||||||
\(429\) | −3.51924 | −0.169911 | ||||||||
\(430\) | 5.90202 | 0.284621 | ||||||||
\(431\) | 21.3448 | 1.02814 | 0.514072 | − | 0.857747i | \(-0.328136\pi\) | ||||
0.514072 | + | 0.857747i | \(0.328136\pi\) | |||||||
\(432\) | 14.7259 | 0.708501 | ||||||||
\(433\) | 19.7426 | 0.948770 | 0.474385 | − | 0.880317i | \(-0.342670\pi\) | ||||
0.474385 | + | 0.880317i | \(0.342670\pi\) | |||||||
\(434\) | 21.2826 | 1.02160 | ||||||||
\(435\) | −5.08301 | −0.243711 | ||||||||
\(436\) | −45.7144 | −2.18932 | ||||||||
\(437\) | 0.587287 | 0.0280938 | ||||||||
\(438\) | 5.08322 | 0.242886 | ||||||||
\(439\) | 20.9962 | 1.00209 | 0.501047 | − | 0.865420i | \(-0.332948\pi\) | ||||
0.501047 | + | 0.865420i | \(0.332948\pi\) | |||||||
\(440\) | −136.739 | −6.51876 | ||||||||
\(441\) | 7.74510 | 0.368814 | ||||||||
\(442\) | 34.2286 | 1.62809 | ||||||||
\(443\) | 37.6209 | 1.78742 | 0.893711 | − | 0.448642i | \(-0.148092\pi\) | ||||
0.893711 | + | 0.448642i | \(0.148092\pi\) | |||||||
\(444\) | 8.47677 | 0.402290 | ||||||||
\(445\) | −48.8159 | −2.31410 | ||||||||
\(446\) | 9.88694 | 0.468160 | ||||||||
\(447\) | 0.234953 | 0.0111129 | ||||||||
\(448\) | 15.9508 | 0.753604 | ||||||||
\(449\) | 17.4333 | 0.822727 | 0.411363 | − | 0.911471i | \(-0.365053\pi\) | ||||
0.411363 | + | 0.911471i | \(0.365053\pi\) | |||||||
\(450\) | 89.9840 | 4.24188 | ||||||||
\(451\) | 52.9687 | 2.49420 | ||||||||
\(452\) | −28.0978 | −1.32161 | ||||||||
\(453\) | −4.27104 | −0.200671 | ||||||||
\(454\) | 36.7117 | 1.72297 | ||||||||
\(455\) | 25.4697 | 1.19404 | ||||||||
\(456\) | −1.43440 | −0.0671717 | ||||||||
\(457\) | 5.70445 | 0.266843 | 0.133421 | − | 0.991059i | \(-0.457404\pi\) | ||||
0.133421 | + | 0.991059i | \(0.457404\pi\) | |||||||
\(458\) | 16.9127 | 0.790278 | ||||||||
\(459\) | 6.77951 | 0.316440 | ||||||||
\(460\) | 15.4058 | 0.718297 | ||||||||
\(461\) | 41.5258 | 1.93405 | 0.967025 | − | 0.254682i | \(-0.0819709\pi\) | ||||
0.967025 | + | 0.254682i | \(0.0819709\pi\) | |||||||
\(462\) | −6.43575 | −0.299418 | ||||||||
\(463\) | −11.1028 | −0.515989 | −0.257994 | − | 0.966146i | \(-0.583062\pi\) | ||||
−0.257994 | + | 0.966146i | \(0.583062\pi\) | |||||||
\(464\) | −45.6809 | −2.12068 | ||||||||
\(465\) | −4.15186 | −0.192538 | ||||||||
\(466\) | −21.1859 | −0.981418 | ||||||||
\(467\) | −36.6735 | −1.69705 | −0.848524 | − | 0.529157i | \(-0.822508\pi\) | ||||
−0.848524 | + | 0.529157i | \(0.822508\pi\) | |||||||
\(468\) | 42.0853 | 1.94539 | ||||||||
\(469\) | −17.4212 | −0.804437 | ||||||||
\(470\) | −14.5208 | −0.669794 | ||||||||
\(471\) | 6.18232 | 0.284866 | ||||||||
\(472\) | 87.5299 | 4.02889 | ||||||||
\(473\) | −2.51067 | −0.115441 | ||||||||
\(474\) | −7.05140 | −0.323882 | ||||||||
\(475\) | −8.83130 | −0.405208 | ||||||||
\(476\) | 44.2257 | 2.02708 | ||||||||
\(477\) | 25.5714 | 1.17083 | ||||||||
\(478\) | 63.2614 | 2.89351 | ||||||||
\(479\) | −22.7530 | −1.03961 | −0.519807 | − | 0.854284i | \(-0.673996\pi\) | ||||
−0.519807 | + | 0.854284i | \(0.673996\pi\) | |||||||
\(480\) | −10.8955 | −0.497311 | ||||||||
\(481\) | 20.1981 | 0.920953 | ||||||||
\(482\) | −32.1356 | −1.46374 | ||||||||
\(483\) | 0.423921 | 0.0192891 | ||||||||
\(484\) | 46.5248 | 2.11476 | ||||||||
\(485\) | 76.0047 | 3.45120 | ||||||||
\(486\) | 17.7639 | 0.805788 | ||||||||
\(487\) | −25.5086 | −1.15590 | −0.577952 | − | 0.816071i | \(-0.696148\pi\) | ||||
−0.577952 | + | 0.816071i | \(0.696148\pi\) | |||||||
\(488\) | 3.46149 | 0.156694 | ||||||||
\(489\) | 5.01633 | 0.226846 | ||||||||
\(490\) | −28.2217 | −1.27493 | ||||||||
\(491\) | −12.1885 | −0.550059 | −0.275030 | − | 0.961436i | \(-0.588688\pi\) | ||||
−0.275030 | + | 0.961436i | \(0.588688\pi\) | |||||||
\(492\) | 14.5757 | 0.657123 | ||||||||
\(493\) | −21.0305 | −0.947168 | ||||||||
\(494\) | −5.84594 | −0.263021 | ||||||||
\(495\) | −54.5616 | −2.45236 | ||||||||
\(496\) | −37.3127 | −1.67539 | ||||||||
\(497\) | 20.9495 | 0.939712 | ||||||||
\(498\) | −9.10570 | −0.408036 | ||||||||
\(499\) | 35.7400 | 1.59994 | 0.799970 | − | 0.600039i | \(-0.204848\pi\) | ||||
0.799970 | + | 0.600039i | \(0.204848\pi\) | |||||||
\(500\) | −133.117 | −5.95315 | ||||||||
\(501\) | −1.08936 | −0.0486688 | ||||||||
\(502\) | 40.6373 | 1.81373 | ||||||||
\(503\) | −5.33213 | −0.237748 | −0.118874 | − | 0.992909i | \(-0.537928\pi\) | ||||
−0.118874 | + | 0.992909i | \(0.537928\pi\) | |||||||
\(504\) | 44.9960 | 2.00428 | ||||||||
\(505\) | 45.8046 | 2.03828 | ||||||||
\(506\) | −9.27550 | −0.412346 | ||||||||
\(507\) | 1.06949 | 0.0474979 | ||||||||
\(508\) | −43.3085 | −1.92150 | ||||||||
\(509\) | 8.18131 | 0.362630 | 0.181315 | − | 0.983425i | \(-0.441965\pi\) | ||||
0.181315 | + | 0.983425i | \(0.441965\pi\) | |||||||
\(510\) | −12.2112 | −0.540719 | ||||||||
\(511\) | 15.6496 | 0.692297 | ||||||||
\(512\) | 42.5355 | 1.87982 | ||||||||
\(513\) | −1.15788 | −0.0511216 | ||||||||
\(514\) | −32.1792 | −1.41936 | ||||||||
\(515\) | −41.8980 | −1.84625 | ||||||||
\(516\) | −0.690876 | −0.0304141 | ||||||||
\(517\) | 6.17703 | 0.271666 | ||||||||
\(518\) | 36.9368 | 1.62291 | ||||||||
\(519\) | −2.97484 | −0.130581 | ||||||||
\(520\) | −89.6563 | −3.93169 | ||||||||
\(521\) | −10.1797 | −0.445979 | −0.222990 | − | 0.974821i | \(-0.571582\pi\) | ||||
−0.222990 | + | 0.974821i | \(0.571582\pi\) | |||||||
\(522\) | −36.5979 | −1.60185 | ||||||||
\(523\) | 4.14289 | 0.181156 | 0.0905780 | − | 0.995889i | \(-0.471129\pi\) | ||||
0.0905780 | + | 0.995889i | \(0.471129\pi\) | |||||||
\(524\) | 36.0562 | 1.57512 | ||||||||
\(525\) | −6.37468 | −0.278214 | ||||||||
\(526\) | 14.5535 | 0.634562 | ||||||||
\(527\) | −17.1780 | −0.748285 | ||||||||
\(528\) | 11.2831 | 0.491036 | ||||||||
\(529\) | −22.3890 | −0.973436 | ||||||||
\(530\) | −93.1776 | −4.04738 | ||||||||
\(531\) | 34.9263 | 1.51567 | ||||||||
\(532\) | −7.55335 | −0.327479 | ||||||||
\(533\) | 34.7303 | 1.50434 | ||||||||
\(534\) | 8.08772 | 0.349990 | ||||||||
\(535\) | −15.4757 | −0.669072 | ||||||||
\(536\) | 61.3247 | 2.64882 | ||||||||
\(537\) | −1.24773 | −0.0538436 | ||||||||
\(538\) | −64.9198 | −2.79889 | ||||||||
\(539\) | 12.0053 | 0.517105 | ||||||||
\(540\) | −30.3736 | −1.30707 | ||||||||
\(541\) | 43.9279 | 1.88861 | 0.944303 | − | 0.329077i | \(-0.106738\pi\) | ||||
0.944303 | + | 0.329077i | \(0.106738\pi\) | |||||||
\(542\) | 37.1809 | 1.59706 | ||||||||
\(543\) | −5.31556 | −0.228113 | ||||||||
\(544\) | −45.0795 | −1.93277 | ||||||||
\(545\) | 38.8597 | 1.66457 | ||||||||
\(546\) | −4.21977 | −0.180589 | ||||||||
\(547\) | 1.21345 | 0.0518835 | 0.0259418 | − | 0.999663i | \(-0.491742\pi\) | ||||
0.0259418 | + | 0.999663i | \(0.491742\pi\) | |||||||
\(548\) | 6.98601 | 0.298427 | ||||||||
\(549\) | 1.38121 | 0.0589485 | ||||||||
\(550\) | 139.480 | 5.94744 | ||||||||
\(551\) | 3.59183 | 0.153017 | ||||||||
\(552\) | −1.49225 | −0.0635143 | ||||||||
\(553\) | −21.7090 | −0.923160 | ||||||||
\(554\) | −84.5417 | −3.59183 | ||||||||
\(555\) | −7.20572 | −0.305866 | ||||||||
\(556\) | −61.5592 | −2.61069 | ||||||||
\(557\) | 4.58400 | 0.194230 | 0.0971152 | − | 0.995273i | \(-0.469038\pi\) | ||||
0.0971152 | + | 0.995273i | \(0.469038\pi\) | |||||||
\(558\) | −29.8936 | −1.26550 | ||||||||
\(559\) | −1.64619 | −0.0696264 | ||||||||
\(560\) | −81.6592 | −3.45073 | ||||||||
\(561\) | 5.19453 | 0.219313 | ||||||||
\(562\) | 13.9750 | 0.589500 | ||||||||
\(563\) | 10.8044 | 0.455351 | 0.227675 | − | 0.973737i | \(-0.426888\pi\) | ||||
0.227675 | + | 0.973737i | \(0.426888\pi\) | |||||||
\(564\) | 1.69977 | 0.0715732 | ||||||||
\(565\) | 23.8846 | 1.00483 | ||||||||
\(566\) | 11.1411 | 0.468297 | ||||||||
\(567\) | 17.5317 | 0.736263 | ||||||||
\(568\) | −73.7445 | −3.09425 | ||||||||
\(569\) | −10.1723 | −0.426444 | −0.213222 | − | 0.977004i | \(-0.568396\pi\) | ||||
−0.213222 | + | 0.977004i | \(0.568396\pi\) | |||||||
\(570\) | 2.08556 | 0.0873543 | ||||||||
\(571\) | 14.4371 | 0.604172 | 0.302086 | − | 0.953281i | \(-0.402317\pi\) | ||||
0.302086 | + | 0.953281i | \(0.402317\pi\) | |||||||
\(572\) | 65.2344 | 2.72759 | ||||||||
\(573\) | 1.59182 | 0.0664994 | ||||||||
\(574\) | 63.5124 | 2.65096 | ||||||||
\(575\) | −9.18749 | −0.383145 | ||||||||
\(576\) | −22.4045 | −0.933520 | ||||||||
\(577\) | −6.36585 | −0.265014 | −0.132507 | − | 0.991182i | \(-0.542303\pi\) | ||||
−0.132507 | + | 0.991182i | \(0.542303\pi\) | |||||||
\(578\) | −6.14269 | −0.255502 | ||||||||
\(579\) | 0.382158 | 0.0158820 | ||||||||
\(580\) | 94.2211 | 3.91232 | ||||||||
\(581\) | −28.0335 | −1.16303 | ||||||||
\(582\) | −12.5923 | −0.521968 | ||||||||
\(583\) | 39.6370 | 1.64160 | ||||||||
\(584\) | −55.0884 | −2.27957 | ||||||||
\(585\) | −35.7748 | −1.47911 | ||||||||
\(586\) | −19.8502 | −0.820002 | ||||||||
\(587\) | 27.5890 | 1.13872 | 0.569361 | − | 0.822088i | \(-0.307191\pi\) | ||||
0.569361 | + | 0.822088i | \(0.307191\pi\) | |||||||
\(588\) | 3.30357 | 0.136237 | ||||||||
\(589\) | 2.93385 | 0.120887 | ||||||||
\(590\) | −127.265 | −5.23942 | ||||||||
\(591\) | 0.133552 | 0.00549358 | ||||||||
\(592\) | −64.7576 | −2.66152 | ||||||||
\(593\) | 7.29011 | 0.299369 | 0.149684 | − | 0.988734i | \(-0.452174\pi\) | ||||
0.149684 | + | 0.988734i | \(0.452174\pi\) | |||||||
\(594\) | 18.2873 | 0.750338 | ||||||||
\(595\) | −37.5942 | −1.54121 | ||||||||
\(596\) | −4.35520 | −0.178396 | ||||||||
\(597\) | −5.35632 | −0.219219 | ||||||||
\(598\) | −6.08173 | −0.248700 | ||||||||
\(599\) | 4.71237 | 0.192542 | 0.0962712 | − | 0.995355i | \(-0.469308\pi\) | ||||
0.0962712 | + | 0.995355i | \(0.469308\pi\) | |||||||
\(600\) | 22.4396 | 0.916093 | ||||||||
\(601\) | −39.4421 | −1.60888 | −0.804439 | − | 0.594035i | \(-0.797534\pi\) | ||||
−0.804439 | + | 0.594035i | \(0.797534\pi\) | |||||||
\(602\) | −3.01044 | −0.122696 | ||||||||
\(603\) | 24.4699 | 0.996490 | ||||||||
\(604\) | 79.1701 | 3.22139 | ||||||||
\(605\) | −39.5486 | −1.60788 | ||||||||
\(606\) | −7.58881 | −0.308274 | ||||||||
\(607\) | −3.10118 | −0.125873 | −0.0629364 | − | 0.998018i | \(-0.520047\pi\) | ||||
−0.0629364 | + | 0.998018i | \(0.520047\pi\) | |||||||
\(608\) | 7.69917 | 0.312243 | ||||||||
\(609\) | 2.59268 | 0.105061 | ||||||||
\(610\) | −5.03287 | −0.203775 | ||||||||
\(611\) | 4.05014 | 0.163851 | ||||||||
\(612\) | −62.1195 | −2.51103 | ||||||||
\(613\) | −4.68215 | −0.189110 | −0.0945552 | − | 0.995520i | \(-0.530143\pi\) | ||||
−0.0945552 | + | 0.995520i | \(0.530143\pi\) | |||||||
\(614\) | −17.8195 | −0.719138 | ||||||||
\(615\) | −12.3901 | −0.499618 | ||||||||
\(616\) | 69.7461 | 2.81015 | ||||||||
\(617\) | −11.6286 | −0.468150 | −0.234075 | − | 0.972219i | \(-0.575206\pi\) | ||||
−0.234075 | + | 0.972219i | \(0.575206\pi\) | |||||||
\(618\) | 6.94158 | 0.279231 | ||||||||
\(619\) | −24.8642 | −0.999377 | −0.499689 | − | 0.866205i | \(-0.666552\pi\) | ||||
−0.499689 | + | 0.866205i | \(0.666552\pi\) | |||||||
\(620\) | 76.9609 | 3.09082 | ||||||||
\(621\) | −1.20458 | −0.0483381 | ||||||||
\(622\) | 59.6712 | 2.39260 | ||||||||
\(623\) | 24.8995 | 0.997577 | ||||||||
\(624\) | 7.39810 | 0.296161 | ||||||||
\(625\) | 54.3863 | 2.17545 | ||||||||
\(626\) | 4.83268 | 0.193153 | ||||||||
\(627\) | −0.887179 | −0.0354305 | ||||||||
\(628\) | −114.599 | −4.57298 | ||||||||
\(629\) | −29.8131 | −1.18873 | ||||||||
\(630\) | −65.4225 | −2.60649 | ||||||||
\(631\) | −43.7745 | −1.74264 | −0.871318 | − | 0.490719i | \(-0.836734\pi\) | ||||
−0.871318 | + | 0.490719i | \(0.836734\pi\) | |||||||
\(632\) | 76.4181 | 3.03975 | ||||||||
\(633\) | 0.0439310 | 0.00174610 | ||||||||
\(634\) | 53.7889 | 2.13623 | ||||||||
\(635\) | 36.8145 | 1.46094 | ||||||||
\(636\) | 10.9072 | 0.432497 | ||||||||
\(637\) | 7.87160 | 0.311884 | ||||||||
\(638\) | −56.7286 | −2.24591 | ||||||||
\(639\) | −29.4257 | −1.16406 | ||||||||
\(640\) | −2.24896 | −0.0888978 | ||||||||
\(641\) | −32.1088 | −1.26822 | −0.634111 | − | 0.773242i | \(-0.718634\pi\) | ||||
−0.634111 | + | 0.773242i | \(0.718634\pi\) | |||||||
\(642\) | 2.56398 | 0.101192 | ||||||||
\(643\) | −36.6281 | −1.44447 | −0.722235 | − | 0.691648i | \(-0.756885\pi\) | ||||
−0.722235 | + | 0.691648i | \(0.756885\pi\) | |||||||
\(644\) | −7.85800 | −0.309649 | ||||||||
\(645\) | 0.587282 | 0.0231242 | ||||||||
\(646\) | 8.62883 | 0.339497 | ||||||||
\(647\) | −26.4551 | −1.04006 | −0.520028 | − | 0.854149i | \(-0.674079\pi\) | ||||
−0.520028 | + | 0.854149i | \(0.674079\pi\) | |||||||
\(648\) | −61.7137 | −2.42434 | ||||||||
\(649\) | 54.1376 | 2.12509 | ||||||||
\(650\) | 91.4536 | 3.58711 | ||||||||
\(651\) | 2.11773 | 0.0830005 | ||||||||
\(652\) | −92.9852 | −3.64158 | ||||||||
\(653\) | 40.1265 | 1.57027 | 0.785136 | − | 0.619324i | \(-0.212593\pi\) | ||||
0.785136 | + | 0.619324i | \(0.212593\pi\) | |||||||
\(654\) | −6.43820 | −0.251754 | ||||||||
\(655\) | −30.6497 | −1.19758 | ||||||||
\(656\) | −111.350 | −4.34748 | ||||||||
\(657\) | −21.9814 | −0.857578 | ||||||||
\(658\) | 7.40661 | 0.288740 | ||||||||
\(659\) | −28.2317 | −1.09975 | −0.549876 | − | 0.835246i | \(-0.685325\pi\) | ||||
−0.549876 | + | 0.835246i | \(0.685325\pi\) | |||||||
\(660\) | −23.2726 | −0.905883 | ||||||||
\(661\) | 0.299228 | 0.0116386 | 0.00581931 | − | 0.999983i | \(-0.498148\pi\) | ||||
0.00581931 | + | 0.999983i | \(0.498148\pi\) | |||||||
\(662\) | 16.5999 | 0.645173 | ||||||||
\(663\) | 3.40593 | 0.132275 | ||||||||
\(664\) | 98.6812 | 3.82957 | ||||||||
\(665\) | 6.42076 | 0.248986 | ||||||||
\(666\) | −51.8815 | −2.01037 | ||||||||
\(667\) | 3.73670 | 0.144685 | ||||||||
\(668\) | 20.1928 | 0.781284 | ||||||||
\(669\) | 0.983803 | 0.0380360 | ||||||||
\(670\) | −89.1637 | −3.44470 | ||||||||
\(671\) | 2.14094 | 0.0826502 | ||||||||
\(672\) | 5.55748 | 0.214384 | ||||||||
\(673\) | −1.75600 | −0.0676889 | −0.0338445 | − | 0.999427i | \(-0.510775\pi\) | ||||
−0.0338445 | + | 0.999427i | \(0.510775\pi\) | |||||||
\(674\) | −19.3220 | −0.744256 | ||||||||
\(675\) | 18.1138 | 0.697201 | ||||||||
\(676\) | −19.8247 | −0.762487 | ||||||||
\(677\) | 7.46432 | 0.286877 | 0.143439 | − | 0.989659i | \(-0.454184\pi\) | ||||
0.143439 | + | 0.989659i | \(0.454184\pi\) | |||||||
\(678\) | −3.95715 | −0.151974 | ||||||||
\(679\) | −38.7677 | −1.48777 | ||||||||
\(680\) | 132.336 | 5.07485 | ||||||||
\(681\) | 3.65301 | 0.139984 | ||||||||
\(682\) | −46.3366 | −1.77432 | ||||||||
\(683\) | 20.7657 | 0.794577 | 0.397288 | − | 0.917694i | \(-0.369951\pi\) | ||||
0.397288 | + | 0.917694i | \(0.369951\pi\) | |||||||
\(684\) | 10.6094 | 0.405662 | ||||||||
\(685\) | −5.93848 | −0.226898 | ||||||||
\(686\) | 52.5477 | 2.00628 | ||||||||
\(687\) | 1.68290 | 0.0642068 | ||||||||
\(688\) | 5.27789 | 0.201218 | ||||||||
\(689\) | 25.9891 | 0.990105 | ||||||||
\(690\) | 2.16967 | 0.0825980 | ||||||||
\(691\) | 27.7378 | 1.05520 | 0.527598 | − | 0.849494i | \(-0.323093\pi\) | ||||
0.527598 | + | 0.849494i | \(0.323093\pi\) | |||||||
\(692\) | 55.1430 | 2.09622 | ||||||||
\(693\) | 27.8302 | 1.05718 | ||||||||
\(694\) | −7.76494 | −0.294753 | ||||||||
\(695\) | 52.3286 | 1.98494 | ||||||||
\(696\) | −9.12654 | −0.345941 | ||||||||
\(697\) | −51.2632 | −1.94173 | ||||||||
\(698\) | 0.823429 | 0.0311672 | ||||||||
\(699\) | −2.10811 | −0.0797360 | ||||||||
\(700\) | 118.164 | 4.46619 | ||||||||
\(701\) | 12.9063 | 0.487466 | 0.243733 | − | 0.969842i | \(-0.421628\pi\) | ||||
0.243733 | + | 0.969842i | \(0.421628\pi\) | |||||||
\(702\) | 11.9906 | 0.452555 | ||||||||
\(703\) | 5.09181 | 0.192041 | ||||||||
\(704\) | −34.7281 | −1.30887 | ||||||||
\(705\) | −1.44490 | −0.0544180 | ||||||||
\(706\) | 61.1721 | 2.30224 | ||||||||
\(707\) | −23.3635 | −0.878675 | ||||||||
\(708\) | 14.8974 | 0.559877 | ||||||||
\(709\) | −16.2486 | −0.610228 | −0.305114 | − | 0.952316i | \(-0.598695\pi\) | ||||
−0.305114 | + | 0.952316i | \(0.598695\pi\) | |||||||
\(710\) | 107.222 | 4.02396 | ||||||||
\(711\) | 30.4925 | 1.14356 | ||||||||
\(712\) | −87.6490 | −3.28479 | ||||||||
\(713\) | 3.05218 | 0.114305 | ||||||||
\(714\) | 6.22853 | 0.233097 | ||||||||
\(715\) | −55.4528 | −2.07382 | ||||||||
\(716\) | 23.1286 | 0.864356 | ||||||||
\(717\) | 6.29485 | 0.235085 | ||||||||
\(718\) | −52.9383 | −1.97564 | ||||||||
\(719\) | 33.5096 | 1.24970 | 0.624849 | − | 0.780745i | \(-0.285160\pi\) | ||||
0.624849 | + | 0.780745i | \(0.285160\pi\) | |||||||
\(720\) | 114.699 | 4.27456 | ||||||||
\(721\) | 21.3709 | 0.795893 | ||||||||
\(722\) | 48.1275 | 1.79112 | ||||||||
\(723\) | −3.19766 | −0.118922 | ||||||||
\(724\) | 98.5318 | 3.66191 | ||||||||
\(725\) | −56.1904 | −2.08686 | ||||||||
\(726\) | 6.55232 | 0.243180 | ||||||||
\(727\) | −25.6974 | −0.953065 | −0.476532 | − | 0.879157i | \(-0.658107\pi\) | ||||
−0.476532 | + | 0.879157i | \(0.658107\pi\) | |||||||
\(728\) | 45.7309 | 1.69490 | ||||||||
\(729\) | −23.4241 | −0.867560 | ||||||||
\(730\) | 80.0964 | 2.96450 | ||||||||
\(731\) | 2.42983 | 0.0898707 | ||||||||
\(732\) | 0.589136 | 0.0217751 | ||||||||
\(733\) | −2.69767 | −0.0996407 | −0.0498203 | − | 0.998758i | \(-0.515865\pi\) | ||||
−0.0498203 | + | 0.998758i | \(0.515865\pi\) | |||||||
\(734\) | 94.7998 | 3.49913 | ||||||||
\(735\) | −2.80821 | −0.103583 | ||||||||
\(736\) | 8.00970 | 0.295241 | ||||||||
\(737\) | 37.9296 | 1.39715 | ||||||||
\(738\) | −89.2096 | −3.28385 | ||||||||
\(739\) | 6.64878 | 0.244579 | 0.122290 | − | 0.992494i | \(-0.460976\pi\) | ||||
0.122290 | + | 0.992494i | \(0.460976\pi\) | |||||||
\(740\) | 133.569 | 4.91008 | ||||||||
\(741\) | −0.581703 | −0.0213694 | ||||||||
\(742\) | 47.5270 | 1.74477 | ||||||||
\(743\) | −26.3333 | −0.966074 | −0.483037 | − | 0.875600i | \(-0.660466\pi\) | ||||
−0.483037 | + | 0.875600i | \(0.660466\pi\) | |||||||
\(744\) | −7.45467 | −0.273301 | ||||||||
\(745\) | 3.70216 | 0.135637 | ||||||||
\(746\) | −9.66651 | −0.353916 | ||||||||
\(747\) | 39.3759 | 1.44069 | ||||||||
\(748\) | −96.2884 | −3.52065 | ||||||||
\(749\) | 7.89366 | 0.288428 | ||||||||
\(750\) | −18.7475 | −0.684562 | ||||||||
\(751\) | −32.0977 | −1.17126 | −0.585630 | − | 0.810578i | \(-0.699153\pi\) | ||||
−0.585630 | + | 0.810578i | \(0.699153\pi\) | |||||||
\(752\) | −12.9853 | −0.473524 | ||||||||
\(753\) | 4.04362 | 0.147358 | ||||||||
\(754\) | −37.1956 | −1.35459 | ||||||||
\(755\) | −67.2989 | −2.44926 | ||||||||
\(756\) | 15.4926 | 0.563461 | ||||||||
\(757\) | 35.0330 | 1.27330 | 0.636648 | − | 0.771155i | \(-0.280320\pi\) | ||||
0.636648 | + | 0.771155i | \(0.280320\pi\) | |||||||
\(758\) | −72.5209 | −2.63408 | ||||||||
\(759\) | −0.922962 | −0.0335014 | ||||||||
\(760\) | −22.6018 | −0.819853 | ||||||||
\(761\) | −29.3804 | −1.06504 | −0.532520 | − | 0.846417i | \(-0.678755\pi\) | ||||
−0.532520 | + | 0.846417i | \(0.678755\pi\) | |||||||
\(762\) | −6.09935 | −0.220956 | ||||||||
\(763\) | −19.8212 | −0.717574 | ||||||||
\(764\) | −29.5068 | −1.06752 | ||||||||
\(765\) | 52.8049 | 1.90917 | ||||||||
\(766\) | −82.2966 | −2.97350 | ||||||||
\(767\) | 35.4968 | 1.28171 | ||||||||
\(768\) | 4.34186 | 0.156673 | ||||||||
\(769\) | 9.96773 | 0.359446 | 0.179723 | − | 0.983717i | \(-0.442480\pi\) | ||||
0.179723 | + | 0.983717i | \(0.442480\pi\) | |||||||
\(770\) | −101.408 | −3.65450 | ||||||||
\(771\) | −3.20200 | −0.115317 | ||||||||
\(772\) | −7.08387 | −0.254954 | ||||||||
\(773\) | −17.4115 | −0.626249 | −0.313124 | − | 0.949712i | \(-0.601376\pi\) | ||||
−0.313124 | + | 0.949712i | \(0.601376\pi\) | |||||||
\(774\) | 4.22846 | 0.151989 | ||||||||
\(775\) | −45.8969 | −1.64867 | ||||||||
\(776\) | 136.467 | 4.89887 | ||||||||
\(777\) | 3.67541 | 0.131855 | ||||||||
\(778\) | −60.6796 | −2.17547 | ||||||||
\(779\) | 8.75530 | 0.313691 | ||||||||
\(780\) | −15.2593 | −0.546369 | ||||||||
\(781\) | −45.6113 | −1.63210 | ||||||||
\(782\) | 8.97685 | 0.321012 | ||||||||
\(783\) | −7.36717 | −0.263281 | ||||||||
\(784\) | −25.2374 | −0.901334 | ||||||||
\(785\) | 97.4150 | 3.47689 | ||||||||
\(786\) | 5.07799 | 0.181126 | ||||||||
\(787\) | 36.6531 | 1.30654 | 0.653271 | − | 0.757124i | \(-0.273396\pi\) | ||||
0.653271 | + | 0.757124i | \(0.273396\pi\) | |||||||
\(788\) | −2.47558 | −0.0881888 | ||||||||
\(789\) | 1.44815 | 0.0515554 | ||||||||
\(790\) | −111.109 | −3.95308 | ||||||||
\(791\) | −12.1828 | −0.433171 | ||||||||
\(792\) | −97.9655 | −3.48105 | ||||||||
\(793\) | 1.40377 | 0.0498492 | ||||||||
\(794\) | 87.9568 | 3.12147 | ||||||||
\(795\) | −9.27167 | −0.328832 | ||||||||
\(796\) | 99.2873 | 3.51915 | ||||||||
\(797\) | −2.56965 | −0.0910217 | −0.0455108 | − | 0.998964i | \(-0.514492\pi\) | ||||
−0.0455108 | + | 0.998964i | \(0.514492\pi\) | |||||||
\(798\) | −1.06378 | −0.0376573 | ||||||||
\(799\) | −5.97815 | −0.211492 | ||||||||
\(800\) | −120.445 | −4.25839 | ||||||||
\(801\) | −34.9738 | −1.23574 | ||||||||
\(802\) | 50.4201 | 1.78040 | ||||||||
\(803\) | −34.0724 | −1.20239 | ||||||||
\(804\) | 10.4373 | 0.368095 | ||||||||
\(805\) | 6.67973 | 0.235429 | ||||||||
\(806\) | −30.3818 | −1.07015 | ||||||||
\(807\) | −6.45987 | −0.227398 | ||||||||
\(808\) | 82.2422 | 2.89327 | ||||||||
\(809\) | −27.1561 | −0.954758 | −0.477379 | − | 0.878698i | \(-0.658413\pi\) | ||||
−0.477379 | + | 0.878698i | \(0.658413\pi\) | |||||||
\(810\) | 89.7293 | 3.15277 | ||||||||
\(811\) | 17.6456 | 0.619621 | 0.309810 | − | 0.950798i | \(-0.399734\pi\) | ||||
0.309810 | + | 0.950798i | \(0.399734\pi\) | |||||||
\(812\) | −48.0593 | −1.68655 | ||||||||
\(813\) | 3.69970 | 0.129754 | ||||||||
\(814\) | −80.4190 | −2.81869 | ||||||||
\(815\) | 79.0424 | 2.76874 | ||||||||
\(816\) | −10.9199 | −0.382271 | ||||||||
\(817\) | −0.414994 | −0.0145188 | ||||||||
\(818\) | −90.0589 | −3.14884 | ||||||||
\(819\) | 18.2476 | 0.637623 | ||||||||
\(820\) | 229.670 | 8.02041 | ||||||||
\(821\) | 16.6200 | 0.580042 | 0.290021 | − | 0.957020i | \(-0.406338\pi\) | ||||
0.290021 | + | 0.957020i | \(0.406338\pi\) | |||||||
\(822\) | 0.983876 | 0.0343166 | ||||||||
\(823\) | 19.9273 | 0.694622 | 0.347311 | − | 0.937750i | \(-0.387095\pi\) | ||||
0.347311 | + | 0.937750i | \(0.387095\pi\) | |||||||
\(824\) | −75.2280 | −2.62069 | ||||||||
\(825\) | 13.8790 | 0.483204 | ||||||||
\(826\) | 64.9140 | 2.25865 | ||||||||
\(827\) | −26.3134 | −0.915006 | −0.457503 | − | 0.889208i | \(-0.651256\pi\) | ||||
−0.457503 | + | 0.889208i | \(0.651256\pi\) | |||||||
\(828\) | 11.0374 | 0.383575 | ||||||||
\(829\) | 37.8647 | 1.31510 | 0.657548 | − | 0.753413i | \(-0.271594\pi\) | ||||
0.657548 | + | 0.753413i | \(0.271594\pi\) | |||||||
\(830\) | −143.479 | −4.98022 | ||||||||
\(831\) | −8.41235 | −0.291821 | ||||||||
\(832\) | −22.7704 | −0.789422 | ||||||||
\(833\) | −11.6188 | −0.402566 | ||||||||
\(834\) | −8.66970 | −0.300207 | ||||||||
\(835\) | −17.1650 | −0.594019 | ||||||||
\(836\) | 16.4452 | 0.568769 | ||||||||
\(837\) | −6.01759 | −0.207998 | ||||||||
\(838\) | −40.2057 | −1.38888 | ||||||||
\(839\) | −40.8660 | −1.41085 | −0.705425 | − | 0.708785i | \(-0.749244\pi\) | ||||
−0.705425 | + | 0.708785i | \(0.749244\pi\) | |||||||
\(840\) | −16.3146 | −0.562908 | ||||||||
\(841\) | −6.14649 | −0.211948 | ||||||||
\(842\) | −105.194 | −3.62522 | ||||||||
\(843\) | 1.39059 | 0.0478944 | ||||||||
\(844\) | −0.814326 | −0.0280302 | ||||||||
\(845\) | 16.8520 | 0.579728 | ||||||||
\(846\) | −10.4033 | −0.357674 | ||||||||
\(847\) | 20.1725 | 0.693135 | ||||||||
\(848\) | −83.3243 | −2.86137 | ||||||||
\(849\) | 1.10860 | 0.0380471 | ||||||||
\(850\) | −134.989 | −4.63008 | ||||||||
\(851\) | 5.29718 | 0.181585 | ||||||||
\(852\) | −12.5511 | −0.429994 | ||||||||
\(853\) | −9.64903 | −0.330376 | −0.165188 | − | 0.986262i | \(-0.552823\pi\) | ||||
−0.165188 | + | 0.986262i | \(0.552823\pi\) | |||||||
\(854\) | 2.56711 | 0.0878447 | ||||||||
\(855\) | −9.01860 | −0.308430 | ||||||||
\(856\) | −27.7866 | −0.949726 | ||||||||
\(857\) | 21.3960 | 0.730873 | 0.365437 | − | 0.930836i | \(-0.380920\pi\) | ||||
0.365437 | + | 0.930836i | \(0.380920\pi\) | |||||||
\(858\) | 9.18730 | 0.313649 | ||||||||
\(859\) | −30.2944 | −1.03363 | −0.516815 | − | 0.856097i | \(-0.672882\pi\) | ||||
−0.516815 | + | 0.856097i | \(0.672882\pi\) | |||||||
\(860\) | −10.8862 | −0.371215 | ||||||||
\(861\) | 6.31982 | 0.215379 | ||||||||
\(862\) | −55.7226 | −1.89792 | ||||||||
\(863\) | 30.0519 | 1.02298 | 0.511489 | − | 0.859290i | \(-0.329094\pi\) | ||||
0.511489 | + | 0.859290i | \(0.329094\pi\) | |||||||
\(864\) | −15.7917 | −0.537245 | ||||||||
\(865\) | −46.8745 | −1.59378 | ||||||||
\(866\) | −51.5399 | −1.75140 | ||||||||
\(867\) | −0.611230 | −0.0207585 | ||||||||
\(868\) | −39.2553 | −1.33241 | ||||||||
\(869\) | 47.2649 | 1.60335 | ||||||||
\(870\) | 13.2696 | 0.449883 | ||||||||
\(871\) | 24.8695 | 0.842672 | ||||||||
\(872\) | 69.7727 | 2.36280 | ||||||||
\(873\) | 54.4531 | 1.84296 | ||||||||
\(874\) | −1.53317 | −0.0518601 | ||||||||
\(875\) | −57.7175 | −1.95121 | ||||||||
\(876\) | −9.37589 | −0.316782 | ||||||||
\(877\) | −26.0876 | −0.880916 | −0.440458 | − | 0.897773i | \(-0.645184\pi\) | ||||
−0.440458 | + | 0.897773i | \(0.645184\pi\) | |||||||
\(878\) | −54.8125 | −1.84983 | ||||||||
\(879\) | −1.97520 | −0.0666217 | ||||||||
\(880\) | 177.789 | 5.99326 | ||||||||
\(881\) | 34.4083 | 1.15925 | 0.579623 | − | 0.814885i | \(-0.303200\pi\) | ||||
0.579623 | + | 0.814885i | \(0.303200\pi\) | |||||||
\(882\) | −20.2193 | −0.680819 | ||||||||
\(883\) | −40.6746 | −1.36881 | −0.684405 | − | 0.729102i | \(-0.739938\pi\) | ||||
−0.684405 | + | 0.729102i | \(0.739938\pi\) | |||||||
\(884\) | −63.1340 | −2.12343 | ||||||||
\(885\) | −12.6636 | −0.425681 | ||||||||
\(886\) | −98.2127 | −3.29952 | ||||||||
\(887\) | −40.9423 | −1.37471 | −0.687354 | − | 0.726322i | \(-0.741228\pi\) | ||||
−0.687354 | + | 0.726322i | \(0.741228\pi\) | |||||||
\(888\) | −12.9379 | −0.434167 | ||||||||
\(889\) | −18.7780 | −0.629792 | ||||||||
\(890\) | 127.438 | 4.27174 | ||||||||
\(891\) | −38.1701 | −1.27875 | ||||||||
\(892\) | −18.2363 | −0.610595 | ||||||||
\(893\) | 1.02101 | 0.0341669 | ||||||||
\(894\) | −0.613366 | −0.0205140 | ||||||||
\(895\) | −19.6605 | −0.657180 | ||||||||
\(896\) | 1.14712 | 0.0383227 | ||||||||
\(897\) | −0.605165 | −0.0202059 | ||||||||
\(898\) | −45.5111 | −1.51873 | ||||||||
\(899\) | 18.6670 | 0.622579 | ||||||||
\(900\) | −165.974 | −5.53245 | ||||||||
\(901\) | −38.3608 | −1.27798 | ||||||||
\(902\) | −138.279 | −4.60420 | ||||||||
\(903\) | −0.299554 | −0.00996855 | ||||||||
\(904\) | 42.8849 | 1.42633 | ||||||||
\(905\) | −83.7574 | −2.78419 | ||||||||
\(906\) | 11.1499 | 0.370432 | ||||||||
\(907\) | −52.5203 | −1.74391 | −0.871953 | − | 0.489589i | \(-0.837147\pi\) | ||||
−0.871953 | + | 0.489589i | \(0.837147\pi\) | |||||||
\(908\) | −67.7140 | −2.24717 | ||||||||
\(909\) | 32.8164 | 1.08845 | ||||||||
\(910\) | −66.4910 | −2.20416 | ||||||||
\(911\) | 18.6592 | 0.618206 | 0.309103 | − | 0.951029i | \(-0.399971\pi\) | ||||
0.309103 | + | 0.951029i | \(0.399971\pi\) | |||||||
\(912\) | 1.86501 | 0.0617568 | ||||||||
\(913\) | 61.0347 | 2.01995 | ||||||||
\(914\) | −14.8920 | −0.492583 | ||||||||
\(915\) | −0.500798 | −0.0165559 | ||||||||
\(916\) | −31.1951 | −1.03072 | ||||||||
\(917\) | 15.6335 | 0.516263 | ||||||||
\(918\) | −17.6985 | −0.584138 | ||||||||
\(919\) | −18.8814 | −0.622840 | −0.311420 | − | 0.950272i | \(-0.600805\pi\) | ||||
−0.311420 | + | 0.950272i | \(0.600805\pi\) | |||||||
\(920\) | −23.5134 | −0.775214 | ||||||||
\(921\) | −1.77314 | −0.0584269 | ||||||||
\(922\) | −108.407 | −3.57019 | ||||||||
\(923\) | −29.9063 | −0.984376 | ||||||||
\(924\) | 11.8706 | 0.390514 | ||||||||
\(925\) | −79.6560 | −2.61907 | ||||||||
\(926\) | 28.9848 | 0.952498 | ||||||||
\(927\) | −30.0176 | −0.985906 | ||||||||
\(928\) | 48.9870 | 1.60808 | ||||||||
\(929\) | −6.17839 | −0.202706 | −0.101353 | − | 0.994851i | \(-0.532317\pi\) | ||||
−0.101353 | + | 0.994851i | \(0.532317\pi\) | |||||||
\(930\) | 10.8388 | 0.355418 | ||||||||
\(931\) | 1.98438 | 0.0650355 | ||||||||
\(932\) | 39.0769 | 1.28001 | ||||||||
\(933\) | 5.93761 | 0.194388 | ||||||||
\(934\) | 95.7395 | 3.13269 | ||||||||
\(935\) | 81.8503 | 2.67679 | ||||||||
\(936\) | −64.2337 | −2.09954 | ||||||||
\(937\) | 7.14764 | 0.233503 | 0.116752 | − | 0.993161i | \(-0.462752\pi\) | ||||
0.116752 | + | 0.993161i | \(0.462752\pi\) | |||||||
\(938\) | 45.4797 | 1.48496 | ||||||||
\(939\) | 0.480877 | 0.0156928 | ||||||||
\(940\) | 26.7833 | 0.873575 | ||||||||
\(941\) | −31.8887 | −1.03954 | −0.519770 | − | 0.854306i | \(-0.673982\pi\) | ||||
−0.519770 | + | 0.854306i | \(0.673982\pi\) | |||||||
\(942\) | −16.1395 | −0.525854 | ||||||||
\(943\) | 9.10843 | 0.296611 | ||||||||
\(944\) | −113.807 | −3.70411 | ||||||||
\(945\) | −13.1696 | −0.428406 | ||||||||
\(946\) | 6.55433 | 0.213100 | ||||||||
\(947\) | 21.9422 | 0.713027 | 0.356513 | − | 0.934290i | \(-0.383965\pi\) | ||||
0.356513 | + | 0.934290i | \(0.383965\pi\) | |||||||
\(948\) | 13.0062 | 0.422421 | ||||||||
\(949\) | −22.3405 | −0.725202 | ||||||||
\(950\) | 23.0549 | 0.747999 | ||||||||
\(951\) | 5.35228 | 0.173560 | ||||||||
\(952\) | −67.5005 | −2.18770 | ||||||||
\(953\) | −46.7805 | −1.51537 | −0.757684 | − | 0.652621i | \(-0.773669\pi\) | ||||
−0.757684 | + | 0.652621i | \(0.773669\pi\) | |||||||
\(954\) | −66.7565 | −2.16132 | ||||||||
\(955\) | 25.0824 | 0.811648 | ||||||||
\(956\) | −116.684 | −3.77384 | ||||||||
\(957\) | −5.64480 | −0.182471 | ||||||||
\(958\) | 59.3989 | 1.91909 | ||||||||
\(959\) | 3.02904 | 0.0978127 | ||||||||
\(960\) | 8.12341 | 0.262182 | ||||||||
\(961\) | −15.7526 | −0.508148 | ||||||||
\(962\) | −52.7289 | −1.70005 | ||||||||
\(963\) | −11.0874 | −0.357288 | ||||||||
\(964\) | 59.2734 | 1.90907 | ||||||||
\(965\) | 6.02167 | 0.193845 | ||||||||
\(966\) | −1.10668 | −0.0356069 | ||||||||
\(967\) | 27.2626 | 0.876706 | 0.438353 | − | 0.898803i | \(-0.355562\pi\) | ||||
0.438353 | + | 0.898803i | \(0.355562\pi\) | |||||||
\(968\) | −71.0095 | −2.28233 | ||||||||
\(969\) | 0.858614 | 0.0275827 | ||||||||
\(970\) | −198.417 | −6.37079 | ||||||||
\(971\) | 30.5592 | 0.980692 | 0.490346 | − | 0.871528i | \(-0.336870\pi\) | ||||
0.490346 | + | 0.871528i | \(0.336870\pi\) | |||||||
\(972\) | −32.7652 | −1.05094 | ||||||||
\(973\) | −26.6912 | −0.855681 | ||||||||
\(974\) | 66.5924 | 2.13376 | ||||||||
\(975\) | 9.10013 | 0.291437 | ||||||||
\(976\) | −4.50066 | −0.144063 | ||||||||
\(977\) | 31.6056 | 1.01115 | 0.505576 | − | 0.862782i | \(-0.331280\pi\) | ||||
0.505576 | + | 0.862782i | \(0.331280\pi\) | |||||||
\(978\) | −13.0956 | −0.418751 | ||||||||
\(979\) | −54.2113 | −1.73260 | ||||||||
\(980\) | 52.0544 | 1.66282 | ||||||||
\(981\) | 27.8408 | 0.888889 | ||||||||
\(982\) | 31.8192 | 1.01539 | ||||||||
\(983\) | 2.31068 | 0.0736993 | 0.0368496 | − | 0.999321i | \(-0.488268\pi\) | ||||
0.0368496 | + | 0.999321i | \(0.488268\pi\) | |||||||
\(984\) | −22.2465 | −0.709193 | ||||||||
\(985\) | 2.10437 | 0.0670509 | ||||||||
\(986\) | 54.9021 | 1.74844 | ||||||||
\(987\) | 0.736997 | 0.0234589 | ||||||||
\(988\) | 10.7827 | 0.343044 | ||||||||
\(989\) | −0.431732 | −0.0137283 | ||||||||
\(990\) | 142.438 | 4.52698 | ||||||||
\(991\) | 53.3558 | 1.69490 | 0.847451 | − | 0.530873i | \(-0.178136\pi\) | ||||
0.847451 | + | 0.530873i | \(0.178136\pi\) | |||||||
\(992\) | 40.0132 | 1.27042 | ||||||||
\(993\) | 1.65178 | 0.0524176 | ||||||||
\(994\) | −54.6905 | −1.73468 | ||||||||
\(995\) | −84.3996 | −2.67565 | ||||||||
\(996\) | 16.7953 | 0.532178 | ||||||||
\(997\) | −6.96753 | −0.220664 | −0.110332 | − | 0.993895i | \(-0.535191\pi\) | ||||
−0.110332 | + | 0.993895i | \(0.535191\pi\) | |||||||
\(998\) | −93.3024 | −2.95344 | ||||||||
\(999\) | −10.4438 | −0.330426 |
(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 | 4001.2.a.b.1.14 | ✓ | 184 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4001.2.a.b.1.14 | ✓ | 184 | 1.1 | even | 1 | trivial |