Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6019,2,Mod(1,6019)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6019, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6019.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6019 = 13 \cdot 463 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6019.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: | \(48.0619569766\) |
Analytic rank: | \(0\) |
Dimension: | \(130\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Character | \(\chi\) | \(=\) | 6019.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.65690 | −1.87871 | −0.939356 | − | 0.342942i | \(-0.888576\pi\) | ||||
−0.939356 | + | 0.342942i | \(0.888576\pi\) | |||||||
\(3\) | −1.17656 | −0.679288 | −0.339644 | − | 0.940554i | \(-0.610307\pi\) | ||||
−0.339644 | + | 0.940554i | \(0.610307\pi\) | |||||||
\(4\) | 5.05912 | 2.52956 | ||||||||
\(5\) | −3.97344 | −1.77697 | −0.888487 | − | 0.458901i | \(-0.848243\pi\) | ||||
−0.888487 | + | 0.458901i | \(0.848243\pi\) | |||||||
\(6\) | 3.12601 | 1.27619 | ||||||||
\(7\) | −1.98444 | −0.750049 | −0.375025 | − | 0.927015i | \(-0.622366\pi\) | ||||
−0.375025 | + | 0.927015i | \(0.622366\pi\) | |||||||
\(8\) | −8.12779 | −2.87361 | ||||||||
\(9\) | −1.61571 | −0.538568 | ||||||||
\(10\) | 10.5570 | 3.33843 | ||||||||
\(11\) | 3.06486 | 0.924090 | 0.462045 | − | 0.886856i | \(-0.347116\pi\) | ||||
0.462045 | + | 0.886856i | \(0.347116\pi\) | |||||||
\(12\) | −5.95237 | −1.71830 | ||||||||
\(13\) | 1.00000 | 0.277350 | ||||||||
\(14\) | 5.27247 | 1.40913 | ||||||||
\(15\) | 4.67499 | 1.20708 | ||||||||
\(16\) | 11.4765 | 2.86912 | ||||||||
\(17\) | 4.82877 | 1.17115 | 0.585574 | − | 0.810619i | \(-0.300869\pi\) | ||||
0.585574 | + | 0.810619i | \(0.300869\pi\) | |||||||
\(18\) | 4.29277 | 1.01182 | ||||||||
\(19\) | −1.87946 | −0.431178 | −0.215589 | − | 0.976484i | \(-0.569167\pi\) | ||||
−0.215589 | + | 0.976484i | \(0.569167\pi\) | |||||||
\(20\) | −20.1021 | −4.49497 | ||||||||
\(21\) | 2.33482 | 0.509499 | ||||||||
\(22\) | −8.14303 | −1.73610 | ||||||||
\(23\) | 3.96518 | 0.826797 | 0.413398 | − | 0.910550i | \(-0.364342\pi\) | ||||
0.413398 | + | 0.910550i | \(0.364342\pi\) | |||||||
\(24\) | 9.56284 | 1.95201 | ||||||||
\(25\) | 10.7882 | 2.15764 | ||||||||
\(26\) | −2.65690 | −0.521061 | ||||||||
\(27\) | 5.43066 | 1.04513 | ||||||||
\(28\) | −10.0395 | −1.89730 | ||||||||
\(29\) | 10.1973 | 1.89359 | 0.946795 | − | 0.321837i | \(-0.104300\pi\) | ||||
0.946795 | + | 0.321837i | \(0.104300\pi\) | |||||||
\(30\) | −12.4210 | −2.26775 | ||||||||
\(31\) | 1.96081 | 0.352172 | 0.176086 | − | 0.984375i | \(-0.443656\pi\) | ||||
0.176086 | + | 0.984375i | \(0.443656\pi\) | |||||||
\(32\) | −14.2363 | −2.51665 | ||||||||
\(33\) | −3.60599 | −0.627723 | ||||||||
\(34\) | −12.8296 | −2.20025 | ||||||||
\(35\) | 7.88506 | 1.33282 | ||||||||
\(36\) | −8.17405 | −1.36234 | ||||||||
\(37\) | −10.4081 | −1.71109 | −0.855543 | − | 0.517732i | \(-0.826776\pi\) | ||||
−0.855543 | + | 0.517732i | \(0.826776\pi\) | |||||||
\(38\) | 4.99355 | 0.810061 | ||||||||
\(39\) | −1.17656 | −0.188400 | ||||||||
\(40\) | 32.2953 | 5.10633 | ||||||||
\(41\) | 10.2820 | 1.60578 | 0.802889 | − | 0.596129i | \(-0.203295\pi\) | ||||
0.802889 | + | 0.596129i | \(0.203295\pi\) | |||||||
\(42\) | −6.20338 | −0.957202 | ||||||||
\(43\) | 9.66829 | 1.47440 | 0.737201 | − | 0.675674i | \(-0.236147\pi\) | ||||
0.737201 | + | 0.675674i | \(0.236147\pi\) | |||||||
\(44\) | 15.5055 | 2.33754 | ||||||||
\(45\) | 6.41990 | 0.957023 | ||||||||
\(46\) | −10.5351 | −1.55331 | ||||||||
\(47\) | 1.09660 | 0.159955 | 0.0799776 | − | 0.996797i | \(-0.474515\pi\) | ||||
0.0799776 | + | 0.996797i | \(0.474515\pi\) | |||||||
\(48\) | −13.5028 | −1.94896 | ||||||||
\(49\) | −3.06198 | −0.437426 | ||||||||
\(50\) | −28.6632 | −4.05358 | ||||||||
\(51\) | −5.68133 | −0.795546 | ||||||||
\(52\) | 5.05912 | 0.701574 | ||||||||
\(53\) | 0.613431 | 0.0842613 | 0.0421306 | − | 0.999112i | \(-0.486585\pi\) | ||||
0.0421306 | + | 0.999112i | \(0.486585\pi\) | |||||||
\(54\) | −14.4287 | −1.96350 | ||||||||
\(55\) | −12.1780 | −1.64209 | ||||||||
\(56\) | 16.1291 | 2.15535 | ||||||||
\(57\) | 2.21130 | 0.292894 | ||||||||
\(58\) | −27.0932 | −3.55751 | ||||||||
\(59\) | 8.78784 | 1.14408 | 0.572040 | − | 0.820226i | \(-0.306152\pi\) | ||||
0.572040 | + | 0.820226i | \(0.306152\pi\) | |||||||
\(60\) | 23.6513 | 3.05338 | ||||||||
\(61\) | 3.09399 | 0.396145 | 0.198072 | − | 0.980187i | \(-0.436532\pi\) | ||||
0.198072 | + | 0.980187i | \(0.436532\pi\) | |||||||
\(62\) | −5.20967 | −0.661629 | ||||||||
\(63\) | 3.20628 | 0.403953 | ||||||||
\(64\) | 14.8715 | 1.85894 | ||||||||
\(65\) | −3.97344 | −0.492844 | ||||||||
\(66\) | 9.58077 | 1.17931 | ||||||||
\(67\) | −5.68402 | −0.694414 | −0.347207 | − | 0.937789i | \(-0.612870\pi\) | ||||
−0.347207 | + | 0.937789i | \(0.612870\pi\) | |||||||
\(68\) | 24.4293 | 2.96249 | ||||||||
\(69\) | −4.66527 | −0.561633 | ||||||||
\(70\) | −20.9498 | −2.50398 | ||||||||
\(71\) | 1.46209 | 0.173518 | 0.0867590 | − | 0.996229i | \(-0.472349\pi\) | ||||
0.0867590 | + | 0.996229i | \(0.472349\pi\) | |||||||
\(72\) | 13.1321 | 1.54763 | ||||||||
\(73\) | −12.1577 | −1.42295 | −0.711474 | − | 0.702712i | \(-0.751972\pi\) | ||||
−0.711474 | + | 0.702712i | \(0.751972\pi\) | |||||||
\(74\) | 27.6534 | 3.21464 | ||||||||
\(75\) | −12.6930 | −1.46566 | ||||||||
\(76\) | −9.50844 | −1.09069 | ||||||||
\(77\) | −6.08204 | −0.693113 | ||||||||
\(78\) | 3.12601 | 0.353950 | ||||||||
\(79\) | 5.94489 | 0.668852 | 0.334426 | − | 0.942422i | \(-0.391458\pi\) | ||||
0.334426 | + | 0.942422i | \(0.391458\pi\) | |||||||
\(80\) | −45.6011 | −5.09836 | ||||||||
\(81\) | −1.54238 | −0.171376 | ||||||||
\(82\) | −27.3182 | −3.01679 | ||||||||
\(83\) | 8.26160 | 0.906829 | 0.453414 | − | 0.891300i | \(-0.350206\pi\) | ||||
0.453414 | + | 0.891300i | \(0.350206\pi\) | |||||||
\(84\) | 11.8121 | 1.28881 | ||||||||
\(85\) | −19.1868 | −2.08110 | ||||||||
\(86\) | −25.6877 | −2.76998 | ||||||||
\(87\) | −11.9977 | −1.28629 | ||||||||
\(88\) | −24.9106 | −2.65547 | ||||||||
\(89\) | −0.0123574 | −0.00130988 | −0.000654940 | − | 1.00000i | \(-0.500208\pi\) | ||||
−0.000654940 | 1.00000i | \(0.500208\pi\) | ||||||||
\(90\) | −17.0570 | −1.79797 | ||||||||
\(91\) | −1.98444 | −0.208026 | ||||||||
\(92\) | 20.0603 | 2.09143 | ||||||||
\(93\) | −2.30701 | −0.239226 | ||||||||
\(94\) | −2.91355 | −0.300510 | ||||||||
\(95\) | 7.46793 | 0.766193 | ||||||||
\(96\) | 16.7499 | 1.70953 | ||||||||
\(97\) | 9.42141 | 0.956600 | 0.478300 | − | 0.878197i | \(-0.341253\pi\) | ||||
0.478300 | + | 0.878197i | \(0.341253\pi\) | |||||||
\(98\) | 8.13539 | 0.821798 | ||||||||
\(99\) | −4.95191 | −0.497686 | ||||||||
\(100\) | 54.5788 | 5.45788 | ||||||||
\(101\) | −10.8874 | −1.08334 | −0.541671 | − | 0.840591i | \(-0.682208\pi\) | ||||
−0.541671 | + | 0.840591i | \(0.682208\pi\) | |||||||
\(102\) | 15.0947 | 1.49460 | ||||||||
\(103\) | 2.12250 | 0.209136 | 0.104568 | − | 0.994518i | \(-0.466654\pi\) | ||||
0.104568 | + | 0.994518i | \(0.466654\pi\) | |||||||
\(104\) | −8.12779 | −0.796995 | ||||||||
\(105\) | −9.27725 | −0.905367 | ||||||||
\(106\) | −1.62983 | −0.158303 | ||||||||
\(107\) | −17.3367 | −1.67600 | −0.838002 | − | 0.545667i | \(-0.816276\pi\) | ||||
−0.838002 | + | 0.545667i | \(0.816276\pi\) | |||||||
\(108\) | 27.4744 | 2.64372 | ||||||||
\(109\) | 16.6563 | 1.59538 | 0.797691 | − | 0.603067i | \(-0.206055\pi\) | ||||
0.797691 | + | 0.603067i | \(0.206055\pi\) | |||||||
\(110\) | 32.3558 | 3.08501 | ||||||||
\(111\) | 12.2458 | 1.16232 | ||||||||
\(112\) | −22.7744 | −2.15198 | ||||||||
\(113\) | −0.437226 | −0.0411308 | −0.0205654 | − | 0.999789i | \(-0.506547\pi\) | ||||
−0.0205654 | + | 0.999789i | \(0.506547\pi\) | |||||||
\(114\) | −5.87521 | −0.550264 | ||||||||
\(115\) | −15.7554 | −1.46920 | ||||||||
\(116\) | 51.5894 | 4.78995 | ||||||||
\(117\) | −1.61571 | −0.149372 | ||||||||
\(118\) | −23.3484 | −2.14940 | ||||||||
\(119\) | −9.58241 | −0.878418 | ||||||||
\(120\) | −37.9973 | −3.46867 | ||||||||
\(121\) | −1.60663 | −0.146057 | ||||||||
\(122\) | −8.22042 | −0.744242 | ||||||||
\(123\) | −12.0974 | −1.09078 | ||||||||
\(124\) | 9.91997 | 0.890840 | ||||||||
\(125\) | −22.9990 | −2.05710 | ||||||||
\(126\) | −8.51876 | −0.758911 | ||||||||
\(127\) | −11.0495 | −0.980485 | −0.490242 | − | 0.871586i | \(-0.663092\pi\) | ||||
−0.490242 | + | 0.871586i | \(0.663092\pi\) | |||||||
\(128\) | −11.0395 | −0.975763 | ||||||||
\(129\) | −11.3753 | −1.00154 | ||||||||
\(130\) | 10.5570 | 0.925913 | ||||||||
\(131\) | −9.01334 | −0.787499 | −0.393750 | − | 0.919218i | \(-0.628822\pi\) | ||||
−0.393750 | + | 0.919218i | \(0.628822\pi\) | |||||||
\(132\) | −18.2432 | −1.58786 | ||||||||
\(133\) | 3.72969 | 0.323405 | ||||||||
\(134\) | 15.1019 | 1.30460 | ||||||||
\(135\) | −21.5784 | −1.85717 | ||||||||
\(136\) | −39.2472 | −3.36542 | ||||||||
\(137\) | −16.9279 | −1.44625 | −0.723126 | − | 0.690716i | \(-0.757295\pi\) | ||||
−0.723126 | + | 0.690716i | \(0.757295\pi\) | |||||||
\(138\) | 12.3952 | 1.05515 | ||||||||
\(139\) | −7.03091 | −0.596354 | −0.298177 | − | 0.954511i | \(-0.596379\pi\) | ||||
−0.298177 | + | 0.954511i | \(0.596379\pi\) | |||||||
\(140\) | 39.8915 | 3.37145 | ||||||||
\(141\) | −1.29021 | −0.108656 | ||||||||
\(142\) | −3.88462 | −0.325990 | ||||||||
\(143\) | 3.06486 | 0.256297 | ||||||||
\(144\) | −18.5426 | −1.54522 | ||||||||
\(145\) | −40.5183 | −3.36486 | ||||||||
\(146\) | 32.3018 | 2.67331 | ||||||||
\(147\) | 3.60261 | 0.297138 | ||||||||
\(148\) | −52.6560 | −4.32830 | ||||||||
\(149\) | 12.2129 | 1.00052 | 0.500262 | − | 0.865874i | \(-0.333237\pi\) | ||||
0.500262 | + | 0.865874i | \(0.333237\pi\) | |||||||
\(150\) | 33.7240 | 2.75355 | ||||||||
\(151\) | 3.66650 | 0.298376 | 0.149188 | − | 0.988809i | \(-0.452334\pi\) | ||||
0.149188 | + | 0.988809i | \(0.452334\pi\) | |||||||
\(152\) | 15.2759 | 1.23904 | ||||||||
\(153\) | −7.80186 | −0.630743 | ||||||||
\(154\) | 16.1594 | 1.30216 | ||||||||
\(155\) | −7.79115 | −0.625800 | ||||||||
\(156\) | −5.95237 | −0.476571 | ||||||||
\(157\) | 11.4086 | 0.910502 | 0.455251 | − | 0.890363i | \(-0.349550\pi\) | ||||
0.455251 | + | 0.890363i | \(0.349550\pi\) | |||||||
\(158\) | −15.7950 | −1.25658 | ||||||||
\(159\) | −0.721739 | −0.0572376 | ||||||||
\(160\) | 56.5671 | 4.47202 | ||||||||
\(161\) | −7.86867 | −0.620138 | ||||||||
\(162\) | 4.09795 | 0.321965 | ||||||||
\(163\) | −4.35309 | −0.340961 | −0.170480 | − | 0.985361i | \(-0.554532\pi\) | ||||
−0.170480 | + | 0.985361i | \(0.554532\pi\) | |||||||
\(164\) | 52.0179 | 4.06191 | ||||||||
\(165\) | 14.3282 | 1.11545 | ||||||||
\(166\) | −21.9503 | −1.70367 | ||||||||
\(167\) | 17.7186 | 1.37111 | 0.685554 | − | 0.728022i | \(-0.259560\pi\) | ||||
0.685554 | + | 0.728022i | \(0.259560\pi\) | |||||||
\(168\) | −18.9769 | −1.46410 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 50.9774 | 3.90979 | ||||||||
\(171\) | 3.03666 | 0.232219 | ||||||||
\(172\) | 48.9131 | 3.72959 | ||||||||
\(173\) | 26.0485 | 1.98043 | 0.990214 | − | 0.139558i | \(-0.0445682\pi\) | ||||
0.990214 | + | 0.139558i | \(0.0445682\pi\) | |||||||
\(174\) | 31.8768 | 2.41657 | ||||||||
\(175\) | −21.4086 | −1.61834 | ||||||||
\(176\) | 35.1738 | 2.65133 | ||||||||
\(177\) | −10.3394 | −0.777159 | ||||||||
\(178\) | 0.0328324 | 0.00246089 | ||||||||
\(179\) | 15.8317 | 1.18332 | 0.591658 | − | 0.806189i | \(-0.298474\pi\) | ||||
0.591658 | + | 0.806189i | \(0.298474\pi\) | |||||||
\(180\) | 32.4791 | 2.42085 | ||||||||
\(181\) | 0.966140 | 0.0718126 | 0.0359063 | − | 0.999355i | \(-0.488568\pi\) | ||||
0.0359063 | + | 0.999355i | \(0.488568\pi\) | |||||||
\(182\) | 5.27247 | 0.390822 | ||||||||
\(183\) | −3.64026 | −0.269096 | ||||||||
\(184\) | −32.2281 | −2.37589 | ||||||||
\(185\) | 41.3560 | 3.04056 | ||||||||
\(186\) | 6.12950 | 0.449436 | ||||||||
\(187\) | 14.7995 | 1.08225 | ||||||||
\(188\) | 5.54782 | 0.404617 | ||||||||
\(189\) | −10.7768 | −0.783899 | ||||||||
\(190\) | −19.8415 | −1.43946 | ||||||||
\(191\) | 24.0959 | 1.74351 | 0.871757 | − | 0.489938i | \(-0.162981\pi\) | ||||
0.871757 | + | 0.489938i | \(0.162981\pi\) | |||||||
\(192\) | −17.4972 | −1.26275 | ||||||||
\(193\) | 21.3639 | 1.53781 | 0.768904 | − | 0.639365i | \(-0.220803\pi\) | ||||
0.768904 | + | 0.639365i | \(0.220803\pi\) | |||||||
\(194\) | −25.0318 | −1.79718 | ||||||||
\(195\) | 4.67499 | 0.334783 | ||||||||
\(196\) | −15.4910 | −1.10650 | ||||||||
\(197\) | 11.0926 | 0.790313 | 0.395157 | − | 0.918614i | \(-0.370690\pi\) | ||||
0.395157 | + | 0.918614i | \(0.370690\pi\) | |||||||
\(198\) | 13.1567 | 0.935009 | ||||||||
\(199\) | 7.03091 | 0.498408 | 0.249204 | − | 0.968451i | \(-0.419831\pi\) | ||||
0.249204 | + | 0.968451i | \(0.419831\pi\) | |||||||
\(200\) | −87.6842 | −6.20021 | ||||||||
\(201\) | 6.68760 | 0.471707 | ||||||||
\(202\) | 28.9269 | 2.03529 | ||||||||
\(203\) | −20.2360 | −1.42029 | ||||||||
\(204\) | −28.7426 | −2.01238 | ||||||||
\(205\) | −40.8548 | −2.85343 | ||||||||
\(206\) | −5.63928 | −0.392907 | ||||||||
\(207\) | −6.40656 | −0.445287 | ||||||||
\(208\) | 11.4765 | 0.795751 | ||||||||
\(209\) | −5.76029 | −0.398448 | ||||||||
\(210\) | 24.6487 | 1.70092 | ||||||||
\(211\) | 6.33567 | 0.436166 | 0.218083 | − | 0.975930i | \(-0.430020\pi\) | ||||
0.218083 | + | 0.975930i | \(0.430020\pi\) | |||||||
\(212\) | 3.10343 | 0.213144 | ||||||||
\(213\) | −1.72024 | −0.117869 | ||||||||
\(214\) | 46.0620 | 3.14873 | ||||||||
\(215\) | −38.4164 | −2.61997 | ||||||||
\(216\) | −44.1392 | −3.00330 | ||||||||
\(217\) | −3.89111 | −0.264146 | ||||||||
\(218\) | −44.2541 | −2.99726 | ||||||||
\(219\) | 14.3042 | 0.966591 | ||||||||
\(220\) | −61.6102 | −4.15376 | ||||||||
\(221\) | 4.82877 | 0.324818 | ||||||||
\(222\) | −32.5359 | −2.18366 | ||||||||
\(223\) | −17.3622 | −1.16266 | −0.581331 | − | 0.813667i | \(-0.697468\pi\) | ||||
−0.581331 | + | 0.813667i | \(0.697468\pi\) | |||||||
\(224\) | 28.2512 | 1.88761 | ||||||||
\(225\) | −17.4305 | −1.16204 | ||||||||
\(226\) | 1.16167 | 0.0772730 | ||||||||
\(227\) | −0.475918 | −0.0315878 | −0.0157939 | − | 0.999875i | \(-0.505028\pi\) | ||||
−0.0157939 | + | 0.999875i | \(0.505028\pi\) | |||||||
\(228\) | 11.1873 | 0.740894 | ||||||||
\(229\) | −24.1579 | −1.59640 | −0.798199 | − | 0.602394i | \(-0.794214\pi\) | ||||
−0.798199 | + | 0.602394i | \(0.794214\pi\) | |||||||
\(230\) | 41.8605 | 2.76020 | ||||||||
\(231\) | 7.15589 | 0.470823 | ||||||||
\(232\) | −82.8815 | −5.44144 | ||||||||
\(233\) | −7.25831 | −0.475508 | −0.237754 | − | 0.971325i | \(-0.576411\pi\) | ||||
−0.237754 | + | 0.971325i | \(0.576411\pi\) | |||||||
\(234\) | 4.29277 | 0.280627 | ||||||||
\(235\) | −4.35726 | −0.284236 | ||||||||
\(236\) | 44.4588 | 2.89402 | ||||||||
\(237\) | −6.99452 | −0.454343 | ||||||||
\(238\) | 25.4595 | 1.65030 | ||||||||
\(239\) | 18.2769 | 1.18223 | 0.591117 | − | 0.806586i | \(-0.298687\pi\) | ||||
0.591117 | + | 0.806586i | \(0.298687\pi\) | |||||||
\(240\) | 53.6525 | 3.46325 | ||||||||
\(241\) | 24.6535 | 1.58807 | 0.794036 | − | 0.607871i | \(-0.207976\pi\) | ||||
0.794036 | + | 0.607871i | \(0.207976\pi\) | |||||||
\(242\) | 4.26865 | 0.274399 | ||||||||
\(243\) | −14.4773 | −0.928717 | ||||||||
\(244\) | 15.6529 | 1.00207 | ||||||||
\(245\) | 12.1666 | 0.777295 | ||||||||
\(246\) | 32.1416 | 2.04927 | ||||||||
\(247\) | −1.87946 | −0.119587 | ||||||||
\(248\) | −15.9370 | −1.01200 | ||||||||
\(249\) | −9.72028 | −0.615998 | ||||||||
\(250\) | 61.1061 | 3.86469 | ||||||||
\(251\) | −15.0931 | −0.952666 | −0.476333 | − | 0.879265i | \(-0.658034\pi\) | ||||
−0.476333 | + | 0.879265i | \(0.658034\pi\) | |||||||
\(252\) | 16.2210 | 1.02182 | ||||||||
\(253\) | 12.1527 | 0.764035 | ||||||||
\(254\) | 29.3574 | 1.84205 | ||||||||
\(255\) | 22.5744 | 1.41367 | ||||||||
\(256\) | −0.412156 | −0.0257598 | ||||||||
\(257\) | −9.89505 | −0.617236 | −0.308618 | − | 0.951186i | \(-0.599867\pi\) | ||||
−0.308618 | + | 0.951186i | \(0.599867\pi\) | |||||||
\(258\) | 30.2231 | 1.88161 | ||||||||
\(259\) | 20.6543 | 1.28340 | ||||||||
\(260\) | −20.1021 | −1.24668 | ||||||||
\(261\) | −16.4758 | −1.01983 | ||||||||
\(262\) | 23.9476 | 1.47949 | ||||||||
\(263\) | −15.1484 | −0.934092 | −0.467046 | − | 0.884233i | \(-0.654682\pi\) | ||||
−0.467046 | + | 0.884233i | \(0.654682\pi\) | |||||||
\(264\) | 29.3088 | 1.80383 | ||||||||
\(265\) | −2.43743 | −0.149730 | ||||||||
\(266\) | −9.90942 | −0.607585 | ||||||||
\(267\) | 0.0145392 | 0.000889785 0 | ||||||||
\(268\) | −28.7562 | −1.75656 | ||||||||
\(269\) | 3.11677 | 0.190033 | 0.0950164 | − | 0.995476i | \(-0.469710\pi\) | ||||
0.0950164 | + | 0.995476i | \(0.469710\pi\) | |||||||
\(270\) | 57.3316 | 3.48909 | ||||||||
\(271\) | −12.4574 | −0.756735 | −0.378368 | − | 0.925655i | \(-0.623514\pi\) | ||||
−0.378368 | + | 0.925655i | \(0.623514\pi\) | |||||||
\(272\) | 55.4173 | 3.36017 | ||||||||
\(273\) | 2.33482 | 0.141310 | ||||||||
\(274\) | 44.9759 | 2.71709 | ||||||||
\(275\) | 33.0643 | 1.99385 | ||||||||
\(276\) | −23.6022 | −1.42069 | ||||||||
\(277\) | −13.9653 | −0.839092 | −0.419546 | − | 0.907734i | \(-0.637811\pi\) | ||||
−0.419546 | + | 0.907734i | \(0.637811\pi\) | |||||||
\(278\) | 18.6804 | 1.12038 | ||||||||
\(279\) | −3.16809 | −0.189668 | ||||||||
\(280\) | −64.0881 | −3.83000 | ||||||||
\(281\) | −13.8823 | −0.828150 | −0.414075 | − | 0.910243i | \(-0.635895\pi\) | ||||
−0.414075 | + | 0.910243i | \(0.635895\pi\) | |||||||
\(282\) | 3.42797 | 0.204133 | ||||||||
\(283\) | 20.4315 | 1.21453 | 0.607263 | − | 0.794501i | \(-0.292267\pi\) | ||||
0.607263 | + | 0.794501i | \(0.292267\pi\) | |||||||
\(284\) | 7.39689 | 0.438924 | ||||||||
\(285\) | −8.78647 | −0.520465 | ||||||||
\(286\) | −8.14303 | −0.481508 | ||||||||
\(287\) | −20.4040 | −1.20441 | ||||||||
\(288\) | 23.0017 | 1.35539 | ||||||||
\(289\) | 6.31697 | 0.371587 | ||||||||
\(290\) | 107.653 | 6.32161 | ||||||||
\(291\) | −11.0849 | −0.649806 | ||||||||
\(292\) | −61.5072 | −3.59944 | ||||||||
\(293\) | −33.9016 | −1.98055 | −0.990277 | − | 0.139113i | \(-0.955575\pi\) | ||||
−0.990277 | + | 0.139113i | \(0.955575\pi\) | |||||||
\(294\) | −9.57177 | −0.558237 | ||||||||
\(295\) | −34.9179 | −2.03300 | ||||||||
\(296\) | 84.5951 | 4.91699 | ||||||||
\(297\) | 16.6442 | 0.965795 | ||||||||
\(298\) | −32.4486 | −1.87970 | ||||||||
\(299\) | 3.96518 | 0.229312 | ||||||||
\(300\) | −64.2153 | −3.70747 | ||||||||
\(301\) | −19.1862 | −1.10587 | ||||||||
\(302\) | −9.74153 | −0.560562 | ||||||||
\(303\) | 12.8097 | 0.735900 | ||||||||
\(304\) | −21.5696 | −1.23710 | ||||||||
\(305\) | −12.2938 | −0.703939 | ||||||||
\(306\) | 20.7288 | 1.18499 | ||||||||
\(307\) | −9.32207 | −0.532039 | −0.266019 | − | 0.963968i | \(-0.585709\pi\) | ||||
−0.266019 | + | 0.963968i | \(0.585709\pi\) | |||||||
\(308\) | −30.7698 | −1.75327 | ||||||||
\(309\) | −2.49725 | −0.142064 | ||||||||
\(310\) | 20.7003 | 1.17570 | ||||||||
\(311\) | −27.6274 | −1.56661 | −0.783304 | − | 0.621639i | \(-0.786467\pi\) | ||||
−0.783304 | + | 0.621639i | \(0.786467\pi\) | |||||||
\(312\) | 9.56284 | 0.541389 | ||||||||
\(313\) | −7.43171 | −0.420065 | −0.210032 | − | 0.977694i | \(-0.567357\pi\) | ||||
−0.210032 | + | 0.977694i | \(0.567357\pi\) | |||||||
\(314\) | −30.3114 | −1.71057 | ||||||||
\(315\) | −12.7399 | −0.717814 | ||||||||
\(316\) | 30.0759 | 1.69190 | ||||||||
\(317\) | 12.9504 | 0.727365 | 0.363682 | − | 0.931523i | \(-0.381519\pi\) | ||||
0.363682 | + | 0.931523i | \(0.381519\pi\) | |||||||
\(318\) | 1.91759 | 0.107533 | ||||||||
\(319\) | 31.2533 | 1.74985 | ||||||||
\(320\) | −59.0910 | −3.30329 | ||||||||
\(321\) | 20.3977 | 1.13849 | ||||||||
\(322\) | 20.9063 | 1.16506 | ||||||||
\(323\) | −9.07549 | −0.504974 | ||||||||
\(324\) | −7.80309 | −0.433505 | ||||||||
\(325\) | 10.7882 | 0.598421 | ||||||||
\(326\) | 11.5657 | 0.640567 | ||||||||
\(327\) | −19.5971 | −1.08372 | ||||||||
\(328\) | −83.5699 | −4.61437 | ||||||||
\(329\) | −2.17614 | −0.119974 | ||||||||
\(330\) | −38.0686 | −2.09561 | ||||||||
\(331\) | 8.48585 | 0.466424 | 0.233212 | − | 0.972426i | \(-0.425076\pi\) | ||||
0.233212 | + | 0.972426i | \(0.425076\pi\) | |||||||
\(332\) | 41.7965 | 2.29388 | ||||||||
\(333\) | 16.8165 | 0.921537 | ||||||||
\(334\) | −47.0766 | −2.57592 | ||||||||
\(335\) | 22.5851 | 1.23396 | ||||||||
\(336\) | 26.7955 | 1.46182 | ||||||||
\(337\) | 9.07019 | 0.494085 | 0.247042 | − | 0.969005i | \(-0.420541\pi\) | ||||
0.247042 | + | 0.969005i | \(0.420541\pi\) | |||||||
\(338\) | −2.65690 | −0.144516 | ||||||||
\(339\) | 0.514423 | 0.0279396 | ||||||||
\(340\) | −97.0684 | −5.26427 | ||||||||
\(341\) | 6.00960 | 0.325438 | ||||||||
\(342\) | −8.06810 | −0.436273 | ||||||||
\(343\) | 19.9674 | 1.07814 | ||||||||
\(344\) | −78.5819 | −4.23685 | ||||||||
\(345\) | 18.5372 | 0.998007 | ||||||||
\(346\) | −69.2082 | −3.72066 | ||||||||
\(347\) | −10.3017 | −0.553022 | −0.276511 | − | 0.961011i | \(-0.589178\pi\) | ||||
−0.276511 | + | 0.961011i | \(0.589178\pi\) | |||||||
\(348\) | −60.6980 | −3.25376 | ||||||||
\(349\) | 12.8012 | 0.685234 | 0.342617 | − | 0.939475i | \(-0.388687\pi\) | ||||
0.342617 | + | 0.939475i | \(0.388687\pi\) | |||||||
\(350\) | 56.8804 | 3.04039 | ||||||||
\(351\) | 5.43066 | 0.289867 | ||||||||
\(352\) | −43.6323 | −2.32561 | ||||||||
\(353\) | −3.02271 | −0.160882 | −0.0804412 | − | 0.996759i | \(-0.525633\pi\) | ||||
−0.0804412 | + | 0.996759i | \(0.525633\pi\) | |||||||
\(354\) | 27.4708 | 1.46006 | ||||||||
\(355\) | −5.80951 | −0.308337 | ||||||||
\(356\) | −0.0625176 | −0.00331342 | ||||||||
\(357\) | 11.2743 | 0.596699 | ||||||||
\(358\) | −42.0632 | −2.22311 | ||||||||
\(359\) | 35.4670 | 1.87188 | 0.935938 | − | 0.352163i | \(-0.114554\pi\) | ||||
0.935938 | + | 0.352163i | \(0.114554\pi\) | |||||||
\(360\) | −52.1796 | −2.75011 | ||||||||
\(361\) | −15.4676 | −0.814085 | ||||||||
\(362\) | −2.56694 | −0.134915 | ||||||||
\(363\) | 1.89029 | 0.0992146 | ||||||||
\(364\) | −10.0395 | −0.526215 | ||||||||
\(365\) | 48.3078 | 2.52854 | ||||||||
\(366\) | 9.67182 | 0.505554 | ||||||||
\(367\) | −13.3714 | −0.697983 | −0.348992 | − | 0.937126i | \(-0.613476\pi\) | ||||
−0.348992 | + | 0.937126i | \(0.613476\pi\) | |||||||
\(368\) | 45.5063 | 2.37218 | ||||||||
\(369\) | −16.6127 | −0.864821 | ||||||||
\(370\) | −109.879 | −5.71233 | ||||||||
\(371\) | −1.21732 | −0.0632001 | ||||||||
\(372\) | −11.6714 | −0.605136 | ||||||||
\(373\) | 16.1585 | 0.836657 | 0.418328 | − | 0.908296i | \(-0.362616\pi\) | ||||
0.418328 | + | 0.908296i | \(0.362616\pi\) | |||||||
\(374\) | −39.3208 | −2.03323 | ||||||||
\(375\) | 27.0597 | 1.39736 | ||||||||
\(376\) | −8.91291 | −0.459648 | ||||||||
\(377\) | 10.1973 | 0.525188 | ||||||||
\(378\) | 28.6330 | 1.47272 | ||||||||
\(379\) | −5.71821 | −0.293725 | −0.146862 | − | 0.989157i | \(-0.546917\pi\) | ||||
−0.146862 | + | 0.989157i | \(0.546917\pi\) | |||||||
\(380\) | 37.7812 | 1.93813 | ||||||||
\(381\) | 13.0004 | 0.666031 | ||||||||
\(382\) | −64.0203 | −3.27556 | ||||||||
\(383\) | −26.2662 | −1.34214 | −0.671069 | − | 0.741394i | \(-0.734165\pi\) | ||||
−0.671069 | + | 0.741394i | \(0.734165\pi\) | |||||||
\(384\) | 12.9886 | 0.662824 | ||||||||
\(385\) | 24.1666 | 1.23164 | ||||||||
\(386\) | −56.7618 | −2.88910 | ||||||||
\(387\) | −15.6211 | −0.794066 | ||||||||
\(388\) | 47.6641 | 2.41978 | ||||||||
\(389\) | 30.3037 | 1.53646 | 0.768230 | − | 0.640174i | \(-0.221138\pi\) | ||||
0.768230 | + | 0.640174i | \(0.221138\pi\) | |||||||
\(390\) | −12.4210 | −0.628961 | ||||||||
\(391\) | 19.1469 | 0.968301 | ||||||||
\(392\) | 24.8872 | 1.25699 | ||||||||
\(393\) | 10.6047 | 0.534938 | ||||||||
\(394\) | −29.4719 | −1.48477 | ||||||||
\(395\) | −23.6216 | −1.18853 | ||||||||
\(396\) | −25.0523 | −1.25893 | ||||||||
\(397\) | 8.20491 | 0.411793 | 0.205896 | − | 0.978574i | \(-0.433989\pi\) | ||||
0.205896 | + | 0.978574i | \(0.433989\pi\) | |||||||
\(398\) | −18.6804 | −0.936365 | ||||||||
\(399\) | −4.38820 | −0.219685 | ||||||||
\(400\) | 123.811 | 6.19053 | ||||||||
\(401\) | −26.7591 | −1.33628 | −0.668142 | − | 0.744034i | \(-0.732910\pi\) | ||||
−0.668142 | + | 0.744034i | \(0.732910\pi\) | |||||||
\(402\) | −17.7683 | −0.886201 | ||||||||
\(403\) | 1.96081 | 0.0976748 | ||||||||
\(404\) | −55.0809 | −2.74038 | ||||||||
\(405\) | 6.12855 | 0.304530 | ||||||||
\(406\) | 53.7650 | 2.66831 | ||||||||
\(407\) | −31.8995 | −1.58120 | ||||||||
\(408\) | 46.1767 | 2.28609 | ||||||||
\(409\) | −32.1955 | −1.59197 | −0.795983 | − | 0.605320i | \(-0.793045\pi\) | ||||
−0.795983 | + | 0.605320i | \(0.793045\pi\) | |||||||
\(410\) | 108.547 | 5.36077 | ||||||||
\(411\) | 19.9167 | 0.982420 | ||||||||
\(412\) | 10.7380 | 0.529024 | ||||||||
\(413\) | −17.4390 | −0.858116 | ||||||||
\(414\) | 17.0216 | 0.836566 | ||||||||
\(415\) | −32.8270 | −1.61141 | ||||||||
\(416\) | −14.2363 | −0.697993 | ||||||||
\(417\) | 8.27229 | 0.405096 | ||||||||
\(418\) | 15.3045 | 0.748569 | ||||||||
\(419\) | −20.5499 | −1.00393 | −0.501963 | − | 0.864889i | \(-0.667389\pi\) | ||||
−0.501963 | + | 0.864889i | \(0.667389\pi\) | |||||||
\(420\) | −46.9348 | −2.29018 | ||||||||
\(421\) | −5.75164 | −0.280318 | −0.140159 | − | 0.990129i | \(-0.544761\pi\) | ||||
−0.140159 | + | 0.990129i | \(0.544761\pi\) | |||||||
\(422\) | −16.8333 | −0.819430 | ||||||||
\(423\) | −1.77178 | −0.0861468 | ||||||||
\(424\) | −4.98584 | −0.242134 | ||||||||
\(425\) | 52.0937 | 2.52691 | ||||||||
\(426\) | 4.57050 | 0.221441 | ||||||||
\(427\) | −6.13984 | −0.297128 | ||||||||
\(428\) | −87.7086 | −4.23956 | ||||||||
\(429\) | −3.60599 | −0.174099 | ||||||||
\(430\) | 102.068 | 4.92218 | ||||||||
\(431\) | 26.1633 | 1.26024 | 0.630122 | − | 0.776496i | \(-0.283005\pi\) | ||||
0.630122 | + | 0.776496i | \(0.283005\pi\) | |||||||
\(432\) | 62.3249 | 2.99861 | ||||||||
\(433\) | −0.476113 | −0.0228805 | −0.0114403 | − | 0.999935i | \(-0.503642\pi\) | ||||
−0.0114403 | + | 0.999935i | \(0.503642\pi\) | |||||||
\(434\) | 10.3383 | 0.496254 | ||||||||
\(435\) | 47.6722 | 2.28571 | ||||||||
\(436\) | 84.2661 | 4.03562 | ||||||||
\(437\) | −7.45241 | −0.356497 | ||||||||
\(438\) | −38.0050 | −1.81595 | ||||||||
\(439\) | 15.3683 | 0.733489 | 0.366744 | − | 0.930322i | \(-0.380472\pi\) | ||||
0.366744 | + | 0.930322i | \(0.380472\pi\) | |||||||
\(440\) | 98.9805 | 4.71871 | ||||||||
\(441\) | 4.94726 | 0.235584 | ||||||||
\(442\) | −12.8296 | −0.610240 | ||||||||
\(443\) | −6.57632 | −0.312451 | −0.156225 | − | 0.987721i | \(-0.549933\pi\) | ||||
−0.156225 | + | 0.987721i | \(0.549933\pi\) | |||||||
\(444\) | 61.9530 | 2.94016 | ||||||||
\(445\) | 0.0491013 | 0.00232762 | ||||||||
\(446\) | 46.1298 | 2.18431 | ||||||||
\(447\) | −14.3693 | −0.679643 | ||||||||
\(448\) | −29.5117 | −1.39430 | ||||||||
\(449\) | −14.9077 | −0.703537 | −0.351768 | − | 0.936087i | \(-0.614420\pi\) | ||||
−0.351768 | + | 0.936087i | \(0.614420\pi\) | |||||||
\(450\) | 46.3112 | 2.18313 | ||||||||
\(451\) | 31.5129 | 1.48388 | ||||||||
\(452\) | −2.21198 | −0.104043 | ||||||||
\(453\) | −4.31386 | −0.202683 | ||||||||
\(454\) | 1.26447 | 0.0593444 | ||||||||
\(455\) | 7.88506 | 0.369657 | ||||||||
\(456\) | −17.9730 | −0.841663 | ||||||||
\(457\) | −15.8093 | −0.739530 | −0.369765 | − | 0.929125i | \(-0.620562\pi\) | ||||
−0.369765 | + | 0.929125i | \(0.620562\pi\) | |||||||
\(458\) | 64.1851 | 2.99917 | ||||||||
\(459\) | 26.2234 | 1.22400 | ||||||||
\(460\) | −79.7084 | −3.71643 | ||||||||
\(461\) | −12.1802 | −0.567288 | −0.283644 | − | 0.958930i | \(-0.591543\pi\) | ||||
−0.283644 | + | 0.958930i | \(0.591543\pi\) | |||||||
\(462\) | −19.0125 | −0.884542 | ||||||||
\(463\) | −1.00000 | −0.0464739 | ||||||||
\(464\) | 117.029 | 5.43294 | ||||||||
\(465\) | 9.16675 | 0.425098 | ||||||||
\(466\) | 19.2846 | 0.893342 | ||||||||
\(467\) | 12.0447 | 0.557362 | 0.278681 | − | 0.960384i | \(-0.410103\pi\) | ||||
0.278681 | + | 0.960384i | \(0.410103\pi\) | |||||||
\(468\) | −8.17405 | −0.377846 | ||||||||
\(469\) | 11.2796 | 0.520845 | ||||||||
\(470\) | 11.5768 | 0.533998 | ||||||||
\(471\) | −13.4229 | −0.618493 | ||||||||
\(472\) | −71.4257 | −3.28764 | ||||||||
\(473\) | 29.6320 | 1.36248 | ||||||||
\(474\) | 18.5837 | 0.853580 | ||||||||
\(475\) | −20.2760 | −0.930327 | ||||||||
\(476\) | −48.4786 | −2.22201 | ||||||||
\(477\) | −0.991124 | −0.0453805 | ||||||||
\(478\) | −48.5599 | −2.22108 | ||||||||
\(479\) | 27.4121 | 1.25249 | 0.626245 | − | 0.779626i | \(-0.284591\pi\) | ||||
0.626245 | + | 0.779626i | \(0.284591\pi\) | |||||||
\(480\) | −66.5546 | −3.03779 | ||||||||
\(481\) | −10.4081 | −0.474570 | ||||||||
\(482\) | −65.5019 | −2.98353 | ||||||||
\(483\) | 9.25797 | 0.421252 | ||||||||
\(484\) | −8.12812 | −0.369460 | ||||||||
\(485\) | −37.4354 | −1.69985 | ||||||||
\(486\) | 38.4647 | 1.74479 | ||||||||
\(487\) | 25.6063 | 1.16033 | 0.580166 | − | 0.814498i | \(-0.302988\pi\) | ||||
0.580166 | + | 0.814498i | \(0.302988\pi\) | |||||||
\(488\) | −25.1473 | −1.13836 | ||||||||
\(489\) | 5.12168 | 0.231610 | ||||||||
\(490\) | −32.3254 | −1.46031 | ||||||||
\(491\) | 27.1838 | 1.22679 | 0.613393 | − | 0.789778i | \(-0.289804\pi\) | ||||
0.613393 | + | 0.789778i | \(0.289804\pi\) | |||||||
\(492\) | −61.2022 | −2.75921 | ||||||||
\(493\) | 49.2404 | 2.21767 | ||||||||
\(494\) | 4.99355 | 0.224670 | ||||||||
\(495\) | 19.6761 | 0.884375 | ||||||||
\(496\) | 22.5032 | 1.01042 | ||||||||
\(497\) | −2.90143 | −0.130147 | ||||||||
\(498\) | 25.8258 | 1.15728 | ||||||||
\(499\) | 24.7709 | 1.10890 | 0.554449 | − | 0.832218i | \(-0.312929\pi\) | ||||
0.554449 | + | 0.832218i | \(0.312929\pi\) | |||||||
\(500\) | −116.355 | −5.20355 | ||||||||
\(501\) | −20.8470 | −0.931376 | ||||||||
\(502\) | 40.1008 | 1.78979 | ||||||||
\(503\) | 2.17207 | 0.0968480 | 0.0484240 | − | 0.998827i | \(-0.484580\pi\) | ||||
0.0484240 | + | 0.998827i | \(0.484580\pi\) | |||||||
\(504\) | −26.0599 | −1.16080 | ||||||||
\(505\) | 43.2606 | 1.92507 | ||||||||
\(506\) | −32.2886 | −1.43540 | ||||||||
\(507\) | −1.17656 | −0.0522529 | ||||||||
\(508\) | −55.9008 | −2.48020 | ||||||||
\(509\) | 20.5415 | 0.910485 | 0.455243 | − | 0.890367i | \(-0.349552\pi\) | ||||
0.455243 | + | 0.890367i | \(0.349552\pi\) | |||||||
\(510\) | −59.9780 | −2.65587 | ||||||||
\(511\) | 24.1262 | 1.06728 | ||||||||
\(512\) | 23.1741 | 1.02416 | ||||||||
\(513\) | −10.2067 | −0.450638 | ||||||||
\(514\) | 26.2902 | 1.15961 | ||||||||
\(515\) | −8.43363 | −0.371630 | ||||||||
\(516\) | −57.5492 | −2.53346 | ||||||||
\(517\) | 3.36092 | 0.147813 | ||||||||
\(518\) | −54.8766 | −2.41114 | ||||||||
\(519\) | −30.6476 | −1.34528 | ||||||||
\(520\) | 32.2953 | 1.41624 | ||||||||
\(521\) | −32.8503 | −1.43920 | −0.719598 | − | 0.694391i | \(-0.755674\pi\) | ||||
−0.719598 | + | 0.694391i | \(0.755674\pi\) | |||||||
\(522\) | 43.7746 | 1.91596 | ||||||||
\(523\) | 36.4545 | 1.59404 | 0.797022 | − | 0.603950i | \(-0.206407\pi\) | ||||
0.797022 | + | 0.603950i | \(0.206407\pi\) | |||||||
\(524\) | −45.5996 | −1.99203 | ||||||||
\(525\) | 25.1885 | 1.09932 | ||||||||
\(526\) | 40.2479 | 1.75489 | ||||||||
\(527\) | 9.46828 | 0.412445 | ||||||||
\(528\) | −41.3842 | −1.80101 | ||||||||
\(529\) | −7.27736 | −0.316407 | ||||||||
\(530\) | 6.47601 | 0.281300 | ||||||||
\(531\) | −14.1986 | −0.616165 | ||||||||
\(532\) | 18.8690 | 0.818073 | ||||||||
\(533\) | 10.2820 | 0.445362 | ||||||||
\(534\) | −0.0386293 | −0.00167165 | ||||||||
\(535\) | 68.8864 | 2.97822 | ||||||||
\(536\) | 46.1985 | 1.99547 | ||||||||
\(537\) | −18.6269 | −0.803812 | ||||||||
\(538\) | −8.28095 | −0.357017 | ||||||||
\(539\) | −9.38455 | −0.404221 | ||||||||
\(540\) | −109.168 | −4.69783 | ||||||||
\(541\) | 45.1577 | 1.94148 | 0.970740 | − | 0.240132i | \(-0.0771906\pi\) | ||||
0.970740 | + | 0.240132i | \(0.0771906\pi\) | |||||||
\(542\) | 33.0982 | 1.42169 | ||||||||
\(543\) | −1.13672 | −0.0487814 | ||||||||
\(544\) | −68.7438 | −2.94737 | ||||||||
\(545\) | −66.1826 | −2.83495 | ||||||||
\(546\) | −6.20338 | −0.265480 | ||||||||
\(547\) | −41.7375 | −1.78456 | −0.892282 | − | 0.451478i | \(-0.850897\pi\) | ||||
−0.892282 | + | 0.451478i | \(0.850897\pi\) | |||||||
\(548\) | −85.6405 | −3.65838 | ||||||||
\(549\) | −4.99897 | −0.213351 | ||||||||
\(550\) | −87.8486 | −3.74588 | ||||||||
\(551\) | −19.1654 | −0.816475 | ||||||||
\(552\) | 37.9184 | 1.61391 | ||||||||
\(553\) | −11.7973 | −0.501672 | ||||||||
\(554\) | 37.1044 | 1.57641 | ||||||||
\(555\) | −48.6579 | −2.06541 | ||||||||
\(556\) | −35.5702 | −1.50851 | ||||||||
\(557\) | 28.1938 | 1.19461 | 0.597306 | − | 0.802014i | \(-0.296238\pi\) | ||||
0.597306 | + | 0.802014i | \(0.296238\pi\) | |||||||
\(558\) | 8.41730 | 0.356333 | ||||||||
\(559\) | 9.66829 | 0.408925 | ||||||||
\(560\) | 90.4928 | 3.82402 | ||||||||
\(561\) | −17.4125 | −0.735156 | ||||||||
\(562\) | 36.8840 | 1.55586 | ||||||||
\(563\) | 10.5047 | 0.442722 | 0.221361 | − | 0.975192i | \(-0.428950\pi\) | ||||
0.221361 | + | 0.975192i | \(0.428950\pi\) | |||||||
\(564\) | −6.52735 | −0.274851 | ||||||||
\(565\) | 1.73729 | 0.0730884 | ||||||||
\(566\) | −54.2845 | −2.28175 | ||||||||
\(567\) | 3.06077 | 0.128540 | ||||||||
\(568\) | −11.8835 | −0.498623 | ||||||||
\(569\) | −34.5144 | −1.44692 | −0.723459 | − | 0.690367i | \(-0.757449\pi\) | ||||
−0.723459 | + | 0.690367i | \(0.757449\pi\) | |||||||
\(570\) | 23.3448 | 0.977805 | ||||||||
\(571\) | −17.5453 | −0.734247 | −0.367123 | − | 0.930172i | \(-0.619657\pi\) | ||||
−0.367123 | + | 0.930172i | \(0.619657\pi\) | |||||||
\(572\) | 15.5055 | 0.648318 | ||||||||
\(573\) | −28.3502 | −1.18435 | ||||||||
\(574\) | 54.2115 | 2.26274 | ||||||||
\(575\) | 42.7771 | 1.78393 | ||||||||
\(576\) | −24.0280 | −1.00117 | ||||||||
\(577\) | −15.2246 | −0.633810 | −0.316905 | − | 0.948457i | \(-0.602644\pi\) | ||||
−0.316905 | + | 0.948457i | \(0.602644\pi\) | |||||||
\(578\) | −16.7836 | −0.698105 | ||||||||
\(579\) | −25.1359 | −1.04461 | ||||||||
\(580\) | −204.987 | −8.51163 | ||||||||
\(581\) | −16.3947 | −0.680166 | ||||||||
\(582\) | 29.4514 | 1.22080 | ||||||||
\(583\) | 1.88008 | 0.0778650 | ||||||||
\(584\) | 98.8151 | 4.08900 | ||||||||
\(585\) | 6.41990 | 0.265430 | ||||||||
\(586\) | 90.0732 | 3.72089 | ||||||||
\(587\) | −10.8413 | −0.447468 | −0.223734 | − | 0.974650i | \(-0.571825\pi\) | ||||
−0.223734 | + | 0.974650i | \(0.571825\pi\) | |||||||
\(588\) | 18.2260 | 0.751629 | ||||||||
\(589\) | −3.68527 | −0.151849 | ||||||||
\(590\) | 92.7735 | 3.81942 | ||||||||
\(591\) | −13.0511 | −0.536850 | ||||||||
\(592\) | −119.449 | −4.90931 | ||||||||
\(593\) | 8.07669 | 0.331670 | 0.165835 | − | 0.986154i | \(-0.446968\pi\) | ||||
0.165835 | + | 0.986154i | \(0.446968\pi\) | |||||||
\(594\) | −44.2220 | −1.81445 | ||||||||
\(595\) | 38.0751 | 1.56093 | ||||||||
\(596\) | 61.7868 | 2.53089 | ||||||||
\(597\) | −8.27229 | −0.338562 | ||||||||
\(598\) | −10.5351 | −0.430812 | ||||||||
\(599\) | −8.26183 | −0.337569 | −0.168785 | − | 0.985653i | \(-0.553984\pi\) | ||||
−0.168785 | + | 0.985653i | \(0.553984\pi\) | |||||||
\(600\) | 103.166 | 4.21172 | ||||||||
\(601\) | 7.32359 | 0.298736 | 0.149368 | − | 0.988782i | \(-0.452276\pi\) | ||||
0.149368 | + | 0.988782i | \(0.452276\pi\) | |||||||
\(602\) | 50.9758 | 2.07762 | ||||||||
\(603\) | 9.18371 | 0.373989 | ||||||||
\(604\) | 18.5493 | 0.754760 | ||||||||
\(605\) | 6.38382 | 0.259539 | ||||||||
\(606\) | −34.0342 | −1.38255 | ||||||||
\(607\) | 25.9269 | 1.05234 | 0.526170 | − | 0.850380i | \(-0.323628\pi\) | ||||
0.526170 | + | 0.850380i | \(0.323628\pi\) | |||||||
\(608\) | 26.7566 | 1.08512 | ||||||||
\(609\) | 23.8088 | 0.964783 | ||||||||
\(610\) | 32.6633 | 1.32250 | ||||||||
\(611\) | 1.09660 | 0.0443636 | ||||||||
\(612\) | −39.4706 | −1.59550 | ||||||||
\(613\) | −5.12832 | −0.207131 | −0.103565 | − | 0.994623i | \(-0.533025\pi\) | ||||
−0.103565 | + | 0.994623i | \(0.533025\pi\) | |||||||
\(614\) | 24.7678 | 0.999548 | ||||||||
\(615\) | 48.0682 | 1.93830 | ||||||||
\(616\) | 49.4336 | 1.99174 | ||||||||
\(617\) | 22.5852 | 0.909246 | 0.454623 | − | 0.890684i | \(-0.349774\pi\) | ||||
0.454623 | + | 0.890684i | \(0.349774\pi\) | |||||||
\(618\) | 6.63496 | 0.266897 | ||||||||
\(619\) | 44.6843 | 1.79601 | 0.898007 | − | 0.439982i | \(-0.145015\pi\) | ||||
0.898007 | + | 0.439982i | \(0.145015\pi\) | |||||||
\(620\) | −39.4164 | −1.58300 | ||||||||
\(621\) | 21.5335 | 0.864110 | ||||||||
\(622\) | 73.4034 | 2.94321 | ||||||||
\(623\) | 0.0245225 | 0.000982475 0 | ||||||||
\(624\) | −13.5028 | −0.540544 | ||||||||
\(625\) | 37.4442 | 1.49777 | ||||||||
\(626\) | 19.7453 | 0.789181 | ||||||||
\(627\) | 6.77733 | 0.270661 | ||||||||
\(628\) | 57.7173 | 2.30317 | ||||||||
\(629\) | −50.2584 | −2.00393 | ||||||||
\(630\) | 33.8487 | 1.34857 | ||||||||
\(631\) | 1.04529 | 0.0416123 | 0.0208062 | − | 0.999784i | \(-0.493377\pi\) | ||||
0.0208062 | + | 0.999784i | \(0.493377\pi\) | |||||||
\(632\) | −48.3188 | −1.92202 | ||||||||
\(633\) | −7.45430 | −0.296282 | ||||||||
\(634\) | −34.4078 | −1.36651 | ||||||||
\(635\) | 43.9045 | 1.74230 | ||||||||
\(636\) | −3.65137 | −0.144786 | ||||||||
\(637\) | −3.06198 | −0.121320 | ||||||||
\(638\) | −83.0369 | −3.28746 | ||||||||
\(639\) | −2.36230 | −0.0934513 | ||||||||
\(640\) | 43.8648 | 1.73391 | ||||||||
\(641\) | 24.0903 | 0.951512 | 0.475756 | − | 0.879577i | \(-0.342175\pi\) | ||||
0.475756 | + | 0.879577i | \(0.342175\pi\) | |||||||
\(642\) | −54.1947 | −2.13889 | ||||||||
\(643\) | −11.5578 | −0.455797 | −0.227899 | − | 0.973685i | \(-0.573185\pi\) | ||||
−0.227899 | + | 0.973685i | \(0.573185\pi\) | |||||||
\(644\) | −39.8086 | −1.56868 | ||||||||
\(645\) | 45.1992 | 1.77972 | ||||||||
\(646\) | 24.1127 | 0.948700 | ||||||||
\(647\) | 39.6724 | 1.55968 | 0.779841 | − | 0.625978i | \(-0.215300\pi\) | ||||
0.779841 | + | 0.625978i | \(0.215300\pi\) | |||||||
\(648\) | 12.5361 | 0.492466 | ||||||||
\(649\) | 26.9335 | 1.05723 | ||||||||
\(650\) | −28.6632 | −1.12426 | ||||||||
\(651\) | 4.57813 | 0.179431 | ||||||||
\(652\) | −22.0228 | −0.862481 | ||||||||
\(653\) | 7.02959 | 0.275089 | 0.137545 | − | 0.990496i | \(-0.456079\pi\) | ||||
0.137545 | + | 0.990496i | \(0.456079\pi\) | |||||||
\(654\) | 52.0676 | 2.03600 | ||||||||
\(655\) | 35.8139 | 1.39937 | ||||||||
\(656\) | 118.001 | 4.60717 | ||||||||
\(657\) | 19.6432 | 0.766355 | ||||||||
\(658\) | 5.78178 | 0.225397 | ||||||||
\(659\) | 9.20097 | 0.358419 | 0.179210 | − | 0.983811i | \(-0.442646\pi\) | ||||
0.179210 | + | 0.983811i | \(0.442646\pi\) | |||||||
\(660\) | 72.4881 | 2.82160 | ||||||||
\(661\) | 40.8089 | 1.58728 | 0.793642 | − | 0.608385i | \(-0.208182\pi\) | ||||
0.793642 | + | 0.608385i | \(0.208182\pi\) | |||||||
\(662\) | −22.5461 | −0.876277 | ||||||||
\(663\) | −5.68133 | −0.220645 | ||||||||
\(664\) | −67.1486 | −2.60587 | ||||||||
\(665\) | −14.8197 | −0.574683 | ||||||||
\(666\) | −44.6797 | −1.73130 | ||||||||
\(667\) | 40.4341 | 1.56561 | ||||||||
\(668\) | 89.6407 | 3.46830 | ||||||||
\(669\) | 20.4277 | 0.789781 | ||||||||
\(670\) | −60.0064 | −2.31825 | ||||||||
\(671\) | 9.48264 | 0.366073 | ||||||||
\(672\) | −33.2392 | −1.28223 | ||||||||
\(673\) | −40.7545 | −1.57097 | −0.785486 | − | 0.618880i | \(-0.787587\pi\) | ||||
−0.785486 | + | 0.618880i | \(0.787587\pi\) | |||||||
\(674\) | −24.0986 | −0.928244 | ||||||||
\(675\) | 58.5870 | 2.25501 | ||||||||
\(676\) | 5.05912 | 0.194582 | ||||||||
\(677\) | 25.4388 | 0.977693 | 0.488847 | − | 0.872370i | \(-0.337418\pi\) | ||||
0.488847 | + | 0.872370i | \(0.337418\pi\) | |||||||
\(678\) | −1.36677 | −0.0524906 | ||||||||
\(679\) | −18.6963 | −0.717497 | ||||||||
\(680\) | 155.946 | 5.98026 | ||||||||
\(681\) | 0.559946 | 0.0214572 | ||||||||
\(682\) | −15.9669 | −0.611405 | ||||||||
\(683\) | −43.6830 | −1.67148 | −0.835742 | − | 0.549123i | \(-0.814962\pi\) | ||||
−0.835742 | + | 0.549123i | \(0.814962\pi\) | |||||||
\(684\) | 15.3628 | 0.587413 | ||||||||
\(685\) | 67.2621 | 2.56995 | ||||||||
\(686\) | −53.0515 | −2.02552 | ||||||||
\(687\) | 28.4232 | 1.08441 | ||||||||
\(688\) | 110.958 | 4.23024 | ||||||||
\(689\) | 0.613431 | 0.0233699 | ||||||||
\(690\) | −49.2514 | −1.87497 | ||||||||
\(691\) | −21.0404 | −0.800416 | −0.400208 | − | 0.916424i | \(-0.631062\pi\) | ||||
−0.400208 | + | 0.916424i | \(0.631062\pi\) | |||||||
\(692\) | 131.782 | 5.00962 | ||||||||
\(693\) | 9.82679 | 0.373289 | ||||||||
\(694\) | 27.3705 | 1.03897 | ||||||||
\(695\) | 27.9369 | 1.05971 | ||||||||
\(696\) | 97.5151 | 3.69630 | ||||||||
\(697\) | 49.6493 | 1.88060 | ||||||||
\(698\) | −34.0116 | −1.28736 | ||||||||
\(699\) | 8.53984 | 0.323006 | ||||||||
\(700\) | −108.309 | −4.09368 | ||||||||
\(701\) | 9.87176 | 0.372851 | 0.186426 | − | 0.982469i | \(-0.440310\pi\) | ||||
0.186426 | + | 0.982469i | \(0.440310\pi\) | |||||||
\(702\) | −14.4287 | −0.544577 | ||||||||
\(703\) | 19.5617 | 0.737783 | ||||||||
\(704\) | 45.5791 | 1.71783 | ||||||||
\(705\) | 5.12658 | 0.193078 | ||||||||
\(706\) | 8.03103 | 0.302252 | ||||||||
\(707\) | 21.6055 | 0.812559 | ||||||||
\(708\) | −52.3084 | −1.96587 | ||||||||
\(709\) | −37.2705 | −1.39972 | −0.699862 | − | 0.714278i | \(-0.746755\pi\) | ||||
−0.699862 | + | 0.714278i | \(0.746755\pi\) | |||||||
\(710\) | 15.4353 | 0.579277 | ||||||||
\(711\) | −9.60518 | −0.360223 | ||||||||
\(712\) | 0.100438 | 0.00376408 | ||||||||
\(713\) | 7.77495 | 0.291174 | ||||||||
\(714\) | −29.9547 | −1.12103 | ||||||||
\(715\) | −12.1780 | −0.455433 | ||||||||
\(716\) | 80.0945 | 2.99327 | ||||||||
\(717\) | −21.5039 | −0.803077 | ||||||||
\(718\) | −94.2323 | −3.51672 | ||||||||
\(719\) | −34.9981 | −1.30521 | −0.652604 | − | 0.757699i | \(-0.726324\pi\) | ||||
−0.652604 | + | 0.757699i | \(0.726324\pi\) | |||||||
\(720\) | 73.6779 | 2.74581 | ||||||||
\(721\) | −4.21199 | −0.156863 | ||||||||
\(722\) | 41.0959 | 1.52943 | ||||||||
\(723\) | −29.0063 | −1.07876 | ||||||||
\(724\) | 4.88782 | 0.181654 | ||||||||
\(725\) | 110.010 | 4.08568 | ||||||||
\(726\) | −5.02232 | −0.186396 | ||||||||
\(727\) | 17.3768 | 0.644468 | 0.322234 | − | 0.946660i | \(-0.395566\pi\) | ||||
0.322234 | + | 0.946660i | \(0.395566\pi\) | |||||||
\(728\) | 16.1291 | 0.597786 | ||||||||
\(729\) | 21.6605 | 0.802241 | ||||||||
\(730\) | −128.349 | −4.75041 | ||||||||
\(731\) | 46.6859 | 1.72674 | ||||||||
\(732\) | −18.4165 | −0.680695 | ||||||||
\(733\) | −30.5994 | −1.13021 | −0.565107 | − | 0.825017i | \(-0.691165\pi\) | ||||
−0.565107 | + | 0.825017i | \(0.691165\pi\) | |||||||
\(734\) | 35.5266 | 1.31131 | ||||||||
\(735\) | −14.3147 | −0.528007 | ||||||||
\(736\) | −56.4495 | −2.08076 | ||||||||
\(737\) | −17.4207 | −0.641701 | ||||||||
\(738\) | 44.1382 | 1.62475 | ||||||||
\(739\) | 28.2850 | 1.04048 | 0.520241 | − | 0.854020i | \(-0.325842\pi\) | ||||
0.520241 | + | 0.854020i | \(0.325842\pi\) | |||||||
\(740\) | 209.225 | 7.69128 | ||||||||
\(741\) | 2.21130 | 0.0812342 | ||||||||
\(742\) | 3.23430 | 0.118735 | ||||||||
\(743\) | −23.3959 | −0.858311 | −0.429155 | − | 0.903231i | \(-0.641189\pi\) | ||||
−0.429155 | + | 0.903231i | \(0.641189\pi\) | |||||||
\(744\) | 18.7509 | 0.687441 | ||||||||
\(745\) | −48.5274 | −1.77790 | ||||||||
\(746\) | −42.9316 | −1.57184 | ||||||||
\(747\) | −13.3483 | −0.488389 | ||||||||
\(748\) | 74.8725 | 2.73761 | ||||||||
\(749\) | 34.4037 | 1.25709 | ||||||||
\(750\) | −71.8951 | −2.62524 | ||||||||
\(751\) | 49.0605 | 1.79024 | 0.895122 | − | 0.445822i | \(-0.147088\pi\) | ||||
0.895122 | + | 0.445822i | \(0.147088\pi\) | |||||||
\(752\) | 12.5851 | 0.458931 | ||||||||
\(753\) | 17.7579 | 0.647134 | ||||||||
\(754\) | −27.0932 | −0.986677 | ||||||||
\(755\) | −14.5686 | −0.530206 | ||||||||
\(756\) | −54.5213 | −1.98292 | ||||||||
\(757\) | −11.0993 | −0.403412 | −0.201706 | − | 0.979446i | \(-0.564649\pi\) | ||||
−0.201706 | + | 0.979446i | \(0.564649\pi\) | |||||||
\(758\) | 15.1927 | 0.551825 | ||||||||
\(759\) | −14.2984 | −0.518999 | ||||||||
\(760\) | −60.6978 | −2.20174 | ||||||||
\(761\) | −6.43818 | −0.233384 | −0.116692 | − | 0.993168i | \(-0.537229\pi\) | ||||
−0.116692 | + | 0.993168i | \(0.537229\pi\) | |||||||
\(762\) | −34.5408 | −1.25128 | ||||||||
\(763\) | −33.0534 | −1.19661 | ||||||||
\(764\) | 121.904 | 4.41033 | ||||||||
\(765\) | 31.0002 | 1.12081 | ||||||||
\(766\) | 69.7866 | 2.52149 | ||||||||
\(767\) | 8.78784 | 0.317310 | ||||||||
\(768\) | 0.484927 | 0.0174983 | ||||||||
\(769\) | 13.2246 | 0.476892 | 0.238446 | − | 0.971156i | \(-0.423362\pi\) | ||||
0.238446 | + | 0.971156i | \(0.423362\pi\) | |||||||
\(770\) | −64.2083 | −2.31391 | ||||||||
\(771\) | 11.6421 | 0.419281 | ||||||||
\(772\) | 108.083 | 3.88998 | ||||||||
\(773\) | −17.4756 | −0.628553 | −0.314276 | − | 0.949332i | \(-0.601762\pi\) | ||||
−0.314276 | + | 0.949332i | \(0.601762\pi\) | |||||||
\(774\) | 41.5038 | 1.49182 | ||||||||
\(775\) | 21.1536 | 0.759859 | ||||||||
\(776\) | −76.5753 | −2.74889 | ||||||||
\(777\) | −24.3011 | −0.871797 | ||||||||
\(778\) | −80.5140 | −2.88657 | ||||||||
\(779\) | −19.3246 | −0.692376 | ||||||||
\(780\) | 23.6513 | 0.846854 | ||||||||
\(781\) | 4.48110 | 0.160346 | ||||||||
\(782\) | −50.8715 | −1.81916 | ||||||||
\(783\) | 55.3780 | 1.97905 | ||||||||
\(784\) | −35.1408 | −1.25503 | ||||||||
\(785\) | −45.3312 | −1.61794 | ||||||||
\(786\) | −28.1757 | −1.00500 | ||||||||
\(787\) | −17.5036 | −0.623936 | −0.311968 | − | 0.950093i | \(-0.600988\pi\) | ||||
−0.311968 | + | 0.950093i | \(0.600988\pi\) | |||||||
\(788\) | 56.1187 | 1.99915 | ||||||||
\(789\) | 17.8230 | 0.634517 | ||||||||
\(790\) | 62.7603 | 2.23291 | ||||||||
\(791\) | 0.867651 | 0.0308501 | ||||||||
\(792\) | 40.2481 | 1.43015 | ||||||||
\(793\) | 3.09399 | 0.109871 | ||||||||
\(794\) | −21.7996 | −0.773640 | ||||||||
\(795\) | 2.86778 | 0.101710 | ||||||||
\(796\) | 35.5702 | 1.26075 | ||||||||
\(797\) | 22.3330 | 0.791075 | 0.395538 | − | 0.918450i | \(-0.370558\pi\) | ||||
0.395538 | + | 0.918450i | \(0.370558\pi\) | |||||||
\(798\) | 11.6590 | 0.412725 | ||||||||
\(799\) | 5.29521 | 0.187331 | ||||||||
\(800\) | −153.584 | −5.43002 | ||||||||
\(801\) | 0.0199659 | 0.000705460 0 | ||||||||
\(802\) | 71.0962 | 2.51050 | ||||||||
\(803\) | −37.2616 | −1.31493 | ||||||||
\(804\) | 33.8334 | 1.19321 | ||||||||
\(805\) | 31.2657 | 1.10197 | ||||||||
\(806\) | −5.20967 | −0.183503 | ||||||||
\(807\) | −3.66707 | −0.129087 | ||||||||
\(808\) | 88.4909 | 3.11310 | ||||||||
\(809\) | 25.0649 | 0.881235 | 0.440618 | − | 0.897695i | \(-0.354759\pi\) | ||||
0.440618 | + | 0.897695i | \(0.354759\pi\) | |||||||
\(810\) | −16.2829 | −0.572124 | ||||||||
\(811\) | 16.3762 | 0.575046 | 0.287523 | − | 0.957774i | \(-0.407168\pi\) | ||||
0.287523 | + | 0.957774i | \(0.407168\pi\) | |||||||
\(812\) | −102.376 | −3.59270 | ||||||||
\(813\) | 14.6569 | 0.514041 | ||||||||
\(814\) | 84.7537 | 2.97062 | ||||||||
\(815\) | 17.2967 | 0.605878 | ||||||||
\(816\) | −65.2018 | −2.28252 | ||||||||
\(817\) | −18.1712 | −0.635730 | ||||||||
\(818\) | 85.5403 | 2.99085 | ||||||||
\(819\) | 3.20628 | 0.112036 | ||||||||
\(820\) | −206.690 | −7.21792 | ||||||||
\(821\) | 12.2886 | 0.428875 | 0.214437 | − | 0.976738i | \(-0.431208\pi\) | ||||
0.214437 | + | 0.976738i | \(0.431208\pi\) | |||||||
\(822\) | −52.9168 | −1.84569 | ||||||||
\(823\) | −53.6582 | −1.87041 | −0.935203 | − | 0.354111i | \(-0.884783\pi\) | ||||
−0.935203 | + | 0.354111i | \(0.884783\pi\) | |||||||
\(824\) | −17.2513 | −0.600976 | ||||||||
\(825\) | −38.9022 | −1.35440 | ||||||||
\(826\) | 46.3336 | 1.61215 | ||||||||
\(827\) | −38.3316 | −1.33292 | −0.666461 | − | 0.745540i | \(-0.732192\pi\) | ||||
−0.666461 | + | 0.745540i | \(0.732192\pi\) | |||||||
\(828\) | −32.4116 | −1.12638 | ||||||||
\(829\) | −38.0853 | −1.32276 | −0.661378 | − | 0.750053i | \(-0.730028\pi\) | ||||
−0.661378 | + | 0.750053i | \(0.730028\pi\) | |||||||
\(830\) | 87.2180 | 3.02738 | ||||||||
\(831\) | 16.4310 | 0.569985 | ||||||||
\(832\) | 14.8715 | 0.515577 | ||||||||
\(833\) | −14.7856 | −0.512291 | ||||||||
\(834\) | −21.9787 | −0.761059 | ||||||||
\(835\) | −70.4038 | −2.43642 | ||||||||
\(836\) | −29.1420 | −1.00790 | ||||||||
\(837\) | 10.6485 | 0.368065 | ||||||||
\(838\) | 54.5989 | 1.88609 | ||||||||
\(839\) | 25.7616 | 0.889391 | 0.444695 | − | 0.895682i | \(-0.353312\pi\) | ||||
0.444695 | + | 0.895682i | \(0.353312\pi\) | |||||||
\(840\) | 75.4036 | 2.60167 | ||||||||
\(841\) | 74.9849 | 2.58568 | ||||||||
\(842\) | 15.2815 | 0.526637 | ||||||||
\(843\) | 16.3334 | 0.562552 | ||||||||
\(844\) | 32.0530 | 1.10331 | ||||||||
\(845\) | −3.97344 | −0.136690 | ||||||||
\(846\) | 4.70744 | 0.161845 | ||||||||
\(847\) | 3.18826 | 0.109550 | ||||||||
\(848\) | 7.04004 | 0.241756 | ||||||||
\(849\) | −24.0389 | −0.825013 | ||||||||
\(850\) | −138.408 | −4.74735 | ||||||||
\(851\) | −41.2701 | −1.41472 | ||||||||
\(852\) | −8.70288 | −0.298156 | ||||||||
\(853\) | −39.4292 | −1.35003 | −0.675015 | − | 0.737804i | \(-0.735863\pi\) | ||||
−0.675015 | + | 0.737804i | \(0.735863\pi\) | |||||||
\(854\) | 16.3130 | 0.558218 | ||||||||
\(855\) | −12.0660 | −0.412647 | ||||||||
\(856\) | 140.909 | 4.81618 | ||||||||
\(857\) | 24.0158 | 0.820363 | 0.410182 | − | 0.912004i | \(-0.365465\pi\) | ||||
0.410182 | + | 0.912004i | \(0.365465\pi\) | |||||||
\(858\) | 9.58077 | 0.327082 | ||||||||
\(859\) | 19.7622 | 0.674277 | 0.337139 | − | 0.941455i | \(-0.390541\pi\) | ||||
0.337139 | + | 0.941455i | \(0.390541\pi\) | |||||||
\(860\) | −194.353 | −6.62739 | ||||||||
\(861\) | 24.0066 | 0.818142 | ||||||||
\(862\) | −69.5134 | −2.36764 | ||||||||
\(863\) | −27.9906 | −0.952812 | −0.476406 | − | 0.879225i | \(-0.658061\pi\) | ||||
−0.476406 | + | 0.879225i | \(0.658061\pi\) | |||||||
\(864\) | −77.3126 | −2.63023 | ||||||||
\(865\) | −103.502 | −3.51917 | ||||||||
\(866\) | 1.26499 | 0.0429859 | ||||||||
\(867\) | −7.43230 | −0.252414 | ||||||||
\(868\) | −19.6856 | −0.668174 | ||||||||
\(869\) | 18.2203 | 0.618080 | ||||||||
\(870\) | −126.660 | −4.29419 | ||||||||
\(871\) | −5.68402 | −0.192596 | ||||||||
\(872\) | −135.379 | −4.58450 | ||||||||
\(873\) | −15.2222 | −0.515194 | ||||||||
\(874\) | 19.8003 | 0.669755 | ||||||||
\(875\) | 45.6403 | 1.54292 | ||||||||
\(876\) | 72.3670 | 2.44505 | ||||||||
\(877\) | −24.4648 | −0.826118 | −0.413059 | − | 0.910704i | \(-0.635540\pi\) | ||||
−0.413059 | + | 0.910704i | \(0.635540\pi\) | |||||||
\(878\) | −40.8320 | −1.37801 | ||||||||
\(879\) | 39.8873 | 1.34537 | ||||||||
\(880\) | −139.761 | −4.71134 | ||||||||
\(881\) | 10.8885 | 0.366841 | 0.183421 | − | 0.983035i | \(-0.441283\pi\) | ||||
0.183421 | + | 0.983035i | \(0.441283\pi\) | |||||||
\(882\) | −13.1444 | −0.442595 | ||||||||
\(883\) | 58.4943 | 1.96849 | 0.984245 | − | 0.176813i | \(-0.0565787\pi\) | ||||
0.984245 | + | 0.176813i | \(0.0565787\pi\) | |||||||
\(884\) | 24.4293 | 0.821647 | ||||||||
\(885\) | 41.0830 | 1.38099 | ||||||||
\(886\) | 17.4726 | 0.587005 | ||||||||
\(887\) | 46.6267 | 1.56557 | 0.782786 | − | 0.622290i | \(-0.213798\pi\) | ||||
0.782786 | + | 0.622290i | \(0.213798\pi\) | |||||||
\(888\) | −99.5313 | −3.34005 | ||||||||
\(889\) | 21.9271 | 0.735412 | ||||||||
\(890\) | −0.130457 | −0.00437294 | ||||||||
\(891\) | −4.72718 | −0.158367 | ||||||||
\(892\) | −87.8377 | −2.94102 | ||||||||
\(893\) | −2.06101 | −0.0689692 | ||||||||
\(894\) | 38.1777 | 1.27685 | ||||||||
\(895\) | −62.9062 | −2.10272 | ||||||||
\(896\) | 21.9073 | 0.731871 | ||||||||
\(897\) | −4.66527 | −0.155769 | ||||||||
\(898\) | 39.6082 | 1.32174 | ||||||||
\(899\) | 19.9949 | 0.666869 | ||||||||
\(900\) | −88.1833 | −2.93944 | ||||||||
\(901\) | 2.96212 | 0.0986824 | ||||||||
\(902\) | −83.7266 | −2.78779 | ||||||||
\(903\) | 22.5737 | 0.751206 | ||||||||
\(904\) | 3.55368 | 0.118194 | ||||||||
\(905\) | −3.83889 | −0.127609 | ||||||||
\(906\) | 11.4615 | 0.380783 | ||||||||
\(907\) | −26.7541 | −0.888354 | −0.444177 | − | 0.895939i | \(-0.646504\pi\) | ||||
−0.444177 | + | 0.895939i | \(0.646504\pi\) | |||||||
\(908\) | −2.40773 | −0.0799033 | ||||||||
\(909\) | 17.5909 | 0.583453 | ||||||||
\(910\) | −20.9498 | −0.694480 | ||||||||
\(911\) | −46.4151 | −1.53780 | −0.768900 | − | 0.639369i | \(-0.779196\pi\) | ||||
−0.768900 | + | 0.639369i | \(0.779196\pi\) | |||||||
\(912\) | 25.3780 | 0.840349 | ||||||||
\(913\) | 25.3207 | 0.837992 | ||||||||
\(914\) | 42.0039 | 1.38936 | ||||||||
\(915\) | 14.4644 | 0.478177 | ||||||||
\(916\) | −122.218 | −4.03819 | ||||||||
\(917\) | 17.8865 | 0.590663 | ||||||||
\(918\) | −69.6729 | −2.29955 | ||||||||
\(919\) | 23.2605 | 0.767293 | 0.383646 | − | 0.923480i | \(-0.374668\pi\) | ||||
0.383646 | + | 0.923480i | \(0.374668\pi\) | |||||||
\(920\) | 128.056 | 4.22190 | ||||||||
\(921\) | 10.9680 | 0.361407 | ||||||||
\(922\) | 32.3615 | 1.06577 | ||||||||
\(923\) | 1.46209 | 0.0481252 | ||||||||
\(924\) | 36.2026 | 1.19098 | ||||||||
\(925\) | −112.285 | −3.69191 | ||||||||
\(926\) | 2.65690 | 0.0873112 | ||||||||
\(927\) | −3.42934 | −0.112634 | ||||||||
\(928\) | −145.172 | −4.76550 | ||||||||
\(929\) | −2.51259 | −0.0824355 | −0.0412178 | − | 0.999150i | \(-0.513124\pi\) | ||||
−0.0412178 | + | 0.999150i | \(0.513124\pi\) | |||||||
\(930\) | −24.3552 | −0.798637 | ||||||||
\(931\) | 5.75488 | 0.188609 | ||||||||
\(932\) | −36.7207 | −1.20283 | ||||||||
\(933\) | 32.5053 | 1.06418 | ||||||||
\(934\) | −32.0016 | −1.04712 | ||||||||
\(935\) | −58.8049 | −1.92312 | ||||||||
\(936\) | 13.1321 | 0.429237 | ||||||||
\(937\) | −21.5271 | −0.703259 | −0.351630 | − | 0.936139i | \(-0.614372\pi\) | ||||
−0.351630 | + | 0.936139i | \(0.614372\pi\) | |||||||
\(938\) | −29.9688 | −0.978517 | ||||||||
\(939\) | 8.74385 | 0.285345 | ||||||||
\(940\) | −22.0439 | −0.718993 | ||||||||
\(941\) | −8.25916 | −0.269241 | −0.134620 | − | 0.990897i | \(-0.542982\pi\) | ||||
−0.134620 | + | 0.990897i | \(0.542982\pi\) | |||||||
\(942\) | 35.6632 | 1.16197 | ||||||||
\(943\) | 40.7699 | 1.32765 | ||||||||
\(944\) | 100.854 | 3.28250 | ||||||||
\(945\) | 42.8211 | 1.39297 | ||||||||
\(946\) | −78.7293 | −2.55971 | ||||||||
\(947\) | −10.2538 | −0.333203 | −0.166602 | − | 0.986024i | \(-0.553279\pi\) | ||||
−0.166602 | + | 0.986024i | \(0.553279\pi\) | |||||||
\(948\) | −35.3861 | −1.14929 | ||||||||
\(949\) | −12.1577 | −0.394655 | ||||||||
\(950\) | 53.8714 | 1.74782 | ||||||||
\(951\) | −15.2369 | −0.494090 | ||||||||
\(952\) | 77.8839 | 2.52423 | ||||||||
\(953\) | 27.0557 | 0.876420 | 0.438210 | − | 0.898873i | \(-0.355613\pi\) | ||||
0.438210 | + | 0.898873i | \(0.355613\pi\) | |||||||
\(954\) | 2.63332 | 0.0852569 | ||||||||
\(955\) | −95.7433 | −3.09818 | ||||||||
\(956\) | 92.4651 | 2.99054 | ||||||||
\(957\) | −36.7714 | −1.18865 | ||||||||
\(958\) | −72.8312 | −2.35307 | ||||||||
\(959\) | 33.5925 | 1.08476 | ||||||||
\(960\) | 69.5241 | 2.24388 | ||||||||
\(961\) | −27.1552 | −0.875975 | ||||||||
\(962\) | 27.6534 | 0.891580 | ||||||||
\(963\) | 28.0110 | 0.902643 | ||||||||
\(964\) | 124.725 | 4.01713 | ||||||||
\(965\) | −84.8881 | −2.73264 | ||||||||
\(966\) | −24.5975 | −0.791412 | ||||||||
\(967\) | −13.6939 | −0.440367 | −0.220183 | − | 0.975459i | \(-0.570666\pi\) | ||||
−0.220183 | + | 0.975459i | \(0.570666\pi\) | |||||||
\(968\) | 13.0583 | 0.419710 | ||||||||
\(969\) | 10.6779 | 0.343022 | ||||||||
\(970\) | 99.4621 | 3.19354 | ||||||||
\(971\) | −14.4397 | −0.463394 | −0.231697 | − | 0.972788i | \(-0.574428\pi\) | ||||
−0.231697 | + | 0.972788i | \(0.574428\pi\) | |||||||
\(972\) | −73.2423 | −2.34925 | ||||||||
\(973\) | 13.9524 | 0.447295 | ||||||||
\(974\) | −68.0334 | −2.17993 | ||||||||
\(975\) | −12.6930 | −0.406500 | ||||||||
\(976\) | 35.5081 | 1.13659 | ||||||||
\(977\) | 28.1840 | 0.901685 | 0.450842 | − | 0.892604i | \(-0.351124\pi\) | ||||
0.450842 | + | 0.892604i | \(0.351124\pi\) | |||||||
\(978\) | −13.6078 | −0.435129 | ||||||||
\(979\) | −0.0378737 | −0.00121045 | ||||||||
\(980\) | 61.5523 | 1.96622 | ||||||||
\(981\) | −26.9116 | −0.859222 | ||||||||
\(982\) | −72.2246 | −2.30478 | ||||||||
\(983\) | 24.5555 | 0.783197 | 0.391599 | − | 0.920136i | \(-0.371922\pi\) | ||||
0.391599 | + | 0.920136i | \(0.371922\pi\) | |||||||
\(984\) | 98.3250 | 3.13449 | ||||||||
\(985\) | −44.0756 | −1.40437 | ||||||||
\(986\) | −130.827 | −4.16637 | ||||||||
\(987\) | 2.56036 | 0.0814970 | ||||||||
\(988\) | −9.50844 | −0.302504 | ||||||||
\(989\) | 38.3365 | 1.21903 | ||||||||
\(990\) | −52.2775 | −1.66149 | ||||||||
\(991\) | −11.6704 | −0.370724 | −0.185362 | − | 0.982670i | \(-0.559346\pi\) | ||||
−0.185362 | + | 0.982670i | \(0.559346\pi\) | |||||||
\(992\) | −27.9147 | −0.886292 | ||||||||
\(993\) | −9.98411 | −0.316836 | ||||||||
\(994\) | 7.70882 | 0.244509 | ||||||||
\(995\) | −27.9369 | −0.885658 | ||||||||
\(996\) | −49.1761 | −1.55820 | ||||||||
\(997\) | −0.0786553 | −0.00249104 | −0.00124552 | − | 0.999999i | \(-0.500396\pi\) | ||||
−0.00124552 | + | 0.999999i | \(0.500396\pi\) | |||||||
\(998\) | −65.8138 | −2.08330 | ||||||||
\(999\) | −56.5230 | −1.78831 |
(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 | 6019.2.a.e.1.4 | ✓ | 130 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6019.2.a.e.1.4 | ✓ | 130 | 1.1 | even | 1 | trivial |