Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4034,2,Mod(1,4034)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4034, 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("4034.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4034 = 2 \cdot 2017 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4034.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: | \(32.2116521754\) |
Analytic rank: | \(1\) |
Dimension: | \(33\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Character | \(\chi\) | \(=\) | 4034.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | −3.31212 | −1.91225 | −0.956125 | − | 0.292958i | \(-0.905360\pi\) | ||||
−0.956125 | + | 0.292958i | \(0.905360\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −3.97668 | −1.77843 | −0.889213 | − | 0.457494i | \(-0.848747\pi\) | ||||
−0.889213 | + | 0.457494i | \(0.848747\pi\) | |||||||
\(6\) | −3.31212 | −1.35217 | ||||||||
\(7\) | 0.855437 | 0.323325 | 0.161662 | − | 0.986846i | \(-0.448314\pi\) | ||||
0.161662 | + | 0.986846i | \(0.448314\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 7.97011 | 2.65670 | ||||||||
\(10\) | −3.97668 | −1.25754 | ||||||||
\(11\) | −4.89168 | −1.47490 | −0.737449 | − | 0.675403i | \(-0.763970\pi\) | ||||
−0.737449 | + | 0.675403i | \(0.763970\pi\) | |||||||
\(12\) | −3.31212 | −0.956125 | ||||||||
\(13\) | −3.28198 | −0.910259 | −0.455129 | − | 0.890425i | \(-0.650407\pi\) | ||||
−0.455129 | + | 0.890425i | \(0.650407\pi\) | |||||||
\(14\) | 0.855437 | 0.228625 | ||||||||
\(15\) | 13.1712 | 3.40080 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −2.74675 | −0.666186 | −0.333093 | − | 0.942894i | \(-0.608092\pi\) | ||||
−0.333093 | + | 0.942894i | \(0.608092\pi\) | |||||||
\(18\) | 7.97011 | 1.87857 | ||||||||
\(19\) | 6.27503 | 1.43959 | 0.719795 | − | 0.694187i | \(-0.244236\pi\) | ||||
0.719795 | + | 0.694187i | \(0.244236\pi\) | |||||||
\(20\) | −3.97668 | −0.889213 | ||||||||
\(21\) | −2.83331 | −0.618278 | ||||||||
\(22\) | −4.89168 | −1.04291 | ||||||||
\(23\) | 7.31641 | 1.52558 | 0.762789 | − | 0.646648i | \(-0.223830\pi\) | ||||
0.762789 | + | 0.646648i | \(0.223830\pi\) | |||||||
\(24\) | −3.31212 | −0.676083 | ||||||||
\(25\) | 10.8140 | 2.16280 | ||||||||
\(26\) | −3.28198 | −0.643650 | ||||||||
\(27\) | −16.4616 | −3.16803 | ||||||||
\(28\) | 0.855437 | 0.161662 | ||||||||
\(29\) | 7.72086 | 1.43373 | 0.716864 | − | 0.697213i | \(-0.245577\pi\) | ||||
0.716864 | + | 0.697213i | \(0.245577\pi\) | |||||||
\(30\) | 13.1712 | 2.40473 | ||||||||
\(31\) | −7.07071 | −1.26994 | −0.634968 | − | 0.772538i | \(-0.718987\pi\) | ||||
−0.634968 | + | 0.772538i | \(0.718987\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 16.2018 | 2.82037 | ||||||||
\(34\) | −2.74675 | −0.471064 | ||||||||
\(35\) | −3.40180 | −0.575009 | ||||||||
\(36\) | 7.97011 | 1.32835 | ||||||||
\(37\) | −3.37965 | −0.555612 | −0.277806 | − | 0.960637i | \(-0.589607\pi\) | ||||
−0.277806 | + | 0.960637i | \(0.589607\pi\) | |||||||
\(38\) | 6.27503 | 1.01794 | ||||||||
\(39\) | 10.8703 | 1.74064 | ||||||||
\(40\) | −3.97668 | −0.628768 | ||||||||
\(41\) | 4.02227 | 0.628174 | 0.314087 | − | 0.949394i | \(-0.398302\pi\) | ||||
0.314087 | + | 0.949394i | \(0.398302\pi\) | |||||||
\(42\) | −2.83331 | −0.437189 | ||||||||
\(43\) | −4.97249 | −0.758298 | −0.379149 | − | 0.925336i | \(-0.623783\pi\) | ||||
−0.379149 | + | 0.925336i | \(0.623783\pi\) | |||||||
\(44\) | −4.89168 | −0.737449 | ||||||||
\(45\) | −31.6946 | −4.72475 | ||||||||
\(46\) | 7.31641 | 1.07875 | ||||||||
\(47\) | 5.21962 | 0.761360 | 0.380680 | − | 0.924707i | \(-0.375690\pi\) | ||||
0.380680 | + | 0.924707i | \(0.375690\pi\) | |||||||
\(48\) | −3.31212 | −0.478063 | ||||||||
\(49\) | −6.26823 | −0.895461 | ||||||||
\(50\) | 10.8140 | 1.52933 | ||||||||
\(51\) | 9.09757 | 1.27391 | ||||||||
\(52\) | −3.28198 | −0.455129 | ||||||||
\(53\) | 11.2318 | 1.54281 | 0.771405 | − | 0.636344i | \(-0.219554\pi\) | ||||
0.771405 | + | 0.636344i | \(0.219554\pi\) | |||||||
\(54\) | −16.4616 | −2.24014 | ||||||||
\(55\) | 19.4526 | 2.62299 | ||||||||
\(56\) | 0.855437 | 0.114313 | ||||||||
\(57\) | −20.7836 | −2.75286 | ||||||||
\(58\) | 7.72086 | 1.01380 | ||||||||
\(59\) | 8.53741 | 1.11148 | 0.555738 | − | 0.831358i | \(-0.312436\pi\) | ||||
0.555738 | + | 0.831358i | \(0.312436\pi\) | |||||||
\(60\) | 13.1712 | 1.70040 | ||||||||
\(61\) | −7.10692 | −0.909948 | −0.454974 | − | 0.890505i | \(-0.650351\pi\) | ||||
−0.454974 | + | 0.890505i | \(0.650351\pi\) | |||||||
\(62\) | −7.07071 | −0.897980 | ||||||||
\(63\) | 6.81792 | 0.858978 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 13.0514 | 1.61883 | ||||||||
\(66\) | 16.2018 | 1.99430 | ||||||||
\(67\) | 10.0679 | 1.22999 | 0.614997 | − | 0.788529i | \(-0.289157\pi\) | ||||
0.614997 | + | 0.788529i | \(0.289157\pi\) | |||||||
\(68\) | −2.74675 | −0.333093 | ||||||||
\(69\) | −24.2328 | −2.91729 | ||||||||
\(70\) | −3.40180 | −0.406593 | ||||||||
\(71\) | 7.41511 | 0.880011 | 0.440006 | − | 0.897995i | \(-0.354976\pi\) | ||||
0.440006 | + | 0.897995i | \(0.354976\pi\) | |||||||
\(72\) | 7.97011 | 0.939286 | ||||||||
\(73\) | 8.98140 | 1.05119 | 0.525597 | − | 0.850734i | \(-0.323842\pi\) | ||||
0.525597 | + | 0.850734i | \(0.323842\pi\) | |||||||
\(74\) | −3.37965 | −0.392877 | ||||||||
\(75\) | −35.8172 | −4.13581 | ||||||||
\(76\) | 6.27503 | 0.719795 | ||||||||
\(77\) | −4.18452 | −0.476871 | ||||||||
\(78\) | 10.8703 | 1.23082 | ||||||||
\(79\) | −13.0910 | −1.47285 | −0.736426 | − | 0.676518i | \(-0.763488\pi\) | ||||
−0.736426 | + | 0.676518i | \(0.763488\pi\) | |||||||
\(80\) | −3.97668 | −0.444606 | ||||||||
\(81\) | 30.6123 | 3.40137 | ||||||||
\(82\) | 4.02227 | 0.444186 | ||||||||
\(83\) | −12.7934 | −1.40426 | −0.702132 | − | 0.712047i | \(-0.747768\pi\) | ||||
−0.702132 | + | 0.712047i | \(0.747768\pi\) | |||||||
\(84\) | −2.83331 | −0.309139 | ||||||||
\(85\) | 10.9230 | 1.18476 | ||||||||
\(86\) | −4.97249 | −0.536198 | ||||||||
\(87\) | −25.5724 | −2.74165 | ||||||||
\(88\) | −4.89168 | −0.521455 | ||||||||
\(89\) | −15.1636 | −1.60734 | −0.803668 | − | 0.595078i | \(-0.797121\pi\) | ||||
−0.803668 | + | 0.595078i | \(0.797121\pi\) | |||||||
\(90\) | −31.6946 | −3.34090 | ||||||||
\(91\) | −2.80753 | −0.294309 | ||||||||
\(92\) | 7.31641 | 0.762789 | ||||||||
\(93\) | 23.4190 | 2.42844 | ||||||||
\(94\) | 5.21962 | 0.538363 | ||||||||
\(95\) | −24.9538 | −2.56020 | ||||||||
\(96\) | −3.31212 | −0.338041 | ||||||||
\(97\) | −1.64996 | −0.167528 | −0.0837641 | − | 0.996486i | \(-0.526694\pi\) | ||||
−0.0837641 | + | 0.996486i | \(0.526694\pi\) | |||||||
\(98\) | −6.26823 | −0.633187 | ||||||||
\(99\) | −38.9872 | −3.91836 | ||||||||
\(100\) | 10.8140 | 1.08140 | ||||||||
\(101\) | 6.46648 | 0.643439 | 0.321719 | − | 0.946835i | \(-0.395739\pi\) | ||||
0.321719 | + | 0.946835i | \(0.395739\pi\) | |||||||
\(102\) | 9.09757 | 0.900793 | ||||||||
\(103\) | 17.3456 | 1.70911 | 0.854557 | − | 0.519357i | \(-0.173828\pi\) | ||||
0.854557 | + | 0.519357i | \(0.173828\pi\) | |||||||
\(104\) | −3.28198 | −0.321825 | ||||||||
\(105\) | 11.2672 | 1.09956 | ||||||||
\(106\) | 11.2318 | 1.09093 | ||||||||
\(107\) | 6.92793 | 0.669748 | 0.334874 | − | 0.942263i | \(-0.391306\pi\) | ||||
0.334874 | + | 0.942263i | \(0.391306\pi\) | |||||||
\(108\) | −16.4616 | −1.58402 | ||||||||
\(109\) | −13.9130 | −1.33263 | −0.666313 | − | 0.745672i | \(-0.732128\pi\) | ||||
−0.666313 | + | 0.745672i | \(0.732128\pi\) | |||||||
\(110\) | 19.4526 | 1.85474 | ||||||||
\(111\) | 11.1938 | 1.06247 | ||||||||
\(112\) | 0.855437 | 0.0808312 | ||||||||
\(113\) | 2.03299 | 0.191247 | 0.0956237 | − | 0.995418i | \(-0.469515\pi\) | ||||
0.0956237 | + | 0.995418i | \(0.469515\pi\) | |||||||
\(114\) | −20.7836 | −1.94656 | ||||||||
\(115\) | −29.0950 | −2.71313 | ||||||||
\(116\) | 7.72086 | 0.716864 | ||||||||
\(117\) | −26.1578 | −2.41829 | ||||||||
\(118\) | 8.53741 | 0.785932 | ||||||||
\(119\) | −2.34968 | −0.215394 | ||||||||
\(120\) | 13.1712 | 1.20236 | ||||||||
\(121\) | 12.9285 | 1.17532 | ||||||||
\(122\) | −7.10692 | −0.643430 | ||||||||
\(123\) | −13.3222 | −1.20123 | ||||||||
\(124\) | −7.07071 | −0.634968 | ||||||||
\(125\) | −23.1204 | −2.06795 | ||||||||
\(126\) | 6.81792 | 0.607389 | ||||||||
\(127\) | −5.55835 | −0.493224 | −0.246612 | − | 0.969114i | \(-0.579317\pi\) | ||||
−0.246612 | + | 0.969114i | \(0.579317\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 16.4695 | 1.45006 | ||||||||
\(130\) | 13.0514 | 1.14468 | ||||||||
\(131\) | −14.8483 | −1.29731 | −0.648653 | − | 0.761084i | \(-0.724667\pi\) | ||||
−0.648653 | + | 0.761084i | \(0.724667\pi\) | |||||||
\(132\) | 16.2018 | 1.41019 | ||||||||
\(133\) | 5.36789 | 0.465455 | ||||||||
\(134\) | 10.0679 | 0.869737 | ||||||||
\(135\) | 65.4624 | 5.63411 | ||||||||
\(136\) | −2.74675 | −0.235532 | ||||||||
\(137\) | 0.609707 | 0.0520908 | 0.0260454 | − | 0.999661i | \(-0.491709\pi\) | ||||
0.0260454 | + | 0.999661i | \(0.491709\pi\) | |||||||
\(138\) | −24.2328 | −2.06283 | ||||||||
\(139\) | −7.38651 | −0.626515 | −0.313258 | − | 0.949668i | \(-0.601420\pi\) | ||||
−0.313258 | + | 0.949668i | \(0.601420\pi\) | |||||||
\(140\) | −3.40180 | −0.287505 | ||||||||
\(141\) | −17.2880 | −1.45591 | ||||||||
\(142\) | 7.41511 | 0.622262 | ||||||||
\(143\) | 16.0544 | 1.34254 | ||||||||
\(144\) | 7.97011 | 0.664176 | ||||||||
\(145\) | −30.7034 | −2.54978 | ||||||||
\(146\) | 8.98140 | 0.743306 | ||||||||
\(147\) | 20.7611 | 1.71235 | ||||||||
\(148\) | −3.37965 | −0.277806 | ||||||||
\(149\) | −13.9558 | −1.14331 | −0.571653 | − | 0.820495i | \(-0.693698\pi\) | ||||
−0.571653 | + | 0.820495i | \(0.693698\pi\) | |||||||
\(150\) | −35.8172 | −2.92446 | ||||||||
\(151\) | −19.8711 | −1.61708 | −0.808542 | − | 0.588439i | \(-0.799743\pi\) | ||||
−0.808542 | + | 0.588439i | \(0.799743\pi\) | |||||||
\(152\) | 6.27503 | 0.508972 | ||||||||
\(153\) | −21.8919 | −1.76986 | ||||||||
\(154\) | −4.18452 | −0.337199 | ||||||||
\(155\) | 28.1179 | 2.25849 | ||||||||
\(156\) | 10.8703 | 0.870321 | ||||||||
\(157\) | −19.4298 | −1.55067 | −0.775335 | − | 0.631551i | \(-0.782419\pi\) | ||||
−0.775335 | + | 0.631551i | \(0.782419\pi\) | |||||||
\(158\) | −13.0910 | −1.04146 | ||||||||
\(159\) | −37.2011 | −2.95024 | ||||||||
\(160\) | −3.97668 | −0.314384 | ||||||||
\(161\) | 6.25873 | 0.493257 | ||||||||
\(162\) | 30.6123 | 2.40513 | ||||||||
\(163\) | −9.01885 | −0.706410 | −0.353205 | − | 0.935546i | \(-0.614908\pi\) | ||||
−0.353205 | + | 0.935546i | \(0.614908\pi\) | |||||||
\(164\) | 4.02227 | 0.314087 | ||||||||
\(165\) | −64.4294 | −5.01582 | ||||||||
\(166\) | −12.7934 | −0.992964 | ||||||||
\(167\) | 19.4198 | 1.50275 | 0.751375 | − | 0.659876i | \(-0.229391\pi\) | ||||
0.751375 | + | 0.659876i | \(0.229391\pi\) | |||||||
\(168\) | −2.83331 | −0.218594 | ||||||||
\(169\) | −2.22858 | −0.171429 | ||||||||
\(170\) | 10.9230 | 0.837753 | ||||||||
\(171\) | 50.0126 | 3.82456 | ||||||||
\(172\) | −4.97249 | −0.379149 | ||||||||
\(173\) | 11.4945 | 0.873909 | 0.436955 | − | 0.899484i | \(-0.356057\pi\) | ||||
0.436955 | + | 0.899484i | \(0.356057\pi\) | |||||||
\(174\) | −25.5724 | −1.93864 | ||||||||
\(175\) | 9.25068 | 0.699286 | ||||||||
\(176\) | −4.89168 | −0.368724 | ||||||||
\(177\) | −28.2769 | −2.12542 | ||||||||
\(178\) | −15.1636 | −1.13656 | ||||||||
\(179\) | 16.3117 | 1.21920 | 0.609598 | − | 0.792711i | \(-0.291331\pi\) | ||||
0.609598 | + | 0.792711i | \(0.291331\pi\) | |||||||
\(180\) | −31.6946 | −2.36237 | ||||||||
\(181\) | −18.1731 | −1.35080 | −0.675398 | − | 0.737453i | \(-0.736028\pi\) | ||||
−0.675398 | + | 0.737453i | \(0.736028\pi\) | |||||||
\(182\) | −2.80753 | −0.208108 | ||||||||
\(183\) | 23.5389 | 1.74005 | ||||||||
\(184\) | 7.31641 | 0.539373 | ||||||||
\(185\) | 13.4398 | 0.988114 | ||||||||
\(186\) | 23.4190 | 1.71716 | ||||||||
\(187\) | 13.4362 | 0.982555 | ||||||||
\(188\) | 5.21962 | 0.380680 | ||||||||
\(189\) | −14.0818 | −1.02430 | ||||||||
\(190\) | −24.9538 | −1.81034 | ||||||||
\(191\) | −9.28707 | −0.671989 | −0.335994 | − | 0.941864i | \(-0.609072\pi\) | ||||
−0.335994 | + | 0.941864i | \(0.609072\pi\) | |||||||
\(192\) | −3.31212 | −0.239031 | ||||||||
\(193\) | 5.95574 | 0.428704 | 0.214352 | − | 0.976757i | \(-0.431236\pi\) | ||||
0.214352 | + | 0.976757i | \(0.431236\pi\) | |||||||
\(194\) | −1.64996 | −0.118460 | ||||||||
\(195\) | −43.2277 | −3.09560 | ||||||||
\(196\) | −6.26823 | −0.447731 | ||||||||
\(197\) | −18.3039 | −1.30410 | −0.652050 | − | 0.758176i | \(-0.726091\pi\) | ||||
−0.652050 | + | 0.758176i | \(0.726091\pi\) | |||||||
\(198\) | −38.9872 | −2.77070 | ||||||||
\(199\) | −13.5988 | −0.963996 | −0.481998 | − | 0.876172i | \(-0.660089\pi\) | ||||
−0.481998 | + | 0.876172i | \(0.660089\pi\) | |||||||
\(200\) | 10.8140 | 0.764664 | ||||||||
\(201\) | −33.3462 | −2.35206 | ||||||||
\(202\) | 6.46648 | 0.454980 | ||||||||
\(203\) | 6.60471 | 0.463560 | ||||||||
\(204\) | 9.09757 | 0.636957 | ||||||||
\(205\) | −15.9953 | −1.11716 | ||||||||
\(206\) | 17.3456 | 1.20853 | ||||||||
\(207\) | 58.3126 | 4.05301 | ||||||||
\(208\) | −3.28198 | −0.227565 | ||||||||
\(209\) | −30.6954 | −2.12325 | ||||||||
\(210\) | 11.2672 | 0.777507 | ||||||||
\(211\) | −11.6376 | −0.801163 | −0.400581 | − | 0.916261i | \(-0.631192\pi\) | ||||
−0.400581 | + | 0.916261i | \(0.631192\pi\) | |||||||
\(212\) | 11.2318 | 0.771405 | ||||||||
\(213\) | −24.5597 | −1.68280 | ||||||||
\(214\) | 6.92793 | 0.473583 | ||||||||
\(215\) | 19.7740 | 1.34858 | ||||||||
\(216\) | −16.4616 | −1.12007 | ||||||||
\(217\) | −6.04854 | −0.410602 | ||||||||
\(218\) | −13.9130 | −0.942309 | ||||||||
\(219\) | −29.7474 | −2.01015 | ||||||||
\(220\) | 19.4526 | 1.31150 | ||||||||
\(221\) | 9.01480 | 0.606401 | ||||||||
\(222\) | 11.1938 | 0.751279 | ||||||||
\(223\) | 4.79178 | 0.320881 | 0.160441 | − | 0.987045i | \(-0.448708\pi\) | ||||
0.160441 | + | 0.987045i | \(0.448708\pi\) | |||||||
\(224\) | 0.855437 | 0.0571563 | ||||||||
\(225\) | 86.1886 | 5.74591 | ||||||||
\(226\) | 2.03299 | 0.135232 | ||||||||
\(227\) | 16.2988 | 1.08179 | 0.540895 | − | 0.841090i | \(-0.318086\pi\) | ||||
0.540895 | + | 0.841090i | \(0.318086\pi\) | |||||||
\(228\) | −20.7836 | −1.37643 | ||||||||
\(229\) | 26.7092 | 1.76499 | 0.882496 | − | 0.470321i | \(-0.155862\pi\) | ||||
0.882496 | + | 0.470321i | \(0.155862\pi\) | |||||||
\(230\) | −29.0950 | −1.91847 | ||||||||
\(231\) | 13.8596 | 0.911897 | ||||||||
\(232\) | 7.72086 | 0.506899 | ||||||||
\(233\) | −8.65945 | −0.567299 | −0.283650 | − | 0.958928i | \(-0.591545\pi\) | ||||
−0.283650 | + | 0.958928i | \(0.591545\pi\) | |||||||
\(234\) | −26.1578 | −1.70999 | ||||||||
\(235\) | −20.7568 | −1.35402 | ||||||||
\(236\) | 8.53741 | 0.555738 | ||||||||
\(237\) | 43.3589 | 2.81646 | ||||||||
\(238\) | −2.34968 | −0.152307 | ||||||||
\(239\) | 9.49796 | 0.614372 | 0.307186 | − | 0.951649i | \(-0.400613\pi\) | ||||
0.307186 | + | 0.951649i | \(0.400613\pi\) | |||||||
\(240\) | 13.1712 | 0.850199 | ||||||||
\(241\) | −9.36709 | −0.603387 | −0.301694 | − | 0.953405i | \(-0.597552\pi\) | ||||
−0.301694 | + | 0.953405i | \(0.597552\pi\) | |||||||
\(242\) | 12.9285 | 0.831078 | ||||||||
\(243\) | −52.0067 | −3.33623 | ||||||||
\(244\) | −7.10692 | −0.454974 | ||||||||
\(245\) | 24.9267 | 1.59251 | ||||||||
\(246\) | −13.3222 | −0.849395 | ||||||||
\(247\) | −20.5945 | −1.31040 | ||||||||
\(248\) | −7.07071 | −0.448990 | ||||||||
\(249\) | 42.3734 | 2.68530 | ||||||||
\(250\) | −23.1204 | −1.46226 | ||||||||
\(251\) | −20.8698 | −1.31729 | −0.658644 | − | 0.752454i | \(-0.728870\pi\) | ||||
−0.658644 | + | 0.752454i | \(0.728870\pi\) | |||||||
\(252\) | 6.81792 | 0.429489 | ||||||||
\(253\) | −35.7896 | −2.25007 | ||||||||
\(254\) | −5.55835 | −0.348762 | ||||||||
\(255\) | −36.1781 | −2.26556 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −3.94016 | −0.245780 | −0.122890 | − | 0.992420i | \(-0.539216\pi\) | ||||
−0.122890 | + | 0.992420i | \(0.539216\pi\) | |||||||
\(258\) | 16.4695 | 1.02534 | ||||||||
\(259\) | −2.89108 | −0.179643 | ||||||||
\(260\) | 13.0514 | 0.809413 | ||||||||
\(261\) | 61.5361 | 3.80899 | ||||||||
\(262\) | −14.8483 | −0.917334 | ||||||||
\(263\) | 16.6206 | 1.02487 | 0.512434 | − | 0.858726i | \(-0.328744\pi\) | ||||
0.512434 | + | 0.858726i | \(0.328744\pi\) | |||||||
\(264\) | 16.2018 | 0.997152 | ||||||||
\(265\) | −44.6654 | −2.74377 | ||||||||
\(266\) | 5.36789 | 0.329127 | ||||||||
\(267\) | 50.2235 | 3.07363 | ||||||||
\(268\) | 10.0679 | 0.614997 | ||||||||
\(269\) | 23.6989 | 1.44495 | 0.722475 | − | 0.691397i | \(-0.243004\pi\) | ||||
0.722475 | + | 0.691397i | \(0.243004\pi\) | |||||||
\(270\) | 65.4624 | 3.98391 | ||||||||
\(271\) | 14.1471 | 0.859374 | 0.429687 | − | 0.902978i | \(-0.358624\pi\) | ||||
0.429687 | + | 0.902978i | \(0.358624\pi\) | |||||||
\(272\) | −2.74675 | −0.166546 | ||||||||
\(273\) | 9.29886 | 0.562793 | ||||||||
\(274\) | 0.609707 | 0.0368338 | ||||||||
\(275\) | −52.8986 | −3.18990 | ||||||||
\(276\) | −24.2328 | −1.45864 | ||||||||
\(277\) | −0.941415 | −0.0565641 | −0.0282821 | − | 0.999600i | \(-0.509004\pi\) | ||||
−0.0282821 | + | 0.999600i | \(0.509004\pi\) | |||||||
\(278\) | −7.38651 | −0.443013 | ||||||||
\(279\) | −56.3543 | −3.37384 | ||||||||
\(280\) | −3.40180 | −0.203296 | ||||||||
\(281\) | −11.5510 | −0.689074 | −0.344537 | − | 0.938773i | \(-0.611964\pi\) | ||||
−0.344537 | + | 0.938773i | \(0.611964\pi\) | |||||||
\(282\) | −17.2880 | −1.02948 | ||||||||
\(283\) | 9.51125 | 0.565385 | 0.282692 | − | 0.959211i | \(-0.408772\pi\) | ||||
0.282692 | + | 0.959211i | \(0.408772\pi\) | |||||||
\(284\) | 7.41511 | 0.440006 | ||||||||
\(285\) | 82.6498 | 4.89575 | ||||||||
\(286\) | 16.0544 | 0.949317 | ||||||||
\(287\) | 3.44080 | 0.203104 | ||||||||
\(288\) | 7.97011 | 0.469643 | ||||||||
\(289\) | −9.45534 | −0.556196 | ||||||||
\(290\) | −30.7034 | −1.80297 | ||||||||
\(291\) | 5.46487 | 0.320356 | ||||||||
\(292\) | 8.98140 | 0.525597 | ||||||||
\(293\) | −17.9313 | −1.04756 | −0.523778 | − | 0.851855i | \(-0.675478\pi\) | ||||
−0.523778 | + | 0.851855i | \(0.675478\pi\) | |||||||
\(294\) | 20.7611 | 1.21081 | ||||||||
\(295\) | −33.9505 | −1.97668 | ||||||||
\(296\) | −3.37965 | −0.196438 | ||||||||
\(297\) | 80.5247 | 4.67252 | ||||||||
\(298\) | −13.9558 | −0.808440 | ||||||||
\(299\) | −24.0123 | −1.38867 | ||||||||
\(300\) | −35.8172 | −2.06791 | ||||||||
\(301\) | −4.25366 | −0.245177 | ||||||||
\(302\) | −19.8711 | −1.14345 | ||||||||
\(303\) | −21.4177 | −1.23042 | ||||||||
\(304\) | 6.27503 | 0.359898 | ||||||||
\(305\) | 28.2620 | 1.61827 | ||||||||
\(306\) | −21.8919 | −1.25148 | ||||||||
\(307\) | 24.3758 | 1.39120 | 0.695601 | − | 0.718429i | \(-0.255138\pi\) | ||||
0.695601 | + | 0.718429i | \(0.255138\pi\) | |||||||
\(308\) | −4.18452 | −0.238435 | ||||||||
\(309\) | −57.4507 | −3.26826 | ||||||||
\(310\) | 28.1179 | 1.59699 | ||||||||
\(311\) | −12.2328 | −0.693660 | −0.346830 | − | 0.937928i | \(-0.612742\pi\) | ||||
−0.346830 | + | 0.937928i | \(0.612742\pi\) | |||||||
\(312\) | 10.8703 | 0.615410 | ||||||||
\(313\) | −16.4905 | −0.932098 | −0.466049 | − | 0.884759i | \(-0.654323\pi\) | ||||
−0.466049 | + | 0.884759i | \(0.654323\pi\) | |||||||
\(314\) | −19.4298 | −1.09649 | ||||||||
\(315\) | −27.1127 | −1.52763 | ||||||||
\(316\) | −13.0910 | −0.736426 | ||||||||
\(317\) | −20.6396 | −1.15923 | −0.579617 | − | 0.814889i | \(-0.696798\pi\) | ||||
−0.579617 | + | 0.814889i | \(0.696798\pi\) | |||||||
\(318\) | −37.2011 | −2.08613 | ||||||||
\(319\) | −37.7680 | −2.11460 | ||||||||
\(320\) | −3.97668 | −0.222303 | ||||||||
\(321\) | −22.9461 | −1.28073 | ||||||||
\(322\) | 6.25873 | 0.348785 | ||||||||
\(323\) | −17.2360 | −0.959035 | ||||||||
\(324\) | 30.6123 | 1.70068 | ||||||||
\(325\) | −35.4913 | −1.96870 | ||||||||
\(326\) | −9.01885 | −0.499508 | ||||||||
\(327\) | 46.0815 | 2.54831 | ||||||||
\(328\) | 4.02227 | 0.222093 | ||||||||
\(329\) | 4.46506 | 0.246167 | ||||||||
\(330\) | −64.4294 | −3.54672 | ||||||||
\(331\) | 18.7141 | 1.02862 | 0.514311 | − | 0.857604i | \(-0.328048\pi\) | ||||
0.514311 | + | 0.857604i | \(0.328048\pi\) | |||||||
\(332\) | −12.7934 | −0.702132 | ||||||||
\(333\) | −26.9362 | −1.47609 | ||||||||
\(334\) | 19.4198 | 1.06260 | ||||||||
\(335\) | −40.0370 | −2.18745 | ||||||||
\(336\) | −2.83331 | −0.154570 | ||||||||
\(337\) | −14.6929 | −0.800372 | −0.400186 | − | 0.916434i | \(-0.631055\pi\) | ||||
−0.400186 | + | 0.916434i | \(0.631055\pi\) | |||||||
\(338\) | −2.22858 | −0.121219 | ||||||||
\(339\) | −6.73349 | −0.365713 | ||||||||
\(340\) | 10.9230 | 0.592381 | ||||||||
\(341\) | 34.5876 | 1.87303 | ||||||||
\(342\) | 50.0126 | 2.70437 | ||||||||
\(343\) | −11.3501 | −0.612850 | ||||||||
\(344\) | −4.97249 | −0.268099 | ||||||||
\(345\) | 96.3661 | 5.18818 | ||||||||
\(346\) | 11.4945 | 0.617947 | ||||||||
\(347\) | 6.47579 | 0.347639 | 0.173819 | − | 0.984778i | \(-0.444389\pi\) | ||||
0.173819 | + | 0.984778i | \(0.444389\pi\) | |||||||
\(348\) | −25.5724 | −1.37082 | ||||||||
\(349\) | −12.4695 | −0.667479 | −0.333739 | − | 0.942665i | \(-0.608311\pi\) | ||||
−0.333739 | + | 0.942665i | \(0.608311\pi\) | |||||||
\(350\) | 9.25068 | 0.494470 | ||||||||
\(351\) | 54.0266 | 2.88373 | ||||||||
\(352\) | −4.89168 | −0.260727 | ||||||||
\(353\) | 23.7610 | 1.26467 | 0.632335 | − | 0.774695i | \(-0.282097\pi\) | ||||
0.632335 | + | 0.774695i | \(0.282097\pi\) | |||||||
\(354\) | −28.2769 | −1.50290 | ||||||||
\(355\) | −29.4875 | −1.56503 | ||||||||
\(356\) | −15.1636 | −0.803668 | ||||||||
\(357\) | 7.78240 | 0.411888 | ||||||||
\(358\) | 16.3117 | 0.862102 | ||||||||
\(359\) | −33.1864 | −1.75151 | −0.875757 | − | 0.482752i | \(-0.839637\pi\) | ||||
−0.875757 | + | 0.482752i | \(0.839637\pi\) | |||||||
\(360\) | −31.6946 | −1.67045 | ||||||||
\(361\) | 20.3760 | 1.07242 | ||||||||
\(362\) | −18.1731 | −0.955157 | ||||||||
\(363\) | −42.8208 | −2.24751 | ||||||||
\(364\) | −2.80753 | −0.147155 | ||||||||
\(365\) | −35.7162 | −1.86947 | ||||||||
\(366\) | 23.5389 | 1.23040 | ||||||||
\(367\) | 15.1489 | 0.790766 | 0.395383 | − | 0.918516i | \(-0.370612\pi\) | ||||
0.395383 | + | 0.918516i | \(0.370612\pi\) | |||||||
\(368\) | 7.31641 | 0.381394 | ||||||||
\(369\) | 32.0580 | 1.66887 | ||||||||
\(370\) | 13.4398 | 0.698702 | ||||||||
\(371\) | 9.60812 | 0.498829 | ||||||||
\(372\) | 23.4190 | 1.21422 | ||||||||
\(373\) | −12.2667 | −0.635144 | −0.317572 | − | 0.948234i | \(-0.602868\pi\) | ||||
−0.317572 | + | 0.948234i | \(0.602868\pi\) | |||||||
\(374\) | 13.4362 | 0.694772 | ||||||||
\(375\) | 76.5773 | 3.95444 | ||||||||
\(376\) | 5.21962 | 0.269181 | ||||||||
\(377\) | −25.3397 | −1.30506 | ||||||||
\(378\) | −14.0818 | −0.724291 | ||||||||
\(379\) | 2.22253 | 0.114164 | 0.0570819 | − | 0.998370i | \(-0.481820\pi\) | ||||
0.0570819 | + | 0.998370i | \(0.481820\pi\) | |||||||
\(380\) | −24.9538 | −1.28010 | ||||||||
\(381\) | 18.4099 | 0.943167 | ||||||||
\(382\) | −9.28707 | −0.475168 | ||||||||
\(383\) | −7.09815 | −0.362699 | −0.181349 | − | 0.983419i | \(-0.558046\pi\) | ||||
−0.181349 | + | 0.983419i | \(0.558046\pi\) | |||||||
\(384\) | −3.31212 | −0.169021 | ||||||||
\(385\) | 16.6405 | 0.848079 | ||||||||
\(386\) | 5.95574 | 0.303139 | ||||||||
\(387\) | −39.6313 | −2.01457 | ||||||||
\(388\) | −1.64996 | −0.0837641 | ||||||||
\(389\) | −29.9360 | −1.51781 | −0.758907 | − | 0.651199i | \(-0.774266\pi\) | ||||
−0.758907 | + | 0.651199i | \(0.774266\pi\) | |||||||
\(390\) | −43.2277 | −2.18892 | ||||||||
\(391\) | −20.0964 | −1.01632 | ||||||||
\(392\) | −6.26823 | −0.316593 | ||||||||
\(393\) | 49.1794 | 2.48077 | ||||||||
\(394\) | −18.3039 | −0.922138 | ||||||||
\(395\) | 52.0587 | 2.61936 | ||||||||
\(396\) | −38.9872 | −1.95918 | ||||||||
\(397\) | −16.5297 | −0.829599 | −0.414800 | − | 0.909913i | \(-0.636148\pi\) | ||||
−0.414800 | + | 0.909913i | \(0.636148\pi\) | |||||||
\(398\) | −13.5988 | −0.681648 | ||||||||
\(399\) | −17.7791 | −0.890067 | ||||||||
\(400\) | 10.8140 | 0.540699 | ||||||||
\(401\) | −1.55115 | −0.0774609 | −0.0387305 | − | 0.999250i | \(-0.512331\pi\) | ||||
−0.0387305 | + | 0.999250i | \(0.512331\pi\) | |||||||
\(402\) | −33.3462 | −1.66316 | ||||||||
\(403\) | 23.2059 | 1.15597 | ||||||||
\(404\) | 6.46648 | 0.321719 | ||||||||
\(405\) | −121.735 | −6.04907 | ||||||||
\(406\) | 6.60471 | 0.327786 | ||||||||
\(407\) | 16.5322 | 0.819470 | ||||||||
\(408\) | 9.09757 | 0.450397 | ||||||||
\(409\) | −3.93256 | −0.194453 | −0.0972263 | − | 0.995262i | \(-0.530997\pi\) | ||||
−0.0972263 | + | 0.995262i | \(0.530997\pi\) | |||||||
\(410\) | −15.9953 | −0.789951 | ||||||||
\(411\) | −2.01942 | −0.0996107 | ||||||||
\(412\) | 17.3456 | 0.854557 | ||||||||
\(413\) | 7.30321 | 0.359368 | ||||||||
\(414\) | 58.3126 | 2.86591 | ||||||||
\(415\) | 50.8754 | 2.49738 | ||||||||
\(416\) | −3.28198 | −0.160912 | ||||||||
\(417\) | 24.4650 | 1.19805 | ||||||||
\(418\) | −30.6954 | −1.50136 | ||||||||
\(419\) | 22.1606 | 1.08262 | 0.541308 | − | 0.840825i | \(-0.317929\pi\) | ||||
0.541308 | + | 0.840825i | \(0.317929\pi\) | |||||||
\(420\) | 11.2672 | 0.549781 | ||||||||
\(421\) | 7.33855 | 0.357659 | 0.178830 | − | 0.983880i | \(-0.442769\pi\) | ||||
0.178830 | + | 0.983880i | \(0.442769\pi\) | |||||||
\(422\) | −11.6376 | −0.566507 | ||||||||
\(423\) | 41.6009 | 2.02271 | ||||||||
\(424\) | 11.2318 | 0.545466 | ||||||||
\(425\) | −29.7034 | −1.44082 | ||||||||
\(426\) | −24.5597 | −1.18992 | ||||||||
\(427\) | −6.07952 | −0.294209 | ||||||||
\(428\) | 6.92793 | 0.334874 | ||||||||
\(429\) | −53.1741 | −2.56727 | ||||||||
\(430\) | 19.7740 | 0.953588 | ||||||||
\(431\) | 6.05414 | 0.291618 | 0.145809 | − | 0.989313i | \(-0.453422\pi\) | ||||
0.145809 | + | 0.989313i | \(0.453422\pi\) | |||||||
\(432\) | −16.4616 | −0.792008 | ||||||||
\(433\) | −12.2248 | −0.587484 | −0.293742 | − | 0.955885i | \(-0.594901\pi\) | ||||
−0.293742 | + | 0.955885i | \(0.594901\pi\) | |||||||
\(434\) | −6.04854 | −0.290339 | ||||||||
\(435\) | 101.693 | 4.87581 | ||||||||
\(436\) | −13.9130 | −0.666313 | ||||||||
\(437\) | 45.9107 | 2.19621 | ||||||||
\(438\) | −29.7474 | −1.42139 | ||||||||
\(439\) | 18.9382 | 0.903873 | 0.451936 | − | 0.892050i | \(-0.350733\pi\) | ||||
0.451936 | + | 0.892050i | \(0.350733\pi\) | |||||||
\(440\) | 19.4526 | 0.927369 | ||||||||
\(441\) | −49.9584 | −2.37897 | ||||||||
\(442\) | 9.01480 | 0.428790 | ||||||||
\(443\) | 21.9860 | 1.04458 | 0.522292 | − | 0.852767i | \(-0.325077\pi\) | ||||
0.522292 | + | 0.852767i | \(0.325077\pi\) | |||||||
\(444\) | 11.1938 | 0.531234 | ||||||||
\(445\) | 60.3007 | 2.85853 | ||||||||
\(446\) | 4.79178 | 0.226897 | ||||||||
\(447\) | 46.2233 | 2.18629 | ||||||||
\(448\) | 0.855437 | 0.0404156 | ||||||||
\(449\) | 16.3688 | 0.772489 | 0.386245 | − | 0.922396i | \(-0.373772\pi\) | ||||
0.386245 | + | 0.922396i | \(0.373772\pi\) | |||||||
\(450\) | 86.1886 | 4.06297 | ||||||||
\(451\) | −19.6757 | −0.926492 | ||||||||
\(452\) | 2.03299 | 0.0956237 | ||||||||
\(453\) | 65.8152 | 3.09227 | ||||||||
\(454\) | 16.2988 | 0.764941 | ||||||||
\(455\) | 11.1647 | 0.523407 | ||||||||
\(456\) | −20.7836 | −0.973282 | ||||||||
\(457\) | −15.8092 | −0.739523 | −0.369761 | − | 0.929127i | \(-0.620561\pi\) | ||||
−0.369761 | + | 0.929127i | \(0.620561\pi\) | |||||||
\(458\) | 26.7092 | 1.24804 | ||||||||
\(459\) | 45.2159 | 2.11050 | ||||||||
\(460\) | −29.0950 | −1.35656 | ||||||||
\(461\) | −8.41358 | −0.391860 | −0.195930 | − | 0.980618i | \(-0.562772\pi\) | ||||
−0.195930 | + | 0.980618i | \(0.562772\pi\) | |||||||
\(462\) | 13.8596 | 0.644808 | ||||||||
\(463\) | 14.0178 | 0.651464 | 0.325732 | − | 0.945462i | \(-0.394389\pi\) | ||||
0.325732 | + | 0.945462i | \(0.394389\pi\) | |||||||
\(464\) | 7.72086 | 0.358432 | ||||||||
\(465\) | −93.1298 | −4.31879 | ||||||||
\(466\) | −8.65945 | −0.401141 | ||||||||
\(467\) | 13.8392 | 0.640402 | 0.320201 | − | 0.947350i | \(-0.396250\pi\) | ||||
0.320201 | + | 0.947350i | \(0.396250\pi\) | |||||||
\(468\) | −26.1578 | −1.20914 | ||||||||
\(469\) | 8.61248 | 0.397688 | ||||||||
\(470\) | −20.7568 | −0.957438 | ||||||||
\(471\) | 64.3538 | 2.96527 | ||||||||
\(472\) | 8.53741 | 0.392966 | ||||||||
\(473\) | 24.3238 | 1.11841 | ||||||||
\(474\) | 43.3589 | 1.99154 | ||||||||
\(475\) | 67.8581 | 3.11354 | ||||||||
\(476\) | −2.34968 | −0.107697 | ||||||||
\(477\) | 89.5189 | 4.09879 | ||||||||
\(478\) | 9.49796 | 0.434427 | ||||||||
\(479\) | 10.4904 | 0.479320 | 0.239660 | − | 0.970857i | \(-0.422964\pi\) | ||||
0.239660 | + | 0.970857i | \(0.422964\pi\) | |||||||
\(480\) | 13.1712 | 0.601181 | ||||||||
\(481\) | 11.0920 | 0.505750 | ||||||||
\(482\) | −9.36709 | −0.426659 | ||||||||
\(483\) | −20.7296 | −0.943231 | ||||||||
\(484\) | 12.9285 | 0.587661 | ||||||||
\(485\) | 6.56137 | 0.297937 | ||||||||
\(486\) | −52.0067 | −2.35907 | ||||||||
\(487\) | −4.56912 | −0.207047 | −0.103523 | − | 0.994627i | \(-0.533012\pi\) | ||||
−0.103523 | + | 0.994627i | \(0.533012\pi\) | |||||||
\(488\) | −7.10692 | −0.321715 | ||||||||
\(489\) | 29.8715 | 1.35083 | ||||||||
\(490\) | 24.9267 | 1.12608 | ||||||||
\(491\) | −5.26184 | −0.237463 | −0.118732 | − | 0.992926i | \(-0.537883\pi\) | ||||
−0.118732 | + | 0.992926i | \(0.537883\pi\) | |||||||
\(492\) | −13.3222 | −0.600613 | ||||||||
\(493\) | −21.2073 | −0.955129 | ||||||||
\(494\) | −20.5945 | −0.926592 | ||||||||
\(495\) | 155.040 | 6.96852 | ||||||||
\(496\) | −7.07071 | −0.317484 | ||||||||
\(497\) | 6.34316 | 0.284530 | ||||||||
\(498\) | 42.3734 | 1.89880 | ||||||||
\(499\) | 5.52192 | 0.247195 | 0.123598 | − | 0.992332i | \(-0.460557\pi\) | ||||
0.123598 | + | 0.992332i | \(0.460557\pi\) | |||||||
\(500\) | −23.1204 | −1.03397 | ||||||||
\(501\) | −64.3206 | −2.87363 | ||||||||
\(502\) | −20.8698 | −0.931464 | ||||||||
\(503\) | 11.0229 | 0.491487 | 0.245743 | − | 0.969335i | \(-0.420968\pi\) | ||||
0.245743 | + | 0.969335i | \(0.420968\pi\) | |||||||
\(504\) | 6.81792 | 0.303695 | ||||||||
\(505\) | −25.7151 | −1.14431 | ||||||||
\(506\) | −35.7896 | −1.59104 | ||||||||
\(507\) | 7.38132 | 0.327816 | ||||||||
\(508\) | −5.55835 | −0.246612 | ||||||||
\(509\) | 23.6351 | 1.04761 | 0.523804 | − | 0.851839i | \(-0.324512\pi\) | ||||
0.523804 | + | 0.851839i | \(0.324512\pi\) | |||||||
\(510\) | −36.1781 | −1.60199 | ||||||||
\(511\) | 7.68303 | 0.339877 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −103.297 | −4.56067 | ||||||||
\(514\) | −3.94016 | −0.173793 | ||||||||
\(515\) | −68.9780 | −3.03953 | ||||||||
\(516\) | 16.4695 | 0.725028 | ||||||||
\(517\) | −25.5327 | −1.12293 | ||||||||
\(518\) | −2.89108 | −0.127027 | ||||||||
\(519\) | −38.0711 | −1.67113 | ||||||||
\(520\) | 13.0514 | 0.572342 | ||||||||
\(521\) | 43.8366 | 1.92052 | 0.960259 | − | 0.279110i | \(-0.0900395\pi\) | ||||
0.960259 | + | 0.279110i | \(0.0900395\pi\) | |||||||
\(522\) | 61.5361 | 2.69336 | ||||||||
\(523\) | −13.7026 | −0.599171 | −0.299585 | − | 0.954069i | \(-0.596848\pi\) | ||||
−0.299585 | + | 0.954069i | \(0.596848\pi\) | |||||||
\(524\) | −14.8483 | −0.648653 | ||||||||
\(525\) | −30.6393 | −1.33721 | ||||||||
\(526\) | 16.6206 | 0.724692 | ||||||||
\(527\) | 19.4215 | 0.846013 | ||||||||
\(528\) | 16.2018 | 0.705093 | ||||||||
\(529\) | 30.5299 | 1.32739 | ||||||||
\(530\) | −44.6654 | −1.94014 | ||||||||
\(531\) | 68.0440 | 2.95286 | ||||||||
\(532\) | 5.36789 | 0.232728 | ||||||||
\(533\) | −13.2010 | −0.571800 | ||||||||
\(534\) | 50.2235 | 2.17338 | ||||||||
\(535\) | −27.5502 | −1.19110 | ||||||||
\(536\) | 10.0679 | 0.434869 | ||||||||
\(537\) | −54.0263 | −2.33141 | ||||||||
\(538\) | 23.6989 | 1.02173 | ||||||||
\(539\) | 30.6622 | 1.32071 | ||||||||
\(540\) | 65.4624 | 2.81705 | ||||||||
\(541\) | −22.2254 | −0.955545 | −0.477772 | − | 0.878484i | \(-0.658556\pi\) | ||||
−0.477772 | + | 0.878484i | \(0.658556\pi\) | |||||||
\(542\) | 14.1471 | 0.607669 | ||||||||
\(543\) | 60.1914 | 2.58306 | ||||||||
\(544\) | −2.74675 | −0.117766 | ||||||||
\(545\) | 55.3276 | 2.36998 | ||||||||
\(546\) | 9.29886 | 0.397955 | ||||||||
\(547\) | −40.5695 | −1.73463 | −0.867314 | − | 0.497761i | \(-0.834156\pi\) | ||||
−0.867314 | + | 0.497761i | \(0.834156\pi\) | |||||||
\(548\) | 0.609707 | 0.0260454 | ||||||||
\(549\) | −56.6429 | −2.41746 | ||||||||
\(550\) | −52.8986 | −2.25560 | ||||||||
\(551\) | 48.4486 | 2.06398 | ||||||||
\(552\) | −24.2328 | −1.03142 | ||||||||
\(553\) | −11.1985 | −0.476209 | ||||||||
\(554\) | −0.941415 | −0.0399969 | ||||||||
\(555\) | −44.5142 | −1.88952 | ||||||||
\(556\) | −7.38651 | −0.313258 | ||||||||
\(557\) | 17.2950 | 0.732812 | 0.366406 | − | 0.930455i | \(-0.380588\pi\) | ||||
0.366406 | + | 0.930455i | \(0.380588\pi\) | |||||||
\(558\) | −56.3543 | −2.38567 | ||||||||
\(559\) | 16.3196 | 0.690247 | ||||||||
\(560\) | −3.40180 | −0.143752 | ||||||||
\(561\) | −44.5024 | −1.87889 | ||||||||
\(562\) | −11.5510 | −0.487249 | ||||||||
\(563\) | −26.9089 | −1.13407 | −0.567036 | − | 0.823693i | \(-0.691910\pi\) | ||||
−0.567036 | + | 0.823693i | \(0.691910\pi\) | |||||||
\(564\) | −17.2880 | −0.727955 | ||||||||
\(565\) | −8.08454 | −0.340119 | ||||||||
\(566\) | 9.51125 | 0.399788 | ||||||||
\(567\) | 26.1869 | 1.09975 | ||||||||
\(568\) | 7.41511 | 0.311131 | ||||||||
\(569\) | 4.49562 | 0.188466 | 0.0942331 | − | 0.995550i | \(-0.469960\pi\) | ||||
0.0942331 | + | 0.995550i | \(0.469960\pi\) | |||||||
\(570\) | 82.6498 | 3.46182 | ||||||||
\(571\) | 10.3471 | 0.433014 | 0.216507 | − | 0.976281i | \(-0.430534\pi\) | ||||
0.216507 | + | 0.976281i | \(0.430534\pi\) | |||||||
\(572\) | 16.0544 | 0.671269 | ||||||||
\(573\) | 30.7598 | 1.28501 | ||||||||
\(574\) | 3.44080 | 0.143616 | ||||||||
\(575\) | 79.1196 | 3.29952 | ||||||||
\(576\) | 7.97011 | 0.332088 | ||||||||
\(577\) | −24.5284 | −1.02113 | −0.510565 | − | 0.859839i | \(-0.670564\pi\) | ||||
−0.510565 | + | 0.859839i | \(0.670564\pi\) | |||||||
\(578\) | −9.45534 | −0.393290 | ||||||||
\(579\) | −19.7261 | −0.819789 | ||||||||
\(580\) | −30.7034 | −1.27489 | ||||||||
\(581\) | −10.9440 | −0.454033 | ||||||||
\(582\) | 5.46487 | 0.226526 | ||||||||
\(583\) | −54.9425 | −2.27549 | ||||||||
\(584\) | 8.98140 | 0.371653 | ||||||||
\(585\) | 104.021 | 4.30074 | ||||||||
\(586\) | −17.9313 | −0.740734 | ||||||||
\(587\) | −30.0531 | −1.24042 | −0.620212 | − | 0.784434i | \(-0.712954\pi\) | ||||
−0.620212 | + | 0.784434i | \(0.712954\pi\) | |||||||
\(588\) | 20.7611 | 0.856173 | ||||||||
\(589\) | −44.3689 | −1.82819 | ||||||||
\(590\) | −33.9505 | −1.39772 | ||||||||
\(591\) | 60.6247 | 2.49377 | ||||||||
\(592\) | −3.37965 | −0.138903 | ||||||||
\(593\) | 21.2526 | 0.872738 | 0.436369 | − | 0.899768i | \(-0.356264\pi\) | ||||
0.436369 | + | 0.899768i | \(0.356264\pi\) | |||||||
\(594\) | 80.5247 | 3.30397 | ||||||||
\(595\) | 9.34391 | 0.383063 | ||||||||
\(596\) | −13.9558 | −0.571653 | ||||||||
\(597\) | 45.0409 | 1.84340 | ||||||||
\(598\) | −24.0123 | −0.981938 | ||||||||
\(599\) | 0.983806 | 0.0401972 | 0.0200986 | − | 0.999798i | \(-0.493602\pi\) | ||||
0.0200986 | + | 0.999798i | \(0.493602\pi\) | |||||||
\(600\) | −35.8172 | −1.46223 | ||||||||
\(601\) | −11.6587 | −0.475570 | −0.237785 | − | 0.971318i | \(-0.576421\pi\) | ||||
−0.237785 | + | 0.971318i | \(0.576421\pi\) | |||||||
\(602\) | −4.25366 | −0.173366 | ||||||||
\(603\) | 80.2425 | 3.26773 | ||||||||
\(604\) | −19.8711 | −0.808542 | ||||||||
\(605\) | −51.4127 | −2.09022 | ||||||||
\(606\) | −21.4177 | −0.870036 | ||||||||
\(607\) | 35.2497 | 1.43074 | 0.715371 | − | 0.698744i | \(-0.246258\pi\) | ||||
0.715371 | + | 0.698744i | \(0.246258\pi\) | |||||||
\(608\) | 6.27503 | 0.254486 | ||||||||
\(609\) | −21.8756 | −0.886443 | ||||||||
\(610\) | 28.2620 | 1.14429 | ||||||||
\(611\) | −17.1307 | −0.693034 | ||||||||
\(612\) | −21.8919 | −0.884929 | ||||||||
\(613\) | 36.4150 | 1.47079 | 0.735393 | − | 0.677640i | \(-0.236997\pi\) | ||||
0.735393 | + | 0.677640i | \(0.236997\pi\) | |||||||
\(614\) | 24.3758 | 0.983728 | ||||||||
\(615\) | 52.9783 | 2.13629 | ||||||||
\(616\) | −4.18452 | −0.168599 | ||||||||
\(617\) | −32.6775 | −1.31555 | −0.657774 | − | 0.753215i | \(-0.728502\pi\) | ||||
−0.657774 | + | 0.753215i | \(0.728502\pi\) | |||||||
\(618\) | −57.4507 | −2.31101 | ||||||||
\(619\) | 6.83385 | 0.274676 | 0.137338 | − | 0.990524i | \(-0.456145\pi\) | ||||
0.137338 | + | 0.990524i | \(0.456145\pi\) | |||||||
\(620\) | 28.1179 | 1.12924 | ||||||||
\(621\) | −120.440 | −4.83308 | ||||||||
\(622\) | −12.2328 | −0.490492 | ||||||||
\(623\) | −12.9715 | −0.519692 | ||||||||
\(624\) | 10.8703 | 0.435161 | ||||||||
\(625\) | 37.8724 | 1.51489 | ||||||||
\(626\) | −16.4905 | −0.659093 | ||||||||
\(627\) | 101.667 | 4.06018 | ||||||||
\(628\) | −19.4298 | −0.775335 | ||||||||
\(629\) | 9.28308 | 0.370141 | ||||||||
\(630\) | −27.1127 | −1.08020 | ||||||||
\(631\) | 23.8248 | 0.948451 | 0.474226 | − | 0.880403i | \(-0.342728\pi\) | ||||
0.474226 | + | 0.880403i | \(0.342728\pi\) | |||||||
\(632\) | −13.0910 | −0.520732 | ||||||||
\(633\) | 38.5449 | 1.53202 | ||||||||
\(634\) | −20.6396 | −0.819702 | ||||||||
\(635\) | 22.1038 | 0.877162 | ||||||||
\(636\) | −37.2011 | −1.47512 | ||||||||
\(637\) | 20.5722 | 0.815101 | ||||||||
\(638\) | −37.7680 | −1.49525 | ||||||||
\(639\) | 59.0992 | 2.33793 | ||||||||
\(640\) | −3.97668 | −0.157192 | ||||||||
\(641\) | −1.37219 | −0.0541983 | −0.0270992 | − | 0.999633i | \(-0.508627\pi\) | ||||
−0.0270992 | + | 0.999633i | \(0.508627\pi\) | |||||||
\(642\) | −22.9461 | −0.905610 | ||||||||
\(643\) | 21.8486 | 0.861625 | 0.430812 | − | 0.902442i | \(-0.358227\pi\) | ||||
0.430812 | + | 0.902442i | \(0.358227\pi\) | |||||||
\(644\) | 6.25873 | 0.246629 | ||||||||
\(645\) | −65.4938 | −2.57882 | ||||||||
\(646\) | −17.2360 | −0.678140 | ||||||||
\(647\) | −27.0979 | −1.06533 | −0.532665 | − | 0.846326i | \(-0.678809\pi\) | ||||
−0.532665 | + | 0.846326i | \(0.678809\pi\) | |||||||
\(648\) | 30.6123 | 1.20256 | ||||||||
\(649\) | −41.7623 | −1.63931 | ||||||||
\(650\) | −35.4913 | −1.39208 | ||||||||
\(651\) | 20.0335 | 0.785174 | ||||||||
\(652\) | −9.01885 | −0.353205 | ||||||||
\(653\) | −11.4227 | −0.447006 | −0.223503 | − | 0.974703i | \(-0.571749\pi\) | ||||
−0.223503 | + | 0.974703i | \(0.571749\pi\) | |||||||
\(654\) | 46.0815 | 1.80193 | ||||||||
\(655\) | 59.0471 | 2.30716 | ||||||||
\(656\) | 4.02227 | 0.157043 | ||||||||
\(657\) | 71.5827 | 2.79271 | ||||||||
\(658\) | 4.46506 | 0.174066 | ||||||||
\(659\) | −19.0063 | −0.740380 | −0.370190 | − | 0.928956i | \(-0.620707\pi\) | ||||
−0.370190 | + | 0.928956i | \(0.620707\pi\) | |||||||
\(660\) | −64.4294 | −2.50791 | ||||||||
\(661\) | 36.5946 | 1.42337 | 0.711683 | − | 0.702501i | \(-0.247933\pi\) | ||||
0.711683 | + | 0.702501i | \(0.247933\pi\) | |||||||
\(662\) | 18.7141 | 0.727346 | ||||||||
\(663\) | −29.8581 | −1.15959 | ||||||||
\(664\) | −12.7934 | −0.496482 | ||||||||
\(665\) | −21.3464 | −0.827777 | ||||||||
\(666\) | −26.9362 | −1.04376 | ||||||||
\(667\) | 56.4890 | 2.18726 | ||||||||
\(668\) | 19.4198 | 0.751375 | ||||||||
\(669\) | −15.8709 | −0.613605 | ||||||||
\(670\) | −40.0370 | −1.54676 | ||||||||
\(671\) | 34.7648 | 1.34208 | ||||||||
\(672\) | −2.83331 | −0.109297 | ||||||||
\(673\) | −29.4403 | −1.13484 | −0.567419 | − | 0.823429i | \(-0.692058\pi\) | ||||
−0.567419 | + | 0.823429i | \(0.692058\pi\) | |||||||
\(674\) | −14.6929 | −0.565949 | ||||||||
\(675\) | −178.015 | −6.85181 | ||||||||
\(676\) | −2.22858 | −0.0857147 | ||||||||
\(677\) | −17.8650 | −0.686608 | −0.343304 | − | 0.939224i | \(-0.611546\pi\) | ||||
−0.343304 | + | 0.939224i | \(0.611546\pi\) | |||||||
\(678\) | −6.73349 | −0.258598 | ||||||||
\(679\) | −1.41144 | −0.0541661 | ||||||||
\(680\) | 10.9230 | 0.418877 | ||||||||
\(681\) | −53.9835 | −2.06865 | ||||||||
\(682\) | 34.5876 | 1.32443 | ||||||||
\(683\) | 31.7788 | 1.21598 | 0.607992 | − | 0.793943i | \(-0.291975\pi\) | ||||
0.607992 | + | 0.793943i | \(0.291975\pi\) | |||||||
\(684\) | 50.0126 | 1.91228 | ||||||||
\(685\) | −2.42461 | −0.0926396 | ||||||||
\(686\) | −11.3501 | −0.433350 | ||||||||
\(687\) | −88.4638 | −3.37511 | ||||||||
\(688\) | −4.97249 | −0.189575 | ||||||||
\(689\) | −36.8627 | −1.40436 | ||||||||
\(690\) | 96.3661 | 3.66860 | ||||||||
\(691\) | 20.2153 | 0.769028 | 0.384514 | − | 0.923119i | \(-0.374369\pi\) | ||||
0.384514 | + | 0.923119i | \(0.374369\pi\) | |||||||
\(692\) | 11.4945 | 0.436955 | ||||||||
\(693\) | −33.3511 | −1.26690 | ||||||||
\(694\) | 6.47579 | 0.245818 | ||||||||
\(695\) | 29.3738 | 1.11421 | ||||||||
\(696\) | −25.5724 | −0.969319 | ||||||||
\(697\) | −11.0482 | −0.418480 | ||||||||
\(698\) | −12.4695 | −0.471979 | ||||||||
\(699\) | 28.6811 | 1.08482 | ||||||||
\(700\) | 9.25068 | 0.349643 | ||||||||
\(701\) | −22.2866 | −0.841755 | −0.420877 | − | 0.907117i | \(-0.638278\pi\) | ||||
−0.420877 | + | 0.907117i | \(0.638278\pi\) | |||||||
\(702\) | 54.0266 | 2.03910 | ||||||||
\(703\) | −21.2074 | −0.799853 | ||||||||
\(704\) | −4.89168 | −0.184362 | ||||||||
\(705\) | 68.7488 | 2.58923 | ||||||||
\(706\) | 23.7610 | 0.894257 | ||||||||
\(707\) | 5.53167 | 0.208040 | ||||||||
\(708\) | −28.2769 | −1.06271 | ||||||||
\(709\) | −34.2975 | −1.28807 | −0.644035 | − | 0.764996i | \(-0.722741\pi\) | ||||
−0.644035 | + | 0.764996i | \(0.722741\pi\) | |||||||
\(710\) | −29.4875 | −1.10665 | ||||||||
\(711\) | −104.337 | −3.91293 | ||||||||
\(712\) | −15.1636 | −0.568279 | ||||||||
\(713\) | −51.7322 | −1.93739 | ||||||||
\(714\) | 7.78240 | 0.291249 | ||||||||
\(715\) | −63.8433 | −2.38760 | ||||||||
\(716\) | 16.3117 | 0.609598 | ||||||||
\(717\) | −31.4583 | −1.17483 | ||||||||
\(718\) | −33.1864 | −1.23851 | ||||||||
\(719\) | −47.9723 | −1.78906 | −0.894532 | − | 0.447004i | \(-0.852491\pi\) | ||||
−0.894532 | + | 0.447004i | \(0.852491\pi\) | |||||||
\(720\) | −31.6946 | −1.18119 | ||||||||
\(721\) | 14.8381 | 0.552599 | ||||||||
\(722\) | 20.3760 | 0.758315 | ||||||||
\(723\) | 31.0249 | 1.15383 | ||||||||
\(724\) | −18.1731 | −0.675398 | ||||||||
\(725\) | 83.4933 | 3.10086 | ||||||||
\(726\) | −42.8208 | −1.58923 | ||||||||
\(727\) | −20.0838 | −0.744865 | −0.372433 | − | 0.928059i | \(-0.621476\pi\) | ||||
−0.372433 | + | 0.928059i | \(0.621476\pi\) | |||||||
\(728\) | −2.80753 | −0.104054 | ||||||||
\(729\) | 80.4154 | 2.97835 | ||||||||
\(730\) | −35.7162 | −1.32191 | ||||||||
\(731\) | 13.6582 | 0.505167 | ||||||||
\(732\) | 23.5389 | 0.870024 | ||||||||
\(733\) | 29.8249 | 1.10161 | 0.550803 | − | 0.834635i | \(-0.314321\pi\) | ||||
0.550803 | + | 0.834635i | \(0.314321\pi\) | |||||||
\(734\) | 15.1489 | 0.559156 | ||||||||
\(735\) | −82.5602 | −3.04528 | ||||||||
\(736\) | 7.31641 | 0.269687 | ||||||||
\(737\) | −49.2491 | −1.81411 | ||||||||
\(738\) | 32.0580 | 1.18007 | ||||||||
\(739\) | −28.0876 | −1.03322 | −0.516610 | − | 0.856221i | \(-0.672806\pi\) | ||||
−0.516610 | + | 0.856221i | \(0.672806\pi\) | |||||||
\(740\) | 13.4398 | 0.494057 | ||||||||
\(741\) | 68.2115 | 2.50581 | ||||||||
\(742\) | 9.60812 | 0.352725 | ||||||||
\(743\) | 15.9967 | 0.586863 | 0.293431 | − | 0.955980i | \(-0.405203\pi\) | ||||
0.293431 | + | 0.955980i | \(0.405203\pi\) | |||||||
\(744\) | 23.4190 | 0.858582 | ||||||||
\(745\) | 55.4979 | 2.03328 | ||||||||
\(746\) | −12.2667 | −0.449115 | ||||||||
\(747\) | −101.965 | −3.73071 | ||||||||
\(748\) | 13.4362 | 0.491278 | ||||||||
\(749\) | 5.92641 | 0.216546 | ||||||||
\(750\) | 76.5773 | 2.79621 | ||||||||
\(751\) | 4.89620 | 0.178665 | 0.0893324 | − | 0.996002i | \(-0.471527\pi\) | ||||
0.0893324 | + | 0.996002i | \(0.471527\pi\) | |||||||
\(752\) | 5.21962 | 0.190340 | ||||||||
\(753\) | 69.1231 | 2.51899 | ||||||||
\(754\) | −25.3397 | −0.922819 | ||||||||
\(755\) | 79.0208 | 2.87586 | ||||||||
\(756\) | −14.0818 | −0.512151 | ||||||||
\(757\) | 40.4645 | 1.47071 | 0.735354 | − | 0.677684i | \(-0.237016\pi\) | ||||
0.735354 | + | 0.677684i | \(0.237016\pi\) | |||||||
\(758\) | 2.22253 | 0.0807260 | ||||||||
\(759\) | 118.539 | 4.30270 | ||||||||
\(760\) | −24.9538 | −0.905169 | ||||||||
\(761\) | −38.8638 | −1.40881 | −0.704405 | − | 0.709798i | \(-0.748786\pi\) | ||||
−0.704405 | + | 0.709798i | \(0.748786\pi\) | |||||||
\(762\) | 18.4099 | 0.666920 | ||||||||
\(763\) | −11.9017 | −0.430871 | ||||||||
\(764\) | −9.28707 | −0.335994 | ||||||||
\(765\) | 87.0572 | 3.14756 | ||||||||
\(766\) | −7.09815 | −0.256467 | ||||||||
\(767\) | −28.0196 | −1.01173 | ||||||||
\(768\) | −3.31212 | −0.119516 | ||||||||
\(769\) | 19.2216 | 0.693150 | 0.346575 | − | 0.938022i | \(-0.387345\pi\) | ||||
0.346575 | + | 0.938022i | \(0.387345\pi\) | |||||||
\(770\) | 16.6405 | 0.599683 | ||||||||
\(771\) | 13.0502 | 0.469993 | ||||||||
\(772\) | 5.95574 | 0.214352 | ||||||||
\(773\) | −39.6644 | −1.42663 | −0.713314 | − | 0.700845i | \(-0.752807\pi\) | ||||
−0.713314 | + | 0.700845i | \(0.752807\pi\) | |||||||
\(774\) | −39.6313 | −1.42452 | ||||||||
\(775\) | −76.4625 | −2.74661 | ||||||||
\(776\) | −1.64996 | −0.0592302 | ||||||||
\(777\) | 9.57559 | 0.343522 | ||||||||
\(778\) | −29.9360 | −1.07326 | ||||||||
\(779\) | 25.2399 | 0.904313 | ||||||||
\(780\) | −43.2277 | −1.54780 | ||||||||
\(781\) | −36.2723 | −1.29793 | ||||||||
\(782\) | −20.0964 | −0.718645 | ||||||||
\(783\) | −127.097 | −4.54209 | ||||||||
\(784\) | −6.26823 | −0.223865 | ||||||||
\(785\) | 77.2662 | 2.75775 | ||||||||
\(786\) | 49.1794 | 1.75417 | ||||||||
\(787\) | −18.6831 | −0.665981 | −0.332991 | − | 0.942930i | \(-0.608058\pi\) | ||||
−0.332991 | + | 0.942930i | \(0.608058\pi\) | |||||||
\(788\) | −18.3039 | −0.652050 | ||||||||
\(789\) | −55.0493 | −1.95981 | ||||||||
\(790\) | 52.0587 | 1.85216 | ||||||||
\(791\) | 1.73909 | 0.0618350 | ||||||||
\(792\) | −38.9872 | −1.38535 | ||||||||
\(793\) | 23.3248 | 0.828288 | ||||||||
\(794\) | −16.5297 | −0.586615 | ||||||||
\(795\) | 147.937 | 5.24678 | ||||||||
\(796\) | −13.5988 | −0.481998 | ||||||||
\(797\) | −48.3585 | −1.71295 | −0.856474 | − | 0.516191i | \(-0.827350\pi\) | ||||
−0.856474 | + | 0.516191i | \(0.827350\pi\) | |||||||
\(798\) | −17.7791 | −0.629372 | ||||||||
\(799\) | −14.3370 | −0.507207 | ||||||||
\(800\) | 10.8140 | 0.382332 | ||||||||
\(801\) | −120.855 | −4.27021 | ||||||||
\(802\) | −1.55115 | −0.0547731 | ||||||||
\(803\) | −43.9342 | −1.55040 | ||||||||
\(804\) | −33.3462 | −1.17603 | ||||||||
\(805\) | −24.8890 | −0.877221 | ||||||||
\(806\) | 23.2059 | 0.817394 | ||||||||
\(807\) | −78.4936 | −2.76311 | ||||||||
\(808\) | 6.46648 | 0.227490 | ||||||||
\(809\) | 3.12392 | 0.109831 | 0.0549157 | − | 0.998491i | \(-0.482511\pi\) | ||||
0.0549157 | + | 0.998491i | \(0.482511\pi\) | |||||||
\(810\) | −121.735 | −4.27734 | ||||||||
\(811\) | −5.42327 | −0.190437 | −0.0952183 | − | 0.995456i | \(-0.530355\pi\) | ||||
−0.0952183 | + | 0.995456i | \(0.530355\pi\) | |||||||
\(812\) | 6.60471 | 0.231780 | ||||||||
\(813\) | −46.8567 | −1.64334 | ||||||||
\(814\) | 16.5322 | 0.579453 | ||||||||
\(815\) | 35.8651 | 1.25630 | ||||||||
\(816\) | 9.09757 | 0.318479 | ||||||||
\(817\) | −31.2025 | −1.09164 | ||||||||
\(818\) | −3.93256 | −0.137499 | ||||||||
\(819\) | −22.3763 | −0.781892 | ||||||||
\(820\) | −15.9953 | −0.558580 | ||||||||
\(821\) | −10.5461 | −0.368060 | −0.184030 | − | 0.982921i | \(-0.558914\pi\) | ||||
−0.184030 | + | 0.982921i | \(0.558914\pi\) | |||||||
\(822\) | −2.01942 | −0.0704354 | ||||||||
\(823\) | −3.36285 | −0.117222 | −0.0586109 | − | 0.998281i | \(-0.518667\pi\) | ||||
−0.0586109 | + | 0.998281i | \(0.518667\pi\) | |||||||
\(824\) | 17.3456 | 0.604263 | ||||||||
\(825\) | 175.206 | 6.09989 | ||||||||
\(826\) | 7.30321 | 0.254111 | ||||||||
\(827\) | −10.7581 | −0.374094 | −0.187047 | − | 0.982351i | \(-0.559892\pi\) | ||||
−0.187047 | + | 0.982351i | \(0.559892\pi\) | |||||||
\(828\) | 58.3126 | 2.02650 | ||||||||
\(829\) | −18.7899 | −0.652601 | −0.326300 | − | 0.945266i | \(-0.605802\pi\) | ||||
−0.326300 | + | 0.945266i | \(0.605802\pi\) | |||||||
\(830\) | 50.8754 | 1.76591 | ||||||||
\(831\) | 3.11807 | 0.108165 | ||||||||
\(832\) | −3.28198 | −0.113782 | ||||||||
\(833\) | 17.2173 | 0.596543 | ||||||||
\(834\) | 24.4650 | 0.847152 | ||||||||
\(835\) | −77.2263 | −2.67253 | ||||||||
\(836\) | −30.6954 | −1.06162 | ||||||||
\(837\) | 116.395 | 4.02320 | ||||||||
\(838\) | 22.1606 | 0.765525 | ||||||||
\(839\) | −34.2303 | −1.18176 | −0.590880 | − | 0.806759i | \(-0.701219\pi\) | ||||
−0.590880 | + | 0.806759i | \(0.701219\pi\) | |||||||
\(840\) | 11.2672 | 0.388754 | ||||||||
\(841\) | 30.6117 | 1.05558 | ||||||||
\(842\) | 7.33855 | 0.252903 | ||||||||
\(843\) | 38.2582 | 1.31768 | ||||||||
\(844\) | −11.6376 | −0.400581 | ||||||||
\(845\) | 8.86236 | 0.304874 | ||||||||
\(846\) | 41.6009 | 1.43027 | ||||||||
\(847\) | 11.0595 | 0.380011 | ||||||||
\(848\) | 11.2318 | 0.385703 | ||||||||
\(849\) | −31.5023 | −1.08116 | ||||||||
\(850\) | −29.7034 | −1.01882 | ||||||||
\(851\) | −24.7269 | −0.847629 | ||||||||
\(852\) | −24.5597 | −0.841401 | ||||||||
\(853\) | −35.6390 | −1.22026 | −0.610129 | − | 0.792302i | \(-0.708882\pi\) | ||||
−0.610129 | + | 0.792302i | \(0.708882\pi\) | |||||||
\(854\) | −6.07952 | −0.208037 | ||||||||
\(855\) | −198.884 | −6.80170 | ||||||||
\(856\) | 6.92793 | 0.236792 | ||||||||
\(857\) | −33.5365 | −1.14559 | −0.572793 | − | 0.819700i | \(-0.694140\pi\) | ||||
−0.572793 | + | 0.819700i | \(0.694140\pi\) | |||||||
\(858\) | −53.1741 | −1.81533 | ||||||||
\(859\) | −4.01706 | −0.137060 | −0.0685302 | − | 0.997649i | \(-0.521831\pi\) | ||||
−0.0685302 | + | 0.997649i | \(0.521831\pi\) | |||||||
\(860\) | 19.7740 | 0.674288 | ||||||||
\(861\) | −11.3963 | −0.388386 | ||||||||
\(862\) | 6.05414 | 0.206205 | ||||||||
\(863\) | 21.1975 | 0.721572 | 0.360786 | − | 0.932649i | \(-0.382509\pi\) | ||||
0.360786 | + | 0.932649i | \(0.382509\pi\) | |||||||
\(864\) | −16.4616 | −0.560034 | ||||||||
\(865\) | −45.7099 | −1.55418 | ||||||||
\(866\) | −12.2248 | −0.415414 | ||||||||
\(867\) | 31.3172 | 1.06359 | ||||||||
\(868\) | −6.04854 | −0.205301 | ||||||||
\(869\) | 64.0369 | 2.17230 | ||||||||
\(870\) | 101.693 | 3.44772 | ||||||||
\(871\) | −33.0428 | −1.11961 | ||||||||
\(872\) | −13.9130 | −0.471154 | ||||||||
\(873\) | −13.1504 | −0.445073 | ||||||||
\(874\) | 45.9107 | 1.55295 | ||||||||
\(875\) | −19.7780 | −0.668619 | ||||||||
\(876\) | −29.7474 | −1.00507 | ||||||||
\(877\) | −16.2533 | −0.548835 | −0.274418 | − | 0.961611i | \(-0.588485\pi\) | ||||
−0.274418 | + | 0.961611i | \(0.588485\pi\) | |||||||
\(878\) | 18.9382 | 0.639135 | ||||||||
\(879\) | 59.3905 | 2.00319 | ||||||||
\(880\) | 19.4526 | 0.655749 | ||||||||
\(881\) | −51.3185 | −1.72896 | −0.864482 | − | 0.502663i | \(-0.832354\pi\) | ||||
−0.864482 | + | 0.502663i | \(0.832354\pi\) | |||||||
\(882\) | −49.9584 | −1.68219 | ||||||||
\(883\) | −15.0695 | −0.507129 | −0.253564 | − | 0.967319i | \(-0.581603\pi\) | ||||
−0.253564 | + | 0.967319i | \(0.581603\pi\) | |||||||
\(884\) | 9.01480 | 0.303201 | ||||||||
\(885\) | 112.448 | 3.77990 | ||||||||
\(886\) | 21.9860 | 0.738633 | ||||||||
\(887\) | −10.3731 | −0.348295 | −0.174148 | − | 0.984720i | \(-0.555717\pi\) | ||||
−0.174148 | + | 0.984720i | \(0.555717\pi\) | |||||||
\(888\) | 11.1938 | 0.375639 | ||||||||
\(889\) | −4.75482 | −0.159471 | ||||||||
\(890\) | 60.3007 | 2.02128 | ||||||||
\(891\) | −149.746 | −5.01666 | ||||||||
\(892\) | 4.79178 | 0.160441 | ||||||||
\(893\) | 32.7533 | 1.09605 | ||||||||
\(894\) | 46.2233 | 1.54594 | ||||||||
\(895\) | −64.8665 | −2.16825 | ||||||||
\(896\) | 0.855437 | 0.0285781 | ||||||||
\(897\) | 79.5317 | 2.65549 | ||||||||
\(898\) | 16.3688 | 0.546232 | ||||||||
\(899\) | −54.5919 | −1.82074 | ||||||||
\(900\) | 86.1886 | 2.87295 | ||||||||
\(901\) | −30.8511 | −1.02780 | ||||||||
\(902\) | −19.6757 | −0.655128 | ||||||||
\(903\) | 14.0886 | 0.468839 | ||||||||
\(904\) | 2.03299 | 0.0676161 | ||||||||
\(905\) | 72.2686 | 2.40229 | ||||||||
\(906\) | 65.8152 | 2.18656 | ||||||||
\(907\) | 31.1543 | 1.03446 | 0.517232 | − | 0.855845i | \(-0.326963\pi\) | ||||
0.517232 | + | 0.855845i | \(0.326963\pi\) | |||||||
\(908\) | 16.2988 | 0.540895 | ||||||||
\(909\) | 51.5385 | 1.70943 | ||||||||
\(910\) | 11.1647 | 0.370105 | ||||||||
\(911\) | −30.7928 | −1.02021 | −0.510105 | − | 0.860112i | \(-0.670393\pi\) | ||||
−0.510105 | + | 0.860112i | \(0.670393\pi\) | |||||||
\(912\) | −20.7836 | −0.688214 | ||||||||
\(913\) | 62.5815 | 2.07114 | ||||||||
\(914\) | −15.8092 | −0.522921 | ||||||||
\(915\) | −93.6068 | −3.09455 | ||||||||
\(916\) | 26.7092 | 0.882496 | ||||||||
\(917\) | −12.7018 | −0.419451 | ||||||||
\(918\) | 45.2159 | 1.49235 | ||||||||
\(919\) | −23.8736 | −0.787518 | −0.393759 | − | 0.919214i | \(-0.628826\pi\) | ||||
−0.393759 | + | 0.919214i | \(0.628826\pi\) | |||||||
\(920\) | −29.0950 | −0.959235 | ||||||||
\(921\) | −80.7355 | −2.66033 | ||||||||
\(922\) | −8.41358 | −0.277087 | ||||||||
\(923\) | −24.3363 | −0.801038 | ||||||||
\(924\) | 13.8596 | 0.455948 | ||||||||
\(925\) | −36.5475 | −1.20168 | ||||||||
\(926\) | 14.0178 | 0.460654 | ||||||||
\(927\) | 138.246 | 4.54061 | ||||||||
\(928\) | 7.72086 | 0.253450 | ||||||||
\(929\) | 1.50590 | 0.0494068 | 0.0247034 | − | 0.999695i | \(-0.492136\pi\) | ||||
0.0247034 | + | 0.999695i | \(0.492136\pi\) | |||||||
\(930\) | −93.1298 | −3.05385 | ||||||||
\(931\) | −39.3333 | −1.28910 | ||||||||
\(932\) | −8.65945 | −0.283650 | ||||||||
\(933\) | 40.5165 | 1.32645 | ||||||||
\(934\) | 13.8392 | 0.452833 | ||||||||
\(935\) | −53.4316 | −1.74740 | ||||||||
\(936\) | −26.1578 | −0.854993 | ||||||||
\(937\) | 1.49201 | 0.0487418 | 0.0243709 | − | 0.999703i | \(-0.492242\pi\) | ||||
0.0243709 | + | 0.999703i | \(0.492242\pi\) | |||||||
\(938\) | 8.61248 | 0.281208 | ||||||||
\(939\) | 54.6184 | 1.78240 | ||||||||
\(940\) | −20.7568 | −0.677011 | ||||||||
\(941\) | 1.47577 | 0.0481086 | 0.0240543 | − | 0.999711i | \(-0.492343\pi\) | ||||
0.0240543 | + | 0.999711i | \(0.492343\pi\) | |||||||
\(942\) | 64.3538 | 2.09676 | ||||||||
\(943\) | 29.4286 | 0.958328 | ||||||||
\(944\) | 8.53741 | 0.277869 | ||||||||
\(945\) | 55.9990 | 1.82165 | ||||||||
\(946\) | 24.3238 | 0.790837 | ||||||||
\(947\) | −9.75887 | −0.317121 | −0.158560 | − | 0.987349i | \(-0.550685\pi\) | ||||
−0.158560 | + | 0.987349i | \(0.550685\pi\) | |||||||
\(948\) | 43.3589 | 1.40823 | ||||||||
\(949\) | −29.4768 | −0.956858 | ||||||||
\(950\) | 67.8581 | 2.20161 | ||||||||
\(951\) | 68.3606 | 2.21675 | ||||||||
\(952\) | −2.34968 | −0.0761534 | ||||||||
\(953\) | −10.1264 | −0.328025 | −0.164012 | − | 0.986458i | \(-0.552444\pi\) | ||||
−0.164012 | + | 0.986458i | \(0.552444\pi\) | |||||||
\(954\) | 89.5189 | 2.89828 | ||||||||
\(955\) | 36.9317 | 1.19508 | ||||||||
\(956\) | 9.49796 | 0.307186 | ||||||||
\(957\) | 125.092 | 4.04365 | ||||||||
\(958\) | 10.4904 | 0.338930 | ||||||||
\(959\) | 0.521566 | 0.0168422 | ||||||||
\(960\) | 13.1712 | 0.425099 | ||||||||
\(961\) | 18.9949 | 0.612738 | ||||||||
\(962\) | 11.0920 | 0.357619 | ||||||||
\(963\) | 55.2163 | 1.77932 | ||||||||
\(964\) | −9.36709 | −0.301694 | ||||||||
\(965\) | −23.6841 | −0.762417 | ||||||||
\(966\) | −20.7296 | −0.666965 | ||||||||
\(967\) | −47.0815 | −1.51404 | −0.757019 | − | 0.653392i | \(-0.773345\pi\) | ||||
−0.757019 | + | 0.653392i | \(0.773345\pi\) | |||||||
\(968\) | 12.9285 | 0.415539 | ||||||||
\(969\) | 57.0875 | 1.83391 | ||||||||
\(970\) | 6.56137 | 0.210673 | ||||||||
\(971\) | 7.05243 | 0.226323 | 0.113162 | − | 0.993577i | \(-0.463902\pi\) | ||||
0.113162 | + | 0.993577i | \(0.463902\pi\) | |||||||
\(972\) | −52.0067 | −1.66812 | ||||||||
\(973\) | −6.31869 | −0.202568 | ||||||||
\(974\) | −4.56912 | −0.146404 | ||||||||
\(975\) | 117.551 | 3.76466 | ||||||||
\(976\) | −7.10692 | −0.227487 | ||||||||
\(977\) | −42.6704 | −1.36515 | −0.682573 | − | 0.730818i | \(-0.739139\pi\) | ||||
−0.682573 | + | 0.730818i | \(0.739139\pi\) | |||||||
\(978\) | 29.8715 | 0.955184 | ||||||||
\(979\) | 74.1754 | 2.37066 | ||||||||
\(980\) | 24.9267 | 0.796255 | ||||||||
\(981\) | −110.888 | −3.54039 | ||||||||
\(982\) | −5.26184 | −0.167912 | ||||||||
\(983\) | 28.7096 | 0.915695 | 0.457848 | − | 0.889031i | \(-0.348621\pi\) | ||||
0.457848 | + | 0.889031i | \(0.348621\pi\) | |||||||
\(984\) | −13.3222 | −0.424697 | ||||||||
\(985\) | 72.7888 | 2.31924 | ||||||||
\(986\) | −21.2073 | −0.675378 | ||||||||
\(987\) | −14.7888 | −0.470732 | ||||||||
\(988\) | −20.5945 | −0.655200 | ||||||||
\(989\) | −36.3808 | −1.15684 | ||||||||
\(990\) | 155.040 | 4.92748 | ||||||||
\(991\) | −10.8436 | −0.344457 | −0.172228 | − | 0.985057i | \(-0.555097\pi\) | ||||
−0.172228 | + | 0.985057i | \(0.555097\pi\) | |||||||
\(992\) | −7.07071 | −0.224495 | ||||||||
\(993\) | −61.9834 | −1.96698 | ||||||||
\(994\) | 6.34316 | 0.201193 | ||||||||
\(995\) | 54.0782 | 1.71440 | ||||||||
\(996\) | 42.3734 | 1.34265 | ||||||||
\(997\) | −10.8630 | −0.344035 | −0.172017 | − | 0.985094i | \(-0.555028\pi\) | ||||
−0.172017 | + | 0.985094i | \(0.555028\pi\) | |||||||
\(998\) | 5.52192 | 0.174793 | ||||||||
\(999\) | 55.6344 | 1.76019 |
(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 | 4034.2.a.a.1.2 | ✓ | 33 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4034.2.a.a.1.2 | ✓ | 33 | 1.1 | even | 1 | trivial |