Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6007,2,Mod(1,6007)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6007, 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("6007.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6007 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6007.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: | \(47.9661364942\) |
Analytic rank: | \(0\) |
Dimension: | \(261\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.7 | ||
Character | \(\chi\) | \(=\) | 6007.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.63601 | −1.86394 | −0.931971 | − | 0.362533i | \(-0.881912\pi\) | ||||
−0.931971 | + | 0.362533i | \(0.881912\pi\) | |||||||
\(3\) | 0.145552 | 0.0840347 | 0.0420174 | − | 0.999117i | \(-0.486622\pi\) | ||||
0.0420174 | + | 0.999117i | \(0.486622\pi\) | |||||||
\(4\) | 4.94856 | 2.47428 | ||||||||
\(5\) | 0.530894 | 0.237423 | 0.118711 | − | 0.992929i | \(-0.462124\pi\) | ||||
0.118711 | + | 0.992929i | \(0.462124\pi\) | |||||||
\(6\) | −0.383678 | −0.156636 | ||||||||
\(7\) | 0.464377 | 0.175518 | 0.0877590 | − | 0.996142i | \(-0.472029\pi\) | ||||
0.0877590 | + | 0.996142i | \(0.472029\pi\) | |||||||
\(8\) | −7.77243 | −2.74797 | ||||||||
\(9\) | −2.97881 | −0.992938 | ||||||||
\(10\) | −1.39944 | −0.442543 | ||||||||
\(11\) | 3.49469 | 1.05369 | 0.526845 | − | 0.849961i | \(-0.323375\pi\) | ||||
0.526845 | + | 0.849961i | \(0.323375\pi\) | |||||||
\(12\) | 0.720274 | 0.207925 | ||||||||
\(13\) | 5.14638 | 1.42735 | 0.713674 | − | 0.700478i | \(-0.247030\pi\) | ||||
0.713674 | + | 0.700478i | \(0.247030\pi\) | |||||||
\(14\) | −1.22410 | −0.327155 | ||||||||
\(15\) | 0.0772729 | 0.0199518 | ||||||||
\(16\) | 10.5911 | 2.64777 | ||||||||
\(17\) | −1.13332 | −0.274870 | −0.137435 | − | 0.990511i | \(-0.543886\pi\) | ||||
−0.137435 | + | 0.990511i | \(0.543886\pi\) | |||||||
\(18\) | 7.85219 | 1.85078 | ||||||||
\(19\) | −4.89648 | −1.12333 | −0.561665 | − | 0.827365i | \(-0.689839\pi\) | ||||
−0.561665 | + | 0.827365i | \(0.689839\pi\) | |||||||
\(20\) | 2.62716 | 0.587450 | ||||||||
\(21\) | 0.0675912 | 0.0147496 | ||||||||
\(22\) | −9.21205 | −1.96402 | ||||||||
\(23\) | −7.53211 | −1.57055 | −0.785276 | − | 0.619145i | \(-0.787479\pi\) | ||||
−0.785276 | + | 0.619145i | \(0.787479\pi\) | |||||||
\(24\) | −1.13130 | −0.230925 | ||||||||
\(25\) | −4.71815 | −0.943630 | ||||||||
\(26\) | −13.5659 | −2.66049 | ||||||||
\(27\) | −0.870231 | −0.167476 | ||||||||
\(28\) | 2.29800 | 0.434281 | ||||||||
\(29\) | 3.17919 | 0.590361 | 0.295180 | − | 0.955442i | \(-0.404620\pi\) | ||||
0.295180 | + | 0.955442i | \(0.404620\pi\) | |||||||
\(30\) | −0.203692 | −0.0371889 | ||||||||
\(31\) | −0.803639 | −0.144338 | −0.0721689 | − | 0.997392i | \(-0.522992\pi\) | ||||
−0.0721689 | + | 0.997392i | \(0.522992\pi\) | |||||||
\(32\) | −12.3734 | −2.18733 | ||||||||
\(33\) | 0.508661 | 0.0885466 | ||||||||
\(34\) | 2.98744 | 0.512342 | ||||||||
\(35\) | 0.246535 | 0.0416720 | ||||||||
\(36\) | −14.7408 | −2.45681 | ||||||||
\(37\) | −2.21469 | −0.364093 | −0.182047 | − | 0.983290i | \(-0.558272\pi\) | ||||
−0.182047 | + | 0.983290i | \(0.558272\pi\) | |||||||
\(38\) | 12.9072 | 2.09382 | ||||||||
\(39\) | 0.749068 | 0.119947 | ||||||||
\(40\) | −4.12633 | −0.652431 | ||||||||
\(41\) | 7.88114 | 1.23083 | 0.615413 | − | 0.788205i | \(-0.288989\pi\) | ||||
0.615413 | + | 0.788205i | \(0.288989\pi\) | |||||||
\(42\) | −0.178171 | −0.0274924 | ||||||||
\(43\) | −4.69155 | −0.715455 | −0.357727 | − | 0.933826i | \(-0.616448\pi\) | ||||
−0.357727 | + | 0.933826i | \(0.616448\pi\) | |||||||
\(44\) | 17.2937 | 2.60712 | ||||||||
\(45\) | −1.58143 | −0.235746 | ||||||||
\(46\) | 19.8547 | 2.92742 | ||||||||
\(47\) | 6.42226 | 0.936783 | 0.468391 | − | 0.883521i | \(-0.344834\pi\) | ||||
0.468391 | + | 0.883521i | \(0.344834\pi\) | |||||||
\(48\) | 1.54156 | 0.222505 | ||||||||
\(49\) | −6.78435 | −0.969193 | ||||||||
\(50\) | 12.4371 | 1.75887 | ||||||||
\(51\) | −0.164957 | −0.0230986 | ||||||||
\(52\) | 25.4671 | 3.53166 | ||||||||
\(53\) | 5.01065 | 0.688266 | 0.344133 | − | 0.938921i | \(-0.388173\pi\) | ||||
0.344133 | + | 0.938921i | \(0.388173\pi\) | |||||||
\(54\) | 2.29394 | 0.312166 | ||||||||
\(55\) | 1.85531 | 0.250170 | ||||||||
\(56\) | −3.60934 | −0.482318 | ||||||||
\(57\) | −0.712695 | −0.0943988 | ||||||||
\(58\) | −8.38038 | −1.10040 | ||||||||
\(59\) | 8.41858 | 1.09601 | 0.548003 | − | 0.836476i | \(-0.315388\pi\) | ||||
0.548003 | + | 0.836476i | \(0.315388\pi\) | |||||||
\(60\) | 0.382389 | 0.0493662 | ||||||||
\(61\) | −8.02261 | −1.02719 | −0.513595 | − | 0.858033i | \(-0.671686\pi\) | ||||
−0.513595 | + | 0.858033i | \(0.671686\pi\) | |||||||
\(62\) | 2.11840 | 0.269037 | ||||||||
\(63\) | −1.38329 | −0.174279 | ||||||||
\(64\) | 11.4342 | 1.42928 | ||||||||
\(65\) | 2.73218 | 0.338885 | ||||||||
\(66\) | −1.34084 | −0.165046 | ||||||||
\(67\) | 6.98917 | 0.853863 | 0.426931 | − | 0.904284i | \(-0.359595\pi\) | ||||
0.426931 | + | 0.904284i | \(0.359595\pi\) | |||||||
\(68\) | −5.60829 | −0.680105 | ||||||||
\(69\) | −1.09632 | −0.131981 | ||||||||
\(70\) | −0.649869 | −0.0776742 | ||||||||
\(71\) | −5.36420 | −0.636613 | −0.318306 | − | 0.947988i | \(-0.603114\pi\) | ||||
−0.318306 | + | 0.947988i | \(0.603114\pi\) | |||||||
\(72\) | 23.1526 | 2.72856 | ||||||||
\(73\) | 0.136320 | 0.0159551 | 0.00797754 | − | 0.999968i | \(-0.497461\pi\) | ||||
0.00797754 | + | 0.999968i | \(0.497461\pi\) | |||||||
\(74\) | 5.83796 | 0.678649 | ||||||||
\(75\) | −0.686739 | −0.0792977 | ||||||||
\(76\) | −24.2305 | −2.77943 | ||||||||
\(77\) | 1.62286 | 0.184942 | ||||||||
\(78\) | −1.97455 | −0.223574 | ||||||||
\(79\) | −11.6822 | −1.31435 | −0.657173 | − | 0.753740i | \(-0.728248\pi\) | ||||
−0.657173 | + | 0.753740i | \(0.728248\pi\) | |||||||
\(80\) | 5.62275 | 0.628642 | ||||||||
\(81\) | 8.80978 | 0.978864 | ||||||||
\(82\) | −20.7748 | −2.29419 | ||||||||
\(83\) | 5.50982 | 0.604781 | 0.302390 | − | 0.953184i | \(-0.402215\pi\) | ||||
0.302390 | + | 0.953184i | \(0.402215\pi\) | |||||||
\(84\) | 0.334479 | 0.0364947 | ||||||||
\(85\) | −0.601672 | −0.0652604 | ||||||||
\(86\) | 12.3670 | 1.33357 | ||||||||
\(87\) | 0.462739 | 0.0496108 | ||||||||
\(88\) | −27.1623 | −2.89551 | ||||||||
\(89\) | 15.4879 | 1.64171 | 0.820855 | − | 0.571137i | \(-0.193497\pi\) | ||||
0.820855 | + | 0.571137i | \(0.193497\pi\) | |||||||
\(90\) | 4.16868 | 0.439417 | ||||||||
\(91\) | 2.38986 | 0.250526 | ||||||||
\(92\) | −37.2731 | −3.88598 | ||||||||
\(93\) | −0.116972 | −0.0121294 | ||||||||
\(94\) | −16.9292 | −1.74611 | ||||||||
\(95\) | −2.59951 | −0.266704 | ||||||||
\(96\) | −1.80098 | −0.183812 | ||||||||
\(97\) | 10.1553 | 1.03112 | 0.515559 | − | 0.856854i | \(-0.327584\pi\) | ||||
0.515559 | + | 0.856854i | \(0.327584\pi\) | |||||||
\(98\) | 17.8836 | 1.80652 | ||||||||
\(99\) | −10.4100 | −1.04625 | ||||||||
\(100\) | −23.3480 | −2.33480 | ||||||||
\(101\) | −11.0329 | −1.09782 | −0.548909 | − | 0.835882i | \(-0.684957\pi\) | ||||
−0.548909 | + | 0.835882i | \(0.684957\pi\) | |||||||
\(102\) | 0.434829 | 0.0430545 | ||||||||
\(103\) | 11.5710 | 1.14013 | 0.570063 | − | 0.821601i | \(-0.306919\pi\) | ||||
0.570063 | + | 0.821601i | \(0.306919\pi\) | |||||||
\(104\) | −39.9999 | −3.92231 | ||||||||
\(105\) | 0.0358838 | 0.00350190 | ||||||||
\(106\) | −13.2081 | −1.28289 | ||||||||
\(107\) | 3.42860 | 0.331455 | 0.165727 | − | 0.986172i | \(-0.447003\pi\) | ||||
0.165727 | + | 0.986172i | \(0.447003\pi\) | |||||||
\(108\) | −4.30639 | −0.414382 | ||||||||
\(109\) | 16.8798 | 1.61679 | 0.808396 | − | 0.588639i | \(-0.200336\pi\) | ||||
0.808396 | + | 0.588639i | \(0.200336\pi\) | |||||||
\(110\) | −4.89062 | −0.466303 | ||||||||
\(111\) | −0.322354 | −0.0305965 | ||||||||
\(112\) | 4.91826 | 0.464732 | ||||||||
\(113\) | −0.114943 | −0.0108129 | −0.00540647 | − | 0.999985i | \(-0.501721\pi\) | ||||
−0.00540647 | + | 0.999985i | \(0.501721\pi\) | |||||||
\(114\) | 1.87867 | 0.175954 | ||||||||
\(115\) | −3.99875 | −0.372885 | ||||||||
\(116\) | 15.7324 | 1.46072 | ||||||||
\(117\) | −15.3301 | −1.41727 | ||||||||
\(118\) | −22.1915 | −2.04289 | ||||||||
\(119\) | −0.526287 | −0.0482447 | ||||||||
\(120\) | −0.600598 | −0.0548268 | ||||||||
\(121\) | 1.21289 | 0.110263 | ||||||||
\(122\) | 21.1477 | 1.91462 | ||||||||
\(123\) | 1.14712 | 0.103432 | ||||||||
\(124\) | −3.97685 | −0.357132 | ||||||||
\(125\) | −5.15931 | −0.461462 | ||||||||
\(126\) | 3.64638 | 0.324845 | ||||||||
\(127\) | 2.21966 | 0.196963 | 0.0984813 | − | 0.995139i | \(-0.468602\pi\) | ||||
0.0984813 | + | 0.995139i | \(0.468602\pi\) | |||||||
\(128\) | −5.39393 | −0.476761 | ||||||||
\(129\) | −0.682867 | −0.0601230 | ||||||||
\(130\) | −7.20206 | −0.631662 | ||||||||
\(131\) | −9.03676 | −0.789545 | −0.394773 | − | 0.918779i | \(-0.629177\pi\) | ||||
−0.394773 | + | 0.918779i | \(0.629177\pi\) | |||||||
\(132\) | 2.51714 | 0.219089 | ||||||||
\(133\) | −2.27382 | −0.197165 | ||||||||
\(134\) | −18.4235 | −1.59155 | ||||||||
\(135\) | −0.462000 | −0.0397627 | ||||||||
\(136\) | 8.80863 | 0.755334 | ||||||||
\(137\) | 21.0127 | 1.79524 | 0.897618 | − | 0.440774i | \(-0.145296\pi\) | ||||
0.897618 | + | 0.440774i | \(0.145296\pi\) | |||||||
\(138\) | 2.88990 | 0.246005 | ||||||||
\(139\) | 8.17664 | 0.693533 | 0.346767 | − | 0.937951i | \(-0.387280\pi\) | ||||
0.346767 | + | 0.937951i | \(0.387280\pi\) | |||||||
\(140\) | 1.21999 | 0.103108 | ||||||||
\(141\) | 0.934776 | 0.0787223 | ||||||||
\(142\) | 14.1401 | 1.18661 | ||||||||
\(143\) | 17.9850 | 1.50398 | ||||||||
\(144\) | −31.5489 | −2.62908 | ||||||||
\(145\) | 1.68781 | 0.140165 | ||||||||
\(146\) | −0.359342 | −0.0297393 | ||||||||
\(147\) | −0.987479 | −0.0814459 | ||||||||
\(148\) | −10.9595 | −0.900868 | ||||||||
\(149\) | 10.3436 | 0.847378 | 0.423689 | − | 0.905808i | \(-0.360735\pi\) | ||||
0.423689 | + | 0.905808i | \(0.360735\pi\) | |||||||
\(150\) | 1.81025 | 0.147806 | ||||||||
\(151\) | 2.24726 | 0.182880 | 0.0914398 | − | 0.995811i | \(-0.470853\pi\) | ||||
0.0914398 | + | 0.995811i | \(0.470853\pi\) | |||||||
\(152\) | 38.0576 | 3.08688 | ||||||||
\(153\) | 3.37594 | 0.272929 | ||||||||
\(154\) | −4.27787 | −0.344720 | ||||||||
\(155\) | −0.426647 | −0.0342691 | ||||||||
\(156\) | 3.70681 | 0.296782 | ||||||||
\(157\) | −11.7734 | −0.939617 | −0.469809 | − | 0.882768i | \(-0.655677\pi\) | ||||
−0.469809 | + | 0.882768i | \(0.655677\pi\) | |||||||
\(158\) | 30.7943 | 2.44986 | ||||||||
\(159\) | 0.729313 | 0.0578383 | ||||||||
\(160\) | −6.56896 | −0.519322 | ||||||||
\(161\) | −3.49774 | −0.275660 | ||||||||
\(162\) | −23.2227 | −1.82455 | ||||||||
\(163\) | −6.22278 | −0.487406 | −0.243703 | − | 0.969850i | \(-0.578362\pi\) | ||||
−0.243703 | + | 0.969850i | \(0.578362\pi\) | |||||||
\(164\) | 39.0002 | 3.04541 | ||||||||
\(165\) | 0.270045 | 0.0210230 | ||||||||
\(166\) | −14.5239 | −1.12728 | ||||||||
\(167\) | 7.95673 | 0.615711 | 0.307855 | − | 0.951433i | \(-0.400389\pi\) | ||||
0.307855 | + | 0.951433i | \(0.400389\pi\) | |||||||
\(168\) | −0.525348 | −0.0405315 | ||||||||
\(169\) | 13.4852 | 1.03732 | ||||||||
\(170\) | 1.58601 | 0.121642 | ||||||||
\(171\) | 14.5857 | 1.11540 | ||||||||
\(172\) | −23.2164 | −1.77023 | ||||||||
\(173\) | 11.0349 | 0.838967 | 0.419483 | − | 0.907763i | \(-0.362211\pi\) | ||||
0.419483 | + | 0.907763i | \(0.362211\pi\) | |||||||
\(174\) | −1.21978 | −0.0924716 | ||||||||
\(175\) | −2.19100 | −0.165624 | ||||||||
\(176\) | 37.0126 | 2.78993 | ||||||||
\(177\) | 1.22535 | 0.0921026 | ||||||||
\(178\) | −40.8262 | −3.06005 | ||||||||
\(179\) | 23.3320 | 1.74391 | 0.871956 | − | 0.489584i | \(-0.162851\pi\) | ||||
0.871956 | + | 0.489584i | \(0.162851\pi\) | |||||||
\(180\) | −7.82582 | −0.583302 | ||||||||
\(181\) | 8.44649 | 0.627823 | 0.313911 | − | 0.949452i | \(-0.398360\pi\) | ||||
0.313911 | + | 0.949452i | \(0.398360\pi\) | |||||||
\(182\) | −6.29970 | −0.466965 | ||||||||
\(183\) | −1.16771 | −0.0863196 | ||||||||
\(184\) | 58.5428 | 4.31583 | ||||||||
\(185\) | −1.17577 | −0.0864441 | ||||||||
\(186\) | 0.308339 | 0.0226085 | ||||||||
\(187\) | −3.96060 | −0.289628 | ||||||||
\(188\) | 31.7809 | 2.31786 | ||||||||
\(189\) | −0.404116 | −0.0293951 | ||||||||
\(190\) | 6.85235 | 0.497122 | ||||||||
\(191\) | −1.43300 | −0.103688 | −0.0518442 | − | 0.998655i | \(-0.516510\pi\) | ||||
−0.0518442 | + | 0.998655i | \(0.516510\pi\) | |||||||
\(192\) | 1.66428 | 0.120109 | ||||||||
\(193\) | −0.640689 | −0.0461178 | −0.0230589 | − | 0.999734i | \(-0.507341\pi\) | ||||
−0.0230589 | + | 0.999734i | \(0.507341\pi\) | |||||||
\(194\) | −26.7696 | −1.92194 | ||||||||
\(195\) | 0.397676 | 0.0284781 | ||||||||
\(196\) | −33.5728 | −2.39805 | ||||||||
\(197\) | 6.86801 | 0.489325 | 0.244663 | − | 0.969608i | \(-0.421323\pi\) | ||||
0.244663 | + | 0.969608i | \(0.421323\pi\) | |||||||
\(198\) | 27.4410 | 1.95015 | ||||||||
\(199\) | −5.01432 | −0.355455 | −0.177728 | − | 0.984080i | \(-0.556875\pi\) | ||||
−0.177728 | + | 0.984080i | \(0.556875\pi\) | |||||||
\(200\) | 36.6715 | 2.59307 | ||||||||
\(201\) | 1.01729 | 0.0717542 | ||||||||
\(202\) | 29.0829 | 2.04627 | ||||||||
\(203\) | 1.47634 | 0.103619 | ||||||||
\(204\) | −0.816300 | −0.0571524 | ||||||||
\(205\) | 4.18405 | 0.292227 | ||||||||
\(206\) | −30.5013 | −2.12513 | ||||||||
\(207\) | 22.4368 | 1.55946 | ||||||||
\(208\) | 54.5058 | 3.77930 | ||||||||
\(209\) | −17.1117 | −1.18364 | ||||||||
\(210\) | −0.0945900 | −0.00652733 | ||||||||
\(211\) | −6.15793 | −0.423929 | −0.211965 | − | 0.977277i | \(-0.567986\pi\) | ||||
−0.211965 | + | 0.977277i | \(0.567986\pi\) | |||||||
\(212\) | 24.7955 | 1.70296 | ||||||||
\(213\) | −0.780772 | −0.0534976 | ||||||||
\(214\) | −9.03782 | −0.617813 | ||||||||
\(215\) | −2.49071 | −0.169865 | ||||||||
\(216\) | 6.76381 | 0.460219 | ||||||||
\(217\) | −0.373192 | −0.0253339 | ||||||||
\(218\) | −44.4954 | −3.01361 | ||||||||
\(219\) | 0.0198417 | 0.00134078 | ||||||||
\(220\) | 9.18111 | 0.618991 | ||||||||
\(221\) | −5.83248 | −0.392335 | ||||||||
\(222\) | 0.849729 | 0.0570301 | ||||||||
\(223\) | −1.59962 | −0.107119 | −0.0535593 | − | 0.998565i | \(-0.517057\pi\) | ||||
−0.0535593 | + | 0.998565i | \(0.517057\pi\) | |||||||
\(224\) | −5.74592 | −0.383916 | ||||||||
\(225\) | 14.0545 | 0.936967 | ||||||||
\(226\) | 0.302992 | 0.0201547 | ||||||||
\(227\) | 2.71787 | 0.180391 | 0.0901956 | − | 0.995924i | \(-0.471251\pi\) | ||||
0.0901956 | + | 0.995924i | \(0.471251\pi\) | |||||||
\(228\) | −3.52681 | −0.233569 | ||||||||
\(229\) | 21.1403 | 1.39699 | 0.698495 | − | 0.715615i | \(-0.253853\pi\) | ||||
0.698495 | + | 0.715615i | \(0.253853\pi\) | |||||||
\(230\) | 10.5407 | 0.695036 | ||||||||
\(231\) | 0.236211 | 0.0155415 | ||||||||
\(232\) | −24.7100 | −1.62229 | ||||||||
\(233\) | −5.27553 | −0.345611 | −0.172806 | − | 0.984956i | \(-0.555283\pi\) | ||||
−0.172806 | + | 0.984956i | \(0.555283\pi\) | |||||||
\(234\) | 40.4103 | 2.64171 | ||||||||
\(235\) | 3.40954 | 0.222414 | ||||||||
\(236\) | 41.6598 | 2.71182 | ||||||||
\(237\) | −1.70037 | −0.110451 | ||||||||
\(238\) | 1.38730 | 0.0899252 | ||||||||
\(239\) | −13.2777 | −0.858863 | −0.429432 | − | 0.903099i | \(-0.641286\pi\) | ||||
−0.429432 | + | 0.903099i | \(0.641286\pi\) | |||||||
\(240\) | 0.818405 | 0.0528278 | ||||||||
\(241\) | 3.64256 | 0.234638 | 0.117319 | − | 0.993094i | \(-0.462570\pi\) | ||||
0.117319 | + | 0.993094i | \(0.462570\pi\) | |||||||
\(242\) | −3.19719 | −0.205523 | ||||||||
\(243\) | 3.89298 | 0.249735 | ||||||||
\(244\) | −39.7003 | −2.54155 | ||||||||
\(245\) | −3.60177 | −0.230109 | ||||||||
\(246\) | −3.02382 | −0.192792 | ||||||||
\(247\) | −25.1992 | −1.60338 | ||||||||
\(248\) | 6.24623 | 0.396636 | ||||||||
\(249\) | 0.801967 | 0.0508226 | ||||||||
\(250\) | 13.6000 | 0.860139 | ||||||||
\(251\) | 0.0182307 | 0.00115071 | 0.000575356 | − | 1.00000i | \(-0.499817\pi\) | ||||
0.000575356 | 1.00000i | \(0.499817\pi\) | ||||||||
\(252\) | −6.84531 | −0.431214 | ||||||||
\(253\) | −26.3224 | −1.65488 | ||||||||
\(254\) | −5.85104 | −0.367127 | ||||||||
\(255\) | −0.0875748 | −0.00548415 | ||||||||
\(256\) | −8.64996 | −0.540623 | ||||||||
\(257\) | 22.0359 | 1.37456 | 0.687281 | − | 0.726392i | \(-0.258804\pi\) | ||||
0.687281 | + | 0.726392i | \(0.258804\pi\) | |||||||
\(258\) | 1.80004 | 0.112066 | ||||||||
\(259\) | −1.02845 | −0.0639050 | ||||||||
\(260\) | 13.5204 | 0.838497 | ||||||||
\(261\) | −9.47022 | −0.586192 | ||||||||
\(262\) | 23.8210 | 1.47167 | ||||||||
\(263\) | −10.5274 | −0.649146 | −0.324573 | − | 0.945861i | \(-0.605221\pi\) | ||||
−0.324573 | + | 0.945861i | \(0.605221\pi\) | |||||||
\(264\) | −3.95353 | −0.243323 | ||||||||
\(265\) | 2.66013 | 0.163410 | ||||||||
\(266\) | 5.99380 | 0.367504 | ||||||||
\(267\) | 2.25430 | 0.137961 | ||||||||
\(268\) | 34.5863 | 2.11269 | ||||||||
\(269\) | −24.6221 | −1.50124 | −0.750619 | − | 0.660735i | \(-0.770245\pi\) | ||||
−0.750619 | + | 0.660735i | \(0.770245\pi\) | |||||||
\(270\) | 1.21784 | 0.0741153 | ||||||||
\(271\) | −5.27947 | −0.320705 | −0.160353 | − | 0.987060i | \(-0.551263\pi\) | ||||
−0.160353 | + | 0.987060i | \(0.551263\pi\) | |||||||
\(272\) | −12.0031 | −0.727794 | ||||||||
\(273\) | 0.347850 | 0.0210528 | ||||||||
\(274\) | −55.3897 | −3.34622 | ||||||||
\(275\) | −16.4885 | −0.994294 | ||||||||
\(276\) | −5.42518 | −0.326558 | ||||||||
\(277\) | 17.1113 | 1.02812 | 0.514058 | − | 0.857756i | \(-0.328142\pi\) | ||||
0.514058 | + | 0.857756i | \(0.328142\pi\) | |||||||
\(278\) | −21.5537 | −1.29271 | ||||||||
\(279\) | 2.39389 | 0.143319 | ||||||||
\(280\) | −1.91618 | −0.114513 | ||||||||
\(281\) | −8.24845 | −0.492061 | −0.246031 | − | 0.969262i | \(-0.579126\pi\) | ||||
−0.246031 | + | 0.969262i | \(0.579126\pi\) | |||||||
\(282\) | −2.46408 | −0.146734 | ||||||||
\(283\) | −2.56891 | −0.152706 | −0.0763528 | − | 0.997081i | \(-0.524328\pi\) | ||||
−0.0763528 | + | 0.997081i | \(0.524328\pi\) | |||||||
\(284\) | −26.5450 | −1.57516 | ||||||||
\(285\) | −0.378366 | −0.0224124 | ||||||||
\(286\) | −47.4087 | −2.80334 | ||||||||
\(287\) | 3.65982 | 0.216032 | ||||||||
\(288\) | 36.8580 | 2.17188 | ||||||||
\(289\) | −15.7156 | −0.924446 | ||||||||
\(290\) | −4.44909 | −0.261260 | ||||||||
\(291\) | 1.47813 | 0.0866497 | ||||||||
\(292\) | 0.674588 | 0.0394773 | ||||||||
\(293\) | 15.7408 | 0.919585 | 0.459792 | − | 0.888026i | \(-0.347924\pi\) | ||||
0.459792 | + | 0.888026i | \(0.347924\pi\) | |||||||
\(294\) | 2.60301 | 0.151810 | ||||||||
\(295\) | 4.46937 | 0.260217 | ||||||||
\(296\) | 17.2135 | 1.00052 | ||||||||
\(297\) | −3.04119 | −0.176468 | ||||||||
\(298\) | −27.2658 | −1.57946 | ||||||||
\(299\) | −38.7631 | −2.24173 | ||||||||
\(300\) | −3.39836 | −0.196205 | ||||||||
\(301\) | −2.17865 | −0.125575 | ||||||||
\(302\) | −5.92381 | −0.340877 | ||||||||
\(303\) | −1.60587 | −0.0922548 | ||||||||
\(304\) | −51.8591 | −2.97433 | ||||||||
\(305\) | −4.25915 | −0.243878 | ||||||||
\(306\) | −8.89903 | −0.508724 | ||||||||
\(307\) | −13.1574 | −0.750934 | −0.375467 | − | 0.926836i | \(-0.622518\pi\) | ||||
−0.375467 | + | 0.926836i | \(0.622518\pi\) | |||||||
\(308\) | 8.03080 | 0.457597 | ||||||||
\(309\) | 1.68419 | 0.0958102 | ||||||||
\(310\) | 1.12465 | 0.0638756 | ||||||||
\(311\) | 3.66100 | 0.207596 | 0.103798 | − | 0.994598i | \(-0.466900\pi\) | ||||
0.103798 | + | 0.994598i | \(0.466900\pi\) | |||||||
\(312\) | −5.82208 | −0.329610 | ||||||||
\(313\) | −17.5814 | −0.993762 | −0.496881 | − | 0.867819i | \(-0.665521\pi\) | ||||
−0.496881 | + | 0.867819i | \(0.665521\pi\) | |||||||
\(314\) | 31.0347 | 1.75139 | ||||||||
\(315\) | −0.734382 | −0.0413777 | ||||||||
\(316\) | −57.8098 | −3.25206 | ||||||||
\(317\) | −8.63558 | −0.485023 | −0.242511 | − | 0.970149i | \(-0.577971\pi\) | ||||
−0.242511 | + | 0.970149i | \(0.577971\pi\) | |||||||
\(318\) | −1.92248 | −0.107807 | ||||||||
\(319\) | 11.1103 | 0.622057 | ||||||||
\(320\) | 6.07035 | 0.339343 | ||||||||
\(321\) | 0.499041 | 0.0278537 | ||||||||
\(322\) | 9.22008 | 0.513815 | ||||||||
\(323\) | 5.54927 | 0.308770 | ||||||||
\(324\) | 43.5957 | 2.42198 | ||||||||
\(325\) | −24.2814 | −1.34689 | ||||||||
\(326\) | 16.4033 | 0.908496 | ||||||||
\(327\) | 2.45690 | 0.135867 | ||||||||
\(328\) | −61.2556 | −3.38227 | ||||||||
\(329\) | 2.98235 | 0.164422 | ||||||||
\(330\) | −0.711842 | −0.0391856 | ||||||||
\(331\) | 16.1864 | 0.889686 | 0.444843 | − | 0.895608i | \(-0.353259\pi\) | ||||
0.444843 | + | 0.895608i | \(0.353259\pi\) | |||||||
\(332\) | 27.2656 | 1.49640 | ||||||||
\(333\) | 6.59716 | 0.361522 | ||||||||
\(334\) | −20.9740 | −1.14765 | ||||||||
\(335\) | 3.71051 | 0.202727 | ||||||||
\(336\) | 0.715865 | 0.0390537 | ||||||||
\(337\) | 16.1610 | 0.880346 | 0.440173 | − | 0.897913i | \(-0.354917\pi\) | ||||
0.440173 | + | 0.897913i | \(0.354917\pi\) | |||||||
\(338\) | −35.5472 | −1.93351 | ||||||||
\(339\) | −0.0167303 | −0.000908663 0 | ||||||||
\(340\) | −2.97741 | −0.161472 | ||||||||
\(341\) | −2.80847 | −0.152087 | ||||||||
\(342\) | −38.4481 | −2.07904 | ||||||||
\(343\) | −6.40114 | −0.345629 | ||||||||
\(344\) | 36.4647 | 1.96605 | ||||||||
\(345\) | −0.582028 | −0.0313353 | ||||||||
\(346\) | −29.0881 | −1.56378 | ||||||||
\(347\) | 10.1340 | 0.544021 | 0.272010 | − | 0.962294i | \(-0.412312\pi\) | ||||
0.272010 | + | 0.962294i | \(0.412312\pi\) | |||||||
\(348\) | 2.28989 | 0.122751 | ||||||||
\(349\) | −11.5947 | −0.620648 | −0.310324 | − | 0.950631i | \(-0.600438\pi\) | ||||
−0.310324 | + | 0.950631i | \(0.600438\pi\) | |||||||
\(350\) | 5.77551 | 0.308714 | ||||||||
\(351\) | −4.47854 | −0.239047 | ||||||||
\(352\) | −43.2412 | −2.30476 | ||||||||
\(353\) | −14.2967 | −0.760936 | −0.380468 | − | 0.924794i | \(-0.624237\pi\) | ||||
−0.380468 | + | 0.924794i | \(0.624237\pi\) | |||||||
\(354\) | −3.23002 | −0.171674 | ||||||||
\(355\) | −2.84782 | −0.151147 | ||||||||
\(356\) | 76.6426 | 4.06205 | ||||||||
\(357\) | −0.0766024 | −0.00405423 | ||||||||
\(358\) | −61.5033 | −3.25055 | ||||||||
\(359\) | −4.18574 | −0.220915 | −0.110457 | − | 0.993881i | \(-0.535232\pi\) | ||||
−0.110457 | + | 0.993881i | \(0.535232\pi\) | |||||||
\(360\) | 12.2916 | 0.647823 | ||||||||
\(361\) | 4.97556 | 0.261872 | ||||||||
\(362\) | −22.2651 | −1.17023 | ||||||||
\(363\) | 0.176539 | 0.00926589 | ||||||||
\(364\) | 11.8264 | 0.619870 | ||||||||
\(365\) | 0.0723716 | 0.00378810 | ||||||||
\(366\) | 3.07810 | 0.160895 | ||||||||
\(367\) | 4.59241 | 0.239722 | 0.119861 | − | 0.992791i | \(-0.461755\pi\) | ||||
0.119861 | + | 0.992791i | \(0.461755\pi\) | |||||||
\(368\) | −79.7733 | −4.15847 | ||||||||
\(369\) | −23.4764 | −1.22213 | ||||||||
\(370\) | 3.09934 | 0.161127 | ||||||||
\(371\) | 2.32683 | 0.120803 | ||||||||
\(372\) | −0.578841 | −0.0300115 | ||||||||
\(373\) | 29.4920 | 1.52704 | 0.763519 | − | 0.645786i | \(-0.223470\pi\) | ||||
0.763519 | + | 0.645786i | \(0.223470\pi\) | |||||||
\(374\) | 10.4402 | 0.539849 | ||||||||
\(375\) | −0.750950 | −0.0387789 | ||||||||
\(376\) | −49.9165 | −2.57425 | ||||||||
\(377\) | 16.3613 | 0.842651 | ||||||||
\(378\) | 1.06525 | 0.0547907 | ||||||||
\(379\) | 13.3926 | 0.687931 | 0.343965 | − | 0.938982i | \(-0.388230\pi\) | ||||
0.343965 | + | 0.938982i | \(0.388230\pi\) | |||||||
\(380\) | −12.8638 | −0.659901 | ||||||||
\(381\) | 0.323076 | 0.0165517 | ||||||||
\(382\) | 3.77741 | 0.193269 | ||||||||
\(383\) | 3.52042 | 0.179885 | 0.0899425 | − | 0.995947i | \(-0.471332\pi\) | ||||
0.0899425 | + | 0.995947i | \(0.471332\pi\) | |||||||
\(384\) | −0.785100 | −0.0400645 | ||||||||
\(385\) | 0.861565 | 0.0439094 | ||||||||
\(386\) | 1.68886 | 0.0859609 | ||||||||
\(387\) | 13.9753 | 0.710402 | ||||||||
\(388\) | 50.2542 | 2.55127 | ||||||||
\(389\) | 11.3354 | 0.574727 | 0.287364 | − | 0.957822i | \(-0.407221\pi\) | ||||
0.287364 | + | 0.957822i | \(0.407221\pi\) | |||||||
\(390\) | −1.04828 | −0.0530816 | ||||||||
\(391\) | 8.53627 | 0.431698 | ||||||||
\(392\) | 52.7309 | 2.66331 | ||||||||
\(393\) | −1.31532 | −0.0663492 | ||||||||
\(394\) | −18.1041 | −0.912074 | ||||||||
\(395\) | −6.20199 | −0.312056 | ||||||||
\(396\) | −51.5147 | −2.58871 | ||||||||
\(397\) | 20.5737 | 1.03256 | 0.516282 | − | 0.856419i | \(-0.327316\pi\) | ||||
0.516282 | + | 0.856419i | \(0.327316\pi\) | |||||||
\(398\) | 13.2178 | 0.662548 | ||||||||
\(399\) | −0.330959 | −0.0165687 | ||||||||
\(400\) | −49.9704 | −2.49852 | ||||||||
\(401\) | 23.1609 | 1.15660 | 0.578299 | − | 0.815825i | \(-0.303717\pi\) | ||||
0.578299 | + | 0.815825i | \(0.303717\pi\) | |||||||
\(402\) | −2.68159 | −0.133746 | ||||||||
\(403\) | −4.13583 | −0.206020 | ||||||||
\(404\) | −54.5971 | −2.71631 | ||||||||
\(405\) | 4.67706 | 0.232405 | ||||||||
\(406\) | −3.89166 | −0.193140 | ||||||||
\(407\) | −7.73968 | −0.383642 | ||||||||
\(408\) | 1.28212 | 0.0634743 | ||||||||
\(409\) | 1.59562 | 0.0788985 | 0.0394492 | − | 0.999222i | \(-0.487440\pi\) | ||||
0.0394492 | + | 0.999222i | \(0.487440\pi\) | |||||||
\(410\) | −11.0292 | −0.544693 | ||||||||
\(411\) | 3.05845 | 0.150862 | ||||||||
\(412\) | 57.2598 | 2.82099 | ||||||||
\(413\) | 3.90940 | 0.192369 | ||||||||
\(414\) | −59.1435 | −2.90675 | ||||||||
\(415\) | 2.92513 | 0.143589 | ||||||||
\(416\) | −63.6782 | −3.12208 | ||||||||
\(417\) | 1.19013 | 0.0582809 | ||||||||
\(418\) | 45.1067 | 2.20624 | ||||||||
\(419\) | 26.5678 | 1.29792 | 0.648961 | − | 0.760822i | \(-0.275204\pi\) | ||||
0.648961 | + | 0.760822i | \(0.275204\pi\) | |||||||
\(420\) | 0.177573 | 0.00866467 | ||||||||
\(421\) | 8.94543 | 0.435974 | 0.217987 | − | 0.975952i | \(-0.430051\pi\) | ||||
0.217987 | + | 0.975952i | \(0.430051\pi\) | |||||||
\(422\) | 16.2324 | 0.790179 | ||||||||
\(423\) | −19.1307 | −0.930167 | ||||||||
\(424\) | −38.9449 | −1.89133 | ||||||||
\(425\) | 5.34717 | 0.259376 | ||||||||
\(426\) | 2.05812 | 0.0997164 | ||||||||
\(427\) | −3.72552 | −0.180290 | ||||||||
\(428\) | 16.9666 | 0.820112 | ||||||||
\(429\) | 2.61776 | 0.126387 | ||||||||
\(430\) | 6.56555 | 0.316619 | ||||||||
\(431\) | −12.0067 | −0.578343 | −0.289171 | − | 0.957277i | \(-0.593380\pi\) | ||||
−0.289171 | + | 0.957277i | \(0.593380\pi\) | |||||||
\(432\) | −9.21670 | −0.443439 | ||||||||
\(433\) | −12.8340 | −0.616762 | −0.308381 | − | 0.951263i | \(-0.599787\pi\) | ||||
−0.308381 | + | 0.951263i | \(0.599787\pi\) | |||||||
\(434\) | 0.983737 | 0.0472209 | ||||||||
\(435\) | 0.245665 | 0.0117787 | ||||||||
\(436\) | 83.5307 | 4.00039 | ||||||||
\(437\) | 36.8808 | 1.76425 | ||||||||
\(438\) | −0.0523031 | −0.00249914 | ||||||||
\(439\) | −17.0890 | −0.815616 | −0.407808 | − | 0.913068i | \(-0.633707\pi\) | ||||
−0.407808 | + | 0.913068i | \(0.633707\pi\) | |||||||
\(440\) | −14.4203 | −0.687460 | ||||||||
\(441\) | 20.2093 | 0.962349 | ||||||||
\(442\) | 15.3745 | 0.731290 | ||||||||
\(443\) | −14.2718 | −0.678072 | −0.339036 | − | 0.940773i | \(-0.610101\pi\) | ||||
−0.339036 | + | 0.940773i | \(0.610101\pi\) | |||||||
\(444\) | −1.59519 | −0.0757043 | ||||||||
\(445\) | 8.22241 | 0.389780 | ||||||||
\(446\) | 4.21662 | 0.199663 | ||||||||
\(447\) | 1.50553 | 0.0712092 | ||||||||
\(448\) | 5.30979 | 0.250864 | ||||||||
\(449\) | −39.1732 | −1.84870 | −0.924348 | − | 0.381550i | \(-0.875390\pi\) | ||||
−0.924348 | + | 0.381550i | \(0.875390\pi\) | |||||||
\(450\) | −37.0478 | −1.74645 | ||||||||
\(451\) | 27.5422 | 1.29691 | ||||||||
\(452\) | −0.568803 | −0.0267542 | ||||||||
\(453\) | 0.327094 | 0.0153682 | ||||||||
\(454\) | −7.16433 | −0.336239 | ||||||||
\(455\) | 1.26876 | 0.0594805 | ||||||||
\(456\) | 5.53937 | 0.259405 | ||||||||
\(457\) | −25.9395 | −1.21340 | −0.606699 | − | 0.794931i | \(-0.707507\pi\) | ||||
−0.606699 | + | 0.794931i | \(0.707507\pi\) | |||||||
\(458\) | −55.7260 | −2.60391 | ||||||||
\(459\) | 0.986249 | 0.0460341 | ||||||||
\(460\) | −19.7880 | −0.922622 | ||||||||
\(461\) | 29.5030 | 1.37409 | 0.687045 | − | 0.726615i | \(-0.258908\pi\) | ||||
0.687045 | + | 0.726615i | \(0.258908\pi\) | |||||||
\(462\) | −0.622654 | −0.0289685 | ||||||||
\(463\) | 5.14067 | 0.238907 | 0.119454 | − | 0.992840i | \(-0.461886\pi\) | ||||
0.119454 | + | 0.992840i | \(0.461886\pi\) | |||||||
\(464\) | 33.6711 | 1.56314 | ||||||||
\(465\) | −0.0620995 | −0.00287980 | ||||||||
\(466\) | 13.9064 | 0.644199 | ||||||||
\(467\) | −2.28720 | −0.105839 | −0.0529194 | − | 0.998599i | \(-0.516853\pi\) | ||||
−0.0529194 | + | 0.998599i | \(0.516853\pi\) | |||||||
\(468\) | −75.8619 | −3.50672 | ||||||||
\(469\) | 3.24561 | 0.149868 | ||||||||
\(470\) | −8.98758 | −0.414566 | ||||||||
\(471\) | −1.71364 | −0.0789605 | ||||||||
\(472\) | −65.4328 | −3.01179 | ||||||||
\(473\) | −16.3955 | −0.753867 | ||||||||
\(474\) | 4.48219 | 0.205874 | ||||||||
\(475\) | 23.1024 | 1.06001 | ||||||||
\(476\) | −2.60436 | −0.119371 | ||||||||
\(477\) | −14.9258 | −0.683406 | ||||||||
\(478\) | 35.0002 | 1.60087 | ||||||||
\(479\) | 17.2926 | 0.790117 | 0.395059 | − | 0.918656i | \(-0.370724\pi\) | ||||
0.395059 | + | 0.918656i | \(0.370724\pi\) | |||||||
\(480\) | −0.956128 | −0.0436411 | ||||||||
\(481\) | −11.3977 | −0.519688 | ||||||||
\(482\) | −9.60183 | −0.437352 | ||||||||
\(483\) | −0.509105 | −0.0231651 | ||||||||
\(484\) | 6.00204 | 0.272820 | ||||||||
\(485\) | 5.39140 | 0.244811 | ||||||||
\(486\) | −10.2619 | −0.465491 | ||||||||
\(487\) | 13.6833 | 0.620050 | 0.310025 | − | 0.950728i | \(-0.399663\pi\) | ||||
0.310025 | + | 0.950728i | \(0.399663\pi\) | |||||||
\(488\) | 62.3551 | 2.82268 | ||||||||
\(489\) | −0.905741 | −0.0409590 | ||||||||
\(490\) | 9.49431 | 0.428909 | ||||||||
\(491\) | 11.4210 | 0.515424 | 0.257712 | − | 0.966222i | \(-0.417031\pi\) | ||||
0.257712 | + | 0.966222i | \(0.417031\pi\) | |||||||
\(492\) | 5.67658 | 0.255920 | ||||||||
\(493\) | −3.60303 | −0.162272 | ||||||||
\(494\) | 66.4253 | 2.98861 | ||||||||
\(495\) | −5.52663 | −0.248404 | ||||||||
\(496\) | −8.51142 | −0.382174 | ||||||||
\(497\) | −2.49101 | −0.111737 | ||||||||
\(498\) | −2.11399 | −0.0947304 | ||||||||
\(499\) | 11.7922 | 0.527893 | 0.263947 | − | 0.964537i | \(-0.414976\pi\) | ||||
0.263947 | + | 0.964537i | \(0.414976\pi\) | |||||||
\(500\) | −25.5311 | −1.14179 | ||||||||
\(501\) | 1.15812 | 0.0517411 | ||||||||
\(502\) | −0.0480564 | −0.00214486 | ||||||||
\(503\) | −29.4568 | −1.31342 | −0.656708 | − | 0.754145i | \(-0.728052\pi\) | ||||
−0.656708 | + | 0.754145i | \(0.728052\pi\) | |||||||
\(504\) | 10.7515 | 0.478912 | ||||||||
\(505\) | −5.85731 | −0.260647 | ||||||||
\(506\) | 69.3862 | 3.08459 | ||||||||
\(507\) | 1.96281 | 0.0871713 | ||||||||
\(508\) | 10.9841 | 0.487340 | ||||||||
\(509\) | −14.6039 | −0.647306 | −0.323653 | − | 0.946176i | \(-0.604911\pi\) | ||||
−0.323653 | + | 0.946176i | \(0.604911\pi\) | |||||||
\(510\) | 0.230848 | 0.0102221 | ||||||||
\(511\) | 0.0633040 | 0.00280040 | ||||||||
\(512\) | 33.5893 | 1.48445 | ||||||||
\(513\) | 4.26107 | 0.188131 | ||||||||
\(514\) | −58.0869 | −2.56210 | ||||||||
\(515\) | 6.14298 | 0.270692 | ||||||||
\(516\) | −3.37920 | −0.148761 | ||||||||
\(517\) | 22.4438 | 0.987079 | ||||||||
\(518\) | 2.71102 | 0.119115 | ||||||||
\(519\) | 1.60615 | 0.0705023 | ||||||||
\(520\) | −21.2357 | −0.931246 | ||||||||
\(521\) | −31.4069 | −1.37596 | −0.687980 | − | 0.725729i | \(-0.741502\pi\) | ||||
−0.687980 | + | 0.725729i | \(0.741502\pi\) | |||||||
\(522\) | 24.9636 | 1.09263 | ||||||||
\(523\) | 36.9604 | 1.61616 | 0.808082 | − | 0.589070i | \(-0.200506\pi\) | ||||
0.808082 | + | 0.589070i | \(0.200506\pi\) | |||||||
\(524\) | −44.7189 | −1.95355 | ||||||||
\(525\) | −0.318906 | −0.0139182 | ||||||||
\(526\) | 27.7503 | 1.20997 | ||||||||
\(527\) | 0.910778 | 0.0396741 | ||||||||
\(528\) | 5.38728 | 0.234451 | ||||||||
\(529\) | 33.7326 | 1.46664 | ||||||||
\(530\) | −7.01212 | −0.304587 | ||||||||
\(531\) | −25.0774 | −1.08827 | ||||||||
\(532\) | −11.2521 | −0.487841 | ||||||||
\(533\) | 40.5593 | 1.75682 | ||||||||
\(534\) | −5.94235 | −0.257151 | ||||||||
\(535\) | 1.82022 | 0.0786950 | ||||||||
\(536\) | −54.3228 | −2.34639 | ||||||||
\(537\) | 3.39602 | 0.146549 | ||||||||
\(538\) | 64.9043 | 2.79822 | ||||||||
\(539\) | −23.7092 | −1.02123 | ||||||||
\(540\) | −2.28623 | −0.0983839 | ||||||||
\(541\) | 34.9476 | 1.50251 | 0.751257 | − | 0.660009i | \(-0.229448\pi\) | ||||
0.751257 | + | 0.660009i | \(0.229448\pi\) | |||||||
\(542\) | 13.9168 | 0.597776 | ||||||||
\(543\) | 1.22941 | 0.0527589 | ||||||||
\(544\) | 14.0230 | 0.601231 | ||||||||
\(545\) | 8.96138 | 0.383864 | ||||||||
\(546\) | −0.916937 | −0.0392413 | ||||||||
\(547\) | 0.0554230 | 0.00236972 | 0.00118486 | − | 0.999999i | \(-0.499623\pi\) | ||||
0.00118486 | + | 0.999999i | \(0.499623\pi\) | |||||||
\(548\) | 103.983 | 4.44191 | ||||||||
\(549\) | 23.8979 | 1.01994 | ||||||||
\(550\) | 43.4639 | 1.85331 | ||||||||
\(551\) | −15.5669 | −0.663170 | ||||||||
\(552\) | 8.52104 | 0.362680 | ||||||||
\(553\) | −5.42493 | −0.230692 | ||||||||
\(554\) | −45.1055 | −1.91635 | ||||||||
\(555\) | −0.171136 | −0.00726431 | ||||||||
\(556\) | 40.4625 | 1.71599 | ||||||||
\(557\) | 12.8773 | 0.545629 | 0.272814 | − | 0.962067i | \(-0.412046\pi\) | ||||
0.272814 | + | 0.962067i | \(0.412046\pi\) | |||||||
\(558\) | −6.31032 | −0.267137 | ||||||||
\(559\) | −24.1445 | −1.02120 | ||||||||
\(560\) | 2.61108 | 0.110338 | ||||||||
\(561\) | −0.576475 | −0.0243388 | ||||||||
\(562\) | 21.7430 | 0.917174 | ||||||||
\(563\) | 8.78995 | 0.370452 | 0.185226 | − | 0.982696i | \(-0.440698\pi\) | ||||
0.185226 | + | 0.982696i | \(0.440698\pi\) | |||||||
\(564\) | 4.62579 | 0.194781 | ||||||||
\(565\) | −0.0610226 | −0.00256724 | ||||||||
\(566\) | 6.77167 | 0.284634 | ||||||||
\(567\) | 4.09106 | 0.171808 | ||||||||
\(568\) | 41.6928 | 1.74939 | ||||||||
\(569\) | −28.2277 | −1.18337 | −0.591683 | − | 0.806171i | \(-0.701536\pi\) | ||||
−0.591683 | + | 0.806171i | \(0.701536\pi\) | |||||||
\(570\) | 0.997376 | 0.0417755 | ||||||||
\(571\) | −12.8869 | −0.539302 | −0.269651 | − | 0.962958i | \(-0.586908\pi\) | ||||
−0.269651 | + | 0.962958i | \(0.586908\pi\) | |||||||
\(572\) | 88.9999 | 3.72127 | ||||||||
\(573\) | −0.208577 | −0.00871343 | ||||||||
\(574\) | −9.64733 | −0.402672 | ||||||||
\(575\) | 35.5376 | 1.48202 | ||||||||
\(576\) | −34.0604 | −1.41918 | ||||||||
\(577\) | 16.1725 | 0.673269 | 0.336634 | − | 0.941635i | \(-0.390711\pi\) | ||||
0.336634 | + | 0.941635i | \(0.390711\pi\) | |||||||
\(578\) | 41.4265 | 1.72311 | ||||||||
\(579\) | −0.0932538 | −0.00387550 | ||||||||
\(580\) | 8.35223 | 0.346808 | ||||||||
\(581\) | 2.55863 | 0.106150 | ||||||||
\(582\) | −3.89638 | −0.161510 | ||||||||
\(583\) | 17.5107 | 0.725219 | ||||||||
\(584\) | −1.05954 | −0.0438440 | ||||||||
\(585\) | −8.13866 | −0.336492 | ||||||||
\(586\) | −41.4928 | −1.71405 | ||||||||
\(587\) | −11.6784 | −0.482019 | −0.241010 | − | 0.970523i | \(-0.577479\pi\) | ||||
−0.241010 | + | 0.970523i | \(0.577479\pi\) | |||||||
\(588\) | −4.88660 | −0.201520 | ||||||||
\(589\) | 3.93501 | 0.162139 | ||||||||
\(590\) | −11.7813 | −0.485029 | ||||||||
\(591\) | 0.999655 | 0.0411203 | ||||||||
\(592\) | −23.4560 | −0.964037 | ||||||||
\(593\) | −9.14424 | −0.375509 | −0.187755 | − | 0.982216i | \(-0.560121\pi\) | ||||
−0.187755 | + | 0.982216i | \(0.560121\pi\) | |||||||
\(594\) | 8.01662 | 0.328926 | ||||||||
\(595\) | −0.279403 | −0.0114544 | ||||||||
\(596\) | 51.1857 | 2.09665 | ||||||||
\(597\) | −0.729846 | −0.0298706 | ||||||||
\(598\) | 102.180 | 4.17845 | ||||||||
\(599\) | −11.4158 | −0.466437 | −0.233219 | − | 0.972424i | \(-0.574926\pi\) | ||||
−0.233219 | + | 0.972424i | \(0.574926\pi\) | |||||||
\(600\) | 5.33763 | 0.217908 | ||||||||
\(601\) | −3.06977 | −0.125218 | −0.0626092 | − | 0.998038i | \(-0.519942\pi\) | ||||
−0.0626092 | + | 0.998038i | \(0.519942\pi\) | |||||||
\(602\) | 5.74294 | 0.234065 | ||||||||
\(603\) | −20.8194 | −0.847833 | ||||||||
\(604\) | 11.1207 | 0.452495 | ||||||||
\(605\) | 0.643915 | 0.0261789 | ||||||||
\(606\) | 4.23309 | 0.171958 | ||||||||
\(607\) | 21.6585 | 0.879092 | 0.439546 | − | 0.898220i | \(-0.355139\pi\) | ||||
0.439546 | + | 0.898220i | \(0.355139\pi\) | |||||||
\(608\) | 60.5861 | 2.45709 | ||||||||
\(609\) | 0.214885 | 0.00870759 | ||||||||
\(610\) | 11.2272 | 0.454575 | ||||||||
\(611\) | 33.0514 | 1.33712 | ||||||||
\(612\) | 16.7060 | 0.675302 | ||||||||
\(613\) | 35.4461 | 1.43165 | 0.715827 | − | 0.698277i | \(-0.246050\pi\) | ||||
0.715827 | + | 0.698277i | \(0.246050\pi\) | |||||||
\(614\) | 34.6831 | 1.39970 | ||||||||
\(615\) | 0.608998 | 0.0245572 | ||||||||
\(616\) | −12.6135 | −0.508214 | ||||||||
\(617\) | −8.44095 | −0.339820 | −0.169910 | − | 0.985460i | \(-0.554348\pi\) | ||||
−0.169910 | + | 0.985460i | \(0.554348\pi\) | |||||||
\(618\) | −4.43954 | −0.178585 | ||||||||
\(619\) | −25.1410 | −1.01050 | −0.505252 | − | 0.862972i | \(-0.668600\pi\) | ||||
−0.505252 | + | 0.862972i | \(0.668600\pi\) | |||||||
\(620\) | −2.11129 | −0.0847913 | ||||||||
\(621\) | 6.55467 | 0.263030 | ||||||||
\(622\) | −9.65043 | −0.386947 | ||||||||
\(623\) | 7.19221 | 0.288150 | ||||||||
\(624\) | 7.93345 | 0.317592 | ||||||||
\(625\) | 20.8517 | 0.834069 | ||||||||
\(626\) | 46.3449 | 1.85231 | ||||||||
\(627\) | −2.49065 | −0.0994671 | ||||||||
\(628\) | −58.2612 | −2.32487 | ||||||||
\(629\) | 2.50995 | 0.100078 | ||||||||
\(630\) | 1.93584 | 0.0771257 | ||||||||
\(631\) | 11.1522 | 0.443960 | 0.221980 | − | 0.975051i | \(-0.428748\pi\) | ||||
0.221980 | + | 0.975051i | \(0.428748\pi\) | |||||||
\(632\) | 90.7988 | 3.61178 | ||||||||
\(633\) | −0.896302 | −0.0356248 | ||||||||
\(634\) | 22.7635 | 0.904054 | ||||||||
\(635\) | 1.17840 | 0.0467635 | ||||||||
\(636\) | 3.60905 | 0.143108 | ||||||||
\(637\) | −34.9149 | −1.38338 | ||||||||
\(638\) | −29.2869 | −1.15948 | ||||||||
\(639\) | 15.9789 | 0.632117 | ||||||||
\(640\) | −2.86361 | −0.113194 | ||||||||
\(641\) | 17.5609 | 0.693615 | 0.346807 | − | 0.937936i | \(-0.387266\pi\) | ||||
0.346807 | + | 0.937936i | \(0.387266\pi\) | |||||||
\(642\) | −1.31548 | −0.0519177 | ||||||||
\(643\) | 27.7343 | 1.09373 | 0.546867 | − | 0.837219i | \(-0.315820\pi\) | ||||
0.546867 | + | 0.837219i | \(0.315820\pi\) | |||||||
\(644\) | −17.3088 | −0.682061 | ||||||||
\(645\) | −0.362530 | −0.0142746 | ||||||||
\(646\) | −14.6280 | −0.575529 | ||||||||
\(647\) | 33.4666 | 1.31571 | 0.657855 | − | 0.753145i | \(-0.271464\pi\) | ||||
0.657855 | + | 0.753145i | \(0.271464\pi\) | |||||||
\(648\) | −68.4734 | −2.68989 | ||||||||
\(649\) | 29.4204 | 1.15485 | ||||||||
\(650\) | 64.0060 | 2.51052 | ||||||||
\(651\) | −0.0543190 | −0.00212893 | ||||||||
\(652\) | −30.7938 | −1.20598 | ||||||||
\(653\) | 11.9381 | 0.467176 | 0.233588 | − | 0.972336i | \(-0.424953\pi\) | ||||
0.233588 | + | 0.972336i | \(0.424953\pi\) | |||||||
\(654\) | −6.47641 | −0.253248 | ||||||||
\(655\) | −4.79756 | −0.187456 | ||||||||
\(656\) | 83.4699 | 3.25895 | ||||||||
\(657\) | −0.406073 | −0.0158424 | ||||||||
\(658\) | −7.86151 | −0.306474 | ||||||||
\(659\) | 49.1115 | 1.91311 | 0.956555 | − | 0.291551i | \(-0.0941713\pi\) | ||||
0.956555 | + | 0.291551i | \(0.0941713\pi\) | |||||||
\(660\) | 1.33633 | 0.0520167 | ||||||||
\(661\) | −25.8028 | −1.00361 | −0.501807 | − | 0.864980i | \(-0.667331\pi\) | ||||
−0.501807 | + | 0.864980i | \(0.667331\pi\) | |||||||
\(662\) | −42.6676 | −1.65832 | ||||||||
\(663\) | −0.848932 | −0.0329698 | ||||||||
\(664\) | −42.8246 | −1.66192 | ||||||||
\(665\) | −1.20715 | −0.0468115 | ||||||||
\(666\) | −17.3902 | −0.673856 | ||||||||
\(667\) | −23.9460 | −0.927193 | ||||||||
\(668\) | 39.3743 | 1.52344 | ||||||||
\(669\) | −0.232829 | −0.00900168 | ||||||||
\(670\) | −9.78094 | −0.377871 | ||||||||
\(671\) | −28.0366 | −1.08234 | ||||||||
\(672\) | −0.836333 | −0.0322622 | ||||||||
\(673\) | −2.24519 | −0.0865459 | −0.0432729 | − | 0.999063i | \(-0.513779\pi\) | ||||
−0.0432729 | + | 0.999063i | \(0.513779\pi\) | |||||||
\(674\) | −42.6006 | −1.64091 | ||||||||
\(675\) | 4.10588 | 0.158035 | ||||||||
\(676\) | 66.7324 | 2.56663 | ||||||||
\(677\) | 19.4441 | 0.747296 | 0.373648 | − | 0.927570i | \(-0.378107\pi\) | ||||
0.373648 | + | 0.927570i | \(0.378107\pi\) | |||||||
\(678\) | 0.0441012 | 0.00169369 | ||||||||
\(679\) | 4.71591 | 0.180980 | ||||||||
\(680\) | 4.67645 | 0.179334 | ||||||||
\(681\) | 0.395592 | 0.0151591 | ||||||||
\(682\) | 7.40316 | 0.283482 | ||||||||
\(683\) | 21.6887 | 0.829893 | 0.414947 | − | 0.909846i | \(-0.363800\pi\) | ||||
0.414947 | + | 0.909846i | \(0.363800\pi\) | |||||||
\(684\) | 72.1782 | 2.75980 | ||||||||
\(685\) | 11.1555 | 0.426230 | ||||||||
\(686\) | 16.8735 | 0.644232 | ||||||||
\(687\) | 3.07702 | 0.117396 | ||||||||
\(688\) | −49.6886 | −1.89436 | ||||||||
\(689\) | 25.7867 | 0.982396 | ||||||||
\(690\) | 1.53423 | 0.0584072 | ||||||||
\(691\) | −21.1301 | −0.803828 | −0.401914 | − | 0.915677i | \(-0.631655\pi\) | ||||
−0.401914 | + | 0.915677i | \(0.631655\pi\) | |||||||
\(692\) | 54.6067 | 2.07584 | ||||||||
\(693\) | −4.83419 | −0.183636 | ||||||||
\(694\) | −26.7133 | −1.01402 | ||||||||
\(695\) | 4.34093 | 0.164661 | ||||||||
\(696\) | −3.59660 | −0.136329 | ||||||||
\(697\) | −8.93183 | −0.338317 | ||||||||
\(698\) | 30.5637 | 1.15685 | ||||||||
\(699\) | −0.767866 | −0.0290434 | ||||||||
\(700\) | −10.8423 | −0.409800 | ||||||||
\(701\) | −30.7681 | −1.16210 | −0.581048 | − | 0.813869i | \(-0.697357\pi\) | ||||
−0.581048 | + | 0.813869i | \(0.697357\pi\) | |||||||
\(702\) | 11.8055 | 0.445569 | ||||||||
\(703\) | 10.8442 | 0.408997 | ||||||||
\(704\) | 39.9591 | 1.50601 | ||||||||
\(705\) | 0.496267 | 0.0186905 | ||||||||
\(706\) | 37.6862 | 1.41834 | ||||||||
\(707\) | −5.12344 | −0.192687 | ||||||||
\(708\) | 6.06369 | 0.227887 | ||||||||
\(709\) | −3.23862 | −0.121629 | −0.0608144 | − | 0.998149i | \(-0.519370\pi\) | ||||
−0.0608144 | + | 0.998149i | \(0.519370\pi\) | |||||||
\(710\) | 7.50688 | 0.281728 | ||||||||
\(711\) | 34.7990 | 1.30506 | ||||||||
\(712\) | −120.378 | −4.51137 | ||||||||
\(713\) | 6.05309 | 0.226690 | ||||||||
\(714\) | 0.201925 | 0.00755684 | ||||||||
\(715\) | 9.54814 | 0.357080 | ||||||||
\(716\) | 115.459 | 4.31492 | ||||||||
\(717\) | −1.93260 | −0.0721744 | ||||||||
\(718\) | 11.0337 | 0.411773 | ||||||||
\(719\) | −2.84703 | −0.106176 | −0.0530882 | − | 0.998590i | \(-0.516906\pi\) | ||||
−0.0530882 | + | 0.998590i | \(0.516906\pi\) | |||||||
\(720\) | −16.7491 | −0.624203 | ||||||||
\(721\) | 5.37332 | 0.200113 | ||||||||
\(722\) | −13.1156 | −0.488113 | ||||||||
\(723\) | 0.530184 | 0.0197177 | ||||||||
\(724\) | 41.7979 | 1.55341 | ||||||||
\(725\) | −14.9999 | −0.557082 | ||||||||
\(726\) | −0.465358 | −0.0172711 | ||||||||
\(727\) | −45.1722 | −1.67535 | −0.837673 | − | 0.546172i | \(-0.816084\pi\) | ||||
−0.837673 | + | 0.546172i | \(0.816084\pi\) | |||||||
\(728\) | −18.5750 | −0.688436 | ||||||||
\(729\) | −25.8627 | −0.957878 | ||||||||
\(730\) | −0.190772 | −0.00706080 | ||||||||
\(731\) | 5.31702 | 0.196657 | ||||||||
\(732\) | −5.77848 | −0.213579 | ||||||||
\(733\) | 9.18130 | 0.339119 | 0.169559 | − | 0.985520i | \(-0.445766\pi\) | ||||
0.169559 | + | 0.985520i | \(0.445766\pi\) | |||||||
\(734\) | −12.1056 | −0.446828 | ||||||||
\(735\) | −0.524247 | −0.0193371 | ||||||||
\(736\) | 93.1977 | 3.43531 | ||||||||
\(737\) | 24.4250 | 0.899707 | ||||||||
\(738\) | 61.8842 | 2.27799 | ||||||||
\(739\) | 38.5849 | 1.41937 | 0.709685 | − | 0.704519i | \(-0.248837\pi\) | ||||
0.709685 | + | 0.704519i | \(0.248837\pi\) | |||||||
\(740\) | −5.81835 | −0.213887 | ||||||||
\(741\) | −3.66780 | −0.134740 | ||||||||
\(742\) | −6.13356 | −0.225170 | ||||||||
\(743\) | 7.31389 | 0.268321 | 0.134160 | − | 0.990960i | \(-0.457166\pi\) | ||||
0.134160 | + | 0.990960i | \(0.457166\pi\) | |||||||
\(744\) | 0.909153 | 0.0333312 | ||||||||
\(745\) | 5.49134 | 0.201187 | ||||||||
\(746\) | −77.7412 | −2.84631 | ||||||||
\(747\) | −16.4127 | −0.600510 | ||||||||
\(748\) | −19.5993 | −0.716620 | ||||||||
\(749\) | 1.59216 | 0.0581763 | ||||||||
\(750\) | 1.97951 | 0.0722816 | ||||||||
\(751\) | −37.0356 | −1.35145 | −0.675725 | − | 0.737154i | \(-0.736169\pi\) | ||||
−0.675725 | + | 0.737154i | \(0.736169\pi\) | |||||||
\(752\) | 68.0188 | 2.48039 | ||||||||
\(753\) | 0.00265353 | 9.66999e−5 0 | ||||||||
\(754\) | −43.1286 | −1.57065 | ||||||||
\(755\) | 1.19306 | 0.0434198 | ||||||||
\(756\) | −1.99979 | −0.0727316 | ||||||||
\(757\) | −12.4669 | −0.453118 | −0.226559 | − | 0.973997i | \(-0.572748\pi\) | ||||
−0.226559 | + | 0.973997i | \(0.572748\pi\) | |||||||
\(758\) | −35.3030 | −1.28226 | ||||||||
\(759\) | −3.83129 | −0.139067 | ||||||||
\(760\) | 20.2045 | 0.732895 | ||||||||
\(761\) | −8.41470 | −0.305033 | −0.152516 | − | 0.988301i | \(-0.548738\pi\) | ||||
−0.152516 | + | 0.988301i | \(0.548738\pi\) | |||||||
\(762\) | −0.851633 | −0.0308514 | ||||||||
\(763\) | 7.83860 | 0.283776 | ||||||||
\(764\) | −7.09130 | −0.256554 | ||||||||
\(765\) | 1.79227 | 0.0647996 | ||||||||
\(766\) | −9.27987 | −0.335295 | ||||||||
\(767\) | 43.3252 | 1.56438 | ||||||||
\(768\) | −1.25902 | −0.0454311 | ||||||||
\(769\) | 19.2318 | 0.693517 | 0.346759 | − | 0.937954i | \(-0.387282\pi\) | ||||
0.346759 | + | 0.937954i | \(0.387282\pi\) | |||||||
\(770\) | −2.27109 | −0.0818445 | ||||||||
\(771\) | 3.20738 | 0.115511 | ||||||||
\(772\) | −3.17048 | −0.114108 | ||||||||
\(773\) | −26.0713 | −0.937718 | −0.468859 | − | 0.883273i | \(-0.655335\pi\) | ||||
−0.468859 | + | 0.883273i | \(0.655335\pi\) | |||||||
\(774\) | −36.8389 | −1.32415 | ||||||||
\(775\) | 3.79169 | 0.136202 | ||||||||
\(776\) | −78.9316 | −2.83348 | ||||||||
\(777\) | −0.149694 | −0.00537024 | ||||||||
\(778\) | −29.8802 | −1.07126 | ||||||||
\(779\) | −38.5899 | −1.38263 | ||||||||
\(780\) | 1.96792 | 0.0704628 | ||||||||
\(781\) | −18.7462 | −0.670793 | ||||||||
\(782\) | −22.5017 | −0.804660 | ||||||||
\(783\) | −2.76663 | −0.0988713 | ||||||||
\(784\) | −71.8537 | −2.56620 | ||||||||
\(785\) | −6.25041 | −0.223087 | ||||||||
\(786\) | 3.46721 | 0.123671 | ||||||||
\(787\) | 14.3786 | 0.512540 | 0.256270 | − | 0.966605i | \(-0.417506\pi\) | ||||
0.256270 | + | 0.966605i | \(0.417506\pi\) | |||||||
\(788\) | 33.9867 | 1.21073 | ||||||||
\(789\) | −1.53228 | −0.0545508 | ||||||||
\(790\) | 16.3485 | 0.581654 | ||||||||
\(791\) | −0.0533770 | −0.00189787 | ||||||||
\(792\) | 80.9113 | 2.87506 | ||||||||
\(793\) | −41.2874 | −1.46616 | ||||||||
\(794\) | −54.2325 | −1.92464 | ||||||||
\(795\) | 0.387188 | 0.0137321 | ||||||||
\(796\) | −24.8136 | −0.879496 | ||||||||
\(797\) | 38.2513 | 1.35493 | 0.677465 | − | 0.735555i | \(-0.263079\pi\) | ||||
0.677465 | + | 0.735555i | \(0.263079\pi\) | |||||||
\(798\) | 0.872413 | 0.0308831 | ||||||||
\(799\) | −7.27846 | −0.257494 | ||||||||
\(800\) | 58.3795 | 2.06403 | ||||||||
\(801\) | −46.1355 | −1.63012 | ||||||||
\(802\) | −61.0523 | −2.15583 | ||||||||
\(803\) | 0.476397 | 0.0168117 | ||||||||
\(804\) | 5.03412 | 0.177540 | ||||||||
\(805\) | −1.85693 | −0.0654481 | ||||||||
\(806\) | 10.9021 | 0.384010 | ||||||||
\(807\) | −3.58381 | −0.126156 | ||||||||
\(808\) | 85.7526 | 3.01677 | ||||||||
\(809\) | −47.7550 | −1.67898 | −0.839488 | − | 0.543378i | \(-0.817145\pi\) | ||||
−0.839488 | + | 0.543378i | \(0.817145\pi\) | |||||||
\(810\) | −12.3288 | −0.433189 | ||||||||
\(811\) | −23.6336 | −0.829888 | −0.414944 | − | 0.909847i | \(-0.636199\pi\) | ||||
−0.414944 | + | 0.909847i | \(0.636199\pi\) | |||||||
\(812\) | 7.30577 | 0.256382 | ||||||||
\(813\) | −0.768440 | −0.0269504 | ||||||||
\(814\) | 20.4019 | 0.715086 | ||||||||
\(815\) | −3.30364 | −0.115721 | ||||||||
\(816\) | −1.74708 | −0.0611600 | ||||||||
\(817\) | 22.9721 | 0.803692 | ||||||||
\(818\) | −4.20608 | −0.147062 | ||||||||
\(819\) | −7.11895 | −0.248756 | ||||||||
\(820\) | 20.7050 | 0.723050 | ||||||||
\(821\) | 54.4910 | 1.90175 | 0.950874 | − | 0.309579i | \(-0.100188\pi\) | ||||
0.950874 | + | 0.309579i | \(0.100188\pi\) | |||||||
\(822\) | −8.06211 | −0.281198 | ||||||||
\(823\) | 10.6729 | 0.372036 | 0.186018 | − | 0.982546i | \(-0.440442\pi\) | ||||
0.186018 | + | 0.982546i | \(0.440442\pi\) | |||||||
\(824\) | −89.9349 | −3.13303 | ||||||||
\(825\) | −2.39994 | −0.0835552 | ||||||||
\(826\) | −10.3052 | −0.358564 | ||||||||
\(827\) | 35.8210 | 1.24562 | 0.622809 | − | 0.782374i | \(-0.285991\pi\) | ||||
0.622809 | + | 0.782374i | \(0.285991\pi\) | |||||||
\(828\) | 111.030 | 3.85854 | ||||||||
\(829\) | 45.8189 | 1.59136 | 0.795678 | − | 0.605719i | \(-0.207115\pi\) | ||||
0.795678 | + | 0.605719i | \(0.207115\pi\) | |||||||
\(830\) | −7.71067 | −0.267641 | ||||||||
\(831\) | 2.49058 | 0.0863974 | ||||||||
\(832\) | 58.8448 | 2.04008 | ||||||||
\(833\) | 7.68883 | 0.266402 | ||||||||
\(834\) | −3.13719 | −0.108632 | ||||||||
\(835\) | 4.22418 | 0.146184 | ||||||||
\(836\) | −84.6783 | −2.92866 | ||||||||
\(837\) | 0.699352 | 0.0241731 | ||||||||
\(838\) | −70.0330 | −2.41925 | ||||||||
\(839\) | 28.6828 | 0.990241 | 0.495121 | − | 0.868824i | \(-0.335124\pi\) | ||||
0.495121 | + | 0.868824i | \(0.335124\pi\) | |||||||
\(840\) | −0.278904 | −0.00962310 | ||||||||
\(841\) | −18.8928 | −0.651474 | ||||||||
\(842\) | −23.5803 | −0.812629 | ||||||||
\(843\) | −1.20058 | −0.0413503 | ||||||||
\(844\) | −30.4729 | −1.04892 | ||||||||
\(845\) | 7.15922 | 0.246285 | ||||||||
\(846\) | 50.4288 | 1.73378 | ||||||||
\(847\) | 0.563238 | 0.0193531 | ||||||||
\(848\) | 53.0683 | 1.82237 | ||||||||
\(849\) | −0.373911 | −0.0128326 | ||||||||
\(850\) | −14.0952 | −0.483461 | ||||||||
\(851\) | 16.6813 | 0.571828 | ||||||||
\(852\) | −3.86369 | −0.132368 | ||||||||
\(853\) | −15.1726 | −0.519499 | −0.259749 | − | 0.965676i | \(-0.583640\pi\) | ||||
−0.259749 | + | 0.965676i | \(0.583640\pi\) | |||||||
\(854\) | 9.82050 | 0.336051 | ||||||||
\(855\) | 7.74347 | 0.264821 | ||||||||
\(856\) | −26.6485 | −0.910828 | ||||||||
\(857\) | 31.7470 | 1.08446 | 0.542229 | − | 0.840231i | \(-0.317580\pi\) | ||||
0.542229 | + | 0.840231i | \(0.317580\pi\) | |||||||
\(858\) | −6.90046 | −0.235578 | ||||||||
\(859\) | −9.38987 | −0.320378 | −0.160189 | − | 0.987086i | \(-0.551210\pi\) | ||||
−0.160189 | + | 0.987086i | \(0.551210\pi\) | |||||||
\(860\) | −12.3254 | −0.420294 | ||||||||
\(861\) | 0.532696 | 0.0181542 | ||||||||
\(862\) | 31.6498 | 1.07800 | ||||||||
\(863\) | −36.4580 | −1.24105 | −0.620523 | − | 0.784188i | \(-0.713080\pi\) | ||||
−0.620523 | + | 0.784188i | \(0.713080\pi\) | |||||||
\(864\) | 10.7677 | 0.366325 | ||||||||
\(865\) | 5.85835 | 0.199190 | ||||||||
\(866\) | 33.8306 | 1.14961 | ||||||||
\(867\) | −2.28744 | −0.0776856 | ||||||||
\(868\) | −1.84676 | −0.0626831 | ||||||||
\(869\) | −40.8256 | −1.38491 | ||||||||
\(870\) | −0.647576 | −0.0219549 | ||||||||
\(871\) | 35.9689 | 1.21876 | ||||||||
\(872\) | −131.197 | −4.44289 | ||||||||
\(873\) | −30.2509 | −1.02384 | ||||||||
\(874\) | −97.2183 | −3.28846 | ||||||||
\(875\) | −2.39586 | −0.0809950 | ||||||||
\(876\) | 0.0981880 | 0.00331746 | ||||||||
\(877\) | 0.500309 | 0.0168942 | 0.00844712 | − | 0.999964i | \(-0.497311\pi\) | ||||
0.00844712 | + | 0.999964i | \(0.497311\pi\) | |||||||
\(878\) | 45.0469 | 1.52026 | ||||||||
\(879\) | 2.29111 | 0.0772771 | ||||||||
\(880\) | 19.6498 | 0.662394 | ||||||||
\(881\) | −49.6396 | −1.67240 | −0.836201 | − | 0.548423i | \(-0.815228\pi\) | ||||
−0.836201 | + | 0.548423i | \(0.815228\pi\) | |||||||
\(882\) | −53.2720 | −1.79376 | ||||||||
\(883\) | 3.65213 | 0.122904 | 0.0614519 | − | 0.998110i | \(-0.480427\pi\) | ||||
0.0614519 | + | 0.998110i | \(0.480427\pi\) | |||||||
\(884\) | −28.8624 | −0.970747 | ||||||||
\(885\) | 0.650528 | 0.0218673 | ||||||||
\(886\) | 37.6205 | 1.26389 | ||||||||
\(887\) | 16.4471 | 0.552240 | 0.276120 | − | 0.961123i | \(-0.410951\pi\) | ||||
0.276120 | + | 0.961123i | \(0.410951\pi\) | |||||||
\(888\) | 2.50547 | 0.0840782 | ||||||||
\(889\) | 1.03076 | 0.0345705 | ||||||||
\(890\) | −21.6744 | −0.726527 | ||||||||
\(891\) | 30.7875 | 1.03142 | ||||||||
\(892\) | −7.91581 | −0.265041 | ||||||||
\(893\) | −31.4465 | −1.05232 | ||||||||
\(894\) | −3.96860 | −0.132730 | ||||||||
\(895\) | 12.3868 | 0.414045 | ||||||||
\(896\) | −2.50482 | −0.0836801 | ||||||||
\(897\) | −5.64206 | −0.188383 | ||||||||
\(898\) | 103.261 | 3.44586 | ||||||||
\(899\) | −2.55492 | −0.0852114 | ||||||||
\(900\) | 69.5495 | 2.31832 | ||||||||
\(901\) | −5.67866 | −0.189184 | ||||||||
\(902\) | −72.6015 | −2.41736 | ||||||||
\(903\) | −0.317108 | −0.0105527 | ||||||||
\(904\) | 0.893388 | 0.0297136 | ||||||||
\(905\) | 4.48419 | 0.149060 | ||||||||
\(906\) | −0.862225 | −0.0286455 | ||||||||
\(907\) | 24.4458 | 0.811709 | 0.405854 | − | 0.913938i | \(-0.366974\pi\) | ||||
0.405854 | + | 0.913938i | \(0.366974\pi\) | |||||||
\(908\) | 13.4495 | 0.446338 | ||||||||
\(909\) | 32.8650 | 1.09006 | ||||||||
\(910\) | −3.34447 | −0.110868 | ||||||||
\(911\) | 52.9608 | 1.75467 | 0.877334 | − | 0.479880i | \(-0.159320\pi\) | ||||
0.877334 | + | 0.479880i | \(0.159320\pi\) | |||||||
\(912\) | −7.54822 | −0.249947 | ||||||||
\(913\) | 19.2551 | 0.637252 | ||||||||
\(914\) | 68.3768 | 2.26170 | ||||||||
\(915\) | −0.619930 | −0.0204943 | ||||||||
\(916\) | 104.614 | 3.45654 | ||||||||
\(917\) | −4.19647 | −0.138579 | ||||||||
\(918\) | −2.59976 | −0.0858050 | ||||||||
\(919\) | 20.5426 | 0.677638 | 0.338819 | − | 0.940852i | \(-0.389973\pi\) | ||||
0.338819 | + | 0.940852i | \(0.389973\pi\) | |||||||
\(920\) | 31.0800 | 1.02468 | ||||||||
\(921\) | −1.91510 | −0.0631045 | ||||||||
\(922\) | −77.7701 | −2.56122 | ||||||||
\(923\) | −27.6062 | −0.908669 | ||||||||
\(924\) | 1.16890 | 0.0384541 | ||||||||
\(925\) | 10.4493 | 0.343570 | ||||||||
\(926\) | −13.5509 | −0.445309 | ||||||||
\(927\) | −34.4679 | −1.13207 | ||||||||
\(928\) | −39.3374 | −1.29131 | ||||||||
\(929\) | 18.4959 | 0.606831 | 0.303416 | − | 0.952858i | \(-0.401873\pi\) | ||||
0.303416 | + | 0.952858i | \(0.401873\pi\) | |||||||
\(930\) | 0.163695 | 0.00536777 | ||||||||
\(931\) | 33.2195 | 1.08872 | ||||||||
\(932\) | −26.1062 | −0.855139 | ||||||||
\(933\) | 0.532867 | 0.0174453 | ||||||||
\(934\) | 6.02908 | 0.197277 | ||||||||
\(935\) | −2.10266 | −0.0687643 | ||||||||
\(936\) | 119.152 | 3.89461 | ||||||||
\(937\) | −30.8582 | −1.00809 | −0.504047 | − | 0.863676i | \(-0.668156\pi\) | ||||
−0.504047 | + | 0.863676i | \(0.668156\pi\) | |||||||
\(938\) | −8.55547 | −0.279346 | ||||||||
\(939\) | −2.55902 | −0.0835105 | ||||||||
\(940\) | 16.8723 | 0.550313 | ||||||||
\(941\) | 37.4581 | 1.22110 | 0.610550 | − | 0.791978i | \(-0.290948\pi\) | ||||
0.610550 | + | 0.791978i | \(0.290948\pi\) | |||||||
\(942\) | 4.51718 | 0.147178 | ||||||||
\(943\) | −59.3616 | −1.93308 | ||||||||
\(944\) | 89.1620 | 2.90198 | ||||||||
\(945\) | −0.214542 | −0.00697907 | ||||||||
\(946\) | 43.2188 | 1.40516 | ||||||||
\(947\) | 55.5568 | 1.80535 | 0.902676 | − | 0.430320i | \(-0.141599\pi\) | ||||
0.902676 | + | 0.430320i | \(0.141599\pi\) | |||||||
\(948\) | −8.41437 | −0.273286 | ||||||||
\(949\) | 0.701555 | 0.0227735 | ||||||||
\(950\) | −60.8981 | −1.97579 | ||||||||
\(951\) | −1.25693 | −0.0407588 | ||||||||
\(952\) | 4.09053 | 0.132575 | ||||||||
\(953\) | 14.0637 | 0.455568 | 0.227784 | − | 0.973712i | \(-0.426852\pi\) | ||||
0.227784 | + | 0.973712i | \(0.426852\pi\) | |||||||
\(954\) | 39.3446 | 1.27383 | ||||||||
\(955\) | −0.760773 | −0.0246180 | ||||||||
\(956\) | −65.7055 | −2.12507 | ||||||||
\(957\) | 1.61713 | 0.0522744 | ||||||||
\(958\) | −45.5834 | −1.47273 | ||||||||
\(959\) | 9.75782 | 0.315096 | ||||||||
\(960\) | 0.883555 | 0.0285166 | ||||||||
\(961\) | −30.3542 | −0.979167 | ||||||||
\(962\) | 30.0443 | 0.968669 | ||||||||
\(963\) | −10.2132 | −0.329114 | ||||||||
\(964\) | 18.0254 | 0.580560 | ||||||||
\(965\) | −0.340138 | −0.0109494 | ||||||||
\(966\) | 1.34201 | 0.0431783 | ||||||||
\(967\) | 32.6962 | 1.05144 | 0.525720 | − | 0.850658i | \(-0.323796\pi\) | ||||
0.525720 | + | 0.850658i | \(0.323796\pi\) | |||||||
\(968\) | −9.42708 | −0.302998 | ||||||||
\(969\) | 0.807711 | 0.0259474 | ||||||||
\(970\) | −14.2118 | −0.456314 | ||||||||
\(971\) | −42.4585 | −1.36256 | −0.681278 | − | 0.732024i | \(-0.738576\pi\) | ||||
−0.681278 | + | 0.732024i | \(0.738576\pi\) | |||||||
\(972\) | 19.2646 | 0.617913 | ||||||||
\(973\) | 3.79704 | 0.121728 | ||||||||
\(974\) | −36.0694 | −1.15574 | ||||||||
\(975\) | −3.53422 | −0.113186 | ||||||||
\(976\) | −84.9682 | −2.71977 | ||||||||
\(977\) | 21.5642 | 0.689898 | 0.344949 | − | 0.938621i | \(-0.387896\pi\) | ||||
0.344949 | + | 0.938621i | \(0.387896\pi\) | |||||||
\(978\) | 2.38754 | 0.0763452 | ||||||||
\(979\) | 54.1253 | 1.72985 | ||||||||
\(980\) | −17.8236 | −0.569353 | ||||||||
\(981\) | −50.2818 | −1.60537 | ||||||||
\(982\) | −30.1060 | −0.960721 | ||||||||
\(983\) | 11.8067 | 0.376574 | 0.188287 | − | 0.982114i | \(-0.439706\pi\) | ||||
0.188287 | + | 0.982114i | \(0.439706\pi\) | |||||||
\(984\) | −8.91590 | −0.284228 | ||||||||
\(985\) | 3.64618 | 0.116177 | ||||||||
\(986\) | 9.49764 | 0.302466 | ||||||||
\(987\) | 0.434089 | 0.0138172 | ||||||||
\(988\) | −124.699 | −3.96722 | ||||||||
\(989\) | 35.3373 | 1.12366 | ||||||||
\(990\) | 14.5683 | 0.463010 | ||||||||
\(991\) | 16.9327 | 0.537886 | 0.268943 | − | 0.963156i | \(-0.413326\pi\) | ||||
0.268943 | + | 0.963156i | \(0.413326\pi\) | |||||||
\(992\) | 9.94374 | 0.315714 | ||||||||
\(993\) | 2.35597 | 0.0747646 | ||||||||
\(994\) | 6.56633 | 0.208271 | ||||||||
\(995\) | −2.66207 | −0.0843933 | ||||||||
\(996\) | 3.96858 | 0.125749 | ||||||||
\(997\) | 21.6310 | 0.685061 | 0.342530 | − | 0.939507i | \(-0.388716\pi\) | ||||
0.342530 | + | 0.939507i | \(0.388716\pi\) | |||||||
\(998\) | −31.0845 | −0.983962 | ||||||||
\(999\) | 1.92730 | 0.0609769 |
(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 | 6007.2.a.c.1.7 | ✓ | 261 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6007.2.a.c.1.7 | ✓ | 261 | 1.1 | even | 1 | trivial |