Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1334,2,Mod(1,1334)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1334, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1334.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1334 = 2 \cdot 23 \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1334.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: | \(10.6520436296\) |
Analytic rank: | \(0\) |
Dimension: | \(10\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{10} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{10} - 5x^{9} - 8x^{8} + 60x^{7} + 13x^{6} - 241x^{5} + 6x^{4} + 346x^{3} + 16x^{2} - 64x - 12 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Root | \(-0.267188\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1334.1 |
$q$-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 | ||||||||
\(3\) | 1.26719 | 0.731612 | 0.365806 | − | 0.930691i | \(-0.380793\pi\) | ||||
0.365806 | + | 0.930691i | \(0.380793\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 1.36043 | 0.608401 | 0.304201 | − | 0.952608i | \(-0.401611\pi\) | ||||
0.304201 | + | 0.952608i | \(0.401611\pi\) | |||||||
\(6\) | 1.26719 | 0.517328 | ||||||||
\(7\) | 1.67775 | 0.634130 | 0.317065 | − | 0.948404i | \(-0.397303\pi\) | ||||
0.317065 | + | 0.948404i | \(0.397303\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | −1.39423 | −0.464744 | ||||||||
\(10\) | 1.36043 | 0.430205 | ||||||||
\(11\) | 4.80785 | 1.44962 | 0.724810 | − | 0.688949i | \(-0.241927\pi\) | ||||
0.724810 | + | 0.688949i | \(0.241927\pi\) | |||||||
\(12\) | 1.26719 | 0.365806 | ||||||||
\(13\) | −1.92323 | −0.533407 | −0.266704 | − | 0.963779i | \(-0.585935\pi\) | ||||
−0.266704 | + | 0.963779i | \(0.585935\pi\) | |||||||
\(14\) | 1.67775 | 0.448398 | ||||||||
\(15\) | 1.72392 | 0.445113 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 3.00120 | 0.727897 | 0.363948 | − | 0.931419i | \(-0.381428\pi\) | ||||
0.363948 | + | 0.931419i | \(0.381428\pi\) | |||||||
\(18\) | −1.39423 | −0.328624 | ||||||||
\(19\) | −2.45647 | −0.563553 | −0.281777 | − | 0.959480i | \(-0.590924\pi\) | ||||
−0.281777 | + | 0.959480i | \(0.590924\pi\) | |||||||
\(20\) | 1.36043 | 0.304201 | ||||||||
\(21\) | 2.12603 | 0.463937 | ||||||||
\(22\) | 4.80785 | 1.02504 | ||||||||
\(23\) | 1.00000 | 0.208514 | ||||||||
\(24\) | 1.26719 | 0.258664 | ||||||||
\(25\) | −3.14924 | −0.629848 | ||||||||
\(26\) | −1.92323 | −0.377176 | ||||||||
\(27\) | −5.56832 | −1.07162 | ||||||||
\(28\) | 1.67775 | 0.317065 | ||||||||
\(29\) | 1.00000 | 0.185695 | ||||||||
\(30\) | 1.72392 | 0.314743 | ||||||||
\(31\) | −6.93732 | −1.24598 | −0.622990 | − | 0.782230i | \(-0.714082\pi\) | ||||
−0.622990 | + | 0.782230i | \(0.714082\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 6.09245 | 1.06056 | ||||||||
\(34\) | 3.00120 | 0.514701 | ||||||||
\(35\) | 2.28246 | 0.385805 | ||||||||
\(36\) | −1.39423 | −0.232372 | ||||||||
\(37\) | 8.33349 | 1.37002 | 0.685008 | − | 0.728535i | \(-0.259798\pi\) | ||||
0.685008 | + | 0.728535i | \(0.259798\pi\) | |||||||
\(38\) | −2.45647 | −0.398492 | ||||||||
\(39\) | −2.43709 | −0.390247 | ||||||||
\(40\) | 1.36043 | 0.215102 | ||||||||
\(41\) | −1.49177 | −0.232975 | −0.116488 | − | 0.993192i | \(-0.537164\pi\) | ||||
−0.116488 | + | 0.993192i | \(0.537164\pi\) | |||||||
\(42\) | 2.12603 | 0.328053 | ||||||||
\(43\) | 0.840503 | 0.128175 | 0.0640877 | − | 0.997944i | \(-0.479586\pi\) | ||||
0.0640877 | + | 0.997944i | \(0.479586\pi\) | |||||||
\(44\) | 4.80785 | 0.724810 | ||||||||
\(45\) | −1.89675 | −0.282751 | ||||||||
\(46\) | 1.00000 | 0.147442 | ||||||||
\(47\) | −0.754099 | −0.109997 | −0.0549983 | − | 0.998486i | \(-0.517515\pi\) | ||||
−0.0549983 | + | 0.998486i | \(0.517515\pi\) | |||||||
\(48\) | 1.26719 | 0.182903 | ||||||||
\(49\) | −4.18516 | −0.597879 | ||||||||
\(50\) | −3.14924 | −0.445370 | ||||||||
\(51\) | 3.80308 | 0.532538 | ||||||||
\(52\) | −1.92323 | −0.266704 | ||||||||
\(53\) | 4.47440 | 0.614606 | 0.307303 | − | 0.951612i | \(-0.400573\pi\) | ||||
0.307303 | + | 0.951612i | \(0.400573\pi\) | |||||||
\(54\) | −5.56832 | −0.757753 | ||||||||
\(55\) | 6.54072 | 0.881951 | ||||||||
\(56\) | 1.67775 | 0.224199 | ||||||||
\(57\) | −3.11281 | −0.412302 | ||||||||
\(58\) | 1.00000 | 0.131306 | ||||||||
\(59\) | 10.0339 | 1.30631 | 0.653153 | − | 0.757226i | \(-0.273446\pi\) | ||||
0.653153 | + | 0.757226i | \(0.273446\pi\) | |||||||
\(60\) | 1.72392 | 0.222557 | ||||||||
\(61\) | 5.19712 | 0.665423 | 0.332712 | − | 0.943029i | \(-0.392036\pi\) | ||||
0.332712 | + | 0.943029i | \(0.392036\pi\) | |||||||
\(62\) | −6.93732 | −0.881041 | ||||||||
\(63\) | −2.33918 | −0.294708 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −2.61641 | −0.324526 | ||||||||
\(66\) | 6.09245 | 0.749928 | ||||||||
\(67\) | −14.7127 | −1.79744 | −0.898721 | − | 0.438520i | \(-0.855503\pi\) | ||||
−0.898721 | + | 0.438520i | \(0.855503\pi\) | |||||||
\(68\) | 3.00120 | 0.363948 | ||||||||
\(69\) | 1.26719 | 0.152552 | ||||||||
\(70\) | 2.28246 | 0.272806 | ||||||||
\(71\) | −5.76111 | −0.683718 | −0.341859 | − | 0.939751i | \(-0.611057\pi\) | ||||
−0.341859 | + | 0.939751i | \(0.611057\pi\) | |||||||
\(72\) | −1.39423 | −0.164312 | ||||||||
\(73\) | −0.364931 | −0.0427119 | −0.0213560 | − | 0.999772i | \(-0.506798\pi\) | ||||
−0.0213560 | + | 0.999772i | \(0.506798\pi\) | |||||||
\(74\) | 8.33349 | 0.968748 | ||||||||
\(75\) | −3.99068 | −0.460804 | ||||||||
\(76\) | −2.45647 | −0.281777 | ||||||||
\(77\) | 8.06636 | 0.919248 | ||||||||
\(78\) | −2.43709 | −0.275946 | ||||||||
\(79\) | −14.4028 | −1.62044 | −0.810222 | − | 0.586123i | \(-0.800653\pi\) | ||||
−0.810222 | + | 0.586123i | \(0.800653\pi\) | |||||||
\(80\) | 1.36043 | 0.152100 | ||||||||
\(81\) | −2.87341 | −0.319268 | ||||||||
\(82\) | −1.49177 | −0.164738 | ||||||||
\(83\) | 4.02625 | 0.441938 | 0.220969 | − | 0.975281i | \(-0.429078\pi\) | ||||
0.220969 | + | 0.975281i | \(0.429078\pi\) | |||||||
\(84\) | 2.12603 | 0.231968 | ||||||||
\(85\) | 4.08291 | 0.442853 | ||||||||
\(86\) | 0.840503 | 0.0906337 | ||||||||
\(87\) | 1.26719 | 0.135857 | ||||||||
\(88\) | 4.80785 | 0.512518 | ||||||||
\(89\) | −5.58835 | −0.592363 | −0.296182 | − | 0.955132i | \(-0.595713\pi\) | ||||
−0.296182 | + | 0.955132i | \(0.595713\pi\) | |||||||
\(90\) | −1.89675 | −0.199935 | ||||||||
\(91\) | −3.22670 | −0.338250 | ||||||||
\(92\) | 1.00000 | 0.104257 | ||||||||
\(93\) | −8.79089 | −0.911573 | ||||||||
\(94\) | −0.754099 | −0.0777794 | ||||||||
\(95\) | −3.34185 | −0.342867 | ||||||||
\(96\) | 1.26719 | 0.129332 | ||||||||
\(97\) | 16.2117 | 1.64604 | 0.823022 | − | 0.568010i | \(-0.192286\pi\) | ||||
0.823022 | + | 0.568010i | \(0.192286\pi\) | |||||||
\(98\) | −4.18516 | −0.422765 | ||||||||
\(99\) | −6.70326 | −0.673703 | ||||||||
\(100\) | −3.14924 | −0.314924 | ||||||||
\(101\) | 5.25982 | 0.523372 | 0.261686 | − | 0.965153i | \(-0.415722\pi\) | ||||
0.261686 | + | 0.965153i | \(0.415722\pi\) | |||||||
\(102\) | 3.80308 | 0.376561 | ||||||||
\(103\) | 7.07418 | 0.697039 | 0.348520 | − | 0.937301i | \(-0.386684\pi\) | ||||
0.348520 | + | 0.937301i | \(0.386684\pi\) | |||||||
\(104\) | −1.92323 | −0.188588 | ||||||||
\(105\) | 2.89230 | 0.282260 | ||||||||
\(106\) | 4.47440 | 0.434592 | ||||||||
\(107\) | 2.68162 | 0.259242 | 0.129621 | − | 0.991564i | \(-0.458624\pi\) | ||||
0.129621 | + | 0.991564i | \(0.458624\pi\) | |||||||
\(108\) | −5.56832 | −0.535812 | ||||||||
\(109\) | −11.8123 | −1.13141 | −0.565704 | − | 0.824608i | \(-0.691396\pi\) | ||||
−0.565704 | + | 0.824608i | \(0.691396\pi\) | |||||||
\(110\) | 6.54072 | 0.623633 | ||||||||
\(111\) | 10.5601 | 1.00232 | ||||||||
\(112\) | 1.67775 | 0.158532 | ||||||||
\(113\) | −14.8431 | −1.39633 | −0.698163 | − | 0.715939i | \(-0.745999\pi\) | ||||
−0.698163 | + | 0.715939i | \(0.745999\pi\) | |||||||
\(114\) | −3.11281 | −0.291542 | ||||||||
\(115\) | 1.36043 | 0.126860 | ||||||||
\(116\) | 1.00000 | 0.0928477 | ||||||||
\(117\) | 2.68143 | 0.247898 | ||||||||
\(118\) | 10.0339 | 0.923697 | ||||||||
\(119\) | 5.03526 | 0.461581 | ||||||||
\(120\) | 1.72392 | 0.157371 | ||||||||
\(121\) | 12.1154 | 1.10140 | ||||||||
\(122\) | 5.19712 | 0.470525 | ||||||||
\(123\) | −1.89035 | −0.170447 | ||||||||
\(124\) | −6.93732 | −0.622990 | ||||||||
\(125\) | −11.0864 | −0.991602 | ||||||||
\(126\) | −2.33918 | −0.208390 | ||||||||
\(127\) | −13.9826 | −1.24076 | −0.620379 | − | 0.784302i | \(-0.713021\pi\) | ||||
−0.620379 | + | 0.784302i | \(0.713021\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 1.06508 | 0.0937747 | ||||||||
\(130\) | −2.61641 | −0.229474 | ||||||||
\(131\) | −1.69582 | −0.148165 | −0.0740824 | − | 0.997252i | \(-0.523603\pi\) | ||||
−0.0740824 | + | 0.997252i | \(0.523603\pi\) | |||||||
\(132\) | 6.09245 | 0.530280 | ||||||||
\(133\) | −4.12135 | −0.357366 | ||||||||
\(134\) | −14.7127 | −1.27098 | ||||||||
\(135\) | −7.57529 | −0.651977 | ||||||||
\(136\) | 3.00120 | 0.257350 | ||||||||
\(137\) | 12.1768 | 1.04034 | 0.520168 | − | 0.854064i | \(-0.325869\pi\) | ||||
0.520168 | + | 0.854064i | \(0.325869\pi\) | |||||||
\(138\) | 1.26719 | 0.107870 | ||||||||
\(139\) | 4.82859 | 0.409556 | 0.204778 | − | 0.978808i | \(-0.434353\pi\) | ||||
0.204778 | + | 0.978808i | \(0.434353\pi\) | |||||||
\(140\) | 2.28246 | 0.192903 | ||||||||
\(141\) | −0.955586 | −0.0804748 | ||||||||
\(142\) | −5.76111 | −0.483462 | ||||||||
\(143\) | −9.24659 | −0.773238 | ||||||||
\(144\) | −1.39423 | −0.116186 | ||||||||
\(145\) | 1.36043 | 0.112977 | ||||||||
\(146\) | −0.364931 | −0.0302019 | ||||||||
\(147\) | −5.30338 | −0.437415 | ||||||||
\(148\) | 8.33349 | 0.685008 | ||||||||
\(149\) | −20.4742 | −1.67731 | −0.838657 | − | 0.544660i | \(-0.816659\pi\) | ||||
−0.838657 | + | 0.544660i | \(0.816659\pi\) | |||||||
\(150\) | −3.99068 | −0.325838 | ||||||||
\(151\) | 14.9617 | 1.21757 | 0.608784 | − | 0.793336i | \(-0.291658\pi\) | ||||
0.608784 | + | 0.793336i | \(0.291658\pi\) | |||||||
\(152\) | −2.45647 | −0.199246 | ||||||||
\(153\) | −4.18437 | −0.338286 | ||||||||
\(154\) | 8.06636 | 0.650006 | ||||||||
\(155\) | −9.43772 | −0.758056 | ||||||||
\(156\) | −2.43709 | −0.195124 | ||||||||
\(157\) | −7.35532 | −0.587019 | −0.293509 | − | 0.955956i | \(-0.594823\pi\) | ||||
−0.293509 | + | 0.955956i | \(0.594823\pi\) | |||||||
\(158\) | −14.4028 | −1.14583 | ||||||||
\(159\) | 5.66991 | 0.449653 | ||||||||
\(160\) | 1.36043 | 0.107551 | ||||||||
\(161\) | 1.67775 | 0.132225 | ||||||||
\(162\) | −2.87341 | −0.225757 | ||||||||
\(163\) | 23.8132 | 1.86519 | 0.932596 | − | 0.360923i | \(-0.117538\pi\) | ||||
0.932596 | + | 0.360923i | \(0.117538\pi\) | |||||||
\(164\) | −1.49177 | −0.116488 | ||||||||
\(165\) | 8.28833 | 0.645246 | ||||||||
\(166\) | 4.02625 | 0.312498 | ||||||||
\(167\) | 13.1045 | 1.01406 | 0.507029 | − | 0.861929i | \(-0.330744\pi\) | ||||
0.507029 | + | 0.861929i | \(0.330744\pi\) | |||||||
\(168\) | 2.12603 | 0.164026 | ||||||||
\(169\) | −9.30119 | −0.715476 | ||||||||
\(170\) | 4.08291 | 0.313145 | ||||||||
\(171\) | 3.42490 | 0.261908 | ||||||||
\(172\) | 0.840503 | 0.0640877 | ||||||||
\(173\) | −13.2765 | −1.00940 | −0.504698 | − | 0.863296i | \(-0.668396\pi\) | ||||
−0.504698 | + | 0.863296i | \(0.668396\pi\) | |||||||
\(174\) | 1.26719 | 0.0960653 | ||||||||
\(175\) | −5.28364 | −0.399405 | ||||||||
\(176\) | 4.80785 | 0.362405 | ||||||||
\(177\) | 12.7149 | 0.955708 | ||||||||
\(178\) | −5.58835 | −0.418864 | ||||||||
\(179\) | −3.06552 | −0.229127 | −0.114564 | − | 0.993416i | \(-0.536547\pi\) | ||||
−0.114564 | + | 0.993416i | \(0.536547\pi\) | |||||||
\(180\) | −1.89675 | −0.141376 | ||||||||
\(181\) | 1.51768 | 0.112809 | 0.0564043 | − | 0.998408i | \(-0.482036\pi\) | ||||
0.0564043 | + | 0.998408i | \(0.482036\pi\) | |||||||
\(182\) | −3.22670 | −0.239179 | ||||||||
\(183\) | 6.58573 | 0.486831 | ||||||||
\(184\) | 1.00000 | 0.0737210 | ||||||||
\(185\) | 11.3371 | 0.833520 | ||||||||
\(186\) | −8.79089 | −0.644579 | ||||||||
\(187\) | 14.4293 | 1.05517 | ||||||||
\(188\) | −0.754099 | −0.0549983 | ||||||||
\(189\) | −9.34225 | −0.679549 | ||||||||
\(190\) | −3.34185 | −0.242443 | ||||||||
\(191\) | 14.9770 | 1.08370 | 0.541850 | − | 0.840475i | \(-0.317724\pi\) | ||||
0.541850 | + | 0.840475i | \(0.317724\pi\) | |||||||
\(192\) | 1.26719 | 0.0914514 | ||||||||
\(193\) | −15.0546 | −1.08365 | −0.541825 | − | 0.840491i | \(-0.682267\pi\) | ||||
−0.541825 | + | 0.840491i | \(0.682267\pi\) | |||||||
\(194\) | 16.2117 | 1.16393 | ||||||||
\(195\) | −3.31549 | −0.237427 | ||||||||
\(196\) | −4.18516 | −0.298940 | ||||||||
\(197\) | −14.4974 | −1.03290 | −0.516448 | − | 0.856318i | \(-0.672746\pi\) | ||||
−0.516448 | + | 0.856318i | \(0.672746\pi\) | |||||||
\(198\) | −6.70326 | −0.476380 | ||||||||
\(199\) | 0.866870 | 0.0614508 | 0.0307254 | − | 0.999528i | \(-0.490218\pi\) | ||||
0.0307254 | + | 0.999528i | \(0.490218\pi\) | |||||||
\(200\) | −3.14924 | −0.222685 | ||||||||
\(201\) | −18.6438 | −1.31503 | ||||||||
\(202\) | 5.25982 | 0.370080 | ||||||||
\(203\) | 1.67775 | 0.117755 | ||||||||
\(204\) | 3.80308 | 0.266269 | ||||||||
\(205\) | −2.02944 | −0.141742 | ||||||||
\(206\) | 7.07418 | 0.492881 | ||||||||
\(207\) | −1.39423 | −0.0969059 | ||||||||
\(208\) | −1.92323 | −0.133352 | ||||||||
\(209\) | −11.8103 | −0.816938 | ||||||||
\(210\) | 2.89230 | 0.199588 | ||||||||
\(211\) | 18.4414 | 1.26956 | 0.634779 | − | 0.772694i | \(-0.281091\pi\) | ||||
0.634779 | + | 0.772694i | \(0.281091\pi\) | |||||||
\(212\) | 4.47440 | 0.307303 | ||||||||
\(213\) | −7.30041 | −0.500216 | ||||||||
\(214\) | 2.68162 | 0.183312 | ||||||||
\(215\) | 1.14344 | 0.0779821 | ||||||||
\(216\) | −5.56832 | −0.378876 | ||||||||
\(217\) | −11.6391 | −0.790113 | ||||||||
\(218\) | −11.8123 | −0.800027 | ||||||||
\(219\) | −0.462436 | −0.0312485 | ||||||||
\(220\) | 6.54072 | 0.440975 | ||||||||
\(221\) | −5.77198 | −0.388266 | ||||||||
\(222\) | 10.5601 | 0.708747 | ||||||||
\(223\) | −2.35395 | −0.157632 | −0.0788161 | − | 0.996889i | \(-0.525114\pi\) | ||||
−0.0788161 | + | 0.996889i | \(0.525114\pi\) | |||||||
\(224\) | 1.67775 | 0.112099 | ||||||||
\(225\) | 4.39077 | 0.292718 | ||||||||
\(226\) | −14.8431 | −0.987351 | ||||||||
\(227\) | −19.0700 | −1.26572 | −0.632859 | − | 0.774267i | \(-0.718119\pi\) | ||||
−0.632859 | + | 0.774267i | \(0.718119\pi\) | |||||||
\(228\) | −3.11281 | −0.206151 | ||||||||
\(229\) | −8.57773 | −0.566832 | −0.283416 | − | 0.958997i | \(-0.591468\pi\) | ||||
−0.283416 | + | 0.958997i | \(0.591468\pi\) | |||||||
\(230\) | 1.36043 | 0.0897039 | ||||||||
\(231\) | 10.2216 | 0.672532 | ||||||||
\(232\) | 1.00000 | 0.0656532 | ||||||||
\(233\) | −15.3009 | −1.00240 | −0.501198 | − | 0.865332i | \(-0.667107\pi\) | ||||
−0.501198 | + | 0.865332i | \(0.667107\pi\) | |||||||
\(234\) | 2.68143 | 0.175290 | ||||||||
\(235\) | −1.02590 | −0.0669221 | ||||||||
\(236\) | 10.0339 | 0.653153 | ||||||||
\(237\) | −18.2511 | −1.18554 | ||||||||
\(238\) | 5.03526 | 0.326387 | ||||||||
\(239\) | −13.7120 | −0.886954 | −0.443477 | − | 0.896286i | \(-0.646255\pi\) | ||||
−0.443477 | + | 0.896286i | \(0.646255\pi\) | |||||||
\(240\) | 1.72392 | 0.111278 | ||||||||
\(241\) | −10.7067 | −0.689678 | −0.344839 | − | 0.938662i | \(-0.612066\pi\) | ||||
−0.344839 | + | 0.938662i | \(0.612066\pi\) | |||||||
\(242\) | 12.1154 | 0.778807 | ||||||||
\(243\) | 13.0638 | 0.838044 | ||||||||
\(244\) | 5.19712 | 0.332712 | ||||||||
\(245\) | −5.69360 | −0.363751 | ||||||||
\(246\) | −1.89035 | −0.120524 | ||||||||
\(247\) | 4.72436 | 0.300604 | ||||||||
\(248\) | −6.93732 | −0.440520 | ||||||||
\(249\) | 5.10202 | 0.323327 | ||||||||
\(250\) | −11.0864 | −0.701168 | ||||||||
\(251\) | −9.17063 | −0.578845 | −0.289422 | − | 0.957201i | \(-0.593463\pi\) | ||||
−0.289422 | + | 0.957201i | \(0.593463\pi\) | |||||||
\(252\) | −2.33918 | −0.147354 | ||||||||
\(253\) | 4.80785 | 0.302267 | ||||||||
\(254\) | −13.9826 | −0.877349 | ||||||||
\(255\) | 5.17381 | 0.323997 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −5.17021 | −0.322509 | −0.161255 | − | 0.986913i | \(-0.551554\pi\) | ||||
−0.161255 | + | 0.986913i | \(0.551554\pi\) | |||||||
\(258\) | 1.06508 | 0.0663087 | ||||||||
\(259\) | 13.9815 | 0.868769 | ||||||||
\(260\) | −2.61641 | −0.162263 | ||||||||
\(261\) | −1.39423 | −0.0863009 | ||||||||
\(262\) | −1.69582 | −0.104768 | ||||||||
\(263\) | −10.8593 | −0.669613 | −0.334806 | − | 0.942287i | \(-0.608671\pi\) | ||||
−0.334806 | + | 0.942287i | \(0.608671\pi\) | |||||||
\(264\) | 6.09245 | 0.374964 | ||||||||
\(265\) | 6.08709 | 0.373927 | ||||||||
\(266\) | −4.12135 | −0.252696 | ||||||||
\(267\) | −7.08149 | −0.433380 | ||||||||
\(268\) | −14.7127 | −0.898721 | ||||||||
\(269\) | 22.5988 | 1.37787 | 0.688935 | − | 0.724823i | \(-0.258078\pi\) | ||||
0.688935 | + | 0.724823i | \(0.258078\pi\) | |||||||
\(270\) | −7.57529 | −0.461018 | ||||||||
\(271\) | −22.9257 | −1.39264 | −0.696320 | − | 0.717732i | \(-0.745180\pi\) | ||||
−0.696320 | + | 0.717732i | \(0.745180\pi\) | |||||||
\(272\) | 3.00120 | 0.181974 | ||||||||
\(273\) | −4.08883 | −0.247467 | ||||||||
\(274\) | 12.1768 | 0.735628 | ||||||||
\(275\) | −15.1411 | −0.913040 | ||||||||
\(276\) | 1.26719 | 0.0762758 | ||||||||
\(277\) | 6.16710 | 0.370545 | 0.185273 | − | 0.982687i | \(-0.440683\pi\) | ||||
0.185273 | + | 0.982687i | \(0.440683\pi\) | |||||||
\(278\) | 4.82859 | 0.289600 | ||||||||
\(279\) | 9.67224 | 0.579062 | ||||||||
\(280\) | 2.28246 | 0.136403 | ||||||||
\(281\) | 24.4453 | 1.45828 | 0.729141 | − | 0.684364i | \(-0.239920\pi\) | ||||
0.729141 | + | 0.684364i | \(0.239920\pi\) | |||||||
\(282\) | −0.955586 | −0.0569043 | ||||||||
\(283\) | −12.9213 | −0.768089 | −0.384044 | − | 0.923315i | \(-0.625469\pi\) | ||||
−0.384044 | + | 0.923315i | \(0.625469\pi\) | |||||||
\(284\) | −5.76111 | −0.341859 | ||||||||
\(285\) | −4.23475 | −0.250845 | ||||||||
\(286\) | −9.24659 | −0.546762 | ||||||||
\(287\) | −2.50281 | −0.147736 | ||||||||
\(288\) | −1.39423 | −0.0821560 | ||||||||
\(289\) | −7.99282 | −0.470166 | ||||||||
\(290\) | 1.36043 | 0.0798870 | ||||||||
\(291\) | 20.5432 | 1.20426 | ||||||||
\(292\) | −0.364931 | −0.0213560 | ||||||||
\(293\) | 19.3518 | 1.13055 | 0.565273 | − | 0.824904i | \(-0.308771\pi\) | ||||
0.565273 | + | 0.824904i | \(0.308771\pi\) | |||||||
\(294\) | −5.30338 | −0.309299 | ||||||||
\(295\) | 13.6504 | 0.794758 | ||||||||
\(296\) | 8.33349 | 0.484374 | ||||||||
\(297\) | −26.7716 | −1.55345 | ||||||||
\(298\) | −20.4742 | −1.18604 | ||||||||
\(299\) | −1.92323 | −0.111223 | ||||||||
\(300\) | −3.99068 | −0.230402 | ||||||||
\(301\) | 1.41015 | 0.0812799 | ||||||||
\(302\) | 14.9617 | 0.860951 | ||||||||
\(303\) | 6.66519 | 0.382905 | ||||||||
\(304\) | −2.45647 | −0.140888 | ||||||||
\(305\) | 7.07030 | 0.404844 | ||||||||
\(306\) | −4.18437 | −0.239204 | ||||||||
\(307\) | 26.5296 | 1.51413 | 0.757064 | − | 0.653341i | \(-0.226633\pi\) | ||||
0.757064 | + | 0.653341i | \(0.226633\pi\) | |||||||
\(308\) | 8.06636 | 0.459624 | ||||||||
\(309\) | 8.96432 | 0.509962 | ||||||||
\(310\) | −9.43772 | −0.536026 | ||||||||
\(311\) | 1.44899 | 0.0821648 | 0.0410824 | − | 0.999156i | \(-0.486919\pi\) | ||||
0.0410824 | + | 0.999156i | \(0.486919\pi\) | |||||||
\(312\) | −2.43709 | −0.137973 | ||||||||
\(313\) | 11.4897 | 0.649436 | 0.324718 | − | 0.945811i | \(-0.394731\pi\) | ||||
0.324718 | + | 0.945811i | \(0.394731\pi\) | |||||||
\(314\) | −7.35532 | −0.415085 | ||||||||
\(315\) | −3.18228 | −0.179301 | ||||||||
\(316\) | −14.4028 | −0.810222 | ||||||||
\(317\) | 12.2314 | 0.686986 | 0.343493 | − | 0.939155i | \(-0.388390\pi\) | ||||
0.343493 | + | 0.939155i | \(0.388390\pi\) | |||||||
\(318\) | 5.66991 | 0.317953 | ||||||||
\(319\) | 4.80785 | 0.269188 | ||||||||
\(320\) | 1.36043 | 0.0760502 | ||||||||
\(321\) | 3.39812 | 0.189664 | ||||||||
\(322\) | 1.67775 | 0.0934973 | ||||||||
\(323\) | −7.37235 | −0.410209 | ||||||||
\(324\) | −2.87341 | −0.159634 | ||||||||
\(325\) | 6.05670 | 0.335966 | ||||||||
\(326\) | 23.8132 | 1.31889 | ||||||||
\(327\) | −14.9684 | −0.827752 | ||||||||
\(328\) | −1.49177 | −0.0823691 | ||||||||
\(329\) | −1.26519 | −0.0697522 | ||||||||
\(330\) | 8.28833 | 0.456257 | ||||||||
\(331\) | −3.46211 | −0.190295 | −0.0951473 | − | 0.995463i | \(-0.530332\pi\) | ||||
−0.0951473 | + | 0.995463i | \(0.530332\pi\) | |||||||
\(332\) | 4.02625 | 0.220969 | ||||||||
\(333\) | −11.6188 | −0.636708 | ||||||||
\(334\) | 13.1045 | 0.717047 | ||||||||
\(335\) | −20.0156 | −1.09357 | ||||||||
\(336\) | 2.12603 | 0.115984 | ||||||||
\(337\) | 10.6391 | 0.579548 | 0.289774 | − | 0.957095i | \(-0.406420\pi\) | ||||
0.289774 | + | 0.957095i | \(0.406420\pi\) | |||||||
\(338\) | −9.30119 | −0.505918 | ||||||||
\(339\) | −18.8091 | −1.02157 | ||||||||
\(340\) | 4.08291 | 0.221427 | ||||||||
\(341\) | −33.3536 | −1.80620 | ||||||||
\(342\) | 3.42490 | 0.185197 | ||||||||
\(343\) | −18.7659 | −1.01326 | ||||||||
\(344\) | 0.840503 | 0.0453169 | ||||||||
\(345\) | 1.72392 | 0.0928126 | ||||||||
\(346\) | −13.2765 | −0.713750 | ||||||||
\(347\) | 1.01251 | 0.0543542 | 0.0271771 | − | 0.999631i | \(-0.491348\pi\) | ||||
0.0271771 | + | 0.999631i | \(0.491348\pi\) | |||||||
\(348\) | 1.26719 | 0.0679284 | ||||||||
\(349\) | 31.6050 | 1.69178 | 0.845888 | − | 0.533360i | \(-0.179071\pi\) | ||||
0.845888 | + | 0.533360i | \(0.179071\pi\) | |||||||
\(350\) | −5.28364 | −0.282422 | ||||||||
\(351\) | 10.7092 | 0.571612 | ||||||||
\(352\) | 4.80785 | 0.256259 | ||||||||
\(353\) | −34.4148 | −1.83171 | −0.915857 | − | 0.401505i | \(-0.868487\pi\) | ||||
−0.915857 | + | 0.401505i | \(0.868487\pi\) | |||||||
\(354\) | 12.7149 | 0.675788 | ||||||||
\(355\) | −7.83757 | −0.415975 | ||||||||
\(356\) | −5.58835 | −0.296182 | ||||||||
\(357\) | 6.38062 | 0.337698 | ||||||||
\(358\) | −3.06552 | −0.162018 | ||||||||
\(359\) | 5.12711 | 0.270598 | 0.135299 | − | 0.990805i | \(-0.456800\pi\) | ||||
0.135299 | + | 0.990805i | \(0.456800\pi\) | |||||||
\(360\) | −1.89675 | −0.0999676 | ||||||||
\(361\) | −12.9657 | −0.682408 | ||||||||
\(362\) | 1.51768 | 0.0797677 | ||||||||
\(363\) | 15.3525 | 0.805796 | ||||||||
\(364\) | −3.22670 | −0.169125 | ||||||||
\(365\) | −0.496462 | −0.0259860 | ||||||||
\(366\) | 6.58573 | 0.344242 | ||||||||
\(367\) | −22.6211 | −1.18081 | −0.590405 | − | 0.807107i | \(-0.701032\pi\) | ||||
−0.590405 | + | 0.807107i | \(0.701032\pi\) | |||||||
\(368\) | 1.00000 | 0.0521286 | ||||||||
\(369\) | 2.07987 | 0.108274 | ||||||||
\(370\) | 11.3371 | 0.589388 | ||||||||
\(371\) | 7.50692 | 0.389740 | ||||||||
\(372\) | −8.79089 | −0.455787 | ||||||||
\(373\) | 6.33703 | 0.328119 | 0.164060 | − | 0.986450i | \(-0.447541\pi\) | ||||
0.164060 | + | 0.986450i | \(0.447541\pi\) | |||||||
\(374\) | 14.4293 | 0.746121 | ||||||||
\(375\) | −14.0486 | −0.725467 | ||||||||
\(376\) | −0.754099 | −0.0388897 | ||||||||
\(377\) | −1.92323 | −0.0990513 | ||||||||
\(378\) | −9.34225 | −0.480514 | ||||||||
\(379\) | 27.1482 | 1.39451 | 0.697255 | − | 0.716823i | \(-0.254404\pi\) | ||||
0.697255 | + | 0.716823i | \(0.254404\pi\) | |||||||
\(380\) | −3.34185 | −0.171433 | ||||||||
\(381\) | −17.7186 | −0.907753 | ||||||||
\(382\) | 14.9770 | 0.766292 | ||||||||
\(383\) | −2.29092 | −0.117060 | −0.0585302 | − | 0.998286i | \(-0.518641\pi\) | ||||
−0.0585302 | + | 0.998286i | \(0.518641\pi\) | |||||||
\(384\) | 1.26719 | 0.0646659 | ||||||||
\(385\) | 10.9737 | 0.559271 | ||||||||
\(386\) | −15.0546 | −0.766257 | ||||||||
\(387\) | −1.17186 | −0.0595688 | ||||||||
\(388\) | 16.2117 | 0.823022 | ||||||||
\(389\) | −32.7508 | −1.66053 | −0.830267 | − | 0.557366i | \(-0.811812\pi\) | ||||
−0.830267 | + | 0.557366i | \(0.811812\pi\) | |||||||
\(390\) | −3.31549 | −0.167886 | ||||||||
\(391\) | 3.00120 | 0.151777 | ||||||||
\(392\) | −4.18516 | −0.211382 | ||||||||
\(393\) | −2.14893 | −0.108399 | ||||||||
\(394\) | −14.4974 | −0.730368 | ||||||||
\(395\) | −19.5940 | −0.985880 | ||||||||
\(396\) | −6.70326 | −0.336852 | ||||||||
\(397\) | 2.74992 | 0.138015 | 0.0690073 | − | 0.997616i | \(-0.478017\pi\) | ||||
0.0690073 | + | 0.997616i | \(0.478017\pi\) | |||||||
\(398\) | 0.866870 | 0.0434523 | ||||||||
\(399\) | −5.22252 | −0.261453 | ||||||||
\(400\) | −3.14924 | −0.157462 | ||||||||
\(401\) | 12.5672 | 0.627578 | 0.313789 | − | 0.949493i | \(-0.398402\pi\) | ||||
0.313789 | + | 0.949493i | \(0.398402\pi\) | |||||||
\(402\) | −18.6438 | −0.929867 | ||||||||
\(403\) | 13.3420 | 0.664615 | ||||||||
\(404\) | 5.25982 | 0.261686 | ||||||||
\(405\) | −3.90907 | −0.194243 | ||||||||
\(406\) | 1.67775 | 0.0832653 | ||||||||
\(407\) | 40.0661 | 1.98600 | ||||||||
\(408\) | 3.80308 | 0.188281 | ||||||||
\(409\) | −35.5121 | −1.75596 | −0.877981 | − | 0.478696i | \(-0.841110\pi\) | ||||
−0.877981 | + | 0.478696i | \(0.841110\pi\) | |||||||
\(410\) | −2.02944 | −0.100227 | ||||||||
\(411\) | 15.4303 | 0.761121 | ||||||||
\(412\) | 7.07418 | 0.348520 | ||||||||
\(413\) | 16.8344 | 0.828367 | ||||||||
\(414\) | −1.39423 | −0.0685228 | ||||||||
\(415\) | 5.47742 | 0.268876 | ||||||||
\(416\) | −1.92323 | −0.0942940 | ||||||||
\(417\) | 6.11874 | 0.299636 | ||||||||
\(418\) | −11.8103 | −0.577663 | ||||||||
\(419\) | 26.3900 | 1.28924 | 0.644618 | − | 0.764505i | \(-0.277016\pi\) | ||||
0.644618 | + | 0.764505i | \(0.277016\pi\) | |||||||
\(420\) | 2.89230 | 0.141130 | ||||||||
\(421\) | 16.7524 | 0.816460 | 0.408230 | − | 0.912879i | \(-0.366146\pi\) | ||||
0.408230 | + | 0.912879i | \(0.366146\pi\) | |||||||
\(422\) | 18.4414 | 0.897713 | ||||||||
\(423\) | 1.05139 | 0.0511203 | ||||||||
\(424\) | 4.47440 | 0.217296 | ||||||||
\(425\) | −9.45148 | −0.458464 | ||||||||
\(426\) | −7.30041 | −0.353706 | ||||||||
\(427\) | 8.71947 | 0.421965 | ||||||||
\(428\) | 2.68162 | 0.129621 | ||||||||
\(429\) | −11.7172 | −0.565710 | ||||||||
\(430\) | 1.14344 | 0.0551417 | ||||||||
\(431\) | 28.3187 | 1.36406 | 0.682032 | − | 0.731323i | \(-0.261097\pi\) | ||||
0.682032 | + | 0.731323i | \(0.261097\pi\) | |||||||
\(432\) | −5.56832 | −0.267906 | ||||||||
\(433\) | 21.9376 | 1.05425 | 0.527127 | − | 0.849787i | \(-0.323269\pi\) | ||||
0.527127 | + | 0.849787i | \(0.323269\pi\) | |||||||
\(434\) | −11.6391 | −0.558694 | ||||||||
\(435\) | 1.72392 | 0.0826555 | ||||||||
\(436\) | −11.8123 | −0.565704 | ||||||||
\(437\) | −2.45647 | −0.117509 | ||||||||
\(438\) | −0.462436 | −0.0220961 | ||||||||
\(439\) | 5.61332 | 0.267909 | 0.133955 | − | 0.990987i | \(-0.457232\pi\) | ||||
0.133955 | + | 0.990987i | \(0.457232\pi\) | |||||||
\(440\) | 6.54072 | 0.311817 | ||||||||
\(441\) | 5.83508 | 0.277861 | ||||||||
\(442\) | −5.77198 | −0.274545 | ||||||||
\(443\) | 16.4683 | 0.782435 | 0.391217 | − | 0.920298i | \(-0.372054\pi\) | ||||
0.391217 | + | 0.920298i | \(0.372054\pi\) | |||||||
\(444\) | 10.5601 | 0.501160 | ||||||||
\(445\) | −7.60253 | −0.360395 | ||||||||
\(446\) | −2.35395 | −0.111463 | ||||||||
\(447\) | −25.9447 | −1.22714 | ||||||||
\(448\) | 1.67775 | 0.0792662 | ||||||||
\(449\) | −11.0487 | −0.521420 | −0.260710 | − | 0.965417i | \(-0.583957\pi\) | ||||
−0.260710 | + | 0.965417i | \(0.583957\pi\) | |||||||
\(450\) | 4.39077 | 0.206983 | ||||||||
\(451\) | −7.17219 | −0.337725 | ||||||||
\(452\) | −14.8431 | −0.698163 | ||||||||
\(453\) | 18.9593 | 0.890787 | ||||||||
\(454\) | −19.0700 | −0.894997 | ||||||||
\(455\) | −4.38968 | −0.205791 | ||||||||
\(456\) | −3.11281 | −0.145771 | ||||||||
\(457\) | −0.859524 | −0.0402068 | −0.0201034 | − | 0.999798i | \(-0.506400\pi\) | ||||
−0.0201034 | + | 0.999798i | \(0.506400\pi\) | |||||||
\(458\) | −8.57773 | −0.400811 | ||||||||
\(459\) | −16.7116 | −0.780032 | ||||||||
\(460\) | 1.36043 | 0.0634302 | ||||||||
\(461\) | −12.9533 | −0.603297 | −0.301649 | − | 0.953419i | \(-0.597537\pi\) | ||||
−0.301649 | + | 0.953419i | \(0.597537\pi\) | |||||||
\(462\) | 10.2216 | 0.475552 | ||||||||
\(463\) | −32.4852 | −1.50971 | −0.754856 | − | 0.655890i | \(-0.772294\pi\) | ||||
−0.754856 | + | 0.655890i | \(0.772294\pi\) | |||||||
\(464\) | 1.00000 | 0.0464238 | ||||||||
\(465\) | −11.9594 | −0.554602 | ||||||||
\(466\) | −15.3009 | −0.708802 | ||||||||
\(467\) | 6.04140 | 0.279563 | 0.139781 | − | 0.990182i | \(-0.455360\pi\) | ||||
0.139781 | + | 0.990182i | \(0.455360\pi\) | |||||||
\(468\) | 2.68143 | 0.123949 | ||||||||
\(469\) | −24.6842 | −1.13981 | ||||||||
\(470\) | −1.02590 | −0.0473211 | ||||||||
\(471\) | −9.32058 | −0.429470 | ||||||||
\(472\) | 10.0339 | 0.461849 | ||||||||
\(473\) | 4.04101 | 0.185806 | ||||||||
\(474\) | −18.2511 | −0.838300 | ||||||||
\(475\) | 7.73602 | 0.354953 | ||||||||
\(476\) | 5.03526 | 0.230791 | ||||||||
\(477\) | −6.23836 | −0.285635 | ||||||||
\(478\) | −13.7120 | −0.627171 | ||||||||
\(479\) | 15.0832 | 0.689168 | 0.344584 | − | 0.938755i | \(-0.388020\pi\) | ||||
0.344584 | + | 0.938755i | \(0.388020\pi\) | |||||||
\(480\) | 1.72392 | 0.0786857 | ||||||||
\(481\) | −16.0272 | −0.730777 | ||||||||
\(482\) | −10.7067 | −0.487676 | ||||||||
\(483\) | 2.12603 | 0.0967375 | ||||||||
\(484\) | 12.1154 | 0.550700 | ||||||||
\(485\) | 22.0548 | 1.00146 | ||||||||
\(486\) | 13.0638 | 0.592586 | ||||||||
\(487\) | 28.7409 | 1.30238 | 0.651188 | − | 0.758917i | \(-0.274271\pi\) | ||||
0.651188 | + | 0.758917i | \(0.274271\pi\) | |||||||
\(488\) | 5.19712 | 0.235263 | ||||||||
\(489\) | 30.1758 | 1.36460 | ||||||||
\(490\) | −5.69360 | −0.257211 | ||||||||
\(491\) | −31.7016 | −1.43067 | −0.715336 | − | 0.698781i | \(-0.753726\pi\) | ||||
−0.715336 | + | 0.698781i | \(0.753726\pi\) | |||||||
\(492\) | −1.89035 | −0.0852236 | ||||||||
\(493\) | 3.00120 | 0.135167 | ||||||||
\(494\) | 4.72436 | 0.212559 | ||||||||
\(495\) | −9.11930 | −0.409882 | ||||||||
\(496\) | −6.93732 | −0.311495 | ||||||||
\(497\) | −9.66570 | −0.433566 | ||||||||
\(498\) | 5.10202 | 0.228627 | ||||||||
\(499\) | −7.15558 | −0.320328 | −0.160164 | − | 0.987090i | \(-0.551202\pi\) | ||||
−0.160164 | + | 0.987090i | \(0.551202\pi\) | |||||||
\(500\) | −11.0864 | −0.495801 | ||||||||
\(501\) | 16.6059 | 0.741896 | ||||||||
\(502\) | −9.17063 | −0.409305 | ||||||||
\(503\) | 6.70427 | 0.298929 | 0.149464 | − | 0.988767i | \(-0.452245\pi\) | ||||
0.149464 | + | 0.988767i | \(0.452245\pi\) | |||||||
\(504\) | −2.33918 | −0.104195 | ||||||||
\(505\) | 7.15561 | 0.318420 | ||||||||
\(506\) | 4.80785 | 0.213735 | ||||||||
\(507\) | −11.7864 | −0.523451 | ||||||||
\(508\) | −13.9826 | −0.620379 | ||||||||
\(509\) | −8.99690 | −0.398781 | −0.199390 | − | 0.979920i | \(-0.563896\pi\) | ||||
−0.199390 | + | 0.979920i | \(0.563896\pi\) | |||||||
\(510\) | 5.17381 | 0.229100 | ||||||||
\(511\) | −0.612263 | −0.0270849 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 13.6784 | 0.603917 | ||||||||
\(514\) | −5.17021 | −0.228048 | ||||||||
\(515\) | 9.62390 | 0.424080 | ||||||||
\(516\) | 1.06508 | 0.0468873 | ||||||||
\(517\) | −3.62559 | −0.159453 | ||||||||
\(518\) | 13.9815 | 0.614312 | ||||||||
\(519\) | −16.8239 | −0.738485 | ||||||||
\(520\) | −2.61641 | −0.114737 | ||||||||
\(521\) | 37.9054 | 1.66067 | 0.830334 | − | 0.557266i | \(-0.188150\pi\) | ||||
0.830334 | + | 0.557266i | \(0.188150\pi\) | |||||||
\(522\) | −1.39423 | −0.0610239 | ||||||||
\(523\) | 34.2143 | 1.49609 | 0.748044 | − | 0.663649i | \(-0.230993\pi\) | ||||
0.748044 | + | 0.663649i | \(0.230993\pi\) | |||||||
\(524\) | −1.69582 | −0.0740824 | ||||||||
\(525\) | −6.69536 | −0.292210 | ||||||||
\(526\) | −10.8593 | −0.473488 | ||||||||
\(527\) | −20.8203 | −0.906945 | ||||||||
\(528\) | 6.09245 | 0.265140 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 6.08709 | 0.264406 | ||||||||
\(531\) | −13.9896 | −0.607098 | ||||||||
\(532\) | −4.12135 | −0.178683 | ||||||||
\(533\) | 2.86901 | 0.124271 | ||||||||
\(534\) | −7.08149 | −0.306446 | ||||||||
\(535\) | 3.64815 | 0.157723 | ||||||||
\(536\) | −14.7127 | −0.635492 | ||||||||
\(537\) | −3.88459 | −0.167632 | ||||||||
\(538\) | 22.5988 | 0.974301 | ||||||||
\(539\) | −20.1216 | −0.866698 | ||||||||
\(540\) | −7.57529 | −0.325989 | ||||||||
\(541\) | −6.07269 | −0.261085 | −0.130543 | − | 0.991443i | \(-0.541672\pi\) | ||||
−0.130543 | + | 0.991443i | \(0.541672\pi\) | |||||||
\(542\) | −22.9257 | −0.984745 | ||||||||
\(543\) | 1.92319 | 0.0825321 | ||||||||
\(544\) | 3.00120 | 0.128675 | ||||||||
\(545\) | −16.0697 | −0.688351 | ||||||||
\(546\) | −4.08883 | −0.174986 | ||||||||
\(547\) | 44.4162 | 1.89910 | 0.949549 | − | 0.313619i | \(-0.101542\pi\) | ||||
0.949549 | + | 0.313619i | \(0.101542\pi\) | |||||||
\(548\) | 12.1768 | 0.520168 | ||||||||
\(549\) | −7.24600 | −0.309252 | ||||||||
\(550\) | −15.1411 | −0.645617 | ||||||||
\(551\) | −2.45647 | −0.104649 | ||||||||
\(552\) | 1.26719 | 0.0539351 | ||||||||
\(553\) | −24.1643 | −1.02757 | ||||||||
\(554\) | 6.16710 | 0.262015 | ||||||||
\(555\) | 14.3662 | 0.609813 | ||||||||
\(556\) | 4.82859 | 0.204778 | ||||||||
\(557\) | 3.21542 | 0.136242 | 0.0681209 | − | 0.997677i | \(-0.478300\pi\) | ||||
0.0681209 | + | 0.997677i | \(0.478300\pi\) | |||||||
\(558\) | 9.67224 | 0.409459 | ||||||||
\(559\) | −1.61648 | −0.0683697 | ||||||||
\(560\) | 2.28246 | 0.0964514 | ||||||||
\(561\) | 18.2846 | 0.771978 | ||||||||
\(562\) | 24.4453 | 1.03116 | ||||||||
\(563\) | 11.9237 | 0.502525 | 0.251262 | − | 0.967919i | \(-0.419154\pi\) | ||||
0.251262 | + | 0.967919i | \(0.419154\pi\) | |||||||
\(564\) | −0.955586 | −0.0402374 | ||||||||
\(565\) | −20.1930 | −0.849526 | ||||||||
\(566\) | −12.9213 | −0.543121 | ||||||||
\(567\) | −4.82087 | −0.202457 | ||||||||
\(568\) | −5.76111 | −0.241731 | ||||||||
\(569\) | −10.8574 | −0.455167 | −0.227584 | − | 0.973759i | \(-0.573082\pi\) | ||||
−0.227584 | + | 0.973759i | \(0.573082\pi\) | |||||||
\(570\) | −4.23475 | −0.177374 | ||||||||
\(571\) | −1.83362 | −0.0767345 | −0.0383673 | − | 0.999264i | \(-0.512216\pi\) | ||||
−0.0383673 | + | 0.999264i | \(0.512216\pi\) | |||||||
\(572\) | −9.24659 | −0.386619 | ||||||||
\(573\) | 18.9787 | 0.792847 | ||||||||
\(574\) | −2.50281 | −0.104465 | ||||||||
\(575\) | −3.14924 | −0.131332 | ||||||||
\(576\) | −1.39423 | −0.0580931 | ||||||||
\(577\) | 15.0644 | 0.627140 | 0.313570 | − | 0.949565i | \(-0.398475\pi\) | ||||
0.313570 | + | 0.949565i | \(0.398475\pi\) | |||||||
\(578\) | −7.99282 | −0.332458 | ||||||||
\(579\) | −19.0770 | −0.792811 | ||||||||
\(580\) | 1.36043 | 0.0564886 | ||||||||
\(581\) | 6.75504 | 0.280246 | ||||||||
\(582\) | 20.5432 | 0.851544 | ||||||||
\(583\) | 21.5122 | 0.890945 | ||||||||
\(584\) | −0.364931 | −0.0151009 | ||||||||
\(585\) | 3.64789 | 0.150822 | ||||||||
\(586\) | 19.3518 | 0.799417 | ||||||||
\(587\) | 18.8131 | 0.776499 | 0.388250 | − | 0.921554i | \(-0.373080\pi\) | ||||
0.388250 | + | 0.921554i | \(0.373080\pi\) | |||||||
\(588\) | −5.30338 | −0.218708 | ||||||||
\(589\) | 17.0413 | 0.702176 | ||||||||
\(590\) | 13.6504 | 0.561979 | ||||||||
\(591\) | −18.3709 | −0.755679 | ||||||||
\(592\) | 8.33349 | 0.342504 | ||||||||
\(593\) | 39.1535 | 1.60784 | 0.803921 | − | 0.594736i | \(-0.202744\pi\) | ||||
0.803921 | + | 0.594736i | \(0.202744\pi\) | |||||||
\(594\) | −26.7716 | −1.09845 | ||||||||
\(595\) | 6.85010 | 0.280827 | ||||||||
\(596\) | −20.4742 | −0.838657 | ||||||||
\(597\) | 1.09849 | 0.0449581 | ||||||||
\(598\) | −1.92323 | −0.0786466 | ||||||||
\(599\) | 10.7095 | 0.437577 | 0.218789 | − | 0.975772i | \(-0.429790\pi\) | ||||
0.218789 | + | 0.975772i | \(0.429790\pi\) | |||||||
\(600\) | −3.99068 | −0.162919 | ||||||||
\(601\) | 23.5653 | 0.961247 | 0.480623 | − | 0.876927i | \(-0.340410\pi\) | ||||
0.480623 | + | 0.876927i | \(0.340410\pi\) | |||||||
\(602\) | 1.41015 | 0.0574736 | ||||||||
\(603\) | 20.5129 | 0.835352 | ||||||||
\(604\) | 14.9617 | 0.608784 | ||||||||
\(605\) | 16.4821 | 0.670093 | ||||||||
\(606\) | 6.66519 | 0.270755 | ||||||||
\(607\) | 30.9235 | 1.25514 | 0.627572 | − | 0.778558i | \(-0.284049\pi\) | ||||
0.627572 | + | 0.778558i | \(0.284049\pi\) | |||||||
\(608\) | −2.45647 | −0.0996231 | ||||||||
\(609\) | 2.12603 | 0.0861509 | ||||||||
\(610\) | 7.07030 | 0.286268 | ||||||||
\(611\) | 1.45030 | 0.0586730 | ||||||||
\(612\) | −4.18437 | −0.169143 | ||||||||
\(613\) | −14.7372 | −0.595229 | −0.297614 | − | 0.954686i | \(-0.596191\pi\) | ||||
−0.297614 | + | 0.954686i | \(0.596191\pi\) | |||||||
\(614\) | 26.5296 | 1.07065 | ||||||||
\(615\) | −2.57168 | −0.103700 | ||||||||
\(616\) | 8.06636 | 0.325003 | ||||||||
\(617\) | −31.0254 | −1.24904 | −0.624518 | − | 0.781011i | \(-0.714704\pi\) | ||||
−0.624518 | + | 0.781011i | \(0.714704\pi\) | |||||||
\(618\) | 8.96432 | 0.360598 | ||||||||
\(619\) | 38.0968 | 1.53124 | 0.765620 | − | 0.643293i | \(-0.222432\pi\) | ||||
0.765620 | + | 0.643293i | \(0.222432\pi\) | |||||||
\(620\) | −9.43772 | −0.379028 | ||||||||
\(621\) | −5.56832 | −0.223449 | ||||||||
\(622\) | 1.44899 | 0.0580993 | ||||||||
\(623\) | −9.37585 | −0.375635 | ||||||||
\(624\) | −2.43709 | −0.0975618 | ||||||||
\(625\) | 0.663903 | 0.0265561 | ||||||||
\(626\) | 11.4897 | 0.459221 | ||||||||
\(627\) | −14.9659 | −0.597682 | ||||||||
\(628\) | −7.35532 | −0.293509 | ||||||||
\(629\) | 25.0104 | 0.997231 | ||||||||
\(630\) | −3.18228 | −0.126785 | ||||||||
\(631\) | −19.6621 | −0.782736 | −0.391368 | − | 0.920234i | \(-0.627998\pi\) | ||||
−0.391368 | + | 0.920234i | \(0.627998\pi\) | |||||||
\(632\) | −14.4028 | −0.572913 | ||||||||
\(633\) | 23.3687 | 0.928824 | ||||||||
\(634\) | 12.2314 | 0.485772 | ||||||||
\(635\) | −19.0224 | −0.754879 | ||||||||
\(636\) | 5.66991 | 0.224826 | ||||||||
\(637\) | 8.04901 | 0.318913 | ||||||||
\(638\) | 4.80785 | 0.190344 | ||||||||
\(639\) | 8.03233 | 0.317754 | ||||||||
\(640\) | 1.36043 | 0.0537756 | ||||||||
\(641\) | −22.7454 | −0.898390 | −0.449195 | − | 0.893434i | \(-0.648289\pi\) | ||||
−0.449195 | + | 0.893434i | \(0.648289\pi\) | |||||||
\(642\) | 3.39812 | 0.134113 | ||||||||
\(643\) | −36.1762 | −1.42665 | −0.713325 | − | 0.700833i | \(-0.752812\pi\) | ||||
−0.713325 | + | 0.700833i | \(0.752812\pi\) | |||||||
\(644\) | 1.67775 | 0.0661126 | ||||||||
\(645\) | 1.44896 | 0.0570526 | ||||||||
\(646\) | −7.37235 | −0.290061 | ||||||||
\(647\) | 35.9675 | 1.41403 | 0.707013 | − | 0.707200i | \(-0.250042\pi\) | ||||
0.707013 | + | 0.707200i | \(0.250042\pi\) | |||||||
\(648\) | −2.87341 | −0.112878 | ||||||||
\(649\) | 48.2416 | 1.89365 | ||||||||
\(650\) | 6.05670 | 0.237564 | ||||||||
\(651\) | −14.7489 | −0.578056 | ||||||||
\(652\) | 23.8132 | 0.932596 | ||||||||
\(653\) | −6.58068 | −0.257522 | −0.128761 | − | 0.991676i | \(-0.541100\pi\) | ||||
−0.128761 | + | 0.991676i | \(0.541100\pi\) | |||||||
\(654\) | −14.9684 | −0.585309 | ||||||||
\(655\) | −2.30704 | −0.0901437 | ||||||||
\(656\) | −1.49177 | −0.0582438 | ||||||||
\(657\) | 0.508799 | 0.0198501 | ||||||||
\(658\) | −1.26519 | −0.0493222 | ||||||||
\(659\) | 16.7980 | 0.654356 | 0.327178 | − | 0.944963i | \(-0.393902\pi\) | ||||
0.327178 | + | 0.944963i | \(0.393902\pi\) | |||||||
\(660\) | 8.28833 | 0.322623 | ||||||||
\(661\) | 2.79814 | 0.108835 | 0.0544175 | − | 0.998518i | \(-0.482670\pi\) | ||||
0.0544175 | + | 0.998518i | \(0.482670\pi\) | |||||||
\(662\) | −3.46211 | −0.134559 | ||||||||
\(663\) | −7.31419 | −0.284060 | ||||||||
\(664\) | 4.02625 | 0.156249 | ||||||||
\(665\) | −5.60679 | −0.217422 | ||||||||
\(666\) | −11.6188 | −0.450220 | ||||||||
\(667\) | 1.00000 | 0.0387202 | ||||||||
\(668\) | 13.1045 | 0.507029 | ||||||||
\(669\) | −2.98290 | −0.115326 | ||||||||
\(670\) | −20.0156 | −0.773268 | ||||||||
\(671\) | 24.9870 | 0.964611 | ||||||||
\(672\) | 2.12603 | 0.0820132 | ||||||||
\(673\) | 43.8643 | 1.69085 | 0.845423 | − | 0.534097i | \(-0.179348\pi\) | ||||
0.845423 | + | 0.534097i | \(0.179348\pi\) | |||||||
\(674\) | 10.6391 | 0.409802 | ||||||||
\(675\) | 17.5360 | 0.674960 | ||||||||
\(676\) | −9.30119 | −0.357738 | ||||||||
\(677\) | 16.9798 | 0.652587 | 0.326293 | − | 0.945269i | \(-0.394200\pi\) | ||||
0.326293 | + | 0.945269i | \(0.394200\pi\) | |||||||
\(678\) | −18.8091 | −0.722358 | ||||||||
\(679\) | 27.1991 | 1.04381 | ||||||||
\(680\) | 4.08291 | 0.156572 | ||||||||
\(681\) | −24.1652 | −0.926013 | ||||||||
\(682\) | −33.3536 | −1.27717 | ||||||||
\(683\) | 27.1983 | 1.04072 | 0.520358 | − | 0.853948i | \(-0.325799\pi\) | ||||
0.520358 | + | 0.853948i | \(0.325799\pi\) | |||||||
\(684\) | 3.42490 | 0.130954 | ||||||||
\(685\) | 16.5657 | 0.632941 | ||||||||
\(686\) | −18.7659 | −0.716485 | ||||||||
\(687\) | −10.8696 | −0.414701 | ||||||||
\(688\) | 0.840503 | 0.0320439 | ||||||||
\(689\) | −8.60529 | −0.327835 | ||||||||
\(690\) | 1.72392 | 0.0656284 | ||||||||
\(691\) | −0.269591 | −0.0102557 | −0.00512786 | − | 0.999987i | \(-0.501632\pi\) | ||||
−0.00512786 | + | 0.999987i | \(0.501632\pi\) | |||||||
\(692\) | −13.2765 | −0.504698 | ||||||||
\(693\) | −11.2464 | −0.427215 | ||||||||
\(694\) | 1.01251 | 0.0384342 | ||||||||
\(695\) | 6.56895 | 0.249174 | ||||||||
\(696\) | 1.26719 | 0.0480327 | ||||||||
\(697\) | −4.47709 | −0.169582 | ||||||||
\(698\) | 31.6050 | 1.19627 | ||||||||
\(699\) | −19.3892 | −0.733365 | ||||||||
\(700\) | −5.28364 | −0.199703 | ||||||||
\(701\) | −8.53751 | −0.322457 | −0.161229 | − | 0.986917i | \(-0.551546\pi\) | ||||
−0.161229 | + | 0.986917i | \(0.551546\pi\) | |||||||
\(702\) | 10.7092 | 0.404191 | ||||||||
\(703\) | −20.4710 | −0.772078 | ||||||||
\(704\) | 4.80785 | 0.181203 | ||||||||
\(705\) | −1.30000 | −0.0489610 | ||||||||
\(706\) | −34.4148 | −1.29522 | ||||||||
\(707\) | 8.82467 | 0.331886 | ||||||||
\(708\) | 12.7149 | 0.477854 | ||||||||
\(709\) | −0.578454 | −0.0217243 | −0.0108621 | − | 0.999941i | \(-0.503458\pi\) | ||||
−0.0108621 | + | 0.999941i | \(0.503458\pi\) | |||||||
\(710\) | −7.83757 | −0.294139 | ||||||||
\(711\) | 20.0809 | 0.753092 | ||||||||
\(712\) | −5.58835 | −0.209432 | ||||||||
\(713\) | −6.93732 | −0.259805 | ||||||||
\(714\) | 6.38062 | 0.238789 | ||||||||
\(715\) | −12.5793 | −0.470439 | ||||||||
\(716\) | −3.06552 | −0.114564 | ||||||||
\(717\) | −17.3757 | −0.648906 | ||||||||
\(718\) | 5.12711 | 0.191342 | ||||||||
\(719\) | −8.24661 | −0.307546 | −0.153773 | − | 0.988106i | \(-0.549143\pi\) | ||||
−0.153773 | + | 0.988106i | \(0.549143\pi\) | |||||||
\(720\) | −1.89675 | −0.0706878 | ||||||||
\(721\) | 11.8687 | 0.442014 | ||||||||
\(722\) | −12.9657 | −0.482535 | ||||||||
\(723\) | −13.5674 | −0.504576 | ||||||||
\(724\) | 1.51768 | 0.0564043 | ||||||||
\(725\) | −3.14924 | −0.116960 | ||||||||
\(726\) | 15.3525 | 0.569784 | ||||||||
\(727\) | −22.4965 | −0.834349 | −0.417175 | − | 0.908826i | \(-0.636980\pi\) | ||||
−0.417175 | + | 0.908826i | \(0.636980\pi\) | |||||||
\(728\) | −3.22670 | −0.119589 | ||||||||
\(729\) | 25.1745 | 0.932391 | ||||||||
\(730\) | −0.496462 | −0.0183749 | ||||||||
\(731\) | 2.52251 | 0.0932985 | ||||||||
\(732\) | 6.58573 | 0.243416 | ||||||||
\(733\) | −28.0468 | −1.03593 | −0.517967 | − | 0.855401i | \(-0.673311\pi\) | ||||
−0.517967 | + | 0.855401i | \(0.673311\pi\) | |||||||
\(734\) | −22.6211 | −0.834959 | ||||||||
\(735\) | −7.21486 | −0.266124 | ||||||||
\(736\) | 1.00000 | 0.0368605 | ||||||||
\(737\) | −70.7364 | −2.60561 | ||||||||
\(738\) | 2.07987 | 0.0765612 | ||||||||
\(739\) | −8.86610 | −0.326145 | −0.163072 | − | 0.986614i | \(-0.552140\pi\) | ||||
−0.163072 | + | 0.986614i | \(0.552140\pi\) | |||||||
\(740\) | 11.3371 | 0.416760 | ||||||||
\(741\) | 5.98665 | 0.219925 | ||||||||
\(742\) | 7.50692 | 0.275588 | ||||||||
\(743\) | −17.8425 | −0.654576 | −0.327288 | − | 0.944925i | \(-0.606135\pi\) | ||||
−0.327288 | + | 0.944925i | \(0.606135\pi\) | |||||||
\(744\) | −8.79089 | −0.322290 | ||||||||
\(745\) | −27.8537 | −1.02048 | ||||||||
\(746\) | 6.33703 | 0.232015 | ||||||||
\(747\) | −5.61353 | −0.205388 | ||||||||
\(748\) | 14.4293 | 0.527587 | ||||||||
\(749\) | 4.49909 | 0.164393 | ||||||||
\(750\) | −14.0486 | −0.512983 | ||||||||
\(751\) | 31.2394 | 1.13994 | 0.569972 | − | 0.821664i | \(-0.306954\pi\) | ||||
0.569972 | + | 0.821664i | \(0.306954\pi\) | |||||||
\(752\) | −0.754099 | −0.0274992 | ||||||||
\(753\) | −11.6209 | −0.423490 | ||||||||
\(754\) | −1.92323 | −0.0700398 | ||||||||
\(755\) | 20.3543 | 0.740770 | ||||||||
\(756\) | −9.34225 | −0.339774 | ||||||||
\(757\) | 24.1891 | 0.879166 | 0.439583 | − | 0.898202i | \(-0.355126\pi\) | ||||
0.439583 | + | 0.898202i | \(0.355126\pi\) | |||||||
\(758\) | 27.1482 | 0.986068 | ||||||||
\(759\) | 6.09245 | 0.221142 | ||||||||
\(760\) | −3.34185 | −0.121222 | ||||||||
\(761\) | 5.37248 | 0.194752 | 0.0973761 | − | 0.995248i | \(-0.468955\pi\) | ||||
0.0973761 | + | 0.995248i | \(0.468955\pi\) | |||||||
\(762\) | −17.7186 | −0.641878 | ||||||||
\(763\) | −19.8180 | −0.717460 | ||||||||
\(764\) | 14.9770 | 0.541850 | ||||||||
\(765\) | −5.69253 | −0.205814 | ||||||||
\(766\) | −2.29092 | −0.0827742 | ||||||||
\(767\) | −19.2975 | −0.696793 | ||||||||
\(768\) | 1.26719 | 0.0457257 | ||||||||
\(769\) | 25.1668 | 0.907539 | 0.453769 | − | 0.891119i | \(-0.350079\pi\) | ||||
0.453769 | + | 0.891119i | \(0.350079\pi\) | |||||||
\(770\) | 10.9737 | 0.395465 | ||||||||
\(771\) | −6.55164 | −0.235951 | ||||||||
\(772\) | −15.0546 | −0.541825 | ||||||||
\(773\) | −40.9003 | −1.47108 | −0.735540 | − | 0.677481i | \(-0.763072\pi\) | ||||
−0.735540 | + | 0.677481i | \(0.763072\pi\) | |||||||
\(774\) | −1.17186 | −0.0421215 | ||||||||
\(775\) | 21.8473 | 0.784778 | ||||||||
\(776\) | 16.2117 | 0.581964 | ||||||||
\(777\) | 17.7172 | 0.635601 | ||||||||
\(778\) | −32.7508 | −1.17417 | ||||||||
\(779\) | 3.66449 | 0.131294 | ||||||||
\(780\) | −3.31549 | −0.118713 | ||||||||
\(781\) | −27.6985 | −0.991131 | ||||||||
\(782\) | 3.00120 | 0.107323 | ||||||||
\(783\) | −5.56832 | −0.198996 | ||||||||
\(784\) | −4.18516 | −0.149470 | ||||||||
\(785\) | −10.0064 | −0.357143 | ||||||||
\(786\) | −2.14893 | −0.0766498 | ||||||||
\(787\) | 41.2713 | 1.47116 | 0.735582 | − | 0.677436i | \(-0.236909\pi\) | ||||
0.735582 | + | 0.677436i | \(0.236909\pi\) | |||||||
\(788\) | −14.4974 | −0.516448 | ||||||||
\(789\) | −13.7608 | −0.489896 | ||||||||
\(790\) | −19.5940 | −0.697122 | ||||||||
\(791\) | −24.9031 | −0.885452 | ||||||||
\(792\) | −6.70326 | −0.238190 | ||||||||
\(793\) | −9.99525 | −0.354942 | ||||||||
\(794\) | 2.74992 | 0.0975910 | ||||||||
\(795\) | 7.71349 | 0.273569 | ||||||||
\(796\) | 0.866870 | 0.0307254 | ||||||||
\(797\) | 0.713375 | 0.0252691 | 0.0126345 | − | 0.999920i | \(-0.495978\pi\) | ||||
0.0126345 | + | 0.999920i | \(0.495978\pi\) | |||||||
\(798\) | −5.22252 | −0.184875 | ||||||||
\(799\) | −2.26320 | −0.0800662 | ||||||||
\(800\) | −3.14924 | −0.111342 | ||||||||
\(801\) | 7.79146 | 0.275298 | ||||||||
\(802\) | 12.5672 | 0.443764 | ||||||||
\(803\) | −1.75453 | −0.0619161 | ||||||||
\(804\) | −18.6438 | −0.657515 | ||||||||
\(805\) | 2.28246 | 0.0804460 | ||||||||
\(806\) | 13.3420 | 0.469954 | ||||||||
\(807\) | 28.6369 | 1.00807 | ||||||||
\(808\) | 5.25982 | 0.185040 | ||||||||
\(809\) | 12.0415 | 0.423357 | 0.211679 | − | 0.977339i | \(-0.432107\pi\) | ||||
0.211679 | + | 0.977339i | \(0.432107\pi\) | |||||||
\(810\) | −3.90907 | −0.137351 | ||||||||
\(811\) | 43.6002 | 1.53101 | 0.765505 | − | 0.643430i | \(-0.222489\pi\) | ||||
0.765505 | + | 0.643430i | \(0.222489\pi\) | |||||||
\(812\) | 1.67775 | 0.0588775 | ||||||||
\(813\) | −29.0512 | −1.01887 | ||||||||
\(814\) | 40.0661 | 1.40432 | ||||||||
\(815\) | 32.3961 | 1.13478 | ||||||||
\(816\) | 3.80308 | 0.133134 | ||||||||
\(817\) | −2.06467 | −0.0722337 | ||||||||
\(818\) | −35.5121 | −1.24165 | ||||||||
\(819\) | 4.49877 | 0.157200 | ||||||||
\(820\) | −2.02944 | −0.0708712 | ||||||||
\(821\) | 12.0620 | 0.420966 | 0.210483 | − | 0.977597i | \(-0.432496\pi\) | ||||
0.210483 | + | 0.977597i | \(0.432496\pi\) | |||||||
\(822\) | 15.4303 | 0.538194 | ||||||||
\(823\) | 36.9766 | 1.28892 | 0.644461 | − | 0.764637i | \(-0.277082\pi\) | ||||
0.644461 | + | 0.764637i | \(0.277082\pi\) | |||||||
\(824\) | 7.07418 | 0.246441 | ||||||||
\(825\) | −19.1866 | −0.667991 | ||||||||
\(826\) | 16.8344 | 0.585744 | ||||||||
\(827\) | −1.19387 | −0.0415151 | −0.0207575 | − | 0.999785i | \(-0.506608\pi\) | ||||
−0.0207575 | + | 0.999785i | \(0.506608\pi\) | |||||||
\(828\) | −1.39423 | −0.0484530 | ||||||||
\(829\) | 28.8452 | 1.00184 | 0.500918 | − | 0.865495i | \(-0.332996\pi\) | ||||
0.500918 | + | 0.865495i | \(0.332996\pi\) | |||||||
\(830\) | 5.47742 | 0.190124 | ||||||||
\(831\) | 7.81488 | 0.271095 | ||||||||
\(832\) | −1.92323 | −0.0666759 | ||||||||
\(833\) | −12.5605 | −0.435194 | ||||||||
\(834\) | 6.11874 | 0.211875 | ||||||||
\(835\) | 17.8277 | 0.616954 | ||||||||
\(836\) | −11.8103 | −0.408469 | ||||||||
\(837\) | 38.6292 | 1.33522 | ||||||||
\(838\) | 26.3900 | 0.911628 | ||||||||
\(839\) | −20.7303 | −0.715688 | −0.357844 | − | 0.933781i | \(-0.616488\pi\) | ||||
−0.357844 | + | 0.933781i | \(0.616488\pi\) | |||||||
\(840\) | 2.89230 | 0.0997939 | ||||||||
\(841\) | 1.00000 | 0.0344828 | ||||||||
\(842\) | 16.7524 | 0.577325 | ||||||||
\(843\) | 30.9767 | 1.06690 | ||||||||
\(844\) | 18.4414 | 0.634779 | ||||||||
\(845\) | −12.6536 | −0.435297 | ||||||||
\(846\) | 1.05139 | 0.0361475 | ||||||||
\(847\) | 20.3266 | 0.698430 | ||||||||
\(848\) | 4.47440 | 0.153652 | ||||||||
\(849\) | −16.3737 | −0.561943 | ||||||||
\(850\) | −9.45148 | −0.324183 | ||||||||
\(851\) | 8.33349 | 0.285668 | ||||||||
\(852\) | −7.30041 | −0.250108 | ||||||||
\(853\) | −29.8055 | −1.02052 | −0.510261 | − | 0.860020i | \(-0.670451\pi\) | ||||
−0.510261 | + | 0.860020i | \(0.670451\pi\) | |||||||
\(854\) | 8.71947 | 0.298374 | ||||||||
\(855\) | 4.65932 | 0.159345 | ||||||||
\(856\) | 2.68162 | 0.0916559 | ||||||||
\(857\) | 55.0638 | 1.88094 | 0.940471 | − | 0.339874i | \(-0.110384\pi\) | ||||
0.940471 | + | 0.339874i | \(0.110384\pi\) | |||||||
\(858\) | −11.7172 | −0.400017 | ||||||||
\(859\) | 42.7439 | 1.45840 | 0.729201 | − | 0.684299i | \(-0.239892\pi\) | ||||
0.729201 | + | 0.684299i | \(0.239892\pi\) | |||||||
\(860\) | 1.14344 | 0.0389911 | ||||||||
\(861\) | −3.17154 | −0.108086 | ||||||||
\(862\) | 28.3187 | 0.964538 | ||||||||
\(863\) | 0.0487062 | 0.00165798 | 0.000828990 | − | 1.00000i | \(-0.499736\pi\) | ||||
0.000828990 | 1.00000i | \(0.499736\pi\) | ||||||||
\(864\) | −5.56832 | −0.189438 | ||||||||
\(865\) | −18.0617 | −0.614117 | ||||||||
\(866\) | 21.9376 | 0.745470 | ||||||||
\(867\) | −10.1284 | −0.343979 | ||||||||
\(868\) | −11.6391 | −0.395056 | ||||||||
\(869\) | −69.2465 | −2.34903 | ||||||||
\(870\) | 1.72392 | 0.0584463 | ||||||||
\(871\) | 28.2959 | 0.958769 | ||||||||
\(872\) | −11.8123 | −0.400013 | ||||||||
\(873\) | −22.6028 | −0.764990 | ||||||||
\(874\) | −2.45647 | −0.0830914 | ||||||||
\(875\) | −18.6003 | −0.628804 | ||||||||
\(876\) | −0.462436 | −0.0156243 | ||||||||
\(877\) | 2.82793 | 0.0954925 | 0.0477463 | − | 0.998859i | \(-0.484796\pi\) | ||||
0.0477463 | + | 0.998859i | \(0.484796\pi\) | |||||||
\(878\) | 5.61332 | 0.189440 | ||||||||
\(879\) | 24.5224 | 0.827121 | ||||||||
\(880\) | 6.54072 | 0.220488 | ||||||||
\(881\) | 19.5533 | 0.658767 | 0.329383 | − | 0.944196i | \(-0.393159\pi\) | ||||
0.329383 | + | 0.944196i | \(0.393159\pi\) | |||||||
\(882\) | 5.83508 | 0.196477 | ||||||||
\(883\) | 41.0246 | 1.38059 | 0.690294 | − | 0.723529i | \(-0.257481\pi\) | ||||
0.690294 | + | 0.723529i | \(0.257481\pi\) | |||||||
\(884\) | −5.77198 | −0.194133 | ||||||||
\(885\) | 17.2977 | 0.581454 | ||||||||
\(886\) | 16.4683 | 0.553265 | ||||||||
\(887\) | 10.3756 | 0.348380 | 0.174190 | − | 0.984712i | \(-0.444269\pi\) | ||||
0.174190 | + | 0.984712i | \(0.444269\pi\) | |||||||
\(888\) | 10.5601 | 0.354374 | ||||||||
\(889\) | −23.4594 | −0.786802 | ||||||||
\(890\) | −7.60253 | −0.254838 | ||||||||
\(891\) | −13.8149 | −0.462817 | ||||||||
\(892\) | −2.35395 | −0.0788161 | ||||||||
\(893\) | 1.85242 | 0.0619890 | ||||||||
\(894\) | −25.9447 | −0.867721 | ||||||||
\(895\) | −4.17041 | −0.139401 | ||||||||
\(896\) | 1.67775 | 0.0560497 | ||||||||
\(897\) | −2.43709 | −0.0813721 | ||||||||
\(898\) | −11.0487 | −0.368700 | ||||||||
\(899\) | −6.93732 | −0.231373 | ||||||||
\(900\) | 4.39077 | 0.146359 | ||||||||
\(901\) | 13.4285 | 0.447370 | ||||||||
\(902\) | −7.17219 | −0.238808 | ||||||||
\(903\) | 1.78693 | 0.0594653 | ||||||||
\(904\) | −14.8431 | −0.493676 | ||||||||
\(905\) | 2.06470 | 0.0686329 | ||||||||
\(906\) | 18.9593 | 0.629882 | ||||||||
\(907\) | −24.1680 | −0.802485 | −0.401243 | − | 0.915972i | \(-0.631422\pi\) | ||||
−0.401243 | + | 0.915972i | \(0.631422\pi\) | |||||||
\(908\) | −19.0700 | −0.632859 | ||||||||
\(909\) | −7.33342 | −0.243234 | ||||||||
\(910\) | −4.38968 | −0.145517 | ||||||||
\(911\) | 20.8063 | 0.689344 | 0.344672 | − | 0.938723i | \(-0.387990\pi\) | ||||
0.344672 | + | 0.938723i | \(0.387990\pi\) | |||||||
\(912\) | −3.11281 | −0.103076 | ||||||||
\(913\) | 19.3576 | 0.640643 | ||||||||
\(914\) | −0.859524 | −0.0284305 | ||||||||
\(915\) | 8.95940 | 0.296189 | ||||||||
\(916\) | −8.57773 | −0.283416 | ||||||||
\(917\) | −2.84517 | −0.0939558 | ||||||||
\(918\) | −16.7116 | −0.551566 | ||||||||
\(919\) | 7.76601 | 0.256177 | 0.128089 | − | 0.991763i | \(-0.459116\pi\) | ||||
0.128089 | + | 0.991763i | \(0.459116\pi\) | |||||||
\(920\) | 1.36043 | 0.0448519 | ||||||||
\(921\) | 33.6181 | 1.10775 | ||||||||
\(922\) | −12.9533 | −0.426596 | ||||||||
\(923\) | 11.0799 | 0.364700 | ||||||||
\(924\) | 10.2216 | 0.336266 | ||||||||
\(925\) | −26.2441 | −0.862902 | ||||||||
\(926\) | −32.4852 | −1.06753 | ||||||||
\(927\) | −9.86306 | −0.323945 | ||||||||
\(928\) | 1.00000 | 0.0328266 | ||||||||
\(929\) | 47.6223 | 1.56244 | 0.781218 | − | 0.624258i | \(-0.214599\pi\) | ||||
0.781218 | + | 0.624258i | \(0.214599\pi\) | |||||||
\(930\) | −11.9594 | −0.392163 | ||||||||
\(931\) | 10.2807 | 0.336937 | ||||||||
\(932\) | −15.3009 | −0.501198 | ||||||||
\(933\) | 1.83615 | 0.0601127 | ||||||||
\(934\) | 6.04140 | 0.197681 | ||||||||
\(935\) | 19.6300 | 0.641969 | ||||||||
\(936\) | 2.68143 | 0.0876452 | ||||||||
\(937\) | 17.0990 | 0.558599 | 0.279300 | − | 0.960204i | \(-0.409898\pi\) | ||||
0.279300 | + | 0.960204i | \(0.409898\pi\) | |||||||
\(938\) | −24.6842 | −0.805969 | ||||||||
\(939\) | 14.5596 | 0.475135 | ||||||||
\(940\) | −1.02590 | −0.0334611 | ||||||||
\(941\) | 27.6093 | 0.900037 | 0.450019 | − | 0.893019i | \(-0.351417\pi\) | ||||
0.450019 | + | 0.893019i | \(0.351417\pi\) | |||||||
\(942\) | −9.32058 | −0.303681 | ||||||||
\(943\) | −1.49177 | −0.0485787 | ||||||||
\(944\) | 10.0339 | 0.326576 | ||||||||
\(945\) | −12.7094 | −0.413438 | ||||||||
\(946\) | 4.04101 | 0.131385 | ||||||||
\(947\) | −38.2847 | −1.24409 | −0.622043 | − | 0.782983i | \(-0.713697\pi\) | ||||
−0.622043 | + | 0.782983i | \(0.713697\pi\) | |||||||
\(948\) | −18.2511 | −0.592768 | ||||||||
\(949\) | 0.701845 | 0.0227829 | ||||||||
\(950\) | 7.73602 | 0.250990 | ||||||||
\(951\) | 15.4995 | 0.502607 | ||||||||
\(952\) | 5.03526 | 0.163194 | ||||||||
\(953\) | −3.44005 | −0.111434 | −0.0557171 | − | 0.998447i | \(-0.517744\pi\) | ||||
−0.0557171 | + | 0.998447i | \(0.517744\pi\) | |||||||
\(954\) | −6.23836 | −0.201974 | ||||||||
\(955\) | 20.3752 | 0.659325 | ||||||||
\(956\) | −13.7120 | −0.443477 | ||||||||
\(957\) | 6.09245 | 0.196941 | ||||||||
\(958\) | 15.0832 | 0.487315 | ||||||||
\(959\) | 20.4296 | 0.659708 | ||||||||
\(960\) | 1.72392 | 0.0556392 | ||||||||
\(961\) | 17.1264 | 0.552465 | ||||||||
\(962\) | −16.0272 | −0.516738 | ||||||||
\(963\) | −3.73880 | −0.120481 | ||||||||
\(964\) | −10.7067 | −0.344839 | ||||||||
\(965\) | −20.4806 | −0.659294 | ||||||||
\(966\) | 2.12603 | 0.0684037 | ||||||||
\(967\) | −55.4650 | −1.78363 | −0.891817 | − | 0.452396i | \(-0.850569\pi\) | ||||
−0.891817 | + | 0.452396i | \(0.850569\pi\) | |||||||
\(968\) | 12.1154 | 0.389403 | ||||||||
\(969\) | −9.34216 | −0.300113 | ||||||||
\(970\) | 22.0548 | 0.708136 | ||||||||
\(971\) | −54.8260 | −1.75945 | −0.879725 | − | 0.475483i | \(-0.842273\pi\) | ||||
−0.879725 | + | 0.475483i | \(0.842273\pi\) | |||||||
\(972\) | 13.0638 | 0.419022 | ||||||||
\(973\) | 8.10117 | 0.259712 | ||||||||
\(974\) | 28.7409 | 0.920918 | ||||||||
\(975\) | 7.67499 | 0.245796 | ||||||||
\(976\) | 5.19712 | 0.166356 | ||||||||
\(977\) | −34.4063 | −1.10076 | −0.550378 | − | 0.834915i | \(-0.685516\pi\) | ||||
−0.550378 | + | 0.834915i | \(0.685516\pi\) | |||||||
\(978\) | 30.1758 | 0.964915 | ||||||||
\(979\) | −26.8679 | −0.858702 | ||||||||
\(980\) | −5.69360 | −0.181875 | ||||||||
\(981\) | 16.4690 | 0.525816 | ||||||||
\(982\) | −31.7016 | −1.01164 | ||||||||
\(983\) | −46.9384 | −1.49710 | −0.748552 | − | 0.663076i | \(-0.769250\pi\) | ||||
−0.748552 | + | 0.663076i | \(0.769250\pi\) | |||||||
\(984\) | −1.89035 | −0.0602622 | ||||||||
\(985\) | −19.7226 | −0.628416 | ||||||||
\(986\) | 3.00120 | 0.0955775 | ||||||||
\(987\) | −1.60323 | −0.0510315 | ||||||||
\(988\) | 4.72436 | 0.150302 | ||||||||
\(989\) | 0.840503 | 0.0267264 | ||||||||
\(990\) | −9.11930 | −0.289830 | ||||||||
\(991\) | 27.4682 | 0.872555 | 0.436277 | − | 0.899812i | \(-0.356297\pi\) | ||||
0.436277 | + | 0.899812i | \(0.356297\pi\) | |||||||
\(992\) | −6.93732 | −0.220260 | ||||||||
\(993\) | −4.38714 | −0.139222 | ||||||||
\(994\) | −9.66570 | −0.306577 | ||||||||
\(995\) | 1.17931 | 0.0373867 | ||||||||
\(996\) | 5.10202 | 0.161664 | ||||||||
\(997\) | 41.7387 | 1.32188 | 0.660939 | − | 0.750440i | \(-0.270158\pi\) | ||||
0.660939 | + | 0.750440i | \(0.270158\pi\) | |||||||
\(998\) | −7.15558 | −0.226506 | ||||||||
\(999\) | −46.4035 | −1.46814 |
(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 | 1334.2.a.k.1.6 | ✓ | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1334.2.a.k.1.6 | ✓ | 10 | 1.1 | even | 1 | trivial |