Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5103,2,Mod(1,5103)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5103, 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("5103.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5103 = 3^{6} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5103.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: | \(40.7476601515\) |
Analytic rank: | \(1\) |
Dimension: | \(27\) |
Twist minimal: | no (minimal twist has level 189) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.14 | ||
Character | \(\chi\) | \(=\) | 5103.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.268830 | −0.190092 | −0.0950459 | − | 0.995473i | \(-0.530300\pi\) | ||||
−0.0950459 | + | 0.995473i | \(0.530300\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.92773 | −0.963865 | ||||||||
\(5\) | −1.98449 | −0.887490 | −0.443745 | − | 0.896153i | \(-0.646350\pi\) | ||||
−0.443745 | + | 0.896153i | \(0.646350\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 1.05589 | 0.373315 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0.533491 | 0.168705 | ||||||||
\(11\) | 4.25324 | 1.28240 | 0.641200 | − | 0.767374i | \(-0.278437\pi\) | ||||
0.641200 | + | 0.767374i | \(0.278437\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.109391 | −0.0303395 | −0.0151698 | − | 0.999885i | \(-0.504829\pi\) | ||||
−0.0151698 | + | 0.999885i | \(0.504829\pi\) | |||||||
\(14\) | −0.268830 | −0.0718479 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 3.57160 | 0.892901 | ||||||||
\(17\) | −1.06748 | −0.258902 | −0.129451 | − | 0.991586i | \(-0.541322\pi\) | ||||
−0.129451 | + | 0.991586i | \(0.541322\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −6.42242 | −1.47341 | −0.736703 | − | 0.676217i | \(-0.763618\pi\) | ||||
−0.736703 | + | 0.676217i | \(0.763618\pi\) | |||||||
\(20\) | 3.82556 | 0.855421 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −1.14340 | −0.243774 | ||||||||
\(23\) | −0.0715490 | −0.0149190 | −0.00745950 | − | 0.999972i | \(-0.502374\pi\) | ||||
−0.00745950 | + | 0.999972i | \(0.502374\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.06180 | −0.212361 | ||||||||
\(26\) | 0.0294076 | 0.00576730 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −1.92773 | −0.364307 | ||||||||
\(29\) | −7.27006 | −1.35002 | −0.675008 | − | 0.737810i | \(-0.735860\pi\) | ||||
−0.675008 | + | 0.737810i | \(0.735860\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.69167 | −0.483438 | −0.241719 | − | 0.970346i | \(-0.577711\pi\) | ||||
−0.241719 | + | 0.970346i | \(0.577711\pi\) | |||||||
\(32\) | −3.07194 | −0.543048 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0.286971 | 0.0492152 | ||||||||
\(35\) | −1.98449 | −0.335440 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 9.47793 | 1.55816 | 0.779081 | − | 0.626923i | \(-0.215686\pi\) | ||||
0.779081 | + | 0.626923i | \(0.215686\pi\) | |||||||
\(38\) | 1.72654 | 0.280082 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −2.09541 | −0.331313 | ||||||||
\(41\) | 3.10599 | 0.485075 | 0.242537 | − | 0.970142i | \(-0.422020\pi\) | ||||
0.242537 | + | 0.970142i | \(0.422020\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 6.55295 | 0.999316 | 0.499658 | − | 0.866223i | \(-0.333459\pi\) | ||||
0.499658 | + | 0.866223i | \(0.333459\pi\) | |||||||
\(44\) | −8.19910 | −1.23606 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0.0192345 | 0.00283598 | ||||||||
\(47\) | 11.1287 | 1.62329 | 0.811645 | − | 0.584151i | \(-0.198572\pi\) | ||||
0.811645 | + | 0.584151i | \(0.198572\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0.285445 | 0.0403680 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0.210876 | 0.0292432 | ||||||||
\(53\) | −6.12296 | −0.841053 | −0.420526 | − | 0.907280i | \(-0.638155\pi\) | ||||
−0.420526 | + | 0.907280i | \(0.638155\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −8.44050 | −1.13812 | ||||||||
\(56\) | 1.05589 | 0.141100 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 1.95441 | 0.256627 | ||||||||
\(59\) | −5.37482 | −0.699742 | −0.349871 | − | 0.936798i | \(-0.613775\pi\) | ||||
−0.349871 | + | 0.936798i | \(0.613775\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.70539 | 0.602464 | 0.301232 | − | 0.953551i | \(-0.402602\pi\) | ||||
0.301232 | + | 0.953551i | \(0.402602\pi\) | |||||||
\(62\) | 0.723602 | 0.0918975 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −6.31738 | −0.789672 | ||||||||
\(65\) | 0.217085 | 0.0269260 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 5.23154 | 0.639134 | 0.319567 | − | 0.947564i | \(-0.396463\pi\) | ||||
0.319567 | + | 0.947564i | \(0.396463\pi\) | |||||||
\(68\) | 2.05781 | 0.249547 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0.533491 | 0.0637644 | ||||||||
\(71\) | −11.5301 | −1.36837 | −0.684184 | − | 0.729310i | \(-0.739841\pi\) | ||||
−0.684184 | + | 0.729310i | \(0.739841\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 13.8468 | 1.62065 | 0.810325 | − | 0.585981i | \(-0.199290\pi\) | ||||
0.810325 | + | 0.585981i | \(0.199290\pi\) | |||||||
\(74\) | −2.54796 | −0.296194 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 12.3807 | 1.42016 | ||||||||
\(77\) | 4.25324 | 0.484701 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −8.28311 | −0.931923 | −0.465961 | − | 0.884805i | \(-0.654291\pi\) | ||||
−0.465961 | + | 0.884805i | \(0.654291\pi\) | |||||||
\(80\) | −7.08781 | −0.792441 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −0.834985 | −0.0922087 | ||||||||
\(83\) | 16.2719 | 1.78608 | 0.893038 | − | 0.449981i | \(-0.148569\pi\) | ||||
0.893038 | + | 0.449981i | \(0.148569\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.11840 | 0.229773 | ||||||||
\(86\) | −1.76163 | −0.189962 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 4.49097 | 0.478739 | ||||||||
\(89\) | −10.5989 | −1.12348 | −0.561741 | − | 0.827313i | \(-0.689868\pi\) | ||||
−0.561741 | + | 0.827313i | \(0.689868\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −0.109391 | −0.0114673 | ||||||||
\(92\) | 0.137927 | 0.0143799 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −2.99174 | −0.308574 | ||||||||
\(95\) | 12.7452 | 1.30763 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.76383 | 0.179089 | 0.0895447 | − | 0.995983i | \(-0.471459\pi\) | ||||
0.0895447 | + | 0.995983i | \(0.471459\pi\) | |||||||
\(98\) | −0.268830 | −0.0271560 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 2.04687 | 0.204687 | ||||||||
\(101\) | −7.25947 | −0.722344 | −0.361172 | − | 0.932499i | \(-0.617623\pi\) | ||||
−0.361172 | + | 0.932499i | \(0.617623\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 16.2067 | 1.59689 | 0.798446 | − | 0.602066i | \(-0.205656\pi\) | ||||
0.798446 | + | 0.602066i | \(0.205656\pi\) | |||||||
\(104\) | −0.115505 | −0.0113262 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1.64604 | 0.159877 | ||||||||
\(107\) | −7.58438 | −0.733210 | −0.366605 | − | 0.930377i | \(-0.619480\pi\) | ||||
−0.366605 | + | 0.930377i | \(0.619480\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −4.68262 | −0.448513 | −0.224257 | − | 0.974530i | \(-0.571995\pi\) | ||||
−0.224257 | + | 0.974530i | \(0.571995\pi\) | |||||||
\(110\) | 2.26906 | 0.216347 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 3.57160 | 0.337485 | ||||||||
\(113\) | 3.37177 | 0.317190 | 0.158595 | − | 0.987344i | \(-0.449304\pi\) | ||||
0.158595 | + | 0.987344i | \(0.449304\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.141988 | 0.0132405 | ||||||||
\(116\) | 14.0147 | 1.30123 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 1.44491 | 0.133015 | ||||||||
\(119\) | −1.06748 | −0.0978558 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 7.09003 | 0.644548 | ||||||||
\(122\) | −1.26495 | −0.114523 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 5.18881 | 0.465969 | ||||||||
\(125\) | 12.0296 | 1.07596 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −9.01219 | −0.799702 | −0.399851 | − | 0.916580i | \(-0.630938\pi\) | ||||
−0.399851 | + | 0.916580i | \(0.630938\pi\) | |||||||
\(128\) | 7.84219 | 0.693158 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −0.0583590 | −0.00511842 | ||||||||
\(131\) | −7.38926 | −0.645602 | −0.322801 | − | 0.946467i | \(-0.604625\pi\) | ||||
−0.322801 | + | 0.946467i | \(0.604625\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −6.42242 | −0.556895 | ||||||||
\(134\) | −1.40640 | −0.121494 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −1.12715 | −0.0966519 | ||||||||
\(137\) | −16.2358 | −1.38712 | −0.693558 | − | 0.720400i | \(-0.743958\pi\) | ||||
−0.693558 | + | 0.720400i | \(0.743958\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −7.34736 | −0.623195 | −0.311597 | − | 0.950214i | \(-0.600864\pi\) | ||||
−0.311597 | + | 0.950214i | \(0.600864\pi\) | |||||||
\(140\) | 3.82556 | 0.323319 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 3.09963 | 0.260115 | ||||||||
\(143\) | −0.465265 | −0.0389074 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 14.4274 | 1.19813 | ||||||||
\(146\) | −3.72245 | −0.308072 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −18.2709 | −1.50186 | ||||||||
\(149\) | −16.4309 | −1.34607 | −0.673035 | − | 0.739611i | \(-0.735010\pi\) | ||||
−0.673035 | + | 0.739611i | \(0.735010\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −21.2936 | −1.73285 | −0.866424 | − | 0.499309i | \(-0.833587\pi\) | ||||
−0.866424 | + | 0.499309i | \(0.833587\pi\) | |||||||
\(152\) | −6.78140 | −0.550044 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −1.14340 | −0.0921378 | ||||||||
\(155\) | 5.34158 | 0.429046 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −4.84201 | −0.386435 | −0.193217 | − | 0.981156i | \(-0.561892\pi\) | ||||
−0.193217 | + | 0.981156i | \(0.561892\pi\) | |||||||
\(158\) | 2.22675 | 0.177151 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 6.09624 | 0.481950 | ||||||||
\(161\) | −0.0715490 | −0.00563885 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 17.1250 | 1.34133 | 0.670665 | − | 0.741760i | \(-0.266009\pi\) | ||||
0.670665 | + | 0.741760i | \(0.266009\pi\) | |||||||
\(164\) | −5.98752 | −0.467546 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −4.37439 | −0.339518 | ||||||||
\(167\) | 2.54016 | 0.196563 | 0.0982817 | − | 0.995159i | \(-0.468665\pi\) | ||||
0.0982817 | + | 0.995159i | \(0.468665\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.9880 | −0.999080 | ||||||||
\(170\) | −0.569491 | −0.0436780 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −12.6323 | −0.963206 | ||||||||
\(173\) | 11.7993 | 0.897086 | 0.448543 | − | 0.893761i | \(-0.351943\pi\) | ||||
0.448543 | + | 0.893761i | \(0.351943\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.06180 | −0.0802648 | ||||||||
\(176\) | 15.1909 | 1.14506 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 2.84931 | 0.213565 | ||||||||
\(179\) | −23.1128 | −1.72753 | −0.863766 | − | 0.503893i | \(-0.831901\pi\) | ||||
−0.863766 | + | 0.503893i | \(0.831901\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 13.2932 | 0.988076 | 0.494038 | − | 0.869440i | \(-0.335520\pi\) | ||||
0.494038 | + | 0.869440i | \(0.335520\pi\) | |||||||
\(182\) | 0.0294076 | 0.00217983 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −0.0755481 | −0.00556948 | ||||||||
\(185\) | −18.8088 | −1.38285 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −4.54025 | −0.332016 | ||||||||
\(188\) | −21.4532 | −1.56463 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −3.42631 | −0.248570 | ||||||||
\(191\) | −5.65034 | −0.408844 | −0.204422 | − | 0.978883i | \(-0.565532\pi\) | ||||
−0.204422 | + | 0.978883i | \(0.565532\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −12.0026 | −0.863964 | −0.431982 | − | 0.901882i | \(-0.642186\pi\) | ||||
−0.431982 | + | 0.901882i | \(0.642186\pi\) | |||||||
\(194\) | −0.474170 | −0.0340434 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1.92773 | −0.137695 | ||||||||
\(197\) | −21.1585 | −1.50748 | −0.753742 | − | 0.657171i | \(-0.771753\pi\) | ||||
−0.753742 | + | 0.657171i | \(0.771753\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 4.92519 | 0.349137 | 0.174569 | − | 0.984645i | \(-0.444147\pi\) | ||||
0.174569 | + | 0.984645i | \(0.444147\pi\) | |||||||
\(200\) | −1.12115 | −0.0792773 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 1.95157 | 0.137312 | ||||||||
\(203\) | −7.27006 | −0.510258 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −6.16381 | −0.430499 | ||||||||
\(206\) | −4.35685 | −0.303556 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −0.390700 | −0.0270902 | ||||||||
\(209\) | −27.3161 | −1.88949 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −19.5738 | −1.34752 | −0.673758 | − | 0.738952i | \(-0.735321\pi\) | ||||
−0.673758 | + | 0.738952i | \(0.735321\pi\) | |||||||
\(212\) | 11.8034 | 0.810662 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 2.03891 | 0.139377 | ||||||||
\(215\) | −13.0043 | −0.886883 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2.69167 | −0.182722 | ||||||||
\(218\) | 1.25883 | 0.0852587 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 16.2710 | 1.09699 | ||||||||
\(221\) | 0.116772 | 0.00785497 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −2.57522 | −0.172450 | −0.0862248 | − | 0.996276i | \(-0.527480\pi\) | ||||
−0.0862248 | + | 0.996276i | \(0.527480\pi\) | |||||||
\(224\) | −3.07194 | −0.205253 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −0.906435 | −0.0602951 | ||||||||
\(227\) | −18.1727 | −1.20617 | −0.603084 | − | 0.797678i | \(-0.706062\pi\) | ||||
−0.603084 | + | 0.797678i | \(0.706062\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 23.7111 | 1.56687 | 0.783436 | − | 0.621473i | \(-0.213465\pi\) | ||||
0.783436 | + | 0.621473i | \(0.213465\pi\) | |||||||
\(230\) | −0.0381707 | −0.00251690 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −7.67641 | −0.503981 | ||||||||
\(233\) | −9.63100 | −0.630948 | −0.315474 | − | 0.948934i | \(-0.602163\pi\) | ||||
−0.315474 | + | 0.948934i | \(0.602163\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −22.0848 | −1.44065 | ||||||||
\(236\) | 10.3612 | 0.674456 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0.286971 | 0.0186016 | ||||||||
\(239\) | 10.0032 | 0.647050 | 0.323525 | − | 0.946220i | \(-0.395132\pi\) | ||||
0.323525 | + | 0.946220i | \(0.395132\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.69924 | 0.109458 | 0.0547289 | − | 0.998501i | \(-0.482571\pi\) | ||||
0.0547289 | + | 0.998501i | \(0.482571\pi\) | |||||||
\(242\) | −1.90602 | −0.122523 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −9.07073 | −0.580694 | ||||||||
\(245\) | −1.98449 | −0.126784 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.702554 | 0.0447024 | ||||||||
\(248\) | −2.84211 | −0.180474 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −3.23392 | −0.204531 | ||||||||
\(251\) | −21.2530 | −1.34148 | −0.670740 | − | 0.741692i | \(-0.734023\pi\) | ||||
−0.670740 | + | 0.741692i | \(0.734023\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −0.304315 | −0.0191321 | ||||||||
\(254\) | 2.42275 | 0.152017 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 10.5265 | 0.657908 | ||||||||
\(257\) | −4.75606 | −0.296675 | −0.148338 | − | 0.988937i | \(-0.547392\pi\) | ||||
−0.148338 | + | 0.988937i | \(0.547392\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 9.47793 | 0.588930 | ||||||||
\(260\) | −0.418481 | −0.0259531 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 1.98646 | 0.122724 | ||||||||
\(263\) | −0.0455692 | −0.00280992 | −0.00140496 | − | 0.999999i | \(-0.500447\pi\) | ||||
−0.00140496 | + | 0.999999i | \(0.500447\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 12.1509 | 0.746426 | ||||||||
\(266\) | 1.72654 | 0.105861 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −10.0850 | −0.616039 | ||||||||
\(269\) | 3.67995 | 0.224371 | 0.112185 | − | 0.993687i | \(-0.464215\pi\) | ||||
0.112185 | + | 0.993687i | \(0.464215\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 21.3658 | 1.29788 | 0.648939 | − | 0.760841i | \(-0.275213\pi\) | ||||
0.648939 | + | 0.760841i | \(0.275213\pi\) | |||||||
\(272\) | −3.81262 | −0.231174 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 4.36467 | 0.263680 | ||||||||
\(275\) | −4.51610 | −0.272331 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 14.8421 | 0.891773 | 0.445887 | − | 0.895089i | \(-0.352888\pi\) | ||||
0.445887 | + | 0.895089i | \(0.352888\pi\) | |||||||
\(278\) | 1.97519 | 0.118464 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −2.09541 | −0.125225 | ||||||||
\(281\) | 6.11526 | 0.364806 | 0.182403 | − | 0.983224i | \(-0.441612\pi\) | ||||
0.182403 | + | 0.983224i | \(0.441612\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −16.1655 | −0.960937 | −0.480468 | − | 0.877012i | \(-0.659533\pi\) | ||||
−0.480468 | + | 0.877012i | \(0.659533\pi\) | |||||||
\(284\) | 22.2269 | 1.31892 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0.125077 | 0.00739598 | ||||||||
\(287\) | 3.10599 | 0.183341 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −15.8605 | −0.932970 | ||||||||
\(290\) | −3.87851 | −0.227754 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −26.6930 | −1.56209 | ||||||||
\(293\) | 8.28460 | 0.483991 | 0.241996 | − | 0.970277i | \(-0.422198\pi\) | ||||
0.241996 | + | 0.970277i | \(0.422198\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 10.6663 | 0.621014 | ||||||||
\(296\) | 10.0077 | 0.581685 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 4.41712 | 0.255877 | ||||||||
\(299\) | 0.00782680 | 0.000452635 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 6.55295 | 0.377706 | ||||||||
\(302\) | 5.72436 | 0.329400 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −22.9384 | −1.31561 | ||||||||
\(305\) | −9.33780 | −0.534681 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −25.3127 | −1.44467 | −0.722336 | − | 0.691542i | \(-0.756932\pi\) | ||||
−0.722336 | + | 0.691542i | \(0.756932\pi\) | |||||||
\(308\) | −8.19910 | −0.467187 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −1.43598 | −0.0815582 | ||||||||
\(311\) | −33.2635 | −1.88620 | −0.943100 | − | 0.332509i | \(-0.892105\pi\) | ||||
−0.943100 | + | 0.332509i | \(0.892105\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −13.4885 | −0.762418 | −0.381209 | − | 0.924489i | \(-0.624492\pi\) | ||||
−0.381209 | + | 0.924489i | \(0.624492\pi\) | |||||||
\(314\) | 1.30168 | 0.0734581 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 15.9676 | 0.898248 | ||||||||
\(317\) | −30.4736 | −1.71157 | −0.855785 | − | 0.517332i | \(-0.826925\pi\) | ||||
−0.855785 | + | 0.517332i | \(0.826925\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −30.9213 | −1.73126 | ||||||||
\(320\) | 12.5368 | 0.700826 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0.0192345 | 0.00107190 | ||||||||
\(323\) | 6.85581 | 0.381468 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0.116151 | 0.00644292 | ||||||||
\(326\) | −4.60371 | −0.254976 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 3.27960 | 0.181085 | ||||||||
\(329\) | 11.1287 | 0.613546 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −4.01992 | −0.220955 | −0.110477 | − | 0.993879i | \(-0.535238\pi\) | ||||
−0.110477 | + | 0.993879i | \(0.535238\pi\) | |||||||
\(332\) | −31.3679 | −1.72154 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −0.682872 | −0.0373651 | ||||||||
\(335\) | −10.3819 | −0.567225 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −11.8565 | −0.645863 | −0.322931 | − | 0.946422i | \(-0.604668\pi\) | ||||
−0.322931 | + | 0.946422i | \(0.604668\pi\) | |||||||
\(338\) | 3.49158 | 0.189917 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −4.08371 | −0.221470 | ||||||||
\(341\) | −11.4483 | −0.619960 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 6.91922 | 0.373059 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −3.17202 | −0.170529 | ||||||||
\(347\) | −10.2831 | −0.552024 | −0.276012 | − | 0.961154i | \(-0.589013\pi\) | ||||
−0.276012 | + | 0.961154i | \(0.589013\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 4.27567 | 0.228871 | 0.114436 | − | 0.993431i | \(-0.463494\pi\) | ||||
0.114436 | + | 0.993431i | \(0.463494\pi\) | |||||||
\(350\) | 0.285445 | 0.0152577 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −13.0657 | −0.696404 | ||||||||
\(353\) | 26.3971 | 1.40498 | 0.702489 | − | 0.711695i | \(-0.252072\pi\) | ||||
0.702489 | + | 0.711695i | \(0.252072\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 22.8813 | 1.21441 | ||||||||
\(356\) | 20.4318 | 1.08289 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 6.21343 | 0.328390 | ||||||||
\(359\) | −21.6348 | −1.14184 | −0.570921 | − | 0.821005i | \(-0.693414\pi\) | ||||
−0.570921 | + | 0.821005i | \(0.693414\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 22.2475 | 1.17092 | ||||||||
\(362\) | −3.57362 | −0.187825 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0.210876 | 0.0110529 | ||||||||
\(365\) | −27.4789 | −1.43831 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −2.25742 | −0.117836 | −0.0589182 | − | 0.998263i | \(-0.518765\pi\) | ||||
−0.0589182 | + | 0.998263i | \(0.518765\pi\) | |||||||
\(368\) | −0.255545 | −0.0133212 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 5.05639 | 0.262869 | ||||||||
\(371\) | −6.12296 | −0.317888 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 10.3806 | 0.537487 | 0.268743 | − | 0.963212i | \(-0.413392\pi\) | ||||
0.268743 | + | 0.963212i | \(0.413392\pi\) | |||||||
\(374\) | 1.22056 | 0.0631135 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 11.7507 | 0.605998 | ||||||||
\(377\) | 0.795277 | 0.0409589 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 10.1524 | 0.521496 | 0.260748 | − | 0.965407i | \(-0.416031\pi\) | ||||
0.260748 | + | 0.965407i | \(0.416031\pi\) | |||||||
\(380\) | −24.5694 | −1.26038 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 1.51898 | 0.0777180 | ||||||||
\(383\) | −7.61267 | −0.388989 | −0.194495 | − | 0.980904i | \(-0.562307\pi\) | ||||
−0.194495 | + | 0.980904i | \(0.562307\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −8.44050 | −0.430168 | ||||||||
\(386\) | 3.22666 | 0.164232 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −3.40018 | −0.172618 | ||||||||
\(389\) | −4.50304 | −0.228313 | −0.114157 | − | 0.993463i | \(-0.536417\pi\) | ||||
−0.114157 | + | 0.993463i | \(0.536417\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0.0763771 | 0.00386256 | ||||||||
\(392\) | 1.05589 | 0.0533307 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 5.68806 | 0.286560 | ||||||||
\(395\) | 16.4377 | 0.827072 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −1.41325 | −0.0709289 | −0.0354644 | − | 0.999371i | \(-0.511291\pi\) | ||||
−0.0354644 | + | 0.999371i | \(0.511291\pi\) | |||||||
\(398\) | −1.32404 | −0.0663681 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −3.79234 | −0.189617 | ||||||||
\(401\) | −27.3096 | −1.36377 | −0.681887 | − | 0.731457i | \(-0.738841\pi\) | ||||
−0.681887 | + | 0.731457i | \(0.738841\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0.294443 | 0.0146673 | ||||||||
\(404\) | 13.9943 | 0.696242 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 1.95441 | 0.0969959 | ||||||||
\(407\) | 40.3119 | 1.99819 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −18.9077 | −0.934924 | −0.467462 | − | 0.884013i | \(-0.654831\pi\) | ||||
−0.467462 | + | 0.884013i | \(0.654831\pi\) | |||||||
\(410\) | 1.65702 | 0.0818343 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −31.2421 | −1.53919 | ||||||||
\(413\) | −5.37482 | −0.264477 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −32.2915 | −1.58513 | ||||||||
\(416\) | 0.336042 | 0.0164758 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 7.34340 | 0.359177 | ||||||||
\(419\) | −19.9807 | −0.976119 | −0.488060 | − | 0.872810i | \(-0.662295\pi\) | ||||
−0.488060 | + | 0.872810i | \(0.662295\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 25.3479 | 1.23538 | 0.617692 | − | 0.786420i | \(-0.288068\pi\) | ||||
0.617692 | + | 0.786420i | \(0.288068\pi\) | |||||||
\(422\) | 5.26203 | 0.256152 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −6.46519 | −0.313977 | ||||||||
\(425\) | 1.13345 | 0.0549806 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 4.70539 | 0.227710 | ||||||||
\(428\) | 14.6206 | 0.706715 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 3.49594 | 0.168589 | ||||||||
\(431\) | −9.73667 | −0.468999 | −0.234499 | − | 0.972116i | \(-0.575345\pi\) | ||||
−0.234499 | + | 0.972116i | \(0.575345\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −10.2203 | −0.491155 | −0.245578 | − | 0.969377i | \(-0.578978\pi\) | ||||
−0.245578 | + | 0.969377i | \(0.578978\pi\) | |||||||
\(434\) | 0.723602 | 0.0347340 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 9.02682 | 0.432306 | ||||||||
\(437\) | 0.459518 | 0.0219817 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 33.7275 | 1.60973 | 0.804863 | − | 0.593461i | \(-0.202239\pi\) | ||||
0.804863 | + | 0.593461i | \(0.202239\pi\) | |||||||
\(440\) | −8.91227 | −0.424876 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −0.0313920 | −0.00149317 | ||||||||
\(443\) | −21.1342 | −1.00412 | −0.502059 | − | 0.864833i | \(-0.667424\pi\) | ||||
−0.502059 | + | 0.864833i | \(0.667424\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 21.0334 | 0.997080 | ||||||||
\(446\) | 0.692298 | 0.0327812 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −6.31738 | −0.298468 | ||||||||
\(449\) | 18.4182 | 0.869208 | 0.434604 | − | 0.900622i | \(-0.356888\pi\) | ||||
0.434604 | + | 0.900622i | \(0.356888\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 13.2105 | 0.622059 | ||||||||
\(452\) | −6.49987 | −0.305728 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 4.88539 | 0.229283 | ||||||||
\(455\) | 0.217085 | 0.0101771 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 38.8038 | 1.81517 | 0.907584 | − | 0.419872i | \(-0.137925\pi\) | ||||
0.907584 | + | 0.419872i | \(0.137925\pi\) | |||||||
\(458\) | −6.37426 | −0.297849 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −0.273715 | −0.0127620 | ||||||||
\(461\) | 36.5473 | 1.70218 | 0.851088 | − | 0.525024i | \(-0.175944\pi\) | ||||
0.851088 | + | 0.525024i | \(0.175944\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −17.3513 | −0.806382 | −0.403191 | − | 0.915116i | \(-0.632099\pi\) | ||||
−0.403191 | + | 0.915116i | \(0.632099\pi\) | |||||||
\(464\) | −25.9658 | −1.20543 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 2.58911 | 0.119938 | ||||||||
\(467\) | 23.2819 | 1.07736 | 0.538680 | − | 0.842511i | \(-0.318923\pi\) | ||||
0.538680 | + | 0.842511i | \(0.318923\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 5.23154 | 0.241570 | ||||||||
\(470\) | 5.93707 | 0.273857 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −5.67523 | −0.261224 | ||||||||
\(473\) | 27.8713 | 1.28152 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 6.81935 | 0.312893 | ||||||||
\(476\) | 2.05781 | 0.0943198 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −2.68915 | −0.122999 | ||||||||
\(479\) | 0.779751 | 0.0356278 | 0.0178139 | − | 0.999841i | \(-0.494329\pi\) | ||||
0.0178139 | + | 0.999841i | \(0.494329\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.03680 | −0.0472739 | ||||||||
\(482\) | −0.456808 | −0.0208070 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −13.6677 | −0.621258 | ||||||||
\(485\) | −3.50029 | −0.158940 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 35.3660 | 1.60259 | 0.801293 | − | 0.598272i | \(-0.204146\pi\) | ||||
0.801293 | + | 0.598272i | \(0.204146\pi\) | |||||||
\(488\) | 4.96839 | 0.224909 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0.533491 | 0.0241007 | ||||||||
\(491\) | 40.1437 | 1.81166 | 0.905830 | − | 0.423642i | \(-0.139248\pi\) | ||||
0.905830 | + | 0.423642i | \(0.139248\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 7.76065 | 0.349522 | ||||||||
\(494\) | −0.188868 | −0.00849757 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −9.61357 | −0.431662 | ||||||||
\(497\) | −11.5301 | −0.517194 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 5.85631 | 0.262164 | 0.131082 | − | 0.991372i | \(-0.458155\pi\) | ||||
0.131082 | + | 0.991372i | \(0.458155\pi\) | |||||||
\(500\) | −23.1898 | −1.03708 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 5.71346 | 0.255004 | ||||||||
\(503\) | −8.23611 | −0.367230 | −0.183615 | − | 0.982998i | \(-0.558780\pi\) | ||||
−0.183615 | + | 0.982998i | \(0.558780\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 14.4063 | 0.641073 | ||||||||
\(506\) | 0.0818091 | 0.00363686 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 17.3731 | 0.770805 | ||||||||
\(509\) | −21.7206 | −0.962748 | −0.481374 | − | 0.876515i | \(-0.659862\pi\) | ||||
−0.481374 | + | 0.876515i | \(0.659862\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 13.8468 | 0.612548 | ||||||||
\(512\) | −18.5142 | −0.818221 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 1.27857 | 0.0563955 | ||||||||
\(515\) | −32.1620 | −1.41723 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 47.3331 | 2.08171 | ||||||||
\(518\) | −2.54796 | −0.111951 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0.229218 | 0.0100519 | ||||||||
\(521\) | −7.58951 | −0.332502 | −0.166251 | − | 0.986083i | \(-0.553166\pi\) | ||||
−0.166251 | + | 0.986083i | \(0.553166\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −16.6859 | −0.729623 | −0.364811 | − | 0.931081i | \(-0.618866\pi\) | ||||
−0.364811 | + | 0.931081i | \(0.618866\pi\) | |||||||
\(524\) | 14.2445 | 0.622274 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0.0122504 | 0.000534142 0 | ||||||||
\(527\) | 2.87330 | 0.125163 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.9949 | −0.999777 | ||||||||
\(530\) | −3.26654 | −0.141890 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 12.3807 | 0.536771 | ||||||||
\(533\) | −0.339767 | −0.0147169 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 15.0511 | 0.650717 | ||||||||
\(536\) | 5.52394 | 0.238598 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −0.989284 | −0.0426510 | ||||||||
\(539\) | 4.25324 | 0.183200 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 17.7745 | 0.764187 | 0.382093 | − | 0.924124i | \(-0.375203\pi\) | ||||
0.382093 | + | 0.924124i | \(0.375203\pi\) | |||||||
\(542\) | −5.74377 | −0.246716 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 3.27924 | 0.140596 | ||||||||
\(545\) | 9.29260 | 0.398051 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 2.60865 | 0.111538 | 0.0557690 | − | 0.998444i | \(-0.482239\pi\) | ||||
0.0557690 | + | 0.998444i | \(0.482239\pi\) | |||||||
\(548\) | 31.2982 | 1.33699 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 1.21407 | 0.0517679 | ||||||||
\(551\) | 46.6914 | 1.98912 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −8.28311 | −0.352234 | ||||||||
\(554\) | −3.99000 | −0.169519 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 14.1637 | 0.600676 | ||||||||
\(557\) | −20.4485 | −0.866429 | −0.433215 | − | 0.901291i | \(-0.642621\pi\) | ||||
−0.433215 | + | 0.901291i | \(0.642621\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −0.716832 | −0.0303188 | ||||||||
\(560\) | −7.08781 | −0.299515 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −1.64397 | −0.0693466 | ||||||||
\(563\) | −24.2667 | −1.02272 | −0.511359 | − | 0.859367i | \(-0.670858\pi\) | ||||
−0.511359 | + | 0.859367i | \(0.670858\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −6.69124 | −0.281503 | ||||||||
\(566\) | 4.34577 | 0.182666 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −12.1745 | −0.510832 | ||||||||
\(569\) | −3.27147 | −0.137147 | −0.0685735 | − | 0.997646i | \(-0.521845\pi\) | ||||
−0.0685735 | + | 0.997646i | \(0.521845\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −39.9363 | −1.67128 | −0.835641 | − | 0.549276i | \(-0.814904\pi\) | ||||
−0.835641 | + | 0.549276i | \(0.814904\pi\) | |||||||
\(572\) | 0.896905 | 0.0375015 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −0.834985 | −0.0348516 | ||||||||
\(575\) | 0.0759709 | 0.00316821 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −28.5036 | −1.18662 | −0.593311 | − | 0.804973i | \(-0.702179\pi\) | ||||
−0.593311 | + | 0.804973i | \(0.702179\pi\) | |||||||
\(578\) | 4.26378 | 0.177350 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −27.8120 | −1.15483 | ||||||||
\(581\) | 16.2719 | 0.675073 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −26.0424 | −1.07857 | ||||||||
\(584\) | 14.6208 | 0.605013 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −2.22715 | −0.0920028 | ||||||||
\(587\) | 37.4354 | 1.54512 | 0.772562 | − | 0.634940i | \(-0.218975\pi\) | ||||
0.772562 | + | 0.634940i | \(0.218975\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 17.2870 | 0.712300 | ||||||||
\(590\) | −2.86742 | −0.118050 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 33.8514 | 1.39128 | ||||||||
\(593\) | 1.95349 | 0.0802204 | 0.0401102 | − | 0.999195i | \(-0.487229\pi\) | ||||
0.0401102 | + | 0.999195i | \(0.487229\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 2.11840 | 0.0868461 | ||||||||
\(596\) | 31.6743 | 1.29743 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −0.00210408 | −8.60423e−5 0 | ||||||||
\(599\) | −38.2229 | −1.56175 | −0.780873 | − | 0.624690i | \(-0.785225\pi\) | ||||
−0.780873 | + | 0.624690i | \(0.785225\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 16.0872 | 0.656210 | 0.328105 | − | 0.944641i | \(-0.393590\pi\) | ||||
0.328105 | + | 0.944641i | \(0.393590\pi\) | |||||||
\(602\) | −1.76163 | −0.0717988 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 41.0483 | 1.67023 | ||||||||
\(605\) | −14.0701 | −0.572031 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 2.80440 | 0.113827 | 0.0569135 | − | 0.998379i | \(-0.481874\pi\) | ||||
0.0569135 | + | 0.998379i | \(0.481874\pi\) | |||||||
\(608\) | 19.7293 | 0.800130 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 2.51029 | 0.101638 | ||||||||
\(611\) | −1.21738 | −0.0492499 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −24.6455 | −0.995424 | −0.497712 | − | 0.867342i | \(-0.665826\pi\) | ||||
−0.497712 | + | 0.867342i | \(0.665826\pi\) | |||||||
\(614\) | 6.80482 | 0.274620 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 4.49097 | 0.180946 | ||||||||
\(617\) | 12.9429 | 0.521061 | 0.260531 | − | 0.965466i | \(-0.416103\pi\) | ||||
0.260531 | + | 0.965466i | \(0.416103\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −8.70764 | −0.349990 | −0.174995 | − | 0.984569i | \(-0.555991\pi\) | ||||
−0.174995 | + | 0.984569i | \(0.555991\pi\) | |||||||
\(620\) | −10.2971 | −0.413543 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 8.94224 | 0.358551 | ||||||||
\(623\) | −10.5989 | −0.424637 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −18.5636 | −0.742542 | ||||||||
\(626\) | 3.62613 | 0.144929 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 9.33410 | 0.372471 | ||||||||
\(629\) | −10.1175 | −0.403411 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 14.8276 | 0.590277 | 0.295139 | − | 0.955454i | \(-0.404634\pi\) | ||||
0.295139 | + | 0.955454i | \(0.404634\pi\) | |||||||
\(632\) | −8.74608 | −0.347900 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 8.19224 | 0.325355 | ||||||||
\(635\) | 17.8846 | 0.709728 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −0.109391 | −0.00433422 | ||||||||
\(638\) | 8.31258 | 0.329098 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −15.5627 | −0.615171 | ||||||||
\(641\) | 13.2604 | 0.523753 | 0.261876 | − | 0.965101i | \(-0.415659\pi\) | ||||
0.261876 | + | 0.965101i | \(0.415659\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −33.9031 | −1.33701 | −0.668504 | − | 0.743709i | \(-0.733065\pi\) | ||||
−0.668504 | + | 0.743709i | \(0.733065\pi\) | |||||||
\(644\) | 0.137927 | 0.00543509 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −1.84305 | −0.0725139 | ||||||||
\(647\) | −15.4959 | −0.609207 | −0.304604 | − | 0.952479i | \(-0.598524\pi\) | ||||
−0.304604 | + | 0.952479i | \(0.598524\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −22.8604 | −0.897348 | ||||||||
\(650\) | −0.0312250 | −0.00122475 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −33.0123 | −1.29286 | ||||||||
\(653\) | 18.1551 | 0.710463 | 0.355232 | − | 0.934778i | \(-0.384402\pi\) | ||||
0.355232 | + | 0.934778i | \(0.384402\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 14.6639 | 0.572966 | ||||||||
\(656\) | 11.0934 | 0.433124 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −2.99174 | −0.116630 | ||||||||
\(659\) | 12.5102 | 0.487330 | 0.243665 | − | 0.969859i | \(-0.421650\pi\) | ||||
0.243665 | + | 0.969859i | \(0.421650\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −24.0089 | −0.933837 | −0.466918 | − | 0.884300i | \(-0.654636\pi\) | ||||
−0.466918 | + | 0.884300i | \(0.654636\pi\) | |||||||
\(662\) | 1.08068 | 0.0420017 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 17.1814 | 0.666768 | ||||||||
\(665\) | 12.7452 | 0.494239 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0.520165 | 0.0201409 | ||||||||
\(668\) | −4.89674 | −0.189461 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 2.79098 | 0.107825 | ||||||||
\(671\) | 20.0132 | 0.772599 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −33.4131 | −1.28798 | −0.643990 | − | 0.765034i | \(-0.722722\pi\) | ||||
−0.643990 | + | 0.765034i | \(0.722722\pi\) | |||||||
\(674\) | 3.18738 | 0.122773 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 25.0374 | 0.962978 | ||||||||
\(677\) | 21.5096 | 0.826680 | 0.413340 | − | 0.910577i | \(-0.364362\pi\) | ||||
0.413340 | + | 0.910577i | \(0.364362\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1.76383 | 0.0676894 | ||||||||
\(680\) | 2.23681 | 0.0857777 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 3.07765 | 0.117849 | ||||||||
\(683\) | 42.4410 | 1.62396 | 0.811979 | − | 0.583687i | \(-0.198390\pi\) | ||||
0.811979 | + | 0.583687i | \(0.198390\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 32.2197 | 1.23105 | ||||||||
\(686\) | −0.268830 | −0.0102640 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 23.4046 | 0.892290 | ||||||||
\(689\) | 0.669795 | 0.0255172 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −33.5025 | −1.27449 | −0.637247 | − | 0.770659i | \(-0.719927\pi\) | ||||
−0.637247 | + | 0.770659i | \(0.719927\pi\) | |||||||
\(692\) | −22.7459 | −0.864669 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 2.76440 | 0.104935 | ||||||||
\(695\) | 14.5808 | 0.553080 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −3.31559 | −0.125587 | ||||||||
\(698\) | −1.14943 | −0.0435066 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 2.04687 | 0.0773644 | ||||||||
\(701\) | 4.77624 | 0.180396 | 0.0901980 | − | 0.995924i | \(-0.471250\pi\) | ||||
0.0901980 | + | 0.995924i | \(0.471250\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −60.8713 | −2.29580 | ||||||||
\(704\) | −26.8693 | −1.01268 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −7.09635 | −0.267075 | ||||||||
\(707\) | −7.25947 | −0.273020 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 3.75143 | 0.140888 | 0.0704439 | − | 0.997516i | \(-0.477558\pi\) | ||||
0.0704439 | + | 0.997516i | \(0.477558\pi\) | |||||||
\(710\) | −6.15119 | −0.230850 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −11.1913 | −0.419413 | ||||||||
\(713\) | 0.192586 | 0.00721240 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0.923313 | 0.0345299 | ||||||||
\(716\) | 44.5553 | 1.66511 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 5.81609 | 0.217055 | ||||||||
\(719\) | −32.8054 | −1.22344 | −0.611718 | − | 0.791076i | \(-0.709521\pi\) | ||||
−0.611718 | + | 0.791076i | \(0.709521\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 16.2067 | 0.603569 | ||||||||
\(722\) | −5.98081 | −0.222583 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −25.6257 | −0.952372 | ||||||||
\(725\) | 7.71937 | 0.286690 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −3.66946 | −0.136093 | −0.0680463 | − | 0.997682i | \(-0.521677\pi\) | ||||
−0.0680463 | + | 0.997682i | \(0.521677\pi\) | |||||||
\(728\) | −0.115505 | −0.00428090 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 7.38717 | 0.273411 | ||||||||
\(731\) | −6.99515 | −0.258725 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −27.0739 | −0.999997 | −0.499998 | − | 0.866026i | \(-0.666666\pi\) | ||||
−0.499998 | + | 0.866026i | \(0.666666\pi\) | |||||||
\(734\) | 0.606864 | 0.0223998 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0.219794 | 0.00810173 | ||||||||
\(737\) | 22.2510 | 0.819625 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 19.1679 | 0.705101 | 0.352551 | − | 0.935793i | \(-0.385314\pi\) | ||||
0.352551 | + | 0.935793i | \(0.385314\pi\) | |||||||
\(740\) | 36.2584 | 1.33288 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 1.64604 | 0.0604279 | ||||||||
\(743\) | −3.66732 | −0.134541 | −0.0672705 | − | 0.997735i | \(-0.521429\pi\) | ||||
−0.0672705 | + | 0.997735i | \(0.521429\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 32.6069 | 1.19462 | ||||||||
\(746\) | −2.79062 | −0.102172 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 8.75237 | 0.320018 | ||||||||
\(749\) | −7.58438 | −0.277127 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −32.3105 | −1.17903 | −0.589514 | − | 0.807758i | \(-0.700681\pi\) | ||||
−0.589514 | + | 0.807758i | \(0.700681\pi\) | |||||||
\(752\) | 39.7474 | 1.44944 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −0.213795 | −0.00778594 | ||||||||
\(755\) | 42.2569 | 1.53789 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −22.9786 | −0.835170 | −0.417585 | − | 0.908638i | \(-0.637123\pi\) | ||||
−0.417585 | + | 0.908638i | \(0.637123\pi\) | |||||||
\(758\) | −2.72929 | −0.0991322 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 13.4576 | 0.488159 | ||||||||
\(761\) | −38.9742 | −1.41281 | −0.706407 | − | 0.707806i | \(-0.749685\pi\) | ||||
−0.706407 | + | 0.707806i | \(0.749685\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −4.68262 | −0.169522 | ||||||||
\(764\) | 10.8923 | 0.394071 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 2.04652 | 0.0739436 | ||||||||
\(767\) | 0.587955 | 0.0212298 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −4.00488 | −0.144420 | −0.0722098 | − | 0.997389i | \(-0.523005\pi\) | ||||
−0.0722098 | + | 0.997389i | \(0.523005\pi\) | |||||||
\(770\) | 2.26906 | 0.0817714 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 23.1377 | 0.832745 | ||||||||
\(773\) | 8.99583 | 0.323558 | 0.161779 | − | 0.986827i | \(-0.448277\pi\) | ||||
0.161779 | + | 0.986827i | \(0.448277\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 2.85802 | 0.102663 | ||||||||
\(776\) | 1.86241 | 0.0668567 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 1.21056 | 0.0434005 | ||||||||
\(779\) | −19.9480 | −0.714711 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −49.0401 | −1.75479 | ||||||||
\(782\) | −0.0205325 | −0.000734241 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 3.57160 | 0.127557 | ||||||||
\(785\) | 9.60893 | 0.342957 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 6.14098 | 0.218902 | 0.109451 | − | 0.993992i | \(-0.465091\pi\) | ||||
0.109451 | + | 0.993992i | \(0.465091\pi\) | |||||||
\(788\) | 40.7880 | 1.45301 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −4.41896 | −0.157220 | ||||||||
\(791\) | 3.37177 | 0.119886 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −0.514727 | −0.0182785 | ||||||||
\(794\) | 0.379924 | 0.0134830 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −9.49443 | −0.336521 | ||||||||
\(797\) | −42.8217 | −1.51682 | −0.758412 | − | 0.651776i | \(-0.774024\pi\) | ||||
−0.758412 | + | 0.651776i | \(0.774024\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −11.8797 | −0.420273 | ||||||||
\(800\) | 3.26180 | 0.115322 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 7.34164 | 0.259242 | ||||||||
\(803\) | 58.8939 | 2.07832 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0.141988 | 0.00500442 | ||||||||
\(806\) | −0.0791554 | −0.00278813 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −7.66522 | −0.269662 | ||||||||
\(809\) | 51.9664 | 1.82704 | 0.913521 | − | 0.406791i | \(-0.133352\pi\) | ||||
0.913521 | + | 0.406791i | \(0.133352\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 0.845745 | 0.0296981 | 0.0148491 | − | 0.999890i | \(-0.495273\pi\) | ||||
0.0148491 | + | 0.999890i | \(0.495273\pi\) | |||||||
\(812\) | 14.0147 | 0.491820 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −10.8371 | −0.379839 | ||||||||
\(815\) | −33.9843 | −1.19042 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −42.0858 | −1.47240 | ||||||||
\(818\) | 5.08295 | 0.177721 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 11.8822 | 0.414943 | ||||||||
\(821\) | 7.01109 | 0.244689 | 0.122344 | − | 0.992488i | \(-0.460959\pi\) | ||||
0.122344 | + | 0.992488i | \(0.460959\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −4.80802 | −0.167597 | −0.0837984 | − | 0.996483i | \(-0.526705\pi\) | ||||
−0.0837984 | + | 0.996483i | \(0.526705\pi\) | |||||||
\(824\) | 17.1125 | 0.596144 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 1.44491 | 0.0502750 | ||||||||
\(827\) | 41.2756 | 1.43529 | 0.717646 | − | 0.696408i | \(-0.245220\pi\) | ||||
0.717646 | + | 0.696408i | \(0.245220\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −28.8000 | −1.00027 | −0.500133 | − | 0.865948i | \(-0.666716\pi\) | ||||
−0.500133 | + | 0.865948i | \(0.666716\pi\) | |||||||
\(830\) | 8.68093 | 0.301319 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0.691063 | 0.0239583 | ||||||||
\(833\) | −1.06748 | −0.0369860 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −5.04092 | −0.174448 | ||||||||
\(836\) | 52.6581 | 1.82122 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 5.37141 | 0.185552 | ||||||||
\(839\) | −33.3431 | −1.15113 | −0.575566 | − | 0.817755i | \(-0.695218\pi\) | ||||
−0.575566 | + | 0.817755i | \(0.695218\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 23.8538 | 0.822543 | ||||||||
\(842\) | −6.81430 | −0.234836 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 37.7330 | 1.29882 | ||||||||
\(845\) | 25.7746 | 0.886674 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 7.09003 | 0.243616 | ||||||||
\(848\) | −21.8688 | −0.750977 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −0.304707 | −0.0104514 | ||||||||
\(851\) | −0.678136 | −0.0232462 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 42.1899 | 1.44455 | 0.722277 | − | 0.691604i | \(-0.243096\pi\) | ||||
0.722277 | + | 0.691604i | \(0.243096\pi\) | |||||||
\(854\) | −1.26495 | −0.0432858 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −8.00829 | −0.273718 | ||||||||
\(857\) | −29.7978 | −1.01787 | −0.508937 | − | 0.860804i | \(-0.669961\pi\) | ||||
−0.508937 | + | 0.860804i | \(0.669961\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 8.99932 | 0.307053 | 0.153526 | − | 0.988145i | \(-0.450937\pi\) | ||||
0.153526 | + | 0.988145i | \(0.450937\pi\) | |||||||
\(860\) | 25.0687 | 0.854836 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 2.61751 | 0.0891529 | ||||||||
\(863\) | −7.45910 | −0.253911 | −0.126955 | − | 0.991908i | \(-0.540521\pi\) | ||||
−0.126955 | + | 0.991908i | \(0.540521\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −23.4156 | −0.796155 | ||||||||
\(866\) | 2.74752 | 0.0933646 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 5.18881 | 0.176120 | ||||||||
\(869\) | −35.2300 | −1.19510 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −0.572282 | −0.0193910 | ||||||||
\(872\) | −4.94434 | −0.167437 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −0.123532 | −0.00417854 | ||||||||
\(875\) | 12.0296 | 0.406674 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −28.5129 | −0.962812 | −0.481406 | − | 0.876498i | \(-0.659874\pi\) | ||||
−0.481406 | + | 0.876498i | \(0.659874\pi\) | |||||||
\(878\) | −9.06698 | −0.305996 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −30.1461 | −1.01623 | ||||||||
\(881\) | 38.9446 | 1.31208 | 0.656038 | − | 0.754728i | \(-0.272231\pi\) | ||||
0.656038 | + | 0.754728i | \(0.272231\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 20.3440 | 0.684631 | 0.342315 | − | 0.939585i | \(-0.388789\pi\) | ||||
0.342315 | + | 0.939585i | \(0.388789\pi\) | |||||||
\(884\) | −0.225106 | −0.00757113 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 5.68153 | 0.190875 | ||||||||
\(887\) | −2.30968 | −0.0775514 | −0.0387757 | − | 0.999248i | \(-0.512346\pi\) | ||||
−0.0387757 | + | 0.999248i | \(0.512346\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −9.01219 | −0.302259 | ||||||||
\(890\) | −5.65443 | −0.189537 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 4.96433 | 0.166218 | ||||||||
\(893\) | −71.4733 | −2.39176 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 45.8671 | 1.53317 | ||||||||
\(896\) | 7.84219 | 0.261989 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −4.95137 | −0.165229 | ||||||||
\(899\) | 19.5686 | 0.652649 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 6.53614 | 0.217750 | ||||||||
\(902\) | −3.55139 | −0.118248 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 3.56023 | 0.118412 | ||||||||
\(905\) | −26.3802 | −0.876908 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 16.2959 | 0.541095 | 0.270548 | − | 0.962707i | \(-0.412795\pi\) | ||||
0.270548 | + | 0.962707i | \(0.412795\pi\) | |||||||
\(908\) | 35.0322 | 1.16258 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −0.0583590 | −0.00193458 | ||||||||
\(911\) | 14.8774 | 0.492909 | 0.246455 | − | 0.969154i | \(-0.420734\pi\) | ||||
0.246455 | + | 0.969154i | \(0.420734\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 69.2084 | 2.29046 | ||||||||
\(914\) | −10.4317 | −0.345048 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −45.7085 | −1.51025 | ||||||||
\(917\) | −7.38926 | −0.244015 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −25.7942 | −0.850871 | −0.425435 | − | 0.904989i | \(-0.639879\pi\) | ||||
−0.425435 | + | 0.904989i | \(0.639879\pi\) | |||||||
\(920\) | 0.149924 | 0.00494286 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −9.82501 | −0.323570 | ||||||||
\(923\) | 1.26128 | 0.0415156 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −10.0637 | −0.330892 | ||||||||
\(926\) | 4.66455 | 0.153287 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 22.3332 | 0.733123 | ||||||||
\(929\) | 57.1521 | 1.87510 | 0.937550 | − | 0.347851i | \(-0.113089\pi\) | ||||
0.937550 | + | 0.347851i | \(0.113089\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −6.42242 | −0.210486 | ||||||||
\(932\) | 18.5660 | 0.608149 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −6.25889 | −0.204797 | ||||||||
\(935\) | 9.01007 | 0.294661 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −22.7694 | −0.743845 | −0.371922 | − | 0.928264i | \(-0.621301\pi\) | ||||
−0.371922 | + | 0.928264i | \(0.621301\pi\) | |||||||
\(938\) | −1.40640 | −0.0459205 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 42.5736 | 1.38860 | ||||||||
\(941\) | −5.93953 | −0.193623 | −0.0968115 | − | 0.995303i | \(-0.530864\pi\) | ||||
−0.0968115 | + | 0.995303i | \(0.530864\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −0.222231 | −0.00723682 | ||||||||
\(944\) | −19.1967 | −0.624800 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −7.49264 | −0.243607 | ||||||||
\(947\) | −8.11730 | −0.263777 | −0.131888 | − | 0.991265i | \(-0.542104\pi\) | ||||
−0.131888 | + | 0.991265i | \(0.542104\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1.51472 | −0.0491698 | ||||||||
\(950\) | −1.83325 | −0.0594784 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −1.12715 | −0.0365310 | ||||||||
\(953\) | −14.4797 | −0.469044 | −0.234522 | − | 0.972111i | \(-0.575352\pi\) | ||||
−0.234522 | + | 0.972111i | \(0.575352\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 11.2130 | 0.362846 | ||||||||
\(956\) | −19.2834 | −0.623669 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −0.209621 | −0.00677254 | ||||||||
\(959\) | −16.2358 | −0.524281 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −23.7549 | −0.766288 | ||||||||
\(962\) | 0.278723 | 0.00898638 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −3.27568 | −0.105503 | ||||||||
\(965\) | 23.8190 | 0.766760 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 29.6967 | 0.954981 | 0.477491 | − | 0.878637i | \(-0.341546\pi\) | ||||
0.477491 | + | 0.878637i | \(0.341546\pi\) | |||||||
\(968\) | 7.48632 | 0.240619 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0.940985 | 0.0302132 | ||||||||
\(971\) | −40.4986 | −1.29966 | −0.649831 | − | 0.760079i | \(-0.725160\pi\) | ||||
−0.649831 | + | 0.760079i | \(0.725160\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −7.34736 | −0.235546 | ||||||||
\(974\) | −9.50746 | −0.304639 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 16.8058 | 0.537941 | ||||||||
\(977\) | −24.0412 | −0.769145 | −0.384573 | − | 0.923095i | \(-0.625651\pi\) | ||||
−0.384573 | + | 0.923095i | \(0.625651\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −45.0797 | −1.44075 | ||||||||
\(980\) | 3.82556 | 0.122203 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −10.7918 | −0.344382 | ||||||||
\(983\) | −39.8861 | −1.27217 | −0.636085 | − | 0.771619i | \(-0.719447\pi\) | ||||
−0.636085 | + | 0.771619i | \(0.719447\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 41.9889 | 1.33788 | ||||||||
\(986\) | −2.08630 | −0.0664413 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −1.35433 | −0.0430871 | ||||||||
\(989\) | −0.468857 | −0.0149088 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −41.0288 | −1.30332 | −0.651661 | − | 0.758510i | \(-0.725928\pi\) | ||||
−0.651661 | + | 0.758510i | \(0.725928\pi\) | |||||||
\(992\) | 8.26865 | 0.262530 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 3.09963 | 0.0983144 | ||||||||
\(995\) | −9.77398 | −0.309856 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −18.0838 | −0.572721 | −0.286360 | − | 0.958122i | \(-0.592445\pi\) | ||||
−0.286360 | + | 0.958122i | \(0.592445\pi\) | |||||||
\(998\) | −1.57435 | −0.0498353 | ||||||||
\(999\) | 0 | 0 |
(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 | 5103.2.a.f.1.14 | 27 | ||
3.2 | odd | 2 | 5103.2.a.i.1.14 | 27 | |||
27.2 | odd | 18 | 189.2.v.a.85.5 | ✓ | 54 | ||
27.13 | even | 9 | 567.2.v.b.505.5 | 54 | |||
27.14 | odd | 18 | 189.2.v.a.169.5 | yes | 54 | ||
27.25 | even | 9 | 567.2.v.b.64.5 | 54 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
189.2.v.a.85.5 | ✓ | 54 | 27.2 | odd | 18 | ||
189.2.v.a.169.5 | yes | 54 | 27.14 | odd | 18 | ||
567.2.v.b.64.5 | 54 | 27.25 | even | 9 | |||
567.2.v.b.505.5 | 54 | 27.13 | even | 9 | |||
5103.2.a.f.1.14 | 27 | 1.1 | even | 1 | trivial | ||
5103.2.a.i.1.14 | 27 | 3.2 | odd | 2 |