Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8048,2,Mod(1,8048)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8048, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("8048.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8048 = 2^{4} \cdot 503 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8048.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: | \(64.2636035467\) |
Analytic rank: | \(1\) |
Dimension: | \(33\) |
Twist minimal: | no (minimal twist has level 4024) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Character | \(\chi\) | \(=\) | 8048.1 |
$q$-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 | 0 | ||||||||
\(3\) | −2.91492 | −1.68293 | −0.841464 | − | 0.540313i | \(-0.818306\pi\) | ||||
−0.841464 | + | 0.540313i | \(0.818306\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.91993 | 0.858619 | 0.429310 | − | 0.903157i | \(-0.358757\pi\) | ||||
0.429310 | + | 0.903157i | \(0.358757\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −3.81516 | −1.44200 | −0.720998 | − | 0.692937i | \(-0.756316\pi\) | ||||
−0.720998 | + | 0.692937i | \(0.756316\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 5.49674 | 1.83225 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.0492775 | 0.0148577 | 0.00742886 | − | 0.999972i | \(-0.497635\pi\) | ||||
0.00742886 | + | 0.999972i | \(0.497635\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.32659 | 0.645281 | 0.322641 | − | 0.946522i | \(-0.395429\pi\) | ||||
0.322641 | + | 0.946522i | \(0.395429\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −5.59644 | −1.44499 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −6.76001 | −1.63954 | −0.819771 | − | 0.572691i | \(-0.805900\pi\) | ||||
−0.819771 | + | 0.572691i | \(0.805900\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 8.12242 | 1.86341 | 0.931706 | − | 0.363214i | \(-0.118321\pi\) | ||||
0.931706 | + | 0.363214i | \(0.118321\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 11.1209 | 2.42678 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −6.65471 | −1.38760 | −0.693801 | − | 0.720166i | \(-0.744065\pi\) | ||||
−0.693801 | + | 0.720166i | \(0.744065\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.31387 | −0.262773 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −7.27780 | −1.40061 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 9.38336 | 1.74245 | 0.871224 | − | 0.490886i | \(-0.163327\pi\) | ||||
0.871224 | + | 0.490886i | \(0.163327\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.64599 | 0.475233 | 0.237617 | − | 0.971359i | \(-0.423634\pi\) | ||||
0.237617 | + | 0.971359i | \(0.423634\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −0.143640 | −0.0250045 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −7.32485 | −1.23813 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −0.740541 | −0.121744 | −0.0608721 | − | 0.998146i | \(-0.519388\pi\) | ||||
−0.0608721 | + | 0.998146i | \(0.519388\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −6.78183 | −1.08596 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −10.7106 | −1.67272 | −0.836358 | − | 0.548183i | \(-0.815320\pi\) | ||||
−0.836358 | + | 0.548183i | \(0.815320\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −10.8939 | −1.66131 | −0.830653 | − | 0.556790i | \(-0.812033\pi\) | ||||
−0.830653 | + | 0.556790i | \(0.812033\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 10.5534 | 1.57320 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 8.22628 | 1.19993 | 0.599963 | − | 0.800028i | \(-0.295182\pi\) | ||||
0.599963 | + | 0.800028i | \(0.295182\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 7.55546 | 1.07935 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 19.7049 | 2.75923 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 8.63256 | 1.18577 | 0.592887 | − | 0.805286i | \(-0.297988\pi\) | ||||
0.592887 | + | 0.805286i | \(0.297988\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.0946094 | 0.0127571 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −23.6762 | −3.13599 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −12.7530 | −1.66030 | −0.830151 | − | 0.557539i | \(-0.811746\pi\) | ||||
−0.830151 | + | 0.557539i | \(0.811746\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.76090 | 0.865645 | 0.432822 | − | 0.901479i | \(-0.357518\pi\) | ||||
0.432822 | + | 0.901479i | \(0.357518\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −20.9710 | −2.64209 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 4.46690 | 0.554051 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3.07357 | 0.375496 | 0.187748 | − | 0.982217i | \(-0.439881\pi\) | ||||
0.187748 | + | 0.982217i | \(0.439881\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 19.3979 | 2.33524 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 5.82993 | 0.691886 | 0.345943 | − | 0.938256i | \(-0.387559\pi\) | ||||
0.345943 | + | 0.938256i | \(0.387559\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 8.06072 | 0.943436 | 0.471718 | − | 0.881750i | \(-0.343634\pi\) | ||||
0.471718 | + | 0.881750i | \(0.343634\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 3.82981 | 0.442228 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −0.188002 | −0.0214248 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −3.75511 | −0.422482 | −0.211241 | − | 0.977434i | \(-0.567751\pi\) | ||||
−0.211241 | + | 0.977434i | \(0.567751\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 4.72395 | 0.524883 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 4.63757 | 0.509039 | 0.254520 | − | 0.967068i | \(-0.418083\pi\) | ||||
0.254520 | + | 0.967068i | \(0.418083\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −12.9787 | −1.40774 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −27.3517 | −2.93241 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 6.74306 | 0.714763 | 0.357381 | − | 0.933959i | \(-0.383670\pi\) | ||||
0.357381 | + | 0.933959i | \(0.383670\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −8.87634 | −0.930493 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −7.71283 | −0.799783 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 15.5945 | 1.59996 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −9.93673 | −1.00892 | −0.504461 | − | 0.863434i | \(-0.668309\pi\) | ||||
−0.504461 | + | 0.863434i | \(0.668309\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0.270866 | 0.0272230 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.33314 | −0.132653 | −0.0663264 | − | 0.997798i | \(-0.521128\pi\) | ||||
−0.0663264 | + | 0.997798i | \(0.521128\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 6.78884 | 0.668924 | 0.334462 | − | 0.942409i | \(-0.391445\pi\) | ||||
0.334462 | + | 0.942409i | \(0.391445\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 21.3513 | 2.08368 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 17.4430 | 1.68628 | 0.843140 | − | 0.537694i | \(-0.180705\pi\) | ||||
0.843140 | + | 0.537694i | \(0.180705\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −3.42253 | −0.327819 | −0.163910 | − | 0.986475i | \(-0.552411\pi\) | ||||
−0.163910 | + | 0.986475i | \(0.552411\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 2.15862 | 0.204887 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −15.0455 | −1.41537 | −0.707683 | − | 0.706530i | \(-0.750260\pi\) | ||||
−0.707683 | + | 0.706530i | \(0.750260\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −12.7766 | −1.19142 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 12.7887 | 1.18231 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 25.7905 | 2.36421 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.9976 | −0.999779 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 31.2205 | 2.81506 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −12.1222 | −1.08424 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.44797 | −0.128486 | −0.0642432 | − | 0.997934i | \(-0.520463\pi\) | ||||
−0.0642432 | + | 0.997934i | \(0.520463\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 31.7548 | 2.79586 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2.80644 | −0.245200 | −0.122600 | − | 0.992456i | \(-0.539123\pi\) | ||||
−0.122600 | + | 0.992456i | \(0.539123\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −30.9884 | −2.68703 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −13.9729 | −1.20259 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 13.6495 | 1.16616 | 0.583079 | − | 0.812415i | \(-0.301848\pi\) | ||||
0.583079 | + | 0.812415i | \(0.301848\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2.09368 | −0.177584 | −0.0887918 | − | 0.996050i | \(-0.528301\pi\) | ||||
−0.0887918 | + | 0.996050i | \(0.528301\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −23.9789 | −2.01939 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0.114649 | 0.00958741 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 18.0154 | 1.49610 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −22.0235 | −1.81647 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 15.0301 | 1.23131 | 0.615656 | − | 0.788015i | \(-0.288891\pi\) | ||||
0.615656 | + | 0.788015i | \(0.288891\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 21.8858 | 1.78104 | 0.890520 | − | 0.454944i | \(-0.150341\pi\) | ||||
0.890520 | + | 0.454944i | \(0.150341\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −37.1580 | −3.00405 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 5.08011 | 0.408044 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −4.55666 | −0.363661 | −0.181831 | − | 0.983330i | \(-0.558202\pi\) | ||||
−0.181831 | + | 0.983330i | \(0.558202\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −25.1632 | −1.99557 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 25.3888 | 2.00092 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −16.8610 | −1.32065 | −0.660326 | − | 0.750979i | \(-0.729582\pi\) | ||||
−0.660326 | + | 0.750979i | \(0.729582\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −0.275779 | −0.0214693 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −2.57459 | −0.199228 | −0.0996140 | − | 0.995026i | \(-0.531761\pi\) | ||||
−0.0996140 | + | 0.995026i | \(0.531761\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −7.58696 | −0.583612 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 44.6469 | 3.41423 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 3.27149 | 0.248727 | 0.124363 | − | 0.992237i | \(-0.460311\pi\) | ||||
0.124363 | + | 0.992237i | \(0.460311\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 5.01261 | 0.378918 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 37.1740 | 2.79417 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 15.3592 | 1.14800 | 0.574002 | − | 0.818854i | \(-0.305390\pi\) | ||||
0.574002 | + | 0.818854i | \(0.305390\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −16.8666 | −1.25368 | −0.626842 | − | 0.779146i | \(-0.715653\pi\) | ||||
−0.626842 | + | 0.779146i | \(0.715653\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −19.7075 | −1.45682 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −1.42179 | −0.104532 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −0.333116 | −0.0243599 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 27.7660 | 2.01968 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 2.20431 | 0.159498 | 0.0797492 | − | 0.996815i | \(-0.474588\pi\) | ||||
0.0797492 | + | 0.996815i | \(0.474588\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 7.82115 | 0.562979 | 0.281489 | − | 0.959564i | \(-0.409172\pi\) | ||||
0.281489 | + | 0.959564i | \(0.409172\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −13.0206 | −0.932428 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 7.75701 | 0.552664 | 0.276332 | − | 0.961062i | \(-0.410881\pi\) | ||||
0.276332 | + | 0.961062i | \(0.410881\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 23.1998 | 1.64459 | 0.822295 | − | 0.569062i | \(-0.192694\pi\) | ||||
0.822295 | + | 0.569062i | \(0.192694\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −8.95919 | −0.631933 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −35.7991 | −2.51260 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −20.5636 | −1.43623 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −36.5792 | −2.54243 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0.400253 | 0.0276861 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 7.11100 | 0.489542 | 0.244771 | − | 0.969581i | \(-0.421287\pi\) | ||||
0.244771 | + | 0.969581i | \(0.421287\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −16.9938 | −1.16439 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −20.9156 | −1.42643 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −10.0949 | −0.685284 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −23.4963 | −1.58773 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −15.7278 | −1.05797 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −14.9352 | −1.00013 | −0.500067 | − | 0.865987i | \(-0.666691\pi\) | ||||
−0.500067 | + | 0.865987i | \(0.666691\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −7.22198 | −0.481465 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −8.03714 | −0.533444 | −0.266722 | − | 0.963774i | \(-0.585941\pi\) | ||||
−0.266722 | + | 0.963774i | \(0.585941\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −0.403582 | −0.0266694 | −0.0133347 | − | 0.999911i | \(-0.504245\pi\) | ||||
−0.0133347 | + | 0.999911i | \(0.504245\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0.548009 | 0.0360564 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −18.7111 | −1.22581 | −0.612903 | − | 0.790158i | \(-0.709998\pi\) | ||||
−0.612903 | + | 0.790158i | \(0.709998\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 15.7939 | 1.03028 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 10.9458 | 0.711007 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −10.1106 | −0.654000 | −0.327000 | − | 0.945024i | \(-0.606038\pi\) | ||||
−0.327000 | + | 0.945024i | \(0.606038\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 7.18094 | 0.462565 | 0.231283 | − | 0.972887i | \(-0.425708\pi\) | ||||
0.231283 | + | 0.972887i | \(0.425708\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 8.06348 | 0.517272 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 14.5060 | 0.926752 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 18.8976 | 1.20242 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −13.5181 | −0.856677 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 10.0999 | 0.637500 | 0.318750 | − | 0.947839i | \(-0.396737\pi\) | ||||
0.318750 | + | 0.947839i | \(0.396737\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −0.327927 | −0.0206166 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 37.8320 | 2.36913 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 6.02742 | 0.375980 | 0.187990 | − | 0.982171i | \(-0.439803\pi\) | ||||
0.187990 | + | 0.982171i | \(0.439803\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2.82528 | 0.175555 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 51.5779 | 3.19259 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −10.2511 | −0.632109 | −0.316055 | − | 0.948741i | \(-0.602358\pi\) | ||||
−0.316055 | + | 0.948741i | \(0.602358\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 16.5739 | 1.01813 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −19.6555 | −1.20289 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −27.9144 | −1.70197 | −0.850986 | − | 0.525188i | \(-0.823995\pi\) | ||||
−0.850986 | + | 0.525188i | \(0.823995\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −31.0863 | −1.88836 | −0.944180 | − | 0.329430i | \(-0.893143\pi\) | ||||
−0.944180 | + | 0.329430i | \(0.893143\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 25.8738 | 1.56595 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −0.0647440 | −0.00390421 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −19.9609 | −1.19933 | −0.599667 | − | 0.800250i | \(-0.704700\pi\) | ||||
−0.599667 | + | 0.800250i | \(0.704700\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 14.5443 | 0.870745 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 19.7244 | 1.17666 | 0.588329 | − | 0.808621i | \(-0.299786\pi\) | ||||
0.588329 | + | 0.808621i | \(0.299786\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −12.8936 | −0.766447 | −0.383223 | − | 0.923656i | \(-0.625186\pi\) | ||||
−0.383223 | + | 0.923656i | \(0.625186\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −45.4566 | −2.69262 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 40.8627 | 2.41205 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 28.6977 | 1.68810 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 28.9648 | 1.69794 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 22.5403 | 1.31682 | 0.658411 | − | 0.752659i | \(-0.271229\pi\) | ||||
0.658411 | + | 0.752659i | \(0.271229\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −24.4849 | −1.42557 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −0.358632 | −0.0208099 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −15.4828 | −0.895394 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 41.5620 | 2.39560 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 3.88601 | 0.223245 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 12.9805 | 0.743259 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 23.9314 | 1.36584 | 0.682918 | − | 0.730495i | \(-0.260710\pi\) | ||||
0.682918 | + | 0.730495i | \(0.260710\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −19.7889 | −1.12575 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −1.33343 | −0.0756120 | −0.0378060 | − | 0.999285i | \(-0.512037\pi\) | ||||
−0.0378060 | + | 0.999285i | \(0.512037\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −29.3797 | −1.66064 | −0.830318 | − | 0.557289i | \(-0.811841\pi\) | ||||
−0.830318 | + | 0.557289i | \(0.811841\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −40.2628 | −2.26855 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −4.85921 | −0.272921 | −0.136460 | − | 0.990646i | \(-0.543573\pi\) | ||||
−0.136460 | + | 0.990646i | \(0.543573\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0.462389 | 0.0258888 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −50.8449 | −2.83789 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −54.9076 | −3.05514 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −3.05683 | −0.169562 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 9.97640 | 0.551696 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −31.3846 | −1.73029 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 14.7431 | 0.810357 | 0.405178 | − | 0.914238i | \(-0.367209\pi\) | ||||
0.405178 | + | 0.914238i | \(0.367209\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −4.07056 | −0.223066 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 5.90104 | 0.322408 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 8.27405 | 0.450716 | 0.225358 | − | 0.974276i | \(-0.427645\pi\) | ||||
0.225358 | + | 0.974276i | \(0.427645\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 43.8565 | 2.38196 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0.130388 | 0.00706088 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −2.11917 | −0.114424 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 37.2427 | 2.00508 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −19.5548 | −1.04976 | −0.524879 | − | 0.851177i | \(-0.675889\pi\) | ||||
−0.524879 | + | 0.851177i | \(0.675889\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −35.6012 | −1.90569 | −0.952843 | − | 0.303464i | \(-0.901857\pi\) | ||||
−0.952843 | + | 0.303464i | \(0.901857\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −16.9325 | −0.903789 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −15.9871 | −0.850910 | −0.425455 | − | 0.904980i | \(-0.639886\pi\) | ||||
−0.425455 | + | 0.904980i | \(0.639886\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 11.1931 | 0.594066 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −75.1772 | −3.97880 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −20.6664 | −1.09073 | −0.545366 | − | 0.838198i | \(-0.683609\pi\) | ||||
−0.545366 | + | 0.838198i | \(0.683609\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 46.9737 | 2.47230 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 32.0570 | 1.68256 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 15.4760 | 0.810052 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 5.83969 | 0.304829 | 0.152415 | − | 0.988317i | \(-0.451295\pi\) | ||||
0.152415 | + | 0.988317i | \(0.451295\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −58.8735 | −3.06483 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −32.9346 | −1.70988 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −10.3104 | −0.533853 | −0.266927 | − | 0.963717i | \(-0.586008\pi\) | ||||
−0.266927 | + | 0.963717i | \(0.586008\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 35.3352 | 1.82470 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 21.8313 | 1.12437 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1.97374 | −0.101384 | −0.0506921 | − | 0.998714i | \(-0.516143\pi\) | ||||
−0.0506921 | + | 0.998714i | \(0.516143\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 4.22071 | 0.216233 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 34.7397 | 1.77512 | 0.887559 | − | 0.460695i | \(-0.152400\pi\) | ||||
0.887559 | + | 0.460695i | \(0.152400\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −0.360950 | −0.0183957 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −59.8810 | −3.04392 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 7.51098 | 0.380822 | 0.190411 | − | 0.981704i | \(-0.439018\pi\) | ||||
0.190411 | + | 0.981704i | \(0.439018\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 44.9859 | 2.27503 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 8.18054 | 0.412654 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −7.20954 | −0.362751 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 2.80451 | 0.140754 | 0.0703771 | − | 0.997520i | \(-0.477580\pi\) | ||||
0.0703771 | + | 0.997520i | \(0.477580\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 90.3285 | 4.52208 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −13.7828 | −0.688278 | −0.344139 | − | 0.938919i | \(-0.611829\pi\) | ||||
−0.344139 | + | 0.938919i | \(0.611829\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 6.15614 | 0.306659 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 9.06965 | 0.450674 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −0.0364920 | −0.00180884 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −14.7252 | −0.728112 | −0.364056 | − | 0.931377i | \(-0.618608\pi\) | ||||
−0.364056 | + | 0.931377i | \(0.618608\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −39.7873 | −1.96256 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 48.6548 | 2.39415 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 8.90381 | 0.437071 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 6.10290 | 0.298860 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −16.4707 | −0.804649 | −0.402324 | − | 0.915497i | \(-0.631798\pi\) | ||||
−0.402324 | + | 0.915497i | \(0.631798\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2.08683 | −0.101706 | −0.0508528 | − | 0.998706i | \(-0.516194\pi\) | ||||
−0.0508528 | + | 0.998706i | \(0.516194\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 45.2177 | 2.19856 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 8.88174 | 0.430828 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −25.7939 | −1.24826 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −0.334192 | −0.0161349 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −33.9574 | −1.63567 | −0.817834 | − | 0.575454i | \(-0.804825\pi\) | ||||
−0.817834 | + | 0.575454i | \(0.804825\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −12.2573 | −0.589048 | −0.294524 | − | 0.955644i | \(-0.595161\pi\) | ||||
−0.294524 | + | 0.955644i | \(0.595161\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −52.5134 | −2.51783 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −54.0524 | −2.58567 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −4.67197 | −0.222981 | −0.111490 | − | 0.993766i | \(-0.535562\pi\) | ||||
−0.111490 | + | 0.993766i | \(0.535562\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 41.5304 | 1.97764 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −1.83465 | −0.0871670 | −0.0435835 | − | 0.999050i | \(-0.513877\pi\) | ||||
−0.0435835 | + | 0.999050i | \(0.513877\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 12.9462 | 0.613709 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −43.8114 | −2.07221 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −26.5909 | −1.25490 | −0.627452 | − | 0.778656i | \(-0.715902\pi\) | ||||
−0.627452 | + | 0.778656i | \(0.715902\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −0.527792 | −0.0248528 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −63.7953 | −2.99736 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −17.0420 | −0.798939 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −3.41740 | −0.159859 | −0.0799296 | − | 0.996801i | \(-0.525470\pi\) | ||||
−0.0799296 | + | 0.996801i | \(0.525470\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 49.1980 | 2.29636 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 14.1968 | 0.661213 | 0.330607 | − | 0.943769i | \(-0.392747\pi\) | ||||
0.330607 | + | 0.943769i | \(0.392747\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −40.8064 | −1.89643 | −0.948217 | − | 0.317623i | \(-0.897115\pi\) | ||||
−0.948217 | + | 0.317623i | \(0.897115\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −14.8081 | −0.686709 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −9.42953 | −0.436346 | −0.218173 | − | 0.975910i | \(-0.570010\pi\) | ||||
−0.218173 | + | 0.975910i | \(0.570010\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −11.7262 | −0.541464 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 13.2823 | 0.612015 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −0.536825 | −0.0246832 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −10.6718 | −0.489654 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 47.4510 | 2.17263 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −31.6403 | −1.44568 | −0.722842 | − | 0.691014i | \(-0.757164\pi\) | ||||
−0.722842 | + | 0.691014i | \(0.757164\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.72294 | −0.0785593 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −74.0062 | −3.36740 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −19.0778 | −0.866280 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −13.9987 | −0.634339 | −0.317170 | − | 0.948369i | \(-0.602732\pi\) | ||||
−0.317170 | + | 0.948369i | \(0.602732\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 49.1483 | 2.22256 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −19.8085 | −0.893944 | −0.446972 | − | 0.894548i | \(-0.647498\pi\) | ||||
−0.446972 | + | 0.894548i | \(0.647498\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −63.4316 | −2.85682 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0.520043 | 0.0233742 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −22.2421 | −0.997696 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −12.2517 | −0.548459 | −0.274230 | − | 0.961664i | \(-0.588423\pi\) | ||||
−0.274230 | + | 0.961664i | \(0.588423\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 7.50473 | 0.335286 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −1.00000 | −0.0445878 | ||||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −2.55955 | −0.113898 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 22.1154 | 0.982177 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 26.7007 | 1.18349 | 0.591744 | − | 0.806126i | \(-0.298440\pi\) | ||||
0.591744 | + | 0.806126i | \(0.298440\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −30.7529 | −1.36043 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −59.1133 | −2.60992 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 13.0341 | 0.574351 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0.405370 | 0.0178282 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −9.53613 | −0.418590 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 19.1798 | 0.840283 | 0.420141 | − | 0.907459i | \(-0.361980\pi\) | ||||
0.420141 | + | 0.907459i | \(0.361980\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 0.290547 | 0.0127047 | 0.00635236 | − | 0.999980i | \(-0.497978\pi\) | ||||
0.00635236 | + | 0.999980i | \(0.497978\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −14.6113 | −0.637691 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −17.8869 | −0.779165 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 21.2852 | 0.925441 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −70.1000 | −3.04208 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −24.9193 | −1.07937 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 33.4894 | 1.44787 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −44.7709 | −1.93201 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0.372314 | 0.0160367 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −18.5726 | −0.798497 | −0.399249 | − | 0.916843i | \(-0.630729\pi\) | ||||
−0.399249 | + | 0.916843i | \(0.630729\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 49.1647 | 2.10986 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −6.57103 | −0.281472 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 15.5449 | 0.664650 | 0.332325 | − | 0.943165i | \(-0.392167\pi\) | ||||
0.332325 | + | 0.943165i | \(0.392167\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 37.1629 | 1.58608 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 76.2157 | 3.24690 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 14.3263 | 0.609218 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 4.14439 | 0.175920 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −34.0341 | −1.44207 | −0.721036 | − | 0.692897i | \(-0.756334\pi\) | ||||
−0.721036 | + | 0.692897i | \(0.756334\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −25.3457 | −1.07201 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0.971006 | 0.0409959 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −29.3438 | −1.23669 | −0.618346 | − | 0.785906i | \(-0.712197\pi\) | ||||
−0.618346 | + | 0.785906i | \(0.712197\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −28.8864 | −1.21526 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −18.0226 | −0.756879 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −37.6423 | −1.57805 | −0.789025 | − | 0.614362i | \(-0.789414\pi\) | ||||
−0.789025 | + | 0.614362i | \(0.789414\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −30.6908 | −1.28437 | −0.642185 | − | 0.766550i | \(-0.721972\pi\) | ||||
−0.642185 | + | 0.766550i | \(0.721972\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −6.42538 | −0.268424 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 8.74339 | 0.364625 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −18.5886 | −0.773853 | −0.386927 | − | 0.922111i | \(-0.626463\pi\) | ||||
−0.386927 | + | 0.922111i | \(0.626463\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −22.7980 | −0.947453 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −17.6931 | −0.734033 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0.425391 | 0.0176179 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 24.5534 | 1.01516 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −25.5566 | −1.05484 | −0.527418 | − | 0.849606i | \(-0.676840\pi\) | ||||
−0.527418 | + | 0.849606i | \(0.676840\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 21.4918 | 0.885555 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −22.6110 | −0.930094 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −5.02195 | −0.206227 | −0.103113 | − | 0.994670i | \(-0.532880\pi\) | ||||
−0.103113 | + | 0.994670i | \(0.532880\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 49.5160 | 2.02996 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −67.6255 | −2.76773 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 28.8801 | 1.18001 | 0.590004 | − | 0.807400i | \(-0.299126\pi\) | ||||
0.590004 | + | 0.807400i | \(0.299126\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −33.3107 | −1.35877 | −0.679386 | − | 0.733781i | \(-0.737754\pi\) | ||||
−0.679386 | + | 0.733781i | \(0.737754\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 16.8946 | 0.688002 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −21.1146 | −0.858430 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −33.7256 | −1.36888 | −0.684441 | − | 0.729069i | \(-0.739954\pi\) | ||||
−0.684441 | + | 0.729069i | \(0.739954\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 104.351 | 4.22853 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 19.1392 | 0.774290 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −31.6932 | −1.28008 | −0.640039 | − | 0.768343i | \(-0.721082\pi\) | ||||
−0.640039 | + | 0.768343i | \(0.721082\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 59.9413 | 2.41707 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 38.7409 | 1.55965 | 0.779824 | − | 0.625998i | \(-0.215308\pi\) | ||||
0.779824 | + | 0.625998i | \(0.215308\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 24.8896 | 1.00040 | 0.500200 | − | 0.865910i | \(-0.333260\pi\) | ||||
0.500200 | + | 0.865910i | \(0.333260\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 48.4316 | 1.94349 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −25.7259 | −1.03068 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −16.7044 | −0.668177 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −1.16670 | −0.0465936 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 5.00606 | 0.199605 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −17.8569 | −0.710871 | −0.355435 | − | 0.934701i | \(-0.615667\pi\) | ||||
−0.355435 | + | 0.934701i | \(0.615667\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −20.7280 | −0.823863 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −2.78000 | −0.110321 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 17.5785 | 0.696485 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 32.0456 | 1.26771 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −41.5304 | −1.64035 | −0.820177 | − | 0.572110i | \(-0.806125\pi\) | ||||
−0.820177 | + | 0.572110i | \(0.806125\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −10.8973 | −0.429748 | −0.214874 | − | 0.976642i | \(-0.568934\pi\) | ||||
−0.214874 | + | 0.976642i | \(0.568934\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 60.9671 | 2.40058 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −8.49716 | −0.334058 | −0.167029 | − | 0.985952i | \(-0.553417\pi\) | ||||
−0.167029 | + | 0.985952i | \(0.553417\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −0.628437 | −0.0246683 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 29.4257 | 1.15328 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 26.2695 | 1.02801 | 0.514003 | − | 0.857789i | \(-0.328162\pi\) | ||||
0.514003 | + | 0.857789i | \(0.328162\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −5.38817 | −0.210533 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 44.3077 | 1.72861 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −0.748762 | −0.0291676 | −0.0145838 | − | 0.999894i | \(-0.504642\pi\) | ||||
−0.0145838 | + | 0.999894i | \(0.504642\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 6.21166 | 0.241606 | 0.120803 | − | 0.992677i | \(-0.461453\pi\) | ||||
0.120803 | + | 0.992677i | \(0.461453\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 45.8452 | 1.78048 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −59.4955 | −2.30714 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −62.4436 | −2.41782 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 43.5348 | 1.68315 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0.333160 | 0.0128615 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 30.2232 | 1.16502 | 0.582510 | − | 0.812823i | \(-0.302071\pi\) | ||||
0.582510 | + | 0.812823i | \(0.302071\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 9.56204 | 0.368043 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −0.0861188 | −0.00330982 | −0.00165491 | − | 0.999999i | \(-0.500527\pi\) | ||||
−0.00165491 | + | 0.999999i | \(0.500527\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 37.9102 | 1.45486 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 23.4276 | 0.897747 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −21.0287 | −0.804640 | −0.402320 | − | 0.915499i | \(-0.631796\pi\) | ||||
−0.402320 | + | 0.915499i | \(0.631796\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 26.2062 | 1.00129 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 1.17641 | 0.0448827 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 20.0845 | 0.765157 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 27.1755 | 1.03380 | 0.516902 | − | 0.856045i | \(-0.327085\pi\) | ||||
0.516902 | + | 0.856045i | \(0.327085\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −1.03340 | −0.0392555 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −4.01972 | −0.152477 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 72.4038 | 2.74249 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 54.5413 | 2.06294 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −6.85723 | −0.258994 | −0.129497 | − | 0.991580i | \(-0.541336\pi\) | ||||
−0.129497 | + | 0.991580i | \(0.541336\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −6.01499 | −0.226860 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −46.0379 | −1.73389 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 5.08616 | 0.191285 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 8.04815 | 0.302254 | 0.151127 | − | 0.988514i | \(-0.451710\pi\) | ||||
0.151127 | + | 0.988514i | \(0.451710\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −20.6408 | −0.774092 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −17.6083 | −0.659435 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0.220118 | 0.00823194 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 29.4715 | 1.10064 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 8.57264 | 0.319705 | 0.159853 | − | 0.987141i | \(-0.448898\pi\) | ||||
0.159853 | + | 0.987141i | \(0.448898\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −25.9005 | −0.964586 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −20.9318 | −0.778464 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −12.3285 | −0.457868 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 20.6702 | 0.766617 | 0.383308 | − | 0.923620i | \(-0.374785\pi\) | ||||
0.383308 | + | 0.923620i | \(0.374785\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −37.6762 | −1.39541 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 73.6429 | 2.72378 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 21.4859 | 0.793600 | 0.396800 | − | 0.917905i | \(-0.370121\pi\) | ||||
0.396800 | + | 0.917905i | \(0.370121\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −42.2837 | −1.55966 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 0.151458 | 0.00557902 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 36.4769 | 1.34182 | 0.670912 | − | 0.741537i | \(-0.265903\pi\) | ||||
0.670912 | + | 0.741537i | \(0.265903\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −55.0849 | −2.02359 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −24.7307 | −0.907282 | −0.453641 | − | 0.891185i | \(-0.649875\pi\) | ||||
−0.453641 | + | 0.891185i | \(0.649875\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 28.8567 | 1.05723 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 25.4915 | 0.932686 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −66.5479 | −2.43161 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −38.4930 | −1.40463 | −0.702315 | − | 0.711867i | \(-0.747850\pi\) | ||||
−0.702315 | + | 0.711867i | \(0.747850\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −29.4404 | −1.07287 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 42.0192 | 1.52924 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 0.613093 | 0.0222832 | 0.0111416 | − | 0.999938i | \(-0.496453\pi\) | ||||
0.0111416 | + | 0.999938i | \(0.496453\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0.955881 | 0.0346963 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −49.4532 | −1.79268 | −0.896338 | − | 0.443372i | \(-0.853782\pi\) | ||||
−0.896338 | + | 0.443372i | \(0.853782\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 13.0575 | 0.472714 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −71.3408 | −2.57933 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −29.6711 | −1.07136 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −38.3625 | −1.38339 | −0.691694 | − | 0.722190i | \(-0.743135\pi\) | ||||
−0.691694 | + | 0.722190i | \(0.743135\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −17.5694 | −0.632747 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 13.0048 | 0.467749 | 0.233875 | − | 0.972267i | \(-0.424859\pi\) | ||||
0.233875 | + | 0.972267i | \(0.424859\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −3.47647 | −0.124878 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −8.23547 | −0.295446 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −86.9961 | −3.11696 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0.287285 | 0.0102798 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −68.2902 | −2.44049 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −8.74847 | −0.312246 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −39.9722 | −1.42486 | −0.712428 | − | 0.701745i | \(-0.752404\pi\) | ||||
−0.712428 | + | 0.701745i | \(0.752404\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 29.8811 | 1.06379 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 57.4012 | 2.04095 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 15.7299 | 0.558584 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −48.3116 | −1.71344 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −0.903441 | −0.0320015 | −0.0160008 | − | 0.999872i | \(-0.505093\pi\) | ||||
−0.0160008 | + | 0.999872i | \(0.505093\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −55.6097 | −1.96733 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 37.0649 | 1.30962 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0.397212 | 0.0140173 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 48.7447 | 1.71803 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 81.3682 | 2.86430 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −12.8707 | −0.452510 | −0.226255 | − | 0.974068i | \(-0.572648\pi\) | ||||
−0.226255 | + | 0.974068i | \(0.572648\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −34.8684 | −1.22440 | −0.612198 | − | 0.790705i | \(-0.709714\pi\) | ||||
−0.612198 | + | 0.790705i | \(0.709714\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 90.6141 | 3.17797 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −32.3719 | −1.13394 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −88.4850 | −3.09570 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −48.7909 | −1.70489 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 38.5797 | 1.34644 | 0.673220 | − | 0.739443i | \(-0.264911\pi\) | ||||
0.673220 | + | 0.739443i | \(0.264911\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −10.5735 | −0.368571 | −0.184285 | − | 0.982873i | \(-0.558997\pi\) | ||||
−0.184285 | + | 0.982873i | \(0.558997\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0.188723 | 0.00657050 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 42.6187 | 1.48200 | 0.740998 | − | 0.671507i | \(-0.234353\pi\) | ||||
0.740998 | + | 0.671507i | \(0.234353\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 15.1668 | 0.526766 | 0.263383 | − | 0.964691i | \(-0.415162\pi\) | ||||
0.263383 | + | 0.964691i | \(0.415162\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 58.1844 | 2.01839 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −51.0750 | −1.76964 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −4.94304 | −0.171061 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −19.2569 | −0.665617 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −31.3287 | −1.08159 | −0.540793 | − | 0.841156i | \(-0.681876\pi\) | ||||
−0.540793 | + | 0.841156i | \(0.681876\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 59.0475 | 2.03612 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −57.4950 | −1.98023 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −14.5664 | −0.501101 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 41.9575 | 1.44168 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 37.5839 | 1.28988 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 4.92809 | 0.168933 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 33.3531 | 1.14199 | 0.570993 | − | 0.820955i | \(-0.306558\pi\) | ||||
0.570993 | + | 0.820955i | \(0.306558\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 85.7189 | 2.93152 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 31.9922 | 1.09283 | 0.546417 | − | 0.837513i | \(-0.315991\pi\) | ||||
0.546417 | + | 0.837513i | \(0.315991\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −5.83878 | −0.199217 | −0.0996083 | − | 0.995027i | \(-0.531759\pi\) | ||||
−0.0996083 | + | 0.995027i | \(0.531759\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −119.111 | −4.05931 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −39.9498 | −1.35991 | −0.679953 | − | 0.733256i | \(-0.738000\pi\) | ||||
−0.679953 | + | 0.733256i | \(0.738000\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 6.28104 | 0.213562 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −83.6514 | −2.84095 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −0.185042 | −0.00627713 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 7.15095 | 0.242301 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −54.6197 | −1.84860 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 46.2481 | 1.56347 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 25.4088 | 0.857993 | 0.428997 | − | 0.903306i | \(-0.358867\pi\) | ||||
0.428997 | + | 0.903306i | \(0.358867\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −65.7033 | −2.21612 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −54.3860 | −1.83231 | −0.916155 | − | 0.400825i | \(-0.868724\pi\) | ||||
−0.916155 | + | 0.400825i | \(0.868724\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −3.88025 | −0.130581 | −0.0652905 | − | 0.997866i | \(-0.520797\pi\) | ||||
−0.0652905 | + | 0.997866i | \(0.520797\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 71.3715 | 2.39913 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −45.1782 | −1.51693 | −0.758467 | − | 0.651711i | \(-0.774051\pi\) | ||||
−0.758467 | + | 0.651711i | \(0.774051\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 5.52423 | 0.185277 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0.232784 | 0.00779856 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 66.8173 | 2.23596 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 29.4887 | 0.985698 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 45.1311 | 1.50688 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 24.8283 | 0.828069 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −58.3562 | −1.94413 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −121.150 | −4.03162 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −32.3827 | −1.07644 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 45.3498 | 1.50582 | 0.752908 | − | 0.658126i | \(-0.228650\pi\) | ||||
0.752908 | + | 0.658126i | \(0.228650\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −7.32795 | −0.243053 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 34.3520 | 1.13813 | 0.569066 | − | 0.822292i | \(-0.307305\pi\) | ||||
0.569066 | + | 0.822292i | \(0.307305\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0.228528 | 0.00756317 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −37.8370 | −1.25085 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 10.7070 | 0.353577 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 6.66121 | 0.219733 | 0.109866 | − | 0.993946i | \(-0.464958\pi\) | ||||
0.109866 | + | 0.993946i | \(0.464958\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −69.7580 | −2.29860 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 13.5639 | 0.446461 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0.972971 | 0.0319911 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 37.3165 | 1.22563 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 26.0988 | 0.856275 | 0.428138 | − | 0.903713i | \(-0.359170\pi\) | ||||
0.428138 | + | 0.903713i | \(0.359170\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 61.3686 | 2.01128 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 3.88685 | 0.127250 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −0.639560 | −0.0209159 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 24.4264 | 0.797975 | 0.398987 | − | 0.916956i | \(-0.369362\pi\) | ||||
0.398987 | + | 0.916956i | \(0.369362\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 85.6393 | 2.79473 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 33.8986 | 1.10506 | 0.552532 | − | 0.833492i | \(-0.313662\pi\) | ||||
0.552532 | + | 0.833492i | \(0.313662\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 71.2760 | 2.32107 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 53.3087 | 1.73413 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 28.1887 | 0.916010 | 0.458005 | − | 0.888950i | \(-0.348564\pi\) | ||||
0.458005 | + | 0.888950i | \(0.348564\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 18.7540 | 0.608781 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 14.1642 | 0.459306 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −21.3674 | −0.692157 | −0.346079 | − | 0.938206i | \(-0.612487\pi\) | ||||
−0.346079 | + | 0.938206i | \(0.612487\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 4.23212 | 0.136948 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −1.34782 | −0.0435690 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −52.0752 | −1.68160 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −23.9988 | −0.774153 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 95.8797 | 3.08968 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 15.0161 | 0.483385 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −51.7347 | −1.66367 | −0.831837 | − | 0.555020i | \(-0.812711\pi\) | ||||
−0.831837 | + | 0.555020i | \(0.812711\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 160.051 | 5.14159 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −4.78933 | −0.153697 | −0.0768484 | − | 0.997043i | \(-0.524486\pi\) | ||||
−0.0768484 | + | 0.997043i | \(0.524486\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 7.98773 | 0.256075 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 8.91041 | 0.285362 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 53.9391 | 1.72566 | 0.862832 | − | 0.505491i | \(-0.168689\pi\) | ||||
0.862832 | + | 0.505491i | \(0.168689\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0.332281 | 0.0106198 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −18.8128 | −0.600646 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −17.4039 | −0.555098 | −0.277549 | − | 0.960712i | \(-0.589522\pi\) | ||||
−0.277549 | + | 0.960712i | \(0.589522\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 14.8929 | 0.474528 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 91.4834 | 2.91195 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 72.4958 | 2.30523 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 44.5225 | 1.41430 | 0.707152 | − | 0.707062i | \(-0.249980\pi\) | ||||
0.707152 | + | 0.707062i | \(0.249980\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −42.9751 | −1.36377 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 44.5420 | 1.41208 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −39.2457 | −1.24292 | −0.621462 | − | 0.783444i | \(-0.713461\pi\) | ||||
−0.621462 | + | 0.783444i | \(0.713461\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 5.38951 | 0.170516 |
(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 | 8048.2.a.x.1.4 | 33 | ||
4.3 | odd | 2 | 4024.2.a.g.1.30 | ✓ | 33 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4024.2.a.g.1.30 | ✓ | 33 | 4.3 | odd | 2 | ||
8048.2.a.x.1.4 | 33 | 1.1 | even | 1 | trivial |