Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4007,2,Mod(1,4007)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4007, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4007.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4007 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4007.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: | \(31.9960560899\) |
Analytic rank: | \(1\) |
Dimension: | \(139\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.10 | ||
Character | \(\chi\) | \(=\) | 4007.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.51027 | −1.77503 | −0.887514 | − | 0.460781i | \(-0.847569\pi\) | ||||
−0.887514 | + | 0.460781i | \(0.847569\pi\) | |||||||
\(3\) | −1.47560 | −0.851937 | −0.425968 | − | 0.904738i | \(-0.640067\pi\) | ||||
−0.425968 | + | 0.904738i | \(0.640067\pi\) | |||||||
\(4\) | 4.30145 | 2.15072 | ||||||||
\(5\) | −0.0269498 | −0.0120523 | −0.00602616 | − | 0.999982i | \(-0.501918\pi\) | ||||
−0.00602616 | + | 0.999982i | \(0.501918\pi\) | |||||||
\(6\) | 3.70415 | 1.51221 | ||||||||
\(7\) | 2.66833 | 1.00853 | 0.504267 | − | 0.863548i | \(-0.331763\pi\) | ||||
0.504267 | + | 0.863548i | \(0.331763\pi\) | |||||||
\(8\) | −5.77725 | −2.04256 | ||||||||
\(9\) | −0.822611 | −0.274204 | ||||||||
\(10\) | 0.0676513 | 0.0213932 | ||||||||
\(11\) | −2.54459 | −0.767222 | −0.383611 | − | 0.923495i | \(-0.625320\pi\) | ||||
−0.383611 | + | 0.923495i | \(0.625320\pi\) | |||||||
\(12\) | −6.34720 | −1.83228 | ||||||||
\(13\) | −4.66719 | −1.29445 | −0.647223 | − | 0.762301i | \(-0.724070\pi\) | ||||
−0.647223 | + | 0.762301i | \(0.724070\pi\) | |||||||
\(14\) | −6.69822 | −1.79018 | ||||||||
\(15\) | 0.0397671 | 0.0102678 | ||||||||
\(16\) | 5.89954 | 1.47489 | ||||||||
\(17\) | 5.31669 | 1.28949 | 0.644744 | − | 0.764399i | \(-0.276964\pi\) | ||||
0.644744 | + | 0.764399i | \(0.276964\pi\) | |||||||
\(18\) | 2.06498 | 0.486719 | ||||||||
\(19\) | −3.22201 | −0.739181 | −0.369590 | − | 0.929195i | \(-0.620502\pi\) | ||||
−0.369590 | + | 0.929195i | \(0.620502\pi\) | |||||||
\(20\) | −0.115923 | −0.0259212 | ||||||||
\(21\) | −3.93738 | −0.859207 | ||||||||
\(22\) | 6.38759 | 1.36184 | ||||||||
\(23\) | −1.00526 | −0.209612 | −0.104806 | − | 0.994493i | \(-0.533422\pi\) | ||||
−0.104806 | + | 0.994493i | \(0.533422\pi\) | |||||||
\(24\) | 8.52489 | 1.74014 | ||||||||
\(25\) | −4.99927 | −0.999855 | ||||||||
\(26\) | 11.7159 | 2.29768 | ||||||||
\(27\) | 5.64064 | 1.08554 | ||||||||
\(28\) | 11.4777 | 2.16908 | ||||||||
\(29\) | 6.05354 | 1.12411 | 0.562057 | − | 0.827098i | \(-0.310010\pi\) | ||||
0.562057 | + | 0.827098i | \(0.310010\pi\) | |||||||
\(30\) | −0.0998261 | −0.0182257 | ||||||||
\(31\) | 7.05805 | 1.26766 | 0.633831 | − | 0.773471i | \(-0.281481\pi\) | ||||
0.633831 | + | 0.773471i | \(0.281481\pi\) | |||||||
\(32\) | −3.25494 | −0.575398 | ||||||||
\(33\) | 3.75479 | 0.653624 | ||||||||
\(34\) | −13.3463 | −2.28888 | ||||||||
\(35\) | −0.0719110 | −0.0121552 | ||||||||
\(36\) | −3.53842 | −0.589736 | ||||||||
\(37\) | −1.01221 | −0.166407 | −0.0832034 | − | 0.996533i | \(-0.526515\pi\) | ||||
−0.0832034 | + | 0.996533i | \(0.526515\pi\) | |||||||
\(38\) | 8.08812 | 1.31207 | ||||||||
\(39\) | 6.88690 | 1.10279 | ||||||||
\(40\) | 0.155696 | 0.0246177 | ||||||||
\(41\) | 5.65268 | 0.882800 | 0.441400 | − | 0.897310i | \(-0.354482\pi\) | ||||
0.441400 | + | 0.897310i | \(0.354482\pi\) | |||||||
\(42\) | 9.88388 | 1.52512 | ||||||||
\(43\) | −2.44526 | −0.372899 | −0.186450 | − | 0.982465i | \(-0.559698\pi\) | ||||
−0.186450 | + | 0.982465i | \(0.559698\pi\) | |||||||
\(44\) | −10.9454 | −1.65008 | ||||||||
\(45\) | 0.0221692 | 0.00330479 | ||||||||
\(46\) | 2.52348 | 0.372067 | ||||||||
\(47\) | −10.0099 | −1.46009 | −0.730044 | − | 0.683401i | \(-0.760500\pi\) | ||||
−0.730044 | + | 0.683401i | \(0.760500\pi\) | |||||||
\(48\) | −8.70535 | −1.25651 | ||||||||
\(49\) | 0.119985 | 0.0171407 | ||||||||
\(50\) | 12.5495 | 1.77477 | ||||||||
\(51\) | −7.84530 | −1.09856 | ||||||||
\(52\) | −20.0757 | −2.78400 | ||||||||
\(53\) | 9.53728 | 1.31005 | 0.655023 | − | 0.755609i | \(-0.272659\pi\) | ||||
0.655023 | + | 0.755609i | \(0.272659\pi\) | |||||||
\(54\) | −14.1595 | −1.92687 | ||||||||
\(55\) | 0.0685762 | 0.00924681 | ||||||||
\(56\) | −15.4156 | −2.06000 | ||||||||
\(57\) | 4.75440 | 0.629735 | ||||||||
\(58\) | −15.1960 | −1.99533 | ||||||||
\(59\) | 7.79484 | 1.01480 | 0.507401 | − | 0.861710i | \(-0.330606\pi\) | ||||
0.507401 | + | 0.861710i | \(0.330606\pi\) | |||||||
\(60\) | 0.171056 | 0.0220832 | ||||||||
\(61\) | 0.720735 | 0.0922807 | 0.0461403 | − | 0.998935i | \(-0.485308\pi\) | ||||
0.0461403 | + | 0.998935i | \(0.485308\pi\) | |||||||
\(62\) | −17.7176 | −2.25014 | ||||||||
\(63\) | −2.19500 | −0.276544 | ||||||||
\(64\) | −3.62830 | −0.453538 | ||||||||
\(65\) | 0.125780 | 0.0156011 | ||||||||
\(66\) | −9.42552 | −1.16020 | ||||||||
\(67\) | 5.95035 | 0.726951 | 0.363475 | − | 0.931604i | \(-0.381590\pi\) | ||||
0.363475 | + | 0.931604i | \(0.381590\pi\) | |||||||
\(68\) | 22.8695 | 2.77333 | ||||||||
\(69\) | 1.48336 | 0.178576 | ||||||||
\(70\) | 0.180516 | 0.0215758 | ||||||||
\(71\) | −5.50883 | −0.653778 | −0.326889 | − | 0.945063i | \(-0.606000\pi\) | ||||
−0.326889 | + | 0.945063i | \(0.606000\pi\) | |||||||
\(72\) | 4.75243 | 0.560079 | ||||||||
\(73\) | −10.4037 | −1.21766 | −0.608829 | − | 0.793301i | \(-0.708360\pi\) | ||||
−0.608829 | + | 0.793301i | \(0.708360\pi\) | |||||||
\(74\) | 2.54093 | 0.295377 | ||||||||
\(75\) | 7.37692 | 0.851813 | ||||||||
\(76\) | −13.8593 | −1.58977 | ||||||||
\(77\) | −6.78980 | −0.773769 | ||||||||
\(78\) | −17.2880 | −1.95748 | ||||||||
\(79\) | −8.50548 | −0.956942 | −0.478471 | − | 0.878103i | \(-0.658809\pi\) | ||||
−0.478471 | + | 0.878103i | \(0.658809\pi\) | |||||||
\(80\) | −0.158992 | −0.0177758 | ||||||||
\(81\) | −5.85548 | −0.650608 | ||||||||
\(82\) | −14.1897 | −1.56699 | ||||||||
\(83\) | 11.2651 | 1.23651 | 0.618253 | − | 0.785979i | \(-0.287841\pi\) | ||||
0.618253 | + | 0.785979i | \(0.287841\pi\) | |||||||
\(84\) | −16.9364 | −1.84792 | ||||||||
\(85\) | −0.143284 | −0.0155413 | ||||||||
\(86\) | 6.13826 | 0.661906 | ||||||||
\(87\) | −8.93259 | −0.957674 | ||||||||
\(88\) | 14.7007 | 1.56710 | ||||||||
\(89\) | −0.278394 | −0.0295097 | −0.0147548 | − | 0.999891i | \(-0.504697\pi\) | ||||
−0.0147548 | + | 0.999891i | \(0.504697\pi\) | |||||||
\(90\) | −0.0556507 | −0.00586610 | ||||||||
\(91\) | −12.4536 | −1.30549 | ||||||||
\(92\) | −4.32408 | −0.450817 | ||||||||
\(93\) | −10.4148 | −1.07997 | ||||||||
\(94\) | 25.1274 | 2.59169 | ||||||||
\(95\) | 0.0868327 | 0.00890885 | ||||||||
\(96\) | 4.80299 | 0.490203 | ||||||||
\(97\) | −11.4105 | −1.15856 | −0.579280 | − | 0.815129i | \(-0.696666\pi\) | ||||
−0.579280 | + | 0.815129i | \(0.696666\pi\) | |||||||
\(98\) | −0.301193 | −0.0304251 | ||||||||
\(99\) | 2.09321 | 0.210375 | ||||||||
\(100\) | −21.5041 | −2.15041 | ||||||||
\(101\) | 2.42278 | 0.241075 | 0.120538 | − | 0.992709i | \(-0.461538\pi\) | ||||
0.120538 | + | 0.992709i | \(0.461538\pi\) | |||||||
\(102\) | 19.6938 | 1.94998 | ||||||||
\(103\) | 12.9362 | 1.27465 | 0.637323 | − | 0.770597i | \(-0.280042\pi\) | ||||
0.637323 | + | 0.770597i | \(0.280042\pi\) | |||||||
\(104\) | 26.9635 | 2.64399 | ||||||||
\(105\) | 0.106112 | 0.0103554 | ||||||||
\(106\) | −23.9411 | −2.32537 | ||||||||
\(107\) | −14.8815 | −1.43865 | −0.719326 | − | 0.694672i | \(-0.755549\pi\) | ||||
−0.719326 | + | 0.694672i | \(0.755549\pi\) | |||||||
\(108\) | 24.2629 | 2.33470 | ||||||||
\(109\) | 2.61026 | 0.250017 | 0.125009 | − | 0.992156i | \(-0.460104\pi\) | ||||
0.125009 | + | 0.992156i | \(0.460104\pi\) | |||||||
\(110\) | −0.172145 | −0.0164133 | ||||||||
\(111\) | 1.49362 | 0.141768 | ||||||||
\(112\) | 15.7419 | 1.48747 | ||||||||
\(113\) | −6.39100 | −0.601215 | −0.300607 | − | 0.953748i | \(-0.597189\pi\) | ||||
−0.300607 | + | 0.953748i | \(0.597189\pi\) | |||||||
\(114\) | −11.9348 | −1.11780 | ||||||||
\(115\) | 0.0270917 | 0.00252631 | ||||||||
\(116\) | 26.0390 | 2.41766 | ||||||||
\(117\) | 3.83929 | 0.354942 | ||||||||
\(118\) | −19.5671 | −1.80130 | ||||||||
\(119\) | 14.1867 | 1.30049 | ||||||||
\(120\) | −0.229744 | −0.0209727 | ||||||||
\(121\) | −4.52508 | −0.411371 | ||||||||
\(122\) | −1.80924 | −0.163801 | ||||||||
\(123\) | −8.34108 | −0.752090 | ||||||||
\(124\) | 30.3598 | 2.72639 | ||||||||
\(125\) | 0.269479 | 0.0241029 | ||||||||
\(126\) | 5.51004 | 0.490873 | ||||||||
\(127\) | 4.50010 | 0.399319 | 0.199660 | − | 0.979865i | \(-0.436016\pi\) | ||||
0.199660 | + | 0.979865i | \(0.436016\pi\) | |||||||
\(128\) | 15.6179 | 1.38044 | ||||||||
\(129\) | 3.60822 | 0.317686 | ||||||||
\(130\) | −0.315742 | −0.0276924 | ||||||||
\(131\) | 3.46003 | 0.302304 | 0.151152 | − | 0.988511i | \(-0.451702\pi\) | ||||
0.151152 | + | 0.988511i | \(0.451702\pi\) | |||||||
\(132\) | 16.1510 | 1.40576 | ||||||||
\(133\) | −8.59739 | −0.745489 | ||||||||
\(134\) | −14.9370 | −1.29036 | ||||||||
\(135\) | −0.152014 | −0.0130833 | ||||||||
\(136\) | −30.7158 | −2.63386 | ||||||||
\(137\) | 18.1298 | 1.54894 | 0.774468 | − | 0.632613i | \(-0.218018\pi\) | ||||
0.774468 | + | 0.632613i | \(0.218018\pi\) | |||||||
\(138\) | −3.72364 | −0.316977 | ||||||||
\(139\) | 18.1267 | 1.53748 | 0.768741 | − | 0.639560i | \(-0.220883\pi\) | ||||
0.768741 | + | 0.639560i | \(0.220883\pi\) | |||||||
\(140\) | −0.309321 | −0.0261424 | ||||||||
\(141\) | 14.7705 | 1.24390 | ||||||||
\(142\) | 13.8286 | 1.16047 | ||||||||
\(143\) | 11.8761 | 0.993127 | ||||||||
\(144\) | −4.85303 | −0.404419 | ||||||||
\(145\) | −0.163142 | −0.0135482 | ||||||||
\(146\) | 26.1160 | 2.16138 | ||||||||
\(147\) | −0.177049 | −0.0146028 | ||||||||
\(148\) | −4.35398 | −0.357895 | ||||||||
\(149\) | −7.04588 | −0.577221 | −0.288611 | − | 0.957447i | \(-0.593193\pi\) | ||||
−0.288611 | + | 0.957447i | \(0.593193\pi\) | |||||||
\(150\) | −18.5180 | −1.51199 | ||||||||
\(151\) | 8.33478 | 0.678275 | 0.339137 | − | 0.940737i | \(-0.389865\pi\) | ||||
0.339137 | + | 0.940737i | \(0.389865\pi\) | |||||||
\(152\) | 18.6144 | 1.50982 | ||||||||
\(153\) | −4.37357 | −0.353582 | ||||||||
\(154\) | 17.0442 | 1.37346 | ||||||||
\(155\) | −0.190213 | −0.0152783 | ||||||||
\(156\) | 29.6236 | 2.37179 | ||||||||
\(157\) | 4.46433 | 0.356293 | 0.178146 | − | 0.984004i | \(-0.442990\pi\) | ||||
0.178146 | + | 0.984004i | \(0.442990\pi\) | |||||||
\(158\) | 21.3510 | 1.69860 | ||||||||
\(159\) | −14.0732 | −1.11608 | ||||||||
\(160\) | 0.0877202 | 0.00693489 | ||||||||
\(161\) | −2.68237 | −0.211401 | ||||||||
\(162\) | 14.6988 | 1.15485 | ||||||||
\(163\) | −9.90060 | −0.775475 | −0.387737 | − | 0.921770i | \(-0.626743\pi\) | ||||
−0.387737 | + | 0.921770i | \(0.626743\pi\) | |||||||
\(164\) | 24.3147 | 1.89866 | ||||||||
\(165\) | −0.101191 | −0.00787770 | ||||||||
\(166\) | −28.2785 | −2.19483 | ||||||||
\(167\) | −21.8663 | −1.69206 | −0.846032 | − | 0.533132i | \(-0.821015\pi\) | ||||
−0.846032 | + | 0.533132i | \(0.821015\pi\) | |||||||
\(168\) | 22.7472 | 1.75499 | ||||||||
\(169\) | 8.78269 | 0.675592 | ||||||||
\(170\) | 0.359681 | 0.0275863 | ||||||||
\(171\) | 2.65047 | 0.202686 | ||||||||
\(172\) | −10.5182 | −0.802003 | ||||||||
\(173\) | −11.0883 | −0.843030 | −0.421515 | − | 0.906821i | \(-0.638502\pi\) | ||||
−0.421515 | + | 0.906821i | \(0.638502\pi\) | |||||||
\(174\) | 22.4232 | 1.69990 | ||||||||
\(175\) | −13.3397 | −1.00839 | ||||||||
\(176\) | −15.0119 | −1.13156 | ||||||||
\(177\) | −11.5021 | −0.864547 | ||||||||
\(178\) | 0.698843 | 0.0523805 | ||||||||
\(179\) | 5.73934 | 0.428978 | 0.214489 | − | 0.976726i | \(-0.431191\pi\) | ||||
0.214489 | + | 0.976726i | \(0.431191\pi\) | |||||||
\(180\) | 0.0953598 | 0.00710770 | ||||||||
\(181\) | −20.8064 | −1.54653 | −0.773265 | − | 0.634083i | \(-0.781378\pi\) | ||||
−0.773265 | + | 0.634083i | \(0.781378\pi\) | |||||||
\(182\) | 31.2619 | 2.31729 | ||||||||
\(183\) | −1.06351 | −0.0786173 | ||||||||
\(184\) | 5.80765 | 0.428146 | ||||||||
\(185\) | 0.0272790 | 0.00200559 | ||||||||
\(186\) | 26.1440 | 1.91697 | ||||||||
\(187\) | −13.5288 | −0.989323 | ||||||||
\(188\) | −43.0568 | −3.14024 | ||||||||
\(189\) | 15.0511 | 1.09480 | ||||||||
\(190\) | −0.217973 | −0.0158135 | ||||||||
\(191\) | 19.4735 | 1.40905 | 0.704525 | − | 0.709679i | \(-0.251160\pi\) | ||||
0.704525 | + | 0.709679i | \(0.251160\pi\) | |||||||
\(192\) | 5.35392 | 0.386386 | ||||||||
\(193\) | −19.7535 | −1.42189 | −0.710944 | − | 0.703249i | \(-0.751732\pi\) | ||||
−0.710944 | + | 0.703249i | \(0.751732\pi\) | |||||||
\(194\) | 28.6434 | 2.05648 | ||||||||
\(195\) | −0.185601 | −0.0132911 | ||||||||
\(196\) | 0.516107 | 0.0368648 | ||||||||
\(197\) | 23.1001 | 1.64581 | 0.822907 | − | 0.568176i | \(-0.192351\pi\) | ||||
0.822907 | + | 0.568176i | \(0.192351\pi\) | |||||||
\(198\) | −5.25451 | −0.373422 | ||||||||
\(199\) | −15.8669 | −1.12477 | −0.562387 | − | 0.826874i | \(-0.690117\pi\) | ||||
−0.562387 | + | 0.826874i | \(0.690117\pi\) | |||||||
\(200\) | 28.8820 | 2.04227 | ||||||||
\(201\) | −8.78032 | −0.619316 | ||||||||
\(202\) | −6.08182 | −0.427915 | ||||||||
\(203\) | 16.1528 | 1.13371 | ||||||||
\(204\) | −33.7461 | −2.36270 | ||||||||
\(205\) | −0.152339 | −0.0106398 | ||||||||
\(206\) | −32.4734 | −2.26253 | ||||||||
\(207\) | 0.826941 | 0.0574764 | ||||||||
\(208\) | −27.5343 | −1.90916 | ||||||||
\(209\) | 8.19869 | 0.567115 | ||||||||
\(210\) | −0.266369 | −0.0183812 | ||||||||
\(211\) | −1.92286 | −0.132375 | −0.0661876 | − | 0.997807i | \(-0.521084\pi\) | ||||
−0.0661876 | + | 0.997807i | \(0.521084\pi\) | |||||||
\(212\) | 41.0241 | 2.81755 | ||||||||
\(213\) | 8.12882 | 0.556977 | ||||||||
\(214\) | 37.3567 | 2.55365 | ||||||||
\(215\) | 0.0658994 | 0.00449430 | ||||||||
\(216\) | −32.5873 | −2.21729 | ||||||||
\(217\) | 18.8332 | 1.27848 | ||||||||
\(218\) | −6.55244 | −0.443787 | ||||||||
\(219\) | 15.3516 | 1.03737 | ||||||||
\(220\) | 0.294977 | 0.0198873 | ||||||||
\(221\) | −24.8140 | −1.66917 | ||||||||
\(222\) | −3.74938 | −0.251642 | ||||||||
\(223\) | −9.12539 | −0.611081 | −0.305541 | − | 0.952179i | \(-0.598837\pi\) | ||||
−0.305541 | + | 0.952179i | \(0.598837\pi\) | |||||||
\(224\) | −8.68527 | −0.580309 | ||||||||
\(225\) | 4.11246 | 0.274164 | ||||||||
\(226\) | 16.0431 | 1.06717 | ||||||||
\(227\) | −6.30892 | −0.418738 | −0.209369 | − | 0.977837i | \(-0.567141\pi\) | ||||
−0.209369 | + | 0.977837i | \(0.567141\pi\) | |||||||
\(228\) | 20.4508 | 1.35439 | ||||||||
\(229\) | 17.5489 | 1.15966 | 0.579832 | − | 0.814736i | \(-0.303118\pi\) | ||||
0.579832 | + | 0.814736i | \(0.303118\pi\) | |||||||
\(230\) | −0.0680074 | −0.00448427 | ||||||||
\(231\) | 10.0190 | 0.659202 | ||||||||
\(232\) | −34.9728 | −2.29608 | ||||||||
\(233\) | 17.0777 | 1.11880 | 0.559399 | − | 0.828899i | \(-0.311032\pi\) | ||||
0.559399 | + | 0.828899i | \(0.311032\pi\) | |||||||
\(234\) | −9.63764 | −0.630032 | ||||||||
\(235\) | 0.269764 | 0.0175975 | ||||||||
\(236\) | 33.5291 | 2.18256 | ||||||||
\(237\) | 12.5507 | 0.815254 | ||||||||
\(238\) | −35.6124 | −2.30841 | ||||||||
\(239\) | 10.7585 | 0.695908 | 0.347954 | − | 0.937512i | \(-0.386876\pi\) | ||||
0.347954 | + | 0.937512i | \(0.386876\pi\) | |||||||
\(240\) | 0.234608 | 0.0151439 | ||||||||
\(241\) | 11.2449 | 0.724348 | 0.362174 | − | 0.932110i | \(-0.382035\pi\) | ||||
0.362174 | + | 0.932110i | \(0.382035\pi\) | |||||||
\(242\) | 11.3592 | 0.730195 | ||||||||
\(243\) | −8.28158 | −0.531264 | ||||||||
\(244\) | 3.10020 | 0.198470 | ||||||||
\(245\) | −0.00323356 | −0.000206585 0 | ||||||||
\(246\) | 20.9383 | 1.33498 | ||||||||
\(247\) | 15.0378 | 0.956830 | ||||||||
\(248\) | −40.7761 | −2.58928 | ||||||||
\(249\) | −16.6228 | −1.05343 | ||||||||
\(250\) | −0.676464 | −0.0427833 | ||||||||
\(251\) | 16.0113 | 1.01062 | 0.505312 | − | 0.862937i | \(-0.331377\pi\) | ||||
0.505312 | + | 0.862937i | \(0.331377\pi\) | |||||||
\(252\) | −9.44167 | −0.594769 | ||||||||
\(253\) | 2.55798 | 0.160819 | ||||||||
\(254\) | −11.2965 | −0.708803 | ||||||||
\(255\) | 0.211429 | 0.0132402 | ||||||||
\(256\) | −31.9485 | −1.99678 | ||||||||
\(257\) | −25.7049 | −1.60343 | −0.801715 | − | 0.597707i | \(-0.796079\pi\) | ||||
−0.801715 | + | 0.597707i | \(0.796079\pi\) | |||||||
\(258\) | −9.05761 | −0.563902 | ||||||||
\(259\) | −2.70092 | −0.167827 | ||||||||
\(260\) | 0.541036 | 0.0335536 | ||||||||
\(261\) | −4.97971 | −0.308236 | ||||||||
\(262\) | −8.68560 | −0.536598 | ||||||||
\(263\) | −19.6388 | −1.21098 | −0.605491 | − | 0.795852i | \(-0.707023\pi\) | ||||
−0.605491 | + | 0.795852i | \(0.707023\pi\) | |||||||
\(264\) | −21.6923 | −1.33507 | ||||||||
\(265\) | −0.257028 | −0.0157891 | ||||||||
\(266\) | 21.5818 | 1.32326 | ||||||||
\(267\) | 0.410797 | 0.0251404 | ||||||||
\(268\) | 25.5951 | 1.56347 | ||||||||
\(269\) | −11.3937 | −0.694685 | −0.347343 | − | 0.937738i | \(-0.612916\pi\) | ||||
−0.347343 | + | 0.937738i | \(0.612916\pi\) | |||||||
\(270\) | 0.381596 | 0.0232232 | ||||||||
\(271\) | −30.0407 | −1.82484 | −0.912422 | − | 0.409252i | \(-0.865790\pi\) | ||||
−0.912422 | + | 0.409252i | \(0.865790\pi\) | |||||||
\(272\) | 31.3661 | 1.90185 | ||||||||
\(273\) | 18.3765 | 1.11220 | ||||||||
\(274\) | −45.5107 | −2.74940 | ||||||||
\(275\) | 12.7211 | 0.767110 | ||||||||
\(276\) | 6.38061 | 0.384068 | ||||||||
\(277\) | 20.9521 | 1.25889 | 0.629445 | − | 0.777045i | \(-0.283282\pi\) | ||||
0.629445 | + | 0.777045i | \(0.283282\pi\) | |||||||
\(278\) | −45.5028 | −2.72907 | ||||||||
\(279\) | −5.80603 | −0.347598 | ||||||||
\(280\) | 0.415448 | 0.0248277 | ||||||||
\(281\) | 12.5921 | 0.751182 | 0.375591 | − | 0.926786i | \(-0.377440\pi\) | ||||
0.375591 | + | 0.926786i | \(0.377440\pi\) | |||||||
\(282\) | −37.0780 | −2.20796 | ||||||||
\(283\) | −29.0888 | −1.72915 | −0.864574 | − | 0.502506i | \(-0.832411\pi\) | ||||
−0.864574 | + | 0.502506i | \(0.832411\pi\) | |||||||
\(284\) | −23.6959 | −1.40609 | ||||||||
\(285\) | −0.128130 | −0.00758978 | ||||||||
\(286\) | −29.8121 | −1.76283 | ||||||||
\(287\) | 15.0832 | 0.890334 | ||||||||
\(288\) | 2.67755 | 0.157776 | ||||||||
\(289\) | 11.2672 | 0.662778 | ||||||||
\(290\) | 0.409530 | 0.0240484 | ||||||||
\(291\) | 16.8373 | 0.987020 | ||||||||
\(292\) | −44.7508 | −2.61885 | ||||||||
\(293\) | −17.8617 | −1.04349 | −0.521746 | − | 0.853101i | \(-0.674719\pi\) | ||||
−0.521746 | + | 0.853101i | \(0.674719\pi\) | |||||||
\(294\) | 0.444440 | 0.0259203 | ||||||||
\(295\) | −0.210070 | −0.0122307 | ||||||||
\(296\) | 5.84780 | 0.339897 | ||||||||
\(297\) | −14.3531 | −0.832851 | ||||||||
\(298\) | 17.6870 | 1.02458 | ||||||||
\(299\) | 4.69176 | 0.271331 | ||||||||
\(300\) | 31.7314 | 1.83201 | ||||||||
\(301\) | −6.52477 | −0.376081 | ||||||||
\(302\) | −20.9225 | −1.20396 | ||||||||
\(303\) | −3.57504 | −0.205381 | ||||||||
\(304\) | −19.0084 | −1.09021 | ||||||||
\(305\) | −0.0194237 | −0.00111220 | ||||||||
\(306\) | 10.9788 | 0.627618 | ||||||||
\(307\) | −3.66712 | −0.209294 | −0.104647 | − | 0.994509i | \(-0.533371\pi\) | ||||
−0.104647 | + | 0.994509i | \(0.533371\pi\) | |||||||
\(308\) | −29.2059 | −1.66416 | ||||||||
\(309\) | −19.0887 | −1.08592 | ||||||||
\(310\) | 0.477486 | 0.0271194 | ||||||||
\(311\) | −3.37948 | −0.191633 | −0.0958164 | − | 0.995399i | \(-0.530546\pi\) | ||||
−0.0958164 | + | 0.995399i | \(0.530546\pi\) | |||||||
\(312\) | −39.7873 | −2.25251 | ||||||||
\(313\) | 8.91967 | 0.504170 | 0.252085 | − | 0.967705i | \(-0.418884\pi\) | ||||
0.252085 | + | 0.967705i | \(0.418884\pi\) | |||||||
\(314\) | −11.2067 | −0.632429 | ||||||||
\(315\) | 0.0591548 | 0.00333300 | ||||||||
\(316\) | −36.5859 | −2.05812 | ||||||||
\(317\) | −11.8836 | −0.667450 | −0.333725 | − | 0.942670i | \(-0.608306\pi\) | ||||
−0.333725 | + | 0.942670i | \(0.608306\pi\) | |||||||
\(318\) | 35.3275 | 1.98107 | ||||||||
\(319\) | −15.4038 | −0.862445 | ||||||||
\(320\) | 0.0977822 | 0.00546619 | ||||||||
\(321\) | 21.9592 | 1.22564 | ||||||||
\(322\) | 6.73348 | 0.375242 | ||||||||
\(323\) | −17.1305 | −0.953164 | ||||||||
\(324\) | −25.1870 | −1.39928 | ||||||||
\(325\) | 23.3326 | 1.29426 | ||||||||
\(326\) | 24.8532 | 1.37649 | ||||||||
\(327\) | −3.85169 | −0.212999 | ||||||||
\(328\) | −32.6569 | −1.80318 | ||||||||
\(329\) | −26.7096 | −1.47255 | ||||||||
\(330\) | 0.254016 | 0.0139831 | ||||||||
\(331\) | −16.2327 | −0.892229 | −0.446114 | − | 0.894976i | \(-0.647193\pi\) | ||||
−0.446114 | + | 0.894976i | \(0.647193\pi\) | |||||||
\(332\) | 48.4563 | 2.65938 | ||||||||
\(333\) | 0.832658 | 0.0456294 | ||||||||
\(334\) | 54.8902 | 3.00346 | ||||||||
\(335\) | −0.160361 | −0.00876145 | ||||||||
\(336\) | −23.2288 | −1.26723 | ||||||||
\(337\) | 25.0372 | 1.36386 | 0.681931 | − | 0.731416i | \(-0.261140\pi\) | ||||
0.681931 | + | 0.731416i | \(0.261140\pi\) | |||||||
\(338\) | −22.0469 | −1.19919 | ||||||||
\(339\) | 9.43054 | 0.512197 | ||||||||
\(340\) | −0.616328 | −0.0334251 | ||||||||
\(341\) | −17.9598 | −0.972578 | ||||||||
\(342\) | −6.65338 | −0.359773 | ||||||||
\(343\) | −18.3582 | −0.991247 | ||||||||
\(344\) | 14.1269 | 0.761671 | ||||||||
\(345\) | −0.0399764 | −0.00215226 | ||||||||
\(346\) | 27.8347 | 1.49640 | ||||||||
\(347\) | −14.8312 | −0.796182 | −0.398091 | − | 0.917346i | \(-0.630327\pi\) | ||||
−0.398091 | + | 0.917346i | \(0.630327\pi\) | |||||||
\(348\) | −38.4230 | −2.05969 | ||||||||
\(349\) | 21.4424 | 1.14778 | 0.573892 | − | 0.818931i | \(-0.305433\pi\) | ||||
0.573892 | + | 0.818931i | \(0.305433\pi\) | |||||||
\(350\) | 33.4863 | 1.78992 | ||||||||
\(351\) | −26.3259 | −1.40517 | ||||||||
\(352\) | 8.28249 | 0.441458 | ||||||||
\(353\) | −25.9394 | −1.38061 | −0.690306 | − | 0.723517i | \(-0.742524\pi\) | ||||
−0.690306 | + | 0.723517i | \(0.742524\pi\) | |||||||
\(354\) | 28.8732 | 1.53460 | ||||||||
\(355\) | 0.148462 | 0.00787955 | ||||||||
\(356\) | −1.19750 | −0.0634672 | ||||||||
\(357\) | −20.9338 | −1.10794 | ||||||||
\(358\) | −14.4073 | −0.761448 | ||||||||
\(359\) | 31.9560 | 1.68657 | 0.843286 | − | 0.537466i | \(-0.180618\pi\) | ||||
0.843286 | + | 0.537466i | \(0.180618\pi\) | |||||||
\(360\) | −0.128077 | −0.00675026 | ||||||||
\(361\) | −8.61863 | −0.453612 | ||||||||
\(362\) | 52.2297 | 2.74513 | ||||||||
\(363\) | 6.67720 | 0.350462 | ||||||||
\(364\) | −53.5685 | −2.80775 | ||||||||
\(365\) | 0.280377 | 0.0146756 | ||||||||
\(366\) | 2.66971 | 0.139548 | ||||||||
\(367\) | −18.5096 | −0.966191 | −0.483095 | − | 0.875568i | \(-0.660488\pi\) | ||||
−0.483095 | + | 0.875568i | \(0.660488\pi\) | |||||||
\(368\) | −5.93059 | −0.309154 | ||||||||
\(369\) | −4.64996 | −0.242067 | ||||||||
\(370\) | −0.0684775 | −0.00355998 | ||||||||
\(371\) | 25.4486 | 1.32123 | ||||||||
\(372\) | −44.7989 | −2.32271 | ||||||||
\(373\) | −17.5243 | −0.907373 | −0.453687 | − | 0.891161i | \(-0.649891\pi\) | ||||
−0.453687 | + | 0.891161i | \(0.649891\pi\) | |||||||
\(374\) | 33.9609 | 1.75608 | ||||||||
\(375\) | −0.397642 | −0.0205342 | ||||||||
\(376\) | 57.8294 | 2.98232 | ||||||||
\(377\) | −28.2530 | −1.45511 | ||||||||
\(378\) | −37.7822 | −1.94331 | ||||||||
\(379\) | 1.43101 | 0.0735060 | 0.0367530 | − | 0.999324i | \(-0.488299\pi\) | ||||
0.0367530 | + | 0.999324i | \(0.488299\pi\) | |||||||
\(380\) | 0.373506 | 0.0191605 | ||||||||
\(381\) | −6.64034 | −0.340195 | ||||||||
\(382\) | −48.8836 | −2.50110 | ||||||||
\(383\) | −17.2330 | −0.880565 | −0.440282 | − | 0.897859i | \(-0.645122\pi\) | ||||
−0.440282 | + | 0.897859i | \(0.645122\pi\) | |||||||
\(384\) | −23.0457 | −1.17605 | ||||||||
\(385\) | 0.182984 | 0.00932572 | ||||||||
\(386\) | 49.5866 | 2.52389 | ||||||||
\(387\) | 2.01150 | 0.102250 | ||||||||
\(388\) | −49.0816 | −2.49174 | ||||||||
\(389\) | 17.8047 | 0.902735 | 0.451368 | − | 0.892338i | \(-0.350936\pi\) | ||||
0.451368 | + | 0.892338i | \(0.350936\pi\) | |||||||
\(390\) | 0.465908 | 0.0235922 | ||||||||
\(391\) | −5.34468 | −0.270292 | ||||||||
\(392\) | −0.693180 | −0.0350109 | ||||||||
\(393\) | −5.10561 | −0.257544 | ||||||||
\(394\) | −57.9874 | −2.92136 | ||||||||
\(395\) | 0.229221 | 0.0115334 | ||||||||
\(396\) | 9.00381 | 0.452459 | ||||||||
\(397\) | −6.41463 | −0.321941 | −0.160970 | − | 0.986959i | \(-0.551462\pi\) | ||||
−0.160970 | + | 0.986959i | \(0.551462\pi\) | |||||||
\(398\) | 39.8302 | 1.99651 | ||||||||
\(399\) | 12.6863 | 0.635109 | ||||||||
\(400\) | −29.4934 | −1.47467 | ||||||||
\(401\) | −20.4424 | −1.02084 | −0.510422 | − | 0.859924i | \(-0.670511\pi\) | ||||
−0.510422 | + | 0.859924i | \(0.670511\pi\) | |||||||
\(402\) | 22.0410 | 1.09930 | ||||||||
\(403\) | −32.9413 | −1.64092 | ||||||||
\(404\) | 10.4214 | 0.518486 | ||||||||
\(405\) | 0.157804 | 0.00784135 | ||||||||
\(406\) | −40.5480 | −2.01236 | ||||||||
\(407\) | 2.57566 | 0.127671 | ||||||||
\(408\) | 45.3242 | 2.24388 | ||||||||
\(409\) | 35.7642 | 1.76842 | 0.884212 | − | 0.467086i | \(-0.154696\pi\) | ||||
0.884212 | + | 0.467086i | \(0.154696\pi\) | |||||||
\(410\) | 0.382411 | 0.0188859 | ||||||||
\(411\) | −26.7523 | −1.31960 | ||||||||
\(412\) | 55.6445 | 2.74141 | ||||||||
\(413\) | 20.7992 | 1.02346 | ||||||||
\(414\) | −2.07584 | −0.102022 | ||||||||
\(415\) | −0.303593 | −0.0149028 | ||||||||
\(416\) | 15.1915 | 0.744822 | ||||||||
\(417\) | −26.7476 | −1.30984 | ||||||||
\(418\) | −20.5809 | −1.00665 | ||||||||
\(419\) | −13.8844 | −0.678298 | −0.339149 | − | 0.940733i | \(-0.610139\pi\) | ||||
−0.339149 | + | 0.940733i | \(0.610139\pi\) | |||||||
\(420\) | 0.456434 | 0.0222717 | ||||||||
\(421\) | 8.99892 | 0.438580 | 0.219290 | − | 0.975660i | \(-0.429626\pi\) | ||||
0.219290 | + | 0.975660i | \(0.429626\pi\) | |||||||
\(422\) | 4.82689 | 0.234970 | ||||||||
\(423\) | 8.23422 | 0.400361 | ||||||||
\(424\) | −55.0992 | −2.67586 | ||||||||
\(425\) | −26.5796 | −1.28930 | ||||||||
\(426\) | −20.4055 | −0.988650 | ||||||||
\(427\) | 1.92316 | 0.0930682 | ||||||||
\(428\) | −64.0121 | −3.09414 | ||||||||
\(429\) | −17.5243 | −0.846082 | ||||||||
\(430\) | −0.165425 | −0.00797751 | ||||||||
\(431\) | −15.9942 | −0.770413 | −0.385207 | − | 0.922830i | \(-0.625870\pi\) | ||||
−0.385207 | + | 0.922830i | \(0.625870\pi\) | |||||||
\(432\) | 33.2772 | 1.60105 | ||||||||
\(433\) | −7.98316 | −0.383646 | −0.191823 | − | 0.981430i | \(-0.561440\pi\) | ||||
−0.191823 | + | 0.981430i | \(0.561440\pi\) | |||||||
\(434\) | −47.2764 | −2.26934 | ||||||||
\(435\) | 0.240732 | 0.0115422 | ||||||||
\(436\) | 11.2279 | 0.537718 | ||||||||
\(437\) | 3.23897 | 0.154941 | ||||||||
\(438\) | −38.5367 | −1.84136 | ||||||||
\(439\) | −6.62890 | −0.316380 | −0.158190 | − | 0.987409i | \(-0.550566\pi\) | ||||
−0.158190 | + | 0.987409i | \(0.550566\pi\) | |||||||
\(440\) | −0.396181 | −0.0188872 | ||||||||
\(441\) | −0.0987007 | −0.00470003 | ||||||||
\(442\) | 62.2899 | 2.96283 | ||||||||
\(443\) | 1.29844 | 0.0616907 | 0.0308454 | − | 0.999524i | \(-0.490180\pi\) | ||||
0.0308454 | + | 0.999524i | \(0.490180\pi\) | |||||||
\(444\) | 6.42472 | 0.304904 | ||||||||
\(445\) | 0.00750267 | 0.000355661 0 | ||||||||
\(446\) | 22.9072 | 1.08469 | ||||||||
\(447\) | 10.3969 | 0.491756 | ||||||||
\(448\) | −9.68151 | −0.457408 | ||||||||
\(449\) | −30.9324 | −1.45979 | −0.729894 | − | 0.683560i | \(-0.760431\pi\) | ||||
−0.729894 | + | 0.683560i | \(0.760431\pi\) | |||||||
\(450\) | −10.3234 | −0.486649 | ||||||||
\(451\) | −14.3837 | −0.677303 | ||||||||
\(452\) | −27.4905 | −1.29305 | ||||||||
\(453\) | −12.2988 | −0.577847 | ||||||||
\(454\) | 15.8371 | 0.743271 | ||||||||
\(455\) | 0.335623 | 0.0157342 | ||||||||
\(456\) | −27.4673 | −1.28627 | ||||||||
\(457\) | −20.6604 | −0.966454 | −0.483227 | − | 0.875495i | \(-0.660536\pi\) | ||||
−0.483227 | + | 0.875495i | \(0.660536\pi\) | |||||||
\(458\) | −44.0524 | −2.05843 | ||||||||
\(459\) | 29.9895 | 1.39979 | ||||||||
\(460\) | 0.116533 | 0.00543340 | ||||||||
\(461\) | −8.64742 | −0.402751 | −0.201375 | − | 0.979514i | \(-0.564541\pi\) | ||||
−0.201375 | + | 0.979514i | \(0.564541\pi\) | |||||||
\(462\) | −25.1504 | −1.17010 | ||||||||
\(463\) | −12.2277 | −0.568269 | −0.284135 | − | 0.958784i | \(-0.591706\pi\) | ||||
−0.284135 | + | 0.958784i | \(0.591706\pi\) | |||||||
\(464\) | 35.7131 | 1.65794 | ||||||||
\(465\) | 0.280678 | 0.0130161 | ||||||||
\(466\) | −42.8696 | −1.98590 | ||||||||
\(467\) | −34.0814 | −1.57710 | −0.788550 | − | 0.614971i | \(-0.789168\pi\) | ||||
−0.788550 | + | 0.614971i | \(0.789168\pi\) | |||||||
\(468\) | 16.5145 | 0.763382 | ||||||||
\(469\) | 15.8775 | 0.733154 | ||||||||
\(470\) | −0.677179 | −0.0312360 | ||||||||
\(471\) | −6.58756 | −0.303539 | ||||||||
\(472\) | −45.0327 | −2.07280 | ||||||||
\(473\) | 6.22218 | 0.286096 | ||||||||
\(474\) | −31.5055 | −1.44710 | ||||||||
\(475\) | 16.1077 | 0.739073 | ||||||||
\(476\) | 61.0233 | 2.79700 | ||||||||
\(477\) | −7.84548 | −0.359220 | ||||||||
\(478\) | −27.0067 | −1.23526 | ||||||||
\(479\) | 23.7116 | 1.08341 | 0.541706 | − | 0.840568i | \(-0.317779\pi\) | ||||
0.541706 | + | 0.840568i | \(0.317779\pi\) | |||||||
\(480\) | −0.129440 | −0.00590809 | ||||||||
\(481\) | 4.72419 | 0.215405 | ||||||||
\(482\) | −28.2277 | −1.28574 | ||||||||
\(483\) | 3.95810 | 0.180100 | ||||||||
\(484\) | −19.4644 | −0.884745 | ||||||||
\(485\) | 0.307511 | 0.0139633 | ||||||||
\(486\) | 20.7890 | 0.943008 | ||||||||
\(487\) | −13.7837 | −0.624601 | −0.312301 | − | 0.949983i | \(-0.601100\pi\) | ||||
−0.312301 | + | 0.949983i | \(0.601100\pi\) | |||||||
\(488\) | −4.16386 | −0.188489 | ||||||||
\(489\) | 14.6093 | 0.660655 | ||||||||
\(490\) | 0.00811711 | 0.000366694 0 | ||||||||
\(491\) | 32.5513 | 1.46902 | 0.734509 | − | 0.678599i | \(-0.237413\pi\) | ||||
0.734509 | + | 0.678599i | \(0.237413\pi\) | |||||||
\(492\) | −35.8787 | −1.61754 | ||||||||
\(493\) | 32.1848 | 1.44953 | ||||||||
\(494\) | −37.7488 | −1.69840 | ||||||||
\(495\) | −0.0564115 | −0.00253551 | ||||||||
\(496\) | 41.6393 | 1.86966 | ||||||||
\(497\) | −14.6994 | −0.659357 | ||||||||
\(498\) | 41.7276 | 1.86986 | ||||||||
\(499\) | 39.1068 | 1.75066 | 0.875330 | − | 0.483527i | \(-0.160644\pi\) | ||||
0.875330 | + | 0.483527i | \(0.160644\pi\) | |||||||
\(500\) | 1.15915 | 0.0518387 | ||||||||
\(501\) | 32.2658 | 1.44153 | ||||||||
\(502\) | −40.1926 | −1.79389 | ||||||||
\(503\) | −19.1271 | −0.852836 | −0.426418 | − | 0.904526i | \(-0.640225\pi\) | ||||
−0.426418 | + | 0.904526i | \(0.640225\pi\) | |||||||
\(504\) | 12.6810 | 0.564859 | ||||||||
\(505\) | −0.0652934 | −0.00290552 | ||||||||
\(506\) | −6.42121 | −0.285458 | ||||||||
\(507\) | −12.9597 | −0.575561 | ||||||||
\(508\) | 19.3569 | 0.858826 | ||||||||
\(509\) | 14.0852 | 0.624314 | 0.312157 | − | 0.950030i | \(-0.398948\pi\) | ||||
0.312157 | + | 0.950030i | \(0.398948\pi\) | |||||||
\(510\) | −0.530745 | −0.0235018 | ||||||||
\(511\) | −27.7604 | −1.22805 | ||||||||
\(512\) | 48.9635 | 2.16390 | ||||||||
\(513\) | −18.1742 | −0.802411 | ||||||||
\(514\) | 64.5263 | 2.84613 | ||||||||
\(515\) | −0.348629 | −0.0153624 | ||||||||
\(516\) | 15.5206 | 0.683255 | ||||||||
\(517\) | 25.4709 | 1.12021 | ||||||||
\(518\) | 6.78003 | 0.297897 | ||||||||
\(519\) | 16.3619 | 0.718209 | ||||||||
\(520\) | −0.726662 | −0.0318662 | ||||||||
\(521\) | −16.8238 | −0.737062 | −0.368531 | − | 0.929615i | \(-0.620139\pi\) | ||||
−0.368531 | + | 0.929615i | \(0.620139\pi\) | |||||||
\(522\) | 12.5004 | 0.547128 | ||||||||
\(523\) | 17.4809 | 0.764386 | 0.382193 | − | 0.924083i | \(-0.375169\pi\) | ||||
0.382193 | + | 0.924083i | \(0.375169\pi\) | |||||||
\(524\) | 14.8831 | 0.650173 | ||||||||
\(525\) | 19.6840 | 0.859082 | ||||||||
\(526\) | 49.2987 | 2.14953 | ||||||||
\(527\) | 37.5255 | 1.63463 | ||||||||
\(528\) | 22.1515 | 0.964021 | ||||||||
\(529\) | −21.9894 | −0.956063 | ||||||||
\(530\) | 0.645210 | 0.0280261 | ||||||||
\(531\) | −6.41213 | −0.278263 | ||||||||
\(532\) | −36.9812 | −1.60334 | ||||||||
\(533\) | −26.3821 | −1.14274 | ||||||||
\(534\) | −1.03121 | −0.0446249 | ||||||||
\(535\) | 0.401055 | 0.0173391 | ||||||||
\(536\) | −34.3766 | −1.48484 | ||||||||
\(537\) | −8.46895 | −0.365462 | ||||||||
\(538\) | 28.6012 | 1.23309 | ||||||||
\(539\) | −0.305311 | −0.0131507 | ||||||||
\(540\) | −0.653881 | −0.0281385 | ||||||||
\(541\) | −32.6820 | −1.40511 | −0.702555 | − | 0.711630i | \(-0.747957\pi\) | ||||
−0.702555 | + | 0.711630i | \(0.747957\pi\) | |||||||
\(542\) | 75.4102 | 3.23915 | ||||||||
\(543\) | 30.7019 | 1.31755 | ||||||||
\(544\) | −17.3055 | −0.741969 | ||||||||
\(545\) | −0.0703460 | −0.00301329 | ||||||||
\(546\) | −46.1300 | −1.97418 | ||||||||
\(547\) | −19.7584 | −0.844808 | −0.422404 | − | 0.906408i | \(-0.638814\pi\) | ||||
−0.422404 | + | 0.906408i | \(0.638814\pi\) | |||||||
\(548\) | 77.9845 | 3.33133 | ||||||||
\(549\) | −0.592885 | −0.0253037 | ||||||||
\(550\) | −31.9333 | −1.36164 | ||||||||
\(551\) | −19.5046 | −0.830923 | ||||||||
\(552\) | −8.56976 | −0.364753 | ||||||||
\(553\) | −22.6954 | −0.965108 | ||||||||
\(554\) | −52.5954 | −2.23457 | ||||||||
\(555\) | −0.0402528 | −0.00170864 | ||||||||
\(556\) | 77.9708 | 3.30670 | ||||||||
\(557\) | 24.9745 | 1.05820 | 0.529102 | − | 0.848558i | \(-0.322529\pi\) | ||||
0.529102 | + | 0.848558i | \(0.322529\pi\) | |||||||
\(558\) | 14.5747 | 0.616996 | ||||||||
\(559\) | 11.4125 | 0.482698 | ||||||||
\(560\) | −0.424242 | −0.0179275 | ||||||||
\(561\) | 19.9630 | 0.842840 | ||||||||
\(562\) | −31.6096 | −1.33337 | ||||||||
\(563\) | 12.9818 | 0.547117 | 0.273558 | − | 0.961855i | \(-0.411799\pi\) | ||||
0.273558 | + | 0.961855i | \(0.411799\pi\) | |||||||
\(564\) | 63.5346 | 2.67529 | ||||||||
\(565\) | 0.172236 | 0.00724604 | ||||||||
\(566\) | 73.0206 | 3.06928 | ||||||||
\(567\) | −15.6243 | −0.656161 | ||||||||
\(568\) | 31.8259 | 1.33538 | ||||||||
\(569\) | 3.32206 | 0.139268 | 0.0696340 | − | 0.997573i | \(-0.477817\pi\) | ||||
0.0696340 | + | 0.997573i | \(0.477817\pi\) | |||||||
\(570\) | 0.321641 | 0.0134721 | ||||||||
\(571\) | −11.9313 | −0.499311 | −0.249655 | − | 0.968335i | \(-0.580317\pi\) | ||||
−0.249655 | + | 0.968335i | \(0.580317\pi\) | |||||||
\(572\) | 51.0843 | 2.13594 | ||||||||
\(573\) | −28.7350 | −1.20042 | ||||||||
\(574\) | −37.8629 | −1.58037 | ||||||||
\(575\) | 5.02559 | 0.209581 | ||||||||
\(576\) | 2.98468 | 0.124362 | ||||||||
\(577\) | −27.7745 | −1.15627 | −0.578134 | − | 0.815942i | \(-0.696219\pi\) | ||||
−0.578134 | + | 0.815942i | \(0.696219\pi\) | |||||||
\(578\) | −28.2838 | −1.17645 | ||||||||
\(579\) | 29.1482 | 1.21136 | ||||||||
\(580\) | −0.701746 | −0.0291384 | ||||||||
\(581\) | 30.0590 | 1.24706 | ||||||||
\(582\) | −42.2661 | −1.75199 | ||||||||
\(583\) | −24.2684 | −1.00510 | ||||||||
\(584\) | 60.1046 | 2.48715 | ||||||||
\(585\) | −0.103468 | −0.00427788 | ||||||||
\(586\) | 44.8377 | 1.85223 | ||||||||
\(587\) | −15.0417 | −0.620839 | −0.310419 | − | 0.950600i | \(-0.600469\pi\) | ||||
−0.310419 | + | 0.950600i | \(0.600469\pi\) | |||||||
\(588\) | −0.761567 | −0.0314065 | ||||||||
\(589\) | −22.7411 | −0.937032 | ||||||||
\(590\) | 0.527331 | 0.0217099 | ||||||||
\(591\) | −34.0865 | −1.40213 | ||||||||
\(592\) | −5.97160 | −0.245431 | ||||||||
\(593\) | −32.8038 | −1.34709 | −0.673545 | − | 0.739146i | \(-0.735229\pi\) | ||||
−0.673545 | + | 0.739146i | \(0.735229\pi\) | |||||||
\(594\) | 36.0301 | 1.47833 | ||||||||
\(595\) | −0.382329 | −0.0156740 | ||||||||
\(596\) | −30.3075 | −1.24144 | ||||||||
\(597\) | 23.4132 | 0.958237 | ||||||||
\(598\) | −11.7776 | −0.481621 | ||||||||
\(599\) | −22.2344 | −0.908472 | −0.454236 | − | 0.890881i | \(-0.650088\pi\) | ||||
−0.454236 | + | 0.890881i | \(0.650088\pi\) | |||||||
\(600\) | −42.6183 | −1.73988 | ||||||||
\(601\) | −48.2179 | −1.96685 | −0.983426 | − | 0.181312i | \(-0.941965\pi\) | ||||
−0.983426 | + | 0.181312i | \(0.941965\pi\) | |||||||
\(602\) | 16.3789 | 0.667555 | ||||||||
\(603\) | −4.89482 | −0.199333 | ||||||||
\(604\) | 35.8516 | 1.45878 | ||||||||
\(605\) | 0.121950 | 0.00495798 | ||||||||
\(606\) | 8.97432 | 0.364557 | ||||||||
\(607\) | 0.840739 | 0.0341246 | 0.0170623 | − | 0.999854i | \(-0.494569\pi\) | ||||
0.0170623 | + | 0.999854i | \(0.494569\pi\) | |||||||
\(608\) | 10.4875 | 0.425323 | ||||||||
\(609\) | −23.8351 | −0.965847 | ||||||||
\(610\) | 0.0487587 | 0.00197418 | ||||||||
\(611\) | 46.7179 | 1.89000 | ||||||||
\(612\) | −18.8127 | −0.760458 | ||||||||
\(613\) | −16.5518 | −0.668521 | −0.334260 | − | 0.942481i | \(-0.608486\pi\) | ||||
−0.334260 | + | 0.942481i | \(0.608486\pi\) | |||||||
\(614\) | 9.20546 | 0.371502 | ||||||||
\(615\) | 0.224791 | 0.00906444 | ||||||||
\(616\) | 39.2263 | 1.58047 | ||||||||
\(617\) | 2.49491 | 0.100441 | 0.0502207 | − | 0.998738i | \(-0.484008\pi\) | ||||
0.0502207 | + | 0.998738i | \(0.484008\pi\) | |||||||
\(618\) | 47.9177 | 1.92753 | ||||||||
\(619\) | 35.0504 | 1.40879 | 0.704397 | − | 0.709806i | \(-0.251218\pi\) | ||||
0.704397 | + | 0.709806i | \(0.251218\pi\) | |||||||
\(620\) | −0.818191 | −0.0328594 | ||||||||
\(621\) | −5.67032 | −0.227542 | ||||||||
\(622\) | 8.48340 | 0.340153 | ||||||||
\(623\) | −0.742847 | −0.0297615 | ||||||||
\(624\) | 40.6296 | 1.62648 | ||||||||
\(625\) | 24.9891 | 0.999564 | ||||||||
\(626\) | −22.3908 | −0.894915 | ||||||||
\(627\) | −12.0980 | −0.483146 | ||||||||
\(628\) | 19.2031 | 0.766286 | ||||||||
\(629\) | −5.38163 | −0.214579 | ||||||||
\(630\) | −0.148495 | −0.00591616 | ||||||||
\(631\) | 7.14118 | 0.284286 | 0.142143 | − | 0.989846i | \(-0.454601\pi\) | ||||
0.142143 | + | 0.989846i | \(0.454601\pi\) | |||||||
\(632\) | 49.1383 | 1.95462 | ||||||||
\(633\) | 2.83737 | 0.112775 | ||||||||
\(634\) | 29.8310 | 1.18474 | ||||||||
\(635\) | −0.121277 | −0.00481273 | ||||||||
\(636\) | −60.5351 | −2.40037 | ||||||||
\(637\) | −0.559991 | −0.0221877 | ||||||||
\(638\) | 38.6676 | 1.53086 | ||||||||
\(639\) | 4.53163 | 0.179268 | ||||||||
\(640\) | −0.420900 | −0.0166375 | ||||||||
\(641\) | −39.3954 | −1.55603 | −0.778013 | − | 0.628248i | \(-0.783772\pi\) | ||||
−0.778013 | + | 0.628248i | \(0.783772\pi\) | |||||||
\(642\) | −55.1234 | −2.17555 | ||||||||
\(643\) | 5.01172 | 0.197643 | 0.0988215 | − | 0.995105i | \(-0.468493\pi\) | ||||
0.0988215 | + | 0.995105i | \(0.468493\pi\) | |||||||
\(644\) | −11.5381 | −0.454664 | ||||||||
\(645\) | −0.0972410 | −0.00382886 | ||||||||
\(646\) | 43.0020 | 1.69189 | ||||||||
\(647\) | 42.4392 | 1.66846 | 0.834229 | − | 0.551419i | \(-0.185913\pi\) | ||||
0.834229 | + | 0.551419i | \(0.185913\pi\) | |||||||
\(648\) | 33.8285 | 1.32891 | ||||||||
\(649\) | −19.8347 | −0.778578 | ||||||||
\(650\) | −58.5710 | −2.29734 | ||||||||
\(651\) | −27.7902 | −1.08918 | ||||||||
\(652\) | −42.5869 | −1.66783 | ||||||||
\(653\) | −27.9842 | −1.09511 | −0.547553 | − | 0.836771i | \(-0.684440\pi\) | ||||
−0.547553 | + | 0.836771i | \(0.684440\pi\) | |||||||
\(654\) | 9.66877 | 0.378079 | ||||||||
\(655\) | −0.0932472 | −0.00364347 | ||||||||
\(656\) | 33.3482 | 1.30203 | ||||||||
\(657\) | 8.55818 | 0.333887 | ||||||||
\(658\) | 67.0482 | 2.61381 | ||||||||
\(659\) | 9.25126 | 0.360378 | 0.180189 | − | 0.983632i | \(-0.442329\pi\) | ||||
0.180189 | + | 0.983632i | \(0.442329\pi\) | |||||||
\(660\) | −0.435267 | −0.0169427 | ||||||||
\(661\) | −8.03659 | −0.312587 | −0.156294 | − | 0.987711i | \(-0.549955\pi\) | ||||
−0.156294 | + | 0.987711i | \(0.549955\pi\) | |||||||
\(662\) | 40.7484 | 1.58373 | ||||||||
\(663\) | 36.6155 | 1.42203 | ||||||||
\(664\) | −65.0813 | −2.52565 | ||||||||
\(665\) | 0.231698 | 0.00898488 | ||||||||
\(666\) | −2.09019 | −0.0809934 | ||||||||
\(667\) | −6.08540 | −0.235628 | ||||||||
\(668\) | −94.0567 | −3.63916 | ||||||||
\(669\) | 13.4654 | 0.520603 | ||||||||
\(670\) | 0.402549 | 0.0155518 | ||||||||
\(671\) | −1.83397 | −0.0707997 | ||||||||
\(672\) | 12.8160 | 0.494386 | ||||||||
\(673\) | 4.19885 | 0.161854 | 0.0809269 | − | 0.996720i | \(-0.474212\pi\) | ||||
0.0809269 | + | 0.996720i | \(0.474212\pi\) | |||||||
\(674\) | −62.8501 | −2.42089 | ||||||||
\(675\) | −28.1991 | −1.08538 | ||||||||
\(676\) | 37.7783 | 1.45301 | ||||||||
\(677\) | −34.2807 | −1.31751 | −0.658757 | − | 0.752356i | \(-0.728918\pi\) | ||||
−0.658757 | + | 0.752356i | \(0.728918\pi\) | |||||||
\(678\) | −23.6732 | −0.909163 | ||||||||
\(679\) | −30.4470 | −1.16845 | ||||||||
\(680\) | 0.827787 | 0.0317442 | ||||||||
\(681\) | 9.30942 | 0.356738 | ||||||||
\(682\) | 45.0839 | 1.72635 | ||||||||
\(683\) | 11.7185 | 0.448396 | 0.224198 | − | 0.974544i | \(-0.428024\pi\) | ||||
0.224198 | + | 0.974544i | \(0.428024\pi\) | |||||||
\(684\) | 11.4008 | 0.435922 | ||||||||
\(685\) | −0.488596 | −0.0186683 | ||||||||
\(686\) | 46.0839 | 1.75949 | ||||||||
\(687\) | −25.8951 | −0.987960 | ||||||||
\(688\) | −14.4259 | −0.549984 | ||||||||
\(689\) | −44.5123 | −1.69579 | ||||||||
\(690\) | 0.100351 | 0.00382032 | ||||||||
\(691\) | 33.0781 | 1.25835 | 0.629176 | − | 0.777263i | \(-0.283393\pi\) | ||||
0.629176 | + | 0.777263i | \(0.283393\pi\) | |||||||
\(692\) | −47.6959 | −1.81312 | ||||||||
\(693\) | 5.58536 | 0.212170 | ||||||||
\(694\) | 37.2304 | 1.41325 | ||||||||
\(695\) | −0.488510 | −0.0185302 | ||||||||
\(696\) | 51.6058 | 1.95611 | ||||||||
\(697\) | 30.0536 | 1.13836 | ||||||||
\(698\) | −53.8261 | −2.03735 | ||||||||
\(699\) | −25.1998 | −0.953145 | ||||||||
\(700\) | −57.3800 | −2.16876 | ||||||||
\(701\) | −7.92623 | −0.299369 | −0.149685 | − | 0.988734i | \(-0.547826\pi\) | ||||
−0.149685 | + | 0.988734i | \(0.547826\pi\) | |||||||
\(702\) | 66.0852 | 2.49422 | ||||||||
\(703\) | 3.26136 | 0.123005 | ||||||||
\(704\) | 9.23253 | 0.347964 | ||||||||
\(705\) | −0.398063 | −0.0149919 | ||||||||
\(706\) | 65.1147 | 2.45063 | ||||||||
\(707\) | 6.46477 | 0.243133 | ||||||||
\(708\) | −49.4755 | −1.85940 | ||||||||
\(709\) | −20.3863 | −0.765623 | −0.382812 | − | 0.923826i | \(-0.625044\pi\) | ||||
−0.382812 | + | 0.923826i | \(0.625044\pi\) | |||||||
\(710\) | −0.372679 | −0.0139864 | ||||||||
\(711\) | 6.99671 | 0.262397 | ||||||||
\(712\) | 1.60835 | 0.0602755 | ||||||||
\(713\) | −7.09519 | −0.265717 | ||||||||
\(714\) | 52.5496 | 1.96662 | ||||||||
\(715\) | −0.320058 | −0.0119695 | ||||||||
\(716\) | 24.6874 | 0.922613 | ||||||||
\(717\) | −15.8752 | −0.592870 | ||||||||
\(718\) | −80.2180 | −2.99371 | ||||||||
\(719\) | 11.8222 | 0.440894 | 0.220447 | − | 0.975399i | \(-0.429248\pi\) | ||||
0.220447 | + | 0.975399i | \(0.429248\pi\) | |||||||
\(720\) | 0.130788 | 0.00487420 | ||||||||
\(721\) | 34.5182 | 1.28552 | ||||||||
\(722\) | 21.6351 | 0.805174 | ||||||||
\(723\) | −16.5930 | −0.617099 | ||||||||
\(724\) | −89.4977 | −3.32616 | ||||||||
\(725\) | −30.2633 | −1.12395 | ||||||||
\(726\) | −16.7616 | −0.622080 | ||||||||
\(727\) | −9.11018 | −0.337878 | −0.168939 | − | 0.985627i | \(-0.554034\pi\) | ||||
−0.168939 | + | 0.985627i | \(0.554034\pi\) | |||||||
\(728\) | 71.9476 | 2.66655 | ||||||||
\(729\) | 29.7867 | 1.10321 | ||||||||
\(730\) | −0.703822 | −0.0260496 | ||||||||
\(731\) | −13.0007 | −0.480849 | ||||||||
\(732\) | −4.57465 | −0.169084 | ||||||||
\(733\) | 9.26626 | 0.342257 | 0.171128 | − | 0.985249i | \(-0.445259\pi\) | ||||
0.171128 | + | 0.985249i | \(0.445259\pi\) | |||||||
\(734\) | 46.4639 | 1.71502 | ||||||||
\(735\) | 0.00477144 | 0.000175997 0 | ||||||||
\(736\) | 3.27208 | 0.120610 | ||||||||
\(737\) | −15.1412 | −0.557732 | ||||||||
\(738\) | 11.6726 | 0.429676 | ||||||||
\(739\) | −3.00749 | −0.110632 | −0.0553161 | − | 0.998469i | \(-0.517617\pi\) | ||||
−0.0553161 | + | 0.998469i | \(0.517617\pi\) | |||||||
\(740\) | 0.117339 | 0.00431347 | ||||||||
\(741\) | −22.1897 | −0.815158 | ||||||||
\(742\) | −63.8829 | −2.34521 | ||||||||
\(743\) | −18.2252 | −0.668618 | −0.334309 | − | 0.942464i | \(-0.608503\pi\) | ||||
−0.334309 | + | 0.942464i | \(0.608503\pi\) | |||||||
\(744\) | 60.1691 | 2.20591 | ||||||||
\(745\) | 0.189885 | 0.00695686 | ||||||||
\(746\) | 43.9907 | 1.61061 | ||||||||
\(747\) | −9.26681 | −0.339055 | ||||||||
\(748\) | −58.1933 | −2.12776 | ||||||||
\(749\) | −39.7089 | −1.45093 | ||||||||
\(750\) | 0.998188 | 0.0364487 | ||||||||
\(751\) | −40.8227 | −1.48964 | −0.744820 | − | 0.667265i | \(-0.767465\pi\) | ||||
−0.744820 | + | 0.667265i | \(0.767465\pi\) | |||||||
\(752\) | −59.0536 | −2.15346 | ||||||||
\(753\) | −23.6262 | −0.860988 | ||||||||
\(754\) | 70.9227 | 2.58285 | ||||||||
\(755\) | −0.224621 | −0.00817479 | ||||||||
\(756\) | 64.7414 | 2.35462 | ||||||||
\(757\) | −35.1246 | −1.27662 | −0.638312 | − | 0.769778i | \(-0.720367\pi\) | ||||
−0.638312 | + | 0.769778i | \(0.720367\pi\) | |||||||
\(758\) | −3.59222 | −0.130475 | ||||||||
\(759\) | −3.77455 | −0.137007 | ||||||||
\(760\) | −0.501654 | −0.0181969 | ||||||||
\(761\) | −32.9129 | −1.19309 | −0.596545 | − | 0.802579i | \(-0.703460\pi\) | ||||
−0.596545 | + | 0.802579i | \(0.703460\pi\) | |||||||
\(762\) | 16.6690 | 0.603855 | ||||||||
\(763\) | 6.96502 | 0.252151 | ||||||||
\(764\) | 83.7640 | 3.03048 | ||||||||
\(765\) | 0.117867 | 0.00426149 | ||||||||
\(766\) | 43.2594 | 1.56303 | ||||||||
\(767\) | −36.3800 | −1.31361 | ||||||||
\(768\) | 47.1432 | 1.70113 | ||||||||
\(769\) | 6.93883 | 0.250221 | 0.125110 | − | 0.992143i | \(-0.460072\pi\) | ||||
0.125110 | + | 0.992143i | \(0.460072\pi\) | |||||||
\(770\) | −0.459339 | −0.0165534 | ||||||||
\(771\) | 37.9301 | 1.36602 | ||||||||
\(772\) | −84.9686 | −3.05809 | ||||||||
\(773\) | −30.2446 | −1.08782 | −0.543911 | − | 0.839143i | \(-0.683057\pi\) | ||||
−0.543911 | + | 0.839143i | \(0.683057\pi\) | |||||||
\(774\) | −5.04941 | −0.181497 | ||||||||
\(775\) | −35.2851 | −1.26748 | ||||||||
\(776\) | 65.9212 | 2.36643 | ||||||||
\(777\) | 3.98547 | 0.142978 | ||||||||
\(778\) | −44.6946 | −1.60238 | ||||||||
\(779\) | −18.2130 | −0.652549 | ||||||||
\(780\) | −0.798352 | −0.0285856 | ||||||||
\(781\) | 14.0177 | 0.501593 | ||||||||
\(782\) | 13.4166 | 0.479776 | ||||||||
\(783\) | 34.1458 | 1.22027 | ||||||||
\(784\) | 0.707854 | 0.0252805 | ||||||||
\(785\) | −0.120313 | −0.00429415 | ||||||||
\(786\) | 12.8165 | 0.457148 | ||||||||
\(787\) | 24.3925 | 0.869498 | 0.434749 | − | 0.900552i | \(-0.356837\pi\) | ||||
0.434749 | + | 0.900552i | \(0.356837\pi\) | |||||||
\(788\) | 99.3638 | 3.53969 | ||||||||
\(789\) | 28.9790 | 1.03168 | ||||||||
\(790\) | −0.575407 | −0.0204721 | ||||||||
\(791\) | −17.0533 | −0.606345 | ||||||||
\(792\) | −12.0930 | −0.429705 | ||||||||
\(793\) | −3.36381 | −0.119452 | ||||||||
\(794\) | 16.1024 | 0.571454 | ||||||||
\(795\) | 0.379270 | 0.0134513 | ||||||||
\(796\) | −68.2506 | −2.41908 | ||||||||
\(797\) | −31.9350 | −1.13120 | −0.565599 | − | 0.824681i | \(-0.691355\pi\) | ||||
−0.565599 | + | 0.824681i | \(0.691355\pi\) | |||||||
\(798\) | −31.8460 | −1.12734 | ||||||||
\(799\) | −53.2193 | −1.88276 | ||||||||
\(800\) | 16.2724 | 0.575315 | ||||||||
\(801\) | 0.229010 | 0.00809167 | ||||||||
\(802\) | 51.3158 | 1.81202 | ||||||||
\(803\) | 26.4731 | 0.934214 | ||||||||
\(804\) | −37.7681 | −1.33198 | ||||||||
\(805\) | 0.0722895 | 0.00254787 | ||||||||
\(806\) | 82.6914 | 2.91268 | ||||||||
\(807\) | 16.8125 | 0.591828 | ||||||||
\(808\) | −13.9970 | −0.492412 | ||||||||
\(809\) | −13.0809 | −0.459901 | −0.229950 | − | 0.973202i | \(-0.573856\pi\) | ||||
−0.229950 | + | 0.973202i | \(0.573856\pi\) | |||||||
\(810\) | −0.396131 | −0.0139186 | ||||||||
\(811\) | 41.8983 | 1.47125 | 0.735624 | − | 0.677391i | \(-0.236889\pi\) | ||||
0.735624 | + | 0.677391i | \(0.236889\pi\) | |||||||
\(812\) | 69.4806 | 2.43829 | ||||||||
\(813\) | 44.3280 | 1.55465 | ||||||||
\(814\) | −6.46561 | −0.226619 | ||||||||
\(815\) | 0.266819 | 0.00934628 | ||||||||
\(816\) | −46.2837 | −1.62025 | ||||||||
\(817\) | 7.87867 | 0.275640 | ||||||||
\(818\) | −89.7776 | −3.13900 | ||||||||
\(819\) | 10.2445 | 0.357971 | ||||||||
\(820\) | −0.655277 | −0.0228833 | ||||||||
\(821\) | −8.81603 | −0.307682 | −0.153841 | − | 0.988096i | \(-0.549164\pi\) | ||||
−0.153841 | + | 0.988096i | \(0.549164\pi\) | |||||||
\(822\) | 67.1555 | 2.34232 | ||||||||
\(823\) | 32.1300 | 1.11998 | 0.559990 | − | 0.828499i | \(-0.310805\pi\) | ||||
0.559990 | + | 0.828499i | \(0.310805\pi\) | |||||||
\(824\) | −74.7358 | −2.60355 | ||||||||
\(825\) | −18.7712 | −0.653529 | ||||||||
\(826\) | −52.2116 | −1.81667 | ||||||||
\(827\) | −16.5459 | −0.575356 | −0.287678 | − | 0.957727i | \(-0.592883\pi\) | ||||
−0.287678 | + | 0.957727i | \(0.592883\pi\) | |||||||
\(828\) | 3.55704 | 0.123616 | ||||||||
\(829\) | −27.5184 | −0.955752 | −0.477876 | − | 0.878427i | \(-0.658593\pi\) | ||||
−0.477876 | + | 0.878427i | \(0.658593\pi\) | |||||||
\(830\) | 0.762099 | 0.0264529 | ||||||||
\(831\) | −30.9169 | −1.07250 | ||||||||
\(832\) | 16.9340 | 0.587081 | ||||||||
\(833\) | 0.637921 | 0.0221027 | ||||||||
\(834\) | 67.1438 | 2.32500 | ||||||||
\(835\) | 0.589293 | 0.0203933 | ||||||||
\(836\) | 35.2662 | 1.21971 | ||||||||
\(837\) | 39.8119 | 1.37610 | ||||||||
\(838\) | 34.8536 | 1.20400 | ||||||||
\(839\) | −17.1000 | −0.590359 | −0.295179 | − | 0.955442i | \(-0.595379\pi\) | ||||
−0.295179 | + | 0.955442i | \(0.595379\pi\) | |||||||
\(840\) | −0.613034 | −0.0211517 | ||||||||
\(841\) | 7.64534 | 0.263633 | ||||||||
\(842\) | −22.5897 | −0.778492 | ||||||||
\(843\) | −18.5809 | −0.639959 | ||||||||
\(844\) | −8.27108 | −0.284702 | ||||||||
\(845\) | −0.236692 | −0.00814245 | ||||||||
\(846\) | −20.6701 | −0.710653 | ||||||||
\(847\) | −12.0744 | −0.414881 | ||||||||
\(848\) | 56.2656 | 1.93217 | ||||||||
\(849\) | 42.9233 | 1.47312 | ||||||||
\(850\) | 66.7219 | 2.28854 | ||||||||
\(851\) | 1.01754 | 0.0348808 | ||||||||
\(852\) | 34.9657 | 1.19790 | ||||||||
\(853\) | −24.9815 | −0.855351 | −0.427676 | − | 0.903932i | \(-0.640667\pi\) | ||||
−0.427676 | + | 0.903932i | \(0.640667\pi\) | |||||||
\(854\) | −4.82764 | −0.165199 | ||||||||
\(855\) | −0.0714296 | −0.00244284 | ||||||||
\(856\) | 85.9743 | 2.93854 | ||||||||
\(857\) | 6.32454 | 0.216042 | 0.108021 | − | 0.994149i | \(-0.465549\pi\) | ||||
0.108021 | + | 0.994149i | \(0.465549\pi\) | |||||||
\(858\) | 43.9907 | 1.50182 | ||||||||
\(859\) | 44.6477 | 1.52336 | 0.761680 | − | 0.647954i | \(-0.224375\pi\) | ||||
0.761680 | + | 0.647954i | \(0.224375\pi\) | |||||||
\(860\) | 0.283463 | 0.00966600 | ||||||||
\(861\) | −22.2568 | −0.758508 | ||||||||
\(862\) | 40.1497 | 1.36751 | ||||||||
\(863\) | 33.8143 | 1.15105 | 0.575526 | − | 0.817783i | \(-0.304797\pi\) | ||||
0.575526 | + | 0.817783i | \(0.304797\pi\) | |||||||
\(864\) | −18.3600 | −0.624619 | ||||||||
\(865\) | 0.298829 | 0.0101605 | ||||||||
\(866\) | 20.0399 | 0.680983 | ||||||||
\(867\) | −16.6259 | −0.564645 | ||||||||
\(868\) | 81.0100 | 2.74966 | ||||||||
\(869\) | 21.6429 | 0.734186 | ||||||||
\(870\) | −0.604301 | −0.0204877 | ||||||||
\(871\) | −27.7714 | −0.940999 | ||||||||
\(872\) | −15.0801 | −0.510676 | ||||||||
\(873\) | 9.38640 | 0.317682 | ||||||||
\(874\) | −8.13069 | −0.275025 | ||||||||
\(875\) | 0.719058 | 0.0243086 | ||||||||
\(876\) | 66.0342 | 2.23109 | ||||||||
\(877\) | −14.6392 | −0.494330 | −0.247165 | − | 0.968973i | \(-0.579499\pi\) | ||||
−0.247165 | + | 0.968973i | \(0.579499\pi\) | |||||||
\(878\) | 16.6403 | 0.561583 | ||||||||
\(879\) | 26.3567 | 0.888989 | ||||||||
\(880\) | 0.404568 | 0.0136380 | ||||||||
\(881\) | 10.1670 | 0.342535 | 0.171268 | − | 0.985225i | \(-0.445214\pi\) | ||||
0.171268 | + | 0.985225i | \(0.445214\pi\) | |||||||
\(882\) | 0.247765 | 0.00834269 | ||||||||
\(883\) | 28.5414 | 0.960493 | 0.480247 | − | 0.877134i | \(-0.340547\pi\) | ||||
0.480247 | + | 0.877134i | \(0.340547\pi\) | |||||||
\(884\) | −106.736 | −3.58993 | ||||||||
\(885\) | 0.309978 | 0.0104198 | ||||||||
\(886\) | −3.25943 | −0.109503 | ||||||||
\(887\) | −7.43313 | −0.249580 | −0.124790 | − | 0.992183i | \(-0.539826\pi\) | ||||
−0.124790 | + | 0.992183i | \(0.539826\pi\) | |||||||
\(888\) | −8.62901 | −0.289570 | ||||||||
\(889\) | 12.0078 | 0.402727 | ||||||||
\(890\) | −0.0188337 | −0.000631307 0 | ||||||||
\(891\) | 14.8998 | 0.499161 | ||||||||
\(892\) | −39.2524 | −1.31427 | ||||||||
\(893\) | 32.2519 | 1.07927 | ||||||||
\(894\) | −26.0990 | −0.872880 | ||||||||
\(895\) | −0.154674 | −0.00517019 | ||||||||
\(896\) | 41.6737 | 1.39222 | ||||||||
\(897\) | −6.92315 | −0.231157 | ||||||||
\(898\) | 77.6485 | 2.59116 | ||||||||
\(899\) | 42.7262 | 1.42500 | ||||||||
\(900\) | 17.6895 | 0.589651 | ||||||||
\(901\) | 50.7068 | 1.68929 | ||||||||
\(902\) | 36.1070 | 1.20223 | ||||||||
\(903\) | 9.62793 | 0.320398 | ||||||||
\(904\) | 36.9224 | 1.22802 | ||||||||
\(905\) | 0.560730 | 0.0186393 | ||||||||
\(906\) | 30.8732 | 1.02569 | ||||||||
\(907\) | 36.2192 | 1.20264 | 0.601320 | − | 0.799008i | \(-0.294642\pi\) | ||||
0.601320 | + | 0.799008i | \(0.294642\pi\) | |||||||
\(908\) | −27.1375 | −0.900588 | ||||||||
\(909\) | −1.99300 | −0.0661038 | ||||||||
\(910\) | −0.842503 | −0.0279287 | ||||||||
\(911\) | 38.2935 | 1.26872 | 0.634360 | − | 0.773038i | \(-0.281264\pi\) | ||||
0.634360 | + | 0.773038i | \(0.281264\pi\) | |||||||
\(912\) | 28.0488 | 0.928787 | ||||||||
\(913\) | −28.6651 | −0.948675 | ||||||||
\(914\) | 51.8632 | 1.71548 | ||||||||
\(915\) | 0.0286615 | 0.000947521 0 | ||||||||
\(916\) | 75.4856 | 2.49411 | ||||||||
\(917\) | 9.23250 | 0.304884 | ||||||||
\(918\) | −75.2818 | −2.48467 | ||||||||
\(919\) | −11.2696 | −0.371750 | −0.185875 | − | 0.982573i | \(-0.559512\pi\) | ||||
−0.185875 | + | 0.982573i | \(0.559512\pi\) | |||||||
\(920\) | −0.156515 | −0.00516015 | ||||||||
\(921\) | 5.41120 | 0.178305 | ||||||||
\(922\) | 21.7074 | 0.714894 | ||||||||
\(923\) | 25.7108 | 0.846280 | ||||||||
\(924\) | 43.0962 | 1.41776 | ||||||||
\(925\) | 5.06033 | 0.166383 | ||||||||
\(926\) | 30.6948 | 1.00869 | ||||||||
\(927\) | −10.6415 | −0.349513 | ||||||||
\(928\) | −19.7039 | −0.646813 | ||||||||
\(929\) | 0.394018 | 0.0129273 | 0.00646365 | − | 0.999979i | \(-0.497943\pi\) | ||||
0.00646365 | + | 0.999979i | \(0.497943\pi\) | |||||||
\(930\) | −0.704577 | −0.0231040 | ||||||||
\(931\) | −0.386592 | −0.0126700 | ||||||||
\(932\) | 73.4588 | 2.40622 | ||||||||
\(933\) | 4.98675 | 0.163259 | ||||||||
\(934\) | 85.5535 | 2.79940 | ||||||||
\(935\) | 0.364598 | 0.0119236 | ||||||||
\(936\) | −22.1805 | −0.724992 | ||||||||
\(937\) | −50.0343 | −1.63455 | −0.817274 | − | 0.576249i | \(-0.804516\pi\) | ||||
−0.817274 | + | 0.576249i | \(0.804516\pi\) | |||||||
\(938\) | −39.8568 | −1.30137 | ||||||||
\(939\) | −13.1618 | −0.429521 | ||||||||
\(940\) | 1.16037 | 0.0378472 | ||||||||
\(941\) | 20.1417 | 0.656601 | 0.328301 | − | 0.944573i | \(-0.393524\pi\) | ||||
0.328301 | + | 0.944573i | \(0.393524\pi\) | |||||||
\(942\) | 16.5365 | 0.538790 | ||||||||
\(943\) | −5.68243 | −0.185045 | ||||||||
\(944\) | 45.9860 | 1.49672 | ||||||||
\(945\) | −0.405624 | −0.0131950 | ||||||||
\(946\) | −15.6193 | −0.507829 | ||||||||
\(947\) | −13.6663 | −0.444094 | −0.222047 | − | 0.975036i | \(-0.571274\pi\) | ||||
−0.222047 | + | 0.975036i | \(0.571274\pi\) | |||||||
\(948\) | 53.9860 | 1.75338 | ||||||||
\(949\) | 48.5560 | 1.57619 | ||||||||
\(950\) | −40.4347 | −1.31188 | ||||||||
\(951\) | 17.5354 | 0.568625 | ||||||||
\(952\) | −81.9600 | −2.65634 | ||||||||
\(953\) | −29.2291 | −0.946824 | −0.473412 | − | 0.880841i | \(-0.656978\pi\) | ||||
−0.473412 | + | 0.880841i | \(0.656978\pi\) | |||||||
\(954\) | 19.6943 | 0.637625 | ||||||||
\(955\) | −0.524806 | −0.0169823 | ||||||||
\(956\) | 46.2770 | 1.49671 | ||||||||
\(957\) | 22.7297 | 0.734748 | ||||||||
\(958\) | −59.5226 | −1.92309 | ||||||||
\(959\) | 48.3764 | 1.56215 | ||||||||
\(960\) | −0.144287 | −0.00465685 | ||||||||
\(961\) | 18.8160 | 0.606968 | ||||||||
\(962\) | −11.8590 | −0.382349 | ||||||||
\(963\) | 12.2417 | 0.394484 | ||||||||
\(964\) | 48.3694 | 1.55787 | ||||||||
\(965\) | 0.532353 | 0.0171371 | ||||||||
\(966\) | −9.93590 | −0.319682 | ||||||||
\(967\) | 18.4625 | 0.593715 | 0.296858 | − | 0.954922i | \(-0.404061\pi\) | ||||
0.296858 | + | 0.954922i | \(0.404061\pi\) | |||||||
\(968\) | 26.1425 | 0.840252 | ||||||||
\(969\) | 25.2777 | 0.812036 | ||||||||
\(970\) | −0.771935 | −0.0247853 | ||||||||
\(971\) | −2.55091 | −0.0818627 | −0.0409314 | − | 0.999162i | \(-0.513032\pi\) | ||||
−0.0409314 | + | 0.999162i | \(0.513032\pi\) | |||||||
\(972\) | −35.6228 | −1.14260 | ||||||||
\(973\) | 48.3679 | 1.55060 | ||||||||
\(974\) | 34.6009 | 1.10868 | ||||||||
\(975\) | −34.4295 | −1.10263 | ||||||||
\(976\) | 4.25201 | 0.136103 | ||||||||
\(977\) | −24.2975 | −0.777345 | −0.388672 | − | 0.921376i | \(-0.627066\pi\) | ||||
−0.388672 | + | 0.921376i | \(0.627066\pi\) | |||||||
\(978\) | −36.6733 | −1.17268 | ||||||||
\(979\) | 0.708397 | 0.0226405 | ||||||||
\(980\) | −0.0139090 | −0.000444307 0 | ||||||||
\(981\) | −2.14723 | −0.0685557 | ||||||||
\(982\) | −81.7124 | −2.60755 | ||||||||
\(983\) | 54.5719 | 1.74057 | 0.870287 | − | 0.492545i | \(-0.163933\pi\) | ||||
0.870287 | + | 0.492545i | \(0.163933\pi\) | |||||||
\(984\) | 48.1885 | 1.53619 | ||||||||
\(985\) | −0.622544 | −0.0198359 | ||||||||
\(986\) | −80.7925 | −2.57296 | ||||||||
\(987\) | 39.4126 | 1.25452 | ||||||||
\(988\) | 64.6841 | 2.05788 | ||||||||
\(989\) | 2.45813 | 0.0781641 | ||||||||
\(990\) | 0.141608 | 0.00450060 | ||||||||
\(991\) | −3.12892 | −0.0993933 | −0.0496967 | − | 0.998764i | \(-0.515825\pi\) | ||||
−0.0496967 | + | 0.998764i | \(0.515825\pi\) | |||||||
\(992\) | −22.9736 | −0.729411 | ||||||||
\(993\) | 23.9529 | 0.760122 | ||||||||
\(994\) | 36.8994 | 1.17038 | ||||||||
\(995\) | 0.427610 | 0.0135562 | ||||||||
\(996\) | −71.5020 | −2.26563 | ||||||||
\(997\) | −39.2772 | −1.24392 | −0.621961 | − | 0.783049i | \(-0.713664\pi\) | ||||
−0.621961 | + | 0.783049i | \(0.713664\pi\) | |||||||
\(998\) | −98.1685 | −3.10747 | ||||||||
\(999\) | −5.70953 | −0.180641 |
(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 | 4007.2.a.a.1.10 | ✓ | 139 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4007.2.a.a.1.10 | ✓ | 139 | 1.1 | even | 1 | trivial |