Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8009,2,Mod(1,8009)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8009, 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("8009.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8009 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8009.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: | \(63.9521869788\) |
Analytic rank: | \(1\) |
Dimension: | \(306\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.18 | ||
Character | \(\chi\) | \(=\) | 8009.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.52963 | −1.78872 | −0.894359 | − | 0.447350i | \(-0.852368\pi\) | ||||
−0.894359 | + | 0.447350i | \(0.852368\pi\) | |||||||
\(3\) | 0.577486 | 0.333412 | 0.166706 | − | 0.986007i | \(-0.446687\pi\) | ||||
0.166706 | + | 0.986007i | \(0.446687\pi\) | |||||||
\(4\) | 4.39902 | 2.19951 | ||||||||
\(5\) | −1.57582 | −0.704728 | −0.352364 | − | 0.935863i | \(-0.614622\pi\) | ||||
−0.352364 | + | 0.935863i | \(0.614622\pi\) | |||||||
\(6\) | −1.46082 | −0.596379 | ||||||||
\(7\) | −2.02955 | −0.767099 | −0.383549 | − | 0.923520i | \(-0.625298\pi\) | ||||
−0.383549 | + | 0.923520i | \(0.625298\pi\) | |||||||
\(8\) | −6.06864 | −2.14559 | ||||||||
\(9\) | −2.66651 | −0.888837 | ||||||||
\(10\) | 3.98624 | 1.26056 | ||||||||
\(11\) | 1.54104 | 0.464640 | 0.232320 | − | 0.972639i | \(-0.425368\pi\) | ||||
0.232320 | + | 0.972639i | \(0.425368\pi\) | |||||||
\(12\) | 2.54037 | 0.733342 | ||||||||
\(13\) | −2.97088 | −0.823974 | −0.411987 | − | 0.911190i | \(-0.635165\pi\) | ||||
−0.411987 | + | 0.911190i | \(0.635165\pi\) | |||||||
\(14\) | 5.13402 | 1.37212 | ||||||||
\(15\) | −0.910013 | −0.234964 | ||||||||
\(16\) | 6.55335 | 1.63834 | ||||||||
\(17\) | 5.26544 | 1.27706 | 0.638528 | − | 0.769598i | \(-0.279543\pi\) | ||||
0.638528 | + | 0.769598i | \(0.279543\pi\) | |||||||
\(18\) | 6.74528 | 1.58988 | ||||||||
\(19\) | 0.106614 | 0.0244589 | 0.0122294 | − | 0.999925i | \(-0.496107\pi\) | ||||
0.0122294 | + | 0.999925i | \(0.496107\pi\) | |||||||
\(20\) | −6.93206 | −1.55006 | ||||||||
\(21\) | −1.17204 | −0.255760 | ||||||||
\(22\) | −3.89825 | −0.831110 | ||||||||
\(23\) | −3.47995 | −0.725619 | −0.362809 | − | 0.931863i | \(-0.618182\pi\) | ||||
−0.362809 | + | 0.931863i | \(0.618182\pi\) | |||||||
\(24\) | −3.50455 | −0.715363 | ||||||||
\(25\) | −2.51679 | −0.503359 | ||||||||
\(26\) | 7.51522 | 1.47386 | ||||||||
\(27\) | −3.27233 | −0.629760 | ||||||||
\(28\) | −8.92805 | −1.68724 | ||||||||
\(29\) | −0.567612 | −0.105403 | −0.0527014 | − | 0.998610i | \(-0.516783\pi\) | ||||
−0.0527014 | + | 0.998610i | \(0.516783\pi\) | |||||||
\(30\) | 2.30200 | 0.420285 | ||||||||
\(31\) | 9.64704 | 1.73266 | 0.866330 | − | 0.499472i | \(-0.166473\pi\) | ||||
0.866330 | + | 0.499472i | \(0.166473\pi\) | |||||||
\(32\) | −4.44028 | −0.784938 | ||||||||
\(33\) | 0.889926 | 0.154916 | ||||||||
\(34\) | −13.3196 | −2.28429 | ||||||||
\(35\) | 3.19821 | 0.540596 | ||||||||
\(36\) | −11.7300 | −1.95501 | ||||||||
\(37\) | 8.29375 | 1.36348 | 0.681742 | − | 0.731592i | \(-0.261222\pi\) | ||||
0.681742 | + | 0.731592i | \(0.261222\pi\) | |||||||
\(38\) | −0.269693 | −0.0437500 | ||||||||
\(39\) | −1.71564 | −0.274722 | ||||||||
\(40\) | 9.56307 | 1.51205 | ||||||||
\(41\) | −5.00824 | −0.782156 | −0.391078 | − | 0.920357i | \(-0.627898\pi\) | ||||
−0.391078 | + | 0.920357i | \(0.627898\pi\) | |||||||
\(42\) | 2.96482 | 0.457482 | ||||||||
\(43\) | −2.17640 | −0.331899 | −0.165949 | − | 0.986134i | \(-0.553069\pi\) | ||||
−0.165949 | + | 0.986134i | \(0.553069\pi\) | |||||||
\(44\) | 6.77905 | 1.02198 | ||||||||
\(45\) | 4.20194 | 0.626388 | ||||||||
\(46\) | 8.80297 | 1.29793 | ||||||||
\(47\) | −1.86539 | −0.272095 | −0.136047 | − | 0.990702i | \(-0.543440\pi\) | ||||
−0.136047 | + | 0.990702i | \(0.543440\pi\) | |||||||
\(48\) | 3.78447 | 0.546241 | ||||||||
\(49\) | −2.88091 | −0.411559 | ||||||||
\(50\) | 6.36655 | 0.900367 | ||||||||
\(51\) | 3.04072 | 0.425786 | ||||||||
\(52\) | −13.0690 | −1.81234 | ||||||||
\(53\) | 13.0403 | 1.79122 | 0.895612 | − | 0.444837i | \(-0.146738\pi\) | ||||
0.895612 | + | 0.444837i | \(0.146738\pi\) | |||||||
\(54\) | 8.27778 | 1.12646 | ||||||||
\(55\) | −2.42839 | −0.327445 | ||||||||
\(56\) | 12.3166 | 1.64588 | ||||||||
\(57\) | 0.0615680 | 0.00815487 | ||||||||
\(58\) | 1.43585 | 0.188536 | ||||||||
\(59\) | −14.4740 | −1.88435 | −0.942174 | − | 0.335123i | \(-0.891222\pi\) | ||||
−0.942174 | + | 0.335123i | \(0.891222\pi\) | |||||||
\(60\) | −4.00317 | −0.516807 | ||||||||
\(61\) | 13.3263 | 1.70626 | 0.853130 | − | 0.521698i | \(-0.174701\pi\) | ||||
0.853130 | + | 0.521698i | \(0.174701\pi\) | |||||||
\(62\) | −24.4034 | −3.09924 | ||||||||
\(63\) | 5.41182 | 0.681826 | ||||||||
\(64\) | −1.87445 | −0.234306 | ||||||||
\(65\) | 4.68157 | 0.580677 | ||||||||
\(66\) | −2.25118 | −0.277102 | ||||||||
\(67\) | −2.56018 | −0.312776 | −0.156388 | − | 0.987696i | \(-0.549985\pi\) | ||||
−0.156388 | + | 0.987696i | \(0.549985\pi\) | |||||||
\(68\) | 23.1628 | 2.80890 | ||||||||
\(69\) | −2.00962 | −0.241930 | ||||||||
\(70\) | −8.09028 | −0.966974 | ||||||||
\(71\) | −2.02974 | −0.240885 | −0.120443 | − | 0.992720i | \(-0.538431\pi\) | ||||
−0.120443 | + | 0.992720i | \(0.538431\pi\) | |||||||
\(72\) | 16.1821 | 1.90708 | ||||||||
\(73\) | −9.31908 | −1.09072 | −0.545358 | − | 0.838203i | \(-0.683606\pi\) | ||||
−0.545358 | + | 0.838203i | \(0.683606\pi\) | |||||||
\(74\) | −20.9801 | −2.43889 | ||||||||
\(75\) | −1.45341 | −0.167826 | ||||||||
\(76\) | 0.468997 | 0.0537976 | ||||||||
\(77\) | −3.12761 | −0.356425 | ||||||||
\(78\) | 4.33993 | 0.491401 | ||||||||
\(79\) | −13.9983 | −1.57494 | −0.787468 | − | 0.616355i | \(-0.788609\pi\) | ||||
−0.787468 | + | 0.616355i | \(0.788609\pi\) | |||||||
\(80\) | −10.3269 | −1.15458 | ||||||||
\(81\) | 6.10981 | 0.678868 | ||||||||
\(82\) | 12.6690 | 1.39906 | ||||||||
\(83\) | −8.30188 | −0.911250 | −0.455625 | − | 0.890172i | \(-0.650584\pi\) | ||||
−0.455625 | + | 0.890172i | \(0.650584\pi\) | |||||||
\(84\) | −5.15582 | −0.562546 | ||||||||
\(85\) | −8.29738 | −0.899978 | ||||||||
\(86\) | 5.50550 | 0.593673 | ||||||||
\(87\) | −0.327788 | −0.0351425 | ||||||||
\(88\) | −9.35199 | −0.996925 | ||||||||
\(89\) | 12.4061 | 1.31504 | 0.657521 | − | 0.753436i | \(-0.271605\pi\) | ||||
0.657521 | + | 0.753436i | \(0.271605\pi\) | |||||||
\(90\) | −10.6293 | −1.12043 | ||||||||
\(91\) | 6.02956 | 0.632070 | ||||||||
\(92\) | −15.3084 | −1.59601 | ||||||||
\(93\) | 5.57103 | 0.577689 | ||||||||
\(94\) | 4.71873 | 0.486700 | ||||||||
\(95\) | −0.168004 | −0.0172369 | ||||||||
\(96\) | −2.56420 | −0.261707 | ||||||||
\(97\) | 13.7317 | 1.39424 | 0.697121 | − | 0.716953i | \(-0.254464\pi\) | ||||
0.697121 | + | 0.716953i | \(0.254464\pi\) | |||||||
\(98\) | 7.28765 | 0.736163 | ||||||||
\(99\) | −4.10919 | −0.412989 | ||||||||
\(100\) | −11.0714 | −1.10714 | ||||||||
\(101\) | 9.47232 | 0.942532 | 0.471266 | − | 0.881991i | \(-0.343797\pi\) | ||||
0.471266 | + | 0.881991i | \(0.343797\pi\) | |||||||
\(102\) | −7.69189 | −0.761610 | ||||||||
\(103\) | 5.43537 | 0.535563 | 0.267782 | − | 0.963480i | \(-0.413709\pi\) | ||||
0.267782 | + | 0.963480i | \(0.413709\pi\) | |||||||
\(104\) | 18.0292 | 1.76791 | ||||||||
\(105\) | 1.84692 | 0.180241 | ||||||||
\(106\) | −32.9871 | −3.20399 | ||||||||
\(107\) | 10.9215 | 1.05582 | 0.527909 | − | 0.849301i | \(-0.322976\pi\) | ||||
0.527909 | + | 0.849301i | \(0.322976\pi\) | |||||||
\(108\) | −14.3950 | −1.38516 | ||||||||
\(109\) | 11.2703 | 1.07950 | 0.539751 | − | 0.841825i | \(-0.318518\pi\) | ||||
0.539751 | + | 0.841825i | \(0.318518\pi\) | |||||||
\(110\) | 6.14294 | 0.585706 | ||||||||
\(111\) | 4.78952 | 0.454602 | ||||||||
\(112\) | −13.3004 | −1.25677 | ||||||||
\(113\) | 12.1763 | 1.14545 | 0.572724 | − | 0.819748i | \(-0.305887\pi\) | ||||
0.572724 | + | 0.819748i | \(0.305887\pi\) | |||||||
\(114\) | −0.155744 | −0.0145868 | ||||||||
\(115\) | 5.48377 | 0.511364 | ||||||||
\(116\) | −2.49694 | −0.231835 | ||||||||
\(117\) | 7.92188 | 0.732378 | ||||||||
\(118\) | 36.6137 | 3.37057 | ||||||||
\(119\) | −10.6865 | −0.979629 | ||||||||
\(120\) | 5.52254 | 0.504137 | ||||||||
\(121\) | −8.62521 | −0.784110 | ||||||||
\(122\) | −33.7106 | −3.05202 | ||||||||
\(123\) | −2.89219 | −0.260780 | ||||||||
\(124\) | 42.4376 | 3.81100 | ||||||||
\(125\) | 11.8451 | 1.05946 | ||||||||
\(126\) | −13.6899 | −1.21959 | ||||||||
\(127\) | −2.85204 | −0.253077 | −0.126539 | − | 0.991962i | \(-0.540387\pi\) | ||||
−0.126539 | + | 0.991962i | \(0.540387\pi\) | |||||||
\(128\) | 13.6222 | 1.20405 | ||||||||
\(129\) | −1.25684 | −0.110659 | ||||||||
\(130\) | −11.8426 | −1.03867 | ||||||||
\(131\) | 15.9974 | 1.39770 | 0.698851 | − | 0.715268i | \(-0.253695\pi\) | ||||
0.698851 | + | 0.715268i | \(0.253695\pi\) | |||||||
\(132\) | 3.91481 | 0.340740 | ||||||||
\(133\) | −0.216378 | −0.0187624 | ||||||||
\(134\) | 6.47631 | 0.559468 | ||||||||
\(135\) | 5.15660 | 0.443809 | ||||||||
\(136\) | −31.9540 | −2.74004 | ||||||||
\(137\) | 19.2710 | 1.64643 | 0.823215 | − | 0.567729i | \(-0.192178\pi\) | ||||
0.823215 | + | 0.567729i | \(0.192178\pi\) | |||||||
\(138\) | 5.08359 | 0.432744 | ||||||||
\(139\) | −11.9024 | −1.00955 | −0.504774 | − | 0.863251i | \(-0.668424\pi\) | ||||
−0.504774 | + | 0.863251i | \(0.668424\pi\) | |||||||
\(140\) | 14.0690 | 1.18905 | ||||||||
\(141\) | −1.07723 | −0.0907194 | ||||||||
\(142\) | 5.13448 | 0.430876 | ||||||||
\(143\) | −4.57823 | −0.382851 | ||||||||
\(144\) | −17.4746 | −1.45622 | ||||||||
\(145\) | 0.894454 | 0.0742804 | ||||||||
\(146\) | 23.5738 | 1.95098 | ||||||||
\(147\) | −1.66369 | −0.137219 | ||||||||
\(148\) | 36.4844 | 2.99900 | ||||||||
\(149\) | −4.74061 | −0.388366 | −0.194183 | − | 0.980965i | \(-0.562205\pi\) | ||||
−0.194183 | + | 0.980965i | \(0.562205\pi\) | |||||||
\(150\) | 3.67659 | 0.300193 | ||||||||
\(151\) | −4.97433 | −0.404806 | −0.202403 | − | 0.979302i | \(-0.564875\pi\) | ||||
−0.202403 | + | 0.979302i | \(0.564875\pi\) | |||||||
\(152\) | −0.647000 | −0.0524787 | ||||||||
\(153\) | −14.0404 | −1.13510 | ||||||||
\(154\) | 7.91170 | 0.637543 | ||||||||
\(155\) | −15.2020 | −1.22105 | ||||||||
\(156\) | −7.54714 | −0.604255 | ||||||||
\(157\) | −10.3181 | −0.823475 | −0.411738 | − | 0.911302i | \(-0.635078\pi\) | ||||
−0.411738 | + | 0.911302i | \(0.635078\pi\) | |||||||
\(158\) | 35.4106 | 2.81712 | ||||||||
\(159\) | 7.53059 | 0.597215 | ||||||||
\(160\) | 6.99708 | 0.553167 | ||||||||
\(161\) | 7.06274 | 0.556622 | ||||||||
\(162\) | −15.4555 | −1.21430 | ||||||||
\(163\) | 8.34247 | 0.653432 | 0.326716 | − | 0.945122i | \(-0.394058\pi\) | ||||
0.326716 | + | 0.945122i | \(0.394058\pi\) | |||||||
\(164\) | −22.0314 | −1.72036 | ||||||||
\(165\) | −1.40236 | −0.109174 | ||||||||
\(166\) | 21.0007 | 1.62997 | ||||||||
\(167\) | 1.14915 | 0.0889239 | 0.0444620 | − | 0.999011i | \(-0.485843\pi\) | ||||
0.0444620 | + | 0.999011i | \(0.485843\pi\) | |||||||
\(168\) | 7.11267 | 0.548754 | ||||||||
\(169\) | −4.17387 | −0.321067 | ||||||||
\(170\) | 20.9893 | 1.60981 | ||||||||
\(171\) | −0.284287 | −0.0217400 | ||||||||
\(172\) | −9.57405 | −0.730015 | ||||||||
\(173\) | 6.33437 | 0.481593 | 0.240797 | − | 0.970576i | \(-0.422591\pi\) | ||||
0.240797 | + | 0.970576i | \(0.422591\pi\) | |||||||
\(174\) | 0.829182 | 0.0628601 | ||||||||
\(175\) | 5.10797 | 0.386126 | ||||||||
\(176\) | 10.0990 | 0.761237 | ||||||||
\(177\) | −8.35850 | −0.628264 | ||||||||
\(178\) | −31.3828 | −2.35224 | ||||||||
\(179\) | 0.271048 | 0.0202591 | 0.0101295 | − | 0.999949i | \(-0.496776\pi\) | ||||
0.0101295 | + | 0.999949i | \(0.496776\pi\) | |||||||
\(180\) | 18.4844 | 1.37775 | ||||||||
\(181\) | −26.2785 | −1.95327 | −0.976633 | − | 0.214915i | \(-0.931053\pi\) | ||||
−0.976633 | + | 0.214915i | \(0.931053\pi\) | |||||||
\(182\) | −15.2525 | −1.13059 | ||||||||
\(183\) | 7.69576 | 0.568887 | ||||||||
\(184\) | 21.1185 | 1.55688 | ||||||||
\(185\) | −13.0695 | −0.960886 | ||||||||
\(186\) | −14.0926 | −1.03332 | ||||||||
\(187\) | 8.11424 | 0.593372 | ||||||||
\(188\) | −8.20587 | −0.598475 | ||||||||
\(189\) | 6.64136 | 0.483088 | ||||||||
\(190\) | 0.424988 | 0.0308319 | ||||||||
\(191\) | 12.7717 | 0.924129 | 0.462064 | − | 0.886846i | \(-0.347109\pi\) | ||||
0.462064 | + | 0.886846i | \(0.347109\pi\) | |||||||
\(192\) | −1.08247 | −0.0781204 | ||||||||
\(193\) | 10.1400 | 0.729890 | 0.364945 | − | 0.931029i | \(-0.381088\pi\) | ||||
0.364945 | + | 0.931029i | \(0.381088\pi\) | |||||||
\(194\) | −34.7361 | −2.49391 | ||||||||
\(195\) | 2.70354 | 0.193605 | ||||||||
\(196\) | −12.6732 | −0.905229 | ||||||||
\(197\) | −20.6470 | −1.47103 | −0.735517 | − | 0.677506i | \(-0.763061\pi\) | ||||
−0.735517 | + | 0.677506i | \(0.763061\pi\) | |||||||
\(198\) | 10.3947 | 0.738721 | ||||||||
\(199\) | −3.85601 | −0.273345 | −0.136673 | − | 0.990616i | \(-0.543641\pi\) | ||||
−0.136673 | + | 0.990616i | \(0.543641\pi\) | |||||||
\(200\) | 15.2735 | 1.08000 | ||||||||
\(201\) | −1.47847 | −0.104283 | ||||||||
\(202\) | −23.9615 | −1.68592 | ||||||||
\(203\) | 1.15200 | 0.0808545 | ||||||||
\(204\) | 13.3762 | 0.936520 | ||||||||
\(205\) | 7.89209 | 0.551207 | ||||||||
\(206\) | −13.7495 | −0.957971 | ||||||||
\(207\) | 9.27931 | 0.644957 | ||||||||
\(208\) | −19.4692 | −1.34995 | ||||||||
\(209\) | 0.164296 | 0.0113646 | ||||||||
\(210\) | −4.67202 | −0.322400 | ||||||||
\(211\) | −14.9307 | −1.02787 | −0.513937 | − | 0.857828i | \(-0.671814\pi\) | ||||
−0.513937 | + | 0.857828i | \(0.671814\pi\) | |||||||
\(212\) | 57.3646 | 3.93982 | ||||||||
\(213\) | −1.17214 | −0.0803140 | ||||||||
\(214\) | −27.6272 | −1.88856 | ||||||||
\(215\) | 3.42962 | 0.233898 | ||||||||
\(216\) | 19.8586 | 1.35120 | ||||||||
\(217\) | −19.5792 | −1.32912 | ||||||||
\(218\) | −28.5097 | −1.93092 | ||||||||
\(219\) | −5.38163 | −0.363657 | ||||||||
\(220\) | −10.6826 | −0.720218 | ||||||||
\(221\) | −15.6430 | −1.05226 | ||||||||
\(222\) | −12.1157 | −0.813154 | ||||||||
\(223\) | −11.3457 | −0.759764 | −0.379882 | − | 0.925035i | \(-0.624035\pi\) | ||||
−0.379882 | + | 0.925035i | \(0.624035\pi\) | |||||||
\(224\) | 9.01178 | 0.602125 | ||||||||
\(225\) | 6.71105 | 0.447404 | ||||||||
\(226\) | −30.8015 | −2.04888 | ||||||||
\(227\) | −14.4999 | −0.962394 | −0.481197 | − | 0.876612i | \(-0.659798\pi\) | ||||
−0.481197 | + | 0.876612i | \(0.659798\pi\) | |||||||
\(228\) | 0.270839 | 0.0179367 | ||||||||
\(229\) | −6.86488 | −0.453644 | −0.226822 | − | 0.973936i | \(-0.572834\pi\) | ||||
−0.226822 | + | 0.973936i | \(0.572834\pi\) | |||||||
\(230\) | −13.8719 | −0.914686 | ||||||||
\(231\) | −1.80615 | −0.118836 | ||||||||
\(232\) | 3.44463 | 0.226151 | ||||||||
\(233\) | 13.8280 | 0.905903 | 0.452951 | − | 0.891535i | \(-0.350371\pi\) | ||||
0.452951 | + | 0.891535i | \(0.350371\pi\) | |||||||
\(234\) | −20.0394 | −1.31002 | ||||||||
\(235\) | 2.93951 | 0.191753 | ||||||||
\(236\) | −63.6713 | −4.14465 | ||||||||
\(237\) | −8.08384 | −0.525102 | ||||||||
\(238\) | 27.0329 | 1.75228 | ||||||||
\(239\) | −6.43481 | −0.416233 | −0.208117 | − | 0.978104i | \(-0.566733\pi\) | ||||
−0.208117 | + | 0.978104i | \(0.566733\pi\) | |||||||
\(240\) | −5.96364 | −0.384951 | ||||||||
\(241\) | 14.7804 | 0.952087 | 0.476044 | − | 0.879422i | \(-0.342070\pi\) | ||||
0.476044 | + | 0.879422i | \(0.342070\pi\) | |||||||
\(242\) | 21.8186 | 1.40255 | ||||||||
\(243\) | 13.3453 | 0.856102 | ||||||||
\(244\) | 58.6228 | 3.75294 | ||||||||
\(245\) | 4.53980 | 0.290037 | ||||||||
\(246\) | 7.31617 | 0.466462 | ||||||||
\(247\) | −0.316737 | −0.0201535 | ||||||||
\(248\) | −58.5444 | −3.71757 | ||||||||
\(249\) | −4.79422 | −0.303821 | ||||||||
\(250\) | −29.9637 | −1.89507 | ||||||||
\(251\) | −4.44745 | −0.280720 | −0.140360 | − | 0.990101i | \(-0.544826\pi\) | ||||
−0.140360 | + | 0.990101i | \(0.544826\pi\) | |||||||
\(252\) | 23.8067 | 1.49968 | ||||||||
\(253\) | −5.36272 | −0.337152 | ||||||||
\(254\) | 7.21459 | 0.452684 | ||||||||
\(255\) | −4.79162 | −0.300063 | ||||||||
\(256\) | −30.7103 | −1.91939 | ||||||||
\(257\) | −23.2825 | −1.45232 | −0.726161 | − | 0.687525i | \(-0.758697\pi\) | ||||
−0.726161 | + | 0.687525i | \(0.758697\pi\) | |||||||
\(258\) | 3.17935 | 0.197937 | ||||||||
\(259\) | −16.8326 | −1.04593 | ||||||||
\(260\) | 20.5943 | 1.27721 | ||||||||
\(261\) | 1.51354 | 0.0936860 | ||||||||
\(262\) | −40.4675 | −2.50009 | ||||||||
\(263\) | 9.82150 | 0.605619 | 0.302810 | − | 0.953051i | \(-0.402075\pi\) | ||||
0.302810 | + | 0.953051i | \(0.402075\pi\) | |||||||
\(264\) | −5.40064 | −0.332386 | ||||||||
\(265\) | −20.5492 | −1.26233 | ||||||||
\(266\) | 0.547357 | 0.0335606 | ||||||||
\(267\) | 7.16434 | 0.438450 | ||||||||
\(268\) | −11.2623 | −0.687954 | ||||||||
\(269\) | 10.9090 | 0.665131 | 0.332566 | − | 0.943080i | \(-0.392086\pi\) | ||||
0.332566 | + | 0.943080i | \(0.392086\pi\) | |||||||
\(270\) | −13.0443 | −0.793850 | ||||||||
\(271\) | 9.42960 | 0.572808 | 0.286404 | − | 0.958109i | \(-0.407540\pi\) | ||||
0.286404 | + | 0.958109i | \(0.407540\pi\) | |||||||
\(272\) | 34.5063 | 2.09225 | ||||||||
\(273\) | 3.48198 | 0.210739 | ||||||||
\(274\) | −48.7484 | −2.94500 | ||||||||
\(275\) | −3.87847 | −0.233881 | ||||||||
\(276\) | −8.84036 | −0.532127 | ||||||||
\(277\) | 13.2115 | 0.793800 | 0.396900 | − | 0.917862i | \(-0.370086\pi\) | ||||
0.396900 | + | 0.917862i | \(0.370086\pi\) | |||||||
\(278\) | 30.1087 | 1.80580 | ||||||||
\(279\) | −25.7239 | −1.54005 | ||||||||
\(280\) | −19.4088 | −1.15990 | ||||||||
\(281\) | −16.3299 | −0.974158 | −0.487079 | − | 0.873358i | \(-0.661938\pi\) | ||||
−0.487079 | + | 0.873358i | \(0.661938\pi\) | |||||||
\(282\) | 2.72500 | 0.162271 | ||||||||
\(283\) | 12.1223 | 0.720595 | 0.360298 | − | 0.932837i | \(-0.382675\pi\) | ||||
0.360298 | + | 0.932837i | \(0.382675\pi\) | |||||||
\(284\) | −8.92886 | −0.529830 | ||||||||
\(285\) | −0.0970200 | −0.00574697 | ||||||||
\(286\) | 11.5812 | 0.684813 | ||||||||
\(287\) | 10.1645 | 0.599991 | ||||||||
\(288\) | 11.8400 | 0.697681 | ||||||||
\(289\) | 10.7249 | 0.630875 | ||||||||
\(290\) | −2.26264 | −0.132867 | ||||||||
\(291\) | 7.92986 | 0.464856 | ||||||||
\(292\) | −40.9948 | −2.39904 | ||||||||
\(293\) | −16.3448 | −0.954871 | −0.477436 | − | 0.878667i | \(-0.658434\pi\) | ||||
−0.477436 | + | 0.878667i | \(0.658434\pi\) | |||||||
\(294\) | 4.20851 | 0.245445 | ||||||||
\(295\) | 22.8083 | 1.32795 | ||||||||
\(296\) | −50.3318 | −2.92548 | ||||||||
\(297\) | −5.04278 | −0.292612 | ||||||||
\(298\) | 11.9920 | 0.694676 | ||||||||
\(299\) | 10.3385 | 0.597891 | ||||||||
\(300\) | −6.39359 | −0.369134 | ||||||||
\(301\) | 4.41713 | 0.254599 | ||||||||
\(302\) | 12.5832 | 0.724083 | ||||||||
\(303\) | 5.47013 | 0.314251 | ||||||||
\(304\) | 0.698678 | 0.0400719 | ||||||||
\(305\) | −20.9999 | −1.20245 | ||||||||
\(306\) | 35.5169 | 2.03036 | ||||||||
\(307\) | 12.6810 | 0.723743 | 0.361871 | − | 0.932228i | \(-0.382138\pi\) | ||||
0.361871 | + | 0.932228i | \(0.382138\pi\) | |||||||
\(308\) | −13.7584 | −0.783960 | ||||||||
\(309\) | 3.13885 | 0.178563 | ||||||||
\(310\) | 38.4554 | 2.18412 | ||||||||
\(311\) | 20.0795 | 1.13860 | 0.569301 | − | 0.822129i | \(-0.307214\pi\) | ||||
0.569301 | + | 0.822129i | \(0.307214\pi\) | |||||||
\(312\) | 10.4116 | 0.589441 | ||||||||
\(313\) | −30.7965 | −1.74072 | −0.870361 | − | 0.492414i | \(-0.836115\pi\) | ||||
−0.870361 | + | 0.492414i | \(0.836115\pi\) | |||||||
\(314\) | 26.1010 | 1.47296 | ||||||||
\(315\) | −8.52806 | −0.480502 | ||||||||
\(316\) | −61.5790 | −3.46409 | ||||||||
\(317\) | −14.4214 | −0.809986 | −0.404993 | − | 0.914320i | \(-0.632726\pi\) | ||||
−0.404993 | + | 0.914320i | \(0.632726\pi\) | |||||||
\(318\) | −19.0496 | −1.06825 | ||||||||
\(319\) | −0.874711 | −0.0489744 | ||||||||
\(320\) | 2.95379 | 0.165122 | ||||||||
\(321\) | 6.30699 | 0.352022 | ||||||||
\(322\) | −17.8661 | −0.995639 | ||||||||
\(323\) | 0.561369 | 0.0312354 | ||||||||
\(324\) | 26.8772 | 1.49318 | ||||||||
\(325\) | 7.47709 | 0.414754 | ||||||||
\(326\) | −21.1033 | −1.16881 | ||||||||
\(327\) | 6.50845 | 0.359918 | ||||||||
\(328\) | 30.3932 | 1.67818 | ||||||||
\(329\) | 3.78590 | 0.208723 | ||||||||
\(330\) | 3.54746 | 0.195281 | ||||||||
\(331\) | 3.65452 | 0.200870 | 0.100435 | − | 0.994944i | \(-0.467976\pi\) | ||||
0.100435 | + | 0.994944i | \(0.467976\pi\) | |||||||
\(332\) | −36.5202 | −2.00430 | ||||||||
\(333\) | −22.1154 | −1.21192 | ||||||||
\(334\) | −2.90692 | −0.159060 | ||||||||
\(335\) | 4.03438 | 0.220422 | ||||||||
\(336\) | −7.68078 | −0.419021 | ||||||||
\(337\) | −7.97610 | −0.434486 | −0.217243 | − | 0.976118i | \(-0.569706\pi\) | ||||
−0.217243 | + | 0.976118i | \(0.569706\pi\) | |||||||
\(338\) | 10.5583 | 0.574298 | ||||||||
\(339\) | 7.03163 | 0.381906 | ||||||||
\(340\) | −36.5004 | −1.97951 | ||||||||
\(341\) | 14.8664 | 0.805063 | ||||||||
\(342\) | 0.719140 | 0.0388866 | ||||||||
\(343\) | 20.0538 | 1.08281 | ||||||||
\(344\) | 13.2078 | 0.712117 | ||||||||
\(345\) | 3.16680 | 0.170495 | ||||||||
\(346\) | −16.0236 | −0.861434 | ||||||||
\(347\) | 15.7710 | 0.846630 | 0.423315 | − | 0.905983i | \(-0.360866\pi\) | ||||
0.423315 | + | 0.905983i | \(0.360866\pi\) | |||||||
\(348\) | −1.44195 | −0.0772964 | ||||||||
\(349\) | −25.1619 | −1.34689 | −0.673443 | − | 0.739239i | \(-0.735185\pi\) | ||||
−0.673443 | + | 0.739239i | \(0.735185\pi\) | |||||||
\(350\) | −12.9213 | −0.690670 | ||||||||
\(351\) | 9.72170 | 0.518906 | ||||||||
\(352\) | −6.84263 | −0.364713 | ||||||||
\(353\) | 18.7315 | 0.996977 | 0.498489 | − | 0.866896i | \(-0.333889\pi\) | ||||
0.498489 | + | 0.866896i | \(0.333889\pi\) | |||||||
\(354\) | 21.1439 | 1.12379 | ||||||||
\(355\) | 3.19850 | 0.169759 | ||||||||
\(356\) | 54.5746 | 2.89245 | ||||||||
\(357\) | −6.17130 | −0.326620 | ||||||||
\(358\) | −0.685652 | −0.0362378 | ||||||||
\(359\) | −20.4138 | −1.07740 | −0.538698 | − | 0.842499i | \(-0.681084\pi\) | ||||
−0.538698 | + | 0.842499i | \(0.681084\pi\) | |||||||
\(360\) | −25.5000 | −1.34397 | ||||||||
\(361\) | −18.9886 | −0.999402 | ||||||||
\(362\) | 66.4749 | 3.49384 | ||||||||
\(363\) | −4.98093 | −0.261431 | ||||||||
\(364\) | 26.5242 | 1.39024 | ||||||||
\(365\) | 14.6852 | 0.768658 | ||||||||
\(366\) | −19.4674 | −1.01758 | ||||||||
\(367\) | −14.3699 | −0.750104 | −0.375052 | − | 0.927004i | \(-0.622375\pi\) | ||||
−0.375052 | + | 0.927004i | \(0.622375\pi\) | |||||||
\(368\) | −22.8053 | −1.18881 | ||||||||
\(369\) | 13.3545 | 0.695209 | ||||||||
\(370\) | 33.0609 | 1.71875 | ||||||||
\(371\) | −26.4660 | −1.37405 | ||||||||
\(372\) | 24.5071 | 1.27063 | ||||||||
\(373\) | −15.9217 | −0.824392 | −0.412196 | − | 0.911095i | \(-0.635238\pi\) | ||||
−0.412196 | + | 0.911095i | \(0.635238\pi\) | |||||||
\(374\) | −20.5260 | −1.06137 | ||||||||
\(375\) | 6.84038 | 0.353236 | ||||||||
\(376\) | 11.3203 | 0.583802 | ||||||||
\(377\) | 1.68631 | 0.0868492 | ||||||||
\(378\) | −16.8002 | −0.864108 | ||||||||
\(379\) | −6.99928 | −0.359529 | −0.179764 | − | 0.983710i | \(-0.557534\pi\) | ||||
−0.179764 | + | 0.983710i | \(0.557534\pi\) | |||||||
\(380\) | −0.739054 | −0.0379127 | ||||||||
\(381\) | −1.64701 | −0.0843789 | ||||||||
\(382\) | −32.3077 | −1.65301 | ||||||||
\(383\) | 10.3949 | 0.531153 | 0.265576 | − | 0.964090i | \(-0.414438\pi\) | ||||
0.265576 | + | 0.964090i | \(0.414438\pi\) | |||||||
\(384\) | 7.86664 | 0.401443 | ||||||||
\(385\) | 4.92856 | 0.251182 | ||||||||
\(386\) | −25.6503 | −1.30557 | ||||||||
\(387\) | 5.80341 | 0.295004 | ||||||||
\(388\) | 60.4060 | 3.06665 | ||||||||
\(389\) | −22.1215 | −1.12160 | −0.560802 | − | 0.827950i | \(-0.689507\pi\) | ||||
−0.560802 | + | 0.827950i | \(0.689507\pi\) | |||||||
\(390\) | −6.83895 | −0.346304 | ||||||||
\(391\) | −18.3235 | −0.926657 | ||||||||
\(392\) | 17.4832 | 0.883036 | ||||||||
\(393\) | 9.23828 | 0.466010 | ||||||||
\(394\) | 52.2291 | 2.63127 | ||||||||
\(395\) | 22.0589 | 1.10990 | ||||||||
\(396\) | −18.0764 | −0.908374 | ||||||||
\(397\) | 11.7331 | 0.588866 | 0.294433 | − | 0.955672i | \(-0.404869\pi\) | ||||
0.294433 | + | 0.955672i | \(0.404869\pi\) | |||||||
\(398\) | 9.75428 | 0.488938 | ||||||||
\(399\) | −0.124955 | −0.00625560 | ||||||||
\(400\) | −16.4934 | −0.824672 | ||||||||
\(401\) | −6.42865 | −0.321031 | −0.160516 | − | 0.987033i | \(-0.551316\pi\) | ||||
−0.160516 | + | 0.987033i | \(0.551316\pi\) | |||||||
\(402\) | 3.73997 | 0.186533 | ||||||||
\(403\) | −28.6602 | −1.42767 | ||||||||
\(404\) | 41.6690 | 2.07311 | ||||||||
\(405\) | −9.62795 | −0.478417 | ||||||||
\(406\) | −2.91413 | −0.144626 | ||||||||
\(407\) | 12.7810 | 0.633529 | ||||||||
\(408\) | −18.4530 | −0.913560 | ||||||||
\(409\) | 1.19610 | 0.0591433 | 0.0295716 | − | 0.999563i | \(-0.490586\pi\) | ||||
0.0295716 | + | 0.999563i | \(0.490586\pi\) | |||||||
\(410\) | −19.9641 | −0.985955 | ||||||||
\(411\) | 11.1287 | 0.548939 | ||||||||
\(412\) | 23.9103 | 1.17798 | ||||||||
\(413\) | 29.3757 | 1.44548 | ||||||||
\(414\) | −23.4732 | −1.15365 | ||||||||
\(415\) | 13.0823 | 0.642183 | ||||||||
\(416\) | 13.1915 | 0.646768 | ||||||||
\(417\) | −6.87347 | −0.336595 | ||||||||
\(418\) | −0.415607 | −0.0203280 | ||||||||
\(419\) | −6.33558 | −0.309513 | −0.154757 | − | 0.987953i | \(-0.549459\pi\) | ||||
−0.154757 | + | 0.987953i | \(0.549459\pi\) | |||||||
\(420\) | 8.12464 | 0.396442 | ||||||||
\(421\) | −28.6739 | −1.39748 | −0.698741 | − | 0.715375i | \(-0.746256\pi\) | ||||
−0.698741 | + | 0.715375i | \(0.746256\pi\) | |||||||
\(422\) | 37.7692 | 1.83858 | ||||||||
\(423\) | 4.97407 | 0.241848 | ||||||||
\(424\) | −79.1369 | −3.84323 | ||||||||
\(425\) | −13.2520 | −0.642818 | ||||||||
\(426\) | 2.96509 | 0.143659 | ||||||||
\(427\) | −27.0465 | −1.30887 | ||||||||
\(428\) | 48.0438 | 2.32228 | ||||||||
\(429\) | −2.64386 | −0.127647 | ||||||||
\(430\) | −8.67567 | −0.418378 | ||||||||
\(431\) | −12.0146 | −0.578724 | −0.289362 | − | 0.957220i | \(-0.593443\pi\) | ||||
−0.289362 | + | 0.957220i | \(0.593443\pi\) | |||||||
\(432\) | −21.4447 | −1.03176 | ||||||||
\(433\) | 4.45511 | 0.214099 | 0.107050 | − | 0.994254i | \(-0.465860\pi\) | ||||
0.107050 | + | 0.994254i | \(0.465860\pi\) | |||||||
\(434\) | 49.5281 | 2.37742 | ||||||||
\(435\) | 0.516534 | 0.0247659 | ||||||||
\(436\) | 49.5784 | 2.37438 | ||||||||
\(437\) | −0.371010 | −0.0177478 | ||||||||
\(438\) | 13.6135 | 0.650480 | ||||||||
\(439\) | −25.7040 | −1.22679 | −0.613393 | − | 0.789778i | \(-0.710196\pi\) | ||||
−0.613393 | + | 0.789778i | \(0.710196\pi\) | |||||||
\(440\) | 14.7370 | 0.702561 | ||||||||
\(441\) | 7.68199 | 0.365809 | ||||||||
\(442\) | 39.5710 | 1.88220 | ||||||||
\(443\) | −33.4065 | −1.58719 | −0.793597 | − | 0.608444i | \(-0.791794\pi\) | ||||
−0.793597 | + | 0.608444i | \(0.791794\pi\) | |||||||
\(444\) | 21.0692 | 0.999901 | ||||||||
\(445\) | −19.5497 | −0.926747 | ||||||||
\(446\) | 28.7004 | 1.35900 | ||||||||
\(447\) | −2.73763 | −0.129486 | ||||||||
\(448\) | 3.80430 | 0.179736 | ||||||||
\(449\) | 28.2214 | 1.33185 | 0.665924 | − | 0.746019i | \(-0.268037\pi\) | ||||
0.665924 | + | 0.746019i | \(0.268037\pi\) | |||||||
\(450\) | −16.9765 | −0.800279 | ||||||||
\(451\) | −7.71789 | −0.363421 | ||||||||
\(452\) | 53.5637 | 2.51943 | ||||||||
\(453\) | −2.87261 | −0.134967 | ||||||||
\(454\) | 36.6794 | 1.72145 | ||||||||
\(455\) | −9.50150 | −0.445437 | ||||||||
\(456\) | −0.373634 | −0.0174970 | ||||||||
\(457\) | −0.0250571 | −0.00117212 | −0.000586061 | − | 1.00000i | \(-0.500187\pi\) | ||||
−0.000586061 | 1.00000i | \(0.500187\pi\) | ||||||||
\(458\) | 17.3656 | 0.811441 | ||||||||
\(459\) | −17.2303 | −0.804239 | ||||||||
\(460\) | 24.1232 | 1.12475 | ||||||||
\(461\) | 30.0540 | 1.39975 | 0.699877 | − | 0.714263i | \(-0.253238\pi\) | ||||
0.699877 | + | 0.714263i | \(0.253238\pi\) | |||||||
\(462\) | 4.56890 | 0.212564 | ||||||||
\(463\) | 16.9027 | 0.785535 | 0.392767 | − | 0.919638i | \(-0.371518\pi\) | ||||
0.392767 | + | 0.919638i | \(0.371518\pi\) | |||||||
\(464\) | −3.71976 | −0.172686 | ||||||||
\(465\) | −8.77894 | −0.407113 | ||||||||
\(466\) | −34.9797 | −1.62040 | ||||||||
\(467\) | 10.7325 | 0.496640 | 0.248320 | − | 0.968678i | \(-0.420121\pi\) | ||||
0.248320 | + | 0.968678i | \(0.420121\pi\) | |||||||
\(468\) | 34.8485 | 1.61087 | ||||||||
\(469\) | 5.19602 | 0.239930 | ||||||||
\(470\) | −7.43587 | −0.342991 | ||||||||
\(471\) | −5.95856 | −0.274556 | ||||||||
\(472\) | 87.8372 | 4.04303 | ||||||||
\(473\) | −3.35392 | −0.154213 | ||||||||
\(474\) | 20.4491 | 0.939259 | ||||||||
\(475\) | −0.268325 | −0.0123116 | ||||||||
\(476\) | −47.0101 | −2.15470 | ||||||||
\(477\) | −34.7721 | −1.59211 | ||||||||
\(478\) | 16.2777 | 0.744524 | ||||||||
\(479\) | 20.9272 | 0.956190 | 0.478095 | − | 0.878308i | \(-0.341328\pi\) | ||||
0.478095 | + | 0.878308i | \(0.341328\pi\) | |||||||
\(480\) | 4.04071 | 0.184432 | ||||||||
\(481\) | −24.6398 | −1.12348 | ||||||||
\(482\) | −37.3889 | −1.70302 | ||||||||
\(483\) | 4.07863 | 0.185584 | ||||||||
\(484\) | −37.9425 | −1.72466 | ||||||||
\(485\) | −21.6387 | −0.982561 | ||||||||
\(486\) | −33.7587 | −1.53133 | ||||||||
\(487\) | −22.9441 | −1.03969 | −0.519847 | − | 0.854259i | \(-0.674011\pi\) | ||||
−0.519847 | + | 0.854259i | \(0.674011\pi\) | |||||||
\(488\) | −80.8726 | −3.66093 | ||||||||
\(489\) | 4.81766 | 0.217862 | ||||||||
\(490\) | −11.4840 | −0.518795 | ||||||||
\(491\) | 15.2557 | 0.688478 | 0.344239 | − | 0.938882i | \(-0.388137\pi\) | ||||
0.344239 | + | 0.938882i | \(0.388137\pi\) | |||||||
\(492\) | −12.7228 | −0.573588 | ||||||||
\(493\) | −2.98873 | −0.134606 | ||||||||
\(494\) | 0.801227 | 0.0360489 | ||||||||
\(495\) | 6.47534 | 0.291045 | ||||||||
\(496\) | 63.2205 | 2.83868 | ||||||||
\(497\) | 4.11946 | 0.184783 | ||||||||
\(498\) | 12.1276 | 0.543450 | ||||||||
\(499\) | 1.70219 | 0.0762005 | 0.0381003 | − | 0.999274i | \(-0.487869\pi\) | ||||
0.0381003 | + | 0.999274i | \(0.487869\pi\) | |||||||
\(500\) | 52.1069 | 2.33029 | ||||||||
\(501\) | 0.663618 | 0.0296483 | ||||||||
\(502\) | 11.2504 | 0.502130 | ||||||||
\(503\) | 3.31243 | 0.147694 | 0.0738470 | − | 0.997270i | \(-0.476472\pi\) | ||||
0.0738470 | + | 0.997270i | \(0.476472\pi\) | |||||||
\(504\) | −32.8424 | −1.46292 | ||||||||
\(505\) | −14.9267 | −0.664228 | ||||||||
\(506\) | 13.5657 | 0.603069 | ||||||||
\(507\) | −2.41035 | −0.107047 | ||||||||
\(508\) | −12.5462 | −0.556646 | ||||||||
\(509\) | −34.6962 | −1.53788 | −0.768942 | − | 0.639319i | \(-0.779216\pi\) | ||||
−0.768942 | + | 0.639319i | \(0.779216\pi\) | |||||||
\(510\) | 12.1210 | 0.536728 | ||||||||
\(511\) | 18.9136 | 0.836687 | ||||||||
\(512\) | 50.4411 | 2.22920 | ||||||||
\(513\) | −0.348875 | −0.0154032 | ||||||||
\(514\) | 58.8961 | 2.59779 | ||||||||
\(515\) | −8.56516 | −0.377426 | ||||||||
\(516\) | −5.52888 | −0.243395 | ||||||||
\(517\) | −2.87463 | −0.126426 | ||||||||
\(518\) | 42.5803 | 1.87087 | ||||||||
\(519\) | 3.65801 | 0.160569 | ||||||||
\(520\) | −28.4107 | −1.24589 | ||||||||
\(521\) | 8.33417 | 0.365127 | 0.182563 | − | 0.983194i | \(-0.441561\pi\) | ||||
0.182563 | + | 0.983194i | \(0.441561\pi\) | |||||||
\(522\) | −3.82870 | −0.167578 | ||||||||
\(523\) | −9.78912 | −0.428048 | −0.214024 | − | 0.976828i | \(-0.568657\pi\) | ||||
−0.214024 | + | 0.976828i | \(0.568657\pi\) | |||||||
\(524\) | 70.3730 | 3.07426 | ||||||||
\(525\) | 2.94978 | 0.128739 | ||||||||
\(526\) | −24.8447 | −1.08328 | ||||||||
\(527\) | 50.7959 | 2.21271 | ||||||||
\(528\) | 5.83200 | 0.253805 | ||||||||
\(529\) | −10.8900 | −0.473477 | ||||||||
\(530\) | 51.9818 | 2.25794 | ||||||||
\(531\) | 38.5950 | 1.67488 | ||||||||
\(532\) | −0.951853 | −0.0412681 | ||||||||
\(533\) | 14.8789 | 0.644477 | ||||||||
\(534\) | −18.1231 | −0.784264 | ||||||||
\(535\) | −17.2103 | −0.744064 | ||||||||
\(536\) | 15.5368 | 0.671088 | ||||||||
\(537\) | 0.156526 | 0.00675462 | ||||||||
\(538\) | −27.5956 | −1.18973 | ||||||||
\(539\) | −4.43959 | −0.191227 | ||||||||
\(540\) | 22.6840 | 0.976164 | ||||||||
\(541\) | −33.2973 | −1.43156 | −0.715782 | − | 0.698324i | \(-0.753930\pi\) | ||||
−0.715782 | + | 0.698324i | \(0.753930\pi\) | |||||||
\(542\) | −23.8534 | −1.02459 | ||||||||
\(543\) | −15.1755 | −0.651241 | ||||||||
\(544\) | −23.3800 | −1.00241 | ||||||||
\(545\) | −17.7600 | −0.760755 | ||||||||
\(546\) | −8.80813 | −0.376953 | ||||||||
\(547\) | −0.00795725 | −0.000340227 0 | −0.000170114 | − | 1.00000i | \(-0.500054\pi\) | ||||
−0.000170114 | 1.00000i | \(0.500054\pi\) | ||||||||
\(548\) | 84.7735 | 3.62134 | ||||||||
\(549\) | −35.5348 | −1.51659 | ||||||||
\(550\) | 9.81109 | 0.418346 | ||||||||
\(551\) | −0.0605153 | −0.00257804 | ||||||||
\(552\) | 12.1956 | 0.519081 | ||||||||
\(553\) | 28.4104 | 1.20813 | ||||||||
\(554\) | −33.4201 | −1.41988 | ||||||||
\(555\) | −7.54743 | −0.320370 | ||||||||
\(556\) | −52.3590 | −2.22051 | ||||||||
\(557\) | 39.2934 | 1.66492 | 0.832458 | − | 0.554088i | \(-0.186933\pi\) | ||||
0.832458 | + | 0.554088i | \(0.186933\pi\) | |||||||
\(558\) | 65.0720 | 2.75472 | ||||||||
\(559\) | 6.46584 | 0.273476 | ||||||||
\(560\) | 20.9590 | 0.885679 | ||||||||
\(561\) | 4.68585 | 0.197837 | ||||||||
\(562\) | 41.3085 | 1.74249 | ||||||||
\(563\) | −45.6737 | −1.92492 | −0.962458 | − | 0.271431i | \(-0.912503\pi\) | ||||
−0.962458 | + | 0.271431i | \(0.912503\pi\) | |||||||
\(564\) | −4.73878 | −0.199538 | ||||||||
\(565\) | −19.1876 | −0.807229 | ||||||||
\(566\) | −30.6649 | −1.28894 | ||||||||
\(567\) | −12.4002 | −0.520759 | ||||||||
\(568\) | 12.3177 | 0.516841 | ||||||||
\(569\) | −25.3923 | −1.06450 | −0.532251 | − | 0.846587i | \(-0.678654\pi\) | ||||
−0.532251 | + | 0.846587i | \(0.678654\pi\) | |||||||
\(570\) | 0.245425 | 0.0102797 | ||||||||
\(571\) | −27.0741 | −1.13302 | −0.566508 | − | 0.824056i | \(-0.691706\pi\) | ||||
−0.566508 | + | 0.824056i | \(0.691706\pi\) | |||||||
\(572\) | −20.1398 | −0.842085 | ||||||||
\(573\) | 7.37548 | 0.308115 | ||||||||
\(574\) | −25.7124 | −1.07322 | ||||||||
\(575\) | 8.75830 | 0.365247 | ||||||||
\(576\) | 4.99824 | 0.208260 | ||||||||
\(577\) | 1.46468 | 0.0609752 | 0.0304876 | − | 0.999535i | \(-0.490294\pi\) | ||||
0.0304876 | + | 0.999535i | \(0.490294\pi\) | |||||||
\(578\) | −27.1299 | −1.12846 | ||||||||
\(579\) | 5.85568 | 0.243354 | ||||||||
\(580\) | 3.93472 | 0.163380 | ||||||||
\(581\) | 16.8491 | 0.699019 | ||||||||
\(582\) | −20.0596 | −0.831497 | ||||||||
\(583\) | 20.0956 | 0.832274 | ||||||||
\(584\) | 56.5541 | 2.34022 | ||||||||
\(585\) | −12.4835 | −0.516127 | ||||||||
\(586\) | 41.3462 | 1.70800 | ||||||||
\(587\) | 22.8204 | 0.941900 | 0.470950 | − | 0.882160i | \(-0.343911\pi\) | ||||
0.470950 | + | 0.882160i | \(0.343911\pi\) | |||||||
\(588\) | −7.31860 | −0.301814 | ||||||||
\(589\) | 1.02851 | 0.0423789 | ||||||||
\(590\) | −57.6966 | −2.37533 | ||||||||
\(591\) | −11.9233 | −0.490460 | ||||||||
\(592\) | 54.3519 | 2.23385 | ||||||||
\(593\) | 8.86170 | 0.363907 | 0.181953 | − | 0.983307i | \(-0.441758\pi\) | ||||
0.181953 | + | 0.983307i | \(0.441758\pi\) | |||||||
\(594\) | 12.7564 | 0.523400 | ||||||||
\(595\) | 16.8400 | 0.690372 | ||||||||
\(596\) | −20.8540 | −0.854214 | ||||||||
\(597\) | −2.22679 | −0.0911365 | ||||||||
\(598\) | −26.1526 | −1.06946 | ||||||||
\(599\) | 28.7869 | 1.17620 | 0.588100 | − | 0.808788i | \(-0.299876\pi\) | ||||
0.588100 | + | 0.808788i | \(0.299876\pi\) | |||||||
\(600\) | 8.82023 | 0.360084 | ||||||||
\(601\) | 10.6460 | 0.434258 | 0.217129 | − | 0.976143i | \(-0.430331\pi\) | ||||
0.217129 | + | 0.976143i | \(0.430331\pi\) | |||||||
\(602\) | −11.1737 | −0.455406 | ||||||||
\(603\) | 6.82675 | 0.278007 | ||||||||
\(604\) | −21.8822 | −0.890374 | ||||||||
\(605\) | 13.5918 | 0.552584 | ||||||||
\(606\) | −13.8374 | −0.562106 | ||||||||
\(607\) | −39.4007 | −1.59923 | −0.799613 | − | 0.600516i | \(-0.794962\pi\) | ||||
−0.799613 | + | 0.600516i | \(0.794962\pi\) | |||||||
\(608\) | −0.473395 | −0.0191987 | ||||||||
\(609\) | 0.665263 | 0.0269578 | ||||||||
\(610\) | 53.1219 | 2.15084 | ||||||||
\(611\) | 5.54184 | 0.224199 | ||||||||
\(612\) | −61.7638 | −2.49665 | ||||||||
\(613\) | −17.3233 | −0.699682 | −0.349841 | − | 0.936809i | \(-0.613764\pi\) | ||||
−0.349841 | + | 0.936809i | \(0.613764\pi\) | |||||||
\(614\) | −32.0782 | −1.29457 | ||||||||
\(615\) | 4.55757 | 0.183779 | ||||||||
\(616\) | 18.9804 | 0.764740 | ||||||||
\(617\) | 42.8238 | 1.72402 | 0.862011 | − | 0.506890i | \(-0.169205\pi\) | ||||
0.862011 | + | 0.506890i | \(0.169205\pi\) | |||||||
\(618\) | −7.94012 | −0.319399 | ||||||||
\(619\) | 24.6484 | 0.990705 | 0.495352 | − | 0.868692i | \(-0.335039\pi\) | ||||
0.495352 | + | 0.868692i | \(0.335039\pi\) | |||||||
\(620\) | −66.8739 | −2.68572 | ||||||||
\(621\) | 11.3875 | 0.456966 | ||||||||
\(622\) | −50.7936 | −2.03664 | ||||||||
\(623\) | −25.1788 | −1.00877 | ||||||||
\(624\) | −11.2432 | −0.450088 | ||||||||
\(625\) | −6.08179 | −0.243271 | ||||||||
\(626\) | 77.9038 | 3.11366 | ||||||||
\(627\) | 0.0948785 | 0.00378908 | ||||||||
\(628\) | −45.3896 | −1.81124 | ||||||||
\(629\) | 43.6703 | 1.74125 | ||||||||
\(630\) | 21.5728 | 0.859482 | ||||||||
\(631\) | −11.5495 | −0.459780 | −0.229890 | − | 0.973217i | \(-0.573837\pi\) | ||||
−0.229890 | + | 0.973217i | \(0.573837\pi\) | |||||||
\(632\) | 84.9508 | 3.37916 | ||||||||
\(633\) | −8.62229 | −0.342705 | ||||||||
\(634\) | 36.4807 | 1.44884 | ||||||||
\(635\) | 4.49429 | 0.178351 | ||||||||
\(636\) | 33.1272 | 1.31358 | ||||||||
\(637\) | 8.55885 | 0.339114 | ||||||||
\(638\) | 2.21269 | 0.0876014 | ||||||||
\(639\) | 5.41231 | 0.214108 | ||||||||
\(640\) | −21.4662 | −0.848524 | ||||||||
\(641\) | −3.19212 | −0.126081 | −0.0630406 | − | 0.998011i | \(-0.520080\pi\) | ||||
−0.0630406 | + | 0.998011i | \(0.520080\pi\) | |||||||
\(642\) | −15.9543 | −0.629668 | ||||||||
\(643\) | −1.52316 | −0.0600676 | −0.0300338 | − | 0.999549i | \(-0.509561\pi\) | ||||
−0.0300338 | + | 0.999549i | \(0.509561\pi\) | |||||||
\(644\) | 31.0691 | 1.22430 | ||||||||
\(645\) | 1.98056 | 0.0779844 | ||||||||
\(646\) | −1.42005 | −0.0558713 | ||||||||
\(647\) | −33.4498 | −1.31505 | −0.657524 | − | 0.753433i | \(-0.728396\pi\) | ||||
−0.657524 | + | 0.753433i | \(0.728396\pi\) | |||||||
\(648\) | −37.0782 | −1.45657 | ||||||||
\(649\) | −22.3049 | −0.875544 | ||||||||
\(650\) | −18.9143 | −0.741879 | ||||||||
\(651\) | −11.3067 | −0.443144 | ||||||||
\(652\) | 36.6987 | 1.43723 | ||||||||
\(653\) | 42.7948 | 1.67469 | 0.837345 | − | 0.546674i | \(-0.184106\pi\) | ||||
0.837345 | + | 0.546674i | \(0.184106\pi\) | |||||||
\(654\) | −16.4640 | −0.643792 | ||||||||
\(655\) | −25.2090 | −0.984999 | ||||||||
\(656\) | −32.8208 | −1.28144 | ||||||||
\(657\) | 24.8494 | 0.969468 | ||||||||
\(658\) | −9.57692 | −0.373347 | ||||||||
\(659\) | −2.23351 | −0.0870051 | −0.0435026 | − | 0.999053i | \(-0.513852\pi\) | ||||
−0.0435026 | + | 0.999053i | \(0.513852\pi\) | |||||||
\(660\) | −6.16903 | −0.240129 | ||||||||
\(661\) | 34.1335 | 1.32764 | 0.663820 | − | 0.747892i | \(-0.268934\pi\) | ||||
0.663820 | + | 0.747892i | \(0.268934\pi\) | |||||||
\(662\) | −9.24457 | −0.359300 | ||||||||
\(663\) | −9.03361 | −0.350836 | ||||||||
\(664\) | 50.3811 | 1.95517 | ||||||||
\(665\) | 0.340973 | 0.0132224 | ||||||||
\(666\) | 55.9437 | 2.16777 | ||||||||
\(667\) | 1.97526 | 0.0764823 | ||||||||
\(668\) | 5.05514 | 0.195589 | ||||||||
\(669\) | −6.55198 | −0.253314 | ||||||||
\(670\) | −10.2055 | −0.394272 | ||||||||
\(671\) | 20.5363 | 0.792797 | ||||||||
\(672\) | 5.20417 | 0.200755 | ||||||||
\(673\) | 20.0627 | 0.773360 | 0.386680 | − | 0.922214i | \(-0.373622\pi\) | ||||
0.386680 | + | 0.922214i | \(0.373622\pi\) | |||||||
\(674\) | 20.1766 | 0.777173 | ||||||||
\(675\) | 8.23577 | 0.316995 | ||||||||
\(676\) | −18.3609 | −0.706190 | ||||||||
\(677\) | −18.0048 | −0.691979 | −0.345990 | − | 0.938238i | \(-0.612457\pi\) | ||||
−0.345990 | + | 0.938238i | \(0.612457\pi\) | |||||||
\(678\) | −17.7874 | −0.683122 | ||||||||
\(679\) | −27.8692 | −1.06952 | ||||||||
\(680\) | 50.3538 | 1.93098 | ||||||||
\(681\) | −8.37350 | −0.320873 | ||||||||
\(682\) | −37.6066 | −1.44003 | ||||||||
\(683\) | −36.7868 | −1.40761 | −0.703805 | − | 0.710394i | \(-0.748517\pi\) | ||||
−0.703805 | + | 0.710394i | \(0.748517\pi\) | |||||||
\(684\) | −1.25058 | −0.0478173 | ||||||||
\(685\) | −30.3676 | −1.16029 | ||||||||
\(686\) | −50.7288 | −1.93683 | ||||||||
\(687\) | −3.96437 | −0.151250 | ||||||||
\(688\) | −14.2627 | −0.543762 | ||||||||
\(689\) | −38.7412 | −1.47592 | ||||||||
\(690\) | −8.01082 | −0.304967 | ||||||||
\(691\) | −23.9990 | −0.912966 | −0.456483 | − | 0.889732i | \(-0.650891\pi\) | ||||
−0.456483 | + | 0.889732i | \(0.650891\pi\) | |||||||
\(692\) | 27.8650 | 1.05927 | ||||||||
\(693\) | 8.33982 | 0.316803 | ||||||||
\(694\) | −39.8947 | −1.51438 | ||||||||
\(695\) | 18.7560 | 0.711457 | ||||||||
\(696\) | 1.98922 | 0.0754014 | ||||||||
\(697\) | −26.3706 | −0.998858 | ||||||||
\(698\) | 63.6503 | 2.40920 | ||||||||
\(699\) | 7.98547 | 0.302038 | ||||||||
\(700\) | 22.4701 | 0.849288 | ||||||||
\(701\) | 23.5312 | 0.888760 | 0.444380 | − | 0.895838i | \(-0.353424\pi\) | ||||
0.444380 | + | 0.895838i | \(0.353424\pi\) | |||||||
\(702\) | −24.5923 | −0.928176 | ||||||||
\(703\) | 0.884229 | 0.0333493 | ||||||||
\(704\) | −2.88860 | −0.108868 | ||||||||
\(705\) | 1.69753 | 0.0639325 | ||||||||
\(706\) | −47.3837 | −1.78331 | ||||||||
\(707\) | −19.2246 | −0.723015 | ||||||||
\(708\) | −36.7692 | −1.38187 | ||||||||
\(709\) | −14.9623 | −0.561921 | −0.280960 | − | 0.959719i | \(-0.590653\pi\) | ||||
−0.280960 | + | 0.959719i | \(0.590653\pi\) | |||||||
\(710\) | −8.09101 | −0.303650 | ||||||||
\(711\) | 37.3267 | 1.39986 | ||||||||
\(712\) | −75.2880 | −2.82154 | ||||||||
\(713\) | −33.5712 | −1.25725 | ||||||||
\(714\) | 15.6111 | 0.584230 | ||||||||
\(715\) | 7.21447 | 0.269806 | ||||||||
\(716\) | 1.19235 | 0.0445601 | ||||||||
\(717\) | −3.71601 | −0.138777 | ||||||||
\(718\) | 51.6392 | 1.92716 | ||||||||
\(719\) | −41.9054 | −1.56281 | −0.781404 | − | 0.624026i | \(-0.785496\pi\) | ||||
−0.781404 | + | 0.624026i | \(0.785496\pi\) | |||||||
\(720\) | 27.5368 | 1.02624 | ||||||||
\(721\) | −11.0314 | −0.410830 | ||||||||
\(722\) | 48.0342 | 1.78765 | ||||||||
\(723\) | 8.53545 | 0.317437 | ||||||||
\(724\) | −115.600 | −4.29623 | ||||||||
\(725\) | 1.42856 | 0.0530555 | ||||||||
\(726\) | 12.5999 | 0.467627 | ||||||||
\(727\) | 31.8351 | 1.18070 | 0.590350 | − | 0.807147i | \(-0.298990\pi\) | ||||
0.590350 | + | 0.807147i | \(0.298990\pi\) | |||||||
\(728\) | −36.5912 | −1.35616 | ||||||||
\(729\) | −10.6227 | −0.393433 | ||||||||
\(730\) | −37.1481 | −1.37491 | ||||||||
\(731\) | −11.4597 | −0.423853 | ||||||||
\(732\) | 33.8538 | 1.25127 | ||||||||
\(733\) | 8.20871 | 0.303195 | 0.151598 | − | 0.988442i | \(-0.451558\pi\) | ||||
0.151598 | + | 0.988442i | \(0.451558\pi\) | |||||||
\(734\) | 36.3506 | 1.34172 | ||||||||
\(735\) | 2.62167 | 0.0967018 | ||||||||
\(736\) | 15.4519 | 0.569566 | ||||||||
\(737\) | −3.94533 | −0.145328 | ||||||||
\(738\) | −33.7820 | −1.24353 | ||||||||
\(739\) | 24.0820 | 0.885872 | 0.442936 | − | 0.896553i | \(-0.353937\pi\) | ||||
0.442936 | + | 0.896553i | \(0.353937\pi\) | |||||||
\(740\) | −57.4928 | −2.11348 | ||||||||
\(741\) | −0.182911 | −0.00671940 | ||||||||
\(742\) | 66.9491 | 2.45778 | ||||||||
\(743\) | −48.0518 | −1.76285 | −0.881425 | − | 0.472324i | \(-0.843415\pi\) | ||||
−0.881425 | + | 0.472324i | \(0.843415\pi\) | |||||||
\(744\) | −33.8085 | −1.23948 | ||||||||
\(745\) | 7.47034 | 0.273692 | ||||||||
\(746\) | 40.2759 | 1.47460 | ||||||||
\(747\) | 22.1370 | 0.809952 | ||||||||
\(748\) | 35.6947 | 1.30513 | ||||||||
\(749\) | −22.1657 | −0.809917 | ||||||||
\(750\) | −17.3036 | −0.631839 | ||||||||
\(751\) | −4.96165 | −0.181053 | −0.0905267 | − | 0.995894i | \(-0.528855\pi\) | ||||
−0.0905267 | + | 0.995894i | \(0.528855\pi\) | |||||||
\(752\) | −12.2245 | −0.445783 | ||||||||
\(753\) | −2.56834 | −0.0935954 | ||||||||
\(754\) | −4.26573 | −0.155349 | ||||||||
\(755\) | 7.83865 | 0.285278 | ||||||||
\(756\) | 29.2155 | 1.06256 | ||||||||
\(757\) | −37.2218 | −1.35285 | −0.676424 | − | 0.736512i | \(-0.736471\pi\) | ||||
−0.676424 | + | 0.736512i | \(0.736471\pi\) | |||||||
\(758\) | 17.7056 | 0.643096 | ||||||||
\(759\) | −3.09690 | −0.112410 | ||||||||
\(760\) | 1.01956 | 0.0369832 | ||||||||
\(761\) | −53.7809 | −1.94955 | −0.974777 | − | 0.223180i | \(-0.928356\pi\) | ||||
−0.974777 | + | 0.223180i | \(0.928356\pi\) | |||||||
\(762\) | 4.16632 | 0.150930 | ||||||||
\(763\) | −22.8737 | −0.828085 | ||||||||
\(764\) | 56.1830 | 2.03263 | ||||||||
\(765\) | 22.1251 | 0.799933 | ||||||||
\(766\) | −26.2952 | −0.950083 | ||||||||
\(767\) | 43.0004 | 1.55265 | ||||||||
\(768\) | −17.7347 | −0.639947 | ||||||||
\(769\) | 15.5669 | 0.561358 | 0.280679 | − | 0.959802i | \(-0.409440\pi\) | ||||
0.280679 | + | 0.959802i | \(0.409440\pi\) | |||||||
\(770\) | −12.4674 | −0.449295 | ||||||||
\(771\) | −13.4453 | −0.484221 | ||||||||
\(772\) | 44.6059 | 1.60540 | ||||||||
\(773\) | 34.2086 | 1.23040 | 0.615199 | − | 0.788372i | \(-0.289076\pi\) | ||||
0.615199 | + | 0.788372i | \(0.289076\pi\) | |||||||
\(774\) | −14.6805 | −0.527678 | ||||||||
\(775\) | −24.2796 | −0.872149 | ||||||||
\(776\) | −83.3327 | −2.99147 | ||||||||
\(777\) | −9.72059 | −0.348724 | ||||||||
\(778\) | 55.9591 | 2.00623 | ||||||||
\(779\) | −0.533948 | −0.0191307 | ||||||||
\(780\) | 11.8929 | 0.425835 | ||||||||
\(781\) | −3.12790 | −0.111925 | ||||||||
\(782\) | 46.3515 | 1.65753 | ||||||||
\(783\) | 1.85741 | 0.0663785 | ||||||||
\(784\) | −18.8797 | −0.674273 | ||||||||
\(785\) | 16.2595 | 0.580326 | ||||||||
\(786\) | −23.3694 | −0.833560 | ||||||||
\(787\) | −11.0271 | −0.393075 | −0.196538 | − | 0.980496i | \(-0.562970\pi\) | ||||
−0.196538 | + | 0.980496i | \(0.562970\pi\) | |||||||
\(788\) | −90.8264 | −3.23556 | ||||||||
\(789\) | 5.67177 | 0.201921 | ||||||||
\(790\) | −55.8007 | −1.98530 | ||||||||
\(791\) | −24.7124 | −0.878672 | ||||||||
\(792\) | 24.9372 | 0.886104 | ||||||||
\(793\) | −39.5909 | −1.40591 | ||||||||
\(794\) | −29.6803 | −1.05332 | ||||||||
\(795\) | −11.8668 | −0.420874 | ||||||||
\(796\) | −16.9627 | −0.601226 | ||||||||
\(797\) | −22.2583 | −0.788428 | −0.394214 | − | 0.919019i | \(-0.628983\pi\) | ||||
−0.394214 | + | 0.919019i | \(0.628983\pi\) | |||||||
\(798\) | 0.316091 | 0.0111895 | ||||||||
\(799\) | −9.82208 | −0.347480 | ||||||||
\(800\) | 11.1753 | 0.395105 | ||||||||
\(801\) | −33.0810 | −1.16886 | ||||||||
\(802\) | 16.2621 | 0.574235 | ||||||||
\(803\) | −14.3610 | −0.506790 | ||||||||
\(804\) | −6.50381 | −0.229372 | ||||||||
\(805\) | −11.1296 | −0.392267 | ||||||||
\(806\) | 72.4997 | 2.55369 | ||||||||
\(807\) | 6.29977 | 0.221762 | ||||||||
\(808\) | −57.4841 | −2.02228 | ||||||||
\(809\) | 25.7295 | 0.904603 | 0.452301 | − | 0.891865i | \(-0.350603\pi\) | ||||
0.452301 | + | 0.891865i | \(0.350603\pi\) | |||||||
\(810\) | 24.3551 | 0.855753 | ||||||||
\(811\) | −10.4208 | −0.365924 | −0.182962 | − | 0.983120i | \(-0.558568\pi\) | ||||
−0.182962 | + | 0.983120i | \(0.558568\pi\) | |||||||
\(812\) | 5.06767 | 0.177840 | ||||||||
\(813\) | 5.44546 | 0.190981 | ||||||||
\(814\) | −32.3311 | −1.13321 | ||||||||
\(815\) | −13.1462 | −0.460492 | ||||||||
\(816\) | 19.9269 | 0.697581 | ||||||||
\(817\) | −0.232035 | −0.00811787 | ||||||||
\(818\) | −3.02568 | −0.105791 | ||||||||
\(819\) | −16.0779 | −0.561807 | ||||||||
\(820\) | 34.7175 | 1.21239 | ||||||||
\(821\) | −18.4271 | −0.643112 | −0.321556 | − | 0.946891i | \(-0.604206\pi\) | ||||
−0.321556 | + | 0.946891i | \(0.604206\pi\) | |||||||
\(822\) | −28.1515 | −0.981897 | ||||||||
\(823\) | 9.91467 | 0.345604 | 0.172802 | − | 0.984957i | \(-0.444718\pi\) | ||||
0.172802 | + | 0.984957i | \(0.444718\pi\) | |||||||
\(824\) | −32.9853 | −1.14910 | ||||||||
\(825\) | −2.23976 | −0.0779785 | ||||||||
\(826\) | −74.3095 | −2.58556 | ||||||||
\(827\) | 32.0818 | 1.11559 | 0.557796 | − | 0.829978i | \(-0.311647\pi\) | ||||
0.557796 | + | 0.829978i | \(0.311647\pi\) | |||||||
\(828\) | 40.8199 | 1.41859 | ||||||||
\(829\) | −22.4879 | −0.781035 | −0.390518 | − | 0.920595i | \(-0.627704\pi\) | ||||
−0.390518 | + | 0.920595i | \(0.627704\pi\) | |||||||
\(830\) | −33.0933 | −1.14868 | ||||||||
\(831\) | 7.62943 | 0.264662 | ||||||||
\(832\) | 5.56877 | 0.193062 | ||||||||
\(833\) | −15.1693 | −0.525585 | ||||||||
\(834\) | 17.3873 | 0.602074 | ||||||||
\(835\) | −1.81085 | −0.0626672 | ||||||||
\(836\) | 0.722741 | 0.0249965 | ||||||||
\(837\) | −31.5683 | −1.09116 | ||||||||
\(838\) | 16.0267 | 0.553632 | ||||||||
\(839\) | −41.7385 | −1.44097 | −0.720487 | − | 0.693468i | \(-0.756082\pi\) | ||||
−0.720487 | + | 0.693468i | \(0.756082\pi\) | |||||||
\(840\) | −11.2083 | −0.386723 | ||||||||
\(841\) | −28.6778 | −0.988890 | ||||||||
\(842\) | 72.5344 | 2.49970 | ||||||||
\(843\) | −9.43026 | −0.324796 | ||||||||
\(844\) | −65.6807 | −2.26082 | ||||||||
\(845\) | 6.57727 | 0.226265 | ||||||||
\(846\) | −12.5826 | −0.432597 | ||||||||
\(847\) | 17.5053 | 0.601490 | ||||||||
\(848\) | 85.4577 | 2.93463 | ||||||||
\(849\) | 7.00045 | 0.240255 | ||||||||
\(850\) | 33.5227 | 1.14982 | ||||||||
\(851\) | −28.8618 | −0.989370 | ||||||||
\(852\) | −5.15629 | −0.176651 | ||||||||
\(853\) | −9.97034 | −0.341378 | −0.170689 | − | 0.985325i | \(-0.554599\pi\) | ||||
−0.170689 | + | 0.985325i | \(0.554599\pi\) | |||||||
\(854\) | 68.4175 | 2.34120 | ||||||||
\(855\) | 0.447985 | 0.0153208 | ||||||||
\(856\) | −66.2784 | −2.26535 | ||||||||
\(857\) | 6.67851 | 0.228133 | 0.114067 | − | 0.993473i | \(-0.463612\pi\) | ||||
0.114067 | + | 0.993473i | \(0.463612\pi\) | |||||||
\(858\) | 6.68800 | 0.228324 | ||||||||
\(859\) | −55.5705 | −1.89604 | −0.948020 | − | 0.318210i | \(-0.896918\pi\) | ||||
−0.948020 | + | 0.318210i | \(0.896918\pi\) | |||||||
\(860\) | 15.0870 | 0.514462 | ||||||||
\(861\) | 5.86985 | 0.200044 | ||||||||
\(862\) | 30.3926 | 1.03517 | ||||||||
\(863\) | −50.2541 | −1.71067 | −0.855335 | − | 0.518076i | \(-0.826649\pi\) | ||||
−0.855335 | + | 0.518076i | \(0.826649\pi\) | |||||||
\(864\) | 14.5300 | 0.494322 | ||||||||
\(865\) | −9.98182 | −0.339392 | ||||||||
\(866\) | −11.2698 | −0.382963 | ||||||||
\(867\) | 6.19346 | 0.210341 | ||||||||
\(868\) | −86.1293 | −2.92342 | ||||||||
\(869\) | −21.5720 | −0.731778 | ||||||||
\(870\) | −1.30664 | −0.0442993 | ||||||||
\(871\) | 7.60599 | 0.257719 | ||||||||
\(872\) | −68.3955 | −2.31616 | ||||||||
\(873\) | −36.6157 | −1.23925 | ||||||||
\(874\) | 0.938518 | 0.0317459 | ||||||||
\(875\) | −24.0403 | −0.812710 | ||||||||
\(876\) | −23.6739 | −0.799868 | ||||||||
\(877\) | −50.0313 | −1.68944 | −0.844718 | − | 0.535212i | \(-0.820232\pi\) | ||||
−0.844718 | + | 0.535212i | \(0.820232\pi\) | |||||||
\(878\) | 65.0216 | 2.19437 | ||||||||
\(879\) | −9.43887 | −0.318365 | ||||||||
\(880\) | −15.9141 | −0.536465 | ||||||||
\(881\) | 41.8745 | 1.41079 | 0.705394 | − | 0.708816i | \(-0.250770\pi\) | ||||
0.705394 | + | 0.708816i | \(0.250770\pi\) | |||||||
\(882\) | −19.4326 | −0.654329 | ||||||||
\(883\) | 2.77390 | 0.0933492 | 0.0466746 | − | 0.998910i | \(-0.485138\pi\) | ||||
0.0466746 | + | 0.998910i | \(0.485138\pi\) | |||||||
\(884\) | −68.8139 | −2.31446 | ||||||||
\(885\) | 13.1715 | 0.442755 | ||||||||
\(886\) | 84.5062 | 2.83904 | ||||||||
\(887\) | −43.4158 | −1.45776 | −0.728881 | − | 0.684641i | \(-0.759959\pi\) | ||||
−0.728881 | + | 0.684641i | \(0.759959\pi\) | |||||||
\(888\) | −29.0659 | −0.975387 | ||||||||
\(889\) | 5.78836 | 0.194135 | ||||||||
\(890\) | 49.4536 | 1.65769 | ||||||||
\(891\) | 9.41544 | 0.315429 | ||||||||
\(892\) | −49.9100 | −1.67111 | ||||||||
\(893\) | −0.198876 | −0.00665513 | ||||||||
\(894\) | 6.92519 | 0.231613 | ||||||||
\(895\) | −0.427123 | −0.0142772 | ||||||||
\(896\) | −27.6470 | −0.923622 | ||||||||
\(897\) | 5.97034 | 0.199344 | ||||||||
\(898\) | −71.3896 | −2.38230 | ||||||||
\(899\) | −5.47578 | −0.182627 | ||||||||
\(900\) | 29.5221 | 0.984069 | ||||||||
\(901\) | 68.6629 | 2.28749 | ||||||||
\(902\) | 19.5234 | 0.650058 | ||||||||
\(903\) | 2.55083 | 0.0848863 | ||||||||
\(904\) | −73.8934 | −2.45766 | ||||||||
\(905\) | 41.4102 | 1.37652 | ||||||||
\(906\) | 7.26663 | 0.241418 | ||||||||
\(907\) | 27.6191 | 0.917078 | 0.458539 | − | 0.888674i | \(-0.348373\pi\) | ||||
0.458539 | + | 0.888674i | \(0.348373\pi\) | |||||||
\(908\) | −63.7855 | −2.11680 | ||||||||
\(909\) | −25.2581 | −0.837757 | ||||||||
\(910\) | 24.0353 | 0.796761 | ||||||||
\(911\) | −30.8043 | −1.02059 | −0.510296 | − | 0.859999i | \(-0.670464\pi\) | ||||
−0.510296 | + | 0.859999i | \(0.670464\pi\) | |||||||
\(912\) | 0.403477 | 0.0133604 | ||||||||
\(913\) | −12.7935 | −0.423403 | ||||||||
\(914\) | 0.0633852 | 0.00209659 | ||||||||
\(915\) | −12.1271 | −0.400910 | ||||||||
\(916\) | −30.1988 | −0.997795 | ||||||||
\(917\) | −32.4676 | −1.07218 | ||||||||
\(918\) | 43.5861 | 1.43856 | ||||||||
\(919\) | −24.3447 | −0.803057 | −0.401528 | − | 0.915847i | \(-0.631521\pi\) | ||||
−0.401528 | + | 0.915847i | \(0.631521\pi\) | |||||||
\(920\) | −33.2790 | −1.09718 | ||||||||
\(921\) | 7.32309 | 0.241304 | ||||||||
\(922\) | −76.0254 | −2.50376 | ||||||||
\(923\) | 6.03010 | 0.198483 | ||||||||
\(924\) | −7.94531 | −0.261381 | ||||||||
\(925\) | −20.8737 | −0.686322 | ||||||||
\(926\) | −42.7575 | −1.40510 | ||||||||
\(927\) | −14.4935 | −0.476028 | ||||||||
\(928\) | 2.52036 | 0.0827347 | ||||||||
\(929\) | −2.77615 | −0.0910826 | −0.0455413 | − | 0.998962i | \(-0.514501\pi\) | ||||
−0.0455413 | + | 0.998962i | \(0.514501\pi\) | |||||||
\(930\) | 22.2074 | 0.728211 | ||||||||
\(931\) | −0.307145 | −0.0100663 | ||||||||
\(932\) | 60.8297 | 1.99254 | ||||||||
\(933\) | 11.5956 | 0.379623 | ||||||||
\(934\) | −27.1492 | −0.888349 | ||||||||
\(935\) | −12.7866 | −0.418166 | ||||||||
\(936\) | −48.0750 | −1.57138 | ||||||||
\(937\) | −14.9429 | −0.488162 | −0.244081 | − | 0.969755i | \(-0.578486\pi\) | ||||
−0.244081 | + | 0.969755i | \(0.578486\pi\) | |||||||
\(938\) | −13.1440 | −0.429167 | ||||||||
\(939\) | −17.7846 | −0.580377 | ||||||||
\(940\) | 12.9310 | 0.421762 | ||||||||
\(941\) | −21.4863 | −0.700434 | −0.350217 | − | 0.936669i | \(-0.613892\pi\) | ||||
−0.350217 | + | 0.936669i | \(0.613892\pi\) | |||||||
\(942\) | 15.0730 | 0.491103 | ||||||||
\(943\) | 17.4284 | 0.567548 | ||||||||
\(944\) | −94.8529 | −3.08720 | ||||||||
\(945\) | −10.4656 | −0.340446 | ||||||||
\(946\) | 8.48417 | 0.275844 | ||||||||
\(947\) | −49.1986 | −1.59874 | −0.799370 | − | 0.600839i | \(-0.794833\pi\) | ||||
−0.799370 | + | 0.600839i | \(0.794833\pi\) | |||||||
\(948\) | −35.5610 | −1.15497 | ||||||||
\(949\) | 27.6859 | 0.898721 | ||||||||
\(950\) | 0.678762 | 0.0220220 | ||||||||
\(951\) | −8.32814 | −0.270059 | ||||||||
\(952\) | 64.8524 | 2.10188 | ||||||||
\(953\) | −29.3187 | −0.949725 | −0.474863 | − | 0.880060i | \(-0.657502\pi\) | ||||
−0.474863 | + | 0.880060i | \(0.657502\pi\) | |||||||
\(954\) | 87.9605 | 2.84783 | ||||||||
\(955\) | −20.1259 | −0.651259 | ||||||||
\(956\) | −28.3069 | −0.915510 | ||||||||
\(957\) | −0.505133 | −0.0163286 | ||||||||
\(958\) | −52.9381 | −1.71035 | ||||||||
\(959\) | −39.1115 | −1.26298 | ||||||||
\(960\) | 1.70577 | 0.0550536 | ||||||||
\(961\) | 62.0654 | 2.00211 | ||||||||
\(962\) | 62.3294 | 2.00958 | ||||||||
\(963\) | −29.1222 | −0.938450 | ||||||||
\(964\) | 65.0192 | 2.09413 | ||||||||
\(965\) | −15.9787 | −0.514374 | ||||||||
\(966\) | −10.3174 | −0.331957 | ||||||||
\(967\) | 53.2020 | 1.71086 | 0.855430 | − | 0.517918i | \(-0.173293\pi\) | ||||
0.855430 | + | 0.517918i | \(0.173293\pi\) | |||||||
\(968\) | 52.3432 | 1.68238 | ||||||||
\(969\) | 0.324182 | 0.0104142 | ||||||||
\(970\) | 54.7378 | 1.75753 | ||||||||
\(971\) | 42.3611 | 1.35943 | 0.679716 | − | 0.733476i | \(-0.262103\pi\) | ||||
0.679716 | + | 0.733476i | \(0.262103\pi\) | |||||||
\(972\) | 58.7063 | 1.88301 | ||||||||
\(973\) | 24.1566 | 0.774424 | ||||||||
\(974\) | 58.0399 | 1.85972 | ||||||||
\(975\) | 4.31791 | 0.138284 | ||||||||
\(976\) | 87.3321 | 2.79543 | ||||||||
\(977\) | 49.5988 | 1.58681 | 0.793403 | − | 0.608697i | \(-0.208308\pi\) | ||||
0.793403 | + | 0.608697i | \(0.208308\pi\) | |||||||
\(978\) | −12.1869 | −0.389693 | ||||||||
\(979\) | 19.1182 | 0.611021 | ||||||||
\(980\) | 19.9707 | 0.637940 | ||||||||
\(981\) | −30.0524 | −0.959501 | ||||||||
\(982\) | −38.5911 | −1.23149 | ||||||||
\(983\) | 16.9012 | 0.539064 | 0.269532 | − | 0.962991i | \(-0.413131\pi\) | ||||
0.269532 | + | 0.962991i | \(0.413131\pi\) | |||||||
\(984\) | 17.5516 | 0.559526 | ||||||||
\(985\) | 32.5359 | 1.03668 | ||||||||
\(986\) | 7.56037 | 0.240771 | ||||||||
\(987\) | 2.18630 | 0.0695908 | ||||||||
\(988\) | −1.39333 | −0.0443278 | ||||||||
\(989\) | 7.57377 | 0.240832 | ||||||||
\(990\) | −16.3802 | −0.520597 | ||||||||
\(991\) | −0.262728 | −0.00834582 | −0.00417291 | − | 0.999991i | \(-0.501328\pi\) | ||||
−0.00417291 | + | 0.999991i | \(0.501328\pi\) | |||||||
\(992\) | −42.8355 | −1.36003 | ||||||||
\(993\) | 2.11043 | 0.0669725 | ||||||||
\(994\) | −10.4207 | −0.330524 | ||||||||
\(995\) | 6.07638 | 0.192634 | ||||||||
\(996\) | −21.0899 | −0.668258 | ||||||||
\(997\) | −57.6486 | −1.82575 | −0.912875 | − | 0.408240i | \(-0.866143\pi\) | ||||
−0.912875 | + | 0.408240i | \(0.866143\pi\) | |||||||
\(998\) | −4.30591 | −0.136301 | ||||||||
\(999\) | −27.1399 | −0.858668 |
(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 | 8009.2.a.a.1.18 | ✓ | 306 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8009.2.a.a.1.18 | ✓ | 306 | 1.1 | even | 1 | trivial |