Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8041,2,Mod(1,8041)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8041, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8041.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8041 = 11 \cdot 17 \cdot 43 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8041.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(64.2077082653\) |
Analytic rank: | \(1\) |
Dimension: | \(69\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.4 | ||
Character | \(\chi\) | \(=\) | 8041.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.67122 | −1.88883 | −0.944417 | − | 0.328749i | \(-0.893373\pi\) | ||||
−0.944417 | + | 0.328749i | \(0.893373\pi\) | |||||||
\(3\) | 2.62074 | 1.51308 | 0.756542 | − | 0.653945i | \(-0.226887\pi\) | ||||
0.756542 | + | 0.653945i | \(0.226887\pi\) | |||||||
\(4\) | 5.13539 | 2.56770 | ||||||||
\(5\) | 0.949400 | 0.424585 | 0.212292 | − | 0.977206i | \(-0.431907\pi\) | ||||
0.212292 | + | 0.977206i | \(0.431907\pi\) | |||||||
\(6\) | −7.00056 | −2.85797 | ||||||||
\(7\) | −4.03564 | −1.52533 | −0.762664 | − | 0.646795i | \(-0.776109\pi\) | ||||
−0.762664 | + | 0.646795i | \(0.776109\pi\) | |||||||
\(8\) | −8.37532 | −2.96112 | ||||||||
\(9\) | 3.86827 | 1.28942 | ||||||||
\(10\) | −2.53605 | −0.801970 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | 13.4585 | 3.88514 | ||||||||
\(13\) | 0.167776 | 0.0465327 | 0.0232664 | − | 0.999729i | \(-0.492593\pi\) | ||||
0.0232664 | + | 0.999729i | \(0.492593\pi\) | |||||||
\(14\) | 10.7801 | 2.88109 | ||||||||
\(15\) | 2.48813 | 0.642432 | ||||||||
\(16\) | 12.1015 | 3.02537 | ||||||||
\(17\) | 1.00000 | 0.242536 | ||||||||
\(18\) | −10.3330 | −2.43551 | ||||||||
\(19\) | −8.43016 | −1.93401 | −0.967006 | − | 0.254755i | \(-0.918005\pi\) | ||||
−0.967006 | + | 0.254755i | \(0.918005\pi\) | |||||||
\(20\) | 4.87554 | 1.09020 | ||||||||
\(21\) | −10.5764 | −2.30795 | ||||||||
\(22\) | 2.67122 | 0.569505 | ||||||||
\(23\) | 5.22814 | 1.09014 | 0.545072 | − | 0.838389i | \(-0.316502\pi\) | ||||
0.545072 | + | 0.838389i | \(0.316502\pi\) | |||||||
\(24\) | −21.9495 | −4.48042 | ||||||||
\(25\) | −4.09864 | −0.819728 | ||||||||
\(26\) | −0.448166 | −0.0878926 | ||||||||
\(27\) | 2.27550 | 0.437920 | ||||||||
\(28\) | −20.7246 | −3.91658 | ||||||||
\(29\) | 8.85167 | 1.64371 | 0.821857 | − | 0.569694i | \(-0.192938\pi\) | ||||
0.821857 | + | 0.569694i | \(0.192938\pi\) | |||||||
\(30\) | −6.64633 | −1.21345 | ||||||||
\(31\) | 5.94666 | 1.06805 | 0.534026 | − | 0.845468i | \(-0.320678\pi\) | ||||
0.534026 | + | 0.845468i | \(0.320678\pi\) | |||||||
\(32\) | −15.5751 | −2.75331 | ||||||||
\(33\) | −2.62074 | −0.456212 | ||||||||
\(34\) | −2.67122 | −0.458110 | ||||||||
\(35\) | −3.83144 | −0.647631 | ||||||||
\(36\) | 19.8651 | 3.31085 | ||||||||
\(37\) | 5.66287 | 0.930970 | 0.465485 | − | 0.885056i | \(-0.345880\pi\) | ||||
0.465485 | + | 0.885056i | \(0.345880\pi\) | |||||||
\(38\) | 22.5188 | 3.65303 | ||||||||
\(39\) | 0.439697 | 0.0704079 | ||||||||
\(40\) | −7.95152 | −1.25725 | ||||||||
\(41\) | −1.71029 | −0.267102 | −0.133551 | − | 0.991042i | \(-0.542638\pi\) | ||||
−0.133551 | + | 0.991042i | \(0.542638\pi\) | |||||||
\(42\) | 28.2517 | 4.35934 | ||||||||
\(43\) | 1.00000 | 0.152499 | ||||||||
\(44\) | −5.13539 | −0.774190 | ||||||||
\(45\) | 3.67253 | 0.547469 | ||||||||
\(46\) | −13.9655 | −2.05910 | ||||||||
\(47\) | 2.40992 | 0.351523 | 0.175761 | − | 0.984433i | \(-0.443761\pi\) | ||||
0.175761 | + | 0.984433i | \(0.443761\pi\) | |||||||
\(48\) | 31.7148 | 4.57764 | ||||||||
\(49\) | 9.28639 | 1.32663 | ||||||||
\(50\) | 10.9484 | 1.54833 | ||||||||
\(51\) | 2.62074 | 0.366977 | ||||||||
\(52\) | 0.861596 | 0.119482 | ||||||||
\(53\) | −7.83596 | −1.07635 | −0.538176 | − | 0.842833i | \(-0.680886\pi\) | ||||
−0.538176 | + | 0.842833i | \(0.680886\pi\) | |||||||
\(54\) | −6.07835 | −0.827159 | ||||||||
\(55\) | −0.949400 | −0.128017 | ||||||||
\(56\) | 33.7998 | 4.51668 | ||||||||
\(57\) | −22.0932 | −2.92632 | ||||||||
\(58\) | −23.6447 | −3.10470 | ||||||||
\(59\) | −9.07751 | −1.18179 | −0.590896 | − | 0.806748i | \(-0.701225\pi\) | ||||
−0.590896 | + | 0.806748i | \(0.701225\pi\) | |||||||
\(60\) | 12.7775 | 1.64957 | ||||||||
\(61\) | 6.13333 | 0.785293 | 0.392646 | − | 0.919690i | \(-0.371560\pi\) | ||||
0.392646 | + | 0.919690i | \(0.371560\pi\) | |||||||
\(62\) | −15.8848 | −2.01737 | ||||||||
\(63\) | −15.6109 | −1.96679 | ||||||||
\(64\) | 17.4014 | 2.17517 | ||||||||
\(65\) | 0.159287 | 0.0197571 | ||||||||
\(66\) | 7.00056 | 0.861709 | ||||||||
\(67\) | −4.24323 | −0.518393 | −0.259196 | − | 0.965825i | \(-0.583458\pi\) | ||||
−0.259196 | + | 0.965825i | \(0.583458\pi\) | |||||||
\(68\) | 5.13539 | 0.622758 | ||||||||
\(69\) | 13.7016 | 1.64948 | ||||||||
\(70\) | 10.2346 | 1.22327 | ||||||||
\(71\) | −11.5783 | −1.37409 | −0.687043 | − | 0.726616i | \(-0.741092\pi\) | ||||
−0.687043 | + | 0.726616i | \(0.741092\pi\) | |||||||
\(72\) | −32.3980 | −3.81814 | ||||||||
\(73\) | 4.99497 | 0.584617 | 0.292308 | − | 0.956324i | \(-0.405577\pi\) | ||||
0.292308 | + | 0.956324i | \(0.405577\pi\) | |||||||
\(74\) | −15.1267 | −1.75845 | ||||||||
\(75\) | −10.7415 | −1.24032 | ||||||||
\(76\) | −43.2922 | −4.96595 | ||||||||
\(77\) | 4.03564 | 0.459904 | ||||||||
\(78\) | −1.17453 | −0.132989 | ||||||||
\(79\) | 4.03713 | 0.454212 | 0.227106 | − | 0.973870i | \(-0.427074\pi\) | ||||
0.227106 | + | 0.973870i | \(0.427074\pi\) | |||||||
\(80\) | 11.4892 | 1.28453 | ||||||||
\(81\) | −5.64131 | −0.626813 | ||||||||
\(82\) | 4.56855 | 0.504512 | ||||||||
\(83\) | −7.69890 | −0.845064 | −0.422532 | − | 0.906348i | \(-0.638859\pi\) | ||||
−0.422532 | + | 0.906348i | \(0.638859\pi\) | |||||||
\(84\) | −54.3137 | −5.92612 | ||||||||
\(85\) | 0.949400 | 0.102977 | ||||||||
\(86\) | −2.67122 | −0.288045 | ||||||||
\(87\) | 23.1979 | 2.48708 | ||||||||
\(88\) | 8.37532 | 0.892812 | ||||||||
\(89\) | 3.38193 | 0.358484 | 0.179242 | − | 0.983805i | \(-0.442636\pi\) | ||||
0.179242 | + | 0.983805i | \(0.442636\pi\) | |||||||
\(90\) | −9.81013 | −1.03408 | ||||||||
\(91\) | −0.677084 | −0.0709777 | ||||||||
\(92\) | 26.8486 | 2.79916 | ||||||||
\(93\) | 15.5846 | 1.61605 | ||||||||
\(94\) | −6.43741 | −0.663968 | ||||||||
\(95\) | −8.00359 | −0.821151 | ||||||||
\(96\) | −40.8181 | −4.16598 | ||||||||
\(97\) | −6.26604 | −0.636220 | −0.318110 | − | 0.948054i | \(-0.603048\pi\) | ||||
−0.318110 | + | 0.948054i | \(0.603048\pi\) | |||||||
\(98\) | −24.8059 | −2.50578 | ||||||||
\(99\) | −3.86827 | −0.388775 | ||||||||
\(100\) | −21.0481 | −2.10481 | ||||||||
\(101\) | 13.5038 | 1.34367 | 0.671837 | − | 0.740699i | \(-0.265505\pi\) | ||||
0.671837 | + | 0.740699i | \(0.265505\pi\) | |||||||
\(102\) | −7.00056 | −0.693158 | ||||||||
\(103\) | −19.6363 | −1.93482 | −0.967410 | − | 0.253215i | \(-0.918512\pi\) | ||||
−0.967410 | + | 0.253215i | \(0.918512\pi\) | |||||||
\(104\) | −1.40518 | −0.137789 | ||||||||
\(105\) | −10.0412 | −0.979920 | ||||||||
\(106\) | 20.9315 | 2.03305 | ||||||||
\(107\) | 15.0067 | 1.45075 | 0.725374 | − | 0.688355i | \(-0.241667\pi\) | ||||
0.725374 | + | 0.688355i | \(0.241667\pi\) | |||||||
\(108\) | 11.6856 | 1.12445 | ||||||||
\(109\) | −18.2609 | −1.74907 | −0.874537 | − | 0.484958i | \(-0.838835\pi\) | ||||
−0.874537 | + | 0.484958i | \(0.838835\pi\) | |||||||
\(110\) | 2.53605 | 0.241803 | ||||||||
\(111\) | 14.8409 | 1.40864 | ||||||||
\(112\) | −48.8372 | −4.61468 | ||||||||
\(113\) | −0.831552 | −0.0782258 | −0.0391129 | − | 0.999235i | \(-0.512453\pi\) | ||||
−0.0391129 | + | 0.999235i | \(0.512453\pi\) | |||||||
\(114\) | 59.0158 | 5.52734 | ||||||||
\(115\) | 4.96360 | 0.462858 | ||||||||
\(116\) | 45.4568 | 4.22056 | ||||||||
\(117\) | 0.649003 | 0.0600003 | ||||||||
\(118\) | 24.2480 | 2.23221 | ||||||||
\(119\) | −4.03564 | −0.369946 | ||||||||
\(120\) | −20.8389 | −1.90232 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | −16.3835 | −1.48329 | ||||||||
\(123\) | −4.48222 | −0.404148 | ||||||||
\(124\) | 30.5385 | 2.74243 | ||||||||
\(125\) | −8.63825 | −0.772628 | ||||||||
\(126\) | 41.7002 | 3.71495 | ||||||||
\(127\) | 10.0286 | 0.889894 | 0.444947 | − | 0.895557i | \(-0.353222\pi\) | ||||
0.444947 | + | 0.895557i | \(0.353222\pi\) | |||||||
\(128\) | −15.3327 | −1.35523 | ||||||||
\(129\) | 2.62074 | 0.230743 | ||||||||
\(130\) | −0.425489 | −0.0373179 | ||||||||
\(131\) | −18.2205 | −1.59194 | −0.795968 | − | 0.605339i | \(-0.793038\pi\) | ||||
−0.795968 | + | 0.605339i | \(0.793038\pi\) | |||||||
\(132\) | −13.4585 | −1.17141 | ||||||||
\(133\) | 34.0211 | 2.95000 | ||||||||
\(134\) | 11.3346 | 0.979158 | ||||||||
\(135\) | 2.16036 | 0.185934 | ||||||||
\(136\) | −8.37532 | −0.718177 | ||||||||
\(137\) | −0.803989 | −0.0686894 | −0.0343447 | − | 0.999410i | \(-0.510934\pi\) | ||||
−0.0343447 | + | 0.999410i | \(0.510934\pi\) | |||||||
\(138\) | −36.5999 | −3.11559 | ||||||||
\(139\) | −18.8259 | −1.59679 | −0.798397 | − | 0.602132i | \(-0.794318\pi\) | ||||
−0.798397 | + | 0.602132i | \(0.794318\pi\) | |||||||
\(140\) | −19.6759 | −1.66292 | ||||||||
\(141\) | 6.31576 | 0.531883 | ||||||||
\(142\) | 30.9280 | 2.59542 | ||||||||
\(143\) | −0.167776 | −0.0140301 | ||||||||
\(144\) | 46.8118 | 3.90098 | ||||||||
\(145\) | 8.40377 | 0.697895 | ||||||||
\(146\) | −13.3426 | −1.10424 | ||||||||
\(147\) | 24.3372 | 2.00730 | ||||||||
\(148\) | 29.0811 | 2.39045 | ||||||||
\(149\) | 21.8999 | 1.79411 | 0.897053 | − | 0.441922i | \(-0.145703\pi\) | ||||
0.897053 | + | 0.441922i | \(0.145703\pi\) | |||||||
\(150\) | 28.6928 | 2.34275 | ||||||||
\(151\) | −9.65566 | −0.785766 | −0.392883 | − | 0.919588i | \(-0.628522\pi\) | ||||
−0.392883 | + | 0.919588i | \(0.628522\pi\) | |||||||
\(152\) | 70.6052 | 5.72684 | ||||||||
\(153\) | 3.86827 | 0.312731 | ||||||||
\(154\) | −10.7801 | −0.868682 | ||||||||
\(155\) | 5.64576 | 0.453479 | ||||||||
\(156\) | 2.25802 | 0.180786 | ||||||||
\(157\) | 16.0423 | 1.28031 | 0.640156 | − | 0.768245i | \(-0.278870\pi\) | ||||
0.640156 | + | 0.768245i | \(0.278870\pi\) | |||||||
\(158\) | −10.7840 | −0.857932 | ||||||||
\(159\) | −20.5360 | −1.62861 | ||||||||
\(160\) | −14.7870 | −1.16901 | ||||||||
\(161\) | −21.0989 | −1.66283 | ||||||||
\(162\) | 15.0692 | 1.18395 | ||||||||
\(163\) | 15.6179 | 1.22329 | 0.611643 | − | 0.791134i | \(-0.290509\pi\) | ||||
0.611643 | + | 0.791134i | \(0.290509\pi\) | |||||||
\(164\) | −8.78301 | −0.685838 | ||||||||
\(165\) | −2.48813 | −0.193701 | ||||||||
\(166\) | 20.5654 | 1.59619 | ||||||||
\(167\) | 1.52626 | 0.118105 | 0.0590526 | − | 0.998255i | \(-0.481192\pi\) | ||||
0.0590526 | + | 0.998255i | \(0.481192\pi\) | |||||||
\(168\) | 88.5803 | 6.83412 | ||||||||
\(169\) | −12.9719 | −0.997835 | ||||||||
\(170\) | −2.53605 | −0.194506 | ||||||||
\(171\) | −32.6101 | −2.49376 | ||||||||
\(172\) | 5.13539 | 0.391570 | ||||||||
\(173\) | −10.9673 | −0.833825 | −0.416913 | − | 0.908947i | \(-0.636888\pi\) | ||||
−0.416913 | + | 0.908947i | \(0.636888\pi\) | |||||||
\(174\) | −61.9666 | −4.69768 | ||||||||
\(175\) | 16.5406 | 1.25035 | ||||||||
\(176\) | −12.1015 | −0.912184 | ||||||||
\(177\) | −23.7898 | −1.78815 | ||||||||
\(178\) | −9.03386 | −0.677117 | ||||||||
\(179\) | −16.9601 | −1.26766 | −0.633828 | − | 0.773474i | \(-0.718517\pi\) | ||||
−0.633828 | + | 0.773474i | \(0.718517\pi\) | |||||||
\(180\) | 18.8599 | 1.40573 | ||||||||
\(181\) | 8.65716 | 0.643482 | 0.321741 | − | 0.946828i | \(-0.395732\pi\) | ||||
0.321741 | + | 0.946828i | \(0.395732\pi\) | |||||||
\(182\) | 1.80864 | 0.134065 | ||||||||
\(183\) | 16.0739 | 1.18821 | ||||||||
\(184\) | −43.7874 | −3.22805 | ||||||||
\(185\) | 5.37633 | 0.395276 | ||||||||
\(186\) | −41.6300 | −3.05246 | ||||||||
\(187\) | −1.00000 | −0.0731272 | ||||||||
\(188\) | 12.3759 | 0.902604 | ||||||||
\(189\) | −9.18309 | −0.667972 | ||||||||
\(190\) | 21.3793 | 1.55102 | ||||||||
\(191\) | −18.3254 | −1.32598 | −0.662989 | − | 0.748629i | \(-0.730712\pi\) | ||||
−0.662989 | + | 0.748629i | \(0.730712\pi\) | |||||||
\(192\) | 45.6044 | 3.29121 | ||||||||
\(193\) | 2.71391 | 0.195352 | 0.0976759 | − | 0.995218i | \(-0.468859\pi\) | ||||
0.0976759 | + | 0.995218i | \(0.468859\pi\) | |||||||
\(194\) | 16.7380 | 1.20172 | ||||||||
\(195\) | 0.417448 | 0.0298941 | ||||||||
\(196\) | 47.6892 | 3.40637 | ||||||||
\(197\) | −20.0277 | −1.42692 | −0.713458 | − | 0.700698i | \(-0.752872\pi\) | ||||
−0.713458 | + | 0.700698i | \(0.752872\pi\) | |||||||
\(198\) | 10.3330 | 0.734333 | ||||||||
\(199\) | 17.7250 | 1.25649 | 0.628244 | − | 0.778016i | \(-0.283774\pi\) | ||||
0.628244 | + | 0.778016i | \(0.283774\pi\) | |||||||
\(200\) | 34.3274 | 2.42731 | ||||||||
\(201\) | −11.1204 | −0.784371 | ||||||||
\(202\) | −36.0715 | −2.53798 | ||||||||
\(203\) | −35.7221 | −2.50720 | ||||||||
\(204\) | 13.4585 | 0.942285 | ||||||||
\(205\) | −1.62375 | −0.113408 | ||||||||
\(206\) | 52.4527 | 3.65456 | ||||||||
\(207\) | 20.2239 | 1.40566 | ||||||||
\(208\) | 2.03034 | 0.140779 | ||||||||
\(209\) | 8.43016 | 0.583126 | ||||||||
\(210\) | 26.8222 | 1.85091 | ||||||||
\(211\) | −6.59004 | −0.453677 | −0.226838 | − | 0.973932i | \(-0.572839\pi\) | ||||
−0.226838 | + | 0.973932i | \(0.572839\pi\) | |||||||
\(212\) | −40.2407 | −2.76374 | ||||||||
\(213\) | −30.3436 | −2.07911 | ||||||||
\(214\) | −40.0860 | −2.74022 | ||||||||
\(215\) | 0.949400 | 0.0647485 | ||||||||
\(216\) | −19.0580 | −1.29673 | ||||||||
\(217\) | −23.9986 | −1.62913 | ||||||||
\(218\) | 48.7787 | 3.30371 | ||||||||
\(219\) | 13.0905 | 0.884574 | ||||||||
\(220\) | −4.87554 | −0.328709 | ||||||||
\(221\) | 0.167776 | 0.0112858 | ||||||||
\(222\) | −39.6432 | −2.66068 | ||||||||
\(223\) | 2.99779 | 0.200747 | 0.100373 | − | 0.994950i | \(-0.467996\pi\) | ||||
0.100373 | + | 0.994950i | \(0.467996\pi\) | |||||||
\(224\) | 62.8553 | 4.19970 | ||||||||
\(225\) | −15.8546 | −1.05698 | ||||||||
\(226\) | 2.22125 | 0.147756 | ||||||||
\(227\) | −15.8023 | −1.04883 | −0.524416 | − | 0.851462i | \(-0.675716\pi\) | ||||
−0.524416 | + | 0.851462i | \(0.675716\pi\) | |||||||
\(228\) | −113.457 | −7.51391 | ||||||||
\(229\) | −22.5758 | −1.49185 | −0.745926 | − | 0.666028i | \(-0.767993\pi\) | ||||
−0.745926 | + | 0.666028i | \(0.767993\pi\) | |||||||
\(230\) | −13.2588 | −0.874262 | ||||||||
\(231\) | 10.5764 | 0.695873 | ||||||||
\(232\) | −74.1355 | −4.86723 | ||||||||
\(233\) | −18.4714 | −1.21010 | −0.605051 | − | 0.796186i | \(-0.706847\pi\) | ||||
−0.605051 | + | 0.796186i | \(0.706847\pi\) | |||||||
\(234\) | −1.73363 | −0.113331 | ||||||||
\(235\) | 2.28798 | 0.149251 | ||||||||
\(236\) | −46.6166 | −3.03448 | ||||||||
\(237\) | 10.5803 | 0.687261 | ||||||||
\(238\) | 10.7801 | 0.698768 | ||||||||
\(239\) | −8.75515 | −0.566323 | −0.283162 | − | 0.959072i | \(-0.591383\pi\) | ||||
−0.283162 | + | 0.959072i | \(0.591383\pi\) | |||||||
\(240\) | 30.1101 | 1.94360 | ||||||||
\(241\) | 7.41689 | 0.477764 | 0.238882 | − | 0.971049i | \(-0.423219\pi\) | ||||
0.238882 | + | 0.971049i | \(0.423219\pi\) | |||||||
\(242\) | −2.67122 | −0.171712 | ||||||||
\(243\) | −21.6109 | −1.38634 | ||||||||
\(244\) | 31.4971 | 2.01639 | ||||||||
\(245\) | 8.81649 | 0.563265 | ||||||||
\(246\) | 11.9730 | 0.763369 | ||||||||
\(247\) | −1.41438 | −0.0899948 | ||||||||
\(248\) | −49.8052 | −3.16263 | ||||||||
\(249\) | −20.1768 | −1.27865 | ||||||||
\(250\) | 23.0746 | 1.45937 | ||||||||
\(251\) | −7.83995 | −0.494853 | −0.247427 | − | 0.968907i | \(-0.579585\pi\) | ||||
−0.247427 | + | 0.968907i | \(0.579585\pi\) | |||||||
\(252\) | −80.1683 | −5.05013 | ||||||||
\(253\) | −5.22814 | −0.328691 | ||||||||
\(254\) | −26.7886 | −1.68086 | ||||||||
\(255\) | 2.48813 | 0.155813 | ||||||||
\(256\) | 6.15416 | 0.384635 | ||||||||
\(257\) | −1.22987 | −0.0767174 | −0.0383587 | − | 0.999264i | \(-0.512213\pi\) | ||||
−0.0383587 | + | 0.999264i | \(0.512213\pi\) | |||||||
\(258\) | −7.00056 | −0.435836 | ||||||||
\(259\) | −22.8533 | −1.42004 | ||||||||
\(260\) | 0.818000 | 0.0507302 | ||||||||
\(261\) | 34.2406 | 2.11944 | ||||||||
\(262\) | 48.6710 | 3.00690 | ||||||||
\(263\) | 8.64291 | 0.532945 | 0.266472 | − | 0.963843i | \(-0.414142\pi\) | ||||
0.266472 | + | 0.963843i | \(0.414142\pi\) | |||||||
\(264\) | 21.9495 | 1.35090 | ||||||||
\(265\) | −7.43946 | −0.457002 | ||||||||
\(266\) | −90.8777 | −5.57207 | ||||||||
\(267\) | 8.86315 | 0.542416 | ||||||||
\(268\) | −21.7906 | −1.33108 | ||||||||
\(269\) | −19.0649 | −1.16241 | −0.581203 | − | 0.813759i | \(-0.697418\pi\) | ||||
−0.581203 | + | 0.813759i | \(0.697418\pi\) | |||||||
\(270\) | −5.77079 | −0.351199 | ||||||||
\(271\) | 1.05569 | 0.0641285 | 0.0320643 | − | 0.999486i | \(-0.489792\pi\) | ||||
0.0320643 | + | 0.999486i | \(0.489792\pi\) | |||||||
\(272\) | 12.1015 | 0.733760 | ||||||||
\(273\) | −1.77446 | −0.107395 | ||||||||
\(274\) | 2.14763 | 0.129743 | ||||||||
\(275\) | 4.09864 | 0.247157 | ||||||||
\(276\) | 70.3631 | 4.23536 | ||||||||
\(277\) | −7.96483 | −0.478560 | −0.239280 | − | 0.970951i | \(-0.576911\pi\) | ||||
−0.239280 | + | 0.970951i | \(0.576911\pi\) | |||||||
\(278\) | 50.2881 | 3.01608 | ||||||||
\(279\) | 23.0033 | 1.37717 | ||||||||
\(280\) | 32.0895 | 1.91771 | ||||||||
\(281\) | −4.96841 | −0.296391 | −0.148195 | − | 0.988958i | \(-0.547346\pi\) | ||||
−0.148195 | + | 0.988958i | \(0.547346\pi\) | |||||||
\(282\) | −16.8708 | −1.00464 | ||||||||
\(283\) | −20.8777 | −1.24105 | −0.620526 | − | 0.784186i | \(-0.713081\pi\) | ||||
−0.620526 | + | 0.784186i | \(0.713081\pi\) | |||||||
\(284\) | −59.4589 | −3.52824 | ||||||||
\(285\) | −20.9753 | −1.24247 | ||||||||
\(286\) | 0.448166 | 0.0265006 | ||||||||
\(287\) | 6.90211 | 0.407419 | ||||||||
\(288\) | −60.2485 | −3.55017 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | −22.4483 | −1.31821 | ||||||||
\(291\) | −16.4217 | −0.962655 | ||||||||
\(292\) | 25.6511 | 1.50112 | ||||||||
\(293\) | −6.95187 | −0.406133 | −0.203066 | − | 0.979165i | \(-0.565091\pi\) | ||||
−0.203066 | + | 0.979165i | \(0.565091\pi\) | |||||||
\(294\) | −65.0099 | −3.79145 | ||||||||
\(295\) | −8.61819 | −0.501770 | ||||||||
\(296\) | −47.4283 | −2.75672 | ||||||||
\(297\) | −2.27550 | −0.132038 | ||||||||
\(298\) | −58.4993 | −3.38877 | ||||||||
\(299\) | 0.877158 | 0.0507273 | ||||||||
\(300\) | −55.1616 | −3.18476 | ||||||||
\(301\) | −4.03564 | −0.232610 | ||||||||
\(302\) | 25.7923 | 1.48418 | ||||||||
\(303\) | 35.3898 | 2.03309 | ||||||||
\(304\) | −102.017 | −5.85110 | ||||||||
\(305\) | 5.82298 | 0.333423 | ||||||||
\(306\) | −10.3330 | −0.590697 | ||||||||
\(307\) | 22.5669 | 1.28796 | 0.643981 | − | 0.765041i | \(-0.277282\pi\) | ||||
0.643981 | + | 0.765041i | \(0.277282\pi\) | |||||||
\(308\) | 20.7246 | 1.18089 | ||||||||
\(309\) | −51.4615 | −2.92755 | ||||||||
\(310\) | −15.0810 | −0.856546 | ||||||||
\(311\) | −14.5578 | −0.825500 | −0.412750 | − | 0.910844i | \(-0.635432\pi\) | ||||
−0.412750 | + | 0.910844i | \(0.635432\pi\) | |||||||
\(312\) | −3.68260 | −0.208486 | ||||||||
\(313\) | −3.55013 | −0.200665 | −0.100333 | − | 0.994954i | \(-0.531991\pi\) | ||||
−0.100333 | + | 0.994954i | \(0.531991\pi\) | |||||||
\(314\) | −42.8523 | −2.41830 | ||||||||
\(315\) | −14.8210 | −0.835070 | ||||||||
\(316\) | 20.7322 | 1.16628 | ||||||||
\(317\) | −30.2570 | −1.69940 | −0.849702 | − | 0.527263i | \(-0.823218\pi\) | ||||
−0.849702 | + | 0.527263i | \(0.823218\pi\) | |||||||
\(318\) | 54.8561 | 3.07617 | ||||||||
\(319\) | −8.85167 | −0.495598 | ||||||||
\(320\) | 16.5208 | 0.923543 | ||||||||
\(321\) | 39.3285 | 2.19510 | ||||||||
\(322\) | 56.3597 | 3.14080 | ||||||||
\(323\) | −8.43016 | −0.469067 | ||||||||
\(324\) | −28.9704 | −1.60946 | ||||||||
\(325\) | −0.687654 | −0.0381442 | ||||||||
\(326\) | −41.7187 | −2.31058 | ||||||||
\(327\) | −47.8570 | −2.64650 | ||||||||
\(328\) | 14.3242 | 0.790923 | ||||||||
\(329\) | −9.72556 | −0.536188 | ||||||||
\(330\) | 6.64633 | 0.365868 | ||||||||
\(331\) | −16.7959 | −0.923184 | −0.461592 | − | 0.887092i | \(-0.652722\pi\) | ||||
−0.461592 | + | 0.887092i | \(0.652722\pi\) | |||||||
\(332\) | −39.5369 | −2.16987 | ||||||||
\(333\) | 21.9055 | 1.20041 | ||||||||
\(334\) | −4.07696 | −0.223081 | ||||||||
\(335\) | −4.02852 | −0.220101 | ||||||||
\(336\) | −127.990 | −6.98240 | ||||||||
\(337\) | 8.22214 | 0.447888 | 0.223944 | − | 0.974602i | \(-0.428107\pi\) | ||||
0.223944 | + | 0.974602i | \(0.428107\pi\) | |||||||
\(338\) | 34.6506 | 1.88474 | ||||||||
\(339\) | −2.17928 | −0.118362 | ||||||||
\(340\) | 4.87554 | 0.264413 | ||||||||
\(341\) | −5.94666 | −0.322030 | ||||||||
\(342\) | 87.1086 | 4.71029 | ||||||||
\(343\) | −9.22703 | −0.498213 | ||||||||
\(344\) | −8.37532 | −0.451567 | ||||||||
\(345\) | 13.0083 | 0.700343 | ||||||||
\(346\) | 29.2959 | 1.57496 | ||||||||
\(347\) | 8.49821 | 0.456208 | 0.228104 | − | 0.973637i | \(-0.426747\pi\) | ||||
0.228104 | + | 0.973637i | \(0.426747\pi\) | |||||||
\(348\) | 119.130 | 6.38606 | ||||||||
\(349\) | 27.7391 | 1.48484 | 0.742420 | − | 0.669934i | \(-0.233678\pi\) | ||||
0.742420 | + | 0.669934i | \(0.233678\pi\) | |||||||
\(350\) | −44.1836 | −2.36171 | ||||||||
\(351\) | 0.381774 | 0.0203776 | ||||||||
\(352\) | 15.5751 | 0.830153 | ||||||||
\(353\) | −7.63207 | −0.406214 | −0.203107 | − | 0.979157i | \(-0.565104\pi\) | ||||
−0.203107 | + | 0.979157i | \(0.565104\pi\) | |||||||
\(354\) | 63.5476 | 3.37752 | ||||||||
\(355\) | −10.9924 | −0.583416 | ||||||||
\(356\) | 17.3675 | 0.920478 | ||||||||
\(357\) | −10.5764 | −0.559760 | ||||||||
\(358\) | 45.3040 | 2.39439 | ||||||||
\(359\) | −34.4022 | −1.81568 | −0.907839 | − | 0.419318i | \(-0.862269\pi\) | ||||
−0.907839 | + | 0.419318i | \(0.862269\pi\) | |||||||
\(360\) | −30.7586 | −1.62112 | ||||||||
\(361\) | 52.0676 | 2.74040 | ||||||||
\(362\) | −23.1251 | −1.21543 | ||||||||
\(363\) | 2.62074 | 0.137553 | ||||||||
\(364\) | −3.47709 | −0.182249 | ||||||||
\(365\) | 4.74222 | 0.248219 | ||||||||
\(366\) | −42.9367 | −2.24434 | ||||||||
\(367\) | 25.6282 | 1.33778 | 0.668891 | − | 0.743360i | \(-0.266769\pi\) | ||||
0.668891 | + | 0.743360i | \(0.266769\pi\) | |||||||
\(368\) | 63.2683 | 3.29809 | ||||||||
\(369\) | −6.61586 | −0.344408 | ||||||||
\(370\) | −14.3613 | −0.746610 | ||||||||
\(371\) | 31.6231 | 1.64179 | ||||||||
\(372\) | 80.0333 | 4.14953 | ||||||||
\(373\) | −35.5160 | −1.83895 | −0.919476 | − | 0.393147i | \(-0.871386\pi\) | ||||
−0.919476 | + | 0.393147i | \(0.871386\pi\) | |||||||
\(374\) | 2.67122 | 0.138125 | ||||||||
\(375\) | −22.6386 | −1.16905 | ||||||||
\(376\) | −20.1838 | −1.04090 | ||||||||
\(377\) | 1.48510 | 0.0764865 | ||||||||
\(378\) | 24.5300 | 1.26169 | ||||||||
\(379\) | −0.741015 | −0.0380634 | −0.0190317 | − | 0.999819i | \(-0.506058\pi\) | ||||
−0.0190317 | + | 0.999819i | \(0.506058\pi\) | |||||||
\(380\) | −41.1016 | −2.10847 | ||||||||
\(381\) | 26.2823 | 1.34648 | ||||||||
\(382\) | 48.9511 | 2.50455 | ||||||||
\(383\) | −1.63497 | −0.0835432 | −0.0417716 | − | 0.999127i | \(-0.513300\pi\) | ||||
−0.0417716 | + | 0.999127i | \(0.513300\pi\) | |||||||
\(384\) | −40.1829 | −2.05058 | ||||||||
\(385\) | 3.83144 | 0.195268 | ||||||||
\(386\) | −7.24945 | −0.368987 | ||||||||
\(387\) | 3.86827 | 0.196635 | ||||||||
\(388\) | −32.1786 | −1.63362 | ||||||||
\(389\) | −17.2922 | −0.876747 | −0.438373 | − | 0.898793i | \(-0.644445\pi\) | ||||
−0.438373 | + | 0.898793i | \(0.644445\pi\) | |||||||
\(390\) | −1.11510 | −0.0564650 | ||||||||
\(391\) | 5.22814 | 0.264399 | ||||||||
\(392\) | −77.7764 | −3.92830 | ||||||||
\(393\) | −47.7513 | −2.40873 | ||||||||
\(394\) | 53.4984 | 2.69521 | ||||||||
\(395\) | 3.83285 | 0.192852 | ||||||||
\(396\) | −19.8651 | −0.998258 | ||||||||
\(397\) | −6.13451 | −0.307882 | −0.153941 | − | 0.988080i | \(-0.549197\pi\) | ||||
−0.153941 | + | 0.988080i | \(0.549197\pi\) | |||||||
\(398\) | −47.3472 | −2.37330 | ||||||||
\(399\) | 89.1603 | 4.46360 | ||||||||
\(400\) | −49.5996 | −2.47998 | ||||||||
\(401\) | −4.41238 | −0.220344 | −0.110172 | − | 0.993913i | \(-0.535140\pi\) | ||||
−0.110172 | + | 0.993913i | \(0.535140\pi\) | |||||||
\(402\) | 29.7049 | 1.48155 | ||||||||
\(403\) | 0.997708 | 0.0496994 | ||||||||
\(404\) | 69.3472 | 3.45015 | ||||||||
\(405\) | −5.35586 | −0.266135 | ||||||||
\(406\) | 95.4216 | 4.73569 | ||||||||
\(407\) | −5.66287 | −0.280698 | ||||||||
\(408\) | −21.9495 | −1.08666 | ||||||||
\(409\) | 3.56821 | 0.176437 | 0.0882184 | − | 0.996101i | \(-0.471883\pi\) | ||||
0.0882184 | + | 0.996101i | \(0.471883\pi\) | |||||||
\(410\) | 4.33738 | 0.214208 | ||||||||
\(411\) | −2.10704 | −0.103933 | ||||||||
\(412\) | −100.840 | −4.96803 | ||||||||
\(413\) | 36.6336 | 1.80262 | ||||||||
\(414\) | −54.0223 | −2.65505 | ||||||||
\(415\) | −7.30934 | −0.358801 | ||||||||
\(416\) | −2.61312 | −0.128119 | ||||||||
\(417\) | −49.3378 | −2.41608 | ||||||||
\(418\) | −22.5188 | −1.10143 | ||||||||
\(419\) | −19.3093 | −0.943320 | −0.471660 | − | 0.881780i | \(-0.656345\pi\) | ||||
−0.471660 | + | 0.881780i | \(0.656345\pi\) | |||||||
\(420\) | −51.5655 | −2.51614 | ||||||||
\(421\) | 21.6769 | 1.05647 | 0.528234 | − | 0.849099i | \(-0.322854\pi\) | ||||
0.528234 | + | 0.849099i | \(0.322854\pi\) | |||||||
\(422\) | 17.6034 | 0.856921 | ||||||||
\(423\) | 9.32221 | 0.453261 | ||||||||
\(424\) | 65.6286 | 3.18721 | ||||||||
\(425\) | −4.09864 | −0.198813 | ||||||||
\(426\) | 81.0543 | 3.92709 | ||||||||
\(427\) | −24.7519 | −1.19783 | ||||||||
\(428\) | 77.0651 | 3.72508 | ||||||||
\(429\) | −0.439697 | −0.0212288 | ||||||||
\(430\) | −2.53605 | −0.122299 | ||||||||
\(431\) | 34.1955 | 1.64714 | 0.823570 | − | 0.567215i | \(-0.191979\pi\) | ||||
0.823570 | + | 0.567215i | \(0.191979\pi\) | |||||||
\(432\) | 27.5369 | 1.32487 | ||||||||
\(433\) | 25.9097 | 1.24514 | 0.622570 | − | 0.782564i | \(-0.286089\pi\) | ||||
0.622570 | + | 0.782564i | \(0.286089\pi\) | |||||||
\(434\) | 64.1054 | 3.07716 | ||||||||
\(435\) | 22.0241 | 1.05597 | ||||||||
\(436\) | −93.7768 | −4.49109 | ||||||||
\(437\) | −44.0741 | −2.10835 | ||||||||
\(438\) | −34.9676 | −1.67081 | ||||||||
\(439\) | −29.3524 | −1.40091 | −0.700456 | − | 0.713695i | \(-0.747020\pi\) | ||||
−0.700456 | + | 0.713695i | \(0.747020\pi\) | |||||||
\(440\) | 7.95152 | 0.379074 | ||||||||
\(441\) | 35.9222 | 1.71058 | ||||||||
\(442\) | −0.448166 | −0.0213171 | ||||||||
\(443\) | −19.2972 | −0.916838 | −0.458419 | − | 0.888736i | \(-0.651584\pi\) | ||||
−0.458419 | + | 0.888736i | \(0.651584\pi\) | |||||||
\(444\) | 76.2139 | 3.61695 | ||||||||
\(445\) | 3.21080 | 0.152207 | ||||||||
\(446\) | −8.00774 | −0.379177 | ||||||||
\(447\) | 57.3938 | 2.71463 | ||||||||
\(448\) | −70.2256 | −3.31785 | ||||||||
\(449\) | 0.450571 | 0.0212637 | 0.0106319 | − | 0.999943i | \(-0.496616\pi\) | ||||
0.0106319 | + | 0.999943i | \(0.496616\pi\) | |||||||
\(450\) | 42.3511 | 1.99645 | ||||||||
\(451\) | 1.71029 | 0.0805344 | ||||||||
\(452\) | −4.27035 | −0.200860 | ||||||||
\(453\) | −25.3049 | −1.18893 | ||||||||
\(454\) | 42.2112 | 1.98107 | ||||||||
\(455\) | −0.642823 | −0.0301360 | ||||||||
\(456\) | 185.038 | 8.66519 | ||||||||
\(457\) | 6.88978 | 0.322290 | 0.161145 | − | 0.986931i | \(-0.448481\pi\) | ||||
0.161145 | + | 0.986931i | \(0.448481\pi\) | |||||||
\(458\) | 60.3049 | 2.81786 | ||||||||
\(459\) | 2.27550 | 0.106211 | ||||||||
\(460\) | 25.4900 | 1.18848 | ||||||||
\(461\) | −4.39969 | −0.204914 | −0.102457 | − | 0.994737i | \(-0.532670\pi\) | ||||
−0.102457 | + | 0.994737i | \(0.532670\pi\) | |||||||
\(462\) | −28.2517 | −1.31439 | ||||||||
\(463\) | 8.95224 | 0.416046 | 0.208023 | − | 0.978124i | \(-0.433297\pi\) | ||||
0.208023 | + | 0.978124i | \(0.433297\pi\) | |||||||
\(464\) | 107.118 | 4.97284 | ||||||||
\(465\) | 14.7961 | 0.686151 | ||||||||
\(466\) | 49.3411 | 2.28568 | ||||||||
\(467\) | 42.2207 | 1.95374 | 0.976870 | − | 0.213835i | \(-0.0685954\pi\) | ||||
0.976870 | + | 0.213835i | \(0.0685954\pi\) | |||||||
\(468\) | 3.33288 | 0.154063 | ||||||||
\(469\) | 17.1241 | 0.790719 | ||||||||
\(470\) | −6.11168 | −0.281911 | ||||||||
\(471\) | 42.0425 | 1.93722 | ||||||||
\(472\) | 76.0270 | 3.49943 | ||||||||
\(473\) | −1.00000 | −0.0459800 | ||||||||
\(474\) | −28.2621 | −1.29812 | ||||||||
\(475\) | 34.5522 | 1.58536 | ||||||||
\(476\) | −20.7246 | −0.949910 | ||||||||
\(477\) | −30.3116 | −1.38787 | ||||||||
\(478\) | 23.3869 | 1.06969 | ||||||||
\(479\) | −25.7835 | −1.17808 | −0.589038 | − | 0.808105i | \(-0.700493\pi\) | ||||
−0.589038 | + | 0.808105i | \(0.700493\pi\) | |||||||
\(480\) | −38.7527 | −1.76881 | ||||||||
\(481\) | 0.950094 | 0.0433206 | ||||||||
\(482\) | −19.8121 | −0.902418 | ||||||||
\(483\) | −55.2947 | −2.51600 | ||||||||
\(484\) | 5.13539 | 0.233427 | ||||||||
\(485\) | −5.94898 | −0.270129 | ||||||||
\(486\) | 57.7274 | 2.61857 | ||||||||
\(487\) | −23.0585 | −1.04488 | −0.522439 | − | 0.852676i | \(-0.674978\pi\) | ||||
−0.522439 | + | 0.852676i | \(0.674978\pi\) | |||||||
\(488\) | −51.3686 | −2.32535 | ||||||||
\(489\) | 40.9303 | 1.85093 | ||||||||
\(490\) | −23.5508 | −1.06391 | ||||||||
\(491\) | 0.592782 | 0.0267519 | 0.0133759 | − | 0.999911i | \(-0.495742\pi\) | ||||
0.0133759 | + | 0.999911i | \(0.495742\pi\) | |||||||
\(492\) | −23.0180 | −1.03773 | ||||||||
\(493\) | 8.85167 | 0.398659 | ||||||||
\(494\) | 3.77811 | 0.169985 | ||||||||
\(495\) | −3.67253 | −0.165068 | ||||||||
\(496\) | 71.9635 | 3.23126 | ||||||||
\(497\) | 46.7257 | 2.09593 | ||||||||
\(498\) | 53.8966 | 2.41516 | ||||||||
\(499\) | −15.1449 | −0.677980 | −0.338990 | − | 0.940790i | \(-0.610085\pi\) | ||||
−0.338990 | + | 0.940790i | \(0.610085\pi\) | |||||||
\(500\) | −44.3608 | −1.98388 | ||||||||
\(501\) | 3.99991 | 0.178703 | ||||||||
\(502\) | 20.9422 | 0.934697 | ||||||||
\(503\) | −14.0043 | −0.624419 | −0.312210 | − | 0.950013i | \(-0.601069\pi\) | ||||
−0.312210 | + | 0.950013i | \(0.601069\pi\) | |||||||
\(504\) | 130.746 | 5.82391 | ||||||||
\(505\) | 12.8205 | 0.570504 | ||||||||
\(506\) | 13.9655 | 0.620842 | ||||||||
\(507\) | −33.9958 | −1.50981 | ||||||||
\(508\) | 51.5008 | 2.28498 | ||||||||
\(509\) | 7.75138 | 0.343574 | 0.171787 | − | 0.985134i | \(-0.445046\pi\) | ||||
0.171787 | + | 0.985134i | \(0.445046\pi\) | |||||||
\(510\) | −6.64633 | −0.294304 | ||||||||
\(511\) | −20.1579 | −0.891733 | ||||||||
\(512\) | 14.2262 | 0.628717 | ||||||||
\(513\) | −19.1828 | −0.846942 | ||||||||
\(514\) | 3.28526 | 0.144907 | ||||||||
\(515\) | −18.6427 | −0.821495 | ||||||||
\(516\) | 13.4585 | 0.592478 | ||||||||
\(517\) | −2.40992 | −0.105988 | ||||||||
\(518\) | 61.0461 | 2.68221 | ||||||||
\(519\) | −28.7423 | −1.26165 | ||||||||
\(520\) | −1.33408 | −0.0585031 | ||||||||
\(521\) | 4.15859 | 0.182191 | 0.0910956 | − | 0.995842i | \(-0.470963\pi\) | ||||
0.0910956 | + | 0.995842i | \(0.470963\pi\) | |||||||
\(522\) | −91.4641 | −4.00327 | ||||||||
\(523\) | −29.0024 | −1.26819 | −0.634094 | − | 0.773256i | \(-0.718627\pi\) | ||||
−0.634094 | + | 0.773256i | \(0.718627\pi\) | |||||||
\(524\) | −93.5697 | −4.08761 | ||||||||
\(525\) | 43.3487 | 1.89189 | ||||||||
\(526\) | −23.0871 | −1.00664 | ||||||||
\(527\) | 5.94666 | 0.259041 | ||||||||
\(528\) | −31.7148 | −1.38021 | ||||||||
\(529\) | 4.33349 | 0.188412 | ||||||||
\(530\) | 19.8724 | 0.863202 | ||||||||
\(531\) | −35.1142 | −1.52383 | ||||||||
\(532\) | 174.712 | 7.57471 | ||||||||
\(533\) | −0.286946 | −0.0124290 | ||||||||
\(534\) | −23.6754 | −1.02453 | ||||||||
\(535\) | 14.2473 | 0.615965 | ||||||||
\(536\) | 35.5384 | 1.53502 | ||||||||
\(537\) | −44.4479 | −1.91807 | ||||||||
\(538\) | 50.9264 | 2.19559 | ||||||||
\(539\) | −9.28639 | −0.399993 | ||||||||
\(540\) | 11.0943 | 0.477422 | ||||||||
\(541\) | −7.47108 | −0.321207 | −0.160604 | − | 0.987019i | \(-0.551344\pi\) | ||||
−0.160604 | + | 0.987019i | \(0.551344\pi\) | |||||||
\(542\) | −2.81997 | −0.121128 | ||||||||
\(543\) | 22.6882 | 0.973642 | ||||||||
\(544\) | −15.5751 | −0.667775 | ||||||||
\(545\) | −17.3369 | −0.742630 | ||||||||
\(546\) | 4.73996 | 0.202852 | ||||||||
\(547\) | −15.6496 | −0.669128 | −0.334564 | − | 0.942373i | \(-0.608589\pi\) | ||||
−0.334564 | + | 0.942373i | \(0.608589\pi\) | |||||||
\(548\) | −4.12880 | −0.176374 | ||||||||
\(549\) | 23.7254 | 1.01257 | ||||||||
\(550\) | −10.9484 | −0.466839 | ||||||||
\(551\) | −74.6210 | −3.17896 | ||||||||
\(552\) | −114.755 | −4.88430 | ||||||||
\(553\) | −16.2924 | −0.692823 | ||||||||
\(554\) | 21.2758 | 0.903921 | ||||||||
\(555\) | 14.0899 | 0.598085 | ||||||||
\(556\) | −96.6785 | −4.10008 | ||||||||
\(557\) | 9.34255 | 0.395857 | 0.197928 | − | 0.980216i | \(-0.436579\pi\) | ||||
0.197928 | + | 0.980216i | \(0.436579\pi\) | |||||||
\(558\) | −61.4467 | −2.60125 | ||||||||
\(559\) | 0.167776 | 0.00709617 | ||||||||
\(560\) | −46.3661 | −1.95932 | ||||||||
\(561\) | −2.62074 | −0.110648 | ||||||||
\(562\) | 13.2717 | 0.559833 | ||||||||
\(563\) | 16.4963 | 0.695236 | 0.347618 | − | 0.937636i | \(-0.386991\pi\) | ||||
0.347618 | + | 0.937636i | \(0.386991\pi\) | |||||||
\(564\) | 32.4339 | 1.36572 | ||||||||
\(565\) | −0.789475 | −0.0332135 | ||||||||
\(566\) | 55.7689 | 2.34414 | ||||||||
\(567\) | 22.7663 | 0.956095 | ||||||||
\(568\) | 96.9716 | 4.06884 | ||||||||
\(569\) | 4.77889 | 0.200341 | 0.100171 | − | 0.994970i | \(-0.468061\pi\) | ||||
0.100171 | + | 0.994970i | \(0.468061\pi\) | |||||||
\(570\) | 56.0296 | 2.34682 | ||||||||
\(571\) | 36.5704 | 1.53043 | 0.765213 | − | 0.643778i | \(-0.222634\pi\) | ||||
0.765213 | + | 0.643778i | \(0.222634\pi\) | |||||||
\(572\) | −0.861596 | −0.0360252 | ||||||||
\(573\) | −48.0260 | −2.00632 | ||||||||
\(574\) | −18.4370 | −0.769547 | ||||||||
\(575\) | −21.4283 | −0.893621 | ||||||||
\(576\) | 67.3131 | 2.80471 | ||||||||
\(577\) | −26.2557 | −1.09304 | −0.546519 | − | 0.837447i | \(-0.684047\pi\) | ||||
−0.546519 | + | 0.837447i | \(0.684047\pi\) | |||||||
\(578\) | −2.67122 | −0.111108 | ||||||||
\(579\) | 7.11245 | 0.295583 | ||||||||
\(580\) | 43.1567 | 1.79198 | ||||||||
\(581\) | 31.0700 | 1.28900 | ||||||||
\(582\) | 43.8658 | 1.81830 | ||||||||
\(583\) | 7.83596 | 0.324532 | ||||||||
\(584\) | −41.8344 | −1.73112 | ||||||||
\(585\) | 0.616163 | 0.0254752 | ||||||||
\(586\) | 18.5699 | 0.767117 | ||||||||
\(587\) | 10.1219 | 0.417776 | 0.208888 | − | 0.977940i | \(-0.433016\pi\) | ||||
0.208888 | + | 0.977940i | \(0.433016\pi\) | |||||||
\(588\) | 124.981 | 5.15413 | ||||||||
\(589\) | −50.1313 | −2.06563 | ||||||||
\(590\) | 23.0210 | 0.947761 | ||||||||
\(591\) | −52.4874 | −2.15904 | ||||||||
\(592\) | 68.5291 | 2.81653 | ||||||||
\(593\) | 13.2856 | 0.545575 | 0.272787 | − | 0.962074i | \(-0.412054\pi\) | ||||
0.272787 | + | 0.962074i | \(0.412054\pi\) | |||||||
\(594\) | 6.07835 | 0.249398 | ||||||||
\(595\) | −3.83144 | −0.157074 | ||||||||
\(596\) | 112.464 | 4.60672 | ||||||||
\(597\) | 46.4525 | 1.90117 | ||||||||
\(598\) | −2.34308 | −0.0958156 | ||||||||
\(599\) | −35.6049 | −1.45478 | −0.727388 | − | 0.686227i | \(-0.759266\pi\) | ||||
−0.727388 | + | 0.686227i | \(0.759266\pi\) | |||||||
\(600\) | 89.9631 | 3.67273 | ||||||||
\(601\) | −5.60169 | −0.228498 | −0.114249 | − | 0.993452i | \(-0.536446\pi\) | ||||
−0.114249 | + | 0.993452i | \(0.536446\pi\) | |||||||
\(602\) | 10.7801 | 0.439363 | ||||||||
\(603\) | −16.4139 | −0.668427 | ||||||||
\(604\) | −49.5856 | −2.01761 | ||||||||
\(605\) | 0.949400 | 0.0385986 | ||||||||
\(606\) | −94.5339 | −3.84018 | ||||||||
\(607\) | −34.1744 | −1.38710 | −0.693548 | − | 0.720410i | \(-0.743954\pi\) | ||||
−0.693548 | + | 0.720410i | \(0.743954\pi\) | |||||||
\(608\) | 131.300 | 5.32492 | ||||||||
\(609\) | −93.6184 | −3.79361 | ||||||||
\(610\) | −15.5544 | −0.629781 | ||||||||
\(611\) | 0.404327 | 0.0163573 | ||||||||
\(612\) | 19.8651 | 0.802998 | ||||||||
\(613\) | 18.7263 | 0.756348 | 0.378174 | − | 0.925735i | \(-0.376552\pi\) | ||||
0.378174 | + | 0.925735i | \(0.376552\pi\) | |||||||
\(614\) | −60.2811 | −2.43275 | ||||||||
\(615\) | −4.25542 | −0.171595 | ||||||||
\(616\) | −33.7998 | −1.36183 | ||||||||
\(617\) | −24.0661 | −0.968865 | −0.484433 | − | 0.874829i | \(-0.660974\pi\) | ||||
−0.484433 | + | 0.874829i | \(0.660974\pi\) | |||||||
\(618\) | 137.465 | 5.52965 | ||||||||
\(619\) | 5.08877 | 0.204535 | 0.102267 | − | 0.994757i | \(-0.467390\pi\) | ||||
0.102267 | + | 0.994757i | \(0.467390\pi\) | |||||||
\(620\) | 28.9932 | 1.16440 | ||||||||
\(621\) | 11.8966 | 0.477396 | ||||||||
\(622\) | 38.8872 | 1.55923 | ||||||||
\(623\) | −13.6482 | −0.546806 | ||||||||
\(624\) | 5.32099 | 0.213010 | ||||||||
\(625\) | 12.2920 | 0.491682 | ||||||||
\(626\) | 9.48317 | 0.379024 | ||||||||
\(627\) | 22.0932 | 0.882319 | ||||||||
\(628\) | 82.3833 | 3.28745 | ||||||||
\(629\) | 5.66287 | 0.225793 | ||||||||
\(630\) | 39.5901 | 1.57731 | ||||||||
\(631\) | 29.8693 | 1.18908 | 0.594539 | − | 0.804067i | \(-0.297335\pi\) | ||||
0.594539 | + | 0.804067i | \(0.297335\pi\) | |||||||
\(632\) | −33.8122 | −1.34498 | ||||||||
\(633\) | −17.2708 | −0.686451 | ||||||||
\(634\) | 80.8231 | 3.20989 | ||||||||
\(635\) | 9.52115 | 0.377835 | ||||||||
\(636\) | −105.460 | −4.18178 | ||||||||
\(637\) | 1.55803 | 0.0617315 | ||||||||
\(638\) | 23.6447 | 0.936103 | ||||||||
\(639\) | −44.7878 | −1.77178 | ||||||||
\(640\) | −14.5568 | −0.575410 | ||||||||
\(641\) | −39.0237 | −1.54134 | −0.770672 | − | 0.637232i | \(-0.780079\pi\) | ||||
−0.770672 | + | 0.637232i | \(0.780079\pi\) | |||||||
\(642\) | −105.055 | −4.14619 | ||||||||
\(643\) | −9.14378 | −0.360595 | −0.180298 | − | 0.983612i | \(-0.557706\pi\) | ||||
−0.180298 | + | 0.983612i | \(0.557706\pi\) | |||||||
\(644\) | −108.351 | −4.26963 | ||||||||
\(645\) | 2.48813 | 0.0979700 | ||||||||
\(646\) | 22.5188 | 0.885989 | ||||||||
\(647\) | −4.33675 | −0.170495 | −0.0852477 | − | 0.996360i | \(-0.527168\pi\) | ||||
−0.0852477 | + | 0.996360i | \(0.527168\pi\) | |||||||
\(648\) | 47.2478 | 1.85607 | ||||||||
\(649\) | 9.07751 | 0.356323 | ||||||||
\(650\) | 1.83687 | 0.0720480 | ||||||||
\(651\) | −62.8940 | −2.46501 | ||||||||
\(652\) | 80.2039 | 3.14103 | ||||||||
\(653\) | 6.98784 | 0.273455 | 0.136728 | − | 0.990609i | \(-0.456342\pi\) | ||||
0.136728 | + | 0.990609i | \(0.456342\pi\) | |||||||
\(654\) | 127.836 | 4.99879 | ||||||||
\(655\) | −17.2986 | −0.675912 | ||||||||
\(656\) | −20.6970 | −0.808084 | ||||||||
\(657\) | 19.3219 | 0.753818 | ||||||||
\(658\) | 25.9791 | 1.01277 | ||||||||
\(659\) | 32.3388 | 1.25974 | 0.629871 | − | 0.776700i | \(-0.283108\pi\) | ||||
0.629871 | + | 0.776700i | \(0.283108\pi\) | |||||||
\(660\) | −12.7775 | −0.497364 | ||||||||
\(661\) | −37.6419 | −1.46410 | −0.732050 | − | 0.681251i | \(-0.761436\pi\) | ||||
−0.732050 | + | 0.681251i | \(0.761436\pi\) | |||||||
\(662\) | 44.8654 | 1.74374 | ||||||||
\(663\) | 0.439697 | 0.0170764 | ||||||||
\(664\) | 64.4807 | 2.50234 | ||||||||
\(665\) | 32.2996 | 1.25253 | ||||||||
\(666\) | −58.5143 | −2.26738 | ||||||||
\(667\) | 46.2778 | 1.79188 | ||||||||
\(668\) | 7.83792 | 0.303258 | ||||||||
\(669\) | 7.85642 | 0.303747 | ||||||||
\(670\) | 10.7610 | 0.415735 | ||||||||
\(671\) | −6.13333 | −0.236775 | ||||||||
\(672\) | 164.727 | 6.35449 | ||||||||
\(673\) | 28.4658 | 1.09728 | 0.548639 | − | 0.836060i | \(-0.315146\pi\) | ||||
0.548639 | + | 0.836060i | \(0.315146\pi\) | |||||||
\(674\) | −21.9631 | −0.845987 | ||||||||
\(675\) | −9.32645 | −0.358975 | ||||||||
\(676\) | −66.6156 | −2.56214 | ||||||||
\(677\) | 9.69865 | 0.372749 | 0.186375 | − | 0.982479i | \(-0.440326\pi\) | ||||
0.186375 | + | 0.982479i | \(0.440326\pi\) | |||||||
\(678\) | 5.82133 | 0.223567 | ||||||||
\(679\) | 25.2875 | 0.970445 | ||||||||
\(680\) | −7.95152 | −0.304927 | ||||||||
\(681\) | −41.4136 | −1.58697 | ||||||||
\(682\) | 15.8848 | 0.608261 | ||||||||
\(683\) | 9.07541 | 0.347261 | 0.173630 | − | 0.984811i | \(-0.444450\pi\) | ||||
0.173630 | + | 0.984811i | \(0.444450\pi\) | |||||||
\(684\) | −167.466 | −6.40321 | ||||||||
\(685\) | −0.763307 | −0.0291645 | ||||||||
\(686\) | 24.6474 | 0.941041 | ||||||||
\(687\) | −59.1653 | −2.25730 | ||||||||
\(688\) | 12.1015 | 0.461365 | ||||||||
\(689\) | −1.31469 | −0.0500856 | ||||||||
\(690\) | −34.7480 | −1.32283 | ||||||||
\(691\) | 41.2002 | 1.56733 | 0.783665 | − | 0.621184i | \(-0.213348\pi\) | ||||
0.783665 | + | 0.621184i | \(0.213348\pi\) | |||||||
\(692\) | −56.3212 | −2.14101 | ||||||||
\(693\) | 15.6109 | 0.593010 | ||||||||
\(694\) | −22.7005 | −0.861701 | ||||||||
\(695\) | −17.8733 | −0.677974 | ||||||||
\(696\) | −194.290 | −7.36453 | ||||||||
\(697\) | −1.71029 | −0.0647818 | ||||||||
\(698\) | −74.0972 | −2.80462 | ||||||||
\(699\) | −48.4087 | −1.83099 | ||||||||
\(700\) | 84.9427 | 3.21053 | ||||||||
\(701\) | 10.0973 | 0.381368 | 0.190684 | − | 0.981651i | \(-0.438929\pi\) | ||||
0.190684 | + | 0.981651i | \(0.438929\pi\) | |||||||
\(702\) | −1.01980 | −0.0384899 | ||||||||
\(703\) | −47.7389 | −1.80051 | ||||||||
\(704\) | −17.4014 | −0.655838 | ||||||||
\(705\) | 5.99619 | 0.225829 | ||||||||
\(706\) | 20.3869 | 0.767271 | ||||||||
\(707\) | −54.4963 | −2.04955 | ||||||||
\(708\) | −122.170 | −4.59142 | ||||||||
\(709\) | 11.6574 | 0.437804 | 0.218902 | − | 0.975747i | \(-0.429752\pi\) | ||||
0.218902 | + | 0.975747i | \(0.429752\pi\) | |||||||
\(710\) | 29.3631 | 1.10198 | ||||||||
\(711\) | 15.6167 | 0.585671 | ||||||||
\(712\) | −28.3247 | −1.06151 | ||||||||
\(713\) | 31.0900 | 1.16433 | ||||||||
\(714\) | 28.2517 | 1.05729 | ||||||||
\(715\) | −0.159287 | −0.00595698 | ||||||||
\(716\) | −87.0967 | −3.25496 | ||||||||
\(717\) | −22.9449 | −0.856895 | ||||||||
\(718\) | 91.8957 | 3.42952 | ||||||||
\(719\) | −36.3273 | −1.35478 | −0.677390 | − | 0.735624i | \(-0.736889\pi\) | ||||
−0.677390 | + | 0.735624i | \(0.736889\pi\) | |||||||
\(720\) | 44.4431 | 1.65630 | ||||||||
\(721\) | 79.2450 | 2.95124 | ||||||||
\(722\) | −139.084 | −5.17616 | ||||||||
\(723\) | 19.4377 | 0.722897 | ||||||||
\(724\) | 44.4579 | 1.65227 | ||||||||
\(725\) | −36.2798 | −1.34740 | ||||||||
\(726\) | −7.00056 | −0.259815 | ||||||||
\(727\) | −15.6139 | −0.579087 | −0.289543 | − | 0.957165i | \(-0.593503\pi\) | ||||
−0.289543 | + | 0.957165i | \(0.593503\pi\) | |||||||
\(728\) | 5.67079 | 0.210173 | ||||||||
\(729\) | −39.7126 | −1.47084 | ||||||||
\(730\) | −12.6675 | −0.468845 | ||||||||
\(731\) | 1.00000 | 0.0369863 | ||||||||
\(732\) | 82.5456 | 3.05097 | ||||||||
\(733\) | −3.11550 | −0.115073 | −0.0575367 | − | 0.998343i | \(-0.518325\pi\) | ||||
−0.0575367 | + | 0.998343i | \(0.518325\pi\) | |||||||
\(734\) | −68.4585 | −2.52685 | ||||||||
\(735\) | 23.1057 | 0.852267 | ||||||||
\(736\) | −81.4286 | −3.00150 | ||||||||
\(737\) | 4.24323 | 0.156301 | ||||||||
\(738\) | 17.6724 | 0.650529 | ||||||||
\(739\) | 51.5071 | 1.89472 | 0.947359 | − | 0.320174i | \(-0.103741\pi\) | ||||
0.947359 | + | 0.320174i | \(0.103741\pi\) | |||||||
\(740\) | 27.6096 | 1.01495 | ||||||||
\(741\) | −3.70672 | −0.136170 | ||||||||
\(742\) | −84.4721 | −3.10107 | ||||||||
\(743\) | 50.6592 | 1.85851 | 0.929253 | − | 0.369444i | \(-0.120452\pi\) | ||||
0.929253 | + | 0.369444i | \(0.120452\pi\) | |||||||
\(744\) | −130.526 | −4.78533 | ||||||||
\(745\) | 20.7917 | 0.761750 | ||||||||
\(746\) | 94.8710 | 3.47348 | ||||||||
\(747\) | −29.7814 | −1.08964 | ||||||||
\(748\) | −5.13539 | −0.187769 | ||||||||
\(749\) | −60.5615 | −2.21287 | ||||||||
\(750\) | 60.4725 | 2.20815 | ||||||||
\(751\) | −22.8286 | −0.833029 | −0.416514 | − | 0.909129i | \(-0.636748\pi\) | ||||
−0.416514 | + | 0.909129i | \(0.636748\pi\) | |||||||
\(752\) | 29.1636 | 1.06349 | ||||||||
\(753\) | −20.5465 | −0.748755 | ||||||||
\(754\) | −3.96702 | −0.144470 | ||||||||
\(755\) | −9.16708 | −0.333624 | ||||||||
\(756\) | −47.1588 | −1.71515 | ||||||||
\(757\) | 41.9916 | 1.52621 | 0.763105 | − | 0.646275i | \(-0.223674\pi\) | ||||
0.763105 | + | 0.646275i | \(0.223674\pi\) | |||||||
\(758\) | 1.97941 | 0.0718954 | ||||||||
\(759\) | −13.7016 | −0.497336 | ||||||||
\(760\) | 67.0326 | 2.43153 | ||||||||
\(761\) | 46.4945 | 1.68542 | 0.842711 | − | 0.538366i | \(-0.180958\pi\) | ||||
0.842711 | + | 0.538366i | \(0.180958\pi\) | |||||||
\(762\) | −70.2058 | −2.54329 | ||||||||
\(763\) | 73.6943 | 2.66791 | ||||||||
\(764\) | −94.1081 | −3.40471 | ||||||||
\(765\) | 3.67253 | 0.132781 | ||||||||
\(766\) | 4.36736 | 0.157799 | ||||||||
\(767\) | −1.52299 | −0.0549920 | ||||||||
\(768\) | 16.1285 | 0.581985 | ||||||||
\(769\) | 9.22702 | 0.332735 | 0.166367 | − | 0.986064i | \(-0.446796\pi\) | ||||
0.166367 | + | 0.986064i | \(0.446796\pi\) | |||||||
\(770\) | −10.2346 | −0.368829 | ||||||||
\(771\) | −3.22318 | −0.116080 | ||||||||
\(772\) | 13.9370 | 0.501604 | ||||||||
\(773\) | 24.3518 | 0.875875 | 0.437937 | − | 0.899005i | \(-0.355709\pi\) | ||||
0.437937 | + | 0.899005i | \(0.355709\pi\) | |||||||
\(774\) | −10.3330 | −0.371411 | ||||||||
\(775\) | −24.3732 | −0.875512 | ||||||||
\(776\) | 52.4801 | 1.88393 | ||||||||
\(777\) | −59.8925 | −2.14863 | ||||||||
\(778\) | 46.1911 | 1.65603 | ||||||||
\(779\) | 14.4180 | 0.516579 | ||||||||
\(780\) | 2.14376 | 0.0767590 | ||||||||
\(781\) | 11.5783 | 0.414303 | ||||||||
\(782\) | −13.9655 | −0.499405 | ||||||||
\(783\) | 20.1420 | 0.719815 | ||||||||
\(784\) | 112.379 | 4.01354 | ||||||||
\(785\) | 15.2305 | 0.543600 | ||||||||
\(786\) | 127.554 | 4.54970 | ||||||||
\(787\) | −26.1069 | −0.930609 | −0.465304 | − | 0.885151i | \(-0.654055\pi\) | ||||
−0.465304 | + | 0.885151i | \(0.654055\pi\) | |||||||
\(788\) | −102.850 | −3.66389 | ||||||||
\(789\) | 22.6508 | 0.806390 | ||||||||
\(790\) | −10.2384 | −0.364265 | ||||||||
\(791\) | 3.35584 | 0.119320 | ||||||||
\(792\) | 32.3980 | 1.15121 | ||||||||
\(793\) | 1.02903 | 0.0365418 | ||||||||
\(794\) | 16.3866 | 0.581539 | ||||||||
\(795\) | −19.4969 | −0.691483 | ||||||||
\(796\) | 91.0246 | 3.22628 | ||||||||
\(797\) | 54.5131 | 1.93095 | 0.965476 | − | 0.260493i | \(-0.0838850\pi\) | ||||
0.965476 | + | 0.260493i | \(0.0838850\pi\) | |||||||
\(798\) | −238.167 | −8.43100 | ||||||||
\(799\) | 2.40992 | 0.0852568 | ||||||||
\(800\) | 63.8365 | 2.25696 | ||||||||
\(801\) | 13.0822 | 0.462237 | ||||||||
\(802\) | 11.7864 | 0.416193 | ||||||||
\(803\) | −4.99497 | −0.176269 | ||||||||
\(804\) | −57.1076 | −2.01403 | ||||||||
\(805\) | −20.0313 | −0.706010 | ||||||||
\(806\) | −2.66509 | −0.0938739 | ||||||||
\(807\) | −49.9640 | −1.75882 | ||||||||
\(808\) | −113.098 | −3.97878 | ||||||||
\(809\) | −33.3485 | −1.17247 | −0.586235 | − | 0.810141i | \(-0.699390\pi\) | ||||
−0.586235 | + | 0.810141i | \(0.699390\pi\) | |||||||
\(810\) | 14.3067 | 0.502685 | ||||||||
\(811\) | −22.8260 | −0.801530 | −0.400765 | − | 0.916181i | \(-0.631256\pi\) | ||||
−0.400765 | + | 0.916181i | \(0.631256\pi\) | |||||||
\(812\) | −183.447 | −6.43774 | ||||||||
\(813\) | 2.76668 | 0.0970318 | ||||||||
\(814\) | 15.1267 | 0.530192 | ||||||||
\(815\) | 14.8276 | 0.519388 | ||||||||
\(816\) | 31.7148 | 1.11024 | ||||||||
\(817\) | −8.43016 | −0.294934 | ||||||||
\(818\) | −9.53146 | −0.333260 | ||||||||
\(819\) | −2.61914 | −0.0915202 | ||||||||
\(820\) | −8.33859 | −0.291196 | ||||||||
\(821\) | −48.9846 | −1.70958 | −0.854788 | − | 0.518978i | \(-0.826313\pi\) | ||||
−0.854788 | + | 0.518978i | \(0.826313\pi\) | |||||||
\(822\) | 5.62837 | 0.196312 | ||||||||
\(823\) | 45.9147 | 1.60049 | 0.800243 | − | 0.599676i | \(-0.204704\pi\) | ||||
0.800243 | + | 0.599676i | \(0.204704\pi\) | |||||||
\(824\) | 164.460 | 5.72924 | ||||||||
\(825\) | 10.7415 | 0.373970 | ||||||||
\(826\) | −97.8561 | −3.40485 | ||||||||
\(827\) | −7.96108 | −0.276834 | −0.138417 | − | 0.990374i | \(-0.544201\pi\) | ||||
−0.138417 | + | 0.990374i | \(0.544201\pi\) | |||||||
\(828\) | 103.857 | 3.60930 | ||||||||
\(829\) | 10.8082 | 0.375386 | 0.187693 | − | 0.982228i | \(-0.439899\pi\) | ||||
0.187693 | + | 0.982228i | \(0.439899\pi\) | |||||||
\(830\) | 19.5248 | 0.677716 | ||||||||
\(831\) | −20.8737 | −0.724101 | ||||||||
\(832\) | 2.91953 | 0.101217 | ||||||||
\(833\) | 9.28639 | 0.321754 | ||||||||
\(834\) | 131.792 | 4.56358 | ||||||||
\(835\) | 1.44903 | 0.0501456 | ||||||||
\(836\) | 43.2922 | 1.49729 | ||||||||
\(837\) | 13.5316 | 0.467722 | ||||||||
\(838\) | 51.5793 | 1.78178 | ||||||||
\(839\) | 10.8435 | 0.374357 | 0.187179 | − | 0.982326i | \(-0.440066\pi\) | ||||
0.187179 | + | 0.982326i | \(0.440066\pi\) | |||||||
\(840\) | 84.0981 | 2.90166 | ||||||||
\(841\) | 49.3520 | 1.70179 | ||||||||
\(842\) | −57.9037 | −1.99549 | ||||||||
\(843\) | −13.0209 | −0.448464 | ||||||||
\(844\) | −33.8424 | −1.16490 | ||||||||
\(845\) | −12.3155 | −0.423665 | ||||||||
\(846\) | −24.9016 | −0.856136 | ||||||||
\(847\) | −4.03564 | −0.138666 | ||||||||
\(848\) | −94.8267 | −3.25636 | ||||||||
\(849\) | −54.7151 | −1.87782 | ||||||||
\(850\) | 10.9484 | 0.375525 | ||||||||
\(851\) | 29.6063 | 1.01489 | ||||||||
\(852\) | −155.826 | −5.33852 | ||||||||
\(853\) | 29.0348 | 0.994132 | 0.497066 | − | 0.867713i | \(-0.334411\pi\) | ||||
0.497066 | + | 0.867713i | \(0.334411\pi\) | |||||||
\(854\) | 66.1177 | 2.26250 | ||||||||
\(855\) | −30.9600 | −1.05881 | ||||||||
\(856\) | −125.685 | −4.29584 | ||||||||
\(857\) | −22.9067 | −0.782479 | −0.391240 | − | 0.920289i | \(-0.627954\pi\) | ||||
−0.391240 | + | 0.920289i | \(0.627954\pi\) | |||||||
\(858\) | 1.17453 | 0.0400977 | ||||||||
\(859\) | 50.8516 | 1.73503 | 0.867517 | − | 0.497408i | \(-0.165715\pi\) | ||||
0.867517 | + | 0.497408i | \(0.165715\pi\) | |||||||
\(860\) | 4.87554 | 0.166255 | ||||||||
\(861\) | 18.0886 | 0.616459 | ||||||||
\(862\) | −91.3436 | −3.11117 | ||||||||
\(863\) | 53.3484 | 1.81600 | 0.908000 | − | 0.418969i | \(-0.137609\pi\) | ||||
0.908000 | + | 0.418969i | \(0.137609\pi\) | |||||||
\(864\) | −35.4410 | −1.20573 | ||||||||
\(865\) | −10.4123 | −0.354029 | ||||||||
\(866\) | −69.2103 | −2.35186 | ||||||||
\(867\) | 2.62074 | 0.0890049 | ||||||||
\(868\) | −123.242 | −4.18311 | ||||||||
\(869\) | −4.03713 | −0.136950 | ||||||||
\(870\) | −58.8311 | −1.99456 | ||||||||
\(871\) | −0.711912 | −0.0241222 | ||||||||
\(872\) | 152.941 | 5.17922 | ||||||||
\(873\) | −24.2387 | −0.820357 | ||||||||
\(874\) | 117.731 | 3.98232 | ||||||||
\(875\) | 34.8609 | 1.17851 | ||||||||
\(876\) | 67.2249 | 2.27132 | ||||||||
\(877\) | −3.72789 | −0.125882 | −0.0629409 | − | 0.998017i | \(-0.520048\pi\) | ||||
−0.0629409 | + | 0.998017i | \(0.520048\pi\) | |||||||
\(878\) | 78.4066 | 2.64609 | ||||||||
\(879\) | −18.2190 | −0.614513 | ||||||||
\(880\) | −11.4892 | −0.387299 | ||||||||
\(881\) | −12.4484 | −0.419399 | −0.209699 | − | 0.977766i | \(-0.567249\pi\) | ||||
−0.209699 | + | 0.977766i | \(0.567249\pi\) | |||||||
\(882\) | −95.9560 | −3.23101 | ||||||||
\(883\) | 23.2800 | 0.783433 | 0.391716 | − | 0.920086i | \(-0.371881\pi\) | ||||
0.391716 | + | 0.920086i | \(0.371881\pi\) | |||||||
\(884\) | 0.861596 | 0.0289786 | ||||||||
\(885\) | −22.5860 | −0.759220 | ||||||||
\(886\) | 51.5470 | 1.73176 | ||||||||
\(887\) | −18.0951 | −0.607575 | −0.303788 | − | 0.952740i | \(-0.598251\pi\) | ||||
−0.303788 | + | 0.952740i | \(0.598251\pi\) | |||||||
\(888\) | −124.297 | −4.17114 | ||||||||
\(889\) | −40.4718 | −1.35738 | ||||||||
\(890\) | −8.57675 | −0.287493 | ||||||||
\(891\) | 5.64131 | 0.188991 | ||||||||
\(892\) | 15.3948 | 0.515457 | ||||||||
\(893\) | −20.3160 | −0.679849 | ||||||||
\(894\) | −153.311 | −5.12749 | ||||||||
\(895\) | −16.1019 | −0.538227 | ||||||||
\(896\) | 61.8771 | 2.06717 | ||||||||
\(897\) | 2.29880 | 0.0767547 | ||||||||
\(898\) | −1.20357 | −0.0401637 | ||||||||
\(899\) | 52.6379 | 1.75557 | ||||||||
\(900\) | −81.4198 | −2.71399 | ||||||||
\(901\) | −7.83596 | −0.261054 | ||||||||
\(902\) | −4.56855 | −0.152116 | ||||||||
\(903\) | −10.5764 | −0.351959 | ||||||||
\(904\) | 6.96451 | 0.231636 | ||||||||
\(905\) | 8.21911 | 0.273212 | ||||||||
\(906\) | 67.5950 | 2.24569 | ||||||||
\(907\) | 32.6032 | 1.08257 | 0.541286 | − | 0.840839i | \(-0.317938\pi\) | ||||
0.541286 | + | 0.840839i | \(0.317938\pi\) | |||||||
\(908\) | −81.1508 | −2.69308 | ||||||||
\(909\) | 52.2362 | 1.73256 | ||||||||
\(910\) | 1.71712 | 0.0569220 | ||||||||
\(911\) | −16.7868 | −0.556171 | −0.278086 | − | 0.960556i | \(-0.589700\pi\) | ||||
−0.278086 | + | 0.960556i | \(0.589700\pi\) | |||||||
\(912\) | −267.361 | −8.85321 | ||||||||
\(913\) | 7.69890 | 0.254796 | ||||||||
\(914\) | −18.4041 | −0.608753 | ||||||||
\(915\) | 15.2605 | 0.504497 | ||||||||
\(916\) | −115.936 | −3.83063 | ||||||||
\(917\) | 73.5315 | 2.42823 | ||||||||
\(918\) | −6.07835 | −0.200615 | ||||||||
\(919\) | −18.7918 | −0.619884 | −0.309942 | − | 0.950755i | \(-0.600310\pi\) | ||||
−0.309942 | + | 0.950755i | \(0.600310\pi\) | |||||||
\(920\) | −41.5717 | −1.37058 | ||||||||
\(921\) | 59.1420 | 1.94879 | ||||||||
\(922\) | 11.7525 | 0.387049 | ||||||||
\(923\) | −1.94256 | −0.0639400 | ||||||||
\(924\) | 54.3137 | 1.78679 | ||||||||
\(925\) | −23.2101 | −0.763142 | ||||||||
\(926\) | −23.9134 | −0.785842 | ||||||||
\(927\) | −75.9584 | −2.49480 | ||||||||
\(928\) | −137.865 | −4.52565 | ||||||||
\(929\) | 3.05221 | 0.100140 | 0.0500698 | − | 0.998746i | \(-0.484056\pi\) | ||||
0.0500698 | + | 0.998746i | \(0.484056\pi\) | |||||||
\(930\) | −39.5235 | −1.29603 | ||||||||
\(931\) | −78.2857 | −2.56571 | ||||||||
\(932\) | −94.8580 | −3.10718 | ||||||||
\(933\) | −38.1523 | −1.24905 | ||||||||
\(934\) | −112.781 | −3.69029 | ||||||||
\(935\) | −0.949400 | −0.0310487 | ||||||||
\(936\) | −5.43560 | −0.177668 | ||||||||
\(937\) | −46.5580 | −1.52098 | −0.760492 | − | 0.649347i | \(-0.775042\pi\) | ||||
−0.760492 | + | 0.649347i | \(0.775042\pi\) | |||||||
\(938\) | −45.7423 | −1.49354 | ||||||||
\(939\) | −9.30396 | −0.303623 | ||||||||
\(940\) | 11.7497 | 0.383232 | ||||||||
\(941\) | 6.32792 | 0.206284 | 0.103142 | − | 0.994667i | \(-0.467110\pi\) | ||||
0.103142 | + | 0.994667i | \(0.467110\pi\) | |||||||
\(942\) | −112.305 | −3.65908 | ||||||||
\(943\) | −8.94164 | −0.291180 | ||||||||
\(944\) | −109.851 | −3.57536 | ||||||||
\(945\) | −8.71843 | −0.283611 | ||||||||
\(946\) | 2.67122 | 0.0868487 | ||||||||
\(947\) | −44.3781 | −1.44209 | −0.721047 | − | 0.692886i | \(-0.756339\pi\) | ||||
−0.721047 | + | 0.692886i | \(0.756339\pi\) | |||||||
\(948\) | 54.3338 | 1.76468 | ||||||||
\(949\) | 0.838036 | 0.0272038 | ||||||||
\(950\) | −92.2963 | −2.99449 | ||||||||
\(951\) | −79.2958 | −2.57134 | ||||||||
\(952\) | 33.7998 | 1.09546 | ||||||||
\(953\) | −26.2801 | −0.851296 | −0.425648 | − | 0.904889i | \(-0.639954\pi\) | ||||
−0.425648 | + | 0.904889i | \(0.639954\pi\) | |||||||
\(954\) | 80.9687 | 2.62146 | ||||||||
\(955\) | −17.3981 | −0.562990 | ||||||||
\(956\) | −44.9611 | −1.45415 | ||||||||
\(957\) | −23.1979 | −0.749882 | ||||||||
\(958\) | 68.8732 | 2.22519 | ||||||||
\(959\) | 3.24461 | 0.104774 | ||||||||
\(960\) | 43.2968 | 1.39740 | ||||||||
\(961\) | 4.36281 | 0.140736 | ||||||||
\(962\) | −2.53791 | −0.0818254 | ||||||||
\(963\) | 58.0497 | 1.87063 | ||||||||
\(964\) | 38.0887 | 1.22675 | ||||||||
\(965\) | 2.57659 | 0.0829433 | ||||||||
\(966\) | 147.704 | 4.75230 | ||||||||
\(967\) | 42.2745 | 1.35946 | 0.679728 | − | 0.733465i | \(-0.262098\pi\) | ||||
0.679728 | + | 0.733465i | \(0.262098\pi\) | |||||||
\(968\) | −8.37532 | −0.269193 | ||||||||
\(969\) | −22.0932 | −0.709737 | ||||||||
\(970\) | 15.8910 | 0.510230 | ||||||||
\(971\) | −26.9582 | −0.865129 | −0.432564 | − | 0.901603i | \(-0.642391\pi\) | ||||
−0.432564 | + | 0.901603i | \(0.642391\pi\) | |||||||
\(972\) | −110.980 | −3.55970 | ||||||||
\(973\) | 75.9746 | 2.43563 | ||||||||
\(974\) | 61.5941 | 1.97360 | ||||||||
\(975\) | −1.80216 | −0.0577153 | ||||||||
\(976\) | 74.2224 | 2.37580 | ||||||||
\(977\) | 30.4031 | 0.972682 | 0.486341 | − | 0.873769i | \(-0.338331\pi\) | ||||
0.486341 | + | 0.873769i | \(0.338331\pi\) | |||||||
\(978\) | −109.334 | −3.49611 | ||||||||
\(979\) | −3.38193 | −0.108087 | ||||||||
\(980\) | 45.2762 | 1.44629 | ||||||||
\(981\) | −70.6379 | −2.25530 | ||||||||
\(982\) | −1.58345 | −0.0505299 | ||||||||
\(983\) | 30.5554 | 0.974566 | 0.487283 | − | 0.873244i | \(-0.337988\pi\) | ||||
0.487283 | + | 0.873244i | \(0.337988\pi\) | |||||||
\(984\) | 37.5400 | 1.19673 | ||||||||
\(985\) | −19.0143 | −0.605847 | ||||||||
\(986\) | −23.6447 | −0.753001 | ||||||||
\(987\) | −25.4881 | −0.811297 | ||||||||
\(988\) | −7.26340 | −0.231079 | ||||||||
\(989\) | 5.22814 | 0.166245 | ||||||||
\(990\) | 9.81013 | 0.311786 | ||||||||
\(991\) | −3.75012 | −0.119127 | −0.0595633 | − | 0.998225i | \(-0.518971\pi\) | ||||
−0.0595633 | + | 0.998225i | \(0.518971\pi\) | |||||||
\(992\) | −92.6196 | −2.94068 | ||||||||
\(993\) | −44.0175 | −1.39685 | ||||||||
\(994\) | −124.814 | −3.95887 | ||||||||
\(995\) | 16.8281 | 0.533486 | ||||||||
\(996\) | −103.616 | −3.28319 | ||||||||
\(997\) | 49.4156 | 1.56501 | 0.782504 | − | 0.622645i | \(-0.213942\pi\) | ||||
0.782504 | + | 0.622645i | \(0.213942\pi\) | |||||||
\(998\) | 40.4553 | 1.28059 | ||||||||
\(999\) | 12.8859 | 0.407690 |
(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 | 8041.2.a.g.1.4 | ✓ | 69 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8041.2.a.g.1.4 | ✓ | 69 | 1.1 | even | 1 | trivial |