Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6023,2,Mod(1,6023)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6023, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("6023.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6023 = 19 \cdot 317 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6023.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: | \(48.0938971374\) |
Analytic rank: | \(1\) |
Dimension: | \(99\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.16 | ||
Character | \(\chi\) | \(=\) | 6023.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.15033 | −1.52051 | −0.760255 | − | 0.649625i | \(-0.774926\pi\) | ||||
−0.760255 | + | 0.649625i | \(0.774926\pi\) | |||||||
\(3\) | −0.758271 | −0.437788 | −0.218894 | − | 0.975749i | \(-0.570245\pi\) | ||||
−0.218894 | + | 0.975749i | \(0.570245\pi\) | |||||||
\(4\) | 2.62390 | 1.31195 | ||||||||
\(5\) | −3.61423 | −1.61633 | −0.808167 | − | 0.588953i | \(-0.799540\pi\) | ||||
−0.808167 | + | 0.588953i | \(0.799540\pi\) | |||||||
\(6\) | 1.63053 | 0.665661 | ||||||||
\(7\) | −3.46519 | −1.30972 | −0.654859 | − | 0.755751i | \(-0.727272\pi\) | ||||
−0.654859 | + | 0.755751i | \(0.727272\pi\) | |||||||
\(8\) | −1.34159 | −0.474324 | ||||||||
\(9\) | −2.42502 | −0.808342 | ||||||||
\(10\) | 7.77178 | 2.45765 | ||||||||
\(11\) | −2.36321 | −0.712534 | −0.356267 | − | 0.934384i | \(-0.615951\pi\) | ||||
−0.356267 | + | 0.934384i | \(0.615951\pi\) | |||||||
\(12\) | −1.98963 | −0.574356 | ||||||||
\(13\) | −5.83434 | −1.61815 | −0.809077 | − | 0.587703i | \(-0.800032\pi\) | ||||
−0.809077 | + | 0.587703i | \(0.800032\pi\) | |||||||
\(14\) | 7.45128 | 1.99144 | ||||||||
\(15\) | 2.74057 | 0.707612 | ||||||||
\(16\) | −2.36294 | −0.590736 | ||||||||
\(17\) | −1.13828 | −0.276074 | −0.138037 | − | 0.990427i | \(-0.544079\pi\) | ||||
−0.138037 | + | 0.990427i | \(0.544079\pi\) | |||||||
\(18\) | 5.21459 | 1.22909 | ||||||||
\(19\) | −1.00000 | −0.229416 | ||||||||
\(20\) | −9.48339 | −2.12055 | ||||||||
\(21\) | 2.62755 | 0.573379 | ||||||||
\(22\) | 5.08167 | 1.08342 | ||||||||
\(23\) | −8.30329 | −1.73136 | −0.865678 | − | 0.500601i | \(-0.833112\pi\) | ||||
−0.865678 | + | 0.500601i | \(0.833112\pi\) | |||||||
\(24\) | 1.01729 | 0.207653 | ||||||||
\(25\) | 8.06268 | 1.61254 | ||||||||
\(26\) | 12.5457 | 2.46042 | ||||||||
\(27\) | 4.11364 | 0.791671 | ||||||||
\(28\) | −9.09231 | −1.71828 | ||||||||
\(29\) | −0.468033 | −0.0869116 | −0.0434558 | − | 0.999055i | \(-0.513837\pi\) | ||||
−0.0434558 | + | 0.999055i | \(0.513837\pi\) | |||||||
\(30\) | −5.89312 | −1.07593 | ||||||||
\(31\) | 5.31029 | 0.953757 | 0.476879 | − | 0.878969i | \(-0.341768\pi\) | ||||
0.476879 | + | 0.878969i | \(0.341768\pi\) | |||||||
\(32\) | 7.76428 | 1.37254 | ||||||||
\(33\) | 1.79195 | 0.311939 | ||||||||
\(34\) | 2.44768 | 0.419773 | ||||||||
\(35\) | 12.5240 | 2.11694 | ||||||||
\(36\) | −6.36302 | −1.06050 | ||||||||
\(37\) | −8.64931 | −1.42194 | −0.710969 | − | 0.703224i | \(-0.751743\pi\) | ||||
−0.710969 | + | 0.703224i | \(0.751743\pi\) | |||||||
\(38\) | 2.15033 | 0.348829 | ||||||||
\(39\) | 4.42401 | 0.708409 | ||||||||
\(40\) | 4.84882 | 0.766666 | ||||||||
\(41\) | 0.0804774 | 0.0125685 | 0.00628423 | − | 0.999980i | \(-0.498000\pi\) | ||||
0.00628423 | + | 0.999980i | \(0.498000\pi\) | |||||||
\(42\) | −5.65009 | −0.871828 | ||||||||
\(43\) | 3.27407 | 0.499291 | 0.249646 | − | 0.968337i | \(-0.419686\pi\) | ||||
0.249646 | + | 0.968337i | \(0.419686\pi\) | |||||||
\(44\) | −6.20082 | −0.934809 | ||||||||
\(45\) | 8.76460 | 1.30655 | ||||||||
\(46\) | 17.8548 | 2.63254 | ||||||||
\(47\) | 6.11975 | 0.892657 | 0.446329 | − | 0.894869i | \(-0.352731\pi\) | ||||
0.446329 | + | 0.894869i | \(0.352731\pi\) | |||||||
\(48\) | 1.79175 | 0.258617 | ||||||||
\(49\) | 5.00751 | 0.715359 | ||||||||
\(50\) | −17.3374 | −2.45188 | ||||||||
\(51\) | 0.863126 | 0.120862 | ||||||||
\(52\) | −15.3087 | −2.12294 | ||||||||
\(53\) | 5.60205 | 0.769500 | 0.384750 | − | 0.923021i | \(-0.374288\pi\) | ||||
0.384750 | + | 0.923021i | \(0.374288\pi\) | |||||||
\(54\) | −8.84567 | −1.20374 | ||||||||
\(55\) | 8.54119 | 1.15169 | ||||||||
\(56\) | 4.64886 | 0.621230 | ||||||||
\(57\) | 0.758271 | 0.100435 | ||||||||
\(58\) | 1.00642 | 0.132150 | ||||||||
\(59\) | −2.48579 | −0.323623 | −0.161811 | − | 0.986822i | \(-0.551734\pi\) | ||||
−0.161811 | + | 0.986822i | \(0.551734\pi\) | |||||||
\(60\) | 7.19098 | 0.928352 | ||||||||
\(61\) | 3.79889 | 0.486399 | 0.243199 | − | 0.969976i | \(-0.421803\pi\) | ||||
0.243199 | + | 0.969976i | \(0.421803\pi\) | |||||||
\(62\) | −11.4189 | −1.45020 | ||||||||
\(63\) | 8.40316 | 1.05870 | ||||||||
\(64\) | −11.9698 | −1.49623 | ||||||||
\(65\) | 21.0867 | 2.61548 | ||||||||
\(66\) | −3.85328 | −0.474306 | ||||||||
\(67\) | −7.78246 | −0.950779 | −0.475390 | − | 0.879775i | \(-0.657693\pi\) | ||||
−0.475390 | + | 0.879775i | \(0.657693\pi\) | |||||||
\(68\) | −2.98674 | −0.362195 | ||||||||
\(69\) | 6.29615 | 0.757967 | ||||||||
\(70\) | −26.9307 | −3.21883 | ||||||||
\(71\) | 8.94185 | 1.06120 | 0.530601 | − | 0.847622i | \(-0.321966\pi\) | ||||
0.530601 | + | 0.847622i | \(0.321966\pi\) | |||||||
\(72\) | 3.25339 | 0.383416 | ||||||||
\(73\) | −3.10520 | −0.363436 | −0.181718 | − | 0.983351i | \(-0.558166\pi\) | ||||
−0.181718 | + | 0.983351i | \(0.558166\pi\) | |||||||
\(74\) | 18.5988 | 2.16207 | ||||||||
\(75\) | −6.11370 | −0.705950 | ||||||||
\(76\) | −2.62390 | −0.300982 | ||||||||
\(77\) | 8.18896 | 0.933218 | ||||||||
\(78\) | −9.51306 | −1.07714 | ||||||||
\(79\) | −8.07936 | −0.908999 | −0.454500 | − | 0.890747i | \(-0.650182\pi\) | ||||
−0.454500 | + | 0.890747i | \(0.650182\pi\) | |||||||
\(80\) | 8.54023 | 0.954827 | ||||||||
\(81\) | 4.15582 | 0.461757 | ||||||||
\(82\) | −0.173053 | −0.0191105 | ||||||||
\(83\) | 4.70994 | 0.516983 | 0.258492 | − | 0.966014i | \(-0.416775\pi\) | ||||
0.258492 | + | 0.966014i | \(0.416775\pi\) | |||||||
\(84\) | 6.89444 | 0.752245 | ||||||||
\(85\) | 4.11401 | 0.446227 | ||||||||
\(86\) | −7.04032 | −0.759177 | ||||||||
\(87\) | 0.354896 | 0.0380489 | ||||||||
\(88\) | 3.17046 | 0.337972 | ||||||||
\(89\) | −8.02104 | −0.850229 | −0.425114 | − | 0.905140i | \(-0.639766\pi\) | ||||
−0.425114 | + | 0.905140i | \(0.639766\pi\) | |||||||
\(90\) | −18.8468 | −1.98662 | ||||||||
\(91\) | 20.2171 | 2.11932 | ||||||||
\(92\) | −21.7870 | −2.27145 | ||||||||
\(93\) | −4.02664 | −0.417544 | ||||||||
\(94\) | −13.1595 | −1.35729 | ||||||||
\(95\) | 3.61423 | 0.370813 | ||||||||
\(96\) | −5.88743 | −0.600884 | ||||||||
\(97\) | 4.78710 | 0.486056 | 0.243028 | − | 0.970019i | \(-0.421859\pi\) | ||||
0.243028 | + | 0.970019i | \(0.421859\pi\) | |||||||
\(98\) | −10.7678 | −1.08771 | ||||||||
\(99\) | 5.73084 | 0.575971 | ||||||||
\(100\) | 21.1557 | 2.11557 | ||||||||
\(101\) | 5.92423 | 0.589483 | 0.294741 | − | 0.955577i | \(-0.404767\pi\) | ||||
0.294741 | + | 0.955577i | \(0.404767\pi\) | |||||||
\(102\) | −1.85600 | −0.183772 | ||||||||
\(103\) | −9.60535 | −0.946443 | −0.473221 | − | 0.880943i | \(-0.656909\pi\) | ||||
−0.473221 | + | 0.880943i | \(0.656909\pi\) | |||||||
\(104\) | 7.82729 | 0.767529 | ||||||||
\(105\) | −9.49658 | −0.926772 | ||||||||
\(106\) | −12.0462 | −1.17003 | ||||||||
\(107\) | −8.76418 | −0.847265 | −0.423633 | − | 0.905834i | \(-0.639245\pi\) | ||||
−0.423633 | + | 0.905834i | \(0.639245\pi\) | |||||||
\(108\) | 10.7938 | 1.03863 | ||||||||
\(109\) | 4.75916 | 0.455845 | 0.227923 | − | 0.973679i | \(-0.426807\pi\) | ||||
0.227923 | + | 0.973679i | \(0.426807\pi\) | |||||||
\(110\) | −18.3663 | −1.75116 | ||||||||
\(111\) | 6.55852 | 0.622507 | ||||||||
\(112\) | 8.18804 | 0.773697 | ||||||||
\(113\) | 1.20485 | 0.113343 | 0.0566713 | − | 0.998393i | \(-0.481951\pi\) | ||||
0.0566713 | + | 0.998393i | \(0.481951\pi\) | |||||||
\(114\) | −1.63053 | −0.152713 | ||||||||
\(115\) | 30.0100 | 2.79845 | ||||||||
\(116\) | −1.22807 | −0.114024 | ||||||||
\(117\) | 14.1484 | 1.30802 | ||||||||
\(118\) | 5.34527 | 0.492072 | ||||||||
\(119\) | 3.94436 | 0.361578 | ||||||||
\(120\) | −3.67672 | −0.335637 | ||||||||
\(121\) | −5.41525 | −0.492295 | ||||||||
\(122\) | −8.16886 | −0.739574 | ||||||||
\(123\) | −0.0610237 | −0.00550232 | ||||||||
\(124\) | 13.9337 | 1.25128 | ||||||||
\(125\) | −11.0693 | −0.990064 | ||||||||
\(126\) | −18.0695 | −1.60976 | ||||||||
\(127\) | 12.3801 | 1.09856 | 0.549279 | − | 0.835639i | \(-0.314902\pi\) | ||||
0.549279 | + | 0.835639i | \(0.314902\pi\) | |||||||
\(128\) | 10.2105 | 0.902490 | ||||||||
\(129\) | −2.48263 | −0.218584 | ||||||||
\(130\) | −45.3432 | −3.97686 | ||||||||
\(131\) | 4.57409 | 0.399640 | 0.199820 | − | 0.979833i | \(-0.435964\pi\) | ||||
0.199820 | + | 0.979833i | \(0.435964\pi\) | |||||||
\(132\) | 4.70191 | 0.409249 | ||||||||
\(133\) | 3.46519 | 0.300470 | ||||||||
\(134\) | 16.7348 | 1.44567 | ||||||||
\(135\) | −14.8677 | −1.27960 | ||||||||
\(136\) | 1.52711 | 0.130948 | ||||||||
\(137\) | 12.7303 | 1.08762 | 0.543809 | − | 0.839209i | \(-0.316981\pi\) | ||||
0.543809 | + | 0.839209i | \(0.316981\pi\) | |||||||
\(138\) | −13.5388 | −1.15250 | ||||||||
\(139\) | −20.5528 | −1.74327 | −0.871634 | − | 0.490158i | \(-0.836939\pi\) | ||||
−0.871634 | + | 0.490158i | \(0.836939\pi\) | |||||||
\(140\) | 32.8617 | 2.77732 | ||||||||
\(141\) | −4.64043 | −0.390795 | ||||||||
\(142\) | −19.2279 | −1.61357 | ||||||||
\(143\) | 13.7878 | 1.15299 | ||||||||
\(144\) | 5.73020 | 0.477517 | ||||||||
\(145\) | 1.69158 | 0.140478 | ||||||||
\(146\) | 6.67719 | 0.552608 | ||||||||
\(147\) | −3.79705 | −0.313176 | ||||||||
\(148\) | −22.6949 | −1.86551 | ||||||||
\(149\) | 12.2221 | 1.00127 | 0.500635 | − | 0.865658i | \(-0.333100\pi\) | ||||
0.500635 | + | 0.865658i | \(0.333100\pi\) | |||||||
\(150\) | 13.1465 | 1.07340 | ||||||||
\(151\) | 4.74717 | 0.386320 | 0.193160 | − | 0.981167i | \(-0.438126\pi\) | ||||
0.193160 | + | 0.981167i | \(0.438126\pi\) | |||||||
\(152\) | 1.34159 | 0.108817 | ||||||||
\(153\) | 2.76036 | 0.223162 | ||||||||
\(154\) | −17.6089 | −1.41897 | ||||||||
\(155\) | −19.1926 | −1.54159 | ||||||||
\(156\) | 11.6082 | 0.929397 | ||||||||
\(157\) | 10.7757 | 0.859991 | 0.429996 | − | 0.902831i | \(-0.358515\pi\) | ||||
0.429996 | + | 0.902831i | \(0.358515\pi\) | |||||||
\(158\) | 17.3733 | 1.38214 | ||||||||
\(159\) | −4.24787 | −0.336878 | ||||||||
\(160\) | −28.0619 | −2.21849 | ||||||||
\(161\) | 28.7724 | 2.26759 | ||||||||
\(162\) | −8.93636 | −0.702107 | ||||||||
\(163\) | −20.1957 | −1.58185 | −0.790925 | − | 0.611913i | \(-0.790400\pi\) | ||||
−0.790925 | + | 0.611913i | \(0.790400\pi\) | |||||||
\(164\) | 0.211165 | 0.0164892 | ||||||||
\(165\) | −6.47654 | −0.504198 | ||||||||
\(166\) | −10.1279 | −0.786078 | ||||||||
\(167\) | −10.7629 | −0.832860 | −0.416430 | − | 0.909168i | \(-0.636719\pi\) | ||||
−0.416430 | + | 0.909168i | \(0.636719\pi\) | |||||||
\(168\) | −3.52510 | −0.271967 | ||||||||
\(169\) | 21.0395 | 1.61842 | ||||||||
\(170\) | −8.84647 | −0.678493 | ||||||||
\(171\) | 2.42502 | 0.185446 | ||||||||
\(172\) | 8.59084 | 0.655045 | ||||||||
\(173\) | −10.9655 | −0.833694 | −0.416847 | − | 0.908977i | \(-0.636865\pi\) | ||||
−0.416847 | + | 0.908977i | \(0.636865\pi\) | |||||||
\(174\) | −0.763143 | −0.0578537 | ||||||||
\(175\) | −27.9387 | −2.11197 | ||||||||
\(176\) | 5.58413 | 0.420920 | ||||||||
\(177\) | 1.88491 | 0.141678 | ||||||||
\(178\) | 17.2479 | 1.29278 | ||||||||
\(179\) | 6.23241 | 0.465832 | 0.232916 | − | 0.972497i | \(-0.425173\pi\) | ||||
0.232916 | + | 0.972497i | \(0.425173\pi\) | |||||||
\(180\) | 22.9975 | 1.71413 | ||||||||
\(181\) | 7.73278 | 0.574773 | 0.287387 | − | 0.957815i | \(-0.407214\pi\) | ||||
0.287387 | + | 0.957815i | \(0.407214\pi\) | |||||||
\(182\) | −43.4733 | −3.22245 | ||||||||
\(183\) | −2.88059 | −0.212940 | ||||||||
\(184\) | 11.1396 | 0.821224 | ||||||||
\(185\) | 31.2606 | 2.29833 | ||||||||
\(186\) | 8.65860 | 0.634879 | ||||||||
\(187\) | 2.69000 | 0.196712 | ||||||||
\(188\) | 16.0576 | 1.17112 | ||||||||
\(189\) | −14.2545 | −1.03686 | ||||||||
\(190\) | −7.77178 | −0.563824 | ||||||||
\(191\) | −0.228860 | −0.0165597 | −0.00827986 | − | 0.999966i | \(-0.502636\pi\) | ||||
−0.00827986 | + | 0.999966i | \(0.502636\pi\) | |||||||
\(192\) | 9.07639 | 0.655032 | ||||||||
\(193\) | −16.2349 | −1.16861 | −0.584306 | − | 0.811534i | \(-0.698633\pi\) | ||||
−0.584306 | + | 0.811534i | \(0.698633\pi\) | |||||||
\(194\) | −10.2938 | −0.739054 | ||||||||
\(195\) | −15.9894 | −1.14503 | ||||||||
\(196\) | 13.1392 | 0.938516 | ||||||||
\(197\) | 19.6254 | 1.39825 | 0.699126 | − | 0.714998i | \(-0.253572\pi\) | ||||
0.699126 | + | 0.714998i | \(0.253572\pi\) | |||||||
\(198\) | −12.3232 | −0.875769 | ||||||||
\(199\) | −6.74121 | −0.477872 | −0.238936 | − | 0.971035i | \(-0.576799\pi\) | ||||
−0.238936 | + | 0.971035i | \(0.576799\pi\) | |||||||
\(200\) | −10.8168 | −0.764865 | ||||||||
\(201\) | 5.90122 | 0.416240 | ||||||||
\(202\) | −12.7390 | −0.896314 | ||||||||
\(203\) | 1.62182 | 0.113830 | ||||||||
\(204\) | 2.26476 | 0.158565 | ||||||||
\(205\) | −0.290864 | −0.0203148 | ||||||||
\(206\) | 20.6546 | 1.43908 | ||||||||
\(207\) | 20.1357 | 1.39953 | ||||||||
\(208\) | 13.7862 | 0.955902 | ||||||||
\(209\) | 2.36321 | 0.163467 | ||||||||
\(210\) | 20.4207 | 1.40917 | ||||||||
\(211\) | 27.6002 | 1.90008 | 0.950039 | − | 0.312130i | \(-0.101042\pi\) | ||||
0.950039 | + | 0.312130i | \(0.101042\pi\) | |||||||
\(212\) | 14.6992 | 1.00955 | ||||||||
\(213\) | −6.78035 | −0.464582 | ||||||||
\(214\) | 18.8458 | 1.28827 | ||||||||
\(215\) | −11.8333 | −0.807021 | ||||||||
\(216\) | −5.51882 | −0.375508 | ||||||||
\(217\) | −18.4012 | −1.24915 | ||||||||
\(218\) | −10.2338 | −0.693117 | ||||||||
\(219\) | 2.35458 | 0.159108 | ||||||||
\(220\) | 22.4112 | 1.51096 | ||||||||
\(221\) | 6.64111 | 0.446730 | ||||||||
\(222\) | −14.1030 | −0.946529 | ||||||||
\(223\) | −21.6754 | −1.45149 | −0.725747 | − | 0.687962i | \(-0.758506\pi\) | ||||
−0.725747 | + | 0.687962i | \(0.758506\pi\) | |||||||
\(224\) | −26.9047 | −1.79764 | ||||||||
\(225\) | −19.5522 | −1.30348 | ||||||||
\(226\) | −2.59082 | −0.172339 | ||||||||
\(227\) | −5.48628 | −0.364137 | −0.182069 | − | 0.983286i | \(-0.558279\pi\) | ||||
−0.182069 | + | 0.983286i | \(0.558279\pi\) | |||||||
\(228\) | 1.98963 | 0.131766 | ||||||||
\(229\) | 15.0026 | 0.991398 | 0.495699 | − | 0.868494i | \(-0.334912\pi\) | ||||
0.495699 | + | 0.868494i | \(0.334912\pi\) | |||||||
\(230\) | −64.5314 | −4.25507 | ||||||||
\(231\) | −6.20945 | −0.408552 | ||||||||
\(232\) | 0.627909 | 0.0412243 | ||||||||
\(233\) | −28.5124 | −1.86791 | −0.933955 | − | 0.357392i | \(-0.883666\pi\) | ||||
−0.933955 | + | 0.357392i | \(0.883666\pi\) | |||||||
\(234\) | −30.4237 | −1.98886 | ||||||||
\(235\) | −22.1182 | −1.44283 | ||||||||
\(236\) | −6.52248 | −0.424577 | ||||||||
\(237\) | 6.12635 | 0.397949 | ||||||||
\(238\) | −8.48165 | −0.549784 | ||||||||
\(239\) | 20.4845 | 1.32503 | 0.662516 | − | 0.749048i | \(-0.269489\pi\) | ||||
0.662516 | + | 0.749048i | \(0.269489\pi\) | |||||||
\(240\) | −6.47582 | −0.418012 | ||||||||
\(241\) | −17.7303 | −1.14211 | −0.571054 | − | 0.820912i | \(-0.693465\pi\) | ||||
−0.571054 | + | 0.820912i | \(0.693465\pi\) | |||||||
\(242\) | 11.6445 | 0.748540 | ||||||||
\(243\) | −15.4922 | −0.993823 | ||||||||
\(244\) | 9.96792 | 0.638131 | ||||||||
\(245\) | −18.0983 | −1.15626 | ||||||||
\(246\) | 0.131221 | 0.00836633 | ||||||||
\(247\) | 5.83434 | 0.371230 | ||||||||
\(248\) | −7.12424 | −0.452390 | ||||||||
\(249\) | −3.57141 | −0.226329 | ||||||||
\(250\) | 23.8025 | 1.50540 | ||||||||
\(251\) | 16.7542 | 1.05752 | 0.528758 | − | 0.848773i | \(-0.322658\pi\) | ||||
0.528758 | + | 0.848773i | \(0.322658\pi\) | |||||||
\(252\) | 22.0491 | 1.38896 | ||||||||
\(253\) | 19.6224 | 1.23365 | ||||||||
\(254\) | −26.6213 | −1.67037 | ||||||||
\(255\) | −3.11954 | −0.195353 | ||||||||
\(256\) | 1.98378 | 0.123986 | ||||||||
\(257\) | −13.2088 | −0.823940 | −0.411970 | − | 0.911197i | \(-0.635159\pi\) | ||||
−0.411970 | + | 0.911197i | \(0.635159\pi\) | |||||||
\(258\) | 5.33847 | 0.332359 | ||||||||
\(259\) | 29.9715 | 1.86234 | ||||||||
\(260\) | 55.3293 | 3.43138 | ||||||||
\(261\) | 1.13499 | 0.0702543 | ||||||||
\(262\) | −9.83579 | −0.607657 | ||||||||
\(263\) | 24.0246 | 1.48142 | 0.740709 | − | 0.671826i | \(-0.234490\pi\) | ||||
0.740709 | + | 0.671826i | \(0.234490\pi\) | |||||||
\(264\) | −2.40407 | −0.147960 | ||||||||
\(265\) | −20.2471 | −1.24377 | ||||||||
\(266\) | −7.45128 | −0.456867 | ||||||||
\(267\) | 6.08213 | 0.372220 | ||||||||
\(268\) | −20.4204 | −1.24738 | ||||||||
\(269\) | 21.4987 | 1.31080 | 0.655398 | − | 0.755283i | \(-0.272501\pi\) | ||||
0.655398 | + | 0.755283i | \(0.272501\pi\) | |||||||
\(270\) | 31.9703 | 1.94565 | ||||||||
\(271\) | −3.54406 | −0.215286 | −0.107643 | − | 0.994190i | \(-0.534330\pi\) | ||||
−0.107643 | + | 0.994190i | \(0.534330\pi\) | |||||||
\(272\) | 2.68970 | 0.163087 | ||||||||
\(273\) | −15.3300 | −0.927815 | ||||||||
\(274\) | −27.3742 | −1.65374 | ||||||||
\(275\) | −19.0538 | −1.14899 | ||||||||
\(276\) | 16.5205 | 0.994416 | ||||||||
\(277\) | −10.1076 | −0.607306 | −0.303653 | − | 0.952783i | \(-0.598206\pi\) | ||||
−0.303653 | + | 0.952783i | \(0.598206\pi\) | |||||||
\(278\) | 44.1953 | 2.65066 | ||||||||
\(279\) | −12.8776 | −0.770961 | ||||||||
\(280\) | −16.8021 | −1.00412 | ||||||||
\(281\) | −16.4244 | −0.979799 | −0.489900 | − | 0.871779i | \(-0.662967\pi\) | ||||
−0.489900 | + | 0.871779i | \(0.662967\pi\) | |||||||
\(282\) | 9.97844 | 0.594208 | ||||||||
\(283\) | −12.1933 | −0.724815 | −0.362408 | − | 0.932020i | \(-0.618045\pi\) | ||||
−0.362408 | + | 0.932020i | \(0.618045\pi\) | |||||||
\(284\) | 23.4625 | 1.39224 | ||||||||
\(285\) | −2.74057 | −0.162337 | ||||||||
\(286\) | −29.6482 | −1.75313 | ||||||||
\(287\) | −0.278869 | −0.0164611 | ||||||||
\(288\) | −18.8286 | −1.10948 | ||||||||
\(289\) | −15.7043 | −0.923783 | ||||||||
\(290\) | −3.63745 | −0.213599 | ||||||||
\(291\) | −3.62992 | −0.212790 | ||||||||
\(292\) | −8.14774 | −0.476810 | ||||||||
\(293\) | −0.684535 | −0.0399910 | −0.0199955 | − | 0.999800i | \(-0.506365\pi\) | ||||
−0.0199955 | + | 0.999800i | \(0.506365\pi\) | |||||||
\(294\) | 8.16490 | 0.476187 | ||||||||
\(295\) | 8.98424 | 0.523083 | ||||||||
\(296\) | 11.6038 | 0.674459 | ||||||||
\(297\) | −9.72139 | −0.564092 | ||||||||
\(298\) | −26.2814 | −1.52244 | ||||||||
\(299\) | 48.4442 | 2.80160 | ||||||||
\(300\) | −16.0418 | −0.926171 | ||||||||
\(301\) | −11.3453 | −0.653930 | ||||||||
\(302\) | −10.2080 | −0.587403 | ||||||||
\(303\) | −4.49217 | −0.258069 | ||||||||
\(304\) | 2.36294 | 0.135524 | ||||||||
\(305\) | −13.7301 | −0.786183 | ||||||||
\(306\) | −5.93567 | −0.339320 | ||||||||
\(307\) | 24.1375 | 1.37760 | 0.688800 | − | 0.724952i | \(-0.258138\pi\) | ||||
0.688800 | + | 0.724952i | \(0.258138\pi\) | |||||||
\(308\) | 21.4870 | 1.22434 | ||||||||
\(309\) | 7.28346 | 0.414342 | ||||||||
\(310\) | 41.2704 | 2.34400 | ||||||||
\(311\) | −23.0170 | −1.30517 | −0.652587 | − | 0.757714i | \(-0.726316\pi\) | ||||
−0.652587 | + | 0.757714i | \(0.726316\pi\) | |||||||
\(312\) | −5.93521 | −0.336015 | ||||||||
\(313\) | 7.33966 | 0.414862 | 0.207431 | − | 0.978250i | \(-0.433490\pi\) | ||||
0.207431 | + | 0.978250i | \(0.433490\pi\) | |||||||
\(314\) | −23.1712 | −1.30763 | ||||||||
\(315\) | −30.3710 | −1.71121 | ||||||||
\(316\) | −21.1994 | −1.19256 | ||||||||
\(317\) | −1.00000 | −0.0561656 | ||||||||
\(318\) | 9.13431 | 0.512227 | ||||||||
\(319\) | 1.10606 | 0.0619275 | ||||||||
\(320\) | 43.2618 | 2.41841 | ||||||||
\(321\) | 6.64563 | 0.370923 | ||||||||
\(322\) | −61.8701 | −3.44789 | ||||||||
\(323\) | 1.13828 | 0.0633357 | ||||||||
\(324\) | 10.9045 | 0.605803 | ||||||||
\(325\) | −47.0404 | −2.60933 | ||||||||
\(326\) | 43.4273 | 2.40522 | ||||||||
\(327\) | −3.60874 | −0.199564 | ||||||||
\(328\) | −0.107968 | −0.00596152 | ||||||||
\(329\) | −21.2061 | −1.16913 | ||||||||
\(330\) | 13.9267 | 0.766638 | ||||||||
\(331\) | −1.89396 | −0.104102 | −0.0520508 | − | 0.998644i | \(-0.516576\pi\) | ||||
−0.0520508 | + | 0.998644i | \(0.516576\pi\) | |||||||
\(332\) | 12.3584 | 0.678256 | ||||||||
\(333\) | 20.9748 | 1.14941 | ||||||||
\(334\) | 23.1438 | 1.26637 | ||||||||
\(335\) | 28.1276 | 1.53678 | ||||||||
\(336\) | −6.20876 | −0.338716 | ||||||||
\(337\) | 7.38817 | 0.402459 | 0.201230 | − | 0.979544i | \(-0.435506\pi\) | ||||
0.201230 | + | 0.979544i | \(0.435506\pi\) | |||||||
\(338\) | −45.2417 | −2.46083 | ||||||||
\(339\) | −0.913602 | −0.0496201 | ||||||||
\(340\) | 10.7948 | 0.585428 | ||||||||
\(341\) | −12.5493 | −0.679584 | ||||||||
\(342\) | −5.21459 | −0.281973 | ||||||||
\(343\) | 6.90434 | 0.372799 | ||||||||
\(344\) | −4.39246 | −0.236826 | ||||||||
\(345\) | −22.7558 | −1.22513 | ||||||||
\(346\) | 23.5795 | 1.26764 | ||||||||
\(347\) | −20.0658 | −1.07719 | −0.538593 | − | 0.842566i | \(-0.681044\pi\) | ||||
−0.538593 | + | 0.842566i | \(0.681044\pi\) | |||||||
\(348\) | 0.931213 | 0.0499182 | ||||||||
\(349\) | 19.8296 | 1.06145 | 0.530727 | − | 0.847543i | \(-0.321919\pi\) | ||||
0.530727 | + | 0.847543i | \(0.321919\pi\) | |||||||
\(350\) | 60.0773 | 3.21127 | ||||||||
\(351\) | −24.0004 | −1.28104 | ||||||||
\(352\) | −18.3486 | −0.977985 | ||||||||
\(353\) | 25.3562 | 1.34957 | 0.674787 | − | 0.738012i | \(-0.264235\pi\) | ||||
0.674787 | + | 0.738012i | \(0.264235\pi\) | |||||||
\(354\) | −4.05316 | −0.215423 | ||||||||
\(355\) | −32.3179 | −1.71526 | ||||||||
\(356\) | −21.0464 | −1.11546 | ||||||||
\(357\) | −2.99089 | −0.158295 | ||||||||
\(358\) | −13.4017 | −0.708302 | ||||||||
\(359\) | 25.8296 | 1.36324 | 0.681618 | − | 0.731708i | \(-0.261277\pi\) | ||||
0.681618 | + | 0.731708i | \(0.261277\pi\) | |||||||
\(360\) | −11.7585 | −0.619728 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | −16.6280 | −0.873948 | ||||||||
\(363\) | 4.10623 | 0.215521 | ||||||||
\(364\) | 53.0476 | 2.78045 | ||||||||
\(365\) | 11.2229 | 0.587434 | ||||||||
\(366\) | 6.19421 | 0.323777 | ||||||||
\(367\) | −15.3089 | −0.799119 | −0.399559 | − | 0.916707i | \(-0.630837\pi\) | ||||
−0.399559 | + | 0.916707i | \(0.630837\pi\) | |||||||
\(368\) | 19.6202 | 1.02277 | ||||||||
\(369\) | −0.195160 | −0.0101596 | ||||||||
\(370\) | −67.2205 | −3.49463 | ||||||||
\(371\) | −19.4121 | −1.00783 | ||||||||
\(372\) | −10.5655 | −0.547797 | ||||||||
\(373\) | 25.1146 | 1.30039 | 0.650193 | − | 0.759769i | \(-0.274688\pi\) | ||||
0.650193 | + | 0.759769i | \(0.274688\pi\) | |||||||
\(374\) | −5.78437 | −0.299102 | ||||||||
\(375\) | 8.39350 | 0.433438 | ||||||||
\(376\) | −8.21020 | −0.423409 | ||||||||
\(377\) | 2.73066 | 0.140636 | ||||||||
\(378\) | 30.6519 | 1.57656 | ||||||||
\(379\) | 21.9503 | 1.12751 | 0.563754 | − | 0.825942i | \(-0.309356\pi\) | ||||
0.563754 | + | 0.825942i | \(0.309356\pi\) | |||||||
\(380\) | 9.48339 | 0.486488 | ||||||||
\(381\) | −9.38750 | −0.480936 | ||||||||
\(382\) | 0.492123 | 0.0251792 | ||||||||
\(383\) | 9.37501 | 0.479041 | 0.239520 | − | 0.970891i | \(-0.423010\pi\) | ||||
0.239520 | + | 0.970891i | \(0.423010\pi\) | |||||||
\(384\) | −7.74234 | −0.395099 | ||||||||
\(385\) | −29.5968 | −1.50839 | ||||||||
\(386\) | 34.9103 | 1.77689 | ||||||||
\(387\) | −7.93970 | −0.403598 | ||||||||
\(388\) | 12.5609 | 0.637682 | ||||||||
\(389\) | −4.17034 | −0.211445 | −0.105722 | − | 0.994396i | \(-0.533715\pi\) | ||||
−0.105722 | + | 0.994396i | \(0.533715\pi\) | |||||||
\(390\) | 34.3824 | 1.74102 | ||||||||
\(391\) | 9.45148 | 0.477982 | ||||||||
\(392\) | −6.71803 | −0.339312 | ||||||||
\(393\) | −3.46840 | −0.174958 | ||||||||
\(394\) | −42.2010 | −2.12606 | ||||||||
\(395\) | 29.2007 | 1.46925 | ||||||||
\(396\) | 15.0372 | 0.755645 | ||||||||
\(397\) | −10.6613 | −0.535077 | −0.267539 | − | 0.963547i | \(-0.586210\pi\) | ||||
−0.267539 | + | 0.963547i | \(0.586210\pi\) | |||||||
\(398\) | 14.4958 | 0.726609 | ||||||||
\(399\) | −2.62755 | −0.131542 | ||||||||
\(400\) | −19.0517 | −0.952584 | ||||||||
\(401\) | −3.02541 | −0.151082 | −0.0755408 | − | 0.997143i | \(-0.524068\pi\) | ||||
−0.0755408 | + | 0.997143i | \(0.524068\pi\) | |||||||
\(402\) | −12.6895 | −0.632897 | ||||||||
\(403\) | −30.9820 | −1.54333 | ||||||||
\(404\) | 15.5446 | 0.773372 | ||||||||
\(405\) | −15.0201 | −0.746354 | ||||||||
\(406\) | −3.48745 | −0.173079 | ||||||||
\(407\) | 20.4401 | 1.01318 | ||||||||
\(408\) | −1.15796 | −0.0573277 | ||||||||
\(409\) | −23.5038 | −1.16219 | −0.581094 | − | 0.813836i | \(-0.697375\pi\) | ||||
−0.581094 | + | 0.813836i | \(0.697375\pi\) | |||||||
\(410\) | 0.625452 | 0.0308889 | ||||||||
\(411\) | −9.65299 | −0.476147 | ||||||||
\(412\) | −25.2035 | −1.24169 | ||||||||
\(413\) | 8.61374 | 0.423854 | ||||||||
\(414\) | −43.2983 | −2.12799 | ||||||||
\(415\) | −17.0228 | −0.835617 | ||||||||
\(416\) | −45.2994 | −2.22099 | ||||||||
\(417\) | 15.5846 | 0.763182 | ||||||||
\(418\) | −5.08167 | −0.248552 | ||||||||
\(419\) | 24.2611 | 1.18523 | 0.592617 | − | 0.805485i | \(-0.298095\pi\) | ||||
0.592617 | + | 0.805485i | \(0.298095\pi\) | |||||||
\(420\) | −24.9181 | −1.21588 | ||||||||
\(421\) | 18.6543 | 0.909156 | 0.454578 | − | 0.890707i | \(-0.349790\pi\) | ||||
0.454578 | + | 0.890707i | \(0.349790\pi\) | |||||||
\(422\) | −59.3495 | −2.88909 | ||||||||
\(423\) | −14.8405 | −0.721572 | ||||||||
\(424\) | −7.51566 | −0.364993 | ||||||||
\(425\) | −9.17760 | −0.445179 | ||||||||
\(426\) | 14.5800 | 0.706401 | ||||||||
\(427\) | −13.1639 | −0.637044 | ||||||||
\(428\) | −22.9963 | −1.11157 | ||||||||
\(429\) | −10.4549 | −0.504765 | ||||||||
\(430\) | 25.4454 | 1.22708 | ||||||||
\(431\) | −8.20581 | −0.395260 | −0.197630 | − | 0.980277i | \(-0.563324\pi\) | ||||
−0.197630 | + | 0.980277i | \(0.563324\pi\) | |||||||
\(432\) | −9.72031 | −0.467668 | ||||||||
\(433\) | −0.0290442 | −0.00139578 | −0.000697888 | − | 1.00000i | \(-0.500222\pi\) | ||||
−0.000697888 | 1.00000i | \(0.500222\pi\) | ||||||||
\(434\) | 39.5685 | 1.89935 | ||||||||
\(435\) | −1.28268 | −0.0614997 | ||||||||
\(436\) | 12.4876 | 0.598046 | ||||||||
\(437\) | 8.30329 | 0.397200 | ||||||||
\(438\) | −5.06312 | −0.241925 | ||||||||
\(439\) | 4.22968 | 0.201872 | 0.100936 | − | 0.994893i | \(-0.467816\pi\) | ||||
0.100936 | + | 0.994893i | \(0.467816\pi\) | |||||||
\(440\) | −11.4588 | −0.546276 | ||||||||
\(441\) | −12.1433 | −0.578254 | ||||||||
\(442\) | −14.2806 | −0.679257 | ||||||||
\(443\) | 10.2463 | 0.486817 | 0.243409 | − | 0.969924i | \(-0.421734\pi\) | ||||
0.243409 | + | 0.969924i | \(0.421734\pi\) | |||||||
\(444\) | 17.2089 | 0.816699 | ||||||||
\(445\) | 28.9899 | 1.37425 | ||||||||
\(446\) | 46.6092 | 2.20701 | ||||||||
\(447\) | −9.26764 | −0.438344 | ||||||||
\(448\) | 41.4778 | 1.95964 | ||||||||
\(449\) | −14.4468 | −0.681787 | −0.340893 | − | 0.940102i | \(-0.610730\pi\) | ||||
−0.340893 | + | 0.940102i | \(0.610730\pi\) | |||||||
\(450\) | 42.0436 | 1.98195 | ||||||||
\(451\) | −0.190185 | −0.00895545 | ||||||||
\(452\) | 3.16140 | 0.148700 | ||||||||
\(453\) | −3.59965 | −0.169126 | ||||||||
\(454\) | 11.7973 | 0.553675 | ||||||||
\(455\) | −73.0692 | −3.42554 | ||||||||
\(456\) | −1.01729 | −0.0476390 | ||||||||
\(457\) | 13.3265 | 0.623386 | 0.311693 | − | 0.950183i | \(-0.399104\pi\) | ||||
0.311693 | + | 0.950183i | \(0.399104\pi\) | |||||||
\(458\) | −32.2604 | −1.50743 | ||||||||
\(459\) | −4.68248 | −0.218559 | ||||||||
\(460\) | 78.7434 | 3.67143 | ||||||||
\(461\) | −9.56243 | −0.445367 | −0.222683 | − | 0.974891i | \(-0.571482\pi\) | ||||
−0.222683 | + | 0.974891i | \(0.571482\pi\) | |||||||
\(462\) | 13.3523 | 0.621207 | ||||||||
\(463\) | 1.93850 | 0.0900898 | 0.0450449 | − | 0.998985i | \(-0.485657\pi\) | ||||
0.0450449 | + | 0.998985i | \(0.485657\pi\) | |||||||
\(464\) | 1.10594 | 0.0513418 | ||||||||
\(465\) | 14.5532 | 0.674890 | ||||||||
\(466\) | 61.3109 | 2.84017 | ||||||||
\(467\) | −9.09582 | −0.420904 | −0.210452 | − | 0.977604i | \(-0.567494\pi\) | ||||
−0.210452 | + | 0.977604i | \(0.567494\pi\) | |||||||
\(468\) | 37.1240 | 1.71606 | ||||||||
\(469\) | 26.9677 | 1.24525 | ||||||||
\(470\) | 47.5614 | 2.19384 | ||||||||
\(471\) | −8.17087 | −0.376494 | ||||||||
\(472\) | 3.33492 | 0.153502 | ||||||||
\(473\) | −7.73731 | −0.355762 | ||||||||
\(474\) | −13.1736 | −0.605086 | ||||||||
\(475\) | −8.06268 | −0.369941 | ||||||||
\(476\) | 10.3496 | 0.474373 | ||||||||
\(477\) | −13.5851 | −0.622019 | ||||||||
\(478\) | −44.0483 | −2.01472 | ||||||||
\(479\) | 12.3698 | 0.565191 | 0.282595 | − | 0.959239i | \(-0.408805\pi\) | ||||
0.282595 | + | 0.959239i | \(0.408805\pi\) | |||||||
\(480\) | 21.2786 | 0.971229 | ||||||||
\(481\) | 50.4630 | 2.30091 | ||||||||
\(482\) | 38.1259 | 1.73659 | ||||||||
\(483\) | −21.8173 | −0.992723 | ||||||||
\(484\) | −14.2091 | −0.645867 | ||||||||
\(485\) | −17.3017 | −0.785630 | ||||||||
\(486\) | 33.3132 | 1.51112 | ||||||||
\(487\) | 27.7348 | 1.25678 | 0.628391 | − | 0.777898i | \(-0.283714\pi\) | ||||
0.628391 | + | 0.777898i | \(0.283714\pi\) | |||||||
\(488\) | −5.09656 | −0.230710 | ||||||||
\(489\) | 15.3138 | 0.692515 | ||||||||
\(490\) | 38.9173 | 1.75810 | ||||||||
\(491\) | 1.58105 | 0.0713520 | 0.0356760 | − | 0.999363i | \(-0.488642\pi\) | ||||
0.0356760 | + | 0.999363i | \(0.488642\pi\) | |||||||
\(492\) | −0.160120 | −0.00721877 | ||||||||
\(493\) | 0.532754 | 0.0239940 | ||||||||
\(494\) | −12.5457 | −0.564459 | ||||||||
\(495\) | −20.7126 | −0.930961 | ||||||||
\(496\) | −12.5479 | −0.563419 | ||||||||
\(497\) | −30.9852 | −1.38987 | ||||||||
\(498\) | 7.67970 | 0.344136 | ||||||||
\(499\) | −43.2795 | −1.93746 | −0.968728 | − | 0.248125i | \(-0.920186\pi\) | ||||
−0.968728 | + | 0.248125i | \(0.920186\pi\) | |||||||
\(500\) | −29.0446 | −1.29892 | ||||||||
\(501\) | 8.16122 | 0.364616 | ||||||||
\(502\) | −36.0270 | −1.60796 | ||||||||
\(503\) | −26.8724 | −1.19818 | −0.599090 | − | 0.800682i | \(-0.704471\pi\) | ||||
−0.599090 | + | 0.800682i | \(0.704471\pi\) | |||||||
\(504\) | −11.2736 | −0.502166 | ||||||||
\(505\) | −21.4115 | −0.952801 | ||||||||
\(506\) | −42.1946 | −1.87578 | ||||||||
\(507\) | −15.9536 | −0.708526 | ||||||||
\(508\) | 32.4842 | 1.44125 | ||||||||
\(509\) | −3.59201 | −0.159213 | −0.0796066 | − | 0.996826i | \(-0.525366\pi\) | ||||
−0.0796066 | + | 0.996826i | \(0.525366\pi\) | |||||||
\(510\) | 6.70802 | 0.297036 | ||||||||
\(511\) | 10.7601 | 0.475999 | ||||||||
\(512\) | −24.6868 | −1.09101 | ||||||||
\(513\) | −4.11364 | −0.181622 | ||||||||
\(514\) | 28.4031 | 1.25281 | ||||||||
\(515\) | 34.7160 | 1.52977 | ||||||||
\(516\) | −6.51419 | −0.286771 | ||||||||
\(517\) | −14.4622 | −0.636049 | ||||||||
\(518\) | −64.4484 | −2.83170 | ||||||||
\(519\) | 8.31485 | 0.364982 | ||||||||
\(520\) | −28.2897 | −1.24058 | ||||||||
\(521\) | 8.48645 | 0.371798 | 0.185899 | − | 0.982569i | \(-0.440480\pi\) | ||||
0.185899 | + | 0.982569i | \(0.440480\pi\) | |||||||
\(522\) | −2.44060 | −0.106822 | ||||||||
\(523\) | −38.5797 | −1.68697 | −0.843486 | − | 0.537151i | \(-0.819501\pi\) | ||||
−0.843486 | + | 0.537151i | \(0.819501\pi\) | |||||||
\(524\) | 12.0020 | 0.524308 | ||||||||
\(525\) | 21.1851 | 0.924594 | ||||||||
\(526\) | −51.6606 | −2.25251 | ||||||||
\(527\) | −6.04461 | −0.263307 | ||||||||
\(528\) | −4.23429 | −0.184274 | ||||||||
\(529\) | 45.9447 | 1.99759 | ||||||||
\(530\) | 43.5379 | 1.89116 | ||||||||
\(531\) | 6.02811 | 0.261598 | ||||||||
\(532\) | 9.09231 | 0.394201 | ||||||||
\(533\) | −0.469532 | −0.0203377 | ||||||||
\(534\) | −13.0786 | −0.565964 | ||||||||
\(535\) | 31.6758 | 1.36946 | ||||||||
\(536\) | 10.4409 | 0.450977 | ||||||||
\(537\) | −4.72586 | −0.203936 | ||||||||
\(538\) | −46.2291 | −1.99308 | ||||||||
\(539\) | −11.8338 | −0.509718 | ||||||||
\(540\) | −39.0113 | −1.67878 | ||||||||
\(541\) | 10.3721 | 0.445933 | 0.222966 | − | 0.974826i | \(-0.428426\pi\) | ||||
0.222966 | + | 0.974826i | \(0.428426\pi\) | |||||||
\(542\) | 7.62088 | 0.327345 | ||||||||
\(543\) | −5.86355 | −0.251629 | ||||||||
\(544\) | −8.83794 | −0.378923 | ||||||||
\(545\) | −17.2007 | −0.736798 | ||||||||
\(546\) | 32.9645 | 1.41075 | ||||||||
\(547\) | −14.0713 | −0.601647 | −0.300824 | − | 0.953680i | \(-0.597262\pi\) | ||||
−0.300824 | + | 0.953680i | \(0.597262\pi\) | |||||||
\(548\) | 33.4029 | 1.42690 | ||||||||
\(549\) | −9.21241 | −0.393176 | ||||||||
\(550\) | 40.9719 | 1.74705 | ||||||||
\(551\) | 0.468033 | 0.0199389 | ||||||||
\(552\) | −8.44686 | −0.359522 | ||||||||
\(553\) | 27.9965 | 1.19053 | ||||||||
\(554\) | 21.7346 | 0.923415 | ||||||||
\(555\) | −23.7040 | −1.00618 | ||||||||
\(556\) | −53.9286 | −2.28708 | ||||||||
\(557\) | −37.5748 | −1.59209 | −0.796047 | − | 0.605235i | \(-0.793079\pi\) | ||||
−0.796047 | + | 0.605235i | \(0.793079\pi\) | |||||||
\(558\) | 27.6910 | 1.17225 | ||||||||
\(559\) | −19.1020 | −0.807930 | ||||||||
\(560\) | −29.5935 | −1.25055 | ||||||||
\(561\) | −2.03975 | −0.0861182 | ||||||||
\(562\) | 35.3179 | 1.48979 | ||||||||
\(563\) | 21.8906 | 0.922578 | 0.461289 | − | 0.887250i | \(-0.347387\pi\) | ||||
0.461289 | + | 0.887250i | \(0.347387\pi\) | |||||||
\(564\) | −12.1760 | −0.512704 | ||||||||
\(565\) | −4.35460 | −0.183200 | ||||||||
\(566\) | 26.2195 | 1.10209 | ||||||||
\(567\) | −14.4007 | −0.604772 | ||||||||
\(568\) | −11.9963 | −0.503354 | ||||||||
\(569\) | 15.9919 | 0.670416 | 0.335208 | − | 0.942144i | \(-0.391193\pi\) | ||||
0.335208 | + | 0.942144i | \(0.391193\pi\) | |||||||
\(570\) | 5.89312 | 0.246836 | ||||||||
\(571\) | −8.06717 | −0.337601 | −0.168800 | − | 0.985650i | \(-0.553989\pi\) | ||||
−0.168800 | + | 0.985650i | \(0.553989\pi\) | |||||||
\(572\) | 36.1777 | 1.51267 | ||||||||
\(573\) | 0.173538 | 0.00724965 | ||||||||
\(574\) | 0.599659 | 0.0250293 | ||||||||
\(575\) | −66.9468 | −2.79188 | ||||||||
\(576\) | 29.0272 | 1.20947 | ||||||||
\(577\) | 6.69031 | 0.278521 | 0.139261 | − | 0.990256i | \(-0.455527\pi\) | ||||
0.139261 | + | 0.990256i | \(0.455527\pi\) | |||||||
\(578\) | 33.7694 | 1.40462 | ||||||||
\(579\) | 12.3104 | 0.511604 | ||||||||
\(580\) | 4.43854 | 0.184300 | ||||||||
\(581\) | −16.3208 | −0.677102 | ||||||||
\(582\) | 7.80551 | 0.323549 | ||||||||
\(583\) | −13.2388 | −0.548295 | ||||||||
\(584\) | 4.16591 | 0.172386 | ||||||||
\(585\) | −51.1357 | −2.11420 | ||||||||
\(586\) | 1.47197 | 0.0608066 | ||||||||
\(587\) | 35.8224 | 1.47855 | 0.739275 | − | 0.673404i | \(-0.235168\pi\) | ||||
0.739275 | + | 0.673404i | \(0.235168\pi\) | |||||||
\(588\) | −9.96309 | −0.410871 | ||||||||
\(589\) | −5.31029 | −0.218807 | ||||||||
\(590\) | −19.3190 | −0.795352 | ||||||||
\(591\) | −14.8814 | −0.612139 | ||||||||
\(592\) | 20.4378 | 0.839990 | ||||||||
\(593\) | 3.06515 | 0.125871 | 0.0629354 | − | 0.998018i | \(-0.479954\pi\) | ||||
0.0629354 | + | 0.998018i | \(0.479954\pi\) | |||||||
\(594\) | 20.9042 | 0.857708 | ||||||||
\(595\) | −14.2558 | −0.584432 | ||||||||
\(596\) | 32.0695 | 1.31362 | ||||||||
\(597\) | 5.11167 | 0.209207 | ||||||||
\(598\) | −104.171 | −4.25986 | ||||||||
\(599\) | 28.4937 | 1.16422 | 0.582111 | − | 0.813109i | \(-0.302227\pi\) | ||||
0.582111 | + | 0.813109i | \(0.302227\pi\) | |||||||
\(600\) | 8.20209 | 0.334849 | ||||||||
\(601\) | −40.3516 | −1.64597 | −0.822987 | − | 0.568060i | \(-0.807694\pi\) | ||||
−0.822987 | + | 0.568060i | \(0.807694\pi\) | |||||||
\(602\) | 24.3960 | 0.994307 | ||||||||
\(603\) | 18.8727 | 0.768554 | ||||||||
\(604\) | 12.4561 | 0.506832 | ||||||||
\(605\) | 19.5720 | 0.795714 | ||||||||
\(606\) | 9.65963 | 0.392396 | ||||||||
\(607\) | 15.3266 | 0.622086 | 0.311043 | − | 0.950396i | \(-0.399322\pi\) | ||||
0.311043 | + | 0.950396i | \(0.399322\pi\) | |||||||
\(608\) | −7.76428 | −0.314883 | ||||||||
\(609\) | −1.22978 | −0.0498333 | ||||||||
\(610\) | 29.5242 | 1.19540 | ||||||||
\(611\) | −35.7047 | −1.44446 | ||||||||
\(612\) | 7.24291 | 0.292777 | ||||||||
\(613\) | −34.7133 | −1.40206 | −0.701028 | − | 0.713133i | \(-0.747275\pi\) | ||||
−0.701028 | + | 0.713133i | \(0.747275\pi\) | |||||||
\(614\) | −51.9035 | −2.09465 | ||||||||
\(615\) | 0.220554 | 0.00889359 | ||||||||
\(616\) | −10.9862 | −0.442648 | ||||||||
\(617\) | 9.27524 | 0.373407 | 0.186704 | − | 0.982416i | \(-0.440220\pi\) | ||||
0.186704 | + | 0.982416i | \(0.440220\pi\) | |||||||
\(618\) | −15.6618 | −0.630010 | ||||||||
\(619\) | −20.5227 | −0.824875 | −0.412438 | − | 0.910986i | \(-0.635322\pi\) | ||||
−0.412438 | + | 0.910986i | \(0.635322\pi\) | |||||||
\(620\) | −50.3596 | −2.02249 | ||||||||
\(621\) | −34.1568 | −1.37066 | ||||||||
\(622\) | 49.4940 | 1.98453 | ||||||||
\(623\) | 27.7944 | 1.11356 | ||||||||
\(624\) | −10.4537 | −0.418483 | ||||||||
\(625\) | −0.306549 | −0.0122620 | ||||||||
\(626\) | −15.7827 | −0.630802 | ||||||||
\(627\) | −1.79195 | −0.0715637 | ||||||||
\(628\) | 28.2743 | 1.12827 | ||||||||
\(629\) | 9.84534 | 0.392559 | ||||||||
\(630\) | 65.3075 | 2.60191 | ||||||||
\(631\) | −35.1992 | −1.40126 | −0.700629 | − | 0.713526i | \(-0.747097\pi\) | ||||
−0.700629 | + | 0.713526i | \(0.747097\pi\) | |||||||
\(632\) | 10.8392 | 0.431160 | ||||||||
\(633\) | −20.9285 | −0.831832 | ||||||||
\(634\) | 2.15033 | 0.0854003 | ||||||||
\(635\) | −44.7447 | −1.77564 | ||||||||
\(636\) | −11.1460 | −0.441968 | ||||||||
\(637\) | −29.2155 | −1.15756 | ||||||||
\(638\) | −2.37839 | −0.0941614 | ||||||||
\(639\) | −21.6842 | −0.857814 | ||||||||
\(640\) | −36.9032 | −1.45873 | ||||||||
\(641\) | −21.7477 | −0.858982 | −0.429491 | − | 0.903071i | \(-0.641307\pi\) | ||||
−0.429491 | + | 0.903071i | \(0.641307\pi\) | |||||||
\(642\) | −14.2903 | −0.563992 | ||||||||
\(643\) | 24.6227 | 0.971025 | 0.485512 | − | 0.874230i | \(-0.338633\pi\) | ||||
0.485512 | + | 0.874230i | \(0.338633\pi\) | |||||||
\(644\) | 75.4961 | 2.97496 | ||||||||
\(645\) | 8.97282 | 0.353304 | ||||||||
\(646\) | −2.44768 | −0.0963025 | ||||||||
\(647\) | −23.1956 | −0.911915 | −0.455957 | − | 0.890002i | \(-0.650703\pi\) | ||||
−0.455957 | + | 0.890002i | \(0.650703\pi\) | |||||||
\(648\) | −5.57541 | −0.219023 | ||||||||
\(649\) | 5.87445 | 0.230592 | ||||||||
\(650\) | 101.152 | 3.96752 | ||||||||
\(651\) | 13.9531 | 0.546864 | ||||||||
\(652\) | −52.9915 | −2.07531 | ||||||||
\(653\) | 3.65615 | 0.143076 | 0.0715380 | − | 0.997438i | \(-0.477209\pi\) | ||||
0.0715380 | + | 0.997438i | \(0.477209\pi\) | |||||||
\(654\) | 7.75996 | 0.303438 | ||||||||
\(655\) | −16.5318 | −0.645952 | ||||||||
\(656\) | −0.190164 | −0.00742464 | ||||||||
\(657\) | 7.53019 | 0.293781 | ||||||||
\(658\) | 45.6000 | 1.77767 | ||||||||
\(659\) | 25.1423 | 0.979403 | 0.489702 | − | 0.871890i | \(-0.337106\pi\) | ||||
0.489702 | + | 0.871890i | \(0.337106\pi\) | |||||||
\(660\) | −16.9938 | −0.661483 | ||||||||
\(661\) | −48.5827 | −1.88965 | −0.944824 | − | 0.327580i | \(-0.893767\pi\) | ||||
−0.944824 | + | 0.327580i | \(0.893767\pi\) | |||||||
\(662\) | 4.07264 | 0.158287 | ||||||||
\(663\) | −5.03577 | −0.195573 | ||||||||
\(664\) | −6.31881 | −0.245217 | ||||||||
\(665\) | −12.5240 | −0.485660 | ||||||||
\(666\) | −45.1026 | −1.74769 | ||||||||
\(667\) | 3.88622 | 0.150475 | ||||||||
\(668\) | −28.2408 | −1.09267 | ||||||||
\(669\) | 16.4359 | 0.635447 | ||||||||
\(670\) | −60.4836 | −2.33669 | ||||||||
\(671\) | −8.97758 | −0.346576 | ||||||||
\(672\) | 20.4011 | 0.786988 | ||||||||
\(673\) | −51.6039 | −1.98918 | −0.994592 | − | 0.103863i | \(-0.966880\pi\) | ||||
−0.994592 | + | 0.103863i | \(0.966880\pi\) | |||||||
\(674\) | −15.8870 | −0.611944 | ||||||||
\(675\) | 33.1670 | 1.27660 | ||||||||
\(676\) | 55.2055 | 2.12329 | ||||||||
\(677\) | 47.2366 | 1.81545 | 0.907725 | − | 0.419565i | \(-0.137818\pi\) | ||||
0.907725 | + | 0.419565i | \(0.137818\pi\) | |||||||
\(678\) | 1.96454 | 0.0754478 | ||||||||
\(679\) | −16.5882 | −0.636596 | ||||||||
\(680\) | −5.51932 | −0.211656 | ||||||||
\(681\) | 4.16009 | 0.159415 | ||||||||
\(682\) | 26.9852 | 1.03331 | ||||||||
\(683\) | −11.5833 | −0.443223 | −0.221611 | − | 0.975135i | \(-0.571132\pi\) | ||||
−0.221611 | + | 0.975135i | \(0.571132\pi\) | |||||||
\(684\) | 6.36302 | 0.243296 | ||||||||
\(685\) | −46.0101 | −1.75796 | ||||||||
\(686\) | −14.8466 | −0.566845 | ||||||||
\(687\) | −11.3760 | −0.434022 | ||||||||
\(688\) | −7.73645 | −0.294949 | ||||||||
\(689\) | −32.6842 | −1.24517 | ||||||||
\(690\) | 48.9323 | 1.86282 | ||||||||
\(691\) | 11.4576 | 0.435867 | 0.217933 | − | 0.975964i | \(-0.430068\pi\) | ||||
0.217933 | + | 0.975964i | \(0.430068\pi\) | |||||||
\(692\) | −28.7725 | −1.09377 | ||||||||
\(693\) | −19.8584 | −0.754359 | ||||||||
\(694\) | 43.1479 | 1.63787 | ||||||||
\(695\) | 74.2827 | 2.81770 | ||||||||
\(696\) | −0.476126 | −0.0180475 | ||||||||
\(697\) | −0.0916059 | −0.00346982 | ||||||||
\(698\) | −42.6401 | −1.61395 | ||||||||
\(699\) | 21.6201 | 0.817749 | ||||||||
\(700\) | −73.3084 | −2.77080 | ||||||||
\(701\) | 1.52904 | 0.0577512 | 0.0288756 | − | 0.999583i | \(-0.490807\pi\) | ||||
0.0288756 | + | 0.999583i | \(0.490807\pi\) | |||||||
\(702\) | 51.6086 | 1.94784 | ||||||||
\(703\) | 8.64931 | 0.326215 | ||||||||
\(704\) | 28.2872 | 1.06612 | ||||||||
\(705\) | 16.7716 | 0.631655 | ||||||||
\(706\) | −54.5241 | −2.05204 | ||||||||
\(707\) | −20.5285 | −0.772056 | ||||||||
\(708\) | 4.94581 | 0.185875 | ||||||||
\(709\) | −2.00829 | −0.0754230 | −0.0377115 | − | 0.999289i | \(-0.512007\pi\) | ||||
−0.0377115 | + | 0.999289i | \(0.512007\pi\) | |||||||
\(710\) | 69.4941 | 2.60807 | ||||||||
\(711\) | 19.5927 | 0.734782 | ||||||||
\(712\) | 10.7610 | 0.403284 | ||||||||
\(713\) | −44.0929 | −1.65129 | ||||||||
\(714\) | 6.43139 | 0.240689 | ||||||||
\(715\) | −49.8321 | −1.86362 | ||||||||
\(716\) | 16.3532 | 0.611148 | ||||||||
\(717\) | −15.5328 | −0.580083 | ||||||||
\(718\) | −55.5421 | −2.07281 | ||||||||
\(719\) | 6.73336 | 0.251112 | 0.125556 | − | 0.992087i | \(-0.459929\pi\) | ||||
0.125556 | + | 0.992087i | \(0.459929\pi\) | |||||||
\(720\) | −20.7103 | −0.771826 | ||||||||
\(721\) | 33.2843 | 1.23957 | ||||||||
\(722\) | −2.15033 | −0.0800268 | ||||||||
\(723\) | 13.4444 | 0.500002 | ||||||||
\(724\) | 20.2901 | 0.754074 | ||||||||
\(725\) | −3.77361 | −0.140148 | ||||||||
\(726\) | −8.82973 | −0.327702 | ||||||||
\(727\) | −48.5715 | −1.80142 | −0.900708 | − | 0.434426i | \(-0.856951\pi\) | ||||
−0.900708 | + | 0.434426i | \(0.856951\pi\) | |||||||
\(728\) | −27.1230 | −1.00525 | ||||||||
\(729\) | −0.720190 | −0.0266737 | ||||||||
\(730\) | −24.1329 | −0.893200 | ||||||||
\(731\) | −3.72681 | −0.137841 | ||||||||
\(732\) | −7.55839 | −0.279366 | ||||||||
\(733\) | 46.6878 | 1.72445 | 0.862226 | − | 0.506523i | \(-0.169070\pi\) | ||||
0.862226 | + | 0.506523i | \(0.169070\pi\) | |||||||
\(734\) | 32.9191 | 1.21507 | ||||||||
\(735\) | 13.7234 | 0.506197 | ||||||||
\(736\) | −64.4691 | −2.37636 | ||||||||
\(737\) | 18.3916 | 0.677463 | ||||||||
\(738\) | 0.419657 | 0.0154478 | ||||||||
\(739\) | 21.3621 | 0.785818 | 0.392909 | − | 0.919577i | \(-0.371469\pi\) | ||||
0.392909 | + | 0.919577i | \(0.371469\pi\) | |||||||
\(740\) | 82.0248 | 3.01529 | ||||||||
\(741\) | −4.42401 | −0.162520 | ||||||||
\(742\) | 41.7424 | 1.53241 | ||||||||
\(743\) | −25.4167 | −0.932447 | −0.466223 | − | 0.884667i | \(-0.654386\pi\) | ||||
−0.466223 | + | 0.884667i | \(0.654386\pi\) | |||||||
\(744\) | 5.40211 | 0.198051 | ||||||||
\(745\) | −44.1734 | −1.61839 | ||||||||
\(746\) | −54.0046 | −1.97725 | ||||||||
\(747\) | −11.4217 | −0.417899 | ||||||||
\(748\) | 7.05828 | 0.258076 | ||||||||
\(749\) | 30.3695 | 1.10968 | ||||||||
\(750\) | −18.0488 | −0.659047 | ||||||||
\(751\) | −34.0142 | −1.24120 | −0.620599 | − | 0.784128i | \(-0.713110\pi\) | ||||
−0.620599 | + | 0.784128i | \(0.713110\pi\) | |||||||
\(752\) | −14.4606 | −0.527325 | ||||||||
\(753\) | −12.7042 | −0.462968 | ||||||||
\(754\) | −5.87182 | −0.213839 | ||||||||
\(755\) | −17.1574 | −0.624422 | ||||||||
\(756\) | −37.4025 | −1.36032 | ||||||||
\(757\) | −32.3114 | −1.17438 | −0.587188 | − | 0.809450i | \(-0.699765\pi\) | ||||
−0.587188 | + | 0.809450i | \(0.699765\pi\) | |||||||
\(758\) | −47.2002 | −1.71439 | ||||||||
\(759\) | −14.8791 | −0.540077 | ||||||||
\(760\) | −4.84882 | −0.175885 | ||||||||
\(761\) | −21.5197 | −0.780088 | −0.390044 | − | 0.920796i | \(-0.627540\pi\) | ||||
−0.390044 | + | 0.920796i | \(0.627540\pi\) | |||||||
\(762\) | 20.1862 | 0.731268 | ||||||||
\(763\) | −16.4914 | −0.597028 | ||||||||
\(764\) | −0.600506 | −0.0217255 | ||||||||
\(765\) | −9.97658 | −0.360704 | ||||||||
\(766\) | −20.1593 | −0.728386 | ||||||||
\(767\) | 14.5030 | 0.523671 | ||||||||
\(768\) | −1.50424 | −0.0542796 | ||||||||
\(769\) | −10.9627 | −0.395325 | −0.197663 | − | 0.980270i | \(-0.563335\pi\) | ||||
−0.197663 | + | 0.980270i | \(0.563335\pi\) | |||||||
\(770\) | 63.6428 | 2.29353 | ||||||||
\(771\) | 10.0158 | 0.360711 | ||||||||
\(772\) | −42.5987 | −1.53316 | ||||||||
\(773\) | 35.2590 | 1.26818 | 0.634090 | − | 0.773259i | \(-0.281375\pi\) | ||||
0.634090 | + | 0.773259i | \(0.281375\pi\) | |||||||
\(774\) | 17.0729 | 0.613674 | ||||||||
\(775\) | 42.8152 | 1.53797 | ||||||||
\(776\) | −6.42233 | −0.230548 | ||||||||
\(777\) | −22.7265 | −0.815309 | ||||||||
\(778\) | 8.96760 | 0.321504 | ||||||||
\(779\) | −0.0804774 | −0.00288340 | ||||||||
\(780\) | −41.9546 | −1.50222 | ||||||||
\(781\) | −21.1314 | −0.756143 | ||||||||
\(782\) | −20.3238 | −0.726776 | ||||||||
\(783\) | −1.92532 | −0.0688054 | ||||||||
\(784\) | −11.8325 | −0.422588 | ||||||||
\(785\) | −38.9457 | −1.39003 | ||||||||
\(786\) | 7.45820 | 0.266025 | ||||||||
\(787\) | −46.7499 | −1.66646 | −0.833228 | − | 0.552930i | \(-0.813510\pi\) | ||||
−0.833228 | + | 0.552930i | \(0.813510\pi\) | |||||||
\(788\) | 51.4951 | 1.83444 | ||||||||
\(789\) | −18.2171 | −0.648547 | ||||||||
\(790\) | −62.7910 | −2.23400 | ||||||||
\(791\) | −4.17502 | −0.148447 | ||||||||
\(792\) | −7.68844 | −0.273197 | ||||||||
\(793\) | −22.1640 | −0.787068 | ||||||||
\(794\) | 22.9253 | 0.813590 | ||||||||
\(795\) | 15.3528 | 0.544508 | ||||||||
\(796\) | −17.6883 | −0.626944 | ||||||||
\(797\) | 38.6354 | 1.36854 | 0.684269 | − | 0.729230i | \(-0.260122\pi\) | ||||
0.684269 | + | 0.729230i | \(0.260122\pi\) | |||||||
\(798\) | 5.65009 | 0.200011 | ||||||||
\(799\) | −6.96600 | −0.246439 | ||||||||
\(800\) | 62.6010 | 2.21328 | ||||||||
\(801\) | 19.4512 | 0.687275 | ||||||||
\(802\) | 6.50561 | 0.229721 | ||||||||
\(803\) | 7.33823 | 0.258961 | ||||||||
\(804\) | 15.4842 | 0.546086 | ||||||||
\(805\) | −103.990 | −3.66518 | ||||||||
\(806\) | 66.6215 | 2.34664 | ||||||||
\(807\) | −16.3018 | −0.573851 | ||||||||
\(808\) | −7.94789 | −0.279606 | ||||||||
\(809\) | 12.4315 | 0.437070 | 0.218535 | − | 0.975829i | \(-0.429872\pi\) | ||||
0.218535 | + | 0.975829i | \(0.429872\pi\) | |||||||
\(810\) | 32.2981 | 1.13484 | ||||||||
\(811\) | −19.9461 | −0.700403 | −0.350201 | − | 0.936674i | \(-0.613887\pi\) | ||||
−0.350201 | + | 0.936674i | \(0.613887\pi\) | |||||||
\(812\) | 4.25550 | 0.149339 | ||||||||
\(813\) | 2.68736 | 0.0942498 | ||||||||
\(814\) | −43.9529 | −1.54055 | ||||||||
\(815\) | 72.9920 | 2.55680 | ||||||||
\(816\) | −2.03952 | −0.0713974 | ||||||||
\(817\) | −3.27407 | −0.114545 | ||||||||
\(818\) | 50.5408 | 1.76712 | ||||||||
\(819\) | −49.0269 | −1.71314 | ||||||||
\(820\) | −0.763198 | −0.0266520 | ||||||||
\(821\) | 31.0579 | 1.08393 | 0.541964 | − | 0.840402i | \(-0.317681\pi\) | ||||
0.541964 | + | 0.840402i | \(0.317681\pi\) | |||||||
\(822\) | 20.7571 | 0.723986 | ||||||||
\(823\) | 22.2263 | 0.774761 | 0.387381 | − | 0.921920i | \(-0.373380\pi\) | ||||
0.387381 | + | 0.921920i | \(0.373380\pi\) | |||||||
\(824\) | 12.8864 | 0.448921 | ||||||||
\(825\) | 14.4480 | 0.503013 | ||||||||
\(826\) | −18.5223 | −0.644475 | ||||||||
\(827\) | −12.4274 | −0.432145 | −0.216072 | − | 0.976377i | \(-0.569325\pi\) | ||||
−0.216072 | + | 0.976377i | \(0.569325\pi\) | |||||||
\(828\) | 52.8341 | 1.83611 | ||||||||
\(829\) | −43.7789 | −1.52050 | −0.760252 | − | 0.649629i | \(-0.774924\pi\) | ||||
−0.760252 | + | 0.649629i | \(0.774924\pi\) | |||||||
\(830\) | 36.6046 | 1.27056 | ||||||||
\(831\) | 7.66429 | 0.265871 | ||||||||
\(832\) | 69.8361 | 2.42113 | ||||||||
\(833\) | −5.69996 | −0.197492 | ||||||||
\(834\) | −33.5120 | −1.16043 | ||||||||
\(835\) | 38.8997 | 1.34618 | ||||||||
\(836\) | 6.20082 | 0.214460 | ||||||||
\(837\) | 21.8446 | 0.755061 | ||||||||
\(838\) | −52.1693 | −1.80216 | ||||||||
\(839\) | 1.26369 | 0.0436276 | 0.0218138 | − | 0.999762i | \(-0.493056\pi\) | ||||
0.0218138 | + | 0.999762i | \(0.493056\pi\) | |||||||
\(840\) | 12.7405 | 0.439590 | ||||||||
\(841\) | −28.7809 | −0.992446 | ||||||||
\(842\) | −40.1129 | −1.38238 | ||||||||
\(843\) | 12.4542 | 0.428945 | ||||||||
\(844\) | 72.4203 | 2.49281 | ||||||||
\(845\) | −76.0416 | −2.61591 | ||||||||
\(846\) | 31.9120 | 1.09716 | ||||||||
\(847\) | 18.7648 | 0.644767 | ||||||||
\(848\) | −13.2373 | −0.454572 | ||||||||
\(849\) | 9.24582 | 0.317316 | ||||||||
\(850\) | 19.7348 | 0.676899 | ||||||||
\(851\) | 71.8177 | 2.46188 | ||||||||
\(852\) | −17.7910 | −0.609508 | ||||||||
\(853\) | 15.6806 | 0.536894 | 0.268447 | − | 0.963295i | \(-0.413490\pi\) | ||||
0.268447 | + | 0.963295i | \(0.413490\pi\) | |||||||
\(854\) | 28.3066 | 0.968632 | ||||||||
\(855\) | −8.76460 | −0.299743 | ||||||||
\(856\) | 11.7579 | 0.401878 | ||||||||
\(857\) | 56.2918 | 1.92289 | 0.961446 | − | 0.274994i | \(-0.0886760\pi\) | ||||
0.961446 | + | 0.274994i | \(0.0886760\pi\) | |||||||
\(858\) | 22.4813 | 0.767501 | ||||||||
\(859\) | −15.3109 | −0.522402 | −0.261201 | − | 0.965284i | \(-0.584119\pi\) | ||||
−0.261201 | + | 0.965284i | \(0.584119\pi\) | |||||||
\(860\) | −31.0493 | −1.05877 | ||||||||
\(861\) | 0.211458 | 0.00720648 | ||||||||
\(862\) | 17.6452 | 0.600997 | ||||||||
\(863\) | 33.5179 | 1.14096 | 0.570482 | − | 0.821310i | \(-0.306757\pi\) | ||||
0.570482 | + | 0.821310i | \(0.306757\pi\) | |||||||
\(864\) | 31.9395 | 1.08660 | ||||||||
\(865\) | 39.6320 | 1.34753 | ||||||||
\(866\) | 0.0624545 | 0.00212229 | ||||||||
\(867\) | 11.9081 | 0.404421 | ||||||||
\(868\) | −48.2828 | −1.63883 | ||||||||
\(869\) | 19.0932 | 0.647693 | ||||||||
\(870\) | 2.75818 | 0.0935109 | ||||||||
\(871\) | 45.4055 | 1.53851 | ||||||||
\(872\) | −6.38485 | −0.216218 | ||||||||
\(873\) | −11.6088 | −0.392900 | ||||||||
\(874\) | −17.8548 | −0.603947 | ||||||||
\(875\) | 38.3570 | 1.29670 | ||||||||
\(876\) | 6.17820 | 0.208742 | ||||||||
\(877\) | 21.9876 | 0.742469 | 0.371234 | − | 0.928539i | \(-0.378935\pi\) | ||||
0.371234 | + | 0.928539i | \(0.378935\pi\) | |||||||
\(878\) | −9.09520 | −0.306948 | ||||||||
\(879\) | 0.519063 | 0.0175076 | ||||||||
\(880\) | −20.1824 | −0.680347 | ||||||||
\(881\) | 9.04553 | 0.304752 | 0.152376 | − | 0.988323i | \(-0.451308\pi\) | ||||
0.152376 | + | 0.988323i | \(0.451308\pi\) | |||||||
\(882\) | 26.1121 | 0.879242 | ||||||||
\(883\) | −20.7042 | −0.696752 | −0.348376 | − | 0.937355i | \(-0.613267\pi\) | ||||
−0.348376 | + | 0.937355i | \(0.613267\pi\) | |||||||
\(884\) | 17.4256 | 0.586087 | ||||||||
\(885\) | −6.81249 | −0.228999 | ||||||||
\(886\) | −22.0329 | −0.740210 | ||||||||
\(887\) | −3.71329 | −0.124680 | −0.0623400 | − | 0.998055i | \(-0.519856\pi\) | ||||
−0.0623400 | + | 0.998055i | \(0.519856\pi\) | |||||||
\(888\) | −8.79885 | −0.295270 | ||||||||
\(889\) | −42.8994 | −1.43880 | ||||||||
\(890\) | −62.3378 | −2.08957 | ||||||||
\(891\) | −9.82106 | −0.329018 | ||||||||
\(892\) | −56.8742 | −1.90429 | ||||||||
\(893\) | −6.11975 | −0.204790 | ||||||||
\(894\) | 19.9285 | 0.666507 | ||||||||
\(895\) | −22.5254 | −0.752940 | ||||||||
\(896\) | −35.3813 | −1.18201 | ||||||||
\(897\) | −36.7338 | −1.22651 | ||||||||
\(898\) | 31.0653 | 1.03666 | ||||||||
\(899\) | −2.48539 | −0.0828926 | ||||||||
\(900\) | −51.3031 | −1.71010 | ||||||||
\(901\) | −6.37670 | −0.212439 | ||||||||
\(902\) | 0.408959 | 0.0136169 | ||||||||
\(903\) | 8.60279 | 0.286283 | ||||||||
\(904\) | −1.61641 | −0.0537611 | ||||||||
\(905\) | −27.9481 | −0.929026 | ||||||||
\(906\) | 7.74041 | 0.257158 | ||||||||
\(907\) | 1.21719 | 0.0404162 | 0.0202081 | − | 0.999796i | \(-0.493567\pi\) | ||||
0.0202081 | + | 0.999796i | \(0.493567\pi\) | |||||||
\(908\) | −14.3955 | −0.477730 | ||||||||
\(909\) | −14.3664 | −0.476503 | ||||||||
\(910\) | 157.123 | 5.20856 | ||||||||
\(911\) | 58.4949 | 1.93802 | 0.969012 | − | 0.247015i | \(-0.0794498\pi\) | ||||
0.969012 | + | 0.247015i | \(0.0794498\pi\) | |||||||
\(912\) | −1.79175 | −0.0593309 | ||||||||
\(913\) | −11.1306 | −0.368368 | ||||||||
\(914\) | −28.6562 | −0.947864 | ||||||||
\(915\) | 10.4111 | 0.344181 | ||||||||
\(916\) | 39.3653 | 1.30066 | ||||||||
\(917\) | −15.8501 | −0.523416 | ||||||||
\(918\) | 10.0689 | 0.332322 | ||||||||
\(919\) | 21.3438 | 0.704066 | 0.352033 | − | 0.935987i | \(-0.385490\pi\) | ||||
0.352033 | + | 0.935987i | \(0.385490\pi\) | |||||||
\(920\) | −40.2612 | −1.32737 | ||||||||
\(921\) | −18.3028 | −0.603097 | ||||||||
\(922\) | 20.5623 | 0.677185 | ||||||||
\(923\) | −52.1697 | −1.71719 | ||||||||
\(924\) | −16.2930 | −0.536000 | ||||||||
\(925\) | −69.7366 | −2.29293 | ||||||||
\(926\) | −4.16841 | −0.136982 | ||||||||
\(927\) | 23.2932 | 0.765049 | ||||||||
\(928\) | −3.63394 | −0.119290 | ||||||||
\(929\) | 2.60236 | 0.0853806 | 0.0426903 | − | 0.999088i | \(-0.486407\pi\) | ||||
0.0426903 | + | 0.999088i | \(0.486407\pi\) | |||||||
\(930\) | −31.2942 | −1.02618 | ||||||||
\(931\) | −5.00751 | −0.164115 | ||||||||
\(932\) | −74.8137 | −2.45060 | ||||||||
\(933\) | 17.4531 | 0.571389 | ||||||||
\(934\) | 19.5590 | 0.639989 | ||||||||
\(935\) | −9.72227 | −0.317952 | ||||||||
\(936\) | −18.9814 | −0.620426 | ||||||||
\(937\) | −24.3756 | −0.796317 | −0.398158 | − | 0.917317i | \(-0.630351\pi\) | ||||
−0.398158 | + | 0.917317i | \(0.630351\pi\) | |||||||
\(938\) | −57.9893 | −1.89342 | ||||||||
\(939\) | −5.56546 | −0.181622 | ||||||||
\(940\) | −58.0360 | −1.89293 | ||||||||
\(941\) | 26.8171 | 0.874212 | 0.437106 | − | 0.899410i | \(-0.356003\pi\) | ||||
0.437106 | + | 0.899410i | \(0.356003\pi\) | |||||||
\(942\) | 17.5700 | 0.572463 | ||||||||
\(943\) | −0.668227 | −0.0217605 | ||||||||
\(944\) | 5.87379 | 0.191176 | ||||||||
\(945\) | 51.5192 | 1.67592 | ||||||||
\(946\) | 16.6377 | 0.540940 | ||||||||
\(947\) | 6.66067 | 0.216443 | 0.108221 | − | 0.994127i | \(-0.465485\pi\) | ||||
0.108221 | + | 0.994127i | \(0.465485\pi\) | |||||||
\(948\) | 16.0749 | 0.522090 | ||||||||
\(949\) | 18.1168 | 0.588096 | ||||||||
\(950\) | 17.3374 | 0.562499 | ||||||||
\(951\) | 0.758271 | 0.0245886 | ||||||||
\(952\) | −5.29171 | −0.171505 | ||||||||
\(953\) | 3.23814 | 0.104894 | 0.0524468 | − | 0.998624i | \(-0.483298\pi\) | ||||
0.0524468 | + | 0.998624i | \(0.483298\pi\) | |||||||
\(954\) | 29.2124 | 0.945786 | ||||||||
\(955\) | 0.827153 | 0.0267660 | ||||||||
\(956\) | 53.7493 | 1.73838 | ||||||||
\(957\) | −0.838694 | −0.0271111 | ||||||||
\(958\) | −26.5991 | −0.859378 | ||||||||
\(959\) | −44.1127 | −1.42447 | ||||||||
\(960\) | −32.8042 | −1.05875 | ||||||||
\(961\) | −2.80077 | −0.0903476 | ||||||||
\(962\) | −108.512 | −3.49856 | ||||||||
\(963\) | 21.2533 | 0.684880 | ||||||||
\(964\) | −46.5225 | −1.49839 | ||||||||
\(965\) | 58.6766 | 1.88887 | ||||||||
\(966\) | 46.9144 | 1.50944 | ||||||||
\(967\) | 23.7419 | 0.763487 | 0.381743 | − | 0.924268i | \(-0.375324\pi\) | ||||
0.381743 | + | 0.924268i | \(0.375324\pi\) | |||||||
\(968\) | 7.26505 | 0.233507 | ||||||||
\(969\) | −0.863126 | −0.0277276 | ||||||||
\(970\) | 37.2043 | 1.19456 | ||||||||
\(971\) | −43.3690 | −1.39178 | −0.695890 | − | 0.718149i | \(-0.744990\pi\) | ||||
−0.695890 | + | 0.718149i | \(0.744990\pi\) | |||||||
\(972\) | −40.6499 | −1.30385 | ||||||||
\(973\) | 71.2193 | 2.28319 | ||||||||
\(974\) | −59.6388 | −1.91095 | ||||||||
\(975\) | 35.6694 | 1.14233 | ||||||||
\(976\) | −8.97658 | −0.287333 | ||||||||
\(977\) | 17.6134 | 0.563504 | 0.281752 | − | 0.959487i | \(-0.409084\pi\) | ||||
0.281752 | + | 0.959487i | \(0.409084\pi\) | |||||||
\(978\) | −32.9297 | −1.05298 | ||||||||
\(979\) | 18.9554 | 0.605817 | ||||||||
\(980\) | −47.4882 | −1.51696 | ||||||||
\(981\) | −11.5411 | −0.368479 | ||||||||
\(982\) | −3.39978 | −0.108491 | ||||||||
\(983\) | −7.98009 | −0.254525 | −0.127263 | − | 0.991869i | \(-0.540619\pi\) | ||||
−0.127263 | + | 0.991869i | \(0.540619\pi\) | |||||||
\(984\) | 0.0818688 | 0.00260988 | ||||||||
\(985\) | −70.9308 | −2.26004 | ||||||||
\(986\) | −1.14559 | −0.0364831 | ||||||||
\(987\) | 16.0800 | 0.511831 | ||||||||
\(988\) | 15.3087 | 0.487035 | ||||||||
\(989\) | −27.1856 | −0.864451 | ||||||||
\(990\) | 44.5388 | 1.41554 | ||||||||
\(991\) | 42.2817 | 1.34312 | 0.671561 | − | 0.740949i | \(-0.265624\pi\) | ||||
0.671561 | + | 0.740949i | \(0.265624\pi\) | |||||||
\(992\) | 41.2306 | 1.30907 | ||||||||
\(993\) | 1.43614 | 0.0455744 | ||||||||
\(994\) | 66.6282 | 2.11332 | ||||||||
\(995\) | 24.3643 | 0.772400 | ||||||||
\(996\) | −9.37103 | −0.296933 | ||||||||
\(997\) | 30.4877 | 0.965554 | 0.482777 | − | 0.875743i | \(-0.339628\pi\) | ||||
0.482777 | + | 0.875743i | \(0.339628\pi\) | |||||||
\(998\) | 93.0650 | 2.94592 | ||||||||
\(999\) | −35.5801 | −1.12571 |
(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 | 6023.2.a.b.1.16 | ✓ | 99 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6023.2.a.b.1.16 | ✓ | 99 | 1.1 | even | 1 | trivial |