Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5077,2,Mod(1,5077)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5077, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("5077.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5077 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5077.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: | \(40.5400491062\) |
Analytic rank: | \(1\) |
Dimension: | \(205\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Character | \(\chi\) | \(=\) | 5077.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.77001 | −1.95869 | −0.979345 | − | 0.202195i | \(-0.935192\pi\) | ||||
−0.979345 | + | 0.202195i | \(0.935192\pi\) | |||||||
\(3\) | −0.453815 | −0.262010 | −0.131005 | − | 0.991382i | \(-0.541820\pi\) | ||||
−0.131005 | + | 0.991382i | \(0.541820\pi\) | |||||||
\(4\) | 5.67294 | 2.83647 | ||||||||
\(5\) | −2.74837 | −1.22911 | −0.614554 | − | 0.788875i | \(-0.710664\pi\) | ||||
−0.614554 | + | 0.788875i | \(0.710664\pi\) | |||||||
\(6\) | 1.25707 | 0.513197 | ||||||||
\(7\) | −3.66610 | −1.38565 | −0.692827 | − | 0.721104i | \(-0.743635\pi\) | ||||
−0.692827 | + | 0.721104i | \(0.743635\pi\) | |||||||
\(8\) | −10.1741 | −3.59707 | ||||||||
\(9\) | −2.79405 | −0.931351 | ||||||||
\(10\) | 7.61300 | 2.40744 | ||||||||
\(11\) | −3.29970 | −0.994898 | −0.497449 | − | 0.867493i | \(-0.665730\pi\) | ||||
−0.497449 | + | 0.867493i | \(0.665730\pi\) | |||||||
\(12\) | −2.57446 | −0.743184 | ||||||||
\(13\) | −2.96983 | −0.823683 | −0.411841 | − | 0.911256i | \(-0.635114\pi\) | ||||
−0.411841 | + | 0.911256i | \(0.635114\pi\) | |||||||
\(14\) | 10.1551 | 2.71407 | ||||||||
\(15\) | 1.24725 | 0.322039 | ||||||||
\(16\) | 16.8363 | 4.20909 | ||||||||
\(17\) | 0.979742 | 0.237622 | 0.118811 | − | 0.992917i | \(-0.462092\pi\) | ||||
0.118811 | + | 0.992917i | \(0.462092\pi\) | |||||||
\(18\) | 7.73954 | 1.82423 | ||||||||
\(19\) | −2.27616 | −0.522188 | −0.261094 | − | 0.965313i | \(-0.584083\pi\) | ||||
−0.261094 | + | 0.965313i | \(0.584083\pi\) | |||||||
\(20\) | −15.5913 | −3.48632 | ||||||||
\(21\) | 1.66373 | 0.363055 | ||||||||
\(22\) | 9.14020 | 1.94870 | ||||||||
\(23\) | −2.05068 | −0.427596 | −0.213798 | − | 0.976878i | \(-0.568583\pi\) | ||||
−0.213798 | + | 0.976878i | \(0.568583\pi\) | |||||||
\(24\) | 4.61714 | 0.942470 | ||||||||
\(25\) | 2.55352 | 0.510705 | ||||||||
\(26\) | 8.22645 | 1.61334 | ||||||||
\(27\) | 2.62943 | 0.506033 | ||||||||
\(28\) | −20.7975 | −3.93036 | ||||||||
\(29\) | 0.750007 | 0.139273 | 0.0696364 | − | 0.997572i | \(-0.477816\pi\) | ||||
0.0696364 | + | 0.997572i | \(0.477816\pi\) | |||||||
\(30\) | −3.45489 | −0.630774 | ||||||||
\(31\) | 7.68000 | 1.37937 | 0.689684 | − | 0.724110i | \(-0.257749\pi\) | ||||
0.689684 | + | 0.724110i | \(0.257749\pi\) | |||||||
\(32\) | −26.2887 | −4.64722 | ||||||||
\(33\) | 1.49745 | 0.260673 | ||||||||
\(34\) | −2.71389 | −0.465429 | ||||||||
\(35\) | 10.0758 | 1.70312 | ||||||||
\(36\) | −15.8505 | −2.64175 | ||||||||
\(37\) | −6.11894 | −1.00595 | −0.502974 | − | 0.864302i | \(-0.667761\pi\) | ||||
−0.502974 | + | 0.864302i | \(0.667761\pi\) | |||||||
\(38\) | 6.30499 | 1.02280 | ||||||||
\(39\) | 1.34775 | 0.215813 | ||||||||
\(40\) | 27.9621 | 4.42119 | ||||||||
\(41\) | 4.59256 | 0.717238 | 0.358619 | − | 0.933484i | \(-0.383248\pi\) | ||||
0.358619 | + | 0.933484i | \(0.383248\pi\) | |||||||
\(42\) | −4.60854 | −0.711113 | ||||||||
\(43\) | 4.12047 | 0.628366 | 0.314183 | − | 0.949363i | \(-0.398270\pi\) | ||||
0.314183 | + | 0.949363i | \(0.398270\pi\) | |||||||
\(44\) | −18.7190 | −2.82200 | ||||||||
\(45\) | 7.67908 | 1.14473 | ||||||||
\(46\) | 5.68039 | 0.837527 | ||||||||
\(47\) | −1.26549 | −0.184590 | −0.0922952 | − | 0.995732i | \(-0.529420\pi\) | ||||
−0.0922952 | + | 0.995732i | \(0.529420\pi\) | |||||||
\(48\) | −7.64058 | −1.10282 | ||||||||
\(49\) | 6.44027 | 0.920038 | ||||||||
\(50\) | −7.07328 | −1.00031 | ||||||||
\(51\) | −0.444622 | −0.0622595 | ||||||||
\(52\) | −16.8477 | −2.33635 | ||||||||
\(53\) | −4.52493 | −0.621546 | −0.310773 | − | 0.950484i | \(-0.600588\pi\) | ||||
−0.310773 | + | 0.950484i | \(0.600588\pi\) | |||||||
\(54\) | −7.28353 | −0.991163 | ||||||||
\(55\) | 9.06880 | 1.22284 | ||||||||
\(56\) | 37.2991 | 4.98430 | ||||||||
\(57\) | 1.03296 | 0.136818 | ||||||||
\(58\) | −2.07752 | −0.272792 | ||||||||
\(59\) | 4.39496 | 0.572175 | 0.286087 | − | 0.958203i | \(-0.407645\pi\) | ||||
0.286087 | + | 0.958203i | \(0.407645\pi\) | |||||||
\(60\) | 7.07557 | 0.913452 | ||||||||
\(61\) | 10.4117 | 1.33309 | 0.666543 | − | 0.745467i | \(-0.267773\pi\) | ||||
0.666543 | + | 0.745467i | \(0.267773\pi\) | |||||||
\(62\) | −21.2736 | −2.70176 | ||||||||
\(63\) | 10.2433 | 1.29053 | ||||||||
\(64\) | 39.1471 | 4.89338 | ||||||||
\(65\) | 8.16219 | 1.01239 | ||||||||
\(66\) | −4.14796 | −0.510578 | ||||||||
\(67\) | 0.130613 | 0.0159569 | 0.00797845 | − | 0.999968i | \(-0.497460\pi\) | ||||
0.00797845 | + | 0.999968i | \(0.497460\pi\) | |||||||
\(68\) | 5.55801 | 0.674008 | ||||||||
\(69\) | 0.930627 | 0.112034 | ||||||||
\(70\) | −27.9100 | −3.33588 | ||||||||
\(71\) | −4.55199 | −0.540222 | −0.270111 | − | 0.962829i | \(-0.587060\pi\) | ||||
−0.270111 | + | 0.962829i | \(0.587060\pi\) | |||||||
\(72\) | 28.4269 | 3.35014 | ||||||||
\(73\) | 13.5446 | 1.58528 | 0.792638 | − | 0.609692i | \(-0.208707\pi\) | ||||
0.792638 | + | 0.609692i | \(0.208707\pi\) | |||||||
\(74\) | 16.9495 | 1.97034 | ||||||||
\(75\) | −1.15883 | −0.133810 | ||||||||
\(76\) | −12.9125 | −1.48117 | ||||||||
\(77\) | 12.0970 | 1.37858 | ||||||||
\(78\) | −3.73329 | −0.422711 | ||||||||
\(79\) | 15.0185 | 1.68972 | 0.844859 | − | 0.534989i | \(-0.179684\pi\) | ||||
0.844859 | + | 0.534989i | \(0.179684\pi\) | |||||||
\(80\) | −46.2725 | −5.17342 | ||||||||
\(81\) | 7.18888 | 0.798765 | ||||||||
\(82\) | −12.7214 | −1.40485 | ||||||||
\(83\) | 1.79303 | 0.196811 | 0.0984055 | − | 0.995146i | \(-0.468626\pi\) | ||||
0.0984055 | + | 0.995146i | \(0.468626\pi\) | |||||||
\(84\) | 9.43823 | 1.02980 | ||||||||
\(85\) | −2.69269 | −0.292063 | ||||||||
\(86\) | −11.4137 | −1.23077 | ||||||||
\(87\) | −0.340364 | −0.0364909 | ||||||||
\(88\) | 33.5714 | 3.57872 | ||||||||
\(89\) | −8.62803 | −0.914569 | −0.457285 | − | 0.889320i | \(-0.651178\pi\) | ||||
−0.457285 | + | 0.889320i | \(0.651178\pi\) | |||||||
\(90\) | −21.2711 | −2.24217 | ||||||||
\(91\) | 10.8877 | 1.14134 | ||||||||
\(92\) | −11.6334 | −1.21286 | ||||||||
\(93\) | −3.48530 | −0.361408 | ||||||||
\(94\) | 3.50541 | 0.361555 | ||||||||
\(95\) | 6.25573 | 0.641825 | ||||||||
\(96\) | 11.9302 | 1.21762 | ||||||||
\(97\) | −5.07395 | −0.515182 | −0.257591 | − | 0.966254i | \(-0.582929\pi\) | ||||
−0.257591 | + | 0.966254i | \(0.582929\pi\) | |||||||
\(98\) | −17.8396 | −1.80207 | ||||||||
\(99\) | 9.21954 | 0.926599 | ||||||||
\(100\) | 14.4860 | 1.44860 | ||||||||
\(101\) | −13.6434 | −1.35757 | −0.678784 | − | 0.734338i | \(-0.737493\pi\) | ||||
−0.678784 | + | 0.734338i | \(0.737493\pi\) | |||||||
\(102\) | 1.23160 | 0.121947 | ||||||||
\(103\) | 3.40598 | 0.335601 | 0.167801 | − | 0.985821i | \(-0.446334\pi\) | ||||
0.167801 | + | 0.985821i | \(0.446334\pi\) | |||||||
\(104\) | 30.2152 | 2.96285 | ||||||||
\(105\) | −4.57254 | −0.446234 | ||||||||
\(106\) | 12.5341 | 1.21742 | ||||||||
\(107\) | −10.2554 | −0.991431 | −0.495715 | − | 0.868485i | \(-0.665094\pi\) | ||||
−0.495715 | + | 0.868485i | \(0.665094\pi\) | |||||||
\(108\) | 14.9166 | 1.43535 | ||||||||
\(109\) | 3.18609 | 0.305172 | 0.152586 | − | 0.988290i | \(-0.451240\pi\) | ||||
0.152586 | + | 0.988290i | \(0.451240\pi\) | |||||||
\(110\) | −25.1206 | −2.39516 | ||||||||
\(111\) | 2.77687 | 0.263569 | ||||||||
\(112\) | −61.7237 | −5.83234 | ||||||||
\(113\) | 10.0315 | 0.943689 | 0.471844 | − | 0.881682i | \(-0.343588\pi\) | ||||
0.471844 | + | 0.881682i | \(0.343588\pi\) | |||||||
\(114\) | −2.86130 | −0.267985 | ||||||||
\(115\) | 5.63601 | 0.525561 | ||||||||
\(116\) | 4.25474 | 0.395043 | ||||||||
\(117\) | 8.29786 | 0.767138 | ||||||||
\(118\) | −12.1741 | −1.12071 | ||||||||
\(119\) | −3.59183 | −0.329262 | ||||||||
\(120\) | −12.6896 | −1.15840 | ||||||||
\(121\) | −0.111956 | −0.0101778 | ||||||||
\(122\) | −28.8406 | −2.61110 | ||||||||
\(123\) | −2.08417 | −0.187924 | ||||||||
\(124\) | 43.5681 | 3.91253 | ||||||||
\(125\) | 6.72381 | 0.601396 | ||||||||
\(126\) | −28.3739 | −2.52775 | ||||||||
\(127\) | 4.03807 | 0.358321 | 0.179161 | − | 0.983820i | \(-0.442662\pi\) | ||||
0.179161 | + | 0.983820i | \(0.442662\pi\) | |||||||
\(128\) | −55.8603 | −4.93740 | ||||||||
\(129\) | −1.86993 | −0.164638 | ||||||||
\(130\) | −22.6093 | −1.98297 | ||||||||
\(131\) | 14.6660 | 1.28138 | 0.640689 | − | 0.767800i | \(-0.278649\pi\) | ||||
0.640689 | + | 0.767800i | \(0.278649\pi\) | |||||||
\(132\) | 8.49497 | 0.739392 | ||||||||
\(133\) | 8.34463 | 0.723572 | ||||||||
\(134\) | −0.361799 | −0.0312546 | ||||||||
\(135\) | −7.22663 | −0.621969 | ||||||||
\(136\) | −9.96795 | −0.854745 | ||||||||
\(137\) | −15.6534 | −1.33736 | −0.668681 | − | 0.743549i | \(-0.733141\pi\) | ||||
−0.668681 | + | 0.743549i | \(0.733141\pi\) | |||||||
\(138\) | −2.57784 | −0.219441 | ||||||||
\(139\) | −23.0205 | −1.95257 | −0.976285 | − | 0.216490i | \(-0.930539\pi\) | ||||
−0.976285 | + | 0.216490i | \(0.930539\pi\) | |||||||
\(140\) | 57.1593 | 4.83084 | ||||||||
\(141\) | 0.574297 | 0.0483645 | ||||||||
\(142\) | 12.6091 | 1.05813 | ||||||||
\(143\) | 9.79956 | 0.819480 | ||||||||
\(144\) | −47.0416 | −3.92013 | ||||||||
\(145\) | −2.06129 | −0.171181 | ||||||||
\(146\) | −37.5187 | −3.10507 | ||||||||
\(147\) | −2.92269 | −0.241059 | ||||||||
\(148\) | −34.7124 | −2.85334 | ||||||||
\(149\) | −16.9382 | −1.38763 | −0.693815 | − | 0.720153i | \(-0.744072\pi\) | ||||
−0.693815 | + | 0.720153i | \(0.744072\pi\) | |||||||
\(150\) | 3.20996 | 0.262092 | ||||||||
\(151\) | 0.822424 | 0.0669279 | 0.0334640 | − | 0.999440i | \(-0.489346\pi\) | ||||
0.0334640 | + | 0.999440i | \(0.489346\pi\) | |||||||
\(152\) | 23.1578 | 1.87835 | ||||||||
\(153\) | −2.73745 | −0.221310 | ||||||||
\(154\) | −33.5089 | −2.70022 | ||||||||
\(155\) | −21.1075 | −1.69539 | ||||||||
\(156\) | 7.64572 | 0.612148 | ||||||||
\(157\) | 10.8646 | 0.867090 | 0.433545 | − | 0.901132i | \(-0.357263\pi\) | ||||
0.433545 | + | 0.901132i | \(0.357263\pi\) | |||||||
\(158\) | −41.6015 | −3.30964 | ||||||||
\(159\) | 2.05348 | 0.162851 | ||||||||
\(160\) | 72.2509 | 5.71193 | ||||||||
\(161\) | 7.51798 | 0.592500 | ||||||||
\(162\) | −19.9133 | −1.56453 | ||||||||
\(163\) | −10.8043 | −0.846257 | −0.423129 | − | 0.906070i | \(-0.639068\pi\) | ||||
−0.423129 | + | 0.906070i | \(0.639068\pi\) | |||||||
\(164\) | 26.0533 | 2.03442 | ||||||||
\(165\) | −4.11556 | −0.320396 | ||||||||
\(166\) | −4.96671 | −0.385492 | ||||||||
\(167\) | −12.3818 | −0.958129 | −0.479064 | − | 0.877780i | \(-0.659024\pi\) | ||||
−0.479064 | + | 0.877780i | \(0.659024\pi\) | |||||||
\(168\) | −16.9269 | −1.30594 | ||||||||
\(169\) | −4.18011 | −0.321547 | ||||||||
\(170\) | 7.45877 | 0.572062 | ||||||||
\(171\) | 6.35972 | 0.486340 | ||||||||
\(172\) | 23.3752 | 1.78234 | ||||||||
\(173\) | −10.7755 | −0.819244 | −0.409622 | − | 0.912255i | \(-0.634339\pi\) | ||||
−0.409622 | + | 0.912255i | \(0.634339\pi\) | |||||||
\(174\) | 0.942811 | 0.0714743 | ||||||||
\(175\) | −9.36147 | −0.707660 | ||||||||
\(176\) | −55.5549 | −4.18761 | ||||||||
\(177\) | −1.99450 | −0.149916 | ||||||||
\(178\) | 23.8997 | 1.79136 | ||||||||
\(179\) | 16.5051 | 1.23365 | 0.616824 | − | 0.787101i | \(-0.288419\pi\) | ||||
0.616824 | + | 0.787101i | \(0.288419\pi\) | |||||||
\(180\) | 43.5629 | 3.24699 | ||||||||
\(181\) | 5.77800 | 0.429475 | 0.214738 | − | 0.976672i | \(-0.431110\pi\) | ||||
0.214738 | + | 0.976672i | \(0.431110\pi\) | |||||||
\(182\) | −30.1590 | −2.23553 | ||||||||
\(183\) | −4.72500 | −0.349282 | ||||||||
\(184\) | 20.8637 | 1.53809 | ||||||||
\(185\) | 16.8171 | 1.23642 | ||||||||
\(186\) | 9.65430 | 0.707887 | ||||||||
\(187\) | −3.23286 | −0.236410 | ||||||||
\(188\) | −7.17903 | −0.523585 | ||||||||
\(189\) | −9.63973 | −0.701187 | ||||||||
\(190\) | −17.3284 | −1.25714 | ||||||||
\(191\) | 6.70763 | 0.485347 | 0.242674 | − | 0.970108i | \(-0.421976\pi\) | ||||
0.242674 | + | 0.970108i | \(0.421976\pi\) | |||||||
\(192\) | −17.7655 | −1.28212 | ||||||||
\(193\) | 4.68338 | 0.337117 | 0.168558 | − | 0.985692i | \(-0.446089\pi\) | ||||
0.168558 | + | 0.985692i | \(0.446089\pi\) | |||||||
\(194\) | 14.0549 | 1.00908 | ||||||||
\(195\) | −3.70412 | −0.265258 | ||||||||
\(196\) | 36.5352 | 2.60966 | ||||||||
\(197\) | 11.7303 | 0.835750 | 0.417875 | − | 0.908505i | \(-0.362775\pi\) | ||||
0.417875 | + | 0.908505i | \(0.362775\pi\) | |||||||
\(198\) | −25.5382 | −1.81492 | ||||||||
\(199\) | 15.8724 | 1.12516 | 0.562582 | − | 0.826742i | \(-0.309808\pi\) | ||||
0.562582 | + | 0.826742i | \(0.309808\pi\) | |||||||
\(200\) | −25.9797 | −1.83704 | ||||||||
\(201\) | −0.0592741 | −0.00418087 | ||||||||
\(202\) | 37.7923 | 2.65905 | ||||||||
\(203\) | −2.74960 | −0.192984 | ||||||||
\(204\) | −2.52231 | −0.176597 | ||||||||
\(205\) | −12.6221 | −0.881562 | ||||||||
\(206\) | −9.43459 | −0.657339 | ||||||||
\(207\) | 5.72970 | 0.398241 | ||||||||
\(208\) | −50.0011 | −3.46695 | ||||||||
\(209\) | 7.51066 | 0.519524 | ||||||||
\(210\) | 12.6660 | 0.874035 | ||||||||
\(211\) | −20.4531 | −1.40805 | −0.704026 | − | 0.710174i | \(-0.748616\pi\) | ||||
−0.704026 | + | 0.710174i | \(0.748616\pi\) | |||||||
\(212\) | −25.6696 | −1.76300 | ||||||||
\(213\) | 2.06576 | 0.141544 | ||||||||
\(214\) | 28.4076 | 1.94191 | ||||||||
\(215\) | −11.3246 | −0.772329 | ||||||||
\(216\) | −26.7519 | −1.82024 | ||||||||
\(217\) | −28.1556 | −1.91133 | ||||||||
\(218\) | −8.82549 | −0.597738 | ||||||||
\(219\) | −6.14674 | −0.415358 | ||||||||
\(220\) | 51.4467 | 3.46854 | ||||||||
\(221\) | −2.90967 | −0.195725 | ||||||||
\(222\) | −7.69194 | −0.516249 | ||||||||
\(223\) | −3.19195 | −0.213749 | −0.106874 | − | 0.994273i | \(-0.534084\pi\) | ||||
−0.106874 | + | 0.994273i | \(0.534084\pi\) | |||||||
\(224\) | 96.3768 | 6.43944 | ||||||||
\(225\) | −7.13468 | −0.475645 | ||||||||
\(226\) | −27.7875 | −1.84839 | ||||||||
\(227\) | −2.32334 | −0.154205 | −0.0771026 | − | 0.997023i | \(-0.524567\pi\) | ||||
−0.0771026 | + | 0.997023i | \(0.524567\pi\) | |||||||
\(228\) | 5.85990 | 0.388081 | ||||||||
\(229\) | 10.9869 | 0.726035 | 0.363017 | − | 0.931782i | \(-0.381747\pi\) | ||||
0.363017 | + | 0.931782i | \(0.381747\pi\) | |||||||
\(230\) | −15.6118 | −1.02941 | ||||||||
\(231\) | −5.48981 | −0.361203 | ||||||||
\(232\) | −7.63062 | −0.500974 | ||||||||
\(233\) | −1.46796 | −0.0961692 | −0.0480846 | − | 0.998843i | \(-0.515312\pi\) | ||||
−0.0480846 | + | 0.998843i | \(0.515312\pi\) | |||||||
\(234\) | −22.9851 | −1.50259 | ||||||||
\(235\) | 3.47803 | 0.226881 | ||||||||
\(236\) | 24.9323 | 1.62296 | ||||||||
\(237\) | −6.81564 | −0.442723 | ||||||||
\(238\) | 9.94939 | 0.644923 | ||||||||
\(239\) | −15.6932 | −1.01511 | −0.507554 | − | 0.861620i | \(-0.669450\pi\) | ||||
−0.507554 | + | 0.861620i | \(0.669450\pi\) | |||||||
\(240\) | 20.9991 | 1.35549 | ||||||||
\(241\) | 20.4302 | 1.31602 | 0.658011 | − | 0.753008i | \(-0.271398\pi\) | ||||
0.658011 | + | 0.753008i | \(0.271398\pi\) | |||||||
\(242\) | 0.310118 | 0.0199352 | ||||||||
\(243\) | −11.1507 | −0.715318 | ||||||||
\(244\) | 59.0651 | 3.78126 | ||||||||
\(245\) | −17.7002 | −1.13083 | ||||||||
\(246\) | 5.77317 | 0.368084 | ||||||||
\(247\) | 6.75982 | 0.430117 | ||||||||
\(248\) | −78.1368 | −4.96169 | ||||||||
\(249\) | −0.813705 | −0.0515665 | ||||||||
\(250\) | −18.6250 | −1.17795 | ||||||||
\(251\) | −15.3821 | −0.970907 | −0.485454 | − | 0.874262i | \(-0.661346\pi\) | ||||
−0.485454 | + | 0.874262i | \(0.661346\pi\) | |||||||
\(252\) | 58.1094 | 3.66055 | ||||||||
\(253\) | 6.76662 | 0.425414 | ||||||||
\(254\) | −11.1855 | −0.701840 | ||||||||
\(255\) | 1.22198 | 0.0765236 | ||||||||
\(256\) | 76.4394 | 4.77746 | ||||||||
\(257\) | −6.93175 | −0.432391 | −0.216195 | − | 0.976350i | \(-0.569365\pi\) | ||||
−0.216195 | + | 0.976350i | \(0.569365\pi\) | |||||||
\(258\) | 5.17972 | 0.322475 | ||||||||
\(259\) | 22.4326 | 1.39390 | ||||||||
\(260\) | 46.3036 | 2.87163 | ||||||||
\(261\) | −2.09556 | −0.129712 | ||||||||
\(262\) | −40.6250 | −2.50982 | ||||||||
\(263\) | 14.4344 | 0.890064 | 0.445032 | − | 0.895515i | \(-0.353192\pi\) | ||||
0.445032 | + | 0.895515i | \(0.353192\pi\) | |||||||
\(264\) | −15.2352 | −0.937661 | ||||||||
\(265\) | 12.4362 | 0.763947 | ||||||||
\(266\) | −23.1147 | −1.41725 | ||||||||
\(267\) | 3.91553 | 0.239626 | ||||||||
\(268\) | 0.740959 | 0.0452613 | ||||||||
\(269\) | 7.75215 | 0.472657 | 0.236329 | − | 0.971673i | \(-0.424056\pi\) | ||||
0.236329 | + | 0.971673i | \(0.424056\pi\) | |||||||
\(270\) | 20.0178 | 1.21825 | ||||||||
\(271\) | 1.51990 | 0.0923272 | 0.0461636 | − | 0.998934i | \(-0.485300\pi\) | ||||
0.0461636 | + | 0.998934i | \(0.485300\pi\) | |||||||
\(272\) | 16.4953 | 1.00017 | ||||||||
\(273\) | −4.94099 | −0.299043 | ||||||||
\(274\) | 43.3601 | 2.61948 | ||||||||
\(275\) | −8.42587 | −0.508099 | ||||||||
\(276\) | 5.27939 | 0.317782 | ||||||||
\(277\) | 27.0614 | 1.62596 | 0.812982 | − | 0.582288i | \(-0.197843\pi\) | ||||
0.812982 | + | 0.582288i | \(0.197843\pi\) | |||||||
\(278\) | 63.7668 | 3.82448 | ||||||||
\(279\) | −21.4583 | −1.28468 | ||||||||
\(280\) | −102.512 | −6.12624 | ||||||||
\(281\) | 26.0726 | 1.55536 | 0.777682 | − | 0.628658i | \(-0.216396\pi\) | ||||
0.777682 | + | 0.628658i | \(0.216396\pi\) | |||||||
\(282\) | −1.59081 | −0.0947312 | ||||||||
\(283\) | −21.5785 | −1.28271 | −0.641355 | − | 0.767244i | \(-0.721627\pi\) | ||||
−0.641355 | + | 0.767244i | \(0.721627\pi\) | |||||||
\(284\) | −25.8232 | −1.53232 | ||||||||
\(285\) | −2.83895 | −0.168165 | ||||||||
\(286\) | −27.1449 | −1.60511 | ||||||||
\(287\) | −16.8368 | −0.993844 | ||||||||
\(288\) | 73.4519 | 4.32819 | ||||||||
\(289\) | −16.0401 | −0.943536 | ||||||||
\(290\) | 5.70980 | 0.335291 | ||||||||
\(291\) | 2.30264 | 0.134983 | ||||||||
\(292\) | 76.8377 | 4.49659 | ||||||||
\(293\) | −11.1908 | −0.653771 | −0.326885 | − | 0.945064i | \(-0.605999\pi\) | ||||
−0.326885 | + | 0.945064i | \(0.605999\pi\) | |||||||
\(294\) | 8.09587 | 0.472160 | ||||||||
\(295\) | −12.0790 | −0.703264 | ||||||||
\(296\) | 62.2545 | 3.61847 | ||||||||
\(297\) | −8.67633 | −0.503452 | ||||||||
\(298\) | 46.9189 | 2.71794 | ||||||||
\(299\) | 6.09016 | 0.352203 | ||||||||
\(300\) | −6.57396 | −0.379547 | ||||||||
\(301\) | −15.1060 | −0.870698 | ||||||||
\(302\) | −2.27812 | −0.131091 | ||||||||
\(303\) | 6.19157 | 0.355696 | ||||||||
\(304\) | −38.3223 | −2.19793 | ||||||||
\(305\) | −28.6153 | −1.63851 | ||||||||
\(306\) | 7.58276 | 0.433477 | ||||||||
\(307\) | 30.7810 | 1.75677 | 0.878383 | − | 0.477957i | \(-0.158623\pi\) | ||||
0.878383 | + | 0.477957i | \(0.158623\pi\) | |||||||
\(308\) | 68.6257 | 3.91031 | ||||||||
\(309\) | −1.54568 | −0.0879309 | ||||||||
\(310\) | 58.4678 | 3.32075 | ||||||||
\(311\) | 9.33936 | 0.529587 | 0.264793 | − | 0.964305i | \(-0.414696\pi\) | ||||
0.264793 | + | 0.964305i | \(0.414696\pi\) | |||||||
\(312\) | −13.7121 | −0.776296 | ||||||||
\(313\) | 33.8024 | 1.91063 | 0.955313 | − | 0.295597i | \(-0.0955186\pi\) | ||||
0.955313 | + | 0.295597i | \(0.0955186\pi\) | |||||||
\(314\) | −30.0950 | −1.69836 | ||||||||
\(315\) | −28.1523 | −1.58620 | ||||||||
\(316\) | 85.1993 | 4.79283 | ||||||||
\(317\) | 13.0245 | 0.731530 | 0.365765 | − | 0.930707i | \(-0.380807\pi\) | ||||
0.365765 | + | 0.930707i | \(0.380807\pi\) | |||||||
\(318\) | −5.68815 | −0.318976 | ||||||||
\(319\) | −2.47480 | −0.138562 | ||||||||
\(320\) | −107.591 | −6.01449 | ||||||||
\(321\) | 4.65407 | 0.259765 | ||||||||
\(322\) | −20.8248 | −1.16052 | ||||||||
\(323\) | −2.23005 | −0.124083 | ||||||||
\(324\) | 40.7821 | 2.26567 | ||||||||
\(325\) | −7.58354 | −0.420659 | ||||||||
\(326\) | 29.9280 | 1.65756 | ||||||||
\(327\) | −1.44589 | −0.0799582 | ||||||||
\(328\) | −46.7250 | −2.57996 | ||||||||
\(329\) | 4.63940 | 0.255778 | ||||||||
\(330\) | 11.4001 | 0.627556 | ||||||||
\(331\) | 17.5961 | 0.967172 | 0.483586 | − | 0.875297i | \(-0.339334\pi\) | ||||
0.483586 | + | 0.875297i | \(0.339334\pi\) | |||||||
\(332\) | 10.1718 | 0.558248 | ||||||||
\(333\) | 17.0966 | 0.936890 | ||||||||
\(334\) | 34.2975 | 1.87668 | ||||||||
\(335\) | −0.358972 | −0.0196127 | ||||||||
\(336\) | 28.0111 | 1.52813 | ||||||||
\(337\) | −0.723998 | −0.0394387 | −0.0197193 | − | 0.999806i | \(-0.506277\pi\) | ||||
−0.0197193 | + | 0.999806i | \(0.506277\pi\) | |||||||
\(338\) | 11.5789 | 0.629810 | ||||||||
\(339\) | −4.55247 | −0.247256 | ||||||||
\(340\) | −15.2755 | −0.828429 | ||||||||
\(341\) | −25.3417 | −1.37233 | ||||||||
\(342\) | −17.6165 | −0.952589 | ||||||||
\(343\) | 2.05204 | 0.110800 | ||||||||
\(344\) | −41.9219 | −2.26028 | ||||||||
\(345\) | −2.55771 | −0.137702 | ||||||||
\(346\) | 29.8481 | 1.60465 | ||||||||
\(347\) | 4.95238 | 0.265858 | 0.132929 | − | 0.991126i | \(-0.457562\pi\) | ||||
0.132929 | + | 0.991126i | \(0.457562\pi\) | |||||||
\(348\) | −1.93087 | −0.103505 | ||||||||
\(349\) | 12.1255 | 0.649064 | 0.324532 | − | 0.945875i | \(-0.394793\pi\) | ||||
0.324532 | + | 0.945875i | \(0.394793\pi\) | |||||||
\(350\) | 25.9313 | 1.38609 | ||||||||
\(351\) | −7.80895 | −0.416811 | ||||||||
\(352\) | 86.7448 | 4.62351 | ||||||||
\(353\) | −22.4537 | −1.19509 | −0.597546 | − | 0.801835i | \(-0.703857\pi\) | ||||
−0.597546 | + | 0.801835i | \(0.703857\pi\) | |||||||
\(354\) | 5.52477 | 0.293638 | ||||||||
\(355\) | 12.5106 | 0.663991 | ||||||||
\(356\) | −48.9463 | −2.59415 | ||||||||
\(357\) | 1.63003 | 0.0862701 | ||||||||
\(358\) | −45.7192 | −2.41634 | ||||||||
\(359\) | 18.3685 | 0.969450 | 0.484725 | − | 0.874667i | \(-0.338920\pi\) | ||||
0.484725 | + | 0.874667i | \(0.338920\pi\) | |||||||
\(360\) | −78.1274 | −4.11768 | ||||||||
\(361\) | −13.8191 | −0.727320 | ||||||||
\(362\) | −16.0051 | −0.841209 | ||||||||
\(363\) | 0.0508072 | 0.00266669 | ||||||||
\(364\) | 61.7652 | 3.23737 | ||||||||
\(365\) | −37.2256 | −1.94847 | ||||||||
\(366\) | 13.0883 | 0.684136 | ||||||||
\(367\) | 24.7449 | 1.29167 | 0.645836 | − | 0.763476i | \(-0.276509\pi\) | ||||
0.645836 | + | 0.763476i | \(0.276509\pi\) | |||||||
\(368\) | −34.5259 | −1.79979 | ||||||||
\(369\) | −12.8319 | −0.668000 | ||||||||
\(370\) | −46.5835 | −2.42176 | ||||||||
\(371\) | 16.5888 | 0.861248 | ||||||||
\(372\) | −19.7719 | −1.02512 | ||||||||
\(373\) | −20.4524 | −1.05899 | −0.529494 | − | 0.848314i | \(-0.677618\pi\) | ||||
−0.529494 | + | 0.848314i | \(0.677618\pi\) | |||||||
\(374\) | 8.95504 | 0.463054 | ||||||||
\(375\) | −3.05137 | −0.157572 | ||||||||
\(376\) | 12.8751 | 0.663985 | ||||||||
\(377\) | −2.22739 | −0.114717 | ||||||||
\(378\) | 26.7021 | 1.37341 | ||||||||
\(379\) | −14.8428 | −0.762425 | −0.381212 | − | 0.924488i | \(-0.624493\pi\) | ||||
−0.381212 | + | 0.924488i | \(0.624493\pi\) | |||||||
\(380\) | 35.4884 | 1.82052 | ||||||||
\(381\) | −1.83254 | −0.0938838 | ||||||||
\(382\) | −18.5802 | −0.950645 | ||||||||
\(383\) | −12.5466 | −0.641103 | −0.320551 | − | 0.947231i | \(-0.603868\pi\) | ||||
−0.320551 | + | 0.947231i | \(0.603868\pi\) | |||||||
\(384\) | 25.3503 | 1.29365 | ||||||||
\(385\) | −33.2471 | −1.69443 | ||||||||
\(386\) | −12.9730 | −0.660308 | ||||||||
\(387\) | −11.5128 | −0.585229 | ||||||||
\(388\) | −28.7842 | −1.46130 | ||||||||
\(389\) | 25.5944 | 1.29769 | 0.648845 | − | 0.760921i | \(-0.275253\pi\) | ||||
0.648845 | + | 0.760921i | \(0.275253\pi\) | |||||||
\(390\) | 10.2604 | 0.519558 | ||||||||
\(391\) | −2.00913 | −0.101606 | ||||||||
\(392\) | −65.5236 | −3.30944 | ||||||||
\(393\) | −6.65567 | −0.335734 | ||||||||
\(394\) | −32.4930 | −1.63697 | ||||||||
\(395\) | −41.2765 | −2.07685 | ||||||||
\(396\) | 52.3019 | 2.62827 | ||||||||
\(397\) | −22.0990 | −1.10912 | −0.554558 | − | 0.832145i | \(-0.687113\pi\) | ||||
−0.554558 | + | 0.832145i | \(0.687113\pi\) | |||||||
\(398\) | −43.9666 | −2.20385 | ||||||||
\(399\) | −3.78692 | −0.189583 | ||||||||
\(400\) | 42.9920 | 2.14960 | ||||||||
\(401\) | 5.48851 | 0.274083 | 0.137041 | − | 0.990565i | \(-0.456241\pi\) | ||||
0.137041 | + | 0.990565i | \(0.456241\pi\) | |||||||
\(402\) | 0.164190 | 0.00818903 | ||||||||
\(403\) | −22.8083 | −1.13616 | ||||||||
\(404\) | −77.3980 | −3.85070 | ||||||||
\(405\) | −19.7577 | −0.981768 | ||||||||
\(406\) | 7.61640 | 0.377996 | ||||||||
\(407\) | 20.1907 | 1.00082 | ||||||||
\(408\) | 4.52361 | 0.223952 | ||||||||
\(409\) | −25.4927 | −1.26053 | −0.630267 | − | 0.776378i | \(-0.717055\pi\) | ||||
−0.630267 | + | 0.776378i | \(0.717055\pi\) | |||||||
\(410\) | 34.9632 | 1.72671 | ||||||||
\(411\) | 7.10376 | 0.350402 | ||||||||
\(412\) | 19.3219 | 0.951922 | ||||||||
\(413\) | −16.1123 | −0.792837 | ||||||||
\(414\) | −15.8713 | −0.780032 | ||||||||
\(415\) | −4.92791 | −0.241902 | ||||||||
\(416\) | 78.0729 | 3.82784 | ||||||||
\(417\) | 10.4470 | 0.511593 | ||||||||
\(418\) | −20.8046 | −1.01759 | ||||||||
\(419\) | −22.2973 | −1.08929 | −0.544647 | − | 0.838665i | \(-0.683336\pi\) | ||||
−0.544647 | + | 0.838665i | \(0.683336\pi\) | |||||||
\(420\) | −25.9397 | −1.26573 | ||||||||
\(421\) | −23.9500 | −1.16725 | −0.583626 | − | 0.812023i | \(-0.698366\pi\) | ||||
−0.583626 | + | 0.812023i | \(0.698366\pi\) | |||||||
\(422\) | 56.6553 | 2.75794 | ||||||||
\(423\) | 3.53584 | 0.171918 | ||||||||
\(424\) | 46.0369 | 2.23575 | ||||||||
\(425\) | 2.50180 | 0.121355 | ||||||||
\(426\) | −5.72218 | −0.277240 | ||||||||
\(427\) | −38.1704 | −1.84720 | ||||||||
\(428\) | −58.1785 | −2.81216 | ||||||||
\(429\) | −4.44719 | −0.214712 | ||||||||
\(430\) | 31.3691 | 1.51275 | ||||||||
\(431\) | 4.42706 | 0.213244 | 0.106622 | − | 0.994300i | \(-0.465997\pi\) | ||||
0.106622 | + | 0.994300i | \(0.465997\pi\) | |||||||
\(432\) | 44.2699 | 2.12994 | ||||||||
\(433\) | −6.81306 | −0.327415 | −0.163707 | − | 0.986509i | \(-0.552345\pi\) | ||||
−0.163707 | + | 0.986509i | \(0.552345\pi\) | |||||||
\(434\) | 77.9912 | 3.74370 | ||||||||
\(435\) | 0.935446 | 0.0448512 | ||||||||
\(436\) | 18.0745 | 0.865611 | ||||||||
\(437\) | 4.66767 | 0.223285 | ||||||||
\(438\) | 17.0265 | 0.813559 | ||||||||
\(439\) | 26.0996 | 1.24567 | 0.622833 | − | 0.782355i | \(-0.285982\pi\) | ||||
0.622833 | + | 0.782355i | \(0.285982\pi\) | |||||||
\(440\) | −92.2665 | −4.39863 | ||||||||
\(441\) | −17.9944 | −0.856878 | ||||||||
\(442\) | 8.05980 | 0.383366 | ||||||||
\(443\) | −26.9424 | −1.28007 | −0.640037 | − | 0.768344i | \(-0.721081\pi\) | ||||
−0.640037 | + | 0.768344i | \(0.721081\pi\) | |||||||
\(444\) | 15.7530 | 0.747604 | ||||||||
\(445\) | 23.7130 | 1.12410 | ||||||||
\(446\) | 8.84172 | 0.418668 | ||||||||
\(447\) | 7.68680 | 0.363573 | ||||||||
\(448\) | −143.517 | −6.78054 | ||||||||
\(449\) | 22.0242 | 1.03939 | 0.519693 | − | 0.854353i | \(-0.326046\pi\) | ||||
0.519693 | + | 0.854353i | \(0.326046\pi\) | |||||||
\(450\) | 19.7631 | 0.931642 | ||||||||
\(451\) | −15.1541 | −0.713579 | ||||||||
\(452\) | 56.9084 | 2.67674 | ||||||||
\(453\) | −0.373228 | −0.0175358 | ||||||||
\(454\) | 6.43566 | 0.302040 | ||||||||
\(455\) | −29.9234 | −1.40283 | ||||||||
\(456\) | −10.5094 | −0.492146 | ||||||||
\(457\) | −10.9497 | −0.512205 | −0.256102 | − | 0.966650i | \(-0.582438\pi\) | ||||
−0.256102 | + | 0.966650i | \(0.582438\pi\) | |||||||
\(458\) | −30.4338 | −1.42208 | ||||||||
\(459\) | 2.57616 | 0.120245 | ||||||||
\(460\) | 31.9727 | 1.49074 | ||||||||
\(461\) | 16.2581 | 0.757215 | 0.378607 | − | 0.925557i | \(-0.376403\pi\) | ||||
0.378607 | + | 0.925557i | \(0.376403\pi\) | |||||||
\(462\) | 15.2068 | 0.707485 | ||||||||
\(463\) | −19.5275 | −0.907522 | −0.453761 | − | 0.891123i | \(-0.649918\pi\) | ||||
−0.453761 | + | 0.891123i | \(0.649918\pi\) | |||||||
\(464\) | 12.6274 | 0.586211 | ||||||||
\(465\) | 9.57888 | 0.444210 | ||||||||
\(466\) | 4.06626 | 0.188366 | ||||||||
\(467\) | 37.0618 | 1.71502 | 0.857508 | − | 0.514471i | \(-0.172012\pi\) | ||||
0.857508 | + | 0.514471i | \(0.172012\pi\) | |||||||
\(468\) | 47.0732 | 2.17596 | ||||||||
\(469\) | −0.478839 | −0.0221108 | ||||||||
\(470\) | −9.63415 | −0.444390 | ||||||||
\(471\) | −4.93052 | −0.227186 | ||||||||
\(472\) | −44.7146 | −2.05816 | ||||||||
\(473\) | −13.5963 | −0.625160 | ||||||||
\(474\) | 18.8794 | 0.867158 | ||||||||
\(475\) | −5.81224 | −0.266684 | ||||||||
\(476\) | −20.3762 | −0.933943 | ||||||||
\(477\) | 12.6429 | 0.578878 | ||||||||
\(478\) | 43.4703 | 1.98828 | ||||||||
\(479\) | −27.8668 | −1.27327 | −0.636634 | − | 0.771166i | \(-0.719674\pi\) | ||||
−0.636634 | + | 0.771166i | \(0.719674\pi\) | |||||||
\(480\) | −32.7885 | −1.49658 | ||||||||
\(481\) | 18.1722 | 0.828582 | ||||||||
\(482\) | −56.5917 | −2.57768 | ||||||||
\(483\) | −3.41177 | −0.155241 | ||||||||
\(484\) | −0.635118 | −0.0288690 | ||||||||
\(485\) | 13.9451 | 0.633214 | ||||||||
\(486\) | 30.8875 | 1.40109 | ||||||||
\(487\) | −21.4182 | −0.970553 | −0.485277 | − | 0.874361i | \(-0.661281\pi\) | ||||
−0.485277 | + | 0.874361i | \(0.661281\pi\) | |||||||
\(488\) | −105.930 | −4.79521 | ||||||||
\(489\) | 4.90315 | 0.221728 | ||||||||
\(490\) | 49.0297 | 2.21494 | ||||||||
\(491\) | 15.9681 | 0.720629 | 0.360314 | − | 0.932831i | \(-0.382669\pi\) | ||||
0.360314 | + | 0.932831i | \(0.382669\pi\) | |||||||
\(492\) | −11.8234 | −0.533039 | ||||||||
\(493\) | 0.734813 | 0.0330943 | ||||||||
\(494\) | −18.7247 | −0.842466 | ||||||||
\(495\) | −25.3387 | −1.13889 | ||||||||
\(496\) | 129.303 | 5.80588 | ||||||||
\(497\) | 16.6881 | 0.748561 | ||||||||
\(498\) | 2.25397 | 0.101003 | ||||||||
\(499\) | −25.3815 | −1.13623 | −0.568116 | − | 0.822949i | \(-0.692327\pi\) | ||||
−0.568116 | + | 0.822949i | \(0.692327\pi\) | |||||||
\(500\) | 38.1438 | 1.70584 | ||||||||
\(501\) | 5.61902 | 0.251039 | ||||||||
\(502\) | 42.6084 | 1.90171 | ||||||||
\(503\) | 38.5387 | 1.71836 | 0.859178 | − | 0.511677i | \(-0.170976\pi\) | ||||
0.859178 | + | 0.511677i | \(0.170976\pi\) | |||||||
\(504\) | −104.216 | −4.64213 | ||||||||
\(505\) | 37.4970 | 1.66860 | ||||||||
\(506\) | −18.7436 | −0.833254 | ||||||||
\(507\) | 1.89699 | 0.0842485 | ||||||||
\(508\) | 22.9077 | 1.01637 | ||||||||
\(509\) | 16.2262 | 0.719214 | 0.359607 | − | 0.933104i | \(-0.382911\pi\) | ||||
0.359607 | + | 0.933104i | \(0.382911\pi\) | |||||||
\(510\) | −3.38490 | −0.149886 | ||||||||
\(511\) | −49.6558 | −2.19664 | ||||||||
\(512\) | −100.017 | −4.42016 | ||||||||
\(513\) | −5.98501 | −0.264244 | ||||||||
\(514\) | 19.2010 | 0.846919 | ||||||||
\(515\) | −9.36088 | −0.412490 | ||||||||
\(516\) | −10.6080 | −0.466991 | ||||||||
\(517\) | 4.17573 | 0.183649 | ||||||||
\(518\) | −62.1386 | −2.73021 | ||||||||
\(519\) | 4.89007 | 0.214650 | ||||||||
\(520\) | −83.0426 | −3.64166 | ||||||||
\(521\) | 34.2941 | 1.50245 | 0.751227 | − | 0.660044i | \(-0.229462\pi\) | ||||
0.751227 | + | 0.660044i | \(0.229462\pi\) | |||||||
\(522\) | 5.80471 | 0.254065 | ||||||||
\(523\) | −32.3929 | −1.41644 | −0.708222 | − | 0.705990i | \(-0.750502\pi\) | ||||
−0.708222 | + | 0.705990i | \(0.750502\pi\) | |||||||
\(524\) | 83.1995 | 3.63459 | ||||||||
\(525\) | 4.24837 | 0.185414 | ||||||||
\(526\) | −39.9834 | −1.74336 | ||||||||
\(527\) | 7.52442 | 0.327769 | ||||||||
\(528\) | 25.2117 | 1.09720 | ||||||||
\(529\) | −18.7947 | −0.817162 | ||||||||
\(530\) | −34.4482 | −1.49634 | ||||||||
\(531\) | −12.2797 | −0.532896 | ||||||||
\(532\) | 47.3386 | 2.05239 | ||||||||
\(533\) | −13.6391 | −0.590777 | ||||||||
\(534\) | −10.8460 | −0.469354 | ||||||||
\(535\) | 28.1857 | 1.21857 | ||||||||
\(536\) | −1.32886 | −0.0573982 | ||||||||
\(537\) | −7.49025 | −0.323228 | ||||||||
\(538\) | −21.4735 | −0.925789 | ||||||||
\(539\) | −21.2510 | −0.915344 | ||||||||
\(540\) | −40.9962 | −1.76420 | ||||||||
\(541\) | 25.1036 | 1.07929 | 0.539645 | − | 0.841893i | \(-0.318559\pi\) | ||||
0.539645 | + | 0.841893i | \(0.318559\pi\) | |||||||
\(542\) | −4.21013 | −0.180840 | ||||||||
\(543\) | −2.62214 | −0.112527 | ||||||||
\(544\) | −25.7561 | −1.10428 | ||||||||
\(545\) | −8.75655 | −0.375089 | ||||||||
\(546\) | 13.6866 | 0.585732 | ||||||||
\(547\) | −30.6241 | −1.30939 | −0.654697 | − | 0.755892i | \(-0.727204\pi\) | ||||
−0.654697 | + | 0.755892i | \(0.727204\pi\) | |||||||
\(548\) | −88.8009 | −3.79339 | ||||||||
\(549\) | −29.0909 | −1.24157 | ||||||||
\(550\) | 23.3397 | 0.995209 | ||||||||
\(551\) | −1.70714 | −0.0727265 | ||||||||
\(552\) | −9.46826 | −0.402996 | ||||||||
\(553\) | −55.0594 | −2.34137 | ||||||||
\(554\) | −74.9604 | −3.18476 | ||||||||
\(555\) | −7.63185 | −0.323954 | ||||||||
\(556\) | −130.594 | −5.53840 | ||||||||
\(557\) | −21.4771 | −0.910015 | −0.455007 | − | 0.890488i | \(-0.650363\pi\) | ||||
−0.455007 | + | 0.890488i | \(0.650363\pi\) | |||||||
\(558\) | 59.4397 | 2.51628 | ||||||||
\(559\) | −12.2371 | −0.517574 | ||||||||
\(560\) | 169.639 | 7.16857 | ||||||||
\(561\) | 1.46712 | 0.0619418 | ||||||||
\(562\) | −72.2214 | −3.04648 | ||||||||
\(563\) | 46.7467 | 1.97014 | 0.985070 | − | 0.172156i | \(-0.0550732\pi\) | ||||
0.985070 | + | 0.172156i | \(0.0550732\pi\) | |||||||
\(564\) | 3.25795 | 0.137185 | ||||||||
\(565\) | −27.5704 | −1.15989 | ||||||||
\(566\) | 59.7727 | 2.51243 | ||||||||
\(567\) | −26.3551 | −1.10681 | ||||||||
\(568\) | 46.3123 | 1.94322 | ||||||||
\(569\) | 17.5040 | 0.733804 | 0.366902 | − | 0.930260i | \(-0.380418\pi\) | ||||
0.366902 | + | 0.930260i | \(0.380418\pi\) | |||||||
\(570\) | 7.86390 | 0.329382 | ||||||||
\(571\) | −32.3897 | −1.35547 | −0.677733 | − | 0.735308i | \(-0.737037\pi\) | ||||
−0.677733 | + | 0.735308i | \(0.737037\pi\) | |||||||
\(572\) | 55.5923 | 2.32443 | ||||||||
\(573\) | −3.04402 | −0.127166 | ||||||||
\(574\) | 46.6380 | 1.94663 | ||||||||
\(575\) | −5.23645 | −0.218375 | ||||||||
\(576\) | −109.379 | −4.55746 | ||||||||
\(577\) | −17.3114 | −0.720681 | −0.360341 | − | 0.932821i | \(-0.617340\pi\) | ||||
−0.360341 | + | 0.932821i | \(0.617340\pi\) | |||||||
\(578\) | 44.4312 | 1.84809 | ||||||||
\(579\) | −2.12539 | −0.0883280 | ||||||||
\(580\) | −11.6936 | −0.485550 | ||||||||
\(581\) | −6.57343 | −0.272712 | ||||||||
\(582\) | −6.37832 | −0.264390 | ||||||||
\(583\) | 14.9309 | 0.618375 | ||||||||
\(584\) | −137.804 | −5.70236 | ||||||||
\(585\) | −22.8056 | −0.942894 | ||||||||
\(586\) | 30.9985 | 1.28053 | ||||||||
\(587\) | −15.4541 | −0.637858 | −0.318929 | − | 0.947779i | \(-0.603323\pi\) | ||||
−0.318929 | + | 0.947779i | \(0.603323\pi\) | |||||||
\(588\) | −16.5802 | −0.683757 | ||||||||
\(589\) | −17.4809 | −0.720289 | ||||||||
\(590\) | 33.4588 | 1.37748 | ||||||||
\(591\) | −5.32339 | −0.218975 | ||||||||
\(592\) | −103.021 | −4.23412 | ||||||||
\(593\) | 20.9145 | 0.858855 | 0.429428 | − | 0.903101i | \(-0.358715\pi\) | ||||
0.429428 | + | 0.903101i | \(0.358715\pi\) | |||||||
\(594\) | 24.0335 | 0.986106 | ||||||||
\(595\) | 9.87167 | 0.404699 | ||||||||
\(596\) | −96.0893 | −3.93597 | ||||||||
\(597\) | −7.20312 | −0.294804 | ||||||||
\(598\) | −16.8698 | −0.689857 | ||||||||
\(599\) | 7.93391 | 0.324171 | 0.162085 | − | 0.986777i | \(-0.448178\pi\) | ||||
0.162085 | + | 0.986777i | \(0.448178\pi\) | |||||||
\(600\) | 11.7900 | 0.481324 | ||||||||
\(601\) | 9.93108 | 0.405097 | 0.202549 | − | 0.979272i | \(-0.435078\pi\) | ||||
0.202549 | + | 0.979272i | \(0.435078\pi\) | |||||||
\(602\) | 41.8438 | 1.70543 | ||||||||
\(603\) | −0.364939 | −0.0148615 | ||||||||
\(604\) | 4.66556 | 0.189839 | ||||||||
\(605\) | 0.307696 | 0.0125096 | ||||||||
\(606\) | −17.1507 | −0.696699 | ||||||||
\(607\) | 15.9424 | 0.647081 | 0.323540 | − | 0.946214i | \(-0.395127\pi\) | ||||
0.323540 | + | 0.946214i | \(0.395127\pi\) | |||||||
\(608\) | 59.8373 | 2.42672 | ||||||||
\(609\) | 1.24781 | 0.0505637 | ||||||||
\(610\) | 79.2645 | 3.20933 | ||||||||
\(611\) | 3.75828 | 0.152044 | ||||||||
\(612\) | −15.5294 | −0.627738 | ||||||||
\(613\) | 24.3333 | 0.982811 | 0.491406 | − | 0.870931i | \(-0.336483\pi\) | ||||
0.491406 | + | 0.870931i | \(0.336483\pi\) | |||||||
\(614\) | −85.2637 | −3.44096 | ||||||||
\(615\) | 5.72808 | 0.230978 | ||||||||
\(616\) | −123.076 | −4.95887 | ||||||||
\(617\) | −42.2289 | −1.70007 | −0.850036 | − | 0.526724i | \(-0.823420\pi\) | ||||
−0.850036 | + | 0.526724i | \(0.823420\pi\) | |||||||
\(618\) | 4.28156 | 0.172229 | ||||||||
\(619\) | 19.9759 | 0.802898 | 0.401449 | − | 0.915881i | \(-0.368507\pi\) | ||||
0.401449 | + | 0.915881i | \(0.368507\pi\) | |||||||
\(620\) | −119.741 | −4.80893 | ||||||||
\(621\) | −5.39210 | −0.216378 | ||||||||
\(622\) | −25.8701 | −1.03730 | ||||||||
\(623\) | 31.6312 | 1.26728 | ||||||||
\(624\) | 22.6912 | 0.908376 | ||||||||
\(625\) | −31.2471 | −1.24989 | ||||||||
\(626\) | −93.6329 | −3.74232 | ||||||||
\(627\) | −3.40845 | −0.136120 | ||||||||
\(628\) | 61.6342 | 2.45947 | ||||||||
\(629\) | −5.99499 | −0.239036 | ||||||||
\(630\) | 77.9819 | 3.10687 | ||||||||
\(631\) | 19.1345 | 0.761734 | 0.380867 | − | 0.924630i | \(-0.375626\pi\) | ||||
0.380867 | + | 0.924630i | \(0.375626\pi\) | |||||||
\(632\) | −152.800 | −6.07804 | ||||||||
\(633\) | 9.28194 | 0.368924 | ||||||||
\(634\) | −36.0780 | −1.43284 | ||||||||
\(635\) | −11.0981 | −0.440415 | ||||||||
\(636\) | 11.6493 | 0.461923 | ||||||||
\(637\) | −19.1265 | −0.757819 | ||||||||
\(638\) | 6.85521 | 0.271401 | ||||||||
\(639\) | 12.7185 | 0.503136 | ||||||||
\(640\) | 153.525 | 6.06860 | ||||||||
\(641\) | −3.24092 | −0.128008 | −0.0640042 | − | 0.997950i | \(-0.520387\pi\) | ||||
−0.0640042 | + | 0.997950i | \(0.520387\pi\) | |||||||
\(642\) | −12.8918 | −0.508799 | ||||||||
\(643\) | 19.7549 | 0.779059 | 0.389530 | − | 0.921014i | \(-0.372638\pi\) | ||||
0.389530 | + | 0.921014i | \(0.372638\pi\) | |||||||
\(644\) | 42.6490 | 1.68061 | ||||||||
\(645\) | 5.13926 | 0.202358 | ||||||||
\(646\) | 6.17726 | 0.243041 | ||||||||
\(647\) | −21.3018 | −0.837458 | −0.418729 | − | 0.908111i | \(-0.637524\pi\) | ||||
−0.418729 | + | 0.908111i | \(0.637524\pi\) | |||||||
\(648\) | −73.1401 | −2.87322 | ||||||||
\(649\) | −14.5021 | −0.569256 | ||||||||
\(650\) | 21.0064 | 0.823941 | ||||||||
\(651\) | 12.7774 | 0.500787 | ||||||||
\(652\) | −61.2921 | −2.40038 | ||||||||
\(653\) | 45.6267 | 1.78551 | 0.892755 | − | 0.450542i | \(-0.148769\pi\) | ||||
0.892755 | + | 0.450542i | \(0.148769\pi\) | |||||||
\(654\) | 4.00514 | 0.156613 | ||||||||
\(655\) | −40.3077 | −1.57495 | ||||||||
\(656\) | 77.3220 | 3.01892 | ||||||||
\(657\) | −37.8443 | −1.47645 | ||||||||
\(658\) | −12.8512 | −0.500991 | ||||||||
\(659\) | −2.38239 | −0.0928047 | −0.0464024 | − | 0.998923i | \(-0.514776\pi\) | ||||
−0.0464024 | + | 0.998923i | \(0.514776\pi\) | |||||||
\(660\) | −23.3473 | −0.908792 | ||||||||
\(661\) | 12.0865 | 0.470112 | 0.235056 | − | 0.971982i | \(-0.424473\pi\) | ||||
0.235056 | + | 0.971982i | \(0.424473\pi\) | |||||||
\(662\) | −48.7414 | −1.89439 | ||||||||
\(663\) | 1.32045 | 0.0512821 | ||||||||
\(664\) | −18.2424 | −0.707943 | ||||||||
\(665\) | −22.9341 | −0.889347 | ||||||||
\(666\) | −47.3578 | −1.83508 | ||||||||
\(667\) | −1.53802 | −0.0595524 | ||||||||
\(668\) | −70.2409 | −2.71770 | ||||||||
\(669\) | 1.44855 | 0.0560043 | ||||||||
\(670\) | 0.994355 | 0.0384153 | ||||||||
\(671\) | −34.3556 | −1.32628 | ||||||||
\(672\) | −43.7372 | −1.68720 | ||||||||
\(673\) | 43.3388 | 1.67059 | 0.835295 | − | 0.549803i | \(-0.185297\pi\) | ||||
0.835295 | + | 0.549803i | \(0.185297\pi\) | |||||||
\(674\) | 2.00548 | 0.0772482 | ||||||||
\(675\) | 6.71431 | 0.258434 | ||||||||
\(676\) | −23.7135 | −0.912057 | ||||||||
\(677\) | 14.4629 | 0.555856 | 0.277928 | − | 0.960602i | \(-0.410352\pi\) | ||||
0.277928 | + | 0.960602i | \(0.410352\pi\) | |||||||
\(678\) | 12.6104 | 0.484298 | ||||||||
\(679\) | 18.6016 | 0.713864 | ||||||||
\(680\) | 27.3956 | 1.05057 | ||||||||
\(681\) | 1.05436 | 0.0404034 | ||||||||
\(682\) | 70.1967 | 2.68797 | ||||||||
\(683\) | −24.2843 | −0.929215 | −0.464607 | − | 0.885517i | \(-0.653805\pi\) | ||||
−0.464607 | + | 0.885517i | \(0.653805\pi\) | |||||||
\(684\) | 36.0783 | 1.37949 | ||||||||
\(685\) | 43.0214 | 1.64376 | ||||||||
\(686\) | −5.68417 | −0.217023 | ||||||||
\(687\) | −4.98602 | −0.190228 | ||||||||
\(688\) | 69.3736 | 2.64484 | ||||||||
\(689\) | 13.4383 | 0.511957 | ||||||||
\(690\) | 7.08486 | 0.269716 | ||||||||
\(691\) | 8.52572 | 0.324334 | 0.162167 | − | 0.986763i | \(-0.448152\pi\) | ||||
0.162167 | + | 0.986763i | \(0.448152\pi\) | |||||||
\(692\) | −61.1286 | −2.32376 | ||||||||
\(693\) | −33.7997 | −1.28395 | ||||||||
\(694\) | −13.7181 | −0.520733 | ||||||||
\(695\) | 63.2687 | 2.39992 | ||||||||
\(696\) | 3.46289 | 0.131260 | ||||||||
\(697\) | 4.49953 | 0.170432 | ||||||||
\(698\) | −33.5878 | −1.27132 | ||||||||
\(699\) | 0.666182 | 0.0251973 | ||||||||
\(700\) | −53.1070 | −2.00726 | ||||||||
\(701\) | −29.1666 | −1.10161 | −0.550804 | − | 0.834635i | \(-0.685679\pi\) | ||||
−0.550804 | + | 0.834635i | \(0.685679\pi\) | |||||||
\(702\) | 21.6309 | 0.816404 | ||||||||
\(703\) | 13.9277 | 0.525294 | ||||||||
\(704\) | −129.174 | −4.86842 | ||||||||
\(705\) | −1.57838 | −0.0594452 | ||||||||
\(706\) | 62.1970 | 2.34081 | ||||||||
\(707\) | 50.0180 | 1.88112 | ||||||||
\(708\) | −11.3147 | −0.425231 | ||||||||
\(709\) | 8.89435 | 0.334034 | 0.167017 | − | 0.985954i | \(-0.446586\pi\) | ||||
0.167017 | + | 0.985954i | \(0.446586\pi\) | |||||||
\(710\) | −34.6543 | −1.30055 | ||||||||
\(711\) | −41.9626 | −1.57372 | ||||||||
\(712\) | 87.7821 | 3.28977 | ||||||||
\(713\) | −15.7492 | −0.589812 | ||||||||
\(714\) | −4.51518 | −0.168976 | ||||||||
\(715\) | −26.9328 | −1.00723 | ||||||||
\(716\) | 93.6323 | 3.49920 | ||||||||
\(717\) | 7.12181 | 0.265969 | ||||||||
\(718\) | −50.8808 | −1.89885 | ||||||||
\(719\) | −20.1059 | −0.749822 | −0.374911 | − | 0.927061i | \(-0.622327\pi\) | ||||
−0.374911 | + | 0.927061i | \(0.622327\pi\) | |||||||
\(720\) | 129.288 | 4.81827 | ||||||||
\(721\) | −12.4866 | −0.465027 | ||||||||
\(722\) | 38.2789 | 1.42459 | ||||||||
\(723\) | −9.27151 | −0.344811 | ||||||||
\(724\) | 32.7782 | 1.21819 | ||||||||
\(725\) | 1.91516 | 0.0711273 | ||||||||
\(726\) | −0.140736 | −0.00522321 | ||||||||
\(727\) | −20.2989 | −0.752846 | −0.376423 | − | 0.926448i | \(-0.622846\pi\) | ||||
−0.376423 | + | 0.926448i | \(0.622846\pi\) | |||||||
\(728\) | −110.772 | −4.10548 | ||||||||
\(729\) | −16.5063 | −0.611344 | ||||||||
\(730\) | 103.115 | 3.81646 | ||||||||
\(731\) | 4.03700 | 0.149314 | ||||||||
\(732\) | −26.8046 | −0.990728 | ||||||||
\(733\) | −6.33091 | −0.233837 | −0.116919 | − | 0.993141i | \(-0.537302\pi\) | ||||
−0.116919 | + | 0.993141i | \(0.537302\pi\) | |||||||
\(734\) | −68.5435 | −2.52999 | ||||||||
\(735\) | 8.03262 | 0.296288 | ||||||||
\(736\) | 53.9095 | 1.98713 | ||||||||
\(737\) | −0.430984 | −0.0158755 | ||||||||
\(738\) | 35.5443 | 1.30841 | ||||||||
\(739\) | −48.6350 | −1.78907 | −0.894534 | − | 0.447000i | \(-0.852492\pi\) | ||||
−0.894534 | + | 0.447000i | \(0.852492\pi\) | |||||||
\(740\) | 95.4024 | 3.50706 | ||||||||
\(741\) | −3.06771 | −0.112695 | ||||||||
\(742\) | −45.9511 | −1.68692 | ||||||||
\(743\) | 26.2443 | 0.962812 | 0.481406 | − | 0.876498i | \(-0.340126\pi\) | ||||
0.481406 | + | 0.876498i | \(0.340126\pi\) | |||||||
\(744\) | 35.4596 | 1.30001 | ||||||||
\(745\) | 46.5524 | 1.70555 | ||||||||
\(746\) | 56.6534 | 2.07423 | ||||||||
\(747\) | −5.00983 | −0.183300 | ||||||||
\(748\) | −18.3398 | −0.670570 | ||||||||
\(749\) | 37.5974 | 1.37378 | ||||||||
\(750\) | 8.45231 | 0.308635 | ||||||||
\(751\) | −2.70661 | −0.0987657 | −0.0493829 | − | 0.998780i | \(-0.515725\pi\) | ||||
−0.0493829 | + | 0.998780i | \(0.515725\pi\) | |||||||
\(752\) | −21.3062 | −0.776956 | ||||||||
\(753\) | 6.98061 | 0.254388 | ||||||||
\(754\) | 6.16989 | 0.224694 | ||||||||
\(755\) | −2.26032 | −0.0822616 | ||||||||
\(756\) | −54.6856 | −1.98890 | ||||||||
\(757\) | −7.60354 | −0.276356 | −0.138178 | − | 0.990407i | \(-0.544125\pi\) | ||||
−0.138178 | + | 0.990407i | \(0.544125\pi\) | |||||||
\(758\) | 41.1147 | 1.49335 | ||||||||
\(759\) | −3.07079 | −0.111463 | ||||||||
\(760\) | −63.6462 | −2.30869 | ||||||||
\(761\) | 36.5550 | 1.32512 | 0.662558 | − | 0.749010i | \(-0.269471\pi\) | ||||
0.662558 | + | 0.749010i | \(0.269471\pi\) | |||||||
\(762\) | 5.07614 | 0.183889 | ||||||||
\(763\) | −11.6805 | −0.422863 | ||||||||
\(764\) | 38.0520 | 1.37667 | ||||||||
\(765\) | 7.52352 | 0.272013 | ||||||||
\(766\) | 34.7542 | 1.25572 | ||||||||
\(767\) | −13.0523 | −0.471291 | ||||||||
\(768\) | −34.6893 | −1.25174 | ||||||||
\(769\) | 21.4810 | 0.774625 | 0.387312 | − | 0.921949i | \(-0.373404\pi\) | ||||
0.387312 | + | 0.921949i | \(0.373404\pi\) | |||||||
\(770\) | 92.0947 | 3.31886 | ||||||||
\(771\) | 3.14573 | 0.113291 | ||||||||
\(772\) | 26.5685 | 0.956221 | ||||||||
\(773\) | −15.8644 | −0.570602 | −0.285301 | − | 0.958438i | \(-0.592093\pi\) | ||||
−0.285301 | + | 0.958438i | \(0.592093\pi\) | |||||||
\(774\) | 31.8905 | 1.14628 | ||||||||
\(775\) | 19.6111 | 0.704450 | ||||||||
\(776\) | 51.6227 | 1.85315 | ||||||||
\(777\) | −10.1803 | −0.365215 | ||||||||
\(778\) | −70.8967 | −2.54177 | ||||||||
\(779\) | −10.4534 | −0.374533 | ||||||||
\(780\) | −21.0132 | −0.752395 | ||||||||
\(781\) | 15.0202 | 0.537466 | ||||||||
\(782\) | 5.56531 | 0.199015 | ||||||||
\(783\) | 1.97209 | 0.0704767 | ||||||||
\(784\) | 108.430 | 3.87252 | ||||||||
\(785\) | −29.8599 | −1.06575 | ||||||||
\(786\) | 18.4362 | 0.657599 | ||||||||
\(787\) | 6.71771 | 0.239460 | 0.119730 | − | 0.992806i | \(-0.461797\pi\) | ||||
0.119730 | + | 0.992806i | \(0.461797\pi\) | |||||||
\(788\) | 66.5453 | 2.37058 | ||||||||
\(789\) | −6.55055 | −0.233206 | ||||||||
\(790\) | 114.336 | 4.06790 | ||||||||
\(791\) | −36.7766 | −1.30763 | ||||||||
\(792\) | −93.8002 | −3.33304 | ||||||||
\(793\) | −30.9211 | −1.09804 | ||||||||
\(794\) | 61.2143 | 2.17242 | ||||||||
\(795\) | −5.64371 | −0.200162 | ||||||||
\(796\) | 90.0430 | 3.19149 | ||||||||
\(797\) | 5.48198 | 0.194182 | 0.0970908 | − | 0.995276i | \(-0.469046\pi\) | ||||
0.0970908 | + | 0.995276i | \(0.469046\pi\) | |||||||
\(798\) | 10.4898 | 0.371335 | ||||||||
\(799\) | −1.23985 | −0.0438628 | ||||||||
\(800\) | −67.1287 | −2.37336 | ||||||||
\(801\) | 24.1072 | 0.851785 | ||||||||
\(802\) | −15.2032 | −0.536844 | ||||||||
\(803\) | −44.6932 | −1.57719 | ||||||||
\(804\) | −0.336258 | −0.0118589 | ||||||||
\(805\) | −20.6622 | −0.728246 | ||||||||
\(806\) | 63.1791 | 2.22539 | ||||||||
\(807\) | −3.51804 | −0.123841 | ||||||||
\(808\) | 138.809 | 4.88327 | ||||||||
\(809\) | 31.6107 | 1.11137 | 0.555687 | − | 0.831392i | \(-0.312455\pi\) | ||||
0.555687 | + | 0.831392i | \(0.312455\pi\) | |||||||
\(810\) | 54.7289 | 1.92298 | ||||||||
\(811\) | 10.8681 | 0.381629 | 0.190815 | − | 0.981626i | \(-0.438887\pi\) | ||||
0.190815 | + | 0.981626i | \(0.438887\pi\) | |||||||
\(812\) | −15.5983 | −0.547393 | ||||||||
\(813\) | −0.689752 | −0.0241907 | ||||||||
\(814\) | −55.9284 | −1.96029 | ||||||||
\(815\) | 29.6942 | 1.04014 | ||||||||
\(816\) | −7.48580 | −0.262055 | ||||||||
\(817\) | −9.37886 | −0.328125 | ||||||||
\(818\) | 70.6150 | 2.46900 | ||||||||
\(819\) | −30.4208 | −1.06299 | ||||||||
\(820\) | −71.6041 | −2.50052 | ||||||||
\(821\) | 9.80523 | 0.342205 | 0.171102 | − | 0.985253i | \(-0.445267\pi\) | ||||
0.171102 | + | 0.985253i | \(0.445267\pi\) | |||||||
\(822\) | −19.6775 | −0.686330 | ||||||||
\(823\) | −5.53124 | −0.192807 | −0.0964035 | − | 0.995342i | \(-0.530734\pi\) | ||||
−0.0964035 | + | 0.995342i | \(0.530734\pi\) | |||||||
\(824\) | −34.6526 | −1.20718 | ||||||||
\(825\) | 3.82379 | 0.133127 | ||||||||
\(826\) | 44.6313 | 1.55292 | ||||||||
\(827\) | −23.5441 | −0.818708 | −0.409354 | − | 0.912376i | \(-0.634246\pi\) | ||||
−0.409354 | + | 0.912376i | \(0.634246\pi\) | |||||||
\(828\) | 32.5042 | 1.12960 | ||||||||
\(829\) | 50.4382 | 1.75179 | 0.875895 | − | 0.482502i | \(-0.160272\pi\) | ||||
0.875895 | + | 0.482502i | \(0.160272\pi\) | |||||||
\(830\) | 13.6504 | 0.473811 | ||||||||
\(831\) | −12.2809 | −0.426019 | ||||||||
\(832\) | −116.260 | −4.03060 | ||||||||
\(833\) | 6.30980 | 0.218622 | ||||||||
\(834\) | −28.9383 | −1.00205 | ||||||||
\(835\) | 34.0296 | 1.17764 | ||||||||
\(836\) | 42.6075 | 1.47361 | ||||||||
\(837\) | 20.1940 | 0.698007 | ||||||||
\(838\) | 61.7636 | 2.13359 | ||||||||
\(839\) | −39.2420 | −1.35478 | −0.677392 | − | 0.735623i | \(-0.736890\pi\) | ||||
−0.677392 | + | 0.735623i | \(0.736890\pi\) | |||||||
\(840\) | 46.5213 | 1.60514 | ||||||||
\(841\) | −28.4375 | −0.980603 | ||||||||
\(842\) | 66.3416 | 2.28628 | ||||||||
\(843\) | −11.8322 | −0.407521 | ||||||||
\(844\) | −116.029 | −3.99390 | ||||||||
\(845\) | 11.4885 | 0.395215 | ||||||||
\(846\) | −9.79430 | −0.336735 | ||||||||
\(847\) | 0.410441 | 0.0141029 | ||||||||
\(848\) | −76.1832 | −2.61614 | ||||||||
\(849\) | 9.79266 | 0.336083 | ||||||||
\(850\) | −6.92999 | −0.237697 | ||||||||
\(851\) | 12.5480 | 0.430139 | ||||||||
\(852\) | 11.7189 | 0.401484 | ||||||||
\(853\) | −32.2363 | −1.10375 | −0.551874 | − | 0.833927i | \(-0.686087\pi\) | ||||
−0.551874 | + | 0.833927i | \(0.686087\pi\) | |||||||
\(854\) | 105.732 | 3.61809 | ||||||||
\(855\) | −17.4788 | −0.597764 | ||||||||
\(856\) | 104.339 | 3.56625 | ||||||||
\(857\) | −1.95981 | −0.0669458 | −0.0334729 | − | 0.999440i | \(-0.510657\pi\) | ||||
−0.0334729 | + | 0.999440i | \(0.510657\pi\) | |||||||
\(858\) | 12.3187 | 0.420555 | ||||||||
\(859\) | 13.2145 | 0.450874 | 0.225437 | − | 0.974258i | \(-0.427619\pi\) | ||||
0.225437 | + | 0.974258i | \(0.427619\pi\) | |||||||
\(860\) | −64.2435 | −2.19069 | ||||||||
\(861\) | 7.64078 | 0.260397 | ||||||||
\(862\) | −12.2630 | −0.417679 | ||||||||
\(863\) | −20.9152 | −0.711960 | −0.355980 | − | 0.934494i | \(-0.615853\pi\) | ||||
−0.355980 | + | 0.934494i | \(0.615853\pi\) | |||||||
\(864\) | −69.1241 | −2.35165 | ||||||||
\(865\) | 29.6150 | 1.00694 | ||||||||
\(866\) | 18.8722 | 0.641304 | ||||||||
\(867\) | 7.27924 | 0.247216 | ||||||||
\(868\) | −159.725 | −5.42142 | ||||||||
\(869\) | −49.5567 | −1.68110 | ||||||||
\(870\) | −2.59119 | −0.0878496 | ||||||||
\(871\) | −0.387898 | −0.0131434 | ||||||||
\(872\) | −32.4155 | −1.09773 | ||||||||
\(873\) | 14.1769 | 0.479815 | ||||||||
\(874\) | −12.9295 | −0.437346 | ||||||||
\(875\) | −24.6502 | −0.833327 | ||||||||
\(876\) | −34.8701 | −1.17815 | ||||||||
\(877\) | −14.3841 | −0.485716 | −0.242858 | − | 0.970062i | \(-0.578085\pi\) | ||||
−0.242858 | + | 0.970062i | \(0.578085\pi\) | |||||||
\(878\) | −72.2961 | −2.43987 | ||||||||
\(879\) | 5.07853 | 0.171295 | ||||||||
\(880\) | 152.685 | 5.14702 | ||||||||
\(881\) | −32.5760 | −1.09751 | −0.548756 | − | 0.835983i | \(-0.684898\pi\) | ||||
−0.548756 | + | 0.835983i | \(0.684898\pi\) | |||||||
\(882\) | 49.8447 | 1.67836 | ||||||||
\(883\) | −56.0790 | −1.88721 | −0.943604 | − | 0.331076i | \(-0.892588\pi\) | ||||
−0.943604 | + | 0.331076i | \(0.892588\pi\) | |||||||
\(884\) | −16.5064 | −0.555169 | ||||||||
\(885\) | 5.48161 | 0.184262 | ||||||||
\(886\) | 74.6308 | 2.50727 | ||||||||
\(887\) | 14.8633 | 0.499059 | 0.249530 | − | 0.968367i | \(-0.419724\pi\) | ||||
0.249530 | + | 0.968367i | \(0.419724\pi\) | |||||||
\(888\) | −28.2520 | −0.948076 | ||||||||
\(889\) | −14.8040 | −0.496509 | ||||||||
\(890\) | −65.6852 | −2.20177 | ||||||||
\(891\) | −23.7212 | −0.794690 | ||||||||
\(892\) | −18.1077 | −0.606292 | ||||||||
\(893\) | 2.88046 | 0.0963908 | ||||||||
\(894\) | −21.2925 | −0.712127 | ||||||||
\(895\) | −45.3620 | −1.51629 | ||||||||
\(896\) | 204.789 | 6.84153 | ||||||||
\(897\) | −2.76381 | −0.0922808 | ||||||||
\(898\) | −61.0072 | −2.03584 | ||||||||
\(899\) | 5.76005 | 0.192108 | ||||||||
\(900\) | −40.4746 | −1.34915 | ||||||||
\(901\) | −4.43326 | −0.147693 | ||||||||
\(902\) | 41.9770 | 1.39768 | ||||||||
\(903\) | 6.85534 | 0.228132 | ||||||||
\(904\) | −102.062 | −3.39452 | ||||||||
\(905\) | −15.8801 | −0.527871 | ||||||||
\(906\) | 1.03384 | 0.0343472 | ||||||||
\(907\) | −5.30131 | −0.176027 | −0.0880136 | − | 0.996119i | \(-0.528052\pi\) | ||||
−0.0880136 | + | 0.996119i | \(0.528052\pi\) | |||||||
\(908\) | −13.1801 | −0.437398 | ||||||||
\(909\) | 38.1203 | 1.26437 | ||||||||
\(910\) | 82.8879 | 2.74771 | ||||||||
\(911\) | −42.6404 | −1.41274 | −0.706370 | − | 0.707843i | \(-0.749668\pi\) | ||||
−0.706370 | + | 0.707843i | \(0.749668\pi\) | |||||||
\(912\) | 17.3912 | 0.575881 | ||||||||
\(913\) | −5.91648 | −0.195807 | ||||||||
\(914\) | 30.3307 | 1.00325 | ||||||||
\(915\) | 12.9860 | 0.429305 | ||||||||
\(916\) | 62.3280 | 2.05937 | ||||||||
\(917\) | −53.7671 | −1.77555 | ||||||||
\(918\) | −7.13598 | −0.235522 | ||||||||
\(919\) | 52.4702 | 1.73083 | 0.865416 | − | 0.501054i | \(-0.167054\pi\) | ||||
0.865416 | + | 0.501054i | \(0.167054\pi\) | |||||||
\(920\) | −57.3411 | −1.89048 | ||||||||
\(921\) | −13.9689 | −0.460291 | ||||||||
\(922\) | −45.0350 | −1.48315 | ||||||||
\(923\) | 13.5187 | 0.444972 | ||||||||
\(924\) | −31.1434 | −1.02454 | ||||||||
\(925\) | −15.6249 | −0.513743 | ||||||||
\(926\) | 54.0914 | 1.77755 | ||||||||
\(927\) | −9.51648 | −0.312562 | ||||||||
\(928\) | −19.7167 | −0.647231 | ||||||||
\(929\) | 40.3864 | 1.32503 | 0.662517 | − | 0.749047i | \(-0.269488\pi\) | ||||
0.662517 | + | 0.749047i | \(0.269488\pi\) | |||||||
\(930\) | −26.5336 | −0.870070 | ||||||||
\(931\) | −14.6591 | −0.480432 | ||||||||
\(932\) | −8.32764 | −0.272781 | ||||||||
\(933\) | −4.23834 | −0.138757 | ||||||||
\(934\) | −102.661 | −3.35918 | ||||||||
\(935\) | 8.88508 | 0.290573 | ||||||||
\(936\) | −84.4229 | −2.75945 | ||||||||
\(937\) | 31.9884 | 1.04501 | 0.522507 | − | 0.852635i | \(-0.324997\pi\) | ||||
0.522507 | + | 0.852635i | \(0.324997\pi\) | |||||||
\(938\) | 1.32639 | 0.0433081 | ||||||||
\(939\) | −15.3400 | −0.500603 | ||||||||
\(940\) | 19.7306 | 0.643542 | ||||||||
\(941\) | 46.6973 | 1.52229 | 0.761143 | − | 0.648584i | \(-0.224638\pi\) | ||||
0.761143 | + | 0.648584i | \(0.224638\pi\) | |||||||
\(942\) | 13.6576 | 0.444988 | ||||||||
\(943\) | −9.41786 | −0.306688 | ||||||||
\(944\) | 73.9950 | 2.40833 | ||||||||
\(945\) | 26.4935 | 0.861835 | ||||||||
\(946\) | 37.6619 | 1.22449 | ||||||||
\(947\) | 6.98863 | 0.227100 | 0.113550 | − | 0.993532i | \(-0.463778\pi\) | ||||
0.113550 | + | 0.993532i | \(0.463778\pi\) | |||||||
\(948\) | −38.6647 | −1.25577 | ||||||||
\(949\) | −40.2252 | −1.30576 | ||||||||
\(950\) | 16.0999 | 0.522351 | ||||||||
\(951\) | −5.91072 | −0.191668 | ||||||||
\(952\) | 36.5435 | 1.18438 | ||||||||
\(953\) | 16.5590 | 0.536399 | 0.268199 | − | 0.963363i | \(-0.413571\pi\) | ||||
0.268199 | + | 0.963363i | \(0.413571\pi\) | |||||||
\(954\) | −35.0209 | −1.13384 | ||||||||
\(955\) | −18.4350 | −0.596544 | ||||||||
\(956\) | −89.0265 | −2.87932 | ||||||||
\(957\) | 1.12310 | 0.0363047 | ||||||||
\(958\) | 77.1913 | 2.49394 | ||||||||
\(959\) | 57.3870 | 1.85312 | ||||||||
\(960\) | 48.8262 | 1.57586 | ||||||||
\(961\) | 27.9824 | 0.902657 | ||||||||
\(962\) | −50.3372 | −1.62294 | ||||||||
\(963\) | 28.6542 | 0.923370 | ||||||||
\(964\) | 115.899 | 3.73286 | ||||||||
\(965\) | −12.8716 | −0.414353 | ||||||||
\(966\) | 9.45062 | 0.304069 | ||||||||
\(967\) | 30.3934 | 0.977387 | 0.488693 | − | 0.872456i | \(-0.337474\pi\) | ||||
0.488693 | + | 0.872456i | \(0.337474\pi\) | |||||||
\(968\) | 1.13905 | 0.0366103 | ||||||||
\(969\) | 1.01203 | 0.0325111 | ||||||||
\(970\) | −38.6280 | −1.24027 | ||||||||
\(971\) | −11.9447 | −0.383323 | −0.191662 | − | 0.981461i | \(-0.561388\pi\) | ||||
−0.191662 | + | 0.981461i | \(0.561388\pi\) | |||||||
\(972\) | −63.2572 | −2.02898 | ||||||||
\(973\) | 84.3952 | 2.70559 | ||||||||
\(974\) | 59.3287 | 1.90101 | ||||||||
\(975\) | 3.44152 | 0.110217 | ||||||||
\(976\) | 175.296 | 5.61107 | ||||||||
\(977\) | −38.2074 | −1.22236 | −0.611181 | − | 0.791491i | \(-0.709305\pi\) | ||||
−0.611181 | + | 0.791491i | \(0.709305\pi\) | |||||||
\(978\) | −13.5818 | −0.434297 | ||||||||
\(979\) | 28.4699 | 0.909903 | ||||||||
\(980\) | −100.412 | −3.20755 | ||||||||
\(981\) | −8.90210 | −0.284222 | ||||||||
\(982\) | −44.2317 | −1.41149 | ||||||||
\(983\) | 22.3415 | 0.712583 | 0.356292 | − | 0.934375i | \(-0.384041\pi\) | ||||
0.356292 | + | 0.934375i | \(0.384041\pi\) | |||||||
\(984\) | 21.2045 | 0.675975 | ||||||||
\(985\) | −32.2392 | −1.02723 | ||||||||
\(986\) | −2.03544 | −0.0648215 | ||||||||
\(987\) | −2.10543 | −0.0670165 | ||||||||
\(988\) | 38.3480 | 1.22001 | ||||||||
\(989\) | −8.44975 | −0.268686 | ||||||||
\(990\) | 70.1884 | 2.23073 | ||||||||
\(991\) | −21.0809 | −0.669657 | −0.334829 | − | 0.942279i | \(-0.608678\pi\) | ||||
−0.334829 | + | 0.942279i | \(0.608678\pi\) | |||||||
\(992\) | −201.897 | −6.41023 | ||||||||
\(993\) | −7.98539 | −0.253409 | ||||||||
\(994\) | −46.2260 | −1.46620 | ||||||||
\(995\) | −43.6231 | −1.38295 | ||||||||
\(996\) | −4.61610 | −0.146267 | ||||||||
\(997\) | −12.8127 | −0.405781 | −0.202890 | − | 0.979201i | \(-0.565034\pi\) | ||||
−0.202890 | + | 0.979201i | \(0.565034\pi\) | |||||||
\(998\) | 70.3069 | 2.22553 | ||||||||
\(999\) | −16.0893 | −0.509043 |
(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 | 5077.2.a.b.1.5 | ✓ | 205 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
5077.2.a.b.1.5 | ✓ | 205 | 1.1 | even | 1 | trivial |