Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8026,2,Mod(1,8026)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8026, 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("8026.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8026 = 2 \cdot 4013 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8026.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(64.0879326623\) |
Analytic rank: | \(0\) |
Dimension: | \(96\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.12 | ||
Character | \(\chi\) | \(=\) | 8026.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | −2.75991 | −1.59344 | −0.796718 | − | 0.604351i | \(-0.793432\pi\) | ||||
−0.796718 | + | 0.604351i | \(0.793432\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 1.94869 | 0.871483 | 0.435741 | − | 0.900072i | \(-0.356486\pi\) | ||||
0.435741 | + | 0.900072i | \(0.356486\pi\) | |||||||
\(6\) | −2.75991 | −1.12673 | ||||||||
\(7\) | −1.07781 | −0.407375 | −0.203688 | − | 0.979036i | \(-0.565293\pi\) | ||||
−0.203688 | + | 0.979036i | \(0.565293\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 4.61711 | 1.53904 | ||||||||
\(10\) | 1.94869 | 0.616231 | ||||||||
\(11\) | −0.979671 | −0.295382 | −0.147691 | − | 0.989034i | \(-0.547184\pi\) | ||||
−0.147691 | + | 0.989034i | \(0.547184\pi\) | |||||||
\(12\) | −2.75991 | −0.796718 | ||||||||
\(13\) | 2.80600 | 0.778243 | 0.389122 | − | 0.921186i | \(-0.372779\pi\) | ||||
0.389122 | + | 0.921186i | \(0.372779\pi\) | |||||||
\(14\) | −1.07781 | −0.288058 | ||||||||
\(15\) | −5.37822 | −1.38865 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 6.13809 | 1.48870 | 0.744352 | − | 0.667787i | \(-0.232758\pi\) | ||||
0.744352 | + | 0.667787i | \(0.232758\pi\) | |||||||
\(18\) | 4.61711 | 1.08826 | ||||||||
\(19\) | −5.84597 | −1.34116 | −0.670579 | − | 0.741839i | \(-0.733954\pi\) | ||||
−0.670579 | + | 0.741839i | \(0.733954\pi\) | |||||||
\(20\) | 1.94869 | 0.435741 | ||||||||
\(21\) | 2.97467 | 0.649127 | ||||||||
\(22\) | −0.979671 | −0.208867 | ||||||||
\(23\) | 0.812960 | 0.169514 | 0.0847569 | − | 0.996402i | \(-0.472989\pi\) | ||||
0.0847569 | + | 0.996402i | \(0.472989\pi\) | |||||||
\(24\) | −2.75991 | −0.563365 | ||||||||
\(25\) | −1.20259 | −0.240518 | ||||||||
\(26\) | 2.80600 | 0.550301 | ||||||||
\(27\) | −4.46309 | −0.858922 | ||||||||
\(28\) | −1.07781 | −0.203688 | ||||||||
\(29\) | 6.89766 | 1.28086 | 0.640431 | − | 0.768016i | \(-0.278756\pi\) | ||||
0.640431 | + | 0.768016i | \(0.278756\pi\) | |||||||
\(30\) | −5.37822 | −0.981925 | ||||||||
\(31\) | 2.82331 | 0.507081 | 0.253540 | − | 0.967325i | \(-0.418405\pi\) | ||||
0.253540 | + | 0.967325i | \(0.418405\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 2.70381 | 0.470672 | ||||||||
\(34\) | 6.13809 | 1.05267 | ||||||||
\(35\) | −2.10033 | −0.355021 | ||||||||
\(36\) | 4.61711 | 0.769519 | ||||||||
\(37\) | 2.48058 | 0.407804 | 0.203902 | − | 0.978991i | \(-0.434638\pi\) | ||||
0.203902 | + | 0.978991i | \(0.434638\pi\) | |||||||
\(38\) | −5.84597 | −0.948341 | ||||||||
\(39\) | −7.74430 | −1.24008 | ||||||||
\(40\) | 1.94869 | 0.308116 | ||||||||
\(41\) | 9.53441 | 1.48903 | 0.744513 | − | 0.667608i | \(-0.232682\pi\) | ||||
0.744513 | + | 0.667608i | \(0.232682\pi\) | |||||||
\(42\) | 2.97467 | 0.459002 | ||||||||
\(43\) | −11.3478 | −1.73052 | −0.865261 | − | 0.501321i | \(-0.832848\pi\) | ||||
−0.865261 | + | 0.501321i | \(0.832848\pi\) | |||||||
\(44\) | −0.979671 | −0.147691 | ||||||||
\(45\) | 8.99734 | 1.34124 | ||||||||
\(46\) | 0.812960 | 0.119864 | ||||||||
\(47\) | 6.34815 | 0.925973 | 0.462986 | − | 0.886365i | \(-0.346778\pi\) | ||||
0.462986 | + | 0.886365i | \(0.346778\pi\) | |||||||
\(48\) | −2.75991 | −0.398359 | ||||||||
\(49\) | −5.83832 | −0.834045 | ||||||||
\(50\) | −1.20259 | −0.170072 | ||||||||
\(51\) | −16.9406 | −2.37216 | ||||||||
\(52\) | 2.80600 | 0.389122 | ||||||||
\(53\) | −2.87238 | −0.394551 | −0.197276 | − | 0.980348i | \(-0.563209\pi\) | ||||
−0.197276 | + | 0.980348i | \(0.563209\pi\) | |||||||
\(54\) | −4.46309 | −0.607350 | ||||||||
\(55\) | −1.90908 | −0.257420 | ||||||||
\(56\) | −1.07781 | −0.144029 | ||||||||
\(57\) | 16.1344 | 2.13705 | ||||||||
\(58\) | 6.89766 | 0.905707 | ||||||||
\(59\) | −11.5474 | −1.50334 | −0.751670 | − | 0.659539i | \(-0.770751\pi\) | ||||
−0.751670 | + | 0.659539i | \(0.770751\pi\) | |||||||
\(60\) | −5.37822 | −0.694326 | ||||||||
\(61\) | −1.18561 | −0.151802 | −0.0759009 | − | 0.997115i | \(-0.524183\pi\) | ||||
−0.0759009 | + | 0.997115i | \(0.524183\pi\) | |||||||
\(62\) | 2.82331 | 0.358560 | ||||||||
\(63\) | −4.97639 | −0.626966 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 5.46803 | 0.678225 | ||||||||
\(66\) | 2.70381 | 0.332816 | ||||||||
\(67\) | 12.4222 | 1.51761 | 0.758806 | − | 0.651317i | \(-0.225783\pi\) | ||||
0.758806 | + | 0.651317i | \(0.225783\pi\) | |||||||
\(68\) | 6.13809 | 0.744352 | ||||||||
\(69\) | −2.24370 | −0.270109 | ||||||||
\(70\) | −2.10033 | −0.251037 | ||||||||
\(71\) | 0.804562 | 0.0954840 | 0.0477420 | − | 0.998860i | \(-0.484797\pi\) | ||||
0.0477420 | + | 0.998860i | \(0.484797\pi\) | |||||||
\(72\) | 4.61711 | 0.544132 | ||||||||
\(73\) | −1.00335 | −0.117433 | −0.0587165 | − | 0.998275i | \(-0.518701\pi\) | ||||
−0.0587165 | + | 0.998275i | \(0.518701\pi\) | |||||||
\(74\) | 2.48058 | 0.288361 | ||||||||
\(75\) | 3.31904 | 0.383250 | ||||||||
\(76\) | −5.84597 | −0.670579 | ||||||||
\(77\) | 1.05590 | 0.120331 | ||||||||
\(78\) | −7.74430 | −0.876870 | ||||||||
\(79\) | 17.3763 | 1.95499 | 0.977494 | − | 0.210965i | \(-0.0676605\pi\) | ||||
0.977494 | + | 0.210965i | \(0.0676605\pi\) | |||||||
\(80\) | 1.94869 | 0.217871 | ||||||||
\(81\) | −1.53360 | −0.170400 | ||||||||
\(82\) | 9.53441 | 1.05290 | ||||||||
\(83\) | −13.6050 | −1.49334 | −0.746672 | − | 0.665193i | \(-0.768349\pi\) | ||||
−0.746672 | + | 0.665193i | \(0.768349\pi\) | |||||||
\(84\) | 2.97467 | 0.324563 | ||||||||
\(85\) | 11.9613 | 1.29738 | ||||||||
\(86\) | −11.3478 | −1.22366 | ||||||||
\(87\) | −19.0369 | −2.04097 | ||||||||
\(88\) | −0.979671 | −0.104433 | ||||||||
\(89\) | 4.49866 | 0.476857 | 0.238429 | − | 0.971160i | \(-0.423368\pi\) | ||||
0.238429 | + | 0.971160i | \(0.423368\pi\) | |||||||
\(90\) | 8.99734 | 0.948403 | ||||||||
\(91\) | −3.02434 | −0.317037 | ||||||||
\(92\) | 0.812960 | 0.0847569 | ||||||||
\(93\) | −7.79208 | −0.808001 | ||||||||
\(94\) | 6.34815 | 0.654762 | ||||||||
\(95\) | −11.3920 | −1.16879 | ||||||||
\(96\) | −2.75991 | −0.281682 | ||||||||
\(97\) | 6.91840 | 0.702457 | 0.351228 | − | 0.936290i | \(-0.385764\pi\) | ||||
0.351228 | + | 0.936290i | \(0.385764\pi\) | |||||||
\(98\) | −5.83832 | −0.589759 | ||||||||
\(99\) | −4.52325 | −0.454604 | ||||||||
\(100\) | −1.20259 | −0.120259 | ||||||||
\(101\) | 15.8733 | 1.57946 | 0.789728 | − | 0.613457i | \(-0.210222\pi\) | ||||
0.789728 | + | 0.613457i | \(0.210222\pi\) | |||||||
\(102\) | −16.9406 | −1.67737 | ||||||||
\(103\) | −6.02551 | −0.593711 | −0.296855 | − | 0.954922i | \(-0.595938\pi\) | ||||
−0.296855 | + | 0.954922i | \(0.595938\pi\) | |||||||
\(104\) | 2.80600 | 0.275151 | ||||||||
\(105\) | 5.79673 | 0.565703 | ||||||||
\(106\) | −2.87238 | −0.278990 | ||||||||
\(107\) | 3.14456 | 0.303996 | 0.151998 | − | 0.988381i | \(-0.451429\pi\) | ||||
0.151998 | + | 0.988381i | \(0.451429\pi\) | |||||||
\(108\) | −4.46309 | −0.429461 | ||||||||
\(109\) | 5.80426 | 0.555947 | 0.277974 | − | 0.960589i | \(-0.410337\pi\) | ||||
0.277974 | + | 0.960589i | \(0.410337\pi\) | |||||||
\(110\) | −1.90908 | −0.182024 | ||||||||
\(111\) | −6.84617 | −0.649810 | ||||||||
\(112\) | −1.07781 | −0.101844 | ||||||||
\(113\) | 6.71337 | 0.631541 | 0.315771 | − | 0.948836i | \(-0.397737\pi\) | ||||
0.315771 | + | 0.948836i | \(0.397737\pi\) | |||||||
\(114\) | 16.1344 | 1.51112 | ||||||||
\(115\) | 1.58421 | 0.147728 | ||||||||
\(116\) | 6.89766 | 0.640431 | ||||||||
\(117\) | 12.9556 | 1.19775 | ||||||||
\(118\) | −11.5474 | −1.06302 | ||||||||
\(119\) | −6.61572 | −0.606462 | ||||||||
\(120\) | −5.37822 | −0.490962 | ||||||||
\(121\) | −10.0402 | −0.912749 | ||||||||
\(122\) | −1.18561 | −0.107340 | ||||||||
\(123\) | −26.3141 | −2.37267 | ||||||||
\(124\) | 2.82331 | 0.253540 | ||||||||
\(125\) | −12.0870 | −1.08109 | ||||||||
\(126\) | −4.97639 | −0.443332 | ||||||||
\(127\) | 10.3462 | 0.918075 | 0.459038 | − | 0.888417i | \(-0.348194\pi\) | ||||
0.459038 | + | 0.888417i | \(0.348194\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 31.3189 | 2.75748 | ||||||||
\(130\) | 5.46803 | 0.479578 | ||||||||
\(131\) | −20.9417 | −1.82968 | −0.914841 | − | 0.403815i | \(-0.867684\pi\) | ||||
−0.914841 | + | 0.403815i | \(0.867684\pi\) | |||||||
\(132\) | 2.70381 | 0.235336 | ||||||||
\(133\) | 6.30087 | 0.546354 | ||||||||
\(134\) | 12.4222 | 1.07311 | ||||||||
\(135\) | −8.69720 | −0.748536 | ||||||||
\(136\) | 6.13809 | 0.526337 | ||||||||
\(137\) | −13.9708 | −1.19360 | −0.596801 | − | 0.802389i | \(-0.703562\pi\) | ||||
−0.596801 | + | 0.802389i | \(0.703562\pi\) | |||||||
\(138\) | −2.24370 | −0.190996 | ||||||||
\(139\) | 11.5737 | 0.981668 | 0.490834 | − | 0.871253i | \(-0.336692\pi\) | ||||
0.490834 | + | 0.871253i | \(0.336692\pi\) | |||||||
\(140\) | −2.10033 | −0.177510 | ||||||||
\(141\) | −17.5203 | −1.47548 | ||||||||
\(142\) | 0.804562 | 0.0675174 | ||||||||
\(143\) | −2.74895 | −0.229879 | ||||||||
\(144\) | 4.61711 | 0.384759 | ||||||||
\(145\) | 13.4414 | 1.11625 | ||||||||
\(146\) | −1.00335 | −0.0830377 | ||||||||
\(147\) | 16.1132 | 1.32900 | ||||||||
\(148\) | 2.48058 | 0.203902 | ||||||||
\(149\) | −20.9446 | −1.71585 | −0.857925 | − | 0.513774i | \(-0.828247\pi\) | ||||
−0.857925 | + | 0.513774i | \(0.828247\pi\) | |||||||
\(150\) | 3.31904 | 0.270999 | ||||||||
\(151\) | 16.3586 | 1.33124 | 0.665621 | − | 0.746290i | \(-0.268167\pi\) | ||||
0.665621 | + | 0.746290i | \(0.268167\pi\) | |||||||
\(152\) | −5.84597 | −0.474171 | ||||||||
\(153\) | 28.3402 | 2.29117 | ||||||||
\(154\) | 1.05590 | 0.0850871 | ||||||||
\(155\) | 5.50176 | 0.441912 | ||||||||
\(156\) | −7.74430 | −0.620040 | ||||||||
\(157\) | 10.0426 | 0.801484 | 0.400742 | − | 0.916191i | \(-0.368752\pi\) | ||||
0.400742 | + | 0.916191i | \(0.368752\pi\) | |||||||
\(158\) | 17.3763 | 1.38238 | ||||||||
\(159\) | 7.92750 | 0.628692 | ||||||||
\(160\) | 1.94869 | 0.154058 | ||||||||
\(161\) | −0.876220 | −0.0690558 | ||||||||
\(162\) | −1.53360 | −0.120491 | ||||||||
\(163\) | 11.6883 | 0.915502 | 0.457751 | − | 0.889081i | \(-0.348655\pi\) | ||||
0.457751 | + | 0.889081i | \(0.348655\pi\) | |||||||
\(164\) | 9.53441 | 0.744513 | ||||||||
\(165\) | 5.26889 | 0.410183 | ||||||||
\(166\) | −13.6050 | −1.05595 | ||||||||
\(167\) | 8.90188 | 0.688848 | 0.344424 | − | 0.938814i | \(-0.388074\pi\) | ||||
0.344424 | + | 0.938814i | \(0.388074\pi\) | |||||||
\(168\) | 2.97467 | 0.229501 | ||||||||
\(169\) | −5.12639 | −0.394337 | ||||||||
\(170\) | 11.9613 | 0.917386 | ||||||||
\(171\) | −26.9915 | −2.06409 | ||||||||
\(172\) | −11.3478 | −0.865261 | ||||||||
\(173\) | −23.5687 | −1.79190 | −0.895949 | − | 0.444156i | \(-0.853504\pi\) | ||||
−0.895949 | + | 0.444156i | \(0.853504\pi\) | |||||||
\(174\) | −19.0369 | −1.44319 | ||||||||
\(175\) | 1.29617 | 0.0979812 | ||||||||
\(176\) | −0.979671 | −0.0738455 | ||||||||
\(177\) | 31.8697 | 2.39548 | ||||||||
\(178\) | 4.49866 | 0.337189 | ||||||||
\(179\) | −0.131051 | −0.00979525 | −0.00489762 | − | 0.999988i | \(-0.501559\pi\) | ||||
−0.00489762 | + | 0.999988i | \(0.501559\pi\) | |||||||
\(180\) | 8.99734 | 0.670622 | ||||||||
\(181\) | 2.51657 | 0.187055 | 0.0935274 | − | 0.995617i | \(-0.470186\pi\) | ||||
0.0935274 | + | 0.995617i | \(0.470186\pi\) | |||||||
\(182\) | −3.02434 | −0.224179 | ||||||||
\(183\) | 3.27218 | 0.241886 | ||||||||
\(184\) | 0.812960 | 0.0599322 | ||||||||
\(185\) | 4.83388 | 0.355394 | ||||||||
\(186\) | −7.79208 | −0.571343 | ||||||||
\(187\) | −6.01331 | −0.439737 | ||||||||
\(188\) | 6.34815 | 0.462986 | ||||||||
\(189\) | 4.81038 | 0.349904 | ||||||||
\(190\) | −11.3920 | −0.826463 | ||||||||
\(191\) | 7.60721 | 0.550438 | 0.275219 | − | 0.961382i | \(-0.411250\pi\) | ||||
0.275219 | + | 0.961382i | \(0.411250\pi\) | |||||||
\(192\) | −2.75991 | −0.199179 | ||||||||
\(193\) | 8.64913 | 0.622578 | 0.311289 | − | 0.950315i | \(-0.399239\pi\) | ||||
0.311289 | + | 0.950315i | \(0.399239\pi\) | |||||||
\(194\) | 6.91840 | 0.496712 | ||||||||
\(195\) | −15.0913 | −1.08071 | ||||||||
\(196\) | −5.83832 | −0.417023 | ||||||||
\(197\) | −3.46928 | −0.247176 | −0.123588 | − | 0.992334i | \(-0.539440\pi\) | ||||
−0.123588 | + | 0.992334i | \(0.539440\pi\) | |||||||
\(198\) | −4.52325 | −0.321454 | ||||||||
\(199\) | −6.46451 | −0.458257 | −0.229128 | − | 0.973396i | \(-0.573588\pi\) | ||||
−0.229128 | + | 0.973396i | \(0.573588\pi\) | |||||||
\(200\) | −1.20259 | −0.0850360 | ||||||||
\(201\) | −34.2842 | −2.41822 | ||||||||
\(202\) | 15.8733 | 1.11684 | ||||||||
\(203\) | −7.43439 | −0.521792 | ||||||||
\(204\) | −16.9406 | −1.18608 | ||||||||
\(205\) | 18.5797 | 1.29766 | ||||||||
\(206\) | −6.02551 | −0.419817 | ||||||||
\(207\) | 3.75353 | 0.260888 | ||||||||
\(208\) | 2.80600 | 0.194561 | ||||||||
\(209\) | 5.72713 | 0.396154 | ||||||||
\(210\) | 5.79673 | 0.400012 | ||||||||
\(211\) | 20.1627 | 1.38806 | 0.694030 | − | 0.719946i | \(-0.255833\pi\) | ||||
0.694030 | + | 0.719946i | \(0.255833\pi\) | |||||||
\(212\) | −2.87238 | −0.197276 | ||||||||
\(213\) | −2.22052 | −0.152148 | ||||||||
\(214\) | 3.14456 | 0.214958 | ||||||||
\(215\) | −22.1134 | −1.50812 | ||||||||
\(216\) | −4.46309 | −0.303675 | ||||||||
\(217\) | −3.04300 | −0.206572 | ||||||||
\(218\) | 5.80426 | 0.393114 | ||||||||
\(219\) | 2.76915 | 0.187122 | ||||||||
\(220\) | −1.90908 | −0.128710 | ||||||||
\(221\) | 17.2234 | 1.15857 | ||||||||
\(222\) | −6.84617 | −0.459485 | ||||||||
\(223\) | −2.31323 | −0.154905 | −0.0774525 | − | 0.996996i | \(-0.524679\pi\) | ||||
−0.0774525 | + | 0.996996i | \(0.524679\pi\) | |||||||
\(224\) | −1.07781 | −0.0720145 | ||||||||
\(225\) | −5.55250 | −0.370167 | ||||||||
\(226\) | 6.71337 | 0.446567 | ||||||||
\(227\) | 19.3373 | 1.28346 | 0.641731 | − | 0.766929i | \(-0.278216\pi\) | ||||
0.641731 | + | 0.766929i | \(0.278216\pi\) | |||||||
\(228\) | 16.1344 | 1.06852 | ||||||||
\(229\) | −24.3476 | −1.60894 | −0.804469 | − | 0.593995i | \(-0.797550\pi\) | ||||
−0.804469 | + | 0.593995i | \(0.797550\pi\) | |||||||
\(230\) | 1.58421 | 0.104460 | ||||||||
\(231\) | −2.91420 | −0.191740 | ||||||||
\(232\) | 6.89766 | 0.452853 | ||||||||
\(233\) | 17.8808 | 1.17141 | 0.585706 | − | 0.810523i | \(-0.300817\pi\) | ||||
0.585706 | + | 0.810523i | \(0.300817\pi\) | |||||||
\(234\) | 12.9556 | 0.846934 | ||||||||
\(235\) | 12.3706 | 0.806969 | ||||||||
\(236\) | −11.5474 | −0.751670 | ||||||||
\(237\) | −47.9571 | −3.11515 | ||||||||
\(238\) | −6.61572 | −0.428833 | ||||||||
\(239\) | −2.47497 | −0.160093 | −0.0800464 | − | 0.996791i | \(-0.525507\pi\) | ||||
−0.0800464 | + | 0.996791i | \(0.525507\pi\) | |||||||
\(240\) | −5.37822 | −0.347163 | ||||||||
\(241\) | 16.3687 | 1.05440 | 0.527199 | − | 0.849742i | \(-0.323242\pi\) | ||||
0.527199 | + | 0.849742i | \(0.323242\pi\) | |||||||
\(242\) | −10.0402 | −0.645411 | ||||||||
\(243\) | 17.6219 | 1.13044 | ||||||||
\(244\) | −1.18561 | −0.0759009 | ||||||||
\(245\) | −11.3771 | −0.726856 | ||||||||
\(246\) | −26.3141 | −1.67773 | ||||||||
\(247\) | −16.4038 | −1.04375 | ||||||||
\(248\) | 2.82331 | 0.179280 | ||||||||
\(249\) | 37.5486 | 2.37955 | ||||||||
\(250\) | −12.0870 | −0.764446 | ||||||||
\(251\) | −17.8088 | −1.12408 | −0.562042 | − | 0.827109i | \(-0.689984\pi\) | ||||
−0.562042 | + | 0.827109i | \(0.689984\pi\) | |||||||
\(252\) | −4.97639 | −0.313483 | ||||||||
\(253\) | −0.796433 | −0.0500713 | ||||||||
\(254\) | 10.3462 | 0.649177 | ||||||||
\(255\) | −33.0120 | −2.06729 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 8.77644 | 0.547460 | 0.273730 | − | 0.961807i | \(-0.411743\pi\) | ||||
0.273730 | + | 0.961807i | \(0.411743\pi\) | |||||||
\(258\) | 31.3189 | 1.94983 | ||||||||
\(259\) | −2.67360 | −0.166129 | ||||||||
\(260\) | 5.46803 | 0.339113 | ||||||||
\(261\) | 31.8473 | 1.97130 | ||||||||
\(262\) | −20.9417 | −1.29378 | ||||||||
\(263\) | −5.38526 | −0.332070 | −0.166035 | − | 0.986120i | \(-0.553096\pi\) | ||||
−0.166035 | + | 0.986120i | \(0.553096\pi\) | |||||||
\(264\) | 2.70381 | 0.166408 | ||||||||
\(265\) | −5.59738 | −0.343844 | ||||||||
\(266\) | 6.30087 | 0.386331 | ||||||||
\(267\) | −12.4159 | −0.759842 | ||||||||
\(268\) | 12.4222 | 0.758806 | ||||||||
\(269\) | −4.20717 | −0.256516 | −0.128258 | − | 0.991741i | \(-0.540939\pi\) | ||||
−0.128258 | + | 0.991741i | \(0.540939\pi\) | |||||||
\(270\) | −8.69720 | −0.529295 | ||||||||
\(271\) | 27.9024 | 1.69495 | 0.847474 | − | 0.530836i | \(-0.178122\pi\) | ||||
0.847474 | + | 0.530836i | \(0.178122\pi\) | |||||||
\(272\) | 6.13809 | 0.372176 | ||||||||
\(273\) | 8.34692 | 0.505178 | ||||||||
\(274\) | −13.9708 | −0.844004 | ||||||||
\(275\) | 1.17814 | 0.0710447 | ||||||||
\(276\) | −2.24370 | −0.135055 | ||||||||
\(277\) | −5.19763 | −0.312295 | −0.156148 | − | 0.987734i | \(-0.549908\pi\) | ||||
−0.156148 | + | 0.987734i | \(0.549908\pi\) | |||||||
\(278\) | 11.5737 | 0.694144 | ||||||||
\(279\) | 13.0355 | 0.780417 | ||||||||
\(280\) | −2.10033 | −0.125519 | ||||||||
\(281\) | 0.149335 | 0.00890861 | 0.00445430 | − | 0.999990i | \(-0.498582\pi\) | ||||
0.00445430 | + | 0.999990i | \(0.498582\pi\) | |||||||
\(282\) | −17.5203 | −1.04332 | ||||||||
\(283\) | 3.98574 | 0.236928 | 0.118464 | − | 0.992958i | \(-0.462203\pi\) | ||||
0.118464 | + | 0.992958i | \(0.462203\pi\) | |||||||
\(284\) | 0.804562 | 0.0477420 | ||||||||
\(285\) | 31.4409 | 1.86240 | ||||||||
\(286\) | −2.74895 | −0.162549 | ||||||||
\(287\) | −10.2763 | −0.606592 | ||||||||
\(288\) | 4.61711 | 0.272066 | ||||||||
\(289\) | 20.6761 | 1.21624 | ||||||||
\(290\) | 13.4414 | 0.789307 | ||||||||
\(291\) | −19.0942 | −1.11932 | ||||||||
\(292\) | −1.00335 | −0.0587165 | ||||||||
\(293\) | 13.0709 | 0.763611 | 0.381805 | − | 0.924243i | \(-0.375302\pi\) | ||||
0.381805 | + | 0.924243i | \(0.375302\pi\) | |||||||
\(294\) | 16.1132 | 0.939743 | ||||||||
\(295\) | −22.5023 | −1.31013 | ||||||||
\(296\) | 2.48058 | 0.144181 | ||||||||
\(297\) | 4.37236 | 0.253710 | ||||||||
\(298\) | −20.9446 | −1.21329 | ||||||||
\(299\) | 2.28116 | 0.131923 | ||||||||
\(300\) | 3.31904 | 0.191625 | ||||||||
\(301\) | 12.2308 | 0.704973 | ||||||||
\(302\) | 16.3586 | 0.941331 | ||||||||
\(303\) | −43.8090 | −2.51676 | ||||||||
\(304\) | −5.84597 | −0.335289 | ||||||||
\(305\) | −2.31039 | −0.132293 | ||||||||
\(306\) | 28.3402 | 1.62010 | ||||||||
\(307\) | 26.2437 | 1.49781 | 0.748905 | − | 0.662678i | \(-0.230580\pi\) | ||||
0.748905 | + | 0.662678i | \(0.230580\pi\) | |||||||
\(308\) | 1.05590 | 0.0601657 | ||||||||
\(309\) | 16.6299 | 0.946040 | ||||||||
\(310\) | 5.50176 | 0.312479 | ||||||||
\(311\) | 16.4523 | 0.932923 | 0.466461 | − | 0.884542i | \(-0.345529\pi\) | ||||
0.466461 | + | 0.884542i | \(0.345529\pi\) | |||||||
\(312\) | −7.74430 | −0.438435 | ||||||||
\(313\) | −12.2007 | −0.689624 | −0.344812 | − | 0.938672i | \(-0.612057\pi\) | ||||
−0.344812 | + | 0.938672i | \(0.612057\pi\) | |||||||
\(314\) | 10.0426 | 0.566735 | ||||||||
\(315\) | −9.69746 | −0.546390 | ||||||||
\(316\) | 17.3763 | 0.977494 | ||||||||
\(317\) | 1.51828 | 0.0852749 | 0.0426374 | − | 0.999091i | \(-0.486424\pi\) | ||||
0.0426374 | + | 0.999091i | \(0.486424\pi\) | |||||||
\(318\) | 7.92750 | 0.444552 | ||||||||
\(319\) | −6.75743 | −0.378344 | ||||||||
\(320\) | 1.94869 | 0.108935 | ||||||||
\(321\) | −8.67871 | −0.484399 | ||||||||
\(322\) | −0.876220 | −0.0488298 | ||||||||
\(323\) | −35.8831 | −1.99659 | ||||||||
\(324\) | −1.53360 | −0.0852002 | ||||||||
\(325\) | −3.37446 | −0.187182 | ||||||||
\(326\) | 11.6883 | 0.647357 | ||||||||
\(327\) | −16.0192 | −0.885866 | ||||||||
\(328\) | 9.53441 | 0.526450 | ||||||||
\(329\) | −6.84213 | −0.377219 | ||||||||
\(330\) | 5.26889 | 0.290043 | ||||||||
\(331\) | 29.2707 | 1.60886 | 0.804432 | − | 0.594045i | \(-0.202470\pi\) | ||||
0.804432 | + | 0.594045i | \(0.202470\pi\) | |||||||
\(332\) | −13.6050 | −0.746672 | ||||||||
\(333\) | 11.4531 | 0.627626 | ||||||||
\(334\) | 8.90188 | 0.487089 | ||||||||
\(335\) | 24.2071 | 1.32257 | ||||||||
\(336\) | 2.97467 | 0.162282 | ||||||||
\(337\) | −16.3957 | −0.893131 | −0.446565 | − | 0.894751i | \(-0.647353\pi\) | ||||
−0.446565 | + | 0.894751i | \(0.647353\pi\) | |||||||
\(338\) | −5.12639 | −0.278839 | ||||||||
\(339\) | −18.5283 | −1.00632 | ||||||||
\(340\) | 11.9613 | 0.648690 | ||||||||
\(341\) | −2.76591 | −0.149783 | ||||||||
\(342\) | −26.9915 | −1.45953 | ||||||||
\(343\) | 13.8373 | 0.747145 | ||||||||
\(344\) | −11.3478 | −0.611832 | ||||||||
\(345\) | −4.37228 | −0.235396 | ||||||||
\(346\) | −23.5687 | −1.26706 | ||||||||
\(347\) | 32.4629 | 1.74270 | 0.871349 | − | 0.490664i | \(-0.163246\pi\) | ||||
0.871349 | + | 0.490664i | \(0.163246\pi\) | |||||||
\(348\) | −19.0369 | −1.02049 | ||||||||
\(349\) | 9.69041 | 0.518716 | 0.259358 | − | 0.965781i | \(-0.416489\pi\) | ||||
0.259358 | + | 0.965781i | \(0.416489\pi\) | |||||||
\(350\) | 1.29617 | 0.0692832 | ||||||||
\(351\) | −12.5234 | −0.668450 | ||||||||
\(352\) | −0.979671 | −0.0522166 | ||||||||
\(353\) | 17.9689 | 0.956389 | 0.478195 | − | 0.878254i | \(-0.341291\pi\) | ||||
0.478195 | + | 0.878254i | \(0.341291\pi\) | |||||||
\(354\) | 31.8697 | 1.69386 | ||||||||
\(355\) | 1.56785 | 0.0832126 | ||||||||
\(356\) | 4.49866 | 0.238429 | ||||||||
\(357\) | 18.2588 | 0.966358 | ||||||||
\(358\) | −0.131051 | −0.00692628 | ||||||||
\(359\) | 1.40738 | 0.0742787 | 0.0371394 | − | 0.999310i | \(-0.488175\pi\) | ||||
0.0371394 | + | 0.999310i | \(0.488175\pi\) | |||||||
\(360\) | 8.99734 | 0.474202 | ||||||||
\(361\) | 15.1753 | 0.798702 | ||||||||
\(362\) | 2.51657 | 0.132268 | ||||||||
\(363\) | 27.7102 | 1.45441 | ||||||||
\(364\) | −3.02434 | −0.158519 | ||||||||
\(365\) | −1.95522 | −0.102341 | ||||||||
\(366\) | 3.27218 | 0.171040 | ||||||||
\(367\) | −0.423661 | −0.0221149 | −0.0110575 | − | 0.999939i | \(-0.503520\pi\) | ||||
−0.0110575 | + | 0.999939i | \(0.503520\pi\) | |||||||
\(368\) | 0.812960 | 0.0423785 | ||||||||
\(369\) | 44.0215 | 2.29167 | ||||||||
\(370\) | 4.83388 | 0.251302 | ||||||||
\(371\) | 3.09589 | 0.160730 | ||||||||
\(372\) | −7.79208 | −0.404000 | ||||||||
\(373\) | 6.59142 | 0.341291 | 0.170645 | − | 0.985332i | \(-0.445415\pi\) | ||||
0.170645 | + | 0.985332i | \(0.445415\pi\) | |||||||
\(374\) | −6.01331 | −0.310941 | ||||||||
\(375\) | 33.3589 | 1.72265 | ||||||||
\(376\) | 6.34815 | 0.327381 | ||||||||
\(377\) | 19.3548 | 0.996823 | ||||||||
\(378\) | 4.81038 | 0.247419 | ||||||||
\(379\) | 10.1493 | 0.521334 | 0.260667 | − | 0.965429i | \(-0.416057\pi\) | ||||
0.260667 | + | 0.965429i | \(0.416057\pi\) | |||||||
\(380\) | −11.3920 | −0.584397 | ||||||||
\(381\) | −28.5546 | −1.46289 | ||||||||
\(382\) | 7.60721 | 0.389219 | ||||||||
\(383\) | −30.9076 | −1.57931 | −0.789653 | − | 0.613554i | \(-0.789739\pi\) | ||||
−0.789653 | + | 0.613554i | \(0.789739\pi\) | |||||||
\(384\) | −2.75991 | −0.140841 | ||||||||
\(385\) | 2.05763 | 0.104867 | ||||||||
\(386\) | 8.64913 | 0.440229 | ||||||||
\(387\) | −52.3941 | −2.66334 | ||||||||
\(388\) | 6.91840 | 0.351228 | ||||||||
\(389\) | 22.0663 | 1.11880 | 0.559402 | − | 0.828897i | \(-0.311031\pi\) | ||||
0.559402 | + | 0.828897i | \(0.311031\pi\) | |||||||
\(390\) | −15.0913 | −0.764176 | ||||||||
\(391\) | 4.99002 | 0.252356 | ||||||||
\(392\) | −5.83832 | −0.294880 | ||||||||
\(393\) | 57.7971 | 2.91548 | ||||||||
\(394\) | −3.46928 | −0.174780 | ||||||||
\(395\) | 33.8611 | 1.70374 | ||||||||
\(396\) | −4.52325 | −0.227302 | ||||||||
\(397\) | 20.6663 | 1.03721 | 0.518607 | − | 0.855013i | \(-0.326451\pi\) | ||||
0.518607 | + | 0.855013i | \(0.326451\pi\) | |||||||
\(398\) | −6.46451 | −0.324037 | ||||||||
\(399\) | −17.3898 | −0.870581 | ||||||||
\(400\) | −1.20259 | −0.0601295 | ||||||||
\(401\) | 12.1495 | 0.606715 | 0.303357 | − | 0.952877i | \(-0.401892\pi\) | ||||
0.303357 | + | 0.952877i | \(0.401892\pi\) | |||||||
\(402\) | −34.2842 | −1.70994 | ||||||||
\(403\) | 7.92219 | 0.394632 | ||||||||
\(404\) | 15.8733 | 0.789728 | ||||||||
\(405\) | −2.98852 | −0.148501 | ||||||||
\(406\) | −7.43439 | −0.368963 | ||||||||
\(407\) | −2.43015 | −0.120458 | ||||||||
\(408\) | −16.9406 | −0.838684 | ||||||||
\(409\) | −2.08319 | −0.103007 | −0.0515037 | − | 0.998673i | \(-0.516401\pi\) | ||||
−0.0515037 | + | 0.998673i | \(0.516401\pi\) | |||||||
\(410\) | 18.5797 | 0.917584 | ||||||||
\(411\) | 38.5580 | 1.90193 | ||||||||
\(412\) | −6.02551 | −0.296855 | ||||||||
\(413\) | 12.4459 | 0.612424 | ||||||||
\(414\) | 3.75353 | 0.184476 | ||||||||
\(415\) | −26.5120 | −1.30142 | ||||||||
\(416\) | 2.80600 | 0.137575 | ||||||||
\(417\) | −31.9424 | −1.56422 | ||||||||
\(418\) | 5.72713 | 0.280123 | ||||||||
\(419\) | −30.5228 | −1.49113 | −0.745567 | − | 0.666430i | \(-0.767821\pi\) | ||||
−0.745567 | + | 0.666430i | \(0.767821\pi\) | |||||||
\(420\) | 5.79673 | 0.282851 | ||||||||
\(421\) | −34.4862 | −1.68075 | −0.840377 | − | 0.542003i | \(-0.817666\pi\) | ||||
−0.840377 | + | 0.542003i | \(0.817666\pi\) | |||||||
\(422\) | 20.1627 | 0.981507 | ||||||||
\(423\) | 29.3101 | 1.42511 | ||||||||
\(424\) | −2.87238 | −0.139495 | ||||||||
\(425\) | −7.38161 | −0.358060 | ||||||||
\(426\) | −2.22052 | −0.107585 | ||||||||
\(427\) | 1.27787 | 0.0618403 | ||||||||
\(428\) | 3.14456 | 0.151998 | ||||||||
\(429\) | 7.58687 | 0.366297 | ||||||||
\(430\) | −22.1134 | −1.06640 | ||||||||
\(431\) | −0.285310 | −0.0137429 | −0.00687145 | − | 0.999976i | \(-0.502187\pi\) | ||||
−0.00687145 | + | 0.999976i | \(0.502187\pi\) | |||||||
\(432\) | −4.46309 | −0.214731 | ||||||||
\(433\) | 9.69131 | 0.465735 | 0.232867 | − | 0.972509i | \(-0.425189\pi\) | ||||
0.232867 | + | 0.972509i | \(0.425189\pi\) | |||||||
\(434\) | −3.04300 | −0.146069 | ||||||||
\(435\) | −37.0971 | −1.77867 | ||||||||
\(436\) | 5.80426 | 0.277974 | ||||||||
\(437\) | −4.75254 | −0.227345 | ||||||||
\(438\) | 2.76915 | 0.132315 | ||||||||
\(439\) | −20.4018 | −0.973727 | −0.486863 | − | 0.873478i | \(-0.661859\pi\) | ||||
−0.486863 | + | 0.873478i | \(0.661859\pi\) | |||||||
\(440\) | −1.90908 | −0.0910118 | ||||||||
\(441\) | −26.9562 | −1.28363 | ||||||||
\(442\) | 17.2234 | 0.819236 | ||||||||
\(443\) | 16.8381 | 0.800004 | 0.400002 | − | 0.916514i | \(-0.369009\pi\) | ||||
0.400002 | + | 0.916514i | \(0.369009\pi\) | |||||||
\(444\) | −6.84617 | −0.324905 | ||||||||
\(445\) | 8.76652 | 0.415573 | ||||||||
\(446\) | −2.31323 | −0.109534 | ||||||||
\(447\) | 57.8053 | 2.73410 | ||||||||
\(448\) | −1.07781 | −0.0509219 | ||||||||
\(449\) | −31.2864 | −1.47649 | −0.738247 | − | 0.674530i | \(-0.764346\pi\) | ||||
−0.738247 | + | 0.674530i | \(0.764346\pi\) | |||||||
\(450\) | −5.55250 | −0.261747 | ||||||||
\(451\) | −9.34059 | −0.439831 | ||||||||
\(452\) | 6.71337 | 0.315771 | ||||||||
\(453\) | −45.1483 | −2.12125 | ||||||||
\(454\) | 19.3373 | 0.907545 | ||||||||
\(455\) | −5.89352 | −0.276292 | ||||||||
\(456\) | 16.1344 | 0.755560 | ||||||||
\(457\) | −20.5708 | −0.962260 | −0.481130 | − | 0.876649i | \(-0.659774\pi\) | ||||
−0.481130 | + | 0.876649i | \(0.659774\pi\) | |||||||
\(458\) | −24.3476 | −1.13769 | ||||||||
\(459\) | −27.3948 | −1.27868 | ||||||||
\(460\) | 1.58421 | 0.0738642 | ||||||||
\(461\) | 38.1200 | 1.77543 | 0.887713 | − | 0.460398i | \(-0.152293\pi\) | ||||
0.887713 | + | 0.460398i | \(0.152293\pi\) | |||||||
\(462\) | −2.91420 | −0.135581 | ||||||||
\(463\) | 4.21206 | 0.195751 | 0.0978754 | − | 0.995199i | \(-0.468795\pi\) | ||||
0.0978754 | + | 0.995199i | \(0.468795\pi\) | |||||||
\(464\) | 6.89766 | 0.320216 | ||||||||
\(465\) | −15.1844 | −0.704159 | ||||||||
\(466\) | 17.8808 | 0.828314 | ||||||||
\(467\) | 0.467726 | 0.0216438 | 0.0108219 | − | 0.999941i | \(-0.496555\pi\) | ||||
0.0108219 | + | 0.999941i | \(0.496555\pi\) | |||||||
\(468\) | 12.9556 | 0.598873 | ||||||||
\(469\) | −13.3888 | −0.618238 | ||||||||
\(470\) | 12.3706 | 0.570613 | ||||||||
\(471\) | −27.7166 | −1.27711 | ||||||||
\(472\) | −11.5474 | −0.531511 | ||||||||
\(473\) | 11.1171 | 0.511165 | ||||||||
\(474\) | −47.9571 | −2.20274 | ||||||||
\(475\) | 7.03031 | 0.322573 | ||||||||
\(476\) | −6.61572 | −0.303231 | ||||||||
\(477\) | −13.2621 | −0.607229 | ||||||||
\(478\) | −2.47497 | −0.113203 | ||||||||
\(479\) | 27.3789 | 1.25098 | 0.625488 | − | 0.780234i | \(-0.284900\pi\) | ||||
0.625488 | + | 0.780234i | \(0.284900\pi\) | |||||||
\(480\) | −5.37822 | −0.245481 | ||||||||
\(481\) | 6.96048 | 0.317371 | ||||||||
\(482\) | 16.3687 | 0.745572 | ||||||||
\(483\) | 2.41829 | 0.110036 | ||||||||
\(484\) | −10.0402 | −0.456375 | ||||||||
\(485\) | 13.4818 | 0.612179 | ||||||||
\(486\) | 17.6219 | 0.799345 | ||||||||
\(487\) | 20.9230 | 0.948112 | 0.474056 | − | 0.880495i | \(-0.342789\pi\) | ||||
0.474056 | + | 0.880495i | \(0.342789\pi\) | |||||||
\(488\) | −1.18561 | −0.0536700 | ||||||||
\(489\) | −32.2588 | −1.45879 | ||||||||
\(490\) | −11.3771 | −0.513965 | ||||||||
\(491\) | 31.5076 | 1.42192 | 0.710959 | − | 0.703234i | \(-0.248261\pi\) | ||||
0.710959 | + | 0.703234i | \(0.248261\pi\) | |||||||
\(492\) | −26.3141 | −1.18633 | ||||||||
\(493\) | 42.3384 | 1.90683 | ||||||||
\(494\) | −16.4038 | −0.738040 | ||||||||
\(495\) | −8.81444 | −0.396179 | ||||||||
\(496\) | 2.82331 | 0.126770 | ||||||||
\(497\) | −0.867169 | −0.0388978 | ||||||||
\(498\) | 37.5486 | 1.68259 | ||||||||
\(499\) | −1.46096 | −0.0654016 | −0.0327008 | − | 0.999465i | \(-0.510411\pi\) | ||||
−0.0327008 | + | 0.999465i | \(0.510411\pi\) | |||||||
\(500\) | −12.0870 | −0.540545 | ||||||||
\(501\) | −24.5684 | −1.09763 | ||||||||
\(502\) | −17.8088 | −0.794847 | ||||||||
\(503\) | −9.96582 | −0.444354 | −0.222177 | − | 0.975006i | \(-0.571316\pi\) | ||||
−0.222177 | + | 0.975006i | \(0.571316\pi\) | |||||||
\(504\) | −4.97639 | −0.221666 | ||||||||
\(505\) | 30.9323 | 1.37647 | ||||||||
\(506\) | −0.796433 | −0.0354058 | ||||||||
\(507\) | 14.1484 | 0.628351 | ||||||||
\(508\) | 10.3462 | 0.459038 | ||||||||
\(509\) | 4.10846 | 0.182104 | 0.0910522 | − | 0.995846i | \(-0.470977\pi\) | ||||
0.0910522 | + | 0.995846i | \(0.470977\pi\) | |||||||
\(510\) | −33.0120 | −1.46180 | ||||||||
\(511\) | 1.08142 | 0.0478393 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 26.0911 | 1.15195 | ||||||||
\(514\) | 8.77644 | 0.387112 | ||||||||
\(515\) | −11.7419 | −0.517409 | ||||||||
\(516\) | 31.3189 | 1.37874 | ||||||||
\(517\) | −6.21910 | −0.273516 | ||||||||
\(518\) | −2.67360 | −0.117471 | ||||||||
\(519\) | 65.0477 | 2.85528 | ||||||||
\(520\) | 5.46803 | 0.239789 | ||||||||
\(521\) | 28.5129 | 1.24917 | 0.624585 | − | 0.780957i | \(-0.285268\pi\) | ||||
0.624585 | + | 0.780957i | \(0.285268\pi\) | |||||||
\(522\) | 31.8473 | 1.39392 | ||||||||
\(523\) | 42.9607 | 1.87854 | 0.939270 | − | 0.343178i | \(-0.111503\pi\) | ||||
0.939270 | + | 0.343178i | \(0.111503\pi\) | |||||||
\(524\) | −20.9417 | −0.914841 | ||||||||
\(525\) | −3.57731 | −0.156127 | ||||||||
\(526\) | −5.38526 | −0.234809 | ||||||||
\(527\) | 17.3297 | 0.754894 | ||||||||
\(528\) | 2.70381 | 0.117668 | ||||||||
\(529\) | −22.3391 | −0.971265 | ||||||||
\(530\) | −5.59738 | −0.243135 | ||||||||
\(531\) | −53.3155 | −2.31370 | ||||||||
\(532\) | 6.30087 | 0.273177 | ||||||||
\(533\) | 26.7535 | 1.15882 | ||||||||
\(534\) | −12.4159 | −0.537289 | ||||||||
\(535\) | 6.12779 | 0.264927 | ||||||||
\(536\) | 12.4222 | 0.536557 | ||||||||
\(537\) | 0.361690 | 0.0156081 | ||||||||
\(538\) | −4.20717 | −0.181384 | ||||||||
\(539\) | 5.71963 | 0.246362 | ||||||||
\(540\) | −8.69720 | −0.374268 | ||||||||
\(541\) | 41.8976 | 1.80132 | 0.900658 | − | 0.434528i | \(-0.143085\pi\) | ||||
0.900658 | + | 0.434528i | \(0.143085\pi\) | |||||||
\(542\) | 27.9024 | 1.19851 | ||||||||
\(543\) | −6.94550 | −0.298060 | ||||||||
\(544\) | 6.13809 | 0.263168 | ||||||||
\(545\) | 11.3107 | 0.484498 | ||||||||
\(546\) | 8.34692 | 0.357215 | ||||||||
\(547\) | 2.45563 | 0.104995 | 0.0524975 | − | 0.998621i | \(-0.483282\pi\) | ||||
0.0524975 | + | 0.998621i | \(0.483282\pi\) | |||||||
\(548\) | −13.9708 | −0.596801 | ||||||||
\(549\) | −5.47410 | −0.233629 | ||||||||
\(550\) | 1.17814 | 0.0502362 | ||||||||
\(551\) | −40.3235 | −1.71784 | ||||||||
\(552\) | −2.24370 | −0.0954981 | ||||||||
\(553\) | −18.7284 | −0.796414 | ||||||||
\(554\) | −5.19763 | −0.220826 | ||||||||
\(555\) | −13.3411 | −0.566298 | ||||||||
\(556\) | 11.5737 | 0.490834 | ||||||||
\(557\) | −38.0194 | −1.61093 | −0.805466 | − | 0.592642i | \(-0.798085\pi\) | ||||
−0.805466 | + | 0.592642i | \(0.798085\pi\) | |||||||
\(558\) | 13.0355 | 0.551838 | ||||||||
\(559\) | −31.8419 | −1.34677 | ||||||||
\(560\) | −2.10033 | −0.0887552 | ||||||||
\(561\) | 16.5962 | 0.700692 | ||||||||
\(562\) | 0.149335 | 0.00629934 | ||||||||
\(563\) | 15.7669 | 0.664495 | 0.332247 | − | 0.943192i | \(-0.392193\pi\) | ||||
0.332247 | + | 0.943192i | \(0.392193\pi\) | |||||||
\(564\) | −17.5203 | −0.737739 | ||||||||
\(565\) | 13.0823 | 0.550377 | ||||||||
\(566\) | 3.98574 | 0.167533 | ||||||||
\(567\) | 1.65294 | 0.0694169 | ||||||||
\(568\) | 0.804562 | 0.0337587 | ||||||||
\(569\) | 22.1317 | 0.927809 | 0.463905 | − | 0.885885i | \(-0.346448\pi\) | ||||
0.463905 | + | 0.885885i | \(0.346448\pi\) | |||||||
\(570\) | 31.4409 | 1.31692 | ||||||||
\(571\) | 10.2704 | 0.429804 | 0.214902 | − | 0.976636i | \(-0.431057\pi\) | ||||
0.214902 | + | 0.976636i | \(0.431057\pi\) | |||||||
\(572\) | −2.74895 | −0.114940 | ||||||||
\(573\) | −20.9952 | −0.877088 | ||||||||
\(574\) | −10.2763 | −0.428926 | ||||||||
\(575\) | −0.977658 | −0.0407712 | ||||||||
\(576\) | 4.61711 | 0.192380 | ||||||||
\(577\) | 20.6211 | 0.858467 | 0.429234 | − | 0.903193i | \(-0.358784\pi\) | ||||
0.429234 | + | 0.903193i | \(0.358784\pi\) | |||||||
\(578\) | 20.6761 | 0.860013 | ||||||||
\(579\) | −23.8708 | −0.992038 | ||||||||
\(580\) | 13.4414 | 0.558125 | ||||||||
\(581\) | 14.6637 | 0.608352 | ||||||||
\(582\) | −19.0942 | −0.791479 | ||||||||
\(583\) | 2.81398 | 0.116543 | ||||||||
\(584\) | −1.00335 | −0.0415189 | ||||||||
\(585\) | 25.2465 | 1.04381 | ||||||||
\(586\) | 13.0709 | 0.539954 | ||||||||
\(587\) | −9.44050 | −0.389651 | −0.194826 | − | 0.980838i | \(-0.562414\pi\) | ||||
−0.194826 | + | 0.980838i | \(0.562414\pi\) | |||||||
\(588\) | 16.1132 | 0.664499 | ||||||||
\(589\) | −16.5050 | −0.680075 | ||||||||
\(590\) | −22.5023 | −0.926405 | ||||||||
\(591\) | 9.57490 | 0.393859 | ||||||||
\(592\) | 2.48058 | 0.101951 | ||||||||
\(593\) | 24.9189 | 1.02330 | 0.511648 | − | 0.859195i | \(-0.329035\pi\) | ||||
0.511648 | + | 0.859195i | \(0.329035\pi\) | |||||||
\(594\) | 4.37236 | 0.179400 | ||||||||
\(595\) | −12.8920 | −0.528521 | ||||||||
\(596\) | −20.9446 | −0.857925 | ||||||||
\(597\) | 17.8415 | 0.730203 | ||||||||
\(598\) | 2.28116 | 0.0932836 | ||||||||
\(599\) | 38.5056 | 1.57329 | 0.786647 | − | 0.617402i | \(-0.211815\pi\) | ||||
0.786647 | + | 0.617402i | \(0.211815\pi\) | |||||||
\(600\) | 3.31904 | 0.135499 | ||||||||
\(601\) | 17.6057 | 0.718151 | 0.359076 | − | 0.933308i | \(-0.383092\pi\) | ||||
0.359076 | + | 0.933308i | \(0.383092\pi\) | |||||||
\(602\) | 12.2308 | 0.498491 | ||||||||
\(603\) | 57.3547 | 2.33566 | ||||||||
\(604\) | 16.3586 | 0.665621 | ||||||||
\(605\) | −19.5654 | −0.795445 | ||||||||
\(606\) | −43.8090 | −1.77962 | ||||||||
\(607\) | 19.4163 | 0.788085 | 0.394042 | − | 0.919092i | \(-0.371076\pi\) | ||||
0.394042 | + | 0.919092i | \(0.371076\pi\) | |||||||
\(608\) | −5.84597 | −0.237085 | ||||||||
\(609\) | 20.5183 | 0.831442 | ||||||||
\(610\) | −2.31039 | −0.0935450 | ||||||||
\(611\) | 17.8129 | 0.720632 | ||||||||
\(612\) | 28.3402 | 1.14559 | ||||||||
\(613\) | −45.5552 | −1.83996 | −0.919978 | − | 0.391971i | \(-0.871793\pi\) | ||||
−0.919978 | + | 0.391971i | \(0.871793\pi\) | |||||||
\(614\) | 26.2437 | 1.05911 | ||||||||
\(615\) | −51.2782 | −2.06774 | ||||||||
\(616\) | 1.05590 | 0.0425436 | ||||||||
\(617\) | −12.7964 | −0.515164 | −0.257582 | − | 0.966256i | \(-0.582926\pi\) | ||||
−0.257582 | + | 0.966256i | \(0.582926\pi\) | |||||||
\(618\) | 16.6299 | 0.668951 | ||||||||
\(619\) | −8.36623 | −0.336267 | −0.168134 | − | 0.985764i | \(-0.553774\pi\) | ||||
−0.168134 | + | 0.985764i | \(0.553774\pi\) | |||||||
\(620\) | 5.50176 | 0.220956 | ||||||||
\(621\) | −3.62831 | −0.145599 | ||||||||
\(622\) | 16.4523 | 0.659676 | ||||||||
\(623\) | −4.84872 | −0.194260 | ||||||||
\(624\) | −7.74430 | −0.310020 | ||||||||
\(625\) | −17.5408 | −0.701633 | ||||||||
\(626\) | −12.2007 | −0.487638 | ||||||||
\(627\) | −15.8064 | −0.631245 | ||||||||
\(628\) | 10.0426 | 0.400742 | ||||||||
\(629\) | 15.2260 | 0.607100 | ||||||||
\(630\) | −9.69746 | −0.386356 | ||||||||
\(631\) | −21.0840 | −0.839339 | −0.419670 | − | 0.907677i | \(-0.637854\pi\) | ||||
−0.419670 | + | 0.907677i | \(0.637854\pi\) | |||||||
\(632\) | 17.3763 | 0.691192 | ||||||||
\(633\) | −55.6474 | −2.21178 | ||||||||
\(634\) | 1.51828 | 0.0602985 | ||||||||
\(635\) | 20.1615 | 0.800087 | ||||||||
\(636\) | 7.92750 | 0.314346 | ||||||||
\(637\) | −16.3823 | −0.649090 | ||||||||
\(638\) | −6.75743 | −0.267529 | ||||||||
\(639\) | 3.71476 | 0.146953 | ||||||||
\(640\) | 1.94869 | 0.0770289 | ||||||||
\(641\) | 15.0917 | 0.596084 | 0.298042 | − | 0.954553i | \(-0.403666\pi\) | ||||
0.298042 | + | 0.954553i | \(0.403666\pi\) | |||||||
\(642\) | −8.67871 | −0.342521 | ||||||||
\(643\) | −11.5376 | −0.454999 | −0.227499 | − | 0.973778i | \(-0.573055\pi\) | ||||
−0.227499 | + | 0.973778i | \(0.573055\pi\) | |||||||
\(644\) | −0.876220 | −0.0345279 | ||||||||
\(645\) | 61.0310 | 2.40309 | ||||||||
\(646\) | −35.8831 | −1.41180 | ||||||||
\(647\) | 13.0312 | 0.512311 | 0.256155 | − | 0.966636i | \(-0.417544\pi\) | ||||
0.256155 | + | 0.966636i | \(0.417544\pi\) | |||||||
\(648\) | −1.53360 | −0.0602456 | ||||||||
\(649\) | 11.3126 | 0.444060 | ||||||||
\(650\) | −3.37446 | −0.132357 | ||||||||
\(651\) | 8.39841 | 0.329160 | ||||||||
\(652\) | 11.6883 | 0.457751 | ||||||||
\(653\) | 29.3440 | 1.14832 | 0.574160 | − | 0.818743i | \(-0.305329\pi\) | ||||
0.574160 | + | 0.818743i | \(0.305329\pi\) | |||||||
\(654\) | −16.0192 | −0.626402 | ||||||||
\(655\) | −40.8089 | −1.59454 | ||||||||
\(656\) | 9.53441 | 0.372256 | ||||||||
\(657\) | −4.63257 | −0.180734 | ||||||||
\(658\) | −6.84213 | −0.266734 | ||||||||
\(659\) | −22.3510 | −0.870673 | −0.435336 | − | 0.900268i | \(-0.643371\pi\) | ||||
−0.435336 | + | 0.900268i | \(0.643371\pi\) | |||||||
\(660\) | 5.26889 | 0.205091 | ||||||||
\(661\) | 1.02423 | 0.0398377 | 0.0199189 | − | 0.999802i | \(-0.493659\pi\) | ||||
0.0199189 | + | 0.999802i | \(0.493659\pi\) | |||||||
\(662\) | 29.2707 | 1.13764 | ||||||||
\(663\) | −47.5352 | −1.84611 | ||||||||
\(664\) | −13.6050 | −0.527977 | ||||||||
\(665\) | 12.2785 | 0.476138 | ||||||||
\(666\) | 11.4531 | 0.443799 | ||||||||
\(667\) | 5.60752 | 0.217124 | ||||||||
\(668\) | 8.90188 | 0.344424 | ||||||||
\(669\) | 6.38430 | 0.246831 | ||||||||
\(670\) | 24.2071 | 0.935200 | ||||||||
\(671\) | 1.16151 | 0.0448395 | ||||||||
\(672\) | 2.97467 | 0.114750 | ||||||||
\(673\) | −35.7299 | −1.37729 | −0.688644 | − | 0.725099i | \(-0.741794\pi\) | ||||
−0.688644 | + | 0.725099i | \(0.741794\pi\) | |||||||
\(674\) | −16.3957 | −0.631539 | ||||||||
\(675\) | 5.36727 | 0.206586 | ||||||||
\(676\) | −5.12639 | −0.197169 | ||||||||
\(677\) | 1.99090 | 0.0765166 | 0.0382583 | − | 0.999268i | \(-0.487819\pi\) | ||||
0.0382583 | + | 0.999268i | \(0.487819\pi\) | |||||||
\(678\) | −18.5283 | −0.711576 | ||||||||
\(679\) | −7.45675 | −0.286164 | ||||||||
\(680\) | 11.9613 | 0.458693 | ||||||||
\(681\) | −53.3693 | −2.04512 | ||||||||
\(682\) | −2.76591 | −0.105912 | ||||||||
\(683\) | 13.3001 | 0.508913 | 0.254456 | − | 0.967084i | \(-0.418103\pi\) | ||||
0.254456 | + | 0.967084i | \(0.418103\pi\) | |||||||
\(684\) | −26.9915 | −1.03205 | ||||||||
\(685\) | −27.2247 | −1.04020 | ||||||||
\(686\) | 13.8373 | 0.528311 | ||||||||
\(687\) | 67.1973 | 2.56374 | ||||||||
\(688\) | −11.3478 | −0.432631 | ||||||||
\(689\) | −8.05987 | −0.307057 | ||||||||
\(690\) | −4.37228 | −0.166450 | ||||||||
\(691\) | 47.1513 | 1.79372 | 0.896861 | − | 0.442313i | \(-0.145842\pi\) | ||||
0.896861 | + | 0.442313i | \(0.145842\pi\) | |||||||
\(692\) | −23.5687 | −0.895949 | ||||||||
\(693\) | 4.87523 | 0.185195 | ||||||||
\(694\) | 32.4629 | 1.23227 | ||||||||
\(695\) | 22.5536 | 0.855506 | ||||||||
\(696\) | −19.0369 | −0.721593 | ||||||||
\(697\) | 58.5231 | 2.21672 | ||||||||
\(698\) | 9.69041 | 0.366788 | ||||||||
\(699\) | −49.3495 | −1.86657 | ||||||||
\(700\) | 1.29617 | 0.0489906 | ||||||||
\(701\) | −3.19487 | −0.120668 | −0.0603342 | − | 0.998178i | \(-0.519217\pi\) | ||||
−0.0603342 | + | 0.998178i | \(0.519217\pi\) | |||||||
\(702\) | −12.5234 | −0.472666 | ||||||||
\(703\) | −14.5014 | −0.546929 | ||||||||
\(704\) | −0.979671 | −0.0369227 | ||||||||
\(705\) | −34.1418 | −1.28585 | ||||||||
\(706\) | 17.9689 | 0.676269 | ||||||||
\(707\) | −17.1085 | −0.643431 | ||||||||
\(708\) | 31.8697 | 1.19774 | ||||||||
\(709\) | −9.31234 | −0.349732 | −0.174866 | − | 0.984592i | \(-0.555949\pi\) | ||||
−0.174866 | + | 0.984592i | \(0.555949\pi\) | |||||||
\(710\) | 1.56785 | 0.0588402 | ||||||||
\(711\) | 80.2284 | 3.00880 | ||||||||
\(712\) | 4.49866 | 0.168595 | ||||||||
\(713\) | 2.29523 | 0.0859572 | ||||||||
\(714\) | 18.2588 | 0.683318 | ||||||||
\(715\) | −5.35687 | −0.200336 | ||||||||
\(716\) | −0.131051 | −0.00489762 | ||||||||
\(717\) | 6.83071 | 0.255098 | ||||||||
\(718\) | 1.40738 | 0.0525230 | ||||||||
\(719\) | 14.4611 | 0.539308 | 0.269654 | − | 0.962957i | \(-0.413091\pi\) | ||||
0.269654 | + | 0.962957i | \(0.413091\pi\) | |||||||
\(720\) | 8.99734 | 0.335311 | ||||||||
\(721\) | 6.49438 | 0.241863 | ||||||||
\(722\) | 15.1753 | 0.564768 | ||||||||
\(723\) | −45.1760 | −1.68012 | ||||||||
\(724\) | 2.51657 | 0.0935274 | ||||||||
\(725\) | −8.29506 | −0.308071 | ||||||||
\(726\) | 27.7102 | 1.02842 | ||||||||
\(727\) | −39.3755 | −1.46036 | −0.730179 | − | 0.683256i | \(-0.760563\pi\) | ||||
−0.730179 | + | 0.683256i | \(0.760563\pi\) | |||||||
\(728\) | −3.02434 | −0.112090 | ||||||||
\(729\) | −44.0340 | −1.63089 | ||||||||
\(730\) | −1.95522 | −0.0723659 | ||||||||
\(731\) | −69.6538 | −2.57624 | ||||||||
\(732\) | 3.27218 | 0.120943 | ||||||||
\(733\) | 8.91663 | 0.329343 | 0.164672 | − | 0.986348i | \(-0.447344\pi\) | ||||
0.164672 | + | 0.986348i | \(0.447344\pi\) | |||||||
\(734\) | −0.423661 | −0.0156376 | ||||||||
\(735\) | 31.3998 | 1.15820 | ||||||||
\(736\) | 0.812960 | 0.0299661 | ||||||||
\(737\) | −12.1697 | −0.448275 | ||||||||
\(738\) | 44.0215 | 1.62045 | ||||||||
\(739\) | −7.35201 | −0.270448 | −0.135224 | − | 0.990815i | \(-0.543175\pi\) | ||||
−0.135224 | + | 0.990815i | \(0.543175\pi\) | |||||||
\(740\) | 4.83388 | 0.177697 | ||||||||
\(741\) | 45.2729 | 1.66314 | ||||||||
\(742\) | 3.09589 | 0.113654 | ||||||||
\(743\) | −38.1743 | −1.40048 | −0.700240 | − | 0.713907i | \(-0.746924\pi\) | ||||
−0.700240 | + | 0.713907i | \(0.746924\pi\) | |||||||
\(744\) | −7.79208 | −0.285671 | ||||||||
\(745\) | −40.8147 | −1.49533 | ||||||||
\(746\) | 6.59142 | 0.241329 | ||||||||
\(747\) | −62.8159 | −2.29831 | ||||||||
\(748\) | −6.01331 | −0.219868 | ||||||||
\(749\) | −3.38925 | −0.123841 | ||||||||
\(750\) | 33.3589 | 1.21810 | ||||||||
\(751\) | −39.9738 | −1.45867 | −0.729333 | − | 0.684159i | \(-0.760169\pi\) | ||||
−0.729333 | + | 0.684159i | \(0.760169\pi\) | |||||||
\(752\) | 6.34815 | 0.231493 | ||||||||
\(753\) | 49.1508 | 1.79116 | ||||||||
\(754\) | 19.3548 | 0.704860 | ||||||||
\(755\) | 31.8779 | 1.16015 | ||||||||
\(756\) | 4.81038 | 0.174952 | ||||||||
\(757\) | −40.3248 | −1.46563 | −0.732815 | − | 0.680428i | \(-0.761794\pi\) | ||||
−0.732815 | + | 0.680428i | \(0.761794\pi\) | |||||||
\(758\) | 10.1493 | 0.368639 | ||||||||
\(759\) | 2.19809 | 0.0797855 | ||||||||
\(760\) | −11.3920 | −0.413231 | ||||||||
\(761\) | 23.9110 | 0.866772 | 0.433386 | − | 0.901208i | \(-0.357319\pi\) | ||||
0.433386 | + | 0.901208i | \(0.357319\pi\) | |||||||
\(762\) | −28.5546 | −1.03442 | ||||||||
\(763\) | −6.25591 | −0.226479 | ||||||||
\(764\) | 7.60721 | 0.275219 | ||||||||
\(765\) | 55.2265 | 1.99672 | ||||||||
\(766\) | −30.9076 | −1.11674 | ||||||||
\(767\) | −32.4019 | −1.16996 | ||||||||
\(768\) | −2.75991 | −0.0995897 | ||||||||
\(769\) | 35.6971 | 1.28727 | 0.643636 | − | 0.765332i | \(-0.277425\pi\) | ||||
0.643636 | + | 0.765332i | \(0.277425\pi\) | |||||||
\(770\) | 2.05763 | 0.0741519 | ||||||||
\(771\) | −24.2222 | −0.872342 | ||||||||
\(772\) | 8.64913 | 0.311289 | ||||||||
\(773\) | −45.7212 | −1.64448 | −0.822239 | − | 0.569143i | \(-0.807275\pi\) | ||||
−0.822239 | + | 0.569143i | \(0.807275\pi\) | |||||||
\(774\) | −52.3941 | −1.88327 | ||||||||
\(775\) | −3.39528 | −0.121962 | ||||||||
\(776\) | 6.91840 | 0.248356 | ||||||||
\(777\) | 7.37890 | 0.264717 | ||||||||
\(778\) | 22.0663 | 0.791114 | ||||||||
\(779\) | −55.7379 | −1.99702 | ||||||||
\(780\) | −15.0913 | −0.540354 | ||||||||
\(781\) | −0.788207 | −0.0282042 | ||||||||
\(782\) | 4.99002 | 0.178443 | ||||||||
\(783\) | −30.7849 | −1.10016 | ||||||||
\(784\) | −5.83832 | −0.208511 | ||||||||
\(785\) | 19.5699 | 0.698479 | ||||||||
\(786\) | 57.7971 | 2.06156 | ||||||||
\(787\) | 18.9694 | 0.676187 | 0.338093 | − | 0.941113i | \(-0.390218\pi\) | ||||
0.338093 | + | 0.941113i | \(0.390218\pi\) | |||||||
\(788\) | −3.46928 | −0.123588 | ||||||||
\(789\) | 14.8629 | 0.529131 | ||||||||
\(790\) | 33.8611 | 1.20472 | ||||||||
\(791\) | −7.23577 | −0.257274 | ||||||||
\(792\) | −4.52325 | −0.160727 | ||||||||
\(793\) | −3.32682 | −0.118139 | ||||||||
\(794\) | 20.6663 | 0.733420 | ||||||||
\(795\) | 15.4483 | 0.547894 | ||||||||
\(796\) | −6.46451 | −0.229128 | ||||||||
\(797\) | −0.359493 | −0.0127339 | −0.00636696 | − | 0.999980i | \(-0.502027\pi\) | ||||
−0.00636696 | + | 0.999980i | \(0.502027\pi\) | |||||||
\(798\) | −17.3898 | −0.615594 | ||||||||
\(799\) | 38.9655 | 1.37850 | ||||||||
\(800\) | −1.20259 | −0.0425180 | ||||||||
\(801\) | 20.7708 | 0.733902 | ||||||||
\(802\) | 12.1495 | 0.429012 | ||||||||
\(803\) | 0.982952 | 0.0346876 | ||||||||
\(804\) | −34.2842 | −1.20911 | ||||||||
\(805\) | −1.70748 | −0.0601809 | ||||||||
\(806\) | 7.92219 | 0.279047 | ||||||||
\(807\) | 11.6114 | 0.408742 | ||||||||
\(808\) | 15.8733 | 0.558422 | ||||||||
\(809\) | −17.9681 | −0.631725 | −0.315863 | − | 0.948805i | \(-0.602294\pi\) | ||||
−0.315863 | + | 0.948805i | \(0.602294\pi\) | |||||||
\(810\) | −2.98852 | −0.105006 | ||||||||
\(811\) | −25.8396 | −0.907351 | −0.453676 | − | 0.891167i | \(-0.649887\pi\) | ||||
−0.453676 | + | 0.891167i | \(0.649887\pi\) | |||||||
\(812\) | −7.43439 | −0.260896 | ||||||||
\(813\) | −77.0081 | −2.70079 | ||||||||
\(814\) | −2.43015 | −0.0851766 | ||||||||
\(815\) | 22.7770 | 0.797844 | ||||||||
\(816\) | −16.9406 | −0.593039 | ||||||||
\(817\) | 66.3389 | 2.32090 | ||||||||
\(818\) | −2.08319 | −0.0728372 | ||||||||
\(819\) | −13.9637 | −0.487932 | ||||||||
\(820\) | 18.5797 | 0.648830 | ||||||||
\(821\) | 15.3699 | 0.536413 | 0.268207 | − | 0.963361i | \(-0.413569\pi\) | ||||
0.268207 | + | 0.963361i | \(0.413569\pi\) | |||||||
\(822\) | 38.5580 | 1.34487 | ||||||||
\(823\) | −48.7044 | −1.69773 | −0.848865 | − | 0.528610i | \(-0.822713\pi\) | ||||
−0.848865 | + | 0.528610i | \(0.822713\pi\) | |||||||
\(824\) | −6.02551 | −0.209908 | ||||||||
\(825\) | −3.25157 | −0.113205 | ||||||||
\(826\) | 12.4459 | 0.433049 | ||||||||
\(827\) | −52.6902 | −1.83222 | −0.916110 | − | 0.400928i | \(-0.868688\pi\) | ||||
−0.916110 | + | 0.400928i | \(0.868688\pi\) | |||||||
\(828\) | 3.75353 | 0.130444 | ||||||||
\(829\) | −20.4754 | −0.711141 | −0.355570 | − | 0.934650i | \(-0.615713\pi\) | ||||
−0.355570 | + | 0.934650i | \(0.615713\pi\) | |||||||
\(830\) | −26.5120 | −0.920245 | ||||||||
\(831\) | 14.3450 | 0.497622 | ||||||||
\(832\) | 2.80600 | 0.0972804 | ||||||||
\(833\) | −35.8361 | −1.24165 | ||||||||
\(834\) | −31.9424 | −1.10607 | ||||||||
\(835\) | 17.3470 | 0.600319 | ||||||||
\(836\) | 5.72713 | 0.198077 | ||||||||
\(837\) | −12.6007 | −0.435543 | ||||||||
\(838\) | −30.5228 | −1.05439 | ||||||||
\(839\) | 44.4620 | 1.53500 | 0.767499 | − | 0.641050i | \(-0.221501\pi\) | ||||
0.767499 | + | 0.641050i | \(0.221501\pi\) | |||||||
\(840\) | 5.79673 | 0.200006 | ||||||||
\(841\) | 18.5776 | 0.640609 | ||||||||
\(842\) | −34.4862 | −1.18847 | ||||||||
\(843\) | −0.412153 | −0.0141953 | ||||||||
\(844\) | 20.1627 | 0.694030 | ||||||||
\(845\) | −9.98976 | −0.343658 | ||||||||
\(846\) | 29.3101 | 1.00770 | ||||||||
\(847\) | 10.8215 | 0.371832 | ||||||||
\(848\) | −2.87238 | −0.0986378 | ||||||||
\(849\) | −11.0003 | −0.377529 | ||||||||
\(850\) | −7.38161 | −0.253187 | ||||||||
\(851\) | 2.01661 | 0.0691284 | ||||||||
\(852\) | −2.22052 | −0.0760738 | ||||||||
\(853\) | −41.1419 | −1.40867 | −0.704336 | − | 0.709867i | \(-0.748755\pi\) | ||||
−0.704336 | + | 0.709867i | \(0.748755\pi\) | |||||||
\(854\) | 1.27787 | 0.0437277 | ||||||||
\(855\) | −52.5982 | −1.79882 | ||||||||
\(856\) | 3.14456 | 0.107479 | ||||||||
\(857\) | 25.7476 | 0.879521 | 0.439761 | − | 0.898115i | \(-0.355063\pi\) | ||||
0.439761 | + | 0.898115i | \(0.355063\pi\) | |||||||
\(858\) | 7.58687 | 0.259011 | ||||||||
\(859\) | 13.4030 | 0.457306 | 0.228653 | − | 0.973508i | \(-0.426568\pi\) | ||||
0.228653 | + | 0.973508i | \(0.426568\pi\) | |||||||
\(860\) | −22.1134 | −0.754060 | ||||||||
\(861\) | 28.3618 | 0.966566 | ||||||||
\(862\) | −0.285310 | −0.00971769 | ||||||||
\(863\) | 25.0039 | 0.851142 | 0.425571 | − | 0.904925i | \(-0.360073\pi\) | ||||
0.425571 | + | 0.904925i | \(0.360073\pi\) | |||||||
\(864\) | −4.46309 | −0.151837 | ||||||||
\(865\) | −45.9283 | −1.56161 | ||||||||
\(866\) | 9.69131 | 0.329324 | ||||||||
\(867\) | −57.0642 | −1.93800 | ||||||||
\(868\) | −3.04300 | −0.103286 | ||||||||
\(869\) | −17.0231 | −0.577468 | ||||||||
\(870\) | −37.0971 | −1.25771 | ||||||||
\(871\) | 34.8566 | 1.18107 | ||||||||
\(872\) | 5.80426 | 0.196557 | ||||||||
\(873\) | 31.9430 | 1.08111 | ||||||||
\(874\) | −4.75254 | −0.160757 | ||||||||
\(875\) | 13.0275 | 0.440410 | ||||||||
\(876\) | 2.76915 | 0.0935610 | ||||||||
\(877\) | 9.80661 | 0.331146 | 0.165573 | − | 0.986198i | \(-0.447053\pi\) | ||||
0.165573 | + | 0.986198i | \(0.447053\pi\) | |||||||
\(878\) | −20.4018 | −0.688529 | ||||||||
\(879\) | −36.0746 | −1.21676 | ||||||||
\(880\) | −1.90908 | −0.0643551 | ||||||||
\(881\) | 15.3207 | 0.516167 | 0.258083 | − | 0.966123i | \(-0.416909\pi\) | ||||
0.258083 | + | 0.966123i | \(0.416909\pi\) | |||||||
\(882\) | −26.9562 | −0.907661 | ||||||||
\(883\) | −36.2701 | −1.22058 | −0.610292 | − | 0.792176i | \(-0.708948\pi\) | ||||
−0.610292 | + | 0.792176i | \(0.708948\pi\) | |||||||
\(884\) | 17.2234 | 0.579287 | ||||||||
\(885\) | 62.1044 | 2.08762 | ||||||||
\(886\) | 16.8381 | 0.565688 | ||||||||
\(887\) | −6.41568 | −0.215417 | −0.107709 | − | 0.994183i | \(-0.534351\pi\) | ||||
−0.107709 | + | 0.994183i | \(0.534351\pi\) | |||||||
\(888\) | −6.84617 | −0.229742 | ||||||||
\(889\) | −11.1513 | −0.374001 | ||||||||
\(890\) | 8.76652 | 0.293854 | ||||||||
\(891\) | 1.50243 | 0.0503332 | ||||||||
\(892\) | −2.31323 | −0.0774525 | ||||||||
\(893\) | −37.1111 | −1.24187 | ||||||||
\(894\) | 57.8053 | 1.93330 | ||||||||
\(895\) | −0.255379 | −0.00853639 | ||||||||
\(896\) | −1.07781 | −0.0360072 | ||||||||
\(897\) | −6.29581 | −0.210211 | ||||||||
\(898\) | −31.2864 | −1.04404 | ||||||||
\(899\) | 19.4742 | 0.649501 | ||||||||
\(900\) | −5.55250 | −0.185083 | ||||||||
\(901\) | −17.6309 | −0.587370 | ||||||||
\(902\) | −9.34059 | −0.311008 | ||||||||
\(903\) | −33.7560 | −1.12333 | ||||||||
\(904\) | 6.71337 | 0.223284 | ||||||||
\(905\) | 4.90402 | 0.163015 | ||||||||
\(906\) | −45.1483 | −1.49995 | ||||||||
\(907\) | −45.8274 | −1.52167 | −0.760837 | − | 0.648942i | \(-0.775212\pi\) | ||||
−0.760837 | + | 0.648942i | \(0.775212\pi\) | |||||||
\(908\) | 19.3373 | 0.641731 | ||||||||
\(909\) | 73.2890 | 2.43084 | ||||||||
\(910\) | −5.89352 | −0.195368 | ||||||||
\(911\) | −38.5475 | −1.27714 | −0.638568 | − | 0.769565i | \(-0.720473\pi\) | ||||
−0.638568 | + | 0.769565i | \(0.720473\pi\) | |||||||
\(912\) | 16.1344 | 0.534262 | ||||||||
\(913\) | 13.3284 | 0.441107 | ||||||||
\(914\) | −20.5708 | −0.680421 | ||||||||
\(915\) | 6.37648 | 0.210800 | ||||||||
\(916\) | −24.3476 | −0.804469 | ||||||||
\(917\) | 22.5712 | 0.745367 | ||||||||
\(918\) | −27.3948 | −0.904164 | ||||||||
\(919\) | 12.0676 | 0.398072 | 0.199036 | − | 0.979992i | \(-0.436219\pi\) | ||||
0.199036 | + | 0.979992i | \(0.436219\pi\) | |||||||
\(920\) | 1.58421 | 0.0522299 | ||||||||
\(921\) | −72.4304 | −2.38666 | ||||||||
\(922\) | 38.1200 | 1.25542 | ||||||||
\(923\) | 2.25760 | 0.0743098 | ||||||||
\(924\) | −2.91420 | −0.0958702 | ||||||||
\(925\) | −2.98312 | −0.0980843 | ||||||||
\(926\) | 4.21206 | 0.138417 | ||||||||
\(927\) | −27.8204 | −0.913743 | ||||||||
\(928\) | 6.89766 | 0.226427 | ||||||||
\(929\) | −19.4079 | −0.636753 | −0.318377 | − | 0.947964i | \(-0.603138\pi\) | ||||
−0.318377 | + | 0.947964i | \(0.603138\pi\) | |||||||
\(930\) | −15.1844 | −0.497915 | ||||||||
\(931\) | 34.1306 | 1.11859 | ||||||||
\(932\) | 17.8808 | 0.585706 | ||||||||
\(933\) | −45.4068 | −1.48655 | ||||||||
\(934\) | 0.467726 | 0.0153044 | ||||||||
\(935\) | −11.7181 | −0.383223 | ||||||||
\(936\) | 12.9556 | 0.423467 | ||||||||
\(937\) | 10.0986 | 0.329908 | 0.164954 | − | 0.986301i | \(-0.447252\pi\) | ||||
0.164954 | + | 0.986301i | \(0.447252\pi\) | |||||||
\(938\) | −13.3888 | −0.437160 | ||||||||
\(939\) | 33.6728 | 1.09887 | ||||||||
\(940\) | 12.3706 | 0.403485 | ||||||||
\(941\) | 11.8119 | 0.385058 | 0.192529 | − | 0.981291i | \(-0.438331\pi\) | ||||
0.192529 | + | 0.981291i | \(0.438331\pi\) | |||||||
\(942\) | −27.7166 | −0.903055 | ||||||||
\(943\) | 7.75109 | 0.252410 | ||||||||
\(944\) | −11.5474 | −0.375835 | ||||||||
\(945\) | 9.37396 | 0.304935 | ||||||||
\(946\) | 11.1171 | 0.361448 | ||||||||
\(947\) | −51.4580 | −1.67216 | −0.836080 | − | 0.548607i | \(-0.815158\pi\) | ||||
−0.836080 | + | 0.548607i | \(0.815158\pi\) | |||||||
\(948\) | −47.9571 | −1.55757 | ||||||||
\(949\) | −2.81539 | −0.0913915 | ||||||||
\(950\) | 7.03031 | 0.228093 | ||||||||
\(951\) | −4.19031 | −0.135880 | ||||||||
\(952\) | −6.61572 | −0.214417 | ||||||||
\(953\) | 45.8690 | 1.48584 | 0.742922 | − | 0.669378i | \(-0.233439\pi\) | ||||
0.742922 | + | 0.669378i | \(0.233439\pi\) | |||||||
\(954\) | −13.2621 | −0.429376 | ||||||||
\(955\) | 14.8241 | 0.479697 | ||||||||
\(956\) | −2.47497 | −0.0800464 | ||||||||
\(957\) | 18.6499 | 0.602866 | ||||||||
\(958\) | 27.3789 | 0.884573 | ||||||||
\(959\) | 15.0579 | 0.486244 | ||||||||
\(960\) | −5.37822 | −0.173581 | ||||||||
\(961\) | −23.0289 | −0.742869 | ||||||||
\(962\) | 6.96048 | 0.224415 | ||||||||
\(963\) | 14.5188 | 0.467862 | ||||||||
\(964\) | 16.3687 | 0.527199 | ||||||||
\(965\) | 16.8545 | 0.542566 | ||||||||
\(966\) | 2.41829 | 0.0778072 | ||||||||
\(967\) | −36.9900 | −1.18952 | −0.594760 | − | 0.803904i | \(-0.702753\pi\) | ||||
−0.594760 | + | 0.803904i | \(0.702753\pi\) | |||||||
\(968\) | −10.0402 | −0.322706 | ||||||||
\(969\) | 99.0341 | 3.18143 | ||||||||
\(970\) | 13.4818 | 0.432876 | ||||||||
\(971\) | −7.18233 | −0.230492 | −0.115246 | − | 0.993337i | \(-0.536766\pi\) | ||||
−0.115246 | + | 0.993337i | \(0.536766\pi\) | |||||||
\(972\) | 17.6219 | 0.565222 | ||||||||
\(973\) | −12.4743 | −0.399907 | ||||||||
\(974\) | 20.9230 | 0.670416 | ||||||||
\(975\) | 9.31323 | 0.298262 | ||||||||
\(976\) | −1.18561 | −0.0379504 | ||||||||
\(977\) | 19.0271 | 0.608731 | 0.304365 | − | 0.952555i | \(-0.401556\pi\) | ||||
0.304365 | + | 0.952555i | \(0.401556\pi\) | |||||||
\(978\) | −32.2588 | −1.03152 | ||||||||
\(979\) | −4.40721 | −0.140855 | ||||||||
\(980\) | −11.3771 | −0.363428 | ||||||||
\(981\) | 26.7989 | 0.855624 | ||||||||
\(982\) | 31.5076 | 1.00545 | ||||||||
\(983\) | −19.3901 | −0.618447 | −0.309223 | − | 0.950989i | \(-0.600069\pi\) | ||||
−0.309223 | + | 0.950989i | \(0.600069\pi\) | |||||||
\(984\) | −26.3141 | −0.838864 | ||||||||
\(985\) | −6.76056 | −0.215409 | ||||||||
\(986\) | 42.3384 | 1.34833 | ||||||||
\(987\) | 18.8837 | 0.601074 | ||||||||
\(988\) | −16.4038 | −0.521873 | ||||||||
\(989\) | −9.22530 | −0.293348 | ||||||||
\(990\) | −8.81444 | −0.280141 | ||||||||
\(991\) | −15.8049 | −0.502059 | −0.251030 | − | 0.967979i | \(-0.580769\pi\) | ||||
−0.251030 | + | 0.967979i | \(0.580769\pi\) | |||||||
\(992\) | 2.82331 | 0.0896401 | ||||||||
\(993\) | −80.7846 | −2.56362 | ||||||||
\(994\) | −0.867169 | −0.0275049 | ||||||||
\(995\) | −12.5974 | −0.399363 | ||||||||
\(996\) | 37.5486 | 1.18977 | ||||||||
\(997\) | −6.20291 | −0.196448 | −0.0982241 | − | 0.995164i | \(-0.531316\pi\) | ||||
−0.0982241 | + | 0.995164i | \(0.531316\pi\) | |||||||
\(998\) | −1.46096 | −0.0462459 | ||||||||
\(999\) | −11.0710 | −0.350272 |
(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 | 8026.2.a.d.1.12 | ✓ | 96 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8026.2.a.d.1.12 | ✓ | 96 | 1.1 | even | 1 | trivial |