Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4034,2,Mod(1,4034)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4034, 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("4034.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4034 = 2 \cdot 2017 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4034.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: | \(32.2116521754\) |
Analytic rank: | \(0\) |
Dimension: | \(49\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.8 | ||
Character | \(\chi\) | \(=\) | 4034.1 |
$q$-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 | ||||||||
\(3\) | −2.62176 | −1.51367 | −0.756837 | − | 0.653603i | \(-0.773257\pi\) | ||||
−0.756837 | + | 0.653603i | \(0.773257\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 1.44534 | 0.646375 | 0.323187 | − | 0.946335i | \(-0.395246\pi\) | ||||
0.323187 | + | 0.946335i | \(0.395246\pi\) | |||||||
\(6\) | 2.62176 | 1.07033 | ||||||||
\(7\) | −4.09354 | −1.54721 | −0.773606 | − | 0.633667i | \(-0.781549\pi\) | ||||
−0.773606 | + | 0.633667i | \(0.781549\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 3.87363 | 1.29121 | ||||||||
\(10\) | −1.44534 | −0.457056 | ||||||||
\(11\) | 1.36002 | 0.410063 | 0.205031 | − | 0.978755i | \(-0.434270\pi\) | ||||
0.205031 | + | 0.978755i | \(0.434270\pi\) | |||||||
\(12\) | −2.62176 | −0.756837 | ||||||||
\(13\) | −5.47069 | −1.51730 | −0.758649 | − | 0.651500i | \(-0.774140\pi\) | ||||
−0.758649 | + | 0.651500i | \(0.774140\pi\) | |||||||
\(14\) | 4.09354 | 1.09404 | ||||||||
\(15\) | −3.78933 | −0.978401 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −6.54138 | −1.58652 | −0.793258 | − | 0.608885i | \(-0.791617\pi\) | ||||
−0.793258 | + | 0.608885i | \(0.791617\pi\) | |||||||
\(18\) | −3.87363 | −0.913024 | ||||||||
\(19\) | −7.18152 | −1.64755 | −0.823777 | − | 0.566914i | \(-0.808137\pi\) | ||||
−0.823777 | + | 0.566914i | \(0.808137\pi\) | |||||||
\(20\) | 1.44534 | 0.323187 | ||||||||
\(21\) | 10.7323 | 2.34198 | ||||||||
\(22\) | −1.36002 | −0.289958 | ||||||||
\(23\) | 0.364985 | 0.0761046 | 0.0380523 | − | 0.999276i | \(-0.487885\pi\) | ||||
0.0380523 | + | 0.999276i | \(0.487885\pi\) | |||||||
\(24\) | 2.62176 | 0.535165 | ||||||||
\(25\) | −2.91100 | −0.582200 | ||||||||
\(26\) | 5.47069 | 1.07289 | ||||||||
\(27\) | −2.29046 | −0.440799 | ||||||||
\(28\) | −4.09354 | −0.773606 | ||||||||
\(29\) | −8.13182 | −1.51004 | −0.755021 | − | 0.655701i | \(-0.772373\pi\) | ||||
−0.755021 | + | 0.655701i | \(0.772373\pi\) | |||||||
\(30\) | 3.78933 | 0.691834 | ||||||||
\(31\) | 5.99102 | 1.07602 | 0.538009 | − | 0.842939i | \(-0.319176\pi\) | ||||
0.538009 | + | 0.842939i | \(0.319176\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | −3.56566 | −0.620702 | ||||||||
\(34\) | 6.54138 | 1.12184 | ||||||||
\(35\) | −5.91655 | −1.00008 | ||||||||
\(36\) | 3.87363 | 0.645605 | ||||||||
\(37\) | −10.8895 | −1.79023 | −0.895115 | − | 0.445836i | \(-0.852906\pi\) | ||||
−0.895115 | + | 0.445836i | \(0.852906\pi\) | |||||||
\(38\) | 7.18152 | 1.16500 | ||||||||
\(39\) | 14.3429 | 2.29670 | ||||||||
\(40\) | −1.44534 | −0.228528 | ||||||||
\(41\) | −0.609989 | −0.0952643 | −0.0476322 | − | 0.998865i | \(-0.515168\pi\) | ||||
−0.0476322 | + | 0.998865i | \(0.515168\pi\) | |||||||
\(42\) | −10.7323 | −1.65603 | ||||||||
\(43\) | −3.38869 | −0.516771 | −0.258385 | − | 0.966042i | \(-0.583190\pi\) | ||||
−0.258385 | + | 0.966042i | \(0.583190\pi\) | |||||||
\(44\) | 1.36002 | 0.205031 | ||||||||
\(45\) | 5.59871 | 0.834606 | ||||||||
\(46\) | −0.364985 | −0.0538141 | ||||||||
\(47\) | 6.02904 | 0.879425 | 0.439713 | − | 0.898138i | \(-0.355080\pi\) | ||||
0.439713 | + | 0.898138i | \(0.355080\pi\) | |||||||
\(48\) | −2.62176 | −0.378419 | ||||||||
\(49\) | 9.75706 | 1.39387 | ||||||||
\(50\) | 2.91100 | 0.411677 | ||||||||
\(51\) | 17.1499 | 2.40147 | ||||||||
\(52\) | −5.47069 | −0.758649 | ||||||||
\(53\) | −3.46241 | −0.475599 | −0.237800 | − | 0.971314i | \(-0.576426\pi\) | ||||
−0.237800 | + | 0.971314i | \(0.576426\pi\) | |||||||
\(54\) | 2.29046 | 0.311692 | ||||||||
\(55\) | 1.96570 | 0.265054 | ||||||||
\(56\) | 4.09354 | 0.547022 | ||||||||
\(57\) | 18.8282 | 2.49386 | ||||||||
\(58\) | 8.13182 | 1.06776 | ||||||||
\(59\) | 1.05886 | 0.137852 | 0.0689260 | − | 0.997622i | \(-0.478043\pi\) | ||||
0.0689260 | + | 0.997622i | \(0.478043\pi\) | |||||||
\(60\) | −3.78933 | −0.489201 | ||||||||
\(61\) | 3.80729 | 0.487473 | 0.243737 | − | 0.969841i | \(-0.421627\pi\) | ||||
0.243737 | + | 0.969841i | \(0.421627\pi\) | |||||||
\(62\) | −5.99102 | −0.760860 | ||||||||
\(63\) | −15.8569 | −1.99778 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −7.90700 | −0.980743 | ||||||||
\(66\) | 3.56566 | 0.438902 | ||||||||
\(67\) | −13.4770 | −1.64648 | −0.823239 | − | 0.567694i | \(-0.807836\pi\) | ||||
−0.823239 | + | 0.567694i | \(0.807836\pi\) | |||||||
\(68\) | −6.54138 | −0.793258 | ||||||||
\(69\) | −0.956904 | −0.115198 | ||||||||
\(70\) | 5.91655 | 0.707163 | ||||||||
\(71\) | 4.01685 | 0.476712 | 0.238356 | − | 0.971178i | \(-0.423391\pi\) | ||||
0.238356 | + | 0.971178i | \(0.423391\pi\) | |||||||
\(72\) | −3.87363 | −0.456512 | ||||||||
\(73\) | −16.8267 | −1.96942 | −0.984710 | − | 0.174204i | \(-0.944265\pi\) | ||||
−0.984710 | + | 0.174204i | \(0.944265\pi\) | |||||||
\(74\) | 10.8895 | 1.26588 | ||||||||
\(75\) | 7.63194 | 0.881261 | ||||||||
\(76\) | −7.18152 | −0.823777 | ||||||||
\(77\) | −5.56731 | −0.634454 | ||||||||
\(78\) | −14.3429 | −1.62401 | ||||||||
\(79\) | −7.89704 | −0.888486 | −0.444243 | − | 0.895906i | \(-0.646527\pi\) | ||||
−0.444243 | + | 0.895906i | \(0.646527\pi\) | |||||||
\(80\) | 1.44534 | 0.161594 | ||||||||
\(81\) | −5.61587 | −0.623985 | ||||||||
\(82\) | 0.609989 | 0.0673621 | ||||||||
\(83\) | −1.45700 | −0.159926 | −0.0799630 | − | 0.996798i | \(-0.525480\pi\) | ||||
−0.0799630 | + | 0.996798i | \(0.525480\pi\) | |||||||
\(84\) | 10.7323 | 1.17099 | ||||||||
\(85\) | −9.45450 | −1.02548 | ||||||||
\(86\) | 3.38869 | 0.365412 | ||||||||
\(87\) | 21.3197 | 2.28571 | ||||||||
\(88\) | −1.36002 | −0.144979 | ||||||||
\(89\) | 12.9834 | 1.37624 | 0.688118 | − | 0.725599i | \(-0.258437\pi\) | ||||
0.688118 | + | 0.725599i | \(0.258437\pi\) | |||||||
\(90\) | −5.59871 | −0.590156 | ||||||||
\(91\) | 22.3945 | 2.34758 | ||||||||
\(92\) | 0.364985 | 0.0380523 | ||||||||
\(93\) | −15.7070 | −1.62874 | ||||||||
\(94\) | −6.02904 | −0.621848 | ||||||||
\(95\) | −10.3797 | −1.06494 | ||||||||
\(96\) | 2.62176 | 0.267582 | ||||||||
\(97\) | −1.54670 | −0.157044 | −0.0785218 | − | 0.996912i | \(-0.525020\pi\) | ||||
−0.0785218 | + | 0.996912i | \(0.525020\pi\) | |||||||
\(98\) | −9.75706 | −0.985612 | ||||||||
\(99\) | 5.26824 | 0.529478 | ||||||||
\(100\) | −2.91100 | −0.291100 | ||||||||
\(101\) | 4.12010 | 0.409965 | 0.204983 | − | 0.978766i | \(-0.434286\pi\) | ||||
0.204983 | + | 0.978766i | \(0.434286\pi\) | |||||||
\(102\) | −17.1499 | −1.69810 | ||||||||
\(103\) | −5.24149 | −0.516459 | −0.258230 | − | 0.966084i | \(-0.583139\pi\) | ||||
−0.258230 | + | 0.966084i | \(0.583139\pi\) | |||||||
\(104\) | 5.47069 | 0.536446 | ||||||||
\(105\) | 15.5118 | 1.51379 | ||||||||
\(106\) | 3.46241 | 0.336299 | ||||||||
\(107\) | 15.2504 | 1.47431 | 0.737156 | − | 0.675722i | \(-0.236168\pi\) | ||||
0.737156 | + | 0.675722i | \(0.236168\pi\) | |||||||
\(108\) | −2.29046 | −0.220399 | ||||||||
\(109\) | −4.96261 | −0.475332 | −0.237666 | − | 0.971347i | \(-0.576382\pi\) | ||||
−0.237666 | + | 0.971347i | \(0.576382\pi\) | |||||||
\(110\) | −1.96570 | −0.187422 | ||||||||
\(111\) | 28.5498 | 2.70982 | ||||||||
\(112\) | −4.09354 | −0.386803 | ||||||||
\(113\) | −13.4851 | −1.26857 | −0.634287 | − | 0.773097i | \(-0.718706\pi\) | ||||
−0.634287 | + | 0.773097i | \(0.718706\pi\) | |||||||
\(114\) | −18.8282 | −1.76343 | ||||||||
\(115\) | 0.527527 | 0.0491921 | ||||||||
\(116\) | −8.13182 | −0.755021 | ||||||||
\(117\) | −21.1915 | −1.95915 | ||||||||
\(118\) | −1.05886 | −0.0974760 | ||||||||
\(119\) | 26.7774 | 2.45468 | ||||||||
\(120\) | 3.78933 | 0.345917 | ||||||||
\(121\) | −9.15033 | −0.831848 | ||||||||
\(122\) | −3.80729 | −0.344696 | ||||||||
\(123\) | 1.59925 | 0.144199 | ||||||||
\(124\) | 5.99102 | 0.538009 | ||||||||
\(125\) | −11.4341 | −1.02269 | ||||||||
\(126\) | 15.8569 | 1.41264 | ||||||||
\(127\) | 8.13770 | 0.722104 | 0.361052 | − | 0.932546i | \(-0.382418\pi\) | ||||
0.361052 | + | 0.932546i | \(0.382418\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 8.88434 | 0.782223 | ||||||||
\(130\) | 7.90700 | 0.693490 | ||||||||
\(131\) | −15.0648 | −1.31621 | −0.658107 | − | 0.752925i | \(-0.728642\pi\) | ||||
−0.658107 | + | 0.752925i | \(0.728642\pi\) | |||||||
\(132\) | −3.56566 | −0.310351 | ||||||||
\(133\) | 29.3978 | 2.54912 | ||||||||
\(134\) | 13.4770 | 1.16424 | ||||||||
\(135\) | −3.31048 | −0.284921 | ||||||||
\(136\) | 6.54138 | 0.560918 | ||||||||
\(137\) | 18.0039 | 1.53817 | 0.769087 | − | 0.639144i | \(-0.220711\pi\) | ||||
0.769087 | + | 0.639144i | \(0.220711\pi\) | |||||||
\(138\) | 0.956904 | 0.0814570 | ||||||||
\(139\) | −21.2018 | −1.79832 | −0.899158 | − | 0.437624i | \(-0.855820\pi\) | ||||
−0.899158 | + | 0.437624i | \(0.855820\pi\) | |||||||
\(140\) | −5.91655 | −0.500039 | ||||||||
\(141\) | −15.8067 | −1.33116 | ||||||||
\(142\) | −4.01685 | −0.337086 | ||||||||
\(143\) | −7.44028 | −0.622187 | ||||||||
\(144\) | 3.87363 | 0.322803 | ||||||||
\(145\) | −11.7532 | −0.976053 | ||||||||
\(146\) | 16.8267 | 1.39259 | ||||||||
\(147\) | −25.5807 | −2.10986 | ||||||||
\(148\) | −10.8895 | −0.895115 | ||||||||
\(149\) | −7.49989 | −0.614415 | −0.307208 | − | 0.951643i | \(-0.599395\pi\) | ||||
−0.307208 | + | 0.951643i | \(0.599395\pi\) | |||||||
\(150\) | −7.63194 | −0.623146 | ||||||||
\(151\) | −16.9662 | −1.38069 | −0.690347 | − | 0.723479i | \(-0.742542\pi\) | ||||
−0.690347 | + | 0.723479i | \(0.742542\pi\) | |||||||
\(152\) | 7.18152 | 0.582498 | ||||||||
\(153\) | −25.3389 | −2.04853 | ||||||||
\(154\) | 5.56731 | 0.448627 | ||||||||
\(155\) | 8.65905 | 0.695511 | ||||||||
\(156\) | 14.3429 | 1.14835 | ||||||||
\(157\) | −9.19808 | −0.734086 | −0.367043 | − | 0.930204i | \(-0.619630\pi\) | ||||
−0.367043 | + | 0.930204i | \(0.619630\pi\) | |||||||
\(158\) | 7.89704 | 0.628254 | ||||||||
\(159\) | 9.07762 | 0.719902 | ||||||||
\(160\) | −1.44534 | −0.114264 | ||||||||
\(161\) | −1.49408 | −0.117750 | ||||||||
\(162\) | 5.61587 | 0.441224 | ||||||||
\(163\) | 13.3398 | 1.04485 | 0.522425 | − | 0.852685i | \(-0.325027\pi\) | ||||
0.522425 | + | 0.852685i | \(0.325027\pi\) | |||||||
\(164\) | −0.609989 | −0.0476322 | ||||||||
\(165\) | −5.15358 | −0.401206 | ||||||||
\(166\) | 1.45700 | 0.113085 | ||||||||
\(167\) | 13.9074 | 1.07619 | 0.538095 | − | 0.842884i | \(-0.319144\pi\) | ||||
0.538095 | + | 0.842884i | \(0.319144\pi\) | |||||||
\(168\) | −10.7323 | −0.828013 | ||||||||
\(169\) | 16.9285 | 1.30219 | ||||||||
\(170\) | 9.45450 | 0.725127 | ||||||||
\(171\) | −27.8186 | −2.12734 | ||||||||
\(172\) | −3.38869 | −0.258385 | ||||||||
\(173\) | −14.7694 | −1.12290 | −0.561448 | − | 0.827512i | \(-0.689756\pi\) | ||||
−0.561448 | + | 0.827512i | \(0.689756\pi\) | |||||||
\(174\) | −21.3197 | −1.61624 | ||||||||
\(175\) | 11.9163 | 0.900786 | ||||||||
\(176\) | 1.36002 | 0.102516 | ||||||||
\(177\) | −2.77608 | −0.208663 | ||||||||
\(178\) | −12.9834 | −0.973145 | ||||||||
\(179\) | −13.4258 | −1.00349 | −0.501746 | − | 0.865015i | \(-0.667309\pi\) | ||||
−0.501746 | + | 0.865015i | \(0.667309\pi\) | |||||||
\(180\) | 5.59871 | 0.417303 | ||||||||
\(181\) | 1.06095 | 0.0788597 | 0.0394299 | − | 0.999222i | \(-0.487446\pi\) | ||||
0.0394299 | + | 0.999222i | \(0.487446\pi\) | |||||||
\(182\) | −22.3945 | −1.65999 | ||||||||
\(183\) | −9.98180 | −0.737876 | ||||||||
\(184\) | −0.364985 | −0.0269071 | ||||||||
\(185\) | −15.7391 | −1.15716 | ||||||||
\(186\) | 15.7070 | 1.15169 | ||||||||
\(187\) | −8.89643 | −0.650572 | ||||||||
\(188\) | 6.02904 | 0.439713 | ||||||||
\(189\) | 9.37607 | 0.682009 | ||||||||
\(190\) | 10.3797 | 0.753025 | ||||||||
\(191\) | −24.7184 | −1.78856 | −0.894281 | − | 0.447505i | \(-0.852313\pi\) | ||||
−0.894281 | + | 0.447505i | \(0.852313\pi\) | |||||||
\(192\) | −2.62176 | −0.189209 | ||||||||
\(193\) | −3.02058 | −0.217426 | −0.108713 | − | 0.994073i | \(-0.534673\pi\) | ||||
−0.108713 | + | 0.994073i | \(0.534673\pi\) | |||||||
\(194\) | 1.54670 | 0.111047 | ||||||||
\(195\) | 20.7303 | 1.48453 | ||||||||
\(196\) | 9.75706 | 0.696933 | ||||||||
\(197\) | 18.7157 | 1.33344 | 0.666720 | − | 0.745308i | \(-0.267698\pi\) | ||||
0.666720 | + | 0.745308i | \(0.267698\pi\) | |||||||
\(198\) | −5.26824 | −0.374397 | ||||||||
\(199\) | 7.74076 | 0.548728 | 0.274364 | − | 0.961626i | \(-0.411533\pi\) | ||||
0.274364 | + | 0.961626i | \(0.411533\pi\) | |||||||
\(200\) | 2.91100 | 0.205839 | ||||||||
\(201\) | 35.3335 | 2.49223 | ||||||||
\(202\) | −4.12010 | −0.289889 | ||||||||
\(203\) | 33.2879 | 2.33635 | ||||||||
\(204\) | 17.1499 | 1.20074 | ||||||||
\(205\) | −0.881641 | −0.0615765 | ||||||||
\(206\) | 5.24149 | 0.365192 | ||||||||
\(207\) | 1.41382 | 0.0982671 | ||||||||
\(208\) | −5.47069 | −0.379324 | ||||||||
\(209\) | −9.76705 | −0.675601 | ||||||||
\(210\) | −15.5118 | −1.07041 | ||||||||
\(211\) | 5.83190 | 0.401484 | 0.200742 | − | 0.979644i | \(-0.435665\pi\) | ||||
0.200742 | + | 0.979644i | \(0.435665\pi\) | |||||||
\(212\) | −3.46241 | −0.237800 | ||||||||
\(213\) | −10.5312 | −0.721587 | ||||||||
\(214\) | −15.2504 | −1.04250 | ||||||||
\(215\) | −4.89780 | −0.334027 | ||||||||
\(216\) | 2.29046 | 0.155846 | ||||||||
\(217\) | −24.5245 | −1.66483 | ||||||||
\(218\) | 4.96261 | 0.336111 | ||||||||
\(219\) | 44.1157 | 2.98106 | ||||||||
\(220\) | 1.96570 | 0.132527 | ||||||||
\(221\) | 35.7859 | 2.40722 | ||||||||
\(222\) | −28.5498 | −1.91614 | ||||||||
\(223\) | 1.68068 | 0.112547 | 0.0562734 | − | 0.998415i | \(-0.482078\pi\) | ||||
0.0562734 | + | 0.998415i | \(0.482078\pi\) | |||||||
\(224\) | 4.09354 | 0.273511 | ||||||||
\(225\) | −11.2761 | −0.751743 | ||||||||
\(226\) | 13.4851 | 0.897018 | ||||||||
\(227\) | 19.5353 | 1.29661 | 0.648303 | − | 0.761382i | \(-0.275479\pi\) | ||||
0.648303 | + | 0.761382i | \(0.275479\pi\) | |||||||
\(228\) | 18.8282 | 1.24693 | ||||||||
\(229\) | −5.15115 | −0.340398 | −0.170199 | − | 0.985410i | \(-0.554441\pi\) | ||||
−0.170199 | + | 0.985410i | \(0.554441\pi\) | |||||||
\(230\) | −0.527527 | −0.0347841 | ||||||||
\(231\) | 14.5962 | 0.960357 | ||||||||
\(232\) | 8.13182 | 0.533880 | ||||||||
\(233\) | −8.24409 | −0.540088 | −0.270044 | − | 0.962848i | \(-0.587038\pi\) | ||||
−0.270044 | + | 0.962848i | \(0.587038\pi\) | |||||||
\(234\) | 21.1915 | 1.38533 | ||||||||
\(235\) | 8.71400 | 0.568438 | ||||||||
\(236\) | 1.05886 | 0.0689260 | ||||||||
\(237\) | 20.7041 | 1.34488 | ||||||||
\(238\) | −26.7774 | −1.73572 | ||||||||
\(239\) | 11.2771 | 0.729453 | 0.364726 | − | 0.931115i | \(-0.381163\pi\) | ||||
0.364726 | + | 0.931115i | \(0.381163\pi\) | |||||||
\(240\) | −3.78933 | −0.244600 | ||||||||
\(241\) | 5.90314 | 0.380254 | 0.190127 | − | 0.981759i | \(-0.439110\pi\) | ||||
0.190127 | + | 0.981759i | \(0.439110\pi\) | |||||||
\(242\) | 9.15033 | 0.588206 | ||||||||
\(243\) | 21.5948 | 1.38531 | ||||||||
\(244\) | 3.80729 | 0.243737 | ||||||||
\(245\) | 14.1022 | 0.900959 | ||||||||
\(246\) | −1.59925 | −0.101964 | ||||||||
\(247\) | 39.2879 | 2.49983 | ||||||||
\(248\) | −5.99102 | −0.380430 | ||||||||
\(249\) | 3.81989 | 0.242076 | ||||||||
\(250\) | 11.4341 | 0.723154 | ||||||||
\(251\) | 8.33837 | 0.526313 | 0.263157 | − | 0.964753i | \(-0.415236\pi\) | ||||
0.263157 | + | 0.964753i | \(0.415236\pi\) | |||||||
\(252\) | −15.8569 | −0.998889 | ||||||||
\(253\) | 0.496389 | 0.0312077 | ||||||||
\(254\) | −8.13770 | −0.510605 | ||||||||
\(255\) | 24.7874 | 1.55225 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 31.9857 | 1.99521 | 0.997607 | − | 0.0691432i | \(-0.0220265\pi\) | ||||
0.997607 | + | 0.0691432i | \(0.0220265\pi\) | |||||||
\(258\) | −8.88434 | −0.553115 | ||||||||
\(259\) | 44.5767 | 2.76986 | ||||||||
\(260\) | −7.90700 | −0.490371 | ||||||||
\(261\) | −31.4997 | −1.94978 | ||||||||
\(262\) | 15.0648 | 0.930704 | ||||||||
\(263\) | 7.92671 | 0.488782 | 0.244391 | − | 0.969677i | \(-0.421412\pi\) | ||||
0.244391 | + | 0.969677i | \(0.421412\pi\) | |||||||
\(264\) | 3.56566 | 0.219451 | ||||||||
\(265\) | −5.00436 | −0.307415 | ||||||||
\(266\) | −29.3978 | −1.80250 | ||||||||
\(267\) | −34.0393 | −2.08317 | ||||||||
\(268\) | −13.4770 | −0.823239 | ||||||||
\(269\) | −27.5788 | −1.68151 | −0.840754 | − | 0.541418i | \(-0.817888\pi\) | ||||
−0.840754 | + | 0.541418i | \(0.817888\pi\) | |||||||
\(270\) | 3.31048 | 0.201470 | ||||||||
\(271\) | −23.1705 | −1.40751 | −0.703755 | − | 0.710443i | \(-0.748495\pi\) | ||||
−0.703755 | + | 0.710443i | \(0.748495\pi\) | |||||||
\(272\) | −6.54138 | −0.396629 | ||||||||
\(273\) | −58.7130 | −3.55347 | ||||||||
\(274\) | −18.0039 | −1.08765 | ||||||||
\(275\) | −3.95903 | −0.238738 | ||||||||
\(276\) | −0.956904 | −0.0575988 | ||||||||
\(277\) | −14.1382 | −0.849480 | −0.424740 | − | 0.905315i | \(-0.639634\pi\) | ||||
−0.424740 | + | 0.905315i | \(0.639634\pi\) | |||||||
\(278\) | 21.2018 | 1.27160 | ||||||||
\(279\) | 23.2070 | 1.38937 | ||||||||
\(280\) | 5.91655 | 0.353581 | ||||||||
\(281\) | −4.87885 | −0.291048 | −0.145524 | − | 0.989355i | \(-0.546487\pi\) | ||||
−0.145524 | + | 0.989355i | \(0.546487\pi\) | |||||||
\(282\) | 15.8067 | 0.941275 | ||||||||
\(283\) | −12.8107 | −0.761516 | −0.380758 | − | 0.924675i | \(-0.624337\pi\) | ||||
−0.380758 | + | 0.924675i | \(0.624337\pi\) | |||||||
\(284\) | 4.01685 | 0.238356 | ||||||||
\(285\) | 27.2132 | 1.61197 | ||||||||
\(286\) | 7.44028 | 0.439953 | ||||||||
\(287\) | 2.49701 | 0.147394 | ||||||||
\(288\) | −3.87363 | −0.228256 | ||||||||
\(289\) | 25.7896 | 1.51704 | ||||||||
\(290\) | 11.7532 | 0.690173 | ||||||||
\(291\) | 4.05508 | 0.237713 | ||||||||
\(292\) | −16.8267 | −0.984710 | ||||||||
\(293\) | −22.7712 | −1.33031 | −0.665154 | − | 0.746706i | \(-0.731634\pi\) | ||||
−0.665154 | + | 0.746706i | \(0.731634\pi\) | |||||||
\(294\) | 25.5807 | 1.49190 | ||||||||
\(295\) | 1.53041 | 0.0891040 | ||||||||
\(296\) | 10.8895 | 0.632942 | ||||||||
\(297\) | −3.11508 | −0.180755 | ||||||||
\(298\) | 7.49989 | 0.434457 | ||||||||
\(299\) | −1.99672 | −0.115473 | ||||||||
\(300\) | 7.63194 | 0.440630 | ||||||||
\(301\) | 13.8717 | 0.799554 | ||||||||
\(302\) | 16.9662 | 0.976298 | ||||||||
\(303\) | −10.8019 | −0.620554 | ||||||||
\(304\) | −7.18152 | −0.411889 | ||||||||
\(305\) | 5.50282 | 0.315090 | ||||||||
\(306\) | 25.3389 | 1.44853 | ||||||||
\(307\) | 26.5484 | 1.51520 | 0.757599 | − | 0.652721i | \(-0.226372\pi\) | ||||
0.757599 | + | 0.652721i | \(0.226372\pi\) | |||||||
\(308\) | −5.56731 | −0.317227 | ||||||||
\(309\) | 13.7419 | 0.781751 | ||||||||
\(310\) | −8.65905 | −0.491801 | ||||||||
\(311\) | −18.3052 | −1.03799 | −0.518995 | − | 0.854777i | \(-0.673694\pi\) | ||||
−0.518995 | + | 0.854777i | \(0.673694\pi\) | |||||||
\(312\) | −14.3429 | −0.812004 | ||||||||
\(313\) | −1.74796 | −0.0988004 | −0.0494002 | − | 0.998779i | \(-0.515731\pi\) | ||||
−0.0494002 | + | 0.998779i | \(0.515731\pi\) | |||||||
\(314\) | 9.19808 | 0.519078 | ||||||||
\(315\) | −22.9185 | −1.29131 | ||||||||
\(316\) | −7.89704 | −0.444243 | ||||||||
\(317\) | 4.85941 | 0.272931 | 0.136466 | − | 0.990645i | \(-0.456426\pi\) | ||||
0.136466 | + | 0.990645i | \(0.456426\pi\) | |||||||
\(318\) | −9.07762 | −0.509048 | ||||||||
\(319\) | −11.0595 | −0.619212 | ||||||||
\(320\) | 1.44534 | 0.0807968 | ||||||||
\(321\) | −39.9829 | −2.23163 | ||||||||
\(322\) | 1.49408 | 0.0832618 | ||||||||
\(323\) | 46.9770 | 2.61387 | ||||||||
\(324\) | −5.61587 | −0.311993 | ||||||||
\(325\) | 15.9252 | 0.883370 | ||||||||
\(326\) | −13.3398 | −0.738821 | ||||||||
\(327\) | 13.0108 | 0.719498 | ||||||||
\(328\) | 0.609989 | 0.0336810 | ||||||||
\(329\) | −24.6801 | −1.36066 | ||||||||
\(330\) | 5.15358 | 0.283695 | ||||||||
\(331\) | 14.5539 | 0.799953 | 0.399977 | − | 0.916525i | \(-0.369018\pi\) | ||||
0.399977 | + | 0.916525i | \(0.369018\pi\) | |||||||
\(332\) | −1.45700 | −0.0799630 | ||||||||
\(333\) | −42.1821 | −2.31156 | ||||||||
\(334\) | −13.9074 | −0.760981 | ||||||||
\(335\) | −19.4788 | −1.06424 | ||||||||
\(336\) | 10.7323 | 0.585494 | ||||||||
\(337\) | 23.1858 | 1.26301 | 0.631505 | − | 0.775372i | \(-0.282438\pi\) | ||||
0.631505 | + | 0.775372i | \(0.282438\pi\) | |||||||
\(338\) | −16.9285 | −0.920789 | ||||||||
\(339\) | 35.3548 | 1.92021 | ||||||||
\(340\) | −9.45450 | −0.512742 | ||||||||
\(341\) | 8.14793 | 0.441235 | ||||||||
\(342\) | 27.8186 | 1.50426 | ||||||||
\(343\) | −11.2861 | −0.609393 | ||||||||
\(344\) | 3.38869 | 0.182706 | ||||||||
\(345\) | −1.38305 | −0.0744609 | ||||||||
\(346\) | 14.7694 | 0.794008 | ||||||||
\(347\) | 27.3960 | 1.47069 | 0.735346 | − | 0.677692i | \(-0.237020\pi\) | ||||
0.735346 | + | 0.677692i | \(0.237020\pi\) | |||||||
\(348\) | 21.3197 | 1.14286 | ||||||||
\(349\) | 26.3999 | 1.41315 | 0.706577 | − | 0.707636i | \(-0.250238\pi\) | ||||
0.706577 | + | 0.707636i | \(0.250238\pi\) | |||||||
\(350\) | −11.9163 | −0.636952 | ||||||||
\(351\) | 12.5304 | 0.668823 | ||||||||
\(352\) | −1.36002 | −0.0724896 | ||||||||
\(353\) | −13.7470 | −0.731681 | −0.365840 | − | 0.930678i | \(-0.619218\pi\) | ||||
−0.365840 | + | 0.930678i | \(0.619218\pi\) | |||||||
\(354\) | 2.77608 | 0.147547 | ||||||||
\(355\) | 5.80570 | 0.308135 | ||||||||
\(356\) | 12.9834 | 0.688118 | ||||||||
\(357\) | −70.2039 | −3.71558 | ||||||||
\(358\) | 13.4258 | 0.709575 | ||||||||
\(359\) | −3.82307 | −0.201774 | −0.100887 | − | 0.994898i | \(-0.532168\pi\) | ||||
−0.100887 | + | 0.994898i | \(0.532168\pi\) | |||||||
\(360\) | −5.59871 | −0.295078 | ||||||||
\(361\) | 32.5743 | 1.71444 | ||||||||
\(362\) | −1.06095 | −0.0557622 | ||||||||
\(363\) | 23.9900 | 1.25915 | ||||||||
\(364\) | 22.3945 | 1.17379 | ||||||||
\(365\) | −24.3203 | −1.27298 | ||||||||
\(366\) | 9.98180 | 0.521757 | ||||||||
\(367\) | 23.1945 | 1.21074 | 0.605372 | − | 0.795943i | \(-0.293024\pi\) | ||||
0.605372 | + | 0.795943i | \(0.293024\pi\) | |||||||
\(368\) | 0.364985 | 0.0190262 | ||||||||
\(369\) | −2.36287 | −0.123006 | ||||||||
\(370\) | 15.7391 | 0.818235 | ||||||||
\(371\) | 14.1735 | 0.735853 | ||||||||
\(372\) | −15.7070 | −0.814371 | ||||||||
\(373\) | 13.4254 | 0.695138 | 0.347569 | − | 0.937654i | \(-0.387007\pi\) | ||||
0.347569 | + | 0.937654i | \(0.387007\pi\) | |||||||
\(374\) | 8.89643 | 0.460024 | ||||||||
\(375\) | 29.9774 | 1.54803 | ||||||||
\(376\) | −6.02904 | −0.310924 | ||||||||
\(377\) | 44.4867 | 2.29118 | ||||||||
\(378\) | −9.37607 | −0.482253 | ||||||||
\(379\) | 14.3281 | 0.735985 | 0.367993 | − | 0.929829i | \(-0.380045\pi\) | ||||
0.367993 | + | 0.929829i | \(0.380045\pi\) | |||||||
\(380\) | −10.3797 | −0.532469 | ||||||||
\(381\) | −21.3351 | −1.09303 | ||||||||
\(382\) | 24.7184 | 1.26470 | ||||||||
\(383\) | −4.47181 | −0.228499 | −0.114249 | − | 0.993452i | \(-0.536446\pi\) | ||||
−0.114249 | + | 0.993452i | \(0.536446\pi\) | |||||||
\(384\) | 2.62176 | 0.133791 | ||||||||
\(385\) | −8.04665 | −0.410095 | ||||||||
\(386\) | 3.02058 | 0.153743 | ||||||||
\(387\) | −13.1265 | −0.667260 | ||||||||
\(388\) | −1.54670 | −0.0785218 | ||||||||
\(389\) | −15.9884 | −0.810643 | −0.405322 | − | 0.914174i | \(-0.632840\pi\) | ||||
−0.405322 | + | 0.914174i | \(0.632840\pi\) | |||||||
\(390\) | −20.7303 | −1.04972 | ||||||||
\(391\) | −2.38750 | −0.120741 | ||||||||
\(392\) | −9.75706 | −0.492806 | ||||||||
\(393\) | 39.4962 | 1.99232 | ||||||||
\(394\) | −18.7157 | −0.942884 | ||||||||
\(395\) | −11.4139 | −0.574295 | ||||||||
\(396\) | 5.26824 | 0.264739 | ||||||||
\(397\) | −8.14136 | −0.408603 | −0.204302 | − | 0.978908i | \(-0.565492\pi\) | ||||
−0.204302 | + | 0.978908i | \(0.565492\pi\) | |||||||
\(398\) | −7.74076 | −0.388009 | ||||||||
\(399\) | −77.0741 | −3.85853 | ||||||||
\(400\) | −2.91100 | −0.145550 | ||||||||
\(401\) | −28.3772 | −1.41709 | −0.708545 | − | 0.705665i | \(-0.750648\pi\) | ||||
−0.708545 | + | 0.705665i | \(0.750648\pi\) | |||||||
\(402\) | −35.3335 | −1.76228 | ||||||||
\(403\) | −32.7750 | −1.63264 | ||||||||
\(404\) | 4.12010 | 0.204983 | ||||||||
\(405\) | −8.11683 | −0.403328 | ||||||||
\(406\) | −33.2879 | −1.65205 | ||||||||
\(407\) | −14.8100 | −0.734106 | ||||||||
\(408\) | −17.1499 | −0.849048 | ||||||||
\(409\) | 29.1329 | 1.44053 | 0.720264 | − | 0.693700i | \(-0.244021\pi\) | ||||
0.720264 | + | 0.693700i | \(0.244021\pi\) | |||||||
\(410\) | 0.881641 | 0.0435411 | ||||||||
\(411\) | −47.2018 | −2.32829 | ||||||||
\(412\) | −5.24149 | −0.258230 | ||||||||
\(413\) | −4.33449 | −0.213286 | ||||||||
\(414\) | −1.41382 | −0.0694854 | ||||||||
\(415\) | −2.10585 | −0.103372 | ||||||||
\(416\) | 5.47069 | 0.268223 | ||||||||
\(417\) | 55.5861 | 2.72207 | ||||||||
\(418\) | 9.76705 | 0.477722 | ||||||||
\(419\) | 10.9845 | 0.536628 | 0.268314 | − | 0.963331i | \(-0.413533\pi\) | ||||
0.268314 | + | 0.963331i | \(0.413533\pi\) | |||||||
\(420\) | 15.5118 | 0.756897 | ||||||||
\(421\) | 11.3632 | 0.553807 | 0.276903 | − | 0.960898i | \(-0.410692\pi\) | ||||
0.276903 | + | 0.960898i | \(0.410692\pi\) | |||||||
\(422\) | −5.83190 | −0.283892 | ||||||||
\(423\) | 23.3543 | 1.13552 | ||||||||
\(424\) | 3.46241 | 0.168150 | ||||||||
\(425\) | 19.0419 | 0.923670 | ||||||||
\(426\) | 10.5312 | 0.510239 | ||||||||
\(427\) | −15.5853 | −0.754225 | ||||||||
\(428\) | 15.2504 | 0.737156 | ||||||||
\(429\) | 19.5066 | 0.941789 | ||||||||
\(430\) | 4.89780 | 0.236193 | ||||||||
\(431\) | 37.3716 | 1.80012 | 0.900062 | − | 0.435761i | \(-0.143521\pi\) | ||||
0.900062 | + | 0.435761i | \(0.143521\pi\) | |||||||
\(432\) | −2.29046 | −0.110200 | ||||||||
\(433\) | 14.2547 | 0.685038 | 0.342519 | − | 0.939511i | \(-0.388720\pi\) | ||||
0.342519 | + | 0.939511i | \(0.388720\pi\) | |||||||
\(434\) | 24.5245 | 1.17721 | ||||||||
\(435\) | 30.8142 | 1.47743 | ||||||||
\(436\) | −4.96261 | −0.237666 | ||||||||
\(437\) | −2.62115 | −0.125387 | ||||||||
\(438\) | −44.1157 | −2.10793 | ||||||||
\(439\) | −2.48473 | −0.118590 | −0.0592948 | − | 0.998241i | \(-0.518885\pi\) | ||||
−0.0592948 | + | 0.998241i | \(0.518885\pi\) | |||||||
\(440\) | −1.96570 | −0.0937108 | ||||||||
\(441\) | 37.7953 | 1.79977 | ||||||||
\(442\) | −35.7859 | −1.70216 | ||||||||
\(443\) | −27.4112 | −1.30235 | −0.651173 | − | 0.758930i | \(-0.725723\pi\) | ||||
−0.651173 | + | 0.758930i | \(0.725723\pi\) | |||||||
\(444\) | 28.5498 | 1.35491 | ||||||||
\(445\) | 18.7654 | 0.889564 | ||||||||
\(446\) | −1.68068 | −0.0795827 | ||||||||
\(447\) | 19.6629 | 0.930025 | ||||||||
\(448\) | −4.09354 | −0.193402 | ||||||||
\(449\) | −18.5159 | −0.873822 | −0.436911 | − | 0.899505i | \(-0.643927\pi\) | ||||
−0.436911 | + | 0.899505i | \(0.643927\pi\) | |||||||
\(450\) | 11.2761 | 0.531562 | ||||||||
\(451\) | −0.829601 | −0.0390644 | ||||||||
\(452\) | −13.4851 | −0.634287 | ||||||||
\(453\) | 44.4814 | 2.08992 | ||||||||
\(454\) | −19.5353 | −0.916839 | ||||||||
\(455\) | 32.3676 | 1.51742 | ||||||||
\(456\) | −18.8282 | −0.881713 | ||||||||
\(457\) | −19.1505 | −0.895821 | −0.447911 | − | 0.894078i | \(-0.647832\pi\) | ||||
−0.447911 | + | 0.894078i | \(0.647832\pi\) | |||||||
\(458\) | 5.15115 | 0.240698 | ||||||||
\(459\) | 14.9827 | 0.699334 | ||||||||
\(460\) | 0.527527 | 0.0245961 | ||||||||
\(461\) | −14.9860 | −0.697968 | −0.348984 | − | 0.937129i | \(-0.613473\pi\) | ||||
−0.348984 | + | 0.937129i | \(0.613473\pi\) | |||||||
\(462\) | −14.5962 | −0.679075 | ||||||||
\(463\) | −34.3496 | −1.59636 | −0.798180 | − | 0.602419i | \(-0.794204\pi\) | ||||
−0.798180 | + | 0.602419i | \(0.794204\pi\) | |||||||
\(464\) | −8.13182 | −0.377510 | ||||||||
\(465\) | −22.7020 | −1.05278 | ||||||||
\(466\) | 8.24409 | 0.381900 | ||||||||
\(467\) | 6.33991 | 0.293376 | 0.146688 | − | 0.989183i | \(-0.453139\pi\) | ||||
0.146688 | + | 0.989183i | \(0.453139\pi\) | |||||||
\(468\) | −21.1915 | −0.979576 | ||||||||
\(469\) | 55.1687 | 2.54745 | ||||||||
\(470\) | −8.71400 | −0.401947 | ||||||||
\(471\) | 24.1152 | 1.11117 | ||||||||
\(472\) | −1.05886 | −0.0487380 | ||||||||
\(473\) | −4.60870 | −0.211908 | ||||||||
\(474\) | −20.7041 | −0.950973 | ||||||||
\(475\) | 20.9054 | 0.959206 | ||||||||
\(476\) | 26.7774 | 1.22734 | ||||||||
\(477\) | −13.4121 | −0.614099 | ||||||||
\(478\) | −11.2771 | −0.515801 | ||||||||
\(479\) | −32.6955 | −1.49389 | −0.746947 | − | 0.664883i | \(-0.768481\pi\) | ||||
−0.746947 | + | 0.664883i | \(0.768481\pi\) | |||||||
\(480\) | 3.78933 | 0.172958 | ||||||||
\(481\) | 59.5733 | 2.71631 | ||||||||
\(482\) | −5.90314 | −0.268880 | ||||||||
\(483\) | 3.91712 | 0.178235 | ||||||||
\(484\) | −9.15033 | −0.415924 | ||||||||
\(485\) | −2.23550 | −0.101509 | ||||||||
\(486\) | −21.5948 | −0.979562 | ||||||||
\(487\) | −2.28521 | −0.103553 | −0.0517764 | − | 0.998659i | \(-0.516488\pi\) | ||||
−0.0517764 | + | 0.998659i | \(0.516488\pi\) | |||||||
\(488\) | −3.80729 | −0.172348 | ||||||||
\(489\) | −34.9737 | −1.58156 | ||||||||
\(490\) | −14.1022 | −0.637074 | ||||||||
\(491\) | −32.2680 | −1.45623 | −0.728117 | − | 0.685453i | \(-0.759604\pi\) | ||||
−0.728117 | + | 0.685453i | \(0.759604\pi\) | |||||||
\(492\) | 1.59925 | 0.0720996 | ||||||||
\(493\) | 53.1933 | 2.39571 | ||||||||
\(494\) | −39.2879 | −1.76765 | ||||||||
\(495\) | 7.61438 | 0.342241 | ||||||||
\(496\) | 5.99102 | 0.269005 | ||||||||
\(497\) | −16.4431 | −0.737575 | ||||||||
\(498\) | −3.81989 | −0.171174 | ||||||||
\(499\) | −17.9334 | −0.802808 | −0.401404 | − | 0.915901i | \(-0.631478\pi\) | ||||
−0.401404 | + | 0.915901i | \(0.631478\pi\) | |||||||
\(500\) | −11.4341 | −0.511347 | ||||||||
\(501\) | −36.4620 | −1.62900 | ||||||||
\(502\) | −8.33837 | −0.372160 | ||||||||
\(503\) | 35.0425 | 1.56247 | 0.781235 | − | 0.624238i | \(-0.214590\pi\) | ||||
0.781235 | + | 0.624238i | \(0.214590\pi\) | |||||||
\(504\) | 15.8569 | 0.706321 | ||||||||
\(505\) | 5.95494 | 0.264991 | ||||||||
\(506\) | −0.496389 | −0.0220672 | ||||||||
\(507\) | −44.3825 | −1.97110 | ||||||||
\(508\) | 8.13770 | 0.361052 | ||||||||
\(509\) | 30.9489 | 1.37178 | 0.685892 | − | 0.727703i | \(-0.259412\pi\) | ||||
0.685892 | + | 0.727703i | \(0.259412\pi\) | |||||||
\(510\) | −24.7874 | −1.09761 | ||||||||
\(511\) | 68.8808 | 3.04711 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 16.4490 | 0.726240 | ||||||||
\(514\) | −31.9857 | −1.41083 | ||||||||
\(515\) | −7.57572 | −0.333826 | ||||||||
\(516\) | 8.88434 | 0.391111 | ||||||||
\(517\) | 8.19964 | 0.360620 | ||||||||
\(518\) | −44.5767 | −1.95859 | ||||||||
\(519\) | 38.7219 | 1.69970 | ||||||||
\(520\) | 7.90700 | 0.346745 | ||||||||
\(521\) | 16.1727 | 0.708539 | 0.354270 | − | 0.935143i | \(-0.384730\pi\) | ||||
0.354270 | + | 0.935143i | \(0.384730\pi\) | |||||||
\(522\) | 31.4997 | 1.37870 | ||||||||
\(523\) | 41.9849 | 1.83587 | 0.917936 | − | 0.396729i | \(-0.129855\pi\) | ||||
0.917936 | + | 0.396729i | \(0.129855\pi\) | |||||||
\(524\) | −15.0648 | −0.658107 | ||||||||
\(525\) | −31.2417 | −1.36350 | ||||||||
\(526\) | −7.92671 | −0.345621 | ||||||||
\(527\) | −39.1895 | −1.70712 | ||||||||
\(528\) | −3.56566 | −0.155175 | ||||||||
\(529\) | −22.8668 | −0.994208 | ||||||||
\(530\) | 5.00436 | 0.217375 | ||||||||
\(531\) | 4.10164 | 0.177996 | ||||||||
\(532\) | 29.3978 | 1.27456 | ||||||||
\(533\) | 3.33707 | 0.144544 | ||||||||
\(534\) | 34.0393 | 1.47303 | ||||||||
\(535\) | 22.0420 | 0.952959 | ||||||||
\(536\) | 13.4770 | 0.582118 | ||||||||
\(537\) | 35.1992 | 1.51896 | ||||||||
\(538\) | 27.5788 | 1.18901 | ||||||||
\(539\) | 13.2698 | 0.571572 | ||||||||
\(540\) | −3.31048 | −0.142461 | ||||||||
\(541\) | 3.66219 | 0.157450 | 0.0787248 | − | 0.996896i | \(-0.474915\pi\) | ||||
0.0787248 | + | 0.996896i | \(0.474915\pi\) | |||||||
\(542\) | 23.1705 | 0.995259 | ||||||||
\(543\) | −2.78155 | −0.119368 | ||||||||
\(544\) | 6.54138 | 0.280459 | ||||||||
\(545\) | −7.17265 | −0.307243 | ||||||||
\(546\) | 58.7130 | 2.51269 | ||||||||
\(547\) | −37.4615 | −1.60174 | −0.800869 | − | 0.598839i | \(-0.795629\pi\) | ||||
−0.800869 | + | 0.598839i | \(0.795629\pi\) | |||||||
\(548\) | 18.0039 | 0.769087 | ||||||||
\(549\) | 14.7480 | 0.629431 | ||||||||
\(550\) | 3.95903 | 0.168814 | ||||||||
\(551\) | 58.3989 | 2.48788 | ||||||||
\(552\) | 0.956904 | 0.0407285 | ||||||||
\(553\) | 32.3268 | 1.37468 | ||||||||
\(554\) | 14.1382 | 0.600673 | ||||||||
\(555\) | 41.2641 | 1.75156 | ||||||||
\(556\) | −21.2018 | −0.899158 | ||||||||
\(557\) | −31.2437 | −1.32384 | −0.661919 | − | 0.749576i | \(-0.730258\pi\) | ||||
−0.661919 | + | 0.749576i | \(0.730258\pi\) | |||||||
\(558\) | −23.2070 | −0.982431 | ||||||||
\(559\) | 18.5385 | 0.784095 | ||||||||
\(560\) | −5.91655 | −0.250020 | ||||||||
\(561\) | 23.3243 | 0.984754 | ||||||||
\(562\) | 4.87885 | 0.205802 | ||||||||
\(563\) | −40.1601 | −1.69254 | −0.846272 | − | 0.532750i | \(-0.821158\pi\) | ||||
−0.846272 | + | 0.532750i | \(0.821158\pi\) | |||||||
\(564\) | −15.8067 | −0.665582 | ||||||||
\(565\) | −19.4906 | −0.819975 | ||||||||
\(566\) | 12.8107 | 0.538473 | ||||||||
\(567\) | 22.9888 | 0.965438 | ||||||||
\(568\) | −4.01685 | −0.168543 | ||||||||
\(569\) | 29.1994 | 1.22410 | 0.612052 | − | 0.790817i | \(-0.290344\pi\) | ||||
0.612052 | + | 0.790817i | \(0.290344\pi\) | |||||||
\(570\) | −27.2132 | −1.13983 | ||||||||
\(571\) | 5.97277 | 0.249953 | 0.124976 | − | 0.992160i | \(-0.460114\pi\) | ||||
0.124976 | + | 0.992160i | \(0.460114\pi\) | |||||||
\(572\) | −7.44028 | −0.311094 | ||||||||
\(573\) | 64.8058 | 2.70730 | ||||||||
\(574\) | −2.49701 | −0.104223 | ||||||||
\(575\) | −1.06247 | −0.0443081 | ||||||||
\(576\) | 3.87363 | 0.161401 | ||||||||
\(577\) | −28.5601 | −1.18897 | −0.594486 | − | 0.804106i | \(-0.702644\pi\) | ||||
−0.594486 | + | 0.804106i | \(0.702644\pi\) | |||||||
\(578\) | −25.7896 | −1.07271 | ||||||||
\(579\) | 7.91923 | 0.329112 | ||||||||
\(580\) | −11.7532 | −0.488026 | ||||||||
\(581\) | 5.96427 | 0.247440 | ||||||||
\(582\) | −4.05508 | −0.168088 | ||||||||
\(583\) | −4.70897 | −0.195026 | ||||||||
\(584\) | 16.8267 | 0.696295 | ||||||||
\(585\) | −30.6288 | −1.26635 | ||||||||
\(586\) | 22.7712 | 0.940670 | ||||||||
\(587\) | 10.9831 | 0.453322 | 0.226661 | − | 0.973974i | \(-0.427219\pi\) | ||||
0.226661 | + | 0.973974i | \(0.427219\pi\) | |||||||
\(588\) | −25.5807 | −1.05493 | ||||||||
\(589\) | −43.0246 | −1.77280 | ||||||||
\(590\) | −1.53041 | −0.0630060 | ||||||||
\(591\) | −49.0681 | −2.01839 | ||||||||
\(592\) | −10.8895 | −0.447557 | ||||||||
\(593\) | −34.2296 | −1.40564 | −0.702822 | − | 0.711366i | \(-0.748077\pi\) | ||||
−0.702822 | + | 0.711366i | \(0.748077\pi\) | |||||||
\(594\) | 3.11508 | 0.127813 | ||||||||
\(595\) | 38.7024 | 1.58664 | ||||||||
\(596\) | −7.49989 | −0.307208 | ||||||||
\(597\) | −20.2944 | −0.830595 | ||||||||
\(598\) | 1.99672 | 0.0816520 | ||||||||
\(599\) | 0.488672 | 0.0199666 | 0.00998330 | − | 0.999950i | \(-0.496822\pi\) | ||||
0.00998330 | + | 0.999950i | \(0.496822\pi\) | |||||||
\(600\) | −7.63194 | −0.311573 | ||||||||
\(601\) | −11.1034 | −0.452918 | −0.226459 | − | 0.974021i | \(-0.572715\pi\) | ||||
−0.226459 | + | 0.974021i | \(0.572715\pi\) | |||||||
\(602\) | −13.8717 | −0.565370 | ||||||||
\(603\) | −52.2050 | −2.12595 | ||||||||
\(604\) | −16.9662 | −0.690347 | ||||||||
\(605\) | −13.2253 | −0.537686 | ||||||||
\(606\) | 10.8019 | 0.438798 | ||||||||
\(607\) | 30.3342 | 1.23123 | 0.615614 | − | 0.788048i | \(-0.288908\pi\) | ||||
0.615614 | + | 0.788048i | \(0.288908\pi\) | |||||||
\(608\) | 7.18152 | 0.291249 | ||||||||
\(609\) | −87.2730 | −3.53648 | ||||||||
\(610\) | −5.50282 | −0.222803 | ||||||||
\(611\) | −32.9830 | −1.33435 | ||||||||
\(612\) | −25.3389 | −1.02426 | ||||||||
\(613\) | 16.0652 | 0.648869 | 0.324434 | − | 0.945908i | \(-0.394826\pi\) | ||||
0.324434 | + | 0.945908i | \(0.394826\pi\) | |||||||
\(614\) | −26.5484 | −1.07141 | ||||||||
\(615\) | 2.31145 | 0.0932067 | ||||||||
\(616\) | 5.56731 | 0.224313 | ||||||||
\(617\) | −27.7335 | −1.11651 | −0.558255 | − | 0.829669i | \(-0.688529\pi\) | ||||
−0.558255 | + | 0.829669i | \(0.688529\pi\) | |||||||
\(618\) | −13.7419 | −0.552782 | ||||||||
\(619\) | 21.0334 | 0.845405 | 0.422703 | − | 0.906268i | \(-0.361081\pi\) | ||||
0.422703 | + | 0.906268i | \(0.361081\pi\) | |||||||
\(620\) | 8.65905 | 0.347756 | ||||||||
\(621\) | −0.835982 | −0.0335468 | ||||||||
\(622\) | 18.3052 | 0.733970 | ||||||||
\(623\) | −53.1480 | −2.12933 | ||||||||
\(624\) | 14.3429 | 0.574174 | ||||||||
\(625\) | −1.97109 | −0.0788438 | ||||||||
\(626\) | 1.74796 | 0.0698624 | ||||||||
\(627\) | 25.6069 | 1.02264 | ||||||||
\(628\) | −9.19808 | −0.367043 | ||||||||
\(629\) | 71.2326 | 2.84023 | ||||||||
\(630\) | 22.9185 | 0.913096 | ||||||||
\(631\) | −4.31983 | −0.171970 | −0.0859849 | − | 0.996296i | \(-0.527404\pi\) | ||||
−0.0859849 | + | 0.996296i | \(0.527404\pi\) | |||||||
\(632\) | 7.89704 | 0.314127 | ||||||||
\(633\) | −15.2898 | −0.607717 | ||||||||
\(634\) | −4.85941 | −0.192992 | ||||||||
\(635\) | 11.7617 | 0.466750 | ||||||||
\(636\) | 9.07762 | 0.359951 | ||||||||
\(637\) | −53.3779 | −2.11491 | ||||||||
\(638\) | 11.0595 | 0.437849 | ||||||||
\(639\) | 15.5598 | 0.615536 | ||||||||
\(640\) | −1.44534 | −0.0571320 | ||||||||
\(641\) | 3.77164 | 0.148971 | 0.0744855 | − | 0.997222i | \(-0.476269\pi\) | ||||
0.0744855 | + | 0.997222i | \(0.476269\pi\) | |||||||
\(642\) | 39.9829 | 1.57800 | ||||||||
\(643\) | −12.1021 | −0.477261 | −0.238630 | − | 0.971110i | \(-0.576698\pi\) | ||||
−0.238630 | + | 0.971110i | \(0.576698\pi\) | |||||||
\(644\) | −1.49408 | −0.0588750 | ||||||||
\(645\) | 12.8409 | 0.505609 | ||||||||
\(646\) | −46.9770 | −1.84829 | ||||||||
\(647\) | −35.5611 | −1.39805 | −0.699026 | − | 0.715096i | \(-0.746383\pi\) | ||||
−0.699026 | + | 0.715096i | \(0.746383\pi\) | |||||||
\(648\) | 5.61587 | 0.220612 | ||||||||
\(649\) | 1.44008 | 0.0565280 | ||||||||
\(650\) | −15.9252 | −0.624637 | ||||||||
\(651\) | 64.2973 | 2.52001 | ||||||||
\(652\) | 13.3398 | 0.522425 | ||||||||
\(653\) | 27.2904 | 1.06796 | 0.533978 | − | 0.845499i | \(-0.320697\pi\) | ||||
0.533978 | + | 0.845499i | \(0.320697\pi\) | |||||||
\(654\) | −13.0108 | −0.508762 | ||||||||
\(655\) | −21.7737 | −0.850767 | ||||||||
\(656\) | −0.609989 | −0.0238161 | ||||||||
\(657\) | −65.1806 | −2.54294 | ||||||||
\(658\) | 24.6801 | 0.962130 | ||||||||
\(659\) | −31.5019 | −1.22714 | −0.613570 | − | 0.789640i | \(-0.710267\pi\) | ||||
−0.613570 | + | 0.789640i | \(0.710267\pi\) | |||||||
\(660\) | −5.15358 | −0.200603 | ||||||||
\(661\) | 3.66417 | 0.142520 | 0.0712599 | − | 0.997458i | \(-0.477298\pi\) | ||||
0.0712599 | + | 0.997458i | \(0.477298\pi\) | |||||||
\(662\) | −14.5539 | −0.565652 | ||||||||
\(663\) | −93.8220 | −3.64375 | ||||||||
\(664\) | 1.45700 | 0.0565424 | ||||||||
\(665\) | 42.4898 | 1.64768 | ||||||||
\(666\) | 42.1821 | 1.63452 | ||||||||
\(667\) | −2.96799 | −0.114921 | ||||||||
\(668\) | 13.9074 | 0.538095 | ||||||||
\(669\) | −4.40635 | −0.170359 | ||||||||
\(670\) | 19.4788 | 0.752533 | ||||||||
\(671\) | 5.17801 | 0.199895 | ||||||||
\(672\) | −10.7323 | −0.414007 | ||||||||
\(673\) | −22.7724 | −0.877810 | −0.438905 | − | 0.898533i | \(-0.644634\pi\) | ||||
−0.438905 | + | 0.898533i | \(0.644634\pi\) | |||||||
\(674\) | −23.1858 | −0.893082 | ||||||||
\(675\) | 6.66751 | 0.256633 | ||||||||
\(676\) | 16.9285 | 0.651096 | ||||||||
\(677\) | −1.62301 | −0.0623773 | −0.0311887 | − | 0.999514i | \(-0.509929\pi\) | ||||
−0.0311887 | + | 0.999514i | \(0.509929\pi\) | |||||||
\(678\) | −35.3548 | −1.35779 | ||||||||
\(679\) | 6.33148 | 0.242980 | ||||||||
\(680\) | 9.45450 | 0.362563 | ||||||||
\(681\) | −51.2170 | −1.96264 | ||||||||
\(682\) | −8.14793 | −0.312001 | ||||||||
\(683\) | −21.3377 | −0.816464 | −0.408232 | − | 0.912878i | \(-0.633855\pi\) | ||||
−0.408232 | + | 0.912878i | \(0.633855\pi\) | |||||||
\(684\) | −27.8186 | −1.06367 | ||||||||
\(685\) | 26.0217 | 0.994237 | ||||||||
\(686\) | 11.2861 | 0.430906 | ||||||||
\(687\) | 13.5051 | 0.515252 | ||||||||
\(688\) | −3.38869 | −0.129193 | ||||||||
\(689\) | 18.9418 | 0.721625 | ||||||||
\(690\) | 1.38305 | 0.0526518 | ||||||||
\(691\) | −14.3975 | −0.547707 | −0.273853 | − | 0.961771i | \(-0.588298\pi\) | ||||
−0.273853 | + | 0.961771i | \(0.588298\pi\) | |||||||
\(692\) | −14.7694 | −0.561448 | ||||||||
\(693\) | −21.5657 | −0.819214 | ||||||||
\(694\) | −27.3960 | −1.03994 | ||||||||
\(695\) | −30.6438 | −1.16239 | ||||||||
\(696\) | −21.3197 | −0.808121 | ||||||||
\(697\) | 3.99017 | 0.151138 | ||||||||
\(698\) | −26.3999 | −0.999251 | ||||||||
\(699\) | 21.6140 | 0.817518 | ||||||||
\(700\) | 11.9163 | 0.450393 | ||||||||
\(701\) | −5.04224 | −0.190443 | −0.0952213 | − | 0.995456i | \(-0.530356\pi\) | ||||
−0.0952213 | + | 0.995456i | \(0.530356\pi\) | |||||||
\(702\) | −12.5304 | −0.472929 | ||||||||
\(703\) | 78.2035 | 2.94950 | ||||||||
\(704\) | 1.36002 | 0.0512579 | ||||||||
\(705\) | −22.8460 | −0.860431 | ||||||||
\(706\) | 13.7470 | 0.517376 | ||||||||
\(707\) | −16.8658 | −0.634304 | ||||||||
\(708\) | −2.77608 | −0.104331 | ||||||||
\(709\) | −36.7624 | −1.38064 | −0.690320 | − | 0.723504i | \(-0.742530\pi\) | ||||
−0.690320 | + | 0.723504i | \(0.742530\pi\) | |||||||
\(710\) | −5.80570 | −0.217884 | ||||||||
\(711\) | −30.5902 | −1.14722 | ||||||||
\(712\) | −12.9834 | −0.486573 | ||||||||
\(713\) | 2.18663 | 0.0818900 | ||||||||
\(714\) | 70.2039 | 2.62731 | ||||||||
\(715\) | −10.7537 | −0.402166 | ||||||||
\(716\) | −13.4258 | −0.501746 | ||||||||
\(717\) | −29.5658 | −1.10415 | ||||||||
\(718\) | 3.82307 | 0.142676 | ||||||||
\(719\) | 41.7979 | 1.55880 | 0.779400 | − | 0.626527i | \(-0.215524\pi\) | ||||
0.779400 | + | 0.626527i | \(0.215524\pi\) | |||||||
\(720\) | 5.59871 | 0.208652 | ||||||||
\(721\) | 21.4562 | 0.799072 | ||||||||
\(722\) | −32.5743 | −1.21229 | ||||||||
\(723\) | −15.4766 | −0.575582 | ||||||||
\(724\) | 1.06095 | 0.0394299 | ||||||||
\(725\) | 23.6717 | 0.879146 | ||||||||
\(726\) | −23.9900 | −0.890352 | ||||||||
\(727\) | −40.7724 | −1.51216 | −0.756082 | − | 0.654477i | \(-0.772889\pi\) | ||||
−0.756082 | + | 0.654477i | \(0.772889\pi\) | |||||||
\(728\) | −22.3945 | −0.829995 | ||||||||
\(729\) | −39.7689 | −1.47292 | ||||||||
\(730\) | 24.3203 | 0.900135 | ||||||||
\(731\) | 22.1667 | 0.819865 | ||||||||
\(732\) | −9.98180 | −0.368938 | ||||||||
\(733\) | 34.8986 | 1.28901 | 0.644505 | − | 0.764600i | \(-0.277064\pi\) | ||||
0.644505 | + | 0.764600i | \(0.277064\pi\) | |||||||
\(734\) | −23.1945 | −0.856126 | ||||||||
\(735\) | −36.9727 | −1.36376 | ||||||||
\(736\) | −0.364985 | −0.0134535 | ||||||||
\(737\) | −18.3291 | −0.675160 | ||||||||
\(738\) | 2.36287 | 0.0869786 | ||||||||
\(739\) | 35.4057 | 1.30242 | 0.651210 | − | 0.758897i | \(-0.274262\pi\) | ||||
0.651210 | + | 0.758897i | \(0.274262\pi\) | |||||||
\(740\) | −15.7391 | −0.578579 | ||||||||
\(741\) | −103.004 | −3.78393 | ||||||||
\(742\) | −14.1735 | −0.520326 | ||||||||
\(743\) | 18.3569 | 0.673450 | 0.336725 | − | 0.941603i | \(-0.390681\pi\) | ||||
0.336725 | + | 0.941603i | \(0.390681\pi\) | |||||||
\(744\) | 15.7070 | 0.575847 | ||||||||
\(745\) | −10.8399 | −0.397142 | ||||||||
\(746\) | −13.4254 | −0.491537 | ||||||||
\(747\) | −5.64387 | −0.206498 | ||||||||
\(748\) | −8.89643 | −0.325286 | ||||||||
\(749\) | −62.4281 | −2.28107 | ||||||||
\(750\) | −29.9774 | −1.09462 | ||||||||
\(751\) | −14.6150 | −0.533308 | −0.266654 | − | 0.963792i | \(-0.585918\pi\) | ||||
−0.266654 | + | 0.963792i | \(0.585918\pi\) | |||||||
\(752\) | 6.02904 | 0.219856 | ||||||||
\(753\) | −21.8612 | −0.796667 | ||||||||
\(754\) | −44.4867 | −1.62011 | ||||||||
\(755\) | −24.5220 | −0.892445 | ||||||||
\(756\) | 9.37607 | 0.341004 | ||||||||
\(757\) | 12.2314 | 0.444558 | 0.222279 | − | 0.974983i | \(-0.428650\pi\) | ||||
0.222279 | + | 0.974983i | \(0.428650\pi\) | |||||||
\(758\) | −14.3281 | −0.520420 | ||||||||
\(759\) | −1.30141 | −0.0472383 | ||||||||
\(760\) | 10.3797 | 0.376512 | ||||||||
\(761\) | 19.6543 | 0.712468 | 0.356234 | − | 0.934397i | \(-0.384061\pi\) | ||||
0.356234 | + | 0.934397i | \(0.384061\pi\) | |||||||
\(762\) | 21.3351 | 0.772890 | ||||||||
\(763\) | 20.3146 | 0.735440 | ||||||||
\(764\) | −24.7184 | −0.894281 | ||||||||
\(765\) | −36.6233 | −1.32412 | ||||||||
\(766\) | 4.47181 | 0.161573 | ||||||||
\(767\) | −5.79270 | −0.209162 | ||||||||
\(768\) | −2.62176 | −0.0946047 | ||||||||
\(769\) | −15.1372 | −0.545862 | −0.272931 | − | 0.962034i | \(-0.587993\pi\) | ||||
−0.272931 | + | 0.962034i | \(0.587993\pi\) | |||||||
\(770\) | 8.04665 | 0.289981 | ||||||||
\(771\) | −83.8589 | −3.02010 | ||||||||
\(772\) | −3.02058 | −0.108713 | ||||||||
\(773\) | −31.6582 | −1.13867 | −0.569333 | − | 0.822107i | \(-0.692799\pi\) | ||||
−0.569333 | + | 0.822107i | \(0.692799\pi\) | |||||||
\(774\) | 13.1265 | 0.471824 | ||||||||
\(775\) | −17.4398 | −0.626458 | ||||||||
\(776\) | 1.54670 | 0.0555233 | ||||||||
\(777\) | −116.870 | −4.19267 | ||||||||
\(778\) | 15.9884 | 0.573211 | ||||||||
\(779\) | 4.38065 | 0.156953 | ||||||||
\(780\) | 20.7303 | 0.742263 | ||||||||
\(781\) | 5.46301 | 0.195482 | ||||||||
\(782\) | 2.38750 | 0.0853770 | ||||||||
\(783\) | 18.6256 | 0.665624 | ||||||||
\(784\) | 9.75706 | 0.348466 | ||||||||
\(785\) | −13.2943 | −0.474495 | ||||||||
\(786\) | −39.4962 | −1.40878 | ||||||||
\(787\) | 8.55072 | 0.304800 | 0.152400 | − | 0.988319i | \(-0.451300\pi\) | ||||
0.152400 | + | 0.988319i | \(0.451300\pi\) | |||||||
\(788\) | 18.7157 | 0.666720 | ||||||||
\(789\) | −20.7819 | −0.739856 | ||||||||
\(790\) | 11.4139 | 0.406088 | ||||||||
\(791\) | 55.2019 | 1.96275 | ||||||||
\(792\) | −5.26824 | −0.187199 | ||||||||
\(793\) | −20.8285 | −0.739642 | ||||||||
\(794\) | 8.14136 | 0.288926 | ||||||||
\(795\) | 13.1202 | 0.465327 | ||||||||
\(796\) | 7.74076 | 0.274364 | ||||||||
\(797\) | 13.7192 | 0.485960 | 0.242980 | − | 0.970031i | \(-0.421875\pi\) | ||||
0.242980 | + | 0.970031i | \(0.421875\pi\) | |||||||
\(798\) | 77.0741 | 2.72839 | ||||||||
\(799\) | −39.4382 | −1.39522 | ||||||||
\(800\) | 2.91100 | 0.102919 | ||||||||
\(801\) | 50.2928 | 1.77701 | ||||||||
\(802\) | 28.3772 | 1.00203 | ||||||||
\(803\) | −22.8848 | −0.807586 | ||||||||
\(804\) | 35.3335 | 1.24612 | ||||||||
\(805\) | −2.15945 | −0.0761106 | ||||||||
\(806\) | 32.7750 | 1.15445 | ||||||||
\(807\) | 72.3049 | 2.54525 | ||||||||
\(808\) | −4.12010 | −0.144945 | ||||||||
\(809\) | −23.6652 | −0.832024 | −0.416012 | − | 0.909359i | \(-0.636573\pi\) | ||||
−0.416012 | + | 0.909359i | \(0.636573\pi\) | |||||||
\(810\) | 8.11683 | 0.285196 | ||||||||
\(811\) | 9.23019 | 0.324116 | 0.162058 | − | 0.986781i | \(-0.448187\pi\) | ||||
0.162058 | + | 0.986781i | \(0.448187\pi\) | |||||||
\(812\) | 33.2879 | 1.16818 | ||||||||
\(813\) | 60.7476 | 2.13051 | ||||||||
\(814\) | 14.8100 | 0.519092 | ||||||||
\(815\) | 19.2805 | 0.675365 | ||||||||
\(816\) | 17.1499 | 0.600368 | ||||||||
\(817\) | 24.3360 | 0.851408 | ||||||||
\(818\) | −29.1329 | −1.01861 | ||||||||
\(819\) | 86.7481 | 3.03122 | ||||||||
\(820\) | −0.881641 | −0.0307882 | ||||||||
\(821\) | −2.22857 | −0.0777776 | −0.0388888 | − | 0.999244i | \(-0.512382\pi\) | ||||
−0.0388888 | + | 0.999244i | \(0.512382\pi\) | |||||||
\(822\) | 47.2018 | 1.64635 | ||||||||
\(823\) | −29.0424 | −1.01235 | −0.506177 | − | 0.862430i | \(-0.668942\pi\) | ||||
−0.506177 | + | 0.862430i | \(0.668942\pi\) | |||||||
\(824\) | 5.24149 | 0.182596 | ||||||||
\(825\) | 10.3796 | 0.361372 | ||||||||
\(826\) | 4.33449 | 0.150816 | ||||||||
\(827\) | −40.1550 | −1.39633 | −0.698163 | − | 0.715939i | \(-0.745999\pi\) | ||||
−0.698163 | + | 0.715939i | \(0.745999\pi\) | |||||||
\(828\) | 1.41382 | 0.0491336 | ||||||||
\(829\) | −34.3636 | −1.19350 | −0.596749 | − | 0.802428i | \(-0.703541\pi\) | ||||
−0.596749 | + | 0.802428i | \(0.703541\pi\) | |||||||
\(830\) | 2.10585 | 0.0730952 | ||||||||
\(831\) | 37.0669 | 1.28584 | ||||||||
\(832\) | −5.47069 | −0.189662 | ||||||||
\(833\) | −63.8246 | −2.21139 | ||||||||
\(834\) | −55.5861 | −1.92479 | ||||||||
\(835\) | 20.1009 | 0.695621 | ||||||||
\(836\) | −9.76705 | −0.337800 | ||||||||
\(837\) | −13.7222 | −0.474308 | ||||||||
\(838\) | −10.9845 | −0.379454 | ||||||||
\(839\) | −19.2038 | −0.662988 | −0.331494 | − | 0.943457i | \(-0.607553\pi\) | ||||
−0.331494 | + | 0.943457i | \(0.607553\pi\) | |||||||
\(840\) | −15.5118 | −0.535207 | ||||||||
\(841\) | 37.1265 | 1.28022 | ||||||||
\(842\) | −11.3632 | −0.391600 | ||||||||
\(843\) | 12.7912 | 0.440552 | ||||||||
\(844\) | 5.83190 | 0.200742 | ||||||||
\(845\) | 24.4674 | 0.841704 | ||||||||
\(846\) | −23.3543 | −0.802937 | ||||||||
\(847\) | 37.4572 | 1.28705 | ||||||||
\(848\) | −3.46241 | −0.118900 | ||||||||
\(849\) | 33.5865 | 1.15269 | ||||||||
\(850\) | −19.0419 | −0.653133 | ||||||||
\(851\) | −3.97452 | −0.136245 | ||||||||
\(852\) | −10.5312 | −0.360794 | ||||||||
\(853\) | −24.0892 | −0.824798 | −0.412399 | − | 0.911003i | \(-0.635309\pi\) | ||||
−0.412399 | + | 0.911003i | \(0.635309\pi\) | |||||||
\(854\) | 15.5853 | 0.533317 | ||||||||
\(855\) | −40.2073 | −1.37506 | ||||||||
\(856\) | −15.2504 | −0.521248 | ||||||||
\(857\) | −38.7433 | −1.32345 | −0.661724 | − | 0.749748i | \(-0.730175\pi\) | ||||
−0.661724 | + | 0.749748i | \(0.730175\pi\) | |||||||
\(858\) | −19.5066 | −0.665946 | ||||||||
\(859\) | −6.26889 | −0.213892 | −0.106946 | − | 0.994265i | \(-0.534107\pi\) | ||||
−0.106946 | + | 0.994265i | \(0.534107\pi\) | |||||||
\(860\) | −4.89780 | −0.167014 | ||||||||
\(861\) | −6.54658 | −0.223107 | ||||||||
\(862\) | −37.3716 | −1.27288 | ||||||||
\(863\) | 5.49493 | 0.187050 | 0.0935248 | − | 0.995617i | \(-0.470187\pi\) | ||||
0.0935248 | + | 0.995617i | \(0.470187\pi\) | |||||||
\(864\) | 2.29046 | 0.0779229 | ||||||||
\(865\) | −21.3468 | −0.725812 | ||||||||
\(866\) | −14.2547 | −0.484395 | ||||||||
\(867\) | −67.6142 | −2.29630 | ||||||||
\(868\) | −24.5245 | −0.832415 | ||||||||
\(869\) | −10.7402 | −0.364335 | ||||||||
\(870\) | −30.8142 | −1.04470 | ||||||||
\(871\) | 73.7286 | 2.49820 | ||||||||
\(872\) | 4.96261 | 0.168055 | ||||||||
\(873\) | −5.99135 | −0.202776 | ||||||||
\(874\) | 2.62115 | 0.0886617 | ||||||||
\(875\) | 46.8058 | 1.58232 | ||||||||
\(876\) | 44.1157 | 1.49053 | ||||||||
\(877\) | −49.7005 | −1.67827 | −0.839134 | − | 0.543925i | \(-0.816938\pi\) | ||||
−0.839134 | + | 0.543925i | \(0.816938\pi\) | |||||||
\(878\) | 2.48473 | 0.0838555 | ||||||||
\(879\) | 59.7007 | 2.01365 | ||||||||
\(880\) | 1.96570 | 0.0662636 | ||||||||
\(881\) | −37.4577 | −1.26198 | −0.630992 | − | 0.775790i | \(-0.717352\pi\) | ||||
−0.630992 | + | 0.775790i | \(0.717352\pi\) | |||||||
\(882\) | −37.7953 | −1.27263 | ||||||||
\(883\) | 1.97579 | 0.0664905 | 0.0332453 | − | 0.999447i | \(-0.489416\pi\) | ||||
0.0332453 | + | 0.999447i | \(0.489416\pi\) | |||||||
\(884\) | 35.7859 | 1.20361 | ||||||||
\(885\) | −4.01237 | −0.134874 | ||||||||
\(886\) | 27.4112 | 0.920897 | ||||||||
\(887\) | 6.98812 | 0.234638 | 0.117319 | − | 0.993094i | \(-0.462570\pi\) | ||||
0.117319 | + | 0.993094i | \(0.462570\pi\) | |||||||
\(888\) | −28.5498 | −0.958068 | ||||||||
\(889\) | −33.3120 | −1.11725 | ||||||||
\(890\) | −18.7654 | −0.629017 | ||||||||
\(891\) | −7.63772 | −0.255873 | ||||||||
\(892\) | 1.68068 | 0.0562734 | ||||||||
\(893\) | −43.2977 | −1.44890 | ||||||||
\(894\) | −19.6629 | −0.657627 | ||||||||
\(895\) | −19.4048 | −0.648631 | ||||||||
\(896\) | 4.09354 | 0.136756 | ||||||||
\(897\) | 5.23493 | 0.174789 | ||||||||
\(898\) | 18.5159 | 0.617885 | ||||||||
\(899\) | −48.7179 | −1.62483 | ||||||||
\(900\) | −11.2761 | −0.375871 | ||||||||
\(901\) | 22.6490 | 0.754546 | ||||||||
\(902\) | 0.829601 | 0.0276227 | ||||||||
\(903\) | −36.3684 | −1.21026 | ||||||||
\(904\) | 13.4851 | 0.448509 | ||||||||
\(905\) | 1.53343 | 0.0509729 | ||||||||
\(906\) | −44.4814 | −1.47780 | ||||||||
\(907\) | −24.5916 | −0.816550 | −0.408275 | − | 0.912859i | \(-0.633870\pi\) | ||||
−0.408275 | + | 0.912859i | \(0.633870\pi\) | |||||||
\(908\) | 19.5353 | 0.648303 | ||||||||
\(909\) | 15.9598 | 0.529352 | ||||||||
\(910\) | −32.3676 | −1.07298 | ||||||||
\(911\) | −4.08295 | −0.135274 | −0.0676370 | − | 0.997710i | \(-0.521546\pi\) | ||||
−0.0676370 | + | 0.997710i | \(0.521546\pi\) | |||||||
\(912\) | 18.8282 | 0.623465 | ||||||||
\(913\) | −1.98155 | −0.0655797 | ||||||||
\(914\) | 19.1505 | 0.633441 | ||||||||
\(915\) | −14.4271 | −0.476944 | ||||||||
\(916\) | −5.15115 | −0.170199 | ||||||||
\(917\) | 61.6681 | 2.03646 | ||||||||
\(918\) | −14.9827 | −0.494504 | ||||||||
\(919\) | −44.3861 | −1.46416 | −0.732081 | − | 0.681217i | \(-0.761451\pi\) | ||||
−0.732081 | + | 0.681217i | \(0.761451\pi\) | |||||||
\(920\) | −0.527527 | −0.0173920 | ||||||||
\(921\) | −69.6036 | −2.29352 | ||||||||
\(922\) | 14.9860 | 0.493538 | ||||||||
\(923\) | −21.9749 | −0.723314 | ||||||||
\(924\) | 14.5962 | 0.480179 | ||||||||
\(925\) | 31.6994 | 1.04227 | ||||||||
\(926\) | 34.3496 | 1.12880 | ||||||||
\(927\) | −20.3036 | −0.666858 | ||||||||
\(928\) | 8.13182 | 0.266940 | ||||||||
\(929\) | −11.6401 | −0.381899 | −0.190950 | − | 0.981600i | \(-0.561157\pi\) | ||||
−0.190950 | + | 0.981600i | \(0.561157\pi\) | |||||||
\(930\) | 22.7020 | 0.744426 | ||||||||
\(931\) | −70.0705 | −2.29647 | ||||||||
\(932\) | −8.24409 | −0.270044 | ||||||||
\(933\) | 47.9918 | 1.57118 | ||||||||
\(934\) | −6.33991 | −0.207448 | ||||||||
\(935\) | −12.8584 | −0.420513 | ||||||||
\(936\) | 21.1915 | 0.692665 | ||||||||
\(937\) | 33.4034 | 1.09124 | 0.545621 | − | 0.838032i | \(-0.316294\pi\) | ||||
0.545621 | + | 0.838032i | \(0.316294\pi\) | |||||||
\(938\) | −55.1687 | −1.80132 | ||||||||
\(939\) | 4.58273 | 0.149552 | ||||||||
\(940\) | 8.71400 | 0.284219 | ||||||||
\(941\) | 2.77334 | 0.0904084 | 0.0452042 | − | 0.998978i | \(-0.485606\pi\) | ||||
0.0452042 | + | 0.998978i | \(0.485606\pi\) | |||||||
\(942\) | −24.1152 | −0.785714 | ||||||||
\(943\) | −0.222637 | −0.00725006 | ||||||||
\(944\) | 1.05886 | 0.0344630 | ||||||||
\(945\) | 13.5516 | 0.440833 | ||||||||
\(946\) | 4.60870 | 0.149842 | ||||||||
\(947\) | 29.1477 | 0.947174 | 0.473587 | − | 0.880747i | \(-0.342959\pi\) | ||||
0.473587 | + | 0.880747i | \(0.342959\pi\) | |||||||
\(948\) | 20.7041 | 0.672439 | ||||||||
\(949\) | 92.0539 | 2.98820 | ||||||||
\(950\) | −20.9054 | −0.678261 | ||||||||
\(951\) | −12.7402 | −0.413129 | ||||||||
\(952\) | −26.7774 | −0.867860 | ||||||||
\(953\) | −25.4242 | −0.823570 | −0.411785 | − | 0.911281i | \(-0.635095\pi\) | ||||
−0.411785 | + | 0.911281i | \(0.635095\pi\) | |||||||
\(954\) | 13.4121 | 0.434233 | ||||||||
\(955\) | −35.7265 | −1.15608 | ||||||||
\(956\) | 11.2771 | 0.364726 | ||||||||
\(957\) | 28.9953 | 0.937285 | ||||||||
\(958\) | 32.6955 | 1.05634 | ||||||||
\(959\) | −73.6995 | −2.37988 | ||||||||
\(960\) | −3.78933 | −0.122300 | ||||||||
\(961\) | 4.89232 | 0.157817 | ||||||||
\(962\) | −59.5733 | −1.92072 | ||||||||
\(963\) | 59.0745 | 1.90365 | ||||||||
\(964\) | 5.90314 | 0.190127 | ||||||||
\(965\) | −4.36575 | −0.140539 | ||||||||
\(966\) | −3.91712 | −0.126031 | ||||||||
\(967\) | −55.4611 | −1.78351 | −0.891755 | − | 0.452519i | \(-0.850525\pi\) | ||||
−0.891755 | + | 0.452519i | \(0.850525\pi\) | |||||||
\(968\) | 9.15033 | 0.294103 | ||||||||
\(969\) | −123.163 | −3.95655 | ||||||||
\(970\) | 2.23550 | 0.0717777 | ||||||||
\(971\) | −21.4603 | −0.688693 | −0.344347 | − | 0.938843i | \(-0.611900\pi\) | ||||
−0.344347 | + | 0.938843i | \(0.611900\pi\) | |||||||
\(972\) | 21.5948 | 0.692655 | ||||||||
\(973\) | 86.7905 | 2.78238 | ||||||||
\(974\) | 2.28521 | 0.0732229 | ||||||||
\(975\) | −41.7520 | −1.33714 | ||||||||
\(976\) | 3.80729 | 0.121868 | ||||||||
\(977\) | −57.1863 | −1.82955 | −0.914775 | − | 0.403963i | \(-0.867632\pi\) | ||||
−0.914775 | + | 0.403963i | \(0.867632\pi\) | |||||||
\(978\) | 34.9737 | 1.11833 | ||||||||
\(979\) | 17.6577 | 0.564343 | ||||||||
\(980\) | 14.1022 | 0.450480 | ||||||||
\(981\) | −19.2233 | −0.613754 | ||||||||
\(982\) | 32.2680 | 1.02971 | ||||||||
\(983\) | 32.3333 | 1.03127 | 0.515637 | − | 0.856807i | \(-0.327555\pi\) | ||||
0.515637 | + | 0.856807i | \(0.327555\pi\) | |||||||
\(984\) | −1.59925 | −0.0509821 | ||||||||
\(985\) | 27.0505 | 0.861902 | ||||||||
\(986\) | −53.1933 | −1.69402 | ||||||||
\(987\) | 64.7053 | 2.05959 | ||||||||
\(988\) | 39.2879 | 1.24992 | ||||||||
\(989\) | −1.23682 | −0.0393286 | ||||||||
\(990\) | −7.61438 | −0.242001 | ||||||||
\(991\) | −14.6307 | −0.464760 | −0.232380 | − | 0.972625i | \(-0.574651\pi\) | ||||
−0.232380 | + | 0.972625i | \(0.574651\pi\) | |||||||
\(992\) | −5.99102 | −0.190215 | ||||||||
\(993\) | −38.1568 | −1.21087 | ||||||||
\(994\) | 16.4431 | 0.521544 | ||||||||
\(995\) | 11.1880 | 0.354684 | ||||||||
\(996\) | 3.81989 | 0.121038 | ||||||||
\(997\) | 5.52588 | 0.175006 | 0.0875032 | − | 0.996164i | \(-0.472111\pi\) | ||||
0.0875032 | + | 0.996164i | \(0.472111\pi\) | |||||||
\(998\) | 17.9334 | 0.567671 | ||||||||
\(999\) | 24.9420 | 0.789130 |
(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 | 4034.2.a.c.1.8 | ✓ | 49 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4034.2.a.c.1.8 | ✓ | 49 | 1.1 | even | 1 | trivial |