Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8043,2,Mod(1,8043)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8043, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8043.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8043 = 3 \cdot 7 \cdot 383 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8043.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: | \(64.2236783457\) |
Analytic rank: | \(1\) |
Dimension: | \(46\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.15 | ||
Character | \(\chi\) | \(=\) | 8043.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.944841 | −0.668104 | −0.334052 | − | 0.942555i | \(-0.608416\pi\) | ||||
−0.334052 | + | 0.942555i | \(0.608416\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | −1.10728 | −0.553638 | ||||||||
\(5\) | 3.73621 | 1.67088 | 0.835442 | − | 0.549579i | \(-0.185212\pi\) | ||||
0.835442 | + | 0.549579i | \(0.185212\pi\) | |||||||
\(6\) | 0.944841 | 0.385730 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 2.93588 | 1.03799 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | −3.53012 | −1.11632 | ||||||||
\(11\) | 6.47318 | 1.95174 | 0.975868 | − | 0.218361i | \(-0.0700711\pi\) | ||||
0.975868 | + | 0.218361i | \(0.0700711\pi\) | |||||||
\(12\) | 1.10728 | 0.319643 | ||||||||
\(13\) | −5.12465 | −1.42132 | −0.710661 | − | 0.703535i | \(-0.751604\pi\) | ||||
−0.710661 | + | 0.703535i | \(0.751604\pi\) | |||||||
\(14\) | 0.944841 | 0.252519 | ||||||||
\(15\) | −3.73621 | −0.964685 | ||||||||
\(16\) | −0.559391 | −0.139848 | ||||||||
\(17\) | −5.30213 | −1.28596 | −0.642978 | − | 0.765884i | \(-0.722301\pi\) | ||||
−0.642978 | + | 0.765884i | \(0.722301\pi\) | |||||||
\(18\) | −0.944841 | −0.222701 | ||||||||
\(19\) | 3.63286 | 0.833436 | 0.416718 | − | 0.909036i | \(-0.363180\pi\) | ||||
0.416718 | + | 0.909036i | \(0.363180\pi\) | |||||||
\(20\) | −4.13701 | −0.925064 | ||||||||
\(21\) | 1.00000 | 0.218218 | ||||||||
\(22\) | −6.11612 | −1.30396 | ||||||||
\(23\) | −0.278452 | −0.0580613 | −0.0290306 | − | 0.999579i | \(-0.509242\pi\) | ||||
−0.0290306 | + | 0.999579i | \(0.509242\pi\) | |||||||
\(24\) | −2.93588 | −0.599284 | ||||||||
\(25\) | 8.95926 | 1.79185 | ||||||||
\(26\) | 4.84198 | 0.949590 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 1.10728 | 0.209255 | ||||||||
\(29\) | 7.59321 | 1.41002 | 0.705011 | − | 0.709196i | \(-0.250942\pi\) | ||||
0.705011 | + | 0.709196i | \(0.250942\pi\) | |||||||
\(30\) | 3.53012 | 0.644510 | ||||||||
\(31\) | −9.50320 | −1.70683 | −0.853413 | − | 0.521236i | \(-0.825471\pi\) | ||||
−0.853413 | + | 0.521236i | \(0.825471\pi\) | |||||||
\(32\) | −5.34323 | −0.944558 | ||||||||
\(33\) | −6.47318 | −1.12684 | ||||||||
\(34\) | 5.00968 | 0.859152 | ||||||||
\(35\) | −3.73621 | −0.631535 | ||||||||
\(36\) | −1.10728 | −0.184546 | ||||||||
\(37\) | −4.28310 | −0.704138 | −0.352069 | − | 0.935974i | \(-0.614522\pi\) | ||||
−0.352069 | + | 0.935974i | \(0.614522\pi\) | |||||||
\(38\) | −3.43248 | −0.556822 | ||||||||
\(39\) | 5.12465 | 0.820601 | ||||||||
\(40\) | 10.9691 | 1.73436 | ||||||||
\(41\) | 4.15413 | 0.648766 | 0.324383 | − | 0.945926i | \(-0.394843\pi\) | ||||
0.324383 | + | 0.945926i | \(0.394843\pi\) | |||||||
\(42\) | −0.944841 | −0.145792 | ||||||||
\(43\) | −3.18694 | −0.486004 | −0.243002 | − | 0.970026i | \(-0.578132\pi\) | ||||
−0.243002 | + | 0.970026i | \(0.578132\pi\) | |||||||
\(44\) | −7.16759 | −1.08055 | ||||||||
\(45\) | 3.73621 | 0.556961 | ||||||||
\(46\) | 0.263093 | 0.0387910 | ||||||||
\(47\) | 1.88454 | 0.274889 | 0.137444 | − | 0.990509i | \(-0.456111\pi\) | ||||
0.137444 | + | 0.990509i | \(0.456111\pi\) | |||||||
\(48\) | 0.559391 | 0.0807412 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −8.46508 | −1.19714 | ||||||||
\(51\) | 5.30213 | 0.742447 | ||||||||
\(52\) | 5.67440 | 0.786897 | ||||||||
\(53\) | −10.9878 | −1.50929 | −0.754644 | − | 0.656134i | \(-0.772191\pi\) | ||||
−0.754644 | + | 0.656134i | \(0.772191\pi\) | |||||||
\(54\) | 0.944841 | 0.128577 | ||||||||
\(55\) | 24.1851 | 3.26112 | ||||||||
\(56\) | −2.93588 | −0.392324 | ||||||||
\(57\) | −3.63286 | −0.481185 | ||||||||
\(58\) | −7.17437 | −0.942041 | ||||||||
\(59\) | −13.4972 | −1.75718 | −0.878590 | − | 0.477577i | \(-0.841515\pi\) | ||||
−0.878590 | + | 0.477577i | \(0.841515\pi\) | |||||||
\(60\) | 4.13701 | 0.534086 | ||||||||
\(61\) | 0.0371054 | 0.00475086 | 0.00237543 | − | 0.999997i | \(-0.499244\pi\) | ||||
0.00237543 | + | 0.999997i | \(0.499244\pi\) | |||||||
\(62\) | 8.97902 | 1.14034 | ||||||||
\(63\) | −1.00000 | −0.125988 | ||||||||
\(64\) | 6.16728 | 0.770910 | ||||||||
\(65\) | −19.1468 | −2.37486 | ||||||||
\(66\) | 6.11612 | 0.752843 | ||||||||
\(67\) | 14.1396 | 1.72742 | 0.863711 | − | 0.503987i | \(-0.168134\pi\) | ||||
0.863711 | + | 0.503987i | \(0.168134\pi\) | |||||||
\(68\) | 5.87092 | 0.711954 | ||||||||
\(69\) | 0.278452 | 0.0335217 | ||||||||
\(70\) | 3.53012 | 0.421931 | ||||||||
\(71\) | −16.3543 | −1.94090 | −0.970451 | − | 0.241297i | \(-0.922427\pi\) | ||||
−0.970451 | + | 0.241297i | \(0.922427\pi\) | |||||||
\(72\) | 2.93588 | 0.345997 | ||||||||
\(73\) | −3.07307 | −0.359675 | −0.179838 | − | 0.983696i | \(-0.557557\pi\) | ||||
−0.179838 | + | 0.983696i | \(0.557557\pi\) | |||||||
\(74\) | 4.04685 | 0.470437 | ||||||||
\(75\) | −8.95926 | −1.03453 | ||||||||
\(76\) | −4.02258 | −0.461422 | ||||||||
\(77\) | −6.47318 | −0.737687 | ||||||||
\(78\) | −4.84198 | −0.548246 | ||||||||
\(79\) | −10.8106 | −1.21629 | −0.608144 | − | 0.793826i | \(-0.708086\pi\) | ||||
−0.608144 | + | 0.793826i | \(0.708086\pi\) | |||||||
\(80\) | −2.09000 | −0.233670 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −3.92499 | −0.433443 | ||||||||
\(83\) | −11.4875 | −1.26091 | −0.630457 | − | 0.776224i | \(-0.717132\pi\) | ||||
−0.630457 | + | 0.776224i | \(0.717132\pi\) | |||||||
\(84\) | −1.10728 | −0.120814 | ||||||||
\(85\) | −19.8099 | −2.14868 | ||||||||
\(86\) | 3.01115 | 0.324701 | ||||||||
\(87\) | −7.59321 | −0.814077 | ||||||||
\(88\) | 19.0045 | 2.02588 | ||||||||
\(89\) | 1.46286 | 0.155063 | 0.0775315 | − | 0.996990i | \(-0.475296\pi\) | ||||
0.0775315 | + | 0.996990i | \(0.475296\pi\) | |||||||
\(90\) | −3.53012 | −0.372108 | ||||||||
\(91\) | 5.12465 | 0.537209 | ||||||||
\(92\) | 0.308323 | 0.0321449 | ||||||||
\(93\) | 9.50320 | 0.985436 | ||||||||
\(94\) | −1.78059 | −0.183654 | ||||||||
\(95\) | 13.5731 | 1.39257 | ||||||||
\(96\) | 5.34323 | 0.545341 | ||||||||
\(97\) | −16.2372 | −1.64864 | −0.824318 | − | 0.566127i | \(-0.808441\pi\) | ||||
−0.824318 | + | 0.566127i | \(0.808441\pi\) | |||||||
\(98\) | −0.944841 | −0.0954434 | ||||||||
\(99\) | 6.47318 | 0.650579 | ||||||||
\(100\) | −9.92037 | −0.992037 | ||||||||
\(101\) | −9.24335 | −0.919748 | −0.459874 | − | 0.887984i | \(-0.652105\pi\) | ||||
−0.459874 | + | 0.887984i | \(0.652105\pi\) | |||||||
\(102\) | −5.00968 | −0.496032 | ||||||||
\(103\) | 1.52895 | 0.150652 | 0.0753258 | − | 0.997159i | \(-0.476000\pi\) | ||||
0.0753258 | + | 0.997159i | \(0.476000\pi\) | |||||||
\(104\) | −15.0454 | −1.47532 | ||||||||
\(105\) | 3.73621 | 0.364617 | ||||||||
\(106\) | 10.3817 | 1.00836 | ||||||||
\(107\) | −9.14736 | −0.884309 | −0.442154 | − | 0.896939i | \(-0.645786\pi\) | ||||
−0.442154 | + | 0.896939i | \(0.645786\pi\) | |||||||
\(108\) | 1.10728 | 0.106548 | ||||||||
\(109\) | −19.5235 | −1.87001 | −0.935005 | − | 0.354635i | \(-0.884605\pi\) | ||||
−0.935005 | + | 0.354635i | \(0.884605\pi\) | |||||||
\(110\) | −22.8511 | −2.17877 | ||||||||
\(111\) | 4.28310 | 0.406534 | ||||||||
\(112\) | 0.559391 | 0.0528575 | ||||||||
\(113\) | 6.82703 | 0.642233 | 0.321117 | − | 0.947040i | \(-0.395942\pi\) | ||||
0.321117 | + | 0.947040i | \(0.395942\pi\) | |||||||
\(114\) | 3.43248 | 0.321481 | ||||||||
\(115\) | −1.04036 | −0.0970137 | ||||||||
\(116\) | −8.40777 | −0.780642 | ||||||||
\(117\) | −5.12465 | −0.473774 | ||||||||
\(118\) | 12.7527 | 1.17398 | ||||||||
\(119\) | 5.30213 | 0.486046 | ||||||||
\(120\) | −10.9691 | −1.00133 | ||||||||
\(121\) | 30.9020 | 2.80927 | ||||||||
\(122\) | −0.0350587 | −0.00317407 | ||||||||
\(123\) | −4.15413 | −0.374565 | ||||||||
\(124\) | 10.5227 | 0.944963 | ||||||||
\(125\) | 14.7926 | 1.32309 | ||||||||
\(126\) | 0.944841 | 0.0841731 | ||||||||
\(127\) | 10.5712 | 0.938043 | 0.469021 | − | 0.883187i | \(-0.344607\pi\) | ||||
0.469021 | + | 0.883187i | \(0.344607\pi\) | |||||||
\(128\) | 4.85935 | 0.429510 | ||||||||
\(129\) | 3.18694 | 0.280594 | ||||||||
\(130\) | 18.0906 | 1.58665 | ||||||||
\(131\) | −9.04132 | −0.789944 | −0.394972 | − | 0.918693i | \(-0.629246\pi\) | ||||
−0.394972 | + | 0.918693i | \(0.629246\pi\) | |||||||
\(132\) | 7.16759 | 0.623858 | ||||||||
\(133\) | −3.63286 | −0.315009 | ||||||||
\(134\) | −13.3596 | −1.15410 | ||||||||
\(135\) | −3.73621 | −0.321562 | ||||||||
\(136\) | −15.5664 | −1.33481 | ||||||||
\(137\) | 9.10325 | 0.777743 | 0.388871 | − | 0.921292i | \(-0.372865\pi\) | ||||
0.388871 | + | 0.921292i | \(0.372865\pi\) | |||||||
\(138\) | −0.263093 | −0.0223960 | ||||||||
\(139\) | −3.56848 | −0.302674 | −0.151337 | − | 0.988482i | \(-0.548358\pi\) | ||||
−0.151337 | + | 0.988482i | \(0.548358\pi\) | |||||||
\(140\) | 4.13701 | 0.349641 | ||||||||
\(141\) | −1.88454 | −0.158707 | ||||||||
\(142\) | 15.4523 | 1.29672 | ||||||||
\(143\) | −33.1728 | −2.77405 | ||||||||
\(144\) | −0.559391 | −0.0466160 | ||||||||
\(145\) | 28.3698 | 2.35598 | ||||||||
\(146\) | 2.90356 | 0.240300 | ||||||||
\(147\) | −1.00000 | −0.0824786 | ||||||||
\(148\) | 4.74257 | 0.389837 | ||||||||
\(149\) | 17.3492 | 1.42130 | 0.710652 | − | 0.703544i | \(-0.248400\pi\) | ||||
0.710652 | + | 0.703544i | \(0.248400\pi\) | |||||||
\(150\) | 8.46508 | 0.691171 | ||||||||
\(151\) | 5.91767 | 0.481573 | 0.240787 | − | 0.970578i | \(-0.422595\pi\) | ||||
0.240787 | + | 0.970578i | \(0.422595\pi\) | |||||||
\(152\) | 10.6657 | 0.865099 | ||||||||
\(153\) | −5.30213 | −0.428652 | ||||||||
\(154\) | 6.11612 | 0.492851 | ||||||||
\(155\) | −35.5059 | −2.85191 | ||||||||
\(156\) | −5.67440 | −0.454315 | ||||||||
\(157\) | 6.46779 | 0.516186 | 0.258093 | − | 0.966120i | \(-0.416906\pi\) | ||||
0.258093 | + | 0.966120i | \(0.416906\pi\) | |||||||
\(158\) | 10.2143 | 0.812607 | ||||||||
\(159\) | 10.9878 | 0.871388 | ||||||||
\(160\) | −19.9634 | −1.57825 | ||||||||
\(161\) | 0.278452 | 0.0219451 | ||||||||
\(162\) | −0.944841 | −0.0742337 | ||||||||
\(163\) | 14.0864 | 1.10333 | 0.551664 | − | 0.834066i | \(-0.313993\pi\) | ||||
0.551664 | + | 0.834066i | \(0.313993\pi\) | |||||||
\(164\) | −4.59976 | −0.359181 | ||||||||
\(165\) | −24.1851 | −1.88281 | ||||||||
\(166\) | 10.8538 | 0.842421 | ||||||||
\(167\) | −15.9505 | −1.23428 | −0.617142 | − | 0.786852i | \(-0.711710\pi\) | ||||
−0.617142 | + | 0.786852i | \(0.711710\pi\) | |||||||
\(168\) | 2.93588 | 0.226508 | ||||||||
\(169\) | 13.2620 | 1.02016 | ||||||||
\(170\) | 18.7172 | 1.43554 | ||||||||
\(171\) | 3.63286 | 0.277812 | ||||||||
\(172\) | 3.52882 | 0.269070 | ||||||||
\(173\) | 11.5900 | 0.881171 | 0.440585 | − | 0.897711i | \(-0.354771\pi\) | ||||
0.440585 | + | 0.897711i | \(0.354771\pi\) | |||||||
\(174\) | 7.17437 | 0.543888 | ||||||||
\(175\) | −8.95926 | −0.677256 | ||||||||
\(176\) | −3.62104 | −0.272946 | ||||||||
\(177\) | 13.4972 | 1.01451 | ||||||||
\(178\) | −1.38217 | −0.103598 | ||||||||
\(179\) | −12.5110 | −0.935116 | −0.467558 | − | 0.883962i | \(-0.654866\pi\) | ||||
−0.467558 | + | 0.883962i | \(0.654866\pi\) | |||||||
\(180\) | −4.13701 | −0.308355 | ||||||||
\(181\) | −23.7664 | −1.76654 | −0.883270 | − | 0.468865i | \(-0.844663\pi\) | ||||
−0.883270 | + | 0.468865i | \(0.844663\pi\) | |||||||
\(182\) | −4.84198 | −0.358911 | ||||||||
\(183\) | −0.0371054 | −0.00274291 | ||||||||
\(184\) | −0.817503 | −0.0602671 | ||||||||
\(185\) | −16.0026 | −1.17653 | ||||||||
\(186\) | −8.97902 | −0.658373 | ||||||||
\(187\) | −34.3216 | −2.50985 | ||||||||
\(188\) | −2.08671 | −0.152189 | ||||||||
\(189\) | 1.00000 | 0.0727393 | ||||||||
\(190\) | −12.8245 | −0.930384 | ||||||||
\(191\) | 15.7867 | 1.14229 | 0.571143 | − | 0.820851i | \(-0.306500\pi\) | ||||
0.571143 | + | 0.820851i | \(0.306500\pi\) | |||||||
\(192\) | −6.16728 | −0.445085 | ||||||||
\(193\) | −9.25361 | −0.666090 | −0.333045 | − | 0.942911i | \(-0.608076\pi\) | ||||
−0.333045 | + | 0.942911i | \(0.608076\pi\) | |||||||
\(194\) | 15.3416 | 1.10146 | ||||||||
\(195\) | 19.1468 | 1.37113 | ||||||||
\(196\) | −1.10728 | −0.0790911 | ||||||||
\(197\) | −25.7315 | −1.83330 | −0.916648 | − | 0.399695i | \(-0.869116\pi\) | ||||
−0.916648 | + | 0.399695i | \(0.869116\pi\) | |||||||
\(198\) | −6.11612 | −0.434654 | ||||||||
\(199\) | 2.53649 | 0.179807 | 0.0899033 | − | 0.995950i | \(-0.471344\pi\) | ||||
0.0899033 | + | 0.995950i | \(0.471344\pi\) | |||||||
\(200\) | 26.3033 | 1.85993 | ||||||||
\(201\) | −14.1396 | −0.997328 | ||||||||
\(202\) | 8.73350 | 0.614487 | ||||||||
\(203\) | −7.59321 | −0.532939 | ||||||||
\(204\) | −5.87092 | −0.411047 | ||||||||
\(205\) | 15.5207 | 1.08401 | ||||||||
\(206\) | −1.44461 | −0.100651 | ||||||||
\(207\) | −0.278452 | −0.0193538 | ||||||||
\(208\) | 2.86669 | 0.198769 | ||||||||
\(209\) | 23.5162 | 1.62665 | ||||||||
\(210\) | −3.53012 | −0.243602 | ||||||||
\(211\) | 21.4603 | 1.47739 | 0.738694 | − | 0.674040i | \(-0.235443\pi\) | ||||
0.738694 | + | 0.674040i | \(0.235443\pi\) | |||||||
\(212\) | 12.1665 | 0.835599 | ||||||||
\(213\) | 16.3543 | 1.12058 | ||||||||
\(214\) | 8.64280 | 0.590810 | ||||||||
\(215\) | −11.9071 | −0.812056 | ||||||||
\(216\) | −2.93588 | −0.199761 | ||||||||
\(217\) | 9.50320 | 0.645119 | ||||||||
\(218\) | 18.4466 | 1.24936 | ||||||||
\(219\) | 3.07307 | 0.207659 | ||||||||
\(220\) | −26.7796 | −1.80548 | ||||||||
\(221\) | 27.1716 | 1.82776 | ||||||||
\(222\) | −4.04685 | −0.271607 | ||||||||
\(223\) | −19.0986 | −1.27894 | −0.639470 | − | 0.768816i | \(-0.720846\pi\) | ||||
−0.639470 | + | 0.768816i | \(0.720846\pi\) | |||||||
\(224\) | 5.34323 | 0.357009 | ||||||||
\(225\) | 8.95926 | 0.597284 | ||||||||
\(226\) | −6.45046 | −0.429078 | ||||||||
\(227\) | −12.6892 | −0.842214 | −0.421107 | − | 0.907011i | \(-0.638358\pi\) | ||||
−0.421107 | + | 0.907011i | \(0.638358\pi\) | |||||||
\(228\) | 4.02258 | 0.266402 | ||||||||
\(229\) | 13.1299 | 0.867649 | 0.433825 | − | 0.900997i | \(-0.357164\pi\) | ||||
0.433825 | + | 0.900997i | \(0.357164\pi\) | |||||||
\(230\) | 0.982971 | 0.0648152 | ||||||||
\(231\) | 6.47318 | 0.425904 | ||||||||
\(232\) | 22.2928 | 1.46359 | ||||||||
\(233\) | 22.8584 | 1.49751 | 0.748753 | − | 0.662849i | \(-0.230653\pi\) | ||||
0.748753 | + | 0.662849i | \(0.230653\pi\) | |||||||
\(234\) | 4.84198 | 0.316530 | ||||||||
\(235\) | 7.04105 | 0.459307 | ||||||||
\(236\) | 14.9451 | 0.972841 | ||||||||
\(237\) | 10.8106 | 0.702225 | ||||||||
\(238\) | −5.00968 | −0.324729 | ||||||||
\(239\) | −6.19886 | −0.400971 | −0.200485 | − | 0.979697i | \(-0.564252\pi\) | ||||
−0.200485 | + | 0.979697i | \(0.564252\pi\) | |||||||
\(240\) | 2.09000 | 0.134909 | ||||||||
\(241\) | 3.91505 | 0.252190 | 0.126095 | − | 0.992018i | \(-0.459756\pi\) | ||||
0.126095 | + | 0.992018i | \(0.459756\pi\) | |||||||
\(242\) | −29.1975 | −1.87689 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −0.0410859 | −0.00263025 | ||||||||
\(245\) | 3.73621 | 0.238698 | ||||||||
\(246\) | 3.92499 | 0.250248 | ||||||||
\(247\) | −18.6172 | −1.18458 | ||||||||
\(248\) | −27.9003 | −1.77167 | ||||||||
\(249\) | 11.4875 | 0.727989 | ||||||||
\(250\) | −13.9767 | −0.883963 | ||||||||
\(251\) | 15.8405 | 0.999843 | 0.499921 | − | 0.866071i | \(-0.333362\pi\) | ||||
0.499921 | + | 0.866071i | \(0.333362\pi\) | |||||||
\(252\) | 1.10728 | 0.0697518 | ||||||||
\(253\) | −1.80247 | −0.113320 | ||||||||
\(254\) | −9.98811 | −0.626710 | ||||||||
\(255\) | 19.8099 | 1.24054 | ||||||||
\(256\) | −16.9259 | −1.05787 | ||||||||
\(257\) | −10.6024 | −0.661362 | −0.330681 | − | 0.943743i | \(-0.607278\pi\) | ||||
−0.330681 | + | 0.943743i | \(0.607278\pi\) | |||||||
\(258\) | −3.01115 | −0.187466 | ||||||||
\(259\) | 4.28310 | 0.266139 | ||||||||
\(260\) | 21.2007 | 1.31481 | ||||||||
\(261\) | 7.59321 | 0.470008 | ||||||||
\(262\) | 8.54261 | 0.527764 | ||||||||
\(263\) | 11.4422 | 0.705556 | 0.352778 | − | 0.935707i | \(-0.385237\pi\) | ||||
0.352778 | + | 0.935707i | \(0.385237\pi\) | |||||||
\(264\) | −19.0045 | −1.16964 | ||||||||
\(265\) | −41.0527 | −2.52185 | ||||||||
\(266\) | 3.43248 | 0.210459 | ||||||||
\(267\) | −1.46286 | −0.0895257 | ||||||||
\(268\) | −15.6564 | −0.956366 | ||||||||
\(269\) | −8.70422 | −0.530705 | −0.265353 | − | 0.964151i | \(-0.585488\pi\) | ||||
−0.265353 | + | 0.964151i | \(0.585488\pi\) | |||||||
\(270\) | 3.53012 | 0.214837 | ||||||||
\(271\) | 17.5628 | 1.06687 | 0.533434 | − | 0.845842i | \(-0.320901\pi\) | ||||
0.533434 | + | 0.845842i | \(0.320901\pi\) | |||||||
\(272\) | 2.96597 | 0.179838 | ||||||||
\(273\) | −5.12465 | −0.310158 | ||||||||
\(274\) | −8.60112 | −0.519613 | ||||||||
\(275\) | 57.9949 | 3.49722 | ||||||||
\(276\) | −0.308323 | −0.0185589 | ||||||||
\(277\) | −12.4469 | −0.747862 | −0.373931 | − | 0.927457i | \(-0.621990\pi\) | ||||
−0.373931 | + | 0.927457i | \(0.621990\pi\) | |||||||
\(278\) | 3.37165 | 0.202218 | ||||||||
\(279\) | −9.50320 | −0.568942 | ||||||||
\(280\) | −10.9691 | −0.655527 | ||||||||
\(281\) | 17.3914 | 1.03748 | 0.518741 | − | 0.854931i | \(-0.326401\pi\) | ||||
0.518741 | + | 0.854931i | \(0.326401\pi\) | |||||||
\(282\) | 1.78059 | 0.106033 | ||||||||
\(283\) | 17.0134 | 1.01134 | 0.505670 | − | 0.862727i | \(-0.331245\pi\) | ||||
0.505670 | + | 0.862727i | \(0.331245\pi\) | |||||||
\(284\) | 18.1087 | 1.07456 | ||||||||
\(285\) | −13.5731 | −0.804004 | ||||||||
\(286\) | 31.3430 | 1.85335 | ||||||||
\(287\) | −4.15413 | −0.245211 | ||||||||
\(288\) | −5.34323 | −0.314853 | ||||||||
\(289\) | 11.1126 | 0.653684 | ||||||||
\(290\) | −26.8050 | −1.57404 | ||||||||
\(291\) | 16.2372 | 0.951840 | ||||||||
\(292\) | 3.40273 | 0.199130 | ||||||||
\(293\) | −4.69883 | −0.274509 | −0.137254 | − | 0.990536i | \(-0.543828\pi\) | ||||
−0.137254 | + | 0.990536i | \(0.543828\pi\) | |||||||
\(294\) | 0.944841 | 0.0551043 | ||||||||
\(295\) | −50.4282 | −2.93604 | ||||||||
\(296\) | −12.5747 | −0.730888 | ||||||||
\(297\) | −6.47318 | −0.375612 | ||||||||
\(298\) | −16.3923 | −0.949578 | ||||||||
\(299\) | 1.42697 | 0.0825238 | ||||||||
\(300\) | 9.92037 | 0.572753 | ||||||||
\(301\) | 3.18694 | 0.183692 | ||||||||
\(302\) | −5.59126 | −0.321741 | ||||||||
\(303\) | 9.24335 | 0.531017 | ||||||||
\(304\) | −2.03219 | −0.116554 | ||||||||
\(305\) | 0.138633 | 0.00793813 | ||||||||
\(306\) | 5.00968 | 0.286384 | ||||||||
\(307\) | 1.94371 | 0.110933 | 0.0554667 | − | 0.998461i | \(-0.482335\pi\) | ||||
0.0554667 | + | 0.998461i | \(0.482335\pi\) | |||||||
\(308\) | 7.16759 | 0.408411 | ||||||||
\(309\) | −1.52895 | −0.0869787 | ||||||||
\(310\) | 33.5475 | 1.90537 | ||||||||
\(311\) | 21.5224 | 1.22042 | 0.610212 | − | 0.792238i | \(-0.291084\pi\) | ||||
0.610212 | + | 0.792238i | \(0.291084\pi\) | |||||||
\(312\) | 15.0454 | 0.851776 | ||||||||
\(313\) | −23.9927 | −1.35615 | −0.678073 | − | 0.734994i | \(-0.737185\pi\) | ||||
−0.678073 | + | 0.734994i | \(0.737185\pi\) | |||||||
\(314\) | −6.11104 | −0.344866 | ||||||||
\(315\) | −3.73621 | −0.210512 | ||||||||
\(316\) | 11.9703 | 0.673383 | ||||||||
\(317\) | −3.80509 | −0.213715 | −0.106858 | − | 0.994274i | \(-0.534079\pi\) | ||||
−0.106858 | + | 0.994274i | \(0.534079\pi\) | |||||||
\(318\) | −10.3817 | −0.582178 | ||||||||
\(319\) | 49.1522 | 2.75199 | ||||||||
\(320\) | 23.0423 | 1.28810 | ||||||||
\(321\) | 9.14736 | 0.510556 | ||||||||
\(322\) | −0.263093 | −0.0146616 | ||||||||
\(323\) | −19.2619 | −1.07176 | ||||||||
\(324\) | −1.10728 | −0.0615153 | ||||||||
\(325\) | −45.9131 | −2.54680 | ||||||||
\(326\) | −13.3094 | −0.737138 | ||||||||
\(327\) | 19.5235 | 1.07965 | ||||||||
\(328\) | 12.1960 | 0.673413 | ||||||||
\(329\) | −1.88454 | −0.103898 | ||||||||
\(330\) | 22.8511 | 1.25791 | ||||||||
\(331\) | 24.3553 | 1.33869 | 0.669345 | − | 0.742952i | \(-0.266575\pi\) | ||||
0.669345 | + | 0.742952i | \(0.266575\pi\) | |||||||
\(332\) | 12.7198 | 0.698089 | ||||||||
\(333\) | −4.28310 | −0.234713 | ||||||||
\(334\) | 15.0707 | 0.824630 | ||||||||
\(335\) | 52.8284 | 2.88632 | ||||||||
\(336\) | −0.559391 | −0.0305173 | ||||||||
\(337\) | −0.254338 | −0.0138547 | −0.00692733 | − | 0.999976i | \(-0.502205\pi\) | ||||
−0.00692733 | + | 0.999976i | \(0.502205\pi\) | |||||||
\(338\) | −12.5305 | −0.681570 | ||||||||
\(339\) | −6.82703 | −0.370793 | ||||||||
\(340\) | 21.9350 | 1.18959 | ||||||||
\(341\) | −61.5159 | −3.33127 | ||||||||
\(342\) | −3.43248 | −0.185607 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | −9.35648 | −0.504468 | ||||||||
\(345\) | 1.04036 | 0.0560109 | ||||||||
\(346\) | −10.9507 | −0.588713 | ||||||||
\(347\) | 7.73657 | 0.415321 | 0.207660 | − | 0.978201i | \(-0.433415\pi\) | ||||
0.207660 | + | 0.978201i | \(0.433415\pi\) | |||||||
\(348\) | 8.40777 | 0.450704 | ||||||||
\(349\) | 27.9850 | 1.49800 | 0.749000 | − | 0.662570i | \(-0.230534\pi\) | ||||
0.749000 | + | 0.662570i | \(0.230534\pi\) | |||||||
\(350\) | 8.46508 | 0.452477 | ||||||||
\(351\) | 5.12465 | 0.273534 | ||||||||
\(352\) | −34.5876 | −1.84353 | ||||||||
\(353\) | −12.7351 | −0.677822 | −0.338911 | − | 0.940818i | \(-0.610059\pi\) | ||||
−0.338911 | + | 0.940818i | \(0.610059\pi\) | |||||||
\(354\) | −12.7527 | −0.677797 | ||||||||
\(355\) | −61.1032 | −3.24302 | ||||||||
\(356\) | −1.61979 | −0.0858487 | ||||||||
\(357\) | −5.30213 | −0.280619 | ||||||||
\(358\) | 11.8209 | 0.624755 | ||||||||
\(359\) | −24.3489 | −1.28509 | −0.642543 | − | 0.766249i | \(-0.722121\pi\) | ||||
−0.642543 | + | 0.766249i | \(0.722121\pi\) | |||||||
\(360\) | 10.9691 | 0.578121 | ||||||||
\(361\) | −5.80230 | −0.305384 | ||||||||
\(362\) | 22.4554 | 1.18023 | ||||||||
\(363\) | −30.9020 | −1.62193 | ||||||||
\(364\) | −5.67440 | −0.297419 | ||||||||
\(365\) | −11.4816 | −0.600976 | ||||||||
\(366\) | 0.0350587 | 0.00183255 | ||||||||
\(367\) | 24.3239 | 1.26970 | 0.634850 | − | 0.772636i | \(-0.281062\pi\) | ||||
0.634850 | + | 0.772636i | \(0.281062\pi\) | |||||||
\(368\) | 0.155764 | 0.00811975 | ||||||||
\(369\) | 4.15413 | 0.216255 | ||||||||
\(370\) | 15.1199 | 0.786045 | ||||||||
\(371\) | 10.9878 | 0.570457 | ||||||||
\(372\) | −10.5227 | −0.545574 | ||||||||
\(373\) | −25.4732 | −1.31895 | −0.659476 | − | 0.751725i | \(-0.729222\pi\) | ||||
−0.659476 | + | 0.751725i | \(0.729222\pi\) | |||||||
\(374\) | 32.4285 | 1.67684 | ||||||||
\(375\) | −14.7926 | −0.763888 | ||||||||
\(376\) | 5.53280 | 0.285332 | ||||||||
\(377\) | −38.9125 | −2.00410 | ||||||||
\(378\) | −0.944841 | −0.0485974 | ||||||||
\(379\) | 17.4613 | 0.896928 | 0.448464 | − | 0.893801i | \(-0.351971\pi\) | ||||
0.448464 | + | 0.893801i | \(0.351971\pi\) | |||||||
\(380\) | −15.0292 | −0.770982 | ||||||||
\(381\) | −10.5712 | −0.541579 | ||||||||
\(382\) | −14.9159 | −0.763165 | ||||||||
\(383\) | −1.00000 | −0.0510976 | ||||||||
\(384\) | −4.85935 | −0.247978 | ||||||||
\(385\) | −24.1851 | −1.23259 | ||||||||
\(386\) | 8.74319 | 0.445017 | ||||||||
\(387\) | −3.18694 | −0.162001 | ||||||||
\(388\) | 17.9790 | 0.912747 | ||||||||
\(389\) | 11.6344 | 0.589888 | 0.294944 | − | 0.955515i | \(-0.404699\pi\) | ||||
0.294944 | + | 0.955515i | \(0.404699\pi\) | |||||||
\(390\) | −18.0906 | −0.916056 | ||||||||
\(391\) | 1.47639 | 0.0746643 | ||||||||
\(392\) | 2.93588 | 0.148284 | ||||||||
\(393\) | 9.04132 | 0.456074 | ||||||||
\(394\) | 24.3122 | 1.22483 | ||||||||
\(395\) | −40.3907 | −2.03228 | ||||||||
\(396\) | −7.16759 | −0.360185 | ||||||||
\(397\) | 0.102318 | 0.00513518 | 0.00256759 | − | 0.999997i | \(-0.499183\pi\) | ||||
0.00256759 | + | 0.999997i | \(0.499183\pi\) | |||||||
\(398\) | −2.39658 | −0.120129 | ||||||||
\(399\) | 3.63286 | 0.181871 | ||||||||
\(400\) | −5.01173 | −0.250587 | ||||||||
\(401\) | −26.2737 | −1.31204 | −0.656022 | − | 0.754741i | \(-0.727762\pi\) | ||||
−0.656022 | + | 0.754741i | \(0.727762\pi\) | |||||||
\(402\) | 13.3596 | 0.666318 | ||||||||
\(403\) | 48.7006 | 2.42595 | ||||||||
\(404\) | 10.2349 | 0.509207 | ||||||||
\(405\) | 3.73621 | 0.185654 | ||||||||
\(406\) | 7.17437 | 0.356058 | ||||||||
\(407\) | −27.7253 | −1.37429 | ||||||||
\(408\) | 15.5664 | 0.770654 | ||||||||
\(409\) | −15.7495 | −0.778761 | −0.389381 | − | 0.921077i | \(-0.627311\pi\) | ||||
−0.389381 | + | 0.921077i | \(0.627311\pi\) | |||||||
\(410\) | −14.6646 | −0.724233 | ||||||||
\(411\) | −9.10325 | −0.449030 | ||||||||
\(412\) | −1.69296 | −0.0834063 | ||||||||
\(413\) | 13.4972 | 0.664152 | ||||||||
\(414\) | 0.263093 | 0.0129303 | ||||||||
\(415\) | −42.9196 | −2.10684 | ||||||||
\(416\) | 27.3822 | 1.34252 | ||||||||
\(417\) | 3.56848 | 0.174749 | ||||||||
\(418\) | −22.2190 | −1.08677 | ||||||||
\(419\) | 3.93006 | 0.191996 | 0.0959980 | − | 0.995382i | \(-0.469396\pi\) | ||||
0.0959980 | + | 0.995382i | \(0.469396\pi\) | |||||||
\(420\) | −4.13701 | −0.201866 | ||||||||
\(421\) | 14.5684 | 0.710018 | 0.355009 | − | 0.934863i | \(-0.384478\pi\) | ||||
0.355009 | + | 0.934863i | \(0.384478\pi\) | |||||||
\(422\) | −20.2766 | −0.987049 | ||||||||
\(423\) | 1.88454 | 0.0916296 | ||||||||
\(424\) | −32.2588 | −1.56663 | ||||||||
\(425\) | −47.5032 | −2.30424 | ||||||||
\(426\) | −15.4523 | −0.748664 | ||||||||
\(427\) | −0.0371054 | −0.00179566 | ||||||||
\(428\) | 10.1286 | 0.489587 | ||||||||
\(429\) | 33.1728 | 1.60160 | ||||||||
\(430\) | 11.2503 | 0.542537 | ||||||||
\(431\) | −28.2912 | −1.36274 | −0.681369 | − | 0.731940i | \(-0.738615\pi\) | ||||
−0.681369 | + | 0.731940i | \(0.738615\pi\) | |||||||
\(432\) | 0.559391 | 0.0269137 | ||||||||
\(433\) | −32.7988 | −1.57621 | −0.788106 | − | 0.615540i | \(-0.788938\pi\) | ||||
−0.788106 | + | 0.615540i | \(0.788938\pi\) | |||||||
\(434\) | −8.97902 | −0.431007 | ||||||||
\(435\) | −28.3698 | −1.36023 | ||||||||
\(436\) | 21.6179 | 1.03531 | ||||||||
\(437\) | −1.01158 | −0.0483904 | ||||||||
\(438\) | −2.90356 | −0.138737 | ||||||||
\(439\) | −9.95764 | −0.475252 | −0.237626 | − | 0.971357i | \(-0.576369\pi\) | ||||
−0.237626 | + | 0.971357i | \(0.576369\pi\) | |||||||
\(440\) | 71.0047 | 3.38502 | ||||||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | −25.6728 | −1.22113 | ||||||||
\(443\) | −19.8469 | −0.942953 | −0.471477 | − | 0.881879i | \(-0.656279\pi\) | ||||
−0.471477 | + | 0.881879i | \(0.656279\pi\) | |||||||
\(444\) | −4.74257 | −0.225073 | ||||||||
\(445\) | 5.46556 | 0.259092 | ||||||||
\(446\) | 18.0452 | 0.854464 | ||||||||
\(447\) | −17.3492 | −0.820590 | ||||||||
\(448\) | −6.16728 | −0.291377 | ||||||||
\(449\) | −9.56848 | −0.451564 | −0.225782 | − | 0.974178i | \(-0.572494\pi\) | ||||
−0.225782 | + | 0.974178i | \(0.572494\pi\) | |||||||
\(450\) | −8.46508 | −0.399048 | ||||||||
\(451\) | 26.8904 | 1.26622 | ||||||||
\(452\) | −7.55940 | −0.355564 | ||||||||
\(453\) | −5.91767 | −0.278037 | ||||||||
\(454\) | 11.9893 | 0.562687 | ||||||||
\(455\) | 19.1468 | 0.897614 | ||||||||
\(456\) | −10.6657 | −0.499465 | ||||||||
\(457\) | −13.9465 | −0.652392 | −0.326196 | − | 0.945302i | \(-0.605767\pi\) | ||||
−0.326196 | + | 0.945302i | \(0.605767\pi\) | |||||||
\(458\) | −12.4057 | −0.579680 | ||||||||
\(459\) | 5.30213 | 0.247482 | ||||||||
\(460\) | 1.15196 | 0.0537104 | ||||||||
\(461\) | −5.98078 | −0.278553 | −0.139276 | − | 0.990254i | \(-0.544478\pi\) | ||||
−0.139276 | + | 0.990254i | \(0.544478\pi\) | |||||||
\(462\) | −6.11612 | −0.284548 | ||||||||
\(463\) | −18.8469 | −0.875890 | −0.437945 | − | 0.899002i | \(-0.644294\pi\) | ||||
−0.437945 | + | 0.899002i | \(0.644294\pi\) | |||||||
\(464\) | −4.24757 | −0.197189 | ||||||||
\(465\) | 35.5059 | 1.64655 | ||||||||
\(466\) | −21.5976 | −1.00049 | ||||||||
\(467\) | 22.6056 | 1.04606 | 0.523032 | − | 0.852313i | \(-0.324801\pi\) | ||||
0.523032 | + | 0.852313i | \(0.324801\pi\) | |||||||
\(468\) | 5.67440 | 0.262299 | ||||||||
\(469\) | −14.1396 | −0.652904 | ||||||||
\(470\) | −6.65267 | −0.306865 | ||||||||
\(471\) | −6.46779 | −0.298020 | ||||||||
\(472\) | −39.6260 | −1.82394 | ||||||||
\(473\) | −20.6296 | −0.948551 | ||||||||
\(474\) | −10.2143 | −0.469159 | ||||||||
\(475\) | 32.5478 | 1.49339 | ||||||||
\(476\) | −5.87092 | −0.269093 | ||||||||
\(477\) | −10.9878 | −0.503096 | ||||||||
\(478\) | 5.85693 | 0.267890 | ||||||||
\(479\) | 17.7002 | 0.808742 | 0.404371 | − | 0.914595i | \(-0.367491\pi\) | ||||
0.404371 | + | 0.914595i | \(0.367491\pi\) | |||||||
\(480\) | 19.9634 | 0.911201 | ||||||||
\(481\) | 21.9494 | 1.00081 | ||||||||
\(482\) | −3.69910 | −0.168489 | ||||||||
\(483\) | −0.278452 | −0.0126700 | ||||||||
\(484\) | −34.2170 | −1.55532 | ||||||||
\(485\) | −60.6655 | −2.75468 | ||||||||
\(486\) | 0.944841 | 0.0428589 | ||||||||
\(487\) | −19.8867 | −0.901153 | −0.450576 | − | 0.892738i | \(-0.648781\pi\) | ||||
−0.450576 | + | 0.892738i | \(0.648781\pi\) | |||||||
\(488\) | 0.108937 | 0.00493135 | ||||||||
\(489\) | −14.0864 | −0.637007 | ||||||||
\(490\) | −3.53012 | −0.159475 | ||||||||
\(491\) | 8.01984 | 0.361930 | 0.180965 | − | 0.983489i | \(-0.442078\pi\) | ||||
0.180965 | + | 0.983489i | \(0.442078\pi\) | |||||||
\(492\) | 4.59976 | 0.207373 | ||||||||
\(493\) | −40.2602 | −1.81323 | ||||||||
\(494\) | 17.5903 | 0.791423 | ||||||||
\(495\) | 24.1851 | 1.08704 | ||||||||
\(496\) | 5.31601 | 0.238696 | ||||||||
\(497\) | 16.3543 | 0.733592 | ||||||||
\(498\) | −10.8538 | −0.486372 | ||||||||
\(499\) | 4.88699 | 0.218772 | 0.109386 | − | 0.993999i | \(-0.465112\pi\) | ||||
0.109386 | + | 0.993999i | \(0.465112\pi\) | |||||||
\(500\) | −16.3795 | −0.732514 | ||||||||
\(501\) | 15.9505 | 0.712614 | ||||||||
\(502\) | −14.9667 | −0.667999 | ||||||||
\(503\) | 22.9160 | 1.02178 | 0.510888 | − | 0.859647i | \(-0.329317\pi\) | ||||
0.510888 | + | 0.859647i | \(0.329317\pi\) | |||||||
\(504\) | −2.93588 | −0.130775 | ||||||||
\(505\) | −34.5351 | −1.53679 | ||||||||
\(506\) | 1.70305 | 0.0757097 | ||||||||
\(507\) | −13.2620 | −0.588987 | ||||||||
\(508\) | −11.7052 | −0.519336 | ||||||||
\(509\) | −4.50555 | −0.199705 | −0.0998524 | − | 0.995002i | \(-0.531837\pi\) | ||||
−0.0998524 | + | 0.995002i | \(0.531837\pi\) | |||||||
\(510\) | −18.7172 | −0.828811 | ||||||||
\(511\) | 3.07307 | 0.135944 | ||||||||
\(512\) | 6.27357 | 0.277255 | ||||||||
\(513\) | −3.63286 | −0.160395 | ||||||||
\(514\) | 10.0176 | 0.441859 | ||||||||
\(515\) | 5.71246 | 0.251721 | ||||||||
\(516\) | −3.52882 | −0.155348 | ||||||||
\(517\) | 12.1990 | 0.536511 | ||||||||
\(518\) | −4.04685 | −0.177808 | ||||||||
\(519\) | −11.5900 | −0.508744 | ||||||||
\(520\) | −56.2126 | −2.46509 | ||||||||
\(521\) | 11.8206 | 0.517872 | 0.258936 | − | 0.965894i | \(-0.416628\pi\) | ||||
0.258936 | + | 0.965894i | \(0.416628\pi\) | |||||||
\(522\) | −7.17437 | −0.314014 | ||||||||
\(523\) | −37.2939 | −1.63075 | −0.815374 | − | 0.578934i | \(-0.803469\pi\) | ||||
−0.815374 | + | 0.578934i | \(0.803469\pi\) | |||||||
\(524\) | 10.0112 | 0.437342 | ||||||||
\(525\) | 8.95926 | 0.391014 | ||||||||
\(526\) | −10.8111 | −0.471384 | ||||||||
\(527\) | 50.3873 | 2.19490 | ||||||||
\(528\) | 3.62104 | 0.157586 | ||||||||
\(529\) | −22.9225 | −0.996629 | ||||||||
\(530\) | 38.7883 | 1.68485 | ||||||||
\(531\) | −13.4972 | −0.585727 | ||||||||
\(532\) | 4.02258 | 0.174401 | ||||||||
\(533\) | −21.2885 | −0.922106 | ||||||||
\(534\) | 1.38217 | 0.0598124 | ||||||||
\(535\) | −34.1765 | −1.47758 | ||||||||
\(536\) | 41.5121 | 1.79305 | ||||||||
\(537\) | 12.5110 | 0.539890 | ||||||||
\(538\) | 8.22410 | 0.354566 | ||||||||
\(539\) | 6.47318 | 0.278819 | ||||||||
\(540\) | 4.13701 | 0.178029 | ||||||||
\(541\) | −23.6543 | −1.01698 | −0.508488 | − | 0.861069i | \(-0.669795\pi\) | ||||
−0.508488 | + | 0.861069i | \(0.669795\pi\) | |||||||
\(542\) | −16.5941 | −0.712778 | ||||||||
\(543\) | 23.7664 | 1.01991 | ||||||||
\(544\) | 28.3305 | 1.21466 | ||||||||
\(545\) | −72.9438 | −3.12457 | ||||||||
\(546\) | 4.84198 | 0.207218 | ||||||||
\(547\) | −19.9032 | −0.850998 | −0.425499 | − | 0.904959i | \(-0.639901\pi\) | ||||
−0.425499 | + | 0.904959i | \(0.639901\pi\) | |||||||
\(548\) | −10.0798 | −0.430588 | ||||||||
\(549\) | 0.0371054 | 0.00158362 | ||||||||
\(550\) | −54.7959 | −2.33651 | ||||||||
\(551\) | 27.5851 | 1.17516 | ||||||||
\(552\) | 0.817503 | 0.0347952 | ||||||||
\(553\) | 10.8106 | 0.459714 | ||||||||
\(554\) | 11.7603 | 0.499649 | ||||||||
\(555\) | 16.0026 | 0.679271 | ||||||||
\(556\) | 3.95129 | 0.167572 | ||||||||
\(557\) | −2.21512 | −0.0938576 | −0.0469288 | − | 0.998898i | \(-0.514943\pi\) | ||||
−0.0469288 | + | 0.998898i | \(0.514943\pi\) | |||||||
\(558\) | 8.97902 | 0.380112 | ||||||||
\(559\) | 16.3320 | 0.690768 | ||||||||
\(560\) | 2.09000 | 0.0883188 | ||||||||
\(561\) | 34.3216 | 1.44906 | ||||||||
\(562\) | −16.4321 | −0.693146 | ||||||||
\(563\) | 14.0710 | 0.593022 | 0.296511 | − | 0.955029i | \(-0.404177\pi\) | ||||
0.296511 | + | 0.955029i | \(0.404177\pi\) | |||||||
\(564\) | 2.08671 | 0.0878663 | ||||||||
\(565\) | 25.5072 | 1.07310 | ||||||||
\(566\) | −16.0749 | −0.675679 | ||||||||
\(567\) | −1.00000 | −0.0419961 | ||||||||
\(568\) | −48.0144 | −2.01464 | ||||||||
\(569\) | 11.0651 | 0.463874 | 0.231937 | − | 0.972731i | \(-0.425494\pi\) | ||||
0.231937 | + | 0.972731i | \(0.425494\pi\) | |||||||
\(570\) | 12.8245 | 0.537158 | ||||||||
\(571\) | −15.5384 | −0.650262 | −0.325131 | − | 0.945669i | \(-0.605408\pi\) | ||||
−0.325131 | + | 0.945669i | \(0.605408\pi\) | |||||||
\(572\) | 36.7314 | 1.53582 | ||||||||
\(573\) | −15.7867 | −0.659499 | ||||||||
\(574\) | 3.92499 | 0.163826 | ||||||||
\(575\) | −2.49473 | −0.104037 | ||||||||
\(576\) | 6.16728 | 0.256970 | ||||||||
\(577\) | 33.1582 | 1.38039 | 0.690196 | − | 0.723622i | \(-0.257524\pi\) | ||||
0.690196 | + | 0.723622i | \(0.257524\pi\) | |||||||
\(578\) | −10.4997 | −0.436729 | ||||||||
\(579\) | 9.25361 | 0.384567 | ||||||||
\(580\) | −31.4132 | −1.30436 | ||||||||
\(581\) | 11.4875 | 0.476581 | ||||||||
\(582\) | −15.3416 | −0.635928 | ||||||||
\(583\) | −71.1259 | −2.94573 | ||||||||
\(584\) | −9.02216 | −0.373340 | ||||||||
\(585\) | −19.1468 | −0.791621 | ||||||||
\(586\) | 4.43965 | 0.183400 | ||||||||
\(587\) | −20.1697 | −0.832491 | −0.416245 | − | 0.909252i | \(-0.636654\pi\) | ||||
−0.416245 | + | 0.909252i | \(0.636654\pi\) | |||||||
\(588\) | 1.10728 | 0.0456633 | ||||||||
\(589\) | −34.5238 | −1.42253 | ||||||||
\(590\) | 47.6466 | 1.96158 | ||||||||
\(591\) | 25.7315 | 1.05845 | ||||||||
\(592\) | 2.39593 | 0.0984721 | ||||||||
\(593\) | 5.68382 | 0.233407 | 0.116703 | − | 0.993167i | \(-0.462767\pi\) | ||||
0.116703 | + | 0.993167i | \(0.462767\pi\) | |||||||
\(594\) | 6.11612 | 0.250948 | ||||||||
\(595\) | 19.8099 | 0.812126 | ||||||||
\(596\) | −19.2104 | −0.786887 | ||||||||
\(597\) | −2.53649 | −0.103811 | ||||||||
\(598\) | −1.34826 | −0.0551344 | ||||||||
\(599\) | 17.2044 | 0.702954 | 0.351477 | − | 0.936196i | \(-0.385679\pi\) | ||||
0.351477 | + | 0.936196i | \(0.385679\pi\) | |||||||
\(600\) | −26.3033 | −1.07383 | ||||||||
\(601\) | −2.43307 | −0.0992469 | −0.0496234 | − | 0.998768i | \(-0.515802\pi\) | ||||
−0.0496234 | + | 0.998768i | \(0.515802\pi\) | |||||||
\(602\) | −3.01115 | −0.122725 | ||||||||
\(603\) | 14.1396 | 0.575807 | ||||||||
\(604\) | −6.55249 | −0.266617 | ||||||||
\(605\) | 115.456 | 4.69397 | ||||||||
\(606\) | −8.73350 | −0.354774 | ||||||||
\(607\) | 20.3386 | 0.825518 | 0.412759 | − | 0.910840i | \(-0.364565\pi\) | ||||
0.412759 | + | 0.910840i | \(0.364565\pi\) | |||||||
\(608\) | −19.4112 | −0.787229 | ||||||||
\(609\) | 7.59321 | 0.307692 | ||||||||
\(610\) | −0.130987 | −0.00530349 | ||||||||
\(611\) | −9.65763 | −0.390706 | ||||||||
\(612\) | 5.87092 | 0.237318 | ||||||||
\(613\) | 19.0284 | 0.768551 | 0.384275 | − | 0.923219i | \(-0.374451\pi\) | ||||
0.384275 | + | 0.923219i | \(0.374451\pi\) | |||||||
\(614\) | −1.83650 | −0.0741149 | ||||||||
\(615\) | −15.5207 | −0.625855 | ||||||||
\(616\) | −19.0045 | −0.765712 | ||||||||
\(617\) | 8.61548 | 0.346846 | 0.173423 | − | 0.984847i | \(-0.444517\pi\) | ||||
0.173423 | + | 0.984847i | \(0.444517\pi\) | |||||||
\(618\) | 1.44461 | 0.0581108 | ||||||||
\(619\) | −2.27320 | −0.0913675 | −0.0456838 | − | 0.998956i | \(-0.514547\pi\) | ||||
−0.0456838 | + | 0.998956i | \(0.514547\pi\) | |||||||
\(620\) | 39.3149 | 1.57892 | ||||||||
\(621\) | 0.278452 | 0.0111739 | ||||||||
\(622\) | −20.3353 | −0.815370 | ||||||||
\(623\) | −1.46286 | −0.0586083 | ||||||||
\(624\) | −2.86669 | −0.114759 | ||||||||
\(625\) | 10.4720 | 0.418882 | ||||||||
\(626\) | 22.6693 | 0.906046 | ||||||||
\(627\) | −23.5162 | −0.939145 | ||||||||
\(628\) | −7.16163 | −0.285780 | ||||||||
\(629\) | 22.7096 | 0.905490 | ||||||||
\(630\) | 3.53012 | 0.140644 | ||||||||
\(631\) | −3.46104 | −0.137782 | −0.0688909 | − | 0.997624i | \(-0.521946\pi\) | ||||
−0.0688909 | + | 0.997624i | \(0.521946\pi\) | |||||||
\(632\) | −31.7387 | −1.26250 | ||||||||
\(633\) | −21.4603 | −0.852971 | ||||||||
\(634\) | 3.59521 | 0.142784 | ||||||||
\(635\) | 39.4962 | 1.56736 | ||||||||
\(636\) | −12.1665 | −0.482433 | ||||||||
\(637\) | −5.12465 | −0.203046 | ||||||||
\(638\) | −46.4410 | −1.83862 | ||||||||
\(639\) | −16.3543 | −0.646968 | ||||||||
\(640\) | 18.1555 | 0.717661 | ||||||||
\(641\) | −22.6478 | −0.894534 | −0.447267 | − | 0.894401i | \(-0.647603\pi\) | ||||
−0.447267 | + | 0.894401i | \(0.647603\pi\) | |||||||
\(642\) | −8.64280 | −0.341104 | ||||||||
\(643\) | 4.47086 | 0.176313 | 0.0881567 | − | 0.996107i | \(-0.471902\pi\) | ||||
0.0881567 | + | 0.996107i | \(0.471902\pi\) | |||||||
\(644\) | −0.308323 | −0.0121496 | ||||||||
\(645\) | 11.9071 | 0.468841 | ||||||||
\(646\) | 18.1995 | 0.716049 | ||||||||
\(647\) | −18.6291 | −0.732385 | −0.366192 | − | 0.930539i | \(-0.619339\pi\) | ||||
−0.366192 | + | 0.930539i | \(0.619339\pi\) | |||||||
\(648\) | 2.93588 | 0.115332 | ||||||||
\(649\) | −87.3694 | −3.42955 | ||||||||
\(650\) | 43.3806 | 1.70153 | ||||||||
\(651\) | −9.50320 | −0.372460 | ||||||||
\(652\) | −15.5975 | −0.610844 | ||||||||
\(653\) | −39.6339 | −1.55099 | −0.775497 | − | 0.631351i | \(-0.782501\pi\) | ||||
−0.775497 | + | 0.631351i | \(0.782501\pi\) | |||||||
\(654\) | −18.4466 | −0.721319 | ||||||||
\(655\) | −33.7803 | −1.31990 | ||||||||
\(656\) | −2.32378 | −0.0907286 | ||||||||
\(657\) | −3.07307 | −0.119892 | ||||||||
\(658\) | 1.78059 | 0.0694148 | ||||||||
\(659\) | −13.3293 | −0.519236 | −0.259618 | − | 0.965711i | \(-0.583597\pi\) | ||||
−0.259618 | + | 0.965711i | \(0.583597\pi\) | |||||||
\(660\) | 26.7796 | 1.04239 | ||||||||
\(661\) | −12.8878 | −0.501277 | −0.250639 | − | 0.968081i | \(-0.580641\pi\) | ||||
−0.250639 | + | 0.968081i | \(0.580641\pi\) | |||||||
\(662\) | −23.0119 | −0.894383 | ||||||||
\(663\) | −27.1716 | −1.05526 | ||||||||
\(664\) | −33.7259 | −1.30882 | ||||||||
\(665\) | −13.5731 | −0.526344 | ||||||||
\(666\) | 4.04685 | 0.156812 | ||||||||
\(667\) | −2.11434 | −0.0818678 | ||||||||
\(668\) | 17.6616 | 0.683346 | ||||||||
\(669\) | 19.0986 | 0.738396 | ||||||||
\(670\) | −49.9144 | −1.92836 | ||||||||
\(671\) | 0.240190 | 0.00927242 | ||||||||
\(672\) | −5.34323 | −0.206119 | ||||||||
\(673\) | 33.5509 | 1.29329 | 0.646646 | − | 0.762791i | \(-0.276171\pi\) | ||||
0.646646 | + | 0.762791i | \(0.276171\pi\) | |||||||
\(674\) | 0.240309 | 0.00925635 | ||||||||
\(675\) | −8.95926 | −0.344842 | ||||||||
\(676\) | −14.6847 | −0.564797 | ||||||||
\(677\) | −6.79747 | −0.261248 | −0.130624 | − | 0.991432i | \(-0.541698\pi\) | ||||
−0.130624 | + | 0.991432i | \(0.541698\pi\) | |||||||
\(678\) | 6.45046 | 0.247728 | ||||||||
\(679\) | 16.2372 | 0.623126 | ||||||||
\(680\) | −58.1595 | −2.23031 | ||||||||
\(681\) | 12.6892 | 0.486253 | ||||||||
\(682\) | 58.1227 | 2.22564 | ||||||||
\(683\) | 27.5708 | 1.05497 | 0.527484 | − | 0.849565i | \(-0.323136\pi\) | ||||
0.527484 | + | 0.849565i | \(0.323136\pi\) | |||||||
\(684\) | −4.02258 | −0.153807 | ||||||||
\(685\) | 34.0116 | 1.29952 | ||||||||
\(686\) | 0.944841 | 0.0360742 | ||||||||
\(687\) | −13.1299 | −0.500938 | ||||||||
\(688\) | 1.78275 | 0.0679666 | ||||||||
\(689\) | 56.3085 | 2.14518 | ||||||||
\(690\) | −0.982971 | −0.0374211 | ||||||||
\(691\) | 4.79103 | 0.182259 | 0.0911296 | − | 0.995839i | \(-0.470952\pi\) | ||||
0.0911296 | + | 0.995839i | \(0.470952\pi\) | |||||||
\(692\) | −12.8333 | −0.487849 | ||||||||
\(693\) | −6.47318 | −0.245896 | ||||||||
\(694\) | −7.30983 | −0.277477 | ||||||||
\(695\) | −13.3326 | −0.505734 | ||||||||
\(696\) | −22.2928 | −0.845005 | ||||||||
\(697\) | −22.0258 | −0.834285 | ||||||||
\(698\) | −26.4413 | −1.00082 | ||||||||
\(699\) | −22.8584 | −0.864586 | ||||||||
\(700\) | 9.92037 | 0.374955 | ||||||||
\(701\) | 30.8363 | 1.16467 | 0.582335 | − | 0.812949i | \(-0.302139\pi\) | ||||
0.582335 | + | 0.812949i | \(0.302139\pi\) | |||||||
\(702\) | −4.84198 | −0.182749 | ||||||||
\(703\) | −15.5599 | −0.586854 | ||||||||
\(704\) | 39.9219 | 1.50461 | ||||||||
\(705\) | −7.04105 | −0.265181 | ||||||||
\(706\) | 12.0327 | 0.452855 | ||||||||
\(707\) | 9.24335 | 0.347632 | ||||||||
\(708\) | −14.9451 | −0.561670 | ||||||||
\(709\) | −13.3569 | −0.501630 | −0.250815 | − | 0.968035i | \(-0.580699\pi\) | ||||
−0.250815 | + | 0.968035i | \(0.580699\pi\) | |||||||
\(710\) | 57.7328 | 2.16667 | ||||||||
\(711\) | −10.8106 | −0.405430 | ||||||||
\(712\) | 4.29479 | 0.160954 | ||||||||
\(713\) | 2.64619 | 0.0991005 | ||||||||
\(714\) | 5.00968 | 0.187482 | ||||||||
\(715\) | −123.940 | −4.63511 | ||||||||
\(716\) | 13.8531 | 0.517716 | ||||||||
\(717\) | 6.19886 | 0.231501 | ||||||||
\(718\) | 23.0059 | 0.858571 | ||||||||
\(719\) | −24.8389 | −0.926336 | −0.463168 | − | 0.886271i | \(-0.653287\pi\) | ||||
−0.463168 | + | 0.886271i | \(0.653287\pi\) | |||||||
\(720\) | −2.09000 | −0.0778898 | ||||||||
\(721\) | −1.52895 | −0.0569409 | ||||||||
\(722\) | 5.48225 | 0.204028 | ||||||||
\(723\) | −3.91505 | −0.145602 | ||||||||
\(724\) | 26.3159 | 0.978023 | ||||||||
\(725\) | 68.0295 | 2.52655 | ||||||||
\(726\) | 29.1975 | 1.08362 | ||||||||
\(727\) | −24.4015 | −0.905000 | −0.452500 | − | 0.891764i | \(-0.649468\pi\) | ||||
−0.452500 | + | 0.891764i | \(0.649468\pi\) | |||||||
\(728\) | 15.0454 | 0.557618 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 10.8483 | 0.401514 | ||||||||
\(731\) | 16.8976 | 0.624980 | ||||||||
\(732\) | 0.0410859 | 0.00151858 | ||||||||
\(733\) | −5.48668 | −0.202655 | −0.101328 | − | 0.994853i | \(-0.532309\pi\) | ||||
−0.101328 | + | 0.994853i | \(0.532309\pi\) | |||||||
\(734\) | −22.9823 | −0.848291 | ||||||||
\(735\) | −3.73621 | −0.137812 | ||||||||
\(736\) | 1.48783 | 0.0548423 | ||||||||
\(737\) | 91.5279 | 3.37147 | ||||||||
\(738\) | −3.92499 | −0.144481 | ||||||||
\(739\) | −8.18683 | −0.301157 | −0.150579 | − | 0.988598i | \(-0.548114\pi\) | ||||
−0.150579 | + | 0.988598i | \(0.548114\pi\) | |||||||
\(740\) | 17.7192 | 0.651372 | ||||||||
\(741\) | 18.6172 | 0.683918 | ||||||||
\(742\) | −10.3817 | −0.381125 | ||||||||
\(743\) | −13.4114 | −0.492017 | −0.246009 | − | 0.969268i | \(-0.579119\pi\) | ||||
−0.246009 | + | 0.969268i | \(0.579119\pi\) | |||||||
\(744\) | 27.9003 | 1.02287 | ||||||||
\(745\) | 64.8203 | 2.37483 | ||||||||
\(746\) | 24.0681 | 0.881197 | ||||||||
\(747\) | −11.4875 | −0.420305 | ||||||||
\(748\) | 38.0035 | 1.38955 | ||||||||
\(749\) | 9.14736 | 0.334237 | ||||||||
\(750\) | 13.9767 | 0.510356 | ||||||||
\(751\) | 32.1013 | 1.17139 | 0.585697 | − | 0.810530i | \(-0.300821\pi\) | ||||
0.585697 | + | 0.810530i | \(0.300821\pi\) | |||||||
\(752\) | −1.05420 | −0.0384426 | ||||||||
\(753\) | −15.8405 | −0.577260 | ||||||||
\(754\) | 36.7661 | 1.33894 | ||||||||
\(755\) | 22.1097 | 0.804653 | ||||||||
\(756\) | −1.10728 | −0.0402712 | ||||||||
\(757\) | 52.5913 | 1.91147 | 0.955733 | − | 0.294237i | \(-0.0950655\pi\) | ||||
0.955733 | + | 0.294237i | \(0.0950655\pi\) | |||||||
\(758\) | −16.4982 | −0.599241 | ||||||||
\(759\) | 1.80247 | 0.0654255 | ||||||||
\(760\) | 39.8491 | 1.44548 | ||||||||
\(761\) | −34.8173 | −1.26213 | −0.631064 | − | 0.775731i | \(-0.717381\pi\) | ||||
−0.631064 | + | 0.775731i | \(0.717381\pi\) | |||||||
\(762\) | 9.98811 | 0.361831 | ||||||||
\(763\) | 19.5235 | 0.706797 | ||||||||
\(764\) | −17.4802 | −0.632412 | ||||||||
\(765\) | −19.8099 | −0.716228 | ||||||||
\(766\) | 0.944841 | 0.0341385 | ||||||||
\(767\) | 69.1682 | 2.49752 | ||||||||
\(768\) | 16.9259 | 0.610760 | ||||||||
\(769\) | −32.4849 | −1.17143 | −0.585717 | − | 0.810516i | \(-0.699187\pi\) | ||||
−0.585717 | + | 0.810516i | \(0.699187\pi\) | |||||||
\(770\) | 22.8511 | 0.823497 | ||||||||
\(771\) | 10.6024 | 0.381838 | ||||||||
\(772\) | 10.2463 | 0.368772 | ||||||||
\(773\) | 21.9140 | 0.788192 | 0.394096 | − | 0.919069i | \(-0.371058\pi\) | ||||
0.394096 | + | 0.919069i | \(0.371058\pi\) | |||||||
\(774\) | 3.01115 | 0.108234 | ||||||||
\(775\) | −85.1417 | −3.05838 | ||||||||
\(776\) | −47.6704 | −1.71127 | ||||||||
\(777\) | −4.28310 | −0.153655 | ||||||||
\(778\) | −10.9927 | −0.394106 | ||||||||
\(779\) | 15.0914 | 0.540705 | ||||||||
\(780\) | −21.2007 | −0.759108 | ||||||||
\(781\) | −105.864 | −3.78813 | ||||||||
\(782\) | −1.39495 | −0.0498835 | ||||||||
\(783\) | −7.59321 | −0.271359 | ||||||||
\(784\) | −0.559391 | −0.0199783 | ||||||||
\(785\) | 24.1650 | 0.862487 | ||||||||
\(786\) | −8.54261 | −0.304705 | ||||||||
\(787\) | 21.2378 | 0.757047 | 0.378523 | − | 0.925592i | \(-0.376432\pi\) | ||||
0.378523 | + | 0.925592i | \(0.376432\pi\) | |||||||
\(788\) | 28.4919 | 1.01498 | ||||||||
\(789\) | −11.4422 | −0.407353 | ||||||||
\(790\) | 38.1628 | 1.35777 | ||||||||
\(791\) | −6.82703 | −0.242741 | ||||||||
\(792\) | 19.0045 | 0.675295 | ||||||||
\(793\) | −0.190152 | −0.00675250 | ||||||||
\(794\) | −0.0966740 | −0.00343083 | ||||||||
\(795\) | 41.0527 | 1.45599 | ||||||||
\(796\) | −2.80859 | −0.0995477 | ||||||||
\(797\) | −52.7511 | −1.86854 | −0.934271 | − | 0.356564i | \(-0.883948\pi\) | ||||
−0.934271 | + | 0.356564i | \(0.883948\pi\) | |||||||
\(798\) | −3.43248 | −0.121508 | ||||||||
\(799\) | −9.99210 | −0.353495 | ||||||||
\(800\) | −47.8714 | −1.69251 | ||||||||
\(801\) | 1.46286 | 0.0516877 | ||||||||
\(802\) | 24.8245 | 0.876582 | ||||||||
\(803\) | −19.8925 | −0.701991 | ||||||||
\(804\) | 15.6564 | 0.552158 | ||||||||
\(805\) | 1.04036 | 0.0366677 | ||||||||
\(806\) | −46.0143 | −1.62078 | ||||||||
\(807\) | 8.70422 | 0.306403 | ||||||||
\(808\) | −27.1374 | −0.954690 | ||||||||
\(809\) | −51.0058 | −1.79327 | −0.896634 | − | 0.442772i | \(-0.853995\pi\) | ||||
−0.896634 | + | 0.442772i | \(0.853995\pi\) | |||||||
\(810\) | −3.53012 | −0.124036 | ||||||||
\(811\) | 36.2768 | 1.27385 | 0.636925 | − | 0.770926i | \(-0.280206\pi\) | ||||
0.636925 | + | 0.770926i | \(0.280206\pi\) | |||||||
\(812\) | 8.40777 | 0.295055 | ||||||||
\(813\) | −17.5628 | −0.615956 | ||||||||
\(814\) | 26.1960 | 0.918169 | ||||||||
\(815\) | 52.6296 | 1.84353 | ||||||||
\(816\) | −2.96597 | −0.103830 | ||||||||
\(817\) | −11.5777 | −0.405053 | ||||||||
\(818\) | 14.8807 | 0.520293 | ||||||||
\(819\) | 5.12465 | 0.179070 | ||||||||
\(820\) | −17.1857 | −0.600150 | ||||||||
\(821\) | 30.4544 | 1.06286 | 0.531432 | − | 0.847101i | \(-0.321654\pi\) | ||||
0.531432 | + | 0.847101i | \(0.321654\pi\) | |||||||
\(822\) | 8.60112 | 0.299999 | ||||||||
\(823\) | 20.0670 | 0.699493 | 0.349747 | − | 0.936844i | \(-0.386268\pi\) | ||||
0.349747 | + | 0.936844i | \(0.386268\pi\) | |||||||
\(824\) | 4.48880 | 0.156375 | ||||||||
\(825\) | −57.9949 | −2.01912 | ||||||||
\(826\) | −12.7527 | −0.443722 | ||||||||
\(827\) | 32.0817 | 1.11559 | 0.557795 | − | 0.829979i | \(-0.311648\pi\) | ||||
0.557795 | + | 0.829979i | \(0.311648\pi\) | |||||||
\(828\) | 0.308323 | 0.0107150 | ||||||||
\(829\) | −16.1028 | −0.559274 | −0.279637 | − | 0.960106i | \(-0.590214\pi\) | ||||
−0.279637 | + | 0.960106i | \(0.590214\pi\) | |||||||
\(830\) | 40.5522 | 1.40759 | ||||||||
\(831\) | 12.4469 | 0.431778 | ||||||||
\(832\) | −31.6052 | −1.09571 | ||||||||
\(833\) | −5.30213 | −0.183708 | ||||||||
\(834\) | −3.37165 | −0.116751 | ||||||||
\(835\) | −59.5943 | −2.06235 | ||||||||
\(836\) | −26.0389 | −0.900573 | ||||||||
\(837\) | 9.50320 | 0.328479 | ||||||||
\(838\) | −3.71328 | −0.128273 | ||||||||
\(839\) | 15.6199 | 0.539258 | 0.269629 | − | 0.962964i | \(-0.413099\pi\) | ||||
0.269629 | + | 0.962964i | \(0.413099\pi\) | |||||||
\(840\) | 10.9691 | 0.378469 | ||||||||
\(841\) | 28.6568 | 0.988165 | ||||||||
\(842\) | −13.7648 | −0.474366 | ||||||||
\(843\) | −17.3914 | −0.598991 | ||||||||
\(844\) | −23.7625 | −0.817938 | ||||||||
\(845\) | 49.5497 | 1.70456 | ||||||||
\(846\) | −1.78059 | −0.0612181 | ||||||||
\(847\) | −30.9020 | −1.06181 | ||||||||
\(848\) | 6.14647 | 0.211071 | ||||||||
\(849\) | −17.0134 | −0.583897 | ||||||||
\(850\) | 44.8830 | 1.53947 | ||||||||
\(851\) | 1.19264 | 0.0408831 | ||||||||
\(852\) | −18.1087 | −0.620396 | ||||||||
\(853\) | −52.7653 | −1.80665 | −0.903325 | − | 0.428957i | \(-0.858881\pi\) | ||||
−0.903325 | + | 0.428957i | \(0.858881\pi\) | |||||||
\(854\) | 0.0350587 | 0.00119968 | ||||||||
\(855\) | 13.5731 | 0.464192 | ||||||||
\(856\) | −26.8556 | −0.917905 | ||||||||
\(857\) | −22.6476 | −0.773627 | −0.386814 | − | 0.922158i | \(-0.626424\pi\) | ||||
−0.386814 | + | 0.922158i | \(0.626424\pi\) | |||||||
\(858\) | −31.3430 | −1.07003 | ||||||||
\(859\) | −25.0295 | −0.853995 | −0.426998 | − | 0.904253i | \(-0.640429\pi\) | ||||
−0.426998 | + | 0.904253i | \(0.640429\pi\) | |||||||
\(860\) | 13.1844 | 0.449585 | ||||||||
\(861\) | 4.15413 | 0.141572 | ||||||||
\(862\) | 26.7307 | 0.910450 | ||||||||
\(863\) | 6.12003 | 0.208328 | 0.104164 | − | 0.994560i | \(-0.466783\pi\) | ||||
0.104164 | + | 0.994560i | \(0.466783\pi\) | |||||||
\(864\) | 5.34323 | 0.181780 | ||||||||
\(865\) | 43.3026 | 1.47233 | ||||||||
\(866\) | 30.9897 | 1.05307 | ||||||||
\(867\) | −11.1126 | −0.377405 | ||||||||
\(868\) | −10.5227 | −0.357162 | ||||||||
\(869\) | −69.9790 | −2.37387 | ||||||||
\(870\) | 26.8050 | 0.908773 | ||||||||
\(871\) | −72.4603 | −2.45522 | ||||||||
\(872\) | −57.3186 | −1.94105 | ||||||||
\(873\) | −16.2372 | −0.549545 | ||||||||
\(874\) | 0.955782 | 0.0323298 | ||||||||
\(875\) | −14.7926 | −0.500082 | ||||||||
\(876\) | −3.40273 | −0.114968 | ||||||||
\(877\) | 33.8899 | 1.14438 | 0.572190 | − | 0.820121i | \(-0.306094\pi\) | ||||
0.572190 | + | 0.820121i | \(0.306094\pi\) | |||||||
\(878\) | 9.40839 | 0.317518 | ||||||||
\(879\) | 4.69883 | 0.158488 | ||||||||
\(880\) | −13.5290 | −0.456061 | ||||||||
\(881\) | −7.63399 | −0.257196 | −0.128598 | − | 0.991697i | \(-0.541048\pi\) | ||||
−0.128598 | + | 0.991697i | \(0.541048\pi\) | |||||||
\(882\) | −0.944841 | −0.0318145 | ||||||||
\(883\) | −3.95306 | −0.133031 | −0.0665155 | − | 0.997785i | \(-0.521188\pi\) | ||||
−0.0665155 | + | 0.997785i | \(0.521188\pi\) | |||||||
\(884\) | −30.0864 | −1.01192 | ||||||||
\(885\) | 50.4282 | 1.69513 | ||||||||
\(886\) | 18.7521 | 0.629991 | ||||||||
\(887\) | −47.3071 | −1.58842 | −0.794209 | − | 0.607645i | \(-0.792114\pi\) | ||||
−0.794209 | + | 0.607645i | \(0.792114\pi\) | |||||||
\(888\) | 12.5747 | 0.421979 | ||||||||
\(889\) | −10.5712 | −0.354547 | ||||||||
\(890\) | −5.16408 | −0.173101 | ||||||||
\(891\) | 6.47318 | 0.216860 | ||||||||
\(892\) | 21.1474 | 0.708069 | ||||||||
\(893\) | 6.84629 | 0.229102 | ||||||||
\(894\) | 16.3923 | 0.548239 | ||||||||
\(895\) | −46.7437 | −1.56247 | ||||||||
\(896\) | −4.85935 | −0.162339 | ||||||||
\(897\) | −1.42697 | −0.0476451 | ||||||||
\(898\) | 9.04069 | 0.301692 | ||||||||
\(899\) | −72.1598 | −2.40666 | ||||||||
\(900\) | −9.92037 | −0.330679 | ||||||||
\(901\) | 58.2587 | 1.94088 | ||||||||
\(902\) | −25.4072 | −0.845966 | ||||||||
\(903\) | −3.18694 | −0.106055 | ||||||||
\(904\) | 20.0434 | 0.666632 | ||||||||
\(905\) | −88.7961 | −2.95168 | ||||||||
\(906\) | 5.59126 | 0.185757 | ||||||||
\(907\) | 21.2732 | 0.706365 | 0.353182 | − | 0.935555i | \(-0.385100\pi\) | ||||
0.353182 | + | 0.935555i | \(0.385100\pi\) | |||||||
\(908\) | 14.0505 | 0.466282 | ||||||||
\(909\) | −9.24335 | −0.306583 | ||||||||
\(910\) | −18.0906 | −0.599699 | ||||||||
\(911\) | −11.4264 | −0.378574 | −0.189287 | − | 0.981922i | \(-0.560618\pi\) | ||||
−0.189287 | + | 0.981922i | \(0.560618\pi\) | |||||||
\(912\) | 2.03219 | 0.0672926 | ||||||||
\(913\) | −74.3604 | −2.46097 | ||||||||
\(914\) | 13.1773 | 0.435865 | ||||||||
\(915\) | −0.138633 | −0.00458308 | ||||||||
\(916\) | −14.5384 | −0.480363 | ||||||||
\(917\) | 9.04132 | 0.298571 | ||||||||
\(918\) | −5.00968 | −0.165344 | ||||||||
\(919\) | −26.8004 | −0.884062 | −0.442031 | − | 0.897000i | \(-0.645742\pi\) | ||||
−0.442031 | + | 0.897000i | \(0.645742\pi\) | |||||||
\(920\) | −3.05436 | −0.100699 | ||||||||
\(921\) | −1.94371 | −0.0640474 | ||||||||
\(922\) | 5.65089 | 0.186102 | ||||||||
\(923\) | 83.8102 | 2.75865 | ||||||||
\(924\) | −7.16759 | −0.235796 | ||||||||
\(925\) | −38.3734 | −1.26171 | ||||||||
\(926\) | 17.8073 | 0.585185 | ||||||||
\(927\) | 1.52895 | 0.0502172 | ||||||||
\(928\) | −40.5722 | −1.33185 | ||||||||
\(929\) | −36.9136 | −1.21110 | −0.605548 | − | 0.795808i | \(-0.707046\pi\) | ||||
−0.605548 | + | 0.795808i | \(0.707046\pi\) | |||||||
\(930\) | −33.5475 | −1.10007 | ||||||||
\(931\) | 3.63286 | 0.119062 | ||||||||
\(932\) | −25.3106 | −0.829076 | ||||||||
\(933\) | −21.5224 | −0.704612 | ||||||||
\(934\) | −21.3587 | −0.698879 | ||||||||
\(935\) | −128.233 | −4.19366 | ||||||||
\(936\) | −15.0454 | −0.491773 | ||||||||
\(937\) | 35.8406 | 1.17086 | 0.585431 | − | 0.810722i | \(-0.300925\pi\) | ||||
0.585431 | + | 0.810722i | \(0.300925\pi\) | |||||||
\(938\) | 13.3596 | 0.436208 | ||||||||
\(939\) | 23.9927 | 0.782971 | ||||||||
\(940\) | −7.79638 | −0.254290 | ||||||||
\(941\) | 9.52369 | 0.310464 | 0.155232 | − | 0.987878i | \(-0.450388\pi\) | ||||
0.155232 | + | 0.987878i | \(0.450388\pi\) | |||||||
\(942\) | 6.11104 | 0.199108 | ||||||||
\(943\) | −1.15673 | −0.0376682 | ||||||||
\(944\) | 7.55019 | 0.245738 | ||||||||
\(945\) | 3.73621 | 0.121539 | ||||||||
\(946\) | 19.4917 | 0.633730 | ||||||||
\(947\) | −23.2013 | −0.753941 | −0.376971 | − | 0.926225i | \(-0.623034\pi\) | ||||
−0.376971 | + | 0.926225i | \(0.623034\pi\) | |||||||
\(948\) | −11.9703 | −0.388778 | ||||||||
\(949\) | 15.7484 | 0.511214 | ||||||||
\(950\) | −30.7525 | −0.997742 | ||||||||
\(951\) | 3.80509 | 0.123389 | ||||||||
\(952\) | 15.5664 | 0.504511 | ||||||||
\(953\) | −21.3002 | −0.689982 | −0.344991 | − | 0.938606i | \(-0.612118\pi\) | ||||
−0.344991 | + | 0.938606i | \(0.612118\pi\) | |||||||
\(954\) | 10.3817 | 0.336120 | ||||||||
\(955\) | 58.9824 | 1.90863 | ||||||||
\(956\) | 6.86384 | 0.221992 | ||||||||
\(957\) | −49.1522 | −1.58886 | ||||||||
\(958\) | −16.7239 | −0.540323 | ||||||||
\(959\) | −9.10325 | −0.293959 | ||||||||
\(960\) | −23.0423 | −0.743686 | ||||||||
\(961\) | 59.3108 | 1.91325 | ||||||||
\(962\) | −20.7387 | −0.668642 | ||||||||
\(963\) | −9.14736 | −0.294770 | ||||||||
\(964\) | −4.33504 | −0.139622 | ||||||||
\(965\) | −34.5734 | −1.11296 | ||||||||
\(966\) | 0.263093 | 0.00846488 | ||||||||
\(967\) | −33.8778 | −1.08944 | −0.544718 | − | 0.838619i | \(-0.683363\pi\) | ||||
−0.544718 | + | 0.838619i | \(0.683363\pi\) | |||||||
\(968\) | 90.7246 | 2.91600 | ||||||||
\(969\) | 19.2619 | 0.618783 | ||||||||
\(970\) | 57.3193 | 1.84041 | ||||||||
\(971\) | 31.6379 | 1.01531 | 0.507654 | − | 0.861561i | \(-0.330513\pi\) | ||||
0.507654 | + | 0.861561i | \(0.330513\pi\) | |||||||
\(972\) | 1.10728 | 0.0355159 | ||||||||
\(973\) | 3.56848 | 0.114400 | ||||||||
\(974\) | 18.7898 | 0.602063 | ||||||||
\(975\) | 45.9131 | 1.47039 | ||||||||
\(976\) | −0.0207564 | −0.000664397 0 | ||||||||
\(977\) | −1.30470 | −0.0417412 | −0.0208706 | − | 0.999782i | \(-0.506644\pi\) | ||||
−0.0208706 | + | 0.999782i | \(0.506644\pi\) | |||||||
\(978\) | 13.3094 | 0.425587 | ||||||||
\(979\) | 9.46936 | 0.302642 | ||||||||
\(980\) | −4.13701 | −0.132152 | ||||||||
\(981\) | −19.5235 | −0.623337 | ||||||||
\(982\) | −7.57748 | −0.241807 | ||||||||
\(983\) | −2.15632 | −0.0687760 | −0.0343880 | − | 0.999409i | \(-0.510948\pi\) | ||||
−0.0343880 | + | 0.999409i | \(0.510948\pi\) | |||||||
\(984\) | −12.1960 | −0.388795 | ||||||||
\(985\) | −96.1384 | −3.06323 | ||||||||
\(986\) | 38.0395 | 1.21142 | ||||||||
\(987\) | 1.88454 | 0.0599857 | ||||||||
\(988\) | 20.6143 | 0.655829 | ||||||||
\(989\) | 0.887410 | 0.0282180 | ||||||||
\(990\) | −22.8511 | −0.726256 | ||||||||
\(991\) | −24.3042 | −0.772049 | −0.386025 | − | 0.922488i | \(-0.626152\pi\) | ||||
−0.386025 | + | 0.922488i | \(0.626152\pi\) | |||||||
\(992\) | 50.7778 | 1.61220 | ||||||||
\(993\) | −24.3553 | −0.772893 | ||||||||
\(994\) | −15.4523 | −0.490116 | ||||||||
\(995\) | 9.47684 | 0.300436 | ||||||||
\(996\) | −12.7198 | −0.403042 | ||||||||
\(997\) | −42.7177 | −1.35288 | −0.676441 | − | 0.736497i | \(-0.736479\pi\) | ||||
−0.676441 | + | 0.736497i | \(0.736479\pi\) | |||||||
\(998\) | −4.61743 | −0.146162 | ||||||||
\(999\) | 4.28310 | 0.135511 |
(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 | 8043.2.a.r.1.15 | ✓ | 46 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8043.2.a.r.1.15 | ✓ | 46 | 1.1 | even | 1 | trivial |