Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4730,2,Mod(1,4730)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4730, 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("4730.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4730 = 2 \cdot 5 \cdot 11 \cdot 43 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4730.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: | \(37.7692401561\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 3 x^{11} - 26 x^{10} + 79 x^{9} + 247 x^{8} - 766 x^{7} - 1023 x^{6} + 3281 x^{5} + 1634 x^{4} + \cdots + 392 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-2.56242\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4730.1 |
$q$-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 | ||||||||
\(3\) | −2.56242 | −1.47941 | −0.739707 | − | 0.672929i | \(-0.765036\pi\) | ||||
−0.739707 | + | 0.672929i | \(0.765036\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | −2.56242 | −1.04610 | ||||||||
\(7\) | 3.71438 | 1.40390 | 0.701952 | − | 0.712224i | \(-0.252312\pi\) | ||||
0.701952 | + | 0.712224i | \(0.252312\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 3.56600 | 1.18867 | ||||||||
\(10\) | 1.00000 | 0.316228 | ||||||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | −2.56242 | −0.739707 | ||||||||
\(13\) | 5.57975 | 1.54754 | 0.773772 | − | 0.633465i | \(-0.218368\pi\) | ||||
0.773772 | + | 0.633465i | \(0.218368\pi\) | |||||||
\(14\) | 3.71438 | 0.992710 | ||||||||
\(15\) | −2.56242 | −0.661614 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 3.56825 | 0.865427 | 0.432713 | − | 0.901532i | \(-0.357556\pi\) | ||||
0.432713 | + | 0.901532i | \(0.357556\pi\) | |||||||
\(18\) | 3.56600 | 0.840514 | ||||||||
\(19\) | 7.50849 | 1.72257 | 0.861283 | − | 0.508126i | \(-0.169662\pi\) | ||||
0.861283 | + | 0.508126i | \(0.169662\pi\) | |||||||
\(20\) | 1.00000 | 0.223607 | ||||||||
\(21\) | −9.51780 | −2.07696 | ||||||||
\(22\) | −1.00000 | −0.213201 | ||||||||
\(23\) | −3.57975 | −0.746429 | −0.373214 | − | 0.927745i | \(-0.621744\pi\) | ||||
−0.373214 | + | 0.927745i | \(0.621744\pi\) | |||||||
\(24\) | −2.56242 | −0.523052 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 5.57975 | 1.09428 | ||||||||
\(27\) | −1.45032 | −0.279115 | ||||||||
\(28\) | 3.71438 | 0.701952 | ||||||||
\(29\) | 10.4694 | 1.94411 | 0.972056 | − | 0.234751i | \(-0.0754274\pi\) | ||||
0.972056 | + | 0.234751i | \(0.0754274\pi\) | |||||||
\(30\) | −2.56242 | −0.467832 | ||||||||
\(31\) | −8.61067 | −1.54652 | −0.773261 | − | 0.634088i | \(-0.781376\pi\) | ||||
−0.773261 | + | 0.634088i | \(0.781376\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 2.56242 | 0.446060 | ||||||||
\(34\) | 3.56825 | 0.611949 | ||||||||
\(35\) | 3.71438 | 0.627845 | ||||||||
\(36\) | 3.56600 | 0.594333 | ||||||||
\(37\) | −1.18834 | −0.195362 | −0.0976808 | − | 0.995218i | \(-0.531142\pi\) | ||||
−0.0976808 | + | 0.995218i | \(0.531142\pi\) | |||||||
\(38\) | 7.50849 | 1.21804 | ||||||||
\(39\) | −14.2977 | −2.28946 | ||||||||
\(40\) | 1.00000 | 0.158114 | ||||||||
\(41\) | 9.18919 | 1.43511 | 0.717556 | − | 0.696501i | \(-0.245261\pi\) | ||||
0.717556 | + | 0.696501i | \(0.245261\pi\) | |||||||
\(42\) | −9.51780 | −1.46863 | ||||||||
\(43\) | 1.00000 | 0.152499 | ||||||||
\(44\) | −1.00000 | −0.150756 | ||||||||
\(45\) | 3.56600 | 0.531588 | ||||||||
\(46\) | −3.57975 | −0.527805 | ||||||||
\(47\) | −8.24604 | −1.20281 | −0.601404 | − | 0.798945i | \(-0.705392\pi\) | ||||
−0.601404 | + | 0.798945i | \(0.705392\pi\) | |||||||
\(48\) | −2.56242 | −0.369854 | ||||||||
\(49\) | 6.79662 | 0.970946 | ||||||||
\(50\) | 1.00000 | 0.141421 | ||||||||
\(51\) | −9.14335 | −1.28032 | ||||||||
\(52\) | 5.57975 | 0.773772 | ||||||||
\(53\) | −9.37658 | −1.28797 | −0.643986 | − | 0.765037i | \(-0.722721\pi\) | ||||
−0.643986 | + | 0.765037i | \(0.722721\pi\) | |||||||
\(54\) | −1.45032 | −0.197364 | ||||||||
\(55\) | −1.00000 | −0.134840 | ||||||||
\(56\) | 3.71438 | 0.496355 | ||||||||
\(57\) | −19.2399 | −2.54839 | ||||||||
\(58\) | 10.4694 | 1.37469 | ||||||||
\(59\) | −4.51898 | −0.588321 | −0.294160 | − | 0.955756i | \(-0.595040\pi\) | ||||
−0.294160 | + | 0.955756i | \(0.595040\pi\) | |||||||
\(60\) | −2.56242 | −0.330807 | ||||||||
\(61\) | −10.7548 | −1.37701 | −0.688507 | − | 0.725229i | \(-0.741734\pi\) | ||||
−0.688507 | + | 0.725229i | \(0.741734\pi\) | |||||||
\(62\) | −8.61067 | −1.09356 | ||||||||
\(63\) | 13.2455 | 1.66877 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 5.57975 | 0.692082 | ||||||||
\(66\) | 2.56242 | 0.315412 | ||||||||
\(67\) | 6.61761 | 0.808470 | 0.404235 | − | 0.914655i | \(-0.367538\pi\) | ||||
0.404235 | + | 0.914655i | \(0.367538\pi\) | |||||||
\(68\) | 3.56825 | 0.432713 | ||||||||
\(69\) | 9.17281 | 1.10428 | ||||||||
\(70\) | 3.71438 | 0.443953 | ||||||||
\(71\) | −0.469439 | −0.0557122 | −0.0278561 | − | 0.999612i | \(-0.508868\pi\) | ||||
−0.0278561 | + | 0.999612i | \(0.508868\pi\) | |||||||
\(72\) | 3.56600 | 0.420257 | ||||||||
\(73\) | −1.64340 | −0.192345 | −0.0961725 | − | 0.995365i | \(-0.530660\pi\) | ||||
−0.0961725 | + | 0.995365i | \(0.530660\pi\) | |||||||
\(74\) | −1.18834 | −0.138142 | ||||||||
\(75\) | −2.56242 | −0.295883 | ||||||||
\(76\) | 7.50849 | 0.861283 | ||||||||
\(77\) | −3.71438 | −0.423293 | ||||||||
\(78\) | −14.2977 | −1.61889 | ||||||||
\(79\) | −4.43404 | −0.498868 | −0.249434 | − | 0.968392i | \(-0.580245\pi\) | ||||
−0.249434 | + | 0.968392i | \(0.580245\pi\) | |||||||
\(80\) | 1.00000 | 0.111803 | ||||||||
\(81\) | −6.98165 | −0.775739 | ||||||||
\(82\) | 9.18919 | 1.01478 | ||||||||
\(83\) | 10.4132 | 1.14300 | 0.571498 | − | 0.820603i | \(-0.306362\pi\) | ||||
0.571498 | + | 0.820603i | \(0.306362\pi\) | |||||||
\(84\) | −9.51780 | −1.03848 | ||||||||
\(85\) | 3.56825 | 0.387031 | ||||||||
\(86\) | 1.00000 | 0.107833 | ||||||||
\(87\) | −26.8269 | −2.87615 | ||||||||
\(88\) | −1.00000 | −0.106600 | ||||||||
\(89\) | 10.8354 | 1.14855 | 0.574273 | − | 0.818664i | \(-0.305285\pi\) | ||||
0.574273 | + | 0.818664i | \(0.305285\pi\) | |||||||
\(90\) | 3.56600 | 0.375889 | ||||||||
\(91\) | 20.7253 | 2.17260 | ||||||||
\(92\) | −3.57975 | −0.373214 | ||||||||
\(93\) | 22.0642 | 2.28795 | ||||||||
\(94\) | −8.24604 | −0.850514 | ||||||||
\(95\) | 7.50849 | 0.770355 | ||||||||
\(96\) | −2.56242 | −0.261526 | ||||||||
\(97\) | 0.511402 | 0.0519250 | 0.0259625 | − | 0.999663i | \(-0.491735\pi\) | ||||
0.0259625 | + | 0.999663i | \(0.491735\pi\) | |||||||
\(98\) | 6.79662 | 0.686562 | ||||||||
\(99\) | −3.56600 | −0.358396 | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | 5.73226 | 0.570381 | 0.285191 | − | 0.958471i | \(-0.407943\pi\) | ||||
0.285191 | + | 0.958471i | \(0.407943\pi\) | |||||||
\(102\) | −9.14335 | −0.905326 | ||||||||
\(103\) | 7.60241 | 0.749087 | 0.374544 | − | 0.927209i | \(-0.377799\pi\) | ||||
0.374544 | + | 0.927209i | \(0.377799\pi\) | |||||||
\(104\) | 5.57975 | 0.547139 | ||||||||
\(105\) | −9.51780 | −0.928843 | ||||||||
\(106\) | −9.37658 | −0.910734 | ||||||||
\(107\) | −2.53696 | −0.245257 | −0.122629 | − | 0.992453i | \(-0.539132\pi\) | ||||
−0.122629 | + | 0.992453i | \(0.539132\pi\) | |||||||
\(108\) | −1.45032 | −0.139558 | ||||||||
\(109\) | −10.5718 | −1.01259 | −0.506295 | − | 0.862360i | \(-0.668985\pi\) | ||||
−0.506295 | + | 0.862360i | \(0.668985\pi\) | |||||||
\(110\) | −1.00000 | −0.0953463 | ||||||||
\(111\) | 3.04502 | 0.289021 | ||||||||
\(112\) | 3.71438 | 0.350976 | ||||||||
\(113\) | −16.3289 | −1.53609 | −0.768046 | − | 0.640395i | \(-0.778771\pi\) | ||||
−0.768046 | + | 0.640395i | \(0.778771\pi\) | |||||||
\(114\) | −19.2399 | −1.80198 | ||||||||
\(115\) | −3.57975 | −0.333813 | ||||||||
\(116\) | 10.4694 | 0.972056 | ||||||||
\(117\) | 19.8974 | 1.83951 | ||||||||
\(118\) | −4.51898 | −0.416005 | ||||||||
\(119\) | 13.2538 | 1.21498 | ||||||||
\(120\) | −2.56242 | −0.233916 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | −10.7548 | −0.973697 | ||||||||
\(123\) | −23.5466 | −2.12312 | ||||||||
\(124\) | −8.61067 | −0.773261 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 13.2455 | 1.18000 | ||||||||
\(127\) | −1.55955 | −0.138388 | −0.0691938 | − | 0.997603i | \(-0.522043\pi\) | ||||
−0.0691938 | + | 0.997603i | \(0.522043\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | −2.56242 | −0.225609 | ||||||||
\(130\) | 5.57975 | 0.489376 | ||||||||
\(131\) | −18.8774 | −1.64933 | −0.824664 | − | 0.565623i | \(-0.808636\pi\) | ||||
−0.824664 | + | 0.565623i | \(0.808636\pi\) | |||||||
\(132\) | 2.56242 | 0.223030 | ||||||||
\(133\) | 27.8894 | 2.41832 | ||||||||
\(134\) | 6.61761 | 0.571675 | ||||||||
\(135\) | −1.45032 | −0.124824 | ||||||||
\(136\) | 3.56825 | 0.305975 | ||||||||
\(137\) | −6.16582 | −0.526782 | −0.263391 | − | 0.964689i | \(-0.584841\pi\) | ||||
−0.263391 | + | 0.964689i | \(0.584841\pi\) | |||||||
\(138\) | 9.17281 | 0.780842 | ||||||||
\(139\) | −20.7119 | −1.75676 | −0.878378 | − | 0.477966i | \(-0.841374\pi\) | ||||
−0.878378 | + | 0.477966i | \(0.841374\pi\) | |||||||
\(140\) | 3.71438 | 0.313922 | ||||||||
\(141\) | 21.1298 | 1.77945 | ||||||||
\(142\) | −0.469439 | −0.0393944 | ||||||||
\(143\) | −5.57975 | −0.466602 | ||||||||
\(144\) | 3.56600 | 0.297166 | ||||||||
\(145\) | 10.4694 | 0.869433 | ||||||||
\(146\) | −1.64340 | −0.136009 | ||||||||
\(147\) | −17.4158 | −1.43643 | ||||||||
\(148\) | −1.18834 | −0.0976808 | ||||||||
\(149\) | 4.55818 | 0.373420 | 0.186710 | − | 0.982415i | \(-0.440217\pi\) | ||||
0.186710 | + | 0.982415i | \(0.440217\pi\) | |||||||
\(150\) | −2.56242 | −0.209221 | ||||||||
\(151\) | −19.4030 | −1.57900 | −0.789498 | − | 0.613753i | \(-0.789659\pi\) | ||||
−0.789498 | + | 0.613753i | \(0.789659\pi\) | |||||||
\(152\) | 7.50849 | 0.609019 | ||||||||
\(153\) | 12.7244 | 1.02870 | ||||||||
\(154\) | −3.71438 | −0.299313 | ||||||||
\(155\) | −8.61067 | −0.691626 | ||||||||
\(156\) | −14.2977 | −1.14473 | ||||||||
\(157\) | 9.75708 | 0.778700 | 0.389350 | − | 0.921090i | \(-0.372700\pi\) | ||||
0.389350 | + | 0.921090i | \(0.372700\pi\) | |||||||
\(158\) | −4.43404 | −0.352753 | ||||||||
\(159\) | 24.0267 | 1.90544 | ||||||||
\(160\) | 1.00000 | 0.0790569 | ||||||||
\(161\) | −13.2965 | −1.04791 | ||||||||
\(162\) | −6.98165 | −0.548530 | ||||||||
\(163\) | −7.12889 | −0.558378 | −0.279189 | − | 0.960236i | \(-0.590066\pi\) | ||||
−0.279189 | + | 0.960236i | \(0.590066\pi\) | |||||||
\(164\) | 9.18919 | 0.717556 | ||||||||
\(165\) | 2.56242 | 0.199484 | ||||||||
\(166\) | 10.4132 | 0.808220 | ||||||||
\(167\) | 6.12444 | 0.473923 | 0.236962 | − | 0.971519i | \(-0.423848\pi\) | ||||
0.236962 | + | 0.971519i | \(0.423848\pi\) | |||||||
\(168\) | −9.51780 | −0.734315 | ||||||||
\(169\) | 18.1336 | 1.39489 | ||||||||
\(170\) | 3.56825 | 0.273672 | ||||||||
\(171\) | 26.7753 | 2.04756 | ||||||||
\(172\) | 1.00000 | 0.0762493 | ||||||||
\(173\) | −18.6132 | −1.41513 | −0.707567 | − | 0.706646i | \(-0.750207\pi\) | ||||
−0.707567 | + | 0.706646i | \(0.750207\pi\) | |||||||
\(174\) | −26.8269 | −2.03374 | ||||||||
\(175\) | 3.71438 | 0.280781 | ||||||||
\(176\) | −1.00000 | −0.0753778 | ||||||||
\(177\) | 11.5795 | 0.870370 | ||||||||
\(178\) | 10.8354 | 0.812145 | ||||||||
\(179\) | −8.07746 | −0.603738 | −0.301869 | − | 0.953349i | \(-0.597611\pi\) | ||||
−0.301869 | + | 0.953349i | \(0.597611\pi\) | |||||||
\(180\) | 3.56600 | 0.265794 | ||||||||
\(181\) | −12.2583 | −0.911153 | −0.455576 | − | 0.890197i | \(-0.650567\pi\) | ||||
−0.455576 | + | 0.890197i | \(0.650567\pi\) | |||||||
\(182\) | 20.7253 | 1.53626 | ||||||||
\(183\) | 27.5584 | 2.03718 | ||||||||
\(184\) | −3.57975 | −0.263902 | ||||||||
\(185\) | −1.18834 | −0.0873684 | ||||||||
\(186\) | 22.0642 | 1.61782 | ||||||||
\(187\) | −3.56825 | −0.260936 | ||||||||
\(188\) | −8.24604 | −0.601404 | ||||||||
\(189\) | −5.38706 | −0.391851 | ||||||||
\(190\) | 7.50849 | 0.544723 | ||||||||
\(191\) | 25.8507 | 1.87049 | 0.935244 | − | 0.354004i | \(-0.115180\pi\) | ||||
0.935244 | + | 0.354004i | \(0.115180\pi\) | |||||||
\(192\) | −2.56242 | −0.184927 | ||||||||
\(193\) | 12.9265 | 0.930467 | 0.465233 | − | 0.885188i | \(-0.345970\pi\) | ||||
0.465233 | + | 0.885188i | \(0.345970\pi\) | |||||||
\(194\) | 0.511402 | 0.0367165 | ||||||||
\(195\) | −14.2977 | −1.02388 | ||||||||
\(196\) | 6.79662 | 0.485473 | ||||||||
\(197\) | 9.14995 | 0.651907 | 0.325953 | − | 0.945386i | \(-0.394315\pi\) | ||||
0.325953 | + | 0.945386i | \(0.394315\pi\) | |||||||
\(198\) | −3.56600 | −0.253424 | ||||||||
\(199\) | 17.2884 | 1.22554 | 0.612771 | − | 0.790260i | \(-0.290055\pi\) | ||||
0.612771 | + | 0.790260i | \(0.290055\pi\) | |||||||
\(200\) | 1.00000 | 0.0707107 | ||||||||
\(201\) | −16.9571 | −1.19606 | ||||||||
\(202\) | 5.73226 | 0.403320 | ||||||||
\(203\) | 38.8872 | 2.72935 | ||||||||
\(204\) | −9.14335 | −0.640162 | ||||||||
\(205\) | 9.18919 | 0.641801 | ||||||||
\(206\) | 7.60241 | 0.529685 | ||||||||
\(207\) | −12.7654 | −0.887254 | ||||||||
\(208\) | 5.57975 | 0.386886 | ||||||||
\(209\) | −7.50849 | −0.519373 | ||||||||
\(210\) | −9.51780 | −0.656791 | ||||||||
\(211\) | 1.34818 | 0.0928123 | 0.0464062 | − | 0.998923i | \(-0.485223\pi\) | ||||
0.0464062 | + | 0.998923i | \(0.485223\pi\) | |||||||
\(212\) | −9.37658 | −0.643986 | ||||||||
\(213\) | 1.20290 | 0.0824214 | ||||||||
\(214\) | −2.53696 | −0.173423 | ||||||||
\(215\) | 1.00000 | 0.0681994 | ||||||||
\(216\) | −1.45032 | −0.0986821 | ||||||||
\(217\) | −31.9833 | −2.17117 | ||||||||
\(218\) | −10.5718 | −0.716010 | ||||||||
\(219\) | 4.21107 | 0.284558 | ||||||||
\(220\) | −1.00000 | −0.0674200 | ||||||||
\(221\) | 19.9099 | 1.33929 | ||||||||
\(222\) | 3.04502 | 0.204369 | ||||||||
\(223\) | 26.8745 | 1.79965 | 0.899824 | − | 0.436253i | \(-0.143695\pi\) | ||||
0.899824 | + | 0.436253i | \(0.143695\pi\) | |||||||
\(224\) | 3.71438 | 0.248177 | ||||||||
\(225\) | 3.56600 | 0.237733 | ||||||||
\(226\) | −16.3289 | −1.08618 | ||||||||
\(227\) | −0.00729015 | −0.000483864 0 | −0.000241932 | − | 1.00000i | \(-0.500077\pi\) | ||||
−0.000241932 | 1.00000i | \(0.500077\pi\) | ||||||||
\(228\) | −19.2399 | −1.27419 | ||||||||
\(229\) | 27.4701 | 1.81528 | 0.907639 | − | 0.419753i | \(-0.137883\pi\) | ||||
0.907639 | + | 0.419753i | \(0.137883\pi\) | |||||||
\(230\) | −3.57975 | −0.236041 | ||||||||
\(231\) | 9.51780 | 0.626226 | ||||||||
\(232\) | 10.4694 | 0.687347 | ||||||||
\(233\) | −3.41771 | −0.223901 | −0.111951 | − | 0.993714i | \(-0.535710\pi\) | ||||
−0.111951 | + | 0.993714i | \(0.535710\pi\) | |||||||
\(234\) | 19.8974 | 1.30073 | ||||||||
\(235\) | −8.24604 | −0.537912 | ||||||||
\(236\) | −4.51898 | −0.294160 | ||||||||
\(237\) | 11.3619 | 0.738033 | ||||||||
\(238\) | 13.2538 | 0.859118 | ||||||||
\(239\) | −20.9593 | −1.35574 | −0.677872 | − | 0.735180i | \(-0.737098\pi\) | ||||
−0.677872 | + | 0.735180i | \(0.737098\pi\) | |||||||
\(240\) | −2.56242 | −0.165404 | ||||||||
\(241\) | 22.6301 | 1.45773 | 0.728865 | − | 0.684657i | \(-0.240048\pi\) | ||||
0.728865 | + | 0.684657i | \(0.240048\pi\) | |||||||
\(242\) | 1.00000 | 0.0642824 | ||||||||
\(243\) | 22.2409 | 1.42675 | ||||||||
\(244\) | −10.7548 | −0.688507 | ||||||||
\(245\) | 6.79662 | 0.434220 | ||||||||
\(246\) | −23.5466 | −1.50127 | ||||||||
\(247\) | 41.8955 | 2.66574 | ||||||||
\(248\) | −8.61067 | −0.546778 | ||||||||
\(249\) | −26.6830 | −1.69096 | ||||||||
\(250\) | 1.00000 | 0.0632456 | ||||||||
\(251\) | −17.7734 | −1.12185 | −0.560923 | − | 0.827868i | \(-0.689554\pi\) | ||||
−0.560923 | + | 0.827868i | \(0.689554\pi\) | |||||||
\(252\) | 13.2455 | 0.834386 | ||||||||
\(253\) | 3.57975 | 0.225057 | ||||||||
\(254\) | −1.55955 | −0.0978548 | ||||||||
\(255\) | −9.14335 | −0.572579 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 1.56620 | 0.0976970 | 0.0488485 | − | 0.998806i | \(-0.484445\pi\) | ||||
0.0488485 | + | 0.998806i | \(0.484445\pi\) | |||||||
\(258\) | −2.56242 | −0.159529 | ||||||||
\(259\) | −4.41394 | −0.274269 | ||||||||
\(260\) | 5.57975 | 0.346041 | ||||||||
\(261\) | 37.3337 | 2.31090 | ||||||||
\(262\) | −18.8774 | −1.16625 | ||||||||
\(263\) | 17.4609 | 1.07668 | 0.538342 | − | 0.842726i | \(-0.319051\pi\) | ||||
0.538342 | + | 0.842726i | \(0.319051\pi\) | |||||||
\(264\) | 2.56242 | 0.157706 | ||||||||
\(265\) | −9.37658 | −0.575999 | ||||||||
\(266\) | 27.8894 | 1.71001 | ||||||||
\(267\) | −27.7647 | −1.69918 | ||||||||
\(268\) | 6.61761 | 0.404235 | ||||||||
\(269\) | 9.08000 | 0.553618 | 0.276809 | − | 0.960925i | \(-0.410723\pi\) | ||||
0.276809 | + | 0.960925i | \(0.410723\pi\) | |||||||
\(270\) | −1.45032 | −0.0882639 | ||||||||
\(271\) | 23.7248 | 1.44118 | 0.720590 | − | 0.693362i | \(-0.243871\pi\) | ||||
0.720590 | + | 0.693362i | \(0.243871\pi\) | |||||||
\(272\) | 3.56825 | 0.216357 | ||||||||
\(273\) | −53.1069 | −3.21418 | ||||||||
\(274\) | −6.16582 | −0.372491 | ||||||||
\(275\) | −1.00000 | −0.0603023 | ||||||||
\(276\) | 9.17281 | 0.552139 | ||||||||
\(277\) | 24.6479 | 1.48095 | 0.740475 | − | 0.672084i | \(-0.234601\pi\) | ||||
0.740475 | + | 0.672084i | \(0.234601\pi\) | |||||||
\(278\) | −20.7119 | −1.24221 | ||||||||
\(279\) | −30.7056 | −1.83830 | ||||||||
\(280\) | 3.71438 | 0.221977 | ||||||||
\(281\) | 1.06479 | 0.0635202 | 0.0317601 | − | 0.999496i | \(-0.489889\pi\) | ||||
0.0317601 | + | 0.999496i | \(0.489889\pi\) | |||||||
\(282\) | 21.1298 | 1.25826 | ||||||||
\(283\) | 8.26267 | 0.491165 | 0.245582 | − | 0.969376i | \(-0.421021\pi\) | ||||
0.245582 | + | 0.969376i | \(0.421021\pi\) | |||||||
\(284\) | −0.469439 | −0.0278561 | ||||||||
\(285\) | −19.2399 | −1.13967 | ||||||||
\(286\) | −5.57975 | −0.329937 | ||||||||
\(287\) | 34.1322 | 2.01476 | ||||||||
\(288\) | 3.56600 | 0.210128 | ||||||||
\(289\) | −4.26762 | −0.251036 | ||||||||
\(290\) | 10.4694 | 0.614782 | ||||||||
\(291\) | −1.31043 | −0.0768185 | ||||||||
\(292\) | −1.64340 | −0.0961725 | ||||||||
\(293\) | −15.1924 | −0.887551 | −0.443776 | − | 0.896138i | \(-0.646361\pi\) | ||||
−0.443776 | + | 0.896138i | \(0.646361\pi\) | |||||||
\(294\) | −17.4158 | −1.01571 | ||||||||
\(295\) | −4.51898 | −0.263105 | ||||||||
\(296\) | −1.18834 | −0.0690708 | ||||||||
\(297\) | 1.45032 | 0.0841564 | ||||||||
\(298\) | 4.55818 | 0.264048 | ||||||||
\(299\) | −19.9741 | −1.15513 | ||||||||
\(300\) | −2.56242 | −0.147941 | ||||||||
\(301\) | 3.71438 | 0.214093 | ||||||||
\(302\) | −19.4030 | −1.11652 | ||||||||
\(303\) | −14.6885 | −0.843830 | ||||||||
\(304\) | 7.50849 | 0.430641 | ||||||||
\(305\) | −10.7548 | −0.615820 | ||||||||
\(306\) | 12.7244 | 0.727403 | ||||||||
\(307\) | −15.3667 | −0.877026 | −0.438513 | − | 0.898725i | \(-0.644495\pi\) | ||||
−0.438513 | + | 0.898725i | \(0.644495\pi\) | |||||||
\(308\) | −3.71438 | −0.211646 | ||||||||
\(309\) | −19.4806 | −1.10821 | ||||||||
\(310\) | −8.61067 | −0.489053 | ||||||||
\(311\) | −25.1532 | −1.42631 | −0.713154 | − | 0.701007i | \(-0.752734\pi\) | ||||
−0.713154 | + | 0.701007i | \(0.752734\pi\) | |||||||
\(312\) | −14.2977 | −0.809445 | ||||||||
\(313\) | 11.8493 | 0.669762 | 0.334881 | − | 0.942260i | \(-0.391304\pi\) | ||||
0.334881 | + | 0.942260i | \(0.391304\pi\) | |||||||
\(314\) | 9.75708 | 0.550624 | ||||||||
\(315\) | 13.2455 | 0.746298 | ||||||||
\(316\) | −4.43404 | −0.249434 | ||||||||
\(317\) | −14.0466 | −0.788933 | −0.394467 | − | 0.918910i | \(-0.629071\pi\) | ||||
−0.394467 | + | 0.918910i | \(0.629071\pi\) | |||||||
\(318\) | 24.0267 | 1.34735 | ||||||||
\(319\) | −10.4694 | −0.586172 | ||||||||
\(320\) | 1.00000 | 0.0559017 | ||||||||
\(321\) | 6.50076 | 0.362837 | ||||||||
\(322\) | −13.2965 | −0.740987 | ||||||||
\(323\) | 26.7921 | 1.49075 | ||||||||
\(324\) | −6.98165 | −0.387870 | ||||||||
\(325\) | 5.57975 | 0.309509 | ||||||||
\(326\) | −7.12889 | −0.394833 | ||||||||
\(327\) | 27.0893 | 1.49804 | ||||||||
\(328\) | 9.18919 | 0.507388 | ||||||||
\(329\) | −30.6289 | −1.68863 | ||||||||
\(330\) | 2.56242 | 0.141057 | ||||||||
\(331\) | 27.3606 | 1.50388 | 0.751938 | − | 0.659234i | \(-0.229119\pi\) | ||||
0.751938 | + | 0.659234i | \(0.229119\pi\) | |||||||
\(332\) | 10.4132 | 0.571498 | ||||||||
\(333\) | −4.23761 | −0.232220 | ||||||||
\(334\) | 6.12444 | 0.335114 | ||||||||
\(335\) | 6.61761 | 0.361559 | ||||||||
\(336\) | −9.51780 | −0.519239 | ||||||||
\(337\) | 25.1191 | 1.36832 | 0.684162 | − | 0.729330i | \(-0.260168\pi\) | ||||
0.684162 | + | 0.729330i | \(0.260168\pi\) | |||||||
\(338\) | 18.1336 | 0.986336 | ||||||||
\(339\) | 41.8414 | 2.27252 | ||||||||
\(340\) | 3.56825 | 0.193515 | ||||||||
\(341\) | 8.61067 | 0.466294 | ||||||||
\(342\) | 26.7753 | 1.44784 | ||||||||
\(343\) | −0.755424 | −0.0407891 | ||||||||
\(344\) | 1.00000 | 0.0539164 | ||||||||
\(345\) | 9.17281 | 0.493848 | ||||||||
\(346\) | −18.6132 | −1.00065 | ||||||||
\(347\) | 11.8815 | 0.637832 | 0.318916 | − | 0.947783i | \(-0.396681\pi\) | ||||
0.318916 | + | 0.947783i | \(0.396681\pi\) | |||||||
\(348\) | −26.8269 | −1.43807 | ||||||||
\(349\) | 1.12629 | 0.0602888 | 0.0301444 | − | 0.999546i | \(-0.490403\pi\) | ||||
0.0301444 | + | 0.999546i | \(0.490403\pi\) | |||||||
\(350\) | 3.71438 | 0.198542 | ||||||||
\(351\) | −8.09244 | −0.431943 | ||||||||
\(352\) | −1.00000 | −0.0533002 | ||||||||
\(353\) | −33.2259 | −1.76844 | −0.884219 | − | 0.467072i | \(-0.845309\pi\) | ||||
−0.884219 | + | 0.467072i | \(0.845309\pi\) | |||||||
\(354\) | 11.5795 | 0.615444 | ||||||||
\(355\) | −0.469439 | −0.0249152 | ||||||||
\(356\) | 10.8354 | 0.574273 | ||||||||
\(357\) | −33.9619 | −1.79745 | ||||||||
\(358\) | −8.07746 | −0.426907 | ||||||||
\(359\) | −37.3416 | −1.97082 | −0.985408 | − | 0.170210i | \(-0.945555\pi\) | ||||
−0.985408 | + | 0.170210i | \(0.945555\pi\) | |||||||
\(360\) | 3.56600 | 0.187945 | ||||||||
\(361\) | 37.3774 | 1.96723 | ||||||||
\(362\) | −12.2583 | −0.644282 | ||||||||
\(363\) | −2.56242 | −0.134492 | ||||||||
\(364\) | 20.7253 | 1.08630 | ||||||||
\(365\) | −1.64340 | −0.0860193 | ||||||||
\(366\) | 27.5584 | 1.44050 | ||||||||
\(367\) | 6.58389 | 0.343676 | 0.171838 | − | 0.985125i | \(-0.445029\pi\) | ||||
0.171838 | + | 0.985125i | \(0.445029\pi\) | |||||||
\(368\) | −3.57975 | −0.186607 | ||||||||
\(369\) | 32.7686 | 1.70587 | ||||||||
\(370\) | −1.18834 | −0.0617788 | ||||||||
\(371\) | −34.8282 | −1.80819 | ||||||||
\(372\) | 22.0642 | 1.14397 | ||||||||
\(373\) | 25.4328 | 1.31686 | 0.658429 | − | 0.752642i | \(-0.271221\pi\) | ||||
0.658429 | + | 0.752642i | \(0.271221\pi\) | |||||||
\(374\) | −3.56825 | −0.184510 | ||||||||
\(375\) | −2.56242 | −0.132323 | ||||||||
\(376\) | −8.24604 | −0.425257 | ||||||||
\(377\) | 58.4164 | 3.00860 | ||||||||
\(378\) | −5.38706 | −0.277080 | ||||||||
\(379\) | 32.8805 | 1.68896 | 0.844479 | − | 0.535589i | \(-0.179910\pi\) | ||||
0.844479 | + | 0.535589i | \(0.179910\pi\) | |||||||
\(380\) | 7.50849 | 0.385177 | ||||||||
\(381\) | 3.99622 | 0.204733 | ||||||||
\(382\) | 25.8507 | 1.32263 | ||||||||
\(383\) | 7.85906 | 0.401579 | 0.200789 | − | 0.979634i | \(-0.435649\pi\) | ||||
0.200789 | + | 0.979634i | \(0.435649\pi\) | |||||||
\(384\) | −2.56242 | −0.130763 | ||||||||
\(385\) | −3.71438 | −0.189302 | ||||||||
\(386\) | 12.9265 | 0.657939 | ||||||||
\(387\) | 3.56600 | 0.181270 | ||||||||
\(388\) | 0.511402 | 0.0259625 | ||||||||
\(389\) | −31.5297 | −1.59862 | −0.799310 | − | 0.600919i | \(-0.794802\pi\) | ||||
−0.799310 | + | 0.600919i | \(0.794802\pi\) | |||||||
\(390\) | −14.2977 | −0.723990 | ||||||||
\(391\) | −12.7734 | −0.645979 | ||||||||
\(392\) | 6.79662 | 0.343281 | ||||||||
\(393\) | 48.3719 | 2.44004 | ||||||||
\(394\) | 9.14995 | 0.460968 | ||||||||
\(395\) | −4.43404 | −0.223101 | ||||||||
\(396\) | −3.56600 | −0.179198 | ||||||||
\(397\) | −30.6110 | −1.53632 | −0.768160 | − | 0.640258i | \(-0.778828\pi\) | ||||
−0.768160 | + | 0.640258i | \(0.778828\pi\) | |||||||
\(398\) | 17.2884 | 0.866589 | ||||||||
\(399\) | −71.4643 | −3.57769 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | 15.8986 | 0.793937 | 0.396969 | − | 0.917832i | \(-0.370062\pi\) | ||||
0.396969 | + | 0.917832i | \(0.370062\pi\) | |||||||
\(402\) | −16.9571 | −0.845744 | ||||||||
\(403\) | −48.0454 | −2.39331 | ||||||||
\(404\) | 5.73226 | 0.285191 | ||||||||
\(405\) | −6.98165 | −0.346921 | ||||||||
\(406\) | 38.8872 | 1.92994 | ||||||||
\(407\) | 1.18834 | 0.0589037 | ||||||||
\(408\) | −9.14335 | −0.452663 | ||||||||
\(409\) | −8.57948 | −0.424228 | −0.212114 | − | 0.977245i | \(-0.568035\pi\) | ||||
−0.212114 | + | 0.977245i | \(0.568035\pi\) | |||||||
\(410\) | 9.18919 | 0.453822 | ||||||||
\(411\) | 15.7994 | 0.779328 | ||||||||
\(412\) | 7.60241 | 0.374544 | ||||||||
\(413\) | −16.7852 | −0.825945 | ||||||||
\(414\) | −12.7654 | −0.627384 | ||||||||
\(415\) | 10.4132 | 0.511164 | ||||||||
\(416\) | 5.57975 | 0.273570 | ||||||||
\(417\) | 53.0725 | 2.59897 | ||||||||
\(418\) | −7.50849 | −0.367252 | ||||||||
\(419\) | −14.1402 | −0.690793 | −0.345396 | − | 0.938457i | \(-0.612256\pi\) | ||||
−0.345396 | + | 0.938457i | \(0.612256\pi\) | |||||||
\(420\) | −9.51780 | −0.464421 | ||||||||
\(421\) | −2.26240 | −0.110263 | −0.0551313 | − | 0.998479i | \(-0.517558\pi\) | ||||
−0.0551313 | + | 0.998479i | \(0.517558\pi\) | |||||||
\(422\) | 1.34818 | 0.0656282 | ||||||||
\(423\) | −29.4054 | −1.42974 | ||||||||
\(424\) | −9.37658 | −0.455367 | ||||||||
\(425\) | 3.56825 | 0.173085 | ||||||||
\(426\) | 1.20290 | 0.0582807 | ||||||||
\(427\) | −39.9475 | −1.93320 | ||||||||
\(428\) | −2.53696 | −0.122629 | ||||||||
\(429\) | 14.2977 | 0.690297 | ||||||||
\(430\) | 1.00000 | 0.0482243 | ||||||||
\(431\) | 15.9360 | 0.767612 | 0.383806 | − | 0.923414i | \(-0.374613\pi\) | ||||
0.383806 | + | 0.923414i | \(0.374613\pi\) | |||||||
\(432\) | −1.45032 | −0.0697788 | ||||||||
\(433\) | 36.2384 | 1.74151 | 0.870754 | − | 0.491720i | \(-0.163632\pi\) | ||||
0.870754 | + | 0.491720i | \(0.163632\pi\) | |||||||
\(434\) | −31.9833 | −1.53525 | ||||||||
\(435\) | −26.8269 | −1.28625 | ||||||||
\(436\) | −10.5718 | −0.506295 | ||||||||
\(437\) | −26.8785 | −1.28577 | ||||||||
\(438\) | 4.21107 | 0.201213 | ||||||||
\(439\) | −31.2479 | −1.49138 | −0.745690 | − | 0.666293i | \(-0.767880\pi\) | ||||
−0.745690 | + | 0.666293i | \(0.767880\pi\) | |||||||
\(440\) | −1.00000 | −0.0476731 | ||||||||
\(441\) | 24.2367 | 1.15413 | ||||||||
\(442\) | 19.9099 | 0.947018 | ||||||||
\(443\) | −31.0221 | −1.47391 | −0.736953 | − | 0.675944i | \(-0.763736\pi\) | ||||
−0.736953 | + | 0.675944i | \(0.763736\pi\) | |||||||
\(444\) | 3.04502 | 0.144510 | ||||||||
\(445\) | 10.8354 | 0.513645 | ||||||||
\(446\) | 26.8745 | 1.27254 | ||||||||
\(447\) | −11.6800 | −0.552443 | ||||||||
\(448\) | 3.71438 | 0.175488 | ||||||||
\(449\) | −30.6147 | −1.44480 | −0.722398 | − | 0.691478i | \(-0.756960\pi\) | ||||
−0.722398 | + | 0.691478i | \(0.756960\pi\) | |||||||
\(450\) | 3.56600 | 0.168103 | ||||||||
\(451\) | −9.18919 | −0.432702 | ||||||||
\(452\) | −16.3289 | −0.768046 | ||||||||
\(453\) | 49.7187 | 2.33599 | ||||||||
\(454\) | −0.00729015 | −0.000342144 0 | ||||||||
\(455\) | 20.7253 | 0.971617 | ||||||||
\(456\) | −19.2399 | −0.900991 | ||||||||
\(457\) | 8.31983 | 0.389185 | 0.194593 | − | 0.980884i | \(-0.437661\pi\) | ||||
0.194593 | + | 0.980884i | \(0.437661\pi\) | |||||||
\(458\) | 27.4701 | 1.28359 | ||||||||
\(459\) | −5.17512 | −0.241554 | ||||||||
\(460\) | −3.57975 | −0.166907 | ||||||||
\(461\) | −8.69871 | −0.405140 | −0.202570 | − | 0.979268i | \(-0.564929\pi\) | ||||
−0.202570 | + | 0.979268i | \(0.564929\pi\) | |||||||
\(462\) | 9.51780 | 0.442808 | ||||||||
\(463\) | 7.27816 | 0.338245 | 0.169122 | − | 0.985595i | \(-0.445907\pi\) | ||||
0.169122 | + | 0.985595i | \(0.445907\pi\) | |||||||
\(464\) | 10.4694 | 0.486028 | ||||||||
\(465\) | 22.0642 | 1.02320 | ||||||||
\(466\) | −3.41771 | −0.158322 | ||||||||
\(467\) | −5.45479 | −0.252418 | −0.126209 | − | 0.992004i | \(-0.540281\pi\) | ||||
−0.126209 | + | 0.992004i | \(0.540281\pi\) | |||||||
\(468\) | 19.8974 | 0.919756 | ||||||||
\(469\) | 24.5803 | 1.13501 | ||||||||
\(470\) | −8.24604 | −0.380361 | ||||||||
\(471\) | −25.0017 | −1.15202 | ||||||||
\(472\) | −4.51898 | −0.208003 | ||||||||
\(473\) | −1.00000 | −0.0459800 | ||||||||
\(474\) | 11.3619 | 0.521868 | ||||||||
\(475\) | 7.50849 | 0.344513 | ||||||||
\(476\) | 13.2538 | 0.607488 | ||||||||
\(477\) | −33.4369 | −1.53097 | ||||||||
\(478\) | −20.9593 | −0.958656 | ||||||||
\(479\) | −32.5974 | −1.48941 | −0.744706 | − | 0.667393i | \(-0.767410\pi\) | ||||
−0.744706 | + | 0.667393i | \(0.767410\pi\) | |||||||
\(480\) | −2.56242 | −0.116958 | ||||||||
\(481\) | −6.63063 | −0.302331 | ||||||||
\(482\) | 22.6301 | 1.03077 | ||||||||
\(483\) | 34.0713 | 1.55030 | ||||||||
\(484\) | 1.00000 | 0.0454545 | ||||||||
\(485\) | 0.511402 | 0.0232215 | ||||||||
\(486\) | 22.2409 | 1.00887 | ||||||||
\(487\) | 3.63248 | 0.164603 | 0.0823017 | − | 0.996607i | \(-0.473773\pi\) | ||||
0.0823017 | + | 0.996607i | \(0.473773\pi\) | |||||||
\(488\) | −10.7548 | −0.486848 | ||||||||
\(489\) | 18.2672 | 0.826072 | ||||||||
\(490\) | 6.79662 | 0.307040 | ||||||||
\(491\) | 5.31772 | 0.239985 | 0.119993 | − | 0.992775i | \(-0.461713\pi\) | ||||
0.119993 | + | 0.992775i | \(0.461713\pi\) | |||||||
\(492\) | −23.5466 | −1.06156 | ||||||||
\(493\) | 37.3573 | 1.68249 | ||||||||
\(494\) | 41.8955 | 1.88497 | ||||||||
\(495\) | −3.56600 | −0.160280 | ||||||||
\(496\) | −8.61067 | −0.386630 | ||||||||
\(497\) | −1.74368 | −0.0782145 | ||||||||
\(498\) | −26.6830 | −1.19569 | ||||||||
\(499\) | −13.4007 | −0.599899 | −0.299950 | − | 0.953955i | \(-0.596970\pi\) | ||||
−0.299950 | + | 0.953955i | \(0.596970\pi\) | |||||||
\(500\) | 1.00000 | 0.0447214 | ||||||||
\(501\) | −15.6934 | −0.701129 | ||||||||
\(502\) | −17.7734 | −0.793265 | ||||||||
\(503\) | 39.5123 | 1.76177 | 0.880884 | − | 0.473332i | \(-0.156949\pi\) | ||||
0.880884 | + | 0.473332i | \(0.156949\pi\) | |||||||
\(504\) | 13.2455 | 0.590000 | ||||||||
\(505\) | 5.73226 | 0.255082 | ||||||||
\(506\) | 3.57975 | 0.159139 | ||||||||
\(507\) | −46.4658 | −2.06362 | ||||||||
\(508\) | −1.55955 | −0.0691938 | ||||||||
\(509\) | −27.7161 | −1.22850 | −0.614248 | − | 0.789113i | \(-0.710541\pi\) | ||||
−0.614248 | + | 0.789113i | \(0.710541\pi\) | |||||||
\(510\) | −9.14335 | −0.404874 | ||||||||
\(511\) | −6.10420 | −0.270034 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −10.8897 | −0.480794 | ||||||||
\(514\) | 1.56620 | 0.0690822 | ||||||||
\(515\) | 7.60241 | 0.335002 | ||||||||
\(516\) | −2.56242 | −0.112804 | ||||||||
\(517\) | 8.24604 | 0.362660 | ||||||||
\(518\) | −4.41394 | −0.193937 | ||||||||
\(519\) | 47.6948 | 2.09357 | ||||||||
\(520\) | 5.57975 | 0.244688 | ||||||||
\(521\) | −18.2117 | −0.797867 | −0.398934 | − | 0.916980i | \(-0.630620\pi\) | ||||
−0.398934 | + | 0.916980i | \(0.630620\pi\) | |||||||
\(522\) | 37.3337 | 1.63405 | ||||||||
\(523\) | −13.3213 | −0.582502 | −0.291251 | − | 0.956647i | \(-0.594071\pi\) | ||||
−0.291251 | + | 0.956647i | \(0.594071\pi\) | |||||||
\(524\) | −18.8774 | −0.824664 | ||||||||
\(525\) | −9.51780 | −0.415391 | ||||||||
\(526\) | 17.4609 | 0.761331 | ||||||||
\(527\) | −30.7250 | −1.33840 | ||||||||
\(528\) | 2.56242 | 0.111515 | ||||||||
\(529\) | −10.1854 | −0.442844 | ||||||||
\(530\) | −9.37658 | −0.407293 | ||||||||
\(531\) | −16.1147 | −0.699317 | ||||||||
\(532\) | 27.8894 | 1.20916 | ||||||||
\(533\) | 51.2734 | 2.22090 | ||||||||
\(534\) | −27.7647 | −1.20150 | ||||||||
\(535\) | −2.53696 | −0.109682 | ||||||||
\(536\) | 6.61761 | 0.285837 | ||||||||
\(537\) | 20.6979 | 0.893178 | ||||||||
\(538\) | 9.08000 | 0.391467 | ||||||||
\(539\) | −6.79662 | −0.292751 | ||||||||
\(540\) | −1.45032 | −0.0624120 | ||||||||
\(541\) | −12.5715 | −0.540493 | −0.270246 | − | 0.962791i | \(-0.587105\pi\) | ||||
−0.270246 | + | 0.962791i | \(0.587105\pi\) | |||||||
\(542\) | 23.7248 | 1.01907 | ||||||||
\(543\) | 31.4109 | 1.34797 | ||||||||
\(544\) | 3.56825 | 0.152987 | ||||||||
\(545\) | −10.5718 | −0.452844 | ||||||||
\(546\) | −53.1069 | −2.27277 | ||||||||
\(547\) | −27.8264 | −1.18977 | −0.594885 | − | 0.803811i | \(-0.702802\pi\) | ||||
−0.594885 | + | 0.803811i | \(0.702802\pi\) | |||||||
\(548\) | −6.16582 | −0.263391 | ||||||||
\(549\) | −38.3517 | −1.63681 | ||||||||
\(550\) | −1.00000 | −0.0426401 | ||||||||
\(551\) | 78.6091 | 3.34886 | ||||||||
\(552\) | 9.17281 | 0.390421 | ||||||||
\(553\) | −16.4697 | −0.700363 | ||||||||
\(554\) | 24.6479 | 1.04719 | ||||||||
\(555\) | 3.04502 | 0.129254 | ||||||||
\(556\) | −20.7119 | −0.878378 | ||||||||
\(557\) | 15.1781 | 0.643115 | 0.321557 | − | 0.946890i | \(-0.395794\pi\) | ||||
0.321557 | + | 0.946890i | \(0.395794\pi\) | |||||||
\(558\) | −30.7056 | −1.29987 | ||||||||
\(559\) | 5.57975 | 0.235998 | ||||||||
\(560\) | 3.71438 | 0.156961 | ||||||||
\(561\) | 9.14335 | 0.386032 | ||||||||
\(562\) | 1.06479 | 0.0449156 | ||||||||
\(563\) | −28.3603 | −1.19524 | −0.597622 | − | 0.801778i | \(-0.703888\pi\) | ||||
−0.597622 | + | 0.801778i | \(0.703888\pi\) | |||||||
\(564\) | 21.1298 | 0.889726 | ||||||||
\(565\) | −16.3289 | −0.686961 | ||||||||
\(566\) | 8.26267 | 0.347306 | ||||||||
\(567\) | −25.9325 | −1.08906 | ||||||||
\(568\) | −0.469439 | −0.0196972 | ||||||||
\(569\) | 30.9562 | 1.29775 | 0.648875 | − | 0.760895i | \(-0.275240\pi\) | ||||
0.648875 | + | 0.760895i | \(0.275240\pi\) | |||||||
\(570\) | −19.2399 | −0.805871 | ||||||||
\(571\) | −15.9479 | −0.667399 | −0.333700 | − | 0.942679i | \(-0.608297\pi\) | ||||
−0.333700 | + | 0.942679i | \(0.608297\pi\) | |||||||
\(572\) | −5.57975 | −0.233301 | ||||||||
\(573\) | −66.2402 | −2.76723 | ||||||||
\(574\) | 34.1322 | 1.42465 | ||||||||
\(575\) | −3.57975 | −0.149286 | ||||||||
\(576\) | 3.56600 | 0.148583 | ||||||||
\(577\) | 7.63594 | 0.317888 | 0.158944 | − | 0.987288i | \(-0.449191\pi\) | ||||
0.158944 | + | 0.987288i | \(0.449191\pi\) | |||||||
\(578\) | −4.26762 | −0.177509 | ||||||||
\(579\) | −33.1230 | −1.37655 | ||||||||
\(580\) | 10.4694 | 0.434716 | ||||||||
\(581\) | 38.6786 | 1.60466 | ||||||||
\(582\) | −1.31043 | −0.0543189 | ||||||||
\(583\) | 9.37658 | 0.388338 | ||||||||
\(584\) | −1.64340 | −0.0680043 | ||||||||
\(585\) | 19.8974 | 0.822655 | ||||||||
\(586\) | −15.1924 | −0.627594 | ||||||||
\(587\) | −38.5469 | −1.59100 | −0.795501 | − | 0.605952i | \(-0.792792\pi\) | ||||
−0.795501 | + | 0.605952i | \(0.792792\pi\) | |||||||
\(588\) | −17.4158 | −0.718216 | ||||||||
\(589\) | −64.6531 | −2.66399 | ||||||||
\(590\) | −4.51898 | −0.186043 | ||||||||
\(591\) | −23.4460 | −0.964440 | ||||||||
\(592\) | −1.18834 | −0.0488404 | ||||||||
\(593\) | −42.3404 | −1.73871 | −0.869356 | − | 0.494187i | \(-0.835466\pi\) | ||||
−0.869356 | + | 0.494187i | \(0.835466\pi\) | |||||||
\(594\) | 1.45032 | 0.0595075 | ||||||||
\(595\) | 13.2538 | 0.543354 | ||||||||
\(596\) | 4.55818 | 0.186710 | ||||||||
\(597\) | −44.3002 | −1.81308 | ||||||||
\(598\) | −19.9741 | −0.816801 | ||||||||
\(599\) | −16.2466 | −0.663817 | −0.331908 | − | 0.943312i | \(-0.607692\pi\) | ||||
−0.331908 | + | 0.943312i | \(0.607692\pi\) | |||||||
\(600\) | −2.56242 | −0.104610 | ||||||||
\(601\) | −29.8453 | −1.21741 | −0.608707 | − | 0.793395i | \(-0.708312\pi\) | ||||
−0.608707 | + | 0.793395i | \(0.708312\pi\) | |||||||
\(602\) | 3.71438 | 0.151387 | ||||||||
\(603\) | 23.5984 | 0.961001 | ||||||||
\(604\) | −19.4030 | −0.789498 | ||||||||
\(605\) | 1.00000 | 0.0406558 | ||||||||
\(606\) | −14.6885 | −0.596678 | ||||||||
\(607\) | 11.3631 | 0.461214 | 0.230607 | − | 0.973047i | \(-0.425929\pi\) | ||||
0.230607 | + | 0.973047i | \(0.425929\pi\) | |||||||
\(608\) | 7.50849 | 0.304509 | ||||||||
\(609\) | −99.6453 | −4.03783 | ||||||||
\(610\) | −10.7548 | −0.435450 | ||||||||
\(611\) | −46.0108 | −1.86140 | ||||||||
\(612\) | 12.7244 | 0.514352 | ||||||||
\(613\) | 25.1962 | 1.01766 | 0.508832 | − | 0.860866i | \(-0.330077\pi\) | ||||
0.508832 | + | 0.860866i | \(0.330077\pi\) | |||||||
\(614\) | −15.3667 | −0.620151 | ||||||||
\(615\) | −23.5466 | −0.949490 | ||||||||
\(616\) | −3.71438 | −0.149657 | ||||||||
\(617\) | 26.2533 | 1.05692 | 0.528460 | − | 0.848958i | \(-0.322770\pi\) | ||||
0.528460 | + | 0.848958i | \(0.322770\pi\) | |||||||
\(618\) | −19.4806 | −0.783623 | ||||||||
\(619\) | −44.1153 | −1.77314 | −0.886572 | − | 0.462591i | \(-0.846920\pi\) | ||||
−0.886572 | + | 0.462591i | \(0.846920\pi\) | |||||||
\(620\) | −8.61067 | −0.345813 | ||||||||
\(621\) | 5.19179 | 0.208339 | ||||||||
\(622\) | −25.1532 | −1.00855 | ||||||||
\(623\) | 40.2467 | 1.61245 | ||||||||
\(624\) | −14.2977 | −0.572364 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 11.8493 | 0.473594 | ||||||||
\(627\) | 19.2399 | 0.768368 | ||||||||
\(628\) | 9.75708 | 0.389350 | ||||||||
\(629\) | −4.24028 | −0.169071 | ||||||||
\(630\) | 13.2455 | 0.527712 | ||||||||
\(631\) | −33.3429 | −1.32736 | −0.663681 | − | 0.748016i | \(-0.731007\pi\) | ||||
−0.663681 | + | 0.748016i | \(0.731007\pi\) | |||||||
\(632\) | −4.43404 | −0.176377 | ||||||||
\(633\) | −3.45460 | −0.137308 | ||||||||
\(634\) | −14.0466 | −0.557860 | ||||||||
\(635\) | −1.55955 | −0.0618888 | ||||||||
\(636\) | 24.0267 | 0.952722 | ||||||||
\(637\) | 37.9234 | 1.50258 | ||||||||
\(638\) | −10.4694 | −0.414486 | ||||||||
\(639\) | −1.67402 | −0.0662232 | ||||||||
\(640\) | 1.00000 | 0.0395285 | ||||||||
\(641\) | −26.5788 | −1.04980 | −0.524900 | − | 0.851164i | \(-0.675897\pi\) | ||||
−0.524900 | + | 0.851164i | \(0.675897\pi\) | |||||||
\(642\) | 6.50076 | 0.256565 | ||||||||
\(643\) | −18.0000 | −0.709850 | −0.354925 | − | 0.934895i | \(-0.615494\pi\) | ||||
−0.354925 | + | 0.934895i | \(0.615494\pi\) | |||||||
\(644\) | −13.2965 | −0.523957 | ||||||||
\(645\) | −2.56242 | −0.100895 | ||||||||
\(646\) | 26.7921 | 1.05412 | ||||||||
\(647\) | −23.4896 | −0.923470 | −0.461735 | − | 0.887018i | \(-0.652773\pi\) | ||||
−0.461735 | + | 0.887018i | \(0.652773\pi\) | |||||||
\(648\) | −6.98165 | −0.274265 | ||||||||
\(649\) | 4.51898 | 0.177385 | ||||||||
\(650\) | 5.57975 | 0.218856 | ||||||||
\(651\) | 81.9547 | 3.21206 | ||||||||
\(652\) | −7.12889 | −0.279189 | ||||||||
\(653\) | 4.77348 | 0.186801 | 0.0934003 | − | 0.995629i | \(-0.470226\pi\) | ||||
0.0934003 | + | 0.995629i | \(0.470226\pi\) | |||||||
\(654\) | 27.0893 | 1.05928 | ||||||||
\(655\) | −18.8774 | −0.737602 | ||||||||
\(656\) | 9.18919 | 0.358778 | ||||||||
\(657\) | −5.86035 | −0.228634 | ||||||||
\(658\) | −30.6289 | −1.19404 | ||||||||
\(659\) | 28.3906 | 1.10594 | 0.552971 | − | 0.833200i | \(-0.313494\pi\) | ||||
0.552971 | + | 0.833200i | \(0.313494\pi\) | |||||||
\(660\) | 2.56242 | 0.0997421 | ||||||||
\(661\) | −21.5499 | −0.838195 | −0.419097 | − | 0.907941i | \(-0.637653\pi\) | ||||
−0.419097 | + | 0.907941i | \(0.637653\pi\) | |||||||
\(662\) | 27.3606 | 1.06340 | ||||||||
\(663\) | −51.0176 | −1.98136 | ||||||||
\(664\) | 10.4132 | 0.404110 | ||||||||
\(665\) | 27.8894 | 1.08150 | ||||||||
\(666\) | −4.23761 | −0.164204 | ||||||||
\(667\) | −37.4776 | −1.45114 | ||||||||
\(668\) | 6.12444 | 0.236962 | ||||||||
\(669\) | −68.8637 | −2.66243 | ||||||||
\(670\) | 6.61761 | 0.255661 | ||||||||
\(671\) | 10.7548 | 0.415186 | ||||||||
\(672\) | −9.51780 | −0.367157 | ||||||||
\(673\) | 12.9526 | 0.499285 | 0.249642 | − | 0.968338i | \(-0.419687\pi\) | ||||
0.249642 | + | 0.968338i | \(0.419687\pi\) | |||||||
\(674\) | 25.1191 | 0.967552 | ||||||||
\(675\) | −1.45032 | −0.0558230 | ||||||||
\(676\) | 18.1336 | 0.697445 | ||||||||
\(677\) | 24.9006 | 0.957009 | 0.478504 | − | 0.878085i | \(-0.341179\pi\) | ||||
0.478504 | + | 0.878085i | \(0.341179\pi\) | |||||||
\(678\) | 41.8414 | 1.60691 | ||||||||
\(679\) | 1.89954 | 0.0728977 | ||||||||
\(680\) | 3.56825 | 0.136836 | ||||||||
\(681\) | 0.0186804 | 0.000715836 0 | ||||||||
\(682\) | 8.61067 | 0.329720 | ||||||||
\(683\) | 2.19027 | 0.0838085 | 0.0419043 | − | 0.999122i | \(-0.486658\pi\) | ||||
0.0419043 | + | 0.999122i | \(0.486658\pi\) | |||||||
\(684\) | 26.7753 | 1.02378 | ||||||||
\(685\) | −6.16582 | −0.235584 | ||||||||
\(686\) | −0.755424 | −0.0288422 | ||||||||
\(687\) | −70.3900 | −2.68555 | ||||||||
\(688\) | 1.00000 | 0.0381246 | ||||||||
\(689\) | −52.3189 | −1.99319 | ||||||||
\(690\) | 9.17281 | 0.349203 | ||||||||
\(691\) | −33.4753 | −1.27346 | −0.636730 | − | 0.771087i | \(-0.719713\pi\) | ||||
−0.636730 | + | 0.771087i | \(0.719713\pi\) | |||||||
\(692\) | −18.6132 | −0.707567 | ||||||||
\(693\) | −13.2455 | −0.503154 | ||||||||
\(694\) | 11.8815 | 0.451015 | ||||||||
\(695\) | −20.7119 | −0.785646 | ||||||||
\(696\) | −26.8269 | −1.01687 | ||||||||
\(697\) | 32.7893 | 1.24198 | ||||||||
\(698\) | 1.12629 | 0.0426306 | ||||||||
\(699\) | 8.75760 | 0.331243 | ||||||||
\(700\) | 3.71438 | 0.140390 | ||||||||
\(701\) | 20.3654 | 0.769191 | 0.384596 | − | 0.923085i | \(-0.374341\pi\) | ||||
0.384596 | + | 0.923085i | \(0.374341\pi\) | |||||||
\(702\) | −8.09244 | −0.305430 | ||||||||
\(703\) | −8.92263 | −0.336523 | ||||||||
\(704\) | −1.00000 | −0.0376889 | ||||||||
\(705\) | 21.1298 | 0.795795 | ||||||||
\(706\) | −33.2259 | −1.25048 | ||||||||
\(707\) | 21.2918 | 0.800760 | ||||||||
\(708\) | 11.5795 | 0.435185 | ||||||||
\(709\) | 34.6244 | 1.30035 | 0.650174 | − | 0.759786i | \(-0.274696\pi\) | ||||
0.650174 | + | 0.759786i | \(0.274696\pi\) | |||||||
\(710\) | −0.469439 | −0.0176177 | ||||||||
\(711\) | −15.8118 | −0.592988 | ||||||||
\(712\) | 10.8354 | 0.406072 | ||||||||
\(713\) | 30.8240 | 1.15437 | ||||||||
\(714\) | −33.9619 | −1.27099 | ||||||||
\(715\) | −5.57975 | −0.208671 | ||||||||
\(716\) | −8.07746 | −0.301869 | ||||||||
\(717\) | 53.7065 | 2.00571 | ||||||||
\(718\) | −37.3416 | −1.39358 | ||||||||
\(719\) | 18.7362 | 0.698741 | 0.349370 | − | 0.936985i | \(-0.386396\pi\) | ||||
0.349370 | + | 0.936985i | \(0.386396\pi\) | |||||||
\(720\) | 3.56600 | 0.132897 | ||||||||
\(721\) | 28.2382 | 1.05165 | ||||||||
\(722\) | 37.3774 | 1.39104 | ||||||||
\(723\) | −57.9877 | −2.15659 | ||||||||
\(724\) | −12.2583 | −0.455576 | ||||||||
\(725\) | 10.4694 | 0.388822 | ||||||||
\(726\) | −2.56242 | −0.0951003 | ||||||||
\(727\) | −36.0943 | −1.33866 | −0.669331 | − | 0.742964i | \(-0.733419\pi\) | ||||
−0.669331 | + | 0.742964i | \(0.733419\pi\) | |||||||
\(728\) | 20.7253 | 0.768131 | ||||||||
\(729\) | −36.0456 | −1.33502 | ||||||||
\(730\) | −1.64340 | −0.0608249 | ||||||||
\(731\) | 3.56825 | 0.131976 | ||||||||
\(732\) | 27.5584 | 1.01859 | ||||||||
\(733\) | 25.9853 | 0.959789 | 0.479894 | − | 0.877326i | \(-0.340675\pi\) | ||||
0.479894 | + | 0.877326i | \(0.340675\pi\) | |||||||
\(734\) | 6.58389 | 0.243016 | ||||||||
\(735\) | −17.4158 | −0.642392 | ||||||||
\(736\) | −3.57975 | −0.131951 | ||||||||
\(737\) | −6.61761 | −0.243763 | ||||||||
\(738\) | 32.7686 | 1.20623 | ||||||||
\(739\) | 12.4010 | 0.456179 | 0.228090 | − | 0.973640i | \(-0.426752\pi\) | ||||
0.228090 | + | 0.973640i | \(0.426752\pi\) | |||||||
\(740\) | −1.18834 | −0.0436842 | ||||||||
\(741\) | −107.354 | −3.94374 | ||||||||
\(742\) | −34.8282 | −1.27858 | ||||||||
\(743\) | 28.0197 | 1.02794 | 0.513972 | − | 0.857807i | \(-0.328173\pi\) | ||||
0.513972 | + | 0.857807i | \(0.328173\pi\) | |||||||
\(744\) | 22.0642 | 0.808911 | ||||||||
\(745\) | 4.55818 | 0.166999 | ||||||||
\(746\) | 25.4328 | 0.931160 | ||||||||
\(747\) | 37.1334 | 1.35864 | ||||||||
\(748\) | −3.56825 | −0.130468 | ||||||||
\(749\) | −9.42324 | −0.344318 | ||||||||
\(750\) | −2.56242 | −0.0935664 | ||||||||
\(751\) | −9.01153 | −0.328835 | −0.164418 | − | 0.986391i | \(-0.552574\pi\) | ||||
−0.164418 | + | 0.986391i | \(0.552574\pi\) | |||||||
\(752\) | −8.24604 | −0.300702 | ||||||||
\(753\) | 45.5429 | 1.65968 | ||||||||
\(754\) | 58.4164 | 2.12740 | ||||||||
\(755\) | −19.4030 | −0.706148 | ||||||||
\(756\) | −5.38706 | −0.195925 | ||||||||
\(757\) | 22.1670 | 0.805672 | 0.402836 | − | 0.915272i | \(-0.368025\pi\) | ||||
0.402836 | + | 0.915272i | \(0.368025\pi\) | |||||||
\(758\) | 32.8805 | 1.19427 | ||||||||
\(759\) | −9.17281 | −0.332952 | ||||||||
\(760\) | 7.50849 | 0.272362 | ||||||||
\(761\) | 7.77879 | 0.281981 | 0.140991 | − | 0.990011i | \(-0.454971\pi\) | ||||
0.140991 | + | 0.990011i | \(0.454971\pi\) | |||||||
\(762\) | 3.99622 | 0.144768 | ||||||||
\(763\) | −39.2675 | −1.42158 | ||||||||
\(764\) | 25.8507 | 0.935244 | ||||||||
\(765\) | 12.7244 | 0.460050 | ||||||||
\(766\) | 7.85906 | 0.283959 | ||||||||
\(767\) | −25.2147 | −0.910451 | ||||||||
\(768\) | −2.56242 | −0.0924634 | ||||||||
\(769\) | 15.2820 | 0.551083 | 0.275542 | − | 0.961289i | \(-0.411143\pi\) | ||||
0.275542 | + | 0.961289i | \(0.411143\pi\) | |||||||
\(770\) | −3.71438 | −0.133857 | ||||||||
\(771\) | −4.01327 | −0.144534 | ||||||||
\(772\) | 12.9265 | 0.465233 | ||||||||
\(773\) | 3.28862 | 0.118284 | 0.0591418 | − | 0.998250i | \(-0.481164\pi\) | ||||
0.0591418 | + | 0.998250i | \(0.481164\pi\) | |||||||
\(774\) | 3.56600 | 0.128177 | ||||||||
\(775\) | −8.61067 | −0.309304 | ||||||||
\(776\) | 0.511402 | 0.0183582 | ||||||||
\(777\) | 11.3104 | 0.405757 | ||||||||
\(778\) | −31.5297 | −1.13040 | ||||||||
\(779\) | 68.9970 | 2.47207 | ||||||||
\(780\) | −14.2977 | −0.511938 | ||||||||
\(781\) | 0.469439 | 0.0167978 | ||||||||
\(782\) | −12.7734 | −0.456776 | ||||||||
\(783\) | −15.1840 | −0.542631 | ||||||||
\(784\) | 6.79662 | 0.242736 | ||||||||
\(785\) | 9.75708 | 0.348245 | ||||||||
\(786\) | 48.3719 | 1.72537 | ||||||||
\(787\) | 38.8675 | 1.38548 | 0.692739 | − | 0.721188i | \(-0.256404\pi\) | ||||
0.692739 | + | 0.721188i | \(0.256404\pi\) | |||||||
\(788\) | 9.14995 | 0.325953 | ||||||||
\(789\) | −44.7421 | −1.59286 | ||||||||
\(790\) | −4.43404 | −0.157756 | ||||||||
\(791\) | −60.6517 | −2.15652 | ||||||||
\(792\) | −3.56600 | −0.126712 | ||||||||
\(793\) | −60.0092 | −2.13099 | ||||||||
\(794\) | −30.6110 | −1.08634 | ||||||||
\(795\) | 24.0267 | 0.852140 | ||||||||
\(796\) | 17.2884 | 0.612771 | ||||||||
\(797\) | 36.9300 | 1.30813 | 0.654063 | − | 0.756440i | \(-0.273063\pi\) | ||||
0.654063 | + | 0.756440i | \(0.273063\pi\) | |||||||
\(798\) | −71.4643 | −2.52981 | ||||||||
\(799\) | −29.4239 | −1.04094 | ||||||||
\(800\) | 1.00000 | 0.0353553 | ||||||||
\(801\) | 38.6389 | 1.36524 | ||||||||
\(802\) | 15.8986 | 0.561398 | ||||||||
\(803\) | 1.64340 | 0.0579942 | ||||||||
\(804\) | −16.9571 | −0.598031 | ||||||||
\(805\) | −13.2965 | −0.468641 | ||||||||
\(806\) | −48.0454 | −1.69233 | ||||||||
\(807\) | −23.2668 | −0.819030 | ||||||||
\(808\) | 5.73226 | 0.201660 | ||||||||
\(809\) | −31.6994 | −1.11449 | −0.557246 | − | 0.830348i | \(-0.688142\pi\) | ||||
−0.557246 | + | 0.830348i | \(0.688142\pi\) | |||||||
\(810\) | −6.98165 | −0.245310 | ||||||||
\(811\) | −13.1924 | −0.463246 | −0.231623 | − | 0.972806i | \(-0.574404\pi\) | ||||
−0.231623 | + | 0.972806i | \(0.574404\pi\) | |||||||
\(812\) | 38.8872 | 1.36467 | ||||||||
\(813\) | −60.7929 | −2.13210 | ||||||||
\(814\) | 1.18834 | 0.0416512 | ||||||||
\(815\) | −7.12889 | −0.249714 | ||||||||
\(816\) | −9.14335 | −0.320081 | ||||||||
\(817\) | 7.50849 | 0.262689 | ||||||||
\(818\) | −8.57948 | −0.299975 | ||||||||
\(819\) | 73.9064 | 2.58250 | ||||||||
\(820\) | 9.18919 | 0.320901 | ||||||||
\(821\) | −19.4667 | −0.679392 | −0.339696 | − | 0.940535i | \(-0.610324\pi\) | ||||
−0.339696 | + | 0.940535i | \(0.610324\pi\) | |||||||
\(822\) | 15.7994 | 0.551068 | ||||||||
\(823\) | 27.8888 | 0.972142 | 0.486071 | − | 0.873919i | \(-0.338430\pi\) | ||||
0.486071 | + | 0.873919i | \(0.338430\pi\) | |||||||
\(824\) | 7.60241 | 0.264842 | ||||||||
\(825\) | 2.56242 | 0.0892120 | ||||||||
\(826\) | −16.7852 | −0.584032 | ||||||||
\(827\) | −9.43030 | −0.327924 | −0.163962 | − | 0.986467i | \(-0.552427\pi\) | ||||
−0.163962 | + | 0.986467i | \(0.552427\pi\) | |||||||
\(828\) | −12.7654 | −0.443627 | ||||||||
\(829\) | −45.8021 | −1.59077 | −0.795386 | − | 0.606103i | \(-0.792732\pi\) | ||||
−0.795386 | + | 0.606103i | \(0.792732\pi\) | |||||||
\(830\) | 10.4132 | 0.361447 | ||||||||
\(831\) | −63.1583 | −2.19094 | ||||||||
\(832\) | 5.57975 | 0.193443 | ||||||||
\(833\) | 24.2520 | 0.840283 | ||||||||
\(834\) | 53.0725 | 1.83775 | ||||||||
\(835\) | 6.12444 | 0.211945 | ||||||||
\(836\) | −7.50849 | −0.259687 | ||||||||
\(837\) | 12.4883 | 0.431658 | ||||||||
\(838\) | −14.1402 | −0.488464 | ||||||||
\(839\) | 7.18828 | 0.248167 | 0.124083 | − | 0.992272i | \(-0.460401\pi\) | ||||
0.124083 | + | 0.992272i | \(0.460401\pi\) | |||||||
\(840\) | −9.51780 | −0.328395 | ||||||||
\(841\) | 80.6075 | 2.77957 | ||||||||
\(842\) | −2.26240 | −0.0779675 | ||||||||
\(843\) | −2.72845 | −0.0939727 | ||||||||
\(844\) | 1.34818 | 0.0464062 | ||||||||
\(845\) | 18.1336 | 0.623814 | ||||||||
\(846\) | −29.4054 | −1.01098 | ||||||||
\(847\) | 3.71438 | 0.127628 | ||||||||
\(848\) | −9.37658 | −0.321993 | ||||||||
\(849\) | −21.1724 | −0.726636 | ||||||||
\(850\) | 3.56825 | 0.122390 | ||||||||
\(851\) | 4.25395 | 0.145824 | ||||||||
\(852\) | 1.20290 | 0.0412107 | ||||||||
\(853\) | 3.57962 | 0.122564 | 0.0612820 | − | 0.998120i | \(-0.480481\pi\) | ||||
0.0612820 | + | 0.998120i | \(0.480481\pi\) | |||||||
\(854\) | −39.9475 | −1.36698 | ||||||||
\(855\) | 26.7753 | 0.915694 | ||||||||
\(856\) | −2.53696 | −0.0867116 | ||||||||
\(857\) | 18.9411 | 0.647014 | 0.323507 | − | 0.946226i | \(-0.395138\pi\) | ||||
0.323507 | + | 0.946226i | \(0.395138\pi\) | |||||||
\(858\) | 14.2977 | 0.488114 | ||||||||
\(859\) | 19.8700 | 0.677957 | 0.338978 | − | 0.940794i | \(-0.389919\pi\) | ||||
0.338978 | + | 0.940794i | \(0.389919\pi\) | |||||||
\(860\) | 1.00000 | 0.0340997 | ||||||||
\(861\) | −87.4609 | −2.98066 | ||||||||
\(862\) | 15.9360 | 0.542783 | ||||||||
\(863\) | 18.6340 | 0.634308 | 0.317154 | − | 0.948374i | \(-0.397273\pi\) | ||||
0.317154 | + | 0.948374i | \(0.397273\pi\) | |||||||
\(864\) | −1.45032 | −0.0493410 | ||||||||
\(865\) | −18.6132 | −0.632868 | ||||||||
\(866\) | 36.2384 | 1.23143 | ||||||||
\(867\) | 10.9354 | 0.371387 | ||||||||
\(868\) | −31.9833 | −1.08558 | ||||||||
\(869\) | 4.43404 | 0.150414 | ||||||||
\(870\) | −26.8269 | −0.909517 | ||||||||
\(871\) | 36.9246 | 1.25114 | ||||||||
\(872\) | −10.5718 | −0.358005 | ||||||||
\(873\) | 1.82366 | 0.0617214 | ||||||||
\(874\) | −26.8785 | −0.909178 | ||||||||
\(875\) | 3.71438 | 0.125569 | ||||||||
\(876\) | 4.21107 | 0.142279 | ||||||||
\(877\) | 11.1192 | 0.375469 | 0.187735 | − | 0.982220i | \(-0.439886\pi\) | ||||
0.187735 | + | 0.982220i | \(0.439886\pi\) | |||||||
\(878\) | −31.2479 | −1.05456 | ||||||||
\(879\) | 38.9294 | 1.31306 | ||||||||
\(880\) | −1.00000 | −0.0337100 | ||||||||
\(881\) | −9.06242 | −0.305321 | −0.152660 | − | 0.988279i | \(-0.548784\pi\) | ||||
−0.152660 | + | 0.988279i | \(0.548784\pi\) | |||||||
\(882\) | 24.2367 | 0.816093 | ||||||||
\(883\) | 14.2250 | 0.478710 | 0.239355 | − | 0.970932i | \(-0.423064\pi\) | ||||
0.239355 | + | 0.970932i | \(0.423064\pi\) | |||||||
\(884\) | 19.9099 | 0.669643 | ||||||||
\(885\) | 11.5795 | 0.389241 | ||||||||
\(886\) | −31.0221 | −1.04221 | ||||||||
\(887\) | 20.5493 | 0.689977 | 0.344988 | − | 0.938607i | \(-0.387883\pi\) | ||||
0.344988 | + | 0.938607i | \(0.387883\pi\) | |||||||
\(888\) | 3.04502 | 0.102184 | ||||||||
\(889\) | −5.79276 | −0.194283 | ||||||||
\(890\) | 10.8354 | 0.363202 | ||||||||
\(891\) | 6.98165 | 0.233894 | ||||||||
\(892\) | 26.8745 | 0.899824 | ||||||||
\(893\) | −61.9153 | −2.07192 | ||||||||
\(894\) | −11.6800 | −0.390637 | ||||||||
\(895\) | −8.07746 | −0.270000 | ||||||||
\(896\) | 3.71438 | 0.124089 | ||||||||
\(897\) | 51.1820 | 1.70892 | ||||||||
\(898\) | −30.6147 | −1.02162 | ||||||||
\(899\) | −90.1482 | −3.00661 | ||||||||
\(900\) | 3.56600 | 0.118867 | ||||||||
\(901\) | −33.4579 | −1.11465 | ||||||||
\(902\) | −9.18919 | −0.305967 | ||||||||
\(903\) | −9.51780 | −0.316733 | ||||||||
\(904\) | −16.3289 | −0.543090 | ||||||||
\(905\) | −12.2583 | −0.407480 | ||||||||
\(906\) | 49.7187 | 1.65179 | ||||||||
\(907\) | 4.79684 | 0.159276 | 0.0796382 | − | 0.996824i | \(-0.474623\pi\) | ||||
0.0796382 | + | 0.996824i | \(0.474623\pi\) | |||||||
\(908\) | −0.00729015 | −0.000241932 0 | ||||||||
\(909\) | 20.4412 | 0.677992 | ||||||||
\(910\) | 20.7253 | 0.687037 | ||||||||
\(911\) | −28.3419 | −0.939010 | −0.469505 | − | 0.882930i | \(-0.655568\pi\) | ||||
−0.469505 | + | 0.882930i | \(0.655568\pi\) | |||||||
\(912\) | −19.2399 | −0.637097 | ||||||||
\(913\) | −10.4132 | −0.344626 | ||||||||
\(914\) | 8.31983 | 0.275196 | ||||||||
\(915\) | 27.5584 | 0.911052 | ||||||||
\(916\) | 27.4701 | 0.907639 | ||||||||
\(917\) | −70.1179 | −2.31550 | ||||||||
\(918\) | −5.17512 | −0.170804 | ||||||||
\(919\) | 16.8779 | 0.556750 | 0.278375 | − | 0.960473i | \(-0.410204\pi\) | ||||
0.278375 | + | 0.960473i | \(0.410204\pi\) | |||||||
\(920\) | −3.57975 | −0.118021 | ||||||||
\(921\) | 39.3760 | 1.29748 | ||||||||
\(922\) | −8.69871 | −0.286477 | ||||||||
\(923\) | −2.61935 | −0.0862170 | ||||||||
\(924\) | 9.51780 | 0.313113 | ||||||||
\(925\) | −1.18834 | −0.0390723 | ||||||||
\(926\) | 7.27816 | 0.239175 | ||||||||
\(927\) | 27.1102 | 0.890415 | ||||||||
\(928\) | 10.4694 | 0.343674 | ||||||||
\(929\) | 23.7461 | 0.779084 | 0.389542 | − | 0.921009i | \(-0.372633\pi\) | ||||
0.389542 | + | 0.921009i | \(0.372633\pi\) | |||||||
\(930\) | 22.0642 | 0.723512 | ||||||||
\(931\) | 51.0324 | 1.67252 | ||||||||
\(932\) | −3.41771 | −0.111951 | ||||||||
\(933\) | 64.4531 | 2.11010 | ||||||||
\(934\) | −5.45479 | −0.178486 | ||||||||
\(935\) | −3.56825 | −0.116694 | ||||||||
\(936\) | 19.8974 | 0.650366 | ||||||||
\(937\) | 24.3243 | 0.794641 | 0.397321 | − | 0.917680i | \(-0.369940\pi\) | ||||
0.397321 | + | 0.917680i | \(0.369940\pi\) | |||||||
\(938\) | 24.5803 | 0.802576 | ||||||||
\(939\) | −30.3629 | −0.990856 | ||||||||
\(940\) | −8.24604 | −0.268956 | ||||||||
\(941\) | −9.98359 | −0.325456 | −0.162728 | − | 0.986671i | \(-0.552029\pi\) | ||||
−0.162728 | + | 0.986671i | \(0.552029\pi\) | |||||||
\(942\) | −25.0017 | −0.814601 | ||||||||
\(943\) | −32.8950 | −1.07121 | ||||||||
\(944\) | −4.51898 | −0.147080 | ||||||||
\(945\) | −5.38706 | −0.175241 | ||||||||
\(946\) | −1.00000 | −0.0325128 | ||||||||
\(947\) | 21.7353 | 0.706304 | 0.353152 | − | 0.935566i | \(-0.385110\pi\) | ||||
0.353152 | + | 0.935566i | \(0.385110\pi\) | |||||||
\(948\) | 11.3619 | 0.369016 | ||||||||
\(949\) | −9.16974 | −0.297662 | ||||||||
\(950\) | 7.50849 | 0.243608 | ||||||||
\(951\) | 35.9932 | 1.16716 | ||||||||
\(952\) | 13.2538 | 0.429559 | ||||||||
\(953\) | 10.1753 | 0.329611 | 0.164806 | − | 0.986326i | \(-0.447300\pi\) | ||||
0.164806 | + | 0.986326i | \(0.447300\pi\) | |||||||
\(954\) | −33.4369 | −1.08256 | ||||||||
\(955\) | 25.8507 | 0.836507 | ||||||||
\(956\) | −20.9593 | −0.677872 | ||||||||
\(957\) | 26.8269 | 0.867190 | ||||||||
\(958\) | −32.5974 | −1.05317 | ||||||||
\(959\) | −22.9022 | −0.739551 | ||||||||
\(960\) | −2.56242 | −0.0827018 | ||||||||
\(961\) | 43.1436 | 1.39173 | ||||||||
\(962\) | −6.63063 | −0.213780 | ||||||||
\(963\) | −9.04680 | −0.291529 | ||||||||
\(964\) | 22.6301 | 0.728865 | ||||||||
\(965\) | 12.9265 | 0.416117 | ||||||||
\(966\) | 34.0713 | 1.09623 | ||||||||
\(967\) | 54.7081 | 1.75929 | 0.879647 | − | 0.475627i | \(-0.157779\pi\) | ||||
0.879647 | + | 0.475627i | \(0.157779\pi\) | |||||||
\(968\) | 1.00000 | 0.0321412 | ||||||||
\(969\) | −68.6527 | −2.20544 | ||||||||
\(970\) | 0.511402 | 0.0164201 | ||||||||
\(971\) | 23.0305 | 0.739083 | 0.369541 | − | 0.929214i | \(-0.379515\pi\) | ||||
0.369541 | + | 0.929214i | \(0.379515\pi\) | |||||||
\(972\) | 22.2409 | 0.713377 | ||||||||
\(973\) | −76.9317 | −2.46632 | ||||||||
\(974\) | 3.63248 | 0.116392 | ||||||||
\(975\) | −14.2977 | −0.457891 | ||||||||
\(976\) | −10.7548 | −0.344254 | ||||||||
\(977\) | −28.5369 | −0.912976 | −0.456488 | − | 0.889730i | \(-0.650893\pi\) | ||||
−0.456488 | + | 0.889730i | \(0.650893\pi\) | |||||||
\(978\) | 18.2672 | 0.584121 | ||||||||
\(979\) | −10.8354 | −0.346300 | ||||||||
\(980\) | 6.79662 | 0.217110 | ||||||||
\(981\) | −37.6989 | −1.20363 | ||||||||
\(982\) | 5.31772 | 0.169695 | ||||||||
\(983\) | −15.7180 | −0.501328 | −0.250664 | − | 0.968074i | \(-0.580649\pi\) | ||||
−0.250664 | + | 0.968074i | \(0.580649\pi\) | |||||||
\(984\) | −23.5466 | −0.750637 | ||||||||
\(985\) | 9.14995 | 0.291542 | ||||||||
\(986\) | 37.3573 | 1.18970 | ||||||||
\(987\) | 78.4842 | 2.49818 | ||||||||
\(988\) | 41.8955 | 1.33287 | ||||||||
\(989\) | −3.57975 | −0.113829 | ||||||||
\(990\) | −3.56600 | −0.113335 | ||||||||
\(991\) | −26.1846 | −0.831781 | −0.415890 | − | 0.909415i | \(-0.636530\pi\) | ||||
−0.415890 | + | 0.909415i | \(0.636530\pi\) | |||||||
\(992\) | −8.61067 | −0.273389 | ||||||||
\(993\) | −70.1094 | −2.22486 | ||||||||
\(994\) | −1.74368 | −0.0553060 | ||||||||
\(995\) | 17.2884 | 0.548079 | ||||||||
\(996\) | −26.6830 | −0.845482 | ||||||||
\(997\) | 31.1336 | 0.986012 | 0.493006 | − | 0.870026i | \(-0.335898\pi\) | ||||
0.493006 | + | 0.870026i | \(0.335898\pi\) | |||||||
\(998\) | −13.4007 | −0.424193 | ||||||||
\(999\) | 1.72348 | 0.0545284 |
(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 | 4730.2.a.be.1.2 | ✓ | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4730.2.a.be.1.2 | ✓ | 12 | 1.1 | even | 1 | trivial |