Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [115,2,Mod(1,115)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(115, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("115.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 115 = 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 115.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: | \(0.918279623245\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.15317.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 2x^{3} - 4x^{2} + 5x + 2 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-1.69353\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 115.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.69353 | −1.19750 | −0.598752 | − | 0.800935i | \(-0.704336\pi\) | ||||
−0.598752 | + | 0.800935i | \(0.704336\pi\) | |||||||
\(3\) | −2.56155 | −1.47891 | −0.739457 | − | 0.673204i | \(-0.764917\pi\) | ||||
−0.739457 | + | 0.673204i | \(0.764917\pi\) | |||||||
\(4\) | 0.868028 | 0.434014 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | 4.33805 | 1.77100 | ||||||||
\(7\) | −0.819031 | −0.309565 | −0.154782 | − | 0.987949i | \(-0.549468\pi\) | ||||
−0.154782 | + | 0.987949i | \(0.549468\pi\) | |||||||
\(8\) | 1.91702 | 0.677770 | ||||||||
\(9\) | 3.56155 | 1.18718 | ||||||||
\(10\) | −1.69353 | −0.535540 | ||||||||
\(11\) | 5.38705 | 1.62426 | 0.812128 | − | 0.583479i | \(-0.198309\pi\) | ||||
0.812128 | + | 0.583479i | \(0.198309\pi\) | |||||||
\(12\) | −2.22350 | −0.641869 | ||||||||
\(13\) | 2.46356 | 0.683269 | 0.341634 | − | 0.939833i | \(-0.389020\pi\) | ||||
0.341634 | + | 0.939833i | \(0.389020\pi\) | |||||||
\(14\) | 1.38705 | 0.370705 | ||||||||
\(15\) | −2.56155 | −0.661390 | ||||||||
\(16\) | −4.98258 | −1.24565 | ||||||||
\(17\) | 4.20608 | 1.02012 | 0.510062 | − | 0.860137i | \(-0.329622\pi\) | ||||
0.510062 | + | 0.860137i | \(0.329622\pi\) | |||||||
\(18\) | −6.03158 | −1.42166 | ||||||||
\(19\) | −5.38705 | −1.23587 | −0.617937 | − | 0.786228i | \(-0.712031\pi\) | ||||
−0.617937 | + | 0.786228i | \(0.712031\pi\) | |||||||
\(20\) | 0.868028 | 0.194097 | ||||||||
\(21\) | 2.09799 | 0.457819 | ||||||||
\(22\) | −9.12311 | −1.94505 | ||||||||
\(23\) | −1.00000 | −0.208514 | ||||||||
\(24\) | −4.91056 | −1.00236 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −4.17210 | −0.818216 | ||||||||
\(27\) | −1.43845 | −0.276829 | ||||||||
\(28\) | −0.710942 | −0.134355 | ||||||||
\(29\) | 2.35547 | 0.437400 | 0.218700 | − | 0.975792i | \(-0.429818\pi\) | ||||
0.218700 | + | 0.975792i | \(0.429818\pi\) | |||||||
\(30\) | 4.33805 | 0.792017 | ||||||||
\(31\) | 6.66964 | 1.19790 | 0.598952 | − | 0.800785i | \(-0.295584\pi\) | ||||
0.598952 | + | 0.800785i | \(0.295584\pi\) | |||||||
\(32\) | 4.60408 | 0.813895 | ||||||||
\(33\) | −13.7992 | −2.40213 | ||||||||
\(34\) | −7.12311 | −1.22160 | ||||||||
\(35\) | −0.819031 | −0.138442 | ||||||||
\(36\) | 3.09153 | 0.515254 | ||||||||
\(37\) | 7.42718 | 1.22102 | 0.610510 | − | 0.792008i | \(-0.290964\pi\) | ||||
0.610510 | + | 0.792008i | \(0.290964\pi\) | |||||||
\(38\) | 9.12311 | 1.47996 | ||||||||
\(39\) | −6.31054 | −1.01050 | ||||||||
\(40\) | 1.91702 | 0.303108 | ||||||||
\(41\) | 5.64453 | 0.881527 | 0.440764 | − | 0.897623i | \(-0.354708\pi\) | ||||
0.440764 | + | 0.897623i | \(0.354708\pi\) | |||||||
\(42\) | −3.55300 | −0.548240 | ||||||||
\(43\) | −1.90201 | −0.290053 | −0.145027 | − | 0.989428i | \(-0.546327\pi\) | ||||
−0.145027 | + | 0.989428i | \(0.546327\pi\) | |||||||
\(44\) | 4.67611 | 0.704950 | ||||||||
\(45\) | 3.56155 | 0.530925 | ||||||||
\(46\) | 1.69353 | 0.249697 | ||||||||
\(47\) | −9.33565 | −1.36175 | −0.680873 | − | 0.732402i | \(-0.738399\pi\) | ||||
−0.680873 | + | 0.732402i | \(0.738399\pi\) | |||||||
\(48\) | 12.7632 | 1.84220 | ||||||||
\(49\) | −6.32919 | −0.904170 | ||||||||
\(50\) | −1.69353 | −0.239501 | ||||||||
\(51\) | −10.7741 | −1.50868 | ||||||||
\(52\) | 2.13844 | 0.296548 | ||||||||
\(53\) | 13.8571 | 1.90342 | 0.951708 | − | 0.307005i | \(-0.0993268\pi\) | ||||
0.951708 | + | 0.307005i | \(0.0993268\pi\) | |||||||
\(54\) | 2.43605 | 0.331504 | ||||||||
\(55\) | 5.38705 | 0.726390 | ||||||||
\(56\) | −1.57010 | −0.209814 | ||||||||
\(57\) | 13.7992 | 1.82775 | ||||||||
\(58\) | −3.98905 | −0.523788 | ||||||||
\(59\) | 5.27896 | 0.687262 | 0.343631 | − | 0.939105i | \(-0.388343\pi\) | ||||
0.343631 | + | 0.939105i | \(0.388343\pi\) | |||||||
\(60\) | −2.22350 | −0.287052 | ||||||||
\(61\) | −8.51016 | −1.08961 | −0.544807 | − | 0.838562i | \(-0.683397\pi\) | ||||
−0.544807 | + | 0.838562i | \(0.683397\pi\) | |||||||
\(62\) | −11.2952 | −1.43449 | ||||||||
\(63\) | −2.91702 | −0.367510 | ||||||||
\(64\) | 2.16804 | 0.271005 | ||||||||
\(65\) | 2.46356 | 0.305567 | ||||||||
\(66\) | 23.3693 | 2.87656 | ||||||||
\(67\) | 4.10809 | 0.501883 | 0.250942 | − | 0.968002i | \(-0.419260\pi\) | ||||
0.250942 | + | 0.968002i | \(0.419260\pi\) | |||||||
\(68\) | 3.65100 | 0.442748 | ||||||||
\(69\) | 2.56155 | 0.308375 | ||||||||
\(70\) | 1.38705 | 0.165784 | ||||||||
\(71\) | −11.7927 | −1.39954 | −0.699771 | − | 0.714367i | \(-0.746715\pi\) | ||||
−0.699771 | + | 0.714367i | \(0.746715\pi\) | |||||||
\(72\) | 6.82758 | 0.804638 | ||||||||
\(73\) | −10.4636 | −1.22467 | −0.612334 | − | 0.790600i | \(-0.709769\pi\) | ||||
−0.612334 | + | 0.790600i | \(0.709769\pi\) | |||||||
\(74\) | −12.5781 | −1.46218 | ||||||||
\(75\) | −2.56155 | −0.295783 | ||||||||
\(76\) | −4.67611 | −0.536386 | ||||||||
\(77\) | −4.41216 | −0.502813 | ||||||||
\(78\) | 10.6871 | 1.21007 | ||||||||
\(79\) | 13.7992 | 1.55253 | 0.776266 | − | 0.630405i | \(-0.217111\pi\) | ||||
0.776266 | + | 0.630405i | \(0.217111\pi\) | |||||||
\(80\) | −4.98258 | −0.557070 | ||||||||
\(81\) | −7.00000 | −0.777778 | ||||||||
\(82\) | −9.55915 | −1.05563 | ||||||||
\(83\) | 3.32919 | 0.365426 | 0.182713 | − | 0.983166i | \(-0.441512\pi\) | ||||
0.182713 | + | 0.983166i | \(0.441512\pi\) | |||||||
\(84\) | 1.82112 | 0.198700 | ||||||||
\(85\) | 4.20608 | 0.456214 | ||||||||
\(86\) | 3.22110 | 0.347340 | ||||||||
\(87\) | −6.03366 | −0.646877 | ||||||||
\(88\) | 10.3271 | 1.10087 | ||||||||
\(89\) | −3.58304 | −0.379801 | −0.189900 | − | 0.981803i | \(-0.560817\pi\) | ||||
−0.189900 | + | 0.981803i | \(0.560817\pi\) | |||||||
\(90\) | −6.03158 | −0.635784 | ||||||||
\(91\) | −2.01773 | −0.211516 | ||||||||
\(92\) | −0.868028 | −0.0904981 | ||||||||
\(93\) | −17.0846 | −1.77159 | ||||||||
\(94\) | 15.8102 | 1.63069 | ||||||||
\(95\) | −5.38705 | −0.552700 | ||||||||
\(96\) | −11.7936 | −1.20368 | ||||||||
\(97\) | −9.02511 | −0.916361 | −0.458181 | − | 0.888859i | \(-0.651499\pi\) | ||||
−0.458181 | + | 0.888859i | \(0.651499\pi\) | |||||||
\(98\) | 10.7186 | 1.08275 | ||||||||
\(99\) | 19.1863 | 1.92829 | ||||||||
\(100\) | 0.868028 | 0.0868028 | ||||||||
\(101\) | −12.1033 | −1.20432 | −0.602161 | − | 0.798375i | \(-0.705694\pi\) | ||||
−0.602161 | + | 0.798375i | \(0.705694\pi\) | |||||||
\(102\) | 18.2462 | 1.80664 | ||||||||
\(103\) | −3.80402 | −0.374821 | −0.187410 | − | 0.982282i | \(-0.560009\pi\) | ||||
−0.187410 | + | 0.982282i | \(0.560009\pi\) | |||||||
\(104\) | 4.72270 | 0.463099 | ||||||||
\(105\) | 2.09799 | 0.204743 | ||||||||
\(106\) | −23.4673 | −2.27935 | ||||||||
\(107\) | −2.47003 | −0.238786 | −0.119393 | − | 0.992847i | \(-0.538095\pi\) | ||||
−0.119393 | + | 0.992847i | \(0.538095\pi\) | |||||||
\(108\) | −1.24861 | −0.120148 | ||||||||
\(109\) | −4.49722 | −0.430756 | −0.215378 | − | 0.976531i | \(-0.569098\pi\) | ||||
−0.215378 | + | 0.976531i | \(0.569098\pi\) | |||||||
\(110\) | −9.12311 | −0.869854 | ||||||||
\(111\) | −19.0251 | −1.80578 | ||||||||
\(112\) | 4.08089 | 0.385608 | ||||||||
\(113\) | 6.30407 | 0.593037 | 0.296519 | − | 0.955027i | \(-0.404174\pi\) | ||||
0.296519 | + | 0.955027i | \(0.404174\pi\) | |||||||
\(114\) | −23.3693 | −2.18874 | ||||||||
\(115\) | −1.00000 | −0.0932505 | ||||||||
\(116\) | 2.04461 | 0.189838 | ||||||||
\(117\) | 8.77410 | 0.811166 | ||||||||
\(118\) | −8.94005 | −0.822999 | ||||||||
\(119\) | −3.44491 | −0.315795 | ||||||||
\(120\) | −4.91056 | −0.448271 | ||||||||
\(121\) | 18.0203 | 1.63821 | ||||||||
\(122\) | 14.4122 | 1.30482 | ||||||||
\(123\) | −14.4588 | −1.30370 | ||||||||
\(124\) | 5.78943 | 0.519906 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | 4.94005 | 0.440095 | ||||||||
\(127\) | −0.910558 | −0.0807989 | −0.0403995 | − | 0.999184i | \(-0.512863\pi\) | ||||
−0.0403995 | + | 0.999184i | \(0.512863\pi\) | |||||||
\(128\) | −12.8798 | −1.13842 | ||||||||
\(129\) | 4.87209 | 0.428964 | ||||||||
\(130\) | −4.17210 | −0.365918 | ||||||||
\(131\) | 18.6070 | 1.62570 | 0.812850 | − | 0.582474i | \(-0.197915\pi\) | ||||
0.812850 | + | 0.582474i | \(0.197915\pi\) | |||||||
\(132\) | −11.9781 | −1.04256 | ||||||||
\(133\) | 4.41216 | 0.382583 | ||||||||
\(134\) | −6.95715 | −0.601006 | ||||||||
\(135\) | −1.43845 | −0.123802 | ||||||||
\(136\) | 8.06316 | 0.691410 | ||||||||
\(137\) | −14.4251 | −1.23242 | −0.616210 | − | 0.787582i | \(-0.711333\pi\) | ||||
−0.616210 | + | 0.787582i | \(0.711333\pi\) | |||||||
\(138\) | −4.33805 | −0.369280 | ||||||||
\(139\) | 18.3507 | 1.55648 | 0.778242 | − | 0.627965i | \(-0.216112\pi\) | ||||
0.778242 | + | 0.627965i | \(0.216112\pi\) | |||||||
\(140\) | −0.710942 | −0.0600856 | ||||||||
\(141\) | 23.9138 | 2.01390 | ||||||||
\(142\) | 19.9713 | 1.67596 | ||||||||
\(143\) | 13.2713 | 1.10980 | ||||||||
\(144\) | −17.7457 | −1.47881 | ||||||||
\(145\) | 2.35547 | 0.195611 | ||||||||
\(146\) | 17.7203 | 1.46654 | ||||||||
\(147\) | 16.2125 | 1.33719 | ||||||||
\(148\) | 6.44700 | 0.529940 | ||||||||
\(149\) | 7.63806 | 0.625734 | 0.312867 | − | 0.949797i | \(-0.398711\pi\) | ||||
0.312867 | + | 0.949797i | \(0.398711\pi\) | |||||||
\(150\) | 4.33805 | 0.354201 | ||||||||
\(151\) | −0.659545 | −0.0536730 | −0.0268365 | − | 0.999640i | \(-0.508543\pi\) | ||||
−0.0268365 | + | 0.999640i | \(0.508543\pi\) | |||||||
\(152\) | −10.3271 | −0.837639 | ||||||||
\(153\) | 14.9802 | 1.21108 | ||||||||
\(154\) | 7.47211 | 0.602120 | ||||||||
\(155\) | 6.66964 | 0.535719 | ||||||||
\(156\) | −5.47772 | −0.438569 | ||||||||
\(157\) | 3.94214 | 0.314617 | 0.157308 | − | 0.987550i | \(-0.449718\pi\) | ||||
0.157308 | + | 0.987550i | \(0.449718\pi\) | |||||||
\(158\) | −23.3693 | −1.85916 | ||||||||
\(159\) | −35.4956 | −2.81499 | ||||||||
\(160\) | 4.60408 | 0.363985 | ||||||||
\(161\) | 0.819031 | 0.0645487 | ||||||||
\(162\) | 11.8547 | 0.931391 | ||||||||
\(163\) | −3.80038 | −0.297669 | −0.148835 | − | 0.988862i | \(-0.547552\pi\) | ||||
−0.148835 | + | 0.988862i | \(0.547552\pi\) | |||||||
\(164\) | 4.89961 | 0.382595 | ||||||||
\(165\) | −13.7992 | −1.07427 | ||||||||
\(166\) | −5.63806 | −0.437599 | ||||||||
\(167\) | −2.24621 | −0.173817 | −0.0869085 | − | 0.996216i | \(-0.527699\pi\) | ||||
−0.0869085 | + | 0.996216i | \(0.527699\pi\) | |||||||
\(168\) | 4.02190 | 0.310296 | ||||||||
\(169\) | −6.93087 | −0.533144 | ||||||||
\(170\) | −7.12311 | −0.546317 | ||||||||
\(171\) | −19.1863 | −1.46721 | ||||||||
\(172\) | −1.65100 | −0.125887 | ||||||||
\(173\) | −13.3822 | −1.01743 | −0.508717 | − | 0.860934i | \(-0.669880\pi\) | ||||
−0.508717 | + | 0.860934i | \(0.669880\pi\) | |||||||
\(174\) | 10.2182 | 0.774637 | ||||||||
\(175\) | −0.819031 | −0.0619130 | ||||||||
\(176\) | −26.8414 | −2.02325 | ||||||||
\(177\) | −13.5223 | −1.01640 | ||||||||
\(178\) | 6.06796 | 0.454813 | ||||||||
\(179\) | 18.2077 | 1.36091 | 0.680455 | − | 0.732789i | \(-0.261782\pi\) | ||||
0.680455 | + | 0.732789i | \(0.261782\pi\) | |||||||
\(180\) | 3.09153 | 0.230429 | ||||||||
\(181\) | −1.01218 | −0.0752348 | −0.0376174 | − | 0.999292i | \(-0.511977\pi\) | ||||
−0.0376174 | + | 0.999292i | \(0.511977\pi\) | |||||||
\(182\) | 3.41708 | 0.253291 | ||||||||
\(183\) | 21.7992 | 1.61144 | ||||||||
\(184\) | −1.91702 | −0.141325 | ||||||||
\(185\) | 7.42718 | 0.546057 | ||||||||
\(186\) | 28.9333 | 2.12149 | ||||||||
\(187\) | 22.6584 | 1.65694 | ||||||||
\(188\) | −8.10361 | −0.591016 | ||||||||
\(189\) | 1.17813 | 0.0856966 | ||||||||
\(190\) | 9.12311 | 0.661860 | ||||||||
\(191\) | −13.1231 | −0.949555 | −0.474777 | − | 0.880106i | \(-0.657471\pi\) | ||||
−0.474777 | + | 0.880106i | \(0.657471\pi\) | |||||||
\(192\) | −5.55354 | −0.400792 | ||||||||
\(193\) | −21.3179 | −1.53450 | −0.767249 | − | 0.641350i | \(-0.778375\pi\) | ||||
−0.767249 | + | 0.641350i | \(0.778375\pi\) | |||||||
\(194\) | 15.2843 | 1.09735 | ||||||||
\(195\) | −6.31054 | −0.451907 | ||||||||
\(196\) | −5.49391 | −0.392422 | ||||||||
\(197\) | 26.3608 | 1.87813 | 0.939063 | − | 0.343744i | \(-0.111695\pi\) | ||||
0.939063 | + | 0.343744i | \(0.111695\pi\) | |||||||
\(198\) | −32.4924 | −2.30914 | ||||||||
\(199\) | −4.16115 | −0.294976 | −0.147488 | − | 0.989064i | \(-0.547119\pi\) | ||||
−0.147488 | + | 0.989064i | \(0.547119\pi\) | |||||||
\(200\) | 1.91702 | 0.135554 | ||||||||
\(201\) | −10.5231 | −0.742241 | ||||||||
\(202\) | 20.4972 | 1.44218 | ||||||||
\(203\) | −1.92920 | −0.135404 | ||||||||
\(204\) | −9.35222 | −0.654786 | ||||||||
\(205\) | 5.64453 | 0.394231 | ||||||||
\(206\) | 6.44220 | 0.448849 | ||||||||
\(207\) | −3.56155 | −0.247545 | ||||||||
\(208\) | −12.2749 | −0.851111 | ||||||||
\(209\) | −29.0203 | −2.00738 | ||||||||
\(210\) | −3.55300 | −0.245180 | ||||||||
\(211\) | −15.7414 | −1.08368 | −0.541840 | − | 0.840482i | \(-0.682272\pi\) | ||||
−0.541840 | + | 0.840482i | \(0.682272\pi\) | |||||||
\(212\) | 12.0283 | 0.826109 | ||||||||
\(213\) | 30.2077 | 2.06980 | ||||||||
\(214\) | 4.18305 | 0.285948 | ||||||||
\(215\) | −1.90201 | −0.129716 | ||||||||
\(216\) | −2.75754 | −0.187627 | ||||||||
\(217\) | −5.46265 | −0.370829 | ||||||||
\(218\) | 7.61616 | 0.515832 | ||||||||
\(219\) | 26.8030 | 1.81118 | ||||||||
\(220\) | 4.67611 | 0.315263 | ||||||||
\(221\) | 10.3619 | 0.697019 | ||||||||
\(222\) | 32.2195 | 2.16243 | ||||||||
\(223\) | 0.0802588 | 0.00537453 | 0.00268726 | − | 0.999996i | \(-0.499145\pi\) | ||||
0.00268726 | + | 0.999996i | \(0.499145\pi\) | |||||||
\(224\) | −3.77089 | −0.251953 | ||||||||
\(225\) | 3.56155 | 0.237437 | ||||||||
\(226\) | −10.6761 | −0.710164 | ||||||||
\(227\) | −28.4705 | −1.88965 | −0.944827 | − | 0.327568i | \(-0.893771\pi\) | ||||
−0.944827 | + | 0.327568i | \(0.893771\pi\) | |||||||
\(228\) | 11.9781 | 0.793269 | ||||||||
\(229\) | −0.612950 | −0.0405048 | −0.0202524 | − | 0.999795i | \(-0.506447\pi\) | ||||
−0.0202524 | + | 0.999795i | \(0.506447\pi\) | |||||||
\(230\) | 1.69353 | 0.111668 | ||||||||
\(231\) | 11.3020 | 0.743616 | ||||||||
\(232\) | 4.51549 | 0.296457 | ||||||||
\(233\) | 3.79558 | 0.248657 | 0.124328 | − | 0.992241i | \(-0.460322\pi\) | ||||
0.124328 | + | 0.992241i | \(0.460322\pi\) | |||||||
\(234\) | −14.8592 | −0.971374 | ||||||||
\(235\) | −9.33565 | −0.608991 | ||||||||
\(236\) | 4.58228 | 0.298281 | ||||||||
\(237\) | −35.3474 | −2.29606 | ||||||||
\(238\) | 5.83405 | 0.378165 | ||||||||
\(239\) | 21.1118 | 1.36561 | 0.682806 | − | 0.730600i | \(-0.260760\pi\) | ||||
0.682806 | + | 0.730600i | \(0.260760\pi\) | |||||||
\(240\) | 12.7632 | 0.823858 | ||||||||
\(241\) | −0.774101 | −0.0498642 | −0.0249321 | − | 0.999689i | \(-0.507937\pi\) | ||||
−0.0249321 | + | 0.999689i | \(0.507937\pi\) | |||||||
\(242\) | −30.5179 | −1.96176 | ||||||||
\(243\) | 22.2462 | 1.42710 | ||||||||
\(244\) | −7.38705 | −0.472907 | ||||||||
\(245\) | −6.32919 | −0.404357 | ||||||||
\(246\) | 24.4863 | 1.56119 | ||||||||
\(247\) | −13.2713 | −0.844434 | ||||||||
\(248\) | 12.7859 | 0.811903 | ||||||||
\(249\) | −8.52789 | −0.540433 | ||||||||
\(250\) | −1.69353 | −0.107108 | ||||||||
\(251\) | −16.8041 | −1.06067 | −0.530334 | − | 0.847789i | \(-0.677933\pi\) | ||||
−0.530334 | + | 0.847789i | \(0.677933\pi\) | |||||||
\(252\) | −2.53206 | −0.159505 | ||||||||
\(253\) | −5.38705 | −0.338681 | ||||||||
\(254\) | 1.54205 | 0.0967570 | ||||||||
\(255\) | −10.7741 | −0.674700 | ||||||||
\(256\) | 17.4762 | 1.09226 | ||||||||
\(257\) | −5.12428 | −0.319644 | −0.159822 | − | 0.987146i | \(-0.551092\pi\) | ||||
−0.159822 | + | 0.987146i | \(0.551092\pi\) | |||||||
\(258\) | −8.25101 | −0.513686 | ||||||||
\(259\) | −6.08309 | −0.377985 | ||||||||
\(260\) | 2.13844 | 0.132620 | ||||||||
\(261\) | 8.38913 | 0.519274 | ||||||||
\(262\) | −31.5114 | −1.94678 | ||||||||
\(263\) | 6.97205 | 0.429915 | 0.214958 | − | 0.976623i | \(-0.431039\pi\) | ||||
0.214958 | + | 0.976623i | \(0.431039\pi\) | |||||||
\(264\) | −26.4534 | −1.62810 | ||||||||
\(265\) | 13.8571 | 0.851233 | ||||||||
\(266\) | −7.47211 | −0.458144 | ||||||||
\(267\) | 9.17813 | 0.561693 | ||||||||
\(268\) | 3.56594 | 0.217824 | ||||||||
\(269\) | −21.3328 | −1.30068 | −0.650342 | − | 0.759641i | \(-0.725375\pi\) | ||||
−0.650342 | + | 0.759641i | \(0.725375\pi\) | |||||||
\(270\) | 2.43605 | 0.148253 | ||||||||
\(271\) | −0.751071 | −0.0456243 | −0.0228122 | − | 0.999740i | \(-0.507262\pi\) | ||||
−0.0228122 | + | 0.999740i | \(0.507262\pi\) | |||||||
\(272\) | −20.9572 | −1.27071 | ||||||||
\(273\) | 5.16853 | 0.312814 | ||||||||
\(274\) | 24.4293 | 1.47583 | ||||||||
\(275\) | 5.38705 | 0.324851 | ||||||||
\(276\) | 2.22350 | 0.133839 | ||||||||
\(277\) | −8.20775 | −0.493156 | −0.246578 | − | 0.969123i | \(-0.579306\pi\) | ||||
−0.246578 | + | 0.969123i | \(0.579306\pi\) | |||||||
\(278\) | −31.0773 | −1.86389 | ||||||||
\(279\) | 23.7543 | 1.42213 | ||||||||
\(280\) | −1.57010 | −0.0938316 | ||||||||
\(281\) | 14.9749 | 0.893327 | 0.446663 | − | 0.894702i | \(-0.352612\pi\) | ||||
0.446663 | + | 0.894702i | \(0.352612\pi\) | |||||||
\(282\) | −40.4986 | −2.41165 | ||||||||
\(283\) | −23.4224 | −1.39232 | −0.696158 | − | 0.717889i | \(-0.745109\pi\) | ||||
−0.696158 | + | 0.717889i | \(0.745109\pi\) | |||||||
\(284\) | −10.2364 | −0.607420 | ||||||||
\(285\) | 13.7992 | 0.817395 | ||||||||
\(286\) | −22.4753 | −1.32899 | ||||||||
\(287\) | −4.62305 | −0.272890 | ||||||||
\(288\) | 16.3977 | 0.966243 | ||||||||
\(289\) | 0.691125 | 0.0406544 | ||||||||
\(290\) | −3.98905 | −0.234245 | ||||||||
\(291\) | 23.1183 | 1.35522 | ||||||||
\(292\) | −9.08266 | −0.531522 | ||||||||
\(293\) | 14.9600 | 0.873972 | 0.436986 | − | 0.899468i | \(-0.356046\pi\) | ||||
0.436986 | + | 0.899468i | \(0.356046\pi\) | |||||||
\(294\) | −27.4564 | −1.60129 | ||||||||
\(295\) | 5.27896 | 0.307353 | ||||||||
\(296\) | 14.2381 | 0.827572 | ||||||||
\(297\) | −7.74899 | −0.449642 | ||||||||
\(298\) | −12.9353 | −0.749319 | ||||||||
\(299\) | −2.46356 | −0.142471 | ||||||||
\(300\) | −2.22350 | −0.128374 | ||||||||
\(301\) | 1.55780 | 0.0897903 | ||||||||
\(302\) | 1.11696 | 0.0642736 | ||||||||
\(303\) | 31.0032 | 1.78109 | ||||||||
\(304\) | 26.8414 | 1.53946 | ||||||||
\(305\) | −8.51016 | −0.487290 | ||||||||
\(306\) | −25.3693 | −1.45027 | ||||||||
\(307\) | −19.1863 | −1.09502 | −0.547509 | − | 0.836800i | \(-0.684424\pi\) | ||||
−0.547509 | + | 0.836800i | \(0.684424\pi\) | |||||||
\(308\) | −3.82988 | −0.218228 | ||||||||
\(309\) | 9.74419 | 0.554327 | ||||||||
\(310\) | −11.2952 | −0.641525 | ||||||||
\(311\) | −19.4336 | −1.10198 | −0.550990 | − | 0.834512i | \(-0.685750\pi\) | ||||
−0.550990 | + | 0.834512i | \(0.685750\pi\) | |||||||
\(312\) | −12.0975 | −0.684884 | ||||||||
\(313\) | −20.9300 | −1.18303 | −0.591516 | − | 0.806294i | \(-0.701470\pi\) | ||||
−0.591516 | + | 0.806294i | \(0.701470\pi\) | |||||||
\(314\) | −6.67611 | −0.376755 | ||||||||
\(315\) | −2.91702 | −0.164356 | ||||||||
\(316\) | 11.9781 | 0.673821 | ||||||||
\(317\) | 10.8041 | 0.606821 | 0.303410 | − | 0.952860i | \(-0.401875\pi\) | ||||
0.303410 | + | 0.952860i | \(0.401875\pi\) | |||||||
\(318\) | 60.1128 | 3.37096 | ||||||||
\(319\) | 12.6890 | 0.710450 | ||||||||
\(320\) | 2.16804 | 0.121197 | ||||||||
\(321\) | 6.32710 | 0.353144 | ||||||||
\(322\) | −1.38705 | −0.0772973 | ||||||||
\(323\) | −22.6584 | −1.26075 | ||||||||
\(324\) | −6.07619 | −0.337566 | ||||||||
\(325\) | 2.46356 | 0.136654 | ||||||||
\(326\) | 6.43605 | 0.356460 | ||||||||
\(327\) | 11.5199 | 0.637051 | ||||||||
\(328\) | 10.8207 | 0.597473 | ||||||||
\(329\) | 7.64619 | 0.421548 | ||||||||
\(330\) | 23.3693 | 1.28644 | ||||||||
\(331\) | 22.7628 | 1.25116 | 0.625579 | − | 0.780161i | \(-0.284863\pi\) | ||||
0.625579 | + | 0.780161i | \(0.284863\pi\) | |||||||
\(332\) | 2.88983 | 0.158600 | ||||||||
\(333\) | 26.4523 | 1.44958 | ||||||||
\(334\) | 3.80402 | 0.208146 | ||||||||
\(335\) | 4.10809 | 0.224449 | ||||||||
\(336\) | −10.4534 | −0.570281 | ||||||||
\(337\) | −2.97489 | −0.162052 | −0.0810262 | − | 0.996712i | \(-0.525820\pi\) | ||||
−0.0810262 | + | 0.996712i | \(0.525820\pi\) | |||||||
\(338\) | 11.7376 | 0.638441 | ||||||||
\(339\) | −16.1482 | −0.877051 | ||||||||
\(340\) | 3.65100 | 0.198003 | ||||||||
\(341\) | 35.9297 | 1.94570 | ||||||||
\(342\) | 32.4924 | 1.75699 | ||||||||
\(343\) | 10.9170 | 0.589464 | ||||||||
\(344\) | −3.64619 | −0.196590 | ||||||||
\(345\) | 2.56155 | 0.137909 | ||||||||
\(346\) | 22.6632 | 1.21838 | ||||||||
\(347\) | 35.4024 | 1.90050 | 0.950251 | − | 0.311484i | \(-0.100826\pi\) | ||||
0.950251 | + | 0.311484i | \(0.100826\pi\) | |||||||
\(348\) | −5.23739 | −0.280753 | ||||||||
\(349\) | 22.4818 | 1.20342 | 0.601711 | − | 0.798714i | \(-0.294486\pi\) | ||||
0.601711 | + | 0.798714i | \(0.294486\pi\) | |||||||
\(350\) | 1.38705 | 0.0741410 | ||||||||
\(351\) | −3.54370 | −0.189149 | ||||||||
\(352\) | 24.8024 | 1.32197 | ||||||||
\(353\) | 6.28051 | 0.334278 | 0.167139 | − | 0.985933i | \(-0.446547\pi\) | ||||
0.167139 | + | 0.985933i | \(0.446547\pi\) | |||||||
\(354\) | 22.9004 | 1.21714 | ||||||||
\(355\) | −11.7927 | −0.625894 | ||||||||
\(356\) | −3.11017 | −0.164839 | ||||||||
\(357\) | 8.82433 | 0.467033 | ||||||||
\(358\) | −30.8353 | −1.62970 | ||||||||
\(359\) | 7.35702 | 0.388289 | 0.194144 | − | 0.980973i | \(-0.437807\pi\) | ||||
0.194144 | + | 0.980973i | \(0.437807\pi\) | |||||||
\(360\) | 6.82758 | 0.359845 | ||||||||
\(361\) | 10.0203 | 0.527385 | ||||||||
\(362\) | 1.71415 | 0.0900939 | ||||||||
\(363\) | −46.1600 | −2.42277 | ||||||||
\(364\) | −1.75145 | −0.0918008 | ||||||||
\(365\) | −10.4636 | −0.547688 | ||||||||
\(366\) | −36.9175 | −1.92971 | ||||||||
\(367\) | −0.886992 | −0.0463006 | −0.0231503 | − | 0.999732i | \(-0.507370\pi\) | ||||
−0.0231503 | + | 0.999732i | \(0.507370\pi\) | |||||||
\(368\) | 4.98258 | 0.259735 | ||||||||
\(369\) | 20.1033 | 1.04654 | ||||||||
\(370\) | −12.5781 | −0.653905 | ||||||||
\(371\) | −11.3494 | −0.589231 | ||||||||
\(372\) | −14.8299 | −0.768897 | ||||||||
\(373\) | −14.6283 | −0.757427 | −0.378713 | − | 0.925514i | \(-0.623633\pi\) | ||||
−0.378713 | + | 0.925514i | \(0.623633\pi\) | |||||||
\(374\) | −38.3725 | −1.98420 | ||||||||
\(375\) | −2.56155 | −0.132278 | ||||||||
\(376\) | −17.8967 | −0.922950 | ||||||||
\(377\) | 5.80285 | 0.298862 | ||||||||
\(378\) | −1.99520 | −0.102622 | ||||||||
\(379\) | −32.5183 | −1.67035 | −0.835176 | − | 0.549983i | \(-0.814634\pi\) | ||||
−0.835176 | + | 0.549983i | \(0.814634\pi\) | |||||||
\(380\) | −4.67611 | −0.239879 | ||||||||
\(381\) | 2.33244 | 0.119495 | ||||||||
\(382\) | 22.2243 | 1.13709 | ||||||||
\(383\) | 21.8393 | 1.11594 | 0.557969 | − | 0.829862i | \(-0.311581\pi\) | ||||
0.557969 | + | 0.829862i | \(0.311581\pi\) | |||||||
\(384\) | 32.9923 | 1.68363 | ||||||||
\(385\) | −4.41216 | −0.224865 | ||||||||
\(386\) | 36.1024 | 1.83757 | ||||||||
\(387\) | −6.77410 | −0.344347 | ||||||||
\(388\) | −7.83405 | −0.397714 | ||||||||
\(389\) | −15.1490 | −0.768083 | −0.384042 | − | 0.923316i | \(-0.625468\pi\) | ||||
−0.384042 | + | 0.923316i | \(0.625468\pi\) | |||||||
\(390\) | 10.6871 | 0.541160 | ||||||||
\(391\) | −4.20608 | −0.212711 | ||||||||
\(392\) | −12.1332 | −0.612819 | ||||||||
\(393\) | −47.6628 | −2.40427 | ||||||||
\(394\) | −44.6426 | −2.24906 | ||||||||
\(395\) | 13.7992 | 0.694314 | ||||||||
\(396\) | 16.6542 | 0.836905 | ||||||||
\(397\) | −7.70239 | −0.386572 | −0.193286 | − | 0.981142i | \(-0.561915\pi\) | ||||
−0.193286 | + | 0.981142i | \(0.561915\pi\) | |||||||
\(398\) | 7.04701 | 0.353235 | ||||||||
\(399\) | −11.3020 | −0.565807 | ||||||||
\(400\) | −4.98258 | −0.249129 | ||||||||
\(401\) | −23.7442 | −1.18573 | −0.592864 | − | 0.805303i | \(-0.702003\pi\) | ||||
−0.592864 | + | 0.805303i | \(0.702003\pi\) | |||||||
\(402\) | 17.8211 | 0.888836 | ||||||||
\(403\) | 16.4311 | 0.818490 | ||||||||
\(404\) | −10.5060 | −0.522692 | ||||||||
\(405\) | −7.00000 | −0.347833 | ||||||||
\(406\) | 3.26716 | 0.162146 | ||||||||
\(407\) | 40.0106 | 1.98325 | ||||||||
\(408\) | −20.6542 | −1.02254 | ||||||||
\(409\) | 10.2397 | 0.506323 | 0.253161 | − | 0.967424i | \(-0.418530\pi\) | ||||
0.253161 | + | 0.967424i | \(0.418530\pi\) | |||||||
\(410\) | −9.55915 | −0.472093 | ||||||||
\(411\) | 36.9506 | 1.82264 | ||||||||
\(412\) | −3.30199 | −0.162677 | ||||||||
\(413\) | −4.32363 | −0.212752 | ||||||||
\(414\) | 6.03158 | 0.296436 | ||||||||
\(415\) | 3.32919 | 0.163423 | ||||||||
\(416\) | 11.3424 | 0.556109 | ||||||||
\(417\) | −47.0062 | −2.30190 | ||||||||
\(418\) | 49.1466 | 2.40384 | ||||||||
\(419\) | −9.98227 | −0.487666 | −0.243833 | − | 0.969817i | \(-0.578405\pi\) | ||||
−0.243833 | + | 0.969817i | \(0.578405\pi\) | |||||||
\(420\) | 1.82112 | 0.0888613 | ||||||||
\(421\) | −17.2470 | −0.840566 | −0.420283 | − | 0.907393i | \(-0.638069\pi\) | ||||
−0.420283 | + | 0.907393i | \(0.638069\pi\) | |||||||
\(422\) | 26.6584 | 1.29771 | ||||||||
\(423\) | −33.2494 | −1.61664 | ||||||||
\(424\) | 26.5643 | 1.29008 | ||||||||
\(425\) | 4.20608 | 0.204025 | ||||||||
\(426\) | −51.1576 | −2.47859 | ||||||||
\(427\) | 6.97009 | 0.337306 | ||||||||
\(428\) | −2.14405 | −0.103637 | ||||||||
\(429\) | −33.9952 | −1.64130 | ||||||||
\(430\) | 3.22110 | 0.155335 | ||||||||
\(431\) | −3.15377 | −0.151912 | −0.0759559 | − | 0.997111i | \(-0.524201\pi\) | ||||
−0.0759559 | + | 0.997111i | \(0.524201\pi\) | |||||||
\(432\) | 7.16718 | 0.344831 | ||||||||
\(433\) | −26.1333 | −1.25589 | −0.627944 | − | 0.778259i | \(-0.716103\pi\) | ||||
−0.627944 | + | 0.778259i | \(0.716103\pi\) | |||||||
\(434\) | 9.25113 | 0.444068 | ||||||||
\(435\) | −6.03366 | −0.289292 | ||||||||
\(436\) | −3.90371 | −0.186954 | ||||||||
\(437\) | 5.38705 | 0.257698 | ||||||||
\(438\) | −45.3915 | −2.16889 | ||||||||
\(439\) | 2.08143 | 0.0993412 | 0.0496706 | − | 0.998766i | \(-0.484183\pi\) | ||||
0.0496706 | + | 0.998766i | \(0.484183\pi\) | |||||||
\(440\) | 10.3271 | 0.492325 | ||||||||
\(441\) | −22.5417 | −1.07342 | ||||||||
\(442\) | −17.5482 | −0.834683 | ||||||||
\(443\) | −12.2799 | −0.583434 | −0.291717 | − | 0.956505i | \(-0.594227\pi\) | ||||
−0.291717 | + | 0.956505i | \(0.594227\pi\) | |||||||
\(444\) | −16.5143 | −0.783735 | ||||||||
\(445\) | −3.58304 | −0.169852 | ||||||||
\(446\) | −0.135920 | −0.00643601 | ||||||||
\(447\) | −19.5653 | −0.925407 | ||||||||
\(448\) | −1.77569 | −0.0838935 | ||||||||
\(449\) | −19.3794 | −0.914571 | −0.457286 | − | 0.889320i | \(-0.651178\pi\) | ||||
−0.457286 | + | 0.889320i | \(0.651178\pi\) | |||||||
\(450\) | −6.03158 | −0.284331 | ||||||||
\(451\) | 30.4074 | 1.43183 | ||||||||
\(452\) | 5.47211 | 0.257386 | ||||||||
\(453\) | 1.68946 | 0.0793777 | ||||||||
\(454\) | 48.2155 | 2.26287 | ||||||||
\(455\) | −2.01773 | −0.0945928 | ||||||||
\(456\) | 26.4534 | 1.23879 | ||||||||
\(457\) | −2.65788 | −0.124330 | −0.0621652 | − | 0.998066i | \(-0.519801\pi\) | ||||
−0.0621652 | + | 0.998066i | \(0.519801\pi\) | |||||||
\(458\) | 1.03805 | 0.0485047 | ||||||||
\(459\) | −6.05023 | −0.282400 | ||||||||
\(460\) | −0.868028 | −0.0404720 | ||||||||
\(461\) | 8.49423 | 0.395616 | 0.197808 | − | 0.980241i | \(-0.436618\pi\) | ||||
0.197808 | + | 0.980241i | \(0.436618\pi\) | |||||||
\(462\) | −19.1402 | −0.890483 | ||||||||
\(463\) | 15.1604 | 0.704564 | 0.352282 | − | 0.935894i | \(-0.385406\pi\) | ||||
0.352282 | + | 0.935894i | \(0.385406\pi\) | |||||||
\(464\) | −11.7363 | −0.544845 | ||||||||
\(465\) | −17.0846 | −0.792281 | ||||||||
\(466\) | −6.42792 | −0.297767 | ||||||||
\(467\) | −12.7039 | −0.587868 | −0.293934 | − | 0.955826i | \(-0.594965\pi\) | ||||
−0.293934 | + | 0.955826i | \(0.594965\pi\) | |||||||
\(468\) | 7.61616 | 0.352057 | ||||||||
\(469\) | −3.36465 | −0.155365 | ||||||||
\(470\) | 15.8102 | 0.729269 | ||||||||
\(471\) | −10.0980 | −0.465291 | ||||||||
\(472\) | 10.1199 | 0.465806 | ||||||||
\(473\) | −10.2462 | −0.471121 | ||||||||
\(474\) | 59.8617 | 2.74954 | ||||||||
\(475\) | −5.38705 | −0.247175 | ||||||||
\(476\) | −2.99028 | −0.137059 | ||||||||
\(477\) | 49.3527 | 2.25971 | ||||||||
\(478\) | −35.7534 | −1.63532 | ||||||||
\(479\) | −11.6681 | −0.533129 | −0.266564 | − | 0.963817i | \(-0.585889\pi\) | ||||
−0.266564 | + | 0.963817i | \(0.585889\pi\) | |||||||
\(480\) | −11.7936 | −0.538302 | ||||||||
\(481\) | 18.2973 | 0.834285 | ||||||||
\(482\) | 1.31096 | 0.0597126 | ||||||||
\(483\) | −2.09799 | −0.0954620 | ||||||||
\(484\) | 15.6421 | 0.711006 | ||||||||
\(485\) | −9.02511 | −0.409809 | ||||||||
\(486\) | −37.6745 | −1.70895 | ||||||||
\(487\) | 31.7778 | 1.43999 | 0.719996 | − | 0.693978i | \(-0.244144\pi\) | ||||
0.719996 | + | 0.693978i | \(0.244144\pi\) | |||||||
\(488\) | −16.3142 | −0.738508 | ||||||||
\(489\) | 9.73489 | 0.440227 | ||||||||
\(490\) | 10.7186 | 0.484219 | ||||||||
\(491\) | −6.17722 | −0.278774 | −0.139387 | − | 0.990238i | \(-0.544513\pi\) | ||||
−0.139387 | + | 0.990238i | \(0.544513\pi\) | |||||||
\(492\) | −12.5506 | −0.565825 | ||||||||
\(493\) | 9.90730 | 0.446203 | ||||||||
\(494\) | 22.4753 | 1.01121 | ||||||||
\(495\) | 19.1863 | 0.862358 | ||||||||
\(496\) | −33.2320 | −1.49216 | ||||||||
\(497\) | 9.65863 | 0.433249 | ||||||||
\(498\) | 14.4422 | 0.647170 | ||||||||
\(499\) | −37.3409 | −1.67161 | −0.835805 | − | 0.549026i | \(-0.814999\pi\) | ||||
−0.835805 | + | 0.549026i | \(0.814999\pi\) | |||||||
\(500\) | 0.868028 | 0.0388194 | ||||||||
\(501\) | 5.75379 | 0.257060 | ||||||||
\(502\) | 28.4582 | 1.27015 | ||||||||
\(503\) | 9.36648 | 0.417631 | 0.208815 | − | 0.977955i | \(-0.433039\pi\) | ||||
0.208815 | + | 0.977955i | \(0.433039\pi\) | |||||||
\(504\) | −5.59200 | −0.249088 | ||||||||
\(505\) | −12.1033 | −0.538589 | ||||||||
\(506\) | 9.12311 | 0.405572 | ||||||||
\(507\) | 17.7538 | 0.788473 | ||||||||
\(508\) | −0.790389 | −0.0350678 | ||||||||
\(509\) | −21.0798 | −0.934347 | −0.467174 | − | 0.884166i | \(-0.654728\pi\) | ||||
−0.467174 | + | 0.884166i | \(0.654728\pi\) | |||||||
\(510\) | 18.2462 | 0.807956 | ||||||||
\(511\) | 8.56999 | 0.379114 | ||||||||
\(512\) | −3.83676 | −0.169563 | ||||||||
\(513\) | 7.74899 | 0.342126 | ||||||||
\(514\) | 8.67809 | 0.382774 | ||||||||
\(515\) | −3.80402 | −0.167625 | ||||||||
\(516\) | 4.22911 | 0.186176 | ||||||||
\(517\) | −50.2916 | −2.21182 | ||||||||
\(518\) | 10.3019 | 0.452638 | ||||||||
\(519\) | 34.2793 | 1.50470 | ||||||||
\(520\) | 4.72270 | 0.207104 | ||||||||
\(521\) | −8.87689 | −0.388904 | −0.194452 | − | 0.980912i | \(-0.562293\pi\) | ||||
−0.194452 | + | 0.980912i | \(0.562293\pi\) | |||||||
\(522\) | −14.2072 | −0.621833 | ||||||||
\(523\) | −2.82187 | −0.123392 | −0.0616958 | − | 0.998095i | \(-0.519651\pi\) | ||||
−0.0616958 | + | 0.998095i | \(0.519651\pi\) | |||||||
\(524\) | 16.1514 | 0.705576 | ||||||||
\(525\) | 2.09799 | 0.0915639 | ||||||||
\(526\) | −11.8073 | −0.514825 | ||||||||
\(527\) | 28.0531 | 1.22201 | ||||||||
\(528\) | 68.7557 | 2.99221 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | −23.4673 | −1.01935 | ||||||||
\(531\) | 18.8013 | 0.815907 | ||||||||
\(532\) | 3.82988 | 0.166046 | ||||||||
\(533\) | 13.9056 | 0.602320 | ||||||||
\(534\) | −15.5434 | −0.672629 | ||||||||
\(535\) | −2.47003 | −0.106789 | ||||||||
\(536\) | 7.87531 | 0.340161 | ||||||||
\(537\) | −46.6401 | −2.01267 | ||||||||
\(538\) | 36.1277 | 1.55757 | ||||||||
\(539\) | −34.0957 | −1.46860 | ||||||||
\(540\) | −1.24861 | −0.0537317 | ||||||||
\(541\) | 21.3786 | 0.919139 | 0.459569 | − | 0.888142i | \(-0.348004\pi\) | ||||
0.459569 | + | 0.888142i | \(0.348004\pi\) | |||||||
\(542\) | 1.27196 | 0.0546353 | ||||||||
\(543\) | 2.59276 | 0.111266 | ||||||||
\(544\) | 19.3651 | 0.830274 | ||||||||
\(545\) | −4.49722 | −0.192640 | ||||||||
\(546\) | −8.75304 | −0.374595 | ||||||||
\(547\) | 7.28543 | 0.311502 | 0.155751 | − | 0.987796i | \(-0.450220\pi\) | ||||
0.155751 | + | 0.987796i | \(0.450220\pi\) | |||||||
\(548\) | −12.5214 | −0.534887 | ||||||||
\(549\) | −30.3094 | −1.29357 | ||||||||
\(550\) | −9.12311 | −0.389011 | ||||||||
\(551\) | −12.6890 | −0.540571 | ||||||||
\(552\) | 4.91056 | 0.209007 | ||||||||
\(553\) | −11.3020 | −0.480610 | ||||||||
\(554\) | 13.9000 | 0.590556 | ||||||||
\(555\) | −19.0251 | −0.807571 | ||||||||
\(556\) | 15.9289 | 0.675535 | ||||||||
\(557\) | 41.4101 | 1.75460 | 0.877301 | − | 0.479941i | \(-0.159342\pi\) | ||||
0.877301 | + | 0.479941i | \(0.159342\pi\) | |||||||
\(558\) | −40.2285 | −1.70301 | ||||||||
\(559\) | −4.68571 | −0.198184 | ||||||||
\(560\) | 4.08089 | 0.172449 | ||||||||
\(561\) | −58.0406 | −2.45048 | ||||||||
\(562\) | −25.3603 | −1.06976 | ||||||||
\(563\) | 21.5210 | 0.907002 | 0.453501 | − | 0.891256i | \(-0.350175\pi\) | ||||
0.453501 | + | 0.891256i | \(0.350175\pi\) | |||||||
\(564\) | 20.7578 | 0.874062 | ||||||||
\(565\) | 6.30407 | 0.265214 | ||||||||
\(566\) | 39.6664 | 1.66730 | ||||||||
\(567\) | 5.73322 | 0.240773 | ||||||||
\(568\) | −22.6070 | −0.948568 | ||||||||
\(569\) | 21.9645 | 0.920801 | 0.460401 | − | 0.887711i | \(-0.347706\pi\) | ||||
0.460401 | + | 0.887711i | \(0.347706\pi\) | |||||||
\(570\) | −23.3693 | −0.978833 | ||||||||
\(571\) | −24.4924 | −1.02498 | −0.512488 | − | 0.858694i | \(-0.671276\pi\) | ||||
−0.512488 | + | 0.858694i | \(0.671276\pi\) | |||||||
\(572\) | 11.5199 | 0.481670 | ||||||||
\(573\) | 33.6155 | 1.40431 | ||||||||
\(574\) | 7.82925 | 0.326786 | ||||||||
\(575\) | −1.00000 | −0.0417029 | ||||||||
\(576\) | 7.72158 | 0.321732 | ||||||||
\(577\) | −10.0159 | −0.416969 | −0.208484 | − | 0.978026i | \(-0.566853\pi\) | ||||
−0.208484 | + | 0.978026i | \(0.566853\pi\) | |||||||
\(578\) | −1.17044 | −0.0486838 | ||||||||
\(579\) | 54.6070 | 2.26939 | ||||||||
\(580\) | 2.04461 | 0.0848980 | ||||||||
\(581\) | −2.72671 | −0.113123 | ||||||||
\(582\) | −39.1514 | −1.62288 | ||||||||
\(583\) | 74.6488 | 3.09164 | ||||||||
\(584\) | −20.0589 | −0.830043 | ||||||||
\(585\) | 8.77410 | 0.362764 | ||||||||
\(586\) | −25.3351 | −1.04658 | ||||||||
\(587\) | −5.64736 | −0.233092 | −0.116546 | − | 0.993185i | \(-0.537182\pi\) | ||||
−0.116546 | + | 0.993185i | \(0.537182\pi\) | |||||||
\(588\) | 14.0729 | 0.580358 | ||||||||
\(589\) | −35.9297 | −1.48046 | ||||||||
\(590\) | −8.94005 | −0.368056 | ||||||||
\(591\) | −67.5245 | −2.77759 | ||||||||
\(592\) | −37.0065 | −1.52096 | ||||||||
\(593\) | 12.4624 | 0.511769 | 0.255885 | − | 0.966707i | \(-0.417633\pi\) | ||||
0.255885 | + | 0.966707i | \(0.417633\pi\) | |||||||
\(594\) | 13.1231 | 0.538448 | ||||||||
\(595\) | −3.44491 | −0.141228 | ||||||||
\(596\) | 6.63005 | 0.271577 | ||||||||
\(597\) | 10.6590 | 0.436244 | ||||||||
\(598\) | 4.17210 | 0.170610 | ||||||||
\(599\) | 24.7985 | 1.01324 | 0.506619 | − | 0.862170i | \(-0.330895\pi\) | ||||
0.506619 | + | 0.862170i | \(0.330895\pi\) | |||||||
\(600\) | −4.91056 | −0.200473 | ||||||||
\(601\) | 9.10371 | 0.371348 | 0.185674 | − | 0.982611i | \(-0.440553\pi\) | ||||
0.185674 | + | 0.982611i | \(0.440553\pi\) | |||||||
\(602\) | −2.63818 | −0.107524 | ||||||||
\(603\) | 14.6312 | 0.595828 | ||||||||
\(604\) | −0.572503 | −0.0232948 | ||||||||
\(605\) | 18.0203 | 0.732630 | ||||||||
\(606\) | −52.5047 | −2.13286 | ||||||||
\(607\) | 20.6283 | 0.837279 | 0.418639 | − | 0.908153i | \(-0.362507\pi\) | ||||
0.418639 | + | 0.908153i | \(0.362507\pi\) | |||||||
\(608\) | −24.8024 | −1.00587 | ||||||||
\(609\) | 4.94176 | 0.200250 | ||||||||
\(610\) | 14.4122 | 0.583531 | ||||||||
\(611\) | −22.9989 | −0.930438 | ||||||||
\(612\) | 13.0032 | 0.525624 | ||||||||
\(613\) | −11.7514 | −0.474637 | −0.237318 | − | 0.971432i | \(-0.576268\pi\) | ||||
−0.237318 | + | 0.971432i | \(0.576268\pi\) | |||||||
\(614\) | 32.4924 | 1.31129 | ||||||||
\(615\) | −14.4588 | −0.583033 | ||||||||
\(616\) | −8.45822 | −0.340792 | ||||||||
\(617\) | 0.462764 | 0.0186302 | 0.00931510 | − | 0.999957i | \(-0.497035\pi\) | ||||
0.00931510 | + | 0.999957i | \(0.497035\pi\) | |||||||
\(618\) | −16.5020 | −0.663809 | ||||||||
\(619\) | −21.7183 | −0.872933 | −0.436467 | − | 0.899720i | \(-0.643770\pi\) | ||||
−0.436467 | + | 0.899720i | \(0.643770\pi\) | |||||||
\(620\) | 5.78943 | 0.232509 | ||||||||
\(621\) | 1.43845 | 0.0577229 | ||||||||
\(622\) | 32.9114 | 1.31963 | ||||||||
\(623\) | 2.93462 | 0.117573 | ||||||||
\(624\) | 31.4428 | 1.25872 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 35.4454 | 1.41668 | ||||||||
\(627\) | 74.3371 | 2.96874 | ||||||||
\(628\) | 3.42188 | 0.136548 | ||||||||
\(629\) | 31.2393 | 1.24559 | ||||||||
\(630\) | 4.94005 | 0.196816 | ||||||||
\(631\) | −4.18369 | −0.166550 | −0.0832750 | − | 0.996527i | \(-0.526538\pi\) | ||||
−0.0832750 | + | 0.996527i | \(0.526538\pi\) | |||||||
\(632\) | 26.4534 | 1.05226 | ||||||||
\(633\) | 40.3223 | 1.60267 | ||||||||
\(634\) | −18.2971 | −0.726670 | ||||||||
\(635\) | −0.910558 | −0.0361344 | ||||||||
\(636\) | −30.8112 | −1.22174 | ||||||||
\(637\) | −15.5923 | −0.617791 | ||||||||
\(638\) | −21.4892 | −0.850766 | ||||||||
\(639\) | −42.0005 | −1.66151 | ||||||||
\(640\) | −12.8798 | −0.509118 | ||||||||
\(641\) | −13.6535 | −0.539279 | −0.269640 | − | 0.962961i | \(-0.586905\pi\) | ||||
−0.269640 | + | 0.962961i | \(0.586905\pi\) | |||||||
\(642\) | −10.7151 | −0.422892 | ||||||||
\(643\) | 39.5583 | 1.56003 | 0.780014 | − | 0.625763i | \(-0.215212\pi\) | ||||
0.780014 | + | 0.625763i | \(0.215212\pi\) | |||||||
\(644\) | 0.710942 | 0.0280150 | ||||||||
\(645\) | 4.87209 | 0.191838 | ||||||||
\(646\) | 38.3725 | 1.50975 | ||||||||
\(647\) | 9.12674 | 0.358809 | 0.179405 | − | 0.983775i | \(-0.442583\pi\) | ||||
0.179405 | + | 0.983775i | \(0.442583\pi\) | |||||||
\(648\) | −13.4192 | −0.527155 | ||||||||
\(649\) | 28.4380 | 1.11629 | ||||||||
\(650\) | −4.17210 | −0.163643 | ||||||||
\(651\) | 13.9929 | 0.548423 | ||||||||
\(652\) | −3.29884 | −0.129192 | ||||||||
\(653\) | 0.745239 | 0.0291634 | 0.0145817 | − | 0.999894i | \(-0.495358\pi\) | ||||
0.0145817 | + | 0.999894i | \(0.495358\pi\) | |||||||
\(654\) | −19.5092 | −0.762870 | ||||||||
\(655\) | 18.6070 | 0.727035 | ||||||||
\(656\) | −28.1243 | −1.09807 | ||||||||
\(657\) | −37.2665 | −1.45391 | ||||||||
\(658\) | −12.9490 | −0.504805 | ||||||||
\(659\) | −33.6285 | −1.30998 | −0.654989 | − | 0.755638i | \(-0.727327\pi\) | ||||
−0.654989 | + | 0.755638i | \(0.727327\pi\) | |||||||
\(660\) | −11.9781 | −0.466247 | ||||||||
\(661\) | 22.0000 | 0.855701 | 0.427850 | − | 0.903850i | \(-0.359271\pi\) | ||||
0.427850 | + | 0.903850i | \(0.359271\pi\) | |||||||
\(662\) | −38.5494 | −1.49827 | ||||||||
\(663\) | −26.5426 | −1.03083 | ||||||||
\(664\) | 6.38213 | 0.247675 | ||||||||
\(665\) | 4.41216 | 0.171096 | ||||||||
\(666\) | −44.7976 | −1.73587 | ||||||||
\(667\) | −2.35547 | −0.0912042 | ||||||||
\(668\) | −1.94977 | −0.0754390 | ||||||||
\(669\) | −0.205587 | −0.00794846 | ||||||||
\(670\) | −6.95715 | −0.268778 | ||||||||
\(671\) | −45.8446 | −1.76981 | ||||||||
\(672\) | 9.65933 | 0.372617 | ||||||||
\(673\) | 19.5641 | 0.754142 | 0.377071 | − | 0.926184i | \(-0.376931\pi\) | ||||
0.377071 | + | 0.926184i | \(0.376931\pi\) | |||||||
\(674\) | 5.03805 | 0.194058 | ||||||||
\(675\) | −1.43845 | −0.0553659 | ||||||||
\(676\) | −6.01619 | −0.231392 | ||||||||
\(677\) | −12.7412 | −0.489685 | −0.244843 | − | 0.969563i | \(-0.578736\pi\) | ||||
−0.244843 | + | 0.969563i | \(0.578736\pi\) | |||||||
\(678\) | 27.3474 | 1.05027 | ||||||||
\(679\) | 7.39185 | 0.283673 | ||||||||
\(680\) | 8.06316 | 0.309208 | ||||||||
\(681\) | 72.9287 | 2.79464 | ||||||||
\(682\) | −60.8479 | −2.32998 | ||||||||
\(683\) | −12.5186 | −0.479010 | −0.239505 | − | 0.970895i | \(-0.576985\pi\) | ||||
−0.239505 | + | 0.970895i | \(0.576985\pi\) | |||||||
\(684\) | −16.6542 | −0.636790 | ||||||||
\(685\) | −14.4251 | −0.551155 | ||||||||
\(686\) | −18.4883 | −0.705885 | ||||||||
\(687\) | 1.57010 | 0.0599032 | ||||||||
\(688\) | 9.47691 | 0.361304 | ||||||||
\(689\) | 34.1377 | 1.30054 | ||||||||
\(690\) | −4.33805 | −0.165147 | ||||||||
\(691\) | 3.70356 | 0.140890 | 0.0704451 | − | 0.997516i | \(-0.477558\pi\) | ||||
0.0704451 | + | 0.997516i | \(0.477558\pi\) | |||||||
\(692\) | −11.6162 | −0.441580 | ||||||||
\(693\) | −15.7142 | −0.596931 | ||||||||
\(694\) | −59.9549 | −2.27586 | ||||||||
\(695\) | 18.3507 | 0.696081 | ||||||||
\(696\) | −11.5667 | −0.438434 | ||||||||
\(697\) | 23.7414 | 0.899268 | ||||||||
\(698\) | −38.0735 | −1.44110 | ||||||||
\(699\) | −9.72259 | −0.367742 | ||||||||
\(700\) | −0.710942 | −0.0268711 | ||||||||
\(701\) | 12.6388 | 0.477361 | 0.238681 | − | 0.971098i | \(-0.423285\pi\) | ||||
0.238681 | + | 0.971098i | \(0.423285\pi\) | |||||||
\(702\) | 6.00135 | 0.226506 | ||||||||
\(703\) | −40.0106 | −1.50903 | ||||||||
\(704\) | 11.6793 | 0.440181 | ||||||||
\(705\) | 23.9138 | 0.900645 | ||||||||
\(706\) | −10.6362 | −0.400299 | ||||||||
\(707\) | 9.91297 | 0.372816 | ||||||||
\(708\) | −11.7378 | −0.441132 | ||||||||
\(709\) | 21.5978 | 0.811122 | 0.405561 | − | 0.914068i | \(-0.367076\pi\) | ||||
0.405561 | + | 0.914068i | \(0.367076\pi\) | |||||||
\(710\) | 19.9713 | 0.749510 | ||||||||
\(711\) | 49.1466 | 1.84314 | ||||||||
\(712\) | −6.86876 | −0.257418 | ||||||||
\(713\) | −6.66964 | −0.249780 | ||||||||
\(714\) | −14.9442 | −0.559273 | ||||||||
\(715\) | 13.2713 | 0.496319 | ||||||||
\(716\) | 15.8048 | 0.590654 | ||||||||
\(717\) | −54.0791 | −2.01962 | ||||||||
\(718\) | −12.4593 | −0.464977 | ||||||||
\(719\) | −31.8418 | −1.18750 | −0.593749 | − | 0.804650i | \(-0.702353\pi\) | ||||
−0.593749 | + | 0.804650i | \(0.702353\pi\) | |||||||
\(720\) | −17.7457 | −0.661344 | ||||||||
\(721\) | 3.11561 | 0.116031 | ||||||||
\(722\) | −16.9697 | −0.631545 | ||||||||
\(723\) | 1.98290 | 0.0737448 | ||||||||
\(724\) | −0.878601 | −0.0326530 | ||||||||
\(725\) | 2.35547 | 0.0874800 | ||||||||
\(726\) | 78.1731 | 2.90128 | ||||||||
\(727\) | −32.0507 | −1.18870 | −0.594348 | − | 0.804208i | \(-0.702590\pi\) | ||||
−0.594348 | + | 0.804208i | \(0.702590\pi\) | |||||||
\(728\) | −3.86804 | −0.143359 | ||||||||
\(729\) | −35.9848 | −1.33277 | ||||||||
\(730\) | 17.7203 | 0.655858 | ||||||||
\(731\) | −8.00000 | −0.295891 | ||||||||
\(732\) | 18.9223 | 0.699389 | ||||||||
\(733\) | −35.9202 | −1.32674 | −0.663372 | − | 0.748290i | \(-0.730875\pi\) | ||||
−0.663372 | + | 0.748290i | \(0.730875\pi\) | |||||||
\(734\) | 1.50214 | 0.0554451 | ||||||||
\(735\) | 16.2125 | 0.598009 | ||||||||
\(736\) | −4.60408 | −0.169709 | ||||||||
\(737\) | 22.1305 | 0.815187 | ||||||||
\(738\) | −34.0454 | −1.25323 | ||||||||
\(739\) | 1.74252 | 0.0640997 | 0.0320498 | − | 0.999486i | \(-0.489796\pi\) | ||||
0.0320498 | + | 0.999486i | \(0.489796\pi\) | |||||||
\(740\) | 6.44700 | 0.236996 | ||||||||
\(741\) | 33.9952 | 1.24884 | ||||||||
\(742\) | 19.2205 | 0.705605 | ||||||||
\(743\) | −3.80402 | −0.139556 | −0.0697779 | − | 0.997563i | \(-0.522229\pi\) | ||||
−0.0697779 | + | 0.997563i | \(0.522229\pi\) | |||||||
\(744\) | −32.7517 | −1.20073 | ||||||||
\(745\) | 7.63806 | 0.279837 | ||||||||
\(746\) | 24.7735 | 0.907021 | ||||||||
\(747\) | 11.8571 | 0.433828 | ||||||||
\(748\) | 19.6681 | 0.719137 | ||||||||
\(749\) | 2.02303 | 0.0739199 | ||||||||
\(750\) | 4.33805 | 0.158403 | ||||||||
\(751\) | 22.3046 | 0.813905 | 0.406953 | − | 0.913449i | \(-0.366591\pi\) | ||||
0.406953 | + | 0.913449i | \(0.366591\pi\) | |||||||
\(752\) | 46.5157 | 1.69625 | ||||||||
\(753\) | 43.0447 | 1.56864 | ||||||||
\(754\) | −9.82726 | −0.357888 | ||||||||
\(755\) | −0.659545 | −0.0240033 | ||||||||
\(756\) | 1.02265 | 0.0371935 | ||||||||
\(757\) | −34.3973 | −1.25019 | −0.625095 | − | 0.780549i | \(-0.714940\pi\) | ||||
−0.625095 | + | 0.780549i | \(0.714940\pi\) | |||||||
\(758\) | 55.0705 | 2.00025 | ||||||||
\(759\) | 13.7992 | 0.500880 | ||||||||
\(760\) | −10.3271 | −0.374603 | ||||||||
\(761\) | −28.1069 | −1.01888 | −0.509438 | − | 0.860508i | \(-0.670147\pi\) | ||||
−0.509438 | + | 0.860508i | \(0.670147\pi\) | |||||||
\(762\) | −3.95005 | −0.143095 | ||||||||
\(763\) | 3.68337 | 0.133347 | ||||||||
\(764\) | −11.3912 | −0.412120 | ||||||||
\(765\) | 14.9802 | 0.541610 | ||||||||
\(766\) | −36.9855 | −1.33634 | ||||||||
\(767\) | 13.0050 | 0.469585 | ||||||||
\(768\) | −44.7661 | −1.61536 | ||||||||
\(769\) | 5.49230 | 0.198058 | 0.0990288 | − | 0.995085i | \(-0.468426\pi\) | ||||
0.0990288 | + | 0.995085i | \(0.468426\pi\) | |||||||
\(770\) | 7.47211 | 0.269276 | ||||||||
\(771\) | 13.1261 | 0.472725 | ||||||||
\(772\) | −18.5045 | −0.665993 | ||||||||
\(773\) | 27.5678 | 0.991543 | 0.495772 | − | 0.868453i | \(-0.334885\pi\) | ||||
0.495772 | + | 0.868453i | \(0.334885\pi\) | |||||||
\(774\) | 11.4721 | 0.412356 | ||||||||
\(775\) | 6.66964 | 0.239581 | ||||||||
\(776\) | −17.3014 | −0.621083 | ||||||||
\(777\) | 15.5822 | 0.559007 | ||||||||
\(778\) | 25.6552 | 0.919782 | ||||||||
\(779\) | −30.4074 | −1.08946 | ||||||||
\(780\) | −5.47772 | −0.196134 | ||||||||
\(781\) | −63.5281 | −2.27322 | ||||||||
\(782\) | 7.12311 | 0.254722 | ||||||||
\(783\) | −3.38822 | −0.121085 | ||||||||
\(784\) | 31.5357 | 1.12628 | ||||||||
\(785\) | 3.94214 | 0.140701 | ||||||||
\(786\) | 80.7181 | 2.87912 | ||||||||
\(787\) | 26.7316 | 0.952880 | 0.476440 | − | 0.879207i | \(-0.341927\pi\) | ||||
0.476440 | + | 0.879207i | \(0.341927\pi\) | |||||||
\(788\) | 22.8819 | 0.815133 | ||||||||
\(789\) | −17.8593 | −0.635807 | ||||||||
\(790\) | −23.3693 | −0.831443 | ||||||||
\(791\) | −5.16324 | −0.183584 | ||||||||
\(792\) | 36.7805 | 1.30694 | ||||||||
\(793\) | −20.9653 | −0.744499 | ||||||||
\(794\) | 13.0442 | 0.462921 | ||||||||
\(795\) | −35.4956 | −1.25890 | ||||||||
\(796\) | −3.61199 | −0.128024 | ||||||||
\(797\) | −34.3017 | −1.21503 | −0.607515 | − | 0.794308i | \(-0.707833\pi\) | ||||
−0.607515 | + | 0.794308i | \(0.707833\pi\) | |||||||
\(798\) | 19.1402 | 0.677556 | ||||||||
\(799\) | −39.2665 | −1.38915 | ||||||||
\(800\) | 4.60408 | 0.162779 | ||||||||
\(801\) | −12.7612 | −0.450894 | ||||||||
\(802\) | 40.2114 | 1.41991 | ||||||||
\(803\) | −56.3677 | −1.98917 | ||||||||
\(804\) | −9.13433 | −0.322143 | ||||||||
\(805\) | 0.819031 | 0.0288671 | ||||||||
\(806\) | −27.8264 | −0.980144 | ||||||||
\(807\) | 54.6451 | 1.92360 | ||||||||
\(808\) | −23.2023 | −0.816254 | ||||||||
\(809\) | −25.9575 | −0.912618 | −0.456309 | − | 0.889821i | \(-0.650829\pi\) | ||||
−0.456309 | + | 0.889821i | \(0.650829\pi\) | |||||||
\(810\) | 11.8547 | 0.416531 | ||||||||
\(811\) | −25.2252 | −0.885777 | −0.442889 | − | 0.896577i | \(-0.646046\pi\) | ||||
−0.442889 | + | 0.896577i | \(0.646046\pi\) | |||||||
\(812\) | −1.67460 | −0.0587670 | ||||||||
\(813\) | 1.92391 | 0.0674744 | ||||||||
\(814\) | −67.7589 | −2.37495 | ||||||||
\(815\) | −3.80038 | −0.133122 | ||||||||
\(816\) | 53.6829 | 1.87928 | ||||||||
\(817\) | 10.2462 | 0.358470 | ||||||||
\(818\) | −17.3413 | −0.606323 | ||||||||
\(819\) | −7.18626 | −0.251108 | ||||||||
\(820\) | 4.89961 | 0.171102 | ||||||||
\(821\) | 25.2761 | 0.882143 | 0.441071 | − | 0.897472i | \(-0.354599\pi\) | ||||
0.441071 | + | 0.897472i | \(0.354599\pi\) | |||||||
\(822\) | −62.5768 | −2.18262 | ||||||||
\(823\) | −22.0337 | −0.768045 | −0.384023 | − | 0.923324i | \(-0.625462\pi\) | ||||
−0.384023 | + | 0.923324i | \(0.625462\pi\) | |||||||
\(824\) | −7.29239 | −0.254042 | ||||||||
\(825\) | −13.7992 | −0.480427 | ||||||||
\(826\) | 7.32218 | 0.254771 | ||||||||
\(827\) | −16.0531 | −0.558220 | −0.279110 | − | 0.960259i | \(-0.590039\pi\) | ||||
−0.279110 | + | 0.960259i | \(0.590039\pi\) | |||||||
\(828\) | −3.09153 | −0.107438 | ||||||||
\(829\) | −20.5251 | −0.712865 | −0.356432 | − | 0.934321i | \(-0.616007\pi\) | ||||
−0.356432 | + | 0.934321i | \(0.616007\pi\) | |||||||
\(830\) | −5.63806 | −0.195700 | ||||||||
\(831\) | 21.0246 | 0.729334 | ||||||||
\(832\) | 5.34109 | 0.185169 | ||||||||
\(833\) | −26.6211 | −0.922366 | ||||||||
\(834\) | 79.6062 | 2.75654 | ||||||||
\(835\) | −2.24621 | −0.0777333 | ||||||||
\(836\) | −25.1904 | −0.871229 | ||||||||
\(837\) | −9.59393 | −0.331615 | ||||||||
\(838\) | 16.9052 | 0.583981 | ||||||||
\(839\) | 43.0284 | 1.48551 | 0.742753 | − | 0.669565i | \(-0.233519\pi\) | ||||
0.742753 | + | 0.669565i | \(0.233519\pi\) | |||||||
\(840\) | 4.02190 | 0.138769 | ||||||||
\(841\) | −23.4518 | −0.808681 | ||||||||
\(842\) | 29.2082 | 1.00658 | ||||||||
\(843\) | −38.3590 | −1.32115 | ||||||||
\(844\) | −13.6639 | −0.470332 | ||||||||
\(845\) | −6.93087 | −0.238429 | ||||||||
\(846\) | 56.3087 | 1.93593 | ||||||||
\(847\) | −14.7592 | −0.507132 | ||||||||
\(848\) | −69.0440 | −2.37098 | ||||||||
\(849\) | 59.9977 | 2.05911 | ||||||||
\(850\) | −7.12311 | −0.244321 | ||||||||
\(851\) | −7.42718 | −0.254600 | ||||||||
\(852\) | 26.2212 | 0.898322 | ||||||||
\(853\) | 29.8203 | 1.02103 | 0.510513 | − | 0.859870i | \(-0.329455\pi\) | ||||
0.510513 | + | 0.859870i | \(0.329455\pi\) | |||||||
\(854\) | −11.8040 | −0.403925 | ||||||||
\(855\) | −19.1863 | −0.656156 | ||||||||
\(856\) | −4.73510 | −0.161842 | ||||||||
\(857\) | −20.4465 | −0.698438 | −0.349219 | − | 0.937041i | \(-0.613553\pi\) | ||||
−0.349219 | + | 0.937041i | \(0.613553\pi\) | |||||||
\(858\) | 57.5717 | 1.96547 | ||||||||
\(859\) | 50.6000 | 1.72645 | 0.863224 | − | 0.504820i | \(-0.168441\pi\) | ||||
0.863224 | + | 0.504820i | \(0.168441\pi\) | |||||||
\(860\) | −1.65100 | −0.0562985 | ||||||||
\(861\) | 11.8422 | 0.403580 | ||||||||
\(862\) | 5.34099 | 0.181915 | ||||||||
\(863\) | 28.1900 | 0.959599 | 0.479800 | − | 0.877378i | \(-0.340709\pi\) | ||||
0.479800 | + | 0.877378i | \(0.340709\pi\) | |||||||
\(864\) | −6.62273 | −0.225310 | ||||||||
\(865\) | −13.3822 | −0.455010 | ||||||||
\(866\) | 44.2574 | 1.50393 | ||||||||
\(867\) | −1.77035 | −0.0601243 | ||||||||
\(868\) | −4.74173 | −0.160945 | ||||||||
\(869\) | 74.3371 | 2.52171 | ||||||||
\(870\) | 10.2182 | 0.346428 | ||||||||
\(871\) | 10.1205 | 0.342921 | ||||||||
\(872\) | −8.62128 | −0.291954 | ||||||||
\(873\) | −32.1434 | −1.08789 | ||||||||
\(874\) | −9.12311 | −0.308594 | ||||||||
\(875\) | −0.819031 | −0.0276883 | ||||||||
\(876\) | 23.2657 | 0.786076 | ||||||||
\(877\) | 3.25176 | 0.109804 | 0.0549021 | − | 0.998492i | \(-0.482515\pi\) | ||||
0.0549021 | + | 0.998492i | \(0.482515\pi\) | |||||||
\(878\) | −3.52495 | −0.118961 | ||||||||
\(879\) | −38.3208 | −1.29253 | ||||||||
\(880\) | −26.8414 | −0.904824 | ||||||||
\(881\) | 40.4455 | 1.36264 | 0.681322 | − | 0.731984i | \(-0.261405\pi\) | ||||
0.681322 | + | 0.731984i | \(0.261405\pi\) | |||||||
\(882\) | 38.1750 | 1.28542 | ||||||||
\(883\) | −12.4178 | −0.417893 | −0.208947 | − | 0.977927i | \(-0.567004\pi\) | ||||
−0.208947 | + | 0.977927i | \(0.567004\pi\) | |||||||
\(884\) | 8.99445 | 0.302516 | ||||||||
\(885\) | −13.5223 | −0.454548 | ||||||||
\(886\) | 20.7963 | 0.698665 | ||||||||
\(887\) | −13.2199 | −0.443882 | −0.221941 | − | 0.975060i | \(-0.571239\pi\) | ||||
−0.221941 | + | 0.975060i | \(0.571239\pi\) | |||||||
\(888\) | −36.4716 | −1.22391 | ||||||||
\(889\) | 0.745775 | 0.0250125 | ||||||||
\(890\) | 6.06796 | 0.203398 | ||||||||
\(891\) | −37.7094 | −1.26331 | ||||||||
\(892\) | 0.0696668 | 0.00233262 | ||||||||
\(893\) | 50.2916 | 1.68295 | ||||||||
\(894\) | 33.1343 | 1.10818 | ||||||||
\(895\) | 18.2077 | 0.608618 | ||||||||
\(896\) | 10.5490 | 0.352416 | ||||||||
\(897\) | 6.31054 | 0.210703 | ||||||||
\(898\) | 32.8195 | 1.09520 | ||||||||
\(899\) | 15.7101 | 0.523963 | ||||||||
\(900\) | 3.09153 | 0.103051 | ||||||||
\(901\) | 58.2840 | 1.94172 | ||||||||
\(902\) | −51.4956 | −1.71462 | ||||||||
\(903\) | −3.99040 | −0.132792 | ||||||||
\(904\) | 12.0851 | 0.401943 | ||||||||
\(905\) | −1.01218 | −0.0336460 | ||||||||
\(906\) | −2.86114 | −0.0950551 | ||||||||
\(907\) | −58.2386 | −1.93378 | −0.966890 | − | 0.255193i | \(-0.917861\pi\) | ||||
−0.966890 | + | 0.255193i | \(0.917861\pi\) | |||||||
\(908\) | −24.7132 | −0.820136 | ||||||||
\(909\) | −43.1065 | −1.42975 | ||||||||
\(910\) | 3.41708 | 0.113275 | ||||||||
\(911\) | −46.5977 | −1.54385 | −0.771925 | − | 0.635714i | \(-0.780706\pi\) | ||||
−0.771925 | + | 0.635714i | \(0.780706\pi\) | |||||||
\(912\) | −68.7557 | −2.27673 | ||||||||
\(913\) | 17.9345 | 0.593545 | ||||||||
\(914\) | 4.50119 | 0.148886 | ||||||||
\(915\) | 21.7992 | 0.720660 | ||||||||
\(916\) | −0.532057 | −0.0175797 | ||||||||
\(917\) | −15.2397 | −0.503259 | ||||||||
\(918\) | 10.2462 | 0.338175 | ||||||||
\(919\) | 20.1386 | 0.664312 | 0.332156 | − | 0.943225i | \(-0.392224\pi\) | ||||
0.332156 | + | 0.943225i | \(0.392224\pi\) | |||||||
\(920\) | −1.91702 | −0.0632024 | ||||||||
\(921\) | 49.1466 | 1.61944 | ||||||||
\(922\) | −14.3852 | −0.473751 | ||||||||
\(923\) | −29.0521 | −0.956263 | ||||||||
\(924\) | 9.81044 | 0.322740 | ||||||||
\(925\) | 7.42718 | 0.244204 | ||||||||
\(926\) | −25.6745 | −0.843717 | ||||||||
\(927\) | −13.5482 | −0.444981 | ||||||||
\(928\) | 10.8448 | 0.355997 | ||||||||
\(929\) | −1.01385 | −0.0332632 | −0.0166316 | − | 0.999862i | \(-0.505294\pi\) | ||||
−0.0166316 | + | 0.999862i | \(0.505294\pi\) | |||||||
\(930\) | 28.9333 | 0.948759 | ||||||||
\(931\) | 34.0957 | 1.11744 | ||||||||
\(932\) | 3.29467 | 0.107921 | ||||||||
\(933\) | 49.7803 | 1.62973 | ||||||||
\(934\) | 21.5144 | 0.703974 | ||||||||
\(935\) | 22.6584 | 0.741008 | ||||||||
\(936\) | 16.8202 | 0.549784 | ||||||||
\(937\) | 32.5904 | 1.06468 | 0.532341 | − | 0.846530i | \(-0.321312\pi\) | ||||
0.532341 | + | 0.846530i | \(0.321312\pi\) | |||||||
\(938\) | 5.69813 | 0.186050 | ||||||||
\(939\) | 53.6132 | 1.74960 | ||||||||
\(940\) | −8.10361 | −0.264310 | ||||||||
\(941\) | −1.01848 | −0.0332017 | −0.0166008 | − | 0.999862i | \(-0.505284\pi\) | ||||
−0.0166008 | + | 0.999862i | \(0.505284\pi\) | |||||||
\(942\) | 17.1012 | 0.557187 | ||||||||
\(943\) | −5.64453 | −0.183811 | ||||||||
\(944\) | −26.3029 | −0.856085 | ||||||||
\(945\) | 1.17813 | 0.0383247 | ||||||||
\(946\) | 17.3522 | 0.564169 | ||||||||
\(947\) | 0.212548 | 0.00690688 | 0.00345344 | − | 0.999994i | \(-0.498901\pi\) | ||||
0.00345344 | + | 0.999994i | \(0.498901\pi\) | |||||||
\(948\) | −30.6825 | −0.996522 | ||||||||
\(949\) | −25.7776 | −0.836777 | ||||||||
\(950\) | 9.12311 | 0.295993 | ||||||||
\(951\) | −27.6754 | −0.897435 | ||||||||
\(952\) | −6.60398 | −0.214036 | ||||||||
\(953\) | 47.2067 | 1.52917 | 0.764587 | − | 0.644520i | \(-0.222943\pi\) | ||||
0.764587 | + | 0.644520i | \(0.222943\pi\) | |||||||
\(954\) | −83.5801 | −2.70600 | ||||||||
\(955\) | −13.1231 | −0.424654 | ||||||||
\(956\) | 18.3257 | 0.592694 | ||||||||
\(957\) | −32.5036 | −1.05069 | ||||||||
\(958\) | 19.7602 | 0.638424 | ||||||||
\(959\) | 11.8146 | 0.381514 | ||||||||
\(960\) | −5.55354 | −0.179240 | ||||||||
\(961\) | 13.4841 | 0.434972 | ||||||||
\(962\) | −30.9870 | −0.999059 | ||||||||
\(963\) | −8.79713 | −0.283484 | ||||||||
\(964\) | −0.671941 | −0.0216418 | ||||||||
\(965\) | −21.3179 | −0.686248 | ||||||||
\(966\) | 3.55300 | 0.114316 | ||||||||
\(967\) | −23.7851 | −0.764878 | −0.382439 | − | 0.923981i | \(-0.624916\pi\) | ||||
−0.382439 | + | 0.923981i | \(0.624916\pi\) | |||||||
\(968\) | 34.5454 | 1.11033 | ||||||||
\(969\) | 58.0406 | 1.86453 | ||||||||
\(970\) | 15.2843 | 0.490748 | ||||||||
\(971\) | −47.7012 | −1.53081 | −0.765403 | − | 0.643552i | \(-0.777460\pi\) | ||||
−0.765403 | + | 0.643552i | \(0.777460\pi\) | |||||||
\(972\) | 19.3103 | 0.619379 | ||||||||
\(973\) | −15.0298 | −0.481832 | ||||||||
\(974\) | −53.8166 | −1.72439 | ||||||||
\(975\) | −6.31054 | −0.202099 | ||||||||
\(976\) | 42.4026 | 1.35727 | ||||||||
\(977\) | −5.04505 | −0.161405 | −0.0807027 | − | 0.996738i | \(-0.525716\pi\) | ||||
−0.0807027 | + | 0.996738i | \(0.525716\pi\) | |||||||
\(978\) | −16.4863 | −0.527173 | ||||||||
\(979\) | −19.3020 | −0.616894 | ||||||||
\(980\) | −5.49391 | −0.175497 | ||||||||
\(981\) | −16.0171 | −0.511387 | ||||||||
\(982\) | 10.4613 | 0.333833 | ||||||||
\(983\) | −3.52184 | −0.112329 | −0.0561647 | − | 0.998422i | \(-0.517887\pi\) | ||||
−0.0561647 | + | 0.998422i | \(0.517887\pi\) | |||||||
\(984\) | −27.7178 | −0.883611 | ||||||||
\(985\) | 26.3608 | 0.839924 | ||||||||
\(986\) | −16.7783 | −0.534329 | ||||||||
\(987\) | −19.5861 | −0.623433 | ||||||||
\(988\) | −11.5199 | −0.366496 | ||||||||
\(989\) | 1.90201 | 0.0604803 | ||||||||
\(990\) | −32.4924 | −1.03268 | ||||||||
\(991\) | 53.3794 | 1.69565 | 0.847826 | − | 0.530274i | \(-0.177911\pi\) | ||||
0.847826 | + | 0.530274i | \(0.177911\pi\) | |||||||
\(992\) | 30.7076 | 0.974967 | ||||||||
\(993\) | −58.3082 | −1.85035 | ||||||||
\(994\) | −16.3571 | −0.518817 | ||||||||
\(995\) | −4.16115 | −0.131917 | ||||||||
\(996\) | −7.40244 | −0.234555 | ||||||||
\(997\) | 55.2269 | 1.74905 | 0.874527 | − | 0.484978i | \(-0.161172\pi\) | ||||
0.874527 | + | 0.484978i | \(0.161172\pi\) | |||||||
\(998\) | 63.2378 | 2.00176 | ||||||||
\(999\) | −10.6836 | −0.338014 |
(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 | 115.2.a.c.1.1 | ✓ | 4 | |
3.2 | odd | 2 | 1035.2.a.o.1.4 | 4 | |||
4.3 | odd | 2 | 1840.2.a.u.1.3 | 4 | |||
5.2 | odd | 4 | 575.2.b.e.24.2 | 8 | |||
5.3 | odd | 4 | 575.2.b.e.24.7 | 8 | |||
5.4 | even | 2 | 575.2.a.h.1.4 | 4 | |||
7.6 | odd | 2 | 5635.2.a.v.1.1 | 4 | |||
8.3 | odd | 2 | 7360.2.a.cg.1.1 | 4 | |||
8.5 | even | 2 | 7360.2.a.cj.1.4 | 4 | |||
15.14 | odd | 2 | 5175.2.a.bx.1.1 | 4 | |||
20.19 | odd | 2 | 9200.2.a.cl.1.2 | 4 | |||
23.22 | odd | 2 | 2645.2.a.m.1.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
115.2.a.c.1.1 | ✓ | 4 | 1.1 | even | 1 | trivial | |
575.2.a.h.1.4 | 4 | 5.4 | even | 2 | |||
575.2.b.e.24.2 | 8 | 5.2 | odd | 4 | |||
575.2.b.e.24.7 | 8 | 5.3 | odd | 4 | |||
1035.2.a.o.1.4 | 4 | 3.2 | odd | 2 | |||
1840.2.a.u.1.3 | 4 | 4.3 | odd | 2 | |||
2645.2.a.m.1.1 | 4 | 23.22 | odd | 2 | |||
5175.2.a.bx.1.1 | 4 | 15.14 | odd | 2 | |||
5635.2.a.v.1.1 | 4 | 7.6 | odd | 2 | |||
7360.2.a.cg.1.1 | 4 | 8.3 | odd | 2 | |||
7360.2.a.cj.1.4 | 4 | 8.5 | even | 2 | |||
9200.2.a.cl.1.2 | 4 | 20.19 | odd | 2 |