Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4030,2,Mod(1,4030)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4030, 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("4030.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4030 = 2 \cdot 5 \cdot 13 \cdot 31 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4030.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(32.1797120146\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 14x^{6} - 6x^{5} + 54x^{4} + 46x^{3} - 32x^{2} - 43x - 11 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.7 | ||
Root | \(-2.55848\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4030.1 |
$q$-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 | ||||||||
\(3\) | 2.53701 | 1.46475 | 0.732373 | − | 0.680904i | \(-0.238413\pi\) | ||||
0.732373 | + | 0.680904i | \(0.238413\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 1.00000 | 0.447214 | ||||||||
\(6\) | −2.53701 | −1.03573 | ||||||||
\(7\) | 1.50878 | 0.570264 | 0.285132 | − | 0.958488i | \(-0.407963\pi\) | ||||
0.285132 | + | 0.958488i | \(0.407963\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 3.43644 | 1.14548 | ||||||||
\(10\) | −1.00000 | −0.316228 | ||||||||
\(11\) | 0.351489 | 0.105978 | 0.0529890 | − | 0.998595i | \(-0.483125\pi\) | ||||
0.0529890 | + | 0.998595i | \(0.483125\pi\) | |||||||
\(12\) | 2.53701 | 0.732373 | ||||||||
\(13\) | −1.00000 | −0.277350 | ||||||||
\(14\) | −1.50878 | −0.403238 | ||||||||
\(15\) | 2.53701 | 0.655054 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 2.31225 | 0.560802 | 0.280401 | − | 0.959883i | \(-0.409533\pi\) | ||||
0.280401 | + | 0.959883i | \(0.409533\pi\) | |||||||
\(18\) | −3.43644 | −0.809977 | ||||||||
\(19\) | 1.18952 | 0.272895 | 0.136448 | − | 0.990647i | \(-0.456431\pi\) | ||||
0.136448 | + | 0.990647i | \(0.456431\pi\) | |||||||
\(20\) | 1.00000 | 0.223607 | ||||||||
\(21\) | 3.82779 | 0.835292 | ||||||||
\(22\) | −0.351489 | −0.0749377 | ||||||||
\(23\) | 5.37024 | 1.11977 | 0.559887 | − | 0.828569i | \(-0.310845\pi\) | ||||
0.559887 | + | 0.828569i | \(0.310845\pi\) | |||||||
\(24\) | −2.53701 | −0.517866 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 1.00000 | 0.196116 | ||||||||
\(27\) | 1.10726 | 0.213091 | ||||||||
\(28\) | 1.50878 | 0.285132 | ||||||||
\(29\) | −0.355403 | −0.0659968 | −0.0329984 | − | 0.999455i | \(-0.510506\pi\) | ||||
−0.0329984 | + | 0.999455i | \(0.510506\pi\) | |||||||
\(30\) | −2.53701 | −0.463193 | ||||||||
\(31\) | −1.00000 | −0.179605 | ||||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 0.891733 | 0.155231 | ||||||||
\(34\) | −2.31225 | −0.396547 | ||||||||
\(35\) | 1.50878 | 0.255030 | ||||||||
\(36\) | 3.43644 | 0.572740 | ||||||||
\(37\) | 7.91157 | 1.30065 | 0.650327 | − | 0.759654i | \(-0.274632\pi\) | ||||
0.650327 | + | 0.759654i | \(0.274632\pi\) | |||||||
\(38\) | −1.18952 | −0.192966 | ||||||||
\(39\) | −2.53701 | −0.406247 | ||||||||
\(40\) | −1.00000 | −0.158114 | ||||||||
\(41\) | 9.73202 | 1.51989 | 0.759943 | − | 0.649990i | \(-0.225227\pi\) | ||||
0.759943 | + | 0.649990i | \(0.225227\pi\) | |||||||
\(42\) | −3.82779 | −0.590641 | ||||||||
\(43\) | −4.51150 | −0.687998 | −0.343999 | − | 0.938970i | \(-0.611782\pi\) | ||||
−0.343999 | + | 0.938970i | \(0.611782\pi\) | |||||||
\(44\) | 0.351489 | 0.0529890 | ||||||||
\(45\) | 3.43644 | 0.512274 | ||||||||
\(46\) | −5.37024 | −0.791799 | ||||||||
\(47\) | −9.03358 | −1.31768 | −0.658842 | − | 0.752282i | \(-0.728953\pi\) | ||||
−0.658842 | + | 0.752282i | \(0.728953\pi\) | |||||||
\(48\) | 2.53701 | 0.366186 | ||||||||
\(49\) | −4.72359 | −0.674799 | ||||||||
\(50\) | −1.00000 | −0.141421 | ||||||||
\(51\) | 5.86620 | 0.821432 | ||||||||
\(52\) | −1.00000 | −0.138675 | ||||||||
\(53\) | −4.72450 | −0.648960 | −0.324480 | − | 0.945893i | \(-0.605189\pi\) | ||||
−0.324480 | + | 0.945893i | \(0.605189\pi\) | |||||||
\(54\) | −1.10726 | −0.150678 | ||||||||
\(55\) | 0.351489 | 0.0473948 | ||||||||
\(56\) | −1.50878 | −0.201619 | ||||||||
\(57\) | 3.01784 | 0.399722 | ||||||||
\(58\) | 0.355403 | 0.0466668 | ||||||||
\(59\) | 4.09595 | 0.533247 | 0.266624 | − | 0.963801i | \(-0.414092\pi\) | ||||
0.266624 | + | 0.963801i | \(0.414092\pi\) | |||||||
\(60\) | 2.53701 | 0.327527 | ||||||||
\(61\) | 3.70865 | 0.474844 | 0.237422 | − | 0.971407i | \(-0.423698\pi\) | ||||
0.237422 | + | 0.971407i | \(0.423698\pi\) | |||||||
\(62\) | 1.00000 | 0.127000 | ||||||||
\(63\) | 5.18482 | 0.653226 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −1.00000 | −0.124035 | ||||||||
\(66\) | −0.891733 | −0.109765 | ||||||||
\(67\) | 11.6316 | 1.42103 | 0.710514 | − | 0.703683i | \(-0.248462\pi\) | ||||
0.710514 | + | 0.703683i | \(0.248462\pi\) | |||||||
\(68\) | 2.31225 | 0.280401 | ||||||||
\(69\) | 13.6244 | 1.64018 | ||||||||
\(70\) | −1.50878 | −0.180333 | ||||||||
\(71\) | −5.16704 | −0.613215 | −0.306607 | − | 0.951836i | \(-0.599194\pi\) | ||||
−0.306607 | + | 0.951836i | \(0.599194\pi\) | |||||||
\(72\) | −3.43644 | −0.404988 | ||||||||
\(73\) | 7.39342 | 0.865334 | 0.432667 | − | 0.901554i | \(-0.357573\pi\) | ||||
0.432667 | + | 0.901554i | \(0.357573\pi\) | |||||||
\(74\) | −7.91157 | −0.919701 | ||||||||
\(75\) | 2.53701 | 0.292949 | ||||||||
\(76\) | 1.18952 | 0.136448 | ||||||||
\(77\) | 0.530319 | 0.0604354 | ||||||||
\(78\) | 2.53701 | 0.287260 | ||||||||
\(79\) | −2.26348 | −0.254661 | −0.127331 | − | 0.991860i | \(-0.540641\pi\) | ||||
−0.127331 | + | 0.991860i | \(0.540641\pi\) | |||||||
\(80\) | 1.00000 | 0.111803 | ||||||||
\(81\) | −7.50020 | −0.833355 | ||||||||
\(82\) | −9.73202 | −1.07472 | ||||||||
\(83\) | −5.61797 | −0.616653 | −0.308326 | − | 0.951281i | \(-0.599769\pi\) | ||||
−0.308326 | + | 0.951281i | \(0.599769\pi\) | |||||||
\(84\) | 3.82779 | 0.417646 | ||||||||
\(85\) | 2.31225 | 0.250798 | ||||||||
\(86\) | 4.51150 | 0.486488 | ||||||||
\(87\) | −0.901663 | −0.0966685 | ||||||||
\(88\) | −0.351489 | −0.0374689 | ||||||||
\(89\) | 11.4134 | 1.20982 | 0.604911 | − | 0.796293i | \(-0.293209\pi\) | ||||
0.604911 | + | 0.796293i | \(0.293209\pi\) | |||||||
\(90\) | −3.43644 | −0.362233 | ||||||||
\(91\) | −1.50878 | −0.158163 | ||||||||
\(92\) | 5.37024 | 0.559887 | ||||||||
\(93\) | −2.53701 | −0.263076 | ||||||||
\(94\) | 9.03358 | 0.931743 | ||||||||
\(95\) | 1.18952 | 0.122043 | ||||||||
\(96\) | −2.53701 | −0.258933 | ||||||||
\(97\) | −14.5519 | −1.47752 | −0.738759 | − | 0.673969i | \(-0.764588\pi\) | ||||
−0.738759 | + | 0.673969i | \(0.764588\pi\) | |||||||
\(98\) | 4.72359 | 0.477155 | ||||||||
\(99\) | 1.20787 | 0.121396 | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | −10.3158 | −1.02646 | −0.513231 | − | 0.858251i | \(-0.671552\pi\) | ||||
−0.513231 | + | 0.858251i | \(0.671552\pi\) | |||||||
\(102\) | −5.86620 | −0.580840 | ||||||||
\(103\) | −1.85938 | −0.183210 | −0.0916049 | − | 0.995795i | \(-0.529200\pi\) | ||||
−0.0916049 | + | 0.995795i | \(0.529200\pi\) | |||||||
\(104\) | 1.00000 | 0.0980581 | ||||||||
\(105\) | 3.82779 | 0.373554 | ||||||||
\(106\) | 4.72450 | 0.458884 | ||||||||
\(107\) | 18.0261 | 1.74265 | 0.871324 | − | 0.490708i | \(-0.163262\pi\) | ||||
0.871324 | + | 0.490708i | \(0.163262\pi\) | |||||||
\(108\) | 1.10726 | 0.106546 | ||||||||
\(109\) | 19.1988 | 1.83891 | 0.919456 | − | 0.393192i | \(-0.128629\pi\) | ||||
0.919456 | + | 0.393192i | \(0.128629\pi\) | |||||||
\(110\) | −0.351489 | −0.0335132 | ||||||||
\(111\) | 20.0718 | 1.90513 | ||||||||
\(112\) | 1.50878 | 0.142566 | ||||||||
\(113\) | 16.7578 | 1.57644 | 0.788220 | − | 0.615394i | \(-0.211003\pi\) | ||||
0.788220 | + | 0.615394i | \(0.211003\pi\) | |||||||
\(114\) | −3.01784 | −0.282646 | ||||||||
\(115\) | 5.37024 | 0.500778 | ||||||||
\(116\) | −0.355403 | −0.0329984 | ||||||||
\(117\) | −3.43644 | −0.317699 | ||||||||
\(118\) | −4.09595 | −0.377063 | ||||||||
\(119\) | 3.48866 | 0.319805 | ||||||||
\(120\) | −2.53701 | −0.231597 | ||||||||
\(121\) | −10.8765 | −0.988769 | ||||||||
\(122\) | −3.70865 | −0.335766 | ||||||||
\(123\) | 24.6903 | 2.22625 | ||||||||
\(124\) | −1.00000 | −0.0898027 | ||||||||
\(125\) | 1.00000 | 0.0894427 | ||||||||
\(126\) | −5.18482 | −0.461901 | ||||||||
\(127\) | −13.6448 | −1.21078 | −0.605388 | − | 0.795930i | \(-0.706982\pi\) | ||||
−0.605388 | + | 0.795930i | \(0.706982\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −11.4457 | −1.00774 | ||||||||
\(130\) | 1.00000 | 0.0877058 | ||||||||
\(131\) | −8.03303 | −0.701849 | −0.350924 | − | 0.936404i | \(-0.614133\pi\) | ||||
−0.350924 | + | 0.936404i | \(0.614133\pi\) | |||||||
\(132\) | 0.891733 | 0.0776154 | ||||||||
\(133\) | 1.79473 | 0.155622 | ||||||||
\(134\) | −11.6316 | −1.00482 | ||||||||
\(135\) | 1.10726 | 0.0952974 | ||||||||
\(136\) | −2.31225 | −0.198273 | ||||||||
\(137\) | −17.7285 | −1.51465 | −0.757323 | − | 0.653040i | \(-0.773493\pi\) | ||||
−0.757323 | + | 0.653040i | \(0.773493\pi\) | |||||||
\(138\) | −13.6244 | −1.15978 | ||||||||
\(139\) | −0.0867283 | −0.00735620 | −0.00367810 | − | 0.999993i | \(-0.501171\pi\) | ||||
−0.00367810 | + | 0.999993i | \(0.501171\pi\) | |||||||
\(140\) | 1.50878 | 0.127515 | ||||||||
\(141\) | −22.9183 | −1.93007 | ||||||||
\(142\) | 5.16704 | 0.433608 | ||||||||
\(143\) | −0.351489 | −0.0293930 | ||||||||
\(144\) | 3.43644 | 0.286370 | ||||||||
\(145\) | −0.355403 | −0.0295146 | ||||||||
\(146\) | −7.39342 | −0.611884 | ||||||||
\(147\) | −11.9838 | −0.988408 | ||||||||
\(148\) | 7.91157 | 0.650327 | ||||||||
\(149\) | 2.85650 | 0.234014 | 0.117007 | − | 0.993131i | \(-0.462670\pi\) | ||||
0.117007 | + | 0.993131i | \(0.462670\pi\) | |||||||
\(150\) | −2.53701 | −0.207146 | ||||||||
\(151\) | 10.5015 | 0.854600 | 0.427300 | − | 0.904110i | \(-0.359465\pi\) | ||||
0.427300 | + | 0.904110i | \(0.359465\pi\) | |||||||
\(152\) | −1.18952 | −0.0964831 | ||||||||
\(153\) | 7.94589 | 0.642387 | ||||||||
\(154\) | −0.530319 | −0.0427343 | ||||||||
\(155\) | −1.00000 | −0.0803219 | ||||||||
\(156\) | −2.53701 | −0.203124 | ||||||||
\(157\) | 0.674228 | 0.0538092 | 0.0269046 | − | 0.999638i | \(-0.491435\pi\) | ||||
0.0269046 | + | 0.999638i | \(0.491435\pi\) | |||||||
\(158\) | 2.26348 | 0.180073 | ||||||||
\(159\) | −11.9861 | −0.950562 | ||||||||
\(160\) | −1.00000 | −0.0790569 | ||||||||
\(161\) | 8.10250 | 0.638567 | ||||||||
\(162\) | 7.50020 | 0.589271 | ||||||||
\(163\) | 11.8583 | 0.928815 | 0.464407 | − | 0.885622i | \(-0.346267\pi\) | ||||
0.464407 | + | 0.885622i | \(0.346267\pi\) | |||||||
\(164\) | 9.73202 | 0.759943 | ||||||||
\(165\) | 0.891733 | 0.0694213 | ||||||||
\(166\) | 5.61797 | 0.436039 | ||||||||
\(167\) | 22.2641 | 1.72285 | 0.861426 | − | 0.507884i | \(-0.169572\pi\) | ||||
0.861426 | + | 0.507884i | \(0.169572\pi\) | |||||||
\(168\) | −3.82779 | −0.295320 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | −2.31225 | −0.177341 | ||||||||
\(171\) | 4.08773 | 0.312596 | ||||||||
\(172\) | −4.51150 | −0.343999 | ||||||||
\(173\) | 11.2452 | 0.854960 | 0.427480 | − | 0.904025i | \(-0.359402\pi\) | ||||
0.427480 | + | 0.904025i | \(0.359402\pi\) | |||||||
\(174\) | 0.901663 | 0.0683549 | ||||||||
\(175\) | 1.50878 | 0.114053 | ||||||||
\(176\) | 0.351489 | 0.0264945 | ||||||||
\(177\) | 10.3915 | 0.781072 | ||||||||
\(178\) | −11.4134 | −0.855474 | ||||||||
\(179\) | 14.5315 | 1.08613 | 0.543067 | − | 0.839689i | \(-0.317263\pi\) | ||||
0.543067 | + | 0.839689i | \(0.317263\pi\) | |||||||
\(180\) | 3.43644 | 0.256137 | ||||||||
\(181\) | −7.28922 | −0.541804 | −0.270902 | − | 0.962607i | \(-0.587322\pi\) | ||||
−0.270902 | + | 0.962607i | \(0.587322\pi\) | |||||||
\(182\) | 1.50878 | 0.111838 | ||||||||
\(183\) | 9.40890 | 0.695526 | ||||||||
\(184\) | −5.37024 | −0.395900 | ||||||||
\(185\) | 7.91157 | 0.581670 | ||||||||
\(186\) | 2.53701 | 0.186023 | ||||||||
\(187\) | 0.812729 | 0.0594326 | ||||||||
\(188\) | −9.03358 | −0.658842 | ||||||||
\(189\) | 1.67060 | 0.121518 | ||||||||
\(190\) | −1.18952 | −0.0862971 | ||||||||
\(191\) | −3.20157 | −0.231658 | −0.115829 | − | 0.993269i | \(-0.536952\pi\) | ||||
−0.115829 | + | 0.993269i | \(0.536952\pi\) | |||||||
\(192\) | 2.53701 | 0.183093 | ||||||||
\(193\) | −17.2768 | −1.24361 | −0.621806 | − | 0.783172i | \(-0.713601\pi\) | ||||
−0.621806 | + | 0.783172i | \(0.713601\pi\) | |||||||
\(194\) | 14.5519 | 1.04476 | ||||||||
\(195\) | −2.53701 | −0.181679 | ||||||||
\(196\) | −4.72359 | −0.337399 | ||||||||
\(197\) | −11.8553 | −0.844654 | −0.422327 | − | 0.906443i | \(-0.638787\pi\) | ||||
−0.422327 | + | 0.906443i | \(0.638787\pi\) | |||||||
\(198\) | −1.20787 | −0.0858397 | ||||||||
\(199\) | −0.350989 | −0.0248809 | −0.0124405 | − | 0.999923i | \(-0.503960\pi\) | ||||
−0.0124405 | + | 0.999923i | \(0.503960\pi\) | |||||||
\(200\) | −1.00000 | −0.0707107 | ||||||||
\(201\) | 29.5096 | 2.08145 | ||||||||
\(202\) | 10.3158 | 0.725818 | ||||||||
\(203\) | −0.536225 | −0.0376356 | ||||||||
\(204\) | 5.86620 | 0.410716 | ||||||||
\(205\) | 9.73202 | 0.679714 | ||||||||
\(206\) | 1.85938 | 0.129549 | ||||||||
\(207\) | 18.4545 | 1.28268 | ||||||||
\(208\) | −1.00000 | −0.0693375 | ||||||||
\(209\) | 0.418104 | 0.0289209 | ||||||||
\(210\) | −3.82779 | −0.264143 | ||||||||
\(211\) | −22.3354 | −1.53763 | −0.768815 | − | 0.639471i | \(-0.779153\pi\) | ||||
−0.768815 | + | 0.639471i | \(0.779153\pi\) | |||||||
\(212\) | −4.72450 | −0.324480 | ||||||||
\(213\) | −13.1089 | −0.898204 | ||||||||
\(214\) | −18.0261 | −1.23224 | ||||||||
\(215\) | −4.51150 | −0.307682 | ||||||||
\(216\) | −1.10726 | −0.0753392 | ||||||||
\(217\) | −1.50878 | −0.102422 | ||||||||
\(218\) | −19.1988 | −1.30031 | ||||||||
\(219\) | 18.7572 | 1.26749 | ||||||||
\(220\) | 0.351489 | 0.0236974 | ||||||||
\(221\) | −2.31225 | −0.155538 | ||||||||
\(222\) | −20.0718 | −1.34713 | ||||||||
\(223\) | −15.4957 | −1.03767 | −0.518834 | − | 0.854875i | \(-0.673634\pi\) | ||||
−0.518834 | + | 0.854875i | \(0.673634\pi\) | |||||||
\(224\) | −1.50878 | −0.100809 | ||||||||
\(225\) | 3.43644 | 0.229096 | ||||||||
\(226\) | −16.7578 | −1.11471 | ||||||||
\(227\) | −22.2125 | −1.47430 | −0.737148 | − | 0.675731i | \(-0.763828\pi\) | ||||
−0.737148 | + | 0.675731i | \(0.763828\pi\) | |||||||
\(228\) | 3.01784 | 0.199861 | ||||||||
\(229\) | 22.6989 | 1.49998 | 0.749991 | − | 0.661448i | \(-0.230058\pi\) | ||||
0.749991 | + | 0.661448i | \(0.230058\pi\) | |||||||
\(230\) | −5.37024 | −0.354103 | ||||||||
\(231\) | 1.34543 | 0.0885226 | ||||||||
\(232\) | 0.355403 | 0.0233334 | ||||||||
\(233\) | 8.56342 | 0.561008 | 0.280504 | − | 0.959853i | \(-0.409498\pi\) | ||||
0.280504 | + | 0.959853i | \(0.409498\pi\) | |||||||
\(234\) | 3.43644 | 0.224647 | ||||||||
\(235\) | −9.03358 | −0.589286 | ||||||||
\(236\) | 4.09595 | 0.266624 | ||||||||
\(237\) | −5.74247 | −0.373014 | ||||||||
\(238\) | −3.48866 | −0.226136 | ||||||||
\(239\) | −7.34936 | −0.475391 | −0.237695 | − | 0.971340i | \(-0.576392\pi\) | ||||
−0.237695 | + | 0.971340i | \(0.576392\pi\) | |||||||
\(240\) | 2.53701 | 0.163764 | ||||||||
\(241\) | −12.2953 | −0.792010 | −0.396005 | − | 0.918248i | \(-0.629604\pi\) | ||||
−0.396005 | + | 0.918248i | \(0.629604\pi\) | |||||||
\(242\) | 10.8765 | 0.699165 | ||||||||
\(243\) | −22.3499 | −1.43375 | ||||||||
\(244\) | 3.70865 | 0.237422 | ||||||||
\(245\) | −4.72359 | −0.301779 | ||||||||
\(246\) | −24.6903 | −1.57419 | ||||||||
\(247\) | −1.18952 | −0.0756876 | ||||||||
\(248\) | 1.00000 | 0.0635001 | ||||||||
\(249\) | −14.2529 | −0.903239 | ||||||||
\(250\) | −1.00000 | −0.0632456 | ||||||||
\(251\) | −0.765427 | −0.0483133 | −0.0241567 | − | 0.999708i | \(-0.507690\pi\) | ||||
−0.0241567 | + | 0.999708i | \(0.507690\pi\) | |||||||
\(252\) | 5.18482 | 0.326613 | ||||||||
\(253\) | 1.88758 | 0.118671 | ||||||||
\(254\) | 13.6448 | 0.856148 | ||||||||
\(255\) | 5.86620 | 0.367356 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 19.2398 | 1.20015 | 0.600073 | − | 0.799945i | \(-0.295138\pi\) | ||||
0.600073 | + | 0.799945i | \(0.295138\pi\) | |||||||
\(258\) | 11.4457 | 0.712581 | ||||||||
\(259\) | 11.9368 | 0.741717 | ||||||||
\(260\) | −1.00000 | −0.0620174 | ||||||||
\(261\) | −1.22132 | −0.0755980 | ||||||||
\(262\) | 8.03303 | 0.496282 | ||||||||
\(263\) | 17.2134 | 1.06142 | 0.530712 | − | 0.847553i | \(-0.321925\pi\) | ||||
0.530712 | + | 0.847553i | \(0.321925\pi\) | |||||||
\(264\) | −0.891733 | −0.0548824 | ||||||||
\(265\) | −4.72450 | −0.290224 | ||||||||
\(266\) | −1.79473 | −0.110042 | ||||||||
\(267\) | 28.9561 | 1.77208 | ||||||||
\(268\) | 11.6316 | 0.710514 | ||||||||
\(269\) | −17.4818 | −1.06589 | −0.532943 | − | 0.846151i | \(-0.678914\pi\) | ||||
−0.532943 | + | 0.846151i | \(0.678914\pi\) | |||||||
\(270\) | −1.10726 | −0.0673854 | ||||||||
\(271\) | −17.3745 | −1.05543 | −0.527714 | − | 0.849422i | \(-0.676951\pi\) | ||||
−0.527714 | + | 0.849422i | \(0.676951\pi\) | |||||||
\(272\) | 2.31225 | 0.140200 | ||||||||
\(273\) | −3.82779 | −0.231668 | ||||||||
\(274\) | 17.7285 | 1.07102 | ||||||||
\(275\) | 0.351489 | 0.0211956 | ||||||||
\(276\) | 13.6244 | 0.820092 | ||||||||
\(277\) | −14.3045 | −0.859474 | −0.429737 | − | 0.902954i | \(-0.641394\pi\) | ||||
−0.429737 | + | 0.902954i | \(0.641394\pi\) | |||||||
\(278\) | 0.0867283 | 0.00520162 | ||||||||
\(279\) | −3.43644 | −0.205734 | ||||||||
\(280\) | −1.50878 | −0.0901667 | ||||||||
\(281\) | 20.7352 | 1.23696 | 0.618478 | − | 0.785802i | \(-0.287749\pi\) | ||||
0.618478 | + | 0.785802i | \(0.287749\pi\) | |||||||
\(282\) | 22.9183 | 1.36477 | ||||||||
\(283\) | −9.54516 | −0.567401 | −0.283700 | − | 0.958913i | \(-0.591562\pi\) | ||||
−0.283700 | + | 0.958913i | \(0.591562\pi\) | |||||||
\(284\) | −5.16704 | −0.306607 | ||||||||
\(285\) | 3.01784 | 0.178761 | ||||||||
\(286\) | 0.351489 | 0.0207840 | ||||||||
\(287\) | 14.6835 | 0.866737 | ||||||||
\(288\) | −3.43644 | −0.202494 | ||||||||
\(289\) | −11.6535 | −0.685501 | ||||||||
\(290\) | 0.355403 | 0.0208700 | ||||||||
\(291\) | −36.9183 | −2.16419 | ||||||||
\(292\) | 7.39342 | 0.432667 | ||||||||
\(293\) | 23.9946 | 1.40178 | 0.700890 | − | 0.713270i | \(-0.252787\pi\) | ||||
0.700890 | + | 0.713270i | \(0.252787\pi\) | |||||||
\(294\) | 11.9838 | 0.698910 | ||||||||
\(295\) | 4.09595 | 0.238475 | ||||||||
\(296\) | −7.91157 | −0.459851 | ||||||||
\(297\) | 0.389188 | 0.0225830 | ||||||||
\(298\) | −2.85650 | −0.165473 | ||||||||
\(299\) | −5.37024 | −0.310569 | ||||||||
\(300\) | 2.53701 | 0.146475 | ||||||||
\(301\) | −6.80686 | −0.392341 | ||||||||
\(302\) | −10.5015 | −0.604293 | ||||||||
\(303\) | −26.1714 | −1.50351 | ||||||||
\(304\) | 1.18952 | 0.0682238 | ||||||||
\(305\) | 3.70865 | 0.212357 | ||||||||
\(306\) | −7.94589 | −0.454236 | ||||||||
\(307\) | 9.07352 | 0.517853 | 0.258926 | − | 0.965897i | \(-0.416631\pi\) | ||||
0.258926 | + | 0.965897i | \(0.416631\pi\) | |||||||
\(308\) | 0.530319 | 0.0302177 | ||||||||
\(309\) | −4.71726 | −0.268356 | ||||||||
\(310\) | 1.00000 | 0.0567962 | ||||||||
\(311\) | −16.5210 | −0.936822 | −0.468411 | − | 0.883511i | \(-0.655173\pi\) | ||||
−0.468411 | + | 0.883511i | \(0.655173\pi\) | |||||||
\(312\) | 2.53701 | 0.143630 | ||||||||
\(313\) | −20.1373 | −1.13823 | −0.569113 | − | 0.822260i | \(-0.692713\pi\) | ||||
−0.569113 | + | 0.822260i | \(0.692713\pi\) | |||||||
\(314\) | −0.674228 | −0.0380489 | ||||||||
\(315\) | 5.18482 | 0.292132 | ||||||||
\(316\) | −2.26348 | −0.127331 | ||||||||
\(317\) | −28.2431 | −1.58629 | −0.793145 | − | 0.609033i | \(-0.791558\pi\) | ||||
−0.793145 | + | 0.609033i | \(0.791558\pi\) | |||||||
\(318\) | 11.9861 | 0.672149 | ||||||||
\(319\) | −0.124920 | −0.00699420 | ||||||||
\(320\) | 1.00000 | 0.0559017 | ||||||||
\(321\) | 45.7325 | 2.55254 | ||||||||
\(322\) | −8.10250 | −0.451535 | ||||||||
\(323\) | 2.75047 | 0.153040 | ||||||||
\(324\) | −7.50020 | −0.416678 | ||||||||
\(325\) | −1.00000 | −0.0554700 | ||||||||
\(326\) | −11.8583 | −0.656771 | ||||||||
\(327\) | 48.7077 | 2.69354 | ||||||||
\(328\) | −9.73202 | −0.537361 | ||||||||
\(329\) | −13.6297 | −0.751428 | ||||||||
\(330\) | −0.891733 | −0.0490883 | ||||||||
\(331\) | 10.0590 | 0.552894 | 0.276447 | − | 0.961029i | \(-0.410843\pi\) | ||||
0.276447 | + | 0.961029i | \(0.410843\pi\) | |||||||
\(332\) | −5.61797 | −0.308326 | ||||||||
\(333\) | 27.1876 | 1.48987 | ||||||||
\(334\) | −22.2641 | −1.21824 | ||||||||
\(335\) | 11.6316 | 0.635503 | ||||||||
\(336\) | 3.82779 | 0.208823 | ||||||||
\(337\) | −9.40521 | −0.512335 | −0.256167 | − | 0.966632i | \(-0.582460\pi\) | ||||
−0.256167 | + | 0.966632i | \(0.582460\pi\) | |||||||
\(338\) | −1.00000 | −0.0543928 | ||||||||
\(339\) | 42.5147 | 2.30908 | ||||||||
\(340\) | 2.31225 | 0.125399 | ||||||||
\(341\) | −0.351489 | −0.0190342 | ||||||||
\(342\) | −4.08773 | −0.221039 | ||||||||
\(343\) | −17.6883 | −0.955078 | ||||||||
\(344\) | 4.51150 | 0.243244 | ||||||||
\(345\) | 13.6244 | 0.733512 | ||||||||
\(346\) | −11.2452 | −0.604548 | ||||||||
\(347\) | 4.86051 | 0.260926 | 0.130463 | − | 0.991453i | \(-0.458354\pi\) | ||||
0.130463 | + | 0.991453i | \(0.458354\pi\) | |||||||
\(348\) | −0.901663 | −0.0483342 | ||||||||
\(349\) | 14.6340 | 0.783338 | 0.391669 | − | 0.920106i | \(-0.371898\pi\) | ||||
0.391669 | + | 0.920106i | \(0.371898\pi\) | |||||||
\(350\) | −1.50878 | −0.0806476 | ||||||||
\(351\) | −1.10726 | −0.0591009 | ||||||||
\(352\) | −0.351489 | −0.0187344 | ||||||||
\(353\) | −5.66589 | −0.301565 | −0.150783 | − | 0.988567i | \(-0.548179\pi\) | ||||
−0.150783 | + | 0.988567i | \(0.548179\pi\) | |||||||
\(354\) | −10.3915 | −0.552301 | ||||||||
\(355\) | −5.16704 | −0.274238 | ||||||||
\(356\) | 11.4134 | 0.604911 | ||||||||
\(357\) | 8.85079 | 0.468433 | ||||||||
\(358\) | −14.5315 | −0.768013 | ||||||||
\(359\) | 24.3350 | 1.28435 | 0.642177 | − | 0.766556i | \(-0.278031\pi\) | ||||
0.642177 | + | 0.766556i | \(0.278031\pi\) | |||||||
\(360\) | −3.43644 | −0.181116 | ||||||||
\(361\) | −17.5850 | −0.925528 | ||||||||
\(362\) | 7.28922 | 0.383113 | ||||||||
\(363\) | −27.5937 | −1.44829 | ||||||||
\(364\) | −1.50878 | −0.0790814 | ||||||||
\(365\) | 7.39342 | 0.386989 | ||||||||
\(366\) | −9.40890 | −0.491811 | ||||||||
\(367\) | −6.57967 | −0.343456 | −0.171728 | − | 0.985144i | \(-0.554935\pi\) | ||||
−0.171728 | + | 0.985144i | \(0.554935\pi\) | |||||||
\(368\) | 5.37024 | 0.279943 | ||||||||
\(369\) | 33.4435 | 1.74100 | ||||||||
\(370\) | −7.91157 | −0.411303 | ||||||||
\(371\) | −7.12822 | −0.370079 | ||||||||
\(372\) | −2.53701 | −0.131538 | ||||||||
\(373\) | −21.4808 | −1.11223 | −0.556117 | − | 0.831104i | \(-0.687709\pi\) | ||||
−0.556117 | + | 0.831104i | \(0.687709\pi\) | |||||||
\(374\) | −0.812729 | −0.0420252 | ||||||||
\(375\) | 2.53701 | 0.131011 | ||||||||
\(376\) | 9.03358 | 0.465871 | ||||||||
\(377\) | 0.355403 | 0.0183042 | ||||||||
\(378\) | −1.67060 | −0.0859265 | ||||||||
\(379\) | −18.4095 | −0.945633 | −0.472817 | − | 0.881161i | \(-0.656763\pi\) | ||||
−0.472817 | + | 0.881161i | \(0.656763\pi\) | |||||||
\(380\) | 1.18952 | 0.0610213 | ||||||||
\(381\) | −34.6169 | −1.77348 | ||||||||
\(382\) | 3.20157 | 0.163807 | ||||||||
\(383\) | 12.8708 | 0.657666 | 0.328833 | − | 0.944388i | \(-0.393345\pi\) | ||||
0.328833 | + | 0.944388i | \(0.393345\pi\) | |||||||
\(384\) | −2.53701 | −0.129466 | ||||||||
\(385\) | 0.530319 | 0.0270276 | ||||||||
\(386\) | 17.2768 | 0.879366 | ||||||||
\(387\) | −15.5035 | −0.788088 | ||||||||
\(388\) | −14.5519 | −0.738759 | ||||||||
\(389\) | −6.12432 | −0.310515 | −0.155258 | − | 0.987874i | \(-0.549621\pi\) | ||||
−0.155258 | + | 0.987874i | \(0.549621\pi\) | |||||||
\(390\) | 2.53701 | 0.128467 | ||||||||
\(391\) | 12.4173 | 0.627971 | ||||||||
\(392\) | 4.72359 | 0.238577 | ||||||||
\(393\) | −20.3799 | −1.02803 | ||||||||
\(394\) | 11.8553 | 0.597261 | ||||||||
\(395\) | −2.26348 | −0.113888 | ||||||||
\(396\) | 1.20787 | 0.0606978 | ||||||||
\(397\) | 4.08647 | 0.205094 | 0.102547 | − | 0.994728i | \(-0.467301\pi\) | ||||
0.102547 | + | 0.994728i | \(0.467301\pi\) | |||||||
\(398\) | 0.350989 | 0.0175935 | ||||||||
\(399\) | 4.55325 | 0.227947 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | 19.6278 | 0.980167 | 0.490083 | − | 0.871676i | \(-0.336966\pi\) | ||||
0.490083 | + | 0.871676i | \(0.336966\pi\) | |||||||
\(402\) | −29.5096 | −1.47180 | ||||||||
\(403\) | 1.00000 | 0.0498135 | ||||||||
\(404\) | −10.3158 | −0.513231 | ||||||||
\(405\) | −7.50020 | −0.372688 | ||||||||
\(406\) | 0.536225 | 0.0266124 | ||||||||
\(407\) | 2.78083 | 0.137841 | ||||||||
\(408\) | −5.86620 | −0.290420 | ||||||||
\(409\) | 21.7862 | 1.07726 | 0.538629 | − | 0.842543i | \(-0.318942\pi\) | ||||
0.538629 | + | 0.842543i | \(0.318942\pi\) | |||||||
\(410\) | −9.73202 | −0.480630 | ||||||||
\(411\) | −44.9774 | −2.21857 | ||||||||
\(412\) | −1.85938 | −0.0916049 | ||||||||
\(413\) | 6.17988 | 0.304092 | ||||||||
\(414\) | −18.4545 | −0.906990 | ||||||||
\(415\) | −5.61797 | −0.275775 | ||||||||
\(416\) | 1.00000 | 0.0490290 | ||||||||
\(417\) | −0.220031 | −0.0107750 | ||||||||
\(418\) | −0.418104 | −0.0204502 | ||||||||
\(419\) | −14.3735 | −0.702189 | −0.351095 | − | 0.936340i | \(-0.614190\pi\) | ||||
−0.351095 | + | 0.936340i | \(0.614190\pi\) | |||||||
\(420\) | 3.82779 | 0.186777 | ||||||||
\(421\) | −28.7493 | −1.40115 | −0.700577 | − | 0.713577i | \(-0.747074\pi\) | ||||
−0.700577 | + | 0.713577i | \(0.747074\pi\) | |||||||
\(422\) | 22.3354 | 1.08727 | ||||||||
\(423\) | −31.0434 | −1.50938 | ||||||||
\(424\) | 4.72450 | 0.229442 | ||||||||
\(425\) | 2.31225 | 0.112160 | ||||||||
\(426\) | 13.1089 | 0.635126 | ||||||||
\(427\) | 5.59553 | 0.270787 | ||||||||
\(428\) | 18.0261 | 0.871324 | ||||||||
\(429\) | −0.891733 | −0.0430533 | ||||||||
\(430\) | 4.51150 | 0.217564 | ||||||||
\(431\) | −27.6116 | −1.33000 | −0.665002 | − | 0.746842i | \(-0.731569\pi\) | ||||
−0.665002 | + | 0.746842i | \(0.731569\pi\) | |||||||
\(432\) | 1.10726 | 0.0532729 | ||||||||
\(433\) | −6.84402 | −0.328902 | −0.164451 | − | 0.986385i | \(-0.552585\pi\) | ||||
−0.164451 | + | 0.986385i | \(0.552585\pi\) | |||||||
\(434\) | 1.50878 | 0.0724236 | ||||||||
\(435\) | −0.901663 | −0.0432315 | ||||||||
\(436\) | 19.1988 | 0.919456 | ||||||||
\(437\) | 6.38803 | 0.305581 | ||||||||
\(438\) | −18.7572 | −0.896254 | ||||||||
\(439\) | −10.0002 | −0.477284 | −0.238642 | − | 0.971108i | \(-0.576702\pi\) | ||||
−0.238642 | + | 0.971108i | \(0.576702\pi\) | |||||||
\(440\) | −0.351489 | −0.0167566 | ||||||||
\(441\) | −16.2323 | −0.772968 | ||||||||
\(442\) | 2.31225 | 0.109982 | ||||||||
\(443\) | 2.61430 | 0.124209 | 0.0621045 | − | 0.998070i | \(-0.480219\pi\) | ||||
0.0621045 | + | 0.998070i | \(0.480219\pi\) | |||||||
\(444\) | 20.0718 | 0.952564 | ||||||||
\(445\) | 11.4134 | 0.541049 | ||||||||
\(446\) | 15.4957 | 0.733742 | ||||||||
\(447\) | 7.24699 | 0.342771 | ||||||||
\(448\) | 1.50878 | 0.0712830 | ||||||||
\(449\) | 25.5365 | 1.20514 | 0.602571 | − | 0.798065i | \(-0.294143\pi\) | ||||
0.602571 | + | 0.798065i | \(0.294143\pi\) | |||||||
\(450\) | −3.43644 | −0.161995 | ||||||||
\(451\) | 3.42070 | 0.161074 | ||||||||
\(452\) | 16.7578 | 0.788220 | ||||||||
\(453\) | 26.6424 | 1.25177 | ||||||||
\(454\) | 22.2125 | 1.04249 | ||||||||
\(455\) | −1.50878 | −0.0707326 | ||||||||
\(456\) | −3.01784 | −0.141323 | ||||||||
\(457\) | 5.50007 | 0.257282 | 0.128641 | − | 0.991691i | \(-0.458938\pi\) | ||||
0.128641 | + | 0.991691i | \(0.458938\pi\) | |||||||
\(458\) | −22.6989 | −1.06065 | ||||||||
\(459\) | 2.56025 | 0.119502 | ||||||||
\(460\) | 5.37024 | 0.250389 | ||||||||
\(461\) | −39.9050 | −1.85856 | −0.929279 | − | 0.369378i | \(-0.879571\pi\) | ||||
−0.929279 | + | 0.369378i | \(0.879571\pi\) | |||||||
\(462\) | −1.34543 | −0.0625949 | ||||||||
\(463\) | −20.9421 | −0.973264 | −0.486632 | − | 0.873607i | \(-0.661775\pi\) | ||||
−0.486632 | + | 0.873607i | \(0.661775\pi\) | |||||||
\(464\) | −0.355403 | −0.0164992 | ||||||||
\(465\) | −2.53701 | −0.117651 | ||||||||
\(466\) | −8.56342 | −0.396693 | ||||||||
\(467\) | 24.9874 | 1.15628 | 0.578138 | − | 0.815939i | \(-0.303779\pi\) | ||||
0.578138 | + | 0.815939i | \(0.303779\pi\) | |||||||
\(468\) | −3.43644 | −0.158850 | ||||||||
\(469\) | 17.5495 | 0.810362 | ||||||||
\(470\) | 9.03358 | 0.416688 | ||||||||
\(471\) | 1.71053 | 0.0788169 | ||||||||
\(472\) | −4.09595 | −0.188531 | ||||||||
\(473\) | −1.58574 | −0.0729126 | ||||||||
\(474\) | 5.74247 | 0.263761 | ||||||||
\(475\) | 1.18952 | 0.0545791 | ||||||||
\(476\) | 3.48866 | 0.159903 | ||||||||
\(477\) | −16.2355 | −0.743371 | ||||||||
\(478\) | 7.34936 | 0.336152 | ||||||||
\(479\) | 2.03234 | 0.0928598 | 0.0464299 | − | 0.998922i | \(-0.485216\pi\) | ||||
0.0464299 | + | 0.998922i | \(0.485216\pi\) | |||||||
\(480\) | −2.53701 | −0.115798 | ||||||||
\(481\) | −7.91157 | −0.360736 | ||||||||
\(482\) | 12.2953 | 0.560036 | ||||||||
\(483\) | 20.5562 | 0.935338 | ||||||||
\(484\) | −10.8765 | −0.494384 | ||||||||
\(485\) | −14.5519 | −0.660766 | ||||||||
\(486\) | 22.3499 | 1.01381 | ||||||||
\(487\) | 39.5360 | 1.79155 | 0.895773 | − | 0.444512i | \(-0.146623\pi\) | ||||
0.895773 | + | 0.444512i | \(0.146623\pi\) | |||||||
\(488\) | −3.70865 | −0.167883 | ||||||||
\(489\) | 30.0847 | 1.36048 | ||||||||
\(490\) | 4.72359 | 0.213390 | ||||||||
\(491\) | 33.9971 | 1.53427 | 0.767134 | − | 0.641487i | \(-0.221682\pi\) | ||||
0.767134 | + | 0.641487i | \(0.221682\pi\) | |||||||
\(492\) | 24.6903 | 1.11312 | ||||||||
\(493\) | −0.821780 | −0.0370111 | ||||||||
\(494\) | 1.18952 | 0.0535192 | ||||||||
\(495\) | 1.20787 | 0.0542898 | ||||||||
\(496\) | −1.00000 | −0.0449013 | ||||||||
\(497\) | −7.79591 | −0.349695 | ||||||||
\(498\) | 14.2529 | 0.638687 | ||||||||
\(499\) | −20.1001 | −0.899805 | −0.449903 | − | 0.893078i | \(-0.648541\pi\) | ||||
−0.449903 | + | 0.893078i | \(0.648541\pi\) | |||||||
\(500\) | 1.00000 | 0.0447214 | ||||||||
\(501\) | 56.4845 | 2.52354 | ||||||||
\(502\) | 0.765427 | 0.0341627 | ||||||||
\(503\) | 3.03600 | 0.135369 | 0.0676844 | − | 0.997707i | \(-0.478439\pi\) | ||||
0.0676844 | + | 0.997707i | \(0.478439\pi\) | |||||||
\(504\) | −5.18482 | −0.230950 | ||||||||
\(505\) | −10.3158 | −0.459048 | ||||||||
\(506\) | −1.88758 | −0.0839133 | ||||||||
\(507\) | 2.53701 | 0.112673 | ||||||||
\(508\) | −13.6448 | −0.605388 | ||||||||
\(509\) | −14.7664 | −0.654511 | −0.327255 | − | 0.944936i | \(-0.606124\pi\) | ||||
−0.327255 | + | 0.944936i | \(0.606124\pi\) | |||||||
\(510\) | −5.86620 | −0.259760 | ||||||||
\(511\) | 11.1550 | 0.493469 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 1.31711 | 0.0581517 | ||||||||
\(514\) | −19.2398 | −0.848632 | ||||||||
\(515\) | −1.85938 | −0.0819339 | ||||||||
\(516\) | −11.4457 | −0.503871 | ||||||||
\(517\) | −3.17520 | −0.139645 | ||||||||
\(518\) | −11.9368 | −0.524473 | ||||||||
\(519\) | 28.5293 | 1.25230 | ||||||||
\(520\) | 1.00000 | 0.0438529 | ||||||||
\(521\) | −26.8402 | −1.17589 | −0.587945 | − | 0.808901i | \(-0.700063\pi\) | ||||
−0.587945 | + | 0.808901i | \(0.700063\pi\) | |||||||
\(522\) | 1.22132 | 0.0534558 | ||||||||
\(523\) | 1.49464 | 0.0653559 | 0.0326780 | − | 0.999466i | \(-0.489596\pi\) | ||||
0.0326780 | + | 0.999466i | \(0.489596\pi\) | |||||||
\(524\) | −8.03303 | −0.350924 | ||||||||
\(525\) | 3.82779 | 0.167058 | ||||||||
\(526\) | −17.2134 | −0.750539 | ||||||||
\(527\) | −2.31225 | −0.100723 | ||||||||
\(528\) | 0.891733 | 0.0388077 | ||||||||
\(529\) | 5.83952 | 0.253892 | ||||||||
\(530\) | 4.72450 | 0.205219 | ||||||||
\(531\) | 14.0755 | 0.610824 | ||||||||
\(532\) | 1.79473 | 0.0778112 | ||||||||
\(533\) | −9.73202 | −0.421541 | ||||||||
\(534\) | −28.9561 | −1.25305 | ||||||||
\(535\) | 18.0261 | 0.779336 | ||||||||
\(536\) | −11.6316 | −0.502410 | ||||||||
\(537\) | 36.8666 | 1.59091 | ||||||||
\(538\) | 17.4818 | 0.753696 | ||||||||
\(539\) | −1.66029 | −0.0715138 | ||||||||
\(540\) | 1.10726 | 0.0476487 | ||||||||
\(541\) | 26.0272 | 1.11900 | 0.559499 | − | 0.828831i | \(-0.310993\pi\) | ||||
0.559499 | + | 0.828831i | \(0.310993\pi\) | |||||||
\(542\) | 17.3745 | 0.746300 | ||||||||
\(543\) | −18.4929 | −0.793605 | ||||||||
\(544\) | −2.31225 | −0.0991367 | ||||||||
\(545\) | 19.1988 | 0.822387 | ||||||||
\(546\) | 3.82779 | 0.163814 | ||||||||
\(547\) | 33.5020 | 1.43244 | 0.716222 | − | 0.697873i | \(-0.245870\pi\) | ||||
0.716222 | + | 0.697873i | \(0.245870\pi\) | |||||||
\(548\) | −17.7285 | −0.757323 | ||||||||
\(549\) | 12.7446 | 0.543925 | ||||||||
\(550\) | −0.351489 | −0.0149875 | ||||||||
\(551\) | −0.422761 | −0.0180102 | ||||||||
\(552\) | −13.6244 | −0.579892 | ||||||||
\(553\) | −3.41508 | −0.145224 | ||||||||
\(554\) | 14.3045 | 0.607740 | ||||||||
\(555\) | 20.0718 | 0.851999 | ||||||||
\(556\) | −0.0867283 | −0.00367810 | ||||||||
\(557\) | 20.5074 | 0.868928 | 0.434464 | − | 0.900689i | \(-0.356938\pi\) | ||||
0.434464 | + | 0.900689i | \(0.356938\pi\) | |||||||
\(558\) | 3.43644 | 0.145476 | ||||||||
\(559\) | 4.51150 | 0.190816 | ||||||||
\(560\) | 1.50878 | 0.0637575 | ||||||||
\(561\) | 2.06190 | 0.0870537 | ||||||||
\(562\) | −20.7352 | −0.874660 | ||||||||
\(563\) | −24.3668 | −1.02694 | −0.513468 | − | 0.858109i | \(-0.671640\pi\) | ||||
−0.513468 | + | 0.858109i | \(0.671640\pi\) | |||||||
\(564\) | −22.9183 | −0.965035 | ||||||||
\(565\) | 16.7578 | 0.705005 | ||||||||
\(566\) | 9.54516 | 0.401213 | ||||||||
\(567\) | −11.3161 | −0.475233 | ||||||||
\(568\) | 5.16704 | 0.216804 | ||||||||
\(569\) | 24.2023 | 1.01461 | 0.507306 | − | 0.861766i | \(-0.330642\pi\) | ||||
0.507306 | + | 0.861766i | \(0.330642\pi\) | |||||||
\(570\) | −3.01784 | −0.126403 | ||||||||
\(571\) | −30.3985 | −1.27214 | −0.636068 | − | 0.771633i | \(-0.719440\pi\) | ||||
−0.636068 | + | 0.771633i | \(0.719440\pi\) | |||||||
\(572\) | −0.351489 | −0.0146965 | ||||||||
\(573\) | −8.12243 | −0.339319 | ||||||||
\(574\) | −14.6835 | −0.612875 | ||||||||
\(575\) | 5.37024 | 0.223955 | ||||||||
\(576\) | 3.43644 | 0.143185 | ||||||||
\(577\) | 12.8633 | 0.535507 | 0.267753 | − | 0.963487i | \(-0.413719\pi\) | ||||
0.267753 | + | 0.963487i | \(0.413719\pi\) | |||||||
\(578\) | 11.6535 | 0.484723 | ||||||||
\(579\) | −43.8315 | −1.82157 | ||||||||
\(580\) | −0.355403 | −0.0147573 | ||||||||
\(581\) | −8.47627 | −0.351655 | ||||||||
\(582\) | 36.9183 | 1.53031 | ||||||||
\(583\) | −1.66061 | −0.0687755 | ||||||||
\(584\) | −7.39342 | −0.305942 | ||||||||
\(585\) | −3.43644 | −0.142079 | ||||||||
\(586\) | −23.9946 | −0.991208 | ||||||||
\(587\) | −31.6787 | −1.30752 | −0.653760 | − | 0.756702i | \(-0.726809\pi\) | ||||
−0.653760 | + | 0.756702i | \(0.726809\pi\) | |||||||
\(588\) | −11.9838 | −0.494204 | ||||||||
\(589\) | −1.18952 | −0.0490135 | ||||||||
\(590\) | −4.09595 | −0.168628 | ||||||||
\(591\) | −30.0770 | −1.23720 | ||||||||
\(592\) | 7.91157 | 0.325163 | ||||||||
\(593\) | 11.2562 | 0.462238 | 0.231119 | − | 0.972925i | \(-0.425761\pi\) | ||||
0.231119 | + | 0.972925i | \(0.425761\pi\) | |||||||
\(594\) | −0.389188 | −0.0159686 | ||||||||
\(595\) | 3.48866 | 0.143021 | ||||||||
\(596\) | 2.85650 | 0.117007 | ||||||||
\(597\) | −0.890464 | −0.0364442 | ||||||||
\(598\) | 5.37024 | 0.219606 | ||||||||
\(599\) | −40.6496 | −1.66090 | −0.830449 | − | 0.557095i | \(-0.811916\pi\) | ||||
−0.830449 | + | 0.557095i | \(0.811916\pi\) | |||||||
\(600\) | −2.53701 | −0.103573 | ||||||||
\(601\) | −9.73998 | −0.397302 | −0.198651 | − | 0.980070i | \(-0.563656\pi\) | ||||
−0.198651 | + | 0.980070i | \(0.563656\pi\) | |||||||
\(602\) | 6.80686 | 0.277427 | ||||||||
\(603\) | 39.9714 | 1.62776 | ||||||||
\(604\) | 10.5015 | 0.427300 | ||||||||
\(605\) | −10.8765 | −0.442191 | ||||||||
\(606\) | 26.1714 | 1.06314 | ||||||||
\(607\) | 15.4422 | 0.626780 | 0.313390 | − | 0.949625i | \(-0.398535\pi\) | ||||
0.313390 | + | 0.949625i | \(0.398535\pi\) | |||||||
\(608\) | −1.18952 | −0.0482415 | ||||||||
\(609\) | −1.36041 | −0.0551266 | ||||||||
\(610\) | −3.70865 | −0.150159 | ||||||||
\(611\) | 9.03358 | 0.365460 | ||||||||
\(612\) | 7.94589 | 0.321194 | ||||||||
\(613\) | 8.72746 | 0.352499 | 0.176249 | − | 0.984346i | \(-0.443604\pi\) | ||||
0.176249 | + | 0.984346i | \(0.443604\pi\) | |||||||
\(614\) | −9.07352 | −0.366177 | ||||||||
\(615\) | 24.6903 | 0.995608 | ||||||||
\(616\) | −0.530319 | −0.0213672 | ||||||||
\(617\) | 33.0295 | 1.32972 | 0.664859 | − | 0.746969i | \(-0.268491\pi\) | ||||
0.664859 | + | 0.746969i | \(0.268491\pi\) | |||||||
\(618\) | 4.71726 | 0.189756 | ||||||||
\(619\) | −6.35715 | −0.255516 | −0.127758 | − | 0.991805i | \(-0.540778\pi\) | ||||
−0.127758 | + | 0.991805i | \(0.540778\pi\) | |||||||
\(620\) | −1.00000 | −0.0401610 | ||||||||
\(621\) | 5.94623 | 0.238614 | ||||||||
\(622\) | 16.5210 | 0.662433 | ||||||||
\(623\) | 17.2203 | 0.689919 | ||||||||
\(624\) | −2.53701 | −0.101562 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 20.1373 | 0.804847 | ||||||||
\(627\) | 1.06074 | 0.0423618 | ||||||||
\(628\) | 0.674228 | 0.0269046 | ||||||||
\(629\) | 18.2935 | 0.729409 | ||||||||
\(630\) | −5.18482 | −0.206568 | ||||||||
\(631\) | 19.7621 | 0.786718 | 0.393359 | − | 0.919385i | \(-0.371313\pi\) | ||||
0.393359 | + | 0.919385i | \(0.371313\pi\) | |||||||
\(632\) | 2.26348 | 0.0900363 | ||||||||
\(633\) | −56.6652 | −2.25224 | ||||||||
\(634\) | 28.2431 | 1.12168 | ||||||||
\(635\) | −13.6448 | −0.541476 | ||||||||
\(636\) | −11.9861 | −0.475281 | ||||||||
\(637\) | 4.72359 | 0.187155 | ||||||||
\(638\) | 0.124920 | 0.00494565 | ||||||||
\(639\) | −17.7562 | −0.702425 | ||||||||
\(640\) | −1.00000 | −0.0395285 | ||||||||
\(641\) | 12.0771 | 0.477019 | 0.238509 | − | 0.971140i | \(-0.423341\pi\) | ||||
0.238509 | + | 0.971140i | \(0.423341\pi\) | |||||||
\(642\) | −45.7325 | −1.80492 | ||||||||
\(643\) | 25.2053 | 0.993999 | 0.497000 | − | 0.867751i | \(-0.334435\pi\) | ||||
0.497000 | + | 0.867751i | \(0.334435\pi\) | |||||||
\(644\) | 8.10250 | 0.319283 | ||||||||
\(645\) | −11.4457 | −0.450676 | ||||||||
\(646\) | −2.75047 | −0.108216 | ||||||||
\(647\) | 39.1661 | 1.53978 | 0.769890 | − | 0.638177i | \(-0.220311\pi\) | ||||
0.769890 | + | 0.638177i | \(0.220311\pi\) | |||||||
\(648\) | 7.50020 | 0.294636 | ||||||||
\(649\) | 1.43968 | 0.0565124 | ||||||||
\(650\) | 1.00000 | 0.0392232 | ||||||||
\(651\) | −3.82779 | −0.150023 | ||||||||
\(652\) | 11.8583 | 0.464407 | ||||||||
\(653\) | −14.7230 | −0.576157 | −0.288078 | − | 0.957607i | \(-0.593016\pi\) | ||||
−0.288078 | + | 0.957607i | \(0.593016\pi\) | |||||||
\(654\) | −48.7077 | −1.90462 | ||||||||
\(655\) | −8.03303 | −0.313876 | ||||||||
\(656\) | 9.73202 | 0.379971 | ||||||||
\(657\) | 25.4070 | 0.991223 | ||||||||
\(658\) | 13.6297 | 0.531340 | ||||||||
\(659\) | 39.2072 | 1.52729 | 0.763647 | − | 0.645633i | \(-0.223407\pi\) | ||||
0.763647 | + | 0.645633i | \(0.223407\pi\) | |||||||
\(660\) | 0.891733 | 0.0347107 | ||||||||
\(661\) | −14.4903 | −0.563609 | −0.281805 | − | 0.959472i | \(-0.590933\pi\) | ||||
−0.281805 | + | 0.959472i | \(0.590933\pi\) | |||||||
\(662\) | −10.0590 | −0.390955 | ||||||||
\(663\) | −5.86620 | −0.227824 | ||||||||
\(664\) | 5.61797 | 0.218020 | ||||||||
\(665\) | 1.79473 | 0.0695965 | ||||||||
\(666\) | −27.1876 | −1.05350 | ||||||||
\(667\) | −1.90860 | −0.0739014 | ||||||||
\(668\) | 22.2641 | 0.861426 | ||||||||
\(669\) | −39.3128 | −1.51992 | ||||||||
\(670\) | −11.6316 | −0.449369 | ||||||||
\(671\) | 1.30355 | 0.0503230 | ||||||||
\(672\) | −3.82779 | −0.147660 | ||||||||
\(673\) | 17.0240 | 0.656226 | 0.328113 | − | 0.944639i | \(-0.393587\pi\) | ||||
0.328113 | + | 0.944639i | \(0.393587\pi\) | |||||||
\(674\) | 9.40521 | 0.362275 | ||||||||
\(675\) | 1.10726 | 0.0426183 | ||||||||
\(676\) | 1.00000 | 0.0384615 | ||||||||
\(677\) | 33.7663 | 1.29774 | 0.648872 | − | 0.760898i | \(-0.275241\pi\) | ||||
0.648872 | + | 0.760898i | \(0.275241\pi\) | |||||||
\(678\) | −42.5147 | −1.63277 | ||||||||
\(679\) | −21.9555 | −0.842576 | ||||||||
\(680\) | −2.31225 | −0.0886706 | ||||||||
\(681\) | −56.3535 | −2.15947 | ||||||||
\(682\) | 0.351489 | 0.0134592 | ||||||||
\(683\) | 30.4675 | 1.16581 | 0.582904 | − | 0.812541i | \(-0.301916\pi\) | ||||
0.582904 | + | 0.812541i | \(0.301916\pi\) | |||||||
\(684\) | 4.08773 | 0.156298 | ||||||||
\(685\) | −17.7285 | −0.677371 | ||||||||
\(686\) | 17.6883 | 0.675342 | ||||||||
\(687\) | 57.5873 | 2.19709 | ||||||||
\(688\) | −4.51150 | −0.171999 | ||||||||
\(689\) | 4.72450 | 0.179989 | ||||||||
\(690\) | −13.6244 | −0.518671 | ||||||||
\(691\) | 9.26119 | 0.352312 | 0.176156 | − | 0.984362i | \(-0.443634\pi\) | ||||
0.176156 | + | 0.984362i | \(0.443634\pi\) | |||||||
\(692\) | 11.2452 | 0.427480 | ||||||||
\(693\) | 1.82241 | 0.0692276 | ||||||||
\(694\) | −4.86051 | −0.184503 | ||||||||
\(695\) | −0.0867283 | −0.00328979 | ||||||||
\(696\) | 0.901663 | 0.0341775 | ||||||||
\(697\) | 22.5028 | 0.852355 | ||||||||
\(698\) | −14.6340 | −0.553904 | ||||||||
\(699\) | 21.7255 | 0.821734 | ||||||||
\(700\) | 1.50878 | 0.0570264 | ||||||||
\(701\) | −24.3820 | −0.920895 | −0.460447 | − | 0.887687i | \(-0.652311\pi\) | ||||
−0.460447 | + | 0.887687i | \(0.652311\pi\) | |||||||
\(702\) | 1.10726 | 0.0417907 | ||||||||
\(703\) | 9.41100 | 0.354942 | ||||||||
\(704\) | 0.351489 | 0.0132472 | ||||||||
\(705\) | −22.9183 | −0.863154 | ||||||||
\(706\) | 5.66589 | 0.213239 | ||||||||
\(707\) | −15.5643 | −0.585355 | ||||||||
\(708\) | 10.3915 | 0.390536 | ||||||||
\(709\) | −24.5762 | −0.922979 | −0.461490 | − | 0.887146i | \(-0.652685\pi\) | ||||
−0.461490 | + | 0.887146i | \(0.652685\pi\) | |||||||
\(710\) | 5.16704 | 0.193916 | ||||||||
\(711\) | −7.77830 | −0.291709 | ||||||||
\(712\) | −11.4134 | −0.427737 | ||||||||
\(713\) | −5.37024 | −0.201117 | ||||||||
\(714\) | −8.85079 | −0.331232 | ||||||||
\(715\) | −0.351489 | −0.0131449 | ||||||||
\(716\) | 14.5315 | 0.543067 | ||||||||
\(717\) | −18.6454 | −0.696326 | ||||||||
\(718\) | −24.3350 | −0.908176 | ||||||||
\(719\) | −46.8558 | −1.74742 | −0.873712 | − | 0.486443i | \(-0.838294\pi\) | ||||
−0.873712 | + | 0.486443i | \(0.838294\pi\) | |||||||
\(720\) | 3.43644 | 0.128069 | ||||||||
\(721\) | −2.80539 | −0.104478 | ||||||||
\(722\) | 17.5850 | 0.654447 | ||||||||
\(723\) | −31.1933 | −1.16009 | ||||||||
\(724\) | −7.28922 | −0.270902 | ||||||||
\(725\) | −0.355403 | −0.0131994 | ||||||||
\(726\) | 27.5937 | 1.02410 | ||||||||
\(727\) | 13.5076 | 0.500970 | 0.250485 | − | 0.968121i | \(-0.419410\pi\) | ||||
0.250485 | + | 0.968121i | \(0.419410\pi\) | |||||||
\(728\) | 1.50878 | 0.0559190 | ||||||||
\(729\) | −34.2014 | −1.26672 | ||||||||
\(730\) | −7.39342 | −0.273643 | ||||||||
\(731\) | −10.4317 | −0.385831 | ||||||||
\(732\) | 9.40890 | 0.347763 | ||||||||
\(733\) | 21.3998 | 0.790419 | 0.395210 | − | 0.918591i | \(-0.370672\pi\) | ||||
0.395210 | + | 0.918591i | \(0.370672\pi\) | |||||||
\(734\) | 6.57967 | 0.242860 | ||||||||
\(735\) | −11.9838 | −0.442030 | ||||||||
\(736\) | −5.37024 | −0.197950 | ||||||||
\(737\) | 4.08839 | 0.150598 | ||||||||
\(738\) | −33.4435 | −1.23107 | ||||||||
\(739\) | −43.2269 | −1.59013 | −0.795064 | − | 0.606526i | \(-0.792563\pi\) | ||||
−0.795064 | + | 0.606526i | \(0.792563\pi\) | |||||||
\(740\) | 7.91157 | 0.290835 | ||||||||
\(741\) | −3.01784 | −0.110863 | ||||||||
\(742\) | 7.12822 | 0.261685 | ||||||||
\(743\) | −15.8489 | −0.581439 | −0.290720 | − | 0.956808i | \(-0.593895\pi\) | ||||
−0.290720 | + | 0.956808i | \(0.593895\pi\) | |||||||
\(744\) | 2.53701 | 0.0930114 | ||||||||
\(745\) | 2.85650 | 0.104654 | ||||||||
\(746\) | 21.4808 | 0.786468 | ||||||||
\(747\) | −19.3058 | −0.706363 | ||||||||
\(748\) | 0.812729 | 0.0297163 | ||||||||
\(749\) | 27.1974 | 0.993770 | ||||||||
\(750\) | −2.53701 | −0.0926387 | ||||||||
\(751\) | −32.2809 | −1.17795 | −0.588974 | − | 0.808152i | \(-0.700468\pi\) | ||||
−0.588974 | + | 0.808152i | \(0.700468\pi\) | |||||||
\(752\) | −9.03358 | −0.329421 | ||||||||
\(753\) | −1.94190 | −0.0707667 | ||||||||
\(754\) | −0.355403 | −0.0129430 | ||||||||
\(755\) | 10.5015 | 0.382189 | ||||||||
\(756\) | 1.67060 | 0.0607592 | ||||||||
\(757\) | −2.77202 | −0.100751 | −0.0503754 | − | 0.998730i | \(-0.516042\pi\) | ||||
−0.0503754 | + | 0.998730i | \(0.516042\pi\) | |||||||
\(758\) | 18.4095 | 0.668664 | ||||||||
\(759\) | 4.78882 | 0.173823 | ||||||||
\(760\) | −1.18952 | −0.0431485 | ||||||||
\(761\) | −1.32550 | −0.0480492 | −0.0240246 | − | 0.999711i | \(-0.507648\pi\) | ||||
−0.0240246 | + | 0.999711i | \(0.507648\pi\) | |||||||
\(762\) | 34.6169 | 1.25404 | ||||||||
\(763\) | 28.9667 | 1.04867 | ||||||||
\(764\) | −3.20157 | −0.115829 | ||||||||
\(765\) | 7.94589 | 0.287284 | ||||||||
\(766\) | −12.8708 | −0.465040 | ||||||||
\(767\) | −4.09595 | −0.147896 | ||||||||
\(768\) | 2.53701 | 0.0915466 | ||||||||
\(769\) | −22.9980 | −0.829330 | −0.414665 | − | 0.909974i | \(-0.636101\pi\) | ||||
−0.414665 | + | 0.909974i | \(0.636101\pi\) | |||||||
\(770\) | −0.530319 | −0.0191114 | ||||||||
\(771\) | 48.8117 | 1.75791 | ||||||||
\(772\) | −17.2768 | −0.621806 | ||||||||
\(773\) | 5.85021 | 0.210417 | 0.105209 | − | 0.994450i | \(-0.466449\pi\) | ||||
0.105209 | + | 0.994450i | \(0.466449\pi\) | |||||||
\(774\) | 15.5035 | 0.557262 | ||||||||
\(775\) | −1.00000 | −0.0359211 | ||||||||
\(776\) | 14.5519 | 0.522382 | ||||||||
\(777\) | 30.2838 | 1.08643 | ||||||||
\(778\) | 6.12432 | 0.219567 | ||||||||
\(779\) | 11.5765 | 0.414770 | ||||||||
\(780\) | −2.53701 | −0.0908397 | ||||||||
\(781\) | −1.81616 | −0.0649872 | ||||||||
\(782\) | −12.4173 | −0.444043 | ||||||||
\(783\) | −0.393522 | −0.0140633 | ||||||||
\(784\) | −4.72359 | −0.168700 | ||||||||
\(785\) | 0.674228 | 0.0240642 | ||||||||
\(786\) | 20.3799 | 0.726927 | ||||||||
\(787\) | 26.6262 | 0.949122 | 0.474561 | − | 0.880223i | \(-0.342607\pi\) | ||||
0.474561 | + | 0.880223i | \(0.342607\pi\) | |||||||
\(788\) | −11.8553 | −0.422327 | ||||||||
\(789\) | 43.6706 | 1.55471 | ||||||||
\(790\) | 2.26348 | 0.0805309 | ||||||||
\(791\) | 25.2838 | 0.898988 | ||||||||
\(792\) | −1.20787 | −0.0429198 | ||||||||
\(793\) | −3.70865 | −0.131698 | ||||||||
\(794\) | −4.08647 | −0.145023 | ||||||||
\(795\) | −11.9861 | −0.425104 | ||||||||
\(796\) | −0.350989 | −0.0124405 | ||||||||
\(797\) | −27.6444 | −0.979216 | −0.489608 | − | 0.871943i | \(-0.662860\pi\) | ||||
−0.489608 | + | 0.871943i | \(0.662860\pi\) | |||||||
\(798\) | −4.55325 | −0.161183 | ||||||||
\(799\) | −20.8879 | −0.738959 | ||||||||
\(800\) | −1.00000 | −0.0353553 | ||||||||
\(801\) | 39.2216 | 1.38583 | ||||||||
\(802\) | −19.6278 | −0.693083 | ||||||||
\(803\) | 2.59871 | 0.0917063 | ||||||||
\(804\) | 29.5096 | 1.04072 | ||||||||
\(805\) | 8.10250 | 0.285576 | ||||||||
\(806\) | −1.00000 | −0.0352235 | ||||||||
\(807\) | −44.3517 | −1.56125 | ||||||||
\(808\) | 10.3158 | 0.362909 | ||||||||
\(809\) | 1.02448 | 0.0360189 | 0.0180095 | − | 0.999838i | \(-0.494267\pi\) | ||||
0.0180095 | + | 0.999838i | \(0.494267\pi\) | |||||||
\(810\) | 7.50020 | 0.263530 | ||||||||
\(811\) | −49.8840 | −1.75166 | −0.875832 | − | 0.482616i | \(-0.839687\pi\) | ||||
−0.875832 | + | 0.482616i | \(0.839687\pi\) | |||||||
\(812\) | −0.536225 | −0.0188178 | ||||||||
\(813\) | −44.0794 | −1.54593 | ||||||||
\(814\) | −2.78083 | −0.0974680 | ||||||||
\(815\) | 11.8583 | 0.415379 | ||||||||
\(816\) | 5.86620 | 0.205358 | ||||||||
\(817\) | −5.36654 | −0.187751 | ||||||||
\(818\) | −21.7862 | −0.761737 | ||||||||
\(819\) | −5.18482 | −0.181172 | ||||||||
\(820\) | 9.73202 | 0.339857 | ||||||||
\(821\) | 15.4504 | 0.539223 | 0.269612 | − | 0.962969i | \(-0.413105\pi\) | ||||
0.269612 | + | 0.962969i | \(0.413105\pi\) | |||||||
\(822\) | 44.9774 | 1.56877 | ||||||||
\(823\) | 8.02554 | 0.279753 | 0.139876 | − | 0.990169i | \(-0.455330\pi\) | ||||
0.139876 | + | 0.990169i | \(0.455330\pi\) | |||||||
\(824\) | 1.85938 | 0.0647744 | ||||||||
\(825\) | 0.891733 | 0.0310461 | ||||||||
\(826\) | −6.17988 | −0.215025 | ||||||||
\(827\) | 28.4999 | 0.991040 | 0.495520 | − | 0.868596i | \(-0.334977\pi\) | ||||
0.495520 | + | 0.868596i | \(0.334977\pi\) | |||||||
\(828\) | 18.4545 | 0.641339 | ||||||||
\(829\) | −53.5090 | −1.85845 | −0.929223 | − | 0.369520i | \(-0.879522\pi\) | ||||
−0.929223 | + | 0.369520i | \(0.879522\pi\) | |||||||
\(830\) | 5.61797 | 0.195003 | ||||||||
\(831\) | −36.2907 | −1.25891 | ||||||||
\(832\) | −1.00000 | −0.0346688 | ||||||||
\(833\) | −10.9221 | −0.378428 | ||||||||
\(834\) | 0.220031 | 0.00761905 | ||||||||
\(835\) | 22.2641 | 0.770483 | ||||||||
\(836\) | 0.418104 | 0.0144604 | ||||||||
\(837\) | −1.10726 | −0.0382723 | ||||||||
\(838\) | 14.3735 | 0.496523 | ||||||||
\(839\) | 7.20463 | 0.248731 | 0.124366 | − | 0.992236i | \(-0.460310\pi\) | ||||
0.124366 | + | 0.992236i | \(0.460310\pi\) | |||||||
\(840\) | −3.82779 | −0.132071 | ||||||||
\(841\) | −28.8737 | −0.995644 | ||||||||
\(842\) | 28.7493 | 0.990765 | ||||||||
\(843\) | 52.6054 | 1.81183 | ||||||||
\(844\) | −22.3354 | −0.768815 | ||||||||
\(845\) | 1.00000 | 0.0344010 | ||||||||
\(846\) | 31.0434 | 1.06729 | ||||||||
\(847\) | −16.4102 | −0.563859 | ||||||||
\(848\) | −4.72450 | −0.162240 | ||||||||
\(849\) | −24.2162 | −0.831098 | ||||||||
\(850\) | −2.31225 | −0.0793094 | ||||||||
\(851\) | 42.4871 | 1.45644 | ||||||||
\(852\) | −13.1089 | −0.449102 | ||||||||
\(853\) | −50.2269 | −1.71974 | −0.859868 | − | 0.510517i | \(-0.829454\pi\) | ||||
−0.859868 | + | 0.510517i | \(0.829454\pi\) | |||||||
\(854\) | −5.59553 | −0.191475 | ||||||||
\(855\) | 4.08773 | 0.139797 | ||||||||
\(856\) | −18.0261 | −0.616119 | ||||||||
\(857\) | −43.4960 | −1.48579 | −0.742897 | − | 0.669406i | \(-0.766549\pi\) | ||||
−0.742897 | + | 0.669406i | \(0.766549\pi\) | |||||||
\(858\) | 0.891733 | 0.0304433 | ||||||||
\(859\) | −49.4152 | −1.68603 | −0.843013 | − | 0.537893i | \(-0.819221\pi\) | ||||
−0.843013 | + | 0.537893i | \(0.819221\pi\) | |||||||
\(860\) | −4.51150 | −0.153841 | ||||||||
\(861\) | 37.2521 | 1.26955 | ||||||||
\(862\) | 27.6116 | 0.940455 | ||||||||
\(863\) | 8.21167 | 0.279529 | 0.139764 | − | 0.990185i | \(-0.455366\pi\) | ||||
0.139764 | + | 0.990185i | \(0.455366\pi\) | |||||||
\(864\) | −1.10726 | −0.0376696 | ||||||||
\(865\) | 11.2452 | 0.382350 | ||||||||
\(866\) | 6.84402 | 0.232569 | ||||||||
\(867\) | −29.5651 | −1.00409 | ||||||||
\(868\) | −1.50878 | −0.0512112 | ||||||||
\(869\) | −0.795587 | −0.0269885 | ||||||||
\(870\) | 0.901663 | 0.0305693 | ||||||||
\(871\) | −11.6316 | −0.394122 | ||||||||
\(872\) | −19.1988 | −0.650154 | ||||||||
\(873\) | −50.0066 | −1.69247 | ||||||||
\(874\) | −6.38803 | −0.216078 | ||||||||
\(875\) | 1.50878 | 0.0510060 | ||||||||
\(876\) | 18.7572 | 0.633747 | ||||||||
\(877\) | −35.5763 | −1.20133 | −0.600664 | − | 0.799502i | \(-0.705097\pi\) | ||||
−0.600664 | + | 0.799502i | \(0.705097\pi\) | |||||||
\(878\) | 10.0002 | 0.337490 | ||||||||
\(879\) | 60.8746 | 2.05325 | ||||||||
\(880\) | 0.351489 | 0.0118487 | ||||||||
\(881\) | −42.7984 | −1.44191 | −0.720957 | − | 0.692980i | \(-0.756297\pi\) | ||||
−0.720957 | + | 0.692980i | \(0.756297\pi\) | |||||||
\(882\) | 16.2323 | 0.546571 | ||||||||
\(883\) | −34.9828 | −1.17726 | −0.588632 | − | 0.808401i | \(-0.700333\pi\) | ||||
−0.588632 | + | 0.808401i | \(0.700333\pi\) | |||||||
\(884\) | −2.31225 | −0.0777692 | ||||||||
\(885\) | 10.3915 | 0.349306 | ||||||||
\(886\) | −2.61430 | −0.0878291 | ||||||||
\(887\) | 26.3669 | 0.885315 | 0.442657 | − | 0.896691i | \(-0.354036\pi\) | ||||
0.442657 | + | 0.896691i | \(0.354036\pi\) | |||||||
\(888\) | −20.0718 | −0.673564 | ||||||||
\(889\) | −20.5869 | −0.690463 | ||||||||
\(890\) | −11.4134 | −0.382579 | ||||||||
\(891\) | −2.63624 | −0.0883173 | ||||||||
\(892\) | −15.4957 | −0.518834 | ||||||||
\(893\) | −10.7457 | −0.359590 | ||||||||
\(894\) | −7.24699 | −0.242376 | ||||||||
\(895\) | 14.5315 | 0.485734 | ||||||||
\(896\) | −1.50878 | −0.0504047 | ||||||||
\(897\) | −13.6244 | −0.454905 | ||||||||
\(898\) | −25.5365 | −0.852164 | ||||||||
\(899\) | 0.355403 | 0.0118534 | ||||||||
\(900\) | 3.43644 | 0.114548 | ||||||||
\(901\) | −10.9242 | −0.363938 | ||||||||
\(902\) | −3.42070 | −0.113897 | ||||||||
\(903\) | −17.2691 | −0.574679 | ||||||||
\(904\) | −16.7578 | −0.557356 | ||||||||
\(905\) | −7.28922 | −0.242302 | ||||||||
\(906\) | −26.6424 | −0.885136 | ||||||||
\(907\) | 30.6581 | 1.01798 | 0.508992 | − | 0.860771i | \(-0.330018\pi\) | ||||
0.508992 | + | 0.860771i | \(0.330018\pi\) | |||||||
\(908\) | −22.2125 | −0.737148 | ||||||||
\(909\) | −35.4497 | −1.17579 | ||||||||
\(910\) | 1.50878 | 0.0500155 | ||||||||
\(911\) | −39.2573 | −1.30065 | −0.650327 | − | 0.759655i | \(-0.725368\pi\) | ||||
−0.650327 | + | 0.759655i | \(0.725368\pi\) | |||||||
\(912\) | 3.01784 | 0.0999306 | ||||||||
\(913\) | −1.97466 | −0.0653516 | ||||||||
\(914\) | −5.50007 | −0.181926 | ||||||||
\(915\) | 9.40890 | 0.311049 | ||||||||
\(916\) | 22.6989 | 0.749991 | ||||||||
\(917\) | −12.1201 | −0.400239 | ||||||||
\(918\) | −2.56025 | −0.0845007 | ||||||||
\(919\) | −35.4666 | −1.16993 | −0.584967 | − | 0.811057i | \(-0.698893\pi\) | ||||
−0.584967 | + | 0.811057i | \(0.698893\pi\) | |||||||
\(920\) | −5.37024 | −0.177052 | ||||||||
\(921\) | 23.0196 | 0.758523 | ||||||||
\(922\) | 39.9050 | 1.31420 | ||||||||
\(923\) | 5.16704 | 0.170075 | ||||||||
\(924\) | 1.34543 | 0.0442613 | ||||||||
\(925\) | 7.91157 | 0.260131 | ||||||||
\(926\) | 20.9421 | 0.688201 | ||||||||
\(927\) | −6.38964 | −0.209863 | ||||||||
\(928\) | 0.355403 | 0.0116667 | ||||||||
\(929\) | 42.8782 | 1.40679 | 0.703395 | − | 0.710800i | \(-0.251667\pi\) | ||||
0.703395 | + | 0.710800i | \(0.251667\pi\) | |||||||
\(930\) | 2.53701 | 0.0831920 | ||||||||
\(931\) | −5.61882 | −0.184149 | ||||||||
\(932\) | 8.56342 | 0.280504 | ||||||||
\(933\) | −41.9141 | −1.37221 | ||||||||
\(934\) | −24.9874 | −0.817611 | ||||||||
\(935\) | 0.812729 | 0.0265791 | ||||||||
\(936\) | 3.43644 | 0.112324 | ||||||||
\(937\) | 24.9524 | 0.815160 | 0.407580 | − | 0.913170i | \(-0.366373\pi\) | ||||
0.407580 | + | 0.913170i | \(0.366373\pi\) | |||||||
\(938\) | −17.5495 | −0.573012 | ||||||||
\(939\) | −51.0885 | −1.66721 | ||||||||
\(940\) | −9.03358 | −0.294643 | ||||||||
\(941\) | −28.2746 | −0.921725 | −0.460862 | − | 0.887472i | \(-0.652460\pi\) | ||||
−0.460862 | + | 0.887472i | \(0.652460\pi\) | |||||||
\(942\) | −1.71053 | −0.0557319 | ||||||||
\(943\) | 52.2633 | 1.70193 | ||||||||
\(944\) | 4.09595 | 0.133312 | ||||||||
\(945\) | 1.67060 | 0.0543447 | ||||||||
\(946\) | 1.58574 | 0.0515570 | ||||||||
\(947\) | −42.8817 | −1.39347 | −0.696734 | − | 0.717329i | \(-0.745364\pi\) | ||||
−0.696734 | + | 0.717329i | \(0.745364\pi\) | |||||||
\(948\) | −5.74247 | −0.186507 | ||||||||
\(949\) | −7.39342 | −0.240000 | ||||||||
\(950\) | −1.18952 | −0.0385932 | ||||||||
\(951\) | −71.6531 | −2.32351 | ||||||||
\(952\) | −3.48866 | −0.113068 | ||||||||
\(953\) | 25.5367 | 0.827215 | 0.413607 | − | 0.910455i | \(-0.364269\pi\) | ||||
0.413607 | + | 0.910455i | \(0.364269\pi\) | |||||||
\(954\) | 16.2355 | 0.525643 | ||||||||
\(955\) | −3.20157 | −0.103600 | ||||||||
\(956\) | −7.34936 | −0.237695 | ||||||||
\(957\) | −0.316925 | −0.0102447 | ||||||||
\(958\) | −2.03234 | −0.0656618 | ||||||||
\(959\) | −26.7483 | −0.863749 | ||||||||
\(960\) | 2.53701 | 0.0818818 | ||||||||
\(961\) | 1.00000 | 0.0322581 | ||||||||
\(962\) | 7.91157 | 0.255079 | ||||||||
\(963\) | 61.9456 | 1.99617 | ||||||||
\(964\) | −12.2953 | −0.396005 | ||||||||
\(965\) | −17.2768 | −0.556160 | ||||||||
\(966\) | −20.5562 | −0.661384 | ||||||||
\(967\) | −20.4243 | −0.656800 | −0.328400 | − | 0.944539i | \(-0.606509\pi\) | ||||
−0.328400 | + | 0.944539i | \(0.606509\pi\) | |||||||
\(968\) | 10.8765 | 0.349583 | ||||||||
\(969\) | 6.97798 | 0.224165 | ||||||||
\(970\) | 14.5519 | 0.467232 | ||||||||
\(971\) | −20.6215 | −0.661776 | −0.330888 | − | 0.943670i | \(-0.607348\pi\) | ||||
−0.330888 | + | 0.943670i | \(0.607348\pi\) | |||||||
\(972\) | −22.3499 | −0.716873 | ||||||||
\(973\) | −0.130854 | −0.00419498 | ||||||||
\(974\) | −39.5360 | −1.26681 | ||||||||
\(975\) | −2.53701 | −0.0812495 | ||||||||
\(976\) | 3.70865 | 0.118711 | ||||||||
\(977\) | −49.7860 | −1.59279 | −0.796397 | − | 0.604774i | \(-0.793264\pi\) | ||||
−0.796397 | + | 0.604774i | \(0.793264\pi\) | |||||||
\(978\) | −30.0847 | −0.962003 | ||||||||
\(979\) | 4.01170 | 0.128215 | ||||||||
\(980\) | −4.72359 | −0.150890 | ||||||||
\(981\) | 65.9756 | 2.10644 | ||||||||
\(982\) | −33.9971 | −1.08489 | ||||||||
\(983\) | −18.4745 | −0.589244 | −0.294622 | − | 0.955614i | \(-0.595194\pi\) | ||||
−0.294622 | + | 0.955614i | \(0.595194\pi\) | |||||||
\(984\) | −24.6903 | −0.787097 | ||||||||
\(985\) | −11.8553 | −0.377741 | ||||||||
\(986\) | 0.821780 | 0.0261708 | ||||||||
\(987\) | −34.5786 | −1.10065 | ||||||||
\(988\) | −1.18952 | −0.0378438 | ||||||||
\(989\) | −24.2279 | −0.770402 | ||||||||
\(990\) | −1.20787 | −0.0383887 | ||||||||
\(991\) | 39.0056 | 1.23905 | 0.619527 | − | 0.784975i | \(-0.287324\pi\) | ||||
0.619527 | + | 0.784975i | \(0.287324\pi\) | |||||||
\(992\) | 1.00000 | 0.0317500 | ||||||||
\(993\) | 25.5199 | 0.809849 | ||||||||
\(994\) | 7.79591 | 0.247271 | ||||||||
\(995\) | −0.350989 | −0.0111271 | ||||||||
\(996\) | −14.2529 | −0.451620 | ||||||||
\(997\) | −26.3619 | −0.834891 | −0.417446 | − | 0.908702i | \(-0.637075\pi\) | ||||
−0.417446 | + | 0.908702i | \(0.637075\pi\) | |||||||
\(998\) | 20.1001 | 0.636258 | ||||||||
\(999\) | 8.76013 | 0.277158 |
(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 | 4030.2.a.l.1.7 | ✓ | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4030.2.a.l.1.7 | ✓ | 8 | 1.1 | even | 1 | trivial |