Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [287,2,Mod(1,287)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(287, 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("287.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 287 = 7 \cdot 41 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 287.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: | \(2.29170653801\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.257.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 4x + 3 \) |
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 | 1.2 | ||
Root | \(0.713538\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 287.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.713538 | 0.504548 | 0.252274 | − | 0.967656i | \(-0.418822\pi\) | ||||
0.252274 | + | 0.967656i | \(0.418822\pi\) | |||||||
\(3\) | −3.20440 | −1.85006 | −0.925031 | − | 0.379892i | \(-0.875961\pi\) | ||||
−0.925031 | + | 0.379892i | \(0.875961\pi\) | |||||||
\(4\) | −1.49086 | −0.745432 | ||||||||
\(5\) | 2.00000 | 0.894427 | 0.447214 | − | 0.894427i | \(-0.352416\pi\) | ||||
0.447214 | + | 0.894427i | \(0.352416\pi\) | |||||||
\(6\) | −2.28646 | −0.933444 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | −2.49086 | −0.880653 | ||||||||
\(9\) | 7.26819 | 2.42273 | ||||||||
\(10\) | 1.42708 | 0.451281 | ||||||||
\(11\) | −2.00000 | −0.603023 | −0.301511 | − | 0.953463i | \(-0.597491\pi\) | ||||
−0.301511 | + | 0.953463i | \(0.597491\pi\) | |||||||
\(12\) | 4.77733 | 1.37910 | ||||||||
\(13\) | 5.49086 | 1.52289 | 0.761446 | − | 0.648229i | \(-0.224490\pi\) | ||||
0.761446 | + | 0.648229i | \(0.224490\pi\) | |||||||
\(14\) | 0.713538 | 0.190701 | ||||||||
\(15\) | −6.40880 | −1.65475 | ||||||||
\(16\) | 1.20440 | 0.301100 | ||||||||
\(17\) | 5.69527 | 1.38130 | 0.690652 | − | 0.723187i | \(-0.257323\pi\) | ||||
0.690652 | + | 0.723187i | \(0.257323\pi\) | |||||||
\(18\) | 5.18613 | 1.22238 | ||||||||
\(19\) | 4.71354 | 1.08136 | 0.540680 | − | 0.841228i | \(-0.318167\pi\) | ||||
0.540680 | + | 0.841228i | \(0.318167\pi\) | |||||||
\(20\) | −2.98173 | −0.666734 | ||||||||
\(21\) | −3.20440 | −0.699258 | ||||||||
\(22\) | −1.42708 | −0.304254 | ||||||||
\(23\) | −0.795598 | −0.165894 | −0.0829469 | − | 0.996554i | \(-0.526433\pi\) | ||||
−0.0829469 | + | 0.996554i | \(0.526433\pi\) | |||||||
\(24\) | 7.98173 | 1.62926 | ||||||||
\(25\) | −1.00000 | −0.200000 | ||||||||
\(26\) | 3.91794 | 0.768371 | ||||||||
\(27\) | −13.6770 | −2.63214 | ||||||||
\(28\) | −1.49086 | −0.281747 | ||||||||
\(29\) | 2.57292 | 0.477780 | 0.238890 | − | 0.971047i | \(-0.423216\pi\) | ||||
0.238890 | + | 0.971047i | \(0.423216\pi\) | |||||||
\(30\) | −4.57292 | −0.834898 | ||||||||
\(31\) | −1.42708 | −0.256310 | −0.128155 | − | 0.991754i | \(-0.540906\pi\) | ||||
−0.128155 | + | 0.991754i | \(0.540906\pi\) | |||||||
\(32\) | 5.84111 | 1.03257 | ||||||||
\(33\) | 6.40880 | 1.11563 | ||||||||
\(34\) | 4.06379 | 0.696934 | ||||||||
\(35\) | 2.00000 | 0.338062 | ||||||||
\(36\) | −10.8359 | −1.80598 | ||||||||
\(37\) | −11.4543 | −1.88308 | −0.941539 | − | 0.336904i | \(-0.890620\pi\) | ||||
−0.941539 | + | 0.336904i | \(0.890620\pi\) | |||||||
\(38\) | 3.36329 | 0.545597 | ||||||||
\(39\) | −17.5949 | −2.81744 | ||||||||
\(40\) | −4.98173 | −0.787680 | ||||||||
\(41\) | −1.00000 | −0.156174 | ||||||||
\(42\) | −2.28646 | −0.352809 | ||||||||
\(43\) | 11.8228 | 1.80297 | 0.901483 | − | 0.432814i | \(-0.142479\pi\) | ||||
0.901483 | + | 0.432814i | \(0.142479\pi\) | |||||||
\(44\) | 2.98173 | 0.449512 | ||||||||
\(45\) | 14.5364 | 2.16696 | ||||||||
\(46\) | −0.567690 | −0.0837013 | ||||||||
\(47\) | 5.89967 | 0.860555 | 0.430277 | − | 0.902697i | \(-0.358416\pi\) | ||||
0.430277 | + | 0.902697i | \(0.358416\pi\) | |||||||
\(48\) | −3.85939 | −0.557054 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −0.713538 | −0.100910 | ||||||||
\(51\) | −18.2499 | −2.55550 | ||||||||
\(52\) | −8.18613 | −1.13521 | ||||||||
\(53\) | −3.55465 | −0.488269 | −0.244134 | − | 0.969741i | \(-0.578504\pi\) | ||||
−0.244134 | + | 0.969741i | \(0.578504\pi\) | |||||||
\(54\) | −9.75905 | −1.32804 | ||||||||
\(55\) | −4.00000 | −0.539360 | ||||||||
\(56\) | −2.49086 | −0.332856 | ||||||||
\(57\) | −15.1041 | −2.00058 | ||||||||
\(58\) | 1.83588 | 0.241063 | ||||||||
\(59\) | −4.00000 | −0.520756 | −0.260378 | − | 0.965507i | \(-0.583847\pi\) | ||||
−0.260378 | + | 0.965507i | \(0.583847\pi\) | |||||||
\(60\) | 9.55465 | 1.23350 | ||||||||
\(61\) | −5.55465 | −0.711200 | −0.355600 | − | 0.934638i | \(-0.615723\pi\) | ||||
−0.355600 | + | 0.934638i | \(0.615723\pi\) | |||||||
\(62\) | −1.01827 | −0.129321 | ||||||||
\(63\) | 7.26819 | 0.915706 | ||||||||
\(64\) | 1.75905 | 0.219882 | ||||||||
\(65\) | 10.9817 | 1.36212 | ||||||||
\(66\) | 4.57292 | 0.562888 | ||||||||
\(67\) | 7.55465 | 0.922948 | 0.461474 | − | 0.887154i | \(-0.347321\pi\) | ||||
0.461474 | + | 0.887154i | \(0.347321\pi\) | |||||||
\(68\) | −8.49086 | −1.02967 | ||||||||
\(69\) | 2.54942 | 0.306914 | ||||||||
\(70\) | 1.42708 | 0.170568 | ||||||||
\(71\) | 1.83588 | 0.217879 | 0.108939 | − | 0.994048i | \(-0.465255\pi\) | ||||
0.108939 | + | 0.994048i | \(0.465255\pi\) | |||||||
\(72\) | −18.1041 | −2.13358 | ||||||||
\(73\) | 9.39053 | 1.09908 | 0.549539 | − | 0.835468i | \(-0.314803\pi\) | ||||
0.549539 | + | 0.835468i | \(0.314803\pi\) | |||||||
\(74\) | −8.17309 | −0.950102 | ||||||||
\(75\) | 3.20440 | 0.370012 | ||||||||
\(76\) | −7.02724 | −0.806080 | ||||||||
\(77\) | −2.00000 | −0.227921 | ||||||||
\(78\) | −12.5547 | −1.42153 | ||||||||
\(79\) | 10.4088 | 1.17108 | 0.585541 | − | 0.810643i | \(-0.300882\pi\) | ||||
0.585541 | + | 0.810643i | \(0.300882\pi\) | |||||||
\(80\) | 2.40880 | 0.269312 | ||||||||
\(81\) | 22.0220 | 2.44689 | ||||||||
\(82\) | −0.713538 | −0.0787971 | ||||||||
\(83\) | 0.854152 | 0.0937553 | 0.0468777 | − | 0.998901i | \(-0.485073\pi\) | ||||
0.0468777 | + | 0.998901i | \(0.485073\pi\) | |||||||
\(84\) | 4.77733 | 0.521249 | ||||||||
\(85\) | 11.3905 | 1.23548 | ||||||||
\(86\) | 8.43605 | 0.909682 | ||||||||
\(87\) | −8.24468 | −0.883923 | ||||||||
\(88\) | 4.98173 | 0.531054 | ||||||||
\(89\) | 7.19917 | 0.763110 | 0.381555 | − | 0.924346i | \(-0.375389\pi\) | ||||
0.381555 | + | 0.924346i | \(0.375389\pi\) | |||||||
\(90\) | 10.3723 | 1.09333 | ||||||||
\(91\) | 5.49086 | 0.575599 | ||||||||
\(92\) | 1.18613 | 0.123662 | ||||||||
\(93\) | 4.57292 | 0.474190 | ||||||||
\(94\) | 4.20964 | 0.434191 | ||||||||
\(95\) | 9.42708 | 0.967198 | ||||||||
\(96\) | −18.7173 | −1.91032 | ||||||||
\(97\) | 5.36852 | 0.545091 | 0.272545 | − | 0.962143i | \(-0.412134\pi\) | ||||
0.272545 | + | 0.962143i | \(0.412134\pi\) | |||||||
\(98\) | 0.713538 | 0.0720782 | ||||||||
\(99\) | −14.5364 | −1.46096 | ||||||||
\(100\) | 1.49086 | 0.149086 | ||||||||
\(101\) | −9.74078 | −0.969244 | −0.484622 | − | 0.874724i | \(-0.661043\pi\) | ||||
−0.484622 | + | 0.874724i | \(0.661043\pi\) | |||||||
\(102\) | −13.0220 | −1.28937 | ||||||||
\(103\) | 12.8542 | 1.26656 | 0.633279 | − | 0.773924i | \(-0.281709\pi\) | ||||
0.633279 | + | 0.773924i | \(0.281709\pi\) | |||||||
\(104\) | −13.6770 | −1.34114 | ||||||||
\(105\) | −6.40880 | −0.625435 | ||||||||
\(106\) | −2.53638 | −0.246355 | ||||||||
\(107\) | −14.9582 | −1.44607 | −0.723033 | − | 0.690814i | \(-0.757252\pi\) | ||||
−0.723033 | + | 0.690814i | \(0.757252\pi\) | |||||||
\(108\) | 20.3905 | 1.96208 | ||||||||
\(109\) | −14.0910 | −1.34968 | −0.674838 | − | 0.737966i | \(-0.735786\pi\) | ||||
−0.674838 | + | 0.737966i | \(0.735786\pi\) | |||||||
\(110\) | −2.85415 | −0.272133 | ||||||||
\(111\) | 36.7042 | 3.48381 | ||||||||
\(112\) | 1.20440 | 0.113805 | ||||||||
\(113\) | −5.04028 | −0.474150 | −0.237075 | − | 0.971491i | \(-0.576189\pi\) | ||||
−0.237075 | + | 0.971491i | \(0.576189\pi\) | |||||||
\(114\) | −10.7773 | −1.00939 | ||||||||
\(115\) | −1.59120 | −0.148380 | ||||||||
\(116\) | −3.83588 | −0.356152 | ||||||||
\(117\) | 39.9086 | 3.68955 | ||||||||
\(118\) | −2.85415 | −0.262746 | ||||||||
\(119\) | 5.69527 | 0.522084 | ||||||||
\(120\) | 15.9635 | 1.45726 | ||||||||
\(121\) | −7.00000 | −0.636364 | ||||||||
\(122\) | −3.96345 | −0.358834 | ||||||||
\(123\) | 3.20440 | 0.288931 | ||||||||
\(124\) | 2.12758 | 0.191062 | ||||||||
\(125\) | −12.0000 | −1.07331 | ||||||||
\(126\) | 5.18613 | 0.462017 | ||||||||
\(127\) | 4.75382 | 0.421833 | 0.210917 | − | 0.977504i | \(-0.432355\pi\) | ||||
0.210917 | + | 0.977504i | \(0.432355\pi\) | |||||||
\(128\) | −10.4271 | −0.921632 | ||||||||
\(129\) | −37.8851 | −3.33560 | ||||||||
\(130\) | 7.83588 | 0.687252 | ||||||||
\(131\) | −15.8359 | −1.38359 | −0.691794 | − | 0.722095i | \(-0.743179\pi\) | ||||
−0.691794 | + | 0.722095i | \(0.743179\pi\) | |||||||
\(132\) | −9.55465 | −0.831626 | ||||||||
\(133\) | 4.71354 | 0.408716 | ||||||||
\(134\) | 5.39053 | 0.465671 | ||||||||
\(135\) | −27.3540 | −2.35426 | ||||||||
\(136\) | −14.1861 | −1.21645 | ||||||||
\(137\) | 15.9635 | 1.36385 | 0.681925 | − | 0.731422i | \(-0.261143\pi\) | ||||
0.681925 | + | 0.731422i | \(0.261143\pi\) | |||||||
\(138\) | 1.81911 | 0.154853 | ||||||||
\(139\) | −7.26295 | −0.616036 | −0.308018 | − | 0.951381i | \(-0.599666\pi\) | ||||
−0.308018 | + | 0.951381i | \(0.599666\pi\) | |||||||
\(140\) | −2.98173 | −0.252002 | ||||||||
\(141\) | −18.9049 | −1.59208 | ||||||||
\(142\) | 1.30997 | 0.109930 | ||||||||
\(143\) | −10.9817 | −0.918338 | ||||||||
\(144\) | 8.75382 | 0.729485 | ||||||||
\(145\) | 5.14585 | 0.427339 | ||||||||
\(146\) | 6.70050 | 0.554537 | ||||||||
\(147\) | −3.20440 | −0.264295 | ||||||||
\(148\) | 17.0768 | 1.40371 | ||||||||
\(149\) | −22.3723 | −1.83281 | −0.916403 | − | 0.400256i | \(-0.868921\pi\) | ||||
−0.916403 | + | 0.400256i | \(0.868921\pi\) | |||||||
\(150\) | 2.28646 | 0.186689 | ||||||||
\(151\) | −19.3905 | −1.57798 | −0.788989 | − | 0.614407i | \(-0.789395\pi\) | ||||
−0.788989 | + | 0.614407i | \(0.789395\pi\) | |||||||
\(152\) | −11.7408 | −0.952303 | ||||||||
\(153\) | 41.3943 | 3.34653 | ||||||||
\(154\) | −1.42708 | −0.114997 | ||||||||
\(155\) | −2.85415 | −0.229251 | ||||||||
\(156\) | 26.2316 | 2.10021 | ||||||||
\(157\) | 7.65872 | 0.611232 | 0.305616 | − | 0.952155i | \(-0.401138\pi\) | ||||
0.305616 | + | 0.952155i | \(0.401138\pi\) | |||||||
\(158\) | 7.42708 | 0.590866 | ||||||||
\(159\) | 11.3905 | 0.903328 | ||||||||
\(160\) | 11.6822 | 0.923561 | ||||||||
\(161\) | −0.795598 | −0.0627019 | ||||||||
\(162\) | 15.7135 | 1.23457 | ||||||||
\(163\) | 1.35805 | 0.106371 | 0.0531855 | − | 0.998585i | \(-0.483063\pi\) | ||||
0.0531855 | + | 0.998585i | \(0.483063\pi\) | |||||||
\(164\) | 1.49086 | 0.116417 | ||||||||
\(165\) | 12.8176 | 0.997849 | ||||||||
\(166\) | 0.609470 | 0.0473040 | ||||||||
\(167\) | −13.5311 | −1.04707 | −0.523536 | − | 0.852004i | \(-0.675387\pi\) | ||||
−0.523536 | + | 0.852004i | \(0.675387\pi\) | |||||||
\(168\) | 7.98173 | 0.615804 | ||||||||
\(169\) | 17.1496 | 1.31920 | ||||||||
\(170\) | 8.12758 | 0.623357 | ||||||||
\(171\) | 34.2589 | 2.61984 | ||||||||
\(172\) | −17.6262 | −1.34399 | ||||||||
\(173\) | 3.01827 | 0.229475 | 0.114738 | − | 0.993396i | \(-0.463397\pi\) | ||||
0.114738 | + | 0.993396i | \(0.463397\pi\) | |||||||
\(174\) | −5.88289 | −0.445981 | ||||||||
\(175\) | −1.00000 | −0.0755929 | ||||||||
\(176\) | −2.40880 | −0.181570 | ||||||||
\(177\) | 12.8176 | 0.963430 | ||||||||
\(178\) | 5.13688 | 0.385025 | ||||||||
\(179\) | −10.8176 | −0.808546 | −0.404273 | − | 0.914638i | \(-0.632475\pi\) | ||||
−0.404273 | + | 0.914638i | \(0.632475\pi\) | |||||||
\(180\) | −21.6718 | −1.61532 | ||||||||
\(181\) | 15.3320 | 1.13962 | 0.569808 | − | 0.821778i | \(-0.307017\pi\) | ||||
0.569808 | + | 0.821778i | \(0.307017\pi\) | |||||||
\(182\) | 3.91794 | 0.290417 | ||||||||
\(183\) | 17.7993 | 1.31576 | ||||||||
\(184\) | 1.98173 | 0.146095 | ||||||||
\(185\) | −22.9086 | −1.68428 | ||||||||
\(186\) | 3.26295 | 0.239251 | ||||||||
\(187\) | −11.3905 | −0.832958 | ||||||||
\(188\) | −8.79560 | −0.641485 | ||||||||
\(189\) | −13.6770 | −0.994855 | ||||||||
\(190\) | 6.72658 | 0.487997 | ||||||||
\(191\) | −3.01827 | −0.218395 | −0.109197 | − | 0.994020i | \(-0.534828\pi\) | ||||
−0.109197 | + | 0.994020i | \(0.534828\pi\) | |||||||
\(192\) | −5.63671 | −0.406795 | ||||||||
\(193\) | 1.01827 | 0.0732969 | 0.0366484 | − | 0.999328i | \(-0.488332\pi\) | ||||
0.0366484 | + | 0.999328i | \(0.488332\pi\) | |||||||
\(194\) | 3.83064 | 0.275024 | ||||||||
\(195\) | −35.1899 | −2.52000 | ||||||||
\(196\) | −1.49086 | −0.106490 | ||||||||
\(197\) | 14.8411 | 1.05739 | 0.528693 | − | 0.848813i | \(-0.322682\pi\) | ||||
0.528693 | + | 0.848813i | \(0.322682\pi\) | |||||||
\(198\) | −10.3723 | −0.737124 | ||||||||
\(199\) | 9.77209 | 0.692725 | 0.346363 | − | 0.938101i | \(-0.387417\pi\) | ||||
0.346363 | + | 0.938101i | \(0.387417\pi\) | |||||||
\(200\) | 2.49086 | 0.176131 | ||||||||
\(201\) | −24.2081 | −1.70751 | ||||||||
\(202\) | −6.95042 | −0.489030 | ||||||||
\(203\) | 2.57292 | 0.180584 | ||||||||
\(204\) | 27.2081 | 1.90495 | ||||||||
\(205\) | −2.00000 | −0.139686 | ||||||||
\(206\) | 9.17192 | 0.639038 | ||||||||
\(207\) | −5.78256 | −0.401916 | ||||||||
\(208\) | 6.61320 | 0.458543 | ||||||||
\(209\) | −9.42708 | −0.652084 | ||||||||
\(210\) | −4.57292 | −0.315562 | ||||||||
\(211\) | 10.6640 | 0.734137 | 0.367068 | − | 0.930194i | \(-0.380361\pi\) | ||||
0.367068 | + | 0.930194i | \(0.380361\pi\) | |||||||
\(212\) | 5.29950 | 0.363971 | ||||||||
\(213\) | −5.88289 | −0.403089 | ||||||||
\(214\) | −10.6733 | −0.729609 | ||||||||
\(215\) | 23.6457 | 1.61262 | ||||||||
\(216\) | 34.0675 | 2.31800 | ||||||||
\(217\) | −1.42708 | −0.0968762 | ||||||||
\(218\) | −10.0545 | −0.680976 | ||||||||
\(219\) | −30.0910 | −2.03336 | ||||||||
\(220\) | 5.96345 | 0.402056 | ||||||||
\(221\) | 31.2719 | 2.10358 | ||||||||
\(222\) | 26.1899 | 1.75775 | ||||||||
\(223\) | −24.4998 | −1.64063 | −0.820315 | − | 0.571912i | \(-0.806202\pi\) | ||||
−0.820315 | + | 0.571912i | \(0.806202\pi\) | |||||||
\(224\) | 5.84111 | 0.390276 | ||||||||
\(225\) | −7.26819 | −0.484546 | ||||||||
\(226\) | −3.59643 | −0.239231 | ||||||||
\(227\) | −10.8542 | −0.720415 | −0.360208 | − | 0.932872i | \(-0.617294\pi\) | ||||
−0.360208 | + | 0.932872i | \(0.617294\pi\) | |||||||
\(228\) | 22.5181 | 1.49130 | ||||||||
\(229\) | 3.07683 | 0.203322 | 0.101661 | − | 0.994819i | \(-0.467584\pi\) | ||||
0.101661 | + | 0.994819i | \(0.467584\pi\) | |||||||
\(230\) | −1.13538 | −0.0748647 | ||||||||
\(231\) | 6.40880 | 0.421668 | ||||||||
\(232\) | −6.40880 | −0.420759 | ||||||||
\(233\) | 16.3827 | 1.07327 | 0.536634 | − | 0.843815i | \(-0.319696\pi\) | ||||
0.536634 | + | 0.843815i | \(0.319696\pi\) | |||||||
\(234\) | 28.4763 | 1.86156 | ||||||||
\(235\) | 11.7993 | 0.769704 | ||||||||
\(236\) | 5.96345 | 0.388188 | ||||||||
\(237\) | −33.3540 | −2.16657 | ||||||||
\(238\) | 4.06379 | 0.263416 | ||||||||
\(239\) | −14.8281 | −0.959148 | −0.479574 | − | 0.877501i | \(-0.659209\pi\) | ||||
−0.479574 | + | 0.877501i | \(0.659209\pi\) | |||||||
\(240\) | −7.71877 | −0.498245 | ||||||||
\(241\) | −14.7811 | −0.952132 | −0.476066 | − | 0.879410i | \(-0.657938\pi\) | ||||
−0.476066 | + | 0.879410i | \(0.657938\pi\) | |||||||
\(242\) | −4.99477 | −0.321076 | ||||||||
\(243\) | −29.5364 | −1.89476 | ||||||||
\(244\) | 8.28123 | 0.530151 | ||||||||
\(245\) | 2.00000 | 0.127775 | ||||||||
\(246\) | 2.28646 | 0.145779 | ||||||||
\(247\) | 25.8814 | 1.64679 | ||||||||
\(248\) | 3.55465 | 0.225721 | ||||||||
\(249\) | −2.73705 | −0.173453 | ||||||||
\(250\) | −8.56246 | −0.541537 | ||||||||
\(251\) | −10.2812 | −0.648945 | −0.324473 | − | 0.945895i | \(-0.605187\pi\) | ||||
−0.324473 | + | 0.945895i | \(0.605187\pi\) | |||||||
\(252\) | −10.8359 | −0.682596 | ||||||||
\(253\) | 1.59120 | 0.100038 | ||||||||
\(254\) | 3.39203 | 0.212835 | ||||||||
\(255\) | −36.4998 | −2.28571 | ||||||||
\(256\) | −10.9582 | −0.684889 | ||||||||
\(257\) | −1.48563 | −0.0926710 | −0.0463355 | − | 0.998926i | \(-0.514754\pi\) | ||||
−0.0463355 | + | 0.998926i | \(0.514754\pi\) | |||||||
\(258\) | −27.0325 | −1.68297 | ||||||||
\(259\) | −11.4543 | −0.711737 | ||||||||
\(260\) | −16.3723 | −1.01536 | ||||||||
\(261\) | 18.7005 | 1.15753 | ||||||||
\(262\) | −11.2995 | −0.698085 | ||||||||
\(263\) | 28.3357 | 1.74725 | 0.873627 | − | 0.486595i | \(-0.161761\pi\) | ||||
0.873627 | + | 0.486595i | \(0.161761\pi\) | |||||||
\(264\) | −15.9635 | −0.982483 | ||||||||
\(265\) | −7.10930 | −0.436721 | ||||||||
\(266\) | 3.36329 | 0.206216 | ||||||||
\(267\) | −23.0690 | −1.41180 | ||||||||
\(268\) | −11.2630 | −0.687994 | ||||||||
\(269\) | 15.8098 | 0.963941 | 0.481970 | − | 0.876188i | \(-0.339921\pi\) | ||||
0.481970 | + | 0.876188i | \(0.339921\pi\) | |||||||
\(270\) | −19.5181 | −1.18783 | ||||||||
\(271\) | 16.3357 | 0.992324 | 0.496162 | − | 0.868230i | \(-0.334742\pi\) | ||||
0.496162 | + | 0.868230i | \(0.334742\pi\) | |||||||
\(272\) | 6.85939 | 0.415911 | ||||||||
\(273\) | −17.5949 | −1.06489 | ||||||||
\(274\) | 11.3905 | 0.688127 | ||||||||
\(275\) | 2.00000 | 0.120605 | ||||||||
\(276\) | −3.80083 | −0.228783 | ||||||||
\(277\) | −1.93098 | −0.116021 | −0.0580106 | − | 0.998316i | \(-0.518476\pi\) | ||||
−0.0580106 | + | 0.998316i | \(0.518476\pi\) | |||||||
\(278\) | −5.18239 | −0.310819 | ||||||||
\(279\) | −10.3723 | −0.620971 | ||||||||
\(280\) | −4.98173 | −0.297715 | ||||||||
\(281\) | −29.5181 | −1.76090 | −0.880451 | − | 0.474137i | \(-0.842760\pi\) | ||||
−0.880451 | + | 0.474137i | \(0.842760\pi\) | |||||||
\(282\) | −13.4894 | −0.803280 | ||||||||
\(283\) | 8.03655 | 0.477723 | 0.238862 | − | 0.971054i | \(-0.423226\pi\) | ||||
0.238862 | + | 0.971054i | \(0.423226\pi\) | |||||||
\(284\) | −2.73705 | −0.162414 | ||||||||
\(285\) | −30.2081 | −1.78938 | ||||||||
\(286\) | −7.83588 | −0.463345 | ||||||||
\(287\) | −1.00000 | −0.0590281 | ||||||||
\(288\) | 42.4543 | 2.50164 | ||||||||
\(289\) | 15.4360 | 0.908003 | ||||||||
\(290\) | 3.67176 | 0.215613 | ||||||||
\(291\) | −17.2029 | −1.00845 | ||||||||
\(292\) | −14.0000 | −0.819288 | ||||||||
\(293\) | −6.56246 | −0.383383 | −0.191691 | − | 0.981455i | \(-0.561397\pi\) | ||||
−0.191691 | + | 0.981455i | \(0.561397\pi\) | |||||||
\(294\) | −2.28646 | −0.133349 | ||||||||
\(295\) | −8.00000 | −0.465778 | ||||||||
\(296\) | 28.5311 | 1.65834 | ||||||||
\(297\) | 27.3540 | 1.58724 | ||||||||
\(298\) | −15.9635 | −0.924738 | ||||||||
\(299\) | −4.36852 | −0.252638 | ||||||||
\(300\) | −4.77733 | −0.275819 | ||||||||
\(301\) | 11.8228 | 0.681457 | ||||||||
\(302\) | −13.8359 | −0.796165 | ||||||||
\(303\) | 31.2134 | 1.79316 | ||||||||
\(304\) | 5.67699 | 0.325598 | ||||||||
\(305\) | −11.1093 | −0.636117 | ||||||||
\(306\) | 29.5364 | 1.68848 | ||||||||
\(307\) | −19.6457 | −1.12124 | −0.560619 | − | 0.828074i | \(-0.689437\pi\) | ||||
−0.560619 | + | 0.828074i | \(0.689437\pi\) | |||||||
\(308\) | 2.98173 | 0.169900 | ||||||||
\(309\) | −41.1899 | −2.34321 | ||||||||
\(310\) | −2.03655 | −0.115668 | ||||||||
\(311\) | −1.32301 | −0.0750209 | −0.0375104 | − | 0.999296i | \(-0.511943\pi\) | ||||
−0.0375104 | + | 0.999296i | \(0.511943\pi\) | |||||||
\(312\) | 43.8266 | 2.48119 | ||||||||
\(313\) | −17.6222 | −0.996064 | −0.498032 | − | 0.867159i | \(-0.665944\pi\) | ||||
−0.498032 | + | 0.867159i | \(0.665944\pi\) | |||||||
\(314\) | 5.46479 | 0.308396 | ||||||||
\(315\) | 14.5364 | 0.819032 | ||||||||
\(316\) | −15.5181 | −0.872962 | ||||||||
\(317\) | −22.7811 | −1.27951 | −0.639756 | − | 0.768578i | \(-0.720965\pi\) | ||||
−0.639756 | + | 0.768578i | \(0.720965\pi\) | |||||||
\(318\) | 8.12758 | 0.455772 | ||||||||
\(319\) | −5.14585 | −0.288112 | ||||||||
\(320\) | 3.51811 | 0.196668 | ||||||||
\(321\) | 47.9321 | 2.67531 | ||||||||
\(322\) | −0.567690 | −0.0316361 | ||||||||
\(323\) | 26.8448 | 1.49369 | ||||||||
\(324\) | −32.8318 | −1.82399 | ||||||||
\(325\) | −5.49086 | −0.304578 | ||||||||
\(326\) | 0.969023 | 0.0536692 | ||||||||
\(327\) | 45.1533 | 2.49698 | ||||||||
\(328\) | 2.49086 | 0.137535 | ||||||||
\(329\) | 5.89967 | 0.325259 | ||||||||
\(330\) | 9.14585 | 0.503462 | ||||||||
\(331\) | 22.0000 | 1.20923 | 0.604615 | − | 0.796518i | \(-0.293327\pi\) | ||||
0.604615 | + | 0.796518i | \(0.293327\pi\) | |||||||
\(332\) | −1.27342 | −0.0698882 | ||||||||
\(333\) | −83.2522 | −4.56219 | ||||||||
\(334\) | −9.65498 | −0.528297 | ||||||||
\(335\) | 15.1093 | 0.825509 | ||||||||
\(336\) | −3.85939 | −0.210547 | ||||||||
\(337\) | 6.63148 | 0.361240 | 0.180620 | − | 0.983553i | \(-0.442190\pi\) | ||||
0.180620 | + | 0.983553i | \(0.442190\pi\) | |||||||
\(338\) | 12.2369 | 0.665598 | ||||||||
\(339\) | 16.1511 | 0.877206 | ||||||||
\(340\) | −16.9817 | −0.920963 | ||||||||
\(341\) | 2.85415 | 0.154561 | ||||||||
\(342\) | 24.4450 | 1.32184 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | −29.4491 | −1.58779 | ||||||||
\(345\) | 5.09883 | 0.274512 | ||||||||
\(346\) | 2.15365 | 0.115781 | ||||||||
\(347\) | −18.0000 | −0.966291 | −0.483145 | − | 0.875540i | \(-0.660506\pi\) | ||||
−0.483145 | + | 0.875540i | \(0.660506\pi\) | |||||||
\(348\) | 12.2917 | 0.658904 | ||||||||
\(349\) | 34.6274 | 1.85356 | 0.926781 | − | 0.375601i | \(-0.122564\pi\) | ||||
0.926781 | + | 0.375601i | \(0.122564\pi\) | |||||||
\(350\) | −0.713538 | −0.0381402 | ||||||||
\(351\) | −75.0985 | −4.00846 | ||||||||
\(352\) | −11.6822 | −0.622665 | ||||||||
\(353\) | −27.9635 | −1.48834 | −0.744172 | − | 0.667988i | \(-0.767156\pi\) | ||||
−0.744172 | + | 0.667988i | \(0.767156\pi\) | |||||||
\(354\) | 9.14585 | 0.486096 | ||||||||
\(355\) | 3.67176 | 0.194877 | ||||||||
\(356\) | −10.7330 | −0.568847 | ||||||||
\(357\) | −18.2499 | −0.965888 | ||||||||
\(358\) | −7.71877 | −0.407950 | ||||||||
\(359\) | 11.9907 | 0.632845 | 0.316422 | − | 0.948618i | \(-0.397518\pi\) | ||||
0.316422 | + | 0.948618i | \(0.397518\pi\) | |||||||
\(360\) | −36.2081 | −1.90834 | ||||||||
\(361\) | 3.21744 | 0.169339 | ||||||||
\(362\) | 10.9399 | 0.574991 | ||||||||
\(363\) | 22.4308 | 1.17731 | ||||||||
\(364\) | −8.18613 | −0.429070 | ||||||||
\(365\) | 18.7811 | 0.983046 | ||||||||
\(366\) | 12.7005 | 0.663866 | ||||||||
\(367\) | 28.4998 | 1.48768 | 0.743840 | − | 0.668358i | \(-0.233003\pi\) | ||||
0.743840 | + | 0.668358i | \(0.233003\pi\) | |||||||
\(368\) | −0.958220 | −0.0499507 | ||||||||
\(369\) | −7.26819 | −0.378367 | ||||||||
\(370\) | −16.3462 | −0.849797 | ||||||||
\(371\) | −3.55465 | −0.184548 | ||||||||
\(372\) | −6.81761 | −0.353476 | ||||||||
\(373\) | −14.8411 | −0.768444 | −0.384222 | − | 0.923241i | \(-0.625530\pi\) | ||||
−0.384222 | + | 0.923241i | \(0.625530\pi\) | |||||||
\(374\) | −8.12758 | −0.420267 | ||||||||
\(375\) | 38.4528 | 1.98570 | ||||||||
\(376\) | −14.6953 | −0.757850 | ||||||||
\(377\) | 14.1276 | 0.727607 | ||||||||
\(378\) | −9.75905 | −0.501952 | ||||||||
\(379\) | 7.20440 | 0.370065 | 0.185033 | − | 0.982732i | \(-0.440761\pi\) | ||||
0.185033 | + | 0.982732i | \(0.440761\pi\) | |||||||
\(380\) | −14.0545 | −0.720980 | ||||||||
\(381\) | −15.2331 | −0.780418 | ||||||||
\(382\) | −2.15365 | −0.110190 | ||||||||
\(383\) | −5.16786 | −0.264065 | −0.132033 | − | 0.991245i | \(-0.542150\pi\) | ||||
−0.132033 | + | 0.991245i | \(0.542150\pi\) | |||||||
\(384\) | 33.4125 | 1.70508 | ||||||||
\(385\) | −4.00000 | −0.203859 | ||||||||
\(386\) | 0.726576 | 0.0369818 | ||||||||
\(387\) | 85.9306 | 4.36810 | ||||||||
\(388\) | −8.00373 | −0.406328 | ||||||||
\(389\) | −4.34502 | −0.220301 | −0.110151 | − | 0.993915i | \(-0.535133\pi\) | ||||
−0.110151 | + | 0.993915i | \(0.535133\pi\) | |||||||
\(390\) | −25.1093 | −1.27146 | ||||||||
\(391\) | −4.53114 | −0.229150 | ||||||||
\(392\) | −2.49086 | −0.125808 | ||||||||
\(393\) | 50.7445 | 2.55972 | ||||||||
\(394\) | 10.5897 | 0.533501 | ||||||||
\(395\) | 20.8176 | 1.04745 | ||||||||
\(396\) | 21.6718 | 1.08905 | ||||||||
\(397\) | 19.7083 | 0.989131 | 0.494566 | − | 0.869140i | \(-0.335327\pi\) | ||||
0.494566 | + | 0.869140i | \(0.335327\pi\) | |||||||
\(398\) | 6.97276 | 0.349513 | ||||||||
\(399\) | −15.1041 | −0.756149 | ||||||||
\(400\) | −1.20440 | −0.0602201 | ||||||||
\(401\) | −28.3995 | −1.41820 | −0.709102 | − | 0.705106i | \(-0.750899\pi\) | ||||
−0.709102 | + | 0.705106i | \(0.750899\pi\) | |||||||
\(402\) | −17.2734 | −0.861520 | ||||||||
\(403\) | −7.83588 | −0.390333 | ||||||||
\(404\) | 14.5222 | 0.722505 | ||||||||
\(405\) | 44.0440 | 2.18856 | ||||||||
\(406\) | 1.83588 | 0.0911131 | ||||||||
\(407\) | 22.9086 | 1.13554 | ||||||||
\(408\) | 45.4581 | 2.25051 | ||||||||
\(409\) | 19.2734 | 0.953009 | 0.476505 | − | 0.879172i | \(-0.341904\pi\) | ||||
0.476505 | + | 0.879172i | \(0.341904\pi\) | |||||||
\(410\) | −1.42708 | −0.0704783 | ||||||||
\(411\) | −51.1533 | −2.52321 | ||||||||
\(412\) | −19.1638 | −0.944132 | ||||||||
\(413\) | −4.00000 | −0.196827 | ||||||||
\(414\) | −4.12608 | −0.202786 | ||||||||
\(415\) | 1.70830 | 0.0838573 | ||||||||
\(416\) | 32.0728 | 1.57250 | ||||||||
\(417\) | 23.2734 | 1.13970 | ||||||||
\(418\) | −6.72658 | −0.329008 | ||||||||
\(419\) | −15.9530 | −0.779354 | −0.389677 | − | 0.920952i | \(-0.627413\pi\) | ||||
−0.389677 | + | 0.920952i | \(0.627413\pi\) | |||||||
\(420\) | 9.55465 | 0.466219 | ||||||||
\(421\) | −38.0806 | −1.85593 | −0.927966 | − | 0.372664i | \(-0.878445\pi\) | ||||
−0.927966 | + | 0.372664i | \(0.878445\pi\) | |||||||
\(422\) | 7.60914 | 0.370407 | ||||||||
\(423\) | 42.8799 | 2.08489 | ||||||||
\(424\) | 8.85415 | 0.429996 | ||||||||
\(425\) | −5.69527 | −0.276261 | ||||||||
\(426\) | −4.19767 | −0.203378 | ||||||||
\(427\) | −5.55465 | −0.268808 | ||||||||
\(428\) | 22.3007 | 1.07794 | ||||||||
\(429\) | 35.1899 | 1.69898 | ||||||||
\(430\) | 16.8721 | 0.813644 | ||||||||
\(431\) | −10.2917 | −0.495734 | −0.247867 | − | 0.968794i | \(-0.579730\pi\) | ||||
−0.247867 | + | 0.968794i | \(0.579730\pi\) | |||||||
\(432\) | −16.4726 | −0.792538 | ||||||||
\(433\) | 9.98953 | 0.480066 | 0.240033 | − | 0.970765i | \(-0.422842\pi\) | ||||
0.240033 | + | 0.970765i | \(0.422842\pi\) | |||||||
\(434\) | −1.01827 | −0.0488787 | ||||||||
\(435\) | −16.4894 | −0.790604 | ||||||||
\(436\) | 21.0078 | 1.00609 | ||||||||
\(437\) | −3.75008 | −0.179391 | ||||||||
\(438\) | −21.4711 | −1.02593 | ||||||||
\(439\) | 1.61320 | 0.0769941 | 0.0384970 | − | 0.999259i | \(-0.487743\pi\) | ||||
0.0384970 | + | 0.999259i | \(0.487743\pi\) | |||||||
\(440\) | 9.96345 | 0.474989 | ||||||||
\(441\) | 7.26819 | 0.346104 | ||||||||
\(442\) | 22.3137 | 1.06135 | ||||||||
\(443\) | 21.2096 | 1.00770 | 0.503850 | − | 0.863791i | \(-0.331916\pi\) | ||||
0.503850 | + | 0.863791i | \(0.331916\pi\) | |||||||
\(444\) | −54.7210 | −2.59694 | ||||||||
\(445\) | 14.3983 | 0.682546 | ||||||||
\(446\) | −17.4816 | −0.827776 | ||||||||
\(447\) | 71.6897 | 3.39081 | ||||||||
\(448\) | 1.75905 | 0.0831074 | ||||||||
\(449\) | 12.0325 | 0.567848 | 0.283924 | − | 0.958847i | \(-0.408364\pi\) | ||||
0.283924 | + | 0.958847i | \(0.408364\pi\) | |||||||
\(450\) | −5.18613 | −0.244476 | ||||||||
\(451\) | 2.00000 | 0.0941763 | ||||||||
\(452\) | 7.51437 | 0.353446 | ||||||||
\(453\) | 62.1350 | 2.91936 | ||||||||
\(454\) | −7.74485 | −0.363484 | ||||||||
\(455\) | 10.9817 | 0.514831 | ||||||||
\(456\) | 37.6222 | 1.76182 | ||||||||
\(457\) | −0.908636 | −0.0425042 | −0.0212521 | − | 0.999774i | \(-0.506765\pi\) | ||||
−0.0212521 | + | 0.999774i | \(0.506765\pi\) | |||||||
\(458\) | 2.19543 | 0.102586 | ||||||||
\(459\) | −77.8941 | −3.63579 | ||||||||
\(460\) | 2.37226 | 0.110607 | ||||||||
\(461\) | −13.4010 | −0.624147 | −0.312073 | − | 0.950058i | \(-0.601023\pi\) | ||||
−0.312073 | + | 0.950058i | \(0.601023\pi\) | |||||||
\(462\) | 4.57292 | 0.212752 | ||||||||
\(463\) | −7.29950 | −0.339237 | −0.169618 | − | 0.985510i | \(-0.554253\pi\) | ||||
−0.169618 | + | 0.985510i | \(0.554253\pi\) | |||||||
\(464\) | 3.09883 | 0.143860 | ||||||||
\(465\) | 9.14585 | 0.424129 | ||||||||
\(466\) | 11.6897 | 0.541515 | ||||||||
\(467\) | −4.54685 | −0.210403 | −0.105202 | − | 0.994451i | \(-0.533549\pi\) | ||||
−0.105202 | + | 0.994451i | \(0.533549\pi\) | |||||||
\(468\) | −59.4983 | −2.75031 | ||||||||
\(469\) | 7.55465 | 0.348841 | ||||||||
\(470\) | 8.41927 | 0.388352 | ||||||||
\(471\) | −24.5416 | −1.13082 | ||||||||
\(472\) | 9.96345 | 0.458605 | ||||||||
\(473\) | −23.6457 | −1.08723 | ||||||||
\(474\) | −23.7993 | −1.09314 | ||||||||
\(475\) | −4.71354 | −0.216272 | ||||||||
\(476\) | −8.49086 | −0.389178 | ||||||||
\(477\) | −25.8359 | −1.18294 | ||||||||
\(478\) | −10.5804 | −0.483936 | ||||||||
\(479\) | 13.3581 | 0.610345 | 0.305173 | − | 0.952297i | \(-0.401286\pi\) | ||||
0.305173 | + | 0.952297i | \(0.401286\pi\) | |||||||
\(480\) | −37.4345 | −1.70865 | ||||||||
\(481\) | −62.8941 | −2.86772 | ||||||||
\(482\) | −10.5468 | −0.480396 | ||||||||
\(483\) | 2.54942 | 0.116002 | ||||||||
\(484\) | 10.4360 | 0.474366 | ||||||||
\(485\) | 10.7370 | 0.487544 | ||||||||
\(486\) | −21.0753 | −0.955996 | ||||||||
\(487\) | 2.11454 | 0.0958188 | 0.0479094 | − | 0.998852i | \(-0.484744\pi\) | ||||
0.0479094 | + | 0.998852i | \(0.484744\pi\) | |||||||
\(488\) | 13.8359 | 0.626321 | ||||||||
\(489\) | −4.35175 | −0.196793 | ||||||||
\(490\) | 1.42708 | 0.0644687 | ||||||||
\(491\) | −15.5767 | −0.702965 | −0.351482 | − | 0.936194i | \(-0.614322\pi\) | ||||
−0.351482 | + | 0.936194i | \(0.614322\pi\) | |||||||
\(492\) | −4.77733 | −0.215378 | ||||||||
\(493\) | 14.6535 | 0.659960 | ||||||||
\(494\) | 18.4674 | 0.830886 | ||||||||
\(495\) | −29.0728 | −1.30672 | ||||||||
\(496\) | −1.71877 | −0.0771752 | ||||||||
\(497\) | 1.83588 | 0.0823504 | ||||||||
\(498\) | −1.95299 | −0.0875154 | ||||||||
\(499\) | −12.5729 | −0.562841 | −0.281421 | − | 0.959584i | \(-0.590806\pi\) | ||||
−0.281421 | + | 0.959584i | \(0.590806\pi\) | |||||||
\(500\) | 17.8904 | 0.800081 | ||||||||
\(501\) | 43.3592 | 1.93715 | ||||||||
\(502\) | −7.33605 | −0.327424 | ||||||||
\(503\) | −34.4308 | −1.53519 | −0.767597 | − | 0.640933i | \(-0.778548\pi\) | ||||
−0.767597 | + | 0.640933i | \(0.778548\pi\) | |||||||
\(504\) | −18.1041 | −0.806419 | ||||||||
\(505\) | −19.4816 | −0.866918 | ||||||||
\(506\) | 1.13538 | 0.0504738 | ||||||||
\(507\) | −54.9542 | −2.44060 | ||||||||
\(508\) | −7.08729 | −0.314448 | ||||||||
\(509\) | 25.6184 | 1.13552 | 0.567759 | − | 0.823195i | \(-0.307811\pi\) | ||||
0.567759 | + | 0.823195i | \(0.307811\pi\) | |||||||
\(510\) | −26.0440 | −1.15325 | ||||||||
\(511\) | 9.39053 | 0.415413 | ||||||||
\(512\) | 13.0350 | 0.576073 | ||||||||
\(513\) | −64.4670 | −2.84629 | ||||||||
\(514\) | −1.06005 | −0.0467569 | ||||||||
\(515\) | 25.7083 | 1.13284 | ||||||||
\(516\) | 56.4816 | 2.48646 | ||||||||
\(517\) | −11.7993 | −0.518934 | ||||||||
\(518\) | −8.17309 | −0.359105 | ||||||||
\(519\) | −9.67176 | −0.424543 | ||||||||
\(520\) | −27.3540 | −1.19955 | ||||||||
\(521\) | 28.1988 | 1.23541 | 0.617707 | − | 0.786409i | \(-0.288062\pi\) | ||||
0.617707 | + | 0.786409i | \(0.288062\pi\) | |||||||
\(522\) | 13.3435 | 0.584030 | ||||||||
\(523\) | −5.54418 | −0.242430 | −0.121215 | − | 0.992626i | \(-0.538679\pi\) | ||||
−0.121215 | + | 0.992626i | \(0.538679\pi\) | |||||||
\(524\) | 23.6091 | 1.03137 | ||||||||
\(525\) | 3.20440 | 0.139852 | ||||||||
\(526\) | 20.2186 | 0.881573 | ||||||||
\(527\) | −8.12758 | −0.354043 | ||||||||
\(528\) | 7.71877 | 0.335916 | ||||||||
\(529\) | −22.3670 | −0.972479 | ||||||||
\(530\) | −5.07276 | −0.220346 | ||||||||
\(531\) | −29.0728 | −1.26165 | ||||||||
\(532\) | −7.02724 | −0.304670 | ||||||||
\(533\) | −5.49086 | −0.237836 | ||||||||
\(534\) | −16.4606 | −0.712321 | ||||||||
\(535\) | −29.9164 | −1.29340 | ||||||||
\(536\) | −18.8176 | −0.812797 | ||||||||
\(537\) | 34.6640 | 1.49586 | ||||||||
\(538\) | 11.2809 | 0.486354 | ||||||||
\(539\) | −2.00000 | −0.0861461 | ||||||||
\(540\) | 40.7811 | 1.75494 | ||||||||
\(541\) | −7.40357 | −0.318304 | −0.159152 | − | 0.987254i | \(-0.550876\pi\) | ||||
−0.159152 | + | 0.987254i | \(0.550876\pi\) | |||||||
\(542\) | 11.6562 | 0.500675 | ||||||||
\(543\) | −49.1298 | −2.10836 | ||||||||
\(544\) | 33.2667 | 1.42630 | ||||||||
\(545\) | −28.1821 | −1.20719 | ||||||||
\(546\) | −12.5547 | −0.537289 | ||||||||
\(547\) | 36.4633 | 1.55906 | 0.779529 | − | 0.626366i | \(-0.215459\pi\) | ||||
0.779529 | + | 0.626366i | \(0.215459\pi\) | |||||||
\(548\) | −23.7993 | −1.01666 | ||||||||
\(549\) | −40.3723 | −1.72305 | ||||||||
\(550\) | 1.42708 | 0.0608507 | ||||||||
\(551\) | 12.1276 | 0.516652 | ||||||||
\(552\) | −6.35025 | −0.270285 | ||||||||
\(553\) | 10.4088 | 0.442627 | ||||||||
\(554\) | −1.37783 | −0.0585382 | ||||||||
\(555\) | 73.4085 | 3.11602 | ||||||||
\(556\) | 10.8281 | 0.459213 | ||||||||
\(557\) | −22.0545 | −0.934478 | −0.467239 | − | 0.884131i | \(-0.654751\pi\) | ||||
−0.467239 | + | 0.884131i | \(0.654751\pi\) | |||||||
\(558\) | −7.40100 | −0.313309 | ||||||||
\(559\) | 64.9176 | 2.74572 | ||||||||
\(560\) | 2.40880 | 0.101791 | ||||||||
\(561\) | 36.4998 | 1.54102 | ||||||||
\(562\) | −21.0623 | −0.888459 | ||||||||
\(563\) | −40.7538 | −1.71757 | −0.858784 | − | 0.512337i | \(-0.828780\pi\) | ||||
−0.858784 | + | 0.512337i | \(0.828780\pi\) | |||||||
\(564\) | 28.1846 | 1.18679 | ||||||||
\(565\) | −10.0806 | −0.424092 | ||||||||
\(566\) | 5.73438 | 0.241034 | ||||||||
\(567\) | 22.0220 | 0.924837 | ||||||||
\(568\) | −4.57292 | −0.191876 | ||||||||
\(569\) | 30.5860 | 1.28223 | 0.641115 | − | 0.767445i | \(-0.278472\pi\) | ||||
0.641115 | + | 0.767445i | \(0.278472\pi\) | |||||||
\(570\) | −21.5547 | −0.902825 | ||||||||
\(571\) | −14.2007 | −0.594279 | −0.297140 | − | 0.954834i | \(-0.596033\pi\) | ||||
−0.297140 | + | 0.954834i | \(0.596033\pi\) | |||||||
\(572\) | 16.3723 | 0.684558 | ||||||||
\(573\) | 9.67176 | 0.404043 | ||||||||
\(574\) | −0.713538 | −0.0297825 | ||||||||
\(575\) | 0.795598 | 0.0331787 | ||||||||
\(576\) | 12.7851 | 0.532714 | ||||||||
\(577\) | 14.5144 | 0.604241 | 0.302121 | − | 0.953270i | \(-0.402305\pi\) | ||||
0.302121 | + | 0.953270i | \(0.402305\pi\) | |||||||
\(578\) | 11.0142 | 0.458130 | ||||||||
\(579\) | −3.26295 | −0.135604 | ||||||||
\(580\) | −7.67176 | −0.318552 | ||||||||
\(581\) | 0.854152 | 0.0354362 | ||||||||
\(582\) | −12.2749 | −0.508812 | ||||||||
\(583\) | 7.10930 | 0.294437 | ||||||||
\(584\) | −23.3905 | −0.967907 | ||||||||
\(585\) | 79.8173 | 3.30004 | ||||||||
\(586\) | −4.68256 | −0.193435 | ||||||||
\(587\) | 30.3958 | 1.25457 | 0.627284 | − | 0.778791i | \(-0.284167\pi\) | ||||
0.627284 | + | 0.778791i | \(0.284167\pi\) | |||||||
\(588\) | 4.77733 | 0.197014 | ||||||||
\(589\) | −6.72658 | −0.277164 | ||||||||
\(590\) | −5.70830 | −0.235007 | ||||||||
\(591\) | −47.5569 | −1.95623 | ||||||||
\(592\) | −13.7956 | −0.566996 | ||||||||
\(593\) | 4.54568 | 0.186669 | 0.0933344 | − | 0.995635i | \(-0.470247\pi\) | ||||
0.0933344 | + | 0.995635i | \(0.470247\pi\) | |||||||
\(594\) | 19.5181 | 0.800838 | ||||||||
\(595\) | 11.3905 | 0.466966 | ||||||||
\(596\) | 33.3540 | 1.36623 | ||||||||
\(597\) | −31.3137 | −1.28158 | ||||||||
\(598\) | −3.11711 | −0.127468 | ||||||||
\(599\) | −29.9542 | −1.22389 | −0.611947 | − | 0.790899i | \(-0.709613\pi\) | ||||
−0.611947 | + | 0.790899i | \(0.709613\pi\) | |||||||
\(600\) | −7.98173 | −0.325853 | ||||||||
\(601\) | 19.9399 | 0.813367 | 0.406684 | − | 0.913569i | \(-0.366685\pi\) | ||||
0.406684 | + | 0.913569i | \(0.366685\pi\) | |||||||
\(602\) | 8.43605 | 0.343828 | ||||||||
\(603\) | 54.9086 | 2.23605 | ||||||||
\(604\) | 28.9086 | 1.17628 | ||||||||
\(605\) | −14.0000 | −0.569181 | ||||||||
\(606\) | 22.2719 | 0.904735 | ||||||||
\(607\) | −31.0623 | −1.26078 | −0.630390 | − | 0.776279i | \(-0.717105\pi\) | ||||
−0.630390 | + | 0.776279i | \(0.717105\pi\) | |||||||
\(608\) | 27.5323 | 1.11658 | ||||||||
\(609\) | −8.24468 | −0.334091 | ||||||||
\(610\) | −7.92691 | −0.320951 | ||||||||
\(611\) | 32.3943 | 1.31053 | ||||||||
\(612\) | −61.7132 | −2.49461 | ||||||||
\(613\) | 3.77733 | 0.152565 | 0.0762824 | − | 0.997086i | \(-0.475695\pi\) | ||||
0.0762824 | + | 0.997086i | \(0.475695\pi\) | |||||||
\(614\) | −14.0179 | −0.565718 | ||||||||
\(615\) | 6.40880 | 0.258428 | ||||||||
\(616\) | 4.98173 | 0.200720 | ||||||||
\(617\) | −24.8046 | −0.998594 | −0.499297 | − | 0.866431i | \(-0.666408\pi\) | ||||
−0.499297 | + | 0.866431i | \(0.666408\pi\) | |||||||
\(618\) | −29.3905 | −1.18226 | ||||||||
\(619\) | −1.54418 | −0.0620659 | −0.0310330 | − | 0.999518i | \(-0.509880\pi\) | ||||
−0.0310330 | + | 0.999518i | \(0.509880\pi\) | |||||||
\(620\) | 4.25515 | 0.170891 | ||||||||
\(621\) | 10.8814 | 0.436655 | ||||||||
\(622\) | −0.944016 | −0.0378516 | ||||||||
\(623\) | 7.19917 | 0.288429 | ||||||||
\(624\) | −21.1914 | −0.848333 | ||||||||
\(625\) | −19.0000 | −0.760000 | ||||||||
\(626\) | −12.5741 | −0.502562 | ||||||||
\(627\) | 30.2081 | 1.20640 | ||||||||
\(628\) | −11.4181 | −0.455632 | ||||||||
\(629\) | −65.2354 | −2.60110 | ||||||||
\(630\) | 10.3723 | 0.413241 | ||||||||
\(631\) | 13.4438 | 0.535191 | 0.267596 | − | 0.963531i | \(-0.413771\pi\) | ||||
0.267596 | + | 0.963531i | \(0.413771\pi\) | |||||||
\(632\) | −25.9269 | −1.03132 | ||||||||
\(633\) | −34.1716 | −1.35820 | ||||||||
\(634\) | −16.2552 | −0.645575 | ||||||||
\(635\) | 9.50764 | 0.377299 | ||||||||
\(636\) | −16.9817 | −0.673369 | ||||||||
\(637\) | 5.49086 | 0.217556 | ||||||||
\(638\) | −3.67176 | −0.145366 | ||||||||
\(639\) | 13.3435 | 0.527861 | ||||||||
\(640\) | −20.8542 | −0.824333 | ||||||||
\(641\) | −6.31777 | −0.249537 | −0.124769 | − | 0.992186i | \(-0.539819\pi\) | ||||
−0.124769 | + | 0.992186i | \(0.539819\pi\) | |||||||
\(642\) | 34.2014 | 1.34982 | ||||||||
\(643\) | 39.1522 | 1.54401 | 0.772005 | − | 0.635616i | \(-0.219254\pi\) | ||||
0.772005 | + | 0.635616i | \(0.219254\pi\) | |||||||
\(644\) | 1.18613 | 0.0467400 | ||||||||
\(645\) | −75.7703 | −2.98345 | ||||||||
\(646\) | 19.1548 | 0.753636 | ||||||||
\(647\) | −29.6897 | −1.16722 | −0.583611 | − | 0.812033i | \(-0.698361\pi\) | ||||
−0.583611 | + | 0.812033i | \(0.698361\pi\) | |||||||
\(648\) | −54.8538 | −2.15486 | ||||||||
\(649\) | 8.00000 | 0.314027 | ||||||||
\(650\) | −3.91794 | −0.153674 | ||||||||
\(651\) | 4.57292 | 0.179227 | ||||||||
\(652\) | −2.02467 | −0.0792923 | ||||||||
\(653\) | −4.39833 | −0.172120 | −0.0860601 | − | 0.996290i | \(-0.527428\pi\) | ||||
−0.0860601 | + | 0.996290i | \(0.527428\pi\) | |||||||
\(654\) | 32.2186 | 1.25985 | ||||||||
\(655\) | −31.6718 | −1.23752 | ||||||||
\(656\) | −1.20440 | −0.0470240 | ||||||||
\(657\) | 68.2522 | 2.66277 | ||||||||
\(658\) | 4.20964 | 0.164109 | ||||||||
\(659\) | 14.3178 | 0.557741 | 0.278871 | − | 0.960329i | \(-0.410040\pi\) | ||||
0.278871 | + | 0.960329i | \(0.410040\pi\) | |||||||
\(660\) | −19.1093 | −0.743829 | ||||||||
\(661\) | 1.26295 | 0.0491232 | 0.0245616 | − | 0.999698i | \(-0.492181\pi\) | ||||
0.0245616 | + | 0.999698i | \(0.492181\pi\) | |||||||
\(662\) | 15.6978 | 0.610114 | ||||||||
\(663\) | −100.208 | −3.89175 | ||||||||
\(664\) | −2.12758 | −0.0825659 | ||||||||
\(665\) | 9.42708 | 0.365566 | ||||||||
\(666\) | −59.4036 | −2.30184 | ||||||||
\(667\) | −2.04701 | −0.0792607 | ||||||||
\(668\) | 20.1731 | 0.780520 | ||||||||
\(669\) | 78.5073 | 3.03527 | ||||||||
\(670\) | 10.7811 | 0.416509 | ||||||||
\(671\) | 11.1093 | 0.428870 | ||||||||
\(672\) | −18.7173 | −0.722034 | ||||||||
\(673\) | −30.7080 | −1.18371 | −0.591853 | − | 0.806046i | \(-0.701603\pi\) | ||||
−0.591853 | + | 0.806046i | \(0.701603\pi\) | |||||||
\(674\) | 4.73181 | 0.182263 | ||||||||
\(675\) | 13.6770 | 0.526428 | ||||||||
\(676\) | −25.5677 | −0.983373 | ||||||||
\(677\) | 13.8098 | 0.530754 | 0.265377 | − | 0.964145i | \(-0.414504\pi\) | ||||
0.265377 | + | 0.964145i | \(0.414504\pi\) | |||||||
\(678\) | 11.5244 | 0.442592 | ||||||||
\(679\) | 5.36852 | 0.206025 | ||||||||
\(680\) | −28.3723 | −1.08803 | ||||||||
\(681\) | 34.7811 | 1.33281 | ||||||||
\(682\) | 2.03655 | 0.0779834 | ||||||||
\(683\) | 40.5073 | 1.54997 | 0.774984 | − | 0.631980i | \(-0.217758\pi\) | ||||
0.774984 | + | 0.631980i | \(0.217758\pi\) | |||||||
\(684\) | −51.0753 | −1.95291 | ||||||||
\(685\) | 31.9269 | 1.21986 | ||||||||
\(686\) | 0.713538 | 0.0272430 | ||||||||
\(687\) | −9.85939 | −0.376159 | ||||||||
\(688\) | 14.2394 | 0.542874 | ||||||||
\(689\) | −19.5181 | −0.743581 | ||||||||
\(690\) | 3.63821 | 0.138504 | ||||||||
\(691\) | 17.2096 | 0.654685 | 0.327343 | − | 0.944906i | \(-0.393847\pi\) | ||||
0.327343 | + | 0.944906i | \(0.393847\pi\) | |||||||
\(692\) | −4.49983 | −0.171058 | ||||||||
\(693\) | −14.5364 | −0.552191 | ||||||||
\(694\) | −12.8437 | −0.487540 | ||||||||
\(695\) | −14.5259 | −0.550999 | ||||||||
\(696\) | 20.5364 | 0.778429 | ||||||||
\(697\) | −5.69527 | −0.215724 | ||||||||
\(698\) | 24.7080 | 0.935210 | ||||||||
\(699\) | −52.4968 | −1.98561 | ||||||||
\(700\) | 1.49086 | 0.0563493 | ||||||||
\(701\) | 24.9620 | 0.942800 | 0.471400 | − | 0.881920i | \(-0.343749\pi\) | ||||
0.471400 | + | 0.881920i | \(0.343749\pi\) | |||||||
\(702\) | −53.5856 | −2.02246 | ||||||||
\(703\) | −53.9904 | −2.03629 | ||||||||
\(704\) | −3.51811 | −0.132594 | ||||||||
\(705\) | −37.8098 | −1.42400 | ||||||||
\(706\) | −19.9530 | −0.750941 | ||||||||
\(707\) | −9.74078 | −0.366340 | ||||||||
\(708\) | −19.1093 | −0.718172 | ||||||||
\(709\) | 5.89036 | 0.221217 | 0.110609 | − | 0.993864i | \(-0.464720\pi\) | ||||
0.110609 | + | 0.993864i | \(0.464720\pi\) | |||||||
\(710\) | 2.61994 | 0.0983245 | ||||||||
\(711\) | 75.6532 | 2.83721 | ||||||||
\(712\) | −17.9321 | −0.672035 | ||||||||
\(713\) | 1.13538 | 0.0425203 | ||||||||
\(714\) | −13.0220 | −0.487336 | ||||||||
\(715\) | −21.9635 | −0.821387 | ||||||||
\(716\) | 16.1276 | 0.602716 | ||||||||
\(717\) | 47.5151 | 1.77448 | ||||||||
\(718\) | 8.55582 | 0.319300 | ||||||||
\(719\) | 22.2917 | 0.831340 | 0.415670 | − | 0.909516i | \(-0.363547\pi\) | ||||
0.415670 | + | 0.909516i | \(0.363547\pi\) | |||||||
\(720\) | 17.5076 | 0.652471 | ||||||||
\(721\) | 12.8542 | 0.478714 | ||||||||
\(722\) | 2.29577 | 0.0854395 | ||||||||
\(723\) | 47.3645 | 1.76150 | ||||||||
\(724\) | −22.8579 | −0.849507 | ||||||||
\(725\) | −2.57292 | −0.0955560 | ||||||||
\(726\) | 16.0052 | 0.594010 | ||||||||
\(727\) | −21.1768 | −0.785405 | −0.392702 | − | 0.919666i | \(-0.628460\pi\) | ||||
−0.392702 | + | 0.919666i | \(0.628460\pi\) | |||||||
\(728\) | −13.6770 | −0.506903 | ||||||||
\(729\) | 28.5804 | 1.05853 | ||||||||
\(730\) | 13.4010 | 0.495993 | ||||||||
\(731\) | 67.3342 | 2.49045 | ||||||||
\(732\) | −26.5364 | −0.980813 | ||||||||
\(733\) | −30.6900 | −1.13356 | −0.566781 | − | 0.823868i | \(-0.691811\pi\) | ||||
−0.566781 | + | 0.823868i | \(0.691811\pi\) | |||||||
\(734\) | 20.3357 | 0.750605 | ||||||||
\(735\) | −6.40880 | −0.236392 | ||||||||
\(736\) | −4.64718 | −0.171297 | ||||||||
\(737\) | −15.1093 | −0.556558 | ||||||||
\(738\) | −5.18613 | −0.190904 | ||||||||
\(739\) | −39.9176 | −1.46839 | −0.734196 | − | 0.678937i | \(-0.762441\pi\) | ||||
−0.734196 | + | 0.678937i | \(0.762441\pi\) | |||||||
\(740\) | 34.1537 | 1.25551 | ||||||||
\(741\) | −82.9344 | −3.04667 | ||||||||
\(742\) | −2.53638 | −0.0931134 | ||||||||
\(743\) | 24.9478 | 0.915244 | 0.457622 | − | 0.889147i | \(-0.348701\pi\) | ||||
0.457622 | + | 0.889147i | \(0.348701\pi\) | |||||||
\(744\) | −11.3905 | −0.417597 | ||||||||
\(745\) | −44.7445 | −1.63931 | ||||||||
\(746\) | −10.5897 | −0.387716 | ||||||||
\(747\) | 6.20814 | 0.227144 | ||||||||
\(748\) | 16.9817 | 0.620913 | ||||||||
\(749\) | −14.9582 | −0.546561 | ||||||||
\(750\) | 27.4375 | 1.00188 | ||||||||
\(751\) | −35.1899 | −1.28410 | −0.642048 | − | 0.766664i | \(-0.721915\pi\) | ||||
−0.642048 | + | 0.766664i | \(0.721915\pi\) | |||||||
\(752\) | 7.10557 | 0.259113 | ||||||||
\(753\) | 32.9452 | 1.20059 | ||||||||
\(754\) | 10.0806 | 0.367112 | ||||||||
\(755\) | −38.7811 | −1.41139 | ||||||||
\(756\) | 20.3905 | 0.741596 | ||||||||
\(757\) | 12.8542 | 0.467192 | 0.233596 | − | 0.972334i | \(-0.424951\pi\) | ||||
0.233596 | + | 0.972334i | \(0.424951\pi\) | |||||||
\(758\) | 5.14061 | 0.186716 | ||||||||
\(759\) | −5.09883 | −0.185076 | ||||||||
\(760\) | −23.4816 | −0.851766 | ||||||||
\(761\) | 29.3645 | 1.06446 | 0.532230 | − | 0.846600i | \(-0.321354\pi\) | ||||
0.532230 | + | 0.846600i | \(0.321354\pi\) | |||||||
\(762\) | −10.8694 | −0.393758 | ||||||||
\(763\) | −14.0910 | −0.510130 | ||||||||
\(764\) | 4.49983 | 0.162798 | ||||||||
\(765\) | 82.7885 | 2.99323 | ||||||||
\(766\) | −3.68746 | −0.133233 | ||||||||
\(767\) | −21.9635 | −0.793054 | ||||||||
\(768\) | 35.1145 | 1.26709 | ||||||||
\(769\) | −2.00000 | −0.0721218 | −0.0360609 | − | 0.999350i | \(-0.511481\pi\) | ||||
−0.0360609 | + | 0.999350i | \(0.511481\pi\) | |||||||
\(770\) | −2.85415 | −0.102856 | ||||||||
\(771\) | 4.76055 | 0.171447 | ||||||||
\(772\) | −1.51811 | −0.0546378 | ||||||||
\(773\) | −28.1220 | −1.01148 | −0.505739 | − | 0.862686i | \(-0.668780\pi\) | ||||
−0.505739 | + | 0.862686i | \(0.668780\pi\) | |||||||
\(774\) | 61.3148 | 2.20391 | ||||||||
\(775\) | 1.42708 | 0.0512621 | ||||||||
\(776\) | −13.3723 | −0.480036 | ||||||||
\(777\) | 36.7042 | 1.31676 | ||||||||
\(778\) | −3.10033 | −0.111152 | ||||||||
\(779\) | −4.71354 | −0.168880 | ||||||||
\(780\) | 52.4633 | 1.87849 | ||||||||
\(781\) | −3.67176 | −0.131386 | ||||||||
\(782\) | −3.23314 | −0.115617 | ||||||||
\(783\) | −35.1899 | −1.25758 | ||||||||
\(784\) | 1.20440 | 0.0430143 | ||||||||
\(785\) | 15.3174 | 0.546703 | ||||||||
\(786\) | 36.2081 | 1.29150 | ||||||||
\(787\) | −5.51811 | −0.196699 | −0.0983496 | − | 0.995152i | \(-0.531356\pi\) | ||||
−0.0983496 | + | 0.995152i | \(0.531356\pi\) | |||||||
\(788\) | −22.1261 | −0.788209 | ||||||||
\(789\) | −90.7990 | −3.23253 | ||||||||
\(790\) | 14.8542 | 0.528487 | ||||||||
\(791\) | −5.04028 | −0.179212 | ||||||||
\(792\) | 36.2081 | 1.28660 | ||||||||
\(793\) | −30.4998 | −1.08308 | ||||||||
\(794\) | 14.0626 | 0.499064 | ||||||||
\(795\) | 22.7811 | 0.807961 | ||||||||
\(796\) | −14.5689 | −0.516379 | ||||||||
\(797\) | 37.5256 | 1.32922 | 0.664612 | − | 0.747189i | \(-0.268597\pi\) | ||||
0.664612 | + | 0.747189i | \(0.268597\pi\) | |||||||
\(798\) | −10.7773 | −0.381513 | ||||||||
\(799\) | 33.6002 | 1.18869 | ||||||||
\(800\) | −5.84111 | −0.206515 | ||||||||
\(801\) | 52.3249 | 1.84881 | ||||||||
\(802\) | −20.2641 | −0.715551 | ||||||||
\(803\) | −18.7811 | −0.662769 | ||||||||
\(804\) | 36.0910 | 1.27283 | ||||||||
\(805\) | −1.59120 | −0.0560823 | ||||||||
\(806\) | −5.59120 | −0.196942 | ||||||||
\(807\) | −50.6610 | −1.78335 | ||||||||
\(808\) | 24.2630 | 0.853568 | ||||||||
\(809\) | 14.8281 | 0.521327 | 0.260664 | − | 0.965430i | \(-0.416059\pi\) | ||||
0.260664 | + | 0.965430i | \(0.416059\pi\) | |||||||
\(810\) | 31.4271 | 1.10423 | ||||||||
\(811\) | −19.4271 | −0.682177 | −0.341088 | − | 0.940031i | \(-0.610796\pi\) | ||||
−0.341088 | + | 0.940031i | \(0.610796\pi\) | |||||||
\(812\) | −3.83588 | −0.134613 | ||||||||
\(813\) | −52.3462 | −1.83586 | ||||||||
\(814\) | 16.3462 | 0.572933 | ||||||||
\(815\) | 2.71611 | 0.0951411 | ||||||||
\(816\) | −21.9802 | −0.769462 | ||||||||
\(817\) | 55.7274 | 1.94966 | ||||||||
\(818\) | 13.7523 | 0.480839 | ||||||||
\(819\) | 39.9086 | 1.39452 | ||||||||
\(820\) | 2.98173 | 0.104126 | ||||||||
\(821\) | −16.0130 | −0.558859 | −0.279429 | − | 0.960166i | \(-0.590145\pi\) | ||||
−0.279429 | + | 0.960166i | \(0.590145\pi\) | |||||||
\(822\) | −36.4998 | −1.27308 | ||||||||
\(823\) | 18.9086 | 0.659114 | 0.329557 | − | 0.944136i | \(-0.393101\pi\) | ||||
0.329557 | + | 0.944136i | \(0.393101\pi\) | |||||||
\(824\) | −32.0179 | −1.11540 | ||||||||
\(825\) | −6.40880 | −0.223126 | ||||||||
\(826\) | −2.85415 | −0.0993086 | ||||||||
\(827\) | −16.6640 | −0.579462 | −0.289731 | − | 0.957108i | \(-0.593566\pi\) | ||||
−0.289731 | + | 0.957108i | \(0.593566\pi\) | |||||||
\(828\) | 8.62101 | 0.299601 | ||||||||
\(829\) | 5.06229 | 0.175821 | 0.0879103 | − | 0.996128i | \(-0.471981\pi\) | ||||
0.0879103 | + | 0.996128i | \(0.471981\pi\) | |||||||
\(830\) | 1.21894 | 0.0423100 | ||||||||
\(831\) | 6.18763 | 0.214646 | ||||||||
\(832\) | 9.65872 | 0.334856 | ||||||||
\(833\) | 5.69527 | 0.197329 | ||||||||
\(834\) | 16.6065 | 0.575035 | ||||||||
\(835\) | −27.0623 | −0.936529 | ||||||||
\(836\) | 14.0545 | 0.486085 | ||||||||
\(837\) | 19.5181 | 0.674644 | ||||||||
\(838\) | −11.3831 | −0.393221 | ||||||||
\(839\) | 8.86869 | 0.306181 | 0.153091 | − | 0.988212i | \(-0.451077\pi\) | ||||
0.153091 | + | 0.988212i | \(0.451077\pi\) | |||||||
\(840\) | 15.9635 | 0.550792 | ||||||||
\(841\) | −22.3801 | −0.771726 | ||||||||
\(842\) | −27.1719 | −0.936406 | ||||||||
\(843\) | 94.5879 | 3.25778 | ||||||||
\(844\) | −15.8985 | −0.547249 | ||||||||
\(845\) | 34.2992 | 1.17993 | ||||||||
\(846\) | 30.5964 | 1.05193 | ||||||||
\(847\) | −7.00000 | −0.240523 | ||||||||
\(848\) | −4.28123 | −0.147018 | ||||||||
\(849\) | −25.7523 | −0.883817 | ||||||||
\(850\) | −4.06379 | −0.139387 | ||||||||
\(851\) | 9.11304 | 0.312391 | ||||||||
\(852\) | 8.77059 | 0.300476 | ||||||||
\(853\) | −22.5729 | −0.772882 | −0.386441 | − | 0.922314i | \(-0.626296\pi\) | ||||
−0.386441 | + | 0.922314i | \(0.626296\pi\) | |||||||
\(854\) | −3.96345 | −0.135627 | ||||||||
\(855\) | 68.5178 | 2.34326 | ||||||||
\(856\) | 37.2589 | 1.27348 | ||||||||
\(857\) | 44.7811 | 1.52969 | 0.764846 | − | 0.644213i | \(-0.222815\pi\) | ||||
0.764846 | + | 0.644213i | \(0.222815\pi\) | |||||||
\(858\) | 25.1093 | 0.857217 | ||||||||
\(859\) | −39.6352 | −1.35234 | −0.676168 | − | 0.736747i | \(-0.736361\pi\) | ||||
−0.676168 | + | 0.736747i | \(0.736361\pi\) | |||||||
\(860\) | −35.2525 | −1.20210 | ||||||||
\(861\) | 3.20440 | 0.109206 | ||||||||
\(862\) | −7.34352 | −0.250121 | ||||||||
\(863\) | 6.21861 | 0.211684 | 0.105842 | − | 0.994383i | \(-0.466246\pi\) | ||||
0.105842 | + | 0.994383i | \(0.466246\pi\) | |||||||
\(864\) | −79.8889 | −2.71787 | ||||||||
\(865\) | 6.03655 | 0.205249 | ||||||||
\(866\) | 7.12791 | 0.242216 | ||||||||
\(867\) | −49.4633 | −1.67986 | ||||||||
\(868\) | 2.12758 | 0.0722146 | ||||||||
\(869\) | −20.8176 | −0.706189 | ||||||||
\(870\) | −11.7658 | −0.398898 | ||||||||
\(871\) | 41.4816 | 1.40555 | ||||||||
\(872\) | 35.0988 | 1.18860 | ||||||||
\(873\) | 39.0194 | 1.32061 | ||||||||
\(874\) | −2.67583 | −0.0905112 | ||||||||
\(875\) | −12.0000 | −0.405674 | ||||||||
\(876\) | 44.8616 | 1.51573 | ||||||||
\(877\) | 4.08463 | 0.137928 | 0.0689641 | − | 0.997619i | \(-0.478031\pi\) | ||||
0.0689641 | + | 0.997619i | \(0.478031\pi\) | |||||||
\(878\) | 1.15108 | 0.0388472 | ||||||||
\(879\) | 21.0287 | 0.709282 | ||||||||
\(880\) | −4.81761 | −0.162401 | ||||||||
\(881\) | 58.3537 | 1.96598 | 0.982992 | − | 0.183647i | \(-0.0587904\pi\) | ||||
0.982992 | + | 0.183647i | \(0.0587904\pi\) | |||||||
\(882\) | 5.18613 | 0.174626 | ||||||||
\(883\) | 31.8724 | 1.07259 | 0.536296 | − | 0.844030i | \(-0.319823\pi\) | ||||
0.536296 | + | 0.844030i | \(0.319823\pi\) | |||||||
\(884\) | −46.6222 | −1.56807 | ||||||||
\(885\) | 25.6352 | 0.861718 | ||||||||
\(886\) | 15.1339 | 0.508433 | ||||||||
\(887\) | 13.0821 | 0.439253 | 0.219626 | − | 0.975584i | \(-0.429516\pi\) | ||||
0.219626 | + | 0.975584i | \(0.429516\pi\) | |||||||
\(888\) | −91.4252 | −3.06803 | ||||||||
\(889\) | 4.75382 | 0.159438 | ||||||||
\(890\) | 10.2738 | 0.344377 | ||||||||
\(891\) | −44.0440 | −1.47553 | ||||||||
\(892\) | 36.5259 | 1.22298 | ||||||||
\(893\) | 27.8083 | 0.930569 | ||||||||
\(894\) | 51.1533 | 1.71082 | ||||||||
\(895\) | −21.6352 | −0.723185 | ||||||||
\(896\) | −10.4271 | −0.348344 | ||||||||
\(897\) | 13.9985 | 0.467396 | ||||||||
\(898\) | 8.58563 | 0.286506 | ||||||||
\(899\) | −3.67176 | −0.122460 | ||||||||
\(900\) | 10.8359 | 0.361196 | ||||||||
\(901\) | −20.2447 | −0.674448 | ||||||||
\(902\) | 1.42708 | 0.0475164 | ||||||||
\(903\) | −37.8851 | −1.26074 | ||||||||
\(904\) | 12.5547 | 0.417561 | ||||||||
\(905\) | 30.6640 | 1.01930 | ||||||||
\(906\) | 44.3357 | 1.47296 | ||||||||
\(907\) | −44.4256 | −1.47513 | −0.737564 | − | 0.675278i | \(-0.764024\pi\) | ||||
−0.737564 | + | 0.675278i | \(0.764024\pi\) | |||||||
\(908\) | 16.1821 | 0.537021 | ||||||||
\(909\) | −70.7978 | −2.34822 | ||||||||
\(910\) | 7.83588 | 0.259757 | ||||||||
\(911\) | −24.0310 | −0.796182 | −0.398091 | − | 0.917346i | \(-0.630327\pi\) | ||||
−0.398091 | + | 0.917346i | \(0.630327\pi\) | |||||||
\(912\) | −18.1914 | −0.602376 | ||||||||
\(913\) | −1.70830 | −0.0565366 | ||||||||
\(914\) | −0.648346 | −0.0214454 | ||||||||
\(915\) | 35.5987 | 1.17686 | ||||||||
\(916\) | −4.58713 | −0.151563 | ||||||||
\(917\) | −15.8359 | −0.522947 | ||||||||
\(918\) | −55.5804 | −1.83443 | ||||||||
\(919\) | −26.4453 | −0.872352 | −0.436176 | − | 0.899861i | \(-0.643667\pi\) | ||||
−0.436176 | + | 0.899861i | \(0.643667\pi\) | |||||||
\(920\) | 3.96345 | 0.130671 | ||||||||
\(921\) | 62.9527 | 2.07436 | ||||||||
\(922\) | −9.56212 | −0.314912 | ||||||||
\(923\) | 10.0806 | 0.331806 | ||||||||
\(924\) | −9.55465 | −0.314325 | ||||||||
\(925\) | 11.4543 | 0.376616 | ||||||||
\(926\) | −5.20847 | −0.171161 | ||||||||
\(927\) | 93.4264 | 3.06853 | ||||||||
\(928\) | 15.0287 | 0.493343 | ||||||||
\(929\) | −34.3032 | −1.12545 | −0.562726 | − | 0.826643i | \(-0.690248\pi\) | ||||
−0.562726 | + | 0.826643i | \(0.690248\pi\) | |||||||
\(930\) | 6.52591 | 0.213993 | ||||||||
\(931\) | 4.71354 | 0.154480 | ||||||||
\(932\) | −24.4244 | −0.800048 | ||||||||
\(933\) | 4.23945 | 0.138793 | ||||||||
\(934\) | −3.24435 | −0.106158 | ||||||||
\(935\) | −22.7811 | −0.745020 | ||||||||
\(936\) | −99.4070 | −3.24922 | ||||||||
\(937\) | 58.5427 | 1.91251 | 0.956253 | − | 0.292541i | \(-0.0945007\pi\) | ||||
0.956253 | + | 0.292541i | \(0.0945007\pi\) | |||||||
\(938\) | 5.39053 | 0.176007 | ||||||||
\(939\) | 56.4685 | 1.84278 | ||||||||
\(940\) | −17.5912 | −0.573762 | ||||||||
\(941\) | −0.382726 | −0.0124765 | −0.00623826 | − | 0.999981i | \(-0.501986\pi\) | ||||
−0.00623826 | + | 0.999981i | \(0.501986\pi\) | |||||||
\(942\) | −17.5114 | −0.570551 | ||||||||
\(943\) | 0.795598 | 0.0259083 | ||||||||
\(944\) | −4.81761 | −0.156800 | ||||||||
\(945\) | −27.3540 | −0.889825 | ||||||||
\(946\) | −16.8721 | −0.548559 | ||||||||
\(947\) | −28.5323 | −0.927175 | −0.463588 | − | 0.886051i | \(-0.653438\pi\) | ||||
−0.463588 | + | 0.886051i | \(0.653438\pi\) | |||||||
\(948\) | 49.7262 | 1.61503 | ||||||||
\(949\) | 51.5621 | 1.67378 | ||||||||
\(950\) | −3.36329 | −0.109119 | ||||||||
\(951\) | 72.9997 | 2.36718 | ||||||||
\(952\) | −14.1861 | −0.459775 | ||||||||
\(953\) | 18.9440 | 0.613657 | 0.306828 | − | 0.951765i | \(-0.400732\pi\) | ||||
0.306828 | + | 0.951765i | \(0.400732\pi\) | |||||||
\(954\) | −18.4349 | −0.596851 | ||||||||
\(955\) | −6.03655 | −0.195338 | ||||||||
\(956\) | 22.1066 | 0.714980 | ||||||||
\(957\) | 16.4894 | 0.533025 | ||||||||
\(958\) | 9.53148 | 0.307948 | ||||||||
\(959\) | 15.9635 | 0.515487 | ||||||||
\(960\) | −11.2734 | −0.363848 | ||||||||
\(961\) | −28.9635 | −0.934305 | ||||||||
\(962\) | −44.8773 | −1.44690 | ||||||||
\(963\) | −108.719 | −3.50343 | ||||||||
\(964\) | 22.0365 | 0.709749 | ||||||||
\(965\) | 2.03655 | 0.0655587 | ||||||||
\(966\) | 1.81911 | 0.0585288 | ||||||||
\(967\) | −5.93738 | −0.190933 | −0.0954666 | − | 0.995433i | \(-0.530434\pi\) | ||||
−0.0954666 | + | 0.995433i | \(0.530434\pi\) | |||||||
\(968\) | 17.4360 | 0.560416 | ||||||||
\(969\) | −86.0217 | −2.76341 | ||||||||
\(970\) | 7.66129 | 0.245989 | ||||||||
\(971\) | −43.7288 | −1.40332 | −0.701662 | − | 0.712510i | \(-0.747558\pi\) | ||||
−0.701662 | + | 0.712510i | \(0.747558\pi\) | |||||||
\(972\) | 44.0347 | 1.41241 | ||||||||
\(973\) | −7.26295 | −0.232840 | ||||||||
\(974\) | 1.50880 | 0.0483452 | ||||||||
\(975\) | 17.5949 | 0.563489 | ||||||||
\(976\) | −6.69003 | −0.214143 | ||||||||
\(977\) | −43.4920 | −1.39143 | −0.695717 | − | 0.718316i | \(-0.744913\pi\) | ||||
−0.695717 | + | 0.718316i | \(0.744913\pi\) | |||||||
\(978\) | −3.10514 | −0.0992914 | ||||||||
\(979\) | −14.3983 | −0.460173 | ||||||||
\(980\) | −2.98173 | −0.0952478 | ||||||||
\(981\) | −102.416 | −3.26990 | ||||||||
\(982\) | −11.1145 | −0.354679 | ||||||||
\(983\) | −40.6640 | −1.29698 | −0.648489 | − | 0.761224i | \(-0.724599\pi\) | ||||
−0.648489 | + | 0.761224i | \(0.724599\pi\) | |||||||
\(984\) | −7.98173 | −0.254448 | ||||||||
\(985\) | 29.6822 | 0.945754 | ||||||||
\(986\) | 10.4558 | 0.332981 | ||||||||
\(987\) | −18.9049 | −0.601750 | ||||||||
\(988\) | −38.5856 | −1.22757 | ||||||||
\(989\) | −9.40623 | −0.299101 | ||||||||
\(990\) | −20.7445 | −0.659304 | ||||||||
\(991\) | −49.9164 | −1.58565 | −0.792824 | − | 0.609451i | \(-0.791390\pi\) | ||||
−0.792824 | + | 0.609451i | \(0.791390\pi\) | |||||||
\(992\) | −8.33571 | −0.264659 | ||||||||
\(993\) | −70.4968 | −2.23715 | ||||||||
\(994\) | 1.30997 | 0.0415497 | ||||||||
\(995\) | 19.5442 | 0.619592 | ||||||||
\(996\) | 4.08056 | 0.129298 | ||||||||
\(997\) | 1.06122 | 0.0336091 | 0.0168046 | − | 0.999859i | \(-0.494651\pi\) | ||||
0.0168046 | + | 0.999859i | \(0.494651\pi\) | |||||||
\(998\) | −8.97126 | −0.283980 | ||||||||
\(999\) | 156.661 | 4.95652 |
(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 | 287.2.a.c.1.2 | ✓ | 3 | |
3.2 | odd | 2 | 2583.2.a.m.1.2 | 3 | |||
4.3 | odd | 2 | 4592.2.a.t.1.3 | 3 | |||
5.4 | even | 2 | 7175.2.a.k.1.2 | 3 | |||
7.6 | odd | 2 | 2009.2.a.j.1.2 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
287.2.a.c.1.2 | ✓ | 3 | 1.1 | even | 1 | trivial | |
2009.2.a.j.1.2 | 3 | 7.6 | odd | 2 | |||
2583.2.a.m.1.2 | 3 | 3.2 | odd | 2 | |||
4592.2.a.t.1.3 | 3 | 4.3 | odd | 2 | |||
7175.2.a.k.1.2 | 3 | 5.4 | even | 2 |