Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1334,2,Mod(1,1334)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1334, 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("1334.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1334 = 2 \cdot 23 \cdot 29 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1334.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: | \(10.6520436296\) |
Analytic rank: | \(1\) |
Dimension: | \(5\) |
Coefficient field: | 5.5.207184.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{5} - x^{4} - 6x^{3} + 2x^{2} + 7x - 1 \) |
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 | 1.1 | ||
Root | \(0.139666\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1334.1 |
$q$-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 | ||||||||
\(3\) | −2.54471 | −1.46919 | −0.734596 | − | 0.678505i | \(-0.762628\pi\) | ||||
−0.734596 | + | 0.678505i | \(0.762628\pi\) | |||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −0.504925 | −0.225809 | −0.112905 | − | 0.993606i | \(-0.536015\pi\) | ||||
−0.112905 | + | 0.993606i | \(0.536015\pi\) | |||||||
\(6\) | 2.54471 | 1.03888 | ||||||||
\(7\) | 2.12016 | 0.801345 | 0.400672 | − | 0.916221i | \(-0.368777\pi\) | ||||
0.400672 | + | 0.916221i | \(0.368777\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 3.47557 | 1.15852 | ||||||||
\(10\) | 0.504925 | 0.159671 | ||||||||
\(11\) | −0.850485 | −0.256431 | −0.128215 | − | 0.991746i | \(-0.540925\pi\) | ||||
−0.128215 | + | 0.991746i | \(0.540925\pi\) | |||||||
\(12\) | −2.54471 | −0.734596 | ||||||||
\(13\) | −5.05101 | −1.40090 | −0.700450 | − | 0.713702i | \(-0.747017\pi\) | ||||
−0.700450 | + | 0.713702i | \(0.747017\pi\) | |||||||
\(14\) | −2.12016 | −0.566636 | ||||||||
\(15\) | 1.28489 | 0.331757 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 6.51398 | 1.57987 | 0.789936 | − | 0.613189i | \(-0.210114\pi\) | ||||
0.789936 | + | 0.613189i | \(0.210114\pi\) | |||||||
\(18\) | −3.47557 | −0.819199 | ||||||||
\(19\) | −4.69560 | −1.07725 | −0.538623 | − | 0.842547i | \(-0.681055\pi\) | ||||
−0.538623 | + | 0.842547i | \(0.681055\pi\) | |||||||
\(20\) | −0.504925 | −0.112905 | ||||||||
\(21\) | −5.39520 | −1.17733 | ||||||||
\(22\) | 0.850485 | 0.181324 | ||||||||
\(23\) | 1.00000 | 0.208514 | ||||||||
\(24\) | 2.54471 | 0.519438 | ||||||||
\(25\) | −4.74505 | −0.949010 | ||||||||
\(26\) | 5.05101 | 0.990585 | ||||||||
\(27\) | −1.21019 | −0.232901 | ||||||||
\(28\) | 2.12016 | 0.400672 | ||||||||
\(29\) | 1.00000 | 0.185695 | ||||||||
\(30\) | −1.28489 | −0.234588 | ||||||||
\(31\) | 10.4596 | 1.87859 | 0.939296 | − | 0.343107i | \(-0.111479\pi\) | ||||
0.939296 | + | 0.343107i | \(0.111479\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 2.16424 | 0.376746 | ||||||||
\(34\) | −6.51398 | −1.11714 | ||||||||
\(35\) | −1.07052 | −0.180951 | ||||||||
\(36\) | 3.47557 | 0.579261 | ||||||||
\(37\) | 6.58588 | 1.08271 | 0.541356 | − | 0.840794i | \(-0.317911\pi\) | ||||
0.541356 | + | 0.840794i | \(0.317911\pi\) | |||||||
\(38\) | 4.69560 | 0.761728 | ||||||||
\(39\) | 12.8534 | 2.05819 | ||||||||
\(40\) | 0.504925 | 0.0798356 | ||||||||
\(41\) | −8.56343 | −1.33738 | −0.668691 | − | 0.743540i | \(-0.733145\pi\) | ||||
−0.668691 | + | 0.743540i | \(0.733145\pi\) | |||||||
\(42\) | 5.39520 | 0.832497 | ||||||||
\(43\) | 4.24169 | 0.646852 | 0.323426 | − | 0.946253i | \(-0.395165\pi\) | ||||
0.323426 | + | 0.946253i | \(0.395165\pi\) | |||||||
\(44\) | −0.850485 | −0.128215 | ||||||||
\(45\) | −1.75490 | −0.261605 | ||||||||
\(46\) | −1.00000 | −0.147442 | ||||||||
\(47\) | −0.904416 | −0.131923 | −0.0659613 | − | 0.997822i | \(-0.521011\pi\) | ||||
−0.0659613 | + | 0.997822i | \(0.521011\pi\) | |||||||
\(48\) | −2.54471 | −0.367298 | ||||||||
\(49\) | −2.50492 | −0.357846 | ||||||||
\(50\) | 4.74505 | 0.671052 | ||||||||
\(51\) | −16.5762 | −2.32114 | ||||||||
\(52\) | −5.05101 | −0.700450 | ||||||||
\(53\) | 3.47576 | 0.477432 | 0.238716 | − | 0.971089i | \(-0.423273\pi\) | ||||
0.238716 | + | 0.971089i | \(0.423273\pi\) | |||||||
\(54\) | 1.21019 | 0.164686 | ||||||||
\(55\) | 0.429431 | 0.0579044 | ||||||||
\(56\) | −2.12016 | −0.283318 | ||||||||
\(57\) | 11.9490 | 1.58268 | ||||||||
\(58\) | −1.00000 | −0.131306 | ||||||||
\(59\) | 2.19195 | 0.285367 | 0.142683 | − | 0.989768i | \(-0.454427\pi\) | ||||
0.142683 | + | 0.989768i | \(0.454427\pi\) | |||||||
\(60\) | 1.28489 | 0.165878 | ||||||||
\(61\) | −12.9842 | −1.66245 | −0.831227 | − | 0.555933i | \(-0.812361\pi\) | ||||
−0.831227 | + | 0.555933i | \(0.812361\pi\) | |||||||
\(62\) | −10.4596 | −1.32837 | ||||||||
\(63\) | 7.36876 | 0.928376 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 2.55038 | 0.316336 | ||||||||
\(66\) | −2.16424 | −0.266400 | ||||||||
\(67\) | −14.7941 | −1.80739 | −0.903693 | − | 0.428181i | \(-0.859154\pi\) | ||||
−0.903693 | + | 0.428181i | \(0.859154\pi\) | |||||||
\(68\) | 6.51398 | 0.789936 | ||||||||
\(69\) | −2.54471 | −0.306348 | ||||||||
\(70\) | 1.07052 | 0.127952 | ||||||||
\(71\) | −1.16201 | −0.137905 | −0.0689523 | − | 0.997620i | \(-0.521966\pi\) | ||||
−0.0689523 | + | 0.997620i | \(0.521966\pi\) | |||||||
\(72\) | −3.47557 | −0.409600 | ||||||||
\(73\) | −5.09617 | −0.596461 | −0.298231 | − | 0.954494i | \(-0.596396\pi\) | ||||
−0.298231 | + | 0.954494i | \(0.596396\pi\) | |||||||
\(74\) | −6.58588 | −0.765593 | ||||||||
\(75\) | 12.0748 | 1.39428 | ||||||||
\(76\) | −4.69560 | −0.538623 | ||||||||
\(77\) | −1.80316 | −0.205490 | ||||||||
\(78\) | −12.8534 | −1.45536 | ||||||||
\(79\) | 7.30088 | 0.821413 | 0.410707 | − | 0.911768i | \(-0.365282\pi\) | ||||
0.410707 | + | 0.911768i | \(0.365282\pi\) | |||||||
\(80\) | −0.504925 | −0.0564523 | ||||||||
\(81\) | −7.34713 | −0.816348 | ||||||||
\(82\) | 8.56343 | 0.945673 | ||||||||
\(83\) | 6.12415 | 0.672213 | 0.336106 | − | 0.941824i | \(-0.390890\pi\) | ||||
0.336106 | + | 0.941824i | \(0.390890\pi\) | |||||||
\(84\) | −5.39520 | −0.588664 | ||||||||
\(85\) | −3.28907 | −0.356750 | ||||||||
\(86\) | −4.24169 | −0.457394 | ||||||||
\(87\) | −2.54471 | −0.272822 | ||||||||
\(88\) | 0.850485 | 0.0906620 | ||||||||
\(89\) | 2.44271 | 0.258927 | 0.129463 | − | 0.991584i | \(-0.458674\pi\) | ||||
0.129463 | + | 0.991584i | \(0.458674\pi\) | |||||||
\(90\) | 1.75490 | 0.184983 | ||||||||
\(91\) | −10.7090 | −1.12260 | ||||||||
\(92\) | 1.00000 | 0.104257 | ||||||||
\(93\) | −26.6166 | −2.76001 | ||||||||
\(94\) | 0.904416 | 0.0932833 | ||||||||
\(95\) | 2.37093 | 0.243252 | ||||||||
\(96\) | 2.54471 | 0.259719 | ||||||||
\(97\) | −14.5252 | −1.47481 | −0.737406 | − | 0.675450i | \(-0.763949\pi\) | ||||
−0.737406 | + | 0.675450i | \(0.763949\pi\) | |||||||
\(98\) | 2.50492 | 0.253036 | ||||||||
\(99\) | −2.95592 | −0.297081 | ||||||||
\(100\) | −4.74505 | −0.474505 | ||||||||
\(101\) | −2.74730 | −0.273367 | −0.136683 | − | 0.990615i | \(-0.543644\pi\) | ||||
−0.136683 | + | 0.990615i | \(0.543644\pi\) | |||||||
\(102\) | 16.5762 | 1.64129 | ||||||||
\(103\) | 0.112367 | 0.0110718 | 0.00553590 | − | 0.999985i | \(-0.498238\pi\) | ||||
0.00553590 | + | 0.999985i | \(0.498238\pi\) | |||||||
\(104\) | 5.05101 | 0.495293 | ||||||||
\(105\) | 2.72417 | 0.265852 | ||||||||
\(106\) | −3.47576 | −0.337596 | ||||||||
\(107\) | −18.0811 | −1.74797 | −0.873984 | − | 0.485954i | \(-0.838472\pi\) | ||||
−0.873984 | + | 0.485954i | \(0.838472\pi\) | |||||||
\(108\) | −1.21019 | −0.116450 | ||||||||
\(109\) | −15.4803 | −1.48274 | −0.741370 | − | 0.671097i | \(-0.765823\pi\) | ||||
−0.741370 | + | 0.671097i | \(0.765823\pi\) | |||||||
\(110\) | −0.429431 | −0.0409446 | ||||||||
\(111\) | −16.7592 | −1.59071 | ||||||||
\(112\) | 2.12016 | 0.200336 | ||||||||
\(113\) | −7.30730 | −0.687413 | −0.343706 | − | 0.939077i | \(-0.611682\pi\) | ||||
−0.343706 | + | 0.939077i | \(0.611682\pi\) | |||||||
\(114\) | −11.9490 | −1.11912 | ||||||||
\(115\) | −0.504925 | −0.0470845 | ||||||||
\(116\) | 1.00000 | 0.0928477 | ||||||||
\(117\) | −17.5551 | −1.62297 | ||||||||
\(118\) | −2.19195 | −0.201785 | ||||||||
\(119\) | 13.8107 | 1.26602 | ||||||||
\(120\) | −1.28489 | −0.117294 | ||||||||
\(121\) | −10.2767 | −0.934243 | ||||||||
\(122\) | 12.9842 | 1.17553 | ||||||||
\(123\) | 21.7915 | 1.96487 | ||||||||
\(124\) | 10.4596 | 0.939296 | ||||||||
\(125\) | 4.92052 | 0.440104 | ||||||||
\(126\) | −7.36876 | −0.656461 | ||||||||
\(127\) | 1.40232 | 0.124436 | 0.0622181 | − | 0.998063i | \(-0.480183\pi\) | ||||
0.0622181 | + | 0.998063i | \(0.480183\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | −10.7939 | −0.950350 | ||||||||
\(130\) | −2.55038 | −0.223683 | ||||||||
\(131\) | −17.9044 | −1.56431 | −0.782157 | − | 0.623081i | \(-0.785881\pi\) | ||||
−0.782157 | + | 0.623081i | \(0.785881\pi\) | |||||||
\(132\) | 2.16424 | 0.188373 | ||||||||
\(133\) | −9.95543 | −0.863245 | ||||||||
\(134\) | 14.7941 | 1.27801 | ||||||||
\(135\) | 0.611053 | 0.0525911 | ||||||||
\(136\) | −6.51398 | −0.558569 | ||||||||
\(137\) | 21.6999 | 1.85395 | 0.926973 | − | 0.375128i | \(-0.122401\pi\) | ||||
0.926973 | + | 0.375128i | \(0.122401\pi\) | |||||||
\(138\) | 2.54471 | 0.216620 | ||||||||
\(139\) | −14.3121 | −1.21394 | −0.606968 | − | 0.794726i | \(-0.707615\pi\) | ||||
−0.606968 | + | 0.794726i | \(0.707615\pi\) | |||||||
\(140\) | −1.07052 | −0.0904755 | ||||||||
\(141\) | 2.30148 | 0.193819 | ||||||||
\(142\) | 1.16201 | 0.0975133 | ||||||||
\(143\) | 4.29581 | 0.359234 | ||||||||
\(144\) | 3.47557 | 0.289631 | ||||||||
\(145\) | −0.504925 | −0.0419317 | ||||||||
\(146\) | 5.09617 | 0.421762 | ||||||||
\(147\) | 6.37432 | 0.525745 | ||||||||
\(148\) | 6.58588 | 0.541356 | ||||||||
\(149\) | 2.45800 | 0.201367 | 0.100683 | − | 0.994919i | \(-0.467897\pi\) | ||||
0.100683 | + | 0.994919i | \(0.467897\pi\) | |||||||
\(150\) | −12.0748 | −0.985903 | ||||||||
\(151\) | −19.9665 | −1.62485 | −0.812427 | − | 0.583063i | \(-0.801854\pi\) | ||||
−0.812427 | + | 0.583063i | \(0.801854\pi\) | |||||||
\(152\) | 4.69560 | 0.380864 | ||||||||
\(153\) | 22.6398 | 1.83032 | ||||||||
\(154\) | 1.80316 | 0.145303 | ||||||||
\(155\) | −5.28129 | −0.424204 | ||||||||
\(156\) | 12.8534 | 1.02909 | ||||||||
\(157\) | −3.40867 | −0.272042 | −0.136021 | − | 0.990706i | \(-0.543431\pi\) | ||||
−0.136021 | + | 0.990706i | \(0.543431\pi\) | |||||||
\(158\) | −7.30088 | −0.580827 | ||||||||
\(159\) | −8.84482 | −0.701440 | ||||||||
\(160\) | 0.504925 | 0.0399178 | ||||||||
\(161\) | 2.12016 | 0.167092 | ||||||||
\(162\) | 7.34713 | 0.577245 | ||||||||
\(163\) | 14.5175 | 1.13710 | 0.568549 | − | 0.822650i | \(-0.307505\pi\) | ||||
0.568549 | + | 0.822650i | \(0.307505\pi\) | |||||||
\(164\) | −8.56343 | −0.668691 | ||||||||
\(165\) | −1.09278 | −0.0850727 | ||||||||
\(166\) | −6.12415 | −0.475326 | ||||||||
\(167\) | 14.6764 | 1.13569 | 0.567846 | − | 0.823135i | \(-0.307777\pi\) | ||||
0.567846 | + | 0.823135i | \(0.307777\pi\) | |||||||
\(168\) | 5.39520 | 0.416249 | ||||||||
\(169\) | 12.5127 | 0.962519 | ||||||||
\(170\) | 3.28907 | 0.252260 | ||||||||
\(171\) | −16.3199 | −1.24801 | ||||||||
\(172\) | 4.24169 | 0.323426 | ||||||||
\(173\) | −4.89401 | −0.372085 | −0.186042 | − | 0.982542i | \(-0.559566\pi\) | ||||
−0.186042 | + | 0.982542i | \(0.559566\pi\) | |||||||
\(174\) | 2.54471 | 0.192914 | ||||||||
\(175\) | −10.0603 | −0.760484 | ||||||||
\(176\) | −0.850485 | −0.0641077 | ||||||||
\(177\) | −5.57787 | −0.419259 | ||||||||
\(178\) | −2.44271 | −0.183089 | ||||||||
\(179\) | 23.9294 | 1.78857 | 0.894283 | − | 0.447502i | \(-0.147686\pi\) | ||||
0.894283 | + | 0.447502i | \(0.147686\pi\) | |||||||
\(180\) | −1.75490 | −0.130803 | ||||||||
\(181\) | −20.2876 | −1.50797 | −0.753983 | − | 0.656894i | \(-0.771870\pi\) | ||||
−0.753983 | + | 0.656894i | \(0.771870\pi\) | |||||||
\(182\) | 10.7090 | 0.793801 | ||||||||
\(183\) | 33.0410 | 2.44246 | ||||||||
\(184\) | −1.00000 | −0.0737210 | ||||||||
\(185\) | −3.32537 | −0.244486 | ||||||||
\(186\) | 26.6166 | 1.95162 | ||||||||
\(187\) | −5.54004 | −0.405128 | ||||||||
\(188\) | −0.904416 | −0.0659613 | ||||||||
\(189\) | −2.56579 | −0.186634 | ||||||||
\(190\) | −2.37093 | −0.172005 | ||||||||
\(191\) | 3.15447 | 0.228250 | 0.114125 | − | 0.993466i | \(-0.463594\pi\) | ||||
0.114125 | + | 0.993466i | \(0.463594\pi\) | |||||||
\(192\) | −2.54471 | −0.183649 | ||||||||
\(193\) | −12.8415 | −0.924353 | −0.462176 | − | 0.886788i | \(-0.652931\pi\) | ||||
−0.462176 | + | 0.886788i | \(0.652931\pi\) | |||||||
\(194\) | 14.5252 | 1.04285 | ||||||||
\(195\) | −6.48999 | −0.464758 | ||||||||
\(196\) | −2.50492 | −0.178923 | ||||||||
\(197\) | 19.3191 | 1.37643 | 0.688216 | − | 0.725506i | \(-0.258394\pi\) | ||||
0.688216 | + | 0.725506i | \(0.258394\pi\) | |||||||
\(198\) | 2.95592 | 0.210068 | ||||||||
\(199\) | −3.71208 | −0.263143 | −0.131571 | − | 0.991307i | \(-0.542002\pi\) | ||||
−0.131571 | + | 0.991307i | \(0.542002\pi\) | |||||||
\(200\) | 4.74505 | 0.335526 | ||||||||
\(201\) | 37.6467 | 2.65540 | ||||||||
\(202\) | 2.74730 | 0.193299 | ||||||||
\(203\) | 2.12016 | 0.148806 | ||||||||
\(204\) | −16.5762 | −1.16057 | ||||||||
\(205\) | 4.32389 | 0.301993 | ||||||||
\(206\) | −0.112367 | −0.00782895 | ||||||||
\(207\) | 3.47557 | 0.241569 | ||||||||
\(208\) | −5.05101 | −0.350225 | ||||||||
\(209\) | 3.99354 | 0.276239 | ||||||||
\(210\) | −2.72417 | −0.187986 | ||||||||
\(211\) | 4.72835 | 0.325513 | 0.162757 | − | 0.986666i | \(-0.447961\pi\) | ||||
0.162757 | + | 0.986666i | \(0.447961\pi\) | |||||||
\(212\) | 3.47576 | 0.238716 | ||||||||
\(213\) | 2.95697 | 0.202608 | ||||||||
\(214\) | 18.0811 | 1.23600 | ||||||||
\(215\) | −2.14174 | −0.146065 | ||||||||
\(216\) | 1.21019 | 0.0823428 | ||||||||
\(217\) | 22.1759 | 1.50540 | ||||||||
\(218\) | 15.4803 | 1.04846 | ||||||||
\(219\) | 12.9683 | 0.876316 | ||||||||
\(220\) | 0.429431 | 0.0289522 | ||||||||
\(221\) | −32.9022 | −2.21324 | ||||||||
\(222\) | 16.7592 | 1.12480 | ||||||||
\(223\) | −17.8577 | −1.19584 | −0.597920 | − | 0.801556i | \(-0.704006\pi\) | ||||
−0.597920 | + | 0.801556i | \(0.704006\pi\) | |||||||
\(224\) | −2.12016 | −0.141659 | ||||||||
\(225\) | −16.4918 | −1.09945 | ||||||||
\(226\) | 7.30730 | 0.486074 | ||||||||
\(227\) | −15.2508 | −1.01223 | −0.506117 | − | 0.862465i | \(-0.668919\pi\) | ||||
−0.506117 | + | 0.862465i | \(0.668919\pi\) | |||||||
\(228\) | 11.9490 | 0.791340 | ||||||||
\(229\) | −22.6368 | −1.49588 | −0.747940 | − | 0.663766i | \(-0.768957\pi\) | ||||
−0.747940 | + | 0.663766i | \(0.768957\pi\) | |||||||
\(230\) | 0.504925 | 0.0332937 | ||||||||
\(231\) | 4.58853 | 0.301903 | ||||||||
\(232\) | −1.00000 | −0.0656532 | ||||||||
\(233\) | −7.62966 | −0.499835 | −0.249918 | − | 0.968267i | \(-0.580404\pi\) | ||||
−0.249918 | + | 0.968267i | \(0.580404\pi\) | |||||||
\(234\) | 17.5551 | 1.14762 | ||||||||
\(235\) | 0.456662 | 0.0297893 | ||||||||
\(236\) | 2.19195 | 0.142683 | ||||||||
\(237\) | −18.5786 | −1.20681 | ||||||||
\(238\) | −13.8107 | −0.895213 | ||||||||
\(239\) | −16.0383 | −1.03743 | −0.518716 | − | 0.854946i | \(-0.673590\pi\) | ||||
−0.518716 | + | 0.854946i | \(0.673590\pi\) | |||||||
\(240\) | 1.28489 | 0.0829392 | ||||||||
\(241\) | −27.6992 | −1.78426 | −0.892130 | − | 0.451778i | \(-0.850790\pi\) | ||||
−0.892130 | + | 0.451778i | \(0.850790\pi\) | |||||||
\(242\) | 10.2767 | 0.660610 | ||||||||
\(243\) | 22.3269 | 1.43227 | ||||||||
\(244\) | −12.9842 | −0.831227 | ||||||||
\(245\) | 1.26480 | 0.0808050 | ||||||||
\(246\) | −21.7915 | −1.38937 | ||||||||
\(247\) | 23.7176 | 1.50911 | ||||||||
\(248\) | −10.4596 | −0.664183 | ||||||||
\(249\) | −15.5842 | −0.987609 | ||||||||
\(250\) | −4.92052 | −0.311201 | ||||||||
\(251\) | −14.2405 | −0.898852 | −0.449426 | − | 0.893318i | \(-0.648371\pi\) | ||||
−0.449426 | + | 0.893318i | \(0.648371\pi\) | |||||||
\(252\) | 7.36876 | 0.464188 | ||||||||
\(253\) | −0.850485 | −0.0534695 | ||||||||
\(254\) | −1.40232 | −0.0879896 | ||||||||
\(255\) | 8.36974 | 0.524134 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 23.2522 | 1.45043 | 0.725216 | − | 0.688521i | \(-0.241740\pi\) | ||||
0.725216 | + | 0.688521i | \(0.241740\pi\) | |||||||
\(258\) | 10.7939 | 0.671999 | ||||||||
\(259\) | 13.9631 | 0.867626 | ||||||||
\(260\) | 2.55038 | 0.158168 | ||||||||
\(261\) | 3.47557 | 0.215132 | ||||||||
\(262\) | 17.9044 | 1.10614 | ||||||||
\(263\) | 11.5860 | 0.714426 | 0.357213 | − | 0.934023i | \(-0.383727\pi\) | ||||
0.357213 | + | 0.934023i | \(0.383727\pi\) | |||||||
\(264\) | −2.16424 | −0.133200 | ||||||||
\(265\) | −1.75500 | −0.107809 | ||||||||
\(266\) | 9.95543 | 0.610407 | ||||||||
\(267\) | −6.21600 | −0.380413 | ||||||||
\(268\) | −14.7941 | −0.903693 | ||||||||
\(269\) | −25.1049 | −1.53067 | −0.765336 | − | 0.643630i | \(-0.777427\pi\) | ||||
−0.765336 | + | 0.643630i | \(0.777427\pi\) | |||||||
\(270\) | −0.611053 | −0.0371875 | ||||||||
\(271\) | 17.3946 | 1.05665 | 0.528323 | − | 0.849044i | \(-0.322821\pi\) | ||||
0.528323 | + | 0.849044i | \(0.322821\pi\) | |||||||
\(272\) | 6.51398 | 0.394968 | ||||||||
\(273\) | 27.2512 | 1.64932 | ||||||||
\(274\) | −21.6999 | −1.31094 | ||||||||
\(275\) | 4.03559 | 0.243355 | ||||||||
\(276\) | −2.54471 | −0.153174 | ||||||||
\(277\) | 14.8366 | 0.891448 | 0.445724 | − | 0.895171i | \(-0.352946\pi\) | ||||
0.445724 | + | 0.895171i | \(0.352946\pi\) | |||||||
\(278\) | 14.3121 | 0.858383 | ||||||||
\(279\) | 36.3529 | 2.17639 | ||||||||
\(280\) | 1.07052 | 0.0639758 | ||||||||
\(281\) | −17.4702 | −1.04218 | −0.521092 | − | 0.853500i | \(-0.674475\pi\) | ||||
−0.521092 | + | 0.853500i | \(0.674475\pi\) | |||||||
\(282\) | −2.30148 | −0.137051 | ||||||||
\(283\) | 14.4926 | 0.861498 | 0.430749 | − | 0.902472i | \(-0.358249\pi\) | ||||
0.430749 | + | 0.902472i | \(0.358249\pi\) | |||||||
\(284\) | −1.16201 | −0.0689523 | ||||||||
\(285\) | −6.03333 | −0.357384 | ||||||||
\(286\) | −4.29581 | −0.254017 | ||||||||
\(287\) | −18.1558 | −1.07170 | ||||||||
\(288\) | −3.47557 | −0.204800 | ||||||||
\(289\) | 25.4320 | 1.49600 | ||||||||
\(290\) | 0.504925 | 0.0296502 | ||||||||
\(291\) | 36.9625 | 2.16678 | ||||||||
\(292\) | −5.09617 | −0.298231 | ||||||||
\(293\) | 5.92107 | 0.345913 | 0.172956 | − | 0.984929i | \(-0.444668\pi\) | ||||
0.172956 | + | 0.984929i | \(0.444668\pi\) | |||||||
\(294\) | −6.37432 | −0.371758 | ||||||||
\(295\) | −1.10677 | −0.0644385 | ||||||||
\(296\) | −6.58588 | −0.382796 | ||||||||
\(297\) | 1.02925 | 0.0597229 | ||||||||
\(298\) | −2.45800 | −0.142388 | ||||||||
\(299\) | −5.05101 | −0.292108 | ||||||||
\(300\) | 12.0748 | 0.697139 | ||||||||
\(301\) | 8.99307 | 0.518352 | ||||||||
\(302\) | 19.9665 | 1.14895 | ||||||||
\(303\) | 6.99109 | 0.401628 | ||||||||
\(304\) | −4.69560 | −0.269311 | ||||||||
\(305\) | 6.55604 | 0.375398 | ||||||||
\(306\) | −22.6398 | −1.29423 | ||||||||
\(307\) | 17.5305 | 1.00052 | 0.500260 | − | 0.865875i | \(-0.333238\pi\) | ||||
0.500260 | + | 0.865875i | \(0.333238\pi\) | |||||||
\(308\) | −1.80316 | −0.102745 | ||||||||
\(309\) | −0.285941 | −0.0162666 | ||||||||
\(310\) | 5.28129 | 0.299957 | ||||||||
\(311\) | 23.7841 | 1.34867 | 0.674337 | − | 0.738424i | \(-0.264429\pi\) | ||||
0.674337 | + | 0.738424i | \(0.264429\pi\) | |||||||
\(312\) | −12.8534 | −0.727680 | ||||||||
\(313\) | 17.6353 | 0.996808 | 0.498404 | − | 0.866945i | \(-0.333920\pi\) | ||||
0.498404 | + | 0.866945i | \(0.333920\pi\) | |||||||
\(314\) | 3.40867 | 0.192363 | ||||||||
\(315\) | −3.72067 | −0.209636 | ||||||||
\(316\) | 7.30088 | 0.410707 | ||||||||
\(317\) | −16.7350 | −0.939930 | −0.469965 | − | 0.882685i | \(-0.655734\pi\) | ||||
−0.469965 | + | 0.882685i | \(0.655734\pi\) | |||||||
\(318\) | 8.84482 | 0.495993 | ||||||||
\(319\) | −0.850485 | −0.0476180 | ||||||||
\(320\) | −0.504925 | −0.0282261 | ||||||||
\(321\) | 46.0113 | 2.56810 | ||||||||
\(322\) | −2.12016 | −0.118152 | ||||||||
\(323\) | −30.5871 | −1.70191 | ||||||||
\(324\) | −7.34713 | −0.408174 | ||||||||
\(325\) | 23.9673 | 1.32947 | ||||||||
\(326\) | −14.5175 | −0.804049 | ||||||||
\(327\) | 39.3928 | 2.17843 | ||||||||
\(328\) | 8.56343 | 0.472836 | ||||||||
\(329\) | −1.91751 | −0.105715 | ||||||||
\(330\) | 1.09278 | 0.0601555 | ||||||||
\(331\) | 34.5251 | 1.89767 | 0.948836 | − | 0.315770i | \(-0.102263\pi\) | ||||
0.948836 | + | 0.315770i | \(0.102263\pi\) | |||||||
\(332\) | 6.12415 | 0.336106 | ||||||||
\(333\) | 22.8897 | 1.25435 | ||||||||
\(334\) | −14.6764 | −0.803056 | ||||||||
\(335\) | 7.46990 | 0.408124 | ||||||||
\(336\) | −5.39520 | −0.294332 | ||||||||
\(337\) | −26.2706 | −1.43105 | −0.715526 | − | 0.698587i | \(-0.753813\pi\) | ||||
−0.715526 | + | 0.698587i | \(0.753813\pi\) | |||||||
\(338\) | −12.5127 | −0.680604 | ||||||||
\(339\) | 18.5950 | 1.00994 | ||||||||
\(340\) | −3.28907 | −0.178375 | ||||||||
\(341\) | −8.89570 | −0.481729 | ||||||||
\(342\) | 16.3199 | 0.882479 | ||||||||
\(343\) | −20.1520 | −1.08810 | ||||||||
\(344\) | −4.24169 | −0.228697 | ||||||||
\(345\) | 1.28489 | 0.0691761 | ||||||||
\(346\) | 4.89401 | 0.263104 | ||||||||
\(347\) | −18.7646 | −1.00734 | −0.503669 | − | 0.863897i | \(-0.668017\pi\) | ||||
−0.503669 | + | 0.863897i | \(0.668017\pi\) | |||||||
\(348\) | −2.54471 | −0.136411 | ||||||||
\(349\) | −21.6052 | −1.15650 | −0.578250 | − | 0.815860i | \(-0.696264\pi\) | ||||
−0.578250 | + | 0.815860i | \(0.696264\pi\) | |||||||
\(350\) | 10.0603 | 0.537744 | ||||||||
\(351\) | 6.11267 | 0.326270 | ||||||||
\(352\) | 0.850485 | 0.0453310 | ||||||||
\(353\) | −25.0509 | −1.33332 | −0.666662 | − | 0.745360i | \(-0.732278\pi\) | ||||
−0.666662 | + | 0.745360i | \(0.732278\pi\) | |||||||
\(354\) | 5.57787 | 0.296461 | ||||||||
\(355\) | 0.586725 | 0.0311401 | ||||||||
\(356\) | 2.44271 | 0.129463 | ||||||||
\(357\) | −35.1442 | −1.86003 | ||||||||
\(358\) | −23.9294 | −1.26471 | ||||||||
\(359\) | 14.9448 | 0.788754 | 0.394377 | − | 0.918949i | \(-0.370960\pi\) | ||||
0.394377 | + | 0.918949i | \(0.370960\pi\) | |||||||
\(360\) | 1.75490 | 0.0924914 | ||||||||
\(361\) | 3.04870 | 0.160458 | ||||||||
\(362\) | 20.2876 | 1.06629 | ||||||||
\(363\) | 26.1512 | 1.37258 | ||||||||
\(364\) | −10.7090 | −0.561302 | ||||||||
\(365\) | 2.57318 | 0.134686 | ||||||||
\(366\) | −33.0410 | −1.72708 | ||||||||
\(367\) | 19.3929 | 1.01230 | 0.506152 | − | 0.862444i | \(-0.331068\pi\) | ||||
0.506152 | + | 0.862444i | \(0.331068\pi\) | |||||||
\(368\) | 1.00000 | 0.0521286 | ||||||||
\(369\) | −29.7628 | −1.54939 | ||||||||
\(370\) | 3.32537 | 0.172878 | ||||||||
\(371\) | 7.36917 | 0.382588 | ||||||||
\(372\) | −26.6166 | −1.38001 | ||||||||
\(373\) | 2.82893 | 0.146477 | 0.0732383 | − | 0.997314i | \(-0.476667\pi\) | ||||
0.0732383 | + | 0.997314i | \(0.476667\pi\) | |||||||
\(374\) | 5.54004 | 0.286469 | ||||||||
\(375\) | −12.5213 | −0.646598 | ||||||||
\(376\) | 0.904416 | 0.0466417 | ||||||||
\(377\) | −5.05101 | −0.260140 | ||||||||
\(378\) | 2.56579 | 0.131970 | ||||||||
\(379\) | 23.6832 | 1.21652 | 0.608262 | − | 0.793736i | \(-0.291867\pi\) | ||||
0.608262 | + | 0.793736i | \(0.291867\pi\) | |||||||
\(380\) | 2.37093 | 0.121626 | ||||||||
\(381\) | −3.56851 | −0.182820 | ||||||||
\(382\) | −3.15447 | −0.161397 | ||||||||
\(383\) | −22.1269 | −1.13063 | −0.565317 | − | 0.824874i | \(-0.691246\pi\) | ||||
−0.565317 | + | 0.824874i | \(0.691246\pi\) | |||||||
\(384\) | 2.54471 | 0.129859 | ||||||||
\(385\) | 0.910462 | 0.0464014 | ||||||||
\(386\) | 12.8415 | 0.653616 | ||||||||
\(387\) | 14.7423 | 0.749393 | ||||||||
\(388\) | −14.5252 | −0.737406 | ||||||||
\(389\) | 10.9909 | 0.557262 | 0.278631 | − | 0.960398i | \(-0.410119\pi\) | ||||
0.278631 | + | 0.960398i | \(0.410119\pi\) | |||||||
\(390\) | 6.48999 | 0.328633 | ||||||||
\(391\) | 6.51398 | 0.329426 | ||||||||
\(392\) | 2.50492 | 0.126518 | ||||||||
\(393\) | 45.5616 | 2.29828 | ||||||||
\(394\) | −19.3191 | −0.973284 | ||||||||
\(395\) | −3.68639 | −0.185483 | ||||||||
\(396\) | −2.95592 | −0.148541 | ||||||||
\(397\) | 20.2250 | 1.01506 | 0.507531 | − | 0.861634i | \(-0.330558\pi\) | ||||
0.507531 | + | 0.861634i | \(0.330558\pi\) | |||||||
\(398\) | 3.71208 | 0.186070 | ||||||||
\(399\) | 25.3337 | 1.26827 | ||||||||
\(400\) | −4.74505 | −0.237253 | ||||||||
\(401\) | 14.6135 | 0.729761 | 0.364881 | − | 0.931054i | \(-0.381110\pi\) | ||||
0.364881 | + | 0.931054i | \(0.381110\pi\) | |||||||
\(402\) | −37.6467 | −1.87765 | ||||||||
\(403\) | −52.8314 | −2.63172 | ||||||||
\(404\) | −2.74730 | −0.136683 | ||||||||
\(405\) | 3.70975 | 0.184339 | ||||||||
\(406\) | −2.12016 | −0.105222 | ||||||||
\(407\) | −5.60119 | −0.277641 | ||||||||
\(408\) | 16.5762 | 0.820645 | ||||||||
\(409\) | −27.4662 | −1.35812 | −0.679058 | − | 0.734085i | \(-0.737611\pi\) | ||||
−0.679058 | + | 0.734085i | \(0.737611\pi\) | |||||||
\(410\) | −4.32389 | −0.213542 | ||||||||
\(411\) | −55.2200 | −2.72380 | ||||||||
\(412\) | 0.112367 | 0.00553590 | ||||||||
\(413\) | 4.64727 | 0.228677 | ||||||||
\(414\) | −3.47557 | −0.170815 | ||||||||
\(415\) | −3.09223 | −0.151792 | ||||||||
\(416\) | 5.05101 | 0.247646 | ||||||||
\(417\) | 36.4202 | 1.78351 | ||||||||
\(418\) | −3.99354 | −0.195330 | ||||||||
\(419\) | 6.96837 | 0.340427 | 0.170213 | − | 0.985407i | \(-0.445554\pi\) | ||||
0.170213 | + | 0.985407i | \(0.445554\pi\) | |||||||
\(420\) | 2.72417 | 0.132926 | ||||||||
\(421\) | −4.95289 | −0.241389 | −0.120695 | − | 0.992690i | \(-0.538512\pi\) | ||||
−0.120695 | + | 0.992690i | \(0.538512\pi\) | |||||||
\(422\) | −4.72835 | −0.230173 | ||||||||
\(423\) | −3.14336 | −0.152835 | ||||||||
\(424\) | −3.47576 | −0.168798 | ||||||||
\(425\) | −30.9092 | −1.49932 | ||||||||
\(426\) | −2.95697 | −0.143266 | ||||||||
\(427\) | −27.5285 | −1.33220 | ||||||||
\(428\) | −18.0811 | −0.873984 | ||||||||
\(429\) | −10.9316 | −0.527783 | ||||||||
\(430\) | 2.14174 | 0.103284 | ||||||||
\(431\) | −26.2304 | −1.26347 | −0.631736 | − | 0.775183i | \(-0.717657\pi\) | ||||
−0.631736 | + | 0.775183i | \(0.717657\pi\) | |||||||
\(432\) | −1.21019 | −0.0582251 | ||||||||
\(433\) | −13.7429 | −0.660440 | −0.330220 | − | 0.943904i | \(-0.607123\pi\) | ||||
−0.330220 | + | 0.943904i | \(0.607123\pi\) | |||||||
\(434\) | −22.1759 | −1.06448 | ||||||||
\(435\) | 1.28489 | 0.0616057 | ||||||||
\(436\) | −15.4803 | −0.741370 | ||||||||
\(437\) | −4.69560 | −0.224621 | ||||||||
\(438\) | −12.9683 | −0.619649 | ||||||||
\(439\) | −12.9060 | −0.615968 | −0.307984 | − | 0.951392i | \(-0.599654\pi\) | ||||
−0.307984 | + | 0.951392i | \(0.599654\pi\) | |||||||
\(440\) | −0.429431 | −0.0204723 | ||||||||
\(441\) | −8.70604 | −0.414573 | ||||||||
\(442\) | 32.9022 | 1.56500 | ||||||||
\(443\) | −0.0726725 | −0.00345277 | −0.00172639 | − | 0.999999i | \(-0.500550\pi\) | ||||
−0.00172639 | + | 0.999999i | \(0.500550\pi\) | |||||||
\(444\) | −16.7592 | −0.795355 | ||||||||
\(445\) | −1.23339 | −0.0584681 | ||||||||
\(446\) | 17.8577 | 0.845587 | ||||||||
\(447\) | −6.25489 | −0.295846 | ||||||||
\(448\) | 2.12016 | 0.100168 | ||||||||
\(449\) | 26.4195 | 1.24681 | 0.623406 | − | 0.781898i | \(-0.285748\pi\) | ||||
0.623406 | + | 0.781898i | \(0.285748\pi\) | |||||||
\(450\) | 16.4918 | 0.777429 | ||||||||
\(451\) | 7.28307 | 0.342946 | ||||||||
\(452\) | −7.30730 | −0.343706 | ||||||||
\(453\) | 50.8091 | 2.38722 | ||||||||
\(454\) | 15.2508 | 0.715757 | ||||||||
\(455\) | 5.40722 | 0.253494 | ||||||||
\(456\) | −11.9490 | −0.559562 | ||||||||
\(457\) | 12.5126 | 0.585313 | 0.292657 | − | 0.956218i | \(-0.405461\pi\) | ||||
0.292657 | + | 0.956218i | \(0.405461\pi\) | |||||||
\(458\) | 22.6368 | 1.05775 | ||||||||
\(459\) | −7.88313 | −0.367953 | ||||||||
\(460\) | −0.504925 | −0.0235422 | ||||||||
\(461\) | −15.3188 | −0.713468 | −0.356734 | − | 0.934206i | \(-0.616110\pi\) | ||||
−0.356734 | + | 0.934206i | \(0.616110\pi\) | |||||||
\(462\) | −4.58853 | −0.213478 | ||||||||
\(463\) | 20.5657 | 0.955767 | 0.477884 | − | 0.878423i | \(-0.341404\pi\) | ||||
0.477884 | + | 0.878423i | \(0.341404\pi\) | |||||||
\(464\) | 1.00000 | 0.0464238 | ||||||||
\(465\) | 13.4394 | 0.623236 | ||||||||
\(466\) | 7.62966 | 0.353437 | ||||||||
\(467\) | −23.5091 | −1.08787 | −0.543935 | − | 0.839127i | \(-0.683066\pi\) | ||||
−0.543935 | + | 0.839127i | \(0.683066\pi\) | |||||||
\(468\) | −17.5551 | −0.811487 | ||||||||
\(469\) | −31.3658 | −1.44834 | ||||||||
\(470\) | −0.456662 | −0.0210642 | ||||||||
\(471\) | 8.67410 | 0.399681 | ||||||||
\(472\) | −2.19195 | −0.100892 | ||||||||
\(473\) | −3.60750 | −0.165873 | ||||||||
\(474\) | 18.5786 | 0.853346 | ||||||||
\(475\) | 22.2809 | 1.02232 | ||||||||
\(476\) | 13.8107 | 0.633011 | ||||||||
\(477\) | 12.0802 | 0.553116 | ||||||||
\(478\) | 16.0383 | 0.733576 | ||||||||
\(479\) | 23.0640 | 1.05382 | 0.526910 | − | 0.849921i | \(-0.323350\pi\) | ||||
0.526910 | + | 0.849921i | \(0.323350\pi\) | |||||||
\(480\) | −1.28489 | −0.0586469 | ||||||||
\(481\) | −33.2654 | −1.51677 | ||||||||
\(482\) | 27.6992 | 1.26166 | ||||||||
\(483\) | −5.39520 | −0.245490 | ||||||||
\(484\) | −10.2767 | −0.467122 | ||||||||
\(485\) | 7.33414 | 0.333026 | ||||||||
\(486\) | −22.3269 | −1.01277 | ||||||||
\(487\) | −25.9056 | −1.17389 | −0.586947 | − | 0.809625i | \(-0.699670\pi\) | ||||
−0.586947 | + | 0.809625i | \(0.699670\pi\) | |||||||
\(488\) | 12.9842 | 0.587766 | ||||||||
\(489\) | −36.9428 | −1.67061 | ||||||||
\(490\) | −1.26480 | −0.0571378 | ||||||||
\(491\) | −11.9550 | −0.539520 | −0.269760 | − | 0.962928i | \(-0.586944\pi\) | ||||
−0.269760 | + | 0.962928i | \(0.586944\pi\) | |||||||
\(492\) | 21.7915 | 0.982436 | ||||||||
\(493\) | 6.51398 | 0.293375 | ||||||||
\(494\) | −23.7176 | −1.06710 | ||||||||
\(495\) | 1.49252 | 0.0670836 | ||||||||
\(496\) | 10.4596 | 0.469648 | ||||||||
\(497\) | −2.46364 | −0.110509 | ||||||||
\(498\) | 15.5842 | 0.698345 | ||||||||
\(499\) | 11.1509 | 0.499181 | 0.249591 | − | 0.968351i | \(-0.419704\pi\) | ||||
0.249591 | + | 0.968351i | \(0.419704\pi\) | |||||||
\(500\) | 4.92052 | 0.220052 | ||||||||
\(501\) | −37.3472 | −1.66855 | ||||||||
\(502\) | 14.2405 | 0.635584 | ||||||||
\(503\) | 17.9630 | 0.800932 | 0.400466 | − | 0.916312i | \(-0.368848\pi\) | ||||
0.400466 | + | 0.916312i | \(0.368848\pi\) | |||||||
\(504\) | −7.36876 | −0.328231 | ||||||||
\(505\) | 1.38718 | 0.0617287 | ||||||||
\(506\) | 0.850485 | 0.0378087 | ||||||||
\(507\) | −31.8414 | −1.41412 | ||||||||
\(508\) | 1.40232 | 0.0622181 | ||||||||
\(509\) | 41.1077 | 1.82207 | 0.911033 | − | 0.412334i | \(-0.135286\pi\) | ||||
0.911033 | + | 0.412334i | \(0.135286\pi\) | |||||||
\(510\) | −8.36974 | −0.370618 | ||||||||
\(511\) | −10.8047 | −0.477971 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 5.68256 | 0.250891 | ||||||||
\(514\) | −23.2522 | −1.02561 | ||||||||
\(515\) | −0.0567367 | −0.00250012 | ||||||||
\(516\) | −10.7939 | −0.475175 | ||||||||
\(517\) | 0.769192 | 0.0338290 | ||||||||
\(518\) | −13.9631 | −0.613504 | ||||||||
\(519\) | 12.4539 | 0.546663 | ||||||||
\(520\) | −2.55038 | −0.111842 | ||||||||
\(521\) | −17.8595 | −0.782437 | −0.391219 | − | 0.920298i | \(-0.627946\pi\) | ||||
−0.391219 | + | 0.920298i | \(0.627946\pi\) | |||||||
\(522\) | −3.47557 | −0.152122 | ||||||||
\(523\) | 27.7568 | 1.21372 | 0.606861 | − | 0.794808i | \(-0.292428\pi\) | ||||
0.606861 | + | 0.794808i | \(0.292428\pi\) | |||||||
\(524\) | −17.9044 | −0.782157 | ||||||||
\(525\) | 25.6005 | 1.11730 | ||||||||
\(526\) | −11.5860 | −0.505176 | ||||||||
\(527\) | 68.1334 | 2.96794 | ||||||||
\(528\) | 2.16424 | 0.0941865 | ||||||||
\(529\) | 1.00000 | 0.0434783 | ||||||||
\(530\) | 1.75500 | 0.0762322 | ||||||||
\(531\) | 7.61826 | 0.330604 | ||||||||
\(532\) | −9.95543 | −0.431623 | ||||||||
\(533\) | 43.2540 | 1.87354 | ||||||||
\(534\) | 6.21600 | 0.268993 | ||||||||
\(535\) | 9.12961 | 0.394707 | ||||||||
\(536\) | 14.7941 | 0.639007 | ||||||||
\(537\) | −60.8934 | −2.62775 | ||||||||
\(538\) | 25.1049 | 1.08235 | ||||||||
\(539\) | 2.13040 | 0.0917628 | ||||||||
\(540\) | 0.611053 | 0.0262955 | ||||||||
\(541\) | 0.962692 | 0.0413894 | 0.0206947 | − | 0.999786i | \(-0.493412\pi\) | ||||
0.0206947 | + | 0.999786i | \(0.493412\pi\) | |||||||
\(542\) | −17.3946 | −0.747161 | ||||||||
\(543\) | 51.6261 | 2.21549 | ||||||||
\(544\) | −6.51398 | −0.279285 | ||||||||
\(545\) | 7.81636 | 0.334816 | ||||||||
\(546\) | −27.2512 | −1.16624 | ||||||||
\(547\) | −6.40185 | −0.273723 | −0.136862 | − | 0.990590i | \(-0.543702\pi\) | ||||
−0.136862 | + | 0.990590i | \(0.543702\pi\) | |||||||
\(548\) | 21.6999 | 0.926973 | ||||||||
\(549\) | −45.1274 | −1.92599 | ||||||||
\(550\) | −4.03559 | −0.172078 | ||||||||
\(551\) | −4.69560 | −0.200039 | ||||||||
\(552\) | 2.54471 | 0.108310 | ||||||||
\(553\) | 15.4790 | 0.658235 | ||||||||
\(554\) | −14.8366 | −0.630349 | ||||||||
\(555\) | 8.46212 | 0.359197 | ||||||||
\(556\) | −14.3121 | −0.606968 | ||||||||
\(557\) | −0.225527 | −0.00955588 | −0.00477794 | − | 0.999989i | \(-0.501521\pi\) | ||||
−0.00477794 | + | 0.999989i | \(0.501521\pi\) | |||||||
\(558\) | −36.3529 | −1.53894 | ||||||||
\(559\) | −21.4249 | −0.906175 | ||||||||
\(560\) | −1.07052 | −0.0452378 | ||||||||
\(561\) | 14.0978 | 0.595211 | ||||||||
\(562\) | 17.4702 | 0.736935 | ||||||||
\(563\) | 4.86110 | 0.204871 | 0.102435 | − | 0.994740i | \(-0.467336\pi\) | ||||
0.102435 | + | 0.994740i | \(0.467336\pi\) | |||||||
\(564\) | 2.30148 | 0.0969097 | ||||||||
\(565\) | 3.68963 | 0.155224 | ||||||||
\(566\) | −14.4926 | −0.609171 | ||||||||
\(567\) | −15.5771 | −0.654176 | ||||||||
\(568\) | 1.16201 | 0.0487567 | ||||||||
\(569\) | 23.8190 | 0.998543 | 0.499272 | − | 0.866446i | \(-0.333601\pi\) | ||||
0.499272 | + | 0.866446i | \(0.333601\pi\) | |||||||
\(570\) | 6.03333 | 0.252708 | ||||||||
\(571\) | 15.4499 | 0.646559 | 0.323280 | − | 0.946304i | \(-0.395215\pi\) | ||||
0.323280 | + | 0.946304i | \(0.395215\pi\) | |||||||
\(572\) | 4.29581 | 0.179617 | ||||||||
\(573\) | −8.02723 | −0.335342 | ||||||||
\(574\) | 18.1558 | 0.757810 | ||||||||
\(575\) | −4.74505 | −0.197882 | ||||||||
\(576\) | 3.47557 | 0.144815 | ||||||||
\(577\) | −40.4140 | −1.68246 | −0.841228 | − | 0.540680i | \(-0.818167\pi\) | ||||
−0.841228 | + | 0.540680i | \(0.818167\pi\) | |||||||
\(578\) | −25.4320 | −1.05783 | ||||||||
\(579\) | 32.6780 | 1.35805 | ||||||||
\(580\) | −0.504925 | −0.0209659 | ||||||||
\(581\) | 12.9842 | 0.538674 | ||||||||
\(582\) | −36.9625 | −1.53214 | ||||||||
\(583\) | −2.95608 | −0.122428 | ||||||||
\(584\) | 5.09617 | 0.210881 | ||||||||
\(585\) | 8.86403 | 0.366482 | ||||||||
\(586\) | −5.92107 | −0.244597 | ||||||||
\(587\) | 16.5023 | 0.681122 | 0.340561 | − | 0.940222i | \(-0.389383\pi\) | ||||
0.340561 | + | 0.940222i | \(0.389383\pi\) | |||||||
\(588\) | 6.37432 | 0.262872 | ||||||||
\(589\) | −49.1140 | −2.02371 | ||||||||
\(590\) | 1.10677 | 0.0455649 | ||||||||
\(591\) | −49.1617 | −2.02224 | ||||||||
\(592\) | 6.58588 | 0.270678 | ||||||||
\(593\) | −24.9126 | −1.02304 | −0.511519 | − | 0.859272i | \(-0.670917\pi\) | ||||
−0.511519 | + | 0.859272i | \(0.670917\pi\) | |||||||
\(594\) | −1.02925 | −0.0422304 | ||||||||
\(595\) | −6.97335 | −0.285880 | ||||||||
\(596\) | 2.45800 | 0.100683 | ||||||||
\(597\) | 9.44619 | 0.386607 | ||||||||
\(598\) | 5.05101 | 0.206551 | ||||||||
\(599\) | −15.0912 | −0.616609 | −0.308305 | − | 0.951288i | \(-0.599762\pi\) | ||||
−0.308305 | + | 0.951288i | \(0.599762\pi\) | |||||||
\(600\) | −12.0748 | −0.492952 | ||||||||
\(601\) | −2.31951 | −0.0946146 | −0.0473073 | − | 0.998880i | \(-0.515064\pi\) | ||||
−0.0473073 | + | 0.998880i | \(0.515064\pi\) | |||||||
\(602\) | −8.99307 | −0.366530 | ||||||||
\(603\) | −51.4179 | −2.09390 | ||||||||
\(604\) | −19.9665 | −0.812427 | ||||||||
\(605\) | 5.18895 | 0.210961 | ||||||||
\(606\) | −6.99109 | −0.283994 | ||||||||
\(607\) | 26.3854 | 1.07095 | 0.535475 | − | 0.844551i | \(-0.320132\pi\) | ||||
0.535475 | + | 0.844551i | \(0.320132\pi\) | |||||||
\(608\) | 4.69560 | 0.190432 | ||||||||
\(609\) | −5.39520 | −0.218624 | ||||||||
\(610\) | −6.55604 | −0.265446 | ||||||||
\(611\) | 4.56822 | 0.184810 | ||||||||
\(612\) | 22.6398 | 0.915159 | ||||||||
\(613\) | 4.14453 | 0.167396 | 0.0836979 | − | 0.996491i | \(-0.473327\pi\) | ||||
0.0836979 | + | 0.996491i | \(0.473327\pi\) | |||||||
\(614\) | −17.5305 | −0.707475 | ||||||||
\(615\) | −11.0031 | −0.443686 | ||||||||
\(616\) | 1.80316 | 0.0726515 | ||||||||
\(617\) | −2.44707 | −0.0985154 | −0.0492577 | − | 0.998786i | \(-0.515686\pi\) | ||||
−0.0492577 | + | 0.998786i | \(0.515686\pi\) | |||||||
\(618\) | 0.285941 | 0.0115022 | ||||||||
\(619\) | −18.7390 | −0.753186 | −0.376593 | − | 0.926379i | \(-0.622904\pi\) | ||||
−0.376593 | + | 0.926379i | \(0.622904\pi\) | |||||||
\(620\) | −5.28129 | −0.212102 | ||||||||
\(621\) | −1.21019 | −0.0485631 | ||||||||
\(622\) | −23.7841 | −0.953657 | ||||||||
\(623\) | 5.17894 | 0.207490 | ||||||||
\(624\) | 12.8534 | 0.514547 | ||||||||
\(625\) | 21.2408 | 0.849631 | ||||||||
\(626\) | −17.6353 | −0.704849 | ||||||||
\(627\) | −10.1624 | −0.405848 | ||||||||
\(628\) | −3.40867 | −0.136021 | ||||||||
\(629\) | 42.9003 | 1.71055 | ||||||||
\(630\) | 3.72067 | 0.148235 | ||||||||
\(631\) | −39.8482 | −1.58633 | −0.793166 | − | 0.609005i | \(-0.791569\pi\) | ||||
−0.793166 | + | 0.609005i | \(0.791569\pi\) | |||||||
\(632\) | −7.30088 | −0.290413 | ||||||||
\(633\) | −12.0323 | −0.478241 | ||||||||
\(634\) | 16.7350 | 0.664631 | ||||||||
\(635\) | −0.708068 | −0.0280988 | ||||||||
\(636\) | −8.84482 | −0.350720 | ||||||||
\(637\) | 12.6524 | 0.501307 | ||||||||
\(638\) | 0.850485 | 0.0336710 | ||||||||
\(639\) | −4.03863 | −0.159766 | ||||||||
\(640\) | 0.504925 | 0.0199589 | ||||||||
\(641\) | −39.7599 | −1.57042 | −0.785210 | − | 0.619229i | \(-0.787445\pi\) | ||||
−0.785210 | + | 0.619229i | \(0.787445\pi\) | |||||||
\(642\) | −46.0113 | −1.81592 | ||||||||
\(643\) | −27.1807 | −1.07190 | −0.535951 | − | 0.844249i | \(-0.680047\pi\) | ||||
−0.535951 | + | 0.844249i | \(0.680047\pi\) | |||||||
\(644\) | 2.12016 | 0.0835460 | ||||||||
\(645\) | 5.45011 | 0.214598 | ||||||||
\(646\) | 30.5871 | 1.20343 | ||||||||
\(647\) | −32.2716 | −1.26873 | −0.634364 | − | 0.773035i | \(-0.718738\pi\) | ||||
−0.634364 | + | 0.773035i | \(0.718738\pi\) | |||||||
\(648\) | 7.34713 | 0.288622 | ||||||||
\(649\) | −1.86422 | −0.0731769 | ||||||||
\(650\) | −23.9673 | −0.940076 | ||||||||
\(651\) | −56.4314 | −2.21172 | ||||||||
\(652\) | 14.5175 | 0.568549 | ||||||||
\(653\) | −0.535483 | −0.0209551 | −0.0104775 | − | 0.999945i | \(-0.503335\pi\) | ||||
−0.0104775 | + | 0.999945i | \(0.503335\pi\) | |||||||
\(654\) | −39.3928 | −1.54038 | ||||||||
\(655\) | 9.04037 | 0.353237 | ||||||||
\(656\) | −8.56343 | −0.334346 | ||||||||
\(657\) | −17.7121 | −0.691014 | ||||||||
\(658\) | 1.91751 | 0.0747521 | ||||||||
\(659\) | −39.0365 | −1.52065 | −0.760324 | − | 0.649544i | \(-0.774960\pi\) | ||||
−0.760324 | + | 0.649544i | \(0.774960\pi\) | |||||||
\(660\) | −1.09278 | −0.0425363 | ||||||||
\(661\) | 44.2521 | 1.72121 | 0.860603 | − | 0.509276i | \(-0.170087\pi\) | ||||
0.860603 | + | 0.509276i | \(0.170087\pi\) | |||||||
\(662\) | −34.5251 | −1.34186 | ||||||||
\(663\) | 83.7267 | 3.25168 | ||||||||
\(664\) | −6.12415 | −0.237663 | ||||||||
\(665\) | 5.02674 | 0.194929 | ||||||||
\(666\) | −22.8897 | −0.886957 | ||||||||
\(667\) | 1.00000 | 0.0387202 | ||||||||
\(668\) | 14.6764 | 0.567846 | ||||||||
\(669\) | 45.4427 | 1.75692 | ||||||||
\(670\) | −7.46990 | −0.288587 | ||||||||
\(671\) | 11.0429 | 0.426305 | ||||||||
\(672\) | 5.39520 | 0.208124 | ||||||||
\(673\) | 41.7056 | 1.60763 | 0.803816 | − | 0.594879i | \(-0.202800\pi\) | ||||
0.803816 | + | 0.594879i | \(0.202800\pi\) | |||||||
\(674\) | 26.2706 | 1.01191 | ||||||||
\(675\) | 5.74240 | 0.221025 | ||||||||
\(676\) | 12.5127 | 0.481259 | ||||||||
\(677\) | −33.1375 | −1.27358 | −0.636789 | − | 0.771038i | \(-0.719738\pi\) | ||||
−0.636789 | + | 0.771038i | \(0.719738\pi\) | |||||||
\(678\) | −18.5950 | −0.714136 | ||||||||
\(679\) | −30.7958 | −1.18183 | ||||||||
\(680\) | 3.28907 | 0.126130 | ||||||||
\(681\) | 38.8090 | 1.48716 | ||||||||
\(682\) | 8.89570 | 0.340634 | ||||||||
\(683\) | −22.2003 | −0.849472 | −0.424736 | − | 0.905317i | \(-0.639633\pi\) | ||||
−0.424736 | + | 0.905317i | \(0.639633\pi\) | |||||||
\(684\) | −16.3199 | −0.624007 | ||||||||
\(685\) | −10.9568 | −0.418638 | ||||||||
\(686\) | 20.1520 | 0.769405 | ||||||||
\(687\) | 57.6041 | 2.19773 | ||||||||
\(688\) | 4.24169 | 0.161713 | ||||||||
\(689\) | −17.5561 | −0.668835 | ||||||||
\(690\) | −1.28489 | −0.0489149 | ||||||||
\(691\) | −2.71861 | −0.103421 | −0.0517104 | − | 0.998662i | \(-0.516467\pi\) | ||||
−0.0517104 | + | 0.998662i | \(0.516467\pi\) | |||||||
\(692\) | −4.89401 | −0.186042 | ||||||||
\(693\) | −6.26702 | −0.238064 | ||||||||
\(694\) | 18.7646 | 0.712295 | ||||||||
\(695\) | 7.22653 | 0.274118 | ||||||||
\(696\) | 2.54471 | 0.0964571 | ||||||||
\(697\) | −55.7820 | −2.11289 | ||||||||
\(698\) | 21.6052 | 0.817769 | ||||||||
\(699\) | 19.4153 | 0.734354 | ||||||||
\(700\) | −10.0603 | −0.380242 | ||||||||
\(701\) | 41.9653 | 1.58501 | 0.792504 | − | 0.609867i | \(-0.208777\pi\) | ||||
0.792504 | + | 0.609867i | \(0.208777\pi\) | |||||||
\(702\) | −6.11267 | −0.230708 | ||||||||
\(703\) | −30.9247 | −1.16635 | ||||||||
\(704\) | −0.850485 | −0.0320539 | ||||||||
\(705\) | −1.16207 | −0.0437662 | ||||||||
\(706\) | 25.0509 | 0.942803 | ||||||||
\(707\) | −5.82471 | −0.219061 | ||||||||
\(708\) | −5.57787 | −0.209629 | ||||||||
\(709\) | 8.11517 | 0.304772 | 0.152386 | − | 0.988321i | \(-0.451304\pi\) | ||||
0.152386 | + | 0.988321i | \(0.451304\pi\) | |||||||
\(710\) | −0.586725 | −0.0220194 | ||||||||
\(711\) | 25.3747 | 0.951626 | ||||||||
\(712\) | −2.44271 | −0.0915445 | ||||||||
\(713\) | 10.4596 | 0.391714 | ||||||||
\(714\) | 35.1442 | 1.31524 | ||||||||
\(715\) | −2.16906 | −0.0811183 | ||||||||
\(716\) | 23.9294 | 0.894283 | ||||||||
\(717\) | 40.8129 | 1.52419 | ||||||||
\(718\) | −14.9448 | −0.557734 | ||||||||
\(719\) | 50.3076 | 1.87616 | 0.938079 | − | 0.346421i | \(-0.112603\pi\) | ||||
0.938079 | + | 0.346421i | \(0.112603\pi\) | |||||||
\(720\) | −1.75490 | −0.0654013 | ||||||||
\(721\) | 0.238235 | 0.00887234 | ||||||||
\(722\) | −3.04870 | −0.113461 | ||||||||
\(723\) | 70.4865 | 2.62142 | ||||||||
\(724\) | −20.2876 | −0.753983 | ||||||||
\(725\) | −4.74505 | −0.176227 | ||||||||
\(726\) | −26.1512 | −0.970562 | ||||||||
\(727\) | −17.3323 | −0.642818 | −0.321409 | − | 0.946941i | \(-0.604156\pi\) | ||||
−0.321409 | + | 0.946941i | \(0.604156\pi\) | |||||||
\(728\) | 10.7090 | 0.396900 | ||||||||
\(729\) | −34.7742 | −1.28793 | ||||||||
\(730\) | −2.57318 | −0.0952377 | ||||||||
\(731\) | 27.6303 | 1.02194 | ||||||||
\(732\) | 33.0410 | 1.22123 | ||||||||
\(733\) | −30.2353 | −1.11677 | −0.558383 | − | 0.829583i | \(-0.688578\pi\) | ||||
−0.558383 | + | 0.829583i | \(0.688578\pi\) | |||||||
\(734\) | −19.3929 | −0.715807 | ||||||||
\(735\) | −3.21855 | −0.118718 | ||||||||
\(736\) | −1.00000 | −0.0368605 | ||||||||
\(737\) | 12.5821 | 0.463469 | ||||||||
\(738\) | 29.7628 | 1.09558 | ||||||||
\(739\) | 18.1462 | 0.667517 | 0.333759 | − | 0.942659i | \(-0.391683\pi\) | ||||
0.333759 | + | 0.942659i | \(0.391683\pi\) | |||||||
\(740\) | −3.32537 | −0.122243 | ||||||||
\(741\) | −60.3544 | −2.21717 | ||||||||
\(742\) | −7.36917 | −0.270531 | ||||||||
\(743\) | −10.1890 | −0.373797 | −0.186898 | − | 0.982379i | \(-0.559843\pi\) | ||||
−0.186898 | + | 0.982379i | \(0.559843\pi\) | |||||||
\(744\) | 26.6166 | 0.975812 | ||||||||
\(745\) | −1.24110 | −0.0454705 | ||||||||
\(746\) | −2.82893 | −0.103575 | ||||||||
\(747\) | 21.2849 | 0.778774 | ||||||||
\(748\) | −5.54004 | −0.202564 | ||||||||
\(749\) | −38.3349 | −1.40073 | ||||||||
\(750\) | 12.5213 | 0.457213 | ||||||||
\(751\) | −20.5941 | −0.751488 | −0.375744 | − | 0.926723i | \(-0.622613\pi\) | ||||
−0.375744 | + | 0.926723i | \(0.622613\pi\) | |||||||
\(752\) | −0.904416 | −0.0329806 | ||||||||
\(753\) | 36.2380 | 1.32059 | ||||||||
\(754\) | 5.05101 | 0.183947 | ||||||||
\(755\) | 10.0816 | 0.366907 | ||||||||
\(756\) | −2.56579 | −0.0933168 | ||||||||
\(757\) | 32.2007 | 1.17036 | 0.585178 | − | 0.810905i | \(-0.301025\pi\) | ||||
0.585178 | + | 0.810905i | \(0.301025\pi\) | |||||||
\(758\) | −23.6832 | −0.860213 | ||||||||
\(759\) | 2.16424 | 0.0785570 | ||||||||
\(760\) | −2.37093 | −0.0860025 | ||||||||
\(761\) | −3.44428 | −0.124855 | −0.0624275 | − | 0.998050i | \(-0.519884\pi\) | ||||
−0.0624275 | + | 0.998050i | \(0.519884\pi\) | |||||||
\(762\) | 3.56851 | 0.129274 | ||||||||
\(763\) | −32.8206 | −1.18819 | ||||||||
\(764\) | 3.15447 | 0.114125 | ||||||||
\(765\) | −11.4314 | −0.413303 | ||||||||
\(766\) | 22.1269 | 0.799479 | ||||||||
\(767\) | −11.0715 | −0.399770 | ||||||||
\(768\) | −2.54471 | −0.0918245 | ||||||||
\(769\) | 6.46099 | 0.232989 | 0.116495 | − | 0.993191i | \(-0.462834\pi\) | ||||
0.116495 | + | 0.993191i | \(0.462834\pi\) | |||||||
\(770\) | −0.910462 | −0.0328108 | ||||||||
\(771\) | −59.1702 | −2.13096 | ||||||||
\(772\) | −12.8415 | −0.462176 | ||||||||
\(773\) | 1.61735 | 0.0581720 | 0.0290860 | − | 0.999577i | \(-0.490740\pi\) | ||||
0.0290860 | + | 0.999577i | \(0.490740\pi\) | |||||||
\(774\) | −14.7423 | −0.529901 | ||||||||
\(775\) | −49.6312 | −1.78280 | ||||||||
\(776\) | 14.5252 | 0.521425 | ||||||||
\(777\) | −35.5321 | −1.27471 | ||||||||
\(778\) | −10.9909 | −0.394044 | ||||||||
\(779\) | 40.2105 | 1.44069 | ||||||||
\(780\) | −6.48999 | −0.232379 | ||||||||
\(781\) | 0.988268 | 0.0353630 | ||||||||
\(782\) | −6.51398 | −0.232940 | ||||||||
\(783\) | −1.21019 | −0.0432485 | ||||||||
\(784\) | −2.50492 | −0.0894616 | ||||||||
\(785\) | 1.72112 | 0.0614295 | ||||||||
\(786\) | −45.5616 | −1.62513 | ||||||||
\(787\) | −4.54522 | −0.162020 | −0.0810098 | − | 0.996713i | \(-0.525814\pi\) | ||||
−0.0810098 | + | 0.996713i | \(0.525814\pi\) | |||||||
\(788\) | 19.3191 | 0.688216 | ||||||||
\(789\) | −29.4832 | −1.04963 | ||||||||
\(790\) | 3.68639 | 0.131156 | ||||||||
\(791\) | −15.4926 | −0.550855 | ||||||||
\(792\) | 2.95592 | 0.105034 | ||||||||
\(793\) | 65.5833 | 2.32893 | ||||||||
\(794\) | −20.2250 | −0.717757 | ||||||||
\(795\) | 4.46597 | 0.158392 | ||||||||
\(796\) | −3.71208 | −0.131571 | ||||||||
\(797\) | 5.36370 | 0.189992 | 0.0949960 | − | 0.995478i | \(-0.469716\pi\) | ||||
0.0949960 | + | 0.995478i | \(0.469716\pi\) | |||||||
\(798\) | −25.3337 | −0.896804 | ||||||||
\(799\) | −5.89135 | −0.208421 | ||||||||
\(800\) | 4.74505 | 0.167763 | ||||||||
\(801\) | 8.48981 | 0.299973 | ||||||||
\(802\) | −14.6135 | −0.516019 | ||||||||
\(803\) | 4.33421 | 0.152951 | ||||||||
\(804\) | 37.6467 | 1.32770 | ||||||||
\(805\) | −1.07052 | −0.0377309 | ||||||||
\(806\) | 52.8314 | 1.86091 | ||||||||
\(807\) | 63.8848 | 2.24885 | ||||||||
\(808\) | 2.74730 | 0.0966497 | ||||||||
\(809\) | 46.9420 | 1.65039 | 0.825197 | − | 0.564846i | \(-0.191064\pi\) | ||||
0.825197 | + | 0.564846i | \(0.191064\pi\) | |||||||
\(810\) | −3.70975 | −0.130347 | ||||||||
\(811\) | −43.0804 | −1.51276 | −0.756379 | − | 0.654134i | \(-0.773033\pi\) | ||||
−0.756379 | + | 0.654134i | \(0.773033\pi\) | |||||||
\(812\) | 2.12016 | 0.0744030 | ||||||||
\(813\) | −44.2642 | −1.55241 | ||||||||
\(814\) | 5.60119 | 0.196322 | ||||||||
\(815\) | −7.33024 | −0.256767 | ||||||||
\(816\) | −16.5762 | −0.580284 | ||||||||
\(817\) | −19.9173 | −0.696819 | ||||||||
\(818\) | 27.4662 | 0.960333 | ||||||||
\(819\) | −37.2197 | −1.30056 | ||||||||
\(820\) | 4.32389 | 0.150997 | ||||||||
\(821\) | 43.2641 | 1.50993 | 0.754963 | − | 0.655767i | \(-0.227655\pi\) | ||||
0.754963 | + | 0.655767i | \(0.227655\pi\) | |||||||
\(822\) | 55.2200 | 1.92602 | ||||||||
\(823\) | −2.41919 | −0.0843276 | −0.0421638 | − | 0.999111i | \(-0.513425\pi\) | ||||
−0.0421638 | + | 0.999111i | \(0.513425\pi\) | |||||||
\(824\) | −0.112367 | −0.00391448 | ||||||||
\(825\) | −10.2694 | −0.357536 | ||||||||
\(826\) | −4.64727 | −0.161699 | ||||||||
\(827\) | −49.7698 | −1.73066 | −0.865332 | − | 0.501199i | \(-0.832892\pi\) | ||||
−0.865332 | + | 0.501199i | \(0.832892\pi\) | |||||||
\(828\) | 3.47557 | 0.120784 | ||||||||
\(829\) | 14.1282 | 0.490694 | 0.245347 | − | 0.969435i | \(-0.421098\pi\) | ||||
0.245347 | + | 0.969435i | \(0.421098\pi\) | |||||||
\(830\) | 3.09223 | 0.107333 | ||||||||
\(831\) | −37.7550 | −1.30971 | ||||||||
\(832\) | −5.05101 | −0.175112 | ||||||||
\(833\) | −16.3170 | −0.565352 | ||||||||
\(834\) | −36.4202 | −1.26113 | ||||||||
\(835\) | −7.41047 | −0.256450 | ||||||||
\(836\) | 3.99354 | 0.138119 | ||||||||
\(837\) | −12.6580 | −0.437525 | ||||||||
\(838\) | −6.96837 | −0.240718 | ||||||||
\(839\) | −44.5225 | −1.53709 | −0.768544 | − | 0.639797i | \(-0.779018\pi\) | ||||
−0.768544 | + | 0.639797i | \(0.779018\pi\) | |||||||
\(840\) | −2.72417 | −0.0939928 | ||||||||
\(841\) | 1.00000 | 0.0344828 | ||||||||
\(842\) | 4.95289 | 0.170688 | ||||||||
\(843\) | 44.4566 | 1.53117 | ||||||||
\(844\) | 4.72835 | 0.162757 | ||||||||
\(845\) | −6.31799 | −0.217346 | ||||||||
\(846\) | 3.14336 | 0.108071 | ||||||||
\(847\) | −21.7882 | −0.748651 | ||||||||
\(848\) | 3.47576 | 0.119358 | ||||||||
\(849\) | −36.8796 | −1.26571 | ||||||||
\(850\) | 30.9092 | 1.06018 | ||||||||
\(851\) | 6.58588 | 0.225761 | ||||||||
\(852\) | 2.95697 | 0.101304 | ||||||||
\(853\) | 37.3437 | 1.27862 | 0.639312 | − | 0.768947i | \(-0.279219\pi\) | ||||
0.639312 | + | 0.768947i | \(0.279219\pi\) | |||||||
\(854\) | 27.5285 | 0.942007 | ||||||||
\(855\) | 8.24032 | 0.281813 | ||||||||
\(856\) | 18.0811 | 0.618000 | ||||||||
\(857\) | −17.8963 | −0.611325 | −0.305663 | − | 0.952140i | \(-0.598878\pi\) | ||||
−0.305663 | + | 0.952140i | \(0.598878\pi\) | |||||||
\(858\) | 10.9316 | 0.373199 | ||||||||
\(859\) | 3.37267 | 0.115074 | 0.0575370 | − | 0.998343i | \(-0.481675\pi\) | ||||
0.0575370 | + | 0.998343i | \(0.481675\pi\) | |||||||
\(860\) | −2.14174 | −0.0730326 | ||||||||
\(861\) | 46.2014 | 1.57454 | ||||||||
\(862\) | 26.2304 | 0.893410 | ||||||||
\(863\) | 25.3401 | 0.862587 | 0.431294 | − | 0.902212i | \(-0.358057\pi\) | ||||
0.431294 | + | 0.902212i | \(0.358057\pi\) | |||||||
\(864\) | 1.21019 | 0.0411714 | ||||||||
\(865\) | 2.47111 | 0.0840201 | ||||||||
\(866\) | 13.7429 | 0.467002 | ||||||||
\(867\) | −64.7171 | −2.19791 | ||||||||
\(868\) | 22.1759 | 0.752700 | ||||||||
\(869\) | −6.20929 | −0.210636 | ||||||||
\(870\) | −1.28489 | −0.0435618 | ||||||||
\(871\) | 74.7252 | 2.53197 | ||||||||
\(872\) | 15.4803 | 0.524228 | ||||||||
\(873\) | −50.4834 | −1.70860 | ||||||||
\(874\) | 4.69560 | 0.158831 | ||||||||
\(875\) | 10.4323 | 0.352675 | ||||||||
\(876\) | 12.9683 | 0.438158 | ||||||||
\(877\) | 15.7169 | 0.530723 | 0.265362 | − | 0.964149i | \(-0.414509\pi\) | ||||
0.265362 | + | 0.964149i | \(0.414509\pi\) | |||||||
\(878\) | 12.9060 | 0.435555 | ||||||||
\(879\) | −15.0674 | −0.508212 | ||||||||
\(880\) | 0.429431 | 0.0144761 | ||||||||
\(881\) | 12.5620 | 0.423225 | 0.211613 | − | 0.977354i | \(-0.432129\pi\) | ||||
0.211613 | + | 0.977354i | \(0.432129\pi\) | |||||||
\(882\) | 8.70604 | 0.293148 | ||||||||
\(883\) | 22.3539 | 0.752267 | 0.376134 | − | 0.926565i | \(-0.377253\pi\) | ||||
0.376134 | + | 0.926565i | \(0.377253\pi\) | |||||||
\(884\) | −32.9022 | −1.10662 | ||||||||
\(885\) | 2.81641 | 0.0946724 | ||||||||
\(886\) | 0.0726725 | 0.00244148 | ||||||||
\(887\) | −24.9506 | −0.837760 | −0.418880 | − | 0.908042i | \(-0.637577\pi\) | ||||
−0.418880 | + | 0.908042i | \(0.637577\pi\) | |||||||
\(888\) | 16.7592 | 0.562401 | ||||||||
\(889\) | 2.97315 | 0.0997162 | ||||||||
\(890\) | 1.23339 | 0.0413432 | ||||||||
\(891\) | 6.24862 | 0.209337 | ||||||||
\(892\) | −17.8577 | −0.597920 | ||||||||
\(893\) | 4.24678 | 0.142113 | ||||||||
\(894\) | 6.25489 | 0.209195 | ||||||||
\(895\) | −12.0825 | −0.403875 | ||||||||
\(896\) | −2.12016 | −0.0708295 | ||||||||
\(897\) | 12.8534 | 0.429162 | ||||||||
\(898\) | −26.4195 | −0.881630 | ||||||||
\(899\) | 10.4596 | 0.348846 | ||||||||
\(900\) | −16.4918 | −0.549725 | ||||||||
\(901\) | 22.6410 | 0.754283 | ||||||||
\(902\) | −7.28307 | −0.242500 | ||||||||
\(903\) | −22.8848 | −0.761558 | ||||||||
\(904\) | 7.30730 | 0.243037 | ||||||||
\(905\) | 10.2437 | 0.340512 | ||||||||
\(906\) | −50.8091 | −1.68802 | ||||||||
\(907\) | 21.9243 | 0.727983 | 0.363991 | − | 0.931402i | \(-0.381414\pi\) | ||||
0.363991 | + | 0.931402i | \(0.381414\pi\) | |||||||
\(908\) | −15.2508 | −0.506117 | ||||||||
\(909\) | −9.54843 | −0.316701 | ||||||||
\(910\) | −5.40722 | −0.179247 | ||||||||
\(911\) | −3.44740 | −0.114218 | −0.0571088 | − | 0.998368i | \(-0.518188\pi\) | ||||
−0.0571088 | + | 0.998368i | \(0.518188\pi\) | |||||||
\(912\) | 11.9490 | 0.395670 | ||||||||
\(913\) | −5.20850 | −0.172376 | ||||||||
\(914\) | −12.5126 | −0.413879 | ||||||||
\(915\) | −16.6832 | −0.551531 | ||||||||
\(916\) | −22.6368 | −0.747940 | ||||||||
\(917\) | −37.9602 | −1.25356 | ||||||||
\(918\) | 7.88313 | 0.260182 | ||||||||
\(919\) | 21.5035 | 0.709335 | 0.354668 | − | 0.934992i | \(-0.384594\pi\) | ||||
0.354668 | + | 0.934992i | \(0.384594\pi\) | |||||||
\(920\) | 0.504925 | 0.0166469 | ||||||||
\(921\) | −44.6102 | −1.46996 | ||||||||
\(922\) | 15.3188 | 0.504498 | ||||||||
\(923\) | 5.86930 | 0.193191 | ||||||||
\(924\) | 4.58853 | 0.150952 | ||||||||
\(925\) | −31.2503 | −1.02750 | ||||||||
\(926\) | −20.5657 | −0.675830 | ||||||||
\(927\) | 0.390538 | 0.0128269 | ||||||||
\(928\) | −1.00000 | −0.0328266 | ||||||||
\(929\) | −16.5557 | −0.543176 | −0.271588 | − | 0.962414i | \(-0.587549\pi\) | ||||
−0.271588 | + | 0.962414i | \(0.587549\pi\) | |||||||
\(930\) | −13.4394 | −0.440694 | ||||||||
\(931\) | 11.7621 | 0.385488 | ||||||||
\(932\) | −7.62966 | −0.249918 | ||||||||
\(933\) | −60.5238 | −1.98146 | ||||||||
\(934\) | 23.5091 | 0.769240 | ||||||||
\(935\) | 2.79730 | 0.0914816 | ||||||||
\(936\) | 17.5551 | 0.573808 | ||||||||
\(937\) | 15.9139 | 0.519883 | 0.259942 | − | 0.965624i | \(-0.416297\pi\) | ||||
0.259942 | + | 0.965624i | \(0.416297\pi\) | |||||||
\(938\) | 31.3658 | 1.02413 | ||||||||
\(939\) | −44.8769 | −1.46450 | ||||||||
\(940\) | 0.456662 | 0.0148947 | ||||||||
\(941\) | −26.4156 | −0.861124 | −0.430562 | − | 0.902561i | \(-0.641685\pi\) | ||||
−0.430562 | + | 0.902561i | \(0.641685\pi\) | |||||||
\(942\) | −8.67410 | −0.282617 | ||||||||
\(943\) | −8.56343 | −0.278864 | ||||||||
\(944\) | 2.19195 | 0.0713417 | ||||||||
\(945\) | 1.29553 | 0.0421436 | ||||||||
\(946\) | 3.60750 | 0.117290 | ||||||||
\(947\) | 49.7387 | 1.61629 | 0.808146 | − | 0.588982i | \(-0.200471\pi\) | ||||
0.808146 | + | 0.588982i | \(0.200471\pi\) | |||||||
\(948\) | −18.5786 | −0.603406 | ||||||||
\(949\) | 25.7408 | 0.835582 | ||||||||
\(950\) | −22.2809 | −0.722887 | ||||||||
\(951\) | 42.5858 | 1.38094 | ||||||||
\(952\) | −13.8107 | −0.447607 | ||||||||
\(953\) | −6.91727 | −0.224072 | −0.112036 | − | 0.993704i | \(-0.535737\pi\) | ||||
−0.112036 | + | 0.993704i | \(0.535737\pi\) | |||||||
\(954\) | −12.0802 | −0.391112 | ||||||||
\(955\) | −1.59277 | −0.0515409 | ||||||||
\(956\) | −16.0383 | −0.518716 | ||||||||
\(957\) | 2.16424 | 0.0699600 | ||||||||
\(958\) | −23.0640 | −0.745163 | ||||||||
\(959\) | 46.0072 | 1.48565 | ||||||||
\(960\) | 1.28489 | 0.0414696 | ||||||||
\(961\) | 78.4025 | 2.52911 | ||||||||
\(962\) | 33.2654 | 1.07252 | ||||||||
\(963\) | −62.8422 | −2.02506 | ||||||||
\(964\) | −27.6992 | −0.892130 | ||||||||
\(965\) | 6.48400 | 0.208727 | ||||||||
\(966\) | 5.39520 | 0.173588 | ||||||||
\(967\) | −11.7585 | −0.378126 | −0.189063 | − | 0.981965i | \(-0.560545\pi\) | ||||
−0.189063 | + | 0.981965i | \(0.560545\pi\) | |||||||
\(968\) | 10.2767 | 0.330305 | ||||||||
\(969\) | 77.8354 | 2.50043 | ||||||||
\(970\) | −7.33414 | −0.235485 | ||||||||
\(971\) | 21.3961 | 0.686634 | 0.343317 | − | 0.939220i | \(-0.388449\pi\) | ||||
0.343317 | + | 0.939220i | \(0.388449\pi\) | |||||||
\(972\) | 22.3269 | 0.716136 | ||||||||
\(973\) | −30.3439 | −0.972782 | ||||||||
\(974\) | 25.9056 | 0.830068 | ||||||||
\(975\) | −60.9900 | −1.95324 | ||||||||
\(976\) | −12.9842 | −0.415614 | ||||||||
\(977\) | 1.60423 | 0.0513238 | 0.0256619 | − | 0.999671i | \(-0.491831\pi\) | ||||
0.0256619 | + | 0.999671i | \(0.491831\pi\) | |||||||
\(978\) | 36.9428 | 1.18130 | ||||||||
\(979\) | −2.07749 | −0.0663969 | ||||||||
\(980\) | 1.26480 | 0.0404025 | ||||||||
\(981\) | −53.8027 | −1.71779 | ||||||||
\(982\) | 11.9550 | 0.381498 | ||||||||
\(983\) | −2.69905 | −0.0860863 | −0.0430431 | − | 0.999073i | \(-0.513705\pi\) | ||||
−0.0430431 | + | 0.999073i | \(0.513705\pi\) | |||||||
\(984\) | −21.7915 | −0.694687 | ||||||||
\(985\) | −9.75471 | −0.310811 | ||||||||
\(986\) | −6.51398 | −0.207447 | ||||||||
\(987\) | 4.87950 | 0.155316 | ||||||||
\(988\) | 23.7176 | 0.754556 | ||||||||
\(989\) | 4.24169 | 0.134878 | ||||||||
\(990\) | −1.49252 | −0.0474353 | ||||||||
\(991\) | −31.3642 | −0.996317 | −0.498158 | − | 0.867086i | \(-0.665990\pi\) | ||||
−0.498158 | + | 0.867086i | \(0.665990\pi\) | |||||||
\(992\) | −10.4596 | −0.332091 | ||||||||
\(993\) | −87.8565 | −2.78804 | ||||||||
\(994\) | 2.46364 | 0.0781418 | ||||||||
\(995\) | 1.87432 | 0.0594200 | ||||||||
\(996\) | −15.5842 | −0.493804 | ||||||||
\(997\) | −4.19811 | −0.132956 | −0.0664778 | − | 0.997788i | \(-0.521176\pi\) | ||||
−0.0664778 | + | 0.997788i | \(0.521176\pi\) | |||||||
\(998\) | −11.1509 | −0.352974 | ||||||||
\(999\) | −7.97014 | −0.252164 |
(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 | 1334.2.a.f.1.1 | ✓ | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1334.2.a.f.1.1 | ✓ | 5 | 1.1 | even | 1 | trivial |