Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [123,2,Mod(1,123)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(123, 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("123.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 123 = 3 \cdot 41 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 123.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(0.982159944862\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.316.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 4x + 2 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(0.470683\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 123.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.470683 | 0.332823 | 0.166412 | − | 0.986056i | \(-0.446782\pi\) | ||||
0.166412 | + | 0.986056i | \(0.446782\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | −1.77846 | −0.889229 | ||||||||
\(5\) | 4.24914 | 1.90027 | 0.950137 | − | 0.311834i | \(-0.100943\pi\) | ||||
0.950137 | + | 0.311834i | \(0.100943\pi\) | |||||||
\(6\) | −0.470683 | −0.192156 | ||||||||
\(7\) | 3.30777 | 1.25022 | 0.625110 | − | 0.780536i | \(-0.285054\pi\) | ||||
0.625110 | + | 0.780536i | \(0.285054\pi\) | |||||||
\(8\) | −1.77846 | −0.628780 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 2.00000 | 0.632456 | ||||||||
\(11\) | −1.47068 | −0.443428 | −0.221714 | − | 0.975112i | \(-0.571165\pi\) | ||||
−0.221714 | + | 0.975112i | \(0.571165\pi\) | |||||||
\(12\) | 1.77846 | 0.513396 | ||||||||
\(13\) | −0.249141 | −0.0690992 | −0.0345496 | − | 0.999403i | \(-0.511000\pi\) | ||||
−0.0345496 | + | 0.999403i | \(0.511000\pi\) | |||||||
\(14\) | 1.55691 | 0.416103 | ||||||||
\(15\) | −4.24914 | −1.09712 | ||||||||
\(16\) | 2.71982 | 0.679956 | ||||||||
\(17\) | −5.02760 | −1.21937 | −0.609686 | − | 0.792643i | \(-0.708704\pi\) | ||||
−0.609686 | + | 0.792643i | \(0.708704\pi\) | |||||||
\(18\) | 0.470683 | 0.110941 | ||||||||
\(19\) | −2.24914 | −0.515988 | −0.257994 | − | 0.966146i | \(-0.583062\pi\) | ||||
−0.257994 | + | 0.966146i | \(0.583062\pi\) | |||||||
\(20\) | −7.55691 | −1.68978 | ||||||||
\(21\) | −3.30777 | −0.721815 | ||||||||
\(22\) | −0.692226 | −0.147583 | ||||||||
\(23\) | −6.24914 | −1.30304 | −0.651518 | − | 0.758633i | \(-0.725867\pi\) | ||||
−0.651518 | + | 0.758633i | \(0.725867\pi\) | |||||||
\(24\) | 1.77846 | 0.363026 | ||||||||
\(25\) | 13.0552 | 2.61104 | ||||||||
\(26\) | −0.117266 | −0.0229978 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | −5.88273 | −1.11173 | ||||||||
\(29\) | −2.41205 | −0.447906 | −0.223953 | − | 0.974600i | \(-0.571896\pi\) | ||||
−0.223953 | + | 0.974600i | \(0.571896\pi\) | |||||||
\(30\) | −2.00000 | −0.365148 | ||||||||
\(31\) | −2.89572 | −0.520087 | −0.260044 | − | 0.965597i | \(-0.583737\pi\) | ||||
−0.260044 | + | 0.965597i | \(0.583737\pi\) | |||||||
\(32\) | 4.83709 | 0.855085 | ||||||||
\(33\) | 1.47068 | 0.256013 | ||||||||
\(34\) | −2.36641 | −0.405835 | ||||||||
\(35\) | 14.0552 | 2.37576 | ||||||||
\(36\) | −1.77846 | −0.296410 | ||||||||
\(37\) | 9.71982 | 1.59793 | 0.798965 | − | 0.601378i | \(-0.205381\pi\) | ||||
0.798965 | + | 0.601378i | \(0.205381\pi\) | |||||||
\(38\) | −1.05863 | −0.171733 | ||||||||
\(39\) | 0.249141 | 0.0398944 | ||||||||
\(40\) | −7.55691 | −1.19485 | ||||||||
\(41\) | 1.00000 | 0.156174 | ||||||||
\(42\) | −1.55691 | −0.240237 | ||||||||
\(43\) | −10.8337 | −1.65212 | −0.826058 | − | 0.563585i | \(-0.809422\pi\) | ||||
−0.826058 | + | 0.563585i | \(0.809422\pi\) | |||||||
\(44\) | 2.61555 | 0.394309 | ||||||||
\(45\) | 4.24914 | 0.633424 | ||||||||
\(46\) | −2.94137 | −0.433681 | ||||||||
\(47\) | −4.08623 | −0.596038 | −0.298019 | − | 0.954560i | \(-0.596326\pi\) | ||||
−0.298019 | + | 0.954560i | \(0.596326\pi\) | |||||||
\(48\) | −2.71982 | −0.392573 | ||||||||
\(49\) | 3.94137 | 0.563052 | ||||||||
\(50\) | 6.14486 | 0.869015 | ||||||||
\(51\) | 5.02760 | 0.704004 | ||||||||
\(52\) | 0.443086 | 0.0614449 | ||||||||
\(53\) | −1.43965 | −0.197751 | −0.0988754 | − | 0.995100i | \(-0.531525\pi\) | ||||
−0.0988754 | + | 0.995100i | \(0.531525\pi\) | |||||||
\(54\) | −0.470683 | −0.0640519 | ||||||||
\(55\) | −6.24914 | −0.842634 | ||||||||
\(56\) | −5.88273 | −0.786113 | ||||||||
\(57\) | 2.24914 | 0.297906 | ||||||||
\(58\) | −1.13531 | −0.149074 | ||||||||
\(59\) | 2.61555 | 0.340515 | 0.170258 | − | 0.985400i | \(-0.445540\pi\) | ||||
0.170258 | + | 0.985400i | \(0.445540\pi\) | |||||||
\(60\) | 7.55691 | 0.975593 | ||||||||
\(61\) | −5.71982 | −0.732348 | −0.366174 | − | 0.930546i | \(-0.619333\pi\) | ||||
−0.366174 | + | 0.930546i | \(0.619333\pi\) | |||||||
\(62\) | −1.36297 | −0.173097 | ||||||||
\(63\) | 3.30777 | 0.416740 | ||||||||
\(64\) | −3.16291 | −0.395364 | ||||||||
\(65\) | −1.05863 | −0.131307 | ||||||||
\(66\) | 0.692226 | 0.0852072 | ||||||||
\(67\) | 15.9379 | 1.94713 | 0.973564 | − | 0.228415i | \(-0.0733542\pi\) | ||||
0.973564 | + | 0.228415i | \(0.0733542\pi\) | |||||||
\(68\) | 8.94137 | 1.08430 | ||||||||
\(69\) | 6.24914 | 0.752308 | ||||||||
\(70\) | 6.61555 | 0.790709 | ||||||||
\(71\) | −10.5293 | −1.24960 | −0.624800 | − | 0.780785i | \(-0.714819\pi\) | ||||
−0.624800 | + | 0.780785i | \(0.714819\pi\) | |||||||
\(72\) | −1.77846 | −0.209593 | ||||||||
\(73\) | 9.39400 | 1.09949 | 0.549743 | − | 0.835334i | \(-0.314726\pi\) | ||||
0.549743 | + | 0.835334i | \(0.314726\pi\) | |||||||
\(74\) | 4.57496 | 0.531828 | ||||||||
\(75\) | −13.0552 | −1.50748 | ||||||||
\(76\) | 4.00000 | 0.458831 | ||||||||
\(77\) | −4.86469 | −0.554383 | ||||||||
\(78\) | 0.117266 | 0.0132778 | ||||||||
\(79\) | −0.560352 | −0.0630445 | −0.0315223 | − | 0.999503i | \(-0.510036\pi\) | ||||
−0.0315223 | + | 0.999503i | \(0.510036\pi\) | |||||||
\(80\) | 11.5569 | 1.29210 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0.470683 | 0.0519783 | ||||||||
\(83\) | 3.80605 | 0.417769 | 0.208884 | − | 0.977940i | \(-0.433017\pi\) | ||||
0.208884 | + | 0.977940i | \(0.433017\pi\) | |||||||
\(84\) | 5.88273 | 0.641859 | ||||||||
\(85\) | −21.3630 | −2.31714 | ||||||||
\(86\) | −5.09922 | −0.549863 | ||||||||
\(87\) | 2.41205 | 0.258599 | ||||||||
\(88\) | 2.61555 | 0.278818 | ||||||||
\(89\) | 4.11727 | 0.436429 | 0.218215 | − | 0.975901i | \(-0.429977\pi\) | ||||
0.218215 | + | 0.975901i | \(0.429977\pi\) | |||||||
\(90\) | 2.00000 | 0.210819 | ||||||||
\(91\) | −0.824101 | −0.0863892 | ||||||||
\(92\) | 11.1138 | 1.15870 | ||||||||
\(93\) | 2.89572 | 0.300273 | ||||||||
\(94\) | −1.92332 | −0.198375 | ||||||||
\(95\) | −9.55691 | −0.980519 | ||||||||
\(96\) | −4.83709 | −0.493683 | ||||||||
\(97\) | −7.19051 | −0.730085 | −0.365043 | − | 0.930991i | \(-0.618946\pi\) | ||||
−0.365043 | + | 0.930991i | \(0.618946\pi\) | |||||||
\(98\) | 1.85514 | 0.187397 | ||||||||
\(99\) | −1.47068 | −0.147809 | ||||||||
\(100\) | −23.2181 | −2.32181 | ||||||||
\(101\) | −11.1449 | −1.10896 | −0.554478 | − | 0.832199i | \(-0.687082\pi\) | ||||
−0.554478 | + | 0.832199i | \(0.687082\pi\) | |||||||
\(102\) | 2.36641 | 0.234309 | ||||||||
\(103\) | 13.2767 | 1.30820 | 0.654098 | − | 0.756410i | \(-0.273048\pi\) | ||||
0.654098 | + | 0.756410i | \(0.273048\pi\) | |||||||
\(104\) | 0.443086 | 0.0434481 | ||||||||
\(105\) | −14.0552 | −1.37165 | ||||||||
\(106\) | −0.677618 | −0.0658161 | ||||||||
\(107\) | 9.32238 | 0.901229 | 0.450614 | − | 0.892719i | \(-0.351205\pi\) | ||||
0.450614 | + | 0.892719i | \(0.351205\pi\) | |||||||
\(108\) | 1.77846 | 0.171132 | ||||||||
\(109\) | −0.249141 | −0.0238633 | −0.0119317 | − | 0.999929i | \(-0.503798\pi\) | ||||
−0.0119317 | + | 0.999929i | \(0.503798\pi\) | |||||||
\(110\) | −2.94137 | −0.280448 | ||||||||
\(111\) | −9.71982 | −0.922565 | ||||||||
\(112\) | 8.99656 | 0.850095 | ||||||||
\(113\) | 9.24570 | 0.869763 | 0.434881 | − | 0.900488i | \(-0.356790\pi\) | ||||
0.434881 | + | 0.900488i | \(0.356790\pi\) | |||||||
\(114\) | 1.05863 | 0.0991501 | ||||||||
\(115\) | −26.5535 | −2.47612 | ||||||||
\(116\) | 4.28973 | 0.398291 | ||||||||
\(117\) | −0.249141 | −0.0230331 | ||||||||
\(118\) | 1.23109 | 0.113331 | ||||||||
\(119\) | −16.6302 | −1.52448 | ||||||||
\(120\) | 7.55691 | 0.689849 | ||||||||
\(121\) | −8.83709 | −0.803372 | ||||||||
\(122\) | −2.69223 | −0.243743 | ||||||||
\(123\) | −1.00000 | −0.0901670 | ||||||||
\(124\) | 5.14992 | 0.462476 | ||||||||
\(125\) | 34.2277 | 3.06141 | ||||||||
\(126\) | 1.55691 | 0.138701 | ||||||||
\(127\) | −0.824101 | −0.0731271 | −0.0365635 | − | 0.999331i | \(-0.511641\pi\) | ||||
−0.0365635 | + | 0.999331i | \(0.511641\pi\) | |||||||
\(128\) | −11.1629 | −0.986671 | ||||||||
\(129\) | 10.8337 | 0.953850 | ||||||||
\(130\) | −0.498281 | −0.0437021 | ||||||||
\(131\) | 8.13187 | 0.710485 | 0.355243 | − | 0.934774i | \(-0.384398\pi\) | ||||
0.355243 | + | 0.934774i | \(0.384398\pi\) | |||||||
\(132\) | −2.61555 | −0.227654 | ||||||||
\(133\) | −7.43965 | −0.645099 | ||||||||
\(134\) | 7.50172 | 0.648050 | ||||||||
\(135\) | −4.24914 | −0.365708 | ||||||||
\(136\) | 8.94137 | 0.766716 | ||||||||
\(137\) | −12.2035 | −1.04262 | −0.521308 | − | 0.853369i | \(-0.674556\pi\) | ||||
−0.521308 | + | 0.853369i | \(0.674556\pi\) | |||||||
\(138\) | 2.94137 | 0.250386 | ||||||||
\(139\) | 14.2897 | 1.21204 | 0.606019 | − | 0.795450i | \(-0.292765\pi\) | ||||
0.606019 | + | 0.795450i | \(0.292765\pi\) | |||||||
\(140\) | −24.9966 | −2.11260 | ||||||||
\(141\) | 4.08623 | 0.344123 | ||||||||
\(142\) | −4.95597 | −0.415896 | ||||||||
\(143\) | 0.366407 | 0.0306405 | ||||||||
\(144\) | 2.71982 | 0.226652 | ||||||||
\(145\) | −10.2491 | −0.851145 | ||||||||
\(146\) | 4.42160 | 0.365934 | ||||||||
\(147\) | −3.94137 | −0.325078 | ||||||||
\(148\) | −17.2863 | −1.42092 | ||||||||
\(149\) | −22.1104 | −1.81135 | −0.905677 | − | 0.423969i | \(-0.860637\pi\) | ||||
−0.905677 | + | 0.423969i | \(0.860637\pi\) | |||||||
\(150\) | −6.14486 | −0.501726 | ||||||||
\(151\) | 10.1173 | 0.823331 | 0.411666 | − | 0.911335i | \(-0.364947\pi\) | ||||
0.411666 | + | 0.911335i | \(0.364947\pi\) | |||||||
\(152\) | 4.00000 | 0.324443 | ||||||||
\(153\) | −5.02760 | −0.406457 | ||||||||
\(154\) | −2.28973 | −0.184512 | ||||||||
\(155\) | −12.3043 | −0.988308 | ||||||||
\(156\) | −0.443086 | −0.0354753 | ||||||||
\(157\) | 18.7620 | 1.49737 | 0.748686 | − | 0.662924i | \(-0.230685\pi\) | ||||
0.748686 | + | 0.662924i | \(0.230685\pi\) | |||||||
\(158\) | −0.263748 | −0.0209827 | ||||||||
\(159\) | 1.43965 | 0.114172 | ||||||||
\(160\) | 20.5535 | 1.62489 | ||||||||
\(161\) | −20.6707 | −1.62908 | ||||||||
\(162\) | 0.470683 | 0.0369804 | ||||||||
\(163\) | 8.54392 | 0.669212 | 0.334606 | − | 0.942358i | \(-0.391397\pi\) | ||||
0.334606 | + | 0.942358i | \(0.391397\pi\) | |||||||
\(164\) | −1.77846 | −0.138874 | ||||||||
\(165\) | 6.24914 | 0.486495 | ||||||||
\(166\) | 1.79145 | 0.139043 | ||||||||
\(167\) | 5.05863 | 0.391449 | 0.195724 | − | 0.980659i | \(-0.437294\pi\) | ||||
0.195724 | + | 0.980659i | \(0.437294\pi\) | |||||||
\(168\) | 5.88273 | 0.453863 | ||||||||
\(169\) | −12.9379 | −0.995225 | ||||||||
\(170\) | −10.0552 | −0.771198 | ||||||||
\(171\) | −2.24914 | −0.171996 | ||||||||
\(172\) | 19.2672 | 1.46911 | ||||||||
\(173\) | 18.8647 | 1.43426 | 0.717128 | − | 0.696942i | \(-0.245456\pi\) | ||||
0.717128 | + | 0.696942i | \(0.245456\pi\) | |||||||
\(174\) | 1.13531 | 0.0860678 | ||||||||
\(175\) | 43.1836 | 3.26438 | ||||||||
\(176\) | −4.00000 | −0.301511 | ||||||||
\(177\) | −2.61555 | −0.196597 | ||||||||
\(178\) | 1.93793 | 0.145254 | ||||||||
\(179\) | −2.85514 | −0.213403 | −0.106701 | − | 0.994291i | \(-0.534029\pi\) | ||||
−0.106701 | + | 0.994291i | \(0.534029\pi\) | |||||||
\(180\) | −7.55691 | −0.563259 | ||||||||
\(181\) | 13.4396 | 0.998961 | 0.499481 | − | 0.866325i | \(-0.333524\pi\) | ||||
0.499481 | + | 0.866325i | \(0.333524\pi\) | |||||||
\(182\) | −0.387890 | −0.0287524 | ||||||||
\(183\) | 5.71982 | 0.422822 | ||||||||
\(184\) | 11.1138 | 0.819322 | ||||||||
\(185\) | 41.3009 | 3.03650 | ||||||||
\(186\) | 1.36297 | 0.0999377 | ||||||||
\(187\) | 7.39400 | 0.540703 | ||||||||
\(188\) | 7.26719 | 0.530014 | ||||||||
\(189\) | −3.30777 | −0.240605 | ||||||||
\(190\) | −4.49828 | −0.326340 | ||||||||
\(191\) | 13.4948 | 0.976453 | 0.488226 | − | 0.872717i | \(-0.337644\pi\) | ||||
0.488226 | + | 0.872717i | \(0.337644\pi\) | |||||||
\(192\) | 3.16291 | 0.228263 | ||||||||
\(193\) | −8.01461 | −0.576904 | −0.288452 | − | 0.957494i | \(-0.593141\pi\) | ||||
−0.288452 | + | 0.957494i | \(0.593141\pi\) | |||||||
\(194\) | −3.38445 | −0.242990 | ||||||||
\(195\) | 1.05863 | 0.0758103 | ||||||||
\(196\) | −7.00955 | −0.500682 | ||||||||
\(197\) | 13.9785 | 0.995928 | 0.497964 | − | 0.867198i | \(-0.334081\pi\) | ||||
0.497964 | + | 0.867198i | \(0.334081\pi\) | |||||||
\(198\) | −0.692226 | −0.0491944 | ||||||||
\(199\) | −4.86469 | −0.344849 | −0.172424 | − | 0.985023i | \(-0.555160\pi\) | ||||
−0.172424 | + | 0.985023i | \(0.555160\pi\) | |||||||
\(200\) | −23.2181 | −1.64177 | ||||||||
\(201\) | −15.9379 | −1.12417 | ||||||||
\(202\) | −5.24570 | −0.369086 | ||||||||
\(203\) | −7.97852 | −0.559982 | ||||||||
\(204\) | −8.94137 | −0.626021 | ||||||||
\(205\) | 4.24914 | 0.296773 | ||||||||
\(206\) | 6.24914 | 0.435398 | ||||||||
\(207\) | −6.24914 | −0.434345 | ||||||||
\(208\) | −0.677618 | −0.0469844 | ||||||||
\(209\) | 3.30777 | 0.228803 | ||||||||
\(210\) | −6.61555 | −0.456516 | ||||||||
\(211\) | −10.6155 | −0.730804 | −0.365402 | − | 0.930850i | \(-0.619069\pi\) | ||||
−0.365402 | + | 0.930850i | \(0.619069\pi\) | |||||||
\(212\) | 2.56035 | 0.175846 | ||||||||
\(213\) | 10.5293 | 0.721457 | ||||||||
\(214\) | 4.38789 | 0.299950 | ||||||||
\(215\) | −46.0337 | −3.13947 | ||||||||
\(216\) | 1.77846 | 0.121009 | ||||||||
\(217\) | −9.57840 | −0.650224 | ||||||||
\(218\) | −0.117266 | −0.00794228 | ||||||||
\(219\) | −9.39400 | −0.634788 | ||||||||
\(220\) | 11.1138 | 0.749294 | ||||||||
\(221\) | 1.25258 | 0.0842575 | ||||||||
\(222\) | −4.57496 | −0.307051 | ||||||||
\(223\) | −17.9931 | −1.20491 | −0.602454 | − | 0.798153i | \(-0.705810\pi\) | ||||
−0.602454 | + | 0.798153i | \(0.705810\pi\) | |||||||
\(224\) | 16.0000 | 1.06904 | ||||||||
\(225\) | 13.0552 | 0.870346 | ||||||||
\(226\) | 4.35180 | 0.289477 | ||||||||
\(227\) | −0.910331 | −0.0604208 | −0.0302104 | − | 0.999544i | \(-0.509618\pi\) | ||||
−0.0302104 | + | 0.999544i | \(0.509618\pi\) | |||||||
\(228\) | −4.00000 | −0.264906 | ||||||||
\(229\) | −7.42504 | −0.490660 | −0.245330 | − | 0.969440i | \(-0.578896\pi\) | ||||
−0.245330 | + | 0.969440i | \(0.578896\pi\) | |||||||
\(230\) | −12.4983 | −0.824112 | ||||||||
\(231\) | 4.86469 | 0.320073 | ||||||||
\(232\) | 4.28973 | 0.281634 | ||||||||
\(233\) | 14.7620 | 0.967093 | 0.483546 | − | 0.875319i | \(-0.339348\pi\) | ||||
0.483546 | + | 0.875319i | \(0.339348\pi\) | |||||||
\(234\) | −0.117266 | −0.00766594 | ||||||||
\(235\) | −17.3630 | −1.13264 | ||||||||
\(236\) | −4.65164 | −0.302796 | ||||||||
\(237\) | 0.560352 | 0.0363988 | ||||||||
\(238\) | −7.82754 | −0.507384 | ||||||||
\(239\) | −1.38445 | −0.0895528 | −0.0447764 | − | 0.998997i | \(-0.514258\pi\) | ||||
−0.0447764 | + | 0.998997i | \(0.514258\pi\) | |||||||
\(240\) | −11.5569 | −0.745996 | ||||||||
\(241\) | −5.95436 | −0.383554 | −0.191777 | − | 0.981439i | \(-0.561425\pi\) | ||||
−0.191777 | + | 0.981439i | \(0.561425\pi\) | |||||||
\(242\) | −4.15947 | −0.267381 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 10.1725 | 0.651225 | ||||||||
\(245\) | 16.7474 | 1.06995 | ||||||||
\(246\) | −0.470683 | −0.0300097 | ||||||||
\(247\) | 0.560352 | 0.0356543 | ||||||||
\(248\) | 5.14992 | 0.327020 | ||||||||
\(249\) | −3.80605 | −0.241199 | ||||||||
\(250\) | 16.1104 | 1.01891 | ||||||||
\(251\) | 2.70683 | 0.170854 | 0.0854269 | − | 0.996344i | \(-0.472775\pi\) | ||||
0.0854269 | + | 0.996344i | \(0.472775\pi\) | |||||||
\(252\) | −5.88273 | −0.370577 | ||||||||
\(253\) | 9.19051 | 0.577802 | ||||||||
\(254\) | −0.387890 | −0.0243384 | ||||||||
\(255\) | 21.3630 | 1.33780 | ||||||||
\(256\) | 1.07162 | 0.0669764 | ||||||||
\(257\) | −0.793065 | −0.0494700 | −0.0247350 | − | 0.999694i | \(-0.507874\pi\) | ||||
−0.0247350 | + | 0.999694i | \(0.507874\pi\) | |||||||
\(258\) | 5.09922 | 0.317464 | ||||||||
\(259\) | 32.1510 | 1.99776 | ||||||||
\(260\) | 1.88273 | 0.116762 | ||||||||
\(261\) | −2.41205 | −0.149302 | ||||||||
\(262\) | 3.82754 | 0.236466 | ||||||||
\(263\) | −15.5879 | −0.961194 | −0.480597 | − | 0.876942i | \(-0.659580\pi\) | ||||
−0.480597 | + | 0.876942i | \(0.659580\pi\) | |||||||
\(264\) | −2.61555 | −0.160976 | ||||||||
\(265\) | −6.11727 | −0.375781 | ||||||||
\(266\) | −3.50172 | −0.214704 | ||||||||
\(267\) | −4.11727 | −0.251973 | ||||||||
\(268\) | −28.3449 | −1.73144 | ||||||||
\(269\) | 3.05863 | 0.186488 | 0.0932441 | − | 0.995643i | \(-0.470276\pi\) | ||||
0.0932441 | + | 0.995643i | \(0.470276\pi\) | |||||||
\(270\) | −2.00000 | −0.121716 | ||||||||
\(271\) | 12.2802 | 0.745968 | 0.372984 | − | 0.927838i | \(-0.378335\pi\) | ||||
0.372984 | + | 0.927838i | \(0.378335\pi\) | |||||||
\(272\) | −13.6742 | −0.829119 | ||||||||
\(273\) | 0.824101 | 0.0498768 | ||||||||
\(274\) | −5.74398 | −0.347007 | ||||||||
\(275\) | −19.2001 | −1.15781 | ||||||||
\(276\) | −11.1138 | −0.668974 | ||||||||
\(277\) | −8.56990 | −0.514916 | −0.257458 | − | 0.966290i | \(-0.582885\pi\) | ||||
−0.257458 | + | 0.966290i | \(0.582885\pi\) | |||||||
\(278\) | 6.72594 | 0.403395 | ||||||||
\(279\) | −2.89572 | −0.173362 | ||||||||
\(280\) | −24.9966 | −1.49383 | ||||||||
\(281\) | −14.5845 | −0.870039 | −0.435020 | − | 0.900421i | \(-0.643259\pi\) | ||||
−0.435020 | + | 0.900421i | \(0.643259\pi\) | |||||||
\(282\) | 1.92332 | 0.114532 | ||||||||
\(283\) | −20.9509 | −1.24540 | −0.622701 | − | 0.782460i | \(-0.713965\pi\) | ||||
−0.622701 | + | 0.782460i | \(0.713965\pi\) | |||||||
\(284\) | 18.7259 | 1.11118 | ||||||||
\(285\) | 9.55691 | 0.566103 | ||||||||
\(286\) | 0.172462 | 0.0101979 | ||||||||
\(287\) | 3.30777 | 0.195252 | ||||||||
\(288\) | 4.83709 | 0.285028 | ||||||||
\(289\) | 8.27674 | 0.486867 | ||||||||
\(290\) | −4.82410 | −0.283281 | ||||||||
\(291\) | 7.19051 | 0.421515 | ||||||||
\(292\) | −16.7068 | −0.977694 | ||||||||
\(293\) | 31.4086 | 1.83491 | 0.917455 | − | 0.397839i | \(-0.130240\pi\) | ||||
0.917455 | + | 0.397839i | \(0.130240\pi\) | |||||||
\(294\) | −1.85514 | −0.108194 | ||||||||
\(295\) | 11.1138 | 0.647072 | ||||||||
\(296\) | −17.2863 | −1.00475 | ||||||||
\(297\) | 1.47068 | 0.0853377 | ||||||||
\(298\) | −10.4070 | −0.602861 | ||||||||
\(299\) | 1.55691 | 0.0900387 | ||||||||
\(300\) | 23.2181 | 1.34050 | ||||||||
\(301\) | −35.8353 | −2.06551 | ||||||||
\(302\) | 4.76203 | 0.274024 | ||||||||
\(303\) | 11.1449 | 0.640256 | ||||||||
\(304\) | −6.11727 | −0.350849 | ||||||||
\(305\) | −24.3043 | −1.39166 | ||||||||
\(306\) | −2.36641 | −0.135278 | ||||||||
\(307\) | 8.54392 | 0.487628 | 0.243814 | − | 0.969822i | \(-0.421601\pi\) | ||||
0.243814 | + | 0.969822i | \(0.421601\pi\) | |||||||
\(308\) | 8.65164 | 0.492973 | ||||||||
\(309\) | −13.2767 | −0.755287 | ||||||||
\(310\) | −5.79145 | −0.328932 | ||||||||
\(311\) | −5.49484 | −0.311584 | −0.155792 | − | 0.987790i | \(-0.549793\pi\) | ||||
−0.155792 | + | 0.987790i | \(0.549793\pi\) | |||||||
\(312\) | −0.443086 | −0.0250848 | ||||||||
\(313\) | 5.48024 | 0.309761 | 0.154881 | − | 0.987933i | \(-0.450501\pi\) | ||||
0.154881 | + | 0.987933i | \(0.450501\pi\) | |||||||
\(314\) | 8.83098 | 0.498361 | ||||||||
\(315\) | 14.0552 | 0.791921 | ||||||||
\(316\) | 0.996562 | 0.0560610 | ||||||||
\(317\) | −11.3173 | −0.635644 | −0.317822 | − | 0.948150i | \(-0.602951\pi\) | ||||
−0.317822 | + | 0.948150i | \(0.602951\pi\) | |||||||
\(318\) | 0.677618 | 0.0379990 | ||||||||
\(319\) | 3.54736 | 0.198614 | ||||||||
\(320\) | −13.4396 | −0.751299 | ||||||||
\(321\) | −9.32238 | −0.520325 | ||||||||
\(322\) | −9.72938 | −0.542197 | ||||||||
\(323\) | 11.3078 | 0.629181 | ||||||||
\(324\) | −1.77846 | −0.0988032 | ||||||||
\(325\) | −3.25258 | −0.180421 | ||||||||
\(326\) | 4.02148 | 0.222729 | ||||||||
\(327\) | 0.249141 | 0.0137775 | ||||||||
\(328\) | −1.77846 | −0.0981989 | ||||||||
\(329\) | −13.5163 | −0.745179 | ||||||||
\(330\) | 2.94137 | 0.161917 | ||||||||
\(331\) | 33.8613 | 1.86118 | 0.930591 | − | 0.366060i | \(-0.119293\pi\) | ||||
0.930591 | + | 0.366060i | \(0.119293\pi\) | |||||||
\(332\) | −6.76891 | −0.371492 | ||||||||
\(333\) | 9.71982 | 0.532643 | ||||||||
\(334\) | 2.38101 | 0.130283 | ||||||||
\(335\) | 67.7225 | 3.70008 | ||||||||
\(336\) | −8.99656 | −0.490803 | ||||||||
\(337\) | −6.77846 | −0.369246 | −0.184623 | − | 0.982809i | \(-0.559106\pi\) | ||||
−0.184623 | + | 0.982809i | \(0.559106\pi\) | |||||||
\(338\) | −6.08967 | −0.331234 | ||||||||
\(339\) | −9.24570 | −0.502158 | ||||||||
\(340\) | 37.9931 | 2.06047 | ||||||||
\(341\) | 4.25869 | 0.230621 | ||||||||
\(342\) | −1.05863 | −0.0572443 | ||||||||
\(343\) | −10.1173 | −0.546281 | ||||||||
\(344\) | 19.2672 | 1.03882 | ||||||||
\(345\) | 26.5535 | 1.42959 | ||||||||
\(346\) | 8.87930 | 0.477354 | ||||||||
\(347\) | 19.2001 | 1.03071 | 0.515357 | − | 0.856976i | \(-0.327659\pi\) | ||||
0.515357 | + | 0.856976i | \(0.327659\pi\) | |||||||
\(348\) | −4.28973 | −0.229954 | ||||||||
\(349\) | −6.54392 | −0.350288 | −0.175144 | − | 0.984543i | \(-0.556039\pi\) | ||||
−0.175144 | + | 0.984543i | \(0.556039\pi\) | |||||||
\(350\) | 20.3258 | 1.08646 | ||||||||
\(351\) | 0.249141 | 0.0132981 | ||||||||
\(352\) | −7.11383 | −0.379168 | ||||||||
\(353\) | −15.9931 | −0.851228 | −0.425614 | − | 0.904905i | \(-0.639942\pi\) | ||||
−0.425614 | + | 0.904905i | \(0.639942\pi\) | |||||||
\(354\) | −1.23109 | −0.0654320 | ||||||||
\(355\) | −44.7405 | −2.37458 | ||||||||
\(356\) | −7.32238 | −0.388085 | ||||||||
\(357\) | 16.6302 | 0.880161 | ||||||||
\(358\) | −1.34387 | −0.0710255 | ||||||||
\(359\) | −12.1319 | −0.640296 | −0.320148 | − | 0.947368i | \(-0.603733\pi\) | ||||
−0.320148 | + | 0.947368i | \(0.603733\pi\) | |||||||
\(360\) | −7.55691 | −0.398284 | ||||||||
\(361\) | −13.9414 | −0.733756 | ||||||||
\(362\) | 6.32582 | 0.332478 | ||||||||
\(363\) | 8.83709 | 0.463827 | ||||||||
\(364\) | 1.46563 | 0.0768198 | ||||||||
\(365\) | 39.9164 | 2.08932 | ||||||||
\(366\) | 2.69223 | 0.140725 | ||||||||
\(367\) | 6.39744 | 0.333944 | 0.166972 | − | 0.985962i | \(-0.446601\pi\) | ||||
0.166972 | + | 0.985962i | \(0.446601\pi\) | |||||||
\(368\) | −16.9966 | −0.886007 | ||||||||
\(369\) | 1.00000 | 0.0520579 | ||||||||
\(370\) | 19.4396 | 1.01062 | ||||||||
\(371\) | −4.76203 | −0.247232 | ||||||||
\(372\) | −5.14992 | −0.267011 | ||||||||
\(373\) | −7.54049 | −0.390432 | −0.195216 | − | 0.980760i | \(-0.562541\pi\) | ||||
−0.195216 | + | 0.980760i | \(0.562541\pi\) | |||||||
\(374\) | 3.48024 | 0.179959 | ||||||||
\(375\) | −34.2277 | −1.76751 | ||||||||
\(376\) | 7.26719 | 0.374777 | ||||||||
\(377\) | 0.600939 | 0.0309500 | ||||||||
\(378\) | −1.55691 | −0.0800790 | ||||||||
\(379\) | −0.0620710 | −0.00318837 | −0.00159419 | − | 0.999999i | \(-0.500507\pi\) | ||||
−0.00159419 | + | 0.999999i | \(0.500507\pi\) | |||||||
\(380\) | 16.9966 | 0.871905 | ||||||||
\(381\) | 0.824101 | 0.0422199 | ||||||||
\(382\) | 6.35180 | 0.324986 | ||||||||
\(383\) | 23.9329 | 1.22291 | 0.611456 | − | 0.791278i | \(-0.290584\pi\) | ||||
0.611456 | + | 0.791278i | \(0.290584\pi\) | |||||||
\(384\) | 11.1629 | 0.569655 | ||||||||
\(385\) | −20.6707 | −1.05348 | ||||||||
\(386\) | −3.77234 | −0.192007 | ||||||||
\(387\) | −10.8337 | −0.550706 | ||||||||
\(388\) | 12.7880 | 0.649213 | ||||||||
\(389\) | −23.8613 | −1.20981 | −0.604907 | − | 0.796296i | \(-0.706790\pi\) | ||||
−0.604907 | + | 0.796296i | \(0.706790\pi\) | |||||||
\(390\) | 0.498281 | 0.0252314 | ||||||||
\(391\) | 31.4182 | 1.58888 | ||||||||
\(392\) | −7.00955 | −0.354036 | ||||||||
\(393\) | −8.13187 | −0.410199 | ||||||||
\(394\) | 6.57946 | 0.331468 | ||||||||
\(395\) | −2.38101 | −0.119802 | ||||||||
\(396\) | 2.61555 | 0.131436 | ||||||||
\(397\) | 14.6302 | 0.734266 | 0.367133 | − | 0.930168i | \(-0.380339\pi\) | ||||
0.367133 | + | 0.930168i | \(0.380339\pi\) | |||||||
\(398\) | −2.28973 | −0.114774 | ||||||||
\(399\) | 7.43965 | 0.372448 | ||||||||
\(400\) | 35.5078 | 1.77539 | ||||||||
\(401\) | −11.3224 | −0.565413 | −0.282706 | − | 0.959206i | \(-0.591232\pi\) | ||||
−0.282706 | + | 0.959206i | \(0.591232\pi\) | |||||||
\(402\) | −7.50172 | −0.374152 | ||||||||
\(403\) | 0.721442 | 0.0359376 | ||||||||
\(404\) | 19.8207 | 0.986115 | ||||||||
\(405\) | 4.24914 | 0.211141 | ||||||||
\(406\) | −3.75536 | −0.186375 | ||||||||
\(407\) | −14.2948 | −0.708566 | ||||||||
\(408\) | −8.94137 | −0.442664 | ||||||||
\(409\) | −33.8923 | −1.67587 | −0.837933 | − | 0.545773i | \(-0.816236\pi\) | ||||
−0.837933 | + | 0.545773i | \(0.816236\pi\) | |||||||
\(410\) | 2.00000 | 0.0987730 | ||||||||
\(411\) | 12.2035 | 0.601954 | ||||||||
\(412\) | −23.6121 | −1.16329 | ||||||||
\(413\) | 8.65164 | 0.425719 | ||||||||
\(414\) | −2.94137 | −0.144560 | ||||||||
\(415\) | 16.1725 | 0.793875 | ||||||||
\(416\) | −1.20512 | −0.0590856 | ||||||||
\(417\) | −14.2897 | −0.699771 | ||||||||
\(418\) | 1.55691 | 0.0761512 | ||||||||
\(419\) | −1.98539 | −0.0969928 | −0.0484964 | − | 0.998823i | \(-0.515443\pi\) | ||||
−0.0484964 | + | 0.998823i | \(0.515443\pi\) | |||||||
\(420\) | 24.9966 | 1.21971 | ||||||||
\(421\) | −5.67418 | −0.276543 | −0.138271 | − | 0.990394i | \(-0.544155\pi\) | ||||
−0.138271 | + | 0.990394i | \(0.544155\pi\) | |||||||
\(422\) | −4.99656 | −0.243229 | ||||||||
\(423\) | −4.08623 | −0.198679 | ||||||||
\(424\) | 2.56035 | 0.124342 | ||||||||
\(425\) | −65.6363 | −3.18383 | ||||||||
\(426\) | 4.95597 | 0.240118 | ||||||||
\(427\) | −18.9199 | −0.915597 | ||||||||
\(428\) | −16.5795 | −0.801398 | ||||||||
\(429\) | −0.366407 | −0.0176903 | ||||||||
\(430\) | −21.6673 | −1.04489 | ||||||||
\(431\) | 1.75086 | 0.0843359 | 0.0421680 | − | 0.999111i | \(-0.486574\pi\) | ||||
0.0421680 | + | 0.999111i | \(0.486574\pi\) | |||||||
\(432\) | −2.71982 | −0.130858 | ||||||||
\(433\) | −34.0647 | −1.63705 | −0.818524 | − | 0.574473i | \(-0.805207\pi\) | ||||
−0.818524 | + | 0.574473i | \(0.805207\pi\) | |||||||
\(434\) | −4.50839 | −0.216410 | ||||||||
\(435\) | 10.2491 | 0.491409 | ||||||||
\(436\) | 0.443086 | 0.0212200 | ||||||||
\(437\) | 14.0552 | 0.672351 | ||||||||
\(438\) | −4.42160 | −0.211272 | ||||||||
\(439\) | −4.32582 | −0.206460 | −0.103230 | − | 0.994658i | \(-0.532918\pi\) | ||||
−0.103230 | + | 0.994658i | \(0.532918\pi\) | |||||||
\(440\) | 11.1138 | 0.529831 | ||||||||
\(441\) | 3.94137 | 0.187684 | ||||||||
\(442\) | 0.589568 | 0.0280429 | ||||||||
\(443\) | 36.9966 | 1.75776 | 0.878880 | − | 0.477043i | \(-0.158291\pi\) | ||||
0.878880 | + | 0.477043i | \(0.158291\pi\) | |||||||
\(444\) | 17.2863 | 0.820371 | ||||||||
\(445\) | 17.4948 | 0.829335 | ||||||||
\(446\) | −8.46907 | −0.401022 | ||||||||
\(447\) | 22.1104 | 1.04579 | ||||||||
\(448\) | −10.4622 | −0.494292 | ||||||||
\(449\) | −15.9448 | −0.752482 | −0.376241 | − | 0.926522i | \(-0.622784\pi\) | ||||
−0.376241 | + | 0.926522i | \(0.622784\pi\) | |||||||
\(450\) | 6.14486 | 0.289672 | ||||||||
\(451\) | −1.47068 | −0.0692518 | ||||||||
\(452\) | −16.4431 | −0.773418 | ||||||||
\(453\) | −10.1173 | −0.475351 | ||||||||
\(454\) | −0.428478 | −0.0201095 | ||||||||
\(455\) | −3.50172 | −0.164163 | ||||||||
\(456\) | −4.00000 | −0.187317 | ||||||||
\(457\) | −29.4396 | −1.37713 | −0.688564 | − | 0.725175i | \(-0.741759\pi\) | ||||
−0.688564 | + | 0.725175i | \(0.741759\pi\) | |||||||
\(458\) | −3.49484 | −0.163303 | ||||||||
\(459\) | 5.02760 | 0.234668 | ||||||||
\(460\) | 47.2242 | 2.20184 | ||||||||
\(461\) | 21.8759 | 1.01886 | 0.509430 | − | 0.860512i | \(-0.329856\pi\) | ||||
0.509430 | + | 0.860512i | \(0.329856\pi\) | |||||||
\(462\) | 2.28973 | 0.106528 | ||||||||
\(463\) | −18.6561 | −0.867024 | −0.433512 | − | 0.901148i | \(-0.642726\pi\) | ||||
−0.433512 | + | 0.901148i | \(0.642726\pi\) | |||||||
\(464\) | −6.56035 | −0.304557 | ||||||||
\(465\) | 12.3043 | 0.570600 | ||||||||
\(466\) | 6.94824 | 0.321871 | ||||||||
\(467\) | 8.67074 | 0.401234 | 0.200617 | − | 0.979670i | \(-0.435705\pi\) | ||||
0.200617 | + | 0.979670i | \(0.435705\pi\) | |||||||
\(468\) | 0.443086 | 0.0204816 | ||||||||
\(469\) | 52.7191 | 2.43434 | ||||||||
\(470\) | −8.17246 | −0.376968 | ||||||||
\(471\) | −18.7620 | −0.864509 | ||||||||
\(472\) | −4.65164 | −0.214109 | ||||||||
\(473\) | 15.9329 | 0.732594 | ||||||||
\(474\) | 0.263748 | 0.0121144 | ||||||||
\(475\) | −29.3630 | −1.34727 | ||||||||
\(476\) | 29.5760 | 1.35561 | ||||||||
\(477\) | −1.43965 | −0.0659169 | ||||||||
\(478\) | −0.651639 | −0.0298053 | ||||||||
\(479\) | −20.4312 | −0.933523 | −0.466762 | − | 0.884383i | \(-0.654579\pi\) | ||||
−0.466762 | + | 0.884383i | \(0.654579\pi\) | |||||||
\(480\) | −20.5535 | −0.938134 | ||||||||
\(481\) | −2.42160 | −0.110416 | ||||||||
\(482\) | −2.80262 | −0.127656 | ||||||||
\(483\) | 20.6707 | 0.940551 | ||||||||
\(484\) | 15.7164 | 0.714381 | ||||||||
\(485\) | −30.5535 | −1.38736 | ||||||||
\(486\) | −0.470683 | −0.0213506 | ||||||||
\(487\) | −7.00611 | −0.317477 | −0.158739 | − | 0.987321i | \(-0.550743\pi\) | ||||
−0.158739 | + | 0.987321i | \(0.550743\pi\) | |||||||
\(488\) | 10.1725 | 0.460486 | ||||||||
\(489\) | −8.54392 | −0.386370 | ||||||||
\(490\) | 7.88273 | 0.356106 | ||||||||
\(491\) | −15.5715 | −0.702733 | −0.351366 | − | 0.936238i | \(-0.614283\pi\) | ||||
−0.351366 | + | 0.936238i | \(0.614283\pi\) | |||||||
\(492\) | 1.77846 | 0.0801790 | ||||||||
\(493\) | 12.1268 | 0.546164 | ||||||||
\(494\) | 0.263748 | 0.0118666 | ||||||||
\(495\) | −6.24914 | −0.280878 | ||||||||
\(496\) | −7.87586 | −0.353636 | ||||||||
\(497\) | −34.8286 | −1.56228 | ||||||||
\(498\) | −1.79145 | −0.0802767 | ||||||||
\(499\) | −1.61899 | −0.0724757 | −0.0362379 | − | 0.999343i | \(-0.511537\pi\) | ||||
−0.0362379 | + | 0.999343i | \(0.511537\pi\) | |||||||
\(500\) | −60.8724 | −2.72230 | ||||||||
\(501\) | −5.05863 | −0.226003 | ||||||||
\(502\) | 1.27406 | 0.0568642 | ||||||||
\(503\) | −39.3725 | −1.75553 | −0.877767 | − | 0.479088i | \(-0.840968\pi\) | ||||
−0.877767 | + | 0.479088i | \(0.840968\pi\) | |||||||
\(504\) | −5.88273 | −0.262038 | ||||||||
\(505\) | −47.3561 | −2.10732 | ||||||||
\(506\) | 4.32582 | 0.192306 | ||||||||
\(507\) | 12.9379 | 0.574594 | ||||||||
\(508\) | 1.46563 | 0.0650267 | ||||||||
\(509\) | −8.63971 | −0.382948 | −0.191474 | − | 0.981498i | \(-0.561327\pi\) | ||||
−0.191474 | + | 0.981498i | \(0.561327\pi\) | |||||||
\(510\) | 10.0552 | 0.445252 | ||||||||
\(511\) | 31.0732 | 1.37460 | ||||||||
\(512\) | 22.8302 | 1.00896 | ||||||||
\(513\) | 2.24914 | 0.0993020 | ||||||||
\(514\) | −0.373283 | −0.0164648 | ||||||||
\(515\) | 56.4147 | 2.48593 | ||||||||
\(516\) | −19.2672 | −0.848191 | ||||||||
\(517\) | 6.00955 | 0.264300 | ||||||||
\(518\) | 15.1329 | 0.664903 | ||||||||
\(519\) | −18.8647 | −0.828068 | ||||||||
\(520\) | 1.88273 | 0.0825633 | ||||||||
\(521\) | 30.7862 | 1.34877 | 0.674384 | − | 0.738381i | \(-0.264409\pi\) | ||||
0.674384 | + | 0.738381i | \(0.264409\pi\) | |||||||
\(522\) | −1.13531 | −0.0496913 | ||||||||
\(523\) | 17.4036 | 0.761004 | 0.380502 | − | 0.924780i | \(-0.375751\pi\) | ||||
0.380502 | + | 0.924780i | \(0.375751\pi\) | |||||||
\(524\) | −14.4622 | −0.631784 | ||||||||
\(525\) | −43.1836 | −1.88469 | ||||||||
\(526\) | −7.33699 | −0.319908 | ||||||||
\(527\) | 14.5585 | 0.634180 | ||||||||
\(528\) | 4.00000 | 0.174078 | ||||||||
\(529\) | 16.0518 | 0.697902 | ||||||||
\(530\) | −2.87930 | −0.125069 | ||||||||
\(531\) | 2.61555 | 0.113505 | ||||||||
\(532\) | 13.2311 | 0.573641 | ||||||||
\(533\) | −0.249141 | −0.0107915 | ||||||||
\(534\) | −1.93793 | −0.0838624 | ||||||||
\(535\) | 39.6121 | 1.71258 | ||||||||
\(536\) | −28.3449 | −1.22431 | ||||||||
\(537\) | 2.85514 | 0.123208 | ||||||||
\(538\) | 1.43965 | 0.0620676 | ||||||||
\(539\) | −5.79650 | −0.249673 | ||||||||
\(540\) | 7.55691 | 0.325198 | ||||||||
\(541\) | −9.87586 | −0.424596 | −0.212298 | − | 0.977205i | \(-0.568095\pi\) | ||||
−0.212298 | + | 0.977205i | \(0.568095\pi\) | |||||||
\(542\) | 5.78008 | 0.248275 | ||||||||
\(543\) | −13.4396 | −0.576750 | ||||||||
\(544\) | −24.3189 | −1.04267 | ||||||||
\(545\) | −1.05863 | −0.0453469 | ||||||||
\(546\) | 0.387890 | 0.0166002 | ||||||||
\(547\) | −18.1465 | −0.775888 | −0.387944 | − | 0.921683i | \(-0.626815\pi\) | ||||
−0.387944 | + | 0.921683i | \(0.626815\pi\) | |||||||
\(548\) | 21.7034 | 0.927123 | ||||||||
\(549\) | −5.71982 | −0.244116 | ||||||||
\(550\) | −9.03715 | −0.385345 | ||||||||
\(551\) | 5.42504 | 0.231114 | ||||||||
\(552\) | −11.1138 | −0.473036 | ||||||||
\(553\) | −1.85352 | −0.0788196 | ||||||||
\(554\) | −4.03371 | −0.171376 | ||||||||
\(555\) | −41.3009 | −1.75313 | ||||||||
\(556\) | −25.4137 | −1.07778 | ||||||||
\(557\) | 37.3725 | 1.58352 | 0.791762 | − | 0.610829i | \(-0.209164\pi\) | ||||
0.791762 | + | 0.610829i | \(0.209164\pi\) | |||||||
\(558\) | −1.36297 | −0.0576991 | ||||||||
\(559\) | 2.69910 | 0.114160 | ||||||||
\(560\) | 38.2277 | 1.61541 | ||||||||
\(561\) | −7.39400 | −0.312175 | ||||||||
\(562\) | −6.86469 | −0.289569 | ||||||||
\(563\) | 22.8742 | 0.964034 | 0.482017 | − | 0.876162i | \(-0.339904\pi\) | ||||
0.482017 | + | 0.876162i | \(0.339904\pi\) | |||||||
\(564\) | −7.26719 | −0.306004 | ||||||||
\(565\) | 39.2863 | 1.65279 | ||||||||
\(566\) | −9.86125 | −0.414499 | ||||||||
\(567\) | 3.30777 | 0.138913 | ||||||||
\(568\) | 18.7259 | 0.785723 | ||||||||
\(569\) | 34.4147 | 1.44274 | 0.721370 | − | 0.692550i | \(-0.243513\pi\) | ||||
0.721370 | + | 0.692550i | \(0.243513\pi\) | |||||||
\(570\) | 4.49828 | 0.188412 | ||||||||
\(571\) | 36.3449 | 1.52099 | 0.760494 | − | 0.649345i | \(-0.224957\pi\) | ||||
0.760494 | + | 0.649345i | \(0.224957\pi\) | |||||||
\(572\) | −0.651639 | −0.0272464 | ||||||||
\(573\) | −13.4948 | −0.563755 | ||||||||
\(574\) | 1.55691 | 0.0649843 | ||||||||
\(575\) | −81.5838 | −3.40228 | ||||||||
\(576\) | −3.16291 | −0.131788 | ||||||||
\(577\) | 26.1725 | 1.08957 | 0.544787 | − | 0.838575i | \(-0.316611\pi\) | ||||
0.544787 | + | 0.838575i | \(0.316611\pi\) | |||||||
\(578\) | 3.89572 | 0.162041 | ||||||||
\(579\) | 8.01461 | 0.333076 | ||||||||
\(580\) | 18.2277 | 0.756862 | ||||||||
\(581\) | 12.5896 | 0.522303 | ||||||||
\(582\) | 3.38445 | 0.140290 | ||||||||
\(583\) | 2.11727 | 0.0876882 | ||||||||
\(584\) | −16.7068 | −0.691334 | ||||||||
\(585\) | −1.05863 | −0.0437691 | ||||||||
\(586\) | 14.7835 | 0.610701 | ||||||||
\(587\) | −17.8156 | −0.735329 | −0.367664 | − | 0.929959i | \(-0.619842\pi\) | ||||
−0.367664 | + | 0.929959i | \(0.619842\pi\) | |||||||
\(588\) | 7.00955 | 0.289069 | ||||||||
\(589\) | 6.51289 | 0.268359 | ||||||||
\(590\) | 5.23109 | 0.215361 | ||||||||
\(591\) | −13.9785 | −0.574999 | ||||||||
\(592\) | 26.4362 | 1.08652 | ||||||||
\(593\) | −32.7018 | −1.34290 | −0.671451 | − | 0.741049i | \(-0.734328\pi\) | ||||
−0.671451 | + | 0.741049i | \(0.734328\pi\) | |||||||
\(594\) | 0.692226 | 0.0284024 | ||||||||
\(595\) | −70.6639 | −2.89694 | ||||||||
\(596\) | 39.3224 | 1.61071 | ||||||||
\(597\) | 4.86469 | 0.199098 | ||||||||
\(598\) | 0.732814 | 0.0299670 | ||||||||
\(599\) | 10.2784 | 0.419962 | 0.209981 | − | 0.977705i | \(-0.432660\pi\) | ||||
0.209981 | + | 0.977705i | \(0.432660\pi\) | |||||||
\(600\) | 23.2181 | 0.947875 | ||||||||
\(601\) | 31.8398 | 1.29877 | 0.649386 | − | 0.760459i | \(-0.275026\pi\) | ||||
0.649386 | + | 0.760459i | \(0.275026\pi\) | |||||||
\(602\) | −16.8671 | −0.687450 | ||||||||
\(603\) | 15.9379 | 0.649043 | ||||||||
\(604\) | −17.9931 | −0.732130 | ||||||||
\(605\) | −37.5500 | −1.52663 | ||||||||
\(606\) | 5.24570 | 0.213092 | ||||||||
\(607\) | 10.2086 | 0.414352 | 0.207176 | − | 0.978304i | \(-0.433573\pi\) | ||||
0.207176 | + | 0.978304i | \(0.433573\pi\) | |||||||
\(608\) | −10.8793 | −0.441214 | ||||||||
\(609\) | 7.97852 | 0.323306 | ||||||||
\(610\) | −11.4396 | −0.463178 | ||||||||
\(611\) | 1.01805 | 0.0411857 | ||||||||
\(612\) | 8.94137 | 0.361433 | ||||||||
\(613\) | −4.94137 | −0.199580 | −0.0997900 | − | 0.995009i | \(-0.531817\pi\) | ||||
−0.0997900 | + | 0.995009i | \(0.531817\pi\) | |||||||
\(614\) | 4.02148 | 0.162294 | ||||||||
\(615\) | −4.24914 | −0.171342 | ||||||||
\(616\) | 8.65164 | 0.348584 | ||||||||
\(617\) | 15.2526 | 0.614046 | 0.307023 | − | 0.951702i | \(-0.400667\pi\) | ||||
0.307023 | + | 0.951702i | \(0.400667\pi\) | |||||||
\(618\) | −6.24914 | −0.251377 | ||||||||
\(619\) | −20.6543 | −0.830167 | −0.415084 | − | 0.909783i | \(-0.636248\pi\) | ||||
−0.415084 | + | 0.909783i | \(0.636248\pi\) | |||||||
\(620\) | 21.8827 | 0.878832 | ||||||||
\(621\) | 6.24914 | 0.250769 | ||||||||
\(622\) | −2.58633 | −0.103702 | ||||||||
\(623\) | 13.6190 | 0.545633 | ||||||||
\(624\) | 0.677618 | 0.0271264 | ||||||||
\(625\) | 80.1621 | 3.20649 | ||||||||
\(626\) | 2.57946 | 0.103096 | ||||||||
\(627\) | −3.30777 | −0.132100 | ||||||||
\(628\) | −33.3675 | −1.33151 | ||||||||
\(629\) | −48.8674 | −1.94847 | ||||||||
\(630\) | 6.61555 | 0.263570 | ||||||||
\(631\) | 5.83709 | 0.232371 | 0.116185 | − | 0.993228i | \(-0.462933\pi\) | ||||
0.116185 | + | 0.993228i | \(0.462933\pi\) | |||||||
\(632\) | 0.996562 | 0.0396411 | ||||||||
\(633\) | 10.6155 | 0.421930 | ||||||||
\(634\) | −5.32688 | −0.211557 | ||||||||
\(635\) | −3.50172 | −0.138961 | ||||||||
\(636\) | −2.56035 | −0.101525 | ||||||||
\(637\) | −0.981954 | −0.0389064 | ||||||||
\(638\) | 1.66968 | 0.0661034 | ||||||||
\(639\) | −10.5293 | −0.416533 | ||||||||
\(640\) | −47.4328 | −1.87494 | ||||||||
\(641\) | 42.6328 | 1.68390 | 0.841948 | − | 0.539559i | \(-0.181409\pi\) | ||||
0.841948 | + | 0.539559i | \(0.181409\pi\) | |||||||
\(642\) | −4.38789 | −0.173176 | ||||||||
\(643\) | 30.7259 | 1.21171 | 0.605856 | − | 0.795574i | \(-0.292831\pi\) | ||||
0.605856 | + | 0.795574i | \(0.292831\pi\) | |||||||
\(644\) | 36.7620 | 1.44863 | ||||||||
\(645\) | 46.0337 | 1.81258 | ||||||||
\(646\) | 5.32238 | 0.209406 | ||||||||
\(647\) | 18.3595 | 0.721788 | 0.360894 | − | 0.932607i | \(-0.382472\pi\) | ||||
0.360894 | + | 0.932607i | \(0.382472\pi\) | |||||||
\(648\) | −1.77846 | −0.0698644 | ||||||||
\(649\) | −3.84664 | −0.150994 | ||||||||
\(650\) | −1.53093 | −0.0600482 | ||||||||
\(651\) | 9.57840 | 0.375407 | ||||||||
\(652\) | −15.1950 | −0.595082 | ||||||||
\(653\) | −35.5811 | −1.39240 | −0.696198 | − | 0.717850i | \(-0.745126\pi\) | ||||
−0.696198 | + | 0.717850i | \(0.745126\pi\) | |||||||
\(654\) | 0.117266 | 0.00458548 | ||||||||
\(655\) | 34.5535 | 1.35012 | ||||||||
\(656\) | 2.71982 | 0.106191 | ||||||||
\(657\) | 9.39400 | 0.366495 | ||||||||
\(658\) | −6.36191 | −0.248013 | ||||||||
\(659\) | −6.38101 | −0.248569 | −0.124285 | − | 0.992247i | \(-0.539664\pi\) | ||||
−0.124285 | + | 0.992247i | \(0.539664\pi\) | |||||||
\(660\) | −11.1138 | −0.432605 | ||||||||
\(661\) | 30.9053 | 1.20208 | 0.601038 | − | 0.799220i | \(-0.294754\pi\) | ||||
0.601038 | + | 0.799220i | \(0.294754\pi\) | |||||||
\(662\) | 15.9379 | 0.619445 | ||||||||
\(663\) | −1.25258 | −0.0486461 | ||||||||
\(664\) | −6.76891 | −0.262684 | ||||||||
\(665\) | −31.6121 | −1.22587 | ||||||||
\(666\) | 4.57496 | 0.177276 | ||||||||
\(667\) | 15.0732 | 0.583638 | ||||||||
\(668\) | −8.99656 | −0.348087 | ||||||||
\(669\) | 17.9931 | 0.695654 | ||||||||
\(670\) | 31.8759 | 1.23147 | ||||||||
\(671\) | 8.41205 | 0.324744 | ||||||||
\(672\) | −16.0000 | −0.617213 | ||||||||
\(673\) | 36.7259 | 1.41568 | 0.707840 | − | 0.706372i | \(-0.249670\pi\) | ||||
0.707840 | + | 0.706372i | \(0.249670\pi\) | |||||||
\(674\) | −3.19051 | −0.122894 | ||||||||
\(675\) | −13.0552 | −0.502495 | ||||||||
\(676\) | 23.0096 | 0.884983 | ||||||||
\(677\) | −5.66281 | −0.217639 | −0.108820 | − | 0.994062i | \(-0.534707\pi\) | ||||
−0.108820 | + | 0.994062i | \(0.534707\pi\) | |||||||
\(678\) | −4.35180 | −0.167130 | ||||||||
\(679\) | −23.7846 | −0.912768 | ||||||||
\(680\) | 37.9931 | 1.45697 | ||||||||
\(681\) | 0.910331 | 0.0348840 | ||||||||
\(682\) | 2.00450 | 0.0767561 | ||||||||
\(683\) | −29.1690 | −1.11612 | −0.558061 | − | 0.829800i | \(-0.688454\pi\) | ||||
−0.558061 | + | 0.829800i | \(0.688454\pi\) | |||||||
\(684\) | 4.00000 | 0.152944 | ||||||||
\(685\) | −51.8544 | −1.98125 | ||||||||
\(686\) | −4.76203 | −0.181815 | ||||||||
\(687\) | 7.42504 | 0.283283 | ||||||||
\(688\) | −29.4656 | −1.12337 | ||||||||
\(689\) | 0.358675 | 0.0136644 | ||||||||
\(690\) | 12.4983 | 0.475801 | ||||||||
\(691\) | 1.68879 | 0.0642445 | 0.0321223 | − | 0.999484i | \(-0.489773\pi\) | ||||
0.0321223 | + | 0.999484i | \(0.489773\pi\) | |||||||
\(692\) | −33.5500 | −1.27538 | ||||||||
\(693\) | −4.86469 | −0.184794 | ||||||||
\(694\) | 9.03715 | 0.343046 | ||||||||
\(695\) | 60.7191 | 2.30321 | ||||||||
\(696\) | −4.28973 | −0.162602 | ||||||||
\(697\) | −5.02760 | −0.190434 | ||||||||
\(698\) | −3.08012 | −0.116584 | ||||||||
\(699\) | −14.7620 | −0.558351 | ||||||||
\(700\) | −76.8002 | −2.90278 | ||||||||
\(701\) | −20.3810 | −0.769780 | −0.384890 | − | 0.922962i | \(-0.625761\pi\) | ||||
−0.384890 | + | 0.922962i | \(0.625761\pi\) | |||||||
\(702\) | 0.117266 | 0.00442593 | ||||||||
\(703\) | −21.8613 | −0.824513 | ||||||||
\(704\) | 4.65164 | 0.175315 | ||||||||
\(705\) | 17.3630 | 0.653927 | ||||||||
\(706\) | −7.52770 | −0.283309 | ||||||||
\(707\) | −36.8647 | −1.38644 | ||||||||
\(708\) | 4.65164 | 0.174819 | ||||||||
\(709\) | −40.8363 | −1.53364 | −0.766820 | − | 0.641862i | \(-0.778162\pi\) | ||||
−0.766820 | + | 0.641862i | \(0.778162\pi\) | |||||||
\(710\) | −21.0586 | −0.790316 | ||||||||
\(711\) | −0.560352 | −0.0210148 | ||||||||
\(712\) | −7.32238 | −0.274418 | ||||||||
\(713\) | 18.0958 | 0.677692 | ||||||||
\(714\) | 7.82754 | 0.292938 | ||||||||
\(715\) | 1.55691 | 0.0582253 | ||||||||
\(716\) | 5.07774 | 0.189764 | ||||||||
\(717\) | 1.38445 | 0.0517033 | ||||||||
\(718\) | −5.71027 | −0.213105 | ||||||||
\(719\) | 9.14486 | 0.341046 | 0.170523 | − | 0.985354i | \(-0.445454\pi\) | ||||
0.170523 | + | 0.985354i | \(0.445454\pi\) | |||||||
\(720\) | 11.5569 | 0.430701 | ||||||||
\(721\) | 43.9164 | 1.63553 | ||||||||
\(722\) | −6.56197 | −0.244211 | ||||||||
\(723\) | 5.95436 | 0.221445 | ||||||||
\(724\) | −23.9018 | −0.888305 | ||||||||
\(725\) | −31.4898 | −1.16950 | ||||||||
\(726\) | 4.15947 | 0.154372 | ||||||||
\(727\) | −2.13875 | −0.0793218 | −0.0396609 | − | 0.999213i | \(-0.512628\pi\) | ||||
−0.0396609 | + | 0.999213i | \(0.512628\pi\) | |||||||
\(728\) | 1.46563 | 0.0543198 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 18.7880 | 0.695375 | ||||||||
\(731\) | 54.4672 | 2.01454 | ||||||||
\(732\) | −10.1725 | −0.375985 | ||||||||
\(733\) | 15.3388 | 0.566552 | 0.283276 | − | 0.959038i | \(-0.408579\pi\) | ||||
0.283276 | + | 0.959038i | \(0.408579\pi\) | |||||||
\(734\) | 3.01117 | 0.111144 | ||||||||
\(735\) | −16.7474 | −0.617738 | ||||||||
\(736\) | −30.2277 | −1.11421 | ||||||||
\(737\) | −23.4396 | −0.863411 | ||||||||
\(738\) | 0.470683 | 0.0173261 | ||||||||
\(739\) | −15.8111 | −0.581621 | −0.290811 | − | 0.956781i | \(-0.593925\pi\) | ||||
−0.290811 | + | 0.956781i | \(0.593925\pi\) | |||||||
\(740\) | −73.4519 | −2.70014 | ||||||||
\(741\) | −0.560352 | −0.0205850 | ||||||||
\(742\) | −2.24141 | −0.0822847 | ||||||||
\(743\) | −20.2017 | −0.741128 | −0.370564 | − | 0.928807i | \(-0.620836\pi\) | ||||
−0.370564 | + | 0.928807i | \(0.620836\pi\) | |||||||
\(744\) | −5.14992 | −0.188805 | ||||||||
\(745\) | −93.9502 | −3.44207 | ||||||||
\(746\) | −3.54918 | −0.129945 | ||||||||
\(747\) | 3.80605 | 0.139256 | ||||||||
\(748\) | −13.1499 | −0.480809 | ||||||||
\(749\) | 30.8363 | 1.12673 | ||||||||
\(750\) | −16.1104 | −0.588268 | ||||||||
\(751\) | 32.9053 | 1.20073 | 0.600365 | − | 0.799726i | \(-0.295022\pi\) | ||||
0.600365 | + | 0.799726i | \(0.295022\pi\) | |||||||
\(752\) | −11.1138 | −0.405280 | ||||||||
\(753\) | −2.70683 | −0.0986425 | ||||||||
\(754\) | 0.282852 | 0.0103009 | ||||||||
\(755\) | 42.9897 | 1.56455 | ||||||||
\(756\) | 5.88273 | 0.213953 | ||||||||
\(757\) | 11.3009 | 0.410738 | 0.205369 | − | 0.978685i | \(-0.434161\pi\) | ||||
0.205369 | + | 0.978685i | \(0.434161\pi\) | |||||||
\(758\) | −0.0292158 | −0.00106117 | ||||||||
\(759\) | −9.19051 | −0.333594 | ||||||||
\(760\) | 16.9966 | 0.616530 | ||||||||
\(761\) | −2.93449 | −0.106375 | −0.0531876 | − | 0.998585i | \(-0.516938\pi\) | ||||
−0.0531876 | + | 0.998585i | \(0.516938\pi\) | |||||||
\(762\) | 0.387890 | 0.0140518 | ||||||||
\(763\) | −0.824101 | −0.0298344 | ||||||||
\(764\) | −24.0000 | −0.868290 | ||||||||
\(765\) | −21.3630 | −0.772380 | ||||||||
\(766\) | 11.2648 | 0.407014 | ||||||||
\(767\) | −0.651639 | −0.0235293 | ||||||||
\(768\) | −1.07162 | −0.0386689 | ||||||||
\(769\) | −22.7785 | −0.821412 | −0.410706 | − | 0.911768i | \(-0.634718\pi\) | ||||
−0.410706 | + | 0.911768i | \(0.634718\pi\) | |||||||
\(770\) | −9.72938 | −0.350622 | ||||||||
\(771\) | 0.793065 | 0.0285615 | ||||||||
\(772\) | 14.2536 | 0.513000 | ||||||||
\(773\) | 10.5553 | 0.379648 | 0.189824 | − | 0.981818i | \(-0.439208\pi\) | ||||
0.189824 | + | 0.981818i | \(0.439208\pi\) | |||||||
\(774\) | −5.09922 | −0.183288 | ||||||||
\(775\) | −37.8042 | −1.35797 | ||||||||
\(776\) | 12.7880 | 0.459063 | ||||||||
\(777\) | −32.1510 | −1.15341 | ||||||||
\(778\) | −11.2311 | −0.402654 | ||||||||
\(779\) | −2.24914 | −0.0805838 | ||||||||
\(780\) | −1.88273 | −0.0674127 | ||||||||
\(781\) | 15.4853 | 0.554107 | ||||||||
\(782\) | 14.7880 | 0.528818 | ||||||||
\(783\) | 2.41205 | 0.0861996 | ||||||||
\(784\) | 10.7198 | 0.382851 | ||||||||
\(785\) | 79.7225 | 2.84542 | ||||||||
\(786\) | −3.82754 | −0.136524 | ||||||||
\(787\) | −23.0682 | −0.822292 | −0.411146 | − | 0.911570i | \(-0.634871\pi\) | ||||
−0.411146 | + | 0.911570i | \(0.634871\pi\) | |||||||
\(788\) | −24.8602 | −0.885608 | ||||||||
\(789\) | 15.5879 | 0.554946 | ||||||||
\(790\) | −1.12070 | −0.0398729 | ||||||||
\(791\) | 30.5827 | 1.08740 | ||||||||
\(792\) | 2.61555 | 0.0929394 | ||||||||
\(793\) | 1.42504 | 0.0506047 | ||||||||
\(794\) | 6.88617 | 0.244381 | ||||||||
\(795\) | 6.11727 | 0.216957 | ||||||||
\(796\) | 8.65164 | 0.306649 | ||||||||
\(797\) | 0.0360915 | 0.00127843 | 0.000639213 | − | 1.00000i | \(-0.499797\pi\) | ||||
0.000639213 | 1.00000i | \(0.499797\pi\) | ||||||||
\(798\) | 3.50172 | 0.123960 | ||||||||
\(799\) | 20.5439 | 0.726792 | ||||||||
\(800\) | 63.1492 | 2.23266 | ||||||||
\(801\) | 4.11727 | 0.145476 | ||||||||
\(802\) | −5.32926 | −0.188183 | ||||||||
\(803\) | −13.8156 | −0.487542 | ||||||||
\(804\) | 28.3449 | 0.999648 | ||||||||
\(805\) | −87.8329 | −3.09570 | ||||||||
\(806\) | 0.339571 | 0.0119609 | ||||||||
\(807\) | −3.05863 | −0.107669 | ||||||||
\(808\) | 19.8207 | 0.697288 | ||||||||
\(809\) | 33.1430 | 1.16525 | 0.582624 | − | 0.812742i | \(-0.302026\pi\) | ||||
0.582624 | + | 0.812742i | \(0.302026\pi\) | |||||||
\(810\) | 2.00000 | 0.0702728 | ||||||||
\(811\) | −1.10428 | −0.0387764 | −0.0193882 | − | 0.999812i | \(-0.506172\pi\) | ||||
−0.0193882 | + | 0.999812i | \(0.506172\pi\) | |||||||
\(812\) | 14.1894 | 0.497952 | ||||||||
\(813\) | −12.2802 | −0.430685 | ||||||||
\(814\) | −6.72832 | −0.235827 | ||||||||
\(815\) | 36.3043 | 1.27169 | ||||||||
\(816\) | 13.6742 | 0.478692 | ||||||||
\(817\) | 24.3664 | 0.852473 | ||||||||
\(818\) | −15.9525 | −0.557767 | ||||||||
\(819\) | −0.824101 | −0.0287964 | ||||||||
\(820\) | −7.55691 | −0.263899 | ||||||||
\(821\) | −7.42504 | −0.259136 | −0.129568 | − | 0.991571i | \(-0.541359\pi\) | ||||
−0.129568 | + | 0.991571i | \(0.541359\pi\) | |||||||
\(822\) | 5.74398 | 0.200344 | ||||||||
\(823\) | 42.1656 | 1.46980 | 0.734900 | − | 0.678176i | \(-0.237229\pi\) | ||||
0.734900 | + | 0.678176i | \(0.237229\pi\) | |||||||
\(824\) | −23.6121 | −0.822567 | ||||||||
\(825\) | 19.2001 | 0.668460 | ||||||||
\(826\) | 4.07218 | 0.141689 | ||||||||
\(827\) | −54.4863 | −1.89468 | −0.947338 | − | 0.320235i | \(-0.896238\pi\) | ||||
−0.947338 | + | 0.320235i | \(0.896238\pi\) | |||||||
\(828\) | 11.1138 | 0.386232 | ||||||||
\(829\) | 24.0388 | 0.834901 | 0.417450 | − | 0.908700i | \(-0.362924\pi\) | ||||
0.417450 | + | 0.908700i | \(0.362924\pi\) | |||||||
\(830\) | 7.61211 | 0.264220 | ||||||||
\(831\) | 8.56990 | 0.297287 | ||||||||
\(832\) | 0.788009 | 0.0273193 | ||||||||
\(833\) | −19.8156 | −0.686570 | ||||||||
\(834\) | −6.72594 | −0.232900 | ||||||||
\(835\) | 21.4948 | 0.743860 | ||||||||
\(836\) | −5.88273 | −0.203459 | ||||||||
\(837\) | 2.89572 | 0.100091 | ||||||||
\(838\) | −0.934491 | −0.0322815 | ||||||||
\(839\) | −13.6190 | −0.470180 | −0.235090 | − | 0.971974i | \(-0.575538\pi\) | ||||
−0.235090 | + | 0.971974i | \(0.575538\pi\) | |||||||
\(840\) | 24.9966 | 0.862463 | ||||||||
\(841\) | −23.1820 | −0.799380 | ||||||||
\(842\) | −2.67074 | −0.0920399 | ||||||||
\(843\) | 14.5845 | 0.502317 | ||||||||
\(844\) | 18.8793 | 0.649852 | ||||||||
\(845\) | −54.9751 | −1.89120 | ||||||||
\(846\) | −1.92332 | −0.0661251 | ||||||||
\(847\) | −29.2311 | −1.00439 | ||||||||
\(848\) | −3.91559 | −0.134462 | ||||||||
\(849\) | 20.9509 | 0.719034 | ||||||||
\(850\) | −30.8939 | −1.05965 | ||||||||
\(851\) | −60.7405 | −2.08216 | ||||||||
\(852\) | −18.7259 | −0.641540 | ||||||||
\(853\) | −6.93449 | −0.237432 | −0.118716 | − | 0.992928i | \(-0.537878\pi\) | ||||
−0.118716 | + | 0.992928i | \(0.537878\pi\) | |||||||
\(854\) | −8.90528 | −0.304732 | ||||||||
\(855\) | −9.55691 | −0.326840 | ||||||||
\(856\) | −16.5795 | −0.566674 | ||||||||
\(857\) | −34.9345 | −1.19334 | −0.596670 | − | 0.802487i | \(-0.703510\pi\) | ||||
−0.596670 | + | 0.802487i | \(0.703510\pi\) | |||||||
\(858\) | −0.172462 | −0.00588774 | ||||||||
\(859\) | 4.39057 | 0.149804 | 0.0749021 | − | 0.997191i | \(-0.476136\pi\) | ||||
0.0749021 | + | 0.997191i | \(0.476136\pi\) | |||||||
\(860\) | 81.8690 | 2.79171 | ||||||||
\(861\) | −3.30777 | −0.112729 | ||||||||
\(862\) | 0.824101 | 0.0280690 | ||||||||
\(863\) | 15.4611 | 0.526303 | 0.263152 | − | 0.964755i | \(-0.415238\pi\) | ||||
0.263152 | + | 0.964755i | \(0.415238\pi\) | |||||||
\(864\) | −4.83709 | −0.164561 | ||||||||
\(865\) | 80.1587 | 2.72548 | ||||||||
\(866\) | −16.0337 | −0.544848 | ||||||||
\(867\) | −8.27674 | −0.281093 | ||||||||
\(868\) | 17.0348 | 0.578198 | ||||||||
\(869\) | 0.824101 | 0.0279557 | ||||||||
\(870\) | 4.82410 | 0.163552 | ||||||||
\(871\) | −3.97078 | −0.134545 | ||||||||
\(872\) | 0.443086 | 0.0150048 | ||||||||
\(873\) | −7.19051 | −0.243362 | ||||||||
\(874\) | 6.61555 | 0.223774 | ||||||||
\(875\) | 113.217 | 3.82744 | ||||||||
\(876\) | 16.7068 | 0.564472 | ||||||||
\(877\) | −55.2338 | −1.86511 | −0.932556 | − | 0.361025i | \(-0.882427\pi\) | ||||
−0.932556 | + | 0.361025i | \(0.882427\pi\) | |||||||
\(878\) | −2.03609 | −0.0687148 | ||||||||
\(879\) | −31.4086 | −1.05939 | ||||||||
\(880\) | −16.9966 | −0.572954 | ||||||||
\(881\) | −28.4431 | −0.958272 | −0.479136 | − | 0.877741i | \(-0.659050\pi\) | ||||
−0.479136 | + | 0.877741i | \(0.659050\pi\) | |||||||
\(882\) | 1.85514 | 0.0624657 | ||||||||
\(883\) | −24.1319 | −0.812102 | −0.406051 | − | 0.913850i | \(-0.633095\pi\) | ||||
−0.406051 | + | 0.913850i | \(0.633095\pi\) | |||||||
\(884\) | −2.22766 | −0.0749242 | ||||||||
\(885\) | −11.1138 | −0.373587 | ||||||||
\(886\) | 17.4137 | 0.585024 | ||||||||
\(887\) | −2.06025 | −0.0691765 | −0.0345882 | − | 0.999402i | \(-0.511012\pi\) | ||||
−0.0345882 | + | 0.999402i | \(0.511012\pi\) | |||||||
\(888\) | 17.2863 | 0.580090 | ||||||||
\(889\) | −2.72594 | −0.0914250 | ||||||||
\(890\) | 8.23453 | 0.276022 | ||||||||
\(891\) | −1.47068 | −0.0492697 | ||||||||
\(892\) | 32.0000 | 1.07144 | ||||||||
\(893\) | 9.19051 | 0.307549 | ||||||||
\(894\) | 10.4070 | 0.348062 | ||||||||
\(895\) | −12.1319 | −0.405524 | ||||||||
\(896\) | −36.9244 | −1.23356 | ||||||||
\(897\) | −1.55691 | −0.0519839 | ||||||||
\(898\) | −7.50496 | −0.250444 | ||||||||
\(899\) | 6.98463 | 0.232950 | ||||||||
\(900\) | −23.2181 | −0.773937 | ||||||||
\(901\) | 7.23797 | 0.241132 | ||||||||
\(902\) | −0.692226 | −0.0230486 | ||||||||
\(903\) | 35.8353 | 1.19252 | ||||||||
\(904\) | −16.4431 | −0.546889 | ||||||||
\(905\) | 57.1070 | 1.89830 | ||||||||
\(906\) | −4.76203 | −0.158208 | ||||||||
\(907\) | −19.5208 | −0.648178 | −0.324089 | − | 0.946027i | \(-0.605058\pi\) | ||||
−0.324089 | + | 0.946027i | \(0.605058\pi\) | |||||||
\(908\) | 1.61899 | 0.0537279 | ||||||||
\(909\) | −11.1449 | −0.369652 | ||||||||
\(910\) | −1.64820 | −0.0546373 | ||||||||
\(911\) | −39.9785 | −1.32455 | −0.662274 | − | 0.749262i | \(-0.730408\pi\) | ||||
−0.662274 | + | 0.749262i | \(0.730408\pi\) | |||||||
\(912\) | 6.11727 | 0.202563 | ||||||||
\(913\) | −5.59750 | −0.185250 | ||||||||
\(914\) | −13.8568 | −0.458341 | ||||||||
\(915\) | 24.3043 | 0.803477 | ||||||||
\(916\) | 13.2051 | 0.436309 | ||||||||
\(917\) | 26.8984 | 0.888263 | ||||||||
\(918\) | 2.36641 | 0.0781031 | ||||||||
\(919\) | −26.4508 | −0.872532 | −0.436266 | − | 0.899818i | \(-0.643699\pi\) | ||||
−0.436266 | + | 0.899818i | \(0.643699\pi\) | |||||||
\(920\) | 47.2242 | 1.55694 | ||||||||
\(921\) | −8.54392 | −0.281532 | ||||||||
\(922\) | 10.2966 | 0.339101 | ||||||||
\(923\) | 2.62328 | 0.0863463 | ||||||||
\(924\) | −8.65164 | −0.284618 | ||||||||
\(925\) | 126.894 | 4.17226 | ||||||||
\(926\) | −8.78113 | −0.288566 | ||||||||
\(927\) | 13.2767 | 0.436065 | ||||||||
\(928\) | −11.6673 | −0.382998 | ||||||||
\(929\) | 33.2913 | 1.09225 | 0.546127 | − | 0.837703i | \(-0.316102\pi\) | ||||
0.546127 | + | 0.837703i | \(0.316102\pi\) | |||||||
\(930\) | 5.79145 | 0.189909 | ||||||||
\(931\) | −8.86469 | −0.290528 | ||||||||
\(932\) | −26.2536 | −0.859966 | ||||||||
\(933\) | 5.49484 | 0.179893 | ||||||||
\(934\) | 4.08117 | 0.133540 | ||||||||
\(935\) | 31.4182 | 1.02748 | ||||||||
\(936\) | 0.443086 | 0.0144827 | ||||||||
\(937\) | −38.7811 | −1.26692 | −0.633462 | − | 0.773774i | \(-0.718367\pi\) | ||||
−0.633462 | + | 0.773774i | \(0.718367\pi\) | |||||||
\(938\) | 24.8140 | 0.810205 | ||||||||
\(939\) | −5.48024 | −0.178841 | ||||||||
\(940\) | 30.8793 | 1.00717 | ||||||||
\(941\) | 15.6482 | 0.510117 | 0.255058 | − | 0.966926i | \(-0.417905\pi\) | ||||
0.255058 | + | 0.966926i | \(0.417905\pi\) | |||||||
\(942\) | −8.83098 | −0.287729 | ||||||||
\(943\) | −6.24914 | −0.203500 | ||||||||
\(944\) | 7.11383 | 0.231535 | ||||||||
\(945\) | −14.0552 | −0.457216 | ||||||||
\(946\) | 7.49934 | 0.243825 | ||||||||
\(947\) | −47.5500 | −1.54517 | −0.772584 | − | 0.634912i | \(-0.781036\pi\) | ||||
−0.772584 | + | 0.634912i | \(0.781036\pi\) | |||||||
\(948\) | −0.996562 | −0.0323668 | ||||||||
\(949\) | −2.34043 | −0.0759735 | ||||||||
\(950\) | −13.8207 | −0.448402 | ||||||||
\(951\) | 11.3173 | 0.366989 | ||||||||
\(952\) | 29.5760 | 0.958564 | ||||||||
\(953\) | −29.6819 | −0.961491 | −0.480746 | − | 0.876860i | \(-0.659634\pi\) | ||||
−0.480746 | + | 0.876860i | \(0.659634\pi\) | |||||||
\(954\) | −0.677618 | −0.0219387 | ||||||||
\(955\) | 57.3415 | 1.85553 | ||||||||
\(956\) | 2.46219 | 0.0796329 | ||||||||
\(957\) | −3.54736 | −0.114670 | ||||||||
\(958\) | −9.61661 | −0.310698 | ||||||||
\(959\) | −40.3664 | −1.30350 | ||||||||
\(960\) | 13.4396 | 0.433763 | ||||||||
\(961\) | −22.6148 | −0.729509 | ||||||||
\(962\) | −1.13981 | −0.0367489 | ||||||||
\(963\) | 9.32238 | 0.300410 | ||||||||
\(964\) | 10.5896 | 0.341067 | ||||||||
\(965\) | −34.0552 | −1.09628 | ||||||||
\(966\) | 9.72938 | 0.313038 | ||||||||
\(967\) | −1.21199 | −0.0389750 | −0.0194875 | − | 0.999810i | \(-0.506203\pi\) | ||||
−0.0194875 | + | 0.999810i | \(0.506203\pi\) | |||||||
\(968\) | 15.7164 | 0.505144 | ||||||||
\(969\) | −11.3078 | −0.363258 | ||||||||
\(970\) | −14.3810 | −0.461747 | ||||||||
\(971\) | 12.5362 | 0.402306 | 0.201153 | − | 0.979560i | \(-0.435531\pi\) | ||||
0.201153 | + | 0.979560i | \(0.435531\pi\) | |||||||
\(972\) | 1.77846 | 0.0570440 | ||||||||
\(973\) | 47.2672 | 1.51532 | ||||||||
\(974\) | −3.29766 | −0.105664 | ||||||||
\(975\) | 3.25258 | 0.104166 | ||||||||
\(976\) | −15.5569 | −0.497965 | ||||||||
\(977\) | 15.2069 | 0.486513 | 0.243256 | − | 0.969962i | \(-0.421784\pi\) | ||||
0.243256 | + | 0.969962i | \(0.421784\pi\) | |||||||
\(978\) | −4.02148 | −0.128593 | ||||||||
\(979\) | −6.05520 | −0.193525 | ||||||||
\(980\) | −29.7846 | −0.951433 | ||||||||
\(981\) | −0.249141 | −0.00795445 | ||||||||
\(982\) | −7.32926 | −0.233886 | ||||||||
\(983\) | 39.0303 | 1.24487 | 0.622436 | − | 0.782671i | \(-0.286143\pi\) | ||||
0.622436 | + | 0.782671i | \(0.286143\pi\) | |||||||
\(984\) | 1.77846 | 0.0566951 | ||||||||
\(985\) | 59.3967 | 1.89254 | ||||||||
\(986\) | 5.70789 | 0.181776 | ||||||||
\(987\) | 13.5163 | 0.430229 | ||||||||
\(988\) | −0.996562 | −0.0317049 | ||||||||
\(989\) | 67.7010 | 2.15277 | ||||||||
\(990\) | −2.94137 | −0.0934828 | ||||||||
\(991\) | −8.91539 | −0.283207 | −0.141603 | − | 0.989923i | \(-0.545226\pi\) | ||||
−0.141603 | + | 0.989923i | \(0.545226\pi\) | |||||||
\(992\) | −14.0069 | −0.444719 | ||||||||
\(993\) | −33.8613 | −1.07455 | ||||||||
\(994\) | −16.3932 | −0.519962 | ||||||||
\(995\) | −20.6707 | −0.655307 | ||||||||
\(996\) | 6.76891 | 0.214481 | ||||||||
\(997\) | −33.6336 | −1.06519 | −0.532593 | − | 0.846371i | \(-0.678782\pi\) | ||||
−0.532593 | + | 0.846371i | \(0.678782\pi\) | |||||||
\(998\) | −0.762030 | −0.0241216 | ||||||||
\(999\) | −9.71982 | −0.307522 |
(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 | 123.2.a.d.1.2 | ✓ | 3 | |
3.2 | odd | 2 | 369.2.a.e.1.2 | 3 | |||
4.3 | odd | 2 | 1968.2.a.w.1.3 | 3 | |||
5.4 | even | 2 | 3075.2.a.t.1.2 | 3 | |||
7.6 | odd | 2 | 6027.2.a.s.1.2 | 3 | |||
8.3 | odd | 2 | 7872.2.a.bs.1.1 | 3 | |||
8.5 | even | 2 | 7872.2.a.bx.1.1 | 3 | |||
12.11 | even | 2 | 5904.2.a.bd.1.1 | 3 | |||
15.14 | odd | 2 | 9225.2.a.bx.1.2 | 3 | |||
41.40 | even | 2 | 5043.2.a.n.1.2 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
123.2.a.d.1.2 | ✓ | 3 | 1.1 | even | 1 | trivial | |
369.2.a.e.1.2 | 3 | 3.2 | odd | 2 | |||
1968.2.a.w.1.3 | 3 | 4.3 | odd | 2 | |||
3075.2.a.t.1.2 | 3 | 5.4 | even | 2 | |||
5043.2.a.n.1.2 | 3 | 41.40 | even | 2 | |||
5904.2.a.bd.1.1 | 3 | 12.11 | even | 2 | |||
6027.2.a.s.1.2 | 3 | 7.6 | odd | 2 | |||
7872.2.a.bs.1.1 | 3 | 8.3 | odd | 2 | |||
7872.2.a.bx.1.1 | 3 | 8.5 | even | 2 | |||
9225.2.a.bx.1.2 | 3 | 15.14 | odd | 2 |