Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8013,2,Mod(1,8013)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8013, 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("8013.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8013 = 3 \cdot 2671 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8013.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: | \(63.9841271397\) |
Analytic rank: | \(1\) |
Dimension: | \(116\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.8 | ||
Character | \(\chi\) | \(=\) | 8013.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.59210 | −1.83289 | −0.916444 | − | 0.400162i | \(-0.868954\pi\) | ||||
−0.916444 | + | 0.400162i | \(0.868954\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 4.71896 | 2.35948 | ||||||||
\(5\) | −1.33515 | −0.597098 | −0.298549 | − | 0.954394i | \(-0.596503\pi\) | ||||
−0.298549 | + | 0.954394i | \(0.596503\pi\) | |||||||
\(6\) | 2.59210 | 1.05822 | ||||||||
\(7\) | −1.92470 | −0.727468 | −0.363734 | − | 0.931503i | \(-0.618498\pi\) | ||||
−0.363734 | + | 0.931503i | \(0.618498\pi\) | |||||||
\(8\) | −7.04781 | −2.49178 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 3.46084 | 1.09441 | ||||||||
\(11\) | −5.66323 | −1.70753 | −0.853765 | − | 0.520659i | \(-0.825686\pi\) | ||||
−0.853765 | + | 0.520659i | \(0.825686\pi\) | |||||||
\(12\) | −4.71896 | −1.36225 | ||||||||
\(13\) | 2.66191 | 0.738281 | 0.369140 | − | 0.929374i | \(-0.379652\pi\) | ||||
0.369140 | + | 0.929374i | \(0.379652\pi\) | |||||||
\(14\) | 4.98901 | 1.33337 | ||||||||
\(15\) | 1.33515 | 0.344735 | ||||||||
\(16\) | 8.83069 | 2.20767 | ||||||||
\(17\) | −1.18763 | −0.288042 | −0.144021 | − | 0.989575i | \(-0.546003\pi\) | ||||
−0.144021 | + | 0.989575i | \(0.546003\pi\) | |||||||
\(18\) | −2.59210 | −0.610963 | ||||||||
\(19\) | −0.599888 | −0.137624 | −0.0688119 | − | 0.997630i | \(-0.521921\pi\) | ||||
−0.0688119 | + | 0.997630i | \(0.521921\pi\) | |||||||
\(20\) | −6.30053 | −1.40884 | ||||||||
\(21\) | 1.92470 | 0.420004 | ||||||||
\(22\) | 14.6796 | 3.12971 | ||||||||
\(23\) | −8.78251 | −1.83128 | −0.915640 | − | 0.401999i | \(-0.868315\pi\) | ||||
−0.915640 | + | 0.401999i | \(0.868315\pi\) | |||||||
\(24\) | 7.04781 | 1.43863 | ||||||||
\(25\) | −3.21737 | −0.643474 | ||||||||
\(26\) | −6.89992 | −1.35319 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | −9.08259 | −1.71645 | ||||||||
\(29\) | 8.46066 | 1.57110 | 0.785552 | − | 0.618795i | \(-0.212379\pi\) | ||||
0.785552 | + | 0.618795i | \(0.212379\pi\) | |||||||
\(30\) | −3.46084 | −0.631861 | ||||||||
\(31\) | 1.10076 | 0.197702 | 0.0988512 | − | 0.995102i | \(-0.468483\pi\) | ||||
0.0988512 | + | 0.995102i | \(0.468483\pi\) | |||||||
\(32\) | −8.79437 | −1.55464 | ||||||||
\(33\) | 5.66323 | 0.985843 | ||||||||
\(34\) | 3.07845 | 0.527949 | ||||||||
\(35\) | 2.56977 | 0.434370 | ||||||||
\(36\) | 4.71896 | 0.786494 | ||||||||
\(37\) | 6.12882 | 1.00757 | 0.503786 | − | 0.863829i | \(-0.331940\pi\) | ||||
0.503786 | + | 0.863829i | \(0.331940\pi\) | |||||||
\(38\) | 1.55497 | 0.252249 | ||||||||
\(39\) | −2.66191 | −0.426247 | ||||||||
\(40\) | 9.40990 | 1.48784 | ||||||||
\(41\) | −2.71046 | −0.423303 | −0.211652 | − | 0.977345i | \(-0.567884\pi\) | ||||
−0.211652 | + | 0.977345i | \(0.567884\pi\) | |||||||
\(42\) | −4.98901 | −0.769821 | ||||||||
\(43\) | 2.41047 | 0.367593 | 0.183796 | − | 0.982964i | \(-0.441161\pi\) | ||||
0.183796 | + | 0.982964i | \(0.441161\pi\) | |||||||
\(44\) | −26.7246 | −4.02888 | ||||||||
\(45\) | −1.33515 | −0.199033 | ||||||||
\(46\) | 22.7651 | 3.35653 | ||||||||
\(47\) | −6.31667 | −0.921382 | −0.460691 | − | 0.887561i | \(-0.652398\pi\) | ||||
−0.460691 | + | 0.887561i | \(0.652398\pi\) | |||||||
\(48\) | −8.83069 | −1.27460 | ||||||||
\(49\) | −3.29553 | −0.470790 | ||||||||
\(50\) | 8.33973 | 1.17942 | ||||||||
\(51\) | 1.18763 | 0.166301 | ||||||||
\(52\) | 12.5615 | 1.74196 | ||||||||
\(53\) | 8.09769 | 1.11230 | 0.556152 | − | 0.831081i | \(-0.312277\pi\) | ||||
0.556152 | + | 0.831081i | \(0.312277\pi\) | |||||||
\(54\) | 2.59210 | 0.352740 | ||||||||
\(55\) | 7.56128 | 1.01956 | ||||||||
\(56\) | 13.5649 | 1.81269 | ||||||||
\(57\) | 0.599888 | 0.0794572 | ||||||||
\(58\) | −21.9308 | −2.87966 | ||||||||
\(59\) | 2.25320 | 0.293342 | 0.146671 | − | 0.989185i | \(-0.453144\pi\) | ||||
0.146671 | + | 0.989185i | \(0.453144\pi\) | |||||||
\(60\) | 6.30053 | 0.813395 | ||||||||
\(61\) | 13.1292 | 1.68103 | 0.840513 | − | 0.541791i | \(-0.182254\pi\) | ||||
0.840513 | + | 0.541791i | \(0.182254\pi\) | |||||||
\(62\) | −2.85328 | −0.362366 | ||||||||
\(63\) | −1.92470 | −0.242489 | ||||||||
\(64\) | 5.13447 | 0.641808 | ||||||||
\(65\) | −3.55405 | −0.440826 | ||||||||
\(66\) | −14.6796 | −1.80694 | ||||||||
\(67\) | 3.21350 | 0.392592 | 0.196296 | − | 0.980545i | \(-0.437109\pi\) | ||||
0.196296 | + | 0.980545i | \(0.437109\pi\) | |||||||
\(68\) | −5.60438 | −0.679630 | ||||||||
\(69\) | 8.78251 | 1.05729 | ||||||||
\(70\) | −6.66108 | −0.796152 | ||||||||
\(71\) | −13.7699 | −1.63419 | −0.817095 | − | 0.576503i | \(-0.804417\pi\) | ||||
−0.817095 | + | 0.576503i | \(0.804417\pi\) | |||||||
\(72\) | −7.04781 | −0.830593 | ||||||||
\(73\) | −7.59790 | −0.889267 | −0.444634 | − | 0.895713i | \(-0.646666\pi\) | ||||
−0.444634 | + | 0.895713i | \(0.646666\pi\) | |||||||
\(74\) | −15.8865 | −1.84677 | ||||||||
\(75\) | 3.21737 | 0.371510 | ||||||||
\(76\) | −2.83085 | −0.324721 | ||||||||
\(77\) | 10.9000 | 1.24217 | ||||||||
\(78\) | 6.89992 | 0.781263 | ||||||||
\(79\) | 8.17323 | 0.919560 | 0.459780 | − | 0.888033i | \(-0.347928\pi\) | ||||
0.459780 | + | 0.888033i | \(0.347928\pi\) | |||||||
\(80\) | −11.7903 | −1.31820 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 7.02578 | 0.775868 | ||||||||
\(83\) | 3.52602 | 0.387031 | 0.193516 | − | 0.981097i | \(-0.438011\pi\) | ||||
0.193516 | + | 0.981097i | \(0.438011\pi\) | |||||||
\(84\) | 9.08259 | 0.990992 | ||||||||
\(85\) | 1.58566 | 0.171990 | ||||||||
\(86\) | −6.24816 | −0.673757 | ||||||||
\(87\) | −8.46066 | −0.907078 | ||||||||
\(88\) | 39.9134 | 4.25479 | ||||||||
\(89\) | 14.2282 | 1.50818 | 0.754092 | − | 0.656769i | \(-0.228077\pi\) | ||||
0.754092 | + | 0.656769i | \(0.228077\pi\) | |||||||
\(90\) | 3.46084 | 0.364805 | ||||||||
\(91\) | −5.12338 | −0.537076 | ||||||||
\(92\) | −41.4443 | −4.32087 | ||||||||
\(93\) | −1.10076 | −0.114144 | ||||||||
\(94\) | 16.3734 | 1.68879 | ||||||||
\(95\) | 0.800942 | 0.0821749 | ||||||||
\(96\) | 8.79437 | 0.897571 | ||||||||
\(97\) | −13.8523 | −1.40649 | −0.703243 | − | 0.710949i | \(-0.748266\pi\) | ||||
−0.703243 | + | 0.710949i | \(0.748266\pi\) | |||||||
\(98\) | 8.54233 | 0.862906 | ||||||||
\(99\) | −5.66323 | −0.569176 | ||||||||
\(100\) | −15.1826 | −1.51826 | ||||||||
\(101\) | 1.19183 | 0.118591 | 0.0592955 | − | 0.998240i | \(-0.481115\pi\) | ||||
0.0592955 | + | 0.998240i | \(0.481115\pi\) | |||||||
\(102\) | −3.07845 | −0.304812 | ||||||||
\(103\) | 6.40546 | 0.631149 | 0.315574 | − | 0.948901i | \(-0.397803\pi\) | ||||
0.315574 | + | 0.948901i | \(0.397803\pi\) | |||||||
\(104\) | −18.7606 | −1.83963 | ||||||||
\(105\) | −2.56977 | −0.250784 | ||||||||
\(106\) | −20.9900 | −2.03873 | ||||||||
\(107\) | 10.8032 | 1.04438 | 0.522190 | − | 0.852829i | \(-0.325115\pi\) | ||||
0.522190 | + | 0.852829i | \(0.325115\pi\) | |||||||
\(108\) | −4.71896 | −0.454082 | ||||||||
\(109\) | 5.64865 | 0.541043 | 0.270521 | − | 0.962714i | \(-0.412804\pi\) | ||||
0.270521 | + | 0.962714i | \(0.412804\pi\) | |||||||
\(110\) | −19.5996 | −1.86875 | ||||||||
\(111\) | −6.12882 | −0.581721 | ||||||||
\(112\) | −16.9964 | −1.60601 | ||||||||
\(113\) | 7.87519 | 0.740835 | 0.370418 | − | 0.928865i | \(-0.379215\pi\) | ||||
0.370418 | + | 0.928865i | \(0.379215\pi\) | |||||||
\(114\) | −1.55497 | −0.145636 | ||||||||
\(115\) | 11.7260 | 1.09345 | ||||||||
\(116\) | 39.9255 | 3.70699 | ||||||||
\(117\) | 2.66191 | 0.246094 | ||||||||
\(118\) | −5.84052 | −0.537663 | ||||||||
\(119\) | 2.28583 | 0.209542 | ||||||||
\(120\) | −9.40990 | −0.859003 | ||||||||
\(121\) | 21.0722 | 1.91566 | ||||||||
\(122\) | −34.0322 | −3.08113 | ||||||||
\(123\) | 2.71046 | 0.244394 | ||||||||
\(124\) | 5.19445 | 0.466475 | ||||||||
\(125\) | 10.9714 | 0.981315 | ||||||||
\(126\) | 4.98901 | 0.444456 | ||||||||
\(127\) | −17.9013 | −1.58849 | −0.794243 | − | 0.607600i | \(-0.792132\pi\) | ||||
−0.794243 | + | 0.607600i | \(0.792132\pi\) | |||||||
\(128\) | 4.27970 | 0.378276 | ||||||||
\(129\) | −2.41047 | −0.212230 | ||||||||
\(130\) | 9.21245 | 0.807985 | ||||||||
\(131\) | 12.3361 | 1.07781 | 0.538906 | − | 0.842366i | \(-0.318838\pi\) | ||||
0.538906 | + | 0.842366i | \(0.318838\pi\) | |||||||
\(132\) | 26.7246 | 2.32608 | ||||||||
\(133\) | 1.15461 | 0.100117 | ||||||||
\(134\) | −8.32971 | −0.719577 | ||||||||
\(135\) | 1.33515 | 0.114912 | ||||||||
\(136\) | 8.37019 | 0.717738 | ||||||||
\(137\) | 13.7818 | 1.17746 | 0.588728 | − | 0.808331i | \(-0.299629\pi\) | ||||
0.588728 | + | 0.808331i | \(0.299629\pi\) | |||||||
\(138\) | −22.7651 | −1.93789 | ||||||||
\(139\) | 9.89703 | 0.839455 | 0.419728 | − | 0.907650i | \(-0.362126\pi\) | ||||
0.419728 | + | 0.907650i | \(0.362126\pi\) | |||||||
\(140\) | 12.1266 | 1.02489 | ||||||||
\(141\) | 6.31667 | 0.531960 | ||||||||
\(142\) | 35.6930 | 2.99529 | ||||||||
\(143\) | −15.0750 | −1.26064 | ||||||||
\(144\) | 8.83069 | 0.735891 | ||||||||
\(145\) | −11.2963 | −0.938104 | ||||||||
\(146\) | 19.6945 | 1.62993 | ||||||||
\(147\) | 3.29553 | 0.271811 | ||||||||
\(148\) | 28.9217 | 2.37735 | ||||||||
\(149\) | 4.06228 | 0.332795 | 0.166397 | − | 0.986059i | \(-0.446787\pi\) | ||||
0.166397 | + | 0.986059i | \(0.446787\pi\) | |||||||
\(150\) | −8.33973 | −0.680936 | ||||||||
\(151\) | 2.18587 | 0.177884 | 0.0889419 | − | 0.996037i | \(-0.471651\pi\) | ||||
0.0889419 | + | 0.996037i | \(0.471651\pi\) | |||||||
\(152\) | 4.22790 | 0.342928 | ||||||||
\(153\) | −1.18763 | −0.0960141 | ||||||||
\(154\) | −28.2539 | −2.27677 | ||||||||
\(155\) | −1.46968 | −0.118048 | ||||||||
\(156\) | −12.5615 | −1.00572 | ||||||||
\(157\) | −7.10494 | −0.567036 | −0.283518 | − | 0.958967i | \(-0.591502\pi\) | ||||
−0.283518 | + | 0.958967i | \(0.591502\pi\) | |||||||
\(158\) | −21.1858 | −1.68545 | ||||||||
\(159\) | −8.09769 | −0.642189 | ||||||||
\(160\) | 11.7418 | 0.928272 | ||||||||
\(161\) | 16.9037 | 1.33220 | ||||||||
\(162\) | −2.59210 | −0.203654 | ||||||||
\(163\) | 7.99813 | 0.626462 | 0.313231 | − | 0.949677i | \(-0.398589\pi\) | ||||
0.313231 | + | 0.949677i | \(0.398589\pi\) | |||||||
\(164\) | −12.7906 | −0.998776 | ||||||||
\(165\) | −7.56128 | −0.588645 | ||||||||
\(166\) | −9.13979 | −0.709385 | ||||||||
\(167\) | −19.6208 | −1.51831 | −0.759153 | − | 0.650912i | \(-0.774387\pi\) | ||||
−0.759153 | + | 0.650912i | \(0.774387\pi\) | |||||||
\(168\) | −13.5649 | −1.04656 | ||||||||
\(169\) | −5.91424 | −0.454942 | ||||||||
\(170\) | −4.11020 | −0.315238 | ||||||||
\(171\) | −0.599888 | −0.0458746 | ||||||||
\(172\) | 11.3749 | 0.867328 | ||||||||
\(173\) | −12.9471 | −0.984348 | −0.492174 | − | 0.870497i | \(-0.663798\pi\) | ||||
−0.492174 | + | 0.870497i | \(0.663798\pi\) | |||||||
\(174\) | 21.9308 | 1.66257 | ||||||||
\(175\) | 6.19247 | 0.468107 | ||||||||
\(176\) | −50.0103 | −3.76967 | ||||||||
\(177\) | −2.25320 | −0.169361 | ||||||||
\(178\) | −36.8808 | −2.76433 | ||||||||
\(179\) | −20.1566 | −1.50658 | −0.753288 | − | 0.657690i | \(-0.771534\pi\) | ||||
−0.753288 | + | 0.657690i | \(0.771534\pi\) | |||||||
\(180\) | −6.30053 | −0.469614 | ||||||||
\(181\) | 3.86727 | 0.287452 | 0.143726 | − | 0.989618i | \(-0.454092\pi\) | ||||
0.143726 | + | 0.989618i | \(0.454092\pi\) | |||||||
\(182\) | 13.2803 | 0.984400 | ||||||||
\(183\) | −13.1292 | −0.970541 | ||||||||
\(184\) | 61.8975 | 4.56314 | ||||||||
\(185\) | −8.18290 | −0.601619 | ||||||||
\(186\) | 2.85328 | 0.209212 | ||||||||
\(187\) | 6.72582 | 0.491841 | ||||||||
\(188\) | −29.8082 | −2.17398 | ||||||||
\(189\) | 1.92470 | 0.140001 | ||||||||
\(190\) | −2.07612 | −0.150618 | ||||||||
\(191\) | −21.3873 | −1.54753 | −0.773767 | − | 0.633471i | \(-0.781630\pi\) | ||||
−0.773767 | + | 0.633471i | \(0.781630\pi\) | |||||||
\(192\) | −5.13447 | −0.370548 | ||||||||
\(193\) | −13.5814 | −0.977607 | −0.488804 | − | 0.872394i | \(-0.662567\pi\) | ||||
−0.488804 | + | 0.872394i | \(0.662567\pi\) | |||||||
\(194\) | 35.9065 | 2.57793 | ||||||||
\(195\) | 3.55405 | 0.254511 | ||||||||
\(196\) | −15.5515 | −1.11082 | ||||||||
\(197\) | −6.68640 | −0.476386 | −0.238193 | − | 0.971218i | \(-0.576555\pi\) | ||||
−0.238193 | + | 0.971218i | \(0.576555\pi\) | |||||||
\(198\) | 14.6796 | 1.04324 | ||||||||
\(199\) | 7.38514 | 0.523519 | 0.261759 | − | 0.965133i | \(-0.415697\pi\) | ||||
0.261759 | + | 0.965133i | \(0.415697\pi\) | |||||||
\(200\) | 22.6754 | 1.60339 | ||||||||
\(201\) | −3.21350 | −0.226663 | ||||||||
\(202\) | −3.08933 | −0.217364 | ||||||||
\(203\) | −16.2842 | −1.14293 | ||||||||
\(204\) | 5.60438 | 0.392385 | ||||||||
\(205\) | 3.61888 | 0.252754 | ||||||||
\(206\) | −16.6036 | −1.15683 | ||||||||
\(207\) | −8.78251 | −0.610427 | ||||||||
\(208\) | 23.5065 | 1.62988 | ||||||||
\(209\) | 3.39731 | 0.234997 | ||||||||
\(210\) | 6.66108 | 0.459658 | ||||||||
\(211\) | −1.13038 | −0.0778183 | −0.0389091 | − | 0.999243i | \(-0.512388\pi\) | ||||
−0.0389091 | + | 0.999243i | \(0.512388\pi\) | |||||||
\(212\) | 38.2127 | 2.62446 | ||||||||
\(213\) | 13.7699 | 0.943500 | ||||||||
\(214\) | −28.0028 | −1.91423 | ||||||||
\(215\) | −3.21834 | −0.219489 | ||||||||
\(216\) | 7.04781 | 0.479543 | ||||||||
\(217\) | −2.11863 | −0.143822 | ||||||||
\(218\) | −14.6419 | −0.991672 | ||||||||
\(219\) | 7.59790 | 0.513419 | ||||||||
\(220\) | 35.6814 | 2.40564 | ||||||||
\(221\) | −3.16136 | −0.212656 | ||||||||
\(222\) | 15.8865 | 1.06623 | ||||||||
\(223\) | 13.2540 | 0.887552 | 0.443776 | − | 0.896138i | \(-0.353639\pi\) | ||||
0.443776 | + | 0.896138i | \(0.353639\pi\) | |||||||
\(224\) | 16.9265 | 1.13095 | ||||||||
\(225\) | −3.21737 | −0.214491 | ||||||||
\(226\) | −20.4132 | −1.35787 | ||||||||
\(227\) | −10.7444 | −0.713129 | −0.356565 | − | 0.934271i | \(-0.616052\pi\) | ||||
−0.356565 | + | 0.934271i | \(0.616052\pi\) | |||||||
\(228\) | 2.83085 | 0.187478 | ||||||||
\(229\) | 17.4234 | 1.15137 | 0.575687 | − | 0.817670i | \(-0.304735\pi\) | ||||
0.575687 | + | 0.817670i | \(0.304735\pi\) | |||||||
\(230\) | −30.3949 | −2.00418 | ||||||||
\(231\) | −10.9000 | −0.717169 | ||||||||
\(232\) | −59.6292 | −3.91485 | ||||||||
\(233\) | −2.61855 | −0.171547 | −0.0857736 | − | 0.996315i | \(-0.527336\pi\) | ||||
−0.0857736 | + | 0.996315i | \(0.527336\pi\) | |||||||
\(234\) | −6.89992 | −0.451062 | ||||||||
\(235\) | 8.43372 | 0.550155 | ||||||||
\(236\) | 10.6328 | 0.692135 | ||||||||
\(237\) | −8.17323 | −0.530908 | ||||||||
\(238\) | −5.92509 | −0.384066 | ||||||||
\(239\) | 9.90679 | 0.640817 | 0.320408 | − | 0.947280i | \(-0.396180\pi\) | ||||
0.320408 | + | 0.947280i | \(0.396180\pi\) | |||||||
\(240\) | 11.7903 | 0.761061 | ||||||||
\(241\) | 15.2624 | 0.983137 | 0.491568 | − | 0.870839i | \(-0.336424\pi\) | ||||
0.491568 | + | 0.870839i | \(0.336424\pi\) | |||||||
\(242\) | −54.6212 | −3.51119 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 61.9564 | 3.96635 | ||||||||
\(245\) | 4.40003 | 0.281108 | ||||||||
\(246\) | −7.02578 | −0.447947 | ||||||||
\(247\) | −1.59685 | −0.101605 | ||||||||
\(248\) | −7.75795 | −0.492631 | ||||||||
\(249\) | −3.52602 | −0.223453 | ||||||||
\(250\) | −28.4390 | −1.79864 | ||||||||
\(251\) | −5.81591 | −0.367097 | −0.183549 | − | 0.983011i | \(-0.558758\pi\) | ||||
−0.183549 | + | 0.983011i | \(0.558758\pi\) | |||||||
\(252\) | −9.08259 | −0.572149 | ||||||||
\(253\) | 49.7374 | 3.12696 | ||||||||
\(254\) | 46.4020 | 2.91152 | ||||||||
\(255\) | −1.58566 | −0.0992982 | ||||||||
\(256\) | −21.3623 | −1.33515 | ||||||||
\(257\) | 1.02291 | 0.0638072 | 0.0319036 | − | 0.999491i | \(-0.489843\pi\) | ||||
0.0319036 | + | 0.999491i | \(0.489843\pi\) | |||||||
\(258\) | 6.24816 | 0.388994 | ||||||||
\(259\) | −11.7961 | −0.732976 | ||||||||
\(260\) | −16.7714 | −1.04012 | ||||||||
\(261\) | 8.46066 | 0.523702 | ||||||||
\(262\) | −31.9764 | −1.97551 | ||||||||
\(263\) | 18.3259 | 1.13002 | 0.565012 | − | 0.825083i | \(-0.308872\pi\) | ||||
0.565012 | + | 0.825083i | \(0.308872\pi\) | |||||||
\(264\) | −39.9134 | −2.45650 | ||||||||
\(265\) | −10.8116 | −0.664154 | ||||||||
\(266\) | −2.99285 | −0.183503 | ||||||||
\(267\) | −14.2282 | −0.870751 | ||||||||
\(268\) | 15.1644 | 0.926314 | ||||||||
\(269\) | −1.16220 | −0.0708607 | −0.0354303 | − | 0.999372i | \(-0.511280\pi\) | ||||
−0.0354303 | + | 0.999372i | \(0.511280\pi\) | |||||||
\(270\) | −3.46084 | −0.210620 | ||||||||
\(271\) | −7.72761 | −0.469419 | −0.234710 | − | 0.972066i | \(-0.575414\pi\) | ||||
−0.234710 | + | 0.972066i | \(0.575414\pi\) | |||||||
\(272\) | −10.4876 | −0.635903 | ||||||||
\(273\) | 5.12338 | 0.310081 | ||||||||
\(274\) | −35.7237 | −2.15814 | ||||||||
\(275\) | 18.2207 | 1.09875 | ||||||||
\(276\) | 41.4443 | 2.49466 | ||||||||
\(277\) | −7.53433 | −0.452694 | −0.226347 | − | 0.974047i | \(-0.572678\pi\) | ||||
−0.226347 | + | 0.974047i | \(0.572678\pi\) | |||||||
\(278\) | −25.6541 | −1.53863 | ||||||||
\(279\) | 1.10076 | 0.0659008 | ||||||||
\(280\) | −18.1112 | −1.08235 | ||||||||
\(281\) | 22.6337 | 1.35021 | 0.675105 | − | 0.737721i | \(-0.264098\pi\) | ||||
0.675105 | + | 0.737721i | \(0.264098\pi\) | |||||||
\(282\) | −16.3734 | −0.975023 | ||||||||
\(283\) | 13.0683 | 0.776827 | 0.388414 | − | 0.921485i | \(-0.373023\pi\) | ||||
0.388414 | + | 0.921485i | \(0.373023\pi\) | |||||||
\(284\) | −64.9798 | −3.85584 | ||||||||
\(285\) | −0.800942 | −0.0474437 | ||||||||
\(286\) | 39.0759 | 2.31061 | ||||||||
\(287\) | 5.21683 | 0.307940 | ||||||||
\(288\) | −8.79437 | −0.518213 | ||||||||
\(289\) | −15.5895 | −0.917032 | ||||||||
\(290\) | 29.2810 | 1.71944 | ||||||||
\(291\) | 13.8523 | 0.812035 | ||||||||
\(292\) | −35.8542 | −2.09821 | ||||||||
\(293\) | 9.23361 | 0.539433 | 0.269717 | − | 0.962940i | \(-0.413070\pi\) | ||||
0.269717 | + | 0.962940i | \(0.413070\pi\) | |||||||
\(294\) | −8.54233 | −0.498199 | ||||||||
\(295\) | −3.00837 | −0.175154 | ||||||||
\(296\) | −43.1948 | −2.51064 | ||||||||
\(297\) | 5.66323 | 0.328614 | ||||||||
\(298\) | −10.5298 | −0.609976 | ||||||||
\(299\) | −23.3782 | −1.35200 | ||||||||
\(300\) | 15.1826 | 0.876570 | ||||||||
\(301\) | −4.63942 | −0.267412 | ||||||||
\(302\) | −5.66599 | −0.326041 | ||||||||
\(303\) | −1.19183 | −0.0684686 | ||||||||
\(304\) | −5.29743 | −0.303828 | ||||||||
\(305\) | −17.5295 | −1.00374 | ||||||||
\(306\) | 3.07845 | 0.175983 | ||||||||
\(307\) | −24.6556 | −1.40717 | −0.703584 | − | 0.710612i | \(-0.748418\pi\) | ||||
−0.703584 | + | 0.710612i | \(0.748418\pi\) | |||||||
\(308\) | 51.4368 | 2.93089 | ||||||||
\(309\) | −6.40546 | −0.364394 | ||||||||
\(310\) | 3.80956 | 0.216368 | ||||||||
\(311\) | 4.54260 | 0.257587 | 0.128794 | − | 0.991671i | \(-0.458890\pi\) | ||||
0.128794 | + | 0.991671i | \(0.458890\pi\) | |||||||
\(312\) | 18.7606 | 1.06211 | ||||||||
\(313\) | 8.84780 | 0.500107 | 0.250054 | − | 0.968232i | \(-0.419552\pi\) | ||||
0.250054 | + | 0.968232i | \(0.419552\pi\) | |||||||
\(314\) | 18.4167 | 1.03931 | ||||||||
\(315\) | 2.56977 | 0.144790 | ||||||||
\(316\) | 38.5692 | 2.16968 | ||||||||
\(317\) | −13.6484 | −0.766571 | −0.383285 | − | 0.923630i | \(-0.625207\pi\) | ||||
−0.383285 | + | 0.923630i | \(0.625207\pi\) | |||||||
\(318\) | 20.9900 | 1.17706 | ||||||||
\(319\) | −47.9147 | −2.68271 | ||||||||
\(320\) | −6.85529 | −0.383222 | ||||||||
\(321\) | −10.8032 | −0.602973 | ||||||||
\(322\) | −43.8160 | −2.44177 | ||||||||
\(323\) | 0.712445 | 0.0396415 | ||||||||
\(324\) | 4.71896 | 0.262165 | ||||||||
\(325\) | −8.56434 | −0.475064 | ||||||||
\(326\) | −20.7319 | −1.14823 | ||||||||
\(327\) | −5.64865 | −0.312371 | ||||||||
\(328\) | 19.1028 | 1.05478 | ||||||||
\(329\) | 12.1577 | 0.670276 | ||||||||
\(330\) | 19.5996 | 1.07892 | ||||||||
\(331\) | 22.1910 | 1.21973 | 0.609865 | − | 0.792505i | \(-0.291224\pi\) | ||||
0.609865 | + | 0.792505i | \(0.291224\pi\) | |||||||
\(332\) | 16.6392 | 0.913193 | ||||||||
\(333\) | 6.12882 | 0.335857 | ||||||||
\(334\) | 50.8591 | 2.78289 | ||||||||
\(335\) | −4.29052 | −0.234416 | ||||||||
\(336\) | 16.9964 | 0.927231 | ||||||||
\(337\) | 4.77632 | 0.260183 | 0.130091 | − | 0.991502i | \(-0.458473\pi\) | ||||
0.130091 | + | 0.991502i | \(0.458473\pi\) | |||||||
\(338\) | 15.3303 | 0.833857 | ||||||||
\(339\) | −7.87519 | −0.427721 | ||||||||
\(340\) | 7.48269 | 0.405806 | ||||||||
\(341\) | −6.23386 | −0.337583 | ||||||||
\(342\) | 1.55497 | 0.0840831 | ||||||||
\(343\) | 19.8158 | 1.06995 | ||||||||
\(344\) | −16.9885 | −0.915960 | ||||||||
\(345\) | −11.7260 | −0.631306 | ||||||||
\(346\) | 33.5601 | 1.80420 | ||||||||
\(347\) | 22.3770 | 1.20126 | 0.600631 | − | 0.799527i | \(-0.294916\pi\) | ||||
0.600631 | + | 0.799527i | \(0.294916\pi\) | |||||||
\(348\) | −39.9255 | −2.14023 | ||||||||
\(349\) | 31.5679 | 1.68979 | 0.844896 | − | 0.534931i | \(-0.179662\pi\) | ||||
0.844896 | + | 0.534931i | \(0.179662\pi\) | |||||||
\(350\) | −16.0515 | −0.857988 | ||||||||
\(351\) | −2.66191 | −0.142082 | ||||||||
\(352\) | 49.8046 | 2.65459 | ||||||||
\(353\) | −1.42915 | −0.0760660 | −0.0380330 | − | 0.999276i | \(-0.512109\pi\) | ||||
−0.0380330 | + | 0.999276i | \(0.512109\pi\) | |||||||
\(354\) | 5.84052 | 0.310420 | ||||||||
\(355\) | 18.3849 | 0.975772 | ||||||||
\(356\) | 67.1423 | 3.55853 | ||||||||
\(357\) | −2.28583 | −0.120979 | ||||||||
\(358\) | 52.2479 | 2.76139 | ||||||||
\(359\) | −2.79564 | −0.147548 | −0.0737742 | − | 0.997275i | \(-0.523504\pi\) | ||||
−0.0737742 | + | 0.997275i | \(0.523504\pi\) | |||||||
\(360\) | 9.40990 | 0.495946 | ||||||||
\(361\) | −18.6401 | −0.981060 | ||||||||
\(362\) | −10.0243 | −0.526868 | ||||||||
\(363\) | −21.0722 | −1.10600 | ||||||||
\(364\) | −24.1770 | −1.26722 | ||||||||
\(365\) | 10.1444 | 0.530980 | ||||||||
\(366\) | 34.0322 | 1.77889 | ||||||||
\(367\) | −1.72620 | −0.0901067 | −0.0450533 | − | 0.998985i | \(-0.514346\pi\) | ||||
−0.0450533 | + | 0.998985i | \(0.514346\pi\) | |||||||
\(368\) | −77.5556 | −4.04287 | ||||||||
\(369\) | −2.71046 | −0.141101 | ||||||||
\(370\) | 21.2109 | 1.10270 | ||||||||
\(371\) | −15.5856 | −0.809165 | ||||||||
\(372\) | −5.19445 | −0.269320 | ||||||||
\(373\) | 24.1013 | 1.24792 | 0.623960 | − | 0.781456i | \(-0.285523\pi\) | ||||
0.623960 | + | 0.781456i | \(0.285523\pi\) | |||||||
\(374\) | −17.4340 | −0.901489 | ||||||||
\(375\) | −10.9714 | −0.566563 | ||||||||
\(376\) | 44.5188 | 2.29588 | ||||||||
\(377\) | 22.5215 | 1.15992 | ||||||||
\(378\) | −4.98901 | −0.256607 | ||||||||
\(379\) | −1.42692 | −0.0732961 | −0.0366481 | − | 0.999328i | \(-0.511668\pi\) | ||||
−0.0366481 | + | 0.999328i | \(0.511668\pi\) | |||||||
\(380\) | 3.77962 | 0.193890 | ||||||||
\(381\) | 17.9013 | 0.917113 | ||||||||
\(382\) | 55.4380 | 2.83646 | ||||||||
\(383\) | 7.31360 | 0.373707 | 0.186854 | − | 0.982388i | \(-0.440171\pi\) | ||||
0.186854 | + | 0.982388i | \(0.440171\pi\) | |||||||
\(384\) | −4.27970 | −0.218398 | ||||||||
\(385\) | −14.5532 | −0.741699 | ||||||||
\(386\) | 35.2042 | 1.79185 | ||||||||
\(387\) | 2.41047 | 0.122531 | ||||||||
\(388\) | −65.3684 | −3.31858 | ||||||||
\(389\) | 30.3479 | 1.53870 | 0.769351 | − | 0.638827i | \(-0.220580\pi\) | ||||
0.769351 | + | 0.638827i | \(0.220580\pi\) | |||||||
\(390\) | −9.21245 | −0.466490 | ||||||||
\(391\) | 10.4304 | 0.527486 | ||||||||
\(392\) | 23.2263 | 1.17310 | ||||||||
\(393\) | −12.3361 | −0.622275 | ||||||||
\(394\) | 17.3318 | 0.873163 | ||||||||
\(395\) | −10.9125 | −0.549068 | ||||||||
\(396\) | −26.7246 | −1.34296 | ||||||||
\(397\) | −16.0005 | −0.803042 | −0.401521 | − | 0.915850i | \(-0.631518\pi\) | ||||
−0.401521 | + | 0.915850i | \(0.631518\pi\) | |||||||
\(398\) | −19.1430 | −0.959552 | ||||||||
\(399\) | −1.15461 | −0.0578026 | ||||||||
\(400\) | −28.4116 | −1.42058 | ||||||||
\(401\) | 13.3250 | 0.665417 | 0.332708 | − | 0.943030i | \(-0.392038\pi\) | ||||
0.332708 | + | 0.943030i | \(0.392038\pi\) | |||||||
\(402\) | 8.32971 | 0.415448 | ||||||||
\(403\) | 2.93012 | 0.145960 | ||||||||
\(404\) | 5.62418 | 0.279813 | ||||||||
\(405\) | −1.33515 | −0.0663442 | ||||||||
\(406\) | 42.2103 | 2.09486 | ||||||||
\(407\) | −34.7089 | −1.72046 | ||||||||
\(408\) | −8.37019 | −0.414386 | ||||||||
\(409\) | −14.3936 | −0.711719 | −0.355859 | − | 0.934540i | \(-0.615812\pi\) | ||||
−0.355859 | + | 0.934540i | \(0.615812\pi\) | |||||||
\(410\) | −9.38048 | −0.463269 | ||||||||
\(411\) | −13.7818 | −0.679804 | ||||||||
\(412\) | 30.2271 | 1.48918 | ||||||||
\(413\) | −4.33674 | −0.213397 | ||||||||
\(414\) | 22.7651 | 1.11884 | ||||||||
\(415\) | −4.70778 | −0.231096 | ||||||||
\(416\) | −23.4098 | −1.14776 | ||||||||
\(417\) | −9.89703 | −0.484660 | ||||||||
\(418\) | −8.80615 | −0.430723 | ||||||||
\(419\) | 33.7268 | 1.64766 | 0.823832 | − | 0.566834i | \(-0.191832\pi\) | ||||
0.823832 | + | 0.566834i | \(0.191832\pi\) | |||||||
\(420\) | −12.1266 | −0.591719 | ||||||||
\(421\) | −33.8811 | −1.65126 | −0.825631 | − | 0.564211i | \(-0.809181\pi\) | ||||
−0.825631 | + | 0.564211i | \(0.809181\pi\) | |||||||
\(422\) | 2.93004 | 0.142632 | ||||||||
\(423\) | −6.31667 | −0.307127 | ||||||||
\(424\) | −57.0710 | −2.77161 | ||||||||
\(425\) | 3.82104 | 0.185348 | ||||||||
\(426\) | −35.6930 | −1.72933 | ||||||||
\(427\) | −25.2698 | −1.22289 | ||||||||
\(428\) | 50.9797 | 2.46420 | ||||||||
\(429\) | 15.0750 | 0.727829 | ||||||||
\(430\) | 8.34225 | 0.402299 | ||||||||
\(431\) | −31.2746 | −1.50644 | −0.753221 | − | 0.657767i | \(-0.771501\pi\) | ||||
−0.753221 | + | 0.657767i | \(0.771501\pi\) | |||||||
\(432\) | −8.83069 | −0.424867 | ||||||||
\(433\) | 11.3752 | 0.546658 | 0.273329 | − | 0.961921i | \(-0.411875\pi\) | ||||
0.273329 | + | 0.961921i | \(0.411875\pi\) | |||||||
\(434\) | 5.49170 | 0.263610 | ||||||||
\(435\) | 11.2963 | 0.541614 | ||||||||
\(436\) | 26.6558 | 1.27658 | ||||||||
\(437\) | 5.26853 | 0.252028 | ||||||||
\(438\) | −19.6945 | −0.941039 | ||||||||
\(439\) | 3.73198 | 0.178118 | 0.0890590 | − | 0.996026i | \(-0.471614\pi\) | ||||
0.0890590 | + | 0.996026i | \(0.471614\pi\) | |||||||
\(440\) | −53.2905 | −2.54052 | ||||||||
\(441\) | −3.29553 | −0.156930 | ||||||||
\(442\) | 8.19455 | 0.389775 | ||||||||
\(443\) | 20.1972 | 0.959600 | 0.479800 | − | 0.877378i | \(-0.340709\pi\) | ||||
0.479800 | + | 0.877378i | \(0.340709\pi\) | |||||||
\(444\) | −28.9217 | −1.37256 | ||||||||
\(445\) | −18.9968 | −0.900534 | ||||||||
\(446\) | −34.3556 | −1.62678 | ||||||||
\(447\) | −4.06228 | −0.192139 | ||||||||
\(448\) | −9.88231 | −0.466895 | ||||||||
\(449\) | −11.8388 | −0.558707 | −0.279353 | − | 0.960188i | \(-0.590120\pi\) | ||||
−0.279353 | + | 0.960188i | \(0.590120\pi\) | |||||||
\(450\) | 8.33973 | 0.393139 | ||||||||
\(451\) | 15.3500 | 0.722803 | ||||||||
\(452\) | 37.1627 | 1.74799 | ||||||||
\(453\) | −2.18587 | −0.102701 | ||||||||
\(454\) | 27.8504 | 1.30709 | ||||||||
\(455\) | 6.84049 | 0.320687 | ||||||||
\(456\) | −4.22790 | −0.197990 | ||||||||
\(457\) | 11.3715 | 0.531935 | 0.265967 | − | 0.963982i | \(-0.414309\pi\) | ||||
0.265967 | + | 0.963982i | \(0.414309\pi\) | |||||||
\(458\) | −45.1632 | −2.11034 | ||||||||
\(459\) | 1.18763 | 0.0554338 | ||||||||
\(460\) | 55.3345 | 2.57998 | ||||||||
\(461\) | −3.09897 | −0.144333 | −0.0721666 | − | 0.997393i | \(-0.522991\pi\) | ||||
−0.0721666 | + | 0.997393i | \(0.522991\pi\) | |||||||
\(462\) | 28.2539 | 1.31449 | ||||||||
\(463\) | −18.2777 | −0.849439 | −0.424719 | − | 0.905325i | \(-0.639627\pi\) | ||||
−0.424719 | + | 0.905325i | \(0.639627\pi\) | |||||||
\(464\) | 74.7134 | 3.46848 | ||||||||
\(465\) | 1.46968 | 0.0681549 | ||||||||
\(466\) | 6.78754 | 0.314427 | ||||||||
\(467\) | −32.9822 | −1.52623 | −0.763116 | − | 0.646261i | \(-0.776332\pi\) | ||||
−0.763116 | + | 0.646261i | \(0.776332\pi\) | |||||||
\(468\) | 12.5615 | 0.580653 | ||||||||
\(469\) | −6.18503 | −0.285598 | ||||||||
\(470\) | −21.8610 | −1.00837 | ||||||||
\(471\) | 7.10494 | 0.327378 | ||||||||
\(472\) | −15.8802 | −0.730944 | ||||||||
\(473\) | −13.6510 | −0.627675 | ||||||||
\(474\) | 21.1858 | 0.973096 | ||||||||
\(475\) | 1.93006 | 0.0885573 | ||||||||
\(476\) | 10.7867 | 0.494410 | ||||||||
\(477\) | 8.09769 | 0.370768 | ||||||||
\(478\) | −25.6793 | −1.17455 | ||||||||
\(479\) | 18.9496 | 0.865831 | 0.432916 | − | 0.901434i | \(-0.357485\pi\) | ||||
0.432916 | + | 0.901434i | \(0.357485\pi\) | |||||||
\(480\) | −11.7418 | −0.535938 | ||||||||
\(481\) | 16.3143 | 0.743870 | ||||||||
\(482\) | −39.5616 | −1.80198 | ||||||||
\(483\) | −16.9037 | −0.769145 | ||||||||
\(484\) | 99.4391 | 4.51996 | ||||||||
\(485\) | 18.4949 | 0.839810 | ||||||||
\(486\) | 2.59210 | 0.117580 | ||||||||
\(487\) | 6.49942 | 0.294517 | 0.147259 | − | 0.989098i | \(-0.452955\pi\) | ||||
0.147259 | + | 0.989098i | \(0.452955\pi\) | |||||||
\(488\) | −92.5324 | −4.18875 | ||||||||
\(489\) | −7.99813 | −0.361688 | ||||||||
\(490\) | −11.4053 | −0.515239 | ||||||||
\(491\) | 24.4999 | 1.10567 | 0.552833 | − | 0.833292i | \(-0.313547\pi\) | ||||
0.552833 | + | 0.833292i | \(0.313547\pi\) | |||||||
\(492\) | 12.7906 | 0.576644 | ||||||||
\(493\) | −10.0481 | −0.452545 | ||||||||
\(494\) | 4.13918 | 0.186231 | ||||||||
\(495\) | 7.56128 | 0.339854 | ||||||||
\(496\) | 9.72047 | 0.436462 | ||||||||
\(497\) | 26.5030 | 1.18882 | ||||||||
\(498\) | 9.13979 | 0.409564 | ||||||||
\(499\) | −5.46734 | −0.244752 | −0.122376 | − | 0.992484i | \(-0.539051\pi\) | ||||
−0.122376 | + | 0.992484i | \(0.539051\pi\) | |||||||
\(500\) | 51.7738 | 2.31540 | ||||||||
\(501\) | 19.6208 | 0.876595 | ||||||||
\(502\) | 15.0754 | 0.672848 | ||||||||
\(503\) | 4.71432 | 0.210201 | 0.105101 | − | 0.994462i | \(-0.466484\pi\) | ||||
0.105101 | + | 0.994462i | \(0.466484\pi\) | |||||||
\(504\) | 13.5649 | 0.604230 | ||||||||
\(505\) | −1.59127 | −0.0708105 | ||||||||
\(506\) | −128.924 | −5.73138 | ||||||||
\(507\) | 5.91424 | 0.262661 | ||||||||
\(508\) | −84.4757 | −3.74800 | ||||||||
\(509\) | 31.6871 | 1.40451 | 0.702253 | − | 0.711927i | \(-0.252178\pi\) | ||||
0.702253 | + | 0.711927i | \(0.252178\pi\) | |||||||
\(510\) | 4.11020 | 0.182003 | ||||||||
\(511\) | 14.6237 | 0.646914 | ||||||||
\(512\) | 46.8138 | 2.06890 | ||||||||
\(513\) | 0.599888 | 0.0264857 | ||||||||
\(514\) | −2.65147 | −0.116951 | ||||||||
\(515\) | −8.55226 | −0.376858 | ||||||||
\(516\) | −11.3749 | −0.500752 | ||||||||
\(517\) | 35.7728 | 1.57329 | ||||||||
\(518\) | 30.5767 | 1.34346 | ||||||||
\(519\) | 12.9471 | 0.568313 | ||||||||
\(520\) | 25.0483 | 1.09844 | ||||||||
\(521\) | −13.8384 | −0.606271 | −0.303135 | − | 0.952948i | \(-0.598033\pi\) | ||||
−0.303135 | + | 0.952948i | \(0.598033\pi\) | |||||||
\(522\) | −21.9308 | −0.959887 | ||||||||
\(523\) | −0.360105 | −0.0157463 | −0.00787314 | − | 0.999969i | \(-0.502506\pi\) | ||||
−0.00787314 | + | 0.999969i | \(0.502506\pi\) | |||||||
\(524\) | 58.2137 | 2.54308 | ||||||||
\(525\) | −6.19247 | −0.270262 | ||||||||
\(526\) | −47.5025 | −2.07121 | ||||||||
\(527\) | −1.30729 | −0.0569466 | ||||||||
\(528\) | 50.0103 | 2.17642 | ||||||||
\(529\) | 54.1325 | 2.35359 | ||||||||
\(530\) | 28.0248 | 1.21732 | ||||||||
\(531\) | 2.25320 | 0.0977807 | ||||||||
\(532\) | 5.44854 | 0.236224 | ||||||||
\(533\) | −7.21500 | −0.312517 | ||||||||
\(534\) | 36.8808 | 1.59599 | ||||||||
\(535\) | −14.4239 | −0.623598 | ||||||||
\(536\) | −22.6482 | −0.978252 | ||||||||
\(537\) | 20.1566 | 0.869823 | ||||||||
\(538\) | 3.01254 | 0.129880 | ||||||||
\(539\) | 18.6634 | 0.803888 | ||||||||
\(540\) | 6.30053 | 0.271132 | ||||||||
\(541\) | −16.7493 | −0.720110 | −0.360055 | − | 0.932931i | \(-0.617242\pi\) | ||||
−0.360055 | + | 0.932931i | \(0.617242\pi\) | |||||||
\(542\) | 20.0307 | 0.860393 | ||||||||
\(543\) | −3.86727 | −0.165961 | ||||||||
\(544\) | 10.4444 | 0.447802 | ||||||||
\(545\) | −7.54181 | −0.323056 | ||||||||
\(546\) | −13.2803 | −0.568344 | ||||||||
\(547\) | 3.90367 | 0.166909 | 0.0834544 | − | 0.996512i | \(-0.473405\pi\) | ||||
0.0834544 | + | 0.996512i | \(0.473405\pi\) | |||||||
\(548\) | 65.0356 | 2.77818 | ||||||||
\(549\) | 13.1292 | 0.560342 | ||||||||
\(550\) | −47.2298 | −2.01389 | ||||||||
\(551\) | −5.07545 | −0.216221 | ||||||||
\(552\) | −61.8975 | −2.63453 | ||||||||
\(553\) | −15.7310 | −0.668951 | ||||||||
\(554\) | 19.5297 | 0.829738 | ||||||||
\(555\) | 8.18290 | 0.347345 | ||||||||
\(556\) | 46.7037 | 1.98068 | ||||||||
\(557\) | −43.4383 | −1.84054 | −0.920269 | − | 0.391285i | \(-0.872031\pi\) | ||||
−0.920269 | + | 0.391285i | \(0.872031\pi\) | |||||||
\(558\) | −2.85328 | −0.120789 | ||||||||
\(559\) | 6.41644 | 0.271387 | ||||||||
\(560\) | 22.6928 | 0.958946 | ||||||||
\(561\) | −6.72582 | −0.283964 | ||||||||
\(562\) | −58.6686 | −2.47479 | ||||||||
\(563\) | −15.0390 | −0.633819 | −0.316910 | − | 0.948456i | \(-0.602645\pi\) | ||||
−0.316910 | + | 0.948456i | \(0.602645\pi\) | |||||||
\(564\) | 29.8082 | 1.25515 | ||||||||
\(565\) | −10.5146 | −0.442351 | ||||||||
\(566\) | −33.8742 | −1.42384 | ||||||||
\(567\) | −1.92470 | −0.0808298 | ||||||||
\(568\) | 97.0479 | 4.07204 | ||||||||
\(569\) | 18.3737 | 0.770267 | 0.385133 | − | 0.922861i | \(-0.374155\pi\) | ||||
0.385133 | + | 0.922861i | \(0.374155\pi\) | |||||||
\(570\) | 2.07612 | 0.0869591 | ||||||||
\(571\) | 4.40212 | 0.184223 | 0.0921116 | − | 0.995749i | \(-0.470638\pi\) | ||||
0.0921116 | + | 0.995749i | \(0.470638\pi\) | |||||||
\(572\) | −71.1384 | −2.97445 | ||||||||
\(573\) | 21.3873 | 0.893469 | ||||||||
\(574\) | −13.5225 | −0.564419 | ||||||||
\(575\) | 28.2566 | 1.17838 | ||||||||
\(576\) | 5.13447 | 0.213936 | ||||||||
\(577\) | −20.6063 | −0.857850 | −0.428925 | − | 0.903340i | \(-0.641108\pi\) | ||||
−0.428925 | + | 0.903340i | \(0.641108\pi\) | |||||||
\(578\) | 40.4096 | 1.68082 | ||||||||
\(579\) | 13.5814 | 0.564422 | ||||||||
\(580\) | −53.3067 | −2.21344 | ||||||||
\(581\) | −6.78654 | −0.281553 | ||||||||
\(582\) | −35.9065 | −1.48837 | ||||||||
\(583\) | −45.8591 | −1.89929 | ||||||||
\(584\) | 53.5486 | 2.21586 | ||||||||
\(585\) | −3.55405 | −0.146942 | ||||||||
\(586\) | −23.9344 | −0.988721 | ||||||||
\(587\) | 14.4066 | 0.594626 | 0.297313 | − | 0.954780i | \(-0.403910\pi\) | ||||
0.297313 | + | 0.954780i | \(0.403910\pi\) | |||||||
\(588\) | 15.5515 | 0.641332 | ||||||||
\(589\) | −0.660333 | −0.0272086 | ||||||||
\(590\) | 7.79798 | 0.321038 | ||||||||
\(591\) | 6.68640 | 0.275042 | ||||||||
\(592\) | 54.1217 | 2.22439 | ||||||||
\(593\) | −28.8539 | −1.18489 | −0.592445 | − | 0.805611i | \(-0.701837\pi\) | ||||
−0.592445 | + | 0.805611i | \(0.701837\pi\) | |||||||
\(594\) | −14.6796 | −0.602313 | ||||||||
\(595\) | −3.05193 | −0.125117 | ||||||||
\(596\) | 19.1697 | 0.785223 | ||||||||
\(597\) | −7.38514 | −0.302254 | ||||||||
\(598\) | 60.5986 | 2.47806 | ||||||||
\(599\) | −27.2122 | −1.11186 | −0.555930 | − | 0.831229i | \(-0.687638\pi\) | ||||
−0.555930 | + | 0.831229i | \(0.687638\pi\) | |||||||
\(600\) | −22.6754 | −0.925720 | ||||||||
\(601\) | −1.60457 | −0.0654518 | −0.0327259 | − | 0.999464i | \(-0.510419\pi\) | ||||
−0.0327259 | + | 0.999464i | \(0.510419\pi\) | |||||||
\(602\) | 12.0258 | 0.490136 | ||||||||
\(603\) | 3.21350 | 0.130864 | ||||||||
\(604\) | 10.3151 | 0.419714 | ||||||||
\(605\) | −28.1346 | −1.14384 | ||||||||
\(606\) | 3.08933 | 0.125495 | ||||||||
\(607\) | −24.9430 | −1.01241 | −0.506203 | − | 0.862414i | \(-0.668951\pi\) | ||||
−0.506203 | + | 0.862414i | \(0.668951\pi\) | |||||||
\(608\) | 5.27564 | 0.213955 | ||||||||
\(609\) | 16.2842 | 0.659870 | ||||||||
\(610\) | 45.4382 | 1.83974 | ||||||||
\(611\) | −16.8144 | −0.680238 | ||||||||
\(612\) | −5.60438 | −0.226543 | ||||||||
\(613\) | −3.55458 | −0.143568 | −0.0717841 | − | 0.997420i | \(-0.522869\pi\) | ||||
−0.0717841 | + | 0.997420i | \(0.522869\pi\) | |||||||
\(614\) | 63.9096 | 2.57918 | ||||||||
\(615\) | −3.61888 | −0.145927 | ||||||||
\(616\) | −76.8214 | −3.09522 | ||||||||
\(617\) | 9.32917 | 0.375578 | 0.187789 | − | 0.982209i | \(-0.439868\pi\) | ||||
0.187789 | + | 0.982209i | \(0.439868\pi\) | |||||||
\(618\) | 16.6036 | 0.667894 | ||||||||
\(619\) | −19.5010 | −0.783810 | −0.391905 | − | 0.920006i | \(-0.628184\pi\) | ||||
−0.391905 | + | 0.920006i | \(0.628184\pi\) | |||||||
\(620\) | −6.93538 | −0.278531 | ||||||||
\(621\) | 8.78251 | 0.352430 | ||||||||
\(622\) | −11.7749 | −0.472129 | ||||||||
\(623\) | −27.3850 | −1.09716 | ||||||||
\(624\) | −23.5065 | −0.941013 | ||||||||
\(625\) | 1.43831 | 0.0575323 | ||||||||
\(626\) | −22.9343 | −0.916641 | ||||||||
\(627\) | −3.39731 | −0.135675 | ||||||||
\(628\) | −33.5279 | −1.33791 | ||||||||
\(629\) | −7.27876 | −0.290223 | ||||||||
\(630\) | −6.66108 | −0.265384 | ||||||||
\(631\) | 7.31759 | 0.291309 | 0.145654 | − | 0.989336i | \(-0.453471\pi\) | ||||
0.145654 | + | 0.989336i | \(0.453471\pi\) | |||||||
\(632\) | −57.6034 | −2.29134 | ||||||||
\(633\) | 1.13038 | 0.0449284 | ||||||||
\(634\) | 35.3780 | 1.40504 | ||||||||
\(635\) | 23.9010 | 0.948482 | ||||||||
\(636\) | −38.2127 | −1.51523 | ||||||||
\(637\) | −8.77240 | −0.347575 | ||||||||
\(638\) | 124.199 | 4.91710 | ||||||||
\(639\) | −13.7699 | −0.544730 | ||||||||
\(640\) | −5.71405 | −0.225868 | ||||||||
\(641\) | −2.18932 | −0.0864730 | −0.0432365 | − | 0.999065i | \(-0.513767\pi\) | ||||
−0.0432365 | + | 0.999065i | \(0.513767\pi\) | |||||||
\(642\) | 28.0028 | 1.10518 | ||||||||
\(643\) | −43.2781 | −1.70672 | −0.853360 | − | 0.521322i | \(-0.825439\pi\) | ||||
−0.853360 | + | 0.521322i | \(0.825439\pi\) | |||||||
\(644\) | 79.7679 | 3.14330 | ||||||||
\(645\) | 3.21834 | 0.126722 | ||||||||
\(646\) | −1.84673 | −0.0726584 | ||||||||
\(647\) | −49.1548 | −1.93248 | −0.966238 | − | 0.257651i | \(-0.917052\pi\) | ||||
−0.966238 | + | 0.257651i | \(0.917052\pi\) | |||||||
\(648\) | −7.04781 | −0.276864 | ||||||||
\(649\) | −12.7604 | −0.500890 | ||||||||
\(650\) | 22.1996 | 0.870740 | ||||||||
\(651\) | 2.11863 | 0.0830358 | ||||||||
\(652\) | 37.7429 | 1.47812 | ||||||||
\(653\) | −30.1831 | −1.18116 | −0.590579 | − | 0.806980i | \(-0.701101\pi\) | ||||
−0.590579 | + | 0.806980i | \(0.701101\pi\) | |||||||
\(654\) | 14.6419 | 0.572542 | ||||||||
\(655\) | −16.4706 | −0.643560 | ||||||||
\(656\) | −23.9353 | −0.934515 | ||||||||
\(657\) | −7.59790 | −0.296422 | ||||||||
\(658\) | −31.5139 | −1.22854 | ||||||||
\(659\) | 35.8803 | 1.39770 | 0.698850 | − | 0.715269i | \(-0.253696\pi\) | ||||
0.698850 | + | 0.715269i | \(0.253696\pi\) | |||||||
\(660\) | −35.6814 | −1.38890 | ||||||||
\(661\) | −20.3966 | −0.793336 | −0.396668 | − | 0.917962i | \(-0.629834\pi\) | ||||
−0.396668 | + | 0.917962i | \(0.629834\pi\) | |||||||
\(662\) | −57.5213 | −2.23563 | ||||||||
\(663\) | 3.16136 | 0.122777 | ||||||||
\(664\) | −24.8508 | −0.964396 | ||||||||
\(665\) | −1.54157 | −0.0597797 | ||||||||
\(666\) | −15.8865 | −0.615589 | ||||||||
\(667\) | −74.3058 | −2.87713 | ||||||||
\(668\) | −92.5900 | −3.58242 | ||||||||
\(669\) | −13.2540 | −0.512429 | ||||||||
\(670\) | 11.1214 | 0.429658 | ||||||||
\(671\) | −74.3539 | −2.87040 | ||||||||
\(672\) | −16.9265 | −0.652955 | ||||||||
\(673\) | 6.20553 | 0.239205 | 0.119603 | − | 0.992822i | \(-0.461838\pi\) | ||||
0.119603 | + | 0.992822i | \(0.461838\pi\) | |||||||
\(674\) | −12.3807 | −0.476886 | ||||||||
\(675\) | 3.21737 | 0.123837 | ||||||||
\(676\) | −27.9091 | −1.07343 | ||||||||
\(677\) | −20.9317 | −0.804471 | −0.402235 | − | 0.915536i | \(-0.631767\pi\) | ||||
−0.402235 | + | 0.915536i | \(0.631767\pi\) | |||||||
\(678\) | 20.4132 | 0.783966 | ||||||||
\(679\) | 26.6615 | 1.02317 | ||||||||
\(680\) | −11.1755 | −0.428560 | ||||||||
\(681\) | 10.7444 | 0.411725 | ||||||||
\(682\) | 16.1588 | 0.618751 | ||||||||
\(683\) | −23.4911 | −0.898863 | −0.449431 | − | 0.893315i | \(-0.648373\pi\) | ||||
−0.449431 | + | 0.893315i | \(0.648373\pi\) | |||||||
\(684\) | −2.83085 | −0.108240 | ||||||||
\(685\) | −18.4007 | −0.703056 | ||||||||
\(686\) | −51.3645 | −1.96110 | ||||||||
\(687\) | −17.4234 | −0.664746 | ||||||||
\(688\) | 21.2861 | 0.811524 | ||||||||
\(689\) | 21.5553 | 0.821192 | ||||||||
\(690\) | 30.3949 | 1.15711 | ||||||||
\(691\) | 47.6607 | 1.81310 | 0.906550 | − | 0.422099i | \(-0.138707\pi\) | ||||
0.906550 | + | 0.422099i | \(0.138707\pi\) | |||||||
\(692\) | −61.0968 | −2.32255 | ||||||||
\(693\) | 10.9000 | 0.414058 | ||||||||
\(694\) | −58.0034 | −2.20178 | ||||||||
\(695\) | −13.2140 | −0.501237 | ||||||||
\(696\) | 59.6292 | 2.26024 | ||||||||
\(697\) | 3.21902 | 0.121929 | ||||||||
\(698\) | −81.8271 | −3.09720 | ||||||||
\(699\) | 2.61855 | 0.0990428 | ||||||||
\(700\) | 29.2220 | 1.10449 | ||||||||
\(701\) | 19.5223 | 0.737348 | 0.368674 | − | 0.929559i | \(-0.379812\pi\) | ||||
0.368674 | + | 0.929559i | \(0.379812\pi\) | |||||||
\(702\) | 6.89992 | 0.260421 | ||||||||
\(703\) | −3.67661 | −0.138666 | ||||||||
\(704\) | −29.0777 | −1.09591 | ||||||||
\(705\) | −8.43372 | −0.317632 | ||||||||
\(706\) | 3.70449 | 0.139420 | ||||||||
\(707\) | −2.29391 | −0.0862712 | ||||||||
\(708\) | −10.6328 | −0.399605 | ||||||||
\(709\) | −22.8553 | −0.858350 | −0.429175 | − | 0.903221i | \(-0.641196\pi\) | ||||
−0.429175 | + | 0.903221i | \(0.641196\pi\) | |||||||
\(710\) | −47.6556 | −1.78848 | ||||||||
\(711\) | 8.17323 | 0.306520 | ||||||||
\(712\) | −100.278 | −3.75806 | ||||||||
\(713\) | −9.66744 | −0.362048 | ||||||||
\(714\) | 5.92509 | 0.221741 | ||||||||
\(715\) | 20.1274 | 0.752723 | ||||||||
\(716\) | −95.1184 | −3.55474 | ||||||||
\(717\) | −9.90679 | −0.369976 | ||||||||
\(718\) | 7.24658 | 0.270440 | ||||||||
\(719\) | 6.89158 | 0.257013 | 0.128506 | − | 0.991709i | \(-0.458982\pi\) | ||||
0.128506 | + | 0.991709i | \(0.458982\pi\) | |||||||
\(720\) | −11.7903 | −0.439399 | ||||||||
\(721\) | −12.3286 | −0.459141 | ||||||||
\(722\) | 48.3170 | 1.79817 | ||||||||
\(723\) | −15.2624 | −0.567614 | ||||||||
\(724\) | 18.2495 | 0.678238 | ||||||||
\(725\) | −27.2211 | −1.01096 | ||||||||
\(726\) | 54.6212 | 2.02718 | ||||||||
\(727\) | −32.8801 | −1.21945 | −0.609727 | − | 0.792611i | \(-0.708721\pi\) | ||||
−0.609727 | + | 0.792611i | \(0.708721\pi\) | |||||||
\(728\) | 36.1086 | 1.33827 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −26.2951 | −0.973227 | ||||||||
\(731\) | −2.86274 | −0.105882 | ||||||||
\(732\) | −61.9564 | −2.28997 | ||||||||
\(733\) | 18.1015 | 0.668595 | 0.334297 | − | 0.942468i | \(-0.391501\pi\) | ||||
0.334297 | + | 0.942468i | \(0.391501\pi\) | |||||||
\(734\) | 4.47446 | 0.165156 | ||||||||
\(735\) | −4.40003 | −0.162298 | ||||||||
\(736\) | 77.2366 | 2.84698 | ||||||||
\(737\) | −18.1988 | −0.670362 | ||||||||
\(738\) | 7.02578 | 0.258623 | ||||||||
\(739\) | 40.1371 | 1.47647 | 0.738234 | − | 0.674545i | \(-0.235660\pi\) | ||||
0.738234 | + | 0.674545i | \(0.235660\pi\) | |||||||
\(740\) | −38.6148 | −1.41951 | ||||||||
\(741\) | 1.59685 | 0.0586617 | ||||||||
\(742\) | 40.3994 | 1.48311 | ||||||||
\(743\) | −0.331346 | −0.0121559 | −0.00607795 | − | 0.999982i | \(-0.501935\pi\) | ||||
−0.00607795 | + | 0.999982i | \(0.501935\pi\) | |||||||
\(744\) | 7.75795 | 0.284420 | ||||||||
\(745\) | −5.42376 | −0.198711 | ||||||||
\(746\) | −62.4730 | −2.28730 | ||||||||
\(747\) | 3.52602 | 0.129010 | ||||||||
\(748\) | 31.7389 | 1.16049 | ||||||||
\(749\) | −20.7928 | −0.759754 | ||||||||
\(750\) | 28.4390 | 1.03845 | ||||||||
\(751\) | 41.8168 | 1.52592 | 0.762958 | − | 0.646448i | \(-0.223746\pi\) | ||||
0.762958 | + | 0.646448i | \(0.223746\pi\) | |||||||
\(752\) | −55.7806 | −2.03411 | ||||||||
\(753\) | 5.81591 | 0.211944 | ||||||||
\(754\) | −58.3779 | −2.12600 | ||||||||
\(755\) | −2.91847 | −0.106214 | ||||||||
\(756\) | 9.08259 | 0.330331 | ||||||||
\(757\) | −13.5037 | −0.490799 | −0.245399 | − | 0.969422i | \(-0.578919\pi\) | ||||
−0.245399 | + | 0.969422i | \(0.578919\pi\) | |||||||
\(758\) | 3.69872 | 0.134344 | ||||||||
\(759\) | −49.7374 | −1.80535 | ||||||||
\(760\) | −5.64489 | −0.204762 | ||||||||
\(761\) | −19.7797 | −0.717015 | −0.358508 | − | 0.933527i | \(-0.616714\pi\) | ||||
−0.358508 | + | 0.933527i | \(0.616714\pi\) | |||||||
\(762\) | −46.4020 | −1.68097 | ||||||||
\(763\) | −10.8720 | −0.393592 | ||||||||
\(764\) | −100.926 | −3.65138 | ||||||||
\(765\) | 1.58566 | 0.0573298 | ||||||||
\(766\) | −18.9575 | −0.684964 | ||||||||
\(767\) | 5.99782 | 0.216569 | ||||||||
\(768\) | 21.3623 | 0.770847 | ||||||||
\(769\) | −40.6590 | −1.46620 | −0.733100 | − | 0.680121i | \(-0.761927\pi\) | ||||
−0.733100 | + | 0.680121i | \(0.761927\pi\) | |||||||
\(770\) | 37.7233 | 1.35945 | ||||||||
\(771\) | −1.02291 | −0.0368391 | ||||||||
\(772\) | −64.0899 | −2.30665 | ||||||||
\(773\) | −39.5324 | −1.42188 | −0.710941 | − | 0.703252i | \(-0.751731\pi\) | ||||
−0.710941 | + | 0.703252i | \(0.751731\pi\) | |||||||
\(774\) | −6.24816 | −0.224586 | ||||||||
\(775\) | −3.54155 | −0.127216 | ||||||||
\(776\) | 97.6283 | 3.50465 | ||||||||
\(777\) | 11.7961 | 0.423184 | ||||||||
\(778\) | −78.6648 | −2.82027 | ||||||||
\(779\) | 1.62598 | 0.0582566 | ||||||||
\(780\) | 16.7714 | 0.600514 | ||||||||
\(781\) | 77.9823 | 2.79043 | ||||||||
\(782\) | −27.0365 | −0.966823 | ||||||||
\(783\) | −8.46066 | −0.302359 | ||||||||
\(784\) | −29.1018 | −1.03935 | ||||||||
\(785\) | 9.48617 | 0.338576 | ||||||||
\(786\) | 31.9764 | 1.14056 | ||||||||
\(787\) | −0.223829 | −0.00797863 | −0.00398932 | − | 0.999992i | \(-0.501270\pi\) | ||||
−0.00398932 | + | 0.999992i | \(0.501270\pi\) | |||||||
\(788\) | −31.5529 | −1.12402 | ||||||||
\(789\) | −18.3259 | −0.652420 | ||||||||
\(790\) | 28.2863 | 1.00638 | ||||||||
\(791\) | −15.1574 | −0.538934 | ||||||||
\(792\) | 39.9134 | 1.41826 | ||||||||
\(793\) | 34.9488 | 1.24107 | ||||||||
\(794\) | 41.4748 | 1.47189 | ||||||||
\(795\) | 10.8116 | 0.383450 | ||||||||
\(796\) | 34.8502 | 1.23523 | ||||||||
\(797\) | −6.98307 | −0.247353 | −0.123677 | − | 0.992323i | \(-0.539469\pi\) | ||||
−0.123677 | + | 0.992323i | \(0.539469\pi\) | |||||||
\(798\) | 2.99285 | 0.105946 | ||||||||
\(799\) | 7.50186 | 0.265397 | ||||||||
\(800\) | 28.2947 | 1.00037 | ||||||||
\(801\) | 14.2282 | 0.502728 | ||||||||
\(802\) | −34.5396 | −1.21963 | ||||||||
\(803\) | 43.0287 | 1.51845 | ||||||||
\(804\) | −15.1644 | −0.534807 | ||||||||
\(805\) | −22.5690 | −0.795453 | ||||||||
\(806\) | −7.59516 | −0.267528 | ||||||||
\(807\) | 1.16220 | 0.0409114 | ||||||||
\(808\) | −8.39976 | −0.295503 | ||||||||
\(809\) | −16.7969 | −0.590546 | −0.295273 | − | 0.955413i | \(-0.595411\pi\) | ||||
−0.295273 | + | 0.955413i | \(0.595411\pi\) | |||||||
\(810\) | 3.46084 | 0.121602 | ||||||||
\(811\) | −26.3047 | −0.923681 | −0.461841 | − | 0.886963i | \(-0.652811\pi\) | ||||
−0.461841 | + | 0.886963i | \(0.652811\pi\) | |||||||
\(812\) | −76.8447 | −2.69672 | ||||||||
\(813\) | 7.72761 | 0.271019 | ||||||||
\(814\) | 89.9689 | 3.15341 | ||||||||
\(815\) | −10.6787 | −0.374059 | ||||||||
\(816\) | 10.4876 | 0.367139 | ||||||||
\(817\) | −1.44601 | −0.0505895 | ||||||||
\(818\) | 37.3096 | 1.30450 | ||||||||
\(819\) | −5.12338 | −0.179025 | ||||||||
\(820\) | 17.0774 | 0.596367 | ||||||||
\(821\) | −6.57305 | −0.229401 | −0.114701 | − | 0.993400i | \(-0.536591\pi\) | ||||
−0.114701 | + | 0.993400i | \(0.536591\pi\) | |||||||
\(822\) | 35.7237 | 1.24601 | ||||||||
\(823\) | −28.5342 | −0.994638 | −0.497319 | − | 0.867568i | \(-0.665682\pi\) | ||||
−0.497319 | + | 0.867568i | \(0.665682\pi\) | |||||||
\(824\) | −45.1445 | −1.57268 | ||||||||
\(825\) | −18.2207 | −0.634364 | ||||||||
\(826\) | 11.2412 | 0.391133 | ||||||||
\(827\) | −5.47525 | −0.190393 | −0.0951965 | − | 0.995458i | \(-0.530348\pi\) | ||||
−0.0951965 | + | 0.995458i | \(0.530348\pi\) | |||||||
\(828\) | −41.4443 | −1.44029 | ||||||||
\(829\) | 6.60113 | 0.229267 | 0.114633 | − | 0.993408i | \(-0.463431\pi\) | ||||
0.114633 | + | 0.993408i | \(0.463431\pi\) | |||||||
\(830\) | 12.2030 | 0.423573 | ||||||||
\(831\) | 7.53433 | 0.261363 | ||||||||
\(832\) | 13.6675 | 0.473835 | ||||||||
\(833\) | 3.91387 | 0.135607 | ||||||||
\(834\) | 25.6541 | 0.888328 | ||||||||
\(835\) | 26.1968 | 0.906578 | ||||||||
\(836\) | 16.0318 | 0.554471 | ||||||||
\(837\) | −1.10076 | −0.0380478 | ||||||||
\(838\) | −87.4232 | −3.01999 | ||||||||
\(839\) | −30.9677 | −1.06912 | −0.534562 | − | 0.845129i | \(-0.679524\pi\) | ||||
−0.534562 | + | 0.845129i | \(0.679524\pi\) | |||||||
\(840\) | 18.1112 | 0.624897 | ||||||||
\(841\) | 42.5827 | 1.46837 | ||||||||
\(842\) | 87.8230 | 3.02658 | ||||||||
\(843\) | −22.6337 | −0.779544 | ||||||||
\(844\) | −5.33420 | −0.183611 | ||||||||
\(845\) | 7.89641 | 0.271645 | ||||||||
\(846\) | 16.3734 | 0.562930 | ||||||||
\(847\) | −40.5577 | −1.39358 | ||||||||
\(848\) | 71.5082 | 2.45560 | ||||||||
\(849\) | −13.0683 | −0.448502 | ||||||||
\(850\) | −9.90450 | −0.339722 | ||||||||
\(851\) | −53.8264 | −1.84514 | ||||||||
\(852\) | 64.9798 | 2.22617 | ||||||||
\(853\) | 28.3716 | 0.971425 | 0.485713 | − | 0.874119i | \(-0.338560\pi\) | ||||
0.485713 | + | 0.874119i | \(0.338560\pi\) | |||||||
\(854\) | 65.5019 | 2.24143 | ||||||||
\(855\) | 0.800942 | 0.0273916 | ||||||||
\(856\) | −76.1386 | −2.60237 | ||||||||
\(857\) | 16.2830 | 0.556217 | 0.278108 | − | 0.960550i | \(-0.410293\pi\) | ||||
0.278108 | + | 0.960550i | \(0.410293\pi\) | |||||||
\(858\) | −39.0759 | −1.33403 | ||||||||
\(859\) | 10.8126 | 0.368922 | 0.184461 | − | 0.982840i | \(-0.440946\pi\) | ||||
0.184461 | + | 0.982840i | \(0.440946\pi\) | |||||||
\(860\) | −15.1872 | −0.517880 | ||||||||
\(861\) | −5.21683 | −0.177789 | ||||||||
\(862\) | 81.0667 | 2.76114 | ||||||||
\(863\) | 5.45175 | 0.185580 | 0.0927899 | − | 0.995686i | \(-0.470422\pi\) | ||||
0.0927899 | + | 0.995686i | \(0.470422\pi\) | |||||||
\(864\) | 8.79437 | 0.299190 | ||||||||
\(865\) | 17.2863 | 0.587752 | ||||||||
\(866\) | −29.4856 | −1.00196 | ||||||||
\(867\) | 15.5895 | 0.529448 | ||||||||
\(868\) | −9.99775 | −0.339346 | ||||||||
\(869\) | −46.2869 | −1.57018 | ||||||||
\(870\) | −29.2810 | −0.992719 | ||||||||
\(871\) | 8.55405 | 0.289843 | ||||||||
\(872\) | −39.8107 | −1.34816 | ||||||||
\(873\) | −13.8523 | −0.468829 | ||||||||
\(874\) | −13.6565 | −0.461939 | ||||||||
\(875\) | −21.1167 | −0.713876 | ||||||||
\(876\) | 35.8542 | 1.21140 | ||||||||
\(877\) | 12.5455 | 0.423633 | 0.211816 | − | 0.977310i | \(-0.432062\pi\) | ||||
0.211816 | + | 0.977310i | \(0.432062\pi\) | |||||||
\(878\) | −9.67366 | −0.326470 | ||||||||
\(879\) | −9.23361 | −0.311442 | ||||||||
\(880\) | 66.7713 | 2.25086 | ||||||||
\(881\) | −52.6564 | −1.77404 | −0.887019 | − | 0.461732i | \(-0.847228\pi\) | ||||
−0.887019 | + | 0.461732i | \(0.847228\pi\) | |||||||
\(882\) | 8.54233 | 0.287635 | ||||||||
\(883\) | −26.0560 | −0.876856 | −0.438428 | − | 0.898766i | \(-0.644464\pi\) | ||||
−0.438428 | + | 0.898766i | \(0.644464\pi\) | |||||||
\(884\) | −14.9183 | −0.501758 | ||||||||
\(885\) | 3.00837 | 0.101125 | ||||||||
\(886\) | −52.3532 | −1.75884 | ||||||||
\(887\) | 25.6479 | 0.861172 | 0.430586 | − | 0.902550i | \(-0.358307\pi\) | ||||
0.430586 | + | 0.902550i | \(0.358307\pi\) | |||||||
\(888\) | 43.1948 | 1.44952 | ||||||||
\(889\) | 34.4547 | 1.15557 | ||||||||
\(890\) | 49.2415 | 1.65058 | ||||||||
\(891\) | −5.66323 | −0.189725 | ||||||||
\(892\) | 62.5451 | 2.09416 | ||||||||
\(893\) | 3.78930 | 0.126804 | ||||||||
\(894\) | 10.5298 | 0.352170 | ||||||||
\(895\) | 26.9122 | 0.899574 | ||||||||
\(896\) | −8.23714 | −0.275184 | ||||||||
\(897\) | 23.3782 | 0.780577 | ||||||||
\(898\) | 30.6873 | 1.02405 | ||||||||
\(899\) | 9.31316 | 0.310611 | ||||||||
\(900\) | −15.1826 | −0.506088 | ||||||||
\(901\) | −9.61705 | −0.320390 | ||||||||
\(902\) | −39.7886 | −1.32482 | ||||||||
\(903\) | 4.63942 | 0.154390 | ||||||||
\(904\) | −55.5029 | −1.84600 | ||||||||
\(905\) | −5.16340 | −0.171637 | ||||||||
\(906\) | 5.66599 | 0.188240 | ||||||||
\(907\) | −35.9104 | −1.19238 | −0.596192 | − | 0.802842i | \(-0.703320\pi\) | ||||
−0.596192 | + | 0.802842i | \(0.703320\pi\) | |||||||
\(908\) | −50.7023 | −1.68261 | ||||||||
\(909\) | 1.19183 | 0.0395303 | ||||||||
\(910\) | −17.7312 | −0.587784 | ||||||||
\(911\) | −3.39735 | −0.112559 | −0.0562796 | − | 0.998415i | \(-0.517924\pi\) | ||||
−0.0562796 | + | 0.998415i | \(0.517924\pi\) | |||||||
\(912\) | 5.29743 | 0.175415 | ||||||||
\(913\) | −19.9687 | −0.660867 | ||||||||
\(914\) | −29.4759 | −0.974977 | ||||||||
\(915\) | 17.5295 | 0.579508 | ||||||||
\(916\) | 82.2206 | 2.71664 | ||||||||
\(917\) | −23.7433 | −0.784074 | ||||||||
\(918\) | −3.07845 | −0.101604 | ||||||||
\(919\) | 23.3113 | 0.768969 | 0.384484 | − | 0.923131i | \(-0.374379\pi\) | ||||
0.384484 | + | 0.923131i | \(0.374379\pi\) | |||||||
\(920\) | −82.6426 | −2.72465 | ||||||||
\(921\) | 24.6556 | 0.812429 | ||||||||
\(922\) | 8.03282 | 0.264547 | ||||||||
\(923\) | −36.6543 | −1.20649 | ||||||||
\(924\) | −51.4368 | −1.69215 | ||||||||
\(925\) | −19.7187 | −0.648346 | ||||||||
\(926\) | 47.3777 | 1.55693 | ||||||||
\(927\) | 6.40546 | 0.210383 | ||||||||
\(928\) | −74.4061 | −2.44250 | ||||||||
\(929\) | −9.14513 | −0.300042 | −0.150021 | − | 0.988683i | \(-0.547934\pi\) | ||||
−0.150021 | + | 0.988683i | \(0.547934\pi\) | |||||||
\(930\) | −3.80956 | −0.124920 | ||||||||
\(931\) | 1.97695 | 0.0647919 | ||||||||
\(932\) | −12.3569 | −0.404762 | ||||||||
\(933\) | −4.54260 | −0.148718 | ||||||||
\(934\) | 85.4929 | 2.79741 | ||||||||
\(935\) | −8.97999 | −0.293677 | ||||||||
\(936\) | −18.7606 | −0.613211 | ||||||||
\(937\) | −36.3446 | −1.18733 | −0.593663 | − | 0.804714i | \(-0.702319\pi\) | ||||
−0.593663 | + | 0.804714i | \(0.702319\pi\) | |||||||
\(938\) | 16.0322 | 0.523470 | ||||||||
\(939\) | −8.84780 | −0.288737 | ||||||||
\(940\) | 39.7984 | 1.29808 | ||||||||
\(941\) | −53.1095 | −1.73132 | −0.865660 | − | 0.500633i | \(-0.833101\pi\) | ||||
−0.865660 | + | 0.500633i | \(0.833101\pi\) | |||||||
\(942\) | −18.4167 | −0.600048 | ||||||||
\(943\) | 23.8047 | 0.775186 | ||||||||
\(944\) | 19.8973 | 0.647603 | ||||||||
\(945\) | −2.56977 | −0.0835945 | ||||||||
\(946\) | 35.3848 | 1.15046 | ||||||||
\(947\) | 10.0793 | 0.327533 | 0.163766 | − | 0.986499i | \(-0.447636\pi\) | ||||
0.163766 | + | 0.986499i | \(0.447636\pi\) | |||||||
\(948\) | −38.5692 | −1.25267 | ||||||||
\(949\) | −20.2249 | −0.656529 | ||||||||
\(950\) | −5.00291 | −0.162316 | ||||||||
\(951\) | 13.6484 | 0.442580 | ||||||||
\(952\) | −16.1101 | −0.522131 | ||||||||
\(953\) | 34.6734 | 1.12318 | 0.561590 | − | 0.827415i | \(-0.310190\pi\) | ||||
0.561590 | + | 0.827415i | \(0.310190\pi\) | |||||||
\(954\) | −20.9900 | −0.679576 | ||||||||
\(955\) | 28.5553 | 0.924029 | ||||||||
\(956\) | 46.7498 | 1.51200 | ||||||||
\(957\) | 47.9147 | 1.54886 | ||||||||
\(958\) | −49.1193 | −1.58697 | ||||||||
\(959\) | −26.5258 | −0.856561 | ||||||||
\(960\) | 6.85529 | 0.221254 | ||||||||
\(961\) | −29.7883 | −0.960914 | ||||||||
\(962\) | −42.2884 | −1.36343 | ||||||||
\(963\) | 10.8032 | 0.348127 | ||||||||
\(964\) | 72.0227 | 2.31969 | ||||||||
\(965\) | 18.1332 | 0.583728 | ||||||||
\(966\) | 43.8160 | 1.40976 | ||||||||
\(967\) | −52.4429 | −1.68645 | −0.843225 | − | 0.537560i | \(-0.819346\pi\) | ||||
−0.843225 | + | 0.537560i | \(0.819346\pi\) | |||||||
\(968\) | −148.513 | −4.77339 | ||||||||
\(969\) | −0.712445 | −0.0228870 | ||||||||
\(970\) | −47.9406 | −1.53928 | ||||||||
\(971\) | 59.5008 | 1.90947 | 0.954736 | − | 0.297454i | \(-0.0961376\pi\) | ||||
0.954736 | + | 0.297454i | \(0.0961376\pi\) | |||||||
\(972\) | −4.71896 | −0.151361 | ||||||||
\(973\) | −19.0488 | −0.610677 | ||||||||
\(974\) | −16.8471 | −0.539817 | ||||||||
\(975\) | 8.56434 | 0.274278 | ||||||||
\(976\) | 115.940 | 3.71116 | ||||||||
\(977\) | 44.8184 | 1.43387 | 0.716934 | − | 0.697141i | \(-0.245545\pi\) | ||||
0.716934 | + | 0.697141i | \(0.245545\pi\) | |||||||
\(978\) | 20.7319 | 0.662934 | ||||||||
\(979\) | −80.5775 | −2.57527 | ||||||||
\(980\) | 20.7636 | 0.663269 | ||||||||
\(981\) | 5.64865 | 0.180348 | ||||||||
\(982\) | −63.5061 | −2.02656 | ||||||||
\(983\) | −33.0377 | −1.05374 | −0.526869 | − | 0.849946i | \(-0.676634\pi\) | ||||
−0.526869 | + | 0.849946i | \(0.676634\pi\) | |||||||
\(984\) | −19.1028 | −0.608976 | ||||||||
\(985\) | 8.92736 | 0.284449 | ||||||||
\(986\) | 26.0457 | 0.829464 | ||||||||
\(987\) | −12.1577 | −0.386984 | ||||||||
\(988\) | −7.53547 | −0.239735 | ||||||||
\(989\) | −21.1699 | −0.673165 | ||||||||
\(990\) | −19.5996 | −0.622915 | ||||||||
\(991\) | 5.63576 | 0.179026 | 0.0895128 | − | 0.995986i | \(-0.471469\pi\) | ||||
0.0895128 | + | 0.995986i | \(0.471469\pi\) | |||||||
\(992\) | −9.68049 | −0.307356 | ||||||||
\(993\) | −22.1910 | −0.704211 | ||||||||
\(994\) | −68.6983 | −2.17898 | ||||||||
\(995\) | −9.86029 | −0.312592 | ||||||||
\(996\) | −16.6392 | −0.527232 | ||||||||
\(997\) | 29.1755 | 0.923997 | 0.461998 | − | 0.886881i | \(-0.347133\pi\) | ||||
0.461998 | + | 0.886881i | \(0.347133\pi\) | |||||||
\(998\) | 14.1719 | 0.448603 | ||||||||
\(999\) | −6.12882 | −0.193907 |
(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 | 8013.2.a.c.1.8 | ✓ | 116 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8013.2.a.c.1.8 | ✓ | 116 | 1.1 | even | 1 | trivial |