Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4033,2,Mod(1,4033)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4033, 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("4033.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4033 = 37 \cdot 109 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4033.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(32.2036671352\) |
Analytic rank: | \(0\) |
Dimension: | \(85\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 4033.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.76864 | −1.95773 | −0.978864 | − | 0.204514i | \(-0.934439\pi\) | ||||
−0.978864 | + | 0.204514i | \(0.934439\pi\) | |||||||
\(3\) | 3.12213 | 1.80256 | 0.901282 | − | 0.433233i | \(-0.142627\pi\) | ||||
0.901282 | + | 0.433233i | \(0.142627\pi\) | |||||||
\(4\) | 5.66539 | 2.83270 | ||||||||
\(5\) | −1.61337 | −0.721520 | −0.360760 | − | 0.932659i | \(-0.617483\pi\) | ||||
−0.360760 | + | 0.932659i | \(0.617483\pi\) | |||||||
\(6\) | −8.64407 | −3.52893 | ||||||||
\(7\) | −3.34335 | −1.26367 | −0.631833 | − | 0.775105i | \(-0.717697\pi\) | ||||
−0.631833 | + | 0.775105i | \(0.717697\pi\) | |||||||
\(8\) | −10.1482 | −3.58792 | ||||||||
\(9\) | 6.74771 | 2.24924 | ||||||||
\(10\) | 4.46684 | 1.41254 | ||||||||
\(11\) | 3.88769 | 1.17218 | 0.586092 | − | 0.810245i | \(-0.300666\pi\) | ||||
0.586092 | + | 0.810245i | \(0.300666\pi\) | |||||||
\(12\) | 17.6881 | 5.10611 | ||||||||
\(13\) | 3.80642 | 1.05571 | 0.527855 | − | 0.849334i | \(-0.322996\pi\) | ||||
0.527855 | + | 0.849334i | \(0.322996\pi\) | |||||||
\(14\) | 9.25654 | 2.47391 | ||||||||
\(15\) | −5.03714 | −1.30058 | ||||||||
\(16\) | 16.7659 | 4.19147 | ||||||||
\(17\) | 1.84146 | 0.446619 | 0.223309 | − | 0.974748i | \(-0.428314\pi\) | ||||
0.223309 | + | 0.974748i | \(0.428314\pi\) | |||||||
\(18\) | −18.6820 | −4.40339 | ||||||||
\(19\) | −6.95397 | −1.59535 | −0.797676 | − | 0.603087i | \(-0.793937\pi\) | ||||
−0.797676 | + | 0.603087i | \(0.793937\pi\) | |||||||
\(20\) | −9.14036 | −2.04385 | ||||||||
\(21\) | −10.4384 | −2.27784 | ||||||||
\(22\) | −10.7636 | −2.29482 | ||||||||
\(23\) | 4.09671 | 0.854223 | 0.427112 | − | 0.904199i | \(-0.359531\pi\) | ||||
0.427112 | + | 0.904199i | \(0.359531\pi\) | |||||||
\(24\) | −31.6839 | −6.46745 | ||||||||
\(25\) | −2.39705 | −0.479409 | ||||||||
\(26\) | −10.5386 | −2.06679 | ||||||||
\(27\) | 11.7008 | 2.25183 | ||||||||
\(28\) | −18.9414 | −3.57958 | ||||||||
\(29\) | 3.22497 | 0.598861 | 0.299431 | − | 0.954118i | \(-0.403203\pi\) | ||||
0.299431 | + | 0.954118i | \(0.403203\pi\) | |||||||
\(30\) | 13.9461 | 2.54619 | ||||||||
\(31\) | 1.83556 | 0.329676 | 0.164838 | − | 0.986321i | \(-0.447290\pi\) | ||||
0.164838 | + | 0.986321i | \(0.447290\pi\) | |||||||
\(32\) | −26.1224 | −4.61784 | ||||||||
\(33\) | 12.1379 | 2.11293 | ||||||||
\(34\) | −5.09834 | −0.874357 | ||||||||
\(35\) | 5.39404 | 0.911760 | ||||||||
\(36\) | 38.2284 | 6.37140 | ||||||||
\(37\) | 1.00000 | 0.164399 | ||||||||
\(38\) | 19.2531 | 3.12326 | ||||||||
\(39\) | 11.8841 | 1.90298 | ||||||||
\(40\) | 16.3727 | 2.58875 | ||||||||
\(41\) | −2.86442 | −0.447347 | −0.223673 | − | 0.974664i | \(-0.571805\pi\) | ||||
−0.223673 | + | 0.974664i | \(0.571805\pi\) | |||||||
\(42\) | 28.9001 | 4.45939 | ||||||||
\(43\) | −1.93334 | −0.294831 | −0.147416 | − | 0.989075i | \(-0.547095\pi\) | ||||
−0.147416 | + | 0.989075i | \(0.547095\pi\) | |||||||
\(44\) | 22.0253 | 3.32044 | ||||||||
\(45\) | −10.8865 | −1.62287 | ||||||||
\(46\) | −11.3423 | −1.67234 | ||||||||
\(47\) | 7.27647 | 1.06138 | 0.530691 | − | 0.847565i | \(-0.321932\pi\) | ||||
0.530691 | + | 0.847565i | \(0.321932\pi\) | |||||||
\(48\) | 52.3453 | 7.55539 | ||||||||
\(49\) | 4.17796 | 0.596852 | ||||||||
\(50\) | 6.63657 | 0.938553 | ||||||||
\(51\) | 5.74927 | 0.805058 | ||||||||
\(52\) | 21.5648 | 2.99051 | ||||||||
\(53\) | 5.78810 | 0.795057 | 0.397528 | − | 0.917590i | \(-0.369868\pi\) | ||||
0.397528 | + | 0.917590i | \(0.369868\pi\) | |||||||
\(54\) | −32.3954 | −4.40846 | ||||||||
\(55\) | −6.27227 | −0.845753 | ||||||||
\(56\) | 33.9288 | 4.53393 | ||||||||
\(57\) | −21.7112 | −2.87572 | ||||||||
\(58\) | −8.92879 | −1.17241 | ||||||||
\(59\) | −12.5053 | −1.62805 | −0.814023 | − | 0.580832i | \(-0.802727\pi\) | ||||
−0.814023 | + | 0.580832i | \(0.802727\pi\) | |||||||
\(60\) | −28.5374 | −3.68416 | ||||||||
\(61\) | 7.02458 | 0.899405 | 0.449703 | − | 0.893178i | \(-0.351530\pi\) | ||||
0.449703 | + | 0.893178i | \(0.351530\pi\) | |||||||
\(62\) | −5.08200 | −0.645415 | ||||||||
\(63\) | −22.5599 | −2.84228 | ||||||||
\(64\) | 38.7920 | 4.84900 | ||||||||
\(65\) | −6.14115 | −0.761716 | ||||||||
\(66\) | −33.6055 | −4.13655 | ||||||||
\(67\) | 14.0937 | 1.72182 | 0.860909 | − | 0.508759i | \(-0.169896\pi\) | ||||
0.860909 | + | 0.508759i | \(0.169896\pi\) | |||||||
\(68\) | 10.4326 | 1.26513 | ||||||||
\(69\) | 12.7905 | 1.53979 | ||||||||
\(70\) | −14.9342 | −1.78498 | ||||||||
\(71\) | 2.13334 | 0.253181 | 0.126590 | − | 0.991955i | \(-0.459597\pi\) | ||||
0.126590 | + | 0.991955i | \(0.459597\pi\) | |||||||
\(72\) | −68.4769 | −8.07008 | ||||||||
\(73\) | −3.64184 | −0.426245 | −0.213123 | − | 0.977025i | \(-0.568363\pi\) | ||||
−0.213123 | + | 0.977025i | \(0.568363\pi\) | |||||||
\(74\) | −2.76864 | −0.321848 | ||||||||
\(75\) | −7.48390 | −0.864166 | ||||||||
\(76\) | −39.3970 | −4.51915 | ||||||||
\(77\) | −12.9979 | −1.48125 | ||||||||
\(78\) | −32.9029 | −3.72553 | ||||||||
\(79\) | −9.58443 | −1.07833 | −0.539166 | − | 0.842199i | \(-0.681261\pi\) | ||||
−0.539166 | + | 0.842199i | \(0.681261\pi\) | |||||||
\(80\) | −27.0495 | −3.02423 | ||||||||
\(81\) | 16.2884 | 1.80982 | ||||||||
\(82\) | 7.93055 | 0.875783 | ||||||||
\(83\) | 9.85300 | 1.08151 | 0.540754 | − | 0.841181i | \(-0.318139\pi\) | ||||
0.540754 | + | 0.841181i | \(0.318139\pi\) | |||||||
\(84\) | −59.1374 | −6.45242 | ||||||||
\(85\) | −2.97094 | −0.322244 | ||||||||
\(86\) | 5.35272 | 0.577199 | ||||||||
\(87\) | 10.0688 | 1.07949 | ||||||||
\(88\) | −39.4530 | −4.20570 | ||||||||
\(89\) | 14.5544 | 1.54277 | 0.771383 | − | 0.636371i | \(-0.219565\pi\) | ||||
0.771383 | + | 0.636371i | \(0.219565\pi\) | |||||||
\(90\) | 30.1409 | 3.17713 | ||||||||
\(91\) | −12.7262 | −1.33407 | ||||||||
\(92\) | 23.2095 | 2.41976 | ||||||||
\(93\) | 5.73085 | 0.594261 | ||||||||
\(94\) | −20.1460 | −2.07790 | ||||||||
\(95\) | 11.2193 | 1.15108 | ||||||||
\(96\) | −81.5577 | −8.32395 | ||||||||
\(97\) | 2.55129 | 0.259045 | 0.129522 | − | 0.991577i | \(-0.458656\pi\) | ||||
0.129522 | + | 0.991577i | \(0.458656\pi\) | |||||||
\(98\) | −11.5673 | −1.16847 | ||||||||
\(99\) | 26.2330 | 2.63652 | ||||||||
\(100\) | −13.5802 | −1.35802 | ||||||||
\(101\) | 1.73108 | 0.172249 | 0.0861246 | − | 0.996284i | \(-0.472552\pi\) | ||||
0.0861246 | + | 0.996284i | \(0.472552\pi\) | |||||||
\(102\) | −15.9177 | −1.57608 | ||||||||
\(103\) | −14.2240 | −1.40153 | −0.700767 | − | 0.713390i | \(-0.747159\pi\) | ||||
−0.700767 | + | 0.713390i | \(0.747159\pi\) | |||||||
\(104\) | −38.6282 | −3.78780 | ||||||||
\(105\) | 16.8409 | 1.64350 | ||||||||
\(106\) | −16.0252 | −1.55650 | ||||||||
\(107\) | 9.11248 | 0.880937 | 0.440468 | − | 0.897768i | \(-0.354812\pi\) | ||||
0.440468 | + | 0.897768i | \(0.354812\pi\) | |||||||
\(108\) | 66.2898 | 6.37874 | ||||||||
\(109\) | −1.00000 | −0.0957826 | ||||||||
\(110\) | 17.3657 | 1.65575 | ||||||||
\(111\) | 3.12213 | 0.296340 | ||||||||
\(112\) | −56.0542 | −5.29662 | ||||||||
\(113\) | −3.16377 | −0.297622 | −0.148811 | − | 0.988866i | \(-0.547545\pi\) | ||||
−0.148811 | + | 0.988866i | \(0.547545\pi\) | |||||||
\(114\) | 60.1107 | 5.62988 | ||||||||
\(115\) | −6.60950 | −0.616339 | ||||||||
\(116\) | 18.2707 | 1.69639 | ||||||||
\(117\) | 25.6846 | 2.37454 | ||||||||
\(118\) | 34.6226 | 3.18727 | ||||||||
\(119\) | −6.15662 | −0.564377 | ||||||||
\(120\) | 51.1178 | 4.66639 | ||||||||
\(121\) | 4.11415 | 0.374014 | ||||||||
\(122\) | −19.4486 | −1.76079 | ||||||||
\(123\) | −8.94309 | −0.806371 | ||||||||
\(124\) | 10.3991 | 0.933871 | ||||||||
\(125\) | 11.9342 | 1.06742 | ||||||||
\(126\) | 62.4604 | 5.56441 | ||||||||
\(127\) | 14.3425 | 1.27269 | 0.636346 | − | 0.771404i | \(-0.280445\pi\) | ||||
0.636346 | + | 0.771404i | \(0.280445\pi\) | |||||||
\(128\) | −55.1563 | −4.87518 | ||||||||
\(129\) | −6.03613 | −0.531452 | ||||||||
\(130\) | 17.0027 | 1.49123 | ||||||||
\(131\) | −9.83339 | −0.859147 | −0.429574 | − | 0.903032i | \(-0.641336\pi\) | ||||
−0.429574 | + | 0.903032i | \(0.641336\pi\) | |||||||
\(132\) | 68.7659 | 5.98530 | ||||||||
\(133\) | 23.2495 | 2.01599 | ||||||||
\(134\) | −39.0204 | −3.37085 | ||||||||
\(135\) | −18.8777 | −1.62474 | ||||||||
\(136\) | −18.6874 | −1.60243 | ||||||||
\(137\) | −8.50721 | −0.726820 | −0.363410 | − | 0.931629i | \(-0.618388\pi\) | ||||
−0.363410 | + | 0.931629i | \(0.618388\pi\) | |||||||
\(138\) | −35.4123 | −3.01449 | ||||||||
\(139\) | 10.1041 | 0.857019 | 0.428509 | − | 0.903537i | \(-0.359039\pi\) | ||||
0.428509 | + | 0.903537i | \(0.359039\pi\) | |||||||
\(140\) | 30.5594 | 2.58274 | ||||||||
\(141\) | 22.7181 | 1.91321 | ||||||||
\(142\) | −5.90646 | −0.495659 | ||||||||
\(143\) | 14.7982 | 1.23749 | ||||||||
\(144\) | 113.131 | 9.42761 | ||||||||
\(145\) | −5.20306 | −0.432090 | ||||||||
\(146\) | 10.0830 | 0.834472 | ||||||||
\(147\) | 13.0441 | 1.07586 | ||||||||
\(148\) | 5.66539 | 0.465692 | ||||||||
\(149\) | 14.7565 | 1.20890 | 0.604450 | − | 0.796643i | \(-0.293393\pi\) | ||||
0.604450 | + | 0.796643i | \(0.293393\pi\) | |||||||
\(150\) | 20.7203 | 1.69180 | ||||||||
\(151\) | −18.5105 | −1.50636 | −0.753182 | − | 0.657813i | \(-0.771482\pi\) | ||||
−0.753182 | + | 0.657813i | \(0.771482\pi\) | |||||||
\(152\) | 70.5701 | 5.72399 | ||||||||
\(153\) | 12.4256 | 1.00455 | ||||||||
\(154\) | 35.9866 | 2.89988 | ||||||||
\(155\) | −2.96143 | −0.237867 | ||||||||
\(156\) | 67.3283 | 5.39058 | ||||||||
\(157\) | 1.29859 | 0.103639 | 0.0518195 | − | 0.998656i | \(-0.483498\pi\) | ||||
0.0518195 | + | 0.998656i | \(0.483498\pi\) | |||||||
\(158\) | 26.5359 | 2.11108 | ||||||||
\(159\) | 18.0712 | 1.43314 | ||||||||
\(160\) | 42.1451 | 3.33186 | ||||||||
\(161\) | −13.6967 | −1.07945 | ||||||||
\(162\) | −45.0968 | −3.54314 | ||||||||
\(163\) | −10.0122 | −0.784213 | −0.392106 | − | 0.919920i | \(-0.628254\pi\) | ||||
−0.392106 | + | 0.919920i | \(0.628254\pi\) | |||||||
\(164\) | −16.2280 | −1.26720 | ||||||||
\(165\) | −19.5829 | −1.52452 | ||||||||
\(166\) | −27.2795 | −2.11730 | ||||||||
\(167\) | 24.2850 | 1.87923 | 0.939614 | − | 0.342237i | \(-0.111185\pi\) | ||||
0.939614 | + | 0.342237i | \(0.111185\pi\) | |||||||
\(168\) | 105.930 | 8.17270 | ||||||||
\(169\) | 1.48881 | 0.114524 | ||||||||
\(170\) | 8.22549 | 0.630866 | ||||||||
\(171\) | −46.9234 | −3.58832 | ||||||||
\(172\) | −10.9531 | −0.835167 | ||||||||
\(173\) | −25.2346 | −1.91855 | −0.959275 | − | 0.282473i | \(-0.908845\pi\) | ||||
−0.959275 | + | 0.282473i | \(0.908845\pi\) | |||||||
\(174\) | −27.8769 | −2.11334 | ||||||||
\(175\) | 8.01416 | 0.605813 | ||||||||
\(176\) | 65.1806 | 4.91317 | ||||||||
\(177\) | −39.0431 | −2.93466 | ||||||||
\(178\) | −40.2960 | −3.02031 | ||||||||
\(179\) | 23.2089 | 1.73472 | 0.867358 | − | 0.497685i | \(-0.165817\pi\) | ||||
0.867358 | + | 0.497685i | \(0.165817\pi\) | |||||||
\(180\) | −61.6764 | −4.59709 | ||||||||
\(181\) | 12.8021 | 0.951574 | 0.475787 | − | 0.879560i | \(-0.342163\pi\) | ||||
0.475787 | + | 0.879560i | \(0.342163\pi\) | |||||||
\(182\) | 35.2342 | 2.61174 | ||||||||
\(183\) | 21.9317 | 1.62123 | ||||||||
\(184\) | −41.5741 | −3.06488 | ||||||||
\(185\) | −1.61337 | −0.118617 | ||||||||
\(186\) | −15.8667 | −1.16340 | ||||||||
\(187\) | 7.15901 | 0.523519 | ||||||||
\(188\) | 41.2241 | 3.00658 | ||||||||
\(189\) | −39.1199 | −2.84556 | ||||||||
\(190\) | −31.0623 | −2.25350 | ||||||||
\(191\) | 21.2022 | 1.53414 | 0.767068 | − | 0.641566i | \(-0.221715\pi\) | ||||
0.767068 | + | 0.641566i | \(0.221715\pi\) | |||||||
\(192\) | 121.114 | 8.74063 | ||||||||
\(193\) | −8.81889 | −0.634798 | −0.317399 | − | 0.948292i | \(-0.602809\pi\) | ||||
−0.317399 | + | 0.948292i | \(0.602809\pi\) | |||||||
\(194\) | −7.06362 | −0.507139 | ||||||||
\(195\) | −19.1735 | −1.37304 | ||||||||
\(196\) | 23.6698 | 1.69070 | ||||||||
\(197\) | 17.5294 | 1.24892 | 0.624461 | − | 0.781056i | \(-0.285319\pi\) | ||||
0.624461 | + | 0.781056i | \(0.285319\pi\) | |||||||
\(198\) | −72.6299 | −5.16158 | ||||||||
\(199\) | −14.0884 | −0.998697 | −0.499348 | − | 0.866401i | \(-0.666427\pi\) | ||||
−0.499348 | + | 0.866401i | \(0.666427\pi\) | |||||||
\(200\) | 24.3256 | 1.72008 | ||||||||
\(201\) | 44.0023 | 3.10369 | ||||||||
\(202\) | −4.79275 | −0.337217 | ||||||||
\(203\) | −10.7822 | −0.756761 | ||||||||
\(204\) | 32.5718 | 2.28049 | ||||||||
\(205\) | 4.62136 | 0.322769 | ||||||||
\(206\) | 39.3813 | 2.74382 | ||||||||
\(207\) | 27.6434 | 1.92135 | ||||||||
\(208\) | 63.8180 | 4.42498 | ||||||||
\(209\) | −27.0349 | −1.87004 | ||||||||
\(210\) | −46.6265 | −3.21753 | ||||||||
\(211\) | −16.2991 | −1.12208 | −0.561038 | − | 0.827790i | \(-0.689598\pi\) | ||||
−0.561038 | + | 0.827790i | \(0.689598\pi\) | |||||||
\(212\) | 32.7919 | 2.25215 | ||||||||
\(213\) | 6.66057 | 0.456375 | ||||||||
\(214\) | −25.2292 | −1.72463 | ||||||||
\(215\) | 3.11918 | 0.212726 | ||||||||
\(216\) | −118.742 | −8.07937 | ||||||||
\(217\) | −6.13690 | −0.416600 | ||||||||
\(218\) | 2.76864 | 0.187516 | ||||||||
\(219\) | −11.3703 | −0.768335 | ||||||||
\(220\) | −35.5349 | −2.39576 | ||||||||
\(221\) | 7.00935 | 0.471500 | ||||||||
\(222\) | −8.64407 | −0.580152 | ||||||||
\(223\) | 11.5553 | 0.773797 | 0.386899 | − | 0.922122i | \(-0.373546\pi\) | ||||
0.386899 | + | 0.922122i | \(0.373546\pi\) | |||||||
\(224\) | 87.3364 | 5.83541 | ||||||||
\(225\) | −16.1746 | −1.07830 | ||||||||
\(226\) | 8.75934 | 0.582663 | ||||||||
\(227\) | 0.204192 | 0.0135527 | 0.00677635 | − | 0.999977i | \(-0.497843\pi\) | ||||
0.00677635 | + | 0.999977i | \(0.497843\pi\) | |||||||
\(228\) | −123.003 | −8.14605 | ||||||||
\(229\) | 4.75914 | 0.314493 | 0.157246 | − | 0.987559i | \(-0.449738\pi\) | ||||
0.157246 | + | 0.987559i | \(0.449738\pi\) | |||||||
\(230\) | 18.2994 | 1.20662 | ||||||||
\(231\) | −40.5812 | −2.67004 | ||||||||
\(232\) | −32.7275 | −2.14867 | ||||||||
\(233\) | −20.4066 | −1.33688 | −0.668442 | − | 0.743764i | \(-0.733038\pi\) | ||||
−0.668442 | + | 0.743764i | \(0.733038\pi\) | |||||||
\(234\) | −71.1115 | −4.64870 | ||||||||
\(235\) | −11.7396 | −0.765809 | ||||||||
\(236\) | −70.8472 | −4.61176 | ||||||||
\(237\) | −29.9238 | −1.94376 | ||||||||
\(238\) | 17.0455 | 1.10490 | ||||||||
\(239\) | 23.8903 | 1.54534 | 0.772668 | − | 0.634811i | \(-0.218922\pi\) | ||||
0.772668 | + | 0.634811i | \(0.218922\pi\) | |||||||
\(240\) | −84.4522 | −5.45136 | ||||||||
\(241\) | −10.3426 | −0.666224 | −0.333112 | − | 0.942887i | \(-0.608099\pi\) | ||||
−0.333112 | + | 0.942887i | \(0.608099\pi\) | |||||||
\(242\) | −11.3906 | −0.732217 | ||||||||
\(243\) | 15.7521 | 1.01050 | ||||||||
\(244\) | 39.7970 | 2.54774 | ||||||||
\(245\) | −6.74059 | −0.430640 | ||||||||
\(246\) | 24.7602 | 1.57865 | ||||||||
\(247\) | −26.4697 | −1.68423 | ||||||||
\(248\) | −18.6275 | −1.18285 | ||||||||
\(249\) | 30.7624 | 1.94949 | ||||||||
\(250\) | −33.0414 | −2.08972 | ||||||||
\(251\) | 1.75869 | 0.111008 | 0.0555038 | − | 0.998458i | \(-0.482323\pi\) | ||||
0.0555038 | + | 0.998458i | \(0.482323\pi\) | |||||||
\(252\) | −127.811 | −8.05132 | ||||||||
\(253\) | 15.9268 | 1.00131 | ||||||||
\(254\) | −39.7093 | −2.49158 | ||||||||
\(255\) | −9.27568 | −0.580865 | ||||||||
\(256\) | 75.1243 | 4.69527 | ||||||||
\(257\) | 30.8732 | 1.92582 | 0.962908 | − | 0.269828i | \(-0.0869670\pi\) | ||||
0.962908 | + | 0.269828i | \(0.0869670\pi\) | |||||||
\(258\) | 16.7119 | 1.04044 | ||||||||
\(259\) | −3.34335 | −0.207745 | ||||||||
\(260\) | −34.7920 | −2.15771 | ||||||||
\(261\) | 21.7611 | 1.34698 | ||||||||
\(262\) | 27.2252 | 1.68198 | ||||||||
\(263\) | 7.80846 | 0.481491 | 0.240745 | − | 0.970588i | \(-0.422608\pi\) | ||||
0.240745 | + | 0.970588i | \(0.422608\pi\) | |||||||
\(264\) | −123.177 | −7.58104 | ||||||||
\(265\) | −9.33833 | −0.573649 | ||||||||
\(266\) | −64.3697 | −3.94676 | ||||||||
\(267\) | 45.4408 | 2.78093 | ||||||||
\(268\) | 79.8462 | 4.87739 | ||||||||
\(269\) | 11.2276 | 0.684558 | 0.342279 | − | 0.939598i | \(-0.388801\pi\) | ||||
0.342279 | + | 0.939598i | \(0.388801\pi\) | |||||||
\(270\) | 52.2657 | 3.18079 | ||||||||
\(271\) | 0.492152 | 0.0298961 | 0.0149480 | − | 0.999888i | \(-0.495242\pi\) | ||||
0.0149480 | + | 0.999888i | \(0.495242\pi\) | |||||||
\(272\) | 30.8736 | 1.87199 | ||||||||
\(273\) | −39.7328 | −2.40474 | ||||||||
\(274\) | 23.5534 | 1.42291 | ||||||||
\(275\) | −9.31898 | −0.561956 | ||||||||
\(276\) | 72.4630 | 4.36176 | ||||||||
\(277\) | 26.2559 | 1.57757 | 0.788783 | − | 0.614672i | \(-0.210712\pi\) | ||||
0.788783 | + | 0.614672i | \(0.210712\pi\) | |||||||
\(278\) | −27.9747 | −1.67781 | ||||||||
\(279\) | 12.3858 | 0.741518 | ||||||||
\(280\) | −54.7397 | −3.27132 | ||||||||
\(281\) | −18.9457 | −1.13021 | −0.565103 | − | 0.825021i | \(-0.691163\pi\) | ||||
−0.565103 | + | 0.825021i | \(0.691163\pi\) | |||||||
\(282\) | −62.8984 | −3.74554 | ||||||||
\(283\) | 22.5710 | 1.34170 | 0.670852 | − | 0.741591i | \(-0.265928\pi\) | ||||
0.670852 | + | 0.741591i | \(0.265928\pi\) | |||||||
\(284\) | 12.0862 | 0.717185 | ||||||||
\(285\) | 35.0282 | 2.07489 | ||||||||
\(286\) | −40.9709 | −2.42266 | ||||||||
\(287\) | 9.57674 | 0.565297 | ||||||||
\(288\) | −176.267 | −10.3866 | ||||||||
\(289\) | −13.6090 | −0.800532 | ||||||||
\(290\) | 14.4054 | 0.845915 | ||||||||
\(291\) | 7.96547 | 0.466944 | ||||||||
\(292\) | −20.6325 | −1.20742 | ||||||||
\(293\) | 19.5955 | 1.14478 | 0.572392 | − | 0.819980i | \(-0.306016\pi\) | ||||
0.572392 | + | 0.819980i | \(0.306016\pi\) | |||||||
\(294\) | −36.1146 | −2.10625 | ||||||||
\(295\) | 20.1756 | 1.17467 | ||||||||
\(296\) | −10.1482 | −0.589850 | ||||||||
\(297\) | 45.4892 | 2.63955 | ||||||||
\(298\) | −40.8555 | −2.36670 | ||||||||
\(299\) | 15.5938 | 0.901812 | ||||||||
\(300\) | −42.3992 | −2.44792 | ||||||||
\(301\) | 6.46381 | 0.372568 | ||||||||
\(302\) | 51.2490 | 2.94905 | ||||||||
\(303\) | 5.40467 | 0.310490 | ||||||||
\(304\) | −116.590 | −6.68687 | ||||||||
\(305\) | −11.3332 | −0.648938 | ||||||||
\(306\) | −34.4021 | −1.96664 | ||||||||
\(307\) | 33.6617 | 1.92117 | 0.960586 | − | 0.277982i | \(-0.0896657\pi\) | ||||
0.960586 | + | 0.277982i | \(0.0896657\pi\) | |||||||
\(308\) | −73.6382 | −4.19593 | ||||||||
\(309\) | −44.4093 | −2.52635 | ||||||||
\(310\) | 8.19914 | 0.465680 | ||||||||
\(311\) | −0.765802 | −0.0434246 | −0.0217123 | − | 0.999764i | \(-0.506912\pi\) | ||||
−0.0217123 | + | 0.999764i | \(0.506912\pi\) | |||||||
\(312\) | −120.602 | −6.82776 | ||||||||
\(313\) | −8.97560 | −0.507331 | −0.253665 | − | 0.967292i | \(-0.581636\pi\) | ||||
−0.253665 | + | 0.967292i | \(0.581636\pi\) | |||||||
\(314\) | −3.59534 | −0.202897 | ||||||||
\(315\) | 36.3974 | 2.05076 | ||||||||
\(316\) | −54.2995 | −3.05459 | ||||||||
\(317\) | −11.1037 | −0.623645 | −0.311823 | − | 0.950140i | \(-0.600939\pi\) | ||||
−0.311823 | + | 0.950140i | \(0.600939\pi\) | |||||||
\(318\) | −50.0328 | −2.80570 | ||||||||
\(319\) | 12.5377 | 0.701975 | ||||||||
\(320\) | −62.5857 | −3.49865 | ||||||||
\(321\) | 28.4504 | 1.58794 | ||||||||
\(322\) | 37.9214 | 2.11327 | ||||||||
\(323\) | −12.8054 | −0.712513 | ||||||||
\(324\) | 92.2803 | 5.12668 | ||||||||
\(325\) | −9.12416 | −0.506117 | ||||||||
\(326\) | 27.7201 | 1.53527 | ||||||||
\(327\) | −3.12213 | −0.172654 | ||||||||
\(328\) | 29.0686 | 1.60504 | ||||||||
\(329\) | −24.3278 | −1.34123 | ||||||||
\(330\) | 54.2180 | 2.98460 | ||||||||
\(331\) | 18.3752 | 1.00999 | 0.504996 | − | 0.863122i | \(-0.331494\pi\) | ||||
0.504996 | + | 0.863122i | \(0.331494\pi\) | |||||||
\(332\) | 55.8211 | 3.06358 | ||||||||
\(333\) | 6.74771 | 0.369772 | ||||||||
\(334\) | −67.2364 | −3.67901 | ||||||||
\(335\) | −22.7383 | −1.24233 | ||||||||
\(336\) | −175.008 | −9.54749 | ||||||||
\(337\) | 20.6948 | 1.12732 | 0.563658 | − | 0.826008i | \(-0.309394\pi\) | ||||
0.563658 | + | 0.826008i | \(0.309394\pi\) | |||||||
\(338\) | −4.12199 | −0.224207 | ||||||||
\(339\) | −9.87769 | −0.536483 | ||||||||
\(340\) | −16.8316 | −0.912819 | ||||||||
\(341\) | 7.13608 | 0.386440 | ||||||||
\(342\) | 129.914 | 7.02495 | ||||||||
\(343\) | 9.43505 | 0.509445 | ||||||||
\(344\) | 19.6198 | 1.05783 | ||||||||
\(345\) | −20.6357 | −1.11099 | ||||||||
\(346\) | 69.8656 | 3.75600 | ||||||||
\(347\) | −0.106910 | −0.00573921 | −0.00286961 | − | 0.999996i | \(-0.500913\pi\) | ||||
−0.00286961 | + | 0.999996i | \(0.500913\pi\) | |||||||
\(348\) | 57.0436 | 3.05786 | ||||||||
\(349\) | −27.1790 | −1.45486 | −0.727429 | − | 0.686183i | \(-0.759285\pi\) | ||||
−0.727429 | + | 0.686183i | \(0.759285\pi\) | |||||||
\(350\) | −22.1884 | −1.18602 | ||||||||
\(351\) | 44.5382 | 2.37728 | ||||||||
\(352\) | −101.556 | −5.41295 | ||||||||
\(353\) | −30.9054 | −1.64493 | −0.822463 | − | 0.568819i | \(-0.807401\pi\) | ||||
−0.822463 | + | 0.568819i | \(0.807401\pi\) | |||||||
\(354\) | 108.096 | 5.74526 | ||||||||
\(355\) | −3.44186 | −0.182675 | ||||||||
\(356\) | 82.4565 | 4.37019 | ||||||||
\(357\) | −19.2218 | −1.01732 | ||||||||
\(358\) | −64.2572 | −3.39610 | ||||||||
\(359\) | 32.8630 | 1.73444 | 0.867221 | − | 0.497924i | \(-0.165904\pi\) | ||||
0.867221 | + | 0.497924i | \(0.165904\pi\) | |||||||
\(360\) | 110.478 | 5.82272 | ||||||||
\(361\) | 29.3578 | 1.54515 | ||||||||
\(362\) | −35.4445 | −1.86292 | ||||||||
\(363\) | 12.8449 | 0.674184 | ||||||||
\(364\) | −72.0987 | −3.77900 | ||||||||
\(365\) | 5.87563 | 0.307544 | ||||||||
\(366\) | −60.7210 | −3.17394 | ||||||||
\(367\) | −16.4096 | −0.856572 | −0.428286 | − | 0.903643i | \(-0.640882\pi\) | ||||
−0.428286 | + | 0.903643i | \(0.640882\pi\) | |||||||
\(368\) | 68.6850 | 3.58045 | ||||||||
\(369\) | −19.3282 | −1.00619 | ||||||||
\(370\) | 4.46684 | 0.232220 | ||||||||
\(371\) | −19.3516 | −1.00469 | ||||||||
\(372\) | 32.4675 | 1.68336 | ||||||||
\(373\) | −27.6209 | −1.43016 | −0.715079 | − | 0.699043i | \(-0.753609\pi\) | ||||
−0.715079 | + | 0.699043i | \(0.753609\pi\) | |||||||
\(374\) | −19.8208 | −1.02491 | ||||||||
\(375\) | 37.2600 | 1.92410 | ||||||||
\(376\) | −73.8429 | −3.80816 | ||||||||
\(377\) | 12.2756 | 0.632224 | ||||||||
\(378\) | 108.309 | 5.57082 | ||||||||
\(379\) | −11.3449 | −0.582749 | −0.291374 | − | 0.956609i | \(-0.594113\pi\) | ||||
−0.291374 | + | 0.956609i | \(0.594113\pi\) | |||||||
\(380\) | 63.5618 | 3.26065 | ||||||||
\(381\) | 44.7792 | 2.29411 | ||||||||
\(382\) | −58.7013 | −3.00342 | ||||||||
\(383\) | 37.6711 | 1.92490 | 0.962452 | − | 0.271452i | \(-0.0875040\pi\) | ||||
0.962452 | + | 0.271452i | \(0.0875040\pi\) | |||||||
\(384\) | −172.205 | −8.78782 | ||||||||
\(385\) | 20.9704 | 1.06875 | ||||||||
\(386\) | 24.4164 | 1.24276 | ||||||||
\(387\) | −13.0456 | −0.663144 | ||||||||
\(388\) | 14.4541 | 0.733794 | ||||||||
\(389\) | 3.22236 | 0.163380 | 0.0816902 | − | 0.996658i | \(-0.473968\pi\) | ||||
0.0816902 | + | 0.996658i | \(0.473968\pi\) | |||||||
\(390\) | 53.0845 | 2.68804 | ||||||||
\(391\) | 7.54391 | 0.381512 | ||||||||
\(392\) | −42.3987 | −2.14146 | ||||||||
\(393\) | −30.7011 | −1.54867 | ||||||||
\(394\) | −48.5328 | −2.44505 | ||||||||
\(395\) | 15.4632 | 0.778038 | ||||||||
\(396\) | 148.620 | 7.46845 | ||||||||
\(397\) | −3.41350 | −0.171319 | −0.0856594 | − | 0.996324i | \(-0.527300\pi\) | ||||
−0.0856594 | + | 0.996324i | \(0.527300\pi\) | |||||||
\(398\) | 39.0056 | 1.95518 | ||||||||
\(399\) | 72.5881 | 3.63395 | ||||||||
\(400\) | −40.1886 | −2.00943 | ||||||||
\(401\) | −27.5181 | −1.37419 | −0.687095 | − | 0.726568i | \(-0.741114\pi\) | ||||
−0.687095 | + | 0.726568i | \(0.741114\pi\) | |||||||
\(402\) | −121.827 | −6.07617 | ||||||||
\(403\) | 6.98689 | 0.348042 | ||||||||
\(404\) | 9.80726 | 0.487929 | ||||||||
\(405\) | −26.2792 | −1.30582 | ||||||||
\(406\) | 29.8520 | 1.48153 | ||||||||
\(407\) | 3.88769 | 0.192706 | ||||||||
\(408\) | −58.3445 | −2.88848 | ||||||||
\(409\) | 12.6710 | 0.626540 | 0.313270 | − | 0.949664i | \(-0.398575\pi\) | ||||
0.313270 | + | 0.949664i | \(0.398575\pi\) | |||||||
\(410\) | −12.7949 | −0.631895 | ||||||||
\(411\) | −26.5606 | −1.31014 | ||||||||
\(412\) | −80.5847 | −3.97012 | ||||||||
\(413\) | 41.8094 | 2.05731 | ||||||||
\(414\) | −76.5348 | −3.76148 | ||||||||
\(415\) | −15.8965 | −0.780329 | ||||||||
\(416\) | −99.4329 | −4.87510 | ||||||||
\(417\) | 31.5463 | 1.54483 | ||||||||
\(418\) | 74.8501 | 3.66104 | ||||||||
\(419\) | −24.5440 | −1.19905 | −0.599527 | − | 0.800355i | \(-0.704645\pi\) | ||||
−0.599527 | + | 0.800355i | \(0.704645\pi\) | |||||||
\(420\) | 95.4104 | 4.65555 | ||||||||
\(421\) | 21.5089 | 1.04828 | 0.524140 | − | 0.851632i | \(-0.324387\pi\) | ||||
0.524140 | + | 0.851632i | \(0.324387\pi\) | |||||||
\(422\) | 45.1264 | 2.19672 | ||||||||
\(423\) | 49.0995 | 2.38730 | ||||||||
\(424\) | −58.7386 | −2.85260 | ||||||||
\(425\) | −4.41406 | −0.214113 | ||||||||
\(426\) | −18.4407 | −0.893457 | ||||||||
\(427\) | −23.4856 | −1.13655 | ||||||||
\(428\) | 51.6258 | 2.49543 | ||||||||
\(429\) | 46.2019 | 2.23065 | ||||||||
\(430\) | −8.63590 | −0.416460 | ||||||||
\(431\) | −20.0907 | −0.967734 | −0.483867 | − | 0.875142i | \(-0.660768\pi\) | ||||
−0.483867 | + | 0.875142i | \(0.660768\pi\) | |||||||
\(432\) | 196.175 | 9.43847 | ||||||||
\(433\) | 12.6758 | 0.609158 | 0.304579 | − | 0.952487i | \(-0.401484\pi\) | ||||
0.304579 | + | 0.952487i | \(0.401484\pi\) | |||||||
\(434\) | 16.9909 | 0.815589 | ||||||||
\(435\) | −16.2446 | −0.778870 | ||||||||
\(436\) | −5.66539 | −0.271323 | ||||||||
\(437\) | −28.4884 | −1.36279 | ||||||||
\(438\) | 31.4804 | 1.50419 | ||||||||
\(439\) | −17.8879 | −0.853742 | −0.426871 | − | 0.904313i | \(-0.640384\pi\) | ||||
−0.426871 | + | 0.904313i | \(0.640384\pi\) | |||||||
\(440\) | 63.6521 | 3.03449 | ||||||||
\(441\) | 28.1917 | 1.34246 | ||||||||
\(442\) | −19.4064 | −0.923068 | ||||||||
\(443\) | 2.23203 | 0.106047 | 0.0530235 | − | 0.998593i | \(-0.483114\pi\) | ||||
0.0530235 | + | 0.998593i | \(0.483114\pi\) | |||||||
\(444\) | 17.6881 | 0.839440 | ||||||||
\(445\) | −23.4816 | −1.11314 | ||||||||
\(446\) | −31.9924 | −1.51488 | ||||||||
\(447\) | 46.0717 | 2.17912 | ||||||||
\(448\) | −129.695 | −6.12751 | ||||||||
\(449\) | −34.4729 | −1.62688 | −0.813438 | − | 0.581652i | \(-0.802407\pi\) | ||||
−0.813438 | + | 0.581652i | \(0.802407\pi\) | |||||||
\(450\) | 44.7816 | 2.11103 | ||||||||
\(451\) | −11.1360 | −0.524372 | ||||||||
\(452\) | −17.9240 | −0.843073 | ||||||||
\(453\) | −57.7922 | −2.71532 | ||||||||
\(454\) | −0.565335 | −0.0265325 | ||||||||
\(455\) | 20.5320 | 0.962554 | ||||||||
\(456\) | 220.329 | 10.3179 | ||||||||
\(457\) | 17.3065 | 0.809562 | 0.404781 | − | 0.914414i | \(-0.367348\pi\) | ||||
0.404781 | + | 0.914414i | \(0.367348\pi\) | |||||||
\(458\) | −13.1764 | −0.615691 | ||||||||
\(459\) | 21.5466 | 1.00571 | ||||||||
\(460\) | −37.4454 | −1.74590 | ||||||||
\(461\) | 21.8186 | 1.01619 | 0.508097 | − | 0.861300i | \(-0.330349\pi\) | ||||
0.508097 | + | 0.861300i | \(0.330349\pi\) | |||||||
\(462\) | 112.355 | 5.22722 | ||||||||
\(463\) | 36.0980 | 1.67762 | 0.838809 | − | 0.544426i | \(-0.183252\pi\) | ||||
0.838809 | + | 0.544426i | \(0.183252\pi\) | |||||||
\(464\) | 54.0694 | 2.51011 | ||||||||
\(465\) | −9.24596 | −0.428771 | ||||||||
\(466\) | 56.4988 | 2.61725 | ||||||||
\(467\) | 7.60070 | 0.351718 | 0.175859 | − | 0.984415i | \(-0.443730\pi\) | ||||
0.175859 | + | 0.984415i | \(0.443730\pi\) | |||||||
\(468\) | 145.513 | 6.72635 | ||||||||
\(469\) | −47.1201 | −2.17580 | ||||||||
\(470\) | 32.5028 | 1.49924 | ||||||||
\(471\) | 4.05438 | 0.186816 | ||||||||
\(472\) | 126.905 | 5.84130 | ||||||||
\(473\) | −7.51622 | −0.345596 | ||||||||
\(474\) | 82.8485 | 3.80536 | ||||||||
\(475\) | 16.6690 | 0.764827 | ||||||||
\(476\) | −34.8797 | −1.59871 | ||||||||
\(477\) | 39.0564 | 1.78827 | ||||||||
\(478\) | −66.1438 | −3.02534 | ||||||||
\(479\) | −22.9636 | −1.04923 | −0.524616 | − | 0.851339i | \(-0.675791\pi\) | ||||
−0.524616 | + | 0.851339i | \(0.675791\pi\) | |||||||
\(480\) | 131.583 | 6.00589 | ||||||||
\(481\) | 3.80642 | 0.173558 | ||||||||
\(482\) | 28.6349 | 1.30428 | ||||||||
\(483\) | −42.7630 | −1.94578 | ||||||||
\(484\) | 23.3083 | 1.05947 | ||||||||
\(485\) | −4.11617 | −0.186906 | ||||||||
\(486\) | −43.6119 | −1.97828 | ||||||||
\(487\) | 23.7112 | 1.07446 | 0.537229 | − | 0.843436i | \(-0.319471\pi\) | ||||
0.537229 | + | 0.843436i | \(0.319471\pi\) | |||||||
\(488\) | −71.2866 | −3.22699 | ||||||||
\(489\) | −31.2593 | −1.41359 | ||||||||
\(490\) | 18.6623 | 0.843076 | ||||||||
\(491\) | −6.19229 | −0.279454 | −0.139727 | − | 0.990190i | \(-0.544623\pi\) | ||||
−0.139727 | + | 0.990190i | \(0.544623\pi\) | |||||||
\(492\) | −50.6661 | −2.28420 | ||||||||
\(493\) | 5.93863 | 0.267463 | ||||||||
\(494\) | 73.2853 | 3.29726 | ||||||||
\(495\) | −42.3235 | −1.90230 | ||||||||
\(496\) | 30.7747 | 1.38183 | ||||||||
\(497\) | −7.13249 | −0.319936 | ||||||||
\(498\) | −85.1701 | −3.81656 | ||||||||
\(499\) | −40.9988 | −1.83536 | −0.917680 | − | 0.397321i | \(-0.869940\pi\) | ||||
−0.917680 | + | 0.397321i | \(0.869940\pi\) | |||||||
\(500\) | 67.6116 | 3.02368 | ||||||||
\(501\) | 75.8209 | 3.38743 | ||||||||
\(502\) | −4.86919 | −0.217323 | ||||||||
\(503\) | 18.0643 | 0.805446 | 0.402723 | − | 0.915322i | \(-0.368064\pi\) | ||||
0.402723 | + | 0.915322i | \(0.368064\pi\) | |||||||
\(504\) | 228.942 | 10.1979 | ||||||||
\(505\) | −2.79287 | −0.124281 | ||||||||
\(506\) | −44.0955 | −1.96028 | ||||||||
\(507\) | 4.64827 | 0.206437 | ||||||||
\(508\) | 81.2560 | 3.60515 | ||||||||
\(509\) | 21.2323 | 0.941103 | 0.470552 | − | 0.882373i | \(-0.344055\pi\) | ||||
0.470552 | + | 0.882373i | \(0.344055\pi\) | |||||||
\(510\) | 25.6810 | 1.13718 | ||||||||
\(511\) | 12.1759 | 0.538632 | ||||||||
\(512\) | −97.6798 | −4.31688 | ||||||||
\(513\) | −81.3673 | −3.59245 | ||||||||
\(514\) | −85.4769 | −3.77022 | ||||||||
\(515\) | 22.9486 | 1.01123 | ||||||||
\(516\) | −34.1971 | −1.50544 | ||||||||
\(517\) | 28.2887 | 1.24414 | ||||||||
\(518\) | 9.25654 | 0.406709 | ||||||||
\(519\) | −78.7857 | −3.45831 | ||||||||
\(520\) | 62.3214 | 2.73297 | ||||||||
\(521\) | −10.1868 | −0.446292 | −0.223146 | − | 0.974785i | \(-0.571633\pi\) | ||||
−0.223146 | + | 0.974785i | \(0.571633\pi\) | |||||||
\(522\) | −60.2488 | −2.63702 | ||||||||
\(523\) | −12.5749 | −0.549863 | −0.274932 | − | 0.961464i | \(-0.588655\pi\) | ||||
−0.274932 | + | 0.961464i | \(0.588655\pi\) | |||||||
\(524\) | −55.7100 | −2.43370 | ||||||||
\(525\) | 25.0213 | 1.09202 | ||||||||
\(526\) | −21.6189 | −0.942627 | ||||||||
\(527\) | 3.38010 | 0.147239 | ||||||||
\(528\) | 203.502 | 8.85631 | ||||||||
\(529\) | −6.21696 | −0.270302 | ||||||||
\(530\) | 25.8545 | 1.12305 | ||||||||
\(531\) | −84.3818 | −3.66186 | ||||||||
\(532\) | 131.718 | 5.71069 | ||||||||
\(533\) | −10.9032 | −0.472269 | ||||||||
\(534\) | −125.809 | −5.44431 | ||||||||
\(535\) | −14.7018 | −0.635613 | ||||||||
\(536\) | −143.025 | −6.17774 | ||||||||
\(537\) | 72.4613 | 3.12693 | ||||||||
\(538\) | −31.0852 | −1.34018 | ||||||||
\(539\) | 16.2426 | 0.699620 | ||||||||
\(540\) | −106.950 | −4.60239 | ||||||||
\(541\) | −32.3227 | −1.38966 | −0.694831 | − | 0.719173i | \(-0.744521\pi\) | ||||
−0.694831 | + | 0.719173i | \(0.744521\pi\) | |||||||
\(542\) | −1.36259 | −0.0585284 | ||||||||
\(543\) | 39.9699 | 1.71527 | ||||||||
\(544\) | −48.1033 | −2.06241 | ||||||||
\(545\) | 1.61337 | 0.0691090 | ||||||||
\(546\) | 110.006 | 4.70782 | ||||||||
\(547\) | 19.7943 | 0.846342 | 0.423171 | − | 0.906050i | \(-0.360917\pi\) | ||||
0.423171 | + | 0.906050i | \(0.360917\pi\) | |||||||
\(548\) | −48.1967 | −2.05886 | ||||||||
\(549\) | 47.3998 | 2.02297 | ||||||||
\(550\) | 25.8010 | 1.10016 | ||||||||
\(551\) | −22.4263 | −0.955394 | ||||||||
\(552\) | −129.800 | −5.52465 | ||||||||
\(553\) | 32.0441 | 1.36265 | ||||||||
\(554\) | −72.6933 | −3.08844 | ||||||||
\(555\) | −5.03714 | −0.213815 | ||||||||
\(556\) | 57.2437 | 2.42767 | ||||||||
\(557\) | −28.9516 | −1.22672 | −0.613358 | − | 0.789805i | \(-0.710182\pi\) | ||||
−0.613358 | + | 0.789805i | \(0.710182\pi\) | |||||||
\(558\) | −34.2919 | −1.45169 | ||||||||
\(559\) | −7.35909 | −0.311256 | ||||||||
\(560\) | 90.4359 | 3.82162 | ||||||||
\(561\) | 22.3514 | 0.943676 | ||||||||
\(562\) | 52.4539 | 2.21263 | ||||||||
\(563\) | −0.477589 | −0.0201280 | −0.0100640 | − | 0.999949i | \(-0.503204\pi\) | ||||
−0.0100640 | + | 0.999949i | \(0.503204\pi\) | |||||||
\(564\) | 128.707 | 5.41954 | ||||||||
\(565\) | 5.10431 | 0.214740 | ||||||||
\(566\) | −62.4910 | −2.62669 | ||||||||
\(567\) | −54.4578 | −2.28701 | ||||||||
\(568\) | −21.6495 | −0.908393 | ||||||||
\(569\) | −12.6469 | −0.530186 | −0.265093 | − | 0.964223i | \(-0.585403\pi\) | ||||
−0.265093 | + | 0.964223i | \(0.585403\pi\) | |||||||
\(570\) | −96.9806 | −4.06207 | ||||||||
\(571\) | 20.4305 | 0.854990 | 0.427495 | − | 0.904018i | \(-0.359396\pi\) | ||||
0.427495 | + | 0.904018i | \(0.359396\pi\) | |||||||
\(572\) | 83.8375 | 3.50542 | ||||||||
\(573\) | 66.1960 | 2.76538 | ||||||||
\(574\) | −26.5146 | −1.10670 | ||||||||
\(575\) | −9.82001 | −0.409523 | ||||||||
\(576\) | 261.757 | 10.9065 | ||||||||
\(577\) | 34.5195 | 1.43706 | 0.718532 | − | 0.695494i | \(-0.244814\pi\) | ||||
0.718532 | + | 0.695494i | \(0.244814\pi\) | |||||||
\(578\) | 37.6786 | 1.56722 | ||||||||
\(579\) | −27.5337 | −1.14426 | ||||||||
\(580\) | −29.4774 | −1.22398 | ||||||||
\(581\) | −32.9420 | −1.36666 | ||||||||
\(582\) | −22.0536 | −0.914149 | ||||||||
\(583\) | 22.5024 | 0.931952 | ||||||||
\(584\) | 36.9580 | 1.52933 | ||||||||
\(585\) | −41.4387 | −1.71328 | ||||||||
\(586\) | −54.2531 | −2.24117 | ||||||||
\(587\) | 5.38327 | 0.222191 | 0.111096 | − | 0.993810i | \(-0.464564\pi\) | ||||
0.111096 | + | 0.993810i | \(0.464564\pi\) | |||||||
\(588\) | 73.9002 | 3.04759 | ||||||||
\(589\) | −12.7644 | −0.525949 | ||||||||
\(590\) | −55.8590 | −2.29968 | ||||||||
\(591\) | 54.7292 | 2.25126 | ||||||||
\(592\) | 16.7659 | 0.689074 | ||||||||
\(593\) | −13.9864 | −0.574353 | −0.287176 | − | 0.957878i | \(-0.592717\pi\) | ||||
−0.287176 | + | 0.957878i | \(0.592717\pi\) | |||||||
\(594\) | −125.944 | −5.16752 | ||||||||
\(595\) | 9.93289 | 0.407209 | ||||||||
\(596\) | 83.6013 | 3.42444 | ||||||||
\(597\) | −43.9857 | −1.80021 | ||||||||
\(598\) | −43.1737 | −1.76550 | ||||||||
\(599\) | −42.3275 | −1.72945 | −0.864727 | − | 0.502241i | \(-0.832509\pi\) | ||||
−0.864727 | + | 0.502241i | \(0.832509\pi\) | |||||||
\(600\) | 75.9479 | 3.10056 | ||||||||
\(601\) | 15.3659 | 0.626789 | 0.313394 | − | 0.949623i | \(-0.398534\pi\) | ||||
0.313394 | + | 0.949623i | \(0.398534\pi\) | |||||||
\(602\) | −17.8960 | −0.729386 | ||||||||
\(603\) | 95.1000 | 3.87277 | ||||||||
\(604\) | −104.869 | −4.26707 | ||||||||
\(605\) | −6.63764 | −0.269858 | ||||||||
\(606\) | −14.9636 | −0.607855 | ||||||||
\(607\) | −30.1097 | −1.22211 | −0.611057 | − | 0.791587i | \(-0.709255\pi\) | ||||
−0.611057 | + | 0.791587i | \(0.709255\pi\) | |||||||
\(608\) | 181.655 | 7.36708 | ||||||||
\(609\) | −33.6634 | −1.36411 | ||||||||
\(610\) | 31.3777 | 1.27044 | ||||||||
\(611\) | 27.6973 | 1.12051 | ||||||||
\(612\) | 70.3959 | 2.84559 | ||||||||
\(613\) | −46.3485 | −1.87200 | −0.936000 | − | 0.352000i | \(-0.885502\pi\) | ||||
−0.936000 | + | 0.352000i | \(0.885502\pi\) | |||||||
\(614\) | −93.1972 | −3.76113 | ||||||||
\(615\) | 14.4285 | 0.581812 | ||||||||
\(616\) | 131.905 | 5.31460 | ||||||||
\(617\) | 24.7591 | 0.996764 | 0.498382 | − | 0.866957i | \(-0.333928\pi\) | ||||
0.498382 | + | 0.866957i | \(0.333928\pi\) | |||||||
\(618\) | 122.953 | 4.94591 | ||||||||
\(619\) | 13.7396 | 0.552240 | 0.276120 | − | 0.961123i | \(-0.410951\pi\) | ||||
0.276120 | + | 0.961123i | \(0.410951\pi\) | |||||||
\(620\) | −16.7776 | −0.673806 | ||||||||
\(621\) | 47.9349 | 1.92356 | ||||||||
\(622\) | 2.12023 | 0.0850136 | ||||||||
\(623\) | −48.6605 | −1.94954 | ||||||||
\(624\) | 199.248 | 7.97631 | ||||||||
\(625\) | −7.26893 | −0.290757 | ||||||||
\(626\) | 24.8502 | 0.993215 | ||||||||
\(627\) | −84.4066 | −3.37087 | ||||||||
\(628\) | 7.35704 | 0.293578 | ||||||||
\(629\) | 1.84146 | 0.0734236 | ||||||||
\(630\) | −100.772 | −4.01483 | ||||||||
\(631\) | 8.02661 | 0.319534 | 0.159767 | − | 0.987155i | \(-0.448926\pi\) | ||||
0.159767 | + | 0.987155i | \(0.448926\pi\) | |||||||
\(632\) | 97.2644 | 3.86897 | ||||||||
\(633\) | −50.8879 | −2.02261 | ||||||||
\(634\) | 30.7422 | 1.22093 | ||||||||
\(635\) | −23.1397 | −0.918273 | ||||||||
\(636\) | 102.380 | 4.05965 | ||||||||
\(637\) | 15.9031 | 0.630102 | ||||||||
\(638\) | −34.7124 | −1.37428 | ||||||||
\(639\) | 14.3952 | 0.569463 | ||||||||
\(640\) | 88.9874 | 3.51754 | ||||||||
\(641\) | 12.9124 | 0.510009 | 0.255005 | − | 0.966940i | \(-0.417923\pi\) | ||||
0.255005 | + | 0.966940i | \(0.417923\pi\) | |||||||
\(642\) | −78.7689 | −3.10876 | ||||||||
\(643\) | 4.69458 | 0.185136 | 0.0925681 | − | 0.995706i | \(-0.470492\pi\) | ||||
0.0925681 | + | 0.995706i | \(0.470492\pi\) | |||||||
\(644\) | −77.5973 | −3.05776 | ||||||||
\(645\) | 9.73849 | 0.383453 | ||||||||
\(646\) | 35.4537 | 1.39491 | ||||||||
\(647\) | −28.9482 | −1.13807 | −0.569036 | − | 0.822313i | \(-0.692683\pi\) | ||||
−0.569036 | + | 0.822313i | \(0.692683\pi\) | |||||||
\(648\) | −165.298 | −6.49350 | ||||||||
\(649\) | −48.6166 | −1.90837 | ||||||||
\(650\) | 25.2616 | 0.990840 | ||||||||
\(651\) | −19.1602 | −0.750948 | ||||||||
\(652\) | −56.7228 | −2.22144 | ||||||||
\(653\) | −35.6751 | −1.39607 | −0.698037 | − | 0.716062i | \(-0.745943\pi\) | ||||
−0.698037 | + | 0.716062i | \(0.745943\pi\) | |||||||
\(654\) | 8.64407 | 0.338010 | ||||||||
\(655\) | 15.8649 | 0.619892 | ||||||||
\(656\) | −48.0245 | −1.87504 | ||||||||
\(657\) | −24.5741 | −0.958726 | ||||||||
\(658\) | 67.3550 | 2.62577 | ||||||||
\(659\) | −12.1829 | −0.474578 | −0.237289 | − | 0.971439i | \(-0.576259\pi\) | ||||
−0.237289 | + | 0.971439i | \(0.576259\pi\) | |||||||
\(660\) | −110.945 | −4.31851 | ||||||||
\(661\) | 34.9982 | 1.36127 | 0.680635 | − | 0.732622i | \(-0.261704\pi\) | ||||
0.680635 | + | 0.732622i | \(0.261704\pi\) | |||||||
\(662\) | −50.8744 | −1.97729 | ||||||||
\(663\) | 21.8841 | 0.849908 | ||||||||
\(664\) | −99.9900 | −3.88036 | ||||||||
\(665\) | −37.5100 | −1.45458 | ||||||||
\(666\) | −18.6820 | −0.723913 | ||||||||
\(667\) | 13.2118 | 0.511561 | ||||||||
\(668\) | 137.584 | 5.32328 | ||||||||
\(669\) | 36.0770 | 1.39482 | ||||||||
\(670\) | 62.9542 | 2.43213 | ||||||||
\(671\) | 27.3094 | 1.05427 | ||||||||
\(672\) | 272.676 | 10.5187 | ||||||||
\(673\) | 28.9217 | 1.11485 | 0.557424 | − | 0.830228i | \(-0.311790\pi\) | ||||
0.557424 | + | 0.830228i | \(0.311790\pi\) | |||||||
\(674\) | −57.2965 | −2.20698 | ||||||||
\(675\) | −28.0474 | −1.07955 | ||||||||
\(676\) | 8.43471 | 0.324412 | ||||||||
\(677\) | 2.75805 | 0.106000 | 0.0530002 | − | 0.998595i | \(-0.483122\pi\) | ||||
0.0530002 | + | 0.998595i | \(0.483122\pi\) | |||||||
\(678\) | 27.3478 | 1.05029 | ||||||||
\(679\) | −8.52985 | −0.327346 | ||||||||
\(680\) | 30.1496 | 1.15619 | ||||||||
\(681\) | 0.637514 | 0.0244296 | ||||||||
\(682\) | −19.7573 | −0.756545 | ||||||||
\(683\) | 9.78543 | 0.374429 | 0.187215 | − | 0.982319i | \(-0.440054\pi\) | ||||
0.187215 | + | 0.982319i | \(0.440054\pi\) | |||||||
\(684\) | −265.839 | −10.1646 | ||||||||
\(685\) | 13.7252 | 0.524415 | ||||||||
\(686\) | −26.1223 | −0.997354 | ||||||||
\(687\) | 14.8587 | 0.566893 | ||||||||
\(688\) | −32.4141 | −1.23578 | ||||||||
\(689\) | 22.0319 | 0.839349 | ||||||||
\(690\) | 57.1330 | 2.17502 | ||||||||
\(691\) | −3.52814 | −0.134217 | −0.0671084 | − | 0.997746i | \(-0.521377\pi\) | ||||
−0.0671084 | + | 0.997746i | \(0.521377\pi\) | |||||||
\(692\) | −142.964 | −5.43467 | ||||||||
\(693\) | −87.7060 | −3.33168 | ||||||||
\(694\) | 0.295995 | 0.0112358 | ||||||||
\(695\) | −16.3016 | −0.618356 | ||||||||
\(696\) | −102.180 | −3.87311 | ||||||||
\(697\) | −5.27470 | −0.199793 | ||||||||
\(698\) | 75.2489 | 2.84821 | ||||||||
\(699\) | −63.7122 | −2.40982 | ||||||||
\(700\) | 45.4034 | 1.71609 | ||||||||
\(701\) | 35.7474 | 1.35016 | 0.675081 | − | 0.737744i | \(-0.264109\pi\) | ||||
0.675081 | + | 0.737744i | \(0.264109\pi\) | |||||||
\(702\) | −123.311 | −4.65406 | ||||||||
\(703\) | −6.95397 | −0.262274 | ||||||||
\(704\) | 150.811 | 5.68392 | ||||||||
\(705\) | −36.6526 | −1.38042 | ||||||||
\(706\) | 85.5659 | 3.22032 | ||||||||
\(707\) | −5.78761 | −0.217665 | ||||||||
\(708\) | −221.194 | −8.31299 | ||||||||
\(709\) | 3.75615 | 0.141065 | 0.0705325 | − | 0.997509i | \(-0.477530\pi\) | ||||
0.0705325 | + | 0.997509i | \(0.477530\pi\) | |||||||
\(710\) | 9.52929 | 0.357628 | ||||||||
\(711\) | −64.6729 | −2.42542 | ||||||||
\(712\) | −147.701 | −5.53532 | ||||||||
\(713\) | 7.51975 | 0.281617 | ||||||||
\(714\) | 53.2183 | 1.99164 | ||||||||
\(715\) | −23.8749 | −0.892870 | ||||||||
\(716\) | 131.488 | 4.91392 | ||||||||
\(717\) | 74.5887 | 2.78556 | ||||||||
\(718\) | −90.9859 | −3.39556 | ||||||||
\(719\) | −1.18679 | −0.0442599 | −0.0221300 | − | 0.999755i | \(-0.507045\pi\) | ||||
−0.0221300 | + | 0.999755i | \(0.507045\pi\) | |||||||
\(720\) | −182.522 | −6.80220 | ||||||||
\(721\) | 47.5558 | 1.77107 | ||||||||
\(722\) | −81.2812 | −3.02497 | ||||||||
\(723\) | −32.2909 | −1.20091 | ||||||||
\(724\) | 72.5290 | 2.69552 | ||||||||
\(725\) | −7.73040 | −0.287100 | ||||||||
\(726\) | −35.5630 | −1.31987 | ||||||||
\(727\) | 18.0752 | 0.670370 | 0.335185 | − | 0.942152i | \(-0.391201\pi\) | ||||
0.335185 | + | 0.942152i | \(0.391201\pi\) | |||||||
\(728\) | 129.147 | 4.78652 | ||||||||
\(729\) | 0.314846 | 0.0116610 | ||||||||
\(730\) | −16.2675 | −0.602088 | ||||||||
\(731\) | −3.56015 | −0.131677 | ||||||||
\(732\) | 124.251 | 4.59247 | ||||||||
\(733\) | −10.7342 | −0.396478 | −0.198239 | − | 0.980154i | \(-0.563522\pi\) | ||||
−0.198239 | + | 0.980154i | \(0.563522\pi\) | |||||||
\(734\) | 45.4323 | 1.67694 | ||||||||
\(735\) | −21.0450 | −0.776256 | ||||||||
\(736\) | −107.016 | −3.94467 | ||||||||
\(737\) | 54.7919 | 2.01829 | ||||||||
\(738\) | 53.5130 | 1.96984 | ||||||||
\(739\) | 15.1219 | 0.556270 | 0.278135 | − | 0.960542i | \(-0.410284\pi\) | ||||
0.278135 | + | 0.960542i | \(0.410284\pi\) | |||||||
\(740\) | −9.14036 | −0.336006 | ||||||||
\(741\) | −82.6420 | −3.03593 | ||||||||
\(742\) | 53.5778 | 1.96690 | ||||||||
\(743\) | 21.9608 | 0.805664 | 0.402832 | − | 0.915274i | \(-0.368026\pi\) | ||||
0.402832 | + | 0.915274i | \(0.368026\pi\) | |||||||
\(744\) | −58.1576 | −2.13216 | ||||||||
\(745\) | −23.8076 | −0.872245 | ||||||||
\(746\) | 76.4726 | 2.79986 | ||||||||
\(747\) | 66.4852 | 2.43257 | ||||||||
\(748\) | 40.5586 | 1.48297 | ||||||||
\(749\) | −30.4662 | −1.11321 | ||||||||
\(750\) | −103.160 | −3.76686 | ||||||||
\(751\) | −1.79937 | −0.0656599 | −0.0328299 | − | 0.999461i | \(-0.510452\pi\) | ||||
−0.0328299 | + | 0.999461i | \(0.510452\pi\) | |||||||
\(752\) | 121.997 | 4.44876 | ||||||||
\(753\) | 5.49087 | 0.200098 | ||||||||
\(754\) | −33.9867 | −1.23772 | ||||||||
\(755\) | 29.8642 | 1.08687 | ||||||||
\(756\) | −221.630 | −8.06060 | ||||||||
\(757\) | −27.8513 | −1.01227 | −0.506136 | − | 0.862454i | \(-0.668927\pi\) | ||||
−0.506136 | + | 0.862454i | \(0.668927\pi\) | |||||||
\(758\) | 31.4100 | 1.14086 | ||||||||
\(759\) | 49.7254 | 1.80492 | ||||||||
\(760\) | −113.855 | −4.12997 | ||||||||
\(761\) | −44.4277 | −1.61050 | −0.805252 | − | 0.592932i | \(-0.797970\pi\) | ||||
−0.805252 | + | 0.592932i | \(0.797970\pi\) | |||||||
\(762\) | −123.978 | −4.49124 | ||||||||
\(763\) | 3.34335 | 0.121037 | ||||||||
\(764\) | 120.119 | 4.34574 | ||||||||
\(765\) | −20.0470 | −0.724803 | ||||||||
\(766\) | −104.298 | −3.76844 | ||||||||
\(767\) | −47.6002 | −1.71875 | ||||||||
\(768\) | 234.548 | 8.46352 | ||||||||
\(769\) | 8.70981 | 0.314084 | 0.157042 | − | 0.987592i | \(-0.449804\pi\) | ||||
0.157042 | + | 0.987592i | \(0.449804\pi\) | |||||||
\(770\) | −58.0595 | −2.09232 | ||||||||
\(771\) | 96.3902 | 3.47141 | ||||||||
\(772\) | −49.9625 | −1.79819 | ||||||||
\(773\) | 4.26867 | 0.153533 | 0.0767667 | − | 0.997049i | \(-0.475540\pi\) | ||||
0.0767667 | + | 0.997049i | \(0.475540\pi\) | |||||||
\(774\) | 36.1186 | 1.29826 | ||||||||
\(775\) | −4.39992 | −0.158050 | ||||||||
\(776\) | −25.8909 | −0.929431 | ||||||||
\(777\) | −10.4384 | −0.374474 | ||||||||
\(778\) | −8.92158 | −0.319854 | ||||||||
\(779\) | 19.9191 | 0.713675 | ||||||||
\(780\) | −108.625 | −3.88941 | ||||||||
\(781\) | 8.29377 | 0.296774 | ||||||||
\(782\) | −20.8864 | −0.746896 | ||||||||
\(783\) | 37.7348 | 1.34853 | ||||||||
\(784\) | 70.0472 | 2.50169 | ||||||||
\(785\) | −2.09511 | −0.0747775 | ||||||||
\(786\) | 85.0005 | 3.03187 | ||||||||
\(787\) | 4.68347 | 0.166948 | 0.0834739 | − | 0.996510i | \(-0.473398\pi\) | ||||
0.0834739 | + | 0.996510i | \(0.473398\pi\) | |||||||
\(788\) | 99.3112 | 3.53781 | ||||||||
\(789\) | 24.3791 | 0.867917 | ||||||||
\(790\) | −42.8121 | −1.52319 | ||||||||
\(791\) | 10.5776 | 0.376095 | ||||||||
\(792\) | −266.217 | −9.45961 | ||||||||
\(793\) | 26.7385 | 0.949511 | ||||||||
\(794\) | 9.45078 | 0.335396 | ||||||||
\(795\) | −29.1555 | −1.03404 | ||||||||
\(796\) | −79.8160 | −2.82900 | ||||||||
\(797\) | −40.8931 | −1.44851 | −0.724254 | − | 0.689533i | \(-0.757816\pi\) | ||||
−0.724254 | + | 0.689533i | \(0.757816\pi\) | |||||||
\(798\) | −200.971 | −7.11429 | ||||||||
\(799\) | 13.3993 | 0.474033 | ||||||||
\(800\) | 62.6167 | 2.21384 | ||||||||
\(801\) | 98.2090 | 3.47004 | ||||||||
\(802\) | 76.1879 | 2.69029 | ||||||||
\(803\) | −14.1584 | −0.499638 | ||||||||
\(804\) | 249.290 | 8.79180 | ||||||||
\(805\) | 22.0978 | 0.778846 | ||||||||
\(806\) | −19.3442 | −0.681371 | ||||||||
\(807\) | 35.0540 | 1.23396 | ||||||||
\(808\) | −17.5673 | −0.618016 | ||||||||
\(809\) | −48.1269 | −1.69205 | −0.846025 | − | 0.533143i | \(-0.821011\pi\) | ||||
−0.846025 | + | 0.533143i | \(0.821011\pi\) | |||||||
\(810\) | 72.7577 | 2.55645 | ||||||||
\(811\) | 30.7336 | 1.07920 | 0.539601 | − | 0.841921i | \(-0.318575\pi\) | ||||
0.539601 | + | 0.841921i | \(0.318575\pi\) | |||||||
\(812\) | −61.0853 | −2.14367 | ||||||||
\(813\) | 1.53656 | 0.0538896 | ||||||||
\(814\) | −10.7636 | −0.377265 | ||||||||
\(815\) | 16.1533 | 0.565825 | ||||||||
\(816\) | 96.3915 | 3.37438 | ||||||||
\(817\) | 13.4444 | 0.470359 | ||||||||
\(818\) | −35.0815 | −1.22660 | ||||||||
\(819\) | −85.8725 | −3.00063 | ||||||||
\(820\) | 26.1818 | 0.914308 | ||||||||
\(821\) | −6.34502 | −0.221443 | −0.110721 | − | 0.993851i | \(-0.535316\pi\) | ||||
−0.110721 | + | 0.993851i | \(0.535316\pi\) | |||||||
\(822\) | 73.5369 | 2.56489 | ||||||||
\(823\) | −33.4548 | −1.16616 | −0.583080 | − | 0.812415i | \(-0.698153\pi\) | ||||
−0.583080 | + | 0.812415i | \(0.698153\pi\) | |||||||
\(824\) | 144.348 | 5.02859 | ||||||||
\(825\) | −29.0951 | −1.01296 | ||||||||
\(826\) | −115.755 | −4.02765 | ||||||||
\(827\) | −0.434651 | −0.0151143 | −0.00755715 | − | 0.999971i | \(-0.502406\pi\) | ||||
−0.00755715 | + | 0.999971i | \(0.502406\pi\) | |||||||
\(828\) | 156.611 | 5.44260 | ||||||||
\(829\) | 16.1239 | 0.560006 | 0.280003 | − | 0.959999i | \(-0.409664\pi\) | ||||
0.280003 | + | 0.959999i | \(0.409664\pi\) | |||||||
\(830\) | 44.0118 | 1.52767 | ||||||||
\(831\) | 81.9745 | 2.84366 | ||||||||
\(832\) | 147.658 | 5.11914 | ||||||||
\(833\) | 7.69353 | 0.266565 | ||||||||
\(834\) | −87.3406 | −3.02436 | ||||||||
\(835\) | −39.1806 | −1.35590 | ||||||||
\(836\) | −153.163 | −5.29727 | ||||||||
\(837\) | 21.4775 | 0.742372 | ||||||||
\(838\) | 67.9537 | 2.34742 | ||||||||
\(839\) | −34.2038 | −1.18085 | −0.590423 | − | 0.807094i | \(-0.701039\pi\) | ||||
−0.590423 | + | 0.807094i | \(0.701039\pi\) | |||||||
\(840\) | −170.904 | −5.89676 | ||||||||
\(841\) | −18.5996 | −0.641365 | ||||||||
\(842\) | −59.5505 | −2.05224 | ||||||||
\(843\) | −59.1509 | −2.03727 | ||||||||
\(844\) | −92.3408 | −3.17850 | ||||||||
\(845\) | −2.40200 | −0.0826314 | ||||||||
\(846\) | −135.939 | −4.67368 | ||||||||
\(847\) | −13.7550 | −0.472629 | ||||||||
\(848\) | 97.0426 | 3.33246 | ||||||||
\(849\) | 70.4695 | 2.41851 | ||||||||
\(850\) | 12.2210 | 0.419175 | ||||||||
\(851\) | 4.09671 | 0.140433 | ||||||||
\(852\) | 37.7347 | 1.29277 | ||||||||
\(853\) | −7.51665 | −0.257365 | −0.128683 | − | 0.991686i | \(-0.541075\pi\) | ||||
−0.128683 | + | 0.991686i | \(0.541075\pi\) | |||||||
\(854\) | 65.0233 | 2.22505 | ||||||||
\(855\) | 75.7046 | 2.58904 | ||||||||
\(856\) | −92.4750 | −3.16073 | ||||||||
\(857\) | 44.7278 | 1.52787 | 0.763937 | − | 0.645291i | \(-0.223264\pi\) | ||||
0.763937 | + | 0.645291i | \(0.223264\pi\) | |||||||
\(858\) | −127.917 | −4.36700 | ||||||||
\(859\) | −2.95019 | −0.100659 | −0.0503296 | − | 0.998733i | \(-0.516027\pi\) | ||||
−0.0503296 | + | 0.998733i | \(0.516027\pi\) | |||||||
\(860\) | 17.6714 | 0.602589 | ||||||||
\(861\) | 29.8998 | 1.01898 | ||||||||
\(862\) | 55.6240 | 1.89456 | ||||||||
\(863\) | −19.7700 | −0.672980 | −0.336490 | − | 0.941687i | \(-0.609240\pi\) | ||||
−0.336490 | + | 0.941687i | \(0.609240\pi\) | |||||||
\(864\) | −305.654 | −10.3986 | ||||||||
\(865\) | 40.7127 | 1.38427 | ||||||||
\(866\) | −35.0947 | −1.19257 | ||||||||
\(867\) | −42.4892 | −1.44301 | ||||||||
\(868\) | −34.7680 | −1.18010 | ||||||||
\(869\) | −37.2613 | −1.26400 | ||||||||
\(870\) | 44.9756 | 1.52482 | ||||||||
\(871\) | 53.6464 | 1.81774 | ||||||||
\(872\) | 10.1482 | 0.343660 | ||||||||
\(873\) | 17.2154 | 0.582652 | ||||||||
\(874\) | 78.8743 | 2.66796 | ||||||||
\(875\) | −39.9000 | −1.34887 | ||||||||
\(876\) | −64.4173 | −2.17646 | ||||||||
\(877\) | −28.3201 | −0.956303 | −0.478152 | − | 0.878277i | \(-0.658693\pi\) | ||||
−0.478152 | + | 0.878277i | \(0.658693\pi\) | |||||||
\(878\) | 49.5252 | 1.67139 | ||||||||
\(879\) | 61.1799 | 2.06355 | ||||||||
\(880\) | −105.160 | −3.54495 | ||||||||
\(881\) | −21.2395 | −0.715577 | −0.357789 | − | 0.933803i | \(-0.616469\pi\) | ||||
−0.357789 | + | 0.933803i | \(0.616469\pi\) | |||||||
\(882\) | −78.0527 | −2.62817 | ||||||||
\(883\) | 31.3857 | 1.05621 | 0.528107 | − | 0.849178i | \(-0.322902\pi\) | ||||
0.528107 | + | 0.849178i | \(0.322902\pi\) | |||||||
\(884\) | 39.7107 | 1.33562 | ||||||||
\(885\) | 62.9908 | 2.11741 | ||||||||
\(886\) | −6.17970 | −0.207611 | ||||||||
\(887\) | −10.5544 | −0.354381 | −0.177191 | − | 0.984177i | \(-0.556701\pi\) | ||||
−0.177191 | + | 0.984177i | \(0.556701\pi\) | |||||||
\(888\) | −31.6839 | −1.06324 | ||||||||
\(889\) | −47.9520 | −1.60826 | ||||||||
\(890\) | 65.0123 | 2.17922 | ||||||||
\(891\) | 63.3244 | 2.12145 | ||||||||
\(892\) | 65.4651 | 2.19193 | ||||||||
\(893\) | −50.6004 | −1.69328 | ||||||||
\(894\) | −127.556 | −4.26612 | ||||||||
\(895\) | −37.4445 | −1.25163 | ||||||||
\(896\) | 184.407 | 6.16060 | ||||||||
\(897\) | 48.6859 | 1.62557 | ||||||||
\(898\) | 95.4431 | 3.18498 | ||||||||
\(899\) | 5.91961 | 0.197430 | ||||||||
\(900\) | −91.6353 | −3.05451 | ||||||||
\(901\) | 10.6585 | 0.355087 | ||||||||
\(902\) | 30.8315 | 1.02658 | ||||||||
\(903\) | 20.1809 | 0.671577 | ||||||||
\(904\) | 32.1064 | 1.06784 | ||||||||
\(905\) | −20.6545 | −0.686579 | ||||||||
\(906\) | 160.006 | 5.31585 | ||||||||
\(907\) | −37.3604 | −1.24053 | −0.620266 | − | 0.784391i | \(-0.712975\pi\) | ||||
−0.620266 | + | 0.784391i | \(0.712975\pi\) | |||||||
\(908\) | 1.15683 | 0.0383907 | ||||||||
\(909\) | 11.6808 | 0.387429 | ||||||||
\(910\) | −56.8458 | −1.88442 | ||||||||
\(911\) | −20.8312 | −0.690169 | −0.345085 | − | 0.938572i | \(-0.612150\pi\) | ||||
−0.345085 | + | 0.938572i | \(0.612150\pi\) | |||||||
\(912\) | −364.008 | −12.0535 | ||||||||
\(913\) | 38.3055 | 1.26773 | ||||||||
\(914\) | −47.9154 | −1.58490 | ||||||||
\(915\) | −35.3838 | −1.16975 | ||||||||
\(916\) | 26.9624 | 0.890862 | ||||||||
\(917\) | 32.8764 | 1.08568 | ||||||||
\(918\) | −59.6548 | −1.96890 | ||||||||
\(919\) | 49.6950 | 1.63929 | 0.819643 | − | 0.572874i | \(-0.194172\pi\) | ||||
0.819643 | + | 0.572874i | \(0.194172\pi\) | |||||||
\(920\) | 67.0743 | 2.21137 | ||||||||
\(921\) | 105.096 | 3.46304 | ||||||||
\(922\) | −60.4080 | −1.98943 | ||||||||
\(923\) | 8.12038 | 0.267286 | ||||||||
\(924\) | −229.908 | −7.56342 | ||||||||
\(925\) | −2.39705 | −0.0788144 | ||||||||
\(926\) | −99.9426 | −3.28432 | ||||||||
\(927\) | −95.9795 | −3.15238 | ||||||||
\(928\) | −84.2440 | −2.76545 | ||||||||
\(929\) | 25.5061 | 0.836827 | 0.418414 | − | 0.908257i | \(-0.362586\pi\) | ||||
0.418414 | + | 0.908257i | \(0.362586\pi\) | |||||||
\(930\) | 25.5988 | 0.839417 | ||||||||
\(931\) | −29.0534 | −0.952188 | ||||||||
\(932\) | −115.612 | −3.78699 | ||||||||
\(933\) | −2.39093 | −0.0782756 | ||||||||
\(934\) | −21.0436 | −0.688569 | ||||||||
\(935\) | −11.5501 | −0.377729 | ||||||||
\(936\) | −260.652 | −8.51966 | ||||||||
\(937\) | 7.39228 | 0.241495 | 0.120748 | − | 0.992683i | \(-0.461471\pi\) | ||||
0.120748 | + | 0.992683i | \(0.461471\pi\) | |||||||
\(938\) | 130.459 | 4.25963 | ||||||||
\(939\) | −28.0230 | −0.914496 | ||||||||
\(940\) | −66.5096 | −2.16930 | ||||||||
\(941\) | −28.9448 | −0.943574 | −0.471787 | − | 0.881712i | \(-0.656391\pi\) | ||||
−0.471787 | + | 0.881712i | \(0.656391\pi\) | |||||||
\(942\) | −11.2251 | −0.365734 | ||||||||
\(943\) | −11.7347 | −0.382134 | ||||||||
\(944\) | −209.662 | −6.82391 | ||||||||
\(945\) | 63.1148 | 2.05312 | ||||||||
\(946\) | 20.8097 | 0.676583 | ||||||||
\(947\) | 0.591774 | 0.0192301 | 0.00961504 | − | 0.999954i | \(-0.496939\pi\) | ||||
0.00961504 | + | 0.999954i | \(0.496939\pi\) | |||||||
\(948\) | −169.530 | −5.50609 | ||||||||
\(949\) | −13.8624 | −0.449992 | ||||||||
\(950\) | −46.1506 | −1.49732 | ||||||||
\(951\) | −34.6672 | −1.12416 | ||||||||
\(952\) | 62.4784 | 2.02494 | ||||||||
\(953\) | −34.2049 | −1.10801 | −0.554003 | − | 0.832515i | \(-0.686900\pi\) | ||||
−0.554003 | + | 0.832515i | \(0.686900\pi\) | |||||||
\(954\) | −108.133 | −3.50094 | ||||||||
\(955\) | −34.2069 | −1.10691 | ||||||||
\(956\) | 135.348 | 4.37747 | ||||||||
\(957\) | 39.1443 | 1.26536 | ||||||||
\(958\) | 63.5780 | 2.05411 | ||||||||
\(959\) | 28.4425 | 0.918457 | ||||||||
\(960\) | −195.401 | −6.30653 | ||||||||
\(961\) | −27.6307 | −0.891314 | ||||||||
\(962\) | −10.5386 | −0.339779 | ||||||||
\(963\) | 61.4883 | 1.98143 | ||||||||
\(964\) | −58.5947 | −1.88721 | ||||||||
\(965\) | 14.2281 | 0.458019 | ||||||||
\(966\) | 118.395 | 3.80931 | ||||||||
\(967\) | −2.83106 | −0.0910406 | −0.0455203 | − | 0.998963i | \(-0.514495\pi\) | ||||
−0.0455203 | + | 0.998963i | \(0.514495\pi\) | |||||||
\(968\) | −41.7511 | −1.34193 | ||||||||
\(969\) | −39.9803 | −1.28435 | ||||||||
\(970\) | 11.3962 | 0.365910 | ||||||||
\(971\) | 10.2022 | 0.327404 | 0.163702 | − | 0.986510i | \(-0.447656\pi\) | ||||
0.163702 | + | 0.986510i | \(0.447656\pi\) | |||||||
\(972\) | 89.2418 | 2.86243 | ||||||||
\(973\) | −33.7815 | −1.08299 | ||||||||
\(974\) | −65.6480 | −2.10350 | ||||||||
\(975\) | −28.4868 | −0.912309 | ||||||||
\(976\) | 117.773 | 3.76983 | ||||||||
\(977\) | 18.4032 | 0.588771 | 0.294386 | − | 0.955687i | \(-0.404885\pi\) | ||||
0.294386 | + | 0.955687i | \(0.404885\pi\) | |||||||
\(978\) | 86.5458 | 2.76743 | ||||||||
\(979\) | 56.5831 | 1.80840 | ||||||||
\(980\) | −38.1881 | −1.21987 | ||||||||
\(981\) | −6.74771 | −0.215438 | ||||||||
\(982\) | 17.1443 | 0.547095 | ||||||||
\(983\) | −22.6528 | −0.722512 | −0.361256 | − | 0.932467i | \(-0.617652\pi\) | ||||
−0.361256 | + | 0.932467i | \(0.617652\pi\) | |||||||
\(984\) | 90.7560 | 2.89319 | ||||||||
\(985\) | −28.2814 | −0.901121 | ||||||||
\(986\) | −16.4420 | −0.523619 | ||||||||
\(987\) | −75.9545 | −2.41766 | ||||||||
\(988\) | −149.961 | −4.77091 | ||||||||
\(989\) | −7.92032 | −0.251852 | ||||||||
\(990\) | 117.179 | 3.72418 | ||||||||
\(991\) | −24.9346 | −0.792073 | −0.396036 | − | 0.918235i | \(-0.629615\pi\) | ||||
−0.396036 | + | 0.918235i | \(0.629615\pi\) | |||||||
\(992\) | −47.9492 | −1.52239 | ||||||||
\(993\) | 57.3698 | 1.82058 | ||||||||
\(994\) | 19.7473 | 0.626348 | ||||||||
\(995\) | 22.7297 | 0.720579 | ||||||||
\(996\) | 174.281 | 5.52230 | ||||||||
\(997\) | 6.20822 | 0.196616 | 0.0983082 | − | 0.995156i | \(-0.468657\pi\) | ||||
0.0983082 | + | 0.995156i | \(0.468657\pi\) | |||||||
\(998\) | 113.511 | 3.59313 | ||||||||
\(999\) | 11.7008 | 0.370198 |
(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 | 4033.2.a.f.1.1 | ✓ | 85 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4033.2.a.f.1.1 | ✓ | 85 | 1.1 | even | 1 | trivial |