Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6019,2,Mod(1,6019)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6019, 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("6019.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6019 = 13 \cdot 463 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6019.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: | \(48.0619569766\) |
Analytic rank: | \(0\) |
Dimension: | \(123\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.5 | ||
Character | \(\chi\) | \(=\) | 6019.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.68053 | −1.89542 | −0.947709 | − | 0.319136i | \(-0.896607\pi\) | ||||
−0.947709 | + | 0.319136i | \(0.896607\pi\) | |||||||
\(3\) | 2.57455 | 1.48642 | 0.743208 | − | 0.669060i | \(-0.233303\pi\) | ||||
0.743208 | + | 0.669060i | \(0.233303\pi\) | |||||||
\(4\) | 5.18522 | 2.59261 | ||||||||
\(5\) | 0.534092 | 0.238853 | 0.119427 | − | 0.992843i | \(-0.461894\pi\) | ||||
0.119427 | + | 0.992843i | \(0.461894\pi\) | |||||||
\(6\) | −6.90114 | −2.81738 | ||||||||
\(7\) | −0.399106 | −0.150848 | −0.0754240 | − | 0.997152i | \(-0.524031\pi\) | ||||
−0.0754240 | + | 0.997152i | \(0.524031\pi\) | |||||||
\(8\) | −8.53805 | −3.01866 | ||||||||
\(9\) | 3.62830 | 1.20943 | ||||||||
\(10\) | −1.43165 | −0.452726 | ||||||||
\(11\) | 4.50922 | 1.35958 | 0.679791 | − | 0.733406i | \(-0.262071\pi\) | ||||
0.679791 | + | 0.733406i | \(0.262071\pi\) | |||||||
\(12\) | 13.3496 | 3.85370 | ||||||||
\(13\) | −1.00000 | −0.277350 | ||||||||
\(14\) | 1.06981 | 0.285920 | ||||||||
\(15\) | 1.37505 | 0.355035 | ||||||||
\(16\) | 12.5160 | 3.12901 | ||||||||
\(17\) | 1.29289 | 0.313572 | 0.156786 | − | 0.987633i | \(-0.449887\pi\) | ||||
0.156786 | + | 0.987633i | \(0.449887\pi\) | |||||||
\(18\) | −9.72575 | −2.29238 | ||||||||
\(19\) | 7.30769 | 1.67650 | 0.838250 | − | 0.545287i | \(-0.183579\pi\) | ||||
0.838250 | + | 0.545287i | \(0.183579\pi\) | |||||||
\(20\) | 2.76938 | 0.619253 | ||||||||
\(21\) | −1.02752 | −0.224223 | ||||||||
\(22\) | −12.0871 | −2.57698 | ||||||||
\(23\) | −7.37895 | −1.53862 | −0.769308 | − | 0.638878i | \(-0.779399\pi\) | ||||
−0.769308 | + | 0.638878i | \(0.779399\pi\) | |||||||
\(24\) | −21.9816 | −4.48698 | ||||||||
\(25\) | −4.71475 | −0.942949 | ||||||||
\(26\) | 2.68053 | 0.525694 | ||||||||
\(27\) | 1.61759 | 0.311306 | ||||||||
\(28\) | −2.06945 | −0.391090 | ||||||||
\(29\) | 6.66639 | 1.23792 | 0.618959 | − | 0.785423i | \(-0.287555\pi\) | ||||
0.618959 | + | 0.785423i | \(0.287555\pi\) | |||||||
\(30\) | −3.68584 | −0.672940 | ||||||||
\(31\) | −2.72165 | −0.488823 | −0.244412 | − | 0.969672i | \(-0.578595\pi\) | ||||
−0.244412 | + | 0.969672i | \(0.578595\pi\) | |||||||
\(32\) | −16.4735 | −2.91212 | ||||||||
\(33\) | 11.6092 | 2.02090 | ||||||||
\(34\) | −3.46563 | −0.594350 | ||||||||
\(35\) | −0.213159 | −0.0360305 | ||||||||
\(36\) | 18.8135 | 3.13559 | ||||||||
\(37\) | 3.40931 | 0.560487 | 0.280243 | − | 0.959929i | \(-0.409585\pi\) | ||||
0.280243 | + | 0.959929i | \(0.409585\pi\) | |||||||
\(38\) | −19.5885 | −3.17767 | ||||||||
\(39\) | −2.57455 | −0.412258 | ||||||||
\(40\) | −4.56010 | −0.721016 | ||||||||
\(41\) | −4.05490 | −0.633269 | −0.316635 | − | 0.948548i | \(-0.602553\pi\) | ||||
−0.316635 | + | 0.948548i | \(0.602553\pi\) | |||||||
\(42\) | 2.75429 | 0.424996 | ||||||||
\(43\) | −4.22886 | −0.644895 | −0.322447 | − | 0.946587i | \(-0.604506\pi\) | ||||
−0.322447 | + | 0.946587i | \(0.604506\pi\) | |||||||
\(44\) | 23.3813 | 3.52486 | ||||||||
\(45\) | 1.93785 | 0.288877 | ||||||||
\(46\) | 19.7795 | 2.91632 | ||||||||
\(47\) | 9.87568 | 1.44052 | 0.720258 | − | 0.693706i | \(-0.244023\pi\) | ||||
0.720258 | + | 0.693706i | \(0.244023\pi\) | |||||||
\(48\) | 32.2232 | 4.65101 | ||||||||
\(49\) | −6.84071 | −0.977245 | ||||||||
\(50\) | 12.6380 | 1.78728 | ||||||||
\(51\) | 3.32861 | 0.466099 | ||||||||
\(52\) | −5.18522 | −0.719060 | ||||||||
\(53\) | 9.58305 | 1.31633 | 0.658167 | − | 0.752872i | \(-0.271332\pi\) | ||||
0.658167 | + | 0.752872i | \(0.271332\pi\) | |||||||
\(54\) | −4.33600 | −0.590055 | ||||||||
\(55\) | 2.40834 | 0.324740 | ||||||||
\(56\) | 3.40759 | 0.455359 | ||||||||
\(57\) | 18.8140 | 2.49198 | ||||||||
\(58\) | −17.8694 | −2.34637 | ||||||||
\(59\) | 4.38788 | 0.571253 | 0.285627 | − | 0.958341i | \(-0.407798\pi\) | ||||
0.285627 | + | 0.958341i | \(0.407798\pi\) | |||||||
\(60\) | 7.12991 | 0.920467 | ||||||||
\(61\) | −3.61920 | −0.463391 | −0.231696 | − | 0.972788i | \(-0.574427\pi\) | ||||
−0.231696 | + | 0.972788i | \(0.574427\pi\) | |||||||
\(62\) | 7.29546 | 0.926524 | ||||||||
\(63\) | −1.44808 | −0.182441 | ||||||||
\(64\) | 19.1254 | 2.39068 | ||||||||
\(65\) | −0.534092 | −0.0662459 | ||||||||
\(66\) | −31.1188 | −3.83046 | ||||||||
\(67\) | 16.2603 | 1.98651 | 0.993253 | − | 0.115969i | \(-0.0369972\pi\) | ||||
0.993253 | + | 0.115969i | \(0.0369972\pi\) | |||||||
\(68\) | 6.70392 | 0.812969 | ||||||||
\(69\) | −18.9975 | −2.28703 | ||||||||
\(70\) | 0.571379 | 0.0682929 | ||||||||
\(71\) | 10.5362 | 1.25041 | 0.625207 | − | 0.780459i | \(-0.285014\pi\) | ||||
0.625207 | + | 0.780459i | \(0.285014\pi\) | |||||||
\(72\) | −30.9786 | −3.65087 | ||||||||
\(73\) | −9.52713 | −1.11507 | −0.557533 | − | 0.830155i | \(-0.688252\pi\) | ||||
−0.557533 | + | 0.830155i | \(0.688252\pi\) | |||||||
\(74\) | −9.13874 | −1.06236 | ||||||||
\(75\) | −12.1383 | −1.40162 | ||||||||
\(76\) | 37.8920 | 4.34651 | ||||||||
\(77\) | −1.79966 | −0.205090 | ||||||||
\(78\) | 6.90114 | 0.781401 | ||||||||
\(79\) | 16.4921 | 1.85551 | 0.927754 | − | 0.373192i | \(-0.121737\pi\) | ||||
0.927754 | + | 0.373192i | \(0.121737\pi\) | |||||||
\(80\) | 6.68471 | 0.747374 | ||||||||
\(81\) | −6.72033 | −0.746704 | ||||||||
\(82\) | 10.8693 | 1.20031 | ||||||||
\(83\) | 0.686373 | 0.0753392 | 0.0376696 | − | 0.999290i | \(-0.488007\pi\) | ||||
0.0376696 | + | 0.999290i | \(0.488007\pi\) | |||||||
\(84\) | −5.32791 | −0.581322 | ||||||||
\(85\) | 0.690522 | 0.0748976 | ||||||||
\(86\) | 11.3356 | 1.22234 | ||||||||
\(87\) | 17.1630 | 1.84006 | ||||||||
\(88\) | −38.5000 | −4.10411 | ||||||||
\(89\) | 12.1340 | 1.28620 | 0.643099 | − | 0.765783i | \(-0.277649\pi\) | ||||
0.643099 | + | 0.765783i | \(0.277649\pi\) | |||||||
\(90\) | −5.19445 | −0.547543 | ||||||||
\(91\) | 0.399106 | 0.0418377 | ||||||||
\(92\) | −38.2614 | −3.98903 | ||||||||
\(93\) | −7.00702 | −0.726595 | ||||||||
\(94\) | −26.4720 | −2.73038 | ||||||||
\(95\) | 3.90298 | 0.400437 | ||||||||
\(96\) | −42.4117 | −4.32863 | ||||||||
\(97\) | −10.1592 | −1.03151 | −0.515754 | − | 0.856737i | \(-0.672488\pi\) | ||||
−0.515754 | + | 0.856737i | \(0.672488\pi\) | |||||||
\(98\) | 18.3367 | 1.85229 | ||||||||
\(99\) | 16.3608 | 1.64432 | ||||||||
\(100\) | −24.4470 | −2.44470 | ||||||||
\(101\) | −15.2241 | −1.51486 | −0.757428 | − | 0.652919i | \(-0.773544\pi\) | ||||
−0.757428 | + | 0.652919i | \(0.773544\pi\) | |||||||
\(102\) | −8.92242 | −0.883452 | ||||||||
\(103\) | 17.5776 | 1.73198 | 0.865988 | − | 0.500065i | \(-0.166691\pi\) | ||||
0.865988 | + | 0.500065i | \(0.166691\pi\) | |||||||
\(104\) | 8.53805 | 0.837225 | ||||||||
\(105\) | −0.548789 | −0.0535564 | ||||||||
\(106\) | −25.6876 | −2.49500 | ||||||||
\(107\) | −1.70932 | −0.165247 | −0.0826233 | − | 0.996581i | \(-0.526330\pi\) | ||||
−0.0826233 | + | 0.996581i | \(0.526330\pi\) | |||||||
\(108\) | 8.38757 | 0.807094 | ||||||||
\(109\) | 3.14229 | 0.300977 | 0.150488 | − | 0.988612i | \(-0.451915\pi\) | ||||
0.150488 | + | 0.988612i | \(0.451915\pi\) | |||||||
\(110\) | −6.45561 | −0.615519 | ||||||||
\(111\) | 8.77743 | 0.833117 | ||||||||
\(112\) | −4.99523 | −0.472005 | ||||||||
\(113\) | −12.4763 | −1.17367 | −0.586837 | − | 0.809705i | \(-0.699627\pi\) | ||||
−0.586837 | + | 0.809705i | \(0.699627\pi\) | |||||||
\(114\) | −50.4314 | −4.72334 | ||||||||
\(115\) | −3.94103 | −0.367503 | ||||||||
\(116\) | 34.5667 | 3.20944 | ||||||||
\(117\) | −3.62830 | −0.335437 | ||||||||
\(118\) | −11.7618 | −1.08276 | ||||||||
\(119\) | −0.516001 | −0.0473017 | ||||||||
\(120\) | −11.7402 | −1.07173 | ||||||||
\(121\) | 9.33309 | 0.848463 | ||||||||
\(122\) | 9.70136 | 0.878320 | ||||||||
\(123\) | −10.4395 | −0.941302 | ||||||||
\(124\) | −14.1124 | −1.26733 | ||||||||
\(125\) | −5.18857 | −0.464079 | ||||||||
\(126\) | 3.88161 | 0.345801 | ||||||||
\(127\) | −8.07482 | −0.716525 | −0.358262 | − | 0.933621i | \(-0.616631\pi\) | ||||
−0.358262 | + | 0.933621i | \(0.616631\pi\) | |||||||
\(128\) | −18.3193 | −1.61921 | ||||||||
\(129\) | −10.8874 | −0.958582 | ||||||||
\(130\) | 1.43165 | 0.125564 | ||||||||
\(131\) | 8.27049 | 0.722596 | 0.361298 | − | 0.932450i | \(-0.382334\pi\) | ||||
0.361298 | + | 0.932450i | \(0.382334\pi\) | |||||||
\(132\) | 60.1963 | 5.23941 | ||||||||
\(133\) | −2.91655 | −0.252897 | ||||||||
\(134\) | −43.5860 | −3.76526 | ||||||||
\(135\) | 0.863943 | 0.0743564 | ||||||||
\(136\) | −11.0388 | −0.946567 | ||||||||
\(137\) | 9.89499 | 0.845386 | 0.422693 | − | 0.906273i | \(-0.361085\pi\) | ||||
0.422693 | + | 0.906273i | \(0.361085\pi\) | |||||||
\(138\) | 50.9232 | 4.33487 | ||||||||
\(139\) | −6.42624 | −0.545067 | −0.272533 | − | 0.962146i | \(-0.587862\pi\) | ||||
−0.272533 | + | 0.962146i | \(0.587862\pi\) | |||||||
\(140\) | −1.10528 | −0.0934130 | ||||||||
\(141\) | 25.4254 | 2.14121 | ||||||||
\(142\) | −28.2425 | −2.37006 | ||||||||
\(143\) | −4.50922 | −0.377080 | ||||||||
\(144\) | 45.4120 | 3.78433 | ||||||||
\(145\) | 3.56047 | 0.295681 | ||||||||
\(146\) | 25.5377 | 2.11352 | ||||||||
\(147\) | −17.6118 | −1.45259 | ||||||||
\(148\) | 17.6780 | 1.45312 | ||||||||
\(149\) | 21.2671 | 1.74227 | 0.871135 | − | 0.491043i | \(-0.163384\pi\) | ||||
0.871135 | + | 0.491043i | \(0.163384\pi\) | |||||||
\(150\) | 32.5371 | 2.65665 | ||||||||
\(151\) | −14.7604 | −1.20118 | −0.600591 | − | 0.799557i | \(-0.705068\pi\) | ||||
−0.600591 | + | 0.799557i | \(0.705068\pi\) | |||||||
\(152\) | −62.3935 | −5.06078 | ||||||||
\(153\) | 4.69100 | 0.379245 | ||||||||
\(154\) | 4.82403 | 0.388732 | ||||||||
\(155\) | −1.45361 | −0.116757 | ||||||||
\(156\) | −13.3496 | −1.06882 | ||||||||
\(157\) | 10.7573 | 0.858526 | 0.429263 | − | 0.903179i | \(-0.358773\pi\) | ||||
0.429263 | + | 0.903179i | \(0.358773\pi\) | |||||||
\(158\) | −44.2075 | −3.51696 | ||||||||
\(159\) | 24.6720 | 1.95662 | ||||||||
\(160\) | −8.79833 | −0.695569 | ||||||||
\(161\) | 2.94498 | 0.232097 | ||||||||
\(162\) | 18.0140 | 1.41532 | ||||||||
\(163\) | −14.1107 | −1.10524 | −0.552618 | − | 0.833435i | \(-0.686371\pi\) | ||||
−0.552618 | + | 0.833435i | \(0.686371\pi\) | |||||||
\(164\) | −21.0255 | −1.64182 | ||||||||
\(165\) | 6.20039 | 0.482699 | ||||||||
\(166\) | −1.83984 | −0.142799 | ||||||||
\(167\) | −8.49873 | −0.657651 | −0.328826 | − | 0.944391i | \(-0.606653\pi\) | ||||
−0.328826 | + | 0.944391i | \(0.606653\pi\) | |||||||
\(168\) | 8.77301 | 0.676853 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | −1.85096 | −0.141962 | ||||||||
\(171\) | 26.5145 | 2.02761 | ||||||||
\(172\) | −21.9275 | −1.67196 | ||||||||
\(173\) | 1.71633 | 0.130491 | 0.0652453 | − | 0.997869i | \(-0.479217\pi\) | ||||
0.0652453 | + | 0.997869i | \(0.479217\pi\) | |||||||
\(174\) | −46.0057 | −3.48769 | ||||||||
\(175\) | 1.88169 | 0.142242 | ||||||||
\(176\) | 56.4376 | 4.25414 | ||||||||
\(177\) | 11.2968 | 0.849120 | ||||||||
\(178\) | −32.5254 | −2.43788 | ||||||||
\(179\) | 20.1867 | 1.50882 | 0.754412 | − | 0.656402i | \(-0.227922\pi\) | ||||
0.754412 | + | 0.656402i | \(0.227922\pi\) | |||||||
\(180\) | 10.0482 | 0.748945 | ||||||||
\(181\) | 16.6693 | 1.23902 | 0.619511 | − | 0.784988i | \(-0.287331\pi\) | ||||
0.619511 | + | 0.784988i | \(0.287331\pi\) | |||||||
\(182\) | −1.06981 | −0.0793000 | ||||||||
\(183\) | −9.31781 | −0.688792 | ||||||||
\(184\) | 63.0018 | 4.64456 | ||||||||
\(185\) | 1.82088 | 0.133874 | ||||||||
\(186\) | 18.7825 | 1.37720 | ||||||||
\(187\) | 5.82993 | 0.426327 | ||||||||
\(188\) | 51.2075 | 3.73469 | ||||||||
\(189\) | −0.645592 | −0.0469599 | ||||||||
\(190\) | −10.4620 | −0.758995 | ||||||||
\(191\) | −1.23290 | −0.0892094 | −0.0446047 | − | 0.999005i | \(-0.514203\pi\) | ||||
−0.0446047 | + | 0.999005i | \(0.514203\pi\) | |||||||
\(192\) | 49.2394 | 3.55354 | ||||||||
\(193\) | −4.02322 | −0.289598 | −0.144799 | − | 0.989461i | \(-0.546254\pi\) | ||||
−0.144799 | + | 0.989461i | \(0.546254\pi\) | |||||||
\(194\) | 27.2319 | 1.95514 | ||||||||
\(195\) | −1.37505 | −0.0984690 | ||||||||
\(196\) | −35.4706 | −2.53361 | ||||||||
\(197\) | 18.0764 | 1.28789 | 0.643945 | − | 0.765072i | \(-0.277297\pi\) | ||||
0.643945 | + | 0.765072i | \(0.277297\pi\) | |||||||
\(198\) | −43.8556 | −3.11668 | ||||||||
\(199\) | −13.0350 | −0.924028 | −0.462014 | − | 0.886873i | \(-0.652873\pi\) | ||||
−0.462014 | + | 0.886873i | \(0.652873\pi\) | |||||||
\(200\) | 40.2548 | 2.84644 | ||||||||
\(201\) | 41.8628 | 2.95277 | ||||||||
\(202\) | 40.8086 | 2.87128 | ||||||||
\(203\) | −2.66060 | −0.186738 | ||||||||
\(204\) | 17.2596 | 1.20841 | ||||||||
\(205\) | −2.16569 | −0.151258 | ||||||||
\(206\) | −47.1173 | −3.28282 | ||||||||
\(207\) | −26.7730 | −1.86086 | ||||||||
\(208\) | −12.5160 | −0.867831 | ||||||||
\(209\) | 32.9520 | 2.27934 | ||||||||
\(210\) | 1.47104 | 0.101512 | ||||||||
\(211\) | 15.6901 | 1.08015 | 0.540074 | − | 0.841618i | \(-0.318396\pi\) | ||||
0.540074 | + | 0.841618i | \(0.318396\pi\) | |||||||
\(212\) | 49.6902 | 3.41274 | ||||||||
\(213\) | 27.1259 | 1.85864 | ||||||||
\(214\) | 4.58189 | 0.313211 | ||||||||
\(215\) | −2.25860 | −0.154035 | ||||||||
\(216\) | −13.8111 | −0.939726 | ||||||||
\(217\) | 1.08623 | 0.0737380 | ||||||||
\(218\) | −8.42299 | −0.570477 | ||||||||
\(219\) | −24.5281 | −1.65745 | ||||||||
\(220\) | 12.4878 | 0.841924 | ||||||||
\(221\) | −1.29289 | −0.0869692 | ||||||||
\(222\) | −23.5281 | −1.57910 | ||||||||
\(223\) | 21.1053 | 1.41332 | 0.706659 | − | 0.707555i | \(-0.250202\pi\) | ||||
0.706659 | + | 0.707555i | \(0.250202\pi\) | |||||||
\(224\) | 6.57466 | 0.439288 | ||||||||
\(225\) | −17.1065 | −1.14043 | ||||||||
\(226\) | 33.4431 | 2.22460 | ||||||||
\(227\) | 6.40630 | 0.425201 | 0.212601 | − | 0.977139i | \(-0.431807\pi\) | ||||
0.212601 | + | 0.977139i | \(0.431807\pi\) | |||||||
\(228\) | 97.5547 | 6.46072 | ||||||||
\(229\) | −12.5060 | −0.826418 | −0.413209 | − | 0.910636i | \(-0.635592\pi\) | ||||
−0.413209 | + | 0.910636i | \(0.635592\pi\) | |||||||
\(230\) | 10.5640 | 0.696572 | ||||||||
\(231\) | −4.63331 | −0.304850 | ||||||||
\(232\) | −56.9180 | −3.73685 | ||||||||
\(233\) | −11.9281 | −0.781437 | −0.390718 | − | 0.920510i | \(-0.627773\pi\) | ||||
−0.390718 | + | 0.920510i | \(0.627773\pi\) | |||||||
\(234\) | 9.72575 | 0.635792 | ||||||||
\(235\) | 5.27452 | 0.344072 | ||||||||
\(236\) | 22.7521 | 1.48104 | ||||||||
\(237\) | 42.4598 | 2.75806 | ||||||||
\(238\) | 1.38315 | 0.0896565 | ||||||||
\(239\) | 15.9409 | 1.03113 | 0.515566 | − | 0.856850i | \(-0.327582\pi\) | ||||
0.515566 | + | 0.856850i | \(0.327582\pi\) | |||||||
\(240\) | 17.2101 | 1.11091 | ||||||||
\(241\) | −6.11585 | −0.393957 | −0.196978 | − | 0.980408i | \(-0.563113\pi\) | ||||
−0.196978 | + | 0.980408i | \(0.563113\pi\) | |||||||
\(242\) | −25.0176 | −1.60819 | ||||||||
\(243\) | −22.1546 | −1.42122 | ||||||||
\(244\) | −18.7663 | −1.20139 | ||||||||
\(245\) | −3.65357 | −0.233418 | ||||||||
\(246\) | 27.9835 | 1.78416 | ||||||||
\(247\) | −7.30769 | −0.464977 | ||||||||
\(248\) | 23.2376 | 1.47559 | ||||||||
\(249\) | 1.76710 | 0.111985 | ||||||||
\(250\) | 13.9081 | 0.879624 | ||||||||
\(251\) | 17.9038 | 1.13007 | 0.565037 | − | 0.825065i | \(-0.308862\pi\) | ||||
0.565037 | + | 0.825065i | \(0.308862\pi\) | |||||||
\(252\) | −7.50860 | −0.472997 | ||||||||
\(253\) | −33.2733 | −2.09188 | ||||||||
\(254\) | 21.6448 | 1.35811 | ||||||||
\(255\) | 1.77778 | 0.111329 | ||||||||
\(256\) | 10.8545 | 0.678405 | ||||||||
\(257\) | 4.72125 | 0.294503 | 0.147252 | − | 0.989099i | \(-0.452957\pi\) | ||||
0.147252 | + | 0.989099i | \(0.452957\pi\) | |||||||
\(258\) | 29.1840 | 1.81691 | ||||||||
\(259\) | −1.36068 | −0.0845483 | ||||||||
\(260\) | −2.76938 | −0.171750 | ||||||||
\(261\) | 24.1877 | 1.49718 | ||||||||
\(262\) | −22.1693 | −1.36962 | ||||||||
\(263\) | −18.2069 | −1.12269 | −0.561344 | − | 0.827583i | \(-0.689715\pi\) | ||||
−0.561344 | + | 0.827583i | \(0.689715\pi\) | |||||||
\(264\) | −99.1201 | −6.10042 | ||||||||
\(265\) | 5.11823 | 0.314410 | ||||||||
\(266\) | 7.81788 | 0.479345 | ||||||||
\(267\) | 31.2395 | 1.91182 | ||||||||
\(268\) | 84.3129 | 5.15023 | ||||||||
\(269\) | −1.17983 | −0.0719357 | −0.0359679 | − | 0.999353i | \(-0.511451\pi\) | ||||
−0.0359679 | + | 0.999353i | \(0.511451\pi\) | |||||||
\(270\) | −2.31582 | −0.140936 | ||||||||
\(271\) | −15.5142 | −0.942420 | −0.471210 | − | 0.882021i | \(-0.656183\pi\) | ||||
−0.471210 | + | 0.882021i | \(0.656183\pi\) | |||||||
\(272\) | 16.1819 | 0.981170 | ||||||||
\(273\) | 1.02752 | 0.0621883 | ||||||||
\(274\) | −26.5238 | −1.60236 | ||||||||
\(275\) | −21.2598 | −1.28202 | ||||||||
\(276\) | −98.5059 | −5.92936 | ||||||||
\(277\) | −19.9138 | −1.19650 | −0.598251 | − | 0.801309i | \(-0.704137\pi\) | ||||
−0.598251 | + | 0.801309i | \(0.704137\pi\) | |||||||
\(278\) | 17.2257 | 1.03313 | ||||||||
\(279\) | −9.87497 | −0.591199 | ||||||||
\(280\) | 1.81997 | 0.108764 | ||||||||
\(281\) | −3.92335 | −0.234047 | −0.117024 | − | 0.993129i | \(-0.537335\pi\) | ||||
−0.117024 | + | 0.993129i | \(0.537335\pi\) | |||||||
\(282\) | −68.1535 | −4.05848 | ||||||||
\(283\) | −11.8402 | −0.703829 | −0.351914 | − | 0.936032i | \(-0.614469\pi\) | ||||
−0.351914 | + | 0.936032i | \(0.614469\pi\) | |||||||
\(284\) | 54.6324 | 3.24183 | ||||||||
\(285\) | 10.0484 | 0.595216 | ||||||||
\(286\) | 12.0871 | 0.714724 | ||||||||
\(287\) | 1.61834 | 0.0955274 | ||||||||
\(288\) | −59.7706 | −3.52202 | ||||||||
\(289\) | −15.3284 | −0.901673 | ||||||||
\(290\) | −9.54392 | −0.560438 | ||||||||
\(291\) | −26.1553 | −1.53325 | ||||||||
\(292\) | −49.4002 | −2.89093 | ||||||||
\(293\) | −14.3153 | −0.836309 | −0.418154 | − | 0.908376i | \(-0.637323\pi\) | ||||
−0.418154 | + | 0.908376i | \(0.637323\pi\) | |||||||
\(294\) | 47.2087 | 2.75327 | ||||||||
\(295\) | 2.34353 | 0.136446 | ||||||||
\(296\) | −29.1089 | −1.69192 | ||||||||
\(297\) | 7.29409 | 0.423246 | ||||||||
\(298\) | −57.0071 | −3.30233 | ||||||||
\(299\) | 7.37895 | 0.426735 | ||||||||
\(300\) | −62.9399 | −3.63384 | ||||||||
\(301\) | 1.68776 | 0.0972811 | ||||||||
\(302\) | 39.5655 | 2.27674 | ||||||||
\(303\) | −39.1952 | −2.25171 | ||||||||
\(304\) | 91.4633 | 5.24578 | ||||||||
\(305\) | −1.93299 | −0.110682 | ||||||||
\(306\) | −12.5743 | −0.718827 | ||||||||
\(307\) | −27.8312 | −1.58841 | −0.794206 | − | 0.607649i | \(-0.792113\pi\) | ||||
−0.794206 | + | 0.607649i | \(0.792113\pi\) | |||||||
\(308\) | −9.33163 | −0.531719 | ||||||||
\(309\) | 45.2545 | 2.57444 | ||||||||
\(310\) | 3.89644 | 0.221303 | ||||||||
\(311\) | 25.4016 | 1.44039 | 0.720196 | − | 0.693770i | \(-0.244052\pi\) | ||||
0.720196 | + | 0.693770i | \(0.244052\pi\) | |||||||
\(312\) | 21.9816 | 1.24447 | ||||||||
\(313\) | −10.8694 | −0.614377 | −0.307188 | − | 0.951649i | \(-0.599388\pi\) | ||||
−0.307188 | + | 0.951649i | \(0.599388\pi\) | |||||||
\(314\) | −28.8352 | −1.62727 | ||||||||
\(315\) | −0.773407 | −0.0435765 | ||||||||
\(316\) | 85.5152 | 4.81061 | ||||||||
\(317\) | −21.2662 | −1.19443 | −0.597214 | − | 0.802082i | \(-0.703726\pi\) | ||||
−0.597214 | + | 0.802082i | \(0.703726\pi\) | |||||||
\(318\) | −66.1340 | −3.70861 | ||||||||
\(319\) | 30.0603 | 1.68305 | ||||||||
\(320\) | 10.2147 | 0.571021 | ||||||||
\(321\) | −4.40074 | −0.245625 | ||||||||
\(322\) | −7.89411 | −0.439921 | ||||||||
\(323\) | 9.44804 | 0.525703 | ||||||||
\(324\) | −34.8464 | −1.93591 | ||||||||
\(325\) | 4.71475 | 0.261527 | ||||||||
\(326\) | 37.8241 | 2.09488 | ||||||||
\(327\) | 8.08998 | 0.447377 | ||||||||
\(328\) | 34.6210 | 1.91162 | ||||||||
\(329\) | −3.94145 | −0.217299 | ||||||||
\(330\) | −16.6203 | −0.914917 | ||||||||
\(331\) | −10.1876 | −0.559962 | −0.279981 | − | 0.960006i | \(-0.590328\pi\) | ||||
−0.279981 | + | 0.960006i | \(0.590328\pi\) | |||||||
\(332\) | 3.55899 | 0.195325 | ||||||||
\(333\) | 12.3700 | 0.677872 | ||||||||
\(334\) | 22.7811 | 1.24652 | ||||||||
\(335\) | 8.68447 | 0.474483 | ||||||||
\(336\) | −12.8605 | −0.701596 | ||||||||
\(337\) | 8.26483 | 0.450214 | 0.225107 | − | 0.974334i | \(-0.427727\pi\) | ||||
0.225107 | + | 0.974334i | \(0.427727\pi\) | |||||||
\(338\) | −2.68053 | −0.145801 | ||||||||
\(339\) | −32.1209 | −1.74457 | ||||||||
\(340\) | 3.58051 | 0.194180 | ||||||||
\(341\) | −12.2725 | −0.664595 | ||||||||
\(342\) | −71.0728 | −3.84318 | ||||||||
\(343\) | 5.52392 | 0.298264 | ||||||||
\(344\) | 36.1062 | 1.94672 | ||||||||
\(345\) | −10.1464 | −0.546263 | ||||||||
\(346\) | −4.60068 | −0.247334 | ||||||||
\(347\) | 32.5233 | 1.74594 | 0.872972 | − | 0.487771i | \(-0.162190\pi\) | ||||
0.872972 | + | 0.487771i | \(0.162190\pi\) | |||||||
\(348\) | 88.9936 | 4.77056 | ||||||||
\(349\) | 29.9808 | 1.60484 | 0.802419 | − | 0.596761i | \(-0.203546\pi\) | ||||
0.802419 | + | 0.596761i | \(0.203546\pi\) | |||||||
\(350\) | −5.04391 | −0.269608 | ||||||||
\(351\) | −1.61759 | −0.0863407 | ||||||||
\(352\) | −74.2825 | −3.95927 | ||||||||
\(353\) | 4.76639 | 0.253689 | 0.126845 | − | 0.991923i | \(-0.459515\pi\) | ||||
0.126845 | + | 0.991923i | \(0.459515\pi\) | |||||||
\(354\) | −30.2814 | −1.60944 | ||||||||
\(355\) | 5.62729 | 0.298665 | ||||||||
\(356\) | 62.9172 | 3.33461 | ||||||||
\(357\) | −1.32847 | −0.0703101 | ||||||||
\(358\) | −54.1109 | −2.85985 | ||||||||
\(359\) | −22.3661 | −1.18044 | −0.590219 | − | 0.807243i | \(-0.700959\pi\) | ||||
−0.590219 | + | 0.807243i | \(0.700959\pi\) | |||||||
\(360\) | −16.5454 | −0.872021 | ||||||||
\(361\) | 34.4023 | 1.81065 | ||||||||
\(362\) | −44.6826 | −2.34846 | ||||||||
\(363\) | 24.0285 | 1.26117 | ||||||||
\(364\) | 2.06945 | 0.108469 | ||||||||
\(365\) | −5.08836 | −0.266337 | ||||||||
\(366\) | 24.9766 | 1.30555 | ||||||||
\(367\) | −15.8433 | −0.827015 | −0.413508 | − | 0.910501i | \(-0.635697\pi\) | ||||
−0.413508 | + | 0.910501i | \(0.635697\pi\) | |||||||
\(368\) | −92.3552 | −4.81435 | ||||||||
\(369\) | −14.7124 | −0.765897 | ||||||||
\(370\) | −4.88092 | −0.253747 | ||||||||
\(371\) | −3.82466 | −0.198566 | ||||||||
\(372\) | −36.3329 | −1.88378 | ||||||||
\(373\) | 32.5864 | 1.68726 | 0.843631 | − | 0.536924i | \(-0.180414\pi\) | ||||
0.843631 | + | 0.536924i | \(0.180414\pi\) | |||||||
\(374\) | −15.6273 | −0.808067 | ||||||||
\(375\) | −13.3582 | −0.689815 | ||||||||
\(376\) | −84.3191 | −4.34843 | ||||||||
\(377\) | −6.66639 | −0.343337 | ||||||||
\(378\) | 1.73052 | 0.0890086 | ||||||||
\(379\) | 19.5206 | 1.00271 | 0.501354 | − | 0.865242i | \(-0.332836\pi\) | ||||
0.501354 | + | 0.865242i | \(0.332836\pi\) | |||||||
\(380\) | 20.2378 | 1.03818 | ||||||||
\(381\) | −20.7890 | −1.06505 | ||||||||
\(382\) | 3.30482 | 0.169089 | ||||||||
\(383\) | −20.3850 | −1.04163 | −0.520813 | − | 0.853671i | \(-0.674371\pi\) | ||||
−0.520813 | + | 0.853671i | \(0.674371\pi\) | |||||||
\(384\) | −47.1639 | −2.40682 | ||||||||
\(385\) | −0.961183 | −0.0489864 | ||||||||
\(386\) | 10.7843 | 0.548909 | ||||||||
\(387\) | −15.3436 | −0.779958 | ||||||||
\(388\) | −52.6775 | −2.67430 | ||||||||
\(389\) | −29.4252 | −1.49192 | −0.745959 | − | 0.665991i | \(-0.768009\pi\) | ||||
−0.745959 | + | 0.665991i | \(0.768009\pi\) | |||||||
\(390\) | 3.68584 | 0.186640 | ||||||||
\(391\) | −9.54017 | −0.482467 | ||||||||
\(392\) | 58.4064 | 2.94997 | ||||||||
\(393\) | 21.2928 | 1.07408 | ||||||||
\(394\) | −48.4543 | −2.44109 | ||||||||
\(395\) | 8.80831 | 0.443194 | ||||||||
\(396\) | 84.8344 | 4.26309 | ||||||||
\(397\) | 33.3559 | 1.67408 | 0.837042 | − | 0.547138i | \(-0.184283\pi\) | ||||
0.837042 | + | 0.547138i | \(0.184283\pi\) | |||||||
\(398\) | 34.9407 | 1.75142 | ||||||||
\(399\) | −7.50879 | −0.375910 | ||||||||
\(400\) | −59.0099 | −2.95050 | ||||||||
\(401\) | 32.7964 | 1.63777 | 0.818887 | − | 0.573954i | \(-0.194591\pi\) | ||||
0.818887 | + | 0.573954i | \(0.194591\pi\) | |||||||
\(402\) | −112.214 | −5.59674 | ||||||||
\(403\) | 2.72165 | 0.135575 | ||||||||
\(404\) | −78.9403 | −3.92743 | ||||||||
\(405\) | −3.58927 | −0.178352 | ||||||||
\(406\) | 7.13181 | 0.353946 | ||||||||
\(407\) | 15.3733 | 0.762027 | ||||||||
\(408\) | −28.4199 | −1.40699 | ||||||||
\(409\) | −28.8141 | −1.42476 | −0.712382 | − | 0.701791i | \(-0.752384\pi\) | ||||
−0.712382 | + | 0.701791i | \(0.752384\pi\) | |||||||
\(410\) | 5.80519 | 0.286698 | ||||||||
\(411\) | 25.4751 | 1.25660 | ||||||||
\(412\) | 91.1438 | 4.49033 | ||||||||
\(413\) | −1.75123 | −0.0861724 | ||||||||
\(414\) | 71.7658 | 3.52710 | ||||||||
\(415\) | 0.366586 | 0.0179950 | ||||||||
\(416\) | 16.4735 | 0.807677 | ||||||||
\(417\) | −16.5447 | −0.810196 | ||||||||
\(418\) | −88.3287 | −4.32030 | ||||||||
\(419\) | 17.8069 | 0.869924 | 0.434962 | − | 0.900449i | \(-0.356762\pi\) | ||||
0.434962 | + | 0.900449i | \(0.356762\pi\) | |||||||
\(420\) | −2.84559 | −0.138851 | ||||||||
\(421\) | 31.8425 | 1.55191 | 0.775955 | − | 0.630788i | \(-0.217268\pi\) | ||||
0.775955 | + | 0.630788i | \(0.217268\pi\) | |||||||
\(422\) | −42.0576 | −2.04733 | ||||||||
\(423\) | 35.8319 | 1.74221 | ||||||||
\(424\) | −81.8206 | −3.97356 | ||||||||
\(425\) | −6.09565 | −0.295682 | ||||||||
\(426\) | −72.7117 | −3.52289 | ||||||||
\(427\) | 1.44445 | 0.0699017 | ||||||||
\(428\) | −8.86322 | −0.428420 | ||||||||
\(429\) | −11.6092 | −0.560498 | ||||||||
\(430\) | 6.05423 | 0.291961 | ||||||||
\(431\) | 24.1099 | 1.16133 | 0.580666 | − | 0.814142i | \(-0.302792\pi\) | ||||
0.580666 | + | 0.814142i | \(0.302792\pi\) | |||||||
\(432\) | 20.2459 | 0.974079 | ||||||||
\(433\) | −7.24476 | −0.348161 | −0.174080 | − | 0.984731i | \(-0.555695\pi\) | ||||
−0.174080 | + | 0.984731i | \(0.555695\pi\) | |||||||
\(434\) | −2.91166 | −0.139764 | ||||||||
\(435\) | 9.16659 | 0.439504 | ||||||||
\(436\) | 16.2934 | 0.780315 | ||||||||
\(437\) | −53.9231 | −2.57949 | ||||||||
\(438\) | 65.7481 | 3.14157 | ||||||||
\(439\) | −18.9953 | −0.906595 | −0.453298 | − | 0.891359i | \(-0.649753\pi\) | ||||
−0.453298 | + | 0.891359i | \(0.649753\pi\) | |||||||
\(440\) | −20.5625 | −0.980280 | ||||||||
\(441\) | −24.8202 | −1.18191 | ||||||||
\(442\) | 3.46563 | 0.164843 | ||||||||
\(443\) | 18.7614 | 0.891381 | 0.445690 | − | 0.895187i | \(-0.352958\pi\) | ||||
0.445690 | + | 0.895187i | \(0.352958\pi\) | |||||||
\(444\) | 45.5129 | 2.15995 | ||||||||
\(445\) | 6.48065 | 0.307212 | ||||||||
\(446\) | −56.5734 | −2.67883 | ||||||||
\(447\) | 54.7532 | 2.58974 | ||||||||
\(448\) | −7.63308 | −0.360629 | ||||||||
\(449\) | −12.7693 | −0.602620 | −0.301310 | − | 0.953526i | \(-0.597424\pi\) | ||||
−0.301310 | + | 0.953526i | \(0.597424\pi\) | |||||||
\(450\) | 45.8545 | 2.16160 | ||||||||
\(451\) | −18.2845 | −0.860981 | ||||||||
\(452\) | −64.6925 | −3.04288 | ||||||||
\(453\) | −38.0013 | −1.78546 | ||||||||
\(454\) | −17.1723 | −0.805934 | ||||||||
\(455\) | 0.213159 | 0.00999307 | ||||||||
\(456\) | −160.635 | −7.52242 | ||||||||
\(457\) | −32.2774 | −1.50988 | −0.754938 | − | 0.655797i | \(-0.772333\pi\) | ||||
−0.754938 | + | 0.655797i | \(0.772333\pi\) | |||||||
\(458\) | 33.5226 | 1.56641 | ||||||||
\(459\) | 2.09137 | 0.0976168 | ||||||||
\(460\) | −20.4351 | −0.952792 | ||||||||
\(461\) | −3.07885 | −0.143396 | −0.0716982 | − | 0.997426i | \(-0.522842\pi\) | ||||
−0.0716982 | + | 0.997426i | \(0.522842\pi\) | |||||||
\(462\) | 12.4197 | 0.577817 | ||||||||
\(463\) | 1.00000 | 0.0464739 | ||||||||
\(464\) | 83.4368 | 3.87346 | ||||||||
\(465\) | −3.74239 | −0.173549 | ||||||||
\(466\) | 31.9736 | 1.48115 | ||||||||
\(467\) | 5.37733 | 0.248833 | 0.124417 | − | 0.992230i | \(-0.460294\pi\) | ||||
0.124417 | + | 0.992230i | \(0.460294\pi\) | |||||||
\(468\) | −18.8135 | −0.869656 | ||||||||
\(469\) | −6.48957 | −0.299661 | ||||||||
\(470\) | −14.1385 | −0.652160 | ||||||||
\(471\) | 27.6952 | 1.27613 | ||||||||
\(472\) | −37.4639 | −1.72442 | ||||||||
\(473\) | −19.0689 | −0.876787 | ||||||||
\(474\) | −113.814 | −5.22767 | ||||||||
\(475\) | −34.4539 | −1.58085 | ||||||||
\(476\) | −2.67558 | −0.122635 | ||||||||
\(477\) | 34.7702 | 1.59202 | ||||||||
\(478\) | −42.7300 | −1.95443 | ||||||||
\(479\) | 20.0439 | 0.915829 | 0.457914 | − | 0.888996i | \(-0.348597\pi\) | ||||
0.457914 | + | 0.888996i | \(0.348597\pi\) | |||||||
\(480\) | −22.6517 | −1.03391 | ||||||||
\(481\) | −3.40931 | −0.155451 | ||||||||
\(482\) | 16.3937 | 0.746712 | ||||||||
\(483\) | 7.58201 | 0.344993 | ||||||||
\(484\) | 48.3941 | 2.19973 | ||||||||
\(485\) | −5.42593 | −0.246379 | ||||||||
\(486\) | 59.3860 | 2.69380 | ||||||||
\(487\) | −5.29203 | −0.239805 | −0.119902 | − | 0.992786i | \(-0.538258\pi\) | ||||
−0.119902 | + | 0.992786i | \(0.538258\pi\) | |||||||
\(488\) | 30.9009 | 1.39882 | ||||||||
\(489\) | −36.3287 | −1.64284 | ||||||||
\(490\) | 9.79348 | 0.442425 | ||||||||
\(491\) | −1.37754 | −0.0621674 | −0.0310837 | − | 0.999517i | \(-0.509896\pi\) | ||||
−0.0310837 | + | 0.999517i | \(0.509896\pi\) | |||||||
\(492\) | −54.1313 | −2.44043 | ||||||||
\(493\) | 8.61892 | 0.388177 | ||||||||
\(494\) | 19.5885 | 0.881326 | ||||||||
\(495\) | 8.73818 | 0.392752 | ||||||||
\(496\) | −34.0643 | −1.52953 | ||||||||
\(497\) | −4.20506 | −0.188623 | ||||||||
\(498\) | −4.73676 | −0.212259 | ||||||||
\(499\) | −14.4239 | −0.645702 | −0.322851 | − | 0.946450i | \(-0.604641\pi\) | ||||
−0.322851 | + | 0.946450i | \(0.604641\pi\) | |||||||
\(500\) | −26.9038 | −1.20318 | ||||||||
\(501\) | −21.8804 | −0.977544 | ||||||||
\(502\) | −47.9915 | −2.14196 | ||||||||
\(503\) | −20.1771 | −0.899653 | −0.449827 | − | 0.893116i | \(-0.648514\pi\) | ||||
−0.449827 | + | 0.893116i | \(0.648514\pi\) | |||||||
\(504\) | 12.3638 | 0.550726 | ||||||||
\(505\) | −8.13107 | −0.361828 | ||||||||
\(506\) | 89.1900 | 3.96498 | ||||||||
\(507\) | 2.57455 | 0.114340 | ||||||||
\(508\) | −41.8697 | −1.85767 | ||||||||
\(509\) | −38.9812 | −1.72781 | −0.863905 | − | 0.503654i | \(-0.831988\pi\) | ||||
−0.863905 | + | 0.503654i | \(0.831988\pi\) | |||||||
\(510\) | −4.76539 | −0.211015 | ||||||||
\(511\) | 3.80234 | 0.168206 | ||||||||
\(512\) | 7.54288 | 0.333351 | ||||||||
\(513\) | 11.8209 | 0.521904 | ||||||||
\(514\) | −12.6554 | −0.558207 | ||||||||
\(515\) | 9.38807 | 0.413688 | ||||||||
\(516\) | −56.4535 | −2.48523 | ||||||||
\(517\) | 44.5316 | 1.95850 | ||||||||
\(518\) | 3.64733 | 0.160254 | ||||||||
\(519\) | 4.41879 | 0.193963 | ||||||||
\(520\) | 4.56010 | 0.199974 | ||||||||
\(521\) | −26.3797 | −1.15571 | −0.577857 | − | 0.816138i | \(-0.696111\pi\) | ||||
−0.577857 | + | 0.816138i | \(0.696111\pi\) | |||||||
\(522\) | −64.8357 | −2.83778 | ||||||||
\(523\) | −21.3338 | −0.932861 | −0.466430 | − | 0.884558i | \(-0.654460\pi\) | ||||
−0.466430 | + | 0.884558i | \(0.654460\pi\) | |||||||
\(524\) | 42.8843 | 1.87341 | ||||||||
\(525\) | 4.84449 | 0.211431 | ||||||||
\(526\) | 48.8041 | 2.12796 | ||||||||
\(527\) | −3.51880 | −0.153281 | ||||||||
\(528\) | 145.301 | 6.32343 | ||||||||
\(529\) | 31.4488 | 1.36734 | ||||||||
\(530\) | −13.7195 | −0.595939 | ||||||||
\(531\) | 15.9205 | 0.690893 | ||||||||
\(532\) | −15.1229 | −0.655662 | ||||||||
\(533\) | 4.05490 | 0.175637 | ||||||||
\(534\) | −83.7382 | −3.62371 | ||||||||
\(535\) | −0.912936 | −0.0394697 | ||||||||
\(536\) | −138.831 | −5.99658 | ||||||||
\(537\) | 51.9716 | 2.24274 | ||||||||
\(538\) | 3.16257 | 0.136348 | ||||||||
\(539\) | −30.8463 | −1.32864 | ||||||||
\(540\) | 4.47973 | 0.192777 | ||||||||
\(541\) | 22.1475 | 0.952194 | 0.476097 | − | 0.879393i | \(-0.342051\pi\) | ||||
0.476097 | + | 0.879393i | \(0.342051\pi\) | |||||||
\(542\) | 41.5862 | 1.78628 | ||||||||
\(543\) | 42.9160 | 1.84170 | ||||||||
\(544\) | −21.2984 | −0.913160 | ||||||||
\(545\) | 1.67827 | 0.0718892 | ||||||||
\(546\) | −2.75429 | −0.117873 | ||||||||
\(547\) | −32.4608 | −1.38792 | −0.693962 | − | 0.720012i | \(-0.744136\pi\) | ||||
−0.693962 | + | 0.720012i | \(0.744136\pi\) | |||||||
\(548\) | 51.3077 | 2.19176 | ||||||||
\(549\) | −13.1316 | −0.560441 | ||||||||
\(550\) | 56.9875 | 2.42996 | ||||||||
\(551\) | 48.7159 | 2.07537 | ||||||||
\(552\) | 162.201 | 6.90375 | ||||||||
\(553\) | −6.58211 | −0.279900 | ||||||||
\(554\) | 53.3793 | 2.26787 | ||||||||
\(555\) | 4.68795 | 0.198992 | ||||||||
\(556\) | −33.3215 | −1.41314 | ||||||||
\(557\) | −3.19164 | −0.135234 | −0.0676171 | − | 0.997711i | \(-0.521540\pi\) | ||||
−0.0676171 | + | 0.997711i | \(0.521540\pi\) | |||||||
\(558\) | 26.4701 | 1.12057 | ||||||||
\(559\) | 4.22886 | 0.178862 | ||||||||
\(560\) | −2.66791 | −0.112740 | ||||||||
\(561\) | 15.0094 | 0.633699 | ||||||||
\(562\) | 10.5166 | 0.443618 | ||||||||
\(563\) | 0.748163 | 0.0315313 | 0.0157656 | − | 0.999876i | \(-0.494981\pi\) | ||||
0.0157656 | + | 0.999876i | \(0.494981\pi\) | |||||||
\(564\) | 131.836 | 5.55131 | ||||||||
\(565\) | −6.66350 | −0.280336 | ||||||||
\(566\) | 31.7380 | 1.33405 | ||||||||
\(567\) | 2.68213 | 0.112639 | ||||||||
\(568\) | −89.9585 | −3.77457 | ||||||||
\(569\) | −35.8158 | −1.50148 | −0.750738 | − | 0.660600i | \(-0.770302\pi\) | ||||
−0.750738 | + | 0.660600i | \(0.770302\pi\) | |||||||
\(570\) | −26.9350 | −1.12818 | ||||||||
\(571\) | 7.39058 | 0.309286 | 0.154643 | − | 0.987970i | \(-0.450577\pi\) | ||||
0.154643 | + | 0.987970i | \(0.450577\pi\) | |||||||
\(572\) | −23.3813 | −0.977621 | ||||||||
\(573\) | −3.17416 | −0.132602 | ||||||||
\(574\) | −4.33799 | −0.181064 | ||||||||
\(575\) | 34.7899 | 1.45084 | ||||||||
\(576\) | 69.3928 | 2.89137 | ||||||||
\(577\) | −12.6445 | −0.526397 | −0.263198 | − | 0.964742i | \(-0.584777\pi\) | ||||
−0.263198 | + | 0.964742i | \(0.584777\pi\) | |||||||
\(578\) | 41.0883 | 1.70905 | ||||||||
\(579\) | −10.3580 | −0.430463 | ||||||||
\(580\) | 18.4618 | 0.766584 | ||||||||
\(581\) | −0.273936 | −0.0113648 | ||||||||
\(582\) | 70.1100 | 2.90615 | ||||||||
\(583\) | 43.2121 | 1.78966 | ||||||||
\(584\) | 81.3432 | 3.36600 | ||||||||
\(585\) | −1.93785 | −0.0801201 | ||||||||
\(586\) | 38.3725 | 1.58515 | ||||||||
\(587\) | −3.36445 | −0.138866 | −0.0694328 | − | 0.997587i | \(-0.522119\pi\) | ||||
−0.0694328 | + | 0.997587i | \(0.522119\pi\) | |||||||
\(588\) | −91.3208 | −3.76600 | ||||||||
\(589\) | −19.8890 | −0.819511 | ||||||||
\(590\) | −6.28189 | −0.258621 | ||||||||
\(591\) | 46.5386 | 1.91434 | ||||||||
\(592\) | 42.6710 | 1.75377 | ||||||||
\(593\) | 5.86069 | 0.240670 | 0.120335 | − | 0.992733i | \(-0.461603\pi\) | ||||
0.120335 | + | 0.992733i | \(0.461603\pi\) | |||||||
\(594\) | −19.5520 | −0.802228 | ||||||||
\(595\) | −0.275592 | −0.0112982 | ||||||||
\(596\) | 110.275 | 4.51702 | ||||||||
\(597\) | −33.5593 | −1.37349 | ||||||||
\(598\) | −19.7795 | −0.808842 | ||||||||
\(599\) | 33.8138 | 1.38159 | 0.690797 | − | 0.723049i | \(-0.257260\pi\) | ||||
0.690797 | + | 0.723049i | \(0.257260\pi\) | |||||||
\(600\) | 103.638 | 4.23100 | ||||||||
\(601\) | −28.6189 | −1.16739 | −0.583694 | − | 0.811973i | \(-0.698393\pi\) | ||||
−0.583694 | + | 0.811973i | \(0.698393\pi\) | |||||||
\(602\) | −4.52410 | −0.184388 | ||||||||
\(603\) | 58.9971 | 2.40255 | ||||||||
\(604\) | −76.5357 | −3.11419 | ||||||||
\(605\) | 4.98473 | 0.202658 | ||||||||
\(606\) | 105.064 | 4.26792 | ||||||||
\(607\) | 20.9237 | 0.849269 | 0.424634 | − | 0.905365i | \(-0.360403\pi\) | ||||
0.424634 | + | 0.905365i | \(0.360403\pi\) | |||||||
\(608\) | −120.383 | −4.88217 | ||||||||
\(609\) | −6.84985 | −0.277570 | ||||||||
\(610\) | 5.18142 | 0.209789 | ||||||||
\(611\) | −9.87568 | −0.399527 | ||||||||
\(612\) | 24.3238 | 0.983233 | ||||||||
\(613\) | −14.6232 | −0.590626 | −0.295313 | − | 0.955401i | \(-0.595424\pi\) | ||||
−0.295313 | + | 0.955401i | \(0.595424\pi\) | |||||||
\(614\) | 74.6023 | 3.01070 | ||||||||
\(615\) | −5.57567 | −0.224833 | ||||||||
\(616\) | 15.3656 | 0.619097 | ||||||||
\(617\) | 40.9032 | 1.64670 | 0.823350 | − | 0.567533i | \(-0.192102\pi\) | ||||
0.823350 | + | 0.567533i | \(0.192102\pi\) | |||||||
\(618\) | −121.306 | −4.87963 | ||||||||
\(619\) | 39.6735 | 1.59461 | 0.797306 | − | 0.603576i | \(-0.206258\pi\) | ||||
0.797306 | + | 0.603576i | \(0.206258\pi\) | |||||||
\(620\) | −7.53729 | −0.302705 | ||||||||
\(621\) | −11.9361 | −0.478980 | ||||||||
\(622\) | −68.0896 | −2.73015 | ||||||||
\(623\) | −4.84274 | −0.194020 | ||||||||
\(624\) | −32.2232 | −1.28996 | ||||||||
\(625\) | 20.8026 | 0.832102 | ||||||||
\(626\) | 29.1358 | 1.16450 | ||||||||
\(627\) | 84.8365 | 3.38805 | ||||||||
\(628\) | 55.7790 | 2.22582 | ||||||||
\(629\) | 4.40786 | 0.175753 | ||||||||
\(630\) | 2.07314 | 0.0825957 | ||||||||
\(631\) | 34.0368 | 1.35498 | 0.677491 | − | 0.735531i | \(-0.263067\pi\) | ||||
0.677491 | + | 0.735531i | \(0.263067\pi\) | |||||||
\(632\) | −140.811 | −5.60115 | ||||||||
\(633\) | 40.3948 | 1.60555 | ||||||||
\(634\) | 57.0046 | 2.26394 | ||||||||
\(635\) | −4.31270 | −0.171144 | ||||||||
\(636\) | 127.930 | 5.07275 | ||||||||
\(637\) | 6.84071 | 0.271039 | ||||||||
\(638\) | −80.5773 | −3.19008 | ||||||||
\(639\) | 38.2284 | 1.51229 | ||||||||
\(640\) | −9.78418 | −0.386754 | ||||||||
\(641\) | −38.9063 | −1.53671 | −0.768353 | − | 0.640026i | \(-0.778924\pi\) | ||||
−0.768353 | + | 0.640026i | \(0.778924\pi\) | |||||||
\(642\) | 11.7963 | 0.465563 | ||||||||
\(643\) | −30.6463 | −1.20857 | −0.604286 | − | 0.796767i | \(-0.706542\pi\) | ||||
−0.604286 | + | 0.796767i | \(0.706542\pi\) | |||||||
\(644\) | 15.2704 | 0.601737 | ||||||||
\(645\) | −5.81487 | −0.228960 | ||||||||
\(646\) | −25.3257 | −0.996427 | ||||||||
\(647\) | −6.08696 | −0.239303 | −0.119652 | − | 0.992816i | \(-0.538178\pi\) | ||||
−0.119652 | + | 0.992816i | \(0.538178\pi\) | |||||||
\(648\) | 57.3786 | 2.25404 | ||||||||
\(649\) | 19.7859 | 0.776665 | ||||||||
\(650\) | −12.6380 | −0.495703 | ||||||||
\(651\) | 2.79655 | 0.109605 | ||||||||
\(652\) | −73.1671 | −2.86544 | ||||||||
\(653\) | 10.2487 | 0.401063 | 0.200531 | − | 0.979687i | \(-0.435733\pi\) | ||||
0.200531 | + | 0.979687i | \(0.435733\pi\) | |||||||
\(654\) | −21.6854 | −0.847966 | ||||||||
\(655\) | 4.41720 | 0.172594 | ||||||||
\(656\) | −50.7513 | −1.98151 | ||||||||
\(657\) | −34.5673 | −1.34860 | ||||||||
\(658\) | 10.5652 | 0.411872 | ||||||||
\(659\) | 24.0251 | 0.935884 | 0.467942 | − | 0.883759i | \(-0.344996\pi\) | ||||
0.467942 | + | 0.883759i | \(0.344996\pi\) | |||||||
\(660\) | 32.1503 | 1.25145 | ||||||||
\(661\) | −47.0392 | −1.82961 | −0.914806 | − | 0.403893i | \(-0.867657\pi\) | ||||
−0.914806 | + | 0.403893i | \(0.867657\pi\) | |||||||
\(662\) | 27.3081 | 1.06136 | ||||||||
\(663\) | −3.32861 | −0.129272 | ||||||||
\(664\) | −5.86029 | −0.227423 | ||||||||
\(665\) | −1.55770 | −0.0604051 | ||||||||
\(666\) | −33.1581 | −1.28485 | ||||||||
\(667\) | −49.1910 | −1.90468 | ||||||||
\(668\) | −44.0677 | −1.70503 | ||||||||
\(669\) | 54.3367 | 2.10078 | ||||||||
\(670\) | −23.2789 | −0.899344 | ||||||||
\(671\) | −16.3198 | −0.630018 | ||||||||
\(672\) | 16.9268 | 0.652965 | ||||||||
\(673\) | 29.8624 | 1.15111 | 0.575555 | − | 0.817763i | \(-0.304786\pi\) | ||||
0.575555 | + | 0.817763i | \(0.304786\pi\) | |||||||
\(674\) | −22.1541 | −0.853344 | ||||||||
\(675\) | −7.62654 | −0.293546 | ||||||||
\(676\) | 5.18522 | 0.199431 | ||||||||
\(677\) | −6.20140 | −0.238339 | −0.119170 | − | 0.992874i | \(-0.538023\pi\) | ||||
−0.119170 | + | 0.992874i | \(0.538023\pi\) | |||||||
\(678\) | 86.1009 | 3.30669 | ||||||||
\(679\) | 4.05459 | 0.155601 | ||||||||
\(680\) | −5.89572 | −0.226090 | ||||||||
\(681\) | 16.4933 | 0.632026 | ||||||||
\(682\) | 32.8968 | 1.25969 | ||||||||
\(683\) | 22.8985 | 0.876186 | 0.438093 | − | 0.898930i | \(-0.355654\pi\) | ||||
0.438093 | + | 0.898930i | \(0.355654\pi\) | |||||||
\(684\) | 137.483 | 5.25681 | ||||||||
\(685\) | 5.28484 | 0.201923 | ||||||||
\(686\) | −14.8070 | −0.565334 | ||||||||
\(687\) | −32.1972 | −1.22840 | ||||||||
\(688\) | −52.9285 | −2.01788 | ||||||||
\(689\) | −9.58305 | −0.365085 | ||||||||
\(690\) | 27.1976 | 1.03540 | ||||||||
\(691\) | 39.8928 | 1.51759 | 0.758797 | − | 0.651328i | \(-0.225788\pi\) | ||||
0.758797 | + | 0.651328i | \(0.225788\pi\) | |||||||
\(692\) | 8.89957 | 0.338311 | ||||||||
\(693\) | −6.52971 | −0.248043 | ||||||||
\(694\) | −87.1796 | −3.30929 | ||||||||
\(695\) | −3.43220 | −0.130191 | ||||||||
\(696\) | −146.538 | −5.55452 | ||||||||
\(697\) | −5.24254 | −0.198576 | ||||||||
\(698\) | −80.3644 | −3.04184 | ||||||||
\(699\) | −30.7095 | −1.16154 | ||||||||
\(700\) | 9.75695 | 0.368778 | ||||||||
\(701\) | −33.7442 | −1.27450 | −0.637250 | − | 0.770657i | \(-0.719928\pi\) | ||||
−0.637250 | + | 0.770657i | \(0.719928\pi\) | |||||||
\(702\) | 4.33600 | 0.163652 | ||||||||
\(703\) | 24.9142 | 0.939655 | ||||||||
\(704\) | 86.2408 | 3.25032 | ||||||||
\(705\) | 13.5795 | 0.511434 | ||||||||
\(706\) | −12.7764 | −0.480847 | ||||||||
\(707\) | 6.07604 | 0.228513 | ||||||||
\(708\) | 58.5764 | 2.20144 | ||||||||
\(709\) | −21.7408 | −0.816492 | −0.408246 | − | 0.912872i | \(-0.633860\pi\) | ||||
−0.408246 | + | 0.912872i | \(0.633860\pi\) | |||||||
\(710\) | −15.0841 | −0.566096 | ||||||||
\(711\) | 59.8384 | 2.24411 | ||||||||
\(712\) | −103.600 | −3.88259 | ||||||||
\(713\) | 20.0829 | 0.752111 | ||||||||
\(714\) | 3.56100 | 0.133267 | ||||||||
\(715\) | −2.40834 | −0.0900668 | ||||||||
\(716\) | 104.672 | 3.91179 | ||||||||
\(717\) | 41.0407 | 1.53269 | ||||||||
\(718\) | 59.9529 | 2.23742 | ||||||||
\(719\) | 41.5480 | 1.54948 | 0.774740 | − | 0.632280i | \(-0.217881\pi\) | ||||
0.774740 | + | 0.632280i | \(0.217881\pi\) | |||||||
\(720\) | 24.2542 | 0.903899 | ||||||||
\(721\) | −7.01535 | −0.261265 | ||||||||
\(722\) | −92.2164 | −3.43194 | ||||||||
\(723\) | −15.7456 | −0.585584 | ||||||||
\(724\) | 86.4341 | 3.21230 | ||||||||
\(725\) | −31.4304 | −1.16729 | ||||||||
\(726\) | −64.4090 | −2.39044 | ||||||||
\(727\) | 15.7901 | 0.585621 | 0.292810 | − | 0.956171i | \(-0.405410\pi\) | ||||
0.292810 | + | 0.956171i | \(0.405410\pi\) | |||||||
\(728\) | −3.40759 | −0.126294 | ||||||||
\(729\) | −36.8771 | −1.36582 | ||||||||
\(730\) | 13.6395 | 0.504820 | ||||||||
\(731\) | −5.46745 | −0.202221 | ||||||||
\(732\) | −48.3149 | −1.78577 | ||||||||
\(733\) | 25.5095 | 0.942213 | 0.471107 | − | 0.882076i | \(-0.343855\pi\) | ||||
0.471107 | + | 0.882076i | \(0.343855\pi\) | |||||||
\(734\) | 42.4685 | 1.56754 | ||||||||
\(735\) | −9.40629 | −0.346956 | ||||||||
\(736\) | 121.557 | 4.48064 | ||||||||
\(737\) | 73.3211 | 2.70082 | ||||||||
\(738\) | 39.4370 | 1.45170 | ||||||||
\(739\) | −41.1172 | −1.51252 | −0.756260 | − | 0.654271i | \(-0.772976\pi\) | ||||
−0.756260 | + | 0.654271i | \(0.772976\pi\) | |||||||
\(740\) | 9.44167 | 0.347083 | ||||||||
\(741\) | −18.8140 | −0.691150 | ||||||||
\(742\) | 10.2521 | 0.376366 | ||||||||
\(743\) | 4.09095 | 0.150082 | 0.0750412 | − | 0.997180i | \(-0.476091\pi\) | ||||
0.0750412 | + | 0.997180i | \(0.476091\pi\) | |||||||
\(744\) | 59.8264 | 2.19334 | ||||||||
\(745\) | 11.3586 | 0.416147 | ||||||||
\(746\) | −87.3488 | −3.19807 | ||||||||
\(747\) | 2.49037 | 0.0911178 | ||||||||
\(748\) | 30.2295 | 1.10530 | ||||||||
\(749\) | 0.682203 | 0.0249271 | ||||||||
\(750\) | 35.8070 | 1.30749 | ||||||||
\(751\) | 49.9960 | 1.82438 | 0.912190 | − | 0.409767i | \(-0.134390\pi\) | ||||
0.912190 | + | 0.409767i | \(0.134390\pi\) | |||||||
\(752\) | 123.604 | 4.50739 | ||||||||
\(753\) | 46.0941 | 1.67976 | ||||||||
\(754\) | 17.8694 | 0.650767 | ||||||||
\(755\) | −7.88339 | −0.286906 | ||||||||
\(756\) | −3.34753 | −0.121749 | ||||||||
\(757\) | 0.816196 | 0.0296652 | 0.0148326 | − | 0.999890i | \(-0.495278\pi\) | ||||
0.0148326 | + | 0.999890i | \(0.495278\pi\) | |||||||
\(758\) | −52.3255 | −1.90055 | ||||||||
\(759\) | −85.6638 | −3.10940 | ||||||||
\(760\) | −33.3238 | −1.20878 | ||||||||
\(761\) | −16.9510 | −0.614474 | −0.307237 | − | 0.951633i | \(-0.599404\pi\) | ||||
−0.307237 | + | 0.951633i | \(0.599404\pi\) | |||||||
\(762\) | 55.7255 | 2.01872 | ||||||||
\(763\) | −1.25411 | −0.0454017 | ||||||||
\(764\) | −6.39285 | −0.231285 | ||||||||
\(765\) | 2.50542 | 0.0905837 | ||||||||
\(766\) | 54.6426 | 1.97432 | ||||||||
\(767\) | −4.38788 | −0.158437 | ||||||||
\(768\) | 27.9454 | 1.00839 | ||||||||
\(769\) | −47.5932 | −1.71625 | −0.858127 | − | 0.513438i | \(-0.828372\pi\) | ||||
−0.858127 | + | 0.513438i | \(0.828372\pi\) | |||||||
\(770\) | 2.57648 | 0.0928498 | ||||||||
\(771\) | 12.1551 | 0.437754 | ||||||||
\(772\) | −20.8613 | −0.750814 | ||||||||
\(773\) | 23.9051 | 0.859808 | 0.429904 | − | 0.902875i | \(-0.358547\pi\) | ||||
0.429904 | + | 0.902875i | \(0.358547\pi\) | |||||||
\(774\) | 41.1288 | 1.47835 | ||||||||
\(775\) | 12.8319 | 0.460935 | ||||||||
\(776\) | 86.7396 | 3.11377 | ||||||||
\(777\) | −3.50313 | −0.125674 | ||||||||
\(778\) | 78.8751 | 2.82781 | ||||||||
\(779\) | −29.6320 | −1.06168 | ||||||||
\(780\) | −7.12991 | −0.255292 | ||||||||
\(781\) | 47.5100 | 1.70004 | ||||||||
\(782\) | 25.5727 | 0.914477 | ||||||||
\(783\) | 10.7835 | 0.385371 | ||||||||
\(784\) | −85.6186 | −3.05781 | ||||||||
\(785\) | 5.74539 | 0.205062 | ||||||||
\(786\) | −57.0758 | −2.03583 | ||||||||
\(787\) | −13.1609 | −0.469134 | −0.234567 | − | 0.972100i | \(-0.575367\pi\) | ||||
−0.234567 | + | 0.972100i | \(0.575367\pi\) | |||||||
\(788\) | 93.7301 | 3.33899 | ||||||||
\(789\) | −46.8746 | −1.66878 | ||||||||
\(790\) | −23.6109 | −0.840038 | ||||||||
\(791\) | 4.97938 | 0.177046 | ||||||||
\(792\) | −139.690 | −4.96365 | ||||||||
\(793\) | 3.61920 | 0.128522 | ||||||||
\(794\) | −89.4114 | −3.17309 | ||||||||
\(795\) | 13.1771 | 0.467345 | ||||||||
\(796\) | −67.5894 | −2.39564 | ||||||||
\(797\) | 1.17269 | 0.0415388 | 0.0207694 | − | 0.999784i | \(-0.493388\pi\) | ||||
0.0207694 | + | 0.999784i | \(0.493388\pi\) | |||||||
\(798\) | 20.1275 | 0.712506 | ||||||||
\(799\) | 12.7682 | 0.451706 | ||||||||
\(800\) | 77.6681 | 2.74598 | ||||||||
\(801\) | 44.0257 | 1.55557 | ||||||||
\(802\) | −87.9116 | −3.10427 | ||||||||
\(803\) | −42.9600 | −1.51602 | ||||||||
\(804\) | 217.068 | 7.65539 | ||||||||
\(805\) | 1.57289 | 0.0554372 | ||||||||
\(806\) | −7.29546 | −0.256971 | ||||||||
\(807\) | −3.03754 | −0.106926 | ||||||||
\(808\) | 129.984 | 4.57283 | ||||||||
\(809\) | 28.0039 | 0.984565 | 0.492283 | − | 0.870435i | \(-0.336163\pi\) | ||||
0.492283 | + | 0.870435i | \(0.336163\pi\) | |||||||
\(810\) | 9.62114 | 0.338052 | ||||||||
\(811\) | −24.9459 | −0.875967 | −0.437984 | − | 0.898983i | \(-0.644307\pi\) | ||||
−0.437984 | + | 0.898983i | \(0.644307\pi\) | |||||||
\(812\) | −13.7958 | −0.484137 | ||||||||
\(813\) | −39.9421 | −1.40083 | ||||||||
\(814\) | −41.2086 | −1.44436 | ||||||||
\(815\) | −7.53641 | −0.263989 | ||||||||
\(816\) | 41.6610 | 1.45843 | ||||||||
\(817\) | −30.9032 | −1.08117 | ||||||||
\(818\) | 77.2369 | 2.70052 | ||||||||
\(819\) | 1.44808 | 0.0506000 | ||||||||
\(820\) | −11.2296 | −0.392154 | ||||||||
\(821\) | 5.87643 | 0.205089 | 0.102544 | − | 0.994728i | \(-0.467302\pi\) | ||||
0.102544 | + | 0.994728i | \(0.467302\pi\) | |||||||
\(822\) | −68.2868 | −2.38177 | ||||||||
\(823\) | 36.0569 | 1.25687 | 0.628433 | − | 0.777864i | \(-0.283697\pi\) | ||||
0.628433 | + | 0.777864i | \(0.283697\pi\) | |||||||
\(824\) | −150.079 | −5.22824 | ||||||||
\(825\) | −54.7345 | −1.90561 | ||||||||
\(826\) | 4.69422 | 0.163333 | ||||||||
\(827\) | 11.4005 | 0.396433 | 0.198216 | − | 0.980158i | \(-0.436485\pi\) | ||||
0.198216 | + | 0.980158i | \(0.436485\pi\) | |||||||
\(828\) | −138.824 | −4.82447 | ||||||||
\(829\) | −1.75217 | −0.0608554 | −0.0304277 | − | 0.999537i | \(-0.509687\pi\) | ||||
−0.0304277 | + | 0.999537i | \(0.509687\pi\) | |||||||
\(830\) | −0.982643 | −0.0341081 | ||||||||
\(831\) | −51.2689 | −1.77850 | ||||||||
\(832\) | −19.1254 | −0.663055 | ||||||||
\(833\) | −8.84429 | −0.306437 | ||||||||
\(834\) | 44.3484 | 1.53566 | ||||||||
\(835\) | −4.53910 | −0.157082 | ||||||||
\(836\) | 170.863 | 5.90943 | ||||||||
\(837\) | −4.40252 | −0.152173 | ||||||||
\(838\) | −47.7318 | −1.64887 | ||||||||
\(839\) | −20.9643 | −0.723769 | −0.361884 | − | 0.932223i | \(-0.617866\pi\) | ||||
−0.361884 | + | 0.932223i | \(0.617866\pi\) | |||||||
\(840\) | 4.68559 | 0.161668 | ||||||||
\(841\) | 15.4408 | 0.532441 | ||||||||
\(842\) | −85.3547 | −2.94152 | ||||||||
\(843\) | −10.1009 | −0.347892 | ||||||||
\(844\) | 81.3563 | 2.80040 | ||||||||
\(845\) | 0.534092 | 0.0183733 | ||||||||
\(846\) | −96.0485 | −3.30221 | ||||||||
\(847\) | −3.72490 | −0.127989 | ||||||||
\(848\) | 119.942 | 4.11882 | ||||||||
\(849\) | −30.4833 | −1.04618 | ||||||||
\(850\) | 16.3395 | 0.560442 | ||||||||
\(851\) | −25.1571 | −0.862374 | ||||||||
\(852\) | 140.654 | 4.81872 | ||||||||
\(853\) | −20.0121 | −0.685200 | −0.342600 | − | 0.939481i | \(-0.611307\pi\) | ||||
−0.342600 | + | 0.939481i | \(0.611307\pi\) | |||||||
\(854\) | −3.87188 | −0.132493 | ||||||||
\(855\) | 14.1612 | 0.484302 | ||||||||
\(856\) | 14.5943 | 0.498823 | ||||||||
\(857\) | 6.76113 | 0.230956 | 0.115478 | − | 0.993310i | \(-0.463160\pi\) | ||||
0.115478 | + | 0.993310i | \(0.463160\pi\) | |||||||
\(858\) | 31.1188 | 1.06238 | ||||||||
\(859\) | −7.54434 | −0.257409 | −0.128705 | − | 0.991683i | \(-0.541082\pi\) | ||||
−0.128705 | + | 0.991683i | \(0.541082\pi\) | |||||||
\(860\) | −11.7113 | −0.399353 | ||||||||
\(861\) | 4.16649 | 0.141994 | ||||||||
\(862\) | −64.6271 | −2.20121 | ||||||||
\(863\) | 44.4288 | 1.51238 | 0.756188 | − | 0.654355i | \(-0.227060\pi\) | ||||
0.756188 | + | 0.654355i | \(0.227060\pi\) | |||||||
\(864\) | −26.6473 | −0.906561 | ||||||||
\(865\) | 0.916680 | 0.0311681 | ||||||||
\(866\) | 19.4198 | 0.659910 | ||||||||
\(867\) | −39.4638 | −1.34026 | ||||||||
\(868\) | 5.63233 | 0.191174 | ||||||||
\(869\) | 74.3666 | 2.52272 | ||||||||
\(870\) | −24.5713 | −0.833045 | ||||||||
\(871\) | −16.2603 | −0.550958 | ||||||||
\(872\) | −26.8290 | −0.908546 | ||||||||
\(873\) | −36.8606 | −1.24754 | ||||||||
\(874\) | 144.542 | 4.88921 | ||||||||
\(875\) | 2.07079 | 0.0700055 | ||||||||
\(876\) | −127.183 | −4.29713 | ||||||||
\(877\) | 32.6181 | 1.10143 | 0.550717 | − | 0.834692i | \(-0.314354\pi\) | ||||
0.550717 | + | 0.834692i | \(0.314354\pi\) | |||||||
\(878\) | 50.9173 | 1.71838 | ||||||||
\(879\) | −36.8554 | −1.24310 | ||||||||
\(880\) | 30.1429 | 1.01612 | ||||||||
\(881\) | −36.2011 | −1.21965 | −0.609824 | − | 0.792537i | \(-0.708760\pi\) | ||||
−0.609824 | + | 0.792537i | \(0.708760\pi\) | |||||||
\(882\) | 66.5311 | 2.24022 | ||||||||
\(883\) | −36.1826 | −1.21764 | −0.608821 | − | 0.793307i | \(-0.708357\pi\) | ||||
−0.608821 | + | 0.793307i | \(0.708357\pi\) | |||||||
\(884\) | −6.70392 | −0.225477 | ||||||||
\(885\) | 6.03353 | 0.202815 | ||||||||
\(886\) | −50.2904 | −1.68954 | ||||||||
\(887\) | 17.8718 | 0.600078 | 0.300039 | − | 0.953927i | \(-0.403000\pi\) | ||||
0.300039 | + | 0.953927i | \(0.403000\pi\) | |||||||
\(888\) | −74.9422 | −2.51489 | ||||||||
\(889\) | 3.22271 | 0.108086 | ||||||||
\(890\) | −17.3715 | −0.582295 | ||||||||
\(891\) | −30.3035 | −1.01520 | ||||||||
\(892\) | 109.436 | 3.66418 | ||||||||
\(893\) | 72.1684 | 2.41502 | ||||||||
\(894\) | −146.767 | −4.90864 | ||||||||
\(895\) | 10.7815 | 0.360387 | ||||||||
\(896\) | 7.31135 | 0.244255 | ||||||||
\(897\) | 18.9975 | 0.634307 | ||||||||
\(898\) | 34.2284 | 1.14222 | ||||||||
\(899\) | −18.1436 | −0.605123 | ||||||||
\(900\) | −88.7010 | −2.95670 | ||||||||
\(901\) | 12.3898 | 0.412765 | ||||||||
\(902\) | 49.0119 | 1.63192 | ||||||||
\(903\) | 4.34523 | 0.144600 | ||||||||
\(904\) | 106.524 | 3.54292 | ||||||||
\(905\) | 8.90295 | 0.295944 | ||||||||
\(906\) | 101.863 | 3.38419 | ||||||||
\(907\) | −29.1853 | −0.969083 | −0.484541 | − | 0.874768i | \(-0.661013\pi\) | ||||
−0.484541 | + | 0.874768i | \(0.661013\pi\) | |||||||
\(908\) | 33.2181 | 1.10238 | ||||||||
\(909\) | −55.2377 | −1.83212 | ||||||||
\(910\) | −0.571379 | −0.0189410 | ||||||||
\(911\) | −54.3230 | −1.79980 | −0.899901 | − | 0.436094i | \(-0.856361\pi\) | ||||
−0.899901 | + | 0.436094i | \(0.856361\pi\) | |||||||
\(912\) | 235.477 | 7.79742 | ||||||||
\(913\) | 3.09501 | 0.102430 | ||||||||
\(914\) | 86.5205 | 2.86184 | ||||||||
\(915\) | −4.97657 | −0.164520 | ||||||||
\(916\) | −64.8462 | −2.14258 | ||||||||
\(917\) | −3.30080 | −0.109002 | ||||||||
\(918\) | −5.60597 | −0.185025 | ||||||||
\(919\) | 46.5673 | 1.53611 | 0.768057 | − | 0.640381i | \(-0.221223\pi\) | ||||
0.768057 | + | 0.640381i | \(0.221223\pi\) | |||||||
\(920\) | 33.6488 | 1.10937 | ||||||||
\(921\) | −71.6528 | −2.36104 | ||||||||
\(922\) | 8.25293 | 0.271796 | ||||||||
\(923\) | −10.5362 | −0.346803 | ||||||||
\(924\) | −24.0247 | −0.790355 | ||||||||
\(925\) | −16.0740 | −0.528510 | ||||||||
\(926\) | −2.68053 | −0.0880875 | ||||||||
\(927\) | 63.7769 | 2.09471 | ||||||||
\(928\) | −109.819 | −3.60497 | ||||||||
\(929\) | 14.1758 | 0.465093 | 0.232547 | − | 0.972585i | \(-0.425294\pi\) | ||||
0.232547 | + | 0.972585i | \(0.425294\pi\) | |||||||
\(930\) | 10.0316 | 0.328949 | ||||||||
\(931\) | −49.9898 | −1.63835 | ||||||||
\(932\) | −61.8498 | −2.02596 | ||||||||
\(933\) | 65.3977 | 2.14102 | ||||||||
\(934\) | −14.4141 | −0.471643 | ||||||||
\(935\) | 3.11372 | 0.101829 | ||||||||
\(936\) | 30.9786 | 1.01257 | ||||||||
\(937\) | −19.9395 | −0.651397 | −0.325698 | − | 0.945474i | \(-0.605599\pi\) | ||||
−0.325698 | + | 0.945474i | \(0.605599\pi\) | |||||||
\(938\) | 17.3955 | 0.567982 | ||||||||
\(939\) | −27.9839 | −0.913220 | ||||||||
\(940\) | 27.3495 | 0.892043 | ||||||||
\(941\) | −17.7825 | −0.579694 | −0.289847 | − | 0.957073i | \(-0.593604\pi\) | ||||
−0.289847 | + | 0.957073i | \(0.593604\pi\) | |||||||
\(942\) | −74.2377 | −2.41880 | ||||||||
\(943\) | 29.9209 | 0.974359 | ||||||||
\(944\) | 54.9189 | 1.78746 | ||||||||
\(945\) | −0.344805 | −0.0112165 | ||||||||
\(946\) | 51.1146 | 1.66188 | ||||||||
\(947\) | −27.3882 | −0.889997 | −0.444998 | − | 0.895531i | \(-0.646796\pi\) | ||||
−0.444998 | + | 0.895531i | \(0.646796\pi\) | |||||||
\(948\) | 220.163 | 7.15057 | ||||||||
\(949\) | 9.52713 | 0.309264 | ||||||||
\(950\) | 92.3546 | 2.99638 | ||||||||
\(951\) | −54.7509 | −1.77542 | ||||||||
\(952\) | 4.40564 | 0.142788 | ||||||||
\(953\) | 47.9609 | 1.55361 | 0.776803 | − | 0.629743i | \(-0.216840\pi\) | ||||
0.776803 | + | 0.629743i | \(0.216840\pi\) | |||||||
\(954\) | −93.2024 | −3.01754 | ||||||||
\(955\) | −0.658481 | −0.0213079 | ||||||||
\(956\) | 82.6571 | 2.67332 | ||||||||
\(957\) | 77.3916 | 2.50171 | ||||||||
\(958\) | −53.7282 | −1.73588 | ||||||||
\(959\) | −3.94916 | −0.127525 | ||||||||
\(960\) | 26.2983 | 0.848775 | ||||||||
\(961\) | −23.5926 | −0.761052 | ||||||||
\(962\) | 9.13874 | 0.294645 | ||||||||
\(963\) | −6.20195 | −0.199855 | ||||||||
\(964\) | −31.7120 | −1.02138 | ||||||||
\(965\) | −2.14877 | −0.0691713 | ||||||||
\(966\) | −20.3238 | −0.653906 | ||||||||
\(967\) | −48.9064 | −1.57273 | −0.786363 | − | 0.617765i | \(-0.788038\pi\) | ||||
−0.786363 | + | 0.617765i | \(0.788038\pi\) | |||||||
\(968\) | −79.6864 | −2.56122 | ||||||||
\(969\) | 24.3245 | 0.781414 | ||||||||
\(970\) | 14.5444 | 0.466991 | ||||||||
\(971\) | −15.2905 | −0.490696 | −0.245348 | − | 0.969435i | \(-0.578902\pi\) | ||||
−0.245348 | + | 0.969435i | \(0.578902\pi\) | |||||||
\(972\) | −114.876 | −3.68466 | ||||||||
\(973\) | 2.56475 | 0.0822223 | ||||||||
\(974\) | 14.1854 | 0.454530 | ||||||||
\(975\) | 12.1383 | 0.388738 | ||||||||
\(976\) | −45.2981 | −1.44996 | ||||||||
\(977\) | −19.9463 | −0.638137 | −0.319069 | − | 0.947732i | \(-0.603370\pi\) | ||||
−0.319069 | + | 0.947732i | \(0.603370\pi\) | |||||||
\(978\) | 97.3800 | 3.11387 | ||||||||
\(979\) | 54.7147 | 1.74869 | ||||||||
\(980\) | −18.9445 | −0.605161 | ||||||||
\(981\) | 11.4012 | 0.364011 | ||||||||
\(982\) | 3.69252 | 0.117833 | ||||||||
\(983\) | 40.7526 | 1.29980 | 0.649902 | − | 0.760018i | \(-0.274810\pi\) | ||||
0.649902 | + | 0.760018i | \(0.274810\pi\) | |||||||
\(984\) | 89.1334 | 2.84147 | ||||||||
\(985\) | 9.65446 | 0.307617 | ||||||||
\(986\) | −23.1032 | −0.735757 | ||||||||
\(987\) | −10.1474 | −0.322997 | ||||||||
\(988\) | −37.8920 | −1.20550 | ||||||||
\(989\) | 31.2045 | 0.992246 | ||||||||
\(990\) | −23.4229 | −0.744429 | ||||||||
\(991\) | −26.2320 | −0.833286 | −0.416643 | − | 0.909070i | \(-0.636794\pi\) | ||||
−0.416643 | + | 0.909070i | \(0.636794\pi\) | |||||||
\(992\) | 44.8350 | 1.42351 | ||||||||
\(993\) | −26.2285 | −0.832336 | ||||||||
\(994\) | 11.2718 | 0.357519 | ||||||||
\(995\) | −6.96189 | −0.220707 | ||||||||
\(996\) | 9.16280 | 0.290334 | ||||||||
\(997\) | 12.5685 | 0.398050 | 0.199025 | − | 0.979994i | \(-0.436223\pi\) | ||||
0.199025 | + | 0.979994i | \(0.436223\pi\) | |||||||
\(998\) | 38.6636 | 1.22388 | ||||||||
\(999\) | 5.51487 | 0.174483 |
(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 | 6019.2.a.d.1.5 | ✓ | 123 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6019.2.a.d.1.5 | ✓ | 123 | 1.1 | even | 1 | trivial |