Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3234,2,Mod(2155,3234)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3234, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3234.2155");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3234 = 2 \cdot 3 \cdot 7^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3234.e (of order \(2\), degree \(1\), minimal) |
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: | no |
Analytic conductor: | \(25.8236200137\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 8 x^{15} + 74 x^{14} - 378 x^{13} + 1878 x^{12} - 6718 x^{11} + 22086 x^{10} - 56904 x^{9} + \cdots + 13417 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{6} \) |
Twist minimal: | no (minimal twist has level 462) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 2155.12 | ||
Root | \(0.500000 - 1.56688i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3234.2155 |
Dual form | 3234.2.e.a.2155.5 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/3234\mathbb{Z}\right)^\times\).
\(n\) | \(199\) | \(1079\) | \(2059\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000i | 0.707107i | ||||||||
\(3\) | 1.00000i | 0.577350i | ||||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | 0.700858i | 0.313433i | 0.987644 | + | 0.156717i | \(0.0500909\pi\) | ||||
−0.987644 | + | 0.156717i | \(0.949909\pi\) | |||||||
\(6\) | −1.00000 | −0.408248 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | − | 1.00000i | − | 0.353553i | ||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | −0.700858 | −0.221631 | ||||||||
\(11\) | 0.176300 | + | 3.31194i | 0.0531566 | + | 0.998586i | ||||
\(12\) | − | 1.00000i | − | 0.288675i | ||||||
\(13\) | −7.03562 | −1.95133 | −0.975665 | − | 0.219267i | \(-0.929633\pi\) | ||||
−0.975665 | + | 0.219267i | \(0.929633\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.700858 | −0.180961 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 0.617785 | 0.149835 | 0.0749175 | − | 0.997190i | \(-0.476131\pi\) | ||||
0.0749175 | + | 0.997190i | \(0.476131\pi\) | |||||||
\(18\) | − | 1.00000i | − | 0.235702i | ||||||
\(19\) | −0.783393 | −0.179723 | −0.0898613 | − | 0.995954i | \(-0.528642\pi\) | ||||
−0.0898613 | + | 0.995954i | \(0.528642\pi\) | |||||||
\(20\) | − | 0.700858i | − | 0.156717i | ||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −3.31194 | + | 0.176300i | −0.706107 | + | 0.0375874i | ||||
\(23\) | −5.27184 | −1.09925 | −0.549627 | − | 0.835410i | \(-0.685230\pi\) | ||||
−0.549627 | + | 0.835410i | \(0.685230\pi\) | |||||||
\(24\) | 1.00000 | 0.204124 | ||||||||
\(25\) | 4.50880 | 0.901760 | ||||||||
\(26\) | − | 7.03562i | − | 1.37980i | ||||||
\(27\) | − | 1.00000i | − | 0.192450i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 2.09176i | − | 0.388431i | −0.980959 | − | 0.194215i | \(-0.937784\pi\) | ||
0.980959 | − | 0.194215i | \(-0.0622161\pi\) | |||||||
\(30\) | − | 0.700858i | − | 0.127959i | ||||||
\(31\) | − | 6.17793i | − | 1.10959i | −0.831988 | − | 0.554794i | \(-0.812797\pi\) | ||
0.831988 | − | 0.554794i | \(-0.187203\pi\) | |||||||
\(32\) | 1.00000i | 0.176777i | ||||||||
\(33\) | −3.31194 | + | 0.176300i | −0.576534 | + | 0.0306900i | ||||
\(34\) | 0.617785i | 0.105949i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 1.00000 | 0.166667 | ||||||||
\(37\) | −3.99419 | −0.656640 | −0.328320 | − | 0.944567i | \(-0.606482\pi\) | ||||
−0.328320 | + | 0.944567i | \(0.606482\pi\) | |||||||
\(38\) | − | 0.783393i | − | 0.127083i | ||||||
\(39\) | − | 7.03562i | − | 1.12660i | ||||||
\(40\) | 0.700858 | 0.110815 | ||||||||
\(41\) | 5.85343 | 0.914152 | 0.457076 | − | 0.889428i | \(-0.348897\pi\) | ||||
0.457076 | + | 0.889428i | \(0.348897\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.62441i | 0.552717i | 0.961055 | + | 0.276359i | \(0.0891277\pi\) | ||||
−0.961055 | + | 0.276359i | \(0.910872\pi\) | |||||||
\(44\) | −0.176300 | − | 3.31194i | −0.0265783 | − | 0.499293i | ||||
\(45\) | − | 0.700858i | − | 0.104478i | ||||||
\(46\) | − | 5.27184i | − | 0.777290i | ||||||
\(47\) | 2.34976i | 0.342747i | 0.985206 | + | 0.171374i | \(0.0548205\pi\) | ||||
−0.985206 | + | 0.171374i | \(0.945179\pi\) | |||||||
\(48\) | 1.00000i | 0.144338i | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 4.50880i | 0.637640i | ||||||||
\(51\) | 0.617785i | 0.0865072i | ||||||||
\(52\) | 7.03562 | 0.975665 | ||||||||
\(53\) | 7.90136 | 1.08534 | 0.542668 | − | 0.839947i | \(-0.317414\pi\) | ||||
0.542668 | + | 0.839947i | \(0.317414\pi\) | |||||||
\(54\) | 1.00000 | 0.136083 | ||||||||
\(55\) | −2.32120 | + | 0.123562i | −0.312990 | + | 0.0166610i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 0.783393i | − | 0.103763i | ||||||
\(58\) | 2.09176 | 0.274662 | ||||||||
\(59\) | − | 3.76387i | − | 0.490014i | −0.969521 | − | 0.245007i | \(-0.921210\pi\) | ||
0.969521 | − | 0.245007i | \(-0.0787903\pi\) | |||||||
\(60\) | 0.700858 | 0.0904803 | ||||||||
\(61\) | −8.36572 | −1.07112 | −0.535560 | − | 0.844497i | \(-0.679900\pi\) | ||||
−0.535560 | + | 0.844497i | \(0.679900\pi\) | |||||||
\(62\) | 6.17793 | 0.784597 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | − | 4.93097i | − | 0.611611i | ||||||
\(66\) | −0.176300 | − | 3.31194i | −0.0217011 | − | 0.407671i | ||||
\(67\) | 2.14081 | 0.261541 | 0.130771 | − | 0.991413i | \(-0.458255\pi\) | ||||
0.130771 | + | 0.991413i | \(0.458255\pi\) | |||||||
\(68\) | −0.617785 | −0.0749175 | ||||||||
\(69\) | − | 5.27184i | − | 0.634655i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −4.48503 | −0.532275 | −0.266138 | − | 0.963935i | \(-0.585748\pi\) | ||||
−0.266138 | + | 0.963935i | \(0.585748\pi\) | |||||||
\(72\) | 1.00000i | 0.117851i | ||||||||
\(73\) | −5.28943 | −0.619081 | −0.309540 | − | 0.950886i | \(-0.600175\pi\) | ||||
−0.309540 | + | 0.950886i | \(0.600175\pi\) | |||||||
\(74\) | − | 3.99419i | − | 0.464315i | ||||||
\(75\) | 4.50880i | 0.520631i | ||||||||
\(76\) | 0.783393 | 0.0898613 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 7.03562 | 0.796627 | ||||||||
\(79\) | − | 4.33957i | − | 0.488240i | −0.969745 | − | 0.244120i | \(-0.921501\pi\) | ||
0.969745 | − | 0.244120i | \(-0.0784991\pi\) | |||||||
\(80\) | 0.700858i | 0.0783583i | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 5.85343i | 0.646403i | ||||||||
\(83\) | 4.03988 | 0.443435 | 0.221717 | − | 0.975111i | \(-0.428834\pi\) | ||||
0.221717 | + | 0.975111i | \(0.428834\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.432980i | 0.0469632i | ||||||||
\(86\) | −3.62441 | −0.390830 | ||||||||
\(87\) | 2.09176 | 0.224261 | ||||||||
\(88\) | 3.31194 | − | 0.176300i | 0.353054 | − | 0.0187937i | ||||
\(89\) | − | 16.2115i | − | 1.71841i | −0.511628 | − | 0.859207i | \(-0.670957\pi\) | ||
0.511628 | − | 0.859207i | \(-0.329043\pi\) | |||||||
\(90\) | 0.700858 | 0.0738769 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 5.27184 | 0.549627 | ||||||||
\(93\) | 6.17793 | 0.640621 | ||||||||
\(94\) | −2.34976 | −0.242359 | ||||||||
\(95\) | − | 0.549047i | − | 0.0563310i | ||||||
\(96\) | −1.00000 | −0.102062 | ||||||||
\(97\) | − | 10.4926i | − | 1.06536i | −0.846317 | − | 0.532680i | \(-0.821185\pi\) | ||
0.846317 | − | 0.532680i | \(-0.178815\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −0.176300 | − | 3.31194i | −0.0177189 | − | 0.332862i | ||||
\(100\) | −4.50880 | −0.450880 | ||||||||
\(101\) | −14.9947 | −1.49203 | −0.746016 | − | 0.665928i | \(-0.768036\pi\) | ||||
−0.746016 | + | 0.665928i | \(0.768036\pi\) | |||||||
\(102\) | −0.617785 | −0.0611698 | ||||||||
\(103\) | − | 14.3517i | − | 1.41411i | −0.707156 | − | 0.707057i | \(-0.750022\pi\) | ||
0.707156 | − | 0.707057i | \(-0.249978\pi\) | |||||||
\(104\) | 7.03562i | 0.689899i | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 7.90136i | 0.767448i | ||||||||
\(107\) | − | 11.4671i | − | 1.10857i | −0.832328 | − | 0.554284i | \(-0.812992\pi\) | ||
0.832328 | − | 0.554284i | \(-0.187008\pi\) | |||||||
\(108\) | 1.00000i | 0.0962250i | ||||||||
\(109\) | − | 1.45285i | − | 0.139158i | −0.997576 | − | 0.0695788i | \(-0.977834\pi\) | ||
0.997576 | − | 0.0695788i | \(-0.0221655\pi\) | |||||||
\(110\) | −0.123562 | − | 2.32120i | −0.0117811 | − | 0.221317i | ||||
\(111\) | − | 3.99419i | − | 0.379111i | ||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 12.0074 | 1.12956 | 0.564781 | − | 0.825241i | \(-0.308961\pi\) | ||||
0.564781 | + | 0.825241i | \(0.308961\pi\) | |||||||
\(114\) | 0.783393 | 0.0733715 | ||||||||
\(115\) | − | 3.69481i | − | 0.344543i | ||||||
\(116\) | 2.09176i | 0.194215i | ||||||||
\(117\) | 7.03562 | 0.650443 | ||||||||
\(118\) | 3.76387 | 0.346492 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0.700858i | 0.0639793i | ||||||||
\(121\) | −10.9378 | + | 1.16779i | −0.994349 | + | 0.106163i | ||||
\(122\) | − | 8.36572i | − | 0.757397i | ||||||
\(123\) | 5.85343i | 0.527786i | ||||||||
\(124\) | 6.17793i | 0.554794i | ||||||||
\(125\) | 6.66432i | 0.596074i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 3.43188i | 0.304530i | 0.988340 | + | 0.152265i | \(0.0486568\pi\) | ||||
−0.988340 | + | 0.152265i | \(0.951343\pi\) | |||||||
\(128\) | − | 1.00000i | − | 0.0883883i | ||||||
\(129\) | −3.62441 | −0.319111 | ||||||||
\(130\) | 4.93097 | 0.432475 | ||||||||
\(131\) | −14.6058 | −1.27611 | −0.638056 | − | 0.769990i | \(-0.720261\pi\) | ||||
−0.638056 | + | 0.769990i | \(0.720261\pi\) | |||||||
\(132\) | 3.31194 | − | 0.176300i | 0.288267 | − | 0.0153450i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 2.14081i | 0.184938i | ||||||||
\(135\) | 0.700858 | 0.0603202 | ||||||||
\(136\) | − | 0.617785i | − | 0.0529746i | ||||||
\(137\) | 16.7161 | 1.42815 | 0.714075 | − | 0.700069i | \(-0.246847\pi\) | ||||
0.714075 | + | 0.700069i | \(0.246847\pi\) | |||||||
\(138\) | 5.27184 | 0.448769 | ||||||||
\(139\) | −12.9399 | −1.09755 | −0.548775 | − | 0.835970i | \(-0.684906\pi\) | ||||
−0.548775 | + | 0.835970i | \(0.684906\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −2.34976 | −0.197885 | ||||||||
\(142\) | − | 4.48503i | − | 0.376375i | ||||||
\(143\) | −1.24038 | − | 23.3015i | −0.103726 | − | 1.94857i | ||||
\(144\) | −1.00000 | −0.0833333 | ||||||||
\(145\) | 1.46603 | 0.121747 | ||||||||
\(146\) | − | 5.28943i | − | 0.437756i | ||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 3.99419 | 0.328320 | ||||||||
\(149\) | − | 9.72861i | − | 0.796999i | −0.917169 | − | 0.398500i | \(-0.869531\pi\) | ||
0.917169 | − | 0.398500i | \(-0.130469\pi\) | |||||||
\(150\) | −4.50880 | −0.368142 | ||||||||
\(151\) | 19.7877i | 1.61030i | 0.593069 | + | 0.805151i | \(0.297916\pi\) | ||||
−0.593069 | + | 0.805151i | \(0.702084\pi\) | |||||||
\(152\) | 0.783393i | 0.0635416i | ||||||||
\(153\) | −0.617785 | −0.0499450 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 4.32985 | 0.347782 | ||||||||
\(156\) | 7.03562i | 0.563300i | ||||||||
\(157\) | 12.0105i | 0.958539i | 0.877668 | + | 0.479269i | \(0.159098\pi\) | ||||
−0.877668 | + | 0.479269i | \(0.840902\pi\) | |||||||
\(158\) | 4.33957 | 0.345238 | ||||||||
\(159\) | 7.90136i | 0.626619i | ||||||||
\(160\) | −0.700858 | −0.0554077 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 1.00000i | 0.0785674i | ||||||||
\(163\) | 22.3960 | 1.75419 | 0.877094 | − | 0.480319i | \(-0.159479\pi\) | ||||
0.877094 | + | 0.480319i | \(0.159479\pi\) | |||||||
\(164\) | −5.85343 | −0.457076 | ||||||||
\(165\) | −0.123562 | − | 2.32120i | −0.00961926 | − | 0.180705i | ||||
\(166\) | 4.03988i | 0.313556i | ||||||||
\(167\) | −17.9924 | −1.39229 | −0.696145 | − | 0.717901i | \(-0.745103\pi\) | ||||
−0.696145 | + | 0.717901i | \(0.745103\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 36.4999 | 2.80769 | ||||||||
\(170\) | −0.432980 | −0.0332080 | ||||||||
\(171\) | 0.783393 | 0.0599075 | ||||||||
\(172\) | − | 3.62441i | − | 0.276359i | ||||||
\(173\) | 0.378382 | 0.0287679 | 0.0143839 | − | 0.999897i | \(-0.495421\pi\) | ||||
0.0143839 | + | 0.999897i | \(0.495421\pi\) | |||||||
\(174\) | 2.09176i | 0.158576i | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0.176300 | + | 3.31194i | 0.0132891 | + | 0.249647i | ||||
\(177\) | 3.76387 | 0.282910 | ||||||||
\(178\) | 16.2115 | 1.21510 | ||||||||
\(179\) | −4.31093 | −0.322214 | −0.161107 | − | 0.986937i | \(-0.551506\pi\) | ||||
−0.161107 | + | 0.986937i | \(0.551506\pi\) | |||||||
\(180\) | 0.700858i | 0.0522389i | ||||||||
\(181\) | − | 6.96276i | − | 0.517538i | −0.965939 | − | 0.258769i | \(-0.916683\pi\) | ||
0.965939 | − | 0.258769i | \(-0.0833169\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 8.36572i | − | 0.618412i | ||||||
\(184\) | 5.27184i | 0.388645i | ||||||||
\(185\) | − | 2.79936i | − | 0.205813i | ||||||
\(186\) | 6.17793i | 0.452987i | ||||||||
\(187\) | 0.108916 | + | 2.04606i | 0.00796471 | + | 0.149623i | ||||
\(188\) | − | 2.34976i | − | 0.171374i | ||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0.549047 | 0.0398321 | ||||||||
\(191\) | −18.5590 | −1.34288 | −0.671440 | − | 0.741059i | \(-0.734324\pi\) | ||||
−0.671440 | + | 0.741059i | \(0.734324\pi\) | |||||||
\(192\) | − | 1.00000i | − | 0.0721688i | ||||||
\(193\) | − | 17.5212i | − | 1.26120i | −0.776107 | − | 0.630601i | \(-0.782808\pi\) | ||
0.776107 | − | 0.630601i | \(-0.217192\pi\) | |||||||
\(194\) | 10.4926 | 0.753323 | ||||||||
\(195\) | 4.93097 | 0.353114 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 18.8663i | − | 1.34417i | −0.740474 | − | 0.672086i | \(-0.765399\pi\) | ||
0.740474 | − | 0.672086i | \(-0.234601\pi\) | |||||||
\(198\) | 3.31194 | − | 0.176300i | 0.235369 | − | 0.0125291i | ||||
\(199\) | − | 13.5324i | − | 0.959283i | −0.877464 | − | 0.479642i | \(-0.840767\pi\) | ||
0.877464 | − | 0.479642i | \(-0.159233\pi\) | |||||||
\(200\) | − | 4.50880i | − | 0.318820i | ||||||
\(201\) | 2.14081i | 0.151001i | ||||||||
\(202\) | − | 14.9947i | − | 1.05503i | ||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | − | 0.617785i | − | 0.0432536i | ||||||
\(205\) | 4.10242i | 0.286525i | ||||||||
\(206\) | 14.3517 | 0.999930 | ||||||||
\(207\) | 5.27184 | 0.366418 | ||||||||
\(208\) | −7.03562 | −0.487832 | ||||||||
\(209\) | −0.138113 | − | 2.59455i | −0.00955344 | − | 0.179469i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4.94368i | 0.340337i | 0.985415 | + | 0.170168i | \(0.0544312\pi\) | ||||
−0.985415 | + | 0.170168i | \(0.945569\pi\) | |||||||
\(212\) | −7.90136 | −0.542668 | ||||||||
\(213\) | − | 4.48503i | − | 0.307309i | ||||||
\(214\) | 11.4671 | 0.783876 | ||||||||
\(215\) | −2.54020 | −0.173240 | ||||||||
\(216\) | −1.00000 | −0.0680414 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 1.45285 | 0.0983993 | ||||||||
\(219\) | − | 5.28943i | − | 0.357426i | ||||||
\(220\) | 2.32120 | − | 0.123562i | 0.156495 | − | 0.00833052i | ||||
\(221\) | −4.34650 | −0.292377 | ||||||||
\(222\) | 3.99419 | 0.268072 | ||||||||
\(223\) | 22.9194i | 1.53480i | 0.641169 | + | 0.767400i | \(0.278450\pi\) | ||||
−0.641169 | + | 0.767400i | \(0.721550\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −4.50880 | −0.300587 | ||||||||
\(226\) | 12.0074i | 0.798721i | ||||||||
\(227\) | 24.2282 | 1.60808 | 0.804042 | − | 0.594573i | \(-0.202679\pi\) | ||||
0.804042 | + | 0.594573i | \(0.202679\pi\) | |||||||
\(228\) | 0.783393i | 0.0518815i | ||||||||
\(229\) | 13.3778i | 0.884031i | 0.897007 | + | 0.442016i | \(0.145736\pi\) | ||||
−0.897007 | + | 0.442016i | \(0.854264\pi\) | |||||||
\(230\) | 3.69481 | 0.243628 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −2.09176 | −0.137331 | ||||||||
\(233\) | 27.9050i | 1.82811i | 0.405585 | + | 0.914057i | \(0.367068\pi\) | ||||
−0.405585 | + | 0.914057i | \(0.632932\pi\) | |||||||
\(234\) | 7.03562i | 0.459933i | ||||||||
\(235\) | −1.64685 | −0.107428 | ||||||||
\(236\) | 3.76387i | 0.245007i | ||||||||
\(237\) | 4.33957 | 0.281886 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 9.27514i | 0.599959i | 0.953946 | + | 0.299979i | \(0.0969798\pi\) | ||||
−0.953946 | + | 0.299979i | \(0.903020\pi\) | |||||||
\(240\) | −0.700858 | −0.0452402 | ||||||||
\(241\) | 19.0970 | 1.23015 | 0.615074 | − | 0.788470i | \(-0.289126\pi\) | ||||
0.615074 | + | 0.788470i | \(0.289126\pi\) | |||||||
\(242\) | −1.16779 | − | 10.9378i | −0.0750685 | − | 0.703111i | ||||
\(243\) | 1.00000i | 0.0641500i | ||||||||
\(244\) | 8.36572 | 0.535560 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −5.85343 | −0.373201 | ||||||||
\(247\) | 5.51165 | 0.350698 | ||||||||
\(248\) | −6.17793 | −0.392299 | ||||||||
\(249\) | 4.03988i | 0.256017i | ||||||||
\(250\) | −6.66432 | −0.421488 | ||||||||
\(251\) | 12.1328i | 0.765818i | 0.923786 | + | 0.382909i | \(0.125078\pi\) | ||||
−0.923786 | + | 0.382909i | \(0.874922\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −0.929428 | − | 17.4600i | −0.0584326 | − | 1.09770i | ||||
\(254\) | −3.43188 | −0.215335 | ||||||||
\(255\) | −0.432980 | −0.0271142 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | − | 19.9471i | − | 1.24427i | −0.782912 | − | 0.622133i | \(-0.786266\pi\) | ||
0.782912 | − | 0.622133i | \(-0.213734\pi\) | |||||||
\(258\) | − | 3.62441i | − | 0.225646i | ||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 4.93097i | 0.305806i | ||||||||
\(261\) | 2.09176i | 0.129477i | ||||||||
\(262\) | − | 14.6058i | − | 0.902347i | ||||||
\(263\) | − | 16.7867i | − | 1.03511i | −0.855649 | − | 0.517556i | \(-0.826842\pi\) | ||
0.855649 | − | 0.517556i | \(-0.173158\pi\) | |||||||
\(264\) | 0.176300 | + | 3.31194i | 0.0108505 | + | 0.203836i | ||||
\(265\) | 5.53773i | 0.340180i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 16.2115 | 0.992127 | ||||||||
\(268\) | −2.14081 | −0.130771 | ||||||||
\(269\) | − | 19.4953i | − | 1.18865i | −0.804224 | − | 0.594326i | \(-0.797419\pi\) | ||
0.804224 | − | 0.594326i | \(-0.202581\pi\) | |||||||
\(270\) | 0.700858i | 0.0426528i | ||||||||
\(271\) | −10.6826 | −0.648922 | −0.324461 | − | 0.945899i | \(-0.605183\pi\) | ||||
−0.324461 | + | 0.945899i | \(0.605183\pi\) | |||||||
\(272\) | 0.617785 | 0.0374587 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 16.7161i | 1.00986i | ||||||||
\(275\) | 0.794903 | + | 14.9329i | 0.0479345 | + | 0.900485i | ||||
\(276\) | 5.27184i | 0.317327i | ||||||||
\(277\) | 30.7880i | 1.84987i | 0.380127 | + | 0.924934i | \(0.375880\pi\) | ||||
−0.380127 | + | 0.924934i | \(0.624120\pi\) | |||||||
\(278\) | − | 12.9399i | − | 0.776086i | ||||||
\(279\) | 6.17793i | 0.369863i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 21.3381i | − | 1.27292i | −0.771308 | − | 0.636462i | \(-0.780397\pi\) | ||
0.771308 | − | 0.636462i | \(-0.219603\pi\) | |||||||
\(282\) | − | 2.34976i | − | 0.139926i | ||||||
\(283\) | −2.52307 | −0.149981 | −0.0749905 | − | 0.997184i | \(-0.523893\pi\) | ||||
−0.0749905 | + | 0.997184i | \(0.523893\pi\) | |||||||
\(284\) | 4.48503 | 0.266138 | ||||||||
\(285\) | 0.549047 | 0.0325227 | ||||||||
\(286\) | 23.3015 | − | 1.24038i | 1.37785 | − | 0.0733454i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | − | 1.00000i | − | 0.0589256i | ||||||
\(289\) | −16.6183 | −0.977549 | ||||||||
\(290\) | 1.46603i | 0.0860882i | ||||||||
\(291\) | 10.4926 | 0.615086 | ||||||||
\(292\) | 5.28943 | 0.309540 | ||||||||
\(293\) | −5.71831 | −0.334067 | −0.167034 | − | 0.985951i | \(-0.553419\pi\) | ||||
−0.167034 | + | 0.985951i | \(0.553419\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2.63794 | 0.153587 | ||||||||
\(296\) | 3.99419i | 0.232157i | ||||||||
\(297\) | 3.31194 | − | 0.176300i | 0.192178 | − | 0.0102300i | ||||
\(298\) | 9.72861 | 0.563563 | ||||||||
\(299\) | 37.0906 | 2.14501 | ||||||||
\(300\) | − | 4.50880i | − | 0.260316i | ||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −19.7877 | −1.13866 | ||||||||
\(303\) | − | 14.9947i | − | 0.861425i | ||||||
\(304\) | −0.783393 | −0.0449307 | ||||||||
\(305\) | − | 5.86318i | − | 0.335725i | ||||||
\(306\) | − | 0.617785i | − | 0.0353164i | ||||||
\(307\) | −20.7839 | −1.18620 | −0.593099 | − | 0.805130i | \(-0.702096\pi\) | ||||
−0.593099 | + | 0.805130i | \(0.702096\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 14.3517 | 0.816439 | ||||||||
\(310\) | 4.32985i | 0.245919i | ||||||||
\(311\) | − | 7.36751i | − | 0.417773i | −0.977940 | − | 0.208887i | \(-0.933016\pi\) | ||
0.977940 | − | 0.208887i | \(-0.0669840\pi\) | |||||||
\(312\) | −7.03562 | −0.398313 | ||||||||
\(313\) | 7.35395i | 0.415670i | 0.978164 | + | 0.207835i | \(0.0666417\pi\) | ||||
−0.978164 | + | 0.207835i | \(0.933358\pi\) | |||||||
\(314\) | −12.0105 | −0.677789 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 4.33957i | 0.244120i | ||||||||
\(317\) | −14.7806 | −0.830161 | −0.415080 | − | 0.909785i | \(-0.636247\pi\) | ||||
−0.415080 | + | 0.909785i | \(0.636247\pi\) | |||||||
\(318\) | −7.90136 | −0.443087 | ||||||||
\(319\) | 6.92779 | − | 0.368779i | 0.387882 | − | 0.0206477i | ||||
\(320\) | − | 0.700858i | − | 0.0391791i | ||||||
\(321\) | 11.4671 | 0.640032 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −0.483969 | −0.0269287 | ||||||||
\(324\) | −1.00000 | −0.0555556 | ||||||||
\(325\) | −31.7222 | −1.75963 | ||||||||
\(326\) | 22.3960i | 1.24040i | ||||||||
\(327\) | 1.45285 | 0.0803427 | ||||||||
\(328\) | − | 5.85343i | − | 0.323202i | ||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 2.32120 | − | 0.123562i | 0.127778 | − | 0.00680184i | ||||
\(331\) | 27.2898 | 1.49998 | 0.749991 | − | 0.661448i | \(-0.230058\pi\) | ||||
0.749991 | + | 0.661448i | \(0.230058\pi\) | |||||||
\(332\) | −4.03988 | −0.221717 | ||||||||
\(333\) | 3.99419 | 0.218880 | ||||||||
\(334\) | − | 17.9924i | − | 0.984498i | ||||||
\(335\) | 1.50040i | 0.0819757i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 13.0929i | 0.713215i | 0.934254 | + | 0.356607i | \(0.116067\pi\) | ||||
−0.934254 | + | 0.356607i | \(0.883933\pi\) | |||||||
\(338\) | 36.4999i | 1.98533i | ||||||||
\(339\) | 12.0074i | 0.652153i | ||||||||
\(340\) | − | 0.432980i | − | 0.0234816i | ||||||
\(341\) | 20.4609 | − | 1.08917i | 1.10802 | − | 0.0589819i | ||||
\(342\) | 0.783393i | 0.0423610i | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 3.62441 | 0.195415 | ||||||||
\(345\) | 3.69481 | 0.198922 | ||||||||
\(346\) | 0.378382i | 0.0203420i | ||||||||
\(347\) | 11.3473i | 0.609157i | 0.952487 | + | 0.304578i | \(0.0985156\pi\) | ||||
−0.952487 | + | 0.304578i | \(0.901484\pi\) | |||||||
\(348\) | −2.09176 | −0.112130 | ||||||||
\(349\) | −12.4060 | −0.664076 | −0.332038 | − | 0.943266i | \(-0.607736\pi\) | ||||
−0.332038 | + | 0.943266i | \(0.607736\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 7.03562i | 0.375534i | ||||||||
\(352\) | −3.31194 | + | 0.176300i | −0.176527 | + | 0.00939685i | ||||
\(353\) | 6.82398i | 0.363204i | 0.983372 | + | 0.181602i | \(0.0581282\pi\) | ||||
−0.983372 | + | 0.181602i | \(0.941872\pi\) | |||||||
\(354\) | 3.76387i | 0.200047i | ||||||||
\(355\) | − | 3.14337i | − | 0.166833i | ||||||
\(356\) | 16.2115i | 0.859207i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | − | 4.31093i | − | 0.227840i | ||||||
\(359\) | − | 20.4315i | − | 1.07833i | −0.842200 | − | 0.539166i | \(-0.818740\pi\) | ||
0.842200 | − | 0.539166i | \(-0.181260\pi\) | |||||||
\(360\) | −0.700858 | −0.0369384 | ||||||||
\(361\) | −18.3863 | −0.967700 | ||||||||
\(362\) | 6.96276 | 0.365955 | ||||||||
\(363\) | −1.16779 | − | 10.9378i | −0.0612932 | − | 0.574088i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 3.70714i | − | 0.194040i | ||||||
\(366\) | 8.36572 | 0.437283 | ||||||||
\(367\) | 20.1568i | 1.05218i | 0.850430 | + | 0.526088i | \(0.176342\pi\) | ||||
−0.850430 | + | 0.526088i | \(0.823658\pi\) | |||||||
\(368\) | −5.27184 | −0.274814 | ||||||||
\(369\) | −5.85343 | −0.304717 | ||||||||
\(370\) | 2.79936 | 0.145532 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −6.17793 | −0.320311 | ||||||||
\(373\) | − | 8.33854i | − | 0.431753i | −0.976421 | − | 0.215877i | \(-0.930739\pi\) | ||
0.976421 | − | 0.215877i | \(-0.0692609\pi\) | |||||||
\(374\) | −2.04606 | + | 0.108916i | −0.105799 | + | 0.00563190i | ||||
\(375\) | −6.66432 | −0.344144 | ||||||||
\(376\) | 2.34976 | 0.121179 | ||||||||
\(377\) | 14.7169i | 0.757956i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −12.2093 | −0.627151 | −0.313575 | − | 0.949563i | \(-0.601527\pi\) | ||||
−0.313575 | + | 0.949563i | \(0.601527\pi\) | |||||||
\(380\) | 0.549047i | 0.0281655i | ||||||||
\(381\) | −3.43188 | −0.175821 | ||||||||
\(382\) | − | 18.5590i | − | 0.949560i | ||||||
\(383\) | − | 18.6517i | − | 0.953057i | −0.879159 | − | 0.476529i | \(-0.841895\pi\) | ||
0.879159 | − | 0.476529i | \(-0.158105\pi\) | |||||||
\(384\) | 1.00000 | 0.0510310 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 17.5212 | 0.891805 | ||||||||
\(387\) | − | 3.62441i | − | 0.184239i | ||||||
\(388\) | 10.4926i | 0.532680i | ||||||||
\(389\) | −9.51444 | −0.482401 | −0.241201 | − | 0.970475i | \(-0.577541\pi\) | ||||
−0.241201 | + | 0.970475i | \(0.577541\pi\) | |||||||
\(390\) | 4.93097i | 0.249689i | ||||||||
\(391\) | −3.25686 | −0.164707 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 14.6058i | − | 0.736764i | ||||||
\(394\) | 18.8663 | 0.950472 | ||||||||
\(395\) | 3.04142 | 0.153031 | ||||||||
\(396\) | 0.176300 | + | 3.31194i | 0.00885943 | + | 0.166431i | ||||
\(397\) | 34.0696i | 1.70990i | 0.518707 | + | 0.854952i | \(0.326414\pi\) | ||||
−0.518707 | + | 0.854952i | \(0.673586\pi\) | |||||||
\(398\) | 13.5324 | 0.678316 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 4.50880 | 0.225440 | ||||||||
\(401\) | −29.6358 | −1.47994 | −0.739969 | − | 0.672641i | \(-0.765160\pi\) | ||||
−0.739969 | + | 0.672641i | \(0.765160\pi\) | |||||||
\(402\) | −2.14081 | −0.106774 | ||||||||
\(403\) | 43.4655i | 2.16517i | ||||||||
\(404\) | 14.9947 | 0.746016 | ||||||||
\(405\) | 0.700858i | 0.0348259i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −0.704177 | − | 13.2285i | −0.0349048 | − | 0.655712i | ||||
\(408\) | 0.617785 | 0.0305849 | ||||||||
\(409\) | −27.3288 | −1.35132 | −0.675662 | − | 0.737212i | \(-0.736142\pi\) | ||||
−0.675662 | + | 0.737212i | \(0.736142\pi\) | |||||||
\(410\) | −4.10242 | −0.202604 | ||||||||
\(411\) | 16.7161i | 0.824543i | ||||||||
\(412\) | 14.3517i | 0.707057i | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 5.27184i | 0.259097i | ||||||||
\(415\) | 2.83138i | 0.138987i | ||||||||
\(416\) | − | 7.03562i | − | 0.344950i | ||||||
\(417\) | − | 12.9399i | − | 0.633671i | ||||||
\(418\) | 2.59455 | − | 0.138113i | 0.126903 | − | 0.00675531i | ||||
\(419\) | − | 25.6972i | − | 1.25539i | −0.778459 | − | 0.627696i | \(-0.783998\pi\) | ||
0.778459 | − | 0.627696i | \(-0.216002\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −36.9246 | −1.79959 | −0.899797 | − | 0.436309i | \(-0.856285\pi\) | ||||
−0.899797 | + | 0.436309i | \(0.856285\pi\) | |||||||
\(422\) | −4.94368 | −0.240654 | ||||||||
\(423\) | − | 2.34976i | − | 0.114249i | ||||||
\(424\) | − | 7.90136i | − | 0.383724i | ||||||
\(425\) | 2.78547 | 0.135115 | ||||||||
\(426\) | 4.48503 | 0.217300 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 11.4671i | 0.554284i | ||||||||
\(429\) | 23.3015 | − | 1.24038i | 1.12501 | − | 0.0598863i | ||||
\(430\) | − | 2.54020i | − | 0.122499i | ||||||
\(431\) | 20.1287i | 0.969566i | 0.874635 | + | 0.484783i | \(0.161101\pi\) | ||||
−0.874635 | + | 0.484783i | \(0.838899\pi\) | |||||||
\(432\) | − | 1.00000i | − | 0.0481125i | ||||||
\(433\) | − | 38.1992i | − | 1.83574i | −0.396884 | − | 0.917869i | \(-0.629908\pi\) | ||
0.396884 | − | 0.917869i | \(-0.370092\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 1.46603i | 0.0702907i | ||||||||
\(436\) | 1.45285i | 0.0695788i | ||||||||
\(437\) | 4.12992 | 0.197561 | ||||||||
\(438\) | 5.28943 | 0.252739 | ||||||||
\(439\) | −7.32197 | −0.349459 | −0.174729 | − | 0.984616i | \(-0.555905\pi\) | ||||
−0.174729 | + | 0.984616i | \(0.555905\pi\) | |||||||
\(440\) | 0.123562 | + | 2.32120i | 0.00589057 | + | 0.110659i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | − | 4.34650i | − | 0.206742i | ||||||
\(443\) | −33.0248 | −1.56905 | −0.784527 | − | 0.620094i | \(-0.787094\pi\) | ||||
−0.784527 | + | 0.620094i | \(0.787094\pi\) | |||||||
\(444\) | 3.99419i | 0.189556i | ||||||||
\(445\) | 11.3619 | 0.538608 | ||||||||
\(446\) | −22.9194 | −1.08527 | ||||||||
\(447\) | 9.72861 | 0.460148 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −22.5285 | −1.06319 | −0.531594 | − | 0.846999i | \(-0.678407\pi\) | ||||
−0.531594 | + | 0.846999i | \(0.678407\pi\) | |||||||
\(450\) | − | 4.50880i | − | 0.212547i | ||||||
\(451\) | 1.03196 | + | 19.3862i | 0.0485932 | + | 0.912859i | ||||
\(452\) | −12.0074 | −0.564781 | ||||||||
\(453\) | −19.7877 | −0.929709 | ||||||||
\(454\) | 24.2282i | 1.13709i | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −0.783393 | −0.0366857 | ||||||||
\(457\) | − | 33.1752i | − | 1.55187i | −0.630814 | − | 0.775934i | \(-0.717279\pi\) | ||
0.630814 | − | 0.775934i | \(-0.282721\pi\) | |||||||
\(458\) | −13.3778 | −0.625105 | ||||||||
\(459\) | − | 0.617785i | − | 0.0288357i | ||||||
\(460\) | 3.69481i | 0.172271i | ||||||||
\(461\) | −7.42955 | −0.346029 | −0.173014 | − | 0.984919i | \(-0.555351\pi\) | ||||
−0.173014 | + | 0.984919i | \(0.555351\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −15.7504 | −0.731984 | −0.365992 | − | 0.930618i | \(-0.619270\pi\) | ||||
−0.365992 | + | 0.930618i | \(0.619270\pi\) | |||||||
\(464\) | − | 2.09176i | − | 0.0971077i | ||||||
\(465\) | 4.32985i | 0.200792i | ||||||||
\(466\) | −27.9050 | −1.29267 | ||||||||
\(467\) | − | 13.3731i | − | 0.618835i | −0.950926 | − | 0.309418i | \(-0.899866\pi\) | ||
0.950926 | − | 0.309418i | \(-0.100134\pi\) | |||||||
\(468\) | −7.03562 | −0.325222 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | − | 1.64685i | − | 0.0759633i | ||||||
\(471\) | −12.0105 | −0.553413 | ||||||||
\(472\) | −3.76387 | −0.173246 | ||||||||
\(473\) | −12.0038 | + | 0.638985i | −0.551936 | + | 0.0293806i | ||||
\(474\) | 4.33957i | 0.199323i | ||||||||
\(475\) | −3.53216 | −0.162067 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −7.90136 | −0.361779 | ||||||||
\(478\) | −9.27514 | −0.424235 | ||||||||
\(479\) | 11.2610 | 0.514528 | 0.257264 | − | 0.966341i | \(-0.417179\pi\) | ||||
0.257264 | + | 0.966341i | \(0.417179\pi\) | |||||||
\(480\) | − | 0.700858i | − | 0.0319896i | ||||||
\(481\) | 28.1016 | 1.28132 | ||||||||
\(482\) | 19.0970i | 0.869845i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 10.9378 | − | 1.16779i | 0.497174 | − | 0.0530814i | ||||
\(485\) | 7.35380 | 0.333919 | ||||||||
\(486\) | −1.00000 | −0.0453609 | ||||||||
\(487\) | 2.66963 | 0.120972 | 0.0604862 | − | 0.998169i | \(-0.480735\pi\) | ||||
0.0604862 | + | 0.998169i | \(0.480735\pi\) | |||||||
\(488\) | 8.36572i | 0.378698i | ||||||||
\(489\) | 22.3960i | 1.01278i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 11.3063i | − | 0.510245i | −0.966909 | − | 0.255123i | \(-0.917884\pi\) | ||
0.966909 | − | 0.255123i | \(-0.0821158\pi\) | |||||||
\(492\) | − | 5.85343i | − | 0.263893i | ||||||
\(493\) | − | 1.29226i | − | 0.0582005i | ||||||
\(494\) | 5.51165i | 0.247981i | ||||||||
\(495\) | 2.32120 | − | 0.123562i | 0.104330 | − | 0.00555368i | ||||
\(496\) | − | 6.17793i | − | 0.277397i | ||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −4.03988 | −0.181032 | ||||||||
\(499\) | 21.4400 | 0.959787 | 0.479894 | − | 0.877327i | \(-0.340675\pi\) | ||||
0.479894 | + | 0.877327i | \(0.340675\pi\) | |||||||
\(500\) | − | 6.66432i | − | 0.298037i | ||||||
\(501\) | − | 17.9924i | − | 0.803839i | ||||||
\(502\) | −12.1328 | −0.541515 | ||||||||
\(503\) | 30.0822 | 1.34130 | 0.670649 | − | 0.741775i | \(-0.266016\pi\) | ||||
0.670649 | + | 0.741775i | \(0.266016\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 10.5092i | − | 0.467652i | ||||||
\(506\) | 17.4600 | − | 0.929428i | 0.776191 | − | 0.0413181i | ||||
\(507\) | 36.4999i | 1.62102i | ||||||||
\(508\) | − | 3.43188i | − | 0.152265i | ||||||
\(509\) | − | 13.4813i | − | 0.597548i | −0.954324 | − | 0.298774i | \(-0.903422\pi\) | ||
0.954324 | − | 0.298774i | \(-0.0965776\pi\) | |||||||
\(510\) | − | 0.432980i | − | 0.0191727i | ||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | 0.783393i | 0.0345876i | ||||||||
\(514\) | 19.9471 | 0.879829 | ||||||||
\(515\) | 10.0585 | 0.443230 | ||||||||
\(516\) | 3.62441 | 0.159556 | ||||||||
\(517\) | −7.78224 | + | 0.414263i | −0.342263 | + | 0.0182193i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0.378382i | 0.0166091i | ||||||||
\(520\) | −4.93097 | −0.216237 | ||||||||
\(521\) | − | 11.1268i | − | 0.487473i | −0.969841 | − | 0.243737i | \(-0.921627\pi\) | ||
0.969841 | − | 0.243737i | \(-0.0783733\pi\) | |||||||
\(522\) | −2.09176 | −0.0915540 | ||||||||
\(523\) | −14.9088 | −0.651916 | −0.325958 | − | 0.945384i | \(-0.605687\pi\) | ||||
−0.325958 | + | 0.945384i | \(0.605687\pi\) | |||||||
\(524\) | 14.6058 | 0.638056 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 16.7867 | 0.731935 | ||||||||
\(527\) | − | 3.81663i | − | 0.166255i | ||||||
\(528\) | −3.31194 | + | 0.176300i | −0.144134 | + | 0.00767249i | ||||
\(529\) | 4.79227 | 0.208360 | ||||||||
\(530\) | −5.53773 | −0.240544 | ||||||||
\(531\) | 3.76387i | 0.163338i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −41.1825 | −1.78381 | ||||||||
\(534\) | 16.2115i | 0.701540i | ||||||||
\(535\) | 8.03682 | 0.347462 | ||||||||
\(536\) | − | 2.14081i | − | 0.0924688i | ||||||
\(537\) | − | 4.31093i | − | 0.186030i | ||||||
\(538\) | 19.4953 | 0.840504 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −0.700858 | −0.0301601 | ||||||||
\(541\) | 26.5815i | 1.14283i | 0.820663 | + | 0.571413i | \(0.193605\pi\) | ||||
−0.820663 | + | 0.571413i | \(0.806395\pi\) | |||||||
\(542\) | − | 10.6826i | − | 0.458857i | ||||||
\(543\) | 6.96276 | 0.298801 | ||||||||
\(544\) | 0.617785i | 0.0264873i | ||||||||
\(545\) | 1.01824 | 0.0436166 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 18.2285i | 0.779393i | 0.920943 | + | 0.389696i | \(0.127420\pi\) | ||||
−0.920943 | + | 0.389696i | \(0.872580\pi\) | |||||||
\(548\) | −16.7161 | −0.714075 | ||||||||
\(549\) | 8.36572 | 0.357040 | ||||||||
\(550\) | −14.9329 | + | 0.794903i | −0.636739 | + | 0.0338948i | ||||
\(551\) | 1.63867i | 0.0698098i | ||||||||
\(552\) | −5.27184 | −0.224384 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −30.7880 | −1.30805 | ||||||||
\(555\) | 2.79936 | 0.118826 | ||||||||
\(556\) | 12.9399 | 0.548775 | ||||||||
\(557\) | − | 31.4847i | − | 1.33405i | −0.745035 | − | 0.667025i | \(-0.767567\pi\) | ||
0.745035 | − | 0.667025i | \(-0.232433\pi\) | |||||||
\(558\) | −6.17793 | −0.261532 | ||||||||
\(559\) | − | 25.5000i | − | 1.07853i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −2.04606 | + | 0.108916i | −0.0863849 | + | 0.00459843i | ||||
\(562\) | 21.3381 | 0.900094 | ||||||||
\(563\) | 21.9402 | 0.924669 | 0.462335 | − | 0.886705i | \(-0.347012\pi\) | ||||
0.462335 | + | 0.886705i | \(0.347012\pi\) | |||||||
\(564\) | 2.34976 | 0.0989426 | ||||||||
\(565\) | 8.41549i | 0.354042i | ||||||||
\(566\) | − | 2.52307i | − | 0.106053i | ||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 4.48503i | 0.188188i | ||||||||
\(569\) | − | 31.0614i | − | 1.30216i | −0.759009 | − | 0.651080i | \(-0.774316\pi\) | ||
0.759009 | − | 0.651080i | \(-0.225684\pi\) | |||||||
\(570\) | 0.549047i | 0.0229970i | ||||||||
\(571\) | − | 9.76821i | − | 0.408787i | −0.978889 | − | 0.204393i | \(-0.934478\pi\) | ||
0.978889 | − | 0.204393i | \(-0.0655222\pi\) | |||||||
\(572\) | 1.24038 | + | 23.3015i | 0.0518630 | + | 0.974285i | ||||
\(573\) | − | 18.5590i | − | 0.775313i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −23.7697 | −0.991263 | ||||||||
\(576\) | 1.00000 | 0.0416667 | ||||||||
\(577\) | 19.3888i | 0.807168i | 0.914943 | + | 0.403584i | \(0.132236\pi\) | ||||
−0.914943 | + | 0.403584i | \(0.867764\pi\) | |||||||
\(578\) | − | 16.6183i | − | 0.691232i | ||||||
\(579\) | 17.5212 | 0.728156 | ||||||||
\(580\) | −1.46603 | −0.0608735 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 10.4926i | 0.434931i | ||||||||
\(583\) | 1.39301 | + | 26.1688i | 0.0576928 | + | 1.08380i | ||||
\(584\) | 5.28943i | 0.218878i | ||||||||
\(585\) | 4.93097i | 0.203870i | ||||||||
\(586\) | − | 5.71831i | − | 0.236221i | ||||||
\(587\) | 14.0625i | 0.580421i | 0.956963 | + | 0.290210i | \(0.0937253\pi\) | ||||
−0.956963 | + | 0.290210i | \(0.906275\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 4.83974i | 0.199418i | ||||||||
\(590\) | 2.63794i | 0.108602i | ||||||||
\(591\) | 18.8663 | 0.776058 | ||||||||
\(592\) | −3.99419 | −0.164160 | ||||||||
\(593\) | −38.1093 | −1.56496 | −0.782480 | − | 0.622676i | \(-0.786046\pi\) | ||||
−0.782480 | + | 0.622676i | \(0.786046\pi\) | |||||||
\(594\) | 0.176300 | + | 3.31194i | 0.00723370 | + | 0.135890i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 9.72861i | 0.398500i | ||||||||
\(597\) | 13.5324 | 0.553842 | ||||||||
\(598\) | 37.0906i | 1.51675i | ||||||||
\(599\) | −24.5324 | −1.00237 | −0.501183 | − | 0.865342i | \(-0.667101\pi\) | ||||
−0.501183 | + | 0.865342i | \(0.667101\pi\) | |||||||
\(600\) | 4.50880 | 0.184071 | ||||||||
\(601\) | −3.08091 | −0.125673 | −0.0628365 | − | 0.998024i | \(-0.520015\pi\) | ||||
−0.0628365 | + | 0.998024i | \(0.520015\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −2.14081 | −0.0871804 | ||||||||
\(604\) | − | 19.7877i | − | 0.805151i | ||||||
\(605\) | −0.818456 | − | 7.66587i | −0.0332750 | − | 0.311662i | ||||
\(606\) | 14.9947 | 0.609120 | ||||||||
\(607\) | 40.7678 | 1.65471 | 0.827356 | − | 0.561677i | \(-0.189844\pi\) | ||||
0.827356 | + | 0.561677i | \(0.189844\pi\) | |||||||
\(608\) | − | 0.783393i | − | 0.0317708i | ||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 5.86318 | 0.237393 | ||||||||
\(611\) | − | 16.5320i | − | 0.668813i | ||||||
\(612\) | 0.617785 | 0.0249725 | ||||||||
\(613\) | − | 8.95511i | − | 0.361693i | −0.983511 | − | 0.180847i | \(-0.942116\pi\) | ||
0.983511 | − | 0.180847i | \(-0.0578838\pi\) | |||||||
\(614\) | − | 20.7839i | − | 0.838768i | ||||||
\(615\) | −4.10242 | −0.165426 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 19.1914 | 0.772618 | 0.386309 | − | 0.922369i | \(-0.373750\pi\) | ||||
0.386309 | + | 0.922369i | \(0.373750\pi\) | |||||||
\(618\) | 14.3517i | 0.577310i | ||||||||
\(619\) | 3.37081i | 0.135484i | 0.997703 | + | 0.0677422i | \(0.0215795\pi\) | ||||
−0.997703 | + | 0.0677422i | \(0.978420\pi\) | |||||||
\(620\) | −4.32985 | −0.173891 | ||||||||
\(621\) | 5.27184i | 0.211552i | ||||||||
\(622\) | 7.36751 | 0.295410 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | − | 7.03562i | − | 0.281650i | ||||||
\(625\) | 17.8733 | 0.714930 | ||||||||
\(626\) | −7.35395 | −0.293923 | ||||||||
\(627\) | 2.59455 | − | 0.138113i | 0.103616 | − | 0.00551568i | ||||
\(628\) | − | 12.0105i | − | 0.479269i | ||||||
\(629\) | −2.46755 | −0.0983876 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 33.1910 | 1.32131 | 0.660657 | − | 0.750688i | \(-0.270278\pi\) | ||||
0.660657 | + | 0.750688i | \(0.270278\pi\) | |||||||
\(632\) | −4.33957 | −0.172619 | ||||||||
\(633\) | −4.94368 | −0.196494 | ||||||||
\(634\) | − | 14.7806i | − | 0.587012i | ||||||
\(635\) | −2.40526 | −0.0954499 | ||||||||
\(636\) | − | 7.90136i | − | 0.313309i | ||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0.368779 | + | 6.92779i | 0.0146001 | + | 0.274274i | ||||
\(639\) | 4.48503 | 0.177425 | ||||||||
\(640\) | 0.700858 | 0.0277038 | ||||||||
\(641\) | −34.4611 | −1.36113 | −0.680566 | − | 0.732686i | \(-0.738266\pi\) | ||||
−0.680566 | + | 0.732686i | \(0.738266\pi\) | |||||||
\(642\) | 11.4671i | 0.452571i | ||||||||
\(643\) | 2.69205i | 0.106164i | 0.998590 | + | 0.0530821i | \(0.0169045\pi\) | ||||
−0.998590 | + | 0.0530821i | \(0.983095\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − | 2.54020i | − | 0.100020i | ||||||
\(646\) | − | 0.483969i | − | 0.0190415i | ||||||
\(647\) | 46.6810i | 1.83522i | 0.397480 | + | 0.917611i | \(0.369885\pi\) | ||||
−0.397480 | + | 0.917611i | \(0.630115\pi\) | |||||||
\(648\) | − | 1.00000i | − | 0.0392837i | ||||||
\(649\) | 12.4657 | − | 0.663572i | 0.489321 | − | 0.0260475i | ||||
\(650\) | − | 31.7222i | − | 1.24425i | ||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −22.3960 | −0.877094 | ||||||||
\(653\) | 39.9858 | 1.56477 | 0.782383 | − | 0.622798i | \(-0.214004\pi\) | ||||
0.782383 | + | 0.622798i | \(0.214004\pi\) | |||||||
\(654\) | 1.45285i | 0.0568109i | ||||||||
\(655\) | − | 10.2366i | − | 0.399976i | ||||||
\(656\) | 5.85343 | 0.228538 | ||||||||
\(657\) | 5.28943 | 0.206360 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 24.9930i | 0.973590i | 0.873516 | + | 0.486795i | \(0.161834\pi\) | ||||
−0.873516 | + | 0.486795i | \(0.838166\pi\) | |||||||
\(660\) | 0.123562 | + | 2.32120i | 0.00480963 | + | 0.0903524i | ||||
\(661\) | 14.6955i | 0.571588i | 0.958291 | + | 0.285794i | \(0.0922573\pi\) | ||||
−0.958291 | + | 0.285794i | \(0.907743\pi\) | |||||||
\(662\) | 27.2898i | 1.06065i | ||||||||
\(663\) | − | 4.34650i | − | 0.168804i | ||||||
\(664\) | − | 4.03988i | − | 0.156778i | ||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 3.99419i | 0.154772i | ||||||||
\(667\) | 11.0274i | 0.426984i | ||||||||
\(668\) | 17.9924 | 0.696145 | ||||||||
\(669\) | −22.9194 | −0.886117 | ||||||||
\(670\) | −1.50040 | −0.0579655 | ||||||||
\(671\) | −1.47488 | − | 27.7067i | −0.0569371 | − | 1.06961i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 51.7415i | − | 1.99449i | −0.0741830 | − | 0.997245i | \(-0.523635\pi\) | ||
0.0741830 | − | 0.997245i | \(-0.476365\pi\) | |||||||
\(674\) | −13.0929 | −0.504319 | ||||||||
\(675\) | − | 4.50880i | − | 0.173544i | ||||||
\(676\) | −36.4999 | −1.40384 | ||||||||
\(677\) | −37.4530 | −1.43944 | −0.719718 | − | 0.694266i | \(-0.755729\pi\) | ||||
−0.719718 | + | 0.694266i | \(0.755729\pi\) | |||||||
\(678\) | −12.0074 | −0.461142 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0.432980 | 0.0166040 | ||||||||
\(681\) | 24.2282i | 0.928427i | ||||||||
\(682\) | 1.08917 | + | 20.4609i | 0.0417065 | + | 0.783488i | ||||
\(683\) | −42.0158 | −1.60769 | −0.803845 | − | 0.594839i | \(-0.797216\pi\) | ||||
−0.803845 | + | 0.594839i | \(0.797216\pi\) | |||||||
\(684\) | −0.783393 | −0.0299538 | ||||||||
\(685\) | 11.7156i | 0.447630i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −13.3778 | −0.510396 | ||||||||
\(688\) | 3.62441i | 0.138179i | ||||||||
\(689\) | −55.5910 | −2.11785 | ||||||||
\(690\) | 3.69481i | 0.140659i | ||||||||
\(691\) | 27.6503i | 1.05187i | 0.850525 | + | 0.525934i | \(0.176284\pi\) | ||||
−0.850525 | + | 0.525934i | \(0.823716\pi\) | |||||||
\(692\) | −0.378382 | −0.0143839 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −11.3473 | −0.430739 | ||||||||
\(695\) | − | 9.06905i | − | 0.344009i | ||||||
\(696\) | − | 2.09176i | − | 0.0792881i | ||||||
\(697\) | 3.61616 | 0.136972 | ||||||||
\(698\) | − | 12.4060i | − | 0.469573i | ||||||
\(699\) | −27.9050 | −1.05546 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 8.73779i | − | 0.330022i | −0.986292 | − | 0.165011i | \(-0.947234\pi\) | ||
0.986292 | − | 0.165011i | \(-0.0527659\pi\) | |||||||
\(702\) | −7.03562 | −0.265542 | ||||||||
\(703\) | 3.12902 | 0.118013 | ||||||||
\(704\) | −0.176300 | − | 3.31194i | −0.00664457 | − | 0.124823i | ||||
\(705\) | − | 1.64685i | − | 0.0620238i | ||||||
\(706\) | −6.82398 | −0.256824 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −3.76387 | −0.141455 | ||||||||
\(709\) | −33.3365 | −1.25198 | −0.625990 | − | 0.779831i | \(-0.715305\pi\) | ||||
−0.625990 | + | 0.779831i | \(0.715305\pi\) | |||||||
\(710\) | 3.14337 | 0.117969 | ||||||||
\(711\) | 4.33957i | 0.162747i | ||||||||
\(712\) | −16.2115 | −0.607551 | ||||||||
\(713\) | 32.5690i | 1.21972i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 16.3310 | − | 0.869332i | 0.610747 | − | 0.0325112i | ||||
\(716\) | 4.31093 | 0.161107 | ||||||||
\(717\) | −9.27514 | −0.346386 | ||||||||
\(718\) | 20.4315 | 0.762495 | ||||||||
\(719\) | 10.4879i | 0.391132i | 0.980691 | + | 0.195566i | \(0.0626544\pi\) | ||||
−0.980691 | + | 0.195566i | \(0.937346\pi\) | |||||||
\(720\) | − | 0.700858i | − | 0.0261194i | ||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | − | 18.3863i | − | 0.684267i | ||||||
\(723\) | 19.0970i | 0.710226i | ||||||||
\(724\) | 6.96276i | 0.258769i | ||||||||
\(725\) | − | 9.43134i | − | 0.350271i | ||||||
\(726\) | 10.9378 | − | 1.16779i | 0.405941 | − | 0.0433408i | ||||
\(727\) | 9.73041i | 0.360881i | 0.983586 | + | 0.180440i | \(0.0577523\pi\) | ||||
−0.983586 | + | 0.180440i | \(0.942248\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 3.70714 | 0.137207 | ||||||||
\(731\) | 2.23911i | 0.0828163i | ||||||||
\(732\) | 8.36572i | 0.309206i | ||||||||
\(733\) | 1.60100 | 0.0591342 | 0.0295671 | − | 0.999563i | \(-0.490587\pi\) | ||||
0.0295671 | + | 0.999563i | \(0.490587\pi\) | |||||||
\(734\) | −20.1568 | −0.744001 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | − | 5.27184i | − | 0.194323i | ||||||
\(737\) | 0.377425 | + | 7.09021i | 0.0139026 | + | 0.261171i | ||||
\(738\) | − | 5.85343i | − | 0.215468i | ||||||
\(739\) | 27.3381i | 1.00565i | 0.864388 | + | 0.502825i | \(0.167706\pi\) | ||||
−0.864388 | + | 0.502825i | \(0.832294\pi\) | |||||||
\(740\) | 2.79936i | 0.102906i | ||||||||
\(741\) | 5.51165i | 0.202476i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 49.7705i | 1.82590i | 0.408067 | + | 0.912952i | \(0.366203\pi\) | ||||
−0.408067 | + | 0.912952i | \(0.633797\pi\) | |||||||
\(744\) | − | 6.17793i | − | 0.226494i | ||||||
\(745\) | 6.81837 | 0.249806 | ||||||||
\(746\) | 8.33854 | 0.305296 | ||||||||
\(747\) | −4.03988 | −0.147812 | ||||||||
\(748\) | −0.108916 | − | 2.04606i | −0.00398236 | − | 0.0748115i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | − | 6.66432i | − | 0.243346i | ||||||
\(751\) | −23.0637 | −0.841606 | −0.420803 | − | 0.907152i | \(-0.638252\pi\) | ||||
−0.420803 | + | 0.907152i | \(0.638252\pi\) | |||||||
\(752\) | 2.34976i | 0.0856868i | ||||||||
\(753\) | −12.1328 | −0.442145 | ||||||||
\(754\) | −14.7169 | −0.535956 | ||||||||
\(755\) | −13.8684 | −0.504722 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −35.4691 | −1.28915 | −0.644574 | − | 0.764542i | \(-0.722965\pi\) | ||||
−0.644574 | + | 0.764542i | \(0.722965\pi\) | |||||||
\(758\) | − | 12.2093i | − | 0.443463i | ||||||
\(759\) | 17.4600 | − | 0.929428i | 0.633757 | − | 0.0337361i | ||||
\(760\) | −0.549047 | −0.0199160 | ||||||||
\(761\) | −16.2697 | −0.589776 | −0.294888 | − | 0.955532i | \(-0.595282\pi\) | ||||
−0.294888 | + | 0.955532i | \(0.595282\pi\) | |||||||
\(762\) | − | 3.43188i | − | 0.124324i | ||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 18.5590 | 0.671440 | ||||||||
\(765\) | − | 0.432980i | − | 0.0156544i | ||||||
\(766\) | 18.6517 | 0.673913 | ||||||||
\(767\) | 26.4811i | 0.956179i | ||||||||
\(768\) | 1.00000i | 0.0360844i | ||||||||
\(769\) | −31.2492 | −1.12687 | −0.563437 | − | 0.826159i | \(-0.690521\pi\) | ||||
−0.563437 | + | 0.826159i | \(0.690521\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 19.9471 | 0.718377 | ||||||||
\(772\) | 17.5212i | 0.630601i | ||||||||
\(773\) | − | 16.5216i | − | 0.594240i | −0.954840 | − | 0.297120i | \(-0.903974\pi\) | ||
0.954840 | − | 0.297120i | \(-0.0960261\pi\) | |||||||
\(774\) | 3.62441 | 0.130277 | ||||||||
\(775\) | − | 27.8550i | − | 1.00058i | ||||||
\(776\) | −10.4926 | −0.376662 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | − | 9.51444i | − | 0.341109i | ||||||
\(779\) | −4.58553 | −0.164294 | ||||||||
\(780\) | −4.93097 | −0.176557 | ||||||||
\(781\) | −0.790713 | − | 14.8541i | −0.0282939 | − | 0.531523i | ||||
\(782\) | − | 3.25686i | − | 0.116465i | ||||||
\(783\) | −2.09176 | −0.0747535 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −8.41762 | −0.300438 | ||||||||
\(786\) | 14.6058 | 0.520970 | ||||||||
\(787\) | −22.0831 | −0.787177 | −0.393589 | − | 0.919287i | \(-0.628767\pi\) | ||||
−0.393589 | + | 0.919287i | \(0.628767\pi\) | |||||||
\(788\) | 18.8663i | 0.672086i | ||||||||
\(789\) | 16.7867 | 0.597622 | ||||||||
\(790\) | 3.04142i | 0.108209i | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −3.31194 | + | 0.176300i | −0.117685 | + | 0.00626457i | ||||
\(793\) | 58.8580 | 2.09011 | ||||||||
\(794\) | −34.0696 | −1.20909 | ||||||||
\(795\) | −5.53773 | −0.196403 | ||||||||
\(796\) | 13.5324i | 0.479642i | ||||||||
\(797\) | 25.7347i | 0.911571i | 0.890090 | + | 0.455785i | \(0.150642\pi\) | ||||
−0.890090 | + | 0.455785i | \(0.849358\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.45165i | 0.0513555i | ||||||||
\(800\) | 4.50880i | 0.159410i | ||||||||
\(801\) | 16.2115i | 0.572805i | ||||||||
\(802\) | − | 29.6358i | − | 1.04647i | ||||||
\(803\) | −0.932528 | − | 17.5182i | −0.0329082 | − | 0.618205i | ||||
\(804\) | − | 2.14081i | − | 0.0755004i | ||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −43.4655 | −1.53101 | ||||||||
\(807\) | 19.4953 | 0.686268 | ||||||||
\(808\) | 14.9947i | 0.527513i | ||||||||
\(809\) | − | 28.9768i | − | 1.01877i | −0.860539 | − | 0.509385i | \(-0.829873\pi\) | ||
0.860539 | − | 0.509385i | \(-0.170127\pi\) | |||||||
\(810\) | −0.700858 | −0.0246256 | ||||||||
\(811\) | 1.48290 | 0.0520715 | 0.0260358 | − | 0.999661i | \(-0.491712\pi\) | ||||
0.0260358 | + | 0.999661i | \(0.491712\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − | 10.6826i | − | 0.374655i | ||||||
\(814\) | 13.2285 | − | 0.704177i | 0.463658 | − | 0.0246814i | ||||
\(815\) | 15.6964i | 0.549821i | ||||||||
\(816\) | 0.617785i | 0.0216268i | ||||||||
\(817\) | − | 2.83934i | − | 0.0993358i | ||||||
\(818\) | − | 27.3288i | − | 0.955530i | ||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | − | 4.10242i | − | 0.143263i | ||||||
\(821\) | − | 5.52513i | − | 0.192828i | −0.995341 | − | 0.0964142i | \(-0.969263\pi\) | ||
0.995341 | − | 0.0964142i | \(-0.0307373\pi\) | |||||||
\(822\) | −16.7161 | −0.583040 | ||||||||
\(823\) | −16.2218 | −0.565455 | −0.282728 | − | 0.959200i | \(-0.591239\pi\) | ||||
−0.282728 | + | 0.959200i | \(0.591239\pi\) | |||||||
\(824\) | −14.3517 | −0.499965 | ||||||||
\(825\) | −14.9329 | + | 0.794903i | −0.519895 | + | 0.0276750i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 5.86195i | − | 0.203840i | −0.994793 | − | 0.101920i | \(-0.967501\pi\) | ||
0.994793 | − | 0.101920i | \(-0.0324986\pi\) | |||||||
\(828\) | −5.27184 | −0.183209 | ||||||||
\(829\) | − | 19.4082i | − | 0.674074i | −0.941491 | − | 0.337037i | \(-0.890575\pi\) | ||
0.941491 | − | 0.337037i | \(-0.109425\pi\) | |||||||
\(830\) | −2.83138 | −0.0982788 | ||||||||
\(831\) | −30.7880 | −1.06802 | ||||||||
\(832\) | 7.03562 | 0.243916 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 12.9399 | 0.448073 | ||||||||
\(835\) | − | 12.6101i | − | 0.436390i | ||||||
\(836\) | 0.138113 | + | 2.59455i | 0.00477672 | + | 0.0897343i | ||||
\(837\) | −6.17793 | −0.213540 | ||||||||
\(838\) | 25.6972 | 0.887696 | ||||||||
\(839\) | 17.8302i | 0.615565i | 0.951457 | + | 0.307783i | \(0.0995870\pi\) | ||||
−0.951457 | + | 0.307783i | \(0.900413\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 24.6245 | 0.849122 | ||||||||
\(842\) | − | 36.9246i | − | 1.27250i | ||||||
\(843\) | 21.3381 | 0.734924 | ||||||||
\(844\) | − | 4.94368i | − | 0.170168i | ||||||
\(845\) | 25.5813i | 0.880022i | ||||||||
\(846\) | 2.34976 | 0.0807863 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 7.90136 | 0.271334 | ||||||||
\(849\) | − | 2.52307i | − | 0.0865916i | ||||||
\(850\) | 2.78547i | 0.0955408i | ||||||||
\(851\) | 21.0567 | 0.721814 | ||||||||
\(852\) | 4.48503i | 0.153655i | ||||||||
\(853\) | −2.57158 | −0.0880491 | −0.0440246 | − | 0.999030i | \(-0.514018\pi\) | ||||
−0.0440246 | + | 0.999030i | \(0.514018\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0.549047i | 0.0187770i | ||||||||
\(856\) | −11.4671 | −0.391938 | ||||||||
\(857\) | 16.3283 | 0.557763 | 0.278881 | − | 0.960326i | \(-0.410036\pi\) | ||||
0.278881 | + | 0.960326i | \(0.410036\pi\) | |||||||
\(858\) | 1.24038 | + | 23.3015i | 0.0423460 | + | 0.795501i | ||||
\(859\) | 25.8385i | 0.881598i | 0.897606 | + | 0.440799i | \(0.145305\pi\) | ||||
−0.897606 | + | 0.440799i | \(0.854695\pi\) | |||||||
\(860\) | 2.54020 | 0.0866199 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −20.1287 | −0.685586 | ||||||||
\(863\) | 17.7945 | 0.605732 | 0.302866 | − | 0.953033i | \(-0.402056\pi\) | ||||
0.302866 | + | 0.953033i | \(0.402056\pi\) | |||||||
\(864\) | 1.00000 | 0.0340207 | ||||||||
\(865\) | 0.265192i | 0.00901680i | ||||||||
\(866\) | 38.1992 | 1.29806 | ||||||||
\(867\) | − | 16.6183i | − | 0.564388i | ||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 14.3724 | − | 0.765069i | 0.487550 | − | 0.0259532i | ||||
\(870\) | −1.46603 | −0.0497030 | ||||||||
\(871\) | −15.0619 | −0.510353 | ||||||||
\(872\) | −1.45285 | −0.0491997 | ||||||||
\(873\) | 10.4926i | 0.355120i | ||||||||
\(874\) | 4.12992i | 0.139697i | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 5.28943i | 0.178713i | ||||||||
\(877\) | − | 1.51986i | − | 0.0513221i | −0.999671 | − | 0.0256611i | \(-0.991831\pi\) | ||
0.999671 | − | 0.0256611i | \(-0.00816907\pi\) | |||||||
\(878\) | − | 7.32197i | − | 0.247105i | ||||||
\(879\) | − | 5.71831i | − | 0.192874i | ||||||
\(880\) | −2.32120 | + | 0.123562i | −0.0782475 | + | 0.00416526i | ||||
\(881\) | 2.61558i | 0.0881210i | 0.999029 | + | 0.0440605i | \(0.0140294\pi\) | ||||
−0.999029 | + | 0.0440605i | \(0.985971\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −32.7433 | −1.10190 | −0.550950 | − | 0.834538i | \(-0.685735\pi\) | ||||
−0.550950 | + | 0.834538i | \(0.685735\pi\) | |||||||
\(884\) | 4.34650 | 0.146189 | ||||||||
\(885\) | 2.63794i | 0.0886733i | ||||||||
\(886\) | − | 33.0248i | − | 1.10949i | ||||||
\(887\) | −23.2200 | −0.779650 | −0.389825 | − | 0.920889i | \(-0.627465\pi\) | ||||
−0.389825 | + | 0.920889i | \(0.627465\pi\) | |||||||
\(888\) | −3.99419 | −0.134036 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 11.3619i | 0.380853i | ||||||||
\(891\) | 0.176300 | + | 3.31194i | 0.00590629 | + | 0.110954i | ||||
\(892\) | − | 22.9194i | − | 0.767400i | ||||||
\(893\) | − | 1.84078i | − | 0.0615994i | ||||||
\(894\) | 9.72861i | 0.325374i | ||||||||
\(895\) | − | 3.02135i | − | 0.100993i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 37.0906i | 1.23842i | ||||||||
\(898\) | − | 22.5285i | − | 0.751787i | ||||||
\(899\) | −12.9228 | −0.430998 | ||||||||
\(900\) | 4.50880 | 0.150293 | ||||||||
\(901\) | 4.88135 | 0.162621 | ||||||||
\(902\) | −19.3862 | + | 1.03196i | −0.645489 | + | 0.0343606i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | − | 12.0074i | − | 0.399361i | ||||||
\(905\) | 4.87991 | 0.162214 | ||||||||
\(906\) | − | 19.7877i | − | 0.657403i | ||||||
\(907\) | −14.9307 | −0.495766 | −0.247883 | − | 0.968790i | \(-0.579735\pi\) | ||||
−0.247883 | + | 0.968790i | \(0.579735\pi\) | |||||||
\(908\) | −24.2282 | −0.804042 | ||||||||
\(909\) | 14.9947 | 0.497344 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 33.6372 | 1.11445 | 0.557225 | − | 0.830362i | \(-0.311866\pi\) | ||||
0.557225 | + | 0.830362i | \(0.311866\pi\) | |||||||
\(912\) | − | 0.783393i | − | 0.0259407i | ||||||
\(913\) | 0.712234 | + | 13.3798i | 0.0235715 | + | 0.442808i | ||||
\(914\) | 33.1752 | 1.09734 | ||||||||
\(915\) | 5.86318 | 0.193831 | ||||||||
\(916\) | − | 13.3778i | − | 0.442016i | ||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0.617785 | 0.0203899 | ||||||||
\(919\) | − | 27.0021i | − | 0.890718i | −0.895352 | − | 0.445359i | \(-0.853076\pi\) | ||
0.895352 | − | 0.445359i | \(-0.146924\pi\) | |||||||
\(920\) | −3.69481 | −0.121814 | ||||||||
\(921\) | − | 20.7839i | − | 0.684851i | ||||||
\(922\) | − | 7.42955i | − | 0.244679i | ||||||
\(923\) | 31.5550 | 1.03864 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −18.0090 | −0.592131 | ||||||||
\(926\) | − | 15.7504i | − | 0.517591i | ||||||
\(927\) | 14.3517i | 0.471372i | ||||||||
\(928\) | 2.09176 | 0.0686655 | ||||||||
\(929\) | − | 37.7631i | − | 1.23897i | −0.785010 | − | 0.619483i | \(-0.787342\pi\) | ||
0.785010 | − | 0.619483i | \(-0.212658\pi\) | |||||||
\(930\) | −4.32985 | −0.141981 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | − | 27.9050i | − | 0.914057i | ||||||
\(933\) | 7.36751 | 0.241202 | ||||||||
\(934\) | 13.3731 | 0.437583 | ||||||||
\(935\) | −1.43400 | + | 0.0763345i | −0.0468968 | + | 0.00249641i | ||||
\(936\) | − | 7.03562i | − | 0.229966i | ||||||
\(937\) | 33.9310 | 1.10848 | 0.554239 | − | 0.832357i | \(-0.313009\pi\) | ||||
0.554239 | + | 0.832357i | \(0.313009\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −7.35395 | −0.239987 | ||||||||
\(940\) | 1.64685 | 0.0537142 | ||||||||
\(941\) | −26.8943 | −0.876729 | −0.438364 | − | 0.898797i | \(-0.644442\pi\) | ||||
−0.438364 | + | 0.898797i | \(0.644442\pi\) | |||||||
\(942\) | − | 12.0105i | − | 0.391322i | ||||||
\(943\) | −30.8583 | −1.00489 | ||||||||
\(944\) | − | 3.76387i | − | 0.122503i | ||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −0.638985 | − | 12.0038i | −0.0207752 | − | 0.390278i | ||||
\(947\) | −22.7254 | −0.738477 | −0.369239 | − | 0.929335i | \(-0.620381\pi\) | ||||
−0.369239 | + | 0.929335i | \(0.620381\pi\) | |||||||
\(948\) | −4.33957 | −0.140943 | ||||||||
\(949\) | 37.2144 | 1.20803 | ||||||||
\(950\) | − | 3.53216i | − | 0.114598i | ||||||
\(951\) | − | 14.7806i | − | 0.479294i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 15.8105i | 0.512152i | 0.966657 | + | 0.256076i | \(0.0824298\pi\) | ||||
−0.966657 | + | 0.256076i | \(0.917570\pi\) | |||||||
\(954\) | − | 7.90136i | − | 0.255816i | ||||||
\(955\) | − | 13.0072i | − | 0.420903i | ||||||
\(956\) | − | 9.27514i | − | 0.299979i | ||||||
\(957\) | 0.368779 | + | 6.92779i | 0.0119209 | + | 0.223944i | ||||
\(958\) | 11.2610i | 0.363826i | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0.700858 | 0.0226201 | ||||||||
\(961\) | −7.16676 | −0.231186 | ||||||||
\(962\) | 28.1016i | 0.906031i | ||||||||
\(963\) | 11.4671i | 0.369523i | ||||||||
\(964\) | −19.0970 | −0.615074 | ||||||||
\(965\) | 12.2799 | 0.395303 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 50.1237i | 1.61187i | 0.592005 | + | 0.805934i | \(0.298337\pi\) | ||||
−0.592005 | + | 0.805934i | \(0.701663\pi\) | |||||||
\(968\) | 1.16779 | + | 10.9378i | 0.0375343 | + | 0.351555i | ||||
\(969\) | − | 0.483969i | − | 0.0155473i | ||||||
\(970\) | 7.35380i | 0.236116i | ||||||||
\(971\) | 33.3796i | 1.07120i | 0.844471 | + | 0.535602i | \(0.179915\pi\) | ||||
−0.844471 | + | 0.535602i | \(0.820085\pi\) | |||||||
\(972\) | − | 1.00000i | − | 0.0320750i | ||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 2.66963i | 0.0855405i | ||||||||
\(975\) | − | 31.7222i | − | 1.01592i | ||||||
\(976\) | −8.36572 | −0.267780 | ||||||||
\(977\) | −30.8183 | −0.985965 | −0.492983 | − | 0.870039i | \(-0.664093\pi\) | ||||
−0.492983 | + | 0.870039i | \(0.664093\pi\) | |||||||
\(978\) | −22.3960 | −0.716144 | ||||||||
\(979\) | 53.6914 | − | 2.85809i | 1.71598 | − | 0.0913450i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1.45285i | 0.0463859i | ||||||||
\(982\) | 11.3063 | 0.360798 | ||||||||
\(983\) | − | 33.3378i | − | 1.06331i | −0.846961 | − | 0.531656i | \(-0.821570\pi\) | ||
0.846961 | − | 0.531656i | \(-0.178430\pi\) | |||||||
\(984\) | 5.85343 | 0.186600 | ||||||||
\(985\) | 13.2226 | 0.421308 | ||||||||
\(986\) | 1.29226 | 0.0411540 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −5.51165 | −0.175349 | ||||||||
\(989\) | − | 19.1073i | − | 0.607577i | ||||||
\(990\) | 0.123562 | + | 2.32120i | 0.00392704 | + | 0.0737724i | ||||
\(991\) | −58.0685 | −1.84461 | −0.922303 | − | 0.386467i | \(-0.873695\pi\) | ||||
−0.922303 | + | 0.386467i | \(0.873695\pi\) | |||||||
\(992\) | 6.17793 | 0.196149 | ||||||||
\(993\) | 27.2898i | 0.866015i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 9.48426 | 0.300671 | ||||||||
\(996\) | − | 4.03988i | − | 0.128009i | ||||||
\(997\) | −36.6484 | −1.16067 | −0.580334 | − | 0.814379i | \(-0.697078\pi\) | ||||
−0.580334 | + | 0.814379i | \(0.697078\pi\) | |||||||
\(998\) | 21.4400i | 0.678672i | ||||||||
\(999\) | 3.99419i | 0.126370i |
(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 | 3234.2.e.a.2155.12 | 16 | ||
7.4 | even | 3 | 462.2.p.a.439.2 | yes | 16 | ||
7.5 | odd | 6 | 462.2.p.b.241.6 | yes | 16 | ||
7.6 | odd | 2 | 3234.2.e.b.2155.13 | 16 | |||
11.10 | odd | 2 | 3234.2.e.b.2155.4 | 16 | |||
21.5 | even | 6 | 1386.2.bk.b.703.3 | 16 | |||
21.11 | odd | 6 | 1386.2.bk.a.901.7 | 16 | |||
77.32 | odd | 6 | 462.2.p.b.439.6 | yes | 16 | ||
77.54 | even | 6 | 462.2.p.a.241.2 | ✓ | 16 | ||
77.76 | even | 2 | inner | 3234.2.e.a.2155.5 | 16 | ||
231.32 | even | 6 | 1386.2.bk.b.901.3 | 16 | |||
231.131 | odd | 6 | 1386.2.bk.a.703.7 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
462.2.p.a.241.2 | ✓ | 16 | 77.54 | even | 6 | ||
462.2.p.a.439.2 | yes | 16 | 7.4 | even | 3 | ||
462.2.p.b.241.6 | yes | 16 | 7.5 | odd | 6 | ||
462.2.p.b.439.6 | yes | 16 | 77.32 | odd | 6 | ||
1386.2.bk.a.703.7 | 16 | 231.131 | odd | 6 | |||
1386.2.bk.a.901.7 | 16 | 21.11 | odd | 6 | |||
1386.2.bk.b.703.3 | 16 | 21.5 | even | 6 | |||
1386.2.bk.b.901.3 | 16 | 231.32 | even | 6 | |||
3234.2.e.a.2155.5 | 16 | 77.76 | even | 2 | inner | ||
3234.2.e.a.2155.12 | 16 | 1.1 | even | 1 | trivial | ||
3234.2.e.b.2155.4 | 16 | 11.10 | odd | 2 | |||
3234.2.e.b.2155.13 | 16 | 7.6 | odd | 2 |