Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4012,2,Mod(237,4012)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4012, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4012.237");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4012 = 2^{2} \cdot 17 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4012.b (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: | \(32.0359812909\) |
Analytic rank: | \(0\) |
Dimension: | \(46\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 237.40 | ||
Character | \(\chi\) | \(=\) | 4012.237 |
Dual form | 4012.2.b.b.237.7 |
$q$-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 \(\left(\mathbb{Z}/4012\mathbb{Z}\right)^\times\).
\(n\) | \(2007\) | \(3129\) | \(3777\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 2.57223i | 1.48508i | 0.669802 | + | 0.742540i | \(0.266379\pi\) | ||||
−0.669802 | + | 0.742540i | \(0.733621\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − | 2.31913i | − | 1.03715i | −0.855033 | − | 0.518574i | \(-0.826463\pi\) | ||
0.855033 | − | 0.518574i | \(-0.173537\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 3.71324i | − | 1.40347i | −0.712437 | − | 0.701736i | \(-0.752409\pi\) | ||
0.712437 | − | 0.701736i | \(-0.247591\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −3.61638 | −1.20546 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 5.32303i | − | 1.60495i | −0.596683 | − | 0.802477i | \(-0.703515\pi\) | ||
0.596683 | − | 0.802477i | \(-0.296485\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.64206 | −0.732775 | −0.366388 | − | 0.930462i | \(-0.619406\pi\) | ||||
−0.366388 | + | 0.930462i | \(0.619406\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 5.96535 | 1.54025 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.19542 | − | 2.60563i | 0.775002 | − | 0.631958i | ||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −4.86403 | −1.11588 | −0.557942 | − | 0.829880i | \(-0.688409\pi\) | ||||
−0.557942 | + | 0.829880i | \(0.688409\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 9.55131 | 2.08427 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.402486i | 0.0839242i | 0.999119 | + | 0.0419621i | \(0.0133609\pi\) | ||||
−0.999119 | + | 0.0419621i | \(0.986639\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.378384 | −0.0756768 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − | 1.58548i | − | 0.305125i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 7.10049i | 1.31853i | 0.751911 | + | 0.659264i | \(0.229132\pi\) | ||||
−0.751911 | + | 0.659264i | \(0.770868\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5.18537i | 0.931320i | 0.884964 | + | 0.465660i | \(0.154183\pi\) | ||||
−0.884964 | + | 0.465660i | \(0.845817\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 13.6921 | 2.38348 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −8.61149 | −1.45561 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.811616i | 0.133429i | 0.997772 | + | 0.0667144i | \(0.0212516\pi\) | ||||
−0.997772 | + | 0.0667144i | \(0.978748\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | − | 6.79599i | − | 1.08823i | ||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 11.0444i | − | 1.72485i | −0.506185 | − | 0.862425i | \(-0.668945\pi\) | ||
0.506185 | − | 0.862425i | \(-0.331055\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −6.22805 | −0.949769 | −0.474884 | − | 0.880048i | \(-0.657510\pi\) | ||||
−0.474884 | + | 0.880048i | \(0.657510\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 8.38687i | 1.25024i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 4.15852 | 0.606582 | 0.303291 | − | 0.952898i | \(-0.401915\pi\) | ||||
0.303291 | + | 0.952898i | \(0.401915\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.78812 | −0.969732 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 6.70229 | + | 8.21936i | 0.938508 | + | 1.15094i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −9.41694 | −1.29352 | −0.646758 | − | 0.762695i | \(-0.723876\pi\) | ||||
−0.646758 | + | 0.762695i | \(0.723876\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −12.3448 | −1.66458 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 12.5114i | − | 1.65718i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1.00000 | 0.130189 | ||||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 9.06997i | 1.16129i | 0.814157 | + | 0.580645i | \(0.197200\pi\) | ||||
−0.814157 | + | 0.580645i | \(0.802800\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 13.4285i | 1.69183i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 6.12729i | 0.759997i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 14.3241 | 1.74997 | 0.874985 | − | 0.484150i | \(-0.160871\pi\) | ||||
0.874985 | + | 0.484150i | \(0.160871\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −1.03529 | −0.124634 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 13.3448i | − | 1.58374i | −0.610689 | − | 0.791871i | \(-0.709107\pi\) | ||
0.610689 | − | 0.791871i | \(-0.290893\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 13.8115i | 1.61651i | 0.588831 | + | 0.808256i | \(0.299588\pi\) | ||||
−0.588831 | + | 0.808256i | \(0.700412\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | − | 0.973292i | − | 0.112386i | ||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −19.7657 | −2.25251 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 13.1249i | − | 1.47667i | −0.674434 | − | 0.738335i | \(-0.735612\pi\) | ||
0.674434 | − | 0.738335i | \(-0.264388\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −6.77093 | −0.752326 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −12.3267 | −1.35304 | −0.676518 | − | 0.736426i | \(-0.736512\pi\) | ||||
−0.676518 | + | 0.736426i | \(0.736512\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −6.04281 | − | 7.41060i | −0.655434 | − | 0.803793i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −18.2641 | −1.95812 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −14.8859 | −1.57790 | −0.788950 | − | 0.614457i | \(-0.789375\pi\) | ||||
−0.788950 | + | 0.614457i | \(0.789375\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 9.81059i | 1.02843i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −13.3380 | −1.38308 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 11.2803i | 1.15734i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 1.69852i | − | 0.172458i | −0.996275 | − | 0.0862292i | \(-0.972518\pi\) | ||
0.996275 | − | 0.0862292i | \(-0.0274817\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 19.2501i | 1.93471i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.48096 | −0.147361 | −0.0736807 | − | 0.997282i | \(-0.523475\pi\) | ||||
−0.0736807 | + | 0.997282i | \(0.523475\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −11.1542 | −1.09905 | −0.549527 | − | 0.835476i | \(-0.685192\pi\) | ||||
−0.549527 | + | 0.835476i | \(0.685192\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | − | 22.1508i | − | 2.16169i | ||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 7.98392i | − | 0.771834i | −0.922533 | − | 0.385917i | \(-0.873885\pi\) | ||
0.922533 | − | 0.385917i | \(-0.126115\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 2.78131i | − | 0.266402i | −0.991089 | − | 0.133201i | \(-0.957474\pi\) | ||
0.991089 | − | 0.133201i | \(-0.0425255\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −2.08767 | −0.198152 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 6.31139i | 0.593725i | 0.954920 | + | 0.296863i | \(0.0959404\pi\) | ||||
−0.954920 | + | 0.296863i | \(0.904060\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.933420 | 0.0870418 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 9.55469 | 0.883332 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −9.67532 | − | 11.8653i | −0.886935 | − | 1.08769i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −17.3347 | −1.57588 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 28.4088 | 2.56154 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 10.7181i | − | 0.958660i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −3.22852 | −0.286485 | −0.143243 | − | 0.989688i | \(-0.545753\pi\) | ||||
−0.143243 | + | 0.989688i | \(0.545753\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | − | 16.0200i | − | 1.41048i | ||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 6.43250i | 0.562010i | 0.959706 | + | 0.281005i | \(0.0906677\pi\) | ||||
−0.959706 | + | 0.281005i | \(0.909332\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 18.0613i | 1.56611i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −3.67693 | −0.316460 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −13.4755 | −1.15129 | −0.575644 | − | 0.817701i | \(-0.695248\pi\) | ||||
−0.575644 | + | 0.817701i | \(0.695248\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 21.7545i | 1.84520i | 0.385764 | + | 0.922598i | \(0.373938\pi\) | ||||
−0.385764 | + | 0.922598i | \(0.626062\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 10.6967i | 0.900823i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 14.0638i | 1.17607i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 16.4670 | 1.36751 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | − | 17.4606i | − | 1.44013i | ||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 2.38227 | 0.195163 | 0.0975815 | − | 0.995228i | \(-0.468889\pi\) | ||||
0.0975815 | + | 0.995228i | \(0.468889\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 12.6698 | 1.03106 | 0.515528 | − | 0.856873i | \(-0.327596\pi\) | ||||
0.515528 | + | 0.856873i | \(0.327596\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −11.5558 | + | 9.42295i | −0.934235 | + | 0.761801i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 12.0256 | 0.965917 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −22.5994 | −1.80363 | −0.901815 | − | 0.432122i | \(-0.857765\pi\) | ||||
−0.901815 | + | 0.432122i | \(0.857765\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | − | 24.2226i | − | 1.92097i | ||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.49453 | 0.117785 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 8.29301i | − | 0.649559i | −0.945790 | − | 0.324779i | \(-0.894710\pi\) | ||
0.945790 | − | 0.324779i | \(-0.105290\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | − | 31.7538i | − | 2.47203i | ||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 11.5763i | − | 0.895804i | −0.894083 | − | 0.447902i | \(-0.852171\pi\) | ||
0.894083 | − | 0.447902i | \(-0.147829\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −6.01952 | −0.463040 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 17.5902 | 1.34515 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − | 12.8513i | − | 0.977067i | −0.872545 | − | 0.488534i | \(-0.837532\pi\) | ||
0.872545 | − | 0.488534i | \(-0.162468\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.40503i | 0.106210i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 2.57223i | 0.193341i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 5.73192 | 0.428424 | 0.214212 | − | 0.976787i | \(-0.431282\pi\) | ||||
0.214212 | + | 0.976787i | \(0.431282\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 0.416007i | − | 0.0309215i | −0.999880 | − | 0.0154608i | \(-0.995078\pi\) | ||
0.999880 | − | 0.0154608i | \(-0.00492151\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −23.3301 | −1.72461 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1.88225 | 0.138386 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −13.8699 | − | 17.0093i | −1.01426 | − | 1.24384i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −5.88725 | −0.428234 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −2.35405 | −0.170333 | −0.0851665 | − | 0.996367i | \(-0.527142\pi\) | ||||
−0.0851665 | + | 0.996367i | \(0.527142\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 10.0371i | − | 0.722487i | −0.932471 | − | 0.361244i | \(-0.882352\pi\) | ||
0.932471 | − | 0.361244i | \(-0.117648\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −15.7608 | −1.12866 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 23.2730i | 1.65813i | 0.559151 | + | 0.829066i | \(0.311127\pi\) | ||||
−0.559151 | + | 0.829066i | \(0.688873\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 6.09988i | − | 0.432409i | −0.976348 | − | 0.216205i | \(-0.930632\pi\) | ||
0.976348 | − | 0.216205i | \(-0.0693678\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 36.8450i | 2.59884i | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 26.3658 | 1.85052 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −25.6135 | −1.78893 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − | 1.45554i | − | 0.101167i | ||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 25.8914i | 1.79094i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 17.7961i | 1.22513i | 0.790419 | + | 0.612566i | \(0.209863\pi\) | ||||
−0.790419 | + | 0.612566i | \(0.790137\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 34.3260 | 2.35198 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 14.4437i | 0.985051i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 19.2545 | 1.30708 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −35.5264 | −2.40065 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −8.44248 | + | 6.88423i | −0.567903 | + | 0.463083i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1.96657 | 0.131691 | 0.0658455 | − | 0.997830i | \(-0.479026\pi\) | ||||
0.0658455 | + | 0.997830i | \(0.479026\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.36838 | 0.0912254 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − | 12.5249i | − | 0.831304i | −0.909524 | − | 0.415652i | \(-0.863553\pi\) | ||
0.909524 | − | 0.415652i | \(-0.136447\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 19.3439 | 1.27828 | 0.639141 | − | 0.769089i | \(-0.279290\pi\) | ||||
0.639141 | + | 0.769089i | \(0.279290\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | − | 50.8419i | − | 3.34515i | ||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 20.5770i | 1.34804i | 0.738712 | + | 0.674021i | \(0.235434\pi\) | ||||
−0.738712 | + | 0.674021i | \(0.764566\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − | 9.64416i | − | 0.629116i | ||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 33.7604 | 2.19297 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 8.11145 | 0.524686 | 0.262343 | − | 0.964975i | \(-0.415505\pi\) | ||||
0.262343 | + | 0.964975i | \(0.415505\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 26.9970i | 1.73903i | 0.493905 | + | 0.869516i | \(0.335569\pi\) | ||||
−0.493905 | + | 0.869516i | \(0.664431\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − | 22.1728i | − | 1.42239i | ||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 15.7426i | 1.00576i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 12.8510 | 0.817692 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | − | 31.7073i | − | 2.00937i | ||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 14.2903 | 0.901996 | 0.450998 | − | 0.892525i | \(-0.351068\pi\) | ||||
0.450998 | + | 0.892525i | \(0.351068\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.14245 | 0.134694 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 19.0618 | − | 15.5435i | 1.19370 | − | 0.973372i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 23.4765 | 1.46442 | 0.732210 | − | 0.681078i | \(-0.238489\pi\) | ||||
0.732210 | + | 0.681078i | \(0.238489\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 3.01372 | 0.187264 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | − | 25.6781i | − | 1.58943i | ||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −1.24249 | −0.0766152 | −0.0383076 | − | 0.999266i | \(-0.512197\pi\) | ||||
−0.0383076 | + | 0.999266i | \(0.512197\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 21.8391i | 1.34157i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − | 38.2900i | − | 2.34331i | ||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 1.76424i | 0.107567i | 0.998553 | + | 0.0537837i | \(0.0171281\pi\) | ||||
−0.998553 | + | 0.0537837i | \(0.982872\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −3.91306 | −0.237702 | −0.118851 | − | 0.992912i | \(-0.537921\pi\) | ||||
−0.118851 | + | 0.992912i | \(0.537921\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −25.2351 | −1.52730 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 2.01415i | 0.121458i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 17.7866i | − | 1.06869i | −0.845266 | − | 0.534346i | \(-0.820558\pi\) | ||
0.845266 | − | 0.534346i | \(-0.179442\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | − | 18.7523i | − | 1.12267i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 23.3743 | 1.39440 | 0.697198 | − | 0.716878i | \(-0.254430\pi\) | ||||
0.697198 | + | 0.716878i | \(0.254430\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2.29742i | 0.136568i | 0.997666 | + | 0.0682838i | \(0.0217523\pi\) | ||||
−0.997666 | + | 0.0682838i | \(0.978248\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −29.0156 | −1.71874 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −41.0106 | −2.42078 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 3.42138 | − | 16.6522i | 0.201258 | − | 0.979538i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 4.36898 | 0.256114 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −6.28286 | −0.367048 | −0.183524 | − | 0.983015i | \(-0.558751\pi\) | ||||
−0.183524 | + | 0.983015i | \(0.558751\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 2.31913i | − | 0.135025i | ||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −8.43954 | −0.489712 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − | 1.06339i | − | 0.0614976i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 23.1262i | 1.33297i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − | 3.80938i | − | 0.218843i | ||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 21.0345 | 1.20443 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −34.9114 | −1.99250 | −0.996249 | − | 0.0865310i | \(-0.972422\pi\) | ||||
−0.996249 | + | 0.0865310i | \(0.972422\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − | 28.6911i | − | 1.63218i | ||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 16.2144i | − | 0.919435i | −0.888065 | − | 0.459717i | \(-0.847951\pi\) | ||
0.888065 | − | 0.459717i | \(-0.152049\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 4.92509i | − | 0.278382i | −0.990266 | − | 0.139191i | \(-0.955550\pi\) | ||
0.990266 | − | 0.139191i | \(-0.0444503\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 31.1424 | 1.75468 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 9.85029i | 0.553247i | 0.960978 | + | 0.276624i | \(0.0892156\pi\) | ||||
−0.960978 | + | 0.276624i | \(0.910784\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 37.7961 | 2.11618 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 20.5365 | 1.14624 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −15.5426 | + | 12.6739i | −0.864813 | + | 0.705192i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0.999713 | 0.0554541 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 7.15419 | 0.395627 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 15.4416i | − | 0.851321i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −23.1819 | −1.27419 | −0.637097 | − | 0.770784i | \(-0.719865\pi\) | ||||
−0.637097 | + | 0.770784i | \(0.719865\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − | 2.93511i | − | 0.160843i | ||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − | 33.2196i | − | 1.81498i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 0.371583i | 0.0202414i | 0.999949 | + | 0.0101207i | \(0.00322158\pi\) | ||||
−0.999949 | + | 0.0101207i | \(0.996778\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −16.2344 | −0.881729 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 27.6019 | 1.49473 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 0.786747i | − | 0.0424804i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 2.40097i | 0.129264i | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 4.37180i | 0.234690i | 0.993091 | + | 0.117345i | \(0.0374384\pi\) | ||||
−0.993091 | + | 0.117345i | \(0.962562\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −4.53122 | −0.242551 | −0.121275 | − | 0.992619i | \(-0.538698\pi\) | ||||
−0.121275 | + | 0.992619i | \(0.538698\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 4.18892i | 0.223588i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −30.0520 | −1.59951 | −0.799754 | − | 0.600328i | \(-0.795037\pi\) | ||||
−0.799754 | + | 0.600328i | \(0.795037\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −30.9485 | −1.64257 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 30.5204 | − | 24.8872i | 1.61531 | − | 1.31717i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −7.97010 | −0.420646 | −0.210323 | − | 0.977632i | \(-0.567451\pi\) | ||||
−0.210323 | + | 0.977632i | \(0.567451\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 4.65875 | 0.245197 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − | 44.5888i | − | 2.34030i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 32.0307 | 1.67656 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 37.8479i | − | 1.97565i | −0.155581 | − | 0.987823i | \(-0.549725\pi\) | ||
0.155581 | − | 0.987823i | \(-0.450275\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 39.9409i | 2.07924i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 34.9673i | 1.81541i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −1.12201 | −0.0580957 | −0.0290478 | − | 0.999578i | \(-0.509248\pi\) | ||||
−0.0290478 | + | 0.999578i | \(0.509248\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 27.5696 | 1.42369 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 18.7599i | − | 0.966185i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 1.75720i | − | 0.0902615i | −0.998981 | − | 0.0451307i | \(-0.985630\pi\) | ||
0.998981 | − | 0.0451307i | \(-0.0143704\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | − | 8.30452i | − | 0.425453i | ||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 21.7868 | 1.11325 | 0.556626 | − | 0.830763i | \(-0.312096\pi\) | ||||
0.556626 | + | 0.830763i | \(0.312096\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 45.8392i | 2.33618i | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 22.5230 | 1.14491 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 13.0693 | 0.662637 | 0.331319 | − | 0.943519i | \(-0.392506\pi\) | ||||
0.331319 | + | 0.943519i | \(0.392506\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.04873 | + | 1.28611i | 0.0530366 | + | 0.0650415i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −16.5459 | −0.834629 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −30.4385 | −1.53153 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 8.77840i | − | 0.440575i | −0.975435 | − | 0.220288i | \(-0.929300\pi\) | ||
0.975435 | − | 0.220288i | \(-0.0706996\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −46.4578 | −2.32580 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 21.2537i | 1.06136i | 0.847573 | + | 0.530680i | \(0.178063\pi\) | ||||
−0.847573 | + | 0.530680i | \(0.821937\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 13.7001i | − | 0.682448i | ||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 15.7027i | 0.780273i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 4.32026 | 0.214147 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −32.1489 | −1.58966 | −0.794830 | − | 0.606833i | \(-0.792440\pi\) | ||||
−0.794830 | + | 0.606833i | \(0.792440\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − | 34.6621i | − | 1.70975i | ||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − | 3.71324i | − | 0.182716i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 28.5874i | 1.40330i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −55.9577 | −2.74026 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 35.0045i | − | 1.71008i | −0.518562 | − | 0.855040i | \(-0.673533\pi\) | ||
0.518562 | − | 0.855040i | \(-0.326467\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −6.96601 | −0.339503 | −0.169751 | − | 0.985487i | \(-0.554296\pi\) | ||||
−0.169751 | + | 0.985487i | \(0.554296\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −15.0388 | −0.731211 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −1.20909 | + | 0.985929i | −0.0586497 | + | 0.0478246i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 33.6789 | 1.62984 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −36.1753 | −1.74656 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 33.6442i | − | 1.62059i | −0.586025 | − | 0.810293i | \(-0.699308\pi\) | ||
0.586025 | − | 0.810293i | \(-0.300692\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −4.10948 | −0.197489 | −0.0987445 | − | 0.995113i | \(-0.531483\pi\) | ||||
−0.0987445 | + | 0.995113i | \(0.531483\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 42.3569i | 2.03086i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − | 1.95770i | − | 0.0936497i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 6.20204i | − | 0.296007i | −0.988987 | − | 0.148004i | \(-0.952715\pi\) | ||
0.988987 | − | 0.148004i | \(-0.0472848\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 24.5484 | 1.16897 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 25.2223 | 1.19835 | 0.599175 | − | 0.800618i | \(-0.295495\pi\) | ||||
0.599175 | + | 0.800618i | \(0.295495\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 34.5224i | 1.63652i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 6.12775i | 0.289832i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 17.1235i | − | 0.808110i | −0.914735 | − | 0.404055i | \(-0.867600\pi\) | ||
0.914735 | − | 0.404055i | \(-0.132400\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −58.7898 | −2.76831 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 32.5897i | 1.53120i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 22.7521 | 1.06663 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 15.2448 | 0.713121 | 0.356561 | − | 0.934272i | \(-0.383949\pi\) | ||||
0.356561 | + | 0.934272i | \(0.383949\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −4.13117 | − | 5.06626i | −0.192826 | − | 0.236473i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −21.7920 | −1.01496 | −0.507478 | − | 0.861665i | \(-0.669422\pi\) | ||||
−0.507478 | + | 0.861665i | \(0.669422\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 8.97857 | 0.417269 | 0.208635 | − | 0.977994i | \(-0.433098\pi\) | ||||
0.208635 | + | 0.977994i | \(0.433098\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 30.9326i | 1.43446i | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 26.6699 | 1.23413 | 0.617067 | − | 0.786911i | \(-0.288321\pi\) | ||||
0.617067 | + | 0.786911i | \(0.288321\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 53.1889i | − | 2.45603i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − | 58.1310i | − | 2.67853i | ||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 33.1521i | 1.52434i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.84047 | 0.0844466 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 34.0552 | 1.55928 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 36.6325i | 1.67378i | 0.547369 | + | 0.836891i | \(0.315629\pi\) | ||||
−0.547369 | + | 0.836891i | \(0.684371\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − | 2.14434i | − | 0.0977734i | ||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 3.84427i | 0.174920i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −3.93909 | −0.178865 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 17.5363i | − | 0.794646i | −0.917679 | − | 0.397323i | \(-0.869939\pi\) | ||
0.917679 | − | 0.397323i | \(-0.130061\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 21.3316 | 0.964646 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −29.1764 | −1.31671 | −0.658355 | − | 0.752707i | \(-0.728748\pi\) | ||||
−0.658355 | + | 0.752707i | \(0.728748\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 18.5013 | + | 22.6890i | 0.833255 | + | 1.02186i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 44.6436 | 2.00658 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −49.5526 | −2.22274 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 24.9940i | − | 1.11889i | −0.828869 | − | 0.559443i | \(-0.811015\pi\) | ||
0.828869 | − | 0.559443i | \(-0.188985\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 29.7770 | 1.33034 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 5.93744i | − | 0.264737i | −0.991201 | − | 0.132369i | \(-0.957742\pi\) | ||
0.991201 | − | 0.132369i | \(-0.0422583\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 3.43455i | 0.152836i | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − | 15.4836i | − | 0.687651i | ||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 11.7369 | 0.520229 | 0.260115 | − | 0.965578i | \(-0.416240\pi\) | ||||
0.260115 | + | 0.965578i | \(0.416240\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 51.2853 | 2.26873 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 7.71180i | 0.340484i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 25.8680i | 1.13988i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 22.1359i | − | 0.973537i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 33.0566 | 1.45102 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 25.6193i | 1.12240i | 0.827680 | + | 0.561200i | \(0.189660\pi\) | ||||
−0.827680 | + | 0.561200i | \(0.810340\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −19.7900 | −0.865358 | −0.432679 | − | 0.901548i | \(-0.642432\pi\) | ||||
−0.432679 | + | 0.901548i | \(0.642432\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −3.61406 | −0.157731 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 13.5112 | + | 16.5694i | 0.588555 | + | 0.721775i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 22.8380 | 0.992957 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −3.61638 | −0.156938 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 29.1800i | 1.26393i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −18.5158 | −0.800507 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 14.7438i | 0.636243i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 36.1334i | 1.55638i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 8.91469i | − | 0.383272i | −0.981466 | − | 0.191636i | \(-0.938621\pi\) | ||
0.981466 | − | 0.191636i | \(-0.0613794\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 1.07007 | 0.0459209 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −6.45024 | −0.276298 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 14.1018i | − | 0.602951i | −0.953474 | − | 0.301475i | \(-0.902521\pi\) | ||
0.953474 | − | 0.301475i | \(-0.0974791\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | − | 32.8005i | − | 1.39989i | ||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 34.5370i | − | 1.47132i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −48.7360 | −2.07246 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 4.84158i | 0.205513i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 18.1269 | 0.768063 | 0.384031 | − | 0.923320i | \(-0.374535\pi\) | ||||
0.384031 | + | 0.923320i | \(0.374535\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 16.4549 | 0.695967 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 43.7519 | − | 35.6765i | 1.84721 | − | 1.50626i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 27.3726 | 1.15362 | 0.576808 | − | 0.816879i | \(-0.304298\pi\) | ||||
0.576808 | + | 0.816879i | \(0.304298\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 14.6370 | 0.615781 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 25.1421i | 1.05587i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −11.5482 | −0.484124 | −0.242062 | − | 0.970261i | \(-0.577824\pi\) | ||||
−0.242062 | + | 0.970261i | \(0.577824\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 25.3692i | 1.06167i | 0.847476 | + | 0.530834i | \(0.178121\pi\) | ||||
−0.847476 | + | 0.530834i | \(0.821879\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − | 6.05516i | − | 0.252958i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 0.152294i | − | 0.00635112i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −9.37840 | −0.390428 | −0.195214 | − | 0.980761i | \(-0.562540\pi\) | ||||
−0.195214 | + | 0.980761i | \(0.562540\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 25.8178 | 1.07295 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 45.7721i | 1.89895i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 50.1266i | 2.07603i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | − | 22.1586i | − | 0.916146i | ||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −5.11578 | −0.211151 | −0.105576 | − | 0.994411i | \(-0.533668\pi\) | ||||
−0.105576 | + | 0.994411i | \(0.533668\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 25.2218i | − | 1.03924i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −59.8636 | −2.46246 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 19.0784 | 0.783455 | 0.391727 | − | 0.920081i | \(-0.371878\pi\) | ||||
0.391727 | + | 0.920081i | \(0.371878\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −27.5173 | + | 22.4384i | −1.12810 | + | 0.919884i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 15.6903 | 0.642162 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −37.0353 | −1.51322 | −0.756611 | − | 0.653865i | \(-0.773146\pi\) | ||||
−0.756611 | + | 0.653865i | \(0.773146\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 14.6431i | − | 0.597306i | −0.954362 | − | 0.298653i | \(-0.903463\pi\) | ||
0.954362 | − | 0.298653i | \(-0.0965373\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −51.8015 | −2.10952 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 40.2014i | 1.63442i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 2.18191i | 0.0885611i | 0.999019 | + | 0.0442805i | \(0.0140995\pi\) | ||||
−0.999019 | + | 0.0442805i | \(0.985900\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 67.8190i | 2.74816i | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −10.9871 | −0.444489 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −3.18512 | −0.128646 | −0.0643229 | − | 0.997929i | \(-0.520489\pi\) | ||||
−0.0643229 | + | 0.997929i | \(0.520489\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | − | 65.8839i | − | 2.65670i | ||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 25.9128i | 1.04321i | 0.853187 | + | 0.521605i | \(0.174666\pi\) | ||||
−0.853187 | + | 0.521605i | \(0.825334\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 28.8384i | 1.15911i | 0.814932 | + | 0.579557i | \(0.196774\pi\) | ||||
−0.814932 | + | 0.579557i | \(0.803226\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0.638132 | 0.0256074 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 55.2748i | 2.21454i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −26.7487 | −1.06995 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −66.5986 | −2.65969 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 2.11477 | + | 2.59345i | 0.0843215 | + | 0.103408i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 14.9710 | 0.595984 | 0.297992 | − | 0.954568i | \(-0.403683\pi\) | ||||
0.297992 | + | 0.954568i | \(0.403683\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −45.7756 | −1.81942 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 7.48738i | 0.297128i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 17.9346 | 0.710596 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 48.2600i | 1.90914i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 38.3957i | − | 1.51654i | −0.651942 | − | 0.758269i | \(-0.726045\pi\) | ||
0.651942 | − | 0.758269i | \(-0.273955\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 44.4993i | 1.75488i | 0.479684 | + | 0.877441i | \(0.340751\pi\) | ||||
−0.479684 | + | 0.877441i | \(0.659249\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −37.1525 | −1.46288 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −6.85386 | −0.269453 | −0.134726 | − | 0.990883i | \(-0.543016\pi\) | ||||
−0.134726 | + | 0.990883i | \(0.543016\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 5.32303i | − | 0.208947i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 49.5271i | 1.94112i | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 38.3482i | 1.50068i | 0.661052 | + | 0.750340i | \(0.270110\pi\) | ||||
−0.661052 | + | 0.750340i | \(0.729890\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 14.9178 | 0.582888 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 49.9476i | − | 1.94864i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 19.6120 | 0.763975 | 0.381987 | − | 0.924168i | \(-0.375240\pi\) | ||||
0.381987 | + | 0.924168i | \(0.375240\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −30.0416 | −1.16848 | −0.584242 | − | 0.811579i | \(-0.698608\pi\) | ||||
−0.584242 | + | 0.811579i | \(0.698608\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −17.7078 | − | 21.7160i | −0.687716 | − | 0.843381i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 41.8865 | 1.62429 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −2.85785 | −0.110656 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 5.05847i | 0.195572i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 48.2797 | 1.86382 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 20.2512i | − | 0.780626i | −0.920682 | − | 0.390313i | \(-0.872367\pi\) | ||
0.920682 | − | 0.390313i | \(-0.127633\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0.599919i | 0.0230909i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 18.7329i | 0.719964i | 0.932959 | + | 0.359982i | \(0.117217\pi\) | ||||
−0.932959 | + | 0.359982i | \(0.882783\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −6.30700 | −0.242040 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 32.2169 | 1.23455 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 31.0343i | 1.18750i | 0.804651 | + | 0.593748i | \(0.202352\pi\) | ||||
−0.804651 | + | 0.593748i | \(0.797648\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 31.2514i | 1.19406i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 49.7571i | 1.89835i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 24.8801 | 0.947856 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 41.1096i | − | 1.56388i | −0.623353 | − | 0.781941i | \(-0.714230\pi\) | ||
0.623353 | − | 0.781941i | \(-0.285770\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 71.4802 | 2.71531 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 50.4517 | 1.91374 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −28.7777 | − | 35.2916i | −1.09003 | − | 1.33676i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −52.9287 | −2.00195 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 16.9073 | 0.638581 | 0.319290 | − | 0.947657i | \(-0.396556\pi\) | ||||
0.319290 | + | 0.947657i | \(0.396556\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 3.94772i | − | 0.148891i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 24.8070 | 0.934287 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 5.49916i | 0.206817i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 48.7791i | − | 1.83194i | −0.401249 | − | 0.915969i | \(-0.631424\pi\) | ||
0.401249 | − | 0.915969i | \(-0.368576\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 47.4647i | 1.78007i | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −2.08704 | −0.0781602 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 32.6158 | 1.21976 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 20.8645i | 0.779201i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 39.1320i | 1.45938i | 0.683780 | + | 0.729688i | \(0.260335\pi\) | ||||
−0.683780 | + | 0.729688i | \(0.739665\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 41.4181i | 1.54249i | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −69.4427 | −2.58260 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − | 2.68671i | − | 0.0997820i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 6.08016 | 0.225501 | 0.112750 | − | 0.993623i | \(-0.464034\pi\) | ||||
0.112750 | + | 0.993623i | \(0.464034\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 36.7209 | 1.36003 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −19.9012 | + | 16.2280i | −0.736073 | + | 0.600214i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 17.8747 | 0.660216 | 0.330108 | − | 0.943943i | \(-0.392915\pi\) | ||||
0.330108 | + | 0.943943i | \(0.392915\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −40.4936 | −1.49363 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 76.2478i | − | 2.80862i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −4.94281 | −0.181824 | −0.0909120 | − | 0.995859i | \(-0.528978\pi\) | ||||
−0.0909120 | + | 0.995859i | \(0.528978\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 33.0559i | 1.21434i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 20.5661i | − | 0.754497i | −0.926112 | − | 0.377249i | \(-0.876870\pi\) | ||
0.926112 | − | 0.377249i | \(-0.123130\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − | 5.52480i | − | 0.202413i | ||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 44.5782 | 1.63103 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −29.6462 | −1.08325 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 37.8162i | − | 1.37993i | −0.723841 | − | 0.689967i | \(-0.757625\pi\) | ||
0.723841 | − | 0.689967i | \(-0.242375\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 36.7580i | 1.33953i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − | 29.3830i | − | 1.06936i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −16.1887 | −0.588387 | −0.294193 | − | 0.955746i | \(-0.595051\pi\) | ||||
−0.294193 | + | 0.955746i | \(0.595051\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 5.51087i | 0.200032i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 2.06693 | 0.0749261 | 0.0374631 | − | 0.999298i | \(-0.488072\pi\) | ||||
0.0374631 | + | 0.999298i | \(0.488072\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −10.3277 | −0.373887 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 21.8531 | + | 26.7996i | 0.790100 | + | 0.968940i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −2.64206 | −0.0953992 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 13.7996 | 0.497625 | 0.248812 | − | 0.968552i | \(-0.419960\pi\) | ||||
0.248812 | + | 0.968552i | \(0.419960\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 60.3869i | 2.17478i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 48.7429 | 1.75316 | 0.876580 | − | 0.481257i | \(-0.159820\pi\) | ||||
0.876580 | + | 0.481257i | \(0.159820\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 1.96206i | − | 0.0704793i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 7.75200i | 0.278101i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 53.7204i | 1.92473i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −71.0350 | −2.54183 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 11.2577 | 0.402316 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 52.4111i | 1.87063i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 36.0214i | − | 1.28402i | −0.766695 | − | 0.642012i | \(-0.778100\pi\) | ||
0.766695 | − | 0.642012i | \(-0.221900\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | − | 3.19597i | − | 0.113780i | ||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 23.4357 | 0.833277 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 23.9634i | − | 0.850965i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −56.1754 | −1.99233 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −36.4166 | −1.28994 | −0.644970 | − | 0.764208i | \(-0.723130\pi\) | ||||
−0.644970 | + | 0.764208i | \(0.723130\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 13.2882 | − | 10.8356i | 0.470103 | − | 0.383335i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 53.8330 | 1.90210 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 73.5190 | 2.59443 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − | 3.46601i | − | 0.122161i | ||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −4.53802 | −0.159746 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 14.3369i | − | 0.504060i | −0.967719 | − | 0.252030i | \(-0.918902\pi\) | ||
0.967719 | − | 0.252030i | \(-0.0810982\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 1.03880i | − | 0.0364772i | −0.999834 | − | 0.0182386i | \(-0.994194\pi\) | ||
0.999834 | − | 0.0182386i | \(-0.00580585\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − | 10.0653i | − | 0.353006i | ||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −19.2326 | −0.673689 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 30.2934 | 1.05983 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | − | 35.4788i | − | 1.23973i | ||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 8.67847i | − | 0.302881i | −0.988466 | − | 0.151440i | \(-0.951609\pi\) | ||
0.988466 | − | 0.151440i | \(-0.0483912\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 26.6439i | 0.928748i | 0.885639 | + | 0.464374i | \(0.153721\pi\) | ||||
−0.885639 | + | 0.464374i | \(0.846279\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −5.18086 | −0.180374 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 36.9122i | − | 1.28356i | −0.766887 | − | 0.641782i | \(-0.778196\pi\) | ||
0.766887 | − | 0.641782i | \(-0.221804\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 32.9235 | 1.14348 | 0.571741 | − | 0.820434i | \(-0.306268\pi\) | ||||
0.571741 | + | 0.820434i | \(0.306268\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 45.7512 | 1.58709 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −21.6909 | + | 17.6873i | −0.751545 | + | 0.612830i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −26.8471 | −0.929081 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 8.22128 | 0.284169 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 15.2861i | 0.527734i | 0.964559 | + | 0.263867i | \(0.0849980\pi\) | ||||
−0.964559 | + | 0.263867i | \(0.915002\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −21.4170 | −0.738517 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 60.1243i | 2.07079i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 13.9601i | 0.480241i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 64.3677i | 2.21170i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −5.90951 | −0.202814 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −0.326664 | −0.0111979 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 0.774074i | − | 0.0265038i | −0.999912 | − | 0.0132519i | \(-0.995782\pi\) | ||
0.999912 | − | 0.0132519i | \(-0.00421833\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | − | 40.7940i | − | 1.39512i | ||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 19.1606i | 0.654513i | 0.944936 | + | 0.327256i | \(0.106124\pi\) | ||||
−0.944936 | + | 0.327256i | \(0.893876\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −29.9647 | −1.02238 | −0.511191 | − | 0.859467i | \(-0.670795\pi\) | ||||
−0.511191 | + | 0.859467i | \(0.670795\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | − | 105.489i | − | 3.59505i | ||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 25.7359 | 0.876060 | 0.438030 | − | 0.898960i | \(-0.355676\pi\) | ||||
0.438030 | + | 0.898960i | \(0.355676\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −29.8039 | −1.01336 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 42.8332 | + | 8.80058i | 1.45469 | + | 0.298884i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −69.8644 | −2.36999 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −37.8452 | −1.28234 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 6.14249i | 0.207892i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −39.7990 | −1.34545 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 44.8058i | 1.51298i | 0.654003 | + | 0.756492i | \(0.273088\pi\) | ||||
−0.654003 | + | 0.756492i | \(0.726912\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | − | 16.1610i | − | 0.545096i | ||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 10.4923i | − | 0.353496i | −0.984256 | − | 0.176748i | \(-0.943442\pi\) | ||
0.984256 | − | 0.176748i | \(-0.0565578\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −16.3446 | −0.550040 | −0.275020 | − | 0.961438i | \(-0.588685\pi\) | ||||
−0.275020 | + | 0.961438i | \(0.588685\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 5.96535 | 0.200523 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 54.1009i | − | 1.81653i | −0.418396 | − | 0.908265i | \(-0.637407\pi\) | ||
0.418396 | − | 0.908265i | \(-0.362593\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 11.9883i | 0.402074i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 36.0419i | 1.20745i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −20.2271 | −0.676876 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 13.2931i | − | 0.444339i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 2.73529 | 0.0913288 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −36.8187 | −1.22797 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −30.0910 | + | 24.5371i | −1.00248 | + | 0.817448i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −59.4860 | −1.97957 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −0.964775 | −0.0320702 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 19.9045i | − | 0.660920i | −0.943820 | − | 0.330460i | \(-0.892796\pi\) | ||
0.943820 | − | 0.330460i | \(-0.107204\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 5.35573 | 0.177638 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 48.0236i | − | 1.59109i | −0.605892 | − | 0.795547i | \(-0.707184\pi\) | ||
0.605892 | − | 0.795547i | \(-0.292816\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 65.6156i | 2.17156i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 54.1056i | 1.78867i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 23.8854 | 0.788765 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 3.27122 | 0.107908 | 0.0539538 | − | 0.998543i | \(-0.482818\pi\) | ||||
0.0539538 | + | 0.998543i | \(0.482818\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | − | 89.8002i | − | 2.95902i | ||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 35.2579i | 1.16053i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − | 0.307103i | − | 0.0100975i | ||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 40.3378 | 1.32487 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 36.7555i | − | 1.20591i | −0.797775 | − | 0.602955i | \(-0.793990\pi\) | ||
0.797775 | − | 0.602955i | \(-0.206010\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 33.0176 | 1.08211 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 41.7072 | 1.36543 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −39.4469 | + | 32.1660i | −1.29005 | + | 1.05194i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 32.3905 | 1.05815 | 0.529075 | − | 0.848575i | \(-0.322539\pi\) | ||||
0.529075 | + | 0.848575i | \(0.322539\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 12.6685 | 0.413420 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 47.8529i | − | 1.55996i | −0.625804 | − | 0.779980i | \(-0.715229\pi\) | ||
0.625804 | − | 0.779980i | \(-0.284771\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 4.44523 | 0.144757 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 13.6533i | 0.444142i | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 14.0770i | 0.457442i | 0.973492 | + | 0.228721i | \(0.0734543\pi\) | ||||
−0.973492 | + | 0.228721i | \(0.926546\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 36.4908i | − | 1.18454i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −25.3372 | −0.821616 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −14.5759 | −0.472159 | −0.236079 | − | 0.971734i | \(-0.575863\pi\) | ||||
−0.236079 | + | 0.971734i | \(0.575863\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 5.45936i | 0.176661i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 97.2205i | 3.14269i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 50.0376i | 1.61580i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 4.11195 | 0.132644 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 28.8729i | 0.930416i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −23.2774 | −0.749327 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 12.8739 | 0.413998 | 0.206999 | − | 0.978341i | \(-0.433630\pi\) | ||||
0.206999 | + | 0.978341i | \(0.433630\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −32.6001 | − | 39.9792i | −1.04727 | − | 1.28432i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 21.8000 | 0.699594 | 0.349797 | − | 0.936825i | \(-0.386250\pi\) | ||||
0.349797 | + | 0.936825i | \(0.386250\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 80.7797 | 2.58968 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 2.57149i | 0.0823537i | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −52.1698 | −1.66906 | −0.834531 | − | 0.550962i | \(-0.814261\pi\) | ||||
−0.834531 | + | 0.550962i | \(0.814261\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 79.2380i | 2.53246i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 10.0583i | 0.321137i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 51.5444i | − | 1.64401i | −0.569479 | − | 0.822006i | \(-0.692855\pi\) | ||
0.569479 | − | 0.822006i | \(-0.307145\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 53.9732 | 1.71973 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 39.7193 | 1.26428 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 2.50670i | − | 0.0797086i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 55.1297i | − | 1.75125i | −0.482989 | − | 0.875627i | \(-0.660449\pi\) | ||
0.482989 | − | 0.875627i | \(-0.339551\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 59.6293i | − | 1.89228i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −14.1464 | −0.448473 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 49.5810i | − | 1.57025i | −0.619339 | − | 0.785124i | \(-0.712599\pi\) | ||
0.619339 | − | 0.785124i | \(-0.287401\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 1.28680 | 0.0407125 |
(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 | 4012.2.b.b.237.40 | yes | 46 | |
17.16 | even | 2 | inner | 4012.2.b.b.237.7 | ✓ | 46 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4012.2.b.b.237.7 | ✓ | 46 | 17.16 | even | 2 | inner | |
4012.2.b.b.237.40 | yes | 46 | 1.1 | even | 1 | trivial |