Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3150,2,Mod(251,3150)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3150, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3150.251");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3150 = 2 \cdot 3^{2} \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3150.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: | \(25.1528766367\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.40960000.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 7x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{6} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 251.6 | ||
Root | \(-1.14412 + 1.14412i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3150.251 |
Dual form | 3150.2.b.d.251.1 |
$q$-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 \(\left(\mathbb{Z}/3150\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(451\) | \(2801\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) |
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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.41421 | + | 2.23607i | −0.534522 | + | 0.845154i | ||||
\(8\) | − | 1.00000i | − | 0.353553i | ||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 1.41421i | − | 0.426401i | −0.977008 | − | 0.213201i | \(-0.931611\pi\) | ||
0.977008 | − | 0.213201i | \(-0.0683888\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.926210i | 0.256884i | 0.991717 | + | 0.128442i | \(0.0409977\pi\) | ||||
−0.991717 | + | 0.128442i | \(0.959002\pi\) | |||||||
\(14\) | −2.23607 | − | 1.41421i | −0.597614 | − | 0.377964i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −2.23607 | −0.542326 | −0.271163 | − | 0.962533i | \(-0.587408\pi\) | ||||
−0.271163 | + | 0.962533i | \(0.587408\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 7.63441i | − | 1.75145i | −0.482806 | − | 0.875727i | \(-0.660382\pi\) | ||
0.482806 | − | 0.875727i | \(-0.339618\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1.41421 | 0.301511 | ||||||||
\(23\) | − | 1.00000i | − | 0.208514i | −0.994550 | − | 0.104257i | \(-0.966753\pi\) | ||
0.994550 | − | 0.104257i | \(-0.0332465\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −0.926210 | −0.181645 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 1.41421 | − | 2.23607i | 0.267261 | − | 0.422577i | ||||
\(29\) | − | 0.757359i | − | 0.140638i | −0.997525 | − | 0.0703190i | \(-0.977598\pi\) | ||
0.997525 | − | 0.0703190i | \(-0.0224017\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.08849i | 0.734314i | 0.930159 | + | 0.367157i | \(0.119669\pi\) | ||||
−0.930159 | + | 0.367157i | \(0.880331\pi\) | |||||||
\(32\) | 1.00000i | 0.176777i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | − | 2.23607i | − | 0.383482i | ||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.82843 | 0.464991 | 0.232495 | − | 0.972598i | \(-0.425311\pi\) | ||||
0.232495 | + | 0.972598i | \(0.425311\pi\) | |||||||
\(38\) | 7.63441 | 1.23847 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 8.56062 | 1.33694 | 0.668472 | − | 0.743737i | \(-0.266948\pi\) | ||||
0.668472 | + | 0.743737i | \(0.266948\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.58579 | 0.546827 | 0.273414 | − | 0.961897i | \(-0.411847\pi\) | ||||
0.273414 | + | 0.961897i | \(0.411847\pi\) | |||||||
\(44\) | 1.41421i | 0.213201i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.00000 | 0.147442 | ||||||||
\(47\) | 1.30986 | 0.191062 | 0.0955312 | − | 0.995426i | \(-0.469545\pi\) | ||||
0.0955312 | + | 0.995426i | \(0.469545\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −3.00000 | − | 6.32456i | −0.428571 | − | 0.903508i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | − | 0.926210i | − | 0.128442i | ||||||
\(53\) | − | 8.07107i | − | 1.10865i | −0.832301 | − | 0.554323i | \(-0.812977\pi\) | ||
0.832301 | − | 0.554323i | \(-0.187023\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 2.23607 | + | 1.41421i | 0.298807 | + | 0.188982i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0.757359 | 0.0994461 | ||||||||
\(59\) | 7.25077 | 0.943969 | 0.471985 | − | 0.881607i | \(-0.343538\pi\) | ||||
0.471985 | + | 0.881607i | \(0.343538\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.926210i | 0.118589i | 0.998241 | + | 0.0592945i | \(0.0188851\pi\) | ||||
−0.998241 | + | 0.0592945i | \(0.981115\pi\) | |||||||
\(62\) | −4.08849 | −0.519238 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(68\) | 2.23607 | 0.271163 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 15.6569i | − | 1.85813i | −0.369921 | − | 0.929063i | \(-0.620615\pi\) | ||
0.369921 | − | 0.929063i | \(-0.379385\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 13.9590i | 1.63377i | 0.576798 | + | 0.816887i | \(0.304302\pi\) | ||||
−0.576798 | + | 0.816887i | \(0.695698\pi\) | |||||||
\(74\) | 2.82843i | 0.328798i | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 7.63441i | 0.875727i | ||||||||
\(77\) | 3.16228 | + | 2.00000i | 0.360375 | + | 0.227921i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −13.0711 | −1.47061 | −0.735305 | − | 0.677736i | \(-0.762961\pi\) | ||||
−0.735305 | + | 0.677736i | \(0.762961\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 8.56062i | 0.945363i | ||||||||
\(83\) | 14.3426 | 1.57431 | 0.787153 | − | 0.616757i | \(-0.211554\pi\) | ||||
0.787153 | + | 0.616757i | \(0.211554\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 3.58579i | 0.386665i | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −1.41421 | −0.150756 | ||||||||
\(89\) | −2.61972 | −0.277689 | −0.138845 | − | 0.990314i | \(-0.544339\pi\) | ||||
−0.138845 | + | 0.990314i | \(0.544339\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.07107 | − | 1.30986i | −0.217107 | − | 0.137310i | ||||
\(92\) | 1.00000i | 0.104257i | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 1.30986i | 0.135102i | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 0.542561i | 0.0550887i | 0.999621 | + | 0.0275444i | \(0.00876875\pi\) | ||||
−0.999621 | + | 0.0275444i | \(0.991231\pi\) | |||||||
\(98\) | 6.32456 | − | 3.00000i | 0.638877 | − | 0.303046i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 12.1065 | 1.20465 | 0.602323 | − | 0.798252i | \(-0.294242\pi\) | ||||
0.602323 | + | 0.798252i | \(0.294242\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 10.4130i | 1.02603i | 0.858380 | + | 0.513014i | \(0.171471\pi\) | ||||
−0.858380 | + | 0.513014i | \(0.828529\pi\) | |||||||
\(104\) | 0.926210 | 0.0908223 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 8.07107 | 0.783931 | ||||||||
\(107\) | − | 2.00000i | − | 0.193347i | −0.995316 | − | 0.0966736i | \(-0.969180\pi\) | ||
0.995316 | − | 0.0966736i | \(-0.0308203\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −7.07107 | −0.677285 | −0.338643 | − | 0.940915i | \(-0.609968\pi\) | ||||
−0.338643 | + | 0.940915i | \(0.609968\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −1.41421 | + | 2.23607i | −0.133631 | + | 0.211289i | ||||
\(113\) | − | 1.07107i | − | 0.100758i | −0.998730 | − | 0.0503788i | \(-0.983957\pi\) | ||
0.998730 | − | 0.0503788i | \(-0.0160429\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0.757359i | 0.0703190i | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 7.25077i | 0.667487i | ||||||||
\(119\) | 3.16228 | − | 5.00000i | 0.289886 | − | 0.458349i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 9.00000 | 0.818182 | ||||||||
\(122\) | −0.926210 | −0.0838551 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | − | 4.08849i | − | 0.367157i | ||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 10.0000 | 0.887357 | 0.443678 | − | 0.896186i | \(-0.353673\pi\) | ||||
0.443678 | + | 0.896186i | \(0.353673\pi\) | |||||||
\(128\) | − | 1.00000i | − | 0.0883883i | ||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 12.6491 | 1.10516 | 0.552579 | − | 0.833461i | \(-0.313644\pi\) | ||||
0.552579 | + | 0.833461i | \(0.313644\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 17.0711 | + | 10.7967i | 1.48025 | + | 0.936192i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 2.23607i | 0.191741i | ||||||||
\(137\) | − | 12.1421i | − | 1.03737i | −0.854965 | − | 0.518686i | \(-0.826421\pi\) | ||
0.854965 | − | 0.518686i | \(-0.173579\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 10.7967i | − | 0.915763i | −0.889013 | − | 0.457882i | \(-0.848608\pi\) | ||
0.889013 | − | 0.457882i | \(-0.151392\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 15.6569 | 1.31389 | ||||||||
\(143\) | 1.30986 | 0.109536 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −13.9590 | −1.15525 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −2.82843 | −0.232495 | ||||||||
\(149\) | 0.757359i | 0.0620453i | 0.999519 | + | 0.0310226i | \(0.00987640\pi\) | ||||
−0.999519 | + | 0.0310226i | \(0.990124\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −14.1421 | −1.15087 | −0.575435 | − | 0.817847i | \(-0.695167\pi\) | ||||
−0.575435 | + | 0.817847i | \(0.695167\pi\) | |||||||
\(152\) | −7.63441 | −0.619233 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −2.00000 | + | 3.16228i | −0.161165 | + | 0.254824i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 10.7967i | 0.861670i | 0.902431 | + | 0.430835i | \(0.141781\pi\) | ||||
−0.902431 | + | 0.430835i | \(0.858219\pi\) | |||||||
\(158\) | − | 13.0711i | − | 1.03988i | ||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2.23607 | + | 1.41421i | 0.176227 | + | 0.111456i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 7.92893 | 0.621042 | 0.310521 | − | 0.950567i | \(-0.399497\pi\) | ||||
0.310521 | + | 0.950567i | \(0.399497\pi\) | |||||||
\(164\) | −8.56062 | −0.668472 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 14.3426i | 1.11320i | ||||||||
\(167\) | 12.1065 | 0.936833 | 0.468416 | − | 0.883508i | \(-0.344825\pi\) | ||||
0.468416 | + | 0.883508i | \(0.344825\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 12.1421 | 0.934010 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −3.58579 | −0.273414 | ||||||||
\(173\) | 10.2541 | 0.779607 | 0.389804 | − | 0.920898i | \(-0.372543\pi\) | ||||
0.389804 | + | 0.920898i | \(0.372543\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | − | 1.41421i | − | 0.106600i | ||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | − | 2.61972i | − | 0.196356i | ||||||
\(179\) | 11.3137i | 0.845626i | 0.906217 | + | 0.422813i | \(0.138957\pi\) | ||||
−0.906217 | + | 0.422813i | \(0.861043\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 2.61972i | − | 0.194722i | −0.995249 | − | 0.0973610i | \(-0.968960\pi\) | ||
0.995249 | − | 0.0973610i | \(-0.0310401\pi\) | |||||||
\(182\) | 1.30986 | − | 2.07107i | 0.0970932 | − | 0.153518i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −1.00000 | −0.0737210 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 3.16228i | 0.231249i | ||||||||
\(188\) | −1.30986 | −0.0955312 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0.656854i | 0.0475283i | 0.999718 | + | 0.0237642i | \(0.00756508\pi\) | ||||
−0.999718 | + | 0.0237642i | \(0.992435\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 8.48528 | 0.610784 | 0.305392 | − | 0.952227i | \(-0.401213\pi\) | ||||
0.305392 | + | 0.952227i | \(0.401213\pi\) | |||||||
\(194\) | −0.542561 | −0.0389536 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 3.00000 | + | 6.32456i | 0.214286 | + | 0.451754i | ||||
\(197\) | − | 5.92893i | − | 0.422419i | −0.977441 | − | 0.211209i | \(-0.932260\pi\) | ||
0.977441 | − | 0.211209i | \(-0.0677402\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 21.5934i | − | 1.53071i | −0.643606 | − | 0.765357i | \(-0.722562\pi\) | ||
0.643606 | − | 0.765357i | \(-0.277438\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 12.1065i | 0.851814i | ||||||||
\(203\) | 1.69351 | + | 1.07107i | 0.118861 | + | 0.0751742i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −10.4130 | −0.725511 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0.926210i | 0.0642211i | ||||||||
\(209\) | −10.7967 | −0.746823 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 16.2132 | 1.11616 | 0.558081 | − | 0.829786i | \(-0.311538\pi\) | ||||
0.558081 | + | 0.829786i | \(0.311538\pi\) | |||||||
\(212\) | 8.07107i | 0.554323i | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 2.00000 | 0.136717 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −9.14214 | − | 5.78199i | −0.620609 | − | 0.392507i | ||||
\(218\) | − | 7.07107i | − | 0.478913i | ||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 2.07107i | − | 0.139315i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 13.0328i | 0.872738i | 0.899768 | + | 0.436369i | \(0.143736\pi\) | ||||
−0.899768 | + | 0.436369i | \(0.856264\pi\) | |||||||
\(224\) | −2.23607 | − | 1.41421i | −0.149404 | − | 0.0944911i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 1.07107 | 0.0712464 | ||||||||
\(227\) | 25.1393 | 1.66855 | 0.834277 | − | 0.551345i | \(-0.185885\pi\) | ||||
0.834277 | + | 0.551345i | \(0.185885\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 10.7967i | 0.713465i | 0.934206 | + | 0.356733i | \(0.116109\pi\) | ||||
−0.934206 | + | 0.356733i | \(0.883891\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −0.757359 | −0.0497231 | ||||||||
\(233\) | 23.0711i | 1.51144i | 0.654897 | + | 0.755718i | \(0.272712\pi\) | ||||
−0.654897 | + | 0.755718i | \(0.727288\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −7.25077 | −0.471985 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 5.00000 | + | 3.16228i | 0.324102 | + | 0.204980i | ||||
\(239\) | − | 7.17157i | − | 0.463890i | −0.972729 | − | 0.231945i | \(-0.925491\pi\) | ||
0.972729 | − | 0.231945i | \(-0.0745090\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 4.47214i | − | 0.288076i | −0.989572 | − | 0.144038i | \(-0.953991\pi\) | ||
0.989572 | − | 0.144038i | \(-0.0460087\pi\) | |||||||
\(242\) | 9.00000i | 0.578542i | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | − | 0.926210i | − | 0.0592945i | ||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 7.07107 | 0.449921 | ||||||||
\(248\) | 4.08849 | 0.259619 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 18.8148 | 1.18758 | 0.593788 | − | 0.804621i | \(-0.297632\pi\) | ||||
0.593788 | + | 0.804621i | \(0.297632\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.41421 | −0.0889108 | ||||||||
\(254\) | 10.0000i | 0.627456i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 21.2097 | 1.32303 | 0.661513 | − | 0.749933i | \(-0.269914\pi\) | ||||
0.661513 | + | 0.749933i | \(0.269914\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −4.00000 | + | 6.32456i | −0.248548 | + | 0.392989i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 12.6491i | 0.781465i | ||||||||
\(263\) | − | 29.2843i | − | 1.80575i | −0.429908 | − | 0.902873i | \(-0.641454\pi\) | ||
0.429908 | − | 0.902873i | \(-0.358546\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −10.7967 | + | 17.0711i | −0.661988 | + | 1.04669i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −27.9179 | −1.70219 | −0.851093 | − | 0.525014i | \(-0.824060\pi\) | ||||
−0.851093 | + | 0.525014i | \(0.824060\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 7.09185i | − | 0.430799i | −0.976526 | − | 0.215400i | \(-0.930895\pi\) | ||
0.976526 | − | 0.215400i | \(-0.0691054\pi\) | |||||||
\(272\) | −2.23607 | −0.135582 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 12.1421 | 0.733533 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −21.2132 | −1.27458 | −0.637289 | − | 0.770625i | \(-0.719944\pi\) | ||||
−0.637289 | + | 0.770625i | \(0.719944\pi\) | |||||||
\(278\) | 10.7967 | 0.647543 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 28.4853i | − | 1.69929i | −0.527356 | − | 0.849645i | \(-0.676816\pi\) | ||
0.527356 | − | 0.849645i | \(-0.323184\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 7.63441i | − | 0.453819i | −0.973916 | − | 0.226909i | \(-0.927138\pi\) | ||
0.973916 | − | 0.226909i | \(-0.0728621\pi\) | |||||||
\(284\) | 15.6569i | 0.929063i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 1.30986i | 0.0774535i | ||||||||
\(287\) | −12.1065 | + | 19.1421i | −0.714627 | + | 1.12992i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −12.0000 | −0.705882 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | − | 13.9590i | − | 0.816887i | ||||||
\(293\) | −25.2982 | −1.47794 | −0.738969 | − | 0.673740i | \(-0.764687\pi\) | ||||
−0.738969 | + | 0.673740i | \(0.764687\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | − | 2.82843i | − | 0.164399i | ||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −0.757359 | −0.0438726 | ||||||||
\(299\) | 0.926210 | 0.0535641 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −5.07107 | + | 8.01806i | −0.292291 | + | 0.462153i | ||||
\(302\) | − | 14.1421i | − | 0.813788i | ||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | − | 7.63441i | − | 0.437864i | ||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 3.70484i | − | 0.211446i | −0.994396 | − | 0.105723i | \(-0.966284\pi\) | ||
0.994396 | − | 0.105723i | \(-0.0337157\pi\) | |||||||
\(308\) | −3.16228 | − | 2.00000i | −0.180187 | − | 0.113961i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −5.23943 | −0.297101 | −0.148550 | − | 0.988905i | \(-0.547461\pi\) | ||||
−0.148550 | + | 0.988905i | \(0.547461\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 16.5787i | 0.937083i | 0.883442 | + | 0.468541i | \(0.155220\pi\) | ||||
−0.883442 | + | 0.468541i | \(0.844780\pi\) | |||||||
\(314\) | −10.7967 | −0.609293 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 13.0711 | 0.735305 | ||||||||
\(317\) | − | 30.0711i | − | 1.68896i | −0.535588 | − | 0.844480i | \(-0.679910\pi\) | ||
0.535588 | − | 0.844480i | \(-0.320090\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.07107 | −0.0599683 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −1.41421 | + | 2.23607i | −0.0788110 | + | 0.124611i | ||||
\(323\) | 17.0711i | 0.949860i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 7.92893i | 0.439143i | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | − | 8.56062i | − | 0.472681i | ||||||
\(329\) | −1.85242 | + | 2.92893i | −0.102127 | + | 0.161477i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 7.92893 | 0.435814 | 0.217907 | − | 0.975970i | \(-0.430077\pi\) | ||||
0.217907 | + | 0.975970i | \(0.430077\pi\) | |||||||
\(332\) | −14.3426 | −0.787153 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 12.1065i | 0.662441i | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 11.9706 | 0.652078 | 0.326039 | − | 0.945356i | \(-0.394286\pi\) | ||||
0.326039 | + | 0.945356i | \(0.394286\pi\) | |||||||
\(338\) | 12.1421i | 0.660445i | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 5.78199 | 0.313113 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 18.3848 | + | 2.23607i | 0.992685 | + | 0.120736i | ||||
\(344\) | − | 3.58579i | − | 0.193333i | ||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 10.2541i | 0.551265i | ||||||||
\(347\) | − | 9.07107i | − | 0.486960i | −0.969906 | − | 0.243480i | \(-0.921711\pi\) | ||
0.969906 | − | 0.243480i | \(-0.0782891\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 6.16564i | 0.330039i | 0.986290 | + | 0.165020i | \(0.0527688\pi\) | ||||
−0.986290 | + | 0.165020i | \(0.947231\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 1.41421 | 0.0753778 | ||||||||
\(353\) | −18.9737 | −1.00987 | −0.504933 | − | 0.863158i | \(-0.668483\pi\) | ||||
−0.504933 | + | 0.863158i | \(0.668483\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 2.61972 | 0.138845 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −11.3137 | −0.597948 | ||||||||
\(359\) | − | 16.3137i | − | 0.861005i | −0.902589 | − | 0.430502i | \(-0.858336\pi\) | ||
0.902589 | − | 0.430502i | \(-0.141664\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −39.2843 | −2.06759 | ||||||||
\(362\) | 2.61972 | 0.137689 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 2.07107 | + | 1.30986i | 0.108553 | + | 0.0686552i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 24.5967i | − | 1.28394i | −0.766730 | − | 0.641970i | \(-0.778117\pi\) | ||
0.766730 | − | 0.641970i | \(-0.221883\pi\) | |||||||
\(368\) | − | 1.00000i | − | 0.0521286i | ||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 18.0475 | + | 11.4142i | 0.936977 | + | 0.592596i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −7.07107 | −0.366126 | −0.183063 | − | 0.983101i | \(-0.558601\pi\) | ||||
−0.183063 | + | 0.983101i | \(0.558601\pi\) | |||||||
\(374\) | −3.16228 | −0.163517 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | − | 1.30986i | − | 0.0675508i | ||||||
\(377\) | 0.701474 | 0.0361277 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 22.0711 | 1.13371 | 0.566857 | − | 0.823816i | \(-0.308159\pi\) | ||||
0.566857 | + | 0.823816i | \(0.308159\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −0.656854 | −0.0336076 | ||||||||
\(383\) | −16.0361 | −0.819408 | −0.409704 | − | 0.912219i | \(-0.634368\pi\) | ||||
−0.409704 | + | 0.912219i | \(0.634368\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 8.48528i | 0.431889i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | − | 0.542561i | − | 0.0275444i | ||||||
\(389\) | 22.8284i | 1.15745i | 0.815524 | + | 0.578724i | \(0.196449\pi\) | ||||
−0.815524 | + | 0.578724i | \(0.803551\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.23607i | 0.113083i | ||||||||
\(392\) | −6.32456 | + | 3.00000i | −0.319438 | + | 0.151523i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 5.92893 | 0.298695 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 29.6114i | − | 1.48616i | −0.669205 | − | 0.743078i | \(-0.733365\pi\) | ||
0.669205 | − | 0.743078i | \(-0.266635\pi\) | |||||||
\(398\) | 21.5934 | 1.08238 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 9.79899i | 0.489338i | 0.969607 | + | 0.244669i | \(0.0786793\pi\) | ||||
−0.969607 | + | 0.244669i | \(0.921321\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −3.78680 | −0.188634 | ||||||||
\(404\) | −12.1065 | −0.602323 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −1.07107 | + | 1.69351i | −0.0531562 | + | 0.0840473i | ||||
\(407\) | − | 4.00000i | − | 0.198273i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 22.9032i | 1.13249i | 0.824236 | + | 0.566246i | \(0.191605\pi\) | ||||
−0.824236 | + | 0.566246i | \(0.808395\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | − | 10.4130i | − | 0.513014i | ||||||
\(413\) | −10.2541 | + | 16.2132i | −0.504573 | + | 0.797800i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −0.926210 | −0.0454112 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | − | 10.7967i | − | 0.528083i | ||||||
\(419\) | 28.8441 | 1.40913 | 0.704564 | − | 0.709640i | \(-0.251142\pi\) | ||||
0.704564 | + | 0.709640i | \(0.251142\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 33.3553 | 1.62564 | 0.812820 | − | 0.582515i | \(-0.197931\pi\) | ||||
0.812820 | + | 0.582515i | \(0.197931\pi\) | |||||||
\(422\) | 16.2132i | 0.789246i | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −8.07107 | −0.391966 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −2.07107 | − | 1.30986i | −0.100226 | − | 0.0633885i | ||||
\(428\) | 2.00000i | 0.0966736i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 4.79899i | − | 0.231159i | −0.993298 | − | 0.115580i | \(-0.963127\pi\) | ||
0.993298 | − | 0.115580i | \(-0.0368725\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 9.71157i | 0.466708i | 0.972392 | + | 0.233354i | \(0.0749701\pi\) | ||||
−0.972392 | + | 0.233354i | \(0.925030\pi\) | |||||||
\(434\) | 5.78199 | − | 9.14214i | 0.277545 | − | 0.438837i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 7.07107 | 0.338643 | ||||||||
\(437\) | −7.63441 | −0.365204 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 4.08849i | − | 0.195133i | −0.995229 | − | 0.0975664i | \(-0.968894\pi\) | ||
0.995229 | − | 0.0975664i | \(-0.0311058\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 2.07107 | 0.0985106 | ||||||||
\(443\) | 23.0711i | 1.09614i | 0.836433 | + | 0.548070i | \(0.184637\pi\) | ||||
−0.836433 | + | 0.548070i | \(0.815363\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −13.0328 | −0.617119 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 1.41421 | − | 2.23607i | 0.0668153 | − | 0.105644i | ||||
\(449\) | 18.3848i | 0.867631i | 0.901002 | + | 0.433816i | \(0.142833\pi\) | ||||
−0.901002 | + | 0.433816i | \(0.857167\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 12.1065i | − | 0.570075i | ||||||
\(452\) | 1.07107i | 0.0503788i | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 25.1393i | 1.17985i | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −17.8284 | −0.833979 | −0.416989 | − | 0.908911i | \(-0.636915\pi\) | ||||
−0.416989 | + | 0.908911i | \(0.636915\pi\) | |||||||
\(458\) | −10.7967 | −0.504496 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −38.9394 | −1.81359 | −0.906794 | − | 0.421575i | \(-0.861477\pi\) | ||||
−0.906794 | + | 0.421575i | \(0.861477\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −38.2843 | −1.77922 | −0.889610 | − | 0.456720i | \(-0.849024\pi\) | ||||
−0.889610 | + | 0.456720i | \(0.849024\pi\) | |||||||
\(464\) | − | 0.757359i | − | 0.0351595i | ||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −23.0711 | −1.06875 | ||||||||
\(467\) | −29.6114 | −1.37025 | −0.685127 | − | 0.728424i | \(-0.740253\pi\) | ||||
−0.685127 | + | 0.728424i | \(0.740253\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | − | 7.25077i | − | 0.333744i | ||||||
\(473\) | − | 5.07107i | − | 0.233168i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −3.16228 | + | 5.00000i | −0.144943 | + | 0.229175i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 7.17157 | 0.328020 | ||||||||
\(479\) | 33.6999 | 1.53979 | 0.769895 | − | 0.638171i | \(-0.220309\pi\) | ||||
0.769895 | + | 0.638171i | \(0.220309\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.61972i | 0.119449i | ||||||||
\(482\) | 4.47214 | 0.203700 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −9.00000 | −0.409091 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −29.8995 | −1.35488 | −0.677438 | − | 0.735580i | \(-0.736910\pi\) | ||||
−0.677438 | + | 0.735580i | \(0.736910\pi\) | |||||||
\(488\) | 0.926210 | 0.0419275 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 21.5147i | − | 0.970946i | −0.874252 | − | 0.485473i | \(-0.838647\pi\) | ||
0.874252 | − | 0.485473i | \(-0.161353\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1.69351i | 0.0762717i | ||||||||
\(494\) | 7.07107i | 0.318142i | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 4.08849i | 0.183579i | ||||||||
\(497\) | 35.0098 | + | 22.1421i | 1.57040 | + | 0.993211i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −22.0711 | −0.988037 | −0.494018 | − | 0.869451i | \(-0.664472\pi\) | ||||
−0.494018 | + | 0.869451i | \(0.664472\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 18.8148i | 0.839744i | ||||||||
\(503\) | −21.8181 | −0.972822 | −0.486411 | − | 0.873730i | \(-0.661694\pi\) | ||||
−0.486411 | + | 0.873730i | \(0.661694\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | − | 1.41421i | − | 0.0628695i | ||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −10.0000 | −0.443678 | ||||||||
\(509\) | 0.224736 | 0.00996125 | 0.00498063 | − | 0.999988i | \(-0.498415\pi\) | ||||
0.00498063 | + | 0.999988i | \(0.498415\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −31.2132 | − | 19.7410i | −1.38079 | − | 0.873289i | ||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 21.2097i | 0.935521i | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 1.85242i | − | 0.0814693i | ||||||
\(518\) | −6.32456 | − | 4.00000i | −0.277885 | − | 0.175750i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 17.5049 | 0.766903 | 0.383452 | − | 0.923561i | \(-0.374735\pi\) | ||||
0.383452 | + | 0.923561i | \(0.374735\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 28.4605i | − | 1.24449i | −0.782822 | − | 0.622245i | \(-0.786221\pi\) | ||
0.782822 | − | 0.622245i | \(-0.213779\pi\) | |||||||
\(524\) | −12.6491 | −0.552579 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 29.2843 | 1.27685 | ||||||||
\(527\) | − | 9.14214i | − | 0.398238i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 22.0000 | 0.956522 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −17.0711 | − | 10.7967i | −0.740125 | − | 0.468096i | ||||
\(533\) | 7.92893i | 0.343440i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | − | 27.9179i | − | 1.20363i | ||||||
\(539\) | −8.94427 | + | 4.24264i | −0.385257 | + | 0.182743i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 5.07107 | 0.218022 | 0.109011 | − | 0.994041i | \(-0.465232\pi\) | ||||
0.109011 | + | 0.994041i | \(0.465232\pi\) | |||||||
\(542\) | 7.09185 | 0.304621 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | − | 2.23607i | − | 0.0958706i | ||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 16.2132 | 0.693227 | 0.346613 | − | 0.938008i | \(-0.387332\pi\) | ||||
0.346613 | + | 0.938008i | \(0.387332\pi\) | |||||||
\(548\) | 12.1421i | 0.518686i | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −5.78199 | −0.246321 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 18.4853 | − | 29.2278i | 0.786074 | − | 1.24289i | ||||
\(554\) | − | 21.2132i | − | 0.901263i | ||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 10.7967i | 0.457882i | ||||||||
\(557\) | 26.1421i | 1.10768i | 0.832624 | + | 0.553839i | \(0.186838\pi\) | ||||
−0.832624 | + | 0.553839i | \(0.813162\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 3.32119i | 0.140471i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 28.4853 | 1.20158 | ||||||||
\(563\) | 24.3720 | 1.02716 | 0.513579 | − | 0.858042i | \(-0.328319\pi\) | ||||
0.513579 | + | 0.858042i | \(0.328319\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 7.63441 | 0.320898 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −15.6569 | −0.656947 | ||||||||
\(569\) | − | 22.5269i | − | 0.944377i | −0.881498 | − | 0.472189i | \(-0.843464\pi\) | ||
0.881498 | − | 0.472189i | \(-0.156536\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −38.2132 | −1.59917 | −0.799586 | − | 0.600551i | \(-0.794948\pi\) | ||||
−0.799586 | + | 0.600551i | \(0.794948\pi\) | |||||||
\(572\) | −1.30986 | −0.0547679 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −19.1421 | − | 12.1065i | −0.798977 | − | 0.505318i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 23.4458i | − | 0.976062i | −0.872826 | − | 0.488031i | \(-0.837715\pi\) | ||
0.872826 | − | 0.488031i | \(-0.162285\pi\) | |||||||
\(578\) | − | 12.0000i | − | 0.499134i | ||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −20.2835 | + | 32.0711i | −0.841502 | + | 1.33053i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −11.4142 | −0.472728 | ||||||||
\(584\) | 13.9590 | 0.577626 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | − | 25.2982i | − | 1.04506i | ||||||
\(587\) | −15.4277 | −0.636771 | −0.318385 | − | 0.947961i | \(-0.603141\pi\) | ||||
−0.318385 | + | 0.947961i | \(0.603141\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 31.2132 | 1.28612 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 2.82843 | 0.116248 | ||||||||
\(593\) | −46.8916 | −1.92561 | −0.962804 | − | 0.270202i | \(-0.912910\pi\) | ||||
−0.962804 | + | 0.270202i | \(0.912910\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | − | 0.757359i | − | 0.0310226i | ||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0.926210i | 0.0378755i | ||||||||
\(599\) | − | 3.68629i | − | 0.150618i | −0.997160 | − | 0.0753089i | \(-0.976006\pi\) | ||
0.997160 | − | 0.0753089i | \(-0.0239943\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 12.1065i | − | 0.493836i | −0.969036 | − | 0.246918i | \(-0.920582\pi\) | ||
0.969036 | − | 0.246918i | \(-0.0794179\pi\) | |||||||
\(602\) | −8.01806 | − | 5.07107i | −0.326792 | − | 0.206681i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 14.1421 | 0.575435 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 43.9541i | 1.78404i | 0.451996 | + | 0.892020i | \(0.350712\pi\) | ||||
−0.451996 | + | 0.892020i | \(0.649288\pi\) | |||||||
\(608\) | 7.63441 | 0.309616 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.21320i | 0.0490810i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −15.8579 | −0.640493 | −0.320247 | − | 0.947334i | \(-0.603766\pi\) | ||||
−0.320247 | + | 0.947334i | \(0.603766\pi\) | |||||||
\(614\) | 3.70484 | 0.149515 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 2.00000 | − | 3.16228i | 0.0805823 | − | 0.127412i | ||||
\(617\) | − | 32.0000i | − | 1.28827i | −0.764911 | − | 0.644136i | \(-0.777217\pi\) | ||
0.764911 | − | 0.644136i | \(-0.222783\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 18.2064i | 0.731776i | 0.930659 | + | 0.365888i | \(0.119235\pi\) | ||||
−0.930659 | + | 0.365888i | \(0.880765\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | − | 5.23943i | − | 0.210082i | ||||||
\(623\) | 3.70484 | − | 5.85786i | 0.148431 | − | 0.234690i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −16.5787 | −0.662618 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | − | 10.7967i | − | 0.430835i | ||||||
\(629\) | −6.32456 | −0.252177 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 10.2843 | 0.409410 | 0.204705 | − | 0.978824i | \(-0.434376\pi\) | ||||
0.204705 | + | 0.978824i | \(0.434376\pi\) | |||||||
\(632\) | 13.0711i | 0.519939i | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 30.0711 | 1.19427 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 5.85786 | − | 2.77863i | 0.232097 | − | 0.110093i | ||||
\(638\) | − | 1.07107i | − | 0.0424040i | ||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 28.4853i | 1.12510i | 0.826763 | + | 0.562550i | \(0.190180\pi\) | ||||
−0.826763 | + | 0.562550i | \(0.809820\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 29.9951i | − | 1.18289i | −0.806345 | − | 0.591446i | \(-0.798557\pi\) | ||
0.806345 | − | 0.591446i | \(-0.201443\pi\) | |||||||
\(644\) | −2.23607 | − | 1.41421i | −0.0881134 | − | 0.0557278i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −17.0711 | −0.671652 | ||||||||
\(647\) | −37.0869 | −1.45804 | −0.729019 | − | 0.684493i | \(-0.760023\pi\) | ||||
−0.729019 | + | 0.684493i | \(0.760023\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 10.2541i | − | 0.402510i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −7.92893 | −0.310521 | ||||||||
\(653\) | 8.14214i | 0.318626i | 0.987228 | + | 0.159313i | \(0.0509280\pi\) | ||||
−0.987228 | + | 0.159313i | \(0.949072\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 8.56062 | 0.334236 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −2.92893 | − | 1.85242i | −0.114182 | − | 0.0722148i | ||||
\(659\) | − | 48.3848i | − | 1.88480i | −0.334483 | − | 0.942402i | \(-0.608562\pi\) | ||
0.334483 | − | 0.942402i | \(-0.391438\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 18.2064i | − | 0.708146i | −0.935218 | − | 0.354073i | \(-0.884796\pi\) | ||
0.935218 | − | 0.354073i | \(-0.115204\pi\) | |||||||
\(662\) | 7.92893i | 0.308167i | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | − | 14.3426i | − | 0.556602i | ||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −0.757359 | −0.0293251 | ||||||||
\(668\) | −12.1065 | −0.468416 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1.30986 | 0.0505665 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −34.7990 | −1.34140 | −0.670701 | − | 0.741728i | \(-0.734007\pi\) | ||||
−0.670701 | + | 0.741728i | \(0.734007\pi\) | |||||||
\(674\) | 11.9706i | 0.461089i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −12.1421 | −0.467005 | ||||||||
\(677\) | 22.9032 | 0.880243 | 0.440122 | − | 0.897938i | \(-0.354935\pi\) | ||||
0.440122 | + | 0.897938i | \(0.354935\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −1.21320 | − | 0.767297i | −0.0465585 | − | 0.0294462i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 5.78199i | 0.221404i | ||||||||
\(683\) | − | 36.0000i | − | 1.37750i | −0.724998 | − | 0.688751i | \(-0.758159\pi\) | ||
0.724998 | − | 0.688751i | \(-0.241841\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −2.23607 | + | 18.3848i | −0.0853735 | + | 0.701934i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 3.58579 | 0.136707 | ||||||||
\(689\) | 7.47550 | 0.284794 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 23.9884i | − | 0.912560i | −0.889836 | − | 0.456280i | \(-0.849181\pi\) | ||
0.889836 | − | 0.456280i | \(-0.150819\pi\) | |||||||
\(692\) | −10.2541 | −0.389804 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 9.07107 | 0.344333 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −19.1421 | −0.725060 | ||||||||
\(698\) | −6.16564 | −0.233373 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 41.8701i | − | 1.58141i | −0.612197 | − | 0.790705i | \(-0.709714\pi\) | ||
0.612197 | − | 0.790705i | \(-0.290286\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 21.5934i | − | 0.814410i | ||||||
\(704\) | 1.41421i | 0.0533002i | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | − | 18.9737i | − | 0.714083i | ||||||
\(707\) | −17.1212 | + | 27.0711i | −0.643911 | + | 1.01811i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 24.1421 | 0.906677 | 0.453338 | − | 0.891338i | \(-0.350233\pi\) | ||||
0.453338 | + | 0.891338i | \(0.350233\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 2.61972i | 0.0981780i | ||||||||
\(713\) | 4.08849 | 0.153115 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | − | 11.3137i | − | 0.422813i | ||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 16.3137 | 0.608822 | ||||||||
\(719\) | 23.9884 | 0.894615 | 0.447307 | − | 0.894380i | \(-0.352383\pi\) | ||||
0.447307 | + | 0.894380i | \(0.352383\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −23.2843 | − | 14.7263i | −0.867152 | − | 0.548435i | ||||
\(722\) | − | 39.2843i | − | 1.46201i | ||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 2.61972i | 0.0973610i | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 6.70820i | − | 0.248794i | −0.992233 | − | 0.124397i | \(-0.960300\pi\) | ||
0.992233 | − | 0.124397i | \(-0.0396996\pi\) | |||||||
\(728\) | −1.30986 | + | 2.07107i | −0.0485466 | + | 0.0767589i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −8.01806 | −0.296559 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 39.6408i | − | 1.46417i | −0.681214 | − | 0.732084i | \(-0.738548\pi\) | ||
0.681214 | − | 0.732084i | \(-0.261452\pi\) | |||||||
\(734\) | 24.5967 | 0.907883 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.00000 | 0.0368605 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −26.3553 | −0.969497 | −0.484748 | − | 0.874654i | \(-0.661089\pi\) | ||||
−0.484748 | + | 0.874654i | \(0.661089\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −11.4142 | + | 18.0475i | −0.419029 | + | 0.662543i | ||||
\(743\) | 35.1421i | 1.28924i | 0.764503 | + | 0.644620i | \(0.222984\pi\) | ||||
−0.764503 | + | 0.644620i | \(0.777016\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | − | 7.07107i | − | 0.258890i | ||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | − | 3.16228i | − | 0.115624i | ||||||
\(749\) | 4.47214 | + | 2.82843i | 0.163408 | + | 0.103348i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 31.2132 | 1.13899 | 0.569493 | − | 0.821996i | \(-0.307140\pi\) | ||||
0.569493 | + | 0.821996i | \(0.307140\pi\) | |||||||
\(752\) | 1.30986 | 0.0477656 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0.701474i | 0.0255462i | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 44.0416 | 1.60072 | 0.800360 | − | 0.599520i | \(-0.204642\pi\) | ||||
0.800360 | + | 0.599520i | \(0.204642\pi\) | |||||||
\(758\) | 22.0711i | 0.801657i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −31.3050 | −1.13480 | −0.567402 | − | 0.823441i | \(-0.692051\pi\) | ||||
−0.567402 | + | 0.823441i | \(0.692051\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 10.0000 | − | 15.8114i | 0.362024 | − | 0.572411i | ||||
\(764\) | − | 0.656854i | − | 0.0237642i | ||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | − | 16.0361i | − | 0.579409i | ||||||
\(767\) | 6.71573i | 0.242491i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 15.0441i | 0.542504i | 0.962508 | + | 0.271252i | \(0.0874376\pi\) | ||||
−0.962508 | + | 0.271252i | \(0.912562\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −8.48528 | −0.305392 | ||||||||
\(773\) | −17.3460 | −0.623892 | −0.311946 | − | 0.950100i | \(-0.600981\pi\) | ||||
−0.311946 | + | 0.950100i | \(0.600981\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0.542561 | 0.0194768 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −22.8284 | −0.818439 | ||||||||
\(779\) | − | 65.3553i | − | 2.34160i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −22.1421 | −0.792308 | ||||||||
\(782\) | −2.23607 | −0.0799616 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −3.00000 | − | 6.32456i | −0.107143 | − | 0.225877i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 33.9247i | 1.20928i | 0.796497 | + | 0.604642i | \(0.206684\pi\) | ||||
−0.796497 | + | 0.604642i | \(0.793316\pi\) | |||||||
\(788\) | 5.92893i | 0.211209i | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 2.39498 | + | 1.51472i | 0.0851557 | + | 0.0538572i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −0.857864 | −0.0304637 | ||||||||
\(794\) | 29.6114 | 1.05087 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 21.5934i | 0.765357i | ||||||||
\(797\) | 11.0214 | 0.390399 | 0.195199 | − | 0.980764i | \(-0.437465\pi\) | ||||
0.195199 | + | 0.980764i | \(0.437465\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −2.92893 | −0.103618 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −9.79899 | −0.346014 | ||||||||
\(803\) | 19.7410 | 0.696643 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | − | 3.78680i | − | 0.133384i | ||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | − | 12.1065i | − | 0.425907i | ||||||
\(809\) | 19.8995i | 0.699629i | 0.936819 | + | 0.349814i | \(0.113755\pi\) | ||||
−0.936819 | + | 0.349814i | \(0.886245\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 41.1096i | − | 1.44355i | −0.692126 | − | 0.721777i | \(-0.743326\pi\) | ||
0.692126 | − | 0.721777i | \(-0.256674\pi\) | |||||||
\(812\) | −1.69351 | − | 1.07107i | −0.0594304 | − | 0.0375871i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 4.00000 | 0.140200 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 27.3754i | − | 0.957743i | ||||||
\(818\) | −22.9032 | −0.800793 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 43.9411i | 1.53356i | 0.641912 | + | 0.766778i | \(0.278141\pi\) | ||||
−0.641912 | + | 0.766778i | \(0.721859\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −17.0711 | −0.595060 | −0.297530 | − | 0.954712i | \(-0.596163\pi\) | ||||
−0.297530 | + | 0.954712i | \(0.596163\pi\) | |||||||
\(824\) | 10.4130 | 0.362756 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −16.2132 | − | 10.2541i | −0.564129 | − | 0.356787i | ||||
\(827\) | 30.4264i | 1.05803i | 0.848613 | + | 0.529015i | \(0.177438\pi\) | ||||
−0.848613 | + | 0.529015i | \(0.822562\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 21.4345i | 0.744450i | 0.928143 | + | 0.372225i | \(0.121405\pi\) | ||||
−0.928143 | + | 0.372225i | \(0.878595\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | − | 0.926210i | − | 0.0321105i | ||||||
\(833\) | 6.70820 | + | 14.1421i | 0.232425 | + | 0.489996i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 10.7967 | 0.373411 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 28.8441i | 0.996405i | ||||||||
\(839\) | 35.0098 | 1.20867 | 0.604336 | − | 0.796729i | \(-0.293438\pi\) | ||||
0.604336 | + | 0.796729i | \(0.293438\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 28.4264 | 0.980221 | ||||||||
\(842\) | 33.3553i | 1.14950i | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −16.2132 | −0.558081 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −12.7279 | + | 20.1246i | −0.437337 | + | 0.691490i | ||||
\(848\) | − | 8.07107i | − | 0.277162i | ||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 2.82843i | − | 0.0969572i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 9.10318i | − | 0.311687i | −0.987782 | − | 0.155844i | \(-0.950190\pi\) | ||
0.987782 | − | 0.155844i | \(-0.0498096\pi\) | |||||||
\(854\) | 1.30986 | − | 2.07107i | 0.0448224 | − | 0.0708705i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −2.00000 | −0.0683586 | ||||||||
\(857\) | 17.8885 | 0.611061 | 0.305531 | − | 0.952182i | \(-0.401166\pi\) | ||||
0.305531 | + | 0.952182i | \(0.401166\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 2.61972i | − | 0.0893836i | −0.999001 | − | 0.0446918i | \(-0.985769\pi\) | ||
0.999001 | − | 0.0446918i | \(-0.0142306\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 4.79899 | 0.163454 | ||||||||
\(863\) | − | 19.8579i | − | 0.675970i | −0.941152 | − | 0.337985i | \(-0.890255\pi\) | ||
0.941152 | − | 0.337985i | \(-0.109745\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −9.71157 | −0.330013 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 9.14214 | + | 5.78199i | 0.310304 | + | 0.196254i | ||||
\(869\) | 18.4853i | 0.627070i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | 7.07107i | 0.239457i | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | − | 7.63441i | − | 0.258238i | ||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −5.85786 | −0.197806 | −0.0989030 | − | 0.995097i | \(-0.531533\pi\) | ||||
−0.0989030 | + | 0.995097i | \(0.531533\pi\) | |||||||
\(878\) | 4.08849 | 0.137980 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 32.0064 | 1.07832 | 0.539162 | − | 0.842202i | \(-0.318741\pi\) | ||||
0.539162 | + | 0.842202i | \(0.318741\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −36.0122 | −1.21191 | −0.605953 | − | 0.795500i | \(-0.707208\pi\) | ||||
−0.605953 | + | 0.795500i | \(0.707208\pi\) | |||||||
\(884\) | 2.07107i | 0.0696575i | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −23.0711 | −0.775088 | ||||||||
\(887\) | −16.3539 | −0.549112 | −0.274556 | − | 0.961571i | \(-0.588531\pi\) | ||||
−0.274556 | + | 0.961571i | \(0.588531\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −14.1421 | + | 22.3607i | −0.474312 | + | 0.749953i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | − | 13.0328i | − | 0.436369i | ||||||
\(893\) | − | 10.0000i | − | 0.334637i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 2.23607 | + | 1.41421i | 0.0747018 | + | 0.0472456i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −18.3848 | −0.613508 | ||||||||
\(899\) | 3.09645 | 0.103273 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 18.0475i | 0.601248i | ||||||||
\(902\) | 12.1065 | 0.403104 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −1.07107 | −0.0356232 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −14.8995 | −0.494730 | −0.247365 | − | 0.968922i | \(-0.579565\pi\) | ||||
−0.247365 | + | 0.968922i | \(0.579565\pi\) | |||||||
\(908\) | −25.1393 | −0.834277 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 12.3726i | − | 0.409922i | −0.978770 | − | 0.204961i | \(-0.934293\pi\) | ||
0.978770 | − | 0.204961i | \(-0.0657067\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 20.2835i | − | 0.671287i | ||||||
\(914\) | − | 17.8284i | − | 0.589712i | ||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | − | 10.7967i | − | 0.356733i | ||||||
\(917\) | −17.8885 | + | 28.2843i | −0.590732 | + | 0.934029i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 7.07107 | 0.233253 | 0.116627 | − | 0.993176i | \(-0.462792\pi\) | ||||
0.116627 | + | 0.993176i | \(0.462792\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | − | 38.9394i | − | 1.28240i | ||||||
\(923\) | 14.5015 | 0.477324 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | − | 38.2843i | − | 1.25810i | ||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0.757359 | 0.0248615 | ||||||||
\(929\) | 25.3640 | 0.832167 | 0.416084 | − | 0.909326i | \(-0.363402\pi\) | ||||
0.416084 | + | 0.909326i | \(0.363402\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −48.2843 | + | 22.9032i | −1.58245 | + | 0.750623i | ||||
\(932\) | − | 23.0711i | − | 0.755718i | ||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | − | 29.6114i | − | 0.968916i | ||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 5.23943i | − | 0.171165i | −0.996331 | − | 0.0855824i | \(-0.972725\pi\) | ||
0.996331 | − | 0.0855824i | \(-0.0272751\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −44.2719 | −1.44322 | −0.721611 | − | 0.692299i | \(-0.756598\pi\) | ||||
−0.721611 | + | 0.692299i | \(0.756598\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 8.56062i | − | 0.278772i | ||||||
\(944\) | 7.25077 | 0.235992 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 5.07107 | 0.164875 | ||||||||
\(947\) | − | 33.3553i | − | 1.08390i | −0.840410 | − | 0.541951i | \(-0.817686\pi\) | ||
0.840410 | − | 0.541951i | \(-0.182314\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −12.9289 | −0.419691 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −5.00000 | − | 3.16228i | −0.162051 | − | 0.102490i | ||||
\(953\) | 36.0000i | 1.16615i | 0.812417 | + | 0.583077i | \(0.198151\pi\) | ||||
−0.812417 | + | 0.583077i | \(0.801849\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 7.17157i | 0.231945i | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 33.6999i | 1.08880i | ||||||||
\(959\) | 27.1506 | + | 17.1716i | 0.876740 | + | 0.554499i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 14.2843 | 0.460783 | ||||||||
\(962\) | −2.61972 | −0.0844631 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 4.47214i | 0.144038i | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 49.4975 | 1.59173 | 0.795866 | − | 0.605473i | \(-0.207016\pi\) | ||||
0.795866 | + | 0.605473i | \(0.207016\pi\) | |||||||
\(968\) | − | 9.00000i | − | 0.289271i | ||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 27.6001 | 0.885730 | 0.442865 | − | 0.896588i | \(-0.353962\pi\) | ||||
0.442865 | + | 0.896588i | \(0.353962\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 24.1421 | + | 15.2688i | 0.773961 | + | 0.489496i | ||||
\(974\) | − | 29.8995i | − | 0.958042i | ||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0.926210i | 0.0296472i | ||||||||
\(977\) | − | 12.0000i | − | 0.383914i | −0.981403 | − | 0.191957i | \(-0.938517\pi\) | ||
0.981403 | − | 0.191957i | \(-0.0614834\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 3.70484i | 0.118407i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 21.5147 | 0.686562 | ||||||||
\(983\) | 6.32456 | 0.201722 | 0.100861 | − | 0.994901i | \(-0.467840\pi\) | ||||
0.100861 | + | 0.994901i | \(0.467840\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −1.69351 | −0.0539322 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −7.07107 | −0.224961 | ||||||||
\(989\) | − | 3.58579i | − | 0.114021i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −25.3553 | −0.805439 | −0.402719 | − | 0.915323i | \(-0.631935\pi\) | ||||
−0.402719 | + | 0.915323i | \(0.631935\pi\) | |||||||
\(992\) | −4.08849 | −0.129810 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −22.1421 | + | 35.0098i | −0.702306 | + | 1.11044i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1.85242i | 0.0586667i | 0.999570 | + | 0.0293334i | \(0.00933844\pi\) | ||||
−0.999570 | + | 0.0293334i | \(0.990662\pi\) | |||||||
\(998\) | − | 22.0711i | − | 0.698647i | ||||||
\(999\) | 0 | 0 |
(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 | 3150.2.b.d.251.6 | yes | 8 | |
3.2 | odd | 2 | inner | 3150.2.b.d.251.2 | yes | 8 | |
5.2 | odd | 4 | 3150.2.d.b.3149.2 | 8 | |||
5.3 | odd | 4 | 3150.2.d.e.3149.7 | 8 | |||
5.4 | even | 2 | 3150.2.b.a.251.3 | ✓ | 8 | ||
7.6 | odd | 2 | inner | 3150.2.b.d.251.5 | yes | 8 | |
15.2 | even | 4 | 3150.2.d.e.3149.2 | 8 | |||
15.8 | even | 4 | 3150.2.d.b.3149.7 | 8 | |||
15.14 | odd | 2 | 3150.2.b.a.251.7 | yes | 8 | ||
21.20 | even | 2 | inner | 3150.2.b.d.251.1 | yes | 8 | |
35.13 | even | 4 | 3150.2.d.e.3149.4 | 8 | |||
35.27 | even | 4 | 3150.2.d.b.3149.5 | 8 | |||
35.34 | odd | 2 | 3150.2.b.a.251.4 | yes | 8 | ||
105.62 | odd | 4 | 3150.2.d.e.3149.5 | 8 | |||
105.83 | odd | 4 | 3150.2.d.b.3149.4 | 8 | |||
105.104 | even | 2 | 3150.2.b.a.251.8 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3150.2.b.a.251.3 | ✓ | 8 | 5.4 | even | 2 | ||
3150.2.b.a.251.4 | yes | 8 | 35.34 | odd | 2 | ||
3150.2.b.a.251.7 | yes | 8 | 15.14 | odd | 2 | ||
3150.2.b.a.251.8 | yes | 8 | 105.104 | even | 2 | ||
3150.2.b.d.251.1 | yes | 8 | 21.20 | even | 2 | inner | |
3150.2.b.d.251.2 | yes | 8 | 3.2 | odd | 2 | inner | |
3150.2.b.d.251.5 | yes | 8 | 7.6 | odd | 2 | inner | |
3150.2.b.d.251.6 | yes | 8 | 1.1 | even | 1 | trivial | |
3150.2.d.b.3149.2 | 8 | 5.2 | odd | 4 | |||
3150.2.d.b.3149.4 | 8 | 105.83 | odd | 4 | |||
3150.2.d.b.3149.5 | 8 | 35.27 | even | 4 | |||
3150.2.d.b.3149.7 | 8 | 15.8 | even | 4 | |||
3150.2.d.e.3149.2 | 8 | 15.2 | even | 4 | |||
3150.2.d.e.3149.4 | 8 | 35.13 | even | 4 | |||
3150.2.d.e.3149.5 | 8 | 105.62 | odd | 4 | |||
3150.2.d.e.3149.7 | 8 | 5.3 | odd | 4 |