Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3120,2,Mod(1249,3120)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3120, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 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("3120.1249");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3120 = 2^{4} \cdot 3 \cdot 5 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3120.l (of order \(2\), degree \(1\), not 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: | \(24.9133254306\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.1698758656.6 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 18x^{6} + 97x^{4} + 176x^{2} + 64 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | no (minimal twist has level 1560) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1249.8 | ||
Root | \(-2.16053i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3120.1249 |
Dual form | 3120.2.l.o.1249.4 |
$q$-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 \(\left(\mathbb{Z}/3120\mathbb{Z}\right)^\times\).
\(n\) | \(1951\) | \(2081\) | \(2341\) | \(2497\) | \(2641\) |
\(\chi(n)\) | \(1\) | \(1\) | \(1\) | \(-1\) | \(1\) |
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 | ||||||||
\(3\) | 1.00000i | 0.577350i | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.23483 | − | 0.0743018i | 0.999448 | − | 0.0332288i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 2.82843i | − | 1.06904i | −0.845154 | − | 0.534522i | \(-0.820491\pi\) | ||
0.845154 | − | 0.534522i | \(-0.179509\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 6.46967 | 1.95068 | 0.975339 | − | 0.220713i | \(-0.0708383\pi\) | ||||
0.975339 | + | 0.220713i | \(0.0708383\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.00000i | 0.277350i | ||||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.0743018 | + | 2.23483i | 0.0191846 | + | 0.577031i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.49264i | 0.847089i | 0.905875 | + | 0.423544i | \(0.139214\pi\) | ||||
−0.905875 | + | 0.423544i | \(0.860786\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.21016 | −0.507045 | −0.253522 | − | 0.967330i | \(-0.581589\pi\) | ||||
−0.253522 | + | 0.967330i | \(0.581589\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.82843 | 0.617213 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 7.14949i | − | 1.49077i | −0.666633 | − | 0.745386i | \(-0.732265\pi\) | ||
0.666633 | − | 0.745386i | \(-0.267735\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 4.98896 | − | 0.332104i | 0.997792 | − | 0.0664208i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − | 1.00000i | − | 0.192450i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −4.82843 | −0.896616 | −0.448308 | − | 0.893879i | \(-0.647973\pi\) | ||||
−0.448308 | + | 0.893879i | \(0.647973\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 9.65685 | 1.73442 | 0.867211 | − | 0.497941i | \(-0.165910\pi\) | ||||
0.867211 | + | 0.497941i | \(0.165910\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 6.46967i | 1.12622i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −0.210157 | − | 6.32106i | −0.0355231 | − | 1.06845i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 6.93933i | 1.14082i | 0.821360 | + | 0.570410i | \(0.193216\pi\) | ||||
−0.821360 | + | 0.570410i | \(0.806784\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.00000 | −0.160128 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −0.148604 | −0.0232080 | −0.0116040 | − | 0.999933i | \(-0.503694\pi\) | ||||
−0.0116040 | + | 0.999933i | \(0.503694\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.03858i | 0.463380i | 0.972790 | + | 0.231690i | \(0.0744255\pi\) | ||||
−0.972790 | + | 0.231690i | \(0.925575\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −2.23483 | + | 0.0743018i | −0.333149 | + | 0.0110763i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 6.79073i | − | 0.990530i | −0.868742 | − | 0.495265i | \(-0.835071\pi\) | ||
0.868742 | − | 0.495265i | \(-0.164929\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −3.49264 | −0.489067 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 1.70279i | − | 0.233897i | −0.993138 | − | 0.116948i | \(-0.962689\pi\) | ||
0.993138 | − | 0.116948i | \(-0.0373112\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 14.4586 | − | 0.480708i | 1.94960 | − | 0.0648186i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 2.21016i | − | 0.292742i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −6.46967 | −0.842279 | −0.421139 | − | 0.906996i | \(-0.638370\pi\) | ||||
−0.421139 | + | 0.906996i | \(0.638370\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.66421 | 0.341117 | 0.170558 | − | 0.985348i | \(-0.445443\pi\) | ||||
0.170558 | + | 0.985348i | \(0.445443\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 2.82843i | 0.356348i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0.0743018 | + | 2.23483i | 0.00921600 | + | 0.277197i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 7.70279i | 0.941046i | 0.882388 | + | 0.470523i | \(0.155935\pi\) | ||||
−0.882388 | + | 0.470523i | \(0.844065\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 7.14949 | 0.860697 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 11.0879 | 1.31590 | 0.657948 | − | 0.753063i | \(-0.271425\pi\) | ||||
0.657948 | + | 0.753063i | \(0.271425\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 5.76776i | − | 0.675065i | −0.941314 | − | 0.337533i | \(-0.890408\pi\) | ||
0.941314 | − | 0.337533i | \(-0.109592\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0.332104 | + | 4.98896i | 0.0383481 | + | 0.576075i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − | 18.2990i | − | 2.08536i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −10.0239 | −1.12777 | −0.563886 | − | 0.825853i | \(-0.690694\pi\) | ||||
−0.563886 | + | 0.825853i | \(0.690694\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 2.27171i | − | 0.249353i | −0.992197 | − | 0.124676i | \(-0.960211\pi\) | ||
0.992197 | − | 0.124676i | \(-0.0397892\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.259509 | + | 7.80546i | 0.0281477 | + | 0.846621i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − | 4.82843i | − | 0.517662i | ||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 9.21104 | 0.976369 | 0.488184 | − | 0.872741i | \(-0.337659\pi\) | ||||
0.488184 | + | 0.872741i | \(0.337659\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.82843 | 0.296500 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 9.65685i | 1.00137i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −4.93933 | + | 0.164219i | −0.506765 | + | 0.0168485i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 8.11091i | − | 0.823538i | −0.911288 | − | 0.411769i | \(-0.864911\pi\) | ||
0.911288 | − | 0.411769i | \(-0.135089\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −6.46967 | −0.650226 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −16.1421 | −1.60620 | −0.803101 | − | 0.595843i | \(-0.796818\pi\) | ||||
−0.803101 | + | 0.595843i | \(0.796818\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 19.5815i | − | 1.92942i | −0.263318 | − | 0.964709i | \(-0.584817\pi\) | ||
0.263318 | − | 0.964709i | \(-0.415183\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 6.32106 | − | 0.210157i | 0.616873 | − | 0.0205092i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 1.35965i | − | 0.131442i | −0.997838 | − | 0.0657210i | \(-0.979065\pi\) | ||
0.997838 | − | 0.0657210i | \(-0.0209347\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −3.49264 | −0.334534 | −0.167267 | − | 0.985912i | \(-0.553494\pi\) | ||||
−0.167267 | + | 0.985912i | \(0.553494\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −6.93933 | −0.658652 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 12.4320i | 1.16950i | 0.811213 | + | 0.584751i | \(0.198808\pi\) | ||||
−0.811213 | + | 0.584751i | \(0.801192\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −0.531220 | − | 15.9779i | −0.0495365 | − | 1.48995i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − | 1.00000i | − | 0.0924500i | ||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 9.87867 | 0.905576 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 30.8566 | 2.80514 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − | 0.148604i | − | 0.0133991i | ||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 11.1248 | − | 1.11289i | 0.995034 | − | 0.0995396i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 18.6200i | − | 1.65226i | −0.563478 | − | 0.826131i | \(-0.690537\pi\) | ||
0.563478 | − | 0.826131i | \(-0.309463\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −3.03858 | −0.267532 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0.751258 | 0.0656378 | 0.0328189 | − | 0.999461i | \(-0.489552\pi\) | ||||
0.0328189 | + | 0.999461i | \(0.489552\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 6.25127i | 0.542054i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −0.0743018 | − | 2.23483i | −0.00639488 | − | 0.192344i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1.08794i | 0.0929487i | 0.998919 | + | 0.0464743i | \(0.0147986\pi\) | ||||
−0.998919 | + | 0.0464743i | \(0.985201\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0.420314 | 0.0356506 | 0.0178253 | − | 0.999841i | \(-0.494326\pi\) | ||||
0.0178253 | + | 0.999841i | \(0.494326\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 6.79073 | 0.571883 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 6.46967i | 0.541021i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −10.7907 | + | 0.358761i | −0.896121 | + | 0.0297935i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | − | 1.00000i | − | 0.0824786i | ||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 14.1265 | 1.15729 | 0.578645 | − | 0.815580i | \(-0.303582\pi\) | ||||
0.578645 | + | 0.815580i | \(0.303582\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −6.07717 | −0.494553 | −0.247276 | − | 0.968945i | \(-0.579536\pi\) | ||||
−0.247276 | + | 0.968945i | \(0.579536\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 3.49264i | − | 0.282363i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 21.5815 | − | 0.717522i | 1.73346 | − | 0.0576327i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 11.7266i | − | 0.935888i | −0.883758 | − | 0.467944i | \(-0.844995\pi\) | ||
0.883758 | − | 0.467944i | \(-0.155005\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 1.70279 | 0.135040 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −20.2218 | −1.59370 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 7.31371i | 0.572854i | 0.958102 | + | 0.286427i | \(0.0924676\pi\) | ||||
−0.958102 | + | 0.286427i | \(0.907532\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0.480708 | + | 14.4586i | 0.0374231 | + | 1.12560i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 21.0420i | 1.62828i | 0.580670 | + | 0.814139i | \(0.302791\pi\) | ||||
−0.580670 | + | 0.814139i | \(0.697209\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.00000 | −0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 2.21016 | 0.169015 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 18.9706i | 1.44231i | 0.692776 | + | 0.721153i | \(0.256387\pi\) | ||||
−0.692776 | + | 0.721153i | \(0.743613\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −0.939333 | − | 14.1109i | −0.0710069 | − | 1.06668i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − | 6.46967i | − | 0.486290i | ||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 20.4099 | 1.52551 | 0.762753 | − | 0.646690i | \(-0.223847\pi\) | ||||
0.762753 | + | 0.646690i | \(0.223847\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 24.8934 | 1.85031 | 0.925156 | − | 0.379588i | \(-0.123934\pi\) | ||||
0.925156 | + | 0.379588i | \(0.123934\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 2.66421i | 0.196944i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0.515605 | + | 15.5083i | 0.0379080 | + | 1.14019i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 22.5962i | 1.65240i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −2.82843 | −0.205738 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 14.9853 | 1.08430 | 0.542148 | − | 0.840283i | \(-0.317611\pi\) | ||||
0.542148 | + | 0.840283i | \(0.317611\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 18.7990i | 1.35318i | 0.736360 | + | 0.676590i | \(0.236543\pi\) | ||||
−0.736360 | + | 0.676590i | \(0.763457\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −2.23483 | + | 0.0743018i | −0.160040 | + | 0.00532086i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1.92857i | 0.137405i | 0.997637 | + | 0.0687023i | \(0.0218859\pi\) | ||||
−0.997637 | + | 0.0687023i | \(0.978114\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −10.0239 | −0.710572 | −0.355286 | − | 0.934758i | \(-0.615617\pi\) | ||||
−0.355286 | + | 0.934758i | \(0.615617\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −7.70279 | −0.543313 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 13.6569i | 0.958523i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −0.332104 | + | 0.0110415i | −0.0231952 | + | 0.000771173i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 7.14949i | 0.496924i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −14.2990 | −0.989081 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −20.2751 | −1.39580 | −0.697899 | − | 0.716197i | \(-0.745881\pi\) | ||||
−0.697899 | + | 0.716197i | \(0.745881\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 11.0879i | 0.759733i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0.225772 | + | 6.79073i | 0.0153975 | + | 0.463124i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 27.3137i | − | 1.85418i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 5.76776 | 0.389749 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −3.49264 | −0.234940 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 16.1881i | 1.08403i | 0.840368 | + | 0.542017i | \(0.182339\pi\) | ||||
−0.840368 | + | 0.542017i | \(0.817661\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −4.98896 | + | 0.332104i | −0.332597 | + | 0.0221403i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 23.0879i | 1.53240i | 0.642602 | + | 0.766200i | \(0.277855\pi\) | ||||
−0.642602 | + | 0.766200i | \(0.722145\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 4.30886 | 0.284738 | 0.142369 | − | 0.989814i | \(-0.454528\pi\) | ||||
0.142369 | + | 0.989814i | \(0.454528\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 18.2990 | 1.20398 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 1.53857i | 0.100795i | 0.998729 | + | 0.0503977i | \(0.0160489\pi\) | ||||
−0.998729 | + | 0.0503977i | \(0.983951\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −0.504563 | − | 15.1761i | −0.0329141 | − | 0.989983i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − | 10.0239i | − | 0.651119i | ||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −17.8514 | −1.15471 | −0.577355 | − | 0.816493i | \(-0.695915\pi\) | ||||
−0.577355 | + | 0.816493i | \(0.695915\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3.95406 | 0.254703 | 0.127352 | − | 0.991858i | \(-0.459352\pi\) | ||||
0.127352 | + | 0.991858i | \(0.459352\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000i | 0.0641500i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −2.23483 | + | 0.0743018i | −0.142778 | + | 0.00474697i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 2.21016i | − | 0.140629i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 2.27171 | 0.143964 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −3.42284 | −0.216048 | −0.108024 | − | 0.994148i | \(-0.534452\pi\) | ||||
−0.108024 | + | 0.994148i | \(0.534452\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 46.2548i | − | 2.90802i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −7.80546 | + | 0.259509i | −0.488797 | + | 0.0162511i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 3.14772i | − | 0.196349i | −0.995169 | − | 0.0981746i | \(-0.968700\pi\) | ||
0.995169 | − | 0.0981746i | \(-0.0313004\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 19.6274 | 1.21959 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 4.82843 | 0.298872 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 13.7144i | 0.845669i | 0.906207 | + | 0.422835i | \(0.138965\pi\) | ||||
−0.906207 | + | 0.422835i | \(0.861035\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −0.126521 | − | 3.80546i | −0.00777210 | − | 0.233767i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 9.21104i | 0.563707i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −9.84316 | −0.600148 | −0.300074 | − | 0.953916i | \(-0.597011\pi\) | ||||
−0.300074 | + | 0.953916i | \(0.597011\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2.86216 | 0.173864 | 0.0869320 | − | 0.996214i | \(-0.472294\pi\) | ||||
0.0869320 | + | 0.996214i | \(0.472294\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 2.82843i | 0.171184i | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 32.2769 | − | 2.14860i | 1.94637 | − | 0.129566i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 6.24389i | 0.375159i | 0.982249 | + | 0.187580i | \(0.0600643\pi\) | ||||
−0.982249 | + | 0.187580i | \(0.939936\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −9.65685 | −0.578141 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −31.3869 | −1.87239 | −0.936193 | − | 0.351486i | \(-0.885677\pi\) | ||||
−0.936193 | + | 0.351486i | \(0.885677\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2.56496i | 0.152471i | 0.997090 | + | 0.0762354i | \(0.0242901\pi\) | ||||
−0.997090 | + | 0.0762354i | \(0.975710\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −0.164219 | − | 4.93933i | −0.00972747 | − | 0.292581i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0.420314i | 0.0248104i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 4.80150 | 0.282441 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 8.11091 | 0.475470 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 0.834895i | 0.0487751i | 0.999703 | + | 0.0243875i | \(0.00776357\pi\) | ||||
−0.999703 | + | 0.0243875i | \(0.992236\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −14.4586 | + | 0.480708i | −0.841814 | + | 0.0279879i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − | 6.46967i | − | 0.375408i | ||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 7.14949 | 0.413466 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 8.59441 | 0.495374 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − | 16.1421i | − | 0.927341i | ||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 5.95406 | − | 0.197955i | 0.340929 | − | 0.0113349i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 17.7556i | 1.01336i | 0.862133 | + | 0.506682i | \(0.169128\pi\) | ||||
−0.862133 | + | 0.506682i | \(0.830872\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 19.5815 | 1.11395 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1.35965 | 0.0770985 | 0.0385493 | − | 0.999257i | \(-0.487726\pi\) | ||||
0.0385493 | + | 0.999257i | \(0.487726\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 7.75611i | 0.438401i | 0.975680 | + | 0.219201i | \(0.0703449\pi\) | ||||
−0.975680 | + | 0.219201i | \(0.929655\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0.210157 | + | 6.32106i | 0.0118410 | + | 0.356152i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 9.38514i | − | 0.527122i | −0.964643 | − | 0.263561i | \(-0.915103\pi\) | ||
0.964643 | − | 0.263561i | \(-0.0848971\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −31.2383 | −1.74901 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1.35965 | 0.0758881 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 7.71927i | − | 0.429512i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0.332104 | + | 4.98896i | 0.0184218 | + | 0.276738i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − | 3.49264i | − | 0.193143i | ||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −19.2071 | −1.05892 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −16.0576 | −0.882605 | −0.441303 | − | 0.897358i | \(-0.645483\pi\) | ||||
−0.441303 | + | 0.897358i | \(0.645483\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − | 6.93933i | − | 0.380273i | ||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0.572331 | + | 17.2145i | 0.0312698 | + | 0.940526i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 11.0698i | 0.603011i | 0.953464 | + | 0.301506i | \(0.0974892\pi\) | ||||
−0.953464 | + | 0.301506i | \(0.902511\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −12.4320 | −0.675212 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 62.4766 | 3.38330 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 16.9706i | − | 0.916324i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 15.9779 | − | 0.531220i | 0.860222 | − | 0.0285999i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − | 29.6127i | − | 1.58969i | −0.606811 | − | 0.794846i | \(-0.707551\pi\) | ||
0.606811 | − | 0.794846i | \(-0.292449\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −17.1183 | −0.916319 | −0.458160 | − | 0.888870i | \(-0.651491\pi\) | ||||
−0.458160 | + | 0.888870i | \(0.651491\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.00000 | 0.0533761 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 18.3245i | − | 0.975313i | −0.873035 | − | 0.487657i | \(-0.837852\pi\) | ||
0.873035 | − | 0.487657i | \(-0.162148\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 24.7797 | − | 0.823854i | 1.31517 | − | 0.0437256i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 9.87867i | 0.522834i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 27.1356 | 1.43216 | 0.716082 | − | 0.698016i | \(-0.245933\pi\) | ||||
0.716082 | + | 0.698016i | \(0.245933\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −14.1152 | −0.742906 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 30.8566i | 1.61955i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −0.428555 | − | 12.8900i | −0.0224316 | − | 0.674692i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 15.1855i | 0.792679i | 0.918104 | + | 0.396340i | \(0.129720\pi\) | ||||
−0.918104 | + | 0.396340i | \(0.870280\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0.148604 | 0.00773599 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −4.81623 | −0.250046 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 22.1776i | − | 1.14831i | −0.818745 | − | 0.574157i | \(-0.805330\pi\) | ||
0.818745 | − | 0.574157i | \(-0.194670\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1.11289 | + | 11.1248i | 0.0574692 | + | 0.574483i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 4.82843i | − | 0.248677i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 14.7604 | 0.758191 | 0.379096 | − | 0.925358i | \(-0.376235\pi\) | ||||
0.379096 | + | 0.925358i | \(0.376235\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 18.6200 | 0.953934 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 9.33238i | − | 0.476862i | −0.971159 | − | 0.238431i | \(-0.923367\pi\) | ||
0.971159 | − | 0.238431i | \(-0.0766331\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.35965 | − | 40.8952i | −0.0692940 | − | 2.08421i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − | 3.03858i | − | 0.154460i | ||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 3.09618 | 0.156982 | 0.0784912 | − | 0.996915i | \(-0.474990\pi\) | ||||
0.0784912 | + | 0.996915i | \(0.474990\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 24.9706 | 1.26282 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0.751258i | 0.0378960i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −22.4016 | + | 0.744790i | −1.12715 | + | 0.0374745i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 7.26777i | 0.364759i | 0.983228 | + | 0.182379i | \(0.0583799\pi\) | ||||
−0.983228 | + | 0.182379i | \(0.941620\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −6.25127 | −0.312955 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −8.40164 | −0.419558 | −0.209779 | − | 0.977749i | \(-0.567274\pi\) | ||||
−0.209779 | + | 0.977749i | \(0.567274\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 9.65685i | 0.481042i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 2.23483 | − | 0.0743018i | 0.111050 | − | 0.00369209i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 44.8952i | 2.22537i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −11.5815 | −0.572666 | −0.286333 | − | 0.958130i | \(-0.592436\pi\) | ||||
−0.286333 | + | 0.958130i | \(0.592436\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1.08794 | −0.0536639 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 18.2990i | 0.900434i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −0.168792 | − | 5.07689i | −0.00828568 | − | 0.249215i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0.420314i | 0.0205829i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −24.7071 | −1.20702 | −0.603510 | − | 0.797355i | \(-0.706232\pi\) | ||||
−0.603510 | + | 0.797355i | \(0.706232\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −20.7769 | −1.01260 | −0.506302 | − | 0.862356i | \(-0.668988\pi\) | ||||
−0.506302 | + | 0.862356i | \(0.668988\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 6.79073i | 0.330177i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1.15992 | + | 17.4246i | 0.0562643 | + | 0.845218i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 7.53552i | − | 0.364669i | ||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −6.46967 | −0.312358 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −16.6694 | −0.802936 | −0.401468 | − | 0.915873i | \(-0.631500\pi\) | ||||
−0.401468 | + | 0.915873i | \(0.631500\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 12.8860i | − | 0.619263i | −0.950857 | − | 0.309631i | \(-0.899794\pi\) | ||
0.950857 | − | 0.309631i | \(-0.100206\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −0.358761 | − | 10.7907i | −0.0172013 | − | 0.517376i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 15.8015i | 0.755888i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 37.1924 | 1.77510 | 0.887548 | − | 0.460716i | \(-0.152407\pi\) | ||||
0.887548 | + | 0.460716i | \(0.152407\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 33.0693i | − | 1.57117i | −0.618755 | − | 0.785584i | \(-0.712363\pi\) | ||
0.618755 | − | 0.785584i | \(-0.287637\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 20.5851 | − | 0.684397i | 0.975829 | − | 0.0324435i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 14.1265i | 0.668161i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 10.7448 | 0.507078 | 0.253539 | − | 0.967325i | \(-0.418405\pi\) | ||||
0.253539 | + | 0.967325i | \(0.418405\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −0.961416 | −0.0452713 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − | 6.07717i | − | 0.285530i | ||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 6.32106 | − | 0.210157i | 0.296336 | − | 0.00985232i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 21.9419i | − | 1.02640i | −0.858270 | − | 0.513198i | \(-0.828460\pi\) | ||
0.858270 | − | 0.513198i | \(-0.171540\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 3.49264 | 0.163022 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 22.0034 | 1.02480 | 0.512401 | − | 0.858747i | \(-0.328756\pi\) | ||||
0.512401 | + | 0.858747i | \(0.328756\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 32.0208i | − | 1.48813i | −0.668106 | − | 0.744066i | \(-0.732895\pi\) | ||
0.668106 | − | 0.744066i | \(-0.267105\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0.717522 | + | 21.5815i | 0.0332743 | + | 1.00082i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 25.3596i | 1.17350i | 0.809767 | + | 0.586752i | \(0.199594\pi\) | ||||
−0.809767 | + | 0.586752i | \(0.800406\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 21.7868 | 1.00602 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 11.7266 | 0.540335 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 19.6586i | 0.903905i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −11.0264 | + | 0.734003i | −0.505925 | + | 0.0336783i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1.70279i | 0.0779655i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 9.46231 | 0.432344 | 0.216172 | − | 0.976355i | \(-0.430643\pi\) | ||||
0.216172 | + | 0.976355i | \(0.430643\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −6.93933 | −0.316406 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − | 20.2218i | − | 0.920124i | ||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −0.602655 | − | 18.1265i | −0.0273651 | − | 0.823083i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 22.3327i | − | 1.01199i | −0.862536 | − | 0.505996i | \(-0.831125\pi\) | ||
0.862536 | − | 0.505996i | \(-0.168875\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −7.31371 | −0.330737 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −29.8762 | −1.34829 | −0.674146 | − | 0.738598i | \(-0.735488\pi\) | ||||
−0.674146 | + | 0.738598i | \(0.735488\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 16.8639i | − | 0.759513i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −14.4586 | + | 0.480708i | −0.649867 | + | 0.0216062i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 31.3614i | − | 1.40675i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −24.7145 | −1.10637 | −0.553186 | − | 0.833058i | \(-0.686588\pi\) | ||||
−0.553186 | + | 0.833058i | \(0.686588\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −21.0420 | −0.940087 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 17.2267i | 0.768099i | 0.923313 | + | 0.384049i | \(0.125471\pi\) | ||||
−0.923313 | + | 0.384049i | \(0.874529\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −36.0750 | + | 1.19939i | −1.60532 | + | 0.0533721i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − | 1.00000i | − | 0.0444116i | ||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −26.1430 | −1.15877 | −0.579384 | − | 0.815055i | \(-0.696707\pi\) | ||||
−0.579384 | + | 0.815055i | \(0.696707\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −16.3137 | −0.721675 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 2.21016i | 0.0975808i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −1.45494 | − | 43.7613i | −0.0641122 | − | 1.92835i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 43.9338i | − | 1.93220i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −18.9706 | −0.832715 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −33.0165 | −1.44648 | −0.723240 | − | 0.690597i | \(-0.757348\pi\) | ||||
−0.723240 | + | 0.690597i | \(0.757348\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 32.2751i | − | 1.41129i | −0.708564 | − | 0.705646i | \(-0.750657\pi\) | ||
0.708564 | − | 0.705646i | \(-0.249343\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 14.1109 | − | 0.939333i | 0.615850 | − | 0.0409958i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 33.7279i | 1.46921i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −28.1152 | −1.22240 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 6.46967 | 0.280760 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 0.148604i | − | 0.00643674i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −0.101024 | − | 3.03858i | −0.00436766 | − | 0.131369i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 20.4099i | 0.880752i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −6.46967 | −0.278668 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −2.21193 | −0.0950983 | −0.0475491 | − | 0.998869i | \(-0.515141\pi\) | ||||
−0.0475491 | + | 0.998869i | \(0.515141\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 24.8934i | 1.06828i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −7.80546 | + | 0.259509i | −0.334349 | + | 0.0111161i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 31.4822i | − | 1.34608i | −0.739605 | − | 0.673041i | \(-0.764988\pi\) | ||
0.739605 | − | 0.673041i | \(-0.235012\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −2.66421 | −0.113706 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 10.6716 | 0.454625 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 28.3517i | 1.20564i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −15.5083 | + | 0.515605i | −0.658289 | + | 0.0218862i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 35.1209i | 1.48812i | 0.668112 | + | 0.744061i | \(0.267103\pi\) | ||||
−0.668112 | + | 0.744061i | \(0.732897\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −3.03858 | −0.128518 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −22.5962 | −0.954012 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 30.3467i | 1.27896i | 0.768808 | + | 0.639480i | \(0.220850\pi\) | ||||
−0.768808 | + | 0.639480i | \(0.779150\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0.923718 | + | 27.7834i | 0.0388611 | + | 1.16886i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − | 2.82843i | − | 0.118783i | ||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −30.8327 | −1.29257 | −0.646287 | − | 0.763094i | \(-0.723679\pi\) | ||||
−0.646287 | + | 0.763094i | \(0.723679\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −21.1832 | −0.886490 | −0.443245 | − | 0.896400i | \(-0.646173\pi\) | ||||
−0.443245 | + | 0.896400i | \(0.646173\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 14.9853i | 0.626019i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −2.37438 | − | 35.6685i | −0.0990183 | − | 1.48748i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 22.6594i | − | 0.943322i | −0.881780 | − | 0.471661i | \(-0.843655\pi\) | ||
0.881780 | − | 0.471661i | \(-0.156345\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −18.7990 | −0.781259 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −6.42537 | −0.266569 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 11.0165i | − | 0.456257i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −0.0743018 | − | 2.23483i | −0.00307200 | − | 0.0923990i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 13.6529i | − | 0.563515i | −0.959486 | − | 0.281758i | \(-0.909083\pi\) | ||
0.959486 | − | 0.281758i | \(-0.0909174\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −21.3432 | −0.879430 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −1.92857 | −0.0793306 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 18.7448i | − | 0.769756i | −0.922967 | − | 0.384878i | \(-0.874243\pi\) | ||
0.922967 | − | 0.384878i | \(-0.125757\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 22.0772 | − | 0.734003i | 0.905076 | − | 0.0300912i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − | 10.0239i | − | 0.410249i | ||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −48.7885 | −1.99345 | −0.996723 | − | 0.0808922i | \(-0.974223\pi\) | ||||
−0.996723 | + | 0.0808922i | \(0.974223\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 16.5870 | 0.676599 | 0.338300 | − | 0.941038i | \(-0.390148\pi\) | ||||
0.338300 | + | 0.941038i | \(0.390148\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − | 7.70279i | − | 0.313682i | ||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 68.9593 | − | 2.29270i | 2.80359 | − | 0.0932115i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 29.0642i | 1.17968i | 0.807520 | + | 0.589840i | \(0.200809\pi\) | ||||
−0.807520 | + | 0.589840i | \(0.799191\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −13.6569 | −0.553404 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 6.79073 | 0.274723 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 22.3926i | 0.904430i | 0.891909 | + | 0.452215i | \(0.149366\pi\) | ||||
−0.891909 | + | 0.452215i | \(0.850634\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −0.0110415 | − | 0.332104i | −0.000445237 | − | 0.0133917i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1.63136i | 0.0656760i | 0.999461 | + | 0.0328380i | \(0.0104545\pi\) | ||||
−0.999461 | + | 0.0328380i | \(0.989545\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −37.4485 | −1.50518 | −0.752591 | − | 0.658489i | \(-0.771196\pi\) | ||||
−0.752591 | + | 0.658489i | \(0.771196\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −7.14949 | −0.286899 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − | 26.0528i | − | 1.04378i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 24.7794 | − | 3.31371i | 0.991177 | − | 0.132548i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − | 14.2990i | − | 0.571046i | ||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −24.2366 | −0.966375 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −10.7193 | −0.426728 | −0.213364 | − | 0.976973i | \(-0.568442\pi\) | ||||
−0.213364 | + | 0.976973i | \(0.568442\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − | 20.2751i | − | 0.805864i | ||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −1.38350 | − | 41.6127i | −0.0549026 | − | 1.65135i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 1.00000i | − | 0.0396214i | ||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −11.0879 | −0.438632 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −31.0183 | −1.22515 | −0.612574 | − | 0.790413i | \(-0.709866\pi\) | ||||
−0.612574 | + | 0.790413i | \(0.709866\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 12.4515i | 0.491041i | 0.969391 | + | 0.245520i | \(0.0789589\pi\) | ||||
−0.969391 | + | 0.245520i | \(0.921041\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −6.79073 | + | 0.225772i | −0.267385 | + | 0.00888977i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 41.6538i | 1.63758i | 0.574093 | + | 0.818790i | \(0.305355\pi\) | ||||
−0.574093 | + | 0.818790i | \(0.694645\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −41.8566 | −1.64301 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 27.3137 | 1.07051 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 3.83095i | 0.149917i | 0.997187 | + | 0.0749584i | \(0.0238824\pi\) | ||||
−0.997187 | + | 0.0749584i | \(0.976118\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1.67894 | − | 0.0558199i | 0.0656015 | − | 0.00218106i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 5.76776i | 0.225022i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −41.8926 | −1.63191 | −0.815953 | − | 0.578119i | \(-0.803787\pi\) | ||||
−0.815953 | + | 0.578119i | \(0.803787\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 40.8523 | 1.58897 | 0.794485 | − | 0.607284i | \(-0.207741\pi\) | ||||
0.794485 | + | 0.607284i | \(0.207741\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − | 3.49264i | − | 0.135643i | ||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0.464480 | + | 13.9705i | 0.0180118 | + | 0.541754i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 34.5208i | 1.33665i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −16.1881 | −0.625867 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 17.2365 | 0.665409 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 45.2401i | 1.74388i | 0.489615 | + | 0.871939i | \(0.337137\pi\) | ||||
−0.489615 | + | 0.871939i | \(0.662863\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −0.332104 | − | 4.98896i | −0.0127827 | − | 0.192025i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 3.58146i | − | 0.137647i | −0.997629 | − | 0.0688233i | \(-0.978076\pi\) | ||
0.997629 | − | 0.0688233i | \(-0.0219245\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −22.9411 | −0.880399 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −23.0879 | −0.884732 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 44.8402i | 1.71576i | 0.513848 | + | 0.857882i | \(0.328220\pi\) | ||||
−0.513848 | + | 0.857882i | \(0.671780\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0.0808356 | + | 2.43136i | 0.00308857 | + | 0.0928973i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 4.30886i | 0.164393i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 1.70279 | 0.0648712 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −18.2891 | −0.695750 | −0.347875 | − | 0.937541i | \(-0.613097\pi\) | ||||
−0.347875 | + | 0.937541i | \(0.613097\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 18.2990i | 0.695121i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0.939333 | − | 0.0312301i | 0.0356309 | − | 0.00118463i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 0.519018i | − | 0.0196592i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −1.53857 | −0.0581942 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 36.0667 | 1.36222 | 0.681111 | − | 0.732180i | \(-0.261497\pi\) | ||||
0.681111 | + | 0.732180i | \(0.261497\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 15.3370i | − | 0.578447i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 15.1761 | − | 0.504563i | 0.571567 | − | 0.0190030i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 45.6569i | 1.71710i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 11.7769 | 0.442291 | 0.221146 | − | 0.975241i | \(-0.429020\pi\) | ||||
0.221146 | + | 0.975241i | \(0.429020\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 10.0239 | 0.375924 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 69.0416i | − | 2.58563i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0.480708 | + | 14.4586i | 0.0179775 | + | 0.540722i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − | 17.8514i | − | 0.666673i | ||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −46.7261 | −1.74259 | −0.871295 | − | 0.490759i | \(-0.836719\pi\) | ||||
−0.871295 | + | 0.490759i | \(0.836719\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −55.3847 | −2.06264 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 3.95406i | 0.147053i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −24.0888 | + | 1.60354i | −0.894636 | + | 0.0595540i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 37.8038i | − | 1.40207i | −0.713129 | − | 0.701033i | \(-0.752723\pi\) | ||
0.713129 | − | 0.701033i | \(-0.247277\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −10.6127 | −0.392524 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 20.9411i | 0.773477i | 0.922189 | + | 0.386739i | \(0.126398\pi\) | ||||
−0.922189 | + | 0.386739i | \(0.873602\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −0.0743018 | − | 2.23483i | −0.00274066 | − | 0.0824331i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 49.8345i | 1.83568i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 31.5012 | 1.15879 | 0.579396 | − | 0.815046i | \(-0.303289\pi\) | ||||
0.579396 | + | 0.815046i | \(0.303289\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 2.21016 | 0.0811922 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 2.96483i | 0.108769i | 0.998520 | + | 0.0543845i | \(0.0173197\pi\) | ||||
−0.998520 | + | 0.0543845i | \(0.982680\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 31.5704 | − | 1.04963i | 1.15665 | − | 0.0384553i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 2.27171i | 0.0831176i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −3.84566 | −0.140517 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −10.0295 | −0.365980 | −0.182990 | − | 0.983115i | \(-0.558578\pi\) | ||||
−0.182990 | + | 0.983115i | \(0.558578\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − | 3.42284i | − | 0.124735i | ||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −13.5815 | + | 0.451545i | −0.494280 | + | 0.0164334i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 36.4731i | − | 1.32564i | −0.748780 | − | 0.662818i | \(-0.769360\pi\) | ||
0.748780 | − | 0.662818i | \(-0.230640\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 46.2548 | 1.67894 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −9.88085 | −0.358181 | −0.179090 | − | 0.983833i | \(-0.557315\pi\) | ||||
−0.179090 | + | 0.983833i | \(0.557315\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 9.87867i | 0.357632i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −0.259509 | − | 7.80546i | −0.00938257 | − | 0.282207i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 6.46967i | − | 0.233606i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −32.6274 | −1.17657 | −0.588287 | − | 0.808652i | \(-0.700198\pi\) | ||||
−0.588287 | + | 0.808652i | \(0.700198\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 3.14772 | 0.113362 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 44.2950i | 1.59318i | 0.604519 | + | 0.796591i | \(0.293365\pi\) | ||||
−0.604519 | + | 0.796591i | \(0.706635\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 48.1776 | − | 3.20708i | 1.73059 | − | 0.115202i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 19.6274i | 0.704129i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0.328437 | 0.0117675 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 71.7352 | 2.56689 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 4.82843i | 0.172554i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −0.871311 | − | 26.2071i | −0.0310984 | − | 0.935372i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 24.0068i | − | 0.855751i | −0.903838 | − | 0.427875i | \(-0.859262\pi\) | ||
0.903838 | − | 0.427875i | \(-0.140738\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −13.7144 | −0.488247 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 35.1629 | 1.25025 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 2.66421i | 0.0946088i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 3.80546 | − | 0.126521i | 0.134966 | − | 0.00448722i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 42.4271i | 1.50285i | 0.659821 | + | 0.751423i | \(0.270632\pi\) | ||||
−0.659821 | + | 0.751423i | \(0.729368\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 23.7175 | 0.839066 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −9.21104 | −0.325456 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − | 37.3155i | − | 1.31683i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −45.1924 | + | 1.50252i | −1.59282 | + | 0.0529568i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − | 9.84316i | − | 0.346495i | ||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 12.0495 | 0.423637 | 0.211819 | − | 0.977309i | \(-0.432061\pi\) | ||||
0.211819 | + | 0.977309i | \(0.432061\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 34.5619 | 1.21363 | 0.606816 | − | 0.794842i | \(-0.292446\pi\) | ||||
0.606816 | + | 0.794842i | \(0.292446\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 2.86216i | 0.100380i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0.543422 | + | 16.3449i | 0.0190352 | + | 0.572538i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 6.71575i | − | 0.234954i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −2.82843 | −0.0988332 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −1.92119 | −0.0670500 | −0.0335250 | − | 0.999438i | \(-0.510673\pi\) | ||||
−0.0335250 | + | 0.999438i | \(0.510673\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 36.9246i | − | 1.28711i | −0.765399 | − | 0.643556i | \(-0.777458\pi\) | ||
0.765399 | − | 0.643556i | \(-0.222542\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 2.14860 | + | 32.2769i | 0.0748048 | + | 1.12374i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 20.9501i | − | 0.728507i | −0.931300 | − | 0.364254i | \(-0.881324\pi\) | ||
0.931300 | − | 0.364254i | \(-0.118676\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 3.55255 | 0.123385 | 0.0616926 | − | 0.998095i | \(-0.480350\pi\) | ||||
0.0616926 | + | 0.998095i | \(0.480350\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −6.24389 | −0.216598 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 3.49264i | − | 0.121013i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1.56346 | + | 47.0254i | 0.0541057 | + | 1.62738i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − | 9.65685i | − | 0.333790i | ||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −12.2768 | −0.423841 | −0.211920 | − | 0.977287i | \(-0.567972\pi\) | ||||
−0.211920 | + | 0.977287i | \(0.567972\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −5.68629 | −0.196079 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − | 31.3869i | − | 1.08102i | ||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −2.23483 | + | 0.0743018i | −0.0768806 | + | 0.00255606i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 87.2756i | − | 2.99882i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −2.56496 | −0.0880291 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 49.6127 | 1.70070 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 10.6734i | 0.365449i | 0.983164 | + | 0.182724i | \(0.0584916\pi\) | ||||
−0.983164 | + | 0.182724i | \(0.941508\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 4.93933 | − | 0.164219i | 0.168922 | − | 0.00561616i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 54.5324i | 1.86279i | 0.364006 | + | 0.931396i | \(0.381409\pi\) | ||||
−0.364006 | + | 0.931396i | \(0.618591\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −45.6218 | −1.55660 | −0.778298 | − | 0.627894i | \(-0.783917\pi\) | ||||
−0.778298 | + | 0.627894i | \(0.783917\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −0.420314 | −0.0143243 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 18.1798i | − | 0.618849i | −0.950924 | − | 0.309424i | \(-0.899864\pi\) | ||
0.950924 | − | 0.309424i | \(-0.100136\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1.40955 | + | 42.3960i | 0.0479260 | + | 1.44151i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 4.80150i | 0.163067i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −64.8510 | −2.19992 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −7.70279 | −0.260999 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 8.11091i | 0.274513i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −3.14772 | − | 31.4657i | −0.106412 | − | 1.06374i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 23.1611i | − | 0.782096i | −0.920370 | − | 0.391048i | \(-0.872113\pi\) | ||
0.920370 | − | 0.391048i | \(-0.127887\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −0.834895 | −0.0281603 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 16.7358 | 0.563843 | 0.281921 | − | 0.959438i | \(-0.409028\pi\) | ||||
0.281921 | + | 0.959438i | \(0.409028\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 20.3959i | 0.686377i | 0.939267 | + | 0.343189i | \(0.111507\pi\) | ||||
−0.939267 | + | 0.343189i | \(0.888493\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −0.480708 | − | 14.4586i | −0.0161588 | − | 0.486021i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 58.7395i | − | 1.97228i | −0.165912 | − | 0.986140i | \(-0.553057\pi\) | ||
0.165912 | − | 0.986140i | \(-0.446943\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −52.6654 | −1.76634 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 6.46967 | 0.216742 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 15.0086i | 0.502243i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 45.6127 | − | 1.51649i | 1.52466 | − | 0.0506907i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 7.14949i | 0.238715i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −46.6274 | −1.55511 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 5.94723 | 0.198131 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 8.59441i | 0.286004i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 55.6326 | − | 1.84962i | 1.84929 | − | 0.0614836i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 17.9853i | 0.597192i | 0.954380 | + | 0.298596i | \(0.0965183\pi\) | ||||
−0.954380 | + | 0.298596i | \(0.903482\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 16.1421 | 0.535401 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −55.0269 | −1.82312 | −0.911561 | − | 0.411165i | \(-0.865122\pi\) | ||||
−0.911561 | + | 0.411165i | \(0.865122\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 14.6972i | − | 0.486407i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0.197955 | + | 5.95406i | 0.00654421 | + | 0.196835i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − | 2.12488i | − | 0.0701697i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1.00913 | 0.0332880 | 0.0166440 | − | 0.999861i | \(-0.494702\pi\) | ||||
0.0166440 | + | 0.999861i | \(0.494702\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −17.7556 | −0.585066 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 11.0879i | 0.364964i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2.30458 | + | 34.6200i | 0.0757742 | + | 1.13830i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 19.5815i | 0.643139i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 23.1407 | 0.759222 | 0.379611 | − | 0.925146i | \(-0.376058\pi\) | ||||
0.379611 | + | 0.925146i | \(0.376058\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2.21016 | 0.0724350 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 1.35965i | 0.0445128i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 1.67894 | + | 50.4987i | 0.0549071 | + | 1.65148i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 8.72667i | − | 0.285088i | −0.989788 | − | 0.142544i | \(-0.954472\pi\) | ||
0.989788 | − | 0.142544i | \(-0.0455282\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −7.75611 | −0.253111 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 5.24965 | 0.171134 | 0.0855668 | − | 0.996332i | \(-0.472730\pi\) | ||||
0.0855668 | + | 0.996332i | \(0.472730\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1.06244i | 0.0345978i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −6.32106 | + | 0.210157i | −0.205624 | + | 0.00683641i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 17.0420i | 0.553791i | 0.960900 | + | 0.276895i | \(0.0893055\pi\) | ||||
−0.960900 | + | 0.276895i | \(0.910694\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 5.76776 | 0.187229 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 9.38514 | 0.304334 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 5.16243i | − | 0.167227i | −0.996498 | − | 0.0836137i | \(-0.973354\pi\) | ||
0.996498 | − | 0.0836137i | \(-0.0266462\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 33.4896 | − | 1.11343i | 1.08370 | − | 0.0360298i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − | 31.2383i | − | 1.00979i | ||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 3.07715 | 0.0993663 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 62.2548 | 2.00822 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 1.35965i | 0.0438140i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 1.39680 | + | 42.0126i | 0.0449645 | + | 1.35243i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 40.3657i | − | 1.29807i | −0.760757 | − | 0.649037i | \(-0.775172\pi\) | ||
0.760757 | − | 0.649037i | \(-0.224828\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 7.71927 | 0.247979 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 20.2322 | 0.649283 | 0.324642 | − | 0.945837i | \(-0.394756\pi\) | ||||
0.324642 | + | 0.945837i | \(0.394756\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 1.18883i | − | 0.0381121i | ||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −4.98896 | + | 0.332104i | −0.159775 | + | 0.0106358i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 30.4034i | − | 0.972691i | −0.873766 | − | 0.486346i | \(-0.838330\pi\) | ||
0.873766 | − | 0.486346i | \(-0.161670\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 59.5924 | 1.90458 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 3.49264 | 0.111511 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 50.4250i | − | 1.60831i | −0.594422 | − | 0.804153i | \(-0.702619\pi\) | ||
0.594422 | − | 0.804153i | \(-0.297381\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0.143296 | + | 4.31002i | 0.00456579 | + | 0.137329i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − | 19.2071i | − | 0.611368i | ||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 21.7243 | 0.690793 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −54.1005 | −1.71856 | −0.859279 | − | 0.511507i | \(-0.829087\pi\) | ||||
−0.859279 | + | 0.511507i | \(0.829087\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 16.0576i | − | 0.509572i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −22.4016 | + | 0.744790i | −0.710180 | + | 0.0236114i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 39.3921i | 1.24756i | 0.781600 | + | 0.623780i | \(0.214404\pi\) | ||||
−0.781600 | + | 0.623780i | \(0.785596\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 6.93933 | 0.219551 |
(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 | 3120.2.l.o.1249.8 | 8 | ||
4.3 | odd | 2 | 1560.2.l.e.1249.4 | ✓ | 8 | ||
5.4 | even | 2 | inner | 3120.2.l.o.1249.4 | 8 | ||
12.11 | even | 2 | 4680.2.l.f.2809.2 | 8 | |||
20.3 | even | 4 | 7800.2.a.bw.1.3 | 4 | |||
20.7 | even | 4 | 7800.2.a.bv.1.1 | 4 | |||
20.19 | odd | 2 | 1560.2.l.e.1249.8 | yes | 8 | ||
60.59 | even | 2 | 4680.2.l.f.2809.1 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1560.2.l.e.1249.4 | ✓ | 8 | 4.3 | odd | 2 | ||
1560.2.l.e.1249.8 | yes | 8 | 20.19 | odd | 2 | ||
3120.2.l.o.1249.4 | 8 | 5.4 | even | 2 | inner | ||
3120.2.l.o.1249.8 | 8 | 1.1 | even | 1 | trivial | ||
4680.2.l.f.2809.1 | 8 | 60.59 | even | 2 | |||
4680.2.l.f.2809.2 | 8 | 12.11 | even | 2 | |||
7800.2.a.bv.1.1 | 4 | 20.7 | even | 4 | |||
7800.2.a.bw.1.3 | 4 | 20.3 | even | 4 |