Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1710,2,Mod(1369,1710)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1710, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1710.1369");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1710 = 2 \cdot 3^{2} \cdot 5 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1710.d (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: | \(13.6544187456\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.0.5161984.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 4x^{3} + 25x^{2} - 20x + 8 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 190) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1369.4 | ||
Root | \(1.32001 - 1.32001i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1710.1369 |
Dual form | 1710.2.d.d.1369.1 |
$q$-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 \(\left(\mathbb{Z}/1710\mathbb{Z}\right)^\times\).
\(n\) | \(191\) | \(1027\) | \(1351\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) |
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 | ||||||||
\(5\) | −1.80487 | − | 1.32001i | −0.807164 | − | 0.590327i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 4.12489i | − | 1.55906i | −0.626365 | − | 0.779530i | \(-0.715458\pi\) | ||
0.626365 | − | 0.779530i | \(-0.284542\pi\) | |||||||
\(8\) | − | 1.00000i | − | 0.353553i | ||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 1.32001 | − | 1.80487i | 0.417424 | − | 0.570751i | ||||
\(11\) | 2.64002 | 0.795997 | 0.397999 | − | 0.917386i | \(-0.369705\pi\) | ||||
0.397999 | + | 0.917386i | \(0.369705\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.51514i | 0.697574i | 0.937202 | + | 0.348787i | \(0.113406\pi\) | ||||
−0.937202 | + | 0.348787i | \(0.886594\pi\) | |||||||
\(14\) | 4.12489 | 1.10242 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | − | 0.515138i | − | 0.124939i | −0.998047 | − | 0.0624697i | \(-0.980102\pi\) | ||
0.998047 | − | 0.0624697i | \(-0.0198977\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.00000 | −0.229416 | ||||||||
\(20\) | 1.80487 | + | 1.32001i | 0.403582 | + | 0.295164i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 2.64002i | 0.562855i | ||||||||
\(23\) | − | 3.09461i | − | 0.645271i | −0.946523 | − | 0.322635i | \(-0.895431\pi\) | ||
0.946523 | − | 0.322635i | \(-0.104569\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.51514 | + | 4.76491i | 0.303028 | + | 0.952982i | ||||
\(26\) | −2.51514 | −0.493259 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 4.12489i | 0.779530i | ||||||||
\(29\) | −7.79518 | −1.44753 | −0.723765 | − | 0.690047i | \(-0.757590\pi\) | ||||
−0.723765 | + | 0.690047i | \(0.757590\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.67030 | 0.659205 | 0.329603 | − | 0.944120i | \(-0.393085\pi\) | ||||
0.329603 | + | 0.944120i | \(0.393085\pi\) | |||||||
\(32\) | 1.00000i | 0.176777i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0.515138 | 0.0883454 | ||||||||
\(35\) | −5.44490 | + | 7.44490i | −0.920356 | + | 1.25842i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 10.2498i | − | 1.68505i | −0.538656 | − | 0.842526i | \(-0.681068\pi\) | ||
0.538656 | − | 0.842526i | \(-0.318932\pi\) | |||||||
\(38\) | − | 1.00000i | − | 0.162221i | ||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −1.32001 | + | 1.80487i | −0.208712 | + | 0.285376i | ||||
\(41\) | −8.88979 | −1.38835 | −0.694176 | − | 0.719805i | \(-0.744231\pi\) | ||||
−0.694176 | + | 0.719805i | \(0.744231\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 8.64002i | 1.31759i | 0.752322 | + | 0.658796i | \(0.228934\pi\) | ||||
−0.752322 | + | 0.658796i | \(0.771066\pi\) | |||||||
\(44\) | −2.64002 | −0.397999 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 3.09461 | 0.456275 | ||||||||
\(47\) | − | 4.96972i | − | 0.724909i | −0.932002 | − | 0.362454i | \(-0.881939\pi\) | ||
0.932002 | − | 0.362454i | \(-0.118061\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −10.0147 | −1.43067 | ||||||||
\(50\) | −4.76491 | + | 1.51514i | −0.673860 | + | 0.214273i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | − | 2.51514i | − | 0.348787i | ||||||
\(53\) | − | 5.48486i | − | 0.753404i | −0.926335 | − | 0.376702i | \(-0.877058\pi\) | ||
0.926335 | − | 0.376702i | \(-0.122942\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −4.76491 | − | 3.48486i | −0.642500 | − | 0.469899i | ||||
\(56\) | −4.12489 | −0.551211 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | − | 7.79518i | − | 1.02356i | ||||||
\(59\) | 3.15516 | 0.410767 | 0.205384 | − | 0.978682i | \(-0.434156\pi\) | ||||
0.205384 | + | 0.978682i | \(0.434156\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −12.6400 | −1.61839 | −0.809195 | − | 0.587541i | \(-0.800096\pi\) | ||||
−0.809195 | + | 0.587541i | \(0.800096\pi\) | |||||||
\(62\) | 3.67030i | 0.466129i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 3.32001 | − | 4.53951i | 0.411797 | − | 0.563056i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 7.40493i | 0.904656i | 0.891852 | + | 0.452328i | \(0.149406\pi\) | ||||
−0.891852 | + | 0.452328i | \(0.850594\pi\) | |||||||
\(68\) | 0.515138i | 0.0624697i | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −7.44490 | − | 5.44490i | −0.889835 | − | 0.650790i | ||||
\(71\) | −11.1396 | −1.32202 | −0.661012 | − | 0.750376i | \(-0.729873\pi\) | ||||
−0.661012 | + | 0.750376i | \(0.729873\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 2.70436i | − | 0.316521i | −0.987397 | − | 0.158261i | \(-0.949411\pi\) | ||
0.987397 | − | 0.158261i | \(-0.0505886\pi\) | |||||||
\(74\) | 10.2498 | 1.19151 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 1.00000 | 0.114708 | ||||||||
\(77\) | − | 10.8898i | − | 1.24101i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −16.7493 | −1.88444 | −0.942222 | − | 0.334988i | \(-0.891268\pi\) | ||||
−0.942222 | + | 0.334988i | \(0.891268\pi\) | |||||||
\(80\) | −1.80487 | − | 1.32001i | −0.201791 | − | 0.147582i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | − | 8.88979i | − | 0.981714i | ||||||
\(83\) | − | 3.28005i | − | 0.360032i | −0.983664 | − | 0.180016i | \(-0.942385\pi\) | ||
0.983664 | − | 0.180016i | \(-0.0576149\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.679988 | + | 0.929759i | −0.0737551 | + | 0.100847i | ||||
\(86\) | −8.64002 | −0.931678 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | − | 2.64002i | − | 0.281427i | ||||||
\(89\) | −7.60975 | −0.806632 | −0.403316 | − | 0.915061i | \(-0.632142\pi\) | ||||
−0.403316 | + | 0.915061i | \(0.632142\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 10.3747 | 1.08756 | ||||||||
\(92\) | 3.09461i | 0.322635i | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 4.96972 | 0.512588 | ||||||||
\(95\) | 1.80487 | + | 1.32001i | 0.185176 | + | 0.135430i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 3.93945i | − | 0.399990i | −0.979797 | − | 0.199995i | \(-0.935907\pi\) | ||
0.979797 | − | 0.199995i | \(-0.0640926\pi\) | |||||||
\(98\) | − | 10.0147i | − | 1.01164i | ||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −1.51514 | − | 4.76491i | −0.151514 | − | 0.476491i | ||||
\(101\) | 13.7990 | 1.37305 | 0.686524 | − | 0.727107i | \(-0.259136\pi\) | ||||
0.686524 | + | 0.727107i | \(0.259136\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 4.57947i | 0.451229i | 0.974217 | + | 0.225614i | \(0.0724389\pi\) | ||||
−0.974217 | + | 0.225614i | \(0.927561\pi\) | |||||||
\(104\) | 2.51514 | 0.246630 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 5.48486 | 0.532737 | ||||||||
\(107\) | − | 10.3747i | − | 1.00296i | −0.865170 | − | 0.501478i | \(-0.832790\pi\) | ||
0.865170 | − | 0.501478i | \(-0.167210\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −3.01468 | −0.288754 | −0.144377 | − | 0.989523i | \(-0.546118\pi\) | ||||
−0.144377 | + | 0.989523i | \(0.546118\pi\) | |||||||
\(110\) | 3.48486 | − | 4.76491i | 0.332269 | − | 0.454316i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | − | 4.12489i | − | 0.389765i | ||||||
\(113\) | 19.2001i | 1.80620i | 0.429435 | + | 0.903098i | \(0.358713\pi\) | ||||
−0.429435 | + | 0.903098i | \(0.641287\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −4.08492 | + | 5.58538i | −0.380921 | + | 0.520839i | ||||
\(116\) | 7.79518 | 0.723765 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 3.15516i | 0.290456i | ||||||||
\(119\) | −2.12489 | −0.194788 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −4.03028 | −0.366389 | ||||||||
\(122\) | − | 12.6400i | − | 1.14437i | ||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −3.67030 | −0.329603 | ||||||||
\(125\) | 3.55510 | − | 10.6001i | 0.317978 | − | 0.948098i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 14.3103i | − | 1.26984i | −0.772580 | − | 0.634918i | \(-0.781034\pi\) | ||
0.772580 | − | 0.634918i | \(-0.218966\pi\) | |||||||
\(128\) | − | 1.00000i | − | 0.0883883i | ||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 4.53951 | + | 3.32001i | 0.398141 | + | 0.291184i | ||||
\(131\) | 6.56009 | 0.573158 | 0.286579 | − | 0.958057i | \(-0.407482\pi\) | ||||
0.286579 | + | 0.958057i | \(0.407482\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 4.12489i | 0.357673i | ||||||||
\(134\) | −7.40493 | −0.639689 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −0.515138 | −0.0441727 | ||||||||
\(137\) | − | 6.45459i | − | 0.551452i | −0.961236 | − | 0.275726i | \(-0.911082\pi\) | ||
0.961236 | − | 0.275726i | \(-0.0889183\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 23.0596 | 1.95589 | 0.977946 | − | 0.208856i | \(-0.0669740\pi\) | ||||
0.977946 | + | 0.208856i | \(0.0669740\pi\) | |||||||
\(140\) | 5.44490 | − | 7.44490i | 0.460178 | − | 0.629209i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | − | 11.1396i | − | 0.934812i | ||||||
\(143\) | 6.64002i | 0.555267i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 14.0693 | + | 10.2897i | 1.16839 | + | 0.854516i | ||||
\(146\) | 2.70436 | 0.223814 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 10.2498i | 0.842526i | ||||||||
\(149\) | 16.0294 | 1.31318 | 0.656588 | − | 0.754249i | \(-0.271999\pi\) | ||||
0.656588 | + | 0.754249i | \(0.271999\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −14.3103 | −1.16456 | −0.582279 | − | 0.812989i | \(-0.697839\pi\) | ||||
−0.582279 | + | 0.812989i | \(0.697839\pi\) | |||||||
\(152\) | 1.00000i | 0.0811107i | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 10.8898 | 0.877525 | ||||||||
\(155\) | −6.62443 | − | 4.84484i | −0.532087 | − | 0.389147i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 18.0294i | 1.43890i | 0.694544 | + | 0.719450i | \(0.255606\pi\) | ||||
−0.694544 | + | 0.719450i | \(0.744394\pi\) | |||||||
\(158\) | − | 16.7493i | − | 1.33250i | ||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 1.32001 | − | 1.80487i | 0.104356 | − | 0.142688i | ||||
\(161\) | −12.7649 | −1.00602 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2.70058i | 0.211525i | 0.994391 | + | 0.105763i | \(0.0337284\pi\) | ||||
−0.994391 | + | 0.105763i | \(0.966272\pi\) | |||||||
\(164\) | 8.88979 | 0.694176 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 3.28005 | 0.254581 | ||||||||
\(167\) | 8.95035i | 0.692599i | 0.938124 | + | 0.346299i | \(0.112562\pi\) | ||||
−0.938124 | + | 0.346299i | \(0.887438\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 6.67408 | 0.513391 | ||||||||
\(170\) | −0.929759 | − | 0.679988i | −0.0713093 | − | 0.0521527i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | − | 8.64002i | − | 0.658796i | ||||||
\(173\) | − | 0.310323i | − | 0.0235934i | −0.999930 | − | 0.0117967i | \(-0.996245\pi\) | ||
0.999930 | − | 0.0117967i | \(-0.00375510\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 19.6547 | − | 6.24977i | 1.48576 | − | 0.472438i | ||||
\(176\) | 2.64002 | 0.198999 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | − | 7.60975i | − | 0.570375i | ||||||
\(179\) | −1.52982 | −0.114344 | −0.0571720 | − | 0.998364i | \(-0.518208\pi\) | ||||
−0.0571720 | + | 0.998364i | \(0.518208\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −14.7493 | −1.09631 | −0.548154 | − | 0.836377i | \(-0.684669\pi\) | ||||
−0.548154 | + | 0.836377i | \(0.684669\pi\) | |||||||
\(182\) | 10.3747i | 0.769021i | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −3.09461 | −0.228138 | ||||||||
\(185\) | −13.5298 | + | 18.4995i | −0.994732 | + | 1.36011i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 1.35998i | − | 0.0994513i | ||||||
\(188\) | 4.96972i | 0.362454i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −1.32001 | + | 1.80487i | −0.0957637 | + | 0.130939i | ||||
\(191\) | −18.1249 | −1.31147 | −0.655735 | − | 0.754991i | \(-0.727641\pi\) | ||||
−0.655735 | + | 0.754991i | \(0.727641\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 4.56009i | − | 0.328243i | −0.986440 | − | 0.164121i | \(-0.947521\pi\) | ||
0.986440 | − | 0.164121i | \(-0.0524789\pi\) | |||||||
\(194\) | 3.93945 | 0.282836 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 10.0147 | 0.715334 | ||||||||
\(197\) | − | 2.14048i | − | 0.152503i | −0.997089 | − | 0.0762515i | \(-0.975705\pi\) | ||
0.997089 | − | 0.0762515i | \(-0.0242952\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −16.5639 | −1.17418 | −0.587091 | − | 0.809521i | \(-0.699727\pi\) | ||||
−0.587091 | + | 0.809521i | \(0.699727\pi\) | |||||||
\(200\) | 4.76491 | − | 1.51514i | 0.336930 | − | 0.107136i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 13.7990i | 0.970892i | ||||||||
\(203\) | 32.1542i | 2.25679i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 16.0450 | + | 11.7346i | 1.12063 | + | 0.819582i | ||||
\(206\) | −4.57947 | −0.319067 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 2.51514i | 0.174393i | ||||||||
\(209\) | −2.64002 | −0.182614 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −15.2838 | −1.05218 | −0.526091 | − | 0.850428i | \(-0.676343\pi\) | ||||
−0.526091 | + | 0.850428i | \(0.676343\pi\) | |||||||
\(212\) | 5.48486i | 0.376702i | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 10.3747 | 0.709197 | ||||||||
\(215\) | 11.4049 | − | 15.5942i | 0.777810 | − | 1.06351i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 15.1396i | − | 1.02774i | ||||||
\(218\) | − | 3.01468i | − | 0.204180i | ||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 4.76491 | + | 3.48486i | 0.321250 | + | 0.234949i | ||||
\(221\) | 1.29564 | 0.0871544 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 3.75023i | − | 0.251134i | −0.992085 | − | 0.125567i | \(-0.959925\pi\) | ||
0.992085 | − | 0.125567i | \(-0.0400750\pi\) | |||||||
\(224\) | 4.12489 | 0.275606 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −19.2001 | −1.27717 | ||||||||
\(227\) | − | 24.1542i | − | 1.60317i | −0.597878 | − | 0.801587i | \(-0.703989\pi\) | ||
0.597878 | − | 0.801587i | \(-0.296011\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 13.0596 | 0.863005 | 0.431503 | − | 0.902112i | \(-0.357984\pi\) | ||||
0.431503 | + | 0.902112i | \(0.357984\pi\) | |||||||
\(230\) | −5.58538 | − | 4.08492i | −0.368289 | − | 0.269352i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 7.79518i | 0.511779i | ||||||||
\(233\) | 6.43899i | 0.421832i | 0.977504 | + | 0.210916i | \(0.0676447\pi\) | ||||
−0.977504 | + | 0.210916i | \(0.932355\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −6.56009 | + | 8.96972i | −0.427933 | + | 0.585120i | ||||
\(236\) | −3.15516 | −0.205384 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | − | 2.12489i | − | 0.137736i | ||||||
\(239\) | 22.8742 | 1.47961 | 0.739804 | − | 0.672822i | \(-0.234918\pi\) | ||||
0.739804 | + | 0.672822i | \(0.234918\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 4.96972 | 0.320128 | 0.160064 | − | 0.987107i | \(-0.448830\pi\) | ||||
0.160064 | + | 0.987107i | \(0.448830\pi\) | |||||||
\(242\) | − | 4.03028i | − | 0.259076i | ||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 12.6400 | 0.809195 | ||||||||
\(245\) | 18.0752 | + | 13.2195i | 1.15478 | + | 0.844563i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 2.51514i | − | 0.160034i | ||||||
\(248\) | − | 3.67030i | − | 0.233064i | ||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 10.6001 | + | 3.55510i | 0.670407 | + | 0.224844i | ||||
\(251\) | −15.9201 | −1.00487 | −0.502433 | − | 0.864616i | \(-0.667562\pi\) | ||||
−0.502433 | + | 0.864616i | \(0.667562\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 8.16984i | − | 0.513634i | ||||||
\(254\) | 14.3103 | 0.897910 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | − | 1.04965i | − | 0.0654756i | −0.999464 | − | 0.0327378i | \(-0.989577\pi\) | ||
0.999464 | − | 0.0327378i | \(-0.0104226\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −42.2791 | −2.62710 | ||||||||
\(260\) | −3.32001 | + | 4.53951i | −0.205898 | + | 0.281528i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 6.56009i | 0.405284i | ||||||||
\(263\) | 11.9394i | 0.736218i | 0.929783 | + | 0.368109i | \(0.119995\pi\) | ||||
−0.929783 | + | 0.368109i | \(0.880005\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −7.24008 | + | 9.89948i | −0.444755 | + | 0.608120i | ||||
\(266\) | −4.12489 | −0.252913 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | − | 7.40493i | − | 0.452328i | ||||||
\(269\) | −15.9394 | −0.971845 | −0.485923 | − | 0.874002i | \(-0.661516\pi\) | ||||
−0.485923 | + | 0.874002i | \(0.661516\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.46548 | 0.0890218 | 0.0445109 | − | 0.999009i | \(-0.485827\pi\) | ||||
0.0445109 | + | 0.999009i | \(0.485827\pi\) | |||||||
\(272\) | − | 0.515138i | − | 0.0312348i | ||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 6.45459 | 0.389936 | ||||||||
\(275\) | 4.00000 | + | 12.5795i | 0.241209 | + | 0.758571i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 32.4995i | − | 1.95271i | −0.216177 | − | 0.976354i | \(-0.569359\pi\) | ||
0.216177 | − | 0.976354i | \(-0.430641\pi\) | |||||||
\(278\) | 23.0596i | 1.38303i | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 7.44490 | + | 5.44490i | 0.444918 | + | 0.325395i | ||||
\(281\) | −1.04965 | −0.0626171 | −0.0313085 | − | 0.999510i | \(-0.509967\pi\) | ||||
−0.0313085 | + | 0.999510i | \(0.509967\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 9.34060i | − | 0.555241i | −0.960691 | − | 0.277620i | \(-0.910454\pi\) | ||
0.960691 | − | 0.277620i | \(-0.0895458\pi\) | |||||||
\(284\) | 11.1396 | 0.661012 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −6.64002 | −0.392633 | ||||||||
\(287\) | 36.6694i | 2.16453i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 16.7346 | 0.984390 | ||||||||
\(290\) | −10.2897 | + | 14.0693i | −0.604234 | + | 0.826179i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 2.70436i | 0.158261i | ||||||||
\(293\) | − | 25.5748i | − | 1.49409i | −0.664771 | − | 0.747047i | \(-0.731471\pi\) | ||
0.664771 | − | 0.747047i | \(-0.268529\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −5.69467 | − | 4.16485i | −0.331556 | − | 0.242487i | ||||
\(296\) | −10.2498 | −0.595756 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 16.0294i | 0.928556i | ||||||||
\(299\) | 7.78337 | 0.450124 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 35.6391 | 2.05420 | ||||||||
\(302\) | − | 14.3103i | − | 0.823467i | ||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −1.00000 | −0.0573539 | ||||||||
\(305\) | 22.8136 | + | 16.6850i | 1.30631 | + | 0.955379i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 9.43991i | − | 0.538764i | −0.963033 | − | 0.269382i | \(-0.913181\pi\) | ||
0.963033 | − | 0.269382i | \(-0.0868194\pi\) | |||||||
\(308\) | 10.8898i | 0.620504i | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 4.84484 | − | 6.62443i | 0.275168 | − | 0.376242i | ||||
\(311\) | 17.4655 | 0.990377 | 0.495188 | − | 0.868786i | \(-0.335099\pi\) | ||||
0.495188 | + | 0.868786i | \(0.335099\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 10.4546i | − | 0.590928i | −0.955354 | − | 0.295464i | \(-0.904526\pi\) | ||
0.955354 | − | 0.295464i | \(-0.0954743\pi\) | |||||||
\(314\) | −18.0294 | −1.01746 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 16.7493 | 0.942222 | ||||||||
\(317\) | 4.33348i | 0.243393i | 0.992567 | + | 0.121696i | \(0.0388334\pi\) | ||||
−0.992567 | + | 0.121696i | \(0.961167\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −20.5795 | −1.15223 | ||||||||
\(320\) | 1.80487 | + | 1.32001i | 0.100896 | + | 0.0737909i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | − | 12.7649i | − | 0.711361i | ||||||
\(323\) | 0.515138i | 0.0286630i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −11.9844 | + | 3.81078i | −0.664775 | + | 0.211384i | ||||
\(326\) | −2.70058 | −0.149571 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 8.88979i | 0.490857i | ||||||||
\(329\) | −20.4995 | −1.13018 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −4.56387 | −0.250853 | −0.125427 | − | 0.992103i | \(-0.540030\pi\) | ||||
−0.125427 | + | 0.992103i | \(0.540030\pi\) | |||||||
\(332\) | 3.28005i | 0.180016i | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −8.95035 | −0.489741 | ||||||||
\(335\) | 9.77460 | − | 13.3650i | 0.534043 | − | 0.730206i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 13.0109i | − | 0.708749i | −0.935104 | − | 0.354374i | \(-0.884694\pi\) | ||
0.935104 | − | 0.354374i | \(-0.115306\pi\) | |||||||
\(338\) | 6.67408i | 0.363022i | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0.679988 | − | 0.929759i | 0.0368775 | − | 0.0504233i | ||||
\(341\) | 9.68968 | 0.524725 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 12.4352i | 0.671438i | ||||||||
\(344\) | 8.64002 | 0.465839 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0.310323 | 0.0166831 | ||||||||
\(347\) | 13.2195i | 0.709660i | 0.934931 | + | 0.354830i | \(0.115461\pi\) | ||||
−0.934931 | + | 0.354830i | \(0.884539\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 20.4390 | 1.09407 | 0.547037 | − | 0.837108i | \(-0.315756\pi\) | ||||
0.547037 | + | 0.837108i | \(0.315756\pi\) | |||||||
\(350\) | 6.24977 | + | 19.6547i | 0.334064 | + | 1.05059i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 2.64002i | 0.140714i | ||||||||
\(353\) | − | 10.7044i | − | 0.569735i | −0.958567 | − | 0.284868i | \(-0.908050\pi\) | ||
0.958567 | − | 0.284868i | \(-0.0919497\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 20.1055 | + | 14.7044i | 1.06709 | + | 0.780426i | ||||
\(356\) | 7.60975 | 0.403316 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | − | 1.52982i | − | 0.0808534i | ||||||
\(359\) | −4.31410 | −0.227690 | −0.113845 | − | 0.993499i | \(-0.536317\pi\) | ||||
−0.113845 | + | 0.993499i | \(0.536317\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | − | 14.7493i | − | 0.775207i | ||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −10.3747 | −0.543780 | ||||||||
\(365\) | −3.56978 | + | 4.88102i | −0.186851 | + | 0.255484i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 12.8099i | 0.668669i | 0.942454 | + | 0.334335i | \(0.108512\pi\) | ||||
−0.942454 | + | 0.334335i | \(0.891488\pi\) | |||||||
\(368\) | − | 3.09461i | − | 0.161318i | ||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −18.4995 | − | 13.5298i | −0.961745 | − | 0.703382i | ||||
\(371\) | −22.6244 | −1.17460 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 0.704357i | 0.0364702i | 0.999834 | + | 0.0182351i | \(0.00580474\pi\) | ||||
−0.999834 | + | 0.0182351i | \(0.994195\pi\) | |||||||
\(374\) | 1.35998 | 0.0703227 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −4.96972 | −0.256294 | ||||||||
\(377\) | − | 19.6060i | − | 1.00976i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −6.12489 | −0.314614 | −0.157307 | − | 0.987550i | \(-0.550281\pi\) | ||||
−0.157307 | + | 0.987550i | \(0.550281\pi\) | |||||||
\(380\) | −1.80487 | − | 1.32001i | −0.0925881 | − | 0.0677152i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | − | 18.1249i | − | 0.927350i | ||||||
\(383\) | − | 18.6400i | − | 0.952461i | −0.879321 | − | 0.476230i | \(-0.842003\pi\) | ||
0.879321 | − | 0.476230i | \(-0.157997\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −14.3747 | + | 19.6547i | −0.732600 | + | 1.00170i | ||||
\(386\) | 4.56009 | 0.232103 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 3.93945i | 0.199995i | ||||||||
\(389\) | 13.9201 | 0.705776 | 0.352888 | − | 0.935666i | \(-0.385200\pi\) | ||||
0.352888 | + | 0.935666i | \(0.385200\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.59415 | −0.0806197 | ||||||||
\(392\) | 10.0147i | 0.505818i | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 2.14048 | 0.107836 | ||||||||
\(395\) | 30.2304 | + | 22.1093i | 1.52106 | + | 1.11244i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 28.3784i | 1.42427i | 0.702041 | + | 0.712136i | \(0.252272\pi\) | ||||
−0.702041 | + | 0.712136i | \(0.747728\pi\) | |||||||
\(398\) | − | 16.5639i | − | 0.830272i | ||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1.51514 | + | 4.76491i | 0.0757569 | + | 0.238245i | ||||
\(401\) | −5.54920 | −0.277114 | −0.138557 | − | 0.990354i | \(-0.544246\pi\) | ||||
−0.138557 | + | 0.990354i | \(0.544246\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 9.23131i | 0.459844i | ||||||||
\(404\) | −13.7990 | −0.686524 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −32.1542 | −1.59579 | ||||||||
\(407\) | − | 27.0596i | − | 1.34130i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 5.01090 | 0.247773 | 0.123886 | − | 0.992296i | \(-0.460464\pi\) | ||||
0.123886 | + | 0.992296i | \(0.460464\pi\) | |||||||
\(410\) | −11.7346 | + | 16.0450i | −0.579532 | + | 0.792404i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | − | 4.57947i | − | 0.225614i | ||||||
\(413\) | − | 13.0147i | − | 0.640411i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −4.32970 | + | 5.92007i | −0.212537 | + | 0.290605i | ||||
\(416\) | −2.51514 | −0.123315 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | − | 2.64002i | − | 0.129128i | ||||||
\(419\) | −15.8889 | −0.776222 | −0.388111 | − | 0.921613i | \(-0.626872\pi\) | ||||
−0.388111 | + | 0.921613i | \(0.626872\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2.38647 | −0.116310 | −0.0581548 | − | 0.998308i | \(-0.518522\pi\) | ||||
−0.0581548 | + | 0.998308i | \(0.518522\pi\) | |||||||
\(422\) | − | 15.2838i | − | 0.744005i | ||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −5.48486 | −0.266368 | ||||||||
\(425\) | 2.45459 | − | 0.780505i | 0.119065 | − | 0.0378601i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 52.1386i | 2.52317i | ||||||||
\(428\) | 10.3747i | 0.501478i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 15.5942 | + | 11.4049i | 0.752017 | + | 0.549995i | ||||
\(431\) | 2.35906 | 0.113632 | 0.0568160 | − | 0.998385i | \(-0.481905\pi\) | ||||
0.0568160 | + | 0.998385i | \(0.481905\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 0.640023i | − | 0.0307576i | −0.999882 | − | 0.0153788i | \(-0.995105\pi\) | ||
0.999882 | − | 0.0153788i | \(-0.00489541\pi\) | |||||||
\(434\) | 15.1396 | 0.726722 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 3.01468 | 0.144377 | ||||||||
\(437\) | 3.09461i | 0.148035i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 25.4499 | 1.21466 | 0.607328 | − | 0.794451i | \(-0.292241\pi\) | ||||
0.607328 | + | 0.794451i | \(0.292241\pi\) | |||||||
\(440\) | −3.48486 | + | 4.76491i | −0.166134 | + | 0.227158i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 1.29564i | 0.0616275i | ||||||||
\(443\) | 35.6685i | 1.69466i | 0.531067 | + | 0.847330i | \(0.321791\pi\) | ||||
−0.531067 | + | 0.847330i | \(0.678209\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 13.7346 | + | 10.0450i | 0.651084 | + | 0.476177i | ||||
\(446\) | 3.75023 | 0.177578 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 4.12489i | 0.194883i | ||||||||
\(449\) | −11.4399 | −0.539883 | −0.269941 | − | 0.962877i | \(-0.587004\pi\) | ||||
−0.269941 | + | 0.962877i | \(0.587004\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −23.4693 | −1.10512 | ||||||||
\(452\) | − | 19.2001i | − | 0.903098i | ||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 24.1542 | 1.13361 | ||||||||
\(455\) | −18.7249 | − | 13.6947i | −0.877839 | − | 0.642016i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 19.4849i | − | 0.911463i | −0.890117 | − | 0.455732i | \(-0.849378\pi\) | ||
0.890117 | − | 0.455732i | \(-0.150622\pi\) | |||||||
\(458\) | 13.0596i | 0.610237i | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 4.08492 | − | 5.58538i | 0.190460 | − | 0.260420i | ||||
\(461\) | 29.3893 | 1.36880 | 0.684399 | − | 0.729108i | \(-0.260065\pi\) | ||||
0.684399 | + | 0.729108i | \(0.260065\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 12.1892i | 0.566481i | 0.959049 | + | 0.283241i | \(0.0914095\pi\) | ||||
−0.959049 | + | 0.283241i | \(0.908591\pi\) | |||||||
\(464\) | −7.79518 | −0.361882 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −6.43899 | −0.298280 | ||||||||
\(467\) | − | 17.8889i | − | 0.827799i | −0.910323 | − | 0.413899i | \(-0.864167\pi\) | ||
0.910323 | − | 0.413899i | \(-0.135833\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 30.5445 | 1.41041 | ||||||||
\(470\) | −8.96972 | − | 6.56009i | −0.413743 | − | 0.302595i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | − | 3.15516i | − | 0.145228i | ||||||
\(473\) | 22.8099i | 1.04880i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.51514 | − | 4.76491i | −0.0695193 | − | 0.218629i | ||||
\(476\) | 2.12489 | 0.0973940 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 22.8742i | 1.04624i | ||||||||
\(479\) | −1.15894 | −0.0529534 | −0.0264767 | − | 0.999649i | \(-0.508429\pi\) | ||||
−0.0264767 | + | 0.999649i | \(0.508429\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 25.7796 | 1.17545 | ||||||||
\(482\) | 4.96972i | 0.226365i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 4.03028 | 0.183194 | ||||||||
\(485\) | −5.20012 | + | 7.11021i | −0.236125 | + | 0.322858i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 30.6888i | − | 1.39064i | −0.718700 | − | 0.695320i | \(-0.755263\pi\) | ||
0.718700 | − | 0.695320i | \(-0.244737\pi\) | |||||||
\(488\) | 12.6400i | 0.572187i | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −13.2195 | + | 18.0752i | −0.597196 | + | 0.816556i | ||||
\(491\) | −3.67030 | −0.165638 | −0.0828192 | − | 0.996565i | \(-0.526392\pi\) | ||||
−0.0828192 | + | 0.996565i | \(0.526392\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 4.01560i | 0.180853i | ||||||||
\(494\) | 2.51514 | 0.113161 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 3.67030 | 0.164801 | ||||||||
\(497\) | 45.9494i | 2.06111i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −31.3893 | −1.40518 | −0.702590 | − | 0.711595i | \(-0.747973\pi\) | ||||
−0.702590 | + | 0.711595i | \(0.747973\pi\) | |||||||
\(500\) | −3.55510 | + | 10.6001i | −0.158989 | + | 0.474049i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | − | 15.9201i | − | 0.710548i | ||||||
\(503\) | 18.1542i | 0.809458i | 0.914437 | + | 0.404729i | \(0.132634\pi\) | ||||
−0.914437 | + | 0.404729i | \(0.867366\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −24.9054 | − | 18.2148i | −1.10828 | − | 0.810548i | ||||
\(506\) | 8.16984 | 0.363194 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 14.3103i | 0.634918i | ||||||||
\(509\) | 11.5298 | 0.511050 | 0.255525 | − | 0.966802i | \(-0.417752\pi\) | ||||
0.255525 | + | 0.966802i | \(0.417752\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −11.1552 | −0.493475 | ||||||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 1.04965 | 0.0462982 | ||||||||
\(515\) | 6.04496 | − | 8.26537i | 0.266373 | − | 0.364216i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 13.1202i | − | 0.577025i | ||||||
\(518\) | − | 42.2791i | − | 1.85764i | ||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −4.53951 | − | 3.32001i | −0.199071 | − | 0.145592i | ||||
\(521\) | 42.5895 | 1.86588 | 0.932939 | − | 0.360035i | \(-0.117235\pi\) | ||||
0.932939 | + | 0.360035i | \(0.117235\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 1.21571i | 0.0531594i | 0.999647 | + | 0.0265797i | \(0.00846159\pi\) | ||||
−0.999647 | + | 0.0265797i | \(0.991538\pi\) | |||||||
\(524\) | −6.56009 | −0.286579 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −11.9394 | −0.520585 | ||||||||
\(527\) | − | 1.89071i | − | 0.0823607i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 13.4234 | 0.583626 | ||||||||
\(530\) | −9.89948 | − | 7.24008i | −0.430006 | − | 0.314489i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | − | 4.12489i | − | 0.178836i | ||||||
\(533\) | − | 22.3591i | − | 0.968478i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −13.6947 | + | 18.7249i | −0.592072 | + | 0.809550i | ||||
\(536\) | 7.40493 | 0.319844 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | − | 15.9394i | − | 0.687198i | ||||||
\(539\) | −26.4390 | −1.13881 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1.92007 | −0.0825503 | −0.0412751 | − | 0.999148i | \(-0.513142\pi\) | ||||
−0.0412751 | + | 0.999148i | \(0.513142\pi\) | |||||||
\(542\) | 1.46548i | 0.0629480i | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0.515138 | 0.0220864 | ||||||||
\(545\) | 5.44112 | + | 3.97941i | 0.233072 | + | 0.170459i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 10.9697i | − | 0.469032i | −0.972112 | − | 0.234516i | \(-0.924650\pi\) | ||
0.972112 | − | 0.234516i | \(-0.0753504\pi\) | |||||||
\(548\) | 6.45459i | 0.275726i | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −12.5795 | + | 4.00000i | −0.536390 | + | 0.170561i | ||||
\(551\) | 7.79518 | 0.332086 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 69.0890i | 2.93796i | ||||||||
\(554\) | 32.4995 | 1.38077 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −23.0596 | −0.977946 | ||||||||
\(557\) | 23.5005i | 0.995746i | 0.867250 | + | 0.497873i | \(0.165886\pi\) | ||||
−0.867250 | + | 0.497873i | \(0.834114\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −21.7309 | −0.919117 | ||||||||
\(560\) | −5.44490 | + | 7.44490i | −0.230089 | + | 0.314604i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | − | 1.04965i | − | 0.0442770i | ||||||
\(563\) | 7.87890i | 0.332056i | 0.986121 | + | 0.166028i | \(0.0530942\pi\) | ||||
−0.986121 | + | 0.166028i | \(0.946906\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 25.3444 | − | 34.6538i | 1.06625 | − | 1.45790i | ||||
\(566\) | 9.34060 | 0.392615 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 11.1396i | 0.467406i | ||||||||
\(569\) | −1.09083 | −0.0457299 | −0.0228650 | − | 0.999739i | \(-0.507279\pi\) | ||||
−0.0228650 | + | 0.999739i | \(0.507279\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 21.4886 | 0.899272 | 0.449636 | − | 0.893212i | \(-0.351554\pi\) | ||||
0.449636 | + | 0.893212i | \(0.351554\pi\) | |||||||
\(572\) | − | 6.64002i | − | 0.277633i | ||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −36.6694 | −1.53055 | ||||||||
\(575\) | 14.7455 | − | 4.68876i | 0.614931 | − | 0.195535i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 16.1055i | 0.670481i | 0.942133 | + | 0.335241i | \(0.108818\pi\) | ||||
−0.942133 | + | 0.335241i | \(0.891182\pi\) | |||||||
\(578\) | 16.7346i | 0.696069i | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −14.0693 | − | 10.2897i | −0.584197 | − | 0.427258i | ||||
\(581\) | −13.5298 | −0.561311 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 14.4802i | − | 0.599707i | ||||||
\(584\) | −2.70436 | −0.111907 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 25.5748 | 1.05648 | ||||||||
\(587\) | 0.480164i | 0.0198185i | 0.999951 | + | 0.00990925i | \(0.00315426\pi\) | ||||
−0.999951 | + | 0.00990925i | \(0.996846\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −3.67030 | −0.151232 | ||||||||
\(590\) | 4.16485 | − | 5.69467i | 0.171464 | − | 0.234446i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | − | 10.2498i | − | 0.421263i | ||||||
\(593\) | − | 40.4683i | − | 1.66184i | −0.556395 | − | 0.830918i | \(-0.687816\pi\) | ||
0.556395 | − | 0.830918i | \(-0.312184\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 3.83515 | + | 2.80487i | 0.157226 | + | 0.114989i | ||||
\(596\) | −16.0294 | −0.656588 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 7.78337i | 0.318286i | ||||||||
\(599\) | −36.1698 | −1.47786 | −0.738930 | − | 0.673782i | \(-0.764669\pi\) | ||||
−0.738930 | + | 0.673782i | \(0.764669\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 24.3903 | 0.994899 | 0.497450 | − | 0.867493i | \(-0.334270\pi\) | ||||
0.497450 | + | 0.867493i | \(0.334270\pi\) | |||||||
\(602\) | 35.6391i | 1.45254i | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 14.3103 | 0.582279 | ||||||||
\(605\) | 7.27414 | + | 5.32001i | 0.295736 | + | 0.216289i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 21.6897i | − | 0.880357i | −0.897910 | − | 0.440178i | \(-0.854915\pi\) | ||
0.897910 | − | 0.440178i | \(-0.145085\pi\) | |||||||
\(608\) | − | 1.00000i | − | 0.0405554i | ||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −16.6850 | + | 22.8136i | −0.675555 | + | 0.923698i | ||||
\(611\) | 12.4995 | 0.505677 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 26.2304i | − | 1.05944i | −0.848174 | − | 0.529718i | \(-0.822298\pi\) | ||
0.848174 | − | 0.529718i | \(-0.177702\pi\) | |||||||
\(614\) | 9.43991 | 0.380964 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −10.8898 | −0.438762 | ||||||||
\(617\) | − | 22.7200i | − | 0.914671i | −0.889294 | − | 0.457335i | \(-0.848804\pi\) | ||
0.889294 | − | 0.457335i | \(-0.151196\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 32.9192 | 1.32313 | 0.661566 | − | 0.749887i | \(-0.269892\pi\) | ||||
0.661566 | + | 0.749887i | \(0.269892\pi\) | |||||||
\(620\) | 6.62443 | + | 4.84484i | 0.266043 | + | 0.194573i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 17.4655i | 0.700302i | ||||||||
\(623\) | 31.3893i | 1.25759i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −20.4087 | + | 14.4390i | −0.816349 | + | 0.577560i | ||||
\(626\) | 10.4546 | 0.417849 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | − | 18.0294i | − | 0.719450i | ||||||
\(629\) | −5.28005 | −0.210529 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 17.2876 | 0.688209 | 0.344104 | − | 0.938931i | \(-0.388183\pi\) | ||||
0.344104 | + | 0.938931i | \(0.388183\pi\) | |||||||
\(632\) | 16.7493i | 0.666252i | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −4.33348 | −0.172105 | ||||||||
\(635\) | −18.8898 | + | 25.8283i | −0.749619 | + | 1.02497i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 25.1883i | − | 0.997997i | ||||||
\(638\) | − | 20.5795i | − | 0.814749i | ||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −1.32001 | + | 1.80487i | −0.0521780 | + | 0.0713439i | ||||
\(641\) | 9.29942 | 0.367305 | 0.183653 | − | 0.982991i | \(-0.441208\pi\) | ||||
0.183653 | + | 0.982991i | \(0.441208\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 3.40115i | − | 0.134128i | −0.997749 | − | 0.0670642i | \(-0.978637\pi\) | ||
0.997749 | − | 0.0670642i | \(-0.0213632\pi\) | |||||||
\(644\) | 12.7649 | 0.503008 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −0.515138 | −0.0202678 | ||||||||
\(647\) | 14.9348i | 0.587146i | 0.955937 | + | 0.293573i | \(0.0948443\pi\) | ||||
−0.955937 | + | 0.293573i | \(0.905156\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 8.32970 | 0.326969 | ||||||||
\(650\) | −3.81078 | − | 11.9844i | −0.149471 | − | 0.470067i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | − | 2.70058i | − | 0.105763i | ||||||
\(653\) | − | 21.1202i | − | 0.826497i | −0.910618 | − | 0.413248i | \(-0.864394\pi\) | ||
0.910618 | − | 0.413248i | \(-0.135606\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −11.8401 | − | 8.65940i | −0.462633 | − | 0.338351i | ||||
\(656\) | −8.88979 | −0.347088 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | − | 20.4995i | − | 0.799155i | ||||||
\(659\) | 27.6547 | 1.07727 | 0.538637 | − | 0.842538i | \(-0.318939\pi\) | ||||
0.538637 | + | 0.842538i | \(0.318939\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 10.2342 | 0.398063 | 0.199032 | − | 0.979993i | \(-0.436220\pi\) | ||||
0.199032 | + | 0.979993i | \(0.436220\pi\) | |||||||
\(662\) | − | 4.56387i | − | 0.177380i | ||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −3.28005 | −0.127291 | ||||||||
\(665\) | 5.44490 | − | 7.44490i | 0.211144 | − | 0.288701i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 24.1231i | 0.934048i | ||||||||
\(668\) | − | 8.95035i | − | 0.346299i | ||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 13.3650 | + | 9.77460i | 0.516334 | + | 0.377626i | ||||
\(671\) | −33.3700 | −1.28823 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 13.4693i | − | 0.519202i | −0.965716 | − | 0.259601i | \(-0.916409\pi\) | ||
0.965716 | − | 0.259601i | \(-0.0835911\pi\) | |||||||
\(674\) | 13.0109 | 0.501161 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −6.67408 | −0.256695 | ||||||||
\(677\) | 15.1433i | 0.582006i | 0.956722 | + | 0.291003i | \(0.0939890\pi\) | ||||
−0.956722 | + | 0.291003i | \(0.906011\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −16.2498 | −0.623609 | ||||||||
\(680\) | 0.929759 | + | 0.679988i | 0.0356546 | + | 0.0260764i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 9.68968i | 0.371037i | ||||||||
\(683\) | − | 15.8789i | − | 0.607589i | −0.952738 | − | 0.303795i | \(-0.901746\pi\) | ||
0.952738 | − | 0.303795i | \(-0.0982536\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −8.52013 | + | 11.6497i | −0.325537 | + | 0.445113i | ||||
\(686\) | −12.4352 | −0.474778 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 8.64002i | 0.329398i | ||||||||
\(689\) | 13.7952 | 0.525555 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 27.3094 | 1.03890 | 0.519449 | − | 0.854501i | \(-0.326137\pi\) | ||||
0.519449 | + | 0.854501i | \(0.326137\pi\) | |||||||
\(692\) | 0.310323i | 0.0117967i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −13.2195 | −0.501805 | ||||||||
\(695\) | −41.6197 | − | 30.4390i | −1.57873 | − | 1.15462i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 4.57947i | 0.173460i | ||||||||
\(698\) | 20.4390i | 0.773627i | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −19.6547 | + | 6.24977i | −0.742878 | + | 0.236219i | ||||
\(701\) | 20.9697 | 0.792016 | 0.396008 | − | 0.918247i | \(-0.370395\pi\) | ||||
0.396008 | + | 0.918247i | \(0.370395\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 10.2498i | 0.386577i | ||||||||
\(704\) | −2.64002 | −0.0994996 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 10.7044 | 0.402864 | ||||||||
\(707\) | − | 56.9192i | − | 2.14067i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −37.5592 | −1.41056 | −0.705282 | − | 0.708927i | \(-0.749180\pi\) | ||||
−0.705282 | + | 0.708927i | \(0.749180\pi\) | |||||||
\(710\) | −14.7044 | + | 20.1055i | −0.551845 | + | 0.754546i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 7.60975i | 0.285187i | ||||||||
\(713\) | − | 11.3581i | − | 0.425366i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 8.76491 | − | 11.9844i | 0.327789 | − | 0.448191i | ||||
\(716\) | 1.52982 | 0.0571720 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | − | 4.31410i | − | 0.161001i | ||||||
\(719\) | 3.94323 | 0.147058 | 0.0735288 | − | 0.997293i | \(-0.476574\pi\) | ||||
0.0735288 | + | 0.997293i | \(0.476574\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 18.8898 | 0.703493 | ||||||||
\(722\) | 1.00000i | 0.0372161i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 14.7493 | 0.548154 | ||||||||
\(725\) | −11.8108 | − | 37.1433i | −0.438641 | − | 1.37947i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 33.2139i | − | 1.23183i | −0.787811 | − | 0.615917i | \(-0.788786\pi\) | ||
0.787811 | − | 0.615917i | \(-0.211214\pi\) | |||||||
\(728\) | − | 10.3747i | − | 0.384510i | ||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −4.88102 | − | 3.56978i | −0.180655 | − | 0.132124i | ||||
\(731\) | 4.45080 | 0.164619 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 8.62065i | − | 0.318411i | −0.987245 | − | 0.159205i | \(-0.949107\pi\) | ||
0.987245 | − | 0.159205i | \(-0.0508932\pi\) | |||||||
\(734\) | −12.8099 | −0.472821 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 3.09461 | 0.114069 | ||||||||
\(737\) | 19.5492i | 0.720104i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 45.1689 | 1.66157 | 0.830783 | − | 0.556597i | \(-0.187893\pi\) | ||||
0.830783 | + | 0.556597i | \(0.187893\pi\) | |||||||
\(740\) | 13.5298 | − | 18.4995i | 0.497366 | − | 0.680057i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | − | 22.6244i | − | 0.830569i | ||||||
\(743\) | 24.7905i | 0.909475i | 0.890626 | + | 0.454737i | \(0.150267\pi\) | ||||
−0.890626 | + | 0.454737i | \(0.849733\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −28.9310 | − | 21.1589i | −1.05995 | − | 0.775204i | ||||
\(746\) | −0.704357 | −0.0257883 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 1.35998i | 0.0497257i | ||||||||
\(749\) | −42.7943 | −1.56367 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −6.76869 | −0.246993 | −0.123497 | − | 0.992345i | \(-0.539411\pi\) | ||||
−0.123497 | + | 0.992345i | \(0.539411\pi\) | |||||||
\(752\) | − | 4.96972i | − | 0.181227i | ||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 19.6060 | 0.714007 | ||||||||
\(755\) | 25.8283 | + | 18.8898i | 0.939989 | + | 0.687470i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 45.2101i | − | 1.64319i | −0.570072 | − | 0.821595i | \(-0.693085\pi\) | ||
0.570072 | − | 0.821595i | \(-0.306915\pi\) | |||||||
\(758\) | − | 6.12489i | − | 0.222466i | ||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 1.32001 | − | 1.80487i | 0.0478819 | − | 0.0654696i | ||||
\(761\) | −19.8851 | −0.720834 | −0.360417 | − | 0.932791i | \(-0.617366\pi\) | ||||
−0.360417 | + | 0.932791i | \(0.617366\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 12.4352i | 0.450185i | ||||||||
\(764\) | 18.1249 | 0.655735 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 18.6400 | 0.673491 | ||||||||
\(767\) | 7.93567i | 0.286540i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −8.07615 | −0.291233 | −0.145617 | − | 0.989341i | \(-0.546517\pi\) | ||||
−0.145617 | + | 0.989341i | \(0.546517\pi\) | |||||||
\(770\) | −19.6547 | − | 14.3747i | −0.708306 | − | 0.518027i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 4.56009i | 0.164121i | ||||||||
\(773\) | − | 45.9456i | − | 1.65255i | −0.563267 | − | 0.826275i | \(-0.690456\pi\) | ||
0.563267 | − | 0.826275i | \(-0.309544\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 5.56101 | + | 17.4886i | 0.199757 | + | 0.628211i | ||||
\(776\) | −3.93945 | −0.141418 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 13.9201i | 0.499059i | ||||||||
\(779\) | 8.88979 | 0.318510 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −29.4087 | −1.05233 | ||||||||
\(782\) | − | 1.59415i | − | 0.0570067i | ||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −10.0147 | −0.357667 | ||||||||
\(785\) | 23.7990 | − | 32.5407i | 0.849422 | − | 1.16143i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 17.8439i | 0.636067i | 0.948079 | + | 0.318034i | \(0.103022\pi\) | ||||
−0.948079 | + | 0.318034i | \(0.896978\pi\) | |||||||
\(788\) | 2.14048i | 0.0762515i | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −22.1093 | + | 30.2304i | −0.786613 | + | 1.07555i | ||||
\(791\) | 79.1983 | 2.81597 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 31.7914i | − | 1.12895i | ||||||
\(794\) | −28.3784 | −1.00711 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 16.5639 | 0.587091 | ||||||||
\(797\) | − | 37.3326i | − | 1.32239i | −0.750215 | − | 0.661194i | \(-0.770050\pi\) | ||
0.750215 | − | 0.661194i | \(-0.229950\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −2.56009 | −0.0905696 | ||||||||
\(800\) | −4.76491 | + | 1.51514i | −0.168465 | + | 0.0535682i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | − | 5.54920i | − | 0.195949i | ||||||
\(803\) | − | 7.13957i | − | 0.251950i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 23.0390 | + | 16.8498i | 0.812020 | + | 0.593878i | ||||
\(806\) | −9.23131 | −0.325159 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | − | 13.7990i | − | 0.485446i | ||||||
\(809\) | −38.6950 | −1.36044 | −0.680221 | − | 0.733007i | \(-0.738116\pi\) | ||||
−0.680221 | + | 0.733007i | \(0.738116\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 13.3444 | 0.468585 | 0.234292 | − | 0.972166i | \(-0.424723\pi\) | ||||
0.234292 | + | 0.972166i | \(0.424723\pi\) | |||||||
\(812\) | − | 32.1542i | − | 1.12839i | ||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 27.0596 | 0.948440 | ||||||||
\(815\) | 3.56479 | − | 4.87420i | 0.124869 | − | 0.170736i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 8.64002i | − | 0.302276i | ||||||
\(818\) | 5.01090i | 0.175202i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −16.0450 | − | 11.7346i | −0.560314 | − | 0.409791i | ||||
\(821\) | 37.3482 | 1.30346 | 0.651730 | − | 0.758451i | \(-0.274044\pi\) | ||||
0.651730 | + | 0.758451i | \(0.274044\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 51.5630i | − | 1.79737i | −0.438593 | − | 0.898686i | \(-0.644523\pi\) | ||
0.438593 | − | 0.898686i | \(-0.355477\pi\) | |||||||
\(824\) | 4.57947 | 0.159533 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 13.0147 | 0.452839 | ||||||||
\(827\) | − | 48.5639i | − | 1.68873i | −0.535767 | − | 0.844366i | \(-0.679978\pi\) | ||
0.535767 | − | 0.844366i | \(-0.320022\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −0.325919 | −0.0113196 | −0.00565982 | − | 0.999984i | \(-0.501802\pi\) | ||||
−0.00565982 | + | 0.999984i | \(0.501802\pi\) | |||||||
\(830\) | −5.92007 | − | 4.32970i | −0.205489 | − | 0.150286i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | − | 2.51514i | − | 0.0871967i | ||||||
\(833\) | 5.15894i | 0.178747i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 11.8146 | − | 16.1542i | 0.408860 | − | 0.559041i | ||||
\(836\) | 2.64002 | 0.0913071 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | − | 15.8889i | − | 0.548872i | ||||||
\(839\) | −17.1202 | −0.591055 | −0.295527 | − | 0.955334i | \(-0.595495\pi\) | ||||
−0.295527 | + | 0.955334i | \(0.595495\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 31.7649 | 1.09534 | ||||||||
\(842\) | − | 2.38647i | − | 0.0822432i | ||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 15.2838 | 0.526091 | ||||||||
\(845\) | −12.0459 | − | 8.80986i | −0.414391 | − | 0.303069i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 16.6244i | 0.571222i | ||||||||
\(848\) | − | 5.48486i | − | 0.188351i | ||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0.780505 | + | 2.45459i | 0.0267711 | + | 0.0841916i | ||||
\(851\) | −31.7190 | −1.08731 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 24.9092i | − | 0.852874i | −0.904517 | − | 0.426437i | \(-0.859769\pi\) | ||
0.904517 | − | 0.426437i | \(-0.140231\pi\) | |||||||
\(854\) | −52.1386 | −1.78415 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −10.3747 | −0.354598 | ||||||||
\(857\) | − | 11.6509i | − | 0.397988i | −0.980001 | − | 0.198994i | \(-0.936233\pi\) | ||
0.980001 | − | 0.198994i | \(-0.0637674\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 5.35998 | 0.182880 | 0.0914400 | − | 0.995811i | \(-0.470853\pi\) | ||||
0.0914400 | + | 0.995811i | \(0.470853\pi\) | |||||||
\(860\) | −11.4049 | + | 15.5942i | −0.388905 | + | 0.531756i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 2.35906i | 0.0803499i | ||||||||
\(863\) | 41.0790i | 1.39835i | 0.714953 | + | 0.699173i | \(0.246448\pi\) | ||||
−0.714953 | + | 0.699173i | \(0.753552\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −0.409630 | + | 0.560094i | −0.0139278 | + | 0.0190438i | ||||
\(866\) | 0.640023 | 0.0217489 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 15.1396i | 0.513870i | ||||||||
\(869\) | −44.2186 | −1.50001 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −18.6244 | −0.631065 | ||||||||
\(872\) | 3.01468i | 0.102090i | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −3.09461 | −0.104677 | ||||||||
\(875\) | −43.7240 | − | 14.6644i | −1.47814 | − | 0.495747i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 45.9532i | − | 1.55173i | −0.630899 | − | 0.775865i | \(-0.717314\pi\) | ||
0.630899 | − | 0.775865i | \(-0.282686\pi\) | |||||||
\(878\) | 25.4499i | 0.858892i | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −4.76491 | − | 3.48486i | −0.160625 | − | 0.117475i | ||||
\(881\) | 6.90917 | 0.232776 | 0.116388 | − | 0.993204i | \(-0.462868\pi\) | ||||
0.116388 | + | 0.993204i | \(0.462868\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 48.5213i | 1.63287i | 0.577435 | + | 0.816437i | \(0.304054\pi\) | ||||
−0.577435 | + | 0.816437i | \(0.695946\pi\) | |||||||
\(884\) | −1.29564 | −0.0435772 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −35.6685 | −1.19831 | ||||||||
\(887\) | 23.7990i | 0.799091i | 0.916713 | + | 0.399546i | \(0.130832\pi\) | ||||
−0.916713 | + | 0.399546i | \(0.869168\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −59.0284 | −1.97975 | ||||||||
\(890\) | −10.0450 | + | 13.7346i | −0.336708 | + | 0.460386i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 3.75023i | 0.125567i | ||||||||
\(893\) | 4.96972i | 0.166305i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 2.76113 | + | 2.01938i | 0.0922943 | + | 0.0675003i | ||||
\(896\) | −4.12489 | −0.137803 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | − | 11.4399i | − | 0.381755i | ||||||
\(899\) | −28.6107 | −0.954219 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −2.82546 | −0.0941298 | ||||||||
\(902\) | − | 23.4693i | − | 0.781441i | ||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 19.2001 | 0.638586 | ||||||||
\(905\) | 26.6206 | + | 19.4693i | 0.884900 | + | 0.647180i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 17.9726i | − | 0.596770i | −0.954446 | − | 0.298385i | \(-0.903552\pi\) | ||
0.954446 | − | 0.298385i | \(-0.0964479\pi\) | |||||||
\(908\) | 24.1542i | 0.801587i | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 13.6947 | − | 18.7249i | 0.453974 | − | 0.620726i | ||||
\(911\) | −19.5592 | −0.648024 | −0.324012 | − | 0.946053i | \(-0.605032\pi\) | ||||
−0.324012 | + | 0.946053i | \(0.605032\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 8.65940i | − | 0.286584i | ||||||
\(914\) | 19.4849 | 0.644502 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −13.0596 | −0.431503 | ||||||||
\(917\) | − | 27.0596i | − | 0.893588i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −35.4948 | −1.17087 | −0.585433 | − | 0.810720i | \(-0.699076\pi\) | ||||
−0.585433 | + | 0.810720i | \(0.699076\pi\) | |||||||
\(920\) | 5.58538 | + | 4.08492i | 0.184144 | + | 0.134676i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 29.3893i | 0.967886i | ||||||||
\(923\) | − | 28.0175i | − | 0.922209i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 48.8392 | − | 15.5298i | 1.60582 | − | 0.510617i | ||||
\(926\) | −12.1892 | −0.400563 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | − | 7.79518i | − | 0.255889i | ||||||
\(929\) | 17.9532 | 0.589026 | 0.294513 | − | 0.955648i | \(-0.404843\pi\) | ||||
0.294513 | + | 0.955648i | \(0.404843\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 10.0147 | 0.328218 | ||||||||
\(932\) | − | 6.43899i | − | 0.210916i | ||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 17.8889 | 0.585342 | ||||||||
\(935\) | −1.79518 | + | 2.45459i | −0.0587088 | + | 0.0802735i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 5.66652i | 0.185117i | 0.995707 | + | 0.0925585i | \(0.0295045\pi\) | ||||
−0.995707 | + | 0.0925585i | \(0.970495\pi\) | |||||||
\(938\) | 30.5445i | 0.997313i | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 6.56009 | − | 8.96972i | 0.213967 | − | 0.292560i | ||||
\(941\) | 24.7044 | 0.805339 | 0.402670 | − | 0.915345i | \(-0.368082\pi\) | ||||
0.402670 | + | 0.915345i | \(0.368082\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 27.5104i | 0.895863i | ||||||||
\(944\) | 3.15516 | 0.102692 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −22.8099 | −0.741613 | ||||||||
\(947\) | 13.5904i | 0.441628i | 0.975316 | + | 0.220814i | \(0.0708713\pi\) | ||||
−0.975316 | + | 0.220814i | \(0.929129\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 6.80183 | 0.220797 | ||||||||
\(950\) | 4.76491 | − | 1.51514i | 0.154594 | − | 0.0491576i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 2.12489i | 0.0688679i | ||||||||
\(953\) | − | 24.7375i | − | 0.801326i | −0.916225 | − | 0.400663i | \(-0.868780\pi\) | ||
0.916225 | − | 0.400663i | \(-0.131220\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 32.7131 | + | 23.9251i | 1.05857 | + | 0.774197i | ||||
\(956\) | −22.8742 | −0.739804 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | − | 1.15894i | − | 0.0374437i | ||||||
\(959\) | −26.6244 | −0.859748 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −17.5289 | −0.565448 | ||||||||
\(962\) | 25.7796i | 0.831167i | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −4.96972 | −0.160064 | ||||||||
\(965\) | −6.01938 | + | 8.23039i | −0.193771 | + | 0.264946i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 35.6897i | 1.14770i | 0.818960 | + | 0.573851i | \(0.194551\pi\) | ||||
−0.818960 | + | 0.573851i | \(0.805449\pi\) | |||||||
\(968\) | 4.03028i | 0.129538i | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −7.11021 | − | 5.20012i | −0.228295 | − | 0.166966i | ||||
\(971\) | −16.4995 | −0.529495 | −0.264748 | − | 0.964318i | \(-0.585289\pi\) | ||||
−0.264748 | + | 0.964318i | \(0.585289\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 95.1184i | − | 3.04935i | ||||||
\(974\) | 30.6888 | 0.983331 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −12.6400 | −0.404597 | ||||||||
\(977\) | 49.8501i | 1.59485i | 0.603420 | + | 0.797423i | \(0.293804\pi\) | ||||
−0.603420 | + | 0.797423i | \(0.706196\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −20.0899 | −0.642076 | ||||||||
\(980\) | −18.0752 | − | 13.2195i | −0.577392 | − | 0.422281i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | − | 3.67030i | − | 0.117124i | ||||||
\(983\) | 5.19014i | 0.165540i | 0.996569 | + | 0.0827698i | \(0.0263766\pi\) | ||||
−0.996569 | + | 0.0827698i | \(0.973623\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −2.82546 | + | 3.86330i | −0.0900267 | + | 0.123095i | ||||
\(986\) | −4.01560 | −0.127883 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 2.51514i | 0.0800172i | ||||||||
\(989\) | 26.7375 | 0.850203 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −32.4272 | −1.03008 | −0.515042 | − | 0.857165i | \(-0.672224\pi\) | ||||
−0.515042 | + | 0.857165i | \(0.672224\pi\) | |||||||
\(992\) | 3.67030i | 0.116532i | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −45.9494 | −1.45743 | ||||||||
\(995\) | 29.8957 | + | 21.8645i | 0.947757 | + | 0.693152i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 10.1992i | − | 0.323012i | −0.986872 | − | 0.161506i | \(-0.948365\pi\) | ||
0.986872 | − | 0.161506i | \(-0.0516351\pi\) | |||||||
\(998\) | − | 31.3893i | − | 0.993612i | ||||||
\(999\) | 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 | 1710.2.d.d.1369.4 | 6 | ||
3.2 | odd | 2 | 190.2.b.b.39.1 | ✓ | 6 | ||
5.2 | odd | 4 | 8550.2.a.ck.1.3 | 3 | |||
5.3 | odd | 4 | 8550.2.a.cl.1.1 | 3 | |||
5.4 | even | 2 | inner | 1710.2.d.d.1369.1 | 6 | ||
12.11 | even | 2 | 1520.2.d.j.609.5 | 6 | |||
15.2 | even | 4 | 950.2.a.n.1.1 | 3 | |||
15.8 | even | 4 | 950.2.a.i.1.3 | 3 | |||
15.14 | odd | 2 | 190.2.b.b.39.6 | yes | 6 | ||
60.23 | odd | 4 | 7600.2.a.cd.1.1 | 3 | |||
60.47 | odd | 4 | 7600.2.a.bi.1.3 | 3 | |||
60.59 | even | 2 | 1520.2.d.j.609.2 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
190.2.b.b.39.1 | ✓ | 6 | 3.2 | odd | 2 | ||
190.2.b.b.39.6 | yes | 6 | 15.14 | odd | 2 | ||
950.2.a.i.1.3 | 3 | 15.8 | even | 4 | |||
950.2.a.n.1.1 | 3 | 15.2 | even | 4 | |||
1520.2.d.j.609.2 | 6 | 60.59 | even | 2 | |||
1520.2.d.j.609.5 | 6 | 12.11 | even | 2 | |||
1710.2.d.d.1369.1 | 6 | 5.4 | even | 2 | inner | ||
1710.2.d.d.1369.4 | 6 | 1.1 | even | 1 | trivial | ||
7600.2.a.bi.1.3 | 3 | 60.47 | odd | 4 | |||
7600.2.a.cd.1.1 | 3 | 60.23 | odd | 4 | |||
8550.2.a.ck.1.3 | 3 | 5.2 | odd | 4 | |||
8550.2.a.cl.1.1 | 3 | 5.3 | odd | 4 |