Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1045,2,Mod(626,1045)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1045, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1045.626");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1045 = 5 \cdot 11 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1045.f (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: | \(8.34436701122\) |
Analytic rank: | \(0\) |
Dimension: | \(40\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 626.6 | ||
Character | \(\chi\) | \(=\) | 1045.626 |
Dual form | 1045.2.f.a.626.5 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1045\mathbb{Z}\right)^\times\).
\(n\) | \(496\) | \(761\) | \(837\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.08652 | −1.47539 | −0.737697 | − | 0.675131i | \(-0.764087\pi\) | ||||
−0.737697 | + | 0.675131i | \(0.764087\pi\) | |||||||
\(3\) | − | 2.80799i | − | 1.62119i | −0.585607 | − | 0.810595i | \(-0.699144\pi\) | ||
0.585607 | − | 0.810595i | \(-0.300856\pi\) | |||||||
\(4\) | 2.35358 | 1.17679 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 5.85893i | 2.39190i | ||||||||
\(7\) | 0.950248i | 0.359160i | 0.983743 | + | 0.179580i | \(0.0574739\pi\) | ||||
−0.983743 | + | 0.179580i | \(0.942526\pi\) | |||||||
\(8\) | −0.737755 | −0.260836 | ||||||||
\(9\) | −4.88478 | −1.62826 | ||||||||
\(10\) | 2.08652 | 0.659817 | ||||||||
\(11\) | 0.932412 | + | 3.18286i | 0.281133 | + | 0.959669i | ||||
\(12\) | − | 6.60882i | − | 1.90780i | ||||||
\(13\) | 3.48762 | 0.967291 | 0.483646 | − | 0.875264i | \(-0.339312\pi\) | ||||
0.483646 | + | 0.875264i | \(0.339312\pi\) | |||||||
\(14\) | − | 1.98271i | − | 0.529903i | ||||||
\(15\) | 2.80799i | 0.725019i | ||||||||
\(16\) | −3.16782 | −0.791955 | ||||||||
\(17\) | 1.26303i | 0.306331i | 0.988201 | + | 0.153165i | \(0.0489467\pi\) | ||||
−0.988201 | + | 0.153165i | \(0.951053\pi\) | |||||||
\(18\) | 10.1922 | 2.40233 | ||||||||
\(19\) | −3.21612 | − | 2.94221i | −0.737828 | − | 0.674989i | ||||
\(20\) | −2.35358 | −0.526277 | ||||||||
\(21\) | 2.66828 | 0.582267 | ||||||||
\(22\) | −1.94550 | − | 6.64112i | −0.414782 | − | 1.41589i | ||||
\(23\) | 4.91539 | 1.02493 | 0.512465 | − | 0.858708i | \(-0.328733\pi\) | ||||
0.512465 | + | 0.858708i | \(0.328733\pi\) | |||||||
\(24\) | 2.07160i | 0.422864i | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | −7.27700 | −1.42714 | ||||||||
\(27\) | 5.29243i | 1.01853i | ||||||||
\(28\) | 2.23649i | 0.422656i | ||||||||
\(29\) | 4.16032 | 0.772552 | 0.386276 | − | 0.922383i | \(-0.373761\pi\) | ||||
0.386276 | + | 0.922383i | \(0.373761\pi\) | |||||||
\(30\) | − | 5.85893i | − | 1.06969i | ||||||
\(31\) | − | 6.79836i | − | 1.22102i | −0.792008 | − | 0.610511i | \(-0.790964\pi\) | ||
0.792008 | − | 0.610511i | \(-0.209036\pi\) | |||||||
\(32\) | 8.08524 | 1.42928 | ||||||||
\(33\) | 8.93743 | − | 2.61820i | 1.55581 | − | 0.455770i | ||||
\(34\) | − | 2.63535i | − | 0.451959i | ||||||
\(35\) | − | 0.950248i | − | 0.160621i | ||||||
\(36\) | −11.4967 | −1.91612 | ||||||||
\(37\) | − | 3.59157i | − | 0.590451i | −0.955428 | − | 0.295225i | \(-0.904605\pi\) | ||
0.955428 | − | 0.295225i | \(-0.0953948\pi\) | |||||||
\(38\) | 6.71050 | + | 6.13899i | 1.08859 | + | 0.995876i | ||||
\(39\) | − | 9.79318i | − | 1.56816i | ||||||
\(40\) | 0.737755 | 0.116649 | ||||||||
\(41\) | −3.33055 | −0.520145 | −0.260072 | − | 0.965589i | \(-0.583746\pi\) | ||||
−0.260072 | + | 0.965589i | \(0.583746\pi\) | |||||||
\(42\) | −5.56743 | −0.859074 | ||||||||
\(43\) | − | 2.02665i | − | 0.309061i | −0.987988 | − | 0.154530i | \(-0.950614\pi\) | ||
0.987988 | − | 0.154530i | \(-0.0493864\pi\) | |||||||
\(44\) | 2.19451 | + | 7.49112i | 0.330835 | + | 1.12933i | ||||
\(45\) | 4.88478 | 0.728180 | ||||||||
\(46\) | −10.2561 | −1.51218 | ||||||||
\(47\) | 9.25227 | 1.34958 | 0.674791 | − | 0.738009i | \(-0.264234\pi\) | ||||
0.674791 | + | 0.738009i | \(0.264234\pi\) | |||||||
\(48\) | 8.89519i | 1.28391i | ||||||||
\(49\) | 6.09703 | 0.871004 | ||||||||
\(50\) | −2.08652 | −0.295079 | ||||||||
\(51\) | 3.54658 | 0.496621 | ||||||||
\(52\) | 8.20839 | 1.13830 | ||||||||
\(53\) | − | 3.95431i | − | 0.543167i | −0.962415 | − | 0.271583i | \(-0.912453\pi\) | ||
0.962415 | − | 0.271583i | \(-0.0875473\pi\) | |||||||
\(54\) | − | 11.0428i | − | 1.50273i | ||||||
\(55\) | −0.932412 | − | 3.18286i | −0.125726 | − | 0.429177i | ||||
\(56\) | − | 0.701050i | − | 0.0936817i | ||||||
\(57\) | −8.26168 | + | 9.03081i | −1.09429 | + | 1.19616i | ||||
\(58\) | −8.68061 | −1.13982 | ||||||||
\(59\) | − | 3.82704i | − | 0.498238i | −0.968473 | − | 0.249119i | \(-0.919859\pi\) | ||
0.968473 | − | 0.249119i | \(-0.0801411\pi\) | |||||||
\(60\) | 6.60882i | 0.853195i | ||||||||
\(61\) | − | 3.98693i | − | 0.510474i | −0.966879 | − | 0.255237i | \(-0.917847\pi\) | ||
0.966879 | − | 0.255237i | \(-0.0821535\pi\) | |||||||
\(62\) | 14.1849i | 1.80149i | ||||||||
\(63\) | − | 4.64175i | − | 0.584806i | ||||||
\(64\) | −10.5344 | −1.31680 | ||||||||
\(65\) | −3.48762 | −0.432586 | ||||||||
\(66\) | −18.6482 | + | 5.46294i | −2.29543 | + | 0.672441i | ||||
\(67\) | 7.67189i | 0.937270i | 0.883392 | + | 0.468635i | \(0.155254\pi\) | ||||
−0.883392 | + | 0.468635i | \(0.844746\pi\) | |||||||
\(68\) | 2.97265i | 0.360487i | ||||||||
\(69\) | − | 13.8023i | − | 1.66161i | ||||||
\(70\) | 1.98271i | 0.236980i | ||||||||
\(71\) | 8.48153i | 1.00657i | 0.864120 | + | 0.503286i | \(0.167876\pi\) | ||||
−0.864120 | + | 0.503286i | \(0.832124\pi\) | |||||||
\(72\) | 3.60377 | 0.424708 | ||||||||
\(73\) | − | 6.81980i | − | 0.798197i | −0.916908 | − | 0.399098i | \(-0.869323\pi\) | ||
0.916908 | − | 0.399098i | \(-0.130677\pi\) | |||||||
\(74\) | 7.49390i | 0.871148i | ||||||||
\(75\) | − | 2.80799i | − | 0.324238i | ||||||
\(76\) | −7.56939 | − | 6.92473i | −0.868268 | − | 0.794321i | ||||
\(77\) | −3.02451 | + | 0.886023i | −0.344675 | + | 0.100972i | ||||
\(78\) | 20.4337i | 2.31366i | ||||||||
\(79\) | −14.7309 | −1.65735 | −0.828676 | − | 0.559728i | \(-0.810905\pi\) | ||||
−0.828676 | + | 0.559728i | \(0.810905\pi\) | |||||||
\(80\) | 3.16782 | 0.354173 | ||||||||
\(81\) | 0.206737 | 0.0229708 | ||||||||
\(82\) | 6.94927 | 0.767419 | ||||||||
\(83\) | 10.4685i | 1.14906i | 0.818482 | + | 0.574532i | \(0.194816\pi\) | ||||
−0.818482 | + | 0.574532i | \(0.805184\pi\) | |||||||
\(84\) | 6.28002 | 0.685206 | ||||||||
\(85\) | − | 1.26303i | − | 0.136995i | ||||||
\(86\) | 4.22864i | 0.455986i | ||||||||
\(87\) | − | 11.6821i | − | 1.25245i | ||||||
\(88\) | −0.687892 | − | 2.34817i | −0.0733295 | − | 0.250316i | ||||
\(89\) | − | 4.45627i | − | 0.472364i | −0.971709 | − | 0.236182i | \(-0.924104\pi\) | ||
0.971709 | − | 0.236182i | \(-0.0758961\pi\) | |||||||
\(90\) | −10.1922 | −1.07435 | ||||||||
\(91\) | 3.31410i | 0.347412i | ||||||||
\(92\) | 11.5688 | 1.20613 | ||||||||
\(93\) | −19.0897 | −1.97951 | ||||||||
\(94\) | −19.3051 | −1.99117 | ||||||||
\(95\) | 3.21612 | + | 2.94221i | 0.329967 | + | 0.301864i | ||||
\(96\) | − | 22.7032i | − | 2.31714i | ||||||
\(97\) | − | 10.0583i | − | 1.02127i | −0.859798 | − | 0.510635i | \(-0.829410\pi\) | ||
0.859798 | − | 0.510635i | \(-0.170590\pi\) | |||||||
\(98\) | −12.7216 | −1.28508 | ||||||||
\(99\) | −4.55463 | − | 15.5476i | −0.457758 | − | 1.56259i | ||||
\(100\) | 2.35358 | 0.235358 | ||||||||
\(101\) | 0.514789i | 0.0512234i | 0.999672 | + | 0.0256117i | \(0.00815335\pi\) | ||||
−0.999672 | + | 0.0256117i | \(0.991847\pi\) | |||||||
\(102\) | −7.40002 | −0.732711 | ||||||||
\(103\) | − | 14.7928i | − | 1.45757i | −0.684740 | − | 0.728787i | \(-0.740084\pi\) | ||
0.684740 | − | 0.728787i | \(-0.259916\pi\) | |||||||
\(104\) | −2.57301 | −0.252304 | ||||||||
\(105\) | −2.66828 | −0.260398 | ||||||||
\(106\) | 8.25077i | 0.801386i | ||||||||
\(107\) | −0.507132 | −0.0490263 | −0.0245131 | − | 0.999700i | \(-0.507804\pi\) | ||||
−0.0245131 | + | 0.999700i | \(0.507804\pi\) | |||||||
\(108\) | 12.4562i | 1.19860i | ||||||||
\(109\) | 5.33073 | 0.510591 | 0.255296 | − | 0.966863i | \(-0.417827\pi\) | ||||
0.255296 | + | 0.966863i | \(0.417827\pi\) | |||||||
\(110\) | 1.94550 | + | 6.64112i | 0.185496 | + | 0.633206i | ||||
\(111\) | −10.0851 | −0.957234 | ||||||||
\(112\) | − | 3.01021i | − | 0.284438i | ||||||
\(113\) | − | 6.94230i | − | 0.653077i | −0.945184 | − | 0.326538i | \(-0.894118\pi\) | ||
0.945184 | − | 0.326538i | \(-0.105882\pi\) | |||||||
\(114\) | 17.2382 | − | 18.8430i | 1.61450 | − | 1.76481i | ||||
\(115\) | −4.91539 | −0.458362 | ||||||||
\(116\) | 9.79165 | 0.909132 | ||||||||
\(117\) | −17.0362 | −1.57500 | ||||||||
\(118\) | 7.98521i | 0.735098i | ||||||||
\(119\) | −1.20020 | −0.110022 | ||||||||
\(120\) | − | 2.07160i | − | 0.189111i | ||||||
\(121\) | −9.26121 | + | 5.93548i | −0.841929 | + | 0.539589i | ||||
\(122\) | 8.31882i | 0.753151i | ||||||||
\(123\) | 9.35213i | 0.843254i | ||||||||
\(124\) | − | 16.0005i | − | 1.43689i | ||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 9.68513i | 0.862820i | ||||||||
\(127\) | −5.90787 | −0.524239 | −0.262120 | − | 0.965035i | \(-0.584421\pi\) | ||||
−0.262120 | + | 0.965035i | \(0.584421\pi\) | |||||||
\(128\) | 5.80980 | 0.513519 | ||||||||
\(129\) | −5.69079 | −0.501046 | ||||||||
\(130\) | 7.27700 | 0.638235 | ||||||||
\(131\) | − | 5.48750i | − | 0.479445i | −0.970841 | − | 0.239722i | \(-0.922944\pi\) | ||
0.970841 | − | 0.239722i | \(-0.0770564\pi\) | |||||||
\(132\) | 21.0350 | − | 6.16215i | 1.83086 | − | 0.536346i | ||||
\(133\) | 2.79583 | − | 3.05611i | 0.242429 | − | 0.264998i | ||||
\(134\) | − | 16.0076i | − | 1.38284i | ||||||
\(135\) | − | 5.29243i | − | 0.455500i | ||||||
\(136\) | − | 0.931809i | − | 0.0799020i | ||||||
\(137\) | 18.1170 | 1.54784 | 0.773921 | − | 0.633282i | \(-0.218293\pi\) | ||||
0.773921 | + | 0.633282i | \(0.218293\pi\) | |||||||
\(138\) | 28.7989i | 2.45152i | ||||||||
\(139\) | − | 9.63153i | − | 0.816935i | −0.912773 | − | 0.408468i | \(-0.866063\pi\) | ||
0.912773 | − | 0.408468i | \(-0.133937\pi\) | |||||||
\(140\) | − | 2.23649i | − | 0.189018i | ||||||
\(141\) | − | 25.9802i | − | 2.18793i | ||||||
\(142\) | − | 17.6969i | − | 1.48509i | ||||||
\(143\) | 3.25190 | + | 11.1006i | 0.271937 | + | 0.928279i | ||||
\(144\) | 15.4741 | 1.28951 | ||||||||
\(145\) | −4.16032 | −0.345496 | ||||||||
\(146\) | 14.2297i | 1.17766i | ||||||||
\(147\) | − | 17.1204i | − | 1.41206i | ||||||
\(148\) | − | 8.45306i | − | 0.694837i | ||||||
\(149\) | − | 20.0757i | − | 1.64466i | −0.569010 | − | 0.822331i | \(-0.692673\pi\) | ||
0.569010 | − | 0.822331i | \(-0.307327\pi\) | |||||||
\(150\) | 5.85893i | 0.478379i | ||||||||
\(151\) | 22.4123 | 1.82389 | 0.911943 | − | 0.410318i | \(-0.134582\pi\) | ||||
0.911943 | + | 0.410318i | \(0.134582\pi\) | |||||||
\(152\) | 2.37270 | + | 2.17063i | 0.192452 | + | 0.176061i | ||||
\(153\) | − | 6.16964i | − | 0.498786i | ||||||
\(154\) | 6.31071 | − | 1.84871i | 0.508531 | − | 0.148973i | ||||
\(155\) | 6.79836i | 0.546057i | ||||||||
\(156\) | − | 23.0490i | − | 1.84540i | ||||||
\(157\) | 20.9743 | 1.67393 | 0.836966 | − | 0.547255i | \(-0.184327\pi\) | ||||
0.836966 | + | 0.547255i | \(0.184327\pi\) | |||||||
\(158\) | 30.7363 | 2.44525 | ||||||||
\(159\) | −11.1037 | −0.880577 | ||||||||
\(160\) | −8.08524 | −0.639194 | ||||||||
\(161\) | 4.67084i | 0.368114i | ||||||||
\(162\) | −0.431362 | −0.0338910 | ||||||||
\(163\) | 3.09195 | 0.242180 | 0.121090 | − | 0.992642i | \(-0.461361\pi\) | ||||
0.121090 | + | 0.992642i | \(0.461361\pi\) | |||||||
\(164\) | −7.83872 | −0.612101 | ||||||||
\(165\) | −8.93743 | + | 2.61820i | −0.695778 | + | 0.203827i | ||||
\(166\) | − | 21.8427i | − | 1.69532i | ||||||
\(167\) | −6.49141 | −0.502320 | −0.251160 | − | 0.967946i | \(-0.580812\pi\) | ||||
−0.251160 | + | 0.967946i | \(0.580812\pi\) | |||||||
\(168\) | −1.96854 | −0.151876 | ||||||||
\(169\) | −0.836519 | −0.0643476 | ||||||||
\(170\) | 2.63535i | 0.202122i | ||||||||
\(171\) | 15.7100 | + | 14.3720i | 1.20138 | + | 1.09906i | ||||
\(172\) | − | 4.76987i | − | 0.363699i | ||||||
\(173\) | −10.6352 | −0.808579 | −0.404290 | − | 0.914631i | \(-0.632481\pi\) | ||||
−0.404290 | + | 0.914631i | \(0.632481\pi\) | |||||||
\(174\) | 24.3750i | 1.84787i | ||||||||
\(175\) | 0.950248i | 0.0718320i | ||||||||
\(176\) | −2.95371 | − | 10.0827i | −0.222645 | − | 0.760014i | ||||
\(177\) | −10.7463 | −0.807739 | ||||||||
\(178\) | 9.29812i | 0.696923i | ||||||||
\(179\) | 17.5731i | 1.31347i | 0.754119 | + | 0.656737i | \(0.228064\pi\) | ||||
−0.754119 | + | 0.656737i | \(0.771936\pi\) | |||||||
\(180\) | 11.4967 | 0.856915 | ||||||||
\(181\) | 15.8579i | 1.17871i | 0.807875 | + | 0.589354i | \(0.200618\pi\) | ||||
−0.807875 | + | 0.589354i | \(0.799382\pi\) | |||||||
\(182\) | − | 6.91495i | − | 0.512570i | ||||||
\(183\) | −11.1952 | −0.827576 | ||||||||
\(184\) | −3.62635 | −0.267338 | ||||||||
\(185\) | 3.59157i | 0.264058i | ||||||||
\(186\) | 39.8311 | 2.92056 | ||||||||
\(187\) | −4.02006 | + | 1.17767i | −0.293976 | + | 0.0861196i | ||||
\(188\) | 21.7760 | 1.58817 | ||||||||
\(189\) | −5.02913 | −0.365815 | ||||||||
\(190\) | −6.71050 | − | 6.13899i | −0.486831 | − | 0.445369i | ||||
\(191\) | −7.01749 | −0.507768 | −0.253884 | − | 0.967235i | \(-0.581708\pi\) | ||||
−0.253884 | + | 0.967235i | \(0.581708\pi\) | |||||||
\(192\) | 29.5804i | 2.13478i | ||||||||
\(193\) | 13.1516 | 0.946671 | 0.473335 | − | 0.880882i | \(-0.343050\pi\) | ||||
0.473335 | + | 0.880882i | \(0.343050\pi\) | |||||||
\(194\) | 20.9870i | 1.50678i | ||||||||
\(195\) | 9.79318i | 0.701304i | ||||||||
\(196\) | 14.3498 | 1.02499 | ||||||||
\(197\) | − | 14.1879i | − | 1.01085i | −0.862871 | − | 0.505423i | \(-0.831336\pi\) | ||
0.862871 | − | 0.505423i | \(-0.168664\pi\) | |||||||
\(198\) | 9.50334 | + | 32.4404i | 0.675373 | + | 2.30544i | ||||
\(199\) | −10.7532 | −0.762277 | −0.381138 | − | 0.924518i | \(-0.624468\pi\) | ||||
−0.381138 | + | 0.924518i | \(0.624468\pi\) | |||||||
\(200\) | −0.737755 | −0.0521671 | ||||||||
\(201\) | 21.5425 | 1.51949 | ||||||||
\(202\) | − | 1.07412i | − | 0.0755747i | ||||||
\(203\) | 3.95334i | 0.277470i | ||||||||
\(204\) | 8.34716 | 0.584418 | ||||||||
\(205\) | 3.33055 | 0.232616 | ||||||||
\(206\) | 30.8655i | 2.15050i | ||||||||
\(207\) | −24.0106 | −1.66885 | ||||||||
\(208\) | −11.0481 | −0.766051 | ||||||||
\(209\) | 6.36590 | − | 12.9798i | 0.440339 | − | 0.897832i | ||||
\(210\) | 5.56743 | 0.384189 | ||||||||
\(211\) | −4.70262 | −0.323742 | −0.161871 | − | 0.986812i | \(-0.551753\pi\) | ||||
−0.161871 | + | 0.986812i | \(0.551753\pi\) | |||||||
\(212\) | − | 9.30680i | − | 0.639194i | ||||||
\(213\) | 23.8160 | 1.63185 | ||||||||
\(214\) | 1.05814 | 0.0723331 | ||||||||
\(215\) | 2.02665i | 0.138216i | ||||||||
\(216\) | − | 3.90452i | − | 0.265669i | ||||||
\(217\) | 6.46013 | 0.438542 | ||||||||
\(218\) | −11.1227 | −0.753324 | ||||||||
\(219\) | −19.1499 | −1.29403 | ||||||||
\(220\) | −2.19451 | − | 7.49112i | −0.147954 | − | 0.505051i | ||||
\(221\) | 4.40498i | 0.296311i | ||||||||
\(222\) | 21.0428 | 1.41230 | ||||||||
\(223\) | − | 21.1126i | − | 1.41380i | −0.707312 | − | 0.706901i | \(-0.750093\pi\) | ||
0.707312 | − | 0.706901i | \(-0.249907\pi\) | |||||||
\(224\) | 7.68298i | 0.513341i | ||||||||
\(225\) | −4.88478 | −0.325652 | ||||||||
\(226\) | 14.4853i | 0.963546i | ||||||||
\(227\) | −15.9318 | −1.05743 | −0.528716 | − | 0.848799i | \(-0.677326\pi\) | ||||
−0.528716 | + | 0.848799i | \(0.677326\pi\) | |||||||
\(228\) | −19.4445 | + | 21.2547i | −1.28775 | + | 1.40763i | ||||
\(229\) | −5.82050 | −0.384630 | −0.192315 | − | 0.981333i | \(-0.561599\pi\) | ||||
−0.192315 | + | 0.981333i | \(0.561599\pi\) | |||||||
\(230\) | 10.2561 | 0.676265 | ||||||||
\(231\) | 2.48794 | + | 8.49277i | 0.163694 | + | 0.558783i | ||||
\(232\) | −3.06930 | −0.201509 | ||||||||
\(233\) | 12.5412i | 0.821599i | 0.911726 | + | 0.410799i | \(0.134750\pi\) | ||||
−0.911726 | + | 0.410799i | \(0.865250\pi\) | |||||||
\(234\) | 35.5465 | 2.32375 | ||||||||
\(235\) | −9.25227 | −0.603551 | ||||||||
\(236\) | − | 9.00725i | − | 0.586322i | ||||||
\(237\) | 41.3641i | 2.68688i | ||||||||
\(238\) | 2.50424 | 0.162326 | ||||||||
\(239\) | 18.9852i | 1.22805i | 0.789286 | + | 0.614026i | \(0.210451\pi\) | ||||
−0.789286 | + | 0.614026i | \(0.789549\pi\) | |||||||
\(240\) | − | 8.89519i | − | 0.574182i | ||||||
\(241\) | −15.6024 | −1.00504 | −0.502520 | − | 0.864565i | \(-0.667594\pi\) | ||||
−0.502520 | + | 0.864565i | \(0.667594\pi\) | |||||||
\(242\) | 19.3237 | − | 12.3845i | 1.24218 | − | 0.796107i | ||||
\(243\) | 15.2968i | 0.981289i | ||||||||
\(244\) | − | 9.38356i | − | 0.600721i | ||||||
\(245\) | −6.09703 | −0.389525 | ||||||||
\(246\) | − | 19.5134i | − | 1.24413i | ||||||
\(247\) | −11.2166 | − | 10.2613i | −0.713694 | − | 0.652911i | ||||
\(248\) | 5.01552i | 0.318486i | ||||||||
\(249\) | 29.3953 | 1.86285 | ||||||||
\(250\) | 2.08652 | 0.131963 | ||||||||
\(251\) | 4.08182 | 0.257642 | 0.128821 | − | 0.991668i | \(-0.458881\pi\) | ||||
0.128821 | + | 0.991668i | \(0.458881\pi\) | |||||||
\(252\) | − | 10.9247i | − | 0.688194i | ||||||
\(253\) | 4.58317 | + | 15.6450i | 0.288141 | + | 0.983592i | ||||
\(254\) | 12.3269 | 0.773460 | ||||||||
\(255\) | −3.54658 | −0.222095 | ||||||||
\(256\) | 8.94651 | 0.559157 | ||||||||
\(257\) | − | 22.3096i | − | 1.39163i | −0.718220 | − | 0.695816i | \(-0.755043\pi\) | ||
0.718220 | − | 0.695816i | \(-0.244957\pi\) | |||||||
\(258\) | 11.8740 | 0.739241 | ||||||||
\(259\) | 3.41289 | 0.212066 | ||||||||
\(260\) | −8.20839 | −0.509063 | ||||||||
\(261\) | −20.3223 | −1.25792 | ||||||||
\(262\) | 11.4498i | 0.707371i | ||||||||
\(263\) | − | 14.7638i | − | 0.910374i | −0.890396 | − | 0.455187i | \(-0.849572\pi\) | ||
0.890396 | − | 0.455187i | \(-0.150428\pi\) | |||||||
\(264\) | −6.59363 | + | 1.93159i | −0.405810 | + | 0.118881i | ||||
\(265\) | 3.95431i | 0.242912i | ||||||||
\(266\) | −5.83356 | + | 6.37664i | −0.357679 | + | 0.390977i | ||||
\(267\) | −12.5131 | −0.765792 | ||||||||
\(268\) | 18.0564i | 1.10297i | ||||||||
\(269\) | 21.1294i | 1.28828i | 0.764906 | + | 0.644142i | \(0.222785\pi\) | ||||
−0.764906 | + | 0.644142i | \(0.777215\pi\) | |||||||
\(270\) | 11.0428i | 0.672043i | ||||||||
\(271\) | − | 21.8317i | − | 1.32618i | −0.748539 | − | 0.663090i | \(-0.769245\pi\) | ||
0.748539 | − | 0.663090i | \(-0.230755\pi\) | |||||||
\(272\) | − | 4.00106i | − | 0.242600i | ||||||
\(273\) | 9.30595 | 0.563222 | ||||||||
\(274\) | −37.8016 | −2.28368 | ||||||||
\(275\) | 0.932412 | + | 3.18286i | 0.0562266 | + | 0.191934i | ||||
\(276\) | − | 32.4849i | − | 1.95536i | ||||||
\(277\) | − | 9.20960i | − | 0.553351i | −0.960963 | − | 0.276676i | \(-0.910767\pi\) | ||
0.960963 | − | 0.276676i | \(-0.0892328\pi\) | |||||||
\(278\) | 20.0964i | 1.20530i | ||||||||
\(279\) | 33.2085i | 1.98814i | ||||||||
\(280\) | 0.701050i | 0.0418957i | ||||||||
\(281\) | 30.4292 | 1.81525 | 0.907626 | − | 0.419780i | \(-0.137893\pi\) | ||||
0.907626 | + | 0.419780i | \(0.137893\pi\) | |||||||
\(282\) | 54.2083i | 3.22806i | ||||||||
\(283\) | 6.01030i | 0.357276i | 0.983915 | + | 0.178638i | \(0.0571690\pi\) | ||||
−0.983915 | + | 0.178638i | \(0.942831\pi\) | |||||||
\(284\) | 19.9620i | 1.18452i | ||||||||
\(285\) | 8.26168 | − | 9.03081i | 0.489380 | − | 0.534939i | ||||
\(286\) | −6.78516 | − | 23.1617i | −0.401215 | − | 1.36958i | ||||
\(287\) | − | 3.16485i | − | 0.186815i | ||||||
\(288\) | −39.4946 | −2.32724 | ||||||||
\(289\) | 15.4047 | 0.906162 | ||||||||
\(290\) | 8.68061 | 0.509743 | ||||||||
\(291\) | −28.2437 | −1.65567 | ||||||||
\(292\) | − | 16.0509i | − | 0.939310i | ||||||
\(293\) | 4.39914 | 0.257000 | 0.128500 | − | 0.991709i | \(-0.458984\pi\) | ||||
0.128500 | + | 0.991709i | \(0.458984\pi\) | |||||||
\(294\) | 35.7220i | 2.08335i | ||||||||
\(295\) | 3.82704i | 0.222819i | ||||||||
\(296\) | 2.64970i | 0.154011i | ||||||||
\(297\) | −16.8451 | + | 4.93473i | −0.977451 | + | 0.286342i | ||||
\(298\) | 41.8883i | 2.42653i | ||||||||
\(299\) | 17.1430 | 0.991405 | ||||||||
\(300\) | − | 6.60882i | − | 0.381560i | ||||||
\(301\) | 1.92582 | 0.111002 | ||||||||
\(302\) | −46.7637 | −2.69095 | ||||||||
\(303\) | 1.44552 | 0.0830429 | ||||||||
\(304\) | 10.1881 | + | 9.32039i | 0.584326 | + | 0.534561i | ||||
\(305\) | 3.98693i | 0.228291i | ||||||||
\(306\) | 12.8731i | 0.735906i | ||||||||
\(307\) | 23.5683 | 1.34512 | 0.672558 | − | 0.740045i | \(-0.265196\pi\) | ||||
0.672558 | + | 0.740045i | \(0.265196\pi\) | |||||||
\(308\) | −7.11842 | + | 2.08533i | −0.405610 | + | 0.118823i | ||||
\(309\) | −41.5379 | −2.36301 | ||||||||
\(310\) | − | 14.1849i | − | 0.805650i | ||||||
\(311\) | 15.3269 | 0.869107 | 0.434554 | − | 0.900646i | \(-0.356906\pi\) | ||||
0.434554 | + | 0.900646i | \(0.356906\pi\) | |||||||
\(312\) | 7.22496i | 0.409033i | ||||||||
\(313\) | −2.74950 | −0.155411 | −0.0777054 | − | 0.996976i | \(-0.524759\pi\) | ||||
−0.0777054 | + | 0.996976i | \(0.524759\pi\) | |||||||
\(314\) | −43.7634 | −2.46971 | ||||||||
\(315\) | 4.64175i | 0.261533i | ||||||||
\(316\) | −34.6703 | −1.95036 | ||||||||
\(317\) | 31.9622i | 1.79517i | 0.440837 | + | 0.897587i | \(0.354682\pi\) | ||||
−0.440837 | + | 0.897587i | \(0.645318\pi\) | |||||||
\(318\) | 23.1680 | 1.29920 | ||||||||
\(319\) | 3.87914 | + | 13.2417i | 0.217190 | + | 0.741394i | ||||
\(320\) | 10.5344 | 0.588891 | ||||||||
\(321\) | 1.42402i | 0.0794809i | ||||||||
\(322\) | − | 9.74581i | − | 0.543113i | ||||||
\(323\) | 3.71611 | − | 4.06206i | 0.206770 | − | 0.226019i | ||||
\(324\) | 0.486573 | 0.0270318 | ||||||||
\(325\) | 3.48762 | 0.193458 | ||||||||
\(326\) | −6.45142 | −0.357311 | ||||||||
\(327\) | − | 14.9686i | − | 0.827766i | ||||||
\(328\) | 2.45713 | 0.135672 | ||||||||
\(329\) | 8.79195i | 0.484716i | ||||||||
\(330\) | 18.6482 | − | 5.46294i | 1.02655 | − | 0.300725i | ||||
\(331\) | − | 18.4799i | − | 1.01575i | −0.861432 | − | 0.507873i | \(-0.830432\pi\) | ||
0.861432 | − | 0.507873i | \(-0.169568\pi\) | |||||||
\(332\) | 24.6384i | 1.35221i | ||||||||
\(333\) | 17.5440i | 0.961408i | ||||||||
\(334\) | 13.5445 | 0.741120 | ||||||||
\(335\) | − | 7.67189i | − | 0.419160i | ||||||
\(336\) | −8.45264 | −0.461129 | ||||||||
\(337\) | 29.1007 | 1.58522 | 0.792609 | − | 0.609730i | \(-0.208722\pi\) | ||||
0.792609 | + | 0.609730i | \(0.208722\pi\) | |||||||
\(338\) | 1.74542 | 0.0949381 | ||||||||
\(339\) | −19.4939 | −1.05876 | ||||||||
\(340\) | − | 2.97265i | − | 0.161215i | ||||||
\(341\) | 21.6382 | − | 6.33887i | 1.17178 | − | 0.343269i | ||||
\(342\) | −32.7793 | − | 29.9876i | −1.77250 | − | 1.62154i | ||||
\(343\) | 12.4454i | 0.671990i | ||||||||
\(344\) | 1.49517i | 0.0806140i | ||||||||
\(345\) | 13.8023i | 0.743093i | ||||||||
\(346\) | 22.1906 | 1.19297 | ||||||||
\(347\) | − | 33.5456i | − | 1.80082i | −0.435042 | − | 0.900410i | \(-0.643266\pi\) | ||
0.435042 | − | 0.900410i | \(-0.356734\pi\) | |||||||
\(348\) | − | 27.4948i | − | 1.47388i | ||||||
\(349\) | − | 9.62017i | − | 0.514956i | −0.966284 | − | 0.257478i | \(-0.917109\pi\) | ||
0.966284 | − | 0.257478i | \(-0.0828915\pi\) | |||||||
\(350\) | − | 1.98271i | − | 0.105981i | ||||||
\(351\) | 18.4580i | 0.985215i | ||||||||
\(352\) | 7.53878 | + | 25.7342i | 0.401818 | + | 1.37164i | ||||
\(353\) | 28.5325 | 1.51863 | 0.759317 | − | 0.650721i | \(-0.225533\pi\) | ||||
0.759317 | + | 0.650721i | \(0.225533\pi\) | |||||||
\(354\) | 22.4224 | 1.19173 | ||||||||
\(355\) | − | 8.48153i | − | 0.450153i | ||||||
\(356\) | − | 10.4882i | − | 0.555873i | ||||||
\(357\) | 3.37013i | 0.178366i | ||||||||
\(358\) | − | 36.6667i | − | 1.93789i | ||||||
\(359\) | − | 6.37196i | − | 0.336299i | −0.985761 | − | 0.168150i | \(-0.946221\pi\) | ||
0.985761 | − | 0.168150i | \(-0.0537792\pi\) | |||||||
\(360\) | −3.60377 | −0.189935 | ||||||||
\(361\) | 1.68680 | + | 18.9250i | 0.0887790 | + | 0.996051i | ||||
\(362\) | − | 33.0879i | − | 1.73906i | ||||||
\(363\) | 16.6667 | + | 26.0054i | 0.874777 | + | 1.36493i | ||||
\(364\) | 7.80001i | 0.408831i | ||||||||
\(365\) | 6.81980i | 0.356964i | ||||||||
\(366\) | 23.3591 | 1.22100 | ||||||||
\(367\) | −28.4067 | −1.48282 | −0.741409 | − | 0.671053i | \(-0.765842\pi\) | ||||
−0.741409 | + | 0.671053i | \(0.765842\pi\) | |||||||
\(368\) | −15.5711 | −0.811697 | ||||||||
\(369\) | 16.2690 | 0.846931 | ||||||||
\(370\) | − | 7.49390i | − | 0.389589i | ||||||
\(371\) | 3.75758 | 0.195084 | ||||||||
\(372\) | −44.9291 | −2.32947 | ||||||||
\(373\) | 12.6887 | 0.656997 | 0.328499 | − | 0.944504i | \(-0.393457\pi\) | ||||
0.328499 | + | 0.944504i | \(0.393457\pi\) | |||||||
\(374\) | 8.38795 | − | 2.45723i | 0.433731 | − | 0.127060i | ||||
\(375\) | 2.80799i | 0.145004i | ||||||||
\(376\) | −6.82590 | −0.352019 | ||||||||
\(377\) | 14.5096 | 0.747283 | ||||||||
\(378\) | 10.4934 | 0.539722 | ||||||||
\(379\) | − | 7.43879i | − | 0.382105i | −0.981580 | − | 0.191052i | \(-0.938810\pi\) | ||
0.981580 | − | 0.191052i | \(-0.0611901\pi\) | |||||||
\(380\) | 7.56939 | + | 6.92473i | 0.388301 | + | 0.355231i | ||||
\(381\) | 16.5892i | 0.849892i | ||||||||
\(382\) | 14.6422 | 0.749158 | ||||||||
\(383\) | 3.69512i | 0.188812i | 0.995534 | + | 0.0944059i | \(0.0300951\pi\) | ||||
−0.995534 | + | 0.0944059i | \(0.969905\pi\) | |||||||
\(384\) | − | 16.3138i | − | 0.832512i | ||||||
\(385\) | 3.02451 | − | 0.886023i | 0.154143 | − | 0.0451559i | ||||
\(386\) | −27.4411 | −1.39671 | ||||||||
\(387\) | 9.89972i | 0.503231i | ||||||||
\(388\) | − | 23.6731i | − | 1.20182i | ||||||
\(389\) | −25.9011 | −1.31324 | −0.656618 | − | 0.754223i | \(-0.728014\pi\) | ||||
−0.656618 | + | 0.754223i | \(0.728014\pi\) | |||||||
\(390\) | − | 20.4337i | − | 1.03470i | ||||||
\(391\) | 6.20830i | 0.313967i | ||||||||
\(392\) | −4.49811 | −0.227189 | ||||||||
\(393\) | −15.4088 | −0.777272 | ||||||||
\(394\) | 29.6034i | 1.49140i | ||||||||
\(395\) | 14.7309 | 0.741190 | ||||||||
\(396\) | −10.7197 | − | 36.5925i | −0.538685 | − | 1.83884i | ||||
\(397\) | 23.0974 | 1.15923 | 0.579613 | − | 0.814892i | \(-0.303204\pi\) | ||||
0.579613 | + | 0.814892i | \(0.303204\pi\) | |||||||
\(398\) | 22.4369 | 1.12466 | ||||||||
\(399\) | −8.58150 | − | 7.85065i | −0.429613 | − | 0.393024i | ||||
\(400\) | −3.16782 | −0.158391 | ||||||||
\(401\) | 7.33323i | 0.366204i | 0.983094 | + | 0.183102i | \(0.0586139\pi\) | ||||
−0.983094 | + | 0.183102i | \(0.941386\pi\) | |||||||
\(402\) | −44.9490 | −2.24185 | ||||||||
\(403\) | − | 23.7101i | − | 1.18108i | ||||||
\(404\) | 1.21160i | 0.0602792i | ||||||||
\(405\) | −0.206737 | −0.0102729 | ||||||||
\(406\) | − | 8.24873i | − | 0.409378i | ||||||
\(407\) | 11.4315 | − | 3.34883i | 0.566637 | − | 0.165995i | ||||
\(408\) | −2.61651 | −0.129536 | ||||||||
\(409\) | 10.4417 | 0.516310 | 0.258155 | − | 0.966104i | \(-0.416885\pi\) | ||||
0.258155 | + | 0.966104i | \(0.416885\pi\) | |||||||
\(410\) | −6.94927 | −0.343200 | ||||||||
\(411\) | − | 50.8724i | − | 2.50935i | ||||||
\(412\) | − | 34.8160i | − | 1.71526i | ||||||
\(413\) | 3.63664 | 0.178947 | ||||||||
\(414\) | 50.0987 | 2.46221 | ||||||||
\(415\) | − | 10.4685i | − | 0.513877i | ||||||
\(416\) | 28.1982 | 1.38253 | ||||||||
\(417\) | −27.0452 | −1.32441 | ||||||||
\(418\) | −13.2826 | + | 27.0827i | −0.649673 | + | 1.32466i | ||||
\(419\) | 23.1341 | 1.13018 | 0.565088 | − | 0.825031i | \(-0.308842\pi\) | ||||
0.565088 | + | 0.825031i | \(0.308842\pi\) | |||||||
\(420\) | −6.28002 | −0.306434 | ||||||||
\(421\) | 11.8661i | 0.578317i | 0.957281 | + | 0.289159i | \(0.0933755\pi\) | ||||
−0.957281 | + | 0.289159i | \(0.906624\pi\) | |||||||
\(422\) | 9.81213 | 0.477647 | ||||||||
\(423\) | −45.1953 | −2.19747 | ||||||||
\(424\) | 2.91731i | 0.141677i | ||||||||
\(425\) | 1.26303i | 0.0612661i | ||||||||
\(426\) | −49.6927 | −2.40762 | ||||||||
\(427\) | 3.78857 | 0.183342 | ||||||||
\(428\) | −1.19358 | −0.0576936 | ||||||||
\(429\) | 31.1703 | − | 9.13128i | 1.50492 | − | 0.440863i | ||||
\(430\) | − | 4.22864i | − | 0.203923i | ||||||
\(431\) | 20.8611 | 1.00485 | 0.502423 | − | 0.864622i | \(-0.332442\pi\) | ||||
0.502423 | + | 0.864622i | \(0.332442\pi\) | |||||||
\(432\) | − | 16.7655i | − | 0.806629i | ||||||
\(433\) | − | 34.7817i | − | 1.67150i | −0.549110 | − | 0.835750i | \(-0.685033\pi\) | ||
0.549110 | − | 0.835750i | \(-0.314967\pi\) | |||||||
\(434\) | −13.4792 | −0.647023 | ||||||||
\(435\) | 11.6821i | 0.560115i | ||||||||
\(436\) | 12.5463 | 0.600859 | ||||||||
\(437\) | −15.8085 | − | 14.4621i | −0.756221 | − | 0.691816i | ||||
\(438\) | 39.9567 | 1.90920 | ||||||||
\(439\) | −3.35497 | −0.160124 | −0.0800621 | − | 0.996790i | \(-0.525512\pi\) | ||||
−0.0800621 | + | 0.996790i | \(0.525512\pi\) | |||||||
\(440\) | 0.687892 | + | 2.34817i | 0.0327940 | + | 0.111945i | ||||
\(441\) | −29.7826 | −1.41822 | ||||||||
\(442\) | − | 9.19109i | − | 0.437176i | ||||||
\(443\) | −11.9525 | −0.567882 | −0.283941 | − | 0.958842i | \(-0.591642\pi\) | ||||
−0.283941 | + | 0.958842i | \(0.591642\pi\) | |||||||
\(444\) | −23.7361 | −1.12646 | ||||||||
\(445\) | 4.45627i | 0.211248i | ||||||||
\(446\) | 44.0519i | 2.08592i | ||||||||
\(447\) | −56.3721 | −2.66631 | ||||||||
\(448\) | − | 10.0103i | − | 0.472942i | ||||||
\(449\) | − | 36.3872i | − | 1.71722i | −0.512632 | − | 0.858609i | \(-0.671329\pi\) | ||
0.512632 | − | 0.858609i | \(-0.328671\pi\) | |||||||
\(450\) | 10.1922 | 0.480465 | ||||||||
\(451\) | −3.10545 | − | 10.6007i | −0.146230 | − | 0.499166i | ||||
\(452\) | − | 16.3393i | − | 0.768535i | ||||||
\(453\) | − | 62.9333i | − | 2.95687i | ||||||
\(454\) | 33.2421 | 1.56013 | ||||||||
\(455\) | − | 3.31410i | − | 0.155368i | ||||||
\(456\) | 6.09509 | − | 6.66252i | 0.285429 | − | 0.312001i | ||||
\(457\) | 0.115471i | 0.00540151i | 0.999996 | + | 0.00270075i | \(0.000859678\pi\) | ||||
−0.999996 | + | 0.00270075i | \(0.999140\pi\) | |||||||
\(458\) | 12.1446 | 0.567481 | ||||||||
\(459\) | −6.68452 | −0.312007 | ||||||||
\(460\) | −11.5688 | −0.539396 | ||||||||
\(461\) | 11.3135i | 0.526921i | 0.964670 | + | 0.263460i | \(0.0848638\pi\) | ||||
−0.964670 | + | 0.263460i | \(0.915136\pi\) | |||||||
\(462\) | −5.19115 | − | 17.7204i | −0.241514 | − | 0.824426i | ||||
\(463\) | −3.86544 | −0.179642 | −0.0898211 | − | 0.995958i | \(-0.528630\pi\) | ||||
−0.0898211 | + | 0.995958i | \(0.528630\pi\) | |||||||
\(464\) | −13.1791 | −0.611826 | ||||||||
\(465\) | 19.0897 | 0.885263 | ||||||||
\(466\) | − | 26.1674i | − | 1.21218i | ||||||
\(467\) | −39.4161 | −1.82396 | −0.911979 | − | 0.410236i | \(-0.865446\pi\) | ||||
−0.911979 | + | 0.410236i | \(0.865446\pi\) | |||||||
\(468\) | −40.0962 | −1.85345 | ||||||||
\(469\) | −7.29019 | −0.336630 | ||||||||
\(470\) | 19.3051 | 0.890476 | ||||||||
\(471\) | − | 58.8955i | − | 2.71376i | ||||||
\(472\) | 2.82342i | 0.129958i | ||||||||
\(473\) | 6.45053 | − | 1.88967i | 0.296596 | − | 0.0868871i | ||||
\(474\) | − | 86.3071i | − | 3.96422i | ||||||
\(475\) | −3.21612 | − | 2.94221i | −0.147566 | − | 0.134998i | ||||
\(476\) | −2.82476 | −0.129473 | ||||||||
\(477\) | 19.3160i | 0.884417i | ||||||||
\(478\) | − | 39.6131i | − | 1.81186i | ||||||
\(479\) | − | 32.7400i | − | 1.49593i | −0.663739 | − | 0.747965i | \(-0.731031\pi\) | ||
0.663739 | − | 0.747965i | \(-0.268969\pi\) | |||||||
\(480\) | 22.7032i | 1.03626i | ||||||||
\(481\) | − | 12.5260i | − | 0.571138i | ||||||
\(482\) | 32.5548 | 1.48283 | ||||||||
\(483\) | 13.1156 | 0.596782 | ||||||||
\(484\) | −21.7970 | + | 13.9696i | −0.990773 | + | 0.634983i | ||||
\(485\) | 10.0583i | 0.456726i | ||||||||
\(486\) | − | 31.9171i | − | 1.44779i | ||||||
\(487\) | 26.3250i | 1.19290i | 0.802651 | + | 0.596449i | \(0.203422\pi\) | ||||
−0.802651 | + | 0.596449i | \(0.796578\pi\) | |||||||
\(488\) | 2.94138i | 0.133150i | ||||||||
\(489\) | − | 8.68214i | − | 0.392620i | ||||||
\(490\) | 12.7216 | 0.574703 | ||||||||
\(491\) | 19.7041i | 0.889232i | 0.895721 | + | 0.444616i | \(0.146660\pi\) | ||||
−0.895721 | + | 0.444616i | \(0.853340\pi\) | |||||||
\(492\) | 22.0110i | 0.992333i | ||||||||
\(493\) | 5.25463i | 0.236656i | ||||||||
\(494\) | 23.4037 | + | 21.4105i | 1.05298 | + | 0.963302i | ||||
\(495\) | 4.55463 | + | 15.5476i | 0.204715 | + | 0.698812i | ||||
\(496\) | 21.5360i | 0.966993i | ||||||||
\(497\) | −8.05956 | −0.361521 | ||||||||
\(498\) | −61.3340 | −2.74844 | ||||||||
\(499\) | −44.2332 | −1.98015 | −0.990075 | − | 0.140543i | \(-0.955115\pi\) | ||||
−0.990075 | + | 0.140543i | \(0.955115\pi\) | |||||||
\(500\) | −2.35358 | −0.105255 | ||||||||
\(501\) | 18.2278i | 0.814357i | ||||||||
\(502\) | −8.51682 | −0.380124 | ||||||||
\(503\) | − | 2.95430i | − | 0.131726i | −0.997829 | − | 0.0658629i | \(-0.979020\pi\) | ||
0.997829 | − | 0.0658629i | \(-0.0209800\pi\) | |||||||
\(504\) | 3.42448i | 0.152538i | ||||||||
\(505\) | − | 0.514789i | − | 0.0229078i | ||||||
\(506\) | −9.56289 | − | 32.6437i | −0.425122 | − | 1.45119i | ||||
\(507\) | 2.34893i | 0.104320i | ||||||||
\(508\) | −13.9047 | −0.616920 | ||||||||
\(509\) | 27.9392i | 1.23838i | 0.785241 | + | 0.619191i | \(0.212539\pi\) | ||||
−0.785241 | + | 0.619191i | \(0.787461\pi\) | |||||||
\(510\) | 7.40002 | 0.327679 | ||||||||
\(511\) | 6.48050 | 0.286680 | ||||||||
\(512\) | −30.2867 | −1.33850 | ||||||||
\(513\) | 15.5715 | − | 17.0211i | 0.687497 | − | 0.751499i | ||||
\(514\) | 46.5494i | 2.05321i | ||||||||
\(515\) | 14.7928i | 0.651847i | ||||||||
\(516\) | −13.3937 | −0.589626 | ||||||||
\(517\) | 8.62693 | + | 29.4487i | 0.379412 | + | 1.29515i | ||||
\(518\) | −7.12107 | −0.312882 | ||||||||
\(519\) | 29.8635i | 1.31086i | ||||||||
\(520\) | 2.57301 | 0.112834 | ||||||||
\(521\) | − | 15.8769i | − | 0.695577i | −0.937573 | − | 0.347789i | \(-0.886933\pi\) | ||
0.937573 | − | 0.347789i | \(-0.113067\pi\) | |||||||
\(522\) | 42.4029 | 1.85592 | ||||||||
\(523\) | −30.4812 | −1.33285 | −0.666425 | − | 0.745572i | \(-0.732176\pi\) | ||||
−0.666425 | + | 0.745572i | \(0.732176\pi\) | |||||||
\(524\) | − | 12.9153i | − | 0.564206i | ||||||
\(525\) | 2.66828 | 0.116453 | ||||||||
\(526\) | 30.8050i | 1.34316i | ||||||||
\(527\) | 8.58656 | 0.374036 | ||||||||
\(528\) | −28.3122 | + | 8.29398i | −1.23213 | + | 0.360949i | ||||
\(529\) | 1.16103 | 0.0504795 | ||||||||
\(530\) | − | 8.25077i | − | 0.358391i | ||||||
\(531\) | 18.6943i | 0.811261i | ||||||||
\(532\) | 6.58021 | − | 7.19280i | 0.285288 | − | 0.311847i | ||||
\(533\) | −11.6157 | −0.503131 | ||||||||
\(534\) | 26.1090 | 1.12985 | ||||||||
\(535\) | 0.507132 | 0.0219252 | ||||||||
\(536\) | − | 5.65997i | − | 0.244473i | ||||||
\(537\) | 49.3450 | 2.12939 | ||||||||
\(538\) | − | 44.0871i | − | 1.90073i | ||||||
\(539\) | 5.68495 | + | 19.4060i | 0.244868 | + | 0.835875i | ||||
\(540\) | − | 12.4562i | − | 0.536028i | ||||||
\(541\) | 3.80497i | 0.163589i | 0.996649 | + | 0.0817943i | \(0.0260651\pi\) | ||||
−0.996649 | + | 0.0817943i | \(0.973935\pi\) | |||||||
\(542\) | 45.5523i | 1.95664i | ||||||||
\(543\) | 44.5287 | 1.91091 | ||||||||
\(544\) | 10.2119i | 0.437833i | ||||||||
\(545\) | −5.33073 | −0.228343 | ||||||||
\(546\) | −19.4171 | −0.830975 | ||||||||
\(547\) | −7.11949 | −0.304408 | −0.152204 | − | 0.988349i | \(-0.548637\pi\) | ||||
−0.152204 | + | 0.988349i | \(0.548637\pi\) | |||||||
\(548\) | 42.6399 | 1.82149 | ||||||||
\(549\) | 19.4753i | 0.831184i | ||||||||
\(550\) | −1.94550 | − | 6.64112i | −0.0829564 | − | 0.283178i | ||||
\(551\) | −13.3801 | − | 12.2405i | −0.570010 | − | 0.521465i | ||||
\(552\) | 10.1827i | 0.433406i | ||||||||
\(553\) | − | 13.9980i | − | 0.595255i | ||||||
\(554\) | 19.2161i | 0.816412i | ||||||||
\(555\) | 10.0851 | 0.428088 | ||||||||
\(556\) | − | 22.6686i | − | 0.961362i | ||||||
\(557\) | − | 35.6661i | − | 1.51122i | −0.655021 | − | 0.755611i | \(-0.727340\pi\) | ||
0.655021 | − | 0.755611i | \(-0.272660\pi\) | |||||||
\(558\) | − | 69.2903i | − | 2.93329i | ||||||
\(559\) | − | 7.06816i | − | 0.298952i | ||||||
\(560\) | 3.01021i | 0.127205i | ||||||||
\(561\) | 3.30688 | + | 11.2883i | 0.139616 | + | 0.476591i | ||||
\(562\) | −63.4912 | −2.67821 | ||||||||
\(563\) | −23.1419 | −0.975315 | −0.487657 | − | 0.873035i | \(-0.662148\pi\) | ||||
−0.487657 | + | 0.873035i | \(0.662148\pi\) | |||||||
\(564\) | − | 61.1466i | − | 2.57473i | ||||||
\(565\) | 6.94230i | 0.292065i | ||||||||
\(566\) | − | 12.5406i | − | 0.527123i | ||||||
\(567\) | 0.196452i | 0.00825020i | ||||||||
\(568\) | − | 6.25729i | − | 0.262550i | ||||||
\(569\) | −40.8965 | −1.71447 | −0.857236 | − | 0.514924i | \(-0.827820\pi\) | ||||
−0.857236 | + | 0.514924i | \(0.827820\pi\) | |||||||
\(570\) | −17.2382 | + | 18.8430i | −0.722028 | + | 0.789246i | ||||
\(571\) | 25.7532i | 1.07774i | 0.842390 | + | 0.538869i | \(0.181148\pi\) | ||||
−0.842390 | + | 0.538869i | \(0.818852\pi\) | |||||||
\(572\) | 7.65361 | + | 26.1262i | 0.320013 | + | 1.09239i | ||||
\(573\) | 19.7050i | 0.823189i | ||||||||
\(574\) | 6.60353i | 0.275626i | ||||||||
\(575\) | 4.91539 | 0.204986 | ||||||||
\(576\) | 51.4582 | 2.14409 | ||||||||
\(577\) | 17.6323 | 0.734043 | 0.367022 | − | 0.930212i | \(-0.380377\pi\) | ||||
0.367022 | + | 0.930212i | \(0.380377\pi\) | |||||||
\(578\) | −32.1424 | −1.33695 | ||||||||
\(579\) | − | 36.9294i | − | 1.53473i | ||||||
\(580\) | −9.79165 | −0.406576 | ||||||||
\(581\) | −9.94764 | −0.412697 | ||||||||
\(582\) | 58.9311 | 2.44277 | ||||||||
\(583\) | 12.5860 | − | 3.68705i | 0.521260 | − | 0.152702i | ||||
\(584\) | 5.03134i | 0.208198i | ||||||||
\(585\) | 17.0362 | 0.704362 | ||||||||
\(586\) | −9.17891 | −0.379177 | ||||||||
\(587\) | 16.5493 | 0.683065 | 0.341532 | − | 0.939870i | \(-0.389054\pi\) | ||||
0.341532 | + | 0.939870i | \(0.389054\pi\) | |||||||
\(588\) | − | 40.2942i | − | 1.66170i | ||||||
\(589\) | −20.0022 | + | 21.8643i | −0.824176 | + | 0.900903i | ||||
\(590\) | − | 7.98521i | − | 0.328746i | ||||||
\(591\) | −39.8394 | −1.63878 | ||||||||
\(592\) | 11.3775i | 0.467610i | ||||||||
\(593\) | 45.0420i | 1.84965i | 0.380389 | + | 0.924827i | \(0.375790\pi\) | ||||
−0.380389 | + | 0.924827i | \(0.624210\pi\) | |||||||
\(594\) | 35.1477 | − | 10.2964i | 1.44213 | − | 0.422468i | ||||
\(595\) | 1.20020 | 0.0492032 | ||||||||
\(596\) | − | 47.2497i | − | 1.93542i | ||||||
\(597\) | 30.1949i | 1.23580i | ||||||||
\(598\) | −35.7693 | −1.46271 | ||||||||
\(599\) | − | 0.394109i | − | 0.0161029i | −0.999968 | − | 0.00805143i | \(-0.997437\pi\) | ||
0.999968 | − | 0.00805143i | \(-0.00256288\pi\) | |||||||
\(600\) | 2.07160i | 0.0845729i | ||||||||
\(601\) | −11.6008 | −0.473209 | −0.236604 | − | 0.971606i | \(-0.576034\pi\) | ||||
−0.236604 | + | 0.971606i | \(0.576034\pi\) | |||||||
\(602\) | −4.01826 | −0.163772 | ||||||||
\(603\) | − | 37.4755i | − | 1.52612i | ||||||
\(604\) | 52.7491 | 2.14633 | ||||||||
\(605\) | 9.26121 | − | 5.93548i | 0.376522 | − | 0.241312i | ||||
\(606\) | −3.01611 | −0.122521 | ||||||||
\(607\) | 34.0839 | 1.38342 | 0.691712 | − | 0.722174i | \(-0.256857\pi\) | ||||
0.691712 | + | 0.722174i | \(0.256857\pi\) | |||||||
\(608\) | −26.0031 | − | 23.7885i | −1.05456 | − | 0.964750i | ||||
\(609\) | 11.1009 | 0.449832 | ||||||||
\(610\) | − | 8.31882i | − | 0.336819i | ||||||
\(611\) | 32.2684 | 1.30544 | ||||||||
\(612\) | − | 14.5208i | − | 0.586967i | ||||||
\(613\) | 21.0030i | 0.848303i | 0.905591 | + | 0.424151i | \(0.139428\pi\) | ||||
−0.905591 | + | 0.424151i | \(0.860572\pi\) | |||||||
\(614\) | −49.1759 | −1.98458 | ||||||||
\(615\) | − | 9.35213i | − | 0.377114i | ||||||
\(616\) | 2.23134 | − | 0.653668i | 0.0899034 | − | 0.0263370i | ||||
\(617\) | 47.0050 | 1.89235 | 0.946174 | − | 0.323658i | \(-0.104913\pi\) | ||||
0.946174 | + | 0.323658i | \(0.104913\pi\) | |||||||
\(618\) | 86.6697 | 3.48637 | ||||||||
\(619\) | −6.66187 | −0.267763 | −0.133882 | − | 0.990997i | \(-0.542744\pi\) | ||||
−0.133882 | + | 0.990997i | \(0.542744\pi\) | |||||||
\(620\) | 16.0005i | 0.642595i | ||||||||
\(621\) | 26.0144i | 1.04392i | ||||||||
\(622\) | −31.9799 | −1.28228 | ||||||||
\(623\) | 4.23456 | 0.169654 | ||||||||
\(624\) | 31.0230i | 1.24191i | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 5.73689 | 0.229292 | ||||||||
\(627\) | −36.4471 | − | 17.8754i | −1.45556 | − | 0.713873i | ||||
\(628\) | 49.3647 | 1.96987 | ||||||||
\(629\) | 4.53628 | 0.180873 | ||||||||
\(630\) | − | 9.68513i | − | 0.385865i | ||||||
\(631\) | 35.0854 | 1.39673 | 0.698363 | − | 0.715743i | \(-0.253912\pi\) | ||||
0.698363 | + | 0.715743i | \(0.253912\pi\) | |||||||
\(632\) | 10.8678 | 0.432297 | ||||||||
\(633\) | 13.2049i | 0.524847i | ||||||||
\(634\) | − | 66.6898i | − | 2.64859i | ||||||
\(635\) | 5.90787 | 0.234447 | ||||||||
\(636\) | −26.1334 | −1.03625 | ||||||||
\(637\) | 21.2641 | 0.842515 | ||||||||
\(638\) | −8.09391 | − | 27.6292i | −0.320441 | − | 1.09385i | ||||
\(639\) | − | 41.4304i | − | 1.63896i | ||||||
\(640\) | −5.80980 | −0.229653 | ||||||||
\(641\) | 17.1106i | 0.675830i | 0.941177 | + | 0.337915i | \(0.109722\pi\) | ||||
−0.941177 | + | 0.337915i | \(0.890278\pi\) | |||||||
\(642\) | − | 2.97125i | − | 0.117266i | ||||||
\(643\) | −2.50261 | −0.0986931 | −0.0493466 | − | 0.998782i | \(-0.515714\pi\) | ||||
−0.0493466 | + | 0.998782i | \(0.515714\pi\) | |||||||
\(644\) | 10.9932i | 0.433192i | ||||||||
\(645\) | 5.69079 | 0.224075 | ||||||||
\(646\) | −7.75375 | + | 8.47559i | −0.305067 | + | 0.333468i | ||||
\(647\) | 15.5165 | 0.610018 | 0.305009 | − | 0.952350i | \(-0.401341\pi\) | ||||
0.305009 | + | 0.952350i | \(0.401341\pi\) | |||||||
\(648\) | −0.152521 | −0.00599161 | ||||||||
\(649\) | 12.1809 | − | 3.56838i | 0.478144 | − | 0.140071i | ||||
\(650\) | −7.27700 | −0.285427 | ||||||||
\(651\) | − | 18.1399i | − | 0.710960i | ||||||
\(652\) | 7.27714 | 0.284995 | ||||||||
\(653\) | 18.2898 | 0.715737 | 0.357869 | − | 0.933772i | \(-0.383504\pi\) | ||||
0.357869 | + | 0.933772i | \(0.383504\pi\) | |||||||
\(654\) | 31.2323i | 1.22128i | ||||||||
\(655\) | 5.48750i | 0.214414i | ||||||||
\(656\) | 10.5506 | 0.411931 | ||||||||
\(657\) | 33.3132i | 1.29967i | ||||||||
\(658\) | − | 18.3446i | − | 0.715147i | ||||||
\(659\) | −43.1272 | −1.68000 | −0.840000 | − | 0.542587i | \(-0.817445\pi\) | ||||
−0.840000 | + | 0.542587i | \(0.817445\pi\) | |||||||
\(660\) | −21.0350 | + | 6.16215i | −0.818785 | + | 0.239861i | ||||
\(661\) | − | 4.89356i | − | 0.190337i | −0.995461 | − | 0.0951687i | \(-0.969661\pi\) | ||
0.995461 | − | 0.0951687i | \(-0.0303390\pi\) | |||||||
\(662\) | 38.5587i | 1.49863i | ||||||||
\(663\) | 12.3691 | 0.480377 | ||||||||
\(664\) | − | 7.72316i | − | 0.299717i | ||||||
\(665\) | −2.79583 | + | 3.05611i | −0.108418 | + | 0.118511i | ||||
\(666\) | − | 36.6061i | − | 1.41846i | ||||||
\(667\) | 20.4496 | 0.791811 | ||||||||
\(668\) | −15.2780 | −0.591125 | ||||||||
\(669\) | −59.2838 | −2.29204 | ||||||||
\(670\) | 16.0076i | 0.618426i | ||||||||
\(671\) | 12.6898 | − | 3.71746i | 0.489886 | − | 0.143511i | ||||
\(672\) | 21.5737 | 0.832224 | ||||||||
\(673\) | −0.745574 | −0.0287398 | −0.0143699 | − | 0.999897i | \(-0.504574\pi\) | ||||
−0.0143699 | + | 0.999897i | \(0.504574\pi\) | |||||||
\(674\) | −60.7194 | −2.33882 | ||||||||
\(675\) | 5.29243i | 0.203706i | ||||||||
\(676\) | −1.96882 | −0.0757237 | ||||||||
\(677\) | 2.57238 | 0.0988645 | 0.0494322 | − | 0.998777i | \(-0.484259\pi\) | ||||
0.0494322 | + | 0.998777i | \(0.484259\pi\) | |||||||
\(678\) | 40.6744 | 1.56209 | ||||||||
\(679\) | 9.55792 | 0.366799 | ||||||||
\(680\) | 0.931809i | 0.0357332i | ||||||||
\(681\) | 44.7363i | 1.71430i | ||||||||
\(682\) | −45.1487 | + | 13.2262i | −1.72883 | + | 0.506458i | ||||
\(683\) | 10.0637i | 0.385079i | 0.981289 | + | 0.192539i | \(0.0616723\pi\) | ||||
−0.981289 | + | 0.192539i | \(0.938328\pi\) | |||||||
\(684\) | 36.9748 | + | 33.8258i | 1.41377 | + | 1.29336i | ||||
\(685\) | −18.1170 | −0.692216 | ||||||||
\(686\) | − | 25.9677i | − | 0.991450i | ||||||
\(687\) | 16.3439i | 0.623558i | ||||||||
\(688\) | 6.42005i | 0.244762i | ||||||||
\(689\) | − | 13.7911i | − | 0.525401i | ||||||
\(690\) | − | 28.7989i | − | 1.09636i | ||||||
\(691\) | 35.6112 | 1.35471 | 0.677357 | − | 0.735655i | \(-0.263125\pi\) | ||||
0.677357 | + | 0.735655i | \(0.263125\pi\) | |||||||
\(692\) | −25.0308 | −0.951528 | ||||||||
\(693\) | 14.7741 | − | 4.32803i | 0.561220 | − | 0.164408i | ||||
\(694\) | 69.9936i | 2.65692i | ||||||||
\(695\) | 9.63153i | 0.365345i | ||||||||
\(696\) | 8.61854i | 0.326685i | ||||||||
\(697\) | − | 4.20660i | − | 0.159336i | ||||||
\(698\) | 20.0727i | 0.759763i | ||||||||
\(699\) | 35.2154 | 1.33197 | ||||||||
\(700\) | 2.23649i | 0.0845312i | ||||||||
\(701\) | 25.3000i | 0.955570i | 0.878477 | + | 0.477785i | \(0.158560\pi\) | ||||
−0.878477 | + | 0.477785i | \(0.841440\pi\) | |||||||
\(702\) | − | 38.5130i | − | 1.45358i | ||||||
\(703\) | −10.5672 | + | 11.5509i | −0.398548 | + | 0.435651i | ||||
\(704\) | −9.82241 | − | 33.5295i | −0.370196 | − | 1.26369i | ||||
\(705\) | 25.9802i | 0.978472i | ||||||||
\(706\) | −59.5338 | −2.24058 | ||||||||
\(707\) | −0.489177 | −0.0183974 | ||||||||
\(708\) | −25.2922 | −0.950540 | ||||||||
\(709\) | −35.7058 | −1.34096 | −0.670479 | − | 0.741928i | \(-0.733911\pi\) | ||||
−0.670479 | + | 0.741928i | \(0.733911\pi\) | |||||||
\(710\) | 17.6969i | 0.664153i | ||||||||
\(711\) | 71.9571 | 2.69860 | ||||||||
\(712\) | 3.28764i | 0.123209i | ||||||||
\(713\) | − | 33.4166i | − | 1.25146i | ||||||
\(714\) | − | 7.03186i | − | 0.263161i | ||||||
\(715\) | −3.25190 | − | 11.1006i | −0.121614 | − | 0.415139i | ||||
\(716\) | 41.3597i | 1.54568i | ||||||||
\(717\) | 53.3102 | 1.99091 | ||||||||
\(718\) | 13.2952i | 0.496174i | ||||||||
\(719\) | −37.7536 | −1.40797 | −0.703987 | − | 0.710213i | \(-0.748599\pi\) | ||||
−0.703987 | + | 0.710213i | \(0.748599\pi\) | |||||||
\(720\) | −15.4741 | −0.576686 | ||||||||
\(721\) | 14.0568 | 0.523503 | ||||||||
\(722\) | −3.51955 | − | 39.4874i | −0.130984 | − | 1.46957i | ||||
\(723\) | 43.8114i | 1.62936i | ||||||||
\(724\) | 37.3228i | 1.38709i | ||||||||
\(725\) | 4.16032 | 0.154510 | ||||||||
\(726\) | −34.7755 | − | 54.2608i | −1.29064 | − | 2.01381i | ||||
\(727\) | −5.16410 | −0.191526 | −0.0957629 | − | 0.995404i | \(-0.530529\pi\) | ||||
−0.0957629 | + | 0.995404i | \(0.530529\pi\) | |||||||
\(728\) | − | 2.44499i | − | 0.0906175i | ||||||
\(729\) | 43.5734 | 1.61383 | ||||||||
\(730\) | − | 14.2297i | − | 0.526664i | ||||||
\(731\) | 2.55972 | 0.0946747 | ||||||||
\(732\) | −26.3489 | −0.973883 | ||||||||
\(733\) | − | 10.5131i | − | 0.388311i | −0.980971 | − | 0.194156i | \(-0.937803\pi\) | ||
0.980971 | − | 0.194156i | \(-0.0621967\pi\) | |||||||
\(734\) | 59.2713 | 2.18774 | ||||||||
\(735\) | 17.1204i | 0.631494i | ||||||||
\(736\) | 39.7421 | 1.46491 | ||||||||
\(737\) | −24.4185 | + | 7.15336i | −0.899469 | + | 0.263497i | ||||
\(738\) | −33.9457 | −1.24956 | ||||||||
\(739\) | 49.6200i | 1.82530i | 0.408742 | + | 0.912650i | \(0.365968\pi\) | ||||
−0.408742 | + | 0.912650i | \(0.634032\pi\) | |||||||
\(740\) | 8.45306i | 0.310741i | ||||||||
\(741\) | −28.8136 | + | 31.4960i | −1.05849 | + | 1.15703i | ||||
\(742\) | −7.84028 | −0.287826 | ||||||||
\(743\) | −38.6120 | −1.41654 | −0.708269 | − | 0.705943i | \(-0.750524\pi\) | ||||
−0.708269 | + | 0.705943i | \(0.750524\pi\) | |||||||
\(744\) | 14.0835 | 0.516326 | ||||||||
\(745\) | 20.0757i | 0.735515i | ||||||||
\(746\) | −26.4753 | −0.969331 | ||||||||
\(747\) | − | 51.1361i | − | 1.87097i | ||||||
\(748\) | −9.46154 | + | 2.77174i | −0.345948 | + | 0.101345i | ||||
\(749\) | − | 0.481901i | − | 0.0176083i | ||||||
\(750\) | − | 5.85893i | − | 0.213938i | ||||||
\(751\) | 6.50018i | 0.237195i | 0.992942 | + | 0.118597i | \(0.0378398\pi\) | ||||
−0.992942 | + | 0.118597i | \(0.962160\pi\) | |||||||
\(752\) | −29.3095 | −1.06881 | ||||||||
\(753\) | − | 11.4617i | − | 0.417687i | ||||||
\(754\) | −30.2747 | −1.10254 | ||||||||
\(755\) | −22.4123 | −0.815666 | ||||||||
\(756\) | −11.8365 | −0.430488 | ||||||||
\(757\) | 26.8511 | 0.975921 | 0.487961 | − | 0.872866i | \(-0.337741\pi\) | ||||
0.487961 | + | 0.872866i | \(0.337741\pi\) | |||||||
\(758\) | 15.5212i | 0.563756i | ||||||||
\(759\) | 43.9309 | − | 12.8695i | 1.59459 | − | 0.467132i | ||||
\(760\) | −2.37270 | − | 2.17063i | −0.0860670 | − | 0.0787370i | ||||
\(761\) | − | 34.3608i | − | 1.24558i | −0.782389 | − | 0.622790i | \(-0.785999\pi\) | ||
0.782389 | − | 0.622790i | \(-0.214001\pi\) | |||||||
\(762\) | − | 34.6138i | − | 1.25393i | ||||||
\(763\) | 5.06551i | 0.183384i | ||||||||
\(764\) | −16.5162 | −0.597536 | ||||||||
\(765\) | 6.16964i | 0.223064i | ||||||||
\(766\) | − | 7.70995i | − | 0.278572i | ||||||
\(767\) | − | 13.3473i | − | 0.481942i | ||||||
\(768\) | − | 25.1217i | − | 0.906500i | ||||||
\(769\) | 17.5008i | 0.631094i | 0.948910 | + | 0.315547i | \(0.102188\pi\) | ||||
−0.948910 | + | 0.315547i | \(0.897812\pi\) | |||||||
\(770\) | −6.31071 | + | 1.84871i | −0.227422 | + | 0.0666228i | ||||
\(771\) | −62.6449 | −2.25610 | ||||||||
\(772\) | 30.9533 | 1.11403 | ||||||||
\(773\) | − | 24.8812i | − | 0.894914i | −0.894305 | − | 0.447457i | \(-0.852330\pi\) | ||
0.894305 | − | 0.447457i | \(-0.147670\pi\) | |||||||
\(774\) | − | 20.6560i | − | 0.742464i | ||||||
\(775\) | − | 6.79836i | − | 0.244204i | ||||||
\(776\) | 7.42059i | 0.266384i | ||||||||
\(777\) | − | 9.58333i | − | 0.343800i | ||||||
\(778\) | 54.0432 | 1.93754 | ||||||||
\(779\) | 10.7114 | + | 9.79918i | 0.383777 | + | 0.351092i | ||||
\(780\) | 23.0490i | 0.825288i | ||||||||
\(781\) | −26.9955 | + | 7.90828i | −0.965976 | + | 0.282981i | ||||
\(782\) | − | 12.9538i | − | 0.463226i | ||||||
\(783\) | 22.0182i | 0.786867i | ||||||||
\(784\) | −19.3143 | −0.689796 | ||||||||
\(785\) | −20.9743 | −0.748605 | ||||||||
\(786\) | 32.1508 | 1.14678 | ||||||||
\(787\) | −28.5417 | −1.01740 | −0.508700 | − | 0.860944i | \(-0.669874\pi\) | ||||
−0.508700 | + | 0.860944i | \(0.669874\pi\) | |||||||
\(788\) | − | 33.3924i | − | 1.18955i | ||||||
\(789\) | −41.4565 | −1.47589 | ||||||||
\(790\) | −30.7363 | −1.09355 | ||||||||
\(791\) | 6.59691 | 0.234559 | ||||||||
\(792\) | 3.36020 | + | 11.4703i | 0.119400 | + | 0.407579i | ||||
\(793\) | − | 13.9049i | − | 0.493777i | ||||||
\(794\) | −48.1933 | −1.71031 | ||||||||
\(795\) | 11.1037 | 0.393806 | ||||||||
\(796\) | −25.3086 | −0.897040 | ||||||||
\(797\) | 23.2530i | 0.823665i | 0.911260 | + | 0.411832i | \(0.135111\pi\) | ||||
−0.911260 | + | 0.411832i | \(0.864889\pi\) | |||||||
\(798\) | 17.9055 | + | 16.3806i | 0.633848 | + | 0.579866i | ||||
\(799\) | 11.6859i | 0.413418i | ||||||||
\(800\) | 8.08524 | 0.285856 | ||||||||
\(801\) | 21.7679i | 0.769131i | ||||||||
\(802\) | − | 15.3010i | − | 0.540296i | ||||||
\(803\) | 21.7065 | − | 6.35886i | 0.766005 | − | 0.224399i | ||||
\(804\) | 50.7021 | 1.78813 | ||||||||
\(805\) | − | 4.67084i | − | 0.164625i | ||||||
\(806\) | 49.4716i | 1.74256i | ||||||||
\(807\) | 59.3311 | 2.08855 | ||||||||
\(808\) | − | 0.379788i | − | 0.0133609i | ||||||
\(809\) | 17.9321i | 0.630457i | 0.949016 | + | 0.315229i | \(0.102081\pi\) | ||||
−0.949016 | + | 0.315229i | \(0.897919\pi\) | |||||||
\(810\) | 0.431362 | 0.0151565 | ||||||||
\(811\) | 17.5303 | 0.615572 | 0.307786 | − | 0.951456i | \(-0.400412\pi\) | ||||
0.307786 | + | 0.951456i | \(0.400412\pi\) | |||||||
\(812\) | 9.30450i | 0.326524i | ||||||||
\(813\) | −61.3031 | −2.14999 | ||||||||
\(814\) | −23.8521 | + | 6.98741i | −0.836014 | + | 0.244909i | ||||
\(815\) | −3.09195 | −0.108306 | ||||||||
\(816\) | −11.2349 | −0.393301 | ||||||||
\(817\) | −5.96282 | + | 6.51793i | −0.208613 | + | 0.228033i | ||||
\(818\) | −21.7869 | −0.761761 | ||||||||
\(819\) | − | 16.1887i | − | 0.565678i | ||||||
\(820\) | 7.83872 | 0.273740 | ||||||||
\(821\) | − | 16.5134i | − | 0.576322i | −0.957582 | − | 0.288161i | \(-0.906956\pi\) | ||
0.957582 | − | 0.288161i | \(-0.0930439\pi\) | |||||||
\(822\) | 106.146i | 3.70228i | ||||||||
\(823\) | −27.2846 | −0.951081 | −0.475540 | − | 0.879694i | \(-0.657747\pi\) | ||||
−0.475540 | + | 0.879694i | \(0.657747\pi\) | |||||||
\(824\) | 10.9134i | 0.380187i | ||||||||
\(825\) | 8.93743 | − | 2.61820i | 0.311161 | − | 0.0911540i | ||||
\(826\) | −7.58793 | −0.264018 | ||||||||
\(827\) | 22.9460 | 0.797909 | 0.398955 | − | 0.916971i | \(-0.369373\pi\) | ||||
0.398955 | + | 0.916971i | \(0.369373\pi\) | |||||||
\(828\) | −56.5109 | −1.96389 | ||||||||
\(829\) | 54.0411i | 1.87693i | 0.345379 | + | 0.938463i | \(0.387750\pi\) | ||||
−0.345379 | + | 0.938463i | \(0.612250\pi\) | |||||||
\(830\) | 21.8427i | 0.758171i | ||||||||
\(831\) | −25.8604 | −0.897088 | ||||||||
\(832\) | −36.7400 | −1.27373 | ||||||||
\(833\) | 7.70075i | 0.266815i | ||||||||
\(834\) | 56.4304 | 1.95403 | ||||||||
\(835\) | 6.49141 | 0.224644 | ||||||||
\(836\) | 14.9827 | − | 30.5490i | 0.518186 | − | 1.05656i | ||||
\(837\) | 35.9799 | 1.24365 | ||||||||
\(838\) | −48.2699 | −1.66746 | ||||||||
\(839\) | − | 38.6207i | − | 1.33333i | −0.745355 | − | 0.666667i | \(-0.767720\pi\) | ||
0.745355 | − | 0.666667i | \(-0.232280\pi\) | |||||||
\(840\) | 1.96854 | 0.0679210 | ||||||||
\(841\) | −11.6917 | −0.403163 | ||||||||
\(842\) | − | 24.7589i | − | 0.853247i | ||||||
\(843\) | − | 85.4447i | − | 2.94287i | ||||||
\(844\) | −11.0680 | −0.380976 | ||||||||
\(845\) | 0.836519 | 0.0287771 | ||||||||
\(846\) | 94.3010 | 3.24214 | ||||||||
\(847\) | −5.64018 | − | 8.80045i | −0.193799 | − | 0.302387i | ||||
\(848\) | 12.5266i | 0.430164i | ||||||||
\(849\) | 16.8768 | 0.579212 | ||||||||
\(850\) | − | 2.63535i | − | 0.0903917i | ||||||
\(851\) | − | 17.6540i | − | 0.605170i | ||||||
\(852\) | 56.0529 | 1.92034 | ||||||||
\(853\) | 51.7098i | 1.77051i | 0.465108 | + | 0.885254i | \(0.346016\pi\) | ||||
−0.465108 | + | 0.885254i | \(0.653984\pi\) | |||||||
\(854\) | −7.90494 | −0.270502 | ||||||||
\(855\) | −15.7100 | − | 14.3720i | −0.537271 | − | 0.491514i | ||||
\(856\) | 0.374139 | 0.0127878 | ||||||||
\(857\) | −18.4927 | −0.631700 | −0.315850 | − | 0.948809i | \(-0.602290\pi\) | ||||
−0.315850 | + | 0.948809i | \(0.602290\pi\) | |||||||
\(858\) | −65.0376 | + | 19.0526i | −2.22035 | + | 0.650446i | ||||
\(859\) | 16.5866 | 0.565926 | 0.282963 | − | 0.959131i | \(-0.408683\pi\) | ||||
0.282963 | + | 0.959131i | \(0.408683\pi\) | |||||||
\(860\) | 4.76987i | 0.162651i | ||||||||
\(861\) | −8.88685 | −0.302863 | ||||||||
\(862\) | −43.5273 | −1.48254 | ||||||||
\(863\) | 19.0806i | 0.649510i | 0.945798 | + | 0.324755i | \(0.105282\pi\) | ||||
−0.945798 | + | 0.324755i | \(0.894718\pi\) | |||||||
\(864\) | 42.7906i | 1.45577i | ||||||||
\(865\) | 10.6352 | 0.361608 | ||||||||
\(866\) | 72.5728i | 2.46612i | ||||||||
\(867\) | − | 43.2563i | − | 1.46906i | ||||||
\(868\) | 15.2044 | 0.516072 | ||||||||
\(869\) | −13.7352 | − | 46.8863i | −0.465936 | − | 1.59051i | ||||
\(870\) | − | 24.3750i | − | 0.826391i | ||||||
\(871\) | 26.7566i | 0.906613i | ||||||||
\(872\) | −3.93277 | −0.133180 | ||||||||
\(873\) | 49.1328i | 1.66289i | ||||||||
\(874\) | 32.9847 | + | 30.1755i | 1.11572 | + | 1.02070i | ||||
\(875\) | − | 0.950248i | − | 0.0321242i | ||||||
\(876\) | −45.0708 | −1.52280 | ||||||||
\(877\) | 13.6363 | 0.460464 | 0.230232 | − | 0.973136i | \(-0.426051\pi\) | ||||
0.230232 | + | 0.973136i | \(0.426051\pi\) | |||||||
\(878\) | 7.00023 | 0.236246 | ||||||||
\(879\) | − | 12.3527i | − | 0.416647i | ||||||
\(880\) | 2.95371 | + | 10.0827i | 0.0995697 | + | 0.339889i | ||||
\(881\) | 5.11244 | 0.172242 | 0.0861212 | − | 0.996285i | \(-0.472553\pi\) | ||||
0.0861212 | + | 0.996285i | \(0.472553\pi\) | |||||||
\(882\) | 62.1422 | 2.09244 | ||||||||
\(883\) | −19.7915 | −0.666038 | −0.333019 | − | 0.942920i | \(-0.608067\pi\) | ||||
−0.333019 | + | 0.942920i | \(0.608067\pi\) | |||||||
\(884\) | 10.3675i | 0.348696i | ||||||||
\(885\) | 10.7463 | 0.361232 | ||||||||
\(886\) | 24.9393 | 0.837851 | ||||||||
\(887\) | −7.37885 | −0.247758 | −0.123879 | − | 0.992297i | \(-0.539533\pi\) | ||||
−0.123879 | + | 0.992297i | \(0.539533\pi\) | |||||||
\(888\) | 7.44032 | 0.249681 | ||||||||
\(889\) | − | 5.61395i | − | 0.188286i | ||||||
\(890\) | − | 9.29812i | − | 0.311674i | ||||||
\(891\) | 0.192764 | + | 0.658016i | 0.00645785 | + | 0.0220444i | ||||
\(892\) | − | 49.6901i | − | 1.66375i | ||||||
\(893\) | −29.7564 | − | 27.2221i | −0.995758 | − | 0.910953i | ||||
\(894\) | 117.622 | 3.93386 | ||||||||
\(895\) | − | 17.5731i | − | 0.587404i | ||||||
\(896\) | 5.52075i | 0.184435i | ||||||||
\(897\) | − | 48.1373i | − | 1.60726i | ||||||
\(898\) | 75.9227i | 2.53357i | ||||||||
\(899\) | − | 28.2834i | − | 0.943303i | ||||||
\(900\) | −11.4967 | −0.383224 | ||||||||
\(901\) | 4.99443 | 0.166389 | ||||||||
\(902\) | 6.47959 | + | 22.1186i | 0.215747 | + | 0.736468i | ||||
\(903\) | − | 5.40766i | − | 0.179956i | ||||||
\(904\) | 5.12172i | 0.170346i | ||||||||
\(905\) | − | 15.8579i | − | 0.527134i | ||||||
\(906\) | 131.312i | 4.36255i | ||||||||
\(907\) | − | 13.8264i | − | 0.459100i | −0.973297 | − | 0.229550i | \(-0.926275\pi\) | ||
0.973297 | − | 0.229550i | \(-0.0737254\pi\) | |||||||
\(908\) | −37.4968 | −1.24437 | ||||||||
\(909\) | − | 2.51463i | − | 0.0834050i | ||||||
\(910\) | 6.91495i | 0.229228i | ||||||||
\(911\) | 55.1464i | 1.82708i | 0.406749 | + | 0.913540i | \(0.366663\pi\) | ||||
−0.406749 | + | 0.913540i | \(0.633337\pi\) | |||||||
\(912\) | 26.1715 | − | 28.6080i | 0.866625 | − | 0.947304i | ||||
\(913\) | −33.3197 | + | 9.76093i | −1.10272 | + | 0.323039i | ||||
\(914\) | − | 0.240933i | − | 0.00796936i | ||||||
\(915\) | 11.1952 | 0.370103 | ||||||||
\(916\) | −13.6990 | −0.452628 | ||||||||
\(917\) | 5.21448 | 0.172197 | ||||||||
\(918\) | 13.9474 | 0.460333 | ||||||||
\(919\) | 44.3304i | 1.46233i | 0.682203 | + | 0.731163i | \(0.261022\pi\) | ||||
−0.682203 | + | 0.731163i | \(0.738978\pi\) | |||||||
\(920\) | 3.62635 | 0.119557 | ||||||||
\(921\) | − | 66.1795i | − | 2.18069i | ||||||
\(922\) | − | 23.6058i | − | 0.777416i | ||||||
\(923\) | 29.5803i | 0.973649i | ||||||||
\(924\) | 5.85557 | + | 19.9884i | 0.192634 | + | 0.657571i | ||||
\(925\) | − | 3.59157i | − | 0.118090i | ||||||
\(926\) | 8.06533 | 0.265043 | ||||||||
\(927\) | 72.2594i | 2.37331i | ||||||||
\(928\) | 33.6372 | 1.10419 | ||||||||
\(929\) | 39.0485 | 1.28114 | 0.640569 | − | 0.767901i | \(-0.278699\pi\) | ||||
0.640569 | + | 0.767901i | \(0.278699\pi\) | |||||||
\(930\) | −39.8311 | −1.30611 | ||||||||
\(931\) | −19.6087 | − | 17.9387i | −0.642651 | − | 0.587918i | ||||
\(932\) | 29.5166i | 0.966850i | ||||||||
\(933\) | − | 43.0376i | − | 1.40899i | ||||||
\(934\) | 82.2426 | 2.69106 | ||||||||
\(935\) | 4.02006 | − | 1.17767i | 0.131470 | − | 0.0385139i | ||||
\(936\) | 12.5686 | 0.410817 | ||||||||
\(937\) | 17.2927i | 0.564927i | 0.959278 | + | 0.282464i | \(0.0911516\pi\) | ||||
−0.959278 | + | 0.282464i | \(0.908848\pi\) | |||||||
\(938\) | 15.2112 | 0.496662 | ||||||||
\(939\) | 7.72055i | 0.251951i | ||||||||
\(940\) | −21.7760 | −0.710253 | ||||||||
\(941\) | 6.95743 | 0.226806 | 0.113403 | − | 0.993549i | \(-0.463825\pi\) | ||||
0.113403 | + | 0.993549i | \(0.463825\pi\) | |||||||
\(942\) | 122.887i | 4.00387i | ||||||||
\(943\) | −16.3709 | −0.533111 | ||||||||
\(944\) | 12.1234i | 0.394582i | ||||||||
\(945\) | 5.02913 | 0.163597 | ||||||||
\(946\) | −13.4592 | + | 3.94284i | −0.437596 | + | 0.128193i | ||||
\(947\) | 52.2670 | 1.69845 | 0.849224 | − | 0.528032i | \(-0.177070\pi\) | ||||
0.849224 | + | 0.528032i | \(0.177070\pi\) | |||||||
\(948\) | 97.3537i | 3.16190i | ||||||||
\(949\) | − | 23.7848i | − | 0.772089i | ||||||
\(950\) | 6.71050 | + | 6.13899i | 0.217717 | + | 0.199175i | ||||
\(951\) | 89.7493 | 2.91032 | ||||||||
\(952\) | 0.885450 | 0.0286976 | ||||||||
\(953\) | −7.08166 | −0.229397 | −0.114699 | − | 0.993400i | \(-0.536590\pi\) | ||||
−0.114699 | + | 0.993400i | \(0.536590\pi\) | |||||||
\(954\) | − | 40.3032i | − | 1.30486i | ||||||
\(955\) | 7.01749 | 0.227081 | ||||||||
\(956\) | 44.6832i | 1.44516i | ||||||||
\(957\) | 37.1826 | − | 10.8926i | 1.20194 | − | 0.352106i | ||||
\(958\) | 68.3128i | 2.20709i | ||||||||
\(959\) | 17.2157i | 0.555923i | ||||||||
\(960\) | − | 29.5804i | − | 0.954705i | ||||||
\(961\) | −15.2177 | −0.490893 | ||||||||
\(962\) | 26.1359i | 0.842654i | ||||||||
\(963\) | 2.47723 | 0.0798275 | ||||||||
\(964\) | −36.7216 | −1.18272 | ||||||||
\(965\) | −13.1516 | −0.423364 | ||||||||
\(966\) | −27.3661 | −0.880490 | ||||||||
\(967\) | − | 6.99645i | − | 0.224991i | −0.993652 | − | 0.112495i | \(-0.964116\pi\) | ||
0.993652 | − | 0.112495i | \(-0.0358843\pi\) | |||||||
\(968\) | 6.83250 | − | 4.37893i | 0.219605 | − | 0.140744i | ||||
\(969\) | −11.4062 | − | 10.4348i | −0.366420 | − | 0.335214i | ||||
\(970\) | − | 20.9870i | − | 0.673851i | ||||||
\(971\) | − | 7.05574i | − | 0.226429i | −0.993571 | − | 0.113215i | \(-0.963885\pi\) | ||
0.993571 | − | 0.113215i | \(-0.0361148\pi\) | |||||||
\(972\) | 36.0022i | 1.15477i | ||||||||
\(973\) | 9.15234 | 0.293410 | ||||||||
\(974\) | − | 54.9277i | − | 1.76000i | ||||||
\(975\) | − | 9.79318i | − | 0.313633i | ||||||
\(976\) | 12.6299i | 0.404272i | ||||||||
\(977\) | 19.9660i | 0.638767i | 0.947625 | + | 0.319384i | \(0.103476\pi\) | ||||
−0.947625 | + | 0.319384i | \(0.896524\pi\) | |||||||
\(978\) | 18.1155i | 0.579269i | ||||||||
\(979\) | 14.1837 | − | 4.15508i | 0.453313 | − | 0.132797i | ||||
\(980\) | −14.3498 | −0.458389 | ||||||||
\(981\) | −26.0394 | −0.831375 | ||||||||
\(982\) | − | 41.1130i | − | 1.31197i | ||||||
\(983\) | 8.39337i | 0.267707i | 0.991001 | + | 0.133853i | \(0.0427351\pi\) | ||||
−0.991001 | + | 0.133853i | \(0.957265\pi\) | |||||||
\(984\) | − | 6.89958i | − | 0.219951i | ||||||
\(985\) | 14.1879i | 0.452064i | ||||||||
\(986\) | − | 10.9639i | − | 0.349162i | ||||||
\(987\) | 24.6877 | 0.785817 | ||||||||
\(988\) | −26.3991 | − | 24.1508i | −0.839868 | − | 0.768340i | ||||
\(989\) | − | 9.96175i | − | 0.316765i | ||||||
\(990\) | −9.50334 | − | 32.4404i | −0.302036 | − | 1.03102i | ||||
\(991\) | 41.1976i | 1.30869i | 0.756198 | + | 0.654343i | \(0.227055\pi\) | ||||
−0.756198 | + | 0.654343i | \(0.772945\pi\) | |||||||
\(992\) | − | 54.9663i | − | 1.74518i | ||||||
\(993\) | −51.8912 | −1.64672 | ||||||||
\(994\) | 16.8165 | 0.533386 | ||||||||
\(995\) | 10.7532 | 0.340901 | ||||||||
\(996\) | 69.1842 | 2.19218 | ||||||||
\(997\) | − | 25.9180i | − | 0.820833i | −0.911898 | − | 0.410416i | \(-0.865383\pi\) | ||
0.911898 | − | 0.410416i | \(-0.134617\pi\) | |||||||
\(998\) | 92.2936 | 2.92150 | ||||||||
\(999\) | 19.0082 | 0.601392 |
(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 | 1045.2.f.a.626.6 | yes | 40 | |
11.10 | odd | 2 | inner | 1045.2.f.a.626.36 | yes | 40 | |
19.18 | odd | 2 | inner | 1045.2.f.a.626.35 | yes | 40 | |
209.208 | even | 2 | inner | 1045.2.f.a.626.5 | ✓ | 40 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1045.2.f.a.626.5 | ✓ | 40 | 209.208 | even | 2 | inner | |
1045.2.f.a.626.6 | yes | 40 | 1.1 | even | 1 | trivial | |
1045.2.f.a.626.35 | yes | 40 | 19.18 | odd | 2 | inner | |
1045.2.f.a.626.36 | yes | 40 | 11.10 | odd | 2 | inner |