Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [975,2,Mod(274,975)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(975, 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("975.274");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 975 = 3 \cdot 5^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 975.c (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(7.78541419707\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.0.5089536.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 2x^{5} + 2x^{4} + 2x^{3} + 16x^{2} - 24x + 18 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 274.4 | ||
Root | \(-1.33641 + 1.33641i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 975.274 |
Dual form | 975.2.c.j.274.3 |
$q$-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 \(\left(\mathbb{Z}/975\mathbb{Z}\right)^\times\).
\(n\) | \(301\) | \(326\) | \(352\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.571993i | 0.404460i | 0.979338 | + | 0.202230i | \(0.0648189\pi\) | ||||
−0.979338 | + | 0.202230i | \(0.935181\pi\) | |||||||
\(3\) | − 1.00000i | − 0.577350i | ||||||||
\(4\) | 1.67282 | 0.836412 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0.571993 | 0.233515 | ||||||||
\(7\) | 1.42801i | 0.539736i | 0.962897 | + | 0.269868i | \(0.0869800\pi\) | ||||
−0.962897 | + | 0.269868i | \(0.913020\pi\) | |||||||
\(8\) | 2.10083i | 0.742756i | ||||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.24482 | 0.978349 | 0.489175 | − | 0.872186i | \(-0.337298\pi\) | ||||
0.489175 | + | 0.872186i | \(0.337298\pi\) | |||||||
\(12\) | − 1.67282i | − 0.482903i | ||||||||
\(13\) | − 1.00000i | − 0.277350i | ||||||||
\(14\) | −0.816810 | −0.218302 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 2.14399 | 0.535997 | ||||||||
\(17\) | 1.85601i | 0.450149i | 0.974342 | + | 0.225075i | \(0.0722626\pi\) | ||||
−0.974342 | + | 0.225075i | \(0.927737\pi\) | |||||||
\(18\) | − 0.571993i | − 0.134820i | ||||||||
\(19\) | 1.81681 | 0.416805 | 0.208402 | − | 0.978043i | \(-0.433174\pi\) | ||||
0.208402 | + | 0.978043i | \(0.433174\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.42801 | 0.311617 | ||||||||
\(22\) | 1.85601i | 0.395703i | ||||||||
\(23\) | 1.52884i | 0.318785i | 0.987215 | + | 0.159392i | \(0.0509535\pi\) | ||||
−0.987215 | + | 0.159392i | \(0.949047\pi\) | |||||||
\(24\) | 2.10083 | 0.428830 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0.571993 | 0.112177 | ||||||||
\(27\) | 1.00000i | 0.192450i | ||||||||
\(28\) | 2.38880i | 0.451441i | ||||||||
\(29\) | −2.34565 | −0.435576 | −0.217788 | − | 0.975996i | \(-0.569884\pi\) | ||||
−0.217788 | + | 0.975996i | \(0.569884\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.38880 | 1.14746 | 0.573731 | − | 0.819043i | \(-0.305495\pi\) | ||||
0.573731 | + | 0.819043i | \(0.305495\pi\) | |||||||
\(32\) | 5.42801i | 0.959545i | ||||||||
\(33\) | − 3.24482i | − 0.564850i | ||||||||
\(34\) | −1.06163 | −0.182068 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −1.67282 | −0.278804 | ||||||||
\(37\) | 3.52884i | 0.580137i | 0.957006 | + | 0.290069i | \(0.0936781\pi\) | ||||
−0.957006 | + | 0.290069i | \(0.906322\pi\) | |||||||
\(38\) | 1.03920i | 0.168581i | ||||||||
\(39\) | −1.00000 | −0.160128 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −3.81681 | −0.596086 | −0.298043 | − | 0.954553i | \(-0.596334\pi\) | ||||
−0.298043 | + | 0.954553i | \(0.596334\pi\) | |||||||
\(42\) | 0.816810i | 0.126037i | ||||||||
\(43\) | − 10.0185i | − 1.52780i | −0.645333 | − | 0.763901i | \(-0.723281\pi\) | ||||
0.645333 | − | 0.763901i | \(-0.276719\pi\) | |||||||
\(44\) | 5.42801 | 0.818303 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −0.874485 | −0.128936 | ||||||||
\(47\) | 11.2633i | 1.64292i | 0.570267 | + | 0.821460i | \(0.306840\pi\) | ||||
−0.570267 | + | 0.821460i | \(0.693160\pi\) | |||||||
\(48\) | − 2.14399i | − 0.309458i | ||||||||
\(49\) | 4.96080 | 0.708685 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.85601 | 0.259894 | ||||||||
\(52\) | − 1.67282i | − 0.231979i | ||||||||
\(53\) | − 6.81681i | − 0.936361i | −0.883633 | − | 0.468180i | \(-0.844910\pi\) | ||||
0.883633 | − | 0.468180i | \(-0.155090\pi\) | |||||||
\(54\) | −0.571993 | −0.0778384 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −3.00000 | −0.400892 | ||||||||
\(57\) | − 1.81681i | − 0.240642i | ||||||||
\(58\) | − 1.34169i | − 0.176173i | ||||||||
\(59\) | 5.91764 | 0.770411 | 0.385206 | − | 0.922831i | \(-0.374131\pi\) | ||||
0.385206 | + | 0.922831i | \(0.374131\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5.48963 | 0.702876 | 0.351438 | − | 0.936211i | \(-0.385693\pi\) | ||||
0.351438 | + | 0.936211i | \(0.385693\pi\) | |||||||
\(62\) | 3.65435i | 0.464103i | ||||||||
\(63\) | − 1.42801i | − 0.179912i | ||||||||
\(64\) | 1.18319 | 0.147899 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 1.85601 | 0.228459 | ||||||||
\(67\) | − 10.3025i | − 1.25865i | −0.777142 | − | 0.629325i | \(-0.783332\pi\) | ||||
0.777142 | − | 0.629325i | \(-0.216668\pi\) | |||||||
\(68\) | 3.10478i | 0.376510i | ||||||||
\(69\) | 1.52884 | 0.184050 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −9.81681 | −1.16504 | −0.582521 | − | 0.812816i | \(-0.697933\pi\) | ||||
−0.582521 | + | 0.812816i | \(0.697933\pi\) | |||||||
\(72\) | − 2.10083i | − 0.247585i | ||||||||
\(73\) | − 5.32718i | − 0.623499i | −0.950164 | − | 0.311749i | \(-0.899085\pi\) | ||||
0.950164 | − | 0.311749i | \(-0.100915\pi\) | |||||||
\(74\) | −2.01847 | −0.234642 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 3.03920 | 0.348621 | ||||||||
\(77\) | 4.63362i | 0.528050i | ||||||||
\(78\) | − 0.571993i | − 0.0647655i | ||||||||
\(79\) | 2.96080 | 0.333116 | 0.166558 | − | 0.986032i | \(-0.446735\pi\) | ||||
0.166558 | + | 0.986032i | \(0.446735\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | − 2.18319i | − 0.241093i | ||||||||
\(83\) | − 3.14003i | − 0.344663i | −0.985039 | − | 0.172332i | \(-0.944870\pi\) | ||||
0.985039 | − | 0.172332i | \(-0.0551301\pi\) | |||||||
\(84\) | 2.38880 | 0.260640 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 5.73050 | 0.617935 | ||||||||
\(87\) | 2.34565i | 0.251480i | ||||||||
\(88\) | 6.81681i | 0.726674i | ||||||||
\(89\) | 4.85601 | 0.514736 | 0.257368 | − | 0.966313i | \(-0.417145\pi\) | ||||
0.257368 | + | 0.966313i | \(0.417145\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.42801 | 0.149696 | ||||||||
\(92\) | 2.55748i | 0.266635i | ||||||||
\(93\) | − 6.38880i | − 0.662488i | ||||||||
\(94\) | −6.44252 | −0.664496 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 5.42801 | 0.553994 | ||||||||
\(97\) | 1.51037i | 0.153354i | 0.997056 | + | 0.0766772i | \(0.0244311\pi\) | ||||
−0.997056 | + | 0.0766772i | \(0.975569\pi\) | |||||||
\(98\) | 2.83754i | 0.286635i | ||||||||
\(99\) | −3.24482 | −0.326116 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −17.0185 | −1.69340 | −0.846701 | − | 0.532070i | \(-0.821414\pi\) | ||||
−0.846701 | + | 0.532070i | \(0.821414\pi\) | |||||||
\(102\) | 1.06163i | 0.105117i | ||||||||
\(103\) | 9.73050i | 0.958774i | 0.877603 | + | 0.479387i | \(0.159141\pi\) | ||||
−0.877603 | + | 0.479387i | \(0.840859\pi\) | |||||||
\(104\) | 2.10083 | 0.206003 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 3.89917 | 0.378721 | ||||||||
\(107\) | − 3.43196i | − 0.331780i | −0.986144 | − | 0.165890i | \(-0.946950\pi\) | ||||
0.986144 | − | 0.165890i | \(-0.0530497\pi\) | |||||||
\(108\) | 1.67282i | 0.160968i | ||||||||
\(109\) | 2.96080 | 0.283593 | 0.141796 | − | 0.989896i | \(-0.454712\pi\) | ||||
0.141796 | + | 0.989896i | \(0.454712\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 3.52884 | 0.334942 | ||||||||
\(112\) | 3.06163i | 0.289297i | ||||||||
\(113\) | 9.54731i | 0.898135i | 0.893498 | + | 0.449068i | \(0.148244\pi\) | ||||
−0.893498 | + | 0.449068i | \(0.851756\pi\) | |||||||
\(114\) | 1.03920 | 0.0973303 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −3.92385 | −0.364321 | ||||||||
\(117\) | 1.00000i | 0.0924500i | ||||||||
\(118\) | 3.38485i | 0.311601i | ||||||||
\(119\) | −2.65040 | −0.242962 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −0.471163 | −0.0428330 | ||||||||
\(122\) | 3.14003i | 0.284285i | ||||||||
\(123\) | 3.81681i | 0.344150i | ||||||||
\(124\) | 10.6873 | 0.959752 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0.816810 | 0.0727672 | ||||||||
\(127\) | − 0.183190i | − 0.0162555i | −0.999967 | − | 0.00812773i | \(-0.997413\pi\) | ||||
0.999967 | − | 0.00812773i | \(-0.00258717\pi\) | |||||||
\(128\) | 11.5328i | 1.01936i | ||||||||
\(129\) | −10.0185 | −0.882077 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −17.4504 | −1.52465 | −0.762326 | − | 0.647194i | \(-0.775942\pi\) | ||||
−0.762326 | + | 0.647194i | \(0.775942\pi\) | |||||||
\(132\) | − 5.42801i | − 0.472447i | ||||||||
\(133\) | 2.59442i | 0.224965i | ||||||||
\(134\) | 5.89296 | 0.509074 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −3.89917 | −0.334351 | ||||||||
\(137\) | 1.79834i | 0.153642i | 0.997045 | + | 0.0768212i | \(0.0244771\pi\) | ||||
−0.997045 | + | 0.0768212i | \(0.975523\pi\) | |||||||
\(138\) | 0.874485i | 0.0744411i | ||||||||
\(139\) | −20.3249 | −1.72394 | −0.861968 | − | 0.506962i | \(-0.830768\pi\) | ||||
−0.861968 | + | 0.506962i | \(0.830768\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 11.2633 | 0.948540 | ||||||||
\(142\) | − 5.61515i | − 0.471213i | ||||||||
\(143\) | − 3.24482i | − 0.271345i | ||||||||
\(144\) | −2.14399 | −0.178666 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 3.04711 | 0.252181 | ||||||||
\(147\) | − 4.96080i | − 0.409160i | ||||||||
\(148\) | 5.90312i | 0.485234i | ||||||||
\(149\) | 17.1809 | 1.40752 | 0.703758 | − | 0.710440i | \(-0.251504\pi\) | ||||
0.703758 | + | 0.710440i | \(0.251504\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 3.99605 | 0.325194 | 0.162597 | − | 0.986693i | \(-0.448013\pi\) | ||||
0.162597 | + | 0.986693i | \(0.448013\pi\) | |||||||
\(152\) | 3.81681i | 0.309584i | ||||||||
\(153\) | − 1.85601i | − 0.150050i | ||||||||
\(154\) | −2.65040 | −0.213575 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −1.67282 | −0.133933 | ||||||||
\(157\) | 7.67282i | 0.612358i | 0.951974 | + | 0.306179i | \(0.0990506\pi\) | ||||
−0.951974 | + | 0.306179i | \(0.900949\pi\) | |||||||
\(158\) | 1.69356i | 0.134732i | ||||||||
\(159\) | −6.81681 | −0.540608 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −2.18319 | −0.172059 | ||||||||
\(162\) | 0.571993i | 0.0449400i | ||||||||
\(163\) | − 0.471163i | − 0.0369043i | −0.999830 | − | 0.0184522i | \(-0.994126\pi\) | ||||
0.999830 | − | 0.0184522i | \(-0.00587384\pi\) | |||||||
\(164\) | −6.38485 | −0.498573 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 1.79608 | 0.139403 | ||||||||
\(167\) | − 18.7098i | − 1.44781i | −0.689902 | − | 0.723903i | \(-0.742346\pi\) | ||||
0.689902 | − | 0.723903i | \(-0.257654\pi\) | |||||||
\(168\) | 3.00000i | 0.231455i | ||||||||
\(169\) | −1.00000 | −0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −1.81681 | −0.138935 | ||||||||
\(172\) | − 16.7591i | − 1.27787i | ||||||||
\(173\) | − 7.96080i | − 0.605248i | −0.953110 | − | 0.302624i | \(-0.902137\pi\) | ||||
0.953110 | − | 0.302624i | \(-0.0978627\pi\) | |||||||
\(174\) | −1.34169 | −0.101714 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 6.95684 | 0.524392 | ||||||||
\(177\) | − 5.91764i | − 0.444797i | ||||||||
\(178\) | 2.77761i | 0.208190i | ||||||||
\(179\) | −15.6521 | −1.16989 | −0.584946 | − | 0.811072i | \(-0.698884\pi\) | ||||
−0.584946 | + | 0.811072i | \(0.698884\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −24.5658 | −1.82596 | −0.912980 | − | 0.408004i | \(-0.866225\pi\) | ||||
−0.912980 | + | 0.408004i | \(0.866225\pi\) | |||||||
\(182\) | 0.816810i | 0.0605460i | ||||||||
\(183\) | − 5.48963i | − 0.405805i | ||||||||
\(184\) | −3.21183 | −0.236779 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 3.65435 | 0.267950 | ||||||||
\(187\) | 6.02242i | 0.440403i | ||||||||
\(188\) | 18.8415i | 1.37416i | ||||||||
\(189\) | −1.42801 | −0.103872 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −21.0577 | −1.52368 | −0.761840 | − | 0.647765i | \(-0.775704\pi\) | ||||
−0.761840 | + | 0.647765i | \(0.775704\pi\) | |||||||
\(192\) | − 1.18319i | − 0.0853894i | ||||||||
\(193\) | − 19.9401i | − 1.43532i | −0.696395 | − | 0.717659i | \(-0.745214\pi\) | ||||
0.696395 | − | 0.717659i | \(-0.254786\pi\) | |||||||
\(194\) | −0.863919 | −0.0620258 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 8.29854 | 0.592753 | ||||||||
\(197\) | − 23.4504i | − 1.67077i | −0.549662 | − | 0.835387i | \(-0.685244\pi\) | ||||
0.549662 | − | 0.835387i | \(-0.314756\pi\) | |||||||
\(198\) | − 1.85601i | − 0.131901i | ||||||||
\(199\) | −16.2880 | −1.15462 | −0.577312 | − | 0.816524i | \(-0.695898\pi\) | ||||
−0.577312 | + | 0.816524i | \(0.695898\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −10.3025 | −0.726682 | ||||||||
\(202\) | − 9.73445i | − 0.684914i | ||||||||
\(203\) | − 3.34960i | − 0.235096i | ||||||||
\(204\) | 3.10478 | 0.217378 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −5.56578 | −0.387786 | ||||||||
\(207\) | − 1.52884i | − 0.106262i | ||||||||
\(208\) | − 2.14399i | − 0.148659i | ||||||||
\(209\) | 5.89522 | 0.407781 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 27.8538 | 1.91753 | 0.958766 | − | 0.284198i | \(-0.0917272\pi\) | ||||
0.958766 | + | 0.284198i | \(0.0917272\pi\) | |||||||
\(212\) | − 11.4033i | − 0.783183i | ||||||||
\(213\) | 9.81681i | 0.672637i | ||||||||
\(214\) | 1.96306 | 0.134192 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −2.10083 | −0.142943 | ||||||||
\(217\) | 9.12325i | 0.619327i | ||||||||
\(218\) | 1.69356i | 0.114702i | ||||||||
\(219\) | −5.32718 | −0.359977 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.85601 | 0.124849 | ||||||||
\(222\) | 2.01847i | 0.135471i | ||||||||
\(223\) | − 11.1625i | − 0.747493i | −0.927531 | − | 0.373747i | \(-0.878073\pi\) | ||||
0.927531 | − | 0.373747i | \(-0.121927\pi\) | |||||||
\(224\) | −7.75123 | −0.517901 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −5.46100 | −0.363260 | ||||||||
\(227\) | 7.93611i | 0.526738i | 0.964695 | + | 0.263369i | \(0.0848337\pi\) | ||||
−0.964695 | + | 0.263369i | \(0.915166\pi\) | |||||||
\(228\) | − 3.03920i | − 0.201276i | ||||||||
\(229\) | −27.9585 | −1.84755 | −0.923776 | − | 0.382933i | \(-0.874914\pi\) | ||||
−0.923776 | + | 0.382933i | \(0.874914\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 4.63362 | 0.304870 | ||||||||
\(232\) | − 4.92781i | − 0.323526i | ||||||||
\(233\) | 1.14399i | 0.0749450i | 0.999298 | + | 0.0374725i | \(0.0119307\pi\) | ||||
−0.999298 | + | 0.0374725i | \(0.988069\pi\) | |||||||
\(234\) | −0.571993 | −0.0373924 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 9.89917 | 0.644381 | ||||||||
\(237\) | − 2.96080i | − 0.192324i | ||||||||
\(238\) | − 1.51601i | − 0.0982684i | ||||||||
\(239\) | 3.34960 | 0.216668 | 0.108334 | − | 0.994115i | \(-0.465448\pi\) | ||||
0.108334 | + | 0.994115i | \(0.465448\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −8.09688 | −0.521566 | −0.260783 | − | 0.965397i | \(-0.583981\pi\) | ||||
−0.260783 | + | 0.965397i | \(0.583981\pi\) | |||||||
\(242\) | − 0.269502i | − 0.0173242i | ||||||||
\(243\) | − 1.00000i | − 0.0641500i | ||||||||
\(244\) | 9.18319 | 0.587893 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −2.18319 | −0.139195 | ||||||||
\(247\) | − 1.81681i | − 0.115601i | ||||||||
\(248\) | 13.4218i | 0.852285i | ||||||||
\(249\) | −3.14003 | −0.198992 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −25.3641 | −1.60097 | −0.800484 | − | 0.599353i | \(-0.795424\pi\) | ||||
−0.800484 | + | 0.599353i | \(0.795424\pi\) | |||||||
\(252\) | − 2.38880i | − 0.150480i | ||||||||
\(253\) | 4.96080i | 0.311883i | ||||||||
\(254\) | 0.104783 | 0.00657469 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −4.23030 | −0.264394 | ||||||||
\(257\) | 19.5865i | 1.22177i | 0.791718 | + | 0.610887i | \(0.209187\pi\) | ||||
−0.791718 | + | 0.610887i | \(0.790813\pi\) | |||||||
\(258\) | − 5.73050i | − 0.356765i | ||||||||
\(259\) | −5.03920 | −0.313121 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2.34565 | 0.145192 | ||||||||
\(262\) | − 9.98153i | − 0.616661i | ||||||||
\(263\) | 7.24877i | 0.446978i | 0.974706 | + | 0.223489i | \(0.0717447\pi\) | ||||
−0.974706 | + | 0.223489i | \(0.928255\pi\) | |||||||
\(264\) | 6.81681 | 0.419546 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −1.48399 | −0.0909892 | ||||||||
\(267\) | − 4.85601i | − 0.297183i | ||||||||
\(268\) | − 17.2343i | − 1.05275i | ||||||||
\(269\) | 14.5104 | 0.884713 | 0.442356 | − | 0.896839i | \(-0.354143\pi\) | ||||
0.442356 | + | 0.896839i | \(0.354143\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −4.19771 | −0.254993 | −0.127496 | − | 0.991839i | \(-0.540694\pi\) | ||||
−0.127496 | + | 0.991839i | \(0.540694\pi\) | |||||||
\(272\) | 3.97927i | 0.241279i | ||||||||
\(273\) | − 1.42801i | − 0.0864269i | ||||||||
\(274\) | −1.02864 | −0.0621423 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 2.55748 | 0.153942 | ||||||||
\(277\) | − 16.6050i | − 0.997697i | −0.866689 | − | 0.498848i | \(-0.833756\pi\) | ||||
0.866689 | − | 0.498848i | \(-0.166244\pi\) | |||||||
\(278\) | − 11.6257i | − 0.697264i | ||||||||
\(279\) | −6.38880 | −0.382488 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 24.3249 | 1.45110 | 0.725551 | − | 0.688168i | \(-0.241585\pi\) | ||||
0.725551 | + | 0.688168i | \(0.241585\pi\) | |||||||
\(282\) | 6.44252i | 0.383647i | ||||||||
\(283\) | 7.71203i | 0.458432i | 0.973376 | + | 0.229216i | \(0.0736163\pi\) | ||||
−0.973376 | + | 0.229216i | \(0.926384\pi\) | |||||||
\(284\) | −16.4218 | −0.974454 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 1.85601 | 0.109748 | ||||||||
\(287\) | − 5.45043i | − 0.321729i | ||||||||
\(288\) | − 5.42801i | − 0.319848i | ||||||||
\(289\) | 13.5552 | 0.797366 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1.51037 | 0.0885392 | ||||||||
\(292\) | − 8.91143i | − 0.521502i | ||||||||
\(293\) | − 6.00000i | − 0.350524i | −0.984522 | − | 0.175262i | \(-0.943923\pi\) | ||||
0.984522 | − | 0.175262i | \(-0.0560772\pi\) | |||||||
\(294\) | 2.83754 | 0.165489 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −7.41349 | −0.430900 | ||||||||
\(297\) | 3.24482i | 0.188283i | ||||||||
\(298\) | 9.82738i | 0.569285i | ||||||||
\(299\) | 1.52884 | 0.0884149 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 14.3064 | 0.824610 | ||||||||
\(302\) | 2.28571i | 0.131528i | ||||||||
\(303\) | 17.0185i | 0.977686i | ||||||||
\(304\) | 3.89522 | 0.223406 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 1.06163 | 0.0606892 | ||||||||
\(307\) | − 12.7882i | − 0.729860i | −0.931035 | − | 0.364930i | \(-0.881093\pi\) | ||||
0.931035 | − | 0.364930i | \(-0.118907\pi\) | |||||||
\(308\) | 7.75123i | 0.441667i | ||||||||
\(309\) | 9.73050 | 0.553549 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −18.0000 | −1.02069 | −0.510343 | − | 0.859971i | \(-0.670482\pi\) | ||||
−0.510343 | + | 0.859971i | \(0.670482\pi\) | |||||||
\(312\) | − 2.10083i | − 0.118936i | ||||||||
\(313\) | − 13.8824i | − 0.784679i | −0.919820 | − | 0.392340i | \(-0.871666\pi\) | ||||
0.919820 | − | 0.392340i | \(-0.128334\pi\) | |||||||
\(314\) | −4.38880 | −0.247675 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 4.95289 | 0.278622 | ||||||||
\(317\) | 8.01847i | 0.450362i | 0.974317 | + | 0.225181i | \(0.0722974\pi\) | ||||
−0.974317 | + | 0.225181i | \(0.927703\pi\) | |||||||
\(318\) | − 3.89917i | − 0.218655i | ||||||||
\(319\) | −7.61120 | −0.426145 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −3.43196 | −0.191553 | ||||||||
\(322\) | − 1.24877i | − 0.0695912i | ||||||||
\(323\) | 3.37202i | 0.187624i | ||||||||
\(324\) | 1.67282 | 0.0929347 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0.269502 | 0.0149263 | ||||||||
\(327\) | − 2.96080i | − 0.163732i | ||||||||
\(328\) | − 8.01847i | − 0.442746i | ||||||||
\(329\) | −16.0841 | −0.886742 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −34.2201 | −1.88091 | −0.940454 | − | 0.339920i | \(-0.889600\pi\) | ||||
−0.940454 | + | 0.339920i | \(0.889600\pi\) | |||||||
\(332\) | − 5.25272i | − 0.288281i | ||||||||
\(333\) | − 3.52884i | − 0.193379i | ||||||||
\(334\) | 10.7019 | 0.585580 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 3.06163 | 0.167025 | ||||||||
\(337\) | 21.4712i | 1.16961i | 0.811174 | + | 0.584804i | \(0.198829\pi\) | ||||
−0.811174 | + | 0.584804i | \(0.801171\pi\) | |||||||
\(338\) | − 0.571993i | − 0.0311123i | ||||||||
\(339\) | 9.54731 | 0.518539 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 20.7305 | 1.12262 | ||||||||
\(342\) | − 1.03920i | − 0.0561937i | ||||||||
\(343\) | 17.0801i | 0.922239i | ||||||||
\(344\) | 21.0471 | 1.13478 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 4.55352 | 0.244799 | ||||||||
\(347\) | − 26.6129i | − 1.42865i | −0.699812 | − | 0.714327i | \(-0.746733\pi\) | ||||
0.699812 | − | 0.714327i | \(-0.253267\pi\) | |||||||
\(348\) | 3.92385i | 0.210341i | ||||||||
\(349\) | 13.8168 | 0.739597 | 0.369798 | − | 0.929112i | \(-0.379427\pi\) | ||||
0.369798 | + | 0.929112i | \(0.379427\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1.00000 | 0.0533761 | ||||||||
\(352\) | 17.6129i | 0.938770i | ||||||||
\(353\) | − 25.5288i | − 1.35876i | −0.733785 | − | 0.679381i | \(-0.762248\pi\) | ||||
0.733785 | − | 0.679381i | \(-0.237752\pi\) | |||||||
\(354\) | 3.38485 | 0.179903 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 8.12325 | 0.430532 | ||||||||
\(357\) | 2.65040i | 0.140274i | ||||||||
\(358\) | − 8.95289i | − 0.473175i | ||||||||
\(359\) | −4.65831 | −0.245856 | −0.122928 | − | 0.992416i | \(-0.539228\pi\) | ||||
−0.122928 | + | 0.992416i | \(0.539228\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −15.6992 | −0.826274 | ||||||||
\(362\) | − 14.0515i | − 0.738528i | ||||||||
\(363\) | 0.471163i | 0.0247296i | ||||||||
\(364\) | 2.38880 | 0.125207 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 3.14003 | 0.164132 | ||||||||
\(367\) | − 19.2672i | − 1.00574i | −0.864362 | − | 0.502871i | \(-0.832277\pi\) | ||||
0.864362 | − | 0.502871i | \(-0.167723\pi\) | |||||||
\(368\) | 3.27781i | 0.170867i | ||||||||
\(369\) | 3.81681 | 0.198695 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 9.73445 | 0.505388 | ||||||||
\(372\) | − 10.6873i | − 0.554113i | ||||||||
\(373\) | 6.12552i | 0.317167i | 0.987346 | + | 0.158584i | \(0.0506927\pi\) | ||||
−0.987346 | + | 0.158584i | \(0.949307\pi\) | |||||||
\(374\) | −3.44479 | −0.178126 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −23.6623 | −1.22029 | ||||||||
\(377\) | 2.34565i | 0.120807i | ||||||||
\(378\) | − 0.816810i | − 0.0420122i | ||||||||
\(379\) | −22.3104 | −1.14601 | −0.573004 | − | 0.819553i | \(-0.694222\pi\) | ||||
−0.573004 | + | 0.819553i | \(0.694222\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −0.183190 | −0.00938510 | ||||||||
\(382\) | − 12.0448i | − 0.616268i | ||||||||
\(383\) | 37.0841i | 1.89491i | 0.319894 | + | 0.947453i | \(0.396353\pi\) | ||||
−0.319894 | + | 0.947453i | \(0.603647\pi\) | |||||||
\(384\) | 11.5328 | 0.588530 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 11.4056 | 0.580529 | ||||||||
\(387\) | 10.0185i | 0.509268i | ||||||||
\(388\) | 2.52658i | 0.128267i | ||||||||
\(389\) | 23.8353 | 1.20850 | 0.604248 | − | 0.796796i | \(-0.293473\pi\) | ||||
0.604248 | + | 0.796796i | \(0.293473\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2.83754 | −0.143501 | ||||||||
\(392\) | 10.4218i | 0.526380i | ||||||||
\(393\) | 17.4504i | 0.880258i | ||||||||
\(394\) | 13.4135 | 0.675762 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −5.42801 | −0.272768 | ||||||||
\(397\) | 26.6992i | 1.33999i | 0.742364 | + | 0.669997i | \(0.233705\pi\) | ||||
−0.742364 | + | 0.669997i | \(0.766295\pi\) | |||||||
\(398\) | − 9.31661i | − 0.467000i | ||||||||
\(399\) | 2.59442 | 0.129883 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 21.8168 | 1.08948 | 0.544740 | − | 0.838605i | \(-0.316628\pi\) | ||||
0.544740 | + | 0.838605i | \(0.316628\pi\) | |||||||
\(402\) | − 5.89296i | − 0.293914i | ||||||||
\(403\) | − 6.38880i | − 0.318249i | ||||||||
\(404\) | −28.4689 | −1.41638 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 1.91595 | 0.0950869 | ||||||||
\(407\) | 11.4504i | 0.567577i | ||||||||
\(408\) | 3.89917i | 0.193038i | ||||||||
\(409\) | 1.16246 | 0.0574798 | 0.0287399 | − | 0.999587i | \(-0.490851\pi\) | ||||
0.0287399 | + | 0.999587i | \(0.490851\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 1.79834 | 0.0887055 | ||||||||
\(412\) | 16.2774i | 0.801930i | ||||||||
\(413\) | 8.45043i | 0.415819i | ||||||||
\(414\) | 0.874485 | 0.0429786 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 5.42801 | 0.266130 | ||||||||
\(417\) | 20.3249i | 0.995315i | ||||||||
\(418\) | 3.37202i | 0.164931i | ||||||||
\(419\) | 2.46326 | 0.120338 | 0.0601690 | − | 0.998188i | \(-0.480836\pi\) | ||||
0.0601690 | + | 0.998188i | \(0.480836\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 27.6336 | 1.34678 | 0.673390 | − | 0.739287i | \(-0.264837\pi\) | ||||
0.673390 | + | 0.739287i | \(0.264837\pi\) | |||||||
\(422\) | 15.9322i | 0.775565i | ||||||||
\(423\) | − 11.2633i | − 0.547640i | ||||||||
\(424\) | 14.3210 | 0.695487 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −5.61515 | −0.272055 | ||||||||
\(427\) | 7.83923i | 0.379367i | ||||||||
\(428\) | − 5.74106i | − 0.277505i | ||||||||
\(429\) | −3.24482 | −0.156661 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 28.9114 | 1.39261 | 0.696307 | − | 0.717744i | \(-0.254825\pi\) | ||||
0.696307 | + | 0.717744i | \(0.254825\pi\) | |||||||
\(432\) | 2.14399i | 0.103153i | ||||||||
\(433\) | 13.7569i | 0.661113i | 0.943786 | + | 0.330557i | \(0.107236\pi\) | ||||
−0.943786 | + | 0.330557i | \(0.892764\pi\) | |||||||
\(434\) | −5.21844 | −0.250493 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 4.95289 | 0.237200 | ||||||||
\(437\) | 2.77761i | 0.132871i | ||||||||
\(438\) | − 3.04711i | − 0.145596i | ||||||||
\(439\) | 30.5081 | 1.45607 | 0.728036 | − | 0.685539i | \(-0.240433\pi\) | ||||
0.728036 | + | 0.685539i | \(0.240433\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −4.96080 | −0.236228 | ||||||||
\(442\) | 1.06163i | 0.0504965i | ||||||||
\(443\) | − 28.3064i | − 1.34488i | −0.740152 | − | 0.672440i | \(-0.765246\pi\) | ||||
0.740152 | − | 0.672440i | \(-0.234754\pi\) | |||||||
\(444\) | 5.90312 | 0.280150 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 6.38485 | 0.302331 | ||||||||
\(447\) | − 17.1809i | − 0.812630i | ||||||||
\(448\) | 1.68960i | 0.0798262i | ||||||||
\(449\) | −0.769701 | −0.0363244 | −0.0181622 | − | 0.999835i | \(-0.505782\pi\) | ||||
−0.0181622 | + | 0.999835i | \(0.505782\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −12.3849 | −0.583180 | ||||||||
\(452\) | 15.9710i | 0.751211i | ||||||||
\(453\) | − 3.99605i | − 0.187751i | ||||||||
\(454\) | −4.53940 | −0.213045 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 3.81681 | 0.178739 | ||||||||
\(457\) | 15.0841i | 0.705602i | 0.935698 | + | 0.352801i | \(0.114771\pi\) | ||||
−0.935698 | + | 0.352801i | \(0.885229\pi\) | |||||||
\(458\) | − 15.9921i | − 0.747261i | ||||||||
\(459\) | −1.85601 | −0.0866313 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 10.3664 | 0.482810 | 0.241405 | − | 0.970424i | \(-0.422392\pi\) | ||||
0.241405 | + | 0.970424i | \(0.422392\pi\) | |||||||
\(462\) | 2.65040i | 0.123308i | ||||||||
\(463\) | 8.06389i | 0.374761i | 0.982287 | + | 0.187380i | \(0.0599997\pi\) | ||||
−0.982287 | + | 0.187380i | \(0.940000\pi\) | |||||||
\(464\) | −5.02904 | −0.233467 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −0.654353 | −0.0303123 | ||||||||
\(467\) | 30.8145i | 1.42593i | 0.701201 | + | 0.712964i | \(0.252648\pi\) | ||||
−0.701201 | + | 0.712964i | \(0.747352\pi\) | |||||||
\(468\) | 1.67282i | 0.0773263i | ||||||||
\(469\) | 14.7120 | 0.679338 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 7.67282 | 0.353545 | ||||||||
\(472\) | 12.4320i | 0.572227i | ||||||||
\(473\) | − 32.5081i | − 1.49472i | ||||||||
\(474\) | 1.69356 | 0.0777876 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −4.43365 | −0.203216 | ||||||||
\(477\) | 6.81681i | 0.312120i | ||||||||
\(478\) | 1.91595i | 0.0876335i | ||||||||
\(479\) | −10.9938 | −0.502319 | −0.251159 | − | 0.967946i | \(-0.580812\pi\) | ||||
−0.251159 | + | 0.967946i | \(0.580812\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 3.52884 | 0.160901 | ||||||||
\(482\) | − 4.63136i | − 0.210953i | ||||||||
\(483\) | 2.18319i | 0.0993386i | ||||||||
\(484\) | −0.788172 | −0.0358260 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0.571993 | 0.0259461 | ||||||||
\(487\) | 29.3602i | 1.33044i | 0.746649 | + | 0.665218i | \(0.231661\pi\) | ||||
−0.746649 | + | 0.665218i | \(0.768339\pi\) | |||||||
\(488\) | 11.5328i | 0.522065i | ||||||||
\(489\) | −0.471163 | −0.0213067 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −21.0577 | −0.950320 | −0.475160 | − | 0.879900i | \(-0.657610\pi\) | ||||
−0.475160 | + | 0.879900i | \(0.657610\pi\) | |||||||
\(492\) | 6.38485i | 0.287851i | ||||||||
\(493\) | − 4.35355i | − 0.196074i | ||||||||
\(494\) | 1.03920 | 0.0467560 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 13.6975 | 0.615036 | ||||||||
\(497\) | − 14.0185i | − 0.628814i | ||||||||
\(498\) | − 1.79608i | − 0.0804842i | ||||||||
\(499\) | −23.8392 | −1.06719 | −0.533595 | − | 0.845740i | \(-0.679159\pi\) | ||||
−0.533595 | + | 0.845740i | \(0.679159\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −18.7098 | −0.835891 | ||||||||
\(502\) | − 14.5081i | − 0.647528i | ||||||||
\(503\) | 21.8168i | 0.972763i | 0.873746 | + | 0.486382i | \(0.161684\pi\) | ||||
−0.873746 | + | 0.486382i | \(0.838316\pi\) | |||||||
\(504\) | 3.00000 | 0.133631 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −2.83754 | −0.126144 | ||||||||
\(507\) | 1.00000i | 0.0444116i | ||||||||
\(508\) | − 0.306444i | − 0.0135963i | ||||||||
\(509\) | −2.01847 | −0.0894672 | −0.0447336 | − | 0.998999i | \(-0.514244\pi\) | ||||
−0.0447336 | + | 0.998999i | \(0.514244\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 7.60724 | 0.336525 | ||||||||
\(512\) | 20.6459i | 0.912428i | ||||||||
\(513\) | 1.81681i | 0.0802141i | ||||||||
\(514\) | −11.2034 | −0.494159 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −16.7591 | −0.737780 | ||||||||
\(517\) | 36.5473i | 1.60735i | ||||||||
\(518\) | − 2.88239i | − 0.126645i | ||||||||
\(519\) | −7.96080 | −0.349440 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 5.02073 | 0.219962 | 0.109981 | − | 0.993934i | \(-0.464921\pi\) | ||||
0.109981 | + | 0.993934i | \(0.464921\pi\) | |||||||
\(522\) | 1.34169i | 0.0587244i | ||||||||
\(523\) | − 18.5266i | − 0.810111i | −0.914292 | − | 0.405055i | \(-0.867252\pi\) | ||||
0.914292 | − | 0.405055i | \(-0.132748\pi\) | |||||||
\(524\) | −29.1915 | −1.27524 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −4.14625 | −0.180785 | ||||||||
\(527\) | 11.8577i | 0.516530i | ||||||||
\(528\) | − 6.95684i | − 0.302758i | ||||||||
\(529\) | 20.6627 | 0.898376 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −5.91764 | −0.256804 | ||||||||
\(532\) | 4.34000i | 0.188163i | ||||||||
\(533\) | 3.81681i | 0.165324i | ||||||||
\(534\) | 2.77761 | 0.120199 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 21.6438 | 0.934869 | ||||||||
\(537\) | 15.6521i | 0.675438i | ||||||||
\(538\) | 8.29983i | 0.357831i | ||||||||
\(539\) | 16.0969 | 0.693342 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 7.61515 | 0.327401 | 0.163700 | − | 0.986510i | \(-0.447657\pi\) | ||||
0.163700 | + | 0.986510i | \(0.447657\pi\) | |||||||
\(542\) | − 2.40106i | − 0.103134i | ||||||||
\(543\) | 24.5658i | 1.05422i | ||||||||
\(544\) | −10.0745 | −0.431939 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0.816810 | 0.0349563 | ||||||||
\(547\) | − 17.9031i | − 0.765482i | −0.923856 | − | 0.382741i | \(-0.874980\pi\) | ||||
0.923856 | − | 0.382741i | \(-0.125020\pi\) | |||||||
\(548\) | 3.00830i | 0.128508i | ||||||||
\(549\) | −5.48963 | −0.234292 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −4.26160 | −0.181550 | ||||||||
\(552\) | 3.21183i | 0.136704i | ||||||||
\(553\) | 4.22804i | 0.179794i | ||||||||
\(554\) | 9.49794 | 0.403529 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −34.0000 | −1.44192 | ||||||||
\(557\) | − 34.4218i | − 1.45850i | −0.684248 | − | 0.729249i | \(-0.739870\pi\) | ||||
0.684248 | − | 0.729249i | \(-0.260130\pi\) | |||||||
\(558\) | − 3.65435i | − 0.154701i | ||||||||
\(559\) | −10.0185 | −0.423736 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 6.02242 | 0.254267 | ||||||||
\(562\) | 13.9137i | 0.586913i | ||||||||
\(563\) | − 41.5658i | − 1.75179i | −0.482503 | − | 0.875894i | \(-0.660272\pi\) | ||||
0.482503 | − | 0.875894i | \(-0.339728\pi\) | |||||||
\(564\) | 18.8415 | 0.793370 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −4.41123 | −0.185418 | ||||||||
\(567\) | 1.42801i | 0.0599706i | ||||||||
\(568\) | − 20.6235i | − 0.865341i | ||||||||
\(569\) | 26.0761 | 1.09317 | 0.546584 | − | 0.837404i | \(-0.315928\pi\) | ||||
0.546584 | + | 0.837404i | \(0.315928\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 3.41349 | 0.142850 | 0.0714250 | − | 0.997446i | \(-0.477245\pi\) | ||||
0.0714250 | + | 0.997446i | \(0.477245\pi\) | |||||||
\(572\) | − 5.42801i | − 0.226956i | ||||||||
\(573\) | 21.0577i | 0.879697i | ||||||||
\(574\) | 3.11761 | 0.130127 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −1.18319 | −0.0492996 | ||||||||
\(577\) | 5.10704i | 0.212609i | 0.994334 | + | 0.106305i | \(0.0339018\pi\) | ||||
−0.994334 | + | 0.106305i | \(0.966098\pi\) | |||||||
\(578\) | 7.75349i | 0.322503i | ||||||||
\(579\) | −19.9401 | −0.828681 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 4.48399 | 0.186027 | ||||||||
\(582\) | 0.863919i | 0.0358106i | ||||||||
\(583\) | − 22.1193i | − 0.916088i | ||||||||
\(584\) | 11.1915 | 0.463107 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 3.43196 | 0.141773 | ||||||||
\(587\) | − 20.8705i | − 0.861419i | −0.902491 | − | 0.430710i | \(-0.858263\pi\) | ||||
0.902491 | − | 0.430710i | \(-0.141737\pi\) | |||||||
\(588\) | − 8.29854i | − 0.342226i | ||||||||
\(589\) | 11.6072 | 0.478268 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −23.4504 | −0.964622 | ||||||||
\(592\) | 7.56578i | 0.310952i | ||||||||
\(593\) | − 30.4403i | − 1.25003i | −0.780612 | − | 0.625016i | \(-0.785092\pi\) | ||||
0.780612 | − | 0.625016i | \(-0.214908\pi\) | |||||||
\(594\) | −1.85601 | −0.0761532 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 28.7407 | 1.17726 | ||||||||
\(597\) | 16.2880i | 0.666622i | ||||||||
\(598\) | 0.874485i | 0.0357603i | ||||||||
\(599\) | −11.5658 | −0.472565 | −0.236282 | − | 0.971684i | \(-0.575929\pi\) | ||||
−0.236282 | + | 0.971684i | \(0.575929\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 13.6728 | 0.557726 | 0.278863 | − | 0.960331i | \(-0.410042\pi\) | ||||
0.278863 | + | 0.960331i | \(0.410042\pi\) | |||||||
\(602\) | 8.18319i | 0.333522i | ||||||||
\(603\) | 10.3025i | 0.419550i | ||||||||
\(604\) | 6.68468 | 0.271996 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −9.73445 | −0.395435 | ||||||||
\(607\) | 15.4689i | 0.627863i | 0.949446 | + | 0.313932i | \(0.101646\pi\) | ||||
−0.949446 | + | 0.313932i | \(0.898354\pi\) | |||||||
\(608\) | 9.86166i | 0.399943i | ||||||||
\(609\) | −3.34960 | −0.135733 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 11.2633 | 0.455664 | ||||||||
\(612\) | − 3.10478i | − 0.125503i | ||||||||
\(613\) | 0.287973i | 0.0116311i | 0.999983 | + | 0.00581556i | \(0.00185116\pi\) | ||||
−0.999983 | + | 0.00581556i | \(0.998149\pi\) | |||||||
\(614\) | 7.31475 | 0.295199 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −9.73445 | −0.392212 | ||||||||
\(617\) | 6.28007i | 0.252826i | 0.991978 | + | 0.126413i | \(0.0403465\pi\) | ||||
−0.991978 | + | 0.126413i | \(0.959654\pi\) | |||||||
\(618\) | 5.56578i | 0.223888i | ||||||||
\(619\) | 20.6314 | 0.829244 | 0.414622 | − | 0.909994i | \(-0.363914\pi\) | ||||
0.414622 | + | 0.909994i | \(0.363914\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.52884 | −0.0613501 | ||||||||
\(622\) | − 10.2959i | − 0.412827i | ||||||||
\(623\) | 6.93442i | 0.277822i | ||||||||
\(624\) | −2.14399 | −0.0858282 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 7.94063 | 0.317372 | ||||||||
\(627\) | − 5.89522i | − 0.235432i | ||||||||
\(628\) | 12.8353i | 0.512183i | ||||||||
\(629\) | −6.54957 | −0.261148 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −11.0392 | −0.439464 | −0.219732 | − | 0.975560i | \(-0.570518\pi\) | ||||
−0.219732 | + | 0.975560i | \(0.570518\pi\) | |||||||
\(632\) | 6.22013i | 0.247424i | ||||||||
\(633\) | − 27.8538i | − 1.10709i | ||||||||
\(634\) | −4.58651 | −0.182154 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −11.4033 | −0.452171 | ||||||||
\(637\) | − 4.96080i | − 0.196554i | ||||||||
\(638\) | − 4.35355i | − 0.172359i | ||||||||
\(639\) | 9.81681 | 0.388347 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 7.97136 | 0.314850 | 0.157425 | − | 0.987531i | \(-0.449681\pi\) | ||||
0.157425 | + | 0.987531i | \(0.449681\pi\) | |||||||
\(642\) | − 1.96306i | − 0.0774757i | ||||||||
\(643\) | 39.5658i | 1.56032i | 0.625579 | + | 0.780161i | \(0.284863\pi\) | ||||
−0.625579 | + | 0.780161i | \(0.715137\pi\) | |||||||
\(644\) | −3.65209 | −0.143913 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −1.92878 | −0.0758866 | ||||||||
\(647\) | − 24.6992i | − 0.971026i | −0.874230 | − | 0.485513i | \(-0.838633\pi\) | ||||
0.874230 | − | 0.485513i | \(-0.161367\pi\) | |||||||
\(648\) | 2.10083i | 0.0825284i | ||||||||
\(649\) | 19.2017 | 0.753731 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 9.12325 | 0.357569 | ||||||||
\(652\) | − 0.788172i | − 0.0308672i | ||||||||
\(653\) | − 37.7361i | − 1.47673i | −0.674402 | − | 0.738365i | \(-0.735598\pi\) | ||||
0.674402 | − | 0.738365i | \(-0.264402\pi\) | |||||||
\(654\) | 1.69356 | 0.0662233 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −8.18319 | −0.319500 | ||||||||
\(657\) | 5.32718i | 0.207833i | ||||||||
\(658\) | − 9.19997i | − 0.358652i | ||||||||
\(659\) | 49.6890 | 1.93561 | 0.967805 | − | 0.251701i | \(-0.0809900\pi\) | ||||
0.967805 | + | 0.251701i | \(0.0809900\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 40.6235 | 1.58007 | 0.790035 | − | 0.613062i | \(-0.210063\pi\) | ||||
0.790035 | + | 0.613062i | \(0.210063\pi\) | |||||||
\(662\) | − 19.5737i | − 0.760753i | ||||||||
\(663\) | − 1.85601i | − 0.0720816i | ||||||||
\(664\) | 6.59668 | 0.256001 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 2.01847 | 0.0782142 | ||||||||
\(667\) | − 3.58611i | − 0.138855i | ||||||||
\(668\) | − 31.2981i | − 1.21096i | ||||||||
\(669\) | −11.1625 | −0.431566 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 17.8129 | 0.687658 | ||||||||
\(672\) | 7.75123i | 0.299010i | ||||||||
\(673\) | 17.7961i | 0.685988i | 0.939338 | + | 0.342994i | \(0.111441\pi\) | ||||
−0.939338 | + | 0.342994i | \(0.888559\pi\) | |||||||
\(674\) | −12.2814 | −0.473060 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −1.67282 | −0.0643394 | ||||||||
\(677\) | − 24.8850i | − 0.956410i | −0.878248 | − | 0.478205i | \(-0.841288\pi\) | ||||
0.878248 | − | 0.478205i | \(-0.158712\pi\) | |||||||
\(678\) | 5.46100i | 0.209728i | ||||||||
\(679\) | −2.15681 | −0.0827709 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 7.93611 | 0.304112 | ||||||||
\(682\) | 11.8577i | 0.454055i | ||||||||
\(683\) | 27.3602i | 1.04691i | 0.852054 | + | 0.523454i | \(0.175357\pi\) | ||||
−0.852054 | + | 0.523454i | \(0.824643\pi\) | |||||||
\(684\) | −3.03920 | −0.116207 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −9.76970 | −0.373009 | ||||||||
\(687\) | 27.9585i | 1.06668i | ||||||||
\(688\) | − 21.4795i | − 0.818897i | ||||||||
\(689\) | −6.81681 | −0.259700 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 20.2919 | 0.771941 | 0.385971 | − | 0.922511i | \(-0.373867\pi\) | ||||
0.385971 | + | 0.922511i | \(0.373867\pi\) | |||||||
\(692\) | − 13.3170i | − 0.506237i | ||||||||
\(693\) | − 4.63362i | − 0.176017i | ||||||||
\(694\) | 15.2224 | 0.577834 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −4.92781 | −0.186788 | ||||||||
\(697\) | − 7.08405i | − 0.268328i | ||||||||
\(698\) | 7.90312i | 0.299138i | ||||||||
\(699\) | 1.14399 | 0.0432695 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 40.1888 | 1.51791 | 0.758956 | − | 0.651142i | \(-0.225710\pi\) | ||||
0.758956 | + | 0.651142i | \(0.225710\pi\) | |||||||
\(702\) | 0.571993i | 0.0215885i | ||||||||
\(703\) | 6.41123i | 0.241804i | ||||||||
\(704\) | 3.83923 | 0.144697 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 14.6023 | 0.549566 | ||||||||
\(707\) | − 24.3025i | − 0.913989i | ||||||||
\(708\) | − 9.89917i | − 0.372034i | ||||||||
\(709\) | −20.9898 | −0.788290 | −0.394145 | − | 0.919048i | \(-0.628959\pi\) | ||||
−0.394145 | + | 0.919048i | \(0.628959\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −2.96080 | −0.111039 | ||||||||
\(712\) | 10.2017i | 0.382323i | ||||||||
\(713\) | 9.76744i | 0.365794i | ||||||||
\(714\) | −1.51601 | −0.0567353 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −26.1832 | −0.978512 | ||||||||
\(717\) | − 3.34960i | − 0.125093i | ||||||||
\(718\) | − 2.66452i | − 0.0994390i | ||||||||
\(719\) | −6.47907 | −0.241628 | −0.120814 | − | 0.992675i | \(-0.538551\pi\) | ||||
−0.120814 | + | 0.992675i | \(0.538551\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −13.8952 | −0.517485 | ||||||||
\(722\) | − 8.97984i | − 0.334195i | ||||||||
\(723\) | 8.09688i | 0.301126i | ||||||||
\(724\) | −41.0942 | −1.52725 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −0.269502 | −0.0100022 | ||||||||
\(727\) | − 22.7098i | − 0.842259i | −0.907001 | − | 0.421129i | \(-0.861634\pi\) | ||||
0.907001 | − | 0.421129i | \(-0.138366\pi\) | |||||||
\(728\) | 3.00000i | 0.111187i | ||||||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 18.5944 | 0.687739 | ||||||||
\(732\) | − 9.18319i | − 0.339420i | ||||||||
\(733\) | 43.0577i | 1.59037i | 0.606366 | + | 0.795186i | \(0.292627\pi\) | ||||
−0.606366 | + | 0.795186i | \(0.707373\pi\) | |||||||
\(734\) | 11.0207 | 0.406783 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −8.29854 | −0.305888 | ||||||||
\(737\) | − 33.4297i | − 1.23140i | ||||||||
\(738\) | 2.18319i | 0.0803643i | ||||||||
\(739\) | 38.4337 | 1.41380 | 0.706902 | − | 0.707311i | \(-0.250092\pi\) | ||||
0.706902 | + | 0.707311i | \(0.250092\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1.81681 | −0.0667422 | ||||||||
\(742\) | 5.56804i | 0.204409i | ||||||||
\(743\) | − 18.2320i | − 0.668867i | −0.942419 | − | 0.334433i | \(-0.891455\pi\) | ||||
0.942419 | − | 0.334433i | \(-0.108545\pi\) | |||||||
\(744\) | 13.4218 | 0.492067 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −3.50375 | −0.128282 | ||||||||
\(747\) | 3.14003i | 0.114888i | ||||||||
\(748\) | 10.0745i | 0.368359i | ||||||||
\(749\) | 4.90086 | 0.179074 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −25.3720 | −0.925838 | −0.462919 | − | 0.886401i | \(-0.653198\pi\) | ||||
−0.462919 | + | 0.886401i | \(0.653198\pi\) | |||||||
\(752\) | 24.1483i | 0.880599i | ||||||||
\(753\) | 25.3641i | 0.924320i | ||||||||
\(754\) | −1.34169 | −0.0488616 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −2.38880 | −0.0868799 | ||||||||
\(757\) | − 32.1888i | − 1.16992i | −0.811061 | − | 0.584962i | \(-0.801110\pi\) | ||||
0.811061 | − | 0.584962i | \(-0.198890\pi\) | |||||||
\(758\) | − 12.7614i | − 0.463515i | ||||||||
\(759\) | 4.96080 | 0.180066 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 32.2280 | 1.16827 | 0.584133 | − | 0.811658i | \(-0.301435\pi\) | ||||
0.584133 | + | 0.811658i | \(0.301435\pi\) | |||||||
\(762\) | − 0.104783i | − 0.00379590i | ||||||||
\(763\) | 4.22804i | 0.153065i | ||||||||
\(764\) | −35.2258 | −1.27442 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −21.2118 | −0.766414 | ||||||||
\(767\) | − 5.91764i | − 0.213674i | ||||||||
\(768\) | 4.23030i | 0.152648i | ||||||||
\(769\) | −39.5843 | −1.42744 | −0.713722 | − | 0.700429i | \(-0.752992\pi\) | ||||
−0.713722 | + | 0.700429i | \(0.752992\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 19.5865 | 0.705391 | ||||||||
\(772\) | − 33.3562i | − 1.20052i | ||||||||
\(773\) | 19.4689i | 0.700248i | 0.936703 | + | 0.350124i | \(0.113861\pi\) | ||||
−0.936703 | + | 0.350124i | \(0.886139\pi\) | |||||||
\(774\) | −5.73050 | −0.205978 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −3.17302 | −0.113905 | ||||||||
\(777\) | 5.03920i | 0.180780i | ||||||||
\(778\) | 13.6336i | 0.488789i | ||||||||
\(779\) | −6.93442 | −0.248451 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −31.8538 | −1.13982 | ||||||||
\(782\) | − 1.62306i | − 0.0580403i | ||||||||
\(783\) | − 2.34565i | − 0.0838266i | ||||||||
\(784\) | 10.6359 | 0.379853 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −9.98153 | −0.356029 | ||||||||
\(787\) | − 17.0722i | − 0.608558i | −0.952583 | − | 0.304279i | \(-0.901584\pi\) | ||||
0.952583 | − | 0.304279i | \(-0.0984155\pi\) | |||||||
\(788\) | − 39.2284i | − 1.39746i | ||||||||
\(789\) | 7.24877 | 0.258063 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −13.6336 | −0.484756 | ||||||||
\(792\) | − 6.81681i | − 0.242225i | ||||||||
\(793\) | − 5.48963i | − 0.194943i | ||||||||
\(794\) | −15.2718 | −0.541975 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −27.2469 | −0.965741 | ||||||||
\(797\) | 17.5187i | 0.620543i | 0.950648 | + | 0.310272i | \(0.100420\pi\) | ||||
−0.950648 | + | 0.310272i | \(0.899580\pi\) | |||||||
\(798\) | 1.48399i | 0.0525326i | ||||||||
\(799\) | −20.9048 | −0.739559 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −4.85601 | −0.171579 | ||||||||
\(802\) | 12.4791i | 0.440651i | ||||||||
\(803\) | − 17.2857i | − 0.610000i | ||||||||
\(804\) | −17.2343 | −0.607805 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 3.65435 | 0.128719 | ||||||||
\(807\) | − 14.5104i | − 0.510789i | ||||||||
\(808\) | − 35.7529i | − 1.25778i | ||||||||
\(809\) | −16.2017 | −0.569620 | −0.284810 | − | 0.958584i | \(-0.591931\pi\) | ||||
−0.284810 | + | 0.958584i | \(0.591931\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 21.5513 | 0.756767 | 0.378384 | − | 0.925649i | \(-0.376480\pi\) | ||||
0.378384 | + | 0.925649i | \(0.376480\pi\) | |||||||
\(812\) | − 5.60329i | − 0.196637i | ||||||||
\(813\) | 4.19771i | 0.147220i | ||||||||
\(814\) | −6.54957 | −0.229562 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 3.97927 | 0.139302 | ||||||||
\(817\) | − 18.2017i | − 0.636796i | ||||||||
\(818\) | 0.664918i | 0.0232483i | ||||||||
\(819\) | −1.42801 | −0.0498986 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 31.5288 | 1.10036 | 0.550182 | − | 0.835045i | \(-0.314558\pi\) | ||||
0.550182 | + | 0.835045i | \(0.314558\pi\) | |||||||
\(822\) | 1.02864i | 0.0358779i | ||||||||
\(823\) | 56.1971i | 1.95891i | 0.201665 | + | 0.979455i | \(0.435365\pi\) | ||||
−0.201665 | + | 0.979455i | \(0.564635\pi\) | |||||||
\(824\) | −20.4421 | −0.712135 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −4.83359 | −0.168182 | ||||||||
\(827\) | − 51.5697i | − 1.79326i | −0.442785 | − | 0.896628i | \(-0.646010\pi\) | ||||
0.442785 | − | 0.896628i | \(-0.353990\pi\) | |||||||
\(828\) | − 2.55748i | − 0.0888784i | ||||||||
\(829\) | 14.0286 | 0.487235 | 0.243617 | − | 0.969871i | \(-0.421666\pi\) | ||||
0.243617 | + | 0.969871i | \(0.421666\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −16.6050 | −0.576020 | ||||||||
\(832\) | − 1.18319i | − 0.0410197i | ||||||||
\(833\) | 9.20731i | 0.319014i | ||||||||
\(834\) | −11.6257 | −0.402566 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 9.86166 | 0.341073 | ||||||||
\(837\) | 6.38880i | 0.220829i | ||||||||
\(838\) | 1.40897i | 0.0486719i | ||||||||
\(839\) | 28.4712 | 0.982934 | 0.491467 | − | 0.870896i | \(-0.336461\pi\) | ||||
0.491467 | + | 0.870896i | \(0.336461\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −23.4979 | −0.810274 | ||||||||
\(842\) | 15.8062i | 0.544719i | ||||||||
\(843\) | − 24.3249i | − 0.837795i | ||||||||
\(844\) | 46.5944 | 1.60385 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 6.44252 | 0.221499 | ||||||||
\(847\) | − 0.672824i | − 0.0231185i | ||||||||
\(848\) | − 14.6151i | − 0.501886i | ||||||||
\(849\) | 7.71203 | 0.264676 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −5.39502 | −0.184939 | ||||||||
\(852\) | 16.4218i | 0.562601i | ||||||||
\(853\) | 33.5552i | 1.14891i | 0.818537 | + | 0.574454i | \(0.194786\pi\) | ||||
−0.818537 | + | 0.574454i | \(0.805214\pi\) | |||||||
\(854\) | −4.48399 | −0.153439 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 7.20997 | 0.246432 | ||||||||
\(857\) | 37.8432i | 1.29270i | 0.763042 | + | 0.646349i | \(0.223705\pi\) | ||||
−0.763042 | + | 0.646349i | \(0.776295\pi\) | |||||||
\(858\) | − 1.85601i | − 0.0633633i | ||||||||
\(859\) | −14.3849 | −0.490805 | −0.245402 | − | 0.969421i | \(-0.578920\pi\) | ||||
−0.245402 | + | 0.969421i | \(0.578920\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −5.45043 | −0.185750 | ||||||||
\(862\) | 16.5371i | 0.563257i | ||||||||
\(863\) | − 32.2610i | − 1.09818i | −0.835764 | − | 0.549089i | \(-0.814975\pi\) | ||||
0.835764 | − | 0.549089i | \(-0.185025\pi\) | |||||||
\(864\) | −5.42801 | −0.184665 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −7.86884 | −0.267394 | ||||||||
\(867\) | − 13.5552i | − 0.460359i | ||||||||
\(868\) | 15.2616i | 0.518012i | ||||||||
\(869\) | 9.60724 | 0.325903 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −10.3025 | −0.349087 | ||||||||
\(872\) | 6.22013i | 0.210640i | ||||||||
\(873\) | − 1.51037i | − 0.0511181i | ||||||||
\(874\) | −1.58877 | −0.0537410 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −8.91143 | −0.301089 | ||||||||
\(877\) | 57.6996i | 1.94838i | 0.225736 | + | 0.974189i | \(0.427521\pi\) | ||||
−0.225736 | + | 0.974189i | \(0.572479\pi\) | |||||||
\(878\) | 17.4504i | 0.588924i | ||||||||
\(879\) | −6.00000 | −0.202375 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −56.6811 | −1.90964 | −0.954818 | − | 0.297192i | \(-0.903950\pi\) | ||||
−0.954818 | + | 0.297192i | \(0.903950\pi\) | |||||||
\(882\) | − 2.83754i | − 0.0955450i | ||||||||
\(883\) | 20.0863i | 0.675958i | 0.941154 | + | 0.337979i | \(0.109743\pi\) | ||||
−0.941154 | + | 0.337979i | \(0.890257\pi\) | |||||||
\(884\) | 3.10478 | 0.104425 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 16.1911 | 0.543950 | ||||||||
\(887\) | − 17.2857i | − 0.580397i | −0.956966 | − | 0.290199i | \(-0.906279\pi\) | ||||
0.956966 | − | 0.290199i | \(-0.0937214\pi\) | |||||||
\(888\) | 7.41349i | 0.248780i | ||||||||
\(889\) | 0.261596 | 0.00877366 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 3.24482 | 0.108705 | ||||||||
\(892\) | − 18.6728i | − 0.625212i | ||||||||
\(893\) | 20.4633i | 0.684777i | ||||||||
\(894\) | 9.82738 | 0.328677 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −16.4689 | −0.550187 | ||||||||
\(897\) | − 1.52884i | − 0.0510464i | ||||||||
\(898\) | − 0.440264i | − 0.0146918i | ||||||||
\(899\) | −14.9859 | −0.499807 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 12.6521 | 0.421502 | ||||||||
\(902\) | − 7.08405i | − 0.235873i | ||||||||
\(903\) | − 14.3064i | − 0.476089i | ||||||||
\(904\) | −20.0573 | −0.667095 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 2.28571 | 0.0759377 | ||||||||
\(907\) | − 48.4033i | − 1.60721i | −0.595166 | − | 0.803603i | \(-0.702914\pi\) | ||||
0.595166 | − | 0.803603i | \(-0.297086\pi\) | |||||||
\(908\) | 13.2757i | 0.440570i | ||||||||
\(909\) | 17.0185 | 0.564467 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −9.16246 | −0.303566 | −0.151783 | − | 0.988414i | \(-0.548501\pi\) | ||||
−0.151783 | + | 0.988414i | \(0.548501\pi\) | |||||||
\(912\) | − 3.89522i | − 0.128984i | ||||||||
\(913\) | − 10.1888i | − 0.337201i | ||||||||
\(914\) | −8.62798 | −0.285388 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −46.7697 | −1.54531 | ||||||||
\(917\) | − 24.9193i | − 0.822909i | ||||||||
\(918\) | − 1.06163i | − 0.0350389i | ||||||||
\(919\) | −7.06558 | −0.233072 | −0.116536 | − | 0.993186i | \(-0.537179\pi\) | ||||
−0.116536 | + | 0.993186i | \(0.537179\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −12.7882 | −0.421385 | ||||||||
\(922\) | 5.92950i | 0.195278i | ||||||||
\(923\) | 9.81681i | 0.323124i | ||||||||
\(924\) | 7.75123 | 0.254997 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −4.61249 | −0.151576 | ||||||||
\(927\) | − 9.73050i | − 0.319591i | ||||||||
\(928\) | − 12.7322i | − 0.417955i | ||||||||
\(929\) | −37.3042 | −1.22391 | −0.611955 | − | 0.790892i | \(-0.709617\pi\) | ||||
−0.611955 | + | 0.790892i | \(0.709617\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 9.01283 | 0.295383 | ||||||||
\(932\) | 1.91369i | 0.0626849i | ||||||||
\(933\) | 18.0000i | 0.589294i | ||||||||
\(934\) | −17.6257 | −0.576731 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −2.10083 | −0.0686678 | ||||||||
\(937\) | − 18.8353i | − 0.615322i | −0.951496 | − | 0.307661i | \(-0.900454\pi\) | ||||
0.951496 | − | 0.307661i | \(-0.0995462\pi\) | |||||||
\(938\) | 8.41518i | 0.274765i | ||||||||
\(939\) | −13.8824 | −0.453035 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −53.6106 | −1.74766 | −0.873828 | − | 0.486235i | \(-0.838370\pi\) | ||||
−0.873828 | + | 0.486235i | \(0.838370\pi\) | |||||||
\(942\) | 4.38880i | 0.142995i | ||||||||
\(943\) | − 5.83528i | − 0.190023i | ||||||||
\(944\) | 12.6873 | 0.412938 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 18.5944 | 0.604557 | ||||||||
\(947\) | − 12.6319i | − 0.410483i | −0.978711 | − | 0.205241i | \(-0.934202\pi\) | ||||
0.978711 | − | 0.205241i | \(-0.0657979\pi\) | |||||||
\(948\) | − 4.95289i | − 0.160862i | ||||||||
\(949\) | −5.32718 | −0.172927 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 8.01847 | 0.260017 | ||||||||
\(952\) | − 5.56804i | − 0.180461i | ||||||||
\(953\) | − 58.8044i | − 1.90486i | −0.304756 | − | 0.952430i | \(-0.598575\pi\) | ||||
0.304756 | − | 0.952430i | \(-0.401425\pi\) | |||||||
\(954\) | −3.89917 | −0.126240 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 5.60329 | 0.181223 | ||||||||
\(957\) | 7.61120i | 0.246035i | ||||||||
\(958\) | − 6.28837i | − 0.203168i | ||||||||
\(959\) | −2.56804 | −0.0829263 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 9.81681 | 0.316671 | ||||||||
\(962\) | 2.01847i | 0.0650781i | ||||||||
\(963\) | 3.43196i | 0.110593i | ||||||||
\(964\) | −13.5446 | −0.436244 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −1.24877 | −0.0401785 | ||||||||
\(967\) | − 6.43027i | − 0.206783i | −0.994641 | − | 0.103392i | \(-0.967030\pi\) | ||||
0.994641 | − | 0.103392i | \(-0.0329695\pi\) | |||||||
\(968\) | − 0.989833i | − 0.0318144i | ||||||||
\(969\) | 3.37202 | 0.108325 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 0.604983 | 0.0194148 | 0.00970741 | − | 0.999953i | \(-0.496910\pi\) | ||||
0.00970741 | + | 0.999953i | \(0.496910\pi\) | |||||||
\(972\) | − 1.67282i | − 0.0536558i | ||||||||
\(973\) | − 29.0241i | − 0.930470i | ||||||||
\(974\) | −16.7938 | −0.538109 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 11.7697 | 0.376739 | ||||||||
\(977\) | − 4.36638i | − 0.139693i | −0.997558 | − | 0.0698464i | \(-0.977749\pi\) | ||||
0.997558 | − | 0.0698464i | \(-0.0222509\pi\) | |||||||
\(978\) | − 0.269502i | − 0.00861772i | ||||||||
\(979\) | 15.7569 | 0.503592 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −2.96080 | −0.0945310 | ||||||||
\(982\) | − 12.0448i | − 0.384367i | ||||||||
\(983\) | 30.3025i | 0.966499i | 0.875483 | + | 0.483250i | \(0.160544\pi\) | ||||
−0.875483 | + | 0.483250i | \(0.839456\pi\) | |||||||
\(984\) | −8.01847 | −0.255620 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 2.49020 | 0.0793042 | ||||||||
\(987\) | 16.0841i | 0.511961i | ||||||||
\(988\) | − 3.03920i | − 0.0966899i | ||||||||
\(989\) | 15.3166 | 0.487040 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −4.96870 | −0.157836 | −0.0789180 | − | 0.996881i | \(-0.525147\pi\) | ||||
−0.0789180 | + | 0.996881i | \(0.525147\pi\) | |||||||
\(992\) | 34.6785i | 1.10104i | ||||||||
\(993\) | 34.2201i | 1.08594i | ||||||||
\(994\) | 8.01847 | 0.254330 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −5.25272 | −0.166439 | ||||||||
\(997\) | − 11.2959i | − 0.357744i | −0.983872 | − | 0.178872i | \(-0.942755\pi\) | ||||
0.983872 | − | 0.178872i | \(-0.0572448\pi\) | |||||||
\(998\) | − 13.6359i | − 0.431636i | ||||||||
\(999\) | −3.52884 | −0.111647 |
(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 | 975.2.c.j.274.4 | 6 | ||
3.2 | odd | 2 | 2925.2.c.x.2224.3 | 6 | |||
5.2 | odd | 4 | 975.2.a.n.1.2 | ✓ | 3 | ||
5.3 | odd | 4 | 975.2.a.p.1.2 | yes | 3 | ||
5.4 | even | 2 | inner | 975.2.c.j.274.3 | 6 | ||
15.2 | even | 4 | 2925.2.a.bi.1.2 | 3 | |||
15.8 | even | 4 | 2925.2.a.bg.1.2 | 3 | |||
15.14 | odd | 2 | 2925.2.c.x.2224.4 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
975.2.a.n.1.2 | ✓ | 3 | 5.2 | odd | 4 | ||
975.2.a.p.1.2 | yes | 3 | 5.3 | odd | 4 | ||
975.2.c.j.274.3 | 6 | 5.4 | even | 2 | inner | ||
975.2.c.j.274.4 | 6 | 1.1 | even | 1 | trivial | ||
2925.2.a.bg.1.2 | 3 | 15.8 | even | 4 | |||
2925.2.a.bi.1.2 | 3 | 15.2 | even | 4 | |||
2925.2.c.x.2224.3 | 6 | 3.2 | odd | 2 | |||
2925.2.c.x.2224.4 | 6 | 15.14 | odd | 2 |