Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1512,2,Mod(865,1512)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1512, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1512.865");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1512 = 2^{3} \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1512.s (of order \(3\), degree \(2\), 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: | \(12.0733807856\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{3})\) |
Coefficient field: | 8.0.9391935744.3 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 4x^{7} + 5x^{6} + 12x^{5} - 76x^{4} + 84x^{3} + 245x^{2} - 1372x + 2401 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{25}]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 1297.4 | ||
Root | \(0.295509 + 2.62920i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1512.1297 |
Dual form | 1512.2.s.m.865.4 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1512\mathbb{Z}\right)^\times\).
\(n\) | \(757\) | \(785\) | \(1081\) | \(1135\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.366025 | − | 0.633975i | 0.163692 | − | 0.283522i | −0.772498 | − | 0.635017i | \(-0.780993\pi\) |
0.936190 | + | 0.351495i | \(0.114326\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.12920 | − | 1.57052i | 0.804761 | − | 0.593599i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.92471 | + | 3.33369i | 0.580321 | + | 1.00514i | 0.995441 | + | 0.0953782i | \(0.0304061\pi\) |
−0.415121 | + | 0.909766i | \(0.636261\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.87308 | −1.35155 | −0.675775 | − | 0.737108i | \(-0.736191\pi\) | ||||
−0.675775 | + | 0.737108i | \(0.736191\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3.09808 | + | 5.36603i | 0.751394 | + | 1.30145i | 0.947147 | + | 0.320799i | \(0.103951\pi\) |
−0.195753 | + | 0.980653i | \(0.562715\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.39715 | + | 2.41993i | −0.320527 | + | 0.555169i | −0.980597 | − | 0.196035i | \(-0.937193\pi\) |
0.660070 | + | 0.751204i | \(0.270527\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3.69971 | − | 6.40809i | 0.771443 | − | 1.33618i | −0.165328 | − | 0.986239i | \(-0.552868\pi\) |
0.936772 | − | 0.349941i | \(-0.113798\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.23205 | + | 3.86603i | 0.446410 | + | 0.773205i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 9.78474 | 1.81698 | 0.908490 | − | 0.417907i | \(-0.137236\pi\) | ||||
0.908490 | + | 0.417907i | \(0.137236\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.15676 | + | 5.46766i | 0.566970 | + | 0.982021i | 0.996863 | + | 0.0791414i | \(0.0252179\pi\) |
−0.429893 | + | 0.902880i | \(0.641449\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −0.216328 | − | 1.92471i | −0.0365660 | − | 0.325335i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.82185 | − | 4.88759i | 0.463909 | − | 0.803515i | −0.535242 | − | 0.844699i | \(-0.679780\pi\) |
0.999152 | + | 0.0411839i | \(0.0131130\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.50267 | 0.234678 | 0.117339 | − | 0.993092i | \(-0.462564\pi\) | ||||
0.117339 | + | 0.993092i | \(0.462564\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −12.1629 | −1.85483 | −0.927414 | − | 0.374036i | \(-0.877974\pi\) | ||||
−0.927414 | + | 0.374036i | \(0.877974\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −2.95704 | + | 5.12175i | −0.431329 | + | 0.747084i | −0.996988 | − | 0.0775554i | \(-0.975289\pi\) |
0.565659 | + | 0.824639i | \(0.308622\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 2.06696 | − | 6.68788i | 0.295279 | − | 0.955411i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −6.43176 | − | 11.1401i | −0.883471 | − | 1.53022i | −0.847456 | − | 0.530865i | \(-0.821867\pi\) |
−0.0360142 | − | 0.999351i | \(-0.511466\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.81796 | 0.379974 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 3.19265 | + | 5.52984i | 0.415648 | + | 0.719924i | 0.995496 | − | 0.0948008i | \(-0.0302214\pi\) |
−0.579848 | + | 0.814725i | \(0.696888\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 6.29779 | − | 10.9081i | 0.806349 | − | 1.39664i | −0.109027 | − | 0.994039i | \(-0.534774\pi\) |
0.915376 | − | 0.402599i | \(-0.131893\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1.78367 | + | 3.08941i | −0.221237 | + | 0.383194i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −0.834905 | − | 1.44610i | −0.102000 | − | 0.176669i | 0.810509 | − | 0.585727i | \(-0.199191\pi\) |
−0.912509 | + | 0.409058i | \(0.865857\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 13.3135 | 1.58002 | 0.790012 | − | 0.613092i | \(-0.210074\pi\) | ||||
0.790012 | + | 0.613092i | \(0.210074\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0.720214 | + | 1.24745i | 0.0842947 | + | 0.146003i | 0.905090 | − | 0.425219i | \(-0.139803\pi\) |
−0.820796 | + | 0.571222i | \(0.806470\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 9.33369 | + | 4.07529i | 1.06367 | + | 0.464423i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −3.55390 | + | 6.15554i | −0.399845 | + | 0.692552i | −0.993706 | − | 0.112015i | \(-0.964269\pi\) |
0.593861 | + | 0.804567i | \(0.297603\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 7.98089 | 0.876016 | 0.438008 | − | 0.898971i | \(-0.355684\pi\) | ||||
0.438008 | + | 0.898971i | \(0.355684\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 4.53590 | 0.491987 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 3.62442 | − | 6.27768i | 0.384188 | − | 0.665432i | −0.607469 | − | 0.794344i | \(-0.707815\pi\) |
0.991656 | + | 0.128911i | \(0.0411483\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −10.3758 | + | 7.65326i | −1.08767 | + | 0.802279i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1.02278 | + | 1.77151i | 0.104935 | + | 0.181753i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 12.1629 | 1.23496 | 0.617479 | − | 0.786587i | \(-0.288154\pi\) | ||||
0.617479 | + | 0.786587i | \(0.288154\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 5.77412 | + | 10.0011i | 0.574546 | + | 0.995143i | 0.996091 | + | 0.0883353i | \(0.0281547\pi\) |
−0.421545 | + | 0.906808i | \(0.638512\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −4.02756 | + | 6.97594i | −0.396847 | + | 0.687360i | −0.993335 | − | 0.115263i | \(-0.963229\pi\) |
0.596488 | + | 0.802622i | \(0.296562\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1.02367 | + | 1.77305i | −0.0989622 | + | 0.171408i | −0.911255 | − | 0.411842i | \(-0.864886\pi\) |
0.812293 | + | 0.583249i | \(0.198219\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −4.29779 | − | 7.44399i | −0.411654 | − | 0.713005i | 0.583417 | − | 0.812173i | \(-0.301715\pi\) |
−0.995071 | + | 0.0991678i | \(0.968382\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 0.260828 | 0.0245366 | 0.0122683 | − | 0.999925i | \(-0.496095\pi\) | ||||
0.0122683 | + | 0.999925i | \(0.496095\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2.70838 | − | 4.69105i | −0.252558 | − | 0.437442i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 15.0238 | + | 6.55974i | 1.37723 | + | 0.601331i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.90898 | + | 3.30645i | −0.173544 | + | 0.300587i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 6.92820 | 0.619677 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −3.15059 | −0.279570 | −0.139785 | − | 0.990182i | \(-0.544641\pi\) | ||||
−0.139785 | + | 0.990182i | \(0.544641\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1.17337 | + | 2.03234i | −0.102518 | + | 0.177566i | −0.912721 | − | 0.408582i | \(-0.866023\pi\) |
0.810204 | + | 0.586149i | \(0.199357\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.825738 | + | 7.34674i | 0.0716006 | + | 0.637043i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 6.28117 | + | 10.8793i | 0.536637 | + | 0.929483i | 0.999082 | + | 0.0428346i | \(0.0136389\pi\) |
−0.462445 | + | 0.886648i | \(0.653028\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 4.48777 | 0.380648 | 0.190324 | − | 0.981721i | \(-0.439046\pi\) | ||||
0.190324 | + | 0.981721i | \(0.439046\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −9.37925 | − | 16.2453i | −0.784332 | − | 1.35850i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 3.58146 | − | 6.20327i | 0.297424 | − | 0.515154i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −1.63397 | + | 2.83013i | −0.133860 | + | 0.231853i | −0.925162 | − | 0.379574i | \(-0.876071\pi\) |
0.791301 | + | 0.611427i | \(0.209404\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −0.307345 | − | 0.532338i | −0.0250114 | − | 0.0433210i | 0.853249 | − | 0.521504i | \(-0.174629\pi\) |
−0.878260 | + | 0.478183i | \(0.841296\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 4.62181 | 0.371233 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1.65326 | − | 2.86353i | −0.131944 | − | 0.228534i | 0.792482 | − | 0.609896i | \(-0.208789\pi\) |
−0.924426 | + | 0.381361i | \(0.875455\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −2.18660 | − | 19.4545i | −0.172328 | − | 1.53323i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 0.241607 | − | 0.418475i | 0.0189241 | − | 0.0327775i | −0.856408 | − | 0.516299i | \(-0.827309\pi\) |
0.875332 | + | 0.483522i | \(0.160643\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −20.7515 | −1.60580 | −0.802900 | − | 0.596114i | \(-0.796711\pi\) | ||||
−0.802900 | + | 0.596114i | \(0.796711\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 10.7469 | 0.826688 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −12.2907 | + | 21.2882i | −0.934447 | + | 1.61851i | −0.158830 | + | 0.987306i | \(0.550772\pi\) |
−0.775617 | + | 0.631204i | \(0.782561\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 10.8241 | + | 4.72606i | 0.818227 | + | 0.357256i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −10.8924 | − | 18.8661i | −0.814134 | − | 1.41012i | −0.909948 | − | 0.414722i | \(-0.863879\pi\) |
0.0958144 | − | 0.995399i | \(-0.469454\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −6.54046 | −0.486148 | −0.243074 | − | 0.970008i | \(-0.578156\pi\) | ||||
−0.243074 | + | 0.970008i | \(0.578156\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −2.06574 | − | 3.57796i | −0.151876 | − | 0.263057i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −11.9258 | + | 20.6560i | −0.872099 | + | 1.51052i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −7.67954 | + | 13.3013i | −0.555672 | + | 0.962452i | 0.442179 | + | 0.896927i | \(0.354206\pi\) |
−0.997851 | + | 0.0655251i | \(0.979128\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −9.47861 | − | 16.4174i | −0.682285 | − | 1.18175i | −0.974282 | − | 0.225333i | \(-0.927653\pi\) |
0.291997 | − | 0.956419i | \(-0.405680\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −8.26295 | −0.588711 | −0.294356 | − | 0.955696i | \(-0.595105\pi\) | ||||
−0.294356 | + | 0.955696i | \(0.595105\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 6.75490 | + | 11.6998i | 0.478842 | + | 0.829378i | 0.999706 | − | 0.0242614i | \(-0.00772340\pi\) |
−0.520864 | + | 0.853640i | \(0.674390\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 20.8336 | − | 15.3671i | 1.46223 | − | 1.07856i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0.550015 | − | 0.952654i | 0.0384147 | − | 0.0665363i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −10.7564 | −0.744034 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −6.87552 | −0.473330 | −0.236665 | − | 0.971591i | \(-0.576054\pi\) | ||||
−0.236665 | + | 0.971591i | \(0.576054\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −4.45194 | + | 7.71098i | −0.303620 | + | 0.525885i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 15.3084 | + | 6.68399i | 1.03920 | + | 0.453739i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −15.0972 | − | 26.1491i | −1.01555 | − | 1.75898i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −13.9809 | −0.936229 | −0.468115 | − | 0.883668i | \(-0.655067\pi\) | ||||
−0.468115 | + | 0.883668i | \(0.655067\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 7.54912 | + | 13.0755i | 0.501053 | + | 0.867849i | 0.999999 | + | 0.00121627i | \(0.000387152\pi\) |
−0.498946 | + | 0.866633i | \(0.666280\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 5.28367 | − | 9.15159i | 0.349155 | − | 0.604754i | −0.636945 | − | 0.770910i | \(-0.719802\pi\) |
0.986100 | + | 0.166155i | \(0.0531354\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 0.740716 | − | 1.28296i | 0.0485259 | − | 0.0840493i | −0.840742 | − | 0.541436i | \(-0.817881\pi\) |
0.889268 | + | 0.457386i | \(0.151214\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2.16471 | + | 3.74938i | 0.141210 | + | 0.244583i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −6.88964 | −0.445653 | −0.222827 | − | 0.974858i | \(-0.571528\pi\) | ||||
−0.222827 | + | 0.974858i | \(0.571528\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −14.1578 | − | 24.5221i | −0.911985 | − | 1.57960i | −0.811256 | − | 0.584691i | \(-0.801216\pi\) |
−0.100729 | − | 0.994914i | \(-0.532118\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −3.48339 | − | 3.75833i | −0.222545 | − | 0.240111i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 6.80841 | − | 11.7925i | 0.433209 | − | 0.750339i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −5.93532 | −0.374634 | −0.187317 | − | 0.982299i | \(-0.559979\pi\) | ||||
−0.187317 | + | 0.982299i | \(0.559979\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 28.4834 | 1.79074 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −3.99044 | + | 6.91165i | −0.248917 | + | 0.431137i | −0.963226 | − | 0.268694i | \(-0.913408\pi\) |
0.714309 | + | 0.699831i | \(0.246741\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.66776 | − | 14.8384i | −0.103630 | − | 0.922013i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −9.97982 | − | 17.2856i | −0.615382 | − | 1.06587i | −0.990317 | − | 0.138822i | \(-0.955668\pi\) |
0.374935 | − | 0.927051i | \(-0.377665\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −9.41676 | −0.578467 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −5.50267 | − | 9.53090i | −0.335504 | − | 0.581109i | 0.648078 | − | 0.761574i | \(-0.275573\pi\) |
−0.983581 | + | 0.180465i | \(0.942240\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 10.9652 | − | 18.9922i | 0.666086 | − | 1.15370i | −0.312903 | − | 0.949785i | \(-0.601302\pi\) |
0.978990 | − | 0.203910i | \(-0.0653651\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −8.59208 | + | 14.8819i | −0.518122 | + | 0.897414i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 8.27412 | + | 14.3312i | 0.497143 | + | 0.861078i | 0.999995 | − | 0.00329530i | \(-0.00104893\pi\) |
−0.502851 | + | 0.864373i | \(0.667716\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 24.8250 | 1.48093 | 0.740466 | − | 0.672093i | \(-0.234605\pi\) | ||||
0.740466 | + | 0.672093i | \(0.234605\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2.23205 | + | 3.86603i | 0.132682 | + | 0.229811i | 0.924709 | − | 0.380674i | \(-0.124308\pi\) |
−0.792028 | + | 0.610485i | \(0.790975\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 3.19948 | − | 2.35997i | 0.188859 | − | 0.139304i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −10.6962 | + | 18.5263i | −0.629185 | + | 1.08978i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −9.20327 | −0.537661 | −0.268830 | − | 0.963188i | \(-0.586637\pi\) | ||||
−0.268830 | + | 0.963188i | \(0.586637\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 4.67437 | 0.272152 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −18.0290 | + | 31.2272i | −1.04264 | + | 1.80591i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −25.8973 | + | 19.1021i | −1.49269 | + | 1.10103i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −4.61030 | − | 7.98528i | −0.263985 | − | 0.457236i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −33.8900 | −1.93420 | −0.967102 | − | 0.254390i | \(-0.918125\pi\) | ||||
−0.967102 | + | 0.254390i | \(0.918125\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 3.68999 | + | 6.39124i | 0.209240 | + | 0.362414i | 0.951475 | − | 0.307725i | \(-0.0995677\pi\) |
−0.742235 | + | 0.670139i | \(0.766234\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −0.657974 | + | 1.13964i | −0.0371909 | + | 0.0644165i | −0.884022 | − | 0.467446i | \(-0.845174\pi\) |
0.846831 | + | 0.531862i | \(0.178508\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 3.59452 | − | 6.22588i | 0.201888 | − | 0.349680i | −0.747249 | − | 0.664545i | \(-0.768626\pi\) |
0.949137 | + | 0.314864i | \(0.101959\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 18.8327 | + | 32.6193i | 1.05443 | + | 1.82633i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −17.3139 | −0.963369 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −10.8770 | − | 18.8395i | −0.603346 | − | 1.04503i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 1.74767 | + | 15.5493i | 0.0963519 | + | 0.857260i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2.41126 | + | 4.17643i | −0.132535 | + | 0.229557i | −0.924653 | − | 0.380811i | \(-0.875645\pi\) |
0.792118 | + | 0.610368i | \(0.208978\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −1.22239 | −0.0667861 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −12.7561 | −0.694867 | −0.347434 | − | 0.937705i | \(-0.612947\pi\) | ||||
−0.347434 | + | 0.937705i | \(0.612947\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −12.1517 | + | 21.0473i | −0.658049 | + | 1.13977i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −6.10247 | − | 17.4860i | −0.329502 | − | 0.944155i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −15.4641 | − | 26.7846i | −0.830156 | − | 1.43787i | −0.897914 | − | 0.440171i | \(-0.854918\pi\) |
0.0677573 | − | 0.997702i | \(-0.478416\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 17.2368 | 0.922667 | 0.461334 | − | 0.887227i | \(-0.347371\pi\) | ||||
0.461334 | + | 0.887227i | \(0.347371\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −5.76350 | − | 9.98267i | −0.306760 | − | 0.531324i | 0.670892 | − | 0.741555i | \(-0.265912\pi\) |
−0.977652 | + | 0.210231i | \(0.932578\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 4.87308 | − | 8.44043i | 0.258636 | − | 0.447971i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 1.02367 | − | 1.77305i | 0.0540274 | − | 0.0935782i | −0.837747 | − | 0.546059i | \(-0.816128\pi\) |
0.891774 | + | 0.452481i | \(0.149461\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 5.59597 | + | 9.69250i | 0.294525 | + | 0.510132i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1.05447 | 0.0551933 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 12.5933 | + | 21.8122i | 0.657365 | + | 1.13859i | 0.981295 | + | 0.192508i | \(0.0616623\pi\) |
−0.323931 | + | 0.946081i | \(0.605004\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −31.1903 | − | 13.6184i | −1.61932 | − | 0.707030i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 4.73677 | − | 8.20432i | 0.245260 | − | 0.424804i | −0.716944 | − | 0.697130i | \(-0.754460\pi\) |
0.962205 | + | 0.272327i | \(0.0877932\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −47.6818 | −2.45574 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −21.6176 | −1.11042 | −0.555211 | − | 0.831710i | \(-0.687362\pi\) | ||||
−0.555211 | + | 0.831710i | \(0.687362\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 11.9045 | − | 20.6193i | 0.608293 | − | 1.05359i | −0.383229 | − | 0.923654i | \(-0.625188\pi\) |
0.991522 | − | 0.129941i | \(-0.0414788\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 6.00000 | − | 4.42566i | 0.305788 | − | 0.225552i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −0.206600 | − | 0.357841i | −0.0104750 | − | 0.0181433i | 0.860740 | − | 0.509044i | \(-0.170001\pi\) |
−0.871215 | + | 0.490901i | \(0.836668\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 45.8480 | 2.31863 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 2.60164 | + | 4.50617i | 0.130903 | + | 0.226730i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −5.14720 | + | 8.91521i | −0.258331 | + | 0.447442i | −0.965795 | − | 0.259307i | \(-0.916506\pi\) |
0.707464 | + | 0.706749i | \(0.249839\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −0.225884 | + | 0.391242i | −0.0112801 | + | 0.0195377i | −0.871610 | − | 0.490199i | \(-0.836924\pi\) |
0.860330 | + | 0.509737i | \(0.170257\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −15.3831 | − | 26.6444i | −0.766289 | − | 1.32725i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 21.7249 | 1.07686 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −2.04061 | − | 3.53445i | −0.100902 | − | 0.174767i | 0.811155 | − | 0.584832i | \(-0.198839\pi\) |
−0.912056 | + | 0.410065i | \(0.865506\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 15.4825 | + | 6.76000i | 0.761844 | + | 0.332638i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 2.92121 | − | 5.05968i | 0.143396 | − | 0.248370i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −9.14347 | −0.446688 | −0.223344 | − | 0.974740i | \(-0.571697\pi\) | ||||
−0.223344 | + | 0.974740i | \(0.571697\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 8.30574 | 0.404797 | 0.202398 | − | 0.979303i | \(-0.435126\pi\) | ||||
0.202398 | + | 0.979303i | \(0.435126\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −13.8301 | + | 23.9545i | −0.670860 | + | 1.16196i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −3.72211 | − | 33.1163i | −0.180125 | − | 1.60261i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −11.6331 | − | 20.1491i | −0.560346 | − | 0.970548i | −0.997466 | − | 0.0711444i | \(-0.977335\pi\) |
0.437120 | − | 0.899403i | \(-0.355998\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 11.7989 | 0.567017 | 0.283508 | − | 0.958970i | \(-0.408502\pi\) | ||||
0.283508 | + | 0.958970i | \(0.408502\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 10.3381 | + | 17.9061i | 0.494537 | + | 0.856564i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 0.447550 | − | 0.775179i | 0.0213604 | − | 0.0369973i | −0.855148 | − | 0.518385i | \(-0.826534\pi\) |
0.876508 | + | 0.481387i | \(0.159867\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 8.02990 | − | 13.9082i | 0.381512 | − | 0.660799i | −0.609766 | − | 0.792581i | \(-0.708737\pi\) |
0.991279 | + | 0.131783i | \(0.0420701\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −2.65326 | − | 4.59558i | −0.125777 | − | 0.217851i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 27.6411 | 1.30447 | 0.652233 | − | 0.758018i | \(-0.273832\pi\) | ||||
0.652233 | + | 0.758018i | \(0.273832\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2.89220 | + | 5.00943i | 0.136188 | + | 0.235885i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 1.05418 | + | 9.37925i | 0.0494208 | + | 0.439706i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 2.93087 | − | 5.07642i | 0.137100 | − | 0.237465i | −0.789297 | − | 0.614011i | \(-0.789555\pi\) |
0.926398 | + | 0.376546i | \(0.122888\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −26.4573 | −1.23224 | −0.616120 | − | 0.787652i | \(-0.711296\pi\) | ||||
−0.616120 | + | 0.787652i | \(0.711296\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 0.727834 | 0.0338253 | 0.0169126 | − | 0.999857i | \(-0.494616\pi\) | ||||
0.0169126 | + | 0.999857i | \(0.494616\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 0.536961 | − | 0.930044i | 0.0248476 | − | 0.0430373i | −0.853334 | − | 0.521364i | \(-0.825423\pi\) |
0.878182 | + | 0.478327i | \(0.158757\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −4.04880 | − | 1.76779i | −0.186956 | − | 0.0816292i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −23.4100 | − | 40.5474i | −1.07640 | − | 1.86437i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −12.4740 | −0.572346 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 5.03340 | + | 8.71811i | 0.229982 | + | 0.398340i | 0.957802 | − | 0.287427i | \(-0.0928000\pi\) |
−0.727821 | + | 0.685768i | \(0.759467\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −13.7511 | + | 23.8176i | −0.626997 | + | 1.08599i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 4.45194 | − | 7.71098i | 0.202152 | − | 0.350138i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 0.964491 | + | 1.67055i | 0.0437052 | + | 0.0756997i | 0.887051 | − | 0.461672i | \(-0.152750\pi\) |
−0.843345 | + | 0.537372i | \(0.819417\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −6.89510 | −0.311172 | −0.155586 | − | 0.987822i | \(-0.549726\pi\) | ||||
−0.155586 | + | 0.987822i | \(0.549726\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 30.3139 | + | 52.5051i | 1.36527 | + | 2.36471i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 28.3471 | − | 20.9091i | 1.27154 | − | 0.937901i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −6.31796 | + | 10.9430i | −0.282831 | + | 0.489878i | −0.972081 | − | 0.234646i | \(-0.924607\pi\) |
0.689250 | + | 0.724524i | \(0.257940\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −25.9493 | −1.15702 | −0.578511 | − | 0.815674i | \(-0.696366\pi\) | ||||
−0.578511 | + | 0.815674i | \(0.696366\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 8.45389 | 0.376193 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 11.1551 | − | 19.3213i | 0.494443 | − | 0.856401i | −0.505536 | − | 0.862805i | \(-0.668705\pi\) |
0.999979 | + | 0.00640446i | \(0.00203862\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 3.49262 | + | 1.52495i | 0.154504 | + | 0.0674600i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 2.94838 | + | 5.10674i | 0.129921 | + | 0.225030i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −22.7657 | −1.00124 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 5.36164 | + | 9.28663i | 0.234898 | + | 0.406855i | 0.959243 | − | 0.282583i | \(-0.0911912\pi\) |
−0.724345 | + | 0.689437i | \(0.757858\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −13.9017 | + | 24.0785i | −0.607879 | + | 1.05288i | 0.383710 | + | 0.923454i | \(0.374646\pi\) |
−0.991589 | + | 0.129424i | \(0.958687\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −19.5597 | + | 33.8785i | −0.852036 | + | 1.47577i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −15.8758 | − | 27.4976i | −0.690250 | − | 1.19555i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −7.32263 | −0.317178 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0.749381 | + | 1.29797i | 0.0323985 | + | 0.0561159i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 26.2736 | − | 5.98161i | 1.13168 | − | 0.257646i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −9.51451 | + | 16.4796i | −0.409061 | + | 0.708514i | −0.994785 | − | 0.101997i | \(-0.967477\pi\) |
0.585724 | + | 0.810510i | \(0.300810\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −6.29240 | −0.269537 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −27.9233 | −1.19392 | −0.596958 | − | 0.802273i | \(-0.703624\pi\) | ||||
−0.596958 | + | 0.802273i | \(0.703624\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −13.6707 | + | 23.6783i | −0.582391 | + | 1.00873i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 2.10042 | + | 18.6878i | 0.0893189 | + | 0.794687i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −8.17687 | − | 14.1628i | −0.346465 | − | 0.600095i | 0.639154 | − | 0.769079i | \(-0.279285\pi\) |
−0.985619 | + | 0.168984i | \(0.945951\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 59.2709 | 2.50689 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 10.8817 | + | 18.8477i | 0.458611 | + | 0.794338i | 0.998888 | − | 0.0471498i | \(-0.0150138\pi\) |
−0.540277 | + | 0.841487i | \(0.681680\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0.0954697 | − | 0.165358i | 0.00401644 | − | 0.00695668i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −8.45105 | + | 14.6376i | −0.354286 | + | 0.613642i | −0.986996 | − | 0.160748i | \(-0.948610\pi\) |
0.632709 | + | 0.774389i | \(0.281943\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 3.31123 | + | 5.73522i | 0.138571 | + | 0.240012i | 0.926956 | − | 0.375170i | \(-0.122416\pi\) |
−0.788385 | + | 0.615182i | \(0.789082\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 33.0318 | 1.37752 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −16.7631 | − | 29.0346i | −0.697857 | − | 1.20872i | −0.969208 | − | 0.246244i | \(-0.920804\pi\) |
0.271351 | − | 0.962481i | \(-0.412530\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 16.9929 | − | 12.5341i | 0.704983 | − | 0.520003i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 24.7585 | − | 42.8830i | 1.02539 | − | 1.77603i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 11.7705 | 0.485820 | 0.242910 | − | 0.970049i | \(-0.421898\pi\) | ||||
0.242910 | + | 0.970049i | \(0.421898\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −17.6418 | −0.726917 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −16.6472 | + | 28.8338i | −0.683619 | + | 1.18406i | 0.290250 | + | 0.956951i | \(0.406261\pi\) |
−0.973869 | + | 0.227111i | \(0.927072\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 9.65782 | − | 7.12370i | 0.395932 | − | 0.292043i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −3.51312 | − | 6.08490i | −0.143542 | − | 0.248622i | 0.785286 | − | 0.619133i | \(-0.212516\pi\) |
−0.928828 | + | 0.370511i | \(0.879183\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −43.0389 | −1.75559 | −0.877797 | − | 0.479033i | \(-0.840987\pi\) | ||||
−0.877797 | + | 0.479033i | \(0.840987\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 1.39747 | + | 2.42049i | 0.0568153 | + | 0.0984070i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −0.526497 | + | 0.911919i | −0.0213698 | + | 0.0370137i | −0.876513 | − | 0.481379i | \(-0.840136\pi\) |
0.855143 | + | 0.518393i | \(0.173469\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 14.4099 | − | 24.9587i | 0.582963 | − | 1.00972i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −4.12353 | − | 7.14216i | −0.166548 | − | 0.288469i | 0.770656 | − | 0.637251i | \(-0.219929\pi\) |
−0.937204 | + | 0.348782i | \(0.886595\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −16.8441 | −0.678117 | −0.339058 | − | 0.940765i | \(-0.610108\pi\) | ||||
−0.339058 | + | 0.940765i | \(0.610108\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −13.0215 | − | 22.5539i | −0.523378 | − | 0.906518i | −0.999630 | − | 0.0272087i | \(-0.991338\pi\) |
0.476251 | − | 0.879309i | \(-0.341995\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −2.14210 | − | 19.0586i | −0.0858213 | − | 0.763567i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −8.62436 | + | 14.9378i | −0.344974 | + | 0.597513i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 34.9692 | 1.39431 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 17.1124 | 0.681232 | 0.340616 | − | 0.940202i | \(-0.389364\pi\) | ||||
0.340616 | + | 0.940202i | \(0.389364\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −1.15320 | + | 1.99739i | −0.0457632 | + | 0.0792641i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −10.0724 | + | 32.5906i | −0.399085 | + | 1.29129i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −10.3399 | − | 17.9093i | −0.408402 | − | 0.707373i | 0.586309 | − | 0.810088i | \(-0.300581\pi\) |
−0.994711 | + | 0.102714i | \(0.967247\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 11.3012 | 0.445675 | 0.222837 | − | 0.974856i | \(-0.428468\pi\) | ||||
0.222837 | + | 0.974856i | \(0.428468\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 7.31351 | + | 12.6674i | 0.287524 | + | 0.498006i | 0.973218 | − | 0.229884i | \(-0.0738346\pi\) |
−0.685694 | + | 0.727890i | \(0.740501\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −12.2898 | + | 21.2866i | −0.482418 | + | 0.835573i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −8.24261 | + | 14.2766i | −0.322558 | + | 0.558687i | −0.981015 | − | 0.193931i | \(-0.937876\pi\) |
0.658457 | + | 0.752618i | \(0.271209\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0.858967 | + | 1.48777i | 0.0335626 | + | 0.0581322i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 44.5836 | 1.73673 | 0.868365 | − | 0.495926i | \(-0.165171\pi\) | ||||
0.868365 | + | 0.495926i | \(0.165171\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −16.5364 | − | 28.6419i | −0.643191 | − | 1.11404i | −0.984716 | − | 0.174167i | \(-0.944277\pi\) |
0.341525 | − | 0.939873i | \(-0.389057\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 4.95989 | + | 2.16560i | 0.192336 | + | 0.0839783i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 36.2007 | − | 62.7015i | 1.40170 | − | 2.42781i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 48.4856 | 1.87176 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 47.2968 | 1.82316 | 0.911580 | − | 0.411124i | \(-0.134864\pi\) | ||||
0.911580 | + | 0.411124i | \(0.134864\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 12.7585 | − | 22.0984i | 0.490349 | − | 0.849309i | −0.509589 | − | 0.860418i | \(-0.670203\pi\) |
0.999938 | + | 0.0111083i | \(0.00353596\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 25.8973 | − | 19.1021i | 0.993845 | − | 0.733070i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 21.4248 | + | 37.1089i | 0.819798 | + | 1.41993i | 0.905831 | + | 0.423639i | \(0.139248\pi\) |
−0.0860333 | + | 0.996292i | \(0.527419\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 9.19628 | 0.351372 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 31.3425 | + | 54.2868i | 1.19406 | + | 2.06816i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 4.87575 | − | 8.44505i | 0.185482 | − | 0.321265i | −0.758257 | − | 0.651956i | \(-0.773949\pi\) |
0.943739 | + | 0.330691i | \(0.107282\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 1.64264 | − | 2.84514i | 0.0623089 | − | 0.107922i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 4.65538 | + | 8.06336i | 0.176335 | + | 0.305422i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 22.2174 | 0.839139 | 0.419570 | − | 0.907723i | \(-0.362181\pi\) | ||||
0.419570 | + | 0.907723i | \(0.362181\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 7.88507 | + | 13.6574i | 0.297391 | + | 0.515097i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 28.0011 | + | 12.2259i | 1.05309 | + | 0.459802i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −10.9439 | + | 18.9554i | −0.411008 | + | 0.711886i | −0.995000 | − | 0.0998727i | \(-0.968156\pi\) |
0.583992 | + | 0.811759i | \(0.301490\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 46.7164 | 1.74954 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −13.7322 | −0.513554 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −23.1523 | + | 40.1010i | −0.863435 | + | 1.49551i | 0.00515726 | + | 0.999987i | \(0.498358\pi\) |
−0.868593 | + | 0.495527i | \(0.834975\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 2.38036 | + | 21.1785i | 0.0886492 | + | 0.788728i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 21.8400 | + | 37.8280i | 0.811118 | + | 1.40490i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 25.3662 | 0.940780 | 0.470390 | − | 0.882459i | \(-0.344113\pi\) | ||||
0.470390 | + | 0.882459i | \(0.344113\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −37.6817 | − | 65.2666i | −1.39371 | − | 2.41397i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 11.4484 | − | 19.8292i | 0.422856 | − | 0.732407i | −0.573362 | − | 0.819302i | \(-0.694361\pi\) |
0.996217 | + | 0.0868950i | \(0.0276944\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 3.21389 | − | 5.56663i | 0.118385 | − | 0.205049i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −4.90898 | − | 8.50261i | −0.180580 | − | 0.312773i | 0.761498 | − | 0.648167i | \(-0.224464\pi\) |
−0.942078 | + | 0.335393i | \(0.891131\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 12.4118 | 0.455343 | 0.227672 | − | 0.973738i | \(-0.426889\pi\) | ||||
0.227672 | + | 0.973738i | \(0.426889\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1.19615 | + | 2.07180i | 0.0438236 | + | 0.0759048i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0.605009 | + | 5.38287i | 0.0221065 | + | 0.196686i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 18.5979 | − | 32.2124i | 0.678646 | − | 1.17545i | −0.296743 | − | 0.954957i | \(-0.595901\pi\) |
0.975389 | − | 0.220491i | \(-0.0707660\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −0.449985 | −0.0163766 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −44.3035 | −1.61024 | −0.805119 | − | 0.593113i | \(-0.797899\pi\) | ||||
−0.805119 | + | 0.593113i | \(0.797899\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 2.25383 | − | 3.90375i | 0.0817014 | − | 0.141511i | −0.822279 | − | 0.569084i | \(-0.807298\pi\) |
0.903981 | + | 0.427573i | \(0.140631\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −20.8417 | − | 9.09997i | −0.754522 | − | 0.329441i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −15.5581 | − | 26.9474i | −0.561769 | − | 0.973013i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −38.9328 | −1.40395 | −0.701976 | − | 0.712201i | \(-0.747698\pi\) | ||||
−0.701976 | + | 0.712201i | \(0.747698\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −8.57280 | − | 14.8485i | −0.308342 | − | 0.534064i | 0.669658 | − | 0.742670i | \(-0.266441\pi\) |
−0.978000 | + | 0.208606i | \(0.933107\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −14.0921 | + | 24.4082i | −0.506202 | + | 0.876768i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −2.09945 | + | 3.63635i | −0.0752205 | + | 0.130286i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 25.6246 | + | 44.3831i | 0.916920 | + | 1.58815i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −2.42054 | −0.0863927 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 13.6551 | + | 23.6514i | 0.486754 | + | 0.843082i | 0.999884 | − | 0.0152288i | \(-0.00484765\pi\) |
−0.513131 | + | 0.858311i | \(0.671514\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0.555354 | − | 0.409635i | 0.0197461 | − | 0.0145649i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −30.6897 | + | 53.1560i | −1.08982 | + | 1.88763i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −4.56201 | −0.161595 | −0.0807973 | − | 0.996731i | \(-0.525747\pi\) | ||||
−0.0807973 | + | 0.996731i | \(0.525747\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −36.6446 | −1.29639 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −2.77240 | + | 4.80194i | −0.0978359 | + | 0.169457i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −13.1340 | − | 5.73461i | −0.462914 | − | 0.202118i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 14.8925 | + | 25.7946i | 0.523594 | + | 0.906891i | 0.999623 | + | 0.0274615i | \(0.00874237\pi\) |
−0.476029 | + | 0.879430i | \(0.657924\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −21.1000 | −0.740922 | −0.370461 | − | 0.928848i | \(-0.620800\pi\) | ||||
−0.370461 | + | 0.928848i | \(0.620800\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −0.176869 | − | 0.306345i | −0.00619543 | − | 0.0107308i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 16.9934 | − | 29.4334i | 0.594523 | − | 1.02974i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 10.2637 | − | 17.7773i | 0.358207 | − | 0.620432i | −0.629455 | − | 0.777037i | \(-0.716722\pi\) |
0.987661 | + | 0.156605i | \(0.0500550\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −3.20232 | − | 5.54658i | −0.111626 | − | 0.193342i | 0.804800 | − | 0.593546i | \(-0.202272\pi\) |
−0.916426 | + | 0.400204i | \(0.868939\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 3.55548 | 0.123636 | 0.0618181 | − | 0.998087i | \(-0.480310\pi\) | ||||
0.0618181 | + | 0.998087i | \(0.480310\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −21.7825 | − | 37.7283i | −0.756536 | − | 1.31036i | −0.944607 | − | 0.328203i | \(-0.893557\pi\) |
0.188071 | − | 0.982155i | \(-0.439776\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 42.2909 | − | 9.62821i | 1.46529 | − | 0.333598i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −7.59558 | + | 13.1559i | −0.262856 | + | 0.455280i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −9.27316 | −0.320145 | −0.160073 | − | 0.987105i | \(-0.551173\pi\) | ||||
−0.160073 | + | 0.987105i | \(0.551173\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 66.7410 | 2.30142 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 3.93366 | − | 6.81329i | 0.135322 | − | 0.234384i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.12824 | + | 10.0382i | 0.0387669 | + | 0.344916i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −20.8801 | − | 36.1654i | −0.715760 | − | 1.23973i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −13.5980 | −0.465587 | −0.232794 | − | 0.972526i | \(-0.574787\pi\) | ||||
−0.232794 | + | 0.972526i | \(0.574787\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −27.2095 | − | 47.1283i | −0.929461 | − | 1.60987i | −0.784226 | − | 0.620476i | \(-0.786940\pi\) |
−0.145235 | − | 0.989397i | \(-0.546394\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 7.96944 | − | 13.8035i | 0.271914 | − | 0.470969i | −0.697438 | − | 0.716645i | \(-0.745677\pi\) |
0.969352 | + | 0.245677i | \(0.0790101\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −7.45544 | + | 12.9132i | −0.253786 | + | 0.439570i | −0.964565 | − | 0.263845i | \(-0.915009\pi\) |
0.710779 | + | 0.703415i | \(0.248343\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 8.99744 | + | 15.5840i | 0.305922 | + | 0.529873i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −27.3609 | −0.928154 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 4.06856 | + | 7.04696i | 0.137858 | + | 0.238777i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 14.7515 | − | 10.8809i | 0.498692 | − | 0.367840i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −13.3670 | + | 23.1524i | −0.451372 | + | 0.781800i | −0.998472 | − | 0.0552679i | \(-0.982399\pi\) |
0.547099 | + | 0.837068i | \(0.315732\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 32.0547 | 1.07995 | 0.539975 | − | 0.841681i | \(-0.318434\pi\) | ||||
0.539975 | + | 0.841681i | \(0.318434\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −20.4442 | −0.688002 | −0.344001 | − | 0.938969i | \(-0.611782\pi\) | ||||
−0.344001 | + | 0.938969i | \(0.611782\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 16.3845 | − | 28.3788i | 0.550139 | − | 0.952868i | −0.448125 | − | 0.893971i | \(-0.647908\pi\) |
0.998264 | − | 0.0588975i | \(-0.0187585\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −6.70822 | + | 4.94805i | −0.224987 | + | 0.165952i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −8.26284 | − | 14.3117i | −0.276505 | − | 0.478921i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −15.9475 | −0.533067 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 30.8880 | + | 53.4996i | 1.03017 | + | 1.78431i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 39.8522 | − | 69.0260i | 1.32767 | − | 2.29959i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −2.39397 | + | 4.14648i | −0.0795784 | + | 0.137834i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 17.1098 | + | 29.6351i | 0.568123 | + | 0.984018i | 0.996752 | + | 0.0805374i | \(0.0256636\pi\) |
−0.428628 | + | 0.903481i | \(0.641003\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 40.8423 | 1.35317 | 0.676583 | − | 0.736367i | \(-0.263460\pi\) | ||||
0.676583 | + | 0.736367i | \(0.263460\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 15.3609 | + | 26.6058i | 0.508370 | + | 0.880523i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0.693483 | + | 6.17004i | 0.0229008 | + | 0.203753i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −13.8862 | + | 24.0517i | −0.458065 | + | 0.793392i | −0.998859 | − | 0.0477634i | \(-0.984791\pi\) |
0.540794 | + | 0.841155i | \(0.318124\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −64.8779 | −2.13548 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 25.1941 | 0.828376 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −25.1988 | + | 43.6455i | −0.826744 | + | 1.43196i | 0.0738343 | + | 0.997271i | \(0.476476\pi\) |
−0.900579 | + | 0.434693i | \(0.856857\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 13.2963 | + | 14.3458i | 0.435770 | + | 0.470165i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 8.73027 | + | 15.1213i | 0.285510 | + | 0.494518i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 11.1099 | 0.362946 | 0.181473 | − | 0.983396i | \(-0.441914\pi\) | ||||
0.181473 | + | 0.983396i | \(0.441914\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 5.35102 | + | 9.26823i | 0.174438 | + | 0.302136i | 0.939967 | − | 0.341266i | \(-0.110856\pi\) |
−0.765529 | + | 0.643402i | \(0.777522\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 5.55945 | − | 9.62924i | 0.181040 | − | 0.313571i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 8.86157 | − | 15.3487i | 0.287962 | − | 0.498766i | −0.685361 | − | 0.728204i | \(-0.740355\pi\) |
0.973323 | + | 0.229438i | \(0.0736888\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −3.50966 | − | 6.07892i | −0.113929 | − | 0.197330i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 44.8253 | 1.45203 | 0.726017 | − | 0.687677i | \(-0.241369\pi\) | ||||
0.726017 | + | 0.687677i | \(0.241369\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 5.62181 | + | 9.73726i | 0.181918 | + | 0.315090i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 30.4600 | + | 13.2995i | 0.983605 | + | 0.429464i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −4.43022 | + | 7.67337i | −0.142910 | + | 0.247528i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −13.8776 | −0.446737 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 35.3043 | 1.13531 | 0.567655 | − | 0.823267i | \(-0.307851\pi\) | ||||
0.567655 | + | 0.823267i | \(0.307851\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −11.7761 | + | 20.3968i | −0.377912 | + | 0.654563i | −0.990758 | − | 0.135639i | \(-0.956691\pi\) |
0.612846 | + | 0.790202i | \(0.290025\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 9.55535 | − | 7.04812i | 0.306331 | − | 0.225952i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −11.2372 | − | 19.4633i | −0.359508 | − | 0.622687i | 0.628370 | − | 0.777914i | \(-0.283722\pi\) |
−0.987879 | + | 0.155227i | \(0.950389\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 27.9038 | 0.891808 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −2.38893 | − | 4.13775i | −0.0761951 | − | 0.131974i | 0.825410 | − | 0.564533i | \(-0.190944\pi\) |
−0.901605 | + | 0.432560i | \(0.857611\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −3.02445 | + | 5.23850i | −0.0963670 | + | 0.166913i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −44.9993 | + | 77.9411i | −1.43090 | + | 2.47838i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −19.3142 | − | 33.4532i | −0.613535 | − | 1.06267i | −0.990640 | − | 0.136504i | \(-0.956413\pi\) |
0.377104 | − | 0.926171i | \(-0.376920\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 9.88985 | 0.313529 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −25.8697 | − | 44.8076i | −0.819301 | − | 1.41907i | −0.906198 | − | 0.422854i | \(-0.861028\pi\) |
0.0868962 | − | 0.996217i | \(-0.472305\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1512.2.s.m.1297.4 | yes | 8 | |
3.2 | odd | 2 | 1512.2.s.p.1297.2 | yes | 8 | ||
7.4 | even | 3 | inner | 1512.2.s.m.865.4 | ✓ | 8 | |
21.11 | odd | 6 | 1512.2.s.p.865.2 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1512.2.s.m.865.4 | ✓ | 8 | 7.4 | even | 3 | inner | |
1512.2.s.m.1297.4 | yes | 8 | 1.1 | even | 1 | trivial | |
1512.2.s.p.865.2 | yes | 8 | 21.11 | odd | 6 | ||
1512.2.s.p.1297.2 | yes | 8 | 3.2 | odd | 2 |