Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [360,3,Mod(73,360)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(360, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 0, 0, 3]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("360.73");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 360 = 2^{3} \cdot 3^{2} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 360.v (of order \(4\), 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: | \(9.80928951697\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(i)\) |
Coefficient field: | \(\Q(i, \sqrt{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 9 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 120) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 217.2 | ||
Root | \(-1.22474 + 1.22474i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 360.217 |
Dual form | 360.3.v.b.73.2 |
$q$-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 \(\left(\mathbb{Z}/360\mathbb{Z}\right)^\times\).
\(n\) | \(181\) | \(217\) | \(271\) | \(281\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{4}\right)\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.67423 | + | 4.22474i | 0.534847 | + | 0.844949i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −5.44949 | − | 5.44949i | −0.778499 | − | 0.778499i | 0.201077 | − | 0.979575i | \(-0.435556\pi\) |
−0.979575 | + | 0.201077i | \(0.935556\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 6.44949 | 0.586317 | 0.293159 | − | 0.956064i | \(-0.405294\pi\) | ||||
0.293159 | + | 0.956064i | \(0.405294\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 14.4495 | − | 14.4495i | 1.11150 | − | 1.11150i | 0.118551 | − | 0.992948i | \(-0.462175\pi\) |
0.992948 | − | 0.118551i | \(-0.0378250\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 23.1464 | + | 23.1464i | 1.36155 | + | 1.36155i | 0.871938 | + | 0.489617i | \(0.162863\pi\) |
0.489617 | + | 0.871938i | \(0.337137\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 16.6969i | 0.878786i | 0.898295 | + | 0.439393i | \(0.144806\pi\) | ||||
−0.898295 | + | 0.439393i | \(0.855194\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 6.65153 | − | 6.65153i | 0.289197 | − | 0.289197i | −0.547566 | − | 0.836763i | \(-0.684445\pi\) |
0.836763 | + | 0.547566i | \(0.184445\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −10.6969 | + | 22.5959i | −0.427878 | + | 0.903837i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0.0454077i | 0.00156578i | 1.00000 | 0.000782891i | \(0.000249202\pi\) | |||||
−1.00000 | 0.000782891i | \(0.999751\pi\) | ||||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.49490 | 0.144997 | 0.0724983 | − | 0.997369i | \(-0.476903\pi\) | ||||
0.0724983 | + | 0.997369i | \(0.476903\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 8.44949 | − | 37.5959i | 0.241414 | − | 1.07417i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 35.3485 | + | 35.3485i | 0.955364 | + | 0.955364i | 0.999046 | − | 0.0436815i | \(-0.0139087\pi\) |
−0.0436815 | + | 0.999046i | \(0.513909\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −20.2929 | −0.494948 | −0.247474 | − | 0.968895i | \(-0.579600\pi\) | ||||
−0.247474 | + | 0.968895i | \(0.579600\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 32.2929 | − | 32.2929i | 0.750997 | − | 0.750997i | −0.223669 | − | 0.974665i | \(-0.571803\pi\) |
0.974665 | + | 0.223669i | \(0.0718033\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 50.5403 | + | 50.5403i | 1.07533 | + | 1.07533i | 0.996922 | + | 0.0784040i | \(0.0249824\pi\) |
0.0784040 | + | 0.996922i | \(0.475018\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 10.3939i | 0.212120i | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 5.50510 | − | 5.50510i | 0.103870 | − | 0.103870i | −0.653262 | − | 0.757132i | \(-0.726600\pi\) |
0.757132 | + | 0.653262i | \(0.226600\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 17.2474 | + | 27.2474i | 0.313590 | + | 0.495408i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − | 55.4393i | − | 0.939649i | −0.882760 | − | 0.469824i | \(-0.844317\pi\) | ||
0.882760 | − | 0.469824i | \(-0.155683\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 47.8888 | 0.785062 | 0.392531 | − | 0.919739i | \(-0.371600\pi\) | ||||
0.392531 | + | 0.919739i | \(0.371600\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 99.6867 | + | 22.4041i | 1.53364 | + | 0.344678i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −85.2827 | − | 85.2827i | −1.27288 | − | 1.27288i | −0.944573 | − | 0.328303i | \(-0.893523\pi\) |
−0.328303 | − | 0.944573i | \(-0.606477\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −48.4041 | −0.681748 | −0.340874 | − | 0.940109i | \(-0.610723\pi\) | ||||
−0.340874 | + | 0.940109i | \(0.610723\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −21.9898 | + | 21.9898i | −0.301230 | + | 0.301230i | −0.841495 | − | 0.540265i | \(-0.818324\pi\) |
0.540265 | + | 0.841495i | \(0.318324\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −35.1464 | − | 35.1464i | −0.456447 | − | 0.456447i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 126.697i | − | 1.60376i | −0.597486 | − | 0.801879i | \(-0.703834\pi\) | ||
0.597486 | − | 0.801879i | \(-0.296166\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −94.9444 | + | 94.9444i | −1.14391 | + | 1.14391i | −0.156180 | + | 0.987729i | \(0.549918\pi\) |
−0.987729 | + | 0.156180i | \(0.950082\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −35.8888 | + | 159.687i | −0.422221 | + | 1.87867i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 71.7980i | 0.806719i | 0.915042 | + | 0.403359i | \(0.132158\pi\) | ||||
−0.915042 | + | 0.403359i | \(0.867842\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −157.485 | −1.73060 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −70.5403 | + | 44.6515i | −0.742530 | + | 0.470016i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −37.0000 | − | 37.0000i | −0.381443 | − | 0.381443i | 0.490179 | − | 0.871622i | \(-0.336932\pi\) |
−0.871622 | + | 0.490179i | \(0.836932\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −94.3383 | −0.934042 | −0.467021 | − | 0.884246i | \(-0.654673\pi\) | ||||
−0.467021 | + | 0.884246i | \(0.654673\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 72.6413 | − | 72.6413i | 0.705256 | − | 0.705256i | −0.260278 | − | 0.965534i | \(-0.583814\pi\) |
0.965534 | + | 0.260278i | \(0.0838142\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 13.0556 | + | 13.0556i | 0.122015 | + | 0.122015i | 0.765478 | − | 0.643463i | \(-0.222503\pi\) |
−0.643463 | + | 0.765478i | \(0.722503\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 69.2827i | − | 0.635621i | −0.948154 | − | 0.317810i | \(-0.897052\pi\) | ||
0.948154 | − | 0.317810i | \(-0.102948\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 102.136 | − | 102.136i | 0.903860 | − | 0.903860i | −0.0919072 | − | 0.995768i | \(-0.529296\pi\) |
0.995768 | + | 0.0919072i | \(0.0292963\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 45.8888 | + | 10.3133i | 0.399033 | + | 0.0896806i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − | 252.272i | − | 2.11994i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −79.4041 | −0.656232 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −124.068 | + | 15.2350i | −0.992545 | + | 0.121880i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 119.944 | + | 119.944i | 0.944444 | + | 0.944444i | 0.998536 | − | 0.0540920i | \(-0.0172264\pi\) |
−0.0540920 | + | 0.998536i | \(0.517226\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −121.146 | −0.924782 | −0.462391 | − | 0.886676i | \(-0.653008\pi\) | ||||
−0.462391 | + | 0.886676i | \(0.653008\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 90.9898 | − | 90.9898i | 0.684134 | − | 0.684134i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −119.530 | − | 119.530i | −0.872482 | − | 0.872482i | 0.120260 | − | 0.992742i | \(-0.461627\pi\) |
−0.992742 | + | 0.120260i | \(0.961627\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 140.788i | 1.01286i | 0.862281 | + | 0.506431i | \(0.169035\pi\) | ||||
−0.862281 | + | 0.506431i | \(0.830965\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 93.1918 | − | 93.1918i | 0.651691 | − | 0.651691i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −0.191836 | + | 0.121431i | −0.00132301 | + | 0.000837454i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 53.5301i | 0.359262i | 0.983734 | + | 0.179631i | \(0.0574904\pi\) | ||||
−0.983734 | + | 0.179631i | \(0.942510\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −232.606 | −1.54044 | −0.770219 | − | 0.637780i | \(-0.779853\pi\) | ||||
−0.770219 | + | 0.637780i | \(0.779853\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 12.0204 | + | 18.9898i | 0.0775510 | + | 0.122515i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 128.631 | + | 128.631i | 0.819306 | + | 0.819306i | 0.986007 | − | 0.166701i | \(-0.0533115\pi\) |
−0.166701 | + | 0.986007i | \(0.553311\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −72.4949 | −0.450279 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −117.576 | + | 117.576i | −0.721322 | + | 0.721322i | −0.968875 | − | 0.247552i | \(-0.920374\pi\) |
0.247552 | + | 0.968875i | \(0.420374\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 33.6617 | + | 33.6617i | 0.201567 | + | 0.201567i | 0.800671 | − | 0.599104i | \(-0.204476\pi\) |
−0.599104 | + | 0.800671i | \(0.704476\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 248.576i | − | 1.47086i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −28.2474 | + | 28.2474i | −0.163280 | + | 0.163280i | −0.784018 | − | 0.620738i | \(-0.786833\pi\) |
0.620738 | + | 0.784018i | \(0.286833\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 181.429 | − | 64.8434i | 1.03674 | − | 0.370534i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 45.2372i | 0.252722i | 0.991984 | + | 0.126361i | \(0.0403298\pi\) | ||||
−0.991984 | + | 0.126361i | \(0.959670\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −260.656 | −1.44009 | −0.720045 | − | 0.693928i | \(-0.755879\pi\) | ||||
−0.720045 | + | 0.693928i | \(0.755879\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −54.8082 | + | 243.868i | −0.296260 | + | 1.31821i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 149.283 | + | 149.283i | 0.798303 | + | 0.798303i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 51.8684 | 0.271562 | 0.135781 | − | 0.990739i | \(-0.456646\pi\) | ||||
0.135781 | + | 0.990739i | \(0.456646\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 16.6163 | − | 16.6163i | 0.0860950 | − | 0.0860950i | −0.662748 | − | 0.748843i | \(-0.730610\pi\) |
0.748843 | + | 0.662748i | \(0.230610\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −86.0908 | − | 86.0908i | −0.437009 | − | 0.437009i | 0.453995 | − | 0.891004i | \(-0.349998\pi\) |
−0.891004 | + | 0.453995i | \(0.849998\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 28.5653i | 0.143544i | 0.997421 | + | 0.0717721i | \(0.0228654\pi\) | ||||
−0.997421 | + | 0.0717721i | \(0.977135\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0.247449 | − | 0.247449i | 0.00121896 | − | 0.00121896i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −54.2679 | − | 85.7321i | −0.264721 | − | 0.418206i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 107.687i | 0.515248i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −197.151 | −0.934365 | −0.467183 | − | 0.884161i | \(-0.654731\pi\) | ||||
−0.467183 | + | 0.884161i | \(0.654731\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 222.788 | + | 50.0704i | 1.03622 | + | 0.232886i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −24.4949 | − | 24.4949i | −0.112880 | − | 0.112880i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 668.908 | 3.02673 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 287.338 | − | 287.338i | 1.28851 | − | 1.28851i | 0.352822 | − | 0.935690i | \(-0.385222\pi\) |
0.935690 | − | 0.352822i | \(-0.114778\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 234.384 | + | 234.384i | 1.03253 | + | 1.03253i | 0.999453 | + | 0.0330743i | \(0.0105298\pi\) |
0.0330743 | + | 0.999453i | \(0.489470\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 284.969i | − | 1.24441i | −0.782855 | − | 0.622204i | \(-0.786237\pi\) | ||
0.782855 | − | 0.622204i | \(-0.213763\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 241.530 | − | 241.530i | 1.03661 | − | 1.03661i | 0.0373060 | − | 0.999304i | \(-0.488122\pi\) |
0.999304 | − | 0.0373060i | \(-0.0118776\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −78.3633 | + | 348.677i | −0.333461 | + | 1.48373i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 327.737i | 1.37128i | 0.727939 | + | 0.685642i | \(0.240478\pi\) | ||||
−0.727939 | + | 0.685642i | \(0.759522\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 269.131 | 1.11672 | 0.558362 | − | 0.829597i | \(-0.311430\pi\) | ||||
0.558362 | + | 0.829597i | \(0.311430\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −43.9115 | + | 27.7957i | −0.179231 | + | 0.113452i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 241.262 | + | 241.262i | 0.976770 | + | 0.976770i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −186.136 | −0.741579 | −0.370789 | − | 0.928717i | \(-0.620913\pi\) | ||||
−0.370789 | + | 0.928717i | \(0.620913\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 42.8990 | − | 42.8990i | 0.169561 | − | 0.169561i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −138.268 | − | 138.268i | −0.538007 | − | 0.538007i | 0.384936 | − | 0.922943i | \(-0.374224\pi\) |
−0.922943 | + | 0.384936i | \(0.874224\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 385.262i | − | 1.48750i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 163.146 | − | 163.146i | 0.620329 | − | 0.620329i | −0.325287 | − | 0.945615i | \(-0.605461\pi\) |
0.945615 | + | 0.325287i | \(0.105461\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 37.9796 | + | 8.53572i | 0.143319 | + | 0.0322103i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 108.227i | − | 0.402331i | −0.979557 | − | 0.201165i | \(-0.935527\pi\) | ||
0.979557 | − | 0.201165i | \(-0.0644729\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 324.384 | 1.19699 | 0.598494 | − | 0.801127i | \(-0.295766\pi\) | ||||
0.598494 | + | 0.801127i | \(0.295766\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −68.9898 | + | 145.732i | −0.250872 | + | 0.529935i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −165.864 | − | 165.864i | −0.598786 | − | 0.598786i | 0.341203 | − | 0.939990i | \(-0.389166\pi\) |
−0.939990 | + | 0.341203i | \(0.889166\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −300.434 | −1.06916 | −0.534579 | − | 0.845118i | \(-0.679530\pi\) | ||||
−0.534579 | + | 0.845118i | \(0.679530\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −352.161 | + | 352.161i | −1.24439 | + | 1.24439i | −0.286223 | + | 0.958163i | \(0.592400\pi\) |
−0.958163 | + | 0.286223i | \(0.907600\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 110.586 | + | 110.586i | 0.385316 | + | 0.385316i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 782.514i | 2.70766i | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 109.414 | − | 109.414i | 0.373428 | − | 0.373428i | −0.495296 | − | 0.868724i | \(-0.664941\pi\) |
0.868724 | + | 0.495296i | \(0.164941\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 234.217 | − | 148.258i | 0.793955 | − | 0.502568i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − | 192.222i | − | 0.642884i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −351.959 | −1.16930 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 128.066 | + | 202.318i | 0.419888 | + | 0.663337i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 110.627 | + | 110.627i | 0.360347 | + | 0.360347i | 0.863941 | − | 0.503594i | \(-0.167989\pi\) |
−0.503594 | + | 0.863941i | \(0.667989\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −2.38367 | −0.00766454 | −0.00383227 | − | 0.999993i | \(-0.501220\pi\) | ||||
−0.00383227 | + | 0.999993i | \(0.501220\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 132.959 | − | 132.959i | 0.424790 | − | 0.424790i | −0.462059 | − | 0.886849i | \(-0.652889\pi\) |
0.886849 | + | 0.462059i | \(0.152889\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 37.1464 | + | 37.1464i | 0.117181 | + | 0.117181i | 0.763266 | − | 0.646085i | \(-0.223595\pi\) |
−0.646085 | + | 0.763266i | \(0.723595\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0.292856i | 0.000918045i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −386.474 | + | 386.474i | −1.19652 | + | 1.19652i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 171.934 | + | 481.065i | 0.529028 | + | 1.48020i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 550.838i | − | 1.67428i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 21.6459 | 0.0653955 | 0.0326978 | − | 0.999465i | \(-0.489590\pi\) | ||||
0.0326978 | + | 0.999465i | \(0.489590\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 132.232 | − | 588.363i | 0.394721 | − | 1.75631i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −136.757 | − | 136.757i | −0.405808 | − | 0.405808i | 0.474466 | − | 0.880274i | \(-0.342641\pi\) |
−0.880274 | + | 0.474466i | \(0.842641\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 28.9898 | 0.0850141 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −210.384 | + | 210.384i | −0.613363 | + | 0.613363i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −33.8480 | − | 33.8480i | −0.0975445 | − | 0.0975445i | 0.656650 | − | 0.754195i | \(-0.271973\pi\) |
−0.754195 | + | 0.656650i | \(0.771973\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 241.283i | − | 0.691354i | −0.938354 | − | 0.345677i | \(-0.887649\pi\) | ||
0.938354 | − | 0.345677i | \(-0.112351\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −126.833 | + | 126.833i | −0.359301 | + | 0.359301i | −0.863555 | − | 0.504254i | \(-0.831767\pi\) |
0.504254 | + | 0.863555i | \(0.331767\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −129.444 | − | 204.495i | −0.364631 | − | 0.576042i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 22.1112i | 0.0615912i | 0.999526 | + | 0.0307956i | \(0.00980409\pi\) | ||||
−0.999526 | + | 0.0307956i | \(0.990196\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 82.2122 | 0.227735 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −151.707 | − | 34.0954i | −0.415636 | − | 0.0934121i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −213.944 | − | 213.944i | −0.582955 | − | 0.582955i | 0.352759 | − | 0.935714i | \(-0.385243\pi\) |
−0.935714 | + | 0.352759i | \(0.885243\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −60.0000 | −0.161725 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 210.025 | − | 210.025i | 0.563070 | − | 0.563070i | −0.367108 | − | 0.930178i | \(-0.619652\pi\) |
0.930178 | + | 0.367108i | \(0.119652\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0.656118 | + | 0.656118i | 0.00174037 | + | 0.00174037i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 124.343i | − | 0.328081i | −0.986454 | − | 0.164041i | \(-0.947547\pi\) | ||
0.986454 | − | 0.164041i | \(-0.0524528\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −418.540 | + | 418.540i | −1.09279 | + | 1.09279i | −0.0975654 | + | 0.995229i | \(0.531106\pi\) |
−0.995229 | + | 0.0975654i | \(0.968894\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 54.4949 | − | 242.474i | 0.141545 | − | 0.629804i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 369.884i | 0.950859i | 0.879754 | + | 0.475430i | \(0.157707\pi\) | ||||
−0.879754 | + | 0.475430i | \(0.842293\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 307.918 | 0.787515 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 535.262 | − | 338.817i | 1.35509 | − | 0.857765i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −373.984 | − | 373.984i | −0.942026 | − | 0.942026i | 0.0563835 | − | 0.998409i | \(-0.482043\pi\) |
−0.998409 | + | 0.0563835i | \(0.982043\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −113.151 | −0.282172 | −0.141086 | − | 0.989997i | \(-0.545059\pi\) | ||||
−0.141086 | + | 0.989997i | \(0.545059\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 64.9490 | − | 64.9490i | 0.161164 | − | 0.161164i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 227.980 | + | 227.980i | 0.560146 | + | 0.560146i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 90.3837i | 0.220987i | 0.993877 | + | 0.110493i | \(0.0352431\pi\) | ||||
−0.993877 | + | 0.110493i | \(0.964757\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −302.116 | + | 302.116i | −0.731515 | + | 0.731515i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −655.019 | − | 147.212i | −1.57836 | − | 0.354728i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − | 334.772i | − | 0.798978i | −0.916738 | − | 0.399489i | \(-0.869188\pi\) | ||
0.916738 | − | 0.399489i | \(-0.130812\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 57.2735 | 0.136042 | 0.0680208 | − | 0.997684i | \(-0.478332\pi\) | ||||
0.0680208 | + | 0.997684i | \(0.478332\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −770.611 | + | 275.419i | −1.81320 | + | 0.648044i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −260.969 | − | 260.969i | −0.611170 | − | 0.611170i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −442.656 | −1.02704 | −0.513522 | − | 0.858076i | \(-0.671660\pi\) | ||||
−0.513522 | + | 0.858076i | \(0.671660\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −14.8684 | + | 14.8684i | −0.0343380 | + | 0.0343380i | −0.724067 | − | 0.689729i | \(-0.757730\pi\) |
0.689729 | + | 0.724067i | \(0.257730\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 111.060 | + | 111.060i | 0.254142 | + | 0.254142i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 233.818i | 0.532616i | 0.963888 | + | 0.266308i | \(0.0858038\pi\) | ||||
−0.963888 | + | 0.266308i | \(0.914196\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 246.747 | − | 246.747i | 0.556991 | − | 0.556991i | −0.371459 | − | 0.928449i | \(-0.621142\pi\) |
0.928449 | + | 0.371459i | \(0.121142\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −303.328 | + | 192.005i | −0.681636 | + | 0.431471i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 282.758i | 0.629751i | 0.949133 | + | 0.314875i | \(0.101963\pi\) | ||||
−0.949133 | + | 0.314875i | \(0.898037\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −130.879 | −0.290196 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −421.151 | − | 665.333i | −0.925607 | − | 1.46227i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −298.171 | − | 298.171i | −0.652454 | − | 0.652454i | 0.301129 | − | 0.953583i | \(-0.402636\pi\) |
−0.953583 | + | 0.301129i | \(0.902636\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 264.318 | 0.573358 | 0.286679 | − | 0.958027i | \(-0.407449\pi\) | ||||
0.286679 | + | 0.958027i | \(0.407449\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 135.116 | − | 135.116i | 0.291827 | − | 0.291827i | −0.545975 | − | 0.837802i | \(-0.683841\pi\) |
0.837802 | + | 0.545975i | \(0.183841\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −558.631 | − | 558.631i | −1.19621 | − | 1.19621i | −0.975292 | − | 0.220920i | \(-0.929094\pi\) |
−0.220920 | − | 0.975292i | \(-0.570906\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 929.494i | 1.98186i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 208.272 | − | 208.272i | 0.440322 | − | 0.440322i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −377.283 | − | 178.606i | −0.794279 | − | 0.376013i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 456.141i | 0.952277i | 0.879370 | + | 0.476139i | \(0.157964\pi\) | ||||
−0.879370 | + | 0.476139i | \(0.842036\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1021.53 | 2.12377 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 57.3689 | − | 255.262i | 0.118286 | − | 0.526314i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 11.9444 | + | 11.9444i | 0.0245265 | + | 0.0245265i | 0.719264 | − | 0.694737i | \(-0.244479\pi\) |
−0.694737 | + | 0.719264i | \(0.744479\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −822.468 | −1.67509 | −0.837544 | − | 0.546370i | \(-0.816009\pi\) | ||||
−0.837544 | + | 0.546370i | \(0.816009\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1.05103 | + | 1.05103i | −0.00213190 | + | 0.00213190i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 263.778 | + | 263.778i | 0.530740 | + | 0.530740i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 312.474i | 0.626201i | 0.949720 | + | 0.313101i | \(0.101368\pi\) | ||||
−0.949720 | + | 0.313101i | \(0.898632\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 371.530 | − | 371.530i | 0.738628 | − | 0.738628i | −0.233684 | − | 0.972313i | \(-0.575078\pi\) |
0.972313 | + | 0.233684i | \(0.0750782\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −252.283 | − | 398.555i | −0.499570 | − | 0.789218i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 171.228i | − | 0.336401i | −0.985753 | − | 0.168200i | \(-0.946204\pi\) | ||
0.985753 | − | 0.168200i | \(-0.0537956\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 239.666 | 0.469014 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 501.151 | + | 112.631i | 0.973109 | + | 0.218701i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 325.959 | + | 325.959i | 0.630482 | + | 0.630482i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 206.313 | 0.395995 | 0.197997 | − | 0.980203i | \(-0.436556\pi\) | ||||
0.197997 | + | 0.980203i | \(0.436556\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −135.526 | + | 135.526i | −0.259131 | + | 0.259131i | −0.824701 | − | 0.565570i | \(-0.808656\pi\) |
0.565570 | + | 0.824701i | \(0.308656\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 104.041 | + | 104.041i | 0.197421 | + | 0.197421i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 440.514i | 0.832730i | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −293.221 | + | 293.221i | −0.550134 | + | 0.550134i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −20.2429 | + | 90.0704i | −0.0378371 | + | 0.168356i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 67.0352i | 0.124370i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 303.485 | 0.560970 | 0.280485 | − | 0.959858i | \(-0.409505\pi\) | ||||
0.280485 | + | 0.959858i | \(0.409505\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 292.702 | − | 185.278i | 0.537067 | − | 0.339960i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −71.3939 | − | 71.3939i | −0.130519 | − | 0.130519i | 0.638829 | − | 0.769348i | \(-0.279419\pi\) |
−0.769348 | + | 0.638829i | \(0.779419\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −0.758169 | −0.00137599 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −690.434 | + | 690.434i | −1.24852 | + | 1.24852i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −753.019 | − | 753.019i | −1.35192 | − | 1.35192i | −0.883513 | − | 0.468407i | \(-0.844828\pi\) |
−0.468407 | − | 0.883513i | \(-0.655172\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 933.231i | − | 1.66946i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −703.464 | + | 703.464i | −1.24949 | + | 1.24949i | −0.293548 | + | 0.955944i | \(0.594836\pi\) |
−0.955944 | + | 0.293548i | \(0.905164\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 704.636 | + | 158.363i | 1.24714 | + | 0.280289i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 434.504i | − | 0.763628i | −0.924239 | − | 0.381814i | \(-0.875300\pi\) | ||
0.924239 | − | 0.381814i | \(-0.124700\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −131.040 | −0.229492 | −0.114746 | − | 0.993395i | \(-0.536605\pi\) | ||||
−0.114746 | + | 0.993395i | \(0.536605\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 79.1464 | + | 221.448i | 0.137646 | + | 0.385128i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 290.444 | + | 290.444i | 0.503369 | + | 0.503369i | 0.912483 | − | 0.409114i | \(-0.134162\pi\) |
−0.409114 | + | 0.912483i | \(0.634162\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1034.80 | 1.78106 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 35.5051 | − | 35.5051i | 0.0609007 | − | 0.0609007i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −180.288 | − | 180.288i | −0.307135 | − | 0.307135i | 0.536662 | − | 0.843797i | \(-0.319685\pi\) |
−0.843797 | + | 0.536662i | \(0.819685\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 75.0510i | 0.127421i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 25.0556 | − | 25.0556i | 0.0422523 | − | 0.0422523i | −0.685665 | − | 0.727917i | \(-0.740488\pi\) |
0.727917 | + | 0.685665i | \(0.240488\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1065.79 | − | 674.636i | 1.79124 | − | 1.13384i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 509.807i | − | 0.851097i | −0.904936 | − | 0.425549i | \(-0.860081\pi\) | ||
0.904936 | − | 0.425549i | \(-0.139919\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 179.757 | 0.299097 | 0.149548 | − | 0.988754i | \(-0.452218\pi\) | ||||
0.149548 | + | 0.988754i | \(0.452218\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −212.345 | − | 335.462i | −0.350984 | − | 0.554483i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 33.1566 | + | 33.1566i | 0.0546238 | + | 0.0546238i | 0.733891 | − | 0.679267i | \(-0.237702\pi\) |
−0.679267 | + | 0.733891i | \(0.737702\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1460.56 | 2.39045 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −261.712 | + | 261.712i | −0.426936 | + | 0.426936i | −0.887583 | − | 0.460647i | \(-0.847617\pi\) |
0.460647 | + | 0.887583i | \(0.347617\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 762.075 | + | 762.075i | 1.23513 | + | 1.23513i | 0.961968 | + | 0.273161i | \(0.0880693\pi\) |
0.273161 | + | 0.961968i | \(0.411931\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 81.6367i | − | 0.131885i | −0.997823 | − | 0.0659424i | \(-0.978995\pi\) | ||
0.997823 | − | 0.0659424i | \(-0.0210054\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 391.262 | − | 391.262i | 0.628029 | − | 0.628029i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −396.151 | − | 483.414i | −0.633842 | − | 0.773463i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 1636.38i | 2.60156i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −16.4133 | −0.0260115 | −0.0130057 | − | 0.999915i | \(-0.504140\pi\) | ||||
−0.0130057 | + | 0.999915i | \(0.504140\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −185.975 | + | 827.494i | −0.292874 | + | 1.30314i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 150.186 | + | 150.186i | 0.235771 | + | 0.235771i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 546.041 | 0.851858 | 0.425929 | − | 0.904757i | \(-0.359947\pi\) | ||||
0.425929 | + | 0.904757i | \(0.359947\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −142.879 | + | 142.879i | −0.222206 | + | 0.222206i | −0.809427 | − | 0.587221i | \(-0.800222\pi\) |
0.587221 | + | 0.809427i | \(0.300222\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 649.691 | + | 649.691i | 1.00416 | + | 1.00416i | 0.999991 | + | 0.00416838i | \(0.00132684\pi\) |
0.00416838 | + | 0.999991i | \(0.498673\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 357.555i | − | 0.550932i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 150.904 | − | 150.904i | 0.231093 | − | 0.231093i | −0.582056 | − | 0.813149i | \(-0.697752\pi\) |
0.813149 | + | 0.582056i | \(0.197752\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −323.974 | − | 511.813i | −0.494617 | − | 0.781394i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 268.802i | 0.407893i | 0.978982 | + | 0.203947i | \(0.0653769\pi\) | ||||
−0.978982 | + | 0.203947i | \(0.934623\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 311.162 | 0.470745 | 0.235372 | − | 0.971905i | \(-0.424369\pi\) | ||||
0.235372 | + | 0.971905i | \(0.424369\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 627.737 | + | 141.081i | 0.943965 | + | 0.212151i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0.302031 | + | 0.302031i | 0.000452820 | + | 0.000452820i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 308.858 | 0.460295 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −547.756 | + | 547.756i | −0.813902 | + | 0.813902i | −0.985216 | − | 0.171314i | \(-0.945199\pi\) |
0.171314 | + | 0.985216i | \(0.445199\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −696.257 | − | 696.257i | −1.02844 | − | 1.02844i | −0.999583 | − | 0.0288606i | \(-0.990812\pi\) |
−0.0288606 | − | 0.999583i | \(-0.509188\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 403.262i | 0.593906i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 84.0250 | − | 84.0250i | 0.123023 | − | 0.123023i | −0.642915 | − | 0.765938i | \(-0.722275\pi\) |
0.765938 | + | 0.642915i | \(0.222275\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 185.333 | − | 824.636i | 0.270559 | − | 1.20385i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 159.092i | − | 0.230903i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1157.06 | 1.67447 | 0.837236 | − | 0.546842i | \(-0.184170\pi\) | ||||
0.837236 | + | 0.546842i | \(0.184170\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −594.792 | + | 376.499i | −0.855816 | + | 0.541726i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −469.707 | − | 469.707i | −0.673898 | − | 0.673898i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −843.691 | −1.20355 | −0.601777 | − | 0.798664i | \(-0.705540\pi\) | ||||
−0.601777 | + | 0.798664i | \(0.705540\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −590.211 | + | 590.211i | −0.839561 | + | 0.839561i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 514.095 | + | 514.095i | 0.727150 | + | 0.727150i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 170.686i | − | 0.240741i | −0.992729 | − | 0.120371i | \(-0.961592\pi\) | ||
0.992729 | − | 0.120371i | \(-0.0384083\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 29.8979 | − | 29.8979i | 0.0419326 | − | 0.0419326i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 642.929 | + | 144.495i | 0.899201 | + | 0.202091i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 605.435i | 0.842051i | 0.907049 | + | 0.421026i | \(0.138330\pi\) | ||||
−0.907049 | + | 0.421026i | \(0.861670\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −791.716 | −1.09808 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −1.02603 | − | 0.485723i | −0.00141521 | − | 0.000669963i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −50.8025 | − | 50.8025i | −0.0698797 | − | 0.0698797i | 0.671303 | − | 0.741183i | \(-0.265735\pi\) |
−0.741183 | + | 0.671303i | \(0.765735\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1494.93 | 2.04505 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 516.529 | − | 516.529i | 0.704678 | − | 0.704678i | −0.260733 | − | 0.965411i | \(-0.583964\pi\) |
0.965411 | + | 0.260733i | \(0.0839642\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −550.030 | − | 550.030i | −0.746309 | − | 0.746309i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 650.109i | 0.879715i | 0.898068 | + | 0.439857i | \(0.144971\pi\) | ||||
−0.898068 | + | 0.439857i | \(0.855029\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −90.6811 | + | 90.6811i | −0.122047 | + | 0.122047i | −0.765492 | − | 0.643445i | \(-0.777504\pi\) |
0.643445 | + | 0.765492i | \(0.277504\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −226.151 | + | 143.152i | −0.303558 | + | 0.192150i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 142.293i | − | 0.189977i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −300.050 | −0.399534 | −0.199767 | − | 0.979843i | \(-0.564019\pi\) | ||||
−0.199767 | + | 0.979843i | \(0.564019\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −622.043 | − | 982.702i | −0.823898 | − | 1.30159i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 523.176 | + | 523.176i | 0.691118 | + | 0.691118i | 0.962478 | − | 0.271360i | \(-0.0874735\pi\) |
−0.271360 | + | 0.962478i | \(0.587473\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 724.130 | 0.951550 | 0.475775 | − | 0.879567i | \(-0.342168\pi\) | ||||
0.475775 | + | 0.879567i | \(0.342168\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −377.555 | + | 377.555i | −0.494830 | + | 0.494830i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −801.069 | − | 801.069i | −1.04442 | − | 1.04442i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 13.7775i | − | 0.0179162i | −0.999960 | − | 0.00895809i | \(-0.997149\pi\) | ||
0.999960 | − | 0.00895809i | \(-0.00285149\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 564.207 | − | 564.207i | 0.729892 | − | 0.729892i | −0.240706 | − | 0.970598i | \(-0.577379\pi\) |
0.970598 | + | 0.240706i | \(0.0773789\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −48.0816 | + | 101.566i | −0.0620408 | + | 0.131053i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − | 338.829i | − | 0.434953i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −312.182 | −0.399720 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −199.444 | + | 887.423i | −0.254069 | + | 1.13048i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −212.424 | − | 212.424i | −0.269917 | − | 0.269917i | 0.559150 | − | 0.829067i | \(-0.311128\pi\) |
−0.829067 | + | 0.559150i | \(0.811128\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −1113.18 | −1.40731 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 691.968 | − | 691.968i | 0.872596 | − | 0.872596i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 15.6617 | + | 15.6617i | 0.0196509 | + | 0.0196509i | 0.716864 | − | 0.697213i | \(-0.245577\pi\) |
−0.697213 | + | 0.716864i | \(0.745577\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2339.66i | 2.92823i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −141.823 | + | 141.823i | −0.176616 | + | 0.176616i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −193.868 | − | 306.272i | −0.240830 | − | 0.380463i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 816.788i | 1.00963i | 0.863229 | + | 0.504813i | \(0.168439\pi\) | ||||
−0.863229 | + | 0.504813i | \(0.831561\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 830.504 | 1.02405 | 0.512025 | − | 0.858971i | \(-0.328896\pi\) | ||||
0.512025 | + | 0.858971i | \(0.328896\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −811.151 | − | 182.302i | −0.995277 | − | 0.223683i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 539.192 | + | 539.192i | 0.659966 | + | 0.659966i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −569.217 | −0.693321 | −0.346661 | − | 0.937991i | \(-0.612684\pi\) | ||||
−0.346661 | + | 0.937991i | \(0.612684\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 497.095 | − | 497.095i | 0.604004 | − | 0.604004i | −0.337369 | − | 0.941373i | \(-0.609537\pi\) |
0.941373 | + | 0.337369i | \(0.109537\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −874.070 | − | 874.070i | −1.05692 | − | 1.05692i | −0.998279 | − | 0.0586377i | \(-0.981324\pi\) |
−0.0586377 | − | 0.998279i | \(-0.518676\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 1548.77i | − | 1.86824i | −0.356954 | − | 0.934122i | \(-0.616185\pi\) | ||
0.356954 | − | 0.934122i | \(-0.383815\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −240.581 | + | 240.581i | −0.288813 | + | 0.288813i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −52.1929 | + | 232.232i | −0.0625064 | + | 0.278122i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 731.523i | − | 0.871899i | −0.899971 | − | 0.435950i | \(-0.856413\pi\) | ||
0.899971 | − | 0.435950i | \(-0.143587\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 840.998 | 0.999998 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1050.17 | − | 664.749i | 1.24280 | − | 0.786685i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 432.712 | + | 432.712i | 0.510876 | + | 0.510876i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 470.243 | 0.552577 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −554.166 | + | 554.166i | −0.649667 | + | 0.649667i | −0.952912 | − | 0.303246i | \(-0.901930\pi\) |
0.303246 | + | 0.952912i | \(0.401930\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −687.206 | − | 687.206i | −0.801874 | − | 0.801874i | 0.181515 | − | 0.983388i | \(-0.441900\pi\) |
−0.983388 | + | 0.181515i | \(0.941900\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 1285.29i | − | 1.49627i | −0.663549 | − | 0.748133i | \(-0.730951\pi\) | ||
0.663549 | − | 0.748133i | \(-0.269049\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 712.985 | − | 712.985i | 0.826171 | − | 0.826171i | −0.160814 | − | 0.986985i | \(-0.551412\pi\) |
0.986985 | + | 0.160814i | \(0.0514120\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −194.879 | − | 43.7980i | −0.225293 | − | 0.0506335i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 817.131i | − | 0.940311i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −2464.58 | −2.82960 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 759.131 | + | 593.085i | 0.867578 | + | 0.677812i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −474.297 | − | 474.297i | −0.540818 | − | 0.540818i | 0.382951 | − | 0.923769i | \(-0.374908\pi\) |
−0.923769 | + | 0.382951i | \(0.874908\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −1652.71 | −1.87594 | −0.937972 | − | 0.346712i | \(-0.887298\pi\) | ||||
−0.937972 | + | 0.346712i | \(0.887298\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 18.9286 | − | 18.9286i | 0.0214367 | − | 0.0214367i | −0.696307 | − | 0.717744i | \(-0.745175\pi\) |
0.717744 | + | 0.696307i | \(0.245175\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 382.338 | + | 382.338i | 0.431047 | + | 0.431047i | 0.888984 | − | 0.457938i | \(-0.151412\pi\) |
−0.457938 | + | 0.888984i | \(0.651412\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 1307.27i | − | 1.47050i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −843.868 | + | 843.868i | −0.944981 | + | 0.944981i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −191.116 | + | 120.975i | −0.213537 | + | 0.135168i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0.204103i | 0.000227033i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 254.847 | 0.282849 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −697.056 | − | 1101.21i | −0.770227 | − | 1.21680i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 725.485 | + | 725.485i | 0.799873 | + | 0.799873i | 0.983075 | − | 0.183202i | \(-0.0586464\pi\) |
−0.183202 | + | 0.983075i | \(0.558646\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 154.474 | 0.169566 | 0.0847829 | − | 0.996399i | \(-0.472980\pi\) | ||||
0.0847829 | + | 0.996399i | \(0.472980\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −612.343 | + | 612.343i | −0.670693 | + | 0.670693i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 660.186 | + | 660.186i | 0.719941 | + | 0.719941i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 659.079i | 0.717169i | 0.933497 | + | 0.358585i | \(0.116741\pi\) | ||||
−0.933497 | + | 0.358585i | \(0.883259\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −699.414 | + | 699.414i | −0.757762 | + | 0.757762i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1176.85 | + | 420.611i | −1.27227 | + | 0.454714i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 368.556i | − | 0.396723i | −0.980129 | − | 0.198362i | \(-0.936438\pi\) | ||
0.980129 | − | 0.198362i | \(-0.0635621\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −173.546 | −0.186408 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −231.464 | + | 1029.90i | −0.247555 | + | 1.10150i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −820.898 | − | 820.898i | −0.876092 | − | 0.876092i | 0.117036 | − | 0.993128i | \(-0.462661\pi\) |
−0.993128 | + | 0.117036i | \(0.962661\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −1758.50 | −1.86875 | −0.934377 | − | 0.356286i | \(-0.884043\pi\) | ||||
−0.934377 | + | 0.356286i | \(0.884043\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −134.979 | + | 134.979i | −0.143137 | + | 0.143137i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 118.080 | + | 118.080i | 0.124688 | + | 0.124688i | 0.766697 | − | 0.642009i | \(-0.221899\pi\) |
−0.642009 | + | 0.766697i | \(0.721899\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 635.483i | 0.669634i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 217.955 | − | 217.955i | 0.228704 | − | 0.228704i | −0.583447 | − | 0.812151i | \(-0.698297\pi\) |
0.812151 | + | 0.583447i | \(0.198297\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 138.708 | + | 219.131i | 0.145244 | + | 0.229456i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 1302.76i | 1.35845i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −940.796 | −0.978976 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 114.636 | + | 25.7638i | 0.118793 | + | 0.0266982i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −323.983 | − | 323.983i | −0.335039 | − | 0.335039i | 0.519457 | − | 0.854497i | \(-0.326134\pi\) |
−0.854497 | + | 0.519457i | \(0.826134\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −743.743 | −0.765956 | −0.382978 | − | 0.923757i | \(-0.625102\pi\) | ||||
−0.382978 | + | 0.923757i | \(0.625102\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 767.221 | − | 767.221i | 0.788511 | − | 0.788511i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 1050.52 | + | 1050.52i | 1.07525 | + | 1.07525i | 0.996928 | + | 0.0783226i | \(0.0249564\pi\) |
0.0783226 | + | 0.996928i | \(0.475044\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 463.060i | 0.472993i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −72.9648 | + | 72.9648i | −0.0742267 | + | 0.0742267i | −0.743245 | − | 0.669019i | \(-0.766715\pi\) |
0.669019 | + | 0.743245i | \(0.266715\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 133.485 | − | 593.939i | 0.135517 | − | 0.602984i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 429.594i | − | 0.434372i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 444.624 | 0.448662 | 0.224331 | − | 0.974513i | \(-0.427980\pi\) | ||||
0.224331 | + | 0.974513i | \(0.427980\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −120.681 | + | 76.3903i | −0.121288 | + | 0.0767742i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 12.6424 | + | 12.6424i | 0.0126804 | + | 0.0126804i | 0.713419 | − | 0.700738i | \(-0.247146\pi\) |
−0.700738 | + | 0.713419i | \(0.747146\pi\) | |||||||
\(998\) | 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 | 360.3.v.b.217.2 | 4 | ||
3.2 | odd | 2 | 120.3.u.a.97.1 | yes | 4 | ||
4.3 | odd | 2 | 720.3.bh.g.577.2 | 4 | |||
5.2 | odd | 4 | 1800.3.v.n.793.2 | 4 | |||
5.3 | odd | 4 | inner | 360.3.v.b.73.2 | 4 | ||
5.4 | even | 2 | 1800.3.v.n.1657.2 | 4 | |||
12.11 | even | 2 | 240.3.bg.c.97.2 | 4 | |||
15.2 | even | 4 | 600.3.u.e.193.2 | 4 | |||
15.8 | even | 4 | 120.3.u.a.73.1 | ✓ | 4 | ||
15.14 | odd | 2 | 600.3.u.e.457.2 | 4 | |||
20.3 | even | 4 | 720.3.bh.g.433.2 | 4 | |||
24.5 | odd | 2 | 960.3.bg.c.577.2 | 4 | |||
24.11 | even | 2 | 960.3.bg.d.577.1 | 4 | |||
60.23 | odd | 4 | 240.3.bg.c.193.2 | 4 | |||
60.47 | odd | 4 | 1200.3.bg.e.193.1 | 4 | |||
60.59 | even | 2 | 1200.3.bg.e.1057.1 | 4 | |||
120.53 | even | 4 | 960.3.bg.c.193.2 | 4 | |||
120.83 | odd | 4 | 960.3.bg.d.193.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
120.3.u.a.73.1 | ✓ | 4 | 15.8 | even | 4 | ||
120.3.u.a.97.1 | yes | 4 | 3.2 | odd | 2 | ||
240.3.bg.c.97.2 | 4 | 12.11 | even | 2 | |||
240.3.bg.c.193.2 | 4 | 60.23 | odd | 4 | |||
360.3.v.b.73.2 | 4 | 5.3 | odd | 4 | inner | ||
360.3.v.b.217.2 | 4 | 1.1 | even | 1 | trivial | ||
600.3.u.e.193.2 | 4 | 15.2 | even | 4 | |||
600.3.u.e.457.2 | 4 | 15.14 | odd | 2 | |||
720.3.bh.g.433.2 | 4 | 20.3 | even | 4 | |||
720.3.bh.g.577.2 | 4 | 4.3 | odd | 2 | |||
960.3.bg.c.193.2 | 4 | 120.53 | even | 4 | |||
960.3.bg.c.577.2 | 4 | 24.5 | odd | 2 | |||
960.3.bg.d.193.1 | 4 | 120.83 | odd | 4 | |||
960.3.bg.d.577.1 | 4 | 24.11 | even | 2 | |||
1200.3.bg.e.193.1 | 4 | 60.47 | odd | 4 | |||
1200.3.bg.e.1057.1 | 4 | 60.59 | even | 2 | |||
1800.3.v.n.793.2 | 4 | 5.2 | odd | 4 | |||
1800.3.v.n.1657.2 | 4 | 5.4 | even | 2 |