Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2880,2,Mod(1151,2880)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2880, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2880.1151");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2880 = 2^{6} \cdot 3^{2} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2880.h (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(22.9969157821\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\zeta_{8})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 1440) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1151.3 | ||
Root | \(0.707107 + 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2880.1151 |
Dual form | 2880.2.h.a.1151.2 |
$q$-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 \(\left(\mathbb{Z}/2880\mathbb{Z}\right)^\times\).
\(n\) | \(577\) | \(641\) | \(901\) | \(2431\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.00000i | 0.447214i | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.585786i | 0.221406i | 0.993854 | + | 0.110703i | \(0.0353103\pi\) | ||||
−0.993854 | + | 0.110703i | \(0.964690\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −5.41421 | −1.63245 | −0.816223 | − | 0.577736i | \(-0.803936\pi\) | ||||
−0.816223 | + | 0.577736i | \(0.803936\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.585786 | 0.162468 | 0.0812340 | − | 0.996695i | \(-0.474114\pi\) | ||||
0.0812340 | + | 0.996695i | \(0.474114\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 6.82843i | 1.65614i | 0.560627 | + | 0.828068i | \(0.310560\pi\) | ||||
−0.560627 | + | 0.828068i | \(0.689440\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −0.828427 | −0.172739 | −0.0863695 | − | 0.996263i | \(-0.527527\pi\) | ||||
−0.0863695 | + | 0.996263i | \(0.527527\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.00000 | −0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − 6.00000i | − 1.11417i | −0.830455 | − | 0.557086i | \(-0.811919\pi\) | ||||
0.830455 | − | 0.557086i | \(-0.188081\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − 10.4853i | − 1.88321i | −0.336717 | − | 0.941606i | \(-0.609316\pi\) | ||||
0.336717 | − | 0.941606i | \(-0.390684\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −0.585786 | −0.0990160 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −5.07107 | −0.833678 | −0.416839 | − | 0.908980i | \(-0.636862\pi\) | ||||
−0.416839 | + | 0.908980i | \(0.636862\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − 3.07107i | − 0.479620i | −0.970820 | − | 0.239810i | \(-0.922915\pi\) | ||||
0.970820 | − | 0.239810i | \(-0.0770852\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.17157i | 0.178663i | 0.996002 | + | 0.0893316i | \(0.0284731\pi\) | ||||
−0.996002 | + | 0.0893316i | \(0.971527\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 5.65685 | 0.825137 | 0.412568 | − | 0.910927i | \(-0.364632\pi\) | ||||
0.412568 | + | 0.910927i | \(0.364632\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.65685 | 0.950979 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − 6.82843i | − 0.937957i | −0.883210 | − | 0.468978i | \(-0.844622\pi\) | ||||
0.883210 | − | 0.468978i | \(-0.155378\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − 5.41421i | − 0.730052i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −9.41421 | −1.22563 | −0.612813 | − | 0.790228i | \(-0.709962\pi\) | ||||
−0.612813 | + | 0.790228i | \(0.709962\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −7.17157 | −0.918226 | −0.459113 | − | 0.888378i | \(-0.651833\pi\) | ||||
−0.459113 | + | 0.888378i | \(0.651833\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0.585786i | 0.0726579i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 8.00000i | − 0.977356i | −0.872464 | − | 0.488678i | \(-0.837479\pi\) | ||||
0.872464 | − | 0.488678i | \(-0.162521\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −5.65685 | −0.671345 | −0.335673 | − | 0.941979i | \(-0.608964\pi\) | ||||
−0.335673 | + | 0.941979i | \(0.608964\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 6.48528 | 0.759045 | 0.379522 | − | 0.925183i | \(-0.376088\pi\) | ||||
0.379522 | + | 0.925183i | \(0.376088\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − 3.17157i | − 0.361434i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − 2.48528i | − 0.279616i | −0.990179 | − | 0.139808i | \(-0.955351\pi\) | ||||
0.990179 | − | 0.139808i | \(-0.0446485\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −14.8284 | −1.62763 | −0.813816 | − | 0.581123i | \(-0.802613\pi\) | ||||
−0.813816 | + | 0.581123i | \(0.802613\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −6.82843 | −0.740647 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 4.24264i | 0.449719i | 0.974391 | + | 0.224860i | \(0.0721923\pi\) | ||||
−0.974391 | + | 0.224860i | \(0.927808\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.343146i | 0.0359714i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −14.4853 | −1.47076 | −0.735379 | − | 0.677656i | \(-0.762996\pi\) | ||||
−0.735379 | + | 0.677656i | \(0.762996\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 0.828427i | 0.0824316i | 0.999150 | + | 0.0412158i | \(0.0131231\pi\) | ||||
−0.999150 | + | 0.0412158i | \(0.986877\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − 13.5563i | − 1.33575i | −0.744275 | − | 0.667873i | \(-0.767205\pi\) | ||||
0.744275 | − | 0.667873i | \(-0.232795\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −9.17157 | −0.886649 | −0.443325 | − | 0.896361i | \(-0.646201\pi\) | ||||
−0.443325 | + | 0.896361i | \(0.646201\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 12.8284 | 1.22874 | 0.614370 | − | 0.789018i | \(-0.289410\pi\) | ||||
0.614370 | + | 0.789018i | \(0.289410\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 9.65685i | 0.908440i | 0.890889 | + | 0.454220i | \(0.150082\pi\) | ||||
−0.890889 | + | 0.454220i | \(0.849918\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − 0.828427i | − 0.0772512i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −4.00000 | −0.366679 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 18.3137 | 1.66488 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − 1.00000i | − 0.0894427i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − 14.7279i | − 1.30689i | −0.756973 | − | 0.653446i | \(-0.773323\pi\) | ||||
0.756973 | − | 0.653446i | \(-0.226677\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 12.7279 | 1.11204 | 0.556022 | − | 0.831168i | \(-0.312327\pi\) | ||||
0.556022 | + | 0.831168i | \(0.312327\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 3.31371i | 0.283109i | 0.989930 | + | 0.141555i | \(0.0452101\pi\) | ||||
−0.989930 | + | 0.141555i | \(0.954790\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − 7.65685i | − 0.649446i | −0.945809 | − | 0.324723i | \(-0.894729\pi\) | ||||
0.945809 | − | 0.324723i | \(-0.105271\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −3.17157 | −0.265220 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 6.00000 | 0.498273 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 3.17157i | 0.259825i | 0.991525 | + | 0.129913i | \(0.0414697\pi\) | ||||
−0.991525 | + | 0.129913i | \(0.958530\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − 4.34315i | − 0.353440i | −0.984261 | − | 0.176720i | \(-0.943451\pi\) | ||||
0.984261 | − | 0.176720i | \(-0.0565487\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 10.4853 | 0.842198 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 18.2426 | 1.45592 | 0.727961 | − | 0.685619i | \(-0.240468\pi\) | ||||
0.727961 | + | 0.685619i | \(0.240468\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − 0.485281i | − 0.0382455i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 16.4853i | − 1.29123i | −0.763664 | − | 0.645613i | \(-0.776602\pi\) | ||||
0.763664 | − | 0.645613i | \(-0.223398\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 17.7990 | 1.37733 | 0.688664 | − | 0.725081i | \(-0.258198\pi\) | ||||
0.688664 | + | 0.725081i | \(0.258198\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.6569 | −0.973604 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 8.48528i | 0.645124i | 0.946548 | + | 0.322562i | \(0.104544\pi\) | ||||
−0.946548 | + | 0.322562i | \(0.895456\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − 0.585786i | − 0.0442813i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −24.0416 | −1.79696 | −0.898478 | − | 0.439019i | \(-0.855326\pi\) | ||||
−0.898478 | + | 0.439019i | \(0.855326\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −18.4853 | −1.37400 | −0.687000 | − | 0.726657i | \(-0.741073\pi\) | ||||
−0.687000 | + | 0.726657i | \(0.741073\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − 5.07107i | − 0.372832i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 36.9706i | − 2.70356i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −20.4853 | −1.48226 | −0.741131 | − | 0.671360i | \(-0.765710\pi\) | ||||
−0.741131 | + | 0.671360i | \(0.765710\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −14.9706 | −1.07760 | −0.538802 | − | 0.842432i | \(-0.681123\pi\) | ||||
−0.538802 | + | 0.842432i | \(0.681123\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 1.31371i | − 0.0935979i | −0.998904 | − | 0.0467989i | \(-0.985098\pi\) | ||||
0.998904 | − | 0.0467989i | \(-0.0149020\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 4.34315i | 0.307877i | 0.988080 | + | 0.153939i | \(0.0491958\pi\) | ||||
−0.988080 | + | 0.153939i | \(0.950804\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 3.51472 | 0.246685 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 3.07107 | 0.214493 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 26.0000i | 1.78991i | 0.446153 | + | 0.894957i | \(0.352794\pi\) | ||||
−0.446153 | + | 0.894957i | \(0.647206\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −1.17157 | −0.0799006 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 6.14214 | 0.416955 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 4.00000i | 0.269069i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 22.7279i | 1.52197i | 0.648767 | + | 0.760987i | \(0.275285\pi\) | ||||
−0.648767 | + | 0.760987i | \(0.724715\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 5.65685 | 0.375459 | 0.187729 | − | 0.982221i | \(-0.439887\pi\) | ||||
0.187729 | + | 0.982221i | \(0.439887\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −18.9706 | −1.25361 | −0.626805 | − | 0.779176i | \(-0.715638\pi\) | ||||
−0.626805 | + | 0.779176i | \(0.715638\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − 26.1421i | − 1.71263i | −0.516455 | − | 0.856314i | \(-0.672749\pi\) | ||||
0.516455 | − | 0.856314i | \(-0.327251\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 5.65685i | 0.369012i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −25.4558 | −1.64660 | −0.823301 | − | 0.567605i | \(-0.807870\pi\) | ||||
−0.823301 | + | 0.567605i | \(0.807870\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −4.97056 | −0.320182 | −0.160091 | − | 0.987102i | \(-0.551179\pi\) | ||||
−0.160091 | + | 0.987102i | \(0.551179\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 6.65685i | 0.425291i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 5.89949 | 0.372373 | 0.186186 | − | 0.982514i | \(-0.440387\pi\) | ||||
0.186186 | + | 0.982514i | \(0.440387\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 4.48528 | 0.281987 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − 2.97056i | − 0.184582i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −26.4853 | −1.63315 | −0.816576 | − | 0.577238i | \(-0.804131\pi\) | ||||
−0.816576 | + | 0.577238i | \(0.804131\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 6.82843 | 0.419467 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − 3.65685i | − 0.222962i | −0.993767 | − | 0.111481i | \(-0.964441\pi\) | ||||
0.993767 | − | 0.111481i | \(-0.0355595\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − 22.0000i | − 1.33640i | −0.743980 | − | 0.668202i | \(-0.767064\pi\) | ||||
0.743980 | − | 0.668202i | \(-0.232936\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 5.41421 | 0.326489 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 30.7279 | 1.84626 | 0.923131 | − | 0.384486i | \(-0.125621\pi\) | ||||
0.923131 | + | 0.384486i | \(0.125621\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − 25.4142i | − 1.51608i | −0.652205 | − | 0.758042i | \(-0.726156\pi\) | ||||
0.652205 | − | 0.758042i | \(-0.273844\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 15.3137i | 0.910305i | 0.890413 | + | 0.455153i | \(0.150415\pi\) | ||||
−0.890413 | + | 0.455153i | \(0.849585\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1.79899 | 0.106191 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −29.6274 | −1.74279 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 6.68629i | 0.390617i | 0.980742 | + | 0.195309i | \(0.0625709\pi\) | ||||
−0.980742 | + | 0.195309i | \(0.937429\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − 9.41421i | − 0.548117i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −0.485281 | −0.0280645 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −0.686292 | −0.0395572 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − 7.17157i | − 0.410643i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 24.0000i | − 1.36975i | −0.728659 | − | 0.684876i | \(-0.759856\pi\) | ||||
0.728659 | − | 0.684876i | \(-0.240144\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −2.14214 | −0.121469 | −0.0607347 | − | 0.998154i | \(-0.519344\pi\) | ||||
−0.0607347 | + | 0.998154i | \(0.519344\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −3.65685 | −0.206698 | −0.103349 | − | 0.994645i | \(-0.532956\pi\) | ||||
−0.103349 | + | 0.994645i | \(0.532956\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − 28.6274i | − 1.60788i | −0.594713 | − | 0.803938i | \(-0.702734\pi\) | ||||
0.594713 | − | 0.803938i | \(-0.297266\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 32.4853i | 1.81883i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −0.585786 | −0.0324936 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 3.31371i | 0.182691i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − 4.97056i | − 0.273207i | −0.990626 | − | 0.136603i | \(-0.956381\pi\) | ||||
0.990626 | − | 0.136603i | \(-0.0436186\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 8.00000 | 0.437087 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −9.51472 | −0.518300 | −0.259150 | − | 0.965837i | \(-0.583442\pi\) | ||||
−0.259150 | + | 0.965837i | \(0.583442\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 56.7696i | 3.07424i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 8.00000i | 0.431959i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 33.6569 | 1.80679 | 0.903397 | − | 0.428805i | \(-0.141065\pi\) | ||||
0.903397 | + | 0.428805i | \(0.141065\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 19.4558 | 1.04145 | 0.520724 | − | 0.853725i | \(-0.325662\pi\) | ||||
0.520724 | + | 0.853725i | \(0.325662\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 30.1421i | 1.60430i | 0.597120 | + | 0.802152i | \(0.296312\pi\) | ||||
−0.597120 | + | 0.802152i | \(0.703688\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − 5.65685i | − 0.300235i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −13.1716 | −0.695169 | −0.347585 | − | 0.937649i | \(-0.612998\pi\) | ||||
−0.347585 | + | 0.937649i | \(0.612998\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 19.0000 | 1.00000 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 6.48528i | 0.339455i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 28.8701i | 1.50700i | 0.657445 | + | 0.753502i | \(0.271637\pi\) | ||||
−0.657445 | + | 0.753502i | \(0.728363\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 4.00000 | 0.207670 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −14.7279 | −0.762583 | −0.381291 | − | 0.924455i | \(-0.624521\pi\) | ||||
−0.381291 | + | 0.924455i | \(0.624521\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − 3.51472i | − 0.181017i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 13.3137i | 0.683879i | 0.939722 | + | 0.341940i | \(0.111084\pi\) | ||||
−0.939722 | + | 0.341940i | \(0.888916\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 21.6569 | 1.10661 | 0.553307 | − | 0.832978i | \(-0.313366\pi\) | ||||
0.553307 | + | 0.832978i | \(0.313366\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 3.17157 | 0.161638 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 23.6569i | 1.19945i | 0.800206 | + | 0.599725i | \(0.204723\pi\) | ||||
−0.800206 | + | 0.599725i | \(0.795277\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − 5.65685i | − 0.286079i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 2.48528 | 0.125048 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 10.7279 | 0.538419 | 0.269209 | − | 0.963082i | \(-0.413238\pi\) | ||||
0.269209 | + | 0.963082i | \(0.413238\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − 24.7279i | − 1.23485i | −0.786628 | − | 0.617427i | \(-0.788175\pi\) | ||||
0.786628 | − | 0.617427i | \(-0.211825\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − 6.14214i | − 0.305962i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 27.4558 | 1.36094 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 18.2843 | 0.904099 | 0.452050 | − | 0.891993i | \(-0.350693\pi\) | ||||
0.452050 | + | 0.891993i | \(0.350693\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − 5.51472i | − 0.271362i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − 14.8284i | − 0.727899i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 1.61522 | 0.0789088 | 0.0394544 | − | 0.999221i | \(-0.487438\pi\) | ||||
0.0394544 | + | 0.999221i | \(0.487438\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 6.00000 | 0.292422 | 0.146211 | − | 0.989253i | \(-0.453292\pi\) | ||||
0.146211 | + | 0.989253i | \(0.453292\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − 6.82843i | − 0.331227i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − 4.20101i | − 0.203301i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −26.1421 | −1.25922 | −0.629611 | − | 0.776910i | \(-0.716786\pi\) | ||||
−0.629611 | + | 0.776910i | \(0.716786\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 2.48528 | 0.119435 | 0.0597175 | − | 0.998215i | \(-0.480980\pi\) | ||||
0.0597175 | + | 0.998215i | \(0.480980\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 38.2843i | 1.82721i | 0.406604 | + | 0.913604i | \(0.366713\pi\) | ||||
−0.406604 | + | 0.913604i | \(0.633287\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −18.6274 | −0.885015 | −0.442508 | − | 0.896765i | \(-0.645911\pi\) | ||||
−0.442508 | + | 0.896765i | \(0.645911\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −4.24264 | −0.201120 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 21.4142i | 1.01060i | 0.862944 | + | 0.505300i | \(0.168618\pi\) | ||||
−0.862944 | + | 0.505300i | \(0.831382\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 16.6274i | 0.782954i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −0.343146 | −0.0160869 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −14.4853 | −0.677593 | −0.338796 | − | 0.940860i | \(-0.610020\pi\) | ||||
−0.338796 | + | 0.940860i | \(0.610020\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − 19.1716i | − 0.892909i | −0.894806 | − | 0.446455i | \(-0.852686\pi\) | ||||
0.894806 | − | 0.446455i | \(-0.147314\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − 2.92893i | − 0.136119i | −0.997681 | − | 0.0680595i | \(-0.978319\pi\) | ||||
0.997681 | − | 0.0680595i | \(-0.0216808\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 31.1127 | 1.43972 | 0.719862 | − | 0.694117i | \(-0.244205\pi\) | ||||
0.719862 | + | 0.694117i | \(0.244205\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 4.68629 | 0.216393 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − 6.34315i | − 0.291658i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 4.68629 | 0.214122 | 0.107061 | − | 0.994252i | \(-0.465856\pi\) | ||||
0.107061 | + | 0.994252i | \(0.465856\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.97056 | −0.135446 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − 14.4853i | − 0.657743i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 14.7279i | 0.667386i | 0.942682 | + | 0.333693i | \(0.108295\pi\) | ||||
−0.942682 | + | 0.333693i | \(0.891705\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 16.9289 | 0.763992 | 0.381996 | − | 0.924164i | \(-0.375237\pi\) | ||||
0.381996 | + | 0.924164i | \(0.375237\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 40.9706 | 1.84522 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − 3.31371i | − 0.148640i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 26.6274i | 1.19201i | 0.802982 | + | 0.596003i | \(0.203246\pi\) | ||||
−0.802982 | + | 0.596003i | \(0.796754\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −20.2843 | −0.904431 | −0.452215 | − | 0.891909i | \(-0.649366\pi\) | ||||
−0.452215 | + | 0.891909i | \(0.649366\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −0.828427 | −0.0368645 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − 20.1421i | − 0.892784i | −0.894837 | − | 0.446392i | \(-0.852709\pi\) | ||||
0.894837 | − | 0.446392i | \(-0.147291\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 3.79899i | 0.168057i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 13.5563 | 0.597364 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −30.6274 | −1.34699 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 24.7279i | 1.08335i | 0.840588 | + | 0.541675i | \(0.182210\pi\) | ||||
−0.840588 | + | 0.541675i | \(0.817790\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 24.4853i | 1.07067i | 0.844641 | + | 0.535333i | \(0.179814\pi\) | ||||
−0.844641 | + | 0.535333i | \(0.820186\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 71.5980 | 3.11886 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −22.3137 | −0.970161 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − 1.79899i | − 0.0779229i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − 9.17157i | − 0.396522i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −36.0416 | −1.55242 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −23.1716 | −0.996224 | −0.498112 | − | 0.867113i | \(-0.665973\pi\) | ||||
−0.498112 | + | 0.867113i | \(0.665973\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 12.8284i | 0.549509i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 0.485281i | 0.0207491i | 0.999946 | + | 0.0103746i | \(0.00330239\pi\) | ||||
−0.999946 | + | 0.0103746i | \(0.996698\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1.45584 | 0.0619088 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 3.51472i | 0.148923i | 0.997224 | + | 0.0744617i | \(0.0237239\pi\) | ||||
−0.997224 | + | 0.0744617i | \(0.976276\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0.686292i | 0.0290270i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 17.6569 | 0.744148 | 0.372074 | − | 0.928203i | \(-0.378647\pi\) | ||||
0.372074 | + | 0.928203i | \(0.378647\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −9.65685 | −0.406267 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − 33.2132i | − 1.39237i | −0.717862 | − | 0.696185i | \(-0.754879\pi\) | ||||
0.717862 | − | 0.696185i | \(-0.245121\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 28.9706i | 1.21238i | 0.795320 | + | 0.606190i | \(0.207303\pi\) | ||||
−0.795320 | + | 0.606190i | \(0.792697\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0.828427 | 0.0345478 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −35.4558 | −1.47605 | −0.738023 | − | 0.674775i | \(-0.764240\pi\) | ||||
−0.738023 | + | 0.674775i | \(0.764240\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − 8.68629i | − 0.360368i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 36.9706i | 1.53116i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 2.14214 | 0.0884154 | 0.0442077 | − | 0.999022i | \(-0.485924\pi\) | ||||
0.0442077 | + | 0.999022i | \(0.485924\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0 | 0 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − 21.6569i | − 0.889340i | −0.895694 | − | 0.444670i | \(-0.853321\pi\) | ||||
0.895694 | − | 0.444670i | \(-0.146679\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − 4.00000i | − 0.163984i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 13.8579 | 0.566217 | 0.283108 | − | 0.959088i | \(-0.408634\pi\) | ||||
0.283108 | + | 0.959088i | \(0.408634\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 39.3137 | 1.60364 | 0.801820 | − | 0.597566i | \(-0.203865\pi\) | ||||
0.801820 | + | 0.597566i | \(0.203865\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 18.3137i | 0.744558i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − 39.2132i | − 1.59161i | −0.605550 | − | 0.795807i | \(-0.707047\pi\) | ||||
0.605550 | − | 0.795807i | \(-0.292953\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 3.31371 | 0.134058 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −39.2132 | −1.58381 | −0.791903 | − | 0.610647i | \(-0.790910\pi\) | ||||
−0.791903 | + | 0.610647i | \(0.790910\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 21.1716i | 0.852335i | 0.904644 | + | 0.426168i | \(0.140137\pi\) | ||||
−0.904644 | + | 0.426168i | \(0.859863\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 10.9706i | 0.440944i | 0.975393 | + | 0.220472i | \(0.0707598\pi\) | ||||
−0.975393 | + | 0.220472i | \(0.929240\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −2.48528 | −0.0995707 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − 34.6274i | − 1.38069i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 12.8284i | 0.510692i | 0.966850 | + | 0.255346i | \(0.0821893\pi\) | ||||
−0.966850 | + | 0.255346i | \(0.917811\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 14.7279 | 0.584460 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 3.89949 | 0.154504 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 12.4437i | 0.491495i | 0.969334 | + | 0.245747i | \(0.0790333\pi\) | ||||
−0.969334 | + | 0.245747i | \(0.920967\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 27.1127i | 1.06922i | 0.845099 | + | 0.534610i | \(0.179542\pi\) | ||||
−0.845099 | + | 0.534610i | \(0.820458\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 35.3137 | 1.38833 | 0.694163 | − | 0.719818i | \(-0.255775\pi\) | ||||
0.694163 | + | 0.719818i | \(0.255775\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 50.9706 | 2.00077 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − 8.34315i | − 0.326493i | −0.986585 | − | 0.163246i | \(-0.947803\pi\) | ||||
0.986585 | − | 0.163246i | \(-0.0521965\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 12.7279i | 0.497321i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −9.41421 | −0.366726 | −0.183363 | − | 0.983045i | \(-0.558698\pi\) | ||||
−0.183363 | + | 0.983045i | \(0.558698\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −44.4264 | −1.72799 | −0.863993 | − | 0.503503i | \(-0.832044\pi\) | ||||
−0.863993 | + | 0.503503i | \(0.832044\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 4.97056i | 0.192461i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 38.8284 | 1.49895 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 0.544156 | 0.0209757 | 0.0104878 | − | 0.999945i | \(-0.496662\pi\) | ||||
0.0104878 | + | 0.999945i | \(0.496662\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 29.3137i | 1.12662i | 0.826247 | + | 0.563309i | \(0.190472\pi\) | ||||
−0.826247 | + | 0.563309i | \(0.809528\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − 8.48528i | − 0.325635i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −5.17157 | −0.197885 | −0.0989424 | − | 0.995093i | \(-0.531546\pi\) | ||||
−0.0989424 | + | 0.995093i | \(0.531546\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −3.31371 | −0.126610 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − 4.00000i | − 0.152388i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − 8.00000i | − 0.304334i | −0.988355 | − | 0.152167i | \(-0.951375\pi\) | ||||
0.988355 | − | 0.152167i | \(-0.0486252\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 7.65685 | 0.290441 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 20.9706 | 0.794317 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − 26.4853i | − 1.00034i | −0.865929 | − | 0.500168i | \(-0.833272\pi\) | ||||
0.865929 | − | 0.500168i | \(-0.166728\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −0.485281 | −0.0182509 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 26.9706 | 1.01290 | 0.506450 | − | 0.862269i | \(-0.330957\pi\) | ||||
0.506450 | + | 0.862269i | \(0.330957\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 8.68629i | 0.325304i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − 3.17157i | − 0.118610i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −5.17157 | −0.192867 | −0.0964336 | − | 0.995339i | \(-0.530744\pi\) | ||||
−0.0964336 | + | 0.995339i | \(0.530744\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 7.94113 | 0.295743 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 6.00000i | 0.222834i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − 41.0711i | − 1.52324i | −0.648023 | − | 0.761621i | \(-0.724404\pi\) | ||||
0.648023 | − | 0.761621i | \(-0.275596\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −8.00000 | −0.295891 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 31.8995 | 1.17823 | 0.589117 | − | 0.808047i | \(-0.299476\pi\) | ||||
0.589117 | + | 0.808047i | \(0.299476\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 43.3137i | 1.59548i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 33.6569i | 1.23809i | 0.785357 | + | 0.619044i | \(0.212480\pi\) | ||||
−0.785357 | + | 0.619044i | \(0.787520\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 48.0000 | 1.76095 | 0.880475 | − | 0.474093i | \(-0.157224\pi\) | ||||
0.880475 | + | 0.474093i | \(0.157224\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −3.17157 | −0.116197 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − 5.37258i | − 0.196310i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 23.1716i | 0.845543i | 0.906236 | + | 0.422771i | \(0.138943\pi\) | ||||
−0.906236 | + | 0.422771i | \(0.861057\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 4.34315 | 0.158063 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −0.870058 | −0.0316228 | −0.0158114 | − | 0.999875i | \(-0.505033\pi\) | ||||
−0.0158114 | + | 0.999875i | \(0.505033\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 22.8701i | 0.829039i | 0.910040 | + | 0.414519i | \(0.136050\pi\) | ||||
−0.910040 | + | 0.414519i | \(0.863950\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 7.51472i | 0.272051i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −5.51472 | −0.199125 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −13.6569 | −0.492479 | −0.246239 | − | 0.969209i | \(-0.579195\pi\) | ||||
−0.246239 | + | 0.969209i | \(0.579195\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − 18.6863i | − 0.672099i | −0.941844 | − | 0.336050i | \(-0.890909\pi\) | ||||
0.941844 | − | 0.336050i | \(-0.109091\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 10.4853i | 0.376642i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 30.6274 | 1.09594 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 18.2426i | 0.651108i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 13.8579i | − 0.493980i | −0.969018 | − | 0.246990i | \(-0.920559\pi\) | ||||
0.969018 | − | 0.246990i | \(-0.0794414\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −5.65685 | −0.201135 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −4.20101 | −0.149182 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − 13.1716i | − 0.466561i | −0.972409 | − | 0.233281i | \(-0.925054\pi\) | ||||
0.972409 | − | 0.233281i | \(-0.0749460\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 38.6274i | 1.36654i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −35.1127 | −1.23910 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0.485281 | 0.0171039 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 12.0416i | 0.423361i | 0.977339 | + | 0.211681i | \(0.0678937\pi\) | ||||
−0.977339 | + | 0.211681i | \(0.932106\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 48.6274i | 1.70754i | 0.520651 | + | 0.853770i | \(0.325689\pi\) | ||||
−0.520651 | + | 0.853770i | \(0.674311\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 16.4853 | 0.577454 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0 | 0 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 6.68629i | 0.233353i | 0.993170 | + | 0.116677i | \(0.0372241\pi\) | ||||
−0.993170 | + | 0.116677i | \(0.962776\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 2.24264i | 0.0781735i | 0.999236 | + | 0.0390868i | \(0.0124449\pi\) | ||||
−0.999236 | + | 0.0390868i | \(0.987555\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 2.62742 | 0.0913642 | 0.0456821 | − | 0.998956i | \(-0.485454\pi\) | ||||
0.0456821 | + | 0.998956i | \(0.485454\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −31.4558 | −1.09251 | −0.546253 | − | 0.837620i | \(-0.683946\pi\) | ||||
−0.546253 | + | 0.837620i | \(0.683946\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 45.4558i | 1.57495i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 17.7990i | 0.615959i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −42.4264 | −1.46472 | −0.732361 | − | 0.680916i | \(-0.761582\pi\) | ||||
−0.732361 | + | 0.680916i | \(0.761582\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −7.00000 | −0.241379 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − 12.6569i | − 0.435409i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 10.7279i | 0.368616i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 4.20101 | 0.144009 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −30.2426 | −1.03549 | −0.517744 | − | 0.855536i | \(-0.673228\pi\) | ||||
−0.517744 | + | 0.855536i | \(0.673228\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 3.79899i | 0.129771i | 0.997893 | + | 0.0648855i | \(0.0206682\pi\) | ||||
−0.997893 | + | 0.0648855i | \(0.979332\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 26.0000i | 0.887109i | 0.896248 | + | 0.443554i | \(0.146283\pi\) | ||||
−0.896248 | + | 0.443554i | \(0.853717\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −45.7990 | −1.55902 | −0.779508 | − | 0.626392i | \(-0.784531\pi\) | ||||
−0.779508 | + | 0.626392i | \(0.784531\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −8.48528 | −0.288508 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 13.4558i | 0.456458i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − 4.68629i | − 0.158789i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0.585786 | 0.0198032 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −29.5563 | −0.998047 | −0.499023 | − | 0.866588i | \(-0.666308\pi\) | ||||
−0.499023 | + | 0.866588i | \(0.666308\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − 35.3553i | − 1.19115i | −0.803299 | − | 0.595576i | \(-0.796924\pi\) | ||||
0.803299 | − | 0.595576i | \(-0.203076\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 42.4264i | 1.42776i | 0.700267 | + | 0.713881i | \(0.253064\pi\) | ||||
−0.700267 | + | 0.713881i | \(0.746936\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −7.17157 | −0.240798 | −0.120399 | − | 0.992726i | \(-0.538417\pi\) | ||||
−0.120399 | + | 0.992726i | \(0.538417\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 8.62742 | 0.289354 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − 24.0416i | − 0.803623i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −62.9117 | −2.09822 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 46.6274 | 1.55338 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − 18.4853i | − 0.614472i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − 30.1421i | − 1.00085i | −0.865779 | − | 0.500427i | \(-0.833177\pi\) | ||||
0.865779 | − | 0.500427i | \(-0.166823\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 29.6569 | 0.982575 | 0.491288 | − | 0.870997i | \(-0.336526\pi\) | ||||
0.491288 | + | 0.870997i | \(0.336526\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 80.2843 | 2.65702 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 7.45584i | 0.246214i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 7.17157i | 0.236568i | 0.992980 | + | 0.118284i | \(0.0377394\pi\) | ||||
−0.992980 | + | 0.118284i | \(0.962261\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −3.31371 | −0.109072 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 5.07107 | 0.166736 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 26.1005i | 0.856330i | 0.903701 | + | 0.428165i | \(0.140840\pi\) | ||||
−0.903701 | + | 0.428165i | \(0.859160\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 36.9706 | 1.20907 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 18.9706 | 0.619741 | 0.309871 | − | 0.950779i | \(-0.399714\pi\) | ||||
0.309871 | + | 0.950779i | \(0.399714\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − 14.2843i | − 0.465654i | −0.972518 | − | 0.232827i | \(-0.925202\pi\) | ||||
0.972518 | − | 0.232827i | \(-0.0747976\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 2.54416i | 0.0828491i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 27.5980 | 0.896814 | 0.448407 | − | 0.893830i | \(-0.351992\pi\) | ||||
0.448407 | + | 0.893830i | \(0.351992\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 3.79899 | 0.123320 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − 45.2548i | − 1.46595i | −0.680257 | − | 0.732974i | \(-0.738132\pi\) | ||||
0.680257 | − | 0.732974i | \(-0.261868\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − 20.4853i | − 0.662888i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −1.94113 | −0.0626822 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −78.9411 | −2.54649 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − 14.9706i | − 0.481919i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − 1.27208i | − 0.0409073i | −0.999791 | − | 0.0204536i | \(-0.993489\pi\) | ||||
0.999791 | − | 0.0204536i | \(-0.00651105\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −12.9289 | −0.414909 | −0.207455 | − | 0.978245i | \(-0.566518\pi\) | ||||
−0.207455 | + | 0.978245i | \(0.566518\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 4.48528 | 0.143792 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − 42.8284i | − 1.37020i | −0.728448 | − | 0.685101i | \(-0.759758\pi\) | ||||
0.728448 | − | 0.685101i | \(-0.240242\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − 22.9706i | − 0.734142i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 39.5980 | 1.26298 | 0.631490 | − | 0.775384i | \(-0.282444\pi\) | ||||
0.631490 | + | 0.775384i | \(0.282444\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1.31371 | 0.0418582 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − 0.970563i | − 0.0308621i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 27.6569i | 0.878549i | 0.898353 | + | 0.439274i | \(0.144764\pi\) | ||||
−0.898353 | + | 0.439274i | \(0.855236\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −4.34315 | −0.137687 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −30.7279 | −0.973163 | −0.486582 | − | 0.873635i | \(-0.661756\pi\) | ||||
−0.486582 | + | 0.873635i | \(0.661756\pi\) | |||||||
\(998\) | 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 | 2880.2.h.a.1151.3 | 4 | ||
3.2 | odd | 2 | 2880.2.h.d.1151.1 | 4 | |||
4.3 | odd | 2 | 2880.2.h.d.1151.4 | 4 | |||
8.3 | odd | 2 | 1440.2.h.a.1151.2 | ✓ | 4 | ||
8.5 | even | 2 | 1440.2.h.d.1151.1 | yes | 4 | ||
12.11 | even | 2 | inner | 2880.2.h.a.1151.2 | 4 | ||
24.5 | odd | 2 | 1440.2.h.a.1151.3 | yes | 4 | ||
24.11 | even | 2 | 1440.2.h.d.1151.4 | yes | 4 | ||
40.3 | even | 4 | 7200.2.o.b.7199.3 | 4 | |||
40.13 | odd | 4 | 7200.2.o.m.7199.1 | 4 | |||
40.19 | odd | 2 | 7200.2.h.c.1151.3 | 4 | |||
40.27 | even | 4 | 7200.2.o.j.7199.2 | 4 | |||
40.29 | even | 2 | 7200.2.h.i.1151.2 | 4 | |||
40.37 | odd | 4 | 7200.2.o.e.7199.4 | 4 | |||
120.29 | odd | 2 | 7200.2.h.c.1151.2 | 4 | |||
120.53 | even | 4 | 7200.2.o.j.7199.1 | 4 | |||
120.59 | even | 2 | 7200.2.h.i.1151.3 | 4 | |||
120.77 | even | 4 | 7200.2.o.b.7199.4 | 4 | |||
120.83 | odd | 4 | 7200.2.o.e.7199.3 | 4 | |||
120.107 | odd | 4 | 7200.2.o.m.7199.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1440.2.h.a.1151.2 | ✓ | 4 | 8.3 | odd | 2 | ||
1440.2.h.a.1151.3 | yes | 4 | 24.5 | odd | 2 | ||
1440.2.h.d.1151.1 | yes | 4 | 8.5 | even | 2 | ||
1440.2.h.d.1151.4 | yes | 4 | 24.11 | even | 2 | ||
2880.2.h.a.1151.2 | 4 | 12.11 | even | 2 | inner | ||
2880.2.h.a.1151.3 | 4 | 1.1 | even | 1 | trivial | ||
2880.2.h.d.1151.1 | 4 | 3.2 | odd | 2 | |||
2880.2.h.d.1151.4 | 4 | 4.3 | odd | 2 | |||
7200.2.h.c.1151.2 | 4 | 120.29 | odd | 2 | |||
7200.2.h.c.1151.3 | 4 | 40.19 | odd | 2 | |||
7200.2.h.i.1151.2 | 4 | 40.29 | even | 2 | |||
7200.2.h.i.1151.3 | 4 | 120.59 | even | 2 | |||
7200.2.o.b.7199.3 | 4 | 40.3 | even | 4 | |||
7200.2.o.b.7199.4 | 4 | 120.77 | even | 4 | |||
7200.2.o.e.7199.3 | 4 | 120.83 | odd | 4 | |||
7200.2.o.e.7199.4 | 4 | 40.37 | odd | 4 | |||
7200.2.o.j.7199.1 | 4 | 120.53 | even | 4 | |||
7200.2.o.j.7199.2 | 4 | 40.27 | even | 4 | |||
7200.2.o.m.7199.1 | 4 | 40.13 | odd | 4 | |||
7200.2.o.m.7199.2 | 4 | 120.107 | odd | 4 |