Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4900,2,Mod(2549,4900)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4900, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4900.2549");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4900 = 2^{2} \cdot 5^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4900.e (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: | \(39.1266969904\) |
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: | \(\Z[a_1, \ldots, a_{23}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 980) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 2549.4 | ||
Root | \(0.707107 + 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4900.2549 |
Dual form | 4900.2.e.q.2549.1 |
$q$-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 \(\left(\mathbb{Z}/4900\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(1177\) | \(2451\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 2.41421i | 1.39385i | 0.717146 | + | 0.696923i | \(0.245448\pi\) | ||||
−0.717146 | + | 0.696923i | \(0.754552\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.82843 | −0.942809 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.82843 | 0.551292 | 0.275646 | − | 0.961259i | \(-0.411108\pi\) | ||||
0.275646 | + | 0.961259i | \(0.411108\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 6.41421i | 1.77898i | 0.456952 | + | 0.889491i | \(0.348941\pi\) | ||||
−0.456952 | + | 0.889491i | \(0.651059\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − 3.58579i | − 0.869681i | −0.900508 | − | 0.434840i | \(-0.856805\pi\) | ||||
0.900508 | − | 0.434840i | \(-0.143195\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −7.65685 | −1.75660 | −0.878301 | − | 0.478107i | \(-0.841323\pi\) | ||||
−0.878301 | + | 0.478107i | \(0.841323\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − 3.41421i | − 0.711913i | −0.934503 | − | 0.355956i | \(-0.884155\pi\) | ||||
0.934503 | − | 0.355956i | \(-0.115845\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0.414214i | 0.0797154i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.65685 | 0.864756 | 0.432378 | − | 0.901692i | \(-0.357675\pi\) | ||||
0.432378 | + | 0.901692i | \(0.357675\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −7.41421 | −1.33163 | −0.665816 | − | 0.746116i | \(-0.731916\pi\) | ||||
−0.665816 | + | 0.746116i | \(0.731916\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 4.41421i | 0.768416i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − 0.585786i | − 0.0963027i | −0.998840 | − | 0.0481513i | \(-0.984667\pi\) | ||||
0.998840 | − | 0.0481513i | \(-0.0153330\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −15.4853 | −2.47963 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −3.41421 | −0.533211 | −0.266605 | − | 0.963806i | \(-0.585902\pi\) | ||||
−0.266605 | + | 0.963806i | \(0.585902\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 0.343146i | − 0.0523292i | −0.999658 | − | 0.0261646i | \(-0.991671\pi\) | ||||
0.999658 | − | 0.0261646i | \(-0.00832941\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − 10.8995i | − 1.58985i | −0.606705 | − | 0.794927i | \(-0.707509\pi\) | ||||
0.606705 | − | 0.794927i | \(-0.292491\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 8.65685 | 1.21220 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 12.2426i | 1.68166i | 0.541302 | + | 0.840828i | \(0.317931\pi\) | ||||
−0.541302 | + | 0.840828i | \(0.682069\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − 18.4853i | − 2.44844i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0.585786 | 0.0762629 | 0.0381314 | − | 0.999273i | \(-0.487859\pi\) | ||||
0.0381314 | + | 0.999273i | \(0.487859\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −10.8284 | −1.38644 | −0.693219 | − | 0.720727i | \(-0.743808\pi\) | ||||
−0.693219 | + | 0.720727i | \(0.743808\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3.07107i | 0.375191i | 0.982246 | + | 0.187595i | \(0.0600694\pi\) | ||||
−0.982246 | + | 0.187595i | \(0.939931\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 8.24264 | 0.992297 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −10.4853 | −1.24437 | −0.622187 | − | 0.782869i | \(-0.713756\pi\) | ||||
−0.622187 | + | 0.782869i | \(0.713756\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 10.8284i | 1.26737i | 0.773591 | + | 0.633686i | \(0.218459\pi\) | ||||
−0.773591 | + | 0.633686i | \(0.781541\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 15.1421 | 1.70362 | 0.851812 | − | 0.523848i | \(-0.175504\pi\) | ||||
0.851812 | + | 0.523848i | \(0.175504\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −9.48528 | −1.05392 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − 8.00000i | − 0.878114i | −0.898459 | − | 0.439057i | \(-0.855313\pi\) | ||||
0.898459 | − | 0.439057i | \(-0.144687\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 11.2426i | 1.20534i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −16.9706 | −1.79888 | −0.899438 | − | 0.437048i | \(-0.856024\pi\) | ||||
−0.899438 | + | 0.437048i | \(0.856024\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − 17.8995i | − 1.85609i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 9.72792i | 0.987721i | 0.869541 | + | 0.493860i | \(0.164415\pi\) | ||||
−0.869541 | + | 0.493860i | \(0.835585\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −5.17157 | −0.519763 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −0.828427 | −0.0824316 | −0.0412158 | − | 0.999150i | \(-0.513123\pi\) | ||||
−0.0412158 | + | 0.999150i | \(0.513123\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 4.41421i | 0.434945i | 0.976066 | + | 0.217473i | \(0.0697813\pi\) | ||||
−0.976066 | + | 0.217473i | \(0.930219\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − 11.1716i | − 1.08000i | −0.841666 | − | 0.539998i | \(-0.818425\pi\) | ||||
0.841666 | − | 0.539998i | \(-0.181575\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −9.00000 | −0.862044 | −0.431022 | − | 0.902342i | \(-0.641847\pi\) | ||||
−0.431022 | + | 0.902342i | \(0.641847\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1.41421 | 0.134231 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − 9.07107i | − 0.853334i | −0.904409 | − | 0.426667i | \(-0.859688\pi\) | ||||
0.904409 | − | 0.426667i | \(-0.140312\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − 18.1421i | − 1.67724i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7.65685 | −0.696078 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − 8.24264i | − 0.743214i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − 2.10051i | − 0.186390i | −0.995648 | − | 0.0931948i | \(-0.970292\pi\) | ||||
0.995648 | − | 0.0931948i | \(-0.0297079\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0.828427 | 0.0729389 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 20.2426 | 1.76861 | 0.884304 | − | 0.466912i | \(-0.154633\pi\) | ||||
0.884304 | + | 0.466912i | \(0.154633\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − 20.9706i | − 1.79164i | −0.444421 | − | 0.895818i | \(-0.646591\pi\) | ||||
0.444421 | − | 0.895818i | \(-0.353409\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 5.89949 | 0.500389 | 0.250194 | − | 0.968196i | \(-0.419505\pi\) | ||||
0.250194 | + | 0.968196i | \(0.419505\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 26.3137 | 2.21601 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 11.7279i | 0.980738i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −20.4853 | −1.67822 | −0.839110 | − | 0.543962i | \(-0.816924\pi\) | ||||
−0.839110 | + | 0.543962i | \(0.816924\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −6.17157 | −0.502235 | −0.251118 | − | 0.967957i | \(-0.580798\pi\) | ||||
−0.251118 | + | 0.967957i | \(0.580798\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 10.1421i | 0.819943i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 6.48528i | 0.517582i | 0.965933 | + | 0.258791i | \(0.0833241\pi\) | ||||
−0.965933 | + | 0.258791i | \(0.916676\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −29.5563 | −2.34397 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 9.55635i | 0.748511i | 0.927326 | + | 0.374256i | \(0.122102\pi\) | ||||
−0.927326 | + | 0.374256i | \(0.877898\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0.414214i | 0.0320528i | 0.999872 | + | 0.0160264i | \(0.00510158\pi\) | ||||
−0.999872 | + | 0.0160264i | \(0.994898\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −28.1421 | −2.16478 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 21.6569 | 1.65614 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − 12.5563i | − 0.954642i | −0.878729 | − | 0.477321i | \(-0.841608\pi\) | ||||
0.878729 | − | 0.477321i | \(-0.158392\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 1.41421i | 0.106299i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 10.4853 | 0.783707 | 0.391853 | − | 0.920028i | \(-0.371834\pi\) | ||||
0.391853 | + | 0.920028i | \(0.371834\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −10.2426 | −0.761329 | −0.380665 | − | 0.924713i | \(-0.624305\pi\) | ||||
−0.380665 | + | 0.924713i | \(0.624305\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − 26.1421i | − 1.93248i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 6.55635i | − 0.479448i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 5.34315 | 0.386616 | 0.193308 | − | 0.981138i | \(-0.438078\pi\) | ||||
0.193308 | + | 0.981138i | \(0.438078\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 5.65685i | 0.407189i | 0.979055 | + | 0.203595i | \(0.0652625\pi\) | ||||
−0.979055 | + | 0.203595i | \(0.934738\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 3.55635i | 0.253379i | 0.991942 | + | 0.126690i | \(0.0404352\pi\) | ||||
−0.991942 | + | 0.126690i | \(0.959565\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1.27208 | −0.0901752 | −0.0450876 | − | 0.998983i | \(-0.514357\pi\) | ||||
−0.0450876 | + | 0.998983i | \(0.514357\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −7.41421 | −0.522958 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 9.65685i | 0.671198i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −14.0000 | −0.968400 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.68629 | −0.116089 | −0.0580445 | − | 0.998314i | \(-0.518487\pi\) | ||||
−0.0580445 | + | 0.998314i | \(0.518487\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − 25.3137i | − 1.73447i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −26.1421 | −1.76652 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 23.0000 | 1.54715 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 9.92893i | 0.664890i | 0.943123 | + | 0.332445i | \(0.107874\pi\) | ||||
−0.943123 | + | 0.332445i | \(0.892126\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 17.7279i | 1.17664i | 0.808627 | + | 0.588322i | \(0.200211\pi\) | ||||
−0.808627 | + | 0.588322i | \(0.799789\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 4.10051 | 0.270969 | 0.135485 | − | 0.990779i | \(-0.456741\pi\) | ||||
0.135485 | + | 0.990779i | \(0.456741\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 14.8284i | 0.971443i | 0.874114 | + | 0.485721i | \(0.161443\pi\) | ||||
−0.874114 | + | 0.485721i | \(0.838557\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 36.5563i | 2.37459i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −19.8284 | −1.28259 | −0.641297 | − | 0.767293i | \(-0.721603\pi\) | ||||
−0.641297 | + | 0.767293i | \(0.721603\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −27.5563 | −1.77506 | −0.887530 | − | 0.460749i | \(-0.847581\pi\) | ||||
−0.887530 | + | 0.460749i | \(0.847581\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − 21.6569i | − 1.38929i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − 49.1127i | − 3.12497i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 19.3137 | 1.22396 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 12.9289 | 0.816067 | 0.408033 | − | 0.912967i | \(-0.366215\pi\) | ||||
0.408033 | + | 0.912967i | \(0.366215\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − 6.24264i | − 0.392471i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − 13.7990i | − 0.860757i | −0.902648 | − | 0.430379i | \(-0.858380\pi\) | ||||
0.902648 | − | 0.430379i | \(-0.141620\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −13.1716 | −0.815300 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − 10.0000i | − 0.616626i | −0.951285 | − | 0.308313i | \(-0.900236\pi\) | ||||
0.951285 | − | 0.308313i | \(-0.0997645\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − 40.9706i | − 2.50736i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 8.72792 | 0.532151 | 0.266075 | − | 0.963952i | \(-0.414273\pi\) | ||||
0.266075 | + | 0.963952i | \(0.414273\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 4.97056 | 0.301940 | 0.150970 | − | 0.988538i | \(-0.451760\pi\) | ||||
0.150970 | + | 0.988538i | \(0.451760\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − 4.58579i | − 0.275533i | −0.990465 | − | 0.137767i | \(-0.956008\pi\) | ||||
0.990465 | − | 0.137767i | \(-0.0439924\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 20.9706 | 1.25547 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1.00000 | −0.0596550 | −0.0298275 | − | 0.999555i | \(-0.509496\pi\) | ||||
−0.0298275 | + | 0.999555i | \(0.509496\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 27.2426i | − 1.61941i | −0.586839 | − | 0.809703i | \(-0.699628\pi\) | ||||
0.586839 | − | 0.809703i | \(-0.300372\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 4.14214 | 0.243655 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −23.4853 | −1.37673 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − 11.5858i | − 0.676849i | −0.940994 | − | 0.338424i | \(-0.890106\pi\) | ||||
0.940994 | − | 0.338424i | \(-0.109894\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0.757359i | 0.0439464i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 21.8995 | 1.26648 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − 2.00000i | − 0.114897i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − 6.41421i | − 0.366079i | −0.983106 | − | 0.183039i | \(-0.941406\pi\) | ||||
0.983106 | − | 0.183039i | \(-0.0585935\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −10.6569 | −0.606247 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 26.9706 | 1.52936 | 0.764680 | − | 0.644410i | \(-0.222897\pi\) | ||||
0.764680 | + | 0.644410i | \(0.222897\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − 14.5563i | − 0.822774i | −0.911461 | − | 0.411387i | \(-0.865045\pi\) | ||||
0.911461 | − | 0.411387i | \(-0.134955\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 18.9706i | 1.06549i | 0.846275 | + | 0.532746i | \(0.178840\pi\) | ||||
−0.846275 | + | 0.532746i | \(0.821160\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 8.51472 | 0.476733 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 26.9706 | 1.50535 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 27.4558i | 1.52768i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − 21.7279i | − 1.20156i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −0.828427 | −0.0455345 | −0.0227672 | − | 0.999741i | \(-0.507248\pi\) | ||||
−0.0227672 | + | 0.999741i | \(0.507248\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1.65685i | 0.0907951i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 6.72792i | 0.366493i | 0.983067 | + | 0.183247i | \(0.0586607\pi\) | ||||
−0.983067 | + | 0.183247i | \(0.941339\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 21.8995 | 1.18942 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −13.5563 | −0.734117 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − 4.58579i | − 0.246178i | −0.992396 | − | 0.123089i | \(-0.960720\pi\) | ||||
0.992396 | − | 0.123089i | \(-0.0392800\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 18.0000 | 0.963518 | 0.481759 | − | 0.876304i | \(-0.339998\pi\) | ||||
0.481759 | + | 0.876304i | \(0.339998\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2.65685 | −0.141812 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 12.0711i | 0.642478i | 0.946998 | + | 0.321239i | \(0.104099\pi\) | ||||
−0.946998 | + | 0.321239i | \(0.895901\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 11.3137 | 0.597115 | 0.298557 | − | 0.954392i | \(-0.403495\pi\) | ||||
0.298557 | + | 0.954392i | \(0.403495\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 39.6274 | 2.08565 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − 18.4853i | − 0.970226i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 5.72792i | 0.298995i | 0.988762 | + | 0.149498i | \(0.0477656\pi\) | ||||
−0.988762 | + | 0.149498i | \(0.952234\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 9.65685 | 0.502716 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 0.485281i | 0.0251269i | 0.999921 | + | 0.0125635i | \(0.00399918\pi\) | ||||
−0.999921 | + | 0.0125635i | \(0.996001\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 29.8701i | 1.53839i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −14.0000 | −0.719132 | −0.359566 | − | 0.933120i | \(-0.617075\pi\) | ||||
−0.359566 | + | 0.933120i | \(0.617075\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 5.07107 | 0.259799 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − 20.4853i | − 1.04675i | −0.852103 | − | 0.523374i | \(-0.824673\pi\) | ||||
0.852103 | − | 0.523374i | \(-0.175327\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0.970563i | 0.0493365i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 15.1421 | 0.767737 | 0.383868 | − | 0.923388i | \(-0.374592\pi\) | ||||
0.383868 | + | 0.923388i | \(0.374592\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −12.2426 | −0.619137 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 48.8701i | 2.46517i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 11.5858i | − 0.581474i | −0.956803 | − | 0.290737i | \(-0.906100\pi\) | ||||
0.956803 | − | 0.290737i | \(-0.0939005\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 17.4853 | 0.873173 | 0.436587 | − | 0.899662i | \(-0.356187\pi\) | ||||
0.436587 | + | 0.899662i | \(0.356187\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − 47.5563i | − 2.36895i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − 1.07107i | − 0.0530909i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 27.1716 | 1.34355 | 0.671774 | − | 0.740756i | \(-0.265533\pi\) | ||||
0.671774 | + | 0.740756i | \(0.265533\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 50.6274 | 2.49727 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 14.2426i | 0.697465i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 21.5563 | 1.05310 | 0.526548 | − | 0.850145i | \(-0.323486\pi\) | ||||
0.526548 | + | 0.850145i | \(0.323486\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2.31371 | −0.112763 | −0.0563816 | − | 0.998409i | \(-0.517956\pi\) | ||||
−0.0563816 | + | 0.998409i | \(0.517956\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 30.8284i | 1.49893i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −28.3137 | −1.36700 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −4.17157 | −0.200938 | −0.100469 | − | 0.994940i | \(-0.532034\pi\) | ||||
−0.100469 | + | 0.994940i | \(0.532034\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 34.2843i | 1.64760i | 0.566883 | + | 0.823798i | \(0.308149\pi\) | ||||
−0.566883 | + | 0.823798i | \(0.691851\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 26.1421i | 1.25055i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 15.7574 | 0.752058 | 0.376029 | − | 0.926608i | \(-0.377289\pi\) | ||||
0.376029 | + | 0.926608i | \(0.377289\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − 15.4558i | − 0.734329i | −0.930156 | − | 0.367165i | \(-0.880329\pi\) | ||||
0.930156 | − | 0.367165i | \(-0.119671\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − 49.4558i | − 2.33918i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −18.1716 | −0.857570 | −0.428785 | − | 0.903407i | \(-0.641058\pi\) | ||||
−0.428785 | + | 0.903407i | \(0.641058\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −6.24264 | −0.293954 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − 14.8995i | − 0.700039i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − 0.928932i | − 0.0434536i | −0.999764 | − | 0.0217268i | \(-0.993084\pi\) | ||||
0.999764 | − | 0.0217268i | \(-0.00691640\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 1.48528 | 0.0693270 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −33.6569 | −1.56756 | −0.783778 | − | 0.621041i | \(-0.786710\pi\) | ||||
−0.783778 | + | 0.621041i | \(0.786710\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − 37.4558i | − 1.74072i | −0.492415 | − | 0.870360i | \(-0.663886\pi\) | ||||
0.492415 | − | 0.870360i | \(-0.336114\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 18.8995i | 0.874564i | 0.899324 | + | 0.437282i | \(0.144059\pi\) | ||||
−0.899324 | + | 0.437282i | \(0.855941\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −15.6569 | −0.721430 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − 0.627417i | − 0.0288487i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − 34.6274i | − 1.58548i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 6.58579 | 0.300912 | 0.150456 | − | 0.988617i | \(-0.451926\pi\) | ||||
0.150456 | + | 0.988617i | \(0.451926\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 3.75736 | 0.171321 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − 4.58579i | − 0.207802i | −0.994588 | − | 0.103901i | \(-0.966868\pi\) | ||||
0.994588 | − | 0.103901i | \(-0.0331325\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −23.0711 | −1.04331 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −39.2843 | −1.77287 | −0.886437 | − | 0.462849i | \(-0.846827\pi\) | ||||
−0.886437 | + | 0.462849i | \(0.846827\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − 16.6985i | − 0.752062i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −31.6274 | −1.41584 | −0.707919 | − | 0.706294i | \(-0.750366\pi\) | ||||
−0.707919 | + | 0.706294i | \(0.750366\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1.00000 | −0.0446767 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − 9.04163i | − 0.403146i | −0.979473 | − | 0.201573i | \(-0.935395\pi\) | ||||
0.979473 | − | 0.201573i | \(-0.0646054\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − 67.9411i | − 3.01737i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −20.9289 | −0.927659 | −0.463829 | − | 0.885925i | \(-0.653525\pi\) | ||||
−0.463829 | + | 0.885925i | \(0.653525\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | − 3.17157i | − 0.140028i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − 19.9289i | − 0.876473i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 30.3137 | 1.33062 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −29.3137 | −1.28426 | −0.642128 | − | 0.766597i | \(-0.721948\pi\) | ||||
−0.642128 | + | 0.766597i | \(0.721948\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 30.1421i | 1.31802i | 0.752133 | + | 0.659012i | \(0.229025\pi\) | ||||
−0.752133 | + | 0.659012i | \(0.770975\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 26.5858i | 1.15810i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 11.3431 | 0.493180 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −1.65685 | −0.0719014 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − 21.8995i | − 0.948572i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 25.3137i | 1.09237i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −17.9706 | −0.772615 | −0.386307 | − | 0.922370i | \(-0.626250\pi\) | ||||
−0.386307 | + | 0.922370i | \(0.626250\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − 24.7279i | − 1.06118i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 24.4853i | 1.04692i | 0.852052 | + | 0.523458i | \(0.175358\pi\) | ||||
−0.852052 | + | 0.523458i | \(0.824642\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 30.6274 | 1.30715 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −35.6569 | −1.51903 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 31.7990i | 1.34737i | 0.739020 | + | 0.673683i | \(0.235289\pi\) | ||||
−0.739020 | + | 0.673683i | \(0.764711\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2.20101 | 0.0930928 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 15.8284 | 0.668277 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 24.6274i | 1.03792i | 0.854798 | + | 0.518961i | \(0.173681\pi\) | ||||
−0.854798 | + | 0.518961i | \(0.826319\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −7.79899 | −0.326951 | −0.163475 | − | 0.986547i | \(-0.552270\pi\) | ||||
−0.163475 | + | 0.986547i | \(0.552270\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −0.828427 | −0.0346686 | −0.0173343 | − | 0.999850i | \(-0.505518\pi\) | ||||
−0.0173343 | + | 0.999850i | \(0.505518\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 12.8995i | 0.538884i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − 0.0710678i | − 0.00295859i | −0.999999 | − | 0.00147930i | \(-0.999529\pi\) | ||||
0.999999 | − | 0.00147930i | \(-0.000470875\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −13.6569 | −0.567559 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 22.3848i | 0.927083i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 25.1716i | 1.03894i | 0.854488 | + | 0.519471i | \(0.173871\pi\) | ||||
−0.854488 | + | 0.519471i | \(0.826129\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 56.7696 | 2.33915 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −8.58579 | −0.353172 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − 7.72792i | − 0.317348i | −0.987331 | − | 0.158674i | \(-0.949278\pi\) | ||||
0.987331 | − | 0.158674i | \(-0.0507218\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − 3.07107i | − 0.125690i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −26.7990 | −1.09498 | −0.547489 | − | 0.836813i | \(-0.684416\pi\) | ||||
−0.547489 | + | 0.836813i | \(0.684416\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −28.3431 | −1.15614 | −0.578071 | − | 0.815987i | \(-0.696194\pi\) | ||||
−0.578071 | + | 0.815987i | \(0.696194\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − 8.68629i | − 0.353733i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − 28.0711i | − 1.13937i | −0.821863 | − | 0.569685i | \(-0.807065\pi\) | ||||
0.821863 | − | 0.569685i | \(-0.192935\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 69.9117 | 2.82832 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 18.6863i | 0.754732i | 0.926064 | + | 0.377366i | \(0.123170\pi\) | ||||
−0.926064 | + | 0.377366i | \(0.876830\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − 12.8701i | − 0.518129i | −0.965860 | − | 0.259065i | \(-0.916586\pi\) | ||||
0.965860 | − | 0.259065i | \(-0.0834142\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −42.8701 | −1.72309 | −0.861547 | − | 0.507679i | \(-0.830504\pi\) | ||||
−0.861547 | + | 0.507679i | \(0.830504\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.41421 | 0.0567504 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − 33.7990i | − 1.34980i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −2.10051 | −0.0837526 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −22.5147 | −0.896297 | −0.448148 | − | 0.893959i | \(-0.647916\pi\) | ||||
−0.448148 | + | 0.893959i | \(0.647916\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − 4.07107i | − 0.161810i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 29.6569 | 1.17321 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 16.6863 | 0.659069 | 0.329534 | − | 0.944144i | \(-0.393108\pi\) | ||||
0.329534 | + | 0.944144i | \(0.393108\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 38.2132i | − 1.50698i | −0.657458 | − | 0.753491i | \(-0.728368\pi\) | ||||
0.657458 | − | 0.753491i | \(-0.271632\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 27.1127i | 1.06591i | 0.846144 | + | 0.532955i | \(0.178919\pi\) | ||||
−0.846144 | + | 0.532955i | \(0.821081\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.07107 | 0.0420431 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 49.3137i | 1.92979i | 0.262628 | + | 0.964897i | \(0.415411\pi\) | ||||
−0.262628 | + | 0.964897i | \(0.584589\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − 30.6274i | − 1.19489i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 9.34315 | 0.363957 | 0.181979 | − | 0.983302i | \(-0.441750\pi\) | ||||
0.181979 | + | 0.983302i | \(0.441750\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 5.85786 | 0.227845 | 0.113922 | − | 0.993490i | \(-0.463659\pi\) | ||||
0.113922 | + | 0.993490i | \(0.463659\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 55.5269i | 2.15649i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 15.8995i | − 0.615631i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −23.9706 | −0.926755 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −19.7990 | −0.764332 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 44.4853i | 1.71478i | 0.514666 | + | 0.857391i | \(0.327916\pi\) | ||||
−0.514666 | + | 0.857391i | \(0.672084\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 35.7279i | 1.37314i | 0.727066 | + | 0.686568i | \(0.240884\pi\) | ||||
−0.727066 | + | 0.686568i | \(0.759116\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −42.7990 | −1.64006 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 27.1127i | 1.03744i | 0.854945 | + | 0.518719i | \(0.173591\pi\) | ||||
−0.854945 | + | 0.518719i | \(0.826409\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 9.89949i | 0.377689i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −78.5269 | −2.99164 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −20.4853 | −0.779297 | −0.389648 | − | 0.920964i | \(-0.627403\pi\) | ||||
−0.389648 | + | 0.920964i | \(0.627403\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 12.2426i | 0.463723i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −35.7990 | −1.35404 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 17.4853 | 0.660410 | 0.330205 | − | 0.943909i | \(-0.392882\pi\) | ||||
0.330205 | + | 0.943909i | \(0.392882\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 4.48528i | 0.169166i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 41.6274 | 1.56335 | 0.781675 | − | 0.623686i | \(-0.214365\pi\) | ||||
0.781675 | + | 0.623686i | \(0.214365\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −42.8284 | −1.60619 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 25.3137i | 0.948006i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − 47.8701i | − 1.78774i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 24.2426 | 0.904098 | 0.452049 | − | 0.891993i | \(-0.350693\pi\) | ||||
0.452049 | + | 0.891993i | \(0.350693\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − 66.5269i | − 2.47416i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 18.0000i | 0.667583i | 0.942647 | + | 0.333792i | \(0.108328\pi\) | ||||
−0.942647 | + | 0.333792i | \(0.891672\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 23.8284 | 0.882534 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1.23045 | −0.0455097 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 28.6985i | 1.06000i | 0.847997 | + | 0.530001i | \(0.177809\pi\) | ||||
−0.847997 | + | 0.530001i | \(0.822191\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 5.61522i | 0.206839i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −9.34315 | −0.343693 | −0.171847 | − | 0.985124i | \(-0.554973\pi\) | ||||
−0.171847 | + | 0.985124i | \(0.554973\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 118.569 | 4.35572 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 23.0711i | 0.846395i | 0.906037 | + | 0.423198i | \(0.139092\pi\) | ||||
−0.906037 | + | 0.423198i | \(0.860908\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 22.6274i | 0.827894i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −27.1421 | −0.990431 | −0.495215 | − | 0.868770i | \(-0.664911\pi\) | ||||
−0.495215 | + | 0.868770i | \(0.664911\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 31.2132i | 1.13747i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 42.8284i | 1.55663i | 0.627877 | + | 0.778313i | \(0.283924\pi\) | ||||
−0.627877 | + | 0.778313i | \(0.716076\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 15.0711 | 0.547045 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −34.8701 | −1.26404 | −0.632019 | − | 0.774953i | \(-0.717774\pi\) | ||||
−0.632019 | + | 0.774953i | \(0.717774\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 3.75736i | 0.135670i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −0.142136 | −0.00512554 | −0.00256277 | − | 0.999997i | \(-0.500816\pi\) | ||||
−0.00256277 | + | 0.999997i | \(0.500816\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 33.3137 | 1.19976 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − 18.2721i | − 0.657201i | −0.944469 | − | 0.328600i | \(-0.893423\pi\) | ||||
0.944469 | − | 0.328600i | \(-0.106577\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 26.1421 | 0.936639 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −19.1716 | −0.686013 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 1.92893i | 0.0689344i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 18.2721i | 0.651329i | 0.945485 | + | 0.325665i | \(0.105588\pi\) | ||||
−0.945485 | + | 0.325665i | \(0.894412\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 24.1421 | 0.859483 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − 69.4558i | − 2.46645i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − 1.38478i | − 0.0490513i | −0.999699 | − | 0.0245256i | \(-0.992192\pi\) | ||||
0.999699 | − | 0.0245256i | \(-0.00780754\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −39.0833 | −1.38267 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 48.0000 | 1.69600 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 19.7990i | 0.698691i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 21.0711i | 0.741737i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −39.9706 | −1.40529 | −0.702645 | − | 0.711541i | \(-0.747998\pi\) | ||||
−0.702645 | + | 0.711541i | \(0.747998\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −11.5563 | −0.405798 | −0.202899 | − | 0.979200i | \(-0.565036\pi\) | ||||
−0.202899 | + | 0.979200i | \(0.565036\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 12.0000i | 0.420858i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2.62742i | 0.0919217i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 42.1716 | 1.47180 | 0.735899 | − | 0.677091i | \(-0.236760\pi\) | ||||
0.735899 | + | 0.677091i | \(0.236760\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 28.5269i | 0.994386i | 0.867640 | + | 0.497193i | \(0.165636\pi\) | ||||
−0.867640 | + | 0.497193i | \(0.834364\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 38.0416i | 1.32284i | 0.750017 | + | 0.661419i | \(0.230045\pi\) | ||||
−0.750017 | + | 0.661419i | \(0.769955\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −2.72792 | −0.0947446 | −0.0473723 | − | 0.998877i | \(-0.515085\pi\) | ||||
−0.0473723 | + | 0.998877i | \(0.515085\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 11.0711 | 0.384051 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − 3.07107i | − 0.106152i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −14.3848 | −0.496618 | −0.248309 | − | 0.968681i | \(-0.579875\pi\) | ||||
−0.248309 | + | 0.968681i | \(0.579875\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −7.31371 | −0.252197 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − 2.41421i | − 0.0831499i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 65.7696 | 2.25721 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −2.00000 | −0.0685591 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 26.2843i | 0.899956i | 0.893040 | + | 0.449978i | \(0.148568\pi\) | ||||
−0.893040 | + | 0.449978i | \(0.851432\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 15.1716i | 0.518251i | 0.965844 | + | 0.259126i | \(0.0834343\pi\) | ||||
−0.965844 | + | 0.259126i | \(0.916566\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 5.45584 | 0.186151 | 0.0930755 | − | 0.995659i | \(-0.470330\pi\) | ||||
0.0930755 | + | 0.995659i | \(0.470330\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 28.2426i | 0.961391i | 0.876888 | + | 0.480695i | \(0.159616\pi\) | ||||
−0.876888 | + | 0.480695i | \(0.840384\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 10.0000i | 0.339618i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 27.6863 | 0.939193 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −19.6985 | −0.667458 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − 27.5147i | − 0.931232i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 33.3137i | 1.12492i | 0.826823 | + | 0.562462i | \(0.190146\pi\) | ||||
−0.826823 | + | 0.562462i | \(0.809854\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 27.9706 | 0.943424 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −0.284271 | −0.00957734 | −0.00478867 | − | 0.999989i | \(-0.501524\pi\) | ||||
−0.00478867 | + | 0.999989i | \(0.501524\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 55.1127i | − 1.85469i | −0.374208 | − | 0.927345i | \(-0.622085\pi\) | ||||
0.374208 | − | 0.927345i | \(-0.377915\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 21.5980i | 0.725189i | 0.931947 | + | 0.362595i | \(0.118109\pi\) | ||||
−0.931947 | + | 0.362595i | \(0.881891\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −17.3431 | −0.581017 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 83.4558i | 2.79274i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 52.8701i | 1.76528i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −34.5269 | −1.15154 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 43.8995 | 1.46250 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − 42.5269i | − 1.41208i | −0.708170 | − | 0.706041i | \(-0.750479\pi\) | ||||
0.708170 | − | 0.706041i | \(-0.249521\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 2.34315 | 0.0777172 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 23.5980 | 0.781836 | 0.390918 | − | 0.920426i | \(-0.372158\pi\) | ||||
0.390918 | + | 0.920426i | \(0.372158\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − 14.6274i | − 0.484097i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 35.4853 | 1.17055 | 0.585276 | − | 0.810834i | \(-0.300986\pi\) | ||||
0.585276 | + | 0.810834i | \(0.300986\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 15.4853 | 0.510257 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − 67.2548i | − 2.21372i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | − 12.4853i | − 0.410070i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −46.7279 | −1.53309 | −0.766547 | − | 0.642189i | \(-0.778027\pi\) | ||||
−0.766547 | + | 0.642189i | \(0.778027\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 65.1127i | 2.13169i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − 17.7279i | − 0.579146i | −0.957156 | − | 0.289573i | \(-0.906487\pi\) | ||||
0.957156 | − | 0.289573i | \(-0.0935133\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 35.1421 | 1.14682 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 4.00000 | 0.130396 | 0.0651981 | − | 0.997872i | \(-0.479232\pi\) | ||||
0.0651981 | + | 0.997872i | \(0.479232\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 11.6569i | 0.379599i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 16.0416i | 0.521283i | 0.965436 | + | 0.260641i | \(0.0839340\pi\) | ||||
−0.965436 | + | 0.260641i | \(0.916066\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −69.4558 | −2.25463 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −45.7990 | −1.48513 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − 14.8701i | − 0.481688i | −0.970564 | − | 0.240844i | \(-0.922576\pi\) | ||||
0.970564 | − | 0.240844i | \(-0.0774243\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 20.5563i | 0.664492i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 23.9706 | 0.773244 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 31.5980i | 1.01823i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 43.4558i | 1.39745i | 0.715392 | + | 0.698723i | \(0.246248\pi\) | ||||
−0.715392 | + | 0.698723i | \(0.753752\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −66.2843 | −2.12936 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −42.5269 | −1.36475 | −0.682377 | − | 0.731001i | \(-0.739054\pi\) | ||||
−0.682377 | + | 0.731001i | \(0.739054\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 20.1421i | 0.644404i | 0.946671 | + | 0.322202i | \(0.104423\pi\) | ||||
−0.946671 | + | 0.322202i | \(0.895577\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −31.0294 | −0.991705 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 25.4558 | 0.812743 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 40.0122i | 1.27619i | 0.769957 | + | 0.638095i | \(0.220277\pi\) | ||||
−0.769957 | + | 0.638095i | \(0.779723\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −1.17157 | −0.0372539 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 2.68629 | 0.0853329 | 0.0426664 | − | 0.999089i | \(-0.486415\pi\) | ||||
0.0426664 | + | 0.999089i | \(0.486415\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − 2.00000i | − 0.0634681i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 36.8406i | − 1.16675i | −0.812201 | − | 0.583377i | \(-0.801731\pi\) | ||||
0.812201 | − | 0.583377i | \(-0.198269\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0.242641 | 0.00767681 |
(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 | 4900.2.e.q.2549.4 | 4 | ||
5.2 | odd | 4 | 4900.2.a.z.1.2 | 2 | |||
5.3 | odd | 4 | 980.2.a.j.1.1 | ✓ | 2 | ||
5.4 | even | 2 | inner | 4900.2.e.q.2549.1 | 4 | ||
7.6 | odd | 2 | 4900.2.e.r.2549.1 | 4 | |||
15.8 | even | 4 | 8820.2.a.bg.1.1 | 2 | |||
20.3 | even | 4 | 3920.2.a.bx.1.2 | 2 | |||
35.3 | even | 12 | 980.2.i.k.961.1 | 4 | |||
35.13 | even | 4 | 980.2.a.k.1.2 | yes | 2 | ||
35.18 | odd | 12 | 980.2.i.l.961.2 | 4 | |||
35.23 | odd | 12 | 980.2.i.l.361.2 | 4 | |||
35.27 | even | 4 | 4900.2.a.x.1.1 | 2 | |||
35.33 | even | 12 | 980.2.i.k.361.1 | 4 | |||
35.34 | odd | 2 | 4900.2.e.r.2549.4 | 4 | |||
105.83 | odd | 4 | 8820.2.a.bl.1.1 | 2 | |||
140.83 | odd | 4 | 3920.2.a.bo.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
980.2.a.j.1.1 | ✓ | 2 | 5.3 | odd | 4 | ||
980.2.a.k.1.2 | yes | 2 | 35.13 | even | 4 | ||
980.2.i.k.361.1 | 4 | 35.33 | even | 12 | |||
980.2.i.k.961.1 | 4 | 35.3 | even | 12 | |||
980.2.i.l.361.2 | 4 | 35.23 | odd | 12 | |||
980.2.i.l.961.2 | 4 | 35.18 | odd | 12 | |||
3920.2.a.bo.1.1 | 2 | 140.83 | odd | 4 | |||
3920.2.a.bx.1.2 | 2 | 20.3 | even | 4 | |||
4900.2.a.x.1.1 | 2 | 35.27 | even | 4 | |||
4900.2.a.z.1.2 | 2 | 5.2 | odd | 4 | |||
4900.2.e.q.2549.1 | 4 | 5.4 | even | 2 | inner | ||
4900.2.e.q.2549.4 | 4 | 1.1 | even | 1 | trivial | ||
4900.2.e.r.2549.1 | 4 | 7.6 | odd | 2 | |||
4900.2.e.r.2549.4 | 4 | 35.34 | odd | 2 | |||
8820.2.a.bg.1.1 | 2 | 15.8 | even | 4 | |||
8820.2.a.bl.1.1 | 2 | 105.83 | odd | 4 |