Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1089,3,Mod(485,1089)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1089, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1089.485");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1089 = 3^{2} \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1089.b (of order \(2\), degree \(1\), 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: | \(29.6731007888\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 48x^{14} + 921x^{12} + 8986x^{10} + 46812x^{8} + 125072x^{6} + 152129x^{4} + 65614x^{2} + 5041 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{2}\cdot 3^{4} \) |
Twist minimal: | no (minimal twist has level 99) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 485.9 | ||
Root | \(0.311356i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1089.485 |
Dual form | 1089.3.b.j.485.8 |
$q$-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 \(\left(\mathbb{Z}/1089\mathbb{Z}\right)^\times\).
\(n\) | \(244\) | \(848\) |
\(\chi(n)\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.311356i | 0.155678i | 0.996966 | + | 0.0778391i | \(0.0248020\pi\) | ||||
−0.996966 | + | 0.0778391i | \(0.975198\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 3.90306 | 0.975764 | ||||||||
\(5\) | − 5.94641i | − 1.18928i | −0.803992 | − | 0.594641i | \(-0.797294\pi\) | ||||
0.803992 | − | 0.594641i | \(-0.202706\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −8.67101 | −1.23872 | −0.619358 | − | 0.785109i | \(-0.712607\pi\) | ||||
−0.619358 | + | 0.785109i | \(0.712607\pi\) | |||||||
\(8\) | 2.46067i | 0.307583i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 1.85145 | 0.185145 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −18.6982 | −1.43832 | −0.719162 | − | 0.694842i | \(-0.755474\pi\) | ||||
−0.719162 | + | 0.694842i | \(0.755474\pi\) | |||||||
\(14\) | − 2.69977i | − 0.192841i | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 14.8461 | 0.927880 | ||||||||
\(17\) | 9.59948i | 0.564675i | 0.959315 | + | 0.282338i | \(0.0911098\pi\) | ||||
−0.959315 | + | 0.282338i | \(0.908890\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −5.76332 | −0.303333 | −0.151666 | − | 0.988432i | \(-0.548464\pi\) | ||||
−0.151666 | + | 0.988432i | \(0.548464\pi\) | |||||||
\(20\) | − 23.2092i | − 1.16046i | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 41.5830i | 1.80796i | 0.427578 | + | 0.903979i | \(0.359367\pi\) | ||||
−0.427578 | + | 0.903979i | \(0.640633\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −10.3598 | −0.414390 | ||||||||
\(26\) | − 5.82181i | − 0.223916i | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −33.8434 | −1.20869 | ||||||||
\(29\) | − 17.3733i | − 0.599078i | −0.954084 | − | 0.299539i | \(-0.903167\pi\) | ||||
0.954084 | − | 0.299539i | \(-0.0968329\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −13.6771 | −0.441198 | −0.220599 | − | 0.975365i | \(-0.570801\pi\) | ||||
−0.220599 | + | 0.975365i | \(0.570801\pi\) | |||||||
\(32\) | 14.4651i | 0.452034i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −2.98886 | −0.0879076 | ||||||||
\(35\) | 51.5613i | 1.47318i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −7.21391 | −0.194970 | −0.0974852 | − | 0.995237i | \(-0.531080\pi\) | ||||
−0.0974852 | + | 0.995237i | \(0.531080\pi\) | |||||||
\(38\) | − 1.79445i | − 0.0472223i | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 14.6321 | 0.365803 | ||||||||
\(41\) | 53.1361i | 1.29600i | 0.761640 | + | 0.648001i | \(0.224395\pi\) | ||||
−0.761640 | + | 0.648001i | \(0.775605\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −43.3682 | −1.00856 | −0.504282 | − | 0.863539i | \(-0.668243\pi\) | ||||
−0.504282 | + | 0.863539i | \(0.668243\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −12.9471 | −0.281459 | ||||||||
\(47\) | 18.8439i | 0.400934i | 0.979700 | + | 0.200467i | \(0.0642460\pi\) | ||||
−0.979700 | + | 0.200467i | \(0.935754\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 26.1864 | 0.534416 | ||||||||
\(50\) | − 3.22558i | − 0.0645115i | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −72.9802 | −1.40347 | ||||||||
\(53\) | 54.5516i | 1.02928i | 0.857408 | + | 0.514638i | \(0.172074\pi\) | ||||
−0.857408 | + | 0.514638i | \(0.827926\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | − 21.3365i | − 0.381008i | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 5.40928 | 0.0932634 | ||||||||
\(59\) | 35.3312i | 0.598833i | 0.954122 | + | 0.299417i | \(0.0967920\pi\) | ||||
−0.954122 | + | 0.299417i | \(0.903208\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 117.852 | 1.93201 | 0.966004 | − | 0.258528i | \(-0.0832375\pi\) | ||||
0.966004 | + | 0.258528i | \(0.0832375\pi\) | |||||||
\(62\) | − 4.25847i | − 0.0686849i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 54.8805 | 0.857508 | ||||||||
\(65\) | 111.187i | 1.71057i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −91.5111 | −1.36584 | −0.682919 | − | 0.730494i | \(-0.739290\pi\) | ||||
−0.682919 | + | 0.730494i | \(0.739290\pi\) | |||||||
\(68\) | 37.4673i | 0.550990i | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −16.0540 | −0.229342 | ||||||||
\(71\) | − 115.816i | − 1.63120i | −0.578613 | − | 0.815602i | \(-0.696406\pi\) | ||||
0.578613 | − | 0.815602i | \(-0.303594\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 52.9453 | 0.725278 | 0.362639 | − | 0.931930i | \(-0.381876\pi\) | ||||
0.362639 | + | 0.931930i | \(0.381876\pi\) | |||||||
\(74\) | − 2.24610i | − 0.0303526i | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −22.4946 | −0.295981 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −2.04912 | −0.0259383 | −0.0129691 | − | 0.999916i | \(-0.504128\pi\) | ||||
−0.0129691 | + | 0.999916i | \(0.504128\pi\) | |||||||
\(80\) | − 88.2809i | − 1.10351i | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −16.5443 | −0.201759 | ||||||||
\(83\) | − 28.8194i | − 0.347222i | −0.984814 | − | 0.173611i | \(-0.944457\pi\) | ||||
0.984814 | − | 0.173611i | \(-0.0555435\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 57.0824 | 0.671558 | ||||||||
\(86\) | − 13.5030i | − 0.157011i | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 134.980i | 1.51663i | 0.651891 | + | 0.758313i | \(0.273976\pi\) | ||||
−0.651891 | + | 0.758313i | \(0.726024\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 162.132 | 1.78168 | ||||||||
\(92\) | 162.301i | 1.76414i | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −5.86717 | −0.0624168 | ||||||||
\(95\) | 34.2710i | 0.360748i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −9.97627 | −0.102848 | −0.0514241 | − | 0.998677i | \(-0.516376\pi\) | ||||
−0.0514241 | + | 0.998677i | \(0.516376\pi\) | |||||||
\(98\) | 8.15330i | 0.0831970i | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −40.4347 | −0.404347 | ||||||||
\(101\) | 172.426i | 1.70719i | 0.520939 | + | 0.853594i | \(0.325582\pi\) | ||||
−0.520939 | + | 0.853594i | \(0.674418\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −113.639 | −1.10329 | −0.551643 | − | 0.834080i | \(-0.685999\pi\) | ||||
−0.551643 | + | 0.834080i | \(0.685999\pi\) | |||||||
\(104\) | − 46.0101i | − 0.442405i | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −16.9850 | −0.160236 | ||||||||
\(107\) | − 83.1724i | − 0.777312i | −0.921383 | − | 0.388656i | \(-0.872939\pi\) | ||||
0.921383 | − | 0.388656i | \(-0.127061\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −125.432 | −1.15075 | −0.575377 | − | 0.817888i | \(-0.695145\pi\) | ||||
−0.575377 | + | 0.817888i | \(0.695145\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −128.731 | −1.14938 | ||||||||
\(113\) | − 101.186i | − 0.895451i | −0.894171 | − | 0.447726i | \(-0.852234\pi\) | ||||
0.894171 | − | 0.447726i | \(-0.147766\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 247.270 | 2.15017 | ||||||||
\(116\) | − 67.8089i | − 0.584559i | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −11.0006 | −0.0932252 | ||||||||
\(119\) | − 83.2372i | − 0.699472i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | 36.6941i | 0.300771i | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −53.3827 | −0.430505 | ||||||||
\(125\) | − 87.0569i | − 0.696455i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −123.996 | −0.976346 | −0.488173 | − | 0.872747i | \(-0.662337\pi\) | ||||
−0.488173 | + | 0.872747i | \(0.662337\pi\) | |||||||
\(128\) | 74.9478i | 0.585529i | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −34.6189 | −0.266299 | ||||||||
\(131\) | 52.5607i | 0.401227i | 0.979670 | + | 0.200614i | \(0.0642935\pi\) | ||||
−0.979670 | + | 0.200614i | \(0.935706\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 49.9738 | 0.375743 | ||||||||
\(134\) | − 28.4926i | − 0.212631i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −23.6211 | −0.173685 | ||||||||
\(137\) | − 125.783i | − 0.918121i | −0.888405 | − | 0.459060i | \(-0.848186\pi\) | ||||
0.888405 | − | 0.459060i | \(-0.151814\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −53.6460 | −0.385943 | −0.192971 | − | 0.981204i | \(-0.561812\pi\) | ||||
−0.192971 | + | 0.981204i | \(0.561812\pi\) | |||||||
\(140\) | 201.247i | 1.43748i | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 36.0599 | 0.253943 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −103.309 | −0.712473 | ||||||||
\(146\) | 16.4848i | 0.112910i | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −28.1563 | −0.190245 | ||||||||
\(149\) | − 4.23732i | − 0.0284384i | −0.999899 | − | 0.0142192i | \(-0.995474\pi\) | ||||
0.999899 | − | 0.0142192i | \(-0.00452626\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −94.3874 | −0.625082 | −0.312541 | − | 0.949904i | \(-0.601180\pi\) | ||||
−0.312541 | + | 0.949904i | \(0.601180\pi\) | |||||||
\(152\) | − 14.1816i | − 0.0933001i | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 81.3299i | 0.524709i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −148.683 | −0.947028 | −0.473514 | − | 0.880786i | \(-0.657015\pi\) | ||||
−0.473514 | + | 0.880786i | \(0.657015\pi\) | |||||||
\(158\) | − 0.638008i | − 0.00403802i | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 86.0153 | 0.537596 | ||||||||
\(161\) | − 360.567i | − 2.23954i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −91.7512 | −0.562891 | −0.281445 | − | 0.959577i | \(-0.590814\pi\) | ||||
−0.281445 | + | 0.959577i | \(0.590814\pi\) | |||||||
\(164\) | 207.393i | 1.26459i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 8.97310 | 0.0540548 | ||||||||
\(167\) | 14.2677i | 0.0854351i | 0.999087 | + | 0.0427175i | \(0.0136016\pi\) | ||||
−0.999087 | + | 0.0427175i | \(0.986398\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 180.623 | 1.06878 | ||||||||
\(170\) | 17.7730i | 0.104547i | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −169.269 | −0.984120 | ||||||||
\(173\) | 232.280i | 1.34266i | 0.741158 | + | 0.671331i | \(0.234277\pi\) | ||||
−0.741158 | + | 0.671331i | \(0.765723\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 89.8295 | 0.513312 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −42.0268 | −0.236105 | ||||||||
\(179\) | 143.658i | 0.802560i | 0.915956 | + | 0.401280i | \(0.131434\pi\) | ||||
−0.915956 | + | 0.401280i | \(0.868566\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −239.706 | −1.32434 | −0.662171 | − | 0.749353i | \(-0.730365\pi\) | ||||
−0.662171 | + | 0.749353i | \(0.730365\pi\) | |||||||
\(182\) | 50.4810i | 0.277368i | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −102.322 | −0.556098 | ||||||||
\(185\) | 42.8968i | 0.231875i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 73.5489i | 0.391218i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −10.6705 | −0.0561606 | ||||||||
\(191\) | − 37.5317i | − 0.196501i | −0.995162 | − | 0.0982506i | \(-0.968675\pi\) | ||||
0.995162 | − | 0.0982506i | \(-0.0313247\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −203.572 | −1.05478 | −0.527389 | − | 0.849624i | \(-0.676829\pi\) | ||||
−0.527389 | + | 0.849624i | \(0.676829\pi\) | |||||||
\(194\) | − 3.10617i | − 0.0160112i | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 102.207 | 0.521464 | ||||||||
\(197\) | − 208.477i | − 1.05826i | −0.848541 | − | 0.529129i | \(-0.822519\pi\) | ||||
0.848541 | − | 0.529129i | \(-0.177481\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −249.874 | −1.25565 | −0.627825 | − | 0.778355i | \(-0.716055\pi\) | ||||
−0.627825 | + | 0.778355i | \(0.716055\pi\) | |||||||
\(200\) | − 25.4919i | − 0.127460i | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −53.6859 | −0.265772 | ||||||||
\(203\) | 150.644i | 0.742088i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 315.969 | 1.54131 | ||||||||
\(206\) | − 35.3821i | − 0.171758i | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −277.595 | −1.33459 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −121.553 | −0.576081 | −0.288040 | − | 0.957618i | \(-0.593004\pi\) | ||||
−0.288040 | + | 0.957618i | \(0.593004\pi\) | |||||||
\(212\) | 212.918i | 1.00433i | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 25.8963 | 0.121011 | ||||||||
\(215\) | 257.885i | 1.19947i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 118.595 | 0.546519 | ||||||||
\(218\) | − 39.0541i | − 0.179147i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − 179.493i | − 0.812186i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −71.8121 | −0.322027 | −0.161014 | − | 0.986952i | \(-0.551476\pi\) | ||||
−0.161014 | + | 0.986952i | \(0.551476\pi\) | |||||||
\(224\) | − 125.427i | − 0.559942i | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 31.5049 | 0.139402 | ||||||||
\(227\) | 234.045i | 1.03104i | 0.856879 | + | 0.515518i | \(0.172400\pi\) | ||||
−0.856879 | + | 0.515518i | \(0.827600\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 68.1310 | 0.297515 | 0.148758 | − | 0.988874i | \(-0.452473\pi\) | ||||
0.148758 | + | 0.988874i | \(0.452473\pi\) | |||||||
\(230\) | 76.9889i | 0.334735i | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 42.7498 | 0.184267 | ||||||||
\(233\) | 106.735i | 0.458090i | 0.973416 | + | 0.229045i | \(0.0735603\pi\) | ||||
−0.973416 | + | 0.229045i | \(0.926440\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 112.054 | 0.476824 | ||||||||
\(236\) | 137.900i | 0.584320i | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 25.9164 | 0.108893 | ||||||||
\(239\) | − 348.588i | − 1.45853i | −0.684232 | − | 0.729265i | \(-0.739862\pi\) | ||||
0.684232 | − | 0.729265i | \(-0.260138\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 377.429 | 1.56609 | 0.783047 | − | 0.621962i | \(-0.213664\pi\) | ||||
0.783047 | + | 0.621962i | \(0.213664\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 459.985 | 1.88518 | ||||||||
\(245\) | − 155.715i | − 0.635571i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 107.764 | 0.436291 | ||||||||
\(248\) | − 33.6549i | − 0.135705i | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 27.1057 | 0.108423 | ||||||||
\(251\) | 301.660i | 1.20183i | 0.799311 | + | 0.600917i | \(0.205198\pi\) | ||||
−0.799311 | + | 0.600917i | \(0.794802\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | − 38.6069i | − 0.151996i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 196.187 | 0.766354 | ||||||||
\(257\) | − 14.9765i | − 0.0582743i | −0.999575 | − | 0.0291372i | \(-0.990724\pi\) | ||||
0.999575 | − | 0.0291372i | \(-0.00927596\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 62.5519 | 0.241513 | ||||||||
\(260\) | 433.970i | 1.66912i | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −16.3651 | −0.0624623 | ||||||||
\(263\) | − 470.671i | − 1.78962i | −0.446443 | − | 0.894812i | \(-0.647309\pi\) | ||||
0.446443 | − | 0.894812i | \(-0.352691\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 324.386 | 1.22410 | ||||||||
\(266\) | 15.5597i | 0.0584950i | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −357.173 | −1.33274 | ||||||||
\(269\) | − 199.826i | − 0.742848i | −0.928463 | − | 0.371424i | \(-0.878870\pi\) | ||||
0.928463 | − | 0.371424i | \(-0.121130\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 87.2697 | 0.322028 | 0.161014 | − | 0.986952i | \(-0.448524\pi\) | ||||
0.161014 | + | 0.986952i | \(0.448524\pi\) | |||||||
\(272\) | 142.515i | 0.523951i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 39.1632 | 0.142931 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 299.219 | 1.08021 | 0.540106 | − | 0.841597i | \(-0.318384\pi\) | ||||
0.540106 | + | 0.841597i | \(0.318384\pi\) | |||||||
\(278\) | − 16.7030i | − 0.0600828i | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −126.875 | −0.453126 | ||||||||
\(281\) | − 298.705i | − 1.06301i | −0.847056 | − | 0.531504i | \(-0.821627\pi\) | ||||
0.847056 | − | 0.531504i | \(-0.178373\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 204.517 | 0.722674 | 0.361337 | − | 0.932435i | \(-0.382320\pi\) | ||||
0.361337 | + | 0.932435i | \(0.382320\pi\) | |||||||
\(284\) | − 452.035i | − 1.59167i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − 460.743i | − 1.60538i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 196.850 | 0.681142 | ||||||||
\(290\) | − 32.1658i | − 0.110916i | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 206.648 | 0.707700 | ||||||||
\(293\) | − 102.843i | − 0.351001i | −0.984479 | − | 0.175500i | \(-0.943846\pi\) | ||||
0.984479 | − | 0.175500i | \(-0.0561543\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 210.093 | 0.712181 | ||||||||
\(296\) | − 17.7510i | − 0.0599697i | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 1.31932 | 0.00442724 | ||||||||
\(299\) | − 777.528i | − 2.60043i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 376.046 | 1.24932 | ||||||||
\(302\) | − 29.3881i | − 0.0973116i | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −85.5627 | −0.281456 | ||||||||
\(305\) | − 700.799i | − 2.29770i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −39.5643 | −0.128874 | −0.0644369 | − | 0.997922i | \(-0.520525\pi\) | ||||
−0.0644369 | + | 0.997922i | \(0.520525\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −25.3226 | −0.0816857 | ||||||||
\(311\) | − 139.455i | − 0.448407i | −0.974542 | − | 0.224203i | \(-0.928022\pi\) | ||||
0.974542 | − | 0.224203i | \(-0.0719780\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −226.078 | −0.722295 | −0.361148 | − | 0.932509i | \(-0.617615\pi\) | ||||
−0.361148 | + | 0.932509i | \(0.617615\pi\) | |||||||
\(314\) | − 46.2935i | − 0.147432i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −7.99784 | −0.0253096 | ||||||||
\(317\) | 352.182i | 1.11098i | 0.831522 | + | 0.555492i | \(0.187470\pi\) | ||||
−0.831522 | + | 0.555492i | \(0.812530\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | − 326.342i | − 1.01982i | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 112.265 | 0.348648 | ||||||||
\(323\) | − 55.3249i | − 0.171284i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 193.709 | 0.596028 | ||||||||
\(326\) | − 28.5673i | − 0.0876298i | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −130.750 | −0.398629 | ||||||||
\(329\) | − 163.396i | − 0.496644i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −84.8580 | −0.256369 | −0.128184 | − | 0.991750i | \(-0.540915\pi\) | ||||
−0.128184 | + | 0.991750i | \(0.540915\pi\) | |||||||
\(332\) | − 112.484i | − 0.338806i | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −4.44233 | −0.0133004 | ||||||||
\(335\) | 544.162i | 1.62437i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −527.174 | −1.56432 | −0.782158 | − | 0.623080i | \(-0.785881\pi\) | ||||
−0.782158 | + | 0.623080i | \(0.785881\pi\) | |||||||
\(338\) | 56.2383i | 0.166385i | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 222.796 | 0.655282 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 197.817 | 0.576726 | ||||||||
\(344\) | − 106.715i | − 0.310217i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −72.3220 | −0.209023 | ||||||||
\(347\) | 126.318i | 0.364029i | 0.983296 | + | 0.182015i | \(0.0582618\pi\) | ||||
−0.983296 | + | 0.182015i | \(0.941738\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 451.455 | 1.29357 | 0.646784 | − | 0.762673i | \(-0.276113\pi\) | ||||
0.646784 | + | 0.762673i | \(0.276113\pi\) | |||||||
\(350\) | 27.9690i | 0.0799114i | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 145.710i | 0.412775i | 0.978470 | + | 0.206388i | \(0.0661708\pi\) | ||||
−0.978470 | + | 0.206388i | \(0.933829\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −688.686 | −1.93996 | ||||||||
\(356\) | 526.833i | 1.47987i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −44.7289 | −0.124941 | ||||||||
\(359\) | − 429.208i | − 1.19557i | −0.801658 | − | 0.597783i | \(-0.796048\pi\) | ||||
0.801658 | − | 0.597783i | \(-0.203952\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −327.784 | −0.907989 | ||||||||
\(362\) | − 74.6339i | − 0.206171i | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 632.812 | 1.73850 | ||||||||
\(365\) | − 314.834i | − 0.862559i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 132.361 | 0.360658 | 0.180329 | − | 0.983606i | \(-0.442284\pi\) | ||||
0.180329 | + | 0.983606i | \(0.442284\pi\) | |||||||
\(368\) | 617.345i | 1.67757i | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −13.3562 | −0.0360978 | ||||||||
\(371\) | − 473.017i | − 1.27498i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 478.180 | 1.28198 | 0.640992 | − | 0.767547i | \(-0.278523\pi\) | ||||
0.640992 | + | 0.767547i | \(0.278523\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −46.3686 | −0.123321 | ||||||||
\(377\) | 324.849i | 0.861669i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −264.206 | −0.697113 | −0.348557 | − | 0.937288i | \(-0.613328\pi\) | ||||
−0.348557 | + | 0.937288i | \(0.613328\pi\) | |||||||
\(380\) | 133.762i | 0.352005i | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 11.6857 | 0.0305909 | ||||||||
\(383\) | 236.431i | 0.617313i | 0.951174 | + | 0.308657i | \(0.0998794\pi\) | ||||
−0.951174 | + | 0.308657i | \(0.900121\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | − 63.3834i | − 0.164206i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −38.9379 | −0.100356 | ||||||||
\(389\) | − 511.217i | − 1.31418i | −0.753811 | − | 0.657091i | \(-0.771787\pi\) | ||||
0.753811 | − | 0.657091i | \(-0.228213\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −399.175 | −1.02091 | ||||||||
\(392\) | 64.4360i | 0.164378i | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 64.9106 | 0.164748 | ||||||||
\(395\) | 12.1849i | 0.0308479i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 389.224 | 0.980413 | 0.490207 | − | 0.871606i | \(-0.336921\pi\) | ||||
0.490207 | + | 0.871606i | \(0.336921\pi\) | |||||||
\(398\) | − 77.7999i | − 0.195477i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −153.802 | −0.384504 | ||||||||
\(401\) | 226.050i | 0.563715i | 0.959456 | + | 0.281858i | \(0.0909506\pi\) | ||||
−0.959456 | + | 0.281858i | \(0.909049\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 255.738 | 0.634586 | ||||||||
\(404\) | 672.988i | 1.66581i | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −46.9039 | −0.115527 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 181.766 | 0.444415 | 0.222208 | − | 0.974999i | \(-0.428674\pi\) | ||||
0.222208 | + | 0.974999i | \(0.428674\pi\) | |||||||
\(410\) | 98.3789i | 0.239948i | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −443.538 | −1.07655 | ||||||||
\(413\) | − 306.357i | − 0.741784i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −171.372 | −0.412944 | ||||||||
\(416\) | − 270.471i | − 0.650172i | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 171.909i | 0.410284i | 0.978732 | + | 0.205142i | \(0.0657656\pi\) | ||||
−0.978732 | + | 0.205142i | \(0.934234\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −120.846 | −0.287046 | −0.143523 | − | 0.989647i | \(-0.545843\pi\) | ||||
−0.143523 | + | 0.989647i | \(0.545843\pi\) | |||||||
\(422\) | − 37.8463i | − 0.0896832i | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −134.233 | −0.316588 | ||||||||
\(425\) | − 99.4482i | − 0.233996i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1021.90 | −2.39321 | ||||||||
\(428\) | − 324.627i | − 0.758473i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −80.2942 | −0.186731 | ||||||||
\(431\) | − 474.296i | − 1.10045i | −0.835015 | − | 0.550227i | \(-0.814541\pi\) | ||||
0.835015 | − | 0.550227i | \(-0.185459\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 254.226 | 0.587127 | 0.293564 | − | 0.955940i | \(-0.405159\pi\) | ||||
0.293564 | + | 0.955940i | \(0.405159\pi\) | |||||||
\(434\) | 36.9252i | 0.0850811i | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −489.569 | −1.12286 | ||||||||
\(437\) | − 239.656i | − 0.548412i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −515.246 | −1.17368 | −0.586841 | − | 0.809703i | \(-0.699628\pi\) | ||||
−0.586841 | + | 0.809703i | \(0.699628\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 55.8863 | 0.126440 | ||||||||
\(443\) | 526.041i | 1.18745i | 0.804668 | + | 0.593726i | \(0.202344\pi\) | ||||
−0.804668 | + | 0.593726i | \(0.797656\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 802.644 | 1.80369 | ||||||||
\(446\) | − 22.3592i | − 0.0501326i | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −475.870 | −1.06221 | ||||||||
\(449\) | − 541.858i | − 1.20681i | −0.797435 | − | 0.603405i | \(-0.793810\pi\) | ||||
0.797435 | − | 0.603405i | \(-0.206190\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | − 394.935i | − 0.873749i | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −72.8714 | −0.160510 | ||||||||
\(455\) | − 964.106i | − 2.11891i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −122.430 | −0.267899 | −0.133950 | − | 0.990988i | \(-0.542766\pi\) | ||||
−0.133950 | + | 0.990988i | \(0.542766\pi\) | |||||||
\(458\) | 21.2130i | 0.0463166i | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 965.107 | 2.09806 | ||||||||
\(461\) | − 308.300i | − 0.668764i | −0.942438 | − | 0.334382i | \(-0.891472\pi\) | ||||
0.942438 | − | 0.334382i | \(-0.108528\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 369.654 | 0.798389 | 0.399195 | − | 0.916866i | \(-0.369290\pi\) | ||||
0.399195 | + | 0.916866i | \(0.369290\pi\) | |||||||
\(464\) | − 257.925i | − 0.555873i | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −33.2326 | −0.0713146 | ||||||||
\(467\) | 108.850i | 0.233084i | 0.993186 | + | 0.116542i | \(0.0371809\pi\) | ||||
−0.993186 | + | 0.116542i | \(0.962819\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 793.494 | 1.69188 | ||||||||
\(470\) | 34.8886i | 0.0742311i | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −86.9382 | −0.184191 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 59.7066 | 0.125698 | ||||||||
\(476\) | − 324.879i | − 0.682520i | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 108.535 | 0.227061 | ||||||||
\(479\) | 302.678i | 0.631897i | 0.948776 | + | 0.315948i | \(0.102323\pi\) | ||||
−0.948776 | + | 0.315948i | \(0.897677\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 134.887 | 0.280431 | ||||||||
\(482\) | 117.515i | 0.243807i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 59.3229i | 0.122315i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 464.193 | 0.953169 | 0.476584 | − | 0.879129i | \(-0.341875\pi\) | ||||
0.476584 | + | 0.879129i | \(0.341875\pi\) | |||||||
\(488\) | 289.996i | 0.594253i | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 48.4829 | 0.0989446 | ||||||||
\(491\) | 347.094i | 0.706913i | 0.935451 | + | 0.353456i | \(0.114994\pi\) | ||||
−0.935451 | + | 0.353456i | \(0.885006\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 166.774 | 0.338285 | ||||||||
\(494\) | 33.5530i | 0.0679210i | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −203.052 | −0.409379 | ||||||||
\(497\) | 1004.24i | 2.02060i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 454.952 | 0.911728 | 0.455864 | − | 0.890049i | \(-0.349330\pi\) | ||||
0.455864 | + | 0.890049i | \(0.349330\pi\) | |||||||
\(500\) | − 339.788i | − 0.679576i | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −93.9239 | −0.187099 | ||||||||
\(503\) | 414.477i | 0.824010i | 0.911182 | + | 0.412005i | \(0.135171\pi\) | ||||
−0.911182 | + | 0.412005i | \(0.864829\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1025.31 | 2.03033 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −483.963 | −0.952684 | ||||||||
\(509\) | 150.010i | 0.294714i | 0.989083 | + | 0.147357i | \(0.0470767\pi\) | ||||
−0.989083 | + | 0.147357i | \(0.952923\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −459.089 | −0.898413 | ||||||||
\(512\) | 360.875i | 0.704834i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 4.66303 | 0.00907204 | ||||||||
\(515\) | 675.741i | 1.31212i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 19.4759i | 0.0375983i | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −273.595 | −0.526144 | ||||||||
\(521\) | 437.080i | 0.838924i | 0.907773 | + | 0.419462i | \(0.137781\pi\) | ||||
−0.907773 | + | 0.419462i | \(0.862219\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 410.273 | 0.784461 | 0.392231 | − | 0.919867i | \(-0.371703\pi\) | ||||
0.392231 | + | 0.919867i | \(0.371703\pi\) | |||||||
\(524\) | 205.148i | 0.391503i | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 146.546 | 0.278605 | ||||||||
\(527\) | − 131.293i | − 0.249134i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1200.15 | −2.26871 | ||||||||
\(530\) | 101.000i | 0.190565i | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 195.051 | 0.366636 | ||||||||
\(533\) | − 993.550i | − 1.86407i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −494.577 | −0.924443 | ||||||||
\(536\) | − 225.178i | − 0.420109i | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 62.2171 | 0.115645 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 499.682 | 0.923626 | 0.461813 | − | 0.886977i | \(-0.347199\pi\) | ||||
0.461813 | + | 0.886977i | \(0.347199\pi\) | |||||||
\(542\) | 27.1720i | 0.0501328i | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −138.857 | −0.255252 | ||||||||
\(545\) | 745.871i | 1.36857i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 695.564 | 1.27160 | 0.635798 | − | 0.771855i | \(-0.280671\pi\) | ||||
0.635798 | + | 0.771855i | \(0.280671\pi\) | |||||||
\(548\) | − 490.936i | − 0.895869i | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 100.128i | 0.181720i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 17.7680 | 0.0321301 | ||||||||
\(554\) | 93.1637i | 0.168165i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −209.383 | −0.376589 | ||||||||
\(557\) | 433.734i | 0.778697i | 0.921091 | + | 0.389348i | \(0.127300\pi\) | ||||
−0.921091 | + | 0.389348i | \(0.872700\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 810.909 | 1.45064 | ||||||||
\(560\) | 765.484i | 1.36694i | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 93.0037 | 0.165487 | ||||||||
\(563\) | 672.668i | 1.19479i | 0.801946 | + | 0.597396i | \(0.203798\pi\) | ||||
−0.801946 | + | 0.597396i | \(0.796202\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −601.693 | −1.06494 | ||||||||
\(566\) | 63.6776i | 0.112505i | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 284.984 | 0.501732 | ||||||||
\(569\) | − 543.176i | − 0.954614i | −0.878737 | − | 0.477307i | \(-0.841613\pi\) | ||||
0.878737 | − | 0.477307i | \(-0.158387\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −607.861 | −1.06456 | −0.532278 | − | 0.846570i | \(-0.678664\pi\) | ||||
−0.532278 | + | 0.846570i | \(0.678664\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 143.455 | 0.249922 | ||||||||
\(575\) | − 430.790i | − 0.749200i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 131.051 | 0.227125 | 0.113562 | − | 0.993531i | \(-0.463774\pi\) | ||||
0.113562 | + | 0.993531i | \(0.463774\pi\) | |||||||
\(578\) | 61.2905i | 0.106039i | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −403.219 | −0.695205 | ||||||||
\(581\) | 249.893i | 0.430109i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 130.281i | 0.223083i | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 32.0209 | 0.0546431 | ||||||||
\(587\) | − 133.668i | − 0.227713i | −0.993497 | − | 0.113857i | \(-0.963680\pi\) | ||||
0.993497 | − | 0.113857i | \(-0.0363204\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 78.8257 | 0.133830 | ||||||||
\(590\) | 65.4139i | 0.110871i | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −107.098 | −0.180909 | ||||||||
\(593\) | − 164.004i | − 0.276567i | −0.990393 | − | 0.138283i | \(-0.955841\pi\) | ||||
0.990393 | − | 0.138283i | \(-0.0441585\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −494.962 | −0.831869 | ||||||||
\(596\) | − 16.5385i | − 0.0277492i | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 242.088 | 0.404830 | ||||||||
\(599\) | 42.8102i | 0.0714694i | 0.999361 | + | 0.0357347i | \(0.0113771\pi\) | ||||
−0.999361 | + | 0.0357347i | \(0.988623\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 311.489 | 0.518284 | 0.259142 | − | 0.965839i | \(-0.416560\pi\) | ||||
0.259142 | + | 0.965839i | \(0.416560\pi\) | |||||||
\(602\) | 117.084i | 0.194492i | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −368.399 | −0.609933 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −1126.14 | −1.85526 | −0.927631 | − | 0.373498i | \(-0.878158\pi\) | ||||
−0.927631 | + | 0.373498i | \(0.878158\pi\) | |||||||
\(608\) | − 83.3669i | − 0.137117i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 218.198 | 0.357702 | ||||||||
\(611\) | − 352.348i | − 0.576674i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −466.854 | −0.761589 | −0.380795 | − | 0.924660i | \(-0.624350\pi\) | ||||
−0.380795 | + | 0.924660i | \(0.624350\pi\) | |||||||
\(614\) | − 12.3186i | − 0.0200628i | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 130.650i | 0.211750i | 0.994379 | + | 0.105875i | \(0.0337644\pi\) | ||||
−0.994379 | + | 0.105875i | \(0.966236\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 1096.95 | 1.77214 | 0.886068 | − | 0.463555i | \(-0.153426\pi\) | ||||
0.886068 | + | 0.463555i | \(0.153426\pi\) | |||||||
\(620\) | 317.435i | 0.511992i | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 43.4200 | 0.0698072 | ||||||||
\(623\) | − 1170.41i | − 1.87867i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −776.669 | −1.24267 | ||||||||
\(626\) | − 70.3909i | − 0.112446i | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −580.320 | −0.924076 | ||||||||
\(629\) | − 69.2497i | − 0.110095i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1161.69 | −1.84102 | −0.920511 | − | 0.390716i | \(-0.872227\pi\) | ||||
−0.920511 | + | 0.390716i | \(0.872227\pi\) | |||||||
\(632\) | − 5.04221i | − 0.00797818i | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −109.654 | −0.172956 | ||||||||
\(635\) | 737.331i | 1.16115i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −489.639 | −0.768664 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 445.670 | 0.696359 | ||||||||
\(641\) | 387.958i | 0.605238i | 0.953112 | + | 0.302619i | \(0.0978610\pi\) | ||||
−0.953112 | + | 0.302619i | \(0.902139\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −115.275 | −0.179277 | −0.0896383 | − | 0.995974i | \(-0.528571\pi\) | ||||
−0.0896383 | + | 0.995974i | \(0.528571\pi\) | |||||||
\(644\) | − 1407.31i | − 2.18527i | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 17.2257 | 0.0266652 | ||||||||
\(647\) | 182.585i | 0.282203i | 0.989995 | + | 0.141101i | \(0.0450643\pi\) | ||||
−0.989995 | + | 0.141101i | \(0.954936\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 60.3125i | 0.0927885i | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −358.110 | −0.549249 | ||||||||
\(653\) | − 10.8119i | − 0.0165573i | −0.999966 | − | 0.00827865i | \(-0.997365\pi\) | ||||
0.999966 | − | 0.00827865i | \(-0.00263521\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 312.548 | 0.477172 | ||||||||
\(656\) | 788.863i | 1.20253i | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 50.8743 | 0.0773166 | ||||||||
\(659\) | 875.394i | 1.32837i | 0.747569 | + | 0.664184i | \(0.231221\pi\) | ||||
−0.747569 | + | 0.664184i | \(0.768779\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1015.92 | 1.53695 | 0.768475 | − | 0.639880i | \(-0.221016\pi\) | ||||
0.768475 | + | 0.639880i | \(0.221016\pi\) | |||||||
\(662\) | − 26.4211i | − 0.0399110i | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 70.9149 | 0.106800 | ||||||||
\(665\) | − 297.165i | − 0.446864i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 722.433 | 1.08311 | ||||||||
\(668\) | 55.6875i | 0.0833645i | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −169.428 | −0.252878 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 113.798 | 0.169091 | 0.0845454 | − | 0.996420i | \(-0.473056\pi\) | ||||
0.0845454 | + | 0.996420i | \(0.473056\pi\) | |||||||
\(674\) | − 164.139i | − 0.243530i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 704.984 | 1.04288 | ||||||||
\(677\) | − 853.302i | − 1.26042i | −0.776426 | − | 0.630208i | \(-0.782969\pi\) | ||||
0.776426 | − | 0.630208i | \(-0.217031\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 86.5043 | 0.127400 | ||||||||
\(680\) | 140.461i | 0.206560i | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 193.740i | 0.283661i | 0.989891 | + | 0.141830i | \(0.0452987\pi\) | ||||
−0.989891 | + | 0.141830i | \(0.954701\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −747.954 | −1.09190 | ||||||||
\(686\) | 61.5916i | 0.0897836i | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −643.848 | −0.935826 | ||||||||
\(689\) | − 1020.02i | − 1.48043i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −253.670 | −0.367106 | −0.183553 | − | 0.983010i | \(-0.558760\pi\) | ||||
−0.183553 | + | 0.983010i | \(0.558760\pi\) | |||||||
\(692\) | 906.604i | 1.31012i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −39.3300 | −0.0566714 | ||||||||
\(695\) | 319.001i | 0.458994i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −510.078 | −0.731820 | ||||||||
\(698\) | 140.563i | 0.201380i | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 350.610 | 0.500871 | ||||||||
\(701\) | 1139.33i | 1.62529i | 0.582760 | + | 0.812644i | \(0.301973\pi\) | ||||
−0.582760 | + | 0.812644i | \(0.698027\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 41.5761 | 0.0591409 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −45.3676 | −0.0642601 | ||||||||
\(707\) | − 1495.11i | − 2.11472i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 374.159 | 0.527728 | 0.263864 | − | 0.964560i | \(-0.415003\pi\) | ||||
0.263864 | + | 0.964560i | \(0.415003\pi\) | |||||||
\(710\) | − 214.427i | − 0.302010i | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −332.140 | −0.466489 | ||||||||
\(713\) | − 568.737i | − 0.797667i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 560.706i | 0.783109i | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 133.637 | 0.186124 | ||||||||
\(719\) | 757.515i | 1.05357i | 0.849999 | + | 0.526784i | \(0.176602\pi\) | ||||
−0.849999 | + | 0.526784i | \(0.823398\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 985.361 | 1.36666 | ||||||||
\(722\) | − 102.058i | − 0.141354i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −935.585 | −1.29224 | ||||||||
\(725\) | 179.983i | 0.248252i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 845.080 | 1.16242 | 0.581211 | − | 0.813753i | \(-0.302579\pi\) | ||||
0.581211 | + | 0.813753i | \(0.302579\pi\) | |||||||
\(728\) | 398.954i | 0.548014i | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 98.0256 | 0.134282 | ||||||||
\(731\) | − 416.312i | − 0.569511i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −1358.08 | −1.85278 | −0.926388 | − | 0.376570i | \(-0.877103\pi\) | ||||
−0.926388 | + | 0.376570i | \(0.877103\pi\) | |||||||
\(734\) | 41.2115i | 0.0561465i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −601.502 | −0.817258 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −801.192 | −1.08416 | −0.542078 | − | 0.840328i | \(-0.682362\pi\) | ||||
−0.542078 | + | 0.840328i | \(0.682362\pi\) | |||||||
\(740\) | 167.429i | 0.226255i | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 147.277 | 0.198487 | ||||||||
\(743\) | 893.596i | 1.20269i | 0.798991 | + | 0.601343i | \(0.205368\pi\) | ||||
−0.798991 | + | 0.601343i | \(0.794632\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −25.1968 | −0.0338213 | ||||||||
\(746\) | 148.884i | 0.199577i | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 721.189i | 0.962868i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 397.035 | 0.528676 | 0.264338 | − | 0.964430i | \(-0.414847\pi\) | ||||
0.264338 | + | 0.964430i | \(0.414847\pi\) | |||||||
\(752\) | 279.758i | 0.372019i | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −101.144 | −0.134143 | ||||||||
\(755\) | 561.266i | 0.743398i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 593.110 | 0.783500 | 0.391750 | − | 0.920072i | \(-0.371870\pi\) | ||||
0.391750 | + | 0.920072i | \(0.371870\pi\) | |||||||
\(758\) | − 82.2622i | − 0.108525i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −84.3296 | −0.110960 | ||||||||
\(761\) | − 409.540i | − 0.538160i | −0.963118 | − | 0.269080i | \(-0.913280\pi\) | ||||
0.963118 | − | 0.269080i | \(-0.0867196\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1087.62 | 1.42546 | ||||||||
\(764\) | − 146.488i | − 0.191739i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −73.6143 | −0.0961022 | ||||||||
\(767\) | − 660.630i | − 0.861316i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −119.029 | −0.154784 | −0.0773921 | − | 0.997001i | \(-0.524659\pi\) | ||||
−0.0773921 | + | 0.997001i | \(0.524659\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −794.553 | −1.02921 | ||||||||
\(773\) | 701.535i | 0.907548i | 0.891117 | + | 0.453774i | \(0.149923\pi\) | ||||
−0.891117 | + | 0.453774i | \(0.850077\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 141.692 | 0.182828 | ||||||||
\(776\) | − 24.5483i | − 0.0316344i | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 159.171 | 0.204590 | ||||||||
\(779\) | − 306.240i | − 0.393120i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | − 124.286i | − 0.158933i | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 388.766 | 0.495874 | ||||||||
\(785\) | 884.132i | 1.12628i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −1539.13 | −1.95569 | −0.977844 | − | 0.209336i | \(-0.932870\pi\) | ||||
−0.977844 | + | 0.209336i | \(0.932870\pi\) | |||||||
\(788\) | − 813.697i | − 1.03261i | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −3.79385 | −0.00480234 | ||||||||
\(791\) | 877.384i | 1.10921i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −2203.63 | −2.77885 | ||||||||
\(794\) | 121.187i | 0.152629i | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −975.273 | −1.22522 | ||||||||
\(797\) | − 989.760i | − 1.24186i | −0.783867 | − | 0.620928i | \(-0.786756\pi\) | ||||
0.783867 | − | 0.620928i | \(-0.213244\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −180.892 | −0.226398 | ||||||||
\(800\) | − 149.855i | − 0.187319i | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −70.3821 | −0.0877582 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −2144.08 | −2.66345 | ||||||||
\(806\) | 79.6257i | 0.0987912i | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −424.283 | −0.525103 | ||||||||
\(809\) | 94.1076i | 0.116326i | 0.998307 | + | 0.0581629i | \(0.0185243\pi\) | ||||
−0.998307 | + | 0.0581629i | \(0.981476\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 370.312 | 0.456612 | 0.228306 | − | 0.973589i | \(-0.426681\pi\) | ||||
0.228306 | + | 0.973589i | \(0.426681\pi\) | |||||||
\(812\) | 587.971i | 0.724103i | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 545.590i | 0.669436i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 249.945 | 0.305930 | ||||||||
\(818\) | 56.5940i | 0.0691858i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 1233.24 | 1.50396 | ||||||||
\(821\) | − 213.696i | − 0.260288i | −0.991495 | − | 0.130144i | \(-0.958456\pi\) | ||||
0.991495 | − | 0.130144i | \(-0.0415439\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 104.216 | 0.126630 | 0.0633148 | − | 0.997994i | \(-0.479833\pi\) | ||||
0.0633148 | + | 0.997994i | \(0.479833\pi\) | |||||||
\(824\) | − 279.627i | − 0.339353i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 95.3861 | 0.115480 | ||||||||
\(827\) | 1329.26i | 1.60732i | 0.595086 | + | 0.803662i | \(0.297118\pi\) | ||||
−0.595086 | + | 0.803662i | \(0.702882\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −350.092 | −0.422306 | −0.211153 | − | 0.977453i | \(-0.567722\pi\) | ||||
−0.211153 | + | 0.977453i | \(0.567722\pi\) | |||||||
\(830\) | − 53.3577i | − 0.0642864i | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −1026.17 | −1.23338 | ||||||||
\(833\) | 251.376i | 0.301772i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 84.8413 | 0.101606 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −53.5250 | −0.0638723 | ||||||||
\(839\) | − 1542.17i | − 1.83811i | −0.394132 | − | 0.919054i | \(-0.628955\pi\) | ||||
0.394132 | − | 0.919054i | \(-0.371045\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 539.169 | 0.641105 | ||||||||
\(842\) | − 37.6263i | − 0.0446868i | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −474.428 | −0.562119 | ||||||||
\(845\) | − 1074.06i | − 1.27108i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 809.878i | 0.955044i | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 30.9638 | 0.0364280 | ||||||||
\(851\) | − 299.976i | − 0.352498i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −53.1329 | −0.0622895 | −0.0311448 | − | 0.999515i | \(-0.509915\pi\) | ||||
−0.0311448 | + | 0.999515i | \(0.509915\pi\) | |||||||
\(854\) | − 318.175i | − 0.372570i | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 204.660 | 0.239088 | ||||||||
\(857\) | − 668.807i | − 0.780405i | −0.920729 | − | 0.390202i | \(-0.872405\pi\) | ||||
0.920729 | − | 0.390202i | \(-0.127595\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 192.579 | 0.224189 | 0.112095 | − | 0.993698i | \(-0.464244\pi\) | ||||
0.112095 | + | 0.993698i | \(0.464244\pi\) | |||||||
\(860\) | 1006.54i | 1.17040i | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 147.675 | 0.171317 | ||||||||
\(863\) | − 851.072i | − 0.986179i | −0.869979 | − | 0.493089i | \(-0.835868\pi\) | ||||
0.869979 | − | 0.493089i | \(-0.164132\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1381.23 | 1.59680 | ||||||||
\(866\) | 79.1549i | 0.0914029i | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 462.882 | 0.533274 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1711.10 | 1.96452 | ||||||||
\(872\) | − 308.647i | − 0.353953i | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 74.6185 | 0.0853758 | ||||||||
\(875\) | 754.871i | 0.862709i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −440.628 | −0.502427 | −0.251213 | − | 0.967932i | \(-0.580830\pi\) | ||||
−0.251213 | + | 0.967932i | \(0.580830\pi\) | |||||||
\(878\) | − 160.425i | − 0.182717i | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 448.427i | 0.508997i | 0.967073 | + | 0.254499i | \(0.0819104\pi\) | ||||
−0.967073 | + | 0.254499i | \(0.918090\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −310.831 | −0.352017 | −0.176009 | − | 0.984389i | \(-0.556319\pi\) | ||||
−0.176009 | + | 0.984389i | \(0.556319\pi\) | |||||||
\(884\) | − 700.572i | − 0.792502i | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −163.786 | −0.184860 | ||||||||
\(887\) | 1292.83i | 1.45754i | 0.684761 | + | 0.728768i | \(0.259907\pi\) | ||||
−0.684761 | + | 0.728768i | \(0.740093\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1075.17 | 1.20942 | ||||||||
\(890\) | 249.908i | 0.280796i | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −280.287 | −0.314223 | ||||||||
\(893\) | − 108.604i | − 0.121617i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 854.250 | 0.954469 | ||||||||
\(896\) | − 649.873i | − 0.725304i | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 168.711 | 0.187874 | ||||||||
\(899\) | 237.617i | 0.264312i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −523.667 | −0.581206 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 248.985 | 0.275426 | ||||||||
\(905\) | 1425.39i | 1.57501i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 815.519 | 0.899139 | 0.449570 | − | 0.893245i | \(-0.351577\pi\) | ||||
0.449570 | + | 0.893245i | \(0.351577\pi\) | |||||||
\(908\) | 913.491i | 1.00605i | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 300.180 | 0.329869 | ||||||||
\(911\) | − 243.043i | − 0.266787i | −0.991063 | − | 0.133393i | \(-0.957413\pi\) | ||||
0.991063 | − | 0.133393i | \(-0.0425874\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | − 38.1193i | − 0.0417061i | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 265.919 | 0.290305 | ||||||||
\(917\) | − 455.755i | − 0.497006i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 290.283 | 0.315868 | 0.157934 | − | 0.987450i | \(-0.449517\pi\) | ||||
0.157934 | + | 0.987450i | \(0.449517\pi\) | |||||||
\(920\) | 608.448i | 0.661357i | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 95.9913 | 0.104112 | ||||||||
\(923\) | 2165.54i | 2.34620i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 74.7343 | 0.0807938 | ||||||||
\(926\) | 115.094i | 0.124292i | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 251.306 | 0.270804 | ||||||||
\(929\) | 295.075i | 0.317627i | 0.987309 | + | 0.158813i | \(0.0507668\pi\) | ||||
−0.987309 | + | 0.158813i | \(0.949233\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −150.921 | −0.162106 | ||||||||
\(932\) | 416.593i | 0.446988i | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −33.8912 | −0.0362861 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 918.143 | 0.979875 | 0.489938 | − | 0.871758i | \(-0.337020\pi\) | ||||
0.489938 | + | 0.871758i | \(0.337020\pi\) | |||||||
\(938\) | 247.059i | 0.263389i | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 437.352 | 0.465268 | ||||||||
\(941\) | − 998.146i | − 1.06073i | −0.847770 | − | 0.530365i | \(-0.822055\pi\) | ||||
0.847770 | − | 0.530365i | \(-0.177945\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −2209.56 | −2.34312 | ||||||||
\(944\) | 524.529i | 0.555645i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − 780.779i | − 0.824476i | −0.911076 | − | 0.412238i | \(-0.864747\pi\) | ||||
0.911076 | − | 0.412238i | \(-0.135253\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −989.982 | −1.04318 | ||||||||
\(950\) | 18.5900i | 0.0195684i | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 204.819 | 0.215146 | ||||||||
\(953\) | 93.2267i | 0.0978245i | 0.998803 | + | 0.0489122i | \(0.0155755\pi\) | ||||
−0.998803 | + | 0.0489122i | \(0.984425\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −223.179 | −0.233695 | ||||||||
\(956\) | − 1360.56i | − 1.42318i | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −94.2409 | −0.0983725 | ||||||||
\(959\) | 1090.66i | 1.13729i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −773.936 | −0.805344 | ||||||||
\(962\) | 41.9980i | 0.0436570i | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 1473.13 | 1.52814 | ||||||||
\(965\) | 1210.52i | 1.25443i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −365.949 | −0.378437 | −0.189219 | − | 0.981935i | \(-0.560595\pi\) | ||||
−0.189219 | + | 0.981935i | \(0.560595\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −18.4706 | −0.0190418 | ||||||||
\(971\) | − 284.163i | − 0.292650i | −0.989237 | − | 0.146325i | \(-0.953256\pi\) | ||||
0.989237 | − | 0.146325i | \(-0.0467445\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 465.165 | 0.478073 | ||||||||
\(974\) | 144.529i | 0.148388i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 1749.65 | 1.79267 | ||||||||
\(977\) | 882.999i | 0.903786i | 0.892072 | + | 0.451893i | \(0.149251\pi\) | ||||
−0.892072 | + | 0.451893i | \(0.850749\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | − 607.765i | − 0.620168i | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −108.070 | −0.110051 | ||||||||
\(983\) | − 1364.76i | − 1.38836i | −0.719799 | − | 0.694182i | \(-0.755766\pi\) | ||||
0.719799 | − | 0.694182i | \(-0.244234\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −1239.69 | −1.25857 | ||||||||
\(986\) | 51.9262i | 0.0526635i | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 420.608 | 0.425717 | ||||||||
\(989\) | − 1803.38i | − 1.82344i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −842.288 | −0.849938 | −0.424969 | − | 0.905208i | \(-0.639715\pi\) | ||||
−0.424969 | + | 0.905208i | \(0.639715\pi\) | |||||||
\(992\) | − 197.841i | − 0.199437i | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −312.676 | −0.314563 | ||||||||
\(995\) | 1485.85i | 1.49332i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 366.417 | 0.367520 | 0.183760 | − | 0.982971i | \(-0.441173\pi\) | ||||
0.183760 | + | 0.982971i | \(0.441173\pi\) | |||||||
\(998\) | 141.652i | 0.141936i | ||||||||
\(999\) | 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 | 1089.3.b.j.485.9 | 16 | ||
3.2 | odd | 2 | inner | 1089.3.b.j.485.8 | 16 | ||
11.7 | odd | 10 | 99.3.l.a.71.5 | yes | 32 | ||
11.8 | odd | 10 | 99.3.l.a.53.4 | ✓ | 32 | ||
11.10 | odd | 2 | 1089.3.b.i.485.8 | 16 | |||
33.8 | even | 10 | 99.3.l.a.53.5 | yes | 32 | ||
33.29 | even | 10 | 99.3.l.a.71.4 | yes | 32 | ||
33.32 | even | 2 | 1089.3.b.i.485.9 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
99.3.l.a.53.4 | ✓ | 32 | 11.8 | odd | 10 | ||
99.3.l.a.53.5 | yes | 32 | 33.8 | even | 10 | ||
99.3.l.a.71.4 | yes | 32 | 33.29 | even | 10 | ||
99.3.l.a.71.5 | yes | 32 | 11.7 | odd | 10 | ||
1089.3.b.i.485.8 | 16 | 11.10 | odd | 2 | |||
1089.3.b.i.485.9 | 16 | 33.32 | even | 2 | |||
1089.3.b.j.485.8 | 16 | 3.2 | odd | 2 | inner | ||
1089.3.b.j.485.9 | 16 | 1.1 | even | 1 | trivial |