Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1150,2,Mod(599,1150)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1150, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("1150.599");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1150 = 2 \cdot 5^{2} \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1150.b (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: | \(9.18279623245\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(i, \sqrt{13})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 7x^{2} + 9 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 230) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 599.4 | ||
Root | \(2.30278i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1150.599 |
Dual form | 1150.2.b.f.599.1 |
$q$-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 \(\left(\mathbb{Z}/1150\mathbb{Z}\right)^\times\).
\(n\) | \(51\) | \(277\) |
\(\chi(n)\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000i | 0.707107i | ||||||||
\(3\) | 3.30278i | 1.90686i | 0.301617 | + | 0.953429i | \(0.402474\pi\) | ||||
−0.301617 | + | 0.953429i | \(0.597526\pi\) | |||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −3.30278 | −1.34835 | ||||||||
\(7\) | 0.302776i | 0.114438i | 0.998362 | + | 0.0572192i | \(0.0182234\pi\) | ||||
−0.998362 | + | 0.0572192i | \(0.981777\pi\) | |||||||
\(8\) | − 1.00000i | − 0.353553i | ||||||||
\(9\) | −7.90833 | −2.63611 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −5.30278 | −1.59885 | −0.799424 | − | 0.600768i | \(-0.794862\pi\) | ||||
−0.799424 | + | 0.600768i | \(0.794862\pi\) | |||||||
\(12\) | − 3.30278i | − 0.953429i | ||||||||
\(13\) | − 0.302776i | − 0.0839749i | −0.999118 | − | 0.0419874i | \(-0.986631\pi\) | ||||
0.999118 | − | 0.0419874i | \(-0.0133689\pi\) | |||||||
\(14\) | −0.302776 | −0.0809202 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 3.90833i | 0.947909i | 0.880549 | + | 0.473954i | \(0.157174\pi\) | ||||
−0.880549 | + | 0.473954i | \(0.842826\pi\) | |||||||
\(18\) | − 7.90833i | − 1.86401i | ||||||||
\(19\) | 4.90833 | 1.12605 | 0.563024 | − | 0.826441i | \(-0.309638\pi\) | ||||
0.563024 | + | 0.826441i | \(0.309638\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.00000 | −0.218218 | ||||||||
\(22\) | − 5.30278i | − 1.13056i | ||||||||
\(23\) | − 1.00000i | − 0.208514i | ||||||||
\(24\) | 3.30278 | 0.674176 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0.302776 | 0.0593792 | ||||||||
\(27\) | − 16.2111i | − 3.11983i | ||||||||
\(28\) | − 0.302776i | − 0.0572192i | ||||||||
\(29\) | −4.60555 | −0.855229 | −0.427615 | − | 0.903961i | \(-0.640646\pi\) | ||||
−0.427615 | + | 0.903961i | \(0.640646\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.90833 | 0.522351 | 0.261175 | − | 0.965291i | \(-0.415890\pi\) | ||||
0.261175 | + | 0.965291i | \(0.415890\pi\) | |||||||
\(32\) | 1.00000i | 0.176777i | ||||||||
\(33\) | − 17.5139i | − 3.04877i | ||||||||
\(34\) | −3.90833 | −0.670273 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 7.90833 | 1.31805 | ||||||||
\(37\) | − 8.00000i | − 1.31519i | −0.753371 | − | 0.657596i | \(-0.771573\pi\) | ||||
0.753371 | − | 0.657596i | \(-0.228427\pi\) | |||||||
\(38\) | 4.90833i | 0.796236i | ||||||||
\(39\) | 1.00000 | 0.160128 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −9.90833 | −1.54742 | −0.773710 | − | 0.633540i | \(-0.781601\pi\) | ||||
−0.773710 | + | 0.633540i | \(0.781601\pi\) | |||||||
\(42\) | − 1.00000i | − 0.154303i | ||||||||
\(43\) | 5.21110i | 0.794686i | 0.917670 | + | 0.397343i | \(0.130068\pi\) | ||||
−0.917670 | + | 0.397343i | \(0.869932\pi\) | |||||||
\(44\) | 5.30278 | 0.799424 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.00000 | 0.147442 | ||||||||
\(47\) | − 4.60555i | − 0.671789i | −0.941900 | − | 0.335894i | \(-0.890961\pi\) | ||||
0.941900 | − | 0.335894i | \(-0.109039\pi\) | |||||||
\(48\) | 3.30278i | 0.476715i | ||||||||
\(49\) | 6.90833 | 0.986904 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −12.9083 | −1.80753 | ||||||||
\(52\) | 0.302776i | 0.0419874i | ||||||||
\(53\) | 3.21110i | 0.441079i | 0.975378 | + | 0.220539i | \(0.0707818\pi\) | ||||
−0.975378 | + | 0.220539i | \(0.929218\pi\) | |||||||
\(54\) | 16.2111 | 2.20605 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0.302776 | 0.0404601 | ||||||||
\(57\) | 16.2111i | 2.14721i | ||||||||
\(58\) | − 4.60555i | − 0.604739i | ||||||||
\(59\) | 10.6056 | 1.38073 | 0.690363 | − | 0.723464i | \(-0.257451\pi\) | ||||
0.690363 | + | 0.723464i | \(0.257451\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −6.51388 | −0.834017 | −0.417008 | − | 0.908903i | \(-0.636921\pi\) | ||||
−0.417008 | + | 0.908903i | \(0.636921\pi\) | |||||||
\(62\) | 2.90833i | 0.369358i | ||||||||
\(63\) | − 2.39445i | − 0.301672i | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 17.5139 | 2.15581 | ||||||||
\(67\) | 4.00000i | 0.488678i | 0.969690 | + | 0.244339i | \(0.0785709\pi\) | ||||
−0.969690 | + | 0.244339i | \(0.921429\pi\) | |||||||
\(68\) | − 3.90833i | − 0.473954i | ||||||||
\(69\) | 3.30278 | 0.397607 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −12.6972 | −1.50688 | −0.753442 | − | 0.657515i | \(-0.771608\pi\) | ||||
−0.753442 | + | 0.657515i | \(0.771608\pi\) | |||||||
\(72\) | 7.90833i | 0.932005i | ||||||||
\(73\) | 15.8167i | 1.85120i | 0.378504 | + | 0.925600i | \(0.376439\pi\) | ||||
−0.378504 | + | 0.925600i | \(0.623561\pi\) | |||||||
\(74\) | 8.00000 | 0.929981 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −4.90833 | −0.563024 | ||||||||
\(77\) | − 1.60555i | − 0.182970i | ||||||||
\(78\) | 1.00000i | 0.113228i | ||||||||
\(79\) | −14.4222 | −1.62262 | −0.811312 | − | 0.584613i | \(-0.801246\pi\) | ||||
−0.811312 | + | 0.584613i | \(0.801246\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 29.8167 | 3.31296 | ||||||||
\(82\) | − 9.90833i | − 1.09419i | ||||||||
\(83\) | − 3.21110i | − 0.352464i | −0.984349 | − | 0.176232i | \(-0.943609\pi\) | ||||
0.984349 | − | 0.176232i | \(-0.0563909\pi\) | |||||||
\(84\) | 1.00000 | 0.109109 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −5.21110 | −0.561928 | ||||||||
\(87\) | − 15.2111i | − 1.63080i | ||||||||
\(88\) | 5.30278i | 0.565278i | ||||||||
\(89\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.0916731 | 0.00960995 | ||||||||
\(92\) | 1.00000i | 0.104257i | ||||||||
\(93\) | 9.60555i | 0.996049i | ||||||||
\(94\) | 4.60555 | 0.475026 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −3.30278 | −0.337088 | ||||||||
\(97\) | − 2.69722i | − 0.273862i | −0.990581 | − | 0.136931i | \(-0.956276\pi\) | ||||
0.990581 | − | 0.136931i | \(-0.0437238\pi\) | |||||||
\(98\) | 6.90833i | 0.697846i | ||||||||
\(99\) | 41.9361 | 4.21473 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −4.60555 | −0.458269 | −0.229135 | − | 0.973395i | \(-0.573590\pi\) | ||||
−0.229135 | + | 0.973395i | \(0.573590\pi\) | |||||||
\(102\) | − 12.9083i | − 1.27811i | ||||||||
\(103\) | − 17.1194i | − 1.68683i | −0.537265 | − | 0.843414i | \(-0.680542\pi\) | ||||
0.537265 | − | 0.843414i | \(-0.319458\pi\) | |||||||
\(104\) | −0.302776 | −0.0296896 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −3.21110 | −0.311890 | ||||||||
\(107\) | − 4.60555i | − 0.445235i | −0.974906 | − | 0.222618i | \(-0.928540\pi\) | ||||
0.974906 | − | 0.222618i | \(-0.0714602\pi\) | |||||||
\(108\) | 16.2111i | 1.55991i | ||||||||
\(109\) | −19.5139 | −1.86909 | −0.934545 | − | 0.355844i | \(-0.884193\pi\) | ||||
−0.934545 | + | 0.355844i | \(0.884193\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 26.4222 | 2.50788 | ||||||||
\(112\) | 0.302776i | 0.0286096i | ||||||||
\(113\) | 12.4222i | 1.16858i | 0.811544 | + | 0.584291i | \(0.198627\pi\) | ||||
−0.811544 | + | 0.584291i | \(0.801373\pi\) | |||||||
\(114\) | −16.2111 | −1.51831 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 4.60555 | 0.427615 | ||||||||
\(117\) | 2.39445i | 0.221367i | ||||||||
\(118\) | 10.6056i | 0.976320i | ||||||||
\(119\) | −1.18335 | −0.108477 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 17.1194 | 1.55631 | ||||||||
\(122\) | − 6.51388i | − 0.589739i | ||||||||
\(123\) | − 32.7250i | − 2.95071i | ||||||||
\(124\) | −2.90833 | −0.261175 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 2.39445 | 0.213314 | ||||||||
\(127\) | 11.8167i | 1.04856i | 0.851546 | + | 0.524279i | \(0.175665\pi\) | ||||
−0.851546 | + | 0.524279i | \(0.824335\pi\) | |||||||
\(128\) | − 1.00000i | − 0.0883883i | ||||||||
\(129\) | −17.2111 | −1.51535 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 3.21110 | 0.280555 | 0.140278 | − | 0.990112i | \(-0.455200\pi\) | ||||
0.140278 | + | 0.990112i | \(0.455200\pi\) | |||||||
\(132\) | 17.5139i | 1.52439i | ||||||||
\(133\) | 1.48612i | 0.128863i | ||||||||
\(134\) | −4.00000 | −0.345547 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 3.90833 | 0.335136 | ||||||||
\(137\) | 6.90833i | 0.590218i | 0.955464 | + | 0.295109i | \(0.0953560\pi\) | ||||
−0.955464 | + | 0.295109i | \(0.904644\pi\) | |||||||
\(138\) | 3.30278i | 0.281151i | ||||||||
\(139\) | 5.39445 | 0.457551 | 0.228776 | − | 0.973479i | \(-0.426528\pi\) | ||||
0.228776 | + | 0.973479i | \(0.426528\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 15.2111 | 1.28101 | ||||||||
\(142\) | − 12.6972i | − 1.06553i | ||||||||
\(143\) | 1.60555i | 0.134263i | ||||||||
\(144\) | −7.90833 | −0.659027 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −15.8167 | −1.30900 | ||||||||
\(147\) | 22.8167i | 1.88189i | ||||||||
\(148\) | 8.00000i | 0.657596i | ||||||||
\(149\) | −9.69722 | −0.794428 | −0.397214 | − | 0.917726i | \(-0.630023\pi\) | ||||
−0.397214 | + | 0.917726i | \(0.630023\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1.90833 | −0.155297 | −0.0776487 | − | 0.996981i | \(-0.524741\pi\) | ||||
−0.0776487 | + | 0.996981i | \(0.524741\pi\) | |||||||
\(152\) | − 4.90833i | − 0.398118i | ||||||||
\(153\) | − 30.9083i | − 2.49879i | ||||||||
\(154\) | 1.60555 | 0.129379 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −1.00000 | −0.0800641 | ||||||||
\(157\) | 11.3944i | 0.909376i | 0.890651 | + | 0.454688i | \(0.150249\pi\) | ||||
−0.890651 | + | 0.454688i | \(0.849751\pi\) | |||||||
\(158\) | − 14.4222i | − 1.14737i | ||||||||
\(159\) | −10.6056 | −0.841075 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0.302776 | 0.0238621 | ||||||||
\(162\) | 29.8167i | 2.34262i | ||||||||
\(163\) | 5.69722i | 0.446241i | 0.974791 | + | 0.223121i | \(0.0716243\pi\) | ||||
−0.974791 | + | 0.223121i | \(0.928376\pi\) | |||||||
\(164\) | 9.90833 | 0.773710 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 3.21110 | 0.249230 | ||||||||
\(167\) | − 21.2111i | − 1.64136i | −0.571385 | − | 0.820682i | \(-0.693594\pi\) | ||||
0.571385 | − | 0.820682i | \(-0.306406\pi\) | |||||||
\(168\) | 1.00000i | 0.0771517i | ||||||||
\(169\) | 12.9083 | 0.992948 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −38.8167 | −2.96838 | ||||||||
\(172\) | − 5.21110i | − 0.397343i | ||||||||
\(173\) | 23.3028i | 1.77168i | 0.463993 | + | 0.885839i | \(0.346416\pi\) | ||||
−0.463993 | + | 0.885839i | \(0.653584\pi\) | |||||||
\(174\) | 15.2111 | 1.15315 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −5.30278 | −0.399712 | ||||||||
\(177\) | 35.0278i | 2.63285i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −16.6056 | −1.24116 | −0.620579 | − | 0.784144i | \(-0.713102\pi\) | ||||
−0.620579 | + | 0.784144i | \(0.713102\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −8.11943 | −0.603512 | −0.301756 | − | 0.953385i | \(-0.597573\pi\) | ||||
−0.301756 | + | 0.953385i | \(0.597573\pi\) | |||||||
\(182\) | 0.0916731i | 0.00679526i | ||||||||
\(183\) | − 21.5139i | − 1.59035i | ||||||||
\(184\) | −1.00000 | −0.0737210 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −9.60555 | −0.704313 | ||||||||
\(187\) | − 20.7250i | − 1.51556i | ||||||||
\(188\) | 4.60555i | 0.335894i | ||||||||
\(189\) | 4.90833 | 0.357028 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1.39445 | −0.100899 | −0.0504494 | − | 0.998727i | \(-0.516065\pi\) | ||||
−0.0504494 | + | 0.998727i | \(0.516065\pi\) | |||||||
\(192\) | − 3.30278i | − 0.238357i | ||||||||
\(193\) | 3.81665i | 0.274729i | 0.990521 | + | 0.137364i | \(0.0438631\pi\) | ||||
−0.990521 | + | 0.137364i | \(0.956137\pi\) | |||||||
\(194\) | 2.69722 | 0.193649 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −6.90833 | −0.493452 | ||||||||
\(197\) | − 0.697224i | − 0.0496752i | −0.999691 | − | 0.0248376i | \(-0.992093\pi\) | ||||
0.999691 | − | 0.0248376i | \(-0.00790686\pi\) | |||||||
\(198\) | 41.9361i | 2.98027i | ||||||||
\(199\) | −8.42221 | −0.597034 | −0.298517 | − | 0.954404i | \(-0.596492\pi\) | ||||
−0.298517 | + | 0.954404i | \(0.596492\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −13.2111 | −0.931839 | ||||||||
\(202\) | − 4.60555i | − 0.324045i | ||||||||
\(203\) | − 1.39445i | − 0.0978711i | ||||||||
\(204\) | 12.9083 | 0.903764 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 17.1194 | 1.19277 | ||||||||
\(207\) | 7.90833i | 0.549667i | ||||||||
\(208\) | − 0.302776i | − 0.0209937i | ||||||||
\(209\) | −26.0278 | −1.80038 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −7.21110 | −0.496433 | −0.248216 | − | 0.968705i | \(-0.579844\pi\) | ||||
−0.248216 | + | 0.968705i | \(0.579844\pi\) | |||||||
\(212\) | − 3.21110i | − 0.220539i | ||||||||
\(213\) | − 41.9361i | − 2.87341i | ||||||||
\(214\) | 4.60555 | 0.314829 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −16.2111 | −1.10303 | ||||||||
\(217\) | 0.880571i | 0.0597770i | ||||||||
\(218\) | − 19.5139i | − 1.32165i | ||||||||
\(219\) | −52.2389 | −3.52997 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.18335 | 0.0796005 | ||||||||
\(222\) | 26.4222i | 1.77334i | ||||||||
\(223\) | − 4.00000i | − 0.267860i | −0.990991 | − | 0.133930i | \(-0.957240\pi\) | ||||
0.990991 | − | 0.133930i | \(-0.0427597\pi\) | |||||||
\(224\) | −0.302776 | −0.0202300 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −12.4222 | −0.826313 | ||||||||
\(227\) | 7.39445i | 0.490787i | 0.969424 | + | 0.245393i | \(0.0789171\pi\) | ||||
−0.969424 | + | 0.245393i | \(0.921083\pi\) | |||||||
\(228\) | − 16.2111i | − 1.07361i | ||||||||
\(229\) | −2.00000 | −0.132164 | −0.0660819 | − | 0.997814i | \(-0.521050\pi\) | ||||
−0.0660819 | + | 0.997814i | \(0.521050\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 5.30278 | 0.348897 | ||||||||
\(232\) | 4.60555i | 0.302369i | ||||||||
\(233\) | 4.18335i | 0.274060i | 0.990567 | + | 0.137030i | \(0.0437557\pi\) | ||||
−0.990567 | + | 0.137030i | \(0.956244\pi\) | |||||||
\(234\) | −2.39445 | −0.156530 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −10.6056 | −0.690363 | ||||||||
\(237\) | − 47.6333i | − 3.09412i | ||||||||
\(238\) | − 1.18335i | − 0.0767049i | ||||||||
\(239\) | 9.21110 | 0.595817 | 0.297908 | − | 0.954594i | \(-0.403711\pi\) | ||||
0.297908 | + | 0.954594i | \(0.403711\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 14.4222 | 0.929016 | 0.464508 | − | 0.885569i | \(-0.346231\pi\) | ||||
0.464508 | + | 0.885569i | \(0.346231\pi\) | |||||||
\(242\) | 17.1194i | 1.10048i | ||||||||
\(243\) | 49.8444i | 3.19752i | ||||||||
\(244\) | 6.51388 | 0.417008 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 32.7250 | 2.08647 | ||||||||
\(247\) | − 1.48612i | − 0.0945597i | ||||||||
\(248\) | − 2.90833i | − 0.184679i | ||||||||
\(249\) | 10.6056 | 0.672100 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −5.51388 | −0.348033 | −0.174016 | − | 0.984743i | \(-0.555675\pi\) | ||||
−0.174016 | + | 0.984743i | \(0.555675\pi\) | |||||||
\(252\) | 2.39445i | 0.150836i | ||||||||
\(253\) | 5.30278i | 0.333383i | ||||||||
\(254\) | −11.8167 | −0.741443 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | − 19.8167i | − 1.23613i | −0.786127 | − | 0.618064i | \(-0.787917\pi\) | ||||
0.786127 | − | 0.618064i | \(-0.212083\pi\) | |||||||
\(258\) | − 17.2111i | − 1.07152i | ||||||||
\(259\) | 2.42221 | 0.150509 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 36.4222 | 2.25448 | ||||||||
\(262\) | 3.21110i | 0.198383i | ||||||||
\(263\) | − 14.5139i | − 0.894964i | −0.894293 | − | 0.447482i | \(-0.852321\pi\) | ||||
0.894293 | − | 0.447482i | \(-0.147679\pi\) | |||||||
\(264\) | −17.5139 | −1.07790 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −1.48612 | −0.0911200 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | − 4.00000i | − 0.244339i | ||||||||
\(269\) | −25.8167 | −1.57407 | −0.787035 | − | 0.616909i | \(-0.788385\pi\) | ||||
−0.787035 | + | 0.616909i | \(0.788385\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −6.30278 | −0.382866 | −0.191433 | − | 0.981506i | \(-0.561314\pi\) | ||||
−0.191433 | + | 0.981506i | \(0.561314\pi\) | |||||||
\(272\) | 3.90833i | 0.236977i | ||||||||
\(273\) | 0.302776i | 0.0183248i | ||||||||
\(274\) | −6.90833 | −0.417347 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −3.30278 | −0.198804 | ||||||||
\(277\) | 12.7889i | 0.768410i | 0.923248 | + | 0.384205i | \(0.125524\pi\) | ||||
−0.923248 | + | 0.384205i | \(0.874476\pi\) | |||||||
\(278\) | 5.39445i | 0.323538i | ||||||||
\(279\) | −23.0000 | −1.37697 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −19.3944 | −1.15698 | −0.578488 | − | 0.815691i | \(-0.696357\pi\) | ||||
−0.578488 | + | 0.815691i | \(0.696357\pi\) | |||||||
\(282\) | 15.2111i | 0.905808i | ||||||||
\(283\) | 2.00000i | 0.118888i | 0.998232 | + | 0.0594438i | \(0.0189327\pi\) | ||||
−0.998232 | + | 0.0594438i | \(0.981067\pi\) | |||||||
\(284\) | 12.6972 | 0.753442 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −1.60555 | −0.0949382 | ||||||||
\(287\) | − 3.00000i | − 0.177084i | ||||||||
\(288\) | − 7.90833i | − 0.466003i | ||||||||
\(289\) | 1.72498 | 0.101469 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 8.90833 | 0.522215 | ||||||||
\(292\) | − 15.8167i | − 0.925600i | ||||||||
\(293\) | 8.78890i | 0.513453i | 0.966484 | + | 0.256726i | \(0.0826439\pi\) | ||||
−0.966484 | + | 0.256726i | \(0.917356\pi\) | |||||||
\(294\) | −22.8167 | −1.33069 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −8.00000 | −0.464991 | ||||||||
\(297\) | 85.9638i | 4.98813i | ||||||||
\(298\) | − 9.69722i | − 0.561745i | ||||||||
\(299\) | −0.302776 | −0.0175100 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.57779 | −0.0909426 | ||||||||
\(302\) | − 1.90833i | − 0.109812i | ||||||||
\(303\) | − 15.2111i | − 0.873855i | ||||||||
\(304\) | 4.90833 | 0.281512 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 30.9083 | 1.76691 | ||||||||
\(307\) | 15.3028i | 0.873376i | 0.899613 | + | 0.436688i | \(0.143849\pi\) | ||||
−0.899613 | + | 0.436688i | \(0.856151\pi\) | |||||||
\(308\) | 1.60555i | 0.0914848i | ||||||||
\(309\) | 56.5416 | 3.21654 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −6.42221 | −0.364170 | −0.182085 | − | 0.983283i | \(-0.558285\pi\) | ||||
−0.182085 | + | 0.983283i | \(0.558285\pi\) | |||||||
\(312\) | − 1.00000i | − 0.0566139i | ||||||||
\(313\) | − 12.7250i | − 0.719258i | −0.933095 | − | 0.359629i | \(-0.882903\pi\) | ||||
0.933095 | − | 0.359629i | \(-0.117097\pi\) | |||||||
\(314\) | −11.3944 | −0.643026 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 14.4222 | 0.811312 | ||||||||
\(317\) | 14.7250i | 0.827037i | 0.910496 | + | 0.413519i | \(0.135700\pi\) | ||||
−0.910496 | + | 0.413519i | \(0.864300\pi\) | |||||||
\(318\) | − 10.6056i | − 0.594730i | ||||||||
\(319\) | 24.4222 | 1.36738 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 15.2111 | 0.849001 | ||||||||
\(322\) | 0.302776i | 0.0168730i | ||||||||
\(323\) | 19.1833i | 1.06739i | ||||||||
\(324\) | −29.8167 | −1.65648 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −5.69722 | −0.315540 | ||||||||
\(327\) | − 64.4500i | − 3.56409i | ||||||||
\(328\) | 9.90833i | 0.547096i | ||||||||
\(329\) | 1.39445 | 0.0768784 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 9.39445 | 0.516366 | 0.258183 | − | 0.966096i | \(-0.416876\pi\) | ||||
0.258183 | + | 0.966096i | \(0.416876\pi\) | |||||||
\(332\) | 3.21110i | 0.176232i | ||||||||
\(333\) | 63.2666i | 3.46699i | ||||||||
\(334\) | 21.2111 | 1.16062 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −1.00000 | −0.0545545 | ||||||||
\(337\) | 4.48612i | 0.244375i | 0.992507 | + | 0.122187i | \(0.0389909\pi\) | ||||
−0.992507 | + | 0.122187i | \(0.961009\pi\) | |||||||
\(338\) | 12.9083i | 0.702120i | ||||||||
\(339\) | −41.0278 | −2.22832 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −15.4222 | −0.835159 | ||||||||
\(342\) | − 38.8167i | − 2.09896i | ||||||||
\(343\) | 4.21110i | 0.227378i | ||||||||
\(344\) | 5.21110 | 0.280964 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −23.3028 | −1.25276 | ||||||||
\(347\) | 25.5416i | 1.37115i | 0.728004 | + | 0.685573i | \(0.240448\pi\) | ||||
−0.728004 | + | 0.685573i | \(0.759552\pi\) | |||||||
\(348\) | 15.2111i | 0.815401i | ||||||||
\(349\) | 12.7889 | 0.684574 | 0.342287 | − | 0.939595i | \(-0.388798\pi\) | ||||
0.342287 | + | 0.939595i | \(0.388798\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −4.90833 | −0.261987 | ||||||||
\(352\) | − 5.30278i | − 0.282639i | ||||||||
\(353\) | 18.4222i | 0.980515i | 0.871578 | + | 0.490258i | \(0.163097\pi\) | ||||
−0.871578 | + | 0.490258i | \(0.836903\pi\) | |||||||
\(354\) | −35.0278 | −1.86170 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | − 3.90833i | − 0.206851i | ||||||||
\(358\) | − 16.6056i | − 0.877631i | ||||||||
\(359\) | 3.21110 | 0.169476 | 0.0847378 | − | 0.996403i | \(-0.472995\pi\) | ||||
0.0847378 | + | 0.996403i | \(0.472995\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 5.09167 | 0.267983 | ||||||||
\(362\) | − 8.11943i | − 0.426748i | ||||||||
\(363\) | 56.5416i | 2.96767i | ||||||||
\(364\) | −0.0916731 | −0.00480498 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 21.5139 | 1.12455 | ||||||||
\(367\) | − 29.2111i | − 1.52481i | −0.647102 | − | 0.762404i | \(-0.724019\pi\) | ||||
0.647102 | − | 0.762404i | \(-0.275981\pi\) | |||||||
\(368\) | − 1.00000i | − 0.0521286i | ||||||||
\(369\) | 78.3583 | 4.07917 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −0.972244 | −0.0504764 | ||||||||
\(372\) | − 9.60555i | − 0.498025i | ||||||||
\(373\) | − 2.60555i | − 0.134910i | −0.997722 | − | 0.0674552i | \(-0.978512\pi\) | ||||
0.997722 | − | 0.0674552i | \(-0.0214880\pi\) | |||||||
\(374\) | 20.7250 | 1.07166 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −4.60555 | −0.237513 | ||||||||
\(377\) | 1.39445i | 0.0718178i | ||||||||
\(378\) | 4.90833i | 0.252457i | ||||||||
\(379\) | −4.09167 | −0.210175 | −0.105088 | − | 0.994463i | \(-0.533512\pi\) | ||||
−0.105088 | + | 0.994463i | \(0.533512\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −39.0278 | −1.99945 | ||||||||
\(382\) | − 1.39445i | − 0.0713462i | ||||||||
\(383\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(384\) | 3.30278 | 0.168544 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −3.81665 | −0.194263 | ||||||||
\(387\) | − 41.2111i | − 2.09488i | ||||||||
\(388\) | 2.69722i | 0.136931i | ||||||||
\(389\) | −20.9361 | −1.06150 | −0.530751 | − | 0.847528i | \(-0.678090\pi\) | ||||
−0.530751 | + | 0.847528i | \(0.678090\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 3.90833 | 0.197653 | ||||||||
\(392\) | − 6.90833i | − 0.348923i | ||||||||
\(393\) | 10.6056i | 0.534979i | ||||||||
\(394\) | 0.697224 | 0.0351257 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −41.9361 | −2.10737 | ||||||||
\(397\) | 21.7250i | 1.09035i | 0.838324 | + | 0.545173i | \(0.183536\pi\) | ||||
−0.838324 | + | 0.545173i | \(0.816464\pi\) | |||||||
\(398\) | − 8.42221i | − 0.422167i | ||||||||
\(399\) | −4.90833 | −0.245724 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −1.39445 | −0.0696354 | −0.0348177 | − | 0.999394i | \(-0.511085\pi\) | ||||
−0.0348177 | + | 0.999394i | \(0.511085\pi\) | |||||||
\(402\) | − 13.2111i | − 0.658910i | ||||||||
\(403\) | − 0.880571i | − 0.0438643i | ||||||||
\(404\) | 4.60555 | 0.229135 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 1.39445 | 0.0692053 | ||||||||
\(407\) | 42.4222i | 2.10279i | ||||||||
\(408\) | 12.9083i | 0.639057i | ||||||||
\(409\) | 15.0917 | 0.746235 | 0.373118 | − | 0.927784i | \(-0.378289\pi\) | ||||
0.373118 | + | 0.927784i | \(0.378289\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −22.8167 | −1.12546 | ||||||||
\(412\) | 17.1194i | 0.843414i | ||||||||
\(413\) | 3.21110i | 0.158008i | ||||||||
\(414\) | −7.90833 | −0.388673 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0.302776 | 0.0148448 | ||||||||
\(417\) | 17.8167i | 0.872485i | ||||||||
\(418\) | − 26.0278i | − 1.27306i | ||||||||
\(419\) | 39.6333 | 1.93621 | 0.968107 | − | 0.250538i | \(-0.0806073\pi\) | ||||
0.968107 | + | 0.250538i | \(0.0806073\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 34.3028 | 1.67181 | 0.835907 | − | 0.548870i | \(-0.184942\pi\) | ||||
0.835907 | + | 0.548870i | \(0.184942\pi\) | |||||||
\(422\) | − 7.21110i | − 0.351031i | ||||||||
\(423\) | 36.4222i | 1.77091i | ||||||||
\(424\) | 3.21110 | 0.155945 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 41.9361 | 2.03181 | ||||||||
\(427\) | − 1.97224i | − 0.0954436i | ||||||||
\(428\) | 4.60555i | 0.222618i | ||||||||
\(429\) | −5.30278 | −0.256020 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 20.2389 | 0.974872 | 0.487436 | − | 0.873159i | \(-0.337932\pi\) | ||||
0.487436 | + | 0.873159i | \(0.337932\pi\) | |||||||
\(432\) | − 16.2111i | − 0.779957i | ||||||||
\(433\) | − 34.9083i | − 1.67759i | −0.544450 | − | 0.838794i | \(-0.683261\pi\) | ||||
0.544450 | − | 0.838794i | \(-0.316739\pi\) | |||||||
\(434\) | −0.880571 | −0.0422687 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 19.5139 | 0.934545 | ||||||||
\(437\) | − 4.90833i | − 0.234797i | ||||||||
\(438\) | − 52.2389i | − 2.49607i | ||||||||
\(439\) | 18.3028 | 0.873544 | 0.436772 | − | 0.899572i | \(-0.356122\pi\) | ||||
0.436772 | + | 0.899572i | \(0.356122\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −54.6333 | −2.60159 | ||||||||
\(442\) | 1.18335i | 0.0562860i | ||||||||
\(443\) | 35.5139i | 1.68732i | 0.536882 | + | 0.843658i | \(0.319602\pi\) | ||||
−0.536882 | + | 0.843658i | \(0.680398\pi\) | |||||||
\(444\) | −26.4222 | −1.25394 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 4.00000 | 0.189405 | ||||||||
\(447\) | − 32.0278i | − 1.51486i | ||||||||
\(448\) | − 0.302776i | − 0.0143048i | ||||||||
\(449\) | 12.9083 | 0.609182 | 0.304591 | − | 0.952483i | \(-0.401480\pi\) | ||||
0.304591 | + | 0.952483i | \(0.401480\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 52.5416 | 2.47409 | ||||||||
\(452\) | − 12.4222i | − 0.584291i | ||||||||
\(453\) | − 6.30278i | − 0.296130i | ||||||||
\(454\) | −7.39445 | −0.347039 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 16.2111 | 0.759154 | ||||||||
\(457\) | 3.57779i | 0.167362i | 0.996493 | + | 0.0836811i | \(0.0266677\pi\) | ||||
−0.996493 | + | 0.0836811i | \(0.973332\pi\) | |||||||
\(458\) | − 2.00000i | − 0.0934539i | ||||||||
\(459\) | 63.3583 | 2.95731 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 31.8167 | 1.48185 | 0.740925 | − | 0.671588i | \(-0.234388\pi\) | ||||
0.740925 | + | 0.671588i | \(0.234388\pi\) | |||||||
\(462\) | 5.30278i | 0.246707i | ||||||||
\(463\) | − 25.6333i | − 1.19128i | −0.803251 | − | 0.595640i | \(-0.796898\pi\) | ||||
0.803251 | − | 0.595640i | \(-0.203102\pi\) | |||||||
\(464\) | −4.60555 | −0.213807 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −4.18335 | −0.193790 | ||||||||
\(467\) | − 19.8167i | − 0.917005i | −0.888693 | − | 0.458503i | \(-0.848386\pi\) | ||||
0.888693 | − | 0.458503i | \(-0.151614\pi\) | |||||||
\(468\) | − 2.39445i | − 0.110683i | ||||||||
\(469\) | −1.21110 | −0.0559235 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −37.6333 | −1.73405 | ||||||||
\(472\) | − 10.6056i | − 0.488160i | ||||||||
\(473\) | − 27.6333i | − 1.27058i | ||||||||
\(474\) | 47.6333 | 2.18787 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 1.18335 | 0.0542386 | ||||||||
\(477\) | − 25.3944i | − 1.16273i | ||||||||
\(478\) | 9.21110i | 0.421306i | ||||||||
\(479\) | 30.0000 | 1.37073 | 0.685367 | − | 0.728197i | \(-0.259642\pi\) | ||||
0.685367 | + | 0.728197i | \(0.259642\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.42221 | −0.110443 | ||||||||
\(482\) | 14.4222i | 0.656913i | ||||||||
\(483\) | 1.00000i | 0.0455016i | ||||||||
\(484\) | −17.1194 | −0.778156 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −49.8444 | −2.26099 | ||||||||
\(487\) | 11.8167i | 0.535464i | 0.963493 | + | 0.267732i | \(0.0862741\pi\) | ||||
−0.963493 | + | 0.267732i | \(0.913726\pi\) | |||||||
\(488\) | 6.51388i | 0.294869i | ||||||||
\(489\) | −18.8167 | −0.850918 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −25.8167 | −1.16509 | −0.582545 | − | 0.812799i | \(-0.697943\pi\) | ||||
−0.582545 | + | 0.812799i | \(0.697943\pi\) | |||||||
\(492\) | 32.7250i | 1.47536i | ||||||||
\(493\) | − 18.0000i | − 0.810679i | ||||||||
\(494\) | 1.48612 | 0.0668638 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 2.90833 | 0.130588 | ||||||||
\(497\) | − 3.84441i | − 0.172445i | ||||||||
\(498\) | 10.6056i | 0.475246i | ||||||||
\(499\) | −11.6333 | −0.520778 | −0.260389 | − | 0.965504i | \(-0.583851\pi\) | ||||
−0.260389 | + | 0.965504i | \(0.583851\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 70.0555 | 3.12985 | ||||||||
\(502\) | − 5.51388i | − 0.246096i | ||||||||
\(503\) | − 2.72498i | − 0.121501i | −0.998153 | − | 0.0607504i | \(-0.980651\pi\) | ||||
0.998153 | − | 0.0607504i | \(-0.0193494\pi\) | |||||||
\(504\) | −2.39445 | −0.106657 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −5.30278 | −0.235737 | ||||||||
\(507\) | 42.6333i | 1.89341i | ||||||||
\(508\) | − 11.8167i | − 0.524279i | ||||||||
\(509\) | −29.4500 | −1.30535 | −0.652673 | − | 0.757639i | \(-0.726353\pi\) | ||||
−0.652673 | + | 0.757639i | \(0.726353\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −4.78890 | −0.211848 | ||||||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | − 79.5694i | − 3.51307i | ||||||||
\(514\) | 19.8167 | 0.874075 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 17.2111 | 0.757677 | ||||||||
\(517\) | 24.4222i | 1.07409i | ||||||||
\(518\) | 2.42221i | 0.106426i | ||||||||
\(519\) | −76.9638 | −3.37834 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 6.00000 | 0.262865 | 0.131432 | − | 0.991325i | \(-0.458042\pi\) | ||||
0.131432 | + | 0.991325i | \(0.458042\pi\) | |||||||
\(522\) | 36.4222i | 1.59416i | ||||||||
\(523\) | 8.42221i | 0.368277i | 0.982900 | + | 0.184139i | \(0.0589495\pi\) | ||||
−0.982900 | + | 0.184139i | \(0.941050\pi\) | |||||||
\(524\) | −3.21110 | −0.140278 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 14.5139 | 0.632835 | ||||||||
\(527\) | 11.3667i | 0.495141i | ||||||||
\(528\) | − 17.5139i | − 0.762194i | ||||||||
\(529\) | −1.00000 | −0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −83.8722 | −3.63974 | ||||||||
\(532\) | − 1.48612i | − 0.0644316i | ||||||||
\(533\) | 3.00000i | 0.129944i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 4.00000 | 0.172774 | ||||||||
\(537\) | − 54.8444i | − 2.36671i | ||||||||
\(538\) | − 25.8167i | − 1.11303i | ||||||||
\(539\) | −36.6333 | −1.57791 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −28.8444 | −1.24012 | −0.620059 | − | 0.784555i | \(-0.712891\pi\) | ||||
−0.620059 | + | 0.784555i | \(0.712891\pi\) | |||||||
\(542\) | − 6.30278i | − 0.270727i | ||||||||
\(543\) | − 26.8167i | − 1.15081i | ||||||||
\(544\) | −3.90833 | −0.167568 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −0.302776 | −0.0129576 | ||||||||
\(547\) | − 7.51388i | − 0.321270i | −0.987014 | − | 0.160635i | \(-0.948646\pi\) | ||||
0.987014 | − | 0.160635i | \(-0.0513542\pi\) | |||||||
\(548\) | − 6.90833i | − 0.295109i | ||||||||
\(549\) | 51.5139 | 2.19856 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −22.6056 | −0.963029 | ||||||||
\(552\) | − 3.30278i | − 0.140575i | ||||||||
\(553\) | − 4.36669i | − 0.185691i | ||||||||
\(554\) | −12.7889 | −0.543348 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −5.39445 | −0.228776 | ||||||||
\(557\) | 6.42221i | 0.272118i | 0.990701 | + | 0.136059i | \(0.0434436\pi\) | ||||
−0.990701 | + | 0.136059i | \(0.956556\pi\) | |||||||
\(558\) | − 23.0000i | − 0.973668i | ||||||||
\(559\) | 1.57779 | 0.0667336 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 68.4500 | 2.88996 | ||||||||
\(562\) | − 19.3944i | − 0.818105i | ||||||||
\(563\) | 39.6333i | 1.67034i | 0.549988 | + | 0.835172i | \(0.314632\pi\) | ||||
−0.549988 | + | 0.835172i | \(0.685368\pi\) | |||||||
\(564\) | −15.2111 | −0.640503 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −2.00000 | −0.0840663 | ||||||||
\(567\) | 9.02776i | 0.379130i | ||||||||
\(568\) | 12.6972i | 0.532764i | ||||||||
\(569\) | 0.422205 | 0.0176998 | 0.00884988 | − | 0.999961i | \(-0.497183\pi\) | ||||
0.00884988 | + | 0.999961i | \(0.497183\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 9.11943 | 0.381636 | 0.190818 | − | 0.981625i | \(-0.438886\pi\) | ||||
0.190818 | + | 0.981625i | \(0.438886\pi\) | |||||||
\(572\) | − 1.60555i | − 0.0671315i | ||||||||
\(573\) | − 4.60555i | − 0.192400i | ||||||||
\(574\) | 3.00000 | 0.125218 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 7.90833 | 0.329514 | ||||||||
\(577\) | − 2.00000i | − 0.0832611i | −0.999133 | − | 0.0416305i | \(-0.986745\pi\) | ||||
0.999133 | − | 0.0416305i | \(-0.0132552\pi\) | |||||||
\(578\) | 1.72498i | 0.0717497i | ||||||||
\(579\) | −12.6056 | −0.523869 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0.972244 | 0.0403355 | ||||||||
\(582\) | 8.90833i | 0.369262i | ||||||||
\(583\) | − 17.0278i | − 0.705218i | ||||||||
\(584\) | 15.8167 | 0.654498 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −8.78890 | −0.363066 | ||||||||
\(587\) | 37.5416i | 1.54951i | 0.632262 | + | 0.774755i | \(0.282127\pi\) | ||||
−0.632262 | + | 0.774755i | \(0.717873\pi\) | |||||||
\(588\) | − 22.8167i | − 0.940943i | ||||||||
\(589\) | 14.2750 | 0.588192 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 2.30278 | 0.0947235 | ||||||||
\(592\) | − 8.00000i | − 0.328798i | ||||||||
\(593\) | 19.8167i | 0.813772i | 0.913479 | + | 0.406886i | \(0.133385\pi\) | ||||
−0.913479 | + | 0.406886i | \(0.866615\pi\) | |||||||
\(594\) | −85.9638 | −3.52714 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 9.69722 | 0.397214 | ||||||||
\(597\) | − 27.8167i | − 1.13846i | ||||||||
\(598\) | − 0.302776i | − 0.0123814i | ||||||||
\(599\) | −4.33053 | −0.176941 | −0.0884704 | − | 0.996079i | \(-0.528198\pi\) | ||||
−0.0884704 | + | 0.996079i | \(0.528198\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −3.93608 | −0.160556 | −0.0802781 | − | 0.996773i | \(-0.525581\pi\) | ||||
−0.0802781 | + | 0.996773i | \(0.525581\pi\) | |||||||
\(602\) | − 1.57779i | − 0.0643061i | ||||||||
\(603\) | − 31.6333i | − 1.28821i | ||||||||
\(604\) | 1.90833 | 0.0776487 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 15.2111 | 0.617909 | ||||||||
\(607\) | 26.0555i | 1.05756i | 0.848759 | + | 0.528780i | \(0.177350\pi\) | ||||
−0.848759 | + | 0.528780i | \(0.822650\pi\) | |||||||
\(608\) | 4.90833i | 0.199059i | ||||||||
\(609\) | 4.60555 | 0.186626 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1.39445 | −0.0564134 | ||||||||
\(612\) | 30.9083i | 1.24940i | ||||||||
\(613\) | 32.4222i | 1.30952i | 0.755837 | + | 0.654760i | \(0.227230\pi\) | ||||
−0.755837 | + | 0.654760i | \(0.772770\pi\) | |||||||
\(614\) | −15.3028 | −0.617570 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −1.60555 | −0.0646895 | ||||||||
\(617\) | − 8.09167i | − 0.325758i | −0.986646 | − | 0.162879i | \(-0.947922\pi\) | ||||
0.986646 | − | 0.162879i | \(-0.0520781\pi\) | |||||||
\(618\) | 56.5416i | 2.27444i | ||||||||
\(619\) | −27.3305 | −1.09851 | −0.549253 | − | 0.835656i | \(-0.685088\pi\) | ||||
−0.549253 | + | 0.835656i | \(0.685088\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −16.2111 | −0.650529 | ||||||||
\(622\) | − 6.42221i | − 0.257507i | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 1.00000 | 0.0400320 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 12.7250 | 0.508593 | ||||||||
\(627\) | − 85.9638i | − 3.43307i | ||||||||
\(628\) | − 11.3944i | − 0.454688i | ||||||||
\(629\) | 31.2666 | 1.24668 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 30.6056 | 1.21839 | 0.609194 | − | 0.793021i | \(-0.291493\pi\) | ||||
0.609194 | + | 0.793021i | \(0.291493\pi\) | |||||||
\(632\) | 14.4222i | 0.573685i | ||||||||
\(633\) | − 23.8167i | − 0.946627i | ||||||||
\(634\) | −14.7250 | −0.584804 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 10.6056 | 0.420537 | ||||||||
\(637\) | − 2.09167i | − 0.0828751i | ||||||||
\(638\) | 24.4222i | 0.966884i | ||||||||
\(639\) | 100.414 | 3.97231 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −36.0000 | −1.42191 | −0.710957 | − | 0.703235i | \(-0.751738\pi\) | ||||
−0.710957 | + | 0.703235i | \(0.751738\pi\) | |||||||
\(642\) | 15.2111i | 0.600334i | ||||||||
\(643\) | 16.2389i | 0.640398i | 0.947350 | + | 0.320199i | \(0.103750\pi\) | ||||
−0.947350 | + | 0.320199i | \(0.896250\pi\) | |||||||
\(644\) | −0.302776 | −0.0119310 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −19.1833 | −0.754759 | ||||||||
\(647\) | 30.8444i | 1.21262i | 0.795229 | + | 0.606309i | \(0.207351\pi\) | ||||
−0.795229 | + | 0.606309i | \(0.792649\pi\) | |||||||
\(648\) | − 29.8167i | − 1.17131i | ||||||||
\(649\) | −56.2389 | −2.20757 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −2.90833 | −0.113986 | ||||||||
\(652\) | − 5.69722i | − 0.223121i | ||||||||
\(653\) | 9.27502i | 0.362960i | 0.983395 | + | 0.181480i | \(0.0580887\pi\) | ||||
−0.983395 | + | 0.181480i | \(0.941911\pi\) | |||||||
\(654\) | 64.4500 | 2.52019 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −9.90833 | −0.386855 | ||||||||
\(657\) | − 125.083i | − 4.87996i | ||||||||
\(658\) | 1.39445i | 0.0543613i | ||||||||
\(659\) | 27.6333 | 1.07644 | 0.538220 | − | 0.842804i | \(-0.319097\pi\) | ||||
0.538220 | + | 0.842804i | \(0.319097\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −24.0917 | −0.937057 | −0.468529 | − | 0.883448i | \(-0.655216\pi\) | ||||
−0.468529 | + | 0.883448i | \(0.655216\pi\) | |||||||
\(662\) | 9.39445i | 0.365126i | ||||||||
\(663\) | 3.90833i | 0.151787i | ||||||||
\(664\) | −3.21110 | −0.124615 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −63.2666 | −2.45153 | ||||||||
\(667\) | 4.60555i | 0.178328i | ||||||||
\(668\) | 21.2111i | 0.820682i | ||||||||
\(669\) | 13.2111 | 0.510771 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 34.5416 | 1.33347 | ||||||||
\(672\) | − 1.00000i | − 0.0385758i | ||||||||
\(673\) | 5.63331i | 0.217148i | 0.994088 | + | 0.108574i | \(0.0346284\pi\) | ||||
−0.994088 | + | 0.108574i | \(0.965372\pi\) | |||||||
\(674\) | −4.48612 | −0.172799 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −12.9083 | −0.496474 | ||||||||
\(677\) | 12.4222i | 0.477424i | 0.971090 | + | 0.238712i | \(0.0767252\pi\) | ||||
−0.971090 | + | 0.238712i | \(0.923275\pi\) | |||||||
\(678\) | − 41.0278i | − 1.57566i | ||||||||
\(679\) | 0.816654 | 0.0313403 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −24.4222 | −0.935861 | ||||||||
\(682\) | − 15.4222i | − 0.590547i | ||||||||
\(683\) | − 32.7250i | − 1.25219i | −0.779748 | − | 0.626093i | \(-0.784653\pi\) | ||||
0.779748 | − | 0.626093i | \(-0.215347\pi\) | |||||||
\(684\) | 38.8167 | 1.48419 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −4.21110 | −0.160781 | ||||||||
\(687\) | − 6.60555i | − 0.252018i | ||||||||
\(688\) | 5.21110i | 0.198671i | ||||||||
\(689\) | 0.972244 | 0.0370395 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 30.1833 | 1.14823 | 0.574114 | − | 0.818775i | \(-0.305347\pi\) | ||||
0.574114 | + | 0.818775i | \(0.305347\pi\) | |||||||
\(692\) | − 23.3028i | − 0.885839i | ||||||||
\(693\) | 12.6972i | 0.482328i | ||||||||
\(694\) | −25.5416 | −0.969547 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −15.2111 | −0.576575 | ||||||||
\(697\) | − 38.7250i | − 1.46681i | ||||||||
\(698\) | 12.7889i | 0.484067i | ||||||||
\(699\) | −13.8167 | −0.522594 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 42.9083 | 1.62063 | 0.810313 | − | 0.585998i | \(-0.199297\pi\) | ||||
0.810313 | + | 0.585998i | \(0.199297\pi\) | |||||||
\(702\) | − 4.90833i | − 0.185253i | ||||||||
\(703\) | − 39.2666i | − 1.48097i | ||||||||
\(704\) | 5.30278 | 0.199856 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −18.4222 | −0.693329 | ||||||||
\(707\) | − 1.39445i | − 0.0524436i | ||||||||
\(708\) | − 35.0278i | − 1.31642i | ||||||||
\(709\) | 41.1194 | 1.54427 | 0.772136 | − | 0.635457i | \(-0.219188\pi\) | ||||
0.772136 | + | 0.635457i | \(0.219188\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 114.056 | 4.27742 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − 2.90833i | − 0.108918i | ||||||||
\(714\) | 3.90833 | 0.146265 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 16.6056 | 0.620579 | ||||||||
\(717\) | 30.4222i | 1.13614i | ||||||||
\(718\) | 3.21110i | 0.119837i | ||||||||
\(719\) | −14.3028 | −0.533404 | −0.266702 | − | 0.963779i | \(-0.585934\pi\) | ||||
−0.266702 | + | 0.963779i | \(0.585934\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 5.18335 | 0.193038 | ||||||||
\(722\) | 5.09167i | 0.189492i | ||||||||
\(723\) | 47.6333i | 1.77150i | ||||||||
\(724\) | 8.11943 | 0.301756 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −56.5416 | −2.09846 | ||||||||
\(727\) | 7.90833i | 0.293304i | 0.989188 | + | 0.146652i | \(0.0468497\pi\) | ||||
−0.989188 | + | 0.146652i | \(0.953150\pi\) | |||||||
\(728\) | − 0.0916731i | − 0.00339763i | ||||||||
\(729\) | −75.1749 | −2.78426 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −20.3667 | −0.753289 | ||||||||
\(732\) | 21.5139i | 0.795176i | ||||||||
\(733\) | − 13.6333i | − 0.503558i | −0.967785 | − | 0.251779i | \(-0.918984\pi\) | ||||
0.967785 | − | 0.251779i | \(-0.0810156\pi\) | |||||||
\(734\) | 29.2111 | 1.07820 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.00000 | 0.0368605 | ||||||||
\(737\) | − 21.2111i | − 0.781321i | ||||||||
\(738\) | 78.3583i | 2.88441i | ||||||||
\(739\) | 7.63331 | 0.280796 | 0.140398 | − | 0.990095i | \(-0.455162\pi\) | ||||
0.140398 | + | 0.990095i | \(0.455162\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 4.90833 | 0.180312 | ||||||||
\(742\) | − 0.972244i | − 0.0356922i | ||||||||
\(743\) | 7.33053i | 0.268931i | 0.990918 | + | 0.134466i | \(0.0429318\pi\) | ||||
−0.990918 | + | 0.134466i | \(0.957068\pi\) | |||||||
\(744\) | 9.60555 | 0.352157 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 2.60555 | 0.0953960 | ||||||||
\(747\) | 25.3944i | 0.929134i | ||||||||
\(748\) | 20.7250i | 0.757780i | ||||||||
\(749\) | 1.39445 | 0.0509520 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 0.183346 | 0.00669040 | 0.00334520 | − | 0.999994i | \(-0.498935\pi\) | ||||
0.00334520 | + | 0.999994i | \(0.498935\pi\) | |||||||
\(752\) | − 4.60555i | − 0.167947i | ||||||||
\(753\) | − 18.2111i | − 0.663649i | ||||||||
\(754\) | −1.39445 | −0.0507828 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −4.90833 | −0.178514 | ||||||||
\(757\) | 1.21110i | 0.0440183i | 0.999758 | + | 0.0220091i | \(0.00700629\pi\) | ||||
−0.999758 | + | 0.0220091i | \(0.992994\pi\) | |||||||
\(758\) | − 4.09167i | − 0.148616i | ||||||||
\(759\) | −17.5139 | −0.635714 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 4.54163 | 0.164634 | 0.0823171 | − | 0.996606i | \(-0.473768\pi\) | ||||
0.0823171 | + | 0.996606i | \(0.473768\pi\) | |||||||
\(762\) | − 39.0278i | − 1.41383i | ||||||||
\(763\) | − 5.90833i | − 0.213896i | ||||||||
\(764\) | 1.39445 | 0.0504494 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − 3.21110i | − 0.115946i | ||||||||
\(768\) | 3.30278i | 0.119179i | ||||||||
\(769\) | 41.2666 | 1.48811 | 0.744056 | − | 0.668117i | \(-0.232900\pi\) | ||||
0.744056 | + | 0.668117i | \(0.232900\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 65.4500 | 2.35712 | ||||||||
\(772\) | − 3.81665i | − 0.137364i | ||||||||
\(773\) | 12.0000i | 0.431610i | 0.976436 | + | 0.215805i | \(0.0692376\pi\) | ||||
−0.976436 | + | 0.215805i | \(0.930762\pi\) | |||||||
\(774\) | 41.2111 | 1.48130 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −2.69722 | −0.0968247 | ||||||||
\(777\) | 8.00000i | 0.286998i | ||||||||
\(778\) | − 20.9361i | − 0.750595i | ||||||||
\(779\) | −48.6333 | −1.74247 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 67.3305 | 2.40928 | ||||||||
\(782\) | 3.90833i | 0.139761i | ||||||||
\(783\) | 74.6611i | 2.66817i | ||||||||
\(784\) | 6.90833 | 0.246726 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −10.6056 | −0.378287 | ||||||||
\(787\) | 27.4500i | 0.978485i | 0.872148 | + | 0.489243i | \(0.162727\pi\) | ||||
−0.872148 | + | 0.489243i | \(0.837273\pi\) | |||||||
\(788\) | 0.697224i | 0.0248376i | ||||||||
\(789\) | 47.9361 | 1.70657 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −3.76114 | −0.133731 | ||||||||
\(792\) | − 41.9361i | − 1.49013i | ||||||||
\(793\) | 1.97224i | 0.0700364i | ||||||||
\(794\) | −21.7250 | −0.770991 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 8.42221 | 0.298517 | ||||||||
\(797\) | 19.8167i | 0.701942i | 0.936386 | + | 0.350971i | \(0.114148\pi\) | ||||
−0.936386 | + | 0.350971i | \(0.885852\pi\) | |||||||
\(798\) | − 4.90833i | − 0.173753i | ||||||||
\(799\) | 18.0000 | 0.636794 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | − 1.39445i | − 0.0492397i | ||||||||
\(803\) | − 83.8722i | − 2.95978i | ||||||||
\(804\) | 13.2111 | 0.465920 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0.880571 | 0.0310168 | ||||||||
\(807\) | − 85.2666i | − 3.00153i | ||||||||
\(808\) | 4.60555i | 0.162023i | ||||||||
\(809\) | −18.2750 | −0.642515 | −0.321258 | − | 0.946992i | \(-0.604106\pi\) | ||||
−0.321258 | + | 0.946992i | \(0.604106\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −4.97224 | −0.174599 | −0.0872995 | − | 0.996182i | \(-0.527824\pi\) | ||||
−0.0872995 | + | 0.996182i | \(0.527824\pi\) | |||||||
\(812\) | 1.39445i | 0.0489356i | ||||||||
\(813\) | − 20.8167i | − 0.730072i | ||||||||
\(814\) | −42.4222 | −1.48690 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −12.9083 | −0.451882 | ||||||||
\(817\) | 25.5778i | 0.894854i | ||||||||
\(818\) | 15.0917i | 0.527668i | ||||||||
\(819\) | −0.724981 | −0.0253329 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −30.0000 | −1.04701 | −0.523504 | − | 0.852023i | \(-0.675375\pi\) | ||||
−0.523504 | + | 0.852023i | \(0.675375\pi\) | |||||||
\(822\) | − 22.8167i | − 0.795822i | ||||||||
\(823\) | − 0.788897i | − 0.0274992i | −0.999905 | − | 0.0137496i | \(-0.995623\pi\) | ||||
0.999905 | − | 0.0137496i | \(-0.00437678\pi\) | |||||||
\(824\) | −17.1194 | −0.596384 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −3.21110 | −0.111729 | ||||||||
\(827\) | − 35.4500i | − 1.23272i | −0.787466 | − | 0.616358i | \(-0.788607\pi\) | ||||
0.787466 | − | 0.616358i | \(-0.211393\pi\) | |||||||
\(828\) | − 7.90833i | − 0.274833i | ||||||||
\(829\) | −16.7889 | −0.583103 | −0.291551 | − | 0.956555i | \(-0.594171\pi\) | ||||
−0.291551 | + | 0.956555i | \(0.594171\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −42.2389 | −1.46525 | ||||||||
\(832\) | 0.302776i | 0.0104969i | ||||||||
\(833\) | 27.0000i | 0.935495i | ||||||||
\(834\) | −17.8167 | −0.616940 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 26.0278 | 0.900189 | ||||||||
\(837\) | − 47.1472i | − 1.62965i | ||||||||
\(838\) | 39.6333i | 1.36911i | ||||||||
\(839\) | 22.1833 | 0.765854 | 0.382927 | − | 0.923779i | \(-0.374916\pi\) | ||||
0.382927 | + | 0.923779i | \(0.374916\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −7.78890 | −0.268583 | ||||||||
\(842\) | 34.3028i | 1.18215i | ||||||||
\(843\) | − 64.0555i | − 2.20619i | ||||||||
\(844\) | 7.21110 | 0.248216 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −36.4222 | −1.25222 | ||||||||
\(847\) | 5.18335i | 0.178102i | ||||||||
\(848\) | 3.21110i | 0.110270i | ||||||||
\(849\) | −6.60555 | −0.226702 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −8.00000 | −0.274236 | ||||||||
\(852\) | 41.9361i | 1.43671i | ||||||||
\(853\) | 10.7250i | 0.367216i | 0.983000 | + | 0.183608i | \(0.0587778\pi\) | ||||
−0.983000 | + | 0.183608i | \(0.941222\pi\) | |||||||
\(854\) | 1.97224 | 0.0674888 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −4.60555 | −0.157415 | ||||||||
\(857\) | 33.6333i | 1.14889i | 0.818543 | + | 0.574446i | \(0.194782\pi\) | ||||
−0.818543 | + | 0.574446i | \(0.805218\pi\) | |||||||
\(858\) | − 5.30278i | − 0.181034i | ||||||||
\(859\) | 14.1833 | 0.483930 | 0.241965 | − | 0.970285i | \(-0.422208\pi\) | ||||
0.241965 | + | 0.970285i | \(0.422208\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 9.90833 | 0.337675 | ||||||||
\(862\) | 20.2389i | 0.689338i | ||||||||
\(863\) | 23.4500i | 0.798246i | 0.916897 | + | 0.399123i | \(0.130685\pi\) | ||||
−0.916897 | + | 0.399123i | \(0.869315\pi\) | |||||||
\(864\) | 16.2111 | 0.551513 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 34.9083 | 1.18623 | ||||||||
\(867\) | 5.69722i | 0.193488i | ||||||||
\(868\) | − 0.880571i | − 0.0298885i | ||||||||
\(869\) | 76.4777 | 2.59433 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.21110 | 0.0410366 | ||||||||
\(872\) | 19.5139i | 0.660823i | ||||||||
\(873\) | 21.3305i | 0.721929i | ||||||||
\(874\) | 4.90833 | 0.166027 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 52.2389 | 1.76499 | ||||||||
\(877\) | − 49.1749i | − 1.66052i | −0.557376 | − | 0.830260i | \(-0.688192\pi\) | ||||
0.557376 | − | 0.830260i | \(-0.311808\pi\) | |||||||
\(878\) | 18.3028i | 0.617689i | ||||||||
\(879\) | −29.0278 | −0.979082 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −31.2666 | −1.05340 | −0.526700 | − | 0.850052i | \(-0.676571\pi\) | ||||
−0.526700 | + | 0.850052i | \(0.676571\pi\) | |||||||
\(882\) | − 54.6333i | − 1.83960i | ||||||||
\(883\) | 40.7250i | 1.37050i | 0.728306 | + | 0.685252i | \(0.240308\pi\) | ||||
−0.728306 | + | 0.685252i | \(0.759692\pi\) | |||||||
\(884\) | −1.18335 | −0.0398002 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −35.5139 | −1.19311 | ||||||||
\(887\) | 15.6333i | 0.524915i | 0.964944 | + | 0.262458i | \(0.0845330\pi\) | ||||
−0.964944 | + | 0.262458i | \(0.915467\pi\) | |||||||
\(888\) | − 26.4222i | − 0.886671i | ||||||||
\(889\) | −3.57779 | −0.119995 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −158.111 | −5.29692 | ||||||||
\(892\) | 4.00000i | 0.133930i | ||||||||
\(893\) | − 22.6056i | − 0.756466i | ||||||||
\(894\) | 32.0278 | 1.07117 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0.302776 | 0.0101150 | ||||||||
\(897\) | − 1.00000i | − 0.0333890i | ||||||||
\(898\) | 12.9083i | 0.430756i | ||||||||
\(899\) | −13.3944 | −0.446730 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −12.5500 | −0.418102 | ||||||||
\(902\) | 52.5416i | 1.74945i | ||||||||
\(903\) | − 5.21110i | − 0.173415i | ||||||||
\(904\) | 12.4222 | 0.413156 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 6.30278 | 0.209396 | ||||||||
\(907\) | 30.6611i | 1.01808i | 0.860742 | + | 0.509042i | \(0.170000\pi\) | ||||
−0.860742 | + | 0.509042i | \(0.830000\pi\) | |||||||
\(908\) | − 7.39445i | − 0.245393i | ||||||||
\(909\) | 36.4222 | 1.20805 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −25.8167 | −0.855344 | −0.427672 | − | 0.903934i | \(-0.640666\pi\) | ||||
−0.427672 | + | 0.903934i | \(0.640666\pi\) | |||||||
\(912\) | 16.2111i | 0.536803i | ||||||||
\(913\) | 17.0278i | 0.563536i | ||||||||
\(914\) | −3.57779 | −0.118343 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 2.00000 | 0.0660819 | ||||||||
\(917\) | 0.972244i | 0.0321063i | ||||||||
\(918\) | 63.3583i | 2.09114i | ||||||||
\(919\) | −44.0000 | −1.45143 | −0.725713 | − | 0.687998i | \(-0.758490\pi\) | ||||
−0.725713 | + | 0.687998i | \(0.758490\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −50.5416 | −1.66540 | ||||||||
\(922\) | 31.8167i | 1.04783i | ||||||||
\(923\) | 3.84441i | 0.126540i | ||||||||
\(924\) | −5.30278 | −0.174449 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 25.6333 | 0.842363 | ||||||||
\(927\) | 135.386i | 4.44666i | ||||||||
\(928\) | − 4.60555i | − 0.151185i | ||||||||
\(929\) | 57.6333 | 1.89089 | 0.945444 | − | 0.325785i | \(-0.105629\pi\) | ||||
0.945444 | + | 0.325785i | \(0.105629\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 33.9083 | 1.11130 | ||||||||
\(932\) | − 4.18335i | − 0.137030i | ||||||||
\(933\) | − 21.2111i | − 0.694420i | ||||||||
\(934\) | 19.8167 | 0.648421 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 2.39445 | 0.0782650 | ||||||||
\(937\) | 44.9638i | 1.46890i | 0.678660 | + | 0.734452i | \(0.262561\pi\) | ||||
−0.678660 | + | 0.734452i | \(0.737439\pi\) | |||||||
\(938\) | − 1.21110i | − 0.0395439i | ||||||||
\(939\) | 42.0278 | 1.37152 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −20.9361 | −0.682497 | −0.341248 | − | 0.939973i | \(-0.610850\pi\) | ||||
−0.341248 | + | 0.939973i | \(0.610850\pi\) | |||||||
\(942\) | − 37.6333i | − 1.22616i | ||||||||
\(943\) | 9.90833i | 0.322660i | ||||||||
\(944\) | 10.6056 | 0.345181 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 27.6333 | 0.898436 | ||||||||
\(947\) | − 41.9361i | − 1.36274i | −0.731939 | − | 0.681370i | \(-0.761385\pi\) | ||||
0.731939 | − | 0.681370i | \(-0.238615\pi\) | |||||||
\(948\) | 47.6333i | 1.54706i | ||||||||
\(949\) | 4.78890 | 0.155454 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −48.6333 | −1.57704 | ||||||||
\(952\) | 1.18335i | 0.0383525i | ||||||||
\(953\) | − 1.66947i | − 0.0540794i | −0.999634 | − | 0.0270397i | \(-0.991392\pi\) | ||||
0.999634 | − | 0.0270397i | \(-0.00860805\pi\) | |||||||
\(954\) | 25.3944 | 0.822176 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −9.21110 | −0.297908 | ||||||||
\(957\) | 80.6611i | 2.60740i | ||||||||
\(958\) | 30.0000i | 0.969256i | ||||||||
\(959\) | −2.09167 | −0.0675436 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −22.5416 | −0.727150 | ||||||||
\(962\) | − 2.42221i | − 0.0780950i | ||||||||
\(963\) | 36.4222i | 1.17369i | ||||||||
\(964\) | −14.4222 | −0.464508 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −1.00000 | −0.0321745 | ||||||||
\(967\) | 5.39445i | 0.173474i | 0.996231 | + | 0.0867369i | \(0.0276439\pi\) | ||||
−0.996231 | + | 0.0867369i | \(0.972356\pi\) | |||||||
\(968\) | − 17.1194i | − 0.550239i | ||||||||
\(969\) | −63.3583 | −2.03536 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −27.9083 | −0.895621 | −0.447810 | − | 0.894129i | \(-0.647796\pi\) | ||||
−0.447810 | + | 0.894129i | \(0.647796\pi\) | |||||||
\(972\) | − 49.8444i | − 1.59876i | ||||||||
\(973\) | 1.63331i | 0.0523614i | ||||||||
\(974\) | −11.8167 | −0.378630 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −6.51388 | −0.208504 | ||||||||
\(977\) | 11.5139i | 0.368362i | 0.982892 | + | 0.184181i | \(0.0589632\pi\) | ||||
−0.982892 | + | 0.184181i | \(0.941037\pi\) | |||||||
\(978\) | − 18.8167i | − 0.601690i | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 154.322 | 4.92713 | ||||||||
\(982\) | − 25.8167i | − 0.823843i | ||||||||
\(983\) | − 19.5416i | − 0.623281i | −0.950200 | − | 0.311641i | \(-0.899121\pi\) | ||||
0.950200 | − | 0.311641i | \(-0.100879\pi\) | |||||||
\(984\) | −32.7250 | −1.04323 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 18.0000 | 0.573237 | ||||||||
\(987\) | 4.60555i | 0.146596i | ||||||||
\(988\) | 1.48612i | 0.0472798i | ||||||||
\(989\) | 5.21110 | 0.165703 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 24.3305 | 0.772885 | 0.386442 | − | 0.922314i | \(-0.373704\pi\) | ||||
0.386442 | + | 0.922314i | \(0.373704\pi\) | |||||||
\(992\) | 2.90833i | 0.0923395i | ||||||||
\(993\) | 31.0278i | 0.984636i | ||||||||
\(994\) | 3.84441 | 0.121937 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −10.6056 | −0.336050 | ||||||||
\(997\) | 31.2111i | 0.988466i | 0.869330 | + | 0.494233i | \(0.164551\pi\) | ||||
−0.869330 | + | 0.494233i | \(0.835449\pi\) | |||||||
\(998\) | − 11.6333i | − 0.368246i | ||||||||
\(999\) | −129.689 | −4.10317 |
(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 | 1150.2.b.f.599.4 | 4 | ||
5.2 | odd | 4 | 230.2.a.b.1.2 | ✓ | 2 | ||
5.3 | odd | 4 | 1150.2.a.m.1.1 | 2 | |||
5.4 | even | 2 | inner | 1150.2.b.f.599.1 | 4 | ||
15.2 | even | 4 | 2070.2.a.w.1.1 | 2 | |||
20.3 | even | 4 | 9200.2.a.ca.1.2 | 2 | |||
20.7 | even | 4 | 1840.2.a.j.1.1 | 2 | |||
40.27 | even | 4 | 7360.2.a.bu.1.2 | 2 | |||
40.37 | odd | 4 | 7360.2.a.bc.1.1 | 2 | |||
115.22 | even | 4 | 5290.2.a.j.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
230.2.a.b.1.2 | ✓ | 2 | 5.2 | odd | 4 | ||
1150.2.a.m.1.1 | 2 | 5.3 | odd | 4 | |||
1150.2.b.f.599.1 | 4 | 5.4 | even | 2 | inner | ||
1150.2.b.f.599.4 | 4 | 1.1 | even | 1 | trivial | ||
1840.2.a.j.1.1 | 2 | 20.7 | even | 4 | |||
2070.2.a.w.1.1 | 2 | 15.2 | even | 4 | |||
5290.2.a.j.1.2 | 2 | 115.22 | even | 4 | |||
7360.2.a.bc.1.1 | 2 | 40.37 | odd | 4 | |||
7360.2.a.bu.1.2 | 2 | 40.27 | even | 4 | |||
9200.2.a.ca.1.2 | 2 | 20.3 | even | 4 |