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 | 599.3 | ||
Root | \(-1.30278i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1150.599 |
Dual form | 1150.2.b.f.599.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1150\mathbb{Z}\right)^\times\).
\(n\) | \(51\) | \(277\) |
\(\chi(n)\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | − 0.302776i | − 0.174808i | −0.996173 | − | 0.0874038i | \(-0.972143\pi\) | ||||
0.996173 | − | 0.0874038i | \(-0.0278570\pi\) | |||||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0.302776 | 0.123608 | ||||||||
\(7\) | − 3.30278i | − 1.24833i | −0.781292 | − | 0.624166i | \(-0.785439\pi\) | ||||
0.781292 | − | 0.624166i | \(-0.214561\pi\) | |||||||
\(8\) | − 1.00000i | − 0.353553i | ||||||||
\(9\) | 2.90833 | 0.969442 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.69722 | −0.511732 | −0.255866 | − | 0.966712i | \(-0.582361\pi\) | ||||
−0.255866 | + | 0.966712i | \(0.582361\pi\) | |||||||
\(12\) | 0.302776i | 0.0874038i | ||||||||
\(13\) | 3.30278i | 0.916025i | 0.888946 | + | 0.458013i | \(0.151439\pi\) | ||||
−0.888946 | + | 0.458013i | \(0.848561\pi\) | |||||||
\(14\) | 3.30278 | 0.882704 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | − 6.90833i | − 1.67552i | −0.546042 | − | 0.837758i | \(-0.683866\pi\) | ||||
0.546042 | − | 0.837758i | \(-0.316134\pi\) | |||||||
\(18\) | 2.90833i | 0.685499i | ||||||||
\(19\) | −5.90833 | −1.35546 | −0.677732 | − | 0.735309i | \(-0.737037\pi\) | ||||
−0.677732 | + | 0.735309i | \(0.737037\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.00000 | −0.218218 | ||||||||
\(22\) | − 1.69722i | − 0.361849i | ||||||||
\(23\) | − 1.00000i | − 0.208514i | ||||||||
\(24\) | −0.302776 | −0.0618038 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −3.30278 | −0.647728 | ||||||||
\(27\) | − 1.78890i | − 0.344273i | ||||||||
\(28\) | 3.30278i | 0.624166i | ||||||||
\(29\) | 2.60555 | 0.483839 | 0.241919 | − | 0.970296i | \(-0.422223\pi\) | ||||
0.241919 | + | 0.970296i | \(0.422223\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −7.90833 | −1.42038 | −0.710189 | − | 0.704011i | \(-0.751390\pi\) | ||||
−0.710189 | + | 0.704011i | \(0.751390\pi\) | |||||||
\(32\) | 1.00000i | 0.176777i | ||||||||
\(33\) | 0.513878i | 0.0894547i | ||||||||
\(34\) | 6.90833 | 1.18477 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −2.90833 | −0.484721 | ||||||||
\(37\) | − 8.00000i | − 1.31519i | −0.753371 | − | 0.657596i | \(-0.771573\pi\) | ||||
0.753371 | − | 0.657596i | \(-0.228427\pi\) | |||||||
\(38\) | − 5.90833i | − 0.958457i | ||||||||
\(39\) | 1.00000 | 0.160128 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0.908327 | 0.141857 | 0.0709284 | − | 0.997481i | \(-0.477404\pi\) | ||||
0.0709284 | + | 0.997481i | \(0.477404\pi\) | |||||||
\(42\) | − 1.00000i | − 0.154303i | ||||||||
\(43\) | − 9.21110i | − 1.40468i | −0.711842 | − | 0.702340i | \(-0.752139\pi\) | ||||
0.711842 | − | 0.702340i | \(-0.247861\pi\) | |||||||
\(44\) | 1.69722 | 0.255866 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.00000 | 0.147442 | ||||||||
\(47\) | 2.60555i | 0.380059i | 0.981778 | + | 0.190029i | \(0.0608583\pi\) | ||||
−0.981778 | + | 0.190029i | \(0.939142\pi\) | |||||||
\(48\) | − 0.302776i | − 0.0437019i | ||||||||
\(49\) | −3.90833 | −0.558332 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −2.09167 | −0.292893 | ||||||||
\(52\) | − 3.30278i | − 0.458013i | ||||||||
\(53\) | − 11.2111i | − 1.53996i | −0.638066 | − | 0.769982i | \(-0.720265\pi\) | ||||
0.638066 | − | 0.769982i | \(-0.279735\pi\) | |||||||
\(54\) | 1.78890 | 0.243438 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −3.30278 | −0.441352 | ||||||||
\(57\) | 1.78890i | 0.236945i | ||||||||
\(58\) | 2.60555i | 0.342126i | ||||||||
\(59\) | 3.39445 | 0.441920 | 0.220960 | − | 0.975283i | \(-0.429081\pi\) | ||||
0.220960 | + | 0.975283i | \(0.429081\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 11.5139 | 1.47420 | 0.737101 | − | 0.675783i | \(-0.236194\pi\) | ||||
0.737101 | + | 0.675783i | \(0.236194\pi\) | |||||||
\(62\) | − 7.90833i | − 1.00436i | ||||||||
\(63\) | − 9.60555i | − 1.21019i | ||||||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −0.513878 | −0.0632540 | ||||||||
\(67\) | 4.00000i | 0.488678i | 0.969690 | + | 0.244339i | \(0.0785709\pi\) | ||||
−0.969690 | + | 0.244339i | \(0.921429\pi\) | |||||||
\(68\) | 6.90833i | 0.837758i | ||||||||
\(69\) | −0.302776 | −0.0364499 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −16.3028 | −1.93478 | −0.967392 | − | 0.253285i | \(-0.918489\pi\) | ||||
−0.967392 | + | 0.253285i | \(0.918489\pi\) | |||||||
\(72\) | − 2.90833i | − 0.342750i | ||||||||
\(73\) | − 5.81665i | − 0.680788i | −0.940283 | − | 0.340394i | \(-0.889440\pi\) | ||||
0.940283 | − | 0.340394i | \(-0.110560\pi\) | |||||||
\(74\) | 8.00000 | 0.929981 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 5.90833 | 0.677732 | ||||||||
\(77\) | 5.60555i | 0.638812i | ||||||||
\(78\) | 1.00000i | 0.113228i | ||||||||
\(79\) | 14.4222 | 1.62262 | 0.811312 | − | 0.584613i | \(-0.198754\pi\) | ||||
0.811312 | + | 0.584613i | \(0.198754\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 8.18335 | 0.909261 | ||||||||
\(82\) | 0.908327i | 0.100308i | ||||||||
\(83\) | 11.2111i | 1.23058i | 0.788301 | + | 0.615289i | \(0.210961\pi\) | ||||
−0.788301 | + | 0.615289i | \(0.789039\pi\) | |||||||
\(84\) | 1.00000 | 0.109109 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 9.21110 | 0.993259 | ||||||||
\(87\) | − 0.788897i | − 0.0845787i | ||||||||
\(88\) | 1.69722i | 0.180925i | ||||||||
\(89\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 10.9083 | 1.14350 | ||||||||
\(92\) | 1.00000i | 0.104257i | ||||||||
\(93\) | 2.39445i | 0.248293i | ||||||||
\(94\) | −2.60555 | −0.268742 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0.302776 | 0.0309019 | ||||||||
\(97\) | − 6.30278i | − 0.639950i | −0.947426 | − | 0.319975i | \(-0.896325\pi\) | ||||
0.947426 | − | 0.319975i | \(-0.103675\pi\) | |||||||
\(98\) | − 3.90833i | − 0.394801i | ||||||||
\(99\) | −4.93608 | −0.496095 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 2.60555 | 0.259262 | 0.129631 | − | 0.991562i | \(-0.458621\pi\) | ||||
0.129631 | + | 0.991562i | \(0.458621\pi\) | |||||||
\(102\) | − 2.09167i | − 0.207106i | ||||||||
\(103\) | 8.11943i | 0.800031i | 0.916508 | + | 0.400016i | \(0.130995\pi\) | ||||
−0.916508 | + | 0.400016i | \(0.869005\pi\) | |||||||
\(104\) | 3.30278 | 0.323864 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 11.2111 | 1.08892 | ||||||||
\(107\) | 2.60555i | 0.251888i | 0.992037 | + | 0.125944i | \(0.0401960\pi\) | ||||
−0.992037 | + | 0.125944i | \(0.959804\pi\) | |||||||
\(108\) | 1.78890i | 0.172137i | ||||||||
\(109\) | −1.48612 | −0.142345 | −0.0711723 | − | 0.997464i | \(-0.522674\pi\) | ||||
−0.0711723 | + | 0.997464i | \(0.522674\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −2.42221 | −0.229906 | ||||||||
\(112\) | − 3.30278i | − 0.312083i | ||||||||
\(113\) | − 16.4222i | − 1.54487i | −0.635093 | − | 0.772436i | \(-0.719038\pi\) | ||||
0.635093 | − | 0.772436i | \(-0.280962\pi\) | |||||||
\(114\) | −1.78890 | −0.167546 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −2.60555 | −0.241919 | ||||||||
\(117\) | 9.60555i | 0.888034i | ||||||||
\(118\) | 3.39445i | 0.312484i | ||||||||
\(119\) | −22.8167 | −2.09160 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −8.11943 | −0.738130 | ||||||||
\(122\) | 11.5139i | 1.04242i | ||||||||
\(123\) | − 0.275019i | − 0.0247977i | ||||||||
\(124\) | 7.90833 | 0.710189 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 9.60555 | 0.855731 | ||||||||
\(127\) | − 9.81665i | − 0.871087i | −0.900168 | − | 0.435544i | \(-0.856556\pi\) | ||||
0.900168 | − | 0.435544i | \(-0.143444\pi\) | |||||||
\(128\) | − 1.00000i | − 0.0883883i | ||||||||
\(129\) | −2.78890 | −0.245549 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −11.2111 | −0.979519 | −0.489759 | − | 0.871858i | \(-0.662915\pi\) | ||||
−0.489759 | + | 0.871858i | \(0.662915\pi\) | |||||||
\(132\) | − 0.513878i | − 0.0447274i | ||||||||
\(133\) | 19.5139i | 1.69207i | ||||||||
\(134\) | −4.00000 | −0.345547 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −6.90833 | −0.592384 | ||||||||
\(137\) | − 3.90833i | − 0.333911i | −0.985964 | − | 0.166955i | \(-0.946606\pi\) | ||||
0.985964 | − | 0.166955i | \(-0.0533936\pi\) | |||||||
\(138\) | − 0.302776i | − 0.0257740i | ||||||||
\(139\) | 12.6056 | 1.06919 | 0.534594 | − | 0.845109i | \(-0.320464\pi\) | ||||
0.534594 | + | 0.845109i | \(0.320464\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0.788897 | 0.0664372 | ||||||||
\(142\) | − 16.3028i | − 1.36810i | ||||||||
\(143\) | − 5.60555i | − 0.468760i | ||||||||
\(144\) | 2.90833 | 0.242361 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 5.81665 | 0.481390 | ||||||||
\(147\) | 1.18335i | 0.0976007i | ||||||||
\(148\) | 8.00000i | 0.657596i | ||||||||
\(149\) | −13.3028 | −1.08981 | −0.544903 | − | 0.838499i | \(-0.683433\pi\) | ||||
−0.544903 | + | 0.838499i | \(0.683433\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 8.90833 | 0.724949 | 0.362475 | − | 0.931994i | \(-0.381932\pi\) | ||||
0.362475 | + | 0.931994i | \(0.381932\pi\) | |||||||
\(152\) | 5.90833i | 0.479229i | ||||||||
\(153\) | − 20.0917i | − 1.62432i | ||||||||
\(154\) | −5.60555 | −0.451708 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −1.00000 | −0.0800641 | ||||||||
\(157\) | 18.6056i | 1.48488i | 0.669910 | + | 0.742442i | \(0.266333\pi\) | ||||
−0.669910 | + | 0.742442i | \(0.733667\pi\) | |||||||
\(158\) | 14.4222i | 1.14737i | ||||||||
\(159\) | −3.39445 | −0.269197 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −3.30278 | −0.260295 | ||||||||
\(162\) | 8.18335i | 0.642944i | ||||||||
\(163\) | 9.30278i | 0.728650i | 0.931272 | + | 0.364325i | \(0.118700\pi\) | ||||
−0.931272 | + | 0.364325i | \(0.881300\pi\) | |||||||
\(164\) | −0.908327 | −0.0709284 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −11.2111 | −0.870150 | ||||||||
\(167\) | − 6.78890i | − 0.525341i | −0.964886 | − | 0.262670i | \(-0.915397\pi\) | ||||
0.964886 | − | 0.262670i | \(-0.0846032\pi\) | |||||||
\(168\) | 1.00000i | 0.0771517i | ||||||||
\(169\) | 2.09167 | 0.160898 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −17.1833 | −1.31404 | ||||||||
\(172\) | 9.21110i | 0.702340i | ||||||||
\(173\) | 19.6972i | 1.49755i | 0.662823 | + | 0.748776i | \(0.269358\pi\) | ||||
−0.662823 | + | 0.748776i | \(0.730642\pi\) | |||||||
\(174\) | 0.788897 | 0.0598062 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −1.69722 | −0.127933 | ||||||||
\(177\) | − 1.02776i | − 0.0772509i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −9.39445 | −0.702174 | −0.351087 | − | 0.936343i | \(-0.614188\pi\) | ||||
−0.351087 | + | 0.936343i | \(0.614188\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 17.1194 | 1.27248 | 0.636239 | − | 0.771492i | \(-0.280489\pi\) | ||||
0.636239 | + | 0.771492i | \(0.280489\pi\) | |||||||
\(182\) | 10.9083i | 0.808579i | ||||||||
\(183\) | − 3.48612i | − 0.257702i | ||||||||
\(184\) | −1.00000 | −0.0737210 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −2.39445 | −0.175569 | ||||||||
\(187\) | 11.7250i | 0.857416i | ||||||||
\(188\) | − 2.60555i | − 0.190029i | ||||||||
\(189\) | −5.90833 | −0.429768 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −8.60555 | −0.622676 | −0.311338 | − | 0.950299i | \(-0.600777\pi\) | ||||
−0.311338 | + | 0.950299i | \(0.600777\pi\) | |||||||
\(192\) | 0.302776i | 0.0218509i | ||||||||
\(193\) | − 17.8167i | − 1.28247i | −0.767344 | − | 0.641235i | \(-0.778422\pi\) | ||||
0.767344 | − | 0.641235i | \(-0.221578\pi\) | |||||||
\(194\) | 6.30278 | 0.452513 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 3.90833 | 0.279166 | ||||||||
\(197\) | − 4.30278i | − 0.306560i | −0.988183 | − | 0.153280i | \(-0.951016\pi\) | ||||
0.988183 | − | 0.153280i | \(-0.0489837\pi\) | |||||||
\(198\) | − 4.93608i | − 0.350792i | ||||||||
\(199\) | 20.4222 | 1.44769 | 0.723846 | − | 0.689962i | \(-0.242373\pi\) | ||||
0.723846 | + | 0.689962i | \(0.242373\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1.21110 | 0.0854246 | ||||||||
\(202\) | 2.60555i | 0.183326i | ||||||||
\(203\) | − 8.60555i | − 0.603991i | ||||||||
\(204\) | 2.09167 | 0.146446 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −8.11943 | −0.565707 | ||||||||
\(207\) | − 2.90833i | − 0.202143i | ||||||||
\(208\) | 3.30278i | 0.229006i | ||||||||
\(209\) | 10.0278 | 0.693634 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 7.21110 | 0.496433 | 0.248216 | − | 0.968705i | \(-0.420156\pi\) | ||||
0.248216 | + | 0.968705i | \(0.420156\pi\) | |||||||
\(212\) | 11.2111i | 0.769982i | ||||||||
\(213\) | 4.93608i | 0.338215i | ||||||||
\(214\) | −2.60555 | −0.178112 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −1.78890 | −0.121719 | ||||||||
\(217\) | 26.1194i | 1.77310i | ||||||||
\(218\) | − 1.48612i | − 0.100653i | ||||||||
\(219\) | −1.76114 | −0.119007 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 22.8167 | 1.53481 | ||||||||
\(222\) | − 2.42221i | − 0.162568i | ||||||||
\(223\) | − 4.00000i | − 0.267860i | −0.990991 | − | 0.133930i | \(-0.957240\pi\) | ||||
0.990991 | − | 0.133930i | \(-0.0427597\pi\) | |||||||
\(224\) | 3.30278 | 0.220676 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 16.4222 | 1.09239 | ||||||||
\(227\) | 14.6056i | 0.969404i | 0.874679 | + | 0.484702i | \(0.161072\pi\) | ||||
−0.874679 | + | 0.484702i | \(0.838928\pi\) | |||||||
\(228\) | − 1.78890i | − 0.118473i | ||||||||
\(229\) | −2.00000 | −0.132164 | −0.0660819 | − | 0.997814i | \(-0.521050\pi\) | ||||
−0.0660819 | + | 0.997814i | \(0.521050\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.69722 | 0.111669 | ||||||||
\(232\) | − 2.60555i | − 0.171063i | ||||||||
\(233\) | 25.8167i | 1.69131i | 0.533734 | + | 0.845653i | \(0.320788\pi\) | ||||
−0.533734 | + | 0.845653i | \(0.679212\pi\) | |||||||
\(234\) | −9.60555 | −0.627935 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −3.39445 | −0.220960 | ||||||||
\(237\) | − 4.36669i | − 0.283647i | ||||||||
\(238\) | − 22.8167i | − 1.47898i | ||||||||
\(239\) | −5.21110 | −0.337078 | −0.168539 | − | 0.985695i | \(-0.553905\pi\) | ||||
−0.168539 | + | 0.985695i | \(0.553905\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −14.4222 | −0.929016 | −0.464508 | − | 0.885569i | \(-0.653769\pi\) | ||||
−0.464508 | + | 0.885569i | \(0.653769\pi\) | |||||||
\(242\) | − 8.11943i | − 0.521937i | ||||||||
\(243\) | − 7.84441i | − 0.503219i | ||||||||
\(244\) | −11.5139 | −0.737101 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0.275019 | 0.0175346 | ||||||||
\(247\) | − 19.5139i | − 1.24164i | ||||||||
\(248\) | 7.90833i | 0.502179i | ||||||||
\(249\) | 3.39445 | 0.215114 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 12.5139 | 0.789869 | 0.394934 | − | 0.918709i | \(-0.370767\pi\) | ||||
0.394934 | + | 0.918709i | \(0.370767\pi\) | |||||||
\(252\) | 9.60555i | 0.605093i | ||||||||
\(253\) | 1.69722i | 0.106704i | ||||||||
\(254\) | 9.81665 | 0.615952 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 1.81665i | 0.113320i | 0.998394 | + | 0.0566599i | \(0.0180451\pi\) | ||||
−0.998394 | + | 0.0566599i | \(0.981955\pi\) | |||||||
\(258\) | − 2.78890i | − 0.173629i | ||||||||
\(259\) | −26.4222 | −1.64180 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 7.57779 | 0.469054 | ||||||||
\(262\) | − 11.2111i | − 0.692624i | ||||||||
\(263\) | 3.51388i | 0.216675i | 0.994114 | + | 0.108338i | \(0.0345527\pi\) | ||||
−0.994114 | + | 0.108338i | \(0.965447\pi\) | |||||||
\(264\) | 0.513878 | 0.0316270 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −19.5139 | −1.19647 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | − 4.00000i | − 0.244339i | ||||||||
\(269\) | −4.18335 | −0.255063 | −0.127532 | − | 0.991835i | \(-0.540705\pi\) | ||||
−0.127532 | + | 0.991835i | \(0.540705\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2.69722 | −0.163845 | −0.0819224 | − | 0.996639i | \(-0.526106\pi\) | ||||
−0.0819224 | + | 0.996639i | \(0.526106\pi\) | |||||||
\(272\) | − 6.90833i | − 0.418879i | ||||||||
\(273\) | − 3.30278i | − 0.199893i | ||||||||
\(274\) | 3.90833 | 0.236111 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0.302776 | 0.0182250 | ||||||||
\(277\) | 27.2111i | 1.63496i | 0.575959 | + | 0.817478i | \(0.304629\pi\) | ||||
−0.575959 | + | 0.817478i | \(0.695371\pi\) | |||||||
\(278\) | 12.6056i | 0.756031i | ||||||||
\(279\) | −23.0000 | −1.37697 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −26.6056 | −1.58715 | −0.793577 | − | 0.608470i | \(-0.791784\pi\) | ||||
−0.793577 | + | 0.608470i | \(0.791784\pi\) | |||||||
\(282\) | 0.788897i | 0.0469782i | ||||||||
\(283\) | 2.00000i | 0.118888i | 0.998232 | + | 0.0594438i | \(0.0189327\pi\) | ||||
−0.998232 | + | 0.0594438i | \(0.981067\pi\) | |||||||
\(284\) | 16.3028 | 0.967392 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 5.60555 | 0.331463 | ||||||||
\(287\) | − 3.00000i | − 0.177084i | ||||||||
\(288\) | 2.90833i | 0.171375i | ||||||||
\(289\) | −30.7250 | −1.80735 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1.90833 | −0.111868 | ||||||||
\(292\) | 5.81665i | 0.340394i | ||||||||
\(293\) | 23.2111i | 1.35601i | 0.735059 | + | 0.678004i | \(0.237155\pi\) | ||||
−0.735059 | + | 0.678004i | \(0.762845\pi\) | |||||||
\(294\) | −1.18335 | −0.0690142 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −8.00000 | −0.464991 | ||||||||
\(297\) | 3.03616i | 0.176176i | ||||||||
\(298\) | − 13.3028i | − 0.770609i | ||||||||
\(299\) | 3.30278 | 0.191004 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −30.4222 | −1.75351 | ||||||||
\(302\) | 8.90833i | 0.512617i | ||||||||
\(303\) | − 0.788897i | − 0.0453210i | ||||||||
\(304\) | −5.90833 | −0.338866 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 20.0917 | 1.14856 | ||||||||
\(307\) | 11.6972i | 0.667596i | 0.942645 | + | 0.333798i | \(0.108330\pi\) | ||||
−0.942645 | + | 0.333798i | \(0.891670\pi\) | |||||||
\(308\) | − 5.60555i | − 0.319406i | ||||||||
\(309\) | 2.45837 | 0.139852 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 22.4222 | 1.27145 | 0.635723 | − | 0.771917i | \(-0.280702\pi\) | ||||
0.635723 | + | 0.771917i | \(0.280702\pi\) | |||||||
\(312\) | − 1.00000i | − 0.0566139i | ||||||||
\(313\) | 19.7250i | 1.11492i | 0.830203 | + | 0.557461i | \(0.188224\pi\) | ||||
−0.830203 | + | 0.557461i | \(0.811776\pi\) | |||||||
\(314\) | −18.6056 | −1.04997 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −14.4222 | −0.811312 | ||||||||
\(317\) | − 17.7250i | − 0.995534i | −0.867311 | − | 0.497767i | \(-0.834153\pi\) | ||||
0.867311 | − | 0.497767i | \(-0.165847\pi\) | |||||||
\(318\) | − 3.39445i | − 0.190351i | ||||||||
\(319\) | −4.42221 | −0.247596 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0.788897 | 0.0440320 | ||||||||
\(322\) | − 3.30278i | − 0.184056i | ||||||||
\(323\) | 40.8167i | 2.27110i | ||||||||
\(324\) | −8.18335 | −0.454630 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −9.30278 | −0.515233 | ||||||||
\(327\) | 0.449961i | 0.0248829i | ||||||||
\(328\) | − 0.908327i | − 0.0501540i | ||||||||
\(329\) | 8.60555 | 0.474439 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 16.6056 | 0.912724 | 0.456362 | − | 0.889794i | \(-0.349152\pi\) | ||||
0.456362 | + | 0.889794i | \(0.349152\pi\) | |||||||
\(332\) | − 11.2111i | − 0.615289i | ||||||||
\(333\) | − 23.2666i | − 1.27500i | ||||||||
\(334\) | 6.78890 | 0.371472 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −1.00000 | −0.0545545 | ||||||||
\(337\) | 22.5139i | 1.22641i | 0.789924 | + | 0.613205i | \(0.210120\pi\) | ||||
−0.789924 | + | 0.613205i | \(0.789880\pi\) | |||||||
\(338\) | 2.09167i | 0.113772i | ||||||||
\(339\) | −4.97224 | −0.270055 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 13.4222 | 0.726853 | ||||||||
\(342\) | − 17.1833i | − 0.929169i | ||||||||
\(343\) | − 10.2111i | − 0.551348i | ||||||||
\(344\) | −9.21110 | −0.496629 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −19.6972 | −1.05893 | ||||||||
\(347\) | − 28.5416i | − 1.53220i | −0.642724 | − | 0.766098i | \(-0.722196\pi\) | ||||
0.642724 | − | 0.766098i | \(-0.277804\pi\) | |||||||
\(348\) | 0.788897i | 0.0422893i | ||||||||
\(349\) | 27.2111 | 1.45658 | 0.728288 | − | 0.685271i | \(-0.240316\pi\) | ||||
0.728288 | + | 0.685271i | \(0.240316\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 5.90833 | 0.315363 | ||||||||
\(352\) | − 1.69722i | − 0.0904624i | ||||||||
\(353\) | − 10.4222i | − 0.554718i | −0.960766 | − | 0.277359i | \(-0.910541\pi\) | ||||
0.960766 | − | 0.277359i | \(-0.0894591\pi\) | |||||||
\(354\) | 1.02776 | 0.0546246 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 6.90833i | 0.365627i | ||||||||
\(358\) | − 9.39445i | − 0.496512i | ||||||||
\(359\) | −11.2111 | −0.591699 | −0.295850 | − | 0.955235i | \(-0.595603\pi\) | ||||
−0.295850 | + | 0.955235i | \(0.595603\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 15.9083 | 0.837280 | ||||||||
\(362\) | 17.1194i | 0.899777i | ||||||||
\(363\) | 2.45837i | 0.129031i | ||||||||
\(364\) | −10.9083 | −0.571752 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 3.48612 | 0.182223 | ||||||||
\(367\) | − 14.7889i | − 0.771974i | −0.922504 | − | 0.385987i | \(-0.873861\pi\) | ||||
0.922504 | − | 0.385987i | \(-0.126139\pi\) | |||||||
\(368\) | − 1.00000i | − 0.0521286i | ||||||||
\(369\) | 2.64171 | 0.137522 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −37.0278 | −1.92239 | ||||||||
\(372\) | − 2.39445i | − 0.124146i | ||||||||
\(373\) | 4.60555i | 0.238466i | 0.992866 | + | 0.119233i | \(0.0380436\pi\) | ||||
−0.992866 | + | 0.119233i | \(0.961956\pi\) | |||||||
\(374\) | −11.7250 | −0.606284 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 2.60555 | 0.134371 | ||||||||
\(377\) | 8.60555i | 0.443208i | ||||||||
\(378\) | − 5.90833i | − 0.303892i | ||||||||
\(379\) | −14.9083 | −0.765789 | −0.382895 | − | 0.923792i | \(-0.625073\pi\) | ||||
−0.382895 | + | 0.923792i | \(0.625073\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −2.97224 | −0.152273 | ||||||||
\(382\) | − 8.60555i | − 0.440298i | ||||||||
\(383\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(384\) | −0.302776 | −0.0154510 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 17.8167 | 0.906844 | ||||||||
\(387\) | − 26.7889i | − 1.36176i | ||||||||
\(388\) | 6.30278i | 0.319975i | ||||||||
\(389\) | 25.9361 | 1.31501 | 0.657506 | − | 0.753449i | \(-0.271612\pi\) | ||||
0.657506 | + | 0.753449i | \(0.271612\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −6.90833 | −0.349369 | ||||||||
\(392\) | 3.90833i | 0.197400i | ||||||||
\(393\) | 3.39445i | 0.171227i | ||||||||
\(394\) | 4.30278 | 0.216771 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 4.93608 | 0.248048 | ||||||||
\(397\) | − 10.7250i | − 0.538271i | −0.963102 | − | 0.269136i | \(-0.913262\pi\) | ||||
0.963102 | − | 0.269136i | \(-0.0867380\pi\) | |||||||
\(398\) | 20.4222i | 1.02367i | ||||||||
\(399\) | 5.90833 | 0.295786 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −8.60555 | −0.429741 | −0.214870 | − | 0.976643i | \(-0.568933\pi\) | ||||
−0.214870 | + | 0.976643i | \(0.568933\pi\) | |||||||
\(402\) | 1.21110i | 0.0604043i | ||||||||
\(403\) | − 26.1194i | − 1.30110i | ||||||||
\(404\) | −2.60555 | −0.129631 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 8.60555 | 0.427086 | ||||||||
\(407\) | 13.5778i | 0.673026i | ||||||||
\(408\) | 2.09167i | 0.103553i | ||||||||
\(409\) | 25.9083 | 1.28108 | 0.640542 | − | 0.767923i | \(-0.278710\pi\) | ||||
0.640542 | + | 0.767923i | \(0.278710\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1.18335 | −0.0583702 | ||||||||
\(412\) | − 8.11943i | − 0.400016i | ||||||||
\(413\) | − 11.2111i | − 0.551662i | ||||||||
\(414\) | 2.90833 | 0.142936 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −3.30278 | −0.161932 | ||||||||
\(417\) | − 3.81665i | − 0.186902i | ||||||||
\(418\) | 10.0278i | 0.490474i | ||||||||
\(419\) | −3.63331 | −0.177499 | −0.0887493 | − | 0.996054i | \(-0.528287\pi\) | ||||
−0.0887493 | + | 0.996054i | \(0.528287\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 30.6972 | 1.49609 | 0.748046 | − | 0.663647i | \(-0.230992\pi\) | ||||
0.748046 | + | 0.663647i | \(0.230992\pi\) | |||||||
\(422\) | 7.21110i | 0.351031i | ||||||||
\(423\) | 7.57779i | 0.368445i | ||||||||
\(424\) | −11.2111 | −0.544459 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −4.93608 | −0.239154 | ||||||||
\(427\) | − 38.0278i | − 1.84029i | ||||||||
\(428\) | − 2.60555i | − 0.125944i | ||||||||
\(429\) | −1.69722 | −0.0819428 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −30.2389 | −1.45655 | −0.728277 | − | 0.685283i | \(-0.759679\pi\) | ||||
−0.728277 | + | 0.685283i | \(0.759679\pi\) | |||||||
\(432\) | − 1.78890i | − 0.0860684i | ||||||||
\(433\) | − 24.0917i | − 1.15777i | −0.815409 | − | 0.578886i | \(-0.803488\pi\) | ||||
0.815409 | − | 0.578886i | \(-0.196512\pi\) | |||||||
\(434\) | −26.1194 | −1.25377 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 1.48612 | 0.0711723 | ||||||||
\(437\) | 5.90833i | 0.282634i | ||||||||
\(438\) | − 1.76114i | − 0.0841506i | ||||||||
\(439\) | 14.6972 | 0.701460 | 0.350730 | − | 0.936477i | \(-0.385933\pi\) | ||||
0.350730 | + | 0.936477i | \(0.385933\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −11.3667 | −0.541271 | ||||||||
\(442\) | 22.8167i | 1.08528i | ||||||||
\(443\) | 17.4861i | 0.830791i | 0.909641 | + | 0.415395i | \(0.136357\pi\) | ||||
−0.909641 | + | 0.415395i | \(0.863643\pi\) | |||||||
\(444\) | 2.42221 | 0.114953 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 4.00000 | 0.189405 | ||||||||
\(447\) | 4.02776i | 0.190506i | ||||||||
\(448\) | 3.30278i | 0.156041i | ||||||||
\(449\) | 2.09167 | 0.0987122 | 0.0493561 | − | 0.998781i | \(-0.484283\pi\) | ||||
0.0493561 | + | 0.998781i | \(0.484283\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.54163 | −0.0725927 | ||||||||
\(452\) | 16.4222i | 0.772436i | ||||||||
\(453\) | − 2.69722i | − 0.126727i | ||||||||
\(454\) | −14.6056 | −0.685472 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 1.78890 | 0.0837728 | ||||||||
\(457\) | 32.4222i | 1.51665i | 0.651879 | + | 0.758323i | \(0.273981\pi\) | ||||
−0.651879 | + | 0.758323i | \(0.726019\pi\) | |||||||
\(458\) | − 2.00000i | − 0.0934539i | ||||||||
\(459\) | −12.3583 | −0.576836 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 10.1833 | 0.474286 | 0.237143 | − | 0.971475i | \(-0.423789\pi\) | ||||
0.237143 | + | 0.971475i | \(0.423789\pi\) | |||||||
\(462\) | 1.69722i | 0.0789620i | ||||||||
\(463\) | 17.6333i | 0.819489i | 0.912200 | + | 0.409745i | \(0.134382\pi\) | ||||
−0.912200 | + | 0.409745i | \(0.865618\pi\) | |||||||
\(464\) | 2.60555 | 0.120960 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −25.8167 | −1.19593 | ||||||||
\(467\) | 1.81665i | 0.0840647i | 0.999116 | + | 0.0420324i | \(0.0133833\pi\) | ||||
−0.999116 | + | 0.0420324i | \(0.986617\pi\) | |||||||
\(468\) | − 9.60555i | − 0.444017i | ||||||||
\(469\) | 13.2111 | 0.610032 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 5.63331 | 0.259569 | ||||||||
\(472\) | − 3.39445i | − 0.156242i | ||||||||
\(473\) | 15.6333i | 0.718820i | ||||||||
\(474\) | 4.36669 | 0.200569 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 22.8167 | 1.04580 | ||||||||
\(477\) | − 32.6056i | − 1.49291i | ||||||||
\(478\) | − 5.21110i | − 0.238350i | ||||||||
\(479\) | 30.0000 | 1.37073 | 0.685367 | − | 0.728197i | \(-0.259642\pi\) | ||||
0.685367 | + | 0.728197i | \(0.259642\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 26.4222 | 1.20475 | ||||||||
\(482\) | − 14.4222i | − 0.656913i | ||||||||
\(483\) | 1.00000i | 0.0455016i | ||||||||
\(484\) | 8.11943 | 0.369065 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 7.84441 | 0.355830 | ||||||||
\(487\) | − 9.81665i | − 0.444835i | −0.974952 | − | 0.222418i | \(-0.928605\pi\) | ||||
0.974952 | − | 0.222418i | \(-0.0713948\pi\) | |||||||
\(488\) | − 11.5139i | − 0.521209i | ||||||||
\(489\) | 2.81665 | 0.127373 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −4.18335 | −0.188792 | −0.0943959 | − | 0.995535i | \(-0.530092\pi\) | ||||
−0.0943959 | + | 0.995535i | \(0.530092\pi\) | |||||||
\(492\) | 0.275019i | 0.0123988i | ||||||||
\(493\) | − 18.0000i | − 0.810679i | ||||||||
\(494\) | 19.5139 | 0.877971 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −7.90833 | −0.355094 | ||||||||
\(497\) | 53.8444i | 2.41525i | ||||||||
\(498\) | 3.39445i | 0.152109i | ||||||||
\(499\) | 31.6333 | 1.41610 | 0.708051 | − | 0.706162i | \(-0.249575\pi\) | ||||
0.708051 | + | 0.706162i | \(0.249575\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −2.05551 | −0.0918335 | ||||||||
\(502\) | 12.5139i | 0.558522i | ||||||||
\(503\) | 29.7250i | 1.32537i | 0.748898 | + | 0.662686i | \(0.230583\pi\) | ||||
−0.748898 | + | 0.662686i | \(0.769417\pi\) | |||||||
\(504\) | −9.60555 | −0.427865 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −1.69722 | −0.0754508 | ||||||||
\(507\) | − 0.633308i | − 0.0281262i | ||||||||
\(508\) | 9.81665i | 0.435544i | ||||||||
\(509\) | 35.4500 | 1.57129 | 0.785646 | − | 0.618676i | \(-0.212331\pi\) | ||||
0.785646 | + | 0.618676i | \(0.212331\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −19.2111 | −0.849849 | ||||||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | 10.5694i | 0.466650i | ||||||||
\(514\) | −1.81665 | −0.0801292 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 2.78890 | 0.122774 | ||||||||
\(517\) | − 4.42221i | − 0.194488i | ||||||||
\(518\) | − 26.4222i | − 1.16093i | ||||||||
\(519\) | 5.96384 | 0.261784 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 6.00000 | 0.262865 | 0.131432 | − | 0.991325i | \(-0.458042\pi\) | ||||
0.131432 | + | 0.991325i | \(0.458042\pi\) | |||||||
\(522\) | 7.57779i | 0.331671i | ||||||||
\(523\) | − 20.4222i | − 0.893001i | −0.894783 | − | 0.446500i | \(-0.852670\pi\) | ||||
0.894783 | − | 0.446500i | \(-0.147330\pi\) | |||||||
\(524\) | 11.2111 | 0.489759 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −3.51388 | −0.153212 | ||||||||
\(527\) | 54.6333i | 2.37986i | ||||||||
\(528\) | 0.513878i | 0.0223637i | ||||||||
\(529\) | −1.00000 | −0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 9.87217 | 0.428416 | ||||||||
\(532\) | − 19.5139i | − 0.846034i | ||||||||
\(533\) | 3.00000i | 0.129944i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 4.00000 | 0.172774 | ||||||||
\(537\) | 2.84441i | 0.122745i | ||||||||
\(538\) | − 4.18335i | − 0.180357i | ||||||||
\(539\) | 6.63331 | 0.285717 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 28.8444 | 1.24012 | 0.620059 | − | 0.784555i | \(-0.287109\pi\) | ||||
0.620059 | + | 0.784555i | \(0.287109\pi\) | |||||||
\(542\) | − 2.69722i | − 0.115856i | ||||||||
\(543\) | − 5.18335i | − 0.222439i | ||||||||
\(544\) | 6.90833 | 0.296192 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 3.30278 | 0.141346 | ||||||||
\(547\) | 10.5139i | 0.449541i | 0.974412 | + | 0.224770i | \(0.0721632\pi\) | ||||
−0.974412 | + | 0.224770i | \(0.927837\pi\) | |||||||
\(548\) | 3.90833i | 0.166955i | ||||||||
\(549\) | 33.4861 | 1.42915 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −15.3944 | −0.655826 | ||||||||
\(552\) | 0.302776i | 0.0128870i | ||||||||
\(553\) | − 47.6333i | − 2.02557i | ||||||||
\(554\) | −27.2111 | −1.15609 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −12.6056 | −0.534594 | ||||||||
\(557\) | − 22.4222i | − 0.950059i | −0.879970 | − | 0.475030i | \(-0.842437\pi\) | ||||
0.879970 | − | 0.475030i | \(-0.157563\pi\) | |||||||
\(558\) | − 23.0000i | − 0.973668i | ||||||||
\(559\) | 30.4222 | 1.28672 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 3.55004 | 0.149883 | ||||||||
\(562\) | − 26.6056i | − 1.12229i | ||||||||
\(563\) | − 3.63331i | − 0.153126i | −0.997065 | − | 0.0765628i | \(-0.975605\pi\) | ||||
0.997065 | − | 0.0765628i | \(-0.0243946\pi\) | |||||||
\(564\) | −0.788897 | −0.0332186 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −2.00000 | −0.0840663 | ||||||||
\(567\) | − 27.0278i | − 1.13506i | ||||||||
\(568\) | 16.3028i | 0.684049i | ||||||||
\(569\) | −28.4222 | −1.19152 | −0.595760 | − | 0.803162i | \(-0.703149\pi\) | ||||
−0.595760 | + | 0.803162i | \(0.703149\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −16.1194 | −0.674577 | −0.337289 | − | 0.941401i | \(-0.609510\pi\) | ||||
−0.337289 | + | 0.941401i | \(0.609510\pi\) | |||||||
\(572\) | 5.60555i | 0.234380i | ||||||||
\(573\) | 2.60555i | 0.108848i | ||||||||
\(574\) | 3.00000 | 0.125218 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −2.90833 | −0.121180 | ||||||||
\(577\) | − 2.00000i | − 0.0832611i | −0.999133 | − | 0.0416305i | \(-0.986745\pi\) | ||||
0.999133 | − | 0.0416305i | \(-0.0132552\pi\) | |||||||
\(578\) | − 30.7250i | − 1.27799i | ||||||||
\(579\) | −5.39445 | −0.224186 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 37.0278 | 1.53617 | ||||||||
\(582\) | − 1.90833i | − 0.0791027i | ||||||||
\(583\) | 19.0278i | 0.788049i | ||||||||
\(584\) | −5.81665 | −0.240695 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −23.2111 | −0.958842 | ||||||||
\(587\) | − 16.5416i | − 0.682746i | −0.939928 | − | 0.341373i | \(-0.889108\pi\) | ||||
0.939928 | − | 0.341373i | \(-0.110892\pi\) | |||||||
\(588\) | − 1.18335i | − 0.0488004i | ||||||||
\(589\) | 46.7250 | 1.92527 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −1.30278 | −0.0535890 | ||||||||
\(592\) | − 8.00000i | − 0.328798i | ||||||||
\(593\) | − 1.81665i | − 0.0746010i | −0.999304 | − | 0.0373005i | \(-0.988124\pi\) | ||||
0.999304 | − | 0.0373005i | \(-0.0118759\pi\) | |||||||
\(594\) | −3.03616 | −0.124575 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 13.3028 | 0.544903 | ||||||||
\(597\) | − 6.18335i | − 0.253068i | ||||||||
\(598\) | 3.30278i | 0.135061i | ||||||||
\(599\) | 35.3305 | 1.44357 | 0.721783 | − | 0.692119i | \(-0.243323\pi\) | ||||
0.721783 | + | 0.692119i | \(0.243323\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 42.9361 | 1.75140 | 0.875700 | − | 0.482856i | \(-0.160401\pi\) | ||||
0.875700 | + | 0.482856i | \(0.160401\pi\) | |||||||
\(602\) | − 30.4222i | − 1.23992i | ||||||||
\(603\) | 11.6333i | 0.473745i | ||||||||
\(604\) | −8.90833 | −0.362475 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0.788897 | 0.0320468 | ||||||||
\(607\) | − 46.0555i | − 1.86934i | −0.355522 | − | 0.934668i | \(-0.615697\pi\) | ||||
0.355522 | − | 0.934668i | \(-0.384303\pi\) | |||||||
\(608\) | − 5.90833i | − 0.239614i | ||||||||
\(609\) | −2.60555 | −0.105582 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −8.60555 | −0.348143 | ||||||||
\(612\) | 20.0917i | 0.812158i | ||||||||
\(613\) | 3.57779i | 0.144506i | 0.997386 | + | 0.0722529i | \(0.0230189\pi\) | ||||
−0.997386 | + | 0.0722529i | \(0.976981\pi\) | |||||||
\(614\) | −11.6972 | −0.472062 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 5.60555 | 0.225854 | ||||||||
\(617\) | − 18.9083i | − 0.761221i | −0.924736 | − | 0.380610i | \(-0.875714\pi\) | ||||
0.924736 | − | 0.380610i | \(-0.124286\pi\) | |||||||
\(618\) | 2.45837i | 0.0988900i | ||||||||
\(619\) | 12.3305 | 0.495606 | 0.247803 | − | 0.968810i | \(-0.420291\pi\) | ||||
0.247803 | + | 0.968810i | \(0.420291\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.78890 | −0.0717860 | ||||||||
\(622\) | 22.4222i | 0.899049i | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 1.00000 | 0.0400320 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −19.7250 | −0.788369 | ||||||||
\(627\) | − 3.03616i | − 0.121253i | ||||||||
\(628\) | − 18.6056i | − 0.742442i | ||||||||
\(629\) | −55.2666 | −2.20362 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 23.3944 | 0.931318 | 0.465659 | − | 0.884964i | \(-0.345817\pi\) | ||||
0.465659 | + | 0.884964i | \(0.345817\pi\) | |||||||
\(632\) | − 14.4222i | − 0.573685i | ||||||||
\(633\) | − 2.18335i | − 0.0867802i | ||||||||
\(634\) | 17.7250 | 0.703949 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 3.39445 | 0.134599 | ||||||||
\(637\) | − 12.9083i | − 0.511447i | ||||||||
\(638\) | − 4.42221i | − 0.175077i | ||||||||
\(639\) | −47.4138 | −1.87566 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −36.0000 | −1.42191 | −0.710957 | − | 0.703235i | \(-0.751738\pi\) | ||||
−0.710957 | + | 0.703235i | \(0.751738\pi\) | |||||||
\(642\) | 0.788897i | 0.0311353i | ||||||||
\(643\) | − 34.2389i | − 1.35025i | −0.737704 | − | 0.675124i | \(-0.764090\pi\) | ||||
0.737704 | − | 0.675124i | \(-0.235910\pi\) | |||||||
\(644\) | 3.30278 | 0.130148 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −40.8167 | −1.60591 | ||||||||
\(647\) | − 26.8444i | − 1.05536i | −0.849442 | − | 0.527681i | \(-0.823062\pi\) | ||||
0.849442 | − | 0.527681i | \(-0.176938\pi\) | |||||||
\(648\) | − 8.18335i | − 0.321472i | ||||||||
\(649\) | −5.76114 | −0.226145 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 7.90833 | 0.309952 | ||||||||
\(652\) | − 9.30278i | − 0.364325i | ||||||||
\(653\) | 41.7250i | 1.63282i | 0.577469 | + | 0.816412i | \(0.304040\pi\) | ||||
−0.577469 | + | 0.816412i | \(0.695960\pi\) | |||||||
\(654\) | −0.449961 | −0.0175949 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0.908327 | 0.0354642 | ||||||||
\(657\) | − 16.9167i | − 0.659985i | ||||||||
\(658\) | 8.60555i | 0.335479i | ||||||||
\(659\) | −15.6333 | −0.608987 | −0.304494 | − | 0.952514i | \(-0.598487\pi\) | ||||
−0.304494 | + | 0.952514i | \(0.598487\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −34.9083 | −1.35778 | −0.678888 | − | 0.734242i | \(-0.737538\pi\) | ||||
−0.678888 | + | 0.734242i | \(0.737538\pi\) | |||||||
\(662\) | 16.6056i | 0.645393i | ||||||||
\(663\) | − 6.90833i | − 0.268297i | ||||||||
\(664\) | 11.2111 | 0.435075 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 23.2666 | 0.901563 | ||||||||
\(667\) | − 2.60555i | − 0.100887i | ||||||||
\(668\) | 6.78890i | 0.262670i | ||||||||
\(669\) | −1.21110 | −0.0468239 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −19.5416 | −0.754396 | ||||||||
\(672\) | − 1.00000i | − 0.0385758i | ||||||||
\(673\) | − 37.6333i | − 1.45066i | −0.688403 | − | 0.725329i | \(-0.741688\pi\) | ||||
0.688403 | − | 0.725329i | \(-0.258312\pi\) | |||||||
\(674\) | −22.5139 | −0.867202 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −2.09167 | −0.0804490 | ||||||||
\(677\) | − 16.4222i | − 0.631157i | −0.948900 | − | 0.315578i | \(-0.897802\pi\) | ||||
0.948900 | − | 0.315578i | \(-0.102198\pi\) | |||||||
\(678\) | − 4.97224i | − 0.190958i | ||||||||
\(679\) | −20.8167 | −0.798870 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 4.42221 | 0.169459 | ||||||||
\(682\) | 13.4222i | 0.513963i | ||||||||
\(683\) | − 0.275019i | − 0.0105233i | −0.999986 | − | 0.00526166i | \(-0.998325\pi\) | ||||
0.999986 | − | 0.00526166i | \(-0.00167485\pi\) | |||||||
\(684\) | 17.1833 | 0.657022 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 10.2111 | 0.389862 | ||||||||
\(687\) | 0.605551i | 0.0231032i | ||||||||
\(688\) | − 9.21110i | − 0.351170i | ||||||||
\(689\) | 37.0278 | 1.41065 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 51.8167 | 1.97120 | 0.985599 | − | 0.169098i | \(-0.0540855\pi\) | ||||
0.985599 | + | 0.169098i | \(0.0540855\pi\) | |||||||
\(692\) | − 19.6972i | − 0.748776i | ||||||||
\(693\) | 16.3028i | 0.619291i | ||||||||
\(694\) | 28.5416 | 1.08343 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −0.788897 | −0.0299031 | ||||||||
\(697\) | − 6.27502i | − 0.237683i | ||||||||
\(698\) | 27.2111i | 1.02996i | ||||||||
\(699\) | 7.81665 | 0.295653 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 32.0917 | 1.21209 | 0.606043 | − | 0.795432i | \(-0.292756\pi\) | ||||
0.606043 | + | 0.795432i | \(0.292756\pi\) | |||||||
\(702\) | 5.90833i | 0.222995i | ||||||||
\(703\) | 47.2666i | 1.78269i | ||||||||
\(704\) | 1.69722 | 0.0639665 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 10.4222 | 0.392245 | ||||||||
\(707\) | − 8.60555i | − 0.323645i | ||||||||
\(708\) | 1.02776i | 0.0386254i | ||||||||
\(709\) | 15.8806 | 0.596407 | 0.298204 | − | 0.954502i | \(-0.403613\pi\) | ||||
0.298204 | + | 0.954502i | \(0.403613\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 41.9445 | 1.57304 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 7.90833i | 0.296169i | ||||||||
\(714\) | −6.90833 | −0.258538 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 9.39445 | 0.351087 | ||||||||
\(717\) | 1.57779i | 0.0589238i | ||||||||
\(718\) | − 11.2111i | − 0.418395i | ||||||||
\(719\) | −10.6972 | −0.398939 | −0.199470 | − | 0.979904i | \(-0.563922\pi\) | ||||
−0.199470 | + | 0.979904i | \(0.563922\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 26.8167 | 0.998704 | ||||||||
\(722\) | 15.9083i | 0.592047i | ||||||||
\(723\) | 4.36669i | 0.162399i | ||||||||
\(724\) | −17.1194 | −0.636239 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −2.45837 | −0.0912385 | ||||||||
\(727\) | − 2.90833i | − 0.107864i | −0.998545 | − | 0.0539319i | \(-0.982825\pi\) | ||||
0.998545 | − | 0.0539319i | \(-0.0171754\pi\) | |||||||
\(728\) | − 10.9083i | − 0.404289i | ||||||||
\(729\) | 22.1749 | 0.821294 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −63.6333 | −2.35356 | ||||||||
\(732\) | 3.48612i | 0.128851i | ||||||||
\(733\) | 29.6333i | 1.09453i | 0.836959 | + | 0.547266i | \(0.184331\pi\) | ||||
−0.836959 | + | 0.547266i | \(0.815669\pi\) | |||||||
\(734\) | 14.7889 | 0.545868 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.00000 | 0.0368605 | ||||||||
\(737\) | − 6.78890i | − 0.250072i | ||||||||
\(738\) | 2.64171i | 0.0972427i | ||||||||
\(739\) | −35.6333 | −1.31079 | −0.655396 | − | 0.755285i | \(-0.727498\pi\) | ||||
−0.655396 | + | 0.755285i | \(0.727498\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −5.90833 | −0.217048 | ||||||||
\(742\) | − 37.0278i | − 1.35933i | ||||||||
\(743\) | − 32.3305i | − 1.18609i | −0.805169 | − | 0.593046i | \(-0.797925\pi\) | ||||
0.805169 | − | 0.593046i | \(-0.202075\pi\) | |||||||
\(744\) | 2.39445 | 0.0877847 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −4.60555 | −0.168621 | ||||||||
\(747\) | 32.6056i | 1.19297i | ||||||||
\(748\) | − 11.7250i | − 0.428708i | ||||||||
\(749\) | 8.60555 | 0.314440 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 21.8167 | 0.796101 | 0.398051 | − | 0.917364i | \(-0.369687\pi\) | ||||
0.398051 | + | 0.917364i | \(0.369687\pi\) | |||||||
\(752\) | 2.60555i | 0.0950147i | ||||||||
\(753\) | − 3.78890i | − 0.138075i | ||||||||
\(754\) | −8.60555 | −0.313396 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 5.90833 | 0.214884 | ||||||||
\(757\) | − 13.2111i | − 0.480166i | −0.970752 | − | 0.240083i | \(-0.922825\pi\) | ||||
0.970752 | − | 0.240083i | \(-0.0771746\pi\) | |||||||
\(758\) | − 14.9083i | − 0.541495i | ||||||||
\(759\) | 0.513878 | 0.0186526 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −49.5416 | −1.79588 | −0.897941 | − | 0.440115i | \(-0.854938\pi\) | ||||
−0.897941 | + | 0.440115i | \(0.854938\pi\) | |||||||
\(762\) | − 2.97224i | − 0.107673i | ||||||||
\(763\) | 4.90833i | 0.177693i | ||||||||
\(764\) | 8.60555 | 0.311338 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 11.2111i | 0.404809i | ||||||||
\(768\) | − 0.302776i | − 0.0109255i | ||||||||
\(769\) | −45.2666 | −1.63236 | −0.816178 | − | 0.577801i | \(-0.803911\pi\) | ||||
−0.816178 | + | 0.577801i | \(0.803911\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0.550039 | 0.0198092 | ||||||||
\(772\) | 17.8167i | 0.641235i | ||||||||
\(773\) | 12.0000i | 0.431610i | 0.976436 | + | 0.215805i | \(0.0692376\pi\) | ||||
−0.976436 | + | 0.215805i | \(0.930762\pi\) | |||||||
\(774\) | 26.7889 | 0.962907 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −6.30278 | −0.226256 | ||||||||
\(777\) | 8.00000i | 0.286998i | ||||||||
\(778\) | 25.9361i | 0.929854i | ||||||||
\(779\) | −5.36669 | −0.192282 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 27.6695 | 0.990091 | ||||||||
\(782\) | − 6.90833i | − 0.247041i | ||||||||
\(783\) | − 4.66106i | − 0.166573i | ||||||||
\(784\) | −3.90833 | −0.139583 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −3.39445 | −0.121076 | ||||||||
\(787\) | − 37.4500i | − 1.33495i | −0.744634 | − | 0.667473i | \(-0.767376\pi\) | ||||
0.744634 | − | 0.667473i | \(-0.232624\pi\) | |||||||
\(788\) | 4.30278i | 0.153280i | ||||||||
\(789\) | 1.06392 | 0.0378764 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −54.2389 | −1.92851 | ||||||||
\(792\) | 4.93608i | 0.175396i | ||||||||
\(793\) | 38.0278i | 1.35041i | ||||||||
\(794\) | 10.7250 | 0.380615 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −20.4222 | −0.723846 | ||||||||
\(797\) | − 1.81665i | − 0.0643492i | −0.999482 | − | 0.0321746i | \(-0.989757\pi\) | ||||
0.999482 | − | 0.0321746i | \(-0.0102433\pi\) | |||||||
\(798\) | 5.90833i | 0.209153i | ||||||||
\(799\) | 18.0000 | 0.636794 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | − 8.60555i | − 0.303873i | ||||||||
\(803\) | 9.87217i | 0.348381i | ||||||||
\(804\) | −1.21110 | −0.0427123 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 26.1194 | 0.920018 | ||||||||
\(807\) | 1.26662i | 0.0445870i | ||||||||
\(808\) | − 2.60555i | − 0.0916630i | ||||||||
\(809\) | −50.7250 | −1.78340 | −0.891698 | − | 0.452631i | \(-0.850485\pi\) | ||||
−0.891698 | + | 0.452631i | \(0.850485\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −41.0278 | −1.44068 | −0.720340 | − | 0.693621i | \(-0.756014\pi\) | ||||
−0.720340 | + | 0.693621i | \(0.756014\pi\) | |||||||
\(812\) | 8.60555i | 0.301996i | ||||||||
\(813\) | 0.816654i | 0.0286413i | ||||||||
\(814\) | −13.5778 | −0.475901 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −2.09167 | −0.0732232 | ||||||||
\(817\) | 54.4222i | 1.90399i | ||||||||
\(818\) | 25.9083i | 0.905863i | ||||||||
\(819\) | 31.7250 | 1.10856 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −30.0000 | −1.04701 | −0.523504 | − | 0.852023i | \(-0.675375\pi\) | ||||
−0.523504 | + | 0.852023i | \(0.675375\pi\) | |||||||
\(822\) | − 1.18335i | − 0.0412739i | ||||||||
\(823\) | − 15.2111i | − 0.530226i | −0.964217 | − | 0.265113i | \(-0.914591\pi\) | ||||
0.964217 | − | 0.265113i | \(-0.0854092\pi\) | |||||||
\(824\) | 8.11943 | 0.282854 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 11.2111 | 0.390084 | ||||||||
\(827\) | 29.4500i | 1.02408i | 0.858963 | + | 0.512038i | \(0.171109\pi\) | ||||
−0.858963 | + | 0.512038i | \(0.828891\pi\) | |||||||
\(828\) | 2.90833i | 0.101071i | ||||||||
\(829\) | −31.2111 | −1.08401 | −0.542003 | − | 0.840376i | \(-0.682334\pi\) | ||||
−0.542003 | + | 0.840376i | \(0.682334\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 8.23886 | 0.285803 | ||||||||
\(832\) | − 3.30278i | − 0.114503i | ||||||||
\(833\) | 27.0000i | 0.935495i | ||||||||
\(834\) | 3.81665 | 0.132160 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −10.0278 | −0.346817 | ||||||||
\(837\) | 14.1472i | 0.488998i | ||||||||
\(838\) | − 3.63331i | − 0.125511i | ||||||||
\(839\) | 43.8167 | 1.51272 | 0.756359 | − | 0.654156i | \(-0.226976\pi\) | ||||
0.756359 | + | 0.654156i | \(0.226976\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −22.2111 | −0.765900 | ||||||||
\(842\) | 30.6972i | 1.05790i | ||||||||
\(843\) | 8.05551i | 0.277447i | ||||||||
\(844\) | −7.21110 | −0.248216 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −7.57779 | −0.260530 | ||||||||
\(847\) | 26.8167i | 0.921431i | ||||||||
\(848\) | − 11.2111i | − 0.384991i | ||||||||
\(849\) | 0.605551 | 0.0207825 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −8.00000 | −0.274236 | ||||||||
\(852\) | − 4.93608i | − 0.169107i | ||||||||
\(853\) | − 21.7250i | − 0.743849i | −0.928263 | − | 0.371925i | \(-0.878698\pi\) | ||||
0.928263 | − | 0.371925i | \(-0.121302\pi\) | |||||||
\(854\) | 38.0278 | 1.30128 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 2.60555 | 0.0890559 | ||||||||
\(857\) | − 9.63331i | − 0.329068i | −0.986371 | − | 0.164534i | \(-0.947388\pi\) | ||||
0.986371 | − | 0.164534i | \(-0.0526119\pi\) | |||||||
\(858\) | − 1.69722i | − 0.0579423i | ||||||||
\(859\) | 35.8167 | 1.22205 | 0.611024 | − | 0.791612i | \(-0.290758\pi\) | ||||
0.611024 | + | 0.791612i | \(0.290758\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −0.908327 | −0.0309557 | ||||||||
\(862\) | − 30.2389i | − 1.02994i | ||||||||
\(863\) | − 41.4500i | − 1.41097i | −0.708723 | − | 0.705487i | \(-0.750729\pi\) | ||||
0.708723 | − | 0.705487i | \(-0.249271\pi\) | |||||||
\(864\) | 1.78890 | 0.0608595 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 24.0917 | 0.818668 | ||||||||
\(867\) | 9.30278i | 0.315939i | ||||||||
\(868\) | − 26.1194i | − 0.886551i | ||||||||
\(869\) | −24.4777 | −0.830350 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −13.2111 | −0.447641 | ||||||||
\(872\) | 1.48612i | 0.0503264i | ||||||||
\(873\) | − 18.3305i | − 0.620395i | ||||||||
\(874\) | −5.90833 | −0.199852 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 1.76114 | 0.0595034 | ||||||||
\(877\) | 48.1749i | 1.62675i | 0.581738 | + | 0.813376i | \(0.302373\pi\) | ||||
−0.581738 | + | 0.813376i | \(0.697627\pi\) | |||||||
\(878\) | 14.6972i | 0.496007i | ||||||||
\(879\) | 7.02776 | 0.237040 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 55.2666 | 1.86198 | 0.930990 | − | 0.365045i | \(-0.118946\pi\) | ||||
0.930990 | + | 0.365045i | \(0.118946\pi\) | |||||||
\(882\) | − 11.3667i | − 0.382736i | ||||||||
\(883\) | 8.27502i | 0.278477i | 0.990259 | + | 0.139238i | \(0.0444654\pi\) | ||||
−0.990259 | + | 0.139238i | \(0.955535\pi\) | |||||||
\(884\) | −22.8167 | −0.767407 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −17.4861 | −0.587458 | ||||||||
\(887\) | − 27.6333i | − 0.927836i | −0.885878 | − | 0.463918i | \(-0.846443\pi\) | ||||
0.885878 | − | 0.463918i | \(-0.153557\pi\) | |||||||
\(888\) | 2.42221i | 0.0812839i | ||||||||
\(889\) | −32.4222 | −1.08741 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −13.8890 | −0.465298 | ||||||||
\(892\) | 4.00000i | 0.133930i | ||||||||
\(893\) | − 15.3944i | − 0.515156i | ||||||||
\(894\) | −4.02776 | −0.134708 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −3.30278 | −0.110338 | ||||||||
\(897\) | − 1.00000i | − 0.0333890i | ||||||||
\(898\) | 2.09167i | 0.0698000i | ||||||||
\(899\) | −20.6056 | −0.687234 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −77.4500 | −2.58023 | ||||||||
\(902\) | − 1.54163i | − 0.0513308i | ||||||||
\(903\) | 9.21110i | 0.306526i | ||||||||
\(904\) | −16.4222 | −0.546194 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 2.69722 | 0.0896093 | ||||||||
\(907\) | − 48.6611i | − 1.61576i | −0.589344 | − | 0.807882i | \(-0.700614\pi\) | ||||
0.589344 | − | 0.807882i | \(-0.299386\pi\) | |||||||
\(908\) | − 14.6056i | − 0.484702i | ||||||||
\(909\) | 7.57779 | 0.251340 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −4.18335 | −0.138600 | −0.0693002 | − | 0.997596i | \(-0.522077\pi\) | ||||
−0.0693002 | + | 0.997596i | \(0.522077\pi\) | |||||||
\(912\) | 1.78890i | 0.0592363i | ||||||||
\(913\) | − 19.0278i | − 0.629727i | ||||||||
\(914\) | −32.4222 | −1.07243 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 2.00000 | 0.0660819 | ||||||||
\(917\) | 37.0278i | 1.22276i | ||||||||
\(918\) | − 12.3583i | − 0.407884i | ||||||||
\(919\) | −44.0000 | −1.45143 | −0.725713 | − | 0.687998i | \(-0.758490\pi\) | ||||
−0.725713 | + | 0.687998i | \(0.758490\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 3.54163 | 0.116701 | ||||||||
\(922\) | 10.1833i | 0.335371i | ||||||||
\(923\) | − 53.8444i | − 1.77231i | ||||||||
\(924\) | −1.69722 | −0.0558346 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −17.6333 | −0.579466 | ||||||||
\(927\) | 23.6140i | 0.775584i | ||||||||
\(928\) | 2.60555i | 0.0855314i | ||||||||
\(929\) | 14.3667 | 0.471356 | 0.235678 | − | 0.971831i | \(-0.424269\pi\) | ||||
0.235678 | + | 0.971831i | \(0.424269\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 23.0917 | 0.756799 | ||||||||
\(932\) | − 25.8167i | − 0.845653i | ||||||||
\(933\) | − 6.78890i | − 0.222259i | ||||||||
\(934\) | −1.81665 | −0.0594427 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 9.60555 | 0.313967 | ||||||||
\(937\) | − 37.9638i | − 1.24022i | −0.784513 | − | 0.620112i | \(-0.787087\pi\) | ||||
0.784513 | − | 0.620112i | \(-0.212913\pi\) | |||||||
\(938\) | 13.2111i | 0.431358i | ||||||||
\(939\) | 5.97224 | 0.194897 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 25.9361 | 0.845492 | 0.422746 | − | 0.906248i | \(-0.361066\pi\) | ||||
0.422746 | + | 0.906248i | \(0.361066\pi\) | |||||||
\(942\) | 5.63331i | 0.183543i | ||||||||
\(943\) | − 0.908327i | − 0.0295792i | ||||||||
\(944\) | 3.39445 | 0.110480 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −15.6333 | −0.508283 | ||||||||
\(947\) | 4.93608i | 0.160401i | 0.996779 | + | 0.0802006i | \(0.0255561\pi\) | ||||
−0.996779 | + | 0.0802006i | \(0.974444\pi\) | |||||||
\(948\) | 4.36669i | 0.141824i | ||||||||
\(949\) | 19.2111 | 0.623619 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −5.36669 | −0.174027 | ||||||||
\(952\) | 22.8167i | 0.739492i | ||||||||
\(953\) | − 41.3305i | − 1.33883i | −0.742890 | − | 0.669414i | \(-0.766545\pi\) | ||||
0.742890 | − | 0.669414i | \(-0.233455\pi\) | |||||||
\(954\) | 32.6056 | 1.05564 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 5.21110 | 0.168539 | ||||||||
\(957\) | 1.33894i | 0.0432817i | ||||||||
\(958\) | 30.0000i | 0.969256i | ||||||||
\(959\) | −12.9083 | −0.416832 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 31.5416 | 1.01747 | ||||||||
\(962\) | 26.4222i | 0.851886i | ||||||||
\(963\) | 7.57779i | 0.244191i | ||||||||
\(964\) | 14.4222 | 0.464508 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −1.00000 | −0.0321745 | ||||||||
\(967\) | 12.6056i | 0.405367i | 0.979244 | + | 0.202684i | \(0.0649663\pi\) | ||||
−0.979244 | + | 0.202684i | \(0.935034\pi\) | |||||||
\(968\) | 8.11943i | 0.260968i | ||||||||
\(969\) | 12.3583 | 0.397005 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −17.0917 | −0.548498 | −0.274249 | − | 0.961659i | \(-0.588429\pi\) | ||||
−0.274249 | + | 0.961659i | \(0.588429\pi\) | |||||||
\(972\) | 7.84441i | 0.251610i | ||||||||
\(973\) | − 41.6333i | − 1.33470i | ||||||||
\(974\) | 9.81665 | 0.314546 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 11.5139 | 0.368550 | ||||||||
\(977\) | − 6.51388i | − 0.208397i | −0.994556 | − | 0.104199i | \(-0.966772\pi\) | ||||
0.994556 | − | 0.104199i | \(-0.0332278\pi\) | |||||||
\(978\) | 2.81665i | 0.0900667i | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −4.32213 | −0.137995 | ||||||||
\(982\) | − 4.18335i | − 0.133496i | ||||||||
\(983\) | 34.5416i | 1.10171i | 0.834602 | + | 0.550854i | \(0.185698\pi\) | ||||
−0.834602 | + | 0.550854i | \(0.814302\pi\) | |||||||
\(984\) | −0.275019 | −0.00876729 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 18.0000 | 0.573237 | ||||||||
\(987\) | − 2.60555i | − 0.0829356i | ||||||||
\(988\) | 19.5139i | 0.620819i | ||||||||
\(989\) | −9.21110 | −0.292896 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −15.3305 | −0.486990 | −0.243495 | − | 0.969902i | \(-0.578294\pi\) | ||||
−0.243495 | + | 0.969902i | \(0.578294\pi\) | |||||||
\(992\) | − 7.90833i | − 0.251090i | ||||||||
\(993\) | − 5.02776i | − 0.159551i | ||||||||
\(994\) | −53.8444 | −1.70784 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −3.39445 | −0.107557 | ||||||||
\(997\) | 16.7889i | 0.531710i | 0.964013 | + | 0.265855i | \(0.0856542\pi\) | ||||
−0.964013 | + | 0.265855i | \(0.914346\pi\) | |||||||
\(998\) | 31.6333i | 1.00133i | ||||||||
\(999\) | −14.3112 | −0.452786 |
(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.599.3 | 4 | ||
5.2 | odd | 4 | 230.2.a.b.1.1 | ✓ | 2 | ||
5.3 | odd | 4 | 1150.2.a.m.1.2 | 2 | |||
5.4 | even | 2 | inner | 1150.2.b.f.599.2 | 4 | ||
15.2 | even | 4 | 2070.2.a.w.1.2 | 2 | |||
20.3 | even | 4 | 9200.2.a.ca.1.1 | 2 | |||
20.7 | even | 4 | 1840.2.a.j.1.2 | 2 | |||
40.27 | even | 4 | 7360.2.a.bu.1.1 | 2 | |||
40.37 | odd | 4 | 7360.2.a.bc.1.2 | 2 | |||
115.22 | even | 4 | 5290.2.a.j.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
230.2.a.b.1.1 | ✓ | 2 | 5.2 | odd | 4 | ||
1150.2.a.m.1.2 | 2 | 5.3 | odd | 4 | |||
1150.2.b.f.599.2 | 4 | 5.4 | even | 2 | inner | ||
1150.2.b.f.599.3 | 4 | 1.1 | even | 1 | trivial | ||
1840.2.a.j.1.2 | 2 | 20.7 | even | 4 | |||
2070.2.a.w.1.2 | 2 | 15.2 | even | 4 | |||
5290.2.a.j.1.1 | 2 | 115.22 | even | 4 | |||
7360.2.a.bc.1.2 | 2 | 40.37 | odd | 4 | |||
7360.2.a.bu.1.1 | 2 | 40.27 | even | 4 | |||
9200.2.a.ca.1.1 | 2 | 20.3 | even | 4 |