Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [384,3,Mod(31,384)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(384, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 1, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("384.31");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 384 = 2^{7} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 384.l (of order \(4\), degree \(2\), 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: | \(10.4632421514\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 6 x^{14} - 4 x^{13} + 10 x^{12} + 56 x^{11} + 88 x^{10} - 128 x^{9} - 496 x^{8} - 512 x^{7} + \cdots + 65536 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{24} \) |
Twist minimal: | no (minimal twist has level 48) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 31.3 | ||
Root | \(-0.455024 - 1.94755i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 384.31 |
Dual form | 384.3.l.b.223.3 |
$q$-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 \(\left(\mathbb{Z}/384\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(133\) | \(257\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{4}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.22474 | − | 1.22474i | −0.408248 | − | 0.408248i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 3.40572 | + | 3.40572i | 0.681145 | + | 0.681145i | 0.960258 | − | 0.279113i | \(-0.0900405\pi\) |
−0.279113 | + | 0.960258i | \(0.590040\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −12.1303 | −1.73290 | −0.866452 | − | 0.499261i | \(-0.833605\pi\) | ||||
−0.866452 | + | 0.499261i | \(0.833605\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 3.00000i | 0.333333i | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 9.81086 | − | 9.81086i | 0.891896 | − | 0.891896i | −0.102805 | − | 0.994702i | \(-0.532782\pi\) |
0.994702 | + | 0.102805i | \(0.0327818\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 7.76859 | − | 7.76859i | 0.597584 | − | 0.597584i | −0.342085 | − | 0.939669i | \(-0.611133\pi\) |
0.939669 | + | 0.342085i | \(0.111133\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | − | 8.34229i | − | 0.556153i | ||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 9.73087 | 0.572404 | 0.286202 | − | 0.958169i | \(-0.407607\pi\) | ||||
0.286202 | + | 0.958169i | \(0.407607\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 11.2823 | + | 11.2823i | 0.593806 | + | 0.593806i | 0.938657 | − | 0.344851i | \(-0.112071\pi\) |
−0.344851 | + | 0.938657i | \(0.612071\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 14.8566 | + | 14.8566i | 0.707455 | + | 0.707455i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 20.2635 | 0.881020 | 0.440510 | − | 0.897748i | \(-0.354798\pi\) | ||||
0.440510 | + | 0.897748i | \(0.354798\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | − | 1.80207i | − | 0.0720830i | ||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 3.67423 | − | 3.67423i | 0.136083 | − | 0.136083i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 16.4069 | − | 16.4069i | 0.565754 | − | 0.565754i | −0.365182 | − | 0.930936i | \(-0.618993\pi\) |
0.930936 | + | 0.365182i | \(0.118993\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 26.3542i | − | 0.850134i | −0.905162 | − | 0.425067i | \(-0.860251\pi\) | ||
0.905162 | − | 0.425067i | \(-0.139749\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −24.0316 | −0.728230 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −41.3125 | − | 41.3125i | −1.18036 | − | 1.18036i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 23.7263 | + | 23.7263i | 0.641250 | + | 0.641250i | 0.950863 | − | 0.309613i | \(-0.100199\pi\) |
−0.309613 | + | 0.950863i | \(0.600199\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −19.0291 | −0.487925 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 24.7452i | 0.603542i | 0.953380 | + | 0.301771i | \(0.0975779\pi\) | ||||
−0.953380 | + | 0.301771i | \(0.902422\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 29.8844 | − | 29.8844i | 0.694987 | − | 0.694987i | −0.268338 | − | 0.963325i | \(-0.586474\pi\) |
0.963325 | + | 0.268338i | \(0.0864744\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −10.2172 | + | 10.2172i | −0.227048 | + | 0.227048i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 31.3325i | − | 0.666648i | −0.942812 | − | 0.333324i | \(-0.891830\pi\) | ||
0.942812 | − | 0.333324i | \(-0.108170\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 98.1448 | 2.00295 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −11.9178 | − | 11.9178i | −0.233683 | − | 0.233683i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −36.8742 | − | 36.8742i | −0.695739 | − | 0.695739i | 0.267750 | − | 0.963489i | \(-0.413720\pi\) |
−0.963489 | + | 0.267750i | \(0.913720\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 66.8262 | 1.21502 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 27.6359i | − | 0.484841i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −14.1325 | + | 14.1325i | −0.239534 | + | 0.239534i | −0.816657 | − | 0.577123i | \(-0.804175\pi\) |
0.577123 | + | 0.816657i | \(0.304175\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 42.5199 | − | 42.5199i | 0.697048 | − | 0.697048i | −0.266725 | − | 0.963773i | \(-0.585941\pi\) |
0.963773 | + | 0.266725i | \(0.0859414\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | − | 36.3910i | − | 0.577634i | ||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 52.9153 | 0.814082 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 48.7789 | + | 48.7789i | 0.728044 | + | 0.728044i | 0.970230 | − | 0.242186i | \(-0.0778644\pi\) |
−0.242186 | + | 0.970230i | \(0.577864\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −24.8176 | − | 24.8176i | −0.359675 | − | 0.359675i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −7.73935 | −0.109005 | −0.0545025 | − | 0.998514i | \(-0.517357\pi\) | ||||
−0.0545025 | + | 0.998514i | \(0.517357\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 85.4163i | − | 1.17009i | −0.811002 | − | 0.585043i | \(-0.801077\pi\) | ||
0.811002 | − | 0.585043i | \(-0.198923\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −2.20708 | + | 2.20708i | −0.0294278 | + | 0.0294278i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −119.009 | + | 119.009i | −1.54557 | + | 1.54557i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 105.294i | 1.33283i | 0.745581 | + | 0.666416i | \(0.232172\pi\) | ||||
−0.745581 | + | 0.666416i | \(0.767828\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −9.00000 | −0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −62.1229 | − | 62.1229i | −0.748469 | − | 0.748469i | 0.225723 | − | 0.974192i | \(-0.427526\pi\) |
−0.974192 | + | 0.225723i | \(0.927526\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 33.1407 | + | 33.1407i | 0.389890 | + | 0.389890i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −40.1885 | −0.461937 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 127.172i | 1.42890i | 0.699685 | + | 0.714451i | \(0.253324\pi\) | ||||
−0.699685 | + | 0.714451i | \(0.746676\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −94.2355 | + | 94.2355i | −1.03555 | + | 1.03555i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −32.2771 | + | 32.2771i | −0.347066 | + | 0.347066i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 76.8489i | 0.808936i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −147.348 | −1.51905 | −0.759525 | − | 0.650478i | \(-0.774569\pi\) | ||||
−0.759525 | + | 0.650478i | \(0.774569\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 29.4326 | + | 29.4326i | 0.297299 | + | 0.297299i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −12.7690 | − | 12.7690i | −0.126426 | − | 0.126426i | 0.641063 | − | 0.767489i | \(-0.278494\pi\) |
−0.767489 | + | 0.641063i | \(0.778494\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 17.7621 | 0.172448 | 0.0862240 | − | 0.996276i | \(-0.472520\pi\) | ||||
0.0862240 | + | 0.996276i | \(0.472520\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 101.195i | 0.963759i | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −15.8889 | + | 15.8889i | −0.148494 | + | 0.148494i | −0.777445 | − | 0.628951i | \(-0.783485\pi\) |
0.628951 | + | 0.777445i | \(0.283485\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 79.3257 | − | 79.3257i | 0.727758 | − | 0.727758i | −0.242414 | − | 0.970173i | \(-0.577939\pi\) |
0.970173 | + | 0.242414i | \(0.0779394\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − | 58.1172i | − | 0.523579i | ||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −167.538 | −1.48263 | −0.741317 | − | 0.671155i | \(-0.765799\pi\) | ||||
−0.741317 | + | 0.671155i | \(0.765799\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 69.0118 | + | 69.0118i | 0.600102 | + | 0.600102i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 23.3058 | + | 23.3058i | 0.199195 | + | 0.199195i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −118.039 | −0.991921 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | − | 71.5059i | − | 0.590958i | ||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 30.3066 | − | 30.3066i | 0.246395 | − | 0.246395i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 91.2805 | − | 91.2805i | 0.730244 | − | 0.730244i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 198.247i | 1.56100i | 0.625156 | + | 0.780500i | \(0.285035\pi\) | ||||
−0.625156 | + | 0.780500i | \(0.714965\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −73.2016 | −0.567454 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 134.339 | + | 134.339i | 1.02549 | + | 1.02549i | 0.999667 | + | 0.0258197i | \(0.00821957\pi\) |
0.0258197 | + | 0.999667i | \(0.491780\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −136.858 | − | 136.858i | −1.02901 | − | 1.02901i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 25.0269 | 0.185384 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 255.937i | − | 1.86816i | −0.357069 | − | 0.934078i | \(-0.616224\pi\) | ||
0.357069 | − | 0.934078i | \(-0.383776\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −21.7231 | + | 21.7231i | −0.156281 | + | 0.156281i | −0.780917 | − | 0.624635i | \(-0.785248\pi\) |
0.624635 | + | 0.780917i | \(0.285248\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −38.3743 | + | 38.3743i | −0.272158 | + | 0.272158i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 152.433i | − | 1.06597i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 111.755 | 0.770722 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −120.202 | − | 120.202i | −0.817703 | − | 0.817703i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 34.2444 | + | 34.2444i | 0.229828 | + | 0.229828i | 0.812621 | − | 0.582793i | \(-0.198040\pi\) |
−0.582793 | + | 0.812621i | \(0.698040\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 14.4645 | 0.0957913 | 0.0478956 | − | 0.998852i | \(-0.484749\pi\) | ||||
0.0478956 | + | 0.998852i | \(0.484749\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 29.1926i | 0.190801i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 89.7550 | − | 89.7550i | 0.579064 | − | 0.579064i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −31.4652 | + | 31.4652i | −0.200415 | + | 0.200415i | −0.800178 | − | 0.599763i | \(-0.795262\pi\) |
0.599763 | + | 0.800178i | \(0.295262\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 90.3229i | 0.568068i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −245.802 | −1.52672 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 31.4002 | + | 31.4002i | 0.192640 | + | 0.192640i | 0.796836 | − | 0.604196i | \(-0.206506\pi\) |
−0.604196 | + | 0.796836i | \(0.706506\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −81.8450 | − | 81.8450i | −0.496030 | − | 0.496030i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −36.4796 | −0.218441 | −0.109220 | − | 0.994018i | \(-0.534835\pi\) | ||||
−0.109220 | + | 0.994018i | \(0.534835\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 48.2981i | 0.285788i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −33.8469 | + | 33.8469i | −0.197935 | + | 0.197935i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −97.6419 | + | 97.6419i | −0.564404 | + | 0.564404i | −0.930555 | − | 0.366151i | \(-0.880675\pi\) |
0.366151 | + | 0.930555i | \(0.380675\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 21.8598i | 0.124913i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 34.6175 | 0.195579 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 89.7427 | + | 89.7427i | 0.501356 | + | 0.501356i | 0.911859 | − | 0.410503i | \(-0.134647\pi\) |
−0.410503 | + | 0.911859i | \(0.634647\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 115.497 | + | 115.497i | 0.638108 | + | 0.638108i | 0.950088 | − | 0.311981i | \(-0.100992\pi\) |
−0.311981 | + | 0.950088i | \(0.600992\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −104.152 | −0.569137 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 161.610i | 0.873569i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 95.4682 | − | 95.4682i | 0.510525 | − | 0.510525i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −44.5697 | + | 44.5697i | −0.235818 | + | 0.235818i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 62.6278i | 0.327894i | 0.986469 | + | 0.163947i | \(0.0524227\pi\) | ||||
−0.986469 | + | 0.163947i | \(0.947577\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 223.342 | 1.15721 | 0.578607 | − | 0.815607i | \(-0.303597\pi\) | ||||
0.578607 | + | 0.815607i | \(0.303597\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −64.8078 | − | 64.8078i | −0.332348 | − | 0.332348i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −29.0959 | − | 29.0959i | −0.147695 | − | 0.147695i | 0.629393 | − | 0.777087i | \(-0.283304\pi\) |
−0.777087 | + | 0.629393i | \(0.783304\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −11.6967 | −0.0587776 | −0.0293888 | − | 0.999568i | \(-0.509356\pi\) | ||||
−0.0293888 | + | 0.999568i | \(0.509356\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | − | 119.484i | − | 0.594445i | ||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −199.021 | + | 199.021i | −0.980398 | + | 0.980398i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −84.2755 | + | 84.2755i | −0.411100 | + | 0.411100i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 60.7904i | 0.293673i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 221.378 | 1.05923 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −0.215765 | − | 0.215765i | −0.00102258 | − | 0.00102258i | 0.706595 | − | 0.707618i | \(-0.250230\pi\) |
−0.707618 | + | 0.706595i | \(0.750230\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 9.47873 | + | 9.47873i | 0.0445011 | + | 0.0445011i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 203.556 | 0.946773 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 319.684i | 1.47320i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −104.613 | + | 104.613i | −0.477686 | + | 0.477686i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 75.5951 | − | 75.5951i | 0.342059 | − | 0.342059i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 371.347i | − | 1.66523i | −0.553850 | − | 0.832617i | \(-0.686842\pi\) | ||
0.553850 | − | 0.832617i | \(-0.313158\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 5.40622 | 0.0240277 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −209.823 | − | 209.823i | −0.924330 | − | 0.924330i | 0.0730018 | − | 0.997332i | \(-0.476742\pi\) |
−0.997332 | + | 0.0730018i | \(0.976742\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −152.751 | − | 152.751i | −0.667037 | − | 0.667037i | 0.289992 | − | 0.957029i | \(-0.406347\pi\) |
−0.957029 | + | 0.289992i | \(0.906347\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 291.511 | 1.26195 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 272.899i | − | 1.17124i | −0.810586 | − | 0.585619i | \(-0.800851\pi\) | ||
0.810586 | − | 0.585619i | \(-0.199149\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 106.710 | − | 106.710i | 0.454084 | − | 0.454084i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 128.958 | − | 128.958i | 0.544126 | − | 0.544126i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 104.650i | − | 0.437866i | −0.975740 | − | 0.218933i | \(-0.929742\pi\) | ||
0.975740 | − | 0.218933i | \(-0.0702576\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 148.875 | 0.617737 | 0.308869 | − | 0.951105i | \(-0.400050\pi\) | ||||
0.308869 | + | 0.951105i | \(0.400050\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 11.0227 | + | 11.0227i | 0.0453609 | + | 0.0453609i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 334.254 | + | 334.254i | 1.36430 | + | 1.36430i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 175.295 | 0.709698 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 152.169i | 0.611122i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 143.712 | − | 143.712i | 0.572558 | − | 0.572558i | −0.360284 | − | 0.932843i | \(-0.617320\pi\) |
0.932843 | + | 0.360284i | \(0.117320\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 198.802 | − | 198.802i | 0.785778 | − | 0.785778i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | − | 81.1777i | − | 0.318344i | ||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 134.023 | 0.521489 | 0.260745 | − | 0.965408i | \(-0.416032\pi\) | ||||
0.260745 | + | 0.965408i | \(0.416032\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −287.807 | − | 287.807i | −1.11122 | − | 1.11122i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 49.2206 | + | 49.2206i | 0.188585 | + | 0.188585i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −290.386 | −1.10413 | −0.552066 | − | 0.833801i | \(-0.686160\pi\) | ||||
−0.552066 | + | 0.833801i | \(0.686160\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 251.166i | − | 0.947798i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 155.754 | − | 155.754i | 0.583347 | − | 0.583347i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 74.2628 | − | 74.2628i | 0.276070 | − | 0.276070i | −0.555468 | − | 0.831538i | \(-0.687461\pi\) |
0.831538 | + | 0.555468i | \(0.187461\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 70.8329i | 0.261376i | 0.991424 | + | 0.130688i | \(0.0417186\pi\) | ||||
−0.991424 | + | 0.130688i | \(0.958281\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 230.829 | 0.845527 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −17.6799 | − | 17.6799i | −0.0642906 | − | 0.0642906i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 96.6953 | + | 96.6953i | 0.349081 | + | 0.349081i | 0.859767 | − | 0.510686i | \(-0.170609\pi\) |
−0.510686 | + | 0.859767i | \(0.670609\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 79.0625 | 0.283378 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 138.151i | 0.491640i | 0.969316 | + | 0.245820i | \(0.0790572\pi\) | ||||
−0.969316 | + | 0.245820i | \(0.920943\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −295.011 | + | 295.011i | −1.04244 | + | 1.04244i | −0.0433821 | + | 0.999059i | \(0.513813\pi\) |
−0.999059 | + | 0.0433821i | \(0.986187\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 94.1203 | − | 94.1203i | 0.330247 | − | 0.330247i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 300.168i | − | 1.04588i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −194.310 | −0.672353 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 180.464 | + | 180.464i | 0.620150 | + | 0.620150i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 33.4759 | + | 33.4759i | 0.114252 | + | 0.114252i | 0.761922 | − | 0.647669i | \(-0.224256\pi\) |
−0.647669 | + | 0.761922i | \(0.724256\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −96.2630 | −0.326315 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − | 72.0948i | − | 0.242743i | ||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 157.418 | − | 157.418i | 0.526483 | − | 0.526483i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −362.508 | + | 362.508i | −1.20434 | + | 1.20434i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 31.2776i | 0.103226i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 289.622 | 0.949582 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −92.6638 | − | 92.6638i | −0.301836 | − | 0.301836i | 0.539896 | − | 0.841732i | \(-0.318464\pi\) |
−0.841732 | + | 0.539896i | \(0.818464\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −21.7541 | − | 21.7541i | −0.0704016 | − | 0.0704016i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 18.5610 | 0.0596817 | 0.0298408 | − | 0.999555i | \(-0.490500\pi\) | ||||
0.0298408 | + | 0.999555i | \(0.490500\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 55.1534i | 0.176209i | 0.996111 | + | 0.0881045i | \(0.0280809\pi\) | ||||
−0.996111 | + | 0.0881045i | \(0.971919\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 123.938 | − | 123.938i | 0.393453 | − | 0.393453i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −62.2977 | + | 62.2977i | −0.196523 | + | 0.196523i | −0.798507 | − | 0.601985i | \(-0.794377\pi\) |
0.601985 | + | 0.798507i | \(0.294377\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 321.931i | − | 1.00919i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 38.9197 | 0.121245 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 109.787 | + | 109.787i | 0.339897 | + | 0.339897i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −13.9996 | − | 13.9996i | −0.0430756 | − | 0.0430756i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −194.307 | −0.594212 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 380.073i | 1.15524i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 373.767 | − | 373.767i | 1.12921 | − | 1.12921i | 0.138899 | − | 0.990307i | \(-0.455644\pi\) |
0.990307 | − | 0.138899i | \(-0.0443564\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −71.1788 | + | 71.1788i | −0.213750 | + | 0.213750i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 332.255i | 0.991807i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −519.936 | −1.54284 | −0.771419 | − | 0.636328i | \(-0.780453\pi\) | ||||
−0.771419 | + | 0.636328i | \(0.780453\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 205.191 | + | 205.191i | 0.605283 | + | 0.605283i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −258.557 | − | 258.557i | −0.758231 | − | 0.758231i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −596.142 | −1.73802 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | − | 169.044i | − | 0.489981i | ||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 122.160 | − | 122.160i | 0.352045 | − | 0.352045i | −0.508825 | − | 0.860870i | \(-0.669920\pi\) |
0.860870 | + | 0.508825i | \(0.169920\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 279.483 | − | 279.483i | 0.800810 | − | 0.800810i | −0.182412 | − | 0.983222i | \(-0.558391\pi\) |
0.983222 | + | 0.182412i | \(0.0583906\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − | 57.0872i | − | 0.162642i | ||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −212.266 | −0.601320 | −0.300660 | − | 0.953731i | \(-0.597207\pi\) | ||||
−0.300660 | + | 0.953731i | \(0.597207\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −26.3581 | − | 26.3581i | −0.0742482 | − | 0.0742482i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 144.567 | + | 144.567i | 0.404950 | + | 0.404950i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 435.033 | 1.21179 | 0.605895 | − | 0.795545i | \(-0.292815\pi\) | ||||
0.605895 | + | 0.795545i | \(0.292815\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | − | 106.419i | − | 0.294789i | ||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −87.5765 | + | 87.5765i | −0.241258 | + | 0.241258i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 290.905 | − | 290.905i | 0.796999 | − | 0.796999i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 125.535i | 0.342058i | 0.985266 | + | 0.171029i | \(0.0547091\pi\) | ||||
−0.985266 | + | 0.171029i | \(0.945291\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −74.2357 | −0.201181 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 447.295 | + | 447.295i | 1.20565 | + | 1.20565i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 302.389 | + | 302.389i | 0.810694 | + | 0.810694i | 0.984738 | − | 0.174044i | \(-0.0556835\pi\) |
−0.174044 | + | 0.984738i | \(0.555683\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −223.591 | −0.596242 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 254.917i | − | 0.676171i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 189.784 | − | 189.784i | 0.500751 | − | 0.500751i | −0.410921 | − | 0.911671i | \(-0.634793\pi\) |
0.911671 | + | 0.410921i | \(0.134793\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 242.802 | − | 242.802i | 0.637275 | − | 0.637275i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 639.916i | 1.67080i | 0.549644 | + | 0.835399i | \(0.314763\pi\) | ||||
−0.549644 | + | 0.835399i | \(0.685237\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −810.623 | −2.10551 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 89.6533 | + | 89.6533i | 0.231662 | + | 0.231662i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −499.333 | − | 499.333i | −1.28363 | − | 1.28363i | −0.938586 | − | 0.345046i | \(-0.887863\pi\) |
−0.345046 | − | 0.938586i | \(-0.612137\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 197.181 | 0.504300 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 329.061i | − | 0.837306i | ||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −358.601 | + | 358.601i | −0.907851 | + | 0.907851i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −492.518 | + | 492.518i | −1.24060 | + | 1.24060i | −0.280846 | + | 0.959753i | \(0.590615\pi\) |
−0.959753 | + | 0.280846i | \(0.909385\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 335.233i | 0.840182i | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 705.045 | 1.75822 | 0.879109 | − | 0.476621i | \(-0.158138\pi\) | ||||
0.879109 | + | 0.476621i | \(0.158138\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −204.735 | − | 204.735i | −0.508026 | − | 0.508026i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −30.6515 | − | 30.6515i | −0.0756828 | − | 0.0756828i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 465.550 | 1.14386 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 279.815i | 0.684144i | 0.939674 | + | 0.342072i | \(0.111129\pi\) | ||||
−0.939674 | + | 0.342072i | \(0.888871\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −313.458 | + | 313.458i | −0.762671 | + | 0.762671i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 171.432 | − | 171.432i | 0.415090 | − | 0.415090i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 423.147i | − | 1.01963i | ||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 53.2106 | 0.127603 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −573.583 | − | 573.583i | −1.36893 | − | 1.36893i | −0.861965 | − | 0.506968i | \(-0.830766\pi\) |
−0.506968 | − | 0.861965i | \(-0.669234\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 213.341 | + | 213.341i | 0.506749 | + | 0.506749i | 0.913527 | − | 0.406778i | \(-0.133348\pi\) |
−0.406778 | + | 0.913527i | \(0.633348\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 93.9974 | 0.222216 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − | 17.5358i | − | 0.0412606i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −515.781 | + | 515.781i | −1.20792 | + | 1.20792i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −186.692 | + | 186.692i | −0.435178 | + | 0.435178i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 166.900i | − | 0.387239i | −0.981077 | − | 0.193619i | \(-0.937977\pi\) | ||
0.981077 | − | 0.193619i | \(-0.0620227\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 233.153 | 0.538459 | 0.269230 | − | 0.963076i | \(-0.413231\pi\) | ||||
0.269230 | + | 0.963076i | \(0.413231\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −136.871 | − | 136.871i | −0.314646 | − | 0.314646i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 228.619 | + | 228.619i | 0.523155 | + | 0.523155i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −440.480 | −1.00337 | −0.501686 | − | 0.865050i | \(-0.667287\pi\) | ||||
−0.501686 | + | 0.865050i | \(0.667287\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 294.434i | 0.667651i | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −312.524 | + | 312.524i | −0.705473 | + | 0.705473i | −0.965580 | − | 0.260107i | \(-0.916242\pi\) |
0.260107 | + | 0.965580i | \(0.416242\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −433.114 | + | 433.114i | −0.973290 | + | 0.973290i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − | 83.8814i | − | 0.187654i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −734.338 | −1.63550 | −0.817748 | − | 0.575576i | \(-0.804778\pi\) | ||||
−0.817748 | + | 0.575576i | \(0.804778\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 242.772 | + | 242.772i | 0.538297 | + | 0.538297i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −17.7153 | − | 17.7153i | −0.0391066 | − | 0.0391066i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −641.880 | −1.41073 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 692.749i | 1.51586i | 0.652335 | + | 0.757931i | \(0.273789\pi\) | ||||
−0.652335 | + | 0.757931i | \(0.726211\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 35.7535 | − | 35.7535i | 0.0778944 | − | 0.0778944i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −298.447 | + | 298.447i | −0.647391 | + | 0.647391i | −0.952362 | − | 0.304971i | \(-0.901353\pi\) |
0.304971 | + | 0.952362i | \(0.401353\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 281.830i | − | 0.608705i | −0.952560 | − | 0.304352i | \(-0.901560\pi\) | ||
0.952560 | − | 0.304352i | \(-0.0984400\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −219.854 | −0.472804 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 198.116 | + | 198.116i | 0.424232 | + | 0.424232i | 0.886658 | − | 0.462426i | \(-0.153021\pi\) |
−0.462426 | + | 0.886658i | \(0.653021\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −591.704 | − | 591.704i | −1.26163 | − | 1.26163i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 77.0737 | 0.163638 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 586.384i | − | 1.23971i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 20.3316 | − | 20.3316i | 0.0428033 | − | 0.0428033i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 110.622 | − | 110.622i | 0.231913 | − | 0.231913i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 917.713i | 1.91589i | 0.286945 | + | 0.957947i | \(0.407360\pi\) | ||||
−0.286945 | + | 0.957947i | \(0.592640\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 368.639 | 0.766401 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 301.045 | + | 301.045i | 0.623282 | + | 0.623282i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −501.826 | − | 501.826i | −1.03469 | − | 1.03469i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 426.183 | 0.875119 | 0.437559 | − | 0.899190i | \(-0.355843\pi\) | ||||
0.437559 | + | 0.899190i | \(0.355843\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 76.9146i | − | 0.157290i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −266.299 | + | 266.299i | −0.542361 | + | 0.542361i | −0.924220 | − | 0.381859i | \(-0.875284\pi\) |
0.381859 | + | 0.924220i | \(0.375284\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 159.653 | − | 159.653i | 0.323840 | − | 0.323840i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 200.479i | 0.405007i | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 93.8809 | 0.188895 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −264.104 | − | 264.104i | −0.529266 | − | 0.529266i | 0.391088 | − | 0.920353i | \(-0.372099\pi\) |
−0.920353 | + | 0.391088i | \(0.872099\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 44.6782 | + | 44.6782i | 0.0891781 | + | 0.0891781i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 574.766 | 1.14268 | 0.571338 | − | 0.820715i | \(-0.306425\pi\) | ||||
0.571338 | + | 0.820715i | \(0.306425\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 86.9756i | − | 0.172229i | ||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 59.1528 | − | 59.1528i | 0.116672 | − | 0.116672i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −170.592 | + | 170.592i | −0.335152 | + | 0.335152i | −0.854539 | − | 0.519387i | \(-0.826160\pi\) |
0.519387 | + | 0.854539i | \(0.326160\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1036.13i | 2.02765i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 82.9077 | 0.161614 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 60.4930 | + | 60.4930i | 0.117462 | + | 0.117462i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −307.398 | − | 307.398i | −0.594581 | − | 0.594581i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 239.173 | 0.460834 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 37.1210i | 0.0712496i | 0.999365 | + | 0.0356248i | \(0.0113421\pi\) | ||||
−0.999365 | + | 0.0356248i | \(0.988658\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −199.555 | + | 199.555i | −0.381558 | + | 0.381558i | −0.871663 | − | 0.490105i | \(-0.836958\pi\) |
0.490105 | + | 0.871663i | \(0.336958\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 26.7726 | − | 26.7726i | 0.0509955 | − | 0.0509955i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 256.449i | − | 0.486620i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −118.392 | −0.223804 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −42.3976 | − | 42.3976i | −0.0798448 | − | 0.0798448i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 192.236 | + | 192.236i | 0.360667 | + | 0.360667i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −108.226 | −0.202292 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − | 219.824i | − | 0.409355i | ||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 962.884 | − | 962.884i | 1.78643 | − | 1.78643i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −278.121 | + | 278.121i | −0.514086 | + | 0.514086i | −0.915776 | − | 0.401690i | \(-0.868423\pi\) |
0.401690 | + | 0.915776i | \(0.368423\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − | 282.910i | − | 0.521013i | ||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 540.323 | 0.991418 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 724.938 | + | 724.938i | 1.32530 | + | 1.32530i | 0.909421 | + | 0.415876i | \(0.136525\pi\) |
0.415876 | + | 0.909421i | \(0.363475\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 127.560 | + | 127.560i | 0.232349 | + | 0.232349i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 370.215 | 0.671897 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 1277.25i | − | 2.30967i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 197.931 | − | 197.931i | 0.356633 | − | 0.356633i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −268.298 | + | 268.298i | −0.481685 | + | 0.481685i | −0.905669 | − | 0.423985i | \(-0.860631\pi\) |
0.423985 | + | 0.905669i | \(0.360631\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 464.320i | − | 0.830625i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −233.848 | −0.416842 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −78.4662 | − | 78.4662i | −0.139372 | − | 0.139372i | 0.633979 | − | 0.773350i | \(-0.281421\pi\) |
−0.773350 | + | 0.633979i | \(0.781421\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −570.587 | − | 570.587i | −1.00989 | − | 1.00989i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 109.173 | 0.192545 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 801.999i | 1.40949i | 0.709461 | + | 0.704744i | \(0.248938\pi\) | ||||
−0.709461 | + | 0.704744i | \(0.751062\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 79.9964 | − | 79.9964i | 0.140099 | − | 0.140099i | −0.633579 | − | 0.773678i | \(-0.718415\pi\) |
0.773678 | + | 0.633579i | \(0.218415\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 76.7031 | − | 76.7031i | 0.133862 | − | 0.133862i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 36.5163i | − | 0.0635066i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −237.186 | −0.411068 | −0.205534 | − | 0.978650i | \(-0.565893\pi\) | ||||
−0.205534 | + | 0.978650i | \(0.565893\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −273.537 | − | 273.537i | −0.472430 | − | 0.472430i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 753.571 | + | 753.571i | 1.29702 | + | 1.29702i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −723.534 | −1.24105 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 158.746i | 0.271361i | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −267.958 | + | 267.958i | −0.456487 | + | 0.456487i | −0.897500 | − | 0.441014i | \(-0.854619\pi\) |
0.441014 | + | 0.897500i | \(0.354619\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 297.336 | − | 297.336i | 0.504815 | − | 0.504815i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 71.2701i | 0.120592i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −607.086 | −1.02375 | −0.511877 | − | 0.859059i | \(-0.671050\pi\) | ||||
−0.511877 | + | 0.859059i | \(0.671050\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −402.007 | − | 402.007i | −0.675642 | − | 0.675642i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 14.3255 | + | 14.3255i | 0.0239958 | + | 0.0239958i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −575.392 | −0.960587 | −0.480294 | − | 0.877108i | \(-0.659470\pi\) | ||||
−0.480294 | + | 0.877108i | \(0.659470\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 310.094i | 0.515963i | 0.966150 | + | 0.257981i | \(0.0830573\pi\) | ||||
−0.966150 | + | 0.257981i | \(0.916943\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −146.337 | + | 146.337i | −0.242681 | + | 0.242681i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 243.529 | − | 243.529i | 0.402528 | − | 0.402528i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 556.510i | − | 0.916820i | −0.888741 | − | 0.458410i | \(-0.848419\pi\) | ||
0.888741 | − | 0.458410i | \(-0.151581\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 487.499 | 0.800492 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −243.409 | − | 243.409i | −0.398378 | − | 0.398378i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 326.241 | + | 326.241i | 0.532204 | + | 0.532204i | 0.921228 | − | 0.389024i | \(-0.127188\pi\) |
−0.389024 | + | 0.921228i | \(0.627188\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 206.432 | 0.335662 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 502.068i | 0.813725i | 0.913490 | + | 0.406862i | \(0.133377\pi\) | ||||
−0.913490 | + | 0.406862i | \(0.866623\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 304.429 | − | 304.429i | 0.491808 | − | 0.491808i | −0.417067 | − | 0.908876i | \(-0.636942\pi\) |
0.908876 | + | 0.417067i | \(0.136942\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 74.4527 | − | 74.4527i | 0.119892 | − | 0.119892i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − | 1542.64i | − | 2.47615i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 576.701 | 0.922721 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −271.132 | − | 271.132i | −0.432428 | − | 0.432428i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 230.877 | + | 230.877i | 0.367054 | + | 0.367054i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −8.60592 | −0.0136385 | −0.00681927 | − | 0.999977i | \(-0.502171\pi\) | ||||
−0.00681927 | + | 0.999977i | \(0.502171\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0.528515i | 0.000834936i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −675.174 | + | 675.174i | −1.06327 | + | 1.06327i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 762.446 | − | 762.446i | 1.19693 | − | 1.19693i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | − | 23.2181i | − | 0.0363350i | ||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −445.780 | −0.695445 | −0.347722 | − | 0.937598i | \(-0.613045\pi\) | ||||
−0.347722 | + | 0.937598i | \(0.613045\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −118.001 | − | 118.001i | −0.183517 | − | 0.183517i | 0.609369 | − | 0.792886i | \(-0.291423\pi\) |
−0.792886 | + | 0.609369i | \(0.791423\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −249.304 | − | 249.304i | −0.386519 | − | 0.386519i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −1081.35 | −1.67132 | −0.835662 | − | 0.549243i | \(-0.814916\pi\) | ||||
−0.835662 | + | 0.549243i | \(0.814916\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 277.305i | 0.427280i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 391.532 | − | 391.532i | 0.601431 | − | 0.601431i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 586.227 | − | 586.227i | 0.897744 | − | 0.897744i | −0.0974927 | − | 0.995236i | \(-0.531082\pi\) |
0.995236 | + | 0.0974927i | \(0.0310823\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 915.041i | 1.39701i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 256.249 | 0.390029 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 469.999 | + | 469.999i | 0.713201 | + | 0.713201i | 0.967204 | − | 0.254003i | \(-0.0817472\pi\) |
−0.254003 | + | 0.967204i | \(0.581747\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 884.745 | + | 884.745i | 1.33849 | + | 1.33849i | 0.897519 | + | 0.440976i | \(0.145368\pi\) |
0.440976 | + | 0.897519i | \(0.354632\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −185.170 | −0.279290 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − | 932.202i | − | 1.40181i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 332.460 | − | 332.460i | 0.498441 | − | 0.498441i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −454.805 | + | 454.805i | −0.679829 | + | 0.679829i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 834.314i | − | 1.24339i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 684.329 | 1.01683 | 0.508417 | − | 0.861111i | \(-0.330231\pi\) | ||||
0.508417 | + | 0.861111i | \(0.330231\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −6.62125 | − | 6.62125i | −0.00980925 | − | 0.00980925i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 383.762 | + | 383.762i | 0.566857 | + | 0.566857i | 0.931246 | − | 0.364390i | \(-0.118722\pi\) |
−0.364390 | + | 0.931246i | \(0.618722\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1787.38 | 2.63237 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 513.959i | 0.754712i | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 903.626 | − | 903.626i | 1.32302 | − | 1.32302i | 0.411709 | − | 0.911315i | \(-0.364932\pi\) |
0.911315 | − | 0.411709i | \(-0.135068\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 871.652 | − | 871.652i | 1.27248 | − | 1.27248i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 374.163i | 0.544633i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −572.920 | −0.831524 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −63.6870 | − | 63.6870i | −0.0921665 | − | 0.0921665i | 0.659520 | − | 0.751687i | \(-0.270759\pi\) |
−0.751687 | + | 0.659520i | \(0.770759\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −357.027 | − | 357.027i | −0.515190 | − | 0.515190i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −147.966 | −0.212901 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 240.793i | 0.345470i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −334.231 | + | 334.231i | −0.478156 | + | 0.478156i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −218.312 | + | 218.312i | −0.311430 | + | 0.311430i | −0.845463 | − | 0.534033i | \(-0.820676\pi\) |
0.534033 | + | 0.845463i | \(0.320676\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 535.374i | 0.761557i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −261.384 | −0.370758 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 154.893 | + | 154.893i | 0.219084 | + | 0.219084i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 822.199 | + | 822.199i | 1.15966 | + | 1.15966i | 0.984548 | + | 0.175112i | \(0.0560288\pi\) |
0.175112 | + | 0.984548i | \(0.443971\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −315.881 | −0.444277 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 534.026i | − | 0.748985i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 519.145 | − | 519.145i | 0.726077 | − | 0.726077i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −128.169 | + | 128.169i | −0.178758 | + | 0.178758i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 340.913i | 0.474149i | 0.971491 | + | 0.237074i | \(0.0761885\pi\) | ||||
−0.971491 | + | 0.237074i | \(0.923811\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −215.461 | −0.298836 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −182.334 | − | 182.334i | −0.252190 | − | 0.252190i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −29.5664 | − | 29.5664i | −0.0407813 | − | 0.0407813i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 803.090 | 1.10466 | 0.552331 | − | 0.833625i | \(-0.313738\pi\) | ||||
0.552331 | + | 0.833625i | \(0.313738\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | − | 27.0000i | − | 0.0370370i | ||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 290.802 | − | 290.802i | 0.397813 | − | 0.397813i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −481.592 | + | 481.592i | −0.657015 | + | 0.657015i | −0.954673 | − | 0.297658i | \(-0.903795\pi\) |
0.297658 | + | 0.954673i | \(0.403795\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | − | 818.752i | − | 1.11395i | ||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 957.127 | 1.29868 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 173.622 | + | 173.622i | 0.234941 | + | 0.234941i | 0.814752 | − | 0.579810i | \(-0.196873\pi\) |
−0.579810 | + | 0.814752i | \(0.696873\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −214.692 | − | 214.692i | −0.289733 | − | 0.289733i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −1316.22 | −1.77149 | −0.885744 | − | 0.464173i | \(-0.846351\pi\) | ||||
−0.885744 | + | 0.464173i | \(0.846351\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 233.254i | 0.313093i | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 186.369 | − | 186.369i | 0.249490 | − | 0.249490i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 192.737 | − | 192.737i | 0.257326 | − | 0.257326i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 322.977i | − | 0.430062i | −0.976607 | − | 0.215031i | \(-0.931015\pi\) | ||
0.976607 | − | 0.215031i | \(-0.0689853\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −352.021 | −0.467492 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 49.2621 | + | 49.2621i | 0.0652478 | + | 0.0652478i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 80.2744 | + | 80.2744i | 0.106043 | + | 0.106043i | 0.758138 | − | 0.652095i | \(-0.226110\pi\) |
−0.652095 | + | 0.758138i | \(0.726110\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −486.963 | −0.641585 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 596.664i | 0.784053i | 0.919954 | + | 0.392027i | \(0.128226\pi\) | ||||
−0.919954 | + | 0.392027i | \(0.871774\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −962.246 | + | 962.246i | −1.26113 | + | 1.26113i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −99.4220 | + | 99.4220i | −0.129963 | + | 0.129963i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 219.580i | 0.286284i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1515.31 | 1.97050 | 0.985249 | − | 0.171129i | \(-0.0547416\pi\) | ||||
0.985249 | + | 0.171129i | \(0.0547416\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −164.144 | − | 164.144i | −0.212897 | − | 0.212897i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −607.901 | − | 607.901i | −0.786418 | − | 0.786418i | 0.194487 | − | 0.980905i | \(-0.437696\pi\) |
−0.980905 | + | 0.194487i | \(0.937696\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −47.4922 | −0.0612802 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 704.981i | 0.907311i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −279.184 | + | 279.184i | −0.358387 | + | 0.358387i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −75.9297 | + | 75.9297i | −0.0972211 | + | 0.0972211i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − | 120.565i | − | 0.153979i | ||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −214.324 | −0.273024 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 356.009 | + | 356.009i | 0.452362 | + | 0.452362i | 0.896138 | − | 0.443776i | \(-0.146361\pi\) |
−0.443776 | + | 0.896138i | \(0.646361\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 355.649 | + | 355.649i | 0.450760 | + | 0.450760i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 2032.29 | 2.56926 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 660.640i | − | 0.833089i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −307.615 | + | 307.615i | −0.386937 | + | 0.386937i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −971.380 | + | 971.380i | −1.21880 | + | 1.21880i | −0.250742 | + | 0.968054i | \(0.580674\pi\) |
−0.968054 | + | 0.250742i | \(0.919326\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 304.892i | − | 0.381592i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −381.517 | −0.476301 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −838.008 | − | 838.008i | −1.04360 | − | 1.04360i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −837.135 | − | 837.135i | −1.03992 | − | 1.03992i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −181.906 | −0.225410 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 678.276i | − | 0.838412i | −0.907891 | − | 0.419206i | \(-0.862308\pi\) | ||
0.907891 | − | 0.419206i | \(-0.137692\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 204.625 | − | 204.625i | 0.252312 | − | 0.252312i | −0.569606 | − | 0.821918i | \(-0.692904\pi\) |
0.821918 | + | 0.569606i | \(0.192904\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 86.7522 | − | 86.7522i | 0.106706 | − | 0.106706i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 213.881i | 0.262431i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 674.331 | 0.825375 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −282.706 | − | 282.706i | −0.345185 | − | 0.345185i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −326.524 | − | 326.524i | −0.397715 | − | 0.397715i | 0.479711 | − | 0.877426i | \(-0.340741\pi\) |
−0.877426 | + | 0.479711i | \(0.840741\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −804.270 | −0.977241 | −0.488621 | − | 0.872496i | \(-0.662500\pi\) | ||||
−0.488621 | + | 0.872496i | \(0.662500\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 43.3067i | 0.0524930i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 848.530 | − | 848.530i | 1.02603 | − | 1.02603i | 0.0263821 | − | 0.999652i | \(-0.491601\pi\) |
0.999652 | − | 0.0263821i | \(-0.00839864\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −49.5139 | + | 49.5139i | −0.0597273 | + | 0.0597273i | −0.736340 | − | 0.676612i | \(-0.763447\pi\) |
0.676612 | + | 0.736340i | \(0.263447\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | − | 236.854i | − | 0.285023i | ||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 955.034 | 1.14650 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −124.240 | − | 124.240i | −0.148790 | − | 0.148790i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −96.8313 | − | 96.8313i | −0.115689 | − | 0.115689i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −866.213 | −1.03244 | −0.516218 | − | 0.856457i | \(-0.672660\pi\) | ||||
−0.516218 | + | 0.856457i | \(0.672660\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 302.629i | 0.359844i | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 169.199 | − | 169.199i | 0.200711 | − | 0.200711i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −164.490 | + | 164.490i | −0.194663 | + | 0.194663i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 867.390i | 1.02407i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 722.626 | 0.851149 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 480.776 | + | 480.776i | 0.564954 | + | 0.564954i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −313.947 | − | 313.947i | −0.368050 | − | 0.368050i | 0.498715 | − | 0.866766i | \(-0.333805\pi\) |
−0.866766 | + | 0.498715i | \(0.833805\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −230.547 | −0.269645 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 473.297i | 0.552272i | 0.961119 | + | 0.276136i | \(0.0890540\pi\) | ||||
−0.961119 | + | 0.276136i | \(0.910946\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −595.383 | + | 595.383i | −0.693112 | + | 0.693112i | −0.962915 | − | 0.269803i | \(-0.913041\pi\) |
0.269803 | + | 0.962915i | \(0.413041\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −367.629 | + | 367.629i | −0.426979 | + | 0.426979i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 742.134i | − | 0.859947i | −0.902842 | − | 0.429973i | \(-0.858523\pi\) | ||
0.902842 | − | 0.429973i | \(-0.141477\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −665.083 | −0.768882 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 237.980 | + | 237.980i | 0.274487 | + | 0.274487i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1033.02 | + | 1033.02i | 1.18875 | + | 1.18875i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 757.887 | 0.870134 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 442.044i | − | 0.506350i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −1107.26 | + | 1107.26i | −1.26544 | + | 1.26544i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 791.224 | − | 791.224i | 0.902194 | − | 0.902194i | −0.0934320 | − | 0.995626i | \(-0.529784\pi\) |
0.995626 | + | 0.0934320i | \(0.0297838\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | − | 81.9989i | − | 0.0932865i | ||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −1524.92 | −1.73090 | −0.865450 | − | 0.500995i | \(-0.832967\pi\) | ||||
−0.865450 | + | 0.500995i | \(0.832967\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −314.328 | − | 314.328i | −0.355978 | − | 0.355978i | 0.506350 | − | 0.862328i | \(-0.330994\pi\) |
−0.862328 | + | 0.506350i | \(0.830994\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 117.898 | + | 117.898i | 0.133218 | + | 0.133218i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 1520.80 | 1.71454 | 0.857271 | − | 0.514866i | \(-0.172158\pi\) | ||||
0.857271 | + | 0.514866i | \(0.172158\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 2404.80i | − | 2.70506i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −88.2977 | + | 88.2977i | −0.0990996 | + | 0.0990996i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 353.503 | − | 353.503i | 0.395860 | − | 0.395860i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 611.278i | 0.682992i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −385.595 | −0.429872 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −432.389 | − | 432.389i | −0.480967 | − | 0.480967i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −358.818 | − | 358.818i | −0.398244 | − | 0.398244i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 887.959 | 0.983343 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 786.705i | 0.869288i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −216.886 | + | 216.886i | −0.239125 | + | 0.239125i | −0.816488 | − | 0.577363i | \(-0.804082\pi\) |
0.577363 | + | 0.816488i | \(0.304082\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 38.3071 | − | 38.3071i | 0.0421420 | − | 0.0421420i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 799.632i | − | 0.877752i | −0.898548 | − | 0.438876i | \(-0.855377\pi\) | ||
0.898548 | − | 0.438876i | \(-0.144623\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1218.96 | −1.33511 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −354.714 | − | 354.714i | −0.387665 | − | 0.387665i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −1629.57 | − | 1629.57i | −1.77707 | − | 1.77707i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 640.590 | 0.697051 | 0.348525 | − | 0.937299i | \(-0.386683\pi\) | ||||
0.348525 | + | 0.937299i | \(0.386683\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 226.979i | 0.246448i | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −60.1238 | + | 60.1238i | −0.0651396 | + | 0.0651396i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 42.7565 | − | 42.7565i | 0.0462232 | − | 0.0462232i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 53.2864i | 0.0574827i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 118.633 | 0.127699 | 0.0638496 | − | 0.997960i | \(-0.479662\pi\) | ||||
0.0638496 | + | 0.997960i | \(0.479662\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1107.30 | + | 1107.30i | 1.18937 | + | 1.18937i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −22.7325 | − | 22.7325i | −0.0243649 | − | 0.0243649i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 650.277 | 0.695483 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 731.334i | 0.780506i | 0.920708 | + | 0.390253i | \(0.127612\pi\) | ||||
−0.920708 | + | 0.390253i | \(0.872388\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 67.5488 | − | 67.5488i | 0.0719370 | − | 0.0719370i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −980.281 | + | 980.281i | −1.04174 | + | 1.04174i | −0.0426536 | + | 0.999090i | \(0.513581\pi\) |
−0.999090 | + | 0.0426536i | \(0.986419\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 501.424i | 0.531733i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −303.584 | −0.321253 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −240.008 | − | 240.008i | −0.253441 | − | 0.253441i | 0.568939 | − | 0.822380i | \(-0.307354\pi\) |
−0.822380 | + | 0.568939i | \(0.807354\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −663.564 | − | 663.564i | −0.699225 | − | 0.699225i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 152.597 | 0.160460 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 780.049i | − | 0.818519i | −0.912418 | − | 0.409259i | \(-0.865787\pi\) | ||
0.912418 | − | 0.409259i | \(-0.134213\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −213.293 | + | 213.293i | −0.223344 | + | 0.223344i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −394.284 | + | 394.284i | −0.412000 | + | 0.412000i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 3104.60i | 3.23733i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 266.459 | 0.277272 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −47.6666 | − | 47.6666i | −0.0494981 | − | 0.0494981i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 760.642 | + | 760.642i | 0.788230 | + | 0.788230i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1783.10 | −1.84395 | −0.921975 | − | 0.387249i | \(-0.873425\pi\) | ||||
−0.921975 | + | 0.387249i | \(0.873425\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | − | 268.922i | − | 0.277525i | ||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −159.340 | + | 159.340i | −0.164099 | + | 0.164099i | −0.784380 | − | 0.620281i | \(-0.787019\pi\) |
0.620281 | + | 0.784380i | \(0.287019\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 263.509 | − | 263.509i | 0.270821 | − | 0.270821i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 34.2918i | 0.0351711i | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −970.922 | −0.993779 | −0.496889 | − | 0.867814i | \(-0.665525\pi\) | ||||
−0.496889 | + | 0.867814i | \(0.665525\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1247.67 | + | 1247.67i | 1.27443 | + | 1.27443i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 237.977 | + | 237.977i | 0.242586 | + | 0.242586i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −1266.90 | −1.28881 | −0.644406 | − | 0.764684i | \(-0.722895\pi\) | ||||
−0.644406 | + | 0.764684i | \(0.722895\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − | 198.185i | − | 0.201203i | ||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 465.492 | − | 465.492i | 0.471623 | − | 0.471623i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 605.562 | − | 605.562i | 0.612297 | − | 0.612297i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 222.422i | 0.224442i | 0.993683 | + | 0.112221i | \(0.0357964\pi\) | ||||
−0.993683 | + | 0.112221i | \(0.964204\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −915.539 | −0.921993 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −39.8359 | − | 39.8359i | −0.0400360 | − | 0.0400360i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 441.746 | + | 441.746i | 0.443075 | + | 0.443075i | 0.893044 | − | 0.449969i | \(-0.148565\pi\) |
−0.449969 | + | 0.893044i | \(0.648565\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 174.352 | 0.174526 |
(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 | 384.3.l.b.31.3 | 16 | ||
3.2 | odd | 2 | 1152.3.m.c.415.3 | 16 | |||
4.3 | odd | 2 | 384.3.l.a.31.7 | 16 | |||
8.3 | odd | 2 | 48.3.l.a.43.5 | yes | 16 | ||
8.5 | even | 2 | 192.3.l.a.79.6 | 16 | |||
12.11 | even | 2 | 1152.3.m.f.415.3 | 16 | |||
16.3 | odd | 4 | inner | 384.3.l.b.223.3 | 16 | ||
16.5 | even | 4 | 48.3.l.a.19.5 | ✓ | 16 | ||
16.11 | odd | 4 | 192.3.l.a.175.6 | 16 | |||
16.13 | even | 4 | 384.3.l.a.223.7 | 16 | |||
24.5 | odd | 2 | 576.3.m.c.271.6 | 16 | |||
24.11 | even | 2 | 144.3.m.c.91.4 | 16 | |||
48.5 | odd | 4 | 144.3.m.c.19.4 | 16 | |||
48.11 | even | 4 | 576.3.m.c.559.6 | 16 | |||
48.29 | odd | 4 | 1152.3.m.f.991.3 | 16 | |||
48.35 | even | 4 | 1152.3.m.c.991.3 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
48.3.l.a.19.5 | ✓ | 16 | 16.5 | even | 4 | ||
48.3.l.a.43.5 | yes | 16 | 8.3 | odd | 2 | ||
144.3.m.c.19.4 | 16 | 48.5 | odd | 4 | |||
144.3.m.c.91.4 | 16 | 24.11 | even | 2 | |||
192.3.l.a.79.6 | 16 | 8.5 | even | 2 | |||
192.3.l.a.175.6 | 16 | 16.11 | odd | 4 | |||
384.3.l.a.31.7 | 16 | 4.3 | odd | 2 | |||
384.3.l.a.223.7 | 16 | 16.13 | even | 4 | |||
384.3.l.b.31.3 | 16 | 1.1 | even | 1 | trivial | ||
384.3.l.b.223.3 | 16 | 16.3 | odd | 4 | inner | ||
576.3.m.c.271.6 | 16 | 24.5 | odd | 2 | |||
576.3.m.c.559.6 | 16 | 48.11 | even | 4 | |||
1152.3.m.c.415.3 | 16 | 3.2 | odd | 2 | |||
1152.3.m.c.991.3 | 16 | 48.35 | even | 4 | |||
1152.3.m.f.415.3 | 16 | 12.11 | even | 2 | |||
1152.3.m.f.991.3 | 16 | 48.29 | odd | 4 |