Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [507,4,Mod(337,507)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(507, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("507.337");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 507 = 3 \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 507.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: | \(29.9139683729\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(i)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 39) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 337.1 | ||
Root | \(-1.00000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 507.337 |
Dual form | 507.4.b.c.337.2 |
$q$-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 \(\left(\mathbb{Z}/507\mathbb{Z}\right)^\times\).
\(n\) | \(170\) | \(340\) |
\(\chi(n)\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − 3.00000i | − 1.06066i | −0.847791 | − | 0.530330i | \(-0.822068\pi\) | ||||
0.847791 | − | 0.530330i | \(-0.177932\pi\) | |||||||
\(3\) | 3.00000 | 0.577350 | ||||||||
\(4\) | −1.00000 | −0.125000 | ||||||||
\(5\) | 9.00000i | 0.804984i | 0.915423 | + | 0.402492i | \(0.131856\pi\) | ||||
−0.915423 | + | 0.402492i | \(0.868144\pi\) | |||||||
\(6\) | − 9.00000i | − 0.612372i | ||||||||
\(7\) | 2.00000i | 0.107990i | 0.998541 | + | 0.0539949i | \(0.0171955\pi\) | ||||
−0.998541 | + | 0.0539949i | \(0.982805\pi\) | |||||||
\(8\) | − 21.0000i | − 0.928078i | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | 27.0000 | 0.853815 | ||||||||
\(11\) | 30.0000i | 0.822304i | 0.911567 | + | 0.411152i | \(0.134873\pi\) | ||||
−0.911567 | + | 0.411152i | \(0.865127\pi\) | |||||||
\(12\) | −3.00000 | −0.0721688 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 6.00000 | 0.114541 | ||||||||
\(15\) | 27.0000i | 0.464758i | ||||||||
\(16\) | −71.0000 | −1.10938 | ||||||||
\(17\) | 111.000 | 1.58361 | 0.791807 | − | 0.610771i | \(-0.209140\pi\) | ||||
0.791807 | + | 0.610771i | \(0.209140\pi\) | |||||||
\(18\) | − 27.0000i | − 0.353553i | ||||||||
\(19\) | 46.0000i | 0.555428i | 0.960664 | + | 0.277714i | \(0.0895767\pi\) | ||||
−0.960664 | + | 0.277714i | \(0.910423\pi\) | |||||||
\(20\) | − 9.00000i | − 0.100623i | ||||||||
\(21\) | 6.00000i | 0.0623480i | ||||||||
\(22\) | 90.0000 | 0.872185 | ||||||||
\(23\) | 6.00000 | 0.0543951 | 0.0271975 | − | 0.999630i | \(-0.491342\pi\) | ||||
0.0271975 | + | 0.999630i | \(0.491342\pi\) | |||||||
\(24\) | − 63.0000i | − 0.535826i | ||||||||
\(25\) | 44.0000 | 0.352000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 27.0000 | 0.192450 | ||||||||
\(28\) | − 2.00000i | − 0.0134987i | ||||||||
\(29\) | −105.000 | −0.672345 | −0.336173 | − | 0.941800i | \(-0.609133\pi\) | ||||
−0.336173 | + | 0.941800i | \(0.609133\pi\) | |||||||
\(30\) | 81.0000 | 0.492950 | ||||||||
\(31\) | 100.000i | 0.579372i | 0.957122 | + | 0.289686i | \(0.0935509\pi\) | ||||
−0.957122 | + | 0.289686i | \(0.906449\pi\) | |||||||
\(32\) | 45.0000i | 0.248592i | ||||||||
\(33\) | 90.0000i | 0.474757i | ||||||||
\(34\) | − 333.000i | − 1.67968i | ||||||||
\(35\) | −18.0000 | −0.0869302 | ||||||||
\(36\) | −9.00000 | −0.0416667 | ||||||||
\(37\) | 17.0000i | 0.0755347i | 0.999287 | + | 0.0377673i | \(0.0120246\pi\) | ||||
−0.999287 | + | 0.0377673i | \(0.987975\pi\) | |||||||
\(38\) | 138.000 | 0.589120 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 189.000 | 0.747088 | ||||||||
\(41\) | 231.000i | 0.879906i | 0.898021 | + | 0.439953i | \(0.145005\pi\) | ||||
−0.898021 | + | 0.439953i | \(0.854995\pi\) | |||||||
\(42\) | 18.0000 | 0.0661300 | ||||||||
\(43\) | 514.000 | 1.82289 | 0.911445 | − | 0.411422i | \(-0.134968\pi\) | ||||
0.911445 | + | 0.411422i | \(0.134968\pi\) | |||||||
\(44\) | − 30.0000i | − 0.102788i | ||||||||
\(45\) | 81.0000i | 0.268328i | ||||||||
\(46\) | − 18.0000i | − 0.0576947i | ||||||||
\(47\) | − 162.000i | − 0.502769i | −0.967887 | − | 0.251384i | \(-0.919114\pi\) | ||||
0.967887 | − | 0.251384i | \(-0.0808858\pi\) | |||||||
\(48\) | −213.000 | −0.640498 | ||||||||
\(49\) | 339.000 | 0.988338 | ||||||||
\(50\) | − 132.000i | − 0.373352i | ||||||||
\(51\) | 333.000 | 0.914301 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 639.000 | 1.65610 | 0.828051 | − | 0.560653i | \(-0.189450\pi\) | ||||
0.828051 | + | 0.560653i | \(0.189450\pi\) | |||||||
\(54\) | − 81.0000i | − 0.204124i | ||||||||
\(55\) | −270.000 | −0.661942 | ||||||||
\(56\) | 42.0000 | 0.100223 | ||||||||
\(57\) | 138.000i | 0.320676i | ||||||||
\(58\) | 315.000i | 0.713130i | ||||||||
\(59\) | 600.000i | 1.32396i | 0.749524 | + | 0.661978i | \(0.230283\pi\) | ||||
−0.749524 | + | 0.661978i | \(0.769717\pi\) | |||||||
\(60\) | − 27.0000i | − 0.0580948i | ||||||||
\(61\) | 233.000 | 0.489059 | 0.244529 | − | 0.969642i | \(-0.421367\pi\) | ||||
0.244529 | + | 0.969642i | \(0.421367\pi\) | |||||||
\(62\) | 300.000 | 0.614517 | ||||||||
\(63\) | 18.0000i | 0.0359966i | ||||||||
\(64\) | −433.000 | −0.845703 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 270.000 | 0.503556 | ||||||||
\(67\) | − 926.000i | − 1.68849i | −0.535957 | − | 0.844246i | \(-0.680049\pi\) | ||||
0.535957 | − | 0.844246i | \(-0.319951\pi\) | |||||||
\(68\) | −111.000 | −0.197952 | ||||||||
\(69\) | 18.0000 | 0.0314050 | ||||||||
\(70\) | 54.0000i | 0.0922033i | ||||||||
\(71\) | 930.000i | 1.55452i | 0.629182 | + | 0.777258i | \(0.283390\pi\) | ||||
−0.629182 | + | 0.777258i | \(0.716610\pi\) | |||||||
\(72\) | − 189.000i | − 0.309359i | ||||||||
\(73\) | − 253.000i | − 0.405636i | −0.979216 | − | 0.202818i | \(-0.934990\pi\) | ||||
0.979216 | − | 0.202818i | \(-0.0650099\pi\) | |||||||
\(74\) | 51.0000 | 0.0801166 | ||||||||
\(75\) | 132.000 | 0.203227 | ||||||||
\(76\) | − 46.0000i | − 0.0694284i | ||||||||
\(77\) | −60.0000 | −0.0888004 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1324.00 | −1.88559 | −0.942795 | − | 0.333373i | \(-0.891813\pi\) | ||||
−0.942795 | + | 0.333373i | \(0.891813\pi\) | |||||||
\(80\) | − 639.000i | − 0.893030i | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 693.000 | 0.933281 | ||||||||
\(83\) | − 810.000i | − 1.07119i | −0.844474 | − | 0.535597i | \(-0.820087\pi\) | ||||
0.844474 | − | 0.535597i | \(-0.179913\pi\) | |||||||
\(84\) | − 6.00000i | − 0.00779350i | ||||||||
\(85\) | 999.000i | 1.27479i | ||||||||
\(86\) | − 1542.00i | − 1.93347i | ||||||||
\(87\) | −315.000 | −0.388179 | ||||||||
\(88\) | 630.000 | 0.763162 | ||||||||
\(89\) | 498.000i | 0.593122i | 0.955014 | + | 0.296561i | \(0.0958399\pi\) | ||||
−0.955014 | + | 0.296561i | \(0.904160\pi\) | |||||||
\(90\) | 243.000 | 0.284605 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −6.00000 | −0.00679938 | ||||||||
\(93\) | 300.000i | 0.334501i | ||||||||
\(94\) | −486.000 | −0.533267 | ||||||||
\(95\) | −414.000 | −0.447111 | ||||||||
\(96\) | 135.000i | 0.143525i | ||||||||
\(97\) | − 1358.00i | − 1.42148i | −0.703452 | − | 0.710742i | \(-0.748359\pi\) | ||||
0.703452 | − | 0.710742i | \(-0.251641\pi\) | |||||||
\(98\) | − 1017.00i | − 1.04829i | ||||||||
\(99\) | 270.000i | 0.274101i | ||||||||
\(100\) | −44.0000 | −0.0440000 | ||||||||
\(101\) | 357.000 | 0.351711 | 0.175856 | − | 0.984416i | \(-0.443731\pi\) | ||||
0.175856 | + | 0.984416i | \(0.443731\pi\) | |||||||
\(102\) | − 999.000i | − 0.969762i | ||||||||
\(103\) | −1118.00 | −1.06951 | −0.534756 | − | 0.845006i | \(-0.679597\pi\) | ||||
−0.534756 | + | 0.845006i | \(0.679597\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −54.0000 | −0.0501891 | ||||||||
\(106\) | − 1917.00i | − 1.75656i | ||||||||
\(107\) | 714.000 | 0.645093 | 0.322547 | − | 0.946554i | \(-0.395461\pi\) | ||||
0.322547 | + | 0.946554i | \(0.395461\pi\) | |||||||
\(108\) | −27.0000 | −0.0240563 | ||||||||
\(109\) | − 2006.00i | − 1.76275i | −0.472416 | − | 0.881376i | \(-0.656618\pi\) | ||||
0.472416 | − | 0.881376i | \(-0.343382\pi\) | |||||||
\(110\) | 810.000i | 0.702095i | ||||||||
\(111\) | 51.0000i | 0.0436100i | ||||||||
\(112\) | − 142.000i | − 0.119801i | ||||||||
\(113\) | −1119.00 | −0.931563 | −0.465782 | − | 0.884900i | \(-0.654227\pi\) | ||||
−0.465782 | + | 0.884900i | \(0.654227\pi\) | |||||||
\(114\) | 414.000 | 0.340129 | ||||||||
\(115\) | 54.0000i | 0.0437872i | ||||||||
\(116\) | 105.000 | 0.0840431 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 1800.00 | 1.40427 | ||||||||
\(119\) | 222.000i | 0.171014i | ||||||||
\(120\) | 567.000 | 0.431332 | ||||||||
\(121\) | 431.000 | 0.323817 | ||||||||
\(122\) | − 699.000i | − 0.518725i | ||||||||
\(123\) | 693.000i | 0.508014i | ||||||||
\(124\) | − 100.000i | − 0.0724215i | ||||||||
\(125\) | 1521.00i | 1.08834i | ||||||||
\(126\) | 54.0000 | 0.0381802 | ||||||||
\(127\) | 604.000 | 0.422018 | 0.211009 | − | 0.977484i | \(-0.432325\pi\) | ||||
0.211009 | + | 0.977484i | \(0.432325\pi\) | |||||||
\(128\) | 1659.00i | 1.14560i | ||||||||
\(129\) | 1542.00 | 1.05245 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −1584.00 | −1.05645 | −0.528224 | − | 0.849105i | \(-0.677142\pi\) | ||||
−0.528224 | + | 0.849105i | \(0.677142\pi\) | |||||||
\(132\) | − 90.0000i | − 0.0593447i | ||||||||
\(133\) | −92.0000 | −0.0599805 | ||||||||
\(134\) | −2778.00 | −1.79092 | ||||||||
\(135\) | 243.000i | 0.154919i | ||||||||
\(136\) | − 2331.00i | − 1.46972i | ||||||||
\(137\) | 717.000i | 0.447135i | 0.974688 | + | 0.223567i | \(0.0717703\pi\) | ||||
−0.974688 | + | 0.223567i | \(0.928230\pi\) | |||||||
\(138\) | − 54.0000i | − 0.0333100i | ||||||||
\(139\) | −820.000 | −0.500370 | −0.250185 | − | 0.968198i | \(-0.580492\pi\) | ||||
−0.250185 | + | 0.968198i | \(0.580492\pi\) | |||||||
\(140\) | 18.0000 | 0.0108663 | ||||||||
\(141\) | − 486.000i | − 0.290274i | ||||||||
\(142\) | 2790.00 | 1.64881 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −639.000 | −0.369792 | ||||||||
\(145\) | − 945.000i | − 0.541227i | ||||||||
\(146\) | −759.000 | −0.430242 | ||||||||
\(147\) | 1017.00 | 0.570617 | ||||||||
\(148\) | − 17.0000i | − 0.00944183i | ||||||||
\(149\) | 1749.00i | 0.961635i | 0.876821 | + | 0.480818i | \(0.159660\pi\) | ||||
−0.876821 | + | 0.480818i | \(0.840340\pi\) | |||||||
\(150\) | − 396.000i | − 0.215555i | ||||||||
\(151\) | − 370.000i | − 0.199405i | −0.995017 | − | 0.0997026i | \(-0.968211\pi\) | ||||
0.995017 | − | 0.0997026i | \(-0.0317891\pi\) | |||||||
\(152\) | 966.000 | 0.515480 | ||||||||
\(153\) | 999.000 | 0.527872 | ||||||||
\(154\) | 180.000i | 0.0941871i | ||||||||
\(155\) | −900.000 | −0.466385 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2611.00 | −1.32726 | −0.663632 | − | 0.748059i | \(-0.730986\pi\) | ||||
−0.663632 | + | 0.748059i | \(0.730986\pi\) | |||||||
\(158\) | 3972.00i | 1.99997i | ||||||||
\(159\) | 1917.00 | 0.956151 | ||||||||
\(160\) | −405.000 | −0.200113 | ||||||||
\(161\) | 12.0000i | 0.00587411i | ||||||||
\(162\) | − 243.000i | − 0.117851i | ||||||||
\(163\) | − 1636.00i | − 0.786144i | −0.919508 | − | 0.393072i | \(-0.871412\pi\) | ||||
0.919508 | − | 0.393072i | \(-0.128588\pi\) | |||||||
\(164\) | − 231.000i | − 0.109988i | ||||||||
\(165\) | −810.000 | −0.382172 | ||||||||
\(166\) | −2430.00 | −1.13617 | ||||||||
\(167\) | 264.000i | 0.122329i | 0.998128 | + | 0.0611645i | \(0.0194814\pi\) | ||||
−0.998128 | + | 0.0611645i | \(0.980519\pi\) | |||||||
\(168\) | 126.000 | 0.0578638 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 2997.00 | 1.35211 | ||||||||
\(171\) | 414.000i | 0.185143i | ||||||||
\(172\) | −514.000 | −0.227861 | ||||||||
\(173\) | −1410.00 | −0.619655 | −0.309827 | − | 0.950793i | \(-0.600271\pi\) | ||||
−0.309827 | + | 0.950793i | \(0.600271\pi\) | |||||||
\(174\) | 945.000i | 0.411726i | ||||||||
\(175\) | 88.0000i | 0.0380124i | ||||||||
\(176\) | − 2130.00i | − 0.912243i | ||||||||
\(177\) | 1800.00i | 0.764386i | ||||||||
\(178\) | 1494.00 | 0.629101 | ||||||||
\(179\) | 474.000 | 0.197924 | 0.0989621 | − | 0.995091i | \(-0.468448\pi\) | ||||
0.0989621 | + | 0.995091i | \(0.468448\pi\) | |||||||
\(180\) | − 81.0000i | − 0.0335410i | ||||||||
\(181\) | −2249.00 | −0.923574 | −0.461787 | − | 0.886991i | \(-0.652792\pi\) | ||||
−0.461787 | + | 0.886991i | \(0.652792\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 699.000 | 0.282358 | ||||||||
\(184\) | − 126.000i | − 0.0504828i | ||||||||
\(185\) | −153.000 | −0.0608042 | ||||||||
\(186\) | 900.000 | 0.354791 | ||||||||
\(187\) | 3330.00i | 1.30221i | ||||||||
\(188\) | 162.000i | 0.0628461i | ||||||||
\(189\) | 54.0000i | 0.0207827i | ||||||||
\(190\) | 1242.00i | 0.474232i | ||||||||
\(191\) | 3444.00 | 1.30471 | 0.652354 | − | 0.757915i | \(-0.273782\pi\) | ||||
0.652354 | + | 0.757915i | \(0.273782\pi\) | |||||||
\(192\) | −1299.00 | −0.488267 | ||||||||
\(193\) | − 4273.00i | − 1.59366i | −0.604201 | − | 0.796832i | \(-0.706507\pi\) | ||||
0.604201 | − | 0.796832i | \(-0.293493\pi\) | |||||||
\(194\) | −4074.00 | −1.50771 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −339.000 | −0.123542 | ||||||||
\(197\) | 1986.00i | 0.718257i | 0.933288 | + | 0.359129i | \(0.116926\pi\) | ||||
−0.933288 | + | 0.359129i | \(0.883074\pi\) | |||||||
\(198\) | 810.000 | 0.290728 | ||||||||
\(199\) | 2386.00 | 0.849945 | 0.424973 | − | 0.905206i | \(-0.360284\pi\) | ||||
0.424973 | + | 0.905206i | \(0.360284\pi\) | |||||||
\(200\) | − 924.000i | − 0.326683i | ||||||||
\(201\) | − 2778.00i | − 0.974851i | ||||||||
\(202\) | − 1071.00i | − 0.373046i | ||||||||
\(203\) | − 210.000i | − 0.0726065i | ||||||||
\(204\) | −333.000 | −0.114288 | ||||||||
\(205\) | −2079.00 | −0.708311 | ||||||||
\(206\) | 3354.00i | 1.13439i | ||||||||
\(207\) | 54.0000 | 0.0181317 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1380.00 | −0.456730 | ||||||||
\(210\) | 162.000i | 0.0532336i | ||||||||
\(211\) | −1600.00 | −0.522031 | −0.261016 | − | 0.965335i | \(-0.584057\pi\) | ||||
−0.261016 | + | 0.965335i | \(0.584057\pi\) | |||||||
\(212\) | −639.000 | −0.207013 | ||||||||
\(213\) | 2790.00i | 0.897501i | ||||||||
\(214\) | − 2142.00i | − 0.684225i | ||||||||
\(215\) | 4626.00i | 1.46740i | ||||||||
\(216\) | − 567.000i | − 0.178609i | ||||||||
\(217\) | −200.000 | −0.0625663 | ||||||||
\(218\) | −6018.00 | −1.86968 | ||||||||
\(219\) | − 759.000i | − 0.234194i | ||||||||
\(220\) | 270.000 | 0.0827427 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 153.000 | 0.0462553 | ||||||||
\(223\) | 3832.00i | 1.15072i | 0.817902 | + | 0.575358i | \(0.195137\pi\) | ||||
−0.817902 | + | 0.575358i | \(0.804863\pi\) | |||||||
\(224\) | −90.0000 | −0.0268454 | ||||||||
\(225\) | 396.000 | 0.117333 | ||||||||
\(226\) | 3357.00i | 0.988072i | ||||||||
\(227\) | 1398.00i | 0.408760i | 0.978892 | + | 0.204380i | \(0.0655178\pi\) | ||||
−0.978892 | + | 0.204380i | \(0.934482\pi\) | |||||||
\(228\) | − 138.000i | − 0.0400845i | ||||||||
\(229\) | 4466.00i | 1.28874i | 0.764714 | + | 0.644370i | \(0.222880\pi\) | ||||
−0.764714 | + | 0.644370i | \(0.777120\pi\) | |||||||
\(230\) | 162.000 | 0.0464433 | ||||||||
\(231\) | −180.000 | −0.0512690 | ||||||||
\(232\) | 2205.00i | 0.623989i | ||||||||
\(233\) | 1638.00 | 0.460553 | 0.230277 | − | 0.973125i | \(-0.426037\pi\) | ||||
0.230277 | + | 0.973125i | \(0.426037\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1458.00 | 0.404721 | ||||||||
\(236\) | − 600.000i | − 0.165494i | ||||||||
\(237\) | −3972.00 | −1.08865 | ||||||||
\(238\) | 666.000 | 0.181388 | ||||||||
\(239\) | 594.000i | 0.160764i | 0.996764 | + | 0.0803821i | \(0.0256141\pi\) | ||||
−0.996764 | + | 0.0803821i | \(0.974386\pi\) | |||||||
\(240\) | − 1917.00i | − 0.515591i | ||||||||
\(241\) | 2303.00i | 0.615557i | 0.951458 | + | 0.307779i | \(0.0995856\pi\) | ||||
−0.951458 | + | 0.307779i | \(0.900414\pi\) | |||||||
\(242\) | − 1293.00i | − 0.343459i | ||||||||
\(243\) | 243.000 | 0.0641500 | ||||||||
\(244\) | −233.000 | −0.0611324 | ||||||||
\(245\) | 3051.00i | 0.795597i | ||||||||
\(246\) | 2079.00 | 0.538830 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | 2100.00 | 0.537702 | ||||||||
\(249\) | − 2430.00i | − 0.618454i | ||||||||
\(250\) | 4563.00 | 1.15436 | ||||||||
\(251\) | −6324.00 | −1.59031 | −0.795154 | − | 0.606407i | \(-0.792610\pi\) | ||||
−0.795154 | + | 0.606407i | \(0.792610\pi\) | |||||||
\(252\) | − 18.0000i | − 0.00449958i | ||||||||
\(253\) | 180.000i | 0.0447293i | ||||||||
\(254\) | − 1812.00i | − 0.447618i | ||||||||
\(255\) | 2997.00i | 0.735998i | ||||||||
\(256\) | 1513.00 | 0.369385 | ||||||||
\(257\) | −7833.00 | −1.90120 | −0.950601 | − | 0.310414i | \(-0.899532\pi\) | ||||
−0.950601 | + | 0.310414i | \(0.899532\pi\) | |||||||
\(258\) | − 4626.00i | − 1.11629i | ||||||||
\(259\) | −34.0000 | −0.00815698 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −945.000 | −0.224115 | ||||||||
\(262\) | 4752.00i | 1.12053i | ||||||||
\(263\) | −3030.00 | −0.710410 | −0.355205 | − | 0.934788i | \(-0.615589\pi\) | ||||
−0.355205 | + | 0.934788i | \(0.615589\pi\) | |||||||
\(264\) | 1890.00 | 0.440612 | ||||||||
\(265\) | 5751.00i | 1.33314i | ||||||||
\(266\) | 276.000i | 0.0636190i | ||||||||
\(267\) | 1494.00i | 0.342439i | ||||||||
\(268\) | 926.000i | 0.211061i | ||||||||
\(269\) | −534.000 | −0.121036 | −0.0605178 | − | 0.998167i | \(-0.519275\pi\) | ||||
−0.0605178 | + | 0.998167i | \(0.519275\pi\) | |||||||
\(270\) | 729.000 | 0.164317 | ||||||||
\(271\) | − 3688.00i | − 0.826679i | −0.910577 | − | 0.413340i | \(-0.864362\pi\) | ||||
0.910577 | − | 0.413340i | \(-0.135638\pi\) | |||||||
\(272\) | −7881.00 | −1.75682 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 2151.00 | 0.474258 | ||||||||
\(275\) | 1320.00i | 0.289451i | ||||||||
\(276\) | −18.0000 | −0.00392563 | ||||||||
\(277\) | −1865.00 | −0.404538 | −0.202269 | − | 0.979330i | \(-0.564832\pi\) | ||||
−0.202269 | + | 0.979330i | \(0.564832\pi\) | |||||||
\(278\) | 2460.00i | 0.530723i | ||||||||
\(279\) | 900.000i | 0.193124i | ||||||||
\(280\) | 378.000i | 0.0806779i | ||||||||
\(281\) | 2997.00i | 0.636249i | 0.948049 | + | 0.318125i | \(0.103053\pi\) | ||||
−0.948049 | + | 0.318125i | \(0.896947\pi\) | |||||||
\(282\) | −1458.00 | −0.307882 | ||||||||
\(283\) | 4114.00 | 0.864141 | 0.432071 | − | 0.901840i | \(-0.357783\pi\) | ||||
0.432071 | + | 0.901840i | \(0.357783\pi\) | |||||||
\(284\) | − 930.000i | − 0.194315i | ||||||||
\(285\) | −1242.00 | −0.258139 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −462.000 | −0.0950209 | ||||||||
\(288\) | 405.000i | 0.0828641i | ||||||||
\(289\) | 7408.00 | 1.50784 | ||||||||
\(290\) | −2835.00 | −0.574058 | ||||||||
\(291\) | − 4074.00i | − 0.820695i | ||||||||
\(292\) | 253.000i | 0.0507045i | ||||||||
\(293\) | − 4665.00i | − 0.930144i | −0.885273 | − | 0.465072i | \(-0.846028\pi\) | ||||
0.885273 | − | 0.465072i | \(-0.153972\pi\) | |||||||
\(294\) | − 3051.00i | − 0.605231i | ||||||||
\(295\) | −5400.00 | −1.06576 | ||||||||
\(296\) | 357.000 | 0.0701020 | ||||||||
\(297\) | 810.000i | 0.158252i | ||||||||
\(298\) | 5247.00 | 1.01997 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | −132.000 | −0.0254034 | ||||||||
\(301\) | 1028.00i | 0.196854i | ||||||||
\(302\) | −1110.00 | −0.211501 | ||||||||
\(303\) | 1071.00 | 0.203061 | ||||||||
\(304\) | − 3266.00i | − 0.616177i | ||||||||
\(305\) | 2097.00i | 0.393685i | ||||||||
\(306\) | − 2997.00i | − 0.559892i | ||||||||
\(307\) | 1502.00i | 0.279230i | 0.990206 | + | 0.139615i | \(0.0445865\pi\) | ||||
−0.990206 | + | 0.139615i | \(0.955413\pi\) | |||||||
\(308\) | 60.0000 | 0.0111001 | ||||||||
\(309\) | −3354.00 | −0.617483 | ||||||||
\(310\) | 2700.00i | 0.494676i | ||||||||
\(311\) | −2106.00 | −0.383988 | −0.191994 | − | 0.981396i | \(-0.561495\pi\) | ||||
−0.191994 | + | 0.981396i | \(0.561495\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −3898.00 | −0.703923 | −0.351962 | − | 0.936014i | \(-0.614485\pi\) | ||||
−0.351962 | + | 0.936014i | \(0.614485\pi\) | |||||||
\(314\) | 7833.00i | 1.40778i | ||||||||
\(315\) | −162.000 | −0.0289767 | ||||||||
\(316\) | 1324.00 | 0.235699 | ||||||||
\(317\) | − 9351.00i | − 1.65680i | −0.560140 | − | 0.828398i | \(-0.689253\pi\) | ||||
0.560140 | − | 0.828398i | \(-0.310747\pi\) | |||||||
\(318\) | − 5751.00i | − 1.01415i | ||||||||
\(319\) | − 3150.00i | − 0.552872i | ||||||||
\(320\) | − 3897.00i | − 0.680778i | ||||||||
\(321\) | 2142.00 | 0.372445 | ||||||||
\(322\) | 36.0000 | 0.00623044 | ||||||||
\(323\) | 5106.00i | 0.879583i | ||||||||
\(324\) | −81.0000 | −0.0138889 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −4908.00 | −0.833831 | ||||||||
\(327\) | − 6018.00i | − 1.01773i | ||||||||
\(328\) | 4851.00 | 0.816621 | ||||||||
\(329\) | 324.000 | 0.0542939 | ||||||||
\(330\) | 2430.00i | 0.405355i | ||||||||
\(331\) | 9172.00i | 1.52308i | 0.648119 | + | 0.761539i | \(0.275556\pi\) | ||||
−0.648119 | + | 0.761539i | \(0.724444\pi\) | |||||||
\(332\) | 810.000i | 0.133899i | ||||||||
\(333\) | 153.000i | 0.0251782i | ||||||||
\(334\) | 792.000 | 0.129749 | ||||||||
\(335\) | 8334.00 | 1.35921 | ||||||||
\(336\) | − 426.000i | − 0.0691673i | ||||||||
\(337\) | 11089.0 | 1.79245 | 0.896226 | − | 0.443598i | \(-0.146298\pi\) | ||||
0.896226 | + | 0.443598i | \(0.146298\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −3357.00 | −0.537838 | ||||||||
\(340\) | − 999.000i | − 0.159348i | ||||||||
\(341\) | −3000.00 | −0.476420 | ||||||||
\(342\) | 1242.00 | 0.196373 | ||||||||
\(343\) | 1364.00i | 0.214720i | ||||||||
\(344\) | − 10794.0i | − 1.69178i | ||||||||
\(345\) | 162.000i | 0.0252805i | ||||||||
\(346\) | 4230.00i | 0.657243i | ||||||||
\(347\) | 9762.00 | 1.51024 | 0.755118 | − | 0.655589i | \(-0.227580\pi\) | ||||
0.755118 | + | 0.655589i | \(0.227580\pi\) | |||||||
\(348\) | 315.000 | 0.0485223 | ||||||||
\(349\) | − 8290.00i | − 1.27150i | −0.771895 | − | 0.635750i | \(-0.780691\pi\) | ||||
0.771895 | − | 0.635750i | \(-0.219309\pi\) | |||||||
\(350\) | 264.000 | 0.0403183 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −1350.00 | −0.204418 | ||||||||
\(353\) | − 12405.0i | − 1.87040i | −0.354119 | − | 0.935200i | \(-0.615219\pi\) | ||||
0.354119 | − | 0.935200i | \(-0.384781\pi\) | |||||||
\(354\) | 5400.00 | 0.810754 | ||||||||
\(355\) | −8370.00 | −1.25136 | ||||||||
\(356\) | − 498.000i | − 0.0741403i | ||||||||
\(357\) | 666.000i | 0.0987352i | ||||||||
\(358\) | − 1422.00i | − 0.209930i | ||||||||
\(359\) | − 1098.00i | − 0.161421i | −0.996738 | − | 0.0807106i | \(-0.974281\pi\) | ||||
0.996738 | − | 0.0807106i | \(-0.0257190\pi\) | |||||||
\(360\) | 1701.00 | 0.249029 | ||||||||
\(361\) | 4743.00 | 0.691500 | ||||||||
\(362\) | 6747.00i | 0.979598i | ||||||||
\(363\) | 1293.00 | 0.186956 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 2277.00 | 0.326530 | ||||||||
\(366\) | − 2097.00i | − 0.299486i | ||||||||
\(367\) | −5734.00 | −0.815565 | −0.407783 | − | 0.913079i | \(-0.633698\pi\) | ||||
−0.407783 | + | 0.913079i | \(0.633698\pi\) | |||||||
\(368\) | −426.000 | −0.0603445 | ||||||||
\(369\) | 2079.00i | 0.293302i | ||||||||
\(370\) | 459.000i | 0.0644926i | ||||||||
\(371\) | 1278.00i | 0.178842i | ||||||||
\(372\) | − 300.000i | − 0.0418126i | ||||||||
\(373\) | −8971.00 | −1.24531 | −0.622655 | − | 0.782496i | \(-0.713946\pi\) | ||||
−0.622655 | + | 0.782496i | \(0.713946\pi\) | |||||||
\(374\) | 9990.00 | 1.38120 | ||||||||
\(375\) | 4563.00i | 0.628353i | ||||||||
\(376\) | −3402.00 | −0.466608 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | 162.000 | 0.0220433 | ||||||||
\(379\) | − 7244.00i | − 0.981792i | −0.871218 | − | 0.490896i | \(-0.836669\pi\) | ||||
0.871218 | − | 0.490896i | \(-0.163331\pi\) | |||||||
\(380\) | 414.000 | 0.0558888 | ||||||||
\(381\) | 1812.00 | 0.243652 | ||||||||
\(382\) | − 10332.0i | − 1.38385i | ||||||||
\(383\) | 6312.00i | 0.842110i | 0.907035 | + | 0.421055i | \(0.138340\pi\) | ||||
−0.907035 | + | 0.421055i | \(0.861660\pi\) | |||||||
\(384\) | 4977.00i | 0.661410i | ||||||||
\(385\) | − 540.000i | − 0.0714830i | ||||||||
\(386\) | −12819.0 | −1.69034 | ||||||||
\(387\) | 4626.00 | 0.607630 | ||||||||
\(388\) | 1358.00i | 0.177686i | ||||||||
\(389\) | −3627.00 | −0.472741 | −0.236370 | − | 0.971663i | \(-0.575958\pi\) | ||||
−0.236370 | + | 0.971663i | \(0.575958\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 666.000 | 0.0861408 | ||||||||
\(392\) | − 7119.00i | − 0.917255i | ||||||||
\(393\) | −4752.00 | −0.609941 | ||||||||
\(394\) | 5958.00 | 0.761827 | ||||||||
\(395\) | − 11916.0i | − 1.51787i | ||||||||
\(396\) | − 270.000i | − 0.0342627i | ||||||||
\(397\) | − 3898.00i | − 0.492783i | −0.969170 | − | 0.246392i | \(-0.920755\pi\) | ||||
0.969170 | − | 0.246392i | \(-0.0792450\pi\) | |||||||
\(398\) | − 7158.00i | − 0.901503i | ||||||||
\(399\) | −276.000 | −0.0346298 | ||||||||
\(400\) | −3124.00 | −0.390500 | ||||||||
\(401\) | − 5703.00i | − 0.710210i | −0.934826 | − | 0.355105i | \(-0.884445\pi\) | ||||
0.934826 | − | 0.355105i | \(-0.115555\pi\) | |||||||
\(402\) | −8334.00 | −1.03399 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | −357.000 | −0.0439639 | ||||||||
\(405\) | 729.000i | 0.0894427i | ||||||||
\(406\) | −630.000 | −0.0770108 | ||||||||
\(407\) | −510.000 | −0.0621124 | ||||||||
\(408\) | − 6993.00i | − 0.848542i | ||||||||
\(409\) | − 6311.00i | − 0.762980i | −0.924373 | − | 0.381490i | \(-0.875411\pi\) | ||||
0.924373 | − | 0.381490i | \(-0.124589\pi\) | |||||||
\(410\) | 6237.00i | 0.751277i | ||||||||
\(411\) | 2151.00i | 0.258153i | ||||||||
\(412\) | 1118.00 | 0.133689 | ||||||||
\(413\) | −1200.00 | −0.142974 | ||||||||
\(414\) | − 162.000i | − 0.0192316i | ||||||||
\(415\) | 7290.00 | 0.862294 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −2460.00 | −0.288889 | ||||||||
\(418\) | 4140.00i | 0.484435i | ||||||||
\(419\) | −2328.00 | −0.271433 | −0.135716 | − | 0.990748i | \(-0.543334\pi\) | ||||
−0.135716 | + | 0.990748i | \(0.543334\pi\) | |||||||
\(420\) | 54.0000 | 0.00627364 | ||||||||
\(421\) | − 2045.00i | − 0.236739i | −0.992970 | − | 0.118370i | \(-0.962233\pi\) | ||||
0.992970 | − | 0.118370i | \(-0.0377668\pi\) | |||||||
\(422\) | 4800.00i | 0.553697i | ||||||||
\(423\) | − 1458.00i | − 0.167590i | ||||||||
\(424\) | − 13419.0i | − 1.53699i | ||||||||
\(425\) | 4884.00 | 0.557432 | ||||||||
\(426\) | 8370.00 | 0.951943 | ||||||||
\(427\) | 466.000i | 0.0528134i | ||||||||
\(428\) | −714.000 | −0.0806367 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 13878.0 | 1.55641 | ||||||||
\(431\) | − 5034.00i | − 0.562597i | −0.959620 | − | 0.281298i | \(-0.909235\pi\) | ||||
0.959620 | − | 0.281298i | \(-0.0907651\pi\) | |||||||
\(432\) | −1917.00 | −0.213499 | ||||||||
\(433\) | −4283.00 | −0.475353 | −0.237676 | − | 0.971344i | \(-0.576386\pi\) | ||||
−0.237676 | + | 0.971344i | \(0.576386\pi\) | |||||||
\(434\) | 600.000i | 0.0663616i | ||||||||
\(435\) | − 2835.00i | − 0.312478i | ||||||||
\(436\) | 2006.00i | 0.220344i | ||||||||
\(437\) | 276.000i | 0.0302125i | ||||||||
\(438\) | −2277.00 | −0.248400 | ||||||||
\(439\) | 1306.00 | 0.141986 | 0.0709931 | − | 0.997477i | \(-0.477383\pi\) | ||||
0.0709931 | + | 0.997477i | \(0.477383\pi\) | |||||||
\(440\) | 5670.00i | 0.614333i | ||||||||
\(441\) | 3051.00 | 0.329446 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −5796.00 | −0.621617 | −0.310808 | − | 0.950473i | \(-0.600600\pi\) | ||||
−0.310808 | + | 0.950473i | \(0.600600\pi\) | |||||||
\(444\) | − 51.0000i | − 0.00545125i | ||||||||
\(445\) | −4482.00 | −0.477454 | ||||||||
\(446\) | 11496.0 | 1.22052 | ||||||||
\(447\) | 5247.00i | 0.555200i | ||||||||
\(448\) | − 866.000i | − 0.0913274i | ||||||||
\(449\) | 2706.00i | 0.284419i | 0.989837 | + | 0.142209i | \(0.0454206\pi\) | ||||
−0.989837 | + | 0.142209i | \(0.954579\pi\) | |||||||
\(450\) | − 1188.00i | − 0.124451i | ||||||||
\(451\) | −6930.00 | −0.723550 | ||||||||
\(452\) | 1119.00 | 0.116445 | ||||||||
\(453\) | − 1110.00i | − 0.115127i | ||||||||
\(454\) | 4194.00 | 0.433555 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 2898.00 | 0.297612 | ||||||||
\(457\) | 829.000i | 0.0848555i | 0.999100 | + | 0.0424278i | \(0.0135092\pi\) | ||||
−0.999100 | + | 0.0424278i | \(0.986491\pi\) | |||||||
\(458\) | 13398.0 | 1.36692 | ||||||||
\(459\) | 2997.00 | 0.304767 | ||||||||
\(460\) | − 54.0000i | − 0.00547340i | ||||||||
\(461\) | 5493.00i | 0.554956i | 0.960732 | + | 0.277478i | \(0.0894985\pi\) | ||||
−0.960732 | + | 0.277478i | \(0.910502\pi\) | |||||||
\(462\) | 540.000i | 0.0543789i | ||||||||
\(463\) | − 15346.0i | − 1.54037i | −0.637823 | − | 0.770183i | \(-0.720165\pi\) | ||||
0.637823 | − | 0.770183i | \(-0.279835\pi\) | |||||||
\(464\) | 7455.00 | 0.745883 | ||||||||
\(465\) | −2700.00 | −0.269268 | ||||||||
\(466\) | − 4914.00i | − 0.488491i | ||||||||
\(467\) | 9594.00 | 0.950658 | 0.475329 | − | 0.879808i | \(-0.342329\pi\) | ||||
0.475329 | + | 0.879808i | \(0.342329\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1852.00 | 0.182340 | ||||||||
\(470\) | − 4374.00i | − 0.429271i | ||||||||
\(471\) | −7833.00 | −0.766296 | ||||||||
\(472\) | 12600.0 | 1.22873 | ||||||||
\(473\) | 15420.0i | 1.49897i | ||||||||
\(474\) | 11916.0i | 1.15468i | ||||||||
\(475\) | 2024.00i | 0.195511i | ||||||||
\(476\) | − 222.000i | − 0.0213768i | ||||||||
\(477\) | 5751.00 | 0.552034 | ||||||||
\(478\) | 1782.00 | 0.170516 | ||||||||
\(479\) | − 12840.0i | − 1.22479i | −0.790552 | − | 0.612395i | \(-0.790206\pi\) | ||||
0.790552 | − | 0.612395i | \(-0.209794\pi\) | |||||||
\(480\) | −1215.00 | −0.115535 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 6909.00 | 0.652897 | ||||||||
\(483\) | 36.0000i | 0.00339142i | ||||||||
\(484\) | −431.000 | −0.0404771 | ||||||||
\(485\) | 12222.0 | 1.14427 | ||||||||
\(486\) | − 729.000i | − 0.0680414i | ||||||||
\(487\) | 14086.0i | 1.31067i | 0.755337 | + | 0.655336i | \(0.227473\pi\) | ||||
−0.755337 | + | 0.655336i | \(0.772527\pi\) | |||||||
\(488\) | − 4893.00i | − 0.453885i | ||||||||
\(489\) | − 4908.00i | − 0.453880i | ||||||||
\(490\) | 9153.00 | 0.843858 | ||||||||
\(491\) | −11694.0 | −1.07483 | −0.537416 | − | 0.843317i | \(-0.680600\pi\) | ||||
−0.537416 | + | 0.843317i | \(0.680600\pi\) | |||||||
\(492\) | − 693.000i | − 0.0635017i | ||||||||
\(493\) | −11655.0 | −1.06474 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −2430.00 | −0.220647 | ||||||||
\(496\) | − 7100.00i | − 0.642741i | ||||||||
\(497\) | −1860.00 | −0.167872 | ||||||||
\(498\) | −7290.00 | −0.655969 | ||||||||
\(499\) | 3688.00i | 0.330857i | 0.986222 | + | 0.165428i | \(0.0529007\pi\) | ||||
−0.986222 | + | 0.165428i | \(0.947099\pi\) | |||||||
\(500\) | − 1521.00i | − 0.136042i | ||||||||
\(501\) | 792.000i | 0.0706266i | ||||||||
\(502\) | 18972.0i | 1.68678i | ||||||||
\(503\) | −4746.00 | −0.420703 | −0.210352 | − | 0.977626i | \(-0.567461\pi\) | ||||
−0.210352 | + | 0.977626i | \(0.567461\pi\) | |||||||
\(504\) | 378.000 | 0.0334077 | ||||||||
\(505\) | 3213.00i | 0.283122i | ||||||||
\(506\) | 540.000 | 0.0474425 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −604.000 | −0.0527523 | ||||||||
\(509\) | 14505.0i | 1.26311i | 0.775331 | + | 0.631555i | \(0.217583\pi\) | ||||
−0.775331 | + | 0.631555i | \(0.782417\pi\) | |||||||
\(510\) | 8991.00 | 0.780643 | ||||||||
\(511\) | 506.000 | 0.0438045 | ||||||||
\(512\) | 8733.00i | 0.753804i | ||||||||
\(513\) | 1242.00i | 0.106892i | ||||||||
\(514\) | 23499.0i | 2.01653i | ||||||||
\(515\) | − 10062.0i | − 0.860941i | ||||||||
\(516\) | −1542.00 | −0.131556 | ||||||||
\(517\) | 4860.00 | 0.413429 | ||||||||
\(518\) | 102.000i | 0.00865178i | ||||||||
\(519\) | −4230.00 | −0.357758 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 5085.00 | 0.427597 | 0.213798 | − | 0.976878i | \(-0.431416\pi\) | ||||
0.213798 | + | 0.976878i | \(0.431416\pi\) | |||||||
\(522\) | 2835.00i | 0.237710i | ||||||||
\(523\) | −10882.0 | −0.909821 | −0.454911 | − | 0.890537i | \(-0.650329\pi\) | ||||
−0.454911 | + | 0.890537i | \(0.650329\pi\) | |||||||
\(524\) | 1584.00 | 0.132056 | ||||||||
\(525\) | 264.000i | 0.0219465i | ||||||||
\(526\) | 9090.00i | 0.753503i | ||||||||
\(527\) | 11100.0i | 0.917502i | ||||||||
\(528\) | − 6390.00i | − 0.526684i | ||||||||
\(529\) | −12131.0 | −0.997041 | ||||||||
\(530\) | 17253.0 | 1.41400 | ||||||||
\(531\) | 5400.00i | 0.441318i | ||||||||
\(532\) | 92.0000 | 0.00749757 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | 4482.00 | 0.363212 | ||||||||
\(535\) | 6426.00i | 0.519290i | ||||||||
\(536\) | −19446.0 | −1.56705 | ||||||||
\(537\) | 1422.00 | 0.114272 | ||||||||
\(538\) | 1602.00i | 0.128378i | ||||||||
\(539\) | 10170.0i | 0.812714i | ||||||||
\(540\) | − 243.000i | − 0.0193649i | ||||||||
\(541\) | − 4699.00i | − 0.373430i | −0.982414 | − | 0.186715i | \(-0.940216\pi\) | ||||
0.982414 | − | 0.186715i | \(-0.0597841\pi\) | |||||||
\(542\) | −11064.0 | −0.876826 | ||||||||
\(543\) | −6747.00 | −0.533226 | ||||||||
\(544\) | 4995.00i | 0.393674i | ||||||||
\(545\) | 18054.0 | 1.41899 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 8270.00 | 0.646434 | 0.323217 | − | 0.946325i | \(-0.395236\pi\) | ||||
0.323217 | + | 0.946325i | \(0.395236\pi\) | |||||||
\(548\) | − 717.000i | − 0.0558918i | ||||||||
\(549\) | 2097.00 | 0.163020 | ||||||||
\(550\) | 3960.00 | 0.307009 | ||||||||
\(551\) | − 4830.00i | − 0.373439i | ||||||||
\(552\) | − 378.000i | − 0.0291463i | ||||||||
\(553\) | − 2648.00i | − 0.203625i | ||||||||
\(554\) | 5595.00i | 0.429077i | ||||||||
\(555\) | −459.000 | −0.0351053 | ||||||||
\(556\) | 820.000 | 0.0625463 | ||||||||
\(557\) | − 22785.0i | − 1.73327i | −0.498943 | − | 0.866635i | \(-0.666278\pi\) | ||||
0.498943 | − | 0.866635i | \(-0.333722\pi\) | |||||||
\(558\) | 2700.00 | 0.204839 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 1278.00 | 0.0964381 | ||||||||
\(561\) | 9990.00i | 0.751833i | ||||||||
\(562\) | 8991.00 | 0.674844 | ||||||||
\(563\) | 11928.0 | 0.892905 | 0.446452 | − | 0.894807i | \(-0.352687\pi\) | ||||
0.446452 | + | 0.894807i | \(0.352687\pi\) | |||||||
\(564\) | 486.000i | 0.0362842i | ||||||||
\(565\) | − 10071.0i | − 0.749894i | ||||||||
\(566\) | − 12342.0i | − 0.916560i | ||||||||
\(567\) | 162.000i | 0.0119989i | ||||||||
\(568\) | 19530.0 | 1.44271 | ||||||||
\(569\) | 7962.00 | 0.586616 | 0.293308 | − | 0.956018i | \(-0.405244\pi\) | ||||
0.293308 | + | 0.956018i | \(0.405244\pi\) | |||||||
\(570\) | 3726.00i | 0.273798i | ||||||||
\(571\) | −20618.0 | −1.51110 | −0.755549 | − | 0.655093i | \(-0.772630\pi\) | ||||
−0.755549 | + | 0.655093i | \(0.772630\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 10332.0 | 0.753273 | ||||||||
\(574\) | 1386.00i | 0.100785i | ||||||||
\(575\) | 264.000 | 0.0191471 | ||||||||
\(576\) | −3897.00 | −0.281901 | ||||||||
\(577\) | 3493.00i | 0.252020i | 0.992029 | + | 0.126010i | \(0.0402171\pi\) | ||||
−0.992029 | + | 0.126010i | \(0.959783\pi\) | |||||||
\(578\) | − 22224.0i | − 1.59930i | ||||||||
\(579\) | − 12819.0i | − 0.920103i | ||||||||
\(580\) | 945.000i | 0.0676534i | ||||||||
\(581\) | 1620.00 | 0.115678 | ||||||||
\(582\) | −12222.0 | −0.870478 | ||||||||
\(583\) | 19170.0i | 1.36182i | ||||||||
\(584\) | −5313.00 | −0.376461 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −13995.0 | −0.986567 | ||||||||
\(587\) | − 10416.0i | − 0.732392i | −0.930538 | − | 0.366196i | \(-0.880660\pi\) | ||||
0.930538 | − | 0.366196i | \(-0.119340\pi\) | |||||||
\(588\) | −1017.00 | −0.0713272 | ||||||||
\(589\) | −4600.00 | −0.321799 | ||||||||
\(590\) | 16200.0i | 1.13041i | ||||||||
\(591\) | 5958.00i | 0.414686i | ||||||||
\(592\) | − 1207.00i | − 0.0837963i | ||||||||
\(593\) | 2061.00i | 0.142724i | 0.997450 | + | 0.0713618i | \(0.0227345\pi\) | ||||
−0.997450 | + | 0.0713618i | \(0.977266\pi\) | |||||||
\(594\) | 2430.00 | 0.167852 | ||||||||
\(595\) | −1998.00 | −0.137664 | ||||||||
\(596\) | − 1749.00i | − 0.120204i | ||||||||
\(597\) | 7158.00 | 0.490716 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 12456.0 | 0.849647 | 0.424823 | − | 0.905276i | \(-0.360336\pi\) | ||||
0.424823 | + | 0.905276i | \(0.360336\pi\) | |||||||
\(600\) | − 2772.00i | − 0.188611i | ||||||||
\(601\) | −781.000 | −0.0530077 | −0.0265039 | − | 0.999649i | \(-0.508437\pi\) | ||||
−0.0265039 | + | 0.999649i | \(0.508437\pi\) | |||||||
\(602\) | 3084.00 | 0.208795 | ||||||||
\(603\) | − 8334.00i | − 0.562830i | ||||||||
\(604\) | 370.000i | 0.0249256i | ||||||||
\(605\) | 3879.00i | 0.260667i | ||||||||
\(606\) | − 3213.00i | − 0.215378i | ||||||||
\(607\) | 19304.0 | 1.29082 | 0.645408 | − | 0.763838i | \(-0.276687\pi\) | ||||
0.645408 | + | 0.763838i | \(0.276687\pi\) | |||||||
\(608\) | −2070.00 | −0.138075 | ||||||||
\(609\) | − 630.000i | − 0.0419194i | ||||||||
\(610\) | 6291.00 | 0.417566 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | −999.000 | −0.0659840 | ||||||||
\(613\) | − 12041.0i | − 0.793363i | −0.917956 | − | 0.396681i | \(-0.870162\pi\) | ||||
0.917956 | − | 0.396681i | \(-0.129838\pi\) | |||||||
\(614\) | 4506.00 | 0.296168 | ||||||||
\(615\) | −6237.00 | −0.408943 | ||||||||
\(616\) | 1260.00i | 0.0824137i | ||||||||
\(617\) | − 9717.00i | − 0.634022i | −0.948422 | − | 0.317011i | \(-0.897321\pi\) | ||||
0.948422 | − | 0.317011i | \(-0.102679\pi\) | |||||||
\(618\) | 10062.0i | 0.654940i | ||||||||
\(619\) | − 21040.0i | − 1.36619i | −0.730332 | − | 0.683093i | \(-0.760634\pi\) | ||||
0.730332 | − | 0.683093i | \(-0.239366\pi\) | |||||||
\(620\) | 900.000 | 0.0582982 | ||||||||
\(621\) | 162.000 | 0.0104683 | ||||||||
\(622\) | 6318.00i | 0.407281i | ||||||||
\(623\) | −996.000 | −0.0640512 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −8189.00 | −0.524096 | ||||||||
\(626\) | 11694.0i | 0.746623i | ||||||||
\(627\) | −4140.00 | −0.263693 | ||||||||
\(628\) | 2611.00 | 0.165908 | ||||||||
\(629\) | 1887.00i | 0.119618i | ||||||||
\(630\) | 486.000i | 0.0307344i | ||||||||
\(631\) | − 5068.00i | − 0.319737i | −0.987138 | − | 0.159868i | \(-0.948893\pi\) | ||||
0.987138 | − | 0.159868i | \(-0.0511070\pi\) | |||||||
\(632\) | 27804.0i | 1.74997i | ||||||||
\(633\) | −4800.00 | −0.301395 | ||||||||
\(634\) | −28053.0 | −1.75730 | ||||||||
\(635\) | 5436.00i | 0.339718i | ||||||||
\(636\) | −1917.00 | −0.119519 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −9450.00 | −0.586409 | ||||||||
\(639\) | 8370.00i | 0.518172i | ||||||||
\(640\) | −14931.0 | −0.922187 | ||||||||
\(641\) | −10185.0 | −0.627587 | −0.313794 | − | 0.949491i | \(-0.601600\pi\) | ||||
−0.313794 | + | 0.949491i | \(0.601600\pi\) | |||||||
\(642\) | − 6426.00i | − 0.395037i | ||||||||
\(643\) | − 25928.0i | − 1.59020i | −0.606476 | − | 0.795101i | \(-0.707418\pi\) | ||||
0.606476 | − | 0.795101i | \(-0.292582\pi\) | |||||||
\(644\) | − 12.0000i | 0 0.000734264i | ||||||||
\(645\) | 13878.0i | 0.847203i | ||||||||
\(646\) | 15318.0 | 0.932939 | ||||||||
\(647\) | −23160.0 | −1.40729 | −0.703643 | − | 0.710554i | \(-0.748444\pi\) | ||||
−0.703643 | + | 0.710554i | \(0.748444\pi\) | |||||||
\(648\) | − 1701.00i | − 0.103120i | ||||||||
\(649\) | −18000.0 | −1.08869 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −600.000 | −0.0361227 | ||||||||
\(652\) | 1636.00i | 0.0982680i | ||||||||
\(653\) | 16626.0 | 0.996364 | 0.498182 | − | 0.867073i | \(-0.334001\pi\) | ||||
0.498182 | + | 0.867073i | \(0.334001\pi\) | |||||||
\(654\) | −18054.0 | −1.07946 | ||||||||
\(655\) | − 14256.0i | − 0.850424i | ||||||||
\(656\) | − 16401.0i | − 0.976146i | ||||||||
\(657\) | − 2277.00i | − 0.135212i | ||||||||
\(658\) | − 972.000i | − 0.0575874i | ||||||||
\(659\) | −14808.0 | −0.875323 | −0.437661 | − | 0.899140i | \(-0.644193\pi\) | ||||
−0.437661 | + | 0.899140i | \(0.644193\pi\) | |||||||
\(660\) | 810.000 | 0.0477715 | ||||||||
\(661\) | 4853.00i | 0.285567i | 0.989754 | + | 0.142784i | \(0.0456053\pi\) | ||||
−0.989754 | + | 0.142784i | \(0.954395\pi\) | |||||||
\(662\) | 27516.0 | 1.61547 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −17010.0 | −0.994151 | ||||||||
\(665\) | − 828.000i | − 0.0482834i | ||||||||
\(666\) | 459.000 | 0.0267055 | ||||||||
\(667\) | −630.000 | −0.0365723 | ||||||||
\(668\) | − 264.000i | − 0.0152911i | ||||||||
\(669\) | 11496.0i | 0.664366i | ||||||||
\(670\) | − 25002.0i | − 1.44166i | ||||||||
\(671\) | 6990.00i | 0.402155i | ||||||||
\(672\) | −270.000 | −0.0154992 | ||||||||
\(673\) | 16165.0 | 0.925877 | 0.462938 | − | 0.886391i | \(-0.346795\pi\) | ||||
0.462938 | + | 0.886391i | \(0.346795\pi\) | |||||||
\(674\) | − 33267.0i | − 1.90118i | ||||||||
\(675\) | 1188.00 | 0.0677424 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −25686.0 | −1.45819 | −0.729094 | − | 0.684414i | \(-0.760058\pi\) | ||||
−0.729094 | + | 0.684414i | \(0.760058\pi\) | |||||||
\(678\) | 10071.0i | 0.570464i | ||||||||
\(679\) | 2716.00 | 0.153506 | ||||||||
\(680\) | 20979.0 | 1.18310 | ||||||||
\(681\) | 4194.00i | 0.235998i | ||||||||
\(682\) | 9000.00i | 0.505319i | ||||||||
\(683\) | − 19056.0i | − 1.06758i | −0.845617 | − | 0.533790i | \(-0.820767\pi\) | ||||
0.845617 | − | 0.533790i | \(-0.179233\pi\) | |||||||
\(684\) | − 414.000i | − 0.0231428i | ||||||||
\(685\) | −6453.00 | −0.359936 | ||||||||
\(686\) | 4092.00 | 0.227745 | ||||||||
\(687\) | 13398.0i | 0.744055i | ||||||||
\(688\) | −36494.0 | −2.02227 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 486.000 | 0.0268141 | ||||||||
\(691\) | 16390.0i | 0.902323i | 0.892442 | + | 0.451161i | \(0.148990\pi\) | ||||
−0.892442 | + | 0.451161i | \(0.851010\pi\) | |||||||
\(692\) | 1410.00 | 0.0774569 | ||||||||
\(693\) | −540.000 | −0.0296001 | ||||||||
\(694\) | − 29286.0i | − 1.60185i | ||||||||
\(695\) | − 7380.00i | − 0.402790i | ||||||||
\(696\) | 6615.00i | 0.360260i | ||||||||
\(697\) | 25641.0i | 1.39343i | ||||||||
\(698\) | −24870.0 | −1.34863 | ||||||||
\(699\) | 4914.00 | 0.265901 | ||||||||
\(700\) | − 88.0000i | − 0.00475155i | ||||||||
\(701\) | 27846.0 | 1.50033 | 0.750163 | − | 0.661253i | \(-0.229975\pi\) | ||||
0.750163 | + | 0.661253i | \(0.229975\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −782.000 | −0.0419540 | ||||||||
\(704\) | − 12990.0i | − 0.695425i | ||||||||
\(705\) | 4374.00 | 0.233666 | ||||||||
\(706\) | −37215.0 | −1.98386 | ||||||||
\(707\) | 714.000i | 0.0379812i | ||||||||
\(708\) | − 1800.00i | − 0.0955482i | ||||||||
\(709\) | − 12283.0i | − 0.650632i | −0.945605 | − | 0.325316i | \(-0.894529\pi\) | ||||
0.945605 | − | 0.325316i | \(-0.105471\pi\) | |||||||
\(710\) | 25110.0i | 1.32727i | ||||||||
\(711\) | −11916.0 | −0.628530 | ||||||||
\(712\) | 10458.0 | 0.550464 | ||||||||
\(713\) | 600.000i | 0.0315150i | ||||||||
\(714\) | 1998.00 | 0.104724 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −474.000 | −0.0247405 | ||||||||
\(717\) | 1782.00i | 0.0928173i | ||||||||
\(718\) | −3294.00 | −0.171213 | ||||||||
\(719\) | −25512.0 | −1.32328 | −0.661639 | − | 0.749822i | \(-0.730139\pi\) | ||||
−0.661639 | + | 0.749822i | \(0.730139\pi\) | |||||||
\(720\) | − 5751.00i | − 0.297677i | ||||||||
\(721\) | − 2236.00i | − 0.115497i | ||||||||
\(722\) | − 14229.0i | − 0.733447i | ||||||||
\(723\) | 6909.00i | 0.355392i | ||||||||
\(724\) | 2249.00 | 0.115447 | ||||||||
\(725\) | −4620.00 | −0.236666 | ||||||||
\(726\) | − 3879.00i | − 0.198296i | ||||||||
\(727\) | −6110.00 | −0.311702 | −0.155851 | − | 0.987781i | \(-0.549812\pi\) | ||||
−0.155851 | + | 0.987781i | \(0.549812\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | − 6831.00i | − 0.346338i | ||||||||
\(731\) | 57054.0 | 2.88676 | ||||||||
\(732\) | −699.000 | −0.0352948 | ||||||||
\(733\) | 27127.0i | 1.36693i | 0.729984 | + | 0.683464i | \(0.239527\pi\) | ||||
−0.729984 | + | 0.683464i | \(0.760473\pi\) | |||||||
\(734\) | 17202.0i | 0.865037i | ||||||||
\(735\) | 9153.00i | 0.459338i | ||||||||
\(736\) | 270.000i | 0.0135222i | ||||||||
\(737\) | 27780.0 | 1.38845 | ||||||||
\(738\) | 6237.00 | 0.311094 | ||||||||
\(739\) | − 880.000i | − 0.0438042i | −0.999760 | − | 0.0219021i | \(-0.993028\pi\) | ||||
0.999760 | − | 0.0219021i | \(-0.00697222\pi\) | |||||||
\(740\) | 153.000 | 0.00760053 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 3834.00 | 0.189691 | ||||||||
\(743\) | 21876.0i | 1.08015i | 0.841616 | + | 0.540076i | \(0.181604\pi\) | ||||
−0.841616 | + | 0.540076i | \(0.818396\pi\) | |||||||
\(744\) | 6300.00 | 0.310442 | ||||||||
\(745\) | −15741.0 | −0.774102 | ||||||||
\(746\) | 26913.0i | 1.32085i | ||||||||
\(747\) | − 7290.00i | − 0.357064i | ||||||||
\(748\) | − 3330.00i | − 0.162777i | ||||||||
\(749\) | 1428.00i | 0.0696635i | ||||||||
\(750\) | 13689.0 | 0.666469 | ||||||||
\(751\) | −11798.0 | −0.573256 | −0.286628 | − | 0.958042i | \(-0.592534\pi\) | ||||
−0.286628 | + | 0.958042i | \(0.592534\pi\) | |||||||
\(752\) | 11502.0i | 0.557759i | ||||||||
\(753\) | −18972.0 | −0.918165 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 3330.00 | 0.160518 | ||||||||
\(756\) | − 54.0000i | − 0.00259783i | ||||||||
\(757\) | −8074.00 | −0.387655 | −0.193827 | − | 0.981036i | \(-0.562090\pi\) | ||||
−0.193827 | + | 0.981036i | \(0.562090\pi\) | |||||||
\(758\) | −21732.0 | −1.04135 | ||||||||
\(759\) | 540.000i | 0.0258245i | ||||||||
\(760\) | 8694.00i | 0.414953i | ||||||||
\(761\) | 19554.0i | 0.931448i | 0.884930 | + | 0.465724i | \(0.154206\pi\) | ||||
−0.884930 | + | 0.465724i | \(0.845794\pi\) | |||||||
\(762\) | − 5436.00i | − 0.258432i | ||||||||
\(763\) | 4012.00 | 0.190359 | ||||||||
\(764\) | −3444.00 | −0.163088 | ||||||||
\(765\) | 8991.00i | 0.424928i | ||||||||
\(766\) | 18936.0 | 0.893193 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 4539.00 | 0.213264 | ||||||||
\(769\) | − 14030.0i | − 0.657913i | −0.944345 | − | 0.328956i | \(-0.893303\pi\) | ||||
0.944345 | − | 0.328956i | \(-0.106697\pi\) | |||||||
\(770\) | −1620.00 | −0.0758192 | ||||||||
\(771\) | −23499.0 | −1.09766 | ||||||||
\(772\) | 4273.00i | 0.199208i | ||||||||
\(773\) | − 36042.0i | − 1.67703i | −0.544882 | − | 0.838513i | \(-0.683426\pi\) | ||||
0.544882 | − | 0.838513i | \(-0.316574\pi\) | |||||||
\(774\) | − 13878.0i | − 0.644489i | ||||||||
\(775\) | 4400.00i | 0.203939i | ||||||||
\(776\) | −28518.0 | −1.31925 | ||||||||
\(777\) | −102.000 | −0.00470943 | ||||||||
\(778\) | 10881.0i | 0.501417i | ||||||||
\(779\) | −10626.0 | −0.488724 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −27900.0 | −1.27828 | ||||||||
\(782\) | − 1998.00i | − 0.0913662i | ||||||||
\(783\) | −2835.00 | −0.129393 | ||||||||
\(784\) | −24069.0 | −1.09644 | ||||||||
\(785\) | − 23499.0i | − 1.06843i | ||||||||
\(786\) | 14256.0i | 0.646940i | ||||||||
\(787\) | 28628.0i | 1.29667i | 0.761356 | + | 0.648334i | \(0.224534\pi\) | ||||
−0.761356 | + | 0.648334i | \(0.775466\pi\) | |||||||
\(788\) | − 1986.00i | − 0.0897821i | ||||||||
\(789\) | −9090.00 | −0.410155 | ||||||||
\(790\) | −35748.0 | −1.60995 | ||||||||
\(791\) | − 2238.00i | − 0.100599i | ||||||||
\(792\) | 5670.00 | 0.254387 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | −11694.0 | −0.522676 | ||||||||
\(795\) | 17253.0i | 0.769687i | ||||||||
\(796\) | −2386.00 | −0.106243 | ||||||||
\(797\) | 37434.0 | 1.66371 | 0.831857 | − | 0.554990i | \(-0.187278\pi\) | ||||
0.831857 | + | 0.554990i | \(0.187278\pi\) | |||||||
\(798\) | 828.000i | 0.0367304i | ||||||||
\(799\) | − 17982.0i | − 0.796192i | ||||||||
\(800\) | 1980.00i | 0.0875045i | ||||||||
\(801\) | 4482.00i | 0.197707i | ||||||||
\(802\) | −17109.0 | −0.753292 | ||||||||
\(803\) | 7590.00 | 0.333556 | ||||||||
\(804\) | 2778.00i | 0.121856i | ||||||||
\(805\) | −108.000 | −0.00472857 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −1602.00 | −0.0698799 | ||||||||
\(808\) | − 7497.00i | − 0.326415i | ||||||||
\(809\) | 37569.0 | 1.63270 | 0.816351 | − | 0.577556i | \(-0.195994\pi\) | ||||
0.816351 | + | 0.577556i | \(0.195994\pi\) | |||||||
\(810\) | 2187.00 | 0.0948683 | ||||||||
\(811\) | − 5516.00i | − 0.238832i | −0.992844 | − | 0.119416i | \(-0.961898\pi\) | ||||
0.992844 | − | 0.119416i | \(-0.0381023\pi\) | |||||||
\(812\) | 210.000i | 0.00907581i | ||||||||
\(813\) | − 11064.0i | − 0.477283i | ||||||||
\(814\) | 1530.00i | 0.0658802i | ||||||||
\(815\) | 14724.0 | 0.632833 | ||||||||
\(816\) | −23643.0 | −1.01430 | ||||||||
\(817\) | 23644.0i | 1.01248i | ||||||||
\(818\) | −18933.0 | −0.809263 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 2079.00 | 0.0885388 | ||||||||
\(821\) | − 8778.00i | − 0.373148i | −0.982441 | − | 0.186574i | \(-0.940262\pi\) | ||||
0.982441 | − | 0.186574i | \(-0.0597384\pi\) | |||||||
\(822\) | 6453.00 | 0.273813 | ||||||||
\(823\) | 3088.00 | 0.130791 | 0.0653955 | − | 0.997859i | \(-0.479169\pi\) | ||||
0.0653955 | + | 0.997859i | \(0.479169\pi\) | |||||||
\(824\) | 23478.0i | 0.992591i | ||||||||
\(825\) | 3960.00i | 0.167115i | ||||||||
\(826\) | 3600.00i | 0.151647i | ||||||||
\(827\) | 13176.0i | 0.554020i | 0.960867 | + | 0.277010i | \(0.0893435\pi\) | ||||
−0.960867 | + | 0.277010i | \(0.910657\pi\) | |||||||
\(828\) | −54.0000 | −0.00226646 | ||||||||
\(829\) | 2359.00 | 0.0988317 | 0.0494158 | − | 0.998778i | \(-0.484264\pi\) | ||||
0.0494158 | + | 0.998778i | \(0.484264\pi\) | |||||||
\(830\) | − 21870.0i | − 0.914601i | ||||||||
\(831\) | −5595.00 | −0.233560 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 37629.0 | 1.56515 | ||||||||
\(834\) | 7380.00i | 0.306413i | ||||||||
\(835\) | −2376.00 | −0.0984729 | ||||||||
\(836\) | 1380.00 | 0.0570913 | ||||||||
\(837\) | 2700.00i | 0.111500i | ||||||||
\(838\) | 6984.00i | 0.287898i | ||||||||
\(839\) | − 2676.00i | − 0.110114i | −0.998483 | − | 0.0550571i | \(-0.982466\pi\) | ||||
0.998483 | − | 0.0550571i | \(-0.0175341\pi\) | |||||||
\(840\) | 1134.00i | 0.0465794i | ||||||||
\(841\) | −13364.0 | −0.547952 | ||||||||
\(842\) | −6135.00 | −0.251100 | ||||||||
\(843\) | 8991.00i | 0.367339i | ||||||||
\(844\) | 1600.00 | 0.0652539 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −4374.00 | −0.177756 | ||||||||
\(847\) | 862.000i | 0.0349689i | ||||||||
\(848\) | −45369.0 | −1.83724 | ||||||||
\(849\) | 12342.0 | 0.498912 | ||||||||
\(850\) | − 14652.0i | − 0.591246i | ||||||||
\(851\) | 102.000i | 0.00410871i | ||||||||
\(852\) | − 2790.00i | − 0.112188i | ||||||||
\(853\) | 2477.00i | 0.0994266i | 0.998764 | + | 0.0497133i | \(0.0158308\pi\) | ||||
−0.998764 | + | 0.0497133i | \(0.984169\pi\) | |||||||
\(854\) | 1398.00 | 0.0560171 | ||||||||
\(855\) | −3726.00 | −0.149037 | ||||||||
\(856\) | − 14994.0i | − 0.598697i | ||||||||
\(857\) | 17199.0 | 0.685539 | 0.342769 | − | 0.939420i | \(-0.388635\pi\) | ||||
0.342769 | + | 0.939420i | \(0.388635\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 24338.0 | 0.966708 | 0.483354 | − | 0.875425i | \(-0.339418\pi\) | ||||
0.483354 | + | 0.875425i | \(0.339418\pi\) | |||||||
\(860\) | − 4626.00i | − 0.183425i | ||||||||
\(861\) | −1386.00 | −0.0548603 | ||||||||
\(862\) | −15102.0 | −0.596724 | ||||||||
\(863\) | − 25146.0i | − 0.991865i | −0.868361 | − | 0.495933i | \(-0.834826\pi\) | ||||
0.868361 | − | 0.495933i | \(-0.165174\pi\) | |||||||
\(864\) | 1215.00i | 0.0478416i | ||||||||
\(865\) | − 12690.0i | − 0.498813i | ||||||||
\(866\) | 12849.0i | 0.504188i | ||||||||
\(867\) | 22224.0 | 0.870550 | ||||||||
\(868\) | 200.000 | 0.00782079 | ||||||||
\(869\) | − 39720.0i | − 1.55053i | ||||||||
\(870\) | −8505.00 | −0.331433 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −42126.0 | −1.63597 | ||||||||
\(873\) | − 12222.0i | − 0.473828i | ||||||||
\(874\) | 828.000 | 0.0320452 | ||||||||
\(875\) | −3042.00 | −0.117530 | ||||||||
\(876\) | 759.000i | 0.0292742i | ||||||||
\(877\) | − 18089.0i | − 0.696490i | −0.937403 | − | 0.348245i | \(-0.886778\pi\) | ||||
0.937403 | − | 0.348245i | \(-0.113222\pi\) | |||||||
\(878\) | − 3918.00i | − 0.150599i | ||||||||
\(879\) | − 13995.0i | − 0.537019i | ||||||||
\(880\) | 19170.0 | 0.734342 | ||||||||
\(881\) | 15099.0 | 0.577410 | 0.288705 | − | 0.957418i | \(-0.406775\pi\) | ||||
0.288705 | + | 0.957418i | \(0.406775\pi\) | |||||||
\(882\) | − 9153.00i | − 0.349430i | ||||||||
\(883\) | −33488.0 | −1.27629 | −0.638143 | − | 0.769918i | \(-0.720297\pi\) | ||||
−0.638143 | + | 0.769918i | \(0.720297\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −16200.0 | −0.615319 | ||||||||
\(886\) | 17388.0i | 0.659324i | ||||||||
\(887\) | −39768.0 | −1.50539 | −0.752694 | − | 0.658371i | \(-0.771246\pi\) | ||||
−0.752694 | + | 0.658371i | \(0.771246\pi\) | |||||||
\(888\) | 1071.00 | 0.0404734 | ||||||||
\(889\) | 1208.00i | 0.0455737i | ||||||||
\(890\) | 13446.0i | 0.506417i | ||||||||
\(891\) | 2430.00i | 0.0913671i | ||||||||
\(892\) | − 3832.00i | − 0.143840i | ||||||||
\(893\) | 7452.00 | 0.279252 | ||||||||
\(894\) | 15741.0 | 0.588879 | ||||||||
\(895\) | 4266.00i | 0.159326i | ||||||||
\(896\) | −3318.00 | −0.123713 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 8118.00 | 0.301672 | ||||||||
\(899\) | − 10500.0i | − 0.389538i | ||||||||
\(900\) | −396.000 | −0.0146667 | ||||||||
\(901\) | 70929.0 | 2.62263 | ||||||||
\(902\) | 20790.0i | 0.767440i | ||||||||
\(903\) | 3084.00i | 0.113653i | ||||||||
\(904\) | 23499.0i | 0.864563i | ||||||||
\(905\) | − 20241.0i | − 0.743463i | ||||||||
\(906\) | −3330.00 | −0.122110 | ||||||||
\(907\) | −32156.0 | −1.17720 | −0.588601 | − | 0.808424i | \(-0.700321\pi\) | ||||
−0.588601 | + | 0.808424i | \(0.700321\pi\) | |||||||
\(908\) | − 1398.00i | − 0.0510950i | ||||||||
\(909\) | 3213.00 | 0.117237 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 11520.0 | 0.418962 | 0.209481 | − | 0.977813i | \(-0.432823\pi\) | ||||
0.209481 | + | 0.977813i | \(0.432823\pi\) | |||||||
\(912\) | − 9798.00i | − 0.355750i | ||||||||
\(913\) | 24300.0 | 0.880846 | ||||||||
\(914\) | 2487.00 | 0.0900029 | ||||||||
\(915\) | 6291.00i | 0.227294i | ||||||||
\(916\) | − 4466.00i | − 0.161093i | ||||||||
\(917\) | − 3168.00i | − 0.114086i | ||||||||
\(918\) | − 8991.00i | − 0.323254i | ||||||||
\(919\) | 4952.00 | 0.177749 | 0.0888745 | − | 0.996043i | \(-0.471673\pi\) | ||||
0.0888745 | + | 0.996043i | \(0.471673\pi\) | |||||||
\(920\) | 1134.00 | 0.0406379 | ||||||||
\(921\) | 4506.00i | 0.161214i | ||||||||
\(922\) | 16479.0 | 0.588619 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 180.000 | 0.00640862 | ||||||||
\(925\) | 748.000i | 0.0265882i | ||||||||
\(926\) | −46038.0 | −1.63380 | ||||||||
\(927\) | −10062.0 | −0.356504 | ||||||||
\(928\) | − 4725.00i | − 0.167140i | ||||||||
\(929\) | − 8781.00i | − 0.310113i | −0.987906 | − | 0.155057i | \(-0.950444\pi\) | ||||
0.987906 | − | 0.155057i | \(-0.0495560\pi\) | |||||||
\(930\) | 8100.00i | 0.285602i | ||||||||
\(931\) | 15594.0i | 0.548950i | ||||||||
\(932\) | −1638.00 | −0.0575692 | ||||||||
\(933\) | −6318.00 | −0.221696 | ||||||||
\(934\) | − 28782.0i | − 1.00833i | ||||||||
\(935\) | −29970.0 | −1.04826 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 50039.0 | 1.74461 | 0.872307 | − | 0.488959i | \(-0.162623\pi\) | ||||
0.872307 | + | 0.488959i | \(0.162623\pi\) | |||||||
\(938\) | − 5556.00i | − 0.193401i | ||||||||
\(939\) | −11694.0 | −0.406410 | ||||||||
\(940\) | −1458.00 | −0.0505901 | ||||||||
\(941\) | 50670.0i | 1.75536i | 0.479246 | + | 0.877681i | \(0.340910\pi\) | ||||
−0.479246 | + | 0.877681i | \(0.659090\pi\) | |||||||
\(942\) | 23499.0i | 0.812780i | ||||||||
\(943\) | 1386.00i | 0.0478625i | ||||||||
\(944\) | − 42600.0i | − 1.46876i | ||||||||
\(945\) | −486.000 | −0.0167297 | ||||||||
\(946\) | 46260.0 | 1.58990 | ||||||||
\(947\) | 42384.0i | 1.45438i | 0.686438 | + | 0.727188i | \(0.259173\pi\) | ||||
−0.686438 | + | 0.727188i | \(0.740827\pi\) | |||||||
\(948\) | 3972.00 | 0.136081 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 6072.00 | 0.207370 | ||||||||
\(951\) | − 28053.0i | − 0.956552i | ||||||||
\(952\) | 4662.00 | 0.158715 | ||||||||
\(953\) | 50538.0 | 1.71782 | 0.858912 | − | 0.512123i | \(-0.171141\pi\) | ||||
0.858912 | + | 0.512123i | \(0.171141\pi\) | |||||||
\(954\) | − 17253.0i | − 0.585520i | ||||||||
\(955\) | 30996.0i | 1.05027i | ||||||||
\(956\) | − 594.000i | − 0.0200955i | ||||||||
\(957\) | − 9450.00i | − 0.319201i | ||||||||
\(958\) | −38520.0 | −1.29909 | ||||||||
\(959\) | −1434.00 | −0.0482860 | ||||||||
\(960\) | − 11691.0i | − 0.393047i | ||||||||
\(961\) | 19791.0 | 0.664328 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 6426.00 | 0.215031 | ||||||||
\(964\) | − 2303.00i | − 0.0769446i | ||||||||
\(965\) | 38457.0 | 1.28288 | ||||||||
\(966\) | 108.000 | 0.00359715 | ||||||||
\(967\) | 6886.00i | 0.228996i | 0.993423 | + | 0.114498i | \(0.0365259\pi\) | ||||
−0.993423 | + | 0.114498i | \(0.963474\pi\) | |||||||
\(968\) | − 9051.00i | − 0.300527i | ||||||||
\(969\) | 15318.0i | 0.507828i | ||||||||
\(970\) | − 36666.0i | − 1.21368i | ||||||||
\(971\) | 9060.00 | 0.299433 | 0.149716 | − | 0.988729i | \(-0.452164\pi\) | ||||
0.149716 | + | 0.988729i | \(0.452164\pi\) | |||||||
\(972\) | −243.000 | −0.00801875 | ||||||||
\(973\) | − 1640.00i | − 0.0540349i | ||||||||
\(974\) | 42258.0 | 1.39018 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −16543.0 | −0.542550 | ||||||||
\(977\) | 28311.0i | 0.927072i | 0.886078 | + | 0.463536i | \(0.153419\pi\) | ||||
−0.886078 | + | 0.463536i | \(0.846581\pi\) | |||||||
\(978\) | −14724.0 | −0.481413 | ||||||||
\(979\) | −14940.0 | −0.487727 | ||||||||
\(980\) | − 3051.00i | − 0.0994496i | ||||||||
\(981\) | − 18054.0i | − 0.587584i | ||||||||
\(982\) | 35082.0i | 1.14003i | ||||||||
\(983\) | 4284.00i | 0.139001i | 0.997582 | + | 0.0695007i | \(0.0221406\pi\) | ||||
−0.997582 | + | 0.0695007i | \(0.977859\pi\) | |||||||
\(984\) | 14553.0 | 0.471476 | ||||||||
\(985\) | −17874.0 | −0.578186 | ||||||||
\(986\) | 34965.0i | 1.12932i | ||||||||
\(987\) | 972.000 | 0.0313466 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 3084.00 | 0.0991562 | ||||||||
\(990\) | 7290.00i | 0.234032i | ||||||||
\(991\) | −2458.00 | −0.0787901 | −0.0393950 | − | 0.999224i | \(-0.512543\pi\) | ||||
−0.0393950 | + | 0.999224i | \(0.512543\pi\) | |||||||
\(992\) | −4500.00 | −0.144027 | ||||||||
\(993\) | 27516.0i | 0.879349i | ||||||||
\(994\) | 5580.00i | 0.178055i | ||||||||
\(995\) | 21474.0i | 0.684193i | ||||||||
\(996\) | 2430.00i | 0.0773067i | ||||||||
\(997\) | 24101.0 | 0.765583 | 0.382792 | − | 0.923835i | \(-0.374963\pi\) | ||||
0.382792 | + | 0.923835i | \(0.374963\pi\) | |||||||
\(998\) | 11064.0 | 0.350927 | ||||||||
\(999\) | 459.000i | 0.0145367i |
(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 | 507.4.b.c.337.1 | 2 | ||
13.5 | odd | 4 | 507.4.a.a.1.1 | 1 | |||
13.7 | odd | 12 | 39.4.e.a.16.1 | ✓ | 2 | ||
13.8 | odd | 4 | 507.4.a.e.1.1 | 1 | |||
13.11 | odd | 12 | 39.4.e.a.22.1 | yes | 2 | ||
13.12 | even | 2 | inner | 507.4.b.c.337.2 | 2 | ||
39.5 | even | 4 | 1521.4.a.j.1.1 | 1 | |||
39.8 | even | 4 | 1521.4.a.c.1.1 | 1 | |||
39.11 | even | 12 | 117.4.g.b.100.1 | 2 | |||
39.20 | even | 12 | 117.4.g.b.55.1 | 2 | |||
52.7 | even | 12 | 624.4.q.b.289.1 | 2 | |||
52.11 | even | 12 | 624.4.q.b.529.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
39.4.e.a.16.1 | ✓ | 2 | 13.7 | odd | 12 | ||
39.4.e.a.22.1 | yes | 2 | 13.11 | odd | 12 | ||
117.4.g.b.55.1 | 2 | 39.20 | even | 12 | |||
117.4.g.b.100.1 | 2 | 39.11 | even | 12 | |||
507.4.a.a.1.1 | 1 | 13.5 | odd | 4 | |||
507.4.a.e.1.1 | 1 | 13.8 | odd | 4 | |||
507.4.b.c.337.1 | 2 | 1.1 | even | 1 | trivial | ||
507.4.b.c.337.2 | 2 | 13.12 | even | 2 | inner | ||
624.4.q.b.289.1 | 2 | 52.7 | even | 12 | |||
624.4.q.b.529.1 | 2 | 52.11 | even | 12 | |||
1521.4.a.c.1.1 | 1 | 39.8 | even | 4 | |||
1521.4.a.j.1.1 | 1 | 39.5 | even | 4 |