Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1089,3,Mod(604,1089)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1089, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1089.604");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1089 = 3^{2} \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1089.c (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(29.6731007888\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.523388583936.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 28x^{6} + 262x^{4} + 948x^{2} + 1089 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2\cdot 11 \) |
Twist minimal: | no (minimal twist has level 121) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 604.6 | ||
Root | \(2.16205i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1089.604 |
Dual form | 1089.3.c.k.604.3 |
$q$-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 \(\left(\mathbb{Z}/1089\mathbb{Z}\right)^\times\).
\(n\) | \(244\) | \(848\) |
\(\chi(n)\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.16205i | 1.08102i | 0.841336 | + | 0.540512i | \(0.181769\pi\) | ||||
−0.841336 | + | 0.540512i | \(0.818231\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.674453 | −0.168613 | ||||||||
\(5\) | −7.64086 | −1.52817 | −0.764086 | − | 0.645115i | \(-0.776810\pi\) | ||||
−0.764086 | + | 0.645115i | \(0.776810\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − 6.05557i | − 0.865081i | −0.901615 | − | 0.432540i | \(-0.857617\pi\) | ||||
0.901615 | − | 0.432540i | \(-0.142383\pi\) | |||||||
\(8\) | 7.18999i | 0.898749i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | − 16.5199i | − 1.65199i | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.21180i | 0.247062i | 0.992341 | + | 0.123531i | \(0.0394218\pi\) | ||||
−0.992341 | + | 0.123531i | \(0.960578\pi\) | |||||||
\(14\) | 13.0924 | 0.935173 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −18.2429 | −1.14018 | ||||||||
\(17\) | 6.22852i | 0.366383i | 0.983077 | + | 0.183192i | \(0.0586429\pi\) | ||||
−0.983077 | + | 0.183192i | \(0.941357\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − 19.4519i | − 1.02379i | −0.859049 | − | 0.511893i | \(-0.828944\pi\) | ||||
0.859049 | − | 0.511893i | \(-0.171056\pi\) | |||||||
\(20\) | 5.15340 | 0.257670 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −3.47096 | −0.150912 | −0.0754558 | − | 0.997149i | \(-0.524041\pi\) | ||||
−0.0754558 | + | 0.997149i | \(0.524041\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 33.3827 | 1.33531 | ||||||||
\(26\) | −6.94407 | −0.267080 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 4.08419i | 0.145864i | ||||||||
\(29\) | − 36.1250i | − 1.24569i | −0.782345 | − | 0.622845i | \(-0.785977\pi\) | ||||
0.782345 | − | 0.622845i | \(-0.214023\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.28901 | −0.106097 | −0.0530486 | − | 0.998592i | \(-0.516894\pi\) | ||||
−0.0530486 | + | 0.998592i | \(0.516894\pi\) | |||||||
\(32\) | − 10.6821i | − 0.333816i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −13.4664 | −0.396069 | ||||||||
\(35\) | 46.2697i | 1.32199i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 63.2118 | 1.70843 | 0.854214 | − | 0.519922i | \(-0.174039\pi\) | ||||
0.854214 | + | 0.519922i | \(0.174039\pi\) | |||||||
\(38\) | 42.0560 | 1.10674 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | − 54.9377i | − 1.37344i | ||||||||
\(41\) | − 31.9231i | − 0.778612i | −0.921108 | − | 0.389306i | \(-0.872715\pi\) | ||||
0.921108 | − | 0.389306i | \(-0.127285\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 43.9407i | 1.02188i | 0.859618 | + | 0.510938i | \(0.170702\pi\) | ||||
−0.859618 | + | 0.510938i | \(0.829298\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | − 7.50439i | − 0.163139i | ||||||||
\(47\) | 34.7799 | 0.739998 | 0.369999 | − | 0.929032i | \(-0.379358\pi\) | ||||
0.369999 | + | 0.929032i | \(0.379358\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 12.3301 | 0.251635 | ||||||||
\(50\) | 72.1750i | 1.44350i | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | − 2.16621i | − 0.0416578i | ||||||||
\(53\) | −16.5478 | −0.312223 | −0.156111 | − | 0.987739i | \(-0.549896\pi\) | ||||
−0.156111 | + | 0.987739i | \(0.549896\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 43.5395 | 0.777491 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 78.1040 | 1.34662 | ||||||||
\(59\) | 63.7608 | 1.08069 | 0.540346 | − | 0.841443i | \(-0.318293\pi\) | ||||
0.540346 | + | 0.841443i | \(0.318293\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 110.544i | 1.81220i | 0.423059 | + | 0.906102i | \(0.360956\pi\) | ||||
−0.423059 | + | 0.906102i | \(0.639044\pi\) | |||||||
\(62\) | − 7.11100i | − 0.114694i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −49.8765 | −0.779320 | ||||||||
\(65\) | − 24.5409i | − 0.377553i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 96.1439 | 1.43498 | 0.717492 | − | 0.696567i | \(-0.245290\pi\) | ||||
0.717492 | + | 0.696567i | \(0.245290\pi\) | |||||||
\(68\) | − 4.20084i | − 0.0617771i | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −100.037 | −1.42911 | ||||||||
\(71\) | 44.8264 | 0.631358 | 0.315679 | − | 0.948866i | \(-0.397768\pi\) | ||||
0.315679 | + | 0.948866i | \(0.397768\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 63.2763i | 0.866798i | 0.901202 | + | 0.433399i | \(0.142686\pi\) | ||||
−0.901202 | + | 0.433399i | \(0.857314\pi\) | |||||||
\(74\) | 136.667i | 1.84685i | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 13.1194i | 0.172624i | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − 14.1046i | − 0.178540i | −0.996007 | − | 0.0892699i | \(-0.971547\pi\) | ||||
0.996007 | − | 0.0892699i | \(-0.0284534\pi\) | |||||||
\(80\) | 139.392 | 1.74239 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 69.0193 | 0.841699 | ||||||||
\(83\) | 88.6120i | 1.06761i | 0.845606 | + | 0.533807i | \(0.179239\pi\) | ||||
−0.845606 | + | 0.533807i | \(0.820761\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − 47.5912i | − 0.559897i | ||||||||
\(86\) | −95.0018 | −1.10467 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −51.3977 | −0.577502 | −0.288751 | − | 0.957404i | \(-0.593240\pi\) | ||||
−0.288751 | + | 0.957404i | \(0.593240\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 19.4493 | 0.213728 | ||||||||
\(92\) | 2.34100 | 0.0254457 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 75.1958i | 0.799956i | ||||||||
\(95\) | 148.630i | 1.56452i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 31.5024 | 0.324767 | 0.162383 | − | 0.986728i | \(-0.448082\pi\) | ||||
0.162383 | + | 0.986728i | \(0.448082\pi\) | |||||||
\(98\) | 26.6583i | 0.272023i | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −22.5151 | −0.225151 | ||||||||
\(101\) | 84.1059i | 0.832732i | 0.909197 | + | 0.416366i | \(0.136696\pi\) | ||||
−0.909197 | + | 0.416366i | \(0.863304\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 76.6144 | 0.743829 | 0.371915 | − | 0.928267i | \(-0.378701\pi\) | ||||
0.371915 | + | 0.928267i | \(0.378701\pi\) | |||||||
\(104\) | −23.0928 | −0.222046 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | − 35.7771i | − 0.337520i | ||||||||
\(107\) | − 128.437i | − 1.20034i | −0.799872 | − | 0.600171i | \(-0.795099\pi\) | ||||
0.799872 | − | 0.600171i | \(-0.204901\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − 150.418i | − 1.37998i | −0.723819 | − | 0.689990i | \(-0.757615\pi\) | ||||
0.723819 | − | 0.689990i | \(-0.242385\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 110.471i | 0.986350i | ||||||||
\(113\) | 102.830 | 0.910004 | 0.455002 | − | 0.890490i | \(-0.349638\pi\) | ||||
0.455002 | + | 0.890490i | \(0.349638\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 26.5212 | 0.230619 | ||||||||
\(116\) | 24.3646i | 0.210040i | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 137.854i | 1.16825i | ||||||||
\(119\) | 37.7172 | 0.316951 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | −239.002 | −1.95904 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 2.21828 | 0.0178894 | ||||||||
\(125\) | −64.0511 | −0.512409 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − 231.035i | − 1.81917i | −0.415517 | − | 0.909585i | \(-0.636399\pi\) | ||||
0.415517 | − | 0.909585i | \(-0.363601\pi\) | |||||||
\(128\) | − 150.564i | − 1.17628i | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 53.0586 | 0.408143 | ||||||||
\(131\) | − 234.208i | − 1.78784i | −0.448223 | − | 0.893922i | \(-0.647943\pi\) | ||||
0.448223 | − | 0.893922i | \(-0.352057\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −117.793 | −0.885658 | ||||||||
\(134\) | 207.868i | 1.55125i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −44.7830 | −0.329287 | ||||||||
\(137\) | 145.175 | 1.05967 | 0.529837 | − | 0.848100i | \(-0.322253\pi\) | ||||
0.529837 | + | 0.848100i | \(0.322253\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 20.6006i | 0.148206i | 0.997251 | + | 0.0741028i | \(0.0236093\pi\) | ||||
−0.997251 | + | 0.0741028i | \(0.976391\pi\) | |||||||
\(140\) | − 31.2067i | − 0.222905i | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 96.9169i | 0.682513i | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 276.026i | 1.90363i | ||||||||
\(146\) | −136.806 | −0.937030 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −42.6334 | −0.288063 | ||||||||
\(149\) | 80.6247i | 0.541105i | 0.962705 | + | 0.270553i | \(0.0872064\pi\) | ||||
−0.962705 | + | 0.270553i | \(0.912794\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 150.438i | 0.996276i | 0.867098 | + | 0.498138i | \(0.165983\pi\) | ||||
−0.867098 | + | 0.498138i | \(0.834017\pi\) | |||||||
\(152\) | 139.859 | 0.920127 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 25.1309 | 0.162135 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −81.4919 | −0.519057 | −0.259528 | − | 0.965735i | \(-0.583567\pi\) | ||||
−0.259528 | + | 0.965735i | \(0.583567\pi\) | |||||||
\(158\) | 30.4949 | 0.193006 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 81.6205i | 0.510128i | ||||||||
\(161\) | 21.0187i | 0.130551i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −23.0774 | −0.141579 | −0.0707895 | − | 0.997491i | \(-0.522552\pi\) | ||||
−0.0707895 | + | 0.997491i | \(0.522552\pi\) | |||||||
\(164\) | 21.5306i | 0.131284i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −191.584 | −1.15412 | ||||||||
\(167\) | − 292.437i | − 1.75112i | −0.483110 | − | 0.875560i | \(-0.660493\pi\) | ||||
0.483110 | − | 0.875560i | \(-0.339507\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 158.684 | 0.938961 | ||||||||
\(170\) | 102.895 | 0.605262 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | − 29.6359i | − 0.172302i | ||||||||
\(173\) | 212.290i | 1.22711i | 0.789651 | + | 0.613556i | \(0.210262\pi\) | ||||
−0.789651 | + | 0.613556i | \(0.789738\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − 202.151i | − 1.15515i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | − 111.124i | − 0.624294i | ||||||||
\(179\) | −52.8561 | −0.295285 | −0.147643 | − | 0.989041i | \(-0.547169\pi\) | ||||
−0.147643 | + | 0.989041i | \(0.547169\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −26.2830 | −0.145210 | −0.0726051 | − | 0.997361i | \(-0.523131\pi\) | ||||
−0.0726051 | + | 0.997361i | \(0.523131\pi\) | |||||||
\(182\) | 42.0503i | 0.231045i | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | − 24.9562i | − 0.135632i | ||||||||
\(185\) | −482.992 | −2.61077 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −23.4574 | −0.124773 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −321.344 | −1.69129 | ||||||||
\(191\) | 115.146 | 0.602861 | 0.301430 | − | 0.953488i | \(-0.402536\pi\) | ||||
0.301430 | + | 0.953488i | \(0.402536\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − 38.6666i | − 0.200345i | −0.994970 | − | 0.100172i | \(-0.968061\pi\) | ||||
0.994970 | − | 0.100172i | \(-0.0319395\pi\) | |||||||
\(194\) | 68.1097i | 0.351081i | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −8.31608 | −0.0424290 | ||||||||
\(197\) | 3.42417i | 0.0173815i | 0.999962 | + | 0.00869077i | \(0.00276639\pi\) | ||||
−0.999962 | + | 0.00869077i | \(0.997234\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −183.079 | −0.919997 | −0.459999 | − | 0.887920i | \(-0.652150\pi\) | ||||
−0.459999 | + | 0.887920i | \(0.652150\pi\) | |||||||
\(200\) | 240.021i | 1.20011i | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −181.841 | −0.900203 | ||||||||
\(203\) | −218.757 | −1.07762 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 243.920i | 1.18985i | ||||||||
\(206\) | 165.644i | 0.804097i | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | − 58.5926i | − 0.281695i | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − 271.800i | − 1.28815i | −0.764961 | − | 0.644077i | \(-0.777242\pi\) | ||||
0.764961 | − | 0.644077i | \(-0.222758\pi\) | |||||||
\(212\) | 11.1607 | 0.0526449 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 277.686 | 1.29760 | ||||||||
\(215\) | − 335.744i | − 1.56160i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 19.9168i | 0.0917826i | ||||||||
\(218\) | 325.211 | 1.49179 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −20.0048 | −0.0905193 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 44.7473 | 0.200661 | 0.100330 | − | 0.994954i | \(-0.468010\pi\) | ||||
0.100330 | + | 0.994954i | \(0.468010\pi\) | |||||||
\(224\) | −64.6862 | −0.288778 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 222.324i | 0.983737i | ||||||||
\(227\) | 131.114i | 0.577596i | 0.957390 | + | 0.288798i | \(0.0932556\pi\) | ||||
−0.957390 | + | 0.288798i | \(0.906744\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −276.449 | −1.20720 | −0.603601 | − | 0.797287i | \(-0.706268\pi\) | ||||
−0.603601 | + | 0.797287i | \(0.706268\pi\) | |||||||
\(230\) | 57.3400i | 0.249304i | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 259.739 | 1.11956 | ||||||||
\(233\) | − 42.8283i | − 0.183812i | −0.995768 | − | 0.0919061i | \(-0.970704\pi\) | ||||
0.995768 | − | 0.0919061i | \(-0.0292960\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −265.748 | −1.13084 | ||||||||
\(236\) | −43.0037 | −0.182219 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 81.5464i | 0.342632i | ||||||||
\(239\) | 13.1360i | 0.0549625i | 0.999622 | + | 0.0274812i | \(0.00874865\pi\) | ||||
−0.999622 | + | 0.0274812i | \(0.991251\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 80.4946i | 0.334002i | 0.985957 | + | 0.167001i | \(0.0534084\pi\) | ||||
−0.985957 | + | 0.167001i | \(0.946592\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | − 74.5570i | − 0.305561i | ||||||||
\(245\) | −94.2127 | −0.384541 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 62.4758 | 0.252938 | ||||||||
\(248\) | − 23.6480i | − 0.0953547i | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | − 138.482i | − 0.553927i | ||||||||
\(251\) | 311.802 | 1.24224 | 0.621120 | − | 0.783716i | \(-0.286678\pi\) | ||||
0.621120 | + | 0.783716i | \(0.286678\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 499.508 | 1.96657 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 126.020 | 0.492267 | ||||||||
\(257\) | 24.7875 | 0.0964496 | 0.0482248 | − | 0.998837i | \(-0.484644\pi\) | ||||
0.0482248 | + | 0.998837i | \(0.484644\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − 382.783i | − 1.47793i | ||||||||
\(260\) | 16.5517i | 0.0636603i | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 506.368 | 1.93270 | ||||||||
\(263\) | 189.407i | 0.720178i | 0.932918 | + | 0.360089i | \(0.117254\pi\) | ||||
−0.932918 | + | 0.360089i | \(0.882746\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 126.439 | 0.477130 | ||||||||
\(266\) | − 254.673i | − 0.957418i | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −64.8445 | −0.241957 | ||||||||
\(269\) | 409.266 | 1.52144 | 0.760718 | − | 0.649082i | \(-0.224847\pi\) | ||||
0.760718 | + | 0.649082i | \(0.224847\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 24.5223i | 0.0904882i | 0.998976 | + | 0.0452441i | \(0.0144066\pi\) | ||||
−0.998976 | + | 0.0452441i | \(0.985593\pi\) | |||||||
\(272\) | − 113.626i | − 0.417744i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 313.876i | 1.14553i | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − 80.5213i | − 0.290691i | −0.989381 | − | 0.145345i | \(-0.953571\pi\) | ||||
0.989381 | − | 0.145345i | \(-0.0464293\pi\) | |||||||
\(278\) | −44.5395 | −0.160214 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −332.679 | −1.18814 | ||||||||
\(281\) | − 58.2626i | − 0.207340i | −0.994612 | − | 0.103670i | \(-0.966941\pi\) | ||||
0.994612 | − | 0.103670i | \(-0.0330586\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − 124.525i | − 0.440016i | −0.975498 | − | 0.220008i | \(-0.929392\pi\) | ||||
0.975498 | − | 0.220008i | \(-0.0706084\pi\) | |||||||
\(284\) | −30.2333 | −0.106455 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −193.312 | −0.673563 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 250.206 | 0.865763 | ||||||||
\(290\) | −596.782 | −2.05787 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | − 42.6769i | − 0.146154i | ||||||||
\(293\) | − 99.0592i | − 0.338086i | −0.985609 | − | 0.169043i | \(-0.945932\pi\) | ||||
0.985609 | − | 0.169043i | \(-0.0540677\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −487.187 | −1.65148 | ||||||||
\(296\) | 454.492i | 1.53545i | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −174.314 | −0.584948 | ||||||||
\(299\) | − 11.1480i | − 0.0372844i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 266.086 | 0.884005 | ||||||||
\(302\) | −325.254 | −1.07700 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 354.860i | 1.16730i | ||||||||
\(305\) | − 844.654i | − 2.76936i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 335.303i | 1.09219i | 0.837723 | + | 0.546096i | \(0.183886\pi\) | ||||
−0.837723 | + | 0.546096i | \(0.816114\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 54.3342i | 0.175271i | ||||||||
\(311\) | −257.049 | −0.826525 | −0.413263 | − | 0.910612i | \(-0.635611\pi\) | ||||
−0.413263 | + | 0.910612i | \(0.635611\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 187.670 | 0.599585 | 0.299792 | − | 0.954004i | \(-0.403083\pi\) | ||||
0.299792 | + | 0.954004i | \(0.403083\pi\) | |||||||
\(314\) | − 176.190i | − 0.561113i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 9.51291i | 0.0301042i | ||||||||
\(317\) | −324.893 | −1.02490 | −0.512449 | − | 0.858718i | \(-0.671262\pi\) | ||||
−0.512449 | + | 0.858718i | \(0.671262\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 381.099 | 1.19093 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −45.4434 | −0.141128 | ||||||||
\(323\) | 121.157 | 0.375098 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 107.219i | 0.329903i | ||||||||
\(326\) | − 49.8944i | − 0.153050i | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 229.527 | 0.699777 | ||||||||
\(329\) | − 210.612i | − 0.640158i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 599.240 | 1.81039 | 0.905196 | − | 0.424993i | \(-0.139724\pi\) | ||||
0.905196 | + | 0.424993i | \(0.139724\pi\) | |||||||
\(332\) | − 59.7646i | − 0.180014i | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 632.263 | 1.89300 | ||||||||
\(335\) | −734.622 | −2.19290 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − 480.354i | − 1.42538i | −0.701477 | − | 0.712692i | \(-0.747476\pi\) | ||||
0.701477 | − | 0.712692i | \(-0.252524\pi\) | |||||||
\(338\) | 343.083i | 1.01504i | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 32.0980i | 0.0944060i | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − 371.389i | − 1.08277i | ||||||||
\(344\) | −315.933 | −0.918410 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −458.982 | −1.32654 | ||||||||
\(347\) | 21.1483i | 0.0609461i | 0.999536 | + | 0.0304731i | \(0.00970138\pi\) | ||||
−0.999536 | + | 0.0304731i | \(0.990299\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − 361.648i | − 1.03624i | −0.855307 | − | 0.518121i | \(-0.826632\pi\) | ||||
0.855307 | − | 0.518121i | \(-0.173368\pi\) | |||||||
\(350\) | 437.061 | 1.24874 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −140.448 | −0.397871 | −0.198935 | − | 0.980013i | \(-0.563748\pi\) | ||||
−0.198935 | + | 0.980013i | \(0.563748\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −342.512 | −0.964823 | ||||||||
\(356\) | 34.6653 | 0.0973745 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | − 114.277i | − 0.319211i | ||||||||
\(359\) | − 433.079i | − 1.20635i | −0.797609 | − | 0.603174i | \(-0.793902\pi\) | ||||
0.797609 | − | 0.603174i | \(-0.206098\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −17.3783 | −0.0481392 | ||||||||
\(362\) | − 56.8252i | − 0.156976i | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −13.1176 | −0.0360374 | ||||||||
\(365\) | − 483.485i | − 1.32462i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 22.0832 | 0.0601723 | 0.0300862 | − | 0.999547i | \(-0.490422\pi\) | ||||
0.0300862 | + | 0.999547i | \(0.490422\pi\) | |||||||
\(368\) | 63.3206 | 0.172067 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | − 1044.25i | − 2.82231i | ||||||||
\(371\) | 100.206i | 0.270098i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − 485.424i | − 1.30140i | −0.759333 | − | 0.650702i | \(-0.774475\pi\) | ||||
0.759333 | − | 0.650702i | \(-0.225525\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 250.067i | 0.665072i | ||||||||
\(377\) | 116.026 | 0.307762 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −710.615 | −1.87497 | −0.937487 | − | 0.348021i | \(-0.886854\pi\) | ||||
−0.937487 | + | 0.348021i | \(0.886854\pi\) | |||||||
\(380\) | − 100.244i | − 0.263799i | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 248.952i | 0.651707i | ||||||||
\(383\) | −70.1703 | −0.183212 | −0.0916061 | − | 0.995795i | \(-0.529200\pi\) | ||||
−0.0916061 | + | 0.995795i | \(0.529200\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 83.5990 | 0.216578 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −21.2469 | −0.0547600 | ||||||||
\(389\) | 503.306 | 1.29385 | 0.646923 | − | 0.762555i | \(-0.276055\pi\) | ||||
0.646923 | + | 0.762555i | \(0.276055\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − 21.6190i | − 0.0552915i | ||||||||
\(392\) | 88.6534i | 0.226157i | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −7.40321 | −0.0187899 | ||||||||
\(395\) | 107.772i | 0.272839i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −144.659 | −0.364380 | −0.182190 | − | 0.983263i | \(-0.558319\pi\) | ||||
−0.182190 | + | 0.983263i | \(0.558319\pi\) | |||||||
\(398\) | − 395.827i | − 0.994539i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −608.998 | −1.52250 | ||||||||
\(401\) | −598.115 | −1.49156 | −0.745779 | − | 0.666194i | \(-0.767922\pi\) | ||||
−0.745779 | + | 0.666194i | \(0.767922\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − 10.5636i | − 0.0262125i | ||||||||
\(404\) | − 56.7255i | − 0.140410i | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | − 472.964i | − 1.16494i | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 209.088i | 0.511217i | 0.966780 | + | 0.255609i | \(0.0822758\pi\) | ||||
−0.966780 | + | 0.255609i | \(0.917724\pi\) | |||||||
\(410\) | −527.367 | −1.28626 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −51.6728 | −0.125419 | ||||||||
\(413\) | − 386.108i | − 0.934886i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − 677.072i | − 1.63150i | ||||||||
\(416\) | 34.3088 | 0.0824731 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 170.309 | 0.406466 | 0.203233 | − | 0.979130i | \(-0.434855\pi\) | ||||
0.203233 | + | 0.979130i | \(0.434855\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 301.865 | 0.717019 | 0.358510 | − | 0.933526i | \(-0.383285\pi\) | ||||
0.358510 | + | 0.933526i | \(0.383285\pi\) | |||||||
\(422\) | 587.646 | 1.39253 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | − 118.979i | − 0.280610i | ||||||||
\(425\) | 207.925i | 0.489235i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 669.409 | 1.56770 | ||||||||
\(428\) | 86.6244i | 0.202393i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 725.895 | 1.68813 | ||||||||
\(431\) | − 416.880i | − 0.967238i | −0.875279 | − | 0.483619i | \(-0.839322\pi\) | ||||
0.875279 | − | 0.483619i | \(-0.160678\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −296.975 | −0.685854 | −0.342927 | − | 0.939362i | \(-0.611418\pi\) | ||||
−0.342927 | + | 0.939362i | \(0.611418\pi\) | |||||||
\(434\) | −43.0611 | −0.0992192 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 101.450i | 0.232683i | ||||||||
\(437\) | 67.5170i | 0.154501i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 690.951i | 1.57392i | 0.617004 | + | 0.786960i | \(0.288346\pi\) | ||||
−0.617004 | + | 0.786960i | \(0.711654\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | − 43.2513i | − 0.0978535i | ||||||||
\(443\) | 769.034 | 1.73597 | 0.867984 | − | 0.496592i | \(-0.165415\pi\) | ||||
0.867984 | + | 0.496592i | \(0.165415\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 392.722 | 0.882522 | ||||||||
\(446\) | 96.7459i | 0.216919i | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 302.030i | 0.674175i | ||||||||
\(449\) | 350.143 | 0.779827 | 0.389914 | − | 0.920851i | \(-0.372505\pi\) | ||||
0.389914 | + | 0.920851i | \(0.372505\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | −69.3543 | −0.153439 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −283.475 | −0.624395 | ||||||||
\(455\) | −148.609 | −0.326613 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 424.881i | 0.929719i | 0.885385 | + | 0.464859i | \(0.153895\pi\) | ||||
−0.885385 | + | 0.464859i | \(0.846105\pi\) | |||||||
\(458\) | − 597.697i | − 1.30501i | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −17.8873 | −0.0388854 | ||||||||
\(461\) | 134.512i | 0.291782i | 0.989301 | + | 0.145891i | \(0.0466049\pi\) | ||||
−0.989301 | + | 0.145891i | \(0.953395\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −186.040 | −0.401815 | −0.200908 | − | 0.979610i | \(-0.564389\pi\) | ||||
−0.200908 | + | 0.979610i | \(0.564389\pi\) | |||||||
\(464\) | 659.026i | 1.42031i | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 92.5968 | 0.198706 | ||||||||
\(467\) | 583.197 | 1.24882 | 0.624408 | − | 0.781099i | \(-0.285340\pi\) | ||||
0.624408 | + | 0.781099i | \(0.285340\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − 582.206i | − 1.24138i | ||||||||
\(470\) | − 574.561i | − 1.22247i | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 458.440i | 0.971271i | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − 649.359i | − 1.36707i | ||||||||
\(476\) | −25.4385 | −0.0534422 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −28.4007 | −0.0594158 | ||||||||
\(479\) | − 734.447i | − 1.53329i | −0.642070 | − | 0.766646i | \(-0.721924\pi\) | ||||
0.642070 | − | 0.766646i | \(-0.278076\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 203.024i | 0.422087i | ||||||||
\(482\) | −174.033 | −0.361065 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −240.705 | −0.496300 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 289.221 | 0.593882 | 0.296941 | − | 0.954896i | \(-0.404033\pi\) | ||||
0.296941 | + | 0.954896i | \(0.404033\pi\) | |||||||
\(488\) | −794.814 | −1.62872 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | − 203.692i | − 0.415699i | ||||||||
\(491\) | 535.540i | 1.09071i | 0.838204 | + | 0.545356i | \(0.183606\pi\) | ||||
−0.838204 | + | 0.545356i | \(0.816394\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 225.005 | 0.456400 | ||||||||
\(494\) | 135.076i | 0.273432i | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 60.0012 | 0.120970 | ||||||||
\(497\) | − 271.449i | − 0.546176i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 446.596 | 0.894982 | 0.447491 | − | 0.894289i | \(-0.352318\pi\) | ||||
0.447491 | + | 0.894289i | \(0.352318\pi\) | |||||||
\(500\) | 43.1995 | 0.0863989 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 674.131i | 1.34289i | ||||||||
\(503\) | − 701.708i | − 1.39505i | −0.716563 | − | 0.697523i | \(-0.754286\pi\) | ||||
0.716563 | − | 0.697523i | \(-0.245714\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − 642.641i | − 1.27256i | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 155.822i | 0.306736i | ||||||||
\(509\) | −169.290 | −0.332594 | −0.166297 | − | 0.986076i | \(-0.553181\pi\) | ||||
−0.166297 | + | 0.986076i | \(0.553181\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 383.174 | 0.749851 | ||||||||
\(512\) | − 329.793i | − 0.644127i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 53.5919i | 0.104264i | ||||||||
\(515\) | −585.400 | −1.13670 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 827.596 | 1.59768 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 176.449 | 0.339325 | ||||||||
\(521\) | −666.820 | −1.27989 | −0.639943 | − | 0.768423i | \(-0.721042\pi\) | ||||
−0.639943 | + | 0.768423i | \(0.721042\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 253.003i | − 0.483754i | −0.970307 | − | 0.241877i | \(-0.922237\pi\) | ||||
0.970307 | − | 0.241877i | \(-0.0777630\pi\) | |||||||
\(524\) | 157.962i | 0.301454i | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −409.507 | −0.778530 | ||||||||
\(527\) | − 20.4857i | − 0.0388722i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −516.952 | −0.977226 | ||||||||
\(530\) | 273.368i | 0.515789i | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 79.4455 | 0.149334 | ||||||||
\(533\) | 102.531 | 0.192365 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 981.366i | 1.83433i | ||||||||
\(536\) | 691.274i | 1.28969i | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 884.854i | 1.64471i | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 383.554i | 0.708971i | 0.935061 | + | 0.354486i | \(0.115344\pi\) | ||||
−0.935061 | + | 0.354486i | \(0.884656\pi\) | |||||||
\(542\) | −53.0184 | −0.0978199 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 66.5337 | 0.122305 | ||||||||
\(545\) | 1149.32i | 2.10885i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 376.753i | 0.688762i | 0.938830 | + | 0.344381i | \(0.111911\pi\) | ||||
−0.938830 | + | 0.344381i | \(0.888089\pi\) | |||||||
\(548\) | −97.9138 | −0.178675 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −702.702 | −1.27532 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −85.4116 | −0.154451 | ||||||||
\(554\) | 174.091 | 0.314244 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | − 13.8941i | − 0.0249894i | ||||||||
\(557\) | 810.940i | 1.45591i | 0.685627 | + | 0.727953i | \(0.259528\pi\) | ||||
−0.685627 | + | 0.727953i | \(0.740472\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −141.129 | −0.252466 | ||||||||
\(560\) | − 844.095i | − 1.50731i | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 125.967 | 0.224140 | ||||||||
\(563\) | 62.2529i | 0.110574i | 0.998471 | + | 0.0552868i | \(0.0176073\pi\) | ||||
−0.998471 | + | 0.0552868i | \(0.982393\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −785.713 | −1.39064 | ||||||||
\(566\) | 269.228 | 0.475668 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 322.302i | 0.567432i | ||||||||
\(569\) | − 128.524i | − 0.225878i | −0.993602 | − | 0.112939i | \(-0.963974\pi\) | ||||
0.993602 | − | 0.112939i | \(-0.0360264\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − 2.62521i | − 0.00459757i | −0.999997 | − | 0.00229879i | \(-0.999268\pi\) | ||||
0.999997 | − | 0.00229879i | \(-0.000731727\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | − 417.951i | − 0.728138i | ||||||||
\(575\) | −115.870 | −0.201513 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −641.965 | −1.11259 | −0.556296 | − | 0.830984i | \(-0.687778\pi\) | ||||
−0.556296 | + | 0.830984i | \(0.687778\pi\) | |||||||
\(578\) | 540.957i | 0.935911i | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | − 186.167i | − 0.320977i | ||||||||
\(581\) | 536.596 | 0.923573 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −454.956 | −0.779034 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 214.171 | 0.365479 | ||||||||
\(587\) | 570.395 | 0.971712 | 0.485856 | − | 0.874039i | \(-0.338508\pi\) | ||||
0.485856 | + | 0.874039i | \(0.338508\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 63.9777i | 0.108621i | ||||||||
\(590\) | − 1053.32i | − 1.78529i | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −1153.17 | −1.94792 | ||||||||
\(593\) | 57.8790i | 0.0976036i | 0.998808 | + | 0.0488018i | \(0.0155403\pi\) | ||||
−0.998808 | + | 0.0488018i | \(0.984460\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −288.192 | −0.484356 | ||||||||
\(596\) | − 54.3775i | − 0.0912375i | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 24.1026 | 0.0403054 | ||||||||
\(599\) | −288.442 | −0.481539 | −0.240769 | − | 0.970582i | \(-0.577400\pi\) | ||||
−0.240769 | + | 0.970582i | \(0.577400\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 666.067i | 1.10827i | 0.832428 | + | 0.554133i | \(0.186950\pi\) | ||||
−0.832428 | + | 0.554133i | \(0.813050\pi\) | |||||||
\(602\) | 575.290i | 0.955631i | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | − 101.463i | − 0.167985i | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 233.869i | 0.385286i | 0.981269 | + | 0.192643i | \(0.0617059\pi\) | ||||
−0.981269 | + | 0.192643i | \(0.938294\pi\) | |||||||
\(608\) | −207.788 | −0.341756 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 1826.18 | 2.99374 | ||||||||
\(611\) | 111.706i | 0.182825i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 447.324i | 0.729729i | 0.931061 | + | 0.364865i | \(0.118885\pi\) | ||||
−0.931061 | + | 0.364865i | \(0.881115\pi\) | |||||||
\(614\) | −724.941 | −1.18069 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 662.279 | 1.07339 | 0.536693 | − | 0.843778i | \(-0.319673\pi\) | ||||
0.536693 | + | 0.843778i | \(0.319673\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −1177.52 | −1.90229 | −0.951145 | − | 0.308746i | \(-0.900091\pi\) | ||||
−0.951145 | + | 0.308746i | \(0.900091\pi\) | |||||||
\(620\) | −16.9496 | −0.0273380 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | − 555.753i | − 0.893494i | ||||||||
\(623\) | 311.242i | 0.499586i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −345.162 | −0.552260 | ||||||||
\(626\) | 405.752i | 0.648165i | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 54.9625 | 0.0875199 | ||||||||
\(629\) | 393.716i | 0.625939i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 663.644 | 1.05173 | 0.525867 | − | 0.850567i | \(-0.323741\pi\) | ||||
0.525867 | + | 0.850567i | \(0.323741\pi\) | |||||||
\(632\) | 101.412 | 0.160462 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | − 702.434i | − 1.10794i | ||||||||
\(635\) | 1765.30i | 2.78001i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 39.6019i | 0.0621693i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 1150.44i | 1.79756i | ||||||||
\(641\) | −186.560 | −0.291045 | −0.145522 | − | 0.989355i | \(-0.546486\pi\) | ||||
−0.145522 | + | 0.989355i | \(0.546486\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −41.4284 | −0.0644298 | −0.0322149 | − | 0.999481i | \(-0.510256\pi\) | ||||
−0.0322149 | + | 0.999481i | \(0.510256\pi\) | |||||||
\(644\) | − 14.1761i | − 0.0220126i | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 261.947i | 0.405491i | ||||||||
\(647\) | 115.776 | 0.178943 | 0.0894716 | − | 0.995989i | \(-0.471482\pi\) | ||||
0.0894716 | + | 0.995989i | \(0.471482\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | −231.812 | −0.356634 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 15.5646 | 0.0238721 | ||||||||
\(653\) | −608.629 | −0.932050 | −0.466025 | − | 0.884772i | \(-0.654314\pi\) | ||||
−0.466025 | + | 0.884772i | \(0.654314\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1789.55i | 2.73213i | ||||||||
\(656\) | 582.371i | 0.887760i | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 455.353 | 0.692026 | ||||||||
\(659\) | 725.000i | 1.10015i | 0.835114 | + | 0.550076i | \(0.185401\pi\) | ||||
−0.835114 | + | 0.550076i | \(0.814599\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −781.088 | −1.18168 | −0.590838 | − | 0.806790i | \(-0.701203\pi\) | ||||
−0.590838 | + | 0.806790i | \(0.701203\pi\) | |||||||
\(662\) | 1295.59i | 1.95708i | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −637.120 | −0.959518 | ||||||||
\(665\) | 900.036 | 1.35344 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 125.389i | 0.187989i | ||||||||
\(668\) | 197.235i | 0.295262i | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | − 1588.29i | − 2.37058i | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − 967.686i | − 1.43787i | −0.695078 | − | 0.718934i | \(-0.744630\pi\) | ||||
0.695078 | − | 0.718934i | \(-0.255370\pi\) | |||||||
\(674\) | 1038.55 | 1.54087 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −107.025 | −0.158321 | ||||||||
\(677\) | 970.132i | 1.43299i | 0.697594 | + | 0.716494i | \(0.254254\pi\) | ||||
−0.697594 | + | 0.716494i | \(0.745746\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − 190.765i | − 0.280950i | ||||||||
\(680\) | 342.181 | 0.503207 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −1104.74 | −1.61749 | −0.808745 | − | 0.588160i | \(-0.799852\pi\) | ||||
−0.808745 | + | 0.588160i | \(0.799852\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −1109.26 | −1.61936 | ||||||||
\(686\) | 802.960 | 1.17050 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | − 801.606i | − 1.16513i | ||||||||
\(689\) | − 53.1482i | − 0.0771382i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 853.354 | 1.23496 | 0.617478 | − | 0.786588i | \(-0.288155\pi\) | ||||
0.617478 | + | 0.786588i | \(0.288155\pi\) | |||||||
\(692\) | − 143.180i | − 0.206907i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −45.7237 | −0.0658842 | ||||||||
\(695\) | − 157.406i | − 0.226484i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 198.834 | 0.285271 | ||||||||
\(698\) | 781.901 | 1.12020 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 136.341i | 0.194774i | ||||||||
\(701\) | − 874.615i | − 1.24767i | −0.781557 | − | 0.623834i | \(-0.785574\pi\) | ||||
0.781557 | − | 0.623834i | \(-0.214426\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − 1229.59i | − 1.74906i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | − 303.656i | − 0.430108i | ||||||||
\(707\) | 509.309 | 0.720380 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 150.786 | 0.212674 | 0.106337 | − | 0.994330i | \(-0.466088\pi\) | ||||
0.106337 | + | 0.994330i | \(0.466088\pi\) | |||||||
\(710\) | − 740.528i | − 1.04300i | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | − 369.549i | − 0.519030i | ||||||||
\(713\) | 11.4160 | 0.0160113 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 35.6489 | 0.0497890 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 936.338 | 1.30409 | ||||||||
\(719\) | 731.799 | 1.01780 | 0.508900 | − | 0.860825i | \(-0.330052\pi\) | ||||
0.508900 | + | 0.860825i | \(0.330052\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − 463.944i | − 0.643473i | ||||||||
\(722\) | − 37.5726i | − 0.0520396i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 17.7267 | 0.0244844 | ||||||||
\(725\) | − 1205.95i | − 1.66338i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −827.657 | −1.13845 | −0.569227 | − | 0.822180i | \(-0.692758\pi\) | ||||
−0.569227 | + | 0.822180i | \(0.692758\pi\) | |||||||
\(728\) | 139.840i | 0.192088i | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 1045.32 | 1.43194 | ||||||||
\(731\) | −273.685 | −0.374398 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − 76.3293i | − 0.104133i | −0.998644 | − | 0.0520664i | \(-0.983419\pi\) | ||||
0.998644 | − | 0.0520664i | \(-0.0165807\pi\) | |||||||
\(734\) | 47.7450i | 0.0650477i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 37.0772i | 0.0503767i | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1358.96i | 1.83892i | 0.393188 | + | 0.919458i | \(0.371372\pi\) | ||||
−0.393188 | + | 0.919458i | \(0.628628\pi\) | |||||||
\(740\) | 325.756 | 0.440210 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −216.651 | −0.291982 | ||||||||
\(743\) | − 389.840i | − 0.524684i | −0.964975 | − | 0.262342i | \(-0.915505\pi\) | ||||
0.964975 | − | 0.262342i | \(-0.0844948\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − 616.042i | − 0.826902i | ||||||||
\(746\) | 1049.51 | 1.40685 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −777.756 | −1.03839 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1254.95 | 1.67103 | 0.835517 | − | 0.549464i | \(-0.185168\pi\) | ||||
0.835517 | + | 0.549464i | \(0.185168\pi\) | |||||||
\(752\) | −634.487 | −0.843733 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 250.854i | 0.332698i | ||||||||
\(755\) | − 1149.47i | − 1.52248i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 298.722 | 0.394613 | 0.197307 | − | 0.980342i | \(-0.436781\pi\) | ||||
0.197307 | + | 0.980342i | \(0.436781\pi\) | |||||||
\(758\) | − 1536.38i | − 2.02689i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −1068.65 | −1.40611 | ||||||||
\(761\) | 575.246i | 0.755908i | 0.925824 | + | 0.377954i | \(0.123372\pi\) | ||||
−0.925824 | + | 0.377954i | \(0.876628\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −910.865 | −1.19379 | ||||||||
\(764\) | −77.6608 | −0.101650 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | − 151.712i | − 0.198057i | ||||||||
\(767\) | 204.787i | 0.266997i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 746.975i | 0.971359i | 0.874137 | + | 0.485680i | \(0.161428\pi\) | ||||
−0.874137 | + | 0.485680i | \(0.838572\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 26.0788i | 0.0337808i | ||||||||
\(773\) | −4.05557 | −0.00524654 | −0.00262327 | − | 0.999997i | \(-0.500835\pi\) | ||||
−0.00262327 | + | 0.999997i | \(0.500835\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −109.796 | −0.141672 | ||||||||
\(776\) | 226.502i | 0.291884i | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 1088.17i | 1.39868i | ||||||||
\(779\) | −620.967 | −0.797133 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 46.7413 | 0.0597714 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −224.937 | −0.286910 | ||||||||
\(785\) | 622.668 | 0.793208 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 59.5811i | 0.0757066i | 0.999283 | + | 0.0378533i | \(0.0120520\pi\) | ||||
−0.999283 | + | 0.0378533i | \(0.987948\pi\) | |||||||
\(788\) | − 2.30944i | − 0.00293076i | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −233.007 | −0.294946 | ||||||||
\(791\) | − 622.697i | − 0.787227i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −355.047 | −0.447726 | ||||||||
\(794\) | − 312.759i | − 0.393903i | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 123.478 | 0.155124 | ||||||||
\(797\) | 187.364 | 0.235086 | 0.117543 | − | 0.993068i | \(-0.462498\pi\) | ||||
0.117543 | + | 0.993068i | \(0.462498\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 216.627i | 0.271123i | ||||||||
\(800\) | − 356.598i | − 0.445747i | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | − 1293.15i | − 1.61241i | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − 160.601i | − 0.199504i | ||||||||
\(806\) | 22.8391 | 0.0283364 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −604.721 | −0.748417 | ||||||||
\(809\) | 1451.43i | 1.79411i | 0.441923 | + | 0.897053i | \(0.354297\pi\) | ||||
−0.441923 | + | 0.897053i | \(0.645703\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1043.47i | 1.28665i | 0.765594 | + | 0.643324i | \(0.222445\pi\) | ||||
−0.765594 | + | 0.643324i | \(0.777555\pi\) | |||||||
\(812\) | 147.541 | 0.181701 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 176.331 | 0.216357 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 854.731 | 1.04618 | ||||||||
\(818\) | −452.058 | −0.552638 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | − 164.512i | − 0.200625i | ||||||||
\(821\) | 165.085i | 0.201078i | 0.994933 | + | 0.100539i | \(0.0320568\pi\) | ||||
−0.994933 | + | 0.100539i | \(0.967943\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −118.929 | −0.144507 | −0.0722535 | − | 0.997386i | \(-0.523019\pi\) | ||||
−0.0722535 | + | 0.997386i | \(0.523019\pi\) | |||||||
\(824\) | 550.857i | 0.668516i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 834.784 | 1.01063 | ||||||||
\(827\) | 1445.00i | 1.74728i | 0.486569 | + | 0.873642i | \(0.338248\pi\) | ||||
−0.486569 | + | 0.873642i | \(0.661752\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −504.206 | −0.608210 | −0.304105 | − | 0.952639i | \(-0.598357\pi\) | ||||
−0.304105 | + | 0.952639i | \(0.598357\pi\) | |||||||
\(830\) | 1463.86 | 1.76369 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | − 160.193i | − 0.192540i | ||||||||
\(833\) | 76.7983i | 0.0921949i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 2234.47i | 2.67601i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 368.216i | 0.439399i | ||||||||
\(839\) | −396.145 | −0.472164 | −0.236082 | − | 0.971733i | \(-0.575863\pi\) | ||||
−0.236082 | + | 0.971733i | \(0.575863\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −464.016 | −0.551743 | ||||||||
\(842\) | 652.647i | 0.775115i | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 183.317i | 0.217200i | ||||||||
\(845\) | −1212.48 | −1.43489 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 301.880 | 0.355991 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −449.544 | −0.528875 | ||||||||
\(851\) | −219.406 | −0.257821 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 56.0848i | 0.0657500i | 0.999459 | + | 0.0328750i | \(0.0104663\pi\) | ||||
−0.999459 | + | 0.0328750i | \(0.989534\pi\) | |||||||
\(854\) | 1447.29i | 1.69472i | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 923.458 | 1.07881 | ||||||||
\(857\) | 108.138i | 0.126182i | 0.998008 | + | 0.0630911i | \(0.0200959\pi\) | ||||
−0.998008 | + | 0.0630911i | \(0.979904\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 910.177 | 1.05958 | 0.529789 | − | 0.848130i | \(-0.322271\pi\) | ||||
0.529789 | + | 0.848130i | \(0.322271\pi\) | |||||||
\(860\) | 226.444i | 0.263307i | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 901.314 | 1.04561 | ||||||||
\(863\) | −979.204 | −1.13465 | −0.567326 | − | 0.823494i | \(-0.692022\pi\) | ||||
−0.567326 | + | 0.823494i | \(0.692022\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | − 1622.08i | − 1.87524i | ||||||||
\(866\) | − 642.074i | − 0.741425i | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | − 13.4330i | − 0.0154758i | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 308.795i | 0.354529i | ||||||||
\(872\) | 1081.50 | 1.24026 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −145.975 | −0.167020 | ||||||||
\(875\) | 387.866i | 0.443275i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − 544.429i | − 0.620785i | −0.950608 | − | 0.310393i | \(-0.899539\pi\) | ||||
0.950608 | − | 0.310393i | \(-0.100461\pi\) | |||||||
\(878\) | −1493.87 | −1.70145 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1232.58 | 1.39907 | 0.699534 | − | 0.714600i | \(-0.253391\pi\) | ||||
0.699534 | + | 0.714600i | \(0.253391\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 762.570 | 0.863613 | 0.431807 | − | 0.901966i | \(-0.357876\pi\) | ||||
0.431807 | + | 0.901966i | \(0.357876\pi\) | |||||||
\(884\) | 13.4923 | 0.0152627 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 1662.69i | 1.87662i | ||||||||
\(887\) | − 361.349i | − 0.407384i | −0.979035 | − | 0.203692i | \(-0.934706\pi\) | ||||
0.979035 | − | 0.203692i | \(-0.0652940\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1399.05 | −1.57373 | ||||||||
\(890\) | 849.085i | 0.954028i | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −30.1800 | −0.0338340 | ||||||||
\(893\) | − 676.537i | − 0.757600i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 403.866 | 0.451247 | ||||||||
\(896\) | −911.749 | −1.01758 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 757.025i | 0.843012i | ||||||||
\(899\) | 118.816i | 0.132164i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − 103.068i | − 0.114393i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 739.351i | 0.817866i | ||||||||
\(905\) | 200.825 | 0.221906 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1330.09 | 1.46647 | 0.733234 | − | 0.679976i | \(-0.238010\pi\) | ||||
0.733234 | + | 0.679976i | \(0.238010\pi\) | |||||||
\(908\) | − 88.4304i | − 0.0973903i | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | − 321.300i | − 0.353077i | ||||||||
\(911\) | 0.221374 | 0.000243001 0 | 0.000121501 | − | 1.00000i | \(-0.499961\pi\) | ||||
0.000121501 | 1.00000i | \(0.499961\pi\) | ||||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | −918.614 | −1.00505 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 186.452 | 0.203550 | ||||||||
\(917\) | −1418.26 | −1.54663 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 443.268i | 0.482338i | 0.970483 | + | 0.241169i | \(0.0775307\pi\) | ||||
−0.970483 | + | 0.241169i | \(0.922469\pi\) | |||||||
\(920\) | 190.687i | 0.207268i | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −290.821 | −0.315424 | ||||||||
\(923\) | 143.974i | 0.155984i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2110.18 | 2.28128 | ||||||||
\(926\) | − 402.229i | − 0.434372i | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −385.891 | −0.415831 | ||||||||
\(929\) | −288.120 | −0.310140 | −0.155070 | − | 0.987904i | \(-0.549560\pi\) | ||||
−0.155070 | + | 0.987904i | \(0.549560\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − 239.845i | − 0.257621i | ||||||||
\(932\) | 28.8856i | 0.0309932i | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 1260.90i | 1.35000i | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − 1462.84i | − 1.56120i | −0.625033 | − | 0.780599i | \(-0.714914\pi\) | ||||
0.625033 | − | 0.780599i | \(-0.285086\pi\) | |||||||
\(938\) | 1258.76 | 1.34196 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 179.235 | 0.190675 | ||||||||
\(941\) | − 1069.21i | − 1.13624i | −0.822944 | − | 0.568122i | \(-0.807670\pi\) | ||||
0.822944 | − | 0.568122i | \(-0.192330\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 110.804i | 0.117502i | ||||||||
\(944\) | −1163.18 | −1.23219 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −356.893 | −0.376867 | −0.188433 | − | 0.982086i | \(-0.560341\pi\) | ||||
−0.188433 | + | 0.982086i | \(0.560341\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −203.231 | −0.214153 | ||||||||
\(950\) | 1403.95 | 1.47784 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 271.186i | 0.284860i | ||||||||
\(953\) | − 1072.25i | − 1.12513i | −0.826753 | − | 0.562565i | \(-0.809815\pi\) | ||||
0.826753 | − | 0.562565i | \(-0.190185\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −879.817 | −0.921275 | ||||||||
\(956\) | − 8.85963i | − 0.00926740i | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 1587.91 | 1.65753 | ||||||||
\(959\) | − 879.118i | − 0.916703i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −950.182 | −0.988743 | ||||||||
\(962\) | −438.947 | −0.456286 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | − 54.2898i | − 0.0563172i | ||||||||
\(965\) | 295.446i | 0.306161i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 273.281i | 0.282607i | 0.989966 | + | 0.141303i | \(0.0451293\pi\) | ||||
−0.989966 | + | 0.141303i | \(0.954871\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | − 520.417i | − 0.536512i | ||||||||
\(971\) | 644.921 | 0.664182 | 0.332091 | − | 0.943247i | \(-0.392246\pi\) | ||||
0.332091 | + | 0.943247i | \(0.392246\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 124.748 | 0.128210 | ||||||||
\(974\) | 625.309i | 0.642001i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | − 2016.65i | − 2.06624i | ||||||||
\(977\) | 1637.62 | 1.67617 | 0.838086 | − | 0.545539i | \(-0.183675\pi\) | ||||
0.838086 | + | 0.545539i | \(0.183675\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 63.5420 | 0.0648388 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −1157.86 | −1.17909 | ||||||||
\(983\) | 913.097 | 0.928888 | 0.464444 | − | 0.885602i | \(-0.346254\pi\) | ||||
0.464444 | + | 0.885602i | \(0.346254\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − 26.1636i | − 0.0265620i | ||||||||
\(986\) | 486.472i | 0.493379i | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −42.1370 | −0.0426487 | ||||||||
\(989\) | − 152.516i | − 0.154213i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1447.57 | −1.46072 | −0.730360 | − | 0.683062i | \(-0.760648\pi\) | ||||
−0.730360 | + | 0.683062i | \(0.760648\pi\) | |||||||
\(992\) | 35.1336i | 0.0354169i | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 586.887 | 0.590429 | ||||||||
\(995\) | 1398.88 | 1.40591 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 909.292i | 0.912028i | 0.889973 | + | 0.456014i | \(0.150723\pi\) | ||||
−0.889973 | + | 0.456014i | \(0.849277\pi\) | |||||||
\(998\) | 965.562i | 0.967497i | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1089.3.c.k.604.6 | 8 | ||
3.2 | odd | 2 | 121.3.b.c.120.3 | ✓ | 8 | ||
11.10 | odd | 2 | inner | 1089.3.c.k.604.3 | 8 | ||
33.2 | even | 10 | 121.3.d.f.40.6 | 32 | |||
33.5 | odd | 10 | 121.3.d.f.118.6 | 32 | |||
33.8 | even | 10 | 121.3.d.f.112.6 | 32 | |||
33.14 | odd | 10 | 121.3.d.f.112.3 | 32 | |||
33.17 | even | 10 | 121.3.d.f.118.3 | 32 | |||
33.20 | odd | 10 | 121.3.d.f.40.3 | 32 | |||
33.26 | odd | 10 | 121.3.d.f.94.6 | 32 | |||
33.29 | even | 10 | 121.3.d.f.94.3 | 32 | |||
33.32 | even | 2 | 121.3.b.c.120.6 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
121.3.b.c.120.3 | ✓ | 8 | 3.2 | odd | 2 | ||
121.3.b.c.120.6 | yes | 8 | 33.32 | even | 2 | ||
121.3.d.f.40.3 | 32 | 33.20 | odd | 10 | |||
121.3.d.f.40.6 | 32 | 33.2 | even | 10 | |||
121.3.d.f.94.3 | 32 | 33.29 | even | 10 | |||
121.3.d.f.94.6 | 32 | 33.26 | odd | 10 | |||
121.3.d.f.112.3 | 32 | 33.14 | odd | 10 | |||
121.3.d.f.112.6 | 32 | 33.8 | even | 10 | |||
121.3.d.f.118.3 | 32 | 33.17 | even | 10 | |||
121.3.d.f.118.6 | 32 | 33.5 | odd | 10 | |||
1089.3.c.k.604.3 | 8 | 11.10 | odd | 2 | inner | ||
1089.3.c.k.604.6 | 8 | 1.1 | even | 1 | trivial |