Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [690,2,Mod(551,690)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(690, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("690.551");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 690.e (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: | \(5.50967773947\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 2 x^{15} + 3 x^{14} - 12 x^{13} + 15 x^{12} - 4 x^{11} + 45 x^{10} - 66 x^{9} - 32 x^{8} + \cdots + 6561 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 551.11 | ||
Root | \(1.53677 - 0.798958i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 690.551 |
Dual form | 690.2.e.a.551.3 |
$q$-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 \(\left(\mathbb{Z}/690\mathbb{Z}\right)^\times\).
\(n\) | \(277\) | \(461\) | \(511\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000i | 0.707107i | ||||||||
\(3\) | −0.798958 | − | 1.53677i | −0.461279 | − | 0.887255i | ||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 1.53677 | − | 0.798958i | 0.627384 | − | 0.326173i | ||||
\(7\) | 0.145234i | 0.0548933i | 0.999623 | + | 0.0274466i | \(0.00873763\pi\) | ||||
−0.999623 | + | 0.0274466i | \(0.991262\pi\) | |||||||
\(8\) | − | 1.00000i | − | 0.353553i | ||||||
\(9\) | −1.72333 | + | 2.45563i | −0.574444 | + | 0.818544i | ||||
\(10\) | − | 1.00000i | − | 0.316228i | ||||||
\(11\) | −3.35877 | −1.01271 | −0.506354 | − | 0.862326i | \(-0.669007\pi\) | ||||
−0.506354 | + | 0.862326i | \(0.669007\pi\) | |||||||
\(12\) | 0.798958 | + | 1.53677i | 0.230639 | + | 0.443628i | ||||
\(13\) | 2.96087 | 0.821199 | 0.410599 | − | 0.911816i | \(-0.365320\pi\) | ||||
0.410599 | + | 0.911816i | \(0.365320\pi\) | |||||||
\(14\) | −0.145234 | −0.0388154 | ||||||||
\(15\) | 0.798958 | + | 1.53677i | 0.206290 | + | 0.396793i | ||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 5.54307 | 1.34439 | 0.672196 | − | 0.740373i | \(-0.265351\pi\) | ||||
0.672196 | + | 0.740373i | \(0.265351\pi\) | |||||||
\(18\) | −2.45563 | − | 1.72333i | −0.578798 | − | 0.406193i | ||||
\(19\) | 6.91126i | 1.58555i | 0.609513 | + | 0.792776i | \(0.291365\pi\) | ||||
−0.609513 | + | 0.792776i | \(0.708635\pi\) | |||||||
\(20\) | 1.00000 | 0.223607 | ||||||||
\(21\) | 0.223191 | − | 0.116036i | 0.0487043 | − | 0.0253211i | ||||
\(22\) | − | 3.35877i | − | 0.716093i | ||||||
\(23\) | −3.26171 | + | 3.51586i | −0.680113 | + | 0.733107i | ||||
\(24\) | −1.53677 | + | 0.798958i | −0.313692 | + | 0.163087i | ||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 2.96087i | 0.580675i | ||||||||
\(27\) | 5.15061 | + | 0.686420i | 0.991236 | + | 0.132102i | ||||
\(28\) | − | 0.145234i | − | 0.0274466i | ||||||
\(29\) | − | 3.58666i | − | 0.666026i | −0.942922 | − | 0.333013i | \(-0.891935\pi\) | ||
0.942922 | − | 0.333013i | \(-0.108065\pi\) | |||||||
\(30\) | −1.53677 | + | 0.798958i | −0.280575 | + | 0.145869i | ||||
\(31\) | 10.6138 | 1.90629 | 0.953147 | − | 0.302506i | \(-0.0978233\pi\) | ||||
0.953147 | + | 0.302506i | \(0.0978233\pi\) | |||||||
\(32\) | 1.00000i | 0.176777i | ||||||||
\(33\) | 2.68352 | + | 5.16167i | 0.467141 | + | 0.898531i | ||||
\(34\) | 5.54307i | 0.950628i | ||||||||
\(35\) | − | 0.145234i | − | 0.0245490i | ||||||
\(36\) | 1.72333 | − | 2.45563i | 0.287222 | − | 0.409272i | ||||
\(37\) | 6.04149i | 0.993214i | 0.867975 | + | 0.496607i | \(0.165421\pi\) | ||||
−0.867975 | + | 0.496607i | \(0.834579\pi\) | |||||||
\(38\) | −6.91126 | −1.12115 | ||||||||
\(39\) | −2.36561 | − | 4.55019i | −0.378801 | − | 0.728613i | ||||
\(40\) | 1.00000i | 0.158114i | ||||||||
\(41\) | − | 8.84450i | − | 1.38128i | −0.723199 | − | 0.690639i | \(-0.757329\pi\) | ||
0.723199 | − | 0.690639i | \(-0.242671\pi\) | |||||||
\(42\) | 0.116036 | + | 0.223191i | 0.0179047 | + | 0.0344392i | ||||
\(43\) | 8.40616i | 1.28193i | 0.767571 | + | 0.640964i | \(0.221465\pi\) | ||||
−0.767571 | + | 0.640964i | \(0.778535\pi\) | |||||||
\(44\) | 3.35877 | 0.506354 | ||||||||
\(45\) | 1.72333 | − | 2.45563i | 0.256899 | − | 0.366064i | ||||
\(46\) | −3.51586 | − | 3.26171i | −0.518385 | − | 0.480912i | ||||
\(47\) | 9.98664i | 1.45670i | 0.685205 | + | 0.728351i | \(0.259713\pi\) | ||||
−0.685205 | + | 0.728351i | \(0.740287\pi\) | |||||||
\(48\) | −0.798958 | − | 1.53677i | −0.115320 | − | 0.221814i | ||||
\(49\) | 6.97891 | 0.996987 | ||||||||
\(50\) | 1.00000i | 0.141421i | ||||||||
\(51\) | −4.42868 | − | 8.51843i | −0.620139 | − | 1.19282i | ||||
\(52\) | −2.96087 | −0.410599 | ||||||||
\(53\) | −3.83589 | −0.526900 | −0.263450 | − | 0.964673i | \(-0.584860\pi\) | ||||
−0.263450 | + | 0.964673i | \(0.584860\pi\) | |||||||
\(54\) | −0.686420 | + | 5.15061i | −0.0934099 | + | 0.700910i | ||||
\(55\) | 3.35877 | 0.452897 | ||||||||
\(56\) | 0.145234 | 0.0194077 | ||||||||
\(57\) | 10.6210 | − | 5.52181i | 1.40679 | − | 0.731382i | ||||
\(58\) | 3.58666 | 0.470952 | ||||||||
\(59\) | 7.91338i | 1.03023i | 0.857120 | + | 0.515117i | \(0.172252\pi\) | ||||
−0.857120 | + | 0.515117i | \(0.827748\pi\) | |||||||
\(60\) | −0.798958 | − | 1.53677i | −0.103145 | − | 0.198396i | ||||
\(61\) | 4.14107i | 0.530209i | 0.964220 | + | 0.265105i | \(0.0854065\pi\) | ||||
−0.964220 | + | 0.265105i | \(0.914594\pi\) | |||||||
\(62\) | 10.6138i | 1.34795i | ||||||||
\(63\) | −0.356641 | − | 0.250286i | −0.0449325 | − | 0.0315331i | ||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | −2.96087 | −0.367251 | ||||||||
\(66\) | −5.16167 | + | 2.68352i | −0.635357 | + | 0.330318i | ||||
\(67\) | 13.0680i | 1.59651i | 0.602322 | + | 0.798253i | \(0.294242\pi\) | ||||
−0.602322 | + | 0.798253i | \(0.705758\pi\) | |||||||
\(68\) | −5.54307 | −0.672196 | ||||||||
\(69\) | 8.00904 | + | 2.20347i | 0.964175 | + | 0.265267i | ||||
\(70\) | 0.145234 | 0.0173588 | ||||||||
\(71\) | 1.26558i | 0.150196i | 0.997176 | + | 0.0750981i | \(0.0239270\pi\) | ||||
−0.997176 | + | 0.0750981i | \(0.976073\pi\) | |||||||
\(72\) | 2.45563 | + | 1.72333i | 0.289399 | + | 0.203097i | ||||
\(73\) | −9.24658 | −1.08223 | −0.541115 | − | 0.840948i | \(-0.681998\pi\) | ||||
−0.541115 | + | 0.840948i | \(0.681998\pi\) | |||||||
\(74\) | −6.04149 | −0.702309 | ||||||||
\(75\) | −0.798958 | − | 1.53677i | −0.0922557 | − | 0.177451i | ||||
\(76\) | − | 6.91126i | − | 0.792776i | ||||||
\(77\) | − | 0.487808i | − | 0.0555909i | ||||||
\(78\) | 4.55019 | − | 2.36561i | 0.515207 | − | 0.267853i | ||||
\(79\) | − | 13.2148i | − | 1.48678i | −0.668857 | − | 0.743391i | \(-0.733216\pi\) | ||
0.668857 | − | 0.743391i | \(-0.266784\pi\) | |||||||
\(80\) | −1.00000 | −0.111803 | ||||||||
\(81\) | −3.06025 | − | 8.46374i | −0.340028 | − | 0.940415i | ||||
\(82\) | 8.84450 | 0.976711 | ||||||||
\(83\) | 9.71029 | 1.06584 | 0.532921 | − | 0.846165i | \(-0.321094\pi\) | ||||
0.532921 | + | 0.846165i | \(0.321094\pi\) | |||||||
\(84\) | −0.223191 | + | 0.116036i | −0.0243522 | + | 0.0126605i | ||||
\(85\) | −5.54307 | −0.601230 | ||||||||
\(86\) | −8.40616 | −0.906460 | ||||||||
\(87\) | −5.51188 | + | 2.86559i | −0.590935 | + | 0.307224i | ||||
\(88\) | 3.35877i | 0.358046i | ||||||||
\(89\) | −15.3774 | −1.63000 | −0.815001 | − | 0.579459i | \(-0.803264\pi\) | ||||
−0.815001 | + | 0.579459i | \(0.803264\pi\) | |||||||
\(90\) | 2.45563 | + | 1.72333i | 0.258846 | + | 0.181655i | ||||
\(91\) | 0.430019i | 0.0450783i | ||||||||
\(92\) | 3.26171 | − | 3.51586i | 0.340056 | − | 0.366554i | ||||
\(93\) | −8.47998 | − | 16.3110i | −0.879333 | − | 1.69137i | ||||
\(94\) | −9.98664 | −1.03004 | ||||||||
\(95\) | − | 6.91126i | − | 0.709081i | ||||||
\(96\) | 1.53677 | − | 0.798958i | 0.156846 | − | 0.0815433i | ||||
\(97\) | − | 11.6097i | − | 1.17879i | −0.807845 | − | 0.589395i | \(-0.799366\pi\) | ||
0.807845 | − | 0.589395i | \(-0.200634\pi\) | |||||||
\(98\) | 6.97891i | 0.704976i | ||||||||
\(99\) | 5.78828 | − | 8.24791i | 0.581744 | − | 0.828946i | ||||
\(100\) | −1.00000 | −0.100000 | ||||||||
\(101\) | 5.20471i | 0.517888i | 0.965892 | + | 0.258944i | \(0.0833745\pi\) | ||||
−0.965892 | + | 0.258944i | \(0.916625\pi\) | |||||||
\(102\) | 8.51843 | − | 4.42868i | 0.843450 | − | 0.438505i | ||||
\(103\) | − | 8.68617i | − | 0.855874i | −0.903809 | − | 0.427937i | \(-0.859241\pi\) | ||
0.903809 | − | 0.427937i | \(-0.140759\pi\) | |||||||
\(104\) | − | 2.96087i | − | 0.290338i | ||||||
\(105\) | −0.223191 | + | 0.116036i | −0.0217812 | + | 0.0113239i | ||||
\(106\) | − | 3.83589i | − | 0.372574i | ||||||
\(107\) | −11.1465 | −1.07757 | −0.538785 | − | 0.842443i | \(-0.681116\pi\) | ||||
−0.538785 | + | 0.842443i | \(0.681116\pi\) | |||||||
\(108\) | −5.15061 | − | 0.686420i | −0.495618 | − | 0.0660508i | ||||
\(109\) | − | 7.19631i | − | 0.689282i | −0.938735 | − | 0.344641i | \(-0.888001\pi\) | ||
0.938735 | − | 0.344641i | \(-0.111999\pi\) | |||||||
\(110\) | 3.35877i | 0.320246i | ||||||||
\(111\) | 9.28438 | − | 4.82690i | 0.881235 | − | 0.458149i | ||||
\(112\) | 0.145234i | 0.0137233i | ||||||||
\(113\) | 13.1580 | 1.23780 | 0.618902 | − | 0.785468i | \(-0.287578\pi\) | ||||
0.618902 | + | 0.785468i | \(0.287578\pi\) | |||||||
\(114\) | 5.52181 | + | 10.6210i | 0.517165 | + | 0.994751i | ||||
\(115\) | 3.26171 | − | 3.51586i | 0.304156 | − | 0.327856i | ||||
\(116\) | 3.58666i | 0.333013i | ||||||||
\(117\) | −5.10257 | + | 7.27082i | −0.471733 | + | 0.672187i | ||||
\(118\) | −7.91338 | −0.728486 | ||||||||
\(119\) | 0.805042i | 0.0737980i | ||||||||
\(120\) | 1.53677 | − | 0.798958i | 0.140287 | − | 0.0729346i | ||||
\(121\) | 0.281357 | 0.0255779 | ||||||||
\(122\) | −4.14107 | −0.374915 | ||||||||
\(123\) | −13.5920 | + | 7.06638i | −1.22555 | + | 0.637154i | ||||
\(124\) | −10.6138 | −0.953147 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0.250286 | − | 0.356641i | 0.0222973 | − | 0.0317721i | ||||
\(127\) | −13.8601 | −1.22989 | −0.614943 | − | 0.788572i | \(-0.710821\pi\) | ||||
−0.614943 | + | 0.788572i | \(0.710821\pi\) | |||||||
\(128\) | − | 1.00000i | − | 0.0883883i | ||||||
\(129\) | 12.9184 | − | 6.71617i | 1.13740 | − | 0.591326i | ||||
\(130\) | − | 2.96087i | − | 0.259686i | ||||||
\(131\) | − | 3.17761i | − | 0.277629i | −0.990318 | − | 0.138815i | \(-0.955671\pi\) | ||
0.990318 | − | 0.138815i | \(-0.0443292\pi\) | |||||||
\(132\) | −2.68352 | − | 5.16167i | −0.233570 | − | 0.449265i | ||||
\(133\) | −1.00375 | −0.0870362 | ||||||||
\(134\) | −13.0680 | −1.12890 | ||||||||
\(135\) | −5.15061 | − | 0.686420i | −0.443294 | − | 0.0590776i | ||||
\(136\) | − | 5.54307i | − | 0.475314i | ||||||
\(137\) | 19.0473 | 1.62732 | 0.813661 | − | 0.581340i | \(-0.197471\pi\) | ||||
0.813661 | + | 0.581340i | \(0.197471\pi\) | |||||||
\(138\) | −2.20347 | + | 8.00904i | −0.187572 | + | 0.681775i | ||||
\(139\) | 10.1337 | 0.859531 | 0.429766 | − | 0.902940i | \(-0.358596\pi\) | ||||
0.429766 | + | 0.902940i | \(0.358596\pi\) | |||||||
\(140\) | 0.145234i | 0.0122745i | ||||||||
\(141\) | 15.3472 | − | 7.97891i | 1.29247 | − | 0.671945i | ||||
\(142\) | −1.26558 | −0.106205 | ||||||||
\(143\) | −9.94490 | −0.831635 | ||||||||
\(144\) | −1.72333 | + | 2.45563i | −0.143611 | + | 0.204636i | ||||
\(145\) | 3.58666i | 0.297856i | ||||||||
\(146\) | − | 9.24658i | − | 0.765253i | ||||||
\(147\) | −5.57585 | − | 10.7250i | −0.459889 | − | 0.884582i | ||||
\(148\) | − | 6.04149i | − | 0.496607i | ||||||
\(149\) | 19.7755 | 1.62008 | 0.810038 | − | 0.586378i | \(-0.199447\pi\) | ||||
0.810038 | + | 0.586378i | \(0.199447\pi\) | |||||||
\(150\) | 1.53677 | − | 0.798958i | 0.125477 | − | 0.0652347i | ||||
\(151\) | −9.13517 | −0.743409 | −0.371705 | − | 0.928351i | \(-0.621227\pi\) | ||||
−0.371705 | + | 0.928351i | \(0.621227\pi\) | |||||||
\(152\) | 6.91126 | 0.560577 | ||||||||
\(153\) | −9.55255 | + | 13.6117i | −0.772278 | + | 1.10044i | ||||
\(154\) | 0.487808 | 0.0393087 | ||||||||
\(155\) | −10.6138 | −0.852521 | ||||||||
\(156\) | 2.36561 | + | 4.55019i | 0.189401 | + | 0.364306i | ||||
\(157\) | 10.3178i | 0.823451i | 0.911308 | + | 0.411726i | \(0.135074\pi\) | ||||
−0.911308 | + | 0.411726i | \(0.864926\pi\) | |||||||
\(158\) | 13.2148 | 1.05131 | ||||||||
\(159\) | 3.06471 | + | 5.89488i | 0.243048 | + | 0.467494i | ||||
\(160\) | − | 1.00000i | − | 0.0790569i | ||||||
\(161\) | −0.510622 | − | 0.473711i | −0.0402427 | − | 0.0373336i | ||||
\(162\) | 8.46374 | − | 3.06025i | 0.664974 | − | 0.240436i | ||||
\(163\) | 11.8046 | 0.924607 | 0.462303 | − | 0.886722i | \(-0.347023\pi\) | ||||
0.462303 | + | 0.886722i | \(0.347023\pi\) | |||||||
\(164\) | 8.84450i | 0.690639i | ||||||||
\(165\) | −2.68352 | − | 5.16167i | −0.208912 | − | 0.401835i | ||||
\(166\) | 9.71029i | 0.753664i | ||||||||
\(167\) | 11.8429i | 0.916428i | 0.888842 | + | 0.458214i | \(0.151511\pi\) | ||||
−0.888842 | + | 0.458214i | \(0.848489\pi\) | |||||||
\(168\) | −0.116036 | − | 0.223191i | −0.00895236 | − | 0.0172196i | ||||
\(169\) | −4.23323 | −0.325633 | ||||||||
\(170\) | − | 5.54307i | − | 0.425134i | ||||||
\(171\) | −16.9715 | − | 11.9104i | −1.29784 | − | 0.910811i | ||||
\(172\) | − | 8.40616i | − | 0.640964i | ||||||
\(173\) | 9.94482i | 0.756090i | 0.925787 | + | 0.378045i | \(0.123404\pi\) | ||||
−0.925787 | + | 0.378045i | \(0.876596\pi\) | |||||||
\(174\) | −2.86559 | − | 5.51188i | −0.217240 | − | 0.417854i | ||||
\(175\) | 0.145234i | 0.0109787i | ||||||||
\(176\) | −3.35877 | −0.253177 | ||||||||
\(177\) | 12.1611 | − | 6.32246i | 0.914081 | − | 0.475225i | ||||
\(178\) | − | 15.3774i | − | 1.15259i | ||||||
\(179\) | 3.37701i | 0.252409i | 0.992004 | + | 0.126205i | \(0.0402796\pi\) | ||||
−0.992004 | + | 0.126205i | \(0.959720\pi\) | |||||||
\(180\) | −1.72333 | + | 2.45563i | −0.128450 | + | 0.183032i | ||||
\(181\) | 5.28230i | 0.392630i | 0.980541 | + | 0.196315i | \(0.0628976\pi\) | ||||
−0.980541 | + | 0.196315i | \(0.937102\pi\) | |||||||
\(182\) | −0.430019 | −0.0318752 | ||||||||
\(183\) | 6.36387 | − | 3.30854i | 0.470431 | − | 0.244574i | ||||
\(184\) | 3.51586 | + | 3.26171i | 0.259193 | + | 0.240456i | ||||
\(185\) | − | 6.04149i | − | 0.444179i | ||||||
\(186\) | 16.3110 | − | 8.47998i | 1.19598 | − | 0.621782i | ||||
\(187\) | −18.6179 | −1.36148 | ||||||||
\(188\) | − | 9.98664i | − | 0.728351i | ||||||
\(189\) | −0.0996915 | + | 0.748044i | −0.00725149 | + | 0.0544122i | ||||
\(190\) | 6.91126 | 0.501396 | ||||||||
\(191\) | −22.1062 | −1.59955 | −0.799775 | − | 0.600300i | \(-0.795048\pi\) | ||||
−0.799775 | + | 0.600300i | \(0.795048\pi\) | |||||||
\(192\) | 0.798958 | + | 1.53677i | 0.0576598 | + | 0.110907i | ||||
\(193\) | 5.62469 | 0.404874 | 0.202437 | − | 0.979295i | \(-0.435114\pi\) | ||||
0.202437 | + | 0.979295i | \(0.435114\pi\) | |||||||
\(194\) | 11.6097 | 0.833530 | ||||||||
\(195\) | 2.36561 | + | 4.55019i | 0.169405 | + | 0.325846i | ||||
\(196\) | −6.97891 | −0.498493 | ||||||||
\(197\) | − | 4.97721i | − | 0.354611i | −0.984156 | − | 0.177306i | \(-0.943262\pi\) | ||
0.984156 | − | 0.177306i | \(-0.0567381\pi\) | |||||||
\(198\) | 8.24791 | + | 5.78828i | 0.586153 | + | 0.411355i | ||||
\(199\) | 5.07219i | 0.359558i | 0.983707 | + | 0.179779i | \(0.0575382\pi\) | ||||
−0.983707 | + | 0.179779i | \(0.942462\pi\) | |||||||
\(200\) | − | 1.00000i | − | 0.0707107i | ||||||
\(201\) | 20.0825 | − | 10.4408i | 1.41651 | − | 0.736434i | ||||
\(202\) | −5.20471 | −0.366202 | ||||||||
\(203\) | 0.520905 | 0.0365603 | ||||||||
\(204\) | 4.42868 | + | 8.51843i | 0.310070 | + | 0.596409i | ||||
\(205\) | 8.84450i | 0.617727i | ||||||||
\(206\) | 8.68617 | 0.605194 | ||||||||
\(207\) | −3.01265 | − | 14.0685i | −0.209394 | − | 0.977831i | ||||
\(208\) | 2.96087 | 0.205300 | ||||||||
\(209\) | − | 23.2134i | − | 1.60570i | ||||||
\(210\) | −0.116036 | − | 0.223191i | −0.00800723 | − | 0.0154017i | ||||
\(211\) | −9.58459 | −0.659830 | −0.329915 | − | 0.944011i | \(-0.607020\pi\) | ||||
−0.329915 | + | 0.944011i | \(0.607020\pi\) | |||||||
\(212\) | 3.83589 | 0.263450 | ||||||||
\(213\) | 1.94490 | − | 1.01114i | 0.133262 | − | 0.0692823i | ||||
\(214\) | − | 11.1465i | − | 0.761957i | ||||||
\(215\) | − | 8.40616i | − | 0.573296i | ||||||
\(216\) | 0.686420 | − | 5.15061i | 0.0467050 | − | 0.350455i | ||||
\(217\) | 1.54148i | 0.104643i | ||||||||
\(218\) | 7.19631 | 0.487396 | ||||||||
\(219\) | 7.38763 | + | 14.2099i | 0.499210 | + | 0.960215i | ||||
\(220\) | −3.35877 | −0.226448 | ||||||||
\(221\) | 16.4123 | 1.10401 | ||||||||
\(222\) | 4.82690 | + | 9.28438i | 0.323960 | + | 0.623127i | ||||
\(223\) | 17.7150 | 1.18628 | 0.593142 | − | 0.805098i | \(-0.297887\pi\) | ||||
0.593142 | + | 0.805098i | \(0.297887\pi\) | |||||||
\(224\) | −0.145234 | −0.00970385 | ||||||||
\(225\) | −1.72333 | + | 2.45563i | −0.114889 | + | 0.163709i | ||||
\(226\) | 13.1580i | 0.875260i | ||||||||
\(227\) | −3.72255 | −0.247074 | −0.123537 | − | 0.992340i | \(-0.539424\pi\) | ||||
−0.123537 | + | 0.992340i | \(0.539424\pi\) | |||||||
\(228\) | −10.6210 | + | 5.52181i | −0.703395 | + | 0.365691i | ||||
\(229\) | − | 4.59060i | − | 0.303355i | −0.988430 | − | 0.151678i | \(-0.951532\pi\) | ||
0.988430 | − | 0.151678i | \(-0.0484676\pi\) | |||||||
\(230\) | 3.51586 | + | 3.26171i | 0.231829 | + | 0.215071i | ||||
\(231\) | −0.749649 | + | 0.389738i | −0.0493233 | + | 0.0256429i | ||||
\(232\) | −3.58666 | −0.235476 | ||||||||
\(233\) | 3.65041i | 0.239147i | 0.992825 | + | 0.119573i | \(0.0381526\pi\) | ||||
−0.992825 | + | 0.119573i | \(0.961847\pi\) | |||||||
\(234\) | −7.27082 | − | 5.10257i | −0.475308 | − | 0.333565i | ||||
\(235\) | − | 9.98664i | − | 0.651457i | ||||||
\(236\) | − | 7.91338i | − | 0.515117i | ||||||
\(237\) | −20.3081 | + | 10.5581i | −1.31916 | + | 0.685821i | ||||
\(238\) | −0.805042 | −0.0521831 | ||||||||
\(239\) | 2.23114i | 0.144321i | 0.997393 | + | 0.0721603i | \(0.0229893\pi\) | ||||
−0.997393 | + | 0.0721603i | \(0.977011\pi\) | |||||||
\(240\) | 0.798958 | + | 1.53677i | 0.0515725 | + | 0.0991982i | ||||
\(241\) | − | 14.8025i | − | 0.953511i | −0.879036 | − | 0.476756i | \(-0.841813\pi\) | ||
0.879036 | − | 0.476756i | \(-0.158187\pi\) | |||||||
\(242\) | 0.281357i | 0.0180863i | ||||||||
\(243\) | −10.5618 | + | 11.4651i | −0.677541 | + | 0.735485i | ||||
\(244\) | − | 4.14107i | − | 0.265105i | ||||||
\(245\) | −6.97891 | −0.445866 | ||||||||
\(246\) | −7.06638 | − | 13.5920i | −0.450536 | − | 0.866592i | ||||
\(247\) | 20.4634i | 1.30205i | ||||||||
\(248\) | − | 10.6138i | − | 0.673977i | ||||||
\(249\) | −7.75811 | − | 14.9225i | −0.491650 | − | 0.945674i | ||||
\(250\) | − | 1.00000i | − | 0.0632456i | ||||||
\(251\) | −13.8618 | −0.874948 | −0.437474 | − | 0.899231i | \(-0.644127\pi\) | ||||
−0.437474 | + | 0.899231i | \(0.644127\pi\) | |||||||
\(252\) | 0.356641 | + | 0.250286i | 0.0224663 | + | 0.0157666i | ||||
\(253\) | 10.9553 | − | 11.8090i | 0.688756 | − | 0.742424i | ||||
\(254\) | − | 13.8601i | − | 0.869660i | ||||||
\(255\) | 4.42868 | + | 8.51843i | 0.277335 | + | 0.533445i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 1.86957i | 0.116621i | 0.998298 | + | 0.0583104i | \(0.0185713\pi\) | ||||
−0.998298 | + | 0.0583104i | \(0.981429\pi\) | |||||||
\(258\) | 6.71617 | + | 12.9184i | 0.418131 | + | 0.804261i | ||||
\(259\) | −0.877429 | −0.0545208 | ||||||||
\(260\) | 2.96087 | 0.183626 | ||||||||
\(261\) | 8.80752 | + | 6.18101i | 0.545172 | + | 0.382595i | ||||
\(262\) | 3.17761 | 0.196313 | ||||||||
\(263\) | 21.2810 | 1.31224 | 0.656120 | − | 0.754656i | \(-0.272196\pi\) | ||||
0.656120 | + | 0.754656i | \(0.272196\pi\) | |||||||
\(264\) | 5.16167 | − | 2.68352i | 0.317679 | − | 0.165159i | ||||
\(265\) | 3.83589 | 0.235637 | ||||||||
\(266\) | − | 1.00375i | − | 0.0615439i | ||||||
\(267\) | 12.2859 | + | 23.6316i | 0.751885 | + | 1.44623i | ||||
\(268\) | − | 13.0680i | − | 0.798253i | ||||||
\(269\) | 21.9822i | 1.34028i | 0.742237 | + | 0.670138i | \(0.233765\pi\) | ||||
−0.742237 | + | 0.670138i | \(0.766235\pi\) | |||||||
\(270\) | 0.686420 | − | 5.15061i | 0.0417742 | − | 0.313456i | ||||
\(271\) | 18.8975 | 1.14794 | 0.573971 | − | 0.818876i | \(-0.305402\pi\) | ||||
0.573971 | + | 0.818876i | \(0.305402\pi\) | |||||||
\(272\) | 5.54307 | 0.336098 | ||||||||
\(273\) | 0.660841 | − | 0.343567i | 0.0399959 | − | 0.0207936i | ||||
\(274\) | 19.0473i | 1.15069i | ||||||||
\(275\) | −3.35877 | −0.202542 | ||||||||
\(276\) | −8.00904 | − | 2.20347i | −0.482088 | − | 0.132633i | ||||
\(277\) | −8.26393 | −0.496532 | −0.248266 | − | 0.968692i | \(-0.579861\pi\) | ||||
−0.248266 | + | 0.968692i | \(0.579861\pi\) | |||||||
\(278\) | 10.1337i | 0.607780i | ||||||||
\(279\) | −18.2911 | + | 26.0636i | −1.09506 | + | 1.56039i | ||||
\(280\) | −0.145234 | −0.00867939 | ||||||||
\(281\) | −13.4017 | −0.799475 | −0.399738 | − | 0.916630i | \(-0.630899\pi\) | ||||
−0.399738 | + | 0.916630i | \(0.630899\pi\) | |||||||
\(282\) | 7.97891 | + | 15.3472i | 0.475137 | + | 0.913911i | ||||
\(283\) | − | 30.2552i | − | 1.79849i | −0.437450 | − | 0.899243i | \(-0.644118\pi\) | ||
0.437450 | − | 0.899243i | \(-0.355882\pi\) | |||||||
\(284\) | − | 1.26558i | − | 0.0750981i | ||||||
\(285\) | −10.6210 | + | 5.52181i | −0.629136 | + | 0.327084i | ||||
\(286\) | − | 9.94490i | − | 0.588054i | ||||||
\(287\) | 1.28452 | 0.0758229 | ||||||||
\(288\) | −2.45563 | − | 1.72333i | −0.144699 | − | 0.101548i | ||||
\(289\) | 13.7256 | 0.807389 | ||||||||
\(290\) | −3.58666 | −0.210616 | ||||||||
\(291\) | −17.8415 | + | 9.27569i | −1.04589 | + | 0.543750i | ||||
\(292\) | 9.24658 | 0.541115 | ||||||||
\(293\) | 7.09896 | 0.414725 | 0.207363 | − | 0.978264i | \(-0.433512\pi\) | ||||
0.207363 | + | 0.978264i | \(0.433512\pi\) | |||||||
\(294\) | 10.7250 | − | 5.57585i | 0.625494 | − | 0.325190i | ||||
\(295\) | − | 7.91338i | − | 0.460735i | ||||||
\(296\) | 6.04149 | 0.351154 | ||||||||
\(297\) | −17.2997 | − | 2.30553i | −1.00383 | − | 0.133780i | ||||
\(298\) | 19.7755i | 1.14557i | ||||||||
\(299\) | −9.65750 | + | 10.4100i | −0.558508 | + | 0.602027i | ||||
\(300\) | 0.798958 | + | 1.53677i | 0.0461279 | + | 0.0887255i | ||||
\(301\) | −1.22086 | −0.0703692 | ||||||||
\(302\) | − | 9.13517i | − | 0.525670i | ||||||
\(303\) | 7.99845 | − | 4.15834i | 0.459499 | − | 0.238891i | ||||
\(304\) | 6.91126i | 0.396388i | ||||||||
\(305\) | − | 4.14107i | − | 0.237117i | ||||||
\(306\) | −13.6117 | − | 9.55255i | −0.778131 | − | 0.546083i | ||||
\(307\) | −27.6286 | −1.57685 | −0.788423 | − | 0.615133i | \(-0.789102\pi\) | ||||
−0.788423 | + | 0.615133i | \(0.789102\pi\) | |||||||
\(308\) | 0.487808i | 0.0277954i | ||||||||
\(309\) | −13.3487 | + | 6.93989i | −0.759379 | + | 0.394796i | ||||
\(310\) | − | 10.6138i | − | 0.602823i | ||||||
\(311\) | − | 30.1469i | − | 1.70948i | −0.519060 | − | 0.854738i | \(-0.673718\pi\) | ||
0.519060 | − | 0.854738i | \(-0.326282\pi\) | |||||||
\(312\) | −4.55019 | + | 2.36561i | −0.257604 | + | 0.133927i | ||||
\(313\) | 5.35060i | 0.302434i | 0.988501 | + | 0.151217i | \(0.0483192\pi\) | ||||
−0.988501 | + | 0.151217i | \(0.951681\pi\) | |||||||
\(314\) | −10.3178 | −0.582268 | ||||||||
\(315\) | 0.356641 | + | 0.250286i | 0.0200944 | + | 0.0141020i | ||||
\(316\) | 13.2148i | 0.743391i | ||||||||
\(317\) | 20.5865i | 1.15625i | 0.815947 | + | 0.578127i | \(0.196216\pi\) | ||||
−0.815947 | + | 0.578127i | \(0.803784\pi\) | |||||||
\(318\) | −5.89488 | + | 3.06471i | −0.330568 | + | 0.171861i | ||||
\(319\) | 12.0468i | 0.674490i | ||||||||
\(320\) | 1.00000 | 0.0559017 | ||||||||
\(321\) | 8.90556 | + | 17.1296i | 0.497060 | + | 0.956079i | ||||
\(322\) | 0.473711 | − | 0.510622i | 0.0263989 | − | 0.0284559i | ||||
\(323\) | 38.3096i | 2.13160i | ||||||||
\(324\) | 3.06025 | + | 8.46374i | 0.170014 | + | 0.470208i | ||||
\(325\) | 2.96087 | 0.164240 | ||||||||
\(326\) | 11.8046i | 0.653796i | ||||||||
\(327\) | −11.0591 | + | 5.74955i | −0.611569 | + | 0.317951i | ||||
\(328\) | −8.84450 | −0.488356 | ||||||||
\(329\) | −1.45040 | −0.0799631 | ||||||||
\(330\) | 5.16167 | − | 2.68352i | 0.284140 | − | 0.147723i | ||||
\(331\) | 0.146593 | 0.00805747 | 0.00402874 | − | 0.999992i | \(-0.498718\pi\) | ||||
0.00402874 | + | 0.999992i | \(0.498718\pi\) | |||||||
\(332\) | −9.71029 | −0.532921 | ||||||||
\(333\) | −14.8357 | − | 10.4115i | −0.812990 | − | 0.570546i | ||||
\(334\) | −11.8429 | −0.648012 | ||||||||
\(335\) | − | 13.0680i | − | 0.713979i | ||||||
\(336\) | 0.223191 | − | 0.116036i | 0.0121761 | − | 0.00633027i | ||||
\(337\) | 24.5559i | 1.33764i | 0.743423 | + | 0.668821i | \(0.233201\pi\) | ||||
−0.743423 | + | 0.668821i | \(0.766799\pi\) | |||||||
\(338\) | − | 4.23323i | − | 0.230257i | ||||||
\(339\) | −10.5127 | − | 20.2209i | −0.570973 | − | 1.09825i | ||||
\(340\) | 5.54307 | 0.300615 | ||||||||
\(341\) | −35.6493 | −1.93052 | ||||||||
\(342\) | 11.9104 | − | 16.9715i | 0.644041 | − | 0.917715i | ||||
\(343\) | 2.03021i | 0.109621i | ||||||||
\(344\) | 8.40616 | 0.453230 | ||||||||
\(345\) | −8.00904 | − | 2.20347i | −0.431192 | − | 0.118631i | ||||
\(346\) | −9.94482 | −0.534637 | ||||||||
\(347\) | 9.62040i | 0.516450i | 0.966085 | + | 0.258225i | \(0.0831376\pi\) | ||||
−0.966085 | + | 0.258225i | \(0.916862\pi\) | |||||||
\(348\) | 5.51188 | − | 2.86559i | 0.295468 | − | 0.153612i | ||||
\(349\) | 23.1850 | 1.24106 | 0.620532 | − | 0.784181i | \(-0.286917\pi\) | ||||
0.620532 | + | 0.784181i | \(0.286917\pi\) | |||||||
\(350\) | −0.145234 | −0.00776308 | ||||||||
\(351\) | 15.2503 | + | 2.03240i | 0.814002 | + | 0.108482i | ||||
\(352\) | − | 3.35877i | − | 0.179023i | ||||||
\(353\) | 9.38131i | 0.499317i | 0.968334 | + | 0.249658i | \(0.0803183\pi\) | ||||
−0.968334 | + | 0.249658i | \(0.919682\pi\) | |||||||
\(354\) | 6.32246 | + | 12.1611i | 0.336035 | + | 0.646353i | ||||
\(355\) | − | 1.26558i | − | 0.0671698i | ||||||
\(356\) | 15.3774 | 0.815001 | ||||||||
\(357\) | 1.23716 | − | 0.643195i | 0.0654777 | − | 0.0340415i | ||||
\(358\) | −3.37701 | −0.178480 | ||||||||
\(359\) | 13.9686 | 0.737234 | 0.368617 | − | 0.929581i | \(-0.379831\pi\) | ||||
0.368617 | + | 0.929581i | \(0.379831\pi\) | |||||||
\(360\) | −2.45563 | − | 1.72333i | −0.129423 | − | 0.0908276i | ||||
\(361\) | −28.7656 | −1.51398 | ||||||||
\(362\) | −5.28230 | −0.277632 | ||||||||
\(363\) | −0.224792 | − | 0.432381i | −0.0117985 | − | 0.0226941i | ||||
\(364\) | − | 0.430019i | − | 0.0225391i | ||||||
\(365\) | 9.24658 | 0.483988 | ||||||||
\(366\) | 3.30854 | + | 6.36387i | 0.172940 | + | 0.332645i | ||||
\(367\) | 11.2257i | 0.585976i | 0.956116 | + | 0.292988i | \(0.0946496\pi\) | ||||
−0.956116 | + | 0.292988i | \(0.905350\pi\) | |||||||
\(368\) | −3.26171 | + | 3.51586i | −0.170028 | + | 0.183277i | ||||
\(369\) | 21.7188 | + | 15.2420i | 1.13064 | + | 0.793467i | ||||
\(370\) | 6.04149 | 0.314082 | ||||||||
\(371\) | − | 0.557101i | − | 0.0289232i | ||||||
\(372\) | 8.47998 | + | 16.3110i | 0.439667 | + | 0.845685i | ||||
\(373\) | 6.04006i | 0.312743i | 0.987698 | + | 0.156371i | \(0.0499797\pi\) | ||||
−0.987698 | + | 0.156371i | \(0.950020\pi\) | |||||||
\(374\) | − | 18.6179i | − | 0.962709i | ||||||
\(375\) | 0.798958 | + | 1.53677i | 0.0412580 | + | 0.0793585i | ||||
\(376\) | 9.98664 | 0.515022 | ||||||||
\(377\) | − | 10.6196i | − | 0.546940i | ||||||
\(378\) | −0.748044 | − | 0.0996915i | −0.0384752 | − | 0.00512758i | ||||
\(379\) | − | 6.58693i | − | 0.338348i | −0.985586 | − | 0.169174i | \(-0.945890\pi\) | ||
0.985586 | − | 0.169174i | \(-0.0541099\pi\) | |||||||
\(380\) | 6.91126i | 0.354540i | ||||||||
\(381\) | 11.0736 | + | 21.2998i | 0.567320 | + | 1.09122i | ||||
\(382\) | − | 22.1062i | − | 1.13105i | ||||||
\(383\) | −25.9655 | −1.32677 | −0.663387 | − | 0.748277i | \(-0.730882\pi\) | ||||
−0.663387 | + | 0.748277i | \(0.730882\pi\) | |||||||
\(384\) | −1.53677 | + | 0.798958i | −0.0784230 | + | 0.0407717i | ||||
\(385\) | 0.487808i | 0.0248610i | ||||||||
\(386\) | 5.62469i | 0.286289i | ||||||||
\(387\) | −20.6424 | − | 14.4866i | −1.04931 | − | 0.736396i | ||||
\(388\) | 11.6097i | 0.589395i | ||||||||
\(389\) | 25.9332 | 1.31486 | 0.657432 | − | 0.753514i | \(-0.271643\pi\) | ||||
0.657432 | + | 0.753514i | \(0.271643\pi\) | |||||||
\(390\) | −4.55019 | + | 2.36561i | −0.230408 | + | 0.119788i | ||||
\(391\) | −18.0799 | + | 19.4887i | −0.914338 | + | 0.985583i | ||||
\(392\) | − | 6.97891i | − | 0.352488i | ||||||
\(393\) | −4.88326 | + | 2.53878i | −0.246328 | + | 0.128064i | ||||
\(394\) | 4.97721 | 0.250748 | ||||||||
\(395\) | 13.2148i | 0.664909i | ||||||||
\(396\) | −5.78828 | + | 8.24791i | −0.290872 | + | 0.414473i | ||||
\(397\) | 11.2187 | 0.563049 | 0.281524 | − | 0.959554i | \(-0.409160\pi\) | ||||
0.281524 | + | 0.959554i | \(0.409160\pi\) | |||||||
\(398\) | −5.07219 | −0.254246 | ||||||||
\(399\) | 0.801954 | + | 1.54253i | 0.0401479 | + | 0.0772233i | ||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | 16.0468 | 0.801337 | 0.400669 | − | 0.916223i | \(-0.368778\pi\) | ||||
0.400669 | + | 0.916223i | \(0.368778\pi\) | |||||||
\(402\) | 10.4408 | + | 20.0825i | 0.520738 | + | 1.00162i | ||||
\(403\) | 31.4261 | 1.56545 | ||||||||
\(404\) | − | 5.20471i | − | 0.258944i | ||||||
\(405\) | 3.06025 | + | 8.46374i | 0.152065 | + | 0.420566i | ||||
\(406\) | 0.520905i | 0.0258521i | ||||||||
\(407\) | − | 20.2920i | − | 1.00584i | ||||||
\(408\) | −8.51843 | + | 4.42868i | −0.421725 | + | 0.219252i | ||||
\(409\) | −25.0421 | −1.23825 | −0.619127 | − | 0.785291i | \(-0.712513\pi\) | ||||
−0.619127 | + | 0.785291i | \(0.712513\pi\) | |||||||
\(410\) | −8.84450 | −0.436799 | ||||||||
\(411\) | −15.2180 | − | 29.2714i | −0.750649 | − | 1.44385i | ||||
\(412\) | 8.68617i | 0.427937i | ||||||||
\(413\) | −1.14929 | −0.0565529 | ||||||||
\(414\) | 14.0685 | − | 3.01265i | 0.691431 | − | 0.148064i | ||||
\(415\) | −9.71029 | −0.476659 | ||||||||
\(416\) | 2.96087i | 0.145169i | ||||||||
\(417\) | −8.09642 | − | 15.5732i | −0.396483 | − | 0.762624i | ||||
\(418\) | 23.2134 | 1.13540 | ||||||||
\(419\) | 0.170219 | 0.00831576 | 0.00415788 | − | 0.999991i | \(-0.498677\pi\) | ||||
0.00415788 | + | 0.999991i | \(0.498677\pi\) | |||||||
\(420\) | 0.223191 | − | 0.116036i | 0.0108906 | − | 0.00566197i | ||||
\(421\) | 3.35189i | 0.163361i | 0.996659 | + | 0.0816807i | \(0.0260288\pi\) | ||||
−0.996659 | + | 0.0816807i | \(0.973971\pi\) | |||||||
\(422\) | − | 9.58459i | − | 0.466571i | ||||||
\(423\) | −24.5235 | − | 17.2103i | −1.19237 | − | 0.836793i | ||||
\(424\) | 3.83589i | 0.186287i | ||||||||
\(425\) | 5.54307 | 0.268878 | ||||||||
\(426\) | 1.01114 | + | 1.94490i | 0.0489900 | + | 0.0942307i | ||||
\(427\) | −0.601423 | −0.0291049 | ||||||||
\(428\) | 11.1465 | 0.538785 | ||||||||
\(429\) | 7.94556 | + | 15.2830i | 0.383615 | + | 0.737872i | ||||
\(430\) | 8.40616 | 0.405381 | ||||||||
\(431\) | 21.5603 | 1.03852 | 0.519262 | − | 0.854615i | \(-0.326207\pi\) | ||||
0.519262 | + | 0.854615i | \(0.326207\pi\) | |||||||
\(432\) | 5.15061 | + | 0.686420i | 0.247809 | + | 0.0330254i | ||||
\(433\) | − | 25.3255i | − | 1.21707i | −0.793529 | − | 0.608533i | \(-0.791758\pi\) | ||
0.793529 | − | 0.608533i | \(-0.208242\pi\) | |||||||
\(434\) | −1.54148 | −0.0739936 | ||||||||
\(435\) | 5.51188 | − | 2.86559i | 0.264274 | − | 0.137395i | ||||
\(436\) | 7.19631i | 0.344641i | ||||||||
\(437\) | −24.2990 | − | 22.5425i | −1.16238 | − | 1.07835i | ||||
\(438\) | −14.2099 | + | 7.38763i | −0.678974 | + | 0.352995i | ||||
\(439\) | −0.917239 | −0.0437774 | −0.0218887 | − | 0.999760i | \(-0.506968\pi\) | ||||
−0.0218887 | + | 0.999760i | \(0.506968\pi\) | |||||||
\(440\) | − | 3.35877i | − | 0.160123i | ||||||
\(441\) | −12.0270 | + | 17.1376i | −0.572713 | + | 0.816077i | ||||
\(442\) | 16.4123i | 0.780655i | ||||||||
\(443\) | − | 4.08632i | − | 0.194147i | −0.995277 | − | 0.0970734i | \(-0.969052\pi\) | ||
0.995277 | − | 0.0970734i | \(-0.0309482\pi\) | |||||||
\(444\) | −9.28438 | + | 4.82690i | −0.440617 | + | 0.229074i | ||||
\(445\) | 15.3774 | 0.728959 | ||||||||
\(446\) | 17.7150i | 0.838829i | ||||||||
\(447\) | −15.7998 | − | 30.3905i | −0.747306 | − | 1.43742i | ||||
\(448\) | − | 0.145234i | − | 0.00686166i | ||||||
\(449\) | 5.31513i | 0.250836i | 0.992104 | + | 0.125418i | \(0.0400273\pi\) | ||||
−0.992104 | + | 0.125418i | \(0.959973\pi\) | |||||||
\(450\) | −2.45563 | − | 1.72333i | −0.115760 | − | 0.0812386i | ||||
\(451\) | 29.7067i | 1.39883i | ||||||||
\(452\) | −13.1580 | −0.618902 | ||||||||
\(453\) | 7.29861 | + | 14.0387i | 0.342919 | + | 0.659594i | ||||
\(454\) | − | 3.72255i | − | 0.174708i | ||||||
\(455\) | − | 0.430019i | − | 0.0201596i | ||||||
\(456\) | −5.52181 | − | 10.6210i | −0.258582 | − | 0.497375i | ||||
\(457\) | 17.8678i | 0.835822i | 0.908488 | + | 0.417911i | \(0.137238\pi\) | ||||
−0.908488 | + | 0.417911i | \(0.862762\pi\) | |||||||
\(458\) | 4.59060 | 0.214505 | ||||||||
\(459\) | 28.5502 | + | 3.80487i | 1.33261 | + | 0.177596i | ||||
\(460\) | −3.26171 | + | 3.51586i | −0.152078 | + | 0.163928i | ||||
\(461\) | − | 0.958482i | − | 0.0446410i | −0.999751 | − | 0.0223205i | \(-0.992895\pi\) | ||
0.999751 | − | 0.0223205i | \(-0.00710542\pi\) | |||||||
\(462\) | −0.389738 | − | 0.749649i | −0.0181323 | − | 0.0348768i | ||||
\(463\) | 41.6838 | 1.93721 | 0.968606 | − | 0.248603i | \(-0.0799714\pi\) | ||||
0.968606 | + | 0.248603i | \(0.0799714\pi\) | |||||||
\(464\) | − | 3.58666i | − | 0.166507i | ||||||
\(465\) | 8.47998 | + | 16.3110i | 0.393250 | + | 0.756404i | ||||
\(466\) | −3.65041 | −0.169102 | ||||||||
\(467\) | 7.07758 | 0.327511 | 0.163756 | − | 0.986501i | \(-0.447639\pi\) | ||||
0.163756 | + | 0.986501i | \(0.447639\pi\) | |||||||
\(468\) | 5.10257 | − | 7.27082i | 0.235866 | − | 0.336094i | ||||
\(469\) | −1.89791 | −0.0876375 | ||||||||
\(470\) | 9.98664 | 0.460649 | ||||||||
\(471\) | 15.8561 | − | 8.24350i | 0.730611 | − | 0.379840i | ||||
\(472\) | 7.91338 | 0.364243 | ||||||||
\(473\) | − | 28.2344i | − | 1.29822i | ||||||
\(474\) | −10.5581 | − | 20.3081i | −0.484949 | − | 0.932784i | ||||
\(475\) | 6.91126i | 0.317111i | ||||||||
\(476\) | − | 0.805042i | − | 0.0368990i | ||||||
\(477\) | 6.61051 | − | 9.41953i | 0.302674 | − | 0.431290i | ||||
\(478\) | −2.23114 | −0.102050 | ||||||||
\(479\) | −12.3246 | −0.563125 | −0.281562 | − | 0.959543i | \(-0.590853\pi\) | ||||
−0.281562 | + | 0.959543i | \(0.590853\pi\) | |||||||
\(480\) | −1.53677 | + | 0.798958i | −0.0701437 | + | 0.0364673i | ||||
\(481\) | 17.8881i | 0.815626i | ||||||||
\(482\) | 14.8025 | 0.674234 | ||||||||
\(483\) | −0.320019 | + | 1.16318i | −0.0145614 | + | 0.0529267i | ||||
\(484\) | −0.281357 | −0.0127890 | ||||||||
\(485\) | 11.6097i | 0.527171i | ||||||||
\(486\) | −11.4651 | − | 10.5618i | −0.520067 | − | 0.479094i | ||||
\(487\) | 7.63905 | 0.346159 | 0.173079 | − | 0.984908i | \(-0.444628\pi\) | ||||
0.173079 | + | 0.984908i | \(0.444628\pi\) | |||||||
\(488\) | 4.14107 | 0.187457 | ||||||||
\(489\) | −9.43137 | − | 18.1410i | −0.426501 | − | 0.820362i | ||||
\(490\) | − | 6.97891i | − | 0.315275i | ||||||
\(491\) | − | 30.8151i | − | 1.39067i | −0.718688 | − | 0.695333i | \(-0.755257\pi\) | ||
0.718688 | − | 0.695333i | \(-0.244743\pi\) | |||||||
\(492\) | 13.5920 | − | 7.06638i | 0.612773 | − | 0.318577i | ||||
\(493\) | − | 19.8811i | − | 0.895400i | ||||||
\(494\) | −20.4634 | −0.920691 | ||||||||
\(495\) | −5.78828 | + | 8.24791i | −0.260164 | + | 0.370716i | ||||
\(496\) | 10.6138 | 0.476574 | ||||||||
\(497\) | −0.183805 | −0.00824476 | ||||||||
\(498\) | 14.9225 | − | 7.75811i | 0.668693 | − | 0.347649i | ||||
\(499\) | −26.4668 | −1.18482 | −0.592409 | − | 0.805638i | \(-0.701823\pi\) | ||||
−0.592409 | + | 0.805638i | \(0.701823\pi\) | |||||||
\(500\) | 1.00000 | 0.0447214 | ||||||||
\(501\) | 18.1998 | − | 9.46194i | 0.813105 | − | 0.422729i | ||||
\(502\) | − | 13.8618i | − | 0.618682i | ||||||
\(503\) | 22.6338 | 1.00919 | 0.504595 | − | 0.863356i | \(-0.331642\pi\) | ||||
0.504595 | + | 0.863356i | \(0.331642\pi\) | |||||||
\(504\) | −0.250286 | + | 0.356641i | −0.0111486 | + | 0.0158861i | ||||
\(505\) | − | 5.20471i | − | 0.231607i | ||||||
\(506\) | 11.8090 | + | 10.9553i | 0.524973 | + | 0.487024i | ||||
\(507\) | 3.38217 | + | 6.50550i | 0.150207 | + | 0.288919i | ||||
\(508\) | 13.8601 | 0.614943 | ||||||||
\(509\) | − | 15.8116i | − | 0.700839i | −0.936593 | − | 0.350419i | \(-0.886039\pi\) | ||
0.936593 | − | 0.350419i | \(-0.113961\pi\) | |||||||
\(510\) | −8.51843 | + | 4.42868i | −0.377202 | + | 0.196105i | ||||
\(511\) | − | 1.34292i | − | 0.0594072i | ||||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | −4.74403 | + | 35.5973i | −0.209454 | + | 1.57166i | ||||
\(514\) | −1.86957 | −0.0824634 | ||||||||
\(515\) | 8.68617i | 0.382758i | ||||||||
\(516\) | −12.9184 | + | 6.71617i | −0.568699 | + | 0.295663i | ||||
\(517\) | − | 33.5429i | − | 1.47521i | ||||||
\(518\) | − | 0.877429i | − | 0.0385520i | ||||||
\(519\) | 15.2829 | − | 7.94549i | 0.670845 | − | 0.348768i | ||||
\(520\) | 2.96087i | 0.129843i | ||||||||
\(521\) | 7.86606 | 0.344618 | 0.172309 | − | 0.985043i | \(-0.444877\pi\) | ||||
0.172309 | + | 0.985043i | \(0.444877\pi\) | |||||||
\(522\) | −6.18101 | + | 8.80752i | −0.270535 | + | 0.385495i | ||||
\(523\) | − | 1.97457i | − | 0.0863418i | −0.999068 | − | 0.0431709i | \(-0.986254\pi\) | ||
0.999068 | − | 0.0431709i | \(-0.0137460\pi\) | |||||||
\(524\) | 3.17761i | 0.138815i | ||||||||
\(525\) | 0.223191 | − | 0.116036i | 0.00974087 | − | 0.00506422i | ||||
\(526\) | 21.2810i | 0.927894i | ||||||||
\(527\) | 58.8330 | 2.56281 | ||||||||
\(528\) | 2.68352 | + | 5.16167i | 0.116785 | + | 0.224633i | ||||
\(529\) | −1.72254 | − | 22.9354i | −0.0748929 | − | 0.997192i | ||||
\(530\) | 3.83589i | 0.166620i | ||||||||
\(531\) | −19.4323 | − | 13.6374i | −0.843292 | − | 0.591812i | ||||
\(532\) | 1.00375 | 0.0435181 | ||||||||
\(533\) | − | 26.1874i | − | 1.13430i | ||||||
\(534\) | −23.6316 | + | 12.2859i | −1.02264 | + | 0.531663i | ||||
\(535\) | 11.1465 | 0.481904 | ||||||||
\(536\) | 13.0680 | 0.564450 | ||||||||
\(537\) | 5.18969 | − | 2.69809i | 0.223952 | − | 0.116431i | ||||
\(538\) | −21.9822 | −0.947718 | ||||||||
\(539\) | −23.4406 | −1.00966 | ||||||||
\(540\) | 5.15061 | + | 0.686420i | 0.221647 | + | 0.0295388i | ||||
\(541\) | 2.33239 | 0.100277 | 0.0501387 | − | 0.998742i | \(-0.484034\pi\) | ||||
0.0501387 | + | 0.998742i | \(0.484034\pi\) | |||||||
\(542\) | 18.8975i | 0.811717i | ||||||||
\(543\) | 8.11769 | − | 4.22034i | 0.348363 | − | 0.181112i | ||||
\(544\) | 5.54307i | 0.237657i | ||||||||
\(545\) | 7.19631i | 0.308256i | ||||||||
\(546\) | 0.343567 | + | 0.660841i | 0.0147033 | + | 0.0282814i | ||||
\(547\) | −8.51715 | −0.364167 | −0.182083 | − | 0.983283i | \(-0.558284\pi\) | ||||
−0.182083 | + | 0.983283i | \(0.558284\pi\) | |||||||
\(548\) | −19.0473 | −0.813661 | ||||||||
\(549\) | −10.1689 | − | 7.13643i | −0.434000 | − | 0.304576i | ||||
\(550\) | − | 3.35877i | − | 0.143219i | ||||||
\(551\) | 24.7884 | 1.05602 | ||||||||
\(552\) | 2.20347 | − | 8.00904i | 0.0937860 | − | 0.340887i | ||||
\(553\) | 1.91924 | 0.0816143 | ||||||||
\(554\) | − | 8.26393i | − | 0.351101i | ||||||
\(555\) | −9.28438 | + | 4.82690i | −0.394100 | + | 0.204890i | ||||
\(556\) | −10.1337 | −0.429766 | ||||||||
\(557\) | −2.38292 | −0.100967 | −0.0504837 | − | 0.998725i | \(-0.516076\pi\) | ||||
−0.0504837 | + | 0.998725i | \(0.516076\pi\) | |||||||
\(558\) | −26.0636 | − | 18.2911i | −1.10336 | − | 0.774324i | ||||
\(559\) | 24.8896i | 1.05272i | ||||||||
\(560\) | − | 0.145234i | − | 0.00613725i | ||||||
\(561\) | 14.8749 | + | 28.6115i | 0.628020 | + | 1.20798i | ||||
\(562\) | − | 13.4017i | − | 0.565315i | ||||||
\(563\) | 6.34926 | 0.267589 | 0.133795 | − | 0.991009i | \(-0.457284\pi\) | ||||
0.133795 | + | 0.991009i | \(0.457284\pi\) | |||||||
\(564\) | −15.3472 | + | 7.97891i | −0.646233 | + | 0.335973i | ||||
\(565\) | −13.1580 | −0.553563 | ||||||||
\(566\) | 30.2552 | 1.27172 | ||||||||
\(567\) | 1.22922 | − | 0.444453i | 0.0516225 | − | 0.0186653i | ||||
\(568\) | 1.26558 | 0.0531024 | ||||||||
\(569\) | 25.7123 | 1.07792 | 0.538958 | − | 0.842333i | \(-0.318818\pi\) | ||||
0.538958 | + | 0.842333i | \(0.318818\pi\) | |||||||
\(570\) | −5.52181 | − | 10.6210i | −0.231283 | − | 0.444866i | ||||
\(571\) | 3.97359i | 0.166290i | 0.996537 | + | 0.0831448i | \(0.0264964\pi\) | ||||
−0.996537 | + | 0.0831448i | \(0.973504\pi\) | |||||||
\(572\) | 9.94490 | 0.415817 | ||||||||
\(573\) | 17.6619 | + | 33.9722i | 0.737838 | + | 1.41921i | ||||
\(574\) | 1.28452i | 0.0536149i | ||||||||
\(575\) | −3.26171 | + | 3.51586i | −0.136023 | + | 0.146621i | ||||
\(576\) | 1.72333 | − | 2.45563i | 0.0718055 | − | 0.102318i | ||||
\(577\) | 3.74728 | 0.156001 | 0.0780007 | − | 0.996953i | \(-0.475146\pi\) | ||||
0.0780007 | + | 0.996953i | \(0.475146\pi\) | |||||||
\(578\) | 13.7256i | 0.570910i | ||||||||
\(579\) | −4.49389 | − | 8.64386i | −0.186760 | − | 0.359227i | ||||
\(580\) | − | 3.58666i | − | 0.148928i | ||||||
\(581\) | 1.41026i | 0.0585076i | ||||||||
\(582\) | −9.27569 | − | 17.8415i | −0.384490 | − | 0.739554i | ||||
\(583\) | 12.8839 | 0.533596 | ||||||||
\(584\) | 9.24658i | 0.382626i | ||||||||
\(585\) | 5.10257 | − | 7.27082i | 0.210965 | − | 0.300611i | ||||
\(586\) | 7.09896i | 0.293255i | ||||||||
\(587\) | − | 14.0119i | − | 0.578333i | −0.957279 | − | 0.289166i | \(-0.906622\pi\) | ||
0.957279 | − | 0.289166i | \(-0.0933781\pi\) | |||||||
\(588\) | 5.57585 | + | 10.7250i | 0.229944 | + | 0.442291i | ||||
\(589\) | 73.3548i | 3.02253i | ||||||||
\(590\) | 7.91338 | 0.325789 | ||||||||
\(591\) | −7.64883 | + | 3.97658i | −0.314631 | + | 0.163575i | ||||
\(592\) | 6.04149i | 0.248304i | ||||||||
\(593\) | − | 37.3930i | − | 1.53555i | −0.640722 | − | 0.767773i | \(-0.721365\pi\) | ||
0.640722 | − | 0.767773i | \(-0.278635\pi\) | |||||||
\(594\) | 2.30553 | − | 17.2997i | 0.0945970 | − | 0.709817i | ||||
\(595\) | − | 0.805042i | − | 0.0330035i | ||||||
\(596\) | −19.7755 | −0.810038 | ||||||||
\(597\) | 7.79479 | − | 4.05246i | 0.319020 | − | 0.165856i | ||||
\(598\) | −10.4100 | − | 9.65750i | −0.425697 | − | 0.394925i | ||||
\(599\) | − | 47.3032i | − | 1.93275i | −0.257128 | − | 0.966377i | \(-0.582776\pi\) | ||
0.257128 | − | 0.966377i | \(-0.417224\pi\) | |||||||
\(600\) | −1.53677 | + | 0.798958i | −0.0627384 | + | 0.0326173i | ||||
\(601\) | −22.4865 | −0.917244 | −0.458622 | − | 0.888631i | \(-0.651657\pi\) | ||||
−0.458622 | + | 0.888631i | \(0.651657\pi\) | |||||||
\(602\) | − | 1.22086i | − | 0.0497586i | ||||||
\(603\) | −32.0901 | − | 22.5204i | −1.30681 | − | 0.917104i | ||||
\(604\) | 9.13517 | 0.371705 | ||||||||
\(605\) | −0.281357 | −0.0114388 | ||||||||
\(606\) | 4.15834 | + | 7.99845i | 0.168921 | + | 0.324915i | ||||
\(607\) | 37.1285 | 1.50700 | 0.753499 | − | 0.657449i | \(-0.228365\pi\) | ||||
0.753499 | + | 0.657449i | \(0.228365\pi\) | |||||||
\(608\) | −6.91126 | −0.280289 | ||||||||
\(609\) | −0.416181 | − | 0.800512i | −0.0168645 | − | 0.0324384i | ||||
\(610\) | 4.14107 | 0.167667 | ||||||||
\(611\) | 29.5692i | 1.19624i | ||||||||
\(612\) | 9.55255 | − | 13.6117i | 0.386139 | − | 0.550222i | ||||
\(613\) | − | 2.91171i | − | 0.117603i | −0.998270 | − | 0.0588014i | \(-0.981272\pi\) | ||
0.998270 | − | 0.0588014i | \(-0.0187279\pi\) | |||||||
\(614\) | − | 27.6286i | − | 1.11500i | ||||||
\(615\) | 13.5920 | − | 7.06638i | 0.548081 | − | 0.284944i | ||||
\(616\) | −0.487808 | −0.0196543 | ||||||||
\(617\) | −16.9070 | −0.680651 | −0.340325 | − | 0.940308i | \(-0.610537\pi\) | ||||
−0.340325 | + | 0.940308i | \(0.610537\pi\) | |||||||
\(618\) | −6.93989 | − | 13.3487i | −0.279163 | − | 0.536962i | ||||
\(619\) | − | 30.6140i | − | 1.23048i | −0.788339 | − | 0.615241i | \(-0.789059\pi\) | ||
0.788339 | − | 0.615241i | \(-0.210941\pi\) | |||||||
\(620\) | 10.6138 | 0.426260 | ||||||||
\(621\) | −19.2132 | + | 15.8699i | −0.770997 | + | 0.636839i | ||||
\(622\) | 30.1469 | 1.20878 | ||||||||
\(623\) | − | 2.23332i | − | 0.0894762i | ||||||
\(624\) | −2.36561 | − | 4.55019i | −0.0947004 | − | 0.182153i | ||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | −5.35060 | −0.213853 | ||||||||
\(627\) | −35.6736 | + | 18.5465i | −1.42467 | + | 0.740676i | ||||
\(628\) | − | 10.3178i | − | 0.411726i | ||||||
\(629\) | 33.4884i | 1.33527i | ||||||||
\(630\) | −0.250286 | + | 0.356641i | −0.00997164 | + | 0.0142089i | ||||
\(631\) | − | 12.9825i | − | 0.516826i | −0.966035 | − | 0.258413i | \(-0.916800\pi\) | ||
0.966035 | − | 0.258413i | \(-0.0831995\pi\) | |||||||
\(632\) | −13.2148 | −0.525657 | ||||||||
\(633\) | 7.65769 | + | 14.7293i | 0.304366 | + | 0.585438i | ||||
\(634\) | −20.5865 | −0.817595 | ||||||||
\(635\) | 13.8601 | 0.550021 | ||||||||
\(636\) | −3.06471 | − | 5.89488i | −0.121524 | − | 0.233747i | ||||
\(637\) | 20.6637 | 0.818724 | ||||||||
\(638\) | −12.0468 | −0.476937 | ||||||||
\(639\) | −3.10779 | − | 2.18101i | −0.122942 | − | 0.0862793i | ||||
\(640\) | 1.00000i | 0.0395285i | ||||||||
\(641\) | 23.4868 | 0.927675 | 0.463837 | − | 0.885920i | \(-0.346472\pi\) | ||||
0.463837 | + | 0.885920i | \(0.346472\pi\) | |||||||
\(642\) | −17.1296 | + | 8.90556i | −0.676050 | + | 0.351474i | ||||
\(643\) | − | 50.0206i | − | 1.97262i | −0.164902 | − | 0.986310i | \(-0.552731\pi\) | ||
0.164902 | − | 0.986310i | \(-0.447269\pi\) | |||||||
\(644\) | 0.510622 | + | 0.473711i | 0.0201213 | + | 0.0186668i | ||||
\(645\) | −12.9184 | + | 6.71617i | −0.508660 | + | 0.264449i | ||||
\(646\) | −38.3096 | −1.50727 | ||||||||
\(647\) | 21.4247i | 0.842290i | 0.906993 | + | 0.421145i | \(0.138372\pi\) | ||||
−0.906993 | + | 0.421145i | \(0.861628\pi\) | |||||||
\(648\) | −8.46374 | + | 3.06025i | −0.332487 | + | 0.120218i | ||||
\(649\) | − | 26.5792i | − | 1.04333i | ||||||
\(650\) | 2.96087i | 0.116135i | ||||||||
\(651\) | 2.36891 | − | 1.23158i | 0.0928448 | − | 0.0482695i | ||||
\(652\) | −11.8046 | −0.462303 | ||||||||
\(653\) | − | 28.4131i | − | 1.11189i | −0.831219 | − | 0.555946i | \(-0.812356\pi\) | ||
0.831219 | − | 0.555946i | \(-0.187644\pi\) | |||||||
\(654\) | −5.74955 | − | 11.0591i | −0.224825 | − | 0.432444i | ||||
\(655\) | 3.17761i | 0.124160i | ||||||||
\(656\) | − | 8.84450i | − | 0.345320i | ||||||
\(657\) | 15.9349 | − | 22.7062i | 0.621681 | − | 0.885853i | ||||
\(658\) | − | 1.45040i | − | 0.0565424i | ||||||
\(659\) | −35.0816 | −1.36658 | −0.683292 | − | 0.730146i | \(-0.739452\pi\) | ||||
−0.683292 | + | 0.730146i | \(0.739452\pi\) | |||||||
\(660\) | 2.68352 | + | 5.16167i | 0.104456 | + | 0.200918i | ||||
\(661\) | − | 13.5864i | − | 0.528450i | −0.964461 | − | 0.264225i | \(-0.914884\pi\) | ||
0.964461 | − | 0.264225i | \(-0.0851162\pi\) | |||||||
\(662\) | 0.146593i | 0.00569749i | ||||||||
\(663\) | −13.1128 | − | 25.2220i | −0.509257 | − | 0.979541i | ||||
\(664\) | − | 9.71029i | − | 0.376832i | ||||||
\(665\) | 1.00375 | 0.0389238 | ||||||||
\(666\) | 10.4115 | − | 14.8357i | 0.403437 | − | 0.574870i | ||||
\(667\) | 12.6102 | + | 11.6986i | 0.488269 | + | 0.452973i | ||||
\(668\) | − | 11.8429i | − | 0.458214i | ||||||
\(669\) | −14.1535 | − | 27.2239i | −0.547207 | − | 1.05254i | ||||
\(670\) | 13.0680 | 0.504860 | ||||||||
\(671\) | − | 13.9089i | − | 0.536947i | ||||||
\(672\) | 0.116036 | + | 0.223191i | 0.00447618 | + | 0.00860979i | ||||
\(673\) | −32.3448 | −1.24680 | −0.623400 | − | 0.781903i | \(-0.714249\pi\) | ||||
−0.623400 | + | 0.781903i | \(0.714249\pi\) | |||||||
\(674\) | −24.5559 | −0.945856 | ||||||||
\(675\) | 5.15061 | + | 0.686420i | 0.198247 | + | 0.0264203i | ||||
\(676\) | 4.23323 | 0.162816 | ||||||||
\(677\) | −17.2030 | −0.661164 | −0.330582 | − | 0.943777i | \(-0.607245\pi\) | ||||
−0.330582 | + | 0.943777i | \(0.607245\pi\) | |||||||
\(678\) | 20.2209 | − | 10.5127i | 0.776579 | − | 0.403739i | ||||
\(679\) | 1.68613 | 0.0647076 | ||||||||
\(680\) | 5.54307i | 0.212567i | ||||||||
\(681\) | 2.97416 | + | 5.72071i | 0.113970 | + | 0.219218i | ||||
\(682\) | − | 35.6493i | − | 1.36508i | ||||||
\(683\) | 7.02091i | 0.268648i | 0.990937 | + | 0.134324i | \(0.0428862\pi\) | ||||
−0.990937 | + | 0.134324i | \(0.957114\pi\) | |||||||
\(684\) | 16.9715 | + | 11.9104i | 0.648922 | + | 0.455406i | ||||
\(685\) | −19.0473 | −0.727760 | ||||||||
\(686\) | −2.03021 | −0.0775138 | ||||||||
\(687\) | −7.05470 | + | 3.66770i | −0.269154 | + | 0.139931i | ||||
\(688\) | 8.40616i | 0.320482i | ||||||||
\(689\) | −11.3576 | −0.432689 | ||||||||
\(690\) | 2.20347 | − | 8.00904i | 0.0838848 | − | 0.304899i | ||||
\(691\) | −42.5068 | −1.61703 | −0.808517 | − | 0.588473i | \(-0.799729\pi\) | ||||
−0.808517 | + | 0.588473i | \(0.799729\pi\) | |||||||
\(692\) | − | 9.94482i | − | 0.378045i | ||||||
\(693\) | 1.19788 | + | 0.840655i | 0.0455036 | + | 0.0319338i | ||||
\(694\) | −9.62040 | −0.365185 | ||||||||
\(695\) | −10.1337 | −0.384394 | ||||||||
\(696\) | 2.86559 | + | 5.51188i | 0.108620 | + | 0.208927i | ||||
\(697\) | − | 49.0257i | − | 1.85698i | ||||||
\(698\) | 23.1850i | 0.877565i | ||||||||
\(699\) | 5.60985 | − | 2.91653i | 0.212184 | − | 0.110313i | ||||
\(700\) | − | 0.145234i | − | 0.00548933i | ||||||
\(701\) | 9.67785 | 0.365527 | 0.182764 | − | 0.983157i | \(-0.441496\pi\) | ||||
0.182764 | + | 0.983157i | \(0.441496\pi\) | |||||||
\(702\) | −2.03240 | + | 15.2503i | −0.0767081 | + | 0.575586i | ||||
\(703\) | −41.7543 | −1.57479 | ||||||||
\(704\) | 3.35877 | 0.126589 | ||||||||
\(705\) | −15.3472 | + | 7.97891i | −0.578008 | + | 0.300503i | ||||
\(706\) | −9.38131 | −0.353070 | ||||||||
\(707\) | −0.755900 | −0.0284286 | ||||||||
\(708\) | −12.1611 | + | 6.32246i | −0.457040 | + | 0.237613i | ||||
\(709\) | − | 11.1186i | − | 0.417569i | −0.977962 | − | 0.208784i | \(-0.933049\pi\) | ||
0.977962 | − | 0.208784i | \(-0.0669507\pi\) | |||||||
\(710\) | 1.26558 | 0.0474962 | ||||||||
\(711\) | 32.4507 | + | 22.7735i | 1.21700 | + | 0.854073i | ||||
\(712\) | 15.3774i | 0.576293i | ||||||||
\(713\) | −34.6191 | + | 37.3166i | −1.29650 | + | 1.39752i | ||||
\(714\) | 0.643195 | + | 1.23716i | 0.0240710 | + | 0.0462997i | ||||
\(715\) | 9.94490 | 0.371918 | ||||||||
\(716\) | − | 3.37701i | − | 0.126205i | ||||||
\(717\) | 3.42876 | − | 1.78259i | 0.128049 | − | 0.0665721i | ||||
\(718\) | 13.9686i | 0.521303i | ||||||||
\(719\) | − | 6.75338i | − | 0.251859i | −0.992039 | − | 0.125929i | \(-0.959809\pi\) | ||
0.992039 | − | 0.125929i | \(-0.0401913\pi\) | |||||||
\(720\) | 1.72333 | − | 2.45563i | 0.0642248 | − | 0.0915160i | ||||
\(721\) | 1.26153 | 0.0469817 | ||||||||
\(722\) | − | 28.7656i | − | 1.07054i | ||||||
\(723\) | −22.7480 | + | 11.8266i | −0.846008 | + | 0.439834i | ||||
\(724\) | − | 5.28230i | − | 0.196315i | ||||||
\(725\) | − | 3.58666i | − | 0.133205i | ||||||
\(726\) | 0.432381 | − | 0.224792i | 0.0160472 | − | 0.00834283i | ||||
\(727\) | 20.3417i | 0.754432i | 0.926125 | + | 0.377216i | \(0.123119\pi\) | ||||
−0.926125 | + | 0.377216i | \(0.876881\pi\) | |||||||
\(728\) | 0.430019 | 0.0159376 | ||||||||
\(729\) | 26.0577 | + | 7.07097i | 0.965098 | + | 0.261888i | ||||
\(730\) | 9.24658i | 0.342231i | ||||||||
\(731\) | 46.5959i | 1.72341i | ||||||||
\(732\) | −6.36387 | + | 3.30854i | −0.235215 | + | 0.122287i | ||||
\(733\) | 38.8545i | 1.43512i | 0.696496 | + | 0.717561i | \(0.254742\pi\) | ||||
−0.696496 | + | 0.717561i | \(0.745258\pi\) | |||||||
\(734\) | −11.2257 | −0.414347 | ||||||||
\(735\) | 5.57585 | + | 10.7250i | 0.205668 | + | 0.395597i | ||||
\(736\) | −3.51586 | − | 3.26171i | −0.129596 | − | 0.120228i | ||||
\(737\) | − | 43.8923i | − | 1.61680i | ||||||
\(738\) | −15.2420 | + | 21.7188i | −0.561066 | + | 0.799481i | ||||
\(739\) | 1.32758 | 0.0488359 | 0.0244179 | − | 0.999702i | \(-0.492227\pi\) | ||||
0.0244179 | + | 0.999702i | \(0.492227\pi\) | |||||||
\(740\) | 6.04149i | 0.222090i | ||||||||
\(741\) | 31.4475 | − | 16.3494i | 1.15525 | − | 0.600610i | ||||
\(742\) | 0.557101 | 0.0204518 | ||||||||
\(743\) | 6.50411 | 0.238613 | 0.119306 | − | 0.992857i | \(-0.461933\pi\) | ||||
0.119306 | + | 0.992857i | \(0.461933\pi\) | |||||||
\(744\) | −16.3110 | + | 8.47998i | −0.597990 | + | 0.310891i | ||||
\(745\) | −19.7755 | −0.724520 | ||||||||
\(746\) | −6.04006 | −0.221142 | ||||||||
\(747\) | −16.7340 | + | 23.8449i | −0.612267 | + | 0.872439i | ||||
\(748\) | 18.6179 | 0.680738 | ||||||||
\(749\) | − | 1.61885i | − | 0.0591513i | ||||||
\(750\) | −1.53677 | + | 0.798958i | −0.0561150 | + | 0.0291738i | ||||
\(751\) | − | 0.826257i | − | 0.0301506i | −0.999886 | − | 0.0150753i | \(-0.995201\pi\) | ||
0.999886 | − | 0.0150753i | \(-0.00479879\pi\) | |||||||
\(752\) | 9.98664i | 0.364175i | ||||||||
\(753\) | 11.0750 | + | 21.3024i | 0.403595 | + | 0.776303i | ||||
\(754\) | 10.6196 | 0.386745 | ||||||||
\(755\) | 9.13517 | 0.332463 | ||||||||
\(756\) | 0.0996915 | − | 0.748044i | 0.00362574 | − | 0.0272061i | ||||
\(757\) | − | 38.9797i | − | 1.41674i | −0.705842 | − | 0.708370i | \(-0.749431\pi\) | ||
0.705842 | − | 0.708370i | \(-0.250569\pi\) | |||||||
\(758\) | 6.58693 | 0.239248 | ||||||||
\(759\) | −26.9005 | − | 7.40097i | −0.976428 | − | 0.268638i | ||||
\(760\) | −6.91126 | −0.250698 | ||||||||
\(761\) | 24.3111i | 0.881276i | 0.897685 | + | 0.440638i | \(0.145248\pi\) | ||||
−0.897685 | + | 0.440638i | \(0.854752\pi\) | |||||||
\(762\) | −21.2998 | + | 11.0736i | −0.771610 | + | 0.401156i | ||||
\(763\) | 1.04515 | 0.0378369 | ||||||||
\(764\) | 22.1062 | 0.799775 | ||||||||
\(765\) | 9.55255 | − | 13.6117i | 0.345373 | − | 0.492133i | ||||
\(766\) | − | 25.9655i | − | 0.938171i | ||||||
\(767\) | 23.4305i | 0.846027i | ||||||||
\(768\) | −0.798958 | − | 1.53677i | −0.0288299 | − | 0.0554535i | ||||
\(769\) | − | 32.2264i | − | 1.16211i | −0.813863 | − | 0.581057i | \(-0.802639\pi\) | ||
0.813863 | − | 0.581057i | \(-0.197361\pi\) | |||||||
\(770\) | −0.487808 | −0.0175794 | ||||||||
\(771\) | 2.87311 | − | 1.49371i | 0.103472 | − | 0.0537947i | ||||
\(772\) | −5.62469 | −0.202437 | ||||||||
\(773\) | 2.00243 | 0.0720223 | 0.0360111 | − | 0.999351i | \(-0.488535\pi\) | ||||
0.0360111 | + | 0.999351i | \(0.488535\pi\) | |||||||
\(774\) | 14.4866 | − | 20.6424i | 0.520710 | − | 0.741977i | ||||
\(775\) | 10.6138 | 0.381259 | ||||||||
\(776\) | −11.6097 | −0.416765 | ||||||||
\(777\) | 0.701029 | + | 1.34841i | 0.0251493 | + | 0.0483739i | ||||
\(778\) | 25.9332i | 0.929750i | ||||||||
\(779\) | 61.1267 | 2.19009 | ||||||||
\(780\) | −2.36561 | − | 4.55019i | −0.0847026 | − | 0.162923i | ||||
\(781\) | − | 4.25078i | − | 0.152105i | ||||||
\(782\) | −19.4887 | − | 18.0799i | −0.696913 | − | 0.646535i | ||||
\(783\) | 2.46196 | − | 18.4735i | 0.0879831 | − | 0.660189i | ||||
\(784\) | 6.97891 | 0.249247 | ||||||||
\(785\) | − | 10.3178i | − | 0.368259i | ||||||
\(786\) | −2.53878 | − | 4.88326i | −0.0905552 | − | 0.174180i | ||||
\(787\) | − | 40.4309i | − | 1.44121i | −0.693347 | − | 0.720603i | \(-0.743865\pi\) | ||
0.693347 | − | 0.720603i | \(-0.256135\pi\) | |||||||
\(788\) | 4.97721i | 0.177306i | ||||||||
\(789\) | −17.0026 | − | 32.7040i | −0.605309 | − | 1.16429i | ||||
\(790\) | −13.2148 | −0.470162 | ||||||||
\(791\) | 1.91099i | 0.0679472i | ||||||||
\(792\) | −8.24791 | − | 5.78828i | −0.293077 | − | 0.205678i | ||||
\(793\) | 12.2612i | 0.435407i | ||||||||
\(794\) | 11.2187i | 0.398136i | ||||||||
\(795\) | −3.06471 | − | 5.89488i | −0.108694 | − | 0.209070i | ||||
\(796\) | − | 5.07219i | − | 0.179779i | ||||||
\(797\) | 12.8995 | 0.456924 | 0.228462 | − | 0.973553i | \(-0.426630\pi\) | ||||
0.228462 | + | 0.973553i | \(0.426630\pi\) | |||||||
\(798\) | −1.54253 | + | 0.801954i | −0.0546051 | + | 0.0283889i | ||||
\(799\) | 55.3566i | 1.95838i | ||||||||
\(800\) | 1.00000i | 0.0353553i | ||||||||
\(801\) | 26.5004 | − | 37.7613i | 0.936345 | − | 1.33423i | ||||
\(802\) | 16.0468i | 0.566631i | ||||||||
\(803\) | 31.0572 | 1.09598 | ||||||||
\(804\) | −20.0825 | + | 10.4408i | −0.708254 | + | 0.368217i | ||||
\(805\) | 0.510622 | + | 0.473711i | 0.0179971 | + | 0.0166961i | ||||
\(806\) | 31.4261i | 1.10694i | ||||||||
\(807\) | 33.7815 | − | 17.5628i | 1.18917 | − | 0.618241i | ||||
\(808\) | 5.20471 | 0.183101 | ||||||||
\(809\) | − | 8.14490i | − | 0.286359i | −0.989697 | − | 0.143180i | \(-0.954267\pi\) | ||
0.989697 | − | 0.143180i | \(-0.0457327\pi\) | |||||||
\(810\) | −8.46374 | + | 3.06025i | −0.297385 | + | 0.107526i | ||||
\(811\) | 18.2134 | 0.639559 | 0.319779 | − | 0.947492i | \(-0.396391\pi\) | ||||
0.319779 | + | 0.947492i | \(0.396391\pi\) | |||||||
\(812\) | −0.520905 | −0.0182802 | ||||||||
\(813\) | −15.0983 | − | 29.0411i | −0.529521 | − | 1.01852i | ||||
\(814\) | 20.2920 | 0.711234 | ||||||||
\(815\) | −11.8046 | −0.413497 | ||||||||
\(816\) | −4.42868 | − | 8.51843i | −0.155035 | − | 0.298205i | ||||
\(817\) | −58.0972 | −2.03256 | ||||||||
\(818\) | − | 25.0421i | − | 0.875577i | ||||||
\(819\) | −1.05597 | − | 0.741066i | −0.0368985 | − | 0.0258949i | ||||
\(820\) | − | 8.84450i | − | 0.308863i | ||||||
\(821\) | − | 3.90097i | − | 0.136145i | −0.997680 | − | 0.0680724i | \(-0.978315\pi\) | ||
0.997680 | − | 0.0680724i | \(-0.0216849\pi\) | |||||||
\(822\) | 29.2714 | − | 15.2180i | 1.02096 | − | 0.530789i | ||||
\(823\) | −1.35194 | −0.0471256 | −0.0235628 | − | 0.999722i | \(-0.507501\pi\) | ||||
−0.0235628 | + | 0.999722i | \(0.507501\pi\) | |||||||
\(824\) | −8.68617 | −0.302597 | ||||||||
\(825\) | 2.68352 | + | 5.16167i | 0.0934281 | + | 0.179706i | ||||
\(826\) | − | 1.14929i | − | 0.0399890i | ||||||
\(827\) | −30.6202 | −1.06477 | −0.532385 | − | 0.846502i | \(-0.678704\pi\) | ||||
−0.532385 | + | 0.846502i | \(0.678704\pi\) | |||||||
\(828\) | 3.01265 | + | 14.0685i | 0.104697 | + | 0.488916i | ||||
\(829\) | 5.29692 | 0.183970 | 0.0919848 | − | 0.995760i | \(-0.470679\pi\) | ||||
0.0919848 | + | 0.995760i | \(0.470679\pi\) | |||||||
\(830\) | − | 9.71029i | − | 0.337049i | ||||||
\(831\) | 6.60253 | + | 12.6998i | 0.229039 | + | 0.440550i | ||||
\(832\) | −2.96087 | −0.102650 | ||||||||
\(833\) | 38.6846 | 1.34034 | ||||||||
\(834\) | 15.5732 | − | 8.09642i | 0.539256 | − | 0.280356i | ||||
\(835\) | − | 11.8429i | − | 0.409839i | ||||||
\(836\) | 23.2134i | 0.802851i | ||||||||
\(837\) | 54.6676 | + | 7.28553i | 1.88959 | + | 0.251825i | ||||
\(838\) | 0.170219i | 0.00588013i | ||||||||
\(839\) | 18.2989 | 0.631749 | 0.315875 | − | 0.948801i | \(-0.397702\pi\) | ||||
0.315875 | + | 0.948801i | \(0.397702\pi\) | |||||||
\(840\) | 0.116036 | + | 0.223191i | 0.00400362 | + | 0.00770083i | ||||
\(841\) | 16.1359 | 0.556409 | ||||||||
\(842\) | −3.35189 | −0.115514 | ||||||||
\(843\) | 10.7074 | + | 20.5953i | 0.368781 | + | 0.709339i | ||||
\(844\) | 9.58459 | 0.329915 | ||||||||
\(845\) | 4.23323 | 0.145627 | ||||||||
\(846\) | 17.2103 | − | 24.5235i | 0.591702 | − | 0.843136i | ||||
\(847\) | 0.0408626i | 0.00140406i | ||||||||
\(848\) | −3.83589 | −0.131725 | ||||||||
\(849\) | −46.4953 | + | 24.1726i | −1.59572 | + | 0.829603i | ||||
\(850\) | 5.54307i | 0.190126i | ||||||||
\(851\) | −21.2410 | − | 19.7056i | −0.728133 | − | 0.675498i | ||||
\(852\) | −1.94490 | + | 1.01114i | −0.0666312 | + | 0.0346411i | ||||
\(853\) | −15.6345 | −0.535315 | −0.267658 | − | 0.963514i | \(-0.586250\pi\) | ||||
−0.267658 | + | 0.963514i | \(0.586250\pi\) | |||||||
\(854\) | − | 0.601423i | − | 0.0205803i | ||||||
\(855\) | 16.9715 | + | 11.9104i | 0.580414 | + | 0.407327i | ||||
\(856\) | 11.1465i | 0.380978i | ||||||||
\(857\) | 41.9165i | 1.43184i | 0.698182 | + | 0.715920i | \(0.253993\pi\) | ||||
−0.698182 | + | 0.715920i | \(0.746007\pi\) | |||||||
\(858\) | −15.2830 | + | 7.94556i | −0.521754 | + | 0.271257i | ||||
\(859\) | −2.84869 | −0.0971961 | −0.0485981 | − | 0.998818i | \(-0.515475\pi\) | ||||
−0.0485981 | + | 0.998818i | \(0.515475\pi\) | |||||||
\(860\) | 8.40616i | 0.286648i | ||||||||
\(861\) | −1.02628 | − | 1.97402i | −0.0349755 | − | 0.0672743i | ||||
\(862\) | 21.5603i | 0.734347i | ||||||||
\(863\) | 2.10886i | 0.0717864i | 0.999356 | + | 0.0358932i | \(0.0114276\pi\) | ||||
−0.999356 | + | 0.0358932i | \(0.988572\pi\) | |||||||
\(864\) | −0.686420 | + | 5.15061i | −0.0233525 | + | 0.175227i | ||||
\(865\) | − | 9.94482i | − | 0.338134i | ||||||
\(866\) | 25.3255 | 0.860596 | ||||||||
\(867\) | −10.9662 | − | 21.0931i | −0.372431 | − | 0.716360i | ||||
\(868\) | − | 1.54148i | − | 0.0523214i | ||||||
\(869\) | 44.3855i | 1.50568i | ||||||||
\(870\) | 2.86559 | + | 5.51188i | 0.0971526 | + | 0.186870i | ||||
\(871\) | 38.6926i | 1.31105i | ||||||||
\(872\) | −7.19631 | −0.243698 | ||||||||
\(873\) | 28.5092 | + | 20.0074i | 0.964891 | + | 0.677148i | ||||
\(874\) | 22.5425 | − | 24.2990i | 0.762512 | − | 0.821927i | ||||
\(875\) | − | 0.145234i | − | 0.00490980i | ||||||
\(876\) | −7.38763 | − | 14.2099i | −0.249605 | − | 0.480107i | ||||
\(877\) | −14.4796 | −0.488940 | −0.244470 | − | 0.969657i | \(-0.578614\pi\) | ||||
−0.244470 | + | 0.969657i | \(0.578614\pi\) | |||||||
\(878\) | − | 0.917239i | − | 0.0309553i | ||||||
\(879\) | −5.67177 | − | 10.9095i | −0.191304 | − | 0.367967i | ||||
\(880\) | 3.35877 | 0.113224 | ||||||||
\(881\) | 6.26949 | 0.211225 | 0.105612 | − | 0.994407i | \(-0.466320\pi\) | ||||
0.105612 | + | 0.994407i | \(0.466320\pi\) | |||||||
\(882\) | −17.1376 | − | 12.0270i | −0.577054 | − | 0.404969i | ||||
\(883\) | 22.7330 | 0.765026 | 0.382513 | − | 0.923950i | \(-0.375059\pi\) | ||||
0.382513 | + | 0.923950i | \(0.375059\pi\) | |||||||
\(884\) | −16.4123 | −0.552006 | ||||||||
\(885\) | −12.1611 | + | 6.32246i | −0.408789 | + | 0.212527i | ||||
\(886\) | 4.08632 | 0.137283 | ||||||||
\(887\) | − | 29.2878i | − | 0.983389i | −0.870768 | − | 0.491694i | \(-0.836378\pi\) | ||
0.870768 | − | 0.491694i | \(-0.163622\pi\) | |||||||
\(888\) | −4.82690 | − | 9.28438i | −0.161980 | − | 0.311564i | ||||
\(889\) | − | 2.01296i | − | 0.0675124i | ||||||
\(890\) | 15.3774i | 0.515452i | ||||||||
\(891\) | 10.2787 | + | 28.4278i | 0.344349 | + | 0.952366i | ||||
\(892\) | −17.7150 | −0.593142 | ||||||||
\(893\) | −69.0203 | −2.30968 | ||||||||
\(894\) | 30.3905 | − | 15.7998i | 1.01641 | − | 0.528425i | ||||
\(895\) | − | 3.37701i | − | 0.112881i | ||||||
\(896\) | 0.145234 | 0.00485193 | ||||||||
\(897\) | 23.7138 | + | 6.52420i | 0.791779 | + | 0.217837i | ||||
\(898\) | −5.31513 | −0.177368 | ||||||||
\(899\) | − | 38.0681i | − | 1.26964i | ||||||
\(900\) | 1.72333 | − | 2.45563i | 0.0574444 | − | 0.0818544i | ||||
\(901\) | −21.2626 | −0.708359 | ||||||||
\(902\) | −29.7067 | −0.989124 | ||||||||
\(903\) | 0.975416 | + | 1.87618i | 0.0324598 | + | 0.0624355i | ||||
\(904\) | − | 13.1580i | − | 0.437630i | ||||||
\(905\) | − | 5.28230i | − | 0.175590i | ||||||
\(906\) | −14.0387 | + | 7.29861i | −0.466403 | + | 0.242480i | ||||
\(907\) | 47.6557i | 1.58238i | 0.611569 | + | 0.791191i | \(0.290539\pi\) | ||||
−0.611569 | + | 0.791191i | \(0.709461\pi\) | |||||||
\(908\) | 3.72255 | 0.123537 | ||||||||
\(909\) | −12.7808 | − | 8.96944i | −0.423914 | − | 0.297498i | ||||
\(910\) | 0.430019 | 0.0142550 | ||||||||
\(911\) | −20.8392 | −0.690432 | −0.345216 | − | 0.938523i | \(-0.612194\pi\) | ||||
−0.345216 | + | 0.938523i | \(0.612194\pi\) | |||||||
\(912\) | 10.6210 | − | 5.52181i | 0.351697 | − | 0.182845i | ||||
\(913\) | −32.6146 | −1.07939 | ||||||||
\(914\) | −17.8678 | −0.591016 | ||||||||
\(915\) | −6.36387 | + | 3.30854i | −0.210383 | + | 0.109377i | ||||
\(916\) | 4.59060i | 0.151678i | ||||||||
\(917\) | 0.461497 | 0.0152400 | ||||||||
\(918\) | −3.80487 | + | 28.5502i | −0.125580 | + | 0.942297i | ||||
\(919\) | − | 39.5739i | − | 1.30542i | −0.757607 | − | 0.652711i | \(-0.773632\pi\) | ||
0.757607 | − | 0.652711i | \(-0.226368\pi\) | |||||||
\(920\) | −3.51586 | − | 3.26171i | −0.115914 | − | 0.107535i | ||||
\(921\) | 22.0741 | + | 42.4588i | 0.727366 | + | 1.39907i | ||||
\(922\) | 0.958482 | 0.0315659 | ||||||||
\(923\) | 3.74721i | 0.123341i | ||||||||
\(924\) | 0.749649 | − | 0.389738i | 0.0246616 | − | 0.0128214i | ||||
\(925\) | 6.04149i | 0.198643i | ||||||||
\(926\) | 41.6838i | 1.36982i | ||||||||
\(927\) | 21.3300 | + | 14.9692i | 0.700570 | + | 0.491652i | ||||
\(928\) | 3.58666 | 0.117738 | ||||||||
\(929\) | 43.9606i | 1.44230i | 0.692779 | + | 0.721150i | \(0.256386\pi\) | ||||
−0.692779 | + | 0.721150i | \(0.743614\pi\) | |||||||
\(930\) | −16.3110 | + | 8.47998i | −0.534858 | + | 0.278070i | ||||
\(931\) | 48.2331i | 1.58077i | ||||||||
\(932\) | − | 3.65041i | − | 0.119573i | ||||||
\(933\) | −46.3289 | + | 24.0861i | −1.51674 | + | 0.788544i | ||||
\(934\) | 7.07758i | 0.231585i | ||||||||
\(935\) | 18.6179 | 0.608871 | ||||||||
\(936\) | 7.27082 | + | 5.10257i | 0.237654 | + | 0.166783i | ||||
\(937\) | − | 16.3199i | − | 0.533149i | −0.963814 | − | 0.266575i | \(-0.914108\pi\) | ||
0.963814 | − | 0.266575i | \(-0.0858919\pi\) | |||||||
\(938\) | − | 1.89791i | − | 0.0619690i | ||||||
\(939\) | 8.22265 | − | 4.27491i | 0.268336 | − | 0.139506i | ||||
\(940\) | 9.98664i | 0.325728i | ||||||||
\(941\) | 50.7684 | 1.65500 | 0.827502 | − | 0.561463i | \(-0.189761\pi\) | ||||
0.827502 | + | 0.561463i | \(0.189761\pi\) | |||||||
\(942\) | 8.24350 | + | 15.8561i | 0.268588 | + | 0.516620i | ||||
\(943\) | 31.0960 | + | 28.8482i | 1.01263 | + | 0.939425i | ||||
\(944\) | 7.91338i | 0.257559i | ||||||||
\(945\) | 0.0996915 | − | 0.748044i | 0.00324296 | − | 0.0243339i | ||||
\(946\) | 28.2344 | 0.917979 | ||||||||
\(947\) | − | 24.6666i | − | 0.801557i | −0.916175 | − | 0.400778i | \(-0.868740\pi\) | ||
0.916175 | − | 0.400778i | \(-0.131260\pi\) | |||||||
\(948\) | 20.3081 | − | 10.5581i | 0.659578 | − | 0.342910i | ||||
\(949\) | −27.3780 | −0.888726 | ||||||||
\(950\) | −6.91126 | −0.224231 | ||||||||
\(951\) | 31.6368 | − | 16.4478i | 1.02589 | − | 0.533356i | ||||
\(952\) | 0.805042 | 0.0260916 | ||||||||
\(953\) | −42.3347 | −1.37135 | −0.685677 | − | 0.727906i | \(-0.740494\pi\) | ||||
−0.685677 | + | 0.727906i | \(0.740494\pi\) | |||||||
\(954\) | 9.41953 | + | 6.61051i | 0.304968 | + | 0.214023i | ||||
\(955\) | 22.1062 | 0.715341 | ||||||||
\(956\) | − | 2.23114i | − | 0.0721603i | ||||||
\(957\) | 18.5131 | − | 9.62487i | 0.598445 | − | 0.311128i | ||||
\(958\) | − | 12.3246i | − | 0.398189i | ||||||
\(959\) | 2.76632i | 0.0893290i | ||||||||
\(960\) | −0.798958 | − | 1.53677i | −0.0257863 | − | 0.0495991i | ||||
\(961\) | 81.6528 | 2.63396 | ||||||||
\(962\) | −17.8881 | −0.576735 | ||||||||
\(963\) | 19.2091 | − | 27.3716i | 0.619003 | − | 0.882038i | ||||
\(964\) | 14.8025i | 0.476756i | ||||||||
\(965\) | −5.62469 | −0.181065 | ||||||||
\(966\) | −1.16318 | − | 0.320019i | −0.0374248 | − | 0.0102964i | ||||
\(967\) | 31.0043 | 0.997030 | 0.498515 | − | 0.866881i | \(-0.333879\pi\) | ||||
0.498515 | + | 0.866881i | \(0.333879\pi\) | |||||||
\(968\) | − | 0.281357i | − | 0.00904316i | ||||||
\(969\) | 58.8731 | − | 30.6078i | 1.89128 | − | 0.983263i | ||||
\(970\) | −11.6097 | −0.372766 | ||||||||
\(971\) | −20.1792 | −0.647582 | −0.323791 | − | 0.946129i | \(-0.604958\pi\) | ||||
−0.323791 | + | 0.946129i | \(0.604958\pi\) | |||||||
\(972\) | 10.5618 | − | 11.4651i | 0.338770 | − | 0.367743i | ||||
\(973\) | 1.47176i | 0.0471825i | ||||||||
\(974\) | 7.63905i | 0.244771i | ||||||||
\(975\) | −2.36561 | − | 4.55019i | −0.0757603 | − | 0.145723i | ||||
\(976\) | 4.14107i | 0.132552i | ||||||||
\(977\) | 16.0570 | 0.513707 | 0.256854 | − | 0.966450i | \(-0.417314\pi\) | ||||
0.256854 | + | 0.966450i | \(0.417314\pi\) | |||||||
\(978\) | 18.1410 | − | 9.43137i | 0.580084 | − | 0.301582i | ||||
\(979\) | 51.6492 | 1.65072 | ||||||||
\(980\) | 6.97891 | 0.222933 | ||||||||
\(981\) | 17.6715 | + | 12.4016i | 0.564207 | + | 0.395954i | ||||
\(982\) | 30.8151 | 0.983350 | ||||||||
\(983\) | −34.9165 | −1.11366 | −0.556831 | − | 0.830626i | \(-0.687983\pi\) | ||||
−0.556831 | + | 0.830626i | \(0.687983\pi\) | |||||||
\(984\) | 7.06638 | + | 13.5920i | 0.225268 | + | 0.433296i | ||||
\(985\) | 4.97721i | 0.158587i | ||||||||
\(986\) | 19.8811 | 0.633143 | ||||||||
\(987\) | 1.15881 | + | 2.22893i | 0.0368853 | + | 0.0709477i | ||||
\(988\) | − | 20.4634i | − | 0.651027i | ||||||
\(989\) | −29.5549 | − | 27.4184i | −0.939791 | − | 0.871856i | ||||
\(990\) | −8.24791 | − | 5.78828i | −0.262136 | − | 0.183964i | ||||
\(991\) | −43.4923 | −1.38158 | −0.690789 | − | 0.723056i | \(-0.742737\pi\) | ||||
−0.690789 | + | 0.723056i | \(0.742737\pi\) | |||||||
\(992\) | 10.6138i | 0.336988i | ||||||||
\(993\) | −0.117122 | − | 0.225280i | −0.00371674 | − | 0.00714903i | ||||
\(994\) | − | 0.183805i | − | 0.00582993i | ||||||
\(995\) | − | 5.07219i | − | 0.160799i | ||||||
\(996\) | 7.75811 | + | 14.9225i | 0.245825 | + | 0.472837i | ||||
\(997\) | 10.9446 | 0.346619 | 0.173309 | − | 0.984867i | \(-0.444554\pi\) | ||||
0.173309 | + | 0.984867i | \(0.444554\pi\) | |||||||
\(998\) | − | 26.4668i | − | 0.837792i | ||||||
\(999\) | −4.14700 | + | 31.1174i | −0.131205 | + | 0.984510i |
(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 | 690.2.e.a.551.11 | yes | 16 | |
3.2 | odd | 2 | 690.2.e.b.551.3 | yes | 16 | ||
23.22 | odd | 2 | 690.2.e.b.551.11 | yes | 16 | ||
69.68 | even | 2 | inner | 690.2.e.a.551.3 | ✓ | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
690.2.e.a.551.3 | ✓ | 16 | 69.68 | even | 2 | inner | |
690.2.e.a.551.11 | yes | 16 | 1.1 | even | 1 | trivial | |
690.2.e.b.551.3 | yes | 16 | 3.2 | odd | 2 | ||
690.2.e.b.551.11 | yes | 16 | 23.22 | odd | 2 |