Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [930,2,Mod(371,930)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(930, 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("930.371");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 930.h (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: | \(7.42608738798\) |
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: | \( x^{16} - 4x^{14} + 6x^{12} + 36x^{10} - 142x^{8} + 324x^{6} + 486x^{4} - 2916x^{2} + 6561 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{31}]\) |
Coefficient ring index: | \( 2^{5} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 371.16 | ||
Root | \(-0.206738 + 1.71967i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 930.371 |
Dual form | 930.2.h.d.371.8 |
$q$-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 \(\left(\mathbb{Z}/930\mathbb{Z}\right)^\times\).
\(n\) | \(187\) | \(311\) | \(871\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) |
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 | ||||||||
\(3\) | 1.71967 | − | 0.206738i | 0.992851 | − | 0.119360i | ||||
\(4\) | −1.00000 | −0.500000 | ||||||||
\(5\) | − | 1.00000i | − | 0.447214i | ||||||
\(6\) | 0.206738 | + | 1.71967i | 0.0844003 | + | 0.702052i | ||||
\(7\) | −1.18164 | −0.446619 | −0.223309 | − | 0.974748i | \(-0.571686\pi\) | ||||
−0.223309 | + | 0.974748i | \(0.571686\pi\) | |||||||
\(8\) | − | 1.00000i | − | 0.353553i | ||||||
\(9\) | 2.91452 | − | 0.711040i | 0.971506 | − | 0.237013i | ||||
\(10\) | 1.00000 | 0.316228 | ||||||||
\(11\) | −1.57649 | −0.475330 | −0.237665 | − | 0.971347i | \(-0.576382\pi\) | ||||
−0.237665 | + | 0.971347i | \(0.576382\pi\) | |||||||
\(12\) | −1.71967 | + | 0.206738i | −0.496426 | + | 0.0596800i | ||||
\(13\) | − | 3.43934i | − | 0.953900i | −0.878930 | − | 0.476950i | \(-0.841742\pi\) | ||
0.878930 | − | 0.476950i | \(-0.158258\pi\) | |||||||
\(14\) | − | 1.18164i | − | 0.315807i | ||||||
\(15\) | −0.206738 | − | 1.71967i | −0.0533794 | − | 0.444016i | ||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 4.55264 | 1.10418 | 0.552089 | − | 0.833785i | \(-0.313831\pi\) | ||||
0.552089 | + | 0.833785i | \(0.313831\pi\) | |||||||
\(18\) | 0.711040 | + | 2.91452i | 0.167594 | + | 0.686959i | ||||
\(19\) | 6.64740 | 1.52502 | 0.762509 | − | 0.646978i | \(-0.223967\pi\) | ||||
0.762509 | + | 0.646978i | \(0.223967\pi\) | |||||||
\(20\) | 1.00000i | 0.223607i | ||||||||
\(21\) | −2.03203 | + | 0.244290i | −0.443426 | + | 0.0533084i | ||||
\(22\) | − | 1.57649i | − | 0.336109i | ||||||
\(23\) | 1.16301 | 0.242505 | 0.121253 | − | 0.992622i | \(-0.461309\pi\) | ||||
0.121253 | + | 0.992622i | \(0.461309\pi\) | |||||||
\(24\) | −0.206738 | − | 1.71967i | −0.0422001 | − | 0.351026i | ||||
\(25\) | −1.00000 | −0.200000 | ||||||||
\(26\) | 3.43934 | 0.674509 | ||||||||
\(27\) | 4.86501 | − | 1.82529i | 0.936271 | − | 0.351278i | ||||
\(28\) | 1.18164 | 0.223309 | ||||||||
\(29\) | 8.20323 | 1.52330 | 0.761651 | − | 0.647987i | \(-0.224389\pi\) | ||||
0.761651 | + | 0.647987i | \(0.224389\pi\) | |||||||
\(30\) | 1.71967 | − | 0.206738i | 0.313967 | − | 0.0377450i | ||||
\(31\) | −5.56676 | − | 0.105626i | −0.999820 | − | 0.0189710i | ||||
\(32\) | 1.00000i | 0.176777i | ||||||||
\(33\) | −2.71104 | + | 0.325920i | −0.471932 | + | 0.0567354i | ||||
\(34\) | 4.55264i | 0.780772i | ||||||||
\(35\) | 1.18164i | 0.199734i | ||||||||
\(36\) | −2.91452 | + | 0.711040i | −0.485753 | + | 0.118507i | ||||
\(37\) | − | 9.82943i | − | 1.61595i | −0.589218 | − | 0.807974i | \(-0.700564\pi\) | ||
0.589218 | − | 0.807974i | \(-0.299436\pi\) | |||||||
\(38\) | 6.64740i | 1.07835i | ||||||||
\(39\) | −0.711040 | − | 5.91452i | −0.113858 | − | 0.947081i | ||||
\(40\) | −1.00000 | −0.158114 | ||||||||
\(41\) | 5.42208i | 0.846787i | 0.905946 | + | 0.423393i | \(0.139161\pi\) | ||||
−0.905946 | + | 0.423393i | \(0.860839\pi\) | |||||||
\(42\) | −0.244290 | − | 2.03203i | −0.0376947 | − | 0.313549i | ||||
\(43\) | 6.82897i | 1.04141i | 0.853737 | + | 0.520704i | \(0.174330\pi\) | ||||
−0.853737 | + | 0.520704i | \(0.825670\pi\) | |||||||
\(44\) | 1.57649 | 0.237665 | ||||||||
\(45\) | −0.711040 | − | 2.91452i | −0.105996 | − | 0.434471i | ||||
\(46\) | 1.16301i | 0.171477i | ||||||||
\(47\) | − | 1.46575i | − | 0.213802i | −0.994270 | − | 0.106901i | \(-0.965907\pi\) | ||
0.994270 | − | 0.106901i | \(-0.0340928\pi\) | |||||||
\(48\) | 1.71967 | − | 0.206738i | 0.248213 | − | 0.0298400i | ||||
\(49\) | −5.60372 | −0.800532 | ||||||||
\(50\) | − | 1.00000i | − | 0.141421i | ||||||
\(51\) | 7.82904 | − | 0.941203i | 1.09628 | − | 0.131795i | ||||
\(52\) | 3.43934i | 0.476950i | ||||||||
\(53\) | 7.16734 | 0.984509 | 0.492255 | − | 0.870451i | \(-0.336173\pi\) | ||||
0.492255 | + | 0.870451i | \(0.336173\pi\) | |||||||
\(54\) | 1.82529 | + | 4.86501i | 0.248391 | + | 0.662044i | ||||
\(55\) | 1.57649i | 0.212574i | ||||||||
\(56\) | 1.18164i | 0.157904i | ||||||||
\(57\) | 11.4313 | − | 1.37427i | 1.51412 | − | 0.182026i | ||||
\(58\) | 8.20323i | 1.07714i | ||||||||
\(59\) | − | 6.84416i | − | 0.891034i | −0.895273 | − | 0.445517i | \(-0.853020\pi\) | ||
0.895273 | − | 0.445517i | \(-0.146980\pi\) | |||||||
\(60\) | 0.206738 | + | 1.71967i | 0.0266897 | + | 0.222008i | ||||
\(61\) | − | 11.8448i | − | 1.51657i | −0.651923 | − | 0.758285i | \(-0.726037\pi\) | ||
0.651923 | − | 0.758285i | \(-0.273963\pi\) | |||||||
\(62\) | 0.105626 | − | 5.56676i | 0.0134145 | − | 0.706980i | ||||
\(63\) | −3.44392 | + | 0.840195i | −0.433893 | + | 0.105855i | ||||
\(64\) | −1.00000 | −0.125000 | ||||||||
\(65\) | −3.43934 | −0.426597 | ||||||||
\(66\) | −0.325920 | − | 2.71104i | −0.0401180 | − | 0.333706i | ||||
\(67\) | −13.6144 | −1.66326 | −0.831632 | − | 0.555327i | \(-0.812593\pi\) | ||||
−0.831632 | + | 0.555327i | \(0.812593\pi\) | |||||||
\(68\) | −4.55264 | −0.552089 | ||||||||
\(69\) | 2.00000 | − | 0.240439i | 0.240772 | − | 0.0289454i | ||||
\(70\) | −1.18164 | −0.141233 | ||||||||
\(71\) | 6.52980i | 0.774945i | 0.921881 | + | 0.387472i | \(0.126652\pi\) | ||||
−0.921881 | + | 0.387472i | \(0.873348\pi\) | |||||||
\(72\) | −0.711040 | − | 2.91452i | −0.0837969 | − | 0.343479i | ||||
\(73\) | 4.67746i | 0.547455i | 0.961807 | + | 0.273727i | \(0.0882566\pi\) | ||||
−0.961807 | + | 0.273727i | \(0.911743\pi\) | |||||||
\(74\) | 9.82943 | 1.14265 | ||||||||
\(75\) | −1.71967 | + | 0.206738i | −0.198570 | + | 0.0238720i | ||||
\(76\) | −6.64740 | −0.762509 | ||||||||
\(77\) | 1.86285 | 0.212291 | ||||||||
\(78\) | 5.91452 | − | 0.711040i | 0.669687 | − | 0.0805095i | ||||
\(79\) | 6.13816i | 0.690597i | 0.938493 | + | 0.345299i | \(0.112222\pi\) | ||||
−0.938493 | + | 0.345299i | \(0.887778\pi\) | |||||||
\(80\) | − | 1.00000i | − | 0.111803i | ||||||
\(81\) | 7.98884 | − | 4.14468i | 0.887649 | − | 0.460520i | ||||
\(82\) | −5.42208 | −0.598769 | ||||||||
\(83\) | 3.86184 | 0.423892 | 0.211946 | − | 0.977281i | \(-0.432020\pi\) | ||||
0.211946 | + | 0.977281i | \(0.432020\pi\) | |||||||
\(84\) | 2.03203 | − | 0.244290i | 0.221713 | − | 0.0266542i | ||||
\(85\) | − | 4.55264i | − | 0.493804i | ||||||
\(86\) | −6.82897 | −0.736386 | ||||||||
\(87\) | 14.1068 | − | 1.69592i | 1.51241 | − | 0.181821i | ||||
\(88\) | 1.57649i | 0.168054i | ||||||||
\(89\) | −10.2683 | −1.08844 | −0.544219 | − | 0.838943i | \(-0.683174\pi\) | ||||
−0.544219 | + | 0.838943i | \(0.683174\pi\) | |||||||
\(90\) | 2.91452 | − | 0.711040i | 0.307217 | − | 0.0749502i | ||||
\(91\) | 4.06406i | 0.426030i | ||||||||
\(92\) | −1.16301 | −0.121253 | ||||||||
\(93\) | −9.59482 | + | 0.969217i | −0.994937 | + | 0.100503i | ||||
\(94\) | 1.46575 | 0.151181 | ||||||||
\(95\) | − | 6.64740i | − | 0.682008i | ||||||
\(96\) | 0.206738 | + | 1.71967i | 0.0211001 | + | 0.175513i | ||||
\(97\) | 3.46575 | 0.351894 | 0.175947 | − | 0.984400i | \(-0.443701\pi\) | ||||
0.175947 | + | 0.984400i | \(0.443701\pi\) | |||||||
\(98\) | − | 5.60372i | − | 0.566061i | ||||||
\(99\) | −4.59471 | + | 1.12095i | −0.461786 | + | 0.112660i | ||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | 13.3740i | 1.33076i | 0.746505 | + | 0.665380i | \(0.231730\pi\) | ||||
−0.746505 | + | 0.665380i | \(0.768270\pi\) | |||||||
\(102\) | 0.941203 | + | 7.82904i | 0.0931930 | + | 0.775190i | ||||
\(103\) | −6.40696 | −0.631296 | −0.315648 | − | 0.948876i | \(-0.602222\pi\) | ||||
−0.315648 | + | 0.948876i | \(0.602222\pi\) | |||||||
\(104\) | −3.43934 | −0.337255 | ||||||||
\(105\) | 0.244290 | + | 2.03203i | 0.0238402 | + | 0.198306i | ||||
\(106\) | 7.16734i | 0.696153i | ||||||||
\(107\) | 9.49156i | 0.917584i | 0.888544 | + | 0.458792i | \(0.151718\pi\) | ||||
−0.888544 | + | 0.458792i | \(0.848282\pi\) | |||||||
\(108\) | −4.86501 | + | 1.82529i | −0.468136 | + | 0.175639i | ||||
\(109\) | −14.8139 | −1.41892 | −0.709458 | − | 0.704748i | \(-0.751060\pi\) | ||||
−0.709458 | + | 0.704748i | \(0.751060\pi\) | |||||||
\(110\) | −1.57649 | −0.150312 | ||||||||
\(111\) | −2.03211 | − | 16.9034i | −0.192880 | − | 1.60440i | ||||
\(112\) | −1.18164 | −0.111655 | ||||||||
\(113\) | 17.6839i | 1.66356i | 0.555106 | + | 0.831780i | \(0.312678\pi\) | ||||
−0.555106 | + | 0.831780i | \(0.687322\pi\) | |||||||
\(114\) | 1.37427 | + | 11.4313i | 0.128712 | + | 1.07064i | ||||
\(115\) | − | 1.16301i | − | 0.108452i | ||||||
\(116\) | −8.20323 | −0.761651 | ||||||||
\(117\) | −2.44551 | − | 10.0240i | −0.226087 | − | 0.926720i | ||||
\(118\) | 6.84416 | 0.630056 | ||||||||
\(119\) | −5.37959 | −0.493147 | ||||||||
\(120\) | −1.71967 | + | 0.206738i | −0.156984 | + | 0.0188725i | ||||
\(121\) | −8.51468 | −0.774062 | ||||||||
\(122\) | 11.8448 | 1.07238 | ||||||||
\(123\) | 1.12095 | + | 9.32418i | 0.101072 | + | 0.840733i | ||||
\(124\) | 5.56676 | + | 0.105626i | 0.499910 | + | 0.00948550i | ||||
\(125\) | 1.00000i | 0.0894427i | ||||||||
\(126\) | −0.840195 | − | 3.44392i | −0.0748505 | − | 0.306809i | ||||
\(127\) | − | 14.7956i | − | 1.31289i | −0.754373 | − | 0.656446i | \(-0.772059\pi\) | ||
0.754373 | − | 0.656446i | \(-0.227941\pi\) | |||||||
\(128\) | − | 1.00000i | − | 0.0883883i | ||||||
\(129\) | 1.41180 | + | 11.7436i | 0.124302 | + | 1.03396i | ||||
\(130\) | − | 3.43934i | − | 0.301650i | ||||||
\(131\) | − | 2.84416i | − | 0.248496i | −0.992251 | − | 0.124248i | \(-0.960348\pi\) | ||
0.992251 | − | 0.124248i | \(-0.0396518\pi\) | |||||||
\(132\) | 2.71104 | − | 0.325920i | 0.235966 | − | 0.0283677i | ||||
\(133\) | −7.85484 | −0.681101 | ||||||||
\(134\) | − | 13.6144i | − | 1.17611i | ||||||
\(135\) | −1.82529 | − | 4.86501i | −0.157096 | − | 0.418713i | ||||
\(136\) | − | 4.55264i | − | 0.390386i | ||||||
\(137\) | 5.52980 | 0.472443 | 0.236221 | − | 0.971699i | \(-0.424091\pi\) | ||||
0.236221 | + | 0.971699i | \(0.424091\pi\) | |||||||
\(138\) | 0.240439 | + | 2.00000i | 0.0204675 | + | 0.170251i | ||||
\(139\) | 21.6833i | 1.83915i | 0.392915 | + | 0.919575i | \(0.371467\pi\) | ||||
−0.392915 | + | 0.919575i | \(0.628533\pi\) | |||||||
\(140\) | − | 1.18164i | − | 0.0998670i | ||||||
\(141\) | −0.303027 | − | 2.52061i | −0.0255194 | − | 0.212274i | ||||
\(142\) | −6.52980 | −0.547969 | ||||||||
\(143\) | 5.42208i | 0.453417i | ||||||||
\(144\) | 2.91452 | − | 0.711040i | 0.242877 | − | 0.0592534i | ||||
\(145\) | − | 8.20323i | − | 0.681241i | ||||||
\(146\) | −4.67746 | −0.387109 | ||||||||
\(147\) | −9.63654 | + | 1.15850i | −0.794809 | + | 0.0955515i | ||||
\(148\) | 9.82943i | 0.807974i | ||||||||
\(149\) | − | 6.52980i | − | 0.534942i | −0.963566 | − | 0.267471i | \(-0.913812\pi\) | ||
0.963566 | − | 0.267471i | \(-0.0861880\pi\) | |||||||
\(150\) | −0.206738 | − | 1.71967i | −0.0168801 | − | 0.140410i | ||||
\(151\) | − | 9.72099i | − | 0.791083i | −0.918448 | − | 0.395541i | \(-0.870557\pi\) | ||
0.918448 | − | 0.395541i | \(-0.129443\pi\) | |||||||
\(152\) | − | 6.64740i | − | 0.539175i | ||||||
\(153\) | 13.2688 | − | 3.23711i | 1.07272 | − | 0.261705i | ||||
\(154\) | 1.86285i | 0.150112i | ||||||||
\(155\) | −0.105626 | + | 5.56676i | −0.00848409 | + | 0.447133i | ||||
\(156\) | 0.711040 | + | 5.91452i | 0.0569288 | + | 0.473541i | ||||
\(157\) | 22.0161 | 1.75708 | 0.878538 | − | 0.477672i | \(-0.158519\pi\) | ||||
0.878538 | + | 0.477672i | \(0.158519\pi\) | |||||||
\(158\) | −6.13816 | −0.488326 | ||||||||
\(159\) | 12.3254 | − | 1.48176i | 0.977471 | − | 0.117511i | ||||
\(160\) | 1.00000 | 0.0790569 | ||||||||
\(161\) | −1.37427 | −0.108307 | ||||||||
\(162\) | 4.14468 | + | 7.98884i | 0.325637 | + | 0.627663i | ||||
\(163\) | 14.4283 | 1.13011 | 0.565057 | − | 0.825052i | \(-0.308854\pi\) | ||||
0.565057 | + | 0.825052i | \(0.308854\pi\) | |||||||
\(164\) | − | 5.42208i | − | 0.423393i | ||||||
\(165\) | 0.325920 | + | 2.71104i | 0.0253728 | + | 0.211054i | ||||
\(166\) | 3.86184i | 0.299737i | ||||||||
\(167\) | 1.16301 | 0.0899968 | 0.0449984 | − | 0.998987i | \(-0.485672\pi\) | ||||
0.0449984 | + | 0.998987i | \(0.485672\pi\) | |||||||
\(168\) | 0.244290 | + | 2.03203i | 0.0188474 | + | 0.156775i | ||||
\(169\) | 1.17096 | 0.0900740 | ||||||||
\(170\) | 4.55264 | 0.349172 | ||||||||
\(171\) | 19.3740 | − | 4.72657i | 1.48156 | − | 0.361450i | ||||
\(172\) | − | 6.82897i | − | 0.520704i | ||||||
\(173\) | 3.88241i | 0.295174i | 0.989049 | + | 0.147587i | \(0.0471506\pi\) | ||||
−0.989049 | + | 0.147587i | \(0.952849\pi\) | |||||||
\(174\) | 1.69592 | + | 14.1068i | 0.128567 | + | 1.06944i | ||||
\(175\) | 1.18164 | 0.0893237 | ||||||||
\(176\) | −1.57649 | −0.118832 | ||||||||
\(177\) | −1.41495 | − | 11.7697i | −0.106354 | − | 0.884664i | ||||
\(178\) | − | 10.2683i | − | 0.769642i | ||||||
\(179\) | −10.6411 | −0.795353 | −0.397677 | − | 0.917526i | \(-0.630183\pi\) | ||||
−0.397677 | + | 0.917526i | \(0.630183\pi\) | |||||||
\(180\) | 0.711040 | + | 2.91452i | 0.0529978 | + | 0.217235i | ||||
\(181\) | 16.8606i | 1.25324i | 0.779325 | + | 0.626620i | \(0.215562\pi\) | ||||
−0.779325 | + | 0.626620i | \(0.784438\pi\) | |||||||
\(182\) | −4.06406 | −0.301248 | ||||||||
\(183\) | −2.44876 | − | 20.3691i | −0.181018 | − | 1.50573i | ||||
\(184\) | − | 1.16301i | − | 0.0857386i | ||||||
\(185\) | −9.82943 | −0.722674 | ||||||||
\(186\) | −0.969217 | − | 9.59482i | −0.0710665 | − | 0.703527i | ||||
\(187\) | −7.17720 | −0.524849 | ||||||||
\(188\) | 1.46575i | 0.106901i | ||||||||
\(189\) | −5.74870 | + | 2.15684i | −0.418156 | + | 0.156887i | ||||
\(190\) | 6.64740 | 0.482253 | ||||||||
\(191\) | 26.2574i | 1.89992i | 0.312378 | + | 0.949958i | \(0.398874\pi\) | ||||
−0.312378 | + | 0.949958i | \(0.601126\pi\) | |||||||
\(192\) | −1.71967 | + | 0.206738i | −0.124106 | + | 0.0149200i | ||||
\(193\) | −20.5459 | −1.47893 | −0.739464 | − | 0.673197i | \(-0.764921\pi\) | ||||
−0.739464 | + | 0.673197i | \(0.764921\pi\) | |||||||
\(194\) | 3.46575i | 0.248827i | ||||||||
\(195\) | −5.91452 | + | 0.711040i | −0.423548 | + | 0.0509187i | ||||
\(196\) | 5.60372 | 0.400266 | ||||||||
\(197\) | −5.40391 | −0.385012 | −0.192506 | − | 0.981296i | \(-0.561662\pi\) | ||||
−0.192506 | + | 0.981296i | \(0.561662\pi\) | |||||||
\(198\) | −1.12095 | − | 4.59471i | −0.0796623 | − | 0.326532i | ||||
\(199\) | − | 6.28837i | − | 0.445771i | −0.974845 | − | 0.222885i | \(-0.928452\pi\) | ||
0.974845 | − | 0.222885i | \(-0.0715476\pi\) | |||||||
\(200\) | 1.00000i | 0.0707107i | ||||||||
\(201\) | −23.4123 | + | 2.81461i | −1.65137 | + | 0.198527i | ||||
\(202\) | −13.3740 | −0.940989 | ||||||||
\(203\) | −9.69328 | −0.680335 | ||||||||
\(204\) | −7.82904 | + | 0.941203i | −0.548142 | + | 0.0658974i | ||||
\(205\) | 5.42208 | 0.378695 | ||||||||
\(206\) | − | 6.40696i | − | 0.446394i | ||||||
\(207\) | 3.38963 | − | 0.826951i | 0.235596 | − | 0.0574770i | ||||
\(208\) | − | 3.43934i | − | 0.238475i | ||||||
\(209\) | −10.4796 | −0.724886 | ||||||||
\(210\) | −2.03203 | + | 0.244290i | −0.140224 | + | 0.0168576i | ||||
\(211\) | −10.0792 | −0.693879 | −0.346939 | − | 0.937888i | \(-0.612779\pi\) | ||||
−0.346939 | + | 0.937888i | \(0.612779\pi\) | |||||||
\(212\) | −7.16734 | −0.492255 | ||||||||
\(213\) | 1.34996 | + | 11.2291i | 0.0924975 | + | 0.769405i | ||||
\(214\) | −9.49156 | −0.648830 | ||||||||
\(215\) | 6.82897 | 0.465732 | ||||||||
\(216\) | −1.82529 | − | 4.86501i | −0.124196 | − | 0.331022i | ||||
\(217\) | 6.57792 | + | 0.124812i | 0.446538 | + | 0.00847280i | ||||
\(218\) | − | 14.8139i | − | 1.00332i | ||||||
\(219\) | 0.967006 | + | 8.04367i | 0.0653442 | + | 0.543541i | ||||
\(220\) | − | 1.57649i | − | 0.106287i | ||||||
\(221\) | − | 15.6581i | − | 1.05328i | ||||||
\(222\) | 16.9034 | − | 2.03211i | 1.13448 | − | 0.136387i | ||||
\(223\) | − | 12.7191i | − | 0.851737i | −0.904785 | − | 0.425868i | \(-0.859969\pi\) | ||
0.904785 | − | 0.425868i | \(-0.140031\pi\) | |||||||
\(224\) | − | 1.18164i | − | 0.0789518i | ||||||
\(225\) | −2.91452 | + | 0.711040i | −0.194301 | + | 0.0474027i | ||||
\(226\) | −17.6839 | −1.17631 | ||||||||
\(227\) | − | 12.3357i | − | 0.818750i | −0.912366 | − | 0.409375i | \(-0.865747\pi\) | ||
0.912366 | − | 0.409375i | \(-0.134253\pi\) | |||||||
\(228\) | −11.4313 | + | 1.37427i | −0.757058 | + | 0.0910131i | ||||
\(229\) | 3.44164i | 0.227430i | 0.993513 | + | 0.113715i | \(0.0362751\pi\) | ||||
−0.993513 | + | 0.113715i | \(0.963725\pi\) | |||||||
\(230\) | 1.16301 | 0.0766869 | ||||||||
\(231\) | 3.20348 | − | 0.385121i | 0.210773 | − | 0.0253391i | ||||
\(232\) | − | 8.20323i | − | 0.538569i | ||||||
\(233\) | − | 14.8397i | − | 0.972182i | −0.873908 | − | 0.486091i | \(-0.838422\pi\) | ||
0.873908 | − | 0.486091i | \(-0.161578\pi\) | |||||||
\(234\) | 10.0240 | − | 2.44551i | 0.655290 | − | 0.159868i | ||||
\(235\) | −1.46575 | −0.0956153 | ||||||||
\(236\) | 6.84416i | 0.445517i | ||||||||
\(237\) | 1.26899 | + | 10.5556i | 0.0824297 | + | 0.685660i | ||||
\(238\) | − | 5.37959i | − | 0.348707i | ||||||
\(239\) | 2.48085 | 0.160473 | 0.0802365 | − | 0.996776i | \(-0.474432\pi\) | ||||
0.0802365 | + | 0.996776i | \(0.474432\pi\) | |||||||
\(240\) | −0.206738 | − | 1.71967i | −0.0133449 | − | 0.111004i | ||||
\(241\) | − | 12.9304i | − | 0.832920i | −0.909154 | − | 0.416460i | \(-0.863271\pi\) | ||
0.909154 | − | 0.416460i | \(-0.136729\pi\) | |||||||
\(242\) | − | 8.51468i | − | 0.547344i | ||||||
\(243\) | 12.8813 | − | 8.77907i | 0.826336 | − | 0.563178i | ||||
\(244\) | 11.8448i | 0.758285i | ||||||||
\(245\) | 5.60372i | 0.358009i | ||||||||
\(246\) | −9.32418 | + | 1.12095i | −0.594488 | + | 0.0714690i | ||||
\(247\) | − | 22.8626i | − | 1.45471i | ||||||
\(248\) | −0.105626 | + | 5.56676i | −0.00670726 | + | 0.353490i | ||||
\(249\) | 6.64109 | − | 0.798388i | 0.420862 | − | 0.0505958i | ||||
\(250\) | −1.00000 | −0.0632456 | ||||||||
\(251\) | −5.73203 | −0.361802 | −0.180901 | − | 0.983501i | \(-0.557901\pi\) | ||||
−0.180901 | + | 0.983501i | \(0.557901\pi\) | |||||||
\(252\) | 3.44392 | − | 0.840195i | 0.216946 | − | 0.0529273i | ||||
\(253\) | −1.83348 | −0.115270 | ||||||||
\(254\) | 14.7956 | 0.928355 | ||||||||
\(255\) | −0.941203 | − | 7.82904i | −0.0589404 | − | 0.490273i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 4.35803i | 0.271847i | 0.990719 | + | 0.135923i | \(0.0434001\pi\) | ||||
−0.990719 | + | 0.135923i | \(0.956600\pi\) | |||||||
\(258\) | −11.7436 | + | 1.41180i | −0.731122 | + | 0.0878951i | ||||
\(259\) | 11.6149i | 0.721713i | ||||||||
\(260\) | 3.43934 | 0.213299 | ||||||||
\(261\) | 23.9085 | − | 5.83283i | 1.47990 | − | 0.361043i | ||||
\(262\) | 2.84416 | 0.175713 | ||||||||
\(263\) | −17.8491 | −1.10062 | −0.550312 | − | 0.834959i | \(-0.685491\pi\) | ||||
−0.550312 | + | 0.834959i | \(0.685491\pi\) | |||||||
\(264\) | 0.325920 | + | 2.71104i | 0.0200590 | + | 0.166853i | ||||
\(265\) | − | 7.16734i | − | 0.440286i | ||||||
\(266\) | − | 7.85484i | − | 0.481611i | ||||||
\(267\) | −17.6581 | + | 2.12284i | −1.08066 | + | 0.129916i | ||||
\(268\) | 13.6144 | 0.831632 | ||||||||
\(269\) | −5.38862 | −0.328550 | −0.164275 | − | 0.986415i | \(-0.552528\pi\) | ||||
−0.164275 | + | 0.986415i | \(0.552528\pi\) | |||||||
\(270\) | 4.86501 | − | 1.82529i | 0.296075 | − | 0.111084i | ||||
\(271\) | 29.0008i | 1.76167i | 0.473421 | + | 0.880837i | \(0.343019\pi\) | ||||
−0.473421 | + | 0.880837i | \(0.656981\pi\) | |||||||
\(272\) | 4.55264 | 0.276045 | ||||||||
\(273\) | 0.840195 | + | 6.98884i | 0.0508509 | + | 0.422984i | ||||
\(274\) | 5.52980i | 0.334068i | ||||||||
\(275\) | 1.57649 | 0.0950659 | ||||||||
\(276\) | −2.00000 | + | 0.240439i | −0.120386 | + | 0.0144727i | ||||
\(277\) | − | 0.131535i | − | 0.00790315i | −0.999992 | − | 0.00395158i | \(-0.998742\pi\) | ||
0.999992 | − | 0.00395158i | \(-0.00125783\pi\) | |||||||
\(278\) | −21.6833 | −1.30048 | ||||||||
\(279\) | −16.2995 | + | 3.65034i | −0.975828 | + | 0.218540i | ||||
\(280\) | 1.18164 | 0.0706166 | ||||||||
\(281\) | 0.682894i | 0.0407380i | 0.999793 | + | 0.0203690i | \(0.00648410\pi\) | ||||
−0.999793 | + | 0.0203690i | \(0.993516\pi\) | |||||||
\(282\) | 2.52061 | − | 0.303027i | 0.150100 | − | 0.0180450i | ||||
\(283\) | 10.0953 | 0.600102 | 0.300051 | − | 0.953923i | \(-0.402996\pi\) | ||||
0.300051 | + | 0.953923i | \(0.402996\pi\) | |||||||
\(284\) | − | 6.52980i | − | 0.387472i | ||||||
\(285\) | −1.37427 | − | 11.4313i | −0.0814046 | − | 0.677133i | ||||
\(286\) | −5.42208 | −0.320614 | ||||||||
\(287\) | − | 6.40696i | − | 0.378191i | ||||||
\(288\) | 0.711040 | + | 2.91452i | 0.0418985 | + | 0.171740i | ||||
\(289\) | 3.72657 | 0.219210 | ||||||||
\(290\) | 8.20323 | 0.481710 | ||||||||
\(291\) | 5.95995 | − | 0.716502i | 0.349378 | − | 0.0420021i | ||||
\(292\) | − | 4.67746i | − | 0.273727i | ||||||
\(293\) | − | 31.3464i | − | 1.83128i | −0.402004 | − | 0.915638i | \(-0.631686\pi\) | ||
0.402004 | − | 0.915638i | \(-0.368314\pi\) | |||||||
\(294\) | −1.15850 | − | 9.63654i | −0.0675651 | − | 0.562015i | ||||
\(295\) | −6.84416 | −0.398482 | ||||||||
\(296\) | −9.82943 | −0.571324 | ||||||||
\(297\) | −7.66964 | + | 2.87756i | −0.445037 | + | 0.166973i | ||||
\(298\) | 6.52980 | 0.378261 | ||||||||
\(299\) | − | 4.00000i | − | 0.231326i | ||||||
\(300\) | 1.71967 | − | 0.206738i | 0.0992851 | − | 0.0119360i | ||||
\(301\) | − | 8.06939i | − | 0.465112i | ||||||
\(302\) | 9.72099 | 0.559380 | ||||||||
\(303\) | 2.76490 | + | 22.9988i | 0.158839 | + | 1.32125i | ||||
\(304\) | 6.64740 | 0.381254 | ||||||||
\(305\) | −11.8448 | −0.678231 | ||||||||
\(306\) | 3.23711 | + | 13.2688i | 0.185053 | + | 0.758525i | ||||
\(307\) | −11.4863 | −0.655558 | −0.327779 | − | 0.944754i | \(-0.606300\pi\) | ||||
−0.327779 | + | 0.944754i | \(0.606300\pi\) | |||||||
\(308\) | −1.86285 | −0.106146 | ||||||||
\(309\) | −11.0178 | + | 1.32456i | −0.626783 | + | 0.0753515i | ||||
\(310\) | −5.56676 | − | 0.105626i | −0.316171 | − | 0.00599916i | ||||
\(311\) | − | 1.22976i | − | 0.0697332i | −0.999392 | − | 0.0348666i | \(-0.988899\pi\) | ||
0.999392 | − | 0.0348666i | \(-0.0111006\pi\) | |||||||
\(312\) | −5.91452 | + | 0.711040i | −0.334844 | + | 0.0402547i | ||||
\(313\) | − | 2.64912i | − | 0.149737i | −0.997193 | − | 0.0748685i | \(-0.976146\pi\) | ||
0.997193 | − | 0.0748685i | \(-0.0238537\pi\) | |||||||
\(314\) | 22.0161i | 1.24244i | ||||||||
\(315\) | 0.840195 | + | 3.44392i | 0.0473396 | + | 0.194043i | ||||
\(316\) | − | 6.13816i | − | 0.345299i | ||||||
\(317\) | − | 17.6581i | − | 0.991776i | −0.868386 | − | 0.495888i | \(-0.834843\pi\) | ||
0.868386 | − | 0.495888i | \(-0.165157\pi\) | |||||||
\(318\) | 1.48176 | + | 12.3254i | 0.0830929 | + | 0.691177i | ||||
\(319\) | −12.9323 | −0.724071 | ||||||||
\(320\) | 1.00000i | 0.0559017i | ||||||||
\(321\) | 1.96226 | + | 16.3223i | 0.109523 | + | 0.911024i | ||||
\(322\) | − | 1.37427i | − | 0.0765849i | ||||||
\(323\) | 30.2632 | 1.68389 | ||||||||
\(324\) | −7.98884 | + | 4.14468i | −0.443825 | + | 0.230260i | ||||
\(325\) | 3.43934i | 0.190780i | ||||||||
\(326\) | 14.4283i | 0.799111i | ||||||||
\(327\) | −25.4750 | + | 3.06259i | −1.40877 | + | 0.169362i | ||||
\(328\) | 5.42208 | 0.299384 | ||||||||
\(329\) | 1.73200i | 0.0954881i | ||||||||
\(330\) | −2.71104 | + | 0.325920i | −0.149238 | + | 0.0179413i | ||||
\(331\) | 36.3183i | 1.99624i | 0.0613165 | + | 0.998118i | \(0.480470\pi\) | ||||
−0.0613165 | + | 0.998118i | \(0.519530\pi\) | |||||||
\(332\) | −3.86184 | −0.211946 | ||||||||
\(333\) | −6.98912 | − | 28.6481i | −0.383002 | − | 1.56990i | ||||
\(334\) | 1.16301i | 0.0636373i | ||||||||
\(335\) | 13.6144i | 0.743834i | ||||||||
\(336\) | −2.03203 | + | 0.244290i | −0.110856 | + | 0.0133271i | ||||
\(337\) | − | 27.9926i | − | 1.52485i | −0.647074 | − | 0.762427i | \(-0.724008\pi\) | ||
0.647074 | − | 0.762427i | \(-0.275992\pi\) | |||||||
\(338\) | 1.17096i | 0.0636919i | ||||||||
\(339\) | 3.65592 | + | 30.4104i | 0.198563 | + | 1.65167i | ||||
\(340\) | 4.55264i | 0.246902i | ||||||||
\(341\) | 8.77595 | + | 0.166518i | 0.475244 | + | 0.00901748i | ||||
\(342\) | 4.72657 | + | 19.3740i | 0.255583 | + | 1.04762i | ||||
\(343\) | 14.8931 | 0.804151 | ||||||||
\(344\) | 6.82897 | 0.368193 | ||||||||
\(345\) | −0.240439 | − | 2.00000i | −0.0129448 | − | 0.107676i | ||||
\(346\) | −3.88241 | −0.208719 | ||||||||
\(347\) | −0.131535 | −0.00706115 | −0.00353058 | − | 0.999994i | \(-0.501124\pi\) | ||||
−0.00353058 | + | 0.999994i | \(0.501124\pi\) | |||||||
\(348\) | −14.1068 | + | 1.69592i | −0.756206 | + | 0.0909107i | ||||
\(349\) | −13.2734 | −0.710511 | −0.355255 | − | 0.934769i | \(-0.615606\pi\) | ||||
−0.355255 | + | 0.934769i | \(0.615606\pi\) | |||||||
\(350\) | 1.18164i | 0.0631614i | ||||||||
\(351\) | −6.27780 | − | 16.7324i | −0.335084 | − | 0.893109i | ||||
\(352\) | − | 1.57649i | − | 0.0840272i | ||||||
\(353\) | 23.1169 | 1.23039 | 0.615193 | − | 0.788376i | \(-0.289078\pi\) | ||||
0.615193 | + | 0.788376i | \(0.289078\pi\) | |||||||
\(354\) | 11.7697 | − | 1.41495i | 0.625552 | − | 0.0752035i | ||||
\(355\) | 6.52980 | 0.346566 | ||||||||
\(356\) | 10.2683 | 0.544219 | ||||||||
\(357\) | −9.25112 | + | 1.11216i | −0.489621 | + | 0.0588620i | ||||
\(358\) | − | 10.6411i | − | 0.562400i | ||||||
\(359\) | 28.5201i | 1.50523i | 0.658459 | + | 0.752617i | \(0.271209\pi\) | ||||
−0.658459 | + | 0.752617i | \(0.728791\pi\) | |||||||
\(360\) | −2.91452 | + | 0.711040i | −0.153609 | + | 0.0374751i | ||||
\(361\) | 25.1879 | 1.32568 | ||||||||
\(362\) | −16.8606 | −0.886175 | ||||||||
\(363\) | −14.6424 | + | 1.76030i | −0.768528 | + | 0.0923920i | ||||
\(364\) | − | 4.06406i | − | 0.213015i | ||||||
\(365\) | 4.67746 | 0.244829 | ||||||||
\(366\) | 20.3691 | − | 2.44876i | 1.06471 | − | 0.127999i | ||||
\(367\) | 17.5260i | 0.914851i | 0.889248 | + | 0.457426i | \(0.151228\pi\) | ||||
−0.889248 | + | 0.457426i | \(0.848772\pi\) | |||||||
\(368\) | 1.16301 | 0.0606263 | ||||||||
\(369\) | 3.85532 | + | 15.8028i | 0.200700 | + | 0.822659i | ||||
\(370\) | − | 9.82943i | − | 0.511008i | ||||||
\(371\) | −8.46922 | −0.439700 | ||||||||
\(372\) | 9.59482 | − | 0.969217i | 0.497468 | − | 0.0502516i | ||||
\(373\) | 9.14170 | 0.473339 | 0.236670 | − | 0.971590i | \(-0.423944\pi\) | ||||
0.236670 | + | 0.971590i | \(0.423944\pi\) | |||||||
\(374\) | − | 7.17720i | − | 0.371124i | ||||||
\(375\) | 0.206738 | + | 1.71967i | 0.0106759 | + | 0.0888033i | ||||
\(376\) | −1.46575 | −0.0755905 | ||||||||
\(377\) | − | 28.2137i | − | 1.45308i | ||||||
\(378\) | −2.15684 | − | 5.74870i | −0.110936 | − | 0.295681i | ||||
\(379\) | −2.25387 | −0.115773 | −0.0578867 | − | 0.998323i | \(-0.518436\pi\) | ||||
−0.0578867 | + | 0.998323i | \(0.518436\pi\) | |||||||
\(380\) | 6.64740i | 0.341004i | ||||||||
\(381\) | −3.05880 | − | 25.4434i | −0.156707 | − | 1.30351i | ||||
\(382\) | −26.2574 | −1.34344 | ||||||||
\(383\) | 5.43602 | 0.277768 | 0.138884 | − | 0.990309i | \(-0.455648\pi\) | ||||
0.138884 | + | 0.990309i | \(0.455648\pi\) | |||||||
\(384\) | −0.206738 | − | 1.71967i | −0.0105500 | − | 0.0877565i | ||||
\(385\) | − | 1.86285i | − | 0.0949395i | ||||||
\(386\) | − | 20.5459i | − | 1.04576i | ||||||
\(387\) | 4.85567 | + | 19.9032i | 0.246828 | + | 1.01173i | ||||
\(388\) | −3.46575 | −0.175947 | ||||||||
\(389\) | −37.6062 | −1.90671 | −0.953354 | − | 0.301854i | \(-0.902395\pi\) | ||||
−0.953354 | + | 0.301854i | \(0.902395\pi\) | |||||||
\(390\) | −0.711040 | − | 5.91452i | −0.0360049 | − | 0.299493i | ||||
\(391\) | 5.29479 | 0.267769 | ||||||||
\(392\) | 5.60372i | 0.283031i | ||||||||
\(393\) | −0.587995 | − | 4.89101i | −0.0296604 | − | 0.246719i | ||||
\(394\) | − | 5.40391i | − | 0.272245i | ||||||
\(395\) | 6.13816 | 0.308845 | ||||||||
\(396\) | 4.59471 | − | 1.12095i | 0.230893 | − | 0.0563298i | ||||
\(397\) | 18.1656 | 0.911704 | 0.455852 | − | 0.890056i | \(-0.349335\pi\) | ||||
0.455852 | + | 0.890056i | \(0.349335\pi\) | |||||||
\(398\) | 6.28837 | 0.315208 | ||||||||
\(399\) | −13.5077 | + | 1.62389i | −0.676232 | + | 0.0812963i | ||||
\(400\) | −1.00000 | −0.0500000 | ||||||||
\(401\) | 27.8508 | 1.39080 | 0.695400 | − | 0.718623i | \(-0.255227\pi\) | ||||
0.695400 | + | 0.718623i | \(0.255227\pi\) | |||||||
\(402\) | −2.81461 | − | 23.4123i | −0.140380 | − | 1.16770i | ||||
\(403\) | −0.363284 | + | 19.1460i | −0.0180964 | + | 0.953729i | ||||
\(404\) | − | 13.3740i | − | 0.665380i | ||||||
\(405\) | −4.14468 | − | 7.98884i | −0.205951 | − | 0.396969i | ||||
\(406\) | − | 9.69328i | − | 0.481070i | ||||||
\(407\) | 15.4960i | 0.768108i | ||||||||
\(408\) | −0.941203 | − | 7.82904i | −0.0465965 | − | 0.387595i | ||||
\(409\) | − | 2.73048i | − | 0.135013i | −0.997719 | − | 0.0675067i | \(-0.978496\pi\) | ||
0.997719 | − | 0.0675067i | \(-0.0215044\pi\) | |||||||
\(410\) | 5.42208i | 0.267777i | ||||||||
\(411\) | 9.50943 | − | 1.14322i | 0.469066 | − | 0.0563908i | ||||
\(412\) | 6.40696 | 0.315648 | ||||||||
\(413\) | 8.08735i | 0.397952i | ||||||||
\(414\) | 0.826951 | + | 3.38963i | 0.0406424 | + | 0.166591i | ||||
\(415\) | − | 3.86184i | − | 0.189570i | ||||||
\(416\) | 3.43934 | 0.168627 | ||||||||
\(417\) | 4.48274 | + | 37.2880i | 0.219521 | + | 1.82600i | ||||
\(418\) | − | 10.4796i | − | 0.512572i | ||||||
\(419\) | − | 3.91265i | − | 0.191146i | −0.995422 | − | 0.0955728i | \(-0.969532\pi\) | ||
0.995422 | − | 0.0955728i | \(-0.0304683\pi\) | |||||||
\(420\) | −0.244290 | − | 2.03203i | −0.0119201 | − | 0.0991530i | ||||
\(421\) | −5.57073 | −0.271501 | −0.135750 | − | 0.990743i | \(-0.543345\pi\) | ||||
−0.135750 | + | 0.990743i | \(0.543345\pi\) | |||||||
\(422\) | − | 10.0792i | − | 0.490646i | ||||||
\(423\) | −1.04221 | − | 4.27197i | −0.0506740 | − | 0.207710i | ||||
\(424\) | − | 7.16734i | − | 0.348077i | ||||||
\(425\) | −4.55264 | −0.220836 | ||||||||
\(426\) | −11.2291 | + | 1.34996i | −0.544051 | + | 0.0654056i | ||||
\(427\) | 13.9963i | 0.677329i | ||||||||
\(428\) | − | 9.49156i | − | 0.458792i | ||||||
\(429\) | 1.12095 | + | 9.32418i | 0.0541199 | + | 0.450176i | ||||
\(430\) | 6.82897i | 0.329322i | ||||||||
\(431\) | 18.9412i | 0.912366i | 0.889886 | + | 0.456183i | \(0.150784\pi\) | ||||
−0.889886 | + | 0.456183i | \(0.849216\pi\) | |||||||
\(432\) | 4.86501 | − | 1.82529i | 0.234068 | − | 0.0878195i | ||||
\(433\) | 33.6653i | 1.61785i | 0.587912 | + | 0.808925i | \(0.299950\pi\) | ||||
−0.587912 | + | 0.808925i | \(0.700050\pi\) | |||||||
\(434\) | −0.124812 | + | 6.57792i | −0.00599118 | + | 0.315750i | ||||
\(435\) | −1.69592 | − | 14.1068i | −0.0813130 | − | 0.676371i | ||||
\(436\) | 14.8139 | 0.709458 | ||||||||
\(437\) | 7.73102 | 0.369825 | ||||||||
\(438\) | −8.04367 | + | 0.967006i | −0.384342 | + | 0.0462053i | ||||
\(439\) | 25.8504 | 1.23377 | 0.616886 | − | 0.787052i | \(-0.288394\pi\) | ||||
0.616886 | + | 0.787052i | \(0.288394\pi\) | |||||||
\(440\) | 1.57649 | 0.0751562 | ||||||||
\(441\) | −16.3322 | + | 3.98447i | −0.777722 | + | 0.189737i | ||||
\(442\) | 15.6581 | 0.744779 | ||||||||
\(443\) | 3.89058i | 0.184847i | 0.995720 | + | 0.0924236i | \(0.0294614\pi\) | ||||
−0.995720 | + | 0.0924236i | \(0.970539\pi\) | |||||||
\(444\) | 2.03211 | + | 16.9034i | 0.0964398 | + | 0.802198i | ||||
\(445\) | 10.2683i | 0.486764i | ||||||||
\(446\) | 12.7191 | 0.602269 | ||||||||
\(447\) | −1.34996 | − | 11.2291i | −0.0638507 | − | 0.531118i | ||||
\(448\) | 1.18164 | 0.0558273 | ||||||||
\(449\) | 16.8673 | 0.796019 | 0.398010 | − | 0.917381i | \(-0.369701\pi\) | ||||
0.398010 | + | 0.917381i | \(0.369701\pi\) | |||||||
\(450\) | −0.711040 | − | 2.91452i | −0.0335188 | − | 0.137392i | ||||
\(451\) | − | 8.54786i | − | 0.402503i | ||||||
\(452\) | − | 17.6839i | − | 0.831780i | ||||||
\(453\) | −2.00969 | − | 16.7169i | −0.0944237 | − | 0.785427i | ||||
\(454\) | 12.3357 | 0.578944 | ||||||||
\(455\) | 4.06406 | 0.190526 | ||||||||
\(456\) | −1.37427 | − | 11.4313i | −0.0643560 | − | 0.535321i | ||||
\(457\) | − | 6.15575i | − | 0.287954i | −0.989581 | − | 0.143977i | \(-0.954011\pi\) | ||
0.989581 | − | 0.143977i | \(-0.0459891\pi\) | |||||||
\(458\) | −3.44164 | −0.160817 | ||||||||
\(459\) | 22.1486 | − | 8.30992i | 1.03381 | − | 0.387874i | ||||
\(460\) | 1.16301i | 0.0542258i | ||||||||
\(461\) | −6.44714 | −0.300273 | −0.150137 | − | 0.988665i | \(-0.547971\pi\) | ||||
−0.150137 | + | 0.988665i | \(0.547971\pi\) | |||||||
\(462\) | 0.385121 | + | 3.20348i | 0.0179174 | + | 0.149039i | ||||
\(463\) | 29.6849i | 1.37957i | 0.724013 | + | 0.689787i | \(0.242296\pi\) | ||||
−0.724013 | + | 0.689787i | \(0.757704\pi\) | |||||||
\(464\) | 8.20323 | 0.380826 | ||||||||
\(465\) | 0.969217 | + | 9.59482i | 0.0449464 | + | 0.444949i | ||||
\(466\) | 14.8397 | 0.687437 | ||||||||
\(467\) | − | 17.1558i | − | 0.793878i | −0.917845 | − | 0.396939i | \(-0.870073\pi\) | ||
0.917845 | − | 0.396939i | \(-0.129927\pi\) | |||||||
\(468\) | 2.44551 | + | 10.0240i | 0.113044 | + | 0.463360i | ||||
\(469\) | 16.0873 | 0.742845 | ||||||||
\(470\) | − | 1.46575i | − | 0.0676102i | ||||||
\(471\) | 37.8604 | − | 4.55156i | 1.74452 | − | 0.209725i | ||||
\(472\) | −6.84416 | −0.315028 | ||||||||
\(473\) | − | 10.7658i | − | 0.495012i | ||||||
\(474\) | −10.5556 | + | 1.26899i | −0.484835 | + | 0.0582866i | ||||
\(475\) | −6.64740 | −0.305003 | ||||||||
\(476\) | 5.37959 | 0.246573 | ||||||||
\(477\) | 20.8893 | − | 5.09627i | 0.956457 | − | 0.233342i | ||||
\(478\) | 2.48085i | 0.113472i | ||||||||
\(479\) | 28.7338i | 1.31288i | 0.754378 | + | 0.656440i | \(0.227939\pi\) | ||||
−0.754378 | + | 0.656440i | \(0.772061\pi\) | |||||||
\(480\) | 1.71967 | − | 0.206738i | 0.0784918 | − | 0.00943624i | ||||
\(481\) | −33.8067 | −1.54145 | ||||||||
\(482\) | 12.9304 | 0.588963 | ||||||||
\(483\) | −2.36328 | + | 0.284113i | −0.107533 | + | 0.0129276i | ||||
\(484\) | 8.51468 | 0.387031 | ||||||||
\(485\) | − | 3.46575i | − | 0.157372i | ||||||
\(486\) | 8.77907 | + | 12.8813i | 0.398227 | + | 0.584308i | ||||
\(487\) | 9.91982i | 0.449510i | 0.974415 | + | 0.224755i | \(0.0721581\pi\) | ||||
−0.974415 | + | 0.224755i | \(0.927842\pi\) | |||||||
\(488\) | −11.8448 | −0.536189 | ||||||||
\(489\) | 24.8119 | − | 2.98288i | 1.12203 | − | 0.134890i | ||||
\(490\) | −5.60372 | −0.253150 | ||||||||
\(491\) | 26.2946 | 1.18666 | 0.593330 | − | 0.804959i | \(-0.297813\pi\) | ||||
0.593330 | + | 0.804959i | \(0.297813\pi\) | |||||||
\(492\) | −1.12095 | − | 9.32418i | −0.0505362 | − | 0.420367i | ||||
\(493\) | 37.3464 | 1.68200 | ||||||||
\(494\) | 22.8626 | 1.02864 | ||||||||
\(495\) | 1.12095 | + | 4.59471i | 0.0503829 | + | 0.206517i | ||||
\(496\) | −5.56676 | − | 0.105626i | −0.249955 | − | 0.00474275i | ||||
\(497\) | − | 7.71589i | − | 0.346105i | ||||||
\(498\) | 0.798388 | + | 6.64109i | 0.0357766 | + | 0.297594i | ||||
\(499\) | 9.24144i | 0.413703i | 0.978372 | + | 0.206852i | \(0.0663218\pi\) | ||||
−0.978372 | + | 0.206852i | \(0.933678\pi\) | |||||||
\(500\) | − | 1.00000i | − | 0.0447214i | ||||||
\(501\) | 2.00000 | − | 0.240439i | 0.0893534 | − | 0.0107420i | ||||
\(502\) | − | 5.73203i | − | 0.255833i | ||||||
\(503\) | − | 16.0953i | − | 0.717653i | −0.933404 | − | 0.358827i | \(-0.883177\pi\) | ||
0.933404 | − | 0.358827i | \(-0.116823\pi\) | |||||||
\(504\) | 0.840195 | + | 3.44392i | 0.0374253 | + | 0.153404i | ||||
\(505\) | 13.3740 | 0.595134 | ||||||||
\(506\) | − | 1.83348i | − | 0.0815082i | ||||||
\(507\) | 2.01367 | − | 0.242082i | 0.0894300 | − | 0.0107512i | ||||
\(508\) | 14.7956i | 0.656446i | ||||||||
\(509\) | 4.54361 | 0.201392 | 0.100696 | − | 0.994917i | \(-0.467893\pi\) | ||||
0.100696 | + | 0.994917i | \(0.467893\pi\) | |||||||
\(510\) | 7.82904 | − | 0.941203i | 0.346676 | − | 0.0416772i | ||||
\(511\) | − | 5.52708i | − | 0.244504i | ||||||
\(512\) | 1.00000i | 0.0441942i | ||||||||
\(513\) | 32.3396 | − | 12.1335i | 1.42783 | − | 0.535705i | ||||
\(514\) | −4.35803 | −0.192225 | ||||||||
\(515\) | 6.40696i | 0.282324i | ||||||||
\(516\) | −1.41180 | − | 11.7436i | −0.0621512 | − | 0.516981i | ||||
\(517\) | 2.31075i | 0.101627i | ||||||||
\(518\) | −11.6149 | −0.510328 | ||||||||
\(519\) | 0.802639 | + | 6.67645i | 0.0352320 | + | 0.293064i | ||||
\(520\) | 3.43934i | 0.150825i | ||||||||
\(521\) | 32.0864i | 1.40573i | 0.711323 | + | 0.702865i | \(0.248096\pi\) | ||||
−0.711323 | + | 0.702865i | \(0.751904\pi\) | |||||||
\(522\) | 5.83283 | + | 23.9085i | 0.255296 | + | 1.04645i | ||||
\(523\) | 34.3945i | 1.50396i | 0.659183 | + | 0.751982i | \(0.270902\pi\) | ||||
−0.659183 | + | 0.751982i | \(0.729098\pi\) | |||||||
\(524\) | 2.84416i | 0.124248i | ||||||||
\(525\) | 2.03203 | − | 0.244290i | 0.0886852 | − | 0.0106617i | ||||
\(526\) | − | 17.8491i | − | 0.778258i | ||||||
\(527\) | −25.3435 | − | 0.480878i | −1.10398 | − | 0.0209474i | ||||
\(528\) | −2.71104 | + | 0.325920i | −0.117983 | + | 0.0141838i | ||||
\(529\) | −21.6474 | −0.941191 | ||||||||
\(530\) | 7.16734 | 0.311329 | ||||||||
\(531\) | −4.86648 | − | 19.9474i | −0.211187 | − | 0.865645i | ||||
\(532\) | 7.85484 | 0.340551 | ||||||||
\(533\) | 18.6484 | 0.807750 | ||||||||
\(534\) | −2.12284 | − | 17.6581i | −0.0918645 | − | 0.764140i | ||||
\(535\) | 9.49156 | 0.410356 | ||||||||
\(536\) | 13.6144i | 0.588053i | ||||||||
\(537\) | −18.2992 | + | 2.19992i | −0.789667 | + | 0.0949334i | ||||
\(538\) | − | 5.38862i | − | 0.232320i | ||||||
\(539\) | 8.83421 | 0.380517 | ||||||||
\(540\) | 1.82529 | + | 4.86501i | 0.0785482 | + | 0.209357i | ||||
\(541\) | 6.24569 | 0.268523 | 0.134262 | − | 0.990946i | \(-0.457134\pi\) | ||||
0.134262 | + | 0.990946i | \(0.457134\pi\) | |||||||
\(542\) | −29.0008 | −1.24569 | ||||||||
\(543\) | 3.48572 | + | 28.9947i | 0.149587 | + | 1.24428i | ||||
\(544\) | 4.55264i | 0.195193i | ||||||||
\(545\) | 14.8139i | 0.634558i | ||||||||
\(546\) | −6.98884 | + | 0.840195i | −0.299095 | + | 0.0359570i | ||||
\(547\) | 8.65265 | 0.369960 | 0.184980 | − | 0.982742i | \(-0.440778\pi\) | ||||
0.184980 | + | 0.982742i | \(0.440778\pi\) | |||||||
\(548\) | −5.52980 | −0.236221 | ||||||||
\(549\) | −8.42213 | − | 34.5219i | −0.359448 | − | 1.47336i | ||||
\(550\) | 1.57649i | 0.0672218i | ||||||||
\(551\) | 54.5301 | 2.32306 | ||||||||
\(552\) | −0.240439 | − | 2.00000i | −0.0102338 | − | 0.0851257i | ||||
\(553\) | − | 7.25311i | − | 0.308434i | ||||||
\(554\) | 0.131535 | 0.00558837 | ||||||||
\(555\) | −16.9034 | + | 2.03211i | −0.717508 | + | 0.0862584i | ||||
\(556\) | − | 21.6833i | − | 0.919575i | ||||||
\(557\) | 10.2362 | 0.433721 | 0.216861 | − | 0.976203i | \(-0.430418\pi\) | ||||
0.216861 | + | 0.976203i | \(0.430418\pi\) | |||||||
\(558\) | −3.65034 | − | 16.2995i | −0.154531 | − | 0.690015i | ||||
\(559\) | 23.4871 | 0.993399 | ||||||||
\(560\) | 1.18164i | 0.0499335i | ||||||||
\(561\) | −12.3424 | + | 1.48380i | −0.521097 | + | 0.0626460i | ||||
\(562\) | −0.682894 | −0.0288061 | ||||||||
\(563\) | 25.3464i | 1.06822i | 0.845414 | + | 0.534112i | \(0.179354\pi\) | ||||
−0.845414 | + | 0.534112i | \(0.820646\pi\) | |||||||
\(564\) | 0.303027 | + | 2.52061i | 0.0127597 | + | 0.106137i | ||||
\(565\) | 17.6839 | 0.743966 | ||||||||
\(566\) | 10.0953i | 0.424336i | ||||||||
\(567\) | −9.43995 | + | 4.89753i | −0.396441 | + | 0.205677i | ||||
\(568\) | 6.52980 | 0.273984 | ||||||||
\(569\) | −18.0733 | −0.757674 | −0.378837 | − | 0.925463i | \(-0.623676\pi\) | ||||
−0.378837 | + | 0.925463i | \(0.623676\pi\) | |||||||
\(570\) | 11.4313 | − | 1.37427i | 0.478805 | − | 0.0575617i | ||||
\(571\) | − | 0.635396i | − | 0.0265905i | −0.999912 | − | 0.0132953i | \(-0.995768\pi\) | ||
0.999912 | − | 0.0132953i | \(-0.00423214\pi\) | |||||||
\(572\) | − | 5.42208i | − | 0.226709i | ||||||
\(573\) | 5.42838 | + | 45.1539i | 0.226774 | + | 1.88633i | ||||
\(574\) | 6.40696 | 0.267421 | ||||||||
\(575\) | −1.16301 | −0.0485011 | ||||||||
\(576\) | −2.91452 | + | 0.711040i | −0.121438 | + | 0.0296267i | ||||
\(577\) | 31.0365 | 1.29207 | 0.646033 | − | 0.763310i | \(-0.276427\pi\) | ||||
0.646033 | + | 0.763310i | \(0.276427\pi\) | |||||||
\(578\) | 3.72657i | 0.155005i | ||||||||
\(579\) | −35.3322 | + | 4.24761i | −1.46835 | + | 0.176525i | ||||
\(580\) | 8.20323i | 0.340621i | ||||||||
\(581\) | −4.56331 | −0.189318 | ||||||||
\(582\) | 0.716502 | + | 5.95995i | 0.0297000 | + | 0.247048i | ||||
\(583\) | −11.2992 | −0.467967 | ||||||||
\(584\) | 4.67746 | 0.193555 | ||||||||
\(585\) | −10.0240 | + | 2.44551i | −0.414442 | + | 0.101109i | ||||
\(586\) | 31.3464 | 1.29491 | ||||||||
\(587\) | 13.3315 | 0.550248 | 0.275124 | − | 0.961409i | \(-0.411281\pi\) | ||||
0.275124 | + | 0.961409i | \(0.411281\pi\) | |||||||
\(588\) | 9.63654 | − | 1.15850i | 0.397404 | − | 0.0477758i | ||||
\(589\) | −37.0045 | − | 0.702138i | −1.52474 | − | 0.0289311i | ||||
\(590\) | − | 6.84416i | − | 0.281770i | ||||||
\(591\) | −9.29293 | + | 1.11719i | −0.382260 | + | 0.0459551i | ||||
\(592\) | − | 9.82943i | − | 0.403987i | ||||||
\(593\) | 0.630480i | 0.0258907i | 0.999916 | + | 0.0129453i | \(0.00412075\pi\) | ||||
−0.999916 | + | 0.0129453i | \(0.995879\pi\) | |||||||
\(594\) | −2.87756 | − | 7.66964i | −0.118068 | − | 0.314689i | ||||
\(595\) | 5.37959i | 0.220542i | ||||||||
\(596\) | 6.52980i | 0.267471i | ||||||||
\(597\) | −1.30004 | − | 10.8139i | −0.0532072 | − | 0.442584i | ||||
\(598\) | 4.00000 | 0.163572 | ||||||||
\(599\) | − | 29.3340i | − | 1.19856i | −0.800541 | − | 0.599278i | \(-0.795454\pi\) | ||
0.800541 | − | 0.599278i | \(-0.204546\pi\) | |||||||
\(600\) | 0.206738 | + | 1.71967i | 0.00844003 | + | 0.0702052i | ||||
\(601\) | − | 28.6093i | − | 1.16700i | −0.812114 | − | 0.583499i | \(-0.801683\pi\) | ||
0.812114 | − | 0.583499i | \(-0.198317\pi\) | |||||||
\(602\) | 8.06939 | 0.328884 | ||||||||
\(603\) | −39.6794 | + | 9.68039i | −1.61587 | + | 0.394216i | ||||
\(604\) | 9.72099i | 0.395541i | ||||||||
\(605\) | 8.51468i | 0.346171i | ||||||||
\(606\) | −22.9988 | + | 2.76490i | −0.934262 | + | 0.112316i | ||||
\(607\) | −20.7561 | −0.842464 | −0.421232 | − | 0.906953i | \(-0.638402\pi\) | ||||
−0.421232 | + | 0.906953i | \(0.638402\pi\) | |||||||
\(608\) | 6.64740i | 0.269588i | ||||||||
\(609\) | −16.6692 | + | 2.00397i | −0.675471 | + | 0.0812048i | ||||
\(610\) | − | 11.8448i | − | 0.479582i | ||||||
\(611\) | −5.04122 | −0.203946 | ||||||||
\(612\) | −13.2688 | + | 3.23711i | −0.536358 | + | 0.130853i | ||||
\(613\) | − | 17.8581i | − | 0.721284i | −0.932704 | − | 0.360642i | \(-0.882558\pi\) | ||
0.932704 | − | 0.360642i | \(-0.117442\pi\) | |||||||
\(614\) | − | 11.4863i | − | 0.463550i | ||||||
\(615\) | 9.32418 | − | 1.12095i | 0.375987 | − | 0.0452010i | ||||
\(616\) | − | 1.86285i | − | 0.0750562i | ||||||
\(617\) | 12.4017i | 0.499274i | 0.968340 | + | 0.249637i | \(0.0803113\pi\) | ||||
−0.968340 | + | 0.249637i | \(0.919689\pi\) | |||||||
\(618\) | −1.32456 | − | 11.0178i | −0.0532816 | − | 0.443203i | ||||
\(619\) | − | 24.5533i | − | 0.986879i | −0.869780 | − | 0.493440i | \(-0.835739\pi\) | ||
0.869780 | − | 0.493440i | \(-0.164261\pi\) | |||||||
\(620\) | 0.105626 | − | 5.56676i | 0.00424205 | − | 0.223567i | ||||
\(621\) | 5.65808 | − | 2.12284i | 0.227051 | − | 0.0851868i | ||||
\(622\) | 1.22976 | 0.0493088 | ||||||||
\(623\) | 12.1335 | 0.486117 | ||||||||
\(624\) | −0.711040 | − | 5.91452i | −0.0284644 | − | 0.236770i | ||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 2.64912 | 0.105880 | ||||||||
\(627\) | −18.0214 | + | 2.16652i | −0.719704 | + | 0.0865224i | ||||
\(628\) | −22.0161 | −0.878538 | ||||||||
\(629\) | − | 44.7499i | − | 1.78430i | ||||||
\(630\) | −3.44392 | + | 0.840195i | −0.137209 | + | 0.0334742i | ||||
\(631\) | − | 20.9901i | − | 0.835604i | −0.908538 | − | 0.417802i | \(-0.862801\pi\) | ||
0.908538 | − | 0.417802i | \(-0.137199\pi\) | |||||||
\(632\) | 6.13816 | 0.244163 | ||||||||
\(633\) | −17.3328 | + | 2.08374i | −0.688918 | + | 0.0828214i | ||||
\(634\) | 17.6581 | 0.701292 | ||||||||
\(635\) | −14.7956 | −0.587144 | ||||||||
\(636\) | −12.3254 | + | 1.48176i | −0.488736 | + | 0.0587555i | ||||
\(637\) | 19.2731i | 0.763628i | ||||||||
\(638\) | − | 12.9323i | − | 0.511995i | ||||||
\(639\) | 4.64295 | + | 19.0312i | 0.183672 | + | 0.752864i | ||||
\(640\) | −1.00000 | −0.0395285 | ||||||||
\(641\) | −30.3243 | −1.19774 | −0.598868 | − | 0.800847i | \(-0.704383\pi\) | ||||
−0.598868 | + | 0.800847i | \(0.704383\pi\) | |||||||
\(642\) | −16.3223 | + | 1.96226i | −0.644191 | + | 0.0774443i | ||||
\(643\) | − | 0.443485i | − | 0.0174893i | −0.999962 | − | 0.00874467i | \(-0.997216\pi\) | ||
0.999962 | − | 0.00874467i | \(-0.00278355\pi\) | |||||||
\(644\) | 1.37427 | 0.0541537 | ||||||||
\(645\) | 11.7436 | − | 1.41180i | 0.462402 | − | 0.0555897i | ||||
\(646\) | 30.2632i | 1.19069i | ||||||||
\(647\) | −42.7074 | −1.67900 | −0.839500 | − | 0.543360i | \(-0.817152\pi\) | ||||
−0.839500 | + | 0.543360i | \(0.817152\pi\) | |||||||
\(648\) | −4.14468 | − | 7.98884i | −0.162818 | − | 0.313831i | ||||
\(649\) | 10.7898i | 0.423535i | ||||||||
\(650\) | −3.43934 | −0.134902 | ||||||||
\(651\) | 11.3376 | − | 1.14527i | 0.444357 | − | 0.0448866i | ||||
\(652\) | −14.4283 | −0.565057 | ||||||||
\(653\) | 10.1390i | 0.396768i | 0.980124 | + | 0.198384i | \(0.0635693\pi\) | ||||
−0.980124 | + | 0.198384i | \(0.936431\pi\) | |||||||
\(654\) | −3.06259 | − | 25.4750i | −0.119757 | − | 0.996152i | ||||
\(655\) | −2.84416 | −0.111131 | ||||||||
\(656\) | 5.42208i | 0.211697i | ||||||||
\(657\) | 3.32586 | + | 13.6325i | 0.129754 | + | 0.531856i | ||||
\(658\) | −1.73200 | −0.0675203 | ||||||||
\(659\) | 8.63922i | 0.336536i | 0.985741 | + | 0.168268i | \(0.0538174\pi\) | ||||
−0.985741 | + | 0.168268i | \(0.946183\pi\) | |||||||
\(660\) | −0.325920 | − | 2.71104i | −0.0126864 | − | 0.105527i | ||||
\(661\) | −36.6412 | −1.42518 | −0.712589 | − | 0.701582i | \(-0.752477\pi\) | ||||
−0.712589 | + | 0.701582i | \(0.752477\pi\) | |||||||
\(662\) | −36.3183 | −1.41155 | ||||||||
\(663\) | −3.23711 | − | 26.9267i | −0.125719 | − | 1.04575i | ||||
\(664\) | − | 3.86184i | − | 0.149869i | ||||||
\(665\) | 7.85484i | 0.304598i | ||||||||
\(666\) | 28.6481 | − | 6.98912i | 1.11009 | − | 0.270823i | ||||
\(667\) | 9.54048 | 0.369409 | ||||||||
\(668\) | −1.16301 | −0.0449984 | ||||||||
\(669\) | −2.62953 | − | 21.8727i | −0.101663 | − | 0.845648i | ||||
\(670\) | −13.6144 | −0.525970 | ||||||||
\(671\) | 18.6732i | 0.720871i | ||||||||
\(672\) | −0.244290 | − | 2.03203i | −0.00942369 | − | 0.0783873i | ||||
\(673\) | − | 44.1754i | − | 1.70284i | −0.524487 | − | 0.851418i | \(-0.675743\pi\) | ||
0.524487 | − | 0.851418i | \(-0.324257\pi\) | |||||||
\(674\) | 27.9926 | 1.07823 | ||||||||
\(675\) | −4.86501 | + | 1.82529i | −0.187254 | + | 0.0702556i | ||||
\(676\) | −1.17096 | −0.0450370 | ||||||||
\(677\) | 39.6526 | 1.52397 | 0.761986 | − | 0.647594i | \(-0.224224\pi\) | ||||
0.761986 | + | 0.647594i | \(0.224224\pi\) | |||||||
\(678\) | −30.4104 | + | 3.65592i | −1.16790 | + | 0.140405i | ||||
\(679\) | −4.09528 | −0.157162 | ||||||||
\(680\) | −4.55264 | −0.174586 | ||||||||
\(681\) | −2.55026 | − | 21.2133i | −0.0977261 | − | 0.812897i | ||||
\(682\) | −0.166518 | + | 8.77595i | −0.00637632 | + | 0.336048i | ||||
\(683\) | 47.0748i | 1.80127i | 0.434581 | + | 0.900633i | \(0.356897\pi\) | ||||
−0.434581 | + | 0.900633i | \(0.643103\pi\) | |||||||
\(684\) | −19.3740 | + | 4.72657i | −0.740782 | + | 0.180725i | ||||
\(685\) | − | 5.52980i | − | 0.211283i | ||||||
\(686\) | 14.8931i | 0.568621i | ||||||||
\(687\) | 0.711517 | + | 5.91849i | 0.0271461 | + | 0.225804i | ||||
\(688\) | 6.82897i | 0.260352i | ||||||||
\(689\) | − | 24.6509i | − | 0.939124i | ||||||
\(690\) | 2.00000 | − | 0.240439i | 0.0761387 | − | 0.00915335i | ||||
\(691\) | 15.3740 | 0.584853 | 0.292427 | − | 0.956288i | \(-0.405537\pi\) | ||||
0.292427 | + | 0.956288i | \(0.405537\pi\) | |||||||
\(692\) | − | 3.88241i | − | 0.147587i | ||||||
\(693\) | 5.42930 | − | 1.32456i | 0.206242 | − | 0.0503158i | ||||
\(694\) | − | 0.131535i | − | 0.00499299i | ||||||
\(695\) | 21.6833 | 0.822493 | ||||||||
\(696\) | −1.69592 | − | 14.1068i | −0.0642836 | − | 0.534718i | ||||
\(697\) | 24.6848i | 0.935004i | ||||||||
\(698\) | − | 13.2734i | − | 0.502407i | ||||||
\(699\) | −3.06793 | − | 25.5194i | −0.116040 | − | 0.965232i | ||||
\(700\) | −1.18164 | −0.0446619 | ||||||||
\(701\) | − | 3.33322i | − | 0.125894i | −0.998017 | − | 0.0629469i | \(-0.979950\pi\) | ||
0.998017 | − | 0.0629469i | \(-0.0200499\pi\) | |||||||
\(702\) | 16.7324 | − | 6.27780i | 0.631524 | − | 0.236940i | ||||
\(703\) | − | 65.3401i | − | 2.46435i | ||||||
\(704\) | 1.57649 | 0.0594162 | ||||||||
\(705\) | −2.52061 | + | 0.303027i | −0.0949317 | + | 0.0114126i | ||||
\(706\) | 23.1169i | 0.870015i | ||||||||
\(707\) | − | 15.8032i | − | 0.594342i | ||||||
\(708\) | 1.41495 | + | 11.7697i | 0.0531769 | + | 0.442332i | ||||
\(709\) | − | 9.73232i | − | 0.365505i | −0.983159 | − | 0.182753i | \(-0.941499\pi\) | ||
0.983159 | − | 0.182753i | \(-0.0585007\pi\) | |||||||
\(710\) | 6.52980i | 0.245059i | ||||||||
\(711\) | 4.36448 | + | 17.8898i | 0.163681 | + | 0.670920i | ||||
\(712\) | 10.2683i | 0.384821i | ||||||||
\(713\) | −6.47423 | − | 0.122845i | −0.242462 | − | 0.00460057i | ||||
\(714\) | −1.11216 | − | 9.25112i | −0.0416217 | − | 0.346214i | ||||
\(715\) | 5.42208 | 0.202774 | ||||||||
\(716\) | 10.6411 | 0.397677 | ||||||||
\(717\) | 4.26624 | − | 0.512885i | 0.159326 | − | 0.0191541i | ||||
\(718\) | −28.5201 | −1.06436 | ||||||||
\(719\) | −44.2748 | −1.65117 | −0.825586 | − | 0.564276i | \(-0.809155\pi\) | ||||
−0.825586 | + | 0.564276i | \(0.809155\pi\) | |||||||
\(720\) | −0.711040 | − | 2.91452i | −0.0264989 | − | 0.108618i | ||||
\(721\) | 7.57073 | 0.281949 | ||||||||
\(722\) | 25.1879i | 0.937396i | ||||||||
\(723\) | −2.67320 | − | 22.2360i | −0.0994174 | − | 0.826966i | ||||
\(724\) | − | 16.8606i | − | 0.626620i | ||||||
\(725\) | −8.20323 | −0.304660 | ||||||||
\(726\) | −1.76030 | − | 14.6424i | −0.0653310 | − | 0.543431i | ||||
\(727\) | 7.70700 | 0.285837 | 0.142918 | − | 0.989734i | \(-0.454351\pi\) | ||||
0.142918 | + | 0.989734i | \(0.454351\pi\) | |||||||
\(728\) | 4.06406 | 0.150624 | ||||||||
\(729\) | 20.3366 | − | 17.7601i | 0.753207 | − | 0.657783i | ||||
\(730\) | 4.67746i | 0.173120i | ||||||||
\(731\) | 31.0899i | 1.14990i | ||||||||
\(732\) | 2.44876 | + | 20.3691i | 0.0905089 | + | 0.752864i | ||||
\(733\) | 34.7400 | 1.28315 | 0.641575 | − | 0.767060i | \(-0.278281\pi\) | ||||
0.641575 | + | 0.767060i | \(0.278281\pi\) | |||||||
\(734\) | −17.5260 | −0.646897 | ||||||||
\(735\) | 1.15850 | + | 9.63654i | 0.0427319 | + | 0.355449i | ||||
\(736\) | 1.16301i | 0.0428693i | ||||||||
\(737\) | 21.4630 | 0.790599 | ||||||||
\(738\) | −15.8028 | + | 3.85532i | −0.581708 | + | 0.141916i | ||||
\(739\) | − | 30.2620i | − | 1.11321i | −0.830779 | − | 0.556603i | \(-0.812104\pi\) | ||
0.830779 | − | 0.556603i | \(-0.187896\pi\) | |||||||
\(740\) | 9.82943 | 0.361337 | ||||||||
\(741\) | −4.72657 | − | 39.3162i | −0.173635 | − | 1.44431i | ||||
\(742\) | − | 8.46922i | − | 0.310915i | ||||||
\(743\) | −15.6965 | −0.575849 | −0.287925 | − | 0.957653i | \(-0.592965\pi\) | ||||
−0.287925 | + | 0.957653i | \(0.592965\pi\) | |||||||
\(744\) | 0.969217 | + | 9.59482i | 0.0355332 | + | 0.351763i | ||||
\(745\) | −6.52980 | −0.239233 | ||||||||
\(746\) | 9.14170i | 0.334701i | ||||||||
\(747\) | 11.2554 | − | 2.74593i | 0.411814 | − | 0.100468i | ||||
\(748\) | 7.17720 | 0.262424 | ||||||||
\(749\) | − | 11.2156i | − | 0.409810i | ||||||
\(750\) | −1.71967 | + | 0.206738i | −0.0627934 | + | 0.00754899i | ||||
\(751\) | −8.88864 | −0.324351 | −0.162176 | − | 0.986762i | \(-0.551851\pi\) | ||||
−0.162176 | + | 0.986762i | \(0.551851\pi\) | |||||||
\(752\) | − | 1.46575i | − | 0.0534506i | ||||||
\(753\) | −9.85719 | + | 1.18503i | −0.359216 | + | 0.0431847i | ||||
\(754\) | 28.2137 | 1.02748 | ||||||||
\(755\) | −9.72099 | −0.353783 | ||||||||
\(756\) | 5.74870 | − | 2.15684i | 0.209078 | − | 0.0784437i | ||||
\(757\) | − | 15.7490i | − | 0.572407i | −0.958169 | − | 0.286204i | \(-0.907607\pi\) | ||
0.958169 | − | 0.286204i | \(-0.0923934\pi\) | |||||||
\(758\) | − | 2.25387i | − | 0.0818641i | ||||||
\(759\) | −3.15298 | + | 0.379050i | −0.114446 | + | 0.0137586i | ||||
\(760\) | −6.64740 | −0.241126 | ||||||||
\(761\) | −27.2961 | −0.989483 | −0.494742 | − | 0.869040i | \(-0.664737\pi\) | ||||
−0.494742 | + | 0.869040i | \(0.664737\pi\) | |||||||
\(762\) | 25.4434 | − | 3.05880i | 0.921719 | − | 0.110809i | ||||
\(763\) | 17.5047 | 0.633714 | ||||||||
\(764\) | − | 26.2574i | − | 0.949958i | ||||||
\(765\) | −3.23711 | − | 13.2688i | −0.117038 | − | 0.479733i | ||||
\(766\) | 5.43602i | 0.196412i | ||||||||
\(767\) | −23.5394 | −0.849958 | ||||||||
\(768\) | 1.71967 | − | 0.206738i | 0.0620532 | − | 0.00746000i | ||||
\(769\) | −34.1753 | −1.23239 | −0.616196 | − | 0.787593i | \(-0.711327\pi\) | ||||
−0.616196 | + | 0.787593i | \(0.711327\pi\) | |||||||
\(770\) | 1.86285 | 0.0671323 | ||||||||
\(771\) | 0.900969 | + | 7.49437i | 0.0324476 | + | 0.269903i | ||||
\(772\) | 20.5459 | 0.739464 | ||||||||
\(773\) | 3.28221 | 0.118053 | 0.0590264 | − | 0.998256i | \(-0.481200\pi\) | ||||
0.0590264 | + | 0.998256i | \(0.481200\pi\) | |||||||
\(774\) | −19.9032 | + | 4.85567i | −0.715404 | + | 0.174533i | ||||
\(775\) | 5.56676 | + | 0.105626i | 0.199964 | + | 0.00379420i | ||||
\(776\) | − | 3.46575i | − | 0.124413i | ||||||
\(777\) | 2.40123 | + | 19.9737i | 0.0861437 | + | 0.716553i | ||||
\(778\) | − | 37.6062i | − | 1.34825i | ||||||
\(779\) | 36.0427i | 1.29136i | ||||||||
\(780\) | 5.91452 | − | 0.711040i | 0.211774 | − | 0.0254593i | ||||
\(781\) | − | 10.2942i | − | 0.368354i | ||||||
\(782\) | 5.29479i | 0.189341i | ||||||||
\(783\) | 39.9088 | − | 14.9733i | 1.42622 | − | 0.535103i | ||||
\(784\) | −5.60372 | −0.200133 | ||||||||
\(785\) | − | 22.0161i | − | 0.785789i | ||||||
\(786\) | 4.89101 | − | 0.587995i | 0.174457 | − | 0.0209731i | ||||
\(787\) | 32.1550i | 1.14620i | 0.819485 | + | 0.573101i | \(0.194260\pi\) | ||||
−0.819485 | + | 0.573101i | \(0.805740\pi\) | |||||||
\(788\) | 5.40391 | 0.192506 | ||||||||
\(789\) | −30.6946 | + | 3.69008i | −1.09276 | + | 0.131370i | ||||
\(790\) | 6.13816i | 0.218386i | ||||||||
\(791\) | − | 20.8960i | − | 0.742977i | ||||||
\(792\) | 1.12095 | + | 4.59471i | 0.0398312 | + | 0.163266i | ||||
\(793\) | −40.7382 | −1.44666 | ||||||||
\(794\) | 18.1656i | 0.644672i | ||||||||
\(795\) | −1.48176 | − | 12.3254i | −0.0525526 | − | 0.437138i | ||||
\(796\) | 6.28837i | 0.222885i | ||||||||
\(797\) | −5.20507 | −0.184373 | −0.0921866 | − | 0.995742i | \(-0.529386\pi\) | ||||
−0.0921866 | + | 0.995742i | \(0.529386\pi\) | |||||||
\(798\) | −1.62389 | − | 13.5077i | −0.0574851 | − | 0.478168i | ||||
\(799\) | − | 6.67306i | − | 0.236076i | ||||||
\(800\) | − | 1.00000i | − | 0.0353553i | ||||||
\(801\) | −29.9272 | + | 7.30118i | −1.05742 | + | 0.257974i | ||||
\(802\) | 27.8508i | 0.983445i | ||||||||
\(803\) | − | 7.37396i | − | 0.260222i | ||||||
\(804\) | 23.4123 | − | 2.81461i | 0.825687 | − | 0.0992636i | ||||
\(805\) | 1.37427i | 0.0484365i | ||||||||
\(806\) | −19.1460 | − | 0.363284i | −0.674388 | − | 0.0127961i | ||||
\(807\) | −9.26665 | + | 1.11403i | −0.326201 | + | 0.0392158i | ||||
\(808\) | 13.3740 | 0.470494 | ||||||||
\(809\) | 37.0068 | 1.30109 | 0.650546 | − | 0.759467i | \(-0.274540\pi\) | ||||
0.650546 | + | 0.759467i | \(0.274540\pi\) | |||||||
\(810\) | 7.98884 | − | 4.14468i | 0.280699 | − | 0.145629i | ||||
\(811\) | −26.6990 | −0.937529 | −0.468764 | − | 0.883323i | \(-0.655301\pi\) | ||||
−0.468764 | + | 0.883323i | \(0.655301\pi\) | |||||||
\(812\) | 9.69328 | 0.340168 | ||||||||
\(813\) | 5.99556 | + | 49.8718i | 0.210273 | + | 1.74908i | ||||
\(814\) | −15.4960 | −0.543135 | ||||||||
\(815\) | − | 14.4283i | − | 0.505402i | ||||||
\(816\) | 7.82904 | − | 0.941203i | 0.274071 | − | 0.0329487i | ||||
\(817\) | 45.3948i | 1.58816i | ||||||||
\(818\) | 2.73048 | 0.0954689 | ||||||||
\(819\) | 2.88971 | + | 11.8448i | 0.100975 | + | 0.413891i | ||||
\(820\) | −5.42208 | −0.189347 | ||||||||
\(821\) | −13.8371 | −0.482917 | −0.241458 | − | 0.970411i | \(-0.577626\pi\) | ||||
−0.241458 | + | 0.970411i | \(0.577626\pi\) | |||||||
\(822\) | 1.14322 | + | 9.50943i | 0.0398743 | + | 0.331679i | ||||
\(823\) | − | 16.8720i | − | 0.588119i | −0.955787 | − | 0.294060i | \(-0.904994\pi\) | ||
0.955787 | − | 0.294060i | \(-0.0950065\pi\) | |||||||
\(824\) | 6.40696i | 0.223197i | ||||||||
\(825\) | 2.71104 | − | 0.325920i | 0.0943863 | − | 0.0113471i | ||||
\(826\) | −8.08735 | −0.281395 | ||||||||
\(827\) | −52.8196 | −1.83672 | −0.918359 | − | 0.395748i | \(-0.870485\pi\) | ||||
−0.918359 | + | 0.395748i | \(0.870485\pi\) | |||||||
\(828\) | −3.38963 | + | 0.826951i | −0.117798 | + | 0.0287385i | ||||
\(829\) | − | 25.2938i | − | 0.878489i | −0.898367 | − | 0.439245i | \(-0.855246\pi\) | ||
0.898367 | − | 0.439245i | \(-0.144754\pi\) | |||||||
\(830\) | 3.86184 | 0.134046 | ||||||||
\(831\) | −0.0271932 | − | 0.226196i | −0.000943320 | − | 0.00784665i | ||||
\(832\) | 3.43934i | 0.119238i | ||||||||
\(833\) | −25.5118 | −0.883930 | ||||||||
\(834\) | −37.2880 | + | 4.48274i | −1.29118 | + | 0.155225i | ||||
\(835\) | − | 1.16301i | − | 0.0402478i | ||||||
\(836\) | 10.4796 | 0.362443 | ||||||||
\(837\) | −27.2751 | + | 9.64711i | −0.942767 | + | 0.333453i | ||||
\(838\) | 3.91265 | 0.135160 | ||||||||
\(839\) | − | 30.6893i | − | 1.05951i | −0.848150 | − | 0.529756i | \(-0.822283\pi\) | ||
0.848150 | − | 0.529756i | \(-0.177717\pi\) | |||||||
\(840\) | 2.03203 | − | 0.244290i | 0.0701118 | − | 0.00842880i | ||||
\(841\) | 38.2930 | 1.32045 | ||||||||
\(842\) | − | 5.57073i | − | 0.191980i | ||||||
\(843\) | 0.141180 | + | 1.17435i | 0.00486249 | + | 0.0404468i | ||||
\(844\) | 10.0792 | 0.346939 | ||||||||
\(845\) | − | 1.17096i | − | 0.0402823i | ||||||
\(846\) | 4.27197 | − | 1.04221i | 0.146873 | − | 0.0358319i | ||||
\(847\) | 10.0613 | 0.345710 | ||||||||
\(848\) | 7.16734 | 0.246127 | ||||||||
\(849\) | 17.3605 | − | 2.08707i | 0.595812 | − | 0.0716282i | ||||
\(850\) | − | 4.55264i | − | 0.156154i | ||||||
\(851\) | − | 11.4318i | − | 0.391876i | ||||||
\(852\) | −1.34996 | − | 11.2291i | −0.0462487 | − | 0.384702i | ||||
\(853\) | 22.9779 | 0.786747 | 0.393374 | − | 0.919379i | \(-0.371308\pi\) | ||||
0.393374 | + | 0.919379i | \(0.371308\pi\) | |||||||
\(854\) | −13.9963 | −0.478944 | ||||||||
\(855\) | −4.72657 | − | 19.3740i | −0.161645 | − | 0.662576i | ||||
\(856\) | 9.49156 | 0.324415 | ||||||||
\(857\) | 32.0982i | 1.09645i | 0.836330 | + | 0.548227i | \(0.184697\pi\) | ||||
−0.836330 | + | 0.548227i | \(0.815303\pi\) | |||||||
\(858\) | −9.32418 | + | 1.12095i | −0.318322 | + | 0.0382685i | ||||
\(859\) | − | 18.3241i | − | 0.625209i | −0.949883 | − | 0.312604i | \(-0.898799\pi\) | ||
0.949883 | − | 0.312604i | \(-0.101201\pi\) | |||||||
\(860\) | −6.82897 | −0.232866 | ||||||||
\(861\) | −1.32456 | − | 11.0178i | −0.0451409 | − | 0.375487i | ||||
\(862\) | −18.9412 | −0.645140 | ||||||||
\(863\) | 36.1664 | 1.23112 | 0.615560 | − | 0.788090i | \(-0.288930\pi\) | ||||
0.615560 | + | 0.788090i | \(0.288930\pi\) | |||||||
\(864\) | 1.82529 | + | 4.86501i | 0.0620978 | + | 0.165511i | ||||
\(865\) | 3.88241 | 0.132006 | ||||||||
\(866\) | −33.6653 | −1.14399 | ||||||||
\(867\) | 6.40846 | − | 0.770422i | 0.217643 | − | 0.0261649i | ||||
\(868\) | −6.57792 | − | 0.124812i | −0.223269 | − | 0.00423640i | ||||
\(869\) | − | 9.67675i | − | 0.328261i | ||||||
\(870\) | 14.1068 | − | 1.69592i | 0.478267 | − | 0.0574970i | ||||
\(871\) | 46.8245i | 1.58659i | ||||||||
\(872\) | 14.8139i | 0.501662i | ||||||||
\(873\) | 10.1010 | − | 2.46429i | 0.341867 | − | 0.0834036i | ||||
\(874\) | 7.73102i | 0.261506i | ||||||||
\(875\) | − | 1.18164i | − | 0.0399468i | ||||||
\(876\) | −0.967006 | − | 8.04367i | −0.0326721 | − | 0.271771i | ||||
\(877\) | −5.02482 | −0.169676 | −0.0848380 | − | 0.996395i | \(-0.527037\pi\) | ||||
−0.0848380 | + | 0.996395i | \(0.527037\pi\) | |||||||
\(878\) | 25.8504i | 0.872409i | ||||||||
\(879\) | −6.48048 | − | 53.9054i | −0.218581 | − | 1.81818i | ||||
\(880\) | 1.57649i | 0.0531435i | ||||||||
\(881\) | 24.6770 | 0.831389 | 0.415695 | − | 0.909504i | \(-0.363539\pi\) | ||||
0.415695 | + | 0.909504i | \(0.363539\pi\) | |||||||
\(882\) | −3.98447 | − | 16.3322i | −0.134164 | − | 0.549932i | ||||
\(883\) | 27.6485i | 0.930447i | 0.885193 | + | 0.465224i | \(0.154026\pi\) | ||||
−0.885193 | + | 0.465224i | \(0.845974\pi\) | |||||||
\(884\) | 15.6581i | 0.526638i | ||||||||
\(885\) | −11.7697 | + | 1.41495i | −0.395634 | + | 0.0475629i | ||||
\(886\) | −3.89058 | −0.130707 | ||||||||
\(887\) | − | 30.8122i | − | 1.03457i | −0.855813 | − | 0.517285i | \(-0.826943\pi\) | ||
0.855813 | − | 0.517285i | \(-0.173057\pi\) | |||||||
\(888\) | −16.9034 | + | 2.03211i | −0.567240 | + | 0.0681933i | ||||
\(889\) | 17.4830i | 0.586362i | ||||||||
\(890\) | −10.2683 | −0.344194 | ||||||||
\(891\) | −12.5943 | + | 6.53405i | −0.421926 | + | 0.218899i | ||||
\(892\) | 12.7191i | 0.425868i | ||||||||
\(893\) | − | 9.74345i | − | 0.326052i | ||||||
\(894\) | 11.2291 | − | 1.34996i | 0.375557 | − | 0.0451493i | ||||
\(895\) | 10.6411i | 0.355693i | ||||||||
\(896\) | 1.18164i | 0.0394759i | ||||||||
\(897\) | −0.826951 | − | 6.87867i | −0.0276111 | − | 0.229672i | ||||
\(898\) | 16.8673i | 0.562871i | ||||||||
\(899\) | −45.6654 | − | 0.866475i | −1.52303 | − | 0.0288986i | ||||
\(900\) | 2.91452 | − | 0.711040i | 0.0971506 | − | 0.0237013i | ||||
\(901\) | 32.6303 | 1.08707 | ||||||||
\(902\) | 8.54786 | 0.284613 | ||||||||
\(903\) | −1.66825 | − | 13.8767i | −0.0555158 | − | 0.461787i | ||||
\(904\) | 17.6839 | 0.588157 | ||||||||
\(905\) | 16.8606 | 0.560466 | ||||||||
\(906\) | 16.7169 | − | 2.00969i | 0.555381 | − | 0.0667676i | ||||
\(907\) | −1.99207 | −0.0661455 | −0.0330727 | − | 0.999453i | \(-0.510529\pi\) | ||||
−0.0330727 | + | 0.999453i | \(0.510529\pi\) | |||||||
\(908\) | 12.3357i | 0.409375i | ||||||||
\(909\) | 9.50943 | + | 38.9787i | 0.315408 | + | 1.29284i | ||||
\(910\) | 4.06406i | 0.134722i | ||||||||
\(911\) | 28.2930 | 0.937390 | 0.468695 | − | 0.883360i | \(-0.344724\pi\) | ||||
0.468695 | + | 0.883360i | \(0.344724\pi\) | |||||||
\(912\) | 11.4313 | − | 1.37427i | 0.378529 | − | 0.0455065i | ||||
\(913\) | −6.08815 | −0.201489 | ||||||||
\(914\) | 6.15575 | 0.203614 | ||||||||
\(915\) | −20.3691 | + | 2.44876i | −0.673382 | + | 0.0809537i | ||||
\(916\) | − | 3.44164i | − | 0.113715i | ||||||
\(917\) | 3.36078i | 0.110983i | ||||||||
\(918\) | 8.30992 | + | 22.1486i | 0.274268 | + | 0.731014i | ||||
\(919\) | 23.2183 | 0.765901 | 0.382951 | − | 0.923769i | \(-0.374908\pi\) | ||||
0.382951 | + | 0.923769i | \(0.374908\pi\) | |||||||
\(920\) | −1.16301 | −0.0383435 | ||||||||
\(921\) | −19.7526 | + | 2.37465i | −0.650872 | + | 0.0782474i | ||||
\(922\) | − | 6.44714i | − | 0.212325i | ||||||
\(923\) | 22.4582 | 0.739220 | ||||||||
\(924\) | −3.20348 | + | 0.385121i | −0.105387 | + | 0.0126695i | ||||
\(925\) | 9.82943i | 0.323190i | ||||||||
\(926\) | −29.6849 | −0.975506 | ||||||||
\(927\) | −18.6732 | + | 4.55561i | −0.613308 | + | 0.149626i | ||||
\(928\) | 8.20323i | 0.269284i | ||||||||
\(929\) | −15.4931 | −0.508311 | −0.254156 | − | 0.967163i | \(-0.581798\pi\) | ||||
−0.254156 | + | 0.967163i | \(0.581798\pi\) | |||||||
\(930\) | −9.59482 | + | 0.969217i | −0.314627 | + | 0.0317819i | ||||
\(931\) | −37.2502 | −1.22082 | ||||||||
\(932\) | 14.8397i | 0.486091i | ||||||||
\(933\) | −0.254237 | − | 2.11478i | −0.00832336 | − | 0.0692347i | ||||
\(934\) | 17.1558 | 0.561356 | ||||||||
\(935\) | 7.17720i | 0.234719i | ||||||||
\(936\) | −10.0240 | + | 2.44551i | −0.327645 | + | 0.0799339i | ||||
\(937\) | 33.8512 | 1.10587 | 0.552935 | − | 0.833224i | \(-0.313508\pi\) | ||||
0.552935 | + | 0.833224i | \(0.313508\pi\) | |||||||
\(938\) | 16.0873i | 0.525271i | ||||||||
\(939\) | −0.547673 | − | 4.55561i | −0.0178726 | − | 0.148667i | ||||
\(940\) | 1.46575 | 0.0478076 | ||||||||
\(941\) | −32.4549 | −1.05800 | −0.528999 | − | 0.848622i | \(-0.677433\pi\) | ||||
−0.528999 | + | 0.848622i | \(0.677433\pi\) | |||||||
\(942\) | 4.55156 | + | 37.8604i | 0.148298 | + | 1.23356i | ||||
\(943\) | 6.30596i | 0.205350i | ||||||||
\(944\) | − | 6.84416i | − | 0.222758i | ||||||
\(945\) | 2.15684 | + | 5.74870i | 0.0701622 | + | 0.187005i | ||||
\(946\) | 10.7658 | 0.350026 | ||||||||
\(947\) | 7.36847 | 0.239443 | 0.119722 | − | 0.992808i | \(-0.461800\pi\) | ||||
0.119722 | + | 0.992808i | \(0.461800\pi\) | |||||||
\(948\) | −1.26899 | − | 10.5556i | −0.0412149 | − | 0.342830i | ||||
\(949\) | 16.0873 | 0.522217 | ||||||||
\(950\) | − | 6.64740i | − | 0.215670i | ||||||
\(951\) | −3.65059 | − | 30.3660i | −0.118378 | − | 0.984686i | ||||
\(952\) | 5.37959i | 0.174354i | ||||||||
\(953\) | −46.3285 | −1.50073 | −0.750364 | − | 0.661024i | \(-0.770122\pi\) | ||||
−0.750364 | + | 0.661024i | \(0.770122\pi\) | |||||||
\(954\) | 5.09627 | + | 20.8893i | 0.164998 | + | 0.676317i | ||||
\(955\) | 26.2574 | 0.849668 | ||||||||
\(956\) | −2.48085 | −0.0802365 | ||||||||
\(957\) | −22.2393 | + | 2.67360i | −0.718894 | + | 0.0864251i | ||||
\(958\) | −28.7338 | −0.928347 | ||||||||
\(959\) | −6.53425 | −0.211002 | ||||||||
\(960\) | 0.206738 | + | 1.71967i | 0.00667243 | + | 0.0555021i | ||||
\(961\) | 30.9777 | + | 1.17599i | 0.999280 | + | 0.0379352i | ||||
\(962\) | − | 33.8067i | − | 1.08997i | ||||||
\(963\) | 6.74888 | + | 27.6633i | 0.217480 | + | 0.891438i | ||||
\(964\) | 12.9304i | 0.416460i | ||||||||
\(965\) | 20.5459i | 0.661396i | ||||||||
\(966\) | −0.284113 | − | 2.36328i | −0.00914118 | − | 0.0760374i | ||||
\(967\) | − | 46.2902i | − | 1.48859i | −0.667850 | − | 0.744296i | \(-0.732785\pi\) | ||
0.667850 | − | 0.744296i | \(-0.267215\pi\) | |||||||
\(968\) | 8.51468i | 0.273672i | ||||||||
\(969\) | 52.0427 | − | 6.25655i | 1.67185 | − | 0.200989i | ||||
\(970\) | 3.46575 | 0.111279 | ||||||||
\(971\) | 50.8264i | 1.63110i | 0.578689 | + | 0.815548i | \(0.303564\pi\) | ||||
−0.578689 | + | 0.815548i | \(0.696436\pi\) | |||||||
\(972\) | −12.8813 | + | 8.77907i | −0.413168 | + | 0.281589i | ||||
\(973\) | − | 25.6218i | − | 0.821398i | ||||||
\(974\) | −9.91982 | −0.317851 | ||||||||
\(975\) | 0.711040 | + | 5.91452i | 0.0227715 | + | 0.189416i | ||||
\(976\) | − | 11.8448i | − | 0.379143i | ||||||
\(977\) | − | 43.9331i | − | 1.40554i | −0.711416 | − | 0.702772i | \(-0.751946\pi\) | ||
0.711416 | − | 0.702772i | \(-0.248054\pi\) | |||||||
\(978\) | 2.98288 | + | 24.8119i | 0.0953819 | + | 0.793398i | ||||
\(979\) | 16.1879 | 0.517367 | ||||||||
\(980\) | − | 5.60372i | − | 0.179004i | ||||||
\(981\) | −43.1754 | + | 10.5333i | −1.37849 | + | 0.336302i | ||||
\(982\) | 26.2946i | 0.839095i | ||||||||
\(983\) | −47.5531 | −1.51671 | −0.758354 | − | 0.651843i | \(-0.773996\pi\) | ||||
−0.758354 | + | 0.651843i | \(0.773996\pi\) | |||||||
\(984\) | 9.32418 | − | 1.12095i | 0.297244 | − | 0.0357345i | ||||
\(985\) | 5.40391i | 0.172183i | ||||||||
\(986\) | 37.3464i | 1.18935i | ||||||||
\(987\) | 0.358069 | + | 2.97846i | 0.0113975 | + | 0.0948054i | ||||
\(988\) | 22.8626i | 0.727357i | ||||||||
\(989\) | 7.94219i | 0.252547i | ||||||||
\(990\) | −4.59471 | + | 1.12095i | −0.146029 | + | 0.0356261i | ||||
\(991\) | − | 50.6232i | − | 1.60810i | −0.594562 | − | 0.804050i | \(-0.702675\pi\) | ||
0.594562 | − | 0.804050i | \(-0.297325\pi\) | |||||||
\(992\) | 0.105626 | − | 5.56676i | 0.00335363 | − | 0.176745i | ||||
\(993\) | 7.50837 | + | 62.4555i | 0.238271 | + | 1.98197i | ||||
\(994\) | 7.71589 | 0.244733 | ||||||||
\(995\) | −6.28837 | −0.199355 | ||||||||
\(996\) | −6.64109 | + | 0.798388i | −0.210431 | + | 0.0252979i | ||||
\(997\) | −38.6333 | −1.22353 | −0.611764 | − | 0.791040i | \(-0.709540\pi\) | ||||
−0.611764 | + | 0.791040i | \(0.709540\pi\) | |||||||
\(998\) | −9.24144 | −0.292533 | ||||||||
\(999\) | −17.9416 | − | 47.8203i | −0.567647 | − | 1.51297i |
(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 | 930.2.h.d.371.16 | yes | 16 | |
3.2 | odd | 2 | inner | 930.2.h.d.371.1 | ✓ | 16 | |
31.30 | odd | 2 | inner | 930.2.h.d.371.9 | yes | 16 | |
93.92 | even | 2 | inner | 930.2.h.d.371.8 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
930.2.h.d.371.1 | ✓ | 16 | 3.2 | odd | 2 | inner | |
930.2.h.d.371.8 | yes | 16 | 93.92 | even | 2 | inner | |
930.2.h.d.371.9 | yes | 16 | 31.30 | odd | 2 | inner | |
930.2.h.d.371.16 | yes | 16 | 1.1 | even | 1 | trivial |