Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [74,2,Mod(47,74)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(74, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("74.47");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 74 = 2 \cdot 37 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 74.c (of order \(3\), degree \(2\), 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: | \(0.590892974957\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Relative dimension: | \(3\) over \(\Q(\zeta_{3})\) |
Coefficient field: | 6.0.4406832.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - x^{5} + 6x^{4} + 7x^{3} + 24x^{2} + 5x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 47.2 | ||
Root | \(1.43310 + 2.48220i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 74.47 |
Dual form | 74.2.c.c.63.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/74\mathbb{Z}\right)^\times\).
\(n\) | \(39\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.500000 | + | 0.866025i | −0.353553 | + | 0.612372i | ||||
\(3\) | −0.258652 | − | 0.447998i | −0.149333 | − | 0.258652i | 0.781648 | − | 0.623720i | \(-0.214379\pi\) |
−0.930981 | + | 0.365067i | \(0.881046\pi\) | |||||||
\(4\) | −0.500000 | − | 0.866025i | −0.250000 | − | 0.433013i | ||||
\(5\) | 2.10755 | + | 3.65038i | 0.942523 | + | 1.63250i | 0.760636 | + | 0.649179i | \(0.224887\pi\) |
0.181888 | + | 0.983319i | \(0.441779\pi\) | |||||||
\(6\) | 0.517304 | 0.211188 | ||||||||
\(7\) | 0.258652 | + | 0.447998i | 0.0977613 | + | 0.169327i | 0.910758 | − | 0.412941i | \(-0.135499\pi\) |
−0.812996 | + | 0.582269i | \(0.802165\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 1.36620 | − | 2.36632i | 0.455399 | − | 0.788775i | ||||
\(10\) | −4.21509 | −1.33293 | ||||||||
\(11\) | −3.73240 | −1.12536 | −0.562680 | − | 0.826675i | \(-0.690230\pi\) | ||||
−0.562680 | + | 0.826675i | \(0.690230\pi\) | |||||||
\(12\) | −0.258652 | + | 0.447998i | −0.0746664 | + | 0.129326i | ||||
\(13\) | −1.00000 | − | 1.73205i | −0.277350 | − | 0.480384i | 0.693375 | − | 0.720577i | \(-0.256123\pi\) |
−0.970725 | + | 0.240192i | \(0.922790\pi\) | |||||||
\(14\) | −0.517304 | −0.138255 | ||||||||
\(15\) | 1.09024 | − | 1.88835i | 0.281499 | − | 0.487571i | ||||
\(16\) | −0.500000 | + | 0.866025i | −0.125000 | + | 0.216506i | ||||
\(17\) | 1.01730 | − | 1.76202i | 0.246732 | − | 0.427353i | −0.715885 | − | 0.698218i | \(-0.753976\pi\) |
0.962617 | + | 0.270865i | \(0.0873098\pi\) | |||||||
\(18\) | 1.36620 | + | 2.36632i | 0.322016 | + | 0.557748i | ||||
\(19\) | −3.34889 | − | 5.80045i | −0.768289 | − | 1.33072i | −0.938490 | − | 0.345306i | \(-0.887775\pi\) |
0.170201 | − | 0.985409i | \(-0.445558\pi\) | |||||||
\(20\) | 2.10755 | − | 3.65038i | 0.471262 | − | 0.816249i | ||||
\(21\) | 0.133802 | − | 0.231751i | 0.0291979 | − | 0.0505723i | ||||
\(22\) | 1.86620 | − | 3.23235i | 0.397875 | − | 0.689139i | ||||
\(23\) | 7.21509 | 1.50445 | 0.752225 | − | 0.658906i | \(-0.228980\pi\) | ||||
0.752225 | + | 0.658906i | \(0.228980\pi\) | |||||||
\(24\) | −0.258652 | − | 0.447998i | −0.0527971 | − | 0.0914473i | ||||
\(25\) | −6.38350 | + | 11.0566i | −1.27670 | + | 2.21131i | ||||
\(26\) | 2.00000 | 0.392232 | ||||||||
\(27\) | −2.96539 | −0.570690 | ||||||||
\(28\) | 0.258652 | − | 0.447998i | 0.0488806 | − | 0.0846637i | ||||
\(29\) | −0.482696 | −0.0896344 | −0.0448172 | − | 0.998995i | \(-0.514271\pi\) | ||||
−0.0448172 | + | 0.998995i | \(0.514271\pi\) | |||||||
\(30\) | 1.09024 | + | 1.88835i | 0.199050 | + | 0.344765i | ||||
\(31\) | −2.69779 | −0.484537 | −0.242269 | − | 0.970209i | \(-0.577892\pi\) | ||||
−0.242269 | + | 0.970209i | \(0.577892\pi\) | |||||||
\(32\) | −0.500000 | − | 0.866025i | −0.0883883 | − | 0.153093i | ||||
\(33\) | 0.965392 | + | 1.67211i | 0.168053 | + | 0.291077i | ||||
\(34\) | 1.01730 | + | 1.76202i | 0.174466 | + | 0.302184i | ||||
\(35\) | −1.09024 | + | 1.88835i | −0.184285 | + | 0.319190i | ||||
\(36\) | −2.73240 | −0.455399 | ||||||||
\(37\) | −4.10755 | + | 4.48643i | −0.675276 | + | 0.737565i | ||||
\(38\) | 6.69779 | 1.08652 | ||||||||
\(39\) | −0.517304 | + | 0.895997i | −0.0828349 | + | 0.143474i | ||||
\(40\) | 2.10755 | + | 3.65038i | 0.333232 | + | 0.577175i | ||||
\(41\) | −0.848894 | − | 1.47033i | −0.132575 | − | 0.229627i | 0.792093 | − | 0.610400i | \(-0.208991\pi\) |
−0.924668 | + | 0.380773i | \(0.875658\pi\) | |||||||
\(42\) | 0.133802 | + | 0.231751i | 0.0206461 | + | 0.0357600i | ||||
\(43\) | 8.24970 | 1.25807 | 0.629034 | − | 0.777378i | \(-0.283451\pi\) | ||||
0.629034 | + | 0.777378i | \(0.283451\pi\) | |||||||
\(44\) | 1.86620 | + | 3.23235i | 0.281340 | + | 0.487295i | ||||
\(45\) | 11.5173 | 1.71690 | ||||||||
\(46\) | −3.60755 | + | 6.24845i | −0.531904 | + | 0.921284i | ||||
\(47\) | −1.30221 | −0.189947 | −0.0949735 | − | 0.995480i | \(-0.530277\pi\) | ||||
−0.0949735 | + | 0.995480i | \(0.530277\pi\) | |||||||
\(48\) | 0.517304 | 0.0746664 | ||||||||
\(49\) | 3.36620 | − | 5.83043i | 0.480885 | − | 0.832918i | ||||
\(50\) | −6.38350 | − | 11.0566i | −0.902764 | − | 1.56363i | ||||
\(51\) | −1.05251 | −0.147381 | ||||||||
\(52\) | −1.00000 | + | 1.73205i | −0.138675 | + | 0.240192i | ||||
\(53\) | −1.13380 | + | 1.96380i | −0.155740 | + | 0.269749i | −0.933328 | − | 0.359025i | \(-0.883109\pi\) |
0.777588 | + | 0.628774i | \(0.216443\pi\) | |||||||
\(54\) | 1.48270 | − | 2.56810i | 0.201769 | − | 0.349475i | ||||
\(55\) | −7.86620 | − | 13.6247i | −1.06068 | − | 1.83715i | ||||
\(56\) | 0.258652 | + | 0.447998i | 0.0345638 | + | 0.0598663i | ||||
\(57\) | −1.73240 | + | 3.00060i | −0.229462 | + | 0.397439i | ||||
\(58\) | 0.241348 | − | 0.418027i | 0.0316905 | − | 0.0548896i | ||||
\(59\) | −6.24970 | + | 10.8248i | −0.813642 | + | 1.40927i | 0.0966574 | + | 0.995318i | \(0.469185\pi\) |
−0.910299 | + | 0.413951i | \(0.864148\pi\) | |||||||
\(60\) | −2.18048 | −0.281499 | ||||||||
\(61\) | −1.24135 | − | 2.15008i | −0.158938 | − | 0.275289i | 0.775548 | − | 0.631289i | \(-0.217474\pi\) |
−0.934486 | + | 0.356000i | \(0.884140\pi\) | |||||||
\(62\) | 1.34889 | − | 2.33635i | 0.171310 | − | 0.296717i | ||||
\(63\) | 1.41348 | 0.178082 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 4.21509 | − | 7.30075i | 0.522818 | − | 0.905547i | ||||
\(66\) | −1.93078 | −0.237663 | ||||||||
\(67\) | 0.133802 | + | 0.231751i | 0.0163465 | + | 0.0283129i | 0.874083 | − | 0.485777i | \(-0.161463\pi\) |
−0.857736 | + | 0.514090i | \(0.828130\pi\) | |||||||
\(68\) | −2.03461 | −0.246732 | ||||||||
\(69\) | −1.86620 | − | 3.23235i | −0.224664 | − | 0.389129i | ||||
\(70\) | −1.09024 | − | 1.88835i | −0.130309 | − | 0.225702i | ||||
\(71\) | 1.74135 | + | 3.01610i | 0.206660 | + | 0.357946i | 0.950660 | − | 0.310234i | \(-0.100407\pi\) |
−0.744000 | + | 0.668179i | \(0.767074\pi\) | |||||||
\(72\) | 1.36620 | − | 2.36632i | 0.161008 | − | 0.278874i | ||||
\(73\) | 5.73240 | 0.670926 | 0.335463 | − | 0.942053i | \(-0.391107\pi\) | ||||
0.335463 | + | 0.942053i | \(0.391107\pi\) | |||||||
\(74\) | −1.83159 | − | 5.80045i | −0.212918 | − | 0.674289i | ||||
\(75\) | 6.60442 | 0.762613 | ||||||||
\(76\) | −3.34889 | + | 5.80045i | −0.384145 | + | 0.665358i | ||||
\(77\) | −0.965392 | − | 1.67211i | −0.110017 | − | 0.190554i | ||||
\(78\) | −0.517304 | − | 0.895997i | −0.0585731 | − | 0.101452i | ||||
\(79\) | −2.38350 | − | 4.12835i | −0.268165 | − | 0.464475i | 0.700223 | − | 0.713924i | \(-0.253084\pi\) |
−0.968388 | + | 0.249449i | \(0.919751\pi\) | |||||||
\(80\) | −4.21509 | −0.471262 | ||||||||
\(81\) | −3.33159 | − | 5.77048i | −0.370177 | − | 0.641165i | ||||
\(82\) | 1.69779 | 0.187489 | ||||||||
\(83\) | −5.47374 | + | 9.48080i | −0.600822 | + | 1.04065i | 0.391875 | + | 0.920018i | \(0.371826\pi\) |
−0.992697 | + | 0.120635i | \(0.961507\pi\) | |||||||
\(84\) | −0.267603 | −0.0291979 | ||||||||
\(85\) | 8.57606 | 0.930204 | ||||||||
\(86\) | −4.12485 | + | 7.14445i | −0.444794 | + | 0.770406i | ||||
\(87\) | 0.124850 | + | 0.216247i | 0.0133854 | + | 0.0231841i | ||||
\(88\) | −3.73240 | −0.397875 | ||||||||
\(89\) | −8.06399 | + | 13.9672i | −0.854781 | + | 1.48052i | 0.0220673 | + | 0.999756i | \(0.492975\pi\) |
−0.876848 | + | 0.480767i | \(0.840358\pi\) | |||||||
\(90\) | −5.75865 | + | 9.97428i | −0.607015 | + | 1.05138i | ||||
\(91\) | 0.517304 | − | 0.895997i | 0.0542282 | − | 0.0939260i | ||||
\(92\) | −3.60755 | − | 6.24845i | −0.376113 | − | 0.651446i | ||||
\(93\) | 0.697788 | + | 1.20861i | 0.0723573 | + | 0.125327i | ||||
\(94\) | 0.651106 | − | 1.12775i | 0.0671564 | − | 0.116318i | ||||
\(95\) | 14.1159 | − | 24.4495i | 1.44826 | − | 2.50846i | ||||
\(96\) | −0.258652 | + | 0.447998i | −0.0263986 | + | 0.0457236i | ||||
\(97\) | 0.302212 | 0.0306849 | 0.0153425 | − | 0.999882i | \(-0.495116\pi\) | ||||
0.0153425 | + | 0.999882i | \(0.495116\pi\) | |||||||
\(98\) | 3.36620 | + | 5.83043i | 0.340037 | + | 0.588962i | ||||
\(99\) | −5.09919 | + | 8.83206i | −0.512488 | + | 0.887656i | ||||
\(100\) | 12.7670 | 1.27670 | ||||||||
\(101\) | −9.24970 | −0.920380 | −0.460190 | − | 0.887821i | \(-0.652219\pi\) | ||||
−0.460190 | + | 0.887821i | \(0.652219\pi\) | |||||||
\(102\) | 0.526255 | − | 0.911501i | 0.0521071 | − | 0.0902521i | ||||
\(103\) | 6.44809 | 0.635349 | 0.317674 | − | 0.948200i | \(-0.397098\pi\) | ||||
0.317674 | + | 0.948200i | \(0.397098\pi\) | |||||||
\(104\) | −1.00000 | − | 1.73205i | −0.0980581 | − | 0.169842i | ||||
\(105\) | 1.12797 | 0.110079 | ||||||||
\(106\) | −1.13380 | − | 1.96380i | −0.110125 | − | 0.190741i | ||||
\(107\) | 6.12485 | + | 10.6086i | 0.592112 | + | 1.02557i | 0.993948 | + | 0.109856i | \(0.0350389\pi\) |
−0.401836 | + | 0.915712i | \(0.631628\pi\) | |||||||
\(108\) | 1.48270 | + | 2.56810i | 0.142672 | + | 0.247116i | ||||
\(109\) | 3.45644 | − | 5.98673i | 0.331067 | − | 0.573425i | −0.651654 | − | 0.758516i | \(-0.725925\pi\) |
0.982721 | + | 0.185091i | \(0.0592581\pi\) | |||||||
\(110\) | 15.7324 | 1.50003 | ||||||||
\(111\) | 3.07234 | + | 0.679750i | 0.291614 | + | 0.0645190i | ||||
\(112\) | −0.517304 | −0.0488806 | ||||||||
\(113\) | 4.86620 | − | 8.42850i | 0.457773 | − | 0.792887i | −0.541070 | − | 0.840978i | \(-0.681980\pi\) |
0.998843 | + | 0.0480910i | \(0.0153138\pi\) | |||||||
\(114\) | −1.73240 | − | 3.00060i | −0.162254 | − | 0.281032i | ||||
\(115\) | 15.2061 | + | 26.3378i | 1.41798 | + | 2.45601i | ||||
\(116\) | 0.241348 | + | 0.418027i | 0.0224086 | + | 0.0388128i | ||||
\(117\) | −5.46479 | −0.505220 | ||||||||
\(118\) | −6.24970 | − | 10.8248i | −0.575332 | − | 0.996504i | ||||
\(119\) | 1.05251 | 0.0964835 | ||||||||
\(120\) | 1.09024 | − | 1.88835i | 0.0995250 | − | 0.172382i | ||||
\(121\) | 2.93078 | 0.266435 | ||||||||
\(122\) | 2.48270 | 0.224773 | ||||||||
\(123\) | −0.439136 | + | 0.760607i | −0.0395956 | + | 0.0685816i | ||||
\(124\) | 1.34889 | + | 2.33635i | 0.121134 | + | 0.209811i | ||||
\(125\) | −32.7386 | −2.92823 | ||||||||
\(126\) | −0.706740 | + | 1.22411i | −0.0629614 | + | 0.109052i | ||||
\(127\) | −7.85725 | + | 13.6092i | −0.697218 | + | 1.20762i | 0.272209 | + | 0.962238i | \(0.412246\pi\) |
−0.969427 | + | 0.245379i | \(0.921088\pi\) | |||||||
\(128\) | −0.500000 | + | 0.866025i | −0.0441942 | + | 0.0765466i | ||||
\(129\) | −2.13380 | − | 3.69585i | −0.187871 | − | 0.325402i | ||||
\(130\) | 4.21509 | + | 7.30075i | 0.369688 | + | 0.640319i | ||||
\(131\) | 6.68884 | − | 11.5854i | 0.584406 | − | 1.01222i | −0.410543 | − | 0.911841i | \(-0.634661\pi\) |
0.994949 | − | 0.100380i | \(-0.0320059\pi\) | |||||||
\(132\) | 0.965392 | − | 1.67211i | 0.0840266 | − | 0.145538i | ||||
\(133\) | 1.73240 | − | 3.00060i | 0.150218 | − | 0.260185i | ||||
\(134\) | −0.267603 | −0.0231174 | ||||||||
\(135\) | −6.24970 | − | 10.8248i | −0.537889 | − | 0.931650i | ||||
\(136\) | 1.01730 | − | 1.76202i | 0.0872331 | − | 0.151092i | ||||
\(137\) | −13.3610 | −1.14150 | −0.570752 | − | 0.821122i | \(-0.693348\pi\) | ||||
−0.570752 | + | 0.821122i | \(0.693348\pi\) | |||||||
\(138\) | 3.73240 | 0.317723 | ||||||||
\(139\) | −7.20614 | + | 12.4814i | −0.611217 | + | 1.05866i | 0.379819 | + | 0.925061i | \(0.375986\pi\) |
−0.991036 | + | 0.133598i | \(0.957347\pi\) | |||||||
\(140\) | 2.18048 | 0.184285 | ||||||||
\(141\) | 0.336820 | + | 0.583389i | 0.0283653 | + | 0.0491302i | ||||
\(142\) | −3.48270 | −0.292261 | ||||||||
\(143\) | 3.73240 | + | 6.46470i | 0.312119 | + | 0.540605i | ||||
\(144\) | 1.36620 | + | 2.36632i | 0.113850 | + | 0.197194i | ||||
\(145\) | −1.01730 | − | 1.76202i | −0.0844825 | − | 0.146328i | ||||
\(146\) | −2.86620 | + | 4.96440i | −0.237208 | + | 0.410857i | ||||
\(147\) | −3.48270 | −0.287248 | ||||||||
\(148\) | 5.93914 | + | 1.31402i | 0.488194 | + | 0.108012i | ||||
\(149\) | 20.9129 | 1.71325 | 0.856625 | − | 0.515940i | \(-0.172557\pi\) | ||||
0.856625 | + | 0.515940i | \(0.172557\pi\) | |||||||
\(150\) | −3.30221 | + | 5.71960i | −0.269624 | + | 0.467003i | ||||
\(151\) | −8.82264 | − | 15.2813i | −0.717976 | − | 1.24357i | −0.961800 | − | 0.273752i | \(-0.911735\pi\) |
0.243824 | − | 0.969819i | \(-0.421598\pi\) | |||||||
\(152\) | −3.34889 | − | 5.80045i | −0.271631 | − | 0.470479i | ||||
\(153\) | −2.77968 | − | 4.81454i | −0.224724 | − | 0.389233i | ||||
\(154\) | 1.93078 | 0.155587 | ||||||||
\(155\) | −5.68571 | − | 9.84795i | −0.456688 | − | 0.791006i | ||||
\(156\) | 1.03461 | 0.0828349 | ||||||||
\(157\) | 5.00835 | − | 8.67472i | 0.399710 | − | 0.692318i | −0.593980 | − | 0.804480i | \(-0.702444\pi\) |
0.993690 | + | 0.112162i | \(0.0357775\pi\) | |||||||
\(158\) | 4.76700 | 0.379243 | ||||||||
\(159\) | 1.17304 | 0.0930282 | ||||||||
\(160\) | 2.10755 | − | 3.65038i | 0.166616 | − | 0.288588i | ||||
\(161\) | 1.86620 | + | 3.23235i | 0.147077 | + | 0.254745i | ||||
\(162\) | 6.66318 | 0.523509 | ||||||||
\(163\) | 3.09024 | − | 5.35246i | 0.242046 | − | 0.419237i | −0.719251 | − | 0.694751i | \(-0.755515\pi\) |
0.961297 | + | 0.275514i | \(0.0888480\pi\) | |||||||
\(164\) | −0.848894 | + | 1.47033i | −0.0662875 | + | 0.114813i | ||||
\(165\) | −4.06922 | + | 7.04809i | −0.316788 | + | 0.548693i | ||||
\(166\) | −5.47374 | − | 9.48080i | −0.424845 | − | 0.735853i | ||||
\(167\) | 6.00000 | + | 10.3923i | 0.464294 | + | 0.804181i | 0.999169 | − | 0.0407502i | \(-0.0129748\pi\) |
−0.534875 | + | 0.844931i | \(0.679641\pi\) | |||||||
\(168\) | 0.133802 | − | 0.231751i | 0.0103230 | − | 0.0178800i | ||||
\(169\) | 4.50000 | − | 7.79423i | 0.346154 | − | 0.599556i | ||||
\(170\) | −4.28803 | + | 7.42709i | −0.328877 | + | 0.569632i | ||||
\(171\) | −18.3010 | −1.39951 | ||||||||
\(172\) | −4.12485 | − | 7.14445i | −0.314517 | − | 0.544759i | ||||
\(173\) | 1.45644 | − | 2.52263i | 0.110731 | − | 0.191792i | −0.805334 | − | 0.592821i | \(-0.798014\pi\) |
0.916065 | + | 0.401029i | \(0.131347\pi\) | |||||||
\(174\) | −0.249701 | −0.0189298 | ||||||||
\(175\) | −6.60442 | −0.499247 | ||||||||
\(176\) | 1.86620 | − | 3.23235i | 0.140670 | − | 0.243648i | ||||
\(177\) | 6.46599 | 0.486014 | ||||||||
\(178\) | −8.06399 | − | 13.9672i | −0.604421 | − | 1.04689i | ||||
\(179\) | −6.96539 | −0.520618 | −0.260309 | − | 0.965525i | \(-0.583824\pi\) | ||||
−0.260309 | + | 0.965525i | \(0.583824\pi\) | |||||||
\(180\) | −5.75865 | − | 9.97428i | −0.429225 | − | 0.743439i | ||||
\(181\) | 3.14215 | + | 5.44237i | 0.233554 | + | 0.404528i | 0.958852 | − | 0.283908i | \(-0.0916309\pi\) |
−0.725297 | + | 0.688436i | \(0.758298\pi\) | |||||||
\(182\) | 0.517304 | + | 0.895997i | 0.0383451 | + | 0.0664157i | ||||
\(183\) | −0.642154 | + | 1.11224i | −0.0474694 | + | 0.0822194i | ||||
\(184\) | 7.21509 | 0.531904 | ||||||||
\(185\) | −25.0340 | − | 5.53873i | −1.84054 | − | 0.407216i | ||||
\(186\) | −1.39558 | −0.102329 | ||||||||
\(187\) | −3.79698 | + | 6.57657i | −0.277663 | + | 0.480926i | ||||
\(188\) | 0.651106 | + | 1.12775i | 0.0474868 | + | 0.0822495i | ||||
\(189\) | −0.767005 | − | 1.32849i | −0.0557914 | − | 0.0966335i | ||||
\(190\) | 14.1159 | + | 24.4495i | 1.02407 | + | 1.77375i | ||||
\(191\) | 11.5761 | 0.837614 | 0.418807 | − | 0.908075i | \(-0.362448\pi\) | ||||
0.418807 | + | 0.908075i | \(0.362448\pi\) | |||||||
\(192\) | −0.258652 | − | 0.447998i | −0.0186666 | − | 0.0323315i | ||||
\(193\) | 13.4302 | 0.966726 | 0.483363 | − | 0.875420i | \(-0.339415\pi\) | ||||
0.483363 | + | 0.875420i | \(0.339415\pi\) | |||||||
\(194\) | −0.151106 | + | 0.261723i | −0.0108488 | + | 0.0187906i | ||||
\(195\) | −4.36097 | −0.312295 | ||||||||
\(196\) | −6.73240 | −0.480885 | ||||||||
\(197\) | 2.75865 | − | 4.77813i | 0.196546 | − | 0.340427i | −0.750860 | − | 0.660461i | \(-0.770361\pi\) |
0.947406 | + | 0.320034i | \(0.103694\pi\) | |||||||
\(198\) | −5.09919 | − | 8.83206i | −0.362384 | − | 0.627667i | ||||
\(199\) | 16.3431 | 1.15853 | 0.579265 | − | 0.815140i | \(-0.303340\pi\) | ||||
0.579265 | + | 0.815140i | \(0.303340\pi\) | |||||||
\(200\) | −6.38350 | + | 11.0566i | −0.451382 | + | 0.781816i | ||||
\(201\) | 0.0692162 | − | 0.119886i | 0.00488213 | − | 0.00845610i | ||||
\(202\) | 4.62485 | − | 8.01048i | 0.325403 | − | 0.563615i | ||||
\(203\) | −0.124850 | − | 0.216247i | −0.00876277 | − | 0.0151776i | ||||
\(204\) | 0.526255 | + | 0.911501i | 0.0368453 | + | 0.0638179i | ||||
\(205\) | 3.57817 | − | 6.19757i | 0.249910 | − | 0.432857i | ||||
\(206\) | −3.22404 | + | 5.58421i | −0.224630 | + | 0.389070i | ||||
\(207\) | 9.85725 | − | 17.0733i | 0.685126 | − | 1.18667i | ||||
\(208\) | 2.00000 | 0.138675 | ||||||||
\(209\) | 12.4994 | + | 21.6496i | 0.864602 | + | 1.49753i | ||||
\(210\) | −0.563987 | + | 0.976854i | −0.0389188 | + | 0.0674093i | ||||
\(211\) | 20.7491 | 1.42843 | 0.714214 | − | 0.699928i | \(-0.246785\pi\) | ||||
0.714214 | + | 0.699928i | \(0.246785\pi\) | |||||||
\(212\) | 2.26760 | 0.155740 | ||||||||
\(213\) | 0.900806 | − | 1.56024i | 0.0617222 | − | 0.106906i | ||||
\(214\) | −12.2497 | −0.837372 | ||||||||
\(215\) | 17.3866 | + | 30.1145i | 1.18576 | + | 2.05379i | ||||
\(216\) | −2.96539 | −0.201769 | ||||||||
\(217\) | −0.697788 | − | 1.20861i | −0.0473690 | − | 0.0820455i | ||||
\(218\) | 3.45644 | + | 5.98673i | 0.234100 | + | 0.405473i | ||||
\(219\) | −1.48270 | − | 2.56810i | −0.100191 | − | 0.173536i | ||||
\(220\) | −7.86620 | + | 13.6247i | −0.530339 | + | 0.918574i | ||||
\(221\) | −4.06922 | −0.273725 | ||||||||
\(222\) | −2.12485 | + | 2.32085i | −0.142611 | + | 0.155765i | ||||
\(223\) | −6.85412 | −0.458986 | −0.229493 | − | 0.973310i | \(-0.573707\pi\) | ||||
−0.229493 | + | 0.973310i | \(0.573707\pi\) | |||||||
\(224\) | 0.258652 | − | 0.447998i | 0.0172819 | − | 0.0299332i | ||||
\(225\) | 17.4423 | + | 30.2109i | 1.16282 | + | 2.01406i | ||||
\(226\) | 4.86620 | + | 8.42850i | 0.323695 | + | 0.560656i | ||||
\(227\) | −10.3835 | − | 17.9848i | −0.689177 | − | 1.19369i | −0.972104 | − | 0.234549i | \(-0.924639\pi\) |
0.282927 | − | 0.959141i | \(-0.408695\pi\) | |||||||
\(228\) | 3.46479 | 0.229462 | ||||||||
\(229\) | 0.939136 | + | 1.62663i | 0.0620599 | + | 0.107491i | 0.895386 | − | 0.445291i | \(-0.146900\pi\) |
−0.833326 | + | 0.552782i | \(0.813566\pi\) | |||||||
\(230\) | −30.4123 | −2.00533 | ||||||||
\(231\) | −0.499401 | + | 0.864988i | −0.0328582 | + | 0.0569120i | ||||
\(232\) | −0.482696 | −0.0316905 | ||||||||
\(233\) | −13.8604 | −0.908023 | −0.454012 | − | 0.890996i | \(-0.650008\pi\) | ||||
−0.454012 | + | 0.890996i | \(0.650008\pi\) | |||||||
\(234\) | 2.73240 | − | 4.73265i | 0.178622 | − | 0.309383i | ||||
\(235\) | −2.74447 | − | 4.75356i | −0.179030 | − | 0.310088i | ||||
\(236\) | 12.4994 | 0.813642 | ||||||||
\(237\) | −1.23300 | + | 2.13561i | −0.0800917 | + | 0.138723i | ||||
\(238\) | −0.526255 | + | 0.911501i | −0.0341121 | + | 0.0590839i | ||||
\(239\) | −0.439136 | + | 0.760607i | −0.0284054 | + | 0.0491995i | −0.879879 | − | 0.475198i | \(-0.842376\pi\) |
0.851473 | + | 0.524398i | \(0.175710\pi\) | |||||||
\(240\) | 1.09024 | + | 1.88835i | 0.0703748 | + | 0.121893i | ||||
\(241\) | −7.90081 | − | 13.6846i | −0.508936 | − | 0.881502i | −0.999946 | − | 0.0103489i | \(-0.996706\pi\) |
0.491011 | − | 0.871154i | \(-0.336628\pi\) | |||||||
\(242\) | −1.46539 | + | 2.53813i | −0.0941990 | + | 0.163157i | ||||
\(243\) | −6.17153 | + | 10.6894i | −0.395904 | + | 0.685726i | ||||
\(244\) | −1.24135 | + | 2.15008i | −0.0794692 | + | 0.137645i | ||||
\(245\) | 28.3777 | 1.81298 | ||||||||
\(246\) | −0.439136 | − | 0.760607i | −0.0279983 | − | 0.0484945i | ||||
\(247\) | −6.69779 | + | 11.6009i | −0.426170 | + | 0.738148i | ||||
\(248\) | −2.69779 | −0.171310 | ||||||||
\(249\) | 5.66318 | 0.358889 | ||||||||
\(250\) | 16.3693 | − | 28.3525i | 1.03529 | − | 1.79317i | ||||
\(251\) | 14.6799 | 0.926586 | 0.463293 | − | 0.886205i | \(-0.346668\pi\) | ||||
0.463293 | + | 0.886205i | \(0.346668\pi\) | |||||||
\(252\) | −0.706740 | − | 1.22411i | −0.0445204 | − | 0.0771116i | ||||
\(253\) | −26.9296 | −1.69305 | ||||||||
\(254\) | −7.85725 | − | 13.6092i | −0.493008 | − | 0.853914i | ||||
\(255\) | −2.21822 | − | 3.84206i | −0.138910 | − | 0.240599i | ||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | −3.70302 | + | 6.41382i | −0.230988 | + | 0.400083i | −0.958099 | − | 0.286437i | \(-0.907529\pi\) |
0.727111 | + | 0.686520i | \(0.240862\pi\) | |||||||
\(258\) | 4.26760 | 0.265689 | ||||||||
\(259\) | −3.07234 | − | 0.679750i | −0.190906 | − | 0.0422376i | ||||
\(260\) | −8.43018 | −0.522818 | ||||||||
\(261\) | −0.659458 | + | 1.14222i | −0.0408194 | + | 0.0707014i | ||||
\(262\) | 6.68884 | + | 11.5854i | 0.413238 | + | 0.715749i | ||||
\(263\) | −4.94749 | − | 8.56930i | −0.305075 | − | 0.528406i | 0.672203 | − | 0.740367i | \(-0.265348\pi\) |
−0.977278 | + | 0.211961i | \(0.932015\pi\) | |||||||
\(264\) | 0.965392 | + | 1.67211i | 0.0594158 | + | 0.102911i | ||||
\(265\) | −9.55816 | −0.587153 | ||||||||
\(266\) | 1.73240 | + | 3.00060i | 0.106220 | + | 0.183979i | ||||
\(267\) | 8.34307 | 0.510587 | ||||||||
\(268\) | 0.133802 | − | 0.231751i | 0.00817324 | − | 0.0141565i | ||||
\(269\) | −5.32636 | −0.324754 | −0.162377 | − | 0.986729i | \(-0.551916\pi\) | ||||
−0.162377 | + | 0.986729i | \(0.551916\pi\) | |||||||
\(270\) | 12.4994 | 0.760689 | ||||||||
\(271\) | −0.203018 | + | 0.351637i | −0.0123325 | + | 0.0213604i | −0.872126 | − | 0.489282i | \(-0.837259\pi\) |
0.859793 | + | 0.510642i | \(0.170592\pi\) | |||||||
\(272\) | 1.01730 | + | 1.76202i | 0.0616831 | + | 0.106838i | ||||
\(273\) | −0.535207 | −0.0323922 | ||||||||
\(274\) | 6.68048 | − | 11.5709i | 0.403583 | − | 0.699026i | ||||
\(275\) | 23.8258 | − | 41.2674i | 1.43675 | − | 2.48852i | ||||
\(276\) | −1.86620 | + | 3.23235i | −0.112332 | + | 0.194565i | ||||
\(277\) | 9.05504 | + | 15.6838i | 0.544064 | + | 0.942347i | 0.998665 | + | 0.0516518i | \(0.0164486\pi\) |
−0.454601 | + | 0.890695i | \(0.650218\pi\) | |||||||
\(278\) | −7.20614 | − | 12.4814i | −0.432196 | − | 0.748585i | ||||
\(279\) | −3.68571 | + | 6.38384i | −0.220658 | + | 0.382191i | ||||
\(280\) | −1.09024 | + | 1.88835i | −0.0651544 | + | 0.112851i | ||||
\(281\) | 9.53461 | − | 16.5144i | 0.568787 | − | 0.985168i | −0.427899 | − | 0.903826i | \(-0.640746\pi\) |
0.996686 | − | 0.0813416i | \(-0.0259205\pi\) | |||||||
\(282\) | −0.673639 | −0.0401146 | ||||||||
\(283\) | −8.57294 | − | 14.8488i | −0.509608 | − | 0.882667i | −0.999938 | − | 0.0111304i | \(-0.996457\pi\) |
0.490330 | − | 0.871537i | \(-0.336876\pi\) | |||||||
\(284\) | 1.74135 | − | 3.01610i | 0.103330 | − | 0.178973i | ||||
\(285\) | −14.6044 | −0.865091 | ||||||||
\(286\) | −7.46479 | −0.441402 | ||||||||
\(287\) | 0.439136 | − | 0.760607i | 0.0259214 | − | 0.0448972i | ||||
\(288\) | −2.73240 | −0.161008 | ||||||||
\(289\) | 6.43018 | + | 11.1374i | 0.378246 | + | 0.655142i | ||||
\(290\) | 2.03461 | 0.119476 | ||||||||
\(291\) | −0.0781676 | − | 0.135390i | −0.00458227 | − | 0.00793672i | ||||
\(292\) | −2.86620 | − | 4.96440i | −0.167732 | − | 0.290520i | ||||
\(293\) | −9.24135 | − | 16.0065i | −0.539885 | − | 0.935109i | −0.998910 | − | 0.0466851i | \(-0.985134\pi\) |
0.459024 | − | 0.888424i | \(-0.348199\pi\) | |||||||
\(294\) | 1.74135 | − | 3.01610i | 0.101557 | − | 0.175903i | ||||
\(295\) | −52.6861 | −3.06751 | ||||||||
\(296\) | −4.10755 | + | 4.48643i | −0.238746 | + | 0.260769i | ||||
\(297\) | 11.0680 | 0.642232 | ||||||||
\(298\) | −10.4564 | + | 18.1111i | −0.605725 | + | 1.04915i | ||||
\(299\) | −7.21509 | − | 12.4969i | −0.417260 | − | 0.722715i | ||||
\(300\) | −3.30221 | − | 5.71960i | −0.190653 | − | 0.330221i | ||||
\(301\) | 2.13380 | + | 3.69585i | 0.122990 | + | 0.213025i | ||||
\(302\) | 17.6453 | 1.01537 | ||||||||
\(303\) | 2.39245 | + | 4.14385i | 0.137443 | + | 0.238058i | ||||
\(304\) | 6.69779 | 0.384145 | ||||||||
\(305\) | 5.23240 | − | 9.06278i | 0.299606 | − | 0.518933i | ||||
\(306\) | 5.55936 | 0.317807 | ||||||||
\(307\) | −11.2151 | −0.640079 | −0.320040 | − | 0.947404i | \(-0.603696\pi\) | ||||
−0.320040 | + | 0.947404i | \(0.603696\pi\) | |||||||
\(308\) | −0.965392 | + | 1.67211i | −0.0550083 | + | 0.0952772i | ||||
\(309\) | −1.66781 | − | 2.88873i | −0.0948785 | − | 0.164334i | ||||
\(310\) | 11.3714 | 0.645854 | ||||||||
\(311\) | 8.95644 | − | 15.5130i | 0.507873 | − | 0.879662i | −0.492085 | − | 0.870547i | \(-0.663765\pi\) |
0.999958 | − | 0.00911511i | \(-0.00290147\pi\) | |||||||
\(312\) | −0.517304 | + | 0.895997i | −0.0292866 | + | 0.0507258i | ||||
\(313\) | −2.41871 | + | 4.18933i | −0.136714 | + | 0.236795i | −0.926251 | − | 0.376908i | \(-0.876987\pi\) |
0.789537 | + | 0.613703i | \(0.210321\pi\) | |||||||
\(314\) | 5.00835 | + | 8.67472i | 0.282638 | + | 0.489543i | ||||
\(315\) | 2.97897 | + | 5.15973i | 0.167846 | + | 0.290718i | ||||
\(316\) | −2.38350 | + | 4.12835i | −0.134082 | + | 0.232238i | ||||
\(317\) | −12.9092 | + | 22.3593i | −0.725051 | + | 1.25582i | 0.233903 | + | 0.972260i | \(0.424850\pi\) |
−0.958953 | + | 0.283564i | \(0.908483\pi\) | |||||||
\(318\) | −0.586520 | + | 1.01588i | −0.0328904 | + | 0.0569679i | ||||
\(319\) | 1.80161 | 0.100871 | ||||||||
\(320\) | 2.10755 | + | 3.65038i | 0.117815 | + | 0.204062i | ||||
\(321\) | 3.16841 | − | 5.48785i | 0.176843 | − | 0.306302i | ||||
\(322\) | −3.73240 | −0.207998 | ||||||||
\(323\) | −13.6274 | −0.758247 | ||||||||
\(324\) | −3.33159 | + | 5.77048i | −0.185088 | + | 0.320582i | ||||
\(325\) | 25.5340 | 1.41637 | ||||||||
\(326\) | 3.09024 | + | 5.35246i | 0.171153 | + | 0.296445i | ||||
\(327\) | −3.57606 | −0.197757 | ||||||||
\(328\) | −0.848894 | − | 1.47033i | −0.0468723 | − | 0.0811853i | ||||
\(329\) | −0.336820 | − | 0.583389i | −0.0185695 | − | 0.0321633i | ||||
\(330\) | −4.06922 | − | 7.04809i | −0.224003 | − | 0.387985i | ||||
\(331\) | −9.66318 | + | 16.7371i | −0.531136 | + | 0.919955i | 0.468203 | + | 0.883621i | \(0.344902\pi\) |
−0.999340 | + | 0.0363345i | \(0.988432\pi\) | |||||||
\(332\) | 10.9475 | 0.600822 | ||||||||
\(333\) | 5.00463 | + | 15.8491i | 0.274252 | + | 0.868528i | ||||
\(334\) | −12.0000 | −0.656611 | ||||||||
\(335\) | −0.563987 | + | 0.976854i | −0.0308139 | + | 0.0533712i | ||||
\(336\) | 0.133802 | + | 0.231751i | 0.00729948 | + | 0.0126431i | ||||
\(337\) | −0.0639867 | − | 0.110828i | −0.00348558 | − | 0.00603720i | 0.864277 | − | 0.503016i | \(-0.167776\pi\) |
−0.867763 | + | 0.496978i | \(0.834443\pi\) | |||||||
\(338\) | 4.50000 | + | 7.79423i | 0.244768 | + | 0.423950i | ||||
\(339\) | −5.03461 | −0.273442 | ||||||||
\(340\) | −4.28803 | − | 7.42709i | −0.232551 | − | 0.402790i | ||||
\(341\) | 10.0692 | 0.545279 | ||||||||
\(342\) | 9.15051 | − | 15.8491i | 0.494803 | − | 0.857023i | ||||
\(343\) | 7.10382 | 0.383570 | ||||||||
\(344\) | 8.24970 | 0.444794 | ||||||||
\(345\) | 7.86620 | − | 13.6247i | 0.423502 | − | 0.733527i | ||||
\(346\) | 1.45644 | + | 2.52263i | 0.0782987 | + | 0.135617i | ||||
\(347\) | −9.69034 | −0.520205 | −0.260102 | − | 0.965581i | \(-0.583756\pi\) | ||||
−0.260102 | + | 0.965581i | \(0.583756\pi\) | |||||||
\(348\) | 0.124850 | − | 0.216247i | 0.00669268 | − | 0.0115921i | ||||
\(349\) | −4.57234 | + | 7.91952i | −0.244752 | + | 0.423922i | −0.962062 | − | 0.272832i | \(-0.912040\pi\) |
0.717310 | + | 0.696754i | \(0.245373\pi\) | |||||||
\(350\) | 3.30221 | − | 5.71960i | 0.176511 | − | 0.305725i | ||||
\(351\) | 2.96539 | + | 5.13621i | 0.158281 | + | 0.274151i | ||||
\(352\) | 1.86620 | + | 3.23235i | 0.0994687 | + | 0.172285i | ||||
\(353\) | −4.66841 | + | 8.08592i | −0.248474 | + | 0.430370i | −0.963103 | − | 0.269134i | \(-0.913263\pi\) |
0.714628 | + | 0.699504i | \(0.246596\pi\) | |||||||
\(354\) | −3.23300 | + | 5.59971i | −0.171832 | + | 0.297621i | ||||
\(355\) | −7.33994 | + | 12.7132i | −0.389564 | + | 0.674744i | ||||
\(356\) | 16.1280 | 0.854781 | ||||||||
\(357\) | −0.272234 | − | 0.471523i | −0.0144082 | − | 0.0249557i | ||||
\(358\) | 3.48270 | − | 6.03221i | 0.184066 | − | 0.318812i | ||||
\(359\) | −13.9308 | −0.735239 | −0.367619 | − | 0.929976i | \(-0.619827\pi\) | ||||
−0.367619 | + | 0.929976i | \(0.619827\pi\) | |||||||
\(360\) | 11.5173 | 0.607015 | ||||||||
\(361\) | −12.9302 | + | 22.3957i | −0.680536 | + | 1.17872i | ||||
\(362\) | −6.28431 | −0.330296 | ||||||||
\(363\) | −0.758053 | − | 1.31299i | −0.0397875 | − | 0.0689139i | ||||
\(364\) | −1.03461 | −0.0542282 | ||||||||
\(365\) | 12.0813 | + | 20.9254i | 0.632364 | + | 1.09529i | ||||
\(366\) | −0.642154 | − | 1.11224i | −0.0335659 | − | 0.0581379i | ||||
\(367\) | 2.00000 | + | 3.46410i | 0.104399 | + | 0.180825i | 0.913493 | − | 0.406855i | \(-0.133375\pi\) |
−0.809093 | + | 0.587680i | \(0.800041\pi\) | |||||||
\(368\) | −3.60755 | + | 6.24845i | −0.188056 | + | 0.325723i | ||||
\(369\) | −4.63903 | −0.241498 | ||||||||
\(370\) | 17.3137 | − | 18.9107i | 0.900096 | − | 0.983122i | ||||
\(371\) | −1.17304 | −0.0609012 | ||||||||
\(372\) | 0.697788 | − | 1.20861i | 0.0361786 | − | 0.0626633i | ||||
\(373\) | −0.00372197 | − | 0.00644664i | −0.000192716 | − | 0.000333794i | 0.865929 | − | 0.500167i | \(-0.166728\pi\) |
−0.866122 | + | 0.499833i | \(0.833395\pi\) | |||||||
\(374\) | −3.79698 | − | 6.57657i | −0.196337 | − | 0.340066i | ||||
\(375\) | 8.46792 | + | 14.6669i | 0.437281 | + | 0.757393i | ||||
\(376\) | −1.30221 | −0.0671564 | ||||||||
\(377\) | 0.482696 | + | 0.836054i | 0.0248601 | + | 0.0430590i | ||||
\(378\) | 1.53401 | 0.0789009 | ||||||||
\(379\) | 9.00312 | − | 15.5939i | 0.462459 | − | 0.801003i | −0.536623 | − | 0.843822i | \(-0.680300\pi\) |
0.999083 | + | 0.0428187i | \(0.0136338\pi\) | |||||||
\(380\) | −28.2318 | −1.44826 | ||||||||
\(381\) | 8.12917 | 0.416470 | ||||||||
\(382\) | −5.78803 | + | 10.0252i | −0.296141 | + | 0.512932i | ||||
\(383\) | 7.90393 | + | 13.6900i | 0.403872 | + | 0.699527i | 0.994189 | − | 0.107644i | \(-0.0343308\pi\) |
−0.590318 | + | 0.807171i | \(0.700997\pi\) | |||||||
\(384\) | 0.517304 | 0.0263986 | ||||||||
\(385\) | 4.06922 | − | 7.04809i | 0.207386 | − | 0.359204i | ||||
\(386\) | −6.71509 | + | 11.6309i | −0.341789 | + | 0.591996i | ||||
\(387\) | 11.2707 | − | 19.5215i | 0.572923 | − | 0.992332i | ||||
\(388\) | −0.151106 | − | 0.261723i | −0.00767123 | − | 0.0132870i | ||||
\(389\) | −0.659458 | − | 1.14222i | −0.0334359 | − | 0.0579126i | 0.848823 | − | 0.528677i | \(-0.177312\pi\) |
−0.882259 | + | 0.470764i | \(0.843978\pi\) | |||||||
\(390\) | 2.18048 | − | 3.77671i | 0.110413 | − | 0.191241i | ||||
\(391\) | 7.33994 | − | 12.7132i | 0.371197 | − | 0.642932i | ||||
\(392\) | 3.36620 | − | 5.83043i | 0.170019 | − | 0.294481i | ||||
\(393\) | −6.92032 | −0.349084 | ||||||||
\(394\) | 2.75865 | + | 4.77813i | 0.138979 | + | 0.240718i | ||||
\(395\) | 10.0467 | − | 17.4014i | 0.505503 | − | 0.875558i | ||||
\(396\) | 10.1984 | 0.512488 | ||||||||
\(397\) | 21.8183 | 1.09503 | 0.547515 | − | 0.836796i | \(-0.315574\pi\) | ||||
0.547515 | + | 0.836796i | \(0.315574\pi\) | |||||||
\(398\) | −8.17153 | + | 14.1535i | −0.409602 | + | 0.709451i | ||||
\(399\) | −1.79235 | −0.0897298 | ||||||||
\(400\) | −6.38350 | − | 11.0566i | −0.319175 | − | 0.552828i | ||||
\(401\) | 4.19839 | 0.209657 | 0.104829 | − | 0.994490i | \(-0.466571\pi\) | ||||
0.104829 | + | 0.994490i | \(0.466571\pi\) | |||||||
\(402\) | 0.0692162 | + | 0.119886i | 0.00345219 | + | 0.00597937i | ||||
\(403\) | 2.69779 | + | 4.67271i | 0.134386 | + | 0.232764i | ||||
\(404\) | 4.62485 | + | 8.01048i | 0.230095 | + | 0.398536i | ||||
\(405\) | 14.0430 | − | 24.3231i | 0.697800 | − | 1.20863i | ||||
\(406\) | 0.249701 | 0.0123924 | ||||||||
\(407\) | 15.3310 | − | 16.7451i | 0.759929 | − | 0.830026i | ||||
\(408\) | −1.05251 | −0.0521071 | ||||||||
\(409\) | 8.27908 | − | 14.3398i | 0.409374 | − | 0.709057i | −0.585446 | − | 0.810712i | \(-0.699080\pi\) |
0.994820 | + | 0.101655i | \(0.0324138\pi\) | |||||||
\(410\) | 3.57817 | + | 6.19757i | 0.176713 | + | 0.306076i | ||||
\(411\) | 3.45584 | + | 5.98569i | 0.170464 | + | 0.295252i | ||||
\(412\) | −3.22404 | − | 5.58421i | −0.158837 | − | 0.275114i | ||||
\(413\) | −6.46599 | −0.318171 | ||||||||
\(414\) | 9.85725 | + | 17.0733i | 0.484457 | + | 0.839105i | ||||
\(415\) | −46.1447 | −2.26515 | ||||||||
\(416\) | −1.00000 | + | 1.73205i | −0.0490290 | + | 0.0849208i | ||||
\(417\) | 7.45553 | 0.365099 | ||||||||
\(418\) | −24.9988 | −1.22273 | ||||||||
\(419\) | −11.1595 | + | 19.3287i | −0.545175 | + | 0.944271i | 0.453421 | + | 0.891297i | \(0.350204\pi\) |
−0.998596 | + | 0.0529745i | \(0.983130\pi\) | |||||||
\(420\) | −0.563987 | − | 0.976854i | −0.0275197 | − | 0.0476656i | ||||
\(421\) | 25.1805 | 1.22722 | 0.613611 | − | 0.789609i | \(-0.289716\pi\) | ||||
0.613611 | + | 0.789609i | \(0.289716\pi\) | |||||||
\(422\) | −10.3746 | + | 17.9692i | −0.505025 | + | 0.874729i | ||||
\(423\) | −1.77908 | + | 3.08146i | −0.0865018 | + | 0.149825i | ||||
\(424\) | −1.13380 | + | 1.96380i | −0.0550623 | + | 0.0953707i | ||||
\(425\) | 12.9879 | + | 22.4957i | 0.630007 | + | 1.09120i | ||||
\(426\) | 0.900806 | + | 1.56024i | 0.0436442 | + | 0.0755940i | ||||
\(427\) | 0.642154 | − | 1.11224i | 0.0310760 | − | 0.0538253i | ||||
\(428\) | 6.12485 | − | 10.6086i | 0.296056 | − | 0.512784i | ||||
\(429\) | 1.93078 | − | 3.34422i | 0.0932191 | − | 0.161460i | ||||
\(430\) | −34.7733 | −1.67692 | ||||||||
\(431\) | 11.3489 | + | 19.6569i | 0.546657 | + | 0.946838i | 0.998501 | + | 0.0547405i | \(0.0174332\pi\) |
−0.451844 | + | 0.892097i | \(0.649233\pi\) | |||||||
\(432\) | 1.48270 | − | 2.56810i | 0.0713362 | − | 0.123558i | ||||
\(433\) | −24.6966 | −1.18684 | −0.593421 | − | 0.804892i | \(-0.702223\pi\) | ||||
−0.593421 | + | 0.804892i | \(0.702223\pi\) | |||||||
\(434\) | 1.39558 | 0.0669898 | ||||||||
\(435\) | −0.526255 | + | 0.911501i | −0.0252320 | + | 0.0437031i | ||||
\(436\) | −6.91288 | −0.331067 | ||||||||
\(437\) | −24.1626 | − | 41.8508i | −1.15585 | − | 2.00200i | ||||
\(438\) | 2.96539 | 0.141692 | ||||||||
\(439\) | −3.91288 | − | 6.77731i | −0.186752 | − | 0.323463i | 0.757414 | − | 0.652935i | \(-0.226463\pi\) |
−0.944165 | + | 0.329472i | \(0.893129\pi\) | |||||||
\(440\) | −7.86620 | − | 13.6247i | −0.375006 | − | 0.649530i | ||||
\(441\) | −9.19779 | − | 15.9310i | −0.437990 | − | 0.758621i | ||||
\(442\) | 2.03461 | − | 3.52404i | 0.0967764 | − | 0.167622i | ||||
\(443\) | 34.3944 | 1.63413 | 0.817063 | − | 0.576548i | \(-0.195601\pi\) | ||||
0.817063 | + | 0.576548i | \(0.195601\pi\) | |||||||
\(444\) | −0.947489 | − | 3.00060i | −0.0449658 | − | 0.142402i | ||||
\(445\) | −67.9809 | −3.22260 | ||||||||
\(446\) | 3.42706 | − | 5.93585i | 0.162276 | − | 0.281070i | ||||
\(447\) | −5.40916 | − | 9.36894i | −0.255844 | − | 0.443136i | ||||
\(448\) | 0.258652 | + | 0.447998i | 0.0122202 | + | 0.0211659i | ||||
\(449\) | −7.63320 | − | 13.2211i | −0.360233 | − | 0.623942i | 0.627766 | − | 0.778402i | \(-0.283970\pi\) |
−0.987999 | + | 0.154460i | \(0.950636\pi\) | |||||||
\(450\) | −34.8845 | −1.64447 | ||||||||
\(451\) | 3.16841 | + | 5.48785i | 0.149195 | + | 0.258413i | ||||
\(452\) | −9.73240 | −0.457773 | ||||||||
\(453\) | −4.56399 | + | 7.90506i | −0.214435 | + | 0.371412i | ||||
\(454\) | 20.7670 | 0.974644 | ||||||||
\(455\) | 4.36097 | 0.204445 | ||||||||
\(456\) | −1.73240 | + | 3.00060i | −0.0811269 | + | 0.140516i | ||||
\(457\) | 8.68048 | + | 15.0350i | 0.406056 | + | 0.703310i | 0.994444 | − | 0.105269i | \(-0.0335705\pi\) |
−0.588388 | + | 0.808579i | \(0.700237\pi\) | |||||||
\(458\) | −1.87827 | −0.0877659 | ||||||||
\(459\) | −3.01671 | + | 5.22509i | −0.140808 | + | 0.243886i | ||||
\(460\) | 15.2061 | − | 26.3378i | 0.708990 | − | 1.22801i | ||||
\(461\) | −3.96539 | + | 6.86826i | −0.184687 | + | 0.319887i | −0.943471 | − | 0.331455i | \(-0.892460\pi\) |
0.758784 | + | 0.651342i | \(0.225794\pi\) | |||||||
\(462\) | −0.499401 | − | 0.864988i | −0.0232342 | − | 0.0402429i | ||||
\(463\) | 5.20614 | + | 9.01730i | 0.241950 | + | 0.419070i | 0.961270 | − | 0.275610i | \(-0.0888797\pi\) |
−0.719320 | + | 0.694679i | \(0.755546\pi\) | |||||||
\(464\) | 0.241348 | − | 0.418027i | 0.0112043 | − | 0.0194064i | ||||
\(465\) | −2.94124 | + | 5.09438i | −0.136397 | + | 0.236246i | ||||
\(466\) | 6.93018 | − | 12.0034i | 0.321035 | − | 0.556048i | ||||
\(467\) | 5.70825 | 0.264146 | 0.132073 | − | 0.991240i | \(-0.457837\pi\) | ||||
0.132073 | + | 0.991240i | \(0.457837\pi\) | |||||||
\(468\) | 2.73240 | + | 4.73265i | 0.126305 | + | 0.218767i | ||||
\(469\) | −0.0692162 | + | 0.119886i | −0.00319611 | + | 0.00553582i | ||||
\(470\) | 5.48894 | 0.253186 | ||||||||
\(471\) | −5.18168 | −0.238759 | ||||||||
\(472\) | −6.24970 | + | 10.8248i | −0.287666 | + | 0.498252i | ||||
\(473\) | −30.7912 | −1.41578 | ||||||||
\(474\) | −1.23300 | − | 2.13561i | −0.0566334 | − | 0.0980918i | ||||
\(475\) | 85.5107 | 3.92350 | ||||||||
\(476\) | −0.526255 | − | 0.911501i | −0.0241209 | − | 0.0417786i | ||||
\(477\) | 3.09800 | + | 5.36589i | 0.141847 | + | 0.245687i | ||||
\(478\) | −0.439136 | − | 0.760607i | −0.0200856 | − | 0.0347893i | ||||
\(479\) | 10.3189 | − | 17.8729i | 0.471483 | − | 0.816633i | −0.527984 | − | 0.849254i | \(-0.677052\pi\) |
0.999468 | + | 0.0326209i | \(0.0103854\pi\) | |||||||
\(480\) | −2.18048 | −0.0995250 | ||||||||
\(481\) | 11.8783 | + | 2.62805i | 0.541603 | + | 0.119829i | ||||
\(482\) | 15.8016 | 0.719744 | ||||||||
\(483\) | 0.965392 | − | 1.67211i | 0.0439269 | − | 0.0760835i | ||||
\(484\) | −1.46539 | − | 2.53813i | −0.0666087 | − | 0.115370i | ||||
\(485\) | 0.636925 | + | 1.10319i | 0.0289213 | + | 0.0500931i | ||||
\(486\) | −6.17153 | − | 10.6894i | −0.279946 | − | 0.484881i | ||||
\(487\) | 32.2497 | 1.46137 | 0.730687 | − | 0.682713i | \(-0.239200\pi\) | ||||
0.730687 | + | 0.682713i | \(0.239200\pi\) | |||||||
\(488\) | −1.24135 | − | 2.15008i | −0.0561932 | − | 0.0973294i | ||||
\(489\) | −3.19719 | −0.144582 | ||||||||
\(490\) | −14.1888 | + | 24.5758i | −0.640986 | + | 1.11022i | ||||
\(491\) | 3.73240 | 0.168441 | 0.0842203 | − | 0.996447i | \(-0.473160\pi\) | ||||
0.0842203 | + | 0.996447i | \(0.473160\pi\) | |||||||
\(492\) | 0.878273 | 0.0395956 | ||||||||
\(493\) | −0.491049 | + | 0.850521i | −0.0221157 | + | 0.0383055i | ||||
\(494\) | −6.69779 | − | 11.6009i | −0.301348 | − | 0.521950i | ||||
\(495\) | −42.9871 | −1.93213 | ||||||||
\(496\) | 1.34889 | − | 2.33635i | 0.0605671 | − | 0.104905i | ||||
\(497\) | −0.900806 | + | 1.56024i | −0.0404067 | + | 0.0699864i | ||||
\(498\) | −2.83159 | + | 4.90446i | −0.126887 | + | 0.219774i | ||||
\(499\) | −14.0467 | − | 24.3296i | −0.628816 | − | 1.08914i | −0.987790 | − | 0.155793i | \(-0.950207\pi\) |
0.358974 | − | 0.933348i | \(-0.383127\pi\) | |||||||
\(500\) | 16.3693 | + | 28.3525i | 0.732058 | + | 1.26796i | ||||
\(501\) | 3.10382 | − | 5.37598i | 0.138669 | − | 0.240181i | ||||
\(502\) | −7.33994 | + | 12.7132i | −0.327598 | + | 0.567416i | ||||
\(503\) | −5.43601 | + | 9.41545i | −0.242380 | + | 0.419814i | −0.961392 | − | 0.275184i | \(-0.911261\pi\) |
0.719012 | + | 0.694998i | \(0.244595\pi\) | |||||||
\(504\) | 1.41348 | 0.0629614 | ||||||||
\(505\) | −19.4942 | − | 33.7649i | −0.867479 | − | 1.50252i | ||||
\(506\) | 13.4648 | − | 23.3217i | 0.598583 | − | 1.03678i | ||||
\(507\) | −4.65574 | −0.206769 | ||||||||
\(508\) | 15.7145 | 0.697218 | ||||||||
\(509\) | 0.892454 | − | 1.54578i | 0.0395573 | − | 0.0685153i | −0.845569 | − | 0.533866i | \(-0.820739\pi\) |
0.885126 | + | 0.465351i | \(0.154072\pi\) | |||||||
\(510\) | 4.43643 | 0.196448 | ||||||||
\(511\) | 1.48270 | + | 2.56810i | 0.0655906 | + | 0.113606i | ||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 9.93078 | + | 17.2006i | 0.438455 | + | 0.759426i | ||||
\(514\) | −3.70302 | − | 6.41382i | −0.163333 | − | 0.282901i | ||||
\(515\) | 13.5896 | + | 23.5380i | 0.598831 | + | 1.03721i | ||||
\(516\) | −2.13380 | + | 3.69585i | −0.0939354 | + | 0.162701i | ||||
\(517\) | 4.86037 | 0.213759 | ||||||||
\(518\) | 2.12485 | − | 2.32085i | 0.0933606 | − | 0.101972i | ||||
\(519\) | −1.50685 | −0.0661432 | ||||||||
\(520\) | 4.21509 | − | 7.30075i | 0.184844 | − | 0.320159i | ||||
\(521\) | −14.5986 | − | 25.2855i | −0.639576 | − | 1.10778i | −0.985526 | − | 0.169525i | \(-0.945777\pi\) |
0.345950 | − | 0.938253i | \(-0.387557\pi\) | |||||||
\(522\) | −0.659458 | − | 1.14222i | −0.0288637 | − | 0.0499934i | ||||
\(523\) | −21.0078 | − | 36.3865i | −0.918605 | − | 1.59107i | −0.801536 | − | 0.597947i | \(-0.795983\pi\) |
−0.117069 | − | 0.993124i | \(-0.537350\pi\) | |||||||
\(524\) | −13.3777 | −0.584406 | ||||||||
\(525\) | 1.70825 | + | 2.95877i | 0.0745540 | + | 0.129131i | ||||
\(526\) | 9.89498 | 0.431442 | ||||||||
\(527\) | −2.74447 | + | 4.75356i | −0.119551 | + | 0.207068i | ||||
\(528\) | −1.93078 | −0.0840266 | ||||||||
\(529\) | 29.0576 | 1.26337 | ||||||||
\(530\) | 4.77908 | − | 8.27761i | 0.207590 | − | 0.359556i | ||||
\(531\) | 17.0767 | + | 29.5776i | 0.741064 | + | 1.28356i | ||||
\(532\) | −3.46479 | −0.150218 | ||||||||
\(533\) | −1.69779 | + | 2.94066i | −0.0735394 | + | 0.127374i | ||||
\(534\) | −4.17153 | + | 7.22531i | −0.180520 | + | 0.312670i | ||||
\(535\) | −25.8168 | + | 44.7160i | −1.11616 | + | 1.93324i | ||||
\(536\) | 0.133802 | + | 0.231751i | 0.00577935 | + | 0.0100101i | ||||
\(537\) | 1.80161 | + | 3.12048i | 0.0777453 | + | 0.134659i | ||||
\(538\) | 2.66318 | − | 4.61276i | 0.114818 | − | 0.198870i | ||||
\(539\) | −12.5640 | + | 21.7615i | −0.541169 | + | 0.937333i | ||||
\(540\) | −6.24970 | + | 10.8248i | −0.268944 | + | 0.465825i | ||||
\(541\) | −19.5865 | −0.842090 | −0.421045 | − | 0.907040i | \(-0.638337\pi\) | ||||
−0.421045 | + | 0.907040i | \(0.638337\pi\) | |||||||
\(542\) | −0.203018 | − | 0.351637i | −0.00872037 | − | 0.0151041i | ||||
\(543\) | 1.62545 | − | 2.81536i | 0.0697547 | − | 0.120819i | ||||
\(544\) | −2.03461 | −0.0872331 | ||||||||
\(545\) | 29.1384 | 1.24815 | ||||||||
\(546\) | 0.267603 | − | 0.463503i | 0.0114524 | − | 0.0198361i | ||||
\(547\) | 1.16378 | 0.0497596 | 0.0248798 | − | 0.999690i | \(-0.492080\pi\) | ||||
0.0248798 | + | 0.999690i | \(0.492080\pi\) | |||||||
\(548\) | 6.68048 | + | 11.5709i | 0.285376 | + | 0.494286i | ||||
\(549\) | −6.78371 | −0.289522 | ||||||||
\(550\) | 23.8258 | + | 41.2674i | 1.01593 | + | 1.75965i | ||||
\(551\) | 1.61650 | + | 2.79986i | 0.0688651 | + | 0.119278i | ||||
\(552\) | −1.86620 | − | 3.23235i | −0.0794307 | − | 0.137578i | ||||
\(553\) | 1.23300 | − | 2.13561i | 0.0524323 | − | 0.0908154i | ||||
\(554\) | −18.1101 | −0.769423 | ||||||||
\(555\) | 3.99375 | + | 12.6478i | 0.169525 | + | 0.536869i | ||||
\(556\) | 14.4123 | 0.611217 | ||||||||
\(557\) | 14.1075 | − | 24.4350i | 0.597756 | − | 1.03534i | −0.395396 | − | 0.918511i | \(-0.629393\pi\) |
0.993152 | − | 0.116833i | \(-0.0372741\pi\) | |||||||
\(558\) | −3.68571 | − | 6.38384i | −0.156029 | − | 0.270250i | ||||
\(559\) | −8.24970 | − | 14.2889i | −0.348925 | − | 0.604356i | ||||
\(560\) | −1.09024 | − | 1.88835i | −0.0460711 | − | 0.0797976i | ||||
\(561\) | 3.92839 | 0.165857 | ||||||||
\(562\) | 9.53461 | + | 16.5144i | 0.402193 | + | 0.696619i | ||||
\(563\) | −6.08712 | −0.256541 | −0.128271 | − | 0.991739i | \(-0.540943\pi\) | ||||
−0.128271 | + | 0.991739i | \(0.540943\pi\) | |||||||
\(564\) | 0.336820 | − | 0.583389i | 0.0141827 | − | 0.0245651i | ||||
\(565\) | 41.0230 | 1.72585 | ||||||||
\(566\) | 17.1459 | 0.720695 | ||||||||
\(567\) | 1.72345 | − | 2.98509i | 0.0723779 | − | 0.125362i | ||||
\(568\) | 1.74135 | + | 3.01610i | 0.0730653 | + | 0.126553i | ||||
\(569\) | 24.7658 | 1.03824 | 0.519118 | − | 0.854702i | \(-0.326260\pi\) | ||||
0.519118 | + | 0.854702i | \(0.326260\pi\) | |||||||
\(570\) | 7.30221 | − | 12.6478i | 0.305856 | − | 0.529758i | ||||
\(571\) | 12.7581 | − | 22.0976i | 0.533908 | − | 0.924756i | −0.465307 | − | 0.885149i | \(-0.654056\pi\) |
0.999215 | − | 0.0396065i | \(-0.0126104\pi\) | |||||||
\(572\) | 3.73240 | − | 6.46470i | 0.156059 | − | 0.270303i | ||||
\(573\) | −2.99417 | − | 5.18606i | −0.125083 | − | 0.216651i | ||||
\(574\) | 0.439136 | + | 0.760607i | 0.0183292 | + | 0.0317471i | ||||
\(575\) | −46.0576 | + | 79.7740i | −1.92073 | + | 3.32681i | ||||
\(576\) | 1.36620 | − | 2.36632i | 0.0569249 | − | 0.0985969i | ||||
\(577\) | −19.7912 | + | 34.2793i | −0.823917 | + | 1.42707i | 0.0788280 | + | 0.996888i | \(0.474882\pi\) |
−0.902745 | + | 0.430177i | \(0.858451\pi\) | |||||||
\(578\) | −12.8604 | −0.534921 | ||||||||
\(579\) | −3.47374 | − | 6.01670i | −0.144364 | − | 0.250046i | ||||
\(580\) | −1.01730 | + | 1.76202i | −0.0422413 | + | 0.0731640i | ||||
\(581\) | −5.66318 | −0.234948 | ||||||||
\(582\) | 0.156335 | 0.00648031 | ||||||||
\(583\) | 4.23180 | − | 7.32969i | 0.175263 | − | 0.303565i | ||||
\(584\) | 5.73240 | 0.237208 | ||||||||
\(585\) | −11.5173 | − | 19.9486i | −0.476182 | − | 0.824771i | ||||
\(586\) | 18.4827 | 0.763513 | ||||||||
\(587\) | −8.36992 | − | 14.4971i | −0.345464 | − | 0.598360i | 0.639974 | − | 0.768396i | \(-0.278945\pi\) |
−0.985438 | + | 0.170036i | \(0.945612\pi\) | |||||||
\(588\) | 1.74135 | + | 3.01610i | 0.0718120 | + | 0.124382i | ||||
\(589\) | 9.03461 | + | 15.6484i | 0.372265 | + | 0.644781i | ||||
\(590\) | 26.3431 | − | 45.6275i | 1.08453 | − | 1.87846i | ||||
\(591\) | −2.85412 | −0.117403 | ||||||||
\(592\) | −1.83159 | − | 5.80045i | −0.0752779 | − | 0.238397i | ||||
\(593\) | −20.1972 | −0.829399 | −0.414700 | − | 0.909958i | \(-0.636113\pi\) | ||||
−0.414700 | + | 0.909958i | \(0.636113\pi\) | |||||||
\(594\) | −5.53401 | + | 9.58519i | −0.227063 | + | 0.393285i | ||||
\(595\) | 2.21822 | + | 3.84206i | 0.0909380 | + | 0.157509i | ||||
\(596\) | −10.4564 | − | 18.1111i | −0.428312 | − | 0.741859i | ||||
\(597\) | −4.22717 | − | 7.32167i | −0.173006 | − | 0.299656i | ||||
\(598\) | 14.4302 | 0.590094 | ||||||||
\(599\) | 5.09919 | + | 8.83206i | 0.208347 | + | 0.360868i | 0.951194 | − | 0.308593i | \(-0.0998582\pi\) |
−0.742847 | + | 0.669462i | \(0.766525\pi\) | |||||||
\(600\) | 6.60442 | 0.269624 | ||||||||
\(601\) | −20.2670 | + | 35.1035i | −0.826708 | + | 1.43190i | 0.0738983 | + | 0.997266i | \(0.476456\pi\) |
−0.900607 | + | 0.434635i | \(0.856877\pi\) | |||||||
\(602\) | −4.26760 | −0.173935 | ||||||||
\(603\) | 0.731199 | 0.0297767 | ||||||||
\(604\) | −8.82264 | + | 15.2813i | −0.358988 | + | 0.621786i | ||||
\(605\) | 6.17676 | + | 10.6985i | 0.251121 | + | 0.434955i | ||||
\(606\) | −4.78491 | −0.194374 | ||||||||
\(607\) | −1.33099 | + | 2.30534i | −0.0540233 | + | 0.0935710i | −0.891772 | − | 0.452484i | \(-0.850538\pi\) |
0.837749 | + | 0.546055i | \(0.183871\pi\) | |||||||
\(608\) | −3.34889 | + | 5.80045i | −0.135816 | + | 0.235240i | ||||
\(609\) | −0.0645856 | + | 0.111865i | −0.00261714 | + | 0.00453302i | ||||
\(610\) | 5.23240 | + | 9.06278i | 0.211854 | + | 0.366941i | ||||
\(611\) | 1.30221 | + | 2.25550i | 0.0526818 | + | 0.0912476i | ||||
\(612\) | −2.77968 | + | 4.81454i | −0.112362 | + | 0.194616i | ||||
\(613\) | 5.90916 | − | 10.2350i | 0.238669 | − | 0.413386i | −0.721664 | − | 0.692244i | \(-0.756622\pi\) |
0.960333 | + | 0.278857i | \(0.0899557\pi\) | |||||||
\(614\) | 5.60755 | − | 9.71255i | 0.226302 | − | 0.391967i | ||||
\(615\) | −3.70200 | −0.149279 | ||||||||
\(616\) | −0.965392 | − | 1.67211i | −0.0388967 | − | 0.0673711i | ||||
\(617\) | 0.796982 | − | 1.38041i | 0.0320853 | − | 0.0555734i | −0.849537 | − | 0.527529i | \(-0.823119\pi\) |
0.881622 | + | 0.471956i | \(0.156452\pi\) | |||||||
\(618\) | 3.33562 | 0.134178 | ||||||||
\(619\) | −22.2831 | −0.895634 | −0.447817 | − | 0.894125i | \(-0.647798\pi\) | ||||
−0.447817 | + | 0.894125i | \(0.647798\pi\) | |||||||
\(620\) | −5.68571 | + | 9.84795i | −0.228344 | + | 0.395503i | ||||
\(621\) | −21.3956 | −0.858575 | ||||||||
\(622\) | 8.95644 | + | 15.5130i | 0.359121 | + | 0.622015i | ||||
\(623\) | −8.34307 | −0.334258 | ||||||||
\(624\) | −0.517304 | − | 0.895997i | −0.0207087 | − | 0.0358686i | ||||
\(625\) | −37.0807 | − | 64.2256i | −1.48323 | − | 2.56903i | ||||
\(626\) | −2.41871 | − | 4.18933i | −0.0966711 | − | 0.167439i | ||||
\(627\) | 6.46599 | − | 11.1994i | 0.258227 | − | 0.447262i | ||||
\(628\) | −10.0167 | −0.399710 | ||||||||
\(629\) | 3.72657 | + | 11.8017i | 0.148588 | + | 0.470563i | ||||
\(630\) | −5.95795 | −0.237370 | ||||||||
\(631\) | 18.4858 | − | 32.0184i | 0.735909 | − | 1.27463i | −0.218415 | − | 0.975856i | \(-0.570089\pi\) |
0.954323 | − | 0.298775i | \(-0.0965782\pi\) | |||||||
\(632\) | −2.38350 | − | 4.12835i | −0.0948106 | − | 0.164217i | ||||
\(633\) | −5.36680 | − | 9.29557i | −0.213311 | − | 0.369466i | ||||
\(634\) | −12.9092 | − | 22.3593i | −0.512688 | − | 0.888002i | ||||
\(635\) | −66.2380 | −2.62858 | ||||||||
\(636\) | −0.586520 | − | 1.01588i | −0.0232570 | − | 0.0402824i | ||||
\(637\) | −13.4648 | −0.533495 | ||||||||
\(638\) | −0.900806 | + | 1.56024i | −0.0356633 | + | 0.0617706i | ||||
\(639\) | 9.51611 | 0.376451 | ||||||||
\(640\) | −4.21509 | −0.166616 | ||||||||
\(641\) | 1.08189 | − | 1.87389i | 0.0427321 | − | 0.0740141i | −0.843868 | − | 0.536550i | \(-0.819727\pi\) |
0.886600 | + | 0.462536i | \(0.153060\pi\) | |||||||
\(642\) | 3.16841 | + | 5.48785i | 0.125047 | + | 0.216588i | ||||
\(643\) | 38.1626 | 1.50499 | 0.752493 | − | 0.658601i | \(-0.228851\pi\) | ||||
0.752493 | + | 0.658601i | \(0.228851\pi\) | |||||||
\(644\) | 1.86620 | − | 3.23235i | 0.0735385 | − | 0.127372i | ||||
\(645\) | 8.99417 | − | 15.5784i | 0.354145 | − | 0.613397i | ||||
\(646\) | 6.81369 | − | 11.8017i | 0.268081 | − | 0.464330i | ||||
\(647\) | 22.1715 | + | 38.4022i | 0.871653 | + | 1.50975i | 0.860286 | + | 0.509812i | \(0.170285\pi\) |
0.0113669 | + | 0.999935i | \(0.496382\pi\) | |||||||
\(648\) | −3.33159 | − | 5.77048i | −0.130877 | − | 0.226686i | ||||
\(649\) | 23.3264 | − | 40.4024i | 0.915640 | − | 1.58593i | ||||
\(650\) | −12.7670 | + | 22.1131i | −0.500763 | + | 0.867347i | ||||
\(651\) | −0.360969 | + | 0.625216i | −0.0141475 | + | 0.0245042i | ||||
\(652\) | −6.18048 | −0.242046 | ||||||||
\(653\) | 0.892454 | + | 1.54578i | 0.0349244 | + | 0.0604909i | 0.882959 | − | 0.469450i | \(-0.155548\pi\) |
−0.848035 | + | 0.529940i | \(0.822214\pi\) | |||||||
\(654\) | 1.78803 | − | 3.09696i | 0.0699175 | − | 0.121101i | ||||
\(655\) | 56.3881 | 2.20327 | ||||||||
\(656\) | 1.69779 | 0.0662875 | ||||||||
\(657\) | 7.83159 | − | 13.5647i | 0.305539 | − | 0.529210i | ||||
\(658\) | 0.673639 | 0.0262612 | ||||||||
\(659\) | −17.8258 | − | 30.8751i | −0.694393 | − | 1.20272i | −0.970385 | − | 0.241564i | \(-0.922340\pi\) |
0.275992 | − | 0.961160i | \(-0.410994\pi\) | |||||||
\(660\) | 8.13843 | 0.316788 | ||||||||
\(661\) | 5.16006 | + | 8.93748i | 0.200703 | + | 0.347628i | 0.948755 | − | 0.316012i | \(-0.102344\pi\) |
−0.748052 | + | 0.663640i | \(0.769011\pi\) | |||||||
\(662\) | −9.66318 | − | 16.7371i | −0.375570 | − | 0.650507i | ||||
\(663\) | 1.05251 | + | 1.82300i | 0.0408761 | + | 0.0707996i | ||||
\(664\) | −5.47374 | + | 9.48080i | −0.212422 | + | 0.367927i | ||||
\(665\) | 14.6044 | 0.566335 | ||||||||
\(666\) | −16.2281 | − | 3.59043i | −0.628825 | − | 0.139126i | ||||
\(667\) | −3.48270 | −0.134851 | ||||||||
\(668\) | 6.00000 | − | 10.3923i | 0.232147 | − | 0.402090i | ||||
\(669\) | 1.77283 | + | 3.07064i | 0.0685417 | + | 0.118718i | ||||
\(670\) | −0.563987 | − | 0.976854i | −0.0217887 | − | 0.0377391i | ||||
\(671\) | 4.63320 | + | 8.02494i | 0.178863 | + | 0.309799i | ||||
\(672\) | −0.267603 | −0.0103230 | ||||||||
\(673\) | 15.9250 | + | 27.5828i | 0.613862 | + | 1.06324i | 0.990583 | + | 0.136913i | \(0.0437182\pi\) |
−0.376721 | + | 0.926327i | \(0.622948\pi\) | |||||||
\(674\) | 0.127973 | 0.00492935 | ||||||||
\(675\) | 18.9296 | − | 32.7870i | 0.728600 | − | 1.26197i | ||||
\(676\) | −9.00000 | −0.346154 | ||||||||
\(677\) | −18.0167 | −0.692438 | −0.346219 | − | 0.938154i | \(-0.612535\pi\) | ||||
−0.346219 | + | 0.938154i | \(0.612535\pi\) | |||||||
\(678\) | 2.51730 | − | 4.36010i | 0.0966765 | − | 0.167449i | ||||
\(679\) | 0.0781676 | + | 0.135390i | 0.00299980 | + | 0.00519580i | ||||
\(680\) | 8.57606 | 0.328877 | ||||||||
\(681\) | −5.37143 | + | 9.30359i | −0.205834 | + | 0.356514i | ||||
\(682\) | −5.03461 | + | 8.72020i | −0.192785 | + | 0.333914i | ||||
\(683\) | 23.7009 | − | 41.0512i | 0.906890 | − | 1.57078i | 0.0885305 | − | 0.996073i | \(-0.471783\pi\) |
0.818360 | − | 0.574706i | \(-0.194884\pi\) | |||||||
\(684\) | 9.15051 | + | 15.8491i | 0.349878 | + | 0.606007i | ||||
\(685\) | −28.1589 | − | 48.7726i | −1.07589 | − | 1.86350i | ||||
\(686\) | −3.55191 | + | 6.15209i | −0.135613 | + | 0.234888i | ||||
\(687\) | 0.485819 | − | 0.841463i | 0.0185352 | − | 0.0321038i | ||||
\(688\) | −4.12485 | + | 7.14445i | −0.157258 | + | 0.272380i | ||||
\(689\) | 4.53521 | 0.172778 | ||||||||
\(690\) | 7.86620 | + | 13.6247i | 0.299461 | + | 0.518682i | ||||
\(691\) | 1.68571 | − | 2.91974i | 0.0641276 | − | 0.111072i | −0.832179 | − | 0.554507i | \(-0.812907\pi\) |
0.896307 | + | 0.443435i | \(0.146240\pi\) | |||||||
\(692\) | −2.91288 | −0.110731 | ||||||||
\(693\) | −5.27567 | −0.200406 | ||||||||
\(694\) | 4.84517 | − | 8.39208i | 0.183920 | − | 0.318559i | ||||
\(695\) | −60.7491 | −2.30434 | ||||||||
\(696\) | 0.124850 | + | 0.216247i | 0.00473244 | + | 0.00819682i | ||||
\(697\) | −3.45433 | −0.130842 | ||||||||
\(698\) | −4.57234 | − | 7.91952i | −0.173066 | − | 0.299758i | ||||
\(699\) | 3.58501 | + | 6.20942i | 0.135598 | + | 0.234862i | ||||
\(700\) | 3.30221 | + | 5.71960i | 0.124812 | + | 0.216180i | ||||
\(701\) | −23.0934 | + | 39.9989i | −0.872224 | + | 1.51074i | −0.0125340 | + | 0.999921i | \(0.503990\pi\) |
−0.859690 | + | 0.510815i | \(0.829344\pi\) | |||||||
\(702\) | −5.93078 | −0.223843 | ||||||||
\(703\) | 39.7791 | + | 8.80105i | 1.50030 | + | 0.331938i | ||||
\(704\) | −3.73240 | −0.140670 | ||||||||
\(705\) | −1.41973 | + | 2.45904i | −0.0534700 | + | 0.0926127i | ||||
\(706\) | −4.66841 | − | 8.08592i | −0.175698 | − | 0.304318i | ||||
\(707\) | −2.39245 | − | 4.14385i | −0.0899775 | − | 0.155846i | ||||
\(708\) | −3.23300 | − | 5.59971i | −0.121503 | − | 0.210450i | ||||
\(709\) | 15.2571 | 0.572994 | 0.286497 | − | 0.958081i | \(-0.407509\pi\) | ||||
0.286497 | + | 0.958081i | \(0.407509\pi\) | |||||||
\(710\) | −7.33994 | − | 12.7132i | −0.275463 | − | 0.477116i | ||||
\(711\) | −13.0253 | −0.488489 | ||||||||
\(712\) | −8.06399 | + | 13.9672i | −0.302211 | + | 0.523444i | ||||
\(713\) | −19.4648 | −0.728962 | ||||||||
\(714\) | 0.544468 | 0.0203762 | ||||||||
\(715\) | −15.7324 | + | 27.2493i | −0.588358 | + | 1.01907i | ||||
\(716\) | 3.48270 | + | 6.03221i | 0.130154 | + | 0.225434i | ||||
\(717\) | 0.454334 | 0.0169674 | ||||||||
\(718\) | 6.96539 | − | 12.0644i | 0.259946 | − | 0.450240i | ||||
\(719\) | −4.48582 | + | 7.76967i | −0.167293 | + | 0.289760i | −0.937467 | − | 0.348074i | \(-0.886836\pi\) |
0.770174 | + | 0.637833i | \(0.220169\pi\) | |||||||
\(720\) | −5.75865 | + | 9.97428i | −0.214612 | + | 0.371719i | ||||
\(721\) | 1.66781 | + | 2.88873i | 0.0621125 | + | 0.107582i | ||||
\(722\) | −12.9302 | − | 22.3957i | −0.481212 | − | 0.833483i | ||||
\(723\) | −4.08712 | + | 7.07910i | −0.152002 | + | 0.263274i | ||||
\(724\) | 3.14215 | − | 5.44237i | 0.116777 | − | 0.202264i | ||||
\(725\) | 3.08129 | − | 5.33695i | 0.114436 | − | 0.198209i | ||||
\(726\) | 1.51611 | 0.0562680 | ||||||||
\(727\) | 16.8425 | + | 29.1720i | 0.624653 | + | 1.08193i | 0.988608 | + | 0.150514i | \(0.0480927\pi\) |
−0.363955 | + | 0.931416i | \(0.618574\pi\) | |||||||
\(728\) | 0.517304 | − | 0.895997i | 0.0191726 | − | 0.0332079i | ||||
\(729\) | −13.6044 | −0.503868 | ||||||||
\(730\) | −24.1626 | −0.894297 | ||||||||
\(731\) | 8.39245 | − | 14.5362i | 0.310406 | − | 0.537639i | ||||
\(732\) | 1.28431 | 0.0474694 | ||||||||
\(733\) | 17.1626 | + | 29.7265i | 0.633914 | + | 1.09797i | 0.986744 | + | 0.162284i | \(0.0518862\pi\) |
−0.352830 | + | 0.935688i | \(0.614780\pi\) | |||||||
\(734\) | −4.00000 | −0.147643 | ||||||||
\(735\) | −7.33994 | − | 12.7132i | −0.270738 | − | 0.468932i | ||||
\(736\) | −3.60755 | − | 6.24845i | −0.132976 | − | 0.230321i | ||||
\(737\) | −0.499401 | − | 0.864988i | −0.0183957 | − | 0.0318622i | ||||
\(738\) | 2.31952 | − | 4.01752i | 0.0853825 | − | 0.147887i | ||||
\(739\) | 6.27385 | 0.230787 | 0.115394 | − | 0.993320i | \(-0.463187\pi\) | ||||
0.115394 | + | 0.993320i | \(0.463187\pi\) | |||||||
\(740\) | 7.72032 | + | 24.4495i | 0.283805 | + | 0.898780i | ||||
\(741\) | 6.92959 | 0.254565 | ||||||||
\(742\) | 0.586520 | − | 1.01588i | 0.0215318 | − | 0.0372942i | ||||
\(743\) | 17.5115 | + | 30.3308i | 0.642434 | + | 1.11273i | 0.984888 | + | 0.173193i | \(0.0554085\pi\) |
−0.342454 | + | 0.939535i | \(0.611258\pi\) | |||||||
\(744\) | 0.697788 | + | 1.20861i | 0.0255822 | + | 0.0443096i | ||||
\(745\) | 44.0749 | + | 76.3399i | 1.61478 | + | 2.79688i | ||||
\(746\) | 0.00744394 | 0.000272542 | ||||||||
\(747\) | 14.9564 | + | 25.9053i | 0.547228 | + | 0.947826i | ||||
\(748\) | 7.59396 | 0.277663 | ||||||||
\(749\) | −3.16841 | + | 5.48785i | −0.115771 | + | 0.200522i | ||||
\(750\) | −16.9358 | −0.618409 | ||||||||
\(751\) | −11.6694 | −0.425823 | −0.212912 | − | 0.977071i | \(-0.568295\pi\) | ||||
−0.212912 | + | 0.977071i | \(0.568295\pi\) | |||||||
\(752\) | 0.651106 | − | 1.12775i | 0.0237434 | − | 0.0411247i | ||||
\(753\) | −3.79698 | − | 6.57657i | −0.138370 | − | 0.239663i | ||||
\(754\) | −0.965392 | −0.0351575 | ||||||||
\(755\) | 37.1882 | − | 64.4119i | 1.35342 | − | 2.34419i | ||||
\(756\) | −0.767005 | + | 1.32849i | −0.0278957 | + | 0.0483167i | ||||
\(757\) | −14.7061 | + | 25.4718i | −0.534504 | + | 0.925788i | 0.464683 | + | 0.885477i | \(0.346168\pi\) |
−0.999187 | + | 0.0403108i | \(0.987165\pi\) | |||||||
\(758\) | 9.00312 | + | 15.5939i | 0.327008 | + | 0.566395i | ||||
\(759\) | 6.96539 | + | 12.0644i | 0.252828 | + | 0.437910i | ||||
\(760\) | 14.1159 | − | 24.4495i | 0.512037 | − | 0.886875i | ||||
\(761\) | −14.0415 | + | 24.3205i | −0.509002 | + | 0.881618i | 0.490943 | + | 0.871191i | \(0.336652\pi\) |
−0.999946 | + | 0.0104263i | \(0.996681\pi\) | |||||||
\(762\) | −4.06459 | + | 7.04007i | −0.147244 | + | 0.255035i | ||||
\(763\) | 3.57606 | 0.129462 | ||||||||
\(764\) | −5.78803 | − | 10.0252i | −0.209404 | − | 0.362698i | ||||
\(765\) | 11.7166 | − | 20.2937i | 0.423615 | − | 0.733722i | ||||
\(766\) | −15.8079 | −0.571161 | ||||||||
\(767\) | 24.9988 | 0.902654 | ||||||||
\(768\) | −0.258652 | + | 0.447998i | −0.00933330 | + | 0.0161658i | ||||
\(769\) | 31.9883 | 1.15353 | 0.576765 | − | 0.816910i | \(-0.304315\pi\) | ||||
0.576765 | + | 0.816910i | \(0.304315\pi\) | |||||||
\(770\) | 4.06922 | + | 7.04809i | 0.146644 | + | 0.253996i | ||||
\(771\) | 3.83117 | 0.137976 | ||||||||
\(772\) | −6.71509 | − | 11.6309i | −0.241681 | − | 0.418605i | ||||
\(773\) | −14.8174 | − | 25.6645i | −0.532945 | − | 0.923088i | −0.999260 | − | 0.0384692i | \(-0.987752\pi\) |
0.466315 | − | 0.884619i | \(-0.345581\pi\) | |||||||
\(774\) | 11.2707 | + | 19.5215i | 0.405118 | + | 0.701685i | ||||
\(775\) | 17.2213 | − | 29.8282i | 0.618609 | − | 1.07146i | ||||
\(776\) | 0.302212 | 0.0108488 | ||||||||
\(777\) | 0.490140 | + | 1.55222i | 0.0175837 | + | 0.0556857i | ||||
\(778\) | 1.31892 | 0.0472855 | ||||||||
\(779\) | −5.68571 | + | 9.84795i | −0.203712 | + | 0.352839i | ||||
\(780\) | 2.18048 | + | 3.77671i | 0.0780739 | + | 0.135228i | ||||
\(781\) | −6.49940 | − | 11.2573i | −0.232567 | − | 0.402818i | ||||
\(782\) | 7.33994 | + | 12.7132i | 0.262476 | + | 0.454621i | ||||
\(783\) | 1.43138 | 0.0511534 | ||||||||
\(784\) | 3.36620 | + | 5.83043i | 0.120221 | + | 0.208230i | ||||
\(785\) | 42.2213 | 1.50694 | ||||||||
\(786\) | 3.46016 | − | 5.99318i | 0.123420 | − | 0.213770i | ||||
\(787\) | −47.7900 | −1.70353 | −0.851764 | − | 0.523926i | \(-0.824467\pi\) | ||||
−0.851764 | + | 0.523926i | \(0.824467\pi\) | |||||||
\(788\) | −5.51730 | −0.196546 | ||||||||
\(789\) | −2.55936 | + | 4.43293i | −0.0911155 | + | 0.157817i | ||||
\(790\) | 10.0467 | + | 17.4014i | 0.357445 | + | 0.619113i | ||||
\(791\) | 5.03461 | 0.179010 | ||||||||
\(792\) | −5.09919 | + | 8.83206i | −0.181192 | + | 0.313834i | ||||
\(793\) | −2.48270 | + | 4.30016i | −0.0881631 | + | 0.152703i | ||||
\(794\) | −10.9092 | + | 18.8952i | −0.387152 | + | 0.670566i | ||||
\(795\) | 2.47224 | + | 4.28204i | 0.0876812 | + | 0.151868i | ||||
\(796\) | −8.17153 | − | 14.1535i | −0.289632 | − | 0.501658i | ||||
\(797\) | 16.9642 | − | 29.3828i | 0.600903 | − | 1.04079i | −0.391782 | − | 0.920058i | \(-0.628141\pi\) |
0.992685 | − | 0.120736i | \(-0.0385254\pi\) | |||||||
\(798\) | 0.896176 | − | 1.55222i | 0.0317243 | − | 0.0549481i | ||||
\(799\) | −1.32475 | + | 2.29453i | −0.0468661 | + | 0.0811745i | ||||
\(800\) | 12.7670 | 0.451382 | ||||||||
\(801\) | 22.0340 | + | 38.1640i | 0.778533 | + | 1.34846i | ||||
\(802\) | −2.09919 | + | 3.63591i | −0.0741251 | + | 0.128388i | ||||
\(803\) | −21.3956 | −0.755034 | ||||||||
\(804\) | −0.138432 | −0.00488213 | ||||||||
\(805\) | −7.86620 | + | 13.6247i | −0.277247 | + | 0.480206i | ||||
\(806\) | −5.39558 | −0.190051 | ||||||||
\(807\) | 1.37767 | + | 2.38620i | 0.0484964 | + | 0.0839983i | ||||
\(808\) | −9.24970 | −0.325403 | ||||||||
\(809\) | 8.26178 | + | 14.3098i | 0.290469 | + | 0.503106i | 0.973921 | − | 0.226889i | \(-0.0728555\pi\) |
−0.683452 | + | 0.729995i | \(0.739522\pi\) | |||||||
\(810\) | 14.0430 | + | 24.3231i | 0.493419 | + | 0.854627i | ||||
\(811\) | −7.10382 | − | 12.3042i | −0.249449 | − | 0.432058i | 0.713924 | − | 0.700223i | \(-0.246916\pi\) |
−0.963373 | + | 0.268165i | \(0.913583\pi\) | |||||||
\(812\) | −0.124850 | + | 0.216247i | −0.00438139 | + | 0.00758878i | ||||
\(813\) | 0.210044 | 0.00736656 | ||||||||
\(814\) | 6.83622 | + | 21.6496i | 0.239609 | + | 0.758818i | ||||
\(815\) | 26.0513 | 0.912538 | ||||||||
\(816\) | 0.526255 | − | 0.911501i | 0.0184226 | − | 0.0319089i | ||||
\(817\) | −27.6274 | − | 47.8520i | −0.966559 | − | 1.67413i | ||||
\(818\) | 8.27908 | + | 14.3398i | 0.289471 | + | 0.501379i | ||||
\(819\) | −1.41348 | − | 2.44822i | −0.0493910 | − | 0.0855477i | ||||
\(820\) | −7.15634 | −0.249910 | ||||||||
\(821\) | −8.66318 | − | 15.0051i | −0.302347 | − | 0.523681i | 0.674320 | − | 0.738439i | \(-0.264437\pi\) |
−0.976667 | + | 0.214759i | \(0.931103\pi\) | |||||||
\(822\) | −6.91168 | −0.241073 | ||||||||
\(823\) | 15.5025 | − | 26.8512i | 0.540384 | − | 0.935973i | −0.458498 | − | 0.888696i | \(-0.651612\pi\) |
0.998882 | − | 0.0472770i | \(-0.0150544\pi\) | |||||||
\(824\) | 6.44809 | 0.224630 | ||||||||
\(825\) | −24.6503 | −0.858214 | ||||||||
\(826\) | 3.23300 | − | 5.59971i | 0.112490 | − | 0.194839i | ||||
\(827\) | −21.0588 | − | 36.4748i | −0.732285 | − | 1.26835i | −0.955904 | − | 0.293678i | \(-0.905121\pi\) |
0.223620 | − | 0.974676i | \(-0.428213\pi\) | |||||||
\(828\) | −19.7145 | −0.685126 | ||||||||
\(829\) | 13.9296 | − | 24.1268i | 0.483795 | − | 0.837957i | −0.516032 | − | 0.856569i | \(-0.672592\pi\) |
0.999827 | + | 0.0186125i | \(0.00592487\pi\) | |||||||
\(830\) | 23.0723 | − | 39.9625i | 0.800853 | − | 1.38712i | ||||
\(831\) | 4.68421 | − | 8.11328i | 0.162493 | − | 0.281447i | ||||
\(832\) | −1.00000 | − | 1.73205i | −0.0346688 | − | 0.0600481i | ||||
\(833\) | −6.84889 | − | 11.8626i | −0.237300 | − | 0.411016i | ||||
\(834\) | −3.72777 | + | 6.45668i | −0.129082 | + | 0.223577i | ||||
\(835\) | −25.2906 | + | 43.8045i | −0.875216 | + | 1.51592i | ||||
\(836\) | 12.4994 | − | 21.6496i | 0.432301 | − | 0.748767i | ||||
\(837\) | 8.00000 | 0.276520 | ||||||||
\(838\) | −11.1595 | − | 19.3287i | −0.385497 | − | 0.667701i | ||||
\(839\) | −19.8814 | + | 34.4356i | −0.686382 | + | 1.18885i | 0.286618 | + | 0.958045i | \(0.407469\pi\) |
−0.973000 | + | 0.230804i | \(0.925864\pi\) | |||||||
\(840\) | 1.12797 | 0.0389188 | ||||||||
\(841\) | −28.7670 | −0.991966 | ||||||||
\(842\) | −12.5902 | + | 21.8069i | −0.433888 | + | 0.751517i | ||||
\(843\) | −9.86458 | −0.339754 | ||||||||
\(844\) | −10.3746 | − | 17.9692i | −0.357107 | − | 0.618527i | ||||
\(845\) | 37.9358 | 1.30503 | ||||||||
\(846\) | −1.77908 | − | 3.08146i | −0.0611660 | − | 0.105943i | ||||
\(847\) | 0.758053 | + | 1.31299i | 0.0260470 | + | 0.0451148i | ||||
\(848\) | −1.13380 | − | 1.96380i | −0.0389349 | − | 0.0674372i | ||||
\(849\) | −4.43482 | + | 7.68133i | −0.152202 | + | 0.263622i | ||||
\(850\) | −25.9759 | −0.890964 | ||||||||
\(851\) | −29.6363 | + | 32.3700i | −1.01592 | + | 1.10963i | ||||
\(852\) | −1.80161 | −0.0617222 | ||||||||
\(853\) | −17.5603 | + | 30.4153i | −0.601252 | + | 1.04140i | 0.391380 | + | 0.920229i | \(0.371998\pi\) |
−0.992632 | + | 0.121170i | \(0.961335\pi\) | |||||||
\(854\) | 0.642154 | + | 1.11224i | 0.0219741 | + | 0.0380602i | ||||
\(855\) | −38.5702 | − | 66.8056i | −1.31907 | − | 2.28470i | ||||
\(856\) | 6.12485 | + | 10.6086i | 0.209343 | + | 0.362593i | ||||
\(857\) | 21.1626 | 0.722900 | 0.361450 | − | 0.932391i | \(-0.382282\pi\) | ||||
0.361450 | + | 0.932391i | \(0.382282\pi\) | |||||||
\(858\) | 1.93078 | + | 3.34422i | 0.0659159 | + | 0.114170i | ||||
\(859\) | −20.1113 | −0.686188 | −0.343094 | − | 0.939301i | \(-0.611475\pi\) | ||||
−0.343094 | + | 0.939301i | \(0.611475\pi\) | |||||||
\(860\) | 17.3866 | − | 30.1145i | 0.592879 | − | 1.02690i | ||||
\(861\) | −0.454334 | −0.0154837 | ||||||||
\(862\) | −22.6978 | −0.773090 | ||||||||
\(863\) | 21.6453 | − | 37.4907i | 0.736814 | − | 1.27620i | −0.217109 | − | 0.976147i | \(-0.569663\pi\) |
0.953923 | − | 0.300052i | \(-0.0970039\pi\) | |||||||
\(864\) | 1.48270 | + | 2.56810i | 0.0504423 | + | 0.0873687i | ||||
\(865\) | 12.2781 | 0.417467 | ||||||||
\(866\) | 12.3483 | − | 21.3879i | 0.419612 | − | 0.726790i | ||||
\(867\) | 3.32636 | − | 5.76143i | 0.112969 | − | 0.195668i | ||||
\(868\) | −0.697788 | + | 1.20861i | −0.0236845 | + | 0.0410227i | ||||
\(869\) | 8.89618 | + | 15.4086i | 0.301782 | + | 0.522702i | ||||
\(870\) | −0.526255 | − | 0.911501i | −0.0178417 | − | 0.0309028i | ||||
\(871\) | 0.267603 | − | 0.463503i | 0.00906740 | − | 0.0157052i | ||||
\(872\) | 3.45644 | − | 5.98673i | 0.117050 | − | 0.202736i | ||||
\(873\) | 0.412881 | − | 0.715131i | 0.0139739 | − | 0.0242035i | ||||
\(874\) | 48.3252 | 1.63462 | ||||||||
\(875\) | −8.46792 | − | 14.6669i | −0.286268 | − | 0.495830i | ||||
\(876\) | −1.48270 | + | 2.56810i | −0.0500957 | + | 0.0867682i | ||||
\(877\) | 29.2831 | 0.988820 | 0.494410 | − | 0.869229i | \(-0.335384\pi\) | ||||
0.494410 | + | 0.869229i | \(0.335384\pi\) | |||||||
\(878\) | 7.82576 | 0.264107 | ||||||||
\(879\) | −4.78059 | + | 8.28022i | −0.161245 | + | 0.279285i | ||||
\(880\) | 15.7324 | 0.530339 | ||||||||
\(881\) | −2.46539 | − | 4.27018i | −0.0830612 | − | 0.143866i | 0.821502 | − | 0.570205i | \(-0.193136\pi\) |
−0.904563 | + | 0.426339i | \(0.859803\pi\) | |||||||
\(882\) | 18.3956 | 0.619411 | ||||||||
\(883\) | 15.8168 | + | 27.3955i | 0.532278 | + | 0.921933i | 0.999290 | + | 0.0376815i | \(0.0119972\pi\) |
−0.467012 | + | 0.884251i | \(0.654669\pi\) | |||||||
\(884\) | 2.03461 | + | 3.52404i | 0.0684313 | + | 0.118526i | ||||
\(885\) | 13.6274 | + | 23.6033i | 0.458079 | + | 0.793416i | ||||
\(886\) | −17.1972 | + | 29.7864i | −0.577751 | + | 1.00069i | ||||
\(887\) | −27.9370 | −0.938034 | −0.469017 | − | 0.883189i | \(-0.655392\pi\) | ||||
−0.469017 | + | 0.883189i | \(0.655392\pi\) | |||||||
\(888\) | 3.07234 | + | 0.679750i | 0.103101 | + | 0.0228109i | ||||
\(889\) | −8.12917 | −0.272644 | ||||||||
\(890\) | 33.9904 | − | 58.8732i | 1.13936 | − | 1.97343i | ||||
\(891\) | 12.4348 | + | 21.5377i | 0.416582 | + | 0.721541i | ||||
\(892\) | 3.42706 | + | 5.93585i | 0.114747 | + | 0.198747i | ||||
\(893\) | 4.36097 | + | 7.55342i | 0.145934 | + | 0.252766i | ||||
\(894\) | 10.8183 | 0.361819 | ||||||||
\(895\) | −14.6799 | − | 25.4263i | −0.490694 | − | 0.849908i | ||||
\(896\) | −0.517304 | −0.0172819 | ||||||||
\(897\) | −3.73240 | + | 6.46470i | −0.124621 | + | 0.215850i | ||||
\(898\) | 15.2664 | 0.509447 | ||||||||
\(899\) | 1.30221 | 0.0434312 | ||||||||
\(900\) | 17.4423 | − | 30.2109i | 0.581409 | − | 1.00703i | ||||
\(901\) | 2.30684 | + | 3.99557i | 0.0768521 | + | 0.133112i | ||||
\(902\) | −6.33682 | −0.210993 | ||||||||
\(903\) | 1.10382 | − | 1.91188i | 0.0367330 | − | 0.0636234i | ||||
\(904\) | 4.86620 | − | 8.42850i | 0.161847 | − | 0.280328i | ||||
\(905\) | −13.2445 | + | 22.9401i | −0.440261 | + | 0.762555i | ||||
\(906\) | −4.56399 | − | 7.90506i | −0.151628 | − | 0.262628i | ||||
\(907\) | −8.29638 | − | 14.3698i | −0.275477 | − | 0.477140i | 0.694778 | − | 0.719224i | \(-0.255502\pi\) |
−0.970255 | + | 0.242084i | \(0.922169\pi\) | |||||||
\(908\) | −10.3835 | + | 17.9848i | −0.344589 | + | 0.596845i | ||||
\(909\) | −12.6369 | + | 21.8878i | −0.419140 | + | 0.725972i | ||||
\(910\) | −2.18048 | + | 3.77671i | −0.0722824 | + | 0.125197i | ||||
\(911\) | −51.6787 | −1.71219 | −0.856096 | − | 0.516817i | \(-0.827117\pi\) | ||||
−0.856096 | + | 0.516817i | \(0.827117\pi\) | |||||||
\(912\) | −1.73240 | − | 3.00060i | −0.0573654 | − | 0.0993598i | ||||
\(913\) | 20.4302 | − | 35.3861i | 0.676140 | − | 1.17111i | ||||
\(914\) | −17.3610 | −0.574250 | ||||||||
\(915\) | −5.41348 | −0.178964 | ||||||||
\(916\) | 0.939136 | − | 1.62663i | 0.0310299 | − | 0.0537454i | ||||
\(917\) | 6.92032 | 0.228529 | ||||||||
\(918\) | −3.01671 | − | 5.22509i | −0.0995661 | − | 0.172454i | ||||
\(919\) | −39.3177 | −1.29697 | −0.648486 | − | 0.761227i | \(-0.724597\pi\) | ||||
−0.648486 | + | 0.761227i | \(0.724597\pi\) | |||||||
\(920\) | 15.2061 | + | 26.3378i | 0.501332 | + | 0.868332i | ||||
\(921\) | 2.90081 | + | 5.02434i | 0.0955848 | + | 0.165558i | ||||
\(922\) | −3.96539 | − | 6.86826i | −0.130593 | − | 0.226194i | ||||
\(923\) | 3.48270 | − | 6.03221i | 0.114634 | − | 0.198552i | ||||
\(924\) | 0.998802 | 0.0328582 | ||||||||
\(925\) | −23.3839 | − | 74.0544i | −0.768859 | − | 2.43489i | ||||
\(926\) | −10.4123 | −0.342169 | ||||||||
\(927\) | 8.80937 | − | 15.2583i | 0.289338 | − | 0.501147i | ||||
\(928\) | 0.241348 | + | 0.418027i | 0.00792264 | + | 0.0137224i | ||||
\(929\) | 5.94226 | + | 10.2923i | 0.194959 | + | 0.337679i | 0.946887 | − | 0.321566i | \(-0.104209\pi\) |
−0.751928 | + | 0.659245i | \(0.770876\pi\) | |||||||
\(930\) | −2.94124 | − | 5.09438i | −0.0964472 | − | 0.167051i | ||||
\(931\) | −45.0922 | −1.47784 | ||||||||
\(932\) | 6.93018 | + | 12.0034i | 0.227006 | + | 0.393186i | ||||
\(933\) | −9.26641 | −0.303369 | ||||||||
\(934\) | −2.85412 | + | 4.94349i | −0.0933898 | + | 0.161756i | ||||
\(935\) | −32.0093 | −1.04681 | ||||||||
\(936\) | −5.46479 | −0.178622 | ||||||||
\(937\) | −7.20362 | + | 12.4770i | −0.235332 | + | 0.407607i | −0.959369 | − | 0.282154i | \(-0.908951\pi\) |
0.724037 | + | 0.689761i | \(0.242284\pi\) | |||||||
\(938\) | −0.0692162 | − | 0.119886i | −0.00225999 | − | 0.00391441i | ||||
\(939\) | 2.50242 | 0.0816633 | ||||||||
\(940\) | −2.74447 | + | 4.75356i | −0.0895148 | + | 0.155044i | ||||
\(941\) | −24.5078 | + | 42.4487i | −0.798930 | + | 1.38379i | 0.121384 | + | 0.992606i | \(0.461267\pi\) |
−0.920314 | + | 0.391182i | \(0.872066\pi\) | |||||||
\(942\) | 2.59084 | − | 4.48747i | 0.0844142 | − | 0.146210i | ||||
\(943\) | −6.12485 | − | 10.6086i | −0.199453 | − | 0.345462i | ||||
\(944\) | −6.24970 | − | 10.8248i | −0.203410 | − | 0.352317i | ||||
\(945\) | 3.23300 | − | 5.59971i | 0.105169 | − | 0.182159i | ||||
\(946\) | 15.3956 | − | 26.6659i | 0.500553 | − | 0.866984i | ||||
\(947\) | 13.2151 | − | 22.8892i | 0.429433 | − | 0.743799i | −0.567390 | − | 0.823449i | \(-0.692047\pi\) |
0.996823 | + | 0.0796497i | \(0.0253802\pi\) | |||||||
\(948\) | 2.46599 | 0.0800917 | ||||||||
\(949\) | −5.73240 | − | 9.92880i | −0.186081 | − | 0.322303i | ||||
\(950\) | −42.7553 | + | 74.0544i | −1.38717 | + | 2.40264i | ||||
\(951\) | 13.3559 | 0.433095 | ||||||||
\(952\) | 1.05251 | 0.0341121 | ||||||||
\(953\) | −3.56399 | + | 6.17301i | −0.115449 | + | 0.199963i | −0.917959 | − | 0.396675i | \(-0.870164\pi\) |
0.802510 | + | 0.596638i | \(0.203497\pi\) | |||||||
\(954\) | −6.19599 | −0.200603 | ||||||||
\(955\) | 24.3971 | + | 42.2570i | 0.789471 | + | 1.36740i | ||||
\(956\) | 0.878273 | 0.0284054 | ||||||||
\(957\) | −0.465991 | − | 0.807120i | −0.0150633 | − | 0.0260905i | ||||
\(958\) | 10.3189 | + | 17.8729i | 0.333389 | + | 0.577447i | ||||
\(959\) | −3.45584 | − | 5.98569i | −0.111595 | − | 0.193288i | ||||
\(960\) | 1.09024 | − | 1.88835i | 0.0351874 | − | 0.0609464i | ||||
\(961\) | −23.7219 | −0.765224 | ||||||||
\(962\) | −8.21509 | + | 8.97286i | −0.264865 | + | 0.289297i | ||||
\(963\) | 33.4710 | 1.07859 | ||||||||
\(964\) | −7.90081 | + | 13.6846i | −0.254468 | + | 0.440751i | ||||
\(965\) | 28.3047 | + | 49.0252i | 0.911162 | + | 1.57818i | ||||
\(966\) | 0.965392 | + | 1.67211i | 0.0310610 | + | 0.0537992i | ||||
\(967\) | −4.87827 | − | 8.44942i | −0.156875 | − | 0.271715i | 0.776865 | − | 0.629667i | \(-0.216809\pi\) |
−0.933740 | + | 0.357952i | \(0.883475\pi\) | |||||||
\(968\) | 2.93078 | 0.0941990 | ||||||||
\(969\) | 3.52475 | + | 6.10504i | 0.113231 | + | 0.196122i | ||||
\(970\) | −1.27385 | −0.0409008 | ||||||||
\(971\) | −1.74135 | + | 3.01610i | −0.0558825 | + | 0.0967914i | −0.892613 | − | 0.450823i | \(-0.851131\pi\) |
0.836731 | + | 0.547614i | \(0.184464\pi\) | |||||||
\(972\) | 12.3431 | 0.395904 | ||||||||
\(973\) | −7.45553 | −0.239013 | ||||||||
\(974\) | −16.1249 | + | 27.9291i | −0.516674 | + | 0.894905i | ||||
\(975\) | −6.60442 | − | 11.4392i | −0.211511 | − | 0.366347i | ||||
\(976\) | 2.48270 | 0.0794692 | ||||||||
\(977\) | −8.43601 | + | 14.6116i | −0.269892 | + | 0.467467i | −0.968834 | − | 0.247712i | \(-0.920321\pi\) |
0.698942 | + | 0.715179i | \(0.253655\pi\) | |||||||
\(978\) | 1.59859 | − | 2.76885i | 0.0511174 | − | 0.0885380i | ||||
\(979\) | 30.0980 | − | 52.1313i | 0.961936 | − | 1.66612i | ||||
\(980\) | −14.1888 | − | 24.5758i | −0.453246 | − | 0.785045i | ||||
\(981\) | −9.44437 | − | 16.3581i | −0.301535 | − | 0.522275i | ||||
\(982\) | −1.86620 | + | 3.23235i | −0.0595528 | + | 0.103148i | ||||
\(983\) | 29.8483 | − | 51.6988i | 0.952013 | − | 1.64893i | 0.210952 | − | 0.977496i | \(-0.432344\pi\) |
0.741061 | − | 0.671438i | \(-0.234323\pi\) | |||||||
\(984\) | −0.439136 | + | 0.760607i | −0.0139992 | + | 0.0242473i | ||||
\(985\) | 23.2559 | 0.740996 | ||||||||
\(986\) | −0.491049 | − | 0.850521i | −0.0156382 | − | 0.0270861i | ||||
\(987\) | −0.174238 | + | 0.301789i | −0.00554606 | + | 0.00960606i | ||||
\(988\) | 13.3956 | 0.426170 | ||||||||
\(989\) | 59.5224 | 1.89270 | ||||||||
\(990\) | 21.4936 | − | 37.2280i | 0.683111 | − | 1.18318i | ||||
\(991\) | −36.1688 | −1.14894 | −0.574470 | − | 0.818525i | \(-0.694792\pi\) | ||||
−0.574470 | + | 0.818525i | \(0.694792\pi\) | |||||||
\(992\) | 1.34889 | + | 2.33635i | 0.0428274 | + | 0.0741793i | ||||
\(993\) | 9.99760 | 0.317264 | ||||||||
\(994\) | −0.900806 | − | 1.56024i | −0.0285718 | − | 0.0494879i | ||||
\(995\) | 34.4438 | + | 59.6584i | 1.09194 | + | 1.89130i | ||||
\(996\) | −2.83159 | − | 4.90446i | −0.0897224 | − | 0.155404i | ||||
\(997\) | −7.29175 | + | 12.6297i | −0.230932 | + | 0.399986i | −0.958083 | − | 0.286492i | \(-0.907511\pi\) |
0.727151 | + | 0.686478i | \(0.240844\pi\) | |||||||
\(998\) | 28.0934 | 0.889280 | ||||||||
\(999\) | 12.1805 | − | 13.3040i | 0.385373 | − | 0.420921i |
(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 | 74.2.c.c.47.2 | ✓ | 6 | |
3.2 | odd | 2 | 666.2.f.j.343.1 | 6 | |||
4.3 | odd | 2 | 592.2.i.e.417.2 | 6 | |||
37.10 | even | 3 | 2738.2.a.o.1.2 | 3 | |||
37.26 | even | 3 | inner | 74.2.c.c.63.2 | yes | 6 | |
37.27 | even | 6 | 2738.2.a.n.1.2 | 3 | |||
111.26 | odd | 6 | 666.2.f.j.433.1 | 6 | |||
148.63 | odd | 6 | 592.2.i.e.433.2 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
74.2.c.c.47.2 | ✓ | 6 | 1.1 | even | 1 | trivial | |
74.2.c.c.63.2 | yes | 6 | 37.26 | even | 3 | inner | |
592.2.i.e.417.2 | 6 | 4.3 | odd | 2 | |||
592.2.i.e.433.2 | 6 | 148.63 | odd | 6 | |||
666.2.f.j.343.1 | 6 | 3.2 | odd | 2 | |||
666.2.f.j.433.1 | 6 | 111.26 | odd | 6 | |||
2738.2.a.n.1.2 | 3 | 37.27 | even | 6 | |||
2738.2.a.o.1.2 | 3 | 37.10 | even | 3 |