Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [546,2,Mod(545,546)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(546, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("546.545");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 546.e (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(4.35983195036\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.303595776.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 5x^{6} + 16x^{4} + 45x^{2} + 81 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 545.3 | ||
Root | \(-0.396143 - 1.68614i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 546.545 |
Dual form | 546.2.e.g.545.4 |
$q$-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 \(\left(\mathbb{Z}/546\mathbb{Z}\right)^\times\).
\(n\) | \(157\) | \(365\) | \(379\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | −0.396143 | − | 1.68614i | −0.228714 | − | 0.973494i | ||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 2.37228i | 1.06092i | 0.847711 | + | 0.530458i | \(0.177980\pi\) | ||||
−0.847711 | + | 0.530458i | \(0.822020\pi\) | |||||||
\(6\) | −0.396143 | − | 1.68614i | −0.161725 | − | 0.688364i | ||||
\(7\) | −0.792287 | + | 2.52434i | −0.299456 | + | 0.954110i | ||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | −2.68614 | + | 1.33591i | −0.895380 | + | 0.445302i | ||||
\(10\) | 2.37228i | 0.750181i | ||||||||
\(11\) | 5.74456 | 1.73205 | 0.866025 | − | 0.500000i | \(-0.166667\pi\) | ||||
0.866025 | + | 0.500000i | \(0.166667\pi\) | |||||||
\(12\) | −0.396143 | − | 1.68614i | −0.114357 | − | 0.486747i | ||||
\(13\) | 3.46410 | − | 1.00000i | 0.960769 | − | 0.277350i | ||||
\(14\) | −0.792287 | + | 2.52434i | −0.211748 | + | 0.674658i | ||||
\(15\) | 4.00000 | − | 0.939764i | 1.03280 | − | 0.242646i | ||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 2.52434 | 0.612242 | 0.306121 | − | 0.951993i | \(-0.400969\pi\) | ||||
0.306121 | + | 0.951993i | \(0.400969\pi\) | |||||||
\(18\) | −2.68614 | + | 1.33591i | −0.633129 | + | 0.314876i | ||||
\(19\) | −7.57301 | −1.73737 | −0.868684 | − | 0.495366i | \(-0.835034\pi\) | ||||
−0.868684 | + | 0.495366i | \(0.835034\pi\) | |||||||
\(20\) | 2.37228i | 0.530458i | ||||||||
\(21\) | 4.57025 | + | 0.335907i | 0.997310 | + | 0.0733010i | ||||
\(22\) | 5.74456 | 1.22474 | ||||||||
\(23\) | 6.78073i | 1.41388i | 0.707274 | + | 0.706940i | \(0.249925\pi\) | ||||
−0.707274 | + | 0.706940i | \(0.750075\pi\) | |||||||
\(24\) | −0.396143 | − | 1.68614i | −0.0808625 | − | 0.344182i | ||||
\(25\) | −0.627719 | −0.125544 | ||||||||
\(26\) | 3.46410 | − | 1.00000i | 0.679366 | − | 0.196116i | ||||
\(27\) | 3.31662 | + | 4.00000i | 0.638285 | + | 0.769800i | ||||
\(28\) | −0.792287 | + | 2.52434i | −0.149728 | + | 0.477055i | ||||
\(29\) | − | 7.57301i | − | 1.40627i | −0.711055 | − | 0.703137i | \(-0.751782\pi\) | ||
0.711055 | − | 0.703137i | \(-0.248218\pi\) | |||||||
\(30\) | 4.00000 | − | 0.939764i | 0.730297 | − | 0.171577i | ||||
\(31\) | 5.84096 | 1.04907 | 0.524534 | − | 0.851390i | \(-0.324240\pi\) | ||||
0.524534 | + | 0.851390i | \(0.324240\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | −2.27567 | − | 9.68614i | −0.396143 | − | 1.68614i | ||||
\(34\) | 2.52434 | 0.432920 | ||||||||
\(35\) | −5.98844 | − | 1.87953i | −1.01223 | − | 0.317698i | ||||
\(36\) | −2.68614 | + | 1.33591i | −0.447690 | + | 0.222651i | ||||
\(37\) | − | 4.90120i | − | 0.805752i | −0.915255 | − | 0.402876i | \(-0.868011\pi\) | ||
0.915255 | − | 0.402876i | \(-0.131989\pi\) | |||||||
\(38\) | −7.57301 | −1.22850 | ||||||||
\(39\) | −3.05842 | − | 5.44482i | −0.489739 | − | 0.871869i | ||||
\(40\) | 2.37228i | 0.375091i | ||||||||
\(41\) | 2.62772i | 0.410381i | 0.978722 | + | 0.205190i | \(0.0657813\pi\) | ||||
−0.978722 | + | 0.205190i | \(0.934219\pi\) | |||||||
\(42\) | 4.57025 | + | 0.335907i | 0.705205 | + | 0.0518316i | ||||
\(43\) | −8.37228 | −1.27676 | −0.638380 | − | 0.769721i | \(-0.720395\pi\) | ||||
−0.638380 | + | 0.769721i | \(0.720395\pi\) | |||||||
\(44\) | 5.74456 | 0.866025 | ||||||||
\(45\) | −3.16915 | − | 6.37228i | −0.472429 | − | 0.949924i | ||||
\(46\) | 6.78073i | 0.999764i | ||||||||
\(47\) | − | 4.62772i | − | 0.675022i | −0.941322 | − | 0.337511i | \(-0.890415\pi\) | ||
0.941322 | − | 0.337511i | \(-0.109585\pi\) | |||||||
\(48\) | −0.396143 | − | 1.68614i | −0.0571784 | − | 0.243373i | ||||
\(49\) | −5.74456 | − | 4.00000i | −0.820652 | − | 0.571429i | ||||
\(50\) | −0.627719 | −0.0887728 | ||||||||
\(51\) | −1.00000 | − | 4.25639i | −0.140028 | − | 0.596014i | ||||
\(52\) | 3.46410 | − | 1.00000i | 0.480384 | − | 0.138675i | ||||
\(53\) | − | 3.16915i | − | 0.435316i | −0.976025 | − | 0.217658i | \(-0.930158\pi\) | ||
0.976025 | − | 0.217658i | \(-0.0698417\pi\) | |||||||
\(54\) | 3.31662 | + | 4.00000i | 0.451335 | + | 0.544331i | ||||
\(55\) | 13.6277i | 1.83756i | ||||||||
\(56\) | −0.792287 | + | 2.52434i | −0.105874 | + | 0.337329i | ||||
\(57\) | 3.00000 | + | 12.7692i | 0.397360 | + | 1.69132i | ||||
\(58\) | − | 7.57301i | − | 0.994385i | ||||||
\(59\) | 8.74456i | 1.13845i | 0.822183 | + | 0.569223i | \(0.192756\pi\) | ||||
−0.822183 | + | 0.569223i | \(0.807244\pi\) | |||||||
\(60\) | 4.00000 | − | 0.939764i | 0.516398 | − | 0.121323i | ||||
\(61\) | − | 3.74456i | − | 0.479442i | −0.970842 | − | 0.239721i | \(-0.922944\pi\) | ||
0.970842 | − | 0.239721i | \(-0.0770560\pi\) | |||||||
\(62\) | 5.84096 | 0.741803 | ||||||||
\(63\) | −1.24409 | − | 7.83915i | −0.156740 | − | 0.987640i | ||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 2.37228 | + | 8.21782i | 0.294245 | + | 1.01930i | ||||
\(66\) | −2.27567 | − | 9.68614i | −0.280116 | − | 1.19228i | ||||
\(67\) | − | 2.67181i | − | 0.326414i | −0.986592 | − | 0.163207i | \(-0.947816\pi\) | ||
0.986592 | − | 0.163207i | \(-0.0521839\pi\) | |||||||
\(68\) | 2.52434 | 0.306121 | ||||||||
\(69\) | 11.4333 | − | 2.68614i | 1.37640 | − | 0.323373i | ||||
\(70\) | −5.98844 | − | 1.87953i | −0.715755 | − | 0.224647i | ||||
\(71\) | −2.00000 | −0.237356 | −0.118678 | − | 0.992933i | \(-0.537866\pi\) | ||||
−0.118678 | + | 0.992933i | \(0.537866\pi\) | |||||||
\(72\) | −2.68614 | + | 1.33591i | −0.316565 | + | 0.157438i | ||||
\(73\) | −3.61158 | −0.422703 | −0.211352 | − | 0.977410i | \(-0.567787\pi\) | ||||
−0.211352 | + | 0.977410i | \(0.567787\pi\) | |||||||
\(74\) | − | 4.90120i | − | 0.569753i | ||||||
\(75\) | 0.248667 | + | 1.05842i | 0.0287136 | + | 0.122216i | ||||
\(76\) | −7.57301 | −0.868684 | ||||||||
\(77\) | −4.55134 | + | 14.5012i | −0.518674 | + | 1.65257i | ||||
\(78\) | −3.05842 | − | 5.44482i | −0.346298 | − | 0.616504i | ||||
\(79\) | −9.37228 | −1.05446 | −0.527232 | − | 0.849721i | \(-0.676770\pi\) | ||||
−0.527232 | + | 0.849721i | \(0.676770\pi\) | |||||||
\(80\) | 2.37228i | 0.265229i | ||||||||
\(81\) | 5.43070 | − | 7.17687i | 0.603411 | − | 0.797430i | ||||
\(82\) | 2.62772i | 0.290183i | ||||||||
\(83\) | 4.74456i | 0.520783i | 0.965503 | + | 0.260392i | \(0.0838517\pi\) | ||||
−0.965503 | + | 0.260392i | \(0.916148\pi\) | |||||||
\(84\) | 4.57025 | + | 0.335907i | 0.498655 | + | 0.0366505i | ||||
\(85\) | 5.98844i | 0.649537i | ||||||||
\(86\) | −8.37228 | −0.902806 | ||||||||
\(87\) | −12.7692 | + | 3.00000i | −1.36900 | + | 0.321634i | ||||
\(88\) | 5.74456 | 0.612372 | ||||||||
\(89\) | 10.0000i | 1.06000i | 0.847998 | + | 0.529999i | \(0.177808\pi\) | ||||
−0.847998 | + | 0.529999i | \(0.822192\pi\) | |||||||
\(90\) | −3.16915 | − | 6.37228i | −0.334058 | − | 0.671697i | ||||
\(91\) | −0.220225 | + | 9.53685i | −0.0230858 | + | 0.999733i | ||||
\(92\) | 6.78073i | 0.706940i | ||||||||
\(93\) | −2.31386 | − | 9.84868i | −0.239936 | − | 1.02126i | ||||
\(94\) | − | 4.62772i | − | 0.477313i | ||||||
\(95\) | − | 17.9653i | − | 1.84320i | ||||||
\(96\) | −0.396143 | − | 1.68614i | −0.0404312 | − | 0.172091i | ||||
\(97\) | 7.42554 | 0.753949 | 0.376975 | − | 0.926224i | \(-0.376964\pi\) | ||||
0.376975 | + | 0.926224i | \(0.376964\pi\) | |||||||
\(98\) | −5.74456 | − | 4.00000i | −0.580288 | − | 0.404061i | ||||
\(99\) | −15.4307 | + | 7.67420i | −1.55084 | + | 0.771286i | ||||
\(100\) | −0.627719 | −0.0627719 | ||||||||
\(101\) | −5.54601 | −0.551849 | −0.275924 | − | 0.961179i | \(-0.588984\pi\) | ||||
−0.275924 | + | 0.961179i | \(0.588984\pi\) | |||||||
\(102\) | −1.00000 | − | 4.25639i | −0.0990148 | − | 0.421445i | ||||
\(103\) | − | 1.62772i | − | 0.160384i | −0.996779 | − | 0.0801919i | \(-0.974447\pi\) | ||
0.996779 | − | 0.0801919i | \(-0.0255533\pi\) | |||||||
\(104\) | 3.46410 | − | 1.00000i | 0.339683 | − | 0.0980581i | ||||
\(105\) | −0.796867 | + | 10.8419i | −0.0777662 | + | 1.05806i | ||||
\(106\) | − | 3.16915i | − | 0.307815i | ||||||
\(107\) | − | 3.75906i | − | 0.363402i | −0.983354 | − | 0.181701i | \(-0.941840\pi\) | ||
0.983354 | − | 0.181701i | \(-0.0581602\pi\) | |||||||
\(108\) | 3.31662 | + | 4.00000i | 0.319142 | + | 0.384900i | ||||
\(109\) | − | 9.74749i | − | 0.933641i | −0.884352 | − | 0.466820i | \(-0.845399\pi\) | ||
0.884352 | − | 0.466820i | \(-0.154601\pi\) | |||||||
\(110\) | 13.6277i | 1.29935i | ||||||||
\(111\) | −8.26411 | + | 1.94158i | −0.784395 | + | 0.184286i | ||||
\(112\) | −0.792287 | + | 2.52434i | −0.0748641 | + | 0.238528i | ||||
\(113\) | − | 10.8896i | − | 1.02441i | −0.858863 | − | 0.512205i | \(-0.828829\pi\) | ||
0.858863 | − | 0.512205i | \(-0.171171\pi\) | |||||||
\(114\) | 3.00000 | + | 12.7692i | 0.280976 | + | 1.19594i | ||||
\(115\) | −16.0858 | −1.50001 | ||||||||
\(116\) | − | 7.57301i | − | 0.703137i | ||||||
\(117\) | −7.96916 | + | 7.31386i | −0.736749 | + | 0.676167i | ||||
\(118\) | 8.74456i | 0.805002i | ||||||||
\(119\) | −2.00000 | + | 6.37228i | −0.183340 | + | 0.584146i | ||||
\(120\) | 4.00000 | − | 0.939764i | 0.365148 | − | 0.0857883i | ||||
\(121\) | 22.0000 | 2.00000 | ||||||||
\(122\) | − | 3.74456i | − | 0.339017i | ||||||
\(123\) | 4.43070 | − | 1.04095i | 0.399503 | − | 0.0938596i | ||||
\(124\) | 5.84096 | 0.524534 | ||||||||
\(125\) | 10.3723i | 0.927725i | ||||||||
\(126\) | −1.24409 | − | 7.83915i | −0.110832 | − | 0.698367i | ||||
\(127\) | −4.62772 | −0.410644 | −0.205322 | − | 0.978695i | \(-0.565824\pi\) | ||||
−0.205322 | + | 0.978695i | \(0.565824\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 3.31662 | + | 14.1168i | 0.292013 | + | 1.24292i | ||||
\(130\) | 2.37228 | + | 8.21782i | 0.208063 | + | 0.720751i | ||||
\(131\) | −12.6217 | −1.10276 | −0.551381 | − | 0.834254i | \(-0.685899\pi\) | ||||
−0.551381 | + | 0.834254i | \(0.685899\pi\) | |||||||
\(132\) | −2.27567 | − | 9.68614i | −0.198072 | − | 0.843070i | ||||
\(133\) | 6.00000 | − | 19.1168i | 0.520266 | − | 1.65764i | ||||
\(134\) | − | 2.67181i | − | 0.230810i | ||||||
\(135\) | −9.48913 | + | 7.86797i | −0.816694 | + | 0.677167i | ||||
\(136\) | 2.52434 | 0.216460 | ||||||||
\(137\) | −0.883156 | −0.0754531 | −0.0377266 | − | 0.999288i | \(-0.512012\pi\) | ||||
−0.0377266 | + | 0.999288i | \(0.512012\pi\) | |||||||
\(138\) | 11.4333 | − | 2.68614i | 0.973264 | − | 0.228659i | ||||
\(139\) | − | 16.7446i | − | 1.42026i | −0.704073 | − | 0.710128i | \(-0.748637\pi\) | ||
0.704073 | − | 0.710128i | \(-0.251363\pi\) | |||||||
\(140\) | −5.98844 | − | 1.87953i | −0.506116 | − | 0.158849i | ||||
\(141\) | −7.80298 | + | 1.83324i | −0.657130 | + | 0.154387i | ||||
\(142\) | −2.00000 | −0.167836 | ||||||||
\(143\) | 19.8997 | − | 5.74456i | 1.66410 | − | 0.480384i | ||||
\(144\) | −2.68614 | + | 1.33591i | −0.223845 | + | 0.111326i | ||||
\(145\) | 17.9653 | 1.49194 | ||||||||
\(146\) | −3.61158 | −0.298896 | ||||||||
\(147\) | −4.46889 | + | 11.2707i | −0.368588 | + | 0.929593i | ||||
\(148\) | − | 4.90120i | − | 0.402876i | ||||||
\(149\) | −13.3723 | −1.09550 | −0.547750 | − | 0.836642i | \(-0.684515\pi\) | ||||
−0.547750 | + | 0.836642i | \(0.684515\pi\) | |||||||
\(150\) | 0.248667 | + | 1.05842i | 0.0203035 | + | 0.0864198i | ||||
\(151\) | 1.23472i | 0.100480i | 0.998737 | + | 0.0502399i | \(0.0159986\pi\) | ||||
−0.998737 | + | 0.0502399i | \(0.984001\pi\) | |||||||
\(152\) | −7.57301 | −0.614252 | ||||||||
\(153\) | −6.78073 | + | 3.37228i | −0.548189 | + | 0.272633i | ||||
\(154\) | −4.55134 | + | 14.5012i | −0.366758 | + | 1.16854i | ||||
\(155\) | 13.8564i | 1.11297i | ||||||||
\(156\) | −3.05842 | − | 5.44482i | −0.244870 | − | 0.435934i | ||||
\(157\) | − | 19.7446i | − | 1.57579i | −0.615811 | − | 0.787894i | \(-0.711172\pi\) | ||
0.615811 | − | 0.787894i | \(-0.288828\pi\) | |||||||
\(158\) | −9.37228 | −0.745619 | ||||||||
\(159\) | −5.34363 | + | 1.25544i | −0.423777 | + | 0.0995627i | ||||
\(160\) | 2.37228i | 0.187545i | ||||||||
\(161\) | −17.1168 | − | 5.37228i | −1.34900 | − | 0.423395i | ||||
\(162\) | 5.43070 | − | 7.17687i | 0.426676 | − | 0.563868i | ||||
\(163\) | − | 11.6819i | − | 0.914999i | −0.889210 | − | 0.457499i | \(-0.848745\pi\) | ||
0.889210 | − | 0.457499i | \(-0.151255\pi\) | |||||||
\(164\) | 2.62772i | 0.205190i | ||||||||
\(165\) | 22.9783 | − | 5.39853i | 1.78885 | − | 0.420275i | ||||
\(166\) | 4.74456i | 0.368249i | ||||||||
\(167\) | − | 18.3723i | − | 1.42169i | −0.703349 | − | 0.710845i | \(-0.748313\pi\) | ||
0.703349 | − | 0.710845i | \(-0.251687\pi\) | |||||||
\(168\) | 4.57025 | + | 0.335907i | 0.352602 | + | 0.0259158i | ||||
\(169\) | 11.0000 | − | 6.92820i | 0.846154 | − | 0.532939i | ||||
\(170\) | 5.98844i | 0.459292i | ||||||||
\(171\) | 20.3422 | − | 10.1168i | 1.55561 | − | 0.773654i | ||||
\(172\) | −8.37228 | −0.638380 | ||||||||
\(173\) | 23.9538 | 1.82117 | 0.910585 | − | 0.413321i | \(-0.135631\pi\) | ||||
0.910585 | + | 0.413321i | \(0.135631\pi\) | |||||||
\(174\) | −12.7692 | + | 3.00000i | −0.968028 | + | 0.227429i | ||||
\(175\) | 0.497333 | − | 1.58457i | 0.0375949 | − | 0.119783i | ||||
\(176\) | 5.74456 | 0.433013 | ||||||||
\(177\) | 14.7446 | − | 3.46410i | 1.10827 | − | 0.260378i | ||||
\(178\) | 10.0000i | 0.749532i | ||||||||
\(179\) | − | 6.33830i | − | 0.473746i | −0.971541 | − | 0.236873i | \(-0.923877\pi\) | ||
0.971541 | − | 0.236873i | \(-0.0761226\pi\) | |||||||
\(180\) | −3.16915 | − | 6.37228i | −0.236214 | − | 0.474962i | ||||
\(181\) | − | 14.6277i | − | 1.08727i | −0.839322 | − | 0.543635i | \(-0.817048\pi\) | ||
0.839322 | − | 0.543635i | \(-0.182952\pi\) | |||||||
\(182\) | −0.220225 | + | 9.53685i | −0.0163242 | + | 0.706918i | ||||
\(183\) | −6.31386 | + | 1.48338i | −0.466734 | + | 0.109655i | ||||
\(184\) | 6.78073i | 0.499882i | ||||||||
\(185\) | 11.6270 | 0.854836 | ||||||||
\(186\) | −2.31386 | − | 9.84868i | −0.169660 | − | 0.722141i | ||||
\(187\) | 14.5012 | 1.06043 | ||||||||
\(188\) | − | 4.62772i | − | 0.337511i | ||||||
\(189\) | −12.7251 | + | 5.20313i | −0.925613 | + | 0.378472i | ||||
\(190\) | − | 17.9653i | − | 1.30334i | ||||||
\(191\) | 19.5499i | 1.41458i | 0.706923 | + | 0.707290i | \(0.250083\pi\) | ||||
−0.706923 | + | 0.707290i | \(0.749917\pi\) | |||||||
\(192\) | −0.396143 | − | 1.68614i | −0.0285892 | − | 0.121687i | ||||
\(193\) | 20.7846i | 1.49611i | 0.663637 | + | 0.748054i | \(0.269012\pi\) | ||||
−0.663637 | + | 0.748054i | \(0.730988\pi\) | |||||||
\(194\) | 7.42554 | 0.533122 | ||||||||
\(195\) | 12.9166 | − | 7.25544i | 0.924980 | − | 0.519573i | ||||
\(196\) | −5.74456 | − | 4.00000i | −0.410326 | − | 0.285714i | ||||
\(197\) | 3.88316 | 0.276663 | 0.138332 | − | 0.990386i | \(-0.455826\pi\) | ||||
0.138332 | + | 0.990386i | \(0.455826\pi\) | |||||||
\(198\) | −15.4307 | + | 7.67420i | −1.09661 | + | 0.545382i | ||||
\(199\) | − | 5.11684i | − | 0.362723i | −0.983416 | − | 0.181362i | \(-0.941950\pi\) | ||
0.983416 | − | 0.181362i | \(-0.0580505\pi\) | |||||||
\(200\) | −0.627719 | −0.0443864 | ||||||||
\(201\) | −4.50506 | + | 1.05842i | −0.317762 | + | 0.0746553i | ||||
\(202\) | −5.54601 | −0.390216 | ||||||||
\(203\) | 19.1168 | + | 6.00000i | 1.34174 | + | 0.421117i | ||||
\(204\) | −1.00000 | − | 4.25639i | −0.0700140 | − | 0.298007i | ||||
\(205\) | −6.23369 | −0.435380 | ||||||||
\(206\) | − | 1.62772i | − | 0.113409i | ||||||
\(207\) | −9.05842 | − | 18.2140i | −0.629604 | − | 1.26596i | ||||
\(208\) | 3.46410 | − | 1.00000i | 0.240192 | − | 0.0693375i | ||||
\(209\) | −43.5036 | −3.00921 | ||||||||
\(210\) | −0.796867 | + | 10.8419i | −0.0549890 | + | 0.748163i | ||||
\(211\) | 11.6277 | 0.800485 | 0.400243 | − | 0.916409i | \(-0.368926\pi\) | ||||
0.400243 | + | 0.916409i | \(0.368926\pi\) | |||||||
\(212\) | − | 3.16915i | − | 0.217658i | ||||||
\(213\) | 0.792287 | + | 3.37228i | 0.0542866 | + | 0.231065i | ||||
\(214\) | − | 3.75906i | − | 0.256964i | ||||||
\(215\) | − | 19.8614i | − | 1.35454i | ||||||
\(216\) | 3.31662 | + | 4.00000i | 0.225668 | + | 0.272166i | ||||
\(217\) | −4.62772 | + | 14.7446i | −0.314150 | + | 1.00093i | ||||
\(218\) | − | 9.74749i | − | 0.660184i | ||||||
\(219\) | 1.43070 | + | 6.08963i | 0.0966780 | + | 0.411499i | ||||
\(220\) | 13.6277i | 0.918781i | ||||||||
\(221\) | 8.74456 | − | 2.52434i | 0.588223 | − | 0.169805i | ||||
\(222\) | −8.26411 | + | 1.94158i | −0.554651 | + | 0.130310i | ||||
\(223\) | 9.30506 | 0.623113 | 0.311557 | − | 0.950228i | \(-0.399150\pi\) | ||||
0.311557 | + | 0.950228i | \(0.399150\pi\) | |||||||
\(224\) | −0.792287 | + | 2.52434i | −0.0529369 | + | 0.168664i | ||||
\(225\) | 1.68614 | − | 0.838574i | 0.112409 | − | 0.0559049i | ||||
\(226\) | − | 10.8896i | − | 0.724368i | ||||||
\(227\) | 11.4891i | 0.762560i | 0.924460 | + | 0.381280i | \(0.124517\pi\) | ||||
−0.924460 | + | 0.381280i | \(0.875483\pi\) | |||||||
\(228\) | 3.00000 | + | 12.7692i | 0.198680 | + | 0.845659i | ||||
\(229\) | −1.58457 | −0.104712 | −0.0523558 | − | 0.998628i | \(-0.516673\pi\) | ||||
−0.0523558 | + | 0.998628i | \(0.516673\pi\) | |||||||
\(230\) | −16.0858 | −1.06067 | ||||||||
\(231\) | 26.2541 | + | 1.92964i | 1.72739 | + | 0.126961i | ||||
\(232\) | − | 7.57301i | − | 0.497193i | ||||||
\(233\) | 12.4742i | 0.817213i | 0.912711 | + | 0.408606i | \(0.133985\pi\) | ||||
−0.912711 | + | 0.408606i | \(0.866015\pi\) | |||||||
\(234\) | −7.96916 | + | 7.31386i | −0.520960 | + | 0.478122i | ||||
\(235\) | 10.9783 | 0.716142 | ||||||||
\(236\) | 8.74456i | 0.569223i | ||||||||
\(237\) | 3.71277 | + | 15.8030i | 0.241170 | + | 1.02651i | ||||
\(238\) | −2.00000 | + | 6.37228i | −0.129641 | + | 0.413054i | ||||
\(239\) | 18.0000 | 1.16432 | 0.582162 | − | 0.813073i | \(-0.302207\pi\) | ||||
0.582162 | + | 0.813073i | \(0.302207\pi\) | |||||||
\(240\) | 4.00000 | − | 0.939764i | 0.258199 | − | 0.0606615i | ||||
\(241\) | −23.3639 | −1.50500 | −0.752499 | − | 0.658593i | \(-0.771152\pi\) | ||||
−0.752499 | + | 0.658593i | \(0.771152\pi\) | |||||||
\(242\) | 22.0000 | 1.41421 | ||||||||
\(243\) | −14.2525 | − | 6.31386i | −0.914302 | − | 0.405034i | ||||
\(244\) | − | 3.74456i | − | 0.239721i | ||||||
\(245\) | 9.48913 | − | 13.6277i | 0.606238 | − | 0.870643i | ||||
\(246\) | 4.43070 | − | 1.04095i | 0.282491 | − | 0.0663688i | ||||
\(247\) | −26.2337 | + | 7.57301i | −1.66921 | + | 0.481859i | ||||
\(248\) | 5.84096 | 0.370901 | ||||||||
\(249\) | 8.00000 | − | 1.87953i | 0.506979 | − | 0.119110i | ||||
\(250\) | 10.3723i | 0.656001i | ||||||||
\(251\) | 0.147477 | 0.00930865 | 0.00465433 | − | 0.999989i | \(-0.498518\pi\) | ||||
0.00465433 | + | 0.999989i | \(0.498518\pi\) | |||||||
\(252\) | −1.24409 | − | 7.83915i | −0.0783701 | − | 0.493820i | ||||
\(253\) | 38.9523i | 2.44891i | ||||||||
\(254\) | −4.62772 | −0.290369 | ||||||||
\(255\) | 10.0974 | − | 2.37228i | 0.632321 | − | 0.148558i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 12.2718 | 0.765496 | 0.382748 | − | 0.923853i | \(-0.374978\pi\) | ||||
0.382748 | + | 0.923853i | \(0.374978\pi\) | |||||||
\(258\) | 3.31662 | + | 14.1168i | 0.206484 | + | 0.878876i | ||||
\(259\) | 12.3723 | + | 3.88316i | 0.768776 | + | 0.241288i | ||||
\(260\) | 2.37228 | + | 8.21782i | 0.147123 | + | 0.509648i | ||||
\(261\) | 10.1168 | + | 20.3422i | 0.626217 | + | 1.25915i | ||||
\(262\) | −12.6217 | −0.779771 | ||||||||
\(263\) | − | 20.4897i | − | 1.26345i | −0.775194 | − | 0.631723i | \(-0.782348\pi\) | ||
0.775194 | − | 0.631723i | \(-0.217652\pi\) | |||||||
\(264\) | −2.27567 | − | 9.68614i | −0.140058 | − | 0.596141i | ||||
\(265\) | 7.51811 | 0.461834 | ||||||||
\(266\) | 6.00000 | − | 19.1168i | 0.367884 | − | 1.17213i | ||||
\(267\) | 16.8614 | − | 3.96143i | 1.03190 | − | 0.242436i | ||||
\(268\) | − | 2.67181i | − | 0.163207i | ||||||
\(269\) | −4.55134 | −0.277500 | −0.138750 | − | 0.990327i | \(-0.544308\pi\) | ||||
−0.138750 | + | 0.990327i | \(0.544308\pi\) | |||||||
\(270\) | −9.48913 | + | 7.86797i | −0.577490 | + | 0.478829i | ||||
\(271\) | −14.6487 | −0.889845 | −0.444922 | − | 0.895569i | \(-0.646769\pi\) | ||||
−0.444922 | + | 0.895569i | \(0.646769\pi\) | |||||||
\(272\) | 2.52434 | 0.153060 | ||||||||
\(273\) | 16.1677 | − | 3.40663i | 0.978514 | − | 0.206179i | ||||
\(274\) | −0.883156 | −0.0533534 | ||||||||
\(275\) | −3.60597 | −0.217448 | ||||||||
\(276\) | 11.4333 | − | 2.68614i | 0.688201 | − | 0.161687i | ||||
\(277\) | −5.48913 | −0.329810 | −0.164905 | − | 0.986309i | \(-0.552732\pi\) | ||||
−0.164905 | + | 0.986309i | \(0.552732\pi\) | |||||||
\(278\) | − | 16.7446i | − | 1.00427i | ||||||
\(279\) | −15.6896 | + | 7.80298i | −0.939315 | + | 0.467152i | ||||
\(280\) | −5.98844 | − | 1.87953i | −0.357878 | − | 0.112323i | ||||
\(281\) | −14.0000 | −0.835170 | −0.417585 | − | 0.908638i | \(-0.637123\pi\) | ||||
−0.417585 | + | 0.908638i | \(0.637123\pi\) | |||||||
\(282\) | −7.80298 | + | 1.83324i | −0.464661 | + | 0.109168i | ||||
\(283\) | 5.37228i | 0.319349i | 0.987170 | + | 0.159674i | \(0.0510445\pi\) | ||||
−0.987170 | + | 0.159674i | \(0.948956\pi\) | |||||||
\(284\) | −2.00000 | −0.118678 | ||||||||
\(285\) | −30.2921 | + | 7.11684i | −1.79435 | + | 0.421565i | ||||
\(286\) | 19.8997 | − | 5.74456i | 1.17670 | − | 0.339683i | ||||
\(287\) | −6.63325 | − | 2.08191i | −0.391548 | − | 0.122891i | ||||
\(288\) | −2.68614 | + | 1.33591i | −0.158282 | + | 0.0787191i | ||||
\(289\) | −10.6277 | −0.625160 | ||||||||
\(290\) | 17.9653 | 1.05496 | ||||||||
\(291\) | −2.94158 | − | 12.5205i | −0.172438 | − | 0.733965i | ||||
\(292\) | −3.61158 | −0.211352 | ||||||||
\(293\) | − | 11.4891i | − | 0.671202i | −0.942004 | − | 0.335601i | \(-0.891061\pi\) | ||
0.942004 | − | 0.335601i | \(-0.108939\pi\) | |||||||
\(294\) | −4.46889 | + | 11.2707i | −0.260631 | + | 0.657321i | ||||
\(295\) | −20.7446 | −1.20780 | ||||||||
\(296\) | − | 4.90120i | − | 0.284876i | ||||||
\(297\) | 19.0526 | + | 22.9783i | 1.10554 | + | 1.33333i | ||||
\(298\) | −13.3723 | −0.774635 | ||||||||
\(299\) | 6.78073 | + | 23.4891i | 0.392140 | + | 1.35841i | ||||
\(300\) | 0.248667 | + | 1.05842i | 0.0143568 | + | 0.0611080i | ||||
\(301\) | 6.63325 | − | 21.1345i | 0.382334 | − | 1.21817i | ||||
\(302\) | 1.23472i | 0.0710500i | ||||||||
\(303\) | 2.19702 | + | 9.35135i | 0.126215 | + | 0.537221i | ||||
\(304\) | −7.57301 | −0.434342 | ||||||||
\(305\) | 8.88316 | 0.508648 | ||||||||
\(306\) | −6.78073 | + | 3.37228i | −0.387628 | + | 0.192780i | ||||
\(307\) | −14.5561 | −0.830762 | −0.415381 | − | 0.909648i | \(-0.636352\pi\) | ||||
−0.415381 | + | 0.909648i | \(0.636352\pi\) | |||||||
\(308\) | −4.55134 | + | 14.5012i | −0.259337 | + | 0.826284i | ||||
\(309\) | −2.74456 | + | 0.644810i | −0.156133 | + | 0.0366820i | ||||
\(310\) | 13.8564i | 0.786991i | ||||||||
\(311\) | −10.3923 | −0.589294 | −0.294647 | − | 0.955606i | \(-0.595202\pi\) | ||||
−0.294647 | + | 0.955606i | \(0.595202\pi\) | |||||||
\(312\) | −3.05842 | − | 5.44482i | −0.173149 | − | 0.308252i | ||||
\(313\) | − | 8.74456i | − | 0.494272i | −0.968981 | − | 0.247136i | \(-0.920511\pi\) | ||
0.968981 | − | 0.247136i | \(-0.0794894\pi\) | |||||||
\(314\) | − | 19.7446i | − | 1.11425i | ||||||
\(315\) | 18.5967 | − | 2.95132i | 1.04780 | − | 0.166288i | ||||
\(316\) | −9.37228 | −0.527232 | ||||||||
\(317\) | 24.8614 | 1.39636 | 0.698178 | − | 0.715924i | \(-0.253994\pi\) | ||||
0.698178 | + | 0.715924i | \(0.253994\pi\) | |||||||
\(318\) | −5.34363 | + | 1.25544i | −0.299656 | + | 0.0704014i | ||||
\(319\) | − | 43.5036i | − | 2.43574i | ||||||
\(320\) | 2.37228i | 0.132615i | ||||||||
\(321\) | −6.33830 | + | 1.48913i | −0.353769 | + | 0.0831149i | ||||
\(322\) | −17.1168 | − | 5.37228i | −0.953884 | − | 0.299386i | ||||
\(323\) | −19.1168 | −1.06369 | ||||||||
\(324\) | 5.43070 | − | 7.17687i | 0.301706 | − | 0.398715i | ||||
\(325\) | −2.17448 | + | 0.627719i | −0.120619 | + | 0.0348196i | ||||
\(326\) | − | 11.6819i | − | 0.647002i | ||||||
\(327\) | −16.4356 | + | 3.86141i | −0.908893 | + | 0.213536i | ||||
\(328\) | 2.62772i | 0.145091i | ||||||||
\(329\) | 11.6819 | + | 3.66648i | 0.644045 | + | 0.202140i | ||||
\(330\) | 22.9783 | − | 5.39853i | 1.26491 | − | 0.297179i | ||||
\(331\) | 32.6689i | 1.79565i | 0.440357 | + | 0.897823i | \(0.354852\pi\) | ||||
−0.440357 | + | 0.897823i | \(0.645148\pi\) | |||||||
\(332\) | 4.74456i | 0.260392i | ||||||||
\(333\) | 6.54755 | + | 13.1653i | 0.358803 | + | 0.721455i | ||||
\(334\) | − | 18.3723i | − | 1.00529i | ||||||
\(335\) | 6.33830 | 0.346298 | ||||||||
\(336\) | 4.57025 | + | 0.335907i | 0.249327 | + | 0.0183252i | ||||
\(337\) | 5.00000 | 0.272367 | 0.136184 | − | 0.990684i | \(-0.456516\pi\) | ||||
0.136184 | + | 0.990684i | \(0.456516\pi\) | |||||||
\(338\) | 11.0000 | − | 6.92820i | 0.598321 | − | 0.376845i | ||||
\(339\) | −18.3615 | + | 4.31386i | −0.997258 | + | 0.234297i | ||||
\(340\) | 5.98844i | 0.324769i | ||||||||
\(341\) | 33.5538 | 1.81704 | ||||||||
\(342\) | 20.3422 | − | 10.1168i | 1.09998 | − | 0.547056i | ||||
\(343\) | 14.6487 | − | 11.3321i | 0.790955 | − | 0.611874i | ||||
\(344\) | −8.37228 | −0.451403 | ||||||||
\(345\) | 6.37228 | + | 27.1229i | 0.343072 | + | 1.46025i | ||||
\(346\) | 23.9538 | 1.28776 | ||||||||
\(347\) | 25.8333i | 1.38680i | 0.720551 | + | 0.693402i | \(0.243889\pi\) | ||||
−0.720551 | + | 0.693402i | \(0.756111\pi\) | |||||||
\(348\) | −12.7692 | + | 3.00000i | −0.684499 | + | 0.160817i | ||||
\(349\) | 23.3639 | 1.25064 | 0.625319 | − | 0.780369i | \(-0.284969\pi\) | ||||
0.625319 | + | 0.780369i | \(0.284969\pi\) | |||||||
\(350\) | 0.497333 | − | 1.58457i | 0.0265836 | − | 0.0846990i | ||||
\(351\) | 15.4891 | + | 10.5398i | 0.826748 | + | 0.562572i | ||||
\(352\) | 5.74456 | 0.306186 | ||||||||
\(353\) | − | 6.11684i | − | 0.325567i | −0.986662 | − | 0.162783i | \(-0.947953\pi\) | ||
0.986662 | − | 0.162783i | \(-0.0520472\pi\) | |||||||
\(354\) | 14.7446 | − | 3.46410i | 0.783665 | − | 0.184115i | ||||
\(355\) | − | 4.74456i | − | 0.251815i | ||||||
\(356\) | 10.0000i | 0.529999i | ||||||||
\(357\) | 11.5368 | + | 0.847944i | 0.610595 | + | 0.0448779i | ||||
\(358\) | − | 6.33830i | − | 0.334989i | ||||||
\(359\) | −28.2337 | −1.49012 | −0.745059 | − | 0.666999i | \(-0.767578\pi\) | ||||
−0.745059 | + | 0.666999i | \(0.767578\pi\) | |||||||
\(360\) | −3.16915 | − | 6.37228i | −0.167029 | − | 0.335849i | ||||
\(361\) | 38.3505 | 2.01845 | ||||||||
\(362\) | − | 14.6277i | − | 0.768816i | ||||||
\(363\) | −8.71516 | − | 37.0951i | −0.457427 | − | 1.94699i | ||||
\(364\) | −0.220225 | + | 9.53685i | −0.0115429 | + | 0.499867i | ||||
\(365\) | − | 8.56768i | − | 0.448453i | ||||||
\(366\) | −6.31386 | + | 1.48338i | −0.330031 | + | 0.0775377i | ||||
\(367\) | 6.74456i | 0.352063i | 0.984385 | + | 0.176032i | \(0.0563261\pi\) | ||||
−0.984385 | + | 0.176032i | \(0.943674\pi\) | |||||||
\(368\) | 6.78073i | 0.353470i | ||||||||
\(369\) | −3.51039 | − | 7.05842i | −0.182744 | − | 0.367447i | ||||
\(370\) | 11.6270 | 0.604460 | ||||||||
\(371\) | 8.00000 | + | 2.51087i | 0.415339 | + | 0.130358i | ||||
\(372\) | −2.31386 | − | 9.84868i | −0.119968 | − | 0.510631i | ||||
\(373\) | 22.2337 | 1.15122 | 0.575608 | − | 0.817726i | \(-0.304765\pi\) | ||||
0.575608 | + | 0.817726i | \(0.304765\pi\) | |||||||
\(374\) | 14.5012 | 0.749840 | ||||||||
\(375\) | 17.4891 | − | 4.10891i | 0.903135 | − | 0.212183i | ||||
\(376\) | − | 4.62772i | − | 0.238656i | ||||||
\(377\) | −7.57301 | − | 26.2337i | −0.390030 | − | 1.35110i | ||||
\(378\) | −12.7251 | + | 5.20313i | −0.654507 | + | 0.267620i | ||||
\(379\) | 14.8511i | 0.762848i | 0.924400 | + | 0.381424i | \(0.124566\pi\) | ||||
−0.924400 | + | 0.381424i | \(0.875434\pi\) | |||||||
\(380\) | − | 17.9653i | − | 0.921601i | ||||||
\(381\) | 1.83324 | + | 7.80298i | 0.0939198 | + | 0.399759i | ||||
\(382\) | 19.5499i | 1.00026i | ||||||||
\(383\) | − | 26.4891i | − | 1.35353i | −0.736199 | − | 0.676766i | \(-0.763381\pi\) | ||
0.736199 | − | 0.676766i | \(-0.236619\pi\) | |||||||
\(384\) | −0.396143 | − | 1.68614i | −0.0202156 | − | 0.0860455i | ||||
\(385\) | −34.4010 | − | 10.7971i | −1.75324 | − | 0.550269i | ||||
\(386\) | 20.7846i | 1.05791i | ||||||||
\(387\) | 22.4891 | − | 11.1846i | 1.14319 | − | 0.568545i | ||||
\(388\) | 7.42554 | 0.376975 | ||||||||
\(389\) | 7.92287i | 0.401705i | 0.979621 | + | 0.200853i | \(0.0643713\pi\) | ||||
−0.979621 | + | 0.200853i | \(0.935629\pi\) | |||||||
\(390\) | 12.9166 | − | 7.25544i | 0.654060 | − | 0.367393i | ||||
\(391\) | 17.1168i | 0.865636i | ||||||||
\(392\) | −5.74456 | − | 4.00000i | −0.290144 | − | 0.202031i | ||||
\(393\) | 5.00000 | + | 21.2819i | 0.252217 | + | 1.07353i | ||||
\(394\) | 3.88316 | 0.195631 | ||||||||
\(395\) | − | 22.2337i | − | 1.11870i | ||||||
\(396\) | −15.4307 | + | 7.67420i | −0.775422 | + | 0.385643i | ||||
\(397\) | 6.63325 | 0.332913 | 0.166457 | − | 0.986049i | \(-0.446767\pi\) | ||||
0.166457 | + | 0.986049i | \(0.446767\pi\) | |||||||
\(398\) | − | 5.11684i | − | 0.256484i | ||||||
\(399\) | −34.6105 | − | 2.54383i | −1.73269 | − | 0.127351i | ||||
\(400\) | −0.627719 | −0.0313859 | ||||||||
\(401\) | −16.9783 | −0.847853 | −0.423927 | − | 0.905697i | \(-0.639349\pi\) | ||||
−0.423927 | + | 0.905697i | \(0.639349\pi\) | |||||||
\(402\) | −4.50506 | + | 1.05842i | −0.224692 | + | 0.0527893i | ||||
\(403\) | 20.2337 | − | 5.84096i | 1.00791 | − | 0.290959i | ||||
\(404\) | −5.54601 | −0.275924 | ||||||||
\(405\) | 17.0256 | + | 12.8832i | 0.846007 | + | 0.640169i | ||||
\(406\) | 19.1168 | + | 6.00000i | 0.948753 | + | 0.297775i | ||||
\(407\) | − | 28.1552i | − | 1.39560i | ||||||
\(408\) | −1.00000 | − | 4.25639i | −0.0495074 | − | 0.210723i | ||||
\(409\) | −6.57835 | −0.325278 | −0.162639 | − | 0.986686i | \(-0.552001\pi\) | ||||
−0.162639 | + | 0.986686i | \(0.552001\pi\) | |||||||
\(410\) | −6.23369 | −0.307860 | ||||||||
\(411\) | 0.349857 | + | 1.48913i | 0.0172571 | + | 0.0734531i | ||||
\(412\) | − | 1.62772i | − | 0.0801919i | ||||||
\(413\) | −22.0742 | − | 6.92820i | −1.08620 | − | 0.340915i | ||||
\(414\) | −9.05842 | − | 18.2140i | −0.445197 | − | 0.895169i | ||||
\(415\) | −11.2554 | −0.552508 | ||||||||
\(416\) | 3.46410 | − | 1.00000i | 0.169842 | − | 0.0490290i | ||||
\(417\) | −28.2337 | + | 6.63325i | −1.38261 | + | 0.324832i | ||||
\(418\) | −43.5036 | −2.12783 | ||||||||
\(419\) | 8.36530 | 0.408672 | 0.204336 | − | 0.978901i | \(-0.434497\pi\) | ||||
0.204336 | + | 0.978901i | \(0.434497\pi\) | |||||||
\(420\) | −0.796867 | + | 10.8419i | −0.0388831 | + | 0.529031i | ||||
\(421\) | 6.43087i | 0.313421i | 0.987645 | + | 0.156711i | \(0.0500890\pi\) | ||||
−0.987645 | + | 0.156711i | \(0.949911\pi\) | |||||||
\(422\) | 11.6277 | 0.566028 | ||||||||
\(423\) | 6.18220 | + | 12.4307i | 0.300589 | + | 0.604401i | ||||
\(424\) | − | 3.16915i | − | 0.153907i | ||||||
\(425\) | −1.58457 | −0.0768631 | ||||||||
\(426\) | 0.792287 | + | 3.37228i | 0.0383864 | + | 0.163388i | ||||
\(427\) | 9.45254 | + | 2.96677i | 0.457441 | + | 0.143572i | ||||
\(428\) | − | 3.75906i | − | 0.181701i | ||||||
\(429\) | −17.5693 | − | 31.2781i | −0.848254 | − | 1.51012i | ||||
\(430\) | − | 19.8614i | − | 0.957802i | ||||||
\(431\) | 6.23369 | 0.300266 | 0.150133 | − | 0.988666i | \(-0.452030\pi\) | ||||
0.150133 | + | 0.988666i | \(0.452030\pi\) | |||||||
\(432\) | 3.31662 | + | 4.00000i | 0.159571 | + | 0.192450i | ||||
\(433\) | 38.4674i | 1.84862i | 0.381638 | + | 0.924312i | \(0.375360\pi\) | ||||
−0.381638 | + | 0.924312i | \(0.624640\pi\) | |||||||
\(434\) | −4.62772 | + | 14.7446i | −0.222138 | + | 0.707762i | ||||
\(435\) | −7.11684 | − | 30.2921i | −0.341227 | − | 1.45239i | ||||
\(436\) | − | 9.74749i | − | 0.466820i | ||||||
\(437\) | − | 51.3505i | − | 2.45643i | ||||||
\(438\) | 1.43070 | + | 6.08963i | 0.0683616 | + | 0.290974i | ||||
\(439\) | 34.6060i | 1.65165i | 0.563924 | + | 0.825826i | \(0.309291\pi\) | ||||
−0.563924 | + | 0.825826i | \(0.690709\pi\) | |||||||
\(440\) | 13.6277i | 0.649676i | ||||||||
\(441\) | 20.7743 | + | 3.07036i | 0.989254 | + | 0.146208i | ||||
\(442\) | 8.74456 | − | 2.52434i | 0.415936 | − | 0.120071i | ||||
\(443\) | − | 9.80240i | − | 0.465726i | −0.972510 | − | 0.232863i | \(-0.925191\pi\) | ||
0.972510 | − | 0.232863i | \(-0.0748094\pi\) | |||||||
\(444\) | −8.26411 | + | 1.94158i | −0.392197 | + | 0.0921432i | ||||
\(445\) | −23.7228 | −1.12457 | ||||||||
\(446\) | 9.30506 | 0.440608 | ||||||||
\(447\) | 5.29734 | + | 22.5475i | 0.250556 | + | 1.06646i | ||||
\(448\) | −0.792287 | + | 2.52434i | −0.0374320 | + | 0.119264i | ||||
\(449\) | −3.11684 | −0.147093 | −0.0735465 | − | 0.997292i | \(-0.523432\pi\) | ||||
−0.0735465 | + | 0.997292i | \(0.523432\pi\) | |||||||
\(450\) | 1.68614 | − | 0.838574i | 0.0794854 | − | 0.0395308i | ||||
\(451\) | 15.0951i | 0.710800i | ||||||||
\(452\) | − | 10.8896i | − | 0.512205i | ||||||
\(453\) | 2.08191 | − | 0.489125i | 0.0978165 | − | 0.0229811i | ||||
\(454\) | 11.4891i | 0.539211i | ||||||||
\(455\) | −22.6241 | − | 0.522435i | −1.06063 | − | 0.0244921i | ||||
\(456\) | 3.00000 | + | 12.7692i | 0.140488 | + | 0.597971i | ||||
\(457\) | 2.87419i | 0.134449i | 0.997738 | + | 0.0672246i | \(0.0214144\pi\) | ||||
−0.997738 | + | 0.0672246i | \(0.978586\pi\) | |||||||
\(458\) | −1.58457 | −0.0740423 | ||||||||
\(459\) | 8.37228 | + | 10.0974i | 0.390785 | + | 0.471304i | ||||
\(460\) | −16.0858 | −0.750004 | ||||||||
\(461\) | 18.6060i | 0.866566i | 0.901258 | + | 0.433283i | \(0.142645\pi\) | ||||
−0.901258 | + | 0.433283i | \(0.857355\pi\) | |||||||
\(462\) | 26.2541 | + | 1.92964i | 1.22145 | + | 0.0897750i | ||||
\(463\) | − | 15.0911i | − | 0.701344i | −0.936498 | − | 0.350672i | \(-0.885953\pi\) | ||
0.936498 | − | 0.350672i | \(-0.114047\pi\) | |||||||
\(464\) | − | 7.57301i | − | 0.351568i | ||||||
\(465\) | 23.3639 | − | 5.48913i | 1.08347 | − | 0.254552i | ||||
\(466\) | 12.4742i | 0.577857i | ||||||||
\(467\) | 18.2603 | 0.844985 | 0.422492 | − | 0.906367i | \(-0.361155\pi\) | ||||
0.422492 | + | 0.906367i | \(0.361155\pi\) | |||||||
\(468\) | −7.96916 | + | 7.31386i | −0.368374 | + | 0.338083i | ||||
\(469\) | 6.74456 | + | 2.11684i | 0.311435 | + | 0.0977468i | ||||
\(470\) | 10.9783 | 0.506389 | ||||||||
\(471\) | −33.2921 | + | 7.82168i | −1.53402 | + | 0.360404i | ||||
\(472\) | 8.74456i | 0.402501i | ||||||||
\(473\) | −48.0951 | −2.21141 | ||||||||
\(474\) | 3.71277 | + | 15.8030i | 0.170533 | + | 0.725855i | ||||
\(475\) | 4.75372 | 0.218116 | ||||||||
\(476\) | −2.00000 | + | 6.37228i | −0.0916698 | + | 0.292073i | ||||
\(477\) | 4.23369 | + | 8.51278i | 0.193847 | + | 0.389773i | ||||
\(478\) | 18.0000 | 0.823301 | ||||||||
\(479\) | 34.3723i | 1.57051i | 0.619173 | + | 0.785255i | \(0.287468\pi\) | ||||
−0.619173 | + | 0.785255i | \(0.712532\pi\) | |||||||
\(480\) | 4.00000 | − | 0.939764i | 0.182574 | − | 0.0428942i | ||||
\(481\) | −4.90120 | − | 16.9783i | −0.223475 | − | 0.774142i | ||||
\(482\) | −23.3639 | −1.06419 | ||||||||
\(483\) | −2.27770 | + | 30.9896i | −0.103639 | + | 1.41008i | ||||
\(484\) | 22.0000 | 1.00000 | ||||||||
\(485\) | 17.6155i | 0.799877i | ||||||||
\(486\) | −14.2525 | − | 6.31386i | −0.646509 | − | 0.286402i | ||||
\(487\) | 10.9822i | 0.497652i | 0.968548 | + | 0.248826i | \(0.0800447\pi\) | ||||
−0.968548 | + | 0.248826i | \(0.919955\pi\) | |||||||
\(488\) | − | 3.74456i | − | 0.169508i | ||||||
\(489\) | −19.6974 | + | 4.62772i | −0.890746 | + | 0.209273i | ||||
\(490\) | 9.48913 | − | 13.6277i | 0.428675 | − | 0.615638i | ||||
\(491\) | − | 8.21782i | − | 0.370865i | −0.982657 | − | 0.185433i | \(-0.940631\pi\) | ||
0.982657 | − | 0.185433i | \(-0.0593686\pi\) | |||||||
\(492\) | 4.43070 | − | 1.04095i | 0.199752 | − | 0.0469298i | ||||
\(493\) | − | 19.1168i | − | 0.860979i | ||||||
\(494\) | −26.2337 | + | 7.57301i | −1.18031 | + | 0.340726i | ||||
\(495\) | −18.2054 | − | 36.6060i | −0.818270 | − | 1.64532i | ||||
\(496\) | 5.84096 | 0.262267 | ||||||||
\(497\) | 1.58457 | − | 5.04868i | 0.0710779 | − | 0.226464i | ||||
\(498\) | 8.00000 | − | 1.87953i | 0.358489 | − | 0.0842236i | ||||
\(499\) | 26.0357i | 1.16552i | 0.812646 | + | 0.582758i | \(0.198027\pi\) | ||||
−0.812646 | + | 0.582758i | \(0.801973\pi\) | |||||||
\(500\) | 10.3723i | 0.463863i | ||||||||
\(501\) | −30.9783 | + | 7.27806i | −1.38401 | + | 0.325160i | ||||
\(502\) | 0.147477 | 0.00658221 | ||||||||
\(503\) | −14.1514 | −0.630978 | −0.315489 | − | 0.948929i | \(-0.602169\pi\) | ||||
−0.315489 | + | 0.948929i | \(0.602169\pi\) | |||||||
\(504\) | −1.24409 | − | 7.83915i | −0.0554160 | − | 0.349183i | ||||
\(505\) | − | 13.1567i | − | 0.585465i | ||||||
\(506\) | 38.9523i | 1.73164i | ||||||||
\(507\) | −16.0395 | − | 15.8030i | −0.712339 | − | 0.701835i | ||||
\(508\) | −4.62772 | −0.205322 | ||||||||
\(509\) | 4.88316i | 0.216442i | 0.994127 | + | 0.108221i | \(0.0345154\pi\) | ||||
−0.994127 | + | 0.108221i | \(0.965485\pi\) | |||||||
\(510\) | 10.0974 | − | 2.37228i | 0.447118 | − | 0.105046i | ||||
\(511\) | 2.86141 | − | 9.11684i | 0.126581 | − | 0.403305i | ||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | −25.1168 | − | 30.2921i | −1.10894 | − | 1.33743i | ||||
\(514\) | 12.2718 | 0.541287 | ||||||||
\(515\) | 3.86141 | 0.170154 | ||||||||
\(516\) | 3.31662 | + | 14.1168i | 0.146006 | + | 0.621459i | ||||
\(517\) | − | 26.5842i | − | 1.16917i | ||||||
\(518\) | 12.3723 | + | 3.88316i | 0.543607 | + | 0.170616i | ||||
\(519\) | −9.48913 | − | 40.3894i | −0.416526 | − | 1.77290i | ||||
\(520\) | 2.37228 | + | 8.21782i | 0.104031 | + | 0.360375i | ||||
\(521\) | −35.9855 | −1.57656 | −0.788278 | − | 0.615320i | \(-0.789027\pi\) | ||||
−0.788278 | + | 0.615320i | \(0.789027\pi\) | |||||||
\(522\) | 10.1168 | + | 20.3422i | 0.442802 | + | 0.890353i | ||||
\(523\) | 14.3505i | 0.627505i | 0.949505 | + | 0.313752i | \(0.101586\pi\) | ||||
−0.949505 | + | 0.313752i | \(0.898414\pi\) | |||||||
\(524\) | −12.6217 | −0.551381 | ||||||||
\(525\) | −2.86883 | − | 0.210855i | −0.125206 | − | 0.00920248i | ||||
\(526\) | − | 20.4897i | − | 0.893391i | ||||||
\(527\) | 14.7446 | 0.642283 | ||||||||
\(528\) | −2.27567 | − | 9.68614i | −0.0990359 | − | 0.421535i | ||||
\(529\) | −22.9783 | −0.999054 | ||||||||
\(530\) | 7.51811 | 0.326566 | ||||||||
\(531\) | −11.6819 | − | 23.4891i | −0.506952 | − | 1.01934i | ||||
\(532\) | 6.00000 | − | 19.1168i | 0.260133 | − | 0.828820i | ||||
\(533\) | 2.62772 | + | 9.10268i | 0.113819 | + | 0.394281i | ||||
\(534\) | 16.8614 | − | 3.96143i | 0.729664 | − | 0.171428i | ||||
\(535\) | 8.91754 | 0.385539 | ||||||||
\(536\) | − | 2.67181i | − | 0.115405i | ||||||
\(537\) | −10.6873 | + | 2.51087i | −0.461189 | + | 0.108352i | ||||
\(538\) | −4.55134 | −0.196222 | ||||||||
\(539\) | −33.0000 | − | 22.9783i | −1.42141 | − | 0.989743i | ||||
\(540\) | −9.48913 | + | 7.86797i | −0.408347 | + | 0.338583i | ||||
\(541\) | − | 5.39853i | − | 0.232101i | −0.993243 | − | 0.116051i | \(-0.962977\pi\) | ||
0.993243 | − | 0.116051i | \(-0.0370234\pi\) | |||||||
\(542\) | −14.6487 | −0.629215 | ||||||||
\(543\) | −24.6644 | + | 5.79468i | −1.05845 | + | 0.248673i | ||||
\(544\) | 2.52434 | 0.108230 | ||||||||
\(545\) | 23.1238 | 0.990515 | ||||||||
\(546\) | 16.1677 | − | 3.40663i | 0.691914 | − | 0.145790i | ||||
\(547\) | 17.4891 | 0.747781 | 0.373890 | − | 0.927473i | \(-0.378024\pi\) | ||||
0.373890 | + | 0.927473i | \(0.378024\pi\) | |||||||
\(548\) | −0.883156 | −0.0377266 | ||||||||
\(549\) | 5.00239 | + | 10.0584i | 0.213497 | + | 0.429283i | ||||
\(550\) | −3.60597 | −0.153759 | ||||||||
\(551\) | 57.3505i | 2.44321i | ||||||||
\(552\) | 11.4333 | − | 2.68614i | 0.486632 | − | 0.114330i | ||||
\(553\) | 7.42554 | − | 23.6588i | 0.315766 | − | 1.00607i | ||||
\(554\) | −5.48913 | −0.233211 | ||||||||
\(555\) | −4.60597 | − | 19.6048i | −0.195513 | − | 0.832177i | ||||
\(556\) | − | 16.7446i | − | 0.710128i | ||||||
\(557\) | 24.6277 | 1.04351 | 0.521755 | − | 0.853095i | \(-0.325278\pi\) | ||||
0.521755 | + | 0.853095i | \(0.325278\pi\) | |||||||
\(558\) | −15.6896 | + | 7.80298i | −0.664196 | + | 0.330327i | ||||
\(559\) | −29.0024 | + | 8.37228i | −1.22667 | + | 0.354110i | ||||
\(560\) | −5.98844 | − | 1.87953i | −0.253058 | − | 0.0794245i | ||||
\(561\) | −5.74456 | − | 24.4511i | −0.242536 | − | 1.03233i | ||||
\(562\) | −14.0000 | −0.590554 | ||||||||
\(563\) | 35.7832 | 1.50808 | 0.754040 | − | 0.656828i | \(-0.228102\pi\) | ||||
0.754040 | + | 0.656828i | \(0.228102\pi\) | |||||||
\(564\) | −7.80298 | + | 1.83324i | −0.328565 | + | 0.0771934i | ||||
\(565\) | 25.8333 | 1.08681 | ||||||||
\(566\) | 5.37228i | 0.225814i | ||||||||
\(567\) | 13.8142 | + | 19.3951i | 0.580141 | + | 0.814516i | ||||
\(568\) | −2.00000 | −0.0839181 | ||||||||
\(569\) | − | 39.5971i | − | 1.66000i | −0.557765 | − | 0.829999i | \(-0.688341\pi\) | ||
0.557765 | − | 0.829999i | \(-0.311659\pi\) | |||||||
\(570\) | −30.2921 | + | 7.11684i | −1.26879 | + | 0.298092i | ||||
\(571\) | −20.0000 | −0.836974 | −0.418487 | − | 0.908223i | \(-0.637439\pi\) | ||||
−0.418487 | + | 0.908223i | \(0.637439\pi\) | |||||||
\(572\) | 19.8997 | − | 5.74456i | 0.832050 | − | 0.240192i | ||||
\(573\) | 32.9639 | − | 7.74456i | 1.37709 | − | 0.323534i | ||||
\(574\) | −6.63325 | − | 2.08191i | −0.276866 | − | 0.0868971i | ||||
\(575\) | − | 4.25639i | − | 0.177504i | ||||||
\(576\) | −2.68614 | + | 1.33591i | −0.111923 | + | 0.0556628i | ||||
\(577\) | −6.92820 | −0.288425 | −0.144212 | − | 0.989547i | \(-0.546065\pi\) | ||||
−0.144212 | + | 0.989547i | \(0.546065\pi\) | |||||||
\(578\) | −10.6277 | −0.442055 | ||||||||
\(579\) | 35.0458 | − | 8.23369i | 1.45645 | − | 0.342180i | ||||
\(580\) | 17.9653 | 0.745969 | ||||||||
\(581\) | −11.9769 | − | 3.75906i | −0.496885 | − | 0.155952i | ||||
\(582\) | −2.94158 | − | 12.5205i | −0.121932 | − | 0.518991i | ||||
\(583\) | − | 18.2054i | − | 0.753989i | ||||||
\(584\) | −3.61158 | −0.149448 | ||||||||
\(585\) | −17.3505 | − | 18.9051i | −0.717356 | − | 0.781629i | ||||
\(586\) | − | 11.4891i | − | 0.474611i | ||||||
\(587\) | − | 5.25544i | − | 0.216915i | −0.994101 | − | 0.108458i | \(-0.965409\pi\) | ||
0.994101 | − | 0.108458i | \(-0.0345912\pi\) | |||||||
\(588\) | −4.46889 | + | 11.2707i | −0.184294 | + | 0.464796i | ||||
\(589\) | −44.2337 | −1.82262 | ||||||||
\(590\) | −20.7446 | −0.854040 | ||||||||
\(591\) | −1.53829 | − | 6.54755i | −0.0632767 | − | 0.269330i | ||||
\(592\) | − | 4.90120i | − | 0.201438i | ||||||
\(593\) | 30.7446i | 1.26253i | 0.775568 | + | 0.631264i | \(0.217464\pi\) | ||||
−0.775568 | + | 0.631264i | \(0.782536\pi\) | |||||||
\(594\) | 19.0526 | + | 22.9783i | 0.781736 | + | 0.942809i | ||||
\(595\) | −15.1168 | − | 4.74456i | −0.619730 | − | 0.194508i | ||||
\(596\) | −13.3723 | −0.547750 | ||||||||
\(597\) | −8.62772 | + | 2.02700i | −0.353109 | + | 0.0829598i | ||||
\(598\) | 6.78073 | + | 23.4891i | 0.277285 | + | 0.960542i | ||||
\(599\) | 1.43710i | 0.0587182i | 0.999569 | + | 0.0293591i | \(0.00934663\pi\) | ||||
−0.999569 | + | 0.0293591i | \(0.990653\pi\) | |||||||
\(600\) | 0.248667 | + | 1.05842i | 0.0101518 | + | 0.0432099i | ||||
\(601\) | − | 26.0000i | − | 1.06056i | −0.847822 | − | 0.530281i | \(-0.822086\pi\) | ||
0.847822 | − | 0.530281i | \(-0.177914\pi\) | |||||||
\(602\) | 6.63325 | − | 21.1345i | 0.270351 | − | 0.861377i | ||||
\(603\) | 3.56930 | + | 7.17687i | 0.145353 | + | 0.292265i | ||||
\(604\) | 1.23472i | 0.0502399i | ||||||||
\(605\) | 52.1902i | 2.12183i | ||||||||
\(606\) | 2.19702 | + | 9.35135i | 0.0892476 | + | 0.379873i | ||||
\(607\) | 0.883156i | 0.0358462i | 0.999839 | + | 0.0179231i | \(0.00570541\pi\) | ||||
−0.999839 | + | 0.0179231i | \(0.994295\pi\) | |||||||
\(608\) | −7.57301 | −0.307126 | ||||||||
\(609\) | 2.54383 | − | 34.6105i | 0.103081 | − | 1.40249i | ||||
\(610\) | 8.88316 | 0.359668 | ||||||||
\(611\) | −4.62772 | − | 16.0309i | −0.187217 | − | 0.648540i | ||||
\(612\) | −6.78073 | + | 3.37228i | −0.274095 | + | 0.136316i | ||||
\(613\) | − | 3.02167i | − | 0.122044i | −0.998136 | − | 0.0610221i | \(-0.980564\pi\) | ||
0.998136 | − | 0.0610221i | \(-0.0194360\pi\) | |||||||
\(614\) | −14.5561 | −0.587437 | ||||||||
\(615\) | 2.46943 | + | 10.5109i | 0.0995772 | + | 0.423839i | ||||
\(616\) | −4.55134 | + | 14.5012i | −0.183379 | + | 0.584271i | ||||
\(617\) | 22.6060 | 0.910082 | 0.455041 | − | 0.890470i | \(-0.349625\pi\) | ||||
0.455041 | + | 0.890470i | \(0.349625\pi\) | |||||||
\(618\) | −2.74456 | + | 0.644810i | −0.110403 | + | 0.0259381i | ||||
\(619\) | −16.3807 | −0.658398 | −0.329199 | − | 0.944261i | \(-0.606779\pi\) | ||||
−0.329199 | + | 0.944261i | \(0.606779\pi\) | |||||||
\(620\) | 13.8564i | 0.556487i | ||||||||
\(621\) | −27.1229 | + | 22.4891i | −1.08840 | + | 0.902458i | ||||
\(622\) | −10.3923 | −0.416693 | ||||||||
\(623\) | −25.2434 | − | 7.92287i | −1.01135 | − | 0.317423i | ||||
\(624\) | −3.05842 | − | 5.44482i | −0.122435 | − | 0.217967i | ||||
\(625\) | −27.7446 | −1.10978 | ||||||||
\(626\) | − | 8.74456i | − | 0.349503i | ||||||
\(627\) | 17.2337 | + | 73.3533i | 0.688247 | + | 2.92945i | ||||
\(628\) | − | 19.7446i | − | 0.787894i | ||||||
\(629\) | − | 12.3723i | − | 0.493315i | ||||||
\(630\) | 18.5967 | − | 2.95132i | 0.740909 | − | 0.117584i | ||||
\(631\) | 24.3036i | 0.967512i | 0.875203 | + | 0.483756i | \(0.160728\pi\) | ||||
−0.875203 | + | 0.483756i | \(0.839272\pi\) | |||||||
\(632\) | −9.37228 | −0.372809 | ||||||||
\(633\) | −4.60625 | − | 19.6060i | −0.183082 | − | 0.779267i | ||||
\(634\) | 24.8614 | 0.987373 | ||||||||
\(635\) | − | 10.9783i | − | 0.435659i | ||||||
\(636\) | −5.34363 | + | 1.25544i | −0.211889 | + | 0.0497813i | ||||
\(637\) | −23.8997 | − | 8.11184i | −0.946943 | − | 0.321403i | ||||
\(638\) | − | 43.5036i | − | 1.72233i | ||||||
\(639\) | 5.37228 | − | 2.67181i | 0.212524 | − | 0.105695i | ||||
\(640\) | 2.37228i | 0.0937727i | ||||||||
\(641\) | 20.9870i | 0.828936i | 0.910064 | + | 0.414468i | \(0.136032\pi\) | ||||
−0.910064 | + | 0.414468i | \(0.863968\pi\) | |||||||
\(642\) | −6.33830 | + | 1.48913i | −0.250153 | + | 0.0587711i | ||||
\(643\) | −28.3576 | −1.11832 | −0.559158 | − | 0.829061i | \(-0.688875\pi\) | ||||
−0.559158 | + | 0.829061i | \(0.688875\pi\) | |||||||
\(644\) | −17.1168 | − | 5.37228i | −0.674498 | − | 0.211698i | ||||
\(645\) | −33.4891 | + | 7.86797i | −1.31863 | + | 0.309801i | ||||
\(646\) | −19.1168 | −0.752142 | ||||||||
\(647\) | −32.7615 | −1.28799 | −0.643994 | − | 0.765031i | \(-0.722724\pi\) | ||||
−0.643994 | + | 0.765031i | \(0.722724\pi\) | |||||||
\(648\) | 5.43070 | − | 7.17687i | 0.213338 | − | 0.281934i | ||||
\(649\) | 50.2337i | 1.97184i | ||||||||
\(650\) | −2.17448 | + | 0.627719i | −0.0852902 | + | 0.0246212i | ||||
\(651\) | 26.6946 | + | 1.96202i | 1.04625 | + | 0.0768977i | ||||
\(652\) | − | 11.6819i | − | 0.457499i | ||||||
\(653\) | − | 11.3321i | − | 0.443458i | −0.975108 | − | 0.221729i | \(-0.928830\pi\) | ||
0.975108 | − | 0.221729i | \(-0.0711701\pi\) | |||||||
\(654\) | −16.4356 | + | 3.86141i | −0.642685 | + | 0.150993i | ||||
\(655\) | − | 29.9422i | − | 1.16994i | ||||||
\(656\) | 2.62772i | 0.102595i | ||||||||
\(657\) | 9.70121 | − | 4.82473i | 0.378480 | − | 0.188231i | ||||
\(658\) | 11.6819 | + | 3.66648i | 0.455409 | + | 0.142934i | ||||
\(659\) | 48.3123i | 1.88198i | 0.338436 | + | 0.940990i | \(0.390102\pi\) | ||||
−0.338436 | + | 0.940990i | \(0.609898\pi\) | |||||||
\(660\) | 22.9783 | − | 5.39853i | 0.894427 | − | 0.210138i | ||||
\(661\) | −4.16381 | −0.161954 | −0.0809768 | − | 0.996716i | \(-0.525804\pi\) | ||||
−0.0809768 | + | 0.996716i | \(0.525804\pi\) | |||||||
\(662\) | 32.6689i | 1.26971i | ||||||||
\(663\) | −7.72049 | − | 13.7446i | −0.299839 | − | 0.533795i | ||||
\(664\) | 4.74456i | 0.184125i | ||||||||
\(665\) | 45.3505 | + | 14.2337i | 1.75862 | + | 0.551959i | ||||
\(666\) | 6.54755 | + | 13.1653i | 0.253712 | + | 0.510145i | ||||
\(667\) | 51.3505 | 1.98830 | ||||||||
\(668\) | − | 18.3723i | − | 0.710845i | ||||||
\(669\) | −3.68614 | − | 15.6896i | −0.142514 | − | 0.606597i | ||||
\(670\) | 6.33830 | 0.244870 | ||||||||
\(671\) | − | 21.5109i | − | 0.830418i | ||||||
\(672\) | 4.57025 | + | 0.335907i | 0.176301 | + | 0.0129579i | ||||
\(673\) | −10.7663 | −0.415011 | −0.207505 | − | 0.978234i | \(-0.566534\pi\) | ||||
−0.207505 | + | 0.978234i | \(0.566534\pi\) | |||||||
\(674\) | 5.00000 | 0.192593 | ||||||||
\(675\) | −2.08191 | − | 2.51087i | −0.0801327 | − | 0.0966436i | ||||
\(676\) | 11.0000 | − | 6.92820i | 0.423077 | − | 0.266469i | ||||
\(677\) | 29.2048 | 1.12243 | 0.561216 | − | 0.827669i | \(-0.310334\pi\) | ||||
0.561216 | + | 0.827669i | \(0.310334\pi\) | |||||||
\(678\) | −18.3615 | + | 4.31386i | −0.705168 | + | 0.165673i | ||||
\(679\) | −5.88316 | + | 18.7446i | −0.225775 | + | 0.719350i | ||||
\(680\) | 5.98844i | 0.229646i | ||||||||
\(681\) | 19.3723 | − | 4.55134i | 0.742347 | − | 0.174408i | ||||
\(682\) | 33.5538 | 1.28484 | ||||||||
\(683\) | −19.0000 | −0.727015 | −0.363507 | − | 0.931591i | \(-0.618421\pi\) | ||||
−0.363507 | + | 0.931591i | \(0.618421\pi\) | |||||||
\(684\) | 20.3422 | − | 10.1168i | 0.777803 | − | 0.386827i | ||||
\(685\) | − | 2.09509i | − | 0.0800494i | ||||||
\(686\) | 14.6487 | − | 11.3321i | 0.559290 | − | 0.432660i | ||||
\(687\) | 0.627719 | + | 2.67181i | 0.0239490 | + | 0.101936i | ||||
\(688\) | −8.37228 | −0.319190 | ||||||||
\(689\) | −3.16915 | − | 10.9783i | −0.120735 | − | 0.418238i | ||||
\(690\) | 6.37228 | + | 27.1229i | 0.242589 | + | 1.03255i | ||||
\(691\) | 31.1769 | 1.18603 | 0.593013 | − | 0.805193i | \(-0.297938\pi\) | ||||
0.593013 | + | 0.805193i | \(0.297938\pi\) | |||||||
\(692\) | 23.9538 | 0.910585 | ||||||||
\(693\) | −7.14674 | − | 45.0325i | −0.271482 | − | 1.71064i | ||||
\(694\) | 25.8333i | 0.980618i | ||||||||
\(695\) | 39.7228 | 1.50677 | ||||||||
\(696\) | −12.7692 | + | 3.00000i | −0.484014 | + | 0.113715i | ||||
\(697\) | 6.63325i | 0.251252i | ||||||||
\(698\) | 23.3639 | 0.884335 | ||||||||
\(699\) | 21.0333 | − | 4.94158i | 0.795552 | − | 0.186908i | ||||
\(700\) | 0.497333 | − | 1.58457i | 0.0187974 | − | 0.0598913i | ||||
\(701\) | 13.2665i | 0.501069i | 0.968108 | + | 0.250534i | \(0.0806063\pi\) | ||||
−0.968108 | + | 0.250534i | \(0.919394\pi\) | |||||||
\(702\) | 15.4891 | + | 10.5398i | 0.584599 | + | 0.397798i | ||||
\(703\) | 37.1168i | 1.39989i | ||||||||
\(704\) | 5.74456 | 0.216506 | ||||||||
\(705\) | −4.34896 | − | 18.5109i | −0.163791 | − | 0.697160i | ||||
\(706\) | − | 6.11684i | − | 0.230210i | ||||||
\(707\) | 4.39403 | − | 14.0000i | 0.165255 | − | 0.526524i | ||||
\(708\) | 14.7446 | − | 3.46410i | 0.554135 | − | 0.130189i | ||||
\(709\) | 30.3846i | 1.14112i | 0.821256 | + | 0.570559i | \(0.193274\pi\) | ||||
−0.821256 | + | 0.570559i | \(0.806726\pi\) | |||||||
\(710\) | − | 4.74456i | − | 0.178060i | ||||||
\(711\) | 25.1753 | − | 12.5205i | 0.944146 | − | 0.469555i | ||||
\(712\) | 10.0000i | 0.374766i | ||||||||
\(713\) | 39.6060i | 1.48326i | ||||||||
\(714\) | 11.5368 | + | 0.847944i | 0.431756 | + | 0.0317335i | ||||
\(715\) | 13.6277 | + | 47.2078i | 0.509648 | + | 1.76547i | ||||
\(716\) | − | 6.33830i | − | 0.236873i | ||||||
\(717\) | −7.13058 | − | 30.3505i | −0.266296 | − | 1.13346i | ||||
\(718\) | −28.2337 | −1.05367 | ||||||||
\(719\) | 23.3639 | 0.871325 | 0.435662 | − | 0.900110i | \(-0.356514\pi\) | ||||
0.435662 | + | 0.900110i | \(0.356514\pi\) | |||||||
\(720\) | −3.16915 | − | 6.37228i | −0.118107 | − | 0.237481i | ||||
\(721\) | 4.10891 | + | 1.28962i | 0.153024 | + | 0.0480280i | ||||
\(722\) | 38.3505 | 1.42726 | ||||||||
\(723\) | 9.25544 | + | 39.3947i | 0.344213 | + | 1.46511i | ||||
\(724\) | − | 14.6277i | − | 0.543635i | ||||||
\(725\) | 4.75372i | 0.176549i | ||||||||
\(726\) | −8.71516 | − | 37.0951i | −0.323450 | − | 1.37673i | ||||
\(727\) | 29.8614i | 1.10750i | 0.832684 | + | 0.553749i | \(0.186803\pi\) | ||||
−0.832684 | + | 0.553749i | \(0.813197\pi\) | |||||||
\(728\) | −0.220225 | + | 9.53685i | −0.00816208 | + | 0.353459i | ||||
\(729\) | −5.00000 | + | 26.5330i | −0.185185 | + | 0.982704i | ||||
\(730\) | − | 8.56768i | − | 0.317104i | ||||||
\(731\) | −21.1345 | −0.781686 | ||||||||
\(732\) | −6.31386 | + | 1.48338i | −0.233367 | + | 0.0548275i | ||||
\(733\) | −1.28962 | −0.0476332 | −0.0238166 | − | 0.999716i | \(-0.507582\pi\) | ||||
−0.0238166 | + | 0.999716i | \(0.507582\pi\) | |||||||
\(734\) | 6.74456i | 0.248946i | ||||||||
\(735\) | −26.7373 | − | 10.6015i | −0.986220 | − | 0.391041i | ||||
\(736\) | 6.78073i | 0.249941i | ||||||||
\(737\) | − | 15.3484i | − | 0.565366i | ||||||
\(738\) | −3.51039 | − | 7.05842i | −0.129219 | − | 0.259824i | ||||
\(739\) | − | 41.3841i | − | 1.52234i | −0.648554 | − | 0.761169i | \(-0.724626\pi\) | ||
0.648554 | − | 0.761169i | \(-0.275374\pi\) | |||||||
\(740\) | 11.6270 | 0.427418 | ||||||||
\(741\) | 23.1615 | + | 41.2337i | 0.850858 | + | 1.51476i | ||||
\(742\) | 8.00000 | + | 2.51087i | 0.293689 | + | 0.0921771i | ||||
\(743\) | −44.9783 | −1.65009 | −0.825046 | − | 0.565066i | \(-0.808851\pi\) | ||||
−0.825046 | + | 0.565066i | \(0.808851\pi\) | |||||||
\(744\) | −2.31386 | − | 9.84868i | −0.0848302 | − | 0.361070i | ||||
\(745\) | − | 31.7228i | − | 1.16223i | ||||||
\(746\) | 22.2337 | 0.814033 | ||||||||
\(747\) | −6.33830 | − | 12.7446i | −0.231906 | − | 0.466299i | ||||
\(748\) | 14.5012 | 0.530217 | ||||||||
\(749\) | 9.48913 | + | 2.97825i | 0.346725 | + | 0.108823i | ||||
\(750\) | 17.4891 | − | 4.10891i | 0.638613 | − | 0.150036i | ||||
\(751\) | −21.6060 | −0.788413 | −0.394207 | − | 0.919022i | \(-0.628981\pi\) | ||||
−0.394207 | + | 0.919022i | \(0.628981\pi\) | |||||||
\(752\) | − | 4.62772i | − | 0.168756i | ||||||
\(753\) | −0.0584220 | − | 0.248667i | −0.00212902 | − | 0.00906192i | ||||
\(754\) | −7.57301 | − | 26.2337i | −0.275793 | − | 0.955375i | ||||
\(755\) | −2.92910 | −0.106601 | ||||||||
\(756\) | −12.7251 | + | 5.20313i | −0.462806 | + | 0.189236i | ||||
\(757\) | −18.4674 | −0.671208 | −0.335604 | − | 0.942003i | \(-0.608940\pi\) | ||||
−0.335604 | + | 0.942003i | \(0.608940\pi\) | |||||||
\(758\) | 14.8511i | 0.539415i | ||||||||
\(759\) | 65.6791 | − | 15.4307i | 2.38400 | − | 0.560099i | ||||
\(760\) | − | 17.9653i | − | 0.651671i | ||||||
\(761\) | − | 30.8614i | − | 1.11873i | −0.828923 | − | 0.559363i | \(-0.811046\pi\) | ||
0.828923 | − | 0.559363i | \(-0.188954\pi\) | |||||||
\(762\) | 1.83324 | + | 7.80298i | 0.0664113 | + | 0.282672i | ||||
\(763\) | 24.6060 | + | 7.72281i | 0.890796 | + | 0.279585i | ||||
\(764\) | 19.5499i | 0.707290i | ||||||||
\(765\) | −8.00000 | − | 16.0858i | −0.289241 | − | 0.581583i | ||||
\(766\) | − | 26.4891i | − | 0.957091i | ||||||
\(767\) | 8.74456 | + | 30.2921i | 0.315748 | + | 1.09378i | ||||
\(768\) | −0.396143 | − | 1.68614i | −0.0142946 | − | 0.0608434i | ||||
\(769\) | −14.2988 | −0.515629 | −0.257815 | − | 0.966194i | \(-0.583002\pi\) | ||||
−0.257815 | + | 0.966194i | \(0.583002\pi\) | |||||||
\(770\) | −34.4010 | − | 10.7971i | −1.23972 | − | 0.389099i | ||||
\(771\) | −4.86141 | − | 20.6920i | −0.175079 | − | 0.745205i | ||||
\(772\) | 20.7846i | 0.748054i | ||||||||
\(773\) | 9.86141i | 0.354690i | 0.984149 | + | 0.177345i | \(0.0567509\pi\) | ||||
−0.984149 | + | 0.177345i | \(0.943249\pi\) | |||||||
\(774\) | 22.4891 | − | 11.1846i | 0.808355 | − | 0.402022i | ||||
\(775\) | −3.66648 | −0.131704 | ||||||||
\(776\) | 7.42554 | 0.266561 | ||||||||
\(777\) | 1.64635 | − | 22.3997i | 0.0590624 | − | 0.803585i | ||||
\(778\) | 7.92287i | 0.284049i | ||||||||
\(779\) | − | 19.8997i | − | 0.712982i | ||||||
\(780\) | 12.9166 | − | 7.25544i | 0.462490 | − | 0.259786i | ||||
\(781\) | −11.4891 | −0.411113 | ||||||||
\(782\) | 17.1168i | 0.612097i | ||||||||
\(783\) | 30.2921 | − | 25.1168i | 1.08255 | − | 0.897603i | ||||
\(784\) | −5.74456 | − | 4.00000i | −0.205163 | − | 0.142857i | ||||
\(785\) | 46.8397 | 1.67178 | ||||||||
\(786\) | 5.00000 | + | 21.2819i | 0.178344 | + | 0.759102i | ||||
\(787\) | 13.5065 | 0.481457 | 0.240728 | − | 0.970593i | \(-0.422614\pi\) | ||||
0.240728 | + | 0.970593i | \(0.422614\pi\) | |||||||
\(788\) | 3.88316 | 0.138332 | ||||||||
\(789\) | −34.5484 | + | 8.11684i | −1.22996 | + | 0.288967i | ||||
\(790\) | − | 22.2337i | − | 0.791039i | ||||||
\(791\) | 27.4891 | + | 8.62772i | 0.977401 | + | 0.306766i | ||||
\(792\) | −15.4307 | + | 7.67420i | −0.548306 | + | 0.272691i | ||||
\(793\) | −3.74456 | − | 12.9715i | −0.132973 | − | 0.460633i | ||||
\(794\) | 6.63325 | 0.235405 | ||||||||
\(795\) | −2.97825 | − | 12.6766i | −0.105628 | − | 0.449592i | ||||
\(796\) | − | 5.11684i | − | 0.181362i | ||||||
\(797\) | −9.01011 | −0.319154 | −0.159577 | − | 0.987185i | \(-0.551013\pi\) | ||||
−0.159577 | + | 0.987185i | \(0.551013\pi\) | |||||||
\(798\) | −34.6105 | − | 2.54383i | −1.22520 | − | 0.0900506i | ||||
\(799\) | − | 11.6819i | − | 0.413277i | ||||||
\(800\) | −0.627719 | −0.0221932 | ||||||||
\(801\) | −13.3591 | − | 26.8614i | −0.472020 | − | 0.949101i | ||||
\(802\) | −16.9783 | −0.599523 | ||||||||
\(803\) | −20.7469 | −0.732144 | ||||||||
\(804\) | −4.50506 | + | 1.05842i | −0.158881 | + | 0.0373277i | ||||
\(805\) | 12.7446 | − | 40.6060i | 0.449187 | − | 1.43117i | ||||
\(806\) | 20.2337 | − | 5.84096i | 0.712701 | − | 0.205739i | ||||
\(807\) | 1.80298 | + | 7.67420i | 0.0634681 | + | 0.270145i | ||||
\(808\) | −5.54601 | −0.195108 | ||||||||
\(809\) | − | 5.04868i | − | 0.177502i | −0.996054 | − | 0.0887510i | \(-0.971712\pi\) | ||
0.996054 | − | 0.0887510i | \(-0.0282875\pi\) | |||||||
\(810\) | 17.0256 | + | 12.8832i | 0.598217 | + | 0.452668i | ||||
\(811\) | −12.9166 | −0.453565 | −0.226782 | − | 0.973945i | \(-0.572821\pi\) | ||||
−0.226782 | + | 0.973945i | \(0.572821\pi\) | |||||||
\(812\) | 19.1168 | + | 6.00000i | 0.670870 | + | 0.210559i | ||||
\(813\) | 5.80298 | + | 24.6998i | 0.203520 | + | 0.866258i | ||||
\(814\) | − | 28.1552i | − | 0.986841i | ||||||
\(815\) | 27.7128 | 0.970737 | ||||||||
\(816\) | −1.00000 | − | 4.25639i | −0.0350070 | − | 0.149003i | ||||
\(817\) | 63.4034 | 2.21820 | ||||||||
\(818\) | −6.57835 | −0.230006 | ||||||||
\(819\) | −12.1488 | − | 25.9115i | −0.424513 | − | 0.905422i | ||||
\(820\) | −6.23369 | −0.217690 | ||||||||
\(821\) | 13.7228 | 0.478929 | 0.239465 | − | 0.970905i | \(-0.423028\pi\) | ||||
0.239465 | + | 0.970905i | \(0.423028\pi\) | |||||||
\(822\) | 0.349857 | + | 1.48913i | 0.0122026 | + | 0.0519392i | ||||
\(823\) | 7.13859 | 0.248836 | 0.124418 | − | 0.992230i | \(-0.460294\pi\) | ||||
0.124418 | + | 0.992230i | \(0.460294\pi\) | |||||||
\(824\) | − | 1.62772i | − | 0.0567043i | ||||||
\(825\) | 1.42848 | + | 6.08017i | 0.0497333 | + | 0.211684i | ||||
\(826\) | −22.0742 | − | 6.92820i | −0.768061 | − | 0.241063i | ||||
\(827\) | 4.88316 | 0.169804 | 0.0849020 | − | 0.996389i | \(-0.472942\pi\) | ||||
0.0849020 | + | 0.996389i | \(0.472942\pi\) | |||||||
\(828\) | −9.05842 | − | 18.2140i | −0.314802 | − | 0.632980i | ||||
\(829\) | 6.60597i | 0.229435i | 0.993398 | + | 0.114717i | \(0.0365963\pi\) | ||||
−0.993398 | + | 0.114717i | \(0.963404\pi\) | |||||||
\(830\) | −11.2554 | −0.390682 | ||||||||
\(831\) | 2.17448 | + | 9.25544i | 0.0754319 | + | 0.321068i | ||||
\(832\) | 3.46410 | − | 1.00000i | 0.120096 | − | 0.0346688i | ||||
\(833\) | −14.5012 | − | 10.0974i | −0.502437 | − | 0.349852i | ||||
\(834\) | −28.2337 | + | 6.63325i | −0.977653 | + | 0.229691i | ||||
\(835\) | 43.5842 | 1.50829 | ||||||||
\(836\) | −43.5036 | −1.50461 | ||||||||
\(837\) | 19.3723 | + | 23.3639i | 0.669604 | + | 0.807573i | ||||
\(838\) | 8.36530 | 0.288975 | ||||||||
\(839\) | 11.3723i | 0.392615i | 0.980542 | + | 0.196307i | \(0.0628950\pi\) | ||||
−0.980542 | + | 0.196307i | \(0.937105\pi\) | |||||||
\(840\) | −0.796867 | + | 10.8419i | −0.0274945 | + | 0.374082i | ||||
\(841\) | −28.3505 | −0.977605 | ||||||||
\(842\) | 6.43087i | 0.221622i | ||||||||
\(843\) | 5.54601 | + | 23.6060i | 0.191015 | + | 0.813033i | ||||
\(844\) | 11.6277 | 0.400243 | ||||||||
\(845\) | 16.4356 | + | 26.0951i | 0.565403 | + | 0.897699i | ||||
\(846\) | 6.18220 | + | 12.4307i | 0.212549 | + | 0.427376i | ||||
\(847\) | −17.4303 | + | 55.5354i | −0.598913 | + | 1.90822i | ||||
\(848\) | − | 3.16915i | − | 0.108829i | ||||||
\(849\) | 9.05842 | − | 2.12819i | 0.310884 | − | 0.0730394i | ||||
\(850\) | −1.58457 | −0.0543504 | ||||||||
\(851\) | 33.2337 | 1.13924 | ||||||||
\(852\) | 0.792287 | + | 3.37228i | 0.0271433 | + | 0.115532i | ||||
\(853\) | −36.8155 | −1.26054 | −0.630269 | − | 0.776377i | \(-0.717056\pi\) | ||||
−0.630269 | + | 0.776377i | \(0.717056\pi\) | |||||||
\(854\) | 9.45254 | + | 2.96677i | 0.323459 | + | 0.101521i | ||||
\(855\) | 24.0000 | + | 48.2574i | 0.820783 | + | 1.65037i | ||||
\(856\) | − | 3.75906i | − | 0.128482i | ||||||
\(857\) | 35.0458 | 1.19714 | 0.598570 | − | 0.801070i | \(-0.295736\pi\) | ||||
0.598570 | + | 0.801070i | \(0.295736\pi\) | |||||||
\(858\) | −17.5693 | − | 31.2781i | −0.599806 | − | 1.06782i | ||||
\(859\) | − | 53.0951i | − | 1.81158i | −0.423726 | − | 0.905791i | \(-0.639278\pi\) | ||
0.423726 | − | 0.905791i | \(-0.360722\pi\) | |||||||
\(860\) | − | 19.8614i | − | 0.677268i | ||||||
\(861\) | −0.882670 | + | 12.0093i | −0.0300813 | + | 0.409277i | ||||
\(862\) | 6.23369 | 0.212320 | ||||||||
\(863\) | −11.4891 | −0.391094 | −0.195547 | − | 0.980694i | \(-0.562648\pi\) | ||||
−0.195547 | + | 0.980694i | \(0.562648\pi\) | |||||||
\(864\) | 3.31662 | + | 4.00000i | 0.112834 | + | 0.136083i | ||||
\(865\) | 56.8251i | 1.93211i | ||||||||
\(866\) | 38.4674i | 1.30717i | ||||||||
\(867\) | 4.21010 | + | 17.9198i | 0.142983 | + | 0.608589i | ||||
\(868\) | −4.62772 | + | 14.7446i | −0.157075 | + | 0.500463i | ||||
\(869\) | −53.8397 | −1.82639 | ||||||||
\(870\) | −7.11684 | − | 30.2921i | −0.241284 | − | 1.02700i | ||||
\(871\) | −2.67181 | − | 9.25544i | −0.0905310 | − | 0.313609i | ||||
\(872\) | − | 9.74749i | − | 0.330092i | ||||||
\(873\) | −19.9460 | + | 9.91983i | −0.675071 | + | 0.335735i | ||||
\(874\) | − | 51.3505i | − | 1.73696i | ||||||
\(875\) | −26.1831 | − | 8.21782i | −0.885152 | − | 0.277813i | ||||
\(876\) | 1.43070 | + | 6.08963i | 0.0483390 | + | 0.205750i | ||||
\(877\) | − | 36.7229i | − | 1.24005i | −0.784584 | − | 0.620023i | \(-0.787123\pi\) | ||
0.784584 | − | 0.620023i | \(-0.212877\pi\) | |||||||
\(878\) | 34.6060i | 1.16789i | ||||||||
\(879\) | −19.3723 | + | 4.55134i | −0.653411 | + | 0.153513i | ||||
\(880\) | 13.6277i | 0.459390i | ||||||||
\(881\) | 7.27806 | 0.245204 | 0.122602 | − | 0.992456i | \(-0.460876\pi\) | ||||
0.122602 | + | 0.992456i | \(0.460876\pi\) | |||||||
\(882\) | 20.7743 | + | 3.07036i | 0.699508 | + | 0.103384i | ||||
\(883\) | 54.0951 | 1.82044 | 0.910222 | − | 0.414120i | \(-0.135911\pi\) | ||||
0.910222 | + | 0.414120i | \(0.135911\pi\) | |||||||
\(884\) | 8.74456 | − | 2.52434i | 0.294111 | − | 0.0849027i | ||||
\(885\) | 8.21782 | + | 34.9783i | 0.276239 | + | 1.17578i | ||||
\(886\) | − | 9.80240i | − | 0.329318i | ||||||
\(887\) | −24.3585 | −0.817879 | −0.408939 | − | 0.912562i | \(-0.634101\pi\) | ||||
−0.408939 | + | 0.912562i | \(0.634101\pi\) | |||||||
\(888\) | −8.26411 | + | 1.94158i | −0.277325 | + | 0.0651551i | ||||
\(889\) | 3.66648 | − | 11.6819i | 0.122970 | − | 0.391799i | ||||
\(890\) | −23.7228 | −0.795191 | ||||||||
\(891\) | 31.1970 | − | 41.2280i | 1.04514 | − | 1.38119i | ||||
\(892\) | 9.30506 | 0.311557 | ||||||||
\(893\) | 35.0458i | 1.17276i | ||||||||
\(894\) | 5.29734 | + | 22.5475i | 0.177170 | + | 0.754103i | ||||
\(895\) | 15.0362 | 0.502605 | ||||||||
\(896\) | −0.792287 | + | 2.52434i | −0.0264685 | + | 0.0843322i | ||||
\(897\) | 36.9198 | − | 20.7383i | 1.23272 | − | 0.692432i | ||||
\(898\) | −3.11684 | −0.104010 | ||||||||
\(899\) | − | 44.2337i | − | 1.47528i | ||||||
\(900\) | 1.68614 | − | 0.838574i | 0.0562047 | − | 0.0279525i | ||||
\(901\) | − | 8.00000i | − | 0.266519i | ||||||
\(902\) | 15.0951i | 0.502612i | ||||||||
\(903\) | −38.2634 | − | 2.81231i | −1.27333 | − | 0.0935878i | ||||
\(904\) | − | 10.8896i | − | 0.362184i | ||||||
\(905\) | 34.7011 | 1.15350 | ||||||||
\(906\) | 2.08191 | − | 0.489125i | 0.0691667 | − | 0.0162501i | ||||
\(907\) | 20.0000 | 0.664089 | 0.332045 | − | 0.943264i | \(-0.392262\pi\) | ||||
0.332045 | + | 0.943264i | \(0.392262\pi\) | |||||||
\(908\) | 11.4891i | 0.381280i | ||||||||
\(909\) | 14.8974 | − | 7.40895i | 0.494114 | − | 0.245739i | ||||
\(910\) | −22.6241 | − | 0.522435i | −0.749981 | − | 0.0173186i | ||||
\(911\) | 18.9600i | 0.628172i | 0.949394 | + | 0.314086i | \(0.101698\pi\) | ||||
−0.949394 | + | 0.314086i | \(0.898302\pi\) | |||||||
\(912\) | 3.00000 | + | 12.7692i | 0.0993399 | + | 0.422829i | ||||
\(913\) | 27.2554i | 0.902023i | ||||||||
\(914\) | 2.87419i | 0.0950699i | ||||||||
\(915\) | −3.51900 | − | 14.9783i | −0.116335 | − | 0.495166i | ||||
\(916\) | −1.58457 | −0.0523558 | ||||||||
\(917\) | 10.0000 | − | 31.8614i | 0.330229 | − | 1.05216i | ||||
\(918\) | 8.37228 | + | 10.0974i | 0.276326 | + | 0.333262i | ||||
\(919\) | 40.5842 | 1.33875 | 0.669375 | − | 0.742925i | \(-0.266562\pi\) | ||||
0.669375 | + | 0.742925i | \(0.266562\pi\) | |||||||
\(920\) | −16.0858 | −0.530333 | ||||||||
\(921\) | 5.76631 | + | 24.5437i | 0.190006 | + | 0.808741i | ||||
\(922\) | 18.6060i | 0.612755i | ||||||||
\(923\) | −6.92820 | + | 2.00000i | −0.228045 | + | 0.0658308i | ||||
\(924\) | 26.2541 | + | 1.92964i | 0.863696 | + | 0.0634805i | ||||
\(925\) | 3.07657i | 0.101157i | ||||||||
\(926\) | − | 15.0911i | − | 0.495925i | ||||||
\(927\) | 2.17448 | + | 4.37228i | 0.0714193 | + | 0.143605i | ||||
\(928\) | − | 7.57301i | − | 0.248596i | ||||||
\(929\) | − | 15.6060i | − | 0.512015i | −0.966675 | − | 0.256008i | \(-0.917593\pi\) | ||
0.966675 | − | 0.256008i | \(-0.0824072\pi\) | |||||||
\(930\) | 23.3639 | − | 5.48913i | 0.766131 | − | 0.179996i | ||||
\(931\) | 43.5036 | + | 30.2921i | 1.42577 | + | 0.992782i | ||||
\(932\) | 12.4742i | 0.408606i | ||||||||
\(933\) | 4.11684 | + | 17.5229i | 0.134779 | + | 0.573674i | ||||
\(934\) | 18.2603 | 0.597494 | ||||||||
\(935\) | 34.4010i | 1.12503i | ||||||||
\(936\) | −7.96916 | + | 7.31386i | −0.260480 | + | 0.239061i | ||||
\(937\) | − | 20.5109i | − | 0.670061i | −0.942207 | − | 0.335031i | \(-0.891253\pi\) | ||
0.942207 | − | 0.335031i | \(-0.108747\pi\) | |||||||
\(938\) | 6.74456 | + | 2.11684i | 0.220218 | + | 0.0691174i | ||||
\(939\) | −14.7446 | + | 3.46410i | −0.481171 | + | 0.113047i | ||||
\(940\) | 10.9783 | 0.358071 | ||||||||
\(941\) | 28.5109i | 0.929428i | 0.885461 | + | 0.464714i | \(0.153843\pi\) | ||||
−0.885461 | + | 0.464714i | \(0.846157\pi\) | |||||||
\(942\) | −33.2921 | + | 7.82168i | −1.08472 | + | 0.254844i | ||||
\(943\) | −17.8178 | −0.580229 | ||||||||
\(944\) | 8.74456i | 0.284611i | ||||||||
\(945\) | −12.3433 | − | 30.1874i | −0.401527 | − | 0.981998i | ||||
\(946\) | −48.0951 | −1.56371 | ||||||||
\(947\) | −4.88316 | −0.158681 | −0.0793406 | − | 0.996848i | \(-0.525281\pi\) | ||||
−0.0793406 | + | 0.996848i | \(0.525281\pi\) | |||||||
\(948\) | 3.71277 | + | 15.8030i | 0.120585 | + | 0.513257i | ||||
\(949\) | −12.5109 | + | 3.61158i | −0.406120 | + | 0.117237i | ||||
\(950\) | 4.75372 | 0.154231 | ||||||||
\(951\) | −9.84868 | − | 41.9198i | −0.319365 | − | 1.35934i | ||||
\(952\) | −2.00000 | + | 6.37228i | −0.0648204 | + | 0.206527i | ||||
\(953\) | 52.9562i | 1.71542i | 0.514134 | + | 0.857710i | \(0.328113\pi\) | ||||
−0.514134 | + | 0.857710i | \(0.671887\pi\) | |||||||
\(954\) | 4.23369 | + | 8.51278i | 0.137071 | + | 0.275611i | ||||
\(955\) | −46.3778 | −1.50075 | ||||||||
\(956\) | 18.0000 | 0.582162 | ||||||||
\(957\) | −73.3533 | + | 17.2337i | −2.37117 | + | 0.557086i | ||||
\(958\) | 34.3723i | 1.11052i | ||||||||
\(959\) | 0.699713 | − | 2.22938i | 0.0225949 | − | 0.0719906i | ||||
\(960\) | 4.00000 | − | 0.939764i | 0.129099 | − | 0.0303307i | ||||
\(961\) | 3.11684 | 0.100543 | ||||||||
\(962\) | −4.90120 | − | 16.9783i | −0.158021 | − | 0.547401i | ||||
\(963\) | 5.02175 | + | 10.0974i | 0.161824 | + | 0.325383i | ||||
\(964\) | −23.3639 | −0.752499 | ||||||||
\(965\) | −49.3069 | −1.58725 | ||||||||
\(966\) | −2.27770 | + | 30.9896i | −0.0732837 | + | 0.997074i | ||||
\(967\) | − | 20.5446i | − | 0.660668i | −0.943864 | − | 0.330334i | \(-0.892839\pi\) | ||
0.943864 | − | 0.330334i | \(-0.107161\pi\) | |||||||
\(968\) | 22.0000 | 0.707107 | ||||||||
\(969\) | 7.57301 | + | 32.2337i | 0.243280 | + | 1.03550i | ||||
\(970\) | 17.6155i | 0.565598i | ||||||||
\(971\) | 46.5253 | 1.49307 | 0.746534 | − | 0.665347i | \(-0.231716\pi\) | ||||
0.746534 | + | 0.665347i | \(0.231716\pi\) | |||||||
\(972\) | −14.2525 | − | 6.31386i | −0.457151 | − | 0.202517i | ||||
\(973\) | 42.2689 | + | 13.2665i | 1.35508 | + | 0.425304i | ||||
\(974\) | 10.9822i | 0.351893i | ||||||||
\(975\) | 1.91983 | + | 3.41781i | 0.0614837 | + | 0.109458i | ||||
\(976\) | − | 3.74456i | − | 0.119861i | ||||||
\(977\) | −11.3505 | −0.363136 | −0.181568 | − | 0.983378i | \(-0.558117\pi\) | ||||
−0.181568 | + | 0.983378i | \(0.558117\pi\) | |||||||
\(978\) | −19.6974 | + | 4.62772i | −0.629852 | + | 0.147978i | ||||
\(979\) | 57.4456i | 1.83597i | ||||||||
\(980\) | 9.48913 | − | 13.6277i | 0.303119 | − | 0.435322i | ||||
\(981\) | 13.0217 | + | 26.1831i | 0.415752 | + | 0.835963i | ||||
\(982\) | − | 8.21782i | − | 0.262241i | ||||||
\(983\) | 36.8832i | 1.17639i | 0.808719 | + | 0.588195i | \(0.200161\pi\) | ||||
−0.808719 | + | 0.588195i | \(0.799839\pi\) | |||||||
\(984\) | 4.43070 | − | 1.04095i | 0.141246 | − | 0.0331844i | ||||
\(985\) | 9.21194i | 0.293517i | ||||||||
\(986\) | − | 19.1168i | − | 0.608804i | ||||||
\(987\) | 1.55448 | − | 21.1498i | 0.0494798 | − | 0.673206i | ||||
\(988\) | −26.2337 | + | 7.57301i | −0.834605 | + | 0.240930i | ||||
\(989\) | − | 56.7701i | − | 1.80519i | ||||||
\(990\) | −18.2054 | − | 36.6060i | −0.578605 | − | 1.16341i | ||||
\(991\) | 2.11684 | 0.0672438 | 0.0336219 | − | 0.999435i | \(-0.489296\pi\) | ||||
0.0336219 | + | 0.999435i | \(0.489296\pi\) | |||||||
\(992\) | 5.84096 | 0.185451 | ||||||||
\(993\) | 55.0844 | − | 12.9416i | 1.74805 | − | 0.410689i | ||||
\(994\) | 1.58457 | − | 5.04868i | 0.0502596 | − | 0.160134i | ||||
\(995\) | 12.1386 | 0.384819 | ||||||||
\(996\) | 8.00000 | − | 1.87953i | 0.253490 | − | 0.0595551i | ||||
\(997\) | − | 2.62772i | − | 0.0832207i | −0.999134 | − | 0.0416103i | \(-0.986751\pi\) | ||
0.999134 | − | 0.0416103i | \(-0.0132488\pi\) | |||||||
\(998\) | 26.0357i | 0.824145i | ||||||||
\(999\) | 19.6048 | − | 16.2554i | 0.620268 | − | 0.514299i |
(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 | 546.2.e.g.545.3 | yes | 8 | |
3.2 | odd | 2 | 546.2.e.e.545.5 | yes | 8 | ||
7.6 | odd | 2 | inner | 546.2.e.g.545.6 | yes | 8 | |
13.12 | even | 2 | 546.2.e.e.545.3 | ✓ | 8 | ||
21.20 | even | 2 | 546.2.e.e.545.4 | yes | 8 | ||
39.38 | odd | 2 | inner | 546.2.e.g.545.5 | yes | 8 | |
91.90 | odd | 2 | 546.2.e.e.545.6 | yes | 8 | ||
273.272 | even | 2 | inner | 546.2.e.g.545.4 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
546.2.e.e.545.3 | ✓ | 8 | 13.12 | even | 2 | ||
546.2.e.e.545.4 | yes | 8 | 21.20 | even | 2 | ||
546.2.e.e.545.5 | yes | 8 | 3.2 | odd | 2 | ||
546.2.e.e.545.6 | yes | 8 | 91.90 | odd | 2 | ||
546.2.e.g.545.3 | yes | 8 | 1.1 | even | 1 | trivial | |
546.2.e.g.545.4 | yes | 8 | 273.272 | even | 2 | inner | |
546.2.e.g.545.5 | yes | 8 | 39.38 | odd | 2 | inner | |
546.2.e.g.545.6 | yes | 8 | 7.6 | odd | 2 | inner |