Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [300,3,Mod(199,300)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(300, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("300.199");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 300 = 2^{2} \cdot 3 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 300.f (of order \(2\), degree \(1\), not 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: | \(8.17440793081\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 4 x^{15} + 8 x^{14} - 14 x^{13} + 23 x^{12} - 26 x^{11} + 18 x^{10} - 10 x^{9} + 9 x^{8} + \cdots + 256 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{20}\cdot 5^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 199.10 | ||
Root | \(1.40592 - 0.152947i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 300.199 |
Dual form | 300.3.f.c.199.9 |
$q$-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 \(\left(\mathbb{Z}/300\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(151\) | \(277\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.305673 | + | 1.97650i | 0.152836 | + | 0.988251i | ||||
\(3\) | −1.73205 | −0.577350 | ||||||||
\(4\) | −3.81313 | + | 1.20833i | −0.953282 | + | 0.302082i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −0.529441 | − | 3.42340i | −0.0882402 | − | 0.570567i | ||||
\(7\) | −0.329898 | −0.0471283 | −0.0235641 | − | 0.999722i | \(-0.507501\pi\) | ||||
−0.0235641 | + | 0.999722i | \(0.507501\pi\) | |||||||
\(8\) | −3.55383 | − | 7.16731i | −0.444229 | − | 0.895913i | ||||
\(9\) | 3.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 20.4920i | − | 1.86291i | −0.363861 | − | 0.931453i | \(-0.618542\pi\) | ||
0.363861 | − | 0.931453i | \(-0.381458\pi\) | |||||||
\(12\) | 6.60453 | − | 2.09288i | 0.550378 | − | 0.174407i | ||||
\(13\) | − | 0.416712i | − | 0.0320548i | −0.999872 | − | 0.0160274i | \(-0.994898\pi\) | ||
0.999872 | − | 0.0160274i | \(-0.00510189\pi\) | |||||||
\(14\) | −0.100841 | − | 0.652044i | −0.00720292 | − | 0.0465746i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 13.0799 | − | 9.21501i | 0.817493 | − | 0.575938i | ||||
\(17\) | 18.5884i | 1.09343i | 0.837317 | + | 0.546717i | \(0.184123\pi\) | ||||
−0.837317 | + | 0.546717i | \(0.815877\pi\) | |||||||
\(18\) | 0.917019 | + | 5.92951i | 0.0509455 | + | 0.329417i | ||||
\(19\) | − | 12.4503i | − | 0.655281i | −0.944803 | − | 0.327640i | \(-0.893747\pi\) | ||
0.944803 | − | 0.327640i | \(-0.106253\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.571400 | 0.0272095 | ||||||||
\(22\) | 40.5024 | − | 6.26384i | 1.84102 | − | 0.284720i | ||||
\(23\) | 23.2304 | 1.01002 | 0.505008 | − | 0.863114i | \(-0.331489\pi\) | ||||
0.505008 | + | 0.863114i | \(0.331489\pi\) | |||||||
\(24\) | 6.15542 | + | 12.4141i | 0.256476 | + | 0.517256i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0.823633 | − | 0.127378i | 0.0316782 | − | 0.00489914i | ||||
\(27\) | −5.19615 | −0.192450 | ||||||||
\(28\) | 1.25794 | − | 0.398624i | 0.0449265 | − | 0.0142366i | ||||
\(29\) | 23.9166 | 0.824712 | 0.412356 | − | 0.911023i | \(-0.364706\pi\) | ||||
0.412356 | + | 0.911023i | \(0.364706\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 42.0148i | − | 1.35532i | −0.735377 | − | 0.677658i | \(-0.762995\pi\) | ||
0.735377 | − | 0.677658i | \(-0.237005\pi\) | |||||||
\(32\) | 22.2117 | + | 23.0357i | 0.694115 | + | 0.719865i | ||||
\(33\) | 35.4931i | 1.07555i | ||||||||
\(34\) | −36.7400 | + | 5.68197i | −1.08059 | + | 0.167117i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −11.4394 | + | 3.62498i | −0.317761 | + | 0.100694i | ||||
\(37\) | − | 50.9523i | − | 1.37709i | −0.725194 | − | 0.688545i | \(-0.758250\pi\) | ||
0.725194 | − | 0.688545i | \(-0.241750\pi\) | |||||||
\(38\) | 24.6081 | − | 3.80573i | 0.647582 | − | 0.100151i | ||||
\(39\) | 0.721767i | 0.0185068i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 46.7073 | 1.13920 | 0.569601 | − | 0.821921i | \(-0.307098\pi\) | ||||
0.569601 | + | 0.821921i | \(0.307098\pi\) | |||||||
\(42\) | 0.174661 | + | 1.12937i | 0.00415861 | + | 0.0268898i | ||||
\(43\) | 55.5866 | 1.29271 | 0.646356 | − | 0.763036i | \(-0.276292\pi\) | ||||
0.646356 | + | 0.763036i | \(0.276292\pi\) | |||||||
\(44\) | 24.7610 | + | 78.1385i | 0.562750 | + | 1.77588i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 7.10090 | + | 45.9149i | 0.154367 | + | 0.998151i | ||||
\(47\) | −81.7616 | −1.73961 | −0.869804 | − | 0.493397i | \(-0.835755\pi\) | ||||
−0.869804 | + | 0.493397i | \(0.835755\pi\) | |||||||
\(48\) | −22.6550 | + | 15.9609i | −0.471980 | + | 0.332518i | ||||
\(49\) | −48.8912 | −0.997779 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | − | 32.1960i | − | 0.631295i | ||||||
\(52\) | 0.503524 | + | 1.58898i | 0.00968316 | + | 0.0305572i | ||||
\(53\) | − | 29.9744i | − | 0.565554i | −0.959186 | − | 0.282777i | \(-0.908744\pi\) | ||
0.959186 | − | 0.282777i | \(-0.0912557\pi\) | |||||||
\(54\) | −1.58832 | − | 10.2702i | −0.0294134 | − | 0.190189i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 1.17240 | + | 2.36448i | 0.0209357 | + | 0.0422228i | ||||
\(57\) | 21.5646i | 0.378326i | ||||||||
\(58\) | 7.31067 | + | 47.2713i | 0.126046 | + | 0.815023i | ||||
\(59\) | − | 24.3311i | − | 0.412391i | −0.978511 | − | 0.206196i | \(-0.933892\pi\) | ||
0.978511 | − | 0.206196i | \(-0.0661083\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −74.8416 | −1.22691 | −0.613456 | − | 0.789729i | \(-0.710221\pi\) | ||||
−0.613456 | + | 0.789729i | \(0.710221\pi\) | |||||||
\(62\) | 83.0424 | − | 12.8428i | 1.33939 | − | 0.207142i | ||||
\(63\) | −0.989693 | −0.0157094 | ||||||||
\(64\) | −38.7406 | + | 50.9428i | −0.605321 | + | 0.795981i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −70.1523 | + | 10.8493i | −1.06291 | + | 0.164383i | ||||
\(67\) | −72.8008 | −1.08658 | −0.543290 | − | 0.839545i | \(-0.682822\pi\) | ||||
−0.543290 | + | 0.839545i | \(0.682822\pi\) | |||||||
\(68\) | −22.4608 | − | 70.8799i | −0.330307 | − | 1.04235i | ||||
\(69\) | −40.2362 | −0.583133 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 39.2803i | 0.553244i | 0.960979 | + | 0.276622i | \(0.0892150\pi\) | ||||
−0.960979 | + | 0.276622i | \(0.910785\pi\) | |||||||
\(72\) | −10.6615 | − | 21.5019i | −0.148076 | − | 0.298638i | ||||
\(73\) | − | 46.5814i | − | 0.638101i | −0.947738 | − | 0.319051i | \(-0.896636\pi\) | ||
0.947738 | − | 0.319051i | \(-0.103364\pi\) | |||||||
\(74\) | 100.707 | − | 15.5747i | 1.36091 | − | 0.210469i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 15.0441 | + | 47.4747i | 0.197948 | + | 0.624667i | ||||
\(77\) | 6.76026i | 0.0877955i | ||||||||
\(78\) | −1.42657 | + | 0.220625i | −0.0182894 | + | 0.00282852i | ||||
\(79\) | − | 101.920i | − | 1.29012i | −0.764131 | − | 0.645062i | \(-0.776832\pi\) | ||
0.764131 | − | 0.645062i | \(-0.223168\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 9.00000 | 0.111111 | ||||||||
\(82\) | 14.2771 | + | 92.3170i | 0.174112 | + | 1.12582i | ||||
\(83\) | 5.88913 | 0.0709534 | 0.0354767 | − | 0.999371i | \(-0.488705\pi\) | ||||
0.0354767 | + | 0.999371i | \(0.488705\pi\) | |||||||
\(84\) | −2.17882 | + | 0.690438i | −0.0259383 | + | 0.00821950i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 16.9913 | + | 109.867i | 0.197574 | + | 1.27752i | ||||
\(87\) | −41.4248 | −0.476148 | ||||||||
\(88\) | −146.872 | + | 72.8250i | −1.66900 | + | 0.827557i | ||||
\(89\) | 61.0100 | 0.685506 | 0.342753 | − | 0.939426i | \(-0.388641\pi\) | ||||
0.342753 | + | 0.939426i | \(0.388641\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.137472i | 0.00151069i | ||||||||
\(92\) | −88.5804 | + | 28.0699i | −0.962831 | + | 0.305108i | ||||
\(93\) | 72.7718i | 0.782492i | ||||||||
\(94\) | −24.9923 | − | 161.602i | −0.265876 | − | 1.71917i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −38.4717 | − | 39.8989i | −0.400747 | − | 0.415614i | ||||
\(97\) | − | 95.5437i | − | 0.984987i | −0.870316 | − | 0.492494i | \(-0.836086\pi\) | ||
0.870316 | − | 0.492494i | \(-0.163914\pi\) | |||||||
\(98\) | −14.9447 | − | 96.6335i | −0.152497 | − | 0.986057i | ||||
\(99\) | − | 61.4759i | − | 0.620969i | ||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 162.675 | 1.61064 | 0.805322 | − | 0.592838i | \(-0.201992\pi\) | ||||
0.805322 | + | 0.592838i | \(0.201992\pi\) | |||||||
\(102\) | 63.6355 | − | 9.84145i | 0.623878 | − | 0.0964848i | ||||
\(103\) | −158.196 | −1.53588 | −0.767941 | − | 0.640521i | \(-0.778718\pi\) | ||||
−0.767941 | + | 0.640521i | \(0.778718\pi\) | |||||||
\(104\) | −2.98670 | + | 1.48092i | −0.0287183 | + | 0.0142397i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 59.2445 | − | 9.16236i | 0.558910 | − | 0.0864373i | ||||
\(107\) | 18.1827 | 0.169932 | 0.0849660 | − | 0.996384i | \(-0.472922\pi\) | ||||
0.0849660 | + | 0.996384i | \(0.472922\pi\) | |||||||
\(108\) | 19.8136 | − | 6.27865i | 0.183459 | − | 0.0581357i | ||||
\(109\) | 156.842 | 1.43891 | 0.719457 | − | 0.694537i | \(-0.244391\pi\) | ||||
0.719457 | + | 0.694537i | \(0.244391\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 88.2520i | 0.795063i | ||||||||
\(112\) | −4.31503 | + | 3.04001i | −0.0385270 | + | 0.0271430i | ||||
\(113\) | − | 98.7245i | − | 0.873668i | −0.899542 | − | 0.436834i | \(-0.856100\pi\) | ||
0.899542 | − | 0.436834i | \(-0.143900\pi\) | |||||||
\(114\) | −42.6225 | + | 6.59172i | −0.373882 | + | 0.0578221i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −91.1972 | + | 28.8991i | −0.786183 | + | 0.249130i | ||||
\(117\) | − | 1.25014i | − | 0.0106849i | ||||||
\(118\) | 48.0904 | − | 7.43735i | 0.407546 | − | 0.0630284i | ||||
\(119\) | − | 6.13227i | − | 0.0515317i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −298.921 | −2.47042 | ||||||||
\(122\) | −22.8770 | − | 147.925i | −0.187517 | − | 1.21250i | ||||
\(123\) | −80.8994 | −0.657718 | ||||||||
\(124\) | 50.7676 | + | 160.208i | 0.409416 | + | 1.29200i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −0.302523 | − | 1.95613i | −0.00240097 | − | 0.0155249i | ||||
\(127\) | 27.0938 | 0.213337 | 0.106669 | − | 0.994295i | \(-0.465982\pi\) | ||||
0.106669 | + | 0.994295i | \(0.465982\pi\) | |||||||
\(128\) | −112.531 | − | 60.9990i | −0.879145 | − | 0.476555i | ||||
\(129\) | −96.2789 | −0.746348 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 4.45811i | − | 0.0340314i | −0.999855 | − | 0.0170157i | \(-0.994583\pi\) | ||
0.999855 | − | 0.0170157i | \(-0.00541653\pi\) | |||||||
\(132\) | −42.8873 | − | 135.340i | −0.324904 | − | 1.02530i | ||||
\(133\) | 4.10734i | 0.0308822i | ||||||||
\(134\) | −22.2533 | − | 143.891i | −0.166069 | − | 1.07381i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 133.229 | − | 66.0600i | 0.979622 | − | 0.485735i | ||||
\(137\) | 181.700i | 1.32628i | 0.748496 | + | 0.663139i | \(0.230776\pi\) | ||||
−0.748496 | + | 0.663139i | \(0.769224\pi\) | |||||||
\(138\) | −12.2991 | − | 79.5270i | −0.0891241 | − | 0.576282i | ||||
\(139\) | 223.419i | 1.60733i | 0.595083 | + | 0.803664i | \(0.297119\pi\) | ||||
−0.595083 | + | 0.803664i | \(0.702881\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 141.615 | 1.00436 | ||||||||
\(142\) | −77.6377 | + | 12.0069i | −0.546744 | + | 0.0845559i | ||||
\(143\) | −8.53925 | −0.0597151 | ||||||||
\(144\) | 39.2397 | − | 27.6450i | 0.272498 | − | 0.191979i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 92.0683 | − | 14.2387i | 0.630604 | − | 0.0975251i | ||||
\(147\) | 84.6820 | 0.576068 | ||||||||
\(148\) | 61.5670 | + | 194.288i | 0.415994 | + | 1.31275i | ||||
\(149\) | −123.867 | −0.831324 | −0.415662 | − | 0.909519i | \(-0.636450\pi\) | ||||
−0.415662 | + | 0.909519i | \(0.636450\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 76.0961i | 0.503948i | 0.967734 | + | 0.251974i | \(0.0810797\pi\) | ||||
−0.967734 | + | 0.251974i | \(0.918920\pi\) | |||||||
\(152\) | −89.2353 | + | 44.2464i | −0.587075 | + | 0.291095i | ||||
\(153\) | 55.7651i | 0.364478i | ||||||||
\(154\) | −13.3617 | + | 2.06643i | −0.0867641 | + | 0.0134184i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −0.872130 | − | 2.75219i | −0.00559058 | − | 0.0176422i | ||||
\(157\) | − | 34.2940i | − | 0.218433i | −0.994018 | − | 0.109217i | \(-0.965166\pi\) | ||
0.994018 | − | 0.109217i | \(-0.0348342\pi\) | |||||||
\(158\) | 201.445 | − | 31.1541i | 1.27497 | − | 0.197178i | ||||
\(159\) | 51.9172i | 0.326523i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −7.66365 | −0.0476003 | ||||||||
\(162\) | 2.75106 | + | 17.7885i | 0.0169818 | + | 0.109806i | ||||
\(163\) | 165.538 | 1.01557 | 0.507786 | − | 0.861483i | \(-0.330464\pi\) | ||||
0.507786 | + | 0.861483i | \(0.330464\pi\) | |||||||
\(164\) | −178.101 | + | 56.4377i | −1.08598 | + | 0.344132i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 1.80015 | + | 11.6399i | 0.0108443 | + | 0.0701198i | ||||
\(167\) | 83.6064 | 0.500637 | 0.250319 | − | 0.968164i | \(-0.419465\pi\) | ||||
0.250319 | + | 0.968164i | \(0.419465\pi\) | |||||||
\(168\) | −2.03066 | − | 4.09540i | −0.0120873 | − | 0.0243774i | ||||
\(169\) | 168.826 | 0.998972 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | − | 37.3510i | − | 0.218427i | ||||||
\(172\) | −211.959 | + | 67.1668i | −1.23232 | + | 0.390505i | ||||
\(173\) | 192.900i | 1.11503i | 0.830168 | + | 0.557513i | \(0.188244\pi\) | ||||
−0.830168 | + | 0.557513i | \(0.811756\pi\) | |||||||
\(174\) | −12.6625 | − | 81.8763i | −0.0727727 | − | 0.470554i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −188.834 | − | 268.033i | −1.07292 | − | 1.52291i | ||||
\(177\) | 42.1427i | 0.238094i | ||||||||
\(178\) | 18.6491 | + | 120.587i | 0.104770 | + | 0.677452i | ||||
\(179\) | 120.939i | 0.675637i | 0.941211 | + | 0.337819i | \(0.109689\pi\) | ||||
−0.941211 | + | 0.337819i | \(0.890311\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −107.583 | −0.594381 | −0.297191 | − | 0.954818i | \(-0.596050\pi\) | ||||
−0.297191 | + | 0.954818i | \(0.596050\pi\) | |||||||
\(182\) | −0.271715 | + | 0.0420216i | −0.00149294 | + | 0.000230888i | ||||
\(183\) | 129.629 | 0.708357 | ||||||||
\(184\) | −82.5569 | − | 166.499i | −0.448679 | − | 0.904887i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −143.834 | + | 22.2444i | −0.773299 | + | 0.119593i | ||||
\(187\) | 380.913 | 2.03697 | ||||||||
\(188\) | 311.767 | − | 98.7947i | 1.65834 | − | 0.525504i | ||||
\(189\) | 1.71420 | 0.00906984 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 279.706i | 1.46443i | 0.681075 | + | 0.732214i | \(0.261513\pi\) | ||||
−0.681075 | + | 0.732214i | \(0.738487\pi\) | |||||||
\(192\) | 67.1006 | − | 88.2355i | 0.349482 | − | 0.459560i | ||||
\(193\) | − | 102.534i | − | 0.531263i | −0.964075 | − | 0.265632i | \(-0.914420\pi\) | ||
0.964075 | − | 0.265632i | \(-0.0855805\pi\) | |||||||
\(194\) | 188.842 | − | 29.2051i | 0.973415 | − | 0.150542i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 186.428 | − | 59.0765i | 0.951165 | − | 0.301411i | ||||
\(197\) | − | 38.9632i | − | 0.197783i | −0.995098 | − | 0.0988913i | \(-0.968470\pi\) | ||
0.995098 | − | 0.0988913i | \(-0.0315296\pi\) | |||||||
\(198\) | 121.507 | − | 18.7915i | 0.613673 | − | 0.0949067i | ||||
\(199\) | 147.646i | 0.741940i | 0.928645 | + | 0.370970i | \(0.120975\pi\) | ||||
−0.928645 | + | 0.370970i | \(0.879025\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 126.095 | 0.627337 | ||||||||
\(202\) | 49.7254 | + | 321.528i | 0.246165 | + | 1.59172i | ||||
\(203\) | −7.89005 | −0.0388672 | ||||||||
\(204\) | 38.9033 | + | 122.768i | 0.190703 | + | 0.601802i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −48.3562 | − | 312.674i | −0.234739 | − | 1.51784i | ||||
\(207\) | 69.6912 | 0.336672 | ||||||||
\(208\) | −3.84001 | − | 5.45055i | −0.0184616 | − | 0.0262046i | ||||
\(209\) | −255.132 | −1.22073 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 233.336i | − | 1.10586i | −0.833229 | − | 0.552928i | \(-0.813510\pi\) | ||
0.833229 | − | 0.552928i | \(-0.186490\pi\) | |||||||
\(212\) | 36.2189 | + | 114.296i | 0.170844 | + | 0.539133i | ||||
\(213\) | − | 68.0355i | − | 0.319416i | ||||||
\(214\) | 5.55797 | + | 35.9382i | 0.0259718 | + | 0.167936i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 18.4663 | + | 37.2424i | 0.0854919 | + | 0.172419i | ||||
\(217\) | 13.8606i | 0.0638737i | ||||||||
\(218\) | 47.9422 | + | 309.998i | 0.219918 | + | 1.42201i | ||||
\(219\) | 80.6813i | 0.368408i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 7.74600 | 0.0350498 | ||||||||
\(222\) | −174.430 | + | 26.9762i | −0.785722 | + | 0.121515i | ||||
\(223\) | −82.7105 | −0.370899 | −0.185450 | − | 0.982654i | \(-0.559374\pi\) | ||||
−0.185450 | + | 0.982654i | \(0.559374\pi\) | |||||||
\(224\) | −7.32758 | − | 7.59941i | −0.0327124 | − | 0.0339260i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 195.129 | − | 30.1774i | 0.863403 | − | 0.133528i | ||||
\(227\) | 361.534 | 1.59266 | 0.796330 | − | 0.604862i | \(-0.206772\pi\) | ||||
0.796330 | + | 0.604862i | \(0.206772\pi\) | |||||||
\(228\) | −26.0571 | − | 82.2286i | −0.114286 | − | 0.360652i | ||||
\(229\) | −121.818 | −0.531955 | −0.265977 | − | 0.963979i | \(-0.585695\pi\) | ||||
−0.265977 | + | 0.963979i | \(0.585695\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | − | 11.7091i | − | 0.0506888i | ||||||
\(232\) | −84.9957 | − | 171.418i | −0.366361 | − | 0.738870i | ||||
\(233\) | 136.615i | 0.586329i | 0.956062 | + | 0.293164i | \(0.0947083\pi\) | ||||
−0.956062 | + | 0.293164i | \(0.905292\pi\) | |||||||
\(234\) | 2.47090 | − | 0.382133i | 0.0105594 | − | 0.00163305i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 29.3999 | + | 92.7775i | 0.124576 | + | 0.393125i | ||||
\(237\) | 176.530i | 0.744853i | ||||||||
\(238\) | 12.1204 | − | 1.87447i | 0.0509262 | − | 0.00787592i | ||||
\(239\) | 56.4632i | 0.236248i | 0.992999 | + | 0.118124i | \(0.0376880\pi\) | ||||
−0.992999 | + | 0.118124i | \(0.962312\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2.24158 | −0.00930117 | −0.00465059 | − | 0.999989i | \(-0.501480\pi\) | ||||
−0.00465059 | + | 0.999989i | \(0.501480\pi\) | |||||||
\(242\) | −91.3720 | − | 590.818i | −0.377570 | − | 2.44140i | ||||
\(243\) | −15.5885 | −0.0641500 | ||||||||
\(244\) | 285.381 | − | 90.4331i | 1.16959 | − | 0.370627i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −24.7287 | − | 159.898i | −0.100523 | − | 0.649991i | ||||
\(247\) | −5.18820 | −0.0210049 | ||||||||
\(248\) | −301.133 | + | 149.314i | −1.21425 | + | 0.602071i | ||||
\(249\) | −10.2003 | −0.0409650 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 395.809i | − | 1.57693i | −0.615081 | − | 0.788464i | \(-0.710877\pi\) | ||
0.615081 | − | 0.788464i | \(-0.289123\pi\) | |||||||
\(252\) | 3.77383 | − | 1.19587i | 0.0149755 | − | 0.00474553i | ||||
\(253\) | − | 476.036i | − | 1.88157i | ||||||
\(254\) | 8.28184 | + | 53.5510i | 0.0326057 | + | 0.210831i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 86.1671 | − | 241.063i | 0.336590 | − | 0.941651i | ||||
\(257\) | − | 109.778i | − | 0.427151i | −0.976927 | − | 0.213576i | \(-0.931489\pi\) | ||
0.976927 | − | 0.213576i | \(-0.0685110\pi\) | |||||||
\(258\) | −29.4298 | − | 190.295i | −0.114069 | − | 0.737579i | ||||
\(259\) | 16.8091i | 0.0648998i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 71.7499 | 0.274904 | ||||||||
\(262\) | 8.81147 | − | 1.36272i | 0.0336316 | − | 0.00520124i | ||||
\(263\) | −327.702 | −1.24601 | −0.623007 | − | 0.782216i | \(-0.714089\pi\) | ||||
−0.623007 | + | 0.782216i | \(0.714089\pi\) | |||||||
\(264\) | 254.390 | − | 126.137i | 0.963599 | − | 0.477790i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −8.11816 | + | 1.25550i | −0.0305194 | + | 0.00471993i | ||||
\(267\) | −105.673 | −0.395777 | ||||||||
\(268\) | 277.599 | − | 87.9672i | 1.03582 | − | 0.328236i | ||||
\(269\) | 130.032 | 0.483392 | 0.241696 | − | 0.970352i | \(-0.422296\pi\) | ||||
0.241696 | + | 0.970352i | \(0.422296\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 329.669i | 1.21649i | 0.793750 | + | 0.608245i | \(0.208126\pi\) | ||||
−0.793750 | + | 0.608245i | \(0.791874\pi\) | |||||||
\(272\) | 171.292 | + | 243.134i | 0.629751 | + | 0.893875i | ||||
\(273\) | − | 0.238109i | − | 0.000872195i | ||||||
\(274\) | −359.131 | + | 55.5408i | −1.31070 | + | 0.202704i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 153.426 | − | 48.6185i | 0.555891 | − | 0.176154i | ||||
\(277\) | − | 304.124i | − | 1.09792i | −0.835849 | − | 0.548960i | \(-0.815024\pi\) | ||
0.835849 | − | 0.548960i | \(-0.184976\pi\) | |||||||
\(278\) | −441.588 | + | 68.2930i | −1.58844 | + | 0.245658i | ||||
\(279\) | − | 126.044i | − | 0.451772i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 240.099 | 0.854446 | 0.427223 | − | 0.904146i | \(-0.359492\pi\) | ||||
0.427223 | + | 0.904146i | \(0.359492\pi\) | |||||||
\(282\) | 43.2879 | + | 279.903i | 0.153503 | + | 0.992563i | ||||
\(283\) | 86.6730 | 0.306265 | 0.153133 | − | 0.988206i | \(-0.451064\pi\) | ||||
0.153133 | + | 0.988206i | \(0.451064\pi\) | |||||||
\(284\) | −47.4635 | − | 149.781i | −0.167125 | − | 0.527398i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −2.61022 | − | 16.8779i | −0.00912664 | − | 0.0590135i | ||||
\(287\) | −15.4086 | −0.0536886 | ||||||||
\(288\) | 66.6350 | + | 69.1070i | 0.231372 | + | 0.239955i | ||||
\(289\) | −56.5280 | −0.195599 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 165.487i | 0.568683i | ||||||||
\(292\) | 56.2856 | + | 177.621i | 0.192759 | + | 0.608290i | ||||
\(293\) | 390.339i | 1.33222i | 0.745855 | + | 0.666108i | \(0.232041\pi\) | ||||
−0.745855 | + | 0.666108i | \(0.767959\pi\) | |||||||
\(294\) | 25.8850 | + | 167.374i | 0.0880442 | + | 0.569300i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −365.191 | + | 181.076i | −1.23375 | + | 0.611743i | ||||
\(297\) | 106.479i | 0.358517i | ||||||||
\(298\) | −37.8629 | − | 244.824i | −0.127057 | − | 0.821557i | ||||
\(299\) | − | 9.68038i | − | 0.0323759i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −18.3379 | −0.0609233 | ||||||||
\(302\) | −150.404 | + | 23.2605i | −0.498027 | + | 0.0770216i | ||||
\(303\) | −281.761 | −0.929906 | ||||||||
\(304\) | −114.730 | − | 162.849i | −0.377401 | − | 0.535687i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −110.220 | + | 17.0459i | −0.360196 | + | 0.0557056i | ||||
\(307\) | −60.2318 | −0.196195 | −0.0980973 | − | 0.995177i | \(-0.531276\pi\) | ||||
−0.0980973 | + | 0.995177i | \(0.531276\pi\) | |||||||
\(308\) | −8.16860 | − | 25.7777i | −0.0265214 | − | 0.0836939i | ||||
\(309\) | 274.003 | 0.886741 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 106.594i | 0.342747i | 0.985206 | + | 0.171373i | \(0.0548205\pi\) | ||||
−0.985206 | + | 0.171373i | \(0.945180\pi\) | |||||||
\(312\) | 5.17312 | − | 2.56504i | 0.0165805 | − | 0.00822127i | ||||
\(313\) | − | 46.2243i | − | 0.147682i | −0.997270 | − | 0.0738408i | \(-0.976474\pi\) | ||
0.997270 | − | 0.0738408i | \(-0.0235257\pi\) | |||||||
\(314\) | 67.7823 | − | 10.4828i | 0.215867 | − | 0.0333846i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 123.152 | + | 388.633i | 0.389723 | + | 1.22985i | ||||
\(317\) | 8.36780i | 0.0263969i | 0.999913 | + | 0.0131984i | \(0.00420131\pi\) | ||||
−0.999913 | + | 0.0131984i | \(0.995799\pi\) | |||||||
\(318\) | −102.614 | + | 15.8697i | −0.322687 | + | 0.0499046i | ||||
\(319\) | − | 490.099i | − | 1.53636i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −31.4934 | −0.0981103 | ||||||||
\(322\) | −2.34257 | − | 15.1472i | −0.00727507 | − | 0.0470411i | ||||
\(323\) | 231.432 | 0.716506 | ||||||||
\(324\) | −34.3182 | + | 10.8749i | −0.105920 | + | 0.0335646i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 50.6006 | + | 327.187i | 0.155217 | + | 1.00364i | ||||
\(327\) | −271.658 | −0.830757 | ||||||||
\(328\) | −165.990 | − | 334.765i | −0.506066 | − | 1.02063i | ||||
\(329\) | 26.9730 | 0.0819847 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 111.072i | − | 0.335564i | −0.985824 | − | 0.167782i | \(-0.946339\pi\) | ||
0.985824 | − | 0.167782i | \(-0.0536605\pi\) | |||||||
\(332\) | −22.4560 | + | 7.11600i | −0.0676386 | + | 0.0214337i | ||||
\(333\) | − | 152.857i | − | 0.459030i | ||||||
\(334\) | 25.5562 | + | 165.248i | 0.0765156 | + | 0.494755i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 7.47385 | − | 5.26546i | 0.0222436 | − | 0.0156710i | ||||
\(337\) | 231.853i | 0.687990i | 0.938972 | + | 0.343995i | \(0.111780\pi\) | ||||
−0.938972 | + | 0.343995i | \(0.888220\pi\) | |||||||
\(338\) | 51.6057 | + | 333.686i | 0.152679 | + | 0.987236i | ||||
\(339\) | 170.996i | 0.504412i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −860.966 | −2.52483 | ||||||||
\(342\) | 73.8244 | − | 11.4172i | 0.215861 | − | 0.0333836i | ||||
\(343\) | 32.2941 | 0.0941518 | ||||||||
\(344\) | −197.546 | − | 398.406i | −0.574260 | − | 1.15816i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −381.266 | + | 58.9642i | −1.10193 | + | 0.170417i | ||||
\(347\) | −402.088 | −1.15875 | −0.579377 | − | 0.815059i | \(-0.696704\pi\) | ||||
−0.579377 | + | 0.815059i | \(0.696704\pi\) | |||||||
\(348\) | 157.958 | − | 50.0548i | 0.453903 | − | 0.143835i | ||||
\(349\) | 163.284 | 0.467864 | 0.233932 | − | 0.972253i | \(-0.424841\pi\) | ||||
0.233932 | + | 0.972253i | \(0.424841\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2.16530i | 0.00616894i | ||||||||
\(352\) | 472.046 | − | 455.161i | 1.34104 | − | 1.29307i | ||||
\(353\) | 175.851i | 0.498161i | 0.968483 | + | 0.249081i | \(0.0801285\pi\) | ||||
−0.968483 | + | 0.249081i | \(0.919872\pi\) | |||||||
\(354\) | −83.2951 | + | 12.8819i | −0.235297 | + | 0.0363895i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −232.639 | + | 73.7201i | −0.653481 | + | 0.207079i | ||||
\(357\) | 10.6214i | 0.0297518i | ||||||||
\(358\) | −239.037 | + | 36.9678i | −0.667700 | + | 0.103262i | ||||
\(359\) | − | 345.628i | − | 0.962753i | −0.876514 | − | 0.481377i | \(-0.840137\pi\) | ||
0.876514 | − | 0.481377i | \(-0.159863\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 205.989 | 0.570607 | ||||||||
\(362\) | −32.8852 | − | 212.638i | −0.0908431 | − | 0.587398i | ||||
\(363\) | 517.746 | 1.42630 | ||||||||
\(364\) | −0.166112 | − | 0.524200i | −0.000456351 | − | 0.00144011i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 39.6242 | + | 256.213i | 0.108263 | + | 0.700035i | ||||
\(367\) | −728.998 | −1.98637 | −0.993185 | − | 0.116546i | \(-0.962818\pi\) | ||||
−0.993185 | + | 0.116546i | \(0.962818\pi\) | |||||||
\(368\) | 303.851 | − | 214.068i | 0.825682 | − | 0.581707i | ||||
\(369\) | 140.122 | 0.379734 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 9.88848i | 0.0266536i | ||||||||
\(372\) | −87.9321 | − | 277.488i | −0.236377 | − | 0.745936i | ||||
\(373\) | − | 46.6749i | − | 0.125134i | −0.998041 | − | 0.0625668i | \(-0.980071\pi\) | ||
0.998041 | − | 0.0625668i | \(-0.0199287\pi\) | |||||||
\(374\) | 116.435 | + | 752.875i | 0.311323 | + | 2.01303i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 290.567 | + | 586.010i | 0.772784 | + | 1.55854i | ||||
\(377\) | − | 9.96635i | − | 0.0264360i | ||||||
\(378\) | 0.523984 | + | 3.38812i | 0.00138620 | + | 0.00896328i | ||||
\(379\) | − | 117.629i | − | 0.310368i | −0.987886 | − | 0.155184i | \(-0.950403\pi\) | ||
0.987886 | − | 0.155184i | \(-0.0495970\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −46.9278 | −0.123170 | ||||||||
\(382\) | −552.839 | + | 85.4985i | −1.44722 | + | 0.223818i | ||||
\(383\) | −251.669 | −0.657100 | −0.328550 | − | 0.944487i | \(-0.606560\pi\) | ||||
−0.328550 | + | 0.944487i | \(0.606560\pi\) | |||||||
\(384\) | 194.909 | + | 105.653i | 0.507575 | + | 0.275139i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 202.658 | − | 31.3418i | 0.525022 | − | 0.0811964i | ||||
\(387\) | 166.760 | 0.430904 | ||||||||
\(388\) | 115.448 | + | 364.321i | 0.297547 | + | 0.938970i | ||||
\(389\) | −356.890 | −0.917454 | −0.458727 | − | 0.888577i | \(-0.651694\pi\) | ||||
−0.458727 | + | 0.888577i | \(0.651694\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 431.815i | 1.10439i | ||||||||
\(392\) | 173.751 | + | 350.418i | 0.443242 | + | 0.893923i | ||||
\(393\) | 7.72168i | 0.0196480i | ||||||||
\(394\) | 77.0108 | − | 11.9100i | 0.195459 | − | 0.0302284i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 74.2830 | + | 234.416i | 0.187583 | + | 0.591958i | ||||
\(397\) | 103.819i | 0.261508i | 0.991415 | + | 0.130754i | \(0.0417398\pi\) | ||||
−0.991415 | + | 0.130754i | \(0.958260\pi\) | |||||||
\(398\) | −291.823 | + | 45.1314i | −0.733224 | + | 0.113396i | ||||
\(399\) | − | 7.11412i | − | 0.0178299i | ||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −121.598 | −0.303237 | −0.151618 | − | 0.988439i | \(-0.548449\pi\) | ||||
−0.151618 | + | 0.988439i | \(0.548449\pi\) | |||||||
\(402\) | 38.5438 | + | 249.227i | 0.0958800 | + | 0.619967i | ||||
\(403\) | −17.5081 | −0.0434444 | ||||||||
\(404\) | −620.301 | + | 196.565i | −1.53540 | + | 0.486546i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −2.41177 | − | 15.5947i | −0.00594033 | − | 0.0384106i | ||||
\(407\) | −1044.11 | −2.56539 | ||||||||
\(408\) | −230.759 | + | 114.419i | −0.565585 | + | 0.280439i | ||||
\(409\) | −182.788 | −0.446915 | −0.223457 | − | 0.974714i | \(-0.571734\pi\) | ||||
−0.223457 | + | 0.974714i | \(0.571734\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − | 314.714i | − | 0.765727i | ||||||
\(412\) | 603.221 | − | 191.152i | 1.46413 | − | 0.463962i | ||||
\(413\) | 8.02677i | 0.0194353i | ||||||||
\(414\) | 21.3027 | + | 137.745i | 0.0514558 | + | 0.332717i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 9.59924 | − | 9.25587i | 0.0230751 | − | 0.0222497i | ||||
\(417\) | − | 386.972i | − | 0.927991i | ||||||
\(418\) | −77.9869 | − | 504.269i | −0.186572 | − | 1.20638i | ||||
\(419\) | − | 168.020i | − | 0.401003i | −0.979693 | − | 0.200502i | \(-0.935743\pi\) | ||
0.979693 | − | 0.200502i | \(-0.0642572\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 625.291 | 1.48525 | 0.742626 | − | 0.669706i | \(-0.233580\pi\) | ||||
0.742626 | + | 0.669706i | \(0.233580\pi\) | |||||||
\(422\) | 461.189 | − | 71.3244i | 1.09286 | − | 0.169015i | ||||
\(423\) | −245.285 | −0.579869 | ||||||||
\(424\) | −214.836 | + | 106.524i | −0.506688 | + | 0.251236i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 134.472 | − | 20.7966i | 0.315663 | − | 0.0488184i | ||||
\(427\) | 24.6901 | 0.0578222 | ||||||||
\(428\) | −69.3331 | + | 21.9707i | −0.161993 | + | 0.0513334i | ||||
\(429\) | 14.7904 | 0.0344765 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 133.413i | 0.309544i | 0.987950 | + | 0.154772i | \(0.0494643\pi\) | ||||
−0.987950 | + | 0.154772i | \(0.950536\pi\) | |||||||
\(432\) | −67.9651 | + | 47.8826i | −0.157327 | + | 0.110839i | ||||
\(433\) | 706.716i | 1.63214i | 0.577954 | + | 0.816069i | \(0.303851\pi\) | ||||
−0.577954 | + | 0.816069i | \(0.696149\pi\) | |||||||
\(434\) | −27.3955 | + | 4.23681i | −0.0631233 | + | 0.00976223i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −598.057 | + | 189.516i | −1.37169 | + | 0.434670i | ||||
\(437\) | − | 289.226i | − | 0.661844i | ||||||
\(438\) | −159.467 | + | 24.6621i | −0.364080 | + | 0.0563062i | ||||
\(439\) | 507.488i | 1.15601i | 0.816033 | + | 0.578005i | \(0.196169\pi\) | ||||
−0.816033 | + | 0.578005i | \(0.803831\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −146.674 | −0.332593 | ||||||||
\(442\) | 2.36774 | + | 15.3100i | 0.00535689 | + | 0.0346380i | ||||
\(443\) | 412.172 | 0.930410 | 0.465205 | − | 0.885203i | \(-0.345981\pi\) | ||||
0.465205 | + | 0.885203i | \(0.345981\pi\) | |||||||
\(444\) | −106.637 | − | 336.516i | −0.240174 | − | 0.757919i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −25.2824 | − | 163.478i | −0.0566869 | − | 0.366542i | ||||
\(447\) | 214.544 | 0.479965 | ||||||||
\(448\) | 12.7804 | − | 16.8059i | 0.0285277 | − | 0.0375132i | ||||
\(449\) | 808.617 | 1.80093 | 0.900465 | − | 0.434929i | \(-0.143227\pi\) | ||||
0.900465 | + | 0.434929i | \(0.143227\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 957.124i | − | 2.12223i | ||||||
\(452\) | 119.291 | + | 376.449i | 0.263919 | + | 0.832852i | ||||
\(453\) | − | 131.802i | − | 0.290955i | ||||||
\(454\) | 110.511 | + | 714.573i | 0.243417 | + | 1.57395i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 154.560 | − | 76.6370i | 0.338948 | − | 0.168064i | ||||
\(457\) | − | 472.873i | − | 1.03473i | −0.855764 | − | 0.517367i | \(-0.826912\pi\) | ||
0.855764 | − | 0.517367i | \(-0.173088\pi\) | |||||||
\(458\) | −37.2364 | − | 240.773i | −0.0813021 | − | 0.525705i | ||||
\(459\) | − | 96.5881i | − | 0.210432i | ||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 433.776 | 0.940946 | 0.470473 | − | 0.882414i | \(-0.344083\pi\) | ||||
0.470473 | + | 0.882414i | \(0.344083\pi\) | |||||||
\(462\) | 23.1431 | − | 3.57916i | 0.0500933 | − | 0.00774709i | ||||
\(463\) | 530.624 | 1.14606 | 0.573028 | − | 0.819536i | \(-0.305769\pi\) | ||||
0.573028 | + | 0.819536i | \(0.305769\pi\) | |||||||
\(464\) | 312.827 | − | 220.392i | 0.674196 | − | 0.474983i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −270.019 | + | 41.7594i | −0.579440 | + | 0.0896124i | ||||
\(467\) | 355.266 | 0.760741 | 0.380370 | − | 0.924834i | \(-0.375797\pi\) | ||||
0.380370 | + | 0.924834i | \(0.375797\pi\) | |||||||
\(468\) | 1.51057 | + | 4.76693i | 0.00322772 | + | 0.0101857i | ||||
\(469\) | 24.0168 | 0.0512086 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 59.3990i | 0.126113i | ||||||||
\(472\) | −174.388 | + | 86.4686i | −0.369467 | + | 0.183196i | ||||
\(473\) | − | 1139.08i | − | 2.40820i | ||||||
\(474\) | −348.912 | + | 53.9605i | −0.736102 | + | 0.113841i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 7.40978 | + | 23.3831i | 0.0155668 | + | 0.0491242i | ||||
\(477\) | − | 89.9232i | − | 0.188518i | ||||||
\(478\) | −111.600 | + | 17.2593i | −0.233472 | + | 0.0361072i | ||||
\(479\) | − | 548.640i | − | 1.14539i | −0.819770 | − | 0.572693i | \(-0.805899\pi\) | ||
0.819770 | − | 0.572693i | \(-0.194101\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −21.2324 | −0.0441423 | ||||||||
\(482\) | −0.685191 | − | 4.43050i | −0.00142156 | − | 0.00919190i | ||||
\(483\) | 13.2738 | 0.0274821 | ||||||||
\(484\) | 1139.82 | − | 361.194i | 2.35501 | − | 0.746269i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −4.76497 | − | 30.8106i | −0.00980446 | − | 0.0633964i | ||||
\(487\) | −134.618 | −0.276422 | −0.138211 | − | 0.990403i | \(-0.544135\pi\) | ||||
−0.138211 | + | 0.990403i | \(0.544135\pi\) | |||||||
\(488\) | 265.974 | + | 536.412i | 0.545029 | + | 1.09921i | ||||
\(489\) | −286.721 | −0.586341 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 756.810i | − | 1.54136i | −0.637220 | − | 0.770682i | \(-0.719916\pi\) | ||
0.637220 | − | 0.770682i | \(-0.280084\pi\) | |||||||
\(492\) | 308.480 | − | 97.7529i | 0.626991 | − | 0.198685i | ||||
\(493\) | 444.572i | 0.901768i | ||||||||
\(494\) | −1.58589 | − | 10.2545i | −0.00321031 | − | 0.0207581i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −387.167 | − | 549.549i | −0.780579 | − | 1.10796i | ||||
\(497\) | − | 12.9585i | − | 0.0260734i | ||||||
\(498\) | −3.11795 | − | 20.1609i | −0.00626094 | − | 0.0404837i | ||||
\(499\) | − | 706.956i | − | 1.41675i | −0.705838 | − | 0.708373i | \(-0.749430\pi\) | ||
0.705838 | − | 0.708373i | \(-0.250570\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −144.811 | −0.289043 | ||||||||
\(502\) | 782.318 | − | 120.988i | 1.55840 | − | 0.241012i | ||||
\(503\) | −100.567 | −0.199935 | −0.0999673 | − | 0.994991i | \(-0.531874\pi\) | ||||
−0.0999673 | + | 0.994991i | \(0.531874\pi\) | |||||||
\(504\) | 3.51720 | + | 7.09344i | 0.00697858 | + | 0.0140743i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 940.887 | − | 145.511i | 1.85946 | − | 0.287572i | ||||
\(507\) | −292.416 | −0.576757 | ||||||||
\(508\) | −103.312 | + | 32.7382i | −0.203370 | + | 0.0644452i | ||||
\(509\) | −753.185 | −1.47973 | −0.739867 | − | 0.672753i | \(-0.765112\pi\) | ||||
−0.739867 | + | 0.672753i | \(0.765112\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 15.3671i | 0.0300726i | ||||||||
\(512\) | 502.800 | + | 96.6232i | 0.982031 | + | 0.188717i | ||||
\(513\) | 64.6938i | 0.126109i | ||||||||
\(514\) | 216.976 | − | 33.5561i | 0.422133 | − | 0.0652843i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 367.124 | − | 116.336i | 0.711480 | − | 0.225458i | ||||
\(517\) | 1675.46i | 3.24073i | ||||||||
\(518\) | −33.2231 | + | 5.13807i | −0.0641373 | + | 0.00991906i | ||||
\(519\) | − | 334.112i | − | 0.643761i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 117.708 | 0.225926 | 0.112963 | − | 0.993599i | \(-0.463966\pi\) | ||||
0.112963 | + | 0.993599i | \(0.463966\pi\) | |||||||
\(522\) | 21.9320 | + | 141.814i | 0.0420153 | + | 0.271674i | ||||
\(523\) | −617.411 | −1.18052 | −0.590259 | − | 0.807214i | \(-0.700974\pi\) | ||||
−0.590259 | + | 0.807214i | \(0.700974\pi\) | |||||||
\(524\) | 5.38686 | + | 16.9994i | 0.0102803 | + | 0.0324415i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −100.170 | − | 647.704i | −0.190437 | − | 1.23138i | ||||
\(527\) | 780.988 | 1.48195 | ||||||||
\(528\) | 327.070 | + | 464.246i | 0.619450 | + | 0.879254i | ||||
\(529\) | 10.6508 | 0.0201338 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 72.9932i | − | 0.137464i | ||||||
\(532\) | −4.96301 | − | 15.6618i | −0.00932896 | − | 0.0294395i | ||||
\(533\) | − | 19.4635i | − | 0.0365169i | ||||||
\(534\) | −32.3012 | − | 208.862i | −0.0604892 | − | 0.391127i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 258.722 | + | 521.786i | 0.482690 | + | 0.973481i | ||||
\(537\) | − | 209.473i | − | 0.390079i | ||||||
\(538\) | 39.7474 | + | 257.009i | 0.0738799 | + | 0.477713i | ||||
\(539\) | 1001.88i | 1.85877i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 352.762 | 0.652056 | 0.326028 | − | 0.945360i | \(-0.394290\pi\) | ||||
0.326028 | + | 0.945360i | \(0.394290\pi\) | |||||||
\(542\) | −651.591 | + | 100.771i | −1.20220 | + | 0.185924i | ||||
\(543\) | 186.339 | 0.343166 | ||||||||
\(544\) | −428.196 | + | 412.879i | −0.787125 | + | 0.758969i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0.470623 | − | 0.0727835i | 0.000861948 | − | 0.000133303i | ||||
\(547\) | 295.110 | 0.539507 | 0.269753 | − | 0.962929i | \(-0.413058\pi\) | ||||
0.269753 | + | 0.962929i | \(0.413058\pi\) | |||||||
\(548\) | −219.553 | − | 692.846i | −0.400644 | − | 1.26432i | ||||
\(549\) | −224.525 | −0.408970 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 297.770i | − | 0.540418i | ||||||
\(552\) | 142.993 | + | 288.385i | 0.259045 | + | 0.522437i | ||||
\(553\) | 33.6231i | 0.0608013i | ||||||||
\(554\) | 601.102 | − | 92.9624i | 1.08502 | − | 0.167802i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −269.963 | − | 851.924i | −0.485545 | − | 1.53224i | ||||
\(557\) | − | 31.8538i | − | 0.0571882i | −0.999591 | − | 0.0285941i | \(-0.990897\pi\) | ||
0.999591 | − | 0.0285941i | \(-0.00910302\pi\) | |||||||
\(558\) | 249.127 | − | 38.5284i | 0.446465 | − | 0.0690473i | ||||
\(559\) | − | 23.1636i | − | 0.0414376i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −659.760 | −1.17604 | ||||||||
\(562\) | 73.3919 | + | 474.557i | 0.130591 | + | 0.844408i | ||||
\(563\) | 906.668 | 1.61042 | 0.805211 | − | 0.592988i | \(-0.202052\pi\) | ||||
0.805211 | + | 0.592988i | \(0.202052\pi\) | |||||||
\(564\) | −539.997 | + | 171.117i | −0.957441 | + | 0.303400i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 26.4936 | + | 171.310i | 0.0468085 | + | 0.302667i | ||||
\(567\) | −2.96908 | −0.00523647 | ||||||||
\(568\) | 281.534 | − | 139.596i | 0.495659 | − | 0.245767i | ||||
\(569\) | 465.009 | 0.817239 | 0.408620 | − | 0.912705i | \(-0.366010\pi\) | ||||
0.408620 | + | 0.912705i | \(0.366010\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 265.895i | − | 0.465666i | −0.972517 | − | 0.232833i | \(-0.925200\pi\) | ||
0.972517 | − | 0.232833i | \(-0.0747995\pi\) | |||||||
\(572\) | 32.5613 | − | 10.3182i | 0.0569253 | − | 0.0180388i | ||||
\(573\) | − | 484.464i | − | 0.845488i | ||||||
\(574\) | −4.71000 | − | 30.4552i | −0.00820557 | − | 0.0530578i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −116.222 | + | 152.828i | −0.201774 | + | 0.265327i | ||||
\(577\) | − | 138.097i | − | 0.239336i | −0.992814 | − | 0.119668i | \(-0.961817\pi\) | ||
0.992814 | − | 0.119668i | \(-0.0381830\pi\) | |||||||
\(578\) | −17.2791 | − | 111.728i | −0.0298946 | − | 0.193301i | ||||
\(579\) | 177.594i | 0.306725i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1.94281 | −0.00334391 | ||||||||
\(582\) | −327.085 | + | 50.5848i | −0.562001 | + | 0.0869154i | ||||
\(583\) | −614.234 | −1.05358 | ||||||||
\(584\) | −333.863 | + | 165.542i | −0.571683 | + | 0.283463i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −771.507 | + | 119.316i | −1.31656 | + | 0.203611i | ||||
\(587\) | 648.473 | 1.10472 | 0.552362 | − | 0.833604i | \(-0.313727\pi\) | ||||
0.552362 | + | 0.833604i | \(0.313727\pi\) | |||||||
\(588\) | −322.903 | + | 102.324i | −0.549155 | + | 0.174020i | ||||
\(589\) | −523.098 | −0.888113 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 67.4862i | 0.114190i | ||||||||
\(592\) | −469.526 | − | 666.451i | −0.793118 | − | 1.12576i | ||||
\(593\) | − | 350.392i | − | 0.590880i | −0.955361 | − | 0.295440i | \(-0.904534\pi\) | ||
0.955361 | − | 0.295440i | \(-0.0954662\pi\) | |||||||
\(594\) | −210.457 | + | 32.5479i | −0.354304 | + | 0.0547944i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 472.322 | − | 149.672i | 0.792486 | − | 0.251128i | ||||
\(597\) | − | 255.731i | − | 0.428359i | ||||||
\(598\) | 19.1333 | − | 2.95903i | 0.0319955 | − | 0.00494821i | ||||
\(599\) | 276.745i | 0.462012i | 0.972952 | + | 0.231006i | \(0.0742017\pi\) | ||||
−0.972952 | + | 0.231006i | \(0.925798\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 815.487 | 1.35688 | 0.678442 | − | 0.734654i | \(-0.262656\pi\) | ||||
0.678442 | + | 0.734654i | \(0.262656\pi\) | |||||||
\(602\) | −5.60540 | − | 36.2449i | −0.00931130 | − | 0.0602075i | ||||
\(603\) | −218.403 | −0.362193 | ||||||||
\(604\) | −91.9490 | − | 290.164i | −0.152233 | − | 0.480405i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −86.1269 | − | 556.902i | −0.142124 | − | 0.918981i | ||||
\(607\) | −247.049 | −0.407001 | −0.203500 | − | 0.979075i | \(-0.565232\pi\) | ||||
−0.203500 | + | 0.979075i | \(0.565232\pi\) | |||||||
\(608\) | 286.802 | − | 276.543i | 0.471713 | − | 0.454840i | ||||
\(609\) | 13.6660 | 0.0224400 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 34.0710i | 0.0557627i | ||||||||
\(612\) | −67.3825 | − | 212.640i | −0.110102 | − | 0.347450i | ||||
\(613\) | 1005.15i | 1.63972i | 0.572561 | + | 0.819862i | \(0.305950\pi\) | ||||
−0.572561 | + | 0.819862i | \(0.694050\pi\) | |||||||
\(614\) | −18.4112 | − | 119.048i | −0.0299857 | − | 0.193890i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 48.4528 | − | 24.0248i | 0.0786572 | − | 0.0390013i | ||||
\(617\) | − | 533.282i | − | 0.864314i | −0.901798 | − | 0.432157i | \(-0.857753\pi\) | ||
0.901798 | − | 0.432157i | \(-0.142247\pi\) | |||||||
\(618\) | 83.7553 | + | 541.568i | 0.135526 | + | 0.876324i | ||||
\(619\) | 1136.85i | 1.83659i | 0.395900 | + | 0.918294i | \(0.370433\pi\) | ||||
−0.395900 | + | 0.918294i | \(0.629567\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −120.709 | −0.194378 | ||||||||
\(622\) | −210.684 | + | 32.5830i | −0.338720 | + | 0.0523842i | ||||
\(623\) | −20.1271 | −0.0323067 | ||||||||
\(624\) | 6.65109 | + | 9.44063i | 0.0106588 | + | 0.0151292i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 91.3625 | − | 14.1295i | 0.145946 | − | 0.0225711i | ||||
\(627\) | 441.901 | 0.704787 | ||||||||
\(628\) | 41.4384 | + | 130.768i | 0.0659847 | + | 0.208229i | ||||
\(629\) | 947.121 | 1.50576 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 936.738i | 1.48453i | 0.670107 | + | 0.742265i | \(0.266248\pi\) | ||||
−0.670107 | + | 0.742265i | \(0.733752\pi\) | |||||||
\(632\) | −730.490 | + | 362.206i | −1.15584 | + | 0.573110i | ||||
\(633\) | 404.149i | 0.638466i | ||||||||
\(634\) | −16.5390 | + | 2.55781i | −0.0260867 | + | 0.00403440i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −62.7329 | − | 197.967i | −0.0986366 | − | 0.311269i | ||||
\(637\) | 20.3735i | 0.0319836i | ||||||||
\(638\) | 968.682 | − | 149.810i | 1.51831 | − | 0.234812i | ||||
\(639\) | 117.841i | 0.184415i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 214.558 | 0.334723 | 0.167362 | − | 0.985896i | \(-0.446475\pi\) | ||||
0.167362 | + | 0.985896i | \(0.446475\pi\) | |||||||
\(642\) | −9.62669 | − | 62.2468i | −0.0149948 | − | 0.0969577i | ||||
\(643\) | 786.394 | 1.22301 | 0.611504 | − | 0.791241i | \(-0.290565\pi\) | ||||
0.611504 | + | 0.791241i | \(0.290565\pi\) | |||||||
\(644\) | 29.2225 | − | 9.26020i | 0.0453765 | − | 0.0143792i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 70.7424 | + | 457.425i | 0.109508 | + | 0.708088i | ||||
\(647\) | −316.550 | −0.489258 | −0.244629 | − | 0.969617i | \(-0.578666\pi\) | ||||
−0.244629 | + | 0.969617i | \(0.578666\pi\) | |||||||
\(648\) | −31.9845 | − | 64.5058i | −0.0493588 | − | 0.0995459i | ||||
\(649\) | −498.592 | −0.768246 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | − | 24.0073i | − | 0.0368775i | ||||||
\(652\) | −631.219 | + | 200.024i | −0.968127 | + | 0.306786i | ||||
\(653\) | − | 516.391i | − | 0.790797i | −0.918510 | − | 0.395399i | \(-0.870606\pi\) | ||
0.918510 | − | 0.395399i | \(-0.129394\pi\) | |||||||
\(654\) | −83.0384 | − | 536.932i | −0.126970 | − | 0.820997i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 610.926 | − | 430.408i | 0.931290 | − | 0.656110i | ||||
\(657\) | − | 139.744i | − | 0.212700i | ||||||
\(658\) | 8.24491 | + | 53.3121i | 0.0125303 | + | 0.0810215i | ||||
\(659\) | 285.118i | 0.432653i | 0.976321 | + | 0.216326i | \(0.0694076\pi\) | ||||
−0.976321 | + | 0.216326i | \(0.930592\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −391.847 | −0.592809 | −0.296405 | − | 0.955062i | \(-0.595788\pi\) | ||||
−0.296405 | + | 0.955062i | \(0.595788\pi\) | |||||||
\(662\) | 219.534 | − | 33.9516i | 0.331622 | − | 0.0512865i | ||||
\(663\) | −13.4165 | −0.0202360 | ||||||||
\(664\) | −20.9290 | − | 42.2092i | −0.0315196 | − | 0.0635681i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 302.122 | − | 46.7242i | 0.453637 | − | 0.0701565i | ||||
\(667\) | 555.593 | 0.832973 | ||||||||
\(668\) | −318.802 | + | 101.024i | −0.477248 | + | 0.151233i | ||||
\(669\) | 143.259 | 0.214139 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1533.65i | 2.28562i | ||||||||
\(672\) | 12.6917 | + | 13.1626i | 0.0188865 | + | 0.0195872i | ||||
\(673\) | 1213.59i | 1.80325i | 0.432517 | + | 0.901626i | \(0.357625\pi\) | ||||
−0.432517 | + | 0.901626i | \(0.642375\pi\) | |||||||
\(674\) | −458.257 | + | 70.8711i | −0.679907 | + | 0.105150i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −643.756 | + | 203.997i | −0.952303 | + | 0.301771i | ||||
\(677\) | 251.863i | 0.372028i | 0.982547 | + | 0.186014i | \(0.0595570\pi\) | ||||
−0.982547 | + | 0.186014i | \(0.940443\pi\) | |||||||
\(678\) | −337.974 | + | 52.2688i | −0.498486 | + | 0.0770926i | ||||
\(679\) | 31.5197i | 0.0464207i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −626.195 | −0.919523 | ||||||||
\(682\) | −263.174 | − | 1701.70i | −0.385886 | − | 2.49517i | ||||
\(683\) | −664.793 | −0.973342 | −0.486671 | − | 0.873585i | \(-0.661789\pi\) | ||||
−0.486671 | + | 0.873585i | \(0.661789\pi\) | |||||||
\(684\) | 45.1322 | + | 142.424i | 0.0659828 | + | 0.208222i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 9.87143 | + | 63.8293i | 0.0143898 | + | 0.0930457i | ||||
\(687\) | 210.994 | 0.307124 | ||||||||
\(688\) | 727.067 | − | 512.231i | 1.05678 | − | 0.744522i | ||||
\(689\) | −12.4907 | −0.0181287 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 654.347i | 0.946957i | 0.880805 | + | 0.473479i | \(0.157002\pi\) | ||||
−0.880805 | + | 0.473479i | \(0.842998\pi\) | |||||||
\(692\) | −233.086 | − | 735.551i | −0.336829 | − | 1.06293i | ||||
\(693\) | 20.2808i | 0.0292652i | ||||||||
\(694\) | −122.907 | − | 794.728i | −0.177100 | − | 1.14514i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 147.217 | + | 296.904i | 0.211519 | + | 0.426587i | ||||
\(697\) | 868.213i | 1.24564i | ||||||||
\(698\) | 49.9117 | + | 322.732i | 0.0715067 | + | 0.462367i | ||||
\(699\) | − | 236.623i | − | 0.338517i | ||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −1266.25 | −1.80635 | −0.903174 | − | 0.429275i | \(-0.858769\pi\) | ||||
−0.903174 | + | 0.429275i | \(0.858769\pi\) | |||||||
\(702\) | −4.27972 | + | 0.661874i | −0.00609647 | + | 0.000942840i | ||||
\(703\) | −634.373 | −0.902380 | ||||||||
\(704\) | 1043.92 | + | 793.870i | 1.48284 | + | 1.12766i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −347.570 | + | 53.7529i | −0.492309 | + | 0.0761372i | ||||
\(707\) | −53.6661 | −0.0759068 | ||||||||
\(708\) | −50.9221 | − | 160.695i | −0.0719239 | − | 0.226971i | ||||
\(709\) | 493.220 | 0.695656 | 0.347828 | − | 0.937558i | \(-0.386919\pi\) | ||||
0.347828 | + | 0.937558i | \(0.386919\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − | 305.759i | − | 0.430041i | ||||||
\(712\) | −216.819 | − | 437.278i | −0.304522 | − | 0.614154i | ||||
\(713\) | − | 976.020i | − | 1.36889i | ||||||
\(714\) | −20.9932 | + | 3.24667i | −0.0294023 | + | 0.00454716i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −146.134 | − | 461.156i | −0.204098 | − | 0.644073i | ||||
\(717\) | − | 97.7971i | − | 0.136398i | ||||||
\(718\) | 683.135 | − | 105.649i | 0.951442 | − | 0.147144i | ||||
\(719\) | 60.3910i | 0.0839930i | 0.999118 | + | 0.0419965i | \(0.0133718\pi\) | ||||
−0.999118 | + | 0.0419965i | \(0.986628\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 52.1884 | 0.0723834 | ||||||||
\(722\) | 62.9653 | + | 407.138i | 0.0872096 | + | 0.563904i | ||||
\(723\) | 3.88254 | 0.00537003 | ||||||||
\(724\) | 410.228 | − | 129.995i | 0.566613 | − | 0.179552i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 158.261 | + | 1023.33i | 0.217990 | + | 1.40954i | ||||
\(727\) | 994.690 | 1.36821 | 0.684106 | − | 0.729383i | \(-0.260193\pi\) | ||||
0.684106 | + | 0.729383i | \(0.260193\pi\) | |||||||
\(728\) | 0.985307 | − | 0.488554i | 0.00135344 | − | 0.000671090i | ||||
\(729\) | 27.0000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1033.27i | 1.41350i | ||||||||
\(732\) | −494.294 | + | 156.635i | −0.675264 | + | 0.213982i | ||||
\(733\) | − | 1167.65i | − | 1.59298i | −0.604654 | − | 0.796488i | \(-0.706689\pi\) | ||
0.604654 | − | 0.796488i | \(-0.293311\pi\) | |||||||
\(734\) | −222.835 | − | 1440.87i | −0.303590 | − | 1.96303i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 515.986 | + | 535.127i | 0.701067 | + | 0.727075i | ||||
\(737\) | 1491.83i | 2.02420i | ||||||||
\(738\) | 42.8314 | + | 276.951i | 0.0580372 | + | 0.375273i | ||||
\(739\) | − | 79.9863i | − | 0.108236i | −0.998535 | − | 0.0541179i | \(-0.982765\pi\) | ||
0.998535 | − | 0.0541179i | \(-0.0172347\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 8.98623 | 0.0121272 | ||||||||
\(742\) | −19.5446 | + | 3.02264i | −0.0263405 | + | 0.00407364i | ||||
\(743\) | −402.122 | −0.541214 | −0.270607 | − | 0.962690i | \(-0.587224\pi\) | ||||
−0.270607 | + | 0.962690i | \(0.587224\pi\) | |||||||
\(744\) | 521.578 | − | 258.619i | 0.701045 | − | 0.347606i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 92.2530 | − | 14.2672i | 0.123664 | − | 0.0191250i | ||||
\(747\) | 17.6674 | 0.0236511 | ||||||||
\(748\) | −1452.47 | + | 460.267i | −1.94180 | + | 0.615330i | ||||
\(749\) | −5.99844 | −0.00800860 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 58.7486i | 0.0782271i | 0.999235 | + | 0.0391136i | \(0.0124534\pi\) | ||||
−0.999235 | + | 0.0391136i | \(0.987547\pi\) | |||||||
\(752\) | −1069.43 | + | 753.434i | −1.42212 | + | 1.00191i | ||||
\(753\) | 685.561i | 0.910440i | ||||||||
\(754\) | 19.6985 | − | 3.04644i | 0.0261254 | − | 0.00404038i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −6.53646 | + | 2.07131i | −0.00864611 | + | 0.00273983i | ||||
\(757\) | − | 1040.91i | − | 1.37504i | −0.726164 | − | 0.687522i | \(-0.758699\pi\) | ||
0.726164 | − | 0.687522i | \(-0.241301\pi\) | |||||||
\(758\) | 232.495 | − | 35.9561i | 0.306721 | − | 0.0474355i | ||||
\(759\) | 824.519i | 1.08632i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 750.095 | 0.985670 | 0.492835 | − | 0.870123i | \(-0.335961\pi\) | ||||
0.492835 | + | 0.870123i | \(0.335961\pi\) | |||||||
\(762\) | −14.3446 | − | 92.7530i | −0.0188249 | − | 0.121723i | ||||
\(763\) | −51.7417 | −0.0678135 | ||||||||
\(764\) | −337.976 | − | 1066.55i | −0.442377 | − | 1.39601i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −76.9285 | − | 497.425i | −0.100429 | − | 0.649380i | ||||
\(767\) | −10.1391 | −0.0132191 | ||||||||
\(768\) | −149.246 | + | 417.533i | −0.194331 | + | 0.543663i | ||||
\(769\) | −1065.98 | −1.38619 | −0.693094 | − | 0.720847i | \(-0.743753\pi\) | ||||
−0.693094 | + | 0.720847i | \(0.743753\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 190.141i | 0.246616i | ||||||||
\(772\) | 123.894 | + | 390.975i | 0.160485 | + | 0.506444i | ||||
\(773\) | 947.271i | 1.22545i | 0.790297 | + | 0.612724i | \(0.209926\pi\) | ||||
−0.790297 | + | 0.612724i | \(0.790074\pi\) | |||||||
\(774\) | 50.9740 | + | 329.601i | 0.0658579 | + | 0.425842i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −684.791 | + | 339.546i | −0.882463 | + | 0.437560i | ||||
\(777\) | − | 29.1141i | − | 0.0374699i | ||||||
\(778\) | −109.092 | − | 705.393i | −0.140220 | − | 0.906675i | ||||
\(779\) | − | 581.521i | − | 0.746497i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 804.931 | 1.03064 | ||||||||
\(782\) | −853.484 | + | 131.994i | −1.09141 | + | 0.168791i | ||||
\(783\) | −124.275 | −0.158716 | ||||||||
\(784\) | −639.491 | + | 450.533i | −0.815678 | + | 0.574659i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −15.2619 | + | 2.36031i | −0.0194172 | + | 0.00300294i | ||||
\(787\) | −11.5874 | −0.0147236 | −0.00736178 | − | 0.999973i | \(-0.502343\pi\) | ||||
−0.00736178 | + | 0.999973i | \(0.502343\pi\) | |||||||
\(788\) | 47.0803 | + | 148.572i | 0.0597465 | + | 0.188543i | ||||
\(789\) | 567.596 | 0.719387 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 32.5690i | 0.0411744i | ||||||||
\(792\) | −440.617 | + | 218.475i | −0.556334 | + | 0.275852i | ||||
\(793\) | 31.1874i | 0.0393284i | ||||||||
\(794\) | −205.198 | + | 31.7345i | −0.258436 | + | 0.0399679i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −178.405 | − | 562.994i | −0.224127 | − | 0.707278i | ||||
\(797\) | − | 780.220i | − | 0.978946i | −0.872018 | − | 0.489473i | \(-0.837189\pi\) | ||
0.872018 | − | 0.489473i | \(-0.162811\pi\) | |||||||
\(798\) | 14.0611 | − | 2.17459i | 0.0176204 | − | 0.00272505i | ||||
\(799\) | − | 1519.82i | − | 1.90215i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 183.030 | 0.228502 | ||||||||
\(802\) | −37.1692 | − | 240.339i | −0.0463457 | − | 0.299674i | ||||
\(803\) | −954.545 | −1.18872 | ||||||||
\(804\) | −480.815 | + | 152.364i | −0.598029 | + | 0.189507i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −5.35175 | − | 34.6048i | −0.00663989 | − | 0.0429340i | ||||
\(807\) | −225.223 | −0.279086 | ||||||||
\(808\) | −578.120 | − | 1165.94i | −0.715495 | − | 1.44300i | ||||
\(809\) | 1061.80 | 1.31249 | 0.656243 | − | 0.754549i | \(-0.272145\pi\) | ||||
0.656243 | + | 0.754549i | \(0.272145\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 309.236i | 0.381302i | 0.981658 | + | 0.190651i | \(0.0610599\pi\) | ||||
−0.981658 | + | 0.190651i | \(0.938940\pi\) | |||||||
\(812\) | 30.0858 | − | 9.53376i | 0.0370514 | − | 0.0117411i | ||||
\(813\) | − | 571.003i | − | 0.702341i | ||||||
\(814\) | −319.157 | − | 2063.69i | −0.392085 | − | 2.53525i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −296.687 | − | 421.121i | −0.363587 | − | 0.516079i | ||||
\(817\) | − | 692.072i | − | 0.847089i | ||||||
\(818\) | −55.8734 | − | 361.281i | −0.0683049 | − | 0.441664i | ||||
\(819\) | 0.412417i | 0.000503562i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −1156.76 | −1.40897 | −0.704483 | − | 0.709721i | \(-0.748821\pi\) | ||||
−0.704483 | + | 0.709721i | \(0.748821\pi\) | |||||||
\(822\) | 622.033 | − | 96.1995i | 0.756731 | − | 0.117031i | ||||
\(823\) | −1441.89 | −1.75200 | −0.875998 | − | 0.482314i | \(-0.839796\pi\) | ||||
−0.875998 | + | 0.482314i | \(0.839796\pi\) | |||||||
\(824\) | 562.201 | + | 1133.84i | 0.682283 | + | 1.37602i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −15.8649 | + | 2.45357i | −0.0192069 | + | 0.00297042i | ||||
\(827\) | −367.599 | −0.444497 | −0.222249 | − | 0.974990i | \(-0.571340\pi\) | ||||
−0.222249 | + | 0.974990i | \(0.571340\pi\) | |||||||
\(828\) | −265.741 | + | 84.2097i | −0.320944 | + | 0.101703i | ||||
\(829\) | −172.743 | −0.208375 | −0.104188 | − | 0.994558i | \(-0.533224\pi\) | ||||
−0.104188 | + | 0.994558i | \(0.533224\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 526.758i | 0.633884i | ||||||||
\(832\) | 21.2285 | + | 16.1437i | 0.0255150 | + | 0.0194034i | ||||
\(833\) | − | 908.808i | − | 1.09101i | ||||||
\(834\) | 764.852 | − | 118.287i | 0.917089 | − | 0.141831i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 972.850 | − | 308.283i | 1.16370 | − | 0.368759i | ||||
\(837\) | 218.315i | 0.260831i | ||||||||
\(838\) | 332.093 | − | 51.3593i | 0.396292 | − | 0.0612879i | ||||
\(839\) | 1083.17i | 1.29103i | 0.763748 | + | 0.645514i | \(0.223357\pi\) | ||||
−0.763748 | + | 0.645514i | \(0.776643\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −268.994 | −0.319850 | ||||||||
\(842\) | 191.135 | + | 1235.89i | 0.227001 | + | 1.46780i | ||||
\(843\) | −415.864 | −0.493315 | ||||||||
\(844\) | 281.946 | + | 889.739i | 0.334059 | + | 1.05419i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −74.9769 | − | 484.806i | −0.0886252 | − | 0.573057i | ||||
\(847\) | 98.6133 | 0.116427 | ||||||||
\(848\) | −276.214 | − | 392.062i | −0.325724 | − | 0.462337i | ||||
\(849\) | −150.122 | −0.176822 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 1183.64i | − | 1.39088i | ||||||
\(852\) | 82.2092 | + | 259.428i | 0.0964896 | + | 0.304493i | ||||
\(853\) | − | 1218.00i | − | 1.42790i | −0.700196 | − | 0.713951i | \(-0.746904\pi\) | ||
0.700196 | − | 0.713951i | \(-0.253096\pi\) | |||||||
\(854\) | 7.54709 | + | 48.8000i | 0.00883734 | + | 0.0571429i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −64.6184 | − | 130.321i | −0.0754888 | − | 0.152244i | ||||
\(857\) | − | 207.055i | − | 0.241604i | −0.992677 | − | 0.120802i | \(-0.961453\pi\) | ||
0.992677 | − | 0.120802i | \(-0.0385466\pi\) | |||||||
\(858\) | 4.52103 | + | 29.2333i | 0.00526927 | + | 0.0340715i | ||||
\(859\) | 1186.36i | 1.38109i | 0.723290 | + | 0.690544i | \(0.242629\pi\) | ||||
−0.723290 | + | 0.690544i | \(0.757371\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 26.6885 | 0.0309971 | ||||||||
\(862\) | −263.692 | + | 40.7809i | −0.305907 | + | 0.0473096i | ||||
\(863\) | 885.953 | 1.02660 | 0.513298 | − | 0.858210i | \(-0.328423\pi\) | ||||
0.513298 | + | 0.858210i | \(0.328423\pi\) | |||||||
\(864\) | −115.415 | − | 119.697i | −0.133582 | − | 0.138538i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −1396.83 | + | 216.024i | −1.61296 | + | 0.249450i | ||||
\(867\) | 97.9093 | 0.112929 | ||||||||
\(868\) | −16.7481 | − | 52.8522i | −0.0192951 | − | 0.0608897i | ||||
\(869\) | −2088.54 | −2.40338 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 30.3370i | 0.0348301i | ||||||||
\(872\) | −557.389 | − | 1124.13i | −0.639207 | − | 1.28914i | ||||
\(873\) | − | 286.631i | − | 0.328329i | ||||||
\(874\) | 571.656 | − | 88.4086i | 0.654069 | − | 0.101154i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −97.4894 | − | 307.648i | −0.111289 | − | 0.351197i | ||||
\(877\) | 643.339i | 0.733567i | 0.930306 | + | 0.366784i | \(0.119541\pi\) | ||||
−0.930306 | + | 0.366784i | \(0.880459\pi\) | |||||||
\(878\) | −1003.05 | + | 155.125i | −1.14243 | + | 0.176680i | ||||
\(879\) | − | 676.088i | − | 0.769155i | ||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 353.918 | 0.401723 | 0.200861 | − | 0.979620i | \(-0.435626\pi\) | ||||
0.200861 | + | 0.979620i | \(0.435626\pi\) | |||||||
\(882\) | −44.8341 | − | 289.901i | −0.0508323 | − | 0.328686i | ||||
\(883\) | 1093.51 | 1.23840 | 0.619200 | − | 0.785233i | \(-0.287457\pi\) | ||||
0.619200 | + | 0.785233i | \(0.287457\pi\) | |||||||
\(884\) | −29.5365 | + | 9.35971i | −0.0334123 | + | 0.0105879i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 125.990 | + | 814.659i | 0.142201 | + | 0.919479i | ||||
\(887\) | 520.234 | 0.586510 | 0.293255 | − | 0.956034i | \(-0.405262\pi\) | ||||
0.293255 | + | 0.956034i | \(0.405262\pi\) | |||||||
\(888\) | 632.529 | − | 313.633i | 0.712307 | − | 0.353190i | ||||
\(889\) | −8.93819 | −0.0100542 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | − | 184.428i | − | 0.206990i | ||||||
\(892\) | 315.386 | − | 99.9413i | 0.353571 | − | 0.112042i | ||||
\(893\) | 1017.96i | 1.13993i | ||||||||
\(894\) | 65.5804 | + | 424.048i | 0.0733562 | + | 0.474326i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 37.1236 | + | 20.1234i | 0.0414326 | + | 0.0224592i | ||||
\(897\) | 16.7669i | 0.0186922i | ||||||||
\(898\) | 247.172 | + | 1598.23i | 0.275248 | + | 1.77977i | ||||
\(899\) | − | 1004.85i | − | 1.11775i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 557.175 | 0.618397 | ||||||||
\(902\) | 1891.76 | − | 292.567i | 2.09729 | − | 0.324354i | ||||
\(903\) | 31.7622 | 0.0351741 | ||||||||
\(904\) | −707.588 | + | 350.850i | −0.782730 | + | 0.388109i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 260.508 | − | 40.2884i | 0.287536 | − | 0.0444685i | ||||
\(907\) | −567.834 | −0.626057 | −0.313029 | − | 0.949744i | \(-0.601344\pi\) | ||||
−0.313029 | + | 0.949744i | \(0.601344\pi\) | |||||||
\(908\) | −1378.58 | + | 436.851i | −1.51825 | + | 0.481114i | ||||
\(909\) | 488.025 | 0.536881 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 1180.19i | − | 1.29549i | −0.761858 | − | 0.647744i | \(-0.775713\pi\) | ||
0.761858 | − | 0.647744i | \(-0.224287\pi\) | |||||||
\(912\) | 198.718 | + | 282.063i | 0.217893 | + | 0.309279i | ||||
\(913\) | − | 120.680i | − | 0.132180i | ||||||
\(914\) | 934.635 | − | 144.545i | 1.02258 | − | 0.158145i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 464.506 | − | 147.196i | 0.507103 | − | 0.160694i | ||||
\(917\) | 1.47072i | 0.00160384i | ||||||||
\(918\) | 190.907 | − | 29.5244i | 0.207959 | − | 0.0321616i | ||||
\(919\) | 54.5449i | 0.0593524i | 0.999560 | + | 0.0296762i | \(0.00944761\pi\) | ||||
−0.999560 | + | 0.0296762i | \(0.990552\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 104.324 | 0.113273 | ||||||||
\(922\) | 132.594 | + | 857.360i | 0.143811 | + | 0.929892i | ||||
\(923\) | 16.3686 | 0.0177341 | ||||||||
\(924\) | 14.1484 | + | 44.6483i | 0.0153122 | + | 0.0483207i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 162.197 | + | 1048.78i | 0.175159 | + | 1.13259i | ||||
\(927\) | −474.587 | −0.511960 | ||||||||
\(928\) | 531.228 | + | 550.936i | 0.572444 | + | 0.593681i | ||||
\(929\) | −175.428 | −0.188835 | −0.0944175 | − | 0.995533i | \(-0.530099\pi\) | ||||
−0.0944175 | + | 0.995533i | \(0.530099\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 608.711i | 0.653825i | ||||||||
\(932\) | −165.075 | − | 520.929i | −0.177119 | − | 0.558937i | ||||
\(933\) | − | 184.627i | − | 0.197885i | ||||||
\(934\) | 108.595 | + | 702.184i | 0.116269 | + | 0.751803i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −8.96011 | + | 4.44277i | −0.00957277 | + | 0.00474655i | ||||
\(937\) | 335.374i | 0.357923i | 0.983856 | + | 0.178962i | \(0.0572738\pi\) | ||||
−0.983856 | + | 0.178962i | \(0.942726\pi\) | |||||||
\(938\) | 7.34130 | + | 47.4694i | 0.00782654 | + | 0.0506070i | ||||
\(939\) | 80.0629i | 0.0852640i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 709.182 | 0.753647 | 0.376823 | − | 0.926285i | \(-0.377016\pi\) | ||||
0.376823 | + | 0.926285i | \(0.377016\pi\) | |||||||
\(942\) | −117.402 | + | 18.1567i | −0.124631 | + | 0.0192746i | ||||
\(943\) | 1085.03 | 1.15061 | ||||||||
\(944\) | −224.211 | − | 318.248i | −0.237512 | − | 0.337127i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 2251.39 | − | 348.186i | 2.37991 | − | 0.368061i | ||||
\(947\) | 992.486 | 1.04803 | 0.524016 | − | 0.851708i | \(-0.324433\pi\) | ||||
0.524016 | + | 0.851708i | \(0.324433\pi\) | |||||||
\(948\) | −213.306 | − | 673.132i | −0.225007 | − | 0.710055i | ||||
\(949\) | −19.4110 | −0.0204542 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 14.4935i | − | 0.0152402i | ||||||
\(952\) | −43.9518 | + | 21.7930i | −0.0461679 | + | 0.0228919i | ||||
\(953\) | 1438.16i | 1.50908i | 0.656251 | + | 0.754542i | \(0.272141\pi\) | ||||
−0.656251 | + | 0.754542i | \(0.727859\pi\) | |||||||
\(954\) | 177.733 | − | 27.4871i | 0.186303 | − | 0.0288124i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −68.2260 | − | 215.301i | −0.0713661 | − | 0.225211i | ||||
\(957\) | 848.877i | 0.887018i | ||||||||
\(958\) | 1084.39 | − | 167.704i | 1.13193 | − | 0.175057i | ||||
\(959\) | − | 59.9425i | − | 0.0625052i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −804.245 | −0.836883 | ||||||||
\(962\) | −6.49018 | − | 41.9660i | −0.00674655 | − | 0.0436237i | ||||
\(963\) | 54.5482 | 0.0566440 | ||||||||
\(964\) | 8.54744 | − | 2.70857i | 0.00886664 | − | 0.00280971i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 4.05745 | + | 26.2358i | 0.00420026 | + | 0.0271592i | ||||
\(967\) | −1376.32 | −1.42329 | −0.711646 | − | 0.702539i | \(-0.752050\pi\) | ||||
−0.711646 | + | 0.702539i | \(0.752050\pi\) | |||||||
\(968\) | 1062.31 | + | 2142.46i | 1.09743 | + | 2.21328i | ||||
\(969\) | −400.851 | −0.413675 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 652.667i | − | 0.672159i | −0.941834 | − | 0.336080i | \(-0.890899\pi\) | ||
0.941834 | − | 0.336080i | \(-0.109101\pi\) | |||||||
\(972\) | 59.4408 | − | 18.8360i | 0.0611531 | − | 0.0193786i | ||||
\(973\) | − | 73.7053i | − | 0.0757506i | ||||||
\(974\) | −41.1490 | − | 266.072i | −0.0422474 | − | 0.273175i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −978.920 | + | 689.666i | −1.00299 | + | 0.706625i | ||||
\(977\) | − | 467.260i | − | 0.478260i | −0.970988 | − | 0.239130i | \(-0.923138\pi\) | ||
0.970988 | − | 0.239130i | \(-0.0768622\pi\) | |||||||
\(978\) | −87.6428 | − | 566.705i | −0.0896143 | − | 0.579453i | ||||
\(979\) | − | 1250.22i | − | 1.27703i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 470.525 | 0.479638 | ||||||||
\(982\) | 1495.84 | − | 231.336i | 1.52326 | − | 0.235577i | ||||
\(983\) | 1044.27 | 1.06233 | 0.531165 | − | 0.847268i | \(-0.321754\pi\) | ||||
0.531165 | + | 0.847268i | \(0.321754\pi\) | |||||||
\(984\) | 287.503 | + | 579.830i | 0.292178 | + | 0.589259i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −878.697 | + | 135.894i | −0.891174 | + | 0.137823i | ||||
\(987\) | −46.7185 | −0.0473339 | ||||||||
\(988\) | 19.7833 | − | 6.26905i | 0.0200236 | − | 0.00634519i | ||||
\(989\) | 1291.30 | 1.30566 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 1705.99i | − | 1.72148i | −0.509044 | − | 0.860740i | \(-0.670001\pi\) | ||
0.509044 | − | 0.860740i | \(-0.329999\pi\) | |||||||
\(992\) | 967.839 | − | 933.219i | 0.975644 | − | 0.940745i | ||||
\(993\) | 192.382i | 0.193738i | ||||||||
\(994\) | 25.6125 | − | 3.96106i | 0.0257671 | − | 0.00398497i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 38.8950 | − | 12.3253i | 0.0390512 | − | 0.0123748i | ||||
\(997\) | − | 1262.24i | − | 1.26604i | −0.774136 | − | 0.633020i | \(-0.781815\pi\) | ||
0.774136 | − | 0.633020i | \(-0.218185\pi\) | |||||||
\(998\) | 1397.30 | − | 216.097i | 1.40010 | − | 0.216530i | ||||
\(999\) | 264.756i | 0.265021i |
(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 | 300.3.f.c.199.10 | 16 | ||
3.2 | odd | 2 | 900.3.f.h.199.7 | 16 | |||
4.3 | odd | 2 | inner | 300.3.f.c.199.8 | 16 | ||
5.2 | odd | 4 | 300.3.c.e.151.2 | yes | 8 | ||
5.3 | odd | 4 | 300.3.c.g.151.7 | yes | 8 | ||
5.4 | even | 2 | inner | 300.3.f.c.199.7 | 16 | ||
12.11 | even | 2 | 900.3.f.h.199.9 | 16 | |||
15.2 | even | 4 | 900.3.c.t.451.7 | 8 | |||
15.8 | even | 4 | 900.3.c.n.451.2 | 8 | |||
15.14 | odd | 2 | 900.3.f.h.199.10 | 16 | |||
20.3 | even | 4 | 300.3.c.g.151.8 | yes | 8 | ||
20.7 | even | 4 | 300.3.c.e.151.1 | ✓ | 8 | ||
20.19 | odd | 2 | inner | 300.3.f.c.199.9 | 16 | ||
60.23 | odd | 4 | 900.3.c.n.451.1 | 8 | |||
60.47 | odd | 4 | 900.3.c.t.451.8 | 8 | |||
60.59 | even | 2 | 900.3.f.h.199.8 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
300.3.c.e.151.1 | ✓ | 8 | 20.7 | even | 4 | ||
300.3.c.e.151.2 | yes | 8 | 5.2 | odd | 4 | ||
300.3.c.g.151.7 | yes | 8 | 5.3 | odd | 4 | ||
300.3.c.g.151.8 | yes | 8 | 20.3 | even | 4 | ||
300.3.f.c.199.7 | 16 | 5.4 | even | 2 | inner | ||
300.3.f.c.199.8 | 16 | 4.3 | odd | 2 | inner | ||
300.3.f.c.199.9 | 16 | 20.19 | odd | 2 | inner | ||
300.3.f.c.199.10 | 16 | 1.1 | even | 1 | trivial | ||
900.3.c.n.451.1 | 8 | 60.23 | odd | 4 | |||
900.3.c.n.451.2 | 8 | 15.8 | even | 4 | |||
900.3.c.t.451.7 | 8 | 15.2 | even | 4 | |||
900.3.c.t.451.8 | 8 | 60.47 | odd | 4 | |||
900.3.f.h.199.7 | 16 | 3.2 | odd | 2 | |||
900.3.f.h.199.8 | 16 | 60.59 | even | 2 | |||
900.3.f.h.199.9 | 16 | 12.11 | even | 2 | |||
900.3.f.h.199.10 | 16 | 15.14 | odd | 2 |