Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [900,3,Mod(451,900)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(900, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("900.451");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 900 = 2^{2} \cdot 3^{2} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 900.c (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: | \(24.5232237924\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.4069419264.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 7x^{6} + 50x^{4} - 84x^{3} + 55x^{2} - 12x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{8} \) |
Twist minimal: | no (minimal twist has level 300) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 451.1 | ||
Root | \(1.65359 - 0.954702i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 900.451 |
Dual form | 900.3.c.n.451.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/900\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(451\) | \(577\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.97650 | − | 0.305673i | −0.988251 | − | 0.152836i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 3.81313 | + | 1.20833i | 0.953282 | + | 0.302082i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 0.329898i | − | 0.0471283i | −0.999722 | − | 0.0235641i | \(-0.992499\pi\) | ||
0.999722 | − | 0.0235641i | \(-0.00750139\pi\) | |||||||
\(8\) | −7.16731 | − | 3.55383i | −0.895913 | − | 0.444229i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 20.4920i | − | 1.86291i | −0.363861 | − | 0.931453i | \(-0.618542\pi\) | ||
0.363861 | − | 0.931453i | \(-0.381458\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.416712 | 0.0320548 | 0.0160274 | − | 0.999872i | \(-0.494898\pi\) | ||||
0.0160274 | + | 0.999872i | \(0.494898\pi\) | |||||||
\(14\) | −0.100841 | + | 0.652044i | −0.00720292 | + | 0.0465746i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 13.0799 | + | 9.21501i | 0.817493 | + | 0.575938i | ||||
\(17\) | −18.5884 | −1.09343 | −0.546717 | − | 0.837317i | \(-0.684123\pi\) | ||||
−0.546717 | + | 0.837317i | \(0.684123\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 12.4503i | − | 0.655281i | −0.944803 | − | 0.327640i | \(-0.893747\pi\) | ||
0.944803 | − | 0.327640i | \(-0.106253\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −6.26384 | + | 40.5024i | −0.284720 | + | 1.84102i | ||||
\(23\) | 23.2304i | 1.01002i | 0.863114 | + | 0.505008i | \(0.168511\pi\) | ||||
−0.863114 | + | 0.505008i | \(0.831489\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −0.823633 | − | 0.127378i | −0.0316782 | − | 0.00489914i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0.398624 | − | 1.25794i | 0.0142366 | − | 0.0449265i | ||||
\(29\) | 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 | \(0.237005\pi\) | ||||
−0.735377 | + | 0.677658i | \(0.762995\pi\) | |||||||
\(32\) | −23.0357 | − | 22.2117i | −0.719865 | − | 0.694115i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 36.7400 | + | 5.68197i | 1.08059 | + | 0.167117i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −50.9523 | −1.37709 | −0.688545 | − | 0.725194i | \(-0.741750\pi\) | ||||
−0.688545 | + | 0.725194i | \(0.741750\pi\) | |||||||
\(38\) | −3.80573 | + | 24.6081i | −0.100151 | + | 0.647582i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −46.7073 | −1.13920 | −0.569601 | − | 0.821921i | \(-0.692902\pi\) | ||||
−0.569601 | + | 0.821921i | \(0.692902\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 55.5866i | − | 1.29271i | −0.763036 | − | 0.646356i | \(-0.776292\pi\) | ||
0.763036 | − | 0.646356i | \(-0.223708\pi\) | |||||||
\(44\) | 24.7610 | − | 78.1385i | 0.562750 | − | 1.77588i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 7.10090 | − | 45.9149i | 0.154367 | − | 0.998151i | ||||
\(47\) | 81.7616i | 1.73961i | 0.493397 | + | 0.869804i | \(0.335755\pi\) | ||||
−0.493397 | + | 0.869804i | \(0.664245\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 48.8912 | 0.997779 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 1.58898 | + | 0.503524i | 0.0305572 | + | 0.00968316i | ||||
\(53\) | −29.9744 | −0.565554 | −0.282777 | − | 0.959186i | \(-0.591256\pi\) | ||||
−0.282777 | + | 0.959186i | \(0.591256\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −1.17240 | + | 2.36448i | −0.0209357 | + | 0.0422228i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −47.2713 | − | 7.31067i | −0.815023 | − | 0.126046i | ||||
\(59\) | 24.3311i | 0.412391i | 0.978511 | + | 0.206196i | \(0.0661083\pi\) | ||||
−0.978511 | + | 0.206196i | \(0.933892\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −74.8416 | −1.22691 | −0.613456 | − | 0.789729i | \(-0.710221\pi\) | ||||
−0.613456 | + | 0.789729i | \(0.710221\pi\) | |||||||
\(62\) | 12.8428 | − | 83.0424i | 0.207142 | − | 1.33939i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 38.7406 | + | 50.9428i | 0.605321 | + | 0.795981i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 72.8008i | − | 1.08658i | −0.839545 | − | 0.543290i | \(-0.817178\pi\) | ||
0.839545 | − | 0.543290i | \(-0.182822\pi\) | |||||||
\(68\) | −70.8799 | − | 22.4608i | −1.04235 | − | 0.330307i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 39.2803i | 0.553244i | 0.960979 | + | 0.276622i | \(0.0892150\pi\) | ||||
−0.960979 | + | 0.276622i | \(0.910785\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 46.5814 | 0.638101 | 0.319051 | − | 0.947738i | \(-0.396636\pi\) | ||||
0.319051 | + | 0.947738i | \(0.396636\pi\) | |||||||
\(74\) | 100.707 | + | 15.5747i | 1.36091 | + | 0.210469i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 15.0441 | − | 47.4747i | 0.197948 | − | 0.624667i | ||||
\(77\) | −6.76026 | −0.0877955 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 101.920i | − | 1.29012i | −0.764131 | − | 0.645062i | \(-0.776832\pi\) | ||
0.764131 | − | 0.645062i | \(-0.223168\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 92.3170 | + | 14.2771i | 1.12582 | + | 0.174112i | ||||
\(83\) | 5.88913i | 0.0709534i | 0.999371 | + | 0.0354767i | \(0.0112950\pi\) | ||||
−0.999371 | + | 0.0354767i | \(0.988705\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −16.9913 | + | 109.867i | −0.197574 | + | 1.27752i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −72.8250 | + | 146.872i | −0.827557 | + | 1.66900i | ||||
\(89\) | 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 | ||||||
\(92\) | −28.0699 | + | 88.5804i | −0.305108 | + | 0.962831i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 24.9923 | − | 161.602i | 0.265876 | − | 1.71917i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −95.5437 | −0.984987 | −0.492494 | − | 0.870316i | \(-0.663914\pi\) | ||||
−0.492494 | + | 0.870316i | \(0.663914\pi\) | |||||||
\(98\) | −96.6335 | − | 14.9447i | −0.986057 | − | 0.152497i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −162.675 | −1.61064 | −0.805322 | − | 0.592838i | \(-0.798008\pi\) | ||||
−0.805322 | + | 0.592838i | \(0.798008\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 158.196i | 1.53588i | 0.640521 | + | 0.767941i | \(0.278718\pi\) | ||||
−0.640521 | + | 0.767941i | \(0.721282\pi\) | |||||||
\(104\) | −2.98670 | − | 1.48092i | −0.0287183 | − | 0.0142397i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 59.2445 | + | 9.16236i | 0.558910 | + | 0.0864373i | ||||
\(107\) | − | 18.1827i | − | 0.169932i | −0.996384 | − | 0.0849660i | \(-0.972922\pi\) | ||
0.996384 | − | 0.0849660i | \(-0.0270782\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −156.842 | −1.43891 | −0.719457 | − | 0.694537i | \(-0.755609\pi\) | ||||
−0.719457 | + | 0.694537i | \(0.755609\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 3.04001 | − | 4.31503i | 0.0271430 | − | 0.0385270i | ||||
\(113\) | −98.7245 | −0.873668 | −0.436834 | − | 0.899542i | \(-0.643900\pi\) | ||||
−0.436834 | + | 0.899542i | \(0.643900\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 91.1972 | + | 28.8991i | 0.786183 | + | 0.249130i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 7.43735 | − | 48.0904i | 0.0630284 | − | 0.407546i | ||||
\(119\) | 6.13227i | 0.0515317i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −298.921 | −2.47042 | ||||||||
\(122\) | 147.925 | + | 22.8770i | 1.21250 | + | 0.187517i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −50.7676 | + | 160.208i | −0.409416 | + | 1.29200i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 27.0938i | 0.213337i | 0.994295 | + | 0.106669i | \(0.0340184\pi\) | ||||
−0.994295 | + | 0.106669i | \(0.965982\pi\) | |||||||
\(128\) | −60.9990 | − | 112.531i | −0.476555 | − | 0.879145i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 4.45811i | − | 0.0340314i | −0.999855 | − | 0.0170157i | \(-0.994583\pi\) | ||
0.999855 | − | 0.0170157i | \(-0.00541653\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −4.10734 | −0.0308822 | ||||||||
\(134\) | −22.2533 | + | 143.891i | −0.166069 | + | 1.07381i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 133.229 | + | 66.0600i | 0.979622 | + | 0.485735i | ||||
\(137\) | −181.700 | −1.32628 | −0.663139 | − | 0.748496i | \(-0.730776\pi\) | ||||
−0.663139 | + | 0.748496i | \(0.730776\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 223.419i | 1.60733i | 0.595083 | + | 0.803664i | \(0.297119\pi\) | ||||
−0.595083 | + | 0.803664i | \(0.702881\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 12.0069 | − | 77.6377i | 0.0845559 | − | 0.546744i | ||||
\(143\) | − | 8.53925i | − | 0.0597151i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −92.0683 | − | 14.2387i | −0.630604 | − | 0.0975251i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −194.288 | − | 61.5670i | −1.31275 | − | 0.415994i | ||||
\(149\) | −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 | \(-0.918920\pi\) | ||
0.967734 | − | 0.251974i | \(-0.0810797\pi\) | |||||||
\(152\) | −44.2464 | + | 89.2353i | −0.291095 | + | 0.587075i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 13.3617 | + | 2.06643i | 0.0867641 | + | 0.0134184i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −34.2940 | −0.218433 | −0.109217 | − | 0.994018i | \(-0.534834\pi\) | ||||
−0.109217 | + | 0.994018i | \(0.534834\pi\) | |||||||
\(158\) | −31.1541 | + | 201.445i | −0.197178 | + | 1.27497i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 7.66365 | 0.0476003 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 165.538i | − | 1.01557i | −0.861483 | − | 0.507786i | \(-0.830464\pi\) | ||
0.861483 | − | 0.507786i | \(-0.169536\pi\) | |||||||
\(164\) | −178.101 | − | 56.4377i | −1.08598 | − | 0.344132i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 1.80015 | − | 11.6399i | 0.0108443 | − | 0.0701198i | ||||
\(167\) | − | 83.6064i | − | 0.500637i | −0.968164 | − | 0.250319i | \(-0.919465\pi\) | ||
0.968164 | − | 0.250319i | \(-0.0805353\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −168.826 | −0.998972 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 67.1668 | − | 211.959i | 0.390505 | − | 1.23232i | ||||
\(173\) | 192.900 | 1.11503 | 0.557513 | − | 0.830168i | \(-0.311756\pi\) | ||||
0.557513 | + | 0.830168i | \(0.311756\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 188.834 | − | 268.033i | 1.07292 | − | 1.52291i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −120.587 | − | 18.6491i | −0.677452 | − | 0.104770i | ||||
\(179\) | − | 120.939i | − | 0.675637i | −0.941211 | − | 0.337819i | \(-0.890311\pi\) | ||
0.941211 | − | 0.337819i | \(-0.109689\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −107.583 | −0.594381 | −0.297191 | − | 0.954818i | \(-0.596050\pi\) | ||||
−0.297191 | + | 0.954818i | \(0.596050\pi\) | |||||||
\(182\) | −0.0420216 | + | 0.271715i | −0.000230888 | + | 0.00149294i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 82.5569 | − | 166.499i | 0.448679 | − | 0.904887i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 380.913i | 2.03697i | ||||||||
\(188\) | −98.7947 | + | 311.767i | −0.525504 | + | 1.65834i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 279.706i | 1.46443i | 0.681075 | + | 0.732214i | \(0.261513\pi\) | ||||
−0.681075 | + | 0.732214i | \(0.738487\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 102.534 | 0.531263 | 0.265632 | − | 0.964075i | \(-0.414420\pi\) | ||||
0.265632 | + | 0.964075i | \(0.414420\pi\) | |||||||
\(194\) | 188.842 | + | 29.2051i | 0.973415 | + | 0.150542i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 186.428 | + | 59.0765i | 0.951165 | + | 0.301411i | ||||
\(197\) | 38.9632 | 0.197783 | 0.0988913 | − | 0.995098i | \(-0.468470\pi\) | ||||
0.0988913 | + | 0.995098i | \(0.468470\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 147.646i | 0.741940i | 0.928645 | + | 0.370970i | \(0.120975\pi\) | ||||
−0.928645 | + | 0.370970i | \(0.879025\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 321.528 | + | 49.7254i | 1.59172 | + | 0.246165i | ||||
\(203\) | − | 7.89005i | − | 0.0388672i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 48.3562 | − | 312.674i | 0.234739 | − | 1.51784i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 5.45055 | + | 3.84001i | 0.0262046 | + | 0.0184616i | ||||
\(209\) | −255.132 | −1.22073 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 233.336i | 1.10586i | 0.833229 | + | 0.552928i | \(0.186490\pi\) | ||||
−0.833229 | + | 0.552928i | \(0.813510\pi\) | |||||||
\(212\) | −114.296 | − | 36.2189i | −0.539133 | − | 0.170844i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −5.55797 | + | 35.9382i | −0.0259718 | + | 0.167936i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 13.8606 | 0.0638737 | ||||||||
\(218\) | 309.998 | + | 47.9422i | 1.42201 | + | 0.219918i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −7.74600 | −0.0350498 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 82.7105i | 0.370899i | 0.982654 | + | 0.185450i | \(0.0593741\pi\) | ||||
−0.982654 | + | 0.185450i | \(0.940626\pi\) | |||||||
\(224\) | −7.32758 | + | 7.59941i | −0.0327124 | + | 0.0339260i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 195.129 | + | 30.1774i | 0.863403 | + | 0.133528i | ||||
\(227\) | − | 361.534i | − | 1.59266i | −0.604862 | − | 0.796330i | \(-0.706772\pi\) | ||
0.604862 | − | 0.796330i | \(-0.293228\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 121.818 | 0.531955 | 0.265977 | − | 0.963979i | \(-0.414305\pi\) | ||||
0.265977 | + | 0.963979i | \(0.414305\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −171.418 | − | 84.9957i | −0.738870 | − | 0.366361i | ||||
\(233\) | 136.615 | 0.586329 | 0.293164 | − | 0.956062i | \(-0.405292\pi\) | ||||
0.293164 | + | 0.956062i | \(0.405292\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −29.3999 | + | 92.7775i | −0.124576 | + | 0.393125i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 1.87447 | − | 12.1204i | 0.00787592 | − | 0.0509262i | ||||
\(239\) | − | 56.4632i | − | 0.236248i | −0.992999 | − | 0.118124i | \(-0.962312\pi\) | ||
0.992999 | − | 0.118124i | \(-0.0376880\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2.24158 | −0.00930117 | −0.00465059 | − | 0.999989i | \(-0.501480\pi\) | ||||
−0.00465059 | + | 0.999989i | \(0.501480\pi\) | |||||||
\(242\) | 590.818 | + | 91.3720i | 2.44140 | + | 0.377570i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −285.381 | − | 90.4331i | −1.16959 | − | 0.370627i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 5.18820i | − | 0.0210049i | ||||||
\(248\) | 149.314 | − | 301.133i | 0.602071 | − | 1.21425i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 395.809i | − | 1.57693i | −0.615081 | − | 0.788464i | \(-0.710877\pi\) | ||
0.615081 | − | 0.788464i | \(-0.289123\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 476.036 | 1.88157 | ||||||||
\(254\) | 8.28184 | − | 53.5510i | 0.0326057 | − | 0.210831i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 86.1671 | + | 241.063i | 0.336590 | + | 0.941651i | ||||
\(257\) | 109.778 | 0.427151 | 0.213576 | − | 0.976927i | \(-0.431489\pi\) | ||||
0.213576 | + | 0.976927i | \(0.431489\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 16.8091i | 0.0648998i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −1.36272 | + | 8.81147i | −0.00520124 | + | 0.0336316i | ||||
\(263\) | − | 327.702i | − | 1.24601i | −0.782216 | − | 0.623007i | \(-0.785911\pi\) | ||
0.782216 | − | 0.623007i | \(-0.214089\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 8.11816 | + | 1.25550i | 0.0305194 | + | 0.00471993i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 87.9672 | − | 277.599i | 0.328236 | − | 1.03582i | ||||
\(269\) | 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 | \(-0.791874\pi\) | ||
0.793750 | − | 0.608245i | \(-0.208126\pi\) | |||||||
\(272\) | −243.134 | − | 171.292i | −0.893875 | − | 0.629751i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 359.131 | + | 55.5408i | 1.31070 | + | 0.202704i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −304.124 | −1.09792 | −0.548960 | − | 0.835849i | \(-0.684976\pi\) | ||||
−0.548960 | + | 0.835849i | \(0.684976\pi\) | |||||||
\(278\) | 68.2930 | − | 441.588i | 0.245658 | − | 1.58844i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −240.099 | −0.854446 | −0.427223 | − | 0.904146i | \(-0.640508\pi\) | ||||
−0.427223 | + | 0.904146i | \(0.640508\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 86.6730i | − | 0.306265i | −0.988206 | − | 0.153133i | \(-0.951064\pi\) | ||
0.988206 | − | 0.153133i | \(-0.0489362\pi\) | |||||||
\(284\) | −47.4635 | + | 149.781i | −0.167125 | + | 0.527398i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −2.61022 | + | 16.8779i | −0.00912664 | + | 0.0590135i | ||||
\(287\) | 15.4086i | 0.0536886i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 56.5280 | 0.195599 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 177.621 | + | 56.2856i | 0.608290 | + | 0.192759i | ||||
\(293\) | 390.339 | 1.33222 | 0.666108 | − | 0.745855i | \(-0.267959\pi\) | ||||
0.666108 | + | 0.745855i | \(0.267959\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 365.191 | + | 181.076i | 1.23375 | + | 0.611743i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 244.824 | + | 37.8629i | 0.821557 | + | 0.127057i | ||||
\(299\) | 9.68038i | 0.0323759i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −18.3379 | −0.0609233 | ||||||||
\(302\) | −23.2605 | + | 150.404i | −0.0770216 | + | 0.498027i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 114.730 | − | 162.849i | 0.377401 | − | 0.535687i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 60.2318i | − | 0.196195i | −0.995177 | − | 0.0980973i | \(-0.968724\pi\) | ||
0.995177 | − | 0.0980973i | \(-0.0312757\pi\) | |||||||
\(308\) | −25.7777 | − | 8.16860i | −0.0836939 | − | 0.0265214i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 106.594i | 0.342747i | 0.985206 | + | 0.171373i | \(0.0548205\pi\) | ||||
−0.985206 | + | 0.171373i | \(0.945180\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 46.2243 | 0.147682 | 0.0738408 | − | 0.997270i | \(-0.476474\pi\) | ||||
0.0738408 | + | 0.997270i | \(0.476474\pi\) | |||||||
\(314\) | 67.7823 | + | 10.4828i | 0.215867 | + | 0.0333846i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 123.152 | − | 388.633i | 0.389723 | − | 1.22985i | ||||
\(317\) | −8.36780 | −0.0263969 | −0.0131984 | − | 0.999913i | \(-0.504201\pi\) | ||||
−0.0131984 | + | 0.999913i | \(0.504201\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 490.099i | − | 1.53636i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −15.1472 | − | 2.34257i | −0.0470411 | − | 0.00727507i | ||||
\(323\) | 231.432i | 0.716506i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −50.6006 | + | 327.187i | −0.155217 | + | 1.00364i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 334.765 | + | 165.990i | 1.02063 | + | 0.506066i | ||||
\(329\) | 26.9730 | 0.0819847 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 111.072i | 0.335564i | 0.985824 | + | 0.167782i | \(0.0536605\pi\) | ||||
−0.985824 | + | 0.167782i | \(0.946339\pi\) | |||||||
\(332\) | −7.11600 | + | 22.4560i | −0.0214337 | + | 0.0676386i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −25.5562 | + | 165.248i | −0.0765156 | + | 0.494755i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 231.853 | 0.687990 | 0.343995 | − | 0.938972i | \(-0.388220\pi\) | ||||
0.343995 | + | 0.938972i | \(0.388220\pi\) | |||||||
\(338\) | 333.686 | + | 51.6057i | 0.987236 | + | 0.152679i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 860.966 | 2.52483 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 32.2941i | − | 0.0941518i | ||||||
\(344\) | −197.546 | + | 398.406i | −0.574260 | + | 1.15816i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −381.266 | − | 58.9642i | −1.10193 | − | 0.170417i | ||||
\(347\) | 402.088i | 1.15875i | 0.815059 | + | 0.579377i | \(0.196704\pi\) | ||||
−0.815059 | + | 0.579377i | \(0.803296\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −163.284 | −0.467864 | −0.233932 | − | 0.972253i | \(-0.575159\pi\) | ||||
−0.233932 | + | 0.972253i | \(0.575159\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −455.161 | + | 472.046i | −1.29307 | + | 1.34104i | ||||
\(353\) | 175.851 | 0.498161 | 0.249081 | − | 0.968483i | \(-0.419872\pi\) | ||||
0.249081 | + | 0.968483i | \(0.419872\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 232.639 | + | 73.7201i | 0.653481 | + | 0.207079i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −36.9678 | + | 239.037i | −0.103262 | + | 0.667700i | ||||
\(359\) | 345.628i | 0.962753i | 0.876514 | + | 0.481377i | \(0.159863\pi\) | ||||
−0.876514 | + | 0.481377i | \(0.840137\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 205.989 | 0.570607 | ||||||||
\(362\) | 212.638 | + | 32.8852i | 0.587398 | + | 0.0908431i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0.166112 | − | 0.524200i | 0.000456351 | − | 0.00144011i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 728.998i | − | 1.98637i | −0.116546 | − | 0.993185i | \(-0.537182\pi\) | ||
0.116546 | − | 0.993185i | \(-0.462818\pi\) | |||||||
\(368\) | −214.068 | + | 303.851i | −0.581707 | + | 0.825682i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 9.88848i | 0.0266536i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 46.6749 | 0.125134 | 0.0625668 | − | 0.998041i | \(-0.480071\pi\) | ||||
0.0625668 | + | 0.998041i | \(0.480071\pi\) | |||||||
\(374\) | 116.435 | − | 752.875i | 0.311323 | − | 2.01303i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 290.567 | − | 586.010i | 0.772784 | − | 1.55854i | ||||
\(377\) | 9.96635 | 0.0264360 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 117.629i | − | 0.310368i | −0.987886 | − | 0.155184i | \(-0.950403\pi\) | ||
0.987886 | − | 0.155184i | \(-0.0495970\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 85.4985 | − | 552.839i | 0.223818 | − | 1.44722i | ||||
\(383\) | − | 251.669i | − | 0.657100i | −0.944487 | − | 0.328550i | \(-0.893440\pi\) | ||
0.944487 | − | 0.328550i | \(-0.106560\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −202.658 | − | 31.3418i | −0.525022 | − | 0.0811964i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −364.321 | − | 115.448i | −0.938970 | − | 0.297547i | ||||
\(389\) | −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 | ||||||
\(392\) | −350.418 | − | 173.751i | −0.893923 | − | 0.443242i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −77.0108 | − | 11.9100i | −0.195459 | − | 0.0302284i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 103.819 | 0.261508 | 0.130754 | − | 0.991415i | \(-0.458260\pi\) | ||||
0.130754 | + | 0.991415i | \(0.458260\pi\) | |||||||
\(398\) | 45.1314 | − | 291.823i | 0.113396 | − | 0.733224i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 121.598 | 0.303237 | 0.151618 | − | 0.988439i | \(-0.451551\pi\) | ||||
0.151618 | + | 0.988439i | \(0.451551\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 17.5081i | 0.0434444i | ||||||||
\(404\) | −620.301 | − | 196.565i | −1.53540 | − | 0.486546i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −2.41177 | + | 15.5947i | −0.00594033 | + | 0.0384106i | ||||
\(407\) | 1044.11i | 2.56539i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 182.788 | 0.446915 | 0.223457 | − | 0.974714i | \(-0.428266\pi\) | ||||
0.223457 | + | 0.974714i | \(0.428266\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −191.152 | + | 603.221i | −0.463962 | + | 1.46413i | ||||
\(413\) | 8.02677 | 0.0194353 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −9.59924 | − | 9.25587i | −0.0230751 | − | 0.0222497i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 504.269 | + | 77.9869i | 1.20638 | + | 0.186572i | ||||
\(419\) | 168.020i | 0.401003i | 0.979693 | + | 0.200502i | \(0.0642572\pi\) | ||||
−0.979693 | + | 0.200502i | \(0.935743\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 625.291 | 1.48525 | 0.742626 | − | 0.669706i | \(-0.233580\pi\) | ||||
0.742626 | + | 0.669706i | \(0.233580\pi\) | |||||||
\(422\) | 71.3244 | − | 461.189i | 0.169015 | − | 1.09286i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 214.836 | + | 106.524i | 0.506688 | + | 0.251236i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 24.6901i | 0.0578222i | ||||||||
\(428\) | 21.9707 | − | 69.3331i | 0.0513334 | − | 0.161993i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 133.413i | 0.309544i | 0.987950 | + | 0.154772i | \(0.0494643\pi\) | ||||
−0.987950 | + | 0.154772i | \(0.950536\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −706.716 | −1.63214 | −0.816069 | − | 0.577954i | \(-0.803851\pi\) | ||||
−0.816069 | + | 0.577954i | \(0.803851\pi\) | |||||||
\(434\) | −27.3955 | − | 4.23681i | −0.0631233 | − | 0.00976223i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −598.057 | − | 189.516i | −1.37169 | − | 0.434670i | ||||
\(437\) | 289.226 | 0.661844 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 507.488i | 1.15601i | 0.816033 | + | 0.578005i | \(0.196169\pi\) | ||||
−0.816033 | + | 0.578005i | \(0.803831\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 15.3100 | + | 2.36774i | 0.0346380 | + | 0.00535689i | ||||
\(443\) | 412.172i | 0.930410i | 0.885203 | + | 0.465205i | \(0.154019\pi\) | ||||
−0.885203 | + | 0.465205i | \(0.845981\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 25.2824 | − | 163.478i | 0.0566869 | − | 0.366542i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 16.8059 | − | 12.7804i | 0.0375132 | − | 0.0285277i | ||||
\(449\) | 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 | ||||||||
\(452\) | −376.449 | − | 119.291i | −0.832852 | − | 0.263919i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −110.511 | + | 714.573i | −0.243417 | + | 1.57395i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −472.873 | −1.03473 | −0.517367 | − | 0.855764i | \(-0.673088\pi\) | ||||
−0.517367 | + | 0.855764i | \(0.673088\pi\) | |||||||
\(458\) | −240.773 | − | 37.2364i | −0.525705 | − | 0.0813021i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −433.776 | −0.940946 | −0.470473 | − | 0.882414i | \(-0.655917\pi\) | ||||
−0.470473 | + | 0.882414i | \(0.655917\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 530.624i | − | 1.14606i | −0.819536 | − | 0.573028i | \(-0.805769\pi\) | ||
0.819536 | − | 0.573028i | \(-0.194231\pi\) | |||||||
\(464\) | 312.827 | + | 220.392i | 0.674196 | + | 0.474983i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −270.019 | − | 41.7594i | −0.579440 | − | 0.0896124i | ||||
\(467\) | − | 355.266i | − | 0.760741i | −0.924834 | − | 0.380370i | \(-0.875797\pi\) | ||
0.924834 | − | 0.380370i | \(-0.124203\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −24.0168 | −0.0512086 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 86.4686 | − | 174.388i | 0.183196 | − | 0.369467i | ||||
\(473\) | −1139.08 | −2.40820 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −7.40978 | + | 23.3831i | −0.0155668 | + | 0.0491242i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −17.2593 | + | 111.600i | −0.0361072 | + | 0.233472i | ||||
\(479\) | 548.640i | 1.14539i | 0.819770 | + | 0.572693i | \(0.194101\pi\) | ||||
−0.819770 | + | 0.572693i | \(0.805899\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −21.2324 | −0.0441423 | ||||||||
\(482\) | 4.43050 | + | 0.685191i | 0.00919190 | + | 0.00142156i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −1139.82 | − | 361.194i | −2.35501 | − | 0.746269i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 134.618i | − | 0.276422i | −0.990403 | − | 0.138211i | \(-0.955865\pi\) | ||
0.990403 | − | 0.138211i | \(-0.0441352\pi\) | |||||||
\(488\) | 536.412 | + | 265.974i | 1.09921 | + | 0.545029i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 756.810i | − | 1.54136i | −0.637220 | − | 0.770682i | \(-0.719916\pi\) | ||
0.637220 | − | 0.770682i | \(-0.280084\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −444.572 | −0.901768 | ||||||||
\(494\) | −1.58589 | + | 10.2545i | −0.00321031 | + | 0.0207581i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −387.167 | + | 549.549i | −0.780579 | + | 1.10796i | ||||
\(497\) | 12.9585 | 0.0260734 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 706.956i | − | 1.41675i | −0.705838 | − | 0.708373i | \(-0.749430\pi\) | ||
0.705838 | − | 0.708373i | \(-0.250570\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −120.988 | + | 782.318i | −0.241012 | + | 1.55840i | ||||
\(503\) | − | 100.567i | − | 0.199935i | −0.994991 | − | 0.0999673i | \(-0.968126\pi\) | ||
0.994991 | − | 0.0999673i | \(-0.0318738\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −940.887 | − | 145.511i | −1.85946 | − | 0.287572i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −32.7382 | + | 103.312i | −0.0644452 | + | 0.203370i | ||||
\(509\) | −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 | ||||||
\(512\) | −96.6232 | − | 502.800i | −0.188717 | − | 0.982031i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −216.976 | − | 33.5561i | −0.422133 | − | 0.0652843i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1675.46 | 3.24073 | ||||||||
\(518\) | 5.13807 | − | 33.2231i | 0.00991906 | − | 0.0641373i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −117.708 | −0.225926 | −0.112963 | − | 0.993599i | \(-0.536034\pi\) | ||||
−0.112963 | + | 0.993599i | \(0.536034\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 617.411i | 1.18052i | 0.807214 | + | 0.590259i | \(0.200974\pi\) | ||||
−0.807214 | + | 0.590259i | \(0.799026\pi\) | |||||||
\(524\) | 5.38686 | − | 16.9994i | 0.0102803 | − | 0.0324415i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −100.170 | + | 647.704i | −0.190437 | + | 1.23138i | ||||
\(527\) | − | 780.988i | − | 1.48195i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −10.6508 | −0.0201338 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −15.6618 | − | 4.96301i | −0.0294395 | − | 0.00932896i | ||||
\(533\) | −19.4635 | −0.0365169 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −258.722 | + | 521.786i | −0.482690 | + | 0.973481i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −257.009 | − | 39.7474i | −0.477713 | − | 0.0738799i | ||||
\(539\) | − | 1001.88i | − | 1.85877i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 352.762 | 0.652056 | 0.326028 | − | 0.945360i | \(-0.394290\pi\) | ||||
0.326028 | + | 0.945360i | \(0.394290\pi\) | |||||||
\(542\) | −100.771 | + | 651.591i | −0.185924 | + | 1.20220i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 428.196 | + | 412.879i | 0.787125 | + | 0.758969i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 295.110i | 0.539507i | 0.962929 | + | 0.269753i | \(0.0869422\pi\) | ||||
−0.962929 | + | 0.269753i | \(0.913058\pi\) | |||||||
\(548\) | −692.846 | − | 219.553i | −1.26432 | − | 0.400644i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 297.770i | − | 0.540418i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −33.6231 | −0.0608013 | ||||||||
\(554\) | 601.102 | + | 92.9624i | 1.08502 | + | 0.167802i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −269.963 | + | 851.924i | −0.485545 | + | 1.53224i | ||||
\(557\) | 31.8538 | 0.0571882 | 0.0285941 | − | 0.999591i | \(-0.490897\pi\) | ||||
0.0285941 | + | 0.999591i | \(0.490897\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 23.1636i | − | 0.0414376i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 474.557 | + | 73.3919i | 0.844408 | + | 0.130591i | ||||
\(563\) | 906.668i | 1.61042i | 0.592988 | + | 0.805211i | \(0.297948\pi\) | ||||
−0.592988 | + | 0.805211i | \(0.702052\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −26.4936 | + | 171.310i | −0.0468085 | + | 0.302667i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 139.596 | − | 281.534i | 0.245767 | − | 0.495659i | ||||
\(569\) | 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 | \(0.0747995\pi\) | ||||
−0.972517 | + | 0.232833i | \(0.925200\pi\) | |||||||
\(572\) | 10.3182 | − | 32.5613i | 0.0180388 | − | 0.0569253i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 4.71000 | − | 30.4552i | 0.00820557 | − | 0.0530578i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −138.097 | −0.239336 | −0.119668 | − | 0.992814i | \(-0.538183\pi\) | ||||
−0.119668 | + | 0.992814i | \(0.538183\pi\) | |||||||
\(578\) | −111.728 | − | 17.2791i | −0.193301 | − | 0.0298946i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1.94281 | 0.00334391 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 614.234i | 1.05358i | ||||||||
\(584\) | −333.863 | − | 165.542i | −0.571683 | − | 0.283463i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −771.507 | − | 119.316i | −1.31656 | − | 0.203611i | ||||
\(587\) | − | 648.473i | − | 1.10472i | −0.833604 | − | 0.552362i | \(-0.813727\pi\) | ||
0.833604 | − | 0.552362i | \(-0.186273\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 523.098 | 0.888113 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −666.451 | − | 469.526i | −1.12576 | − | 0.793118i | ||||
\(593\) | −350.392 | −0.590880 | −0.295440 | − | 0.955361i | \(-0.595466\pi\) | ||||
−0.295440 | + | 0.955361i | \(0.595466\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −472.322 | − | 149.672i | −0.792486 | − | 0.251128i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 2.95903 | − | 19.1333i | 0.00494821 | − | 0.0319955i | ||||
\(599\) | − | 276.745i | − | 0.462012i | −0.972952 | − | 0.231006i | \(-0.925798\pi\) | ||
0.972952 | − | 0.231006i | \(-0.0742017\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 815.487 | 1.35688 | 0.678442 | − | 0.734654i | \(-0.262656\pi\) | ||||
0.678442 | + | 0.734654i | \(0.262656\pi\) | |||||||
\(602\) | 36.2449 | + | 5.60540i | 0.0602075 | + | 0.00931130i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 91.9490 | − | 290.164i | 0.152233 | − | 0.480405i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 247.049i | − | 0.407001i | −0.979075 | − | 0.203500i | \(-0.934768\pi\) | ||
0.979075 | − | 0.203500i | \(-0.0652318\pi\) | |||||||
\(608\) | −276.543 | + | 286.802i | −0.454840 | + | 0.471713i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 34.0710i | 0.0557627i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −1005.15 | −1.63972 | −0.819862 | − | 0.572561i | \(-0.805950\pi\) | ||||
−0.819862 | + | 0.572561i | \(0.805950\pi\) | |||||||
\(614\) | −18.4112 | + | 119.048i | −0.0299857 | + | 0.193890i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 48.4528 | + | 24.0248i | 0.0786572 | + | 0.0390013i | ||||
\(617\) | 533.282 | 0.864314 | 0.432157 | − | 0.901798i | \(-0.357753\pi\) | ||||
0.432157 | + | 0.901798i | \(0.357753\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 1136.85i | 1.83659i | 0.395900 | + | 0.918294i | \(0.370433\pi\) | ||||
−0.395900 | + | 0.918294i | \(0.629567\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 32.5830 | − | 210.684i | 0.0523842 | − | 0.338720i | ||||
\(623\) | − | 20.1271i | − | 0.0323067i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −91.3625 | − | 14.1295i | −0.145946 | − | 0.0225711i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −130.768 | − | 41.4384i | −0.208229 | − | 0.0659847i | ||||
\(629\) | 947.121 | 1.50576 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 936.738i | − | 1.48453i | −0.670107 | − | 0.742265i | \(-0.733752\pi\) | ||
0.670107 | − | 0.742265i | \(-0.266248\pi\) | |||||||
\(632\) | −362.206 | + | 730.490i | −0.573110 | + | 1.15584i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 16.5390 | + | 2.55781i | 0.0260867 | + | 0.00403440i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 20.3735 | 0.0319836 | ||||||||
\(638\) | −149.810 | + | 968.682i | −0.234812 | + | 1.51831i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −214.558 | −0.334723 | −0.167362 | − | 0.985896i | \(-0.553525\pi\) | ||||
−0.167362 | + | 0.985896i | \(0.553525\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 786.394i | − | 1.22301i | −0.791241 | − | 0.611504i | \(-0.790565\pi\) | ||
0.791241 | − | 0.611504i | \(-0.209435\pi\) | |||||||
\(644\) | 29.2225 | + | 9.26020i | 0.0453765 | + | 0.0143792i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 70.7424 | − | 457.425i | 0.109508 | − | 0.708088i | ||||
\(647\) | 316.550i | 0.489258i | 0.969617 | + | 0.244629i | \(0.0786661\pi\) | ||||
−0.969617 | + | 0.244629i | \(0.921334\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 498.592 | 0.768246 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 200.024 | − | 631.219i | 0.306786 | − | 0.968127i | ||||
\(653\) | −516.391 | −0.790797 | −0.395399 | − | 0.918510i | \(-0.629394\pi\) | ||||
−0.395399 | + | 0.918510i | \(0.629394\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −610.926 | − | 430.408i | −0.931290 | − | 0.656110i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −53.3121 | − | 8.24491i | −0.0810215 | − | 0.0125303i | ||||
\(659\) | − | 285.118i | − | 0.432653i | −0.976321 | − | 0.216326i | \(-0.930592\pi\) | ||
0.976321 | − | 0.216326i | \(-0.0694076\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −391.847 | −0.592809 | −0.296405 | − | 0.955062i | \(-0.595788\pi\) | ||||
−0.296405 | + | 0.955062i | \(0.595788\pi\) | |||||||
\(662\) | 33.9516 | − | 219.534i | 0.0512865 | − | 0.331622i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 20.9290 | − | 42.2092i | 0.0315196 | − | 0.0635681i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 555.593i | 0.832973i | ||||||||
\(668\) | 101.024 | − | 318.802i | 0.151233 | − | 0.477248i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1533.65i | 2.28562i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1213.59 | −1.80325 | −0.901626 | − | 0.432517i | \(-0.857625\pi\) | ||||
−0.901626 | + | 0.432517i | \(0.857625\pi\) | |||||||
\(674\) | −458.257 | − | 70.8711i | −0.679907 | − | 0.105150i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −643.756 | − | 203.997i | −0.952303 | − | 0.301771i | ||||
\(677\) | −251.863 | −0.372028 | −0.186014 | − | 0.982547i | \(-0.559557\pi\) | ||||
−0.186014 | + | 0.982547i | \(0.559557\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 31.5197i | 0.0464207i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −1701.70 | − | 263.174i | −2.49517 | − | 0.385886i | ||||
\(683\) | − | 664.793i | − | 0.973342i | −0.873585 | − | 0.486671i | \(-0.838211\pi\) | ||
0.873585 | − | 0.486671i | \(-0.161789\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −9.87143 | + | 63.8293i | −0.0143898 | + | 0.0930457i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 512.231 | − | 727.067i | 0.744522 | − | 1.05678i | ||||
\(689\) | −12.4907 | −0.0181287 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 654.347i | − | 0.946957i | −0.880805 | − | 0.473479i | \(-0.842998\pi\) | ||
0.880805 | − | 0.473479i | \(-0.157002\pi\) | |||||||
\(692\) | 735.551 | + | 233.086i | 1.06293 | + | 0.336829i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 122.907 | − | 794.728i | 0.177100 | − | 1.14514i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 868.213 | 1.24564 | ||||||||
\(698\) | 322.732 | + | 49.9117i | 0.462367 | + | 0.0715067i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1266.25 | 1.80635 | 0.903174 | − | 0.429275i | \(-0.141231\pi\) | ||||
0.903174 | + | 0.429275i | \(0.141231\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 634.373i | 0.902380i | ||||||||
\(704\) | 1043.92 | − | 793.870i | 1.48284 | − | 1.12766i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −347.570 | − | 53.7529i | −0.492309 | − | 0.0761372i | ||||
\(707\) | 53.6661i | 0.0759068i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −493.220 | −0.695656 | −0.347828 | − | 0.937558i | \(-0.613081\pi\) | ||||
−0.347828 | + | 0.937558i | \(0.613081\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −437.278 | − | 216.819i | −0.614154 | − | 0.304522i | ||||
\(713\) | −976.020 | −1.36889 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 146.134 | − | 461.156i | 0.204098 | − | 0.644073i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 105.649 | − | 683.135i | 0.147144 | − | 0.951442i | ||||
\(719\) | − | 60.3910i | − | 0.0839930i | −0.999118 | − | 0.0419965i | \(-0.986628\pi\) | ||
0.999118 | − | 0.0419965i | \(-0.0133718\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 52.1884 | 0.0723834 | ||||||||
\(722\) | −407.138 | − | 62.9653i | −0.563904 | − | 0.0872096i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −410.228 | − | 129.995i | −0.566613 | − | 0.179552i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 994.690i | 1.36821i | 0.729383 | + | 0.684106i | \(0.239807\pi\) | ||||
−0.729383 | + | 0.684106i | \(0.760193\pi\) | |||||||
\(728\) | −0.488554 | + | 0.985307i | −0.000671090 | + | 0.00135344i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1033.27i | 1.41350i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1167.65 | 1.59298 | 0.796488 | − | 0.604654i | \(-0.206689\pi\) | ||||
0.796488 | + | 0.604654i | \(0.206689\pi\) | |||||||
\(734\) | −222.835 | + | 1440.87i | −0.303590 | + | 1.96303i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 515.986 | − | 535.127i | 0.701067 | − | 0.727075i | ||||
\(737\) | −1491.83 | −2.02420 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 79.9863i | − | 0.108236i | −0.998535 | − | 0.0541179i | \(-0.982765\pi\) | ||
0.998535 | − | 0.0541179i | \(-0.0172347\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 3.02264 | − | 19.5446i | 0.00407364 | − | 0.0263405i | ||||
\(743\) | − | 402.122i | − | 0.541214i | −0.962690 | − | 0.270607i | \(-0.912776\pi\) | ||
0.962690 | − | 0.270607i | \(-0.0872244\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −92.2530 | − | 14.2672i | −0.123664 | − | 0.0191250i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −460.267 | + | 1452.47i | −0.615330 | + | 1.94180i | ||||
\(749\) | −5.99844 | −0.00800860 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 58.7486i | − | 0.0782271i | −0.999235 | − | 0.0391136i | \(-0.987547\pi\) | ||
0.999235 | − | 0.0391136i | \(-0.0124534\pi\) | |||||||
\(752\) | −753.434 | + | 1069.43i | −1.00191 | + | 1.42212i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −19.6985 | − | 3.04644i | −0.0261254 | − | 0.00404038i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1040.91 | −1.37504 | −0.687522 | − | 0.726164i | \(-0.741301\pi\) | ||||
−0.687522 | + | 0.726164i | \(0.741301\pi\) | |||||||
\(758\) | −35.9561 | + | 232.495i | −0.0474355 | + | 0.306721i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −750.095 | −0.985670 | −0.492835 | − | 0.870123i | \(-0.664039\pi\) | ||||
−0.492835 | + | 0.870123i | \(0.664039\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 51.7417i | 0.0678135i | ||||||||
\(764\) | −337.976 | + | 1066.55i | −0.442377 | + | 1.39601i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −76.9285 | + | 497.425i | −0.100429 | + | 0.649380i | ||||
\(767\) | 10.1391i | 0.0132191i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1065.98 | 1.38619 | 0.693094 | − | 0.720847i | \(-0.256247\pi\) | ||||
0.693094 | + | 0.720847i | \(0.256247\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 390.975 | + | 123.894i | 0.506444 | + | 0.160485i | ||||
\(773\) | 947.271 | 1.22545 | 0.612724 | − | 0.790297i | \(-0.290074\pi\) | ||||
0.612724 | + | 0.790297i | \(0.290074\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 684.791 | + | 339.546i | 0.882463 | + | 0.437560i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 705.393 | + | 109.092i | 0.906675 | + | 0.140220i | ||||
\(779\) | 581.521i | 0.746497i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 804.931 | 1.03064 | ||||||||
\(782\) | −131.994 | + | 853.484i | −0.168791 | + | 1.09141i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 639.491 | + | 450.533i | 0.815678 | + | 0.574659i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 11.5874i | − | 0.0147236i | −0.999973 | − | 0.00736178i | \(-0.997657\pi\) | ||
0.999973 | − | 0.00736178i | \(-0.00234335\pi\) | |||||||
\(788\) | 148.572 | + | 47.0803i | 0.188543 | + | 0.0597465i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 32.5690i | 0.0411744i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −31.1874 | −0.0393284 | ||||||||
\(794\) | −205.198 | − | 31.7345i | −0.258436 | − | 0.0399679i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −178.405 | + | 562.994i | −0.224127 | + | 0.707278i | ||||
\(797\) | 780.220 | 0.978946 | 0.489473 | − | 0.872018i | \(-0.337189\pi\) | ||||
0.489473 | + | 0.872018i | \(0.337189\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 1519.82i | − | 1.90215i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −240.339 | − | 37.1692i | −0.299674 | − | 0.0463457i | ||||
\(803\) | − | 954.545i | − | 1.18872i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 5.35175 | − | 34.6048i | 0.00663989 | − | 0.0429340i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 1165.94 | + | 578.120i | 1.44300 | + | 0.715495i | ||||
\(809\) | 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 | \(-0.938940\pi\) | ||
0.981658 | − | 0.190651i | \(-0.0610599\pi\) | |||||||
\(812\) | 9.53376 | − | 30.0858i | 0.0117411 | − | 0.0370514i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 319.157 | − | 2063.69i | 0.392085 | − | 2.53525i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −692.072 | −0.847089 | ||||||||
\(818\) | −361.281 | − | 55.8734i | −0.441664 | − | 0.0683049i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1156.76 | 1.40897 | 0.704483 | − | 0.709721i | \(-0.251179\pi\) | ||||
0.704483 | + | 0.709721i | \(0.251179\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1441.89i | 1.75200i | 0.482314 | + | 0.875998i | \(0.339796\pi\) | ||||
−0.482314 | + | 0.875998i | \(0.660204\pi\) | |||||||
\(824\) | 562.201 | − | 1133.84i | 0.682283 | − | 1.37602i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −15.8649 | − | 2.45357i | −0.0192069 | − | 0.00297042i | ||||
\(827\) | 367.599i | 0.444497i | 0.974990 | + | 0.222249i | \(0.0713397\pi\) | ||||
−0.974990 | + | 0.222249i | \(0.928660\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 172.743 | 0.208375 | 0.104188 | − | 0.994558i | \(-0.466776\pi\) | ||||
0.104188 | + | 0.994558i | \(0.466776\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 16.1437 | + | 21.2285i | 0.0194034 | + | 0.0255150i | ||||
\(833\) | −908.808 | −1.09101 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −972.850 | − | 308.283i | −1.16370 | − | 0.368759i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 51.3593 | − | 332.093i | 0.0612879 | − | 0.396292i | ||||
\(839\) | − | 1083.17i | − | 1.29103i | −0.763748 | − | 0.645514i | \(-0.776643\pi\) | ||
0.763748 | − | 0.645514i | \(-0.223357\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −268.994 | −0.319850 | ||||||||
\(842\) | −1235.89 | − | 191.135i | −1.46780 | − | 0.227001i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −281.946 | + | 889.739i | −0.334059 | + | 1.05419i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 98.6133i | 0.116427i | ||||||||
\(848\) | −392.062 | − | 276.214i | −0.462337 | − | 0.325724i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 1183.64i | − | 1.39088i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1218.00 | 1.42790 | 0.713951 | − | 0.700196i | \(-0.246904\pi\) | ||||
0.713951 | + | 0.700196i | \(0.246904\pi\) | |||||||
\(854\) | 7.54709 | − | 48.8000i | 0.00883734 | − | 0.0571429i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −64.6184 | + | 130.321i | −0.0754888 | + | 0.152244i | ||||
\(857\) | 207.055 | 0.241604 | 0.120802 | − | 0.992677i | \(-0.461453\pi\) | ||||
0.120802 | + | 0.992677i | \(0.461453\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1186.36i | 1.38109i | 0.723290 | + | 0.690544i | \(0.242629\pi\) | ||||
−0.723290 | + | 0.690544i | \(0.757371\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 40.7809 | − | 263.692i | 0.0473096 | − | 0.305907i | ||||
\(863\) | 885.953i | 1.02660i | 0.858210 | + | 0.513298i | \(0.171577\pi\) | ||||
−0.858210 | + | 0.513298i | \(0.828423\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 1396.83 | + | 216.024i | 1.61296 | + | 0.249450i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 52.8522 | + | 16.7481i | 0.0608897 | + | 0.0192951i | ||||
\(869\) | −2088.54 | −2.40338 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 30.3370i | − | 0.0348301i | ||||||
\(872\) | 1124.13 | + | 557.389i | 1.28914 | + | 0.639207i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −571.656 | − | 88.4086i | −0.654069 | − | 0.101154i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 643.339 | 0.733567 | 0.366784 | − | 0.930306i | \(-0.380459\pi\) | ||||
0.366784 | + | 0.930306i | \(0.380459\pi\) | |||||||
\(878\) | 155.125 | − | 1003.05i | 0.176680 | − | 1.14243i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −353.918 | −0.401723 | −0.200861 | − | 0.979620i | \(-0.564374\pi\) | ||||
−0.200861 | + | 0.979620i | \(0.564374\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 1093.51i | − | 1.23840i | −0.785233 | − | 0.619200i | \(-0.787457\pi\) | ||
0.785233 | − | 0.619200i | \(-0.212543\pi\) | |||||||
\(884\) | −29.5365 | − | 9.35971i | −0.0334123 | − | 0.0105879i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 125.990 | − | 814.659i | 0.142201 | − | 0.919479i | ||||
\(887\) | − | 520.234i | − | 0.586510i | −0.956034 | − | 0.293255i | \(-0.905262\pi\) | ||
0.956034 | − | 0.293255i | \(-0.0947384\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 8.93819 | 0.0100542 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −99.9413 | + | 315.386i | −0.112042 | + | 0.353571i | ||||
\(893\) | 1017.96 | 1.13993 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −37.1236 | + | 20.1234i | −0.0414326 | + | 0.0224592i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −1598.23 | − | 247.172i | −1.77977 | − | 0.275248i | ||||
\(899\) | 1004.85i | 1.11775i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 557.175 | 0.618397 | ||||||||
\(902\) | 292.567 | − | 1891.76i | 0.324354 | − | 2.09729i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 707.588 | + | 350.850i | 0.782730 | + | 0.388109i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 567.834i | − | 0.626057i | −0.949744 | − | 0.313029i | \(-0.898656\pi\) | ||
0.949744 | − | 0.313029i | \(-0.101344\pi\) | |||||||
\(908\) | 436.851 | − | 1378.58i | 0.481114 | − | 1.51825i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 1180.19i | − | 1.29549i | −0.761858 | − | 0.647744i | \(-0.775713\pi\) | ||
0.761858 | − | 0.647744i | \(-0.224287\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 120.680 | 0.132180 | ||||||||
\(914\) | 934.635 | + | 144.545i | 1.02258 | + | 0.158145i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 464.506 | + | 147.196i | 0.507103 | + | 0.160694i | ||||
\(917\) | −1.47072 | −0.00160384 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 54.5449i | 0.0593524i | 0.999560 | + | 0.0296762i | \(0.00944761\pi\) | ||||
−0.999560 | + | 0.0296762i | \(0.990552\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 857.360 | + | 132.594i | 0.929892 | + | 0.143811i | ||||
\(923\) | 16.3686i | 0.0177341i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −162.197 | + | 1048.78i | −0.175159 | + | 1.13259i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −550.936 | − | 531.228i | −0.593681 | − | 0.572444i | ||||
\(929\) | −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 | ||||||
\(932\) | 520.929 | + | 165.075i | 0.558937 | + | 0.177119i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −108.595 | + | 702.184i | −0.116269 | + | 0.751803i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 335.374 | 0.357923 | 0.178962 | − | 0.983856i | \(-0.442726\pi\) | ||||
0.178962 | + | 0.983856i | \(0.442726\pi\) | |||||||
\(938\) | 47.4694 | + | 7.34130i | 0.0506070 | + | 0.00782654i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −709.182 | −0.753647 | −0.376823 | − | 0.926285i | \(-0.622984\pi\) | ||||
−0.376823 | + | 0.926285i | \(0.622984\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 1085.03i | − | 1.15061i | ||||||
\(944\) | −224.211 | + | 318.248i | −0.237512 | + | 0.337127i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 2251.39 | + | 348.186i | 2.37991 | + | 0.368061i | ||||
\(947\) | − | 992.486i | − | 1.04803i | −0.851708 | − | 0.524016i | \(-0.824433\pi\) | ||
0.851708 | − | 0.524016i | \(-0.175567\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 19.4110 | 0.0204542 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 21.7930 | − | 43.9518i | 0.0228919 | − | 0.0461679i | ||||
\(953\) | 1438.16 | 1.50908 | 0.754542 | − | 0.656251i | \(-0.227859\pi\) | ||||
0.754542 | + | 0.656251i | \(0.227859\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 68.2260 | − | 215.301i | 0.0713661 | − | 0.225211i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 167.704 | − | 1084.39i | 0.175057 | − | 1.13193i | ||||
\(959\) | 59.9425i | 0.0625052i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −804.245 | −0.836883 | ||||||||
\(962\) | 41.9660 | + | 6.49018i | 0.0436237 | + | 0.00674655i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −8.54744 | − | 2.70857i | −0.00886664 | − | 0.00280971i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 1376.32i | − | 1.42329i | −0.702539 | − | 0.711646i | \(-0.747950\pi\) | ||
0.702539 | − | 0.711646i | \(-0.252050\pi\) | |||||||
\(968\) | 2142.46 | + | 1062.31i | 2.21328 | + | 1.09743i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 652.667i | − | 0.672159i | −0.941834 | − | 0.336080i | \(-0.890899\pi\) | ||
0.941834 | − | 0.336080i | \(-0.109101\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 73.7053 | 0.0757506 | ||||||||
\(974\) | −41.1490 | + | 266.072i | −0.0422474 | + | 0.273175i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −978.920 | − | 689.666i | −1.00299 | − | 0.706625i | ||||
\(977\) | 467.260 | 0.478260 | 0.239130 | − | 0.970988i | \(-0.423138\pi\) | ||||
0.239130 | + | 0.970988i | \(0.423138\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 1250.22i | − | 1.27703i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −231.336 | + | 1495.84i | −0.235577 | + | 1.52326i | ||||
\(983\) | 1044.27i | 1.06233i | 0.847268 | + | 0.531165i | \(0.178246\pi\) | ||||
−0.847268 | + | 0.531165i | \(0.821754\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 878.697 | + | 135.894i | 0.891174 | + | 0.137823i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 6.26905 | − | 19.7833i | 0.00634519 | − | 0.0200236i | ||||
\(989\) | 1291.30 | 1.30566 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1705.99i | 1.72148i | 0.509044 | + | 0.860740i | \(0.329999\pi\) | ||||
−0.509044 | + | 0.860740i | \(0.670001\pi\) | |||||||
\(992\) | 933.219 | − | 967.839i | 0.940745 | − | 0.975644i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −25.6125 | − | 3.96106i | −0.0257671 | − | 0.00398497i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −1262.24 | −1.26604 | −0.633020 | − | 0.774136i | \(-0.718185\pi\) | ||||
−0.633020 | + | 0.774136i | \(0.718185\pi\) | |||||||
\(998\) | −216.097 | + | 1397.30i | −0.216530 | + | 1.40010i | ||||
\(999\) | 0 | 0 |
(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 | 900.3.c.n.451.1 | 8 | ||
3.2 | odd | 2 | 300.3.c.g.151.8 | yes | 8 | ||
4.3 | odd | 2 | inner | 900.3.c.n.451.2 | 8 | ||
5.2 | odd | 4 | 900.3.f.h.199.9 | 16 | |||
5.3 | odd | 4 | 900.3.f.h.199.8 | 16 | |||
5.4 | even | 2 | 900.3.c.t.451.8 | 8 | |||
12.11 | even | 2 | 300.3.c.g.151.7 | yes | 8 | ||
15.2 | even | 4 | 300.3.f.c.199.8 | 16 | |||
15.8 | even | 4 | 300.3.f.c.199.9 | 16 | |||
15.14 | odd | 2 | 300.3.c.e.151.1 | ✓ | 8 | ||
20.3 | even | 4 | 900.3.f.h.199.10 | 16 | |||
20.7 | even | 4 | 900.3.f.h.199.7 | 16 | |||
20.19 | odd | 2 | 900.3.c.t.451.7 | 8 | |||
60.23 | odd | 4 | 300.3.f.c.199.7 | 16 | |||
60.47 | odd | 4 | 300.3.f.c.199.10 | 16 | |||
60.59 | even | 2 | 300.3.c.e.151.2 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
300.3.c.e.151.1 | ✓ | 8 | 15.14 | odd | 2 | ||
300.3.c.e.151.2 | yes | 8 | 60.59 | even | 2 | ||
300.3.c.g.151.7 | yes | 8 | 12.11 | even | 2 | ||
300.3.c.g.151.8 | yes | 8 | 3.2 | odd | 2 | ||
300.3.f.c.199.7 | 16 | 60.23 | odd | 4 | |||
300.3.f.c.199.8 | 16 | 15.2 | even | 4 | |||
300.3.f.c.199.9 | 16 | 15.8 | even | 4 | |||
300.3.f.c.199.10 | 16 | 60.47 | odd | 4 | |||
900.3.c.n.451.1 | 8 | 1.1 | even | 1 | trivial | ||
900.3.c.n.451.2 | 8 | 4.3 | odd | 2 | inner | ||
900.3.c.t.451.7 | 8 | 20.19 | odd | 2 | |||
900.3.c.t.451.8 | 8 | 5.4 | even | 2 | |||
900.3.f.h.199.7 | 16 | 20.7 | even | 4 | |||
900.3.f.h.199.8 | 16 | 5.3 | odd | 4 | |||
900.3.f.h.199.9 | 16 | 5.2 | odd | 4 | |||
900.3.f.h.199.10 | 16 | 20.3 | even | 4 |