Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [900,3,Mod(199,900)]
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, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("900.199");
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.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: | \(24.5232237924\) |
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: | \( x^{16} - 4 x^{15} + 8 x^{14} - 14 x^{13} + 23 x^{12} - 26 x^{11} + 18 x^{10} - 10 x^{9} + 9 x^{8} - 20 x^{7} + 72 x^{6} - 208 x^{5} + 368 x^{4} - 448 x^{3} + 512 x^{2} - 512 x + 256 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{20}\cdot 5^{4} \) |
Twist minimal: | no (minimal twist has level 300) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 199.7 | ||
Root | \(1.40592 - 0.152947i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 900.199 |
Dual form | 900.3.f.h.199.8 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/900\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(451\) | \(577\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.305673 | − | 1.97650i | −0.152836 | − | 0.988251i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −3.81313 | + | 1.20833i | −0.953282 | + | 0.302082i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −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 | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 20.4920i | 1.86291i | 0.363861 | + | 0.931453i | \(0.381458\pi\) | ||||
−0.363861 | + | 0.931453i | \(0.618542\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 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 | \(-0.815877\pi\) | ||
0.837317 | − | 0.546717i | \(-0.184123\pi\) | |||||||
\(18\) | 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 | ||||||||
\(22\) | 40.5024 | − | 6.26384i | 1.84102 | − | 0.284720i | ||||
\(23\) | −23.2304 | −1.01002 | −0.505008 | − | 0.863114i | \(-0.668511\pi\) | ||||
−0.505008 | + | 0.863114i | \(0.668511\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −0.823633 | + | 0.127378i | −0.0316782 | + | 0.00489914i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 1.25794 | − | 0.398624i | 0.0449265 | − | 0.0142366i | ||||
\(29\) | −23.9166 | −0.824712 | −0.412356 | − | 0.911023i | \(-0.635294\pi\) | ||||
−0.412356 | + | 0.911023i | \(0.635294\pi\) | |||||||
\(30\) | 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 | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −36.7400 | + | 5.68197i | −1.08059 | + | 0.167117i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 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 | 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 | ||||||||
\(43\) | 55.5866 | 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 | \(-0.164245\pi\) | ||||
0.869804 | + | 0.493397i | \(0.164245\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −48.8912 | −0.997779 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0.503524 | + | 1.58898i | 0.00968316 | + | 0.0305572i | ||||
\(53\) | 29.9744i | 0.565554i | 0.959186 | + | 0.282777i | \(0.0912557\pi\) | ||||
−0.959186 | + | 0.282777i | \(0.908744\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −1.17240 | − | 2.36448i | −0.0209357 | − | 0.0422228i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 7.31067 | + | 47.2713i | 0.126046 | + | 0.815023i | ||||
\(59\) | 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 | \(0.710221\pi\) | |||||||
\(62\) | −83.0424 | + | 12.8428i | −1.33939 | + | 0.207142i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −38.7406 | + | 50.9428i | −0.605321 | + | 0.795981i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −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 | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 39.2803i | − | 0.553244i | −0.960979 | − | 0.276622i | \(-0.910785\pi\) | ||
0.960979 | − | 0.276622i | \(-0.0892150\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 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 | ||||||
\(78\) | 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 | ||||||||
\(82\) | 14.2771 | + | 92.3170i | 0.174112 | + | 1.12582i | ||||
\(83\) | −5.88913 | −0.0709534 | −0.0354767 | − | 0.999371i | \(-0.511295\pi\) | ||||
−0.0354767 | + | 0.999371i | \(0.511295\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −16.9913 | − | 109.867i | −0.197574 | − | 1.27752i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −146.872 | + | 72.8250i | −1.66900 | + | 0.827557i | ||||
\(89\) | −61.0100 | −0.685506 | −0.342753 | − | 0.939426i | \(-0.611359\pi\) | ||||
−0.342753 | + | 0.939426i | \(0.611359\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.137472i | 0.00151069i | ||||||||
\(92\) | 88.5804 | − | 28.0699i | 0.962831 | − | 0.305108i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −24.9923 | − | 161.602i | −0.265876 | − | 1.71917i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 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 | ||||
\(99\) | 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 | ||||||||
\(103\) | −158.196 | −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 | \(-0.527078\pi\) | ||||
−0.0849660 | + | 0.996384i | \(0.527078\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 156.842 | 1.43891 | 0.719457 | − | 0.694537i | \(-0.244391\pi\) | ||||
0.719457 | + | 0.694537i | \(0.244391\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −4.31503 | + | 3.04001i | −0.0385270 | + | 0.0271430i | ||||
\(113\) | 98.7245i | 0.873668i | 0.899542 | + | 0.436834i | \(0.143900\pi\) | ||||
−0.899542 | + | 0.436834i | \(0.856100\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 91.1972 | − | 28.8991i | 0.786183 | − | 0.249130i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 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 | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 50.7676 | + | 160.208i | 0.409416 | + | 1.29200i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 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 | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 4.45811i | 0.0340314i | 0.999855 | + | 0.0170157i | \(0.00541653\pi\) | ||||
−0.999855 | + | 0.0170157i | \(0.994583\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 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 | \(-0.769224\pi\) | ||
0.748496 | − | 0.663139i | \(-0.230776\pi\) | |||||||
\(138\) | 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 | ||||||||
\(142\) | −77.6377 | + | 12.0069i | −0.546744 | + | 0.0845559i | ||||
\(143\) | 8.53925 | 0.0597151 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −92.0683 | + | 14.2387i | −0.630604 | + | 0.0975251i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 61.5670 | + | 194.288i | 0.415994 | + | 1.31275i | ||||
\(149\) | 123.867 | 0.831324 | 0.415662 | − | 0.909519i | \(-0.363550\pi\) | ||||
0.415662 | + | 0.909519i | \(0.363550\pi\) | |||||||
\(150\) | 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 | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −13.3617 | + | 2.06643i | −0.0867641 | + | 0.0134184i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 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 | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 7.66365 | 0.0476003 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 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 | \(-0.580535\pi\) | ||||
−0.250319 | + | 0.968164i | \(0.580535\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 168.826 | 0.998972 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −211.959 | + | 67.1668i | −1.23232 | + | 0.390505i | ||||
\(173\) | − | 192.900i | − | 1.11503i | −0.830168 | − | 0.557513i | \(-0.811756\pi\) | ||
0.830168 | − | 0.557513i | \(-0.188244\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 188.834 | + | 268.033i | 1.07292 | + | 1.52291i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 18.6491 | + | 120.587i | 0.104770 | + | 0.677452i | ||||
\(179\) | − | 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 | \(0.596050\pi\) | |||||||
\(182\) | 0.271715 | − | 0.0420216i | 0.00149294 | − | 0.000230888i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −82.5569 | − | 166.499i | −0.448679 | − | 0.904887i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 380.913 | 2.03697 | ||||||||
\(188\) | −311.767 | + | 98.7947i | −1.65834 | + | 0.525504i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 279.706i | − | 1.46443i | −0.681075 | − | 0.732214i | \(-0.738487\pi\) | ||
0.681075 | − | 0.732214i | \(-0.261513\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 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 | \(0.0315296\pi\) | ||||
−0.995098 | + | 0.0988913i | \(0.968470\pi\) | |||||||
\(198\) | 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 | ||||||||
\(202\) | 49.7254 | + | 321.528i | 0.246165 | + | 1.59172i | ||||
\(203\) | 7.89005 | 0.0388672 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 48.3562 | + | 312.674i | 0.234739 | + | 1.51784i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −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 | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 5.55797 | + | 35.9382i | 0.0259718 | + | 0.167936i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 13.8606i | 0.0638737i | ||||||||
\(218\) | −47.9422 | − | 309.998i | −0.219918 | − | 1.42201i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −7.74600 | −0.0350498 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −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 | \(-0.793228\pi\) | ||||
−0.796330 | + | 0.604862i | \(0.793228\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −121.818 | −0.531955 | −0.265977 | − | 0.963979i | \(-0.585695\pi\) | ||||
−0.265977 | + | 0.963979i | \(0.585695\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −84.9957 | − | 171.418i | −0.366361 | − | 0.738870i | ||||
\(233\) | − | 136.615i | − | 0.586329i | −0.956062 | − | 0.293164i | \(-0.905292\pi\) | ||
0.956062 | − | 0.293164i | \(-0.0947083\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −29.3999 | − | 92.7775i | −0.124576 | − | 0.393125i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 12.1204 | − | 1.87447i | 0.0509262 | − | 0.00787592i | ||||
\(239\) | − | 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 | \(0.501480\pi\) | |||||||
\(242\) | 91.3720 | + | 590.818i | 0.377570 | + | 2.44140i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 285.381 | − | 90.4331i | 1.16959 | − | 0.370627i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −5.18820 | −0.0210049 | ||||||||
\(248\) | 301.133 | − | 149.314i | 1.21425 | − | 0.602071i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 395.809i | 1.57693i | 0.615081 | + | 0.788464i | \(0.289123\pi\) | ||||
−0.615081 | + | 0.788464i | \(0.710877\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 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 | \(0.0685110\pi\) | ||||
−0.976927 | + | 0.213576i | \(0.931489\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 16.8091i | 0.0648998i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 8.81147 | − | 1.36272i | 0.0336316 | − | 0.00520124i | ||||
\(263\) | 327.702 | 1.24601 | 0.623007 | − | 0.782216i | \(-0.285911\pi\) | ||||
0.623007 | + | 0.782216i | \(0.285911\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 8.11816 | − | 1.25550i | 0.0305194 | − | 0.00471993i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 277.599 | − | 87.9672i | 1.03582 | − | 0.328236i | ||||
\(269\) | −130.032 | −0.483392 | −0.241696 | − | 0.970352i | \(-0.577704\pi\) | ||||
−0.241696 | + | 0.970352i | \(0.577704\pi\) | |||||||
\(270\) | 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 | 0 | ||||||||
\(274\) | −359.131 | + | 55.5408i | −1.31070 | + | 0.202704i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 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 | ||||
\(279\) | 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 | ||||||||
\(283\) | 86.6730 | 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 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −56.5280 | −0.195599 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 56.2856 | + | 177.621i | 0.192759 | + | 0.608290i | ||||
\(293\) | − | 390.339i | − | 1.33222i | −0.745855 | − | 0.666108i | \(-0.767959\pi\) | ||
0.745855 | − | 0.666108i | \(-0.232041\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 365.191 | − | 181.076i | 1.23375 | − | 0.611743i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −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 | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −114.730 | − | 162.849i | −0.377401 | − | 0.535687i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −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 | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 106.594i | − | 0.342747i | −0.985206 | − | 0.171373i | \(-0.945180\pi\) | ||
0.985206 | − | 0.171373i | \(-0.0548205\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 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 | \(-0.995799\pi\) | ||
0.999913 | − | 0.0131984i | \(-0.00420131\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 490.099i | − | 1.53636i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −2.34257 | − | 15.1472i | −0.00727507 | − | 0.0470411i | ||||
\(323\) | −231.432 | −0.716506 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −50.6006 | − | 327.187i | −0.155217 | − | 1.00364i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −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 | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 25.5562 | + | 165.248i | 0.0765156 | + | 0.494755i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 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 | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 860.966 | 2.52483 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 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 | \(-0.303296\pi\) | ||||
0.579377 | + | 0.815059i | \(0.303296\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 163.284 | 0.467864 | 0.233932 | − | 0.972253i | \(-0.424841\pi\) | ||||
0.233932 | + | 0.972253i | \(0.424841\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 472.046 | − | 455.161i | 1.34104 | − | 1.29307i | ||||
\(353\) | − | 175.851i | − | 0.498161i | −0.968483 | − | 0.249081i | \(-0.919872\pi\) | ||
0.968483 | − | 0.249081i | \(-0.0801285\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 232.639 | − | 73.7201i | 0.653481 | − | 0.207079i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −239.037 | + | 36.9678i | −0.667700 | + | 0.103262i | ||||
\(359\) | 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 | ||||||||
\(362\) | 32.8852 | + | 212.638i | 0.0908431 | + | 0.587398i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −0.166112 | − | 0.524200i | −0.000456351 | − | 0.00144011i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −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 | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 9.88848i | − | 0.0266536i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 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 | 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 | ||||||||
\(382\) | −552.839 | + | 85.4985i | −1.44722 | + | 0.223818i | ||||
\(383\) | 251.669 | 0.657100 | 0.328550 | − | 0.944487i | \(-0.393440\pi\) | ||||
0.328550 | + | 0.944487i | \(0.393440\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −202.658 | + | 31.3418i | −0.525022 | + | 0.0811964i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 115.448 | + | 364.321i | 0.297547 | + | 0.938970i | ||||
\(389\) | 356.890 | 0.917454 | 0.458727 | − | 0.888577i | \(-0.348306\pi\) | ||||
0.458727 | + | 0.888577i | \(0.348306\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 431.815i | 1.10439i | ||||||||
\(392\) | −173.751 | − | 350.418i | −0.443242 | − | 0.893923i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 77.0108 | − | 11.9100i | 0.195459 | − | 0.0302284i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 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 | ||||
\(399\) | 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 | ||||||||
\(403\) | −17.5081 | −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 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −182.788 | −0.446915 | −0.223457 | − | 0.974714i | \(-0.571734\pi\) | ||||
−0.223457 | + | 0.974714i | \(0.571734\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 603.221 | − | 191.152i | 1.46413 | − | 0.463962i | ||||
\(413\) | − | 8.02677i | − | 0.0194353i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −9.59924 | + | 9.25587i | −0.0230751 | + | 0.0222497i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −77.9869 | − | 504.269i | −0.186572 | − | 1.20638i | ||||
\(419\) | 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 | \(0.233580\pi\) | |||||||
\(422\) | −461.189 | + | 71.3244i | −1.09286 | + | 0.169015i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −214.836 | + | 106.524i | −0.506688 | + | 0.251236i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 24.6901 | 0.0578222 | ||||||||
\(428\) | 69.3331 | − | 21.9707i | 0.161993 | − | 0.0513334i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 133.413i | − | 0.309544i | −0.987950 | − | 0.154772i | \(-0.950536\pi\) | ||
0.987950 | − | 0.154772i | \(-0.0494643\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 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 | ||||||||
\(438\) | 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 | ||||||||
\(442\) | 2.36774 | + | 15.3100i | 0.00535689 | + | 0.0346380i | ||||
\(443\) | −412.172 | −0.930410 | −0.465205 | − | 0.885203i | \(-0.654019\pi\) | ||||
−0.465205 | + | 0.885203i | \(0.654019\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 25.2824 | + | 163.478i | 0.0566869 | + | 0.366542i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 12.7804 | − | 16.8059i | 0.0285277 | − | 0.0375132i | ||||
\(449\) | −808.617 | −1.80093 | −0.900465 | − | 0.434929i | \(-0.856773\pi\) | ||||
−0.900465 | + | 0.434929i | \(0.856773\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 957.124i | − | 2.12223i | ||||||
\(452\) | −119.291 | − | 376.449i | −0.263919 | − | 0.832852i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 110.511 | + | 714.573i | 0.243417 | + | 1.57395i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 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 | ||||
\(459\) | 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 | ||||||||
\(463\) | 530.624 | 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 | \(-0.624203\pi\) | ||||
−0.380370 | + | 0.924834i | \(0.624203\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 24.0168 | 0.0512086 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −174.388 | + | 86.4686i | −0.369467 | + | 0.183196i | ||||
\(473\) | 1139.08i | 2.40820i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −7.40978 | − | 23.3831i | −0.0155668 | − | 0.0491242i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −111.600 | + | 17.2593i | −0.233472 | + | 0.0361072i | ||||
\(479\) | 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 | ||||||||
\(482\) | 0.685191 | + | 4.43050i | 0.00142156 | + | 0.00919190i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 1139.82 | − | 361.194i | 2.35501 | − | 0.746269i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −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 | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 756.810i | 1.54136i | 0.637220 | + | 0.770682i | \(0.280084\pi\) | ||||
−0.637220 | + | 0.770682i | \(0.719916\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 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 | ||||||||
\(498\) | 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 | ||||||||
\(502\) | 782.318 | − | 120.988i | 1.55840 | − | 0.241012i | ||||
\(503\) | 100.567 | 0.199935 | 0.0999673 | − | 0.994991i | \(-0.468126\pi\) | ||||
0.0999673 | + | 0.994991i | \(0.468126\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −940.887 | + | 145.511i | −1.85946 | + | 0.287572i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −103.312 | + | 32.7382i | −0.203370 | + | 0.0644452i | ||||
\(509\) | 753.185 | 1.47973 | 0.739867 | − | 0.672753i | \(-0.234888\pi\) | ||||
0.739867 | + | 0.672753i | \(0.234888\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 15.3671i | 0.0300726i | ||||||||
\(512\) | −502.800 | − | 96.6232i | −0.982031 | − | 0.188717i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 216.976 | − | 33.5561i | 0.422133 | − | 0.0652843i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1675.46i | 3.24073i | ||||||||
\(518\) | 33.2231 | − | 5.13807i | 0.0641373 | − | 0.00991906i | ||||
\(519\) | 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 | ||||||||
\(523\) | −617.411 | −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 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 10.6508 | 0.0201338 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −4.96301 | − | 15.6618i | −0.00932896 | − | 0.0294395i | ||||
\(533\) | 19.4635i | 0.0365169i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −258.722 | − | 521.786i | −0.482690 | − | 0.973481i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 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 | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −428.196 | + | 412.879i | −0.787125 | + | 0.758969i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 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 | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 297.770i | 0.540418i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 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 | \(0.00910302\pi\) | ||||
−0.999591 | + | 0.0285941i | \(0.990897\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 23.1636i | − | 0.0414376i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 73.3919 | + | 474.557i | 0.130591 | + | 0.844408i | ||||
\(563\) | −906.668 | −1.61042 | −0.805211 | − | 0.592988i | \(-0.797948\pi\) | ||||
−0.805211 | + | 0.592988i | \(0.797948\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −26.4936 | − | 171.310i | −0.0468085 | − | 0.302667i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 281.534 | − | 139.596i | 0.495659 | − | 0.245767i | ||||
\(569\) | −465.009 | −0.817239 | −0.408620 | − | 0.912705i | \(-0.633990\pi\) | ||||
−0.408620 | + | 0.912705i | \(0.633990\pi\) | |||||||
\(570\) | 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 | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −4.71000 | − | 30.4552i | −0.00820557 | − | 0.0530578i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 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 | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1.94281 | 0.00334391 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −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 | \(-0.686273\pi\) | ||||
−0.552362 | + | 0.833604i | \(0.686273\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −523.098 | −0.888113 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −469.526 | − | 666.451i | −0.793118 | − | 1.12576i | ||||
\(593\) | 350.392i | 0.590880i | 0.955361 | + | 0.295440i | \(0.0954662\pi\) | ||||
−0.955361 | + | 0.295440i | \(0.904534\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −472.322 | + | 149.672i | −0.792486 | + | 0.251128i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 19.1333 | − | 2.95903i | 0.0319955 | − | 0.00494821i | ||||
\(599\) | − | 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 | \(0.262656\pi\) | |||||||
\(602\) | 5.60540 | + | 36.2449i | 0.00931130 | + | 0.0602075i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −91.9490 | − | 290.164i | −0.152233 | − | 0.480405i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −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 | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 34.0710i | − | 0.0557627i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 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 | \(0.142247\pi\) | ||||
−0.901798 | + | 0.432157i | \(0.857753\pi\) | |||||||
\(618\) | 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 | ||||||||
\(622\) | −210.684 | + | 32.5830i | −0.338720 | + | 0.0523842i | ||||
\(623\) | 20.1271 | 0.0323067 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −91.3625 | + | 14.1295i | −0.145946 | + | 0.0225711i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 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 | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −16.5390 | + | 2.55781i | −0.0260867 | + | 0.00403440i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 20.3735i | 0.0319836i | ||||||||
\(638\) | −968.682 | + | 149.810i | −1.51831 | + | 0.234812i | ||||
\(639\) | 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 | ||||||||
\(643\) | 786.394 | 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 | \(-0.421334\pi\) | ||||
0.244629 | + | 0.969617i | \(0.421334\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −498.592 | −0.768246 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −631.219 | + | 200.024i | −0.968127 | + | 0.306786i | ||||
\(653\) | 516.391i | 0.790797i | 0.918510 | + | 0.395399i | \(0.129394\pi\) | ||||
−0.918510 | + | 0.395399i | \(0.870606\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −610.926 | + | 430.408i | −0.931290 | + | 0.656110i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 8.24491 | + | 53.3121i | 0.0125303 | + | 0.0810215i | ||||
\(659\) | − | 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 | \(0.595788\pi\) | |||||||
\(662\) | −219.534 | + | 33.9516i | −0.331622 | + | 0.0512865i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −20.9290 | − | 42.2092i | −0.0315196 | − | 0.0635681i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 555.593 | 0.832973 | ||||||||
\(668\) | 318.802 | − | 101.024i | 0.477248 | − | 0.151233i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 1533.65i | − | 2.28562i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 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 | \(-0.940443\pi\) | ||
0.982547 | − | 0.186014i | \(-0.0595570\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 31.5197i | 0.0464207i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −263.174 | − | 1701.70i | −0.385886 | − | 2.49517i | ||||
\(683\) | 664.793 | 0.973342 | 0.486671 | − | 0.873585i | \(-0.338211\pi\) | ||||
0.486671 | + | 0.873585i | \(0.338211\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −9.87143 | − | 63.8293i | −0.0143898 | − | 0.0930457i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 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 | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −122.907 | − | 794.728i | −0.177100 | − | 1.14514i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 868.213i | 1.24564i | ||||||||
\(698\) | −49.9117 | − | 322.732i | −0.0715067 | − | 0.462367i | ||||
\(699\) | 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 | ||||||||
\(703\) | −634.373 | −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 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 493.220 | 0.695656 | 0.347828 | − | 0.937558i | \(-0.386919\pi\) | ||||
0.347828 | + | 0.937558i | \(0.386919\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −216.819 | − | 437.278i | −0.304522 | − | 0.614154i | ||||
\(713\) | 976.020i | 1.36889i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 146.134 | + | 461.156i | 0.204098 | + | 0.644073i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 683.135 | − | 105.649i | 0.951442 | − | 0.147144i | ||||
\(719\) | − | 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 | ||||||||
\(722\) | −62.9653 | − | 407.138i | −0.0872096 | − | 0.563904i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 410.228 | − | 129.995i | 0.566613 | − | 0.179552i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 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 | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 1033.27i | − | 1.41350i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 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 | ||||||
\(738\) | 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 | ||||||||
\(742\) | −19.5446 | + | 3.02264i | −0.0263405 | + | 0.00407364i | ||||
\(743\) | 402.122 | 0.541214 | 0.270607 | − | 0.962690i | \(-0.412776\pi\) | ||||
0.270607 | + | 0.962690i | \(0.412776\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −92.2530 | + | 14.2672i | −0.123664 | + | 0.0191250i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −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 | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 19.6985 | − | 3.04644i | 0.0261254 | − | 0.00404038i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 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 | ||||
\(759\) | 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 | ||||||||
\(763\) | −51.7417 | −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 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −1065.98 | −1.38619 | −0.693094 | − | 0.720847i | \(-0.743753\pi\) | ||||
−0.693094 | + | 0.720847i | \(0.743753\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 123.894 | + | 390.975i | 0.160485 | + | 0.506444i | ||||
\(773\) | − | 947.271i | − | 1.22545i | −0.790297 | − | 0.612724i | \(-0.790074\pi\) | ||
0.790297 | − | 0.612724i | \(-0.209926\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 684.791 | − | 339.546i | 0.882463 | − | 0.437560i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −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 | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −639.491 | + | 450.533i | −0.815678 | + | 0.574659i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −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 | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 32.5690i | − | 0.0411744i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 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 | \(0.162811\pi\) | ||||
−0.872018 | + | 0.489473i | \(0.837189\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 1519.82i | − | 1.90215i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −37.1692 | − | 240.339i | −0.0463457 | − | 0.299674i | ||||
\(803\) | 954.545 | 1.18872 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 5.35175 | + | 34.6048i | 0.00663989 | + | 0.0429340i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −578.120 | − | 1165.94i | −0.715495 | − | 1.44300i | ||||
\(809\) | −1061.80 | −1.31249 | −0.656243 | − | 0.754549i | \(-0.727855\pi\) | ||||
−0.656243 | + | 0.754549i | \(0.727855\pi\) | |||||||
\(810\) | 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 | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −319.157 | − | 2063.69i | −0.392085 | − | 2.53525i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 692.072i | − | 0.847089i | ||||||
\(818\) | 55.8734 | + | 361.281i | 0.0683049 | + | 0.441664i | ||||
\(819\) | 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 | ||||||||
\(823\) | −1441.89 | −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 | \(-0.428660\pi\) | ||||
0.222249 | + | 0.974990i | \(0.428660\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −172.743 | −0.208375 | −0.104188 | − | 0.994558i | \(-0.533224\pi\) | ||||
−0.104188 | + | 0.994558i | \(0.533224\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 21.2285 | + | 16.1437i | 0.0255150 | + | 0.0194034i | ||||
\(833\) | 908.808i | 1.09101i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −972.850 | + | 308.283i | −1.16370 | + | 0.368759i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 332.093 | − | 51.3593i | 0.396292 | − | 0.0612879i | ||||
\(839\) | − | 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 | ||||||||
\(842\) | −191.135 | − | 1235.89i | −0.227001 | − | 1.46780i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 281.946 | + | 889.739i | 0.334059 | + | 1.05419i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 98.6133 | 0.116427 | ||||||||
\(848\) | 276.214 | + | 392.062i | 0.325724 | + | 0.462337i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1183.64i | 1.39088i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 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 | \(0.0385466\pi\) | ||||
−0.992677 | + | 0.120802i | \(0.961453\pi\) | |||||||
\(858\) | 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 | ||||||||
\(862\) | −263.692 | + | 40.7809i | −0.305907 | + | 0.0473096i | ||||
\(863\) | −885.953 | −1.02660 | −0.513298 | − | 0.858210i | \(-0.671577\pi\) | ||||
−0.513298 | + | 0.858210i | \(0.671577\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 1396.83 | − | 216.024i | 1.61296 | − | 0.249450i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −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 | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 571.656 | − | 88.4086i | 0.654069 | − | 0.101154i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 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 | ||||
\(879\) | 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 | ||||||||
\(883\) | 1093.51 | 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 | \(-0.594738\pi\) | ||||
−0.293255 | + | 0.956034i | \(0.594738\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −8.93819 | −0.0100542 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 315.386 | − | 99.9413i | 0.353571 | − | 0.112042i | ||||
\(893\) | − | 1017.96i | − | 1.13993i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −37.1236 | − | 20.1234i | −0.0414326 | − | 0.0224592i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 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 | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −707.588 | + | 350.850i | −0.782730 | + | 0.388109i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −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 | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1180.19i | 1.29549i | 0.761858 | + | 0.647744i | \(0.224287\pi\) | ||||
−0.761858 | + | 0.647744i | \(0.775713\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 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 | ||||||
\(918\) | 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 | ||||||||
\(922\) | 132.594 | + | 857.360i | 0.143811 | + | 0.929892i | ||||
\(923\) | −16.3686 | −0.0177341 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −162.197 | − | 1048.78i | −0.175159 | − | 1.13259i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 531.228 | + | 550.936i | 0.572444 | + | 0.593681i | ||||
\(929\) | 175.428 | 0.188835 | 0.0944175 | − | 0.995533i | \(-0.469901\pi\) | ||||
0.0944175 | + | 0.995533i | \(0.469901\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 608.711i | 0.653825i | ||||||||
\(932\) | 165.075 | + | 520.929i | 0.177119 | + | 0.558937i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 108.595 | + | 702.184i | 0.116269 | + | 0.751803i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 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 | ||||
\(939\) | 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 | ||||||||
\(943\) | 1085.03 | 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 | \(-0.675567\pi\) | ||||
−0.524016 | + | 0.851708i | \(0.675567\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −19.4110 | −0.0204542 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −43.9518 | + | 21.7930i | −0.0461679 | + | 0.0228919i | ||||
\(953\) | − | 1438.16i | − | 1.50908i | −0.656251 | − | 0.754542i | \(-0.727859\pi\) | ||
0.656251 | − | 0.754542i | \(-0.272141\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 68.2260 | + | 215.301i | 0.0713661 | + | 0.225211i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 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 | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 8.54744 | − | 2.70857i | 0.00886664 | − | 0.00280971i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −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 | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 652.667i | 0.672159i | 0.941834 | + | 0.336080i | \(0.109101\pi\) | ||||
−0.941834 | + | 0.336080i | \(0.890899\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 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 | \(0.0768622\pi\) | ||||
−0.970988 | + | 0.239130i | \(0.923138\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 1250.22i | − | 1.27703i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 1495.84 | − | 231.336i | 1.52326 | − | 0.235577i | ||||
\(983\) | −1044.27 | −1.06233 | −0.531165 | − | 0.847268i | \(-0.678246\pi\) | ||||
−0.531165 | + | 0.847268i | \(0.678246\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 878.697 | − | 135.894i | 0.891174 | − | 0.137823i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 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 | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 25.6125 | − | 3.96106i | 0.0257671 | − | 0.00398497i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 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 | ||||
\(999\) | 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.f.h.199.7 | 16 | ||
3.2 | odd | 2 | 300.3.f.c.199.10 | 16 | |||
4.3 | odd | 2 | inner | 900.3.f.h.199.9 | 16 | ||
5.2 | odd | 4 | 900.3.c.t.451.7 | 8 | |||
5.3 | odd | 4 | 900.3.c.n.451.2 | 8 | |||
5.4 | even | 2 | inner | 900.3.f.h.199.10 | 16 | ||
12.11 | even | 2 | 300.3.f.c.199.8 | 16 | |||
15.2 | even | 4 | 300.3.c.e.151.2 | yes | 8 | ||
15.8 | even | 4 | 300.3.c.g.151.7 | yes | 8 | ||
15.14 | odd | 2 | 300.3.f.c.199.7 | 16 | |||
20.3 | even | 4 | 900.3.c.n.451.1 | 8 | |||
20.7 | even | 4 | 900.3.c.t.451.8 | 8 | |||
20.19 | odd | 2 | inner | 900.3.f.h.199.8 | 16 | ||
60.23 | odd | 4 | 300.3.c.g.151.8 | yes | 8 | ||
60.47 | odd | 4 | 300.3.c.e.151.1 | ✓ | 8 | ||
60.59 | even | 2 | 300.3.f.c.199.9 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
300.3.c.e.151.1 | ✓ | 8 | 60.47 | odd | 4 | ||
300.3.c.e.151.2 | yes | 8 | 15.2 | even | 4 | ||
300.3.c.g.151.7 | yes | 8 | 15.8 | even | 4 | ||
300.3.c.g.151.8 | yes | 8 | 60.23 | odd | 4 | ||
300.3.f.c.199.7 | 16 | 15.14 | odd | 2 | |||
300.3.f.c.199.8 | 16 | 12.11 | even | 2 | |||
300.3.f.c.199.9 | 16 | 60.59 | even | 2 | |||
300.3.f.c.199.10 | 16 | 3.2 | odd | 2 | |||
900.3.c.n.451.1 | 8 | 20.3 | even | 4 | |||
900.3.c.n.451.2 | 8 | 5.3 | odd | 4 | |||
900.3.c.t.451.7 | 8 | 5.2 | odd | 4 | |||
900.3.c.t.451.8 | 8 | 20.7 | even | 4 | |||
900.3.f.h.199.7 | 16 | 1.1 | even | 1 | trivial | ||
900.3.f.h.199.8 | 16 | 20.19 | odd | 2 | inner | ||
900.3.f.h.199.9 | 16 | 4.3 | odd | 2 | inner | ||
900.3.f.h.199.10 | 16 | 5.4 | even | 2 | inner |