Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [624,4,Mod(49,624)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(624, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 0, 5]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("624.49");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 624 = 2^{4} \cdot 3 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 624.bv (of order \(6\), degree \(2\), 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: | \(36.8171918436\) |
Analytic rank: | \(0\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 39) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 433.1 | ||
Root | \(0.500000 + 0.866025i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 624.433 |
Dual form | 624.4.bv.a.49.1 |
$q$-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 \(\left(\mathbb{Z}/624\mathbb{Z}\right)^\times\).
\(n\) | \(79\) | \(145\) | \(209\) | \(469\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{6}\right)\) | \(1\) | \(1\) |
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 | 0 | ||||||||
\(3\) | −1.50000 | + | 2.59808i | −0.288675 | + | 0.500000i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − | 5.19615i | − | 0.464758i | −0.972625 | − | 0.232379i | \(-0.925349\pi\) | ||
0.972625 | − | 0.232379i | \(-0.0746510\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −9.00000 | + | 5.19615i | −0.485954 | + | 0.280566i | −0.722895 | − | 0.690958i | \(-0.757189\pi\) |
0.236940 | + | 0.971524i | \(0.423855\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −4.50000 | − | 7.79423i | −0.166667 | − | 0.288675i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −45.0000 | − | 25.9808i | −1.23346 | − | 0.712136i | −0.265707 | − | 0.964054i | \(-0.585605\pi\) |
−0.967749 | + | 0.251918i | \(0.918939\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −32.5000 | − | 33.7750i | −0.693375 | − | 0.720577i | ||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 13.5000 | + | 7.79423i | 0.232379 | + | 0.134164i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 58.5000 | + | 101.325i | 0.834608 | + | 1.44558i | 0.894349 | + | 0.447369i | \(0.147639\pi\) |
−0.0597414 | + | 0.998214i | \(0.519028\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 21.0000 | − | 12.1244i | 0.253565 | − | 0.146396i | −0.367831 | − | 0.929893i | \(-0.619899\pi\) |
0.621395 | + | 0.783497i | \(0.286566\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − | 31.1769i | − | 0.323970i | ||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 9.00000 | − | 15.5885i | 0.0815926 | − | 0.141323i | −0.822342 | − | 0.568994i | \(-0.807333\pi\) |
0.903934 | + | 0.427672i | \(0.140666\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 98.0000 | 0.784000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 27.0000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 49.5000 | − | 85.7365i | 0.316963 | − | 0.548996i | −0.662890 | − | 0.748717i | \(-0.730670\pi\) |
0.979853 | + | 0.199721i | \(0.0640037\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 193.990i | 1.12392i | 0.827164 | + | 0.561961i | \(0.189953\pi\) | ||||
−0.827164 | + | 0.561961i | \(0.810047\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 135.000 | − | 77.9423i | 0.712136 | − | 0.411152i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 27.0000 | + | 46.7654i | 0.130395 | + | 0.225851i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 97.5000 | + | 56.2917i | 0.433214 | + | 0.250116i | 0.700715 | − | 0.713442i | \(-0.252865\pi\) |
−0.267501 | + | 0.963558i | \(0.586198\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 136.500 | − | 33.7750i | 0.560449 | − | 0.138675i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −31.5000 | − | 18.1865i | −0.119987 | − | 0.0692746i | 0.438805 | − | 0.898582i | \(-0.355402\pi\) |
−0.558792 | + | 0.829308i | \(0.688735\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −41.0000 | − | 71.0141i | −0.145406 | − | 0.251850i | 0.784119 | − | 0.620611i | \(-0.213115\pi\) |
−0.929524 | + | 0.368761i | \(0.879782\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −40.5000 | + | 23.3827i | −0.134164 | + | 0.0774597i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 72.7461i | − | 0.225768i | −0.993608 | − | 0.112884i | \(-0.963991\pi\) | ||
0.993608 | − | 0.112884i | \(-0.0360089\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −117.500 | + | 203.516i | −0.342566 | + | 0.593341i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −351.000 | −0.963722 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −261.000 | −0.676436 | −0.338218 | − | 0.941068i | \(-0.609824\pi\) | ||||
−0.338218 | + | 0.941068i | \(0.609824\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −135.000 | + | 233.827i | −0.330971 | + | 0.573258i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 72.7461i | 0.169043i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 684.000 | − | 394.908i | 1.50931 | − | 0.871400i | 0.509368 | − | 0.860549i | \(-0.329879\pi\) |
0.999941 | − | 0.0108508i | \(-0.00345397\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 359.500 | + | 622.672i | 0.754578 | + | 1.30697i | 0.945584 | + | 0.325379i | \(0.105492\pi\) |
−0.191006 | + | 0.981589i | \(0.561175\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 81.0000 | + | 46.7654i | 0.161985 | + | 0.0935220i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −175.500 | + | 168.875i | −0.334894 | + | 0.322252i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 609.000 | + | 351.606i | 1.11047 | + | 0.641128i | 0.938950 | − | 0.344054i | \(-0.111800\pi\) |
0.171516 | + | 0.985181i | \(0.445134\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 27.0000 | + | 46.7654i | 0.0471075 | + | 0.0815926i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 405.000 | − | 233.827i | 0.676967 | − | 0.390847i | −0.121744 | − | 0.992561i | \(-0.538849\pi\) |
0.798711 | + | 0.601714i | \(0.205515\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 684.160i | − | 1.09692i | −0.836178 | − | 0.548458i | \(-0.815215\pi\) | ||
0.836178 | − | 0.548458i | \(-0.184785\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −147.000 | + | 254.611i | −0.226321 | + | 0.392000i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 540.000 | 0.799204 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 440.000 | 0.626631 | 0.313316 | − | 0.949649i | \(-0.398560\pi\) | ||||
0.313316 | + | 0.949649i | \(0.398560\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −40.5000 | + | 70.1481i | −0.0555556 | + | 0.0962250i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 1195.12i | 1.58049i | 0.612789 | + | 0.790247i | \(0.290048\pi\) | ||||
−0.612789 | + | 0.790247i | \(0.709952\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 526.500 | − | 303.975i | 0.671846 | − | 0.387891i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 148.500 | + | 257.210i | 0.182999 | + | 0.316963i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1314.00 | + | 758.638i | 1.56499 | + | 0.903545i | 0.996740 | + | 0.0806862i | \(0.0257112\pi\) |
0.568246 | + | 0.822859i | \(0.307622\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 468.000 | + | 135.100i | 0.539118 | + | 0.155630i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −504.000 | − | 290.985i | −0.561961 | − | 0.324448i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −63.0000 | − | 109.119i | −0.0680386 | − | 0.117846i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1002.00 | + | 578.505i | −1.04884 | + | 0.605549i | −0.922325 | − | 0.386415i | \(-0.873713\pi\) |
−0.126517 | + | 0.991964i | \(0.540380\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 467.654i | 0.474757i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −787.500 | + | 1363.99i | −0.775833 | + | 1.34378i | 0.158491 | + | 0.987360i | \(0.449337\pi\) |
−0.934325 | + | 0.356423i | \(0.883996\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −794.000 | −0.759565 | −0.379782 | − | 0.925076i | \(-0.624001\pi\) | ||||
−0.379782 | + | 0.925076i | \(0.624001\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −162.000 | −0.150567 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 225.000 | − | 389.711i | 0.203286 | − | 0.352101i | −0.746299 | − | 0.665610i | \(-0.768171\pi\) |
0.949585 | + | 0.313509i | \(0.101505\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 595.825i | − | 0.523576i | −0.965125 | − | 0.261788i | \(-0.915688\pi\) | ||
0.965125 | − | 0.261788i | \(-0.0843120\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −292.500 | + | 168.875i | −0.250116 | + | 0.144405i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 850.500 | + | 1473.11i | 0.708038 | + | 1.22636i | 0.965584 | + | 0.260092i | \(0.0837529\pi\) |
−0.257546 | + | 0.966266i | \(0.582914\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −81.0000 | − | 46.7654i | −0.0656808 | − | 0.0379208i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −117.000 | + | 405.300i | −0.0924500 | + | 0.320256i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1053.00 | − | 607.950i | −0.811163 | − | 0.468325i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 684.500 | + | 1185.59i | 0.514275 | + | 0.890750i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 94.5000 | − | 54.5596i | 0.0692746 | − | 0.0399957i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 1158.74i | − | 0.829128i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −832.000 | + | 1441.07i | −0.581323 | + | 1.00688i | 0.414000 | + | 0.910277i | \(0.364132\pi\) |
−0.995323 | + | 0.0966044i | \(0.969202\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 246.000 | 0.167900 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1476.00 | 0.984418 | 0.492209 | − | 0.870477i | \(-0.336190\pi\) | ||||
0.492209 | + | 0.870477i | \(0.336190\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −126.000 | + | 218.238i | −0.0821473 | + | 0.142283i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | − | 140.296i | − | 0.0894427i | ||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 877.500 | − | 506.625i | 0.547225 | − | 0.315941i | −0.200777 | − | 0.979637i | \(-0.564347\pi\) |
0.748002 | + | 0.663696i | \(0.231013\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 562.000 | + | 973.413i | 0.342937 | + | 0.593984i | 0.984977 | − | 0.172687i | \(-0.0552450\pi\) |
−0.642040 | + | 0.766671i | \(0.721912\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 189.000 | + | 109.119i | 0.112884 | + | 0.0651737i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 585.000 | + | 2364.25i | 0.342099 | + | 1.38258i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −445.500 | − | 257.210i | −0.255150 | − | 0.147311i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −352.500 | − | 610.548i | −0.197780 | − | 0.342566i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 2830.50 | − | 1634.19i | 1.55627 | − | 0.898510i | 0.558657 | − | 0.829399i | \(-0.311317\pi\) |
0.997609 | − | 0.0691115i | \(-0.0220164\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 1638.52i | − | 0.883052i | −0.897248 | − | 0.441526i | \(-0.854437\pi\) | ||
0.897248 | − | 0.441526i | \(-0.145563\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 526.500 | − | 911.925i | 0.278203 | − | 0.481861i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1008.00 | 0.522352 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1259.00 | 0.639995 | 0.319997 | − | 0.947418i | \(-0.396318\pi\) | ||||
0.319997 | + | 0.947418i | \(0.396318\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 391.500 | − | 678.098i | 0.195270 | − | 0.338218i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 187.061i | 0.0915684i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −2556.00 | + | 1475.71i | −1.22823 | + | 0.709118i | −0.966659 | − | 0.256066i | \(-0.917574\pi\) |
−0.261570 | + | 0.965185i | \(0.584240\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −405.000 | − | 701.481i | −0.191086 | − | 0.330971i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 2718.00 | + | 1569.24i | 1.25943 | + | 0.727133i | 0.972964 | − | 0.230956i | \(-0.0741855\pi\) |
0.286468 | + | 0.958090i | \(0.407519\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −84.5000 | + | 2195.37i | −0.0384615 | + | 0.999260i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −189.000 | − | 109.119i | −0.0845216 | − | 0.0487986i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −2133.00 | − | 3694.46i | −0.937393 | − | 1.62361i | −0.770310 | − | 0.637669i | \(-0.779899\pi\) |
−0.167083 | − | 0.985943i | \(-0.553435\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −882.000 | + | 509.223i | −0.380988 | + | 0.219964i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 2369.45i | 1.00621i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 1503.00 | − | 2603.27i | 0.627595 | − | 1.08703i | −0.360438 | − | 0.932783i | \(-0.617373\pi\) |
0.988033 | − | 0.154243i | \(-0.0492939\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1873.00 | −0.769166 | −0.384583 | − | 0.923090i | \(-0.625655\pi\) | ||||
−0.384583 | + | 0.923090i | \(0.625655\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −2157.00 | −0.871312 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 292.500 | − | 506.625i | 0.116243 | − | 0.201339i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 6079.50i | − | 2.37742i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −243.000 | + | 140.296i | −0.0935220 | + | 0.0539949i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1368.00 | − | 2369.45i | −0.518246 | − | 0.897629i | −0.999775 | − | 0.0211985i | \(-0.993252\pi\) |
0.481529 | − | 0.876430i | \(-0.340082\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2254.50 | − | 1301.64i | −0.840842 | − | 0.485460i | 0.0167085 | − | 0.999860i | \(-0.494681\pi\) |
−0.857550 | + | 0.514400i | \(0.828015\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −175.500 | − | 709.275i | −0.0644503 | − | 0.260473i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 3222.00 | + | 1860.22i | 1.16527 | + | 0.672768i | 0.952561 | − | 0.304347i | \(-0.0984384\pi\) |
0.212708 | + | 0.977116i | \(0.431772\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 599.000 | + | 1037.50i | 0.213377 | + | 0.369579i | 0.952769 | − | 0.303695i | \(-0.0982205\pi\) |
−0.739392 | + | 0.673275i | \(0.764887\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1827.00 | + | 1054.82i | −0.641128 | + | 0.370155i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1028.84i | 0.355716i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −94.5000 | + | 163.679i | −0.0321959 | + | 0.0557650i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −162.000 | −0.0543951 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1260.00 | −0.417014 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1196.00 | − | 2071.53i | 0.390218 | − | 0.675878i | −0.602260 | − | 0.798300i | \(-0.705733\pi\) |
0.992478 | + | 0.122422i | \(0.0390662\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 1402.96i | 0.451311i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −369.000 | + | 213.042i | −0.117049 | + | 0.0675784i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1008.00 | − | 1745.91i | −0.315334 | − | 0.546175i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 1777.50 | + | 1026.24i | 0.548458 | + | 0.316652i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1521.00 | − | 5268.90i | 0.462957 | − | 1.60373i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1764.00 | + | 1018.45i | 0.529714 | + | 0.305830i | 0.740900 | − | 0.671615i | \(-0.234399\pi\) |
−0.211186 | + | 0.977446i | \(0.567733\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −441.000 | − | 763.834i | −0.130667 | − | 0.226321i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −1863.00 | + | 1075.60i | −0.544721 | + | 0.314495i | −0.746990 | − | 0.664835i | \(-0.768502\pi\) |
0.202269 | + | 0.979330i | \(0.435168\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 3471.03i | − | 1.00162i | −0.865556 | − | 0.500812i | \(-0.833035\pi\) | ||
0.865556 | − | 0.500812i | \(-0.166965\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −810.000 | + | 1402.96i | −0.230710 | + | 0.399602i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −1854.00 | −0.521286 | −0.260643 | − | 0.965435i | \(-0.583935\pi\) | ||||
−0.260643 | + | 0.965435i | \(0.583935\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −378.000 | −0.104928 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −660.000 | + | 1143.15i | −0.180893 | + | 0.313316i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 4458.30i | − | 1.20662i | −0.797505 | − | 0.603312i | \(-0.793847\pi\) | ||
0.797505 | − | 0.603312i | \(-0.206153\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −361.500 | + | 208.712i | −0.0966235 | + | 0.0557856i | −0.547533 | − | 0.836784i | \(-0.684433\pi\) |
0.450910 | + | 0.892570i | \(0.351100\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −121.500 | − | 210.444i | −0.0320750 | − | 0.0555556i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1057.50 | + | 610.548i | 0.275760 | + | 0.159210i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1092.00 | − | 315.233i | −0.281305 | − | 0.0812057i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −3105.00 | − | 1792.67i | −0.790247 | − | 0.456249i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 2052.00 | + | 3554.17i | 0.516020 | + | 0.893773i | 0.999827 | + | 0.0185985i | \(0.00592043\pi\) |
−0.483807 | + | 0.875175i | \(0.660746\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −810.000 | + | 467.654i | −0.201282 | + | 0.116210i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 1823.85i | 0.447898i | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −994.500 | + | 1722.52i | −0.241382 | + | 0.418086i | −0.961108 | − | 0.276172i | \(-0.910934\pi\) |
0.719726 | + | 0.694258i | \(0.244267\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1170.00 | −0.280696 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −891.000 | −0.211308 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 369.000 | − | 639.127i | 0.0865153 | − | 0.149849i | −0.819521 | − | 0.573050i | \(-0.805760\pi\) |
0.906036 | + | 0.423201i | \(0.139094\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1356.20i | 0.314379i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −3942.00 | + | 2275.91i | −0.903545 | + | 0.521662i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 1053.00 | + | 1823.85i | 0.238671 | + | 0.413391i | 0.960333 | − | 0.278855i | \(-0.0899549\pi\) |
−0.721662 | + | 0.692246i | \(0.756622\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −594.000 | − | 342.946i | −0.133147 | − | 0.0768727i | 0.431947 | − | 0.901899i | \(-0.357827\pi\) |
−0.565094 | + | 0.825026i | \(0.691160\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −1053.00 | + | 1013.25i | −0.233445 | + | 0.224632i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −4410.00 | − | 2546.11i | −0.967029 | − | 0.558315i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1832.50 | − | 3173.98i | −0.397488 | − | 0.688470i | 0.595927 | − | 0.803039i | \(-0.296785\pi\) |
−0.993415 | + | 0.114569i | \(0.963451\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 1512.00 | − | 872.954i | 0.324448 | − | 0.187320i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1719.93i | 0.365132i | 0.983194 | + | 0.182566i | \(0.0584404\pi\) | ||||
−0.983194 | + | 0.182566i | \(0.941560\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −913.000 | + | 1581.36i | −0.191775 | + | 0.332163i | −0.945838 | − | 0.324638i | \(-0.894758\pi\) |
0.754064 | + | 0.656801i | \(0.228091\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 378.000 | 0.0785642 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 378.000 | 0.0777444 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4388.00 | + | 7600.24i | −0.893141 | + | 1.54696i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − | 3471.03i | − | 0.699228i | ||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −436.500 | + | 252.013i | −0.0870328 | + | 0.0502484i | −0.542885 | − | 0.839807i | \(-0.682668\pi\) |
0.455852 | + | 0.890056i | \(0.349335\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −2052.00 | − | 3554.17i | −0.404990 | − | 0.701463i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −1215.00 | − | 701.481i | −0.237379 | − | 0.137051i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −819.000 | + | 202.650i | −0.158408 | + | 0.0391958i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 738.000 | + | 426.084i | 0.141321 | + | 0.0815917i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −2362.50 | − | 4091.97i | −0.447928 | − | 0.775833i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 3235.50 | − | 1868.02i | 0.607424 | − | 0.350696i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1950.29i | 0.362570i | 0.983431 | + | 0.181285i | \(0.0580256\pi\) | ||||
−0.983431 | + | 0.181285i | \(0.941974\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 1191.00 | − | 2062.87i | 0.219267 | − | 0.379782i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 3798.00 | 0.692491 | 0.346246 | − | 0.938144i | \(-0.387456\pi\) | ||||
0.346246 | + | 0.938144i | \(0.387456\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1378.00 | 0.248847 | 0.124424 | − | 0.992229i | \(-0.460292\pi\) | ||||
0.124424 | + | 0.992229i | \(0.460292\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 243.000 | − | 420.888i | 0.0434651 | − | 0.0752837i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 7103.14i | − | 1.25852i | −0.777193 | − | 0.629262i | \(-0.783357\pi\) | ||
0.777193 | − | 0.629262i | \(-0.216643\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −4455.00 | + | 2572.10i | −0.781919 | + | 0.451441i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 675.000 | + | 1169.13i | 0.117367 | + | 0.203286i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 2457.00 | + | 1418.55i | 0.423254 | + | 0.244366i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −3185.00 | − | 3309.95i | −0.543606 | − | 0.564932i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 1548.00 | + | 893.738i | 0.261788 | + | 0.151143i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 378.000 | + | 654.715i | 0.0633429 | + | 0.109713i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −8724.00 | + | 5036.80i | −1.44868 | + | 0.836398i | −0.998403 | − | 0.0564889i | \(-0.982009\pi\) |
−0.450281 | + | 0.892887i | \(0.648676\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − | 1013.25i | − | 0.166744i | ||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 1827.00 | − | 3164.46i | 0.297969 | − | 0.516098i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 9001.00 | 1.45494 | 0.727471 | − | 0.686138i | \(-0.240695\pi\) | ||||
0.727471 | + | 0.686138i | \(0.240695\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −5103.00 | −0.817572 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 5040.00 | − | 8729.54i | 0.800385 | − | 1.38631i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 6006.75i | − | 0.945581i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 243.000 | − | 140.296i | 0.0379208 | − | 0.0218936i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 1647.00 | + | 2852.69i | 0.254800 | + | 0.441327i | 0.964841 | − | 0.262834i | \(-0.0846570\pi\) |
−0.710041 | + | 0.704160i | \(0.751324\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −9132.00 | − | 5272.36i | −1.40064 | − | 0.808662i | −0.406185 | − | 0.913791i | \(-0.633141\pi\) |
−0.994459 | + | 0.105129i | \(0.966475\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −877.500 | − | 911.925i | −0.133440 | − | 0.138675i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −2146.50 | − | 1239.28i | −0.323645 | − | 0.186856i | 0.329371 | − | 0.944201i | \(-0.393163\pi\) |
−0.653016 | + | 0.757344i | \(0.726497\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1215.00 | − | 2104.44i | −0.181649 | − | 0.314626i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 3159.00 | − | 1823.85i | 0.468325 | − | 0.270388i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 5414.39i | − | 0.795991i | −0.917387 | − | 0.397995i | \(-0.869706\pi\) | ||
0.917387 | − | 0.397995i | \(-0.130294\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3135.50 | + | 5430.85i | −0.457137 | + | 0.791784i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −4107.00 | −0.593834 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −3555.00 | −0.509801 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −4973.00 | + | 8613.49i | −0.707326 | + | 1.22512i | 0.258520 | + | 0.966006i | \(0.416765\pi\) |
−0.965846 | + | 0.259118i | \(0.916568\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 327.358i | 0.0461831i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 2349.00 | − | 1356.20i | 0.328717 | − | 0.189785i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 3650.50 | + | 6322.85i | 0.506745 | + | 0.877707i | 0.999970 | + | 0.00780555i | \(0.00248461\pi\) |
−0.493225 | + | 0.869902i | \(0.664182\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 3010.50 | + | 1738.11i | 0.414564 | + | 0.239349i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −4504.50 | + | 1114.57i | −0.615368 | + | 0.152264i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2964.00 | + | 1711.27i | 0.401716 | + | 0.231931i | 0.687224 | − | 0.726445i | \(-0.258829\pi\) |
−0.285508 | + | 0.958376i | \(0.592162\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −2496.00 | − | 4323.20i | −0.335627 | − | 0.581323i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 5004.00 | − | 2889.06i | 0.667604 | − | 0.385442i | −0.127564 | − | 0.991830i | \(-0.540716\pi\) |
0.795168 | + | 0.606389i | \(0.207382\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | − | 2805.92i | − | 0.371436i | ||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −369.000 | + | 639.127i | −0.0484685 | + | 0.0839500i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 9153.00 | 1.19300 | 0.596498 | − | 0.802614i | \(-0.296558\pi\) | ||||
0.596498 | + | 0.802614i | \(0.296558\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2106.00 | 0.272391 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −2214.00 | + | 3834.76i | −0.284177 | + | 0.492209i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − | 2286.31i | − | 0.291232i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1752.00 | − | 1011.52i | 0.221487 | − | 0.127876i | −0.385152 | − | 0.922853i | \(-0.625851\pi\) |
0.606639 | + | 0.794978i | \(0.292518\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −378.000 | − | 654.715i | −0.0474277 | − | 0.0821473i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 7195.50 | + | 4154.32i | 0.896075 | + | 0.517349i | 0.875925 | − | 0.482448i | \(-0.160252\pi\) |
0.0201504 | + | 0.999797i | \(0.493586\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 6552.00 | − | 6304.66i | 0.809872 | − | 0.779300i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 364.500 | + | 210.444i | 0.0447214 | + | 0.0258199i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −2925.00 | − | 5066.25i | −0.356233 | − | 0.617014i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −9022.50 | + | 5209.14i | −1.09079 | + | 0.629769i | −0.933787 | − | 0.357829i | \(-0.883517\pi\) |
−0.157005 | + | 0.987598i | \(0.550184\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 3039.75i | 0.364817i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −4104.00 | + | 7108.34i | −0.488970 | + | 0.846921i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 6210.00 | 0.734547 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −3372.00 | −0.395989 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 2088.00 | − | 3616.52i | 0.243450 | − | 0.421667i | −0.718245 | − | 0.695790i | \(-0.755054\pi\) |
0.961695 | + | 0.274123i | \(0.0883875\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 14471.3i | − | 1.67527i | −0.546233 | − | 0.837633i | \(-0.683939\pi\) | ||
0.546233 | − | 0.837633i | \(-0.316061\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −567.000 | + | 327.358i | −0.0651737 | + | 0.0376281i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 5733.00 | + | 9929.85i | 0.654333 | + | 1.13334i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −6471.00 | − | 3736.03i | −0.733381 | − | 0.423418i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −7020.00 | − | 2026.50i | −0.790044 | − | 0.228066i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 5697.00 | + | 3289.16i | 0.636693 | + | 0.367595i | 0.783340 | − | 0.621594i | \(-0.213515\pi\) |
−0.146646 | + | 0.989189i | \(0.546848\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 3302.50 | + | 5720.10i | 0.366531 | + | 0.634851i | 0.989021 | − | 0.147778i | \(-0.0472120\pi\) |
−0.622489 | + | 0.782628i | \(0.713879\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 1336.50 | − | 771.629i | 0.147311 | − | 0.0850500i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − | 436.477i | − | 0.0477792i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −4271.00 | + | 7397.59i | −0.464336 | + | 0.804254i | −0.999171 | − | 0.0407023i | \(-0.987040\pi\) |
0.534835 | + | 0.844957i | \(0.320374\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 2115.00 | 0.228377 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 14328.0 | 1.53667 | 0.768334 | − | 0.640049i | \(-0.221086\pi\) | ||||
0.768334 | + | 0.640049i | \(0.221086\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 3942.00 | − | 6827.74i | 0.419930 | − | 0.727340i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 9805.14i | 1.03751i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 2610.00 | − | 1506.88i | 0.274329 | − | 0.158384i | −0.356525 | − | 0.934286i | \(-0.616038\pi\) |
0.630853 | + | 0.775902i | \(0.282705\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 945.000 | + | 1636.79i | 0.0986659 | + | 0.170894i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 4257.00 | + | 2457.78i | 0.441526 | + | 0.254915i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 702.000 | − | 2431.80i | 0.0723303 | − | 0.250559i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −2500.50 | − | 1443.66i | −0.255948 | − | 0.147772i | 0.366536 | − | 0.930404i | \(-0.380543\pi\) |
−0.622485 | + | 0.782632i | \(0.713877\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 1579.50 | + | 2735.77i | 0.160620 | + | 0.278203i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 3118.50 | − | 1800.47i | 0.315061 | − | 0.181900i | −0.334128 | − | 0.942528i | \(-0.608442\pi\) |
0.649189 | + | 0.760627i | \(0.275108\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 2677.75i | 0.268781i | 0.990928 | + | 0.134391i | \(0.0429077\pi\) | ||||
−0.990928 | + | 0.134391i | \(0.957092\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −1512.00 | + | 2618.86i | −0.150790 | + | 0.261176i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −13878.0 | −1.37515 | −0.687577 | − | 0.726111i | \(-0.741326\pi\) | ||||
−0.687577 | + | 0.726111i | \(0.741326\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −7308.00 | −0.719514 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −1888.50 | + | 3270.98i | −0.184751 | + | 0.319997i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 4260.84i | 0.414194i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2058.00 | − | 1188.19i | 0.198795 | − | 0.114774i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1174.50 | + | 2034.29i | 0.112739 | + | 0.195270i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −954.000 | − | 550.792i | −0.0910008 | − | 0.0525393i | 0.453809 | − | 0.891099i | \(-0.350065\pi\) |
−0.544810 | + | 0.838560i | \(0.683398\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1267.50 | − | 5122.54i | −0.120152 | − | 0.485588i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −486.000 | − | 280.592i | −0.0457842 | − | 0.0264335i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 3006.00 | + | 5206.54i | 0.281434 | + | 0.487458i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 14829.0 | − | 8561.53i | 1.37981 | − | 0.796632i | 0.387671 | − | 0.921798i | \(-0.373280\pi\) |
0.992136 | + | 0.125166i | \(0.0399462\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 8854.24i | − | 0.818820i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 225.000 | − | 389.711i | 0.0206805 | − | 0.0358196i | −0.855500 | − | 0.517803i | \(-0.826750\pi\) |
0.876180 | + | 0.481983i | \(0.160083\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 11583.0 | 1.05816 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 2430.00 | 0.220647 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −2430.00 | + | 4208.88i | −0.219317 | + | 0.379868i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 13219.0i | 1.18590i | 0.805239 | + | 0.592950i | \(0.202037\pi\) | ||||
−0.805239 | + | 0.592950i | \(0.797963\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −8154.00 | + | 4707.71i | −0.727133 | + | 0.419811i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 2673.00 | + | 4629.77i | 0.236945 | + | 0.410400i | 0.959836 | − | 0.280561i | \(-0.0905206\pi\) |
−0.722891 | + | 0.690962i | \(0.757187\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 7087.50 | + | 4091.97i | 0.624534 | + | 0.360575i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −5577.00 | − | 3512.60i | −0.488527 | − | 0.307692i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −5080.50 | − | 2933.23i | −0.442415 | − | 0.255428i | 0.262207 | − | 0.965012i | \(-0.415550\pi\) |
−0.704621 | + | 0.709583i | \(0.748883\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 3555.00 | + | 6157.44i | 0.307757 | + | 0.533051i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 567.000 | − | 327.358i | 0.0487986 | − | 0.0281739i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 4125.75i | 0.353014i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1890.00 | + | 3273.58i | −0.160778 | + | 0.278475i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 12798.0 | 1.08241 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −9657.00 | −0.812055 | −0.406028 | − | 0.913861i | \(-0.633086\pi\) | ||||
−0.406028 | + | 0.913861i | \(0.633086\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 10813.0 | − | 18728.7i | 0.904053 | − | 1.56586i | 0.0818685 | − | 0.996643i | \(-0.473911\pi\) |
0.822184 | − | 0.569222i | \(-0.192755\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | − | 3055.34i | − | 0.253992i | ||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −19656.0 | + | 11348.4i | −1.62472 | + | 0.938034i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 5921.50 | + | 10256.3i | 0.486685 | + | 0.842964i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −6156.00 | − | 3554.17i | −0.503103 | − | 0.290467i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 409.500 | + | 1654.97i | 0.0332785 | + | 0.134493i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −2025.00 | − | 1169.13i | −0.163642 | − | 0.0944787i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 4509.00 | + | 7809.82i | 0.362342 | + | 0.627595i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 10575.0 | − | 6105.48i | 0.845079 | − | 0.487906i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 5371.09i | 0.426841i | 0.976960 | + | 0.213421i | \(0.0684605\pi\) | ||||
−0.976960 | + | 0.213421i | \(0.931540\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 2809.50 | − | 4866.20i | 0.222039 | − | 0.384583i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −3096.00 | −0.243336 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −16946.0 | −1.32460 | −0.662302 | − | 0.749237i | \(-0.730421\pi\) | ||||
−0.662302 | + | 0.749237i | \(0.730421\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 3235.50 | − | 5604.05i | 0.251526 | − | 0.435656i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 2400.62i | − | 0.185608i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −3960.00 | + | 2286.31i | −0.304514 | + | 0.175811i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 877.500 | + | 1519.87i | 0.0671132 | + | 0.116243i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 3343.50 | + | 1930.37i | 0.254342 | + | 0.146845i | 0.621751 | − | 0.783215i | \(-0.286422\pi\) |
−0.367409 | + | 0.930060i | \(0.619755\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1066.00 | + | 3692.73i | −0.0806565 | + | 0.279402i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 15795.0 | + | 9119.25i | 1.18871 | + | 0.686301i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 10836.0 | + | 18768.5i | 0.811160 | + | 1.40497i | 0.912053 | + | 0.410073i | \(0.134497\pi\) |
−0.100893 | + | 0.994897i | \(0.532170\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 7654.50 | − | 4419.33i | 0.569960 | − | 0.329066i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − | 841.777i | − | 0.0623480i | ||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 693.000 | − | 1200.31i | 0.0510581 | − | 0.0884353i | −0.839367 | − | 0.543565i | \(-0.817074\pi\) |
0.890425 | + | 0.455130i | \(0.150407\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −1162.00 | −0.0851632 | −0.0425816 | − | 0.999093i | \(-0.513558\pi\) | ||||
−0.0425816 | + | 0.999093i | \(0.513558\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 8208.00 | 0.598419 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 882.000 | − | 1527.67i | 0.0639686 | − | 0.110797i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 8045.38i | 0.580474i | 0.956955 | + | 0.290237i | \(0.0937341\pi\) | ||||
−0.956955 | + | 0.290237i | \(0.906266\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 6763.50 | − | 3904.91i | 0.485460 | − | 0.280281i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −6210.00 | − | 10756.0i | −0.443432 | − | 0.768047i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 11745.0 | + | 6780.98i | 0.834354 | + | 0.481714i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 2106.00 | + | 607.950i | 0.148842 | + | 0.0429669i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 23922.0 | + | 13811.4i | 1.68206 | + | 0.971135i | 0.960293 | + | 0.278995i | \(0.0900013\pi\) |
0.721763 | + | 0.692140i | \(0.243332\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2352.00 | + | 4073.78i | 0.164537 | + | 0.284987i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −9666.00 | + | 5580.67i | −0.672768 | + | 0.388423i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 275.396i | 0.0190711i | 0.999955 | + | 0.00953555i | \(0.00303531\pi\) | ||||
−0.999955 | + | 0.00953555i | \(0.996965\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −3159.00 | + | 5471.55i | −0.217658 | + | 0.376994i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −3594.00 | −0.246386 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −22356.0 | −1.52494 | −0.762472 | − | 0.647021i | \(-0.776014\pi\) | ||||
−0.762472 | + | 0.647021i | \(0.776014\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 9041.50 | − | 15660.3i | 0.613661 | − | 1.06289i | −0.376956 | − | 0.926231i | \(-0.623029\pi\) |
0.990618 | − | 0.136662i | \(-0.0436373\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − | 6328.91i | − | 0.427418i | ||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 6160.50 | − | 3556.77i | 0.413983 | − | 0.239013i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 2740.00 | + | 4745.82i | 0.183218 | + | 0.317342i | 0.942975 | − | 0.332865i | \(-0.108015\pi\) |
−0.759757 | + | 0.650207i | \(0.774682\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −2673.00 | − | 1543.26i | −0.177858 | − | 0.102686i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −2457.00 | + | 2364.25i | −0.162683 | + | 0.156542i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 15361.5 | + | 8868.97i | 1.01215 | + | 0.584362i | 0.911819 | − | 0.410592i | \(-0.134678\pi\) |
0.100326 | + | 0.994955i | \(0.468011\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −283.500 | − | 491.036i | −0.0185883 | − | 0.0321959i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 8545.50 | − | 4933.75i | 0.557583 | − | 0.321921i | −0.194592 | − | 0.980884i | \(-0.562338\pi\) |
0.752175 | + | 0.658963i | \(0.229005\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 4115.35i | 0.267221i | 0.991034 | + | 0.133611i | \(0.0426572\pi\) | ||||
−0.991034 | + | 0.133611i | \(0.957343\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 243.000 | − | 420.888i | 0.0157025 | − | 0.0271975i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −15768.0 | −1.01402 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 6229.00 | 0.398656 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 1890.00 | − | 3273.58i | 0.120382 | − | 0.208507i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 13172.2i | 0.834995i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 10968.0 | − | 6332.38i | 0.691964 | − | 0.399506i | −0.112383 | − | 0.993665i | \(-0.535849\pi\) |
0.804347 | + | 0.594159i | \(0.202515\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 3588.00 | + | 6214.60i | 0.225293 | + | 0.390218i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 7488.00 | + | 4323.20i | 0.467956 | + | 0.270175i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 10692.5 | − | 2645.71i | 0.665074 | − | 0.164563i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −3645.00 | − | 2104.44i | −0.225656 | − | 0.130282i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1894.50 | + | 3281.37i | 0.116737 | + | 0.202194i | 0.918473 | − | 0.395484i | \(-0.129423\pi\) |
−0.801736 | + | 0.597678i | \(0.796090\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −14646.0 | + | 8455.87i | −0.898261 | + | 0.518611i | −0.876636 | − | 0.481155i | \(-0.840217\pi\) |
−0.0216255 | + | 0.999766i | \(0.506884\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − | 1278.25i | − | 0.0780328i | ||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −13896.0 | + | 24068.6i | −0.844371 | + | 1.46249i | 0.0417951 | + | 0.999126i | \(0.486692\pi\) |
−0.886166 | + | 0.463368i | \(0.846641\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −41040.0 | −2.48222 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 6048.00 | 0.364116 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 297.000 | − | 514.419i | 0.0177986 | − | 0.0308281i | −0.856989 | − | 0.515335i | \(-0.827668\pi\) |
0.874788 | + | 0.484507i | \(0.161001\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 7669.52i | − | 0.457516i | ||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −5332.50 | + | 3078.72i | −0.316652 | + | 0.182819i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 8874.00 | + | 15370.2i | 0.524555 | + | 0.908556i | 0.999591 | + | 0.0285901i | \(0.00910174\pi\) |
−0.475036 | + | 0.879966i | \(0.657565\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 13675.5 | + | 7895.55i | 0.804713 | + | 0.464601i | 0.845117 | − | 0.534582i | \(-0.179531\pi\) |
−0.0404035 | + | 0.999183i | \(0.512864\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 11407.5 | + | 11855.0i | 0.668221 | + | 0.694436i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 1134.00 | + | 654.715i | 0.0661273 | + | 0.0381786i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −891.000 | − | 1543.26i | −0.0517236 | − | 0.0895879i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −5292.00 | + | 3055.34i | −0.305830 | + | 0.176571i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 37360.3i | − | 2.14945i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −10466.5 | + | 18128.5i | −0.599486 | + | 1.03834i | 0.393411 | + | 0.919363i | \(0.371295\pi\) |
−0.992897 | + | 0.118977i | \(0.962038\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 2646.00 | 0.150881 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 3402.00 | 0.193131 | 0.0965653 | − | 0.995327i | \(-0.469214\pi\) | ||||
0.0965653 | + | 0.995327i | \(0.469214\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 6012.00 | − | 10413.1i | 0.339793 | − | 0.588539i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | − | 6453.62i | − | 0.363147i | ||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −21636.0 | + | 12491.6i | −1.21212 | + | 0.699818i | −0.963221 | − | 0.268711i | \(-0.913402\pi\) |
−0.248900 | + | 0.968529i | \(0.580069\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −2632.50 | − | 4559.62i | −0.146836 | − | 0.254327i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 9018.00 | + | 5206.54i | 0.500812 | + | 0.289144i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 8482.50 | + | 8815.27i | 0.469024 | + | 0.487424i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −12009.0 | − | 6933.40i | −0.661134 | − | 0.381706i | 0.131575 | − | 0.991306i | \(-0.457997\pi\) |
−0.792709 | + | 0.609600i | \(0.791330\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −2430.00 | − | 4208.88i | −0.133201 | − | 0.230710i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 5058.00 | − | 2920.24i | 0.276059 | − | 0.159383i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 4255.65i | − | 0.231269i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 2781.00 | − | 4816.83i | 0.150482 | − | 0.260643i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −21906.0 | −1.18028 | −0.590141 | − | 0.807300i | \(-0.700928\pi\) | ||||
−0.590141 | + | 0.807300i | \(0.700928\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2730.00 | 0.146464 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 567.000 | − | 982.073i | 0.0302900 | − | 0.0524638i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − | 16367.9i | − | 0.870690i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −11308.5 | + | 6528.97i | −0.599012 | + | 0.345840i | −0.768653 | − | 0.639666i | \(-0.779073\pi\) |
0.169641 | + | 0.985506i | \(0.445739\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1980.00 | − | 3429.46i | −0.104439 | − | 0.180893i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 3024.00 | + | 1745.91i | 0.158835 | + | 0.0917037i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 12285.0 | − | 3039.75i | 0.642564 | − | 0.158993i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 11583.0 | + | 6687.45i | 0.603312 | + | 0.348323i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −7110.00 | − | 12314.9i | −0.368788 | − | 0.638759i | 0.620589 | − | 0.784136i | \(-0.286894\pi\) |
−0.989376 | + | 0.145377i | \(0.953560\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 7146.00 | − | 4125.75i | 0.369114 | − | 0.213108i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − | 1252.27i | − | 0.0644157i | ||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 4851.00 | − | 8402.18i | 0.248499 | − | 0.430413i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 5282.00 | 0.269462 | 0.134731 | − | 0.990882i | \(-0.456983\pi\) | ||||
0.134731 | + | 0.990882i | \(0.456983\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 4797.00 | − | 8308.65i | 0.242713 | − | 0.420392i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 11419.4i | − | 0.575424i | −0.957717 | − | 0.287712i | \(-0.907105\pi\) | ||
0.957717 | − | 0.287712i | \(-0.0928945\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −3172.50 | + | 1831.64i | −0.159210 | + | 0.0919200i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −18270.0 | − | 31644.6i | −0.913140 | − | 1.58160i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 17784.0 | + | 10267.6i | 0.885244 | + | 0.511096i | 0.872384 | − | 0.488822i | \(-0.162573\pi\) |
0.0128599 | + | 0.999917i | \(0.495906\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 2457.00 | − | 2364.25i | 0.121809 | − | 0.117210i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 18036.0 | + | 10413.1i | 0.890547 | + | 0.514158i | 0.874121 | − | 0.485707i | \(-0.161438\pi\) |
0.0164258 | + | 0.999865i | \(0.494771\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −8491.50 | − | 14707.7i | −0.417590 | − | 0.723287i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 9315.00 | − | 5378.02i | 0.456249 | − | 0.263416i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 4676.54i | 0.228140i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −2417.00 | + | 4186.37i | −0.117440 | + | 0.203412i | −0.918753 | − | 0.394834i | \(-0.870802\pi\) |
0.801312 | + | 0.598246i | \(0.204136\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −12312.0 | −0.595849 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −8514.00 | −0.410406 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −4523.00 | + | 7834.07i | −0.217161 | + | 0.376135i | −0.953939 | − | 0.300001i | \(-0.903013\pi\) |
0.736778 | + | 0.676135i | \(0.236346\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | − | 2805.92i | − | 0.134188i | ||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −10422.0 | + | 6017.14i | −0.496448 | + | 0.286625i | −0.727246 | − | 0.686377i | \(-0.759200\pi\) |
0.230797 | + | 0.973002i | \(0.425867\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 3096.00 | + | 5362.43i | 0.146897 | + | 0.254434i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −4738.50 | − | 2735.77i | −0.223949 | − | 0.129297i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −35568.0 | − | 10267.6i | −1.67443 | − | 0.483366i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 32514.0 | + | 18772.0i | 1.52469 | + | 0.880279i | 0.999572 | + | 0.0292479i | \(0.00931121\pi\) |
0.525115 | + | 0.851031i | \(0.324022\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −2983.50 | − | 5167.57i | −0.139362 | − | 0.241382i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −13608.0 | + | 7856.58i | −0.633177 | + | 0.365565i | −0.781981 | − | 0.623302i | \(-0.785791\pi\) |
0.148804 | + | 0.988867i | \(0.452457\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 19011.0i | 0.881155i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 1755.00 | − | 3039.75i | 0.0810300 | − | 0.140348i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −882.000 | −0.0405660 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −24300.0 | −1.11334 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 1336.50 | − | 2314.89i | 0.0609995 | − | 0.105654i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 6541.96i | − | 0.297443i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 3252.00 | − | 1877.54i | 0.147295 | − | 0.0850409i | −0.424541 | − | 0.905409i | \(-0.639565\pi\) |
0.571836 | + | 0.820368i | \(0.306231\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 1107.00 | + | 1917.38i | 0.0499496 | + | 0.0865153i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −15309.0 | − | 8838.66i | −0.688148 | − | 0.397303i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 9347.00 | − | 32379.0i | 0.418565 | − | 1.44995i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −3523.50 | − | 2034.29i | −0.157190 | − | 0.0907534i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 3915.00 | + | 6780.98i | 0.173998 | + | 0.301373i | 0.939814 | − | 0.341686i | \(-0.110998\pi\) |
−0.765816 | + | 0.643060i | \(0.777665\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 7371.00 | − | 4255.65i | 0.326367 | − | 0.188428i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | − | 13655.5i | − | 0.602363i | ||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −17775.0 | + | 30787.2i | −0.781153 | + | 1.35300i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 972.000 | 0.0425571 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −6318.00 | −0.275594 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 3082.50 | − | 5339.05i | 0.133962 | − | 0.232028i | −0.791239 | − | 0.611507i | \(-0.790563\pi\) |
0.925200 | + | 0.379479i | \(0.123897\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 29839.8i | − | 1.29201i | −0.763335 | − | 0.646003i | \(-0.776440\pi\) | ||
0.763335 | − | 0.646003i | \(-0.223560\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 1782.00 | − | 1028.84i | 0.0768727 | − | 0.0443824i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 7668.00 | + | 13281.4i | 0.329568 | + | 0.570829i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1722.00 | − | 994.197i | −0.0737395 | − | 0.0425735i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −1053.00 | − | 4255.65i | −0.0449265 | − | 0.181568i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −25776.0 | − | 14881.8i | −1.09572 | − | 0.632616i | −0.160629 | − | 0.987015i | \(-0.551352\pi\) |
−0.935094 | + | 0.354399i | \(0.884685\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −4460.00 | − | 7724.95i | −0.188901 | − | 0.327187i | 0.755983 | − | 0.654591i | \(-0.227159\pi\) |
−0.944884 | + | 0.327405i | \(0.893826\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 13230.0 | − | 7638.34i | 0.558315 | − | 0.322343i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 18041.0i | − | 0.758583i | −0.925277 | − | 0.379292i | \(-0.876168\pi\) | ||
0.925277 | − | 0.379292i | \(-0.123832\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 10511.5 | − | 18206.5i | 0.440385 | − | 0.762770i | −0.557333 | − | 0.830289i | \(-0.688175\pi\) |
0.997718 | + | 0.0675195i | \(0.0215085\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 10995.0 | 0.458980 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −27495.0 | −1.14363 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 8154.00 | − | 14123.1i | 0.337941 | − | 0.585331i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 5237.72i | 0.216299i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 19116.0 | − | 11036.6i | 0.786600 | − | 0.454144i | −0.0521641 | − | 0.998639i | \(-0.516612\pi\) |
0.838764 | + | 0.544495i | \(0.183279\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 7294.00 | + | 12633.6i | 0.299069 | + | 0.518003i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −4468.50 | − | 2579.89i | −0.182566 | − | 0.105405i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 11407.5 | + | 439.075i | 0.464414 | + | 0.0178753i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −12321.0 | − | 7113.53i | −0.499828 | − | 0.288576i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −2739.00 | − | 4744.09i | −0.110721 | − | 0.191775i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1755.00 | − | 1013.25i | 0.0706940 | − | 0.0408152i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 26609.5i | 1.06810i | 0.845452 | + | 0.534051i | \(0.179331\pi\) | ||||
−0.845452 | + | 0.534051i | \(0.820669\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −567.000 | + | 982.073i | −0.0226795 | + | 0.0392821i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −12771.0 | −0.509042 | −0.254521 | − | 0.967067i | \(-0.581918\pi\) | ||||
−0.254521 | + | 0.967067i | \(0.581918\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −17134.0 | −0.680564 | −0.340282 | − | 0.940323i | \(-0.610523\pi\) | ||||
−0.340282 | + | 0.940323i | \(0.610523\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −567.000 | + | 982.073i | −0.0224429 | + | 0.0388722i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 7929.33i | − | 0.312766i | −0.987696 | − | 0.156383i | \(-0.950017\pi\) | ||
0.987696 | − | 0.156383i | \(-0.0499835\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −19197.0 | + | 11083.4i | −0.754587 | + | 0.435661i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −13164.0 | − | 22800.7i | −0.515655 | − | 0.893141i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −19800.0 | − | 11431.5i | −0.772922 | − | 0.446247i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −7917.00 | − | 31996.2i | −0.307988 | − | 1.24472i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 9018.00 | + | 5206.54i | 0.349614 | + | 0.201850i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 6021.00 | + | 10428.7i | 0.232625 | + | 0.402918i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 8542.50 | − | 4932.01i | 0.328916 | − | 0.189900i | −0.326443 | − | 0.945217i | \(-0.605850\pi\) |
0.655360 | + | 0.755317i | \(0.272517\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | − | 1512.08i | − | 0.0580218i | ||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −14584.5 | + | 25261.1i | −0.557735 | + | 0.966025i | 0.439950 | + | 0.898022i | \(0.354996\pi\) |
−0.997685 | + | 0.0680028i | \(0.978337\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −928.000 | −0.0353677 | −0.0176839 | − | 0.999844i | \(-0.505629\pi\) | ||||
−0.0176839 | + | 0.999844i | \(0.505629\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 12312.0 | 0.467642 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −7200.00 | + | 12470.8i | −0.272551 | + | 0.472071i | −0.969514 | − | 0.245035i | \(-0.921201\pi\) |
0.696964 | + | 0.717106i | \(0.254534\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 17292.8i | − | 0.652398i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 3645.00 | − | 2104.44i | 0.137051 | − | 0.0791262i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −882.000 | − | 1527.67i | −0.0330515 | − | 0.0572469i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −13527.0 | − | 7809.82i | −0.505204 | − | 0.291680i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 702.000 | − | 2431.80i | 0.0261305 | − | 0.0905189i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 16632.0 | + | 9602.49i | 0.617028 | + | 0.356241i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −15268.5 | − | 26445.8i | −0.564559 | − | 0.977845i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −2214.00 | + | 1278.25i | −0.0815917 | + | 0.0471070i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 9732.39i | 0.357476i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 9842.00 | − | 17046.8i | 0.360307 | − | 0.624070i | −0.627704 | − | 0.778452i | \(-0.716005\pi\) |
0.988011 | + | 0.154382i | \(0.0493387\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 14175.0 | 0.517222 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −24480.0 | −0.890295 | −0.445147 | − | 0.895457i | \(-0.646849\pi\) | ||||
−0.445147 | + | 0.895457i | \(0.646849\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 31050.0 | − | 53780.2i | 1.12553 | − | 1.94947i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 11208.1i | 0.404949i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −13284.0 | + | 7669.52i | −0.478382 | + | 0.276194i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 19304.0 | + | 33435.5i | 0.692906 | + | 1.20015i | 0.970882 | + | 0.239560i | \(0.0770031\pi\) |
−0.277976 | + | 0.960588i | \(0.589664\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −5067.00 | − | 2925.43i | −0.181285 | − | 0.104665i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −21060.0 | − | 6079.50i | −0.751027 | − | 0.216803i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 9555.00 | + | 5516.58i | 0.339639 | + | 0.196091i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 3573.00 | + | 6188.62i | 0.126594 | + | 0.219267i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 8842.50 | − | 5105.22i | 0.312285 | − | 0.180298i | −0.335663 | − | 0.941982i | \(-0.608960\pi\) |
0.647949 | + | 0.761684i | \(0.275627\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 5698.45i | 0.200600i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −5697.00 | + | 9867.49i | −0.199905 | + | 0.346246i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −31590.0 | −1.10492 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 28495.0 | 0.993480 | 0.496740 | − | 0.867899i | \(-0.334530\pi\) | ||||
0.496740 | + | 0.867899i | \(0.334530\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −2067.00 | + | 3580.15i | −0.0718360 | + | 0.124424i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 10724.9i | − | 0.371541i | −0.982593 | − | 0.185771i | \(-0.940522\pi\) | ||
0.982593 | − | 0.185771i | \(-0.0594782\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −567.000 | + | 327.358i | −0.0195801 | + | 0.0113046i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 729.000 | + | 1262.67i | 0.0250946 | + | 0.0434651i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −29412.0 | − | 16981.0i | −1.00925 | − | 0.582692i | −0.0982794 | − | 0.995159i | \(-0.531334\pi\) |
−0.910973 | + | 0.412467i | \(0.864667\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −23107.5 | + | 22235.2i | −0.790412 | + | 0.760575i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 18454.5 | + | 10654.7i | 0.629262 | + | 0.363305i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −11907.0 | − | 20623.5i | −0.404728 | − | 0.701009i | 0.589562 | − | 0.807723i | \(-0.299300\pi\) |
−0.994290 | + | 0.106714i | \(0.965967\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −12312.0 | + | 7108.34i | −0.417180 | + | 0.240859i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − | 15432.6i | − | 0.521279i | ||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −5265.00 | + | 9119.25i | −0.177284 | + | 0.307066i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −7841.00 | −0.263200 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −4050.00 | −0.135524 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −6763.50 | + | 11714.7i | −0.225622 | + | 0.390788i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 51549.3i | 1.71429i | 0.515079 | + | 0.857143i | \(0.327762\pi\) | ||||
−0.515079 | + | 0.857143i | \(0.672238\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −7371.00 | + | 4255.65i | −0.244366 | + | 0.141085i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −6156.00 | − | 10662.5i | −0.203456 | − | 0.352396i | 0.746184 | − | 0.665740i | \(-0.231884\pi\) |
−0.949640 | + | 0.313344i | \(0.898551\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −10116.0 | − | 5840.48i | −0.333303 | − | 0.192433i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 13377.0 | − | 3309.95i | 0.439392 | − | 0.108721i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 18652.5 | + | 10769.0i | 0.610795 | + | 0.352642i | 0.773276 | − | 0.634069i | \(-0.218617\pi\) |
−0.162482 | + | 0.986712i | \(0.551950\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −39420.0 | − | 68277.4i | −1.28689 | − | 2.22896i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −4644.00 | + | 2681.21i | −0.151143 | + | 0.0872626i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 32611.1i | − | 1.05812i | −0.848585 | − | 0.529060i | \(-0.822545\pi\) | ||
0.848585 | − | 0.529060i | \(-0.177455\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 9666.00 | − | 16742.0i | 0.312674 | − | 0.541568i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −2268.00 | −0.0731421 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −1476.00 | −0.0474561 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −11165.0 | + | 19338.3i | −0.357889 | + | 0.619882i | −0.987608 | − | 0.156941i | \(-0.949837\pi\) |
0.629719 | + | 0.776823i | \(0.283170\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 30220.8i | − | 0.965789i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 5391.00 | − | 3112.50i | 0.171765 | − | 0.0991686i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 12465.5 | + | 21590.9i | 0.395974 | + | 0.685848i | 0.993225 | − | 0.116207i | \(-0.0370736\pi\) |
−0.597251 | + | 0.802055i | \(0.703740\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 2632.50 | + | 1519.87i | 0.0833720 | + | 0.0481348i |
(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 | 624.4.bv.a.433.1 | 2 | ||
4.3 | odd | 2 | 39.4.j.a.4.1 | ✓ | 2 | ||
12.11 | even | 2 | 117.4.q.b.82.1 | 2 | |||
13.10 | even | 6 | inner | 624.4.bv.a.49.1 | 2 | ||
52.7 | even | 12 | 507.4.a.g.1.2 | 2 | |||
52.19 | even | 12 | 507.4.a.g.1.1 | 2 | |||
52.23 | odd | 6 | 39.4.j.a.10.1 | yes | 2 | ||
52.35 | odd | 6 | 507.4.b.a.337.1 | 2 | |||
52.43 | odd | 6 | 507.4.b.a.337.2 | 2 | |||
156.23 | even | 6 | 117.4.q.b.10.1 | 2 | |||
156.59 | odd | 12 | 1521.4.a.m.1.1 | 2 | |||
156.71 | odd | 12 | 1521.4.a.m.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
39.4.j.a.4.1 | ✓ | 2 | 4.3 | odd | 2 | ||
39.4.j.a.10.1 | yes | 2 | 52.23 | odd | 6 | ||
117.4.q.b.10.1 | 2 | 156.23 | even | 6 | |||
117.4.q.b.82.1 | 2 | 12.11 | even | 2 | |||
507.4.a.g.1.1 | 2 | 52.19 | even | 12 | |||
507.4.a.g.1.2 | 2 | 52.7 | even | 12 | |||
507.4.b.a.337.1 | 2 | 52.35 | odd | 6 | |||
507.4.b.a.337.2 | 2 | 52.43 | odd | 6 | |||
624.4.bv.a.49.1 | 2 | 13.10 | even | 6 | inner | ||
624.4.bv.a.433.1 | 2 | 1.1 | even | 1 | trivial | ||
1521.4.a.m.1.1 | 2 | 156.59 | odd | 12 | |||
1521.4.a.m.1.2 | 2 | 156.71 | odd | 12 |