Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [147,4,Mod(146,147)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(147, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("147.146");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 147 = 3 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 147.c (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(8.67328077084\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 146.4 | ||
Character | \(\chi\) | \(=\) | 147.146 |
Dual form | 147.4.c.b.146.22 |
$q$-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 \(\left(\mathbb{Z}/147\mathbb{Z}\right)^\times\).
\(n\) | \(50\) | \(52\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 4.84485i | − | 1.71291i | −0.516220 | − | 0.856456i | \(-0.672661\pi\) | ||
0.516220 | − | 0.856456i | \(-0.327339\pi\) | |||||||
\(3\) | 5.11673 | − | 0.905040i | 0.984715 | − | 0.174175i | ||||
\(4\) | −15.4725 | −1.93407 | ||||||||
\(5\) | 17.3012 | 1.54746 | 0.773732 | − | 0.633513i | \(-0.218388\pi\) | ||||
0.773732 | + | 0.633513i | \(0.218388\pi\) | |||||||
\(6\) | −4.38478 | − | 24.7898i | −0.298346 | − | 1.68673i | ||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 36.2033i | 1.59998i | ||||||||
\(9\) | 25.3618 | − | 9.26169i | 0.939326 | − | 0.343025i | ||||
\(10\) | − | 83.8216i | − | 2.65067i | ||||||
\(11\) | − | 27.8490i | − | 0.763344i | −0.924298 | − | 0.381672i | \(-0.875348\pi\) | ||
0.924298 | − | 0.381672i | \(-0.124652\pi\) | |||||||
\(12\) | −79.1688 | + | 14.0033i | −1.90450 | + | 0.336866i | ||||
\(13\) | 16.3036i | 0.347830i | 0.984761 | + | 0.173915i | \(0.0556419\pi\) | ||||
−0.984761 | + | 0.173915i | \(0.944358\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 88.5254 | − | 15.6583i | 1.52381 | − | 0.269530i | ||||
\(16\) | 51.6191 | 0.806549 | ||||||||
\(17\) | −40.8263 | −0.582461 | −0.291231 | − | 0.956653i | \(-0.594065\pi\) | ||||
−0.291231 | + | 0.956653i | \(0.594065\pi\) | |||||||
\(18\) | −44.8715 | − | 122.874i | −0.587572 | − | 1.60898i | ||||
\(19\) | − | 68.1627i | − | 0.823031i | −0.911403 | − | 0.411515i | \(-0.865000\pi\) | ||
0.911403 | − | 0.411515i | \(-0.135000\pi\) | |||||||
\(20\) | −267.693 | −2.99290 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −134.924 | −1.30754 | ||||||||
\(23\) | 71.7749i | 0.650700i | 0.945594 | + | 0.325350i | \(0.105482\pi\) | ||||
−0.945594 | + | 0.325350i | \(0.894518\pi\) | |||||||
\(24\) | 32.7654 | + | 185.242i | 0.278676 | + | 1.57552i | ||||
\(25\) | 174.331 | 1.39465 | ||||||||
\(26\) | 78.9883 | 0.595803 | ||||||||
\(27\) | 121.387 | − | 70.3430i | 0.865222 | − | 0.501389i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 216.426i | 1.38584i | 0.721014 | + | 0.692920i | \(0.243676\pi\) | ||||
−0.721014 | + | 0.692920i | \(0.756324\pi\) | |||||||
\(30\) | −75.8619 | − | 428.892i | −0.461681 | − | 2.61015i | ||||
\(31\) | 157.351i | 0.911646i | 0.890070 | + | 0.455823i | \(0.150655\pi\) | ||||
−0.890070 | + | 0.455823i | \(0.849345\pi\) | |||||||
\(32\) | 39.5396i | 0.218428i | ||||||||
\(33\) | −25.2044 | − | 142.496i | −0.132955 | − | 0.751676i | ||||
\(34\) | 197.797i | 0.997705i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −392.412 | + | 143.302i | −1.81672 | + | 0.663434i | ||||
\(37\) | −348.489 | −1.54841 | −0.774207 | − | 0.632933i | \(-0.781851\pi\) | ||||
−0.774207 | + | 0.632933i | \(0.781851\pi\) | |||||||
\(38\) | −330.238 | −1.40978 | ||||||||
\(39\) | 14.7554 | + | 83.4209i | 0.0605834 | + | 0.342514i | ||||
\(40\) | 626.360i | 2.47590i | ||||||||
\(41\) | −153.371 | −0.584208 | −0.292104 | − | 0.956387i | \(-0.594355\pi\) | ||||
−0.292104 | + | 0.956387i | \(0.594355\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 427.584 | 1.51642 | 0.758208 | − | 0.652012i | \(-0.226075\pi\) | ||||
0.758208 | + | 0.652012i | \(0.226075\pi\) | |||||||
\(44\) | 430.894i | 1.47636i | ||||||||
\(45\) | 438.789 | − | 160.238i | 1.45357 | − | 0.530820i | ||||
\(46\) | 347.738 | 1.11459 | ||||||||
\(47\) | −16.8103 | −0.0521708 | −0.0260854 | − | 0.999660i | \(-0.508304\pi\) | ||||
−0.0260854 | + | 0.999660i | \(0.508304\pi\) | |||||||
\(48\) | 264.121 | − | 46.7174i | 0.794221 | − | 0.140481i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | − | 844.606i | − | 2.38891i | ||||||
\(51\) | −208.897 | + | 36.9495i | −0.573558 | + | 0.101450i | ||||
\(52\) | − | 252.258i | − | 0.672727i | ||||||
\(53\) | − | 192.526i | − | 0.498971i | −0.968379 | − | 0.249486i | \(-0.919738\pi\) | ||
0.968379 | − | 0.249486i | \(-0.0802615\pi\) | |||||||
\(54\) | −340.801 | − | 588.103i | −0.858836 | − | 1.48205i | ||||
\(55\) | − | 481.820i | − | 1.18125i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −61.6899 | − | 348.770i | −0.143351 | − | 0.810451i | ||||
\(58\) | 1048.55 | 2.37382 | ||||||||
\(59\) | 287.422 | 0.634224 | 0.317112 | − | 0.948388i | \(-0.397287\pi\) | ||||
0.317112 | + | 0.948388i | \(0.397287\pi\) | |||||||
\(60\) | −1369.71 | + | 242.273i | −2.94715 | + | 0.521289i | ||||
\(61\) | − | 224.297i | − | 0.470792i | −0.971900 | − | 0.235396i | \(-0.924361\pi\) | ||
0.971900 | − | 0.235396i | \(-0.0756387\pi\) | |||||||
\(62\) | 762.340 | 1.56157 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 604.516 | 1.18070 | ||||||||
\(65\) | 282.071i | 0.538255i | ||||||||
\(66\) | −690.370 | + | 122.112i | −1.28755 | + | 0.227741i | ||||
\(67\) | −172.206 | −0.314004 | −0.157002 | − | 0.987598i | \(-0.550183\pi\) | ||||
−0.157002 | + | 0.987598i | \(0.550183\pi\) | |||||||
\(68\) | 631.687 | 1.12652 | ||||||||
\(69\) | 64.9591 | + | 367.252i | 0.113336 | + | 0.640754i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1068.78i | 1.78649i | 0.449569 | + | 0.893246i | \(0.351578\pi\) | ||||
−0.449569 | + | 0.893246i | \(0.648422\pi\) | |||||||
\(72\) | 335.304 | + | 918.181i | 0.548832 | + | 1.50290i | ||||
\(73\) | − | 1078.22i | − | 1.72871i | −0.502881 | − | 0.864356i | \(-0.667726\pi\) | ||
0.502881 | − | 0.864356i | \(-0.332274\pi\) | |||||||
\(74\) | 1688.38i | 2.65230i | ||||||||
\(75\) | 892.004 | − | 157.776i | 1.37333 | − | 0.242913i | ||||
\(76\) | 1054.65i | 1.59180i | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 404.161 | − | 71.4875i | 0.586696 | − | 0.103774i | ||||
\(79\) | 52.0336 | 0.0741043 | 0.0370521 | − | 0.999313i | \(-0.488203\pi\) | ||||
0.0370521 | + | 0.999313i | \(0.488203\pi\) | |||||||
\(80\) | 893.072 | 1.24811 | ||||||||
\(81\) | 557.442 | − | 469.786i | 0.764667 | − | 0.644426i | ||||
\(82\) | 743.059i | 1.00070i | ||||||||
\(83\) | 1023.07 | 1.35298 | 0.676488 | − | 0.736454i | \(-0.263501\pi\) | ||||
0.676488 | + | 0.736454i | \(0.263501\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −706.344 | −0.901338 | ||||||||
\(86\) | − | 2071.58i | − | 2.59749i | ||||||
\(87\) | 195.874 | + | 1107.39i | 0.241379 | + | 1.36466i | ||||
\(88\) | 1008.23 | 1.22133 | ||||||||
\(89\) | −668.570 | −0.796272 | −0.398136 | − | 0.917326i | \(-0.630343\pi\) | ||||
−0.398136 | + | 0.917326i | \(0.630343\pi\) | |||||||
\(90\) | −776.329 | − | 2125.87i | −0.909247 | − | 2.48984i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | − | 1110.54i | − | 1.25850i | ||||||
\(93\) | 142.409 | + | 805.121i | 0.158786 | + | 0.897711i | ||||
\(94\) | 81.4431i | 0.0893640i | ||||||||
\(95\) | − | 1179.29i | − | 1.27361i | ||||||
\(96\) | 35.7849 | + | 202.313i | 0.0380446 | + | 0.215089i | ||||
\(97\) | 1358.39i | 1.42190i | 0.703244 | + | 0.710949i | \(0.251734\pi\) | ||||
−0.703244 | + | 0.710949i | \(0.748266\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −257.929 | − | 706.300i | −0.261846 | − | 0.717029i | ||||
\(100\) | −2697.34 | −2.69734 | ||||||||
\(101\) | −29.0959 | −0.0286649 | −0.0143324 | − | 0.999897i | \(-0.504562\pi\) | ||||
−0.0143324 | + | 0.999897i | \(0.504562\pi\) | |||||||
\(102\) | 179.015 | + | 1012.08i | 0.173775 | + | 0.982455i | ||||
\(103\) | 300.909i | 0.287859i | 0.989588 | + | 0.143929i | \(0.0459738\pi\) | ||||
−0.989588 | + | 0.143929i | \(0.954026\pi\) | |||||||
\(104\) | −590.243 | −0.556520 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −932.759 | −0.854694 | ||||||||
\(107\) | 523.431i | 0.472916i | 0.971642 | + | 0.236458i | \(0.0759866\pi\) | ||||
−0.971642 | + | 0.236458i | \(0.924013\pi\) | |||||||
\(108\) | −1878.17 | + | 1088.38i | −1.67340 | + | 0.969721i | ||||
\(109\) | −62.6812 | −0.0550805 | −0.0275402 | − | 0.999621i | \(-0.508767\pi\) | ||||
−0.0275402 | + | 0.999621i | \(0.508767\pi\) | |||||||
\(110\) | −2334.35 | −2.02337 | ||||||||
\(111\) | −1783.13 | + | 315.397i | −1.52475 | + | 0.269695i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 84.9426i | − | 0.0707144i | −0.999375 | − | 0.0353572i | \(-0.988743\pi\) | ||
0.999375 | − | 0.0353572i | \(-0.0112569\pi\) | |||||||
\(114\) | −1689.74 | + | 298.878i | −1.38823 | + | 0.245548i | ||||
\(115\) | 1241.79i | 1.00693i | ||||||||
\(116\) | − | 3348.66i | − | 2.68031i | ||||||
\(117\) | 150.998 | + | 413.488i | 0.119315 | + | 0.326726i | ||||
\(118\) | − | 1392.52i | − | 1.08637i | ||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 566.881 | + | 3204.91i | 0.431241 | + | 2.43806i | ||||
\(121\) | 555.434 | 0.417306 | ||||||||
\(122\) | −1086.69 | −0.806425 | ||||||||
\(123\) | −784.758 | + | 138.807i | −0.575278 | + | 0.101754i | ||||
\(124\) | − | 2434.62i | − | 1.76318i | ||||||
\(125\) | 853.482 | 0.610702 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1842.84 | −1.28760 | −0.643802 | − | 0.765192i | \(-0.722644\pi\) | ||||
−0.643802 | + | 0.765192i | \(0.722644\pi\) | |||||||
\(128\) | − | 2612.47i | − | 1.80400i | ||||||
\(129\) | 2187.83 | − | 386.981i | 1.49324 | − | 0.264122i | ||||
\(130\) | 1366.59 | 0.921984 | ||||||||
\(131\) | 97.8698 | 0.0652742 | 0.0326371 | − | 0.999467i | \(-0.489609\pi\) | ||||
0.0326371 | + | 0.999467i | \(0.489609\pi\) | |||||||
\(132\) | 389.977 | + | 2204.77i | 0.257145 | + | 1.45379i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 834.310i | 0.537861i | ||||||||
\(135\) | 2100.14 | − | 1217.02i | 1.33890 | − | 0.775882i | ||||
\(136\) | − | 1478.05i | − | 0.931924i | ||||||
\(137\) | 1693.85i | 1.05631i | 0.849147 | + | 0.528157i | \(0.177117\pi\) | ||||
−0.849147 | + | 0.528157i | \(0.822883\pi\) | |||||||
\(138\) | 1779.28 | − | 314.717i | 1.09755 | − | 0.194134i | ||||
\(139\) | − | 1821.25i | − | 1.11134i | −0.831402 | − | 0.555672i | \(-0.812461\pi\) | ||
0.831402 | − | 0.555672i | \(-0.187539\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −86.0135 | + | 15.2139i | −0.0513733 | + | 0.00908685i | ||||
\(142\) | 5178.08 | 3.06010 | ||||||||
\(143\) | 454.038 | 0.265514 | ||||||||
\(144\) | 1309.15 | − | 478.080i | 0.757613 | − | 0.276667i | ||||
\(145\) | 3744.43i | 2.14454i | ||||||||
\(146\) | −5223.80 | −2.96113 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 5392.02 | 2.99474 | ||||||||
\(149\) | 1798.00i | 0.988574i | 0.869299 | + | 0.494287i | \(0.164571\pi\) | ||||
−0.869299 | + | 0.494287i | \(0.835429\pi\) | |||||||
\(150\) | −764.402 | − | 4321.62i | −0.416088 | − | 2.35239i | ||||
\(151\) | −2089.84 | −1.12628 | −0.563141 | − | 0.826361i | \(-0.690407\pi\) | ||||
−0.563141 | + | 0.826361i | \(0.690407\pi\) | |||||||
\(152\) | 2467.71 | 1.31683 | ||||||||
\(153\) | −1035.43 | + | 378.121i | −0.547121 | + | 0.199799i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 2722.35i | 1.41074i | ||||||||
\(156\) | −228.303 | − | 1290.73i | −0.117172 | − | 0.662445i | ||||
\(157\) | 1090.34i | 0.554258i | 0.960833 | + | 0.277129i | \(0.0893829\pi\) | ||||
−0.960833 | + | 0.277129i | \(0.910617\pi\) | |||||||
\(158\) | − | 252.095i | − | 0.126934i | ||||||
\(159\) | −174.244 | − | 985.103i | −0.0869083 | − | 0.491344i | ||||
\(160\) | 684.082i | 0.338009i | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −2276.04 | − | 2700.72i | −1.10384 | − | 1.30981i | ||||
\(163\) | −1940.53 | −0.932478 | −0.466239 | − | 0.884659i | \(-0.654391\pi\) | ||||
−0.466239 | + | 0.884659i | \(0.654391\pi\) | |||||||
\(164\) | 2373.04 | 1.12990 | ||||||||
\(165\) | −436.067 | − | 2465.34i | −0.205744 | − | 1.16319i | ||||
\(166\) | − | 4956.64i | − | 2.31753i | ||||||
\(167\) | 2664.87 | 1.23481 | 0.617406 | − | 0.786645i | \(-0.288184\pi\) | ||||
0.617406 | + | 0.786645i | \(0.288184\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1931.19 | 0.879014 | ||||||||
\(170\) | 3422.13i | 1.54391i | ||||||||
\(171\) | −631.301 | − | 1728.73i | −0.282320 | − | 0.773094i | ||||
\(172\) | −6615.81 | −2.93285 | ||||||||
\(173\) | −3096.19 | −1.36069 | −0.680343 | − | 0.732894i | \(-0.738169\pi\) | ||||
−0.680343 | + | 0.732894i | \(0.738169\pi\) | |||||||
\(174\) | 5365.16 | − | 948.982i | 2.33754 | − | 0.413461i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | − | 1437.54i | − | 0.615674i | ||||||
\(177\) | 1470.66 | − | 260.129i | 0.624529 | − | 0.110466i | ||||
\(178\) | 3239.12i | 1.36394i | ||||||||
\(179\) | 902.641i | 0.376908i | 0.982082 | + | 0.188454i | \(0.0603476\pi\) | ||||
−0.982082 | + | 0.188454i | \(0.939652\pi\) | |||||||
\(180\) | −6789.18 | + | 2479.29i | −2.81131 | + | 1.02664i | ||||
\(181\) | − | 3496.01i | − | 1.43567i | −0.696213 | − | 0.717835i | \(-0.745133\pi\) | ||
0.696213 | − | 0.717835i | \(-0.254867\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −202.998 | − | 1147.67i | −0.0820002 | − | 0.463596i | ||||
\(184\) | −2598.49 | −1.04110 | ||||||||
\(185\) | −6029.28 | −2.39612 | ||||||||
\(186\) | 3900.69 | − | 689.948i | 1.53770 | − | 0.271986i | ||||
\(187\) | 1136.97i | 0.444618i | ||||||||
\(188\) | 260.097 | 0.100902 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −5713.50 | −2.18158 | ||||||||
\(191\) | 354.514i | 0.134302i | 0.997743 | + | 0.0671512i | \(0.0213910\pi\) | ||||
−0.997743 | + | 0.0671512i | \(0.978609\pi\) | |||||||
\(192\) | 3093.15 | − | 547.112i | 1.16265 | − | 0.205648i | ||||
\(193\) | 2839.88 | 1.05917 | 0.529584 | − | 0.848258i | \(-0.322348\pi\) | ||||
0.529584 | + | 0.848258i | \(0.322348\pi\) | |||||||
\(194\) | 6581.21 | 2.43559 | ||||||||
\(195\) | 255.285 | + | 1443.28i | 0.0937506 | + | 0.530028i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 3058.25i | − | 1.10605i | −0.833165 | − | 0.553024i | \(-0.813474\pi\) | ||
0.833165 | − | 0.553024i | \(-0.186526\pi\) | |||||||
\(198\) | −3421.92 | + | 1249.62i | −1.22821 | + | 0.448520i | ||||
\(199\) | − | 1839.48i | − | 0.655264i | −0.944805 | − | 0.327632i | \(-0.893749\pi\) | ||
0.944805 | − | 0.327632i | \(-0.106251\pi\) | |||||||
\(200\) | 6311.35i | 2.23140i | ||||||||
\(201\) | −881.129 | + | 155.853i | −0.309204 | + | 0.0546916i | ||||
\(202\) | 140.965i | 0.0491004i | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 3232.17 | − | 571.702i | 1.10930 | − | 0.196212i | ||||
\(205\) | −2653.50 | −0.904041 | ||||||||
\(206\) | 1457.86 | 0.493077 | ||||||||
\(207\) | 664.756 | + | 1820.34i | 0.223207 | + | 0.611219i | ||||
\(208\) | 841.576i | 0.280542i | ||||||||
\(209\) | −1898.26 | −0.628256 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −644.694 | −0.210344 | −0.105172 | − | 0.994454i | \(-0.533539\pi\) | ||||
−0.105172 | + | 0.994454i | \(0.533539\pi\) | |||||||
\(212\) | 2978.86i | 0.965044i | ||||||||
\(213\) | 967.289 | + | 5468.66i | 0.311162 | + | 1.75918i | ||||
\(214\) | 2535.94 | 0.810063 | ||||||||
\(215\) | 7397.71 | 2.34660 | ||||||||
\(216\) | 2546.65 | + | 4394.62i | 0.802210 | + | 1.38433i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 303.681i | 0.0943480i | ||||||||
\(219\) | −975.831 | − | 5516.95i | −0.301098 | − | 1.70229i | ||||
\(220\) | 7454.98i | 2.28461i | ||||||||
\(221\) | − | 665.615i | − | 0.202598i | ||||||
\(222\) | 1528.05 | + | 8638.97i | 0.461964 | + | 2.61176i | ||||
\(223\) | 3760.55i | 1.12926i | 0.825344 | + | 0.564630i | \(0.190981\pi\) | ||||
−0.825344 | + | 0.564630i | \(0.809019\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 4421.35 | − | 1614.60i | 1.31003 | − | 0.478399i | ||||
\(226\) | −411.534 | −0.121128 | ||||||||
\(227\) | 2836.86 | 0.829467 | 0.414733 | − | 0.909943i | \(-0.363875\pi\) | ||||
0.414733 | + | 0.909943i | \(0.363875\pi\) | |||||||
\(228\) | 954.500 | + | 5396.35i | 0.277251 | + | 1.56747i | ||||
\(229\) | − | 5207.86i | − | 1.50282i | −0.659837 | − | 0.751409i | \(-0.729375\pi\) | ||
0.659837 | − | 0.751409i | \(-0.270625\pi\) | |||||||
\(230\) | 6016.28 | 1.72479 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −7835.35 | −2.21731 | ||||||||
\(233\) | − | 2185.90i | − | 0.614604i | −0.951612 | − | 0.307302i | \(-0.900574\pi\) | ||
0.951612 | − | 0.307302i | \(-0.0994262\pi\) | |||||||
\(234\) | 2003.28 | − | 731.565i | 0.559653 | − | 0.204376i | ||||
\(235\) | −290.837 | −0.0807325 | ||||||||
\(236\) | −4447.15 | −1.22663 | ||||||||
\(237\) | 266.242 | − | 47.0925i | 0.0729716 | − | 0.0129071i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1921.87i | 0.520148i | 0.965589 | + | 0.260074i | \(0.0837469\pi\) | ||||
−0.965589 | + | 0.260074i | \(0.916253\pi\) | |||||||
\(240\) | 4569.61 | − | 808.266i | 1.22903 | − | 0.217389i | ||||
\(241\) | − | 4476.26i | − | 1.19644i | −0.801333 | − | 0.598218i | \(-0.795876\pi\) | ||
0.801333 | − | 0.598218i | \(-0.204124\pi\) | |||||||
\(242\) | − | 2690.99i | − | 0.714809i | ||||||
\(243\) | 2427.11 | − | 2908.28i | 0.640736 | − | 0.767761i | ||||
\(244\) | 3470.45i | 0.910543i | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 672.498 | + | 3802.03i | 0.174296 | + | 0.985401i | ||||
\(247\) | 1111.29 | 0.286275 | ||||||||
\(248\) | −5696.62 | −1.45861 | ||||||||
\(249\) | 5234.79 | − | 925.923i | 1.33230 | − | 0.235655i | ||||
\(250\) | − | 4134.99i | − | 1.04608i | ||||||
\(251\) | −3296.51 | −0.828980 | −0.414490 | − | 0.910054i | \(-0.636040\pi\) | ||||
−0.414490 | + | 0.910054i | \(0.636040\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1998.86 | 0.496708 | ||||||||
\(254\) | 8928.28i | 2.20555i | ||||||||
\(255\) | −3614.17 | + | 639.270i | −0.887561 | + | 0.156991i | ||||
\(256\) | −7820.90 | −1.90940 | ||||||||
\(257\) | −7110.67 | −1.72588 | −0.862940 | − | 0.505307i | \(-0.831379\pi\) | ||||
−0.862940 | + | 0.505307i | \(0.831379\pi\) | |||||||
\(258\) | −1874.86 | − | 10599.7i | −0.452418 | − | 2.55779i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | − | 4364.35i | − | 1.04102i | ||||||
\(261\) | 2004.47 | + | 5488.96i | 0.475378 | + | 1.30176i | ||||
\(262\) | − | 474.164i | − | 0.111809i | ||||||
\(263\) | 6808.88i | 1.59640i | 0.602391 | + | 0.798201i | \(0.294215\pi\) | ||||
−0.602391 | + | 0.798201i | \(0.705785\pi\) | |||||||
\(264\) | 5158.81 | − | 912.484i | 1.20266 | − | 0.212725i | ||||
\(265\) | − | 3330.93i | − | 0.772140i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −3420.89 | + | 605.082i | −0.784101 | + | 0.138691i | ||||
\(268\) | 2664.46 | 0.607305 | ||||||||
\(269\) | −3603.91 | −0.816856 | −0.408428 | − | 0.912791i | \(-0.633923\pi\) | ||||
−0.408428 | + | 0.912791i | \(0.633923\pi\) | |||||||
\(270\) | −5896.26 | − | 10174.9i | −1.32902 | − | 2.29342i | ||||
\(271\) | − | 3376.15i | − | 0.756777i | −0.925647 | − | 0.378388i | \(-0.876478\pi\) | ||
0.925647 | − | 0.378388i | \(-0.123522\pi\) | |||||||
\(272\) | −2107.42 | −0.469784 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 8206.42 | 1.80937 | ||||||||
\(275\) | − | 4854.94i | − | 1.06460i | ||||||
\(276\) | −1005.08 | − | 5682.33i | −0.219199 | − | 1.23926i | ||||
\(277\) | −6940.10 | −1.50538 | −0.752690 | − | 0.658375i | \(-0.771244\pi\) | ||||
−0.752690 | + | 0.658375i | \(0.771244\pi\) | |||||||
\(278\) | −8823.70 | −1.90363 | ||||||||
\(279\) | 1457.33 | + | 3990.70i | 0.312718 | + | 0.856333i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 3834.00i | − | 0.813940i | −0.913441 | − | 0.406970i | \(-0.866585\pi\) | ||
0.913441 | − | 0.406970i | \(-0.133415\pi\) | |||||||
\(282\) | 73.7093 | + | 416.722i | 0.0155650 | + | 0.0879980i | ||||
\(283\) | − | 6443.70i | − | 1.35349i | −0.736217 | − | 0.676746i | \(-0.763390\pi\) | ||
0.736217 | − | 0.676746i | \(-0.236610\pi\) | |||||||
\(284\) | − | 16536.7i | − | 3.45519i | ||||||
\(285\) | −1067.31 | − | 6034.13i | −0.221831 | − | 1.25414i | ||||
\(286\) | − | 2199.74i | − | 0.454802i | ||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 366.203 | + | 1002.80i | 0.0749262 | + | 0.205175i | ||||
\(289\) | −3246.21 | −0.660739 | ||||||||
\(290\) | 18141.2 | 3.67341 | ||||||||
\(291\) | 1229.40 | + | 6950.54i | 0.247659 | + | 1.40016i | ||||
\(292\) | 16682.8i | 3.34344i | ||||||||
\(293\) | −1443.22 | −0.287760 | −0.143880 | − | 0.989595i | \(-0.545958\pi\) | ||||
−0.143880 | + | 0.989595i | \(0.545958\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 4972.74 | 0.981439 | ||||||||
\(296\) | − | 12616.5i | − | 2.47742i | ||||||
\(297\) | −1958.98 | − | 3380.51i | −0.382733 | − | 0.660462i | ||||
\(298\) | 8711.01 | 1.69334 | ||||||||
\(299\) | −1170.19 | −0.226333 | ||||||||
\(300\) | −13801.6 | + | 2441.20i | −2.65611 | + | 0.469809i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 10124.9i | 1.92922i | ||||||||
\(303\) | −148.876 | + | 26.3330i | −0.0282267 | + | 0.00499271i | ||||
\(304\) | − | 3518.50i | − | 0.663815i | ||||||
\(305\) | − | 3880.61i | − | 0.728534i | ||||||
\(306\) | 1831.94 | + | 5016.50i | 0.342238 | + | 0.937170i | ||||
\(307\) | − | 5504.32i | − | 1.02328i | −0.859199 | − | 0.511642i | \(-0.829038\pi\) | ||
0.859199 | − | 0.511642i | \(-0.170962\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 272.335 | + | 1539.67i | 0.0501378 | + | 0.283459i | ||||
\(310\) | 13189.4 | 2.41647 | ||||||||
\(311\) | 2419.45 | 0.441140 | 0.220570 | − | 0.975371i | \(-0.429208\pi\) | ||||
0.220570 | + | 0.975371i | \(0.429208\pi\) | |||||||
\(312\) | −3020.11 | + | 534.193i | −0.548013 | + | 0.0969319i | ||||
\(313\) | 1190.38i | 0.214966i | 0.994207 | + | 0.107483i | \(0.0342791\pi\) | ||||
−0.994207 | + | 0.107483i | \(0.965721\pi\) | |||||||
\(314\) | 5282.52 | 0.949395 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −805.092 | −0.143323 | ||||||||
\(317\) | − | 6628.17i | − | 1.17437i | −0.809453 | − | 0.587185i | \(-0.800236\pi\) | ||
0.809453 | − | 0.587185i | \(-0.199764\pi\) | |||||||
\(318\) | −4772.67 | + | 844.184i | −0.841629 | + | 0.148866i | ||||
\(319\) | 6027.25 | 1.05787 | ||||||||
\(320\) | 10458.8 | 1.82709 | ||||||||
\(321\) | 473.726 | + | 2678.25i | 0.0823701 | + | 0.465687i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 2782.83i | 0.479384i | ||||||||
\(324\) | −8625.05 | + | 7268.78i | −1.47892 | + | 1.24636i | ||||
\(325\) | 2842.21i | 0.485101i | ||||||||
\(326\) | 9401.56i | 1.59725i | ||||||||
\(327\) | −320.723 | + | 56.7290i | −0.0542385 | + | 0.00959364i | ||||
\(328\) | − | 5552.54i | − | 0.934718i | ||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −11944.2 | + | 2112.68i | −1.99245 | + | 0.352421i | ||||
\(331\) | −7185.16 | −1.19315 | −0.596574 | − | 0.802558i | \(-0.703472\pi\) | ||||
−0.596574 | + | 0.802558i | \(0.703472\pi\) | |||||||
\(332\) | −15829.6 | −2.61675 | ||||||||
\(333\) | −8838.32 | + | 3227.60i | −1.45447 | + | 0.531145i | ||||
\(334\) | − | 12910.9i | − | 2.11512i | ||||||
\(335\) | −2979.36 | −0.485910 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −7214.56 | −1.16618 | −0.583090 | − | 0.812408i | \(-0.698156\pi\) | ||||
−0.583090 | + | 0.812408i | \(0.698156\pi\) | |||||||
\(338\) | − | 9356.34i | − | 1.50567i | ||||||
\(339\) | −76.8764 | − | 434.628i | −0.0123167 | − | 0.0696335i | ||||
\(340\) | 10928.9 | 1.74325 | ||||||||
\(341\) | 4382.06 | 0.695899 | ||||||||
\(342\) | −8375.42 | + | 3058.56i | −1.32424 | + | 0.483590i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 15479.9i | 2.42623i | ||||||||
\(345\) | 1123.87 | + | 6353.90i | 0.175383 | + | 0.991543i | ||||
\(346\) | 15000.6i | 2.33074i | ||||||||
\(347\) | − | 8151.04i | − | 1.26101i | −0.776185 | − | 0.630505i | \(-0.782848\pi\) | ||
0.776185 | − | 0.630505i | \(-0.217152\pi\) | |||||||
\(348\) | −3030.68 | − | 17134.2i | −0.466843 | − | 2.63934i | ||||
\(349\) | 491.916i | 0.0754489i | 0.999288 | + | 0.0377245i | \(0.0120109\pi\) | ||||
−0.999288 | + | 0.0377245i | \(0.987989\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1146.84 | + | 1979.04i | 0.174398 | + | 0.300950i | ||||
\(352\) | 1101.14 | 0.166735 | ||||||||
\(353\) | 2923.64 | 0.440820 | 0.220410 | − | 0.975407i | \(-0.429260\pi\) | ||||
0.220410 | + | 0.975407i | \(0.429260\pi\) | |||||||
\(354\) | −1260.28 | − | 7125.13i | −0.189218 | − | 1.06976i | ||||
\(355\) | 18491.2i | 2.76453i | ||||||||
\(356\) | 10344.5 | 1.54004 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 4373.16 | 0.645610 | ||||||||
\(359\) | − | 4802.16i | − | 0.705985i | −0.935626 | − | 0.352992i | \(-0.885164\pi\) | ||
0.935626 | − | 0.352992i | \(-0.114836\pi\) | |||||||
\(360\) | 5801.15 | + | 15885.6i | 0.849298 | + | 2.32568i | ||||
\(361\) | 2212.85 | 0.322620 | ||||||||
\(362\) | −16937.6 | −2.45918 | ||||||||
\(363\) | 2842.01 | − | 502.690i | 0.410927 | − | 0.0726843i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 18654.5i | − | 2.67512i | ||||||
\(366\) | −5560.27 | + | 983.494i | −0.794099 | + | 0.140459i | ||||
\(367\) | 8957.91i | 1.27411i | 0.770817 | + | 0.637056i | \(0.219848\pi\) | ||||
−0.770817 | + | 0.637056i | \(0.780152\pi\) | |||||||
\(368\) | 3704.96i | 0.524821i | ||||||||
\(369\) | −3889.77 | + | 1420.47i | −0.548762 | + | 0.200398i | ||||
\(370\) | 29210.9i | 4.10434i | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −2203.42 | − | 12457.3i | −0.307103 | − | 1.73623i | ||||
\(373\) | −5072.83 | −0.704186 | −0.352093 | − | 0.935965i | \(-0.614530\pi\) | ||||
−0.352093 | + | 0.935965i | \(0.614530\pi\) | |||||||
\(374\) | 5508.45 | 0.761592 | ||||||||
\(375\) | 4367.04 | − | 772.435i | 0.601367 | − | 0.106369i | ||||
\(376\) | − | 608.587i | − | 0.0834720i | ||||||
\(377\) | −3528.52 | −0.482037 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −855.835 | −0.115993 | −0.0579964 | − | 0.998317i | \(-0.518471\pi\) | ||||
−0.0579964 | + | 0.998317i | \(0.518471\pi\) | |||||||
\(380\) | 18246.7i | 2.46325i | ||||||||
\(381\) | −9429.31 | + | 1667.84i | −1.26792 | + | 0.224268i | ||||
\(382\) | 1717.57 | 0.230048 | ||||||||
\(383\) | 7080.61 | 0.944653 | 0.472326 | − | 0.881424i | \(-0.343414\pi\) | ||||
0.472326 | + | 0.881424i | \(0.343414\pi\) | |||||||
\(384\) | −2364.39 | − | 13367.3i | −0.314212 | − | 1.77643i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | − | 13758.8i | − | 1.81426i | ||||||
\(387\) | 10844.3 | − | 3960.15i | 1.42441 | − | 0.520170i | ||||
\(388\) | − | 21017.8i | − | 2.75005i | ||||||
\(389\) | − | 2073.59i | − | 0.270270i | −0.990827 | − | 0.135135i | \(-0.956853\pi\) | ||
0.990827 | − | 0.135135i | \(-0.0431468\pi\) | |||||||
\(390\) | 6992.47 | − | 1236.82i | 0.907891 | − | 0.160587i | ||||
\(391\) | − | 2930.31i | − | 0.379007i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 500.773 | − | 88.5761i | 0.0642765 | − | 0.0113691i | ||||
\(394\) | −14816.8 | −1.89456 | ||||||||
\(395\) | 900.243 | 0.114674 | ||||||||
\(396\) | 3990.81 | + | 10928.3i | 0.506429 | + | 1.38678i | ||||
\(397\) | − | 5722.06i | − | 0.723380i | −0.932298 | − | 0.361690i | \(-0.882200\pi\) | ||
0.932298 | − | 0.361690i | \(-0.117800\pi\) | |||||||
\(398\) | −8912.01 | −1.12241 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 8998.81 | 1.12485 | ||||||||
\(401\) | 11728.9i | 1.46064i | 0.683107 | + | 0.730319i | \(0.260628\pi\) | ||||
−0.683107 | + | 0.730319i | \(0.739372\pi\) | |||||||
\(402\) | 755.084 | + | 4268.94i | 0.0936820 | + | 0.529640i | ||||
\(403\) | −2565.38 | −0.317098 | ||||||||
\(404\) | 450.188 | 0.0554398 | ||||||||
\(405\) | 9644.41 | − | 8127.86i | 1.18330 | − | 0.997226i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 9705.08i | 1.18197i | ||||||||
\(408\) | −1337.69 | − | 7562.77i | −0.162318 | − | 0.917679i | ||||
\(409\) | − | 2623.53i | − | 0.317176i | −0.987345 | − | 0.158588i | \(-0.949306\pi\) | ||
0.987345 | − | 0.158588i | \(-0.0506942\pi\) | |||||||
\(410\) | 12855.8i | 1.54854i | ||||||||
\(411\) | 1533.00 | + | 8666.95i | 0.183983 | + | 1.04017i | ||||
\(412\) | − | 4655.83i | − | 0.556738i | ||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 8819.27 | − | 3220.64i | 1.04696 | − | 0.382333i | ||||
\(415\) | 17700.4 | 2.09368 | ||||||||
\(416\) | −644.637 | −0.0759757 | ||||||||
\(417\) | −1648.31 | − | 9318.86i | −0.193568 | − | 1.09436i | ||||
\(418\) | 9196.78i | 1.07615i | ||||||||
\(419\) | 2183.62 | 0.254598 | 0.127299 | − | 0.991864i | \(-0.459369\pi\) | ||||
0.127299 | + | 0.991864i | \(0.459369\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −12921.5 | −1.49586 | −0.747929 | − | 0.663778i | \(-0.768952\pi\) | ||||
−0.747929 | + | 0.663778i | \(0.768952\pi\) | |||||||
\(422\) | 3123.44i | 0.360300i | ||||||||
\(423\) | −426.338 | + | 155.691i | −0.0490054 | + | 0.0178959i | ||||
\(424\) | 6970.07 | 0.798341 | ||||||||
\(425\) | −7117.29 | −0.812328 | ||||||||
\(426\) | 26494.8 | − | 4686.37i | 3.01333 | − | 0.532993i | ||||
\(427\) | 0 | 0 | ||||||||
\(428\) | − | 8098.81i | − | 0.914651i | ||||||
\(429\) | 2323.19 | − | 410.922i | 0.261456 | − | 0.0462459i | ||||
\(430\) | − | 35840.8i | − | 4.01952i | ||||||
\(431\) | 12619.8i | 1.41038i | 0.709018 | + | 0.705190i | \(0.249138\pi\) | ||||
−0.709018 | + | 0.705190i | \(0.750862\pi\) | |||||||
\(432\) | 6265.91 | − | 3631.04i | 0.697844 | − | 0.404395i | ||||
\(433\) | 14180.4i | 1.57382i | 0.617066 | + | 0.786912i | \(0.288321\pi\) | ||||
−0.617066 | + | 0.786912i | \(0.711679\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 3388.86 | + | 19159.2i | 0.373525 | + | 2.11176i | ||||
\(436\) | 969.837 | 0.106529 | ||||||||
\(437\) | 4892.36 | 0.535546 | ||||||||
\(438\) | −26728.8 | + | 4727.75i | −2.91587 | + | 0.515755i | ||||
\(439\) | 7467.03i | 0.811804i | 0.913917 | + | 0.405902i | \(0.133043\pi\) | ||||
−0.913917 | + | 0.405902i | \(0.866957\pi\) | |||||||
\(440\) | 17443.5 | 1.88997 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −3224.80 | −0.347032 | ||||||||
\(443\) | 363.788i | 0.0390160i | 0.999810 | + | 0.0195080i | \(0.00620998\pi\) | ||||
−0.999810 | + | 0.0195080i | \(0.993790\pi\) | |||||||
\(444\) | 27589.5 | − | 4879.99i | 2.94896 | − | 0.521608i | ||||
\(445\) | −11567.0 | −1.23220 | ||||||||
\(446\) | 18219.3 | 1.93432 | ||||||||
\(447\) | 1627.26 | + | 9199.85i | 0.172185 | + | 0.973463i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 5444.69i | 0.572273i | 0.958189 | + | 0.286136i | \(0.0923711\pi\) | ||||
−0.958189 | + | 0.286136i | \(0.907629\pi\) | |||||||
\(450\) | −7822.48 | − | 21420.7i | −0.819456 | − | 2.24396i | ||||
\(451\) | 4271.23i | 0.445952i | ||||||||
\(452\) | 1314.28i | 0.136766i | ||||||||
\(453\) | −10693.1 | + | 1891.39i | −1.10907 | + | 0.196170i | ||||
\(454\) | − | 13744.1i | − | 1.42080i | ||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 12626.6 | − | 2233.38i | 1.29670 | − | 0.229359i | ||||
\(457\) | 2305.66 | 0.236005 | 0.118003 | − | 0.993013i | \(-0.462351\pi\) | ||||
0.118003 | + | 0.993013i | \(0.462351\pi\) | |||||||
\(458\) | −25231.3 | −2.57419 | ||||||||
\(459\) | −4955.80 | + | 2871.85i | −0.503958 | + | 0.292040i | ||||
\(460\) | − | 19213.6i | − | 1.94748i | ||||||
\(461\) | −585.754 | −0.0591785 | −0.0295892 | − | 0.999562i | \(-0.509420\pi\) | ||||
−0.0295892 | + | 0.999562i | \(0.509420\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 11321.6 | 1.13641 | 0.568205 | − | 0.822887i | \(-0.307638\pi\) | ||||
0.568205 | + | 0.822887i | \(0.307638\pi\) | |||||||
\(464\) | 11171.7i | 1.11775i | ||||||||
\(465\) | 2463.84 | + | 13929.5i | 0.245716 | + | 1.38918i | ||||
\(466\) | −10590.3 | −1.05276 | ||||||||
\(467\) | 9958.30 | 0.986756 | 0.493378 | − | 0.869815i | \(-0.335762\pi\) | ||||
0.493378 | + | 0.869815i | \(0.335762\pi\) | |||||||
\(468\) | −2336.33 | − | 6397.71i | −0.230763 | − | 0.631910i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 1409.06i | 0.138288i | ||||||||
\(471\) | 986.800 | + | 5578.97i | 0.0965379 | + | 0.545786i | ||||
\(472\) | 10405.6i | 1.01474i | ||||||||
\(473\) | − | 11907.8i | − | 1.15755i | ||||||
\(474\) | −228.156 | − | 1289.90i | −0.0221088 | − | 0.124994i | ||||
\(475\) | − | 11882.9i | − | 1.14784i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −1783.11 | − | 4882.81i | −0.171160 | − | 0.468697i | ||||
\(478\) | 9311.16 | 0.890967 | ||||||||
\(479\) | 13832.0 | 1.31942 | 0.659709 | − | 0.751521i | \(-0.270680\pi\) | ||||
0.659709 | + | 0.751521i | \(0.270680\pi\) | |||||||
\(480\) | 619.122 | + | 3500.26i | 0.0588727 | + | 0.332842i | ||||
\(481\) | − | 5681.62i | − | 0.538585i | ||||||
\(482\) | −21686.8 | −2.04939 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −8593.98 | −0.807098 | ||||||||
\(485\) | 23501.8i | 2.20034i | ||||||||
\(486\) | −14090.1 | − | 11759.0i | −1.31511 | − | 1.09752i | ||||
\(487\) | 456.178 | 0.0424464 | 0.0212232 | − | 0.999775i | \(-0.493244\pi\) | ||||
0.0212232 | + | 0.999775i | \(0.493244\pi\) | |||||||
\(488\) | 8120.30 | 0.753256 | ||||||||
\(489\) | −9929.15 | + | 1756.26i | −0.918224 | + | 0.162414i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 17039.5i | − | 1.56616i | −0.621922 | − | 0.783079i | \(-0.713648\pi\) | ||
0.621922 | − | 0.783079i | \(-0.286352\pi\) | |||||||
\(492\) | 12142.2 | − | 2147.70i | 1.11263 | − | 0.196800i | ||||
\(493\) | − | 8835.90i | − | 0.807198i | ||||||
\(494\) | − | 5384.05i | − | 0.490364i | ||||||
\(495\) | −4462.47 | − | 12219.8i | −0.405198 | − | 1.10958i | ||||
\(496\) | 8122.31i | 0.735287i | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −4485.96 | − | 25361.8i | −0.403656 | − | 2.28210i | ||||
\(499\) | −1855.54 | −0.166463 | −0.0832317 | − | 0.996530i | \(-0.526524\pi\) | ||||
−0.0832317 | + | 0.996530i | \(0.526524\pi\) | |||||||
\(500\) | −13205.5 | −1.18114 | ||||||||
\(501\) | 13635.4 | − | 2411.81i | 1.21594 | − | 0.215073i | ||||
\(502\) | 15971.1i | 1.41997i | ||||||||
\(503\) | −5860.64 | −0.519509 | −0.259754 | − | 0.965675i | \(-0.583642\pi\) | ||||
−0.259754 | + | 0.965675i | \(0.583642\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −503.394 | −0.0443579 | ||||||||
\(506\) | − | 9684.15i | − | 0.850816i | ||||||
\(507\) | 9881.39 | − | 1747.81i | 0.865578 | − | 0.153102i | ||||
\(508\) | 28513.4 | 2.49031 | ||||||||
\(509\) | −5456.88 | −0.475191 | −0.237595 | − | 0.971364i | \(-0.576359\pi\) | ||||
−0.237595 | + | 0.971364i | \(0.576359\pi\) | |||||||
\(510\) | 3097.16 | + | 17510.1i | 0.268911 | + | 1.52031i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 16991.3i | 1.46663i | ||||||||
\(513\) | −4794.76 | − | 8274.08i | −0.412659 | − | 0.712104i | ||||
\(514\) | 34450.1i | 2.95628i | ||||||||
\(515\) | 5206.08i | 0.445451i | ||||||||
\(516\) | −33851.3 | + | 5987.57i | −2.88802 | + | 0.510830i | ||||
\(517\) | 468.148i | 0.0398243i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −15842.4 | + | 2802.17i | −1.33989 | + | 0.236998i | ||||
\(520\) | −10211.9 | −0.861195 | ||||||||
\(521\) | 7285.24 | 0.612614 | 0.306307 | − | 0.951933i | \(-0.400907\pi\) | ||||
0.306307 | + | 0.951933i | \(0.400907\pi\) | |||||||
\(522\) | 26593.2 | − | 9711.36i | 2.22979 | − | 0.814281i | ||||
\(523\) | 3415.29i | 0.285545i | 0.989756 | + | 0.142772i | \(0.0456017\pi\) | ||||
−0.989756 | + | 0.142772i | \(0.954398\pi\) | |||||||
\(524\) | −1514.29 | −0.126245 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 32988.0 | 2.73450 | ||||||||
\(527\) | − | 6424.06i | − | 0.530999i | ||||||
\(528\) | −1301.03 | − | 7355.50i | −0.107235 | − | 0.606264i | ||||
\(529\) | 7015.37 | 0.576590 | ||||||||
\(530\) | −16137.8 | −1.32261 | ||||||||
\(531\) | 7289.55 | − | 2662.01i | 0.595743 | − | 0.217555i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 2500.49i | − | 0.203205i | ||||||
\(534\) | 2931.53 | + | 16573.7i | 0.237565 | + | 1.34310i | ||||
\(535\) | 9055.98i | 0.731821i | ||||||||
\(536\) | − | 6234.41i | − | 0.502398i | ||||||
\(537\) | 816.926 | + | 4618.57i | 0.0656480 | + | 0.371147i | ||||
\(538\) | 17460.4i | 1.39920i | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −32494.5 | + | 18830.3i | −2.58952 | + | 1.50061i | ||||
\(541\) | −2381.89 | −0.189289 | −0.0946447 | − | 0.995511i | \(-0.530172\pi\) | ||||
−0.0946447 | + | 0.995511i | \(0.530172\pi\) | |||||||
\(542\) | −16356.9 | −1.29629 | ||||||||
\(543\) | −3164.03 | − | 17888.1i | −0.250058 | − | 1.41373i | ||||
\(544\) | − | 1614.26i | − | 0.127226i | ||||||
\(545\) | −1084.46 | −0.0852351 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −1376.55 | −0.107600 | −0.0537998 | − | 0.998552i | \(-0.517133\pi\) | ||||
−0.0537998 | + | 0.998552i | \(0.517133\pi\) | |||||||
\(548\) | − | 26208.1i | − | 2.04298i | ||||||
\(549\) | −2077.37 | − | 5688.58i | −0.161494 | − | 0.442227i | ||||
\(550\) | −23521.4 | −1.82356 | ||||||||
\(551\) | 14752.2 | 1.14059 | ||||||||
\(552\) | −13295.8 | + | 2351.73i | −1.02519 | + | 0.181334i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 33623.7i | 2.57858i | ||||||||
\(555\) | −30850.2 | + | 5456.74i | −2.35949 | + | 0.417344i | ||||
\(556\) | 28179.4i | 2.14941i | ||||||||
\(557\) | 2037.41i | 0.154987i | 0.996993 | + | 0.0774935i | \(0.0246917\pi\) | ||||
−0.996993 | + | 0.0774935i | \(0.975308\pi\) | |||||||
\(558\) | 19334.3 | − | 7060.56i | 1.46682 | − | 0.535658i | ||||
\(559\) | 6971.14i | 0.527456i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1029.01 | + | 5817.58i | 0.0774414 | + | 0.437822i | ||||
\(562\) | −18575.1 | −1.39421 | ||||||||
\(563\) | −2394.19 | −0.179224 | −0.0896118 | − | 0.995977i | \(-0.528563\pi\) | ||||
−0.0896118 | + | 0.995977i | \(0.528563\pi\) | |||||||
\(564\) | 1330.85 | − | 235.398i | 0.0993595 | − | 0.0175746i | ||||
\(565\) | − | 1469.61i | − | 0.109428i | ||||||
\(566\) | −31218.7 | −2.31841 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −38693.4 | −2.85834 | ||||||||
\(569\) | − | 7635.14i | − | 0.562534i | −0.959630 | − | 0.281267i | \(-0.909245\pi\) | ||
0.959630 | − | 0.281267i | \(-0.0907546\pi\) | |||||||
\(570\) | −29234.4 | + | 5170.95i | −2.14824 | + | 0.379977i | ||||
\(571\) | 2512.52 | 0.184143 | 0.0920715 | − | 0.995752i | \(-0.470651\pi\) | ||||
0.0920715 | + | 0.995752i | \(0.470651\pi\) | |||||||
\(572\) | −7025.11 | −0.513522 | ||||||||
\(573\) | 320.850 | + | 1813.95i | 0.0233921 | + | 0.132249i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 12512.6i | 0.907496i | ||||||||
\(576\) | 15331.6 | − | 5598.84i | 1.10906 | − | 0.405009i | ||||
\(577\) | − | 10906.9i | − | 0.786929i | −0.919340 | − | 0.393465i | \(-0.871276\pi\) | ||
0.919340 | − | 0.393465i | \(-0.128724\pi\) | |||||||
\(578\) | 15727.4i | 1.13179i | ||||||||
\(579\) | 14530.9 | − | 2570.21i | 1.04298 | − | 0.184480i | ||||
\(580\) | − | 57935.9i | − | 4.14768i | ||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 33674.3 | − | 5956.26i | 2.39836 | − | 0.424218i | ||||
\(583\) | −5361.65 | −0.380887 | ||||||||
\(584\) | 39035.1 | 2.76590 | ||||||||
\(585\) | 2612.45 | + | 7153.83i | 0.184635 | + | 0.505597i | ||||
\(586\) | 6992.18i | 0.492908i | ||||||||
\(587\) | 25367.7 | 1.78371 | 0.891855 | − | 0.452321i | \(-0.149404\pi\) | ||||
0.891855 | + | 0.452321i | \(0.149404\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 10725.4 | 0.750313 | ||||||||
\(590\) | − | 24092.2i | − | 1.68112i | ||||||
\(591\) | −2767.84 | − | 15648.2i | −0.192646 | − | 1.08914i | ||||
\(592\) | −17988.7 | −1.24887 | ||||||||
\(593\) | 9834.38 | 0.681028 | 0.340514 | − | 0.940239i | \(-0.389399\pi\) | ||||
0.340514 | + | 0.940239i | \(0.389399\pi\) | |||||||
\(594\) | −16378.1 | + | 9490.96i | −1.13131 | + | 0.655587i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | − | 27819.5i | − | 1.91197i | ||||||
\(597\) | −1664.81 | − | 9412.13i | −0.114131 | − | 0.645248i | ||||
\(598\) | 5669.37i | 0.387689i | ||||||||
\(599\) | − | 6922.43i | − | 0.472192i | −0.971730 | − | 0.236096i | \(-0.924132\pi\) | ||
0.971730 | − | 0.236096i | \(-0.0758679\pi\) | |||||||
\(600\) | 5712.03 | + | 32293.5i | 0.388654 | + | 2.19729i | ||||
\(601\) | − | 15144.9i | − | 1.02791i | −0.857817 | − | 0.513955i | \(-0.828180\pi\) | ||
0.857817 | − | 0.513955i | \(-0.171820\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −4367.44 | + | 1594.91i | −0.294952 | + | 0.107711i | ||||
\(604\) | 32335.1 | 2.17830 | ||||||||
\(605\) | 9609.67 | 0.645766 | ||||||||
\(606\) | 127.579 | + | 721.281i | 0.00855207 | + | 0.0483499i | ||||
\(607\) | − | 27601.0i | − | 1.84562i | −0.385259 | − | 0.922809i | \(-0.625888\pi\) | ||
0.385259 | − | 0.922809i | \(-0.374112\pi\) | |||||||
\(608\) | 2695.12 | 0.179773 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −18800.9 | −1.24791 | ||||||||
\(611\) | − | 274.067i | − | 0.0181466i | ||||||
\(612\) | 16020.7 | − | 5850.49i | 1.05817 | − | 0.386425i | ||||
\(613\) | 12162.1 | 0.801342 | 0.400671 | − | 0.916222i | \(-0.368777\pi\) | ||||
0.400671 | + | 0.916222i | \(0.368777\pi\) | |||||||
\(614\) | −26667.6 | −1.75279 | ||||||||
\(615\) | −13577.2 | + | 2401.52i | −0.890223 | + | 0.157461i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 17715.1i | 1.15589i | 0.816077 | + | 0.577944i | \(0.196145\pi\) | ||||
−0.816077 | + | 0.577944i | \(0.803855\pi\) | |||||||
\(618\) | 7459.46 | − | 1319.42i | 0.485540 | − | 0.0858816i | ||||
\(619\) | − | 4569.82i | − | 0.296731i | −0.988933 | − | 0.148366i | \(-0.952599\pi\) | ||
0.988933 | − | 0.148366i | \(-0.0474013\pi\) | |||||||
\(620\) | − | 42121.7i | − | 2.72847i | ||||||
\(621\) | 5048.86 | + | 8712.55i | 0.326254 | + | 0.563000i | ||||
\(622\) | − | 11721.9i | − | 0.755634i | ||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 761.660 | + | 4306.11i | 0.0488635 | + | 0.276254i | ||||
\(625\) | −7025.11 | −0.449607 | ||||||||
\(626\) | 5767.21 | 0.368218 | ||||||||
\(627\) | −9712.88 | + | 1718.00i | −0.618652 | + | 0.109426i | ||||
\(628\) | − | 16870.3i | − | 1.07197i | ||||||
\(629\) | 14227.6 | 0.901891 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1677.26 | −0.105817 | −0.0529086 | − | 0.998599i | \(-0.516849\pi\) | ||||
−0.0529086 | + | 0.998599i | \(0.516849\pi\) | |||||||
\(632\) | 1883.79i | 0.118565i | ||||||||
\(633\) | −3298.72 | + | 583.474i | −0.207129 | + | 0.0366366i | ||||
\(634\) | −32112.5 | −2.01159 | ||||||||
\(635\) | −31883.3 | −1.99252 | ||||||||
\(636\) | 2695.99 | + | 15242.0i | 0.168087 | + | 0.950293i | ||||
\(637\) | 0 | 0 | ||||||||
\(638\) | − | 29201.1i | − | 1.81204i | ||||||
\(639\) | 9898.71 | + | 27106.2i | 0.612812 | + | 1.67810i | ||||
\(640\) | − | 45198.9i | − | 2.79163i | ||||||
\(641\) | − | 27279.5i | − | 1.68093i | −0.541868 | − | 0.840464i | \(-0.682283\pi\) | ||
0.541868 | − | 0.840464i | \(-0.317717\pi\) | |||||||
\(642\) | 12975.7 | − | 2295.13i | 0.797681 | − | 0.141093i | ||||
\(643\) | 19330.9i | 1.18559i | 0.805353 | + | 0.592796i | \(0.201976\pi\) | ||||
−0.805353 | + | 0.592796i | \(0.798024\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 37852.0 | − | 6695.22i | 2.31073 | − | 0.408719i | ||||
\(646\) | 13482.4 | 0.821142 | ||||||||
\(647\) | −19942.3 | −1.21177 | −0.605884 | − | 0.795553i | \(-0.707181\pi\) | ||||
−0.605884 | + | 0.795553i | \(0.707181\pi\) | |||||||
\(648\) | 17007.8 | + | 20181.3i | 1.03106 | + | 1.22345i | ||||
\(649\) | − | 8004.42i | − | 0.484131i | ||||||
\(650\) | 13770.1 | 0.830935 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 30024.9 | 1.80347 | ||||||||
\(653\) | 12834.9i | 0.769171i | 0.923089 | + | 0.384586i | \(0.125656\pi\) | ||||
−0.923089 | + | 0.384586i | \(0.874344\pi\) | |||||||
\(654\) | 274.843 | + | 1553.85i | 0.0164331 | + | 0.0929059i | ||||
\(655\) | 1693.26 | 0.101010 | ||||||||
\(656\) | −7916.88 | −0.471193 | ||||||||
\(657\) | −9986.12 | − | 27345.6i | −0.592992 | − | 1.62382i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 11112.6i | − | 0.656880i | −0.944525 | − | 0.328440i | \(-0.893477\pi\) | ||
0.944525 | − | 0.328440i | \(-0.106523\pi\) | |||||||
\(660\) | 6747.06 | + | 38145.1i | 0.397922 | + | 2.24969i | ||||
\(661\) | − | 3297.94i | − | 0.194062i | −0.995281 | − | 0.0970312i | \(-0.969065\pi\) | ||
0.995281 | − | 0.0970312i | \(-0.0309346\pi\) | |||||||
\(662\) | 34811.0i | 2.04376i | ||||||||
\(663\) | −602.408 | − | 3405.77i | −0.0352875 | − | 0.199501i | ||||
\(664\) | 37038.7i | 2.16473i | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 15637.2 | + | 42820.3i | 0.909805 | + | 2.49137i | ||||
\(667\) | −15534.0 | −0.901766 | ||||||||
\(668\) | −41232.2 | −2.38821 | ||||||||
\(669\) | 3403.45 | + | 19241.7i | 0.196689 | + | 1.11200i | ||||
\(670\) | 14434.5i | 0.832321i | ||||||||
\(671\) | −6246.45 | −0.359376 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 527.753 | 0.0302279 | 0.0151140 | − | 0.999886i | \(-0.495189\pi\) | ||||
0.0151140 | + | 0.999886i | \(0.495189\pi\) | |||||||
\(674\) | 34953.5i | 1.99756i | ||||||||
\(675\) | 21161.5 | − | 12263.0i | 1.20668 | − | 0.699261i | ||||
\(676\) | −29880.5 | −1.70007 | ||||||||
\(677\) | −214.998 | −0.0122054 | −0.00610269 | − | 0.999981i | \(-0.501943\pi\) | ||||
−0.00610269 | + | 0.999981i | \(0.501943\pi\) | |||||||
\(678\) | −2105.71 | + | 372.454i | −0.119276 | + | 0.0210974i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | − | 25572.0i | − | 1.44212i | ||||||
\(681\) | 14515.4 | − | 2567.47i | 0.816788 | − | 0.144472i | ||||
\(682\) | − | 21230.4i | − | 1.19201i | ||||||
\(683\) | 7314.04i | 0.409757i | 0.978787 | + | 0.204878i | \(0.0656799\pi\) | ||||
−0.978787 | + | 0.204878i | \(0.934320\pi\) | |||||||
\(684\) | 9767.83 | + | 26747.8i | 0.546027 | + | 1.49522i | ||||
\(685\) | 29305.5i | 1.63461i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −4713.32 | − | 26647.2i | −0.261753 | − | 1.47985i | ||||
\(688\) | 22071.5 | 1.22306 | ||||||||
\(689\) | 3138.86 | 0.173557 | ||||||||
\(690\) | 30783.7 | − | 5444.98i | 1.69843 | − | 0.300415i | ||||
\(691\) | − | 31412.9i | − | 1.72938i | −0.502302 | − | 0.864692i | \(-0.667514\pi\) | ||
0.502302 | − | 0.864692i | \(-0.332486\pi\) | |||||||
\(692\) | 47905.9 | 2.63166 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −39490.5 | −2.16000 | ||||||||
\(695\) | − | 31509.9i | − | 1.71977i | ||||||
\(696\) | −40091.3 | + | 7091.30i | −2.18342 | + | 0.386200i | ||||
\(697\) | 6261.58 | 0.340279 | ||||||||
\(698\) | 2383.26 | 0.129237 | ||||||||
\(699\) | −1978.32 | − | 11184.6i | −0.107049 | − | 0.605210i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 11496.6i | 0.619430i | 0.950829 | + | 0.309715i | \(0.100234\pi\) | ||||
−0.950829 | + | 0.309715i | \(0.899766\pi\) | |||||||
\(702\) | 9588.17 | − | 5556.27i | 0.515502 | − | 0.298729i | ||||
\(703\) | 23754.0i | 1.27439i | ||||||||
\(704\) | − | 16835.2i | − | 0.901277i | ||||||
\(705\) | −1488.13 | + | 263.219i | −0.0794984 | + | 0.0140616i | ||||
\(706\) | − | 14164.6i | − | 0.755087i | ||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −22754.9 | + | 4024.85i | −1.20788 | + | 0.213649i | ||||
\(709\) | 21068.2 | 1.11598 | 0.557992 | − | 0.829847i | \(-0.311572\pi\) | ||||
0.557992 | + | 0.829847i | \(0.311572\pi\) | |||||||
\(710\) | 89586.8 | 4.73540 | ||||||||
\(711\) | 1319.67 | − | 481.919i | 0.0696081 | − | 0.0254197i | ||||
\(712\) | − | 24204.4i | − | 1.27402i | ||||||
\(713\) | −11293.8 | −0.593208 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 7855.39 | 0.410874 | ||||||||
\(716\) | − | 13966.1i | − | 0.728966i | ||||||
\(717\) | 1739.37 | + | 9833.68i | 0.0905968 | + | 0.512197i | ||||
\(718\) | −23265.7 | −1.20929 | ||||||||
\(719\) | 7492.00 | 0.388602 | 0.194301 | − | 0.980942i | \(-0.437756\pi\) | ||||
0.194301 | + | 0.980942i | \(0.437756\pi\) | |||||||
\(720\) | 22649.9 | − | 8271.35i | 1.17238 | − | 0.428132i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | − | 10720.9i | − | 0.552620i | ||||||
\(723\) | −4051.19 | − | 22903.8i | −0.208389 | − | 1.17815i | ||||
\(724\) | 54092.1i | 2.77668i | ||||||||
\(725\) | 37729.8i | 1.93276i | ||||||||
\(726\) | −2435.46 | − | 13769.1i | −0.124502 | − | 0.703882i | ||||
\(727\) | − | 19637.5i | − | 1.00181i | −0.865503 | − | 0.500904i | \(-0.833001\pi\) | ||
0.865503 | − | 0.500904i | \(-0.166999\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 9786.73 | − | 17077.5i | 0.497217 | − | 0.867626i | ||||
\(730\) | −90378.0 | −4.58225 | ||||||||
\(731\) | −17456.7 | −0.883254 | ||||||||
\(732\) | 3140.89 | + | 17757.3i | 0.158594 | + | 0.896626i | ||||
\(733\) | 28892.7i | 1.45590i | 0.685629 | + | 0.727951i | \(0.259527\pi\) | ||||
−0.685629 | + | 0.727951i | \(0.740473\pi\) | |||||||
\(734\) | 43399.7 | 2.18244 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −2837.95 | −0.142131 | ||||||||
\(737\) | 4795.75i | 0.239693i | ||||||||
\(738\) | 6881.98 | + | 18845.3i | 0.343265 | + | 0.939981i | ||||
\(739\) | −4114.53 | −0.204811 | −0.102406 | − | 0.994743i | \(-0.532654\pi\) | ||||
−0.102406 | + | 0.994743i | \(0.532654\pi\) | |||||||
\(740\) | 93288.3 | 4.63425 | ||||||||
\(741\) | 5686.19 | − | 1005.77i | 0.281899 | − | 0.0498620i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 19095.9i | 0.942881i | 0.881898 | + | 0.471441i | \(0.156266\pi\) | ||||
−0.881898 | + | 0.471441i | \(0.843734\pi\) | |||||||
\(744\) | −29148.0 | + | 5155.67i | −1.43632 | + | 0.254054i | ||||
\(745\) | 31107.4i | 1.52978i | ||||||||
\(746\) | 24577.1i | 1.20621i | ||||||||
\(747\) | 25947.0 | − | 9475.40i | 1.27089 | − | 0.464105i | ||||
\(748\) | − | 17591.8i | − | 0.859922i | ||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −3742.33 | − | 21157.6i | −0.182201 | − | 1.03009i | ||||
\(751\) | 27352.7 | 1.32905 | 0.664524 | − | 0.747267i | \(-0.268634\pi\) | ||||
0.664524 | + | 0.747267i | \(0.268634\pi\) | |||||||
\(752\) | −867.731 | −0.0420783 | ||||||||
\(753\) | −16867.3 | + | 2983.47i | −0.816308 | + | 0.144388i | ||||
\(754\) | 17095.1i | 0.825687i | ||||||||
\(755\) | −36156.7 | −1.74288 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 2016.86 | 0.0968349 | 0.0484174 | − | 0.998827i | \(-0.484582\pi\) | ||||
0.0484174 | + | 0.998827i | \(0.484582\pi\) | |||||||
\(758\) | 4146.39i | 0.198686i | ||||||||
\(759\) | 10227.6 | − | 1809.05i | 0.489115 | − | 0.0865141i | ||||
\(760\) | 42694.4 | 2.03775 | ||||||||
\(761\) | −28904.7 | −1.37687 | −0.688434 | − | 0.725299i | \(-0.741701\pi\) | ||||
−0.688434 | + | 0.725299i | \(0.741701\pi\) | |||||||
\(762\) | 8080.45 | + | 45683.6i | 0.384152 | + | 2.17184i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | − | 5485.23i | − | 0.259750i | ||||||
\(765\) | −17914.2 | + | 6541.94i | −0.846651 | + | 0.309182i | ||||
\(766\) | − | 34304.4i | − | 1.61811i | ||||||
\(767\) | 4686.01i | 0.220602i | ||||||||
\(768\) | −40017.4 | + | 7078.23i | −1.88021 | + | 0.332570i | ||||
\(769\) | 16726.1i | 0.784343i | 0.919892 | + | 0.392171i | \(0.128276\pi\) | ||||
−0.919892 | + | 0.392171i | \(0.871724\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −36383.3 | + | 6435.44i | −1.69950 | + | 0.300605i | ||||
\(772\) | −43940.2 | −2.04850 | ||||||||
\(773\) | −15197.6 | −0.707139 | −0.353570 | − | 0.935408i | \(-0.615032\pi\) | ||||
−0.353570 | + | 0.935408i | \(0.615032\pi\) | |||||||
\(774\) | −19186.3 | − | 52539.0i | −0.891005 | − | 2.43989i | ||||
\(775\) | 27431.1i | 1.27142i | ||||||||
\(776\) | −49178.4 | −2.27500 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −10046.2 | −0.462949 | ||||||||
\(779\) | 10454.2i | 0.480821i | ||||||||
\(780\) | −3949.91 | − | 22331.2i | −0.181320 | − | 1.02511i | ||||
\(781\) | 29764.4 | 1.36371 | ||||||||
\(782\) | −14196.9 | −0.649206 | ||||||||
\(783\) | 15224.1 | + | 26271.4i | 0.694845 | + | 1.19906i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 18864.1i | 0.857694i | ||||||||
\(786\) | −429.138 | − | 2426.17i | −0.0194743 | − | 0.110100i | ||||
\(787\) | 13333.2i | 0.603910i | 0.953322 | + | 0.301955i | \(0.0976393\pi\) | ||||
−0.953322 | + | 0.301955i | \(0.902361\pi\) | |||||||
\(788\) | 47318.9i | 2.13917i | ||||||||
\(789\) | 6162.31 | + | 34839.2i | 0.278053 | + | 1.57200i | ||||
\(790\) | − | 4361.54i | − | 0.196426i | ||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 25570.4 | − | 9337.86i | 1.14723 | − | 0.418948i | ||||
\(793\) | 3656.84 | 0.163756 | ||||||||
\(794\) | −27722.5 | −1.23909 | ||||||||
\(795\) | −3014.62 | − | 17043.4i | −0.134488 | − | 0.760338i | ||||
\(796\) | 28461.5i | 1.26732i | ||||||||
\(797\) | 31995.7 | 1.42202 | 0.711008 | − | 0.703183i | \(-0.248239\pi\) | ||||
0.711008 | + | 0.703183i | \(0.248239\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 686.301 | 0.0303875 | ||||||||
\(800\) | 6892.97i | 0.304629i | ||||||||
\(801\) | −16956.1 | + | 6192.08i | −0.747959 | + | 0.273142i | ||||
\(802\) | 56824.9 | 2.50194 | ||||||||
\(803\) | −30027.3 | −1.31960 | ||||||||
\(804\) | 13633.3 | − | 2411.44i | 0.598022 | − | 0.105777i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 12428.9i | 0.543161i | ||||||||
\(807\) | −18440.2 | + | 3261.68i | −0.804370 | + | 0.142276i | ||||
\(808\) | − | 1053.37i | − | 0.0458631i | ||||||
\(809\) | 5450.03i | 0.236852i | 0.992963 | + | 0.118426i | \(0.0377848\pi\) | ||||
−0.992963 | + | 0.118426i | \(0.962215\pi\) | |||||||
\(810\) | −39378.2 | − | 46725.7i | −1.70816 | − | 2.02688i | ||||
\(811\) | − | 39222.9i | − | 1.69828i | −0.528171 | − | 0.849138i | \(-0.677122\pi\) | ||
0.528171 | − | 0.849138i | \(-0.322878\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −3055.55 | − | 17274.8i | −0.131812 | − | 0.745209i | ||||
\(814\) | 47019.6 | 2.02461 | ||||||||
\(815\) | −33573.4 | −1.44298 | ||||||||
\(816\) | −10783.1 | + | 1907.30i | −0.462603 | + | 0.0818246i | ||||
\(817\) | − | 29145.3i | − | 1.24806i | ||||||
\(818\) | −12710.6 | −0.543295 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 41056.4 | 1.74848 | ||||||||
\(821\) | − | 14897.1i | − | 0.633267i | −0.948548 | − | 0.316634i | \(-0.897447\pi\) | ||
0.948548 | − | 0.316634i | \(-0.102553\pi\) | |||||||
\(822\) | 41990.0 | − | 7427.14i | 1.78172 | − | 0.315147i | ||||
\(823\) | −33975.1 | −1.43900 | −0.719500 | − | 0.694492i | \(-0.755629\pi\) | ||||
−0.719500 | + | 0.694492i | \(0.755629\pi\) | |||||||
\(824\) | −10893.9 | −0.460567 | ||||||||
\(825\) | −4393.91 | − | 24841.4i | −0.185426 | − | 1.04832i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 5008.85i | − | 0.210610i | −0.994440 | − | 0.105305i | \(-0.966418\pi\) | ||
0.994440 | − | 0.105305i | \(-0.0335819\pi\) | |||||||
\(828\) | −10285.5 | − | 28165.3i | −0.431696 | − | 1.18214i | ||||
\(829\) | − | 33961.3i | − | 1.42283i | −0.702773 | − | 0.711414i | \(-0.748055\pi\) | ||
0.702773 | − | 0.711414i | \(-0.251945\pi\) | |||||||
\(830\) | − | 85755.7i | − | 3.58629i | ||||||
\(831\) | −35510.6 | + | 6281.07i | −1.48237 | + | 0.262199i | ||||
\(832\) | 9855.77i | 0.410682i | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −45148.5 | + | 7985.80i | −1.87454 | + | 0.331566i | ||||
\(835\) | 46105.3 | 1.91083 | ||||||||
\(836\) | 29370.9 | 1.21509 | ||||||||
\(837\) | 11068.5 | + | 19100.4i | 0.457090 | + | 0.788776i | ||||
\(838\) | − | 10579.3i | − | 0.436104i | ||||||
\(839\) | 31564.7 | 1.29885 | 0.649426 | − | 0.760425i | \(-0.275009\pi\) | ||||
0.649426 | + | 0.760425i | \(0.275009\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −22451.4 | −0.920553 | ||||||||
\(842\) | 62602.8i | 2.56227i | ||||||||
\(843\) | −3469.92 | − | 19617.5i | −0.141768 | − | 0.801499i | ||||
\(844\) | 9975.05 | 0.406819 | ||||||||
\(845\) | 33411.9 | 1.36024 | ||||||||
\(846\) | 754.300 | + | 2065.54i | 0.0306541 | + | 0.0839419i | ||||
\(847\) | 0 | 0 | ||||||||
\(848\) | − | 9938.02i | − | 0.402445i | ||||||
\(849\) | −5831.80 | − | 32970.6i | −0.235744 | − | 1.33280i | ||||
\(850\) | 34482.2i | 1.39145i | ||||||||
\(851\) | − | 25012.8i | − | 1.00755i | ||||||
\(852\) | −14966.4 | − | 84614.0i | −0.601809 | − | 3.40238i | ||||
\(853\) | 26673.5i | 1.07067i | 0.844639 | + | 0.535336i | \(0.179815\pi\) | ||||
−0.844639 | + | 0.535336i | \(0.820185\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −10922.3 | − | 29909.0i | −0.436881 | − | 1.19634i | ||||
\(856\) | −18949.9 | −0.756654 | ||||||||
\(857\) | −28604.9 | −1.14017 | −0.570084 | − | 0.821586i | \(-0.693089\pi\) | ||||
−0.570084 | + | 0.821586i | \(0.693089\pi\) | |||||||
\(858\) | −1990.86 | − | 11255.5i | −0.0792152 | − | 0.447851i | ||||
\(859\) | 42152.2i | 1.67429i | 0.546980 | + | 0.837146i | \(0.315777\pi\) | ||||
−0.546980 | + | 0.837146i | \(0.684223\pi\) | |||||||
\(860\) | −114461. | −4.53849 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 61141.0 | 2.41586 | ||||||||
\(863\) | 33862.3i | 1.33567i | 0.744308 | + | 0.667836i | \(0.232779\pi\) | ||||
−0.744308 | + | 0.667836i | \(0.767221\pi\) | |||||||
\(864\) | 2781.33 | + | 4799.60i | 0.109517 | + | 0.188988i | ||||
\(865\) | −53567.7 | −2.10561 | ||||||||
\(866\) | 68701.8 | 2.69582 | ||||||||
\(867\) | −16610.0 | + | 2937.95i | −0.650639 | + | 0.115084i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 1449.08i | − | 0.0565671i | ||||||
\(870\) | 92823.6 | − | 16418.5i | 3.61726 | − | 0.639816i | ||||
\(871\) | − | 2807.56i | − | 0.109220i | ||||||
\(872\) | − | 2269.27i | − | 0.0881274i | ||||||
\(873\) | 12581.0 | + | 34451.3i | 0.487747 | + | 1.33563i | ||||
\(874\) | − | 23702.8i | − | 0.917343i | ||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 15098.6 | + | 85361.2i | 0.582345 | + | 3.29234i | ||||
\(877\) | 14209.4 | 0.547111 | 0.273556 | − | 0.961856i | \(-0.411800\pi\) | ||||
0.273556 | + | 0.961856i | \(0.411800\pi\) | |||||||
\(878\) | 36176.6 | 1.39055 | ||||||||
\(879\) | −7384.56 | + | 1306.17i | −0.283362 | + | 0.0501207i | ||||
\(880\) | − | 24871.1i | − | 0.952734i | ||||||
\(881\) | −40320.8 | −1.54193 | −0.770966 | − | 0.636877i | \(-0.780226\pi\) | ||||
−0.770966 | + | 0.636877i | \(0.780226\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 44671.9 | 1.70252 | 0.851262 | − | 0.524741i | \(-0.175838\pi\) | ||||
0.851262 | + | 0.524741i | \(0.175838\pi\) | |||||||
\(884\) | 10298.8i | 0.391838i | ||||||||
\(885\) | 25444.2 | − | 4500.53i | 0.966437 | − | 0.170942i | ||||
\(886\) | 1762.50 | 0.0668309 | ||||||||
\(887\) | 6917.18 | 0.261845 | 0.130922 | − | 0.991393i | \(-0.458206\pi\) | ||||
0.130922 | + | 0.991393i | \(0.458206\pi\) | |||||||
\(888\) | −11418.4 | − | 64555.0i | −0.431505 | − | 2.43956i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 56040.6i | 2.11066i | ||||||||
\(891\) | −13083.1 | − | 15524.2i | −0.491918 | − | 0.583704i | ||||
\(892\) | − | 58185.3i | − | 2.18407i | ||||||
\(893\) | 1145.83i | 0.0429382i | ||||||||
\(894\) | 44571.9 | − | 7883.81i | 1.66746 | − | 0.294938i | ||||
\(895\) | 15616.8i | 0.583252i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −5987.52 | + | 1059.07i | −0.222874 | + | 0.0394216i | ||||
\(898\) | 26378.7 | 0.980253 | ||||||||
\(899\) | −34054.8 | −1.26340 | ||||||||
\(900\) | −68409.4 | + | 24981.9i | −2.53368 | + | 0.925257i | ||||
\(901\) | 7860.13i | 0.290631i | ||||||||
\(902\) | 20693.4 | 0.763876 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 3075.20 | 0.113141 | ||||||||
\(905\) | − | 60485.1i | − | 2.22165i | ||||||
\(906\) | 9163.48 | + | 51806.6i | 0.336022 | + | 1.89973i | ||||
\(907\) | 3716.85 | 0.136071 | 0.0680353 | − | 0.997683i | \(-0.478327\pi\) | ||||
0.0680353 | + | 0.997683i | \(0.478327\pi\) | |||||||
\(908\) | −43893.4 | −1.60424 | ||||||||
\(909\) | −737.925 | + | 269.477i | −0.0269257 | + | 0.00983278i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 47943.1i | − | 1.74361i | −0.489855 | − | 0.871804i | \(-0.662950\pi\) | ||
0.489855 | − | 0.871804i | \(-0.337050\pi\) | |||||||
\(912\) | −3184.38 | − | 18003.2i | −0.115620 | − | 0.653668i | ||||
\(913\) | − | 28491.6i | − | 1.03279i | ||||||
\(914\) | − | 11170.6i | − | 0.404256i | ||||||
\(915\) | −3512.10 | − | 19856.0i | −0.126892 | − | 0.717398i | ||||
\(916\) | 80578.8i | 2.90655i | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 13913.7 | + | 24010.1i | 0.500239 | + | 0.863236i | ||||
\(919\) | −7853.69 | −0.281904 | −0.140952 | − | 0.990016i | \(-0.545016\pi\) | ||||
−0.140952 | + | 0.990016i | \(0.545016\pi\) | |||||||
\(920\) | −44956.9 | −1.61107 | ||||||||
\(921\) | −4981.63 | − | 28164.1i | −0.178230 | − | 1.00764i | ||||
\(922\) | 2837.89i | 0.101367i | ||||||||
\(923\) | −17424.9 | −0.621396 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −60752.5 | −2.15949 | ||||||||
\(926\) | − | 54851.2i | − | 1.94657i | ||||||
\(927\) | 2786.93 | + | 7631.60i | 0.0987429 | + | 0.270393i | ||||
\(928\) | −8557.41 | −0.302706 | ||||||||
\(929\) | 19541.9 | 0.690148 | 0.345074 | − | 0.938575i | \(-0.387854\pi\) | ||||
0.345074 | + | 0.938575i | \(0.387854\pi\) | |||||||
\(930\) | 67486.5 | − | 11936.9i | 2.37954 | − | 0.420889i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 33821.4i | 1.18869i | ||||||||
\(933\) | 12379.7 | − | 2189.70i | 0.434397 | − | 0.0768355i | ||||
\(934\) | − | 48246.4i | − | 1.69023i | ||||||
\(935\) | 19671.0i | 0.688031i | ||||||||
\(936\) | −14969.6 | + | 5466.64i | −0.522754 | + | 0.190900i | ||||
\(937\) | − | 8670.27i | − | 0.302290i | −0.988512 | − | 0.151145i | \(-0.951704\pi\) | ||
0.988512 | − | 0.151145i | \(-0.0482960\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 1077.34 | + | 6090.86i | 0.0374417 | + | 0.211680i | ||||
\(940\) | 4499.99 | 0.156142 | ||||||||
\(941\) | 49486.9 | 1.71437 | 0.857187 | − | 0.515006i | \(-0.172210\pi\) | ||||
0.857187 | + | 0.515006i | \(0.172210\pi\) | |||||||
\(942\) | 27029.2 | − | 4780.89i | 0.934883 | − | 0.165361i | ||||
\(943\) | − | 11008.2i | − | 0.380144i | ||||||
\(944\) | 14836.5 | 0.511532 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −57691.3 | −1.98278 | ||||||||
\(947\) | 34057.1i | 1.16865i | 0.811521 | + | 0.584323i | \(0.198640\pi\) | ||||
−0.811521 | + | 0.584323i | \(0.801360\pi\) | |||||||
\(948\) | −4119.44 | + | 728.641i | −0.141132 | + | 0.0249632i | ||||
\(949\) | 17578.8 | 0.601298 | ||||||||
\(950\) | −57570.6 | −1.96614 | ||||||||
\(951\) | −5998.76 | − | 33914.6i | −0.204546 | − | 1.15642i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 28600.5i | 0.972152i | 0.873917 | + | 0.486076i | \(0.161572\pi\) | ||||
−0.873917 | + | 0.486076i | \(0.838428\pi\) | |||||||
\(954\) | −23656.4 | + | 8638.92i | −0.802836 | + | 0.293182i | ||||
\(955\) | 6133.51i | 0.207828i | ||||||||
\(956\) | − | 29736.2i | − | 1.00600i | ||||||
\(957\) | 30839.8 | − | 5454.90i | 1.04170 | − | 0.184255i | ||||
\(958\) | − | 67014.0i | − | 2.26005i | ||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 53515.1 | − | 9465.68i | 1.79916 | − | 0.318233i | ||||
\(961\) | 5031.75 | 0.168902 | ||||||||
\(962\) | −27526.6 | −0.922549 | ||||||||
\(963\) | 4847.86 | + | 13275.2i | 0.162222 | + | 0.444222i | ||||
\(964\) | 69259.1i | 2.31399i | ||||||||
\(965\) | 49133.3 | 1.63902 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 10889.4 | 0.362131 | 0.181065 | − | 0.983471i | \(-0.442045\pi\) | ||||
0.181065 | + | 0.983471i | \(0.442045\pi\) | |||||||
\(968\) | 20108.6i | 0.667679i | ||||||||
\(969\) | 2518.57 | + | 14239.0i | 0.0834967 | + | 0.472056i | ||||
\(970\) | 113863. | 3.76898 | ||||||||
\(971\) | −45497.2 | −1.50368 | −0.751841 | − | 0.659344i | \(-0.770834\pi\) | ||||
−0.751841 | + | 0.659344i | \(0.770834\pi\) | |||||||
\(972\) | −37553.5 | + | 44998.4i | −1.23923 | + | 1.48490i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | − | 2210.11i | − | 0.0727069i | ||||||
\(975\) | 2572.32 | + | 14542.8i | 0.0844924 | + | 0.477686i | ||||
\(976\) | − | 11578.0i | − | 0.379717i | ||||||
\(977\) | 27429.6i | 0.898210i | 0.893479 | + | 0.449105i | \(0.148257\pi\) | ||||
−0.893479 | + | 0.449105i | \(0.851743\pi\) | |||||||
\(978\) | 8508.79 | + | 48105.2i | 0.278201 | + | 1.57284i | ||||
\(979\) | 18619.0i | 0.607830i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1589.71 | + | 580.534i | −0.0517385 | + | 0.0188940i | ||||
\(982\) | −82553.9 | −2.68269 | ||||||||
\(983\) | 25943.6 | 0.841783 | 0.420892 | − | 0.907111i | \(-0.361717\pi\) | ||||
0.420892 | + | 0.907111i | \(0.361717\pi\) | |||||||
\(984\) | −5025.27 | − | 28410.8i | −0.162805 | − | 0.920431i | ||||
\(985\) | − | 52911.4i | − | 1.71157i | ||||||
\(986\) | −42808.6 | −1.38266 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −17194.5 | −0.553675 | ||||||||
\(989\) | 30689.8i | 0.986732i | ||||||||
\(990\) | −59203.2 | + | 21620.0i | −1.90061 | + | 0.694069i | ||||
\(991\) | 53486.9 | 1.71450 | 0.857250 | − | 0.514901i | \(-0.172171\pi\) | ||||
0.857250 | + | 0.514901i | \(0.172171\pi\) | |||||||
\(992\) | −6221.59 | −0.199129 | ||||||||
\(993\) | −36764.5 | + | 6502.86i | −1.17491 | + | 0.207817i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 31825.2i | − | 1.01400i | ||||||
\(996\) | −80995.5 | + | 14326.4i | −2.57675 | + | 0.455772i | ||||
\(997\) | − | 797.622i | − | 0.0253369i | −0.999920 | − | 0.0126685i | \(-0.995967\pi\) | ||
0.999920 | − | 0.0126685i | \(-0.00403261\pi\) | |||||||
\(998\) | 8989.79i | 0.285137i | ||||||||
\(999\) | −42302.2 | + | 24513.8i | −1.33972 | + | 0.776358i |
(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 | 147.4.c.b.146.4 | yes | 24 | |
3.2 | odd | 2 | inner | 147.4.c.b.146.21 | yes | 24 | |
7.2 | even | 3 | 147.4.g.e.80.3 | 48 | |||
7.3 | odd | 6 | 147.4.g.e.68.22 | 48 | |||
7.4 | even | 3 | 147.4.g.e.68.21 | 48 | |||
7.5 | odd | 6 | 147.4.g.e.80.4 | 48 | |||
7.6 | odd | 2 | inner | 147.4.c.b.146.3 | ✓ | 24 | |
21.2 | odd | 6 | 147.4.g.e.80.22 | 48 | |||
21.5 | even | 6 | 147.4.g.e.80.21 | 48 | |||
21.11 | odd | 6 | 147.4.g.e.68.4 | 48 | |||
21.17 | even | 6 | 147.4.g.e.68.3 | 48 | |||
21.20 | even | 2 | inner | 147.4.c.b.146.22 | yes | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
147.4.c.b.146.3 | ✓ | 24 | 7.6 | odd | 2 | inner | |
147.4.c.b.146.4 | yes | 24 | 1.1 | even | 1 | trivial | |
147.4.c.b.146.21 | yes | 24 | 3.2 | odd | 2 | inner | |
147.4.c.b.146.22 | yes | 24 | 21.20 | even | 2 | inner | |
147.4.g.e.68.3 | 48 | 21.17 | even | 6 | |||
147.4.g.e.68.4 | 48 | 21.11 | odd | 6 | |||
147.4.g.e.68.21 | 48 | 7.4 | even | 3 | |||
147.4.g.e.68.22 | 48 | 7.3 | odd | 6 | |||
147.4.g.e.80.3 | 48 | 7.2 | even | 3 | |||
147.4.g.e.80.4 | 48 | 7.5 | odd | 6 | |||
147.4.g.e.80.21 | 48 | 21.5 | even | 6 | |||
147.4.g.e.80.22 | 48 | 21.2 | odd | 6 |