Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [300,5,Mod(151,300)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(300, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 0]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("300.151");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 300 = 2^{2} \cdot 3 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 300.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: | \(31.0109889252\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 4 x^{15} - 9 x^{14} + 18 x^{13} + 263 x^{12} - 444 x^{11} - 1732 x^{10} - 832 x^{9} + \cdots + 16777216 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{36}\cdot 3^{4}\cdot 5^{4} \) |
Twist minimal: | no (minimal twist has level 60) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 151.15 | ||
Root | \(2.44021 - 1.43016i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 300.151 |
Dual form | 300.5.c.d.151.16 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/300\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(151\) | \(277\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 3.95975 | − | 0.566024i | 0.989937 | − | 0.141506i | ||||
\(3\) | 5.19615i | 0.577350i | ||||||||
\(4\) | 15.3592 | − | 4.48263i | 0.959952 | − | 0.280164i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 2.94115 | + | 20.5755i | 0.0816986 | + | 0.571541i | ||||
\(7\) | − | 24.1355i | − | 0.492561i | −0.969199 | − | 0.246281i | \(-0.920792\pi\) | ||
0.969199 | − | 0.246281i | \(-0.0792085\pi\) | |||||||
\(8\) | 58.2814 | − | 26.4438i | 0.910648 | − | 0.413184i | ||||
\(9\) | −27.0000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 227.128i | − | 1.87709i | −0.345155 | − | 0.938546i | \(-0.612174\pi\) | ||
0.345155 | − | 0.938546i | \(-0.387826\pi\) | |||||||
\(12\) | 23.2924 | + | 79.8089i | 0.161753 | + | 0.554229i | ||||
\(13\) | −285.216 | −1.68767 | −0.843835 | − | 0.536603i | \(-0.819707\pi\) | ||||
−0.843835 | + | 0.536603i | \(0.819707\pi\) | |||||||
\(14\) | −13.6613 | − | 95.5705i | −0.0697004 | − | 0.487605i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 215.812 | − | 137.699i | 0.843016 | − | 0.537889i | ||||
\(17\) | 301.510 | 1.04329 | 0.521644 | − | 0.853163i | \(-0.325319\pi\) | ||||
0.521644 | + | 0.853163i | \(0.325319\pi\) | |||||||
\(18\) | −106.913 | + | 15.2827i | −0.329979 | + | 0.0471687i | ||||
\(19\) | − | 674.273i | − | 1.86779i | −0.357545 | − | 0.933896i | \(-0.616386\pi\) | ||
0.357545 | − | 0.933896i | \(-0.383614\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 125.412 | 0.284380 | ||||||||
\(22\) | −128.560 | − | 899.370i | −0.265620 | − | 1.85820i | ||||
\(23\) | 459.987i | 0.869541i | 0.900541 | + | 0.434770i | \(0.143170\pi\) | ||||
−0.900541 | + | 0.434770i | \(0.856830\pi\) | |||||||
\(24\) | 137.406 | + | 302.839i | 0.238552 | + | 0.525763i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −1129.38 | + | 161.439i | −1.67069 | + | 0.238815i | ||||
\(27\) | − | 140.296i | − | 0.192450i | ||||||
\(28\) | −108.190 | − | 370.703i | −0.137998 | − | 0.472835i | ||||
\(29\) | 146.681 | 0.174412 | 0.0872061 | − | 0.996190i | \(-0.472206\pi\) | ||||
0.0872061 | + | 0.996190i | \(0.472206\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 702.116i | 0.730610i | 0.930888 | + | 0.365305i | \(0.119035\pi\) | ||||
−0.930888 | + | 0.365305i | \(0.880965\pi\) | |||||||
\(32\) | 776.621 | − | 667.410i | 0.758419 | − | 0.651768i | ||||
\(33\) | 1180.19 | 1.08374 | ||||||||
\(34\) | 1193.91 | − | 170.662i | 1.03279 | − | 0.147632i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −414.699 | + | 121.031i | −0.319984 | + | 0.0933881i | ||||
\(37\) | 100.291 | 0.0732589 | 0.0366295 | − | 0.999329i | \(-0.488338\pi\) | ||||
0.0366295 | + | 0.999329i | \(0.488338\pi\) | |||||||
\(38\) | −381.655 | − | 2669.95i | −0.264304 | − | 1.84900i | ||||
\(39\) | − | 1482.03i | − | 0.974376i | ||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1100.61 | 0.654733 | 0.327367 | − | 0.944897i | \(-0.393839\pi\) | ||||
0.327367 | + | 0.944897i | \(0.393839\pi\) | |||||||
\(42\) | 496.599 | − | 70.9861i | 0.281519 | − | 0.0402415i | ||||
\(43\) | − | 811.156i | − | 0.438700i | −0.975646 | − | 0.219350i | \(-0.929606\pi\) | ||
0.975646 | − | 0.219350i | \(-0.0703936\pi\) | |||||||
\(44\) | −1018.13 | − | 3488.51i | −0.525894 | − | 1.80192i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 260.364 | + | 1821.43i | 0.123045 | + | 0.860791i | ||||
\(47\) | − | 1190.37i | − | 0.538874i | −0.963018 | − | 0.269437i | \(-0.913162\pi\) | ||
0.963018 | − | 0.269437i | \(-0.0868375\pi\) | |||||||
\(48\) | 715.507 | + | 1121.39i | 0.310550 | + | 0.486715i | ||||
\(49\) | 1818.48 | 0.757384 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1566.69i | 0.602343i | ||||||||
\(52\) | −4380.70 | + | 1278.52i | −1.62008 | + | 0.472825i | ||||
\(53\) | −2293.09 | −0.816337 | −0.408168 | − | 0.912907i | \(-0.633832\pi\) | ||||
−0.408168 | + | 0.912907i | \(0.633832\pi\) | |||||||
\(54\) | −79.4110 | − | 555.537i | −0.0272329 | − | 0.190514i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −638.234 | − | 1406.65i | −0.203518 | − | 0.448550i | ||||
\(57\) | 3503.62 | 1.07837 | ||||||||
\(58\) | 580.819 | − | 83.0248i | 0.172657 | − | 0.0246804i | ||||
\(59\) | − | 3143.51i | − | 0.903047i | −0.892259 | − | 0.451523i | \(-0.850881\pi\) | ||
0.892259 | − | 0.451523i | \(-0.149119\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2026.98 | −0.544741 | −0.272370 | − | 0.962193i | \(-0.587808\pi\) | ||||
−0.272370 | + | 0.962193i | \(0.587808\pi\) | |||||||
\(62\) | 397.415 | + | 2780.20i | 0.103386 | + | 0.723258i | ||||
\(63\) | 651.658i | 0.164187i | ||||||||
\(64\) | 2697.45 | − | 3082.36i | 0.658558 | − | 0.752530i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 4673.26 | − | 668.017i | 1.07283 | − | 0.153356i | ||||
\(67\) | − | 2697.71i | − | 0.600959i | −0.953788 | − | 0.300480i | \(-0.902853\pi\) | ||
0.953788 | − | 0.300480i | \(-0.0971468\pi\) | |||||||
\(68\) | 4630.97 | − | 1351.56i | 1.00151 | − | 0.292292i | ||||
\(69\) | −2390.16 | −0.502029 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 8362.76i | 1.65895i | 0.558545 | + | 0.829474i | \(0.311360\pi\) | ||||
−0.558545 | + | 0.829474i | \(0.688640\pi\) | |||||||
\(72\) | −1573.60 | + | 713.982i | −0.303549 | + | 0.137728i | ||||
\(73\) | 6721.01 | 1.26121 | 0.630607 | − | 0.776102i | \(-0.282806\pi\) | ||||
0.630607 | + | 0.776102i | \(0.282806\pi\) | |||||||
\(74\) | 397.129 | − | 56.7674i | 0.0725217 | − | 0.0103666i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −3022.51 | − | 10356.3i | −0.523288 | − | 1.79299i | ||||
\(77\) | −5481.85 | −0.924582 | ||||||||
\(78\) | −838.863 | − | 5868.45i | −0.137880 | − | 0.964571i | ||||
\(79\) | 2839.66i | 0.455000i | 0.973778 | + | 0.227500i | \(0.0730552\pi\) | ||||
−0.973778 | + | 0.227500i | \(0.926945\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 729.000 | 0.111111 | ||||||||
\(82\) | 4358.13 | − | 622.970i | 0.648145 | − | 0.0926487i | ||||
\(83\) | − | 4621.51i | − | 0.670853i | −0.942066 | − | 0.335427i | \(-0.891120\pi\) | ||
0.942066 | − | 0.335427i | \(-0.108880\pi\) | |||||||
\(84\) | 1926.23 | − | 562.174i | 0.272991 | − | 0.0796732i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −459.134 | − | 3211.97i | −0.0620787 | − | 0.434285i | ||||
\(87\) | 762.175i | 0.100697i | ||||||||
\(88\) | −6006.12 | − | 13237.3i | −0.775584 | − | 1.70937i | ||||
\(89\) | −245.915 | −0.0310460 | −0.0155230 | − | 0.999880i | \(-0.504941\pi\) | ||||
−0.0155230 | + | 0.999880i | \(0.504941\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 6883.83i | 0.831280i | ||||||||
\(92\) | 2061.95 | + | 7065.05i | 0.243614 | + | 0.834717i | ||||
\(93\) | −3648.30 | −0.421818 | ||||||||
\(94\) | −673.779 | − | 4713.57i | −0.0762539 | − | 0.533451i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 3467.97 | + | 4035.44i | 0.376298 | + | 0.437873i | ||||
\(97\) | −1571.13 | −0.166982 | −0.0834908 | − | 0.996509i | \(-0.526607\pi\) | ||||
−0.0834908 | + | 0.996509i | \(0.526607\pi\) | |||||||
\(98\) | 7200.72 | − | 1029.30i | 0.749762 | − | 0.107174i | ||||
\(99\) | 6132.46i | 0.625697i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 5857.49 | 0.574208 | 0.287104 | − | 0.957899i | \(-0.407308\pi\) | ||||
0.287104 | + | 0.957899i | \(0.407308\pi\) | |||||||
\(102\) | 886.787 | + | 6203.72i | 0.0852352 | + | 0.596282i | ||||
\(103\) | 13444.3i | 1.26726i | 0.773638 | + | 0.633628i | \(0.218435\pi\) | ||||
−0.773638 | + | 0.633628i | \(0.781565\pi\) | |||||||
\(104\) | −16622.8 | + | 7542.19i | −1.53687 | + | 0.697318i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −9080.06 | + | 1297.94i | −0.808122 | + | 0.115517i | ||||
\(107\) | − | 5130.98i | − | 0.448160i | −0.974571 | − | 0.224080i | \(-0.928062\pi\) | ||
0.974571 | − | 0.224080i | \(-0.0719377\pi\) | |||||||
\(108\) | −628.895 | − | 2154.84i | −0.0539176 | − | 0.184743i | ||||
\(109\) | 2448.93 | 0.206122 | 0.103061 | − | 0.994675i | \(-0.467136\pi\) | ||||
0.103061 | + | 0.994675i | \(0.467136\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 521.130i | 0.0422961i | ||||||||
\(112\) | −3323.45 | − | 5208.73i | −0.264943 | − | 0.415237i | ||||
\(113\) | −4654.07 | −0.364482 | −0.182241 | − | 0.983254i | \(-0.558335\pi\) | ||||
−0.182241 | + | 0.983254i | \(0.558335\pi\) | |||||||
\(114\) | 13873.5 | − | 1983.14i | 1.06752 | − | 0.152596i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 2252.90 | − | 657.515i | 0.167427 | − | 0.0488641i | ||||
\(117\) | 7700.83 | 0.562556 | ||||||||
\(118\) | −1779.30 | − | 12447.5i | −0.127787 | − | 0.893960i | ||||
\(119\) | − | 7277.10i | − | 0.513883i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −36946.1 | −2.52347 | ||||||||
\(122\) | −8026.33 | + | 1147.32i | −0.539259 | + | 0.0770841i | ||||
\(123\) | 5718.92i | 0.378010i | ||||||||
\(124\) | 3147.32 | + | 10784.0i | 0.204691 | + | 0.701350i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 368.854 | + | 2580.40i | 0.0232335 | + | 0.162535i | ||||
\(127\) | 2926.08i | 0.181417i | 0.995877 | + | 0.0907086i | \(0.0289132\pi\) | ||||
−0.995877 | + | 0.0907086i | \(0.971087\pi\) | |||||||
\(128\) | 8936.54 | − | 13732.2i | 0.545443 | − | 0.838148i | ||||
\(129\) | 4214.89 | 0.253283 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 16684.4i | 0.972229i | 0.873895 | + | 0.486114i | \(0.161586\pi\) | ||||
−0.873895 | + | 0.486114i | \(0.838414\pi\) | |||||||
\(132\) | 18126.8 | − | 5290.36i | 1.04034 | − | 0.303625i | ||||
\(133\) | −16273.9 | −0.920002 | ||||||||
\(134\) | −1526.97 | − | 10682.2i | −0.0850394 | − | 0.594912i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 17572.5 | − | 7973.08i | 0.950068 | − | 0.431070i | ||||
\(137\) | −25513.0 | −1.35932 | −0.679659 | − | 0.733529i | \(-0.737872\pi\) | ||||
−0.679659 | + | 0.733529i | \(0.737872\pi\) | |||||||
\(138\) | −9464.44 | + | 1352.89i | −0.496978 | + | 0.0710402i | ||||
\(139\) | − | 1316.26i | − | 0.0681261i | −0.999420 | − | 0.0340630i | \(-0.989155\pi\) | ||
0.999420 | − | 0.0340630i | \(-0.0108447\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 6185.35 | 0.311119 | ||||||||
\(142\) | 4733.52 | + | 33114.4i | 0.234751 | + | 1.64225i | ||||
\(143\) | 64780.6i | 3.16791i | ||||||||
\(144\) | −5826.93 | + | 3717.89i | −0.281005 | + | 0.179296i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 26613.5 | − | 3804.26i | 1.24852 | − | 0.178470i | ||||
\(147\) | 9449.09i | 0.437276i | ||||||||
\(148\) | 1540.40 | − | 449.569i | 0.0703251 | − | 0.0205245i | ||||
\(149\) | −20604.9 | −0.928107 | −0.464054 | − | 0.885807i | \(-0.653606\pi\) | ||||
−0.464054 | + | 0.885807i | \(0.653606\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 9781.71i | − | 0.429004i | −0.976724 | − | 0.214502i | \(-0.931187\pi\) | ||
0.976724 | − | 0.214502i | \(-0.0688128\pi\) | |||||||
\(152\) | −17830.3 | − | 39297.6i | −0.771742 | − | 1.70090i | ||||
\(153\) | −8140.78 | −0.347763 | ||||||||
\(154\) | −21706.7 | + | 3102.86i | −0.915278 | + | 0.130834i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −6643.37 | − | 22762.8i | −0.272985 | − | 0.935354i | ||||
\(157\) | 20309.0 | 0.823929 | 0.411964 | − | 0.911200i | \(-0.364843\pi\) | ||||
0.411964 | + | 0.911200i | \(0.364843\pi\) | |||||||
\(158\) | 1607.31 | + | 11244.3i | 0.0643853 | + | 0.450422i | ||||
\(159\) | − | 11915.2i | − | 0.471312i | ||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 11102.0 | 0.428302 | ||||||||
\(162\) | 2886.66 | − | 412.632i | 0.109993 | − | 0.0157229i | ||||
\(163\) | 34880.4i | 1.31282i | 0.754402 | + | 0.656412i | \(0.227927\pi\) | ||||
−0.754402 | + | 0.656412i | \(0.772073\pi\) | |||||||
\(164\) | 16904.5 | − | 4933.61i | 0.628512 | − | 0.183433i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −2615.89 | − | 18300.0i | −0.0949298 | − | 0.664103i | ||||
\(167\) | − | 26021.4i | − | 0.933036i | −0.884512 | − | 0.466518i | \(-0.845508\pi\) | ||
0.884512 | − | 0.466518i | \(-0.154492\pi\) | |||||||
\(168\) | 7309.18 | − | 3316.36i | 0.258970 | − | 0.117501i | ||||
\(169\) | 52787.2 | 1.84823 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 18205.4i | 0.622597i | ||||||||
\(172\) | −3636.11 | − | 12458.7i | −0.122908 | − | 0.421131i | ||||
\(173\) | 41594.8 | 1.38978 | 0.694891 | − | 0.719115i | \(-0.255453\pi\) | ||||
0.694891 | + | 0.719115i | \(0.255453\pi\) | |||||||
\(174\) | 431.410 | + | 3018.02i | 0.0142492 | + | 0.0996837i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −31275.4 | − | 49017.0i | −1.00967 | − | 1.58242i | ||||
\(177\) | 16334.1 | 0.521374 | ||||||||
\(178\) | −973.764 | + | 139.194i | −0.0307336 | + | 0.00439320i | ||||
\(179\) | 52061.3i | 1.62483i | 0.583078 | + | 0.812416i | \(0.301848\pi\) | ||||
−0.583078 | + | 0.812416i | \(0.698152\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 48399.0 | 1.47734 | 0.738668 | − | 0.674070i | \(-0.235455\pi\) | ||||
0.738668 | + | 0.674070i | \(0.235455\pi\) | |||||||
\(182\) | 3896.42 | + | 27258.2i | 0.117631 | + | 0.822915i | ||||
\(183\) | − | 10532.5i | − | 0.314506i | ||||||
\(184\) | 12163.8 | + | 26808.7i | 0.359280 | + | 0.791845i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −14446.4 | + | 2065.03i | −0.417573 | + | 0.0596897i | ||||
\(187\) | − | 68481.5i | − | 1.95835i | ||||||
\(188\) | −5336.00 | − | 18283.2i | −0.150973 | − | 0.517293i | ||||
\(189\) | −3386.12 | −0.0947934 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 14536.0i | − | 0.398453i | −0.979953 | − | 0.199227i | \(-0.936157\pi\) | ||
0.979953 | − | 0.199227i | \(-0.0638430\pi\) | |||||||
\(192\) | 16016.4 | + | 14016.4i | 0.434474 | + | 0.380218i | ||||
\(193\) | 494.150 | 0.0132661 | 0.00663306 | − | 0.999978i | \(-0.497889\pi\) | ||||
0.00663306 | + | 0.999978i | \(0.497889\pi\) | |||||||
\(194\) | −6221.28 | + | 889.297i | −0.165301 | + | 0.0236289i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 27930.4 | − | 8151.56i | 0.727052 | − | 0.212192i | ||||
\(197\) | 3087.98 | 0.0795686 | 0.0397843 | − | 0.999208i | \(-0.487333\pi\) | ||||
0.0397843 | + | 0.999208i | \(0.487333\pi\) | |||||||
\(198\) | 3471.12 | + | 24283.0i | 0.0885399 | + | 0.619401i | ||||
\(199\) | 48825.3i | 1.23293i | 0.787382 | + | 0.616465i | \(0.211436\pi\) | ||||
−0.787382 | + | 0.616465i | \(0.788564\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 14017.7 | 0.346964 | ||||||||
\(202\) | 23194.2 | − | 3315.48i | 0.568430 | − | 0.0812538i | ||||
\(203\) | − | 3540.21i | − | 0.0859087i | ||||||
\(204\) | 7022.91 | + | 24063.2i | 0.168755 | + | 0.578220i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 7609.81 | + | 53236.2i | 0.179325 | + | 1.25450i | ||||
\(207\) | − | 12419.6i | − | 0.289847i | ||||||
\(208\) | −61553.1 | + | 39274.1i | −1.42273 | + | 0.907778i | ||||
\(209\) | −153146. | −3.50601 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 68422.2i | 1.53685i | 0.639938 | + | 0.768427i | \(0.278960\pi\) | ||||
−0.639938 | + | 0.768427i | \(0.721040\pi\) | |||||||
\(212\) | −35220.1 | + | 10279.1i | −0.783644 | + | 0.228708i | ||||
\(213\) | −43454.2 | −0.957794 | ||||||||
\(214\) | −2904.26 | − | 20317.4i | −0.0634173 | − | 0.443650i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −3709.96 | − | 8176.66i | −0.0795173 | − | 0.175254i | ||||
\(217\) | 16945.9 | 0.359870 | ||||||||
\(218\) | 9697.15 | − | 1386.15i | 0.204047 | − | 0.0291674i | ||||
\(219\) | 34923.4i | 0.728163i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −85995.6 | −1.76073 | ||||||||
\(222\) | 294.972 | + | 2063.54i | 0.00598515 | + | 0.0418704i | ||||
\(223\) | − | 1815.89i | − | 0.0365157i | −0.999833 | − | 0.0182578i | \(-0.994188\pi\) | ||
0.999833 | − | 0.0182578i | \(-0.00581197\pi\) | |||||||
\(224\) | −16108.3 | − | 18744.1i | −0.321036 | − | 0.373568i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −18429.0 | + | 2634.32i | −0.360815 | + | 0.0515764i | ||||
\(227\) | 25286.9i | 0.490731i | 0.969431 | + | 0.245366i | \(0.0789080\pi\) | ||||
−0.969431 | + | 0.245366i | \(0.921092\pi\) | |||||||
\(228\) | 53813.0 | − | 15705.4i | 1.03518 | − | 0.302121i | ||||
\(229\) | 61533.5 | 1.17338 | 0.586692 | − | 0.809810i | \(-0.300430\pi\) | ||||
0.586692 | + | 0.809810i | \(0.300430\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | − | 28484.5i | − | 0.533808i | ||||||
\(232\) | 8548.76 | − | 3878.79i | 0.158828 | − | 0.0720644i | ||||
\(233\) | −78964.4 | −1.45452 | −0.727260 | − | 0.686362i | \(-0.759207\pi\) | ||||
−0.727260 | + | 0.686362i | \(0.759207\pi\) | |||||||
\(234\) | 30493.4 | − | 4358.86i | 0.556896 | − | 0.0796051i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −14091.2 | − | 48281.8i | −0.253001 | − | 0.866882i | ||||
\(237\) | −14755.3 | −0.262694 | ||||||||
\(238\) | −4119.02 | − | 28815.5i | −0.0727176 | − | 0.508712i | ||||
\(239\) | − | 60958.7i | − | 1.06719i | −0.845742 | − | 0.533593i | \(-0.820841\pi\) | ||
0.845742 | − | 0.533593i | \(-0.179159\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 43359.9 | 0.746541 | 0.373271 | − | 0.927723i | \(-0.378236\pi\) | ||||
0.373271 | + | 0.927723i | \(0.378236\pi\) | |||||||
\(242\) | −146297. | + | 20912.4i | −2.49808 | + | 0.357086i | ||||
\(243\) | 3788.00i | 0.0641500i | ||||||||
\(244\) | −31132.9 | + | 9086.20i | −0.522925 | + | 0.152617i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 3237.05 | + | 22645.5i | 0.0534908 | + | 0.374207i | ||||
\(247\) | 192313.i | 3.15221i | ||||||||
\(248\) | 18566.6 | + | 40920.3i | 0.301876 | + | 0.665328i | ||||
\(249\) | 24014.1 | 0.387317 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 4036.99i | − | 0.0640783i | −0.999487 | − | 0.0320391i | \(-0.989800\pi\) | ||
0.999487 | − | 0.0320391i | \(-0.0102001\pi\) | |||||||
\(252\) | 2921.14 | + | 10009.0i | 0.0459993 | + | 0.157612i | ||||
\(253\) | 104476. | 1.63221 | ||||||||
\(254\) | 1656.23 | + | 11586.5i | 0.0256716 | + | 0.179592i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 27613.7 | − | 59434.4i | 0.421352 | − | 0.906897i | ||||
\(257\) | −21219.0 | −0.321261 | −0.160631 | − | 0.987015i | \(-0.551353\pi\) | ||||
−0.160631 | + | 0.987015i | \(0.551353\pi\) | |||||||
\(258\) | 16689.9 | − | 2385.73i | 0.250735 | − | 0.0358411i | ||||
\(259\) | − | 2420.58i | − | 0.0360845i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −3960.38 | −0.0581374 | ||||||||
\(262\) | 9443.79 | + | 66066.1i | 0.137576 | + | 0.962446i | ||||
\(263\) | − | 65565.0i | − | 0.947895i | −0.880553 | − | 0.473948i | \(-0.842829\pi\) | ||
0.880553 | − | 0.473948i | \(-0.157171\pi\) | |||||||
\(264\) | 68783.3 | − | 31208.7i | 0.986904 | − | 0.447784i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −64440.6 | + | 9211.43i | −0.910744 | + | 0.130186i | ||||
\(267\) | − | 1277.81i | − | 0.0179244i | ||||||
\(268\) | −12092.8 | − | 41434.7i | −0.168367 | − | 0.576892i | ||||
\(269\) | 71452.1 | 0.987439 | 0.493720 | − | 0.869621i | \(-0.335637\pi\) | ||||
0.493720 | + | 0.869621i | \(0.335637\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 51926.3i | − | 0.707048i | −0.935426 | − | 0.353524i | \(-0.884983\pi\) | ||
0.935426 | − | 0.353524i | \(-0.115017\pi\) | |||||||
\(272\) | 65069.6 | − | 41517.8i | 0.879509 | − | 0.561173i | ||||
\(273\) | −35769.4 | −0.479940 | ||||||||
\(274\) | −101025. | + | 14441.0i | −1.34564 | + | 0.192352i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −36711.1 | + | 10714.2i | −0.481924 | + | 0.140651i | ||||
\(277\) | 21894.1 | 0.285344 | 0.142672 | − | 0.989770i | \(-0.454431\pi\) | ||||
0.142672 | + | 0.989770i | \(0.454431\pi\) | |||||||
\(278\) | −745.037 | − | 5212.08i | −0.00964025 | − | 0.0674406i | ||||
\(279\) | − | 18957.1i | − | 0.243537i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 8050.35 | 0.101954 | 0.0509768 | − | 0.998700i | \(-0.483767\pi\) | ||||
0.0509768 | + | 0.998700i | \(0.483767\pi\) | |||||||
\(282\) | 24492.5 | − | 3501.06i | 0.307988 | − | 0.0440252i | ||||
\(283\) | − | 55028.7i | − | 0.687094i | −0.939136 | − | 0.343547i | \(-0.888372\pi\) | ||
0.939136 | − | 0.343547i | \(-0.111628\pi\) | |||||||
\(284\) | 37487.1 | + | 128446.i | 0.464778 | + | 1.59251i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 36667.4 | + | 256515.i | 0.448278 | + | 3.13603i | ||||
\(287\) | − | 26563.7i | − | 0.322496i | ||||||
\(288\) | −20968.8 | + | 18020.1i | −0.252806 | + | 0.217256i | ||||
\(289\) | 7387.52 | 0.0884510 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − | 8163.83i | − | 0.0964068i | ||||||
\(292\) | 103230. | − | 30127.8i | 1.21071 | − | 0.353347i | ||||
\(293\) | 84067.6 | 0.979249 | 0.489625 | − | 0.871933i | \(-0.337134\pi\) | ||||
0.489625 | + | 0.871933i | \(0.337134\pi\) | |||||||
\(294\) | 5348.41 | + | 37416.0i | 0.0618771 | + | 0.432875i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 5845.13 | − | 2652.09i | 0.0667131 | − | 0.0302694i | ||||
\(297\) | −31865.2 | −0.361246 | ||||||||
\(298\) | −81590.3 | + | 11662.9i | −0.918768 | + | 0.131333i | ||||
\(299\) | − | 131196.i | − | 1.46750i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −19577.7 | −0.216086 | ||||||||
\(302\) | −5536.68 | − | 38733.1i | −0.0607066 | − | 0.424687i | ||||
\(303\) | 30436.4i | 0.331519i | ||||||||
\(304\) | −92847.0 | − | 145516.i | −1.00466 | − | 1.57458i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −32235.5 | + | 4607.88i | −0.344263 | + | 0.0492106i | ||||
\(307\) | − | 77747.6i | − | 0.824917i | −0.910976 | − | 0.412458i | \(-0.864670\pi\) | ||
0.910976 | − | 0.412458i | \(-0.135330\pi\) | |||||||
\(308\) | −84197.0 | + | 24573.1i | −0.887555 | + | 0.259035i | ||||
\(309\) | −69858.8 | −0.731651 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 94365.6i | − | 0.975648i | −0.872942 | − | 0.487824i | \(-0.837791\pi\) | ||
0.872942 | − | 0.487824i | \(-0.162209\pi\) | |||||||
\(312\) | −39190.4 | − | 86374.6i | −0.402597 | − | 0.887313i | ||||
\(313\) | 95720.9 | 0.977053 | 0.488527 | − | 0.872549i | \(-0.337535\pi\) | ||||
0.488527 | + | 0.872549i | \(0.337535\pi\) | |||||||
\(314\) | 80418.7 | − | 11495.4i | 0.815638 | − | 0.116591i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 12729.1 | + | 43614.9i | 0.127475 | + | 0.436778i | ||||
\(317\) | −164258. | −1.63459 | −0.817295 | − | 0.576220i | \(-0.804527\pi\) | ||||
−0.817295 | + | 0.576220i | \(0.804527\pi\) | |||||||
\(318\) | −6744.32 | − | 47181.4i | −0.0666935 | − | 0.466570i | ||||
\(319\) | − | 33315.3i | − | 0.327388i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 26661.4 | 0.258745 | ||||||||
\(322\) | 43961.2 | − | 6284.01i | 0.423992 | − | 0.0606073i | ||||
\(323\) | − | 203300.i | − | 1.94865i | ||||||
\(324\) | 11196.9 | − | 3267.84i | 0.106661 | − | 0.0311294i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 19743.2 | + | 138118.i | 0.185773 | + | 1.29961i | ||||
\(327\) | 12725.0i | 0.119004i | ||||||||
\(328\) | 64144.9 | − | 29104.2i | 0.596231 | − | 0.270525i | ||||
\(329\) | −28730.2 | −0.265428 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 155573.i | − | 1.41997i | −0.704218 | − | 0.709984i | \(-0.748702\pi\) | ||
0.704218 | − | 0.709984i | \(-0.251298\pi\) | |||||||
\(332\) | −20716.5 | − | 70982.8i | −0.187949 | − | 0.643987i | ||||
\(333\) | −2707.87 | −0.0244196 | ||||||||
\(334\) | −14728.8 | − | 103038.i | −0.132030 | − | 0.923647i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 27065.4 | − | 17269.1i | 0.239737 | − | 0.152965i | ||||
\(337\) | 203622. | 1.79294 | 0.896469 | − | 0.443106i | \(-0.146124\pi\) | ||||
0.896469 | + | 0.443106i | \(0.146124\pi\) | |||||||
\(338\) | 209024. | − | 29878.8i | 1.82963 | − | 0.261535i | ||||
\(339\) | − | 24183.3i | − | 0.210434i | ||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 159470. | 1.37142 | ||||||||
\(342\) | 10304.7 | + | 72088.7i | 0.0881013 | + | 0.616332i | ||||
\(343\) | − | 101839.i | − | 0.865619i | ||||||
\(344\) | −21450.0 | − | 47275.3i | −0.181264 | − | 0.399501i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 164705. | − | 23543.7i | 1.37580 | − | 0.196663i | ||||
\(347\) | 545.776i | 0.00453269i | 0.999997 | + | 0.00226634i | \(0.000721400\pi\) | ||||
−0.999997 | + | 0.00226634i | \(0.999279\pi\) | |||||||
\(348\) | 3416.55 | + | 11706.4i | 0.0282117 | + | 0.0966642i | ||||
\(349\) | 218943. | 1.79755 | 0.898774 | − | 0.438413i | \(-0.144459\pi\) | ||||
0.898774 | + | 0.438413i | \(0.144459\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 40014.7i | 0.324792i | ||||||||
\(352\) | −151588. | − | 176392.i | −1.22343 | − | 1.42362i | ||||
\(353\) | −139457. | −1.11915 | −0.559577 | − | 0.828778i | \(-0.689037\pi\) | ||||
−0.559577 | + | 0.828778i | \(0.689037\pi\) | |||||||
\(354\) | 64679.1 | − | 9245.52i | 0.516128 | − | 0.0737776i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −3777.07 | + | 1102.35i | −0.0298027 | + | 0.00869798i | ||||
\(357\) | 37812.9 | 0.296691 | ||||||||
\(358\) | 29467.9 | + | 206150.i | 0.229924 | + | 1.60848i | ||||
\(359\) | 24598.3i | 0.190861i | 0.995436 | + | 0.0954303i | \(0.0304227\pi\) | ||||
−0.995436 | + | 0.0954303i | \(0.969577\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −324323. | −2.48865 | ||||||||
\(362\) | 191648. | − | 27395.0i | 1.46247 | − | 0.209052i | ||||
\(363\) | − | 191978.i | − | 1.45693i | ||||||
\(364\) | 30857.7 | + | 105730.i | 0.232895 | + | 0.797989i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −5961.65 | − | 41706.0i | −0.0445045 | − | 0.311341i | ||||
\(367\) | − | 9837.44i | − | 0.0730382i | −0.999333 | − | 0.0365191i | \(-0.988373\pi\) | ||
0.999333 | − | 0.0365191i | \(-0.0116270\pi\) | |||||||
\(368\) | 63340.0 | + | 99270.7i | 0.467716 | + | 0.733037i | ||||
\(369\) | −29716.4 | −0.218244 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 55344.9i | 0.402096i | ||||||||
\(372\) | −56035.1 | + | 16354.0i | −0.404925 | + | 0.118178i | ||||
\(373\) | 45612.8 | 0.327845 | 0.163923 | − | 0.986473i | \(-0.447585\pi\) | ||||
0.163923 | + | 0.986473i | \(0.447585\pi\) | |||||||
\(374\) | −38762.2 | − | 271169.i | −0.277118 | − | 1.93864i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −31477.9 | − | 69376.6i | −0.222654 | − | 0.490724i | ||||
\(377\) | −41835.7 | −0.294350 | ||||||||
\(378\) | −13408.2 | + | 1916.62i | −0.0938396 | + | 0.0134138i | ||||
\(379\) | − | 215578.i | − | 1.50081i | −0.660978 | − | 0.750405i | \(-0.729858\pi\) | ||
0.660978 | − | 0.750405i | \(-0.270142\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −15204.4 | −0.104741 | ||||||||
\(382\) | −8227.72 | − | 57558.8i | −0.0563836 | − | 0.394444i | ||||
\(383\) | 59498.4i | 0.405609i | 0.979219 | + | 0.202805i | \(0.0650056\pi\) | ||||
−0.979219 | + | 0.202805i | \(0.934994\pi\) | |||||||
\(384\) | 71354.7 | + | 46435.6i | 0.483905 | + | 0.314912i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 1956.71 | − | 279.701i | 0.0131326 | − | 0.00187724i | ||||
\(387\) | 21901.2i | 0.146233i | ||||||||
\(388\) | −24131.3 | + | 7042.79i | −0.160294 | + | 0.0467823i | ||||
\(389\) | −111361. | −0.735925 | −0.367963 | − | 0.929841i | \(-0.619945\pi\) | ||||
−0.367963 | + | 0.929841i | \(0.619945\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 138691.i | 0.907182i | ||||||||
\(392\) | 105984. | − | 48087.4i | 0.689709 | − | 0.312939i | ||||
\(393\) | −86694.8 | −0.561317 | ||||||||
\(394\) | 12227.6 | − | 1747.87i | 0.0787679 | − | 0.0112594i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 27489.5 | + | 94189.8i | 0.175298 | + | 0.600639i | ||||
\(397\) | −202511. | −1.28489 | −0.642446 | − | 0.766331i | \(-0.722080\pi\) | ||||
−0.642446 | + | 0.766331i | \(0.722080\pi\) | |||||||
\(398\) | 27636.3 | + | 193336.i | 0.174467 | + | 1.22052i | ||||
\(399\) | − | 84561.7i | − | 0.531163i | ||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 54865.9 | 0.341204 | 0.170602 | − | 0.985340i | \(-0.445429\pi\) | ||||
0.170602 | + | 0.985340i | \(0.445429\pi\) | |||||||
\(402\) | 55506.6 | − | 7934.36i | 0.343473 | − | 0.0490975i | ||||
\(403\) | − | 200255.i | − | 1.23303i | ||||||
\(404\) | 89966.6 | − | 26257.0i | 0.551212 | − | 0.160872i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −2003.85 | − | 14018.3i | −0.0121566 | − | 0.0850442i | ||||
\(407\) | − | 22779.0i | − | 0.137514i | ||||||
\(408\) | 41429.3 | + | 91309.2i | 0.248879 | + | 0.548522i | ||||
\(409\) | 194691. | 1.16385 | 0.581927 | − | 0.813241i | \(-0.302299\pi\) | ||||
0.581927 | + | 0.813241i | \(0.302299\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − | 132570.i | − | 0.784802i | ||||||
\(412\) | 60265.9 | + | 206495.i | 0.355040 | + | 1.21651i | ||||
\(413\) | −75870.1 | −0.444806 | ||||||||
\(414\) | −7029.82 | − | 49178.7i | −0.0410151 | − | 0.286930i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −221505. | + | 190356.i | −1.27996 | + | 1.09997i | ||||
\(417\) | 6839.51 | 0.0393326 | ||||||||
\(418\) | −606421. | + | 86684.5i | −3.47074 | + | 0.496122i | ||||
\(419\) | 138559.i | 0.789234i | 0.918846 | + | 0.394617i | \(0.129123\pi\) | ||||
−0.918846 | + | 0.394617i | \(0.870877\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 127025. | 0.716682 | 0.358341 | − | 0.933591i | \(-0.383343\pi\) | ||||
0.358341 | + | 0.933591i | \(0.383343\pi\) | |||||||
\(422\) | 38728.6 | + | 270935.i | 0.217474 | + | 1.52139i | ||||
\(423\) | 32140.0i | 0.179625i | ||||||||
\(424\) | −133645. | + | 60638.0i | −0.743395 | + | 0.337297i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −172068. | + | 24596.1i | −0.948156 | + | 0.135534i | ||||
\(427\) | 48922.2i | 0.268318i | ||||||||
\(428\) | −23000.3 | − | 78808.0i | −0.125558 | − | 0.430212i | ||||
\(429\) | −336610. | −1.82899 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 139485.i | − | 0.750884i | −0.926846 | − | 0.375442i | \(-0.877491\pi\) | ||
0.926846 | − | 0.375442i | \(-0.122509\pi\) | |||||||
\(432\) | −19318.7 | − | 30277.6i | −0.103517 | − | 0.162238i | ||||
\(433\) | 334231. | 1.78267 | 0.891334 | − | 0.453348i | \(-0.149770\pi\) | ||||
0.891334 | + | 0.453348i | \(0.149770\pi\) | |||||||
\(434\) | 67101.6 | − | 9591.80i | 0.356249 | − | 0.0509238i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 37613.7 | − | 10977.6i | 0.197867 | − | 0.0577479i | ||||
\(437\) | 310157. | 1.62412 | ||||||||
\(438\) | 19767.5 | + | 138288.i | 0.103039 | + | 0.720835i | ||||
\(439\) | 290388.i | 1.50678i | 0.657575 | + | 0.753389i | \(0.271582\pi\) | ||||
−0.657575 | + | 0.753389i | \(0.728418\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −49098.9 | −0.252461 | ||||||||
\(442\) | −340521. | + | 48675.6i | −1.74301 | + | 0.249153i | ||||
\(443\) | 31499.4i | 0.160507i | 0.996774 | + | 0.0802537i | \(0.0255731\pi\) | ||||
−0.996774 | + | 0.0802537i | \(0.974427\pi\) | |||||||
\(444\) | 2336.03 | + | 8004.15i | 0.0118498 | + | 0.0406022i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −1027.84 | − | 7190.46i | −0.00516719 | − | 0.0361482i | ||||
\(447\) | − | 107066.i | − | 0.535843i | ||||||
\(448\) | −74394.4 | − | 65104.4i | −0.370667 | − | 0.324380i | ||||
\(449\) | 304272. | 1.50928 | 0.754640 | − | 0.656139i | \(-0.227812\pi\) | ||||
0.754640 | + | 0.656139i | \(0.227812\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 249979.i | − | 1.22899i | ||||||
\(452\) | −71483.0 | + | 20862.5i | −0.349885 | + | 0.102115i | ||||
\(453\) | 50827.3 | 0.247685 | ||||||||
\(454\) | 14313.0 | + | 100130.i | 0.0694414 | + | 0.485793i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 204196. | − | 92649.1i | 0.982015 | − | 0.445565i | ||||
\(457\) | −152004. | −0.727816 | −0.363908 | − | 0.931435i | \(-0.618558\pi\) | ||||
−0.363908 | + | 0.931435i | \(0.618558\pi\) | |||||||
\(458\) | 243657. | − | 34829.4i | 1.16158 | − | 0.166041i | ||||
\(459\) | − | 42300.7i | − | 0.200781i | ||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 161303. | 0.758998 | 0.379499 | − | 0.925192i | \(-0.376096\pi\) | ||||
0.379499 | + | 0.925192i | \(0.376096\pi\) | |||||||
\(462\) | −16122.9 | − | 112792.i | −0.0755370 | − | 0.528436i | ||||
\(463\) | 144022.i | 0.671842i | 0.941890 | + | 0.335921i | \(0.109048\pi\) | ||||
−0.941890 | + | 0.335921i | \(0.890952\pi\) | |||||||
\(464\) | 31655.5 | − | 20197.9i | 0.147032 | − | 0.0938143i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −312679. | + | 44695.8i | −1.43988 | + | 0.205823i | ||||
\(467\) | 286324.i | 1.31288i | 0.754380 | + | 0.656438i | \(0.227938\pi\) | ||||
−0.754380 | + | 0.656438i | \(0.772062\pi\) | |||||||
\(468\) | 118279. | − | 34520.0i | 0.540027 | − | 0.157608i | ||||
\(469\) | −65110.5 | −0.296009 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 105529.i | 0.475696i | ||||||||
\(472\) | −83126.2 | − | 183208.i | −0.373125 | − | 0.822357i | ||||
\(473\) | −184236. | −0.823479 | ||||||||
\(474\) | −58427.2 | + | 8351.85i | −0.260051 | + | 0.0371728i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −32620.5 | − | 111771.i | −0.143972 | − | 0.493303i | ||||
\(477\) | 61913.4 | 0.272112 | ||||||||
\(478\) | −34504.1 | − | 241381.i | −0.151013 | − | 1.05645i | ||||
\(479\) | 261356.i | 1.13910i | 0.821957 | + | 0.569550i | \(0.192883\pi\) | ||||
−0.821957 | + | 0.569550i | \(0.807117\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −28604.7 | −0.123637 | ||||||||
\(482\) | 171694. | − | 24542.7i | 0.739029 | − | 0.105640i | ||||
\(483\) | 57687.8i | 0.247280i | ||||||||
\(484\) | −567464. | + | 165616.i | −2.42241 | + | 0.706986i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 2144.10 | + | 14999.5i | 0.00907762 | + | 0.0635045i | ||||
\(487\) | − | 176611.i | − | 0.744662i | −0.928100 | − | 0.372331i | \(-0.878559\pi\) | ||
0.928100 | − | 0.372331i | \(-0.121441\pi\) | |||||||
\(488\) | −118135. | + | 53601.0i | −0.496067 | + | 0.225078i | ||||
\(489\) | −181244. | −0.757959 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 143358.i | 0.594646i | 0.954777 | + | 0.297323i | \(0.0960938\pi\) | ||||
−0.954777 | + | 0.297323i | \(0.903906\pi\) | |||||||
\(492\) | 25635.8 | + | 87838.2i | 0.105905 | + | 0.362872i | ||||
\(493\) | 44225.7 | 0.181962 | ||||||||
\(494\) | 108854. | + | 761513.i | 0.446057 | + | 3.12049i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 96681.0 | + | 151525.i | 0.392987 | + | 0.615915i | ||||
\(497\) | 201839. | 0.817133 | ||||||||
\(498\) | 95089.7 | − | 13592.5i | 0.383420 | − | 0.0548078i | ||||
\(499\) | 104729.i | 0.420595i | 0.977637 | + | 0.210298i | \(0.0674433\pi\) | ||||
−0.977637 | + | 0.210298i | \(0.932557\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 135211. | 0.538689 | ||||||||
\(502\) | −2285.04 | − | 15985.5i | −0.00906746 | − | 0.0634335i | ||||
\(503\) | − | 187746.i | − | 0.742053i | −0.928622 | − | 0.371026i | \(-0.879006\pi\) | ||
0.928622 | − | 0.371026i | \(-0.120994\pi\) | |||||||
\(504\) | 17232.3 | + | 37979.6i | 0.0678395 | + | 0.149517i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 413698. | − | 59135.9i | 1.61578 | − | 0.230967i | ||||
\(507\) | 274290.i | 1.06707i | ||||||||
\(508\) | 13116.5 | + | 44942.3i | 0.0508266 | + | 0.174152i | ||||
\(509\) | −358820. | −1.38497 | −0.692486 | − | 0.721432i | \(-0.743484\pi\) | ||||
−0.692486 | + | 0.721432i | \(0.743484\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 162215.i | − | 0.621225i | ||||||
\(512\) | 75702.1 | − | 250975.i | 0.288780 | − | 0.957395i | ||||
\(513\) | −94597.8 | −0.359457 | ||||||||
\(514\) | −84021.9 | + | 12010.5i | −0.318029 | + | 0.0454604i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 64737.5 | − | 18893.8i | 0.243140 | − | 0.0709610i | ||||
\(517\) | −270367. | −1.01151 | ||||||||
\(518\) | −1370.11 | − | 9584.91i | −0.00510618 | − | 0.0357214i | ||||
\(519\) | 216133.i | 0.802391i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 62111.6 | 0.228822 | 0.114411 | − | 0.993434i | \(-0.463502\pi\) | ||||
0.114411 | + | 0.993434i | \(0.463502\pi\) | |||||||
\(522\) | −15682.1 | + | 2241.67i | −0.0575524 | + | 0.00822680i | ||||
\(523\) | 439230.i | 1.60579i | 0.596122 | + | 0.802894i | \(0.296707\pi\) | ||||
−0.596122 | + | 0.802894i | \(0.703293\pi\) | |||||||
\(524\) | 74790.1 | + | 256260.i | 0.272384 | + | 0.933293i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −37111.4 | − | 259621.i | −0.134133 | − | 0.938357i | ||||
\(527\) | 211695.i | 0.762237i | ||||||||
\(528\) | 254700. | − | 162512.i | 0.913609 | − | 0.582931i | ||||
\(529\) | 68253.0 | 0.243899 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 84874.6i | 0.301016i | ||||||||
\(532\) | −249955. | + | 72949.9i | −0.883157 | + | 0.257752i | ||||
\(533\) | −313911. | −1.10497 | ||||||||
\(534\) | −723.274 | − | 5059.82i | −0.00253641 | − | 0.0177441i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −71337.6 | − | 157226.i | −0.248307 | − | 0.547262i | ||||
\(537\) | −270518. | −0.938098 | ||||||||
\(538\) | 282932. | − | 40443.6i | 0.977503 | − | 0.139729i | ||||
\(539\) | − | 413027.i | − | 1.42168i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −268086. | −0.915966 | −0.457983 | − | 0.888961i | \(-0.651428\pi\) | ||||
−0.457983 | + | 0.888961i | \(0.651428\pi\) | |||||||
\(542\) | −29391.5 | − | 205615.i | −0.100052 | − | 0.699933i | ||||
\(543\) | 251489.i | 0.852940i | ||||||||
\(544\) | 234159. | − | 201231.i | 0.791249 | − | 0.679982i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −141638. | + | 20246.4i | −0.475110 | + | 0.0679144i | ||||
\(547\) | 86050.0i | 0.287592i | 0.989607 | + | 0.143796i | \(0.0459309\pi\) | ||||
−0.989607 | + | 0.143796i | \(0.954069\pi\) | |||||||
\(548\) | −391860. | + | 114365.i | −1.30488 | + | 0.380832i | ||||
\(549\) | 54728.5 | 0.181580 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 98902.8i | − | 0.325766i | ||||||
\(552\) | −139302. | + | 63204.9i | −0.457172 | + | 0.207431i | ||||
\(553\) | 68536.5 | 0.224115 | ||||||||
\(554\) | 86695.3 | − | 12392.6i | 0.282472 | − | 0.0403778i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −5900.32 | − | 20216.8i | −0.0190865 | − | 0.0653978i | ||||
\(557\) | 246565. | 0.794734 | 0.397367 | − | 0.917660i | \(-0.369924\pi\) | ||||
0.397367 | + | 0.917660i | \(0.369924\pi\) | |||||||
\(558\) | −10730.2 | − | 75065.5i | −0.0344619 | − | 0.241086i | ||||
\(559\) | 231355.i | 0.740380i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 355840. | 1.13065 | ||||||||
\(562\) | 31877.4 | − | 4556.70i | 0.100928 | − | 0.0144270i | ||||
\(563\) | 368835.i | 1.16363i | 0.813321 | + | 0.581816i | \(0.197657\pi\) | ||||
−0.813321 | + | 0.581816i | \(0.802343\pi\) | |||||||
\(564\) | 95002.3 | − | 27726.6i | 0.298659 | − | 0.0871644i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −31147.6 | − | 217900.i | −0.0972279 | − | 0.680180i | ||||
\(567\) | − | 17594.8i | − | 0.0547290i | ||||||
\(568\) | 221143. | + | 487394.i | 0.685451 | + | 1.51072i | ||||
\(569\) | −56443.8 | −0.174338 | −0.0871689 | − | 0.996194i | \(-0.527782\pi\) | ||||
−0.0871689 | + | 0.996194i | \(0.527782\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 143219.i | 0.439265i | 0.975583 | + | 0.219633i | \(0.0704859\pi\) | ||||
−0.975583 | + | 0.219633i | \(0.929514\pi\) | |||||||
\(572\) | 290387. | + | 994980.i | 0.887535 | + | 3.04104i | ||||
\(573\) | 75531.2 | 0.230047 | ||||||||
\(574\) | −15035.7 | − | 105186.i | −0.0456352 | − | 0.319251i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −72831.2 | + | 83223.8i | −0.219519 | + | 0.250843i | ||||
\(577\) | 347057. | 1.04244 | 0.521218 | − | 0.853423i | \(-0.325478\pi\) | ||||
0.521218 | + | 0.853423i | \(0.325478\pi\) | |||||||
\(578\) | 29252.7 | − | 4181.51i | 0.0875609 | − | 0.0125164i | ||||
\(579\) | 2567.68i | 0.00765920i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −111542. | −0.330436 | ||||||||
\(582\) | −4620.92 | − | 32326.7i | −0.0136422 | − | 0.0954367i | ||||
\(583\) | 520825.i | 1.53234i | ||||||||
\(584\) | 391710. | − | 177729.i | 1.14852 | − | 0.521114i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 332887. | − | 47584.3i | 0.969396 | − | 0.138570i | ||||
\(587\) | − | 217679.i | − | 0.631743i | −0.948802 | − | 0.315872i | \(-0.897703\pi\) | ||
0.948802 | − | 0.315872i | \(-0.102297\pi\) | |||||||
\(588\) | 42356.8 | + | 145131.i | 0.122509 | + | 0.419764i | ||||
\(589\) | 473418. | 1.36463 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 16045.6i | 0.0459389i | ||||||||
\(592\) | 21644.1 | − | 13810.1i | 0.0617584 | − | 0.0394051i | ||||
\(593\) | 287874. | 0.818640 | 0.409320 | − | 0.912391i | \(-0.365766\pi\) | ||||
0.409320 | + | 0.912391i | \(0.365766\pi\) | |||||||
\(594\) | −126178. | + | 18036.5i | −0.357611 | + | 0.0511185i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −316476. | + | 92364.2i | −0.890939 | + | 0.260023i | ||||
\(597\) | −253704. | −0.711833 | ||||||||
\(598\) | −74259.9 | − | 519502.i | −0.207660 | − | 1.45273i | ||||
\(599\) | 311200.i | 0.867332i | 0.901074 | + | 0.433666i | \(0.142780\pi\) | ||||
−0.901074 | + | 0.433666i | \(0.857220\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −111234. | −0.307957 | −0.153978 | − | 0.988074i | \(-0.549209\pi\) | ||||
−0.153978 | + | 0.988074i | \(0.549209\pi\) | |||||||
\(602\) | −77522.6 | + | 11081.4i | −0.213912 | + | 0.0305775i | ||||
\(603\) | 72838.1i | 0.200320i | ||||||||
\(604\) | −43847.8 | − | 150240.i | −0.120191 | − | 0.411823i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 17227.7 | + | 120521.i | 0.0469119 | + | 0.328183i | ||||
\(607\) | − | 162372.i | − | 0.440690i | −0.975422 | − | 0.220345i | \(-0.929282\pi\) | ||
0.975422 | − | 0.220345i | \(-0.0707183\pi\) | |||||||
\(608\) | −450017. | − | 523654.i | −1.21737 | − | 1.41657i | ||||
\(609\) | 18395.5 | 0.0495994 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 339513.i | 0.909440i | ||||||||
\(612\) | −125036. | + | 36492.1i | −0.333836 | + | 0.0974307i | ||||
\(613\) | 48840.5 | 0.129975 | 0.0649874 | − | 0.997886i | \(-0.479299\pi\) | ||||
0.0649874 | + | 0.997886i | \(0.479299\pi\) | |||||||
\(614\) | −44007.0 | − | 307861.i | −0.116731 | − | 0.816616i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −319490. | + | 144961.i | −0.841968 | + | 0.382023i | ||||
\(617\) | 75750.5 | 0.198983 | 0.0994913 | − | 0.995038i | \(-0.468278\pi\) | ||||
0.0994913 | + | 0.995038i | \(0.468278\pi\) | |||||||
\(618\) | −276623. | + | 39541.8i | −0.724289 | + | 0.103533i | ||||
\(619\) | − | 156219.i | − | 0.407711i | −0.979001 | − | 0.203856i | \(-0.934653\pi\) | ||
0.979001 | − | 0.203856i | \(-0.0653473\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 64534.4 | 0.167343 | ||||||||
\(622\) | −53413.2 | − | 373664.i | −0.138060 | − | 0.965830i | ||||
\(623\) | 5935.29i | 0.0152921i | ||||||||
\(624\) | −204074. | − | 319839.i | −0.524106 | − | 0.821415i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 379031. | − | 54180.4i | 0.967221 | − | 0.138259i | ||||
\(627\) | − | 795771.i | − | 2.02420i | ||||||
\(628\) | 311931. | − | 91037.8i | 0.790932 | − | 0.230835i | ||||
\(629\) | 30238.9 | 0.0764302 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 505064.i | 1.26849i | 0.773131 | + | 0.634246i | \(0.218690\pi\) | ||||
−0.773131 | + | 0.634246i | \(0.781310\pi\) | |||||||
\(632\) | 75091.2 | + | 165499.i | 0.187999 | + | 0.414345i | ||||
\(633\) | −355532. | −0.887303 | ||||||||
\(634\) | −650421. | + | 92974.1i | −1.61814 | + | 0.231304i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −53411.6 | − | 183009.i | −0.132045 | − | 0.452437i | ||||
\(637\) | −518659. | −1.27821 | ||||||||
\(638\) | −18857.3 | − | 131920.i | −0.0463273 | − | 0.324093i | ||||
\(639\) | − | 225794.i | − | 0.552983i | ||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −277583. | −0.675579 | −0.337790 | − | 0.941222i | \(-0.609679\pi\) | ||||
−0.337790 | + | 0.941222i | \(0.609679\pi\) | |||||||
\(642\) | 105572. | − | 15091.0i | 0.256142 | − | 0.0366140i | ||||
\(643\) | − | 444328.i | − | 1.07469i | −0.843363 | − | 0.537344i | \(-0.819428\pi\) | ||
0.843363 | − | 0.537344i | \(-0.180572\pi\) | |||||||
\(644\) | 170518. | − | 49766.2i | 0.411149 | − | 0.119995i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −115073. | − | 805018.i | −0.275745 | − | 1.92904i | ||||
\(647\) | − | 676912.i | − | 1.61705i | −0.588462 | − | 0.808525i | \(-0.700266\pi\) | ||
0.588462 | − | 0.808525i | \(-0.299734\pi\) | |||||||
\(648\) | 42487.2 | − | 19277.5i | 0.101183 | − | 0.0459093i | ||||
\(649\) | −713978. | −1.69510 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 88053.5i | 0.207771i | ||||||||
\(652\) | 156356. | + | 535737.i | 0.367806 | + | 1.26025i | ||||
\(653\) | −5432.36 | −0.0127398 | −0.00636989 | − | 0.999980i | \(-0.502028\pi\) | ||||
−0.00636989 | + | 0.999980i | \(0.502028\pi\) | |||||||
\(654\) | 7202.67 | + | 50387.9i | 0.0168398 | + | 0.117807i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 237524. | − | 151553.i | 0.551950 | − | 0.352173i | ||||
\(657\) | −181467. | −0.420405 | ||||||||
\(658\) | −113764. | + | 16262.0i | −0.262757 | + | 0.0375597i | ||||
\(659\) | − | 400476.i | − | 0.922159i | −0.887359 | − | 0.461079i | \(-0.847462\pi\) | ||
0.887359 | − | 0.461079i | \(-0.152538\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −293134. | −0.670909 | −0.335455 | − | 0.942056i | \(-0.608890\pi\) | ||||
−0.335455 | + | 0.942056i | \(0.608890\pi\) | |||||||
\(662\) | −88058.2 | − | 616031.i | −0.200934 | − | 1.40568i | ||||
\(663\) | − | 446846.i | − | 1.01656i | ||||||
\(664\) | −122210. | − | 269348.i | −0.277186 | − | 0.610911i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −10722.5 | + | 1532.72i | −0.0241739 | + | 0.00345553i | ||||
\(667\) | 67471.2i | 0.151658i | ||||||||
\(668\) | −116644. | − | 399669.i | −0.261403 | − | 0.895670i | ||||
\(669\) | 9435.63 | 0.0210823 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 460384.i | 1.02253i | ||||||||
\(672\) | 97397.3 | − | 83701.1i | 0.215679 | − | 0.185350i | ||||
\(673\) | −200122. | −0.441839 | −0.220920 | − | 0.975292i | \(-0.570906\pi\) | ||||
−0.220920 | + | 0.975292i | \(0.570906\pi\) | |||||||
\(674\) | 806293. | − | 115255.i | 1.77490 | − | 0.253712i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 810771. | − | 236625.i | 1.77421 | − | 0.517807i | ||||
\(677\) | 631369. | 1.37755 | 0.688773 | − | 0.724977i | \(-0.258150\pi\) | ||||
0.688773 | + | 0.724977i | \(0.258150\pi\) | |||||||
\(678\) | −13688.3 | − | 95759.7i | −0.0297777 | − | 0.208316i | ||||
\(679\) | 37920.0i | 0.0822486i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −131395. | −0.283324 | ||||||||
\(682\) | 631462. | − | 90264.0i | 1.35762 | − | 0.194064i | ||||
\(683\) | 489626.i | 1.04960i | 0.851226 | + | 0.524799i | \(0.175860\pi\) | ||||
−0.851226 | + | 0.524799i | \(0.824140\pi\) | |||||||
\(684\) | 81607.9 | + | 279620.i | 0.174429 | + | 0.597663i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −57643.5 | − | 403258.i | −0.122490 | − | 0.856908i | ||||
\(687\) | 319737.i | 0.677454i | ||||||||
\(688\) | −111696. | − | 175057.i | −0.235972 | − | 0.369831i | ||||
\(689\) | 654026. | 1.37771 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 901400.i | 1.88782i | 0.330197 | + | 0.943912i | \(0.392885\pi\) | ||||
−0.330197 | + | 0.943912i | \(0.607115\pi\) | |||||||
\(692\) | 638864. | − | 186454.i | 1.33412 | − | 0.389367i | ||||
\(693\) | 148010. | 0.308194 | ||||||||
\(694\) | 308.923 | + | 2161.14i | 0.000641403 | + | 0.00448708i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 20154.8 | + | 44420.7i | 0.0416064 | + | 0.0916994i | ||||
\(697\) | 331844. | 0.683076 | ||||||||
\(698\) | 866960. | − | 123927.i | 1.77946 | − | 0.254364i | ||||
\(699\) | − | 410311.i | − | 0.839767i | ||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −547685. | −1.11454 | −0.557269 | − | 0.830332i | \(-0.688151\pi\) | ||||
−0.557269 | + | 0.830332i | \(0.688151\pi\) | |||||||
\(702\) | 22649.3 | + | 158448.i | 0.0459600 | + | 0.321524i | ||||
\(703\) | − | 67623.8i | − | 0.136832i | ||||||
\(704\) | −700091. | − | 612667.i | −1.41257 | − | 1.23617i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −552214. | + | 78935.9i | −1.10789 | + | 0.158367i | ||||
\(707\) | − | 141373.i | − | 0.282832i | ||||||
\(708\) | 250880. | − | 73219.9i | 0.500494 | − | 0.146070i | ||||
\(709\) | 861198. | 1.71321 | 0.856604 | − | 0.515974i | \(-0.172570\pi\) | ||||
0.856604 | + | 0.515974i | \(0.172570\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − | 76670.7i | − | 0.151667i | ||||||
\(712\) | −14332.3 | + | 6502.94i | −0.0282720 | + | 0.0128277i | ||||
\(713\) | −322964. | −0.635295 | ||||||||
\(714\) | 149730. | − | 21403.0i | 0.293705 | − | 0.0419835i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 233371. | + | 799621.i | 0.455220 | + | 1.55976i | ||||
\(717\) | 316751. | 0.616140 | ||||||||
\(718\) | 13923.2 | + | 97403.2i | 0.0270079 | + | 0.188940i | ||||
\(719\) | 865354.i | 1.67393i | 0.547260 | + | 0.836963i | \(0.315671\pi\) | ||||
−0.547260 | + | 0.836963i | \(0.684329\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 324485. | 0.624201 | ||||||||
\(722\) | −1.28424e6 | + | 183575.i | −2.46360 | + | 0.352158i | ||||
\(723\) | 225304.i | 0.431016i | ||||||||
\(724\) | 743371. | − | 216955.i | 1.41817 | − | 0.413897i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −108664. | − | 760184.i | −0.206164 | − | 1.44227i | ||||
\(727\) | − | 525474.i | − | 0.994220i | −0.867687 | − | 0.497110i | \(-0.834394\pi\) | ||
0.867687 | − | 0.497110i | \(-0.165606\pi\) | |||||||
\(728\) | 182035. | + | 401200.i | 0.343472 | + | 0.757003i | ||||
\(729\) | −19683.0 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 244572.i | − | 0.457690i | ||||||
\(732\) | −47213.3 | − | 161771.i | −0.0881134 | − | 0.301911i | ||||
\(733\) | −160865. | −0.299401 | −0.149700 | − | 0.988731i | \(-0.547831\pi\) | ||||
−0.149700 | + | 0.988731i | \(0.547831\pi\) | |||||||
\(734\) | −5568.23 | − | 38953.8i | −0.0103354 | − | 0.0723033i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 307000. | + | 357235.i | 0.566739 | + | 0.659476i | ||||
\(737\) | −612725. | −1.12806 | ||||||||
\(738\) | −117669. | + | 16820.2i | −0.216048 | + | 0.0308829i | ||||
\(739\) | − | 859197.i | − | 1.57327i | −0.617417 | − | 0.786636i | \(-0.711821\pi\) | ||
0.617417 | − | 0.786636i | \(-0.288179\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −999290. | −1.81993 | ||||||||
\(742\) | 31326.5 | + | 219152.i | 0.0568990 | + | 0.398050i | ||||
\(743\) | 647679.i | 1.17323i | 0.809867 | + | 0.586614i | \(0.199539\pi\) | ||||
−0.809867 | + | 0.586614i | \(0.800461\pi\) | |||||||
\(744\) | −212628. | + | 96474.9i | −0.384127 | + | 0.174288i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 180615. | − | 25817.9i | 0.324546 | − | 0.0463921i | ||||
\(747\) | 124781.i | 0.223618i | ||||||||
\(748\) | −306977. | − | 1.05182e6i | −0.548659 | − | 1.87992i | ||||
\(749\) | −123839. | −0.220746 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 990728.i | − | 1.75661i | −0.478104 | − | 0.878303i | \(-0.658676\pi\) | ||
0.478104 | − | 0.878303i | \(-0.341324\pi\) | |||||||
\(752\) | −163914. | − | 256897.i | −0.289854 | − | 0.454279i | ||||
\(753\) | 20976.8 | 0.0369956 | ||||||||
\(754\) | −165659. | + | 23680.0i | −0.291388 | + | 0.0416523i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −52008.2 | + | 15178.7i | −0.0909972 | + | 0.0265577i | ||||
\(757\) | 410201. | 0.715823 | 0.357911 | − | 0.933756i | \(-0.383489\pi\) | ||||
0.357911 | + | 0.933756i | \(0.383489\pi\) | |||||||
\(758\) | −122022. | − | 853634.i | −0.212374 | − | 1.48571i | ||||
\(759\) | 542873.i | 0.942355i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 383591. | 0.662367 | 0.331184 | − | 0.943566i | \(-0.392552\pi\) | ||||
0.331184 | + | 0.943566i | \(0.392552\pi\) | |||||||
\(762\) | −60205.4 | + | 8606.03i | −0.103687 | + | 0.0148215i | ||||
\(763\) | − | 59106.1i | − | 0.101527i | ||||||
\(764\) | −65159.4 | − | 223261.i | −0.111632 | − | 0.382496i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 33677.5 | + | 235599.i | 0.0573961 | + | 0.401528i | ||||
\(767\) | 896578.i | 1.52404i | ||||||||
\(768\) | 308830. | + | 143485.i | 0.523597 | + | 0.243268i | ||||
\(769\) | −880209. | −1.48845 | −0.744223 | − | 0.667932i | \(-0.767180\pi\) | ||||
−0.744223 | + | 0.667932i | \(0.767180\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − | 110257.i | − | 0.185480i | ||||||
\(772\) | 7589.76 | − | 2215.09i | 0.0127348 | − | 0.00371669i | ||||
\(773\) | 657589. | 1.10051 | 0.550257 | − | 0.834995i | \(-0.314530\pi\) | ||||
0.550257 | + | 0.834995i | \(0.314530\pi\) | |||||||
\(774\) | 12396.6 | + | 86723.3i | 0.0206929 | + | 0.144762i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −91567.7 | + | 41546.6i | −0.152061 | + | 0.0689941i | ||||
\(777\) | 12577.7 | 0.0208334 | ||||||||
\(778\) | −440962. | + | 63033.0i | −0.728520 | + | 0.104138i | ||||
\(779\) | − | 742109.i | − | 1.22290i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.89942e6 | 3.11400 | ||||||||
\(782\) | 78502.4 | + | 549181.i | 0.128372 | + | 0.898053i | ||||
\(783\) | − | 20578.7i | − | 0.0335656i | ||||||
\(784\) | 392449. | − | 250403.i | 0.638486 | − | 0.407388i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −343290. | + | 49071.4i | −0.555668 | + | 0.0794297i | ||||
\(787\) | 97654.3i | 0.157667i | 0.996888 | + | 0.0788337i | \(0.0251196\pi\) | ||||
−0.996888 | + | 0.0788337i | \(0.974880\pi\) | |||||||
\(788\) | 47429.0 | − | 13842.3i | 0.0763820 | − | 0.0222923i | ||||
\(789\) | 340686. | 0.547267 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 112328.i | 0.179530i | ||||||||
\(792\) | 162165. | + | 357408.i | 0.258528 | + | 0.569789i | ||||
\(793\) | 578127. | 0.919342 | ||||||||
\(794\) | −801892. | + | 114626.i | −1.27196 | + | 0.181820i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 218866. | + | 749919.i | 0.345423 | + | 1.18355i | ||||
\(797\) | −911016. | −1.43420 | −0.717099 | − | 0.696971i | \(-0.754531\pi\) | ||||
−0.717099 | + | 0.696971i | \(0.754531\pi\) | |||||||
\(798\) | −47864.0 | − | 334843.i | −0.0751628 | − | 0.525818i | ||||
\(799\) | − | 358910.i | − | 0.562201i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 6639.72 | 0.0103487 | ||||||||
\(802\) | 217255. | − | 31055.4i | 0.337770 | − | 0.0482824i | ||||
\(803\) | − | 1.52653e6i | − | 2.36741i | ||||||
\(804\) | 215301. | − | 62836.1i | 0.333069 | − | 0.0972070i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −113349. | − | 792958.i | −0.174481 | − | 1.22062i | ||||
\(807\) | 371276.i | 0.570098i | ||||||||
\(808\) | 341383. | − | 154894.i | 0.522901 | − | 0.237253i | ||||
\(809\) | −535190. | −0.817733 | −0.408866 | − | 0.912594i | \(-0.634076\pi\) | ||||
−0.408866 | + | 0.912594i | \(0.634076\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 441885.i | 0.671842i | 0.941890 | + | 0.335921i | \(0.109048\pi\) | ||||
−0.941890 | + | 0.335921i | \(0.890952\pi\) | |||||||
\(812\) | −15869.5 | − | 54374.9i | −0.0240685 | − | 0.0824682i | ||||
\(813\) | 269817. | 0.408214 | ||||||||
\(814\) | −12893.5 | − | 90199.1i | −0.0194590 | − | 0.136130i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 215733. | + | 338111.i | 0.323993 | + | 0.507785i | ||||
\(817\) | −546940. | −0.819400 | ||||||||
\(818\) | 770926. | − | 110200.i | 1.15214 | − | 0.164692i | ||||
\(819\) | − | 185863.i | − | 0.277093i | ||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 418246. | 0.620505 | 0.310253 | − | 0.950654i | \(-0.399586\pi\) | ||||
0.310253 | + | 0.950654i | \(0.399586\pi\) | |||||||
\(822\) | −75037.6 | − | 524942.i | −0.111054 | − | 0.776905i | ||||
\(823\) | 546065.i | 0.806203i | 0.915155 | + | 0.403101i | \(0.132068\pi\) | ||||
−0.915155 | + | 0.403101i | \(0.867932\pi\) | |||||||
\(824\) | 355519. | + | 783555.i | 0.523610 | + | 1.15402i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −300426. | + | 42944.3i | −0.440330 | + | 0.0629427i | ||||
\(827\) | 170798.i | 0.249731i | 0.992174 | + | 0.124865i | \(0.0398499\pi\) | ||||
−0.992174 | + | 0.124865i | \(0.960150\pi\) | |||||||
\(828\) | −55672.7 | − | 190756.i | −0.0812047 | − | 0.278239i | ||||
\(829\) | −409275. | −0.595534 | −0.297767 | − | 0.954639i | \(-0.596242\pi\) | ||||
−0.297767 | + | 0.954639i | \(0.596242\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 113765.i | 0.164743i | ||||||||
\(832\) | −769357. | + | 879140.i | −1.11143 | + | 1.27002i | ||||
\(833\) | 548290. | 0.790170 | ||||||||
\(834\) | 27082.7 | − | 3871.33i | 0.0389368 | − | 0.00556580i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −2.35221e6 | + | 686498.i | −3.36561 | + | 0.982260i | ||||
\(837\) | 98504.1 | 0.140606 | ||||||||
\(838\) | 78427.6 | + | 548658.i | 0.111681 | + | 0.781293i | ||||
\(839\) | − | 442416.i | − | 0.628502i | −0.949340 | − | 0.314251i | \(-0.898247\pi\) | ||
0.949340 | − | 0.314251i | \(-0.101753\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −685766. | −0.969580 | ||||||||
\(842\) | 502989. | − | 71899.4i | 0.709470 | − | 0.101415i | ||||
\(843\) | 41830.9i | 0.0588629i | ||||||||
\(844\) | 306711. | + | 1.05091e6i | 0.430571 | + | 1.47531i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 18192.0 | + | 127267.i | 0.0254180 | + | 0.177817i | ||||
\(847\) | 891713.i | 1.24296i | ||||||||
\(848\) | −494877. | + | 315757.i | −0.688185 | + | 0.439098i | ||||
\(849\) | 285937. | 0.396694 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 46132.8i | 0.0637016i | ||||||||
\(852\) | −667423. | + | 194789.i | −0.919436 | + | 0.268340i | ||||
\(853\) | −1.02334e6 | −1.40645 | −0.703224 | − | 0.710969i | \(-0.748257\pi\) | ||||
−0.703224 | + | 0.710969i | \(0.748257\pi\) | |||||||
\(854\) | 27691.1 | + | 193720.i | 0.0379686 | + | 0.265618i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −135683. | − | 299041.i | −0.185173 | − | 0.408116i | ||||
\(857\) | −605173. | −0.823982 | −0.411991 | − | 0.911188i | \(-0.635167\pi\) | ||||
−0.411991 | + | 0.911188i | \(0.635167\pi\) | |||||||
\(858\) | −1.33289e6 | + | 190529.i | −1.81059 | + | 0.258814i | ||||
\(859\) | 607227.i | 0.822933i | 0.911425 | + | 0.411467i | \(0.134983\pi\) | ||||
−0.911425 | + | 0.411467i | \(0.865017\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 138029. | 0.186193 | ||||||||
\(862\) | −78951.8 | − | 552325.i | −0.106255 | − | 0.743328i | ||||
\(863\) | 1.41500e6i | 1.89992i | 0.312365 | + | 0.949962i | \(0.398879\pi\) | ||||
−0.312365 | + | 0.949962i | \(0.601121\pi\) | |||||||
\(864\) | −93635.1 | − | 108957.i | −0.125433 | − | 0.145958i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 1.32347e6 | − | 189183.i | 1.76473 | − | 0.252258i | ||||
\(867\) | 38386.7i | 0.0510672i | ||||||||
\(868\) | 260276. | − | 75962.2i | 0.345458 | − | 0.100823i | ||||
\(869\) | 644965. | 0.854076 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 769429.i | 1.01422i | ||||||||
\(872\) | 142727. | − | 64759.0i | 0.187704 | − | 0.0851662i | ||||
\(873\) | 42420.5 | 0.0556605 | ||||||||
\(874\) | 1.22814e6 | − | 175556.i | 1.60778 | − | 0.229823i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 156549. | + | 536397.i | 0.204005 | + | 0.699001i | ||||
\(877\) | 1.26941e6 | 1.65045 | 0.825223 | − | 0.564807i | \(-0.191049\pi\) | ||||
0.825223 | + | 0.564807i | \(0.191049\pi\) | |||||||
\(878\) | 164367. | + | 1.14986e6i | 0.213218 | + | 1.49162i | ||||
\(879\) | 436828.i | 0.565370i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −175455. | −0.226055 | −0.113027 | − | 0.993592i | \(-0.536055\pi\) | ||||
−0.113027 | + | 0.993592i | \(0.536055\pi\) | |||||||
\(882\) | −194419. | + | 27791.2i | −0.249921 | + | 0.0357248i | ||||
\(883\) | − | 1.00549e6i | − | 1.28960i | −0.764349 | − | 0.644802i | \(-0.776940\pi\) | ||
0.764349 | − | 0.644802i | \(-0.223060\pi\) | |||||||
\(884\) | −1.32083e6 | + | 385486.i | −1.69021 | + | 0.493292i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 17829.4 | + | 124730.i | 0.0227128 | + | 0.158892i | ||||
\(887\) | − | 796613.i | − | 1.01251i | −0.862383 | − | 0.506256i | \(-0.831029\pi\) | ||
0.862383 | − | 0.506256i | \(-0.168971\pi\) | |||||||
\(888\) | 13780.6 | + | 30372.2i | 0.0174761 | + | 0.0385168i | ||||
\(889\) | 70622.4 | 0.0893591 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | − | 165576.i | − | 0.208566i | ||||||
\(892\) | −8139.95 | − | 27890.6i | −0.0102304 | − | 0.0350533i | ||||
\(893\) | −802635. | −1.00650 | ||||||||
\(894\) | −60602.1 | − | 423956.i | −0.0758250 | − | 0.530451i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −331434. | − | 215688.i | −0.412839 | − | 0.268664i | ||||
\(897\) | 681713. | 0.847260 | ||||||||
\(898\) | 1.20484e6 | − | 172225.i | 1.49409 | − | 0.213572i | ||||
\(899\) | 102987.i | 0.127427i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −691391. | −0.851675 | ||||||||
\(902\) | −141494. | − | 989852.i | −0.173910 | − | 1.21663i | ||||
\(903\) | − | 101728.i | − | 0.124758i | ||||||
\(904\) | −271246. | + | 123071.i | −0.331915 | + | 0.150598i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 201263. | − | 28769.5i | 0.245193 | − | 0.0350490i | ||||
\(907\) | 1.00997e6i | 1.22770i | 0.789423 | + | 0.613850i | \(0.210380\pi\) | ||||
−0.789423 | + | 0.613850i | \(0.789620\pi\) | |||||||
\(908\) | 113352. | + | 388387.i | 0.137485 | + | 0.471078i | ||||
\(909\) | −158152. | −0.191403 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 243711.i | − | 0.293656i | −0.989162 | − | 0.146828i | \(-0.953094\pi\) | ||
0.989162 | − | 0.146828i | \(-0.0469063\pi\) | |||||||
\(912\) | 756124. | − | 482447.i | 0.909083 | − | 0.580043i | ||||
\(913\) | −1.04967e6 | −1.25925 | ||||||||
\(914\) | −601896. | + | 86037.7i | −0.720492 | + | 0.102990i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 945107. | − | 275832.i | 1.12639 | − | 0.328740i | ||||
\(917\) | 402687. | 0.478882 | ||||||||
\(918\) | −23943.2 | − | 167500.i | −0.0284117 | − | 0.198761i | ||||
\(919\) | 997533.i | 1.18113i | 0.806992 | + | 0.590563i | \(0.201094\pi\) | ||||
−0.806992 | + | 0.590563i | \(0.798906\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 403988. | 0.476266 | ||||||||
\(922\) | 638720. | − | 91301.4i | 0.751361 | − | 0.107403i | ||||
\(923\) | − | 2.38519e6i | − | 2.79976i | ||||||
\(924\) | −127686. | − | 437500.i | −0.149554 | − | 0.512430i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 81520.0 | + | 570292.i | 0.0950698 | + | 0.665082i | ||||
\(927\) | − | 362997.i | − | 0.422419i | ||||||
\(928\) | 113915. | − | 97896.2i | 0.132277 | − | 0.113676i | ||||
\(929\) | −101841. | −0.118003 | −0.0590013 | − | 0.998258i | \(-0.518792\pi\) | ||||
−0.0590013 | + | 0.998258i | \(0.518792\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 1.22615e6i | − | 1.41463i | ||||||
\(932\) | −1.21283e6 | + | 353968.i | −1.39627 | + | 0.407505i | ||||
\(933\) | 490338. | 0.563291 | ||||||||
\(934\) | 162066. | + | 1.13377e6i | 0.185780 | + | 1.29966i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 448816. | − | 203639.i | 0.512291 | − | 0.232439i | ||||
\(937\) | 903469. | 1.02904 | 0.514522 | − | 0.857477i | \(-0.327969\pi\) | ||||
0.514522 | + | 0.857477i | \(0.327969\pi\) | |||||||
\(938\) | −257821. | + | 36854.1i | −0.293031 | + | 0.0418871i | ||||
\(939\) | 497381.i | 0.564102i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −489666. | −0.552995 | −0.276497 | − | 0.961015i | \(-0.589174\pi\) | ||||
−0.276497 | + | 0.961015i | \(0.589174\pi\) | |||||||
\(942\) | 59731.9 | + | 417868.i | 0.0673138 | + | 0.470909i | ||||
\(943\) | 506265.i | 0.569317i | ||||||||
\(944\) | −432859. | − | 678406.i | −0.485738 | − | 0.761283i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −729529. | + | 104282.i | −0.815193 | + | 0.116527i | ||||
\(947\) | − | 1.16141e6i | − | 1.29504i | −0.762047 | − | 0.647521i | \(-0.775806\pi\) | ||
0.762047 | − | 0.647521i | \(-0.224194\pi\) | |||||||
\(948\) | −226630. | + | 66142.4i | −0.252174 | + | 0.0735976i | ||||
\(949\) | −1.91694e6 | −2.12851 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 853511.i | − | 0.943730i | ||||||
\(952\) | −192434. | − | 424120.i | −0.212328 | − | 0.467967i | ||||
\(953\) | 1.02846e6 | 1.13241 | 0.566204 | − | 0.824265i | \(-0.308411\pi\) | ||||
0.566204 | + | 0.824265i | \(0.308411\pi\) | |||||||
\(954\) | 245162. | − | 35044.5i | 0.269374 | − | 0.0385055i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −273255. | − | 936279.i | −0.298987 | − | 1.02445i | ||||
\(957\) | 173111. | 0.189017 | ||||||||
\(958\) | 147934. | + | 1.03491e6i | 0.161190 | + | 1.12764i | ||||
\(959\) | 615770.i | 0.669547i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 430554. | 0.466210 | ||||||||
\(962\) | −113268. | + | 16191.0i | −0.122393 | + | 0.0174954i | ||||
\(963\) | 138537.i | 0.149387i | ||||||||
\(964\) | 665974. | − | 194366.i | 0.716644 | − | 0.209154i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 32652.7 | + | 228429.i | 0.0349916 | + | 0.244792i | ||||
\(967\) | − | 1.38968e6i | − | 1.48615i | −0.669210 | − | 0.743074i | \(-0.733367\pi\) | ||
0.669210 | − | 0.743074i | \(-0.266633\pi\) | |||||||
\(968\) | −2.15327e6 | + | 976996.i | −2.29799 | + | 1.04266i | ||||
\(969\) | 1.05638e6 | 1.12505 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 1.30092e6i | − | 1.37979i | −0.723911 | − | 0.689893i | \(-0.757658\pi\) | ||
0.723911 | − | 0.689893i | \(-0.242342\pi\) | |||||||
\(972\) | 16980.2 | + | 58180.7i | 0.0179725 | + | 0.0615810i | ||||
\(973\) | −31768.7 | −0.0335563 | ||||||||
\(974\) | −99965.9 | − | 699334.i | −0.105374 | − | 0.737168i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −437447. | + | 279114.i | −0.459225 | + | 0.293010i | ||||
\(977\) | −1.20079e6 | −1.25799 | −0.628994 | − | 0.777410i | \(-0.716533\pi\) | ||||
−0.628994 | + | 0.777410i | \(0.716533\pi\) | |||||||
\(978\) | −717681. | + | 102589.i | −0.750332 | + | 0.107256i | ||||
\(979\) | 55854.3i | 0.0582762i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −66121.1 | −0.0687072 | ||||||||
\(982\) | 81144.0 | + | 567661.i | 0.0841460 | + | 0.588662i | ||||
\(983\) | 12695.6i | 0.0131385i | 0.999978 | + | 0.00656923i | \(0.00209107\pi\) | ||||
−0.999978 | + | 0.00656923i | \(0.997909\pi\) | |||||||
\(984\) | 151230. | + | 333307.i | 0.156188 | + | 0.344234i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 175123. | − | 25032.8i | 0.180131 | − | 0.0257488i | ||||
\(987\) | − | 149287.i | − | 0.153245i | ||||||
\(988\) | 862070. | + | 2.95379e6i | 0.883138 | + | 3.02597i | ||||
\(989\) | 373121. | 0.381467 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 1.57211e6i | − | 1.60079i | −0.599470 | − | 0.800397i | \(-0.704622\pi\) | ||
0.599470 | − | 0.800397i | \(-0.295378\pi\) | |||||||
\(992\) | 468599. | + | 545278.i | 0.476188 | + | 0.554108i | ||||
\(993\) | 808382. | 0.819819 | ||||||||
\(994\) | 799233. | − | 114246.i | 0.808911 | − | 0.115629i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 368838. | − | 107646.i | 0.371806 | − | 0.108512i | ||||
\(997\) | −774236. | −0.778902 | −0.389451 | − | 0.921047i | \(-0.627335\pi\) | ||||
−0.389451 | + | 0.921047i | \(0.627335\pi\) | |||||||
\(998\) | 59278.9 | + | 414699.i | 0.0595167 | + | 0.416363i | ||||
\(999\) | − | 14070.5i | − | 0.0140987i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 300.5.c.d.151.15 | 16 | ||
4.3 | odd | 2 | inner | 300.5.c.d.151.16 | 16 | ||
5.2 | odd | 4 | 300.5.f.b.199.18 | 32 | |||
5.3 | odd | 4 | 300.5.f.b.199.15 | 32 | |||
5.4 | even | 2 | 60.5.c.a.31.2 | yes | 16 | ||
15.14 | odd | 2 | 180.5.c.c.91.15 | 16 | |||
20.3 | even | 4 | 300.5.f.b.199.17 | 32 | |||
20.7 | even | 4 | 300.5.f.b.199.16 | 32 | |||
20.19 | odd | 2 | 60.5.c.a.31.1 | ✓ | 16 | ||
40.19 | odd | 2 | 960.5.e.f.511.2 | 16 | |||
40.29 | even | 2 | 960.5.e.f.511.11 | 16 | |||
60.59 | even | 2 | 180.5.c.c.91.16 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
60.5.c.a.31.1 | ✓ | 16 | 20.19 | odd | 2 | ||
60.5.c.a.31.2 | yes | 16 | 5.4 | even | 2 | ||
180.5.c.c.91.15 | 16 | 15.14 | odd | 2 | |||
180.5.c.c.91.16 | 16 | 60.59 | even | 2 | |||
300.5.c.d.151.15 | 16 | 1.1 | even | 1 | trivial | ||
300.5.c.d.151.16 | 16 | 4.3 | odd | 2 | inner | ||
300.5.f.b.199.15 | 32 | 5.3 | odd | 4 | |||
300.5.f.b.199.16 | 32 | 20.7 | even | 4 | |||
300.5.f.b.199.17 | 32 | 20.3 | even | 4 | |||
300.5.f.b.199.18 | 32 | 5.2 | odd | 4 | |||
960.5.e.f.511.2 | 16 | 40.19 | odd | 2 | |||
960.5.e.f.511.11 | 16 | 40.29 | even | 2 |