Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [289,4,Mod(288,289)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(289, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("289.288");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 289 = 17^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 289.b (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(17.0515519917\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 288.1 | ||
Character | \(\chi\) | \(=\) | 289.288 |
Dual form | 289.4.b.f.288.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/289\mathbb{Z}\right)^\times\).
\(n\) | \(3\) |
\(\chi(n)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −4.44354 | −1.57103 | −0.785514 | − | 0.618844i | \(-0.787601\pi\) | ||||
−0.785514 | + | 0.618844i | \(0.787601\pi\) | |||||||
\(3\) | − 0.537336i | − 0.103410i | −0.998662 | − | 0.0517052i | \(-0.983534\pi\) | ||||
0.998662 | − | 0.0517052i | \(-0.0164656\pi\) | |||||||
\(4\) | 11.7450 | 1.46813 | ||||||||
\(5\) | − 17.2592i | − 1.54371i | −0.635800 | − | 0.771854i | \(-0.719330\pi\) | ||||
0.635800 | − | 0.771854i | \(-0.280670\pi\) | |||||||
\(6\) | 2.38767i | 0.162461i | ||||||||
\(7\) | − 6.40763i | − 0.345979i | −0.984924 | − | 0.172990i | \(-0.944657\pi\) | ||||
0.984924 | − | 0.172990i | \(-0.0553427\pi\) | |||||||
\(8\) | −16.6411 | −0.735439 | ||||||||
\(9\) | 26.7113 | 0.989306 | ||||||||
\(10\) | 76.6918i | 2.42521i | ||||||||
\(11\) | 55.3227i | 1.51640i | 0.652020 | + | 0.758201i | \(0.273922\pi\) | ||||
−0.652020 | + | 0.758201i | \(0.726078\pi\) | |||||||
\(12\) | − 6.31102i | − 0.151819i | ||||||||
\(13\) | 58.6637 | 1.25157 | 0.625784 | − | 0.779996i | \(-0.284779\pi\) | ||||
0.625784 | + | 0.779996i | \(0.284779\pi\) | |||||||
\(14\) | 28.4725i | 0.543543i | ||||||||
\(15\) | −9.27398 | −0.159635 | ||||||||
\(16\) | −20.0149 | −0.312732 | ||||||||
\(17\) | 0 | 0 | ||||||||
\(18\) | −118.692 | −1.55423 | ||||||||
\(19\) | 91.1866 | 1.10103 | 0.550517 | − | 0.834824i | \(-0.314431\pi\) | ||||
0.550517 | + | 0.834824i | \(0.314431\pi\) | |||||||
\(20\) | − 202.709i | − 2.26636i | ||||||||
\(21\) | −3.44305 | −0.0357779 | ||||||||
\(22\) | − 245.829i | − 2.38231i | ||||||||
\(23\) | 120.879i | 1.09587i | 0.836521 | + | 0.547935i | \(0.184586\pi\) | ||||
−0.836521 | + | 0.547935i | \(0.815414\pi\) | |||||||
\(24\) | 8.94185i | 0.0760520i | ||||||||
\(25\) | −172.879 | −1.38303 | ||||||||
\(26\) | −260.674 | −1.96625 | ||||||||
\(27\) | − 28.8610i | − 0.205715i | ||||||||
\(28\) | − 75.2576i | − 0.507941i | ||||||||
\(29\) | 215.755i | 1.38154i | 0.723074 | + | 0.690771i | \(0.242729\pi\) | ||||
−0.723074 | + | 0.690771i | \(0.757271\pi\) | |||||||
\(30\) | 41.2093 | 0.250792 | ||||||||
\(31\) | 17.5166i | 0.101486i | 0.998712 | + | 0.0507432i | \(0.0161590\pi\) | ||||
−0.998712 | + | 0.0507432i | \(0.983841\pi\) | |||||||
\(32\) | 222.065 | 1.22675 | ||||||||
\(33\) | 29.7269 | 0.156812 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −110.590 | −0.534091 | ||||||||
\(36\) | 313.724 | 1.45243 | ||||||||
\(37\) | 8.40485i | 0.0373446i | 0.999826 | + | 0.0186723i | \(0.00594392\pi\) | ||||
−0.999826 | + | 0.0186723i | \(0.994056\pi\) | |||||||
\(38\) | −405.191 | −1.72975 | ||||||||
\(39\) | − 31.5221i | − 0.129425i | ||||||||
\(40\) | 287.211i | 1.13530i | ||||||||
\(41\) | 99.9530i | 0.380733i | 0.981713 | + | 0.190366i | \(0.0609676\pi\) | ||||
−0.981713 | + | 0.190366i | \(0.939032\pi\) | |||||||
\(42\) | 15.2993 | 0.0562080 | ||||||||
\(43\) | 81.5297 | 0.289143 | 0.144572 | − | 0.989494i | \(-0.453820\pi\) | ||||
0.144572 | + | 0.989494i | \(0.453820\pi\) | |||||||
\(44\) | 649.766i | 2.22627i | ||||||||
\(45\) | − 461.015i | − 1.52720i | ||||||||
\(46\) | − 537.130i | − 1.72164i | ||||||||
\(47\) | 195.351 | 0.606275 | 0.303137 | − | 0.952947i | \(-0.401966\pi\) | ||||
0.303137 | + | 0.952947i | \(0.401966\pi\) | |||||||
\(48\) | 10.7547i | 0.0323398i | ||||||||
\(49\) | 301.942 | 0.880298 | ||||||||
\(50\) | 768.195 | 2.17278 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 689.006 | 1.83746 | ||||||||
\(53\) | −260.322 | −0.674678 | −0.337339 | − | 0.941383i | \(-0.609527\pi\) | ||||
−0.337339 | + | 0.941383i | \(0.609527\pi\) | |||||||
\(54\) | 128.245i | 0.323184i | ||||||||
\(55\) | 954.825 | 2.34088 | ||||||||
\(56\) | 106.630i | 0.254447i | ||||||||
\(57\) | − 48.9979i | − 0.113858i | ||||||||
\(58\) | − 958.715i | − 2.17044i | ||||||||
\(59\) | 536.401 | 1.18362 | 0.591809 | − | 0.806078i | \(-0.298414\pi\) | ||||
0.591809 | + | 0.806078i | \(0.298414\pi\) | |||||||
\(60\) | −108.923 | −0.234365 | ||||||||
\(61\) | − 265.689i | − 0.557671i | −0.960339 | − | 0.278836i | \(-0.910052\pi\) | ||||
0.960339 | − | 0.278836i | \(-0.0899485\pi\) | |||||||
\(62\) | − 77.8357i | − 0.159438i | ||||||||
\(63\) | − 171.156i | − 0.342280i | ||||||||
\(64\) | −826.636 | −1.61452 | ||||||||
\(65\) | − 1012.49i | − 1.93206i | ||||||||
\(66\) | −132.093 | −0.246356 | ||||||||
\(67\) | 514.794 | 0.938687 | 0.469344 | − | 0.883016i | \(-0.344491\pi\) | ||||
0.469344 | + | 0.883016i | \(0.344491\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 64.9526 | 0.113324 | ||||||||
\(70\) | 491.412 | 0.839071 | ||||||||
\(71\) | 704.023i | 1.17679i | 0.808573 | + | 0.588396i | \(0.200240\pi\) | ||||
−0.808573 | + | 0.588396i | \(0.799760\pi\) | |||||||
\(72\) | −444.504 | −0.727574 | ||||||||
\(73\) | − 184.948i | − 0.296528i | −0.988948 | − | 0.148264i | \(-0.952632\pi\) | ||||
0.988948 | − | 0.148264i | \(-0.0473685\pi\) | |||||||
\(74\) | − 37.3473i | − 0.0586693i | ||||||||
\(75\) | 92.8943i | 0.143020i | ||||||||
\(76\) | 1070.99 | 1.61646 | ||||||||
\(77\) | 354.487 | 0.524644 | ||||||||
\(78\) | 140.070i | 0.203330i | ||||||||
\(79\) | − 34.8358i | − 0.0496118i | −0.999692 | − | 0.0248059i | \(-0.992103\pi\) | ||||
0.999692 | − | 0.0248059i | \(-0.00789678\pi\) | |||||||
\(80\) | 345.440i | 0.482767i | ||||||||
\(81\) | 705.696 | 0.968033 | ||||||||
\(82\) | − 444.145i | − 0.598141i | ||||||||
\(83\) | 647.682 | 0.856534 | 0.428267 | − | 0.903652i | \(-0.359124\pi\) | ||||
0.428267 | + | 0.903652i | \(0.359124\pi\) | |||||||
\(84\) | −40.4386 | −0.0525264 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −362.280 | −0.454252 | ||||||||
\(87\) | 115.933 | 0.142866 | ||||||||
\(88\) | − 920.630i | − 1.11522i | ||||||||
\(89\) | −1060.24 | −1.26275 | −0.631377 | − | 0.775476i | \(-0.717510\pi\) | ||||
−0.631377 | + | 0.775476i | \(0.717510\pi\) | |||||||
\(90\) | 2048.53i | 2.39927i | ||||||||
\(91\) | − 375.895i | − 0.433017i | ||||||||
\(92\) | 1419.72i | 1.60887i | ||||||||
\(93\) | 9.41231 | 0.0104947 | ||||||||
\(94\) | −868.051 | −0.952474 | ||||||||
\(95\) | − 1573.81i | − 1.69967i | ||||||||
\(96\) | − 119.324i | − 0.126859i | ||||||||
\(97\) | 256.409i | 0.268395i | 0.990955 | + | 0.134198i | \(0.0428457\pi\) | ||||
−0.990955 | + | 0.134198i | \(0.957154\pi\) | |||||||
\(98\) | −1341.69 | −1.38297 | ||||||||
\(99\) | 1477.74i | 1.50019i | ||||||||
\(100\) | −2030.47 | −2.03047 | ||||||||
\(101\) | −1465.07 | −1.44337 | −0.721685 | − | 0.692222i | \(-0.756632\pi\) | ||||
−0.721685 | + | 0.692222i | \(0.756632\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −25.6805 | −0.0245668 | −0.0122834 | − | 0.999925i | \(-0.503910\pi\) | ||||
−0.0122834 | + | 0.999925i | \(0.503910\pi\) | |||||||
\(104\) | −976.227 | −0.920452 | ||||||||
\(105\) | 59.4242i | 0.0552306i | ||||||||
\(106\) | 1156.75 | 1.05994 | ||||||||
\(107\) | − 2030.70i | − 1.83472i | −0.398060 | − | 0.917359i | \(-0.630317\pi\) | ||||
0.398060 | − | 0.917359i | \(-0.369683\pi\) | |||||||
\(108\) | − 338.973i | − 0.302015i | ||||||||
\(109\) | − 716.479i | − 0.629598i | −0.949158 | − | 0.314799i | \(-0.898063\pi\) | ||||
0.949158 | − | 0.314799i | \(-0.101937\pi\) | |||||||
\(110\) | −4242.80 | −3.67759 | ||||||||
\(111\) | 4.51623 | 0.00386182 | ||||||||
\(112\) | 128.248i | 0.108199i | ||||||||
\(113\) | 16.9632i | 0.0141218i | 0.999975 | + | 0.00706090i | \(0.00224757\pi\) | ||||
−0.999975 | + | 0.00706090i | \(0.997752\pi\) | |||||||
\(114\) | 217.724i | 0.178875i | ||||||||
\(115\) | 2086.27 | 1.69170 | ||||||||
\(116\) | 2534.05i | 2.02828i | ||||||||
\(117\) | 1566.98 | 1.23818 | ||||||||
\(118\) | −2383.52 | −1.85950 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 154.329 | 0.117402 | ||||||||
\(121\) | −1729.60 | −1.29948 | ||||||||
\(122\) | 1180.60i | 0.876117i | ||||||||
\(123\) | 53.7084 | 0.0393717 | ||||||||
\(124\) | 205.733i | 0.148995i | ||||||||
\(125\) | 826.356i | 0.591292i | ||||||||
\(126\) | 760.537i | 0.537730i | ||||||||
\(127\) | 1138.85 | 0.795724 | 0.397862 | − | 0.917445i | \(-0.369752\pi\) | ||||
0.397862 | + | 0.917445i | \(0.369752\pi\) | |||||||
\(128\) | 1896.67 | 1.30971 | ||||||||
\(129\) | − 43.8089i | − 0.0299004i | ||||||||
\(130\) | 4499.02i | 3.03531i | ||||||||
\(131\) | 618.036i | 0.412199i | 0.978531 | + | 0.206100i | \(0.0660771\pi\) | ||||
−0.978531 | + | 0.206100i | \(0.933923\pi\) | |||||||
\(132\) | 349.143 | 0.230219 | ||||||||
\(133\) | − 584.290i | − 0.380935i | ||||||||
\(134\) | −2287.50 | −1.47470 | ||||||||
\(135\) | −498.117 | −0.317564 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −2255.17 | −1.40637 | −0.703183 | − | 0.711009i | \(-0.748238\pi\) | ||||
−0.703183 | + | 0.711009i | \(0.748238\pi\) | |||||||
\(138\) | −288.619 | −0.178036 | ||||||||
\(139\) | − 1014.29i | − 0.618930i | −0.950911 | − | 0.309465i | \(-0.899850\pi\) | ||||
0.950911 | − | 0.309465i | \(-0.100150\pi\) | |||||||
\(140\) | −1298.88 | −0.784113 | ||||||||
\(141\) | − 104.969i | − 0.0626951i | ||||||||
\(142\) | − 3128.35i | − 1.84877i | ||||||||
\(143\) | 3245.44i | 1.89788i | ||||||||
\(144\) | −534.622 | −0.309388 | ||||||||
\(145\) | 3723.76 | 2.13270 | ||||||||
\(146\) | 821.822i | 0.465853i | ||||||||
\(147\) | − 162.245i | − 0.0910320i | ||||||||
\(148\) | 98.7150i | 0.0548265i | ||||||||
\(149\) | −345.080 | −0.189732 | −0.0948661 | − | 0.995490i | \(-0.530242\pi\) | ||||
−0.0948661 | + | 0.995490i | \(0.530242\pi\) | |||||||
\(150\) | − 412.779i | − 0.224688i | ||||||||
\(151\) | −2555.94 | −1.37748 | −0.688741 | − | 0.725007i | \(-0.741836\pi\) | ||||
−0.688741 | + | 0.725007i | \(0.741836\pi\) | |||||||
\(152\) | −1517.44 | −0.809743 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −1575.18 | −0.824230 | ||||||||
\(155\) | 302.322 | 0.156665 | ||||||||
\(156\) | − 370.228i | − 0.190012i | ||||||||
\(157\) | 3651.08 | 1.85598 | 0.927988 | − | 0.372610i | \(-0.121537\pi\) | ||||
0.927988 | + | 0.372610i | \(0.121537\pi\) | |||||||
\(158\) | 154.794i | 0.0779415i | ||||||||
\(159\) | 139.880i | 0.0697688i | ||||||||
\(160\) | − 3832.66i | − 1.89374i | ||||||||
\(161\) | 774.547 | 0.379148 | ||||||||
\(162\) | −3135.79 | −1.52081 | ||||||||
\(163\) | 211.756i | 0.101755i | 0.998705 | + | 0.0508773i | \(0.0162018\pi\) | ||||
−0.998705 | + | 0.0508773i | \(0.983798\pi\) | |||||||
\(164\) | 1173.95i | 0.558963i | ||||||||
\(165\) | − 513.062i | − 0.242072i | ||||||||
\(166\) | −2878.00 | −1.34564 | ||||||||
\(167\) | − 977.319i | − 0.452858i | −0.974028 | − | 0.226429i | \(-0.927295\pi\) | ||||
0.974028 | − | 0.226429i | \(-0.0727051\pi\) | |||||||
\(168\) | 57.2960 | 0.0263124 | ||||||||
\(169\) | 1244.43 | 0.566424 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 2435.71 | 1.08926 | ||||||||
\(172\) | 957.567 | 0.424499 | ||||||||
\(173\) | − 3607.58i | − 1.58543i | −0.609594 | − | 0.792714i | \(-0.708667\pi\) | ||||
0.609594 | − | 0.792714i | \(-0.291333\pi\) | |||||||
\(174\) | −515.152 | −0.224446 | ||||||||
\(175\) | 1107.75i | 0.478501i | ||||||||
\(176\) | − 1107.28i | − 0.474228i | ||||||||
\(177\) | − 288.228i | − 0.122398i | ||||||||
\(178\) | 4711.21 | 1.98382 | ||||||||
\(179\) | −3180.10 | −1.32789 | −0.663943 | − | 0.747783i | \(-0.731118\pi\) | ||||
−0.663943 | + | 0.747783i | \(0.731118\pi\) | |||||||
\(180\) | − 5414.62i | − 2.24212i | ||||||||
\(181\) | − 1094.34i | − 0.449401i | −0.974428 | − | 0.224701i | \(-0.927860\pi\) | ||||
0.974428 | − | 0.224701i | \(-0.0721404\pi\) | |||||||
\(182\) | 1670.30i | 0.680281i | ||||||||
\(183\) | −142.764 | −0.0576690 | ||||||||
\(184\) | − 2011.56i | − 0.805945i | ||||||||
\(185\) | 145.061 | 0.0576491 | ||||||||
\(186\) | −41.8239 | −0.0164875 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 2294.40 | 0.890088 | ||||||||
\(189\) | −184.931 | −0.0711731 | ||||||||
\(190\) | 6993.26i | 2.67023i | ||||||||
\(191\) | −2323.98 | −0.880406 | −0.440203 | − | 0.897898i | \(-0.645094\pi\) | ||||
−0.440203 | + | 0.897898i | \(0.645094\pi\) | |||||||
\(192\) | 444.182i | 0.166959i | ||||||||
\(193\) | 2521.70i | 0.940498i | 0.882534 | + | 0.470249i | \(0.155836\pi\) | ||||
−0.882534 | + | 0.470249i | \(0.844164\pi\) | |||||||
\(194\) | − 1139.36i | − 0.421656i | ||||||||
\(195\) | −544.046 | −0.199795 | ||||||||
\(196\) | 3546.31 | 1.29239 | ||||||||
\(197\) | − 2196.87i | − 0.794521i | −0.917706 | − | 0.397260i | \(-0.869961\pi\) | ||||
0.917706 | − | 0.397260i | \(-0.130039\pi\) | |||||||
\(198\) | − 6566.39i | − 2.35683i | ||||||||
\(199\) | − 3596.88i | − 1.28129i | −0.767839 | − | 0.640643i | \(-0.778668\pi\) | ||||
0.767839 | − | 0.640643i | \(-0.221332\pi\) | |||||||
\(200\) | 2876.90 | 1.01714 | ||||||||
\(201\) | − 276.617i | − 0.0970700i | ||||||||
\(202\) | 6510.11 | 2.26757 | ||||||||
\(203\) | 1382.48 | 0.477985 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1725.11 | 0.587740 | ||||||||
\(206\) | 114.112 | 0.0385951 | ||||||||
\(207\) | 3228.83i | 1.08415i | ||||||||
\(208\) | −1174.15 | −0.391406 | ||||||||
\(209\) | 5044.69i | 1.66961i | ||||||||
\(210\) | − 264.054i | − 0.0867687i | ||||||||
\(211\) | 3677.29i | 1.19979i | 0.800080 | + | 0.599893i | \(0.204790\pi\) | ||||
−0.800080 | + | 0.599893i | \(0.795210\pi\) | |||||||
\(212\) | −3057.48 | −0.990513 | ||||||||
\(213\) | 378.297 | 0.121692 | ||||||||
\(214\) | 9023.47i | 2.88239i | ||||||||
\(215\) | − 1407.14i | − 0.446353i | ||||||||
\(216\) | 480.278i | 0.151291i | ||||||||
\(217\) | 112.240 | 0.0351122 | ||||||||
\(218\) | 3183.70i | 0.989116i | ||||||||
\(219\) | −99.3792 | −0.0306640 | ||||||||
\(220\) | 11214.4 | 3.43671 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −20.0680 | −0.00606702 | ||||||||
\(223\) | −972.699 | −0.292093 | −0.146047 | − | 0.989278i | \(-0.546655\pi\) | ||||
−0.146047 | + | 0.989278i | \(0.546655\pi\) | |||||||
\(224\) | − 1422.91i | − 0.424430i | ||||||||
\(225\) | −4617.82 | −1.36824 | ||||||||
\(226\) | − 75.3766i | − 0.0221857i | ||||||||
\(227\) | 4696.68i | 1.37326i | 0.727008 | + | 0.686629i | \(0.240910\pi\) | ||||
−0.727008 | + | 0.686629i | \(0.759090\pi\) | |||||||
\(228\) | − 575.480i | − 0.167158i | ||||||||
\(229\) | 2105.80 | 0.607664 | 0.303832 | − | 0.952726i | \(-0.401734\pi\) | ||||
0.303832 | + | 0.952726i | \(0.401734\pi\) | |||||||
\(230\) | −9270.42 | −2.65771 | ||||||||
\(231\) | − 190.479i | − 0.0542537i | ||||||||
\(232\) | − 3590.40i | − 1.01604i | ||||||||
\(233\) | − 641.400i | − 0.180341i | −0.995926 | − | 0.0901706i | \(-0.971259\pi\) | ||||
0.995926 | − | 0.0901706i | \(-0.0287412\pi\) | |||||||
\(234\) | −6962.94 | −1.94522 | ||||||||
\(235\) | − 3371.60i | − 0.935911i | ||||||||
\(236\) | 6300.03 | 1.73770 | ||||||||
\(237\) | −18.7185 | −0.00513038 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 4322.85 | 1.16997 | 0.584984 | − | 0.811045i | \(-0.301101\pi\) | ||||
0.584984 | + | 0.811045i | \(0.301101\pi\) | |||||||
\(240\) | 185.617 | 0.0499231 | ||||||||
\(241\) | − 2462.38i | − 0.658156i | −0.944303 | − | 0.329078i | \(-0.893262\pi\) | ||||
0.944303 | − | 0.329078i | \(-0.106738\pi\) | |||||||
\(242\) | 7685.56 | 2.04151 | ||||||||
\(243\) | − 1158.44i | − 0.305820i | ||||||||
\(244\) | − 3120.52i | − 0.818732i | ||||||||
\(245\) | − 5211.28i | − 1.35892i | ||||||||
\(246\) | −238.655 | −0.0618540 | ||||||||
\(247\) | 5349.35 | 1.37802 | ||||||||
\(248\) | − 291.495i | − 0.0746370i | ||||||||
\(249\) | − 348.023i | − 0.0885746i | ||||||||
\(250\) | − 3671.94i | − 0.928936i | ||||||||
\(251\) | 2631.96 | 0.661865 | 0.330932 | − | 0.943654i | \(-0.392637\pi\) | ||||
0.330932 | + | 0.943654i | \(0.392637\pi\) | |||||||
\(252\) | − 2010.23i | − 0.502509i | ||||||||
\(253\) | −6687.35 | −1.66178 | ||||||||
\(254\) | −5060.54 | −1.25010 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −1814.81 | −0.443068 | ||||||||
\(257\) | 3375.79 | 0.819361 | 0.409680 | − | 0.912229i | \(-0.365640\pi\) | ||||
0.409680 | + | 0.912229i | \(0.365640\pi\) | |||||||
\(258\) | 194.666i | 0.0469744i | ||||||||
\(259\) | 53.8552 | 0.0129204 | ||||||||
\(260\) | − 11891.7i | − 2.83650i | ||||||||
\(261\) | 5763.09i | 1.36677i | ||||||||
\(262\) | − 2746.27i | − 0.647576i | ||||||||
\(263\) | 1603.60 | 0.375977 | 0.187989 | − | 0.982171i | \(-0.439803\pi\) | ||||
0.187989 | + | 0.982171i | \(0.439803\pi\) | |||||||
\(264\) | −494.688 | −0.115325 | ||||||||
\(265\) | 4492.94i | 1.04151i | ||||||||
\(266\) | 2596.31i | 0.598459i | ||||||||
\(267\) | 569.705i | 0.130582i | ||||||||
\(268\) | 6046.26 | 1.37811 | ||||||||
\(269\) | 6543.59i | 1.48316i | 0.670864 | + | 0.741580i | \(0.265923\pi\) | ||||
−0.670864 | + | 0.741580i | \(0.734077\pi\) | |||||||
\(270\) | 2213.40 | 0.498901 | ||||||||
\(271\) | −356.005 | −0.0797998 | −0.0398999 | − | 0.999204i | \(-0.512704\pi\) | ||||
−0.0398999 | + | 0.999204i | \(0.512704\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −201.982 | −0.0447784 | ||||||||
\(274\) | 10020.9 | 2.20944 | ||||||||
\(275\) | − 9564.15i | − 2.09724i | ||||||||
\(276\) | 762.869 | 0.166374 | ||||||||
\(277\) | − 3175.91i | − 0.688887i | −0.938807 | − | 0.344444i | \(-0.888068\pi\) | ||||
0.938807 | − | 0.344444i | \(-0.111932\pi\) | |||||||
\(278\) | 4507.05i | 0.972356i | ||||||||
\(279\) | 467.891i | 0.100401i | ||||||||
\(280\) | 1840.34 | 0.392791 | ||||||||
\(281\) | −1667.30 | −0.353960 | −0.176980 | − | 0.984214i | \(-0.556633\pi\) | ||||
−0.176980 | + | 0.984214i | \(0.556633\pi\) | |||||||
\(282\) | 466.435i | 0.0984957i | ||||||||
\(283\) | 7800.28i | 1.63844i | 0.573479 | + | 0.819220i | \(0.305593\pi\) | ||||
−0.573479 | + | 0.819220i | \(0.694407\pi\) | |||||||
\(284\) | 8268.76i | 1.72768i | ||||||||
\(285\) | −845.663 | −0.175764 | ||||||||
\(286\) | − 14421.2i | − 2.98162i | ||||||||
\(287\) | 640.461 | 0.131726 | ||||||||
\(288\) | 5931.65 | 1.21363 | ||||||||
\(289\) | 0 | 0 | ||||||||
\(290\) | −16546.6 | −3.35052 | ||||||||
\(291\) | 137.778 | 0.0277549 | ||||||||
\(292\) | − 2172.21i | − 0.435340i | ||||||||
\(293\) | −2403.16 | −0.479161 | −0.239580 | − | 0.970877i | \(-0.577010\pi\) | ||||
−0.239580 | + | 0.970877i | \(0.577010\pi\) | |||||||
\(294\) | 720.939i | 0.143014i | ||||||||
\(295\) | − 9257.84i | − 1.82716i | ||||||||
\(296\) | − 139.866i | − 0.0274646i | ||||||||
\(297\) | 1596.67 | 0.311947 | ||||||||
\(298\) | 1533.38 | 0.298074 | ||||||||
\(299\) | 7091.21i | 1.37156i | ||||||||
\(300\) | 1091.04i | 0.209971i | ||||||||
\(301\) | − 522.412i | − 0.100038i | ||||||||
\(302\) | 11357.4 | 2.16406 | ||||||||
\(303\) | 787.238i | 0.149259i | ||||||||
\(304\) | −1825.09 | −0.344329 | ||||||||
\(305\) | −4585.57 | −0.860881 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −4027.80 | −0.748791 | −0.374395 | − | 0.927269i | \(-0.622150\pi\) | ||||
−0.374395 | + | 0.927269i | \(0.622150\pi\) | |||||||
\(308\) | 4163.46 | 0.770244 | ||||||||
\(309\) | 13.7991i | 0.00254046i | ||||||||
\(310\) | −1343.38 | −0.246125 | ||||||||
\(311\) | − 3944.44i | − 0.719192i | −0.933108 | − | 0.359596i | \(-0.882915\pi\) | ||||
0.933108 | − | 0.359596i | \(-0.117085\pi\) | |||||||
\(312\) | 524.562i | 0.0951843i | ||||||||
\(313\) | 6540.41i | 1.18111i | 0.806999 | + | 0.590553i | \(0.201090\pi\) | ||||
−0.806999 | + | 0.590553i | \(0.798910\pi\) | |||||||
\(314\) | −16223.7 | −2.91579 | ||||||||
\(315\) | −2954.01 | −0.528380 | ||||||||
\(316\) | − 409.147i | − 0.0728364i | ||||||||
\(317\) | − 3711.41i | − 0.657582i | −0.944403 | − | 0.328791i | \(-0.893359\pi\) | ||||
0.944403 | − | 0.328791i | \(-0.106641\pi\) | |||||||
\(318\) | − 621.563i | − 0.109609i | ||||||||
\(319\) | −11936.2 | −2.09497 | ||||||||
\(320\) | 14267.1i | 2.49235i | ||||||||
\(321\) | −1091.17 | −0.189729 | ||||||||
\(322\) | −3441.73 | −0.595652 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 8288.41 | 1.42119 | ||||||||
\(325\) | −10141.7 | −1.73096 | ||||||||
\(326\) | − 940.945i | − 0.159859i | ||||||||
\(327\) | −384.990 | −0.0651070 | ||||||||
\(328\) | − 1663.33i | − 0.280005i | ||||||||
\(329\) | − 1251.74i | − 0.209759i | ||||||||
\(330\) | 2279.81i | 0.380301i | ||||||||
\(331\) | −3510.10 | −0.582877 | −0.291439 | − | 0.956590i | \(-0.594134\pi\) | ||||
−0.291439 | + | 0.956590i | \(0.594134\pi\) | |||||||
\(332\) | 7607.03 | 1.25750 | ||||||||
\(333\) | 224.504i | 0.0369452i | ||||||||
\(334\) | 4342.75i | 0.711451i | ||||||||
\(335\) | − 8884.92i | − 1.44906i | ||||||||
\(336\) | 68.9121 | 0.0111889 | ||||||||
\(337\) | 5718.46i | 0.924346i | 0.886790 | + | 0.462173i | \(0.152930\pi\) | ||||
−0.886790 | + | 0.462173i | \(0.847070\pi\) | |||||||
\(338\) | −5529.68 | −0.889867 | ||||||||
\(339\) | 9.11494 | 0.00146034 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −969.067 | −0.153894 | ||||||||
\(342\) | −10823.2 | −1.71126 | ||||||||
\(343\) | − 4132.55i | − 0.650544i | ||||||||
\(344\) | −1356.74 | −0.212647 | ||||||||
\(345\) | − 1121.03i | − 0.174940i | ||||||||
\(346\) | 16030.4i | 2.49075i | ||||||||
\(347\) | 677.787i | 0.104857i | 0.998625 | + | 0.0524287i | \(0.0166962\pi\) | ||||
−0.998625 | + | 0.0524287i | \(0.983304\pi\) | |||||||
\(348\) | 1361.63 | 0.209745 | ||||||||
\(349\) | −12161.8 | −1.86534 | −0.932670 | − | 0.360731i | \(-0.882527\pi\) | ||||
−0.932670 | + | 0.360731i | \(0.882527\pi\) | |||||||
\(350\) | − 4922.31i | − 0.751738i | ||||||||
\(351\) | − 1693.09i | − 0.257466i | ||||||||
\(352\) | 12285.3i | 1.86025i | ||||||||
\(353\) | 5681.58 | 0.856657 | 0.428328 | − | 0.903623i | \(-0.359103\pi\) | ||||
0.428328 | + | 0.903623i | \(0.359103\pi\) | |||||||
\(354\) | 1280.75i | 0.192291i | ||||||||
\(355\) | 12150.9 | 1.81662 | ||||||||
\(356\) | −12452.5 | −1.85388 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 14130.9 | 2.08614 | ||||||||
\(359\) | 5883.91 | 0.865017 | 0.432508 | − | 0.901630i | \(-0.357629\pi\) | ||||
0.432508 | + | 0.901630i | \(0.357629\pi\) | |||||||
\(360\) | 7671.78i | 1.12316i | ||||||||
\(361\) | 1456.00 | 0.212276 | ||||||||
\(362\) | 4862.74i | 0.706022i | ||||||||
\(363\) | 929.379i | 0.134380i | ||||||||
\(364\) | − 4414.89i | − 0.635723i | ||||||||
\(365\) | −3192.05 | −0.457752 | ||||||||
\(366\) | 634.377 | 0.0905996 | ||||||||
\(367\) | − 11526.1i | − 1.63939i | −0.572801 | − | 0.819695i | \(-0.694143\pi\) | ||||
0.572801 | − | 0.819695i | \(-0.305857\pi\) | |||||||
\(368\) | − 2419.37i | − 0.342714i | ||||||||
\(369\) | 2669.87i | 0.376661i | ||||||||
\(370\) | −644.583 | −0.0905683 | ||||||||
\(371\) | 1668.05i | 0.233425i | ||||||||
\(372\) | 110.548 | 0.0154076 | ||||||||
\(373\) | 3533.27 | 0.490471 | 0.245236 | − | 0.969464i | \(-0.421135\pi\) | ||||
0.245236 | + | 0.969464i | \(0.421135\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 444.031 | 0.0611458 | ||||||||
\(376\) | −3250.86 | −0.445878 | ||||||||
\(377\) | 12657.0i | 1.72909i | ||||||||
\(378\) | 821.746 | 0.111815 | ||||||||
\(379\) | 13568.8i | 1.83901i | 0.393082 | + | 0.919503i | \(0.371409\pi\) | ||||
−0.393082 | + | 0.919503i | \(0.628591\pi\) | |||||||
\(380\) | − 18484.4i | − 2.49534i | ||||||||
\(381\) | − 611.947i | − 0.0822861i | ||||||||
\(382\) | 10326.7 | 1.38314 | ||||||||
\(383\) | 12948.4 | 1.72750 | 0.863748 | − | 0.503923i | \(-0.168111\pi\) | ||||
0.863748 | + | 0.503923i | \(0.168111\pi\) | |||||||
\(384\) | − 1019.15i | − 0.135438i | ||||||||
\(385\) | − 6118.16i | − 0.809897i | ||||||||
\(386\) | − 11205.3i | − 1.47755i | ||||||||
\(387\) | 2177.76 | 0.286051 | ||||||||
\(388\) | 3011.52i | 0.394038i | ||||||||
\(389\) | −8901.44 | −1.16021 | −0.580104 | − | 0.814542i | \(-0.696988\pi\) | ||||
−0.580104 | + | 0.814542i | \(0.696988\pi\) | |||||||
\(390\) | 2417.49 | 0.313883 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | −5024.64 | −0.647405 | ||||||||
\(393\) | 332.093 | 0.0426257 | ||||||||
\(394\) | 9761.88i | 1.24821i | ||||||||
\(395\) | −601.237 | −0.0765862 | ||||||||
\(396\) | 17356.1i | 2.20246i | ||||||||
\(397\) | − 7180.09i | − 0.907703i | −0.891077 | − | 0.453852i | \(-0.850050\pi\) | ||||
0.891077 | − | 0.453852i | \(-0.149950\pi\) | |||||||
\(398\) | 15982.9i | 2.01293i | ||||||||
\(399\) | −313.960 | −0.0393926 | ||||||||
\(400\) | 3460.15 | 0.432519 | ||||||||
\(401\) | 5087.50i | 0.633560i | 0.948499 | + | 0.316780i | \(0.102602\pi\) | ||||
−0.948499 | + | 0.316780i | \(0.897398\pi\) | |||||||
\(402\) | 1229.16i | 0.152500i | ||||||||
\(403\) | 1027.59i | 0.127017i | ||||||||
\(404\) | −17207.3 | −2.11905 | ||||||||
\(405\) | − 12179.7i | − 1.49436i | ||||||||
\(406\) | −6143.09 | −0.750927 | ||||||||
\(407\) | −464.979 | −0.0566294 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −5287.62 | −0.639256 | −0.319628 | − | 0.947543i | \(-0.603558\pi\) | ||||
−0.319628 | + | 0.947543i | \(0.603558\pi\) | |||||||
\(410\) | −7665.57 | −0.923355 | ||||||||
\(411\) | 1211.78i | 0.145433i | ||||||||
\(412\) | −301.618 | −0.0360671 | ||||||||
\(413\) | − 3437.06i | − 0.409507i | ||||||||
\(414\) | − 14347.4i | − 1.70323i | ||||||||
\(415\) | − 11178.5i | − 1.32224i | ||||||||
\(416\) | 13027.2 | 1.53536 | ||||||||
\(417\) | −545.017 | −0.0640038 | ||||||||
\(418\) | − 22416.3i | − 2.62300i | ||||||||
\(419\) | 15292.9i | 1.78307i | 0.452956 | + | 0.891533i | \(0.350370\pi\) | ||||
−0.452956 | + | 0.891533i | \(0.649630\pi\) | |||||||
\(420\) | 697.938i | 0.0810854i | ||||||||
\(421\) | −1484.20 | −0.171818 | −0.0859089 | − | 0.996303i | \(-0.527379\pi\) | ||||
−0.0859089 | + | 0.996303i | \(0.527379\pi\) | |||||||
\(422\) | − 16340.2i | − 1.88490i | ||||||||
\(423\) | 5218.08 | 0.599792 | ||||||||
\(424\) | 4332.04 | 0.496185 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −1680.98 | −0.191182 | ||||||||
\(427\) | −1702.43 | −0.192943 | ||||||||
\(428\) | − 23850.6i | − 2.69360i | ||||||||
\(429\) | 1743.89 | 0.196261 | ||||||||
\(430\) | 6252.66i | 0.701232i | ||||||||
\(431\) | 2361.94i | 0.263969i | 0.991252 | + | 0.131984i | \(0.0421348\pi\) | ||||
−0.991252 | + | 0.131984i | \(0.957865\pi\) | |||||||
\(432\) | 577.649i | 0.0643337i | ||||||||
\(433\) | 12384.3 | 1.37449 | 0.687244 | − | 0.726426i | \(-0.258820\pi\) | ||||
0.687244 | + | 0.726426i | \(0.258820\pi\) | |||||||
\(434\) | −498.742 | −0.0551622 | ||||||||
\(435\) | − 2000.91i | − 0.220543i | ||||||||
\(436\) | − 8415.05i | − 0.924330i | ||||||||
\(437\) | 11022.5i | 1.20659i | ||||||||
\(438\) | 441.595 | 0.0481740 | ||||||||
\(439\) | − 7612.65i | − 0.827636i | −0.910360 | − | 0.413818i | \(-0.864195\pi\) | ||||
0.910360 | − | 0.413818i | \(-0.135805\pi\) | |||||||
\(440\) | −15889.3 | −1.72158 | ||||||||
\(441\) | 8065.26 | 0.870885 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 11492.3 | 1.23254 | 0.616272 | − | 0.787533i | \(-0.288642\pi\) | ||||
0.616272 | + | 0.787533i | \(0.288642\pi\) | |||||||
\(444\) | 53.0432 | 0.00566963 | ||||||||
\(445\) | 18298.9i | 1.94932i | ||||||||
\(446\) | 4322.22 | 0.458886 | ||||||||
\(447\) | 185.424i | 0.0196203i | ||||||||
\(448\) | 5296.78i | 0.558592i | ||||||||
\(449\) | − 13654.4i | − 1.43517i | −0.696472 | − | 0.717584i | \(-0.745248\pi\) | ||||
0.696472 | − | 0.717584i | \(-0.254752\pi\) | |||||||
\(450\) | 20519.5 | 2.14955 | ||||||||
\(451\) | −5529.67 | −0.577344 | ||||||||
\(452\) | 199.233i | 0.0207326i | ||||||||
\(453\) | 1373.40i | 0.142446i | ||||||||
\(454\) | − 20869.9i | − 2.15743i | ||||||||
\(455\) | −6487.64 | −0.668451 | ||||||||
\(456\) | 815.377i | 0.0837358i | ||||||||
\(457\) | −12274.9 | −1.25645 | −0.628223 | − | 0.778034i | \(-0.716217\pi\) | ||||
−0.628223 | + | 0.778034i | \(0.716217\pi\) | |||||||
\(458\) | −9357.20 | −0.954657 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 24503.3 | 2.48363 | ||||||||
\(461\) | 932.142 | 0.0941739 | 0.0470869 | − | 0.998891i | \(-0.485006\pi\) | ||||
0.0470869 | + | 0.998891i | \(0.485006\pi\) | |||||||
\(462\) | 846.400i | 0.0852340i | ||||||||
\(463\) | 5569.01 | 0.558993 | 0.279496 | − | 0.960147i | \(-0.409832\pi\) | ||||
0.279496 | + | 0.960147i | \(0.409832\pi\) | |||||||
\(464\) | − 4318.31i | − 0.432053i | ||||||||
\(465\) | − 162.449i | − 0.0162008i | ||||||||
\(466\) | 2850.08i | 0.283321i | ||||||||
\(467\) | −14662.2 | −1.45286 | −0.726428 | − | 0.687243i | \(-0.758821\pi\) | ||||
−0.726428 | + | 0.687243i | \(0.758821\pi\) | |||||||
\(468\) | 18404.2 | 1.81781 | ||||||||
\(469\) | − 3298.61i | − 0.324766i | ||||||||
\(470\) | 14981.8i | 1.47034i | ||||||||
\(471\) | − 1961.86i | − 0.191927i | ||||||||
\(472\) | −8926.29 | −0.870478 | ||||||||
\(473\) | 4510.45i | 0.438458i | ||||||||
\(474\) | 83.1765 | 0.00805996 | ||||||||
\(475\) | −15764.3 | −1.52277 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −6953.53 | −0.667464 | ||||||||
\(478\) | −19208.8 | −1.83805 | ||||||||
\(479\) | 12651.6i | 1.20682i | 0.797432 | + | 0.603409i | \(0.206191\pi\) | ||||
−0.797432 | + | 0.603409i | \(0.793809\pi\) | |||||||
\(480\) | −2059.43 | −0.195833 | ||||||||
\(481\) | 493.060i | 0.0467393i | ||||||||
\(482\) | 10941.7i | 1.03398i | ||||||||
\(483\) | − 416.192i | − 0.0392079i | ||||||||
\(484\) | −20314.2 | −1.90780 | ||||||||
\(485\) | 4425.40 | 0.414324 | ||||||||
\(486\) | 5147.58i | 0.480451i | ||||||||
\(487\) | − 13319.7i | − 1.23937i | −0.784852 | − | 0.619683i | \(-0.787261\pi\) | ||||
0.784852 | − | 0.619683i | \(-0.212739\pi\) | |||||||
\(488\) | 4421.34i | 0.410133i | ||||||||
\(489\) | 113.784 | 0.0105225 | ||||||||
\(490\) | 23156.5i | 2.13491i | ||||||||
\(491\) | 19380.9 | 1.78136 | 0.890679 | − | 0.454633i | \(-0.150229\pi\) | ||||
0.890679 | + | 0.454633i | \(0.150229\pi\) | |||||||
\(492\) | 630.805 | 0.0578026 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | −23770.0 | −2.16491 | ||||||||
\(495\) | 25504.6 | 2.31585 | ||||||||
\(496\) | − 350.593i | − 0.0317381i | ||||||||
\(497\) | 4511.12 | 0.407146 | ||||||||
\(498\) | 1546.45i | 0.139153i | ||||||||
\(499\) | − 20101.1i | − 1.80330i | −0.432466 | − | 0.901650i | \(-0.642356\pi\) | ||||
0.432466 | − | 0.901650i | \(-0.357644\pi\) | |||||||
\(500\) | 9705.56i | 0.868091i | ||||||||
\(501\) | −525.149 | −0.0468302 | ||||||||
\(502\) | −11695.2 | −1.03981 | ||||||||
\(503\) | 6166.84i | 0.546652i | 0.961921 | + | 0.273326i | \(0.0881238\pi\) | ||||
−0.961921 | + | 0.273326i | \(0.911876\pi\) | |||||||
\(504\) | 2848.22i | 0.251726i | ||||||||
\(505\) | 25286.0i | 2.22814i | ||||||||
\(506\) | 29715.5 | 2.61070 | ||||||||
\(507\) | − 668.679i | − 0.0585741i | ||||||||
\(508\) | 13375.8 | 1.16822 | ||||||||
\(509\) | 14496.0 | 1.26233 | 0.631165 | − | 0.775649i | \(-0.282577\pi\) | ||||
0.631165 | + | 0.775649i | \(0.282577\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1185.08 | −0.102592 | ||||||||
\(512\) | −7109.16 | −0.613639 | ||||||||
\(513\) | − 2631.74i | − 0.226499i | ||||||||
\(514\) | −15000.4 | −1.28724 | ||||||||
\(515\) | 443.225i | 0.0379239i | ||||||||
\(516\) | − 514.535i | − 0.0438976i | ||||||||
\(517\) | 10807.4i | 0.919357i | ||||||||
\(518\) | −239.307 | −0.0202984 | ||||||||
\(519\) | −1938.48 | −0.163950 | ||||||||
\(520\) | 16848.9i | 1.42091i | ||||||||
\(521\) | 2642.20i | 0.222182i | 0.993810 | + | 0.111091i | \(0.0354346\pi\) | ||||
−0.993810 | + | 0.111091i | \(0.964565\pi\) | |||||||
\(522\) | − 25608.5i | − 2.14723i | ||||||||
\(523\) | 12574.5 | 1.05133 | 0.525665 | − | 0.850692i | \(-0.323817\pi\) | ||||
0.525665 | + | 0.850692i | \(0.323817\pi\) | |||||||
\(524\) | 7258.84i | 0.605160i | ||||||||
\(525\) | 595.232 | 0.0494820 | ||||||||
\(526\) | −7125.63 | −0.590670 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | −594.980 | −0.0490401 | ||||||||
\(529\) | −2444.72 | −0.200930 | ||||||||
\(530\) | − 19964.5i | − 1.63623i | ||||||||
\(531\) | 14328.0 | 1.17096 | ||||||||
\(532\) | − 6862.49i | − 0.559261i | ||||||||
\(533\) | 5863.61i | 0.476513i | ||||||||
\(534\) | − 2531.50i | − 0.205148i | ||||||||
\(535\) | −35048.2 | −2.83227 | ||||||||
\(536\) | −8566.72 | −0.690347 | ||||||||
\(537\) | 1708.78i | 0.137317i | ||||||||
\(538\) | − 29076.7i | − 2.33008i | ||||||||
\(539\) | 16704.3i | 1.33489i | ||||||||
\(540\) | −5850.39 | −0.466224 | ||||||||
\(541\) | 18289.3i | 1.45345i | 0.686927 | + | 0.726726i | \(0.258959\pi\) | ||||
−0.686927 | + | 0.726726i | \(0.741041\pi\) | |||||||
\(542\) | 1581.92 | 0.125368 | ||||||||
\(543\) | −588.028 | −0.0464728 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −12365.8 | −0.971916 | ||||||||
\(546\) | 897.515 | 0.0703481 | ||||||||
\(547\) | − 9989.86i | − 0.780869i | −0.920631 | − | 0.390435i | \(-0.872325\pi\) | ||||
0.920631 | − | 0.390435i | \(-0.127675\pi\) | |||||||
\(548\) | −26487.0 | −2.06472 | ||||||||
\(549\) | − 7096.88i | − 0.551708i | ||||||||
\(550\) | 42498.6i | 3.29482i | ||||||||
\(551\) | 19674.0i | 1.52112i | ||||||||
\(552\) | −1080.88 | −0.0833431 | ||||||||
\(553\) | −223.215 | −0.0171647 | ||||||||
\(554\) | 14112.3i | 1.08226i | ||||||||
\(555\) | − 77.9464i | − 0.00596152i | ||||||||
\(556\) | − 11912.9i | − 0.908668i | ||||||||
\(557\) | −4181.95 | −0.318124 | −0.159062 | − | 0.987269i | \(-0.550847\pi\) | ||||
−0.159062 | + | 0.987269i | \(0.550847\pi\) | |||||||
\(558\) | − 2079.09i | − 0.157733i | ||||||||
\(559\) | 4782.84 | 0.361883 | ||||||||
\(560\) | 2213.45 | 0.167027 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 7408.70 | 0.556080 | ||||||||
\(563\) | −10429.1 | −0.780697 | −0.390348 | − | 0.920667i | \(-0.627645\pi\) | ||||
−0.390348 | + | 0.920667i | \(0.627645\pi\) | |||||||
\(564\) | − 1232.87i | − 0.0920443i | ||||||||
\(565\) | 292.771 | 0.0217999 | ||||||||
\(566\) | − 34660.8i | − 2.57403i | ||||||||
\(567\) | − 4521.84i | − 0.334920i | ||||||||
\(568\) | − 11715.7i | − 0.865458i | ||||||||
\(569\) | −8440.98 | −0.621906 | −0.310953 | − | 0.950425i | \(-0.600648\pi\) | ||||
−0.310953 | + | 0.950425i | \(0.600648\pi\) | |||||||
\(570\) | 3757.73 | 0.276130 | ||||||||
\(571\) | − 27092.6i | − 1.98562i | −0.119694 | − | 0.992811i | \(-0.538191\pi\) | ||||
0.119694 | − | 0.992811i | \(-0.461809\pi\) | |||||||
\(572\) | 38117.7i | 2.78633i | ||||||||
\(573\) | 1248.76i | 0.0910431i | ||||||||
\(574\) | −2845.91 | −0.206944 | ||||||||
\(575\) | − 20897.5i | − 1.51562i | ||||||||
\(576\) | −22080.5 | −1.59726 | ||||||||
\(577\) | −10864.3 | −0.783857 | −0.391929 | − | 0.919996i | \(-0.628192\pi\) | ||||
−0.391929 | + | 0.919996i | \(0.628192\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 1355.00 | 0.0972572 | ||||||||
\(580\) | 43735.5 | 3.13107 | ||||||||
\(581\) | − 4150.11i | − 0.296343i | ||||||||
\(582\) | −612.220 | −0.0436037 | ||||||||
\(583\) | − 14401.7i | − 1.02308i | ||||||||
\(584\) | 3077.73i | 0.218078i | ||||||||
\(585\) | − 27044.8i | − 1.91140i | ||||||||
\(586\) | 10678.5 | 0.752774 | ||||||||
\(587\) | −25173.8 | −1.77008 | −0.885038 | − | 0.465518i | \(-0.845868\pi\) | ||||
−0.885038 | + | 0.465518i | \(0.845868\pi\) | |||||||
\(588\) | − 1905.56i | − 0.133646i | ||||||||
\(589\) | 1597.28i | 0.111740i | ||||||||
\(590\) | 41137.5i | 2.87052i | ||||||||
\(591\) | −1180.46 | −0.0821617 | ||||||||
\(592\) | − 168.222i | − 0.0116788i | ||||||||
\(593\) | −777.712 | −0.0538563 | −0.0269282 | − | 0.999637i | \(-0.508573\pi\) | ||||
−0.0269282 | + | 0.999637i | \(0.508573\pi\) | |||||||
\(594\) | −7094.86 | −0.490077 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −4052.97 | −0.278551 | ||||||||
\(597\) | −1932.73 | −0.132498 | ||||||||
\(598\) | − 31510.0i | − 2.15475i | ||||||||
\(599\) | 6690.40 | 0.456365 | 0.228182 | − | 0.973618i | \(-0.426722\pi\) | ||||
0.228182 | + | 0.973618i | \(0.426722\pi\) | |||||||
\(600\) | − 1545.86i | − 0.105182i | ||||||||
\(601\) | 1574.80i | 0.106884i | 0.998571 | + | 0.0534421i | \(0.0170193\pi\) | ||||
−0.998571 | + | 0.0534421i | \(0.982981\pi\) | |||||||
\(602\) | 2321.36i | 0.157162i | ||||||||
\(603\) | 13750.8 | 0.928649 | ||||||||
\(604\) | −30019.6 | −2.02232 | ||||||||
\(605\) | 29851.6i | 2.00601i | ||||||||
\(606\) | − 3498.12i | − 0.234491i | ||||||||
\(607\) | − 24567.4i | − 1.64276i | −0.570378 | − | 0.821382i | \(-0.693203\pi\) | ||||
0.570378 | − | 0.821382i | \(-0.306797\pi\) | |||||||
\(608\) | 20249.4 | 1.35069 | ||||||||
\(609\) | − 742.856i | − 0.0494286i | ||||||||
\(610\) | 20376.1 | 1.35247 | ||||||||
\(611\) | 11460.0 | 0.758795 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −27992.8 | −1.84440 | −0.922201 | − | 0.386710i | \(-0.873611\pi\) | ||||
−0.922201 | + | 0.386710i | \(0.873611\pi\) | |||||||
\(614\) | 17897.7 | 1.17637 | ||||||||
\(615\) | − 926.962i | − 0.0607784i | ||||||||
\(616\) | −5899.05 | −0.385843 | ||||||||
\(617\) | − 3787.41i | − 0.247124i | −0.992337 | − | 0.123562i | \(-0.960568\pi\) | ||||
0.992337 | − | 0.123562i | \(-0.0394317\pi\) | |||||||
\(618\) | − 61.3167i | − 0.00399113i | ||||||||
\(619\) | − 4066.72i | − 0.264063i | −0.991246 | − | 0.132032i | \(-0.957850\pi\) | ||||
0.991246 | − | 0.132032i | \(-0.0421500\pi\) | |||||||
\(620\) | 3550.78 | 0.230004 | ||||||||
\(621\) | 3488.69 | 0.225437 | ||||||||
\(622\) | 17527.3i | 1.12987i | ||||||||
\(623\) | 6793.62i | 0.436887i | ||||||||
\(624\) | 630.911i | 0.0404754i | ||||||||
\(625\) | −7347.68 | −0.470251 | ||||||||
\(626\) | − 29062.6i | − 1.85555i | ||||||||
\(627\) | 2710.70 | 0.172655 | ||||||||
\(628\) | 42882.0 | 2.72481 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 13126.2 | 0.830099 | ||||||||
\(631\) | 11686.8 | 0.737309 | 0.368655 | − | 0.929566i | \(-0.379818\pi\) | ||||
0.368655 | + | 0.929566i | \(0.379818\pi\) | |||||||
\(632\) | 579.705i | 0.0364864i | ||||||||
\(633\) | 1975.94 | 0.124070 | ||||||||
\(634\) | 16491.8i | 1.03308i | ||||||||
\(635\) | − 19655.7i | − 1.22836i | ||||||||
\(636\) | 1642.90i | 0.102429i | ||||||||
\(637\) | 17713.1 | 1.10175 | ||||||||
\(638\) | 53038.8 | 3.29126 | ||||||||
\(639\) | 18805.4i | 1.16421i | ||||||||
\(640\) | − 32734.9i | − 2.02181i | ||||||||
\(641\) | − 23652.6i | − 1.45744i | −0.684810 | − | 0.728721i | \(-0.740115\pi\) | ||||
0.684810 | − | 0.728721i | \(-0.259885\pi\) | |||||||
\(642\) | 4848.64 | 0.298069 | ||||||||
\(643\) | 2712.61i | 0.166368i | 0.996534 | + | 0.0831841i | \(0.0265089\pi\) | ||||
−0.996534 | + | 0.0831841i | \(0.973491\pi\) | |||||||
\(644\) | 9097.06 | 0.556637 | ||||||||
\(645\) | −756.105 | −0.0461575 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 3672.97 | 0.223183 | 0.111592 | − | 0.993754i | \(-0.464405\pi\) | ||||
0.111592 | + | 0.993754i | \(0.464405\pi\) | |||||||
\(648\) | −11743.5 | −0.711929 | ||||||||
\(649\) | 29675.2i | 1.79484i | ||||||||
\(650\) | 45065.2 | 2.71939 | ||||||||
\(651\) | − 60.3106i | − 0.00363097i | ||||||||
\(652\) | 2487.08i | 0.149389i | ||||||||
\(653\) | − 26090.8i | − 1.56357i | −0.623548 | − | 0.781785i | \(-0.714309\pi\) | ||||
0.623548 | − | 0.781785i | \(-0.285691\pi\) | |||||||
\(654\) | 1710.72 | 0.102285 | ||||||||
\(655\) | 10666.8 | 0.636315 | ||||||||
\(656\) | − 2000.54i | − 0.119067i | ||||||||
\(657\) | − 4940.19i | − 0.293357i | ||||||||
\(658\) | 5562.14i | 0.329536i | ||||||||
\(659\) | −14303.7 | −0.845515 | −0.422758 | − | 0.906243i | \(-0.638938\pi\) | ||||
−0.422758 | + | 0.906243i | \(0.638938\pi\) | |||||||
\(660\) | − 6025.92i | − 0.355392i | ||||||||
\(661\) | 9780.49 | 0.575517 | 0.287759 | − | 0.957703i | \(-0.407090\pi\) | ||||
0.287759 | + | 0.957703i | \(0.407090\pi\) | |||||||
\(662\) | 15597.2 | 0.915716 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −10778.1 | −0.629928 | ||||||||
\(665\) | −10084.4 | −0.588052 | ||||||||
\(666\) | − 997.593i | − 0.0580419i | ||||||||
\(667\) | −26080.2 | −1.51399 | ||||||||
\(668\) | − 11478.6i | − 0.664852i | ||||||||
\(669\) | 522.667i | 0.0302055i | ||||||||
\(670\) | 39480.4i | 2.27651i | ||||||||
\(671\) | 14698.6 | 0.845654 | ||||||||
\(672\) | −764.582 | −0.0438905 | ||||||||
\(673\) | − 21380.1i | − 1.22458i | −0.790634 | − | 0.612289i | \(-0.790249\pi\) | ||||
0.790634 | − | 0.612289i | \(-0.209751\pi\) | |||||||
\(674\) | − 25410.2i | − 1.45217i | ||||||||
\(675\) | 4989.47i | 0.284511i | ||||||||
\(676\) | 14615.9 | 0.831581 | ||||||||
\(677\) | 7244.51i | 0.411269i | 0.978629 | + | 0.205635i | \(0.0659258\pi\) | ||||
−0.978629 | + | 0.205635i | \(0.934074\pi\) | |||||||
\(678\) | −40.5026 | −0.00229424 | ||||||||
\(679\) | 1642.97 | 0.0928593 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 2523.70 | 0.142009 | ||||||||
\(682\) | 4306.08 | 0.241772 | ||||||||
\(683\) | 4140.24i | 0.231950i | 0.993252 | + | 0.115975i | \(0.0369992\pi\) | ||||
−0.993252 | + | 0.115975i | \(0.963001\pi\) | |||||||
\(684\) | 28607.4 | 1.59917 | ||||||||
\(685\) | 38922.4i | 2.17102i | ||||||||
\(686\) | 18363.1i | 1.02202i | ||||||||
\(687\) | − 1131.52i | − 0.0628388i | ||||||||
\(688\) | −1631.81 | −0.0904244 | ||||||||
\(689\) | −15271.4 | −0.844406 | ||||||||
\(690\) | 4981.33i | 0.274835i | ||||||||
\(691\) | 30750.3i | 1.69290i | 0.532466 | + | 0.846451i | \(0.321265\pi\) | ||||
−0.532466 | + | 0.846451i | \(0.678735\pi\) | |||||||
\(692\) | − 42371.0i | − 2.32761i | ||||||||
\(693\) | 9468.81 | 0.519034 | ||||||||
\(694\) | − 3011.77i | − 0.164734i | ||||||||
\(695\) | −17505.9 | −0.955448 | ||||||||
\(696\) | −1929.25 | −0.105069 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 54041.2 | 2.93050 | ||||||||
\(699\) | −344.647 | −0.0186492 | ||||||||
\(700\) | 13010.5i | 0.702500i | ||||||||
\(701\) | −20466.3 | −1.10271 | −0.551356 | − | 0.834270i | \(-0.685890\pi\) | ||||
−0.551356 | + | 0.834270i | \(0.685890\pi\) | |||||||
\(702\) | 7523.32i | 0.404487i | ||||||||
\(703\) | 766.410i | 0.0411176i | ||||||||
\(704\) | − 45731.8i | − 2.44827i | ||||||||
\(705\) | −1811.68 | −0.0967830 | ||||||||
\(706\) | −25246.3 | −1.34583 | ||||||||
\(707\) | 9387.65i | 0.499376i | ||||||||
\(708\) | − 3385.24i | − 0.179696i | ||||||||
\(709\) | 24814.8i | 1.31444i | 0.753697 | + | 0.657222i | \(0.228269\pi\) | ||||
−0.753697 | + | 0.657222i | \(0.771731\pi\) | |||||||
\(710\) | −53992.8 | −2.85396 | ||||||||
\(711\) | − 930.509i | − 0.0490813i | ||||||||
\(712\) | 17643.5 | 0.928678 | ||||||||
\(713\) | −2117.39 | −0.111216 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 56013.6 | 2.92978 | ||||||||
\(716\) | −37350.3 | −1.94950 | ||||||||
\(717\) | − 2322.83i | − 0.120987i | ||||||||
\(718\) | −26145.4 | −1.35897 | ||||||||
\(719\) | − 24507.8i | − 1.27119i | −0.772021 | − | 0.635597i | \(-0.780754\pi\) | ||||
0.772021 | − | 0.635597i | \(-0.219246\pi\) | |||||||
\(720\) | 9227.14i | 0.477604i | ||||||||
\(721\) | 164.551i | 0.00849960i | ||||||||
\(722\) | −6469.79 | −0.333491 | ||||||||
\(723\) | −1323.12 | −0.0680601 | ||||||||
\(724\) | − 12853.0i | − 0.659778i | ||||||||
\(725\) | − 37299.6i | − 1.91072i | ||||||||
\(726\) | − 4129.73i | − 0.211114i | ||||||||
\(727\) | −7468.67 | −0.381015 | −0.190507 | − | 0.981686i | \(-0.561013\pi\) | ||||
−0.190507 | + | 0.981686i | \(0.561013\pi\) | |||||||
\(728\) | 6255.30i | 0.318457i | ||||||||
\(729\) | 18431.3 | 0.936408 | ||||||||
\(730\) | 14184.0 | 0.719140 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | −1676.77 | −0.0846654 | ||||||||
\(733\) | −2801.95 | −0.141190 | −0.0705952 | − | 0.997505i | \(-0.522490\pi\) | ||||
−0.0705952 | + | 0.997505i | \(0.522490\pi\) | |||||||
\(734\) | 51216.5i | 2.57552i | ||||||||
\(735\) | −2800.21 | −0.140527 | ||||||||
\(736\) | 26843.0i | 1.34436i | ||||||||
\(737\) | 28479.8i | 1.42343i | ||||||||
\(738\) | − 11863.7i | − 0.591745i | ||||||||
\(739\) | −5867.20 | −0.292055 | −0.146027 | − | 0.989281i | \(-0.546649\pi\) | ||||
−0.146027 | + | 0.989281i | \(0.546649\pi\) | |||||||
\(740\) | 1703.74 | 0.0846361 | ||||||||
\(741\) | − 2874.40i | − 0.142502i | ||||||||
\(742\) | − 7412.02i | − 0.366717i | ||||||||
\(743\) | − 23585.7i | − 1.16457i | −0.812984 | − | 0.582286i | \(-0.802159\pi\) | ||||
0.812984 | − | 0.582286i | \(-0.197841\pi\) | |||||||
\(744\) | −156.631 | −0.00771824 | ||||||||
\(745\) | 5955.80i | 0.292891i | ||||||||
\(746\) | −15700.2 | −0.770543 | ||||||||
\(747\) | 17300.4 | 0.847375 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −13011.9 | −0.634775 | ||||||||
\(750\) | −1973.07 | −0.0960616 | ||||||||
\(751\) | 15142.8i | 0.735775i | 0.929870 | + | 0.367887i | \(0.119919\pi\) | ||||
−0.929870 | + | 0.367887i | \(0.880081\pi\) | |||||||
\(752\) | −3909.93 | −0.189602 | ||||||||
\(753\) | − 1414.25i | − 0.0684437i | ||||||||
\(754\) | − 56241.8i | − 2.71645i | ||||||||
\(755\) | 44113.5i | 2.12643i | ||||||||
\(756\) | −2172.01 | −0.104491 | ||||||||
\(757\) | 13149.7 | 0.631353 | 0.315676 | − | 0.948867i | \(-0.397769\pi\) | ||||
0.315676 | + | 0.948867i | \(0.397769\pi\) | |||||||
\(758\) | − 60293.5i | − 2.88913i | ||||||||
\(759\) | 3593.36i | 0.171845i | ||||||||
\(760\) | 26189.8i | 1.25001i | ||||||||
\(761\) | −12831.3 | −0.611213 | −0.305607 | − | 0.952158i | \(-0.598859\pi\) | ||||
−0.305607 | + | 0.952158i | \(0.598859\pi\) | |||||||
\(762\) | 2719.21i | 0.129274i | ||||||||
\(763\) | −4590.93 | −0.217828 | ||||||||
\(764\) | −27295.2 | −1.29255 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −57536.6 | −2.71394 | ||||||||
\(767\) | 31467.3 | 1.48138 | ||||||||
\(768\) | 975.162i | 0.0458179i | ||||||||
\(769\) | −11365.1 | −0.532949 | −0.266474 | − | 0.963842i | \(-0.585859\pi\) | ||||
−0.266474 | + | 0.963842i | \(0.585859\pi\) | |||||||
\(770\) | 27186.3i | 1.27237i | ||||||||
\(771\) | − 1813.93i | − 0.0847304i | ||||||||
\(772\) | 29617.4i | 1.38077i | ||||||||
\(773\) | 16551.8 | 0.770150 | 0.385075 | − | 0.922885i | \(-0.374176\pi\) | ||||
0.385075 | + | 0.922885i | \(0.374176\pi\) | |||||||
\(774\) | −9676.96 | −0.449394 | ||||||||
\(775\) | − 3028.26i | − 0.140359i | ||||||||
\(776\) | − 4266.91i | − 0.197388i | ||||||||
\(777\) | − 28.9383i | − 0.00133611i | ||||||||
\(778\) | 39553.9 | 1.82272 | ||||||||
\(779\) | 9114.37i | 0.419199i | ||||||||
\(780\) | −6389.83 | −0.293324 | ||||||||
\(781\) | −38948.5 | −1.78449 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 6226.91 | 0.284204 | ||||||||
\(784\) | −6043.33 | −0.275298 | ||||||||
\(785\) | − 63014.7i | − 2.86509i | ||||||||
\(786\) | −1475.67 | −0.0669661 | ||||||||
\(787\) | 32051.7i | 1.45174i | 0.687832 | + | 0.725870i | \(0.258562\pi\) | ||||
−0.687832 | + | 0.725870i | \(0.741438\pi\) | |||||||
\(788\) | − 25802.3i | − 1.16646i | ||||||||
\(789\) | − 861.670i | − 0.0388799i | ||||||||
\(790\) | 2671.62 | 0.120319 | ||||||||
\(791\) | 108.694 | 0.00488585 | ||||||||
\(792\) | − 24591.2i | − 1.10330i | ||||||||
\(793\) | − 15586.3i | − 0.697964i | ||||||||
\(794\) | 31905.0i | 1.42603i | ||||||||
\(795\) | 2414.22 | 0.107703 | ||||||||
\(796\) | − 42245.4i | − 1.88109i | ||||||||
\(797\) | −27679.0 | −1.23016 | −0.615082 | − | 0.788463i | \(-0.710877\pi\) | ||||
−0.615082 | + | 0.788463i | \(0.710877\pi\) | |||||||
\(798\) | 1395.09 | 0.0618869 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | −38390.5 | −1.69664 | ||||||||
\(801\) | −28320.3 | −1.24925 | ||||||||
\(802\) | − 22606.5i | − 0.995340i | ||||||||
\(803\) | 10231.8 | 0.449655 | ||||||||
\(804\) | − 3248.87i | − 0.142511i | ||||||||
\(805\) | − 13368.0i | − 0.585294i | ||||||||
\(806\) | − 4566.13i | − 0.199547i | ||||||||
\(807\) | 3516.11 | 0.153374 | ||||||||
\(808\) | 24380.4 | 1.06151 | ||||||||
\(809\) | 7438.60i | 0.323272i | 0.986850 | + | 0.161636i | \(0.0516771\pi\) | ||||
−0.986850 | + | 0.161636i | \(0.948323\pi\) | |||||||
\(810\) | 54121.1i | 2.34768i | ||||||||
\(811\) | − 10261.1i | − 0.444288i | −0.975014 | − | 0.222144i | \(-0.928694\pi\) | ||||
0.975014 | − | 0.222144i | \(-0.0713055\pi\) | |||||||
\(812\) | 16237.2 | 0.701742 | ||||||||
\(813\) | 191.294i | 0.00825213i | ||||||||
\(814\) | 2066.15 | 0.0889663 | ||||||||
\(815\) | 3654.73 | 0.157079 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 7434.42 | 0.318357 | ||||||||
\(818\) | 23495.7 | 1.00429 | ||||||||
\(819\) | − 10040.6i | − 0.428386i | ||||||||
\(820\) | 20261.4 | 0.862876 | ||||||||
\(821\) | 21739.5i | 0.924134i | 0.886845 | + | 0.462067i | \(0.152892\pi\) | ||||
−0.886845 | + | 0.462067i | \(0.847108\pi\) | |||||||
\(822\) | − 5384.60i | − 0.228479i | ||||||||
\(823\) | 23728.9i | 1.00503i | 0.864569 | + | 0.502514i | \(0.167592\pi\) | ||||
−0.864569 | + | 0.502514i | \(0.832408\pi\) | |||||||
\(824\) | 427.352 | 0.0180674 | ||||||||
\(825\) | −5139.16 | −0.216876 | ||||||||
\(826\) | 15272.7i | 0.643347i | ||||||||
\(827\) | 21101.5i | 0.887270i | 0.896207 | + | 0.443635i | \(0.146311\pi\) | ||||
−0.896207 | + | 0.443635i | \(0.853689\pi\) | |||||||
\(828\) | 37922.6i | 1.59167i | ||||||||
\(829\) | −1621.77 | −0.0679448 | −0.0339724 | − | 0.999423i | \(-0.510816\pi\) | ||||
−0.0339724 | + | 0.999423i | \(0.510816\pi\) | |||||||
\(830\) | 49671.9i | 2.07727i | ||||||||
\(831\) | −1706.53 | −0.0712381 | ||||||||
\(832\) | −48493.6 | −2.02069 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 2421.80 | 0.100552 | ||||||||
\(835\) | −16867.7 | −0.699080 | ||||||||
\(836\) | 59250.0i | 2.45120i | ||||||||
\(837\) | 505.547 | 0.0208773 | ||||||||
\(838\) | − 67954.3i | − 2.80124i | ||||||||
\(839\) | − 1287.05i | − 0.0529607i | −0.999649 | − | 0.0264803i | \(-0.991570\pi\) | ||||
0.999649 | − | 0.0264803i | \(-0.00842994\pi\) | |||||||
\(840\) | − 988.883i | − 0.0406187i | ||||||||
\(841\) | −22161.3 | −0.908658 | ||||||||
\(842\) | 6595.08 | 0.269930 | ||||||||
\(843\) | 895.900i | 0.0366031i | ||||||||
\(844\) | 43189.8i | 1.76144i | ||||||||
\(845\) | − 21477.9i | − 0.874392i | ||||||||
\(846\) | −23186.7 | −0.942289 | ||||||||
\(847\) | 11082.7i | 0.449592i | ||||||||
\(848\) | 5210.30 | 0.210994 | ||||||||
\(849\) | 4191.37 | 0.169432 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1015.97 | −0.0409248 | ||||||||
\(852\) | 4443.10 | 0.178660 | ||||||||
\(853\) | − 18173.4i | − 0.729479i | −0.931110 | − | 0.364740i | \(-0.881158\pi\) | ||||
0.931110 | − | 0.364740i | \(-0.118842\pi\) | |||||||
\(854\) | 7564.83 | 0.303118 | ||||||||
\(855\) | − 42038.4i | − 1.68150i | ||||||||
\(856\) | 33793.0i | 1.34932i | ||||||||
\(857\) | − 39590.2i | − 1.57803i | −0.614371 | − | 0.789017i | \(-0.710590\pi\) | ||||
0.614371 | − | 0.789017i | \(-0.289410\pi\) | |||||||
\(858\) | −7749.04 | −0.308331 | ||||||||
\(859\) | 17747.9 | 0.704948 | 0.352474 | − | 0.935822i | \(-0.385341\pi\) | ||||
0.352474 | + | 0.935822i | \(0.385341\pi\) | |||||||
\(860\) | − 16526.8i | − 0.655302i | ||||||||
\(861\) | − 344.143i | − 0.0136218i | ||||||||
\(862\) | − 10495.3i | − 0.414702i | ||||||||
\(863\) | −8155.37 | −0.321683 | −0.160841 | − | 0.986980i | \(-0.551421\pi\) | ||||
−0.160841 | + | 0.986980i | \(0.551421\pi\) | |||||||
\(864\) | − 6409.03i | − 0.252361i | ||||||||
\(865\) | −62263.8 | −2.44744 | ||||||||
\(866\) | −55030.3 | −2.15936 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 1318.26 | 0.0515491 | ||||||||
\(869\) | 1927.21 | 0.0752315 | ||||||||
\(870\) | 8891.11i | 0.346479i | ||||||||
\(871\) | 30199.7 | 1.17483 | ||||||||
\(872\) | 11923.0i | 0.463031i | ||||||||
\(873\) | 6849.00i | 0.265525i | ||||||||
\(874\) | − 48979.1i | − 1.89559i | ||||||||
\(875\) | 5294.98 | 0.204575 | ||||||||
\(876\) | −1167.21 | −0.0450187 | ||||||||
\(877\) | 37979.1i | 1.46233i | 0.682202 | + | 0.731164i | \(0.261023\pi\) | ||||
−0.682202 | + | 0.731164i | \(0.738977\pi\) | |||||||
\(878\) | 33827.1i | 1.30024i | ||||||||
\(879\) | 1291.30i | 0.0495502i | ||||||||
\(880\) | −19110.7 | −0.732069 | ||||||||
\(881\) | − 18289.7i | − 0.699427i | −0.936857 | − | 0.349714i | \(-0.886279\pi\) | ||||
0.936857 | − | 0.349714i | \(-0.113721\pi\) | |||||||
\(882\) | −35838.3 | −1.36818 | ||||||||
\(883\) | 18414.9 | 0.701825 | 0.350912 | − | 0.936408i | \(-0.385871\pi\) | ||||
0.350912 | + | 0.936408i | \(0.385871\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −4974.57 | −0.188947 | ||||||||
\(886\) | −51066.6 | −1.93636 | ||||||||
\(887\) | − 50689.5i | − 1.91881i | −0.282028 | − | 0.959406i | \(-0.591007\pi\) | ||||
0.282028 | − | 0.959406i | \(-0.408993\pi\) | |||||||
\(888\) | −75.1549 | −0.00284013 | ||||||||
\(889\) | − 7297.35i | − 0.275304i | ||||||||
\(890\) | − 81311.6i | − 3.06244i | ||||||||
\(891\) | 39041.0i | 1.46793i | ||||||||
\(892\) | −11424.4 | −0.428830 | ||||||||
\(893\) | 17813.4 | 0.667529 | ||||||||
\(894\) | − 823.939i | − 0.0308240i | ||||||||
\(895\) | 54885.8i | 2.04987i | ||||||||
\(896\) | − 12153.1i | − 0.453133i | ||||||||
\(897\) | 3810.36 | 0.141833 | ||||||||
\(898\) | 60673.8i | 2.25469i | ||||||||
\(899\) | −3779.30 | −0.140208 | ||||||||
\(900\) | −54236.4 | −2.00875 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 24571.3 | 0.907023 | ||||||||
\(903\) | −280.711 | −0.0103449 | ||||||||
\(904\) | − 282.286i | − 0.0103857i | ||||||||
\(905\) | −18887.4 | −0.693744 | ||||||||
\(906\) | − 6102.76i | − 0.223786i | ||||||||
\(907\) | 44568.0i | 1.63160i | 0.578338 | + | 0.815798i | \(0.303702\pi\) | ||||
−0.578338 | + | 0.815798i | \(0.696298\pi\) | |||||||
\(908\) | 55162.5i | 2.01612i | ||||||||
\(909\) | −39134.0 | −1.42794 | ||||||||
\(910\) | 28828.1 | 1.05016 | ||||||||
\(911\) | − 7809.03i | − 0.284001i | −0.989867 | − | 0.142000i | \(-0.954647\pi\) | ||||
0.989867 | − | 0.142000i | \(-0.0453535\pi\) | |||||||
\(912\) | 980.685i | 0.0356072i | ||||||||
\(913\) | 35831.5i | 1.29885i | ||||||||
\(914\) | 54543.9 | 1.97391 | ||||||||
\(915\) | 2463.99i | 0.0890241i | ||||||||
\(916\) | 24732.6 | 0.892128 | ||||||||
\(917\) | 3960.15 | 0.142612 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −36710.8 | −1.31771 | −0.658856 | − | 0.752269i | \(-0.728959\pi\) | ||||
−0.658856 | + | 0.752269i | \(0.728959\pi\) | |||||||
\(920\) | −34717.8 | −1.24414 | ||||||||
\(921\) | 2164.28i | 0.0774328i | ||||||||
\(922\) | −4142.00 | −0.147950 | ||||||||
\(923\) | 41300.6i | 1.47284i | ||||||||
\(924\) | − 2237.18i | − 0.0796512i | ||||||||
\(925\) | − 1453.02i | − 0.0516488i | ||||||||
\(926\) | −24746.1 | −0.878193 | ||||||||
\(927\) | −685.960 | −0.0243041 | ||||||||
\(928\) | 47911.7i | 1.69481i | ||||||||
\(929\) | − 15068.9i | − 0.532180i | −0.963948 | − | 0.266090i | \(-0.914268\pi\) | ||||
0.963948 | − | 0.266090i | \(-0.0857319\pi\) | |||||||
\(930\) | 721.847i | 0.0254519i | ||||||||
\(931\) | 27533.1 | 0.969238 | ||||||||
\(932\) | − 7533.25i | − 0.264764i | ||||||||
\(933\) | −2119.49 | −0.0743719 | ||||||||
\(934\) | 65151.8 | 2.28248 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −26076.3 | −0.910609 | ||||||||
\(937\) | −38416.7 | −1.33940 | −0.669700 | − | 0.742632i | \(-0.733577\pi\) | ||||
−0.669700 | + | 0.742632i | \(0.733577\pi\) | |||||||
\(938\) | 14657.5i | 0.510217i | ||||||||
\(939\) | 3514.40 | 0.122139 | ||||||||
\(940\) | − 39599.5i | − 1.37404i | ||||||||
\(941\) | 34621.7i | 1.19940i | 0.800224 | + | 0.599701i | \(0.204714\pi\) | ||||
−0.800224 | + | 0.599701i | \(0.795286\pi\) | |||||||
\(942\) | 8717.59i | 0.301523i | ||||||||
\(943\) | −12082.2 | −0.417233 | ||||||||
\(944\) | −10736.0 | −0.370155 | ||||||||
\(945\) | 3191.75i | 0.109871i | ||||||||
\(946\) | − 20042.3i | − 0.688829i | ||||||||
\(947\) | − 20331.6i | − 0.697665i | −0.937185 | − | 0.348832i | \(-0.886578\pi\) | ||||
0.937185 | − | 0.348832i | \(-0.113422\pi\) | |||||||
\(948\) | −219.849 | −0.00753204 | ||||||||
\(949\) | − 10849.7i | − 0.371124i | ||||||||
\(950\) | 70049.1 | 2.39231 | ||||||||
\(951\) | −1994.28 | −0.0680009 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 17934.5 | 0.609607 | 0.304803 | − | 0.952415i | \(-0.401409\pi\) | ||||
0.304803 | + | 0.952415i | \(0.401409\pi\) | |||||||
\(954\) | 30898.2 | 1.04860 | ||||||||
\(955\) | 40110.0i | 1.35909i | ||||||||
\(956\) | 50771.9 | 1.71766 | ||||||||
\(957\) | 6413.73i | 0.216642i | ||||||||
\(958\) | − 56217.8i | − 1.89594i | ||||||||
\(959\) | 14450.3i | 0.486573i | ||||||||
\(960\) | 7666.21 | 0.257735 | ||||||||
\(961\) | 29484.2 | 0.989701 | ||||||||
\(962\) | − 2190.93i | − 0.0734287i | ||||||||
\(963\) | − 54242.5i | − 1.81510i | ||||||||
\(964\) | − 28920.6i | − 0.966256i | ||||||||
\(965\) | 43522.5 | 1.45185 | ||||||||
\(966\) | 1849.37i | 0.0615966i | ||||||||
\(967\) | −8758.07 | −0.291252 | −0.145626 | − | 0.989340i | \(-0.546520\pi\) | ||||
−0.145626 | + | 0.989340i | \(0.546520\pi\) | |||||||
\(968\) | 28782.5 | 0.955686 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −19664.4 | −0.650914 | ||||||||
\(971\) | 52844.2 | 1.74650 | 0.873250 | − | 0.487273i | \(-0.162008\pi\) | ||||
0.873250 | + | 0.487273i | \(0.162008\pi\) | |||||||
\(972\) | − 13605.9i | − 0.448982i | ||||||||
\(973\) | −6499.22 | −0.214137 | ||||||||
\(974\) | 59186.4i | 1.94708i | ||||||||
\(975\) | 5449.52i | 0.178999i | ||||||||
\(976\) | 5317.72i | 0.174402i | ||||||||
\(977\) | 45377.7 | 1.48594 | 0.742970 | − | 0.669325i | \(-0.233417\pi\) | ||||
0.742970 | + | 0.669325i | \(0.233417\pi\) | |||||||
\(978\) | −505.604 | −0.0165311 | ||||||||
\(979\) | − 58655.3i | − 1.91484i | ||||||||
\(980\) | − 61206.5i | − 1.99507i | ||||||||
\(981\) | − 19138.1i | − 0.622866i | ||||||||
\(982\) | −86119.6 | −2.79856 | ||||||||
\(983\) | 20092.8i | 0.651944i | 0.945379 | + | 0.325972i | \(0.105691\pi\) | ||||
−0.945379 | + | 0.325972i | \(0.894309\pi\) | |||||||
\(984\) | −893.765 | −0.0289555 | ||||||||
\(985\) | −37916.2 | −1.22651 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −672.604 | −0.0216912 | ||||||||
\(988\) | 62828.1 | 2.02311 | ||||||||
\(989\) | 9855.23i | 0.316863i | ||||||||
\(990\) | −113331. | −3.63826 | ||||||||
\(991\) | − 8915.20i | − 0.285773i | −0.989739 | − | 0.142886i | \(-0.954362\pi\) | ||||
0.989739 | − | 0.142886i | \(-0.0456383\pi\) | |||||||
\(992\) | 3889.83i | 0.124498i | ||||||||
\(993\) | 1886.10i | 0.0602756i | ||||||||
\(994\) | −20045.3 | −0.639637 | ||||||||
\(995\) | −62079.1 | −1.97793 | ||||||||
\(996\) | − 4087.53i | − 0.130039i | ||||||||
\(997\) | 12587.1i | 0.399837i | 0.979812 | + | 0.199919i | \(0.0640678\pi\) | ||||
−0.979812 | + | 0.199919i | \(0.935932\pi\) | |||||||
\(998\) | 89319.8i | 2.83303i | ||||||||
\(999\) | 242.572 | 0.00768234 |
(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 | 289.4.b.f.288.1 | 24 | ||
17.4 | even | 4 | 289.4.a.h.1.12 | ✓ | 12 | ||
17.13 | even | 4 | 289.4.a.i.1.12 | yes | 12 | ||
17.16 | even | 2 | inner | 289.4.b.f.288.2 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
289.4.a.h.1.12 | ✓ | 12 | 17.4 | even | 4 | ||
289.4.a.i.1.12 | yes | 12 | 17.13 | even | 4 | ||
289.4.b.f.288.1 | 24 | 1.1 | even | 1 | trivial | ||
289.4.b.f.288.2 | 24 | 17.16 | even | 2 | inner |