Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [76,5,Mod(13,76)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(76, base_ring=CyclotomicField(18))
chi = DirichletCharacter(H, H._module([0, 5]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("76.13");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 76 = 2^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 76.j (of order \(18\), degree \(6\), 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: | \(7.85611719437\) |
Analytic rank: | \(0\) |
Dimension: | \(42\) |
Relative dimension: | \(7\) over \(\Q(\zeta_{18})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{18}]$ |
Embedding invariants
Embedding label | 41.6 | ||
Character | \(\chi\) | \(=\) | 76.41 |
Dual form | 76.5.j.a.13.6 |
$q$-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 \(\left(\mathbb{Z}/76\mathbb{Z}\right)^\times\).
\(n\) | \(21\) | \(39\) |
\(\chi(n)\) | \(e\left(\frac{13}{18}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 3.28951 | + | 9.03787i | 0.365502 | + | 1.00421i | 0.977052 | + | 0.213002i | \(0.0683240\pi\) |
−0.611550 | + | 0.791206i | \(0.709454\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 7.51461 | − | 42.6175i | 0.300585 | − | 1.70470i | −0.343009 | − | 0.939332i | \(-0.611446\pi\) |
0.643594 | − | 0.765367i | \(-0.277443\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −18.8739 | − | 32.6905i | −0.385181 | − | 0.667153i | 0.606613 | − | 0.794997i | \(-0.292528\pi\) |
−0.991794 | + | 0.127844i | \(0.959194\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −8.81253 | + | 7.39459i | −0.108797 | + | 0.0912912i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 103.948 | − | 180.042i | 0.859070 | − | 1.48795i | −0.0137466 | − | 0.999906i | \(-0.504376\pi\) |
0.872817 | − | 0.488048i | \(-0.162291\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −76.3894 | + | 209.878i | −0.452008 | + | 1.24188i | 0.479300 | + | 0.877651i | \(0.340890\pi\) |
−0.931309 | + | 0.364231i | \(0.881332\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 409.891 | − | 72.2748i | 1.82174 | − | 0.321221i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 361.904 | + | 303.674i | 1.25226 | + | 1.05077i | 0.996462 | + | 0.0840453i | \(0.0267841\pi\) |
0.255802 | + | 0.966729i | \(0.417660\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −54.7631 | − | 356.822i | −0.151698 | − | 0.988427i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 233.366 | − | 278.115i | 0.529175 | − | 0.630647i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −61.0806 | − | 346.405i | −0.115464 | − | 0.654831i | −0.986519 | − | 0.163645i | \(-0.947675\pi\) |
0.871055 | − | 0.491186i | \(-0.163436\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1172.47 | − | 426.745i | −1.87596 | − | 0.682792i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 578.857 | + | 334.203i | 0.794042 | + | 0.458440i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −524.525 | − | 625.105i | −0.623692 | − | 0.743287i | 0.358009 | − | 0.933718i | \(-0.383456\pi\) |
−0.981701 | + | 0.190431i | \(0.939011\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 162.613 | − | 93.8845i | 0.169212 | − | 0.0976946i | −0.413002 | − | 0.910730i | \(-0.635520\pi\) |
0.582214 | + | 0.813035i | \(0.302187\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1969.14 | + | 347.212i | 1.80821 | + | 0.318835i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1535.02 | + | 558.700i | −1.25307 | + | 0.456082i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 914.694i | 0.668148i | 0.942547 | + | 0.334074i | \(0.108423\pi\) | ||||
−0.942547 | + | 0.334074i | \(0.891577\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −2148.13 | −1.41232 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 819.137 | + | 2250.56i | 0.487292 | + | 1.33882i | 0.903123 | + | 0.429381i | \(0.141268\pi\) |
−0.415832 | + | 0.909442i | \(0.636509\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −232.697 | + | 1319.69i | −0.125850 | + | 0.713733i | 0.854949 | + | 0.518712i | \(0.173588\pi\) |
−0.980799 | + | 0.195020i | \(0.937523\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 248.916 | + | 431.135i | 0.122921 | + | 0.212906i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 670.959 | − | 563.001i | 0.303739 | − | 0.254867i | −0.478160 | − | 0.878273i | \(-0.658696\pi\) |
0.781898 | + | 0.623406i | \(0.214252\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 488.055 | − | 845.336i | 0.203272 | − | 0.352077i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1554.07 | + | 4269.78i | −0.597491 | + | 1.64159i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −4531.29 | + | 798.988i | −1.61313 | + | 0.284439i | −0.906202 | − | 0.422845i | \(-0.861032\pi\) |
−0.706930 | + | 0.707283i | \(0.749920\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −6891.83 | − | 5782.93i | −2.27829 | − | 1.91171i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 3044.77 | − | 1668.71i | 0.937140 | − | 0.513608i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 2507.79 | − | 2988.66i | 0.720421 | − | 0.858565i | −0.274250 | − | 0.961658i | \(-0.588430\pi\) |
0.994672 | + | 0.103094i | \(0.0328741\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 173.586 | + | 984.457i | 0.0466504 | + | 0.264568i | 0.999208 | − | 0.0397906i | \(-0.0126691\pi\) |
−0.952558 | + | 0.304358i | \(0.901558\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 408.059 | + | 148.521i | 0.102812 | + | 0.0374203i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 8370.44 | + | 4832.68i | 1.98117 | + | 1.14383i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1694.50 | + | 2019.42i | 0.377477 | + | 0.449860i | 0.921016 | − | 0.389524i | \(-0.127360\pi\) |
−0.543539 | + | 0.839384i | \(0.682916\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 2929.84 | − | 1691.54i | 0.615384 | − | 0.355292i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −2943.73 | − | 519.059i | −0.583958 | − | 0.102968i | −0.126138 | − | 0.992013i | \(-0.540258\pi\) |
−0.457819 | + | 0.889045i | \(0.651369\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 455.176 | − | 165.670i | 0.0854148 | − | 0.0310885i | −0.298959 | − | 0.954266i | \(-0.596639\pi\) |
0.384374 | + | 0.923177i | \(0.374417\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | − | 12000.4i | − | 2.13341i | ||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −7847.56 | −1.32359 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 847.785 | + | 2329.27i | 0.135841 | + | 0.373221i | 0.988898 | − | 0.148598i | \(-0.0474760\pi\) |
−0.853056 | + | 0.521819i | \(0.825254\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −1278.13 | + | 7248.66i | −0.194808 | + | 1.10481i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 1815.81 | + | 3145.08i | 0.263581 | + | 0.456536i | 0.967191 | − | 0.254051i | \(-0.0817630\pi\) |
−0.703610 | + | 0.710587i | \(0.748430\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 15661.4 | − | 13141.5i | 2.16767 | − | 1.81889i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 3924.18 | − | 6796.88i | 0.518454 | − | 0.897989i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −2615.57 | + | 7186.22i | −0.330207 | + | 0.907236i | 0.657850 | + | 0.753149i | \(0.271466\pi\) |
−0.988057 | + | 0.154087i | \(0.950756\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 8302.78 | − | 1464.00i | 1.00263 | − | 0.176791i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1383.43 | + | 1160.84i | 0.159953 | + | 0.134216i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −15618.4 | − | 347.516i | −1.73057 | − | 0.0385059i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 125.731 | − | 149.840i | 0.0133628 | − | 0.0159252i | −0.759322 | − | 0.650715i | \(-0.774469\pi\) |
0.772684 | + | 0.634790i | \(0.218914\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 415.299 | + | 2355.28i | 0.0423731 | + | 0.240310i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 5764.46 | + | 2098.09i | 0.565088 | + | 0.205675i | 0.608737 | − | 0.793372i | \(-0.291676\pi\) |
−0.0436498 | + | 0.999047i | \(0.513899\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 10806.4 | + | 6239.10i | 1.01861 | + | 0.588095i | 0.913701 | − | 0.406387i | \(-0.133212\pi\) |
0.104909 | + | 0.994482i | \(0.466545\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −10098.9 | − | 12035.4i | −0.916001 | − | 1.09165i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1213.06 | + | 700.358i | −0.105953 | + | 0.0611720i | −0.552040 | − | 0.833818i | \(-0.686150\pi\) |
0.446087 | + | 0.894990i | \(0.352817\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 11058.0 | + | 1949.82i | 0.930727 | + | 0.164112i | 0.618401 | − | 0.785863i | \(-0.287781\pi\) |
0.312326 | + | 0.949975i | \(0.398892\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −8266.88 | + | 3008.90i | −0.670959 | + | 0.244209i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 5242.34i | 0.410552i | 0.978704 | + | 0.205276i | \(0.0658092\pi\) | ||||
−0.978704 | + | 0.205276i | \(0.934191\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −15221.9 | −1.15100 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −878.778 | − | 2414.42i | −0.0641960 | − | 0.176377i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 3096.71 | − | 17562.3i | 0.218679 | − | 1.24019i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −14289.7 | − | 24750.4i | −0.976004 | − | 1.69049i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −17645.7 | + | 14806.5i | −1.16635 | + | 0.978684i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −13474.1 | + | 23337.8i | −0.862340 | + | 1.49362i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2155.34 | + | 5921.76i | −0.133632 | + | 0.367150i | −0.988403 | − | 0.151855i | \(-0.951475\pi\) |
0.854771 | + | 0.519005i | \(0.173697\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −12692.7 | + | 2238.06i | −0.762734 | + | 0.134491i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 21564.8 | + | 18095.0i | 1.25662 | + | 1.05443i | 0.996034 | + | 0.0889757i | \(0.0283594\pi\) |
0.260583 | + | 0.965451i | \(0.416085\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −10631.1 | + | 8524.84i | −0.601000 | + | 0.481929i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 18592.8 | − | 22158.0i | 1.02018 | − | 1.21580i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 4797.81 | + | 27209.7i | 0.255624 | + | 1.44972i | 0.794466 | + | 0.607309i | \(0.207751\pi\) |
−0.538842 | + | 0.842407i | \(0.681138\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −7874.43 | − | 2866.06i | −0.407558 | − | 0.148339i | 0.130102 | − | 0.991501i | \(-0.458469\pi\) |
−0.537660 | + | 0.843162i | \(0.680692\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 7295.46 | + | 4212.03i | 0.366956 | + | 0.211862i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 29846.5 | + | 35569.6i | 1.45956 | + | 1.73943i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −30582.0 | + | 17656.5i | −1.45455 | + | 0.839787i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 9245.50 | + | 1630.23i | 0.427854 | + | 0.0754422i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 11813.3 | − | 4299.70i | 0.532108 | − | 0.193671i | −0.0619716 | − | 0.998078i | \(-0.519739\pi\) |
0.594079 | + | 0.804407i | \(0.297517\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1094.46i | 0.0480005i | 0.999712 | + | 0.0240002i | \(0.00764025\pi\) | ||||
−0.999712 | + | 0.0240002i | \(0.992360\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −5434.83 | −0.232169 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −2779.15 | − | 7635.65i | −0.115677 | − | 0.317821i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2873.20 | − | 16294.7i | 0.116565 | − | 0.661071i | −0.869399 | − | 0.494111i | \(-0.835494\pi\) |
0.985964 | − | 0.166960i | \(-0.0533951\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −22126.9 | − | 38324.9i | −0.875238 | − | 1.51596i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −10171.3 | + | 8534.76i | −0.392397 | + | 0.329261i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 8971.48 | − | 15539.1i | 0.337667 | − | 0.584857i | −0.646326 | − | 0.763061i | \(-0.723695\pi\) |
0.983993 | + | 0.178204i | \(0.0570288\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 29594.6 | − | 81310.4i | 1.08704 | − | 2.98661i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −31190.3 | + | 5499.70i | −1.11837 | + | 0.197199i | −0.702127 | − | 0.712052i | \(-0.747766\pi\) |
−0.416247 | + | 0.909252i | \(0.636655\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −16334.5 | − | 13706.3i | −0.571915 | − | 0.479894i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 3121.15 | + | 2739.55i | 0.106739 | + | 0.0936888i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 715.042 | − | 852.154i | 0.0238913 | − | 0.0284725i | −0.753967 | − | 0.656913i | \(-0.771862\pi\) |
0.777858 | + | 0.628440i | \(0.216306\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 8178.58 | + | 46383.0i | 0.267056 | + | 1.51455i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 35260.5 | + | 12833.8i | 1.12549 | + | 0.409646i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −18126.2 | − | 10465.1i | −0.565718 | − | 0.326617i | 0.189719 | − | 0.981838i | \(-0.439242\pi\) |
−0.755437 | + | 0.655221i | \(0.772575\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −21860.1 | − | 26051.8i | −0.667259 | − | 0.795209i | 0.321149 | − | 0.947029i | \(-0.395931\pi\) |
−0.988408 | + | 0.151820i | \(0.951487\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −8326.37 | + | 4807.23i | −0.248630 | + | 0.143547i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 38982.0 | + | 6873.57i | 1.13899 | + | 0.200835i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 92293.2 | − | 33592.0i | 2.63929 | − | 0.960622i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | − | 25230.8i | − | 0.706330i | ||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 42570.4 | 1.16692 | 0.583460 | − | 0.812142i | \(-0.301699\pi\) | ||||
0.583460 | + | 0.812142i | \(0.301699\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −15357.1 | − | 42193.2i | −0.412281 | − | 1.13273i | −0.955975 | − | 0.293449i | \(-0.905197\pi\) |
0.543693 | − | 0.839284i | \(-0.317025\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −16142.4 | + | 91548.1i | −0.424521 | + | 2.40758i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 7105.29 | + | 12306.7i | 0.183083 | + | 0.317110i | 0.942929 | − | 0.332994i | \(-0.108059\pi\) |
−0.759846 | + | 0.650104i | \(0.774725\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −22313.5 | + | 18723.2i | −0.563457 | + | 0.472797i | −0.879467 | − | 0.475959i | \(-0.842101\pi\) |
0.316010 | + | 0.948756i | \(0.397657\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −12677.2 | + | 21957.6i | −0.313784 | + | 0.543490i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −10535.2 | + | 28945.1i | −0.255652 | + | 0.702398i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 102069. | − | 17997.5i | 2.42876 | − | 0.428256i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 3099.80 | + | 2601.04i | 0.0723424 | + | 0.0607025i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −69935.6 | − | 27231.1i | −1.60105 | − | 0.623408i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 19420.0 | − | 23143.9i | 0.436200 | − | 0.519843i | −0.502501 | − | 0.864577i | \(-0.667587\pi\) |
0.938700 | + | 0.344734i | \(0.112031\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −4992.26 | − | 28312.5i | −0.110037 | − | 0.624049i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 54493.3 | + | 19833.9i | 1.17887 | + | 0.429074i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −6138.26 | − | 3543.92i | −0.130354 | − | 0.0752601i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 2994.61 | + | 3568.84i | 0.0624385 | + | 0.0744113i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −91380.1 | + | 52758.3i | −1.87097 | + | 1.08021i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −80813.3 | − | 14249.6i | −1.62507 | − | 0.286544i | −0.714421 | − | 0.699716i | \(-0.753310\pi\) |
−0.910653 | + | 0.413171i | \(0.864421\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 13488.1 | − | 4909.25i | 0.266431 | − | 0.0969728i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − | 47803.2i | − | 0.927695i | −0.885915 | − | 0.463847i | \(-0.846469\pi\) | ||
0.885915 | − | 0.463847i | \(-0.153531\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 32706.7 | 0.623686 | 0.311843 | − | 0.950134i | \(-0.399054\pi\) | ||||
0.311843 | + | 0.950134i | \(0.399054\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −25814.7 | − | 70925.2i | −0.483774 | − | 1.32916i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −8373.17 | + | 47486.6i | −0.154233 | + | 0.874701i | 0.805250 | + | 0.592935i | \(0.202031\pi\) |
−0.959483 | + | 0.281765i | \(0.909080\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −18951.7 | − | 32825.3i | −0.343172 | − | 0.594392i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −18262.8 | + | 15324.3i | −0.325141 | + | 0.272826i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −39420.4 | + | 68278.1i | −0.690121 | + | 1.19532i | 0.281677 | + | 0.959509i | \(0.409109\pi\) |
−0.971798 | + | 0.235815i | \(0.924224\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −30298.5 | + | 83244.4i | −0.521659 | + | 1.43325i | 0.347013 | + | 0.937860i | \(0.387196\pi\) |
−0.868672 | + | 0.495387i | \(0.835026\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −16398.5 | + | 2891.49i | −0.277709 | + | 0.0489677i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −32358.5 | − | 27152.0i | −0.539084 | − | 0.452346i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 79072.5 | + | 15763.9i | 1.29608 | + | 0.258386i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −22451.6 | + | 26756.8i | −0.362117 | + | 0.431555i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −16099.8 | − | 91306.6i | −0.255548 | − | 1.44929i | −0.794661 | − | 0.607054i | \(-0.792351\pi\) |
0.539112 | − | 0.842234i | \(-0.318760\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −68716.8 | − | 25010.9i | −1.07355 | − | 0.390740i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 170289. | + | 98316.5i | 2.61883 | + | 1.51198i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −57015.0 | − | 67947.8i | −0.863223 | − | 1.02875i | −0.999276 | − | 0.0380473i | \(-0.987886\pi\) |
0.136053 | − | 0.990702i | \(-0.456558\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 29901.8 | − | 17263.8i | 0.445756 | − | 0.257358i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 9244.78 | + | 1630.10i | 0.135711 | + | 0.0239295i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 61111.7 | − | 22242.9i | 0.883513 | − | 0.321573i | 0.139887 | − | 0.990168i | \(-0.455326\pi\) |
0.743627 | + | 0.668595i | \(0.233104\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 199116.i | 2.83540i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −73552.0 | −1.03174 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −16485.4 | − | 45293.3i | −0.227822 | − | 0.625936i | 0.772133 | − | 0.635461i | \(-0.219190\pi\) |
−0.999955 | + | 0.00952562i | \(0.996968\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3910.58 | − | 22178.0i | 0.0532479 | − | 0.301984i | −0.946540 | − | 0.322587i | \(-0.895448\pi\) |
0.999788 | + | 0.0206031i | \(0.00655864\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 40543.6 | + | 70223.5i | 0.543997 | + | 0.942231i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −198708. | + | 166736.i | −2.62754 | + | 2.20477i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −6433.92 | + | 11143.9i | −0.0838525 | + | 0.145237i | −0.904902 | − | 0.425621i | \(-0.860056\pi\) |
0.821049 | + | 0.570858i | \(0.193389\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −738.791 | + | 2029.81i | −0.00949103 | + | 0.0260764i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 86611.2 | − | 15271.9i | 1.09689 | − | 0.193411i | 0.404215 | − | 0.914664i | \(-0.367545\pi\) |
0.692671 | + | 0.721254i | \(0.256434\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −89003.0 | − | 74682.4i | −1.11130 | − | 0.932493i | −0.113169 | − | 0.993576i | \(-0.536100\pi\) |
−0.998133 | + | 0.0610832i | \(0.980544\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −48236.1 | − | 142300.i | −0.593858 | − | 1.75192i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 58111.7 | − | 69254.8i | 0.705504 | − | 0.840787i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 24253.7 | + | 137550.i | 0.290391 | + | 1.64689i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1767.83 | + | 643.437i | 0.0208763 | + | 0.00759837i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 64975.6 | + | 37513.7i | 0.756859 | + | 0.436973i | 0.828167 | − | 0.560482i | \(-0.189384\pi\) |
−0.0713079 | + | 0.997454i | \(0.522717\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −108524. | − | 129334.i | −1.24705 | − | 1.48617i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 120341. | − | 69479.1i | 1.36428 | − | 0.787665i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 77368.8 | + | 13642.2i | 0.865413 | + | 0.152596i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 47533.3 | − | 17300.7i | 0.524644 | − | 0.190955i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 59000.1i | 0.642640i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 43259.5 | 0.465031 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −36832.6 | − | 101197.i | −0.390801 | − | 1.07372i | −0.966637 | − | 0.256151i | \(-0.917545\pi\) |
0.575836 | − | 0.817565i | \(-0.304677\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −20840.2 | + | 118191.i | −0.218265 | + | 1.23785i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 33480.2 | + | 57989.4i | 0.346152 | + | 0.599553i | 0.985562 | − | 0.169313i | \(-0.0541548\pi\) |
−0.639410 | + | 0.768866i | \(0.720821\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 34053.8 | − | 28574.5i | 0.347597 | − | 0.291669i | −0.452227 | − | 0.891903i | \(-0.649370\pi\) |
0.799824 | + | 0.600234i | \(0.204926\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 9396.01 | − | 16274.4i | 0.0946940 | − | 0.164015i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 35448.9 | − | 97395.0i | 0.352764 | − | 0.969211i | −0.628714 | − | 0.777636i | \(-0.716418\pi\) |
0.981478 | − | 0.191574i | \(-0.0613593\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −167068. | + | 29458.7i | −1.64177 | + | 0.289489i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −10320.1 | − | 8659.60i | −0.100155 | − | 0.0840403i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 88538.5 | − | 145766.i | 0.848647 | − | 1.39717i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 179129. | − | 213478.i | 1.69590 | − | 2.02109i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 18753.1 | + | 106354.i | 0.175379 | + | 0.994626i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −31068.4 | − | 11308.0i | −0.287029 | − | 0.104470i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 59041.4 | + | 34087.6i | 0.538891 | + | 0.311129i | 0.744629 | − | 0.667478i | \(-0.232626\pi\) |
−0.205739 | + | 0.978607i | \(0.565960\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −6763.78 | − | 8060.76i | −0.0609960 | − | 0.0726922i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 98796.2 | − | 57040.0i | 0.880340 | − | 0.508265i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 74850.9 | + | 13198.2i | 0.659079 | + | 0.116213i | 0.493177 | − | 0.869929i | \(-0.335835\pi\) |
0.165902 | + | 0.986142i | \(0.446947\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −47379.5 | + | 17244.7i | −0.412279 | + | 0.150057i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 39036.2i | − | 0.335706i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −127478. | −1.08355 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −50072.8 | − | 137574.i | −0.420691 | − | 1.15584i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 7554.18 | − | 42841.9i | 0.0627377 | − | 0.355803i | −0.937237 | − | 0.348693i | \(-0.886626\pi\) |
0.999975 | − | 0.00711023i | \(-0.00226328\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 78844.4 | + | 136562.i | 0.647321 | + | 1.12119i | 0.983760 | + | 0.179488i | \(0.0574441\pi\) |
−0.336439 | + | 0.941705i | \(0.609223\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −114360. | + | 95959.7i | −0.928242 | + | 0.778888i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −19855.9 | + | 34391.5i | −0.159346 | + | 0.275995i | −0.934633 | − | 0.355614i | \(-0.884272\pi\) |
0.775287 | + | 0.631609i | \(0.217605\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −44242.0 | + | 121554.i | −0.351057 | + | 0.964522i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 168913. | − | 29783.9i | 1.32534 | − | 0.233692i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −113432. | − | 95180.6i | −0.880128 | − | 0.738515i | 0.0860774 | − | 0.996288i | \(-0.472567\pi\) |
−0.966205 | + | 0.257773i | \(0.917011\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −124323. | + | 39081.3i | −0.953975 | + | 0.299885i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 176685. | − | 210565.i | 1.34087 | − | 1.59799i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −3639.99 | − | 20643.4i | −0.0273221 | − | 0.154951i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 9866.08 | + | 3590.96i | 0.0732508 | + | 0.0266611i | 0.378386 | − | 0.925648i | \(-0.376479\pi\) |
−0.305135 | + | 0.952309i | \(0.598702\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −23860.6 | − | 13775.9i | −0.175238 | − | 0.101174i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 111642. | + | 133050.i | 0.811112 | + | 0.966645i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −88926.0 | + | 51341.5i | −0.639162 | + | 0.369021i | −0.784292 | − | 0.620392i | \(-0.786973\pi\) |
0.145129 | + | 0.989413i | \(0.453640\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −255247. | − | 45006.9i | −1.81509 | − | 0.320049i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 171264. | − | 62335.0i | 1.20499 | − | 0.438580i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 193364.i | 1.34616i | 0.739570 | + | 0.673080i | \(0.235029\pi\) | ||||
−0.739570 | + | 0.673080i | \(0.764971\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −60610.1 | −0.417537 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −31138.5 | − | 85552.4i | −0.212276 | − | 0.583223i | 0.787162 | − | 0.616746i | \(-0.211550\pi\) |
−0.999438 | + | 0.0335230i | \(0.989327\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −58971.4 | + | 334443.i | −0.397850 | + | 2.25632i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −7707.93 | − | 13350.5i | −0.0514654 | − | 0.0891407i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 22260.3 | − | 18678.6i | 0.147107 | − | 0.123437i | −0.566264 | − | 0.824224i | \(-0.691612\pi\) |
0.713371 | + | 0.700787i | \(0.247167\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 83088.9 | − | 143914.i | 0.543488 | − | 0.941348i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −92602.7 | + | 254424.i | −0.599568 | + | 1.64730i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 105638. | − | 18626.9i | 0.677061 | − | 0.119384i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 211925. | + | 177826.i | 1.34462 | + | 1.12827i | 0.980412 | + | 0.196957i | \(0.0631061\pi\) |
0.364212 | + | 0.931316i | \(0.381338\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −112018. | − | 68039.8i | −0.703623 | − | 0.427383i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −187594. | + | 223565.i | −1.16662 | + | 1.39032i | −0.261479 | + | 0.965209i | \(0.584210\pi\) |
−0.905140 | + | 0.425114i | \(0.860234\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 7282.41 | + | 41300.6i | 0.0448400 | + | 0.254300i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 299315. | + | 108942.i | 1.82481 | + | 0.664177i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 164684. | + | 95080.2i | 0.994172 | + | 0.573986i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −184229. | − | 219556.i | −1.10131 | − | 1.31250i | −0.945832 | − | 0.324658i | \(-0.894751\pi\) |
−0.155483 | − | 0.987839i | \(-0.549693\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −230135. | + | 132869.i | −1.36238 | + | 0.786573i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −145032. | − | 25573.1i | −0.850286 | − | 0.149928i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 147680. | − | 53751.3i | 0.857485 | − | 0.312099i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − | 80596.0i | − | 0.463491i | ||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −87412.0 | −0.497901 | −0.248951 | − | 0.968516i | \(-0.580086\pi\) | ||||
−0.248951 | + | 0.968516i | \(0.580086\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −97498.4 | − | 267875.i | −0.550090 | − | 1.51136i | −0.833588 | − | 0.552386i | \(-0.813717\pi\) |
0.283499 | − | 0.958973i | \(-0.408505\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −1749.68 | + | 9922.92i | −0.00977862 | + | 0.0554573i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −294732. | − | 510490.i | −1.63173 | − | 2.82624i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 28906.1 | − | 24255.1i | 0.158538 | − | 0.133029i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −223293. | + | 386755.i | −1.21328 | + | 2.10146i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 102913. | − | 282752.i | 0.554010 | − | 1.52213i | −0.274178 | − | 0.961679i | \(-0.588406\pi\) |
0.828188 | − | 0.560451i | \(-0.189372\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −260545. | + | 45941.1i | −1.38966 | + | 0.245034i | −0.817886 | − | 0.575381i | \(-0.804854\pi\) |
−0.571769 | + | 0.820414i | \(0.693743\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −260177. | − | 218315.i | −1.37496 | − | 1.15373i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −120260. | + | 40765.1i | −0.629737 | + | 0.213465i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −132702. | + | 158148.i | −0.688570 | + | 0.820605i | −0.991182 | − | 0.132509i | \(-0.957697\pi\) |
0.302612 | + | 0.953114i | \(0.402141\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1949.91 | + | 11058.5i | 0.0100262 | + | 0.0568616i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 64757.2 | + | 23569.7i | 0.329975 | + | 0.120101i | 0.501695 | − | 0.865045i | \(-0.332710\pi\) |
−0.171720 | + | 0.985146i | \(0.554932\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 286603. | + | 165471.i | 1.44731 | + | 0.835605i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 77720.2 | + | 92623.3i | 0.388972 | + | 0.463559i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −217623. | + | 125644.i | −1.07947 | + | 0.623233i | −0.930754 | − | 0.365646i | \(-0.880848\pi\) |
−0.148718 | + | 0.988880i | \(0.547515\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 490344. | + | 86460.8i | 2.41072 | + | 0.425076i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −9891.57 | + | 3600.24i | −0.0482024 | + | 0.0175442i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | − | 364845.i | − | 1.76232i | ||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 358067. | 1.71448 | 0.857238 | − | 0.514921i | \(-0.172179\pi\) | ||||
0.857238 | + | 0.514921i | \(0.172179\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 108002. | + | 296733.i | 0.512633 | + | 1.40845i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 54042.7 | − | 306491.i | 0.254293 | − | 1.44217i | −0.543586 | − | 0.839353i | \(-0.682934\pi\) |
0.797880 | − | 0.602817i | \(-0.205955\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 5432.68 | + | 9409.69i | 0.0253427 | + | 0.0438948i | 0.878419 | − | 0.477892i | \(-0.158599\pi\) |
−0.853076 | + | 0.521787i | \(0.825266\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 59867.9 | − | 50235.2i | 0.276878 | − | 0.232328i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −109600. | + | 189833.i | −0.502547 | + | 0.870437i | 0.497448 | + | 0.867494i | \(0.334270\pi\) |
−0.999996 | + | 0.00294375i | \(0.999063\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 34034.2 | − | 93508.2i | 0.154728 | − | 0.425113i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 156721. | − | 27634.2i | 0.706457 | − | 0.124567i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 213412. | + | 179074.i | 0.953887 | + | 0.800406i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −88063.9 | + | 441734.i | −0.390311 | + | 1.95782i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 34023.9 | − | 40548.1i | 0.149537 | − | 0.178211i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 53014.1 | + | 300658.i | 0.231058 | + | 1.31039i | 0.850759 | + | 0.525556i | \(0.176143\pi\) |
−0.619701 | + | 0.784838i | \(0.712746\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −191974. | − | 69872.9i | −0.829761 | − | 0.302008i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −110595. | − | 63851.9i | −0.474068 | − | 0.273703i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −5440.99 | − | 6484.32i | −0.0231310 | − | 0.0275665i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −4289.91 | + | 2476.78i | −0.0180880 | + | 0.0104431i | −0.509017 | − | 0.860757i | \(-0.669991\pi\) |
0.490929 | + | 0.871200i | \(0.336658\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 169952. | + | 29967.1i | 0.710735 | + | 0.125322i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 184130. | − | 67017.8i | 0.763768 | − | 0.277989i | 0.0693808 | − | 0.997590i | \(-0.477898\pi\) |
0.694387 | + | 0.719601i | \(0.255675\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 385513.i | − | 1.58615i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 103497. | 0.422393 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 38591.3 | + | 106029.i | 0.156234 | + | 0.429250i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 176.716 | − | 1002.21i | 0.000709701 | − | 0.00402492i | −0.984451 | − | 0.175660i | \(-0.943794\pi\) |
0.985161 | + | 0.171635i | \(0.0549051\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −152307. | − | 263803.i | −0.606797 | − | 1.05100i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −114887. | + | 96401.4i | −0.454081 | + | 0.381020i | −0.840948 | − | 0.541116i | \(-0.818002\pi\) |
0.386866 | + | 0.922136i | \(0.373557\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 132733. | − | 229900.i | 0.520471 | − | 0.901482i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 70142.8 | − | 192716.i | 0.272877 | − | 0.749724i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 140606. | − | 24792.6i | 0.542709 | − | 0.0956943i | 0.104428 | − | 0.994532i | \(-0.466699\pi\) |
0.438281 | + | 0.898838i | \(0.355588\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −14006.8 | − | 11753.1i | −0.0536409 | − | 0.0450101i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 87551.1 | − | 224851.i | 0.332680 | − | 0.854397i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 347101. | − | 413659.i | 1.30870 | − | 1.55965i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −31619.6 | − | 179324.i | −0.118297 | − | 0.670898i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 10053.8 | + | 3659.28i | 0.0373246 | + | 0.0135851i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −105137. | − | 60701.1i | −0.387331 | − | 0.223625i | 0.293672 | − | 0.955906i | \(-0.405123\pi\) |
−0.681003 | + | 0.732281i | \(0.738456\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 38925.4 | + | 46389.5i | 0.142308 | + | 0.169596i | 0.832491 | − | 0.554039i | \(-0.186914\pi\) |
−0.690182 | + | 0.723635i | \(0.742470\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −392300. | + | 226495.i | −1.42331 | + | 0.821749i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 87360.5 | + | 15404.0i | 0.314553 | + | 0.0554642i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 146699. | − | 53393.9i | 0.524221 | − | 0.190801i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 44881.7i | 0.159177i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −534917. | −1.88292 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 20731.8 | + | 56960.3i | 0.0724320 | + | 0.199005i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 34956.3 | − | 198247.i | 0.121221 | − | 0.687477i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −101464. | − | 175741.i | −0.349249 | − | 0.604917i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −322743. | + | 270814.i | −1.10271 | + | 0.925286i | −0.997605 | − | 0.0691745i | \(-0.977963\pi\) |
−0.105109 | + | 0.994461i | \(0.533519\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 163544. | − | 283266.i | 0.554670 | − | 0.960717i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 166193. | − | 456610.i | 0.559524 | − | 1.53728i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −329113. | + | 58031.6i | −1.09994 | + | 0.193950i | −0.694019 | − | 0.719956i | \(-0.744162\pi\) |
−0.405925 | + | 0.913906i | \(0.633051\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −8809.38 | − | 7391.95i | −0.0292281 | − | 0.0245253i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −194327. | + | 221395.i | −0.640072 | + | 0.729229i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 60144.0 | − | 71676.8i | 0.196672 | − | 0.234384i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 66109.3 | + | 374924.i | 0.214623 | + | 1.21719i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 371939. | + | 135375.i | 1.19884 | + | 0.436342i | 0.862819 | − | 0.505512i | \(-0.168697\pi\) |
0.336021 | + | 0.941855i | \(0.390919\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −259199. | − | 149648.i | −0.829487 | − | 0.478904i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 607200. | + | 723632.i | 1.92933 | + | 2.29928i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 267894. | − | 154669.i | 0.845175 | − | 0.487962i | −0.0138446 | − | 0.999904i | \(-0.504407\pi\) |
0.859020 | + | 0.511942i | \(0.171074\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 223415. | + | 39394.1i | 0.699867 | + | 0.123406i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 261085. | − | 95027.3i | 0.812113 | − | 0.295585i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 282436.i | 0.872360i | 0.899859 | + | 0.436180i | \(0.143669\pi\) | ||||
−0.899859 | + | 0.436180i | \(0.856331\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −162080. | −0.497114 | −0.248557 | − | 0.968617i | \(-0.579956\pi\) | ||||
−0.248557 | + | 0.968617i | \(0.579956\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 140036. | + | 384746.i | 0.426511 | + | 1.17183i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −76211.5 | + | 432217.i | −0.230507 | + | 1.30727i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −320896. | − | 555808.i | −0.963857 | − | 1.66945i | −0.712655 | − | 0.701515i | \(-0.752507\pi\) |
−0.251202 | − | 0.967935i | \(-0.580826\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 330819. | − | 277590.i | 0.986810 | − | 0.828032i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 68542.7 | − | 118719.i | 0.203053 | − | 0.351698i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −327164. | + | 898877.i | −0.962562 | + | 2.64462i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −109500. | + | 19307.9i | −0.319966 | + | 0.0564186i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 342332. | + | 287251.i | 0.993509 | + | 0.833653i | 0.986072 | − | 0.166319i | \(-0.0531882\pi\) |
0.00743718 | + | 0.999972i | \(0.497633\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −42405.2 | − | 52882.4i | −0.122233 | − | 0.152434i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −87853.5 | + | 104700.i | −0.251527 | + | 0.299758i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −4325.64 | − | 24531.9i | −0.0123010 | − | 0.0697625i | 0.978039 | − | 0.208420i | \(-0.0668322\pi\) |
−0.990340 | + | 0.138658i | \(0.955721\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −725192. | − | 263948.i | −2.04842 | − | 0.745564i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −242619. | − | 140076.i | −0.680731 | − | 0.393020i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −362000. | − | 431415.i | −1.00892 | − | 1.20238i | −0.979216 | − | 0.202820i | \(-0.934989\pi\) |
−0.0296996 | − | 0.999559i | \(-0.509455\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −108967. | + | 62911.9i | −0.301679 | + | 0.174174i | −0.643197 | − | 0.765701i | \(-0.722392\pi\) |
0.341518 | + | 0.939875i | \(0.389059\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −29865.6 | − | 5266.11i | −0.0821365 | − | 0.0144829i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −1.16218e6 | + | 423000.i | −3.17514 | + | 1.15566i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 421927.i | − | 1.14514i | −0.819855 | − | 0.572571i | \(-0.805946\pi\) | ||
0.819855 | − | 0.572571i | \(-0.194054\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −296258. | −0.798794 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 66907.5 | + | 183827.i | 0.179222 | + | 0.492410i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −11873.9 | + | 67340.2i | −0.0315989 | + | 0.179206i | −0.996522 | − | 0.0833248i | \(-0.973446\pi\) |
0.964924 | + | 0.262531i | \(0.0845572\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 498415. | + | 863281.i | 1.31777 | + | 2.28245i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 260713. | − | 218764.i | 0.684845 | − | 0.574653i | −0.232573 | − | 0.972579i | \(-0.574714\pi\) |
0.917417 | + | 0.397926i | \(0.130270\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −68974.6 | + | 119468.i | −0.180015 | + | 0.311795i | −0.941885 | − | 0.335935i | \(-0.890948\pi\) |
0.761871 | + | 0.647729i | \(0.224281\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 80412.8 | − | 220932.i | 0.208517 | − | 0.572897i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 284287. | − | 50127.4i | 0.732454 | − | 0.129151i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 295964. | + | 248344.i | 0.757669 | + | 0.635760i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 16056.9 | − | 721645.i | 0.0408439 | − | 1.83565i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −277769. | + | 331032.i | −0.702072 | + | 0.836697i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 14222.2 | + | 80658.1i | 0.0357197 | + | 0.202577i | 0.997445 | − | 0.0714390i | \(-0.0227591\pi\) |
−0.961725 | + | 0.274016i | \(0.911648\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 273054. | + | 99383.6i | 0.681462 | + | 0.248032i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 236174. | + | 136355.i | 0.585713 | + | 0.338161i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 140135. | + | 167007.i | 0.345357 | + | 0.411581i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 29779.9 | − | 17193.5i | 0.0729327 | − | 0.0421077i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −583030. | − | 102804.i | −1.41897 | − | 0.250204i | −0.589058 | − | 0.808091i | \(-0.700501\pi\) |
−0.829917 | + | 0.557887i | \(0.811612\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −640784. | + | 233226.i | −1.54985 | + | 0.564100i | −0.968383 | − | 0.249470i | \(-0.919744\pi\) |
−0.581468 | + | 0.813569i | \(0.697522\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 557747.i | 1.34066i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 21537.2 | 0.0514493 | 0.0257247 | − | 0.999669i | \(-0.491811\pi\) | ||||
0.0257247 | + | 0.999669i | \(0.491811\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −277408. | − | 762172.i | −0.658612 | − | 1.80952i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 11837.6 | − | 67134.5i | 0.0279321 | − | 0.158411i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 220827. | + | 382483.i | 0.517876 | + | 0.896987i | 0.999784 | + | 0.0207656i | \(0.00661036\pi\) |
−0.481909 | + | 0.876221i | \(0.660056\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 933216. | − | 783061.i | 2.17520 | − | 1.82521i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −2786.18 | + | 4825.81i | −0.00645474 | + | 0.0111799i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 40628.8 | − | 111627.i | 0.0935542 | − | 0.257038i | −0.884085 | − | 0.467325i | \(-0.845218\pi\) |
0.977640 | + | 0.210287i | \(0.0674399\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −258721. | + | 45619.5i | −0.592146 | + | 0.104411i | −0.461688 | − | 0.887043i | \(-0.652756\pi\) |
−0.130458 | + | 0.991454i | \(0.541645\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −777419. | − | 652332.i | −1.76859 | − | 1.48403i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 283419. | + | 517131.i | 0.640893 | + | 1.16939i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −184501. | + | 219880.i | −0.414713 | + | 0.494236i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −137051. | − | 777254.i | −0.306217 | − | 1.73664i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 195288. | + | 71078.9i | 0.433740 | + | 0.157869i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 577163. | + | 333225.i | 1.27429 | + | 0.735712i | 0.975792 | − | 0.218699i | \(-0.0701813\pi\) |
0.298497 | + | 0.954410i | \(0.403515\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −536074. | − | 638868.i | −1.17657 | − | 1.40218i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 58995.1 | − | 34060.8i | 0.128718 | − | 0.0743153i | −0.434258 | − | 0.900788i | \(-0.642990\pi\) |
0.562976 | + | 0.826473i | \(0.309656\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −7271.37 | − | 1282.14i | −0.0157716 | − | 0.00278097i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 432039. | − | 157249.i | 0.931598 | − | 0.339074i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 573992.i | 1.23045i | 0.788351 | + | 0.615225i | \(0.210935\pi\) | ||||
−0.788351 | + | 0.615225i | \(0.789065\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1.19566e6 | 2.54817 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 107589. | + | 295599.i | 0.227958 | + | 0.626310i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 178452. | − | 1.01205e6i | 0.375909 | − | 2.13189i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 102921. | + | 178264.i | 0.215549 | + | 0.373342i | 0.953442 | − | 0.301576i | \(-0.0975126\pi\) |
−0.737893 | + | 0.674917i | \(0.764179\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 69156.8 | − | 58029.5i | 0.144002 | − | 0.120832i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −181317. | + | 314051.i | −0.375379 | + | 0.650176i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −386987. | + | 1.06324e6i | −0.796583 | + | 2.18859i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −456722. | + | 80532.3i | −0.934754 | + | 0.164822i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −360259. | − | 302293.i | −0.733127 | − | 0.615167i | 0.197855 | − | 0.980231i | \(-0.436602\pi\) |
−0.930982 | + | 0.365065i | \(0.881047\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 326383. | − | 50091.4i | 0.660415 | − | 0.101357i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 234329. | − | 279262.i | 0.471463 | − | 0.561868i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −40210.0 | − | 228042.i | −0.0804442 | − | 0.456222i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −173573. | − | 63175.4i | −0.345295 | − | 0.125677i | 0.163551 | − | 0.986535i | \(-0.447705\pi\) |
−0.508845 | + | 0.860858i | \(0.669928\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −24695.1 | − | 14257.7i | −0.0488508 | − | 0.0282040i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −42454.6 | − | 50595.4i | −0.0835114 | − | 0.0995250i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.74017e6 | − | 1.00469e6i | 3.40393 | − | 1.96526i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −746762. | − | 131674.i | −1.45259 | − | 0.256131i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −117349. | + | 42711.4i | −0.226997 | + | 0.0826201i | −0.453015 | − | 0.891503i | \(-0.649651\pi\) |
0.226018 | + | 0.974123i | \(0.427429\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 471023.i | − | 0.906091i | ||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −852019. | −1.62994 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 348231. | + | 956757.i | 0.662508 | + | 1.82023i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 8299.90 | − | 47071.1i | 0.0157038 | − | 0.0890605i | −0.975949 | − | 0.218001i | \(-0.930046\pi\) |
0.991652 | + | 0.128940i | \(0.0411576\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 218023. | + | 377628.i | 0.410250 | + | 0.710573i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −484970. | + | 406938.i | −0.907570 | + | 0.761542i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 379709. | − | 657676.i | 0.706713 | − | 1.22406i | −0.259356 | − | 0.965782i | \(-0.583510\pi\) |
0.966070 | − | 0.258282i | \(-0.0831563\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 138953. | − | 381769.i | 0.257213 | − | 0.706686i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 539720. | − | 95167.2i | 0.993651 | − | 0.175207i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 257352. | + | 215944.i | 0.471236 | + | 0.395414i | 0.847245 | − | 0.531202i | \(-0.178259\pi\) |
−0.376009 | + | 0.926616i | \(0.622704\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 117638. | + | 766502.i | 0.214246 | + | 1.39597i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −469418. | + | 559431.i | −0.850320 | + | 1.01337i | 0.149377 | + | 0.988780i | \(0.452273\pi\) |
−0.999698 | + | 0.0245920i | \(0.992171\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −94469.7 | − | 535765.i | −0.170208 | − | 0.965298i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −39258.4 | − | 14288.9i | −0.0703545 | − | 0.0256069i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 45790.1 | + | 26436.9i | 0.0816221 | + | 0.0471245i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 38755.9 | + | 46187.5i | 0.0687160 | + | 0.0818925i | 0.799307 | − | 0.600922i | \(-0.205200\pi\) |
−0.730591 | + | 0.682815i | \(0.760756\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 772256. | − | 445862.i | 1.36198 | − | 0.786341i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 46643.1 | + | 8224.43i | 0.0818264 | + | 0.0144282i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 614099. | − | 223514.i | 1.07163 | − | 0.390043i | 0.254847 | − | 0.966981i | \(-0.417975\pi\) |
0.816788 | + | 0.576938i | \(0.195753\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | − | 703327.i | − | 1.22088i | ||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 149877. | 0.258800 | 0.129400 | − | 0.991592i | \(-0.458695\pi\) | ||||
0.129400 | + | 0.991592i | \(0.458695\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −144966. | − | 398291.i | −0.249010 | − | 0.684150i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −40840.7 | + | 231619.i | −0.0697863 | + | 0.395778i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 435687. | + | 754632.i | 0.740600 | + | 1.28276i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −264461. | + | 221909.i | −0.447208 | + | 0.375252i | −0.838398 | − | 0.545058i | \(-0.816508\pi\) |
0.391191 | + | 0.920310i | \(0.372063\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 426552. | − | 738809.i | 0.717568 | − | 1.24286i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −257582. | + | 707701.i | −0.431079 | + | 1.18438i | 0.514072 | + | 0.857747i | \(0.328136\pi\) |
−0.945151 | + | 0.326633i | \(0.894086\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −230724. | + | 40682.8i | −0.384139 | + | 0.0677341i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 254390. | + | 213459.i | 0.421365 | + | 0.353567i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 758192. | − | 415534.i | 1.24941 | − | 0.684749i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −399446. | + | 476041.i | −0.654872 | + | 0.780446i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −94712.9 | − | 537144.i | −0.154485 | − | 0.876127i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −672850. | − | 244897.i | −1.09189 | − | 0.397415i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −982271. | − | 567114.i | −1.58592 | − | 0.915632i | −0.993969 | − | 0.109659i | \(-0.965024\pi\) |
−0.591952 | − | 0.805973i | \(-0.701643\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 402056. | + | 479152.i | 0.645851 | + | 0.769695i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 171374. | − | 98943.1i | 0.273901 | − | 0.158137i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −219876. | − | 38770.1i | −0.349648 | − | 0.0616524i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −1.79959e6 | + | 654996.i | −2.84733 | + | 1.03634i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 199812.i | 0.314561i | 0.987554 | + | 0.157281i | \(0.0502728\pi\) | ||||
−0.987554 | + | 0.157281i | \(0.949727\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 413792. | 0.648169 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −30089.3 | − | 82669.8i | −0.0468973 | − | 0.128849i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 17486.7 | − | 99171.9i | 0.0271192 | − | 0.153800i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 287297. | + | 497612.i | 0.443342 | + | 0.767890i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 355126. | − | 297986.i | 0.545300 | − | 0.457561i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −265478. | + | 459821.i | −0.405631 | + | 0.702573i | −0.994395 | − | 0.105732i | \(-0.966282\pi\) |
0.588764 | + | 0.808305i | \(0.299615\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 264099. | − | 725607.i | 0.401537 | − | 1.10321i | −0.559989 | − | 0.828500i | \(-0.689195\pi\) |
0.961526 | − | 0.274714i | \(-0.0885832\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 213306. | − | 37611.5i | 0.322717 | − | 0.0569036i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −594818. | − | 499112.i | −0.895507 | − | 0.751420i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 483638. | + | 10761.2i | 0.724564 | + | 0.0161219i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −62342.7 | + | 74297.2i | −0.0929433 | + | 0.110766i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 60839.6 | + | 345039.i | 0.0902610 | + | 0.511895i | 0.996097 | + | 0.0882667i | \(0.0281328\pi\) |
−0.905836 | + | 0.423629i | \(0.860756\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1.20647e6 | − | 439118.i | −1.78121 | − | 0.648308i | −0.999702 | − | 0.0244135i | \(-0.992228\pi\) |
−0.781509 | − | 0.623894i | \(-0.785550\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −2.16059e6 | − | 1.24742e6i | −3.17442 | − | 1.83275i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −111442. | − | 132811.i | −0.162943 | − | 0.194188i | 0.678395 | − | 0.734698i | \(-0.262676\pi\) |
−0.841338 | + | 0.540509i | \(0.818232\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −308829. | + | 178302.i | −0.449375 | + | 0.259447i | −0.707566 | − | 0.706647i | \(-0.750207\pi\) |
0.258191 | + | 0.966094i | \(0.416873\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −121881. | − | 21491.0i | −0.176496 | − | 0.0311210i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 433336. | − | 157721.i | 0.624503 | − | 0.227300i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1.37058e6i | 1.96577i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 125506. | 0.179148 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 309925. | + | 851512.i | 0.440284 | + | 1.20967i | 0.939306 | + | 0.343080i | \(0.111470\pi\) |
−0.499022 | + | 0.866589i | \(0.666307\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 7188.83 | − | 40769.9i | 0.0101640 | − | 0.0576431i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 422934. | + | 732543.i | 0.595138 | + | 1.03081i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −706873. | + | 593137.i | −0.989984 | + | 0.830695i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −539402. | + | 934272.i | −0.751876 | + | 1.30229i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 382193. | − | 1.05007e6i | 0.530234 | − | 1.45680i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 316855. | − | 55870.1i | 0.437524 | − | 0.0771472i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 618755. | + | 519197.i | 0.850395 | + | 0.713566i | 0.959877 | − | 0.280423i | \(-0.0904746\pi\) |
−0.109482 | + | 0.993989i | \(0.534919\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 140207. | − | 112429.i | 0.191795 | − | 0.153796i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −236051. | + | 281314.i | −0.321398 | + | 0.383027i | −0.902418 | − | 0.430862i | \(-0.858209\pi\) |
0.581020 | + | 0.813890i | \(0.302654\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 23909.4 | + | 135597.i | 0.0324028 | + | 0.183766i | 0.996713 | − | 0.0810079i | \(-0.0258139\pi\) |
−0.964311 | + | 0.264774i | \(0.914703\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 817074. | + | 297391.i | 1.10219 | + | 0.401163i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 272435. | + | 157291.i | 0.365799 | + | 0.211194i | 0.671621 | − | 0.740895i | \(-0.265598\pi\) |
−0.305823 | + | 0.952088i | \(0.598932\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −30943.4 | − | 36876.9i | −0.0413557 | − | 0.0492859i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −1.16337e6 | + | 671673.i | −1.54768 | + | 0.893552i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 507492. | + | 89484.6i | 0.672032 | + | 0.118497i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −553274. | + | 201375.i | −0.729296 | + | 0.265442i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 2250.20i | 0.00295252i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1.01723e6 | 1.32863 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 54111.4 | + | 148670.i | 0.0703541 | + | 0.193296i | 0.969886 | − | 0.243558i | \(-0.0783147\pi\) |
−0.899532 | + | 0.436854i | \(0.856092\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −125305. | + | 710642.i | −0.162178 | + | 0.919758i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −251115. | − | 434943.i | −0.323534 | − | 0.560378i | 0.657680 | − | 0.753297i | \(-0.271538\pi\) |
−0.981215 | + | 0.192919i | \(0.938204\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 123938. | − | 103997.i | 0.158959 | − | 0.133382i | −0.559839 | − | 0.828601i | \(-0.689137\pi\) |
0.718798 | + | 0.695219i | \(0.244693\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 811913. | − | 1.40627e6i | 1.03663 | − | 1.79549i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −105807. | + | 290703.i | −0.134483 | + | 0.369490i | −0.988595 | − | 0.150600i | \(-0.951879\pi\) |
0.854111 | + | 0.520090i | \(0.174102\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 234265. | − | 41307.2i | 0.296417 | − | 0.0522664i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.17221e6 | + | 983598.i | 1.47655 | + | 1.23897i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −237635. | − | 208581.i | −0.297994 | − | 0.261561i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −582209. | + | 693850.i | −0.726830 | + | 0.866203i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 131209. | + | 744125.i | 0.163072 | + | 0.924829i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −143982. | − | 52405.2i | −0.178151 | − | 0.0648418i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.88252e6 | − | 1.08688e6i | −2.31895 | − | 1.33885i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 312723. | + | 372688.i | 0.383516 | + | 0.457057i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −1.27453e6 | + | 735853.i | −1.55616 | + | 0.898449i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 161004. | + | 28389.3i | 0.195714 | + | 0.0345096i | 0.270646 | − | 0.962679i | \(-0.412763\pi\) |
−0.0749319 | + | 0.997189i | \(0.523874\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −66313.9 | + | 24136.3i | −0.0802559 | + | 0.0292108i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 900368.i | 1.08488i | 0.840093 | + | 0.542442i | \(0.182500\pi\) | ||||
−0.840093 | + | 0.542442i | \(0.817500\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 754996. | 0.905739 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 142303. | + | 390974.i | 0.169970 | + | 0.466987i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 184524. | − | 1.04649e6i | 0.219439 | − | 1.24450i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −722969. | − | 1.25222e6i | −0.856030 | − | 1.48269i | −0.875687 | − | 0.482880i | \(-0.839591\pi\) |
0.0196571 | − | 0.999807i | \(-0.493743\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 793441. | − | 665776.i | 0.935396 | − | 0.784890i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 333809. | − | 578174.i | 0.391827 | − | 0.678665i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 390341. | − | 1.07245e6i | 0.456206 | − | 1.25342i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −141367. | + | 24926.9i | −0.164509 | + | 0.0290074i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 776900. | + | 651896.i | 0.900188 | + | 0.755348i | 0.970227 | − | 0.242196i | \(-0.0778678\pi\) |
−0.0700387 | + | 0.997544i | \(0.522312\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −328362. | − | 127856.i | −0.378838 | − | 0.147510i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −413967. | + | 493346.i | −0.475556 | + | 0.566746i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −738058. | − | 4.18574e6i | −0.844243 | − | 4.78794i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −382818. | − | 139334.i | −0.436027 | − | 0.158701i | 0.114675 | − | 0.993403i | \(-0.463417\pi\) |
−0.550701 | + | 0.834702i | \(0.685640\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 370273. | + | 213777.i | 0.419943 | + | 0.242454i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 388427. | + | 462909.i | 0.438662 | + | 0.522777i | 0.939401 | − | 0.342821i | \(-0.111383\pi\) |
−0.500738 | + | 0.865599i | \(0.666938\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 729573. | − | 421219.i | 0.820438 | − | 0.473680i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −1.07527e6 | − | 189600.i | −1.20408 | − | 0.212312i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −433842. | + | 157906.i | −0.483762 | + | 0.176075i | −0.572376 | − | 0.819991i | \(-0.693978\pi\) |
0.0886142 | + | 0.996066i | \(0.471756\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 108187.i | 0.120127i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 996853. | 1.10222 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 280335. | + | 770214.i | 0.308668 | + | 0.848059i | 0.992917 | + | 0.118810i | \(0.0379080\pi\) |
−0.684249 | + | 0.729249i | \(0.739870\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 319900. | − | 1.81424e6i | 0.350758 | − | 1.98925i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −815817. | − | 1.41304e6i | −0.890777 | − | 1.54287i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 798946. | − | 670395.i | 0.868721 | − | 0.728943i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −444132. | + | 769259.i | −0.480912 | + | 0.832963i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 5511.22 | − | 15142.0i | 0.00594286 | − | 0.0163279i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −1.91357e6 | + | 337414.i | −2.05489 | + | 0.362333i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −679472. | − | 570145.i | −0.726639 | − | 0.609723i | 0.202574 | − | 0.979267i | \(-0.435069\pi\) |
−0.929213 | + | 0.369544i | \(0.879514\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 1.60866e6 | + | 320702.i | 1.71323 | + | 0.341549i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −96323.4 | + | 114794.i | −0.102163 | + | 0.121753i | −0.814703 | − | 0.579878i | \(-0.803100\pi\) |
0.712540 | + | 0.701631i | \(0.247545\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 54928.1 | + | 311513.i | 0.0580188 | + | 0.329041i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 2.51863e6 | + | 916706.i | 2.64945 | + | 0.964319i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −1.01163e6 | − | 584064.i | −1.05982 | − | 0.611887i | −0.134438 | − | 0.990922i | \(-0.542923\pi\) |
−0.925383 | + | 0.379035i | \(0.876256\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1.02194e6 | + | 1.21790e6i | 1.06625 | + | 1.27071i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −111867. | + | 64586.2i | −0.116242 | + | 0.0671123i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 314368. | + | 55431.6i | 0.325336 | + | 0.0573654i | 0.333931 | − | 0.942598i | \(-0.391625\pi\) |
−0.00859514 | + | 0.999963i | \(0.502736\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 577875. | − | 210329.i | 0.595609 | − | 0.216784i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − | 317989.i | − | 0.326421i | ||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 471362. | 0.481905 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −150707. | − | 414063.i | −0.153456 | − | 0.421618i | 0.839013 | − | 0.544112i | \(-0.183133\pi\) |
−0.992469 | + | 0.122493i | \(0.960911\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −113861. | + | 645740.i | −0.115472 | + | 0.654876i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 630260. | + | 1.09164e6i | 0.636610 | + | 1.10264i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −934386. | + | 784043.i | −0.940018 | + | 0.788769i | −0.977588 | − | 0.210525i | \(-0.932483\pi\) |
0.0375705 | + | 0.999294i | \(0.488038\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −305693. | + | 529477.i | −0.306306 | + | 0.530537i |
(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 | 76.5.j.a.41.6 | yes | 42 | |
19.13 | odd | 18 | inner | 76.5.j.a.13.6 | ✓ | 42 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
76.5.j.a.13.6 | ✓ | 42 | 19.13 | odd | 18 | inner | |
76.5.j.a.41.6 | yes | 42 | 1.1 | even | 1 | trivial |