Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [324,4,Mod(37,324)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(324, base_ring=CyclotomicField(18))
chi = DirichletCharacter(H, H._module([0, 14]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("324.37");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 324 = 2^{2} \cdot 3^{4} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 324.i (of order \(9\), degree \(6\), 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: | \(19.1166188419\) |
Analytic rank: | \(0\) |
Dimension: | \(54\) |
Relative dimension: | \(9\) over \(\Q(\zeta_{9})\) |
Twist minimal: | no (minimal twist has level 108) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{9}]$ |
Embedding invariants
Embedding label | 73.2 | ||
Character | \(\chi\) | \(=\) | 324.73 |
Dual form | 324.4.i.a.253.2 |
$q$-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 \(\left(\mathbb{Z}/324\mathbb{Z}\right)^\times\).
\(n\) | \(163\) | \(245\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{5}{9}\right)\) |
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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −8.18465 | + | 6.86774i | −0.732057 | + | 0.614269i | −0.930692 | − | 0.365805i | \(-0.880794\pi\) |
0.198634 | + | 0.980074i | \(0.436349\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −24.4722 | + | 8.90714i | −1.32137 | + | 0.480941i | −0.903898 | − | 0.427748i | \(-0.859307\pi\) |
−0.417475 | + | 0.908688i | \(0.637085\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.555929 | − | 0.466480i | −0.0152381 | − | 0.0127863i | 0.635137 | − | 0.772400i | \(-0.280944\pi\) |
−0.650375 | + | 0.759613i | \(0.725388\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −12.2754 | − | 69.6174i | −0.261892 | − | 1.48526i | −0.777742 | − | 0.628583i | \(-0.783635\pi\) |
0.515851 | − | 0.856678i | \(-0.327476\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 42.6108 | + | 73.8041i | 0.607920 | + | 1.05295i | 0.991583 | + | 0.129475i | \(0.0413293\pi\) |
−0.383662 | + | 0.923473i | \(0.625337\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 75.7224 | − | 131.155i | 0.914311 | − | 1.58363i | 0.106404 | − | 0.994323i | \(-0.466066\pi\) |
0.807907 | − | 0.589310i | \(-0.200600\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 156.978 | + | 57.1353i | 1.42314 | + | 0.517979i | 0.934956 | − | 0.354764i | \(-0.115439\pi\) |
0.488180 | + | 0.872743i | \(0.337661\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.88334 | + | 10.6810i | −0.0150668 | + | 0.0854478i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 42.3122 | − | 239.964i | 0.270937 | − | 1.53656i | −0.480641 | − | 0.876918i | \(-0.659596\pi\) |
0.751578 | − | 0.659644i | \(-0.229293\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 57.5825 | + | 20.9583i | 0.333617 | + | 0.121427i | 0.503397 | − | 0.864055i | \(-0.332083\pi\) |
−0.169780 | + | 0.985482i | \(0.554306\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 139.124 | − | 240.970i | 0.671894 | − | 1.16375i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 7.30212 | + | 12.6477i | 0.0324449 | + | 0.0561962i | 0.881792 | − | 0.471639i | \(-0.156337\pi\) |
−0.849347 | + | 0.527835i | \(0.823004\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 13.2323 | + | 75.0441i | 0.0504034 | + | 0.285852i | 0.999583 | − | 0.0288839i | \(-0.00919530\pi\) |
−0.949179 | + | 0.314735i | \(0.898084\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −152.644 | − | 128.083i | −0.541348 | − | 0.454245i | 0.330650 | − | 0.943753i | \(-0.392732\pi\) |
−0.871999 | + | 0.489508i | \(0.837176\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −252.257 | + | 91.8142i | −0.782884 | + | 0.284946i | −0.702375 | − | 0.711807i | \(-0.747877\pi\) |
−0.0805091 | + | 0.996754i | \(0.525655\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 256.797 | − | 215.478i | 0.748679 | − | 0.628216i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 52.6859 | 0.136546 | 0.0682732 | − | 0.997667i | \(-0.478251\pi\) | ||||
0.0682732 | + | 0.997667i | \(0.478251\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 7.75374 | 0.0190093 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 575.596 | − | 482.982i | 1.27010 | − | 1.06574i | 0.275576 | − | 0.961279i | \(-0.411131\pi\) |
0.994529 | − | 0.104465i | \(-0.0333130\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −34.9282 | + | 12.7128i | −0.0733130 | + | 0.0266838i | −0.378416 | − | 0.925636i | \(-0.623531\pi\) |
0.305103 | + | 0.952319i | \(0.401309\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 578.584 | + | 485.490i | 1.10407 | + | 0.926424i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −88.9446 | − | 504.430i | −0.162184 | − | 0.919790i | −0.951921 | − | 0.306344i | \(-0.900894\pi\) |
0.789737 | − | 0.613445i | \(-0.210217\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −298.140 | − | 516.394i | −0.498349 | − | 0.863165i | 0.501649 | − | 0.865071i | \(-0.332727\pi\) |
−0.999998 | + | 0.00190566i | \(0.999393\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 187.698 | − | 325.103i | 0.300937 | − | 0.521239i | −0.675411 | − | 0.737441i | \(-0.736034\pi\) |
0.976349 | + | 0.216203i | \(0.0693672\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 17.7598 | + | 6.46403i | 0.0262846 | + | 0.00956682i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 61.3493 | − | 347.929i | 0.0873714 | − | 0.495508i | −0.909448 | − | 0.415817i | \(-0.863496\pi\) |
0.996820 | − | 0.0796906i | \(-0.0253932\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −14.6810 | + | 83.2603i | −0.0194151 | + | 0.110109i | −0.992975 | − | 0.118322i | \(-0.962248\pi\) |
0.973560 | + | 0.228431i | \(0.0733595\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −855.622 | − | 311.421i | −1.09183 | − | 0.397392i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 351.204 | − | 608.304i | 0.418287 | − | 0.724495i | −0.577480 | − | 0.816405i | \(-0.695964\pi\) |
0.995767 | + | 0.0919098i | \(0.0292971\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 920.499 | + | 1594.35i | 1.06038 | + | 1.83663i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 280.977 | + | 1593.50i | 0.303449 | + | 1.72094i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 10.3720 | + | 8.70312i | 0.0108569 | + | 0.00910998i | 0.648200 | − | 0.761470i | \(-0.275522\pi\) |
−0.637343 | + | 0.770580i | \(0.719967\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1713.61 | + | 623.703i | −1.68822 | + | 0.614463i | −0.994400 | − | 0.105683i | \(-0.966297\pi\) |
−0.693823 | + | 0.720146i | \(0.744075\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 547.583 | − | 459.477i | 0.523834 | − | 0.439549i | −0.342132 | − | 0.939652i | \(-0.611149\pi\) |
0.865966 | + | 0.500103i | \(0.166704\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1919.61 | 1.73435 | 0.867175 | − | 0.498004i | \(-0.165934\pi\) | ||||
0.867175 | + | 0.498004i | \(0.165934\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −49.6874 | −0.0436623 | −0.0218311 | − | 0.999762i | \(-0.506950\pi\) | ||||
−0.0218311 | + | 0.999762i | \(0.506950\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1232.86 | + | 1034.49i | −1.02635 | + | 0.861208i | −0.990412 | − | 0.138146i | \(-0.955886\pi\) |
−0.0359359 | + | 0.999354i | \(0.511441\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1677.20 | + | 610.450i | −1.36000 | + | 0.494998i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1700.16 | − | 1426.61i | −1.30970 | − | 1.09896i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −231.034 | − | 1310.26i | −0.173579 | − | 0.984418i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −725.708 | − | 1256.96i | −0.519275 | − | 0.899410i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 410.415 | − | 710.860i | 0.286760 | − | 0.496682i | −0.686275 | − | 0.727342i | \(-0.740755\pi\) |
0.973034 | + | 0.230660i | \(0.0740886\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 586.240 | + | 213.374i | 0.390993 | + | 0.142310i | 0.530033 | − | 0.847977i | \(-0.322180\pi\) |
−0.139040 | + | 0.990287i | \(0.544402\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −684.875 | + | 3884.12i | −0.446513 | + | 2.53230i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −211.268 | + | 1198.16i | −0.131751 | + | 0.747194i | 0.845317 | + | 0.534265i | \(0.179412\pi\) |
−0.977068 | + | 0.212929i | \(0.931700\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −26.9027 | − | 9.79178i | −0.0164162 | − | 0.00597502i | 0.333799 | − | 0.942644i | \(-0.391669\pi\) |
−0.350215 | + | 0.936669i | \(0.613892\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −25.6508 | + | 44.4286i | −0.0150002 | + | 0.0259811i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1301.70 | + | 2254.61i | 0.745520 | + | 1.29128i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 154.781 | + | 877.807i | 0.0851017 | + | 0.482636i | 0.997335 | + | 0.0729639i | \(0.0232458\pi\) |
−0.912233 | + | 0.409672i | \(0.865643\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −222.292 | − | 186.525i | −0.119800 | − | 0.100525i | 0.580919 | − | 0.813961i | \(-0.302693\pi\) |
−0.700720 | + | 0.713437i | \(0.747138\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −615.229 | + | 223.925i | −0.318815 | + | 0.116039i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1213.97 | + | 1018.64i | −0.617104 | + | 0.517812i | −0.896892 | − | 0.442250i | \(-0.854180\pi\) |
0.279788 | + | 0.960062i | \(0.409736\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −4350.50 | −2.12961 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 3469.70 | 1.66729 | 0.833643 | − | 0.552304i | \(-0.186251\pi\) | ||||
0.833643 | + | 0.552304i | \(0.186251\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1868.59 | − | 1567.93i | 0.865843 | − | 0.726529i | −0.0973754 | − | 0.995248i | \(-0.531045\pi\) |
0.963219 | + | 0.268719i | \(0.0866003\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2631.39 | + | 957.749i | −1.19772 | + | 0.435935i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −2917.03 | − | 2447.68i | −1.28195 | − | 1.07569i | −0.992972 | − | 0.118351i | \(-0.962239\pi\) |
−0.288981 | − | 0.957335i | \(-0.593316\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −49.0475 | − | 278.162i | −0.0211865 | − | 0.120155i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 157.552 | + | 272.889i | 0.0657878 | + | 0.113948i | 0.897043 | − | 0.441943i | \(-0.145711\pi\) |
−0.831255 | + | 0.555891i | \(0.812377\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1920.99 | + | 3327.25i | −0.788873 | + | 1.36637i | 0.137785 | + | 0.990462i | \(0.456002\pi\) |
−0.926658 | + | 0.375906i | \(0.877331\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −146.626 | − | 53.3675i | −0.0582711 | − | 0.0212090i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 10.7395 | − | 60.9069i | 0.00419974 | − | 0.0238179i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −436.206 | + | 2473.85i | −0.165250 | + | 0.937180i | 0.783556 | + | 0.621321i | \(0.213404\pi\) |
−0.948806 | + | 0.315859i | \(0.897707\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 3588.62 | + | 1306.15i | 1.33842 | + | 0.487144i | 0.909314 | − | 0.416111i | \(-0.136607\pi\) |
0.429104 | + | 0.903255i | \(0.358829\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1819.27 | − | 3151.06i | 0.657957 | − | 1.13961i | −0.323187 | − | 0.946335i | \(-0.604754\pi\) |
0.981144 | − | 0.193279i | \(-0.0619123\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1745.94 | − | 3024.05i | −0.621941 | − | 1.07723i | −0.989124 | − | 0.147085i | \(-0.953011\pi\) |
0.367183 | − | 0.930149i | \(-0.380322\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1101.93 | + | 6249.33i | 0.380986 | + | 2.16068i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −623.685 | − | 523.334i | −0.212488 | − | 0.178299i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −103.277 | + | 37.5899i | −0.0341811 | + | 0.0124409i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3627.33 | − | 3043.69i | 1.18349 | − | 0.993062i | 0.183536 | − | 0.983013i | \(-0.441246\pi\) |
0.999950 | − | 0.0100489i | \(-0.00319870\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 2128.98 | 0.675327 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1595.85 | −0.499232 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 4614.99 | − | 3872.43i | 1.40469 | − | 1.17868i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 590.712 | − | 215.002i | 0.177386 | − | 0.0645631i | −0.251800 | − | 0.967779i | \(-0.581023\pi\) |
0.429186 | + | 0.903216i | \(0.358800\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 994.390 | + | 834.392i | 0.290749 | + | 0.243967i | 0.776481 | − | 0.630140i | \(-0.217003\pi\) |
−0.485732 | + | 0.874108i | \(0.661447\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 101.719 | + | 576.874i | 0.0293526 | + | 0.166467i | 0.995960 | − | 0.0897934i | \(-0.0286207\pi\) |
−0.966608 | + | 0.256260i | \(0.917510\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 423.007 | + | 732.669i | 0.118936 | + | 0.206003i | 0.919346 | − | 0.393449i | \(-0.128718\pi\) |
−0.800410 | + | 0.599453i | \(0.795385\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1434.08 | − | 2483.90i | 0.398082 | − | 0.689498i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −3912.58 | − | 1424.06i | −1.05893 | − | 0.385419i | −0.246903 | − | 0.969040i | \(-0.579413\pi\) |
−0.812026 | + | 0.583621i | \(0.801635\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 982.311 | − | 5570.96i | 0.262557 | − | 1.48903i | −0.513346 | − | 0.858182i | \(-0.671594\pi\) |
0.775903 | − | 0.630852i | \(-0.217295\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −621.945 | + | 3527.23i | −0.162182 | + | 0.919780i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −10060.2 | − | 3661.61i | −2.59156 | − | 0.943251i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 185.584 | − | 321.441i | 0.0466692 | − | 0.0808334i | −0.841747 | − | 0.539872i | \(-0.818473\pi\) |
0.888416 | + | 0.459039i | \(0.151806\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −60.6160 | − | 104.990i | −0.0150628 | − | 0.0260896i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 523.583 | + | 2969.39i | 0.127083 | + | 0.720721i | 0.980049 | + | 0.198755i | \(0.0636899\pi\) |
−0.852967 | + | 0.521965i | \(0.825199\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −291.353 | − | 244.474i | −0.0698989 | − | 0.0586521i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 3971.62 | − | 1445.55i | 0.931182 | − | 0.338922i | 0.168504 | − | 0.985701i | \(-0.446106\pi\) |
0.762678 | + | 0.646778i | \(0.223884\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −431.215 | + | 361.832i | −0.0999598 | + | 0.0838762i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 1948.75 | 0.441700 | 0.220850 | − | 0.975308i | \(-0.429117\pi\) | ||||
0.220850 | + | 0.975308i | \(0.429117\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 6235.43 | 1.39769 | 0.698847 | − | 0.715271i | \(-0.253697\pi\) | ||||
0.698847 | + | 0.715271i | \(0.253697\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 6.02946 | − | 5.05932i | 0.00132215 | − | 0.00110941i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2656.36 | − | 966.836i | 0.576192 | − | 0.209717i | −0.0374534 | − | 0.999298i | \(-0.511925\pi\) |
0.613646 | + | 0.789582i | \(0.289702\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1579.35 | + | 1325.24i | 0.335290 | + | 0.281341i | 0.794851 | − | 0.606805i | \(-0.207549\pi\) |
−0.459561 | + | 0.888146i | \(0.651993\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1178.94 | − | 6686.12i | −0.247636 | − | 1.40441i | −0.814291 | − | 0.580457i | \(-0.802874\pi\) |
0.566656 | − | 0.823955i | \(-0.308237\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −992.252 | − | 1718.63i | −0.204079 | − | 0.353476i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1174.87 | + | 2034.93i | −0.239134 | + | 0.414192i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −4133.18 | − | 1504.35i | −0.824105 | − | 0.299950i | −0.104668 | − | 0.994507i | \(-0.533378\pi\) |
−0.719437 | + | 0.694557i | \(0.755600\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1394.05 | + | 7906.08i | −0.275136 | + | 1.56037i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 2050.64 | − | 11629.8i | 0.396627 | − | 2.24938i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 4876.39 | + | 1774.86i | 0.933788 | + | 0.339871i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 198.567 | − | 343.927i | 0.0372783 | − | 0.0645679i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 489.447 | + | 847.746i | 0.0909909 | + | 0.157601i | 0.907928 | − | 0.419125i | \(-0.137663\pi\) |
−0.816937 | + | 0.576726i | \(0.804330\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −571.383 | − | 3240.47i | −0.104181 | − | 0.590837i | −0.991544 | − | 0.129767i | \(-0.958577\pi\) |
0.887364 | − | 0.461070i | \(-0.152534\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −591.666 | − | 496.467i | −0.106847 | − | 0.0896549i | 0.587799 | − | 0.809007i | \(-0.299994\pi\) |
−0.694646 | + | 0.719352i | \(0.744439\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −657.562 | + | 239.333i | −0.116506 | + | 0.0424046i | −0.399615 | − | 0.916683i | \(-0.630856\pi\) |
0.283109 | + | 0.959088i | \(0.408634\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −135.461 | + | 113.665i | −0.0237754 | + | 0.0199500i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 12906.4 | 2.22331 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 766.701 | 0.130858 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 5355.49 | − | 4493.79i | 0.897439 | − | 0.753041i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 5019.41 | − | 1826.92i | 0.833509 | − | 0.303373i | 0.110211 | − | 0.993908i | \(-0.464847\pi\) |
0.723298 | + | 0.690536i | \(0.242625\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 4192.27 | + | 3517.73i | 0.683726 | + | 0.573714i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 571.369 | + | 3240.40i | 0.0923575 | + | 0.523785i | 0.995525 | + | 0.0944973i | \(0.0301244\pi\) |
−0.903168 | + | 0.429288i | \(0.858765\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −22.2351 | − | 38.5124i | −0.00353109 | − | 0.00611602i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 101.247 | − | 175.365i | 0.0159383 | − | 0.0276059i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −4481.59 | − | 1631.16i | −0.693326 | − | 0.252350i | −0.0287674 | − | 0.999586i | \(-0.509158\pi\) |
−0.664559 | + | 0.747236i | \(0.731380\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 2217.09 | − | 12573.7i | 0.340052 | − | 1.92853i | −0.0300695 | − | 0.999548i | \(-0.509573\pi\) |
0.370122 | − | 0.928983i | \(-0.379316\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 337.891 | − | 1916.28i | 0.0509465 | − | 0.288932i | −0.948681 | − | 0.316236i | \(-0.897581\pi\) |
0.999627 | + | 0.0273036i | \(0.00869208\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 5986.63 | + | 2178.96i | 0.895035 | + | 0.325766i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −3268.90 | + | 5661.90i | −0.480573 | + | 0.832378i | −0.999752 | − | 0.0222884i | \(-0.992905\pi\) |
0.519178 | + | 0.854666i | \(0.326238\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −8038.26 | − | 13922.7i | −1.17193 | − | 2.02984i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 696.477 | + | 3949.91i | 0.0998774 | + | 0.566433i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 4978.80 | + | 4177.71i | 0.708150 | + | 0.594209i | 0.924079 | − | 0.382200i | \(-0.124834\pi\) |
−0.215929 | + | 0.976409i | \(0.569278\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1289.34 | + | 469.280i | −0.180429 | + | 0.0656707i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −7933.62 | + | 6657.10i | −1.10131 | + | 0.924106i | −0.997512 | − | 0.0704931i | \(-0.977543\pi\) |
−0.103794 | + | 0.994599i | \(0.533098\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −17225.1 | −2.35315 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −12857.0 | −1.74254 | −0.871268 | − | 0.490807i | \(-0.836702\pi\) | ||||
−0.871268 | + | 0.490807i | \(0.836702\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 1960.38 | − | 1644.96i | 0.261543 | − | 0.219461i | −0.502581 | − | 0.864530i | \(-0.667616\pi\) |
0.764124 | + | 0.645070i | \(0.223172\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −189.751 | + | 69.0637i | −0.0251184 | + | 0.00914236i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 8568.05 | + | 7189.45i | 1.11675 | + | 0.937068i | 0.998436 | − | 0.0559072i | \(-0.0178051\pi\) |
0.118319 | + | 0.992976i | \(0.462250\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2472.14 | + | 14020.2i | 0.319748 | + | 1.81338i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 1887.36 | + | 3269.01i | 0.240414 | + | 0.416410i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −1143.34 | + | 1980.33i | −0.144541 | + | 0.250352i | −0.929202 | − | 0.369573i | \(-0.879504\pi\) |
0.784661 | + | 0.619926i | \(0.212837\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −12492.1 | − | 4546.76i | −1.55568 | − | 0.566220i | −0.585935 | − | 0.810358i | \(-0.699273\pi\) |
−0.969740 | + | 0.244138i | \(0.921495\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 752.214 | − | 4266.02i | 0.0929788 | − | 0.527309i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1.84041 | − | 10.4375i | 0.000224142 | − | 0.00127117i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 4155.16 | + | 1512.36i | 0.502346 | + | 0.182839i | 0.580749 | − | 0.814083i | \(-0.302760\pi\) |
−0.0784028 | + | 0.996922i | \(0.524982\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −9784.09 | + | 16946.5i | −1.16572 | + | 2.01909i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −451.651 | − | 782.282i | −0.0534233 | − | 0.0925318i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 1861.24 | + | 10555.6i | 0.217011 | + | 1.23073i | 0.877383 | + | 0.479790i | \(0.159287\pi\) |
−0.660373 | + | 0.750938i | \(0.729602\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −3381.05 | − | 2837.04i | −0.391406 | − | 0.328429i | 0.425754 | − | 0.904839i | \(-0.360009\pi\) |
−0.817161 | + | 0.576410i | \(0.804453\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −868.551 | + | 316.127i | −0.0991316 | + | 0.0360809i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 741.533 | − | 622.220i | 0.0840406 | − | 0.0705184i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −12301.2 | −1.37477 | −0.687385 | − | 0.726293i | \(-0.741242\pi\) | ||||
−0.687385 | + | 0.726293i | \(0.741242\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −8467.47 | −0.939770 | −0.469885 | − | 0.882728i | \(-0.655705\pi\) | ||||
−0.469885 | + | 0.882728i | \(0.655705\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 19380.3 | − | 16262.0i | 2.12148 | − | 1.78013i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −1628.97 | + | 592.898i | −0.177100 | + | 0.0644590i | −0.429048 | − | 0.903282i | \(-0.641151\pi\) |
0.251948 | + | 0.967741i | \(0.418929\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −6356.76 | − | 5333.96i | −0.681758 | − | 0.572063i | 0.234761 | − | 0.972053i | \(-0.424569\pi\) |
−0.916519 | + | 0.399990i | \(0.869014\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1303.19 | + | 7390.73i | 0.138825 | + | 0.787313i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 7397.73 | + | 12813.2i | 0.777551 | + | 1.34676i | 0.933350 | + | 0.358968i | \(0.116871\pi\) |
−0.155799 | + | 0.987789i | \(0.549795\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 27.6503 | − | 47.8918i | 0.00288692 | − | 0.00500030i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −18483.5 | − | 6727.46i | −1.90444 | − | 0.693161i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1618.87 | + | 9181.09i | −0.165706 | + | 0.939767i | 0.782627 | + | 0.622491i | \(0.213879\pi\) |
−0.948333 | + | 0.317276i | \(0.897232\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 889.156 | − | 5042.65i | 0.0898311 | − | 0.509457i | −0.906378 | − | 0.422467i | \(-0.861164\pi\) |
0.996209 | − | 0.0869899i | \(-0.0277248\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −863.470 | − | 314.277i | −0.0866714 | − | 0.0315458i | 0.298321 | − | 0.954466i | \(-0.403574\pi\) |
−0.384992 | + | 0.922920i | \(0.625796\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 2802.50 | − | 4854.08i | 0.277697 | − | 0.480985i | −0.693115 | − | 0.720827i | \(-0.743762\pi\) |
0.970812 | + | 0.239842i | \(0.0770956\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 6669.70 | + | 11552.3i | 0.656669 | + | 1.13738i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 25.1108 | + | 142.411i | 0.00244101 | + | 0.0138436i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1258.25 | + | 1055.80i | 0.121542 | + | 0.101986i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 8793.16 | − | 3200.45i | 0.838768 | − | 0.305286i | 0.113315 | − | 0.993559i | \(-0.463853\pi\) |
0.725452 | + | 0.688273i | \(0.241631\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 790.860 | − | 663.610i | 0.0749691 | − | 0.0629065i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −144.662 | −0.0135438 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −5274.19 | −0.490752 | −0.245376 | − | 0.969428i | \(-0.578911\pi\) | ||||
−0.245376 | + | 0.969428i | \(0.578911\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −10145.4 | + | 8513.01i | −0.932497 | + | 0.782458i | −0.976264 | − | 0.216584i | \(-0.930508\pi\) |
0.0437671 | + | 0.999042i | \(0.486064\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 19513.3 | − | 7102.27i | 1.78263 | − | 0.648824i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 11895.7 | + | 9981.71i | 1.07364 | + | 0.900887i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 1209.51 | + | 6859.46i | 0.108507 | + | 0.615374i | 0.989761 | + | 0.142732i | \(0.0455886\pi\) |
−0.881254 | + | 0.472642i | \(0.843300\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 297.634 | + | 515.517i | 0.0263834 | + | 0.0456974i | 0.878916 | − | 0.476977i | \(-0.158268\pi\) |
−0.852532 | + | 0.522675i | \(0.824934\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 9741.86 | − | 16873.4i | 0.858430 | − | 1.48684i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −18230.3 | − | 6635.30i | −1.58752 | − | 0.577809i | −0.610695 | − | 0.791866i | \(-0.709110\pi\) |
−0.976821 | + | 0.214057i | \(0.931332\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1697.65 | + | 9627.83i | −0.146966 | + | 0.833484i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −1326.21 | + | 7521.31i | −0.113475 | + | 0.643550i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 183.067 | + | 66.6308i | 0.0155730 | + | 0.00566812i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 2437.03 | − | 4221.05i | 0.204929 | − | 0.354948i | −0.745181 | − | 0.666862i | \(-0.767637\pi\) |
0.950110 | + | 0.311915i | \(0.100970\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 4980.61 | + | 8626.67i | 0.416419 | + | 0.721258i | 0.995576 | − | 0.0939573i | \(-0.0299517\pi\) |
−0.579158 | + | 0.815216i | \(0.696618\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 906.828 | + | 5142.88i | 0.0749565 | + | 0.425099i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 12057.1 | + | 10117.1i | 0.990970 | + | 0.831523i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 5061.94 | − | 1842.40i | 0.411364 | − | 0.149724i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −15711.3 | + | 13183.4i | −1.26964 | + | 1.06536i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −243.277 | −0.0194410 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −20408.9 | −1.62190 | −0.810948 | − | 0.585118i | \(-0.801048\pi\) | ||||
−0.810948 | + | 0.585118i | \(0.801048\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 406.674 | − | 341.240i | 0.0319633 | − | 0.0268204i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −15260.6 | + | 5554.42i | −1.19287 | + | 0.434168i | −0.860729 | − | 0.509064i | \(-0.829992\pi\) |
−0.332137 | + | 0.943231i | \(0.607770\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −28268.6 | − | 23720.1i | −2.18563 | − | 1.83396i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1597.71 | + | 9061.04i | 0.122860 | + | 0.696771i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −4689.68 | − | 8122.76i | −0.356747 | − | 0.617904i | 0.630668 | − | 0.776052i | \(-0.282781\pi\) |
−0.987415 | + | 0.158149i | \(0.949447\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −7043.07 | + | 12199.0i | −0.532898 | + | 0.923007i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −10092.1 | − | 3673.21i | −0.755471 | − | 0.274969i | −0.0645648 | − | 0.997914i | \(-0.520566\pi\) |
−0.690906 | + | 0.722945i | \(0.742788\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 2985.89 | − | 16933.9i | 0.222332 | − | 1.26091i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −13.7609 | + | 78.0417i | −0.00101386 | + | 0.00574987i | −0.985310 | − | 0.170773i | \(-0.945374\pi\) |
0.984297 | + | 0.176522i | \(0.0564848\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −17084.1 | − | 6218.11i | −1.25210 | − | 0.455726i | −0.370988 | − | 0.928638i | \(-0.620981\pi\) |
−0.881110 | + | 0.472911i | \(0.843203\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −905.904 | + | 1569.07i | −0.0657023 | + | 0.113800i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −2781.75 | − | 4818.13i | −0.200703 | − | 0.347628i | 0.748052 | − | 0.663640i | \(-0.230989\pi\) |
−0.948755 | + | 0.316012i | \(0.897656\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −382.335 | − | 2168.33i | −0.0273011 | − | 0.154832i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −29.2896 | − | 24.5769i | −0.00208070 | − | 0.00174592i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 2307.80 | − | 839.972i | 0.162271 | − | 0.0590619i | −0.259607 | − | 0.965714i | \(-0.583593\pi\) |
0.421879 | + | 0.906652i | \(0.361371\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 7109.08 | − | 5965.22i | 0.497325 | − | 0.417305i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 17323.9 | 1.19967 | 0.599837 | − | 0.800122i | \(-0.295232\pi\) | ||||
0.599837 | + | 0.800122i | \(0.295232\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 23712.8 | 1.63383 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −1054.57 | + | 884.892i | −0.0719344 | + | 0.0603601i | −0.678046 | − | 0.735020i | \(-0.737173\pi\) |
0.606112 | + | 0.795380i | \(0.292729\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 16841.2 | − | 6129.69i | 1.14304 | − | 0.416032i | 0.300029 | − | 0.953930i | \(-0.403004\pi\) |
0.843010 | + | 0.537898i | \(0.180781\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 10889.5 | + | 9137.34i | 0.731768 | + | 0.614026i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −4434.77 | − | 25150.8i | −0.296543 | − | 1.68178i | −0.660862 | − | 0.750507i | \(-0.729809\pi\) |
0.364319 | − | 0.931274i | \(-0.381302\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 9488.44 | + | 16434.5i | 0.628251 | + | 1.08816i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −6521.06 | + | 11294.8i | −0.429662 | + | 0.744197i | −0.996843 | − | 0.0793963i | \(-0.974701\pi\) |
0.567181 | + | 0.823593i | \(0.308034\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 21565.7 | + | 7849.26i | 1.40713 | + | 0.512154i | 0.930287 | − | 0.366833i | \(-0.119558\pi\) |
0.476845 | + | 0.878987i | \(0.341780\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 1776.31 | − | 10073.9i | 0.115341 | − | 0.654129i | −0.871240 | − | 0.490857i | \(-0.836684\pi\) |
0.986581 | − | 0.163273i | \(-0.0522050\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −3176.49 | + | 18014.7i | −0.204275 | + | 1.15850i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 13298.2 | + | 4840.15i | 0.851085 | + | 0.309770i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −622.299 | + | 1077.85i | −0.0394478 | + | 0.0683257i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −3681.07 | − | 6375.79i | −0.232236 | − | 0.402245i | 0.726230 | − | 0.687452i | \(-0.241271\pi\) |
−0.958466 | + | 0.285207i | \(0.907937\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 1522.89 | + | 8636.76i | 0.0951720 | + | 0.539747i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −18153.3 | − | 15232.5i | −1.12914 | − | 0.947460i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 27630.6 | − | 10056.7i | 1.70256 | − | 0.619683i | 0.706451 | − | 0.707762i | \(-0.250295\pi\) |
0.996114 | + | 0.0880788i | \(0.0280727\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 15587.5 | − | 13079.5i | 0.956004 | − | 0.802182i | −0.0242947 | − | 0.999705i | \(-0.507734\pi\) |
0.980298 | + | 0.197523i | \(0.0632896\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 6586.91 | 0.400244 | 0.200122 | − | 0.979771i | \(-0.435866\pi\) | ||||
0.200122 | + | 0.979771i | \(0.435866\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −545.291 | −0.0329808 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 15535.4 | − | 13035.7i | 0.931004 | − | 0.781205i | −0.0449934 | − | 0.998987i | \(-0.514327\pi\) |
0.975997 | + | 0.217782i | \(0.0698822\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −6263.56 | + | 2279.75i | −0.373645 | + | 0.135996i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 8105.40 | + | 6801.23i | 0.479122 | + | 0.402031i | 0.850109 | − | 0.526607i | \(-0.176536\pi\) |
−0.370987 | + | 0.928638i | \(0.620981\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −2105.13 | − | 11938.8i | −0.123873 | − | 0.702518i | −0.981971 | − | 0.189032i | \(-0.939465\pi\) |
0.858098 | − | 0.513486i | \(-0.171646\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −21069.6 | − | 36493.7i | −1.22864 | − | 2.12807i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 20352.5 | − | 35251.6i | 1.18149 | − | 2.04640i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 25.3478 | + | 9.22586i | 0.00145833 | + | 0.000530790i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1997.23 | − | 11326.8i | 0.114395 | − | 0.648764i | −0.872654 | − | 0.488340i | \(-0.837603\pi\) |
0.987048 | − | 0.160424i | \(-0.0512862\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −1826.50 | + | 10358.6i | −0.103690 | + | 0.588055i | 0.888045 | + | 0.459756i | \(0.152063\pi\) |
−0.991735 | + | 0.128300i | \(0.959048\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −331.345 | − | 120.600i | −0.0187273 | − | 0.00681619i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −2489.30 | + | 4311.59i | −0.139459 | + | 0.241550i | −0.927292 | − | 0.374339i | \(-0.877870\pi\) |
0.787833 | + | 0.615889i | \(0.211203\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −6499.49 | − | 11257.4i | −0.362529 | − | 0.627919i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −646.741 | − | 3667.85i | −0.0357604 | − | 0.202807i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 5474.46 | + | 4593.62i | 0.301387 | + | 0.252893i | 0.780921 | − | 0.624630i | \(-0.214750\pi\) |
−0.479534 | + | 0.877523i | \(0.659194\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 287.436 | − | 104.618i | 0.0156879 | − | 0.00570993i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −4974.72 | + | 4174.29i | −0.270346 | + | 0.226847i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 2134.56 | 0.115009 | 0.0575044 | − | 0.998345i | \(-0.481686\pi\) | ||||
0.0575044 | + | 0.998345i | \(0.481686\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 2211.74 | 0.118659 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 36380.3 | − | 30526.7i | 1.93525 | − | 1.62387i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −10970.4 | + | 3992.90i | −0.581103 | + | 0.211504i | −0.615812 | − | 0.787893i | \(-0.711172\pi\) |
0.0347089 | + | 0.999397i | \(0.488950\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 7841.72 | + | 6579.98i | 0.411886 | + | 0.345613i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −95.1805 | − | 539.795i | −0.00497839 | − | 0.0282338i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 3341.98 | + | 5788.48i | 0.173345 | + | 0.300242i | 0.939587 | − | 0.342310i | \(-0.111209\pi\) |
−0.766242 | + | 0.642552i | \(0.777876\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −9307.92 | + | 16121.8i | −0.480784 | + | 0.832742i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 2483.37 | + | 903.872i | 0.127214 | + | 0.0463020i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −4870.25 | + | 27620.6i | −0.248456 | + | 1.40907i | 0.563871 | + | 0.825863i | \(0.309312\pi\) |
−0.812327 | + | 0.583202i | \(0.801799\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 2948.80 | − | 16723.5i | 0.149200 | − | 0.846157i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 27055.3 | + | 9847.32i | 1.36331 | + | 0.496206i | 0.917078 | − | 0.398709i | \(-0.130542\pi\) |
0.446237 | + | 0.894915i | \(0.352764\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −185.859 | + | 321.918i | −0.00928930 | + | 0.0160895i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 2190.75 | + | 3794.49i | 0.109050 | + | 0.188880i | 0.915386 | − | 0.402578i | \(-0.131886\pi\) |
−0.806336 | + | 0.591458i | \(0.798552\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 5769.87 | + | 32722.6i | 0.284894 | + | 1.61571i | 0.705664 | + | 0.708546i | \(0.250649\pi\) |
−0.420770 | + | 0.907167i | \(0.638240\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −7295.38 | − | 6121.55i | −0.358768 | − | 0.301042i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −46977.0 | + | 17098.2i | −2.29172 | + | 0.834119i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −4666.53 | + | 3915.68i | −0.226743 | + | 0.190260i | −0.749081 | − | 0.662479i | \(-0.769504\pi\) |
0.522338 | + | 0.852739i | \(0.325060\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 3100.39 | 0.149450 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −234.359 | −0.0112522 | −0.00562610 | − | 0.999984i | \(-0.501791\pi\) | ||||
−0.00562610 | + | 0.999984i | \(0.501791\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −5554.52 | + | 4660.79i | −0.264587 | + | 0.222015i | −0.765423 | − | 0.643527i | \(-0.777470\pi\) |
0.500836 | + | 0.865542i | \(0.333026\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1215.96 | − | 442.573i | 0.0576942 | − | 0.0209990i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −40689.7 | − | 34142.7i | −1.91554 | − | 1.60733i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −2924.93 | − | 16588.1i | −0.137160 | − | 0.777871i | −0.973331 | − | 0.229403i | \(-0.926323\pi\) |
0.836172 | − | 0.548467i | \(-0.184789\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 95.1463 | + | 164.798i | 0.00442713 | + | 0.00766802i | 0.868230 | − | 0.496161i | \(-0.165257\pi\) |
−0.863803 | + | 0.503829i | \(0.831924\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −332.303 | + | 575.566i | −0.0154022 | + | 0.0266773i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 10844.4 | + | 3947.04i | 0.498769 | + | 0.181537i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −75.1426 | + | 426.155i | −0.00344278 | + | 0.0195250i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 2940.16 | − | 16674.5i | 0.133680 | − | 0.758136i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −25173.0 | − | 9162.21i | −1.14018 | − | 0.414990i | −0.298200 | − | 0.954503i | \(-0.596386\pi\) |
−0.841977 | + | 0.539513i | \(0.818608\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 20956.3 | − | 36297.4i | 0.941999 | − | 1.63159i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1313.79 | + | 2275.55i | 0.0588324 | + | 0.101901i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 4724.22 | + | 26792.4i | 0.209963 | + | 1.19076i | 0.889437 | + | 0.457058i | \(0.151097\pi\) |
−0.679474 | + | 0.733700i | \(0.737792\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −17525.2 | − | 14705.4i | −0.775965 | − | 0.651112i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −256.001 | + | 93.1766i | −0.0112504 | + | 0.00409481i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 35607.3 | − | 29878.1i | 1.55900 | − | 1.30815i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −623.745 | −0.0271072 | −0.0135536 | − | 0.999908i | \(-0.504314\pi\) | ||||
−0.0135536 | + | 0.999908i | \(0.504314\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 43605.5 | 1.88803 | 0.944017 | − | 0.329896i | \(-0.107014\pi\) | ||||
0.944017 | + | 0.329896i | \(0.107014\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −28398.2 | + | 23828.9i | −1.22055 | + | 1.02416i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −28357.4 | + | 10321.2i | −1.21432 | + | 0.441976i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −3888.07 | − | 3262.48i | −0.165279 | − | 0.138686i | 0.556397 | − | 0.830917i | \(-0.312184\pi\) |
−0.721676 | + | 0.692231i | \(0.756628\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 2079.11 | + | 11791.2i | 0.0880598 | + | 0.499412i | 0.996654 | + | 0.0817325i | \(0.0260453\pi\) |
−0.908595 | + | 0.417679i | \(0.862844\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 5343.27 | + | 9254.81i | 0.224672 | + | 0.389143i | 0.956221 | − | 0.292646i | \(-0.0945357\pi\) |
−0.731549 | + | 0.681789i | \(0.761202\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −162.955 | + | 282.246i | −0.00682710 | + | 0.0118249i | −0.869419 | − | 0.494076i | \(-0.835506\pi\) |
0.862592 | + | 0.505901i | \(0.168840\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 26845.5 | + | 9770.97i | 1.11662 | + | 0.406415i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −4525.60 | + | 25666.0i | −0.187563 | + | 1.06372i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 5536.19 | − | 31397.3i | 0.227808 | − | 1.29196i | −0.629437 | − | 0.777051i | \(-0.716714\pi\) |
0.857245 | − | 0.514909i | \(-0.172174\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −32874.5 | − | 11965.3i | −1.34792 | − | 0.490604i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 14959.5 | − | 25910.6i | 0.609019 | − | 1.05485i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 17324.6 | + | 30007.1i | 0.702810 | + | 1.21730i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 423.645 | + | 2402.61i | 0.0170651 | + | 0.0967807i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 15404.7 | + | 12926.1i | 0.618344 | + | 0.518852i | 0.897282 | − | 0.441457i | \(-0.145538\pi\) |
−0.278939 | + | 0.960309i | \(0.589983\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −29990.8 | + | 10915.8i | −1.19541 | + | 0.435094i | −0.861620 | − | 0.507554i | \(-0.830550\pi\) |
−0.333790 | + | 0.942647i | \(0.608328\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −3000.06 | + | 2517.35i | −0.119163 | + | 0.0999893i | −0.700422 | − | 0.713729i | \(-0.747005\pi\) |
0.581259 | + | 0.813719i | \(0.302560\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −10871.7 | −0.428826 | −0.214413 | − | 0.976743i | \(-0.568784\pi\) | ||||
−0.214413 | + | 0.976743i | \(0.568784\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 40684.9 | 1.59922 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −196.408 | + | 164.806i | −0.00766706 | + | 0.00643343i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −34025.3 | + | 12384.2i | −1.32365 | + | 0.481770i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 28955.6 | + | 24296.6i | 1.11872 | + | 0.938716i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −583.987 | − | 3311.96i | −0.0224856 | − | 0.127522i | 0.971499 | − | 0.237045i | \(-0.0761788\pi\) |
−0.993984 | + | 0.109523i | \(0.965068\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −3132.17 | − | 5425.07i | −0.119779 | − | 0.207464i | 0.799901 | − | 0.600132i | \(-0.204885\pi\) |
−0.919680 | + | 0.392669i | \(0.871552\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −11471.9 | + | 19869.9i | −0.437214 | + | 0.757277i | −0.997473 | − | 0.0710403i | \(-0.977368\pi\) |
0.560259 | + | 0.828317i | \(0.310701\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −29550.4 | − | 10755.5i | −1.11861 | − | 0.407140i | −0.284464 | − | 0.958687i | \(-0.591815\pi\) |
−0.834144 | + | 0.551547i | \(0.814038\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −3712.02 | + | 21051.9i | −0.140042 | + | 0.794217i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −7059.65 | + | 40037.2i | −0.264549 | + | 1.50033i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −3163.64 | − | 1151.47i | −0.118155 | − | 0.0430049i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 7465.70 | − | 12931.0i | 0.276969 | − | 0.479724i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2244.99 | + | 3888.43i | 0.0830093 | + | 0.143776i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −7128.06 | − | 40425.2i | −0.261817 | − | 1.48484i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 36556.9 | + | 30674.9i | 1.33832 | + | 1.12298i | 0.982055 | + | 0.188594i | \(0.0603932\pi\) |
0.356261 | + | 0.934386i | \(0.384051\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −36942.9 | + | 13446.1i | −1.34355 | + | 0.489012i | −0.910928 | − | 0.412564i | \(-0.864633\pi\) |
−0.432620 | + | 0.901576i | \(0.642411\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 47.0008 | − | 39.4384i | 0.00170373 | − | 0.00142960i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −16247.1 | −0.585090 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 7346.12 | 0.263684 | 0.131842 | − | 0.991271i | \(-0.457911\pi\) | ||||
0.131842 | + | 0.991271i | \(0.457911\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −32290.2 | + | 27094.7i | −1.15151 | + | 0.966234i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −148.842 | + | 54.1740i | −0.00529069 | + | 0.00192565i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 11537.2 | + | 9680.83i | 0.407451 | + | 0.341892i | 0.823365 | − | 0.567512i | \(-0.192094\pi\) |
−0.415914 | + | 0.909404i | \(0.636538\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −8815.77 | − | 49996.7i | −0.310339 | − | 1.76002i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 330.393 | + | 572.258i | 0.0115562 | + | 0.0200159i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −16943.9 | + | 29347.8i | −0.590752 | + | 1.02321i | 0.403379 | + | 0.915033i | \(0.367836\pi\) |
−0.994131 | + | 0.108180i | \(0.965498\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 48190.4 | + | 17539.9i | 1.66946 | + | 0.607634i | 0.991807 | − | 0.127746i | \(-0.0407743\pi\) |
0.677654 | + | 0.735381i | \(0.262997\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −2210.49 | + | 12536.3i | −0.0763344 | + | 0.432914i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −1862.24 | + | 10561.3i | −0.0639015 | + | 0.362404i | 0.936043 | + | 0.351885i | \(0.114459\pi\) |
−0.999945 | + | 0.0105183i | \(0.996652\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −24936.9 | − | 9076.29i | −0.852989 | − | 0.310462i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −17911.1 | + | 31022.9i | −0.608810 | + | 1.05449i | 0.382626 | + | 0.923903i | \(0.375020\pi\) |
−0.991437 | + | 0.130587i | \(0.958314\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −13419.5 | − | 23243.3i | −0.454708 | − | 0.787577i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −5501.99 | − | 31203.3i | −0.185264 | − | 1.05069i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −19944.7 | − | 16735.6i | −0.669489 | − | 0.561768i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −38341.9 | + | 13955.3i | −1.27904 | + | 0.465531i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −14813.8 | + | 12430.3i | −0.492637 | + | 0.413372i | −0.854970 | − | 0.518677i | \(-0.826425\pi\) |
0.362333 | + | 0.932049i | \(0.381980\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 13651.7 | 0.451190 | 0.225595 | − | 0.974221i | \(-0.427567\pi\) | ||||
0.225595 | + | 0.974221i | \(0.427567\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 745.584 | 0.0245656 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −35656.0 | + | 29918.9i | −1.16759 | + | 0.979724i | −0.999981 | − | 0.00612912i | \(-0.998049\pi\) |
−0.167609 | + | 0.985854i | \(0.553605\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −479.006 | + | 174.344i | −0.0156375 | + | 0.00569158i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −7929.62 | − | 6653.74i | −0.257290 | − | 0.215892i | 0.505014 | − | 0.863111i | \(-0.331487\pi\) |
−0.762304 | + | 0.647219i | \(0.775932\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 6750.61 | + | 38284.6i | 0.218368 | + | 1.23842i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −16643.6 | − | 28827.6i | −0.535123 | − | 0.926860i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −12434.4 | + | 21537.0i | −0.398579 | + | 0.690359i | −0.993551 | − | 0.113387i | \(-0.963830\pi\) |
0.594972 | + | 0.803747i | \(0.297163\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 35058.3 | + | 12760.2i | 1.11701 | + | 0.406557i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 6107.02 | − | 34634.6i | 0.193993 | − | 1.10019i | −0.719852 | − | 0.694128i | \(-0.755790\pi\) |
0.913845 | − | 0.406063i | \(-0.133099\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(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 | 324.4.i.a.73.2 | 54 | ||
3.2 | odd | 2 | 108.4.i.a.25.2 | yes | 54 | ||
27.13 | even | 9 | inner | 324.4.i.a.253.2 | 54 | ||
27.14 | odd | 18 | 108.4.i.a.13.2 | ✓ | 54 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
108.4.i.a.13.2 | ✓ | 54 | 27.14 | odd | 18 | ||
108.4.i.a.25.2 | yes | 54 | 3.2 | odd | 2 | ||
324.4.i.a.73.2 | 54 | 1.1 | even | 1 | trivial | ||
324.4.i.a.253.2 | 54 | 27.13 | even | 9 | inner |