Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [975,2,Mod(274,975)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(975, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("975.274");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 975 = 3 \cdot 5^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 975.c (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(7.78541419707\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.0.399424.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 2x^{5} + 3x^{4} - 6x^{3} + 6x^{2} - 8x + 8 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | no (minimal twist has level 195) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 274.2 | ||
Root | \(-0.671462 + 1.24464i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 975.274 |
Dual form | 975.2.c.i.274.5 |
$q$-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 \(\left(\mathbb{Z}/975\mathbb{Z}\right)^\times\).
\(n\) | \(301\) | \(326\) | \(352\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − 2.48929i | − 1.76019i | −0.474795 | − | 0.880096i | \(-0.657478\pi\) | ||||
0.474795 | − | 0.880096i | \(-0.342522\pi\) | |||||||
\(3\) | 1.00000i | 0.577350i | ||||||||
\(4\) | −4.19656 | −2.09828 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 2.48929 | 1.01625 | ||||||||
\(7\) | − 1.19656i | − 0.452256i | −0.974098 | − | 0.226128i | \(-0.927393\pi\) | ||||
0.974098 | − | 0.226128i | \(-0.0726068\pi\) | |||||||
\(8\) | 5.46787i | 1.93318i | ||||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.19656 | −0.360776 | −0.180388 | − | 0.983596i | \(-0.557735\pi\) | ||||
−0.180388 | + | 0.983596i | \(0.557735\pi\) | |||||||
\(12\) | − 4.19656i | − 1.21144i | ||||||||
\(13\) | − 1.00000i | − 0.277350i | ||||||||
\(14\) | −2.97858 | −0.796058 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 5.21798 | 1.30450 | ||||||||
\(17\) | 6.17513i | 1.49769i | 0.662745 | + | 0.748845i | \(0.269391\pi\) | ||||
−0.662745 | + | 0.748845i | \(0.730609\pi\) | |||||||
\(18\) | 2.48929i | 0.586731i | ||||||||
\(19\) | −6.97858 | −1.60100 | −0.800498 | − | 0.599336i | \(-0.795431\pi\) | ||||
−0.800498 | + | 0.599336i | \(0.795431\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.19656 | 0.261110 | ||||||||
\(22\) | 2.97858i | 0.635035i | ||||||||
\(23\) | − 4.17513i | − 0.870576i | −0.900291 | − | 0.435288i | \(-0.856647\pi\) | ||||
0.900291 | − | 0.435288i | \(-0.143353\pi\) | |||||||
\(24\) | −5.46787 | −1.11612 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −2.48929 | −0.488190 | ||||||||
\(27\) | − 1.00000i | − 0.192450i | ||||||||
\(28\) | 5.02142i | 0.948960i | ||||||||
\(29\) | −6.00000 | −1.11417 | −0.557086 | − | 0.830455i | \(-0.688081\pi\) | ||||
−0.557086 | + | 0.830455i | \(0.688081\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.97858 | −0.534968 | −0.267484 | − | 0.963562i | \(-0.586192\pi\) | ||||
−0.267484 | + | 0.963562i | \(0.586192\pi\) | |||||||
\(32\) | − 2.05333i | − 0.362980i | ||||||||
\(33\) | − 1.19656i | − 0.208294i | ||||||||
\(34\) | 15.3717 | 2.63622 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 4.19656 | 0.699426 | ||||||||
\(37\) | 7.78202i | 1.27936i | 0.768643 | + | 0.639678i | \(0.220932\pi\) | ||||
−0.768643 | + | 0.639678i | \(0.779068\pi\) | |||||||
\(38\) | 17.3717i | 2.81806i | ||||||||
\(39\) | 1.00000 | 0.160128 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −6.17513 | −0.964394 | −0.482197 | − | 0.876063i | \(-0.660161\pi\) | ||||
−0.482197 | + | 0.876063i | \(0.660161\pi\) | |||||||
\(42\) | − 2.97858i | − 0.459604i | ||||||||
\(43\) | 9.95715i | 1.51845i | 0.650827 | + | 0.759226i | \(0.274422\pi\) | ||||
−0.650827 | + | 0.759226i | \(0.725578\pi\) | |||||||
\(44\) | 5.02142 | 0.757008 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −10.3931 | −1.53238 | ||||||||
\(47\) | − 1.02142i | − 0.148990i | −0.997221 | − | 0.0744949i | \(-0.976266\pi\) | ||||
0.997221 | − | 0.0744949i | \(-0.0237345\pi\) | |||||||
\(48\) | 5.21798i | 0.753151i | ||||||||
\(49\) | 5.56825 | 0.795464 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −6.17513 | −0.864692 | ||||||||
\(52\) | 4.19656i | 0.581958i | ||||||||
\(53\) | − 10.1751i | − 1.39766i | −0.715287 | − | 0.698831i | \(-0.753704\pi\) | ||||
0.715287 | − | 0.698831i | \(-0.246296\pi\) | |||||||
\(54\) | −2.48929 | −0.338749 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 6.54262 | 0.874294 | ||||||||
\(57\) | − 6.97858i | − 0.924335i | ||||||||
\(58\) | 14.9357i | 1.96116i | ||||||||
\(59\) | −5.37169 | −0.699335 | −0.349667 | − | 0.936874i | \(-0.613705\pi\) | ||||
−0.349667 | + | 0.936874i | \(0.613705\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 12.5682 | 1.60920 | 0.804600 | − | 0.593818i | \(-0.202380\pi\) | ||||
0.804600 | + | 0.593818i | \(0.202380\pi\) | |||||||
\(62\) | 7.41454i | 0.941647i | ||||||||
\(63\) | 1.19656i | 0.150752i | ||||||||
\(64\) | 5.32464 | 0.665579 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −2.97858 | −0.366638 | ||||||||
\(67\) | 9.37169i | 1.14493i | 0.819928 | + | 0.572467i | \(0.194014\pi\) | ||||
−0.819928 | + | 0.572467i | \(0.805986\pi\) | |||||||
\(68\) | − 25.9143i | − 3.14257i | ||||||||
\(69\) | 4.17513 | 0.502627 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −5.19656 | −0.616718 | −0.308359 | − | 0.951270i | \(-0.599780\pi\) | ||||
−0.308359 | + | 0.951270i | \(0.599780\pi\) | |||||||
\(72\) | − 5.46787i | − 0.644394i | ||||||||
\(73\) | 11.9572i | 1.39948i | 0.714398 | + | 0.699740i | \(0.246701\pi\) | ||||
−0.714398 | + | 0.699740i | \(0.753299\pi\) | |||||||
\(74\) | 19.3717 | 2.25191 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 29.2860 | 3.35933 | ||||||||
\(77\) | 1.43175i | 0.163163i | ||||||||
\(78\) | − 2.48929i | − 0.281856i | ||||||||
\(79\) | 1.78202 | 0.200493 | 0.100246 | − | 0.994963i | \(-0.468037\pi\) | ||||
0.100246 | + | 0.994963i | \(0.468037\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 15.3717i | 1.69752i | ||||||||
\(83\) | 5.37169i | 0.589620i | 0.955556 | + | 0.294810i | \(0.0952563\pi\) | ||||
−0.955556 | + | 0.294810i | \(0.904744\pi\) | |||||||
\(84\) | −5.02142 | −0.547882 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 24.7862 | 2.67277 | ||||||||
\(87\) | − 6.00000i | − 0.643268i | ||||||||
\(88\) | − 6.54262i | − 0.697445i | ||||||||
\(89\) | −10.1751 | −1.07856 | −0.539281 | − | 0.842126i | \(-0.681304\pi\) | ||||
−0.539281 | + | 0.842126i | \(0.681304\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.19656 | −0.125433 | ||||||||
\(92\) | 17.5212i | 1.82671i | ||||||||
\(93\) | − 2.97858i | − 0.308864i | ||||||||
\(94\) | −2.54262 | −0.262251 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 2.05333 | 0.209567 | ||||||||
\(97\) | − 1.82487i | − 0.185287i | −0.995699 | − | 0.0926435i | \(-0.970468\pi\) | ||||
0.995699 | − | 0.0926435i | \(-0.0295317\pi\) | |||||||
\(98\) | − 13.8610i | − 1.40017i | ||||||||
\(99\) | 1.19656 | 0.120259 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −10.3503 | −1.02989 | −0.514945 | − | 0.857223i | \(-0.672188\pi\) | ||||
−0.514945 | + | 0.857223i | \(0.672188\pi\) | |||||||
\(102\) | 15.3717i | 1.52202i | ||||||||
\(103\) | − 18.7434i | − 1.84684i | −0.383790 | − | 0.923420i | \(-0.625381\pi\) | ||||
0.383790 | − | 0.923420i | \(-0.374619\pi\) | |||||||
\(104\) | 5.46787 | 0.536168 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −25.3288 | −2.46016 | ||||||||
\(107\) | − 18.5682i | − 1.79506i | −0.440953 | − | 0.897530i | \(-0.645359\pi\) | ||||
0.440953 | − | 0.897530i | \(-0.354641\pi\) | |||||||
\(108\) | 4.19656i | 0.403814i | ||||||||
\(109\) | −8.39312 | −0.803915 | −0.401957 | − | 0.915658i | \(-0.631670\pi\) | ||||
−0.401957 | + | 0.915658i | \(0.631670\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −7.78202 | −0.738637 | ||||||||
\(112\) | − 6.24361i | − 0.589966i | ||||||||
\(113\) | − 7.95715i | − 0.748546i | −0.927319 | − | 0.374273i | \(-0.877892\pi\) | ||||
0.927319 | − | 0.374273i | \(-0.122108\pi\) | |||||||
\(114\) | −17.3717 | −1.62701 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 25.1793 | 2.33784 | ||||||||
\(117\) | 1.00000i | 0.0924500i | ||||||||
\(118\) | 13.3717i | 1.23096i | ||||||||
\(119\) | 7.38890 | 0.677340 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −9.56825 | −0.869841 | ||||||||
\(122\) | − 31.2860i | − 2.83250i | ||||||||
\(123\) | − 6.17513i | − 0.556793i | ||||||||
\(124\) | 12.4998 | 1.12251 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 2.97858 | 0.265353 | ||||||||
\(127\) | − 10.3931i | − 0.922240i | −0.887338 | − | 0.461120i | \(-0.847448\pi\) | ||||
0.887338 | − | 0.461120i | \(-0.152552\pi\) | |||||||
\(128\) | − 17.3612i | − 1.53453i | ||||||||
\(129\) | −9.95715 | −0.876679 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −6.39312 | −0.558569 | −0.279285 | − | 0.960208i | \(-0.590097\pi\) | ||||
−0.279285 | + | 0.960208i | \(0.590097\pi\) | |||||||
\(132\) | 5.02142i | 0.437059i | ||||||||
\(133\) | 8.35027i | 0.724060i | ||||||||
\(134\) | 23.3288 | 2.01531 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −33.7648 | −2.89531 | ||||||||
\(137\) | 16.7434i | 1.43048i | 0.698877 | + | 0.715242i | \(0.253684\pi\) | ||||
−0.698877 | + | 0.715242i | \(0.746316\pi\) | |||||||
\(138\) | − 10.3931i | − 0.884721i | ||||||||
\(139\) | −5.78202 | −0.490424 | −0.245212 | − | 0.969469i | \(-0.578858\pi\) | ||||
−0.245212 | + | 0.969469i | \(0.578858\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.02142 | 0.0860193 | ||||||||
\(142\) | 12.9357i | 1.08554i | ||||||||
\(143\) | 1.19656i | 0.100061i | ||||||||
\(144\) | −5.21798 | −0.434832 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 29.7648 | 2.46335 | ||||||||
\(147\) | 5.56825i | 0.459262i | ||||||||
\(148\) | − 32.6577i | − 2.68445i | ||||||||
\(149\) | −15.3461 | −1.25720 | −0.628599 | − | 0.777730i | \(-0.716371\pi\) | ||||
−0.628599 | + | 0.777730i | \(0.716371\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −8.58546 | −0.698675 | −0.349337 | − | 0.936997i | \(-0.613593\pi\) | ||||
−0.349337 | + | 0.936997i | \(0.613593\pi\) | |||||||
\(152\) | − 38.1579i | − 3.09502i | ||||||||
\(153\) | − 6.17513i | − 0.499230i | ||||||||
\(154\) | 3.56404 | 0.287198 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −4.19656 | −0.335994 | ||||||||
\(157\) | 2.78623i | 0.222365i | 0.993800 | + | 0.111183i | \(0.0354639\pi\) | ||||
−0.993800 | + | 0.111183i | \(0.964536\pi\) | |||||||
\(158\) | − 4.43596i | − 0.352906i | ||||||||
\(159\) | 10.1751 | 0.806941 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −4.99579 | −0.393723 | ||||||||
\(162\) | − 2.48929i | − 0.195577i | ||||||||
\(163\) | − 8.76060i | − 0.686183i | −0.939302 | − | 0.343091i | \(-0.888526\pi\) | ||||
0.939302 | − | 0.343091i | \(-0.111474\pi\) | |||||||
\(164\) | 25.9143 | 2.02357 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 13.3717 | 1.03784 | ||||||||
\(167\) | − 17.3717i | − 1.34426i | −0.740432 | − | 0.672131i | \(-0.765379\pi\) | ||||
0.740432 | − | 0.672131i | \(-0.234621\pi\) | |||||||
\(168\) | 6.54262i | 0.504774i | ||||||||
\(169\) | −1.00000 | −0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 6.97858 | 0.533665 | ||||||||
\(172\) | − 41.7858i | − 3.18614i | ||||||||
\(173\) | 7.95715i | 0.604971i | 0.953154 | + | 0.302486i | \(0.0978164\pi\) | ||||
−0.953154 | + | 0.302486i | \(0.902184\pi\) | |||||||
\(174\) | −14.9357 | −1.13227 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −6.24361 | −0.470630 | ||||||||
\(177\) | − 5.37169i | − 0.403761i | ||||||||
\(178\) | 25.3288i | 1.89848i | ||||||||
\(179\) | 15.5640 | 1.16331 | 0.581655 | − | 0.813435i | \(-0.302405\pi\) | ||||
0.581655 | + | 0.813435i | \(0.302405\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 15.7820 | 1.17307 | 0.586534 | − | 0.809925i | \(-0.300492\pi\) | ||||
0.586534 | + | 0.809925i | \(0.300492\pi\) | |||||||
\(182\) | 2.97858i | 0.220787i | ||||||||
\(183\) | 12.5682i | 0.929072i | ||||||||
\(184\) | 22.8291 | 1.68298 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −7.41454 | −0.543660 | ||||||||
\(187\) | − 7.38890i | − 0.540330i | ||||||||
\(188\) | 4.28646i | 0.312622i | ||||||||
\(189\) | −1.19656 | −0.0870368 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 10.7434 | 0.777364 | 0.388682 | − | 0.921372i | \(-0.372930\pi\) | ||||
0.388682 | + | 0.921372i | \(0.372930\pi\) | |||||||
\(192\) | 5.32464i | 0.384272i | ||||||||
\(193\) | − 9.73917i | − 0.701041i | −0.936555 | − | 0.350521i | \(-0.886005\pi\) | ||||
0.936555 | − | 0.350521i | \(-0.113995\pi\) | |||||||
\(194\) | −4.54262 | −0.326141 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −23.3675 | −1.66911 | ||||||||
\(197\) | − 9.56404i | − 0.681410i | −0.940170 | − | 0.340705i | \(-0.889334\pi\) | ||||
0.940170 | − | 0.340705i | \(-0.110666\pi\) | |||||||
\(198\) | − 2.97858i | − 0.211678i | ||||||||
\(199\) | −5.95715 | −0.422291 | −0.211146 | − | 0.977455i | \(-0.567719\pi\) | ||||
−0.211146 | + | 0.977455i | \(0.567719\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −9.37169 | −0.661028 | ||||||||
\(202\) | 25.7648i | 1.81281i | ||||||||
\(203\) | 7.17935i | 0.503891i | ||||||||
\(204\) | 25.9143 | 1.81436 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −46.6577 | −3.25080 | ||||||||
\(207\) | 4.17513i | 0.290192i | ||||||||
\(208\) | − 5.21798i | − 0.361802i | ||||||||
\(209\) | 8.35027 | 0.577600 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 23.9143 | 1.64633 | 0.823164 | − | 0.567803i | \(-0.192206\pi\) | ||||
0.823164 | + | 0.567803i | \(0.192206\pi\) | |||||||
\(212\) | 42.7005i | 2.93269i | ||||||||
\(213\) | − 5.19656i | − 0.356062i | ||||||||
\(214\) | −46.2217 | −3.15965 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 5.46787 | 0.372041 | ||||||||
\(217\) | 3.56404i | 0.241943i | ||||||||
\(218\) | 20.8929i | 1.41504i | ||||||||
\(219\) | −11.9572 | −0.807990 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 6.17513 | 0.415385 | ||||||||
\(222\) | 19.3717i | 1.30014i | ||||||||
\(223\) | − 2.62831i | − 0.176004i | −0.996120 | − | 0.0880022i | \(-0.971952\pi\) | ||||
0.996120 | − | 0.0880022i | \(-0.0280483\pi\) | |||||||
\(224\) | −2.45692 | −0.164160 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −19.8077 | −1.31759 | ||||||||
\(227\) | 15.7648i | 1.04635i | 0.852226 | + | 0.523174i | \(0.175252\pi\) | ||||
−0.852226 | + | 0.523174i | \(0.824748\pi\) | |||||||
\(228\) | 29.2860i | 1.93951i | ||||||||
\(229\) | −8.74338 | −0.577779 | −0.288890 | − | 0.957362i | \(-0.593286\pi\) | ||||
−0.288890 | + | 0.957362i | \(0.593286\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1.43175 | −0.0942022 | ||||||||
\(232\) | − 32.8072i | − 2.15390i | ||||||||
\(233\) | 2.17513i | 0.142498i | 0.997459 | + | 0.0712489i | \(0.0226985\pi\) | ||||
−0.997459 | + | 0.0712489i | \(0.977302\pi\) | |||||||
\(234\) | 2.48929 | 0.162730 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 22.5426 | 1.46740 | ||||||||
\(237\) | 1.78202i | 0.115755i | ||||||||
\(238\) | − 18.3931i | − 1.19225i | ||||||||
\(239\) | −2.80344 | −0.181340 | −0.0906698 | − | 0.995881i | \(-0.528901\pi\) | ||||
−0.0906698 | + | 0.995881i | \(0.528901\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −6.00000 | −0.386494 | −0.193247 | − | 0.981150i | \(-0.561902\pi\) | ||||
−0.193247 | + | 0.981150i | \(0.561902\pi\) | |||||||
\(242\) | 23.8181i | 1.53109i | ||||||||
\(243\) | 1.00000i | 0.0641500i | ||||||||
\(244\) | −52.7434 | −3.37655 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −15.3717 | −0.980063 | ||||||||
\(247\) | 6.97858i | 0.444036i | ||||||||
\(248\) | − 16.2865i | − 1.03419i | ||||||||
\(249\) | −5.37169 | −0.340417 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −23.9143 | −1.50946 | −0.754729 | − | 0.656037i | \(-0.772232\pi\) | ||||
−0.754729 | + | 0.656037i | \(0.772232\pi\) | |||||||
\(252\) | − 5.02142i | − 0.316320i | ||||||||
\(253\) | 4.99579i | 0.314083i | ||||||||
\(254\) | −25.8715 | −1.62332 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −32.5678 | −2.03549 | ||||||||
\(257\) | − 19.9572i | − 1.24489i | −0.782662 | − | 0.622447i | \(-0.786139\pi\) | ||||
0.782662 | − | 0.622447i | \(-0.213861\pi\) | |||||||
\(258\) | 24.7862i | 1.54312i | ||||||||
\(259\) | 9.31163 | 0.578597 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 6.00000 | 0.371391 | ||||||||
\(262\) | 15.9143i | 0.983189i | ||||||||
\(263\) | − 8.00000i | − 0.493301i | −0.969104 | − | 0.246651i | \(-0.920670\pi\) | ||||
0.969104 | − | 0.246651i | \(-0.0793300\pi\) | |||||||
\(264\) | 6.54262 | 0.402670 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 20.7862 | 1.27449 | ||||||||
\(267\) | − 10.1751i | − 0.622708i | ||||||||
\(268\) | − 39.3288i | − 2.40239i | ||||||||
\(269\) | 2.35027 | 0.143298 | 0.0716492 | − | 0.997430i | \(-0.477174\pi\) | ||||
0.0716492 | + | 0.997430i | \(0.477174\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 10.9786 | 0.666901 | 0.333451 | − | 0.942768i | \(-0.391787\pi\) | ||||
0.333451 | + | 0.942768i | \(0.391787\pi\) | |||||||
\(272\) | 32.2217i | 1.95373i | ||||||||
\(273\) | − 1.19656i | − 0.0724190i | ||||||||
\(274\) | 41.6791 | 2.51793 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −17.5212 | −1.05465 | ||||||||
\(277\) | 1.21377i | 0.0729283i | 0.999335 | + | 0.0364642i | \(0.0116095\pi\) | ||||
−0.999335 | + | 0.0364642i | \(0.988391\pi\) | |||||||
\(278\) | 14.3931i | 0.863242i | ||||||||
\(279\) | 2.97858 | 0.178323 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 11.9572 | 0.713304 | 0.356652 | − | 0.934237i | \(-0.383918\pi\) | ||||
0.356652 | + | 0.934237i | \(0.383918\pi\) | |||||||
\(282\) | − 2.54262i | − 0.151411i | ||||||||
\(283\) | 29.8715i | 1.77567i | 0.460158 | + | 0.887837i | \(0.347793\pi\) | ||||
−0.460158 | + | 0.887837i | \(0.652207\pi\) | |||||||
\(284\) | 21.8077 | 1.29405 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 2.97858 | 0.176127 | ||||||||
\(287\) | 7.38890i | 0.436153i | ||||||||
\(288\) | 2.05333i | 0.120993i | ||||||||
\(289\) | −21.1323 | −1.24308 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1.82487 | 0.106975 | ||||||||
\(292\) | − 50.1789i | − 2.93650i | ||||||||
\(293\) | − 0.777809i | − 0.0454401i | −0.999742 | − | 0.0227200i | \(-0.992767\pi\) | ||||
0.999742 | − | 0.0227200i | \(-0.00723263\pi\) | |||||||
\(294\) | 13.8610 | 0.808389 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −42.5510 | −2.47323 | ||||||||
\(297\) | 1.19656i | 0.0694313i | ||||||||
\(298\) | 38.2008i | 2.21291i | ||||||||
\(299\) | −4.17513 | −0.241454 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 11.9143 | 0.686729 | ||||||||
\(302\) | 21.3717i | 1.22980i | ||||||||
\(303\) | − 10.3503i | − 0.594607i | ||||||||
\(304\) | −36.4141 | −2.08849 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | −15.3717 | −0.878741 | ||||||||
\(307\) | 0.760597i | 0.0434095i | 0.999764 | + | 0.0217048i | \(0.00690939\pi\) | ||||
−0.999764 | + | 0.0217048i | \(0.993091\pi\) | |||||||
\(308\) | − 6.00842i | − 0.342362i | ||||||||
\(309\) | 18.7434 | 1.06627 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −23.1281 | −1.31147 | −0.655736 | − | 0.754990i | \(-0.727642\pi\) | ||||
−0.655736 | + | 0.754990i | \(0.727642\pi\) | |||||||
\(312\) | 5.46787i | 0.309557i | ||||||||
\(313\) | 33.9143i | 1.91695i | 0.285176 | + | 0.958475i | \(0.407948\pi\) | ||||
−0.285176 | + | 0.958475i | \(0.592052\pi\) | |||||||
\(314\) | 6.93573 | 0.391406 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −7.47835 | −0.420690 | ||||||||
\(317\) | 9.64973i | 0.541983i | 0.962582 | + | 0.270991i | \(0.0873515\pi\) | ||||
−0.962582 | + | 0.270991i | \(0.912648\pi\) | |||||||
\(318\) | − 25.3288i | − 1.42037i | ||||||||
\(319\) | 7.17935 | 0.401966 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 18.5682 | 1.03638 | ||||||||
\(322\) | 12.4360i | 0.693029i | ||||||||
\(323\) | − 43.0937i | − 2.39780i | ||||||||
\(324\) | −4.19656 | −0.233142 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −21.8077 | −1.20781 | ||||||||
\(327\) | − 8.39312i | − 0.464140i | ||||||||
\(328\) | − 33.7648i | − 1.86435i | ||||||||
\(329\) | −1.22219 | −0.0673816 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 15.3288 | 0.842550 | 0.421275 | − | 0.906933i | \(-0.361583\pi\) | ||||
0.421275 | + | 0.906933i | \(0.361583\pi\) | |||||||
\(332\) | − 22.5426i | − 1.23719i | ||||||||
\(333\) | − 7.78202i | − 0.426452i | ||||||||
\(334\) | −43.2432 | −2.36616 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 6.24361 | 0.340617 | ||||||||
\(337\) | − 22.3503i | − 1.21750i | −0.793363 | − | 0.608748i | \(-0.791672\pi\) | ||||
0.793363 | − | 0.608748i | \(-0.208328\pi\) | |||||||
\(338\) | 2.48929i | 0.135399i | ||||||||
\(339\) | 7.95715 | 0.432173 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 3.56404 | 0.193004 | ||||||||
\(342\) | − 17.3717i | − 0.939354i | ||||||||
\(343\) | − 15.0386i | − 0.812010i | ||||||||
\(344\) | −54.4444 | −2.93544 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 19.8077 | 1.06487 | ||||||||
\(347\) | − 5.78202i | − 0.310395i | −0.987883 | − | 0.155198i | \(-0.950399\pi\) | ||||
0.987883 | − | 0.155198i | \(-0.0496014\pi\) | |||||||
\(348\) | 25.1793i | 1.34975i | ||||||||
\(349\) | 27.5212 | 1.47318 | 0.736588 | − | 0.676342i | \(-0.236436\pi\) | ||||
0.736588 | + | 0.676342i | \(0.236436\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.00000 | −0.0533761 | ||||||||
\(352\) | 2.45692i | 0.130955i | ||||||||
\(353\) | 28.7434i | 1.52986i | 0.644116 | + | 0.764928i | \(0.277225\pi\) | ||||
−0.644116 | + | 0.764928i | \(0.722775\pi\) | |||||||
\(354\) | −13.3717 | −0.710697 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 42.7005 | 2.26312 | ||||||||
\(357\) | 7.38890i | 0.391062i | ||||||||
\(358\) | − 38.7434i | − 2.04765i | ||||||||
\(359\) | 12.5855 | 0.664235 | 0.332118 | − | 0.943238i | \(-0.392237\pi\) | ||||
0.332118 | + | 0.943238i | \(0.392237\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 29.7005 | 1.56319 | ||||||||
\(362\) | − 39.2860i | − 2.06483i | ||||||||
\(363\) | − 9.56825i | − 0.502203i | ||||||||
\(364\) | 5.02142 | 0.263194 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 31.2860 | 1.63535 | ||||||||
\(367\) | − 27.9143i | − 1.45712i | −0.684985 | − | 0.728558i | \(-0.740191\pi\) | ||||
0.684985 | − | 0.728558i | \(-0.259809\pi\) | |||||||
\(368\) | − 21.7858i | − 1.13566i | ||||||||
\(369\) | 6.17513 | 0.321465 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −12.1751 | −0.632102 | ||||||||
\(372\) | 12.4998i | 0.648083i | ||||||||
\(373\) | 2.35027i | 0.121692i | 0.998147 | + | 0.0608462i | \(0.0193799\pi\) | ||||
−0.998147 | + | 0.0608462i | \(0.980620\pi\) | |||||||
\(374\) | −18.3931 | −0.951085 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 5.58500 | 0.288025 | ||||||||
\(377\) | 6.00000i | 0.309016i | ||||||||
\(378\) | 2.97858i | 0.153201i | ||||||||
\(379\) | −24.5510 | −1.26110 | −0.630551 | − | 0.776148i | \(-0.717171\pi\) | ||||
−0.630551 | + | 0.776148i | \(0.717171\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 10.3931 | 0.532455 | ||||||||
\(382\) | − 26.7434i | − 1.36831i | ||||||||
\(383\) | − 5.80765i | − 0.296757i | −0.988931 | − | 0.148379i | \(-0.952595\pi\) | ||||
0.988931 | − | 0.148379i | \(-0.0474054\pi\) | |||||||
\(384\) | 17.3612 | 0.885961 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −24.2436 | −1.23397 | ||||||||
\(387\) | − 9.95715i | − 0.506151i | ||||||||
\(388\) | 7.65815i | 0.388784i | ||||||||
\(389\) | −13.6497 | −0.692069 | −0.346034 | − | 0.938222i | \(-0.612472\pi\) | ||||
−0.346034 | + | 0.938222i | \(0.612472\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 25.7820 | 1.30385 | ||||||||
\(392\) | 30.4464i | 1.53778i | ||||||||
\(393\) | − 6.39312i | − 0.322490i | ||||||||
\(394\) | −23.8077 | −1.19941 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −5.02142 | −0.252336 | ||||||||
\(397\) | − 12.1323i | − 0.608902i | −0.952528 | − | 0.304451i | \(-0.901527\pi\) | ||||
0.952528 | − | 0.304451i | \(-0.0984730\pi\) | |||||||
\(398\) | 14.8291i | 0.743314i | ||||||||
\(399\) | −8.35027 | −0.418036 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −37.4439 | −1.86986 | −0.934930 | − | 0.354832i | \(-0.884538\pi\) | ||||
−0.934930 | + | 0.354832i | \(0.884538\pi\) | |||||||
\(402\) | 23.3288i | 1.16354i | ||||||||
\(403\) | 2.97858i | 0.148373i | ||||||||
\(404\) | 43.4355 | 2.16100 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 17.8715 | 0.886946 | ||||||||
\(407\) | − 9.31163i | − 0.461561i | ||||||||
\(408\) | − 33.7648i | − 1.67161i | ||||||||
\(409\) | 14.0000 | 0.692255 | 0.346128 | − | 0.938187i | \(-0.387496\pi\) | ||||
0.346128 | + | 0.938187i | \(0.387496\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −16.7434 | −0.825890 | ||||||||
\(412\) | 78.6577i | 3.87519i | ||||||||
\(413\) | 6.42754i | 0.316279i | ||||||||
\(414\) | 10.3931 | 0.510794 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −2.05333 | −0.100673 | ||||||||
\(417\) | − 5.78202i | − 0.283147i | ||||||||
\(418\) | − 20.7862i | − 1.01669i | ||||||||
\(419\) | −3.17935 | −0.155321 | −0.0776606 | − | 0.996980i | \(-0.524745\pi\) | ||||
−0.0776606 | + | 0.996980i | \(0.524745\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −16.3074 | −0.794775 | −0.397388 | − | 0.917651i | \(-0.630083\pi\) | ||||
−0.397388 | + | 0.917651i | \(0.630083\pi\) | |||||||
\(422\) | − 59.5296i | − 2.89786i | ||||||||
\(423\) | 1.02142i | 0.0496633i | ||||||||
\(424\) | 55.6363 | 2.70194 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −12.9357 | −0.626738 | ||||||||
\(427\) | − 15.0386i | − 0.727771i | ||||||||
\(428\) | 77.9227i | 3.76654i | ||||||||
\(429\) | −1.19656 | −0.0577703 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 4.58546 | 0.220874 | 0.110437 | − | 0.993883i | \(-0.464775\pi\) | ||||
0.110437 | + | 0.993883i | \(0.464775\pi\) | |||||||
\(432\) | − 5.21798i | − 0.251050i | ||||||||
\(433\) | 38.3503i | 1.84300i | 0.388383 | + | 0.921498i | \(0.373034\pi\) | ||||
−0.388383 | + | 0.921498i | \(0.626966\pi\) | |||||||
\(434\) | 8.87192 | 0.425866 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 35.2222 | 1.68684 | ||||||||
\(437\) | 29.1365i | 1.39379i | ||||||||
\(438\) | 29.7648i | 1.42222i | ||||||||
\(439\) | −7.73917 | −0.369371 | −0.184685 | − | 0.982798i | \(-0.559127\pi\) | ||||
−0.184685 | + | 0.982798i | \(0.559127\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −5.56825 | −0.265155 | ||||||||
\(442\) | − 15.3717i | − 0.731157i | ||||||||
\(443\) | − 34.9185i | − 1.65903i | −0.558485 | − | 0.829514i | \(-0.688617\pi\) | ||||
0.558485 | − | 0.829514i | \(-0.311383\pi\) | |||||||
\(444\) | 32.6577 | 1.54987 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −6.54262 | −0.309802 | ||||||||
\(447\) | − 15.3461i | − 0.725844i | ||||||||
\(448\) | − 6.37123i | − 0.301012i | ||||||||
\(449\) | 6.17513 | 0.291423 | 0.145711 | − | 0.989327i | \(-0.453453\pi\) | ||||
0.145711 | + | 0.989327i | \(0.453453\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 7.38890 | 0.347930 | ||||||||
\(452\) | 33.3927i | 1.57066i | ||||||||
\(453\) | − 8.58546i | − 0.403380i | ||||||||
\(454\) | 39.2432 | 1.84177 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 38.1579 | 1.78691 | ||||||||
\(457\) | 1.38890i | 0.0649702i | 0.999472 | + | 0.0324851i | \(0.0103421\pi\) | ||||
−0.999472 | + | 0.0324851i | \(0.989658\pi\) | |||||||
\(458\) | 21.7648i | 1.01700i | ||||||||
\(459\) | 6.17513 | 0.288231 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 28.4826 | 1.32657 | 0.663283 | − | 0.748369i | \(-0.269163\pi\) | ||||
0.663283 | + | 0.748369i | \(0.269163\pi\) | |||||||
\(462\) | 3.56404i | 0.165814i | ||||||||
\(463\) | − 16.3759i | − 0.761053i | −0.924770 | − | 0.380526i | \(-0.875743\pi\) | ||||
0.924770 | − | 0.380526i | \(-0.124257\pi\) | |||||||
\(464\) | −31.3079 | −1.45343 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 5.41454 | 0.250824 | ||||||||
\(467\) | 25.7476i | 1.19146i | 0.803186 | + | 0.595728i | \(0.203136\pi\) | ||||
−0.803186 | + | 0.595728i | \(0.796864\pi\) | |||||||
\(468\) | − 4.19656i | − 0.193986i | ||||||||
\(469\) | 11.2138 | 0.517804 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −2.78623 | −0.128383 | ||||||||
\(472\) | − 29.3717i | − 1.35194i | ||||||||
\(473\) | − 11.9143i | − 0.547820i | ||||||||
\(474\) | 4.43596 | 0.203750 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −31.0080 | −1.42125 | ||||||||
\(477\) | 10.1751i | 0.465887i | ||||||||
\(478\) | 6.97858i | 0.319193i | ||||||||
\(479\) | 7.58967 | 0.346781 | 0.173391 | − | 0.984853i | \(-0.444528\pi\) | ||||
0.173391 | + | 0.984853i | \(0.444528\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 7.78202 | 0.354830 | ||||||||
\(482\) | 14.9357i | 0.680304i | ||||||||
\(483\) | − 4.99579i | − 0.227316i | ||||||||
\(484\) | 40.1537 | 1.82517 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 2.48929 | 0.112916 | ||||||||
\(487\) | 4.41033i | 0.199851i | 0.994995 | + | 0.0999255i | \(0.0318604\pi\) | ||||
−0.994995 | + | 0.0999255i | \(0.968140\pi\) | |||||||
\(488\) | 68.7215i | 3.11088i | ||||||||
\(489\) | 8.76060 | 0.396168 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −0.0856914 | −0.00386720 | −0.00193360 | − | 0.999998i | \(-0.500615\pi\) | ||||
−0.00193360 | + | 0.999998i | \(0.500615\pi\) | |||||||
\(492\) | 25.9143i | 1.16831i | ||||||||
\(493\) | − 37.0508i | − 1.66868i | ||||||||
\(494\) | 17.3717 | 0.781589 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −15.5422 | −0.697863 | ||||||||
\(497\) | 6.21798i | 0.278915i | ||||||||
\(498\) | 13.3717i | 0.599200i | ||||||||
\(499\) | 17.7220 | 0.793344 | 0.396672 | − | 0.917960i | \(-0.370165\pi\) | ||||
0.396672 | + | 0.917960i | \(0.370165\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 17.3717 | 0.776110 | ||||||||
\(502\) | 59.5296i | 2.65694i | ||||||||
\(503\) | 8.70054i | 0.387938i | 0.981008 | + | 0.193969i | \(0.0621361\pi\) | ||||
−0.981008 | + | 0.193969i | \(0.937864\pi\) | |||||||
\(504\) | −6.54262 | −0.291431 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 12.4360 | 0.552846 | ||||||||
\(507\) | − 1.00000i | − 0.0444116i | ||||||||
\(508\) | 43.6153i | 1.93512i | ||||||||
\(509\) | 33.3545 | 1.47841 | 0.739206 | − | 0.673480i | \(-0.235201\pi\) | ||||
0.739206 | + | 0.673480i | \(0.235201\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 14.3074 | 0.632923 | ||||||||
\(512\) | 46.3482i | 2.04832i | ||||||||
\(513\) | 6.97858i | 0.308112i | ||||||||
\(514\) | −49.6791 | −2.19125 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 41.7858 | 1.83952 | ||||||||
\(517\) | 1.22219i | 0.0537519i | ||||||||
\(518\) | − 23.1793i | − 1.01844i | ||||||||
\(519\) | −7.95715 | −0.349280 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 18.7005 | 0.819285 | 0.409643 | − | 0.912246i | \(-0.365653\pi\) | ||||
0.409643 | + | 0.912246i | \(0.365653\pi\) | |||||||
\(522\) | − 14.9357i | − 0.653719i | ||||||||
\(523\) | 4.00000i | 0.174908i | 0.996169 | + | 0.0874539i | \(0.0278730\pi\) | ||||
−0.996169 | + | 0.0874539i | \(0.972127\pi\) | |||||||
\(524\) | 26.8291 | 1.17203 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −19.9143 | −0.868305 | ||||||||
\(527\) | − 18.3931i | − 0.801217i | ||||||||
\(528\) | − 6.24361i | − 0.271718i | ||||||||
\(529\) | 5.56825 | 0.242098 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 5.37169 | 0.233112 | ||||||||
\(532\) | − 35.0424i | − 1.51928i | ||||||||
\(533\) | 6.17513i | 0.267475i | ||||||||
\(534\) | −25.3288 | −1.09609 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −51.2432 | −2.21337 | ||||||||
\(537\) | 15.5640i | 0.671638i | ||||||||
\(538\) | − 5.85050i | − 0.252233i | ||||||||
\(539\) | −6.66273 | −0.286984 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −41.5296 | −1.78550 | −0.892749 | − | 0.450555i | \(-0.851226\pi\) | ||||
−0.892749 | + | 0.450555i | \(0.851226\pi\) | |||||||
\(542\) | − 27.3288i | − 1.17387i | ||||||||
\(543\) | 15.7820i | 0.677271i | ||||||||
\(544\) | 12.6796 | 0.543632 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −2.97858 | −0.127471 | ||||||||
\(547\) | − 7.91431i | − 0.338391i | −0.985582 | − | 0.169196i | \(-0.945883\pi\) | ||||
0.985582 | − | 0.169196i | \(-0.0541170\pi\) | |||||||
\(548\) | − 70.2646i | − 3.00155i | ||||||||
\(549\) | −12.5682 | −0.536400 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 41.8715 | 1.78378 | ||||||||
\(552\) | 22.8291i | 0.971670i | ||||||||
\(553\) | − 2.13229i | − 0.0906742i | ||||||||
\(554\) | 3.02142 | 0.128368 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 24.2646 | 1.02905 | ||||||||
\(557\) | 42.7005i | 1.80928i | 0.426177 | + | 0.904640i | \(0.359860\pi\) | ||||
−0.426177 | + | 0.904640i | \(0.640140\pi\) | |||||||
\(558\) | − 7.41454i | − 0.313882i | ||||||||
\(559\) | 9.95715 | 0.421143 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 7.38890 | 0.311960 | ||||||||
\(562\) | − 29.7648i | − 1.25555i | ||||||||
\(563\) | − 1.04706i | − 0.0441282i | −0.999757 | − | 0.0220641i | \(-0.992976\pi\) | ||||
0.999757 | − | 0.0220641i | \(-0.00702379\pi\) | |||||||
\(564\) | −4.28646 | −0.180493 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 74.3587 | 3.12553 | ||||||||
\(567\) | − 1.19656i | − 0.0502507i | ||||||||
\(568\) | − 28.4141i | − 1.19223i | ||||||||
\(569\) | −16.7778 | −0.703362 | −0.351681 | − | 0.936120i | \(-0.614390\pi\) | ||||
−0.351681 | + | 0.936120i | \(0.614390\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −20.6111 | −0.862548 | −0.431274 | − | 0.902221i | \(-0.641936\pi\) | ||||
−0.431274 | + | 0.902221i | \(0.641936\pi\) | |||||||
\(572\) | − 5.02142i | − 0.209956i | ||||||||
\(573\) | 10.7434i | 0.448811i | ||||||||
\(574\) | 18.3931 | 0.767714 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −5.32464 | −0.221860 | ||||||||
\(577\) | 1.38890i | 0.0578208i | 0.999582 | + | 0.0289104i | \(0.00920376\pi\) | ||||
−0.999582 | + | 0.0289104i | \(0.990796\pi\) | |||||||
\(578\) | 52.6044i | 2.18805i | ||||||||
\(579\) | 9.73917 | 0.404746 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 6.42754 | 0.266659 | ||||||||
\(582\) | − 4.54262i | − 0.188298i | ||||||||
\(583\) | 12.1751i | 0.504243i | ||||||||
\(584\) | −65.3801 | −2.70545 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −1.93619 | −0.0799833 | ||||||||
\(587\) | − 0.935731i | − 0.0386218i | −0.999814 | − | 0.0193109i | \(-0.993853\pi\) | ||||
0.999814 | − | 0.0193109i | \(-0.00614723\pi\) | |||||||
\(588\) | − 23.3675i | − 0.963659i | ||||||||
\(589\) | 20.7862 | 0.856482 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 9.56404 | 0.393412 | ||||||||
\(592\) | 40.6064i | 1.66891i | ||||||||
\(593\) | 0.478807i | 0.0196622i | 0.999952 | + | 0.00983112i | \(0.00312939\pi\) | ||||
−0.999952 | + | 0.00983112i | \(0.996871\pi\) | |||||||
\(594\) | 2.97858 | 0.122213 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 64.4006 | 2.63795 | ||||||||
\(597\) | − 5.95715i | − 0.243810i | ||||||||
\(598\) | 10.3931i | 0.425006i | ||||||||
\(599\) | −29.0852 | −1.18839 | −0.594195 | − | 0.804321i | \(-0.702529\pi\) | ||||
−0.594195 | + | 0.804321i | \(0.702529\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 11.4318 | 0.466311 | 0.233155 | − | 0.972439i | \(-0.425095\pi\) | ||||
0.233155 | + | 0.972439i | \(0.425095\pi\) | |||||||
\(602\) | − 29.6582i | − 1.20878i | ||||||||
\(603\) | − 9.37169i | − 0.381645i | ||||||||
\(604\) | 36.0294 | 1.46601 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −25.7648 | −1.04662 | ||||||||
\(607\) | 27.9143i | 1.13301i | 0.824059 | + | 0.566503i | \(0.191704\pi\) | ||||
−0.824059 | + | 0.566503i | \(0.808296\pi\) | |||||||
\(608\) | 14.3293i | 0.581130i | ||||||||
\(609\) | −7.17935 | −0.290922 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1.02142 | −0.0413223 | ||||||||
\(612\) | 25.9143i | 1.04752i | ||||||||
\(613\) | 4.65394i | 0.187971i | 0.995574 | + | 0.0939855i | \(0.0299607\pi\) | ||||
−0.995574 | + | 0.0939855i | \(0.970039\pi\) | |||||||
\(614\) | 1.89334 | 0.0764092 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −7.82862 | −0.315424 | ||||||||
\(617\) | − 15.9572i | − 0.642411i | −0.947010 | − | 0.321205i | \(-0.895912\pi\) | ||||
0.947010 | − | 0.321205i | \(-0.104088\pi\) | |||||||
\(618\) | − 46.6577i | − 1.87685i | ||||||||
\(619\) | −1.02142 | −0.0410545 | −0.0205272 | − | 0.999789i | \(-0.506534\pi\) | ||||
−0.0205272 | + | 0.999789i | \(0.506534\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −4.17513 | −0.167542 | ||||||||
\(622\) | 57.5725i | 2.30845i | ||||||||
\(623\) | 12.1751i | 0.487786i | ||||||||
\(624\) | 5.21798 | 0.208886 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 84.4225 | 3.37420 | ||||||||
\(627\) | 8.35027i | 0.333478i | ||||||||
\(628\) | − 11.6926i | − 0.466585i | ||||||||
\(629\) | −48.0550 | −1.91608 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −20.4998 | −0.816083 | −0.408041 | − | 0.912963i | \(-0.633788\pi\) | ||||
−0.408041 | + | 0.912963i | \(0.633788\pi\) | |||||||
\(632\) | 9.74384i | 0.387589i | ||||||||
\(633\) | 23.9143i | 0.950508i | ||||||||
\(634\) | 24.0210 | 0.953994 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −42.7005 | −1.69319 | ||||||||
\(637\) | − 5.56825i | − 0.220622i | ||||||||
\(638\) | − 17.8715i | − 0.707538i | ||||||||
\(639\) | 5.19656 | 0.205573 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 38.2646 | 1.51136 | 0.755680 | − | 0.654941i | \(-0.227307\pi\) | ||||
0.755680 | + | 0.654941i | \(0.227307\pi\) | |||||||
\(642\) | − 46.2217i | − 1.82423i | ||||||||
\(643\) | 33.1109i | 1.30577i | 0.757459 | + | 0.652883i | \(0.226440\pi\) | ||||
−0.757459 | + | 0.652883i | \(0.773560\pi\) | |||||||
\(644\) | 20.9651 | 0.826141 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −107.273 | −4.22058 | ||||||||
\(647\) | − 16.9614i | − 0.666820i | −0.942782 | − | 0.333410i | \(-0.891801\pi\) | ||||
0.942782 | − | 0.333410i | \(-0.108199\pi\) | |||||||
\(648\) | 5.46787i | 0.214798i | ||||||||
\(649\) | 6.42754 | 0.252303 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −3.56404 | −0.139686 | ||||||||
\(652\) | 36.7643i | 1.43980i | ||||||||
\(653\) | 19.1709i | 0.750216i | 0.926981 | + | 0.375108i | \(0.122394\pi\) | ||||
−0.926981 | + | 0.375108i | \(0.877606\pi\) | |||||||
\(654\) | −20.8929 | −0.816976 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −32.2217 | −1.25805 | ||||||||
\(657\) | − 11.9572i | − 0.466493i | ||||||||
\(658\) | 3.04239i | 0.118605i | ||||||||
\(659\) | −37.8715 | −1.47526 | −0.737631 | − | 0.675204i | \(-0.764056\pi\) | ||||
−0.737631 | + | 0.675204i | \(0.764056\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 24.3931 | 0.948782 | 0.474391 | − | 0.880314i | \(-0.342668\pi\) | ||||
0.474391 | + | 0.880314i | \(0.342668\pi\) | |||||||
\(662\) | − 38.1579i | − 1.48305i | ||||||||
\(663\) | 6.17513i | 0.239822i | ||||||||
\(664\) | −29.3717 | −1.13984 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −19.3717 | −0.750638 | ||||||||
\(667\) | 25.0508i | 0.969971i | ||||||||
\(668\) | 72.9013i | 2.82064i | ||||||||
\(669\) | 2.62831 | 0.101616 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −15.0386 | −0.580560 | ||||||||
\(672\) | − 2.45692i | − 0.0947779i | ||||||||
\(673\) | 21.1281i | 0.814428i | 0.913333 | + | 0.407214i | \(0.133500\pi\) | ||||
−0.913333 | + | 0.407214i | \(0.866500\pi\) | |||||||
\(674\) | −55.6363 | −2.14303 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 4.19656 | 0.161406 | ||||||||
\(677\) | − 15.3973i | − 0.591767i | −0.955224 | − | 0.295884i | \(-0.904386\pi\) | ||||
0.955224 | − | 0.295884i | \(-0.0956141\pi\) | |||||||
\(678\) | − 19.8077i | − 0.760708i | ||||||||
\(679\) | −2.18356 | −0.0837972 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −15.7648 | −0.604109 | ||||||||
\(682\) | − 8.87192i | − 0.339723i | ||||||||
\(683\) | − 30.0722i | − 1.15068i | −0.817914 | − | 0.575341i | \(-0.804869\pi\) | ||||
0.817914 | − | 0.575341i | \(-0.195131\pi\) | |||||||
\(684\) | −29.2860 | −1.11978 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −37.4355 | −1.42929 | ||||||||
\(687\) | − 8.74338i | − 0.333581i | ||||||||
\(688\) | 51.9562i | 1.98081i | ||||||||
\(689\) | −10.1751 | −0.387642 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −8.14950 | −0.310022 | −0.155011 | − | 0.987913i | \(-0.549541\pi\) | ||||
−0.155011 | + | 0.987913i | \(0.549541\pi\) | |||||||
\(692\) | − 33.3927i | − 1.26940i | ||||||||
\(693\) | − 1.43175i | − 0.0543877i | ||||||||
\(694\) | −14.3931 | −0.546355 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 32.8072 | 1.24355 | ||||||||
\(697\) | − 38.1323i | − 1.44436i | ||||||||
\(698\) | − 68.5082i | − 2.59307i | ||||||||
\(699\) | −2.17513 | −0.0822712 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −28.6921 | −1.08369 | −0.541843 | − | 0.840480i | \(-0.682273\pi\) | ||||
−0.541843 | + | 0.840480i | \(0.682273\pi\) | |||||||
\(702\) | 2.48929i | 0.0939521i | ||||||||
\(703\) | − 54.3074i | − 2.04824i | ||||||||
\(704\) | −6.37123 | −0.240125 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 71.5506 | 2.69284 | ||||||||
\(707\) | 12.3847i | 0.465774i | ||||||||
\(708\) | 22.5426i | 0.847203i | ||||||||
\(709\) | −12.3074 | −0.462215 | −0.231108 | − | 0.972928i | \(-0.574235\pi\) | ||||
−0.231108 | + | 0.972928i | \(0.574235\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1.78202 | −0.0668310 | ||||||||
\(712\) | − 55.6363i | − 2.08506i | ||||||||
\(713\) | 12.4360i | 0.465730i | ||||||||
\(714\) | 18.3931 | 0.688345 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −65.3154 | −2.44095 | ||||||||
\(717\) | − 2.80344i | − 0.104696i | ||||||||
\(718\) | − 31.3288i | − 1.16918i | ||||||||
\(719\) | 28.7862 | 1.07355 | 0.536773 | − | 0.843727i | \(-0.319643\pi\) | ||||
0.536773 | + | 0.843727i | \(0.319643\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −22.4275 | −0.835245 | ||||||||
\(722\) | − 73.9332i | − 2.75151i | ||||||||
\(723\) | − 6.00000i | − 0.223142i | ||||||||
\(724\) | −66.2302 | −2.46142 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −23.8181 | −0.883974 | ||||||||
\(727\) | 34.3931i | 1.27557i | 0.770214 | + | 0.637785i | \(0.220149\pi\) | ||||
−0.770214 | + | 0.637785i | \(0.779851\pi\) | |||||||
\(728\) | − 6.54262i | − 0.242485i | ||||||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −61.4868 | −2.27417 | ||||||||
\(732\) | − 52.7434i | − 1.94945i | ||||||||
\(733\) | 29.0042i | 1.07129i | 0.844442 | + | 0.535647i | \(0.179932\pi\) | ||||
−0.844442 | + | 0.535647i | \(0.820068\pi\) | |||||||
\(734\) | −69.4868 | −2.56480 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −8.57292 | −0.316002 | ||||||||
\(737\) | − 11.2138i | − 0.413065i | ||||||||
\(738\) | − 15.3717i | − 0.565840i | ||||||||
\(739\) | 6.27804 | 0.230941 | 0.115471 | − | 0.993311i | \(-0.463162\pi\) | ||||
0.115471 | + | 0.993311i | \(0.463162\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −6.97858 | −0.256364 | ||||||||
\(742\) | 30.3074i | 1.11262i | ||||||||
\(743\) | − 12.2352i | − 0.448866i | −0.974490 | − | 0.224433i | \(-0.927947\pi\) | ||||
0.974490 | − | 0.224433i | \(-0.0720529\pi\) | |||||||
\(744\) | 16.2865 | 0.597091 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 5.85050 | 0.214202 | ||||||||
\(747\) | − 5.37169i | − 0.196540i | ||||||||
\(748\) | 31.0080i | 1.13376i | ||||||||
\(749\) | −22.2180 | −0.811827 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −28.8757 | −1.05369 | −0.526844 | − | 0.849962i | \(-0.676625\pi\) | ||||
−0.526844 | + | 0.849962i | \(0.676625\pi\) | |||||||
\(752\) | − 5.32976i | − 0.194357i | ||||||||
\(753\) | − 23.9143i | − 0.871486i | ||||||||
\(754\) | 14.9357 | 0.543927 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 5.02142 | 0.182627 | ||||||||
\(757\) | 30.3503i | 1.10310i | 0.834142 | + | 0.551550i | \(0.185963\pi\) | ||||
−0.834142 | + | 0.551550i | \(0.814037\pi\) | |||||||
\(758\) | 61.1146i | 2.21978i | ||||||||
\(759\) | −4.99579 | −0.181336 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −27.1709 | −0.984945 | −0.492473 | − | 0.870328i | \(-0.663907\pi\) | ||||
−0.492473 | + | 0.870328i | \(0.663907\pi\) | |||||||
\(762\) | − 25.8715i | − 0.937224i | ||||||||
\(763\) | 10.0428i | 0.363575i | ||||||||
\(764\) | −45.0852 | −1.63113 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −14.4569 | −0.522350 | ||||||||
\(767\) | 5.37169i | 0.193961i | ||||||||
\(768\) | − 32.5678i | − 1.17519i | ||||||||
\(769\) | 38.3503 | 1.38295 | 0.691473 | − | 0.722402i | \(-0.256962\pi\) | ||||
0.691473 | + | 0.722402i | \(0.256962\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 19.9572 | 0.718739 | ||||||||
\(772\) | 40.8710i | 1.47098i | ||||||||
\(773\) | 50.2646i | 1.80789i | 0.427647 | + | 0.903946i | \(0.359342\pi\) | ||||
−0.427647 | + | 0.903946i | \(0.640658\pi\) | |||||||
\(774\) | −24.7862 | −0.890923 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 9.97812 | 0.358194 | ||||||||
\(777\) | 9.31163i | 0.334053i | ||||||||
\(778\) | 33.9781i | 1.21817i | ||||||||
\(779\) | 43.0937 | 1.54399 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 6.21798 | 0.222497 | ||||||||
\(782\) | − 64.1789i | − 2.29503i | ||||||||
\(783\) | 6.00000i | 0.214423i | ||||||||
\(784\) | 29.0550 | 1.03768 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −15.9143 | −0.567645 | ||||||||
\(787\) | − 13.2860i | − 0.473595i | −0.971559 | − | 0.236797i | \(-0.923902\pi\) | ||||
0.971559 | − | 0.236797i | \(-0.0760978\pi\) | |||||||
\(788\) | 40.1360i | 1.42979i | ||||||||
\(789\) | 8.00000 | 0.284808 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −9.52119 | −0.338535 | ||||||||
\(792\) | 6.54262i | 0.232482i | ||||||||
\(793\) | − 12.5682i | − 0.446312i | ||||||||
\(794\) | −30.2008 | −1.07179 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 24.9995 | 0.886085 | ||||||||
\(797\) | 9.82487i | 0.348015i | 0.984744 | + | 0.174007i | \(0.0556716\pi\) | ||||
−0.984744 | + | 0.174007i | \(0.944328\pi\) | |||||||
\(798\) | 20.7862i | 0.735825i | ||||||||
\(799\) | 6.30742 | 0.223141 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 10.1751 | 0.359521 | ||||||||
\(802\) | 93.2087i | 3.29131i | ||||||||
\(803\) | − 14.3074i | − 0.504898i | ||||||||
\(804\) | 39.3288 | 1.38702 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 7.41454 | 0.261166 | ||||||||
\(807\) | 2.35027i | 0.0827334i | ||||||||
\(808\) | − 56.5939i | − 1.99097i | ||||||||
\(809\) | 9.91431 | 0.348569 | 0.174284 | − | 0.984695i | \(-0.444239\pi\) | ||||
0.174284 | + | 0.984695i | \(0.444239\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −36.5855 | −1.28469 | −0.642345 | − | 0.766416i | \(-0.722038\pi\) | ||||
−0.642345 | + | 0.766416i | \(0.722038\pi\) | |||||||
\(812\) | − 30.1285i | − 1.05730i | ||||||||
\(813\) | 10.9786i | 0.385036i | ||||||||
\(814\) | −23.1793 | −0.812436 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −32.2217 | −1.12799 | ||||||||
\(817\) | − 69.4868i | − 2.43103i | ||||||||
\(818\) | − 34.8500i | − 1.21850i | ||||||||
\(819\) | 1.19656 | 0.0418111 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −34.4741 | −1.20316 | −0.601578 | − | 0.798814i | \(-0.705461\pi\) | ||||
−0.601578 | + | 0.798814i | \(0.705461\pi\) | |||||||
\(822\) | 41.6791i | 1.45373i | ||||||||
\(823\) | − 13.2566i | − 0.462097i | −0.972942 | − | 0.231048i | \(-0.925784\pi\) | ||||
0.972942 | − | 0.231048i | \(-0.0742155\pi\) | |||||||
\(824\) | 102.486 | 3.57028 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 16.0000 | 0.556711 | ||||||||
\(827\) | 28.1495i | 0.978854i | 0.872044 | + | 0.489427i | \(0.162794\pi\) | ||||
−0.872044 | + | 0.489427i | \(0.837206\pi\) | |||||||
\(828\) | − 17.5212i | − 0.608904i | ||||||||
\(829\) | −16.3418 | −0.567576 | −0.283788 | − | 0.958887i | \(-0.591591\pi\) | ||||
−0.283788 | + | 0.958887i | \(0.591591\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −1.21377 | −0.0421052 | ||||||||
\(832\) | − 5.32464i | − 0.184599i | ||||||||
\(833\) | 34.3847i | 1.19136i | ||||||||
\(834\) | −14.3931 | −0.498393 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −35.0424 | −1.21197 | ||||||||
\(837\) | 2.97858i | 0.102955i | ||||||||
\(838\) | 7.91431i | 0.273395i | ||||||||
\(839\) | 30.3675 | 1.04840 | 0.524201 | − | 0.851595i | \(-0.324364\pi\) | ||||
0.524201 | + | 0.851595i | \(0.324364\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 7.00000 | 0.241379 | ||||||||
\(842\) | 40.5939i | 1.39896i | ||||||||
\(843\) | 11.9572i | 0.411826i | ||||||||
\(844\) | −100.358 | −3.45446 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 2.54262 | 0.0874169 | ||||||||
\(847\) | 11.4490i | 0.393391i | ||||||||
\(848\) | − 53.0937i | − 1.82324i | ||||||||
\(849\) | −29.8715 | −1.02519 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 32.4910 | 1.11378 | ||||||||
\(852\) | 21.8077i | 0.747118i | ||||||||
\(853\) | 42.1407i | 1.44287i | 0.692482 | + | 0.721435i | \(0.256517\pi\) | ||||
−0.692482 | + | 0.721435i | \(0.743483\pi\) | |||||||
\(854\) | −37.4355 | −1.28102 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 101.529 | 3.47018 | ||||||||
\(857\) | − 2.17513i | − 0.0743012i | −0.999310 | − | 0.0371506i | \(-0.988172\pi\) | ||||
0.999310 | − | 0.0371506i | \(-0.0118281\pi\) | |||||||
\(858\) | 2.97858i | 0.101687i | ||||||||
\(859\) | −18.5682 | −0.633541 | −0.316770 | − | 0.948502i | \(-0.602598\pi\) | ||||
−0.316770 | + | 0.948502i | \(0.602598\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −7.38890 | −0.251813 | ||||||||
\(862\) | − 11.4145i | − 0.388781i | ||||||||
\(863\) | − 33.7220i | − 1.14791i | −0.818887 | − | 0.573954i | \(-0.805409\pi\) | ||||
0.818887 | − | 0.573954i | \(-0.194591\pi\) | |||||||
\(864\) | −2.05333 | −0.0698556 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 95.4649 | 3.24403 | ||||||||
\(867\) | − 21.1323i | − 0.717690i | ||||||||
\(868\) | − 14.9567i | − 0.507663i | ||||||||
\(869\) | −2.13229 | −0.0723330 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 9.37169 | 0.317548 | ||||||||
\(872\) | − 45.8924i | − 1.55411i | ||||||||
\(873\) | 1.82487i | 0.0617623i | ||||||||
\(874\) | 72.5292 | 2.45334 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 50.1789 | 1.69539 | ||||||||
\(877\) | 43.4868i | 1.46844i | 0.678910 | + | 0.734222i | \(0.262453\pi\) | ||||
−0.678910 | + | 0.734222i | \(0.737547\pi\) | |||||||
\(878\) | 19.2650i | 0.650164i | ||||||||
\(879\) | 0.777809 | 0.0262348 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 26.7005 | 0.899564 | 0.449782 | − | 0.893138i | \(-0.351502\pi\) | ||||
0.449782 | + | 0.893138i | \(0.351502\pi\) | |||||||
\(882\) | 13.8610i | 0.466724i | ||||||||
\(883\) | − 20.2990i | − 0.683116i | −0.939861 | − | 0.341558i | \(-0.889045\pi\) | ||||
0.939861 | − | 0.341558i | \(-0.110955\pi\) | |||||||
\(884\) | −25.9143 | −0.871593 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −86.9223 | −2.92021 | ||||||||
\(887\) | 36.0550i | 1.21061i | 0.795994 | + | 0.605305i | \(0.206949\pi\) | ||||
−0.795994 | + | 0.605305i | \(0.793051\pi\) | |||||||
\(888\) | − 42.5510i | − 1.42792i | ||||||||
\(889\) | −12.4360 | −0.417089 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.19656 | −0.0400862 | ||||||||
\(892\) | 11.0298i | 0.369307i | ||||||||
\(893\) | 7.12808i | 0.238532i | ||||||||
\(894\) | −38.2008 | −1.27762 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −20.7737 | −0.694000 | ||||||||
\(897\) | − 4.17513i | − 0.139404i | ||||||||
\(898\) | − 15.3717i | − 0.512960i | ||||||||
\(899\) | 17.8715 | 0.596047 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 62.8328 | 2.09326 | ||||||||
\(902\) | − 18.3931i | − 0.612424i | ||||||||
\(903\) | 11.9143i | 0.396483i | ||||||||
\(904\) | 43.5087 | 1.44708 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −21.3717 | −0.710027 | ||||||||
\(907\) | − 7.26504i | − 0.241232i | −0.992699 | − | 0.120616i | \(-0.961513\pi\) | ||||
0.992699 | − | 0.120616i | \(-0.0384869\pi\) | |||||||
\(908\) | − 66.1579i | − 2.19553i | ||||||||
\(909\) | 10.3503 | 0.343297 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −6.65769 | −0.220579 | −0.110290 | − | 0.993899i | \(-0.535178\pi\) | ||||
−0.110290 | + | 0.993899i | \(0.535178\pi\) | |||||||
\(912\) | − 36.4141i | − 1.20579i | ||||||||
\(913\) | − 6.42754i | − 0.212721i | ||||||||
\(914\) | 3.45738 | 0.114360 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 36.6921 | 1.21234 | ||||||||
\(917\) | 7.64973i | 0.252616i | ||||||||
\(918\) | − 15.3717i | − 0.507341i | ||||||||
\(919\) | 27.1831 | 0.896688 | 0.448344 | − | 0.893861i | \(-0.352014\pi\) | ||||
0.448344 | + | 0.893861i | \(0.352014\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −0.760597 | −0.0250625 | ||||||||
\(922\) | − 70.9013i | − 2.33501i | ||||||||
\(923\) | 5.19656i | 0.171047i | ||||||||
\(924\) | 6.00842 | 0.197663 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −40.7643 | −1.33960 | ||||||||
\(927\) | 18.7434i | 0.615614i | ||||||||
\(928\) | 12.3200i | 0.404423i | ||||||||
\(929\) | 15.3973 | 0.505170 | 0.252585 | − | 0.967575i | \(-0.418719\pi\) | ||||
0.252585 | + | 0.967575i | \(0.418719\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −38.8585 | −1.27353 | ||||||||
\(932\) | − 9.12808i | − 0.299000i | ||||||||
\(933\) | − 23.1281i | − 0.757179i | ||||||||
\(934\) | 64.0932 | 2.09719 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −5.46787 | −0.178723 | ||||||||
\(937\) | 1.12808i | 0.0368527i | 0.999830 | + | 0.0184264i | \(0.00586562\pi\) | ||||
−0.999830 | + | 0.0184264i | \(0.994134\pi\) | |||||||
\(938\) | − 27.9143i | − 0.911434i | ||||||||
\(939\) | −33.9143 | −1.10675 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −30.1407 | −0.982559 | −0.491280 | − | 0.871002i | \(-0.663471\pi\) | ||||
−0.491280 | + | 0.871002i | \(0.663471\pi\) | |||||||
\(942\) | 6.93573i | 0.225978i | ||||||||
\(943\) | 25.7820i | 0.839578i | ||||||||
\(944\) | −28.0294 | −0.912279 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −29.6582 | −0.964270 | ||||||||
\(947\) | − 20.0294i | − 0.650868i | −0.945565 | − | 0.325434i | \(-0.894490\pi\) | ||||
0.945565 | − | 0.325434i | \(-0.105510\pi\) | |||||||
\(948\) | − 7.47835i | − 0.242885i | ||||||||
\(949\) | 11.9572 | 0.388146 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −9.64973 | −0.312914 | ||||||||
\(952\) | 40.4015i | 1.30942i | ||||||||
\(953\) | 43.2259i | 1.40023i | 0.714032 | + | 0.700113i | \(0.246867\pi\) | ||||
−0.714032 | + | 0.700113i | \(0.753133\pi\) | |||||||
\(954\) | 25.3288 | 0.820052 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 11.7648 | 0.380501 | ||||||||
\(957\) | 7.17935i | 0.232075i | ||||||||
\(958\) | − 18.8929i | − 0.610401i | ||||||||
\(959\) | 20.0344 | 0.646945 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −22.1281 | −0.713809 | ||||||||
\(962\) | − 19.3717i | − 0.624568i | ||||||||
\(963\) | 18.5682i | 0.598353i | ||||||||
\(964\) | 25.1793 | 0.810972 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −12.4360 | −0.400120 | ||||||||
\(967\) | 57.6875i | 1.85511i | 0.373691 | + | 0.927553i | \(0.378092\pi\) | ||||
−0.373691 | + | 0.927553i | \(0.621908\pi\) | |||||||
\(968\) | − 52.3179i | − 1.68156i | ||||||||
\(969\) | 43.0937 | 1.38437 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −19.5296 | −0.626735 | −0.313368 | − | 0.949632i | \(-0.601457\pi\) | ||||
−0.313368 | + | 0.949632i | \(0.601457\pi\) | |||||||
\(972\) | − 4.19656i | − 0.134605i | ||||||||
\(973\) | 6.91852i | 0.221798i | ||||||||
\(974\) | 10.9786 | 0.351776 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 65.5809 | 2.09919 | ||||||||
\(977\) | − 40.3074i | − 1.28955i | −0.764373 | − | 0.644774i | \(-0.776951\pi\) | ||||
0.764373 | − | 0.644774i | \(-0.223049\pi\) | |||||||
\(978\) | − 21.8077i | − 0.697332i | ||||||||
\(979\) | 12.1751 | 0.389119 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 8.39312 | 0.267972 | ||||||||
\(982\) | 0.213311i | 0.00680702i | ||||||||
\(983\) | − 32.2008i | − 1.02705i | −0.858076 | − | 0.513523i | \(-0.828340\pi\) | ||||
0.858076 | − | 0.513523i | \(-0.171660\pi\) | |||||||
\(984\) | 33.7648 | 1.07638 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −92.2302 | −2.93721 | ||||||||
\(987\) | − 1.22219i | − 0.0389028i | ||||||||
\(988\) | − 29.2860i | − 0.931712i | ||||||||
\(989\) | 41.5725 | 1.32193 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 26.4826 | 0.841246 | 0.420623 | − | 0.907235i | \(-0.361811\pi\) | ||||
0.420623 | + | 0.907235i | \(0.361811\pi\) | |||||||
\(992\) | 6.11599i | 0.194183i | ||||||||
\(993\) | 15.3288i | 0.486446i | ||||||||
\(994\) | 15.4783 | 0.490943 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 22.5426 | 0.714290 | ||||||||
\(997\) | 35.1365i | 1.11278i | 0.830920 | + | 0.556392i | \(0.187815\pi\) | ||||
−0.830920 | + | 0.556392i | \(0.812185\pi\) | |||||||
\(998\) | − 44.1151i | − 1.39644i | ||||||||
\(999\) | 7.78202 | 0.246212 |
(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 | 975.2.c.i.274.2 | 6 | ||
3.2 | odd | 2 | 2925.2.c.w.2224.5 | 6 | |||
5.2 | odd | 4 | 975.2.a.o.1.3 | 3 | |||
5.3 | odd | 4 | 195.2.a.e.1.1 | ✓ | 3 | ||
5.4 | even | 2 | inner | 975.2.c.i.274.5 | 6 | ||
15.2 | even | 4 | 2925.2.a.bh.1.1 | 3 | |||
15.8 | even | 4 | 585.2.a.n.1.3 | 3 | |||
15.14 | odd | 2 | 2925.2.c.w.2224.2 | 6 | |||
20.3 | even | 4 | 3120.2.a.bj.1.2 | 3 | |||
35.13 | even | 4 | 9555.2.a.bq.1.1 | 3 | |||
60.23 | odd | 4 | 9360.2.a.dd.1.2 | 3 | |||
65.38 | odd | 4 | 2535.2.a.bc.1.3 | 3 | |||
195.38 | even | 4 | 7605.2.a.bx.1.1 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
195.2.a.e.1.1 | ✓ | 3 | 5.3 | odd | 4 | ||
585.2.a.n.1.3 | 3 | 15.8 | even | 4 | |||
975.2.a.o.1.3 | 3 | 5.2 | odd | 4 | |||
975.2.c.i.274.2 | 6 | 1.1 | even | 1 | trivial | ||
975.2.c.i.274.5 | 6 | 5.4 | even | 2 | inner | ||
2535.2.a.bc.1.3 | 3 | 65.38 | odd | 4 | |||
2925.2.a.bh.1.1 | 3 | 15.2 | even | 4 | |||
2925.2.c.w.2224.2 | 6 | 15.14 | odd | 2 | |||
2925.2.c.w.2224.5 | 6 | 3.2 | odd | 2 | |||
3120.2.a.bj.1.2 | 3 | 20.3 | even | 4 | |||
7605.2.a.bx.1.1 | 3 | 195.38 | even | 4 | |||
9360.2.a.dd.1.2 | 3 | 60.23 | odd | 4 | |||
9555.2.a.bq.1.1 | 3 | 35.13 | even | 4 |