Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1155,2,Mod(694,1155)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1155, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1155.694");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1155 = 3 \cdot 5 \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1155.c (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(9.22272143346\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} + 33 x^{18} + 456 x^{16} + 3426 x^{14} + 15194 x^{12} + 40320 x^{10} + 61593 x^{8} + 48545 x^{6} + \cdots + 100 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 694.17 | ||
Root | \(2.02181i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1155.694 |
Dual form | 1155.2.c.e.694.4 |
$q$-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 \(\left(\mathbb{Z}/1155\mathbb{Z}\right)^\times\).
\(n\) | \(211\) | \(232\) | \(386\) | \(661\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.02181i | 1.42964i | 0.699309 | + | 0.714819i | \(0.253491\pi\) | ||||
−0.699309 | + | 0.714819i | \(0.746509\pi\) | |||||||
\(3\) | − | 1.00000i | − | 0.577350i | ||||||
\(4\) | −2.08773 | −1.04387 | ||||||||
\(5\) | −0.549616 | − | 2.16747i | −0.245796 | − | 0.969322i | ||||
\(6\) | 2.02181 | 0.825402 | ||||||||
\(7\) | 1.00000i | 0.377964i | ||||||||
\(8\) | − | 0.177380i | − | 0.0627132i | ||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | 4.38222 | − | 1.11122i | 1.38578 | − | 0.351399i | ||||
\(11\) | −1.00000 | −0.301511 | ||||||||
\(12\) | 2.08773i | 0.602677i | ||||||||
\(13\) | − | 5.44833i | − | 1.51110i | −0.655094 | − | 0.755548i | \(-0.727371\pi\) | ||
0.655094 | − | 0.755548i | \(-0.272629\pi\) | |||||||
\(14\) | −2.02181 | −0.540353 | ||||||||
\(15\) | −2.16747 | + | 0.549616i | −0.559638 | + | 0.141910i | ||||
\(16\) | −3.81684 | −0.954209 | ||||||||
\(17\) | 2.57671i | 0.624944i | 0.949927 | + | 0.312472i | \(0.101157\pi\) | ||||
−0.949927 | + | 0.312472i | \(0.898843\pi\) | |||||||
\(18\) | − | 2.02181i | − | 0.476546i | ||||||
\(19\) | 0.801918 | 0.183973 | 0.0919863 | − | 0.995760i | \(-0.470678\pi\) | ||||
0.0919863 | + | 0.995760i | \(0.470678\pi\) | |||||||
\(20\) | 1.14745 | + | 4.52510i | 0.256578 | + | 1.01184i | ||||
\(21\) | 1.00000 | 0.218218 | ||||||||
\(22\) | − | 2.02181i | − | 0.431052i | ||||||
\(23\) | − | 4.06135i | − | 0.846849i | −0.905931 | − | 0.423425i | \(-0.860828\pi\) | ||
0.905931 | − | 0.423425i | \(-0.139172\pi\) | |||||||
\(24\) | −0.177380 | −0.0362075 | ||||||||
\(25\) | −4.39584 | + | 2.38255i | −0.879169 | + | 0.476510i | ||||
\(26\) | 11.0155 | 2.16032 | ||||||||
\(27\) | 1.00000i | 0.192450i | ||||||||
\(28\) | − | 2.08773i | − | 0.394544i | ||||||
\(29\) | −4.72983 | −0.878307 | −0.439154 | − | 0.898412i | \(-0.644722\pi\) | ||||
−0.439154 | + | 0.898412i | \(0.644722\pi\) | |||||||
\(30\) | −1.11122 | − | 4.38222i | −0.202880 | − | 0.800080i | ||||
\(31\) | −9.50964 | −1.70798 | −0.853991 | − | 0.520288i | \(-0.825825\pi\) | ||||
−0.853991 | + | 0.520288i | \(0.825825\pi\) | |||||||
\(32\) | − | 8.07170i | − | 1.42689i | ||||||
\(33\) | 1.00000i | 0.174078i | ||||||||
\(34\) | −5.20963 | −0.893445 | ||||||||
\(35\) | 2.16747 | − | 0.549616i | 0.366369 | − | 0.0929021i | ||||
\(36\) | 2.08773 | 0.347955 | ||||||||
\(37\) | 0.369366i | 0.0607234i | 0.999539 | + | 0.0303617i | \(0.00966592\pi\) | ||||
−0.999539 | + | 0.0303617i | \(0.990334\pi\) | |||||||
\(38\) | 1.62133i | 0.263014i | ||||||||
\(39\) | −5.44833 | −0.872431 | ||||||||
\(40\) | −0.384465 | + | 0.0974908i | −0.0607893 | + | 0.0154146i | ||||
\(41\) | −6.07185 | −0.948263 | −0.474132 | − | 0.880454i | \(-0.657238\pi\) | ||||
−0.474132 | + | 0.880454i | \(0.657238\pi\) | |||||||
\(42\) | 2.02181i | 0.311973i | ||||||||
\(43\) | − | 12.8198i | − | 1.95500i | −0.210926 | − | 0.977502i | \(-0.567648\pi\) | ||
0.210926 | − | 0.977502i | \(-0.432352\pi\) | |||||||
\(44\) | 2.08773 | 0.314738 | ||||||||
\(45\) | 0.549616 | + | 2.16747i | 0.0819319 | + | 0.323107i | ||||
\(46\) | 8.21129 | 1.21069 | ||||||||
\(47\) | 10.4673i | 1.52681i | 0.645920 | + | 0.763405i | \(0.276474\pi\) | ||||
−0.645920 | + | 0.763405i | \(0.723526\pi\) | |||||||
\(48\) | 3.81684i | 0.550913i | ||||||||
\(49\) | −1.00000 | −0.142857 | ||||||||
\(50\) | −4.81708 | − | 8.88758i | −0.681237 | − | 1.25689i | ||||
\(51\) | 2.57671 | 0.360812 | ||||||||
\(52\) | 11.3747i | 1.57738i | ||||||||
\(53\) | − | 8.19730i | − | 1.12599i | −0.826462 | − | 0.562993i | \(-0.809650\pi\) | ||
0.826462 | − | 0.562993i | \(-0.190350\pi\) | |||||||
\(54\) | −2.02181 | −0.275134 | ||||||||
\(55\) | 0.549616 | + | 2.16747i | 0.0741102 | + | 0.292261i | ||||
\(56\) | 0.177380 | 0.0237034 | ||||||||
\(57\) | − | 0.801918i | − | 0.106217i | ||||||
\(58\) | − | 9.56284i | − | 1.25566i | ||||||
\(59\) | 0.232249 | 0.0302362 | 0.0151181 | − | 0.999886i | \(-0.495188\pi\) | ||||
0.0151181 | + | 0.999886i | \(0.495188\pi\) | |||||||
\(60\) | 4.52510 | − | 1.14745i | 0.584187 | − | 0.148135i | ||||
\(61\) | 15.4328 | 1.97597 | 0.987984 | − | 0.154559i | \(-0.0493955\pi\) | ||||
0.987984 | + | 0.154559i | \(0.0493955\pi\) | |||||||
\(62\) | − | 19.2267i | − | 2.44180i | ||||||
\(63\) | − | 1.00000i | − | 0.125988i | ||||||
\(64\) | 8.68579 | 1.08572 | ||||||||
\(65\) | −11.8091 | + | 2.99449i | −1.46474 | + | 0.371421i | ||||
\(66\) | −2.02181 | −0.248868 | ||||||||
\(67\) | − | 14.9167i | − | 1.82236i | −0.412004 | − | 0.911182i | \(-0.635171\pi\) | ||
0.412004 | − | 0.911182i | \(-0.364829\pi\) | |||||||
\(68\) | − | 5.37949i | − | 0.652358i | ||||||
\(69\) | −4.06135 | −0.488929 | ||||||||
\(70\) | 1.11122 | + | 4.38222i | 0.132816 | + | 0.523775i | ||||
\(71\) | −9.27387 | −1.10061 | −0.550303 | − | 0.834965i | \(-0.685488\pi\) | ||||
−0.550303 | + | 0.834965i | \(0.685488\pi\) | |||||||
\(72\) | 0.177380i | 0.0209044i | ||||||||
\(73\) | − | 10.5828i | − | 1.23862i | −0.785145 | − | 0.619312i | \(-0.787412\pi\) | ||
0.785145 | − | 0.619312i | \(-0.212588\pi\) | |||||||
\(74\) | −0.746790 | −0.0868126 | ||||||||
\(75\) | 2.38255 | + | 4.39584i | 0.275113 | + | 0.507588i | ||||
\(76\) | −1.67419 | −0.192043 | ||||||||
\(77\) | − | 1.00000i | − | 0.113961i | ||||||
\(78\) | − | 11.0155i | − | 1.24726i | ||||||
\(79\) | −13.3303 | −1.49978 | −0.749891 | − | 0.661562i | \(-0.769894\pi\) | ||||
−0.749891 | + | 0.661562i | \(0.769894\pi\) | |||||||
\(80\) | 2.09779 | + | 8.27288i | 0.234541 | + | 0.924936i | ||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | − | 12.2761i | − | 1.35567i | ||||||
\(83\) | − | 5.21440i | − | 0.572355i | −0.958177 | − | 0.286177i | \(-0.907615\pi\) | ||
0.958177 | − | 0.286177i | \(-0.0923847\pi\) | |||||||
\(84\) | −2.08773 | −0.227790 | ||||||||
\(85\) | 5.58494 | − | 1.41620i | 0.605772 | − | 0.153609i | ||||
\(86\) | 25.9193 | 2.79495 | ||||||||
\(87\) | 4.72983i | 0.507091i | ||||||||
\(88\) | 0.177380i | 0.0189088i | ||||||||
\(89\) | 10.5734 | 1.12078 | 0.560389 | − | 0.828230i | \(-0.310652\pi\) | ||||
0.560389 | + | 0.828230i | \(0.310652\pi\) | |||||||
\(90\) | −4.38222 | + | 1.11122i | −0.461927 | + | 0.117133i | ||||
\(91\) | 5.44833 | 0.571140 | ||||||||
\(92\) | 8.47901i | 0.883998i | ||||||||
\(93\) | 9.50964i | 0.986104i | ||||||||
\(94\) | −21.1629 | −2.18279 | ||||||||
\(95\) | −0.440747 | − | 1.73813i | −0.0452197 | − | 0.178329i | ||||
\(96\) | −8.07170 | −0.823814 | ||||||||
\(97\) | − | 12.2790i | − | 1.24675i | −0.781924 | − | 0.623374i | \(-0.785761\pi\) | ||
0.781924 | − | 0.623374i | \(-0.214239\pi\) | |||||||
\(98\) | − | 2.02181i | − | 0.204234i | ||||||
\(99\) | 1.00000 | 0.100504 | ||||||||
\(100\) | 9.17735 | − | 4.97413i | 0.917735 | − | 0.497413i | ||||
\(101\) | 2.21466 | 0.220367 | 0.110183 | − | 0.993911i | \(-0.464856\pi\) | ||||
0.110183 | + | 0.993911i | \(0.464856\pi\) | |||||||
\(102\) | 5.20963i | 0.515830i | ||||||||
\(103\) | 14.9953i | 1.47753i | 0.673964 | + | 0.738765i | \(0.264590\pi\) | ||||
−0.673964 | + | 0.738765i | \(0.735410\pi\) | |||||||
\(104\) | −0.966424 | −0.0947657 | ||||||||
\(105\) | −0.549616 | − | 2.16747i | −0.0536370 | − | 0.211523i | ||||
\(106\) | 16.5734 | 1.60975 | ||||||||
\(107\) | 9.79736i | 0.947147i | 0.880754 | + | 0.473573i | \(0.157036\pi\) | ||||
−0.880754 | + | 0.473573i | \(0.842964\pi\) | |||||||
\(108\) | − | 2.08773i | − | 0.200892i | ||||||
\(109\) | 0.805348 | 0.0771384 | 0.0385692 | − | 0.999256i | \(-0.487720\pi\) | ||||
0.0385692 | + | 0.999256i | \(0.487720\pi\) | |||||||
\(110\) | −4.38222 | + | 1.11122i | −0.417828 | + | 0.105951i | ||||
\(111\) | 0.369366 | 0.0350587 | ||||||||
\(112\) | − | 3.81684i | − | 0.360657i | ||||||
\(113\) | 18.3292i | 1.72427i | 0.506681 | + | 0.862134i | \(0.330872\pi\) | ||||
−0.506681 | + | 0.862134i | \(0.669128\pi\) | |||||||
\(114\) | 1.62133 | 0.151851 | ||||||||
\(115\) | −8.80284 | + | 2.23218i | −0.820869 | + | 0.208152i | ||||
\(116\) | 9.87462 | 0.916836 | ||||||||
\(117\) | 5.44833i | 0.503698i | ||||||||
\(118\) | 0.469564i | 0.0432269i | ||||||||
\(119\) | −2.57671 | −0.236207 | ||||||||
\(120\) | 0.0974908 | + | 0.384465i | 0.00889965 | + | 0.0350967i | ||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 31.2023i | 2.82492i | ||||||||
\(123\) | 6.07185i | 0.547480i | ||||||||
\(124\) | 19.8536 | 1.78291 | ||||||||
\(125\) | 7.58013 | + | 8.21837i | 0.677988 | + | 0.735073i | ||||
\(126\) | 2.02181 | 0.180118 | ||||||||
\(127\) | − | 4.11772i | − | 0.365388i | −0.983170 | − | 0.182694i | \(-0.941518\pi\) | ||
0.983170 | − | 0.182694i | \(-0.0584818\pi\) | |||||||
\(128\) | 1.41767i | 0.125306i | ||||||||
\(129\) | −12.8198 | −1.12872 | ||||||||
\(130\) | −6.05430 | − | 23.8758i | −0.530998 | − | 2.09405i | ||||
\(131\) | −7.41340 | −0.647712 | −0.323856 | − | 0.946106i | \(-0.604979\pi\) | ||||
−0.323856 | + | 0.946106i | \(0.604979\pi\) | |||||||
\(132\) | − | 2.08773i | − | 0.181714i | ||||||
\(133\) | 0.801918i | 0.0695351i | ||||||||
\(134\) | 30.1588 | 2.60532 | ||||||||
\(135\) | 2.16747 | − | 0.549616i | 0.186546 | − | 0.0473034i | ||||
\(136\) | 0.457057 | 0.0391923 | ||||||||
\(137\) | 9.06835i | 0.774762i | 0.921920 | + | 0.387381i | \(0.126620\pi\) | ||||
−0.921920 | + | 0.387381i | \(0.873380\pi\) | |||||||
\(138\) | − | 8.21129i | − | 0.698991i | ||||||
\(139\) | 7.21710 | 0.612146 | 0.306073 | − | 0.952008i | \(-0.400985\pi\) | ||||
0.306073 | + | 0.952008i | \(0.400985\pi\) | |||||||
\(140\) | −4.52510 | + | 1.14745i | −0.382440 | + | 0.0969774i | ||||
\(141\) | 10.4673 | 0.881505 | ||||||||
\(142\) | − | 18.7501i | − | 1.57347i | ||||||
\(143\) | 5.44833i | 0.455612i | ||||||||
\(144\) | 3.81684 | 0.318070 | ||||||||
\(145\) | 2.59959 | + | 10.2518i | 0.215884 | + | 0.851362i | ||||
\(146\) | 21.3965 | 1.77078 | ||||||||
\(147\) | 1.00000i | 0.0824786i | ||||||||
\(148\) | − | 0.771138i | − | 0.0633872i | ||||||
\(149\) | 6.63108 | 0.543240 | 0.271620 | − | 0.962405i | \(-0.412441\pi\) | ||||
0.271620 | + | 0.962405i | \(0.412441\pi\) | |||||||
\(150\) | −8.88758 | + | 4.81708i | −0.725668 | + | 0.393313i | ||||
\(151\) | −19.2917 | −1.56993 | −0.784967 | − | 0.619538i | \(-0.787320\pi\) | ||||
−0.784967 | + | 0.619538i | \(0.787320\pi\) | |||||||
\(152\) | − | 0.142244i | − | 0.0115375i | ||||||
\(153\) | − | 2.57671i | − | 0.208315i | ||||||
\(154\) | 2.02181 | 0.162922 | ||||||||
\(155\) | 5.22665 | + | 20.6119i | 0.419815 | + | 1.65558i | ||||
\(156\) | 11.3747 | 0.910702 | ||||||||
\(157\) | 9.60329i | 0.766426i | 0.923660 | + | 0.383213i | \(0.125182\pi\) | ||||
−0.923660 | + | 0.383213i | \(0.874818\pi\) | |||||||
\(158\) | − | 26.9515i | − | 2.14415i | ||||||
\(159\) | −8.19730 | −0.650088 | ||||||||
\(160\) | −17.4951 | + | 4.43633i | −1.38311 | + | 0.350723i | ||||
\(161\) | 4.06135 | 0.320079 | ||||||||
\(162\) | 2.02181i | 0.158849i | ||||||||
\(163\) | 1.09563i | 0.0858166i | 0.999079 | + | 0.0429083i | \(0.0136623\pi\) | ||||
−0.999079 | + | 0.0429083i | \(0.986338\pi\) | |||||||
\(164\) | 12.6764 | 0.989860 | ||||||||
\(165\) | 2.16747 | − | 0.549616i | 0.168737 | − | 0.0427875i | ||||
\(166\) | 10.5425 | 0.818260 | ||||||||
\(167\) | 14.3675i | 1.11179i | 0.831253 | + | 0.555895i | \(0.187624\pi\) | ||||
−0.831253 | + | 0.555895i | \(0.812376\pi\) | |||||||
\(168\) | − | 0.177380i | − | 0.0136852i | ||||||
\(169\) | −16.6843 | −1.28341 | ||||||||
\(170\) | 2.86330 | + | 11.2917i | 0.219605 | + | 0.866035i | ||||
\(171\) | −0.801918 | −0.0613242 | ||||||||
\(172\) | 26.7644i | 2.04076i | ||||||||
\(173\) | − | 14.5699i | − | 1.10773i | −0.832607 | − | 0.553864i | \(-0.813153\pi\) | ||
0.832607 | − | 0.553864i | \(-0.186847\pi\) | |||||||
\(174\) | −9.56284 | −0.724957 | ||||||||
\(175\) | −2.38255 | − | 4.39584i | −0.180104 | − | 0.332295i | ||||
\(176\) | 3.81684 | 0.287705 | ||||||||
\(177\) | − | 0.232249i | − | 0.0174569i | ||||||
\(178\) | 21.3774i | 1.60231i | ||||||||
\(179\) | −22.2817 | −1.66542 | −0.832708 | − | 0.553713i | \(-0.813211\pi\) | ||||
−0.832708 | + | 0.553713i | \(0.813211\pi\) | |||||||
\(180\) | −1.14745 | − | 4.52510i | −0.0855260 | − | 0.337281i | ||||
\(181\) | −0.314870 | −0.0234041 | −0.0117021 | − | 0.999932i | \(-0.503725\pi\) | ||||
−0.0117021 | + | 0.999932i | \(0.503725\pi\) | |||||||
\(182\) | 11.0155i | 0.816524i | ||||||||
\(183\) | − | 15.4328i | − | 1.14083i | ||||||
\(184\) | −0.720401 | −0.0531087 | ||||||||
\(185\) | 0.800590 | − | 0.203010i | 0.0588605 | − | 0.0149256i | ||||
\(186\) | −19.2267 | −1.40977 | ||||||||
\(187\) | − | 2.57671i | − | 0.188428i | ||||||
\(188\) | − | 21.8529i | − | 1.59379i | ||||||
\(189\) | −1.00000 | −0.0727393 | ||||||||
\(190\) | 3.51418 | − | 0.891108i | 0.254945 | − | 0.0646478i | ||||
\(191\) | 25.0569 | 1.81306 | 0.906528 | − | 0.422145i | \(-0.138723\pi\) | ||||
0.906528 | + | 0.422145i | \(0.138723\pi\) | |||||||
\(192\) | − | 8.68579i | − | 0.626843i | ||||||
\(193\) | − | 9.45610i | − | 0.680665i | −0.940305 | − | 0.340333i | \(-0.889460\pi\) | ||
0.940305 | − | 0.340333i | \(-0.110540\pi\) | |||||||
\(194\) | 24.8260 | 1.78240 | ||||||||
\(195\) | 2.99449 | + | 11.8091i | 0.214440 | + | 0.845667i | ||||
\(196\) | 2.08773 | 0.149124 | ||||||||
\(197\) | 4.03568i | 0.287530i | 0.989612 | + | 0.143765i | \(0.0459210\pi\) | ||||
−0.989612 | + | 0.143765i | \(0.954079\pi\) | |||||||
\(198\) | 2.02181i | 0.143684i | ||||||||
\(199\) | 27.6266 | 1.95840 | 0.979199 | − | 0.202903i | \(-0.0650377\pi\) | ||||
0.979199 | + | 0.202903i | \(0.0650377\pi\) | |||||||
\(200\) | 0.422617 | + | 0.779734i | 0.0298835 | + | 0.0551355i | ||||
\(201\) | −14.9167 | −1.05214 | ||||||||
\(202\) | 4.47763i | 0.315045i | ||||||||
\(203\) | − | 4.72983i | − | 0.331969i | ||||||
\(204\) | −5.37949 | −0.376639 | ||||||||
\(205\) | 3.33718 | + | 13.1605i | 0.233079 | + | 0.919172i | ||||
\(206\) | −30.3177 | −2.11233 | ||||||||
\(207\) | 4.06135i | 0.282283i | ||||||||
\(208\) | 20.7954i | 1.44190i | ||||||||
\(209\) | −0.801918 | −0.0554698 | ||||||||
\(210\) | 4.38222 | − | 1.11122i | 0.302402 | − | 0.0766816i | ||||
\(211\) | −12.9896 | −0.894244 | −0.447122 | − | 0.894473i | \(-0.647551\pi\) | ||||
−0.447122 | + | 0.894473i | \(0.647551\pi\) | |||||||
\(212\) | 17.1138i | 1.17538i | ||||||||
\(213\) | 9.27387i | 0.635435i | ||||||||
\(214\) | −19.8085 | −1.35408 | ||||||||
\(215\) | −27.7866 | + | 7.04598i | −1.89503 | + | 0.480532i | ||||
\(216\) | 0.177380 | 0.0120692 | ||||||||
\(217\) | − | 9.50964i | − | 0.645557i | ||||||
\(218\) | 1.62827i | 0.110280i | ||||||||
\(219\) | −10.5828 | −0.715119 | ||||||||
\(220\) | −1.14745 | − | 4.52510i | −0.0773612 | − | 0.305082i | ||||
\(221\) | 14.0388 | 0.944350 | ||||||||
\(222\) | 0.746790i | 0.0501213i | ||||||||
\(223\) | − | 5.10103i | − | 0.341590i | −0.985307 | − | 0.170795i | \(-0.945366\pi\) | ||
0.985307 | − | 0.170795i | \(-0.0546336\pi\) | |||||||
\(224\) | 8.07170 | 0.539313 | ||||||||
\(225\) | 4.39584 | − | 2.38255i | 0.293056 | − | 0.158837i | ||||
\(226\) | −37.0583 | −2.46508 | ||||||||
\(227\) | 8.23018i | 0.546256i | 0.961978 | + | 0.273128i | \(0.0880583\pi\) | ||||
−0.961978 | + | 0.273128i | \(0.911942\pi\) | |||||||
\(228\) | 1.67419i | 0.110876i | ||||||||
\(229\) | −3.29195 | −0.217538 | −0.108769 | − | 0.994067i | \(-0.534691\pi\) | ||||
−0.108769 | + | 0.994067i | \(0.534691\pi\) | |||||||
\(230\) | −4.51306 | − | 17.7977i | −0.297582 | − | 1.17355i | ||||
\(231\) | −1.00000 | −0.0657952 | ||||||||
\(232\) | 0.838976i | 0.0550815i | ||||||||
\(233\) | 3.13826i | 0.205594i | 0.994702 | + | 0.102797i | \(0.0327793\pi\) | ||||
−0.994702 | + | 0.102797i | \(0.967221\pi\) | |||||||
\(234\) | −11.0155 | −0.720107 | ||||||||
\(235\) | 22.6875 | − | 5.75299i | 1.47997 | − | 0.375284i | ||||
\(236\) | −0.484874 | −0.0315626 | ||||||||
\(237\) | 13.3303i | 0.865899i | ||||||||
\(238\) | − | 5.20963i | − | 0.337690i | ||||||
\(239\) | 25.5582 | 1.65322 | 0.826610 | − | 0.562775i | \(-0.190266\pi\) | ||||
0.826610 | + | 0.562775i | \(0.190266\pi\) | |||||||
\(240\) | 8.27288 | − | 2.09779i | 0.534012 | − | 0.135412i | ||||
\(241\) | 1.88461 | 0.121398 | 0.0606991 | − | 0.998156i | \(-0.480667\pi\) | ||||
0.0606991 | + | 0.998156i | \(0.480667\pi\) | |||||||
\(242\) | 2.02181i | 0.129967i | ||||||||
\(243\) | − | 1.00000i | − | 0.0641500i | ||||||
\(244\) | −32.2196 | −2.06265 | ||||||||
\(245\) | 0.549616 | + | 2.16747i | 0.0351137 | + | 0.138475i | ||||
\(246\) | −12.2761 | −0.782699 | ||||||||
\(247\) | − | 4.36911i | − | 0.278000i | ||||||
\(248\) | 1.68682i | 0.107113i | ||||||||
\(249\) | −5.21440 | −0.330449 | ||||||||
\(250\) | −16.6160 | + | 15.3256i | −1.05089 | + | 0.969277i | ||||
\(251\) | −9.74338 | −0.614997 | −0.307498 | − | 0.951549i | \(-0.599492\pi\) | ||||
−0.307498 | + | 0.951549i | \(0.599492\pi\) | |||||||
\(252\) | 2.08773i | 0.131515i | ||||||||
\(253\) | 4.06135i | 0.255335i | ||||||||
\(254\) | 8.32526 | 0.522373 | ||||||||
\(255\) | −1.41620 | − | 5.58494i | −0.0886860 | − | 0.349743i | ||||
\(256\) | 14.5053 | 0.906582 | ||||||||
\(257\) | − | 17.6638i | − | 1.10184i | −0.834558 | − | 0.550920i | \(-0.814277\pi\) | ||
0.834558 | − | 0.550920i | \(-0.185723\pi\) | |||||||
\(258\) | − | 25.9193i | − | 1.61366i | ||||||
\(259\) | −0.369366 | −0.0229513 | ||||||||
\(260\) | 24.6542 | − | 6.25170i | 1.52899 | − | 0.387714i | ||||
\(261\) | 4.72983 | 0.292769 | ||||||||
\(262\) | − | 14.9885i | − | 0.925994i | ||||||
\(263\) | 22.9064i | 1.41247i | 0.707976 | + | 0.706236i | \(0.249608\pi\) | ||||
−0.707976 | + | 0.706236i | \(0.750392\pi\) | |||||||
\(264\) | 0.177380 | 0.0109170 | ||||||||
\(265\) | −17.7674 | + | 4.50536i | −1.09144 | + | 0.276762i | ||||
\(266\) | −1.62133 | −0.0994100 | ||||||||
\(267\) | − | 10.5734i | − | 0.647081i | ||||||
\(268\) | 31.1421i | 1.90230i | ||||||||
\(269\) | −8.26091 | −0.503677 | −0.251838 | − | 0.967769i | \(-0.581035\pi\) | ||||
−0.251838 | + | 0.967769i | \(0.581035\pi\) | |||||||
\(270\) | 1.11122 | + | 4.38222i | 0.0676268 | + | 0.266693i | ||||
\(271\) | 23.9284 | 1.45355 | 0.726773 | − | 0.686878i | \(-0.241019\pi\) | ||||
0.726773 | + | 0.686878i | \(0.241019\pi\) | |||||||
\(272\) | − | 9.83489i | − | 0.596328i | ||||||
\(273\) | − | 5.44833i | − | 0.329748i | ||||||
\(274\) | −18.3345 | −1.10763 | ||||||||
\(275\) | 4.39584 | − | 2.38255i | 0.265079 | − | 0.143673i | ||||
\(276\) | 8.47901 | 0.510376 | ||||||||
\(277\) | − | 17.0380i | − | 1.02371i | −0.859071 | − | 0.511857i | \(-0.828958\pi\) | ||
0.859071 | − | 0.511857i | \(-0.171042\pi\) | |||||||
\(278\) | 14.5916i | 0.875148i | ||||||||
\(279\) | 9.50964 | 0.569327 | ||||||||
\(280\) | −0.0974908 | − | 0.384465i | −0.00582619 | − | 0.0229762i | ||||
\(281\) | −19.6769 | −1.17382 | −0.586912 | − | 0.809651i | \(-0.699656\pi\) | ||||
−0.586912 | + | 0.809651i | \(0.699656\pi\) | |||||||
\(282\) | 21.1629i | 1.26023i | ||||||||
\(283\) | 4.63518i | 0.275533i | 0.990465 | + | 0.137766i | \(0.0439923\pi\) | ||||
−0.990465 | + | 0.137766i | \(0.956008\pi\) | |||||||
\(284\) | 19.3614 | 1.14889 | ||||||||
\(285\) | −1.73813 | + | 0.440747i | −0.102958 | + | 0.0261076i | ||||
\(286\) | −11.0155 | −0.651361 | ||||||||
\(287\) | − | 6.07185i | − | 0.358410i | ||||||
\(288\) | 8.07170i | 0.475629i | ||||||||
\(289\) | 10.3606 | 0.609445 | ||||||||
\(290\) | −20.7272 | + | 5.25589i | −1.21714 | + | 0.308636i | ||||
\(291\) | −12.2790 | −0.719811 | ||||||||
\(292\) | 22.0941i | 1.29296i | ||||||||
\(293\) | − | 17.7414i | − | 1.03646i | −0.855241 | − | 0.518231i | \(-0.826591\pi\) | ||
0.855241 | − | 0.518231i | \(-0.173409\pi\) | |||||||
\(294\) | −2.02181 | −0.117915 | ||||||||
\(295\) | −0.127648 | − | 0.503392i | −0.00743194 | − | 0.0293086i | ||||
\(296\) | 0.0655181 | 0.00380816 | ||||||||
\(297\) | − | 1.00000i | − | 0.0580259i | ||||||
\(298\) | 13.4068i | 0.776636i | ||||||||
\(299\) | −22.1276 | −1.27967 | ||||||||
\(300\) | −4.97413 | − | 9.17735i | −0.287182 | − | 0.529855i | ||||
\(301\) | 12.8198 | 0.738922 | ||||||||
\(302\) | − | 39.0042i | − | 2.24444i | ||||||
\(303\) | − | 2.21466i | − | 0.127229i | ||||||
\(304\) | −3.06079 | −0.175548 | ||||||||
\(305\) | −8.48211 | − | 33.4501i | −0.485684 | − | 1.91535i | ||||
\(306\) | 5.20963 | 0.297815 | ||||||||
\(307\) | − | 13.7194i | − | 0.783008i | −0.920176 | − | 0.391504i | \(-0.871955\pi\) | ||
0.920176 | − | 0.391504i | \(-0.128045\pi\) | |||||||
\(308\) | 2.08773i | 0.118960i | ||||||||
\(309\) | 14.9953 | 0.853052 | ||||||||
\(310\) | −41.6733 | + | 10.5673i | −2.36689 | + | 0.600183i | ||||
\(311\) | −0.512264 | −0.0290478 | −0.0145239 | − | 0.999895i | \(-0.504623\pi\) | ||||
−0.0145239 | + | 0.999895i | \(0.504623\pi\) | |||||||
\(312\) | 0.966424i | 0.0547130i | ||||||||
\(313\) | 3.12863i | 0.176841i | 0.996083 | + | 0.0884204i | \(0.0281819\pi\) | ||||
−0.996083 | + | 0.0884204i | \(0.971818\pi\) | |||||||
\(314\) | −19.4161 | −1.09571 | ||||||||
\(315\) | −2.16747 | + | 0.549616i | −0.122123 | + | 0.0309674i | ||||
\(316\) | 27.8302 | 1.56557 | ||||||||
\(317\) | − | 7.61306i | − | 0.427592i | −0.976878 | − | 0.213796i | \(-0.931417\pi\) | ||
0.976878 | − | 0.213796i | \(-0.0685828\pi\) | |||||||
\(318\) | − | 16.5734i | − | 0.929391i | ||||||
\(319\) | 4.72983 | 0.264820 | ||||||||
\(320\) | −4.77385 | − | 18.8262i | −0.266866 | − | 1.05242i | ||||
\(321\) | 9.79736 | 0.546836 | ||||||||
\(322\) | 8.21129i | 0.457597i | ||||||||
\(323\) | 2.06631i | 0.114973i | ||||||||
\(324\) | −2.08773 | −0.115985 | ||||||||
\(325\) | 12.9809 | + | 23.9500i | 0.720052 | + | 1.32851i | ||||
\(326\) | −2.21517 | −0.122687 | ||||||||
\(327\) | − | 0.805348i | − | 0.0445359i | ||||||
\(328\) | 1.07702i | 0.0594687i | ||||||||
\(329\) | −10.4673 | −0.577080 | ||||||||
\(330\) | 1.11122 | + | 4.38222i | 0.0611707 | + | 0.241233i | ||||
\(331\) | −4.56072 | −0.250680 | −0.125340 | − | 0.992114i | \(-0.540002\pi\) | ||||
−0.125340 | + | 0.992114i | \(0.540002\pi\) | |||||||
\(332\) | 10.8863i | 0.597462i | ||||||||
\(333\) | − | 0.369366i | − | 0.0202411i | ||||||
\(334\) | −29.0484 | −1.58946 | ||||||||
\(335\) | −32.3315 | + | 8.19845i | −1.76646 | + | 0.447929i | ||||
\(336\) | −3.81684 | −0.208226 | ||||||||
\(337\) | − | 10.3709i | − | 0.564938i | −0.959276 | − | 0.282469i | \(-0.908847\pi\) | ||
0.959276 | − | 0.282469i | \(-0.0911535\pi\) | |||||||
\(338\) | − | 33.7326i | − | 1.83481i | ||||||
\(339\) | 18.3292 | 0.995506 | ||||||||
\(340\) | −11.6599 | + | 2.95665i | −0.632345 | + | 0.160347i | ||||
\(341\) | 9.50964 | 0.514976 | ||||||||
\(342\) | − | 1.62133i | − | 0.0876714i | ||||||
\(343\) | − | 1.00000i | − | 0.0539949i | ||||||
\(344\) | −2.27398 | −0.122605 | ||||||||
\(345\) | 2.23218 | + | 8.80284i | 0.120177 | + | 0.473929i | ||||
\(346\) | 29.4576 | 1.58365 | ||||||||
\(347\) | − | 1.74157i | − | 0.0934922i | −0.998907 | − | 0.0467461i | \(-0.985115\pi\) | ||
0.998907 | − | 0.0467461i | \(-0.0148852\pi\) | |||||||
\(348\) | − | 9.87462i | − | 0.529335i | ||||||
\(349\) | −25.0894 | −1.34301 | −0.671503 | − | 0.741002i | \(-0.734351\pi\) | ||||
−0.671503 | + | 0.741002i | \(0.734351\pi\) | |||||||
\(350\) | 8.88758 | − | 4.81708i | 0.475061 | − | 0.257484i | ||||
\(351\) | 5.44833 | 0.290810 | ||||||||
\(352\) | 8.07170i | 0.430223i | ||||||||
\(353\) | − | 18.4717i | − | 0.983150i | −0.870835 | − | 0.491575i | \(-0.836421\pi\) | ||
0.870835 | − | 0.491575i | \(-0.163579\pi\) | |||||||
\(354\) | 0.469564 | 0.0249570 | ||||||||
\(355\) | 5.09707 | + | 20.1008i | 0.270524 | + | 1.06684i | ||||
\(356\) | −22.0744 | −1.16994 | ||||||||
\(357\) | 2.57671i | 0.136374i | ||||||||
\(358\) | − | 45.0495i | − | 2.38094i | ||||||
\(359\) | 19.7245 | 1.04102 | 0.520509 | − | 0.853856i | \(-0.325742\pi\) | ||||
0.520509 | + | 0.853856i | \(0.325742\pi\) | |||||||
\(360\) | 0.384465 | − | 0.0974908i | 0.0202631 | − | 0.00513822i | ||||
\(361\) | −18.3569 | −0.966154 | ||||||||
\(362\) | − | 0.636610i | − | 0.0334595i | ||||||
\(363\) | − | 1.00000i | − | 0.0524864i | ||||||
\(364\) | −11.3747 | −0.596194 | ||||||||
\(365\) | −22.9379 | + | 5.81648i | −1.20062 | + | 0.304448i | ||||
\(366\) | 31.2023 | 1.63097 | ||||||||
\(367\) | 14.4499i | 0.754277i | 0.926157 | + | 0.377138i | \(0.123092\pi\) | ||||
−0.926157 | + | 0.377138i | \(0.876908\pi\) | |||||||
\(368\) | 15.5015i | 0.808071i | ||||||||
\(369\) | 6.07185 | 0.316088 | ||||||||
\(370\) | 0.410448 | + | 1.61864i | 0.0213382 | + | 0.0841493i | ||||
\(371\) | 8.19730 | 0.425582 | ||||||||
\(372\) | − | 19.8536i | − | 1.02936i | ||||||
\(373\) | 18.6903i | 0.967746i | 0.875138 | + | 0.483873i | \(0.160770\pi\) | ||||
−0.875138 | + | 0.483873i | \(0.839230\pi\) | |||||||
\(374\) | 5.20963 | 0.269384 | ||||||||
\(375\) | 8.21837 | − | 7.58013i | 0.424395 | − | 0.391436i | ||||
\(376\) | 1.85669 | 0.0957513 | ||||||||
\(377\) | 25.7697i | 1.32721i | ||||||||
\(378\) | − | 2.02181i | − | 0.103991i | ||||||
\(379\) | 18.7279 | 0.961988 | 0.480994 | − | 0.876724i | \(-0.340276\pi\) | ||||
0.480994 | + | 0.876724i | \(0.340276\pi\) | |||||||
\(380\) | 0.920162 | + | 3.62875i | 0.0472033 | + | 0.186151i | ||||
\(381\) | −4.11772 | −0.210957 | ||||||||
\(382\) | 50.6605i | 2.59202i | ||||||||
\(383\) | 28.9782i | 1.48072i | 0.672213 | + | 0.740358i | \(0.265344\pi\) | ||||
−0.672213 | + | 0.740358i | \(0.734656\pi\) | |||||||
\(384\) | 1.41767 | 0.0723453 | ||||||||
\(385\) | −2.16747 | + | 0.549616i | −0.110464 | + | 0.0280110i | ||||
\(386\) | 19.1185 | 0.973105 | ||||||||
\(387\) | 12.8198i | 0.651668i | ||||||||
\(388\) | 25.6354i | 1.30144i | ||||||||
\(389\) | −0.520340 | −0.0263823 | −0.0131911 | − | 0.999913i | \(-0.504199\pi\) | ||||
−0.0131911 | + | 0.999913i | \(0.504199\pi\) | |||||||
\(390\) | −23.8758 | + | 6.05430i | −1.20900 | + | 0.306572i | ||||
\(391\) | 10.4649 | 0.529234 | ||||||||
\(392\) | 0.177380i | 0.00895903i | ||||||||
\(393\) | 7.41340i | 0.373957i | ||||||||
\(394\) | −8.15940 | −0.411065 | ||||||||
\(395\) | 7.32657 | + | 28.8931i | 0.368640 | + | 1.45377i | ||||
\(396\) | −2.08773 | −0.104913 | ||||||||
\(397\) | 5.41741i | 0.271892i | 0.990716 | + | 0.135946i | \(0.0434074\pi\) | ||||
−0.990716 | + | 0.135946i | \(0.956593\pi\) | |||||||
\(398\) | 55.8559i | 2.79980i | ||||||||
\(399\) | 0.801918 | 0.0401461 | ||||||||
\(400\) | 16.7782 | − | 9.09381i | 0.838911 | − | 0.454691i | ||||
\(401\) | 2.98876 | 0.149251 | 0.0746257 | − | 0.997212i | \(-0.476224\pi\) | ||||
0.0746257 | + | 0.997212i | \(0.476224\pi\) | |||||||
\(402\) | − | 30.1588i | − | 1.50418i | ||||||
\(403\) | 51.8117i | 2.58092i | ||||||||
\(404\) | −4.62361 | −0.230033 | ||||||||
\(405\) | −0.549616 | − | 2.16747i | −0.0273106 | − | 0.107702i | ||||
\(406\) | 9.56284 | 0.474596 | ||||||||
\(407\) | − | 0.369366i | − | 0.0183088i | ||||||
\(408\) | − | 0.457057i | − | 0.0226277i | ||||||
\(409\) | 15.0596 | 0.744648 | 0.372324 | − | 0.928103i | \(-0.378561\pi\) | ||||
0.372324 | + | 0.928103i | \(0.378561\pi\) | |||||||
\(410\) | −26.6082 | + | 6.74717i | −1.31408 | + | 0.333219i | ||||
\(411\) | 9.06835 | 0.447309 | ||||||||
\(412\) | − | 31.3061i | − | 1.54234i | ||||||
\(413\) | 0.232249i | 0.0114282i | ||||||||
\(414\) | −8.21129 | −0.403563 | ||||||||
\(415\) | −11.3021 | + | 2.86592i | −0.554796 | + | 0.140682i | ||||
\(416\) | −43.9773 | −2.15616 | ||||||||
\(417\) | − | 7.21710i | − | 0.353423i | ||||||
\(418\) | − | 1.62133i | − | 0.0793018i | ||||||
\(419\) | 25.7411 | 1.25753 | 0.628767 | − | 0.777594i | \(-0.283560\pi\) | ||||
0.628767 | + | 0.777594i | \(0.283560\pi\) | |||||||
\(420\) | 1.14745 | + | 4.52510i | 0.0559899 | + | 0.220802i | ||||
\(421\) | 5.47012 | 0.266597 | 0.133299 | − | 0.991076i | \(-0.457443\pi\) | ||||
0.133299 | + | 0.991076i | \(0.457443\pi\) | |||||||
\(422\) | − | 26.2627i | − | 1.27845i | ||||||
\(423\) | − | 10.4673i | − | 0.508937i | ||||||
\(424\) | −1.45403 | −0.0706142 | ||||||||
\(425\) | −6.13915 | − | 11.3268i | −0.297792 | − | 0.549432i | ||||
\(426\) | −18.7501 | −0.908443 | ||||||||
\(427\) | 15.4328i | 0.746845i | ||||||||
\(428\) | − | 20.4543i | − | 0.988695i | ||||||
\(429\) | 5.44833 | 0.263048 | ||||||||
\(430\) | −14.2457 | − | 56.1793i | −0.686987 | − | 2.70920i | ||||
\(431\) | −2.40289 | −0.115743 | −0.0578715 | − | 0.998324i | \(-0.518431\pi\) | ||||
−0.0578715 | + | 0.998324i | \(0.518431\pi\) | |||||||
\(432\) | − | 3.81684i | − | 0.183638i | ||||||
\(433\) | 5.28854i | 0.254151i | 0.991893 | + | 0.127075i | \(0.0405590\pi\) | ||||
−0.991893 | + | 0.127075i | \(0.959441\pi\) | |||||||
\(434\) | 19.2267 | 0.922913 | ||||||||
\(435\) | 10.2518 | − | 2.59959i | 0.491534 | − | 0.124641i | ||||
\(436\) | −1.68135 | −0.0805222 | ||||||||
\(437\) | − | 3.25687i | − | 0.155797i | ||||||
\(438\) | − | 21.3965i | − | 1.02236i | ||||||
\(439\) | −3.58440 | −0.171074 | −0.0855370 | − | 0.996335i | \(-0.527261\pi\) | ||||
−0.0855370 | + | 0.996335i | \(0.527261\pi\) | |||||||
\(440\) | 0.384465 | − | 0.0974908i | 0.0183287 | − | 0.00464769i | ||||
\(441\) | 1.00000 | 0.0476190 | ||||||||
\(442\) | 28.3838i | 1.35008i | ||||||||
\(443\) | − | 0.658409i | − | 0.0312820i | −0.999878 | − | 0.0156410i | \(-0.995021\pi\) | ||
0.999878 | − | 0.0156410i | \(-0.00497888\pi\) | |||||||
\(444\) | −0.771138 | −0.0365966 | ||||||||
\(445\) | −5.81131 | − | 22.9175i | −0.275482 | − | 1.08639i | ||||
\(446\) | 10.3133 | 0.488350 | ||||||||
\(447\) | − | 6.63108i | − | 0.313639i | ||||||
\(448\) | 8.68579i | 0.410365i | ||||||||
\(449\) | −18.7482 | −0.884781 | −0.442391 | − | 0.896823i | \(-0.645869\pi\) | ||||
−0.442391 | + | 0.896823i | \(0.645869\pi\) | |||||||
\(450\) | 4.81708 | + | 8.88758i | 0.227079 | + | 0.418965i | ||||
\(451\) | 6.07185 | 0.285912 | ||||||||
\(452\) | − | 38.2665i | − | 1.79991i | ||||||
\(453\) | 19.2917i | 0.906402i | ||||||||
\(454\) | −16.6399 | −0.780949 | ||||||||
\(455\) | −2.99449 | − | 11.8091i | −0.140384 | − | 0.553619i | ||||
\(456\) | −0.142244 | −0.00666119 | ||||||||
\(457\) | − | 29.2056i | − | 1.36618i | −0.730335 | − | 0.683090i | \(-0.760636\pi\) | ||
0.730335 | − | 0.683090i | \(-0.239364\pi\) | |||||||
\(458\) | − | 6.65570i | − | 0.311001i | ||||||
\(459\) | −2.57671 | −0.120271 | ||||||||
\(460\) | 18.3780 | − | 4.66020i | 0.856878 | − | 0.217283i | ||||
\(461\) | −3.97847 | −0.185296 | −0.0926480 | − | 0.995699i | \(-0.529533\pi\) | ||||
−0.0926480 | + | 0.995699i | \(0.529533\pi\) | |||||||
\(462\) | − | 2.02181i | − | 0.0940633i | ||||||
\(463\) | 40.1219i | 1.86463i | 0.361654 | + | 0.932313i | \(0.382212\pi\) | ||||
−0.361654 | + | 0.932313i | \(0.617788\pi\) | |||||||
\(464\) | 18.0530 | 0.838089 | ||||||||
\(465\) | 20.6119 | − | 5.22665i | 0.955852 | − | 0.242380i | ||||
\(466\) | −6.34498 | −0.293926 | ||||||||
\(467\) | − | 33.0723i | − | 1.53040i | −0.643790 | − | 0.765202i | \(-0.722639\pi\) | ||
0.643790 | − | 0.765202i | \(-0.277361\pi\) | |||||||
\(468\) | − | 11.3747i | − | 0.525794i | ||||||
\(469\) | 14.9167 | 0.688789 | ||||||||
\(470\) | 11.6315 | + | 45.8700i | 0.536520 | + | 2.11582i | ||||
\(471\) | 9.60329 | 0.442496 | ||||||||
\(472\) | − | 0.0411963i | − | 0.00189621i | ||||||
\(473\) | 12.8198i | 0.589456i | ||||||||
\(474\) | −26.9515 | −1.23792 | ||||||||
\(475\) | −3.52511 | + | 1.91061i | −0.161743 | + | 0.0876648i | ||||
\(476\) | 5.37949 | 0.246568 | ||||||||
\(477\) | 8.19730i | 0.375328i | ||||||||
\(478\) | 51.6739i | 2.36351i | ||||||||
\(479\) | 12.7565 | 0.582859 | 0.291429 | − | 0.956592i | \(-0.405869\pi\) | ||||
0.291429 | + | 0.956592i | \(0.405869\pi\) | |||||||
\(480\) | 4.43633 | + | 17.4951i | 0.202490 | + | 0.798541i | ||||
\(481\) | 2.01243 | 0.0917589 | ||||||||
\(482\) | 3.81032i | 0.173555i | ||||||||
\(483\) | − | 4.06135i | − | 0.184798i | ||||||
\(484\) | −2.08773 | −0.0948970 | ||||||||
\(485\) | −26.6145 | + | 6.74876i | −1.20850 | + | 0.306445i | ||||
\(486\) | 2.02181 | 0.0917114 | ||||||||
\(487\) | − | 17.8968i | − | 0.810980i | −0.914100 | − | 0.405490i | \(-0.867101\pi\) | ||
0.914100 | − | 0.405490i | \(-0.132899\pi\) | |||||||
\(488\) | − | 2.73747i | − | 0.123919i | ||||||
\(489\) | 1.09563 | 0.0495463 | ||||||||
\(490\) | −4.38222 | + | 1.11122i | −0.197969 | + | 0.0501999i | ||||
\(491\) | −12.4841 | −0.563399 | −0.281699 | − | 0.959503i | \(-0.590898\pi\) | ||||
−0.281699 | + | 0.959503i | \(0.590898\pi\) | |||||||
\(492\) | − | 12.6764i | − | 0.571496i | ||||||
\(493\) | − | 12.1874i | − | 0.548893i | ||||||
\(494\) | 8.83354 | 0.397440 | ||||||||
\(495\) | −0.549616 | − | 2.16747i | −0.0247034 | − | 0.0974205i | ||||
\(496\) | 36.2968 | 1.62977 | ||||||||
\(497\) | − | 9.27387i | − | 0.415990i | ||||||
\(498\) | − | 10.5425i | − | 0.472423i | ||||||
\(499\) | −24.5411 | −1.09861 | −0.549306 | − | 0.835621i | \(-0.685108\pi\) | ||||
−0.549306 | + | 0.835621i | \(0.685108\pi\) | |||||||
\(500\) | −15.8253 | − | 17.1578i | −0.707729 | − | 0.767318i | ||||
\(501\) | 14.3675 | 0.641892 | ||||||||
\(502\) | − | 19.6993i | − | 0.879223i | ||||||
\(503\) | − | 39.7756i | − | 1.77350i | −0.462245 | − | 0.886752i | \(-0.652956\pi\) | ||
0.462245 | − | 0.886752i | \(-0.347044\pi\) | |||||||
\(504\) | −0.177380 | −0.00790113 | ||||||||
\(505\) | −1.21721 | − | 4.80020i | −0.0541652 | − | 0.213606i | ||||
\(506\) | −8.21129 | −0.365036 | ||||||||
\(507\) | 16.6843i | 0.740977i | ||||||||
\(508\) | 8.59670i | 0.381417i | ||||||||
\(509\) | −14.2699 | −0.632502 | −0.316251 | − | 0.948676i | \(-0.602424\pi\) | ||||
−0.316251 | + | 0.948676i | \(0.602424\pi\) | |||||||
\(510\) | 11.2917 | − | 2.86330i | 0.500006 | − | 0.126789i | ||||
\(511\) | 10.5828 | 0.468156 | ||||||||
\(512\) | 32.1624i | 1.42139i | ||||||||
\(513\) | 0.801918i | 0.0354055i | ||||||||
\(514\) | 35.7130 | 1.57523 | ||||||||
\(515\) | 32.5018 | − | 8.24165i | 1.43220 | − | 0.363170i | ||||
\(516\) | 26.7644 | 1.17824 | ||||||||
\(517\) | − | 10.4673i | − | 0.460351i | ||||||
\(518\) | − | 0.746790i | − | 0.0328121i | ||||||
\(519\) | −14.5699 | −0.639547 | ||||||||
\(520\) | 0.531162 | + | 2.09469i | 0.0232930 | + | 0.0918584i | ||||
\(521\) | 12.4960 | 0.547461 | 0.273731 | − | 0.961806i | \(-0.411742\pi\) | ||||
0.273731 | + | 0.961806i | \(0.411742\pi\) | |||||||
\(522\) | 9.56284i | 0.418554i | ||||||||
\(523\) | 29.4581i | 1.28811i | 0.764977 | + | 0.644057i | \(0.222750\pi\) | ||||
−0.764977 | + | 0.644057i | \(0.777250\pi\) | |||||||
\(524\) | 15.4772 | 0.676125 | ||||||||
\(525\) | −4.39584 | + | 2.38255i | −0.191850 | + | 0.103983i | ||||
\(526\) | −46.3126 | −2.01932 | ||||||||
\(527\) | − | 24.5036i | − | 1.06739i | ||||||
\(528\) | − | 3.81684i | − | 0.166107i | ||||||
\(529\) | 6.50546 | 0.282846 | ||||||||
\(530\) | −9.10901 | − | 35.9223i | −0.395670 | − | 1.56037i | ||||
\(531\) | −0.232249 | −0.0100787 | ||||||||
\(532\) | − | 1.67419i | − | 0.0725853i | ||||||
\(533\) | 33.0814i | 1.43292i | ||||||||
\(534\) | 21.3774 | 0.925092 | ||||||||
\(535\) | 21.2355 | − | 5.38479i | 0.918090 | − | 0.232805i | ||||
\(536\) | −2.64592 | −0.114286 | ||||||||
\(537\) | 22.2817i | 0.961528i | ||||||||
\(538\) | − | 16.7020i | − | 0.720076i | ||||||
\(539\) | 1.00000 | 0.0430730 | ||||||||
\(540\) | −4.52510 | + | 1.14745i | −0.194729 | + | 0.0493785i | ||||
\(541\) | 21.0046 | 0.903060 | 0.451530 | − | 0.892256i | \(-0.350878\pi\) | ||||
0.451530 | + | 0.892256i | \(0.350878\pi\) | |||||||
\(542\) | 48.3787i | 2.07805i | ||||||||
\(543\) | 0.314870i | 0.0135124i | ||||||||
\(544\) | 20.7984 | 0.891725 | ||||||||
\(545\) | −0.442632 | − | 1.74557i | −0.0189603 | − | 0.0747719i | ||||
\(546\) | 11.0155 | 0.471421 | ||||||||
\(547\) | − | 16.8542i | − | 0.720634i | −0.932830 | − | 0.360317i | \(-0.882669\pi\) | ||
0.932830 | − | 0.360317i | \(-0.117331\pi\) | |||||||
\(548\) | − | 18.9323i | − | 0.808748i | ||||||
\(549\) | −15.4328 | −0.658656 | ||||||||
\(550\) | 4.81708 | + | 8.88758i | 0.205401 | + | 0.378968i | ||||
\(551\) | −3.79293 | −0.161584 | ||||||||
\(552\) | 0.720401i | 0.0306623i | ||||||||
\(553\) | − | 13.3303i | − | 0.566864i | ||||||
\(554\) | 34.4477 | 1.46354 | ||||||||
\(555\) | −0.203010 | − | 0.800590i | −0.00861728 | − | 0.0339832i | ||||
\(556\) | −15.0674 | −0.638999 | ||||||||
\(557\) | − | 21.2648i | − | 0.901019i | −0.892772 | − | 0.450509i | \(-0.851242\pi\) | ||
0.892772 | − | 0.450509i | \(-0.148758\pi\) | |||||||
\(558\) | 19.2267i | 0.813932i | ||||||||
\(559\) | −69.8466 | −2.95420 | ||||||||
\(560\) | −8.27288 | + | 2.09779i | −0.349593 | + | 0.0886480i | ||||
\(561\) | −2.57671 | −0.108789 | ||||||||
\(562\) | − | 39.7830i | − | 1.67814i | ||||||
\(563\) | − | 29.7983i | − | 1.25585i | −0.778274 | − | 0.627925i | \(-0.783905\pi\) | ||
0.778274 | − | 0.627925i | \(-0.216095\pi\) | |||||||
\(564\) | −21.8529 | −0.920173 | ||||||||
\(565\) | 39.7280 | − | 10.0740i | 1.67137 | − | 0.423818i | ||||
\(566\) | −9.37147 | −0.393912 | ||||||||
\(567\) | 1.00000i | 0.0419961i | ||||||||
\(568\) | 1.64500i | 0.0690226i | ||||||||
\(569\) | 14.3258 | 0.600569 | 0.300284 | − | 0.953850i | \(-0.402918\pi\) | ||||
0.300284 | + | 0.953850i | \(0.402918\pi\) | |||||||
\(570\) | −0.891108 | − | 3.51418i | −0.0373244 | − | 0.147193i | ||||
\(571\) | 15.8350 | 0.662676 | 0.331338 | − | 0.943512i | \(-0.392500\pi\) | ||||
0.331338 | + | 0.943512i | \(0.392500\pi\) | |||||||
\(572\) | − | 11.3747i | − | 0.475598i | ||||||
\(573\) | − | 25.0569i | − | 1.04677i | ||||||
\(574\) | 12.2761 | 0.512397 | ||||||||
\(575\) | 9.67637 | + | 17.8530i | 0.403532 | + | 0.744524i | ||||
\(576\) | −8.68579 | −0.361908 | ||||||||
\(577\) | − | 32.4932i | − | 1.35271i | −0.736576 | − | 0.676355i | \(-0.763559\pi\) | ||
0.736576 | − | 0.676355i | \(-0.236441\pi\) | |||||||
\(578\) | 20.9471i | 0.871285i | ||||||||
\(579\) | −9.45610 | −0.392982 | ||||||||
\(580\) | −5.42725 | − | 21.4029i | −0.225354 | − | 0.888709i | ||||
\(581\) | 5.21440 | 0.216330 | ||||||||
\(582\) | − | 24.8260i | − | 1.02907i | ||||||
\(583\) | 8.19730i | 0.339497i | ||||||||
\(584\) | −1.87718 | −0.0776781 | ||||||||
\(585\) | 11.8091 | − | 2.99449i | 0.488246 | − | 0.123807i | ||||
\(586\) | 35.8697 | 1.48177 | ||||||||
\(587\) | − | 9.23858i | − | 0.381317i | −0.981656 | − | 0.190659i | \(-0.938938\pi\) | ||
0.981656 | − | 0.190659i | \(-0.0610623\pi\) | |||||||
\(588\) | − | 2.08773i | − | 0.0860967i | ||||||
\(589\) | −7.62595 | −0.314222 | ||||||||
\(590\) | 1.01777 | − | 0.258080i | 0.0419007 | − | 0.0106250i | ||||
\(591\) | 4.03568 | 0.166006 | ||||||||
\(592\) | − | 1.40981i | − | 0.0579429i | ||||||
\(593\) | − | 45.0180i | − | 1.84867i | −0.381586 | − | 0.924333i | \(-0.624622\pi\) | ||
0.381586 | − | 0.924333i | \(-0.375378\pi\) | |||||||
\(594\) | 2.02181 | 0.0829560 | ||||||||
\(595\) | 1.41620 | + | 5.58494i | 0.0580586 | + | 0.228960i | ||||
\(596\) | −13.8439 | −0.567070 | ||||||||
\(597\) | − | 27.6266i | − | 1.13068i | ||||||
\(598\) | − | 44.7378i | − | 1.82947i | ||||||
\(599\) | −12.0839 | −0.493735 | −0.246867 | − | 0.969049i | \(-0.579401\pi\) | ||||
−0.246867 | + | 0.969049i | \(0.579401\pi\) | |||||||
\(600\) | 0.779734 | − | 0.422617i | 0.0318325 | − | 0.0172532i | ||||
\(601\) | 9.97876 | 0.407042 | 0.203521 | − | 0.979071i | \(-0.434761\pi\) | ||||
0.203521 | + | 0.979071i | \(0.434761\pi\) | |||||||
\(602\) | 25.9193i | 1.05639i | ||||||||
\(603\) | 14.9167i | 0.607455i | ||||||||
\(604\) | 40.2759 | 1.63880 | ||||||||
\(605\) | −0.549616 | − | 2.16747i | −0.0223451 | − | 0.0881201i | ||||
\(606\) | 4.47763 | 0.181891 | ||||||||
\(607\) | 9.78393i | 0.397118i | 0.980089 | + | 0.198559i | \(0.0636261\pi\) | ||||
−0.980089 | + | 0.198559i | \(0.936374\pi\) | |||||||
\(608\) | − | 6.47283i | − | 0.262508i | ||||||
\(609\) | −4.72983 | −0.191662 | ||||||||
\(610\) | 67.6299 | − | 17.1493i | 2.73826 | − | 0.694353i | ||||
\(611\) | 57.0293 | 2.30716 | ||||||||
\(612\) | 5.37949i | 0.217453i | ||||||||
\(613\) | − | 35.1588i | − | 1.42005i | −0.704176 | − | 0.710025i | \(-0.748683\pi\) | ||
0.704176 | − | 0.710025i | \(-0.251317\pi\) | |||||||
\(614\) | 27.7381 | 1.11942 | ||||||||
\(615\) | 13.1605 | − | 3.33718i | 0.530684 | − | 0.134568i | ||||
\(616\) | −0.177380 | −0.00714684 | ||||||||
\(617\) | − | 21.5575i | − | 0.867871i | −0.900944 | − | 0.433936i | \(-0.857125\pi\) | ||
0.900944 | − | 0.433936i | \(-0.142875\pi\) | |||||||
\(618\) | 30.3177i | 1.21956i | ||||||||
\(619\) | 10.2962 | 0.413840 | 0.206920 | − | 0.978358i | \(-0.433656\pi\) | ||||
0.206920 | + | 0.978358i | \(0.433656\pi\) | |||||||
\(620\) | −10.9119 | − | 43.0321i | −0.438231 | − | 1.72821i | ||||
\(621\) | 4.06135 | 0.162976 | ||||||||
\(622\) | − | 1.03570i | − | 0.0415279i | ||||||
\(623\) | 10.5734i | 0.423614i | ||||||||
\(624\) | 20.7954 | 0.832482 | ||||||||
\(625\) | 13.6469 | − | 20.9467i | 0.545876 | − | 0.837866i | ||||
\(626\) | −6.32552 | −0.252818 | ||||||||
\(627\) | 0.801918i | 0.0320255i | ||||||||
\(628\) | − | 20.0491i | − | 0.800046i | ||||||
\(629\) | −0.951750 | −0.0379488 | ||||||||
\(630\) | −1.11122 | − | 4.38222i | −0.0442721 | − | 0.174592i | ||||
\(631\) | −43.4243 | −1.72869 | −0.864347 | − | 0.502896i | \(-0.832268\pi\) | ||||
−0.864347 | + | 0.502896i | \(0.832268\pi\) | |||||||
\(632\) | 2.36453i | 0.0940561i | ||||||||
\(633\) | 12.9896i | 0.516292i | ||||||||
\(634\) | 15.3922 | 0.611302 | ||||||||
\(635\) | −8.92503 | + | 2.26316i | −0.354179 | + | 0.0898109i | ||||
\(636\) | 17.1138 | 0.678605 | ||||||||
\(637\) | 5.44833i | 0.215871i | ||||||||
\(638\) | 9.56284i | 0.378596i | ||||||||
\(639\) | 9.27387 | 0.366869 | ||||||||
\(640\) | 3.07276 | − | 0.779176i | 0.121462 | − | 0.0307996i | ||||
\(641\) | −16.6086 | −0.656002 | −0.328001 | − | 0.944677i | \(-0.606375\pi\) | ||||
−0.328001 | + | 0.944677i | \(0.606375\pi\) | |||||||
\(642\) | 19.8085i | 0.781777i | ||||||||
\(643\) | 45.9180i | 1.81083i | 0.424527 | + | 0.905415i | \(0.360440\pi\) | ||||
−0.424527 | + | 0.905415i | \(0.639560\pi\) | |||||||
\(644\) | −8.47901 | −0.334120 | ||||||||
\(645\) | 7.04598 | + | 27.7866i | 0.277435 | + | 1.09409i | ||||
\(646\) | −4.17770 | −0.164369 | ||||||||
\(647\) | 14.0765i | 0.553403i | 0.960956 | + | 0.276701i | \(0.0892412\pi\) | ||||
−0.960956 | + | 0.276701i | \(0.910759\pi\) | |||||||
\(648\) | − | 0.177380i | − | 0.00696814i | ||||||
\(649\) | −0.232249 | −0.00911657 | ||||||||
\(650\) | −48.4225 | + | 26.2450i | −1.89929 | + | 1.02941i | ||||
\(651\) | −9.50964 | −0.372712 | ||||||||
\(652\) | − | 2.28739i | − | 0.0895811i | ||||||
\(653\) | 7.20161i | 0.281821i | 0.990022 | + | 0.140910i | \(0.0450030\pi\) | ||||
−0.990022 | + | 0.140910i | \(0.954997\pi\) | |||||||
\(654\) | 1.62827 | 0.0636702 | ||||||||
\(655\) | 4.07453 | + | 16.0683i | 0.159205 | + | 0.627841i | ||||
\(656\) | 23.1753 | 0.904842 | ||||||||
\(657\) | 10.5828i | 0.412874i | ||||||||
\(658\) | − | 21.1629i | − | 0.825016i | ||||||
\(659\) | −5.49951 | −0.214231 | −0.107115 | − | 0.994247i | \(-0.534161\pi\) | ||||
−0.107115 | + | 0.994247i | \(0.534161\pi\) | |||||||
\(660\) | −4.52510 | + | 1.14745i | −0.176139 | + | 0.0446645i | ||||
\(661\) | 33.5903 | 1.30651 | 0.653256 | − | 0.757137i | \(-0.273403\pi\) | ||||
0.653256 | + | 0.757137i | \(0.273403\pi\) | |||||||
\(662\) | − | 9.22093i | − | 0.358381i | ||||||
\(663\) | − | 14.0388i | − | 0.545221i | ||||||
\(664\) | −0.924929 | −0.0358942 | ||||||||
\(665\) | 1.73813 | − | 0.440747i | 0.0674019 | − | 0.0170914i | ||||
\(666\) | 0.746790 | 0.0289375 | ||||||||
\(667\) | 19.2095i | 0.743794i | ||||||||
\(668\) | − | 29.9955i | − | 1.16056i | ||||||
\(669\) | −5.10103 | −0.197217 | ||||||||
\(670\) | −16.5757 | − | 65.3682i | −0.640377 | − | 2.52539i | ||||
\(671\) | −15.4328 | −0.595777 | ||||||||
\(672\) | − | 8.07170i | − | 0.311372i | ||||||
\(673\) | 35.9603i | 1.38617i | 0.720857 | + | 0.693084i | \(0.243749\pi\) | ||||
−0.720857 | + | 0.693084i | \(0.756251\pi\) | |||||||
\(674\) | 20.9680 | 0.807657 | ||||||||
\(675\) | −2.38255 | − | 4.39584i | −0.0917044 | − | 0.169196i | ||||
\(676\) | 34.8324 | 1.33971 | ||||||||
\(677\) | − | 8.06821i | − | 0.310087i | −0.987908 | − | 0.155043i | \(-0.950448\pi\) | ||
0.987908 | − | 0.155043i | \(-0.0495517\pi\) | |||||||
\(678\) | 37.0583i | 1.42321i | ||||||||
\(679\) | 12.2790 | 0.471227 | ||||||||
\(680\) | −0.251206 | − | 0.990656i | −0.00963330 | − | 0.0379899i | ||||
\(681\) | 8.23018 | 0.315381 | ||||||||
\(682\) | 19.2267i | 0.736230i | ||||||||
\(683\) | − | 11.8720i | − | 0.454271i | −0.973863 | − | 0.227135i | \(-0.927064\pi\) | ||
0.973863 | − | 0.227135i | \(-0.0729360\pi\) | |||||||
\(684\) | 1.67419 | 0.0640142 | ||||||||
\(685\) | 19.6554 | − | 4.98411i | 0.750993 | − | 0.190433i | ||||
\(686\) | 2.02181 | 0.0771932 | ||||||||
\(687\) | 3.29195i | 0.125596i | ||||||||
\(688\) | 48.9312i | 1.86548i | ||||||||
\(689\) | −44.6616 | −1.70147 | ||||||||
\(690\) | −17.7977 | + | 4.51306i | −0.677547 | + | 0.171809i | ||||
\(691\) | 16.5331 | 0.628950 | 0.314475 | − | 0.949266i | \(-0.398172\pi\) | ||||
0.314475 | + | 0.949266i | \(0.398172\pi\) | |||||||
\(692\) | 30.4180i | 1.15632i | ||||||||
\(693\) | 1.00000i | 0.0379869i | ||||||||
\(694\) | 3.52112 | 0.133660 | ||||||||
\(695\) | −3.96663 | − | 15.6428i | −0.150463 | − | 0.593366i | ||||
\(696\) | 0.838976 | 0.0318013 | ||||||||
\(697\) | − | 15.6454i | − | 0.592612i | ||||||
\(698\) | − | 50.7261i | − | 1.92001i | ||||||
\(699\) | 3.13826 | 0.118700 | ||||||||
\(700\) | 4.97413 | + | 9.17735i | 0.188004 | + | 0.346871i | ||||
\(701\) | −10.4860 | −0.396052 | −0.198026 | − | 0.980197i | \(-0.563453\pi\) | ||||
−0.198026 | + | 0.980197i | \(0.563453\pi\) | |||||||
\(702\) | 11.0155i | 0.415754i | ||||||||
\(703\) | 0.296201i | 0.0111714i | ||||||||
\(704\) | −8.68579 | −0.327358 | ||||||||
\(705\) | −5.75299 | − | 22.6875i | −0.216670 | − | 0.854462i | ||||
\(706\) | 37.3464 | 1.40555 | ||||||||
\(707\) | 2.21466i | 0.0832908i | ||||||||
\(708\) | 0.484874i | 0.0182227i | ||||||||
\(709\) | −14.3256 | −0.538009 | −0.269004 | − | 0.963139i | \(-0.586695\pi\) | ||||
−0.269004 | + | 0.963139i | \(0.586695\pi\) | |||||||
\(710\) | −40.6402 | + | 10.3053i | −1.52520 | + | 0.386752i | ||||
\(711\) | 13.3303 | 0.499927 | ||||||||
\(712\) | − | 1.87551i | − | 0.0702876i | ||||||
\(713\) | 38.6220i | 1.44640i | ||||||||
\(714\) | −5.20963 | −0.194966 | ||||||||
\(715\) | 11.8091 | − | 2.99449i | 0.441635 | − | 0.111988i | ||||
\(716\) | 46.5183 | 1.73847 | ||||||||
\(717\) | − | 25.5582i | − | 0.954487i | ||||||
\(718\) | 39.8792i | 1.48828i | ||||||||
\(719\) | −9.03703 | −0.337024 | −0.168512 | − | 0.985700i | \(-0.553896\pi\) | ||||
−0.168512 | + | 0.985700i | \(0.553896\pi\) | |||||||
\(720\) | −2.09779 | − | 8.27288i | −0.0781802 | − | 0.308312i | ||||
\(721\) | −14.9953 | −0.558454 | ||||||||
\(722\) | − | 37.1143i | − | 1.38125i | ||||||
\(723\) | − | 1.88461i | − | 0.0700893i | ||||||
\(724\) | 0.657366 | 0.0244308 | ||||||||
\(725\) | 20.7916 | − | 11.2691i | 0.772181 | − | 0.418522i | ||||
\(726\) | 2.02181 | 0.0750366 | ||||||||
\(727\) | − | 16.0207i | − | 0.594176i | −0.954850 | − | 0.297088i | \(-0.903984\pi\) | ||
0.954850 | − | 0.297088i | \(-0.0960155\pi\) | |||||||
\(728\) | − | 0.966424i | − | 0.0358181i | ||||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | −11.7598 | − | 46.3762i | −0.435251 | − | 1.71646i | ||||
\(731\) | 33.0330 | 1.22177 | ||||||||
\(732\) | 32.2196i | 1.19087i | ||||||||
\(733\) | − | 6.95247i | − | 0.256796i | −0.991723 | − | 0.128398i | \(-0.959017\pi\) | ||
0.991723 | − | 0.128398i | \(-0.0409834\pi\) | |||||||
\(734\) | −29.2149 | −1.07834 | ||||||||
\(735\) | 2.16747 | − | 0.549616i | 0.0799483 | − | 0.0202729i | ||||
\(736\) | −32.7820 | −1.20836 | ||||||||
\(737\) | 14.9167i | 0.549463i | ||||||||
\(738\) | 12.2761i | 0.451891i | ||||||||
\(739\) | 14.9743 | 0.550837 | 0.275419 | − | 0.961324i | \(-0.411184\pi\) | ||||
0.275419 | + | 0.961324i | \(0.411184\pi\) | |||||||
\(740\) | −1.67142 | + | 0.423830i | −0.0614426 | + | 0.0155803i | ||||
\(741\) | −4.36911 | −0.160503 | ||||||||
\(742\) | 16.5734i | 0.608429i | ||||||||
\(743\) | 22.7811i | 0.835757i | 0.908503 | + | 0.417878i | \(0.137226\pi\) | ||||
−0.908503 | + | 0.417878i | \(0.862774\pi\) | |||||||
\(744\) | 1.68682 | 0.0618418 | ||||||||
\(745\) | −3.64455 | − | 14.3727i | −0.133526 | − | 0.526574i | ||||
\(746\) | −37.7883 | −1.38353 | ||||||||
\(747\) | 5.21440i | 0.190785i | ||||||||
\(748\) | 5.37949i | 0.196693i | ||||||||
\(749\) | −9.79736 | −0.357988 | ||||||||
\(750\) | 15.3256 | + | 16.6160i | 0.559613 | + | 0.606731i | ||||
\(751\) | −15.6340 | −0.570494 | −0.285247 | − | 0.958454i | \(-0.592076\pi\) | ||||
−0.285247 | + | 0.958454i | \(0.592076\pi\) | |||||||
\(752\) | − | 39.9519i | − | 1.45690i | ||||||
\(753\) | 9.74338i | 0.355068i | ||||||||
\(754\) | −52.1015 | −1.89743 | ||||||||
\(755\) | 10.6030 | + | 41.8141i | 0.385883 | + | 1.52177i | ||||
\(756\) | 2.08773 | 0.0759301 | ||||||||
\(757\) | 31.0417i | 1.12823i | 0.825696 | + | 0.564115i | \(0.190782\pi\) | ||||
−0.825696 | + | 0.564115i | \(0.809218\pi\) | |||||||
\(758\) | 37.8644i | 1.37530i | ||||||||
\(759\) | 4.06135 | 0.147418 | ||||||||
\(760\) | −0.308309 | + | 0.0781796i | −0.0111836 | + | 0.00283587i | ||||
\(761\) | 16.9582 | 0.614734 | 0.307367 | − | 0.951591i | \(-0.400552\pi\) | ||||
0.307367 | + | 0.951591i | \(0.400552\pi\) | |||||||
\(762\) | − | 8.32526i | − | 0.301592i | ||||||
\(763\) | 0.805348i | 0.0291556i | ||||||||
\(764\) | −52.3122 | −1.89259 | ||||||||
\(765\) | −5.58494 | + | 1.41620i | −0.201924 | + | 0.0512029i | ||||
\(766\) | −58.5885 | −2.11689 | ||||||||
\(767\) | − | 1.26537i | − | 0.0456898i | ||||||
\(768\) | − | 14.5053i | − | 0.523416i | ||||||
\(769\) | 17.6273 | 0.635657 | 0.317829 | − | 0.948148i | \(-0.397046\pi\) | ||||
0.317829 | + | 0.948148i | \(0.397046\pi\) | |||||||
\(770\) | −1.11122 | − | 4.38222i | −0.0400456 | − | 0.157924i | ||||
\(771\) | −17.6638 | −0.636148 | ||||||||
\(772\) | 19.7418i | 0.710524i | ||||||||
\(773\) | − | 25.9014i | − | 0.931608i | −0.884888 | − | 0.465804i | \(-0.845765\pi\) | ||
0.884888 | − | 0.465804i | \(-0.154235\pi\) | |||||||
\(774\) | −25.9193 | −0.931650 | ||||||||
\(775\) | 41.8029 | − | 22.6572i | 1.50160 | − | 0.813871i | ||||
\(776\) | −2.17806 | −0.0781876 | ||||||||
\(777\) | 0.369366i | 0.0132509i | ||||||||
\(778\) | − | 1.05203i | − | 0.0377171i | ||||||
\(779\) | −4.86912 | −0.174454 | ||||||||
\(780\) | −6.25170 | − | 24.6542i | −0.223847 | − | 0.882763i | ||||
\(781\) | 9.27387 | 0.331845 | ||||||||
\(782\) | 21.1581i | 0.756613i | ||||||||
\(783\) | − | 4.72983i | − | 0.169030i | ||||||
\(784\) | 3.81684 | 0.136316 | ||||||||
\(785\) | 20.8148 | − | 5.27812i | 0.742913 | − | 0.188384i | ||||
\(786\) | −14.9885 | −0.534623 | ||||||||
\(787\) | − | 14.9659i | − | 0.533478i | −0.963769 | − | 0.266739i | \(-0.914054\pi\) | ||
0.963769 | − | 0.266739i | \(-0.0859461\pi\) | |||||||
\(788\) | − | 8.42543i | − | 0.300143i | ||||||
\(789\) | 22.9064 | 0.815491 | ||||||||
\(790\) | −58.4165 | + | 14.8130i | −2.07837 | + | 0.527022i | ||||
\(791\) | −18.3292 | −0.651712 | ||||||||
\(792\) | − | 0.177380i | − | 0.00630292i | ||||||
\(793\) | − | 84.0830i | − | 2.98587i | ||||||
\(794\) | −10.9530 | −0.388707 | ||||||||
\(795\) | 4.50536 | + | 17.7674i | 0.159789 | + | 0.630144i | ||||
\(796\) | −57.6770 | −2.04431 | ||||||||
\(797\) | 2.54301i | 0.0900781i | 0.998985 | + | 0.0450390i | \(0.0143412\pi\) | ||||
−0.998985 | + | 0.0450390i | \(0.985659\pi\) | |||||||
\(798\) | 1.62133i | 0.0573944i | ||||||||
\(799\) | −26.9712 | −0.954172 | ||||||||
\(800\) | 19.2312 | + | 35.4819i | 0.679927 | + | 1.25448i | ||||
\(801\) | −10.5734 | −0.373593 | ||||||||
\(802\) | 6.04271i | 0.213376i | ||||||||
\(803\) | 10.5828i | 0.373459i | ||||||||
\(804\) | 31.1421 | 1.09830 | ||||||||
\(805\) | −2.23218 | − | 8.80284i | −0.0786740 | − | 0.310259i | ||||
\(806\) | −104.754 | −3.68979 | ||||||||
\(807\) | 8.26091i | 0.290798i | ||||||||
\(808\) | − | 0.392836i | − | 0.0138199i | ||||||
\(809\) | −39.3893 | −1.38485 | −0.692426 | − | 0.721488i | \(-0.743458\pi\) | ||||
−0.692426 | + | 0.721488i | \(0.743458\pi\) | |||||||
\(810\) | 4.38222 | − | 1.11122i | 0.153976 | − | 0.0390443i | ||||
\(811\) | −4.84482 | −0.170125 | −0.0850623 | − | 0.996376i | \(-0.527109\pi\) | ||||
−0.0850623 | + | 0.996376i | \(0.527109\pi\) | |||||||
\(812\) | 9.87462i | 0.346531i | ||||||||
\(813\) | − | 23.9284i | − | 0.839205i | ||||||
\(814\) | 0.746790 | 0.0261750 | ||||||||
\(815\) | 2.37475 | − | 0.602178i | 0.0831839 | − | 0.0210934i | ||||
\(816\) | −9.83489 | −0.344290 | ||||||||
\(817\) | − | 10.2804i | − | 0.359667i | ||||||
\(818\) | 30.4477i | 1.06458i | ||||||||
\(819\) | −5.44833 | −0.190380 | ||||||||
\(820\) | −6.96715 | − | 27.4757i | −0.243303 | − | 0.959493i | ||||
\(821\) | −29.1027 | −1.01569 | −0.507845 | − | 0.861448i | \(-0.669558\pi\) | ||||
−0.507845 | + | 0.861448i | \(0.669558\pi\) | |||||||
\(822\) | 18.3345i | 0.639490i | ||||||||
\(823\) | − | 13.4746i | − | 0.469695i | −0.972032 | − | 0.234847i | \(-0.924541\pi\) | ||
0.972032 | − | 0.234847i | \(-0.0754591\pi\) | |||||||
\(824\) | 2.65986 | 0.0926606 | ||||||||
\(825\) | −2.38255 | − | 4.39584i | −0.0829498 | − | 0.153044i | ||||
\(826\) | −0.469564 | −0.0163382 | ||||||||
\(827\) | 22.3530i | 0.777291i | 0.921387 | + | 0.388645i | \(0.127057\pi\) | ||||
−0.921387 | + | 0.388645i | \(0.872943\pi\) | |||||||
\(828\) | − | 8.47901i | − | 0.294666i | ||||||
\(829\) | 26.1762 | 0.909138 | 0.454569 | − | 0.890711i | \(-0.349793\pi\) | ||||
0.454569 | + | 0.890711i | \(0.349793\pi\) | |||||||
\(830\) | −5.79435 | − | 22.8506i | −0.201125 | − | 0.793158i | ||||
\(831\) | −17.0380 | −0.591042 | ||||||||
\(832\) | − | 47.3231i | − | 1.64063i | ||||||
\(833\) | − | 2.57671i | − | 0.0892778i | ||||||
\(834\) | 14.5916 | 0.505267 | ||||||||
\(835\) | 31.1411 | − | 7.89660i | 1.07768 | − | 0.273273i | ||||
\(836\) | 1.67419 | 0.0579031 | ||||||||
\(837\) | − | 9.50964i | − | 0.328701i | ||||||
\(838\) | 52.0437i | 1.79782i | ||||||||
\(839\) | −47.8883 | −1.65329 | −0.826644 | − | 0.562725i | \(-0.809753\pi\) | ||||
−0.826644 | + | 0.562725i | \(0.809753\pi\) | |||||||
\(840\) | −0.384465 | + | 0.0974908i | −0.0132653 | + | 0.00336375i | ||||
\(841\) | −6.62871 | −0.228576 | ||||||||
\(842\) | 11.0596i | 0.381138i | ||||||||
\(843\) | 19.6769i | 0.677707i | ||||||||
\(844\) | 27.1189 | 0.933471 | ||||||||
\(845\) | 9.16997 | + | 36.1627i | 0.315456 | + | 1.24404i | ||||
\(846\) | 21.1629 | 0.727596 | ||||||||
\(847\) | 1.00000i | 0.0343604i | ||||||||
\(848\) | 31.2877i | 1.07443i | ||||||||
\(849\) | 4.63518 | 0.159079 | ||||||||
\(850\) | 22.9007 | − | 12.4122i | 0.785489 | − | 0.425736i | ||||
\(851\) | 1.50012 | 0.0514236 | ||||||||
\(852\) | − | 19.3614i | − | 0.663310i | ||||||
\(853\) | − | 7.31318i | − | 0.250399i | −0.992132 | − | 0.125199i | \(-0.960043\pi\) | ||
0.992132 | − | 0.125199i | \(-0.0399570\pi\) | |||||||
\(854\) | −31.2023 | −1.06772 | ||||||||
\(855\) | 0.440747 | + | 1.73813i | 0.0150732 | + | 0.0594428i | ||||
\(856\) | 1.73785 | 0.0593986 | ||||||||
\(857\) | − | 35.1097i | − | 1.19932i | −0.800253 | − | 0.599662i | \(-0.795302\pi\) | ||
0.800253 | − | 0.599662i | \(-0.204698\pi\) | |||||||
\(858\) | 11.0155i | 0.376063i | ||||||||
\(859\) | −47.7724 | −1.62997 | −0.814987 | − | 0.579480i | \(-0.803256\pi\) | ||||
−0.814987 | + | 0.579480i | \(0.803256\pi\) | |||||||
\(860\) | 58.0109 | − | 14.7101i | 1.97816 | − | 0.501611i | ||||
\(861\) | −6.07185 | −0.206928 | ||||||||
\(862\) | − | 4.85819i | − | 0.165471i | ||||||
\(863\) | 17.8620i | 0.608028i | 0.952668 | + | 0.304014i | \(0.0983270\pi\) | ||||
−0.952668 | + | 0.304014i | \(0.901673\pi\) | |||||||
\(864\) | 8.07170 | 0.274605 | ||||||||
\(865\) | −31.5798 | + | 8.00785i | −1.07375 | + | 0.272275i | ||||
\(866\) | −10.6924 | −0.363344 | ||||||||
\(867\) | − | 10.3606i | − | 0.351863i | ||||||
\(868\) | 19.8536i | 0.673875i | ||||||||
\(869\) | 13.3303 | 0.452201 | ||||||||
\(870\) | 5.25589 | + | 20.7272i | 0.178191 | + | 0.702716i | ||||
\(871\) | −81.2711 | −2.75377 | ||||||||
\(872\) | − | 0.142853i | − | 0.00483760i | ||||||
\(873\) | 12.2790i | 0.415583i | ||||||||
\(874\) | 6.58478 | 0.222733 | ||||||||
\(875\) | −8.21837 | + | 7.58013i | −0.277832 | + | 0.256255i | ||||
\(876\) | 22.0941 | 0.746489 | ||||||||
\(877\) | − | 28.4812i | − | 0.961742i | −0.876791 | − | 0.480871i | \(-0.840321\pi\) | ||
0.876791 | − | 0.480871i | \(-0.159679\pi\) | |||||||
\(878\) | − | 7.24699i | − | 0.244574i | ||||||
\(879\) | −17.7414 | −0.598401 | ||||||||
\(880\) | −2.09779 | − | 8.27288i | −0.0707166 | − | 0.278879i | ||||
\(881\) | 28.9224 | 0.974420 | 0.487210 | − | 0.873285i | \(-0.338015\pi\) | ||||
0.487210 | + | 0.873285i | \(0.338015\pi\) | |||||||
\(882\) | 2.02181i | 0.0680780i | ||||||||
\(883\) | − | 37.4549i | − | 1.26046i | −0.776410 | − | 0.630228i | \(-0.782961\pi\) | ||
0.776410 | − | 0.630228i | \(-0.217039\pi\) | |||||||
\(884\) | −29.3092 | −0.985776 | ||||||||
\(885\) | −0.503392 | + | 0.127648i | −0.0169213 | + | 0.00429083i | ||||
\(886\) | 1.33118 | 0.0447219 | ||||||||
\(887\) | − | 3.59533i | − | 0.120719i | −0.998177 | − | 0.0603597i | \(-0.980775\pi\) | ||
0.998177 | − | 0.0603597i | \(-0.0192248\pi\) | |||||||
\(888\) | − | 0.0655181i | − | 0.00219864i | ||||||
\(889\) | 4.11772 | 0.138104 | ||||||||
\(890\) | 46.3349 | − | 11.7494i | 1.55315 | − | 0.393840i | ||||
\(891\) | −1.00000 | −0.0335013 | ||||||||
\(892\) | 10.6496i | 0.356575i | ||||||||
\(893\) | 8.39390i | 0.280891i | ||||||||
\(894\) | 13.4068 | 0.448391 | ||||||||
\(895\) | 12.2464 | + | 48.2950i | 0.409352 | + | 1.61432i | ||||
\(896\) | −1.41767 | −0.0473611 | ||||||||
\(897\) | 22.1276i | 0.738818i | ||||||||
\(898\) | − | 37.9053i | − | 1.26492i | ||||||
\(899\) | 44.9790 | 1.50013 | ||||||||
\(900\) | −9.17735 | + | 4.97413i | −0.305912 | + | 0.165804i | ||||
\(901\) | 21.1221 | 0.703678 | ||||||||
\(902\) | 12.2761i | 0.408751i | ||||||||
\(903\) | − | 12.8198i | − | 0.426617i | ||||||
\(904\) | 3.25123 | 0.108134 | ||||||||
\(905\) | 0.173058 | + | 0.682472i | 0.00575264 | + | 0.0226861i | ||||
\(906\) | −39.0042 | −1.29583 | ||||||||
\(907\) | − | 8.77625i | − | 0.291411i | −0.989328 | − | 0.145705i | \(-0.953455\pi\) | ||
0.989328 | − | 0.145705i | \(-0.0465451\pi\) | |||||||
\(908\) | − | 17.1824i | − | 0.570219i | ||||||
\(909\) | −2.21466 | −0.0734556 | ||||||||
\(910\) | 23.8758 | − | 6.05430i | 0.791475 | − | 0.200698i | ||||
\(911\) | 32.2659 | 1.06902 | 0.534509 | − | 0.845163i | \(-0.320497\pi\) | ||||
0.534509 | + | 0.845163i | \(0.320497\pi\) | |||||||
\(912\) | 3.06079i | 0.101353i | ||||||||
\(913\) | 5.21440i | 0.172571i | ||||||||
\(914\) | 59.0483 | 1.95314 | ||||||||
\(915\) | −33.4501 | + | 8.48211i | −1.10583 | + | 0.280410i | ||||
\(916\) | 6.87270 | 0.227081 | ||||||||
\(917\) | − | 7.41340i | − | 0.244812i | ||||||
\(918\) | − | 5.20963i | − | 0.171943i | ||||||
\(919\) | −8.81522 | −0.290787 | −0.145394 | − | 0.989374i | \(-0.546445\pi\) | ||||
−0.145394 | + | 0.989374i | \(0.546445\pi\) | |||||||
\(920\) | 0.395944 | + | 1.56145i | 0.0130539 | + | 0.0514794i | ||||
\(921\) | −13.7194 | −0.452070 | ||||||||
\(922\) | − | 8.04373i | − | 0.264906i | ||||||
\(923\) | 50.5271i | 1.66312i | ||||||||
\(924\) | 2.08773 | 0.0686814 | ||||||||
\(925\) | −0.880034 | − | 1.62368i | −0.0289353 | − | 0.0533862i | ||||
\(926\) | −81.1191 | −2.66574 | ||||||||
\(927\) | − | 14.9953i | − | 0.492510i | ||||||
\(928\) | 38.1777i | 1.25325i | ||||||||
\(929\) | −12.1528 | −0.398722 | −0.199361 | − | 0.979926i | \(-0.563887\pi\) | ||||
−0.199361 | + | 0.979926i | \(0.563887\pi\) | |||||||
\(930\) | 10.5673 | + | 41.6733i | 0.346516 | + | 1.36652i | ||||
\(931\) | −0.801918 | −0.0262818 | ||||||||
\(932\) | − | 6.55185i | − | 0.214613i | ||||||
\(933\) | 0.512264i | 0.0167708i | ||||||||
\(934\) | 66.8661 | 2.18792 | ||||||||
\(935\) | −5.58494 | + | 1.41620i | −0.182647 | + | 0.0463148i | ||||
\(936\) | 0.966424 | 0.0315886 | ||||||||
\(937\) | − | 0.710001i | − | 0.0231947i | −0.999933 | − | 0.0115974i | \(-0.996308\pi\) | ||
0.999933 | − | 0.0115974i | \(-0.00369164\pi\) | |||||||
\(938\) | 30.1588i | 0.984719i | ||||||||
\(939\) | 3.12863 | 0.102099 | ||||||||
\(940\) | −47.3655 | + | 12.0107i | −1.54489 | + | 0.391746i | ||||
\(941\) | 7.19633 | 0.234594 | 0.117297 | − | 0.993097i | \(-0.462577\pi\) | ||||
0.117297 | + | 0.993097i | \(0.462577\pi\) | |||||||
\(942\) | 19.4161i | 0.632610i | ||||||||
\(943\) | 24.6599i | 0.803036i | ||||||||
\(944\) | −0.886456 | −0.0288517 | ||||||||
\(945\) | 0.549616 | + | 2.16747i | 0.0178790 | + | 0.0705078i | ||||
\(946\) | −25.9193 | −0.842709 | ||||||||
\(947\) | − | 24.8433i | − | 0.807300i | −0.914913 | − | 0.403650i | \(-0.867741\pi\) | ||
0.914913 | − | 0.403650i | \(-0.132259\pi\) | |||||||
\(948\) | − | 27.8302i | − | 0.903883i | ||||||
\(949\) | −57.6586 | −1.87168 | ||||||||
\(950\) | −3.86290 | − | 7.12711i | −0.125329 | − | 0.231234i | ||||
\(951\) | −7.61306 | −0.246870 | ||||||||
\(952\) | 0.457057i | 0.0148133i | ||||||||
\(953\) | 4.52824i | 0.146684i | 0.997307 | + | 0.0733421i | \(0.0233665\pi\) | ||||
−0.997307 | + | 0.0733421i | \(0.976634\pi\) | |||||||
\(954\) | −16.5734 | −0.536584 | ||||||||
\(955\) | −13.7717 | − | 54.3102i | −0.445642 | − | 1.75744i | ||||
\(956\) | −53.3586 | −1.72574 | ||||||||
\(957\) | − | 4.72983i | − | 0.152894i | ||||||
\(958\) | 25.7912i | 0.833277i | ||||||||
\(959\) | −9.06835 | −0.292832 | ||||||||
\(960\) | −18.8262 | + | 4.77385i | −0.607613 | + | 0.154075i | ||||
\(961\) | 59.4333 | 1.91720 | ||||||||
\(962\) | 4.06876i | 0.131182i | ||||||||
\(963\) | − | 9.79736i | − | 0.315716i | ||||||
\(964\) | −3.93455 | −0.126723 | ||||||||
\(965\) | −20.4958 | + | 5.19723i | −0.659783 | + | 0.167305i | ||||
\(966\) | 8.21129 | 0.264194 | ||||||||
\(967\) | 6.58048i | 0.211614i | 0.994387 | + | 0.105807i | \(0.0337426\pi\) | ||||
−0.994387 | + | 0.105807i | \(0.966257\pi\) | |||||||
\(968\) | − | 0.177380i | − | 0.00570120i | ||||||
\(969\) | 2.06631 | 0.0663795 | ||||||||
\(970\) | −13.6447 | − | 53.8095i | −0.438106 | − | 1.72772i | ||||
\(971\) | −7.15664 | −0.229667 | −0.114834 | − | 0.993385i | \(-0.536634\pi\) | ||||
−0.114834 | + | 0.993385i | \(0.536634\pi\) | |||||||
\(972\) | 2.08773i | 0.0669641i | ||||||||
\(973\) | 7.21710i | 0.231369i | ||||||||
\(974\) | 36.1839 | 1.15941 | ||||||||
\(975\) | 23.9500 | − | 12.9809i | 0.767014 | − | 0.415722i | ||||
\(976\) | −58.9045 | −1.88549 | ||||||||
\(977\) | − | 59.7619i | − | 1.91195i | −0.293446 | − | 0.955976i | \(-0.594802\pi\) | ||
0.293446 | − | 0.955976i | \(-0.405198\pi\) | |||||||
\(978\) | 2.21517i | 0.0708332i | ||||||||
\(979\) | −10.5734 | −0.337927 | ||||||||
\(980\) | −1.14745 | − | 4.52510i | −0.0366540 | − | 0.144549i | ||||
\(981\) | −0.805348 | −0.0257128 | ||||||||
\(982\) | − | 25.2405i | − | 0.805457i | ||||||
\(983\) | − | 30.2137i | − | 0.963668i | −0.876262 | − | 0.481834i | \(-0.839971\pi\) | ||
0.876262 | − | 0.481834i | \(-0.160029\pi\) | |||||||
\(984\) | 1.07702 | 0.0343342 | ||||||||
\(985\) | 8.74722 | − | 2.21808i | 0.278710 | − | 0.0706738i | ||||
\(986\) | 24.6407 | 0.784719 | ||||||||
\(987\) | 10.4673i | 0.333177i | ||||||||
\(988\) | 9.12154i | 0.290195i | ||||||||
\(989\) | −52.0657 | −1.65559 | ||||||||
\(990\) | 4.38222 | − | 1.11122i | 0.139276 | − | 0.0353169i | ||||
\(991\) | −38.0074 | −1.20734 | −0.603672 | − | 0.797233i | \(-0.706296\pi\) | ||||
−0.603672 | + | 0.797233i | \(0.706296\pi\) | |||||||
\(992\) | 76.7589i | 2.43710i | ||||||||
\(993\) | 4.56072i | 0.144730i | ||||||||
\(994\) | 18.7501 | 0.594715 | ||||||||
\(995\) | −15.1840 | − | 59.8798i | −0.481366 | − | 1.89832i | ||||
\(996\) | 10.8863 | 0.344945 | ||||||||
\(997\) | 28.2891i | 0.895925i | 0.894052 | + | 0.447963i | \(0.147850\pi\) | ||||
−0.894052 | + | 0.447963i | \(0.852150\pi\) | |||||||
\(998\) | − | 49.6176i | − | 1.57062i | ||||||
\(999\) | −0.369366 | −0.0116862 |
(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 | 1155.2.c.e.694.17 | yes | 20 | |
5.2 | odd | 4 | 5775.2.a.cm.1.3 | 10 | |||
5.3 | odd | 4 | 5775.2.a.cp.1.8 | 10 | |||
5.4 | even | 2 | inner | 1155.2.c.e.694.4 | ✓ | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1155.2.c.e.694.4 | ✓ | 20 | 5.4 | even | 2 | inner | |
1155.2.c.e.694.17 | yes | 20 | 1.1 | even | 1 | trivial | |
5775.2.a.cm.1.3 | 10 | 5.2 | odd | 4 | |||
5775.2.a.cp.1.8 | 10 | 5.3 | odd | 4 |