Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [177,2,Mod(176,177)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(177, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("177.176");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 177 = 3 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 177.d (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: | \(1.41335211578\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.0.19298288.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - x^{5} + 3x^{4} - 2x^{3} + 9x^{2} - 9x + 27 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 176.3 | ||
Root | \(-1.16170 + 1.28470i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 177.176 |
Dual form | 177.2.d.c.176.4 |
$q$-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 \(\left(\mathbb{Z}/177\mathbb{Z}\right)^\times\).
\(n\) | \(61\) | \(119\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.46260 | 1.03421 | 0.517107 | − | 0.855921i | \(-0.327009\pi\) | ||||
0.517107 | + | 0.855921i | \(0.327009\pi\) | |||||||
\(3\) | 1.16170 | − | 1.28470i | 0.670709 | − | 0.741721i | ||||
\(4\) | 0.139194 | 0.0695971 | ||||||||
\(5\) | 0.594299i | 0.265779i | 0.991131 | + | 0.132889i | \(0.0424255\pi\) | ||||
−0.991131 | + | 0.132889i | \(0.957575\pi\) | |||||||
\(6\) | 1.69910 | − | 1.87900i | 0.693656 | − | 0.767097i | ||||
\(7\) | 1.86081 | 0.703319 | 0.351659 | − | 0.936128i | \(-0.385618\pi\) | ||||
0.351659 | + | 0.936128i | \(0.385618\pi\) | |||||||
\(8\) | −2.72161 | −0.962235 | ||||||||
\(9\) | −0.300896 | − | 2.98487i | −0.100299 | − | 0.994957i | ||||
\(10\) | 0.869221i | 0.274872i | ||||||||
\(11\) | −0.676596 | −0.204001 | −0.102001 | − | 0.994784i | \(-0.532524\pi\) | ||||
−0.102001 | + | 0.994784i | \(0.532524\pi\) | |||||||
\(12\) | 0.161702 | − | 0.178822i | 0.0466794 | − | 0.0516216i | ||||
\(13\) | 5.37545i | 1.49088i | 0.666573 | + | 0.745440i | \(0.267761\pi\) | ||||
−0.666573 | + | 0.745440i | \(0.732239\pi\) | |||||||
\(14\) | 2.72161 | 0.727381 | ||||||||
\(15\) | 0.763495 | + | 0.690399i | 0.197133 | + | 0.178260i | ||||
\(16\) | −4.25901 | −1.06475 | ||||||||
\(17\) | − | 1.70017i | − | 0.412353i | −0.978515 | − | 0.206176i | \(-0.933898\pi\) | ||
0.978515 | − | 0.206176i | \(-0.0661021\pi\) | |||||||
\(18\) | −0.440090 | − | 4.36567i | −0.103730 | − | 1.02900i | ||||
\(19\) | −2.25901 | −0.518253 | −0.259127 | − | 0.965843i | \(-0.583435\pi\) | ||||
−0.259127 | + | 0.965843i | \(0.583435\pi\) | |||||||
\(20\) | 0.0827230i | 0.0184974i | ||||||||
\(21\) | 2.16170 | − | 2.39057i | 0.471722 | − | 0.521666i | ||||
\(22\) | −0.989588 | −0.210981 | ||||||||
\(23\) | −4.86081 | −1.01355 | −0.506774 | − | 0.862079i | \(-0.669162\pi\) | ||||
−0.506774 | + | 0.862079i | \(0.669162\pi\) | |||||||
\(24\) | −3.16170 | + | 3.49645i | −0.645380 | + | 0.713710i | ||||
\(25\) | 4.64681 | 0.929362 | ||||||||
\(26\) | 7.86212i | 1.54189i | ||||||||
\(27\) | −4.18421 | − | 3.08097i | −0.805252 | − | 0.592933i | ||||
\(28\) | 0.259013 | 0.0489489 | ||||||||
\(29\) | 6.24467i | 1.15961i | 0.814757 | + | 0.579803i | \(0.196870\pi\) | ||||
−0.814757 | + | 0.579803i | \(0.803130\pi\) | |||||||
\(30\) | 1.11669 | + | 1.00978i | 0.203878 | + | 0.184359i | ||||
\(31\) | 2.48667i | 0.446620i | 0.974748 | + | 0.223310i | \(0.0716861\pi\) | ||||
−0.974748 | + | 0.223310i | \(0.928314\pi\) | |||||||
\(32\) | −0.786003 | −0.138947 | ||||||||
\(33\) | −0.786003 | + | 0.869221i | −0.136826 | + | 0.151312i | ||||
\(34\) | − | 2.48667i | − | 0.426461i | ||||||
\(35\) | 1.10588i | 0.186927i | ||||||||
\(36\) | −0.0418830 | − | 0.415477i | −0.00698050 | − | 0.0692461i | ||||
\(37\) | − | 7.86212i | − | 1.29252i | −0.763116 | − | 0.646262i | \(-0.776331\pi\) | ||
0.763116 | − | 0.646262i | \(-0.223669\pi\) | |||||||
\(38\) | −3.30403 | −0.535984 | ||||||||
\(39\) | 6.90582 | + | 6.24467i | 1.10582 | + | 0.999947i | ||||
\(40\) | − | 1.61745i | − | 0.255742i | ||||||
\(41\) | 2.29447i | 0.358337i | 0.983818 | + | 0.179168i | \(0.0573407\pi\) | ||||
−0.983818 | + | 0.179168i | \(0.942659\pi\) | |||||||
\(42\) | 3.16170 | − | 3.49645i | 0.487861 | − | 0.539514i | ||||
\(43\) | − | 7.11389i | − | 1.08486i | −0.840102 | − | 0.542429i | \(-0.817505\pi\) | ||
0.840102 | − | 0.542429i | \(-0.182495\pi\) | |||||||
\(44\) | −0.0941782 | −0.0141979 | ||||||||
\(45\) | 1.77391 | − | 0.178822i | 0.264438 | − | 0.0266573i | ||||
\(46\) | −7.10941 | −1.04822 | ||||||||
\(47\) | 8.46260 | 1.23440 | 0.617198 | − | 0.786808i | \(-0.288268\pi\) | ||||
0.617198 | + | 0.786808i | \(0.288268\pi\) | |||||||
\(48\) | −4.94770 | + | 5.47154i | −0.714140 | + | 0.789749i | ||||
\(49\) | −3.53740 | −0.505343 | ||||||||
\(50\) | 6.79641 | 0.961158 | ||||||||
\(51\) | −2.18421 | − | 1.97510i | −0.305851 | − | 0.276569i | ||||
\(52\) | 0.748230i | 0.103761i | ||||||||
\(53\) | 5.73309i | 0.787500i | 0.919217 | + | 0.393750i | \(0.128823\pi\) | ||||
−0.919217 | + | 0.393750i | \(0.871177\pi\) | |||||||
\(54\) | −6.11982 | − | 4.50622i | −0.832802 | − | 0.613219i | ||||
\(55\) | − | 0.402100i | − | 0.0542192i | ||||||
\(56\) | −5.06439 | −0.676758 | ||||||||
\(57\) | −2.62430 | + | 2.90215i | −0.347597 | + | 0.384399i | ||||
\(58\) | 9.13344i | 1.19928i | ||||||||
\(59\) | −1.93561 | − | 7.43326i | −0.251995 | − | 0.967729i | ||||
\(60\) | 0.106274 | + | 0.0960994i | 0.0137199 | + | 0.0124064i | ||||
\(61\) | − | 10.0027i | − | 1.28071i | −0.768079 | − | 0.640355i | \(-0.778787\pi\) | ||
0.768079 | − | 0.640355i | \(-0.221213\pi\) | |||||||
\(62\) | 3.63700i | 0.461900i | ||||||||
\(63\) | −0.559910 | − | 5.55427i | −0.0705420 | − | 0.699772i | ||||
\(64\) | 7.36842 | 0.921053 | ||||||||
\(65\) | −3.19462 | −0.396244 | ||||||||
\(66\) | −1.14961 | + | 1.27132i | −0.141507 | + | 0.156489i | ||||
\(67\) | − | 5.37545i | − | 0.656715i | −0.944553 | − | 0.328358i | \(-0.893505\pi\) | ||
0.944553 | − | 0.328358i | \(-0.106495\pi\) | |||||||
\(68\) | − | 0.236654i | − | 0.0286986i | ||||||
\(69\) | −5.64681 | + | 6.24467i | −0.679796 | + | 0.751769i | ||||
\(70\) | 1.61745i | 0.193322i | ||||||||
\(71\) | − | 5.92529i | − | 0.703202i | −0.936150 | − | 0.351601i | \(-0.885637\pi\) | ||
0.936150 | − | 0.351601i | \(-0.114363\pi\) | |||||||
\(72\) | 0.818923 | + | 8.12366i | 0.0965110 | + | 0.957383i | ||||
\(73\) | 8.26422i | 0.967254i | 0.875274 | + | 0.483627i | \(0.160681\pi\) | ||||
−0.875274 | + | 0.483627i | \(0.839319\pi\) | |||||||
\(74\) | − | 11.4991i | − | 1.33675i | ||||||
\(75\) | 5.39821 | − | 5.96974i | 0.623331 | − | 0.689327i | ||||
\(76\) | −0.314441 | −0.0360689 | ||||||||
\(77\) | −1.25901 | −0.143478 | ||||||||
\(78\) | 10.1004 | + | 9.13344i | 1.14365 | + | 1.03416i | ||||
\(79\) | 8.29362 | 0.933105 | 0.466552 | − | 0.884494i | \(-0.345496\pi\) | ||||
0.466552 | + | 0.884494i | \(0.345496\pi\) | |||||||
\(80\) | − | 2.53113i | − | 0.282989i | ||||||
\(81\) | −8.81892 | + | 1.79627i | −0.979880 | + | 0.199586i | ||||
\(82\) | 3.35589i | 0.370596i | ||||||||
\(83\) | −0.0941782 | −0.0103374 | −0.00516870 | − | 0.999987i | \(-0.501645\pi\) | ||||
−0.00516870 | + | 0.999987i | \(0.501645\pi\) | |||||||
\(84\) | 0.300896 | − | 0.332754i | 0.0328305 | − | 0.0363064i | ||||
\(85\) | 1.01041 | 0.109595 | ||||||||
\(86\) | − | 10.4048i | − | 1.12197i | ||||||
\(87\) | 8.02251 | + | 7.25444i | 0.860103 | + | 0.777758i | ||||
\(88\) | 1.84143 | 0.196297 | ||||||||
\(89\) | 10.9806 | 1.16394 | 0.581972 | − | 0.813209i | \(-0.302281\pi\) | ||||
0.581972 | + | 0.813209i | \(0.302281\pi\) | |||||||
\(90\) | 2.59451 | − | 0.261545i | 0.273486 | − | 0.0275693i | ||||
\(91\) | 10.0027i | 1.04856i | ||||||||
\(92\) | −0.676596 | −0.0705400 | ||||||||
\(93\) | 3.19462 | + | 2.88877i | 0.331267 | + | 0.299552i | ||||
\(94\) | 12.3774 | 1.27663 | ||||||||
\(95\) | − | 1.34253i | − | 0.137741i | ||||||
\(96\) | −0.913101 | + | 1.00978i | −0.0931930 | + | 0.103060i | ||||
\(97\) | − | 17.8648i | − | 1.81389i | −0.421246 | − | 0.906947i | \(-0.638407\pi\) | ||
0.421246 | − | 0.906947i | \(-0.361593\pi\) | |||||||
\(98\) | −5.17380 | −0.522633 | ||||||||
\(99\) | 0.203585 | + | 2.01955i | 0.0204611 | + | 0.202973i | ||||
\(100\) | 0.646809 | 0.0646809 | ||||||||
\(101\) | −8.36842 | −0.832689 | −0.416344 | − | 0.909207i | \(-0.636689\pi\) | ||||
−0.416344 | + | 0.909207i | \(0.636689\pi\) | |||||||
\(102\) | −3.19462 | − | 2.88877i | −0.316315 | − | 0.286031i | ||||
\(103\) | 1.73844i | 0.171294i | 0.996326 | + | 0.0856469i | \(0.0272957\pi\) | ||||
−0.996326 | + | 0.0856469i | \(0.972704\pi\) | |||||||
\(104\) | − | 14.6299i | − | 1.43458i | ||||||
\(105\) | 1.42072 | + | 1.28470i | 0.138648 | + | 0.125374i | ||||
\(106\) | 8.38521i | 0.814443i | ||||||||
\(107\) | 7.66992i | 0.741479i | 0.928737 | + | 0.370740i | \(0.120896\pi\) | ||||
−0.928737 | + | 0.370740i | \(0.879104\pi\) | |||||||
\(108\) | −0.582418 | − | 0.428853i | −0.0560432 | − | 0.0412664i | ||||
\(109\) | 15.3781i | 1.47296i | 0.676462 | + | 0.736478i | \(0.263512\pi\) | ||||
−0.676462 | + | 0.736478i | \(0.736488\pi\) | |||||||
\(110\) | − | 0.588111i | − | 0.0560742i | ||||||
\(111\) | −10.1004 | − | 9.13344i | −0.958692 | − | 0.866908i | ||||
\(112\) | −7.92520 | −0.748861 | ||||||||
\(113\) | 6.11982 | 0.575704 | 0.287852 | − | 0.957675i | \(-0.407059\pi\) | ||||
0.287852 | + | 0.957675i | \(0.407059\pi\) | |||||||
\(114\) | −3.83830 | + | 4.24468i | −0.359490 | + | 0.397551i | ||||
\(115\) | − | 2.88877i | − | 0.269379i | ||||||
\(116\) | 0.869221i | 0.0807051i | ||||||||
\(117\) | 16.0450 | − | 1.61745i | 1.48336 | − | 0.149533i | ||||
\(118\) | −2.83102 | − | 10.8719i | −0.260616 | − | 1.00084i | ||||
\(119\) | − | 3.16369i | − | 0.290015i | ||||||
\(120\) | −2.07794 | − | 1.87900i | −0.189689 | − | 0.171528i | ||||
\(121\) | −10.5422 | −0.958383 | ||||||||
\(122\) | − | 14.6299i | − | 1.32453i | ||||||
\(123\) | 2.94770 | + | 2.66549i | 0.265786 | + | 0.240340i | ||||
\(124\) | 0.346130i | 0.0310834i | ||||||||
\(125\) | 5.73309i | 0.512783i | ||||||||
\(126\) | −0.818923 | − | 8.12366i | −0.0729554 | − | 0.723713i | ||||
\(127\) | 6.20359 | 0.550479 | 0.275240 | − | 0.961376i | \(-0.411243\pi\) | ||||
0.275240 | + | 0.961376i | \(0.411243\pi\) | |||||||
\(128\) | 12.3490 | 1.09151 | ||||||||
\(129\) | −9.13919 | − | 8.26422i | −0.804661 | − | 0.727624i | ||||
\(130\) | −4.67245 | −0.409801 | ||||||||
\(131\) | 16.5180 | 1.44319 | 0.721593 | − | 0.692317i | \(-0.243410\pi\) | ||||
0.721593 | + | 0.692317i | \(0.243410\pi\) | |||||||
\(132\) | −0.109407 | + | 0.120990i | −0.00952265 | + | 0.0105309i | ||||
\(133\) | −4.20359 | −0.364497 | ||||||||
\(134\) | − | 7.86212i | − | 0.679184i | ||||||
\(135\) | 1.83102 | − | 2.48667i | 0.157589 | − | 0.214019i | ||||
\(136\) | 4.62721i | 0.396780i | ||||||||
\(137\) | 17.5071i | 1.49574i | 0.663848 | + | 0.747868i | \(0.268922\pi\) | ||||
−0.663848 | + | 0.747868i | \(0.731078\pi\) | |||||||
\(138\) | −8.25901 | + | 9.13344i | −0.703054 | + | 0.777490i | ||||
\(139\) | 5.69182 | 0.482774 | 0.241387 | − | 0.970429i | \(-0.422398\pi\) | ||||
0.241387 | + | 0.970429i | \(0.422398\pi\) | |||||||
\(140\) | 0.153931i | 0.0130096i | ||||||||
\(141\) | 9.83102 | − | 10.8719i | 0.827921 | − | 0.915578i | ||||
\(142\) | − | 8.66632i | − | 0.727261i | ||||||
\(143\) | − | 3.63700i | − | 0.304141i | ||||||
\(144\) | 1.28152 | + | 12.7126i | 0.106793 | + | 1.05938i | ||||
\(145\) | −3.71120 | −0.308198 | ||||||||
\(146\) | 12.0872i | 1.00035i | ||||||||
\(147\) | −4.10941 | + | 4.54449i | −0.338938 | + | 0.374823i | ||||
\(148\) | − | 1.09436i | − | 0.0899559i | ||||||
\(149\) | −21.5976 | −1.76935 | −0.884674 | − | 0.466210i | \(-0.845619\pi\) | ||||
−0.884674 | + | 0.466210i | \(0.845619\pi\) | |||||||
\(150\) | 7.89541 | − | 8.73134i | 0.644658 | − | 0.712911i | ||||
\(151\) | 8.26422i | 0.672533i | 0.941767 | + | 0.336266i | \(0.109164\pi\) | ||||
−0.941767 | + | 0.336266i | \(0.890836\pi\) | |||||||
\(152\) | 6.14816 | 0.498681 | ||||||||
\(153\) | −5.07480 | + | 0.511576i | −0.410274 | + | 0.0413585i | ||||
\(154\) | −1.84143 | −0.148387 | ||||||||
\(155\) | −1.47783 | −0.118702 | ||||||||
\(156\) | 0.961250 | + | 0.869221i | 0.0769616 | + | 0.0695934i | ||||
\(157\) | 12.8914i | 1.02885i | 0.857536 | + | 0.514424i | \(0.171994\pi\) | ||||
−0.857536 | + | 0.514424i | \(0.828006\pi\) | |||||||
\(158\) | 12.1302 | 0.965029 | ||||||||
\(159\) | 7.36529 | + | 6.66014i | 0.584105 | + | 0.528184i | ||||
\(160\) | − | 0.467121i | − | 0.0369291i | ||||||
\(161\) | −9.04502 | −0.712847 | ||||||||
\(162\) | −12.8985 | + | 2.62723i | −1.01341 | + | 0.206414i | ||||
\(163\) | −15.7562 | −1.23412 | −0.617061 | − | 0.786915i | \(-0.711677\pi\) | ||||
−0.617061 | + | 0.786915i | \(0.711677\pi\) | |||||||
\(164\) | 0.319377i | 0.0249392i | ||||||||
\(165\) | −0.516577 | − | 0.467121i | −0.0402155 | − | 0.0363653i | ||||
\(166\) | −0.137745 | −0.0106911 | ||||||||
\(167\) | − | 13.0454i | − | 1.00948i | −0.863271 | − | 0.504740i | \(-0.831588\pi\) | ||
0.863271 | − | 0.504740i | \(-0.168412\pi\) | |||||||
\(168\) | −5.88331 | + | 6.50621i | −0.453908 | + | 0.501965i | ||||
\(169\) | −15.8954 | −1.22272 | ||||||||
\(170\) | 1.47783 | 0.113344 | ||||||||
\(171\) | 0.679729 | + | 6.74287i | 0.0519802 | + | 0.515640i | ||||
\(172\) | − | 0.990211i | − | 0.0755029i | ||||||
\(173\) | −9.40862 | −0.715324 | −0.357662 | − | 0.933851i | \(-0.616426\pi\) | ||||
−0.357662 | + | 0.933851i | \(0.616426\pi\) | |||||||
\(174\) | 11.7337 | + | 10.6103i | 0.889530 | + | 0.804367i | ||||
\(175\) | 8.64681 | 0.653637 | ||||||||
\(176\) | 2.88163 | 0.217211 | ||||||||
\(177\) | −11.7981 | − | 6.14857i | −0.886799 | − | 0.462155i | ||||
\(178\) | 16.0602 | 1.20377 | ||||||||
\(179\) | −23.0450 | −1.72247 | −0.861233 | − | 0.508211i | \(-0.830307\pi\) | ||||
−0.861233 | + | 0.508211i | \(0.830307\pi\) | |||||||
\(180\) | 0.246917 | − | 0.0248910i | 0.0184041 | − | 0.00185527i | ||||
\(181\) | −7.58242 | −0.563597 | −0.281798 | − | 0.959474i | \(-0.590931\pi\) | ||||
−0.281798 | + | 0.959474i | \(0.590931\pi\) | |||||||
\(182\) | 14.6299i | 1.08444i | ||||||||
\(183\) | −12.8504 | − | 11.6201i | −0.949928 | − | 0.858983i | ||||
\(184\) | 13.2292 | 0.975271 | ||||||||
\(185\) | 4.67245 | 0.343525 | ||||||||
\(186\) | 4.67245 | + | 4.22511i | 0.342601 | + | 0.309800i | ||||
\(187\) | 1.15033i | 0.0841205i | ||||||||
\(188\) | 1.17794 | 0.0859104 | ||||||||
\(189\) | −7.78600 | − | 5.73309i | −0.566348 | − | 0.417021i | ||||
\(190\) | − | 1.96358i | − | 0.142453i | ||||||
\(191\) | 6.11982 | 0.442815 | 0.221407 | − | 0.975181i | \(-0.428935\pi\) | ||||
0.221407 | + | 0.975181i | \(0.428935\pi\) | |||||||
\(192\) | 8.55991 | − | 9.46619i | 0.617758 | − | 0.683164i | ||||
\(193\) | −8.19462 | −0.589862 | −0.294931 | − | 0.955519i | \(-0.595297\pi\) | ||||
−0.294931 | + | 0.955519i | \(0.595297\pi\) | |||||||
\(194\) | − | 26.1290i | − | 1.87595i | ||||||
\(195\) | −3.71120 | + | 4.10412i | −0.265765 | + | 0.293902i | ||||
\(196\) | −0.492386 | −0.0351704 | ||||||||
\(197\) | 24.4288i | 1.74048i | 0.492627 | + | 0.870241i | \(0.336037\pi\) | ||||
−0.492627 | + | 0.870241i | \(0.663963\pi\) | |||||||
\(198\) | 0.297763 | + | 2.95379i | 0.0211611 | + | 0.209917i | ||||
\(199\) | 11.8608 | 0.840790 | 0.420395 | − | 0.907341i | \(-0.361891\pi\) | ||||
0.420395 | + | 0.907341i | \(0.361891\pi\) | |||||||
\(200\) | −12.6468 | −0.894264 | ||||||||
\(201\) | −6.90582 | − | 6.24467i | −0.487099 | − | 0.440465i | ||||
\(202\) | −12.2396 | −0.861178 | ||||||||
\(203\) | 11.6201i | 0.815572i | ||||||||
\(204\) | −0.304029 | − | 0.274922i | −0.0212863 | − | 0.0192484i | ||||
\(205\) | −1.36360 | −0.0952382 | ||||||||
\(206\) | 2.54264i | 0.177154i | ||||||||
\(207\) | 1.46260 | + | 14.5089i | 0.101658 | + | 1.00844i | ||||
\(208\) | − | 22.8941i | − | 1.58742i | ||||||
\(209\) | 1.52844 | 0.105724 | ||||||||
\(210\) | 2.07794 | + | 1.87900i | 0.143391 | + | 0.129663i | ||||
\(211\) | 17.1165i | 1.17835i | 0.808005 | + | 0.589176i | \(0.200547\pi\) | ||||
−0.808005 | + | 0.589176i | \(0.799453\pi\) | |||||||
\(212\) | 0.798013i | 0.0548077i | ||||||||
\(213\) | −7.61220 | − | 6.88342i | −0.521580 | − | 0.471644i | ||||
\(214\) | 11.2180i | 0.766847i | ||||||||
\(215\) | 4.22778 | 0.288332 | ||||||||
\(216\) | 11.3878 | + | 8.38521i | 0.774841 | + | 0.570541i | ||||
\(217\) | 4.62721i | 0.314116i | ||||||||
\(218\) | 22.4920i | 1.52335i | ||||||||
\(219\) | 10.6170 | + | 9.60056i | 0.717432 | + | 0.648746i | ||||
\(220\) | − | 0.0559700i | − | 0.00377350i | ||||||
\(221\) | 9.13919 | 0.614769 | ||||||||
\(222\) | −14.7729 | − | 13.3586i | −0.991492 | − | 0.896567i | ||||
\(223\) | −7.31444 | −0.489811 | −0.244906 | − | 0.969547i | \(-0.578757\pi\) | ||||
−0.244906 | + | 0.969547i | \(0.578757\pi\) | |||||||
\(224\) | −1.46260 | −0.0977240 | ||||||||
\(225\) | −1.39821 | − | 13.8701i | −0.0932138 | − | 0.924675i | ||||
\(226\) | 8.95084 | 0.595401 | ||||||||
\(227\) | 15.7473 | 1.04518 | 0.522591 | − | 0.852584i | \(-0.324966\pi\) | ||||
0.522591 | + | 0.852584i | \(0.324966\pi\) | |||||||
\(228\) | −0.365287 | + | 0.403962i | −0.0241917 | + | 0.0267530i | ||||
\(229\) | − | 26.5311i | − | 1.75322i | −0.481198 | − | 0.876612i | \(-0.659798\pi\) | ||
0.481198 | − | 0.876612i | \(-0.340202\pi\) | |||||||
\(230\) | − | 4.22511i | − | 0.278596i | ||||||
\(231\) | −1.46260 | + | 1.61745i | −0.0962319 | + | 0.106420i | ||||
\(232\) | − | 16.9956i | − | 1.11581i | ||||||
\(233\) | −15.1648 | −0.993481 | −0.496741 | − | 0.867899i | \(-0.665470\pi\) | ||||
−0.496741 | + | 0.867899i | \(0.665470\pi\) | |||||||
\(234\) | 23.4674 | − | 2.36568i | 1.53411 | − | 0.154649i | ||||
\(235\) | 5.02931i | 0.328076i | ||||||||
\(236\) | −0.269425 | − | 1.03467i | −0.0175381 | − | 0.0673511i | ||||
\(237\) | 9.63471 | − | 10.6548i | 0.625842 | − | 0.692103i | ||||
\(238\) | − | 4.62721i | − | 0.299938i | ||||||
\(239\) | − | 17.0338i | − | 1.10183i | −0.834563 | − | 0.550913i | \(-0.814280\pi\) | ||
0.834563 | − | 0.550913i | \(-0.185720\pi\) | |||||||
\(240\) | −3.25173 | − | 2.94042i | −0.209899 | − | 0.189803i | ||||
\(241\) | −10.2847 | −0.662493 | −0.331246 | − | 0.943544i | \(-0.607469\pi\) | ||||
−0.331246 | + | 0.943544i | \(0.607469\pi\) | |||||||
\(242\) | −15.4190 | −0.991173 | ||||||||
\(243\) | −7.93729 | + | 13.4164i | −0.509178 | + | 0.860661i | ||||
\(244\) | − | 1.39231i | − | 0.0891336i | ||||||
\(245\) | − | 2.10227i | − | 0.134309i | ||||||
\(246\) | 4.31131 | + | 3.89855i | 0.274879 | + | 0.248562i | ||||
\(247\) | − | 12.1432i | − | 0.772653i | ||||||
\(248\) | − | 6.76776i | − | 0.429753i | ||||||
\(249\) | −0.109407 | + | 0.120990i | −0.00693339 | + | 0.00766746i | ||||
\(250\) | 8.38521i | 0.530327i | ||||||||
\(251\) | 15.1299i | 0.954993i | 0.878634 | + | 0.477497i | \(0.158456\pi\) | ||||
−0.878634 | + | 0.477497i | \(0.841544\pi\) | |||||||
\(252\) | −0.0779361 | − | 0.773122i | −0.00490952 | − | 0.0487021i | ||||
\(253\) | 3.28880 | 0.206765 | ||||||||
\(254\) | 9.07335 | 0.569313 | ||||||||
\(255\) | 1.17380 | − | 1.29807i | 0.0735061 | − | 0.0812886i | ||||
\(256\) | 3.32485 | 0.207803 | ||||||||
\(257\) | 6.13519i | 0.382703i | 0.981522 | + | 0.191351i | \(0.0612870\pi\) | ||||
−0.981522 | + | 0.191351i | \(0.938713\pi\) | |||||||
\(258\) | −13.3670 | − | 12.0872i | −0.832191 | − | 0.752518i | ||||
\(259\) | − | 14.6299i | − | 0.909056i | ||||||
\(260\) | −0.444673 | −0.0275774 | ||||||||
\(261\) | 18.6395 | − | 1.87900i | 1.15376 | − | 0.116307i | ||||
\(262\) | 24.1592 | 1.49256 | ||||||||
\(263\) | − | 23.7073i | − | 1.46186i | −0.682454 | − | 0.730929i | \(-0.739087\pi\) | ||
0.682454 | − | 0.730929i | \(-0.260913\pi\) | |||||||
\(264\) | 2.13919 | − | 2.36568i | 0.131658 | − | 0.145598i | ||||
\(265\) | −3.40717 | −0.209301 | ||||||||
\(266\) | −6.14816 | −0.376968 | ||||||||
\(267\) | 12.7562 | − | 14.1068i | 0.780668 | − | 0.863321i | ||||
\(268\) | − | 0.748230i | − | 0.0457055i | ||||||
\(269\) | 26.1890 | 1.59677 | 0.798387 | − | 0.602145i | \(-0.205687\pi\) | ||||
0.798387 | + | 0.602145i | \(0.205687\pi\) | |||||||
\(270\) | 2.67805 | − | 3.63700i | 0.162981 | − | 0.221341i | ||||
\(271\) | 22.3144 | 1.35551 | 0.677753 | − | 0.735290i | \(-0.262954\pi\) | ||||
0.677753 | + | 0.735290i | \(0.262954\pi\) | |||||||
\(272\) | 7.24107i | 0.439054i | ||||||||
\(273\) | 12.8504 | + | 11.6201i | 0.777741 | + | 0.703281i | ||||
\(274\) | 25.6059i | 1.54691i | ||||||||
\(275\) | −3.14401 | −0.189591 | ||||||||
\(276\) | −0.786003 | + | 0.869221i | −0.0473118 | + | 0.0523210i | ||||
\(277\) | 23.8269 | 1.43162 | 0.715809 | − | 0.698296i | \(-0.246058\pi\) | ||||
0.715809 | + | 0.698296i | \(0.246058\pi\) | |||||||
\(278\) | 8.32485 | 0.499292 | ||||||||
\(279\) | 7.42240 | − | 0.748230i | 0.444367 | − | 0.0447954i | ||||
\(280\) | − | 3.00976i | − | 0.179868i | ||||||
\(281\) | 2.40395i | 0.143408i | 0.997426 | + | 0.0717038i | \(0.0228436\pi\) | ||||
−0.997426 | + | 0.0717038i | \(0.977156\pi\) | |||||||
\(282\) | 14.3788 | − | 15.9012i | 0.856247 | − | 0.946902i | ||||
\(283\) | 10.4048i | 0.618499i | 0.950981 | + | 0.309249i | \(0.100078\pi\) | ||||
−0.950981 | + | 0.309249i | \(0.899922\pi\) | |||||||
\(284\) | − | 0.824766i | − | 0.0489408i | ||||||
\(285\) | −1.72474 | − | 1.55962i | −0.102165 | − | 0.0923839i | ||||
\(286\) | − | 5.31948i | − | 0.314547i | ||||||
\(287\) | 4.26957i | 0.252025i | ||||||||
\(288\) | 0.236505 | + | 2.34612i | 0.0139362 | + | 0.138246i | ||||
\(289\) | 14.1094 | 0.829965 | ||||||||
\(290\) | −5.42799 | −0.318743 | ||||||||
\(291\) | −22.9508 | − | 20.7535i | −1.34540 | − | 1.21659i | ||||
\(292\) | 1.15033i | 0.0673180i | ||||||||
\(293\) | 26.3212i | 1.53770i | 0.639429 | + | 0.768850i | \(0.279171\pi\) | ||||
−0.639429 | + | 0.768850i | \(0.720829\pi\) | |||||||
\(294\) | −6.01041 | + | 6.64677i | −0.350534 | + | 0.387647i | ||||
\(295\) | 4.41758 | − | 1.15033i | 0.257202 | − | 0.0669748i | ||||
\(296\) | 21.3976i | 1.24371i | ||||||||
\(297\) | 2.83102 | + | 2.08457i | 0.164272 | + | 0.120959i | ||||
\(298\) | −31.5887 | −1.82988 | ||||||||
\(299\) | − | 26.1290i | − | 1.51108i | ||||||
\(300\) | 0.751399 | − | 0.830953i | 0.0433820 | − | 0.0479751i | ||||
\(301\) | − | 13.2376i | − | 0.763000i | ||||||
\(302\) | 12.0872i | 0.695542i | ||||||||
\(303\) | −9.72161 | + | 10.7509i | −0.558492 | + | 0.617623i | ||||
\(304\) | 9.62117 | 0.551812 | ||||||||
\(305\) | 5.94457 | 0.340385 | ||||||||
\(306\) | −7.42240 | + | 0.748230i | −0.424310 | + | 0.0427735i | ||||
\(307\) | −7.89541 | −0.450615 | −0.225307 | − | 0.974288i | \(-0.572339\pi\) | ||||
−0.225307 | + | 0.974288i | \(0.572339\pi\) | |||||||
\(308\) | −0.175247 | −0.00998564 | ||||||||
\(309\) | 2.23337 | + | 2.01955i | 0.127052 | + | 0.114888i | ||||
\(310\) | −2.16147 | −0.122763 | ||||||||
\(311\) | − | 25.2980i | − | 1.43452i | −0.696805 | − | 0.717260i | \(-0.745396\pi\) | ||
0.696805 | − | 0.717260i | \(-0.254604\pi\) | |||||||
\(312\) | −18.7950 | − | 16.9956i | −1.06406 | − | 0.962184i | ||||
\(313\) | 2.08457i | 0.117827i | 0.998263 | + | 0.0589135i | \(0.0187636\pi\) | ||||
−0.998263 | + | 0.0589135i | \(0.981236\pi\) | |||||||
\(314\) | 18.8550i | 1.06405i | ||||||||
\(315\) | 3.30090 | − | 0.332754i | 0.185984 | − | 0.0187486i | ||||
\(316\) | 1.15442 | 0.0649414 | ||||||||
\(317\) | − | 18.8879i | − | 1.06085i | −0.847731 | − | 0.530426i | \(-0.822032\pi\) | ||
0.847731 | − | 0.530426i | \(-0.177968\pi\) | |||||||
\(318\) | 10.7725 | + | 9.74111i | 0.604089 | + | 0.546255i | ||||
\(319\) | − | 4.22511i | − | 0.236561i | ||||||
\(320\) | 4.37905i | 0.244796i | ||||||||
\(321\) | 9.85353 | + | 8.91016i | 0.549970 | + | 0.497317i | ||||
\(322\) | −13.2292 | −0.737236 | ||||||||
\(323\) | 3.84072i | 0.213703i | ||||||||
\(324\) | −1.22754 | + | 0.250031i | −0.0681968 | + | 0.0138906i | ||||
\(325\) | 24.9787i | 1.38557i | ||||||||
\(326\) | −23.0450 | −1.27635 | ||||||||
\(327\) | 19.7562 | + | 17.8648i | 1.09252 | + | 0.987924i | ||||
\(328\) | − | 6.24467i | − | 0.344804i | ||||||
\(329\) | 15.7473 | 0.868174 | ||||||||
\(330\) | −0.755545 | − | 0.683210i | −0.0415914 | − | 0.0376095i | ||||
\(331\) | 29.3595 | 1.61374 | 0.806871 | − | 0.590728i | \(-0.201159\pi\) | ||||
0.806871 | + | 0.590728i | \(0.201159\pi\) | |||||||
\(332\) | −0.0131090 | −0.000719453 | ||||||||
\(333\) | −23.4674 | + | 2.36568i | −1.28601 | + | 0.129639i | ||||
\(334\) | − | 19.0801i | − | 1.04402i | ||||||
\(335\) | 3.19462 | 0.174541 | ||||||||
\(336\) | −9.20672 | + | 10.1815i | −0.502268 | + | 0.555445i | ||||
\(337\) | 12.8355i | 0.699192i | 0.936901 | + | 0.349596i | \(0.113681\pi\) | ||||
−0.936901 | + | 0.349596i | \(0.886319\pi\) | |||||||
\(338\) | −23.2486 | −1.26456 | ||||||||
\(339\) | 7.10941 | − | 7.86212i | 0.386130 | − | 0.427012i | ||||
\(340\) | 0.140643 | 0.00762746 | ||||||||
\(341\) | − | 1.68247i | − | 0.0911110i | ||||||
\(342\) | 0.994170 | + | 9.86210i | 0.0537586 | + | 0.533282i | ||||
\(343\) | −19.6081 | −1.05874 | ||||||||
\(344\) | 19.3612i | 1.04389i | ||||||||
\(345\) | −3.71120 | − | 3.35589i | −0.199804 | − | 0.180675i | ||||
\(346\) | −13.7610 | −0.739798 | ||||||||
\(347\) | −27.7175 | −1.48795 | −0.743976 | − | 0.668207i | \(-0.767062\pi\) | ||||
−0.743976 | + | 0.668207i | \(0.767062\pi\) | |||||||
\(348\) | 1.11669 | + | 1.00978i | 0.0598607 | + | 0.0541297i | ||||
\(349\) | 7.11389i | 0.380798i | 0.981707 | + | 0.190399i | \(0.0609781\pi\) | ||||
−0.981707 | + | 0.190399i | \(0.939022\pi\) | |||||||
\(350\) | 12.6468 | 0.676000 | ||||||||
\(351\) | 16.5616 | − | 22.4920i | 0.883992 | − | 1.20053i | ||||
\(352\) | 0.531806 | 0.0283454 | ||||||||
\(353\) | −8.00482 | −0.426053 | −0.213027 | − | 0.977046i | \(-0.568332\pi\) | ||||
−0.213027 | + | 0.977046i | \(0.568332\pi\) | |||||||
\(354\) | −17.2559 | − | 8.99288i | −0.917140 | − | 0.477966i | ||||
\(355\) | 3.52139 | 0.186896 | ||||||||
\(356\) | 1.52844 | 0.0810071 | ||||||||
\(357\) | −4.06439 | − | 3.67527i | −0.215110 | − | 0.194516i | ||||
\(358\) | −33.7056 | −1.78140 | ||||||||
\(359\) | − | 3.75799i | − | 0.198339i | −0.995071 | − | 0.0991697i | \(-0.968381\pi\) | ||
0.995071 | − | 0.0991697i | \(-0.0316187\pi\) | |||||||
\(360\) | −4.82789 | + | 0.486685i | −0.254452 | + | 0.0256506i | ||||
\(361\) | −13.8969 | −0.731414 | ||||||||
\(362\) | −11.0900 | −0.582879 | ||||||||
\(363\) | −12.2469 | + | 13.5436i | −0.642796 | + | 0.710853i | ||||
\(364\) | 1.39231i | 0.0729770i | ||||||||
\(365\) | −4.91142 | −0.257075 | ||||||||
\(366\) | −18.7950 | − | 16.9956i | −0.982429 | − | 0.888372i | ||||
\(367\) | 11.1530i | 0.582181i | 0.956695 | + | 0.291091i | \(0.0940181\pi\) | ||||
−0.956695 | + | 0.291091i | \(0.905982\pi\) | |||||||
\(368\) | 20.7022 | 1.07918 | ||||||||
\(369\) | 6.84871 | − | 0.690399i | 0.356530 | − | 0.0359407i | ||||
\(370\) | 6.83392 | 0.355278 | ||||||||
\(371\) | 10.6682i | 0.553864i | ||||||||
\(372\) | 0.444673 | + | 0.402100i | 0.0230552 | + | 0.0208479i | ||||
\(373\) | 12.7320 | 0.659239 | 0.329620 | − | 0.944114i | \(-0.393080\pi\) | ||||
0.329620 | + | 0.944114i | \(0.393080\pi\) | |||||||
\(374\) | 1.68247i | 0.0869986i | ||||||||
\(375\) | 7.36529 | + | 6.66014i | 0.380342 | + | 0.343928i | ||||
\(376\) | −23.0319 | −1.18778 | ||||||||
\(377\) | −33.5679 | −1.72883 | ||||||||
\(378\) | −11.3878 | − | 8.38521i | −0.585725 | − | 0.431289i | ||||
\(379\) | −21.8656 | −1.12316 | −0.561581 | − | 0.827422i | \(-0.689807\pi\) | ||||
−0.561581 | + | 0.827422i | \(0.689807\pi\) | |||||||
\(380\) | − | 0.186872i | − | 0.00958634i | ||||||
\(381\) | 7.20672 | − | 7.96973i | 0.369211 | − | 0.408302i | ||||
\(382\) | 8.95084 | 0.457965 | ||||||||
\(383\) | − | 11.2295i | − | 0.573802i | −0.957960 | − | 0.286901i | \(-0.907375\pi\) | ||
0.957960 | − | 0.286901i | \(-0.0926251\pi\) | |||||||
\(384\) | 14.3459 | − | 15.8648i | 0.732087 | − | 0.809597i | ||||
\(385\) | − | 0.748230i | − | 0.0381334i | ||||||
\(386\) | −11.9854 | −0.610043 | ||||||||
\(387\) | −21.2340 | + | 2.14054i | −1.07939 | + | 0.108810i | ||||
\(388\) | − | 2.48667i | − | 0.126242i | ||||||
\(389\) | 27.3559i | 1.38700i | 0.720458 | + | 0.693499i | \(0.243932\pi\) | ||||
−0.720458 | + | 0.693499i | \(0.756068\pi\) | |||||||
\(390\) | −5.42799 | + | 6.00269i | −0.274857 | + | 0.303958i | ||||
\(391\) | 8.26422i | 0.417939i | ||||||||
\(392\) | 9.62743 | 0.486259 | ||||||||
\(393\) | 19.1890 | − | 21.2207i | 0.967958 | − | 1.07044i | ||||
\(394\) | 35.7296i | 1.80003i | ||||||||
\(395\) | 4.92889i | 0.247999i | ||||||||
\(396\) | 0.0283379 | + | 0.281110i | 0.00142403 | + | 0.0141263i | ||||
\(397\) | − | 10.3488i | − | 0.519391i | −0.965691 | − | 0.259695i | \(-0.916378\pi\) | ||
0.965691 | − | 0.259695i | \(-0.0836222\pi\) | |||||||
\(398\) | 17.3476 | 0.869556 | ||||||||
\(399\) | −4.88331 | + | 5.40034i | −0.244471 | + | 0.270355i | ||||
\(400\) | −19.7908 | −0.989541 | ||||||||
\(401\) | 22.4120 | 1.11920 | 0.559601 | − | 0.828762i | \(-0.310955\pi\) | ||||
0.559601 | + | 0.828762i | \(0.310955\pi\) | |||||||
\(402\) | −10.1004 | − | 9.13344i | −0.503764 | − | 0.455535i | ||||
\(403\) | −13.3670 | −0.665856 | ||||||||
\(404\) | −1.16484 | −0.0579527 | ||||||||
\(405\) | −1.06752 | − | 5.24108i | −0.0530457 | − | 0.260431i | ||||
\(406\) | 16.9956i | 0.843475i | ||||||||
\(407\) | 5.31948i | 0.263677i | ||||||||
\(408\) | 5.94457 | + | 5.37545i | 0.294300 | + | 0.266124i | ||||
\(409\) | − | 21.7438i | − | 1.07516i | −0.843213 | − | 0.537580i | \(-0.819339\pi\) | ||
0.843213 | − | 0.537580i | \(-0.180661\pi\) | |||||||
\(410\) | −1.99440 | −0.0984966 | ||||||||
\(411\) | 22.4914 | + | 20.3381i | 1.10942 | + | 1.00320i | ||||
\(412\) | 0.241981i | 0.0119215i | ||||||||
\(413\) | −3.60179 | − | 13.8319i | −0.177233 | − | 0.680621i | ||||
\(414\) | 2.13919 | + | 21.2207i | 0.105136 | + | 1.04294i | ||||
\(415\) | − | 0.0559700i | − | 0.00274746i | ||||||
\(416\) | − | 4.22511i | − | 0.207153i | ||||||
\(417\) | 6.61220 | − | 7.31227i | 0.323801 | − | 0.358084i | ||||
\(418\) | 2.23549 | 0.109341 | ||||||||
\(419\) | 37.9404 | 1.85351 | 0.926756 | − | 0.375665i | \(-0.122586\pi\) | ||||
0.926756 | + | 0.375665i | \(0.122586\pi\) | |||||||
\(420\) | 0.197755 | + | 0.178822i | 0.00964947 | + | 0.00872564i | ||||
\(421\) | 21.3417i | 1.04013i | 0.854127 | + | 0.520064i | \(0.174092\pi\) | ||||
−0.854127 | + | 0.520064i | \(0.825908\pi\) | |||||||
\(422\) | 25.0346i | 1.21867i | ||||||||
\(423\) | −2.54636 | − | 25.2598i | −0.123808 | − | 1.22817i | ||||
\(424\) | − | 15.6032i | − | 0.757761i | ||||||
\(425\) | − | 7.90038i | − | 0.383225i | ||||||
\(426\) | −11.1336 | − | 10.0677i | −0.539425 | − | 0.487781i | ||||
\(427\) | − | 18.6130i | − | 0.900747i | ||||||
\(428\) | 1.06761i | 0.0516048i | ||||||||
\(429\) | −4.67245 | − | 4.22511i | −0.225588 | − | 0.203990i | ||||
\(430\) | 6.18354 | 0.298197 | ||||||||
\(431\) | 19.5679 | 0.942551 | 0.471275 | − | 0.881986i | \(-0.343794\pi\) | ||||
0.471275 | + | 0.881986i | \(0.343794\pi\) | |||||||
\(432\) | 17.8206 | + | 13.1219i | 0.857394 | + | 0.631328i | ||||
\(433\) | 15.0346 | 0.722517 | 0.361258 | − | 0.932466i | \(-0.382347\pi\) | ||||
0.361258 | + | 0.932466i | \(0.382347\pi\) | |||||||
\(434\) | 6.76776i | 0.324863i | ||||||||
\(435\) | −4.31131 | + | 4.76777i | −0.206711 | + | 0.228597i | ||||
\(436\) | 2.14054i | 0.102513i | ||||||||
\(437\) | 10.9806 | 0.525275 | ||||||||
\(438\) | 15.5284 | + | 14.0418i | 0.741978 | + | 0.670941i | ||||
\(439\) | 9.76518 | 0.466067 | 0.233033 | − | 0.972469i | \(-0.425135\pi\) | ||||
0.233033 | + | 0.972469i | \(0.425135\pi\) | |||||||
\(440\) | 1.09436i | 0.0521716i | ||||||||
\(441\) | 1.06439 | + | 10.5587i | 0.0506853 | + | 0.502795i | ||||
\(442\) | 13.3670 | 0.635802 | ||||||||
\(443\) | −0.0435667 | −0.00206991 | −0.00103496 | − | 0.999999i | \(-0.500329\pi\) | ||||
−0.00103496 | + | 0.999999i | \(0.500329\pi\) | |||||||
\(444\) | −1.40592 | − | 1.27132i | −0.0667221 | − | 0.0603342i | ||||
\(445\) | 6.52578i | 0.309351i | ||||||||
\(446\) | −10.6981 | −0.506569 | ||||||||
\(447\) | −25.0900 | + | 27.7464i | −1.18672 | + | 1.31236i | ||||
\(448\) | 13.7112 | 0.647793 | ||||||||
\(449\) | − | 6.28293i | − | 0.296510i | −0.988949 | − | 0.148255i | \(-0.952634\pi\) | ||
0.988949 | − | 0.148255i | \(-0.0473656\pi\) | |||||||
\(450\) | −2.04502 | − | 20.2864i | −0.0964030 | − | 0.956311i | ||||
\(451\) | − | 1.55243i | − | 0.0731011i | ||||||
\(452\) | 0.851843 | 0.0400673 | ||||||||
\(453\) | 10.6170 | + | 9.60056i | 0.498831 | + | 0.451074i | ||||
\(454\) | 23.0319 | 1.08094 | ||||||||
\(455\) | −5.94457 | −0.278686 | ||||||||
\(456\) | 7.14233 | − | 7.89852i | 0.334470 | − | 0.369882i | ||||
\(457\) | 1.55243i | 0.0726197i | 0.999341 | + | 0.0363098i | \(0.0115603\pi\) | ||||
−0.999341 | + | 0.0363098i | \(0.988440\pi\) | |||||||
\(458\) | − | 38.8043i | − | 1.81321i | ||||||
\(459\) | −5.23819 | + | 7.11389i | −0.244498 | + | 0.332048i | ||||
\(460\) | − | 0.402100i | − | 0.0187480i | ||||||
\(461\) | − | 41.3799i | − | 1.92726i | −0.267249 | − | 0.963628i | \(-0.586115\pi\) | ||
0.267249 | − | 0.963628i | \(-0.413885\pi\) | |||||||
\(462\) | −2.13919 | + | 2.36568i | −0.0995243 | + | 0.110061i | ||||
\(463\) | − | 13.6397i | − | 0.633889i | −0.948444 | − | 0.316944i | \(-0.897343\pi\) | ||
0.948444 | − | 0.316944i | \(-0.102657\pi\) | |||||||
\(464\) | − | 26.5961i | − | 1.23469i | ||||||
\(465\) | −1.71680 | + | 1.89856i | −0.0796145 | + | 0.0880437i | ||||
\(466\) | −22.1801 | −1.02747 | ||||||||
\(467\) | −7.01523 | −0.324626 | −0.162313 | − | 0.986739i | \(-0.551895\pi\) | ||||
−0.162313 | + | 0.986739i | \(0.551895\pi\) | |||||||
\(468\) | 2.23337 | − | 0.225140i | 0.103238 | − | 0.0104071i | ||||
\(469\) | − | 10.0027i | − | 0.461880i | ||||||
\(470\) | 7.35587i | 0.339301i | ||||||||
\(471\) | 16.5616 | + | 14.9760i | 0.763118 | + | 0.690058i | ||||
\(472\) | 5.26798 | + | 20.2305i | 0.242478 | + | 0.931182i | ||||
\(473\) | 4.81323i | 0.221312i | ||||||||
\(474\) | 14.0917 | − | 15.5837i | 0.647254 | − | 0.715782i | ||||
\(475\) | −10.4972 | −0.481645 | ||||||||
\(476\) | − | 0.440368i | − | 0.0201842i | ||||||
\(477\) | 17.1125 | − | 1.72507i | 0.783529 | − | 0.0789853i | ||||
\(478\) | − | 24.9136i | − | 1.13952i | ||||||
\(479\) | − | 9.76601i | − | 0.446220i | −0.974793 | − | 0.223110i | \(-0.928379\pi\) | ||
0.974793 | − | 0.223110i | \(-0.0716209\pi\) | |||||||
\(480\) | −0.600109 | − | 0.542655i | −0.0273911 | − | 0.0247687i | ||||
\(481\) | 42.2624 | 1.92700 | ||||||||
\(482\) | −15.0423 | −0.685159 | ||||||||
\(483\) | −10.5076 | + | 11.6201i | −0.478113 | + | 0.528733i | ||||
\(484\) | −1.46742 | −0.0667007 | ||||||||
\(485\) | 10.6170 | 0.482094 | ||||||||
\(486\) | −11.6091 | + | 19.6228i | −0.526598 | + | 0.890108i | ||||
\(487\) | −11.2922 | −0.511697 | −0.255848 | − | 0.966717i | \(-0.582355\pi\) | ||||
−0.255848 | + | 0.966717i | \(0.582355\pi\) | |||||||
\(488\) | 27.2234i | 1.23234i | ||||||||
\(489\) | −18.3040 | + | 20.2420i | −0.827737 | + | 0.915374i | ||||
\(490\) | − | 3.07478i | − | 0.138905i | ||||||
\(491\) | − | 19.8461i | − | 0.895640i | −0.894124 | − | 0.447820i | \(-0.852201\pi\) | ||
0.894124 | − | 0.447820i | \(-0.147799\pi\) | |||||||
\(492\) | 0.410303 | + | 0.371021i | 0.0184979 | + | 0.0167269i | ||||
\(493\) | 10.6170 | 0.478167 | ||||||||
\(494\) | − | 17.7606i | − | 0.799088i | ||||||
\(495\) | −1.20022 | + | 0.120990i | −0.0539458 | + | 0.00543812i | ||||
\(496\) | − | 10.5908i | − | 0.475540i | ||||||
\(497\) | − | 11.0258i | − | 0.494575i | ||||||
\(498\) | −0.160018 | + | 0.176960i | −0.00717060 | + | 0.00792979i | ||||
\(499\) | −35.8864 | −1.60650 | −0.803249 | − | 0.595643i | \(-0.796897\pi\) | ||||
−0.803249 | + | 0.595643i | \(0.796897\pi\) | |||||||
\(500\) | 0.798013i | 0.0356882i | ||||||||
\(501\) | −16.7593 | − | 15.1548i | −0.748752 | − | 0.677068i | ||||
\(502\) | 22.1290i | 0.987667i | ||||||||
\(503\) | 4.72306 | 0.210591 | 0.105295 | − | 0.994441i | \(-0.466421\pi\) | ||||
0.105295 | + | 0.994441i | \(0.466421\pi\) | |||||||
\(504\) | 1.52386 | + | 15.1166i | 0.0678780 | + | 0.673345i | ||||
\(505\) | − | 4.97334i | − | 0.221311i | ||||||
\(506\) | 4.81019 | 0.213839 | ||||||||
\(507\) | −18.4657 | + | 20.4208i | −0.820092 | + | 0.906919i | ||||
\(508\) | 0.863503 | 0.0383117 | ||||||||
\(509\) | −0.501348 | −0.0222219 | −0.0111109 | − | 0.999938i | \(-0.503537\pi\) | ||||
−0.0111109 | + | 0.999938i | \(0.503537\pi\) | |||||||
\(510\) | 1.71680 | − | 1.89856i | 0.0760210 | − | 0.0840697i | ||||
\(511\) | 15.3781i | 0.680287i | ||||||||
\(512\) | −19.8352 | −0.876599 | ||||||||
\(513\) | 9.45219 | + | 6.95996i | 0.417324 | + | 0.307290i | ||||
\(514\) | 8.97332i | 0.395796i | ||||||||
\(515\) | −1.03315 | −0.0455262 | ||||||||
\(516\) | −1.27212 | − | 1.15033i | −0.0560021 | − | 0.0506405i | ||||
\(517\) | −5.72576 | −0.251819 | ||||||||
\(518\) | − | 21.3976i | − | 0.940158i | ||||||
\(519\) | −10.9300 | + | 12.0872i | −0.479774 | + | 0.530571i | ||||
\(520\) | 8.69452 | 0.381280 | ||||||||
\(521\) | − | 34.5969i | − | 1.51572i | −0.652418 | − | 0.757859i | \(-0.726245\pi\) | ||
0.652418 | − | 0.757859i | \(-0.273755\pi\) | |||||||
\(522\) | 27.2621 | − | 2.74822i | 1.19323 | − | 0.120286i | ||||
\(523\) | 8.38365 | 0.366591 | 0.183296 | − | 0.983058i | \(-0.441323\pi\) | ||||
0.183296 | + | 0.983058i | \(0.441323\pi\) | |||||||
\(524\) | 2.29921 | 0.100442 | ||||||||
\(525\) | 10.0450 | − | 11.1085i | 0.438400 | − | 0.484816i | ||||
\(526\) | − | 34.6743i | − | 1.51187i | ||||||
\(527\) | 4.22778 | 0.184165 | ||||||||
\(528\) | 3.34760 | − | 3.70202i | 0.145685 | − | 0.161110i | ||||
\(529\) | 0.627434 | 0.0272797 | ||||||||
\(530\) | −4.98332 | −0.216462 | ||||||||
\(531\) | −21.6049 | + | 8.01419i | −0.937574 | + | 0.347786i | ||||
\(532\) | −0.585114 | −0.0253679 | ||||||||
\(533\) | −12.3338 | −0.534237 | ||||||||
\(534\) | 18.6572 | − | 20.6326i | 0.807377 | − | 0.892858i | ||||
\(535\) | −4.55823 | −0.197069 | ||||||||
\(536\) | 14.6299i | 0.631914i | ||||||||
\(537\) | −26.7714 | + | 29.6059i | −1.15527 | + | 1.27759i | ||||
\(538\) | 38.3040 | 1.65140 | ||||||||
\(539\) | 2.39339 | 0.103091 | ||||||||
\(540\) | 0.254867 | − | 0.346130i | 0.0109677 | − | 0.0148951i | ||||
\(541\) | 10.3488i | 0.444929i | 0.974941 | + | 0.222465i | \(0.0714102\pi\) | ||||
−0.974941 | + | 0.222465i | \(0.928590\pi\) | |||||||
\(542\) | 32.6371 | 1.40188 | ||||||||
\(543\) | −8.80851 | + | 9.74111i | −0.378009 | + | 0.418031i | ||||
\(544\) | 1.33634i | 0.0572952i | ||||||||
\(545\) | −9.13919 | −0.391480 | ||||||||
\(546\) | 18.7950 | + | 16.9956i | 0.804350 | + | 0.727343i | ||||
\(547\) | −35.9661 | −1.53780 | −0.768899 | − | 0.639370i | \(-0.779195\pi\) | ||||
−0.768899 | + | 0.639370i | \(0.779195\pi\) | |||||||
\(548\) | 2.43689i | 0.104099i | ||||||||
\(549\) | −29.8567 | + | 3.00976i | −1.27425 | + | 0.128454i | ||||
\(550\) | −4.59843 | −0.196078 | ||||||||
\(551\) | − | 14.1068i | − | 0.600969i | ||||||
\(552\) | 15.3684 | − | 16.9956i | 0.654123 | − | 0.723379i | ||||
\(553\) | 15.4328 | 0.656270 | ||||||||
\(554\) | 34.8491 | 1.48060 | ||||||||
\(555\) | 5.42799 | − | 6.00269i | 0.230406 | − | 0.254800i | ||||
\(556\) | 0.792269 | 0.0335997 | ||||||||
\(557\) | 19.5588i | 0.828731i | 0.910110 | + | 0.414366i | \(0.135997\pi\) | ||||
−0.910110 | + | 0.414366i | \(0.864003\pi\) | |||||||
\(558\) | 10.8560 | − | 1.09436i | 0.459571 | − | 0.0463280i | ||||
\(559\) | 38.2403 | 1.61739 | ||||||||
\(560\) | − | 4.70994i | − | 0.199031i | ||||||
\(561\) | 1.47783 | + | 1.33634i | 0.0623939 | + | 0.0564204i | ||||
\(562\) | 3.51601i | 0.148314i | ||||||||
\(563\) | −32.9854 | −1.39017 | −0.695085 | − | 0.718927i | \(-0.744633\pi\) | ||||
−0.695085 | + | 0.718927i | \(0.744633\pi\) | |||||||
\(564\) | 1.36842 | − | 1.51330i | 0.0576209 | − | 0.0637215i | ||||
\(565\) | 3.63700i | 0.153010i | ||||||||
\(566\) | 15.2180i | 0.639660i | ||||||||
\(567\) | −16.4103 | + | 3.34252i | −0.689168 | + | 0.140373i | ||||
\(568\) | 16.1263i | 0.676646i | ||||||||
\(569\) | 14.7202 | 0.617101 | 0.308551 | − | 0.951208i | \(-0.400156\pi\) | ||||
0.308551 | + | 0.951208i | \(0.400156\pi\) | |||||||
\(570\) | −2.52261 | − | 2.28110i | −0.105660 | − | 0.0955446i | ||||
\(571\) | − | 32.0926i | − | 1.34303i | −0.740990 | − | 0.671516i | \(-0.765644\pi\) | ||
0.740990 | − | 0.671516i | \(-0.234356\pi\) | |||||||
\(572\) | − | 0.506250i | − | 0.0211674i | ||||||
\(573\) | 7.10941 | − | 7.86212i | 0.297000 | − | 0.328445i | ||||
\(574\) | 6.24467i | 0.260647i | ||||||||
\(575\) | −22.5872 | −0.941953 | ||||||||
\(576\) | −2.21713 | − | 21.9938i | −0.0923804 | − | 0.916408i | ||||
\(577\) | −7.00000 | −0.291414 | −0.145707 | − | 0.989328i | \(-0.546546\pi\) | ||||
−0.145707 | + | 0.989328i | \(0.546546\pi\) | |||||||
\(578\) | 20.6364 | 0.858361 | ||||||||
\(579\) | −9.51971 | + | 10.5276i | −0.395626 | + | 0.437513i | ||||
\(580\) | −0.516577 | −0.0214497 | ||||||||
\(581\) | −0.175247 | −0.00727048 | ||||||||
\(582\) | −33.5679 | − | 30.3541i | −1.39143 | − | 1.25822i | ||||
\(583\) | − | 3.87898i | − | 0.160651i | ||||||
\(584\) | − | 22.4920i | − | 0.930725i | ||||||
\(585\) | 0.961250 | + | 9.53554i | 0.0397428 | + | 0.394246i | ||||
\(586\) | 38.4973i | 1.59031i | ||||||||
\(587\) | −24.0782 | −0.993812 | −0.496906 | − | 0.867804i | \(-0.665531\pi\) | ||||
−0.496906 | + | 0.867804i | \(0.665531\pi\) | |||||||
\(588\) | −0.572005 | + | 0.632567i | −0.0235891 | + | 0.0260866i | ||||
\(589\) | − | 5.61743i | − | 0.231462i | ||||||
\(590\) | 6.46115 | − | 1.68247i | 0.266001 | − | 0.0692663i | ||||
\(591\) | 31.3836 | + | 28.3790i | 1.29095 | + | 1.16736i | ||||
\(592\) | 33.4849i | 1.37622i | ||||||||
\(593\) | − | 35.9012i | − | 1.47429i | −0.675737 | − | 0.737143i | \(-0.736175\pi\) | ||
0.675737 | − | 0.737143i | \(-0.263825\pi\) | |||||||
\(594\) | 4.14064 | + | 3.04889i | 0.169893 | + | 0.125098i | ||||
\(595\) | 1.88018 | 0.0770799 | ||||||||
\(596\) | −3.00627 | −0.123141 | ||||||||
\(597\) | 13.7787 | − | 15.2375i | 0.563926 | − | 0.623631i | ||||
\(598\) | − | 38.2162i | − | 1.56278i | ||||||
\(599\) | 1.85411i | 0.0757567i | 0.999282 | + | 0.0378784i | \(0.0120599\pi\) | ||||
−0.999282 | + | 0.0378784i | \(0.987940\pi\) | |||||||
\(600\) | −14.6918 | + | 16.2473i | −0.599791 | + | 0.663294i | ||||
\(601\) | 0.346130i | 0.0141189i | 0.999975 | + | 0.00705947i | \(0.00224712\pi\) | ||||
−0.999975 | + | 0.00705947i | \(0.997753\pi\) | |||||||
\(602\) | − | 19.3612i | − | 0.789105i | ||||||
\(603\) | −16.0450 | + | 1.61745i | −0.653404 | + | 0.0658677i | ||||
\(604\) | 1.15033i | 0.0468063i | ||||||||
\(605\) | − | 6.26523i | − | 0.254718i | ||||||
\(606\) | −14.2188 | + | 15.7242i | −0.577600 | + | 0.638753i | ||||
\(607\) | 6.59283 | 0.267595 | 0.133797 | − | 0.991009i | \(-0.457283\pi\) | ||||
0.133797 | + | 0.991009i | \(0.457283\pi\) | |||||||
\(608\) | 1.77559 | 0.0720097 | ||||||||
\(609\) | 14.9283 | + | 13.4991i | 0.604926 | + | 0.547011i | ||||
\(610\) | 8.69452 | 0.352031 | ||||||||
\(611\) | 45.4902i | 1.84034i | ||||||||
\(612\) | −0.706383 | + | 0.0712084i | −0.0285538 | + | 0.00287843i | ||||
\(613\) | − | 18.2669i | − | 0.737792i | −0.929471 | − | 0.368896i | \(-0.879736\pi\) | ||
0.929471 | − | 0.368896i | \(-0.120264\pi\) | |||||||
\(614\) | −11.5478 | −0.466032 | ||||||||
\(615\) | −1.58410 | + | 1.75182i | −0.0638771 | + | 0.0706401i | ||||
\(616\) | 3.42655 | 0.138059 | ||||||||
\(617\) | 25.2215i | 1.01538i | 0.861540 | + | 0.507690i | \(0.169500\pi\) | ||||
−0.861540 | + | 0.507690i | \(0.830500\pi\) | |||||||
\(618\) | 3.26653 | + | 2.95379i | 0.131399 | + | 0.118819i | ||||
\(619\) | −0.700787 | −0.0281670 | −0.0140835 | − | 0.999901i | \(-0.504483\pi\) | ||||
−0.0140835 | + | 0.999901i | \(0.504483\pi\) | |||||||
\(620\) | −0.205705 | −0.00826131 | ||||||||
\(621\) | 20.3386 | + | 14.9760i | 0.816161 | + | 0.600966i | ||||
\(622\) | − | 37.0009i | − | 1.48360i | ||||||
\(623\) | 20.4328 | 0.818623 | ||||||||
\(624\) | −29.4120 | − | 26.5961i | −1.17742 | − | 1.06470i | ||||
\(625\) | 19.8269 | 0.793075 | ||||||||
\(626\) | 3.04889i | 0.121858i | ||||||||
\(627\) | 1.77559 | − | 1.96358i | 0.0709103 | − | 0.0784179i | ||||
\(628\) | 1.79441i | 0.0716048i | ||||||||
\(629\) | −13.3670 | −0.532976 | ||||||||
\(630\) | 4.82789 | − | 0.486685i | 0.192348 | − | 0.0193900i | ||||
\(631\) | −19.1559 | −0.762583 | −0.381292 | − | 0.924455i | \(-0.624521\pi\) | ||||
−0.381292 | + | 0.924455i | \(0.624521\pi\) | |||||||
\(632\) | −22.5720 | −0.897866 | ||||||||
\(633\) | 21.9896 | + | 19.8843i | 0.874008 | + | 0.790331i | ||||
\(634\) | − | 27.6255i | − | 1.09715i | ||||||
\(635\) | 3.68679i | 0.146306i | ||||||||
\(636\) | 1.02520 | + | 0.927053i | 0.0406520 | + | 0.0367600i | ||||
\(637\) | − | 19.0151i | − | 0.753406i | ||||||
\(638\) | − | 6.17965i | − | 0.244655i | ||||||
\(639\) | −17.6862 | + | 1.78290i | −0.699656 | + | 0.0705303i | ||||
\(640\) | 7.33903i | 0.290101i | ||||||||
\(641\) | − | 28.5391i | − | 1.12723i | −0.826038 | − | 0.563614i | \(-0.809411\pi\) | ||
0.826038 | − | 0.563614i | \(-0.190589\pi\) | |||||||
\(642\) | 14.4118 | + | 13.0320i | 0.568787 | + | 0.514332i | ||||
\(643\) | −46.4183 | −1.83056 | −0.915279 | − | 0.402821i | \(-0.868030\pi\) | ||||
−0.915279 | + | 0.402821i | \(0.868030\pi\) | |||||||
\(644\) | −1.25901 | −0.0496121 | ||||||||
\(645\) | 4.91142 | − | 5.43142i | 0.193387 | − | 0.213862i | ||||
\(646\) | 5.61743i | 0.221015i | ||||||||
\(647\) | 17.6014i | 0.691981i | 0.938238 | + | 0.345991i | \(0.112457\pi\) | ||||
−0.938238 | + | 0.345991i | \(0.887543\pi\) | |||||||
\(648\) | 24.0017 | − | 4.88876i | 0.942875 | − | 0.192049i | ||||
\(649\) | 1.30962 | + | 5.02931i | 0.0514073 | + | 0.197418i | ||||
\(650\) | 36.5338i | 1.43297i | ||||||||
\(651\) | 5.94457 | + | 5.37545i | 0.232986 | + | 0.210680i | ||||
\(652\) | −2.19317 | −0.0858913 | ||||||||
\(653\) | 32.0275i | 1.25333i | 0.779287 | + | 0.626667i | \(0.215581\pi\) | ||||
−0.779287 | + | 0.626667i | \(0.784419\pi\) | |||||||
\(654\) | 28.8954 | + | 26.1290i | 1.12990 | + | 1.02172i | ||||
\(655\) | 9.81665i | 0.383568i | ||||||||
\(656\) | − | 9.77219i | − | 0.381540i | ||||||
\(657\) | 24.6676 | − | 2.48667i | 0.962376 | − | 0.0970143i | ||||
\(658\) | 23.0319 | 0.897877 | ||||||||
\(659\) | 36.2236 | 1.41107 | 0.705536 | − | 0.708674i | \(-0.250706\pi\) | ||||
0.705536 | + | 0.708674i | \(0.250706\pi\) | |||||||
\(660\) | −0.0719045 | − | 0.0650205i | −0.00279888 | − | 0.00253092i | ||||
\(661\) | −10.8552 | −0.422219 | −0.211109 | − | 0.977462i | \(-0.567708\pi\) | ||||
−0.211109 | + | 0.977462i | \(0.567708\pi\) | |||||||
\(662\) | 42.9411 | 1.66895 | ||||||||
\(663\) | 10.6170 | − | 11.7411i | 0.412331 | − | 0.455987i | ||||
\(664\) | 0.256316 | 0.00994701 | ||||||||
\(665\) | − | 2.49819i | − | 0.0968755i | ||||||
\(666\) | −34.3234 | + | 3.46004i | −1.33000 | + | 0.134074i | ||||
\(667\) | − | 30.3541i | − | 1.17532i | ||||||
\(668\) | − | 1.81584i | − | 0.0702569i | ||||||
\(669\) | −8.49720 | + | 9.39685i | −0.328521 | + | 0.363303i | ||||
\(670\) | 4.67245 | 0.180512 | ||||||||
\(671\) | 6.76776i | 0.261266i | ||||||||
\(672\) | −1.69910 | + | 1.87900i | −0.0655443 | + | 0.0724839i | ||||
\(673\) | 38.2722i | 1.47528i | 0.675192 | + | 0.737642i | \(0.264061\pi\) | ||||
−0.675192 | + | 0.737642i | \(0.735939\pi\) | |||||||
\(674\) | 18.7731i | 0.723114i | ||||||||
\(675\) | −19.4432 | − | 14.3167i | −0.748370 | − | 0.551049i | ||||
\(676\) | −2.21255 | −0.0850980 | ||||||||
\(677\) | 24.6478i | 0.947291i | 0.880716 | + | 0.473645i | \(0.157062\pi\) | ||||
−0.880716 | + | 0.473645i | \(0.842938\pi\) | |||||||
\(678\) | 10.3982 | − | 11.4991i | 0.399341 | − | 0.441621i | ||||
\(679\) | − | 33.2429i | − | 1.27574i | ||||||
\(680\) | −2.74995 | −0.105456 | ||||||||
\(681\) | 18.2936 | − | 20.2305i | 0.701013 | − | 0.775233i | ||||
\(682\) | − | 2.46078i | − | 0.0942282i | ||||||
\(683\) | 41.1350 | 1.57399 | 0.786994 | − | 0.616960i | \(-0.211636\pi\) | ||||
0.786994 | + | 0.616960i | \(0.211636\pi\) | |||||||
\(684\) | 0.0946143 | + | 0.938567i | 0.00361767 | + | 0.0358870i | ||||
\(685\) | −10.4045 | −0.397534 | ||||||||
\(686\) | −28.6787 | −1.09496 | ||||||||
\(687\) | −34.0844 | − | 30.8212i | −1.30040 | − | 1.17590i | ||||
\(688\) | 30.2981i | 1.15511i | ||||||||
\(689\) | −30.8179 | −1.17407 | ||||||||
\(690\) | −5.42799 | − | 4.90832i | −0.206640 | − | 0.186857i | ||||
\(691\) | − | 48.2189i | − | 1.83433i | −0.398504 | − | 0.917166i | \(-0.630471\pi\) | ||
0.398504 | − | 0.917166i | \(-0.369529\pi\) | |||||||
\(692\) | −1.30962 | −0.0497845 | ||||||||
\(693\) | 0.378832 | + | 3.75799i | 0.0143907 | + | 0.142754i | ||||
\(694\) | −40.5395 | −1.53886 | ||||||||
\(695\) | 3.38265i | 0.128311i | ||||||||
\(696\) | −21.8342 | − | 19.7438i | −0.827621 | − | 0.748386i | ||||
\(697\) | 3.90101 | 0.147761 | ||||||||
\(698\) | 10.4048i | 0.393826i | ||||||||
\(699\) | −17.6170 | + | 19.4822i | −0.666337 | + | 0.736886i | ||||
\(700\) | 1.20359 | 0.0454912 | ||||||||
\(701\) | 17.0498 | 0.643963 | 0.321982 | − | 0.946746i | \(-0.395651\pi\) | ||||
0.321982 | + | 0.946746i | \(0.395651\pi\) | |||||||
\(702\) | 24.2230 | − | 32.8968i | 0.914237 | − | 1.24161i | ||||
\(703\) | 17.7606i | 0.669855i | ||||||||
\(704\) | −4.98544 | −0.187896 | ||||||||
\(705\) | 6.46115 | + | 5.84257i | 0.243341 | + | 0.220044i | ||||
\(706\) | −11.7078 | −0.440630 | ||||||||
\(707\) | −15.5720 | −0.585646 | ||||||||
\(708\) | −1.64223 | − | 0.855844i | −0.0617186 | − | 0.0321646i | ||||
\(709\) | −19.3178 | −0.725496 | −0.362748 | − | 0.931887i | \(-0.618161\pi\) | ||||
−0.362748 | + | 0.931887i | \(0.618161\pi\) | |||||||
\(710\) | 5.15039 | 0.193291 | ||||||||
\(711\) | −2.49552 | − | 24.7554i | −0.0935893 | − | 0.928400i | ||||
\(712\) | −29.8850 | −1.11999 | ||||||||
\(713\) | − | 12.0872i | − | 0.452670i | ||||||
\(714\) | −5.94457 | − | 5.37545i | −0.222470 | − | 0.201171i | ||||
\(715\) | 2.16147 | 0.0808343 | ||||||||
\(716\) | −3.20773 | −0.119879 | ||||||||
\(717\) | −21.8833 | − | 19.7882i | −0.817247 | − | 0.739005i | ||||
\(718\) | − | 5.49644i | − | 0.205125i | ||||||
\(719\) | −21.8165 | −0.813617 | −0.406808 | − | 0.913514i | \(-0.633358\pi\) | ||||
−0.406808 | + | 0.913514i | \(0.633358\pi\) | |||||||
\(720\) | −7.55509 | + | 0.761607i | −0.281562 | + | 0.0283834i | ||||
\(721\) | 3.23490i | 0.120474i | ||||||||
\(722\) | −20.3255 | −0.756438 | ||||||||
\(723\) | −11.9477 | + | 13.2127i | −0.444340 | + | 0.491385i | ||||
\(724\) | −1.05543 | −0.0392247 | ||||||||
\(725\) | 29.0178i | 1.07769i | ||||||||
\(726\) | −17.9123 | + | 19.8088i | −0.664789 | + | 0.735173i | ||||
\(727\) | −3.24523 | −0.120359 | −0.0601795 | − | 0.998188i | \(-0.519167\pi\) | ||||
−0.0601795 | + | 0.998188i | \(0.519167\pi\) | |||||||
\(728\) | − | 27.2234i | − | 1.00896i | ||||||
\(729\) | 8.01523 | + | 25.7829i | 0.296860 | + | 0.954921i | ||||
\(730\) | −7.18343 | −0.265871 | ||||||||
\(731\) | −12.0948 | −0.447344 | ||||||||
\(732\) | −1.78870 | − | 1.61745i | −0.0661122 | − | 0.0597827i | ||||
\(733\) | 28.5754 | 1.05546 | 0.527728 | − | 0.849414i | \(-0.323044\pi\) | ||||
0.527728 | + | 0.849414i | \(0.323044\pi\) | |||||||
\(734\) | 16.3123i | 0.602100i | ||||||||
\(735\) | −2.70079 | − | 2.44222i | −0.0996200 | − | 0.0900825i | ||||
\(736\) | 3.82061 | 0.140829 | ||||||||
\(737\) | 3.63700i | 0.133971i | ||||||||
\(738\) | 10.0169 | − | 1.00978i | 0.368728 | − | 0.0371704i | ||||
\(739\) | 17.9207i | 0.659225i | 0.944116 | + | 0.329613i | \(0.106918\pi\) | ||||
−0.944116 | + | 0.329613i | \(0.893082\pi\) | |||||||
\(740\) | 0.650378 | 0.0239084 | ||||||||
\(741\) | −15.6003 | − | 14.1068i | −0.573093 | − | 0.518226i | ||||
\(742\) | 15.6032i | 0.572813i | ||||||||
\(743\) | 29.3639i | 1.07726i | 0.842543 | + | 0.538628i | \(0.181057\pi\) | ||||
−0.842543 | + | 0.538628i | \(0.818943\pi\) | |||||||
\(744\) | −8.69452 | − | 7.86212i | −0.318757 | − | 0.288239i | ||||
\(745\) | − | 12.8355i | − | 0.470255i | ||||||
\(746\) | 18.6218 | 0.681794 | ||||||||
\(747\) | 0.0283379 | + | 0.281110i | 0.00103683 | + | 0.0102853i | ||||
\(748\) | 0.160119i | 0.00585454i | ||||||||
\(749\) | 14.2722i | 0.521496i | ||||||||
\(750\) | 10.7725 | + | 9.74111i | 0.393355 | + | 0.355695i | ||||
\(751\) | 29.2597i | 1.06770i | 0.845578 | + | 0.533852i | \(0.179256\pi\) | ||||
−0.845578 | + | 0.533852i | \(0.820744\pi\) | |||||||
\(752\) | −36.0423 | −1.31433 | ||||||||
\(753\) | 19.4374 | + | 17.5765i | 0.708338 | + | 0.640522i | ||||
\(754\) | −49.0963 | −1.78798 | ||||||||
\(755\) | −4.91142 | −0.178745 | ||||||||
\(756\) | −1.08377 | − | 0.798013i | −0.0394162 | − | 0.0290234i | ||||
\(757\) | −13.6635 | −0.496608 | −0.248304 | − | 0.968682i | \(-0.579873\pi\) | ||||
−0.248304 | + | 0.968682i | \(0.579873\pi\) | |||||||
\(758\) | −31.9806 | −1.16159 | ||||||||
\(759\) | 3.82061 | − | 4.22511i | 0.138679 | − | 0.153362i | ||||
\(760\) | 3.65384i | 0.132539i | ||||||||
\(761\) | − | 9.99115i | − | 0.362179i | −0.983467 | − | 0.181089i | \(-0.942038\pi\) | ||
0.983467 | − | 0.181089i | \(-0.0579623\pi\) | |||||||
\(762\) | 10.5405 | − | 11.6565i | 0.381843 | − | 0.422271i | ||||
\(763\) | 28.6157i | 1.03596i | ||||||||
\(764\) | 0.851843 | 0.0308186 | ||||||||
\(765\) | −0.304029 | − | 3.01595i | −0.0109922 | − | 0.109042i | ||||
\(766\) | − | 16.4243i | − | 0.593434i | ||||||
\(767\) | 39.9571 | − | 10.4048i | 1.44277 | − | 0.375694i | ||||
\(768\) | 3.86249 | − | 4.27143i | 0.139376 | − | 0.154132i | ||||
\(769\) | − | 11.3390i | − | 0.408895i | −0.978878 | − | 0.204447i | \(-0.934460\pi\) | ||
0.978878 | − | 0.204447i | \(-0.0655397\pi\) | |||||||
\(770\) | − | 1.09436i | − | 0.0394380i | ||||||
\(771\) | 7.88186 | + | 7.12726i | 0.283858 | + | 0.256682i | ||||
\(772\) | −1.14064 | −0.0410527 | ||||||||
\(773\) | 47.4737 | 1.70751 | 0.853755 | − | 0.520675i | \(-0.174320\pi\) | ||||
0.853755 | + | 0.520675i | \(0.174320\pi\) | |||||||
\(774\) | −31.0569 | + | 3.13075i | −1.11632 | + | 0.112533i | ||||
\(775\) | 11.5551i | 0.415071i | ||||||||
\(776\) | 48.6210i | 1.74539i | ||||||||
\(777\) | −18.7950 | − | 16.9956i | −0.674266 | − | 0.609712i | ||||
\(778\) | 40.0106i | 1.43445i | ||||||||
\(779\) | − | 5.18325i | − | 0.185709i | ||||||
\(780\) | −0.516577 | + | 0.571270i | −0.0184964 | + | 0.0204547i | ||||
\(781\) | 4.00903i | 0.143454i | ||||||||
\(782\) | 12.0872i | 0.432239i | ||||||||
\(783\) | 19.2396 | − | 26.1290i | 0.687569 | − | 0.933774i | ||||
\(784\) | 15.0658 | 0.538066 | ||||||||
\(785\) | −7.66137 | −0.273446 | ||||||||
\(786\) | 28.0658 | − | 31.0373i | 1.00108 | − | 1.10706i | ||||
\(787\) | 18.5693 | 0.661924 | 0.330962 | − | 0.943644i | \(-0.392627\pi\) | ||||
0.330962 | + | 0.943644i | \(0.392627\pi\) | |||||||
\(788\) | 3.40035i | 0.121132i | ||||||||
\(789\) | −30.4568 | − | 27.5409i | −1.08429 | − | 0.980481i | ||||
\(790\) | 7.20899i | 0.256484i | ||||||||
\(791\) | 11.3878 | 0.404903 | ||||||||
\(792\) | −0.554080 | − | 5.49644i | −0.0196884 | − | 0.195307i | ||||
\(793\) | 53.7687 | 1.90938 | ||||||||
\(794\) | − | 15.1361i | − | 0.537161i | ||||||
\(795\) | −3.95812 | + | 4.37718i | −0.140380 | + | 0.155243i | ||||
\(796\) | 1.65095 | 0.0585165 | ||||||||
\(797\) | −36.7189 | −1.30065 | −0.650325 | − | 0.759656i | \(-0.725367\pi\) | ||||
−0.650325 | + | 0.759656i | \(0.725367\pi\) | |||||||
\(798\) | −7.14233 | + | 7.89852i | −0.252836 | + | 0.279605i | ||||
\(799\) | − | 14.3879i | − | 0.509007i | ||||||
\(800\) | −3.65240 | −0.129132 | ||||||||
\(801\) | −3.30403 | − | 32.7758i | −0.116742 | − | 1.15807i | ||||
\(802\) | 32.7797 | 1.15749 | ||||||||
\(803\) | − | 5.59153i | − | 0.197321i | ||||||
\(804\) | −0.961250 | − | 0.869221i | −0.0339007 | − | 0.0306551i | ||||
\(805\) | − | 5.37545i | − | 0.189460i | ||||||
\(806\) | −19.5505 | −0.688637 | ||||||||
\(807\) | 30.4238 | − | 33.6450i | 1.07097 | − | 1.18436i | ||||
\(808\) | 22.7756 | 0.801242 | ||||||||
\(809\) | −29.0200 | −1.02029 | −0.510145 | − | 0.860088i | \(-0.670408\pi\) | ||||
−0.510145 | + | 0.860088i | \(0.670408\pi\) | |||||||
\(810\) | −1.56136 | − | 7.66559i | −0.0548606 | − | 0.269341i | ||||
\(811\) | 43.2455i | 1.51856i | 0.650766 | + | 0.759278i | \(0.274448\pi\) | ||||
−0.650766 | + | 0.759278i | \(0.725552\pi\) | |||||||
\(812\) | 1.61745i | 0.0567614i | ||||||||
\(813\) | 25.9227 | − | 28.6673i | 0.909150 | − | 1.00541i | ||||
\(814\) | 7.78026i | 0.272698i | ||||||||
\(815\) | − | 9.36391i | − | 0.328003i | ||||||
\(816\) | 9.30258 | + | 8.41196i | 0.325655 | + | 0.294478i | ||||
\(817\) | 16.0704i | 0.562231i | ||||||||
\(818\) | − | 31.8024i | − | 1.11194i | ||||||
\(819\) | 29.8567 | − | 3.00976i | 1.04328 | − | 0.105170i | ||||
\(820\) | −0.189806 | −0.00662830 | ||||||||
\(821\) | 10.4418 | 0.364420 | 0.182210 | − | 0.983260i | \(-0.441675\pi\) | ||||
0.182210 | + | 0.983260i | \(0.441675\pi\) | |||||||
\(822\) | 32.8958 | + | 29.7464i | 1.14737 | + | 1.03753i | ||||
\(823\) | 31.8506i | 1.11024i | 0.831770 | + | 0.555121i | \(0.187328\pi\) | ||||
−0.831770 | + | 0.555121i | \(0.812672\pi\) | |||||||
\(824\) | − | 4.73136i | − | 0.164825i | ||||||
\(825\) | −3.65240 | + | 4.03910i | −0.127160 | + | 0.140624i | ||||
\(826\) | −5.26798 | − | 20.2305i | −0.183296 | − | 0.703908i | ||||
\(827\) | 30.6085i | 1.06436i | 0.846631 | + | 0.532180i | \(0.178627\pi\) | ||||
−0.846631 | + | 0.532180i | \(0.821373\pi\) | |||||||
\(828\) | 0.203585 | + | 2.01955i | 0.00707507 | + | 0.0701843i | ||||
\(829\) | −44.7085 | −1.55279 | −0.776395 | − | 0.630246i | \(-0.782954\pi\) | ||||
−0.776395 | + | 0.630246i | \(0.782954\pi\) | |||||||
\(830\) | − | 0.0818616i | − | 0.00284146i | ||||||
\(831\) | 27.6797 | − | 30.6103i | 0.960199 | − | 1.06186i | ||||
\(832\) | 39.6085i | 1.37318i | ||||||||
\(833\) | 6.01420i | 0.208380i | ||||||||
\(834\) | 9.67100 | − | 10.6949i | 0.334879 | − | 0.370335i | ||||
\(835\) | 7.75285 | 0.268298 | ||||||||
\(836\) | 0.212750 | 0.00735810 | ||||||||
\(837\) | 7.66137 | − | 10.4048i | 0.264816 | − | 0.359641i | ||||
\(838\) | 55.4916 | 1.91693 | ||||||||
\(839\) | −40.7279 | −1.40608 | −0.703041 | − | 0.711149i | \(-0.748175\pi\) | ||||
−0.703041 | + | 0.711149i | \(0.748175\pi\) | |||||||
\(840\) | −3.86664 | − | 3.49645i | −0.133412 | − | 0.120639i | ||||
\(841\) | −9.99585 | −0.344685 | ||||||||
\(842\) | 31.2143i | 1.07572i | ||||||||
\(843\) | 3.08835 | + | 2.79267i | 0.106368 | + | 0.0961848i | ||||
\(844\) | 2.38252i | 0.0820098i | ||||||||
\(845\) | − | 9.44663i | − | 0.324974i | ||||||
\(846\) | −3.72431 | − | 36.9449i | −0.128044 | − | 1.27019i | ||||
\(847\) | −19.6170 | −0.674049 | ||||||||
\(848\) | − | 24.4173i | − | 0.838494i | ||||||
\(849\) | 13.3670 | + | 12.0872i | 0.458753 | + | 0.414833i | ||||
\(850\) | − | 11.5551i | − | 0.396336i | ||||||
\(851\) | 38.2162i | 1.31004i | ||||||||
\(852\) | −1.05957 | − | 0.958132i | −0.0363004 | − | 0.0328251i | ||||
\(853\) | −38.3795 | −1.31409 | −0.657045 | − | 0.753852i | \(-0.728194\pi\) | ||||
−0.657045 | + | 0.753852i | \(0.728194\pi\) | |||||||
\(854\) | − | 27.2234i | − | 0.931564i | ||||||
\(855\) | −4.00728 | + | 0.403962i | −0.137046 | + | 0.0138152i | ||||
\(856\) | − | 20.8745i | − | 0.713477i | ||||||
\(857\) | 31.9523 | 1.09147 | 0.545735 | − | 0.837958i | \(-0.316251\pi\) | ||||
0.545735 | + | 0.837958i | \(0.316251\pi\) | |||||||
\(858\) | −6.83392 | − | 6.17965i | −0.233306 | − | 0.210970i | ||||
\(859\) | 9.01245i | 0.307501i | 0.988110 | + | 0.153750i | \(0.0491352\pi\) | ||||
−0.988110 | + | 0.153750i | \(0.950865\pi\) | |||||||
\(860\) | 0.588482 | 0.0200671 | ||||||||
\(861\) | 5.48511 | + | 4.95997i | 0.186932 | + | 0.169035i | ||||
\(862\) | 28.6199 | 0.974798 | ||||||||
\(863\) | −13.6364 | −0.464188 | −0.232094 | − | 0.972693i | \(-0.574558\pi\) | ||||
−0.232094 | + | 0.972693i | \(0.574558\pi\) | |||||||
\(864\) | 3.28880 | + | 2.42165i | 0.111887 | + | 0.0823863i | ||||
\(865\) | − | 5.59153i | − | 0.190118i | ||||||
\(866\) | 21.9896 | 0.747237 | ||||||||
\(867\) | 16.3909 | − | 18.1263i | 0.556665 | − | 0.615602i | ||||
\(868\) | 0.644081i | 0.0218615i | ||||||||
\(869\) | −5.61143 | −0.190355 | ||||||||
\(870\) | −6.30571 | + | 6.97333i | −0.213784 | + | 0.236418i | ||||
\(871\) | 28.8954 | 0.979084 | ||||||||
\(872\) | − | 41.8532i | − | 1.41733i | ||||||
\(873\) | −53.3241 | + | 5.37545i | −1.80475 | + | 0.181931i | ||||
\(874\) | 16.0602 | 0.543246 | ||||||||
\(875\) | 10.6682i | 0.360650i | ||||||||
\(876\) | 1.47783 | + | 1.33634i | 0.0499312 | + | 0.0451508i | ||||
\(877\) | 7.95498 | 0.268621 | 0.134310 | − | 0.990939i | \(-0.457118\pi\) | ||||
0.134310 | + | 0.990939i | \(0.457118\pi\) | |||||||
\(878\) | 14.2825 | 0.482012 | ||||||||
\(879\) | 33.8148 | + | 30.5774i | 1.14054 | + | 1.03135i | ||||
\(880\) | 1.71255i | 0.0577301i | ||||||||
\(881\) | 20.8269 | 0.701675 | 0.350838 | − | 0.936436i | \(-0.385897\pi\) | ||||
0.350838 | + | 0.936436i | \(0.385897\pi\) | |||||||
\(882\) | 1.55678 | + | 15.4431i | 0.0524194 | + | 0.519997i | ||||
\(883\) | −1.67660 | −0.0564219 | −0.0282110 | − | 0.999602i | \(-0.508981\pi\) | ||||
−0.0282110 | + | 0.999602i | \(0.508981\pi\) | |||||||
\(884\) | 1.27212 | 0.0427861 | ||||||||
\(885\) | 3.65409 | − | 7.01160i | 0.122831 | − | 0.235692i | ||||
\(886\) | −0.0637205 | −0.00214073 | ||||||||
\(887\) | 1.08377 | 0.0363893 | 0.0181947 | − | 0.999834i | \(-0.494208\pi\) | ||||
0.0181947 | + | 0.999834i | \(0.494208\pi\) | |||||||
\(888\) | 27.4895 | + | 24.8577i | 0.922487 | + | 0.834169i | ||||
\(889\) | 11.5437 | 0.387162 | ||||||||
\(890\) | 9.54459i | 0.319935i | ||||||||
\(891\) | 5.96685 | − | 1.21535i | 0.199897 | − | 0.0407158i | ||||
\(892\) | −1.01813 | −0.0340894 | ||||||||
\(893\) | −19.1171 | −0.639730 | ||||||||
\(894\) | −36.6966 | + | 40.5819i | −1.22732 | + | 1.35726i | ||||
\(895\) | − | 13.6956i | − | 0.457795i | ||||||
\(896\) | 22.9792 | 0.767680 | ||||||||
\(897\) | −33.5679 | − | 30.3541i | −1.12080 | − | 1.01349i | ||||
\(898\) | − | 9.18941i | − | 0.306655i | ||||||
\(899\) | −15.5284 | −0.517902 | ||||||||
\(900\) | −0.194622 | − | 1.93064i | −0.00648741 | − | 0.0643547i | ||||
\(901\) | 9.74725 | 0.324728 | ||||||||
\(902\) | − | 2.27058i | − | 0.0756021i | ||||||
\(903\) | −17.0063 | − | 15.3781i | −0.565933 | − | 0.511751i | ||||
\(904\) | −16.6558 | −0.553963 | ||||||||
\(905\) | − | 4.50622i | − | 0.149792i | ||||||
\(906\) | 15.5284 | + | 14.0418i | 0.515898 | + | 0.466506i | ||||
\(907\) | 7.64681 | 0.253908 | 0.126954 | − | 0.991909i | \(-0.459480\pi\) | ||||
0.126954 | + | 0.991909i | \(0.459480\pi\) | |||||||
\(908\) | 2.19193 | 0.0727416 | ||||||||
\(909\) | 2.51803 | + | 24.9787i | 0.0835177 | + | 0.828490i | ||||
\(910\) | −8.69452 | −0.288221 | ||||||||
\(911\) | − | 34.4582i | − | 1.14165i | −0.821071 | − | 0.570826i | \(-0.806623\pi\) | ||
0.821071 | − | 0.570826i | \(-0.193377\pi\) | |||||||
\(912\) | 11.1769 | − | 12.3603i | 0.370105 | − | 0.409290i | ||||
\(913\) | 0.0637205 | 0.00210884 | ||||||||
\(914\) | 2.27058i | 0.0751042i | ||||||||
\(915\) | 6.90582 | − | 7.63698i | 0.228299 | − | 0.252471i | ||||
\(916\) | − | 3.69297i | − | 0.122019i | ||||||
\(917\) | 30.7368 | 1.01502 | ||||||||
\(918\) | −7.66137 | + | 10.4048i | −0.252863 | + | 0.343408i | ||||
\(919\) | − | 52.0160i | − | 1.71585i | −0.513775 | − | 0.857925i | \(-0.671753\pi\) | ||
0.513775 | − | 0.857925i | \(-0.328247\pi\) | |||||||
\(920\) | 7.86212i | 0.259206i | ||||||||
\(921\) | −9.17211 | + | 10.1432i | −0.302231 | + | 0.334230i | ||||
\(922\) | − | 60.5222i | − | 1.99319i | ||||||
\(923\) | 31.8511 | 1.04839 | ||||||||
\(924\) | −0.203585 | + | 0.225140i | −0.00669746 | + | 0.00740655i | ||||
\(925\) | − | 36.5338i | − | 1.20122i | ||||||
\(926\) | − | 19.9493i | − | 0.655576i | ||||||
\(927\) | 5.18903 | − | 0.523091i | 0.170430 | − | 0.0171806i | ||||
\(928\) | − | 4.90832i | − | 0.161124i | ||||||
\(929\) | 29.0271 | 0.952348 | 0.476174 | − | 0.879351i | \(-0.342023\pi\) | ||||
0.476174 | + | 0.879351i | \(0.342023\pi\) | |||||||
\(930\) | −2.51098 | + | 2.77683i | −0.0823383 | + | 0.0910559i | ||||
\(931\) | 7.99104 | 0.261896 | ||||||||
\(932\) | −2.11086 | −0.0691434 | ||||||||
\(933\) | −32.5003 | − | 29.3888i | −1.06401 | − | 0.962146i | ||||
\(934\) | −10.2605 | −0.335733 | ||||||||
\(935\) | −0.683641 | −0.0223574 | ||||||||
\(936\) | −43.6683 | + | 4.40207i | −1.42734 | + | 0.143886i | ||||
\(937\) | 3.87898i | 0.126721i | 0.997991 | + | 0.0633604i | \(0.0201818\pi\) | ||||
−0.997991 | + | 0.0633604i | \(0.979818\pi\) | |||||||
\(938\) | − | 14.6299i | − | 0.477682i | ||||||
\(939\) | 2.67805 | + | 2.42165i | 0.0873947 | + | 0.0790276i | ||||
\(940\) | 0.700051i | 0.0228332i | ||||||||
\(941\) | −17.7901 | −0.579942 | −0.289971 | − | 0.957035i | \(-0.593646\pi\) | ||||
−0.289971 | + | 0.957035i | \(0.593646\pi\) | |||||||
\(942\) | 24.2230 | + | 21.9039i | 0.789227 | + | 0.713667i | ||||
\(943\) | − | 11.1530i | − | 0.363191i | ||||||
\(944\) | 8.24378 | + | 31.6584i | 0.268312 | + | 1.03039i | ||||
\(945\) | 3.40717 | − | 4.62721i | 0.110835 | − | 0.150523i | ||||
\(946\) | 7.03982i | 0.228884i | ||||||||
\(947\) | − | 6.48665i | − | 0.210788i | −0.994431 | − | 0.105394i | \(-0.966390\pi\) | ||
0.994431 | − | 0.105394i | \(-0.0336103\pi\) | |||||||
\(948\) | 1.34110 | − | 1.48308i | 0.0435568 | − | 0.0481683i | ||||
\(949\) | −44.4238 | −1.44206 | ||||||||
\(950\) | −15.3532 | −0.498123 | ||||||||
\(951\) | −24.2653 | − | 21.9421i | −0.786856 | − | 0.711523i | ||||
\(952\) | 8.61035i | 0.279063i | ||||||||
\(953\) | − | 25.1211i | − | 0.813752i | −0.913483 | − | 0.406876i | \(-0.866618\pi\) | ||
0.913483 | − | 0.406876i | \(-0.133382\pi\) | |||||||
\(954\) | 25.0288 | − | 2.52308i | 0.810336 | − | 0.0816877i | ||||
\(955\) | 3.63700i | 0.117691i | ||||||||
\(956\) | − | 2.37101i | − | 0.0766839i | ||||||
\(957\) | −5.42799 | − | 4.90832i | −0.175462 | − | 0.158664i | ||||
\(958\) | − | 14.2837i | − | 0.461487i | ||||||
\(959\) | 32.5774i | 1.05198i | ||||||||
\(960\) | 5.62575 | + | 5.08715i | 0.181570 | + | 0.164187i | ||||
\(961\) | 24.8165 | 0.800531 | ||||||||
\(962\) | 61.8129 | 1.99293 | ||||||||
\(963\) | 22.8937 | − | 2.30785i | 0.737740 | − | 0.0743694i | ||||
\(964\) | −1.43156 | −0.0461076 | ||||||||
\(965\) | − | 4.87006i | − | 0.156773i | ||||||
\(966\) | −15.3684 | + | 16.9956i | −0.494471 | + | 0.546823i | ||||
\(967\) | 45.3301i | 1.45772i | 0.684664 | + | 0.728859i | \(0.259949\pi\) | ||||
−0.684664 | + | 0.728859i | \(0.740051\pi\) | |||||||
\(968\) | 28.6918 | 0.922190 | ||||||||
\(969\) | 4.93416 | + | 4.46177i | 0.158508 | + | 0.143333i | ||||
\(970\) | 15.5284 | 0.498588 | ||||||||
\(971\) | − | 16.6700i | − | 0.534965i | −0.963563 | − | 0.267483i | \(-0.913808\pi\) | ||
0.963563 | − | 0.267483i | \(-0.0861918\pi\) | |||||||
\(972\) | −1.10482 | + | 1.86748i | −0.0354373 | + | 0.0598995i | ||||
\(973\) | 10.5914 | 0.339544 | ||||||||
\(974\) | −16.5159 | −0.529204 | ||||||||
\(975\) | 32.0900 | + | 29.0178i | 1.02770 | + | 0.929312i | ||||
\(976\) | 42.6015i | 1.36364i | ||||||||
\(977\) | 7.91064 | 0.253084 | 0.126542 | − | 0.991961i | \(-0.459612\pi\) | ||||
0.126542 | + | 0.991961i | \(0.459612\pi\) | |||||||
\(978\) | −26.7714 | + | 29.6059i | −0.856056 | + | 0.946692i | ||||
\(979\) | −7.42944 | −0.237446 | ||||||||
\(980\) | − | 0.292624i | − | 0.00934754i | ||||||
\(981\) | 45.9017 | − | 4.62721i | 1.46553 | − | 0.147736i | ||||
\(982\) | − | 29.0268i | − | 0.926283i | ||||||
\(983\) | −38.4287 | −1.22568 | −0.612842 | − | 0.790205i | \(-0.709974\pi\) | ||||
−0.612842 | + | 0.790205i | \(0.709974\pi\) | |||||||
\(984\) | −8.02251 | − | 7.25444i | −0.255748 | − | 0.231263i | ||||
\(985\) | −14.5180 | −0.462583 | ||||||||
\(986\) | 15.5284 | 0.494526 | ||||||||
\(987\) | 18.2936 | − | 20.2305i | 0.582292 | − | 0.643943i | ||||
\(988\) | − | 1.69026i | − | 0.0537744i | ||||||
\(989\) | 34.5792i | 1.09956i | ||||||||
\(990\) | −1.75544 | + | 0.176960i | −0.0557914 | + | 0.00562417i | ||||
\(991\) | − | 29.6059i | − | 0.940462i | −0.882543 | − | 0.470231i | \(-0.844171\pi\) | ||
0.882543 | − | 0.470231i | \(-0.155829\pi\) | |||||||
\(992\) | − | 1.95453i | − | 0.0620564i | ||||||
\(993\) | 34.1069 | − | 37.7180i | 1.08235 | − | 1.19695i | ||||
\(994\) | − | 16.1263i | − | 0.511496i | ||||||
\(995\) | 7.04887i | 0.223464i | ||||||||
\(996\) | −0.0152288 | + | 0.0168412i | −0.000482543 | + | 0.000533633i | ||||
\(997\) | −9.75285 | −0.308876 | −0.154438 | − | 0.988002i | \(-0.549357\pi\) | ||||
−0.154438 | + | 0.988002i | \(0.549357\pi\) | |||||||
\(998\) | −52.4875 | −1.66146 | ||||||||
\(999\) | −24.2230 | + | 32.8968i | −0.766381 | + | 1.04081i |
(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 | 177.2.d.c.176.3 | yes | 6 | |
3.2 | odd | 2 | 177.2.d.a.176.4 | yes | 6 | ||
59.58 | odd | 2 | 177.2.d.a.176.3 | ✓ | 6 | ||
177.176 | even | 2 | inner | 177.2.d.c.176.4 | yes | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
177.2.d.a.176.3 | ✓ | 6 | 59.58 | odd | 2 | ||
177.2.d.a.176.4 | yes | 6 | 3.2 | odd | 2 | ||
177.2.d.c.176.3 | yes | 6 | 1.1 | even | 1 | trivial | |
177.2.d.c.176.4 | yes | 6 | 177.176 | even | 2 | inner |