Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [690,2,Mod(47,690)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(690, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("690.47");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 690 = 2 \cdot 3 \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 690.i (of order \(4\), degree \(2\), 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: | \(5.50967773947\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Relative dimension: | \(16\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 323.8 | ||
Character | \(\chi\) | \(=\) | 690.323 |
Dual form | 690.2.i.e.47.8 |
$q$-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 \(\left(\mathbb{Z}/690\mathbb{Z}\right)^\times\).
\(n\) | \(277\) | \(461\) | \(511\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.707107 | − | 0.707107i | −0.500000 | − | 0.500000i | ||||
\(3\) | 1.47268 | + | 0.911701i | 0.850255 | + | 0.526371i | ||||
\(4\) | 1.00000i | 0.500000i | ||||||||
\(5\) | 2.23363 | − | 0.104337i | 0.998911 | − | 0.0466609i | ||||
\(6\) | −0.396675 | − | 1.68602i | −0.161942 | − | 0.688313i | ||||
\(7\) | −1.29732 | + | 1.29732i | −0.490341 | + | 0.490341i | −0.908414 | − | 0.418072i | \(-0.862706\pi\) |
0.418072 | + | 0.908414i | \(0.362706\pi\) | |||||||
\(8\) | 0.707107 | − | 0.707107i | 0.250000 | − | 0.250000i | ||||
\(9\) | 1.33760 | + | 2.68530i | 0.445867 | + | 0.895099i | ||||
\(10\) | −1.65319 | − | 1.50564i | −0.522786 | − | 0.476125i | ||||
\(11\) | − | 0.254719i | − | 0.0768006i | −0.999262 | − | 0.0384003i | \(-0.987774\pi\) | ||
0.999262 | − | 0.0384003i | \(-0.0122262\pi\) | |||||||
\(12\) | −0.911701 | + | 1.47268i | −0.263185 | + | 0.425128i | ||||
\(13\) | 0.686574 | + | 0.686574i | 0.190421 | + | 0.190421i | 0.795878 | − | 0.605457i | \(-0.207010\pi\) |
−0.605457 | + | 0.795878i | \(0.707010\pi\) | |||||||
\(14\) | 1.83469 | 0.490341 | ||||||||
\(15\) | 3.38456 | + | 1.88275i | 0.873890 | + | 0.486124i | ||||
\(16\) | −1.00000 | −0.250000 | ||||||||
\(17\) | 2.14714 | + | 2.14714i | 0.520758 | + | 0.520758i | 0.917800 | − | 0.397042i | \(-0.129963\pi\) |
−0.397042 | + | 0.917800i | \(0.629963\pi\) | |||||||
\(18\) | 0.952965 | − | 2.84462i | 0.224616 | − | 0.670483i | ||||
\(19\) | − | 0.235326i | − | 0.0539874i | −0.999636 | − | 0.0269937i | \(-0.991407\pi\) | ||
0.999636 | − | 0.0269937i | \(-0.00859340\pi\) | |||||||
\(20\) | 0.104337 | + | 2.23363i | 0.0233305 | + | 0.499455i | ||||
\(21\) | −3.09331 | + | 0.727776i | −0.675016 | + | 0.158814i | ||||
\(22\) | −0.180113 | + | 0.180113i | −0.0384003 | + | 0.0384003i | ||||
\(23\) | 0.707107 | − | 0.707107i | 0.147442 | − | 0.147442i | ||||
\(24\) | 1.68602 | − | 0.396675i | 0.344156 | − | 0.0809710i | ||||
\(25\) | 4.97823 | − | 0.466101i | 0.995646 | − | 0.0932202i | ||||
\(26\) | − | 0.970962i | − | 0.190421i | ||||||
\(27\) | −0.478323 | + | 5.17409i | −0.0920533 | + | 0.995754i | ||||
\(28\) | −1.29732 | − | 1.29732i | −0.245171 | − | 0.245171i | ||||
\(29\) | 0.789167 | 0.146545 | 0.0732723 | − | 0.997312i | \(-0.476656\pi\) | ||||
0.0732723 | + | 0.997312i | \(0.476656\pi\) | |||||||
\(30\) | −1.06194 | − | 3.72455i | −0.193883 | − | 0.680007i | ||||
\(31\) | −2.07999 | −0.373577 | −0.186788 | − | 0.982400i | \(-0.559808\pi\) | ||||
−0.186788 | + | 0.982400i | \(0.559808\pi\) | |||||||
\(32\) | 0.707107 | + | 0.707107i | 0.125000 | + | 0.125000i | ||||
\(33\) | 0.232227 | − | 0.375120i | 0.0404256 | − | 0.0653001i | ||||
\(34\) | − | 3.03651i | − | 0.520758i | ||||||
\(35\) | −2.76238 | + | 3.03310i | −0.466927 | + | 0.512687i | ||||
\(36\) | −2.68530 | + | 1.33760i | −0.447550 | + | 0.222934i | ||||
\(37\) | −4.51979 | + | 4.51979i | −0.743049 | + | 0.743049i | −0.973164 | − | 0.230114i | \(-0.926090\pi\) |
0.230114 | + | 0.973164i | \(0.426090\pi\) | |||||||
\(38\) | −0.166400 | + | 0.166400i | −0.0269937 | + | 0.0269937i | ||||
\(39\) | 0.385157 | + | 1.63706i | 0.0616744 | + | 0.262139i | ||||
\(40\) | 1.50564 | − | 1.65319i | 0.238062 | − | 0.261393i | ||||
\(41\) | − | 7.61245i | − | 1.18887i | −0.804145 | − | 0.594433i | \(-0.797377\pi\) | ||
0.804145 | − | 0.594433i | \(-0.202623\pi\) | |||||||
\(42\) | 2.70192 | + | 1.67269i | 0.416915 | + | 0.258101i | ||||
\(43\) | 2.43550 | + | 2.43550i | 0.371410 | + | 0.371410i | 0.867991 | − | 0.496580i | \(-0.165411\pi\) |
−0.496580 | + | 0.867991i | \(0.665411\pi\) | |||||||
\(44\) | 0.254719 | 0.0384003 | ||||||||
\(45\) | 3.26789 | + | 5.85841i | 0.487148 | + | 0.873320i | ||||
\(46\) | −1.00000 | −0.147442 | ||||||||
\(47\) | −2.45797 | − | 2.45797i | −0.358531 | − | 0.358531i | 0.504740 | − | 0.863271i | \(-0.331588\pi\) |
−0.863271 | + | 0.504740i | \(0.831588\pi\) | |||||||
\(48\) | −1.47268 | − | 0.911701i | −0.212564 | − | 0.131593i | ||||
\(49\) | 3.63392i | 0.519131i | ||||||||
\(50\) | −3.84972 | − | 3.19056i | −0.544433 | − | 0.451213i | ||||
\(51\) | 1.20451 | + | 5.11961i | 0.168665 | + | 0.716889i | ||||
\(52\) | −0.686574 | + | 0.686574i | −0.0952107 | + | 0.0952107i | ||||
\(53\) | 2.31783 | − | 2.31783i | 0.318378 | − | 0.318378i | −0.529766 | − | 0.848144i | \(-0.677720\pi\) |
0.848144 | + | 0.529766i | \(0.177720\pi\) | |||||||
\(54\) | 3.99686 | − | 3.32041i | 0.543904 | − | 0.451850i | ||||
\(55\) | −0.0265766 | − | 0.568948i | −0.00358359 | − | 0.0767169i | ||||
\(56\) | 1.83469i | 0.245171i | ||||||||
\(57\) | 0.214547 | − | 0.346560i | 0.0284174 | − | 0.0459031i | ||||
\(58\) | −0.558025 | − | 0.558025i | −0.0732723 | − | 0.0732723i | ||||
\(59\) | −10.3269 | −1.34445 | −0.672224 | − | 0.740348i | \(-0.734661\pi\) | ||||
−0.672224 | + | 0.740348i | \(0.734661\pi\) | |||||||
\(60\) | −1.88275 | + | 3.38456i | −0.243062 | + | 0.436945i | ||||
\(61\) | 12.2697 | 1.57098 | 0.785490 | − | 0.618874i | \(-0.212411\pi\) | ||||
0.785490 | + | 0.618874i | \(0.212411\pi\) | |||||||
\(62\) | 1.47077 | + | 1.47077i | 0.186788 | + | 0.186788i | ||||
\(63\) | −5.21899 | − | 1.74839i | −0.657531 | − | 0.220277i | ||||
\(64\) | − | 1.00000i | − | 0.125000i | ||||||
\(65\) | 1.60519 | + | 1.46192i | 0.199099 | + | 0.181329i | ||||
\(66\) | −0.429460 | + | 0.101041i | −0.0528628 | + | 0.0124372i | ||||
\(67\) | 1.01439 | − | 1.01439i | 0.123927 | − | 0.123927i | −0.642423 | − | 0.766350i | \(-0.722071\pi\) |
0.766350 | + | 0.642423i | \(0.222071\pi\) | |||||||
\(68\) | −2.14714 | + | 2.14714i | −0.260379 | + | 0.260379i | ||||
\(69\) | 1.68602 | − | 0.396675i | 0.202972 | − | 0.0477541i | ||||
\(70\) | 4.09802 | − | 0.191426i | 0.489807 | − | 0.0228798i | ||||
\(71\) | − | 1.05315i | − | 0.124985i | −0.998045 | − | 0.0624927i | \(-0.980095\pi\) | ||
0.998045 | − | 0.0624927i | \(-0.0199050\pi\) | |||||||
\(72\) | 2.84462 | + | 0.952965i | 0.335242 | + | 0.112308i | ||||
\(73\) | 6.97373 | + | 6.97373i | 0.816214 | + | 0.816214i | 0.985557 | − | 0.169343i | \(-0.0541646\pi\) |
−0.169343 | + | 0.985557i | \(0.554165\pi\) | |||||||
\(74\) | 6.39195 | 0.743049 | ||||||||
\(75\) | 7.75631 | + | 3.85224i | 0.895621 | + | 0.444818i | ||||
\(76\) | 0.235326 | 0.0269937 | ||||||||
\(77\) | 0.330452 | + | 0.330452i | 0.0376585 | + | 0.0376585i | ||||
\(78\) | 0.885227 | − | 1.42992i | 0.100232 | − | 0.161907i | ||||
\(79\) | − | 12.7539i | − | 1.43492i | −0.696599 | − | 0.717461i | \(-0.745304\pi\) | ||
0.696599 | − | 0.717461i | \(-0.254696\pi\) | |||||||
\(80\) | −2.23363 | + | 0.104337i | −0.249728 | + | 0.0116652i | ||||
\(81\) | −5.42164 | + | 7.18372i | −0.602405 | + | 0.798191i | ||||
\(82\) | −5.38282 | + | 5.38282i | −0.594433 | + | 0.594433i | ||||
\(83\) | 8.88336 | − | 8.88336i | 0.975075 | − | 0.975075i | −0.0246219 | − | 0.999697i | \(-0.507838\pi\) |
0.999697 | + | 0.0246219i | \(0.00783820\pi\) | |||||||
\(84\) | −0.727776 | − | 3.09331i | −0.0794069 | − | 0.337508i | ||||
\(85\) | 5.01995 | + | 4.57190i | 0.544490 | + | 0.495892i | ||||
\(86\) | − | 3.44432i | − | 0.371410i | ||||||
\(87\) | 1.16219 | + | 0.719484i | 0.124600 | + | 0.0771368i | ||||
\(88\) | −0.180113 | − | 0.180113i | −0.0192001 | − | 0.0192001i | ||||
\(89\) | −9.41789 | −0.998294 | −0.499147 | − | 0.866517i | \(-0.666353\pi\) | ||||
−0.499147 | + | 0.866517i | \(0.666353\pi\) | |||||||
\(90\) | 1.83177 | − | 6.45326i | 0.193086 | − | 0.680234i | ||||
\(91\) | −1.78141 | −0.186743 | ||||||||
\(92\) | 0.707107 | + | 0.707107i | 0.0737210 | + | 0.0737210i | ||||
\(93\) | −3.06317 | − | 1.89633i | −0.317635 | − | 0.196640i | ||||
\(94\) | 3.47609i | 0.358531i | ||||||||
\(95\) | −0.0245532 | − | 0.525631i | −0.00251910 | − | 0.0539286i | ||||
\(96\) | 0.396675 | + | 1.68602i | 0.0404855 | + | 0.172078i | ||||
\(97\) | 2.94241 | − | 2.94241i | 0.298757 | − | 0.298757i | −0.541770 | − | 0.840527i | \(-0.682246\pi\) |
0.840527 | + | 0.541770i | \(0.182246\pi\) | |||||||
\(98\) | 2.56957 | − | 2.56957i | 0.259566 | − | 0.259566i | ||||
\(99\) | 0.683996 | − | 0.340712i | 0.0687441 | − | 0.0342429i | ||||
\(100\) | 0.466101 | + | 4.97823i | 0.0466101 | + | 0.497823i | ||||
\(101\) | − | 15.2340i | − | 1.51584i | −0.652350 | − | 0.757918i | \(-0.726217\pi\) | ||
0.652350 | − | 0.757918i | \(-0.273783\pi\) | |||||||
\(102\) | 2.76839 | − | 4.47183i | 0.274112 | − | 0.442777i | ||||
\(103\) | −1.33242 | − | 1.33242i | −0.131288 | − | 0.131288i | 0.638409 | − | 0.769697i | \(-0.279593\pi\) |
−0.769697 | + | 0.638409i | \(0.779593\pi\) | |||||||
\(104\) | 0.970962 | 0.0952107 | ||||||||
\(105\) | −6.83339 | + | 1.94833i | −0.666871 | + | 0.190138i | ||||
\(106\) | −3.27790 | −0.318378 | ||||||||
\(107\) | 0.890386 | + | 0.890386i | 0.0860768 | + | 0.0860768i | 0.748834 | − | 0.662757i | \(-0.230614\pi\) |
−0.662757 | + | 0.748834i | \(0.730614\pi\) | |||||||
\(108\) | −5.17409 | − | 0.478323i | −0.497877 | − | 0.0460266i | ||||
\(109\) | − | 11.3456i | − | 1.08672i | −0.839501 | − | 0.543358i | \(-0.817153\pi\) | ||
0.839501 | − | 0.543358i | \(-0.182847\pi\) | |||||||
\(110\) | −0.383515 | + | 0.421099i | −0.0365667 | + | 0.0401503i | ||||
\(111\) | −10.7769 | + | 2.53553i | −1.02290 | + | 0.240662i | ||||
\(112\) | 1.29732 | − | 1.29732i | 0.122585 | − | 0.122585i | ||||
\(113\) | −2.39356 | + | 2.39356i | −0.225167 | + | 0.225167i | −0.810670 | − | 0.585503i | \(-0.800897\pi\) |
0.585503 | + | 0.810670i | \(0.300897\pi\) | |||||||
\(114\) | −0.396763 | + | 0.0933479i | −0.0371602 | + | 0.00874283i | ||||
\(115\) | 1.50564 | − | 1.65319i | 0.140402 | − | 0.154161i | ||||
\(116\) | 0.789167i | 0.0732723i | ||||||||
\(117\) | −0.925292 | + | 2.76202i | −0.0855433 | + | 0.255349i | ||||
\(118\) | 7.30222 | + | 7.30222i | 0.672224 | + | 0.672224i | ||||
\(119\) | −5.57106 | −0.510698 | ||||||||
\(120\) | 3.72455 | − | 1.06194i | 0.340003 | − | 0.0969415i | ||||
\(121\) | 10.9351 | 0.994102 | ||||||||
\(122\) | −8.67602 | − | 8.67602i | −0.785490 | − | 0.785490i | ||||
\(123\) | 6.94028 | − | 11.2107i | 0.625784 | − | 1.01084i | ||||
\(124\) | − | 2.07999i | − | 0.186788i | ||||||
\(125\) | 11.0709 | − | 1.56051i | 0.990211 | − | 0.139576i | ||||
\(126\) | 2.45408 | + | 4.92668i | 0.218627 | + | 0.438904i | ||||
\(127\) | −11.6705 | + | 11.6705i | −1.03559 | + | 1.03559i | −0.0362444 | + | 0.999343i | \(0.511539\pi\) |
−0.999343 | + | 0.0362444i | \(0.988461\pi\) | |||||||
\(128\) | −0.707107 | + | 0.707107i | −0.0625000 | + | 0.0625000i | ||||
\(129\) | 1.36628 | + | 5.80717i | 0.120294 | + | 0.511293i | ||||
\(130\) | −0.101307 | − | 2.16877i | −0.00888523 | − | 0.190214i | ||||
\(131\) | − | 7.84601i | − | 0.685509i | −0.939425 | − | 0.342755i | \(-0.888640\pi\) | ||
0.939425 | − | 0.342755i | \(-0.111360\pi\) | |||||||
\(132\) | 0.375120 | + | 0.232227i | 0.0326500 | + | 0.0202128i | ||||
\(133\) | 0.305293 | + | 0.305293i | 0.0264722 | + | 0.0264722i | ||||
\(134\) | −1.43456 | −0.123927 | ||||||||
\(135\) | −0.528548 | + | 11.6069i | −0.0454902 | + | 0.998965i | ||||
\(136\) | 3.03651 | 0.260379 | ||||||||
\(137\) | −0.446558 | − | 0.446558i | −0.0381520 | − | 0.0381520i | 0.687773 | − | 0.725925i | \(-0.258588\pi\) |
−0.725925 | + | 0.687773i | \(0.758588\pi\) | |||||||
\(138\) | −1.47268 | − | 0.911701i | −0.125363 | − | 0.0776092i | ||||
\(139\) | − | 12.5052i | − | 1.06067i | −0.847787 | − | 0.530337i | \(-0.822065\pi\) | ||
0.847787 | − | 0.530337i | \(-0.177935\pi\) | |||||||
\(140\) | −3.03310 | − | 2.76238i | −0.256343 | − | 0.233464i | ||||
\(141\) | −1.37888 | − | 5.86074i | −0.116123 | − | 0.493563i | ||||
\(142\) | −0.744687 | + | 0.744687i | −0.0624927 | + | 0.0624927i | ||||
\(143\) | 0.174883 | − | 0.174883i | 0.0146245 | − | 0.0146245i | ||||
\(144\) | −1.33760 | − | 2.68530i | −0.111467 | − | 0.223775i | ||||
\(145\) | 1.76271 | − | 0.0823393i | 0.146385 | − | 0.00683791i | ||||
\(146\) | − | 9.86235i | − | 0.816214i | ||||||
\(147\) | −3.31305 | + | 5.35162i | −0.273255 | + | 0.441394i | ||||
\(148\) | −4.51979 | − | 4.51979i | −0.371525 | − | 0.371525i | ||||
\(149\) | −10.1715 | −0.833281 | −0.416640 | − | 0.909071i | \(-0.636793\pi\) | ||||
−0.416640 | + | 0.909071i | \(0.636793\pi\) | |||||||
\(150\) | −2.76059 | − | 8.20848i | −0.225402 | − | 0.670219i | ||||
\(151\) | −14.1211 | −1.14916 | −0.574581 | − | 0.818448i | \(-0.694835\pi\) | ||||
−0.574581 | + | 0.818448i | \(0.694835\pi\) | |||||||
\(152\) | −0.166400 | − | 0.166400i | −0.0134968 | − | 0.0134968i | ||||
\(153\) | −2.89369 | + | 8.63773i | −0.233941 | + | 0.698319i | ||||
\(154\) | − | 0.467330i | − | 0.0376585i | ||||||
\(155\) | −4.64593 | + | 0.217020i | −0.373170 | + | 0.0174314i | ||||
\(156\) | −1.63706 | + | 0.385157i | −0.131069 | + | 0.0308372i | ||||
\(157\) | −10.7816 | + | 10.7816i | −0.860465 | + | 0.860465i | −0.991392 | − | 0.130927i | \(-0.958205\pi\) |
0.130927 | + | 0.991392i | \(0.458205\pi\) | |||||||
\(158\) | −9.01834 | + | 9.01834i | −0.717461 | + | 0.717461i | ||||
\(159\) | 5.52660 | − | 1.30026i | 0.438288 | − | 0.103118i | ||||
\(160\) | 1.65319 | + | 1.50564i | 0.130696 | + | 0.119031i | ||||
\(161\) | 1.83469i | 0.144594i | ||||||||
\(162\) | 8.91334 | − | 1.24597i | 0.700298 | − | 0.0978930i | ||||
\(163\) | −1.35354 | − | 1.35354i | −0.106017 | − | 0.106017i | 0.652108 | − | 0.758126i | \(-0.273885\pi\) |
−0.758126 | + | 0.652108i | \(0.773885\pi\) | |||||||
\(164\) | 7.61245 | 0.594433 | ||||||||
\(165\) | 0.479572 | − | 0.862111i | 0.0373346 | − | 0.0671153i | ||||
\(166\) | −12.5630 | −0.975075 | ||||||||
\(167\) | −5.90252 | − | 5.90252i | −0.456751 | − | 0.456751i | 0.440837 | − | 0.897587i | \(-0.354682\pi\) |
−0.897587 | + | 0.440837i | \(0.854682\pi\) | |||||||
\(168\) | −1.67269 | + | 2.70192i | −0.129051 | + | 0.208458i | ||||
\(169\) | − | 12.0572i | − | 0.927479i | ||||||
\(170\) | −0.316821 | − | 6.78246i | −0.0242990 | − | 0.520191i | ||||
\(171\) | 0.631919 | − | 0.314772i | 0.0483241 | − | 0.0240712i | ||||
\(172\) | −2.43550 | + | 2.43550i | −0.185705 | + | 0.185705i | ||||
\(173\) | −12.9677 | + | 12.9677i | −0.985916 | + | 0.985916i | −0.999902 | − | 0.0139865i | \(-0.995548\pi\) |
0.0139865 | + | 0.999902i | \(0.495548\pi\) | |||||||
\(174\) | −0.313043 | − | 1.33055i | −0.0237317 | − | 0.100869i | ||||
\(175\) | −5.85368 | + | 7.06304i | −0.442496 | + | 0.533916i | ||||
\(176\) | 0.254719i | 0.0192001i | ||||||||
\(177\) | −15.2083 | − | 9.41504i | −1.14312 | − | 0.707678i | ||||
\(178\) | 6.65945 | + | 6.65945i | 0.499147 | + | 0.499147i | ||||
\(179\) | −17.1909 | −1.28491 | −0.642455 | − | 0.766323i | \(-0.722084\pi\) | ||||
−0.642455 | + | 0.766323i | \(0.722084\pi\) | |||||||
\(180\) | −5.85841 | + | 3.26789i | −0.436660 | + | 0.243574i | ||||
\(181\) | −15.0456 | −1.11833 | −0.559166 | − | 0.829055i | \(-0.688879\pi\) | ||||
−0.559166 | + | 0.829055i | \(0.688879\pi\) | |||||||
\(182\) | 1.25965 | + | 1.25965i | 0.0933714 | + | 0.0933714i | ||||
\(183\) | 18.0695 | + | 11.1863i | 1.33573 | + | 0.826918i | ||||
\(184\) | − | 1.00000i | − | 0.0737210i | ||||||
\(185\) | −9.62397 | + | 10.5671i | −0.707568 | + | 0.776911i | ||||
\(186\) | 0.825080 | + | 3.50689i | 0.0604978 | + | 0.257138i | ||||
\(187\) | 0.546917 | − | 0.546917i | 0.0399945 | − | 0.0399945i | ||||
\(188\) | 2.45797 | − | 2.45797i | 0.179266 | − | 0.179266i | ||||
\(189\) | −6.09192 | − | 7.33299i | −0.443122 | − | 0.533397i | ||||
\(190\) | −0.354315 | + | 0.389039i | −0.0257047 | + | 0.0282238i | ||||
\(191\) | 2.26357i | 0.163786i | 0.996641 | + | 0.0818932i | \(0.0260966\pi\) | ||||
−0.996641 | + | 0.0818932i | \(0.973903\pi\) | |||||||
\(192\) | 0.911701 | − | 1.47268i | 0.0657964 | − | 0.106282i | ||||
\(193\) | 1.03012 | + | 1.03012i | 0.0741495 | + | 0.0741495i | 0.743209 | − | 0.669059i | \(-0.233303\pi\) |
−0.669059 | + | 0.743209i | \(0.733303\pi\) | |||||||
\(194\) | −4.16120 | −0.298757 | ||||||||
\(195\) | 1.03110 | + | 3.61640i | 0.0738389 | + | 0.258976i | ||||
\(196\) | −3.63392 | −0.259566 | ||||||||
\(197\) | 0.571573 | + | 0.571573i | 0.0407229 | + | 0.0407229i | 0.727175 | − | 0.686452i | \(-0.240833\pi\) |
−0.686452 | + | 0.727175i | \(0.740833\pi\) | |||||||
\(198\) | −0.724578 | − | 0.242738i | −0.0514935 | − | 0.0172506i | ||||
\(199\) | − | 18.8518i | − | 1.33637i | −0.743996 | − | 0.668184i | \(-0.767072\pi\) | ||
0.743996 | − | 0.668184i | \(-0.232928\pi\) | |||||||
\(200\) | 3.19056 | − | 3.84972i | 0.225606 | − | 0.272216i | ||||
\(201\) | 2.41869 | − | 0.569054i | 0.170601 | − | 0.0401380i | ||||
\(202\) | −10.7720 | + | 10.7720i | −0.757918 | + | 0.757918i | ||||
\(203\) | −1.02380 | + | 1.02380i | −0.0718568 | + | 0.0718568i | ||||
\(204\) | −5.11961 | + | 1.20451i | −0.358444 | + | 0.0843326i | ||||
\(205\) | −0.794260 | − | 17.0034i | −0.0554736 | − | 1.18757i | ||||
\(206\) | 1.88433i | 0.131288i | ||||||||
\(207\) | 2.84462 | + | 0.952965i | 0.197715 | + | 0.0662356i | ||||
\(208\) | −0.686574 | − | 0.686574i | −0.0476053 | − | 0.0476053i | ||||
\(209\) | −0.0599418 | −0.00414626 | ||||||||
\(210\) | 6.20962 | + | 3.45426i | 0.428504 | + | 0.238367i | ||||
\(211\) | 4.60366 | 0.316929 | 0.158465 | − | 0.987365i | \(-0.449346\pi\) | ||||
0.158465 | + | 0.987365i | \(0.449346\pi\) | |||||||
\(212\) | 2.31783 | + | 2.31783i | 0.159189 | + | 0.159189i | ||||
\(213\) | 0.960155 | − | 1.55095i | 0.0657887 | − | 0.106270i | ||||
\(214\) | − | 1.25920i | − | 0.0860768i | ||||||
\(215\) | 5.69413 | + | 5.18590i | 0.388336 | + | 0.353675i | ||||
\(216\) | 3.32041 | + | 3.99686i | 0.225925 | + | 0.271952i | ||||
\(217\) | 2.69841 | − | 2.69841i | 0.183180 | − | 0.183180i | ||||
\(218\) | −8.02258 | + | 8.02258i | −0.543358 | + | 0.543358i | ||||
\(219\) | 3.91215 | + | 16.6281i | 0.264359 | + | 1.12362i | ||||
\(220\) | 0.568948 | − | 0.0265766i | 0.0383585 | − | 0.00179179i | ||||
\(221\) | 2.94834i | 0.198327i | ||||||||
\(222\) | 9.41333 | + | 5.82755i | 0.631781 | + | 0.391120i | ||||
\(223\) | 7.68075 | + | 7.68075i | 0.514341 | + | 0.514341i | 0.915854 | − | 0.401512i | \(-0.131515\pi\) |
−0.401512 | + | 0.915854i | \(0.631515\pi\) | |||||||
\(224\) | −1.83469 | −0.122585 | ||||||||
\(225\) | 7.91051 | + | 12.7446i | 0.527367 | + | 0.849638i | ||||
\(226\) | 3.38500 | 0.225167 | ||||||||
\(227\) | −0.512571 | − | 0.512571i | −0.0340205 | − | 0.0340205i | 0.689892 | − | 0.723912i | \(-0.257658\pi\) |
−0.723912 | + | 0.689892i | \(0.757658\pi\) | |||||||
\(228\) | 0.346560 | + | 0.214547i | 0.0229515 | + | 0.0142087i | ||||
\(229\) | − | 16.3029i | − | 1.07733i | −0.842521 | − | 0.538664i | \(-0.818929\pi\) | ||
0.842521 | − | 0.538664i | \(-0.181071\pi\) | |||||||
\(230\) | −2.23363 | + | 0.104337i | −0.147281 | + | 0.00687978i | ||||
\(231\) | 0.185378 | + | 0.787925i | 0.0121970 | + | 0.0518417i | ||||
\(232\) | 0.558025 | − | 0.558025i | 0.0366361 | − | 0.0366361i | ||||
\(233\) | −6.11748 | + | 6.11748i | −0.400769 | + | 0.400769i | −0.878504 | − | 0.477735i | \(-0.841458\pi\) |
0.477735 | + | 0.878504i | \(0.341458\pi\) | |||||||
\(234\) | 2.60732 | − | 1.29876i | 0.170446 | − | 0.0849026i | ||||
\(235\) | −5.74665 | − | 5.23373i | −0.374870 | − | 0.341411i | ||||
\(236\) | − | 10.3269i | − | 0.672224i | ||||||
\(237\) | 11.6277 | − | 18.7824i | 0.755301 | − | 1.22005i | ||||
\(238\) | 3.93933 | + | 3.93933i | 0.255349 | + | 0.255349i | ||||
\(239\) | −5.10225 | −0.330037 | −0.165019 | − | 0.986290i | \(-0.552768\pi\) | ||||
−0.165019 | + | 0.986290i | \(0.552768\pi\) | |||||||
\(240\) | −3.38456 | − | 1.88275i | −0.218472 | − | 0.121531i | ||||
\(241\) | 12.6977 | 0.817933 | 0.408966 | − | 0.912549i | \(-0.365889\pi\) | ||||
0.408966 | + | 0.912549i | \(0.365889\pi\) | |||||||
\(242\) | −7.73230 | − | 7.73230i | −0.497051 | − | 0.497051i | ||||
\(243\) | −14.5338 | + | 5.63643i | −0.932342 | + | 0.361577i | ||||
\(244\) | 12.2697i | 0.785490i | ||||||||
\(245\) | 0.379152 | + | 8.11684i | 0.0242231 | + | 0.518566i | ||||
\(246\) | −12.8347 | + | 3.01967i | −0.818312 | + | 0.192527i | ||||
\(247\) | 0.161568 | − | 0.161568i | 0.0102804 | − | 0.0102804i | ||||
\(248\) | −1.47077 | + | 1.47077i | −0.0933942 | + | 0.0933942i | ||||
\(249\) | 21.1813 | − | 4.98342i | 1.34231 | − | 0.315811i | ||||
\(250\) | −8.93176 | − | 6.72486i | −0.564894 | − | 0.425317i | ||||
\(251\) | − | 21.8369i | − | 1.37833i | −0.724602 | − | 0.689167i | \(-0.757976\pi\) | ||
0.724602 | − | 0.689167i | \(-0.242024\pi\) | |||||||
\(252\) | 1.74839 | − | 5.21899i | 0.110138 | − | 0.328766i | ||||
\(253\) | −0.180113 | − | 0.180113i | −0.0113236 | − | 0.0113236i | ||||
\(254\) | 16.5045 | 1.03559 | ||||||||
\(255\) | 3.22460 | + | 11.3097i | 0.201932 | + | 0.708238i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −2.12293 | − | 2.12293i | −0.132425 | − | 0.132425i | 0.637787 | − | 0.770212i | \(-0.279850\pi\) |
−0.770212 | + | 0.637787i | \(0.779850\pi\) | |||||||
\(258\) | 3.14019 | − | 5.07240i | 0.195500 | − | 0.315794i | ||||
\(259\) | − | 11.7272i | − | 0.728695i | ||||||
\(260\) | −1.46192 | + | 1.60519i | −0.0906643 | + | 0.0995496i | ||||
\(261\) | 1.05559 | + | 2.11915i | 0.0653394 | + | 0.131172i | ||||
\(262\) | −5.54797 | + | 5.54797i | −0.342755 | + | 0.342755i | ||||
\(263\) | 19.7112 | − | 19.7112i | 1.21544 | − | 1.21544i | 0.246234 | − | 0.969210i | \(-0.420807\pi\) |
0.969210 | − | 0.246234i | \(-0.0791932\pi\) | |||||||
\(264\) | −0.101041 | − | 0.429460i | −0.00621862 | − | 0.0264314i | ||||
\(265\) | 4.93534 | − | 5.41901i | 0.303176 | − | 0.332887i | ||||
\(266\) | − | 0.431749i | − | 0.0264722i | ||||||
\(267\) | −13.8696 | − | 8.58630i | −0.848804 | − | 0.525473i | ||||
\(268\) | 1.01439 | + | 1.01439i | 0.0619635 | + | 0.0619635i | ||||
\(269\) | 24.6404 | 1.50235 | 0.751176 | − | 0.660102i | \(-0.229487\pi\) | ||||
0.751176 | + | 0.660102i | \(0.229487\pi\) | |||||||
\(270\) | 8.58107 | − | 7.83359i | 0.522227 | − | 0.476737i | ||||
\(271\) | −27.5909 | −1.67603 | −0.838014 | − | 0.545649i | \(-0.816283\pi\) | ||||
−0.838014 | + | 0.545649i | \(0.816283\pi\) | |||||||
\(272\) | −2.14714 | − | 2.14714i | −0.130189 | − | 0.130189i | ||||
\(273\) | −2.62346 | − | 1.62412i | −0.158779 | − | 0.0982960i | ||||
\(274\) | 0.631528i | 0.0381520i | ||||||||
\(275\) | −0.118725 | − | 1.26805i | −0.00715937 | − | 0.0764662i | ||||
\(276\) | 0.396675 | + | 1.68602i | 0.0238771 | + | 0.101486i | ||||
\(277\) | 21.0838 | − | 21.0838i | 1.26680 | − | 1.26680i | 0.319076 | − | 0.947729i | \(-0.396628\pi\) |
0.947729 | − | 0.319076i | \(-0.103372\pi\) | |||||||
\(278\) | −8.84248 | + | 8.84248i | −0.530337 | + | 0.530337i | ||||
\(279\) | −2.78219 | − | 5.58538i | −0.166566 | − | 0.334388i | ||||
\(280\) | 0.191426 | + | 4.09802i | 0.0114399 | + | 0.244904i | ||||
\(281\) | 17.6206i | 1.05115i | 0.850746 | + | 0.525577i | \(0.176151\pi\) | ||||
−0.850746 | + | 0.525577i | \(0.823849\pi\) | |||||||
\(282\) | −3.16915 | + | 5.11918i | −0.188720 | + | 0.304843i | ||||
\(283\) | 17.7774 | + | 17.7774i | 1.05676 | + | 1.05676i | 0.998289 | + | 0.0584697i | \(0.0186221\pi\) |
0.0584697 | + | 0.998289i | \(0.481378\pi\) | |||||||
\(284\) | 1.05315 | 0.0624927 | ||||||||
\(285\) | 0.443059 | − | 0.796474i | 0.0262446 | − | 0.0471790i | ||||
\(286\) | −0.247322 | −0.0146245 | ||||||||
\(287\) | 9.87579 | + | 9.87579i | 0.582950 | + | 0.582950i | ||||
\(288\) | −0.952965 | + | 2.84462i | −0.0561540 | + | 0.167621i | ||||
\(289\) | − | 7.77958i | − | 0.457622i | ||||||
\(290\) | −1.30465 | − | 1.18820i | −0.0766114 | − | 0.0697735i | ||||
\(291\) | 7.01584 | − | 1.65064i | 0.411276 | − | 0.0967625i | ||||
\(292\) | −6.97373 | + | 6.97373i | −0.408107 | + | 0.408107i | ||||
\(293\) | 4.75775 | − | 4.75775i | 0.277951 | − | 0.277951i | −0.554340 | − | 0.832291i | \(-0.687029\pi\) |
0.832291 | + | 0.554340i | \(0.187029\pi\) | |||||||
\(294\) | 6.12684 | − | 1.44149i | 0.357325 | − | 0.0840691i | ||||
\(295\) | −23.0665 | + | 1.07748i | −1.34298 | + | 0.0627332i | ||||
\(296\) | 6.39195i | 0.371525i | ||||||||
\(297\) | 1.31794 | + | 0.121838i | 0.0764745 | + | 0.00706974i | ||||
\(298\) | 7.19233 | + | 7.19233i | 0.416640 | + | 0.416640i | ||||
\(299\) | 0.970962 | 0.0561522 | ||||||||
\(300\) | −3.85224 | + | 7.75631i | −0.222409 | + | 0.447811i | ||||
\(301\) | −6.31925 | −0.364236 | ||||||||
\(302\) | 9.98515 | + | 9.98515i | 0.574581 | + | 0.574581i | ||||
\(303\) | 13.8888 | − | 22.4348i | 0.797892 | − | 1.28885i | ||||
\(304\) | 0.235326i | 0.0134968i | ||||||||
\(305\) | 27.4061 | − | 1.28019i | 1.56927 | − | 0.0733034i | ||||
\(306\) | 8.15394 | − | 4.06165i | 0.466130 | − | 0.232189i | ||||
\(307\) | −23.0519 | + | 23.0519i | −1.31564 | + | 1.31564i | −0.398451 | + | 0.917190i | \(0.630452\pi\) |
−0.917190 | + | 0.398451i | \(0.869548\pi\) | |||||||
\(308\) | −0.330452 | + | 0.330452i | −0.0188292 | + | 0.0188292i | ||||
\(309\) | −0.747468 | − | 3.17701i | −0.0425220 | − | 0.180734i | ||||
\(310\) | 3.43862 | + | 3.13171i | 0.195301 | + | 0.177869i | ||||
\(311\) | 24.8240i | 1.40764i | 0.710377 | + | 0.703821i | \(0.248524\pi\) | ||||
−0.710377 | + | 0.703821i | \(0.751476\pi\) | |||||||
\(312\) | 1.42992 | + | 0.885227i | 0.0809533 | + | 0.0501161i | ||||
\(313\) | 2.31611 | + | 2.31611i | 0.130914 | + | 0.130914i | 0.769528 | − | 0.638614i | \(-0.220492\pi\) |
−0.638614 | + | 0.769528i | \(0.720492\pi\) | |||||||
\(314\) | 15.2475 | 0.860465 | ||||||||
\(315\) | −11.8397 | − | 3.36073i | −0.667093 | − | 0.189356i | ||||
\(316\) | 12.7539 | 0.717461 | ||||||||
\(317\) | −22.5014 | − | 22.5014i | −1.26381 | − | 1.26381i | −0.949233 | − | 0.314574i | \(-0.898138\pi\) |
−0.314574 | − | 0.949233i | \(-0.601862\pi\) | |||||||
\(318\) | −4.82732 | − | 2.98847i | −0.270703 | − | 0.167585i | ||||
\(319\) | − | 0.201016i | − | 0.0112547i | ||||||
\(320\) | −0.104337 | − | 2.23363i | −0.00583261 | − | 0.124864i | ||||
\(321\) | 0.499492 | + | 2.12302i | 0.0278789 | + | 0.118496i | ||||
\(322\) | 1.29732 | − | 1.29732i | 0.0722969 | − | 0.0722969i | ||||
\(323\) | 0.505277 | − | 0.505277i | 0.0281144 | − | 0.0281144i | ||||
\(324\) | −7.18372 | − | 5.42164i | −0.399095 | − | 0.301202i | ||||
\(325\) | 3.73793 | + | 3.09791i | 0.207343 | + | 0.171841i | ||||
\(326\) | 1.91419i | 0.106017i | ||||||||
\(327\) | 10.3438 | − | 16.7086i | 0.572015 | − | 0.923985i | ||||
\(328\) | −5.38282 | − | 5.38282i | −0.297216 | − | 0.297216i | ||||
\(329\) | 6.37754 | 0.351605 | ||||||||
\(330\) | −0.948713 | + | 0.270496i | −0.0522249 | + | 0.0148903i | ||||
\(331\) | −9.35497 | −0.514196 | −0.257098 | − | 0.966385i | \(-0.582766\pi\) | ||||
−0.257098 | + | 0.966385i | \(0.582766\pi\) | |||||||
\(332\) | 8.88336 | + | 8.88336i | 0.487537 | + | 0.487537i | ||||
\(333\) | −18.1827 | − | 6.09130i | −0.996404 | − | 0.333801i | ||||
\(334\) | 8.34742i | 0.456751i | ||||||||
\(335\) | 2.15993 | − | 2.37161i | 0.118010 | − | 0.129575i | ||||
\(336\) | 3.09331 | − | 0.727776i | 0.168754 | − | 0.0397034i | ||||
\(337\) | 19.5467 | − | 19.5467i | 1.06477 | − | 1.06477i | 0.0670235 | − | 0.997751i | \(-0.478650\pi\) |
0.997751 | − | 0.0670235i | \(-0.0213503\pi\) | |||||||
\(338\) | −8.52575 | + | 8.52575i | −0.463740 | + | 0.463740i | ||||
\(339\) | −5.70717 | + | 1.34275i | −0.309971 | + | 0.0729280i | ||||
\(340\) | −4.57190 | + | 5.01995i | −0.247946 | + | 0.272245i | ||||
\(341\) | 0.529812i | 0.0286909i | ||||||||
\(342\) | −0.669412 | − | 0.224257i | −0.0361976 | − | 0.0121264i | ||||
\(343\) | −13.7956 | − | 13.7956i | −0.744893 | − | 0.744893i | ||||
\(344\) | 3.44432 | 0.185705 | ||||||||
\(345\) | 3.72455 | − | 1.06194i | 0.200523 | − | 0.0571730i | ||||
\(346\) | 18.3391 | 0.985916 | ||||||||
\(347\) | 20.1751 | + | 20.1751i | 1.08306 | + | 1.08306i | 0.996223 | + | 0.0868324i | \(0.0276745\pi\) |
0.0868324 | + | 0.996223i | \(0.472326\pi\) | |||||||
\(348\) | −0.719484 | + | 1.16219i | −0.0385684 | + | 0.0623001i | ||||
\(349\) | − | 3.34945i | − | 0.179292i | −0.995974 | − | 0.0896460i | \(-0.971426\pi\) | ||
0.995974 | − | 0.0896460i | \(-0.0285736\pi\) | |||||||
\(350\) | 9.13350 | − | 0.855150i | 0.488206 | − | 0.0457097i | ||||
\(351\) | −3.88080 | + | 3.22399i | −0.207142 | + | 0.172084i | ||||
\(352\) | 0.180113 | − | 0.180113i | 0.00960007 | − | 0.00960007i | ||||
\(353\) | 0.587472 | − | 0.587472i | 0.0312680 | − | 0.0312680i | −0.691300 | − | 0.722568i | \(-0.742962\pi\) |
0.722568 | + | 0.691300i | \(0.242962\pi\) | |||||||
\(354\) | 4.09643 | + | 17.4113i | 0.217723 | + | 0.925401i | ||||
\(355\) | −0.109882 | − | 2.35234i | −0.00583194 | − | 0.124849i | ||||
\(356\) | − | 9.41789i | − | 0.499147i | ||||||
\(357\) | −8.20442 | − | 5.07914i | −0.434224 | − | 0.268817i | ||||
\(358\) | 12.1558 | + | 12.1558i | 0.642455 | + | 0.642455i | ||||
\(359\) | 22.1203 | 1.16746 | 0.583731 | − | 0.811947i | \(-0.301592\pi\) | ||||
0.583731 | + | 0.811947i | \(0.301592\pi\) | |||||||
\(360\) | 6.45326 | + | 1.83177i | 0.340117 | + | 0.0965429i | ||||
\(361\) | 18.9446 | 0.997085 | ||||||||
\(362\) | 10.6389 | + | 10.6389i | 0.559166 | + | 0.559166i | ||||
\(363\) | 16.1040 | + | 9.96956i | 0.845240 | + | 0.523266i | ||||
\(364\) | − | 1.78141i | − | 0.0933714i | ||||||
\(365\) | 16.3044 | + | 14.8491i | 0.853410 | + | 0.777240i | ||||
\(366\) | −4.86711 | − | 20.6870i | −0.254408 | − | 1.08133i | ||||
\(367\) | −10.1692 | + | 10.1692i | −0.530827 | + | 0.530827i | −0.920818 | − | 0.389992i | \(-0.872478\pi\) |
0.389992 | + | 0.920818i | \(0.372478\pi\) | |||||||
\(368\) | −0.707107 | + | 0.707107i | −0.0368605 | + | 0.0368605i | ||||
\(369\) | 20.4417 | − | 10.1824i | 1.06415 | − | 0.530076i | ||||
\(370\) | 14.2773 | − | 0.666917i | 0.742240 | − | 0.0346714i | ||||
\(371\) | 6.01393i | 0.312228i | ||||||||
\(372\) | 1.89633 | − | 3.06317i | 0.0983200 | − | 0.158818i | ||||
\(373\) | 6.32688 | + | 6.32688i | 0.327594 | + | 0.327594i | 0.851671 | − | 0.524077i | \(-0.175590\pi\) |
−0.524077 | + | 0.851671i | \(0.675590\pi\) | |||||||
\(374\) | −0.773457 | −0.0399945 | ||||||||
\(375\) | 17.7267 | + | 7.79521i | 0.915401 | + | 0.402543i | ||||
\(376\) | −3.47609 | −0.179266 | ||||||||
\(377\) | 0.541821 | + | 0.541821i | 0.0279052 | + | 0.0279052i | ||||
\(378\) | −0.877573 | + | 9.49284i | −0.0451375 | + | 0.488259i | ||||
\(379\) | 29.7415i | 1.52772i | 0.645382 | + | 0.763860i | \(0.276698\pi\) | ||||
−0.645382 | + | 0.763860i | \(0.723302\pi\) | |||||||
\(380\) | 0.525631 | − | 0.0245532i | 0.0269643 | − | 0.00125955i | ||||
\(381\) | −27.8269 | + | 6.54695i | −1.42562 | + | 0.335410i | ||||
\(382\) | 1.60059 | − | 1.60059i | 0.0818932 | − | 0.0818932i | ||||
\(383\) | −11.8299 | + | 11.8299i | −0.604479 | + | 0.604479i | −0.941498 | − | 0.337019i | \(-0.890581\pi\) |
0.337019 | + | 0.941498i | \(0.390581\pi\) | |||||||
\(384\) | −1.68602 | + | 0.396675i | −0.0860391 | + | 0.0202428i | ||||
\(385\) | 0.772586 | + | 0.703630i | 0.0393747 | + | 0.0358603i | ||||
\(386\) | − | 1.45681i | − | 0.0741495i | ||||||
\(387\) | −3.28231 | + | 9.79777i | −0.166849 | + | 0.498049i | ||||
\(388\) | 2.94241 | + | 2.94241i | 0.149378 | + | 0.149378i | ||||
\(389\) | 33.8998 | 1.71879 | 0.859394 | − | 0.511315i | \(-0.170841\pi\) | ||||
0.859394 | + | 0.511315i | \(0.170841\pi\) | |||||||
\(390\) | 1.82808 | − | 3.28628i | 0.0925684 | − | 0.166407i | ||||
\(391\) | 3.03651 | 0.153563 | ||||||||
\(392\) | 2.56957 | + | 2.56957i | 0.129783 | + | 0.129783i | ||||
\(393\) | 7.15322 | − | 11.5547i | 0.360832 | − | 0.582858i | ||||
\(394\) | − | 0.808326i | − | 0.0407229i | ||||||
\(395\) | −1.33070 | − | 28.4874i | −0.0669547 | − | 1.43336i | ||||
\(396\) | 0.340712 | + | 0.683996i | 0.0171214 | + | 0.0343721i | ||||
\(397\) | −1.01644 | + | 1.01644i | −0.0510138 | + | 0.0510138i | −0.732153 | − | 0.681140i | \(-0.761485\pi\) |
0.681140 | + | 0.732153i | \(0.261485\pi\) | |||||||
\(398\) | −13.3302 | + | 13.3302i | −0.668184 | + | 0.668184i | ||||
\(399\) | 0.171264 | + | 0.727936i | 0.00857394 | + | 0.0364424i | ||||
\(400\) | −4.97823 | + | 0.466101i | −0.248911 | + | 0.0233050i | ||||
\(401\) | 21.8339i | 1.09033i | 0.838327 | + | 0.545167i | \(0.183534\pi\) | ||||
−0.838327 | + | 0.545167i | \(0.816466\pi\) | |||||||
\(402\) | −2.11265 | − | 1.30789i | −0.105370 | − | 0.0652316i | ||||
\(403\) | −1.42806 | − | 1.42806i | −0.0711370 | − | 0.0711370i | ||||
\(404\) | 15.2340 | 0.757918 | ||||||||
\(405\) | −11.3604 | + | 16.6115i | −0.564504 | + | 0.825430i | ||||
\(406\) | 1.44788 | 0.0718568 | ||||||||
\(407\) | 1.15128 | + | 1.15128i | 0.0570666 | + | 0.0570666i | ||||
\(408\) | 4.47183 | + | 2.76839i | 0.221389 | + | 0.137056i | ||||
\(409\) | 32.4433i | 1.60422i | 0.597177 | + | 0.802109i | \(0.296289\pi\) | ||||
−0.597177 | + | 0.802109i | \(0.703711\pi\) | |||||||
\(410\) | −11.4616 | + | 12.5849i | −0.566049 | + | 0.621522i | ||||
\(411\) | −0.250512 | − | 1.06477i | −0.0123568 | − | 0.0525210i | ||||
\(412\) | 1.33242 | − | 1.33242i | 0.0656438 | − | 0.0656438i | ||||
\(413\) | 13.3973 | − | 13.3973i | 0.659238 | − | 0.659238i | ||||
\(414\) | −1.33760 | − | 2.68530i | −0.0657395 | − | 0.131975i | ||||
\(415\) | 18.9153 | − | 20.7690i | 0.928515 | − | 1.01951i | ||||
\(416\) | 0.970962i | 0.0476053i | ||||||||
\(417\) | 11.4010 | − | 18.4162i | 0.558308 | − | 0.901843i | ||||
\(418\) | 0.0423853 | + | 0.0423853i | 0.00207313 | + | 0.00207313i | ||||
\(419\) | −11.6777 | −0.570495 | −0.285248 | − | 0.958454i | \(-0.592076\pi\) | ||||
−0.285248 | + | 0.958454i | \(0.592076\pi\) | |||||||
\(420\) | −1.94833 | − | 6.83339i | −0.0950688 | − | 0.333435i | ||||
\(421\) | 31.0857 | 1.51502 | 0.757512 | − | 0.652822i | \(-0.226415\pi\) | ||||
0.757512 | + | 0.652822i | \(0.226415\pi\) | |||||||
\(422\) | −3.25528 | − | 3.25528i | −0.158465 | − | 0.158465i | ||||
\(423\) | 3.31259 | − | 9.88815i | 0.161064 | − | 0.480778i | ||||
\(424\) | − | 3.27790i | − | 0.159189i | ||||||
\(425\) | 11.6897 | + | 9.68817i | 0.567036 | + | 0.469945i | ||||
\(426\) | −1.77562 | + | 0.417757i | −0.0860291 | + | 0.0202404i | ||||
\(427\) | −15.9178 | + | 15.9178i | −0.770316 | + | 0.770316i | ||||
\(428\) | −0.890386 | + | 0.890386i | −0.0430384 | + | 0.0430384i | ||||
\(429\) | 0.416989 | − | 0.0981066i | 0.0201324 | − | 0.00473663i | ||||
\(430\) | −0.359370 | − | 7.69334i | −0.0173303 | − | 0.371006i | ||||
\(431\) | 17.3722i | 0.836791i | 0.908265 | + | 0.418395i | \(0.137407\pi\) | ||||
−0.908265 | + | 0.418395i | \(0.862593\pi\) | |||||||
\(432\) | 0.478323 | − | 5.17409i | 0.0230133 | − | 0.248939i | ||||
\(433\) | −3.43595 | − | 3.43595i | −0.165121 | − | 0.165121i | 0.619710 | − | 0.784831i | \(-0.287250\pi\) |
−0.784831 | + | 0.619710i | \(0.787250\pi\) | |||||||
\(434\) | −3.81613 | −0.183180 | ||||||||
\(435\) | 2.67098 | + | 1.48580i | 0.128064 | + | 0.0712388i | ||||
\(436\) | 11.3456 | 0.543358 | ||||||||
\(437\) | −0.166400 | − | 0.166400i | −0.00796001 | − | 0.00796001i | ||||
\(438\) | 8.99152 | − | 14.5241i | 0.429631 | − | 0.693990i | ||||
\(439\) | − | 12.2984i | − | 0.586971i | −0.955964 | − | 0.293486i | \(-0.905185\pi\) | ||
0.955964 | − | 0.293486i | \(-0.0948153\pi\) | |||||||
\(440\) | −0.421099 | − | 0.383515i | −0.0200751 | − | 0.0182833i | ||||
\(441\) | −9.75815 | + | 4.86073i | −0.464674 | + | 0.231464i | ||||
\(442\) | 2.08479 | − | 2.08479i | 0.0991634 | − | 0.0991634i | ||||
\(443\) | −11.2303 | + | 11.2303i | −0.533567 | + | 0.533567i | −0.921632 | − | 0.388065i | \(-0.873144\pi\) |
0.388065 | + | 0.921632i | \(0.373144\pi\) | |||||||
\(444\) | −2.53553 | − | 10.7769i | −0.120331 | − | 0.511450i | ||||
\(445\) | −21.0361 | + | 0.982634i | −0.997207 | + | 0.0465813i | ||||
\(446\) | − | 10.8622i | − | 0.514341i | ||||||
\(447\) | −14.9794 | − | 9.27336i | −0.708501 | − | 0.438615i | ||||
\(448\) | 1.29732 | + | 1.29732i | 0.0612926 | + | 0.0612926i | ||||
\(449\) | 4.18538 | 0.197520 | 0.0987601 | − | 0.995111i | \(-0.468512\pi\) | ||||
0.0987601 | + | 0.995111i | \(0.468512\pi\) | |||||||
\(450\) | 3.41819 | − | 14.6053i | 0.161135 | − | 0.688502i | ||||
\(451\) | −1.93903 | −0.0913056 | ||||||||
\(452\) | −2.39356 | − | 2.39356i | −0.112584 | − | 0.112584i | ||||
\(453\) | −20.7960 | − | 12.8743i | −0.977080 | − | 0.604885i | ||||
\(454\) | 0.724884i | 0.0340205i | ||||||||
\(455\) | −3.97902 | + | 0.185867i | −0.186539 | + | 0.00871359i | ||||
\(456\) | −0.0933479 | − | 0.396763i | −0.00437141 | − | 0.0185801i | ||||
\(457\) | 7.32848 | − | 7.32848i | 0.342812 | − | 0.342812i | −0.514612 | − | 0.857423i | \(-0.672064\pi\) |
0.857423 | + | 0.514612i | \(0.172064\pi\) | |||||||
\(458\) | −11.5279 | + | 11.5279i | −0.538664 | + | 0.538664i | ||||
\(459\) | −12.1365 | + | 10.0825i | −0.566484 | + | 0.470609i | ||||
\(460\) | 1.65319 | + | 1.50564i | 0.0770806 | + | 0.0702008i | ||||
\(461\) | − | 11.7310i | − | 0.546367i | −0.961962 | − | 0.273184i | \(-0.911923\pi\) | ||
0.961962 | − | 0.273184i | \(-0.0880767\pi\) | |||||||
\(462\) | 0.426065 | − | 0.688229i | 0.0198223 | − | 0.0320193i | ||||
\(463\) | −19.3473 | − | 19.3473i | −0.899144 | − | 0.899144i | 0.0962167 | − | 0.995360i | \(-0.469326\pi\) |
−0.995360 | + | 0.0962167i | \(0.969326\pi\) | |||||||
\(464\) | −0.789167 | −0.0366361 | ||||||||
\(465\) | −7.03984 | − | 3.91610i | −0.326465 | − | 0.181605i | ||||
\(466\) | 8.65142 | 0.400769 | ||||||||
\(467\) | 18.8596 | + | 18.8596i | 0.872719 | + | 0.872719i | 0.992768 | − | 0.120049i | \(-0.0383051\pi\) |
−0.120049 | + | 0.992768i | \(0.538305\pi\) | |||||||
\(468\) | −2.76202 | − | 0.925292i | −0.127674 | − | 0.0427717i | ||||
\(469\) | 2.63197i | 0.121533i | ||||||||
\(470\) | 0.362685 | + | 7.76430i | 0.0167294 | + | 0.358141i | ||||
\(471\) | −25.7075 | + | 6.04830i | −1.18454 | + | 0.278691i | ||||
\(472\) | −7.30222 | + | 7.30222i | −0.336112 | + | 0.336112i | ||||
\(473\) | 0.620368 | − | 0.620368i | 0.0285245 | − | 0.0285245i | ||||
\(474\) | −21.5032 | + | 5.05914i | −0.987675 | + | 0.232374i | ||||
\(475\) | −0.109685 | − | 1.17150i | −0.00503272 | − | 0.0537523i | ||||
\(476\) | − | 5.57106i | − | 0.255349i | ||||||
\(477\) | 9.32439 | + | 3.12373i | 0.426934 | + | 0.143026i | ||||
\(478\) | 3.60784 | + | 3.60784i | 0.165019 | + | 0.165019i | ||||
\(479\) | −31.9961 | −1.46194 | −0.730970 | − | 0.682410i | \(-0.760932\pi\) | ||||
−0.730970 | + | 0.682410i | \(0.760932\pi\) | |||||||
\(480\) | 1.06194 | + | 3.72455i | 0.0484707 | + | 0.170002i | ||||
\(481\) | −6.20634 | −0.282985 | ||||||||
\(482\) | −8.97865 | − | 8.97865i | −0.408966 | − | 0.408966i | ||||
\(483\) | −1.67269 | + | 2.70192i | −0.0761099 | + | 0.122942i | ||||
\(484\) | 10.9351i | 0.497051i | ||||||||
\(485\) | 6.26526 | − | 6.87927i | 0.284491 | − | 0.312371i | ||||
\(486\) | 14.2625 | + | 6.29137i | 0.646960 | + | 0.285382i | ||||
\(487\) | 5.57401 | − | 5.57401i | 0.252583 | − | 0.252583i | −0.569446 | − | 0.822029i | \(-0.692842\pi\) |
0.822029 | + | 0.569446i | \(0.192842\pi\) | |||||||
\(488\) | 8.67602 | − | 8.67602i | 0.392745 | − | 0.392745i | ||||
\(489\) | −0.759313 | − | 3.22736i | −0.0343373 | − | 0.145946i | ||||
\(490\) | 5.47137 | − | 6.00757i | 0.247171 | − | 0.271394i | ||||
\(491\) | 10.2383i | 0.462049i | 0.972948 | + | 0.231025i | \(0.0742078\pi\) | ||||
−0.972948 | + | 0.231025i | \(0.925792\pi\) | |||||||
\(492\) | 11.2107 | + | 6.94028i | 0.505419 | + | 0.312892i | ||||
\(493\) | 1.69445 | + | 1.69445i | 0.0763143 | + | 0.0763143i | ||||
\(494\) | −0.228492 | −0.0102804 | ||||||||
\(495\) | 1.49225 | − | 0.832392i | 0.0670715 | − | 0.0374132i | ||||
\(496\) | 2.07999 | 0.0933942 | ||||||||
\(497\) | 1.36627 | + | 1.36627i | 0.0612855 | + | 0.0612855i | ||||
\(498\) | −18.5013 | − | 11.4537i | −0.829062 | − | 0.513251i | ||||
\(499\) | 23.8537i | 1.06784i | 0.845536 | + | 0.533919i | \(0.179281\pi\) | ||||
−0.845536 | + | 0.533919i | \(0.820719\pi\) | |||||||
\(500\) | 1.56051 | + | 11.0709i | 0.0697882 | + | 0.495106i | ||||
\(501\) | −3.31122 | − | 14.0739i | −0.147934 | − | 0.628775i | ||||
\(502\) | −15.4410 | + | 15.4410i | −0.689167 | + | 0.689167i | ||||
\(503\) | 18.1094 | − | 18.1094i | 0.807460 | − | 0.807460i | −0.176789 | − | 0.984249i | \(-0.556571\pi\) |
0.984249 | + | 0.176789i | \(0.0565710\pi\) | |||||||
\(504\) | −4.92668 | + | 2.45408i | −0.219452 | + | 0.109314i | ||||
\(505\) | −1.58947 | − | 34.0271i | −0.0707303 | − | 1.51418i | ||||
\(506\) | 0.254719i | 0.0113236i | ||||||||
\(507\) | 10.9926 | − | 17.7565i | 0.488198 | − | 0.788594i | ||||
\(508\) | −11.6705 | − | 11.6705i | −0.517794 | − | 0.517794i | ||||
\(509\) | −33.2985 | −1.47593 | −0.737966 | − | 0.674838i | \(-0.764213\pi\) | ||||
−0.737966 | + | 0.674838i | \(0.764213\pi\) | |||||||
\(510\) | 5.71700 | − | 10.2773i | 0.253153 | − | 0.455085i | ||||
\(511\) | −18.0943 | −0.800447 | ||||||||
\(512\) | −0.707107 | − | 0.707107i | −0.0312500 | − | 0.0312500i | ||||
\(513\) | 1.21760 | + | 0.112562i | 0.0537582 | + | 0.00496972i | ||||
\(514\) | 3.00228i | 0.132425i | ||||||||
\(515\) | −3.11517 | − | 2.83712i | −0.137271 | − | 0.125019i | ||||
\(516\) | −5.80717 | + | 1.36628i | −0.255647 | + | 0.0601470i | ||||
\(517\) | −0.626090 | + | 0.626090i | −0.0275354 | + | 0.0275354i | ||||
\(518\) | −8.29241 | + | 8.29241i | −0.364348 | + | 0.364348i | ||||
\(519\) | −30.9200 | + | 7.27467i | −1.35724 | + | 0.319322i | ||||
\(520\) | 2.16877 | − | 0.101307i | 0.0951070 | − | 0.00444262i | ||||
\(521\) | 39.9278i | 1.74927i | 0.484782 | + | 0.874635i | \(0.338899\pi\) | ||||
−0.484782 | + | 0.874635i | \(0.661101\pi\) | |||||||
\(522\) | 0.752048 | − | 2.24488i | 0.0329162 | − | 0.0982557i | ||||
\(523\) | 12.0950 | + | 12.0950i | 0.528876 | + | 0.528876i | 0.920237 | − | 0.391361i | \(-0.127996\pi\) |
−0.391361 | + | 0.920237i | \(0.627996\pi\) | |||||||
\(524\) | 7.84601 | 0.342755 | ||||||||
\(525\) | −15.0600 | + | 5.06483i | −0.657272 | + | 0.221047i | ||||
\(526\) | −27.8758 | −1.21544 | ||||||||
\(527\) | −4.46602 | − | 4.46602i | −0.194543 | − | 0.194543i | ||||
\(528\) | −0.232227 | + | 0.375120i | −0.0101064 | + | 0.0163250i | ||||
\(529\) | − | 1.00000i | − | 0.0434783i | ||||||
\(530\) | −7.32163 | + | 0.342007i | −0.318031 | + | 0.0148558i | ||||
\(531\) | −13.8133 | − | 27.7308i | −0.599445 | − | 1.20341i | ||||
\(532\) | −0.305293 | + | 0.305293i | −0.0132361 | + | 0.0132361i | ||||
\(533\) | 5.22651 | − | 5.22651i | 0.226385 | − | 0.226385i | ||||
\(534\) | 3.73584 | + | 15.8787i | 0.161666 | + | 0.687139i | ||||
\(535\) | 2.08169 | + | 1.89589i | 0.0899995 | + | 0.0819666i | ||||
\(536\) | − | 1.43456i | − | 0.0619635i | ||||||
\(537\) | −25.3168 | − | 15.6730i | −1.09250 | − | 0.676339i | ||||
\(538\) | −17.4234 | − | 17.4234i | −0.751176 | − | 0.751176i | ||||
\(539\) | 0.925627 | 0.0398696 | ||||||||
\(540\) | −11.6069 | − | 0.528548i | −0.499482 | − | 0.0227451i | ||||
\(541\) | −2.96852 | −0.127627 | −0.0638134 | − | 0.997962i | \(-0.520326\pi\) | ||||
−0.0638134 | + | 0.997962i | \(0.520326\pi\) | |||||||
\(542\) | 19.5097 | + | 19.5097i | 0.838014 | + | 0.838014i | ||||
\(543\) | −22.1575 | − | 13.7171i | −0.950868 | − | 0.588658i | ||||
\(544\) | 3.03651i | 0.130189i | ||||||||
\(545\) | −1.18377 | − | 25.3420i | −0.0507071 | − | 1.08553i | ||||
\(546\) | 0.706643 | + | 3.00349i | 0.0302415 | + | 0.128538i | ||||
\(547\) | 8.47104 | − | 8.47104i | 0.362195 | − | 0.362195i | −0.502425 | − | 0.864621i | \(-0.667559\pi\) |
0.864621 | + | 0.502425i | \(0.167559\pi\) | |||||||
\(548\) | 0.446558 | − | 0.446558i | 0.0190760 | − | 0.0190760i | ||||
\(549\) | 16.4120 | + | 32.9479i | 0.700449 | + | 1.40618i | ||||
\(550\) | −0.812694 | + | 0.980596i | −0.0346534 | + | 0.0418128i | ||||
\(551\) | − | 0.185711i | − | 0.00791156i | ||||||
\(552\) | 0.911701 | − | 1.47268i | 0.0388046 | − | 0.0626816i | ||||
\(553\) | 16.5458 | + | 16.5458i | 0.703601 | + | 0.703601i | ||||
\(554\) | −29.8170 | −1.26680 | ||||||||
\(555\) | −23.8071 | + | 6.78787i | −1.01056 | + | 0.288129i | ||||
\(556\) | 12.5052 | 0.530337 | ||||||||
\(557\) | −14.3600 | − | 14.3600i | −0.608454 | − | 0.608454i | 0.334088 | − | 0.942542i | \(-0.391572\pi\) |
−0.942542 | + | 0.334088i | \(0.891572\pi\) | |||||||
\(558\) | −1.98215 | + | 5.91677i | −0.0839113 | + | 0.250477i | ||||
\(559\) | 3.34430i | 0.141449i | ||||||||
\(560\) | 2.76238 | − | 3.03310i | 0.116732 | − | 0.128172i | ||||
\(561\) | 1.30406 | − | 0.306811i | 0.0550575 | − | 0.0129536i | ||||
\(562\) | 12.4596 | − | 12.4596i | 0.525577 | − | 0.525577i | ||||
\(563\) | 13.7798 | − | 13.7798i | 0.580751 | − | 0.580751i | −0.354359 | − | 0.935109i | \(-0.615301\pi\) |
0.935109 | + | 0.354359i | \(0.115301\pi\) | |||||||
\(564\) | 5.86074 | − | 1.37888i | 0.246782 | − | 0.0580613i | ||||
\(565\) | −5.09659 | + | 5.59607i | −0.214415 | + | 0.235428i | ||||
\(566\) | − | 25.1411i | − | 1.05676i | ||||||
\(567\) | −2.28598 | − | 16.3532i | −0.0960019 | − | 0.686770i | ||||
\(568\) | −0.744687 | − | 0.744687i | −0.0312464 | − | 0.0312464i | ||||
\(569\) | −29.2322 | −1.22548 | −0.612739 | − | 0.790285i | \(-0.709932\pi\) | ||||
−0.612739 | + | 0.790285i | \(0.709932\pi\) | |||||||
\(570\) | −0.876482 | + | 0.249902i | −0.0367118 | + | 0.0104672i | ||||
\(571\) | −0.323861 | −0.0135532 | −0.00677659 | − | 0.999977i | \(-0.502157\pi\) | ||||
−0.00677659 | + | 0.999977i | \(0.502157\pi\) | |||||||
\(572\) | 0.174883 | + | 0.174883i | 0.00731223 | + | 0.00731223i | ||||
\(573\) | −2.06370 | + | 3.33353i | −0.0862124 | + | 0.139260i | ||||
\(574\) | − | 13.9665i | − | 0.582950i | ||||||
\(575\) | 3.19056 | − | 3.84972i | 0.133055 | − | 0.160544i | ||||
\(576\) | 2.68530 | − | 1.33760i | 0.111887 | − | 0.0557334i | ||||
\(577\) | −16.8926 | + | 16.8926i | −0.703249 | + | 0.703249i | −0.965107 | − | 0.261857i | \(-0.915665\pi\) |
0.261857 | + | 0.965107i | \(0.415665\pi\) | |||||||
\(578\) | −5.50099 | + | 5.50099i | −0.228811 | + | 0.228811i | ||||
\(579\) | 0.577879 | + | 2.45620i | 0.0240158 | + | 0.102076i | ||||
\(580\) | 0.0823393 | + | 1.76271i | 0.00341895 | + | 0.0731925i | ||||
\(581\) | 23.0491i | 0.956239i | ||||||||
\(582\) | −6.12813 | − | 3.79377i | −0.254019 | − | 0.157257i | ||||
\(583\) | −0.590394 | − | 0.590394i | −0.0244516 | − | 0.0244516i | ||||
\(584\) | 9.86235 | 0.408107 | ||||||||
\(585\) | −1.77858 | + | 6.26587i | −0.0735353 | + | 0.259062i | ||||
\(586\) | −6.72848 | −0.277951 | ||||||||
\(587\) | −13.5739 | − | 13.5739i | −0.560257 | − | 0.560257i | 0.369124 | − | 0.929380i | \(-0.379658\pi\) |
−0.929380 | + | 0.369124i | \(0.879658\pi\) | |||||||
\(588\) | −5.35162 | − | 3.31305i | −0.220697 | − | 0.136628i | ||||
\(589\) | 0.489474i | 0.0201684i | ||||||||
\(590\) | 17.0724 | + | 15.5486i | 0.702858 | + | 0.640125i | ||||
\(591\) | 0.320643 | + | 1.36285i | 0.0131895 | + | 0.0560601i | ||||
\(592\) | 4.51979 | − | 4.51979i | 0.185762 | − | 0.185762i | ||||
\(593\) | 12.1444 | − | 12.1444i | 0.498710 | − | 0.498710i | −0.412326 | − | 0.911036i | \(-0.635284\pi\) |
0.911036 | + | 0.412326i | \(0.135284\pi\) | |||||||
\(594\) | −0.845770 | − | 1.01807i | −0.0347024 | − | 0.0417721i | ||||
\(595\) | −12.4437 | + | 0.581268i | −0.510142 | + | 0.0238296i | ||||
\(596\) | − | 10.1715i | − | 0.416640i | ||||||
\(597\) | 17.1872 | − | 27.7628i | 0.703426 | − | 1.13625i | ||||
\(598\) | −0.686574 | − | 0.686574i | −0.0280761 | − | 0.0280761i | ||||
\(599\) | −16.7260 | −0.683406 | −0.341703 | − | 0.939808i | \(-0.611004\pi\) | ||||
−0.341703 | + | 0.939808i | \(0.611004\pi\) | |||||||
\(600\) | 8.20848 | − | 2.76059i | 0.335110 | − | 0.112701i | ||||
\(601\) | 28.9544 | 1.18108 | 0.590538 | − | 0.807010i | \(-0.298915\pi\) | ||||
0.590538 | + | 0.807010i | \(0.298915\pi\) | |||||||
\(602\) | 4.46839 | + | 4.46839i | 0.182118 | + | 0.182118i | ||||
\(603\) | 4.08078 | + | 1.36708i | 0.166182 | + | 0.0556720i | ||||
\(604\) | − | 14.1211i | − | 0.574581i | ||||||
\(605\) | 24.4250 | − | 1.14094i | 0.993019 | − | 0.0463857i | ||||
\(606\) | −25.6847 | + | 6.04294i | −1.04337 | + | 0.245478i | ||||
\(607\) | −21.5740 | + | 21.5740i | −0.875663 | + | 0.875663i | −0.993082 | − | 0.117420i | \(-0.962538\pi\) |
0.117420 | + | 0.993082i | \(0.462538\pi\) | |||||||
\(608\) | 0.166400 | − | 0.166400i | 0.00674842 | − | 0.00674842i | ||||
\(609\) | −2.44114 | + | 0.574337i | −0.0989200 | + | 0.0232733i | ||||
\(610\) | −20.2843 | − | 18.4738i | −0.821286 | − | 0.747983i | ||||
\(611\) | − | 3.37515i | − | 0.136544i | ||||||
\(612\) | −8.63773 | − | 2.89369i | −0.349159 | − | 0.116971i | ||||
\(613\) | 0.222524 | + | 0.222524i | 0.00898766 | + | 0.00898766i | 0.711586 | − | 0.702599i | \(-0.247977\pi\) |
−0.702599 | + | 0.711586i | \(0.747977\pi\) | |||||||
\(614\) | 32.6003 | 1.31564 | ||||||||
\(615\) | 14.3323 | − | 25.7648i | 0.577936 | − | 1.03894i | ||||
\(616\) | 0.467330 | 0.0188292 | ||||||||
\(617\) | −13.9375 | − | 13.9375i | −0.561104 | − | 0.561104i | 0.368517 | − | 0.929621i | \(-0.379866\pi\) |
−0.929621 | + | 0.368517i | \(0.879866\pi\) | |||||||
\(618\) | −1.71795 | + | 2.77503i | −0.0691060 | + | 0.111628i | ||||
\(619\) | 28.4695i | 1.14429i | 0.820154 | + | 0.572143i | \(0.193888\pi\) | ||||
−0.820154 | + | 0.572143i | \(0.806112\pi\) | |||||||
\(620\) | −0.217020 | − | 4.64593i | −0.00871572 | − | 0.186585i | ||||
\(621\) | 3.32041 | + | 3.99686i | 0.133243 | + | 0.160388i | ||||
\(622\) | 17.5532 | − | 17.5532i | 0.703821 | − | 0.703821i | ||||
\(623\) | 12.2180 | − | 12.2180i | 0.489505 | − | 0.489505i | ||||
\(624\) | −0.385157 | − | 1.63706i | −0.0154186 | − | 0.0655347i | ||||
\(625\) | 24.5655 | − | 4.64071i | 0.982620 | − | 0.185629i | ||||
\(626\) | − | 3.27547i | − | 0.130914i | ||||||
\(627\) | −0.0882754 | − | 0.0546490i | −0.00352538 | − | 0.00218247i | ||||
\(628\) | −10.7816 | − | 10.7816i | −0.430232 | − | 0.430232i | ||||
\(629\) | −19.4093 | −0.773898 | ||||||||
\(630\) | 5.99555 | + | 10.7484i | 0.238869 | + | 0.428225i | ||||
\(631\) | 14.9930 | 0.596863 | 0.298431 | − | 0.954431i | \(-0.403537\pi\) | ||||
0.298431 | + | 0.954431i | \(0.403537\pi\) | |||||||
\(632\) | −9.01834 | − | 9.01834i | −0.358730 | − | 0.358730i | ||||
\(633\) | 6.77974 | + | 4.19716i | 0.269471 | + | 0.166822i | ||||
\(634\) | 31.8218i | 1.26381i | ||||||||
\(635\) | −24.8499 | + | 27.2852i | −0.986138 | + | 1.08278i | ||||
\(636\) | 1.30026 | + | 5.52660i | 0.0515588 | + | 0.219144i | ||||
\(637\) | −2.49495 | + | 2.49495i | −0.0988536 | + | 0.0988536i | ||||
\(638\) | −0.142139 | + | 0.142139i | −0.00562736 | + | 0.00562736i | ||||
\(639\) | 2.82801 | − | 1.40869i | 0.111874 | − | 0.0557269i | ||||
\(640\) | −1.50564 | + | 1.65319i | −0.0595156 | + | 0.0653482i | ||||
\(641\) | − | 5.92967i | − | 0.234208i | −0.993120 | − | 0.117104i | \(-0.962639\pi\) | ||
0.993120 | − | 0.117104i | \(-0.0373611\pi\) | |||||||
\(642\) | 1.14801 | − | 1.85440i | 0.0453083 | − | 0.0731872i | ||||
\(643\) | 0.231570 | + | 0.231570i | 0.00913224 | + | 0.00913224i | 0.711658 | − | 0.702526i | \(-0.247945\pi\) |
−0.702526 | + | 0.711658i | \(0.747945\pi\) | |||||||
\(644\) | −1.83469 | −0.0722969 | ||||||||
\(645\) | 3.65766 | + | 12.8285i | 0.144020 | + | 0.505123i | ||||
\(646\) | −0.714570 | −0.0281144 | ||||||||
\(647\) | 25.8635 | + | 25.8635i | 1.01680 | + | 1.01680i | 0.999856 | + | 0.0169438i | \(0.00539363\pi\) |
0.0169438 | + | 0.999856i | \(0.494606\pi\) | |||||||
\(648\) | 1.24597 | + | 8.91334i | 0.0489465 | + | 0.350149i | ||||
\(649\) | 2.63045i | 0.103254i | ||||||||
\(650\) | −0.452566 | − | 4.83367i | −0.0177511 | − | 0.189592i | ||||
\(651\) | 6.43405 | − | 1.51376i | 0.252170 | − | 0.0593291i | ||||
\(652\) | 1.35354 | − | 1.35354i | 0.0530087 | − | 0.0530087i | ||||
\(653\) | −30.6540 | + | 30.6540i | −1.19958 | + | 1.19958i | −0.225292 | + | 0.974291i | \(0.572333\pi\) |
−0.974291 | + | 0.225292i | \(0.927667\pi\) | |||||||
\(654\) | −19.1289 | + | 4.50054i | −0.748000 | + | 0.175985i | ||||
\(655\) | −0.818629 | − | 17.5251i | −0.0319865 | − | 0.684762i | ||||
\(656\) | 7.61245i | 0.297216i | ||||||||
\(657\) | −9.39847 | + | 28.0546i | −0.366669 | + | 1.09452i | ||||
\(658\) | −4.50960 | − | 4.50960i | −0.175803 | − | 0.175803i | ||||
\(659\) | 3.72086 | 0.144944 | 0.0724721 | − | 0.997370i | \(-0.476911\pi\) | ||||
0.0724721 | + | 0.997370i | \(0.476911\pi\) | |||||||
\(660\) | 0.862111 | + | 0.479572i | 0.0335576 | + | 0.0186673i | ||||
\(661\) | 35.1235 | 1.36615 | 0.683073 | − | 0.730350i | \(-0.260643\pi\) | ||||
0.683073 | + | 0.730350i | \(0.260643\pi\) | |||||||
\(662\) | 6.61496 | + | 6.61496i | 0.257098 | + | 0.257098i | ||||
\(663\) | −2.68801 | + | 4.34198i | −0.104393 | + | 0.168628i | ||||
\(664\) | − | 12.5630i | − | 0.487537i | ||||||
\(665\) | 0.713765 | + | 0.650059i | 0.0276786 | + | 0.0252082i | ||||
\(666\) | 8.54988 | + | 17.1643i | 0.331301 | + | 0.665103i | ||||
\(667\) | 0.558025 | − | 0.558025i | 0.0216068 | − | 0.0216068i | ||||
\(668\) | 5.90252 | − | 5.90252i | 0.228375 | − | 0.228375i | ||||
\(669\) | 4.30878 | + | 18.3139i | 0.166587 | + | 0.708056i | ||||
\(670\) | −3.20428 | + | 0.149678i | −0.123792 | + | 0.00578255i | ||||
\(671\) | − | 3.12533i | − | 0.120652i | ||||||
\(672\) | −2.70192 | − | 1.67269i | −0.104229 | − | 0.0645253i | ||||
\(673\) | −6.35962 | − | 6.35962i | −0.245145 | − | 0.245145i | 0.573830 | − | 0.818975i | \(-0.305457\pi\) |
−0.818975 | + | 0.573830i | \(0.805457\pi\) | |||||||
\(674\) | −27.6432 | −1.06477 | ||||||||
\(675\) | 0.0304487 | + | 25.9807i | 0.00117197 | + | 0.999999i | ||||
\(676\) | 12.0572 | 0.463740 | ||||||||
\(677\) | 1.56497 | + | 1.56497i | 0.0601469 | + | 0.0601469i | 0.736540 | − | 0.676394i | \(-0.236458\pi\) |
−0.676394 | + | 0.736540i | \(0.736458\pi\) | |||||||
\(678\) | 4.98504 | + | 3.08611i | 0.191449 | + | 0.118521i | ||||
\(679\) | 7.63450i | 0.292985i | ||||||||
\(680\) | 6.78246 | − | 0.316821i | 0.260095 | − | 0.0121495i | ||||
\(681\) | −0.287544 | − | 1.22217i | −0.0110187 | − | 0.0468335i | ||||
\(682\) | 0.374633 | − | 0.374633i | 0.0143455 | − | 0.0143455i | ||||
\(683\) | −2.23708 | + | 2.23708i | −0.0855996 | + | 0.0855996i | −0.748610 | − | 0.663011i | \(-0.769278\pi\) |
0.663011 | + | 0.748610i | \(0.269278\pi\) | |||||||
\(684\) | 0.314772 | + | 0.631919i | 0.0120356 | + | 0.0241620i | ||||
\(685\) | −1.04404 | − | 0.950853i | −0.0398906 | − | 0.0363302i | ||||
\(686\) | 19.5099i | 0.744893i | ||||||||
\(687\) | 14.8634 | − | 24.0091i | 0.567074 | − | 0.916004i | ||||
\(688\) | −2.43550 | − | 2.43550i | −0.0928526 | − | 0.0928526i | ||||
\(689\) | 3.18272 | 0.121252 | ||||||||
\(690\) | −3.38456 | − | 1.88275i | −0.128848 | − | 0.0716751i | ||||
\(691\) | 50.0983 | 1.90583 | 0.952914 | − | 0.303242i | \(-0.0980690\pi\) | ||||
0.952914 | + | 0.303242i | \(0.0980690\pi\) | |||||||
\(692\) | −12.9677 | − | 12.9677i | −0.492958 | − | 0.492958i | ||||
\(693\) | −0.445349 | + | 1.32937i | −0.0169174 | + | 0.0504988i | ||||
\(694\) | − | 28.5319i | − | 1.08306i | ||||||
\(695\) | −1.30475 | − | 27.9319i | −0.0494920 | − | 1.05952i | ||||
\(696\) | 1.33055 | − | 0.313043i | 0.0504343 | − | 0.0118659i | ||||
\(697\) | 16.3450 | − | 16.3450i | 0.619111 | − | 0.619111i | ||||
\(698\) | −2.36842 | + | 2.36842i | −0.0896460 | + | 0.0896460i | ||||
\(699\) | −14.5864 | + | 3.43181i | −0.551709 | + | 0.129803i | ||||
\(700\) | −7.06304 | − | 5.85368i | −0.266958 | − | 0.221248i | ||||
\(701\) | − | 17.7346i | − | 0.669827i | −0.942249 | − | 0.334913i | \(-0.891293\pi\) | ||
0.942249 | − | 0.334913i | \(-0.108707\pi\) | |||||||
\(702\) | 5.02384 | + | 0.464433i | 0.189613 | + | 0.0175289i | ||||
\(703\) | 1.06362 | + | 1.06362i | 0.0401153 | + | 0.0401153i | ||||
\(704\) | −0.254719 | −0.00960007 | ||||||||
\(705\) | −3.69140 | − | 12.9469i | −0.139026 | − | 0.487607i | ||||
\(706\) | −0.830811 | −0.0312680 | ||||||||
\(707\) | 19.7633 | + | 19.7633i | 0.743277 | + | 0.743277i | ||||
\(708\) | 9.41504 | − | 15.2083i | 0.353839 | − | 0.571562i | ||||
\(709\) | 38.9851i | 1.46411i | 0.681243 | + | 0.732057i | \(0.261440\pi\) | ||||
−0.681243 | + | 0.732057i | \(0.738560\pi\) | |||||||
\(710\) | −1.58566 | + | 1.74106i | −0.0595087 | + | 0.0653406i | ||||
\(711\) | 34.2479 | − | 17.0596i | 1.28440 | − | 0.639784i | ||||
\(712\) | −6.65945 | + | 6.65945i | −0.249573 | + | 0.249573i | ||||
\(713\) | −1.47077 | + | 1.47077i | −0.0550809 | + | 0.0550809i | ||||
\(714\) | 2.20990 | + | 9.39289i | 0.0827035 | + | 0.351520i | ||||
\(715\) | 0.372378 | − | 0.408872i | 0.0139261 | − | 0.0152909i | ||||
\(716\) | − | 17.1909i | − | 0.642455i | ||||||
\(717\) | −7.51401 | − | 4.65173i | −0.280616 | − | 0.173722i | ||||
\(718\) | −15.6414 | − | 15.6414i | −0.583731 | − | 0.583731i | ||||
\(719\) | −24.8193 | −0.925605 | −0.462803 | − | 0.886461i | \(-0.653156\pi\) | ||||
−0.462803 | + | 0.886461i | \(0.653156\pi\) | |||||||
\(720\) | −3.26789 | − | 5.85841i | −0.121787 | − | 0.218330i | ||||
\(721\) | 3.45716 | 0.128751 | ||||||||
\(722\) | −13.3959 | − | 13.3959i | −0.498543 | − | 0.498543i | ||||
\(723\) | 18.6998 | + | 11.5765i | 0.695451 | + | 0.430536i | ||||
\(724\) | − | 15.0456i | − | 0.559166i | ||||||
\(725\) | 3.92865 | − | 0.367831i | 0.145906 | − | 0.0136609i | ||||
\(726\) | −4.33769 | − | 18.4368i | −0.160987 | − | 0.684253i | ||||
\(727\) | 17.7250 | − | 17.7250i | 0.657385 | − | 0.657385i | −0.297376 | − | 0.954761i | \(-0.596111\pi\) |
0.954761 | + | 0.297376i | \(0.0961114\pi\) | |||||||
\(728\) | −1.25965 | + | 1.25965i | −0.0466857 | + | 0.0466857i | ||||
\(729\) | −26.5424 | − | 4.94977i | −0.983052 | − | 0.183325i | ||||
\(730\) | −1.02901 | − | 22.0289i | −0.0380853 | − | 0.815325i | ||||
\(731\) | 10.4587i | 0.386830i | ||||||||
\(732\) | −11.1863 | + | 18.0695i | −0.413459 | + | 0.667867i | ||||
\(733\) | 0.884740 | + | 0.884740i | 0.0326786 | + | 0.0326786i | 0.723257 | − | 0.690579i | \(-0.242644\pi\) |
−0.690579 | + | 0.723257i | \(0.742644\pi\) | |||||||
\(734\) | 14.3814 | 0.530827 | ||||||||
\(735\) | −6.84176 | + | 12.2992i | −0.252362 | + | 0.453663i | ||||
\(736\) | 1.00000 | 0.0368605 | ||||||||
\(737\) | −0.258383 | − | 0.258383i | −0.00951767 | − | 0.00951767i | ||||
\(738\) | −21.6545 | − | 7.25440i | −0.797114 | − | 0.267038i | ||||
\(739\) | − | 30.9488i | − | 1.13847i | −0.822175 | − | 0.569235i | \(-0.807239\pi\) | ||
0.822175 | − | 0.569235i | \(-0.192761\pi\) | |||||||
\(740\) | −10.5671 | − | 9.62397i | −0.388456 | − | 0.353784i | ||||
\(741\) | 0.385241 | − | 0.0906372i | 0.0141522 | − | 0.00332964i | ||||
\(742\) | 4.25249 | − | 4.25249i | 0.156114 | − | 0.156114i | ||||
\(743\) | −9.54480 | + | 9.54480i | −0.350165 | + | 0.350165i | −0.860171 | − | 0.510006i | \(-0.829643\pi\) |
0.510006 | + | 0.860171i | \(0.329643\pi\) | |||||||
\(744\) | −3.50689 | + | 0.825080i | −0.128569 | + | 0.0302489i | ||||
\(745\) | −22.7194 | + | 1.06126i | −0.832373 | + | 0.0388816i | ||||
\(746\) | − | 8.94756i | − | 0.327594i | ||||||
\(747\) | 35.7368 | + | 11.9721i | 1.30754 | + | 0.438035i | ||||
\(748\) | 0.546917 | + | 0.546917i | 0.0199973 | + | 0.0199973i | ||||
\(749\) | −2.31023 | −0.0844140 | ||||||||
\(750\) | −7.02260 | − | 18.0467i | −0.256429 | − | 0.658972i | ||||
\(751\) | 36.9921 | 1.34986 | 0.674930 | − | 0.737882i | \(-0.264174\pi\) | ||||
0.674930 | + | 0.737882i | \(0.264174\pi\) | |||||||
\(752\) | 2.45797 | + | 2.45797i | 0.0896328 | + | 0.0896328i | ||||
\(753\) | 19.9088 | − | 32.1589i | 0.725515 | − | 1.17194i | ||||
\(754\) | − | 0.766251i | − | 0.0279052i | ||||||
\(755\) | −31.5414 | + | 1.47336i | −1.14791 | + | 0.0536209i | ||||
\(756\) | 7.33299 | − | 6.09192i | 0.266698 | − | 0.221561i | ||||
\(757\) | −28.4234 | + | 28.4234i | −1.03306 | + | 1.03306i | −0.0336303 | + | 0.999434i | \(0.510707\pi\) |
−0.999434 | + | 0.0336303i | \(0.989293\pi\) | |||||||
\(758\) | 21.0304 | − | 21.0304i | 0.763860 | − | 0.763860i | ||||
\(759\) | −0.101041 | − | 0.429460i | −0.00366754 | − | 0.0155884i | ||||
\(760\) | −0.389039 | − | 0.354315i | −0.0141119 | − | 0.0128524i | ||||
\(761\) | 33.3114i | 1.20754i | 0.797160 | + | 0.603768i | \(0.206335\pi\) | ||||
−0.797160 | + | 0.603768i | \(0.793665\pi\) | |||||||
\(762\) | 24.3060 | + | 15.0472i | 0.880513 | + | 0.545103i | ||||
\(763\) | 14.7189 | + | 14.7189i | 0.532861 | + | 0.532861i | ||||
\(764\) | −2.26357 | −0.0818932 | ||||||||
\(765\) | −5.56221 | + | 19.5954i | −0.201102 | + | 0.708474i | ||||
\(766\) | 16.7300 | 0.604479 | ||||||||
\(767\) | −7.09018 | − | 7.09018i | −0.256011 | − | 0.256011i | ||||
\(768\) | 1.47268 | + | 0.911701i | 0.0531409 | + | 0.0328982i | ||||
\(769\) | 15.4887i | 0.558538i | 0.960213 | + | 0.279269i | \(0.0900920\pi\) | ||||
−0.960213 | + | 0.279269i | \(0.909908\pi\) | |||||||
\(770\) | −0.0487598 | − | 1.04384i | −0.00175718 | − | 0.0376175i | ||||
\(771\) | −1.19093 | − | 5.06189i | −0.0428903 | − | 0.182300i | ||||
\(772\) | −1.03012 | + | 1.03012i | −0.0370748 | + | 0.0370748i | ||||
\(773\) | 22.3134 | − | 22.3134i | 0.802556 | − | 0.802556i | −0.180938 | − | 0.983494i | \(-0.557913\pi\) |
0.983494 | + | 0.180938i | \(0.0579134\pi\) | |||||||
\(774\) | 9.24902 | − | 4.60713i | 0.332449 | − | 0.165600i | ||||
\(775\) | −10.3546 | + | 0.969484i | −0.371950 | + | 0.0348249i | ||||
\(776\) | − | 4.16120i | − | 0.149378i | ||||||
\(777\) | 10.6917 | − | 17.2705i | 0.383564 | − | 0.619577i | ||||
\(778\) | −23.9708 | − | 23.9708i | −0.859394 | − | 0.859394i | ||||
\(779\) | −1.79141 | −0.0641838 | ||||||||
\(780\) | −3.61640 | + | 1.03110i | −0.129488 | + | 0.0369195i | ||||
\(781\) | −0.268256 | −0.00959896 | ||||||||
\(782\) | −2.14714 | − | 2.14714i | −0.0767816 | − | 0.0767816i | ||||
\(783\) | −0.377476 | + | 4.08322i | −0.0134899 | + | 0.145922i | ||||
\(784\) | − | 3.63392i | − | 0.129783i | ||||||
\(785\) | −22.9572 | + | 25.2070i | −0.819377 | + | 0.899677i | ||||
\(786\) | −13.2285 | + | 3.11232i | −0.471845 | + | 0.111013i | ||||
\(787\) | −17.3064 | + | 17.3064i | −0.616906 | + | 0.616906i | −0.944737 | − | 0.327830i | \(-0.893683\pi\) |
0.327830 | + | 0.944737i | \(0.393683\pi\) | |||||||
\(788\) | −0.571573 | + | 0.571573i | −0.0203614 | + | 0.0203614i | ||||
\(789\) | 46.9991 | − | 11.0577i | 1.67321 | − | 0.393663i | ||||
\(790\) | −19.2027 | + | 21.0846i | −0.683202 | + | 0.750157i | ||||
\(791\) | − | 6.21043i | − | 0.220817i | ||||||
\(792\) | 0.242738 | − | 0.724578i | 0.00862532 | − | 0.0257468i | ||||
\(793\) | 8.42409 | + | 8.42409i | 0.299148 | + | 0.299148i | ||||
\(794\) | 1.43747 | 0.0510138 | ||||||||
\(795\) | 12.2087 | − | 3.48094i | 0.432999 | − | 0.123456i | ||||
\(796\) | 18.8518 | 0.668184 | ||||||||
\(797\) | −32.5163 | − | 32.5163i | −1.15179 | − | 1.15179i | −0.986194 | − | 0.165592i | \(-0.947047\pi\) |
−0.165592 | − | 0.986194i | \(-0.552953\pi\) | |||||||
\(798\) | 0.393626 | − | 0.635831i | 0.0139342 | − | 0.0225082i | ||||
\(799\) | − | 10.5552i | − | 0.373416i | ||||||
\(800\) | 3.84972 | + | 3.19056i | 0.136108 | + | 0.112803i | ||||
\(801\) | −12.5974 | − | 25.2898i | −0.445107 | − | 0.893572i | ||||
\(802\) | 15.4389 | − | 15.4389i | 0.545167 | − | 0.545167i | ||||
\(803\) | 1.77634 | − | 1.77634i | 0.0626857 | − | 0.0626857i | ||||
\(804\) | 0.569054 | + | 2.41869i | 0.0200690 | + | 0.0853006i | ||||
\(805\) | 0.191426 | + | 4.09802i | 0.00674688 | + | 0.144436i | ||||
\(806\) | 2.01959i | 0.0711370i | ||||||||
\(807\) | 36.2876 | + | 22.4647i | 1.27738 | + | 0.790794i | ||||
\(808\) | −10.7720 | − | 10.7720i | −0.378959 | − | 0.378959i | ||||
\(809\) | −23.9795 | −0.843074 | −0.421537 | − | 0.906811i | \(-0.638509\pi\) | ||||
−0.421537 | + | 0.906811i | \(0.638509\pi\) | |||||||
\(810\) | 19.7791 | − | 3.71304i | 0.694967 | − | 0.130463i | ||||
\(811\) | 45.9811 | 1.61461 | 0.807307 | − | 0.590131i | \(-0.200924\pi\) | ||||
0.807307 | + | 0.590131i | \(0.200924\pi\) | |||||||
\(812\) | −1.02380 | − | 1.02380i | −0.0359284 | − | 0.0359284i | ||||
\(813\) | −40.6327 | − | 25.1546i | −1.42505 | − | 0.882212i | ||||
\(814\) | − | 1.62815i | − | 0.0570666i | ||||||
\(815\) | −3.16453 | − | 2.88208i | −0.110849 | − | 0.100955i | ||||
\(816\) | −1.20451 | − | 5.11961i | −0.0421663 | − | 0.179222i | ||||
\(817\) | 0.573136 | − | 0.573136i | 0.0200515 | − | 0.0200515i | ||||
\(818\) | 22.9409 | − | 22.9409i | 0.802109 | − | 0.802109i | ||||
\(819\) | −2.38282 | − | 4.78362i | −0.0832625 | − | 0.167153i | ||||
\(820\) | 17.0034 | − | 0.794260i | 0.593785 | − | 0.0277368i | ||||
\(821\) | − | 9.96541i | − | 0.347795i | −0.984764 | − | 0.173898i | \(-0.944364\pi\) | ||
0.984764 | − | 0.173898i | \(-0.0556362\pi\) | |||||||
\(822\) | −0.575765 | + | 0.930041i | −0.0200821 | + | 0.0324389i | ||||
\(823\) | −21.9898 | − | 21.9898i | −0.766516 | − | 0.766516i | 0.210975 | − | 0.977491i | \(-0.432336\pi\) |
−0.977491 | + | 0.210975i | \(0.932336\pi\) | |||||||
\(824\) | −1.88433 | −0.0656438 | ||||||||
\(825\) | 0.981237 | − | 1.97568i | 0.0341623 | − | 0.0687842i | ||||
\(826\) | −18.9466 | −0.659238 | ||||||||
\(827\) | 17.8372 | + | 17.8372i | 0.620260 | + | 0.620260i | 0.945598 | − | 0.325338i | \(-0.105478\pi\) |
−0.325338 | + | 0.945598i | \(0.605478\pi\) | |||||||
\(828\) | −0.952965 | + | 2.84462i | −0.0331178 | + | 0.0988574i | ||||
\(829\) | 32.1993i | 1.11833i | 0.829058 | + | 0.559163i | \(0.188878\pi\) | ||||
−0.829058 | + | 0.559163i | \(0.811122\pi\) | |||||||
\(830\) | −28.0610 | + | 1.31078i | −0.974013 | + | 0.0454979i | ||||
\(831\) | 50.2720 | − | 11.8277i | 1.74392 | − | 0.410298i | ||||
\(832\) | 0.686574 | − | 0.686574i | 0.0238027 | − | 0.0238027i | ||||
\(833\) | −7.80253 | + | 7.80253i | −0.270342 | + | 0.270342i | ||||
\(834\) | −21.0839 | + | 4.96049i | −0.730075 | + | 0.171768i | ||||
\(835\) | −13.7999 | − | 12.5682i | −0.477566 | − | 0.434941i | ||||
\(836\) | − | 0.0599418i | − | 0.00207313i | ||||||
\(837\) | 0.994905 | − | 10.7620i | 0.0343890 | − | 0.371991i | ||||
\(838\) | 8.25742 | + | 8.25742i | 0.285248 | + | 0.285248i | ||||
\(839\) | 27.6357 | 0.954092 | 0.477046 | − | 0.878878i | \(-0.341708\pi\) | ||||
0.477046 | + | 0.878878i | \(0.341708\pi\) | |||||||
\(840\) | −3.45426 | + | 6.20962i | −0.119183 | + | 0.214252i | ||||
\(841\) | −28.3772 | −0.978525 | ||||||||
\(842\) | −21.9809 | − | 21.9809i | −0.757512 | − | 0.757512i | ||||
\(843\) | −16.0647 | + | 25.9495i | −0.553297 | + | 0.893749i | ||||
\(844\) | 4.60366i | 0.158465i | ||||||||
\(845\) | −1.25802 | − | 26.9314i | −0.0432770 | − | 0.926469i | ||||
\(846\) | −9.33433 | + | 4.64962i | −0.320921 | + | 0.159857i | ||||
\(847\) | −14.1864 | + | 14.1864i | −0.487449 | + | 0.487449i | ||||
\(848\) | −2.31783 | + | 2.31783i | −0.0795945 | + | 0.0795945i | ||||
\(849\) | 9.97285 | + | 42.3883i | 0.342267 | + | 1.45476i | ||||
\(850\) | −1.41532 | − | 15.1165i | −0.0485452 | − | 0.518490i | ||||
\(851\) | 6.39195i | 0.219113i | ||||||||
\(852\) | 1.55095 | + | 0.960155i | 0.0531348 | + | 0.0328944i | ||||
\(853\) | 11.1857 | + | 11.1857i | 0.382990 | + | 0.382990i | 0.872178 | − | 0.489188i | \(-0.162707\pi\) |
−0.489188 | + | 0.872178i | \(0.662707\pi\) | |||||||
\(854\) | 22.5112 | 0.770316 | ||||||||
\(855\) | 1.37863 | − | 0.769017i | 0.0471482 | − | 0.0262998i | ||||
\(856\) | 1.25920 | 0.0430384 | ||||||||
\(857\) | 10.4211 | + | 10.4211i | 0.355979 | + | 0.355979i | 0.862328 | − | 0.506349i | \(-0.169005\pi\) |
−0.506349 | + | 0.862328i | \(0.669005\pi\) | |||||||
\(858\) | −0.364228 | − | 0.225484i | −0.0124345 | − | 0.00769790i | ||||
\(859\) | 29.1495i | 0.994567i | 0.867588 | + | 0.497284i | \(0.165669\pi\) | ||||
−0.867588 | + | 0.497284i | \(0.834331\pi\) | |||||||
\(860\) | −5.18590 | + | 5.69413i | −0.176838 | + | 0.194168i | ||||
\(861\) | 5.54016 | + | 23.5477i | 0.188808 | + | 0.802504i | ||||
\(862\) | 12.2840 | − | 12.2840i | 0.418395 | − | 0.418395i | ||||
\(863\) | 7.86977 | − | 7.86977i | 0.267890 | − | 0.267890i | −0.560359 | − | 0.828250i | \(-0.689337\pi\) |
0.828250 | + | 0.560359i | \(0.189337\pi\) | |||||||
\(864\) | −3.99686 | + | 3.32041i | −0.135976 | + | 0.112963i | ||||
\(865\) | −27.6121 | + | 30.3181i | −0.938838 | + | 1.03085i | ||||
\(866\) | 4.85917i | 0.165121i | ||||||||
\(867\) | 7.09265 | − | 11.4569i | 0.240879 | − | 0.389096i | ||||
\(868\) | 2.69841 | + | 2.69841i | 0.0915900 | + | 0.0915900i | ||||
\(869\) | −3.24865 | −0.110203 | ||||||||
\(870\) | −0.838048 | − | 2.93929i | −0.0284125 | − | 0.0996513i | ||||
\(871\) | 1.39290 | 0.0471967 | ||||||||
\(872\) | −8.02258 | − | 8.02258i | −0.271679 | − | 0.271679i | ||||
\(873\) | 11.8370 | + | 3.96547i | 0.400623 | + | 0.134211i | ||||
\(874\) | 0.235326i | 0.00796001i | ||||||||
\(875\) | −12.3380 | + | 16.3870i | −0.417101 | + | 0.553981i | ||||
\(876\) | −16.6281 | + | 3.91215i | −0.561811 | + | 0.132179i | ||||
\(877\) | −12.4703 | + | 12.4703i | −0.421092 | + | 0.421092i | −0.885580 | − | 0.464488i | \(-0.846238\pi\) |
0.464488 | + | 0.885580i | \(0.346238\pi\) | |||||||
\(878\) | −8.69629 | + | 8.69629i | −0.293486 | + | 0.293486i | ||||
\(879\) | 11.3443 | − | 2.66902i | 0.382634 | − | 0.0900238i | ||||
\(880\) | 0.0265766 | + | 0.568948i | 0.000895897 | + | 0.0191792i | ||||
\(881\) | − | 24.7836i | − | 0.834981i | −0.908681 | − | 0.417490i | \(-0.862910\pi\) | ||
0.908681 | − | 0.417490i | \(-0.137090\pi\) | |||||||
\(882\) | 10.3371 | + | 3.46299i | 0.348069 | + | 0.116605i | ||||
\(883\) | −18.5993 | − | 18.5993i | −0.625916 | − | 0.625916i | 0.321122 | − | 0.947038i | \(-0.395940\pi\) |
−0.947038 | + | 0.321122i | \(0.895940\pi\) | |||||||
\(884\) | −2.94834 | −0.0991634 | ||||||||
\(885\) | −34.9520 | − | 19.4430i | −1.17490 | − | 0.653568i | ||||
\(886\) | 15.8820 | 0.533567 | ||||||||
\(887\) | 10.0096 | + | 10.0096i | 0.336088 | + | 0.336088i | 0.854893 | − | 0.518805i | \(-0.173623\pi\) |
−0.518805 | + | 0.854893i | \(0.673623\pi\) | |||||||
\(888\) | −5.82755 | + | 9.41333i | −0.195560 | + | 0.315891i | ||||
\(889\) | − | 30.2807i | − | 1.01558i | ||||||
\(890\) | 15.5696 | + | 14.1799i | 0.521894 | + | 0.475313i | ||||
\(891\) | 1.82983 | + | 1.38099i | 0.0613015 | + | 0.0462650i | ||||
\(892\) | −7.68075 | + | 7.68075i | −0.257171 | + | 0.257171i | ||||
\(893\) | −0.578422 | + | 0.578422i | −0.0193562 | + | 0.0193562i | ||||
\(894\) | 4.03478 | + | 17.1493i | 0.134943 | + | 0.573558i | ||||
\(895\) | −38.3982 | + | 1.79365i | −1.28351 | + | 0.0599551i | ||||
\(896\) | − | 1.83469i | − | 0.0612926i | ||||||
\(897\) | 1.42992 | + | 0.885227i | 0.0477437 | + | 0.0295569i | ||||
\(898\) | −2.95951 | − | 2.95951i | −0.0987601 | − | 0.0987601i | ||||
\(899\) | −1.64146 | −0.0547456 | ||||||||
\(900\) | −12.7446 | + | 7.91051i | −0.424819 | + | 0.263684i | ||||
\(901\) | 9.95340 | 0.331596 | ||||||||
\(902\) | 1.37110 | + | 1.37110i | 0.0456528 | + | 0.0456528i | ||||
\(903\) | −9.30627 | − | 5.76127i | −0.309693 | − | 0.191723i | ||||
\(904\) | 3.38500i | 0.112584i | ||||||||
\(905\) | −33.6064 | + | 1.56982i | −1.11711 | + | 0.0521824i | ||||
\(906\) | 5.60151 | + | 23.8084i | 0.186098 | + | 0.790983i | ||||
\(907\) | −30.3282 | + | 30.3282i | −1.00703 | + | 1.00703i | −0.00705622 | + | 0.999975i | \(0.502246\pi\) |
−0.999975 | + | 0.00705622i | \(0.997754\pi\) | |||||||
\(908\) | 0.512571 | − | 0.512571i | 0.0170103 | − | 0.0170103i | ||||
\(909\) | 40.9077 | − | 20.3770i | 1.35682 | − | 0.675862i | ||||
\(910\) | 2.94502 | + | 2.68217i | 0.0976265 | + | 0.0889129i | ||||
\(911\) | 21.9257i | 0.726430i | 0.931705 | + | 0.363215i | \(0.118321\pi\) | ||||
−0.931705 | + | 0.363215i | \(0.881679\pi\) | |||||||
\(912\) | −0.214547 | + | 0.346560i | −0.00710435 | + | 0.0114758i | ||||
\(913\) | −2.26276 | − | 2.26276i | −0.0748863 | − | 0.0748863i | ||||
\(914\) | −10.3640 | −0.342812 | ||||||||
\(915\) | 41.5277 | + | 23.1009i | 1.37286 | + | 0.763691i | ||||
\(916\) | 16.3029 | 0.538664 | ||||||||
\(917\) | 10.1788 | + | 10.1788i | 0.336133 | + | 0.336133i | ||||
\(918\) | 15.7112 | + | 1.45243i | 0.518547 | + | 0.0479375i | ||||
\(919\) | − | 24.2711i | − | 0.800630i | −0.916378 | − | 0.400315i | \(-0.868901\pi\) | ||
0.916378 | − | 0.400315i | \(-0.131099\pi\) | |||||||
\(920\) | −0.104337 | − | 2.23363i | −0.00343989 | − | 0.0736407i | ||||
\(921\) | −54.9646 | + | 12.9317i | −1.81115 | + | 0.426115i | ||||
\(922\) | −8.29508 | + | 8.29508i | −0.273184 | + | 0.273184i | ||||
\(923\) | 0.723063 | − | 0.723063i | 0.0237999 | − | 0.0237999i | ||||
\(924\) | −0.787925 | + | 0.185378i | −0.0259208 | + | 0.00609849i | ||||
\(925\) | −20.3939 | + | 24.6072i | −0.670546 | + | 0.809081i | ||||
\(926\) | 27.3612i | 0.899144i | ||||||||
\(927\) | 1.79570 | − | 5.36021i | 0.0589786 | − | 0.176052i | ||||
\(928\) | 0.558025 | + | 0.558025i | 0.0183181 | + | 0.0183181i | ||||
\(929\) | −6.03998 | −0.198165 | −0.0990826 | − | 0.995079i | \(-0.531591\pi\) | ||||
−0.0990826 | + | 0.995079i | \(0.531591\pi\) | |||||||
\(930\) | 2.20882 | + | 7.74702i | 0.0724302 | + | 0.254035i | ||||
\(931\) | 0.855154 | 0.0280265 | ||||||||
\(932\) | −6.11748 | − | 6.11748i | −0.200385 | − | 0.200385i | ||||
\(933\) | −22.6321 | + | 36.5580i | −0.740942 | + | 1.19685i | ||||
\(934\) | − | 26.6715i | − | 0.872719i | ||||||
\(935\) | 1.16455 | − | 1.27867i | 0.0380848 | − | 0.0418171i | ||||
\(936\) | 1.29876 | + | 2.60732i | 0.0424513 | + | 0.0852230i | ||||
\(937\) | 24.7487 | − | 24.7487i | 0.808506 | − | 0.808506i | −0.175902 | − | 0.984408i | \(-0.556284\pi\) |
0.984408 | + | 0.175902i | \(0.0562842\pi\) | |||||||
\(938\) | 1.86108 | − | 1.86108i | 0.0607665 | − | 0.0607665i | ||||
\(939\) | 1.29930 | + | 5.52249i | 0.0424010 | + | 0.180220i | ||||
\(940\) | 5.23373 | − | 5.74665i | 0.170706 | − | 0.187435i | ||||
\(941\) | − | 19.5391i | − | 0.636957i | −0.947930 | − | 0.318479i | \(-0.896828\pi\) | ||
0.947930 | − | 0.318479i | \(-0.103172\pi\) | |||||||
\(942\) | 22.4547 | + | 13.9011i | 0.731614 | + | 0.452924i | ||||
\(943\) | −5.38282 | − | 5.38282i | −0.175289 | − | 0.175289i | ||||
\(944\) | 10.3269 | 0.336112 | ||||||||
\(945\) | −14.3722 | − | 15.7436i | −0.467528 | − | 0.512139i | ||||
\(946\) | −0.877332 | −0.0285245 | ||||||||
\(947\) | 14.5559 | + | 14.5559i | 0.473003 | + | 0.473003i | 0.902885 | − | 0.429882i | \(-0.141445\pi\) |
−0.429882 | + | 0.902885i | \(0.641445\pi\) | |||||||
\(948\) | 18.7824 | + | 11.6277i | 0.610025 | + | 0.377650i | ||||
\(949\) | 9.57597i | 0.310849i | ||||||||
\(950\) | −0.750819 | + | 0.905938i | −0.0243598 | + | 0.0293925i | ||||
\(951\) | −12.6229 | − | 53.6521i | −0.409327 | − | 1.73979i | ||||
\(952\) | −3.93933 | + | 3.93933i | −0.127675 | + | 0.127675i | ||||
\(953\) | 8.38520 | − | 8.38520i | 0.271623 | − | 0.271623i | −0.558130 | − | 0.829753i | \(-0.688481\pi\) |
0.829753 | + | 0.558130i | \(0.188481\pi\) | |||||||
\(954\) | −4.38453 | − | 8.80215i | −0.141954 | − | 0.284980i | ||||
\(955\) | 0.236174 | + | 5.05599i | 0.00764242 | + | 0.163608i | ||||
\(956\) | − | 5.10225i | − | 0.165019i | ||||||
\(957\) | 0.183266 | − | 0.296033i | 0.00592415 | − | 0.00956937i | ||||
\(958\) | 22.6247 | + | 22.6247i | 0.730970 | + | 0.730970i | ||||
\(959\) | 1.15866 | 0.0374150 | ||||||||
\(960\) | 1.88275 | − | 3.38456i | 0.0607655 | − | 0.109236i | ||||
\(961\) | −26.6737 | −0.860440 | ||||||||
\(962\) | 4.38855 | + | 4.38855i | 0.141492 | + | 0.141492i | ||||
\(963\) | −1.19997 | + | 3.58193i | −0.0386684 | + | 0.115426i | ||||
\(964\) | 12.6977i | 0.408966i | ||||||||
\(965\) | 2.40838 | + | 2.19343i | 0.0775286 | + | 0.0706089i | ||||
\(966\) | 3.09331 | − | 0.727776i | 0.0995257 | − | 0.0234158i | ||||
\(967\) | 22.3141 | − | 22.3141i | 0.717574 | − | 0.717574i | −0.250534 | − | 0.968108i | \(-0.580606\pi\) |
0.968108 | + | 0.250534i | \(0.0806060\pi\) | |||||||
\(968\) | 7.73230 | − | 7.73230i | 0.248525 | − | 0.248525i | ||||
\(969\) | 1.20478 | − | 0.283452i | 0.0387030 | − | 0.00910580i | ||||
\(970\) | −9.29459 | + | 0.434167i | −0.298431 | + | 0.0139403i | ||||
\(971\) | 36.3642i | 1.16698i | 0.812120 | + | 0.583491i | \(0.198314\pi\) | ||||
−0.812120 | + | 0.583491i | \(0.801686\pi\) | |||||||
\(972\) | −5.63643 | − | 14.5338i | −0.180789 | − | 0.466171i | ||||
\(973\) | 16.2232 | + | 16.2232i | 0.520092 | + | 0.520092i | ||||
\(974\) | −7.88284 | −0.252583 | ||||||||
\(975\) | 2.68043 | + | 7.97012i | 0.0858425 | + | 0.255248i | ||||
\(976\) | −12.2697 | −0.392745 | ||||||||
\(977\) | −1.24875 | − | 1.24875i | −0.0399511 | − | 0.0399511i | 0.686849 | − | 0.726800i | \(-0.258993\pi\) |
−0.726800 | + | 0.686849i | \(0.758993\pi\) | |||||||
\(978\) | −1.74517 | + | 2.81900i | −0.0558044 | + | 0.0901418i | ||||
\(979\) | 2.39891i | 0.0766696i | ||||||||
\(980\) | −8.11684 | + | 0.379152i | −0.259283 | + | 0.0121116i | ||||
\(981\) | 30.4664 | − | 15.1759i | 0.972718 | − | 0.484531i | ||||
\(982\) | 7.23959 | − | 7.23959i | 0.231025 | − | 0.231025i | ||||
\(983\) | 9.65401 | − | 9.65401i | 0.307915 | − | 0.307915i | −0.536185 | − | 0.844100i | \(-0.680135\pi\) |
0.844100 | + | 0.536185i | \(0.180135\pi\) | |||||||
\(984\) | −3.01967 | − | 12.8347i | −0.0962637 | − | 0.409156i | ||||
\(985\) | 1.33632 | + | 1.21705i | 0.0425787 | + | 0.0387783i | ||||
\(986\) | − | 2.39632i | − | 0.0763143i | ||||||
\(987\) | 9.39211 | + | 5.81441i | 0.298954 | + | 0.185075i | ||||
\(988\) | 0.161568 | + | 0.161568i | 0.00514018 | + | 0.00514018i | ||||
\(989\) | 3.44432 | 0.109523 | ||||||||
\(990\) | −1.64377 | − | 0.466587i | −0.0522423 | − | 0.0148291i | ||||
\(991\) | −15.9477 | −0.506594 | −0.253297 | − | 0.967389i | \(-0.581515\pi\) | ||||
−0.253297 | + | 0.967389i | \(0.581515\pi\) | |||||||
\(992\) | −1.47077 | − | 1.47077i | −0.0466971 | − | 0.0466971i | ||||
\(993\) | −13.7769 | − | 8.52894i | −0.437197 | − | 0.270658i | ||||
\(994\) | − | 1.93220i | − | 0.0612855i | ||||||
\(995\) | −1.96694 | − | 42.1080i | −0.0623562 | − | 1.33491i | ||||
\(996\) | 4.98342 | + | 21.1813i | 0.157906 | + | 0.671157i | ||||
\(997\) | −23.7511 | + | 23.7511i | −0.752204 | + | 0.752204i | −0.974890 | − | 0.222686i | \(-0.928517\pi\) |
0.222686 | + | 0.974890i | \(0.428517\pi\) | |||||||
\(998\) | 16.8671 | − | 16.8671i | 0.533919 | − | 0.533919i | ||||
\(999\) | −21.2239 | − | 25.5477i | −0.671494 | − | 0.808294i |
(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 | 690.2.i.e.323.8 | yes | 32 | |
3.2 | odd | 2 | inner | 690.2.i.e.323.13 | yes | 32 | |
5.2 | odd | 4 | inner | 690.2.i.e.47.13 | yes | 32 | |
15.2 | even | 4 | inner | 690.2.i.e.47.8 | ✓ | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
690.2.i.e.47.8 | ✓ | 32 | 15.2 | even | 4 | inner | |
690.2.i.e.47.13 | yes | 32 | 5.2 | odd | 4 | inner | |
690.2.i.e.323.8 | yes | 32 | 1.1 | even | 1 | trivial | |
690.2.i.e.323.13 | yes | 32 | 3.2 | odd | 2 | inner |