Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [156,2,Mod(155,156)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(156, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 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("156.155");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 156 = 2^{2} \cdot 3 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 156.h (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: | \(1.24566627153\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 43x^{12} + 517x^{8} + 1804x^{4} + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{10} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 155.3 | ||
Root | \(-0.217136 + 0.217136i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 156.155 |
Dual form | 156.2.h.b.155.1 |
$q$-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 \(\left(\mathbb{Z}/156\mathbb{Z}\right)^\times\).
\(n\) | \(53\) | \(79\) | \(145\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.17915 | + | 0.780776i | −0.833783 | + | 0.552092i | ||||
\(3\) | −1.26870 | + | 1.17915i | −0.732487 | + | 0.680781i | ||||
\(4\) | 0.780776 | − | 1.84130i | 0.390388 | − | 0.920650i | ||||
\(5\) | −0.662153 | −0.296124 | −0.148062 | − | 0.988978i | \(-0.547304\pi\) | ||||
−0.148062 | + | 0.988978i | \(0.547304\pi\) | |||||||
\(6\) | 0.575339 | − | 2.38096i | 0.234881 | − | 0.972024i | ||||
\(7\) | −3.83206 | −1.44838 | −0.724191 | − | 0.689600i | \(-0.757786\pi\) | ||||
−0.724191 | + | 0.689600i | \(0.757786\pi\) | |||||||
\(8\) | 0.516994 | + | 2.78078i | 0.182785 | + | 0.983153i | ||||
\(9\) | 0.219224 | − | 2.99198i | 0.0730745 | − | 0.997326i | ||||
\(10\) | 0.780776 | − | 0.516994i | 0.246903 | − | 0.163488i | ||||
\(11\) | − | 2.00000i | − | 0.603023i | −0.953463 | − | 0.301511i | \(-0.902509\pi\) | ||
0.953463 | − | 0.301511i | \(-0.0974911\pi\) | |||||||
\(12\) | 1.18059 | + | 3.25672i | 0.340807 | + | 0.940133i | ||||
\(13\) | −2.56155 | − | 2.53741i | −0.710447 | − | 0.703751i | ||||
\(14\) | 4.51856 | − | 2.99198i | 1.20764 | − | 0.799640i | ||||
\(15\) | 0.840077 | − | 0.780776i | 0.216907 | − | 0.201596i | ||||
\(16\) | −2.78078 | − | 2.87529i | −0.695194 | − | 0.718822i | ||||
\(17\) | − | 1.68015i | − | 0.407497i | −0.979023 | − | 0.203749i | \(-0.934687\pi\) | ||
0.979023 | − | 0.203749i | \(-0.0653125\pi\) | |||||||
\(18\) | 2.07757 | + | 3.69915i | 0.489688 | + | 0.871898i | ||||
\(19\) | 2.15190 | 0.493680 | 0.246840 | − | 0.969056i | \(-0.420608\pi\) | ||||
0.246840 | + | 0.969056i | \(0.420608\pi\) | |||||||
\(20\) | −0.516994 | + | 1.21922i | −0.115603 | + | 0.272627i | ||||
\(21\) | 4.86175 | − | 4.51856i | 1.06092 | − | 0.986030i | ||||
\(22\) | 1.56155 | + | 2.35829i | 0.332924 | + | 0.502790i | ||||
\(23\) | −6.49971 | −1.35528 | −0.677641 | − | 0.735392i | \(-0.736998\pi\) | ||||
−0.677641 | + | 0.735392i | \(0.736998\pi\) | |||||||
\(24\) | −3.93486 | − | 2.91837i | −0.803199 | − | 0.595710i | ||||
\(25\) | −4.56155 | −0.912311 | ||||||||
\(26\) | 5.00160 | + | 0.991979i | 0.980894 | + | 0.194543i | ||||
\(27\) | 3.24985 | + | 4.05444i | 0.625435 | + | 0.780276i | ||||
\(28\) | −2.99198 | + | 7.05597i | −0.565431 | + | 1.33345i | ||||
\(29\) | 7.66411i | 1.42319i | 0.702590 | + | 0.711595i | \(0.252027\pi\) | ||||
−0.702590 | + | 0.711595i | \(0.747973\pi\) | |||||||
\(30\) | −0.380963 | + | 1.57656i | −0.0695540 | + | 0.287840i | ||||
\(31\) | −2.15190 | −0.386493 | −0.193247 | − | 0.981150i | \(-0.561902\pi\) | ||||
−0.193247 | + | 0.981150i | \(0.561902\pi\) | |||||||
\(32\) | 5.52390 | + | 1.21922i | 0.976497 | + | 0.215530i | ||||
\(33\) | 2.35829 | + | 2.53741i | 0.410526 | + | 0.441706i | ||||
\(34\) | 1.31182 | + | 1.98115i | 0.224976 | + | 0.339764i | ||||
\(35\) | 2.53741 | 0.428900 | ||||||||
\(36\) | −5.33797 | − | 2.73972i | −0.889662 | − | 0.456621i | ||||
\(37\) | 9.03712i | 1.48569i | 0.669462 | + | 0.742847i | \(0.266525\pi\) | ||||
−0.669462 | + | 0.742847i | \(0.733475\pi\) | |||||||
\(38\) | −2.53741 | + | 1.68015i | −0.411622 | + | 0.272557i | ||||
\(39\) | 6.24183 | + | 0.198776i | 0.999493 | + | 0.0318296i | ||||
\(40\) | −0.342329 | − | 1.84130i | −0.0541270 | − | 0.291135i | ||||
\(41\) | −6.41273 | −1.00150 | −0.500750 | − | 0.865592i | \(-0.666942\pi\) | ||||
−0.500750 | + | 0.865592i | \(0.666942\pi\) | |||||||
\(42\) | −2.20473 | + | 9.12399i | −0.340198 | + | 1.40786i | ||||
\(43\) | − | 3.68260i | − | 0.561591i | −0.959768 | − | 0.280796i | \(-0.909402\pi\) | ||
0.959768 | − | 0.280796i | \(-0.0905983\pi\) | |||||||
\(44\) | −3.68260 | − | 1.56155i | −0.555173 | − | 0.235413i | ||||
\(45\) | −0.145160 | + | 1.98115i | −0.0216391 | + | 0.295332i | ||||
\(46\) | 7.66411 | − | 5.07482i | 1.13001 | − | 0.748241i | ||||
\(47\) | − | 6.68466i | − | 0.975058i | −0.873107 | − | 0.487529i | \(-0.837898\pi\) | ||
0.873107 | − | 0.487529i | \(-0.162102\pi\) | |||||||
\(48\) | 6.91837 | + | 0.368947i | 0.998581 | + | 0.0532529i | ||||
\(49\) | 7.68466 | 1.09781 | ||||||||
\(50\) | 5.37874 | − | 3.56155i | 0.760669 | − | 0.503680i | ||||
\(51\) | 1.98115 | + | 2.13162i | 0.277416 | + | 0.298487i | ||||
\(52\) | −6.67213 | + | 2.73544i | −0.925258 | + | 0.379337i | ||||
\(53\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(54\) | −6.99766 | − | 2.24337i | −0.952261 | − | 0.305284i | ||||
\(55\) | 1.32431i | 0.178570i | ||||||||
\(56\) | −1.98115 | − | 10.6561i | −0.264742 | − | 1.42398i | ||||
\(57\) | −2.73013 | + | 2.53741i | −0.361614 | + | 0.336088i | ||||
\(58\) | −5.98396 | − | 9.03712i | −0.785732 | − | 1.18663i | ||||
\(59\) | − | 2.87689i | − | 0.374540i | −0.982309 | − | 0.187270i | \(-0.940036\pi\) | ||
0.982309 | − | 0.187270i | \(-0.0599639\pi\) | |||||||
\(60\) | −0.781732 | − | 2.15645i | −0.100921 | − | 0.278396i | ||||
\(61\) | 3.12311 | 0.399873 | 0.199936 | − | 0.979809i | \(-0.435926\pi\) | ||||
0.199936 | + | 0.979809i | \(0.435926\pi\) | |||||||
\(62\) | 2.53741 | − | 1.68015i | 0.322251 | − | 0.213380i | ||||
\(63\) | −0.840077 | + | 11.4654i | −0.105840 | + | 1.44451i | ||||
\(64\) | −7.46543 | + | 2.87529i | −0.933179 | + | 0.359411i | ||||
\(65\) | 1.69614 | + | 1.68015i | 0.210380 | + | 0.208398i | ||||
\(66\) | −4.76193 | − | 1.15068i | −0.586153 | − | 0.141639i | ||||
\(67\) | 5.51221 | 0.673424 | 0.336712 | − | 0.941608i | \(-0.390685\pi\) | ||||
0.336712 | + | 0.941608i | \(0.390685\pi\) | |||||||
\(68\) | −3.09367 | − | 1.31182i | −0.375163 | − | 0.159082i | ||||
\(69\) | 8.24621 | − | 7.66411i | 0.992727 | − | 0.922651i | ||||
\(70\) | −2.99198 | + | 1.98115i | −0.357610 | + | 0.236793i | ||||
\(71\) | 14.6847i | 1.74275i | 0.490619 | + | 0.871374i | \(0.336771\pi\) | ||||
−0.490619 | + | 0.871374i | \(0.663229\pi\) | |||||||
\(72\) | 8.43336 | − | 0.937223i | 0.993881 | − | 0.110453i | ||||
\(73\) | − | 12.9994i | − | 1.52147i | −0.649065 | − | 0.760733i | \(-0.724839\pi\) | ||
0.649065 | − | 0.760733i | \(-0.275161\pi\) | |||||||
\(74\) | −7.05597 | − | 10.6561i | −0.820240 | − | 1.23875i | ||||
\(75\) | 5.78726 | − | 5.37874i | 0.668256 | − | 0.621084i | ||||
\(76\) | 1.68015 | − | 3.96230i | 0.192727 | − | 0.454507i | ||||
\(77\) | 7.66411i | 0.873407i | ||||||||
\(78\) | −7.51524 | + | 4.63909i | −0.850933 | + | 0.525274i | ||||
\(79\) | − | 8.10887i | − | 0.912319i | −0.889898 | − | 0.456160i | \(-0.849225\pi\) | ||
0.889898 | − | 0.456160i | \(-0.150775\pi\) | |||||||
\(80\) | 1.84130 | + | 1.90388i | 0.205864 | + | 0.212860i | ||||
\(81\) | −8.90388 | − | 1.31182i | −0.989320 | − | 0.145758i | ||||
\(82\) | 7.56155 | − | 5.00691i | 0.835034 | − | 0.552921i | ||||
\(83\) | − | 6.00000i | − | 0.658586i | −0.944228 | − | 0.329293i | \(-0.893190\pi\) | ||
0.944228 | − | 0.329293i | \(-0.106810\pi\) | |||||||
\(84\) | −4.52409 | − | 12.4799i | −0.493618 | − | 1.36167i | ||||
\(85\) | 1.11252i | 0.120670i | ||||||||
\(86\) | 2.87529 | + | 4.34233i | 0.310050 | + | 0.468245i | ||||
\(87\) | −9.03712 | − | 9.72350i | −0.968881 | − | 1.04247i | ||||
\(88\) | 5.56155 | − | 1.03399i | 0.592864 | − | 0.110223i | ||||
\(89\) | −11.7100 | −1.24125 | −0.620627 | − | 0.784106i | \(-0.713122\pi\) | ||||
−0.620627 | + | 0.784106i | \(0.713122\pi\) | |||||||
\(90\) | −1.37567 | − | 2.44940i | −0.145008 | − | 0.258190i | ||||
\(91\) | 9.81602 | + | 9.72350i | 1.02900 | + | 1.01930i | ||||
\(92\) | −5.07482 | + | 11.9679i | −0.529086 | + | 1.24774i | ||||
\(93\) | 2.73013 | − | 2.53741i | 0.283101 | − | 0.263117i | ||||
\(94\) | 5.21922 | + | 7.88220i | 0.538322 | + | 0.812986i | ||||
\(95\) | −1.42489 | −0.146191 | ||||||||
\(96\) | −8.44585 | + | 4.96666i | −0.862000 | + | 0.506908i | ||||
\(97\) | 7.92460i | 0.804621i | 0.915503 | + | 0.402311i | \(0.131793\pi\) | ||||
−0.915503 | + | 0.402311i | \(0.868207\pi\) | |||||||
\(98\) | −9.06134 | + | 6.00000i | −0.915334 | + | 0.606092i | ||||
\(99\) | −5.98396 | − | 0.438447i | −0.601410 | − | 0.0440656i | ||||
\(100\) | −3.56155 | + | 8.39919i | −0.356155 | + | 0.839919i | ||||
\(101\) | − | 15.3282i | − | 1.52522i | −0.646861 | − | 0.762608i | \(-0.723919\pi\) | ||
0.646861 | − | 0.762608i | \(-0.276081\pi\) | |||||||
\(102\) | −4.00039 | − | 0.966659i | −0.396097 | − | 0.0957135i | ||||
\(103\) | − | 0.580639i | − | 0.0572120i | −0.999591 | − | 0.0286060i | \(-0.990893\pi\) | ||
0.999591 | − | 0.0286060i | \(-0.00910682\pi\) | |||||||
\(104\) | 5.73166 | − | 8.43493i | 0.562036 | − | 0.827113i | ||||
\(105\) | −3.21922 | + | 2.99198i | −0.314164 | + | 0.291987i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 12.9994 | 1.25670 | 0.628351 | − | 0.777930i | \(-0.283730\pi\) | ||||
0.628351 | + | 0.777930i | \(0.283730\pi\) | |||||||
\(108\) | 10.0028 | − | 2.81835i | 0.962524 | − | 0.271196i | ||||
\(109\) | − | 3.96230i | − | 0.379519i | −0.981831 | − | 0.189760i | \(-0.939229\pi\) | ||
0.981831 | − | 0.189760i | \(-0.0607709\pi\) | |||||||
\(110\) | −1.03399 | − | 1.56155i | −0.0985868 | − | 0.148888i | ||||
\(111\) | −10.6561 | − | 11.4654i | −1.01143 | − | 1.08825i | ||||
\(112\) | 10.6561 | + | 11.0183i | 1.00691 | + | 1.04113i | ||||
\(113\) | 4.30380i | 0.404868i | 0.979296 | + | 0.202434i | \(0.0648851\pi\) | ||||
−0.979296 | + | 0.202434i | \(0.935115\pi\) | |||||||
\(114\) | 1.23807 | − | 5.12360i | 0.115956 | − | 0.479869i | ||||
\(115\) | 4.30380 | 0.401332 | ||||||||
\(116\) | 14.1119 | + | 5.98396i | 1.31026 | + | 0.555597i | ||||
\(117\) | −8.15343 | + | 7.10785i | −0.753785 | + | 0.657121i | ||||
\(118\) | 2.24621 | + | 3.39228i | 0.206781 | + | 0.312285i | ||||
\(119\) | 6.43845i | 0.590211i | ||||||||
\(120\) | 2.60548 | + | 1.93241i | 0.237847 | + | 0.176404i | ||||
\(121\) | 7.00000 | 0.636364 | ||||||||
\(122\) | −3.68260 | + | 2.43845i | −0.333407 | + | 0.220767i | ||||
\(123\) | 8.13586 | − | 7.56155i | 0.733586 | − | 0.681802i | ||||
\(124\) | −1.68015 | + | 3.96230i | −0.150882 | + | 0.355825i | ||||
\(125\) | 6.33122 | 0.566281 | ||||||||
\(126\) | −7.96137 | − | 14.1753i | −0.709255 | − | 1.26284i | ||||
\(127\) | 3.39228i | 0.301016i | 0.988609 | + | 0.150508i | \(0.0480910\pi\) | ||||
−0.988609 | + | 0.150508i | \(0.951909\pi\) | |||||||
\(128\) | 6.55789 | − | 9.21922i | 0.579641 | − | 0.814872i | ||||
\(129\) | 4.34233 | + | 4.67213i | 0.382321 | + | 0.411358i | ||||
\(130\) | −3.31182 | − | 0.656843i | −0.290466 | − | 0.0576089i | ||||
\(131\) | −9.03712 | −0.789577 | −0.394788 | − | 0.918772i | \(-0.629182\pi\) | ||||
−0.394788 | + | 0.918772i | \(0.629182\pi\) | |||||||
\(132\) | 6.51343 | − | 2.36118i | 0.566922 | − | 0.205514i | ||||
\(133\) | −8.24621 | −0.715037 | ||||||||
\(134\) | −6.49971 | + | 4.30380i | −0.561489 | + | 0.371792i | ||||
\(135\) | −2.15190 | − | 2.68466i | −0.185206 | − | 0.231059i | ||||
\(136\) | 4.67213 | − | 0.868629i | 0.400632 | − | 0.0744844i | ||||
\(137\) | 16.4265 | 1.40341 | 0.701707 | − | 0.712465i | \(-0.252421\pi\) | ||||
0.701707 | + | 0.712465i | \(0.252421\pi\) | |||||||
\(138\) | −3.73954 | + | 15.4756i | −0.318331 | + | 1.31737i | ||||
\(139\) | 15.7644i | 1.33712i | 0.743659 | + | 0.668559i | \(0.233089\pi\) | ||||
−0.743659 | + | 0.668559i | \(0.766911\pi\) | |||||||
\(140\) | 1.98115 | − | 4.67213i | 0.167438 | − | 0.394867i | ||||
\(141\) | 7.88220 | + | 8.48086i | 0.663801 | + | 0.714217i | ||||
\(142\) | −11.4654 | − | 17.3154i | −0.962158 | − | 1.45307i | ||||
\(143\) | −5.07482 | + | 5.12311i | −0.424378 | + | 0.428416i | ||||
\(144\) | −9.21242 | + | 7.68969i | −0.767701 | + | 0.640808i | ||||
\(145\) | − | 5.07482i | − | 0.421441i | ||||||
\(146\) | 10.1496 | + | 15.3282i | 0.839990 | + | 1.26857i | ||||
\(147\) | −9.74956 | + | 9.06134i | −0.804130 | + | 0.747367i | ||||
\(148\) | 16.6401 | + | 7.05597i | 1.36780 | + | 0.579997i | ||||
\(149\) | −13.7779 | −1.12873 | −0.564366 | − | 0.825525i | \(-0.690879\pi\) | ||||
−0.564366 | + | 0.825525i | \(0.690879\pi\) | |||||||
\(150\) | −2.62444 | + | 10.8609i | −0.214285 | + | 0.886788i | ||||
\(151\) | −20.1038 | −1.63602 | −0.818011 | − | 0.575202i | \(-0.804923\pi\) | ||||
−0.818011 | + | 0.575202i | \(0.804923\pi\) | |||||||
\(152\) | 1.11252 | + | 5.98396i | 0.0902373 | + | 0.485363i | ||||
\(153\) | −5.02699 | − | 0.368330i | −0.406408 | − | 0.0297777i | ||||
\(154\) | −5.98396 | − | 9.03712i | −0.482201 | − | 0.728232i | ||||
\(155\) | 1.42489 | 0.114450 | ||||||||
\(156\) | 5.23948 | − | 11.3379i | 0.419494 | − | 0.907758i | ||||
\(157\) | −10.2462 | −0.817737 | −0.408868 | − | 0.912593i | \(-0.634076\pi\) | ||||
−0.408868 | + | 0.912593i | \(0.634076\pi\) | |||||||
\(158\) | 6.33122 | + | 9.56155i | 0.503684 | + | 0.760676i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −3.65767 | − | 0.807313i | −0.289164 | − | 0.0638237i | ||||
\(161\) | 24.9073 | 1.96297 | ||||||||
\(162\) | 11.5232 | − | 5.40511i | 0.905350 | − | 0.424665i | ||||
\(163\) | −14.1198 | −1.10595 | −0.552975 | − | 0.833198i | \(-0.686507\pi\) | ||||
−0.552975 | + | 0.833198i | \(0.686507\pi\) | |||||||
\(164\) | −5.00691 | + | 11.8078i | −0.390974 | + | 0.922031i | ||||
\(165\) | −1.56155 | − | 1.68015i | −0.121567 | − | 0.130800i | ||||
\(166\) | 4.68466 | + | 7.07488i | 0.363600 | + | 0.549117i | ||||
\(167\) | − | 7.36932i | − | 0.570255i | −0.958490 | − | 0.285127i | \(-0.907964\pi\) | ||
0.958490 | − | 0.285127i | \(-0.0920359\pi\) | |||||||
\(168\) | 15.0786 | + | 11.1834i | 1.16334 | + | 0.862816i | ||||
\(169\) | 0.123106 | + | 12.9994i | 0.00946966 | + | 0.999955i | ||||
\(170\) | −0.868629 | − | 1.31182i | −0.0666208 | − | 0.100612i | ||||
\(171\) | 0.471748 | − | 6.43845i | 0.0360755 | − | 0.492360i | ||||
\(172\) | −6.78078 | − | 2.87529i | −0.517029 | − | 0.219239i | ||||
\(173\) | − | 11.9679i | − | 0.909904i | −0.890516 | − | 0.454952i | \(-0.849656\pi\) | ||
0.890516 | − | 0.454952i | \(-0.150344\pi\) | |||||||
\(174\) | 18.2480 | + | 4.40947i | 1.38338 | + | 0.334281i | ||||
\(175\) | 17.4801 | 1.32137 | ||||||||
\(176\) | −5.75058 | + | 5.56155i | −0.433466 | + | 0.419218i | ||||
\(177\) | 3.39228 | + | 3.64993i | 0.254980 | + | 0.274346i | ||||
\(178\) | 13.8078 | − | 9.14286i | 1.03494 | − | 0.685286i | ||||
\(179\) | 9.03712 | 0.675466 | 0.337733 | − | 0.941242i | \(-0.390340\pi\) | ||||
0.337733 | + | 0.941242i | \(0.390340\pi\) | |||||||
\(180\) | 3.53455 | + | 1.81412i | 0.263450 | + | 0.135216i | ||||
\(181\) | −5.36932 | −0.399098 | −0.199549 | − | 0.979888i | \(-0.563948\pi\) | ||||
−0.199549 | + | 0.979888i | \(0.563948\pi\) | |||||||
\(182\) | −19.1664 | − | 3.80132i | −1.42071 | − | 0.281773i | ||||
\(183\) | −3.96230 | + | 3.68260i | −0.292902 | + | 0.272226i | ||||
\(184\) | −3.36031 | − | 18.0742i | −0.247725 | − | 1.33245i | ||||
\(185\) | − | 5.98396i | − | 0.439949i | ||||||
\(186\) | −1.23807 | + | 5.12360i | −0.0907800 | + | 0.375681i | ||||
\(187\) | −3.36031 | −0.245730 | ||||||||
\(188\) | −12.3085 | − | 5.21922i | −0.897687 | − | 0.380651i | ||||
\(189\) | −12.4536 | − | 15.5368i | −0.905868 | − | 1.13014i | ||||
\(190\) | 1.68015 | − | 1.11252i | 0.121891 | − | 0.0807107i | ||||
\(191\) | 1.42489 | 0.103101 | 0.0515507 | − | 0.998670i | \(-0.483584\pi\) | ||||
0.0515507 | + | 0.998670i | \(0.483584\pi\) | |||||||
\(192\) | 6.08104 | − | 12.4507i | 0.438862 | − | 0.898555i | ||||
\(193\) | − | 15.2245i | − | 1.09588i | −0.836518 | − | 0.547940i | \(-0.815412\pi\) | ||
0.836518 | − | 0.547940i | \(-0.184588\pi\) | |||||||
\(194\) | −6.18734 | − | 9.34427i | −0.444225 | − | 0.670879i | ||||
\(195\) | −4.13305 | − | 0.131620i | −0.295974 | − | 0.00942550i | ||||
\(196\) | 6.00000 | − | 14.1498i | 0.428571 | − | 1.01070i | ||||
\(197\) | 8.02736 | 0.571925 | 0.285963 | − | 0.958241i | \(-0.407687\pi\) | ||||
0.285963 | + | 0.958241i | \(0.407687\pi\) | |||||||
\(198\) | 7.39830 | − | 4.15514i | 0.525774 | − | 0.295293i | ||||
\(199\) | − | 18.1227i | − | 1.28468i | −0.766418 | − | 0.642342i | \(-0.777963\pi\) | ||
0.766418 | − | 0.642342i | \(-0.222037\pi\) | |||||||
\(200\) | −2.35829 | − | 12.6847i | −0.166757 | − | 0.896941i | ||||
\(201\) | −6.99337 | + | 6.49971i | −0.493274 | + | 0.458454i | ||||
\(202\) | 11.9679 | + | 18.0742i | 0.842060 | + | 1.27170i | ||||
\(203\) | − | 29.3693i | − | 2.06132i | ||||||
\(204\) | 5.47179 | − | 1.98357i | 0.383102 | − | 0.138878i | ||||
\(205\) | 4.24621 | 0.296568 | ||||||||
\(206\) | 0.453349 | + | 0.684658i | 0.0315863 | + | 0.0477024i | ||||
\(207\) | −1.42489 | + | 19.4470i | −0.0990367 | + | 1.35166i | ||||
\(208\) | −0.172678 | + | 14.4212i | −0.0119731 | + | 0.999928i | ||||
\(209\) | − | 4.30380i | − | 0.297700i | ||||||
\(210\) | 1.45987 | − | 6.04148i | 0.100741 | − | 0.416902i | ||||
\(211\) | 2.35829i | 0.162352i | 0.996700 | + | 0.0811758i | \(0.0258675\pi\) | ||||
−0.996700 | + | 0.0811758i | \(0.974132\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −17.3154 | − | 18.6305i | −1.18643 | − | 1.27654i | ||||
\(214\) | −15.3282 | + | 10.1496i | −1.04782 | + | 0.693815i | ||||
\(215\) | 2.43845i | 0.166301i | ||||||||
\(216\) | −9.59432 | + | 11.1332i | −0.652811 | + | 0.757521i | ||||
\(217\) | 8.24621 | 0.559789 | ||||||||
\(218\) | 3.09367 | + | 4.67213i | 0.209530 | + | 0.316437i | ||||
\(219\) | 15.3282 | + | 16.4924i | 1.03579 | + | 1.11445i | ||||
\(220\) | 2.43845 | + | 1.03399i | 0.164400 | + | 0.0697114i | ||||
\(221\) | −4.26324 | + | 4.30380i | −0.286777 | + | 0.289505i | ||||
\(222\) | 21.5170 | + | 5.19941i | 1.44413 | + | 0.348962i | ||||
\(223\) | −10.5527 | −0.706659 | −0.353330 | − | 0.935499i | \(-0.614951\pi\) | ||||
−0.353330 | + | 0.935499i | \(0.614951\pi\) | |||||||
\(224\) | −21.1679 | − | 4.67213i | −1.41434 | − | 0.312170i | ||||
\(225\) | −1.00000 | + | 13.6481i | −0.0666667 | + | 0.909871i | ||||
\(226\) | −3.36031 | − | 5.07482i | −0.223524 | − | 0.337572i | ||||
\(227\) | 24.2462i | 1.60928i | 0.593765 | + | 0.804639i | \(0.297641\pi\) | ||||
−0.593765 | + | 0.804639i | \(0.702359\pi\) | |||||||
\(228\) | 2.54051 | + | 7.00814i | 0.168250 | + | 0.464125i | ||||
\(229\) | 11.2622i | 0.744224i | 0.928188 | + | 0.372112i | \(0.121366\pi\) | ||||
−0.928188 | + | 0.372112i | \(0.878634\pi\) | |||||||
\(230\) | −5.07482 | + | 3.36031i | −0.334624 | + | 0.221572i | ||||
\(231\) | −9.03712 | − | 9.72350i | −0.594599 | − | 0.639759i | ||||
\(232\) | −21.3122 | + | 3.96230i | −1.39921 | + | 0.260138i | ||||
\(233\) | − | 17.9519i | − | 1.17607i | −0.808837 | − | 0.588033i | \(-0.799902\pi\) | ||
0.808837 | − | 0.588033i | \(-0.200098\pi\) | |||||||
\(234\) | 4.06445 | − | 14.7472i | 0.265701 | − | 0.964055i | ||||
\(235\) | 4.42627i | 0.288738i | ||||||||
\(236\) | −5.29723 | − | 2.24621i | −0.344820 | − | 0.146216i | ||||
\(237\) | 9.56155 | + | 10.2878i | 0.621090 | + | 0.668262i | ||||
\(238\) | −5.02699 | − | 7.59188i | −0.325851 | − | 0.492108i | ||||
\(239\) | 8.93087i | 0.577690i | 0.957376 | + | 0.288845i | \(0.0932712\pi\) | ||||
−0.957376 | + | 0.288845i | \(0.906729\pi\) | |||||||
\(240\) | −4.58102 | − | 0.244300i | −0.295704 | − | 0.0157695i | ||||
\(241\) | − | 18.0742i | − | 1.16426i | −0.813094 | − | 0.582132i | \(-0.802219\pi\) | ||
0.813094 | − | 0.582132i | \(-0.197781\pi\) | |||||||
\(242\) | −8.25403 | + | 5.46543i | −0.530589 | + | 0.351331i | ||||
\(243\) | 12.8432 | − | 8.83467i | 0.823894 | − | 0.566744i | ||||
\(244\) | 2.43845 | − | 5.75058i | 0.156106 | − | 0.368143i | ||||
\(245\) | −5.08842 | −0.325087 | ||||||||
\(246\) | −3.68950 | + | 15.2685i | −0.235234 | + | 0.973482i | ||||
\(247\) | −5.51221 | − | 5.46026i | −0.350734 | − | 0.347428i | ||||
\(248\) | −1.11252 | − | 5.98396i | −0.0706451 | − | 0.379982i | ||||
\(249\) | 7.07488 | + | 7.61223i | 0.448353 | + | 0.482405i | ||||
\(250\) | −7.46543 | + | 4.94326i | −0.472156 | + | 0.312639i | ||||
\(251\) | −3.64993 | −0.230382 | −0.115191 | − | 0.993343i | \(-0.536748\pi\) | ||||
−0.115191 | + | 0.993343i | \(0.536748\pi\) | |||||||
\(252\) | 20.4554 | + | 10.4988i | 1.28857 | + | 0.661361i | ||||
\(253\) | 12.9994i | 0.817266i | ||||||||
\(254\) | −2.64861 | − | 4.00000i | −0.166189 | − | 0.250982i | ||||
\(255\) | −1.31182 | − | 1.41146i | −0.0821497 | − | 0.0883890i | ||||
\(256\) | −0.534565 | + | 15.9911i | −0.0334103 | + | 0.999442i | ||||
\(257\) | 21.3122i | 1.32942i | 0.747103 | + | 0.664709i | \(0.231444\pi\) | ||||
−0.747103 | + | 0.664709i | \(0.768556\pi\) | |||||||
\(258\) | −8.76814 | − | 2.11875i | −0.545880 | − | 0.131907i | ||||
\(259\) | − | 34.6307i | − | 2.15185i | ||||||
\(260\) | 4.41798 | − | 1.81128i | 0.273991 | − | 0.112331i | ||||
\(261\) | 22.9309 | + | 1.68015i | 1.41939 | + | 0.103999i | ||||
\(262\) | 10.6561 | − | 7.05597i | 0.658336 | − | 0.435919i | ||||
\(263\) | −18.0742 | −1.11451 | −0.557253 | − | 0.830343i | \(-0.688144\pi\) | ||||
−0.557253 | + | 0.830343i | \(0.688144\pi\) | |||||||
\(264\) | −5.83674 | + | 7.86971i | −0.359227 | + | 0.484347i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 9.72350 | − | 6.43845i | 0.596186 | − | 0.394767i | ||||
\(267\) | 14.8565 | − | 13.8078i | 0.909202 | − | 0.845021i | ||||
\(268\) | 4.30380 | − | 10.1496i | 0.262897 | − | 0.619988i | ||||
\(269\) | − | 16.2717i | − | 0.992104i | −0.868293 | − | 0.496052i | \(-0.834782\pi\) | ||
0.868293 | − | 0.496052i | \(-0.165218\pi\) | |||||||
\(270\) | 4.63353 | + | 1.48545i | 0.281988 | + | 0.0904018i | ||||
\(271\) | 19.1603 | 1.16390 | 0.581952 | − | 0.813223i | \(-0.302289\pi\) | ||||
0.581952 | + | 0.813223i | \(0.302289\pi\) | |||||||
\(272\) | −4.83093 | + | 4.67213i | −0.292918 | + | 0.283290i | ||||
\(273\) | −23.9191 | − | 0.761720i | −1.44765 | − | 0.0461014i | ||||
\(274\) | −19.3693 | + | 12.8255i | −1.17014 | + | 0.774814i | ||||
\(275\) | 9.12311i | 0.550144i | ||||||||
\(276\) | −7.67349 | − | 21.1677i | −0.461890 | − | 1.27415i | ||||
\(277\) | −20.2462 | −1.21648 | −0.608238 | − | 0.793754i | \(-0.708124\pi\) | ||||
−0.608238 | + | 0.793754i | \(0.708124\pi\) | |||||||
\(278\) | −12.3085 | − | 18.5885i | −0.738213 | − | 1.11487i | ||||
\(279\) | −0.471748 | + | 6.43845i | −0.0282428 | + | 0.385460i | ||||
\(280\) | 1.31182 | + | 7.05597i | 0.0783965 | + | 0.421675i | ||||
\(281\) | −19.2382 | −1.14765 | −0.573827 | − | 0.818976i | \(-0.694542\pi\) | ||||
−0.573827 | + | 0.818976i | \(0.694542\pi\) | |||||||
\(282\) | −15.9159 | − | 3.84595i | −0.947779 | − | 0.229023i | ||||
\(283\) | 16.0547i | 0.954354i | 0.878807 | + | 0.477177i | \(0.158340\pi\) | ||||
−0.878807 | + | 0.477177i | \(0.841660\pi\) | |||||||
\(284\) | 27.0389 | + | 11.4654i | 1.60446 | + | 0.680348i | ||||
\(285\) | 1.80776 | − | 1.68015i | 0.107083 | − | 0.0995238i | ||||
\(286\) | 1.98396 | − | 10.0032i | 0.117314 | − | 0.591501i | ||||
\(287\) | 24.5739 | 1.45055 | ||||||||
\(288\) | 4.85886 | − | 16.2601i | 0.286311 | − | 0.958137i | ||||
\(289\) | 14.1771 | 0.833946 | ||||||||
\(290\) | 3.96230 | + | 5.98396i | 0.232674 | + | 0.351390i | ||||
\(291\) | −9.34427 | − | 10.0540i | −0.547771 | − | 0.589374i | ||||
\(292\) | −23.9358 | − | 10.1496i | −1.40074 | − | 0.593963i | ||||
\(293\) | 10.0953 | 0.589776 | 0.294888 | − | 0.955532i | \(-0.404718\pi\) | ||||
0.294888 | + | 0.955532i | \(0.404718\pi\) | |||||||
\(294\) | 4.42129 | − | 18.2969i | 0.257855 | − | 1.06710i | ||||
\(295\) | 1.90495i | 0.110910i | ||||||||
\(296\) | −25.1302 | + | 4.67213i | −1.46066 | + | 0.271562i | ||||
\(297\) | 8.10887 | − | 6.49971i | 0.470524 | − | 0.377151i | ||||
\(298\) | 16.2462 | − | 10.7575i | 0.941118 | − | 0.623164i | ||||
\(299\) | 16.6493 | + | 16.4924i | 0.962857 | + | 0.953781i | ||||
\(300\) | −5.38532 | − | 14.8557i | −0.310922 | − | 0.857694i | ||||
\(301\) | 14.1119i | 0.813399i | ||||||||
\(302\) | 23.7053 | − | 15.6966i | 1.36409 | − | 0.903235i | ||||
\(303\) | 18.0742 | + | 19.4470i | 1.03834 | + | 1.11720i | ||||
\(304\) | −5.98396 | − | 6.18734i | −0.343204 | − | 0.354868i | ||||
\(305\) | −2.06798 | −0.118412 | ||||||||
\(306\) | 6.21514 | − | 3.49064i | 0.355296 | − | 0.199547i | ||||
\(307\) | −9.81602 | −0.560230 | −0.280115 | − | 0.959967i | \(-0.590373\pi\) | ||||
−0.280115 | + | 0.959967i | \(0.590373\pi\) | |||||||
\(308\) | 14.1119 | + | 5.98396i | 0.804102 | + | 0.340968i | ||||
\(309\) | 0.684658 | + | 0.736659i | 0.0389489 | + | 0.0419071i | ||||
\(310\) | −1.68015 | + | 1.11252i | −0.0954264 | + | 0.0631869i | ||||
\(311\) | 8.72475 | 0.494735 | 0.247368 | − | 0.968922i | \(-0.420434\pi\) | ||||
0.247368 | + | 0.968922i | \(0.420434\pi\) | |||||||
\(312\) | 2.67424 | + | 17.4599i | 0.151399 | + | 0.988473i | ||||
\(313\) | 11.5616 | 0.653498 | 0.326749 | − | 0.945111i | \(-0.394047\pi\) | ||||
0.326749 | + | 0.945111i | \(0.394047\pi\) | |||||||
\(314\) | 12.0818 | − | 8.00000i | 0.681815 | − | 0.451466i | ||||
\(315\) | 0.556260 | − | 7.59188i | 0.0313417 | − | 0.427754i | ||||
\(316\) | −14.9309 | − | 6.33122i | −0.839927 | − | 0.356159i | ||||
\(317\) | 13.7779 | 0.773846 | 0.386923 | − | 0.922112i | \(-0.373538\pi\) | ||||
0.386923 | + | 0.922112i | \(0.373538\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 15.3282 | 0.858216 | ||||||||
\(320\) | 4.94326 | − | 1.90388i | 0.276337 | − | 0.106430i | ||||
\(321\) | −16.4924 | + | 15.3282i | −0.920517 | + | 0.855538i | ||||
\(322\) | −29.3693 | + | 19.4470i | −1.63669 | + | 1.08374i | ||||
\(323\) | − | 3.61553i | − | 0.201173i | ||||||
\(324\) | −9.36741 | + | 15.3705i | −0.520411 | + | 0.853916i | ||||
\(325\) | 11.6847 | + | 11.5745i | 0.648148 | + | 0.642039i | ||||
\(326\) | 16.6493 | − | 11.0244i | 0.922122 | − | 0.610586i | ||||
\(327\) | 4.67213 | + | 5.02699i | 0.258370 | + | 0.277993i | ||||
\(328\) | −3.31534 | − | 17.8324i | −0.183059 | − | 0.984628i | ||||
\(329\) | 25.6160i | 1.41226i | ||||||||
\(330\) | 3.15313 | + | 0.761926i | 0.173574 | + | 0.0419426i | ||||
\(331\) | 2.15190 | 0.118279 | 0.0591396 | − | 0.998250i | \(-0.481164\pi\) | ||||
0.0591396 | + | 0.998250i | \(0.481164\pi\) | |||||||
\(332\) | −11.0478 | − | 4.68466i | −0.606327 | − | 0.257104i | ||||
\(333\) | 27.0389 | + | 1.98115i | 1.48172 | + | 0.108566i | ||||
\(334\) | 5.75379 | + | 8.68951i | 0.314833 | + | 0.475469i | ||||
\(335\) | −3.64993 | −0.199417 | ||||||||
\(336\) | −26.5116 | − | 1.41383i | −1.44633 | − | 0.0771305i | ||||
\(337\) | 2.68466 | 0.146243 | 0.0731213 | − | 0.997323i | \(-0.476704\pi\) | ||||
0.0731213 | + | 0.997323i | \(0.476704\pi\) | |||||||
\(338\) | −10.2948 | − | 15.2321i | −0.559963 | − | 0.828517i | ||||
\(339\) | −5.07482 | − | 5.46026i | −0.275626 | − | 0.296560i | ||||
\(340\) | 2.04848 | + | 0.868629i | 0.111095 | + | 0.0471080i | ||||
\(341\) | 4.30380i | 0.233064i | ||||||||
\(342\) | 4.47073 | + | 7.96021i | 0.241749 | + | 0.430439i | ||||
\(343\) | −2.62365 | −0.141664 | ||||||||
\(344\) | 10.2405 | − | 1.90388i | 0.552130 | − | 0.102650i | ||||
\(345\) | −5.46026 | + | 5.07482i | −0.293970 | + | 0.273219i | ||||
\(346\) | 9.34427 | + | 14.1119i | 0.502351 | + | 0.758662i | ||||
\(347\) | −5.38719 | −0.289199 | −0.144600 | − | 0.989490i | \(-0.546189\pi\) | ||||
−0.144600 | + | 0.989490i | \(0.546189\pi\) | |||||||
\(348\) | −24.9599 | + | 9.04817i | −1.33799 | + | 0.485033i | ||||
\(349\) | 9.03712i | 0.483746i | 0.970308 | + | 0.241873i | \(0.0777617\pi\) | ||||
−0.970308 | + | 0.241873i | \(0.922238\pi\) | |||||||
\(350\) | −20.6116 | + | 13.6481i | −1.10174 | + | 0.729520i | ||||
\(351\) | 1.96309 | − | 18.6319i | 0.104782 | − | 0.994495i | ||||
\(352\) | 2.43845 | − | 11.0478i | 0.129970 | − | 0.588850i | ||||
\(353\) | −10.9663 | −0.583677 | −0.291838 | − | 0.956468i | \(-0.594267\pi\) | ||||
−0.291838 | + | 0.956468i | \(0.594267\pi\) | |||||||
\(354\) | −6.84978 | − | 1.65519i | −0.364062 | − | 0.0879724i | ||||
\(355\) | − | 9.72350i | − | 0.516070i | ||||||
\(356\) | −9.14286 | + | 21.5616i | −0.484571 | + | 1.14276i | ||||
\(357\) | −7.59188 | − | 8.16849i | −0.401805 | − | 0.432322i | ||||
\(358\) | −10.6561 | + | 7.05597i | −0.563192 | + | 0.372920i | ||||
\(359\) | 2.87689i | 0.151837i | 0.997114 | + | 0.0759183i | \(0.0241888\pi\) | ||||
−0.997114 | + | 0.0759183i | \(0.975811\pi\) | |||||||
\(360\) | −5.58418 | + | 0.620585i | −0.294312 | + | 0.0327077i | ||||
\(361\) | −14.3693 | −0.756280 | ||||||||
\(362\) | 6.33122 | − | 4.19224i | 0.332761 | − | 0.220339i | ||||
\(363\) | −8.88093 | + | 8.25403i | −0.466128 | + | 0.433224i | ||||
\(364\) | 25.5680 | − | 10.4824i | 1.34013 | − | 0.549425i | ||||
\(365\) | 8.60761i | 0.450543i | ||||||||
\(366\) | 1.79685 | − | 7.43600i | 0.0939226 | − | 0.388686i | ||||
\(367\) | 4.13595i | 0.215895i | 0.994157 | + | 0.107947i | \(0.0344278\pi\) | ||||
−0.994157 | + | 0.107947i | \(0.965572\pi\) | |||||||
\(368\) | 18.0742 | + | 18.6885i | 0.942185 | + | 0.974207i | ||||
\(369\) | −1.40582 | + | 19.1868i | −0.0731842 | + | 0.998823i | ||||
\(370\) | 4.67213 | + | 7.05597i | 0.242893 | + | 0.366822i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −2.54051 | − | 7.00814i | −0.131720 | − | 0.363355i | ||||
\(373\) | −9.12311 | −0.472377 | −0.236188 | − | 0.971707i | \(-0.575898\pi\) | ||||
−0.236188 | + | 0.971707i | \(0.575898\pi\) | |||||||
\(374\) | 3.96230 | − | 2.62365i | 0.204886 | − | 0.135666i | ||||
\(375\) | −8.03244 | + | 7.46543i | −0.414794 | + | 0.385513i | ||||
\(376\) | 18.5885 | − | 3.45593i | 0.958631 | − | 0.178226i | ||||
\(377\) | 19.4470 | − | 19.6320i | 1.00157 | − | 1.01110i | ||||
\(378\) | 26.8154 | + | 8.59671i | 1.37924 | + | 0.442167i | ||||
\(379\) | 5.51221 | 0.283143 | 0.141572 | − | 0.989928i | \(-0.454784\pi\) | ||||
0.141572 | + | 0.989928i | \(0.454784\pi\) | |||||||
\(380\) | −1.11252 | + | 2.62365i | −0.0570711 | + | 0.134590i | ||||
\(381\) | −4.00000 | − | 4.30380i | −0.204926 | − | 0.220491i | ||||
\(382\) | −1.68015 | + | 1.11252i | −0.0859642 | + | 0.0569215i | ||||
\(383\) | − | 23.5616i | − | 1.20394i | −0.798519 | − | 0.601970i | \(-0.794383\pi\) | ||
0.798519 | − | 0.601970i | \(-0.205617\pi\) | |||||||
\(384\) | 2.55080 | + | 19.4292i | 0.130170 | + | 0.991492i | ||||
\(385\) | − | 5.07482i | − | 0.258637i | ||||||
\(386\) | 11.8869 | + | 17.9519i | 0.605027 | + | 0.913726i | ||||
\(387\) | −11.0183 | − | 0.807313i | −0.560090 | − | 0.0410380i | ||||
\(388\) | 14.5916 | + | 6.18734i | 0.740775 | + | 0.314115i | ||||
\(389\) | 12.9114i | 0.654635i | 0.944914 | + | 0.327317i | \(0.106145\pi\) | ||||
−0.944914 | + | 0.327317i | \(0.893855\pi\) | |||||||
\(390\) | 4.97624 | − | 3.07179i | 0.251982 | − | 0.155546i | ||||
\(391\) | 10.9205i | 0.552274i | ||||||||
\(392\) | 3.97292 | + | 21.3693i | 0.200663 | + | 1.07931i | ||||
\(393\) | 11.4654 | − | 10.6561i | 0.578355 | − | 0.537529i | ||||
\(394\) | −9.46543 | + | 6.26757i | −0.476862 | + | 0.315756i | ||||
\(395\) | 5.36932i | 0.270160i | ||||||||
\(396\) | −5.47945 | + | 10.6759i | −0.275353 | + | 0.536486i | ||||
\(397\) | − | 18.0742i | − | 0.907120i | −0.891226 | − | 0.453560i | \(-0.850154\pi\) | ||
0.891226 | − | 0.453560i | \(-0.149846\pi\) | |||||||
\(398\) | 14.1498 | + | 21.3693i | 0.709264 | + | 1.07115i | ||||
\(399\) | 10.4620 | − | 9.72350i | 0.523755 | − | 0.486784i | ||||
\(400\) | 12.6847 | + | 13.1158i | 0.634233 | + | 0.655789i | ||||
\(401\) | −36.0366 | −1.79958 | −0.899790 | − | 0.436323i | \(-0.856281\pi\) | ||||
−0.899790 | + | 0.436323i | \(0.856281\pi\) | |||||||
\(402\) | 3.17139 | − | 13.1244i | 0.158175 | − | 0.654584i | ||||
\(403\) | 5.51221 | + | 5.46026i | 0.274583 | + | 0.271995i | ||||
\(404\) | −28.2239 | − | 11.9679i | −1.40419 | − | 0.595426i | ||||
\(405\) | 5.89574 | + | 0.868629i | 0.292961 | + | 0.0431625i | ||||
\(406\) | 22.9309 | + | 34.6307i | 1.13804 | + | 1.71870i | ||||
\(407\) | 18.0742 | 0.895907 | ||||||||
\(408\) | −4.90332 | + | 6.61117i | −0.242750 | + | 0.327302i | ||||
\(409\) | − | 23.1491i | − | 1.14465i | −0.820028 | − | 0.572324i | \(-0.806042\pi\) | ||
0.820028 | − | 0.572324i | \(-0.193958\pi\) | |||||||
\(410\) | −5.00691 | + | 3.31534i | −0.247274 | + | 0.163733i | ||||
\(411\) | −20.8404 | + | 19.3693i | −1.02798 | + | 0.955418i | ||||
\(412\) | −1.06913 | − | 0.453349i | −0.0526723 | − | 0.0223349i | ||||
\(413\) | 11.0244i | 0.542476i | ||||||||
\(414\) | −13.5036 | − | 24.0434i | −0.663666 | − | 1.18167i | ||||
\(415\) | 3.97292i | 0.195023i | ||||||||
\(416\) | −11.0561 | − | 17.1395i | −0.542070 | − | 0.840333i | ||||
\(417\) | −18.5885 | − | 20.0004i | −0.910285 | − | 0.979422i | ||||
\(418\) | 3.36031 | + | 5.07482i | 0.164358 | + | 0.248218i | ||||
\(419\) | −24.8863 | −1.21578 | −0.607888 | − | 0.794023i | \(-0.707983\pi\) | ||||
−0.607888 | + | 0.794023i | \(0.707983\pi\) | |||||||
\(420\) | 2.99564 | + | 8.26363i | 0.146172 | + | 0.403224i | ||||
\(421\) | − | 3.96230i | − | 0.193111i | −0.995328 | − | 0.0965553i | \(-0.969218\pi\) | ||
0.995328 | − | 0.0965553i | \(-0.0307825\pi\) | |||||||
\(422\) | −1.84130 | − | 2.78078i | −0.0896331 | − | 0.135366i | ||||
\(423\) | −20.0004 | − | 1.46543i | −0.972451 | − | 0.0712519i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 7.66411i | 0.371764i | ||||||||
\(426\) | 34.9636 | + | 8.44866i | 1.69399 | + | 0.409339i | ||||
\(427\) | −11.9679 | −0.579168 | ||||||||
\(428\) | 10.1496 | − | 23.9358i | 0.490601 | − | 1.15698i | ||||
\(429\) | 0.397551 | − | 12.4837i | 0.0191940 | − | 0.602717i | ||||
\(430\) | −1.90388 | − | 2.87529i | −0.0918133 | − | 0.138659i | ||||
\(431\) | − | 29.8078i | − | 1.43579i | −0.696152 | − | 0.717895i | \(-0.745106\pi\) | ||
0.696152 | − | 0.717895i | \(-0.254894\pi\) | |||||||
\(432\) | 2.62055 | − | 20.6187i | 0.126081 | − | 0.992020i | ||||
\(433\) | −9.17708 | −0.441022 | −0.220511 | − | 0.975384i | \(-0.570773\pi\) | ||||
−0.220511 | + | 0.975384i | \(0.570773\pi\) | |||||||
\(434\) | −9.72350 | + | 6.43845i | −0.466743 | + | 0.309055i | ||||
\(435\) | 5.98396 | + | 6.43845i | 0.286909 | + | 0.308700i | ||||
\(436\) | −7.29578 | − | 3.09367i | −0.349405 | − | 0.148160i | ||||
\(437\) | −13.9867 | −0.669076 | ||||||||
\(438\) | −30.9511 | − | 7.47908i | −1.47890 | − | 0.357364i | ||||
\(439\) | 7.94584i | 0.379234i | 0.981858 | + | 0.189617i | \(0.0607247\pi\) | ||||
−0.981858 | + | 0.189617i | \(0.939275\pi\) | |||||||
\(440\) | −3.68260 | + | 0.684658i | −0.175561 | + | 0.0326398i | ||||
\(441\) | 1.68466 | − | 22.9923i | 0.0802218 | − | 1.09487i | ||||
\(442\) | 1.66668 | − | 8.40346i | 0.0792758 | − | 0.399712i | ||||
\(443\) | −9.03712 | −0.429366 | −0.214683 | − | 0.976684i | \(-0.568872\pi\) | ||||
−0.214683 | + | 0.976684i | \(0.568872\pi\) | |||||||
\(444\) | −29.4313 | + | 10.6691i | −1.39675 | + | 0.506335i | ||||
\(445\) | 7.75379 | 0.367565 | ||||||||
\(446\) | 12.4432 | − | 8.23928i | 0.589201 | − | 0.390141i | ||||
\(447\) | 17.4801 | − | 16.2462i | 0.826782 | − | 0.768419i | ||||
\(448\) | 28.6080 | − | 11.0183i | 1.35160 | − | 0.520564i | ||||
\(449\) | 3.76412 | 0.177640 | 0.0888198 | − | 0.996048i | \(-0.471690\pi\) | ||||
0.0888198 | + | 0.996048i | \(0.471690\pi\) | |||||||
\(450\) | −9.47695 | − | 16.8739i | −0.446747 | − | 0.795442i | ||||
\(451\) | 12.8255i | 0.603927i | ||||||||
\(452\) | 7.92460 | + | 3.36031i | 0.372742 | + | 0.158056i | ||||
\(453\) | 25.5058 | − | 23.7053i | 1.19837 | − | 1.11377i | ||||
\(454\) | −18.9309 | − | 28.5899i | −0.888470 | − | 1.34179i | ||||
\(455\) | −6.49971 | − | 6.43845i | −0.304711 | − | 0.301839i | ||||
\(456\) | −8.46743 | − | 6.28005i | −0.396524 | − | 0.294090i | ||||
\(457\) | 5.07482i | 0.237390i | 0.992931 | + | 0.118695i | \(0.0378711\pi\) | ||||
−0.992931 | + | 0.118695i | \(0.962129\pi\) | |||||||
\(458\) | −8.79323 | − | 13.2797i | −0.410881 | − | 0.620522i | ||||
\(459\) | 6.81208 | − | 5.46026i | 0.317961 | − | 0.254863i | ||||
\(460\) | 3.36031 | − | 7.92460i | 0.156675 | − | 0.369486i | ||||
\(461\) | 24.9888 | 1.16384 | 0.581921 | − | 0.813245i | \(-0.302301\pi\) | ||||
0.581921 | + | 0.813245i | \(0.302301\pi\) | |||||||
\(462\) | 18.2480 | + | 4.40947i | 0.848972 | + | 0.205147i | ||||
\(463\) | 10.7595 | 0.500037 | 0.250018 | − | 0.968241i | \(-0.419563\pi\) | ||||
0.250018 | + | 0.968241i | \(0.419563\pi\) | |||||||
\(464\) | 22.0365 | − | 21.3122i | 1.02302 | − | 0.989393i | ||||
\(465\) | −1.80776 | + | 1.68015i | −0.0838331 | + | 0.0779153i | ||||
\(466\) | 14.0164 | + | 21.1679i | 0.649297 | + | 0.980584i | ||||
\(467\) | −39.7984 | −1.84165 | −0.920825 | − | 0.389976i | \(-0.872483\pi\) | ||||
−0.920825 | + | 0.389976i | \(0.872483\pi\) | |||||||
\(468\) | 6.72169 | + | 20.5626i | 0.310710 | + | 0.950505i | ||||
\(469\) | −21.1231 | −0.975374 | ||||||||
\(470\) | −3.45593 | − | 5.21922i | −0.159410 | − | 0.240745i | ||||
\(471\) | 12.9994 | − | 12.0818i | 0.598982 | − | 0.556700i | ||||
\(472\) | 8.00000 | − | 1.48734i | 0.368230 | − | 0.0684602i | ||||
\(473\) | −7.36520 | −0.338652 | ||||||||
\(474\) | −19.3069 | − | 4.66535i | −0.886796 | − | 0.214287i | ||||
\(475\) | −9.81602 | −0.450390 | ||||||||
\(476\) | 11.8551 | + | 5.02699i | 0.543378 | + | 0.230412i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −6.97301 | − | 10.5308i | −0.318938 | − | 0.481668i | ||||
\(479\) | − | 11.5616i | − | 0.528261i | −0.964487 | − | 0.264130i | \(-0.914915\pi\) | ||
0.964487 | − | 0.264130i | \(-0.0850849\pi\) | |||||||
\(480\) | 5.59245 | − | 3.28869i | 0.255259 | − | 0.150107i | ||||
\(481\) | 22.9309 | − | 23.1491i | 1.04556 | − | 1.05551i | ||||
\(482\) | 14.1119 | + | 21.3122i | 0.642781 | + | 0.970743i | ||||
\(483\) | −31.5999 | + | 29.3693i | −1.43785 | + | 1.33635i | ||||
\(484\) | 5.46543 | − | 12.8891i | 0.248429 | − | 0.585868i | ||||
\(485\) | − | 5.24730i | − | 0.238268i | ||||||
\(486\) | −8.24616 | + | 20.4451i | −0.374053 | + | 0.927407i | ||||
\(487\) | 2.15190 | 0.0975120 | 0.0487560 | − | 0.998811i | \(-0.484474\pi\) | ||||
0.0487560 | + | 0.998811i | \(0.484474\pi\) | |||||||
\(488\) | 1.61463 | + | 8.68466i | 0.0730907 | + | 0.393136i | ||||
\(489\) | 17.9139 | − | 16.6493i | 0.810094 | − | 0.752909i | ||||
\(490\) | 6.00000 | − | 3.97292i | 0.271052 | − | 0.179478i | ||||
\(491\) | 17.7619 | 0.801582 | 0.400791 | − | 0.916170i | \(-0.368735\pi\) | ||||
0.400791 | + | 0.916170i | \(0.368735\pi\) | |||||||
\(492\) | −7.57080 | − | 20.8844i | −0.341318 | − | 0.941544i | ||||
\(493\) | 12.8769 | 0.579946 | ||||||||
\(494\) | 10.7629 | + | 2.13464i | 0.484248 | + | 0.0960421i | ||||
\(495\) | 3.96230 | + | 0.290319i | 0.178092 | + | 0.0130489i | ||||
\(496\) | 5.98396 | + | 6.18734i | 0.268688 | + | 0.277820i | ||||
\(497\) | − | 56.2724i | − | 2.52416i | ||||||
\(498\) | −14.2858 | − | 3.45204i | −0.640161 | − | 0.154689i | ||||
\(499\) | −2.15190 | −0.0963324 | −0.0481662 | − | 0.998839i | \(-0.515338\pi\) | ||||
−0.0481662 | + | 0.998839i | \(0.515338\pi\) | |||||||
\(500\) | 4.94326 | − | 11.6577i | 0.221069 | − | 0.521347i | ||||
\(501\) | 8.68951 | + | 9.34949i | 0.388219 | + | 0.417704i | ||||
\(502\) | 4.30380 | − | 2.84978i | 0.192088 | − | 0.127192i | ||||
\(503\) | −38.3735 | −1.71099 | −0.855495 | − | 0.517811i | \(-0.826747\pi\) | ||||
−0.855495 | + | 0.517811i | \(0.826747\pi\) | |||||||
\(504\) | −32.3171 | + | 3.59149i | −1.43952 | + | 0.159978i | ||||
\(505\) | 10.1496i | 0.451653i | ||||||||
\(506\) | −10.1496 | − | 15.3282i | −0.451206 | − | 0.681423i | ||||
\(507\) | −15.4844 | − | 16.3473i | −0.687687 | − | 0.726007i | ||||
\(508\) | 6.24621 | + | 2.64861i | 0.277131 | + | 0.117513i | ||||
\(509\) | −30.7393 | −1.36250 | −0.681249 | − | 0.732052i | \(-0.738563\pi\) | ||||
−0.681249 | + | 0.732052i | \(0.738563\pi\) | |||||||
\(510\) | 2.64887 | + | 0.640077i | 0.117294 | + | 0.0283431i | ||||
\(511\) | 49.8145i | 2.20366i | ||||||||
\(512\) | −11.8551 | − | 19.2732i | −0.523927 | − | 0.851763i | ||||
\(513\) | 6.99337 | + | 8.72475i | 0.308765 | + | 0.385207i | ||||
\(514\) | −16.6401 | − | 25.1302i | −0.733961 | − | 1.10845i | ||||
\(515\) | 0.384472i | 0.0169419i | ||||||||
\(516\) | 11.9932 | − | 4.34764i | 0.527971 | − | 0.191394i | ||||
\(517\) | −13.3693 | −0.587982 | ||||||||
\(518\) | 27.0389 | + | 40.8348i | 1.18802 | + | 1.79418i | ||||
\(519\) | 14.1119 | + | 15.1838i | 0.619445 | + | 0.666493i | ||||
\(520\) | −3.79524 | + | 5.58522i | −0.166432 | + | 0.244928i | ||||
\(521\) | 10.2878i | 0.450715i | 0.974276 | + | 0.225358i | \(0.0723550\pi\) | ||||
−0.974276 | + | 0.225358i | \(0.927645\pi\) | |||||||
\(522\) | −28.3507 | + | 15.9227i | −1.24088 | + | 0.696919i | ||||
\(523\) | 0.580639i | 0.0253896i | 0.999919 | + | 0.0126948i | \(0.00404098\pi\) | ||||
−0.999919 | + | 0.0126948i | \(0.995959\pi\) | |||||||
\(524\) | −7.05597 | + | 16.6401i | −0.308241 | + | 0.726924i | ||||
\(525\) | −22.1771 | + | 20.6116i | −0.967889 | + | 0.899566i | ||||
\(526\) | 21.3122 | − | 14.1119i | 0.929255 | − | 0.615310i | ||||
\(527\) | 3.61553i | 0.157495i | ||||||||
\(528\) | 0.737894 | − | 13.8367i | 0.0321127 | − | 0.602167i | ||||
\(529\) | 19.2462 | 0.836792 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −8.60761 | − | 0.630683i | −0.373538 | − | 0.0273693i | ||||
\(532\) | −6.43845 | + | 15.1838i | −0.279142 | + | 0.658299i | ||||
\(533\) | 16.4265 | + | 16.2717i | 0.711513 | + | 0.704807i | ||||
\(534\) | −6.73720 | + | 27.8810i | −0.291547 | + | 1.20653i | ||||
\(535\) | −8.60761 | −0.372139 | ||||||||
\(536\) | 2.84978 | + | 15.3282i | 0.123092 | + | 0.662079i | ||||
\(537\) | −11.4654 | + | 10.6561i | −0.494770 | + | 0.459844i | ||||
\(538\) | 12.7046 | + | 19.1868i | 0.547733 | + | 0.827200i | ||||
\(539\) | − | 15.3693i | − | 0.662003i | ||||||
\(540\) | −6.62342 | + | 1.86618i | −0.285027 | + | 0.0803076i | ||||
\(541\) | − | 6.18734i | − | 0.266014i | −0.991115 | − | 0.133007i | \(-0.957537\pi\) | ||
0.991115 | − | 0.133007i | \(-0.0424634\pi\) | |||||||
\(542\) | −22.5928 | + | 14.9599i | −0.970444 | + | 0.642583i | ||||
\(543\) | 6.81208 | − | 6.33122i | 0.292334 | − | 0.271698i | ||||
\(544\) | 2.04848 | − | 9.28101i | 0.0878280 | − | 0.397920i | ||||
\(545\) | 2.62365i | 0.112385i | ||||||||
\(546\) | 28.7988 | − | 17.7773i | 1.23248 | − | 0.760796i | ||||
\(547\) | − | 38.7667i | − | 1.65754i | −0.559586 | − | 0.828772i | \(-0.689040\pi\) | ||
0.559586 | − | 0.828772i | \(-0.310960\pi\) | |||||||
\(548\) | 12.8255 | − | 30.2462i | 0.547876 | − | 1.29205i | ||||
\(549\) | 0.684658 | − | 9.34427i | 0.0292205 | − | 0.398804i | ||||
\(550\) | −7.12311 | − | 10.7575i | −0.303730 | − | 0.458701i | ||||
\(551\) | 16.4924i | 0.702601i | ||||||||
\(552\) | 25.5754 | + | 18.9686i | 1.08856 | + | 0.807356i | ||||
\(553\) | 31.0737i | 1.32139i | ||||||||
\(554\) | 23.8733 | − | 15.8078i | 1.01428 | − | 0.671608i | ||||
\(555\) | 7.05597 | + | 7.59188i | 0.299509 | + | 0.322257i | ||||
\(556\) | 29.0270 | + | 12.3085i | 1.23102 | + | 0.521995i | ||||
\(557\) | −21.5965 | −0.915072 | −0.457536 | − | 0.889191i | \(-0.651268\pi\) | ||||
−0.457536 | + | 0.889191i | \(0.651268\pi\) | |||||||
\(558\) | −4.47073 | − | 7.96021i | −0.189261 | − | 0.336982i | ||||
\(559\) | −9.34427 | + | 9.43318i | −0.395220 | + | 0.398981i | ||||
\(560\) | −7.05597 | − | 7.29578i | −0.298169 | − | 0.308303i | ||||
\(561\) | 4.26324 | − | 3.96230i | 0.179994 | − | 0.167288i | ||||
\(562\) | 22.6847 | − | 15.0207i | 0.956895 | − | 0.633611i | ||||
\(563\) | −19.1868 | −0.808625 | −0.404313 | − | 0.914621i | \(-0.632489\pi\) | ||||
−0.404313 | + | 0.914621i | \(0.632489\pi\) | |||||||
\(564\) | 21.7700 | − | 7.89184i | 0.916684 | − | 0.332306i | ||||
\(565\) | − | 2.84978i | − | 0.119891i | ||||||
\(566\) | −12.5351 | − | 18.9309i | −0.526891 | − | 0.795724i | ||||
\(567\) | 34.1202 | + | 5.02699i | 1.43291 | + | 0.211114i | ||||
\(568\) | −40.8348 | + | 7.59188i | −1.71339 | + | 0.318548i | ||||
\(569\) | 21.3122i | 0.893453i | 0.894670 | + | 0.446727i | \(0.147410\pi\) | ||||
−0.894670 | + | 0.446727i | \(0.852590\pi\) | |||||||
\(570\) | −0.819795 | + | 3.39261i | −0.0343374 | + | 0.142101i | ||||
\(571\) | − | 15.0207i | − | 0.628598i | −0.949324 | − | 0.314299i | \(-0.898231\pi\) | ||
0.949324 | − | 0.314299i | \(-0.101769\pi\) | |||||||
\(572\) | 5.47088 | + | 13.3443i | 0.228749 | + | 0.557952i | ||||
\(573\) | −1.80776 | + | 1.68015i | −0.0755204 | + | 0.0701895i | ||||
\(574\) | −28.9763 | + | 19.1868i | −1.20945 | + | 0.800840i | ||||
\(575\) | 29.6488 | 1.23644 | ||||||||
\(576\) | 6.96620 | + | 22.9668i | 0.290258 | + | 0.956948i | ||||
\(577\) | 2.84978i | 0.118638i | 0.998239 | + | 0.0593189i | \(0.0188929\pi\) | ||||
−0.998239 | + | 0.0593189i | \(0.981107\pi\) | |||||||
\(578\) | −16.7169 | + | 11.0691i | −0.695330 | + | 0.460415i | ||||
\(579\) | 17.9519 | + | 19.3153i | 0.746055 | + | 0.802718i | ||||
\(580\) | −9.34427 | − | 3.96230i | −0.388000 | − | 0.164526i | ||||
\(581\) | 22.9923i | 0.953883i | ||||||||
\(582\) | 18.8682 | + | 4.55933i | 0.782111 | + | 0.188990i | ||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 36.1485 | − | 6.72062i | 1.49583 | − | 0.278101i | ||||
\(585\) | 5.39882 | − | 4.70649i | 0.223214 | − | 0.194589i | ||||
\(586\) | −11.9039 | + | 7.88220i | −0.491745 | + | 0.325611i | ||||
\(587\) | − | 25.6155i | − | 1.05727i | −0.848850 | − | 0.528633i | \(-0.822705\pi\) | ||
0.848850 | − | 0.528633i | \(-0.177295\pi\) | |||||||
\(588\) | 9.07243 | + | 25.0268i | 0.374141 | + | 1.03209i | ||||
\(589\) | −4.63068 | −0.190804 | ||||||||
\(590\) | −1.48734 | − | 2.24621i | −0.0612327 | − | 0.0924751i | ||||
\(591\) | −10.1843 | + | 9.46543i | −0.418928 | + | 0.389356i | ||||
\(592\) | 25.9843 | − | 25.1302i | 1.06795 | − | 1.03285i | ||||
\(593\) | 1.53311 | 0.0629573 | 0.0314787 | − | 0.999504i | \(-0.489978\pi\) | ||||
0.0314787 | + | 0.999504i | \(0.489978\pi\) | |||||||
\(594\) | −4.48673 | + | 13.9953i | −0.184093 | + | 0.574235i | ||||
\(595\) | − | 4.26324i | − | 0.174776i | ||||||
\(596\) | −10.7575 | + | 25.3693i | −0.440644 | + | 1.03917i | ||||
\(597\) | 21.3693 | + | 22.9923i | 0.874588 | + | 0.941014i | ||||
\(598\) | −32.5089 | − | 6.44758i | −1.32939 | − | 0.263661i | ||||
\(599\) | −15.8492 | −0.647581 | −0.323790 | − | 0.946129i | \(-0.604957\pi\) | ||||
−0.323790 | + | 0.946129i | \(0.604957\pi\) | |||||||
\(600\) | 17.9491 | + | 13.3123i | 0.732767 | + | 0.543473i | ||||
\(601\) | −17.8078 | −0.726394 | −0.363197 | − | 0.931712i | \(-0.618315\pi\) | ||||
−0.363197 | + | 0.931712i | \(0.618315\pi\) | |||||||
\(602\) | −11.0183 | − | 16.6401i | −0.449071 | − | 0.678198i | ||||
\(603\) | 1.20841 | − | 16.4924i | 0.0492101 | − | 0.671623i | ||||
\(604\) | −15.6966 | + | 37.0171i | −0.638684 | + | 1.50620i | ||||
\(605\) | −4.63507 | −0.188443 | ||||||||
\(606\) | −36.4959 | − | 8.81893i | −1.48255 | − | 0.358245i | ||||
\(607\) | − | 6.78456i | − | 0.275377i | −0.990476 | − | 0.137688i | \(-0.956033\pi\) | ||
0.990476 | − | 0.137688i | \(-0.0439673\pi\) | |||||||
\(608\) | 11.8869 | + | 2.62365i | 0.482077 | + | 0.106403i | ||||
\(609\) | 34.6307 | + | 37.2610i | 1.40331 | + | 1.50989i | ||||
\(610\) | 2.43845 | − | 1.61463i | 0.0987298 | − | 0.0653743i | ||||
\(611\) | −16.9617 | + | 17.1231i | −0.686198 | + | 0.692727i | ||||
\(612\) | −4.60316 | + | 8.96861i | −0.186072 | + | 0.362535i | ||||
\(613\) | 5.07482i | 0.204970i | 0.994735 | + | 0.102485i | \(0.0326794\pi\) | ||||
−0.994735 | + | 0.102485i | \(0.967321\pi\) | |||||||
\(614\) | 11.5745 | − | 7.66411i | 0.467110 | − | 0.309298i | ||||
\(615\) | −5.38719 | + | 5.00691i | −0.217232 | + | 0.201898i | ||||
\(616\) | −21.3122 | + | 3.96230i | −0.858692 | + | 0.159646i | ||||
\(617\) | 2.43981 | 0.0982230 | 0.0491115 | − | 0.998793i | \(-0.484361\pi\) | ||||
0.0491115 | + | 0.998793i | \(0.484361\pi\) | |||||||
\(618\) | −1.38248 | − | 0.334064i | −0.0556115 | − | 0.0134380i | ||||
\(619\) | 37.1122 | 1.49166 | 0.745832 | − | 0.666134i | \(-0.232052\pi\) | ||||
0.745832 | + | 0.666134i | \(0.232052\pi\) | |||||||
\(620\) | 1.11252 | − | 2.62365i | 0.0446799 | − | 0.105368i | ||||
\(621\) | −21.1231 | − | 26.3526i | −0.847641 | − | 1.05750i | ||||
\(622\) | −10.2878 | + | 6.81208i | −0.412502 | + | 0.273139i | ||||
\(623\) | 44.8732 | 1.79781 | ||||||||
\(624\) | −16.7856 | − | 18.4998i | −0.671962 | − | 0.740586i | ||||
\(625\) | 18.6155 | 0.744621 | ||||||||
\(626\) | −13.6328 | + | 9.02699i | −0.544875 | + | 0.360791i | ||||
\(627\) | 5.07482 | + | 5.46026i | 0.202669 | + | 0.218062i | ||||
\(628\) | −8.00000 | + | 18.8664i | −0.319235 | + | 0.752850i | ||||
\(629\) | 15.1838 | 0.605416 | ||||||||
\(630\) | 5.27165 | + | 9.38626i | 0.210027 | + | 0.373957i | ||||
\(631\) | 16.7435 | 0.666547 | 0.333274 | − | 0.942830i | \(-0.391847\pi\) | ||||
0.333274 | + | 0.942830i | \(0.391847\pi\) | |||||||
\(632\) | 22.5490 | − | 4.19224i | 0.896949 | − | 0.166758i | ||||
\(633\) | −2.78078 | − | 2.99198i | −0.110526 | − | 0.118921i | ||||
\(634\) | −16.2462 | + | 10.7575i | −0.645219 | + | 0.427234i | ||||
\(635\) | − | 2.24621i | − | 0.0891382i | ||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −19.6847 | − | 19.4991i | −0.779935 | − | 0.772583i | ||||
\(638\) | −18.0742 | + | 11.9679i | −0.715566 | + | 0.473814i | ||||
\(639\) | 43.9362 | + | 3.21922i | 1.73809 | + | 0.127351i | ||||
\(640\) | −4.34233 | + | 6.10454i | −0.171646 | + | 0.241303i | ||||
\(641\) | 34.9603i | 1.38085i | 0.723405 | + | 0.690424i | \(0.242576\pi\) | ||||
−0.723405 | + | 0.690424i | \(0.757424\pi\) | |||||||
\(642\) | 7.47908 | − | 30.9511i | 0.295176 | − | 1.22154i | ||||
\(643\) | −44.7763 | −1.76580 | −0.882902 | − | 0.469557i | \(-0.844413\pi\) | ||||
−0.882902 | + | 0.469557i | \(0.844413\pi\) | |||||||
\(644\) | 19.4470 | − | 45.8617i | 0.766319 | − | 1.80721i | ||||
\(645\) | −2.87529 | − | 3.09367i | −0.113214 | − | 0.121813i | ||||
\(646\) | 2.82292 | + | 4.26324i | 0.111066 | + | 0.167735i | ||||
\(647\) | 15.8492 | 0.623096 | 0.311548 | − | 0.950230i | \(-0.399152\pi\) | ||||
0.311548 | + | 0.950230i | \(0.399152\pi\) | |||||||
\(648\) | −0.955360 | − | 25.4379i | −0.0375301 | − | 0.999295i | ||||
\(649\) | −5.75379 | −0.225856 | ||||||||
\(650\) | −22.8151 | − | 4.52497i | −0.894880 | − | 0.177484i | ||||
\(651\) | −10.4620 | + | 9.72350i | −0.410038 | + | 0.381094i | ||||
\(652\) | −11.0244 | + | 25.9988i | −0.431750 | + | 1.01819i | ||||
\(653\) | 28.2396i | 1.10510i | 0.833479 | + | 0.552551i | \(0.186346\pi\) | ||||
−0.833479 | + | 0.552551i | \(0.813654\pi\) | |||||||
\(654\) | −9.43409 | − | 2.27967i | −0.368902 | − | 0.0891420i | ||||
\(655\) | 5.98396 | 0.233813 | ||||||||
\(656\) | 17.8324 | + | 18.4384i | 0.696237 | + | 0.719900i | ||||
\(657\) | −38.8940 | − | 2.84978i | −1.51740 | − | 0.111180i | ||||
\(658\) | −20.0004 | − | 30.2050i | −0.779695 | − | 1.17751i | ||||
\(659\) | 49.9480 | 1.94570 | 0.972850 | − | 0.231438i | \(-0.0743430\pi\) | ||||
0.972850 | + | 0.231438i | \(0.0743430\pi\) | |||||||
\(660\) | −4.31289 | + | 1.56346i | −0.167879 | + | 0.0608577i | ||||
\(661\) | 2.22504i | 0.0865440i | 0.999063 | + | 0.0432720i | \(0.0137782\pi\) | ||||
−0.999063 | + | 0.0432720i | \(0.986222\pi\) | |||||||
\(662\) | −2.53741 | + | 1.68015i | −0.0986192 | + | 0.0653011i | ||||
\(663\) | 0.333974 | − | 10.4872i | 0.0129705 | − | 0.407291i | ||||
\(664\) | 16.6847 | − | 3.10196i | 0.647490 | − | 0.120380i | ||||
\(665\) | 5.46026 | 0.211740 | ||||||||
\(666\) | −33.4296 | + | 18.7752i | −1.29537 | + | 0.727526i | ||||
\(667\) | − | 49.8145i | − | 1.92883i | ||||||
\(668\) | −13.5691 | − | 5.75379i | −0.525005 | − | 0.222621i | ||||
\(669\) | 13.3882 | − | 12.4432i | 0.517619 | − | 0.481080i | ||||
\(670\) | 4.30380 | − | 2.84978i | 0.166270 | − | 0.110097i | ||||
\(671\) | − | 6.24621i | − | 0.241132i | ||||||
\(672\) | 32.3650 | − | 19.0325i | 1.24851 | − | 0.734195i | ||||
\(673\) | 0.684658 | 0.0263916 | 0.0131958 | − | 0.999913i | \(-0.495800\pi\) | ||||
0.0131958 | + | 0.999913i | \(0.495800\pi\) | |||||||
\(674\) | −3.16561 | + | 2.09612i | −0.121935 | + | 0.0807394i | ||||
\(675\) | −14.8244 | − | 18.4945i | −0.570591 | − | 0.711854i | ||||
\(676\) | 24.0320 | + | 9.92296i | 0.924306 | + | 0.381652i | ||||
\(677\) | − | 20.5755i | − | 0.790782i | −0.918513 | − | 0.395391i | \(-0.870609\pi\) | ||
0.918513 | − | 0.395391i | \(-0.129391\pi\) | |||||||
\(678\) | 10.2472 | + | 2.47615i | 0.393541 | + | 0.0950959i | ||||
\(679\) | − | 30.3675i | − | 1.16540i | ||||||
\(680\) | −3.09367 | + | 0.575166i | −0.118637 | + | 0.0220566i | ||||
\(681\) | −28.5899 | − | 30.7613i | −1.09557 | − | 1.17877i | ||||
\(682\) | −3.36031 | − | 5.07482i | −0.128673 | − | 0.194325i | ||||
\(683\) | 26.9848i | 1.03255i | 0.856424 | + | 0.516273i | \(0.172681\pi\) | ||||
−0.856424 | + | 0.516273i | \(0.827319\pi\) | |||||||
\(684\) | −11.4868 | − | 5.89562i | −0.439208 | − | 0.225425i | ||||
\(685\) | −10.8769 | −0.415585 | ||||||||
\(686\) | 3.09367 | − | 2.04848i | 0.118117 | − | 0.0782115i | ||||
\(687\) | −13.2797 | − | 14.2884i | −0.506654 | − | 0.545135i | ||||
\(688\) | −10.5885 | + | 10.2405i | −0.403684 | + | 0.390415i | ||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 2.47615 | − | 10.2472i | 0.0942654 | − | 0.390104i | ||||
\(691\) | 31.8649 | 1.21220 | 0.606098 | − | 0.795390i | \(-0.292734\pi\) | ||||
0.606098 | + | 0.795390i | \(0.292734\pi\) | |||||||
\(692\) | −22.0365 | − | 9.34427i | −0.837703 | − | 0.355216i | ||||
\(693\) | 22.9309 | + | 1.68015i | 0.871072 | + | 0.0638238i | ||||
\(694\) | 6.35229 | − | 4.20619i | 0.241130 | − | 0.159665i | ||||
\(695\) | − | 10.4384i | − | 0.395953i | ||||||
\(696\) | 22.3667 | − | 30.1572i | 0.847809 | − | 1.14311i | ||||
\(697\) | 10.7744i | 0.408109i | ||||||||
\(698\) | −7.05597 | − | 10.6561i | −0.267072 | − | 0.403339i | ||||
\(699\) | 21.1679 | + | 22.7756i | 0.800644 | + | 0.861454i | ||||
\(700\) | 13.6481 | − | 32.1862i | 0.515849 | − | 1.21652i | ||||
\(701\) | − | 28.2396i | − | 1.06660i | −0.845927 | − | 0.533298i | \(-0.820952\pi\) | ||
0.845927 | − | 0.533298i | \(-0.179048\pi\) | |||||||
\(702\) | 12.2325 | + | 23.5024i | 0.461688 | + | 0.887043i | ||||
\(703\) | 19.4470i | 0.733457i | ||||||||
\(704\) | 5.75058 | + | 14.9309i | 0.216733 | + | 0.562728i | ||||
\(705\) | −5.21922 | − | 5.61563i | −0.196567 | − | 0.211497i | ||||
\(706\) | 12.9309 | − | 8.56222i | 0.486660 | − | 0.322243i | ||||
\(707\) | 58.7386i | 2.20909i | ||||||||
\(708\) | 9.36923 | − | 3.39643i | 0.352117 | − | 0.127646i | ||||
\(709\) | 44.0731i | 1.65520i | 0.561319 | + | 0.827599i | \(0.310294\pi\) | ||||
−0.561319 | + | 0.827599i | \(0.689706\pi\) | |||||||
\(710\) | 7.59188 | + | 11.4654i | 0.284918 | + | 0.430290i | ||||
\(711\) | −24.2616 | − | 1.77766i | −0.909880 | − | 0.0666673i | ||||
\(712\) | −6.05398 | − | 32.5628i | −0.226882 | − | 1.22034i | ||||
\(713\) | 13.9867 | 0.523807 | ||||||||
\(714\) | 15.3297 | + | 3.70429i | 0.573700 | + | 0.138630i | ||||
\(715\) | 3.36031 | − | 3.39228i | 0.125668 | − | 0.126864i | ||||
\(716\) | 7.05597 | − | 16.6401i | 0.263694 | − | 0.621868i | ||||
\(717\) | −10.5308 | − | 11.3306i | −0.393280 | − | 0.423150i | ||||
\(718\) | −2.24621 | − | 3.39228i | −0.0838279 | − | 0.126599i | ||||
\(719\) | 13.7996 | 0.514637 | 0.257319 | − | 0.966327i | \(-0.417161\pi\) | ||||
0.257319 | + | 0.966327i | \(0.417161\pi\) | |||||||
\(720\) | 6.10003 | − | 5.09176i | 0.227335 | − | 0.189759i | ||||
\(721\) | 2.22504i | 0.0828648i | ||||||||
\(722\) | 16.9435 | − | 11.2192i | 0.630573 | − | 0.417536i | ||||
\(723\) | 21.3122 | + | 22.9309i | 0.792609 | + | 0.852808i | ||||
\(724\) | −4.19224 | + | 9.88653i | −0.155803 | + | 0.367430i | ||||
\(725\) | − | 34.9603i | − | 1.29839i | ||||||
\(726\) | 4.02738 | − | 16.6667i | 0.149470 | − | 0.618561i | ||||
\(727\) | 20.1907i | 0.748830i | 0.927261 | + | 0.374415i | \(0.122156\pi\) | ||||
−0.927261 | + | 0.374415i | \(0.877844\pi\) | |||||||
\(728\) | −21.9641 | + | 32.3231i | −0.814042 | + | 1.19797i | ||||
\(729\) | −5.87689 | + | 26.3526i | −0.217663 | + | 0.976024i | ||||
\(730\) | −6.72062 | − | 10.1496i | −0.248741 | − | 0.375655i | ||||
\(731\) | −6.18734 | −0.228847 | ||||||||
\(732\) | 3.68711 | + | 10.1711i | 0.136279 | + | 0.375934i | ||||
\(733\) | 27.1114i | 1.00138i | 0.865626 | + | 0.500690i | \(0.166920\pi\) | ||||
−0.865626 | + | 0.500690i | \(0.833080\pi\) | |||||||
\(734\) | −3.22925 | − | 4.87689i | −0.119194 | − | 0.180009i | ||||
\(735\) | 6.45571 | − | 6.00000i | 0.238122 | − | 0.221313i | ||||
\(736\) | −35.9038 | − | 7.92460i | −1.32343 | − | 0.292105i | ||||
\(737\) | − | 11.0244i | − | 0.406090i | ||||||
\(738\) | −13.3229 | − | 23.7216i | −0.490423 | − | 0.873206i | ||||
\(739\) | −43.8328 | −1.61241 | −0.806207 | − | 0.591633i | \(-0.798483\pi\) | ||||
−0.806207 | + | 0.591633i | \(0.798483\pi\) | |||||||
\(740\) | −11.0183 | − | 4.67213i | −0.405040 | − | 0.171751i | ||||
\(741\) | 13.4318 | + | 0.427746i | 0.493430 | + | 0.0157136i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 8.43845i | 0.309577i | 0.987948 | + | 0.154788i | \(0.0494695\pi\) | ||||
−0.987948 | + | 0.154788i | \(0.950530\pi\) | |||||||
\(744\) | 8.46743 | + | 6.28005i | 0.310431 | + | 0.230238i | ||||
\(745\) | 9.12311 | 0.334245 | ||||||||
\(746\) | 10.7575 | − | 7.12311i | 0.393860 | − | 0.260795i | ||||
\(747\) | −17.9519 | − | 1.31534i | −0.656825 | − | 0.0481258i | ||||
\(748\) | −2.62365 | + | 6.18734i | −0.0959301 | + | 0.226232i | ||||
\(749\) | −49.8145 | −1.82018 | ||||||||
\(750\) | 3.64260 | − | 15.0744i | 0.133009 | − | 0.550439i | ||||
\(751\) | − | 37.1521i | − | 1.35570i | −0.735201 | − | 0.677849i | \(-0.762912\pi\) | ||
0.735201 | − | 0.677849i | \(-0.237088\pi\) | |||||||
\(752\) | −19.2203 | + | 18.5885i | −0.700893 | + | 0.677854i | ||||
\(753\) | 4.63068 | − | 4.30380i | 0.168751 | − | 0.156839i | ||||
\(754\) | −7.60264 | + | 38.3328i | −0.276872 | + | 1.39600i | ||||
\(755\) | 13.3118 | 0.484466 | ||||||||
\(756\) | −38.3315 | + | 10.8001i | −1.39410 | + | 0.392795i | ||||
\(757\) | 28.4924 | 1.03557 | 0.517787 | − | 0.855509i | \(-0.326756\pi\) | ||||
0.517787 | + | 0.855509i | \(0.326756\pi\) | |||||||
\(758\) | −6.49971 | + | 4.30380i | −0.236080 | + | 0.156321i | ||||
\(759\) | −15.3282 | − | 16.4924i | −0.556379 | − | 0.598637i | ||||
\(760\) | −0.736659 | − | 3.96230i | −0.0267214 | − | 0.143728i | ||||
\(761\) | 11.8730 | 0.430395 | 0.215198 | − | 0.976570i | \(-0.430960\pi\) | ||||
0.215198 | + | 0.976570i | \(0.430960\pi\) | |||||||
\(762\) | 8.07690 | + | 1.95171i | 0.292595 | + | 0.0707031i | ||||
\(763\) | 15.1838i | 0.549689i | ||||||||
\(764\) | 1.11252 | − | 2.62365i | 0.0402496 | − | 0.0949203i | ||||
\(765\) | 3.32864 | + | 0.243891i | 0.120347 | + | 0.00881789i | ||||
\(766\) | 18.3963 | + | 27.7825i | 0.664686 | + | 1.00382i | ||||
\(767\) | −7.29986 | + | 7.36932i | −0.263583 | + | 0.266091i | ||||
\(768\) | −18.1776 | − | 20.9183i | −0.655928 | − | 0.754823i | ||||
\(769\) | − | 43.4483i | − | 1.56679i | −0.621526 | − | 0.783393i | \(-0.713487\pi\) | ||
0.621526 | − | 0.783393i | \(-0.286513\pi\) | |||||||
\(770\) | 3.96230 | + | 5.98396i | 0.142791 | + | 0.215647i | ||||
\(771\) | −25.1302 | − | 27.0389i | −0.905042 | − | 0.973781i | ||||
\(772\) | −28.0328 | − | 11.8869i | −1.00892 | − | 0.427819i | ||||
\(773\) | 0.662153 | 0.0238160 | 0.0119080 | − | 0.999929i | \(-0.496209\pi\) | ||||
0.0119080 | + | 0.999929i | \(0.496209\pi\) | |||||||
\(774\) | 13.6225 | − | 7.65086i | 0.489650 | − | 0.275005i | ||||
\(775\) | 9.81602 | 0.352602 | ||||||||
\(776\) | −22.0365 | + | 4.09697i | −0.791066 | + | 0.147073i | ||||
\(777\) | 40.8348 | + | 43.9362i | 1.46494 | + | 1.57620i | ||||
\(778\) | −10.0809 | − | 15.2245i | −0.361419 | − | 0.545823i | ||||
\(779\) | −13.7996 | −0.494421 | ||||||||
\(780\) | −3.46934 | + | 7.50743i | −0.124222 | + | 0.268809i | ||||
\(781\) | 29.3693 | 1.05092 | ||||||||
\(782\) | −8.52648 | − | 12.8769i | −0.304906 | − | 0.460477i | ||||
\(783\) | −31.0737 | + | 24.9073i | −1.11048 | + | 0.890113i | ||||
\(784\) | −21.3693 | − | 22.0956i | −0.763190 | − | 0.789129i | ||||
\(785\) | 6.78456 | 0.242151 | ||||||||
\(786\) | −5.19941 | + | 21.5170i | −0.185457 | + | 0.767488i | ||||
\(787\) | −19.8969 | −0.709249 | −0.354625 | − | 0.935009i | \(-0.615391\pi\) | ||||
−0.354625 | + | 0.935009i | \(0.615391\pi\) | |||||||
\(788\) | 6.26757 | − | 14.7808i | 0.223273 | − | 0.526543i | ||||
\(789\) | 22.9309 | − | 21.3122i | 0.816361 | − | 0.758734i | ||||
\(790\) | −4.19224 | − | 6.33122i | −0.149153 | − | 0.225255i | ||||
\(791\) | − | 16.4924i | − | 0.586403i | ||||||
\(792\) | −1.87445 | − | 16.8667i | −0.0666055 | − | 0.599333i | ||||
\(793\) | −8.00000 | − | 7.92460i | −0.284088 | − | 0.281411i | ||||
\(794\) | 14.1119 | + | 21.3122i | 0.500814 | + | 0.756341i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −33.3693 | − | 14.1498i | −1.18274 | − | 0.501525i | ||||
\(797\) | − | 38.3206i | − | 1.35738i | −0.734423 | − | 0.678692i | \(-0.762547\pi\) | ||
0.734423 | − | 0.678692i | \(-0.237453\pi\) | |||||||
\(798\) | −4.74437 | + | 19.6339i | −0.167949 | + | 0.695033i | ||||
\(799\) | −11.2313 | −0.397333 | ||||||||
\(800\) | −25.1976 | − | 5.56155i | −0.890869 | − | 0.196631i | ||||
\(801\) | −2.56710 | + | 35.0360i | −0.0907040 | + | 1.23793i | ||||
\(802\) | 42.4924 | − | 28.1365i | 1.50046 | − | 0.993534i | ||||
\(803\) | −25.9988 | −0.917479 | ||||||||
\(804\) | 6.50766 | + | 17.9517i | 0.229507 | + | 0.633108i | ||||
\(805\) | −16.4924 | −0.581282 | ||||||||
\(806\) | −10.7629 | − | 2.13464i | −0.379109 | − | 0.0751896i | ||||
\(807\) | 19.1868 | + | 20.6440i | 0.675406 | + | 0.726704i | ||||
\(808\) | 42.6244 | − | 7.92460i | 1.49952 | − | 0.278786i | ||||
\(809\) | 44.3045i | 1.55766i | 0.627232 | + | 0.778832i | \(0.284188\pi\) | ||||
−0.627232 | + | 0.778832i | \(0.715812\pi\) | |||||||
\(810\) | −7.63015 | + | 3.57901i | −0.268096 | + | 0.125754i | ||||
\(811\) | 18.4236 | 0.646941 | 0.323470 | − | 0.946238i | \(-0.395150\pi\) | ||||
0.323470 | + | 0.946238i | \(0.395150\pi\) | |||||||
\(812\) | −54.0777 | − | 22.9309i | −1.89776 | − | 0.804716i | ||||
\(813\) | −24.3087 | + | 22.5928i | −0.852545 | + | 0.792364i | ||||
\(814\) | −21.3122 | + | 14.1119i | −0.746992 | + | 0.494623i | ||||
\(815\) | 9.34949 | 0.327498 | ||||||||
\(816\) | 0.619888 | − | 11.6239i | 0.0217004 | − | 0.406919i | ||||
\(817\) | − | 7.92460i | − | 0.277247i | ||||||
\(818\) | 18.0742 | + | 27.2961i | 0.631951 | + | 0.954387i | ||||
\(819\) | 31.2444 | − | 27.2377i | 1.09177 | − | 0.951762i | ||||
\(820\) | 3.31534 | − | 7.81855i | 0.115777 | − | 0.273036i | ||||
\(821\) | 24.2451 | 0.846160 | 0.423080 | − | 0.906092i | \(-0.360949\pi\) | ||||
0.423080 | + | 0.906092i | \(0.360949\pi\) | |||||||
\(822\) | 9.45084 | − | 39.1110i | 0.329636 | − | 1.36415i | ||||
\(823\) | 18.8664i | 0.657640i | 0.944393 | + | 0.328820i | \(0.106651\pi\) | ||||
−0.944393 | + | 0.328820i | \(0.893349\pi\) | |||||||
\(824\) | 1.61463 | − | 0.300187i | 0.0562482 | − | 0.0104575i | ||||
\(825\) | −10.7575 | − | 11.5745i | −0.374528 | − | 0.402973i | ||||
\(826\) | −8.60761 | − | 12.9994i | −0.299497 | − | 0.452308i | ||||
\(827\) | 46.4924i | 1.61670i | 0.588702 | + | 0.808350i | \(0.299639\pi\) | ||||
−0.588702 | + | 0.808350i | \(0.700361\pi\) | |||||||
\(828\) | 34.6952 | + | 17.8074i | 1.20574 | + | 0.618850i | ||||
\(829\) | 24.0000 | 0.833554 | 0.416777 | − | 0.909009i | \(-0.363160\pi\) | ||||
0.416777 | + | 0.909009i | \(0.363160\pi\) | |||||||
\(830\) | −3.10196 | − | 4.68466i | −0.107671 | − | 0.162607i | ||||
\(831\) | 25.6865 | − | 23.8733i | 0.891054 | − | 0.828154i | ||||
\(832\) | 26.4189 | + | 11.5777i | 0.915910 | + | 0.401383i | ||||
\(833\) | − | 12.9114i | − | 0.447354i | ||||||
\(834\) | 37.5344 | + | 9.06988i | 1.29971 | + | 0.314064i | ||||
\(835\) | 4.87962i | 0.168866i | ||||||||
\(836\) | −7.92460 | − | 3.36031i | −0.274078 | − | 0.116219i | ||||
\(837\) | −6.99337 | − | 8.72475i | −0.241726 | − | 0.301571i | ||||
\(838\) | 29.3446 | − | 19.4306i | 1.01369 | − | 0.671221i | ||||
\(839\) | 10.8769i | 0.375512i | 0.982216 | + | 0.187756i | \(0.0601214\pi\) | ||||
−0.982216 | + | 0.187756i | \(0.939879\pi\) | |||||||
\(840\) | −9.98434 | − | 7.40511i | −0.344493 | − | 0.255500i | ||||
\(841\) | −29.7386 | −1.02547 | ||||||||
\(842\) | 3.09367 | + | 4.67213i | 0.106615 | + | 0.161012i | ||||
\(843\) | 24.4076 | − | 22.6847i | 0.840642 | − | 0.781301i | ||||
\(844\) | 4.34233 | + | 1.84130i | 0.149469 | + | 0.0633802i | ||||
\(845\) | −0.0815148 | − | 8.60761i | −0.00280419 | − | 0.296111i | ||||
\(846\) | 24.7275 | − | 13.8878i | 0.850151 | − | 0.477474i | ||||
\(847\) | −26.8244 | −0.921697 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −18.9309 | − | 20.3687i | −0.649706 | − | 0.699052i | ||||
\(850\) | −5.98396 | − | 9.03712i | −0.205248 | − | 0.309971i | ||||
\(851\) | − | 58.7386i | − | 2.01353i | ||||||
\(852\) | −47.8238 | + | 17.3366i | −1.63842 | + | 0.593941i | ||||
\(853\) | − | 6.18734i | − | 0.211850i | −0.994374 | − | 0.105925i | \(-0.966220\pi\) | ||
0.994374 | − | 0.105925i | \(-0.0337804\pi\) | |||||||
\(854\) | 14.1119 | − | 9.34427i | 0.482901 | − | 0.319754i | ||||
\(855\) | −0.312369 | + | 4.26324i | −0.0106828 | + | 0.145800i | ||||
\(856\) | 6.72062 | + | 36.1485i | 0.229706 | + | 1.23553i | ||||
\(857\) | − | 1.88699i | − | 0.0644584i | −0.999481 | − | 0.0322292i | \(-0.989739\pi\) | ||
0.999481 | − | 0.0322292i | \(-0.0102606\pi\) | |||||||
\(858\) | 9.27818 | + | 15.0305i | 0.316752 | + | 0.513132i | ||||
\(859\) | 8.10887i | 0.276671i | 0.990385 | + | 0.138336i | \(0.0441752\pi\) | ||||
−0.990385 | + | 0.138336i | \(0.955825\pi\) | |||||||
\(860\) | 4.48991 | + | 1.90388i | 0.153105 | + | 0.0649218i | ||||
\(861\) | −31.1771 | + | 28.9763i | −1.06251 | + | 0.987510i | ||||
\(862\) | 23.2732 | + | 35.1477i | 0.792688 | + | 1.19714i | ||||
\(863\) | 3.56155i | 0.121237i | 0.998161 | + | 0.0606183i | \(0.0193073\pi\) | ||||
−0.998161 | + | 0.0606183i | \(0.980693\pi\) | |||||||
\(864\) | 13.0086 | + | 26.3586i | 0.442562 | + | 0.896738i | ||||
\(865\) | 7.92460i | 0.269444i | ||||||||
\(866\) | 10.8211 | − | 7.16525i | 0.367717 | − | 0.243485i | ||||
\(867\) | −17.9865 | + | 16.7169i | −0.610855 | + | 0.567735i | ||||
\(868\) | 6.43845 | − | 15.1838i | 0.218535 | − | 0.515370i | ||||
\(869\) | −16.2177 | −0.550149 | ||||||||
\(870\) | −12.0830 | − | 2.91974i | −0.409651 | − | 0.0989886i | ||||
\(871\) | −14.1198 | − | 13.9867i | −0.478432 | − | 0.473923i | ||||
\(872\) | 11.0183 | − | 2.04848i | 0.373126 | − | 0.0693704i | ||||
\(873\) | 23.7102 | + | 1.73726i | 0.802470 | + | 0.0587973i | ||||
\(874\) | 16.4924 | − | 10.9205i | 0.557865 | − | 0.369392i | ||||
\(875\) | −24.2616 | −0.820191 | ||||||||
\(876\) | 42.3354 | − | 15.3470i | 1.43038 | − | 0.518526i | ||||
\(877\) | 1.11252i | 0.0375671i | 0.999824 | + | 0.0187836i | \(0.00597935\pi\) | ||||
−0.999824 | + | 0.0187836i | \(0.994021\pi\) | |||||||
\(878\) | −6.20393 | − | 9.36932i | −0.209372 | − | 0.316199i | ||||
\(879\) | −12.8080 | + | 11.9039i | −0.432003 | + | 0.401508i | ||||
\(880\) | 3.80776 | − | 3.68260i | 0.128360 | − | 0.124140i | ||||
\(881\) | − | 31.3931i | − | 1.05766i | −0.848728 | − | 0.528830i | \(-0.822631\pi\) | ||
0.848728 | − | 0.528830i | \(-0.177369\pi\) | |||||||
\(882\) | 15.9654 | + | 28.4267i | 0.537584 | + | 0.957177i | ||||
\(883\) | 22.9666i | 0.772886i | 0.922313 | + | 0.386443i | \(0.126296\pi\) | ||||
−0.922313 | + | 0.386443i | \(0.873704\pi\) | |||||||
\(884\) | 4.59596 | + | 11.2102i | 0.154579 | + | 0.377040i | ||||
\(885\) | −2.24621 | − | 2.41681i | −0.0755056 | − | 0.0812403i | ||||
\(886\) | 10.6561 | − | 7.05597i | 0.357998 | − | 0.237050i | ||||
\(887\) | 4.27467 | 0.143529 | 0.0717647 | − | 0.997422i | \(-0.477137\pi\) | ||||
0.0717647 | + | 0.997422i | \(0.477137\pi\) | |||||||
\(888\) | 26.3737 | − | 35.5598i | 0.885043 | − | 1.19331i | ||||
\(889\) | − | 12.9994i | − | 0.435986i | ||||||
\(890\) | −9.14286 | + | 6.05398i | −0.306469 | + | 0.202930i | ||||
\(891\) | −2.62365 | + | 17.8078i | −0.0878956 | + | 0.596583i | ||||
\(892\) | −8.23928 | + | 19.4306i | −0.275871 | + | 0.650586i | ||||
\(893\) | − | 14.3847i | − | 0.481367i | ||||||
\(894\) | −7.92699 | + | 32.8047i | −0.265118 | + | 1.09715i | ||||
\(895\) | −5.98396 | −0.200022 | ||||||||
\(896\) | −25.1302 | + | 35.3286i | −0.839541 | + | 1.18025i | ||||
\(897\) | −40.5701 | − | 1.29198i | −1.35460 | − | 0.0431381i | ||||
\(898\) | −4.43845 | + | 2.93893i | −0.148113 | + | 0.0980735i | ||||
\(899\) | − | 16.4924i | − | 0.550053i | ||||||
\(900\) | 24.3494 | + | 12.4974i | 0.811648 | + | 0.416580i | ||||
\(901\) | 0 | 0 | ||||||||
\(902\) | −10.0138 | − | 15.1231i | −0.333424 | − | 0.503544i | ||||
\(903\) | −16.6401 | − | 17.9039i | −0.553746 | − | 0.595804i | ||||
\(904\) | −11.9679 | + | 2.22504i | −0.398047 | + | 0.0740037i | ||||
\(905\) | 3.55531 | 0.118183 | ||||||||
\(906\) | −11.5665 | + | 47.8664i | −0.384271 | + | 1.59025i | ||||
\(907\) | 42.1590i | 1.39987i | 0.714209 | + | 0.699933i | \(0.246787\pi\) | ||||
−0.714209 | + | 0.699933i | \(0.753213\pi\) | |||||||
\(908\) | 44.6446 | + | 18.9309i | 1.48158 | + | 0.628243i | ||||
\(909\) | −45.8617 | − | 3.36031i | −1.52114 | − | 0.111454i | ||||
\(910\) | 12.6911 | + | 2.51706i | 0.420706 | + | 0.0834397i | ||||
\(911\) | −24.5739 | −0.814171 | −0.407086 | − | 0.913390i | \(-0.633455\pi\) | ||||
−0.407086 | + | 0.913390i | \(0.633455\pi\) | |||||||
\(912\) | 14.8877 | + | 0.793938i | 0.492980 | + | 0.0262899i | ||||
\(913\) | −12.0000 | −0.397142 | ||||||||
\(914\) | −3.96230 | − | 5.98396i | −0.131061 | − | 0.197932i | ||||
\(915\) | 2.62365 | − | 2.43845i | 0.0867352 | − | 0.0806126i | ||||
\(916\) | 20.7370 | + | 8.79323i | 0.685170 | + | 0.290536i | ||||
\(917\) | 34.6307 | 1.14361 | ||||||||
\(918\) | −3.76920 | + | 11.7572i | −0.124402 | + | 0.388044i | ||||
\(919\) | − | 52.8807i | − | 1.74437i | −0.489172 | − | 0.872187i | \(-0.662701\pi\) | ||
0.489172 | − | 0.872187i | \(-0.337299\pi\) | |||||||
\(920\) | 2.22504 | + | 11.9679i | 0.0733574 | + | 0.394571i | ||||
\(921\) | 12.4536 | − | 11.5745i | 0.410361 | − | 0.381394i | ||||
\(922\) | −29.4654 | + | 19.5106i | −0.970392 | + | 0.642549i | ||||
\(923\) | 37.2610 | − | 37.6155i | 1.22646 | − | 1.23813i | ||||
\(924\) | −24.9599 | + | 9.04817i | −0.821119 | + | 0.297663i | ||||
\(925\) | − | 41.2233i | − | 1.35541i | ||||||
\(926\) | −12.6870 | + | 8.40077i | −0.416922 | + | 0.276067i | ||||
\(927\) | −1.73726 | − | 0.127290i | −0.0570591 | − | 0.00418074i | ||||
\(928\) | −9.34427 | + | 42.3358i | −0.306741 | + | 1.38974i | ||||
\(929\) | 43.9824 | 1.44302 | 0.721508 | − | 0.692406i | \(-0.243449\pi\) | ||||
0.721508 | + | 0.692406i | \(0.243449\pi\) | |||||||
\(930\) | 0.819795 | − | 3.39261i | 0.0268821 | − | 0.111248i | ||||
\(931\) | 16.5366 | 0.541966 | ||||||||
\(932\) | −33.0548 | − | 14.0164i | −1.08275 | − | 0.459123i | ||||
\(933\) | −11.0691 | + | 10.2878i | −0.362387 | + | 0.336806i | ||||
\(934\) | 46.9282 | − | 31.0737i | 1.53554 | − | 1.01676i | ||||
\(935\) | 2.22504 | 0.0727666 | ||||||||
\(936\) | −23.9806 | − | 18.9981i | −0.783831 | − | 0.620974i | ||||
\(937\) | −1.86174 | −0.0608204 | −0.0304102 | − | 0.999538i | \(-0.509681\pi\) | ||||
−0.0304102 | + | 0.999538i | \(0.509681\pi\) | |||||||
\(938\) | 24.9073 | − | 16.4924i | 0.813251 | − | 0.538497i | ||||
\(939\) | −14.6682 | + | 13.6328i | −0.478679 | + | 0.444889i | ||||
\(940\) | 8.15009 | + | 3.45593i | 0.265827 | + | 0.112720i | ||||
\(941\) | 53.5429 | 1.74545 | 0.872724 | − | 0.488214i | \(-0.162351\pi\) | ||||
0.872724 | + | 0.488214i | \(0.162351\pi\) | |||||||
\(942\) | −5.89505 | + | 24.3958i | −0.192071 | + | 0.794860i | ||||
\(943\) | 41.6809 | 1.35732 | ||||||||
\(944\) | −8.27190 | + | 8.00000i | −0.269227 | + | 0.260378i | ||||
\(945\) | 8.24621 | + | 10.2878i | 0.268249 | + | 0.334661i | ||||
\(946\) | 8.68466 | − | 5.75058i | 0.282363 | − | 0.186967i | ||||
\(947\) | − | 2.00000i | − | 0.0649913i | −0.999472 | − | 0.0324956i | \(-0.989654\pi\) | ||
0.999472 | − | 0.0324956i | \(-0.0103455\pi\) | |||||||
\(948\) | 26.4083 | − | 9.57325i | 0.857702 | − | 0.310925i | ||||
\(949\) | −32.9848 | + | 33.2987i | −1.07073 | + | 1.08092i | ||||
\(950\) | 11.5745 | − | 7.66411i | 0.375527 | − | 0.248657i | ||||
\(951\) | −17.4801 | + | 16.2462i | −0.566832 | + | 0.526819i | ||||
\(952\) | −17.9039 | + | 3.32864i | −0.580268 | + | 0.107882i | ||||
\(953\) | − | 28.0328i | − | 0.908072i | −0.890983 | − | 0.454036i | \(-0.849984\pi\) | ||
0.890983 | − | 0.454036i | \(-0.150016\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −0.943495 | −0.0305308 | ||||||||
\(956\) | 16.4444 | + | 6.97301i | 0.531850 | + | 0.225523i | ||||
\(957\) | −19.4470 | + | 18.0742i | −0.628632 | + | 0.584257i | ||||
\(958\) | 9.02699 | + | 13.6328i | 0.291649 | + | 0.440455i | ||||
\(959\) | −62.9475 | −2.03268 | ||||||||
\(960\) | −4.02658 | + | 8.24430i | −0.129957 | + | 0.266084i | ||||
\(961\) | −26.3693 | −0.850623 | ||||||||
\(962\) | −8.96464 | + | 45.2000i | −0.289031 | + | 1.45731i | ||||
\(963\) | 2.84978 | − | 38.8940i | 0.0918328 | − | 1.25334i | ||||
\(964\) | −33.2801 | − | 14.1119i | −1.07188 | − | 0.454515i | ||||
\(965\) | 10.0809i | 0.324517i | ||||||||
\(966\) | 14.3301 | − | 59.3032i | 0.461064 | − | 1.90805i | ||||
\(967\) | 28.7114 | 0.923296 | 0.461648 | − | 0.887063i | \(-0.347258\pi\) | ||||
0.461648 | + | 0.887063i | \(0.347258\pi\) | |||||||
\(968\) | 3.61896 | + | 19.4654i | 0.116318 | + | 0.625643i | ||||
\(969\) | 4.26324 | + | 4.58704i | 0.136955 | + | 0.147357i | ||||
\(970\) | 4.09697 | + | 6.18734i | 0.131546 | + | 0.198663i | ||||
\(971\) | 25.6865 | 0.824318 | 0.412159 | − | 0.911112i | \(-0.364775\pi\) | ||||
0.412159 | + | 0.911112i | \(0.364775\pi\) | |||||||
\(972\) | −6.23959 | − | 30.5462i | −0.200135 | − | 0.979768i | ||||
\(973\) | − | 60.4100i | − | 1.93666i | ||||||
\(974\) | −2.53741 | + | 1.68015i | −0.0813038 | + | 0.0538356i | ||||
\(975\) | −28.4725 | − | 0.906726i | −0.911848 | − | 0.0290385i | ||||
\(976\) | −8.68466 | − | 8.97983i | −0.277989 | − | 0.287437i | ||||
\(977\) | 6.24970 | 0.199946 | 0.0999728 | − | 0.994990i | \(-0.468124\pi\) | ||||
0.0999728 | + | 0.994990i | \(0.468124\pi\) | |||||||
\(978\) | −8.12369 | + | 33.6188i | −0.259767 | + | 1.07501i | ||||
\(979\) | 23.4199i | 0.748504i | ||||||||
\(980\) | −3.97292 | + | 9.36932i | −0.126910 | + | 0.299292i | ||||
\(981\) | −11.8551 | − | 0.868629i | −0.378505 | − | 0.0277332i | ||||
\(982\) | −20.9439 | + | 13.8680i | −0.668345 | + | 0.442547i | ||||
\(983\) | 7.06913i | 0.225470i | 0.993625 | + | 0.112735i | \(0.0359612\pi\) | ||||
−0.993625 | + | 0.112735i | \(0.964039\pi\) | |||||||
\(984\) | 25.2332 | + | 18.7147i | 0.804404 | + | 0.596604i | ||||
\(985\) | −5.31534 | −0.169361 | ||||||||
\(986\) | −15.1838 | + | 10.0540i | −0.483549 | + | 0.320184i | ||||
\(987\) | −30.2050 | − | 32.4991i | −0.961437 | − | 1.03446i | ||||
\(988\) | −14.3578 | + | 5.88640i | −0.456782 | + | 0.187271i | ||||
\(989\) | 23.9358i | 0.761115i | ||||||||
\(990\) | −4.89881 | + | 2.75134i | −0.155694 | + | 0.0874433i | ||||
\(991\) | 42.1232i | 1.33809i | 0.743222 | + | 0.669044i | \(0.233296\pi\) | ||||
−0.743222 | + | 0.669044i | \(0.766704\pi\) | |||||||
\(992\) | −11.8869 | − | 2.62365i | −0.377409 | − | 0.0833010i | ||||
\(993\) | −2.73013 | + | 2.53741i | −0.0866380 | + | 0.0805223i | ||||
\(994\) | 43.9362 | + | 66.3535i | 1.39357 | + | 2.10461i | ||||
\(995\) | 12.0000i | 0.380426i | ||||||||
\(996\) | 19.5403 | − | 7.08354i | 0.619158 | − | 0.224451i | ||||
\(997\) | 10.0000 | 0.316703 | 0.158352 | − | 0.987383i | \(-0.449382\pi\) | ||||
0.158352 | + | 0.987383i | \(0.449382\pi\) | |||||||
\(998\) | 2.53741 | − | 1.68015i | 0.0803203 | − | 0.0531844i | ||||
\(999\) | −36.6404 | + | 29.3693i | −1.15925 | + | 0.929204i |
(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 | 156.2.h.b.155.3 | yes | 16 | |
3.2 | odd | 2 | inner | 156.2.h.b.155.14 | yes | 16 | |
4.3 | odd | 2 | inner | 156.2.h.b.155.2 | yes | 16 | |
12.11 | even | 2 | inner | 156.2.h.b.155.15 | yes | 16 | |
13.12 | even | 2 | inner | 156.2.h.b.155.13 | yes | 16 | |
39.38 | odd | 2 | inner | 156.2.h.b.155.4 | yes | 16 | |
52.51 | odd | 2 | inner | 156.2.h.b.155.16 | yes | 16 | |
156.155 | even | 2 | inner | 156.2.h.b.155.1 | ✓ | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
156.2.h.b.155.1 | ✓ | 16 | 156.155 | even | 2 | inner | |
156.2.h.b.155.2 | yes | 16 | 4.3 | odd | 2 | inner | |
156.2.h.b.155.3 | yes | 16 | 1.1 | even | 1 | trivial | |
156.2.h.b.155.4 | yes | 16 | 39.38 | odd | 2 | inner | |
156.2.h.b.155.13 | yes | 16 | 13.12 | even | 2 | inner | |
156.2.h.b.155.14 | yes | 16 | 3.2 | odd | 2 | inner | |
156.2.h.b.155.15 | yes | 16 | 12.11 | even | 2 | inner | |
156.2.h.b.155.16 | yes | 16 | 52.51 | odd | 2 | inner |