Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [70,2,Mod(13,70)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(70, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([3, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("70.13");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 70 = 2 \cdot 5 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 70.g (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: | \(0.558952814149\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(i)\) |
Coefficient field: | \(\Q(\zeta_{16})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 27.3 | ||
Root | \(-0.923880 + 0.382683i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 70.27 |
Dual form | 70.2.g.a.13.3 |
$q$-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 \(\left(\mathbb{Z}/70\mathbb{Z}\right)^\times\).
\(n\) | \(31\) | \(57\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{4}\right)\) |
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 | ||||
\(3\) | −0.541196 | − | 0.541196i | −0.312460 | − | 0.312460i | 0.533402 | − | 0.845862i | \(-0.320913\pi\) |
−0.845862 | + | 0.533402i | \(0.820913\pi\) | |||||||
\(4\) | 1.00000i | 0.500000i | ||||||||
\(5\) | 2.23044 | − | 0.158513i | 0.997484 | − | 0.0708890i | ||||
\(6\) | − | 0.765367i | − | 0.312460i | ||||||
\(7\) | −2.14065 | + | 1.55487i | −0.809091 | + | 0.587684i | ||||
\(8\) | −0.707107 | + | 0.707107i | −0.250000 | + | 0.250000i | ||||
\(9\) | − | 2.41421i | − | 0.804738i | ||||||
\(10\) | 1.68925 | + | 1.46508i | 0.534187 | + | 0.463298i | ||||
\(11\) | −2.82843 | −0.852803 | −0.426401 | − | 0.904534i | \(-0.640219\pi\) | ||||
−0.426401 | + | 0.904534i | \(0.640219\pi\) | |||||||
\(12\) | 0.541196 | − | 0.541196i | 0.156230 | − | 0.156230i | ||||
\(13\) | −2.83730 | − | 2.83730i | −0.786925 | − | 0.786925i | 0.194064 | − | 0.980989i | \(-0.437833\pi\) |
−0.980989 | + | 0.194064i | \(0.937833\pi\) | |||||||
\(14\) | −2.61313 | − | 0.414214i | −0.698387 | − | 0.110703i | ||||
\(15\) | −1.29289 | − | 1.12132i | −0.333824 | − | 0.289524i | ||||
\(16\) | −1.00000 | −0.250000 | ||||||||
\(17\) | −1.53073 | + | 1.53073i | −0.371257 | + | 0.371257i | −0.867935 | − | 0.496678i | \(-0.834553\pi\) |
0.496678 | + | 0.867935i | \(0.334553\pi\) | |||||||
\(18\) | 1.70711 | − | 1.70711i | 0.402369 | − | 0.402369i | ||||
\(19\) | 7.07401 | 1.62289 | 0.811445 | − | 0.584429i | \(-0.198682\pi\) | ||||
0.811445 | + | 0.584429i | \(0.198682\pi\) | |||||||
\(20\) | 0.158513 | + | 2.23044i | 0.0354445 | + | 0.498742i | ||||
\(21\) | 2.00000 | + | 0.317025i | 0.436436 | + | 0.0691806i | ||||
\(22\) | −2.00000 | − | 2.00000i | −0.426401 | − | 0.426401i | ||||
\(23\) | −2.41421 | + | 2.41421i | −0.503398 | + | 0.503398i | −0.912492 | − | 0.409094i | \(-0.865845\pi\) |
0.409094 | + | 0.912492i | \(0.365845\pi\) | |||||||
\(24\) | 0.765367 | 0.156230 | ||||||||
\(25\) | 4.94975 | − | 0.707107i | 0.989949 | − | 0.141421i | ||||
\(26\) | − | 4.01254i | − | 0.786925i | ||||||
\(27\) | −2.93015 | + | 2.93015i | −0.563908 | + | 0.563908i | ||||
\(28\) | −1.55487 | − | 2.14065i | −0.293842 | − | 0.404545i | ||||
\(29\) | 4.82843i | 0.896616i | 0.893879 | + | 0.448308i | \(0.147973\pi\) | ||||
−0.893879 | + | 0.448308i | \(0.852027\pi\) | |||||||
\(30\) | −0.121320 | − | 1.70711i | −0.0221500 | − | 0.311674i | ||||
\(31\) | − | 3.69552i | − | 0.663735i | −0.943326 | − | 0.331867i | \(-0.892321\pi\) | ||
0.943326 | − | 0.331867i | \(-0.107679\pi\) | |||||||
\(32\) | −0.707107 | − | 0.707107i | −0.125000 | − | 0.125000i | ||||
\(33\) | 1.53073 | + | 1.53073i | 0.266467 | + | 0.266467i | ||||
\(34\) | −2.16478 | −0.371257 | ||||||||
\(35\) | −4.52814 | + | 3.80736i | −0.765395 | + | 0.643561i | ||||
\(36\) | 2.41421 | 0.402369 | ||||||||
\(37\) | 5.41421 | + | 5.41421i | 0.890091 | + | 0.890091i | 0.994531 | − | 0.104440i | \(-0.0333050\pi\) |
−0.104440 | + | 0.994531i | \(0.533305\pi\) | |||||||
\(38\) | 5.00208 | + | 5.00208i | 0.811445 | + | 0.811445i | ||||
\(39\) | 3.07107i | 0.491764i | ||||||||
\(40\) | −1.46508 | + | 1.68925i | −0.231649 | + | 0.267093i | ||||
\(41\) | 1.53073i | 0.239060i | 0.992831 | + | 0.119530i | \(0.0381388\pi\) | ||||
−0.992831 | + | 0.119530i | \(0.961861\pi\) | |||||||
\(42\) | 1.19004 | + | 1.63838i | 0.183628 | + | 0.252808i | ||||
\(43\) | 4.00000 | − | 4.00000i | 0.609994 | − | 0.609994i | −0.332950 | − | 0.942944i | \(-0.608044\pi\) |
0.942944 | + | 0.332950i | \(0.108044\pi\) | |||||||
\(44\) | − | 2.82843i | − | 0.426401i | ||||||
\(45\) | −0.382683 | − | 5.38476i | −0.0570471 | − | 0.802713i | ||||
\(46\) | −3.41421 | −0.503398 | ||||||||
\(47\) | 2.61313 | − | 2.61313i | 0.381164 | − | 0.381164i | −0.490358 | − | 0.871521i | \(-0.663134\pi\) |
0.871521 | + | 0.490358i | \(0.163134\pi\) | |||||||
\(48\) | 0.541196 | + | 0.541196i | 0.0781149 | + | 0.0781149i | ||||
\(49\) | 2.16478 | − | 6.65685i | 0.309255 | − | 0.950979i | ||||
\(50\) | 4.00000 | + | 3.00000i | 0.565685 | + | 0.424264i | ||||
\(51\) | 1.65685 | 0.232006 | ||||||||
\(52\) | 2.83730 | − | 2.83730i | 0.393462 | − | 0.393462i | ||||
\(53\) | 0.242641 | − | 0.242641i | 0.0333293 | − | 0.0333293i | −0.690246 | − | 0.723575i | \(-0.742498\pi\) |
0.723575 | + | 0.690246i | \(0.242498\pi\) | |||||||
\(54\) | −4.14386 | −0.563908 | ||||||||
\(55\) | −6.30864 | + | 0.448342i | −0.850657 | + | 0.0604544i | ||||
\(56\) | 0.414214 | − | 2.61313i | 0.0553516 | − | 0.349194i | ||||
\(57\) | −3.82843 | − | 3.82843i | −0.507088 | − | 0.507088i | ||||
\(58\) | −3.41421 | + | 3.41421i | −0.448308 | + | 0.448308i | ||||
\(59\) | −3.82683 | −0.498211 | −0.249106 | − | 0.968476i | \(-0.580137\pi\) | ||||
−0.249106 | + | 0.968476i | \(0.580137\pi\) | |||||||
\(60\) | 1.12132 | − | 1.29289i | 0.144762 | − | 0.166912i | ||||
\(61\) | 10.3212i | 1.32149i | 0.750609 | + | 0.660746i | \(0.229760\pi\) | ||||
−0.750609 | + | 0.660746i | \(0.770240\pi\) | |||||||
\(62\) | 2.61313 | − | 2.61313i | 0.331867 | − | 0.331867i | ||||
\(63\) | 3.75378 | + | 5.16799i | 0.472932 | + | 0.651106i | ||||
\(64\) | − | 1.00000i | − | 0.125000i | ||||||
\(65\) | −6.77817 | − | 5.87868i | −0.840729 | − | 0.729160i | ||||
\(66\) | 2.16478i | 0.266467i | ||||||||
\(67\) | −6.48528 | − | 6.48528i | −0.792303 | − | 0.792303i | 0.189565 | − | 0.981868i | \(-0.439292\pi\) |
−0.981868 | + | 0.189565i | \(0.939292\pi\) | |||||||
\(68\) | −1.53073 | − | 1.53073i | −0.185629 | − | 0.185629i | ||||
\(69\) | 2.61313 | 0.314583 | ||||||||
\(70\) | −5.89409 | − | 0.509666i | −0.704478 | − | 0.0609167i | ||||
\(71\) | −3.41421 | −0.405193 | −0.202596 | − | 0.979262i | \(-0.564938\pi\) | ||||
−0.202596 | + | 0.979262i | \(0.564938\pi\) | |||||||
\(72\) | 1.70711 | + | 1.70711i | 0.201184 | + | 0.201184i | ||||
\(73\) | −4.77791 | − | 4.77791i | −0.559212 | − | 0.559212i | 0.369871 | − | 0.929083i | \(-0.379402\pi\) |
−0.929083 | + | 0.369871i | \(0.879402\pi\) | |||||||
\(74\) | 7.65685i | 0.890091i | ||||||||
\(75\) | −3.06147 | − | 2.29610i | −0.353508 | − | 0.265131i | ||||
\(76\) | 7.07401i | 0.811445i | ||||||||
\(77\) | 6.05468 | − | 4.39782i | 0.689995 | − | 0.501179i | ||||
\(78\) | −2.17157 | + | 2.17157i | −0.245882 | + | 0.245882i | ||||
\(79\) | − | 9.07107i | − | 1.02057i | −0.860004 | − | 0.510287i | \(-0.829539\pi\) | ||
0.860004 | − | 0.510287i | \(-0.170461\pi\) | |||||||
\(80\) | −2.23044 | + | 0.158513i | −0.249371 | + | 0.0177223i | ||||
\(81\) | −4.07107 | −0.452341 | ||||||||
\(82\) | −1.08239 | + | 1.08239i | −0.119530 | + | 0.119530i | ||||
\(83\) | 5.45042 | + | 5.45042i | 0.598262 | + | 0.598262i | 0.939850 | − | 0.341588i | \(-0.110965\pi\) |
−0.341588 | + | 0.939850i | \(0.610965\pi\) | |||||||
\(84\) | −0.317025 | + | 2.00000i | −0.0345903 | + | 0.218218i | ||||
\(85\) | −3.17157 | + | 3.65685i | −0.344005 | + | 0.396642i | ||||
\(86\) | 5.65685 | 0.609994 | ||||||||
\(87\) | 2.61313 | − | 2.61313i | 0.280157 | − | 0.280157i | ||||
\(88\) | 2.00000 | − | 2.00000i | 0.213201 | − | 0.213201i | ||||
\(89\) | −16.9469 | −1.79636 | −0.898182 | − | 0.439625i | \(-0.855111\pi\) | ||||
−0.898182 | + | 0.439625i | \(0.855111\pi\) | |||||||
\(90\) | 3.53701 | − | 4.07820i | 0.372833 | − | 0.429880i | ||||
\(91\) | 10.4853 | + | 1.66205i | 1.09916 | + | 0.174230i | ||||
\(92\) | −2.41421 | − | 2.41421i | −0.251699 | − | 0.251699i | ||||
\(93\) | −2.00000 | + | 2.00000i | −0.207390 | + | 0.207390i | ||||
\(94\) | 3.69552 | 0.381164 | ||||||||
\(95\) | 15.7782 | − | 1.12132i | 1.61881 | − | 0.115045i | ||||
\(96\) | 0.765367i | 0.0781149i | ||||||||
\(97\) | 11.0866 | − | 11.0866i | 1.12567 | − | 1.12567i | 0.134796 | − | 0.990873i | \(-0.456962\pi\) |
0.990873 | − | 0.134796i | \(-0.0430378\pi\) | |||||||
\(98\) | 6.23784 | − | 3.17637i | 0.630117 | − | 0.320862i | ||||
\(99\) | 6.82843i | 0.686283i | ||||||||
\(100\) | 0.707107 | + | 4.94975i | 0.0707107 | + | 0.494975i | ||||
\(101\) | 11.8519i | 1.17931i | 0.807655 | + | 0.589655i | \(0.200736\pi\) | ||||
−0.807655 | + | 0.589655i | \(0.799264\pi\) | |||||||
\(102\) | 1.17157 | + | 1.17157i | 0.116003 | + | 0.116003i | ||||
\(103\) | −1.97908 | − | 1.97908i | −0.195004 | − | 0.195004i | 0.602850 | − | 0.797854i | \(-0.294032\pi\) |
−0.797854 | + | 0.602850i | \(0.794032\pi\) | |||||||
\(104\) | 4.01254 | 0.393462 | ||||||||
\(105\) | 4.51114 | + | 0.390081i | 0.440242 | + | 0.0380681i | ||||
\(106\) | 0.343146 | 0.0333293 | ||||||||
\(107\) | 7.65685 | + | 7.65685i | 0.740216 | + | 0.740216i | 0.972619 | − | 0.232403i | \(-0.0746590\pi\) |
−0.232403 | + | 0.972619i | \(0.574659\pi\) | |||||||
\(108\) | −2.93015 | − | 2.93015i | −0.281954 | − | 0.281954i | ||||
\(109\) | 16.1421i | 1.54614i | 0.634323 | + | 0.773068i | \(0.281279\pi\) | ||||
−0.634323 | + | 0.773068i | \(0.718721\pi\) | |||||||
\(110\) | −4.77791 | − | 4.14386i | −0.455556 | − | 0.395102i | ||||
\(111\) | − | 5.86030i | − | 0.556235i | ||||||
\(112\) | 2.14065 | − | 1.55487i | 0.202273 | − | 0.146921i | ||||
\(113\) | 6.82843 | − | 6.82843i | 0.642364 | − | 0.642364i | −0.308772 | − | 0.951136i | \(-0.599918\pi\) |
0.951136 | + | 0.308772i | \(0.0999179\pi\) | |||||||
\(114\) | − | 5.41421i | − | 0.507088i | ||||||
\(115\) | −5.00208 | + | 5.76745i | −0.466446 | + | 0.537817i | ||||
\(116\) | −4.82843 | −0.448308 | ||||||||
\(117\) | −6.84984 | + | 6.84984i | −0.633268 | + | 0.633268i | ||||
\(118\) | −2.70598 | − | 2.70598i | −0.249106 | − | 0.249106i | ||||
\(119\) | 0.896683 | − | 5.65685i | 0.0821988 | − | 0.518563i | ||||
\(120\) | 1.70711 | − | 0.121320i | 0.155837 | − | 0.0110750i | ||||
\(121\) | −3.00000 | −0.272727 | ||||||||
\(122\) | −7.29818 | + | 7.29818i | −0.660746 | + | 0.660746i | ||||
\(123\) | 0.828427 | − | 0.828427i | 0.0746968 | − | 0.0746968i | ||||
\(124\) | 3.69552 | 0.331867 | ||||||||
\(125\) | 10.9280 | − | 2.36176i | 0.977434 | − | 0.211242i | ||||
\(126\) | −1.00000 | + | 6.30864i | −0.0890871 | + | 0.562019i | ||||
\(127\) | 6.41421 | + | 6.41421i | 0.569169 | + | 0.569169i | 0.931896 | − | 0.362726i | \(-0.118154\pi\) |
−0.362726 | + | 0.931896i | \(0.618154\pi\) | |||||||
\(128\) | 0.707107 | − | 0.707107i | 0.0625000 | − | 0.0625000i | ||||
\(129\) | −4.32957 | −0.381197 | ||||||||
\(130\) | −0.636039 | − | 8.94975i | −0.0557843 | − | 0.784945i | ||||
\(131\) | − | 16.8925i | − | 1.47590i | −0.674855 | − | 0.737951i | \(-0.735794\pi\) | ||
0.674855 | − | 0.737951i | \(-0.264206\pi\) | |||||||
\(132\) | −1.53073 | + | 1.53073i | −0.133233 | + | 0.133233i | ||||
\(133\) | −15.1430 | + | 10.9991i | −1.31306 | + | 0.953746i | ||||
\(134\) | − | 9.17157i | − | 0.792303i | ||||||
\(135\) | −6.07107 | + | 7.00000i | −0.522514 | + | 0.602464i | ||||
\(136\) | − | 2.16478i | − | 0.185629i | ||||||
\(137\) | −13.8284 | − | 13.8284i | −1.18144 | − | 1.18144i | −0.979371 | − | 0.202071i | \(-0.935233\pi\) |
−0.202071 | − | 0.979371i | \(-0.564767\pi\) | |||||||
\(138\) | 1.84776 | + | 1.84776i | 0.157292 | + | 0.157292i | ||||
\(139\) | 5.09494 | 0.432147 | 0.216073 | − | 0.976377i | \(-0.430675\pi\) | ||||
0.216073 | + | 0.976377i | \(0.430675\pi\) | |||||||
\(140\) | −3.80736 | − | 4.52814i | −0.321781 | − | 0.382697i | ||||
\(141\) | −2.82843 | −0.238197 | ||||||||
\(142\) | −2.41421 | − | 2.41421i | −0.202596 | − | 0.202596i | ||||
\(143\) | 8.02509 | + | 8.02509i | 0.671091 | + | 0.671091i | ||||
\(144\) | 2.41421i | 0.201184i | ||||||||
\(145\) | 0.765367 | + | 10.7695i | 0.0635603 | + | 0.894361i | ||||
\(146\) | − | 6.75699i | − | 0.559212i | ||||||
\(147\) | −4.77424 | + | 2.43109i | −0.393772 | + | 0.200513i | ||||
\(148\) | −5.41421 | + | 5.41421i | −0.445046 | + | 0.445046i | ||||
\(149\) | − | 5.31371i | − | 0.435316i | −0.976025 | − | 0.217658i | \(-0.930158\pi\) | ||
0.976025 | − | 0.217658i | \(-0.0698417\pi\) | |||||||
\(150\) | −0.541196 | − | 3.78837i | −0.0441885 | − | 0.309319i | ||||
\(151\) | −3.17157 | −0.258099 | −0.129049 | − | 0.991638i | \(-0.541193\pi\) | ||||
−0.129049 | + | 0.991638i | \(0.541193\pi\) | |||||||
\(152\) | −5.00208 | + | 5.00208i | −0.405722 | + | 0.405722i | ||||
\(153\) | 3.69552 | + | 3.69552i | 0.298765 | + | 0.298765i | ||||
\(154\) | 7.39104 | + | 1.17157i | 0.595587 | + | 0.0944080i | ||||
\(155\) | −0.585786 | − | 8.24264i | −0.0470515 | − | 0.662065i | ||||
\(156\) | −3.07107 | −0.245882 | ||||||||
\(157\) | −1.17525 | + | 1.17525i | −0.0937949 | + | 0.0937949i | −0.752447 | − | 0.658652i | \(-0.771127\pi\) |
0.658652 | + | 0.752447i | \(0.271127\pi\) | |||||||
\(158\) | 6.41421 | − | 6.41421i | 0.510287 | − | 0.510287i | ||||
\(159\) | −0.262632 | −0.0208281 | ||||||||
\(160\) | −1.68925 | − | 1.46508i | −0.133547 | − | 0.115824i | ||||
\(161\) | 1.41421 | − | 8.92177i | 0.111456 | − | 0.703134i | ||||
\(162\) | −2.87868 | − | 2.87868i | −0.226170 | − | 0.226170i | ||||
\(163\) | 2.34315 | − | 2.34315i | 0.183529 | − | 0.183529i | −0.609362 | − | 0.792892i | \(-0.708575\pi\) |
0.792892 | + | 0.609362i | \(0.208575\pi\) | |||||||
\(164\) | −1.53073 | −0.119530 | ||||||||
\(165\) | 3.65685 | + | 3.17157i | 0.284686 | + | 0.246907i | ||||
\(166\) | 7.70806i | 0.598262i | ||||||||
\(167\) | −11.5349 | + | 11.5349i | −0.892597 | + | 0.892597i | −0.994767 | − | 0.102170i | \(-0.967421\pi\) |
0.102170 | + | 0.994767i | \(0.467421\pi\) | |||||||
\(168\) | −1.63838 | + | 1.19004i | −0.126404 | + | 0.0918138i | ||||
\(169\) | 3.10051i | 0.238500i | ||||||||
\(170\) | −4.82843 | + | 0.343146i | −0.370323 | + | 0.0263181i | ||||
\(171\) | − | 17.0782i | − | 1.30600i | ||||||
\(172\) | 4.00000 | + | 4.00000i | 0.304997 | + | 0.304997i | ||||
\(173\) | −8.56628 | − | 8.56628i | −0.651282 | − | 0.651282i | 0.302019 | − | 0.953302i | \(-0.402339\pi\) |
−0.953302 | + | 0.302019i | \(0.902339\pi\) | |||||||
\(174\) | 3.69552 | 0.280157 | ||||||||
\(175\) | −9.49623 | + | 9.20986i | −0.717848 | + | 0.696200i | ||||
\(176\) | 2.82843 | 0.213201 | ||||||||
\(177\) | 2.07107 | + | 2.07107i | 0.155671 | + | 0.155671i | ||||
\(178\) | −11.9832 | − | 11.9832i | −0.898182 | − | 0.898182i | ||||
\(179\) | − | 2.34315i | − | 0.175135i | −0.996159 | − | 0.0875675i | \(-0.972091\pi\) | ||
0.996159 | − | 0.0875675i | \(-0.0279093\pi\) | |||||||
\(180\) | 5.38476 | − | 0.382683i | 0.401357 | − | 0.0285235i | ||||
\(181\) | − | 10.1355i | − | 0.753364i | −0.926343 | − | 0.376682i | \(-0.877065\pi\) | ||
0.926343 | − | 0.376682i | \(-0.122935\pi\) | |||||||
\(182\) | 6.23897 | + | 8.58946i | 0.462463 | + | 0.636693i | ||||
\(183\) | 5.58579 | − | 5.58579i | 0.412913 | − | 0.412913i | ||||
\(184\) | − | 3.41421i | − | 0.251699i | ||||||
\(185\) | 12.9343 | + | 11.2179i | 0.950950 | + | 0.824754i | ||||
\(186\) | −2.82843 | −0.207390 | ||||||||
\(187\) | 4.32957 | − | 4.32957i | 0.316609 | − | 0.316609i | ||||
\(188\) | 2.61313 | + | 2.61313i | 0.190582 | + | 0.190582i | ||||
\(189\) | 1.71644 | − | 10.8284i | 0.124853 | − | 0.787652i | ||||
\(190\) | 11.9497 | + | 10.3640i | 0.866926 | + | 0.751881i | ||||
\(191\) | 10.2426 | 0.741131 | 0.370566 | − | 0.928806i | \(-0.379164\pi\) | ||||
0.370566 | + | 0.928806i | \(0.379164\pi\) | |||||||
\(192\) | −0.541196 | + | 0.541196i | −0.0390575 | + | 0.0390575i | ||||
\(193\) | −0.242641 | + | 0.242641i | −0.0174657 | + | 0.0174657i | −0.715786 | − | 0.698320i | \(-0.753931\pi\) |
0.698320 | + | 0.715786i | \(0.253931\pi\) | |||||||
\(194\) | 15.6788 | 1.12567 | ||||||||
\(195\) | 0.486803 | + | 6.84984i | 0.0348607 | + | 0.490527i | ||||
\(196\) | 6.65685 | + | 2.16478i | 0.475490 | + | 0.154627i | ||||
\(197\) | 3.41421 | + | 3.41421i | 0.243253 | + | 0.243253i | 0.818194 | − | 0.574942i | \(-0.194975\pi\) |
−0.574942 | + | 0.818194i | \(0.694975\pi\) | |||||||
\(198\) | −4.82843 | + | 4.82843i | −0.343141 | + | 0.343141i | ||||
\(199\) | 15.9414 | 1.13006 | 0.565028 | − | 0.825072i | \(-0.308866\pi\) | ||||
0.565028 | + | 0.825072i | \(0.308866\pi\) | |||||||
\(200\) | −3.00000 | + | 4.00000i | −0.212132 | + | 0.282843i | ||||
\(201\) | 7.01962i | 0.495126i | ||||||||
\(202\) | −8.38057 | + | 8.38057i | −0.589655 | + | 0.589655i | ||||
\(203\) | −7.50756 | − | 10.3360i | −0.526927 | − | 0.725444i | ||||
\(204\) | 1.65685i | 0.116003i | ||||||||
\(205\) | 0.242641 | + | 3.41421i | 0.0169468 | + | 0.238459i | ||||
\(206\) | − | 2.79884i | − | 0.195004i | ||||||
\(207\) | 5.82843 | + | 5.82843i | 0.405104 | + | 0.405104i | ||||
\(208\) | 2.83730 | + | 2.83730i | 0.196731 | + | 0.196731i | ||||
\(209\) | −20.0083 | −1.38400 | ||||||||
\(210\) | 2.91403 | + | 3.46569i | 0.201087 | + | 0.239155i | ||||
\(211\) | −21.6569 | −1.49092 | −0.745460 | − | 0.666551i | \(-0.767770\pi\) | ||||
−0.745460 | + | 0.666551i | \(0.767770\pi\) | |||||||
\(212\) | 0.242641 | + | 0.242641i | 0.0166646 | + | 0.0166646i | ||||
\(213\) | 1.84776 | + | 1.84776i | 0.126606 | + | 0.126606i | ||||
\(214\) | 10.8284i | 0.740216i | ||||||||
\(215\) | 8.28772 | − | 9.55582i | 0.565218 | − | 0.651702i | ||||
\(216\) | − | 4.14386i | − | 0.281954i | ||||||
\(217\) | 5.74603 | + | 7.91082i | 0.390066 | + | 0.537021i | ||||
\(218\) | −11.4142 | + | 11.4142i | −0.773068 | + | 0.773068i | ||||
\(219\) | 5.17157i | 0.349463i | ||||||||
\(220\) | −0.448342 | − | 6.30864i | −0.0302272 | − | 0.425329i | ||||
\(221\) | 8.68629 | 0.584303 | ||||||||
\(222\) | 4.14386 | − | 4.14386i | 0.278118 | − | 0.278118i | ||||
\(223\) | −5.86030 | − | 5.86030i | −0.392435 | − | 0.392435i | 0.483120 | − | 0.875554i | \(-0.339504\pi\) |
−0.875554 | + | 0.483120i | \(0.839504\pi\) | |||||||
\(224\) | 2.61313 | + | 0.414214i | 0.174597 | + | 0.0276758i | ||||
\(225\) | −1.70711 | − | 11.9497i | −0.113807 | − | 0.796650i | ||||
\(226\) | 9.65685 | 0.642364 | ||||||||
\(227\) | 1.94061 | − | 1.94061i | 0.128803 | − | 0.128803i | −0.639766 | − | 0.768569i | \(-0.720969\pi\) |
0.768569 | + | 0.639766i | \(0.220969\pi\) | |||||||
\(228\) | 3.82843 | − | 3.82843i | 0.253544 | − | 0.253544i | ||||
\(229\) | 7.52235 | 0.497091 | 0.248546 | − | 0.968620i | \(-0.420047\pi\) | ||||
0.248546 | + | 0.968620i | \(0.420047\pi\) | |||||||
\(230\) | −7.61521 | + | 0.541196i | −0.502132 | + | 0.0356854i | ||||
\(231\) | −5.65685 | − | 0.896683i | −0.372194 | − | 0.0589974i | ||||
\(232\) | −3.41421 | − | 3.41421i | −0.224154 | − | 0.224154i | ||||
\(233\) | 3.00000 | − | 3.00000i | 0.196537 | − | 0.196537i | −0.601977 | − | 0.798513i | \(-0.705620\pi\) |
0.798513 | + | 0.601977i | \(0.205620\pi\) | |||||||
\(234\) | −9.68714 | −0.633268 | ||||||||
\(235\) | 5.41421 | − | 6.24264i | 0.353184 | − | 0.407225i | ||||
\(236\) | − | 3.82683i | − | 0.249106i | ||||||
\(237\) | −4.90923 | + | 4.90923i | −0.318889 | + | 0.318889i | ||||
\(238\) | 4.63405 | − | 3.36595i | 0.300381 | − | 0.218182i | ||||
\(239\) | 10.4853i | 0.678236i | 0.940744 | + | 0.339118i | \(0.110129\pi\) | ||||
−0.940744 | + | 0.339118i | \(0.889871\pi\) | |||||||
\(240\) | 1.29289 | + | 1.12132i | 0.0834559 | + | 0.0723809i | ||||
\(241\) | 5.86030i | 0.377495i | 0.982026 | + | 0.188748i | \(0.0604428\pi\) | ||||
−0.982026 | + | 0.188748i | \(0.939557\pi\) | |||||||
\(242\) | −2.12132 | − | 2.12132i | −0.136364 | − | 0.136364i | ||||
\(243\) | 10.9937 | + | 10.9937i | 0.705246 | + | 0.705246i | ||||
\(244\) | −10.3212 | −0.660746 | ||||||||
\(245\) | 3.77323 | − | 15.1909i | 0.241063 | − | 0.970509i | ||||
\(246\) | 1.17157 | 0.0746968 | ||||||||
\(247\) | −20.0711 | − | 20.0711i | −1.27709 | − | 1.27709i | ||||
\(248\) | 2.61313 | + | 2.61313i | 0.165934 | + | 0.165934i | ||||
\(249\) | − | 5.89949i | − | 0.373865i | ||||||
\(250\) | 9.39731 | + | 6.05728i | 0.594338 | + | 0.383096i | ||||
\(251\) | 28.7988i | 1.81776i | 0.417055 | + | 0.908881i | \(0.363062\pi\) | ||||
−0.417055 | + | 0.908881i | \(0.636938\pi\) | |||||||
\(252\) | −5.16799 | + | 3.75378i | −0.325553 | + | 0.236466i | ||||
\(253\) | 6.82843 | − | 6.82843i | 0.429300 | − | 0.429300i | ||||
\(254\) | 9.07107i | 0.569169i | ||||||||
\(255\) | 3.69552 | − | 0.262632i | 0.231422 | − | 0.0164467i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 3.24718 | − | 3.24718i | 0.202553 | − | 0.202553i | −0.598540 | − | 0.801093i | \(-0.704252\pi\) |
0.801093 | + | 0.598540i | \(0.204252\pi\) | |||||||
\(258\) | −3.06147 | − | 3.06147i | −0.190599 | − | 0.190599i | ||||
\(259\) | −20.0083 | − | 3.17157i | −1.24326 | − | 0.197072i | ||||
\(260\) | 5.87868 | − | 6.77817i | 0.364580 | − | 0.420365i | ||||
\(261\) | 11.6569 | 0.721541 | ||||||||
\(262\) | 11.9448 | − | 11.9448i | 0.737951 | − | 0.737951i | ||||
\(263\) | −16.5858 | + | 16.5858i | −1.02272 | + | 1.02272i | −0.0229877 | + | 0.999736i | \(0.507318\pi\) |
−0.999736 | + | 0.0229877i | \(0.992682\pi\) | |||||||
\(264\) | −2.16478 | −0.133233 | ||||||||
\(265\) | 0.502734 | − | 0.579658i | 0.0308827 | − | 0.0356081i | ||||
\(266\) | −18.4853 | − | 2.93015i | −1.13341 | − | 0.179659i | ||||
\(267\) | 9.17157 | + | 9.17157i | 0.561291 | + | 0.561291i | ||||
\(268\) | 6.48528 | − | 6.48528i | 0.396152 | − | 0.396152i | ||||
\(269\) | 12.6717 | 0.772606 | 0.386303 | − | 0.922372i | \(-0.373752\pi\) | ||||
0.386303 | + | 0.922372i | \(0.373752\pi\) | |||||||
\(270\) | −9.24264 | + | 0.656854i | −0.562489 | + | 0.0399749i | ||||
\(271\) | − | 13.8854i | − | 0.843477i | −0.906717 | − | 0.421739i | \(-0.861420\pi\) | ||
0.906717 | − | 0.421739i | \(-0.138580\pi\) | |||||||
\(272\) | 1.53073 | − | 1.53073i | 0.0928144 | − | 0.0928144i | ||||
\(273\) | −4.77510 | − | 6.57409i | −0.289002 | − | 0.397882i | ||||
\(274\) | − | 19.5563i | − | 1.18144i | ||||||
\(275\) | −14.0000 | + | 2.00000i | −0.844232 | + | 0.120605i | ||||
\(276\) | 2.61313i | 0.157292i | ||||||||
\(277\) | −10.2426 | − | 10.2426i | −0.615421 | − | 0.615421i | 0.328933 | − | 0.944353i | \(-0.393311\pi\) |
−0.944353 | + | 0.328933i | \(0.893311\pi\) | |||||||
\(278\) | 3.60266 | + | 3.60266i | 0.216073 | + | 0.216073i | ||||
\(279\) | −8.92177 | −0.534132 | ||||||||
\(280\) | 0.509666 | − | 5.89409i | 0.0304584 | − | 0.352239i | ||||
\(281\) | 5.65685 | 0.337460 | 0.168730 | − | 0.985662i | \(-0.446033\pi\) | ||||
0.168730 | + | 0.985662i | \(0.446033\pi\) | |||||||
\(282\) | −2.00000 | − | 2.00000i | −0.119098 | − | 0.119098i | ||||
\(283\) | 0.224171 | + | 0.224171i | 0.0133256 | + | 0.0133256i | 0.713738 | − | 0.700413i | \(-0.247001\pi\) |
−0.700413 | + | 0.713738i | \(0.747001\pi\) | |||||||
\(284\) | − | 3.41421i | − | 0.202596i | ||||||
\(285\) | −9.14594 | − | 7.93223i | −0.541759 | − | 0.469865i | ||||
\(286\) | 11.3492i | 0.671091i | ||||||||
\(287\) | −2.38009 | − | 3.27677i | −0.140492 | − | 0.193422i | ||||
\(288\) | −1.70711 | + | 1.70711i | −0.100592 | + | 0.100592i | ||||
\(289\) | 12.3137i | 0.724336i | ||||||||
\(290\) | −7.07401 | + | 8.15640i | −0.415400 | + | 0.478960i | ||||
\(291\) | −12.0000 | −0.703452 | ||||||||
\(292\) | 4.77791 | − | 4.77791i | 0.279606 | − | 0.279606i | ||||
\(293\) | −2.07193 | − | 2.07193i | −0.121043 | − | 0.121043i | 0.643990 | − | 0.765034i | \(-0.277278\pi\) |
−0.765034 | + | 0.643990i | \(0.777278\pi\) | |||||||
\(294\) | −5.09494 | − | 1.65685i | −0.297143 | − | 0.0966297i | ||||
\(295\) | −8.53553 | + | 0.606602i | −0.496958 | + | 0.0353177i | ||||
\(296\) | −7.65685 | −0.445046 | ||||||||
\(297\) | 8.28772 | − | 8.28772i | 0.480902 | − | 0.480902i | ||||
\(298\) | 3.75736 | − | 3.75736i | 0.217658 | − | 0.217658i | ||||
\(299\) | 13.6997 | 0.792273 | ||||||||
\(300\) | 2.29610 | − | 3.06147i | 0.132565 | − | 0.176754i | ||||
\(301\) | −2.34315 | + | 14.7821i | −0.135057 | + | 0.852024i | ||||
\(302\) | −2.24264 | − | 2.24264i | −0.129049 | − | 0.129049i | ||||
\(303\) | 6.41421 | − | 6.41421i | 0.368487 | − | 0.368487i | ||||
\(304\) | −7.07401 | −0.405722 | ||||||||
\(305\) | 1.63604 | + | 23.0208i | 0.0936793 | + | 1.31817i | ||||
\(306\) | 5.22625i | 0.298765i | ||||||||
\(307\) | 4.18232 | − | 4.18232i | 0.238698 | − | 0.238698i | −0.577613 | − | 0.816311i | \(-0.696016\pi\) |
0.816311 | + | 0.577613i | \(0.196016\pi\) | |||||||
\(308\) | 4.39782 | + | 6.05468i | 0.250589 | + | 0.344997i | ||||
\(309\) | 2.14214i | 0.121862i | ||||||||
\(310\) | 5.41421 | − | 6.24264i | 0.307507 | − | 0.354558i | ||||
\(311\) | 23.0698i | 1.30817i | 0.756422 | + | 0.654084i | \(0.226946\pi\) | ||||
−0.756422 | + | 0.654084i | \(0.773054\pi\) | |||||||
\(312\) | −2.17157 | − | 2.17157i | −0.122941 | − | 0.122941i | ||||
\(313\) | 5.86030 | + | 5.86030i | 0.331244 | + | 0.331244i | 0.853059 | − | 0.521815i | \(-0.174745\pi\) |
−0.521815 | + | 0.853059i | \(0.674745\pi\) | |||||||
\(314\) | −1.66205 | −0.0937949 | ||||||||
\(315\) | 9.19178 | + | 10.9319i | 0.517898 | + | 0.615942i | ||||
\(316\) | 9.07107 | 0.510287 | ||||||||
\(317\) | 2.10051 | + | 2.10051i | 0.117976 | + | 0.117976i | 0.763630 | − | 0.645654i | \(-0.223415\pi\) |
−0.645654 | + | 0.763630i | \(0.723415\pi\) | |||||||
\(318\) | −0.185709 | − | 0.185709i | −0.0104141 | − | 0.0104141i | ||||
\(319\) | − | 13.6569i | − | 0.764637i | ||||||
\(320\) | −0.158513 | − | 2.23044i | −0.00886113 | − | 0.124686i | ||||
\(321\) | − | 8.28772i | − | 0.462575i | ||||||
\(322\) | 7.30864 | − | 5.30864i | 0.407295 | − | 0.295839i | ||||
\(323\) | −10.8284 | + | 10.8284i | −0.602510 | + | 0.602510i | ||||
\(324\) | − | 4.07107i | − | 0.226170i | ||||||
\(325\) | −16.0502 | − | 12.0376i | −0.890303 | − | 0.667728i | ||||
\(326\) | 3.31371 | 0.183529 | ||||||||
\(327\) | 8.73606 | − | 8.73606i | 0.483105 | − | 0.483105i | ||||
\(328\) | −1.08239 | − | 1.08239i | −0.0597651 | − | 0.0597651i | ||||
\(329\) | −1.53073 | + | 9.65685i | −0.0843921 | + | 0.532400i | ||||
\(330\) | 0.343146 | + | 4.82843i | 0.0188896 | + | 0.265796i | ||||
\(331\) | 0.686292 | 0.0377220 | 0.0188610 | − | 0.999822i | \(-0.493996\pi\) | ||||
0.0188610 | + | 0.999822i | \(0.493996\pi\) | |||||||
\(332\) | −5.45042 | + | 5.45042i | −0.299131 | + | 0.299131i | ||||
\(333\) | 13.0711 | − | 13.0711i | 0.716290 | − | 0.716290i | ||||
\(334\) | −16.3128 | −0.892597 | ||||||||
\(335\) | −15.4930 | − | 13.4370i | −0.846476 | − | 0.734144i | ||||
\(336\) | −2.00000 | − | 0.317025i | −0.109109 | − | 0.0172951i | ||||
\(337\) | 12.2426 | + | 12.2426i | 0.666899 | + | 0.666899i | 0.956997 | − | 0.290098i | \(-0.0936879\pi\) |
−0.290098 | + | 0.956997i | \(0.593688\pi\) | |||||||
\(338\) | −2.19239 | + | 2.19239i | −0.119250 | + | 0.119250i | ||||
\(339\) | −7.39104 | −0.401426 | ||||||||
\(340\) | −3.65685 | − | 3.17157i | −0.198321 | − | 0.172003i | ||||
\(341\) | 10.4525i | 0.566035i | ||||||||
\(342\) | 12.0761 | − | 12.0761i | 0.653000 | − | 0.653000i | ||||
\(343\) | 5.71646 | + | 17.6160i | 0.308660 | + | 0.951172i | ||||
\(344\) | 5.65685i | 0.304997i | ||||||||
\(345\) | 5.82843 | − | 0.414214i | 0.313792 | − | 0.0223005i | ||||
\(346\) | − | 12.1146i | − | 0.651282i | ||||||
\(347\) | 17.3137 | + | 17.3137i | 0.929449 | + | 0.929449i | 0.997670 | − | 0.0682216i | \(-0.0217325\pi\) |
−0.0682216 | + | 0.997670i | \(0.521732\pi\) | |||||||
\(348\) | 2.61313 | + | 2.61313i | 0.140078 | + | 0.140078i | ||||
\(349\) | 24.9176 | 1.33381 | 0.666903 | − | 0.745145i | \(-0.267620\pi\) | ||||
0.666903 | + | 0.745145i | \(0.267620\pi\) | |||||||
\(350\) | −13.2272 | − | 0.202493i | −0.707024 | − | 0.0108237i | ||||
\(351\) | 16.6274 | 0.887506 | ||||||||
\(352\) | 2.00000 | + | 2.00000i | 0.106600 | + | 0.106600i | ||||
\(353\) | 5.67459 | + | 5.67459i | 0.302028 | + | 0.302028i | 0.841807 | − | 0.539779i | \(-0.181492\pi\) |
−0.539779 | + | 0.841807i | \(0.681492\pi\) | |||||||
\(354\) | 2.92893i | 0.155671i | ||||||||
\(355\) | −7.61521 | + | 0.541196i | −0.404173 | + | 0.0287237i | ||||
\(356\) | − | 16.9469i | − | 0.898182i | ||||||
\(357\) | −3.54675 | + | 2.57619i | −0.187714 | + | 0.136346i | ||||
\(358\) | 1.65685 | − | 1.65685i | 0.0875675 | − | 0.0875675i | ||||
\(359\) | 16.9706i | 0.895672i | 0.894116 | + | 0.447836i | \(0.147805\pi\) | ||||
−0.894116 | + | 0.447836i | \(0.852195\pi\) | |||||||
\(360\) | 4.07820 | + | 3.53701i | 0.214940 | + | 0.186417i | ||||
\(361\) | 31.0416 | 1.63377 | ||||||||
\(362\) | 7.16687 | − | 7.16687i | 0.376682 | − | 0.376682i | ||||
\(363\) | 1.62359 | + | 1.62359i | 0.0852163 | + | 0.0852163i | ||||
\(364\) | −1.66205 | + | 10.4853i | −0.0871151 | + | 0.549578i | ||||
\(365\) | −11.4142 | − | 9.89949i | −0.597447 | − | 0.518163i | ||||
\(366\) | 7.89949 | 0.412913 | ||||||||
\(367\) | −7.39104 | + | 7.39104i | −0.385809 | + | 0.385809i | −0.873190 | − | 0.487381i | \(-0.837952\pi\) |
0.487381 | + | 0.873190i | \(0.337952\pi\) | |||||||
\(368\) | 2.41421 | − | 2.41421i | 0.125850 | − | 0.125850i | ||||
\(369\) | 3.69552 | 0.192381 | ||||||||
\(370\) | 1.21371 | + | 17.0782i | 0.0630977 | + | 0.887852i | ||||
\(371\) | −0.142136 | + | 0.896683i | −0.00737931 | + | 0.0465535i | ||||
\(372\) | −2.00000 | − | 2.00000i | −0.103695 | − | 0.103695i | ||||
\(373\) | −0.928932 | + | 0.928932i | −0.0480983 | + | 0.0480983i | −0.730747 | − | 0.682649i | \(-0.760828\pi\) |
0.682649 | + | 0.730747i | \(0.260828\pi\) | |||||||
\(374\) | 6.12293 | 0.316609 | ||||||||
\(375\) | −7.19239 | − | 4.63604i | −0.371413 | − | 0.239404i | ||||
\(376\) | 3.69552i | 0.190582i | ||||||||
\(377\) | 13.6997 | − | 13.6997i | 0.705569 | − | 0.705569i | ||||
\(378\) | 8.87056 | − | 6.44315i | 0.456253 | − | 0.331400i | ||||
\(379\) | − | 22.1421i | − | 1.13737i | −0.822557 | − | 0.568683i | \(-0.807453\pi\) | ||
0.822557 | − | 0.568683i | \(-0.192547\pi\) | |||||||
\(380\) | 1.12132 | + | 15.7782i | 0.0575225 | + | 0.809403i | ||||
\(381\) | − | 6.94269i | − | 0.355685i | ||||||
\(382\) | 7.24264 | + | 7.24264i | 0.370566 | + | 0.370566i | ||||
\(383\) | −10.9008 | − | 10.9008i | −0.557007 | − | 0.557007i | 0.371447 | − | 0.928454i | \(-0.378862\pi\) |
−0.928454 | + | 0.371447i | \(0.878862\pi\) | |||||||
\(384\) | −0.765367 | −0.0390575 | ||||||||
\(385\) | 12.8075 | − | 10.7688i | 0.652731 | − | 0.548831i | ||||
\(386\) | −0.343146 | −0.0174657 | ||||||||
\(387\) | −9.65685 | − | 9.65685i | −0.490885 | − | 0.490885i | ||||
\(388\) | 11.0866 | + | 11.0866i | 0.562835 | + | 0.562835i | ||||
\(389\) | − | 28.1421i | − | 1.42686i | −0.700725 | − | 0.713431i | \(-0.747140\pi\) | ||
0.700725 | − | 0.713431i | \(-0.252860\pi\) | |||||||
\(390\) | −4.49935 | + | 5.18779i | −0.227833 | + | 0.262694i | ||||
\(391\) | − | 7.39104i | − | 0.373781i | ||||||
\(392\) | 3.17637 | + | 6.23784i | 0.160431 | + | 0.315059i | ||||
\(393\) | −9.14214 | + | 9.14214i | −0.461160 | + | 0.461160i | ||||
\(394\) | 4.82843i | 0.243253i | ||||||||
\(395\) | −1.43788 | − | 20.2325i | −0.0723476 | − | 1.01801i | ||||
\(396\) | −6.82843 | −0.343141 | ||||||||
\(397\) | −15.7716 | + | 15.7716i | −0.791554 | + | 0.791554i | −0.981747 | − | 0.190192i | \(-0.939089\pi\) |
0.190192 | + | 0.981747i | \(0.439089\pi\) | |||||||
\(398\) | 11.2723 | + | 11.2723i | 0.565028 | + | 0.565028i | ||||
\(399\) | 14.1480 | + | 2.24264i | 0.708287 | + | 0.112272i | ||||
\(400\) | −4.94975 | + | 0.707107i | −0.247487 | + | 0.0353553i | ||||
\(401\) | −28.2426 | −1.41037 | −0.705185 | − | 0.709023i | \(-0.749136\pi\) | ||||
−0.705185 | + | 0.709023i | \(0.749136\pi\) | |||||||
\(402\) | −4.96362 | + | 4.96362i | −0.247563 | + | 0.247563i | ||||
\(403\) | −10.4853 | + | 10.4853i | −0.522309 | + | 0.522309i | ||||
\(404\) | −11.8519 | −0.589655 | ||||||||
\(405\) | −9.08028 | + | 0.645316i | −0.451203 | + | 0.0320660i | ||||
\(406\) | 2.00000 | − | 12.6173i | 0.0992583 | − | 0.626185i | ||||
\(407\) | −15.3137 | − | 15.3137i | −0.759072 | − | 0.759072i | ||||
\(408\) | −1.17157 | + | 1.17157i | −0.0580015 | + | 0.0580015i | ||||
\(409\) | −23.3324 | −1.15371 | −0.576857 | − | 0.816845i | \(-0.695721\pi\) | ||||
−0.576857 | + | 0.816845i | \(0.695721\pi\) | |||||||
\(410\) | −2.24264 | + | 2.58579i | −0.110756 | + | 0.127703i | ||||
\(411\) | 14.9678i | 0.738306i | ||||||||
\(412\) | 1.97908 | − | 1.97908i | 0.0975020 | − | 0.0975020i | ||||
\(413\) | 8.19192 | − | 5.95021i | 0.403098 | − | 0.292791i | ||||
\(414\) | 8.24264i | 0.405104i | ||||||||
\(415\) | 13.0208 | + | 11.2929i | 0.639167 | + | 0.554346i | ||||
\(416\) | 4.01254i | 0.196731i | ||||||||
\(417\) | −2.75736 | − | 2.75736i | −0.135028 | − | 0.135028i | ||||
\(418\) | −14.1480 | − | 14.1480i | −0.692002 | − | 0.692002i | ||||
\(419\) | 24.2835 | 1.18633 | 0.593163 | − | 0.805082i | \(-0.297879\pi\) | ||||
0.593163 | + | 0.805082i | \(0.297879\pi\) | |||||||
\(420\) | −0.390081 | + | 4.51114i | −0.0190340 | + | 0.220121i | ||||
\(421\) | −21.7990 | −1.06242 | −0.531209 | − | 0.847241i | \(-0.678262\pi\) | ||||
−0.531209 | + | 0.847241i | \(0.678262\pi\) | |||||||
\(422\) | −15.3137 | − | 15.3137i | −0.745460 | − | 0.745460i | ||||
\(423\) | −6.30864 | − | 6.30864i | −0.306737 | − | 0.306737i | ||||
\(424\) | 0.343146i | 0.0166646i | ||||||||
\(425\) | −6.49435 | + | 8.65914i | −0.315022 | + | 0.420030i | ||||
\(426\) | 2.61313i | 0.126606i | ||||||||
\(427\) | −16.0481 | − | 22.0941i | −0.776620 | − | 1.06921i | ||||
\(428\) | −7.65685 | + | 7.65685i | −0.370108 | + | 0.370108i | ||||
\(429\) | − | 8.68629i | − | 0.419378i | ||||||
\(430\) | 12.6173 | − | 0.896683i | 0.608460 | − | 0.0432419i | ||||
\(431\) | −5.65685 | −0.272481 | −0.136241 | − | 0.990676i | \(-0.543502\pi\) | ||||
−0.136241 | + | 0.990676i | \(0.543502\pi\) | |||||||
\(432\) | 2.93015 | − | 2.93015i | 0.140977 | − | 0.140977i | ||||
\(433\) | 4.32957 | + | 4.32957i | 0.208066 | + | 0.208066i | 0.803445 | − | 0.595379i | \(-0.202998\pi\) |
−0.595379 | + | 0.803445i | \(0.702998\pi\) | |||||||
\(434\) | −1.53073 | + | 9.65685i | −0.0734776 | + | 0.463544i | ||||
\(435\) | 5.41421 | − | 6.24264i | 0.259592 | − | 0.299312i | ||||
\(436\) | −16.1421 | −0.773068 | ||||||||
\(437\) | −17.0782 | + | 17.0782i | −0.816960 | + | 0.816960i | ||||
\(438\) | −3.65685 | + | 3.65685i | −0.174731 | + | 0.174731i | ||||
\(439\) | −18.7402 | −0.894422 | −0.447211 | − | 0.894428i | \(-0.647583\pi\) | ||||
−0.447211 | + | 0.894428i | \(0.647583\pi\) | |||||||
\(440\) | 4.14386 | − | 4.77791i | 0.197551 | − | 0.227778i | ||||
\(441\) | −16.0711 | − | 5.22625i | −0.765289 | − | 0.248869i | ||||
\(442\) | 6.14214 | + | 6.14214i | 0.292152 | + | 0.292152i | ||||
\(443\) | 24.1421 | − | 24.1421i | 1.14703 | − | 1.14703i | 0.159893 | − | 0.987134i | \(-0.448885\pi\) |
0.987134 | − | 0.159893i | \(-0.0511150\pi\) | |||||||
\(444\) | 5.86030 | 0.278118 | ||||||||
\(445\) | −37.7990 | + | 2.68629i | −1.79184 | + | 0.127342i | ||||
\(446\) | − | 8.28772i | − | 0.392435i | ||||||
\(447\) | −2.87576 | + | 2.87576i | −0.136019 | + | 0.136019i | ||||
\(448\) | 1.55487 | + | 2.14065i | 0.0734605 | + | 0.101136i | ||||
\(449\) | 14.3431i | 0.676895i | 0.940985 | + | 0.338447i | \(0.109902\pi\) | ||||
−0.940985 | + | 0.338447i | \(0.890098\pi\) | |||||||
\(450\) | 7.24264 | − | 9.65685i | 0.341421 | − | 0.455228i | ||||
\(451\) | − | 4.32957i | − | 0.203871i | ||||||
\(452\) | 6.82843 | + | 6.82843i | 0.321182 | + | 0.321182i | ||||
\(453\) | 1.71644 | + | 1.71644i | 0.0806455 | + | 0.0806455i | ||||
\(454\) | 2.74444 | 0.128803 | ||||||||
\(455\) | 23.6503 | + | 2.04506i | 1.10874 | + | 0.0958737i | ||||
\(456\) | 5.41421 | 0.253544 | ||||||||
\(457\) | 9.65685 | + | 9.65685i | 0.451729 | + | 0.451729i | 0.895928 | − | 0.444199i | \(-0.146512\pi\) |
−0.444199 | + | 0.895928i | \(0.646512\pi\) | |||||||
\(458\) | 5.31911 | + | 5.31911i | 0.248546 | + | 0.248546i | ||||
\(459\) | − | 8.97056i | − | 0.418710i | ||||||
\(460\) | −5.76745 | − | 5.00208i | −0.268909 | − | 0.233223i | ||||
\(461\) | 11.9288i | 0.555582i | 0.960642 | + | 0.277791i | \(0.0896022\pi\) | ||||
−0.960642 | + | 0.277791i | \(0.910398\pi\) | |||||||
\(462\) | −3.36595 | − | 4.63405i | −0.156598 | − | 0.215596i | ||||
\(463\) | 20.9706 | − | 20.9706i | 0.974585 | − | 0.974585i | −0.0251002 | − | 0.999685i | \(-0.507990\pi\) |
0.999685 | + | 0.0251002i | \(0.00799049\pi\) | |||||||
\(464\) | − | 4.82843i | − | 0.224154i | ||||||
\(465\) | −4.14386 | + | 4.77791i | −0.192167 | + | 0.221570i | ||||
\(466\) | 4.24264 | 0.196537 | ||||||||
\(467\) | −13.3442 | + | 13.3442i | −0.617496 | + | 0.617496i | −0.944888 | − | 0.327393i | \(-0.893830\pi\) |
0.327393 | + | 0.944888i | \(0.393830\pi\) | |||||||
\(468\) | −6.84984 | − | 6.84984i | −0.316634 | − | 0.316634i | ||||
\(469\) | 23.9665 | + | 3.79899i | 1.10667 | + | 0.175421i | ||||
\(470\) | 8.24264 | − | 0.585786i | 0.380205 | − | 0.0270203i | ||||
\(471\) | 1.27208 | 0.0586143 | ||||||||
\(472\) | 2.70598 | − | 2.70598i | 0.124553 | − | 0.124553i | ||||
\(473\) | −11.3137 | + | 11.3137i | −0.520205 | + | 0.520205i | ||||
\(474\) | −6.94269 | −0.318889 | ||||||||
\(475\) | 35.0146 | − | 5.00208i | 1.60658 | − | 0.229511i | ||||
\(476\) | 5.65685 | + | 0.896683i | 0.259281 | + | 0.0410994i | ||||
\(477\) | −0.585786 | − | 0.585786i | −0.0268213 | − | 0.0268213i | ||||
\(478\) | −7.41421 | + | 7.41421i | −0.339118 | + | 0.339118i | ||||
\(479\) | −4.59220 | −0.209823 | −0.104912 | − | 0.994482i | \(-0.533456\pi\) | ||||
−0.104912 | + | 0.994482i | \(0.533456\pi\) | |||||||
\(480\) | 0.121320 | + | 1.70711i | 0.00553749 | + | 0.0779184i | ||||
\(481\) | − | 30.7235i | − | 1.40087i | ||||||
\(482\) | −4.14386 | + | 4.14386i | −0.188748 | + | 0.188748i | ||||
\(483\) | −5.59379 | + | 4.06306i | −0.254526 | + | 0.184876i | ||||
\(484\) | − | 3.00000i | − | 0.136364i | ||||||
\(485\) | 22.9706 | − | 26.4853i | 1.04304 | − | 1.20263i | ||||
\(486\) | 15.5474i | 0.705246i | ||||||||
\(487\) | 20.8995 | + | 20.8995i | 0.947047 | + | 0.947047i | 0.998667 | − | 0.0516203i | \(-0.0164385\pi\) |
−0.0516203 | + | 0.998667i | \(0.516439\pi\) | |||||||
\(488\) | −7.29818 | − | 7.29818i | −0.330373 | − | 0.330373i | ||||
\(489\) | −2.53620 | −0.114691 | ||||||||
\(490\) | 13.4096 | − | 8.07349i | 0.605786 | − | 0.364723i | ||||
\(491\) | 30.8284 | 1.39127 | 0.695634 | − | 0.718397i | \(-0.255124\pi\) | ||||
0.695634 | + | 0.718397i | \(0.255124\pi\) | |||||||
\(492\) | 0.828427 | + | 0.828427i | 0.0373484 | + | 0.0373484i | ||||
\(493\) | −7.39104 | − | 7.39104i | −0.332876 | − | 0.332876i | ||||
\(494\) | − | 28.3848i | − | 1.27709i | ||||||
\(495\) | 1.08239 | + | 15.2304i | 0.0486499 | + | 0.684556i | ||||
\(496\) | 3.69552i | 0.165934i | ||||||||
\(497\) | 7.30864 | − | 5.30864i | 0.327837 | − | 0.238125i | ||||
\(498\) | 4.17157 | − | 4.17157i | 0.186933 | − | 0.186933i | ||||
\(499\) | 24.4853i | 1.09611i | 0.836442 | + | 0.548056i | \(0.184632\pi\) | ||||
−0.836442 | + | 0.548056i | \(0.815368\pi\) | |||||||
\(500\) | 2.36176 | + | 10.9280i | 0.105621 | + | 0.488717i | ||||
\(501\) | 12.4853 | 0.557801 | ||||||||
\(502\) | −20.3638 | + | 20.3638i | −0.908881 | + | 0.908881i | ||||
\(503\) | −22.8072 | − | 22.8072i | −1.01692 | − | 1.01692i | −0.999854 | − | 0.0170666i | \(-0.994567\pi\) |
−0.0170666 | − | 0.999854i | \(-0.505433\pi\) | |||||||
\(504\) | −6.30864 | − | 1.00000i | −0.281009 | − | 0.0445435i | ||||
\(505\) | 1.87868 | + | 26.4350i | 0.0836001 | + | 1.17634i | ||||
\(506\) | 9.65685 | 0.429300 | ||||||||
\(507\) | 1.67798 | − | 1.67798i | 0.0745218 | − | 0.0745218i | ||||
\(508\) | −6.41421 | + | 6.41421i | −0.284585 | + | 0.284585i | ||||
\(509\) | 1.66205 | 0.0736691 | 0.0368345 | − | 0.999321i | \(-0.488273\pi\) | ||||
0.0368345 | + | 0.999321i | \(0.488273\pi\) | |||||||
\(510\) | 2.79884 | + | 2.42742i | 0.123935 | + | 0.107488i | ||||
\(511\) | 17.6569 | + | 2.79884i | 0.781093 | + | 0.123813i | ||||
\(512\) | 0.707107 | + | 0.707107i | 0.0312500 | + | 0.0312500i | ||||
\(513\) | −20.7279 | + | 20.7279i | −0.915160 | + | 0.915160i | ||||
\(514\) | 4.59220 | 0.202553 | ||||||||
\(515\) | −4.72792 | − | 4.10051i | −0.208337 | − | 0.180690i | ||||
\(516\) | − | 4.32957i | − | 0.190599i | ||||||
\(517\) | −7.39104 | + | 7.39104i | −0.325057 | + | 0.325057i | ||||
\(518\) | −11.9054 | − | 16.3907i | −0.523092 | − | 0.720164i | ||||
\(519\) | 9.27208i | 0.406999i | ||||||||
\(520\) | 8.94975 | − | 0.636039i | 0.392472 | − | 0.0278922i | ||||
\(521\) | − | 36.8464i | − | 1.61427i | −0.590367 | − | 0.807135i | \(-0.701017\pi\) | ||
0.590367 | − | 0.807135i | \(-0.298983\pi\) | |||||||
\(522\) | 8.24264 | + | 8.24264i | 0.360771 | + | 0.360771i | ||||
\(523\) | −6.84984 | − | 6.84984i | −0.299523 | − | 0.299523i | 0.541304 | − | 0.840827i | \(-0.317931\pi\) |
−0.840827 | + | 0.541304i | \(0.817931\pi\) | |||||||
\(524\) | 16.8925 | 0.737951 | ||||||||
\(525\) | 10.1237 | + | 0.154982i | 0.441833 | + | 0.00676396i | ||||
\(526\) | −23.4558 | −1.02272 | ||||||||
\(527\) | 5.65685 | + | 5.65685i | 0.246416 | + | 0.246416i | ||||
\(528\) | −1.53073 | − | 1.53073i | −0.0666166 | − | 0.0666166i | ||||
\(529\) | 11.3431i | 0.493180i | ||||||||
\(530\) | 0.765367 | − | 0.0543929i | 0.0332454 | − | 0.00236268i | ||||
\(531\) | 9.23880i | 0.400930i | ||||||||
\(532\) | −10.9991 | − | 15.1430i | −0.476873 | − | 0.656532i | ||||
\(533\) | 4.34315 | − | 4.34315i | 0.188123 | − | 0.188123i | ||||
\(534\) | 12.9706i | 0.561291i | ||||||||
\(535\) | 18.2919 | + | 15.8645i | 0.790827 | + | 0.685881i | ||||
\(536\) | 9.17157 | 0.396152 | ||||||||
\(537\) | −1.26810 | + | 1.26810i | −0.0547226 | + | 0.0547226i | ||||
\(538\) | 8.96023 | + | 8.96023i | 0.386303 | + | 0.386303i | ||||
\(539\) | −6.12293 | + | 18.8284i | −0.263733 | + | 0.810998i | ||||
\(540\) | −7.00000 | − | 6.07107i | −0.301232 | − | 0.261257i | ||||
\(541\) | −22.9706 | −0.987582 | −0.493791 | − | 0.869581i | \(-0.664389\pi\) | ||||
−0.493791 | + | 0.869581i | \(0.664389\pi\) | |||||||
\(542\) | 9.81845 | − | 9.81845i | 0.421739 | − | 0.421739i | ||||
\(543\) | −5.48528 | + | 5.48528i | −0.235396 | + | 0.235396i | ||||
\(544\) | 2.16478 | 0.0928144 | ||||||||
\(545\) | 2.55873 | + | 36.0041i | 0.109604 | + | 1.54225i | ||||
\(546\) | 1.27208 | − | 8.02509i | 0.0544399 | − | 0.343442i | ||||
\(547\) | 14.6274 | + | 14.6274i | 0.625423 | + | 0.625423i | 0.946913 | − | 0.321490i | \(-0.104184\pi\) |
−0.321490 | + | 0.946913i | \(0.604184\pi\) | |||||||
\(548\) | 13.8284 | − | 13.8284i | 0.590721 | − | 0.590721i | ||||
\(549\) | 24.9176 | 1.06346 | ||||||||
\(550\) | −11.3137 | − | 8.48528i | −0.482418 | − | 0.361814i | ||||
\(551\) | 34.1563i | 1.45511i | ||||||||
\(552\) | −1.84776 | + | 1.84776i | −0.0786458 | + | 0.0786458i | ||||
\(553\) | 14.1043 | + | 19.4180i | 0.599776 | + | 0.825737i | ||||
\(554\) | − | 14.4853i | − | 0.615421i | ||||||
\(555\) | −0.928932 | − | 13.0711i | −0.0394310 | − | 0.554836i | ||||
\(556\) | 5.09494i | 0.216073i | ||||||||
\(557\) | −1.27208 | − | 1.27208i | −0.0538997 | − | 0.0538997i | 0.679643 | − | 0.733543i | \(-0.262135\pi\) |
−0.733543 | + | 0.679643i | \(0.762135\pi\) | |||||||
\(558\) | −6.30864 | − | 6.30864i | −0.267066 | − | 0.267066i | ||||
\(559\) | −22.6984 | −0.960039 | ||||||||
\(560\) | 4.52814 | − | 3.80736i | 0.191349 | − | 0.160890i | ||||
\(561\) | −4.68629 | −0.197855 | ||||||||
\(562\) | 4.00000 | + | 4.00000i | 0.168730 | + | 0.168730i | ||||
\(563\) | −32.0844 | − | 32.0844i | −1.35220 | − | 1.35220i | −0.883200 | − | 0.468997i | \(-0.844615\pi\) |
−0.468997 | − | 0.883200i | \(-0.655385\pi\) | |||||||
\(564\) | − | 2.82843i | − | 0.119098i | ||||||
\(565\) | 14.1480 | − | 16.3128i | 0.595212 | − | 0.686285i | ||||
\(566\) | 0.317025i | 0.0133256i | ||||||||
\(567\) | 8.71474 | − | 6.32996i | 0.365985 | − | 0.265834i | ||||
\(568\) | 2.41421 | − | 2.41421i | 0.101298 | − | 0.101298i | ||||
\(569\) | − | 1.41421i | − | 0.0592869i | −0.999561 | − | 0.0296435i | \(-0.990563\pi\) | ||
0.999561 | − | 0.0296435i | \(-0.00943719\pi\) | |||||||
\(570\) | −0.858221 | − | 12.0761i | −0.0359469 | − | 0.505812i | ||||
\(571\) | 25.4558 | 1.06529 | 0.532647 | − | 0.846338i | \(-0.321197\pi\) | ||||
0.532647 | + | 0.846338i | \(0.321197\pi\) | |||||||
\(572\) | −8.02509 | + | 8.02509i | −0.335546 | + | 0.335546i | ||||
\(573\) | −5.54328 | − | 5.54328i | −0.231574 | − | 0.231574i | ||||
\(574\) | 0.634051 | − | 4.00000i | 0.0264648 | − | 0.166957i | ||||
\(575\) | −10.2426 | + | 13.6569i | −0.427148 | + | 0.569530i | ||||
\(576\) | −2.41421 | −0.100592 | ||||||||
\(577\) | −4.40649 | + | 4.40649i | −0.183445 | + | 0.183445i | −0.792855 | − | 0.609410i | \(-0.791406\pi\) |
0.609410 | + | 0.792855i | \(0.291406\pi\) | |||||||
\(578\) | −8.70711 | + | 8.70711i | −0.362168 | + | 0.362168i | ||||
\(579\) | 0.262632 | 0.0109146 | ||||||||
\(580\) | −10.7695 | + | 0.765367i | −0.447180 | + | 0.0317801i | ||||
\(581\) | −20.1421 | − | 3.19278i | −0.835637 | − | 0.132459i | ||||
\(582\) | −8.48528 | − | 8.48528i | −0.351726 | − | 0.351726i | ||||
\(583\) | −0.686292 | + | 0.686292i | −0.0284233 | + | 0.0284233i | ||||
\(584\) | 6.75699 | 0.279606 | ||||||||
\(585\) | −14.1924 | + | 16.3640i | −0.586783 | + | 0.676567i | ||||
\(586\) | − | 2.93015i | − | 0.121043i | ||||||
\(587\) | 5.58174 | − | 5.58174i | 0.230383 | − | 0.230383i | −0.582470 | − | 0.812853i | \(-0.697913\pi\) |
0.812853 | + | 0.582470i | \(0.197913\pi\) | |||||||
\(588\) | −2.43109 | − | 4.77424i | −0.100256 | − | 0.196886i | ||||
\(589\) | − | 26.1421i | − | 1.07717i | ||||||
\(590\) | −6.46447 | − | 5.60660i | −0.266138 | − | 0.230820i | ||||
\(591\) | − | 3.69552i | − | 0.152013i | ||||||
\(592\) | −5.41421 | − | 5.41421i | −0.222523 | − | 0.222523i | ||||
\(593\) | 18.6633 | + | 18.6633i | 0.766410 | + | 0.766410i | 0.977473 | − | 0.211063i | \(-0.0676924\pi\) |
−0.211063 | + | 0.977473i | \(0.567692\pi\) | |||||||
\(594\) | 11.7206 | 0.480902 | ||||||||
\(595\) | 1.10332 | − | 12.7594i | 0.0452316 | − | 0.523085i | ||||
\(596\) | 5.31371 | 0.217658 | ||||||||
\(597\) | −8.62742 | − | 8.62742i | −0.353097 | − | 0.353097i | ||||
\(598\) | 9.68714 | + | 9.68714i | 0.396136 | + | 0.396136i | ||||
\(599\) | − | 46.5269i | − | 1.90104i | −0.310666 | − | 0.950519i | \(-0.600552\pi\) | ||
0.310666 | − | 0.950519i | \(-0.399448\pi\) | |||||||
\(600\) | 3.78837 | − | 0.541196i | 0.154660 | − | 0.0220942i | ||||
\(601\) | − | 19.1116i | − | 0.779580i | −0.920904 | − | 0.389790i | \(-0.872548\pi\) | ||
0.920904 | − | 0.389790i | \(-0.127452\pi\) | |||||||
\(602\) | −12.1094 | + | 8.79565i | −0.493541 | + | 0.358484i | ||||
\(603\) | −15.6569 | + | 15.6569i | −0.637596 | + | 0.637596i | ||||
\(604\) | − | 3.17157i | − | 0.129049i | ||||||
\(605\) | −6.69133 | + | 0.475538i | −0.272041 | + | 0.0193334i | ||||
\(606\) | 9.07107 | 0.368487 | ||||||||
\(607\) | −0.262632 | + | 0.262632i | −0.0106599 | + | 0.0106599i | −0.712417 | − | 0.701757i | \(-0.752399\pi\) |
0.701757 | + | 0.712417i | \(0.252399\pi\) | |||||||
\(608\) | −5.00208 | − | 5.00208i | −0.202861 | − | 0.202861i | ||||
\(609\) | −1.53073 | + | 9.65685i | −0.0620285 | + | 0.391315i | ||||
\(610\) | −15.1213 | + | 17.4350i | −0.612244 | + | 0.705924i | ||||
\(611\) | −14.8284 | −0.599894 | ||||||||
\(612\) | −3.69552 | + | 3.69552i | −0.149382 | + | 0.149382i | ||||
\(613\) | 0.100505 | − | 0.100505i | 0.00405936 | − | 0.00405936i | −0.705074 | − | 0.709134i | \(-0.749086\pi\) |
0.709134 | + | 0.705074i | \(0.249086\pi\) | |||||||
\(614\) | 5.91470 | 0.238698 | ||||||||
\(615\) | 1.71644 | − | 1.97908i | 0.0692137 | − | 0.0798040i | ||||
\(616\) | −1.17157 | + | 7.39104i | −0.0472040 | + | 0.297793i | ||||
\(617\) | −11.5147 | − | 11.5147i | −0.463565 | − | 0.463565i | 0.436257 | − | 0.899822i | \(-0.356304\pi\) |
−0.899822 | + | 0.436257i | \(0.856304\pi\) | |||||||
\(618\) | −1.51472 | + | 1.51472i | −0.0609309 | + | 0.0609309i | ||||
\(619\) | −34.9217 | −1.40362 | −0.701811 | − | 0.712363i | \(-0.747625\pi\) | ||||
−0.701811 | + | 0.712363i | \(0.747625\pi\) | |||||||
\(620\) | 8.24264 | − | 0.585786i | 0.331032 | − | 0.0235257i | ||||
\(621\) | − | 14.1480i | − | 0.567741i | ||||||
\(622\) | −16.3128 | + | 16.3128i | −0.654084 | + | 0.654084i | ||||
\(623\) | 36.2773 | − | 26.3501i | 1.45342 | − | 1.05569i | ||||
\(624\) | − | 3.07107i | − | 0.122941i | ||||||
\(625\) | 24.0000 | − | 7.00000i | 0.960000 | − | 0.280000i | ||||
\(626\) | 8.28772i | 0.331244i | ||||||||
\(627\) | 10.8284 | + | 10.8284i | 0.432446 | + | 0.432446i | ||||
\(628\) | −1.17525 | − | 1.17525i | −0.0468975 | − | 0.0468975i | ||||
\(629\) | −16.5754 | −0.660906 | ||||||||
\(630\) | −1.23044 | + | 14.2296i | −0.0490220 | + | 0.566920i | ||||
\(631\) | −29.3553 | −1.16862 | −0.584309 | − | 0.811531i | \(-0.698634\pi\) | ||||
−0.584309 | + | 0.811531i | \(0.698634\pi\) | |||||||
\(632\) | 6.41421 | + | 6.41421i | 0.255144 | + | 0.255144i | ||||
\(633\) | 11.7206 | + | 11.7206i | 0.465852 | + | 0.465852i | ||||
\(634\) | 2.97056i | 0.117976i | ||||||||
\(635\) | 15.3233 | + | 13.2898i | 0.608085 | + | 0.527390i | ||||
\(636\) | − | 0.262632i | − | 0.0104141i | ||||||
\(637\) | −25.0296 | + | 12.7453i | −0.991709 | + | 0.504989i | ||||
\(638\) | 9.65685 | − | 9.65685i | 0.382319 | − | 0.382319i | ||||
\(639\) | 8.24264i | 0.326074i | ||||||||
\(640\) | 1.46508 | − | 1.68925i | 0.0579122 | − | 0.0667733i | ||||
\(641\) | 5.21320 | 0.205909 | 0.102955 | − | 0.994686i | \(-0.467170\pi\) | ||||
0.102955 | + | 0.994686i | \(0.467170\pi\) | |||||||
\(642\) | 5.86030 | − | 5.86030i | 0.231288 | − | 0.231288i | ||||
\(643\) | 27.0439 | + | 27.0439i | 1.06651 | + | 1.06651i | 0.997625 | + | 0.0688814i | \(0.0219430\pi\) |
0.0688814 | + | 0.997625i | \(0.478057\pi\) | |||||||
\(644\) | 8.92177 | + | 1.41421i | 0.351567 | + | 0.0557278i | ||||
\(645\) | −9.65685 | + | 0.686292i | −0.380238 | + | 0.0270227i | ||||
\(646\) | −15.3137 | −0.602510 | ||||||||
\(647\) | 20.7193 | − | 20.7193i | 0.814560 | − | 0.814560i | −0.170754 | − | 0.985314i | \(-0.554620\pi\) |
0.985314 | + | 0.170754i | \(0.0546203\pi\) | |||||||
\(648\) | 2.87868 | − | 2.87868i | 0.113085 | − | 0.113085i | ||||
\(649\) | 10.8239 | 0.424876 | ||||||||
\(650\) | −2.83730 | − | 19.8611i | −0.111288 | − | 0.779016i | ||||
\(651\) | 1.17157 | − | 7.39104i | 0.0459176 | − | 0.289678i | ||||
\(652\) | 2.34315 | + | 2.34315i | 0.0917647 | + | 0.0917647i | ||||
\(653\) | −16.7279 | + | 16.7279i | −0.654614 | + | 0.654614i | −0.954101 | − | 0.299486i | \(-0.903185\pi\) |
0.299486 | + | 0.954101i | \(0.403185\pi\) | |||||||
\(654\) | 12.3547 | 0.483105 | ||||||||
\(655\) | −2.67767 | − | 37.6777i | −0.104625 | − | 1.47219i | ||||
\(656\) | − | 1.53073i | − | 0.0597651i | ||||||
\(657\) | −11.5349 | + | 11.5349i | −0.450019 | + | 0.450019i | ||||
\(658\) | −7.91082 | + | 5.74603i | −0.308396 | + | 0.224004i | ||||
\(659\) | − | 18.3431i | − | 0.714548i | −0.934000 | − | 0.357274i | \(-0.883706\pi\) | ||
0.934000 | − | 0.357274i | \(-0.116294\pi\) | |||||||
\(660\) | −3.17157 | + | 3.65685i | −0.123453 | + | 0.142343i | ||||
\(661\) | 0.208239i | 0.00809958i | 0.999992 | + | 0.00404979i | \(0.00128909\pi\) | ||||
−0.999992 | + | 0.00404979i | \(0.998711\pi\) | |||||||
\(662\) | 0.485281 | + | 0.485281i | 0.0188610 | + | 0.0188610i | ||||
\(663\) | −4.70099 | − | 4.70099i | −0.182571 | − | 0.182571i | ||||
\(664\) | −7.70806 | −0.299131 | ||||||||
\(665\) | −32.0321 | + | 26.9333i | −1.24215 | + | 1.04443i | ||||
\(666\) | 18.4853 | 0.716290 | ||||||||
\(667\) | −11.6569 | − | 11.6569i | −0.451355 | − | 0.451355i | ||||
\(668\) | −11.5349 | − | 11.5349i | −0.446299 | − | 0.446299i | ||||
\(669\) | 6.34315i | 0.245240i | ||||||||
\(670\) | −1.45381 | − | 20.4567i | −0.0561656 | − | 0.790310i | ||||
\(671\) | − | 29.1927i | − | 1.12697i | ||||||
\(672\) | −1.19004 | − | 1.63838i | −0.0459069 | − | 0.0632020i | ||||
\(673\) | 16.7990 | − | 16.7990i | 0.647553 | − | 0.647553i | −0.304848 | − | 0.952401i | \(-0.598606\pi\) |
0.952401 | + | 0.304848i | \(0.0986055\pi\) | |||||||
\(674\) | 17.3137i | 0.666899i | ||||||||
\(675\) | −12.4316 | + | 16.5754i | −0.478492 | + | 0.637989i | ||||
\(676\) | −3.10051 | −0.119250 | ||||||||
\(677\) | 30.7394 | − | 30.7394i | 1.18141 | − | 1.18141i | 0.202032 | − | 0.979379i | \(-0.435246\pi\) |
0.979379 | − | 0.202032i | \(-0.0647545\pi\) | |||||||
\(678\) | −5.22625 | − | 5.22625i | −0.200713 | − | 0.200713i | ||||
\(679\) | −6.49435 | + | 40.9706i | −0.249230 | + | 1.57231i | ||||
\(680\) | −0.343146 | − | 4.82843i | −0.0131590 | − | 0.185162i | ||||
\(681\) | −2.10051 | −0.0804915 | ||||||||
\(682\) | −7.39104 | + | 7.39104i | −0.283017 | + | 0.283017i | ||||
\(683\) | −2.68629 | + | 2.68629i | −0.102788 | + | 0.102788i | −0.756631 | − | 0.653843i | \(-0.773156\pi\) |
0.653843 | + | 0.756631i | \(0.273156\pi\) | |||||||
\(684\) | 17.0782 | 0.653000 | ||||||||
\(685\) | −33.0355 | − | 28.6515i | −1.26222 | − | 1.09472i | ||||
\(686\) | −8.41421 | + | 16.4985i | −0.321256 | + | 0.629916i | ||||
\(687\) | −4.07107 | − | 4.07107i | −0.155321 | − | 0.155321i | ||||
\(688\) | −4.00000 | + | 4.00000i | −0.152499 | + | 0.152499i | ||||
\(689\) | −1.37689 | −0.0524552 | ||||||||
\(690\) | 4.41421 | + | 3.82843i | 0.168046 | + | 0.145746i | ||||
\(691\) | 12.5629i | 0.477915i | 0.971030 | + | 0.238958i | \(0.0768057\pi\) | ||||
−0.971030 | + | 0.238958i | \(0.923194\pi\) | |||||||
\(692\) | 8.56628 | − | 8.56628i | 0.325641 | − | 0.325641i | ||||
\(693\) | −10.6173 | − | 14.6173i | −0.403317 | − | 0.555265i | ||||
\(694\) | 24.4853i | 0.929449i | ||||||||
\(695\) | 11.3640 | − | 0.807612i | 0.431060 | − | 0.0306345i | ||||
\(696\) | 3.69552i | 0.140078i | ||||||||
\(697\) | −2.34315 | − | 2.34315i | −0.0887530 | − | 0.0887530i | ||||
\(698\) | 17.6194 | + | 17.6194i | 0.666903 | + | 0.666903i | ||||
\(699\) | −3.24718 | −0.122819 | ||||||||
\(700\) | −9.20986 | − | 9.49623i | −0.348100 | − | 0.358924i | ||||
\(701\) | 49.1127 | 1.85496 | 0.927481 | − | 0.373872i | \(-0.121970\pi\) | ||||
0.927481 | + | 0.373872i | \(0.121970\pi\) | |||||||
\(702\) | 11.7574 | + | 11.7574i | 0.443753 | + | 0.443753i | ||||
\(703\) | 38.3002 | + | 38.3002i | 1.44452 | + | 1.44452i | ||||
\(704\) | 2.82843i | 0.106600i | ||||||||
\(705\) | −6.30864 | + | 0.448342i | −0.237597 | + | 0.0168855i | ||||
\(706\) | 8.02509i | 0.302028i | ||||||||
\(707\) | −18.4281 | − | 25.3708i | −0.693062 | − | 0.954169i | ||||
\(708\) | −2.07107 | + | 2.07107i | −0.0778355 | + | 0.0778355i | ||||
\(709\) | − | 18.6863i | − | 0.701778i | −0.936417 | − | 0.350889i | \(-0.885879\pi\) | ||
0.936417 | − | 0.350889i | \(-0.114121\pi\) | |||||||
\(710\) | −5.76745 | − | 5.00208i | −0.216448 | − | 0.187725i | ||||
\(711\) | −21.8995 | −0.821295 | ||||||||
\(712\) | 11.9832 | − | 11.9832i | 0.449091 | − | 0.449091i | ||||
\(713\) | 8.92177 | + | 8.92177i | 0.334123 | + | 0.334123i | ||||
\(714\) | −4.32957 | − | 0.686292i | −0.162030 | − | 0.0256838i | ||||
\(715\) | 19.1716 | + | 16.6274i | 0.716976 | + | 0.621830i | ||||
\(716\) | 2.34315 | 0.0875675 | ||||||||
\(717\) | 5.67459 | − | 5.67459i | 0.211922 | − | 0.211922i | ||||
\(718\) | −12.0000 | + | 12.0000i | −0.447836 | + | 0.447836i | ||||
\(719\) | 9.44703 | 0.352315 | 0.176157 | − | 0.984362i | \(-0.443633\pi\) | ||||
0.176157 | + | 0.984362i | \(0.443633\pi\) | |||||||
\(720\) | 0.382683 | + | 5.38476i | 0.0142618 | + | 0.200678i | ||||
\(721\) | 7.31371 | + | 1.15932i | 0.272377 | + | 0.0431752i | ||||
\(722\) | 21.9497 | + | 21.9497i | 0.816885 | + | 0.816885i | ||||
\(723\) | 3.17157 | − | 3.17157i | 0.117952 | − | 0.117952i | ||||
\(724\) | 10.1355 | 0.376682 | ||||||||
\(725\) | 3.41421 | + | 23.8995i | 0.126801 | + | 0.887605i | ||||
\(726\) | 2.29610i | 0.0852163i | ||||||||
\(727\) | 18.6633 | − | 18.6633i | 0.692183 | − | 0.692183i | −0.270528 | − | 0.962712i | \(-0.587198\pi\) |
0.962712 | + | 0.270528i | \(0.0871984\pi\) | |||||||
\(728\) | −8.58946 | + | 6.23897i | −0.318347 | + | 0.231231i | ||||
\(729\) | 0.313708i | 0.0116188i | ||||||||
\(730\) | −1.07107 | − | 15.0711i | −0.0396420 | − | 0.557805i | ||||
\(731\) | 12.2459i | 0.452930i | ||||||||
\(732\) | 5.58579 | + | 5.58579i | 0.206457 | + | 0.206457i | ||||
\(733\) | 12.3387 | + | 12.3387i | 0.455741 | + | 0.455741i | 0.897255 | − | 0.441513i | \(-0.145558\pi\) |
−0.441513 | + | 0.897255i | \(0.645558\pi\) | |||||||
\(734\) | −10.4525 | −0.385809 | ||||||||
\(735\) | −10.2633 | + | 6.17918i | −0.378568 | + | 0.227923i | ||||
\(736\) | 3.41421 | 0.125850 | ||||||||
\(737\) | 18.3431 | + | 18.3431i | 0.675678 | + | 0.675678i | ||||
\(738\) | 2.61313 | + | 2.61313i | 0.0961905 | + | 0.0961905i | ||||
\(739\) | 1.65685i | 0.0609484i | 0.999536 | + | 0.0304742i | \(0.00970174\pi\) | ||||
−0.999536 | + | 0.0304742i | \(0.990298\pi\) | |||||||
\(740\) | −11.2179 | + | 12.9343i | −0.412377 | + | 0.475475i | ||||
\(741\) | 21.7248i | 0.798079i | ||||||||
\(742\) | −0.734556 | + | 0.533546i | −0.0269664 | + | 0.0195871i | ||||
\(743\) | −21.0416 | + | 21.0416i | −0.771943 | + | 0.771943i | −0.978446 | − | 0.206503i | \(-0.933792\pi\) |
0.206503 | + | 0.978446i | \(0.433792\pi\) | |||||||
\(744\) | − | 2.82843i | − | 0.103695i | ||||||
\(745\) | −0.842290 | − | 11.8519i | −0.0308591 | − | 0.434221i | ||||
\(746\) | −1.31371 | −0.0480983 | ||||||||
\(747\) | 13.1585 | − | 13.1585i | 0.481444 | − | 0.481444i | ||||
\(748\) | 4.32957 | + | 4.32957i | 0.158305 | + | 0.158305i | ||||
\(749\) | −28.2960 | − | 4.48528i | −1.03391 | − | 0.163889i | ||||
\(750\) | −1.80761 | − | 8.36396i | −0.0660047 | − | 0.305409i | ||||
\(751\) | 14.4853 | 0.528575 | 0.264288 | − | 0.964444i | \(-0.414863\pi\) | ||||
0.264288 | + | 0.964444i | \(0.414863\pi\) | |||||||
\(752\) | −2.61313 | + | 2.61313i | −0.0952909 | + | 0.0952909i | ||||
\(753\) | 15.5858 | − | 15.5858i | 0.567978 | − | 0.567978i | ||||
\(754\) | 19.3743 | 0.705569 | ||||||||
\(755\) | −7.07401 | + | 0.502734i | −0.257450 | + | 0.0182964i | ||||
\(756\) | 10.8284 | + | 1.71644i | 0.393826 | + | 0.0624264i | ||||
\(757\) | −11.8995 | − | 11.8995i | −0.432494 | − | 0.432494i | 0.456982 | − | 0.889476i | \(-0.348931\pi\) |
−0.889476 | + | 0.456982i | \(0.848931\pi\) | |||||||
\(758\) | 15.6569 | − | 15.6569i | 0.568683 | − | 0.568683i | ||||
\(759\) | −7.39104 | −0.268278 | ||||||||
\(760\) | −10.3640 | + | 11.9497i | −0.375940 | + | 0.433463i | ||||
\(761\) | − | 32.3630i | − | 1.17316i | −0.809892 | − | 0.586579i | \(-0.800475\pi\) | ||
0.809892 | − | 0.586579i | \(-0.199525\pi\) | |||||||
\(762\) | 4.90923 | − | 4.90923i | 0.177843 | − | 0.177843i | ||||
\(763\) | −25.0989 | − | 34.5547i | −0.908640 | − | 1.25096i | ||||
\(764\) | 10.2426i | 0.370566i | ||||||||
\(765\) | 8.82843 | + | 7.65685i | 0.319192 | + | 0.276834i | ||||
\(766\) | − | 15.4161i | − | 0.557007i | ||||||
\(767\) | 10.8579 | + | 10.8579i | 0.392055 | + | 0.392055i | ||||
\(768\) | −0.541196 | − | 0.541196i | −0.0195287 | − | 0.0195287i | ||||
\(769\) | −20.2710 | −0.730989 | −0.365495 | − | 0.930813i | \(-0.619100\pi\) | ||||
−0.365495 | + | 0.930813i | \(0.619100\pi\) | |||||||
\(770\) | 16.6710 | + | 1.44155i | 0.600781 | + | 0.0519500i | ||||
\(771\) | −3.51472 | −0.126579 | ||||||||
\(772\) | −0.242641 | − | 0.242641i | −0.00873283 | − | 0.00873283i | ||||
\(773\) | 1.49227 | + | 1.49227i | 0.0536733 | + | 0.0536733i | 0.733434 | − | 0.679761i | \(-0.237916\pi\) |
−0.679761 | + | 0.733434i | \(0.737916\pi\) | |||||||
\(774\) | − | 13.6569i | − | 0.490885i | ||||||
\(775\) | −2.61313 | − | 18.2919i | −0.0938663 | − | 0.657064i | ||||
\(776\) | 15.6788i | 0.562835i | ||||||||
\(777\) | 9.11198 | + | 12.5449i | 0.326891 | + | 0.450045i | ||||
\(778\) | 19.8995 | − | 19.8995i | 0.713431 | − | 0.713431i | ||||
\(779\) | 10.8284i | 0.387969i | ||||||||
\(780\) | −6.84984 | + | 0.486803i | −0.245264 | + | 0.0174303i | ||||
\(781\) | 9.65685 | 0.345549 | ||||||||
\(782\) | 5.22625 | − | 5.22625i | 0.186890 | − | 0.186890i | ||||
\(783\) | −14.1480 | − | 14.1480i | −0.505609 | − | 0.505609i | ||||
\(784\) | −2.16478 | + | 6.65685i | −0.0773137 | + | 0.237745i | ||||
\(785\) | −2.43503 | + | 2.80761i | −0.0869099 | + | 0.100208i | ||||
\(786\) | −12.9289 | −0.461160 | ||||||||
\(787\) | −3.97408 | + | 3.97408i | −0.141661 | + | 0.141661i | −0.774381 | − | 0.632720i | \(-0.781938\pi\) |
0.632720 | + | 0.774381i | \(0.281938\pi\) | |||||||
\(788\) | −3.41421 | + | 3.41421i | −0.121626 | + | 0.121626i | ||||
\(789\) | 17.9523 | 0.639120 | ||||||||
\(790\) | 13.2898 | − | 15.3233i | 0.472830 | − | 0.545177i | ||||
\(791\) | −4.00000 | + | 25.2346i | −0.142224 | + | 0.897238i | ||||
\(792\) | −4.82843 | − | 4.82843i | −0.171571 | − | 0.171571i | ||||
\(793\) | 29.2843 | − | 29.2843i | 1.03991 | − | 1.03991i | ||||
\(794\) | −22.3044 | −0.791554 | ||||||||
\(795\) | −0.585786 | + | 0.0416306i | −0.0207757 | + | 0.00147648i | ||||
\(796\) | 15.9414i | 0.565028i | ||||||||
\(797\) | −11.4964 | + | 11.4964i | −0.407225 | + | 0.407225i | −0.880770 | − | 0.473545i | \(-0.842974\pi\) |
0.473545 | + | 0.880770i | \(0.342974\pi\) | |||||||
\(798\) | 8.41838 | + | 11.5899i | 0.298007 | + | 0.410280i | ||||
\(799\) | 8.00000i | 0.283020i | ||||||||
\(800\) | −4.00000 | − | 3.00000i | −0.141421 | − | 0.106066i | ||||
\(801\) | 40.9133i | 1.44560i | ||||||||
\(802\) | −19.9706 | − | 19.9706i | −0.705185 | − | 0.705185i | ||||
\(803\) | 13.5140 | + | 13.5140i | 0.476898 | + | 0.476898i | ||||
\(804\) | −7.01962 | −0.247563 | ||||||||
\(805\) | 1.74011 | − | 20.1237i | 0.0613308 | − | 0.709266i | ||||
\(806\) | −14.8284 | −0.522309 | ||||||||
\(807\) | −6.85786 | − | 6.85786i | −0.241408 | − | 0.241408i | ||||
\(808\) | −8.38057 | − | 8.38057i | −0.294828 | − | 0.294828i | ||||
\(809\) | 14.1005i | 0.495747i | 0.968792 | + | 0.247874i | \(0.0797318\pi\) | ||||
−0.968792 | + | 0.247874i | \(0.920268\pi\) | |||||||
\(810\) | −6.87704 | − | 5.96442i | −0.241634 | − | 0.209568i | ||||
\(811\) | 7.18280i | 0.252222i | 0.992016 | + | 0.126111i | \(0.0402496\pi\) | ||||
−0.992016 | + | 0.126111i | \(0.959750\pi\) | |||||||
\(812\) | 10.3360 | − | 7.50756i | 0.362722 | − | 0.263464i | ||||
\(813\) | −7.51472 | + | 7.51472i | −0.263553 | + | 0.263553i | ||||
\(814\) | − | 21.6569i | − | 0.759072i | ||||||
\(815\) | 4.85483 | − | 5.59767i | 0.170057 | − | 0.196078i | ||||
\(816\) | −1.65685 | −0.0580015 | ||||||||
\(817\) | 28.2960 | − | 28.2960i | 0.989953 | − | 0.989953i | ||||
\(818\) | −16.4985 | − | 16.4985i | −0.576857 | − | 0.576857i | ||||
\(819\) | 4.01254 | − | 25.3137i | 0.140210 | − | 0.884533i | ||||
\(820\) | −3.41421 | + | 0.242641i | −0.119230 | + | 0.00847338i | ||||
\(821\) | −17.5147 | −0.611268 | −0.305634 | − | 0.952149i | \(-0.598868\pi\) | ||||
−0.305634 | + | 0.952149i | \(0.598868\pi\) | |||||||
\(822\) | −10.5838 | + | 10.5838i | −0.369153 | + | 0.369153i | ||||
\(823\) | −13.6569 | + | 13.6569i | −0.476048 | + | 0.476048i | −0.903865 | − | 0.427817i | \(-0.859283\pi\) |
0.427817 | + | 0.903865i | \(0.359283\pi\) | |||||||
\(824\) | 2.79884 | 0.0975020 | ||||||||
\(825\) | 8.65914 | + | 6.49435i | 0.301472 | + | 0.226104i | ||||
\(826\) | 10.0000 | + | 1.58513i | 0.347945 | + | 0.0551536i | ||||
\(827\) | −24.4853 | − | 24.4853i | −0.851437 | − | 0.851437i | 0.138873 | − | 0.990310i | \(-0.455652\pi\) |
−0.990310 | + | 0.138873i | \(0.955652\pi\) | |||||||
\(828\) | −5.82843 | + | 5.82843i | −0.202552 | + | 0.202552i | ||||
\(829\) | 30.7009 | 1.06629 | 0.533144 | − | 0.846025i | \(-0.321011\pi\) | ||||
0.533144 | + | 0.846025i | \(0.321011\pi\) | |||||||
\(830\) | 1.22183 | + | 17.1924i | 0.0424102 | + | 0.596757i | ||||
\(831\) | 11.0866i | 0.384588i | ||||||||
\(832\) | −2.83730 | + | 2.83730i | −0.0983656 | + | 0.0983656i | ||||
\(833\) | 6.87616 | + | 13.5036i | 0.238245 | + | 0.467871i | ||||
\(834\) | − | 3.89949i | − | 0.135028i | ||||||
\(835\) | −23.8995 | + | 27.5563i | −0.827076 | + | 0.953627i | ||||
\(836\) | − | 20.0083i | − | 0.692002i | ||||||
\(837\) | 10.8284 | + | 10.8284i | 0.374285 | + | 0.374285i | ||||
\(838\) | 17.1710 | + | 17.1710i | 0.593163 | + | 0.593163i | ||||
\(839\) | −12.8799 | −0.444664 | −0.222332 | − | 0.974971i | \(-0.571367\pi\) | ||||
−0.222332 | + | 0.974971i | \(0.571367\pi\) | |||||||
\(840\) | −3.46569 | + | 2.91403i | −0.119577 | + | 0.100543i | ||||
\(841\) | 5.68629 | 0.196079 | ||||||||
\(842\) | −15.4142 | − | 15.4142i | −0.531209 | − | 0.531209i | ||||
\(843\) | −3.06147 | − | 3.06147i | −0.105443 | − | 0.105443i | ||||
\(844\) | − | 21.6569i | − | 0.745460i | ||||||
\(845\) | 0.491469 | + | 6.91550i | 0.0169071 | + | 0.237900i | ||||
\(846\) | − | 8.92177i | − | 0.306737i | ||||||
\(847\) | 6.42196 | − | 4.66460i | 0.220661 | − | 0.160277i | ||||
\(848\) | −0.242641 | + | 0.242641i | −0.00833232 | + | 0.00833232i | ||||
\(849\) | − | 0.242641i | − | 0.00832741i | ||||||
\(850\) | −10.7151 | + | 1.53073i | −0.367526 | + | 0.0525037i | ||||
\(851\) | −26.1421 | −0.896141 | ||||||||
\(852\) | −1.84776 | + | 1.84776i | −0.0633032 | + | 0.0633032i | ||||
\(853\) | 16.4826 | + | 16.4826i | 0.564353 | + | 0.564353i | 0.930541 | − | 0.366188i | \(-0.119337\pi\) |
−0.366188 | + | 0.930541i | \(0.619337\pi\) | |||||||
\(854\) | 4.27518 | − | 26.9706i | 0.146294 | − | 0.922914i | ||||
\(855\) | −2.70711 | − | 38.0919i | −0.0925811 | − | 1.30271i | ||||
\(856\) | −10.8284 | −0.370108 | ||||||||
\(857\) | 35.0530 | − | 35.0530i | 1.19739 | − | 1.19739i | 0.222443 | − | 0.974946i | \(-0.428597\pi\) |
0.974946 | − | 0.222443i | \(-0.0714031\pi\) | |||||||
\(858\) | 6.14214 | − | 6.14214i | 0.209689 | − | 0.209689i | ||||
\(859\) | −45.9313 | −1.56716 | −0.783579 | − | 0.621293i | \(-0.786608\pi\) | ||||
−0.783579 | + | 0.621293i | \(0.786608\pi\) | |||||||
\(860\) | 9.55582 | + | 8.28772i | 0.325851 | + | 0.282609i | ||||
\(861\) | −0.485281 | + | 3.06147i | −0.0165383 | + | 0.104335i | ||||
\(862\) | −4.00000 | − | 4.00000i | −0.136241 | − | 0.136241i | ||||
\(863\) | −33.5563 | + | 33.5563i | −1.14227 | + | 1.14227i | −0.154238 | + | 0.988034i | \(0.549292\pi\) |
−0.988034 | + | 0.154238i | \(0.950708\pi\) | |||||||
\(864\) | 4.14386 | 0.140977 | ||||||||
\(865\) | −20.4645 | − | 17.7487i | −0.695813 | − | 0.603475i | ||||
\(866\) | 6.12293i | 0.208066i | ||||||||
\(867\) | 6.66413 | − | 6.66413i | 0.226326 | − | 0.226326i | ||||
\(868\) | −7.91082 | + | 5.74603i | −0.268511 | + | 0.195033i | ||||
\(869\) | 25.6569i | 0.870349i | ||||||||
\(870\) | 8.24264 | − | 0.585786i | 0.279452 | − | 0.0198600i | ||||
\(871\) | 36.8013i | 1.24697i | ||||||||
\(872\) | −11.4142 | − | 11.4142i | −0.386534 | − | 0.386534i | ||||
\(873\) | −26.7653 | − | 26.7653i | −0.905868 | − | 0.905868i | ||||
\(874\) | −24.1522 | −0.816960 | ||||||||
\(875\) | −19.7209 | + | 22.0473i | −0.666689 | + | 0.745336i | ||||
\(876\) | −5.17157 | −0.174731 | ||||||||
\(877\) | 9.55635 | + | 9.55635i | 0.322695 | + | 0.322695i | 0.849800 | − | 0.527105i | \(-0.176723\pi\) |
−0.527105 | + | 0.849800i | \(0.676723\pi\) | |||||||
\(878\) | −13.2513 | − | 13.2513i | −0.447211 | − | 0.447211i | ||||
\(879\) | 2.24264i | 0.0756424i | ||||||||
\(880\) | 6.30864 | − | 0.448342i | 0.212664 | − | 0.0151136i | ||||
\(881\) | − | 11.7206i | − | 0.394877i | −0.980315 | − | 0.197439i | \(-0.936738\pi\) | ||
0.980315 | − | 0.197439i | \(-0.0632623\pi\) | |||||||
\(882\) | −7.66844 | − | 15.0595i | −0.258210 | − | 0.507079i | ||||
\(883\) | −23.1716 | + | 23.1716i | −0.779786 | + | 0.779786i | −0.979794 | − | 0.200009i | \(-0.935903\pi\) |
0.200009 | + | 0.979794i | \(0.435903\pi\) | |||||||
\(884\) | 8.68629i | 0.292152i | ||||||||
\(885\) | 4.94769 | + | 4.29111i | 0.166315 | + | 0.144244i | ||||
\(886\) | 34.1421 | 1.14703 | ||||||||
\(887\) | −41.6243 | + | 41.6243i | −1.39761 | + | 1.39761i | −0.590760 | + | 0.806847i | \(0.701172\pi\) |
−0.806847 | + | 0.590760i | \(0.798828\pi\) | |||||||
\(888\) | 4.14386 | + | 4.14386i | 0.139059 | + | 0.139059i | ||||
\(889\) | −23.7038 | − | 3.75736i | −0.795001 | − | 0.126018i | ||||
\(890\) | −28.6274 | − | 24.8284i | −0.959593 | − | 0.832251i | ||||
\(891\) | 11.5147 | 0.385758 | ||||||||
\(892\) | 5.86030 | − | 5.86030i | 0.196217 | − | 0.196217i | ||||
\(893\) | 18.4853 | − | 18.4853i | 0.618586 | − | 0.618586i | ||||
\(894\) | −4.06694 | −0.136019 | ||||||||
\(895\) | −0.371418 | − | 5.22625i | −0.0124151 | − | 0.174694i | ||||
\(896\) | −0.414214 | + | 2.61313i | −0.0138379 | + | 0.0872984i | ||||
\(897\) | −7.41421 | − | 7.41421i | −0.247553 | − | 0.247553i | ||||
\(898\) | −10.1421 | + | 10.1421i | −0.338447 | + | 0.338447i | ||||
\(899\) | 17.8435 | 0.595115 | ||||||||
\(900\) | 11.9497 | − | 1.70711i | 0.398325 | − | 0.0569036i | ||||
\(901\) | 0.742837i | 0.0247475i | ||||||||
\(902\) | 3.06147 | − | 3.06147i | 0.101936 | − | 0.101936i | ||||
\(903\) | 9.26810 | − | 6.73190i | 0.308423 | − | 0.224024i | ||||
\(904\) | 9.65685i | 0.321182i | ||||||||
\(905\) | −1.60660 | − | 22.6066i | −0.0534052 | − | 0.751469i | ||||
\(906\) | 2.42742i | 0.0806455i | ||||||||
\(907\) | 16.8284 | + | 16.8284i | 0.558779 | + | 0.558779i | 0.928960 | − | 0.370181i | \(-0.120704\pi\) |
−0.370181 | + | 0.928960i | \(0.620704\pi\) | |||||||
\(908\) | 1.94061 | + | 1.94061i | 0.0644015 | + | 0.0644015i | ||||
\(909\) | 28.6131 | 0.949036 | ||||||||
\(910\) | 15.2772 | + | 18.1693i | 0.506434 | + | 0.602308i | ||||
\(911\) | 0.142136 | 0.00470916 | 0.00235458 | − | 0.999997i | \(-0.499251\pi\) | ||||
0.00235458 | + | 0.999997i | \(0.499251\pi\) | |||||||
\(912\) | 3.82843 | + | 3.82843i | 0.126772 | + | 0.126772i | ||||
\(913\) | −15.4161 | − | 15.4161i | −0.510199 | − | 0.510199i | ||||
\(914\) | 13.6569i | 0.451729i | ||||||||
\(915\) | 11.5734 | − | 13.3442i | 0.382603 | − | 0.441145i | ||||
\(916\) | 7.52235i | 0.248546i | ||||||||
\(917\) | 26.2655 | + | 36.1609i | 0.867364 | + | 1.19414i | ||||
\(918\) | 6.34315 | − | 6.34315i | 0.209355 | − | 0.209355i | ||||
\(919\) | − | 28.3848i | − | 0.936327i | −0.883642 | − | 0.468164i | \(-0.844916\pi\) | ||
0.883642 | − | 0.468164i | \(-0.155084\pi\) | |||||||
\(920\) | −0.541196 | − | 7.61521i | −0.0178427 | − | 0.251066i | ||||
\(921\) | −4.52691 | −0.149167 | ||||||||
\(922\) | −8.43497 | + | 8.43497i | −0.277791 | + | 0.277791i | ||||
\(923\) | 9.68714 | + | 9.68714i | 0.318856 | + | 0.318856i | ||||
\(924\) | 0.896683 | − | 5.65685i | 0.0294987 | − | 0.186097i | ||||
\(925\) | 30.6274 | + | 22.9706i | 1.00702 | + | 0.755267i | ||||
\(926\) | 29.6569 | 0.974585 | ||||||||
\(927\) | −4.77791 | + | 4.77791i | −0.156927 | + | 0.156927i | ||||
\(928\) | 3.41421 | − | 3.41421i | 0.112077 | − | 0.112077i | ||||
\(929\) | −13.7766 | −0.451996 | −0.225998 | − | 0.974128i | \(-0.572564\pi\) | ||||
−0.225998 | + | 0.974128i | \(0.572564\pi\) | |||||||
\(930\) | −6.30864 | + | 0.448342i | −0.206869 | + | 0.0147017i | ||||
\(931\) | 15.3137 | − | 47.0907i | 0.501887 | − | 1.54333i | ||||
\(932\) | 3.00000 | + | 3.00000i | 0.0982683 | + | 0.0982683i | ||||
\(933\) | 12.4853 | − | 12.4853i | 0.408750 | − | 0.408750i | ||||
\(934\) | −18.8715 | −0.617496 | ||||||||
\(935\) | 8.97056 | − | 10.3431i | 0.293369 | − | 0.338257i | ||||
\(936\) | − | 9.68714i | − | 0.316634i | ||||||
\(937\) | −35.5014 | + | 35.5014i | −1.15978 | + | 1.15978i | −0.175256 | + | 0.984523i | \(0.556075\pi\) |
−0.984523 | + | 0.175256i | \(0.943925\pi\) | |||||||
\(938\) | 14.2606 | + | 19.6331i | 0.465624 | + | 0.641045i | ||||
\(939\) | − | 6.34315i | − | 0.207001i | ||||||
\(940\) | 6.24264 | + | 5.41421i | 0.203612 | + | 0.176592i | ||||
\(941\) | − | 37.7975i | − | 1.23216i | −0.787683 | − | 0.616081i | \(-0.788719\pi\) | ||
0.787683 | − | 0.616081i | \(-0.211281\pi\) | |||||||
\(942\) | 0.899495 | + | 0.899495i | 0.0293071 | + | 0.0293071i | ||||
\(943\) | −3.69552 | − | 3.69552i | −0.120343 | − | 0.120343i | ||||
\(944\) | 3.82683 | 0.124553 | ||||||||
\(945\) | 2.11198 | − | 24.4243i | 0.0687029 | − | 0.794521i | ||||
\(946\) | −16.0000 | −0.520205 | ||||||||
\(947\) | −10.9706 | − | 10.9706i | −0.356495 | − | 0.356495i | 0.506024 | − | 0.862519i | \(-0.331115\pi\) |
−0.862519 | + | 0.506024i | \(0.831115\pi\) | |||||||
\(948\) | −4.90923 | − | 4.90923i | −0.159444 | − | 0.159444i | ||||
\(949\) | 27.1127i | 0.880115i | ||||||||
\(950\) | 28.2960 | + | 21.2220i | 0.918045 | + | 0.688534i | ||||
\(951\) | − | 2.27357i | − | 0.0737256i | ||||||
\(952\) | 3.36595 | + | 4.63405i | 0.109091 | + | 0.150190i | ||||
\(953\) | −5.14214 | + | 5.14214i | −0.166570 | + | 0.166570i | −0.785470 | − | 0.618900i | \(-0.787579\pi\) |
0.618900 | + | 0.785470i | \(0.287579\pi\) | |||||||
\(954\) | − | 0.828427i | − | 0.0268213i | ||||||
\(955\) | 22.8456 | − | 1.62359i | 0.739267 | − | 0.0525381i | ||||
\(956\) | −10.4853 | −0.339118 | ||||||||
\(957\) | −7.39104 | + | 7.39104i | −0.238918 | + | 0.238918i | ||||
\(958\) | −3.24718 | − | 3.24718i | −0.104912 | − | 0.104912i | ||||
\(959\) | 51.1032 | + | 8.10051i | 1.65021 | + | 0.261579i | ||||
\(960\) | −1.12132 | + | 1.29289i | −0.0361905 | + | 0.0417279i | ||||
\(961\) | 17.3431 | 0.559456 | ||||||||
\(962\) | 21.7248 | − | 21.7248i | 0.700435 | − | 0.700435i | ||||
\(963\) | 18.4853 | − | 18.4853i | 0.595680 | − | 0.595680i | ||||
\(964\) | −5.86030 | −0.188748 | ||||||||
\(965\) | −0.502734 | + | 0.579658i | −0.0161836 | + | 0.0186598i | ||||
\(966\) | −6.82843 | − | 1.08239i | −0.219701 | − | 0.0348254i | ||||
\(967\) | 40.2132 | + | 40.2132i | 1.29317 | + | 1.29317i | 0.932816 | + | 0.360354i | \(0.117344\pi\) |
0.360354 | + | 0.932816i | \(0.382656\pi\) | |||||||
\(968\) | 2.12132 | − | 2.12132i | 0.0681818 | − | 0.0681818i | ||||
\(969\) | 11.7206 | 0.376520 | ||||||||
\(970\) | 34.9706 | − | 2.48528i | 1.12284 | − | 0.0797976i | ||||
\(971\) | 33.6536i | 1.08000i | 0.841666 | + | 0.539998i | \(0.181575\pi\) | ||||
−0.841666 | + | 0.539998i | \(0.818425\pi\) | |||||||
\(972\) | −10.9937 | + | 10.9937i | −0.352623 | + | 0.352623i | ||||
\(973\) | −10.9065 | + | 7.92194i | −0.349646 | + | 0.253966i | ||||
\(974\) | 29.5563i | 0.947047i | ||||||||
\(975\) | 2.17157 | + | 15.2010i | 0.0695460 | + | 0.486822i | ||||
\(976\) | − | 10.3212i | − | 0.330373i | ||||||
\(977\) | −20.1716 | − | 20.1716i | −0.645346 | − | 0.645346i | 0.306519 | − | 0.951865i | \(-0.400836\pi\) |
−0.951865 | + | 0.306519i | \(0.900836\pi\) | |||||||
\(978\) | −1.79337 | − | 1.79337i | −0.0573455 | − | 0.0573455i | ||||
\(979\) | 47.9329 | 1.53194 | ||||||||
\(980\) | 15.1909 | + | 3.77323i | 0.485255 | + | 0.120531i | ||||
\(981\) | 38.9706 | 1.24423 | ||||||||
\(982\) | 21.7990 | + | 21.7990i | 0.695634 | + | 0.695634i | ||||
\(983\) | −11.9063 | − | 11.9063i | −0.379752 | − | 0.379752i | 0.491260 | − | 0.871013i | \(-0.336536\pi\) |
−0.871013 | + | 0.491260i | \(0.836536\pi\) | |||||||
\(984\) | 1.17157i | 0.0373484i | ||||||||
\(985\) | 8.15640 | + | 7.07401i | 0.259885 | + | 0.225397i | ||||
\(986\) | − | 10.4525i | − | 0.332876i | ||||||
\(987\) | 6.05468 | − | 4.39782i | 0.192723 | − | 0.139984i | ||||
\(988\) | 20.0711 | − | 20.0711i | 0.638546 | − | 0.638546i | ||||
\(989\) | 19.3137i | 0.614140i | ||||||||
\(990\) | −10.0042 | + | 11.5349i | −0.317953 | + | 0.366603i | ||||
\(991\) | −35.4142 | −1.12497 | −0.562485 | − | 0.826808i | \(-0.690155\pi\) | ||||
−0.562485 | + | 0.826808i | \(0.690155\pi\) | |||||||
\(992\) | −2.61313 | + | 2.61313i | −0.0829668 | + | 0.0829668i | ||||
\(993\) | −0.371418 | − | 0.371418i | −0.0117866 | − | 0.0117866i | ||||
\(994\) | 8.92177 | + | 1.41421i | 0.282981 | + | 0.0448561i | ||||
\(995\) | 35.5563 | − | 2.52691i | 1.12721 | − | 0.0801085i | ||||
\(996\) | 5.89949 | 0.186933 | ||||||||
\(997\) | −38.0760 | + | 38.0760i | −1.20588 | + | 1.20588i | −0.233531 | + | 0.972349i | \(0.575028\pi\) |
−0.972349 | + | 0.233531i | \(0.924972\pi\) | |||||||
\(998\) | −17.3137 | + | 17.3137i | −0.548056 | + | 0.548056i | ||||
\(999\) | −31.7289 | −1.00386 |
(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 | 70.2.g.a.27.3 | yes | 8 | |
3.2 | odd | 2 | 630.2.p.a.307.1 | 8 | |||
4.3 | odd | 2 | 560.2.bj.c.97.3 | 8 | |||
5.2 | odd | 4 | 350.2.g.a.293.1 | 8 | |||
5.3 | odd | 4 | inner | 70.2.g.a.13.4 | yes | 8 | |
5.4 | even | 2 | 350.2.g.a.307.2 | 8 | |||
7.2 | even | 3 | 490.2.l.a.227.4 | 16 | |||
7.3 | odd | 6 | 490.2.l.a.117.2 | 16 | |||
7.4 | even | 3 | 490.2.l.a.117.1 | 16 | |||
7.5 | odd | 6 | 490.2.l.a.227.3 | 16 | |||
7.6 | odd | 2 | inner | 70.2.g.a.27.4 | yes | 8 | |
15.8 | even | 4 | 630.2.p.a.433.2 | 8 | |||
20.3 | even | 4 | 560.2.bj.c.433.2 | 8 | |||
21.20 | even | 2 | 630.2.p.a.307.2 | 8 | |||
28.27 | even | 2 | 560.2.bj.c.97.2 | 8 | |||
35.3 | even | 12 | 490.2.l.a.313.4 | 16 | |||
35.13 | even | 4 | inner | 70.2.g.a.13.3 | ✓ | 8 | |
35.18 | odd | 12 | 490.2.l.a.313.3 | 16 | |||
35.23 | odd | 12 | 490.2.l.a.423.2 | 16 | |||
35.27 | even | 4 | 350.2.g.a.293.2 | 8 | |||
35.33 | even | 12 | 490.2.l.a.423.1 | 16 | |||
35.34 | odd | 2 | 350.2.g.a.307.1 | 8 | |||
105.83 | odd | 4 | 630.2.p.a.433.1 | 8 | |||
140.83 | odd | 4 | 560.2.bj.c.433.3 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
70.2.g.a.13.3 | ✓ | 8 | 35.13 | even | 4 | inner | |
70.2.g.a.13.4 | yes | 8 | 5.3 | odd | 4 | inner | |
70.2.g.a.27.3 | yes | 8 | 1.1 | even | 1 | trivial | |
70.2.g.a.27.4 | yes | 8 | 7.6 | odd | 2 | inner | |
350.2.g.a.293.1 | 8 | 5.2 | odd | 4 | |||
350.2.g.a.293.2 | 8 | 35.27 | even | 4 | |||
350.2.g.a.307.1 | 8 | 35.34 | odd | 2 | |||
350.2.g.a.307.2 | 8 | 5.4 | even | 2 | |||
490.2.l.a.117.1 | 16 | 7.4 | even | 3 | |||
490.2.l.a.117.2 | 16 | 7.3 | odd | 6 | |||
490.2.l.a.227.3 | 16 | 7.5 | odd | 6 | |||
490.2.l.a.227.4 | 16 | 7.2 | even | 3 | |||
490.2.l.a.313.3 | 16 | 35.18 | odd | 12 | |||
490.2.l.a.313.4 | 16 | 35.3 | even | 12 | |||
490.2.l.a.423.1 | 16 | 35.33 | even | 12 | |||
490.2.l.a.423.2 | 16 | 35.23 | odd | 12 | |||
560.2.bj.c.97.2 | 8 | 28.27 | even | 2 | |||
560.2.bj.c.97.3 | 8 | 4.3 | odd | 2 | |||
560.2.bj.c.433.2 | 8 | 20.3 | even | 4 | |||
560.2.bj.c.433.3 | 8 | 140.83 | odd | 4 | |||
630.2.p.a.307.1 | 8 | 3.2 | odd | 2 | |||
630.2.p.a.307.2 | 8 | 21.20 | even | 2 | |||
630.2.p.a.433.1 | 8 | 105.83 | odd | 4 | |||
630.2.p.a.433.2 | 8 | 15.8 | even | 4 |