Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [847,2,Mod(148,847)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(847, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("847.148");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 847 = 7 \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 847.f (of order \(5\), degree \(4\), not 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: | \(6.76332905120\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\zeta_{10})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} + x^{2} - x + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 77) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 372.1 | ||
Root | \(-0.309017 - 0.951057i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 847.372 |
Dual form | 847.2.f.a.148.1 |
$q$-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 \(\left(\mathbb{Z}/847\mathbb{Z}\right)^\times\).
\(n\) | \(122\) | \(365\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{3}{5}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.690983 | + | 2.12663i | −0.488599 | + | 1.50375i | 0.338101 | + | 0.941110i | \(0.390215\pi\) |
−0.826700 | + | 0.562643i | \(0.809785\pi\) | |||||||
\(3\) | −2.61803 | + | 1.90211i | −1.51152 | + | 1.09819i | −0.546027 | + | 0.837768i | \(0.683860\pi\) |
−0.965496 | + | 0.260418i | \(0.916140\pi\) | |||||||
\(4\) | −2.42705 | − | 1.76336i | −1.21353 | − | 0.881678i | ||||
\(5\) | −0.618034 | − | 1.90211i | −0.276393 | − | 0.850651i | −0.988847 | − | 0.148932i | \(-0.952416\pi\) |
0.712454 | − | 0.701719i | \(-0.247584\pi\) | |||||||
\(6\) | −2.23607 | − | 6.88191i | −0.912871 | − | 2.80953i | ||||
\(7\) | −0.809017 | − | 0.587785i | −0.305780 | − | 0.222162i | ||||
\(8\) | 1.80902 | − | 1.31433i | 0.639584 | − | 0.464685i | ||||
\(9\) | 2.30902 | − | 7.10642i | 0.769672 | − | 2.36881i | ||||
\(10\) | 4.47214 | 1.41421 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 9.70820 | 2.80252 | ||||||||
\(13\) | −0.381966 | + | 1.17557i | −0.105938 | + | 0.326045i | −0.989950 | − | 0.141421i | \(-0.954833\pi\) |
0.884011 | + | 0.467466i | \(0.154833\pi\) | |||||||
\(14\) | 1.80902 | − | 1.31433i | 0.483480 | − | 0.351269i | ||||
\(15\) | 5.23607 | + | 3.80423i | 1.35195 | + | 0.982247i | ||||
\(16\) | −0.309017 | − | 0.951057i | −0.0772542 | − | 0.237764i | ||||
\(17\) | 0.381966 | + | 1.17557i | 0.0926404 | + | 0.285118i | 0.986632 | − | 0.162967i | \(-0.0521064\pi\) |
−0.893991 | + | 0.448085i | \(0.852106\pi\) | |||||||
\(18\) | 13.5172 | + | 9.82084i | 3.18604 | + | 2.31479i | ||||
\(19\) | 2.00000 | − | 1.45309i | 0.458831 | − | 0.333361i | −0.334241 | − | 0.942488i | \(-0.608480\pi\) |
0.793073 | + | 0.609127i | \(0.208480\pi\) | |||||||
\(20\) | −1.85410 | + | 5.70634i | −0.414590 | + | 1.27598i | ||||
\(21\) | 3.23607 | 0.706168 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −6.47214 | −1.34953 | −0.674767 | − | 0.738031i | \(-0.735756\pi\) | ||||
−0.674767 | + | 0.738031i | \(0.735756\pi\) | |||||||
\(24\) | −2.23607 | + | 6.88191i | −0.456435 | + | 1.40476i | ||||
\(25\) | 0.809017 | − | 0.587785i | 0.161803 | − | 0.117557i | ||||
\(26\) | −2.23607 | − | 1.62460i | −0.438529 | − | 0.318610i | ||||
\(27\) | 4.47214 | + | 13.7638i | 0.860663 | + | 2.64885i | ||||
\(28\) | 0.927051 | + | 2.85317i | 0.175196 | + | 0.539198i | ||||
\(29\) | 0.381966 | + | 0.277515i | 0.0709293 | + | 0.0515332i | 0.622685 | − | 0.782473i | \(-0.286042\pi\) |
−0.551756 | + | 0.834006i | \(0.686042\pi\) | |||||||
\(30\) | −11.7082 | + | 8.50651i | −2.13762 | + | 1.55307i | ||||
\(31\) | −2.23607 | + | 6.88191i | −0.401610 | + | 1.23603i | 0.522083 | + | 0.852894i | \(0.325155\pi\) |
−0.923693 | + | 0.383133i | \(0.874845\pi\) | |||||||
\(32\) | 6.70820 | 1.18585 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −2.76393 | −0.474010 | ||||||||
\(35\) | −0.618034 | + | 1.90211i | −0.104467 | + | 0.321516i | ||||
\(36\) | −18.1353 | + | 13.1760i | −3.02254 | + | 2.19601i | ||||
\(37\) | −0.381966 | − | 0.277515i | −0.0627948 | − | 0.0456231i | 0.555945 | − | 0.831219i | \(-0.312356\pi\) |
−0.618740 | + | 0.785596i | \(0.712356\pi\) | |||||||
\(38\) | 1.70820 | + | 5.25731i | 0.277107 | + | 0.852848i | ||||
\(39\) | −1.23607 | − | 3.80423i | −0.197929 | − | 0.609164i | ||||
\(40\) | −3.61803 | − | 2.62866i | −0.572061 | − | 0.415627i | ||||
\(41\) | 5.47214 | − | 3.97574i | 0.854604 | − | 0.620906i | −0.0718076 | − | 0.997419i | \(-0.522877\pi\) |
0.926412 | + | 0.376512i | \(0.122877\pi\) | |||||||
\(42\) | −2.23607 | + | 6.88191i | −0.345033 | + | 1.06190i | ||||
\(43\) | 8.00000 | 1.21999 | 0.609994 | − | 0.792406i | \(-0.291172\pi\) | ||||
0.609994 | + | 0.792406i | \(0.291172\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −14.9443 | −2.22776 | ||||||||
\(46\) | 4.47214 | − | 13.7638i | 0.659380 | − | 2.02936i | ||||
\(47\) | −5.85410 | + | 4.25325i | −0.853909 | + | 0.620401i | −0.926221 | − | 0.376981i | \(-0.876962\pi\) |
0.0723124 | + | 0.997382i | \(0.476962\pi\) | |||||||
\(48\) | 2.61803 | + | 1.90211i | 0.377881 | + | 0.274546i | ||||
\(49\) | 0.309017 | + | 0.951057i | 0.0441453 | + | 0.135865i | ||||
\(50\) | 0.690983 | + | 2.12663i | 0.0977198 | + | 0.300750i | ||||
\(51\) | −3.23607 | − | 2.35114i | −0.453140 | − | 0.329226i | ||||
\(52\) | 3.00000 | − | 2.17963i | 0.416025 | − | 0.302260i | ||||
\(53\) | 2.61803 | − | 8.05748i | 0.359615 | − | 1.10678i | −0.593671 | − | 0.804708i | \(-0.702322\pi\) |
0.953285 | − | 0.302072i | \(-0.0976782\pi\) | |||||||
\(54\) | −32.3607 | −4.40373 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −2.23607 | −0.298807 | ||||||||
\(57\) | −2.47214 | + | 7.60845i | −0.327442 | + | 1.00776i | ||||
\(58\) | −0.854102 | + | 0.620541i | −0.112149 | + | 0.0814811i | ||||
\(59\) | −2.61803 | − | 1.90211i | −0.340839 | − | 0.247634i | 0.404177 | − | 0.914681i | \(-0.367558\pi\) |
−0.745016 | + | 0.667047i | \(0.767558\pi\) | |||||||
\(60\) | −6.00000 | − | 18.4661i | −0.774597 | − | 2.38396i | ||||
\(61\) | −0.854102 | − | 2.62866i | −0.109357 | − | 0.336565i | 0.881372 | − | 0.472423i | \(-0.156621\pi\) |
−0.990728 | + | 0.135859i | \(0.956621\pi\) | |||||||
\(62\) | −13.0902 | − | 9.51057i | −1.66245 | − | 1.20784i | ||||
\(63\) | −6.04508 | + | 4.39201i | −0.761609 | + | 0.553341i | ||||
\(64\) | −4.01722 | + | 12.3637i | −0.502153 | + | 1.54547i | ||||
\(65\) | 2.47214 | 0.306631 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 5.52786 | 0.675336 | 0.337668 | − | 0.941265i | \(-0.390362\pi\) | ||||
0.337668 | + | 0.941265i | \(0.390362\pi\) | |||||||
\(68\) | 1.14590 | − | 3.52671i | 0.138961 | − | 0.427677i | ||||
\(69\) | 16.9443 | − | 12.3107i | 2.03985 | − | 1.48204i | ||||
\(70\) | −3.61803 | − | 2.62866i | −0.432438 | − | 0.314184i | ||||
\(71\) | −0.472136 | − | 1.45309i | −0.0560322 | − | 0.172449i | 0.919124 | − | 0.393969i | \(-0.128898\pi\) |
−0.975156 | + | 0.221520i | \(0.928898\pi\) | |||||||
\(72\) | −5.16312 | − | 15.8904i | −0.608479 | − | 1.87271i | ||||
\(73\) | 4.23607 | + | 3.07768i | 0.495794 | + | 0.360216i | 0.807408 | − | 0.589993i | \(-0.200870\pi\) |
−0.311614 | + | 0.950209i | \(0.600870\pi\) | |||||||
\(74\) | 0.854102 | − | 0.620541i | 0.0992873 | − | 0.0721365i | ||||
\(75\) | −1.00000 | + | 3.07768i | −0.115470 | + | 0.355380i | ||||
\(76\) | −7.41641 | −0.850720 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 8.94427 | 1.01274 | ||||||||
\(79\) | 2.76393 | − | 8.50651i | 0.310967 | − | 0.957057i | −0.666416 | − | 0.745580i | \(-0.732173\pi\) |
0.977383 | − | 0.211477i | \(-0.0678274\pi\) | |||||||
\(80\) | −1.61803 | + | 1.17557i | −0.180902 | + | 0.131433i | ||||
\(81\) | −19.7533 | − | 14.3516i | −2.19481 | − | 1.59462i | ||||
\(82\) | 4.67376 | + | 14.3844i | 0.516131 | + | 1.58849i | ||||
\(83\) | 4.76393 | + | 14.6619i | 0.522909 | + | 1.60935i | 0.768413 | + | 0.639954i | \(0.221047\pi\) |
−0.245504 | + | 0.969396i | \(0.578953\pi\) | |||||||
\(84\) | −7.85410 | − | 5.70634i | −0.856953 | − | 0.622613i | ||||
\(85\) | 2.00000 | − | 1.45309i | 0.216930 | − | 0.157609i | ||||
\(86\) | −5.52786 | + | 17.0130i | −0.596085 | + | 1.83456i | ||||
\(87\) | −1.52786 | −0.163804 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 2.00000 | 0.212000 | 0.106000 | − | 0.994366i | \(-0.466196\pi\) | ||||
0.106000 | + | 0.994366i | \(0.466196\pi\) | |||||||
\(90\) | 10.3262 | − | 31.7809i | 1.08848 | − | 3.35000i | ||||
\(91\) | 1.00000 | − | 0.726543i | 0.104828 | − | 0.0761624i | ||||
\(92\) | 15.7082 | + | 11.4127i | 1.63769 | + | 1.18985i | ||||
\(93\) | −7.23607 | − | 22.2703i | −0.750345 | − | 2.30933i | ||||
\(94\) | −5.00000 | − | 15.3884i | −0.515711 | − | 1.58719i | ||||
\(95\) | −4.00000 | − | 2.90617i | −0.410391 | − | 0.298167i | ||||
\(96\) | −17.5623 | + | 12.7598i | −1.79245 | + | 1.30229i | ||||
\(97\) | −2.90983 | + | 8.95554i | −0.295448 | + | 0.909297i | 0.687622 | + | 0.726069i | \(0.258655\pi\) |
−0.983070 | + | 0.183228i | \(0.941345\pi\) | |||||||
\(98\) | −2.23607 | −0.225877 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −3.00000 | −0.300000 | ||||||||
\(101\) | −2.85410 | + | 8.78402i | −0.283994 | + | 0.874043i | 0.702705 | + | 0.711482i | \(0.251976\pi\) |
−0.986698 | + | 0.162561i | \(0.948024\pi\) | |||||||
\(102\) | 7.23607 | − | 5.25731i | 0.716477 | − | 0.520551i | ||||
\(103\) | 4.61803 | + | 3.35520i | 0.455028 | + | 0.330597i | 0.791578 | − | 0.611068i | \(-0.209260\pi\) |
−0.336549 | + | 0.941666i | \(0.609260\pi\) | |||||||
\(104\) | 0.854102 | + | 2.62866i | 0.0837516 | + | 0.257761i | ||||
\(105\) | −2.00000 | − | 6.15537i | −0.195180 | − | 0.600702i | ||||
\(106\) | 15.3262 | + | 11.1352i | 1.48862 | + | 1.08154i | ||||
\(107\) | 3.23607 | − | 2.35114i | 0.312842 | − | 0.227293i | −0.420273 | − | 0.907398i | \(-0.638066\pi\) |
0.733115 | + | 0.680104i | \(0.238066\pi\) | |||||||
\(108\) | 13.4164 | − | 41.2915i | 1.29099 | − | 3.97327i | ||||
\(109\) | 4.47214 | 0.428353 | 0.214176 | − | 0.976795i | \(-0.431293\pi\) | ||||
0.214176 | + | 0.976795i | \(0.431293\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1.52786 | 0.145018 | ||||||||
\(112\) | −0.309017 | + | 0.951057i | −0.0291994 | + | 0.0898664i | ||||
\(113\) | −1.61803 | + | 1.17557i | −0.152212 | + | 0.110588i | −0.661285 | − | 0.750135i | \(-0.729988\pi\) |
0.509073 | + | 0.860724i | \(0.329988\pi\) | |||||||
\(114\) | −14.4721 | − | 10.5146i | −1.35544 | − | 0.984785i | ||||
\(115\) | 4.00000 | + | 12.3107i | 0.373002 | + | 1.14798i | ||||
\(116\) | −0.437694 | − | 1.34708i | −0.0406389 | − | 0.125074i | ||||
\(117\) | 7.47214 | + | 5.42882i | 0.690799 | + | 0.501895i | ||||
\(118\) | 5.85410 | − | 4.25325i | 0.538914 | − | 0.391544i | ||||
\(119\) | 0.381966 | − | 1.17557i | 0.0350148 | − | 0.107764i | ||||
\(120\) | 14.4721 | 1.32112 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | 6.18034 | 0.559542 | ||||||||
\(123\) | −6.76393 | + | 20.8172i | −0.609883 | + | 1.87703i | ||||
\(124\) | 17.5623 | − | 12.7598i | 1.57714 | − | 1.14586i | ||||
\(125\) | −9.70820 | − | 7.05342i | −0.868328 | − | 0.630877i | ||||
\(126\) | −5.16312 | − | 15.8904i | −0.459967 | − | 1.41563i | ||||
\(127\) | 6.47214 | + | 19.9192i | 0.574309 | + | 1.76754i | 0.638520 | + | 0.769606i | \(0.279547\pi\) |
−0.0642104 | + | 0.997936i | \(0.520453\pi\) | |||||||
\(128\) | −12.6631 | − | 9.20029i | −1.11927 | − | 0.813199i | ||||
\(129\) | −20.9443 | + | 15.2169i | −1.84404 | + | 1.33977i | ||||
\(130\) | −1.70820 | + | 5.25731i | −0.149819 | + | 0.461097i | ||||
\(131\) | −13.8885 | −1.21345 | −0.606724 | − | 0.794913i | \(-0.707517\pi\) | ||||
−0.606724 | + | 0.794913i | \(0.707517\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.47214 | −0.214361 | ||||||||
\(134\) | −3.81966 | + | 11.7557i | −0.329968 | + | 1.01554i | ||||
\(135\) | 23.4164 | − | 17.0130i | 2.01536 | − | 1.46425i | ||||
\(136\) | 2.23607 | + | 1.62460i | 0.191741 | + | 0.139308i | ||||
\(137\) | 2.32624 | + | 7.15942i | 0.198744 | + | 0.611671i | 0.999912 | + | 0.0132321i | \(0.00421203\pi\) |
−0.801169 | + | 0.598439i | \(0.795788\pi\) | |||||||
\(138\) | 14.4721 | + | 44.5407i | 1.23195 | + | 3.79155i | ||||
\(139\) | 8.47214 | + | 6.15537i | 0.718597 | + | 0.522091i | 0.885936 | − | 0.463808i | \(-0.153517\pi\) |
−0.167339 | + | 0.985899i | \(0.553517\pi\) | |||||||
\(140\) | 4.85410 | − | 3.52671i | 0.410246 | − | 0.298062i | ||||
\(141\) | 7.23607 | − | 22.2703i | 0.609387 | − | 1.87550i | ||||
\(142\) | 3.41641 | 0.286699 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −7.47214 | −0.622678 | ||||||||
\(145\) | 0.291796 | − | 0.898056i | 0.0242323 | − | 0.0745795i | ||||
\(146\) | −9.47214 | + | 6.88191i | −0.783920 | + | 0.569551i | ||||
\(147\) | −2.61803 | − | 1.90211i | −0.215932 | − | 0.156884i | ||||
\(148\) | 0.437694 | + | 1.34708i | 0.0359782 | + | 0.110730i | ||||
\(149\) | 4.32624 | + | 13.3148i | 0.354419 | + | 1.09079i | 0.956345 | + | 0.292239i | \(0.0944001\pi\) |
−0.601926 | + | 0.798552i | \(0.705600\pi\) | |||||||
\(150\) | −5.85410 | − | 4.25325i | −0.477985 | − | 0.347277i | ||||
\(151\) | 7.23607 | − | 5.25731i | 0.588863 | − | 0.427834i | −0.253046 | − | 0.967454i | \(-0.581432\pi\) |
0.841908 | + | 0.539620i | \(0.181432\pi\) | |||||||
\(152\) | 1.70820 | − | 5.25731i | 0.138554 | − | 0.426424i | ||||
\(153\) | 9.23607 | 0.746692 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 14.4721 | 1.16243 | ||||||||
\(156\) | −3.70820 | + | 11.4127i | −0.296894 | + | 0.913746i | ||||
\(157\) | 5.61803 | − | 4.08174i | 0.448368 | − | 0.325758i | −0.340583 | − | 0.940214i | \(-0.610624\pi\) |
0.788951 | + | 0.614456i | \(0.210624\pi\) | |||||||
\(158\) | 16.1803 | + | 11.7557i | 1.28724 | + | 0.935234i | ||||
\(159\) | 8.47214 | + | 26.0746i | 0.671884 | + | 2.06785i | ||||
\(160\) | −4.14590 | − | 12.7598i | −0.327762 | − | 1.00875i | ||||
\(161\) | 5.23607 | + | 3.80423i | 0.412660 | + | 0.299815i | ||||
\(162\) | 44.1697 | − | 32.0912i | 3.47030 | − | 2.52132i | ||||
\(163\) | 7.23607 | − | 22.2703i | 0.566773 | − | 1.74435i | −0.0958527 | − | 0.995396i | \(-0.530558\pi\) |
0.662625 | − | 0.748951i | \(-0.269442\pi\) | |||||||
\(164\) | −20.2918 | −1.58452 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −34.4721 | −2.67556 | ||||||||
\(167\) | −4.00000 | + | 12.3107i | −0.309529 | + | 0.952633i | 0.668419 | + | 0.743785i | \(0.266971\pi\) |
−0.977948 | + | 0.208848i | \(0.933029\pi\) | |||||||
\(168\) | 5.85410 | − | 4.25325i | 0.451654 | − | 0.328146i | ||||
\(169\) | 9.28115 | + | 6.74315i | 0.713935 | + | 0.518704i | ||||
\(170\) | 1.70820 | + | 5.25731i | 0.131013 | + | 0.403217i | ||||
\(171\) | −5.70820 | − | 17.5680i | −0.436517 | − | 1.34346i | ||||
\(172\) | −19.4164 | − | 14.1068i | −1.48049 | − | 1.07564i | ||||
\(173\) | 13.9443 | − | 10.1311i | 1.06016 | − | 0.770254i | 0.0860448 | − | 0.996291i | \(-0.472577\pi\) |
0.974119 | + | 0.226038i | \(0.0725772\pi\) | |||||||
\(174\) | 1.05573 | − | 3.24920i | 0.0800345 | − | 0.246321i | ||||
\(175\) | −1.00000 | −0.0755929 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 10.4721 | 0.787134 | ||||||||
\(178\) | −1.38197 | + | 4.25325i | −0.103583 | + | 0.318795i | ||||
\(179\) | −7.23607 | + | 5.25731i | −0.540849 | + | 0.392950i | −0.824400 | − | 0.566007i | \(-0.808487\pi\) |
0.283551 | + | 0.958957i | \(0.408487\pi\) | |||||||
\(180\) | 36.2705 | + | 26.3521i | 2.70344 | + | 1.96417i | ||||
\(181\) | 0.437694 | + | 1.34708i | 0.0325335 | + | 0.100128i | 0.966005 | − | 0.258525i | \(-0.0832363\pi\) |
−0.933471 | + | 0.358653i | \(0.883236\pi\) | |||||||
\(182\) | 0.854102 | + | 2.62866i | 0.0633102 | + | 0.194849i | ||||
\(183\) | 7.23607 | + | 5.25731i | 0.534906 | + | 0.388632i | ||||
\(184\) | −11.7082 | + | 8.50651i | −0.863140 | + | 0.627108i | ||||
\(185\) | −0.291796 | + | 0.898056i | −0.0214533 | + | 0.0660264i | ||||
\(186\) | 52.3607 | 3.83927 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 21.7082 | 1.58323 | ||||||||
\(189\) | 4.47214 | − | 13.7638i | 0.325300 | − | 1.00117i | ||||
\(190\) | 8.94427 | − | 6.49839i | 0.648886 | − | 0.471443i | ||||
\(191\) | 16.9443 | + | 12.3107i | 1.22604 | + | 0.890773i | 0.996587 | − | 0.0825453i | \(-0.0263049\pi\) |
0.229457 | + | 0.973319i | \(0.426305\pi\) | |||||||
\(192\) | −13.0000 | − | 40.0099i | −0.938194 | − | 2.88746i | ||||
\(193\) | −7.38197 | − | 22.7194i | −0.531366 | − | 1.63537i | −0.751374 | − | 0.659877i | \(-0.770608\pi\) |
0.220008 | − | 0.975498i | \(-0.429392\pi\) | |||||||
\(194\) | −17.0344 | − | 12.3762i | −1.22300 | − | 0.888563i | ||||
\(195\) | −6.47214 | + | 4.70228i | −0.463479 | + | 0.336737i | ||||
\(196\) | 0.927051 | − | 2.85317i | 0.0662179 | − | 0.203798i | ||||
\(197\) | −2.00000 | −0.142494 | −0.0712470 | − | 0.997459i | \(-0.522698\pi\) | ||||
−0.0712470 | + | 0.997459i | \(0.522698\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 20.1803 | 1.43055 | 0.715273 | − | 0.698845i | \(-0.246302\pi\) | ||||
0.715273 | + | 0.698845i | \(0.246302\pi\) | |||||||
\(200\) | 0.690983 | − | 2.12663i | 0.0488599 | − | 0.150375i | ||||
\(201\) | −14.4721 | + | 10.5146i | −1.02079 | + | 0.741644i | ||||
\(202\) | −16.7082 | − | 12.1392i | −1.17559 | − | 0.854113i | ||||
\(203\) | −0.145898 | − | 0.449028i | −0.0102400 | − | 0.0315156i | ||||
\(204\) | 3.70820 | + | 11.4127i | 0.259626 | + | 0.799047i | ||||
\(205\) | −10.9443 | − | 7.95148i | −0.764381 | − | 0.555355i | ||||
\(206\) | −10.3262 | + | 7.50245i | −0.719463 | + | 0.522721i | ||||
\(207\) | −14.9443 | + | 45.9937i | −1.03870 | + | 3.19679i | ||||
\(208\) | 1.23607 | 0.0857059 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 14.4721 | 0.998672 | ||||||||
\(211\) | 6.76393 | − | 20.8172i | 0.465648 | − | 1.43312i | −0.392517 | − | 0.919745i | \(-0.628396\pi\) |
0.858165 | − | 0.513373i | \(-0.171604\pi\) | |||||||
\(212\) | −20.5623 | + | 14.9394i | −1.41222 | + | 1.02604i | ||||
\(213\) | 4.00000 | + | 2.90617i | 0.274075 | + | 0.199127i | ||||
\(214\) | 2.76393 | + | 8.50651i | 0.188939 | + | 0.581493i | ||||
\(215\) | −4.94427 | − | 15.2169i | −0.337197 | − | 1.03778i | ||||
\(216\) | 26.1803 | + | 19.0211i | 1.78135 | + | 1.29422i | ||||
\(217\) | 5.85410 | − | 4.25325i | 0.397402 | − | 0.288730i | ||||
\(218\) | −3.09017 | + | 9.51057i | −0.209293 | + | 0.644137i | ||||
\(219\) | −16.9443 | −1.14499 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.52786 | −0.102775 | ||||||||
\(222\) | −1.05573 | + | 3.24920i | −0.0708558 | + | 0.218072i | ||||
\(223\) | −9.85410 | + | 7.15942i | −0.659879 | + | 0.479431i | −0.866622 | − | 0.498965i | \(-0.833714\pi\) |
0.206743 | + | 0.978395i | \(0.433714\pi\) | |||||||
\(224\) | −5.42705 | − | 3.94298i | −0.362610 | − | 0.263452i | ||||
\(225\) | −2.30902 | − | 7.10642i | −0.153934 | − | 0.473762i | ||||
\(226\) | −1.38197 | − | 4.25325i | −0.0919270 | − | 0.282922i | ||||
\(227\) | 24.1803 | + | 17.5680i | 1.60491 | + | 1.16603i | 0.877177 | + | 0.480166i | \(0.159424\pi\) |
0.727728 | + | 0.685866i | \(0.240576\pi\) | |||||||
\(228\) | 19.4164 | − | 14.1068i | 1.28588 | − | 0.934249i | ||||
\(229\) | 1.38197 | − | 4.25325i | 0.0913229 | − | 0.281063i | −0.894955 | − | 0.446156i | \(-0.852793\pi\) |
0.986278 | + | 0.165093i | \(0.0527925\pi\) | |||||||
\(230\) | −28.9443 | −1.90853 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 1.05573 | 0.0693119 | ||||||||
\(233\) | −5.38197 | + | 16.5640i | −0.352584 | + | 1.08514i | 0.604813 | + | 0.796368i | \(0.293248\pi\) |
−0.957397 | + | 0.288775i | \(0.906752\pi\) | |||||||
\(234\) | −16.7082 | + | 12.1392i | −1.09225 | + | 0.793566i | ||||
\(235\) | 11.7082 | + | 8.50651i | 0.763759 | + | 0.554903i | ||||
\(236\) | 3.00000 | + | 9.23305i | 0.195283 | + | 0.601020i | ||||
\(237\) | 8.94427 | + | 27.5276i | 0.580993 | + | 1.78811i | ||||
\(238\) | 2.23607 | + | 1.62460i | 0.144943 | + | 0.105307i | ||||
\(239\) | −20.9443 | + | 15.2169i | −1.35477 | + | 0.984300i | −0.356014 | + | 0.934481i | \(0.615864\pi\) |
−0.998758 | + | 0.0498191i | \(0.984136\pi\) | |||||||
\(240\) | 2.00000 | − | 6.15537i | 0.129099 | − | 0.397327i | ||||
\(241\) | 27.1246 | 1.74725 | 0.873625 | − | 0.486600i | \(-0.161763\pi\) | ||||
0.873625 | + | 0.486600i | \(0.161763\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 35.5967 | 2.28353 | ||||||||
\(244\) | −2.56231 | + | 7.88597i | −0.164035 | + | 0.504847i | ||||
\(245\) | 1.61803 | − | 1.17557i | 0.103372 | − | 0.0751044i | ||||
\(246\) | −39.5967 | − | 28.7687i | −2.52460 | − | 1.83423i | ||||
\(247\) | 0.944272 | + | 2.90617i | 0.0600826 | + | 0.184915i | ||||
\(248\) | 5.00000 | + | 15.3884i | 0.317500 | + | 0.977166i | ||||
\(249\) | −40.3607 | − | 29.3238i | −2.55775 | − | 1.85832i | ||||
\(250\) | 21.7082 | − | 15.7719i | 1.37295 | − | 0.997505i | ||||
\(251\) | 5.47214 | − | 16.8415i | 0.345398 | − | 1.06303i | −0.615972 | − | 0.787768i | \(-0.711237\pi\) |
0.961370 | − | 0.275258i | \(-0.0887634\pi\) | |||||||
\(252\) | 22.4164 | 1.41210 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −46.8328 | −2.93855 | ||||||||
\(255\) | −2.47214 | + | 7.60845i | −0.154811 | + | 0.476460i | ||||
\(256\) | 7.28115 | − | 5.29007i | 0.455072 | − | 0.330629i | ||||
\(257\) | 4.85410 | + | 3.52671i | 0.302791 | + | 0.219990i | 0.728797 | − | 0.684730i | \(-0.240080\pi\) |
−0.426006 | + | 0.904720i | \(0.640080\pi\) | |||||||
\(258\) | −17.8885 | − | 55.0553i | −1.11369 | − | 3.42759i | ||||
\(259\) | 0.145898 | + | 0.449028i | 0.00906566 | + | 0.0279012i | ||||
\(260\) | −6.00000 | − | 4.35926i | −0.372104 | − | 0.270350i | ||||
\(261\) | 2.85410 | − | 2.07363i | 0.176664 | − | 0.128354i | ||||
\(262\) | 9.59675 | − | 29.5358i | 0.592889 | − | 1.82472i | ||||
\(263\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −16.9443 | −1.04088 | ||||||||
\(266\) | 1.70820 | − | 5.25731i | 0.104737 | − | 0.322346i | ||||
\(267\) | −5.23607 | + | 3.80423i | −0.320442 | + | 0.232815i | ||||
\(268\) | −13.4164 | − | 9.74759i | −0.819538 | − | 0.595429i | ||||
\(269\) | −4.14590 | − | 12.7598i | −0.252780 | − | 0.777976i | −0.994259 | − | 0.107000i | \(-0.965875\pi\) |
0.741479 | − | 0.670976i | \(-0.234125\pi\) | |||||||
\(270\) | 20.0000 | + | 61.5537i | 1.21716 | + | 3.74604i | ||||
\(271\) | 1.23607 | + | 0.898056i | 0.0750858 | + | 0.0545530i | 0.624695 | − | 0.780869i | \(-0.285223\pi\) |
−0.549609 | + | 0.835422i | \(0.685223\pi\) | |||||||
\(272\) | 1.00000 | − | 0.726543i | 0.0606339 | − | 0.0440531i | ||||
\(273\) | −1.23607 | + | 3.80423i | −0.0748102 | + | 0.230242i | ||||
\(274\) | −16.8328 | −1.01691 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −62.8328 | −3.78209 | ||||||||
\(277\) | 4.90983 | − | 15.1109i | 0.295003 | − | 0.907926i | −0.688217 | − | 0.725505i | \(-0.741606\pi\) |
0.983220 | − | 0.182422i | \(-0.0583936\pi\) | |||||||
\(278\) | −18.9443 | + | 13.7638i | −1.13620 | + | 0.825499i | ||||
\(279\) | 43.7426 | + | 31.7809i | 2.61880 | + | 1.90267i | ||||
\(280\) | 1.38197 | + | 4.25325i | 0.0825883 | + | 0.254181i | ||||
\(281\) | −3.85410 | − | 11.8617i | −0.229916 | − | 0.707610i | −0.997755 | − | 0.0669669i | \(-0.978668\pi\) |
0.767839 | − | 0.640643i | \(-0.221332\pi\) | |||||||
\(282\) | 42.3607 | + | 30.7768i | 2.52254 | + | 1.83273i | ||||
\(283\) | 4.76393 | − | 3.46120i | 0.283186 | − | 0.205747i | −0.437120 | − | 0.899403i | \(-0.644001\pi\) |
0.720306 | + | 0.693656i | \(0.244001\pi\) | |||||||
\(284\) | −1.41641 | + | 4.35926i | −0.0840483 | + | 0.258674i | ||||
\(285\) | 16.0000 | 0.947758 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −6.76393 | −0.399262 | ||||||||
\(288\) | 15.4894 | − | 47.6713i | 0.912719 | − | 2.80906i | ||||
\(289\) | 12.5172 | − | 9.09429i | 0.736307 | − | 0.534958i | ||||
\(290\) | 1.70820 | + | 1.24108i | 0.100309 | + | 0.0728789i | ||||
\(291\) | −9.41641 | − | 28.9807i | −0.552000 | − | 1.69888i | ||||
\(292\) | −4.85410 | − | 14.9394i | −0.284065 | − | 0.874262i | ||||
\(293\) | −12.2361 | − | 8.89002i | −0.714839 | − | 0.519361i | 0.169892 | − | 0.985463i | \(-0.445658\pi\) |
−0.884731 | + | 0.466102i | \(0.845658\pi\) | |||||||
\(294\) | 5.85410 | − | 4.25325i | 0.341418 | − | 0.248055i | ||||
\(295\) | −2.00000 | + | 6.15537i | −0.116445 | + | 0.358379i | ||||
\(296\) | −1.05573 | −0.0613629 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −31.3050 | −1.81345 | ||||||||
\(299\) | 2.47214 | − | 7.60845i | 0.142967 | − | 0.440008i | ||||
\(300\) | 7.85410 | − | 5.70634i | 0.453457 | − | 0.329456i | ||||
\(301\) | −6.47214 | − | 4.70228i | −0.373048 | − | 0.271035i | ||||
\(302\) | 6.18034 | + | 19.0211i | 0.355639 | + | 1.09454i | ||||
\(303\) | −9.23607 | − | 28.4257i | −0.530598 | − | 1.63301i | ||||
\(304\) | −2.00000 | − | 1.45309i | −0.114708 | − | 0.0833401i | ||||
\(305\) | −4.47214 | + | 3.24920i | −0.256074 | + | 0.186048i | ||||
\(306\) | −6.38197 | + | 19.6417i | −0.364833 | + | 1.12284i | ||||
\(307\) | 8.94427 | 0.510477 | 0.255238 | − | 0.966878i | \(-0.417846\pi\) | ||||
0.255238 | + | 0.966878i | \(0.417846\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −18.4721 | −1.05084 | ||||||||
\(310\) | −10.0000 | + | 30.7768i | −0.567962 | + | 1.74801i | ||||
\(311\) | 17.5623 | − | 12.7598i | 0.995867 | − | 0.723540i | 0.0346689 | − | 0.999399i | \(-0.488962\pi\) |
0.961198 | + | 0.275859i | \(0.0889623\pi\) | |||||||
\(312\) | −7.23607 | − | 5.25731i | −0.409662 | − | 0.297637i | ||||
\(313\) | −0.909830 | − | 2.80017i | −0.0514266 | − | 0.158275i | 0.922045 | − | 0.387083i | \(-0.126517\pi\) |
−0.973472 | + | 0.228808i | \(0.926517\pi\) | |||||||
\(314\) | 4.79837 | + | 14.7679i | 0.270788 | + | 0.833399i | ||||
\(315\) | 12.0902 | + | 8.78402i | 0.681204 | + | 0.494924i | ||||
\(316\) | −21.7082 | + | 15.7719i | −1.22118 | + | 0.887241i | ||||
\(317\) | 4.32624 | − | 13.3148i | 0.242986 | − | 0.747833i | −0.752975 | − | 0.658049i | \(-0.771382\pi\) |
0.995961 | − | 0.0897846i | \(-0.0286179\pi\) | |||||||
\(318\) | −61.3050 | −3.43781 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 26.0000 | 1.45344 | ||||||||
\(321\) | −4.00000 | + | 12.3107i | −0.223258 | + | 0.687118i | ||||
\(322\) | −11.7082 | + | 8.50651i | −0.652473 | + | 0.474049i | ||||
\(323\) | 2.47214 | + | 1.79611i | 0.137553 | + | 0.0999383i | ||||
\(324\) | 22.6353 | + | 69.6642i | 1.25751 | + | 3.87023i | ||||
\(325\) | 0.381966 | + | 1.17557i | 0.0211877 | + | 0.0652089i | ||||
\(326\) | 42.3607 | + | 30.7768i | 2.34614 | + | 1.70457i | ||||
\(327\) | −11.7082 | + | 8.50651i | −0.647465 | + | 0.470411i | ||||
\(328\) | 4.67376 | − | 14.3844i | 0.258065 | − | 0.794243i | ||||
\(329\) | 7.23607 | 0.398937 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 21.8885 | 1.20310 | 0.601552 | − | 0.798834i | \(-0.294549\pi\) | ||||
0.601552 | + | 0.798834i | \(0.294549\pi\) | |||||||
\(332\) | 14.2918 | − | 43.9856i | 0.784364 | − | 2.41402i | ||||
\(333\) | −2.85410 | + | 2.07363i | −0.156404 | + | 0.113634i | ||||
\(334\) | −23.4164 | − | 17.0130i | −1.28129 | − | 0.930911i | ||||
\(335\) | −3.41641 | − | 10.5146i | −0.186658 | − | 0.574475i | ||||
\(336\) | −1.00000 | − | 3.07768i | −0.0545545 | − | 0.167901i | ||||
\(337\) | 16.5623 | + | 12.0332i | 0.902206 | + | 0.655491i | 0.939032 | − | 0.343830i | \(-0.111725\pi\) |
−0.0368254 | + | 0.999322i | \(0.511725\pi\) | |||||||
\(338\) | −20.7533 | + | 15.0781i | −1.12883 | + | 0.820143i | ||||
\(339\) | 2.00000 | − | 6.15537i | 0.108625 | − | 0.334314i | ||||
\(340\) | −7.41641 | −0.402211 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 41.3050 | 2.23352 | ||||||||
\(343\) | 0.309017 | − | 0.951057i | 0.0166853 | − | 0.0513522i | ||||
\(344\) | 14.4721 | − | 10.5146i | 0.780285 | − | 0.566910i | ||||
\(345\) | −33.8885 | − | 24.6215i | −1.82450 | − | 1.32558i | ||||
\(346\) | 11.9098 | + | 36.6547i | 0.640276 | + | 1.97057i | ||||
\(347\) | 0.944272 | + | 2.90617i | 0.0506912 | + | 0.156011i | 0.973198 | − | 0.229970i | \(-0.0738628\pi\) |
−0.922507 | + | 0.385982i | \(0.873863\pi\) | |||||||
\(348\) | 3.70820 | + | 2.69417i | 0.198781 | + | 0.144423i | ||||
\(349\) | 2.23607 | − | 1.62460i | 0.119694 | − | 0.0869628i | −0.526328 | − | 0.850282i | \(-0.676432\pi\) |
0.646022 | + | 0.763319i | \(0.276432\pi\) | |||||||
\(350\) | 0.690983 | − | 2.12663i | 0.0369346 | − | 0.113673i | ||||
\(351\) | −17.8885 | −0.954820 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −15.8885 | −0.845662 | −0.422831 | − | 0.906209i | \(-0.638964\pi\) | ||||
−0.422831 | + | 0.906209i | \(0.638964\pi\) | |||||||
\(354\) | −7.23607 | + | 22.2703i | −0.384593 | + | 1.18365i | ||||
\(355\) | −2.47214 | + | 1.79611i | −0.131207 | + | 0.0953277i | ||||
\(356\) | −4.85410 | − | 3.52671i | −0.257267 | − | 0.186915i | ||||
\(357\) | 1.23607 | + | 3.80423i | 0.0654197 | + | 0.201341i | ||||
\(358\) | −6.18034 | − | 19.0211i | −0.326641 | − | 1.00530i | ||||
\(359\) | 5.70820 | + | 4.14725i | 0.301267 | + | 0.218884i | 0.728140 | − | 0.685428i | \(-0.240385\pi\) |
−0.426873 | + | 0.904312i | \(0.640385\pi\) | |||||||
\(360\) | −27.0344 | + | 19.6417i | −1.42484 | + | 1.03521i | ||||
\(361\) | −3.98278 | + | 12.2577i | −0.209620 | + | 0.645144i | ||||
\(362\) | −3.16718 | −0.166464 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −3.70820 | −0.194363 | ||||||||
\(365\) | 3.23607 | − | 9.95959i | 0.169384 | − | 0.521309i | ||||
\(366\) | −16.1803 | + | 11.7557i | −0.845760 | + | 0.614481i | ||||
\(367\) | −13.8541 | − | 10.0656i | −0.723178 | − | 0.525420i | 0.164220 | − | 0.986424i | \(-0.447489\pi\) |
−0.887398 | + | 0.461004i | \(0.847489\pi\) | |||||||
\(368\) | 2.00000 | + | 6.15537i | 0.104257 | + | 0.320871i | ||||
\(369\) | −15.6180 | − | 48.0674i | −0.813042 | − | 2.50229i | ||||
\(370\) | −1.70820 | − | 1.24108i | −0.0888053 | − | 0.0645208i | ||||
\(371\) | −6.85410 | + | 4.97980i | −0.355847 | + | 0.258538i | ||||
\(372\) | −21.7082 | + | 66.8110i | −1.12552 | + | 3.46399i | ||||
\(373\) | 6.00000 | 0.310668 | 0.155334 | − | 0.987862i | \(-0.450355\pi\) | ||||
0.155334 | + | 0.987862i | \(0.450355\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 38.8328 | 2.00532 | ||||||||
\(376\) | −5.00000 | + | 15.3884i | −0.257855 | + | 0.793597i | ||||
\(377\) | −0.472136 | + | 0.343027i | −0.0243162 | + | 0.0176668i | ||||
\(378\) | 26.1803 | + | 19.0211i | 1.34657 | + | 0.978341i | ||||
\(379\) | −7.81966 | − | 24.0664i | −0.401669 | − | 1.23621i | −0.923645 | − | 0.383250i | \(-0.874805\pi\) |
0.521976 | − | 0.852960i | \(-0.325195\pi\) | |||||||
\(380\) | 4.58359 | + | 14.1068i | 0.235133 | + | 0.723666i | ||||
\(381\) | −54.8328 | − | 39.8384i | −2.80917 | − | 2.04098i | ||||
\(382\) | −37.8885 | + | 27.5276i | −1.93855 | + | 1.40844i | ||||
\(383\) | 8.23607 | − | 25.3480i | 0.420843 | − | 1.29522i | −0.486075 | − | 0.873917i | \(-0.661572\pi\) |
0.906919 | − | 0.421306i | \(-0.138428\pi\) | |||||||
\(384\) | 50.6525 | 2.58485 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 53.4164 | 2.71882 | ||||||||
\(387\) | 18.4721 | − | 56.8514i | 0.938991 | − | 2.88992i | ||||
\(388\) | 22.8541 | − | 16.6045i | 1.16024 | − | 0.842965i | ||||
\(389\) | 16.0902 | + | 11.6902i | 0.815804 | + | 0.592716i | 0.915508 | − | 0.402301i | \(-0.131789\pi\) |
−0.0997035 | + | 0.995017i | \(0.531789\pi\) | |||||||
\(390\) | −5.52786 | − | 17.0130i | −0.279914 | − | 0.861488i | ||||
\(391\) | −2.47214 | − | 7.60845i | −0.125021 | − | 0.384776i | ||||
\(392\) | 1.80902 | + | 1.31433i | 0.0913692 | + | 0.0663836i | ||||
\(393\) | 36.3607 | − | 26.4176i | 1.83415 | − | 1.33259i | ||||
\(394\) | 1.38197 | − | 4.25325i | 0.0696224 | − | 0.214276i | ||||
\(395\) | −17.8885 | −0.900070 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −0.111456 | −0.00559383 | −0.00279691 | − | 0.999996i | \(-0.500890\pi\) | ||||
−0.00279691 | + | 0.999996i | \(0.500890\pi\) | |||||||
\(398\) | −13.9443 | + | 42.9161i | −0.698963 | + | 2.15119i | ||||
\(399\) | 6.47214 | − | 4.70228i | 0.324012 | − | 0.235409i | ||||
\(400\) | −0.809017 | − | 0.587785i | −0.0404508 | − | 0.0293893i | ||||
\(401\) | 1.56231 | + | 4.80828i | 0.0780178 | + | 0.240114i | 0.982457 | − | 0.186488i | \(-0.0597105\pi\) |
−0.904439 | + | 0.426602i | \(0.859710\pi\) | |||||||
\(402\) | −12.3607 | − | 38.0423i | −0.616495 | − | 1.89738i | ||||
\(403\) | −7.23607 | − | 5.25731i | −0.360454 | − | 0.261885i | ||||
\(404\) | 22.4164 | − | 16.2865i | 1.11526 | − | 0.810282i | ||||
\(405\) | −15.0902 | + | 46.4428i | −0.749837 | + | 2.30776i | ||||
\(406\) | 1.05573 | 0.0523949 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | −8.94427 | −0.442807 | ||||||||
\(409\) | −9.61803 | + | 29.6013i | −0.475581 | + | 1.46369i | 0.369591 | + | 0.929194i | \(0.379498\pi\) |
−0.845172 | + | 0.534494i | \(0.820502\pi\) | |||||||
\(410\) | 24.4721 | − | 17.7800i | 1.20859 | − | 0.878094i | ||||
\(411\) | −19.7082 | − | 14.3188i | −0.972134 | − | 0.706297i | ||||
\(412\) | −5.29180 | − | 16.2865i | −0.260708 | − | 0.802377i | ||||
\(413\) | 1.00000 | + | 3.07768i | 0.0492068 | + | 0.151443i | ||||
\(414\) | −87.4853 | − | 63.5618i | −4.29967 | − | 3.12389i | ||||
\(415\) | 24.9443 | − | 18.1231i | 1.22447 | − | 0.889627i | ||||
\(416\) | −2.56231 | + | 7.88597i | −0.125627 | + | 0.386641i | ||||
\(417\) | −33.8885 | −1.65953 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −6.65248 | −0.324995 | −0.162497 | − | 0.986709i | \(-0.551955\pi\) | ||||
−0.162497 | + | 0.986709i | \(0.551955\pi\) | |||||||
\(420\) | −6.00000 | + | 18.4661i | −0.292770 | + | 0.901053i | ||||
\(421\) | 18.0902 | − | 13.1433i | 0.881661 | − | 0.640564i | −0.0520294 | − | 0.998646i | \(-0.516569\pi\) |
0.933690 | + | 0.358081i | \(0.116569\pi\) | |||||||
\(422\) | 39.5967 | + | 28.7687i | 1.92754 | + | 1.40044i | ||||
\(423\) | 16.7082 | + | 51.4226i | 0.812381 | + | 2.50025i | ||||
\(424\) | −5.85410 | − | 18.0171i | −0.284300 | − | 0.874986i | ||||
\(425\) | 1.00000 | + | 0.726543i | 0.0485071 | + | 0.0352425i | ||||
\(426\) | −8.94427 | + | 6.49839i | −0.433351 | + | 0.314848i | ||||
\(427\) | −0.854102 | + | 2.62866i | −0.0413329 | + | 0.127210i | ||||
\(428\) | −12.0000 | −0.580042 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 35.7771 | 1.72532 | ||||||||
\(431\) | 3.70820 | − | 11.4127i | 0.178618 | − | 0.549729i | −0.821162 | − | 0.570695i | \(-0.806674\pi\) |
0.999780 | + | 0.0209654i | \(0.00667397\pi\) | |||||||
\(432\) | 11.7082 | − | 8.50651i | 0.563311 | − | 0.409270i | ||||
\(433\) | −0.381966 | − | 0.277515i | −0.0183561 | − | 0.0133365i | 0.578569 | − | 0.815633i | \(-0.303611\pi\) |
−0.596925 | + | 0.802297i | \(0.703611\pi\) | |||||||
\(434\) | 5.00000 | + | 15.3884i | 0.240008 | + | 0.738668i | ||||
\(435\) | 0.944272 | + | 2.90617i | 0.0452744 | + | 0.139340i | ||||
\(436\) | −10.8541 | − | 7.88597i | −0.519817 | − | 0.377669i | ||||
\(437\) | −12.9443 | + | 9.40456i | −0.619208 | + | 0.449881i | ||||
\(438\) | 11.7082 | − | 36.0341i | 0.559440 | − | 1.72178i | ||||
\(439\) | 1.52786 | 0.0729210 | 0.0364605 | − | 0.999335i | \(-0.488392\pi\) | ||||
0.0364605 | + | 0.999335i | \(0.488392\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 7.47214 | 0.355816 | ||||||||
\(442\) | 1.05573 | − | 3.24920i | 0.0502159 | − | 0.154549i | ||||
\(443\) | 5.70820 | − | 4.14725i | 0.271205 | − | 0.197042i | −0.443867 | − | 0.896093i | \(-0.646394\pi\) |
0.715072 | + | 0.699051i | \(0.246394\pi\) | |||||||
\(444\) | −3.70820 | − | 2.69417i | −0.175984 | − | 0.127860i | ||||
\(445\) | −1.23607 | − | 3.80423i | −0.0585952 | − | 0.180338i | ||||
\(446\) | −8.41641 | − | 25.9030i | −0.398528 | − | 1.22654i | ||||
\(447\) | −36.6525 | − | 26.6296i | −1.73360 | − | 1.25954i | ||||
\(448\) | 10.5172 | − | 7.64121i | 0.496892 | − | 0.361013i | ||||
\(449\) | −6.03444 | + | 18.5721i | −0.284783 | + | 0.876472i | 0.701681 | + | 0.712492i | \(0.252433\pi\) |
−0.986464 | + | 0.163980i | \(0.947567\pi\) | |||||||
\(450\) | 16.7082 | 0.787632 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 6.00000 | 0.282216 | ||||||||
\(453\) | −8.94427 | + | 27.5276i | −0.420239 | + | 1.29336i | ||||
\(454\) | −54.0689 | + | 39.2833i | −2.53758 | + | 1.84366i | ||||
\(455\) | −2.00000 | − | 1.45309i | −0.0937614 | − | 0.0681217i | ||||
\(456\) | 5.52786 | + | 17.0130i | 0.258866 | + | 0.796707i | ||||
\(457\) | 7.67376 | + | 23.6174i | 0.358963 | + | 1.10478i | 0.953676 | + | 0.300837i | \(0.0972661\pi\) |
−0.594712 | + | 0.803939i | \(0.702734\pi\) | |||||||
\(458\) | 8.09017 | + | 5.87785i | 0.378029 | + | 0.274654i | ||||
\(459\) | −14.4721 | + | 10.5146i | −0.675501 | + | 0.490781i | ||||
\(460\) | 12.0000 | − | 36.9322i | 0.559503 | − | 1.72197i | ||||
\(461\) | 10.1803 | 0.474146 | 0.237073 | − | 0.971492i | \(-0.423812\pi\) | ||||
0.237073 | + | 0.971492i | \(0.423812\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −14.4721 | −0.672577 | −0.336289 | − | 0.941759i | \(-0.609172\pi\) | ||||
−0.336289 | + | 0.941759i | \(0.609172\pi\) | |||||||
\(464\) | 0.145898 | − | 0.449028i | 0.00677315 | − | 0.0208456i | ||||
\(465\) | −37.8885 | + | 27.5276i | −1.75704 | + | 1.27656i | ||||
\(466\) | −31.5066 | − | 22.8909i | −1.45951 | − | 1.06040i | ||||
\(467\) | −10.5279 | − | 32.4014i | −0.487171 | − | 1.49936i | −0.828811 | − | 0.559529i | \(-0.810982\pi\) |
0.341640 | − | 0.939831i | \(-0.389018\pi\) | |||||||
\(468\) | −8.56231 | − | 26.3521i | −0.395793 | − | 1.21812i | ||||
\(469\) | −4.47214 | − | 3.24920i | −0.206504 | − | 0.150034i | ||||
\(470\) | −26.1803 | + | 19.0211i | −1.20761 | + | 0.877379i | ||||
\(471\) | −6.94427 | + | 21.3723i | −0.319975 | + | 0.984782i | ||||
\(472\) | −7.23607 | −0.333067 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | −64.7214 | −2.97275 | ||||||||
\(475\) | 0.763932 | − | 2.35114i | 0.0350516 | − | 0.107878i | ||||
\(476\) | −3.00000 | + | 2.17963i | −0.137505 | + | 0.0999031i | ||||
\(477\) | −51.2148 | − | 37.2097i | −2.34496 | − | 1.70372i | ||||
\(478\) | −17.8885 | − | 55.0553i | −0.818203 | − | 2.51817i | ||||
\(479\) | 6.94427 | + | 21.3723i | 0.317292 | + | 0.976524i | 0.974801 | + | 0.223077i | \(0.0716102\pi\) |
−0.657509 | + | 0.753447i | \(0.728390\pi\) | |||||||
\(480\) | 35.1246 | + | 25.5195i | 1.60321 | + | 1.16480i | ||||
\(481\) | 0.472136 | − | 0.343027i | 0.0215275 | − | 0.0156407i | ||||
\(482\) | −18.7426 | + | 57.6839i | −0.853704 | + | 2.62743i | ||||
\(483\) | −20.9443 | −0.952997 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 18.8328 | 0.855154 | ||||||||
\(486\) | −24.5967 | + | 75.7010i | −1.11573 | + | 3.43387i | ||||
\(487\) | −6.76393 | + | 4.91428i | −0.306503 | + | 0.222687i | −0.730395 | − | 0.683025i | \(-0.760664\pi\) |
0.423892 | + | 0.905713i | \(0.360664\pi\) | |||||||
\(488\) | −5.00000 | − | 3.63271i | −0.226339 | − | 0.164445i | ||||
\(489\) | 23.4164 | + | 72.0683i | 1.05893 | + | 3.25904i | ||||
\(490\) | 1.38197 | + | 4.25325i | 0.0624309 | + | 0.192142i | ||||
\(491\) | 0 | 0 | 0.587785 | − | 0.809017i | \(-0.300000\pi\) | ||||
−0.587785 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(492\) | 53.1246 | − | 38.5973i | 2.39504 | − | 1.74010i | ||||
\(493\) | −0.180340 | + | 0.555029i | −0.00812210 | + | 0.0249973i | ||||
\(494\) | −6.83282 | −0.307423 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 7.23607 | 0.324909 | ||||||||
\(497\) | −0.472136 | + | 1.45309i | −0.0211782 | + | 0.0651798i | ||||
\(498\) | 90.2492 | − | 65.5699i | 4.04416 | − | 2.93826i | ||||
\(499\) | −8.47214 | − | 6.15537i | −0.379265 | − | 0.275552i | 0.381777 | − | 0.924254i | \(-0.375312\pi\) |
−0.761042 | + | 0.648702i | \(0.775312\pi\) | |||||||
\(500\) | 11.1246 | + | 34.2380i | 0.497508 | + | 1.53117i | ||||
\(501\) | −12.9443 | − | 39.8384i | −0.578307 | − | 1.77985i | ||||
\(502\) | 32.0344 | + | 23.2744i | 1.42977 | + | 1.03879i | ||||
\(503\) | 2.76393 | − | 2.00811i | 0.123238 | − | 0.0895374i | −0.524459 | − | 0.851436i | \(-0.675732\pi\) |
0.647697 | + | 0.761898i | \(0.275732\pi\) | |||||||
\(504\) | −5.16312 | + | 15.8904i | −0.229984 | + | 0.707817i | ||||
\(505\) | 18.4721 | 0.821999 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −37.1246 | −1.64876 | ||||||||
\(508\) | 19.4164 | − | 59.7576i | 0.861464 | − | 2.65131i | ||||
\(509\) | −25.5066 | + | 18.5316i | −1.13056 | + | 0.821399i | −0.985776 | − | 0.168064i | \(-0.946248\pi\) |
−0.144783 | + | 0.989463i | \(0.546248\pi\) | |||||||
\(510\) | −14.4721 | − | 10.5146i | −0.640837 | − | 0.465595i | ||||
\(511\) | −1.61803 | − | 4.97980i | −0.0715776 | − | 0.220293i | ||||
\(512\) | −3.45492 | − | 10.6331i | −0.152687 | − | 0.469923i | ||||
\(513\) | 28.9443 | + | 21.0292i | 1.27792 | + | 0.928464i | ||||
\(514\) | −10.8541 | + | 7.88597i | −0.478754 | + | 0.347835i | ||||
\(515\) | 3.52786 | − | 10.8576i | 0.155456 | − | 0.478445i | ||||
\(516\) | 77.6656 | 3.41904 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | −1.05573 | −0.0463860 | ||||||||
\(519\) | −17.2361 | + | 53.0472i | −0.756579 | + | 2.32851i | ||||
\(520\) | 4.47214 | − | 3.24920i | 0.196116 | − | 0.142487i | ||||
\(521\) | 11.6180 | + | 8.44100i | 0.508995 | + | 0.369807i | 0.812442 | − | 0.583042i | \(-0.198138\pi\) |
−0.303447 | + | 0.952848i | \(0.598138\pi\) | |||||||
\(522\) | 2.43769 | + | 7.50245i | 0.106695 | + | 0.328373i | ||||
\(523\) | 13.5967 | + | 41.8465i | 0.594544 | + | 1.82982i | 0.556982 | + | 0.830525i | \(0.311959\pi\) |
0.0375627 | + | 0.999294i | \(0.488041\pi\) | |||||||
\(524\) | 33.7082 | + | 24.4904i | 1.47255 | + | 1.06987i | ||||
\(525\) | 2.61803 | − | 1.90211i | 0.114260 | − | 0.0830150i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −8.94427 | −0.389619 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 18.8885 | 0.821241 | ||||||||
\(530\) | 11.7082 | − | 36.0341i | 0.508572 | − | 1.56522i | ||||
\(531\) | −19.5623 | + | 14.2128i | −0.848932 | + | 0.616785i | ||||
\(532\) | 6.00000 | + | 4.35926i | 0.260133 | + | 0.188998i | ||||
\(533\) | 2.58359 | + | 7.95148i | 0.111908 | + | 0.344417i | ||||
\(534\) | −4.47214 | − | 13.7638i | −0.193528 | − | 0.595619i | ||||
\(535\) | −6.47214 | − | 4.70228i | −0.279815 | − | 0.203297i | ||||
\(536\) | 10.0000 | − | 7.26543i | 0.431934 | − | 0.313819i | ||||
\(537\) | 8.94427 | − | 27.5276i | 0.385974 | − | 1.18791i | ||||
\(538\) | 30.0000 | 1.29339 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −86.8328 | −3.73669 | ||||||||
\(541\) | −10.1459 | + | 31.2259i | −0.436206 | + | 1.34250i | 0.455639 | + | 0.890165i | \(0.349411\pi\) |
−0.891845 | + | 0.452340i | \(0.850589\pi\) | |||||||
\(542\) | −2.76393 | + | 2.00811i | −0.118721 | + | 0.0862559i | ||||
\(543\) | −3.70820 | − | 2.69417i | −0.159134 | − | 0.115618i | ||||
\(544\) | 2.56231 | + | 7.88597i | 0.109858 | + | 0.338108i | ||||
\(545\) | −2.76393 | − | 8.50651i | −0.118394 | − | 0.364379i | ||||
\(546\) | −7.23607 | − | 5.25731i | −0.309675 | − | 0.224992i | ||||
\(547\) | −22.6525 | + | 16.4580i | −0.968550 | + | 0.703693i | −0.955121 | − | 0.296217i | \(-0.904275\pi\) |
−0.0134293 | + | 0.999910i | \(0.504275\pi\) | |||||||
\(548\) | 6.97871 | − | 21.4783i | 0.298116 | − | 0.917506i | ||||
\(549\) | −20.6525 | −0.881426 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.16718 | 0.0497237 | ||||||||
\(552\) | 14.4721 | − | 44.5407i | 0.615975 | − | 1.89578i | ||||
\(553\) | −7.23607 | + | 5.25731i | −0.307709 | + | 0.223564i | ||||
\(554\) | 28.7426 | + | 20.8828i | 1.22116 | + | 0.887223i | ||||
\(555\) | −0.944272 | − | 2.90617i | −0.0400821 | − | 0.123360i | ||||
\(556\) | −9.70820 | − | 29.8788i | −0.411720 | − | 1.26714i | ||||
\(557\) | 17.0344 | + | 12.3762i | 0.721772 | + | 0.524398i | 0.886950 | − | 0.461865i | \(-0.152820\pi\) |
−0.165178 | + | 0.986264i | \(0.552820\pi\) | |||||||
\(558\) | −97.8115 | + | 71.0642i | −4.14069 | + | 3.00839i | ||||
\(559\) | −3.05573 | + | 9.40456i | −0.129244 | + | 0.397771i | ||||
\(560\) | 2.00000 | 0.0845154 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 27.8885 | 1.17641 | ||||||||
\(563\) | 12.1803 | − | 37.4872i | 0.513340 | − | 1.57990i | −0.272942 | − | 0.962031i | \(-0.587997\pi\) |
0.786282 | − | 0.617868i | \(-0.212003\pi\) | |||||||
\(564\) | −56.8328 | + | 41.2915i | −2.39309 | + | 1.73868i | ||||
\(565\) | 3.23607 | + | 2.35114i | 0.136142 | + | 0.0989132i | ||||
\(566\) | 4.06888 | + | 12.5227i | 0.171028 | + | 0.526370i | ||||
\(567\) | 7.54508 | + | 23.2214i | 0.316864 | + | 0.975206i | ||||
\(568\) | −2.76393 | − | 2.00811i | −0.115972 | − | 0.0842586i | ||||
\(569\) | −13.3262 | + | 9.68208i | −0.558665 | + | 0.405894i | −0.830970 | − | 0.556317i | \(-0.812214\pi\) |
0.272305 | + | 0.962211i | \(0.412214\pi\) | |||||||
\(570\) | −11.0557 | + | 34.0260i | −0.463073 | + | 1.42519i | ||||
\(571\) | −32.9443 | −1.37867 | −0.689337 | − | 0.724440i | \(-0.742098\pi\) | ||||
−0.689337 | + | 0.724440i | \(0.742098\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −67.7771 | −2.83143 | ||||||||
\(574\) | 4.67376 | − | 14.3844i | 0.195079 | − | 0.600392i | ||||
\(575\) | −5.23607 | + | 3.80423i | −0.218359 | + | 0.158647i | ||||
\(576\) | 78.5861 | + | 57.0961i | 3.27442 | + | 2.37901i | ||||
\(577\) | −8.79837 | − | 27.0786i | −0.366281 | − | 1.12730i | −0.949175 | − | 0.314749i | \(-0.898080\pi\) |
0.582894 | − | 0.812548i | \(-0.301920\pi\) | |||||||
\(578\) | 10.6910 | + | 32.9035i | 0.444686 | + | 1.36860i | ||||
\(579\) | 62.5410 | + | 45.4387i | 2.59912 | + | 1.88837i | ||||
\(580\) | −2.29180 | + | 1.66509i | −0.0951617 | + | 0.0691390i | ||||
\(581\) | 4.76393 | − | 14.6619i | 0.197641 | − | 0.608277i | ||||
\(582\) | 68.1378 | 2.82440 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | 11.7082 | 0.484489 | ||||||||
\(585\) | 5.70820 | − | 17.5680i | 0.236005 | − | 0.726349i | ||||
\(586\) | 27.3607 | − | 19.8787i | 1.13026 | − | 0.821181i | ||||
\(587\) | 10.6180 | + | 7.71445i | 0.438253 | + | 0.318410i | 0.784940 | − | 0.619571i | \(-0.212693\pi\) |
−0.346687 | + | 0.937981i | \(0.612693\pi\) | |||||||
\(588\) | 3.00000 | + | 9.23305i | 0.123718 | + | 0.380765i | ||||
\(589\) | 5.52786 | + | 17.0130i | 0.227772 | + | 0.701009i | ||||
\(590\) | −11.7082 | − | 8.50651i | −0.482019 | − | 0.350207i | ||||
\(591\) | 5.23607 | − | 3.80423i | 0.215383 | − | 0.156485i | ||||
\(592\) | −0.145898 | + | 0.449028i | −0.00599637 | + | 0.0184549i | ||||
\(593\) | −32.2918 | −1.32607 | −0.663033 | − | 0.748591i | \(-0.730731\pi\) | ||||
−0.663033 | + | 0.748591i | \(0.730731\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −2.47214 | −0.101348 | ||||||||
\(596\) | 12.9787 | − | 39.9444i | 0.531629 | − | 1.63619i | ||||
\(597\) | −52.8328 | + | 38.3853i | −2.16230 | + | 1.57101i | ||||
\(598\) | 14.4721 | + | 10.5146i | 0.591810 | + | 0.429975i | ||||
\(599\) | 1.05573 | + | 3.24920i | 0.0431359 | + | 0.132759i | 0.970305 | − | 0.241884i | \(-0.0777654\pi\) |
−0.927169 | + | 0.374643i | \(0.877765\pi\) | |||||||
\(600\) | 2.23607 | + | 6.88191i | 0.0912871 | + | 0.280953i | ||||
\(601\) | −2.52786 | − | 1.83660i | −0.103114 | − | 0.0749165i | 0.535034 | − | 0.844831i | \(-0.320299\pi\) |
−0.638147 | + | 0.769914i | \(0.720299\pi\) | |||||||
\(602\) | 14.4721 | − | 10.5146i | 0.589840 | − | 0.428544i | ||||
\(603\) | 12.7639 | − | 39.2833i | 0.519787 | − | 1.59974i | ||||
\(604\) | −26.8328 | −1.09181 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 66.8328 | 2.71490 | ||||||||
\(607\) | −1.52786 | + | 4.70228i | −0.0620141 | + | 0.190860i | −0.977264 | − | 0.212028i | \(-0.931993\pi\) |
0.915250 | + | 0.402887i | \(0.131993\pi\) | |||||||
\(608\) | 13.4164 | − | 9.74759i | 0.544107 | − | 0.395317i | ||||
\(609\) | 1.23607 | + | 0.898056i | 0.0500880 | + | 0.0363911i | ||||
\(610\) | −3.81966 | − | 11.7557i | −0.154654 | − | 0.475975i | ||||
\(611\) | −2.76393 | − | 8.50651i | −0.111817 | − | 0.344136i | ||||
\(612\) | −22.4164 | − | 16.2865i | −0.906130 | − | 0.658342i | ||||
\(613\) | 38.2705 | − | 27.8052i | 1.54573 | − | 1.12304i | 0.599121 | − | 0.800658i | \(-0.295517\pi\) |
0.946610 | − | 0.322381i | \(-0.104483\pi\) | |||||||
\(614\) | −6.18034 | + | 19.0211i | −0.249418 | + | 0.767630i | ||||
\(615\) | 43.7771 | 1.76526 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 33.4164 | 1.34529 | 0.672647 | − | 0.739964i | \(-0.265157\pi\) | ||||
0.672647 | + | 0.739964i | \(0.265157\pi\) | |||||||
\(618\) | 12.7639 | − | 39.2833i | 0.513441 | − | 1.58021i | ||||
\(619\) | 23.5623 | − | 17.1190i | 0.947049 | − | 0.688071i | −0.00305805 | − | 0.999995i | \(-0.500973\pi\) |
0.950107 | + | 0.311924i | \(0.100973\pi\) | |||||||
\(620\) | −35.1246 | − | 25.5195i | −1.41064 | − | 1.02489i | ||||
\(621\) | −28.9443 | − | 89.0813i | −1.16149 | − | 3.57471i | ||||
\(622\) | 15.0000 | + | 46.1653i | 0.601445 | + | 1.85106i | ||||
\(623\) | −1.61803 | − | 1.17557i | −0.0648252 | − | 0.0470982i | ||||
\(624\) | −3.23607 | + | 2.35114i | −0.129546 | + | 0.0941210i | ||||
\(625\) | −5.87132 | + | 18.0701i | −0.234853 | + | 0.722803i | ||||
\(626\) | 6.58359 | 0.263133 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −20.8328 | −0.831320 | ||||||||
\(629\) | 0.180340 | − | 0.555029i | 0.00719062 | − | 0.0221305i | ||||
\(630\) | −27.0344 | + | 19.6417i | −1.07708 | + | 0.782543i | ||||
\(631\) | 19.4164 | + | 14.1068i | 0.772955 | + | 0.561585i | 0.902856 | − | 0.429942i | \(-0.141466\pi\) |
−0.129901 | + | 0.991527i | \(0.541466\pi\) | |||||||
\(632\) | −6.18034 | − | 19.0211i | −0.245841 | − | 0.756620i | ||||
\(633\) | 21.8885 | + | 67.3660i | 0.869992 | + | 2.67756i | ||||
\(634\) | 25.3262 | + | 18.4006i | 1.00583 | + | 0.730781i | ||||
\(635\) | 33.8885 | − | 24.6215i | 1.34483 | − | 0.977073i | ||||
\(636\) | 25.4164 | − | 78.2237i | 1.00783 | − | 3.10177i | ||||
\(637\) | −1.23607 | −0.0489748 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −11.4164 | −0.451626 | ||||||||
\(640\) | −9.67376 | + | 29.7728i | −0.382389 | + | 1.17687i | ||||
\(641\) | 19.7984 | − | 14.3844i | 0.781989 | − | 0.568148i | −0.123586 | − | 0.992334i | \(-0.539440\pi\) |
0.905575 | + | 0.424186i | \(0.139440\pi\) | |||||||
\(642\) | −23.4164 | − | 17.0130i | −0.924172 | − | 0.671450i | ||||
\(643\) | −9.00000 | − | 27.6992i | −0.354925 | − | 1.09235i | −0.956053 | − | 0.293195i | \(-0.905282\pi\) |
0.601127 | − | 0.799153i | \(-0.294718\pi\) | |||||||
\(644\) | −6.00000 | − | 18.4661i | −0.236433 | − | 0.727666i | ||||
\(645\) | 41.8885 | + | 30.4338i | 1.64936 | + | 1.19833i | ||||
\(646\) | −5.52786 | + | 4.01623i | −0.217491 | + | 0.158016i | ||||
\(647\) | −6.81966 | + | 20.9888i | −0.268109 | + | 0.825153i | 0.722852 | + | 0.691002i | \(0.242831\pi\) |
−0.990961 | + | 0.134151i | \(0.957169\pi\) | |||||||
\(648\) | −54.5967 | −2.14476 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | −2.76393 | −0.108410 | ||||||||
\(651\) | −7.23607 | + | 22.2703i | −0.283604 | + | 0.872843i | ||||
\(652\) | −56.8328 | + | 41.2915i | −2.22574 | + | 1.61710i | ||||
\(653\) | −34.7426 | − | 25.2420i | −1.35958 | − | 0.987796i | −0.998471 | − | 0.0552743i | \(-0.982397\pi\) |
−0.361114 | − | 0.932522i | \(-0.617603\pi\) | |||||||
\(654\) | −10.0000 | − | 30.7768i | −0.391031 | − | 1.20347i | ||||
\(655\) | 8.58359 | + | 26.4176i | 0.335389 | + | 1.03222i | ||||
\(656\) | −5.47214 | − | 3.97574i | −0.213651 | − | 0.155227i | ||||
\(657\) | 31.6525 | − | 22.9969i | 1.23488 | − | 0.897193i | ||||
\(658\) | −5.00000 | + | 15.3884i | −0.194920 | + | 0.599903i | ||||
\(659\) | 17.8885 | 0.696839 | 0.348419 | − | 0.937339i | \(-0.386719\pi\) | ||||
0.348419 | + | 0.937339i | \(0.386719\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 12.8328 | 0.499139 | 0.249569 | − | 0.968357i | \(-0.419711\pi\) | ||||
0.249569 | + | 0.968357i | \(0.419711\pi\) | |||||||
\(662\) | −15.1246 | + | 46.5488i | −0.587835 | + | 1.80917i | ||||
\(663\) | 4.00000 | − | 2.90617i | 0.155347 | − | 0.112866i | ||||
\(664\) | 27.8885 | + | 20.2622i | 1.08229 | + | 0.786326i | ||||
\(665\) | 1.52786 | + | 4.70228i | 0.0592480 | + | 0.182347i | ||||
\(666\) | −2.43769 | − | 7.50245i | −0.0944587 | − | 0.290714i | ||||
\(667\) | −2.47214 | − | 1.79611i | −0.0957215 | − | 0.0695457i | ||||
\(668\) | 31.4164 | − | 22.8254i | 1.21554 | − | 0.883140i | ||||
\(669\) | 12.1803 | − | 37.4872i | 0.470919 | − | 1.44934i | ||||
\(670\) | 24.7214 | 0.955069 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 21.7082 | 0.837412 | ||||||||
\(673\) | 1.67376 | − | 5.15131i | 0.0645188 | − | 0.198568i | −0.913601 | − | 0.406613i | \(-0.866710\pi\) |
0.978119 | + | 0.208044i | \(0.0667098\pi\) | |||||||
\(674\) | −37.0344 | + | 26.9071i | −1.42651 | + | 1.03642i | ||||
\(675\) | 11.7082 | + | 8.50651i | 0.450649 | + | 0.327416i | ||||
\(676\) | −10.6353 | − | 32.7319i | −0.409048 | − | 1.25892i | ||||
\(677\) | 1.14590 | + | 3.52671i | 0.0440404 | + | 0.135543i | 0.970659 | − | 0.240460i | \(-0.0772983\pi\) |
−0.926619 | + | 0.376003i | \(0.877298\pi\) | |||||||
\(678\) | 11.7082 | + | 8.50651i | 0.449651 | + | 0.326690i | ||||
\(679\) | 7.61803 | − | 5.53483i | 0.292353 | − | 0.212407i | ||||
\(680\) | 1.70820 | − | 5.25731i | 0.0655066 | − | 0.201609i | ||||
\(681\) | −96.7214 | −3.70637 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 29.8885 | 1.14365 | 0.571827 | − | 0.820374i | \(-0.306235\pi\) | ||||
0.571827 | + | 0.820374i | \(0.306235\pi\) | |||||||
\(684\) | −17.1246 | + | 52.7041i | −0.654776 | + | 2.01519i | ||||
\(685\) | 12.1803 | − | 8.84953i | 0.465387 | − | 0.338123i | ||||
\(686\) | 1.80902 | + | 1.31433i | 0.0690686 | + | 0.0501813i | ||||
\(687\) | 4.47214 | + | 13.7638i | 0.170623 | + | 0.525122i | ||||
\(688\) | −2.47214 | − | 7.60845i | −0.0942493 | − | 0.290070i | ||||
\(689\) | 8.47214 | + | 6.15537i | 0.322763 | + | 0.234501i | ||||
\(690\) | 75.7771 | − | 55.0553i | 2.88478 | − | 2.09592i | ||||
\(691\) | −15.0000 | + | 46.1653i | −0.570627 | + | 1.75621i | 0.0799823 | + | 0.996796i | \(0.474514\pi\) |
−0.650609 | + | 0.759413i | \(0.725486\pi\) | |||||||
\(692\) | −51.7082 | −1.96565 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −6.83282 | −0.259370 | ||||||||
\(695\) | 6.47214 | − | 19.9192i | 0.245502 | − | 0.755578i | ||||
\(696\) | −2.76393 | + | 2.00811i | −0.104767 | + | 0.0761174i | ||||
\(697\) | 6.76393 | + | 4.91428i | 0.256202 | + | 0.186142i | ||||
\(698\) | 1.90983 | + | 5.87785i | 0.0722881 | + | 0.222480i | ||||
\(699\) | −17.4164 | − | 53.6022i | −0.658749 | − | 2.02742i | ||||
\(700\) | 2.42705 | + | 1.76336i | 0.0917339 | + | 0.0666486i | ||||
\(701\) | 19.7984 | − | 14.3844i | 0.747774 | − | 0.543290i | −0.147362 | − | 0.989083i | \(-0.547078\pi\) |
0.895136 | + | 0.445793i | \(0.147078\pi\) | |||||||
\(702\) | 12.3607 | − | 38.0423i | 0.466524 | − | 1.43581i | ||||
\(703\) | −1.16718 | −0.0440212 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −46.8328 | −1.76383 | ||||||||
\(706\) | 10.9787 | − | 33.7890i | 0.413189 | − | 1.27167i | ||||
\(707\) | 7.47214 | − | 5.42882i | 0.281019 | − | 0.204172i | ||||
\(708\) | −25.4164 | − | 18.4661i | −0.955207 | − | 0.693999i | ||||
\(709\) | 0.909830 | + | 2.80017i | 0.0341694 | + | 0.105163i | 0.966687 | − | 0.255963i | \(-0.0823926\pi\) |
−0.932517 | + | 0.361126i | \(0.882393\pi\) | |||||||
\(710\) | −2.11146 | − | 6.49839i | −0.0792415 | − | 0.243880i | ||||
\(711\) | −54.0689 | − | 39.2833i | −2.02774 | − | 1.47324i | ||||
\(712\) | 3.61803 | − | 2.62866i | 0.135592 | − | 0.0985130i | ||||
\(713\) | 14.4721 | − | 44.5407i | 0.541986 | − | 1.66806i | ||||
\(714\) | −8.94427 | −0.334731 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 26.8328 | 1.00279 | ||||||||
\(717\) | 25.8885 | − | 79.6767i | 0.966825 | − | 2.97558i | ||||
\(718\) | −12.7639 | + | 9.27354i | −0.476346 | + | 0.346085i | ||||
\(719\) | −27.0902 | − | 19.6822i | −1.01029 | − | 0.734021i | −0.0460224 | − | 0.998940i | \(-0.514655\pi\) |
−0.964270 | + | 0.264920i | \(0.914655\pi\) | |||||||
\(720\) | 4.61803 | + | 14.2128i | 0.172104 | + | 0.529682i | ||||
\(721\) | −1.76393 | − | 5.42882i | −0.0656923 | − | 0.202180i | ||||
\(722\) | −23.3156 | − | 16.9398i | −0.867717 | − | 0.630433i | ||||
\(723\) | −71.0132 | + | 51.5941i | −2.64101 | + | 1.91880i | ||||
\(724\) | 1.31308 | − | 4.04125i | 0.0488003 | − | 0.150192i | ||||
\(725\) | 0.472136 | 0.0175347 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −51.0132 | −1.89197 | −0.945987 | − | 0.324206i | \(-0.894903\pi\) | ||||
−0.945987 | + | 0.324206i | \(0.894903\pi\) | |||||||
\(728\) | 0.854102 | − | 2.62866i | 0.0316551 | − | 0.0974245i | ||||
\(729\) | −33.9336 | + | 24.6542i | −1.25680 | + | 0.913119i | ||||
\(730\) | 18.9443 | + | 13.7638i | 0.701159 | + | 0.509422i | ||||
\(731\) | 3.05573 | + | 9.40456i | 0.113020 | + | 0.347840i | ||||
\(732\) | −8.29180 | − | 25.5195i | −0.306474 | − | 0.943229i | ||||
\(733\) | −10.7082 | − | 7.77997i | −0.395517 | − | 0.287360i | 0.372196 | − | 0.928154i | \(-0.378605\pi\) |
−0.767712 | + | 0.640795i | \(0.778605\pi\) | |||||||
\(734\) | 30.9787 | − | 22.5074i | 1.14345 | − | 0.830762i | ||||
\(735\) | −2.00000 | + | 6.15537i | −0.0737711 | + | 0.227044i | ||||
\(736\) | −43.4164 | −1.60035 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 113.013 | 4.16007 | ||||||||
\(739\) | 2.18034 | − | 6.71040i | 0.0802051 | − | 0.246846i | −0.902911 | − | 0.429827i | \(-0.858575\pi\) |
0.983116 | + | 0.182981i | \(0.0585746\pi\) | |||||||
\(740\) | 2.29180 | − | 1.66509i | 0.0842481 | − | 0.0612098i | ||||
\(741\) | −8.00000 | − | 5.81234i | −0.293887 | − | 0.213522i | ||||
\(742\) | −5.85410 | − | 18.0171i | −0.214911 | − | 0.661428i | ||||
\(743\) | −10.4721 | − | 32.2299i | −0.384185 | − | 1.18240i | −0.937069 | − | 0.349143i | \(-0.886473\pi\) |
0.552884 | − | 0.833258i | \(-0.313527\pi\) | |||||||
\(744\) | −42.3607 | − | 30.7768i | −1.55302 | − | 1.12833i | ||||
\(745\) | 22.6525 | − | 16.4580i | 0.829923 | − | 0.602974i | ||||
\(746\) | −4.14590 | + | 12.7598i | −0.151792 | + | 0.467168i | ||||
\(747\) | 115.193 | 4.21471 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −4.00000 | −0.146157 | ||||||||
\(750\) | −26.8328 | + | 82.5829i | −0.979796 | + | 3.01550i | ||||
\(751\) | −31.1246 | + | 22.6134i | −1.13575 | + | 0.825173i | −0.986522 | − | 0.163629i | \(-0.947680\pi\) |
−0.149231 | + | 0.988802i | \(0.547680\pi\) | |||||||
\(752\) | 5.85410 | + | 4.25325i | 0.213477 | + | 0.155100i | ||||
\(753\) | 17.7082 | + | 54.5002i | 0.645323 | + | 1.98610i | ||||
\(754\) | −0.403252 | − | 1.24108i | −0.0146856 | − | 0.0451976i | ||||
\(755\) | −14.4721 | − | 10.5146i | −0.526695 | − | 0.382666i | ||||
\(756\) | −35.1246 | + | 25.5195i | −1.27747 | + | 0.928136i | ||||
\(757\) | −6.14590 | + | 18.9151i | −0.223376 | + | 0.687482i | 0.775076 | + | 0.631868i | \(0.217712\pi\) |
−0.998452 | + | 0.0556139i | \(0.982288\pi\) | |||||||
\(758\) | 56.5836 | 2.05521 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −11.0557 | −0.401033 | ||||||||
\(761\) | 5.43769 | − | 16.7355i | 0.197116 | − | 0.606661i | −0.802829 | − | 0.596209i | \(-0.796673\pi\) |
0.999945 | − | 0.0104523i | \(-0.00332712\pi\) | |||||||
\(762\) | 122.610 | − | 89.0813i | 4.44169 | − | 3.22708i | ||||
\(763\) | −3.61803 | − | 2.62866i | −0.130982 | − | 0.0951637i | ||||
\(764\) | −19.4164 | − | 59.7576i | −0.702461 | − | 2.16195i | ||||
\(765\) | −5.70820 | − | 17.5680i | −0.206381 | − | 0.635174i | ||||
\(766\) | 48.2148 | + | 35.0301i | 1.74207 | + | 1.26569i | ||||
\(767\) | 3.23607 | − | 2.35114i | 0.116848 | − | 0.0848948i | ||||
\(768\) | −9.00000 | + | 27.6992i | −0.324760 | + | 0.999507i | ||||
\(769\) | 31.7082 | 1.14343 | 0.571714 | − | 0.820453i | \(-0.306279\pi\) | ||||
0.571714 | + | 0.820453i | \(0.306279\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −19.4164 | −0.699265 | ||||||||
\(772\) | −22.1459 | + | 68.1581i | −0.797048 | + | 2.45306i | ||||
\(773\) | −5.14590 | + | 3.73871i | −0.185085 | + | 0.134472i | −0.676470 | − | 0.736471i | \(-0.736491\pi\) |
0.491385 | + | 0.870943i | \(0.336491\pi\) | |||||||
\(774\) | 108.138 | + | 78.5667i | 3.88693 | + | 2.82402i | ||||
\(775\) | 2.23607 | + | 6.88191i | 0.0803219 | + | 0.247205i | ||||
\(776\) | 6.50658 | + | 20.0252i | 0.233573 | + | 0.718862i | ||||
\(777\) | −1.23607 | − | 0.898056i | −0.0443437 | − | 0.0322176i | ||||
\(778\) | −35.9787 | + | 26.1401i | −1.28990 | + | 0.937167i | ||||
\(779\) | 5.16718 | − | 15.9030i | 0.185134 | − | 0.569783i | ||||
\(780\) | 24.0000 | 0.859338 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 17.8885 | 0.639693 | ||||||||
\(783\) | −2.11146 | + | 6.49839i | −0.0754573 | + | 0.232234i | ||||
\(784\) | 0.809017 | − | 0.587785i | 0.0288935 | − | 0.0209923i | ||||
\(785\) | −11.2361 | − | 8.16348i | −0.401032 | − | 0.291367i | ||||
\(786\) | 31.0557 | + | 95.5797i | 1.10772 | + | 3.40922i | ||||
\(787\) | −5.12461 | − | 15.7719i | −0.182673 | − | 0.562209i | 0.817228 | − | 0.576315i | \(-0.195510\pi\) |
−0.999901 | + | 0.0141060i | \(0.995510\pi\) | |||||||
\(788\) | 4.85410 | + | 3.52671i | 0.172920 | + | 0.125634i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 12.3607 | − | 38.0423i | 0.439773 | − | 1.35348i | ||||
\(791\) | 2.00000 | 0.0711118 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 3.41641 | 0.121320 | ||||||||
\(794\) | 0.0770143 | − | 0.237026i | 0.00273314 | − | 0.00841173i | ||||
\(795\) | 44.3607 | − | 32.2299i | 1.57331 | − | 1.14308i | ||||
\(796\) | −48.9787 | − | 35.5851i | −1.73600 | − | 1.26128i | ||||
\(797\) | 0.909830 | + | 2.80017i | 0.0322278 | + | 0.0991871i | 0.965877 | − | 0.259003i | \(-0.0833940\pi\) |
−0.933649 | + | 0.358190i | \(0.883394\pi\) | |||||||
\(798\) | 5.52786 | + | 17.0130i | 0.195684 | + | 0.602254i | ||||
\(799\) | −7.23607 | − | 5.25731i | −0.255994 | − | 0.185990i | ||||
\(800\) | 5.42705 | − | 3.94298i | 0.191875 | − | 0.139406i | ||||
\(801\) | 4.61803 | − | 14.2128i | 0.163170 | − | 0.502186i | ||||
\(802\) | −11.3050 | −0.399192 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 53.6656 | 1.89264 | ||||||||
\(805\) | 4.00000 | − | 12.3107i | 0.140981 | − | 0.433896i | ||||
\(806\) | 16.1803 | − | 11.7557i | 0.569928 | − | 0.414077i | ||||
\(807\) | 35.1246 | + | 25.5195i | 1.23644 | + | 0.898330i | ||||
\(808\) | 6.38197 | + | 19.6417i | 0.224517 | + | 0.690992i | ||||
\(809\) | 12.0344 | + | 37.0382i | 0.423108 | + | 1.30219i | 0.904794 | + | 0.425850i | \(0.140025\pi\) |
−0.481685 | + | 0.876344i | \(0.659975\pi\) | |||||||
\(810\) | −88.3394 | − | 64.1823i | −3.10393 | − | 2.25514i | ||||
\(811\) | −15.2361 | + | 11.0697i | −0.535011 | + | 0.388708i | −0.822229 | − | 0.569157i | \(-0.807270\pi\) |
0.287218 | + | 0.957865i | \(0.407270\pi\) | |||||||
\(812\) | −0.437694 | + | 1.34708i | −0.0153601 | + | 0.0472734i | ||||
\(813\) | −4.94427 | −0.173403 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −46.8328 | −1.64048 | ||||||||
\(816\) | −1.23607 | + | 3.80423i | −0.0432710 | + | 0.133175i | ||||
\(817\) | 16.0000 | − | 11.6247i | 0.559769 | − | 0.406696i | ||||
\(818\) | −56.3050 | − | 40.9079i | −1.96866 | − | 1.43031i | ||||
\(819\) | −2.85410 | − | 8.78402i | −0.0997304 | − | 0.306939i | ||||
\(820\) | 12.5410 | + | 38.5973i | 0.437951 | + | 1.34788i | ||||
\(821\) | 7.14590 | + | 5.19180i | 0.249394 | + | 0.181195i | 0.705458 | − | 0.708752i | \(-0.250741\pi\) |
−0.456064 | + | 0.889947i | \(0.650741\pi\) | |||||||
\(822\) | 44.0689 | − | 32.0179i | 1.53708 | − | 1.11675i | ||||
\(823\) | −15.4164 | + | 47.4468i | −0.537382 | + | 1.65389i | 0.201063 | + | 0.979578i | \(0.435561\pi\) |
−0.738445 | + | 0.674314i | \(0.764439\pi\) | |||||||
\(824\) | 12.7639 | 0.444653 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −7.23607 | −0.251775 | ||||||||
\(827\) | 1.52786 | − | 4.70228i | 0.0531290 | − | 0.163514i | −0.920971 | − | 0.389630i | \(-0.872603\pi\) |
0.974100 | + | 0.226116i | \(0.0726028\pi\) | |||||||
\(828\) | 117.374 | − | 85.2771i | 4.07902 | − | 2.96358i | ||||
\(829\) | 13.6180 | + | 9.89408i | 0.472974 | + | 0.343636i | 0.798599 | − | 0.601863i | \(-0.205575\pi\) |
−0.325625 | + | 0.945499i | \(0.605575\pi\) | |||||||
\(830\) | 21.3050 | + | 65.5699i | 0.739506 | + | 2.27596i | ||||
\(831\) | 15.8885 | + | 48.8999i | 0.551167 | + | 1.69632i | ||||
\(832\) | −13.0000 | − | 9.44505i | −0.450694 | − | 0.327448i | ||||
\(833\) | −1.00000 | + | 0.726543i | −0.0346479 | + | 0.0251732i | ||||
\(834\) | 23.4164 | − | 72.0683i | 0.810844 | − | 2.49552i | ||||
\(835\) | 25.8885 | 0.895910 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −104.721 | −3.61970 | ||||||||
\(838\) | 4.59675 | − | 14.1473i | 0.158792 | − | 0.488712i | ||||
\(839\) | 11.3820 | − | 8.26948i | 0.392949 | − | 0.285494i | −0.373714 | − | 0.927544i | \(-0.621916\pi\) |
0.766663 | + | 0.642050i | \(0.221916\pi\) | |||||||
\(840\) | −11.7082 | − | 8.50651i | −0.403971 | − | 0.293502i | ||||
\(841\) | −8.89261 | − | 27.3686i | −0.306642 | − | 0.943746i | ||||
\(842\) | 15.4508 | + | 47.5528i | 0.532471 | + | 1.63878i | ||||
\(843\) | 32.6525 | + | 23.7234i | 1.12461 | + | 0.817078i | ||||
\(844\) | −53.1246 | + | 38.5973i | −1.82862 | + | 1.32857i | ||||
\(845\) | 7.09017 | − | 21.8213i | 0.243909 | − | 0.750676i | ||||
\(846\) | −120.902 | −4.15669 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −8.47214 | −0.290934 | ||||||||
\(849\) | −5.88854 | + | 18.1231i | −0.202094 | + | 0.621982i | ||||
\(850\) | −2.23607 | + | 1.62460i | −0.0766965 | + | 0.0557233i | ||||
\(851\) | 2.47214 | + | 1.79611i | 0.0847437 | + | 0.0615699i | ||||
\(852\) | −4.58359 | − | 14.1068i | −0.157031 | − | 0.483293i | ||||
\(853\) | 0.201626 | + | 0.620541i | 0.00690355 | + | 0.0212469i | 0.954449 | − | 0.298374i | \(-0.0964443\pi\) |
−0.947545 | + | 0.319621i | \(0.896444\pi\) | |||||||
\(854\) | −5.00000 | − | 3.63271i | −0.171096 | − | 0.124309i | ||||
\(855\) | −29.8885 | + | 21.7153i | −1.02217 | + | 0.742648i | ||||
\(856\) | 2.76393 | − | 8.50651i | 0.0944693 | − | 0.290746i | ||||
\(857\) | 10.7639 | 0.367689 | 0.183844 | − | 0.982955i | \(-0.441146\pi\) | ||||
0.183844 | + | 0.982955i | \(0.441146\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 40.5410 | 1.38324 | 0.691621 | − | 0.722261i | \(-0.256897\pi\) | ||||
0.691621 | + | 0.722261i | \(0.256897\pi\) | |||||||
\(860\) | −14.8328 | + | 45.6507i | −0.505795 | + | 1.55668i | ||||
\(861\) | 17.7082 | − | 12.8658i | 0.603494 | − | 0.438464i | ||||
\(862\) | 21.7082 | + | 15.7719i | 0.739384 | + | 0.537194i | ||||
\(863\) | −6.47214 | − | 19.9192i | −0.220314 | − | 0.678057i | −0.998734 | − | 0.0503125i | \(-0.983978\pi\) |
0.778419 | − | 0.627744i | \(-0.216022\pi\) | |||||||
\(864\) | 30.0000 | + | 92.3305i | 1.02062 | + | 3.14115i | ||||
\(865\) | −27.8885 | − | 20.2622i | −0.948239 | − | 0.688936i | ||||
\(866\) | 0.854102 | − | 0.620541i | 0.0290236 | − | 0.0210869i | ||||
\(867\) | −15.4721 | + | 47.6183i | −0.525461 | + | 1.61720i | ||||
\(868\) | −21.7082 | −0.736824 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | −6.83282 | −0.231654 | ||||||||
\(871\) | −2.11146 | + | 6.49839i | −0.0715440 | + | 0.220190i | ||||
\(872\) | 8.09017 | − | 5.87785i | 0.273968 | − | 0.199049i | ||||
\(873\) | 56.9230 | + | 41.3570i | 1.92655 | + | 1.39972i | ||||
\(874\) | −11.0557 | − | 34.0260i | −0.373966 | − | 1.15095i | ||||
\(875\) | 3.70820 | + | 11.4127i | 0.125360 | + | 0.385819i | ||||
\(876\) | 41.1246 | + | 29.8788i | 1.38947 | + | 1.00951i | ||||
\(877\) | −33.5066 | + | 24.3440i | −1.13144 | + | 0.822037i | −0.985903 | − | 0.167316i | \(-0.946490\pi\) |
−0.145533 | + | 0.989353i | \(0.546490\pi\) | |||||||
\(878\) | −1.05573 | + | 3.24920i | −0.0356291 | + | 0.109655i | ||||
\(879\) | 48.9443 | 1.65085 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 29.4164 | 0.991064 | 0.495532 | − | 0.868590i | \(-0.334973\pi\) | ||||
0.495532 | + | 0.868590i | \(0.334973\pi\) | |||||||
\(882\) | −5.16312 | + | 15.8904i | −0.173851 | + | 0.535059i | ||||
\(883\) | −7.23607 | + | 5.25731i | −0.243513 | + | 0.176923i | −0.702847 | − | 0.711341i | \(-0.748088\pi\) |
0.459334 | + | 0.888264i | \(0.348088\pi\) | |||||||
\(884\) | 3.70820 | + | 2.69417i | 0.124720 | + | 0.0906147i | ||||
\(885\) | −6.47214 | − | 19.9192i | −0.217558 | − | 0.669576i | ||||
\(886\) | 4.87539 | + | 15.0049i | 0.163792 | + | 0.504100i | ||||
\(887\) | −32.6525 | − | 23.7234i | −1.09636 | − | 0.796554i | −0.115900 | − | 0.993261i | \(-0.536975\pi\) |
−0.980462 | + | 0.196707i | \(0.936975\pi\) | |||||||
\(888\) | 2.76393 | − | 2.00811i | 0.0927515 | − | 0.0673879i | ||||
\(889\) | 6.47214 | − | 19.9192i | 0.217068 | − | 0.668068i | ||||
\(890\) | 8.94427 | 0.299813 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 36.5410 | 1.22348 | ||||||||
\(893\) | −5.52786 | + | 17.0130i | −0.184983 | + | 0.569319i | ||||
\(894\) | 81.9574 | − | 59.5456i | 2.74107 | − | 1.99150i | ||||
\(895\) | 14.4721 | + | 10.5146i | 0.483750 | + | 0.351465i | ||||
\(896\) | 4.83688 | + | 14.8864i | 0.161589 | + | 0.497319i | ||||
\(897\) | 8.00000 | + | 24.6215i | 0.267112 | + | 0.822087i | ||||
\(898\) | −35.3262 | − | 25.6660i | −1.17885 | − | 0.856486i | ||||
\(899\) | −2.76393 | + | 2.00811i | −0.0921823 | + | 0.0669744i | ||||
\(900\) | −6.92705 | + | 21.3193i | −0.230902 | + | 0.710642i | ||||
\(901\) | 10.4721 | 0.348877 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 25.8885 | 0.861517 | ||||||||
\(904\) | −1.38197 | + | 4.25325i | −0.0459635 | + | 0.141461i | ||||
\(905\) | 2.29180 | − | 1.66509i | 0.0761819 | − | 0.0553494i | ||||
\(906\) | −52.3607 | − | 38.0423i | −1.73957 | − | 1.26387i | ||||
\(907\) | 4.18034 | + | 12.8658i | 0.138806 | + | 0.427201i | 0.996163 | − | 0.0875221i | \(-0.0278948\pi\) |
−0.857357 | + | 0.514723i | \(0.827895\pi\) | |||||||
\(908\) | −27.7082 | − | 85.2771i | −0.919529 | − | 2.83002i | ||||
\(909\) | 55.8328 | + | 40.5649i | 1.85186 | + | 1.34545i | ||||
\(910\) | 4.47214 | − | 3.24920i | 0.148250 | − | 0.107710i | ||||
\(911\) | 10.3607 | − | 31.8869i | 0.343265 | − | 1.05646i | −0.619242 | − | 0.785200i | \(-0.712560\pi\) |
0.962506 | − | 0.271259i | \(-0.0874401\pi\) | |||||||
\(912\) | 8.00000 | 0.264906 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | −55.5279 | −1.83670 | ||||||||
\(915\) | 5.52786 | − | 17.0130i | 0.182746 | − | 0.562433i | ||||
\(916\) | −10.8541 | + | 7.88597i | −0.358630 | + | 0.260560i | ||||
\(917\) | 11.2361 | + | 8.16348i | 0.371048 | + | 0.269582i | ||||
\(918\) | −12.3607 | − | 38.0423i | −0.407963 | − | 1.25558i | ||||
\(919\) | 1.88854 | + | 5.81234i | 0.0622973 | + | 0.191731i | 0.977361 | − | 0.211577i | \(-0.0678600\pi\) |
−0.915064 | + | 0.403309i | \(0.867860\pi\) | |||||||
\(920\) | 23.4164 | + | 17.0130i | 0.772016 | + | 0.560903i | ||||
\(921\) | −23.4164 | + | 17.0130i | −0.771597 | + | 0.560598i | ||||
\(922\) | −7.03444 | + | 21.6498i | −0.231667 | + | 0.712998i | ||||
\(923\) | 1.88854 | 0.0621622 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −0.472136 | −0.0155237 | ||||||||
\(926\) | 10.0000 | − | 30.7768i | 0.328620 | − | 1.01139i | ||||
\(927\) | 34.5066 | − | 25.0705i | 1.13334 | − | 0.823423i | ||||
\(928\) | 2.56231 | + | 1.86162i | 0.0841118 | + | 0.0611108i | ||||
\(929\) | 8.72949 | + | 26.8666i | 0.286405 | + | 0.881465i | 0.985974 | + | 0.166899i | \(0.0533755\pi\) |
−0.699569 | + | 0.714565i | \(0.746624\pi\) | |||||||
\(930\) | −32.3607 | − | 99.5959i | −1.06115 | − | 3.26588i | ||||
\(931\) | 2.00000 | + | 1.45309i | 0.0655474 | + | 0.0476229i | ||||
\(932\) | 42.2705 | − | 30.7113i | 1.38462 | − | 1.00598i | ||||
\(933\) | −21.7082 | + | 66.8110i | −0.710695 | + | 2.18729i | ||||
\(934\) | 76.1803 | 2.49270 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 20.6525 | 0.675047 | ||||||||
\(937\) | 6.38197 | − | 19.6417i | 0.208490 | − | 0.641665i | −0.791062 | − | 0.611736i | \(-0.790472\pi\) |
0.999552 | − | 0.0299298i | \(-0.00952837\pi\) | |||||||
\(938\) | 10.0000 | − | 7.26543i | 0.326512 | − | 0.237225i | ||||
\(939\) | 7.70820 | + | 5.60034i | 0.251548 | + | 0.182760i | ||||
\(940\) | −13.4164 | − | 41.2915i | −0.437595 | − | 1.34678i | ||||
\(941\) | −12.8541 | − | 39.5609i | −0.419032 | − | 1.28965i | −0.908595 | − | 0.417679i | \(-0.862844\pi\) |
0.489563 | − | 0.871968i | \(-0.337156\pi\) | |||||||
\(942\) | −40.6525 | − | 29.5358i | −1.32453 | − | 0.962327i | ||||
\(943\) | −35.4164 | + | 25.7315i | −1.15332 | + | 0.837934i | ||||
\(944\) | −1.00000 | + | 3.07768i | −0.0325472 | + | 0.100170i | ||||
\(945\) | −28.9443 | −0.941557 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −58.8328 | −1.91181 | −0.955905 | − | 0.293677i | \(-0.905121\pi\) | ||||
−0.955905 | + | 0.293677i | \(0.905121\pi\) | |||||||
\(948\) | 26.8328 | − | 82.5829i | 0.871489 | − | 2.68217i | ||||
\(949\) | −5.23607 | + | 3.80423i | −0.169970 | + | 0.123490i | ||||
\(950\) | 4.47214 | + | 3.24920i | 0.145095 | + | 0.105418i | ||||
\(951\) | 14.0000 | + | 43.0876i | 0.453981 | + | 1.39721i | ||||
\(952\) | −0.854102 | − | 2.62866i | −0.0276816 | − | 0.0851952i | ||||
\(953\) | −4.09017 | − | 2.97168i | −0.132494 | − | 0.0962622i | 0.519565 | − | 0.854431i | \(-0.326094\pi\) |
−0.652058 | + | 0.758169i | \(0.726094\pi\) | |||||||
\(954\) | 114.520 | − | 83.2035i | 3.70771 | − | 2.69381i | ||||
\(955\) | 12.9443 | − | 39.8384i | 0.418867 | − | 1.28914i | ||||
\(956\) | 77.6656 | 2.51189 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −50.2492 | −1.62348 | ||||||||
\(959\) | 2.32624 | − | 7.15942i | 0.0751181 | − | 0.231190i | ||||
\(960\) | −68.0689 | + | 49.4549i | −2.19691 | + | 1.59615i | ||||
\(961\) | −17.2812 | − | 12.5555i | −0.557457 | − | 0.405016i | ||||
\(962\) | 0.403252 | + | 1.24108i | 0.0130014 | + | 0.0400141i | ||||
\(963\) | −9.23607 | − | 28.4257i | −0.297628 | − | 0.916005i | ||||
\(964\) | −65.8328 | − | 47.8303i | −2.12033 | − | 1.54051i | ||||
\(965\) | −38.6525 | + | 28.0827i | −1.24427 | + | 0.904013i | ||||
\(966\) | 14.4721 | − | 44.5407i | 0.465633 | − | 1.43307i | ||||
\(967\) | 21.8885 | 0.703888 | 0.351944 | − | 0.936021i | \(-0.385521\pi\) | ||||
0.351944 | + | 0.936021i | \(0.385521\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −9.88854 | −0.317666 | ||||||||
\(970\) | −13.0132 | + | 40.0504i | −0.417827 | + | 1.28594i | ||||
\(971\) | 23.5623 | − | 17.1190i | 0.756150 | − | 0.549375i | −0.141577 | − | 0.989927i | \(-0.545217\pi\) |
0.897727 | + | 0.440552i | \(0.145217\pi\) | |||||||
\(972\) | −86.3951 | − | 62.7697i | −2.77112 | − | 2.01334i | ||||
\(973\) | −3.23607 | − | 9.95959i | −0.103744 | − | 0.319290i | ||||
\(974\) | −5.77709 | − | 17.7800i | −0.185110 | − | 0.569709i | ||||
\(975\) | −3.23607 | − | 2.35114i | −0.103637 | − | 0.0752968i | ||||
\(976\) | −2.23607 | + | 1.62460i | −0.0715748 | + | 0.0520021i | ||||
\(977\) | 1.56231 | − | 4.80828i | 0.0499826 | − | 0.153831i | −0.922950 | − | 0.384920i | \(-0.874229\pi\) |
0.972933 | + | 0.231089i | \(0.0742290\pi\) | |||||||
\(978\) | −169.443 | −5.41818 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | −6.00000 | −0.191663 | ||||||||
\(981\) | 10.3262 | − | 31.7809i | 0.329691 | − | 1.01469i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −35.7426 | − | 25.9686i | −1.14001 | − | 0.828268i | −0.152892 | − | 0.988243i | \(-0.548859\pi\) |
−0.987121 | + | 0.159975i | \(0.948859\pi\) | |||||||
\(984\) | 15.1246 | + | 46.5488i | 0.482155 | + | 1.48392i | ||||
\(985\) | 1.23607 | + | 3.80423i | 0.0393844 | + | 0.121213i | ||||
\(986\) | −1.05573 | − | 0.767031i | −0.0336212 | − | 0.0244273i | ||||
\(987\) | −18.9443 | + | 13.7638i | −0.603003 | + | 0.438107i | ||||
\(988\) | 2.83282 | − | 8.71851i | 0.0901239 | − | 0.277373i | ||||
\(989\) | −51.7771 | −1.64642 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −26.2492 | −0.833834 | −0.416917 | − | 0.908945i | \(-0.636889\pi\) | ||||
−0.416917 | + | 0.908945i | \(0.636889\pi\) | |||||||
\(992\) | −15.0000 | + | 46.1653i | −0.476250 | + | 1.46575i | ||||
\(993\) | −57.3050 | + | 41.6345i | −1.81852 | + | 1.32123i | ||||
\(994\) | −2.76393 | − | 2.00811i | −0.0876666 | − | 0.0636935i | ||||
\(995\) | −12.4721 | − | 38.3853i | −0.395393 | − | 1.21690i | ||||
\(996\) | 46.2492 | + | 142.340i | 1.46546 | + | 4.51023i | ||||
\(997\) | −26.4164 | − | 19.1926i | −0.836616 | − | 0.607837i | 0.0848073 | − | 0.996397i | \(-0.472973\pi\) |
−0.921423 | + | 0.388560i | \(0.872973\pi\) | |||||||
\(998\) | 18.9443 | − | 13.7638i | 0.599670 | − | 0.435686i | ||||
\(999\) | 2.11146 | − | 6.49839i | 0.0668035 | − | 0.205600i |
(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 | 847.2.f.a.372.1 | 4 | ||
11.2 | odd | 10 | 847.2.f.b.729.1 | 4 | |||
11.3 | even | 5 | 847.2.f.n.323.1 | 4 | |||
11.4 | even | 5 | 77.2.a.d.1.1 | ✓ | 2 | ||
11.5 | even | 5 | inner | 847.2.f.a.148.1 | 4 | ||
11.6 | odd | 10 | 847.2.f.m.148.1 | 4 | |||
11.7 | odd | 10 | 847.2.a.f.1.2 | 2 | |||
11.8 | odd | 10 | 847.2.f.b.323.1 | 4 | |||
11.9 | even | 5 | 847.2.f.n.729.1 | 4 | |||
11.10 | odd | 2 | 847.2.f.m.372.1 | 4 | |||
33.26 | odd | 10 | 693.2.a.h.1.2 | 2 | |||
33.29 | even | 10 | 7623.2.a.bl.1.1 | 2 | |||
44.15 | odd | 10 | 1232.2.a.m.1.1 | 2 | |||
55.4 | even | 10 | 1925.2.a.r.1.2 | 2 | |||
55.37 | odd | 20 | 1925.2.b.h.1849.1 | 4 | |||
55.48 | odd | 20 | 1925.2.b.h.1849.4 | 4 | |||
77.4 | even | 15 | 539.2.e.i.177.2 | 4 | |||
77.26 | odd | 30 | 539.2.e.j.67.2 | 4 | |||
77.37 | even | 15 | 539.2.e.i.67.2 | 4 | |||
77.48 | odd | 10 | 539.2.a.f.1.1 | 2 | |||
77.59 | odd | 30 | 539.2.e.j.177.2 | 4 | |||
77.62 | even | 10 | 5929.2.a.m.1.2 | 2 | |||
88.37 | even | 10 | 4928.2.a.bm.1.1 | 2 | |||
88.59 | odd | 10 | 4928.2.a.bv.1.2 | 2 | |||
231.125 | even | 10 | 4851.2.a.y.1.2 | 2 | |||
308.279 | even | 10 | 8624.2.a.ce.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
77.2.a.d.1.1 | ✓ | 2 | 11.4 | even | 5 | ||
539.2.a.f.1.1 | 2 | 77.48 | odd | 10 | |||
539.2.e.i.67.2 | 4 | 77.37 | even | 15 | |||
539.2.e.i.177.2 | 4 | 77.4 | even | 15 | |||
539.2.e.j.67.2 | 4 | 77.26 | odd | 30 | |||
539.2.e.j.177.2 | 4 | 77.59 | odd | 30 | |||
693.2.a.h.1.2 | 2 | 33.26 | odd | 10 | |||
847.2.a.f.1.2 | 2 | 11.7 | odd | 10 | |||
847.2.f.a.148.1 | 4 | 11.5 | even | 5 | inner | ||
847.2.f.a.372.1 | 4 | 1.1 | even | 1 | trivial | ||
847.2.f.b.323.1 | 4 | 11.8 | odd | 10 | |||
847.2.f.b.729.1 | 4 | 11.2 | odd | 10 | |||
847.2.f.m.148.1 | 4 | 11.6 | odd | 10 | |||
847.2.f.m.372.1 | 4 | 11.10 | odd | 2 | |||
847.2.f.n.323.1 | 4 | 11.3 | even | 5 | |||
847.2.f.n.729.1 | 4 | 11.9 | even | 5 | |||
1232.2.a.m.1.1 | 2 | 44.15 | odd | 10 | |||
1925.2.a.r.1.2 | 2 | 55.4 | even | 10 | |||
1925.2.b.h.1849.1 | 4 | 55.37 | odd | 20 | |||
1925.2.b.h.1849.4 | 4 | 55.48 | odd | 20 | |||
4851.2.a.y.1.2 | 2 | 231.125 | even | 10 | |||
4928.2.a.bm.1.1 | 2 | 88.37 | even | 10 | |||
4928.2.a.bv.1.2 | 2 | 88.59 | odd | 10 | |||
5929.2.a.m.1.2 | 2 | 77.62 | even | 10 | |||
7623.2.a.bl.1.1 | 2 | 33.29 | even | 10 | |||
8624.2.a.ce.1.2 | 2 | 308.279 | even | 10 |