Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [370,2,Mod(159,370)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(370, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("370.159");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 370 = 2 \cdot 5 \cdot 37 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 370.m (of order \(6\), 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: | \(2.95446487479\) |
Analytic rank: | \(1\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\sqrt{-3}, \sqrt{-11})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 2x^{2} - 3x + 9 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 159.1 | ||
Root | \(-1.18614 - 1.26217i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 370.159 |
Dual form | 370.2.m.a.249.1 |
$q$-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 \(\left(\mathbb{Z}/370\mathbb{Z}\right)^\times\).
\(n\) | \(261\) | \(297\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.500000 | − | 0.866025i | −0.353553 | − | 0.612372i | ||||
\(3\) | −2.18614 | − | 1.26217i | −1.26217 | − | 0.728714i | −0.288675 | − | 0.957427i | \(-0.593215\pi\) |
−0.973494 | + | 0.228714i | \(0.926548\pi\) | |||||||
\(4\) | −0.500000 | + | 0.866025i | −0.250000 | + | 0.433013i | ||||
\(5\) | −1.50000 | − | 1.65831i | −0.670820 | − | 0.741620i | ||||
\(6\) | 2.52434i | 1.03056i | ||||||||
\(7\) | −3.00000 | − | 1.73205i | −1.13389 | − | 0.654654i | −0.188982 | − | 0.981981i | \(-0.560519\pi\) |
−0.944911 | + | 0.327327i | \(0.893852\pi\) | |||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 1.68614 | + | 2.92048i | 0.562047 | + | 0.973494i | ||||
\(10\) | −0.686141 | + | 2.12819i | −0.216977 | + | 0.672994i | ||||
\(11\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(12\) | 2.18614 | − | 1.26217i | 0.631084 | − | 0.364357i | ||||
\(13\) | 0.186141 | − | 0.322405i | 0.0516261 | − | 0.0894191i | −0.839057 | − | 0.544043i | \(-0.816893\pi\) |
0.890684 | + | 0.454624i | \(0.150226\pi\) | |||||||
\(14\) | 3.46410i | 0.925820i | ||||||||
\(15\) | 1.18614 | + | 5.51856i | 0.306260 | + | 1.42489i | ||||
\(16\) | −0.500000 | − | 0.866025i | −0.125000 | − | 0.216506i | ||||
\(17\) | 0.686141 | + | 1.18843i | 0.166414 | + | 0.288237i | 0.937156 | − | 0.348910i | \(-0.113448\pi\) |
−0.770743 | + | 0.637146i | \(0.780115\pi\) | |||||||
\(18\) | 1.68614 | − | 2.92048i | 0.397427 | − | 0.688364i | ||||
\(19\) | 0 | 0 | 0.500000 | − | 0.866025i | \(-0.333333\pi\) | ||||
−0.500000 | + | 0.866025i | \(0.666667\pi\) | |||||||
\(20\) | 2.18614 | − | 0.469882i | 0.488836 | − | 0.105069i | ||||
\(21\) | 4.37228 | + | 7.57301i | 0.954110 | + | 1.65257i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.74456 | 0.572281 | 0.286140 | − | 0.958188i | \(-0.407628\pi\) | ||||
0.286140 | + | 0.958188i | \(0.407628\pi\) | |||||||
\(24\) | −2.18614 | − | 1.26217i | −0.446244 | − | 0.257639i | ||||
\(25\) | −0.500000 | + | 4.97494i | −0.100000 | + | 0.994987i | ||||
\(26\) | −0.372281 | −0.0730104 | ||||||||
\(27\) | − | 0.939764i | − | 0.180858i | ||||||
\(28\) | 3.00000 | − | 1.73205i | 0.566947 | − | 0.327327i | ||||
\(29\) | 7.72049i | 1.43366i | 0.697248 | + | 0.716830i | \(0.254407\pi\) | ||||
−0.697248 | + | 0.716830i | \(0.745593\pi\) | |||||||
\(30\) | 4.18614 | − | 3.78651i | 0.764281 | − | 0.691318i | ||||
\(31\) | − | 11.0371i | − | 1.98232i | −0.132656 | − | 0.991162i | \(-0.542350\pi\) | ||
0.132656 | − | 0.991162i | \(-0.457650\pi\) | |||||||
\(32\) | −0.500000 | + | 0.866025i | −0.0883883 | + | 0.153093i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0.686141 | − | 1.18843i | 0.117672 | − | 0.203814i | ||||
\(35\) | 1.62772 | + | 7.57301i | 0.275135 | + | 1.28007i | ||||
\(36\) | −3.37228 | −0.562047 | ||||||||
\(37\) | 0.500000 | + | 6.06218i | 0.0821995 | + | 0.996616i | ||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −0.813859 | + | 0.469882i | −0.130322 | + | 0.0752413i | ||||
\(40\) | −1.50000 | − | 1.65831i | −0.237171 | − | 0.262202i | ||||
\(41\) | 2.87228 | − | 4.97494i | 0.448575 | − | 0.776955i | −0.549719 | − | 0.835350i | \(-0.685265\pi\) |
0.998294 | + | 0.0583953i | \(0.0185984\pi\) | |||||||
\(42\) | 4.37228 | − | 7.57301i | 0.674658 | − | 1.16854i | ||||
\(43\) | −9.11684 | −1.39031 | −0.695153 | − | 0.718862i | \(-0.744663\pi\) | ||||
−0.695153 | + | 0.718862i | \(0.744663\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 2.31386 | − | 7.17687i | 0.344930 | − | 1.06986i | ||||
\(46\) | −1.37228 | − | 2.37686i | −0.202332 | − | 0.350449i | ||||
\(47\) | 5.04868i | 0.736425i | 0.929742 | + | 0.368213i | \(0.120030\pi\) | ||||
−0.929742 | + | 0.368213i | \(0.879970\pi\) | |||||||
\(48\) | 2.52434i | 0.364357i | ||||||||
\(49\) | 2.50000 | + | 4.33013i | 0.357143 | + | 0.618590i | ||||
\(50\) | 4.55842 | − | 2.05446i | 0.644658 | − | 0.290544i | ||||
\(51\) | − | 3.46410i | − | 0.485071i | ||||||
\(52\) | 0.186141 | + | 0.322405i | 0.0258131 | + | 0.0447095i | ||||
\(53\) | 0.813859 | − | 0.469882i | 0.111792 | − | 0.0645432i | −0.443061 | − | 0.896491i | \(-0.646108\pi\) |
0.554854 | + | 0.831948i | \(0.312774\pi\) | |||||||
\(54\) | −0.813859 | + | 0.469882i | −0.110752 | + | 0.0639428i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −3.00000 | − | 1.73205i | −0.400892 | − | 0.231455i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 6.68614 | − | 3.86025i | 0.877933 | − | 0.506875i | ||||
\(59\) | −10.3723 | + | 5.98844i | −1.35036 | + | 0.779628i | −0.988299 | − | 0.152528i | \(-0.951259\pi\) |
−0.362057 | + | 0.932156i | \(0.617925\pi\) | |||||||
\(60\) | −5.37228 | − | 1.73205i | −0.693559 | − | 0.223607i | ||||
\(61\) | 2.05842 | + | 1.18843i | 0.263554 | + | 0.152163i | 0.625955 | − | 0.779859i | \(-0.284709\pi\) |
−0.362401 | + | 0.932022i | \(0.618043\pi\) | |||||||
\(62\) | −9.55842 | + | 5.51856i | −1.21392 | + | 0.700858i | ||||
\(63\) | − | 11.6819i | − | 1.47178i | ||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −0.813859 | + | 0.174928i | −0.100947 | + | 0.0216972i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −7.11684 | − | 4.10891i | −0.869461 | − | 0.501983i | −0.00229183 | − | 0.999997i | \(-0.500730\pi\) |
−0.867169 | + | 0.498014i | \(0.834063\pi\) | |||||||
\(68\) | −1.37228 | −0.166414 | ||||||||
\(69\) | −6.00000 | − | 3.46410i | −0.722315 | − | 0.417029i | ||||
\(70\) | 5.74456 | − | 5.19615i | 0.686607 | − | 0.621059i | ||||
\(71\) | −1.37228 | + | 2.37686i | −0.162860 | + | 0.282082i | −0.935893 | − | 0.352284i | \(-0.885405\pi\) |
0.773033 | + | 0.634365i | \(0.218739\pi\) | |||||||
\(72\) | 1.68614 | + | 2.92048i | 0.198714 | + | 0.344182i | ||||
\(73\) | − | 6.92820i | − | 0.810885i | −0.914121 | − | 0.405442i | \(-0.867117\pi\) | ||
0.914121 | − | 0.405442i | \(-0.132883\pi\) | |||||||
\(74\) | 5.00000 | − | 3.46410i | 0.581238 | − | 0.402694i | ||||
\(75\) | 7.37228 | − | 10.2448i | 0.851278 | − | 1.18297i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0.813859 | + | 0.469882i | 0.0921514 | + | 0.0532036i | ||||
\(79\) | −7.11684 | − | 4.10891i | −0.800708 | − | 0.462289i | 0.0430110 | − | 0.999075i | \(-0.486305\pi\) |
−0.843718 | + | 0.536786i | \(0.819638\pi\) | |||||||
\(80\) | −0.686141 | + | 2.12819i | −0.0767129 | + | 0.237939i | ||||
\(81\) | 3.87228 | − | 6.70699i | 0.430253 | − | 0.745221i | ||||
\(82\) | −5.74456 | −0.634381 | ||||||||
\(83\) | −11.7446 | + | 6.78073i | −1.28913 | + | 0.744281i | −0.978500 | − | 0.206248i | \(-0.933875\pi\) |
−0.310634 | + | 0.950530i | \(0.600541\pi\) | |||||||
\(84\) | −8.74456 | −0.954110 | ||||||||
\(85\) | 0.941578 | − | 2.92048i | 0.102128 | − | 0.316771i | ||||
\(86\) | 4.55842 | + | 7.89542i | 0.491547 | + | 0.851385i | ||||
\(87\) | 9.74456 | − | 16.8781i | 1.04473 | − | 1.80952i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −8.31386 | + | 4.80001i | −0.881267 | + | 0.508800i | −0.871076 | − | 0.491148i | \(-0.836577\pi\) |
−0.0101913 | + | 0.999948i | \(0.503244\pi\) | |||||||
\(90\) | −7.37228 | + | 1.58457i | −0.777107 | + | 0.167029i | ||||
\(91\) | −1.11684 | + | 0.644810i | −0.117077 | + | 0.0675945i | ||||
\(92\) | −1.37228 | + | 2.37686i | −0.143070 | + | 0.247805i | ||||
\(93\) | −13.9307 | + | 24.1287i | −1.44455 | + | 2.50203i | ||||
\(94\) | 4.37228 | − | 2.52434i | 0.450966 | − | 0.260366i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 2.18614 | − | 1.26217i | 0.223122 | − | 0.128820i | ||||
\(97\) | −12.1168 | −1.23028 | −0.615140 | − | 0.788418i | \(-0.710900\pi\) | ||||
−0.615140 | + | 0.788418i | \(0.710900\pi\) | |||||||
\(98\) | 2.50000 | − | 4.33013i | 0.252538 | − | 0.437409i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −4.05842 | − | 2.92048i | −0.405842 | − | 0.292048i | ||||
\(101\) | 1.37228 | 0.136547 | 0.0682735 | − | 0.997667i | \(-0.478251\pi\) | ||||
0.0682735 | + | 0.997667i | \(0.478251\pi\) | |||||||
\(102\) | −3.00000 | + | 1.73205i | −0.297044 | + | 0.171499i | ||||
\(103\) | 15.4891 | 1.52619 | 0.763094 | − | 0.646287i | \(-0.223679\pi\) | ||||
0.763094 | + | 0.646287i | \(0.223679\pi\) | |||||||
\(104\) | 0.186141 | − | 0.322405i | 0.0182526 | − | 0.0316144i | ||||
\(105\) | 6.00000 | − | 18.6101i | 0.585540 | − | 1.81616i | ||||
\(106\) | −0.813859 | − | 0.469882i | −0.0790490 | − | 0.0456390i | ||||
\(107\) | 3.30298 | + | 1.90698i | 0.319312 | + | 0.184355i | 0.651086 | − | 0.759004i | \(-0.274314\pi\) |
−0.331774 | + | 0.943359i | \(0.607647\pi\) | |||||||
\(108\) | 0.813859 | + | 0.469882i | 0.0783137 | + | 0.0452144i | ||||
\(109\) | −2.05842 | + | 1.18843i | −0.197161 | + | 0.113831i | −0.595331 | − | 0.803481i | \(-0.702979\pi\) |
0.398170 | + | 0.917312i | \(0.369646\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 6.55842 | − | 13.8839i | 0.622498 | − | 1.31780i | ||||
\(112\) | 3.46410i | 0.327327i | ||||||||
\(113\) | 10.1168 | + | 17.5229i | 0.951713 | + | 1.64841i | 0.741718 | + | 0.670712i | \(0.234011\pi\) |
0.209995 | + | 0.977702i | \(0.432655\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −4.11684 | − | 4.55134i | −0.383898 | − | 0.424415i | ||||
\(116\) | −6.68614 | − | 3.86025i | −0.620793 | − | 0.358415i | ||||
\(117\) | 1.25544 | 0.116065 | ||||||||
\(118\) | 10.3723 | + | 5.98844i | 0.954846 | + | 0.551281i | ||||
\(119\) | − | 4.75372i | − | 0.435773i | ||||||
\(120\) | 1.18614 | + | 5.51856i | 0.108279 | + | 0.503773i | ||||
\(121\) | −11.0000 | −1.00000 | ||||||||
\(122\) | − | 2.37686i | − | 0.215191i | ||||||
\(123\) | −12.5584 | + | 7.25061i | −1.13235 | + | 0.653765i | ||||
\(124\) | 9.55842 | + | 5.51856i | 0.858372 | + | 0.495581i | ||||
\(125\) | 9.00000 | − | 6.63325i | 0.804984 | − | 0.593296i | ||||
\(126\) | −10.1168 | + | 5.84096i | −0.901280 | + | 0.520354i | ||||
\(127\) | 15.0000 | − | 8.66025i | 1.33103 | − | 0.768473i | 0.345576 | − | 0.938391i | \(-0.387683\pi\) |
0.985458 | + | 0.169917i | \(0.0543501\pi\) | |||||||
\(128\) | −0.500000 | − | 0.866025i | −0.0441942 | − | 0.0765466i | ||||
\(129\) | 19.9307 | + | 11.5070i | 1.75480 | + | 1.01313i | ||||
\(130\) | 0.558422 | + | 0.617359i | 0.0489768 | + | 0.0541459i | ||||
\(131\) | 5.74456 | − | 3.31662i | 0.501905 | − | 0.289775i | −0.227595 | − | 0.973756i | \(-0.573086\pi\) |
0.729500 | + | 0.683981i | \(0.239753\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 8.21782i | 0.709912i | ||||||||
\(135\) | −1.55842 | + | 1.40965i | −0.134128 | + | 0.121323i | ||||
\(136\) | 0.686141 | + | 1.18843i | 0.0588361 | + | 0.101907i | ||||
\(137\) | 2.67181i | 0.228269i | 0.993465 | + | 0.114134i | \(0.0364094\pi\) | ||||
−0.993465 | + | 0.114134i | \(0.963591\pi\) | |||||||
\(138\) | 6.92820i | 0.589768i | ||||||||
\(139\) | 9.37228 | + | 16.2333i | 0.794947 | + | 1.37689i | 0.922873 | + | 0.385104i | \(0.125834\pi\) |
−0.127927 | + | 0.991784i | \(0.540832\pi\) | |||||||
\(140\) | −7.37228 | − | 2.37686i | −0.623071 | − | 0.200881i | ||||
\(141\) | 6.37228 | − | 11.0371i | 0.536643 | − | 0.929493i | ||||
\(142\) | 2.74456 | 0.230319 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 1.68614 | − | 2.92048i | 0.140512 | − | 0.243373i | ||||
\(145\) | 12.8030 | − | 11.5807i | 1.06323 | − | 0.961728i | ||||
\(146\) | −6.00000 | + | 3.46410i | −0.496564 | + | 0.286691i | ||||
\(147\) | − | 12.6217i | − | 1.04102i | ||||||
\(148\) | −5.50000 | − | 2.59808i | −0.452097 | − | 0.213561i | ||||
\(149\) | −10.6277 | −0.870657 | −0.435328 | − | 0.900272i | \(-0.643368\pi\) | ||||
−0.435328 | + | 0.900272i | \(0.643368\pi\) | |||||||
\(150\) | −12.5584 | − | 1.26217i | −1.02539 | − | 0.103056i | ||||
\(151\) | −8.93070 | + | 15.4684i | −0.726770 | + | 1.25880i | 0.231471 | + | 0.972842i | \(0.425646\pi\) |
−0.958241 | + | 0.285961i | \(0.907687\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −2.31386 | + | 4.00772i | −0.187064 | + | 0.324005i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −18.3030 | + | 16.5557i | −1.47013 | + | 1.32978i | ||||
\(156\) | − | 0.939764i | − | 0.0752413i | ||||||
\(157\) | 5.61684 | − | 3.24289i | 0.448273 | − | 0.258811i | −0.258828 | − | 0.965924i | \(-0.583336\pi\) |
0.707101 | + | 0.707113i | \(0.250003\pi\) | |||||||
\(158\) | 8.21782i | 0.653775i | ||||||||
\(159\) | −2.37228 | −0.188134 | ||||||||
\(160\) | 2.18614 | − | 0.469882i | 0.172830 | − | 0.0371474i | ||||
\(161\) | −8.23369 | − | 4.75372i | −0.648906 | − | 0.374646i | ||||
\(162\) | −7.74456 | −0.608470 | ||||||||
\(163\) | −8.55842 | − | 14.8236i | −0.670347 | − | 1.16108i | −0.977806 | − | 0.209514i | \(-0.932812\pi\) |
0.307458 | − | 0.951562i | \(-0.400522\pi\) | |||||||
\(164\) | 2.87228 | + | 4.97494i | 0.224287 | + | 0.388477i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 11.7446 | + | 6.78073i | 0.911555 | + | 0.526286i | ||||
\(167\) | −2.74456 | + | 4.75372i | −0.212381 | + | 0.367854i | −0.952459 | − | 0.304666i | \(-0.901455\pi\) |
0.740078 | + | 0.672521i | \(0.234788\pi\) | |||||||
\(168\) | 4.37228 | + | 7.57301i | 0.337329 | + | 0.584271i | ||||
\(169\) | 6.43070 | + | 11.1383i | 0.494669 | + | 0.856793i | ||||
\(170\) | −3.00000 | + | 0.644810i | −0.230089 | + | 0.0494547i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 4.55842 | − | 7.89542i | 0.347576 | − | 0.602020i | ||||
\(173\) | 10.5475 | − | 6.08963i | 0.801915 | − | 0.462986i | −0.0422252 | − | 0.999108i | \(-0.513445\pi\) |
0.844140 | + | 0.536122i | \(0.180111\pi\) | |||||||
\(174\) | −19.4891 | −1.47747 | ||||||||
\(175\) | 10.1168 | − | 14.0588i | 0.764762 | − | 1.06274i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 30.2337 | 2.27250 | ||||||||
\(178\) | 8.31386 | + | 4.80001i | 0.623150 | + | 0.359776i | ||||
\(179\) | − | 20.1947i | − | 1.50942i | −0.656057 | − | 0.754711i | \(-0.727777\pi\) | ||
0.656057 | − | 0.754711i | \(-0.272223\pi\) | |||||||
\(180\) | 5.05842 | + | 5.59230i | 0.377033 | + | 0.416825i | ||||
\(181\) | 2.43070 | − | 4.21010i | 0.180673 | − | 0.312934i | −0.761437 | − | 0.648239i | \(-0.775506\pi\) |
0.942110 | + | 0.335304i | \(0.108839\pi\) | |||||||
\(182\) | 1.11684 | + | 0.644810i | 0.0827860 | + | 0.0477965i | ||||
\(183\) | −3.00000 | − | 5.19615i | −0.221766 | − | 0.384111i | ||||
\(184\) | 2.74456 | 0.202332 | ||||||||
\(185\) | 9.30298 | − | 9.92242i | 0.683969 | − | 0.729511i | ||||
\(186\) | 27.8614 | 2.04290 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −4.37228 | − | 2.52434i | −0.318881 | − | 0.184106i | ||||
\(189\) | −1.62772 | + | 2.81929i | −0.118399 | + | 0.205073i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 24.5986i | 1.77989i | 0.456068 | + | 0.889945i | \(0.349257\pi\) | ||||
−0.456068 | + | 0.889945i | \(0.650743\pi\) | |||||||
\(192\) | −2.18614 | − | 1.26217i | −0.157771 | − | 0.0910892i | ||||
\(193\) | −6.62772 | −0.477074 | −0.238537 | − | 0.971133i | \(-0.576668\pi\) | ||||
−0.238537 | + | 0.971133i | \(0.576668\pi\) | |||||||
\(194\) | 6.05842 | + | 10.4935i | 0.434969 | + | 0.753389i | ||||
\(195\) | 2.00000 | + | 0.644810i | 0.143223 | + | 0.0461758i | ||||
\(196\) | −5.00000 | −0.357143 | ||||||||
\(197\) | −6.12772 | + | 3.53784i | −0.436582 | + | 0.252061i | −0.702147 | − | 0.712032i | \(-0.747775\pi\) |
0.265565 | + | 0.964093i | \(0.414442\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 8.86263i | − | 0.628255i | −0.949381 | − | 0.314128i | \(-0.898288\pi\) | ||
0.949381 | − | 0.314128i | \(-0.101712\pi\) | |||||||
\(200\) | −0.500000 | + | 4.97494i | −0.0353553 | + | 0.351781i | ||||
\(201\) | 10.3723 | + | 17.9653i | 0.731604 | + | 1.26718i | ||||
\(202\) | −0.686141 | − | 1.18843i | −0.0482767 | − | 0.0836177i | ||||
\(203\) | 13.3723 | − | 23.1615i | 0.938550 | − | 1.62562i | ||||
\(204\) | 3.00000 | + | 1.73205i | 0.210042 | + | 0.121268i | ||||
\(205\) | −12.5584 | + | 2.69927i | −0.877118 | + | 0.188525i | ||||
\(206\) | −7.74456 | − | 13.4140i | −0.539589 | − | 0.934596i | ||||
\(207\) | 4.62772 | + | 8.01544i | 0.321649 | + | 0.557112i | ||||
\(208\) | −0.372281 | −0.0258131 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | −19.1168 | + | 4.10891i | −1.31919 | + | 0.283542i | ||||
\(211\) | −15.4891 | −1.06632 | −0.533158 | − | 0.846016i | \(-0.678995\pi\) | ||||
−0.533158 | + | 0.846016i | \(0.678995\pi\) | |||||||
\(212\) | 0.939764i | 0.0645432i | ||||||||
\(213\) | 6.00000 | − | 3.46410i | 0.411113 | − | 0.237356i | ||||
\(214\) | − | 3.81396i | − | 0.260717i | ||||||
\(215\) | 13.6753 | + | 15.1186i | 0.932645 | + | 1.03108i | ||||
\(216\) | − | 0.939764i | − | 0.0639428i | ||||||
\(217\) | −19.1168 | + | 33.1113i | −1.29774 | + | 2.24774i | ||||
\(218\) | 2.05842 | + | 1.18843i | 0.139414 | + | 0.0804907i | ||||
\(219\) | −8.74456 | + | 15.1460i | −0.590903 | + | 1.02347i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0.510875 | 0.0343652 | ||||||||
\(222\) | −15.3030 | + | 1.26217i | −1.02707 | + | 0.0847112i | ||||
\(223\) | 18.6101i | 1.24623i | 0.782132 | + | 0.623113i | \(0.214132\pi\) | ||||
−0.782132 | + | 0.623113i | \(0.785868\pi\) | |||||||
\(224\) | 3.00000 | − | 1.73205i | 0.200446 | − | 0.115728i | ||||
\(225\) | −15.3723 | + | 6.92820i | −1.02482 | + | 0.461880i | ||||
\(226\) | 10.1168 | − | 17.5229i | 0.672962 | − | 1.16561i | ||||
\(227\) | 5.18614 | − | 8.98266i | 0.344216 | − | 0.596200i | −0.640995 | − | 0.767545i | \(-0.721478\pi\) |
0.985211 | + | 0.171345i | \(0.0548113\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −4.43070 | + | 7.67420i | −0.292789 | + | 0.507126i | −0.974468 | − | 0.224526i | \(-0.927917\pi\) |
0.681679 | + | 0.731651i | \(0.261250\pi\) | |||||||
\(230\) | −1.88316 | + | 5.84096i | −0.124172 | + | 0.385142i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 7.72049i | 0.506875i | ||||||||
\(233\) | − | 14.6487i | − | 0.959668i | −0.877359 | − | 0.479834i | \(-0.840697\pi\) | ||
0.877359 | − | 0.479834i | \(-0.159303\pi\) | |||||||
\(234\) | −0.627719 | − | 1.08724i | −0.0410353 | − | 0.0710751i | ||||
\(235\) | 8.37228 | − | 7.57301i | 0.546147 | − | 0.494009i | ||||
\(236\) | − | 11.9769i | − | 0.779628i | ||||||
\(237\) | 10.3723 | + | 17.9653i | 0.673752 | + | 1.16697i | ||||
\(238\) | −4.11684 | + | 2.37686i | −0.266855 | + | 0.154069i | ||||
\(239\) | −8.48913 | + | 4.90120i | −0.549116 | + | 0.317032i | −0.748765 | − | 0.662835i | \(-0.769353\pi\) |
0.199649 | + | 0.979867i | \(0.436020\pi\) | |||||||
\(240\) | 4.18614 | − | 3.78651i | 0.270214 | − | 0.244418i | ||||
\(241\) | −18.0000 | − | 10.3923i | −1.15948 | − | 0.669427i | −0.208302 | − | 0.978065i | \(-0.566794\pi\) |
−0.951180 | + | 0.308637i | \(0.900127\pi\) | |||||||
\(242\) | 5.50000 | + | 9.52628i | 0.353553 | + | 0.612372i | ||||
\(243\) | −19.3723 | + | 11.1846i | −1.24273 | + | 0.717492i | ||||
\(244\) | −2.05842 | + | 1.18843i | −0.131777 | + | 0.0760815i | ||||
\(245\) | 3.43070 | − | 10.6410i | 0.219180 | − | 0.679827i | ||||
\(246\) | 12.5584 | + | 7.25061i | 0.800696 | + | 0.462282i | ||||
\(247\) | 0 | 0 | ||||||||
\(248\) | − | 11.0371i | − | 0.700858i | ||||||
\(249\) | 34.2337 | 2.16947 | ||||||||
\(250\) | −10.2446 | − | 4.47760i | −0.647923 | − | 0.283189i | ||||
\(251\) | 21.7793i | 1.37470i | 0.726328 | + | 0.687348i | \(0.241225\pi\) | ||||
−0.726328 | + | 0.687348i | \(0.758775\pi\) | |||||||
\(252\) | 10.1168 | + | 5.84096i | 0.637301 | + | 0.367946i | ||||
\(253\) | 0 | 0 | ||||||||
\(254\) | −15.0000 | − | 8.66025i | −0.941184 | − | 0.543393i | ||||
\(255\) | −5.74456 | + | 5.19615i | −0.359738 | + | 0.325396i | ||||
\(256\) | −0.500000 | + | 0.866025i | −0.0312500 | + | 0.0541266i | ||||
\(257\) | −0.430703 | − | 0.746000i | −0.0268665 | − | 0.0465342i | 0.852280 | − | 0.523087i | \(-0.175220\pi\) |
−0.879146 | + | 0.476552i | \(0.841886\pi\) | |||||||
\(258\) | − | 23.0140i | − | 1.43279i | ||||||
\(259\) | 9.00000 | − | 19.0526i | 0.559233 | − | 1.18387i | ||||
\(260\) | 0.255437 | − | 0.792287i | 0.0158416 | − | 0.0491356i | ||||
\(261\) | −22.5475 | + | 13.0178i | −1.39566 | + | 0.805784i | ||||
\(262\) | −5.74456 | − | 3.31662i | −0.354900 | − | 0.204902i | ||||
\(263\) | 2.74456 | + | 1.58457i | 0.169237 | + | 0.0977090i | 0.582226 | − | 0.813027i | \(-0.302182\pi\) |
−0.412989 | + | 0.910736i | \(0.635515\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2.00000 | − | 0.644810i | −0.122859 | − | 0.0396104i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 24.2337 | 1.48308 | ||||||||
\(268\) | 7.11684 | − | 4.10891i | 0.434730 | − | 0.250992i | ||||
\(269\) | −23.4891 | −1.43216 | −0.716079 | − | 0.698020i | \(-0.754065\pi\) | ||||
−0.716079 | + | 0.698020i | \(0.754065\pi\) | |||||||
\(270\) | 2.00000 | + | 0.644810i | 0.121716 | + | 0.0392419i | ||||
\(271\) | −9.18614 | − | 15.9109i | −0.558018 | − | 0.966516i | −0.997662 | − | 0.0683437i | \(-0.978229\pi\) |
0.439644 | − | 0.898172i | \(-0.355105\pi\) | |||||||
\(272\) | 0.686141 | − | 1.18843i | 0.0416034 | − | 0.0720592i | ||||
\(273\) | 3.25544 | 0.197028 | ||||||||
\(274\) | 2.31386 | − | 1.33591i | 0.139785 | − | 0.0807051i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 6.00000 | − | 3.46410i | 0.361158 | − | 0.208514i | ||||
\(277\) | −3.50000 | + | 6.06218i | −0.210295 | + | 0.364241i | −0.951807 | − | 0.306699i | \(-0.900776\pi\) |
0.741512 | + | 0.670940i | \(0.234109\pi\) | |||||||
\(278\) | 9.37228 | − | 16.2333i | 0.562112 | − | 0.973607i | ||||
\(279\) | 32.2337 | − | 18.6101i | 1.92978 | − | 1.11416i | ||||
\(280\) | 1.62772 | + | 7.57301i | 0.0972748 | + | 0.452574i | ||||
\(281\) | 6.12772 | − | 3.53784i | 0.365549 | − | 0.211050i | −0.305963 | − | 0.952043i | \(-0.598978\pi\) |
0.671512 | + | 0.740994i | \(0.265645\pi\) | |||||||
\(282\) | −12.7446 | −0.758928 | ||||||||
\(283\) | −1.44158 | + | 2.49689i | −0.0856929 | + | 0.148424i | −0.905686 | − | 0.423949i | \(-0.860644\pi\) |
0.819993 | + | 0.572373i | \(0.193977\pi\) | |||||||
\(284\) | −1.37228 | − | 2.37686i | −0.0814299 | − | 0.141041i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −17.2337 | + | 9.94987i | −1.01727 | + | 0.587323i | ||||
\(288\) | −3.37228 | −0.198714 | ||||||||
\(289\) | 7.55842 | − | 13.0916i | 0.444613 | − | 0.770092i | ||||
\(290\) | −16.4307 | − | 5.29734i | −0.964844 | − | 0.311071i | ||||
\(291\) | 26.4891 | + | 15.2935i | 1.55282 | + | 0.896521i | ||||
\(292\) | 6.00000 | + | 3.46410i | 0.351123 | + | 0.202721i | ||||
\(293\) | −24.9891 | − | 14.4275i | −1.45988 | − | 0.842862i | −0.460875 | − | 0.887465i | \(-0.652465\pi\) |
−0.999005 | + | 0.0446025i | \(0.985798\pi\) | |||||||
\(294\) | −10.9307 | + | 6.31084i | −0.637492 | + | 0.368056i | ||||
\(295\) | 25.4891 | + | 8.21782i | 1.48403 | + | 0.478460i | ||||
\(296\) | 0.500000 | + | 6.06218i | 0.0290619 | + | 0.352357i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 5.31386 | + | 9.20387i | 0.307824 | + | 0.533166i | ||||
\(299\) | 0.510875 | − | 0.884861i | 0.0295446 | − | 0.0511728i | ||||
\(300\) | 5.18614 | + | 11.5070i | 0.299422 | + | 0.664357i | ||||
\(301\) | 27.3505 | + | 15.7908i | 1.57646 | + | 0.910169i | ||||
\(302\) | 17.8614 | 1.02781 | ||||||||
\(303\) | −3.00000 | − | 1.73205i | −0.172345 | − | 0.0995037i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −1.11684 | − | 5.19615i | −0.0639503 | − | 0.297531i | ||||
\(306\) | 4.62772 | 0.264549 | ||||||||
\(307\) | − | 20.1398i | − | 1.14944i | −0.818350 | − | 0.574720i | \(-0.805111\pi\) | ||
0.818350 | − | 0.574720i | \(-0.194889\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −33.8614 | − | 19.5499i | −1.92631 | − | 1.11215i | ||||
\(310\) | 23.4891 | + | 7.57301i | 1.33409 | + | 0.430118i | ||||
\(311\) | 16.4198 | − | 9.47999i | 0.931083 | − | 0.537561i | 0.0439291 | − | 0.999035i | \(-0.486012\pi\) |
0.887154 | + | 0.461474i | \(0.152679\pi\) | |||||||
\(312\) | −0.813859 | + | 0.469882i | −0.0460757 | + | 0.0266018i | ||||
\(313\) | −14.1753 | − | 24.5523i | −0.801233 | − | 1.38778i | −0.918805 | − | 0.394713i | \(-0.870844\pi\) |
0.117571 | − | 0.993064i | \(-0.462489\pi\) | |||||||
\(314\) | −5.61684 | − | 3.24289i | −0.316977 | − | 0.183007i | ||||
\(315\) | −19.3723 | + | 17.5229i | −1.09150 | + | 0.987303i | ||||
\(316\) | 7.11684 | − | 4.10891i | 0.400354 | − | 0.231144i | ||||
\(317\) | −11.3614 | + | 6.55951i | −0.638120 | + | 0.368419i | −0.783890 | − | 0.620900i | \(-0.786767\pi\) |
0.145770 | + | 0.989319i | \(0.453434\pi\) | |||||||
\(318\) | 1.18614 | + | 2.05446i | 0.0665155 | + | 0.115208i | ||||
\(319\) | 0 | 0 | ||||||||
\(320\) | −1.50000 | − | 1.65831i | −0.0838525 | − | 0.0927025i | ||||
\(321\) | −4.81386 | − | 8.33785i | −0.268683 | − | 0.465373i | ||||
\(322\) | 9.50744i | 0.529829i | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 3.87228 | + | 6.70699i | 0.215127 | + | 0.372610i | ||||
\(325\) | 1.51087 | + | 1.08724i | 0.0838082 | + | 0.0603093i | ||||
\(326\) | −8.55842 | + | 14.8236i | −0.474007 | + | 0.821004i | ||||
\(327\) | 6.00000 | 0.331801 | ||||||||
\(328\) | 2.87228 | − | 4.97494i | 0.158595 | − | 0.274695i | ||||
\(329\) | 8.74456 | − | 15.1460i | 0.482103 | − | 0.835027i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −24.0000 | + | 13.8564i | −1.31916 | + | 0.761617i | −0.983593 | − | 0.180400i | \(-0.942261\pi\) |
−0.335566 | + | 0.942017i | \(0.608928\pi\) | |||||||
\(332\) | − | 13.5615i | − | 0.744281i | ||||||
\(333\) | −16.8614 | + | 11.6819i | −0.923999 | + | 0.640166i | ||||
\(334\) | 5.48913 | 0.300352 | ||||||||
\(335\) | 3.86141 | + | 17.9653i | 0.210971 | + | 0.981550i | ||||
\(336\) | 4.37228 | − | 7.57301i | 0.238528 | − | 0.413142i | ||||
\(337\) | −0.941578 | − | 0.543620i | −0.0512910 | − | 0.0296129i | 0.474135 | − | 0.880452i | \(-0.342761\pi\) |
−0.525426 | + | 0.850839i | \(0.676094\pi\) | |||||||
\(338\) | 6.43070 | − | 11.1383i | 0.349784 | − | 0.605844i | ||||
\(339\) | − | 51.0767i | − | 2.77410i | ||||||
\(340\) | 2.05842 | + | 2.27567i | 0.111634 | + | 0.123416i | ||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 6.92820i | 0.374088i | ||||||||
\(344\) | −9.11684 | −0.491547 | ||||||||
\(345\) | 3.25544 | + | 15.1460i | 0.175267 | + | 0.815435i | ||||
\(346\) | −10.5475 | − | 6.08963i | −0.567040 | − | 0.327380i | ||||
\(347\) | −2.74456 | −0.147336 | −0.0736679 | − | 0.997283i | \(-0.523470\pi\) | ||||
−0.0736679 | + | 0.997283i | \(0.523470\pi\) | |||||||
\(348\) | 9.74456 | + | 16.8781i | 0.522363 | + | 0.904760i | ||||
\(349\) | −0.313859 | − | 0.543620i | −0.0168005 | − | 0.0290993i | 0.857503 | − | 0.514479i | \(-0.172015\pi\) |
−0.874303 | + | 0.485380i | \(0.838681\pi\) | |||||||
\(350\) | −17.2337 | − | 1.73205i | −0.921179 | − | 0.0925820i | ||||
\(351\) | −0.302985 | − | 0.174928i | −0.0161721 | − | 0.00933698i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −12.1753 | − | 21.0882i | −0.648024 | − | 1.12241i | −0.983594 | − | 0.180395i | \(-0.942262\pi\) |
0.335570 | − | 0.942015i | \(-0.391071\pi\) | |||||||
\(354\) | −15.1168 | − | 26.1831i | −0.803451 | − | 1.39162i | ||||
\(355\) | 6.00000 | − | 1.28962i | 0.318447 | − | 0.0684459i | ||||
\(356\) | − | 9.60002i | − | 0.508800i | ||||||
\(357\) | −6.00000 | + | 10.3923i | −0.317554 | + | 0.550019i | ||||
\(358\) | −17.4891 | + | 10.0974i | −0.924329 | + | 0.533662i | ||||
\(359\) | −10.3723 | −0.547428 | −0.273714 | − | 0.961811i | \(-0.588252\pi\) | ||||
−0.273714 | + | 0.961811i | \(0.588252\pi\) | |||||||
\(360\) | 2.31386 | − | 7.17687i | 0.121951 | − | 0.378254i | ||||
\(361\) | −9.50000 | − | 16.4545i | −0.500000 | − | 0.866025i | ||||
\(362\) | −4.86141 | −0.255510 | ||||||||
\(363\) | 24.0475 | + | 13.8839i | 1.26217 | + | 0.728714i | ||||
\(364\) | − | 1.28962i | − | 0.0675945i | ||||||
\(365\) | −11.4891 | + | 10.3923i | −0.601368 | + | 0.543958i | ||||
\(366\) | −3.00000 | + | 5.19615i | −0.156813 | + | 0.271607i | ||||
\(367\) | −19.1168 | − | 11.0371i | −0.997891 | − | 0.576133i | −0.0902675 | − | 0.995918i | \(-0.528772\pi\) |
−0.907624 | + | 0.419785i | \(0.862106\pi\) | |||||||
\(368\) | −1.37228 | − | 2.37686i | −0.0715351 | − | 0.123902i | ||||
\(369\) | 19.3723 | 1.00848 | ||||||||
\(370\) | −13.2446 | − | 3.09541i | −0.688552 | − | 0.160923i | ||||
\(371\) | −3.25544 | −0.169014 | ||||||||
\(372\) | −13.9307 | − | 24.1287i | −0.722273 | − | 1.25101i | ||||
\(373\) | −10.5000 | − | 6.06218i | −0.543669 | − | 0.313888i | 0.202895 | − | 0.979200i | \(-0.434965\pi\) |
−0.746565 | + | 0.665313i | \(0.768298\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −28.0475 | + | 3.14170i | −1.44837 | + | 0.162237i | ||||
\(376\) | 5.04868i | 0.260366i | ||||||||
\(377\) | 2.48913 | + | 1.43710i | 0.128196 | + | 0.0740143i | ||||
\(378\) | 3.25544 | 0.167442 | ||||||||
\(379\) | −5.37228 | − | 9.30506i | −0.275956 | − | 0.477969i | 0.694420 | − | 0.719570i | \(-0.255661\pi\) |
−0.970376 | + | 0.241601i | \(0.922328\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −43.7228 | −2.23999 | ||||||||
\(382\) | 21.3030 | − | 12.2993i | 1.08996 | − | 0.629286i | ||||
\(383\) | 6.25544 | − | 10.8347i | 0.319638 | − | 0.553629i | −0.660775 | − | 0.750584i | \(-0.729772\pi\) |
0.980412 | + | 0.196955i | \(0.0631054\pi\) | |||||||
\(384\) | 2.52434i | 0.128820i | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 3.31386 | + | 5.73977i | 0.168671 | + | 0.292147i | ||||
\(387\) | −15.3723 | − | 26.6256i | −0.781417 | − | 1.35345i | ||||
\(388\) | 6.05842 | − | 10.4935i | 0.307570 | − | 0.532726i | ||||
\(389\) | 7.54755 | + | 4.35758i | 0.382676 | + | 0.220938i | 0.678982 | − | 0.734155i | \(-0.262421\pi\) |
−0.296306 | + | 0.955093i | \(0.595755\pi\) | |||||||
\(390\) | −0.441578 | − | 2.05446i | −0.0223602 | − | 0.104031i | ||||
\(391\) | 1.88316 | + | 3.26172i | 0.0952353 | + | 0.164952i | ||||
\(392\) | 2.50000 | + | 4.33013i | 0.126269 | + | 0.218704i | ||||
\(393\) | −16.7446 | −0.844651 | ||||||||
\(394\) | 6.12772 | + | 3.53784i | 0.308710 | + | 0.178234i | ||||
\(395\) | 3.86141 | + | 17.9653i | 0.194288 | + | 0.903933i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 16.8781i | 0.847086i | 0.905876 | + | 0.423543i | \(0.139214\pi\) | ||||
−0.905876 | + | 0.423543i | \(0.860786\pi\) | |||||||
\(398\) | −7.67527 | + | 4.43132i | −0.384726 | + | 0.222122i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 4.55842 | − | 2.05446i | 0.227921 | − | 0.102723i | ||||
\(401\) | − | 13.2665i | − | 0.662497i | −0.943543 | − | 0.331249i | \(-0.892530\pi\) | ||
0.943543 | − | 0.331249i | \(-0.107470\pi\) | |||||||
\(402\) | 10.3723 | − | 17.9653i | 0.517322 | − | 0.896029i | ||||
\(403\) | −3.55842 | − | 2.05446i | −0.177258 | − | 0.102340i | ||||
\(404\) | −0.686141 | + | 1.18843i | −0.0341368 | + | 0.0591266i | ||||
\(405\) | −16.9307 | + | 3.63903i | −0.841293 | + | 0.180825i | ||||
\(406\) | −26.7446 | −1.32731 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | − | 3.46410i | − | 0.171499i | ||||||
\(409\) | 25.5000 | − | 14.7224i | 1.26089 | − | 0.727977i | 0.287646 | − | 0.957737i | \(-0.407127\pi\) |
0.973247 | + | 0.229759i | \(0.0737939\pi\) | |||||||
\(410\) | 8.61684 | + | 9.52628i | 0.425556 | + | 0.470469i | ||||
\(411\) | 3.37228 | − | 5.84096i | 0.166342 | − | 0.288113i | ||||
\(412\) | −7.74456 | + | 13.4140i | −0.381547 | + | 0.660859i | ||||
\(413\) | 41.4891 | 2.04155 | ||||||||
\(414\) | 4.62772 | − | 8.01544i | 0.227440 | − | 0.393938i | ||||
\(415\) | 28.8614 | + | 9.30506i | 1.41675 | + | 0.456768i | ||||
\(416\) | 0.186141 | + | 0.322405i | 0.00912630 | + | 0.0158072i | ||||
\(417\) | − | 47.3176i | − | 2.31715i | ||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 8.48913 | + | 14.7036i | 0.414721 | + | 0.718318i | 0.995399 | − | 0.0958155i | \(-0.0305459\pi\) |
−0.580678 | + | 0.814133i | \(0.697213\pi\) | |||||||
\(420\) | 13.1168 | + | 14.5012i | 0.640036 | + | 0.707587i | ||||
\(421\) | − | 10.5947i | − | 0.516353i | −0.966098 | − | 0.258177i | \(-0.916878\pi\) | ||
0.966098 | − | 0.258177i | \(-0.0831217\pi\) | |||||||
\(422\) | 7.74456 | + | 13.4140i | 0.376999 | + | 0.652982i | ||||
\(423\) | −14.7446 | + | 8.51278i | −0.716905 | + | 0.413905i | ||||
\(424\) | 0.813859 | − | 0.469882i | 0.0395245 | − | 0.0228195i | ||||
\(425\) | −6.25544 | + | 2.81929i | −0.303433 | + | 0.136756i | ||||
\(426\) | −6.00000 | − | 3.46410i | −0.290701 | − | 0.167836i | ||||
\(427\) | −4.11684 | − | 7.13058i | −0.199228 | − | 0.345073i | ||||
\(428\) | −3.30298 | + | 1.90698i | −0.159656 | + | 0.0921773i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 6.25544 | − | 19.4024i | 0.301664 | − | 0.935668i | ||||
\(431\) | 27.0475 | + | 15.6159i | 1.30283 | + | 0.752192i | 0.980889 | − | 0.194566i | \(-0.0623300\pi\) |
0.321945 | + | 0.946758i | \(0.395663\pi\) | |||||||
\(432\) | −0.813859 | + | 0.469882i | −0.0391568 | + | 0.0226072i | ||||
\(433\) | 20.9870i | 1.00857i | 0.863537 | + | 0.504285i | \(0.168244\pi\) | ||||
−0.863537 | + | 0.504285i | \(0.831756\pi\) | |||||||
\(434\) | 38.2337 | 1.83528 | ||||||||
\(435\) | −42.6060 | + | 9.15759i | −2.04280 | + | 0.439073i | ||||
\(436\) | − | 2.37686i | − | 0.113831i | ||||||
\(437\) | 0 | 0 | ||||||||
\(438\) | 17.4891 | 0.835663 | ||||||||
\(439\) | −14.4416 | − | 8.33785i | −0.689259 | − | 0.397944i | 0.114075 | − | 0.993472i | \(-0.463609\pi\) |
−0.803334 | + | 0.595528i | \(0.796943\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −8.43070 | + | 14.6024i | −0.401462 | + | 0.695353i | ||||
\(442\) | −0.255437 | − | 0.442430i | −0.0121499 | − | 0.0210443i | ||||
\(443\) | 28.6526i | 1.36133i | 0.732597 | + | 0.680663i | \(0.238308\pi\) | ||||
−0.732597 | + | 0.680663i | \(0.761692\pi\) | |||||||
\(444\) | 8.74456 | + | 12.6217i | 0.414999 | + | 0.598999i | ||||
\(445\) | 20.4307 | + | 6.58696i | 0.968508 | + | 0.312252i | ||||
\(446\) | 16.1168 | − | 9.30506i | 0.763155 | − | 0.440608i | ||||
\(447\) | 23.2337 | + | 13.4140i | 1.09892 | + | 0.634459i | ||||
\(448\) | −3.00000 | − | 1.73205i | −0.141737 | − | 0.0818317i | ||||
\(449\) | 5.69702 | + | 3.28917i | 0.268859 | + | 0.155226i | 0.628369 | − | 0.777915i | \(-0.283723\pi\) |
−0.359510 | + | 0.933141i | \(0.617056\pi\) | |||||||
\(450\) | 13.6861 | + | 9.84868i | 0.645171 | + | 0.464271i | ||||
\(451\) | 0 | 0 | ||||||||
\(452\) | −20.2337 | −0.951713 | ||||||||
\(453\) | 39.0475 | − | 22.5441i | 1.83461 | − | 1.05921i | ||||
\(454\) | −10.3723 | −0.486795 | ||||||||
\(455\) | 2.74456 | + | 0.884861i | 0.128667 | + | 0.0414829i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −9.80298 | + | 16.9793i | −0.458564 | + | 0.794257i | −0.998885 | − | 0.0472023i | \(-0.984969\pi\) |
0.540321 | + | 0.841459i | \(0.318303\pi\) | |||||||
\(458\) | 8.86141 | 0.414066 | ||||||||
\(459\) | 1.11684 | − | 0.644810i | 0.0521298 | − | 0.0300972i | ||||
\(460\) | 6.00000 | − | 1.28962i | 0.279751 | − | 0.0601289i | ||||
\(461\) | 27.8614 | − | 16.0858i | 1.29764 | − | 0.749190i | 0.317640 | − | 0.948211i | \(-0.397110\pi\) |
0.979995 | + | 0.199021i | \(0.0637763\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −2.25544 | + | 3.90653i | −0.104819 | + | 0.181552i | −0.913664 | − | 0.406470i | \(-0.866760\pi\) |
0.808845 | + | 0.588022i | \(0.200093\pi\) | |||||||
\(464\) | 6.68614 | − | 3.86025i | 0.310396 | − | 0.179207i | ||||
\(465\) | 60.9090 | − | 13.0916i | 2.82459 | − | 0.607107i | ||||
\(466\) | −12.6861 | + | 7.32435i | −0.587674 | + | 0.339294i | ||||
\(467\) | −22.3723 | −1.03527 | −0.517633 | − | 0.855603i | \(-0.673187\pi\) | ||||
−0.517633 | + | 0.855603i | \(0.673187\pi\) | |||||||
\(468\) | −0.627719 | + | 1.08724i | −0.0290163 | + | 0.0502577i | ||||
\(469\) | 14.2337 | + | 24.6535i | 0.657251 | + | 1.13839i | ||||
\(470\) | −10.7446 | − | 3.46410i | −0.495610 | − | 0.159787i | ||||
\(471\) | −16.3723 | −0.754395 | ||||||||
\(472\) | −10.3723 | + | 5.98844i | −0.477423 | + | 0.275640i | ||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 10.3723 | − | 17.9653i | 0.476415 | − | 0.825174i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 4.11684 | + | 2.37686i | 0.188695 | + | 0.108943i | ||||
\(477\) | 2.74456 | + | 1.58457i | 0.125665 | + | 0.0725527i | ||||
\(478\) | 8.48913 | + | 4.90120i | 0.388284 | + | 0.224176i | ||||
\(479\) | 31.4198 | − | 18.1402i | 1.43561 | − | 0.828849i | 0.438068 | − | 0.898942i | \(-0.355663\pi\) |
0.997540 | + | 0.0700928i | \(0.0223295\pi\) | |||||||
\(480\) | −5.37228 | − | 1.73205i | −0.245210 | − | 0.0790569i | ||||
\(481\) | 2.04755 | + | 0.967215i | 0.0933601 | + | 0.0441012i | ||||
\(482\) | 20.7846i | 0.946713i | ||||||||
\(483\) | 12.0000 | + | 20.7846i | 0.546019 | + | 0.945732i | ||||
\(484\) | 5.50000 | − | 9.52628i | 0.250000 | − | 0.433013i | ||||
\(485\) | 18.1753 | + | 20.0935i | 0.825296 | + | 0.912399i | ||||
\(486\) | 19.3723 | + | 11.1846i | 0.878745 | + | 0.507343i | ||||
\(487\) | −2.00000 | −0.0906287 | −0.0453143 | − | 0.998973i | \(-0.514429\pi\) | ||||
−0.0453143 | + | 0.998973i | \(0.514429\pi\) | |||||||
\(488\) | 2.05842 | + | 1.18843i | 0.0931804 | + | 0.0537977i | ||||
\(489\) | 43.2087i | 1.95396i | ||||||||
\(490\) | −10.9307 | + | 2.34941i | −0.493799 | + | 0.106136i | ||||
\(491\) | −19.7228 | −0.890078 | −0.445039 | − | 0.895511i | \(-0.646810\pi\) | ||||
−0.445039 | + | 0.895511i | \(0.646810\pi\) | |||||||
\(492\) | − | 14.5012i | − | 0.653765i | ||||||
\(493\) | −9.17527 | + | 5.29734i | −0.413233 | + | 0.238580i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −9.55842 | + | 5.51856i | −0.429186 | + | 0.247791i | ||||
\(497\) | 8.23369 | − | 4.75372i | 0.369331 | − | 0.213234i | ||||
\(498\) | −17.1168 | − | 29.6472i | −0.767024 | − | 1.32852i | ||||
\(499\) | 12.0000 | + | 6.92820i | 0.537194 | + | 0.310149i | 0.743941 | − | 0.668245i | \(-0.232954\pi\) |
−0.206747 | + | 0.978394i | \(0.566288\pi\) | |||||||
\(500\) | 1.24456 | + | 11.1109i | 0.0556585 | + | 0.496892i | ||||
\(501\) | 12.0000 | − | 6.92820i | 0.536120 | − | 0.309529i | ||||
\(502\) | 18.8614 | − | 10.8896i | 0.841826 | − | 0.486028i | ||||
\(503\) | 11.4891 | + | 19.8997i | 0.512275 | + | 0.887286i | 0.999899 | + | 0.0142322i | \(0.00453039\pi\) |
−0.487624 | + | 0.873054i | \(0.662136\pi\) | |||||||
\(504\) | − | 11.6819i | − | 0.520354i | ||||||
\(505\) | −2.05842 | − | 2.27567i | −0.0915986 | − | 0.101266i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − | 32.4665i | − | 1.44189i | ||||||
\(508\) | 17.3205i | 0.768473i | ||||||||
\(509\) | −10.8030 | − | 18.7113i | −0.478834 | − | 0.829365i | 0.520872 | − | 0.853635i | \(-0.325607\pi\) |
−0.999705 | + | 0.0242705i | \(0.992274\pi\) | |||||||
\(510\) | 7.37228 | + | 2.37686i | 0.326450 | + | 0.105249i | ||||
\(511\) | −12.0000 | + | 20.7846i | −0.530849 | + | 0.919457i | ||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −0.430703 | + | 0.746000i | −0.0189975 | + | 0.0329046i | ||||
\(515\) | −23.2337 | − | 25.6858i | −1.02380 | − | 1.13185i | ||||
\(516\) | −19.9307 | + | 11.5070i | −0.877400 | + | 0.506567i | ||||
\(517\) | 0 | 0 | ||||||||
\(518\) | −21.0000 | + | 1.73205i | −0.922687 | + | 0.0761019i | ||||
\(519\) | −30.7446 | −1.34954 | ||||||||
\(520\) | −0.813859 | + | 0.174928i | −0.0356901 | + | 0.00767111i | ||||
\(521\) | −2.18614 | + | 3.78651i | −0.0957766 | + | 0.165890i | −0.909932 | − | 0.414756i | \(-0.863867\pi\) |
0.814156 | + | 0.580646i | \(0.197200\pi\) | |||||||
\(522\) | 22.5475 | + | 13.0178i | 0.986879 | + | 0.569775i | ||||
\(523\) | −8.55842 | + | 14.8236i | −0.374234 | + | 0.648192i | −0.990212 | − | 0.139571i | \(-0.955428\pi\) |
0.615978 | + | 0.787763i | \(0.288761\pi\) | |||||||
\(524\) | 6.63325i | 0.289775i | ||||||||
\(525\) | −39.8614 | + | 17.9653i | −1.73969 | + | 0.784071i | ||||
\(526\) | − | 3.16915i | − | 0.138181i | ||||||
\(527\) | 13.1168 | − | 7.57301i | 0.571379 | − | 0.329886i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −15.4674 | −0.672495 | ||||||||
\(530\) | 0.441578 | + | 2.05446i | 0.0191809 | + | 0.0892399i | ||||
\(531\) | −34.9783 | − | 20.1947i | −1.51793 | − | 0.876375i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −1.06930 | − | 1.85208i | −0.0463164 | − | 0.0802223i | ||||
\(534\) | −12.1168 | − | 20.9870i | −0.524347 | − | 0.908196i | ||||
\(535\) | −1.79211 | − | 8.33785i | −0.0774797 | − | 0.360477i | ||||
\(536\) | −7.11684 | − | 4.10891i | −0.307401 | − | 0.177478i | ||||
\(537\) | −25.4891 | + | 44.1485i | −1.09994 | + | 1.90515i | ||||
\(538\) | 11.7446 | + | 20.3422i | 0.506344 | + | 0.877014i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −0.441578 | − | 2.05446i | −0.0190025 | − | 0.0884097i | ||||
\(541\) | 44.3508i | 1.90679i | 0.301723 | + | 0.953396i | \(0.402438\pi\) | ||||
−0.301723 | + | 0.953396i | \(0.597562\pi\) | |||||||
\(542\) | −9.18614 | + | 15.9109i | −0.394579 | + | 0.683430i | ||||
\(543\) | −10.6277 | + | 6.13592i | −0.456079 | + | 0.263317i | ||||
\(544\) | −1.37228 | −0.0588361 | ||||||||
\(545\) | 5.05842 | + | 1.63086i | 0.216679 | + | 0.0698584i | ||||
\(546\) | −1.62772 | − | 2.81929i | −0.0696599 | − | 0.120655i | ||||
\(547\) | 46.0951 | 1.97088 | 0.985442 | − | 0.170012i | \(-0.0543807\pi\) | ||||
0.985442 | + | 0.170012i | \(0.0543807\pi\) | |||||||
\(548\) | −2.31386 | − | 1.33591i | −0.0988432 | − | 0.0570671i | ||||
\(549\) | 8.01544i | 0.342091i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0 | 0 | ||||||||
\(552\) | −6.00000 | − | 3.46410i | −0.255377 | − | 0.147442i | ||||
\(553\) | 14.2337 | + | 24.6535i | 0.605278 | + | 1.04837i | ||||
\(554\) | 7.00000 | 0.297402 | ||||||||
\(555\) | −32.8614 | + | 9.94987i | −1.39489 | + | 0.422349i | ||||
\(556\) | −18.7446 | −0.794947 | ||||||||
\(557\) | −22.2446 | − | 38.5287i | −0.942532 | − | 1.63251i | −0.760618 | − | 0.649200i | \(-0.775104\pi\) |
−0.181914 | − | 0.983314i | \(-0.558229\pi\) | |||||||
\(558\) | −32.2337 | − | 18.6101i | −1.36456 | − | 0.787830i | ||||
\(559\) | −1.69702 | + | 2.93932i | −0.0717761 | + | 0.124320i | ||||
\(560\) | 5.74456 | − | 5.19615i | 0.242752 | − | 0.219578i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −6.12772 | − | 3.53784i | −0.258482 | − | 0.149235i | ||||
\(563\) | −8.23369 | −0.347009 | −0.173504 | − | 0.984833i | \(-0.555509\pi\) | ||||
−0.173504 | + | 0.984833i | \(0.555509\pi\) | |||||||
\(564\) | 6.37228 | + | 11.0371i | 0.268321 | + | 0.464746i | ||||
\(565\) | 13.8832 | − | 43.0612i | 0.584069 | − | 1.81160i | ||||
\(566\) | 2.88316 | 0.121188 | ||||||||
\(567\) | −23.2337 | + | 13.4140i | −0.975723 | + | 0.563334i | ||||
\(568\) | −1.37228 | + | 2.37686i | −0.0575796 | + | 0.0997309i | ||||
\(569\) | 6.19082i | 0.259533i | 0.991545 | + | 0.129766i | \(0.0414227\pi\) | ||||
−0.991545 | + | 0.129766i | \(0.958577\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 19.2337 | + | 33.3137i | 0.804905 | + | 1.39414i | 0.916355 | + | 0.400366i | \(0.131117\pi\) |
−0.111451 | + | 0.993770i | \(0.535550\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 31.0475 | − | 53.7759i | 1.29703 | − | 2.24652i | ||||
\(574\) | 17.2337 | + | 9.94987i | 0.719320 | + | 0.415300i | ||||
\(575\) | −1.37228 | + | 13.6540i | −0.0572281 | + | 0.569412i | ||||
\(576\) | 1.68614 | + | 2.92048i | 0.0702559 | + | 0.121687i | ||||
\(577\) | −13.2337 | − | 22.9214i | −0.550926 | − | 0.954231i | −0.998208 | − | 0.0598384i | \(-0.980941\pi\) |
0.447282 | − | 0.894393i | \(-0.352392\pi\) | |||||||
\(578\) | −15.1168 | −0.628778 | ||||||||
\(579\) | 14.4891 | + | 8.36530i | 0.602147 | + | 0.347650i | ||||
\(580\) | 3.62772 | + | 16.8781i | 0.150633 | + | 0.700824i | ||||
\(581\) | 46.9783 | 1.94899 | ||||||||
\(582\) | − | 30.5870i | − | 1.26787i | ||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | − | 6.92820i | − | 0.286691i | ||||||
\(585\) | −1.88316 | − | 2.08191i | −0.0778589 | − | 0.0860763i | ||||
\(586\) | 28.8550i | 1.19199i | ||||||||
\(587\) | −15.3030 | + | 26.5055i | −0.631622 | + | 1.09400i | 0.355598 | + | 0.934639i | \(0.384277\pi\) |
−0.987220 | + | 0.159362i | \(0.949056\pi\) | |||||||
\(588\) | 10.9307 | + | 6.31084i | 0.450775 | + | 0.260255i | ||||
\(589\) | 0 | 0 | ||||||||
\(590\) | −5.62772 | − | 26.1831i | −0.231690 | − | 1.07794i | ||||
\(591\) | 17.8614 | 0.734720 | ||||||||
\(592\) | 5.00000 | − | 3.46410i | 0.205499 | − | 0.142374i | ||||
\(593\) | 10.8896i | 0.447184i | 0.974683 | + | 0.223592i | \(0.0717783\pi\) | ||||
−0.974683 | + | 0.223592i | \(0.928222\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −7.88316 | + | 7.13058i | −0.323178 | + | 0.292325i | ||||
\(596\) | 5.31386 | − | 9.20387i | 0.217664 | − | 0.377005i | ||||
\(597\) | −11.1861 | + | 19.3750i | −0.457818 | + | 0.792964i | ||||
\(598\) | −1.02175 | −0.0417824 | ||||||||
\(599\) | 6.81386 | − | 11.8020i | 0.278407 | − | 0.482215i | −0.692582 | − | 0.721339i | \(-0.743527\pi\) |
0.970989 | + | 0.239124i | \(0.0768603\pi\) | |||||||
\(600\) | 7.37228 | − | 10.2448i | 0.300972 | − | 0.418243i | ||||
\(601\) | −12.8723 | − | 22.2954i | −0.525071 | − | 0.909450i | −0.999574 | − | 0.0291960i | \(-0.990705\pi\) |
0.474502 | − | 0.880254i | \(-0.342628\pi\) | |||||||
\(602\) | − | 31.5817i | − | 1.28717i | ||||||
\(603\) | − | 27.7128i | − | 1.12855i | ||||||
\(604\) | −8.93070 | − | 15.4684i | −0.363385 | − | 0.629402i | ||||
\(605\) | 16.5000 | + | 18.2414i | 0.670820 | + | 0.741620i | ||||
\(606\) | 3.46410i | 0.140720i | ||||||||
\(607\) | 4.00000 | + | 6.92820i | 0.162355 | + | 0.281207i | 0.935713 | − | 0.352763i | \(-0.114758\pi\) |
−0.773358 | + | 0.633970i | \(0.781424\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −58.4674 | + | 33.7562i | −2.36922 | + | 1.36787i | ||||
\(610\) | −3.94158 | + | 3.56529i | −0.159590 | + | 0.144354i | ||||
\(611\) | 1.62772 | + | 0.939764i | 0.0658504 | + | 0.0380188i | ||||
\(612\) | −2.31386 | − | 4.00772i | −0.0935322 | − | 0.162003i | ||||
\(613\) | −30.9416 | + | 17.8641i | −1.24972 | + | 0.721525i | −0.971053 | − | 0.238863i | \(-0.923225\pi\) |
−0.278665 | + | 0.960388i | \(0.589892\pi\) | |||||||
\(614\) | −17.4416 | + | 10.0699i | −0.703885 | + | 0.406388i | ||||
\(615\) | 30.8614 | + | 9.94987i | 1.24445 | + | 0.401218i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 11.4891 | − | 6.63325i | 0.462535 | − | 0.267045i | −0.250575 | − | 0.968097i | \(-0.580620\pi\) |
0.713109 | + | 0.701053i | \(0.247286\pi\) | |||||||
\(618\) | 39.0998i | 1.57282i | ||||||||
\(619\) | −38.4674 | −1.54613 | −0.773067 | − | 0.634324i | \(-0.781278\pi\) | ||||
−0.773067 | + | 0.634324i | \(0.781278\pi\) | |||||||
\(620\) | −5.18614 | − | 24.1287i | −0.208280 | − | 0.969031i | ||||
\(621\) | − | 2.57924i | − | 0.103501i | ||||||
\(622\) | −16.4198 | − | 9.47999i | −0.658375 | − | 0.380113i | ||||
\(623\) | 33.2554 | 1.33235 | ||||||||
\(624\) | 0.813859 | + | 0.469882i | 0.0325804 | + | 0.0188103i | ||||
\(625\) | −24.5000 | − | 4.97494i | −0.980000 | − | 0.198997i | ||||
\(626\) | −14.1753 | + | 24.5523i | −0.566558 | + | 0.981307i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 6.48577i | 0.258811i | ||||||||
\(629\) | −6.86141 | + | 4.75372i | −0.273582 | + | 0.189543i | ||||
\(630\) | 24.8614 | + | 8.01544i | 0.990502 | + | 0.319343i | ||||
\(631\) | −10.3247 | + | 5.96099i | −0.411021 | + | 0.237303i | −0.691228 | − | 0.722636i | \(-0.742930\pi\) |
0.280207 | + | 0.959940i | \(0.409597\pi\) | |||||||
\(632\) | −7.11684 | − | 4.10891i | −0.283093 | − | 0.163444i | ||||
\(633\) | 33.8614 | + | 19.5499i | 1.34587 | + | 0.777038i | ||||
\(634\) | 11.3614 | + | 6.55951i | 0.451219 | + | 0.260511i | ||||
\(635\) | −36.8614 | − | 11.8843i | −1.46280 | − | 0.471614i | ||||
\(636\) | 1.18614 | − | 2.05446i | 0.0470335 | − | 0.0814645i | ||||
\(637\) | 1.86141 | 0.0737516 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −9.25544 | −0.366139 | ||||||||
\(640\) | −0.686141 | + | 2.12819i | −0.0271221 | + | 0.0841243i | ||||
\(641\) | 13.5000 | + | 23.3827i | 0.533218 | + | 0.923561i | 0.999247 | + | 0.0387913i | \(0.0123508\pi\) |
−0.466029 | + | 0.884769i | \(0.654316\pi\) | |||||||
\(642\) | −4.81386 | + | 8.33785i | −0.189988 | + | 0.329069i | ||||
\(643\) | 7.86141 | 0.310024 | 0.155012 | − | 0.987913i | \(-0.450458\pi\) | ||||
0.155012 | + | 0.987913i | \(0.450458\pi\) | |||||||
\(644\) | 8.23369 | − | 4.75372i | 0.324453 | − | 0.187323i | ||||
\(645\) | −10.8139 | − | 50.3118i | −0.425795 | − | 1.98103i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 11.7446 | − | 20.3422i | 0.461726 | − | 0.799734i | −0.537321 | − | 0.843378i | \(-0.680564\pi\) |
0.999047 | + | 0.0436444i | \(0.0138969\pi\) | |||||||
\(648\) | 3.87228 | − | 6.70699i | 0.152118 | − | 0.263475i | ||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0.186141 | − | 1.85208i | 0.00730104 | − | 0.0726444i | ||||
\(651\) | 83.5842 | − | 48.2574i | 3.27592 | − | 1.89136i | ||||
\(652\) | 17.1168 | 0.670347 | ||||||||
\(653\) | 13.5000 | − | 23.3827i | 0.528296 | − | 0.915035i | −0.471160 | − | 0.882048i | \(-0.656165\pi\) |
0.999456 | − | 0.0329874i | \(-0.0105021\pi\) | |||||||
\(654\) | −3.00000 | − | 5.19615i | −0.117309 | − | 0.203186i | ||||
\(655\) | −14.1168 | − | 4.55134i | −0.551591 | − | 0.177836i | ||||
\(656\) | −5.74456 | −0.224287 | ||||||||
\(657\) | 20.2337 | − | 11.6819i | 0.789391 | − | 0.455755i | ||||
\(658\) | −17.4891 | −0.681797 | ||||||||
\(659\) | −0.510875 | + | 0.884861i | −0.0199009 | + | 0.0344693i | −0.875804 | − | 0.482666i | \(-0.839668\pi\) |
0.855903 | + | 0.517136i | \(0.173002\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 43.2921 | + | 24.9947i | 1.68387 | + | 0.972182i | 0.959048 | + | 0.283243i | \(0.0914103\pi\) |
0.724820 | + | 0.688939i | \(0.241923\pi\) | |||||||
\(662\) | 24.0000 | + | 13.8564i | 0.932786 | + | 0.538545i | ||||
\(663\) | −1.11684 | − | 0.644810i | −0.0433746 | − | 0.0250424i | ||||
\(664\) | −11.7446 | + | 6.78073i | −0.455777 | + | 0.263143i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 18.5475 | + | 8.76144i | 0.718703 | + | 0.339499i | ||||
\(667\) | 21.1894i | 0.820456i | ||||||||
\(668\) | −2.74456 | − | 4.75372i | −0.106190 | − | 0.183927i | ||||
\(669\) | 23.4891 | − | 40.6844i | 0.908142 | − | 1.57295i | ||||
\(670\) | 13.6277 | − | 12.3267i | 0.526485 | − | 0.476223i | ||||
\(671\) | 0 | 0 | ||||||||
\(672\) | −8.74456 | −0.337329 | ||||||||
\(673\) | 6.00000 | + | 3.46410i | 0.231283 | + | 0.133531i | 0.611164 | − | 0.791504i | \(-0.290702\pi\) |
−0.379881 | + | 0.925035i | \(0.624035\pi\) | |||||||
\(674\) | 1.08724i | 0.0418789i | ||||||||
\(675\) | 4.67527 | + | 0.469882i | 0.179951 | + | 0.0180858i | ||||
\(676\) | −12.8614 | −0.494669 | ||||||||
\(677\) | 4.84630i | 0.186258i | 0.995654 | + | 0.0931291i | \(0.0296869\pi\) | ||||
−0.995654 | + | 0.0931291i | \(0.970313\pi\) | |||||||
\(678\) | −44.2337 | + | 25.5383i | −1.69878 | + | 0.980794i | ||||
\(679\) | 36.3505 | + | 20.9870i | 1.39501 | + | 0.805407i | ||||
\(680\) | 0.941578 | − | 2.92048i | 0.0361079 | − | 0.111995i | ||||
\(681\) | −22.6753 | + | 13.0916i | −0.868918 | + | 0.501670i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 5.44158 | + | 9.42509i | 0.208216 | + | 0.360641i | 0.951153 | − | 0.308721i | \(-0.0999009\pi\) |
−0.742936 | + | 0.669362i | \(0.766568\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 4.43070 | − | 4.00772i | 0.169288 | − | 0.153127i | ||||
\(686\) | 6.00000 | − | 3.46410i | 0.229081 | − | 0.132260i | ||||
\(687\) | 19.3723 | − | 11.1846i | 0.739099 | − | 0.426719i | ||||
\(688\) | 4.55842 | + | 7.89542i | 0.173788 | + | 0.301010i | ||||
\(689\) | − | 0.349857i | − | 0.0133285i | ||||||
\(690\) | 11.4891 | − | 10.3923i | 0.437384 | − | 0.395628i | ||||
\(691\) | −6.74456 | − | 11.6819i | −0.256575 | − | 0.444401i | 0.708747 | − | 0.705463i | \(-0.249261\pi\) |
−0.965322 | + | 0.261061i | \(0.915927\pi\) | |||||||
\(692\) | 12.1793i | 0.462986i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 1.37228 | + | 2.37686i | 0.0520911 | + | 0.0902244i | ||||
\(695\) | 12.8614 | − | 39.8921i | 0.487861 | − | 1.51319i | ||||
\(696\) | 9.74456 | − | 16.8781i | 0.369367 | − | 0.639762i | ||||
\(697\) | 7.88316 | 0.298596 | ||||||||
\(698\) | −0.313859 | + | 0.543620i | −0.0118798 | + | 0.0205763i | ||||
\(699\) | −18.4891 | + | 32.0241i | −0.699323 | + | 1.21126i | ||||
\(700\) | 7.11684 | + | 15.7908i | 0.268991 | + | 0.596838i | ||||
\(701\) | 32.7446 | − | 18.9051i | 1.23675 | − | 0.714035i | 0.268318 | − | 0.963331i | \(-0.413532\pi\) |
0.968427 | + | 0.249295i | \(0.0801990\pi\) | |||||||
\(702\) | 0.349857i | 0.0132045i | ||||||||
\(703\) | 0 | 0 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −27.8614 | + | 5.98844i | −1.04932 | + | 0.225538i | ||||
\(706\) | −12.1753 | + | 21.0882i | −0.458222 | + | 0.793664i | ||||
\(707\) | −4.11684 | − | 2.37686i | −0.154830 | − | 0.0893911i | ||||
\(708\) | −15.1168 | + | 26.1831i | −0.568126 | + | 0.984023i | ||||
\(709\) | − | 22.0742i | − | 0.829015i | −0.910046 | − | 0.414508i | \(-0.863954\pi\) | ||
0.910046 | − | 0.414508i | \(-0.136046\pi\) | |||||||
\(710\) | −4.11684 | − | 4.55134i | −0.154502 | − | 0.170809i | ||||
\(711\) | − | 27.7128i | − | 1.03931i | ||||||
\(712\) | −8.31386 | + | 4.80001i | −0.311575 | + | 0.179888i | ||||
\(713\) | − | 30.2921i | − | 1.13445i | ||||||
\(714\) | 12.0000 | 0.449089 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 17.4891 | + | 10.0974i | 0.653599 | + | 0.377356i | ||||
\(717\) | 24.7446 | 0.924103 | ||||||||
\(718\) | 5.18614 | + | 8.98266i | 0.193545 | + | 0.335230i | ||||
\(719\) | −19.6753 | − | 34.0786i | −0.733764 | − | 1.27092i | −0.955264 | − | 0.295755i | \(-0.904429\pi\) |
0.221500 | − | 0.975160i | \(-0.428905\pi\) | |||||||
\(720\) | −7.37228 | + | 1.58457i | −0.274749 | + | 0.0590536i | ||||
\(721\) | −46.4674 | − | 26.8280i | −1.73054 | − | 0.999125i | ||||
\(722\) | −9.50000 | + | 16.4545i | −0.353553 | + | 0.612372i | ||||
\(723\) | 26.2337 | + | 45.4381i | 0.975641 | + | 1.68986i | ||||
\(724\) | 2.43070 | + | 4.21010i | 0.0903364 | + | 0.156467i | ||||
\(725\) | −38.4090 | − | 3.86025i | −1.42647 | − | 0.143366i | ||||
\(726\) | − | 27.7677i | − | 1.03056i | ||||||
\(727\) | 4.00000 | − | 6.92820i | 0.148352 | − | 0.256953i | −0.782267 | − | 0.622944i | \(-0.785937\pi\) |
0.930618 | + | 0.365991i | \(0.119270\pi\) | |||||||
\(728\) | −1.11684 | + | 0.644810i | −0.0413930 | + | 0.0238983i | ||||
\(729\) | 33.2337 | 1.23088 | ||||||||
\(730\) | 14.7446 | + | 4.75372i | 0.545721 | + | 0.175943i | ||||
\(731\) | −6.25544 | − | 10.8347i | −0.231366 | − | 0.400737i | ||||
\(732\) | 6.00000 | 0.221766 | ||||||||
\(733\) | −2.23369 | − | 1.28962i | −0.0825031 | − | 0.0476332i | 0.458181 | − | 0.888859i | \(-0.348501\pi\) |
−0.540684 | + | 0.841226i | \(0.681835\pi\) | |||||||
\(734\) | 22.0742i | 0.814775i | ||||||||
\(735\) | −20.9307 | + | 18.9325i | −0.772041 | + | 0.698337i | ||||
\(736\) | −1.37228 | + | 2.37686i | −0.0505830 | + | 0.0876123i | ||||
\(737\) | 0 | 0 | ||||||||
\(738\) | −9.68614 | − | 16.7769i | −0.356552 | − | 0.617566i | ||||
\(739\) | −20.9783 | −0.771697 | −0.385849 | − | 0.922562i | \(-0.626091\pi\) | ||||
−0.385849 | + | 0.922562i | \(0.626091\pi\) | |||||||
\(740\) | 3.94158 | + | 13.0178i | 0.144895 | + | 0.478545i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 1.62772 | + | 2.81929i | 0.0597554 | + | 0.103499i | ||||
\(743\) | −24.6060 | − | 14.2063i | −0.902705 | − | 0.521177i | −0.0246285 | − | 0.999697i | \(-0.507840\pi\) |
−0.878077 | + | 0.478519i | \(0.841174\pi\) | |||||||
\(744\) | −13.9307 | + | 24.1287i | −0.510724 | + | 0.884601i | ||||
\(745\) | 15.9416 | + | 17.6241i | 0.584054 | + | 0.645696i | ||||
\(746\) | 12.1244i | 0.443904i | ||||||||
\(747\) | −39.6060 | − | 22.8665i | −1.44911 | − | 0.836642i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −6.60597 | − | 11.4419i | −0.241377 | − | 0.418077i | ||||
\(750\) | 16.7446 | + | 22.7190i | 0.611425 | + | 0.829582i | ||||
\(751\) | −19.3505 | −0.706111 | −0.353055 | − | 0.935602i | \(-0.614857\pi\) | ||||
−0.353055 | + | 0.935602i | \(0.614857\pi\) | |||||||
\(752\) | 4.37228 | − | 2.52434i | 0.159441 | − | 0.0920531i | ||||
\(753\) | 27.4891 | − | 47.6126i | 1.00176 | − | 1.73510i | ||||
\(754\) | − | 2.87419i | − | 0.104672i | ||||||
\(755\) | 39.0475 | − | 8.39275i | 1.42109 | − | 0.305444i | ||||
\(756\) | −1.62772 | − | 2.81929i | −0.0591996 | − | 0.102537i | ||||
\(757\) | −13.6168 | − | 23.5851i | −0.494913 | − | 0.857214i | 0.505070 | − | 0.863078i | \(-0.331467\pi\) |
−0.999983 | + | 0.00586448i | \(0.998133\pi\) | |||||||
\(758\) | −5.37228 | + | 9.30506i | −0.195130 | + | 0.337975i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −24.1753 | − | 41.8728i | −0.876353 | − | 1.51789i | −0.855315 | − | 0.518109i | \(-0.826636\pi\) |
−0.0210379 | − | 0.999779i | \(-0.506697\pi\) | |||||||
\(762\) | 21.8614 | + | 37.8651i | 0.791955 | + | 1.37171i | ||||
\(763\) | 8.23369 | 0.298080 | ||||||||
\(764\) | −21.3030 | − | 12.2993i | −0.770715 | − | 0.444972i | ||||
\(765\) | 10.1168 | − | 2.17448i | 0.365775 | − | 0.0786185i | ||||
\(766\) | −12.5109 | −0.452036 | ||||||||
\(767\) | 4.45877i | 0.160997i | ||||||||
\(768\) | 2.18614 | − | 1.26217i | 0.0788856 | − | 0.0455446i | ||||
\(769\) | − | 39.7995i | − | 1.43521i | −0.696452 | − | 0.717603i | \(-0.745239\pi\) | ||
0.696452 | − | 0.717603i | \(-0.254761\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 2.17448i | 0.0783120i | ||||||||
\(772\) | 3.31386 | − | 5.73977i | 0.119268 | − | 0.206579i | ||||
\(773\) | 6.89403 | + | 3.98027i | 0.247961 | + | 0.143160i | 0.618830 | − | 0.785525i | \(-0.287607\pi\) |
−0.370869 | + | 0.928685i | \(0.620940\pi\) | |||||||
\(774\) | −15.3723 | + | 26.6256i | −0.552545 | + | 0.957036i | ||||
\(775\) | 54.9090 | + | 5.51856i | 1.97239 | + | 0.198232i | ||||
\(776\) | −12.1168 | −0.434969 | ||||||||
\(777\) | −43.7228 | + | 30.2921i | −1.56855 | + | 1.08672i | ||||
\(778\) | − | 8.71516i | − | 0.312454i | ||||||
\(779\) | 0 | 0 | ||||||||
\(780\) | −1.55842 | + | 1.40965i | −0.0558005 | + | 0.0504734i | ||||
\(781\) | 0 | 0 | ||||||||
\(782\) | 1.88316 | − | 3.26172i | 0.0673415 | − | 0.116639i | ||||
\(783\) | 7.25544 | 0.259288 | ||||||||
\(784\) | 2.50000 | − | 4.33013i | 0.0892857 | − | 0.154647i | ||||
\(785\) | −13.8030 | − | 4.45015i | −0.492650 | − | 0.158833i | ||||
\(786\) | 8.37228 | + | 14.5012i | 0.298629 | + | 0.517241i | ||||
\(787\) | 20.5446i | 0.732334i | 0.930549 | + | 0.366167i | \(0.119330\pi\) | ||||
−0.930549 | + | 0.366167i | \(0.880670\pi\) | |||||||
\(788\) | − | 7.07568i | − | 0.252061i | ||||||
\(789\) | −4.00000 | − | 6.92820i | −0.142404 | − | 0.246651i | ||||
\(790\) | 13.6277 | − | 12.3267i | 0.484852 | − | 0.438566i | ||||
\(791\) | − | 70.0916i | − | 2.49217i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 0.766312 | − | 0.442430i | 0.0272125 | − | 0.0157112i | ||||
\(794\) | 14.6168 | − | 8.43904i | 0.518732 | − | 0.299490i | ||||
\(795\) | 3.55842 | + | 3.93398i | 0.126204 | + | 0.139524i | ||||
\(796\) | 7.67527 | + | 4.43132i | 0.272043 | + | 0.157064i | ||||
\(797\) | −3.81386 | − | 6.60580i | −0.135094 | − | 0.233989i | 0.790539 | − | 0.612411i | \(-0.209800\pi\) |
−0.925633 | + | 0.378422i | \(0.876467\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −6.00000 | + | 3.46410i | −0.212265 | + | 0.122551i | ||||
\(800\) | −4.05842 | − | 2.92048i | −0.143487 | − | 0.103255i | ||||
\(801\) | −28.0367 | − | 16.1870i | −0.990627 | − | 0.571939i | ||||
\(802\) | −11.4891 | + | 6.63325i | −0.405695 | + | 0.234228i | ||||
\(803\) | 0 | 0 | ||||||||
\(804\) | −20.7446 | −0.731604 | ||||||||
\(805\) | 4.46738 | + | 20.7846i | 0.157454 | + | 0.732561i | ||||
\(806\) | 4.10891i | 0.144730i | ||||||||
\(807\) | 51.3505 | + | 29.6472i | 1.80762 | + | 1.04363i | ||||
\(808\) | 1.37228 | 0.0482767 | ||||||||
\(809\) | −16.0693 | − | 9.27761i | −0.564966 | − | 0.326183i | 0.190170 | − | 0.981751i | \(-0.439096\pi\) |
−0.755136 | + | 0.655568i | \(0.772429\pi\) | |||||||
\(810\) | 11.6168 | + | 12.8429i | 0.408174 | + | 0.451254i | ||||
\(811\) | −5.11684 | + | 8.86263i | −0.179677 | + | 0.311209i | −0.941770 | − | 0.336258i | \(-0.890838\pi\) |
0.762093 | + | 0.647467i | \(0.224172\pi\) | |||||||
\(812\) | 13.3723 | + | 23.1615i | 0.469275 | + | 0.812808i | ||||
\(813\) | 46.3778i | 1.62654i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −11.7446 | + | 36.4280i | −0.411394 | + | 1.27602i | ||||
\(816\) | −3.00000 | + | 1.73205i | −0.105021 | + | 0.0606339i | ||||
\(817\) | 0 | 0 | ||||||||
\(818\) | −25.5000 | − | 14.7224i | −0.891587 | − | 0.514758i | ||||
\(819\) | −3.76631 | − | 2.17448i | −0.131606 | − | 0.0759825i | ||||
\(820\) | 3.94158 | − | 12.2255i | 0.137646 | − | 0.426935i | ||||
\(821\) | 16.1168 | − | 27.9152i | 0.562482 | − | 0.974247i | −0.434797 | − | 0.900528i | \(-0.643180\pi\) |
0.997279 | − | 0.0737186i | \(-0.0234867\pi\) | |||||||
\(822\) | −6.74456 | −0.235244 | ||||||||
\(823\) | −4.11684 | + | 2.37686i | −0.143504 | + | 0.0828522i | −0.570033 | − | 0.821622i | \(-0.693070\pi\) |
0.426529 | + | 0.904474i | \(0.359736\pi\) | |||||||
\(824\) | 15.4891 | 0.539589 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −20.7446 | − | 35.9306i | −0.721796 | − | 1.25019i | ||||
\(827\) | 14.2337 | − | 24.6535i | 0.494954 | − | 0.857285i | −0.505029 | − | 0.863102i | \(-0.668518\pi\) |
0.999983 | + | 0.00581705i | \(0.00185164\pi\) | |||||||
\(828\) | −9.25544 | −0.321649 | ||||||||
\(829\) | −2.23369 | + | 1.28962i | −0.0775792 | + | 0.0447904i | −0.538288 | − | 0.842761i | \(-0.680929\pi\) |
0.460709 | + | 0.887551i | \(0.347595\pi\) | |||||||
\(830\) | −6.37228 | − | 29.6472i | −0.221185 | − | 1.02907i | ||||
\(831\) | 15.3030 | − | 8.83518i | 0.530855 | − | 0.306489i | ||||
\(832\) | 0.186141 | − | 0.322405i | 0.00645327 | − | 0.0111774i | ||||
\(833\) | −3.43070 | + | 5.94215i | −0.118867 | + | 0.205883i | ||||
\(834\) | −40.9783 | + | 23.6588i | −1.41896 | + | 0.819237i | ||||
\(835\) | 12.0000 | − | 2.57924i | 0.415277 | − | 0.0892583i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −10.3723 | −0.358518 | ||||||||
\(838\) | 8.48913 | − | 14.7036i | 0.293252 | − | 0.507927i | ||||
\(839\) | 27.3030 | + | 47.2902i | 0.942604 | + | 1.63264i | 0.760479 | + | 0.649362i | \(0.224964\pi\) |
0.182124 | + | 0.983276i | \(0.441703\pi\) | |||||||
\(840\) | 6.00000 | − | 18.6101i | 0.207020 | − | 0.642110i | ||||
\(841\) | −30.6060 | −1.05538 | ||||||||
\(842\) | −9.17527 | + | 5.29734i | −0.316201 | + | 0.182558i | ||||
\(843\) | −17.8614 | −0.615180 | ||||||||
\(844\) | 7.74456 | − | 13.4140i | 0.266579 | − | 0.461728i | ||||
\(845\) | 8.82473 | − | 27.3716i | 0.303580 | − | 0.941611i | ||||
\(846\) | 14.7446 | + | 8.51278i | 0.506929 | + | 0.292675i | ||||
\(847\) | 33.0000 | + | 19.0526i | 1.13389 | + | 0.654654i | ||||
\(848\) | −0.813859 | − | 0.469882i | −0.0279480 | − | 0.0161358i | ||||
\(849\) | 6.30298 | − | 3.63903i | 0.216318 | − | 0.124891i | ||||
\(850\) | 5.56930 | + | 4.00772i | 0.191025 | + | 0.137464i | ||||
\(851\) | 1.37228 | + | 16.6380i | 0.0470412 | + | 0.570344i | ||||
\(852\) | 6.92820i | 0.237356i | ||||||||
\(853\) | 0.616844 | + | 1.06841i | 0.0211203 | + | 0.0365815i | 0.876392 | − | 0.481598i | \(-0.159943\pi\) |
−0.855272 | + | 0.518179i | \(0.826610\pi\) | |||||||
\(854\) | −4.11684 | + | 7.13058i | −0.140876 | + | 0.244004i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 3.30298 | + | 1.90698i | 0.112894 | + | 0.0651792i | ||||
\(857\) | 18.8614 | 0.644293 | 0.322147 | − | 0.946690i | \(-0.395596\pi\) | ||||
0.322147 | + | 0.946690i | \(0.395596\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 3.46410i | 0.118194i | 0.998252 | + | 0.0590968i | \(0.0188221\pi\) | ||||
−0.998252 | + | 0.0590968i | \(0.981178\pi\) | |||||||
\(860\) | −19.9307 | + | 4.28384i | −0.679631 | + | 0.146078i | ||||
\(861\) | 50.2337 | 1.71196 | ||||||||
\(862\) | − | 31.2318i | − | 1.06376i | ||||||
\(863\) | 6.60597 | − | 3.81396i | 0.224870 | − | 0.129829i | −0.383333 | − | 0.923610i | \(-0.625224\pi\) |
0.608203 | + | 0.793781i | \(0.291891\pi\) | |||||||
\(864\) | 0.813859 | + | 0.469882i | 0.0276881 | + | 0.0159857i | ||||
\(865\) | −25.9198 | − | 8.35668i | −0.881301 | − | 0.284136i | ||||
\(866\) | 18.1753 | − | 10.4935i | 0.617621 | − | 0.356583i | ||||
\(867\) | −33.0475 | + | 19.0800i | −1.12235 | + | 0.647991i | ||||
\(868\) | −19.1168 | − | 33.1113i | −0.648868 | − | 1.12387i | ||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 29.2337 | + | 32.3191i | 0.991115 | + | 1.09572i | ||||
\(871\) | −2.64947 | + | 1.52967i | −0.0897738 | + | 0.0518309i | ||||
\(872\) | −2.05842 | + | 1.18843i | −0.0697070 | + | 0.0402453i | ||||
\(873\) | −20.4307 | − | 35.3870i | −0.691475 | − | 1.19767i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −38.4891 | + | 4.31129i | −1.30117 | + | 0.145748i | ||||
\(876\) | −8.74456 | − | 15.1460i | −0.295451 | − | 0.511737i | ||||
\(877\) | − | 15.9932i | − | 0.540053i | −0.962853 | − | 0.270026i | \(-0.912968\pi\) | ||
0.962853 | − | 0.270026i | \(-0.0870324\pi\) | |||||||
\(878\) | 16.6757i | 0.562778i | ||||||||
\(879\) | 36.4198 | + | 63.0810i | 1.22841 | + | 2.12767i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −8.05842 | + | 13.9576i | −0.271495 | + | 0.470243i | −0.969245 | − | 0.246098i | \(-0.920851\pi\) |
0.697750 | + | 0.716342i | \(0.254185\pi\) | |||||||
\(882\) | 16.8614 | 0.567753 | ||||||||
\(883\) | 29.6753 | − | 51.3991i | 0.998652 | − | 1.72972i | 0.454378 | − | 0.890809i | \(-0.349862\pi\) |
0.544274 | − | 0.838907i | \(-0.316805\pi\) | |||||||
\(884\) | −0.255437 | + | 0.442430i | −0.00859129 | + | 0.0148805i | ||||
\(885\) | −45.3505 | − | 50.1369i | −1.52444 | − | 1.68533i | ||||
\(886\) | 24.8139 | − | 14.3263i | 0.833638 | − | 0.481301i | ||||
\(887\) | − | 21.7793i | − | 0.731277i | −0.930757 | − | 0.365638i | \(-0.880851\pi\) | ||
0.930757 | − | 0.365638i | \(-0.119149\pi\) | |||||||
\(888\) | 6.55842 | − | 13.8839i | 0.220086 | − | 0.465912i | ||||
\(889\) | −60.0000 | −2.01234 | ||||||||
\(890\) | −4.51087 | − | 20.9870i | −0.151205 | − | 0.703485i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −16.1168 | − | 9.30506i | −0.539632 | − | 0.311557i | ||||
\(893\) | 0 | 0 | ||||||||
\(894\) | − | 26.8280i | − | 0.897261i | ||||||
\(895\) | −33.4891 | + | 30.2921i | −1.11942 | + | 1.01255i | ||||
\(896\) | 3.46410i | 0.115728i | ||||||||
\(897\) | −2.23369 | + | 1.28962i | −0.0745807 | + | 0.0430592i | ||||
\(898\) | − | 6.57835i | − | 0.219522i | ||||||
\(899\) | 85.2119 | 2.84198 | ||||||||
\(900\) | 1.68614 | − | 16.7769i | 0.0562047 | − | 0.559230i | ||||
\(901\) | 1.11684 | + | 0.644810i | 0.0372075 | + | 0.0214817i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −39.8614 | − | 69.0420i | −1.32650 | − | 2.29757i | ||||
\(904\) | 10.1168 | + | 17.5229i | 0.336481 | + | 0.582803i | ||||
\(905\) | −10.6277 | + | 2.28429i | −0.353277 | + | 0.0759323i | ||||
\(906\) | −39.0475 | − | 22.5441i | −1.29727 | − | 0.748978i | ||||
\(907\) | 13.2554 | − | 22.9591i | 0.440140 | − | 0.762344i | −0.557560 | − | 0.830137i | \(-0.688262\pi\) |
0.997699 | + | 0.0677926i | \(0.0215956\pi\) | |||||||
\(908\) | 5.18614 | + | 8.98266i | 0.172108 | + | 0.298100i | ||||
\(909\) | 2.31386 | + | 4.00772i | 0.0767459 | + | 0.132928i | ||||
\(910\) | −0.605969 | − | 2.81929i | −0.0200877 | − | 0.0934586i | ||||
\(911\) | 49.2520i | 1.63179i | 0.578198 | + | 0.815896i | \(0.303756\pi\) | ||||
−0.578198 | + | 0.815896i | \(0.696244\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | 19.6060 | 0.648508 | ||||||||
\(915\) | −4.11684 | + | 12.7692i | −0.136099 | + | 0.422136i | ||||
\(916\) | −4.43070 | − | 7.67420i | −0.146395 | − | 0.253563i | ||||
\(917\) | −22.9783 | −0.758809 | ||||||||
\(918\) | −1.11684 | − | 0.644810i | −0.0368613 | − | 0.0212819i | ||||
\(919\) | 3.46410i | 0.114270i | 0.998366 | + | 0.0571351i | \(0.0181966\pi\) | ||||
−0.998366 | + | 0.0571351i | \(0.981803\pi\) | |||||||
\(920\) | −4.11684 | − | 4.55134i | −0.135728 | − | 0.150053i | ||||
\(921\) | −25.4198 | + | 44.0284i | −0.837612 | + | 1.45079i | ||||
\(922\) | −27.8614 | − | 16.0858i | −0.917567 | − | 0.529757i | ||||
\(923\) | 0.510875 | + | 0.884861i | 0.0168156 | + | 0.0291256i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −30.4090 | − | 0.543620i | −0.999840 | − | 0.0178741i | ||||
\(926\) | 4.51087 | 0.148237 | ||||||||
\(927\) | 26.1168 | + | 45.2357i | 0.857790 | + | 1.48574i | ||||
\(928\) | −6.68614 | − | 3.86025i | −0.219483 | − | 0.126719i | ||||
\(929\) | −18.9891 | + | 32.8901i | −0.623013 | + | 1.07909i | 0.365909 | + | 0.930651i | \(0.380758\pi\) |
−0.988922 | + | 0.148439i | \(0.952575\pi\) | |||||||
\(930\) | −41.7921 | − | 46.2029i | −1.37042 | − | 1.51505i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 12.6861 | + | 7.32435i | 0.415548 | + | 0.239917i | ||||
\(933\) | −47.8614 | −1.56691 | ||||||||
\(934\) | 11.1861 | + | 19.3750i | 0.366022 | + | 0.633968i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 1.25544 | 0.0410353 | ||||||||
\(937\) | −42.9416 | + | 24.7923i | −1.40284 | + | 0.809930i | −0.994683 | − | 0.102982i | \(-0.967162\pi\) |
−0.408157 | + | 0.912912i | \(0.633828\pi\) | |||||||
\(938\) | 14.2337 | − | 24.6535i | 0.464746 | − | 0.804964i | ||||
\(939\) | 71.5663i | 2.33548i | ||||||||
\(940\) | 2.37228 | + | 11.0371i | 0.0773753 | + | 0.359991i | ||||
\(941\) | 6.43070 | + | 11.1383i | 0.209635 | + | 0.363098i | 0.951600 | − | 0.307341i | \(-0.0994391\pi\) |
−0.741965 | + | 0.670439i | \(0.766106\pi\) | |||||||
\(942\) | 8.18614 | + | 14.1788i | 0.266719 | + | 0.461971i | ||||
\(943\) | 7.88316 | − | 13.6540i | 0.256711 | − | 0.444636i | ||||
\(944\) | 10.3723 | + | 5.98844i | 0.337589 | + | 0.194907i | ||||
\(945\) | 7.11684 | − | 1.52967i | 0.231511 | − | 0.0497602i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −19.9307 | − | 34.5210i | −0.647661 | − | 1.12178i | −0.983680 | − | 0.179926i | \(-0.942414\pi\) |
0.336019 | − | 0.941855i | \(-0.390919\pi\) | |||||||
\(948\) | −20.7446 | −0.673752 | ||||||||
\(949\) | −2.23369 | − | 1.28962i | −0.0725086 | − | 0.0418628i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 33.1168 | 1.07389 | ||||||||
\(952\) | − | 4.75372i | − | 0.154069i | ||||||
\(953\) | 11.4891 | − | 6.63325i | 0.372169 | − | 0.214872i | −0.302236 | − | 0.953233i | \(-0.597733\pi\) |
0.674406 | + | 0.738361i | \(0.264400\pi\) | |||||||
\(954\) | − | 3.16915i | − | 0.102605i | ||||||
\(955\) | 40.7921 | − | 36.8979i | 1.32000 | − | 1.19399i | ||||
\(956\) | − | 9.80240i | − | 0.317032i | ||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −31.4198 | − | 18.1402i | −1.01513 | − | 0.586085i | ||||
\(959\) | 4.62772 | − | 8.01544i | 0.149437 | − | 0.258832i | ||||
\(960\) | 1.18614 | + | 5.51856i | 0.0382825 | + | 0.178111i | ||||
\(961\) | −90.8179 | −2.92961 | ||||||||
\(962\) | −0.186141 | − | 2.25684i | −0.00600142 | − | 0.0727633i | ||||
\(963\) | 12.8617i | 0.414464i | ||||||||
\(964\) | 18.0000 | − | 10.3923i | 0.579741 | − | 0.334714i | ||||
\(965\) | 9.94158 | + | 10.9908i | 0.320031 | + | 0.353807i | ||||
\(966\) | 12.0000 | − | 20.7846i | 0.386094 | − | 0.668734i | ||||
\(967\) | 17.1168 | − | 29.6472i | 0.550441 | − | 0.953391i | −0.447802 | − | 0.894133i | \(-0.647793\pi\) |
0.998243 | − | 0.0592584i | \(-0.0188736\pi\) | |||||||
\(968\) | −11.0000 | −0.353553 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 8.31386 | − | 25.7870i | 0.266942 | − | 0.827971i | ||||
\(971\) | 8.48913 | + | 14.7036i | 0.272429 | + | 0.471861i | 0.969483 | − | 0.245158i | \(-0.0788397\pi\) |
−0.697054 | + | 0.717018i | \(0.745506\pi\) | |||||||
\(972\) | − | 22.3692i | − | 0.717492i | ||||||
\(973\) | − | 64.9331i | − | 2.08166i | ||||||
\(974\) | 1.00000 | + | 1.73205i | 0.0320421 | + | 0.0554985i | ||||
\(975\) | −1.93070 | − | 4.28384i | −0.0618320 | − | 0.137193i | ||||
\(976\) | − | 2.37686i | − | 0.0760815i | ||||||
\(977\) | 28.1168 | + | 48.6998i | 0.899538 | + | 1.55804i | 0.828086 | + | 0.560601i | \(0.189430\pi\) |
0.0714512 | + | 0.997444i | \(0.477237\pi\) | |||||||
\(978\) | 37.4198 | − | 21.6043i | 1.19655 | − | 0.690831i | ||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 7.50000 | + | 8.29156i | 0.239579 | + | 0.264864i | ||||
\(981\) | −6.94158 | − | 4.00772i | −0.221628 | − | 0.127957i | ||||
\(982\) | 9.86141 | + | 17.0805i | 0.314690 | + | 0.545059i | ||||
\(983\) | −37.6277 | + | 21.7244i | −1.20014 | + | 0.692900i | −0.960586 | − | 0.277984i | \(-0.910334\pi\) |
−0.239552 | + | 0.970884i | \(0.577001\pi\) | |||||||
\(984\) | −12.5584 | + | 7.25061i | −0.400348 | + | 0.231141i | ||||
\(985\) | 15.0584 | + | 4.85491i | 0.479801 | + | 0.154690i | ||||
\(986\) | 9.17527 | + | 5.29734i | 0.292200 | + | 0.168702i | ||||
\(987\) | −38.2337 | + | 22.0742i | −1.21699 | + | 0.702630i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −25.0217 | −0.795645 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 6.28339i | 0.199599i | 0.995008 | + | 0.0997993i | \(0.0318201\pi\) | ||||
−0.995008 | + | 0.0997993i | \(0.968180\pi\) | |||||||
\(992\) | 9.55842 | + | 5.51856i | 0.303480 | + | 0.175214i | ||||
\(993\) | 69.9565 | 2.22000 | ||||||||
\(994\) | −8.23369 | − | 4.75372i | −0.261157 | − | 0.150779i | ||||
\(995\) | −14.6970 | + | 13.2940i | −0.465927 | + | 0.421447i | ||||
\(996\) | −17.1168 | + | 29.6472i | −0.542368 | + | 0.939409i | ||||
\(997\) | 16.5584 | + | 28.6800i | 0.524410 | + | 0.908306i | 0.999596 | + | 0.0284200i | \(0.00904759\pi\) |
−0.475186 | + | 0.879886i | \(0.657619\pi\) | |||||||
\(998\) | − | 13.8564i | − | 0.438617i | ||||||
\(999\) | 5.69702 | − | 0.469882i | 0.180246 | − | 0.0148664i |
(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 | 370.2.m.a.159.1 | ✓ | 4 | |
5.4 | even | 2 | 370.2.m.b.159.2 | yes | 4 | ||
37.27 | even | 6 | 370.2.m.b.249.2 | yes | 4 | ||
185.64 | even | 6 | inner | 370.2.m.a.249.1 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
370.2.m.a.159.1 | ✓ | 4 | 1.1 | even | 1 | trivial | |
370.2.m.a.249.1 | yes | 4 | 185.64 | even | 6 | inner | |
370.2.m.b.159.2 | yes | 4 | 5.4 | even | 2 | ||
370.2.m.b.249.2 | yes | 4 | 37.27 | even | 6 |