Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [230,2,Mod(137,230)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(230, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([1, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("230.137");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 230 = 2 \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 230.e (of order \(4\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(1.83655924649\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(i)\) |
Coefficient field: | 8.0.110166016.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 10x^{6} + 19x^{4} + 10x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 183.4 | ||
Root | \(1.22833i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 230.183 |
Dual form | 230.2.e.b.137.4 |
$q$-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 \(\left(\mathbb{Z}/230\mathbb{Z}\right)^\times\).
\(n\) | \(47\) | \(51\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.707107 | − | 0.707107i | 0.500000 | − | 0.500000i | ||||
\(3\) | 0.575666 | + | 0.575666i | 0.332361 | + | 0.332361i | 0.853482 | − | 0.521122i | \(-0.174486\pi\) |
−0.521122 | + | 0.853482i | \(0.674486\pi\) | |||||||
\(4\) | − | 1.00000i | − | 0.500000i | ||||||
\(5\) | 0.185885 | − | 2.22833i | 0.0831305 | − | 0.996539i | ||||
\(6\) | 0.814115 | 0.332361 | ||||||||
\(7\) | −2.09689 | − | 2.09689i | −0.792549 | − | 0.792549i | 0.189359 | − | 0.981908i | \(-0.439359\pi\) |
−0.981908 | + | 0.189359i | \(0.939359\pi\) | |||||||
\(8\) | −0.707107 | − | 0.707107i | −0.250000 | − | 0.250000i | ||||
\(9\) | − | 2.33722i | − | 0.779072i | ||||||
\(10\) | −1.44423 | − | 1.70711i | −0.456704 | − | 0.539835i | ||||
\(11\) | 1.39990i | 0.422086i | 0.977477 | + | 0.211043i | \(0.0676860\pi\) | ||||
−0.977477 | + | 0.211043i | \(0.932314\pi\) | |||||||
\(12\) | 0.575666 | − | 0.575666i | 0.166180 | − | 0.166180i | ||||
\(13\) | 4.24822 | + | 4.24822i | 1.17824 | + | 1.17824i | 0.980191 | + | 0.198053i | \(0.0634617\pi\) |
0.198053 | + | 0.980191i | \(0.436538\pi\) | |||||||
\(14\) | −2.96545 | −0.792549 | ||||||||
\(15\) | 1.38978 | − | 1.17576i | 0.358840 | − | 0.303581i | ||||
\(16\) | −1.00000 | −0.250000 | ||||||||
\(17\) | 4.38978 | + | 4.38978i | 1.06468 | + | 1.06468i | 0.997758 | + | 0.0669198i | \(0.0213172\pi\) |
0.0669198 | + | 0.997758i | \(0.478683\pi\) | |||||||
\(18\) | −1.65266 | − | 1.65266i | −0.389536 | − | 0.389536i | ||||
\(19\) | 2.37966 | 0.545931 | 0.272966 | − | 0.962024i | \(-0.411995\pi\) | ||||
0.272966 | + | 0.962024i | \(0.411995\pi\) | |||||||
\(20\) | −2.22833 | − | 0.185885i | −0.498269 | − | 0.0415652i | ||||
\(21\) | − | 2.41421i | − | 0.526825i | ||||||
\(22\) | 0.989880 | + | 0.989880i | 0.211043 | + | 0.211043i | ||||
\(23\) | −4.74955 | + | 0.664664i | −0.990350 | + | 0.138592i | ||||
\(24\) | − | 0.814115i | − | 0.166180i | ||||||
\(25\) | −4.93089 | − | 0.828427i | −0.986179 | − | 0.165685i | ||||
\(26\) | 6.00789 | 1.17824 | ||||||||
\(27\) | 3.07245 | − | 3.07245i | 0.591294 | − | 0.591294i | ||||
\(28\) | −2.09689 | + | 2.09689i | −0.396274 | + | 0.396274i | ||||
\(29\) | 3.87087i | 0.718803i | 0.933183 | + | 0.359401i | \(0.117019\pi\) | ||||
−0.933183 | + | 0.359401i | \(0.882981\pi\) | |||||||
\(30\) | 0.151332 | − | 1.81411i | 0.0276293 | − | 0.331211i | ||||
\(31\) | −5.74501 | −1.03183 | −0.515917 | − | 0.856639i | \(-0.672549\pi\) | ||||
−0.515917 | + | 0.856639i | \(0.672549\pi\) | |||||||
\(32\) | −0.707107 | + | 0.707107i | −0.125000 | + | 0.125000i | ||||
\(33\) | −0.805875 | + | 0.805875i | −0.140285 | + | 0.140285i | ||||
\(34\) | 6.20809 | 1.06468 | ||||||||
\(35\) | −5.06233 | + | 4.28277i | −0.855691 | + | 0.723921i | ||||
\(36\) | −2.33722 | −0.389536 | ||||||||
\(37\) | 2.27719 | + | 2.27719i | 0.374368 | + | 0.374368i | 0.869065 | − | 0.494697i | \(-0.164721\pi\) |
−0.494697 | + | 0.869065i | \(0.664721\pi\) | |||||||
\(38\) | 1.68267 | − | 1.68267i | 0.272966 | − | 0.272966i | ||||
\(39\) | 4.89111i | 0.783205i | ||||||||
\(40\) | −1.70711 | + | 1.44423i | −0.269917 | + | 0.228352i | ||||
\(41\) | 2.49121 | 0.389062 | 0.194531 | − | 0.980896i | \(-0.437682\pi\) | ||||
0.194531 | + | 0.980896i | \(0.437682\pi\) | |||||||
\(42\) | −1.70711 | − | 1.70711i | −0.263412 | − | 0.263412i | ||||
\(43\) | 2.85390 | − | 2.85390i | 0.435215 | − | 0.435215i | −0.455183 | − | 0.890398i | \(-0.650426\pi\) |
0.890398 | + | 0.455183i | \(0.150426\pi\) | |||||||
\(44\) | 1.39990 | 0.211043 | ||||||||
\(45\) | −5.20809 | − | 0.434454i | −0.776376 | − | 0.0647646i | ||||
\(46\) | −2.88845 | + | 3.82843i | −0.425879 | + | 0.564471i | ||||
\(47\) | −1.26288 | + | 1.26288i | −0.184210 | + | 0.184210i | −0.793188 | − | 0.608977i | \(-0.791580\pi\) |
0.608977 | + | 0.793188i | \(0.291580\pi\) | |||||||
\(48\) | −0.575666 | − | 0.575666i | −0.0830902 | − | 0.0830902i | ||||
\(49\) | 1.79387i | 0.256268i | ||||||||
\(50\) | −4.07245 | + | 2.90088i | −0.575932 | + | 0.410247i | ||||
\(51\) | 5.05409i | 0.707715i | ||||||||
\(52\) | 4.24822 | − | 4.24822i | 0.589122 | − | 0.589122i | ||||
\(53\) | −4.13375 | + | 4.13375i | −0.567814 | + | 0.567814i | −0.931516 | − | 0.363701i | \(-0.881513\pi\) |
0.363701 | + | 0.931516i | \(0.381513\pi\) | |||||||
\(54\) | − | 4.34511i | − | 0.591294i | ||||||
\(55\) | 3.11944 | + | 0.260221i | 0.420625 | + | 0.0350882i | ||||
\(56\) | 2.96545i | 0.396274i | ||||||||
\(57\) | 1.36989 | + | 1.36989i | 0.181446 | + | 0.181446i | ||||
\(58\) | 2.73712 | + | 2.73712i | 0.359401 | + | 0.359401i | ||||
\(59\) | − | 5.66801i | − | 0.737912i | −0.929447 | − | 0.368956i | \(-0.879715\pi\) | ||
0.929447 | − | 0.368956i | \(-0.120285\pi\) | |||||||
\(60\) | −1.17576 | − | 1.38978i | −0.151791 | − | 0.179420i | ||||
\(61\) | − | 13.1168i | − | 1.67943i | −0.543026 | − | 0.839716i | \(-0.682722\pi\) | ||
0.543026 | − | 0.839716i | \(-0.317278\pi\) | |||||||
\(62\) | −4.06233 | + | 4.06233i | −0.515917 | + | 0.515917i | ||||
\(63\) | −4.90088 | + | 4.90088i | −0.617453 | + | 0.617453i | ||||
\(64\) | 1.00000i | 0.125000i | ||||||||
\(65\) | 10.2561 | − | 8.67675i | 1.27211 | − | 1.07622i | ||||
\(66\) | 1.13968i | 0.140285i | ||||||||
\(67\) | 11.1390 | + | 11.1390i | 1.36084 | + | 1.36084i | 0.872844 | + | 0.487999i | \(0.162273\pi\) |
0.487999 | + | 0.872844i | \(0.337727\pi\) | |||||||
\(68\) | 4.38978 | − | 4.38978i | 0.532339 | − | 0.532339i | ||||
\(69\) | −3.11678 | − | 2.35153i | −0.375216 | − | 0.283091i | ||||
\(70\) | −0.551233 | + | 6.60799i | −0.0658850 | + | 0.789806i | ||||
\(71\) | −9.16188 | −1.08732 | −0.543658 | − | 0.839307i | \(-0.682961\pi\) | ||||
−0.543658 | + | 0.839307i | \(0.682961\pi\) | |||||||
\(72\) | −1.65266 | + | 1.65266i | −0.194768 | + | 0.194768i | ||||
\(73\) | 10.7875 | + | 10.7875i | 1.26258 | + | 1.26258i | 0.949840 | + | 0.312735i | \(0.101245\pi\) |
0.312735 | + | 0.949840i | \(0.398755\pi\) | |||||||
\(74\) | 3.22044 | 0.374368 | ||||||||
\(75\) | −2.36165 | − | 3.31544i | −0.272700 | − | 0.382835i | ||||
\(76\) | − | 2.37966i | − | 0.272966i | ||||||
\(77\) | 2.93543 | − | 2.93543i | 0.334524 | − | 0.334524i | ||||
\(78\) | 3.45854 | + | 3.45854i | 0.391602 | + | 0.391602i | ||||
\(79\) | 5.70196 | 0.641520 | 0.320760 | − | 0.947160i | \(-0.396062\pi\) | ||||
0.320760 | + | 0.947160i | \(0.396062\pi\) | |||||||
\(80\) | −0.185885 | + | 2.22833i | −0.0207826 | + | 0.249135i | ||||
\(81\) | −3.47424 | −0.386026 | ||||||||
\(82\) | 1.76155 | − | 1.76155i | 0.194531 | − | 0.194531i | ||||
\(83\) | −11.6335 | + | 11.6335i | −1.27694 | + | 1.27694i | −0.334565 | + | 0.942373i | \(0.608590\pi\) |
−0.942373 | + | 0.334565i | \(0.891410\pi\) | |||||||
\(84\) | −2.41421 | −0.263412 | ||||||||
\(85\) | 10.5979 | − | 8.96588i | 1.14950 | − | 0.972486i | ||||
\(86\) | − | 4.03602i | − | 0.435215i | ||||||
\(87\) | −2.22833 | + | 2.22833i | −0.238902 | + | 0.238902i | ||||
\(88\) | 0.989880 | − | 0.989880i | 0.105522 | − | 0.105522i | ||||
\(89\) | −1.31441 | −0.139327 | −0.0696635 | − | 0.997571i | \(-0.522193\pi\) | ||||
−0.0696635 | + | 0.997571i | \(0.522193\pi\) | |||||||
\(90\) | −3.98988 | + | 3.37547i | −0.420570 | + | 0.355806i | ||||
\(91\) | − | 17.8161i | − | 1.86763i | ||||||
\(92\) | 0.664664 | + | 4.74955i | 0.0692960 | + | 0.495175i | ||||
\(93\) | −3.30721 | − | 3.30721i | −0.342941 | − | 0.342941i | ||||
\(94\) | 1.78598i | 0.184210i | ||||||||
\(95\) | 0.442344 | − | 5.30266i | 0.0453835 | − | 0.544042i | ||||
\(96\) | −0.814115 | −0.0830902 | ||||||||
\(97\) | −7.84001 | − | 7.84001i | −0.796033 | − | 0.796033i | 0.186435 | − | 0.982467i | \(-0.440307\pi\) |
−0.982467 | + | 0.186435i | \(0.940307\pi\) | |||||||
\(98\) | 1.26846 | + | 1.26846i | 0.128134 | + | 0.128134i | ||||
\(99\) | 3.27187 | 0.328836 | ||||||||
\(100\) | −0.828427 | + | 4.93089i | −0.0828427 | + | 0.493089i | ||||
\(101\) | −1.61707 | −0.160905 | −0.0804523 | − | 0.996758i | \(-0.525636\pi\) | ||||
−0.0804523 | + | 0.996758i | \(0.525636\pi\) | |||||||
\(102\) | 3.57378 | + | 3.57378i | 0.353857 | + | 0.353857i | ||||
\(103\) | −5.23579 | + | 5.23579i | −0.515898 | + | 0.515898i | −0.916327 | − | 0.400430i | \(-0.868861\pi\) |
0.400430 | + | 0.916327i | \(0.368861\pi\) | |||||||
\(104\) | − | 6.00789i | − | 0.589122i | ||||||
\(105\) | −5.37966 | − | 0.448767i | −0.525001 | − | 0.0437952i | ||||
\(106\) | 5.84601i | 0.567814i | ||||||||
\(107\) | −7.78598 | − | 7.78598i | −0.752700 | − | 0.752700i | 0.222283 | − | 0.974982i | \(-0.428649\pi\) |
−0.974982 | + | 0.222283i | \(0.928649\pi\) | |||||||
\(108\) | −3.07245 | − | 3.07245i | −0.295647 | − | 0.295647i | ||||
\(109\) | −11.8899 | −1.13885 | −0.569424 | − | 0.822044i | \(-0.692834\pi\) | ||||
−0.569424 | + | 0.822044i | \(0.692834\pi\) | |||||||
\(110\) | 2.38978 | − | 2.02177i | 0.227857 | − | 0.192768i | ||||
\(111\) | 2.62181i | 0.248851i | ||||||||
\(112\) | 2.09689 | + | 2.09689i | 0.198137 | + | 0.198137i | ||||
\(113\) | 7.91065 | − | 7.91065i | 0.744172 | − | 0.744172i | −0.229206 | − | 0.973378i | \(-0.573613\pi\) |
0.973378 | + | 0.229206i | \(0.0736130\pi\) | |||||||
\(114\) | 1.93732 | 0.181446 | ||||||||
\(115\) | 0.598218 | + | 10.7071i | 0.0557841 | + | 0.998443i | ||||
\(116\) | 3.87087 | 0.359401 | ||||||||
\(117\) | 9.92901 | − | 9.92901i | 0.917937 | − | 0.917937i | ||||
\(118\) | −4.00789 | − | 4.00789i | −0.368956 | − | 0.368956i | ||||
\(119\) | − | 18.4098i | − | 1.68762i | ||||||
\(120\) | −1.81411 | − | 0.151332i | −0.165605 | − | 0.0138147i | ||||
\(121\) | 9.04028 | 0.821843 | ||||||||
\(122\) | −9.27496 | − | 9.27496i | −0.839716 | − | 0.839716i | ||||
\(123\) | 1.43410 | + | 1.43410i | 0.129309 | + | 0.129309i | ||||
\(124\) | 5.74501i | 0.515917i | ||||||||
\(125\) | −2.76259 | + | 10.8337i | −0.247093 | + | 0.968992i | ||||
\(126\) | 6.93089i | 0.617453i | ||||||||
\(127\) | 6.93732 | − | 6.93732i | 0.615587 | − | 0.615587i | −0.328809 | − | 0.944396i | \(-0.606647\pi\) |
0.944396 | + | 0.328809i | \(0.106647\pi\) | |||||||
\(128\) | 0.707107 | + | 0.707107i | 0.0625000 | + | 0.0625000i | ||||
\(129\) | 3.28578 | 0.289297 | ||||||||
\(130\) | 1.11678 | − | 13.3875i | 0.0979480 | − | 1.17417i | ||||
\(131\) | −11.7906 | −1.03015 | −0.515075 | − | 0.857145i | \(-0.672236\pi\) | ||||
−0.515075 | + | 0.857145i | \(0.672236\pi\) | |||||||
\(132\) | 0.805875 | + | 0.805875i | 0.0701425 | + | 0.0701425i | ||||
\(133\) | −4.98988 | − | 4.98988i | −0.432677 | − | 0.432677i | ||||
\(134\) | 15.7529 | 1.36084 | ||||||||
\(135\) | −6.27531 | − | 7.41756i | −0.540093 | − | 0.638402i | ||||
\(136\) | − | 6.20809i | − | 0.532339i | ||||||
\(137\) | −3.78830 | − | 3.78830i | −0.323656 | − | 0.323656i | 0.526512 | − | 0.850168i | \(-0.323500\pi\) |
−0.850168 | + | 0.526512i | \(0.823500\pi\) | |||||||
\(138\) | −3.86668 | + | 0.541113i | −0.329153 | + | 0.0460626i | ||||
\(139\) | − | 5.75082i | − | 0.487778i | −0.969803 | − | 0.243889i | \(-0.921577\pi\) | ||
0.969803 | − | 0.243889i | \(-0.0784233\pi\) | |||||||
\(140\) | 4.28277 | + | 5.06233i | 0.361960 | + | 0.427845i | ||||
\(141\) | −1.45400 | −0.122449 | ||||||||
\(142\) | −6.47843 | + | 6.47843i | −0.543658 | + | 0.543658i | ||||
\(143\) | −5.94709 | + | 5.94709i | −0.497320 | + | 0.497320i | ||||
\(144\) | 2.33722i | 0.194768i | ||||||||
\(145\) | 8.62557 | + | 0.719538i | 0.716315 | + | 0.0597544i | ||||
\(146\) | 15.2558 | 1.26258 | ||||||||
\(147\) | −1.03267 | + | 1.03267i | −0.0851734 | + | 0.0851734i | ||||
\(148\) | 2.27719 | − | 2.27719i | 0.187184 | − | 0.187184i | ||||
\(149\) | 1.83898 | 0.150655 | 0.0753274 | − | 0.997159i | \(-0.476000\pi\) | ||||
0.0753274 | + | 0.997159i | \(0.476000\pi\) | |||||||
\(150\) | −4.01431 | − | 0.674435i | −0.327767 | − | 0.0550674i | ||||
\(151\) | 1.79191 | 0.145824 | 0.0729119 | − | 0.997338i | \(-0.476771\pi\) | ||||
0.0729119 | + | 0.997338i | \(0.476771\pi\) | |||||||
\(152\) | −1.68267 | − | 1.68267i | −0.136483 | − | 0.136483i | ||||
\(153\) | 10.2599 | − | 10.2599i | 0.829461 | − | 0.829461i | ||||
\(154\) | − | 4.15133i | − | 0.334524i | ||||||
\(155\) | −1.06791 | + | 12.8018i | −0.0857768 | + | 1.02826i | ||||
\(156\) | 4.89111 | 0.391602 | ||||||||
\(157\) | −2.30909 | − | 2.30909i | −0.184285 | − | 0.184285i | 0.608935 | − | 0.793220i | \(-0.291597\pi\) |
−0.793220 | + | 0.608935i | \(0.791597\pi\) | |||||||
\(158\) | 4.03189 | − | 4.03189i | 0.320760 | − | 0.320760i | ||||
\(159\) | −4.75932 | −0.377439 | ||||||||
\(160\) | 1.44423 | + | 1.70711i | 0.114176 | + | 0.134959i | ||||
\(161\) | 11.3530 | + | 8.56555i | 0.894741 | + | 0.675060i | ||||
\(162\) | −2.45666 | + | 2.45666i | −0.193013 | + | 0.193013i | ||||
\(163\) | 14.4525 | + | 14.4525i | 1.13201 | + | 1.13201i | 0.989843 | + | 0.142168i | \(0.0454074\pi\) |
0.142168 | + | 0.989843i | \(0.454593\pi\) | |||||||
\(164\) | − | 2.49121i | − | 0.194531i | ||||||
\(165\) | 1.64595 | + | 1.94556i | 0.128137 | + | 0.151461i | ||||
\(166\) | 16.4522i | 1.27694i | ||||||||
\(167\) | −11.7423 | + | 11.7423i | −0.908650 | + | 0.908650i | −0.996163 | − | 0.0875132i | \(-0.972108\pi\) |
0.0875132 | + | 0.996163i | \(0.472108\pi\) | |||||||
\(168\) | −1.70711 | + | 1.70711i | −0.131706 | + | 0.131706i | ||||
\(169\) | 23.0947i | 1.77652i | ||||||||
\(170\) | 1.15399 | − | 13.8337i | 0.0885072 | − | 1.06099i | ||||
\(171\) | − | 5.56178i | − | 0.425320i | ||||||
\(172\) | −2.85390 | − | 2.85390i | −0.217608 | − | 0.217608i | ||||
\(173\) | −7.36165 | − | 7.36165i | −0.559696 | − | 0.559696i | 0.369525 | − | 0.929221i | \(-0.379520\pi\) |
−0.929221 | + | 0.369525i | \(0.879520\pi\) | |||||||
\(174\) | 3.15133i | 0.238902i | ||||||||
\(175\) | 8.60241 | + | 12.0766i | 0.650281 | + | 0.912909i | ||||
\(176\) | − | 1.39990i | − | 0.105522i | ||||||
\(177\) | 3.26288 | − | 3.26288i | 0.245253 | − | 0.245253i | ||||
\(178\) | −0.929427 | + | 0.929427i | −0.0696635 | + | 0.0696635i | ||||
\(179\) | 5.55173i | 0.414956i | 0.978240 | + | 0.207478i | \(0.0665255\pi\) | ||||
−0.978240 | + | 0.207478i | \(0.933475\pi\) | |||||||
\(180\) | −0.434454 | + | 5.20809i | −0.0323823 | + | 0.388188i | ||||
\(181\) | − | 23.0901i | − | 1.71627i | −0.513420 | − | 0.858137i | \(-0.671622\pi\) | ||
0.513420 | − | 0.858137i | \(-0.328378\pi\) | |||||||
\(182\) | −12.5979 | − | 12.5979i | −0.933816 | − | 0.933816i | ||||
\(183\) | 7.55088 | − | 7.55088i | 0.558177 | − | 0.558177i | ||||
\(184\) | 3.82843 | + | 2.88845i | 0.282235 | + | 0.212939i | ||||
\(185\) | 5.49763 | − | 4.65104i | 0.404194 | − | 0.341951i | ||||
\(186\) | −4.67710 | −0.342941 | ||||||||
\(187\) | −6.14526 | + | 6.14526i | −0.449386 | + | 0.449386i | ||||
\(188\) | 1.26288 | + | 1.26288i | 0.0921051 | + | 0.0921051i | ||||
\(189\) | −12.8852 | −0.937259 | ||||||||
\(190\) | −3.43677 | − | 4.06233i | −0.249329 | − | 0.294713i | ||||
\(191\) | − | 7.88579i | − | 0.570596i | −0.958439 | − | 0.285298i | \(-0.907907\pi\) | ||
0.958439 | − | 0.285298i | \(-0.0920925\pi\) | |||||||
\(192\) | −0.575666 | + | 0.575666i | −0.0415451 | + | 0.0415451i | ||||
\(193\) | −5.18469 | − | 5.18469i | −0.373202 | − | 0.373202i | 0.495440 | − | 0.868642i | \(-0.335007\pi\) |
−0.868642 | + | 0.495440i | \(0.835007\pi\) | |||||||
\(194\) | −11.0875 | −0.796033 | ||||||||
\(195\) | 10.8990 | + | 0.909186i | 0.780494 | + | 0.0651082i | ||||
\(196\) | 1.79387 | 0.128134 | ||||||||
\(197\) | −3.44191 | + | 3.44191i | −0.245226 | + | 0.245226i | −0.819008 | − | 0.573782i | \(-0.805476\pi\) |
0.573782 | + | 0.819008i | \(0.305476\pi\) | |||||||
\(198\) | 2.31356 | − | 2.31356i | 0.164418 | − | 0.164418i | ||||
\(199\) | 15.8241 | 1.12174 | 0.560870 | − | 0.827904i | \(-0.310467\pi\) | ||||
0.560870 | + | 0.827904i | \(0.310467\pi\) | |||||||
\(200\) | 2.90088 | + | 4.07245i | 0.205123 | + | 0.287966i | ||||
\(201\) | 12.8247i | 0.904582i | ||||||||
\(202\) | −1.14344 | + | 1.14344i | −0.0804523 | + | 0.0804523i | ||||
\(203\) | 8.11678 | − | 8.11678i | 0.569686 | − | 0.569686i | ||||
\(204\) | 5.05409 | 0.353857 | ||||||||
\(205\) | 0.463079 | − | 5.55123i | 0.0323429 | − | 0.387715i | ||||
\(206\) | 7.40452i | 0.515898i | ||||||||
\(207\) | 1.55346 | + | 11.1007i | 0.107973 | + | 0.771554i | ||||
\(208\) | −4.24822 | − | 4.24822i | −0.294561 | − | 0.294561i | ||||
\(209\) | 3.33129i | 0.230430i | ||||||||
\(210\) | −4.12132 | + | 3.48667i | −0.284398 | + | 0.240603i | ||||
\(211\) | −17.0575 | −1.17429 | −0.587144 | − | 0.809482i | \(-0.699748\pi\) | ||||
−0.587144 | + | 0.809482i | \(0.699748\pi\) | |||||||
\(212\) | 4.13375 | + | 4.13375i | 0.283907 | + | 0.283907i | ||||
\(213\) | −5.27418 | − | 5.27418i | −0.361381 | − | 0.361381i | ||||
\(214\) | −11.0110 | −0.752700 | ||||||||
\(215\) | −5.82892 | − | 6.88992i | −0.397529 | − | 0.469888i | ||||
\(216\) | −4.34511 | −0.295647 | ||||||||
\(217\) | 12.0466 | + | 12.0466i | 0.817779 | + | 0.817779i | ||||
\(218\) | −8.40744 | + | 8.40744i | −0.569424 | + | 0.569424i | ||||
\(219\) | 12.4199i | 0.839262i | ||||||||
\(220\) | 0.260221 | − | 3.11944i | 0.0175441 | − | 0.210313i | ||||
\(221\) | 37.2975i | 2.50890i | ||||||||
\(222\) | 1.85390 | + | 1.85390i | 0.124425 | + | 0.124425i | ||||
\(223\) | −1.18915 | − | 1.18915i | −0.0796316 | − | 0.0796316i | 0.666169 | − | 0.745801i | \(-0.267933\pi\) |
−0.745801 | + | 0.666169i | \(0.767933\pi\) | |||||||
\(224\) | 2.96545 | 0.198137 | ||||||||
\(225\) | −1.93621 | + | 11.5246i | −0.129081 | + | 0.768305i | ||||
\(226\) | − | 11.1874i | − | 0.744172i | ||||||
\(227\) | −14.3791 | − | 14.3791i | −0.954371 | − | 0.954371i | 0.0446322 | − | 0.999003i | \(-0.485788\pi\) |
−0.999003 | + | 0.0446322i | \(0.985788\pi\) | |||||||
\(228\) | 1.36989 | − | 1.36989i | 0.0907231 | − | 0.0907231i | ||||
\(229\) | −4.32083 | −0.285529 | −0.142764 | − | 0.989757i | \(-0.545599\pi\) | ||||
−0.142764 | + | 0.989757i | \(0.545599\pi\) | |||||||
\(230\) | 7.99407 | + | 7.14806i | 0.527113 | + | 0.471329i | ||||
\(231\) | 3.37966 | 0.222365 | ||||||||
\(232\) | 2.73712 | − | 2.73712i | 0.179701 | − | 0.179701i | ||||
\(233\) | 0.921537 | + | 0.921537i | 0.0603719 | + | 0.0603719i | 0.736648 | − | 0.676276i | \(-0.236407\pi\) |
−0.676276 | + | 0.736648i | \(0.736407\pi\) | |||||||
\(234\) | − | 14.0417i | − | 0.917937i | ||||||
\(235\) | 2.57936 | + | 3.04887i | 0.168259 | + | 0.198886i | ||||
\(236\) | −5.66801 | −0.368956 | ||||||||
\(237\) | 3.28242 | + | 3.28242i | 0.213216 | + | 0.213216i | ||||
\(238\) | −13.0177 | − | 13.0177i | −0.843810 | − | 0.843810i | ||||
\(239\) | 9.30740i | 0.602046i | 0.953617 | + | 0.301023i | \(0.0973280\pi\) | ||||
−0.953617 | + | 0.301023i | \(0.902672\pi\) | |||||||
\(240\) | −1.38978 | + | 1.17576i | −0.0897100 | + | 0.0758953i | ||||
\(241\) | 21.4247i | 1.38008i | 0.723769 | + | 0.690042i | \(0.242408\pi\) | ||||
−0.723769 | + | 0.690042i | \(0.757592\pi\) | |||||||
\(242\) | 6.39244 | − | 6.39244i | 0.410922 | − | 0.410922i | ||||
\(243\) | −11.2174 | − | 11.2174i | −0.719594 | − | 0.719594i | ||||
\(244\) | −13.1168 | −0.839716 | ||||||||
\(245\) | 3.99734 | + | 0.333455i | 0.255381 | + | 0.0213036i | ||||
\(246\) | 2.02813 | 0.129309 | ||||||||
\(247\) | 10.1093 | + | 10.1093i | 0.643241 | + | 0.643241i | ||||
\(248\) | 4.06233 | + | 4.06233i | 0.257958 | + | 0.257958i | ||||
\(249\) | −13.3940 | −0.848809 | ||||||||
\(250\) | 5.70711 | + | 9.61400i | 0.360949 | + | 0.608043i | ||||
\(251\) | 6.28824i | 0.396910i | 0.980110 | + | 0.198455i | \(0.0635924\pi\) | ||||
−0.980110 | + | 0.198455i | \(0.936408\pi\) | |||||||
\(252\) | 4.90088 | + | 4.90088i | 0.308727 | + | 0.308727i | ||||
\(253\) | −0.930464 | − | 6.64890i | −0.0584978 | − | 0.418013i | ||||
\(254\) | − | 9.81085i | − | 0.615587i | ||||||
\(255\) | 11.2622 | + | 0.939482i | 0.705265 | + | 0.0588327i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −18.5108 | + | 18.5108i | −1.15467 | + | 1.15467i | −0.169064 | + | 0.985605i | \(0.554074\pi\) |
−0.985605 | + | 0.169064i | \(0.945926\pi\) | |||||||
\(258\) | 2.32340 | − | 2.32340i | 0.144649 | − | 0.144649i | ||||
\(259\) | − | 9.55004i | − | 0.593411i | ||||||
\(260\) | −8.67675 | − | 10.2561i | −0.538109 | − | 0.636057i | ||||
\(261\) | 9.04706 | 0.559999 | ||||||||
\(262\) | −8.33722 | + | 8.33722i | −0.515075 | + | 0.515075i | ||||
\(263\) | 1.46351 | − | 1.46351i | 0.0902438 | − | 0.0902438i | −0.660544 | − | 0.750788i | \(-0.729674\pi\) |
0.750788 | + | 0.660544i | \(0.229674\pi\) | |||||||
\(264\) | 1.13968 | 0.0701425 | ||||||||
\(265\) | 8.44295 | + | 9.97976i | 0.518646 | + | 0.613052i | ||||
\(266\) | −7.05676 | −0.432677 | ||||||||
\(267\) | −0.756660 | − | 0.756660i | −0.0463068 | − | 0.0463068i | ||||
\(268\) | 11.1390 | − | 11.1390i | 0.680422 | − | 0.680422i | ||||
\(269\) | 4.31914i | 0.263343i | 0.991293 | + | 0.131671i | \(0.0420344\pi\) | ||||
−0.991293 | + | 0.131671i | \(0.957966\pi\) | |||||||
\(270\) | −9.68232 | − | 0.807692i | −0.589247 | − | 0.0491546i | ||||
\(271\) | 1.68875 | 0.102584 | 0.0512920 | − | 0.998684i | \(-0.483666\pi\) | ||||
0.0512920 | + | 0.998684i | \(0.483666\pi\) | |||||||
\(272\) | −4.38978 | − | 4.38978i | −0.266170 | − | 0.266170i | ||||
\(273\) | 10.2561 | − | 10.2561i | 0.620728 | − | 0.620728i | ||||
\(274\) | −5.35746 | −0.323656 | ||||||||
\(275\) | 1.15972 | − | 6.90276i | 0.0699335 | − | 0.416252i | ||||
\(276\) | −2.35153 | + | 3.11678i | −0.141545 | + | 0.187608i | ||||
\(277\) | −5.49170 | + | 5.49170i | −0.329965 | + | 0.329965i | −0.852573 | − | 0.522608i | \(-0.824959\pi\) |
0.522608 | + | 0.852573i | \(0.324959\pi\) | |||||||
\(278\) | −4.06645 | − | 4.06645i | −0.243889 | − | 0.243889i | ||||
\(279\) | 13.4273i | 0.803873i | ||||||||
\(280\) | 6.60799 | + | 0.551233i | 0.394903 | + | 0.0329425i | ||||
\(281\) | − | 4.64597i | − | 0.277155i | −0.990352 | − | 0.138578i | \(-0.955747\pi\) | ||
0.990352 | − | 0.138578i | \(-0.0442531\pi\) | |||||||
\(282\) | −1.02813 | + | 1.02813i | −0.0612243 | + | 0.0612243i | ||||
\(283\) | 18.5426 | − | 18.5426i | 1.10225 | − | 1.10225i | 0.108106 | − | 0.994139i | \(-0.465521\pi\) |
0.994139 | − | 0.108106i | \(-0.0344787\pi\) | |||||||
\(284\) | 9.16188i | 0.543658i | ||||||||
\(285\) | 3.30721 | − | 2.79792i | 0.195902 | − | 0.165735i | ||||
\(286\) | 8.41045i | 0.497320i | ||||||||
\(287\) | −5.22379 | − | 5.22379i | −0.308350 | − | 0.308350i | ||||
\(288\) | 1.65266 | + | 1.65266i | 0.0973841 | + | 0.0973841i | ||||
\(289\) | 21.5403i | 1.26708i | ||||||||
\(290\) | 6.60799 | − | 5.59041i | 0.388034 | − | 0.328280i | ||||
\(291\) | − | 9.02646i | − | 0.529140i | ||||||
\(292\) | 10.7875 | − | 10.7875i | 0.631288 | − | 0.631288i | ||||
\(293\) | 4.84916 | − | 4.84916i | 0.283291 | − | 0.283291i | −0.551129 | − | 0.834420i | \(-0.685803\pi\) |
0.834420 | + | 0.551129i | \(0.185803\pi\) | |||||||
\(294\) | 1.46042i | 0.0851734i | ||||||||
\(295\) | −12.6302 | − | 1.05360i | −0.735358 | − | 0.0613430i | ||||
\(296\) | − | 3.22044i | − | 0.187184i | ||||||
\(297\) | 4.30113 | + | 4.30113i | 0.249577 | + | 0.249577i | ||||
\(298\) | 1.30035 | − | 1.30035i | 0.0753274 | − | 0.0753274i | ||||
\(299\) | −23.0008 | − | 17.3535i | −1.33017 | − | 1.00358i | ||||
\(300\) | −3.31544 | + | 2.36165i | −0.191417 | + | 0.136350i | ||||
\(301\) | −11.9686 | −0.689859 | ||||||||
\(302\) | 1.26707 | − | 1.26707i | 0.0729119 | − | 0.0729119i | ||||
\(303\) | −0.930893 | − | 0.930893i | −0.0534784 | − | 0.0534784i | ||||
\(304\) | −2.37966 | −0.136483 | ||||||||
\(305\) | −29.2285 | − | 2.43822i | −1.67362 | − | 0.139612i | ||||
\(306\) | − | 14.5096i | − | 0.829461i | ||||||
\(307\) | 14.4992 | − | 14.4992i | 0.827511 | − | 0.827511i | −0.159661 | − | 0.987172i | \(-0.551040\pi\) |
0.987172 | + | 0.159661i | \(0.0510401\pi\) | |||||||
\(308\) | −2.93543 | − | 2.93543i | −0.167262 | − | 0.167262i | ||||
\(309\) | −6.02813 | −0.342928 | ||||||||
\(310\) | 8.29709 | + | 9.80734i | 0.471243 | + | 0.557020i | ||||
\(311\) | 22.7346 | 1.28916 | 0.644581 | − | 0.764536i | \(-0.277032\pi\) | ||||
0.644581 | + | 0.764536i | \(0.277032\pi\) | |||||||
\(312\) | 3.45854 | − | 3.45854i | 0.195801 | − | 0.195801i | ||||
\(313\) | −12.5099 | + | 12.5099i | −0.707102 | + | 0.707102i | −0.965925 | − | 0.258823i | \(-0.916665\pi\) |
0.258823 | + | 0.965925i | \(0.416665\pi\) | |||||||
\(314\) | −3.26554 | −0.184285 | ||||||||
\(315\) | 10.0098 | + | 11.8318i | 0.563987 | + | 0.666645i | ||||
\(316\) | − | 5.70196i | − | 0.320760i | ||||||
\(317\) | 14.7988 | − | 14.7988i | 0.831186 | − | 0.831186i | −0.156493 | − | 0.987679i | \(-0.550019\pi\) |
0.987679 | + | 0.156493i | \(0.0500189\pi\) | |||||||
\(318\) | −3.36535 | + | 3.36535i | −0.188719 | + | 0.188719i | ||||
\(319\) | −5.41884 | −0.303397 | ||||||||
\(320\) | 2.22833 | + | 0.185885i | 0.124567 | + | 0.0103913i | ||||
\(321\) | − | 8.96425i | − | 0.500336i | ||||||
\(322\) | 14.0845 | − | 1.97103i | 0.784901 | − | 0.109841i | ||||
\(323\) | 10.4462 | + | 10.4462i | 0.581241 | + | 0.581241i | ||||
\(324\) | 3.47424i | 0.193013i | ||||||||
\(325\) | −17.4282 | − | 24.4669i | −0.966741 | − | 1.35718i | ||||
\(326\) | 20.4390 | 1.13201 | ||||||||
\(327\) | −6.84462 | − | 6.84462i | −0.378508 | − | 0.378508i | ||||
\(328\) | −1.76155 | − | 1.76155i | −0.0972654 | − | 0.0972654i | ||||
\(329\) | 5.29624 | 0.291991 | ||||||||
\(330\) | 2.53958 | + | 0.211850i | 0.139799 | + | 0.0116619i | ||||
\(331\) | 14.3184 | 0.787013 | 0.393506 | − | 0.919322i | \(-0.371262\pi\) | ||||
0.393506 | + | 0.919322i | \(0.371262\pi\) | |||||||
\(332\) | 11.6335 | + | 11.6335i | 0.638469 | + | 0.638469i | ||||
\(333\) | 5.32230 | − | 5.32230i | 0.291660 | − | 0.291660i | ||||
\(334\) | 16.6062i | 0.908650i | ||||||||
\(335\) | 26.8919 | − | 22.7507i | 1.46926 | − | 1.24301i | ||||
\(336\) | 2.41421i | 0.131706i | ||||||||
\(337\) | −1.89342 | − | 1.89342i | −0.103141 | − | 0.103141i | 0.653653 | − | 0.756794i | \(-0.273236\pi\) |
−0.756794 | + | 0.653653i | \(0.773236\pi\) | |||||||
\(338\) | 16.3304 | + | 16.3304i | 0.888259 | + | 0.888259i | ||||
\(339\) | 9.10779 | 0.494667 | ||||||||
\(340\) | −8.96588 | − | 10.5979i | −0.486243 | − | 0.574750i | ||||
\(341\) | − | 8.04244i | − | 0.435523i | ||||||
\(342\) | −3.93277 | − | 3.93277i | −0.212660 | − | 0.212660i | ||||
\(343\) | −10.9167 | + | 10.9167i | −0.589444 | + | 0.589444i | ||||
\(344\) | −4.03602 | −0.217608 | ||||||||
\(345\) | −5.81934 | + | 6.50809i | −0.313303 | + | 0.350384i | ||||
\(346\) | −10.4109 | −0.559696 | ||||||||
\(347\) | 5.57833 | − | 5.57833i | 0.299460 | − | 0.299460i | −0.541342 | − | 0.840802i | \(-0.682084\pi\) |
0.840802 | + | 0.541342i | \(0.182084\pi\) | |||||||
\(348\) | 2.22833 | + | 2.22833i | 0.119451 | + | 0.119451i | ||||
\(349\) | − | 4.82635i | − | 0.258349i | −0.991622 | − | 0.129174i | \(-0.958767\pi\) | ||
0.991622 | − | 0.129174i | \(-0.0412327\pi\) | |||||||
\(350\) | 14.6223 | + | 2.45666i | 0.781595 | + | 0.131314i | ||||
\(351\) | 26.1049 | 1.39338 | ||||||||
\(352\) | −0.989880 | − | 0.989880i | −0.0527608 | − | 0.0527608i | ||||
\(353\) | −16.3035 | − | 16.3035i | −0.867749 | − | 0.867749i | 0.124474 | − | 0.992223i | \(-0.460276\pi\) |
−0.992223 | + | 0.124474i | \(0.960276\pi\) | |||||||
\(354\) | − | 4.61441i | − | 0.245253i | ||||||
\(355\) | −1.70306 | + | 20.4157i | −0.0903890 | + | 1.08355i | ||||
\(356\) | 1.31441i | 0.0696635i | ||||||||
\(357\) | 10.5979 | − | 10.5979i | 0.560899 | − | 0.560899i | ||||
\(358\) | 3.92566 | + | 3.92566i | 0.207478 | + | 0.207478i | ||||
\(359\) | 29.7585 | 1.57059 | 0.785297 | − | 0.619119i | \(-0.212510\pi\) | ||||
0.785297 | + | 0.619119i | \(0.212510\pi\) | |||||||
\(360\) | 3.37547 | + | 3.98988i | 0.177903 | + | 0.210285i | ||||
\(361\) | −13.3372 | −0.701959 | ||||||||
\(362\) | −16.3272 | − | 16.3272i | −0.858137 | − | 0.858137i | ||||
\(363\) | 5.20418 | + | 5.20418i | 0.273149 | + | 0.273149i | ||||
\(364\) | −17.8161 | −0.933816 | ||||||||
\(365\) | 26.0432 | − | 22.0328i | 1.36316 | − | 1.15325i | ||||
\(366\) | − | 10.6786i | − | 0.558177i | ||||||
\(367\) | −22.0933 | − | 22.0933i | −1.15326 | − | 1.15326i | −0.985895 | − | 0.167364i | \(-0.946474\pi\) |
−0.167364 | − | 0.985895i | \(-0.553526\pi\) | |||||||
\(368\) | 4.74955 | − | 0.664664i | 0.247587 | − | 0.0346480i | ||||
\(369\) | − | 5.82250i | − | 0.303107i | ||||||
\(370\) | 0.598632 | − | 7.17619i | 0.0311214 | − | 0.373073i | ||||
\(371\) | 17.3360 | 0.900041 | ||||||||
\(372\) | −3.30721 | + | 3.30721i | −0.171471 | + | 0.171471i | ||||
\(373\) | −5.68302 | + | 5.68302i | −0.294256 | + | 0.294256i | −0.838759 | − | 0.544503i | \(-0.816718\pi\) |
0.544503 | + | 0.838759i | \(0.316718\pi\) | |||||||
\(374\) | 8.69071i | 0.449386i | ||||||||
\(375\) | −7.82690 | + | 4.64624i | −0.404179 | + | 0.239931i | ||||
\(376\) | 1.78598 | 0.0921051 | ||||||||
\(377\) | −16.4443 | + | 16.4443i | −0.846925 | + | 0.846925i | ||||
\(378\) | −9.11120 | + | 9.11120i | −0.468630 | + | 0.468630i | ||||
\(379\) | −28.4530 | −1.46153 | −0.730765 | − | 0.682629i | \(-0.760837\pi\) | ||||
−0.730765 | + | 0.682629i | \(0.760837\pi\) | |||||||
\(380\) | −5.30266 | − | 0.442344i | −0.272021 | − | 0.0226918i | ||||
\(381\) | 7.98715 | 0.409194 | ||||||||
\(382\) | −5.57610 | − | 5.57610i | −0.285298 | − | 0.285298i | ||||
\(383\) | 4.38293 | − | 4.38293i | 0.223957 | − | 0.223957i | −0.586205 | − | 0.810163i | \(-0.699379\pi\) |
0.810163 | + | 0.586205i | \(0.199379\pi\) | |||||||
\(384\) | 0.814115i | 0.0415451i | ||||||||
\(385\) | −5.99546 | − | 7.08677i | −0.305557 | − | 0.361175i | ||||
\(386\) | −7.33226 | −0.373202 | ||||||||
\(387\) | −6.67018 | − | 6.67018i | −0.339064 | − | 0.339064i | ||||
\(388\) | −7.84001 | + | 7.84001i | −0.398016 | + | 0.398016i | ||||
\(389\) | −5.98569 | −0.303486 | −0.151743 | − | 0.988420i | \(-0.548489\pi\) | ||||
−0.151743 | + | 0.988420i | \(0.548489\pi\) | |||||||
\(390\) | 8.34965 | − | 7.06387i | 0.422801 | − | 0.357693i | ||||
\(391\) | −23.7672 | − | 17.9318i | −1.20196 | − | 0.906848i | ||||
\(392\) | 1.26846 | − | 1.26846i | 0.0640669 | − | 0.0640669i | ||||
\(393\) | −6.78745 | − | 6.78745i | −0.342382 | − | 0.342382i | ||||
\(394\) | 4.86760i | 0.245226i | ||||||||
\(395\) | 1.05991 | − | 12.7058i | 0.0533299 | − | 0.639300i | ||||
\(396\) | − | 3.27187i | − | 0.164418i | ||||||
\(397\) | 22.2577 | − | 22.2577i | 1.11708 | − | 1.11708i | 0.124912 | − | 0.992168i | \(-0.460135\pi\) |
0.992168 | − | 0.124912i | \(-0.0398648\pi\) | |||||||
\(398\) | 11.1893 | − | 11.1893i | 0.560870 | − | 0.560870i | ||||
\(399\) | − | 5.74501i | − | 0.287610i | ||||||
\(400\) | 4.93089 | + | 0.828427i | 0.246545 | + | 0.0414214i | ||||
\(401\) | 23.0951i | 1.15331i | 0.816987 | + | 0.576656i | \(0.195643\pi\) | ||||
−0.816987 | + | 0.576656i | \(0.804357\pi\) | |||||||
\(402\) | 9.06841 | + | 9.06841i | 0.452291 | + | 0.452291i | ||||
\(403\) | −24.4061 | − | 24.4061i | −1.21575 | − | 1.21575i | ||||
\(404\) | 1.61707i | 0.0804523i | ||||||||
\(405\) | −0.645810 | + | 7.74174i | −0.0320905 | + | 0.384690i | ||||
\(406\) | − | 11.4789i | − | 0.569686i | ||||||
\(407\) | −3.18785 | + | 3.18785i | −0.158016 | + | 0.158016i | ||||
\(408\) | 3.57378 | − | 3.57378i | 0.176929 | − | 0.176929i | ||||
\(409\) | − | 20.1346i | − | 0.995593i | −0.867294 | − | 0.497797i | \(-0.834143\pi\) | ||
0.867294 | − | 0.497797i | \(-0.165857\pi\) | |||||||
\(410\) | −3.59787 | − | 4.25276i | −0.177686 | − | 0.210029i | ||||
\(411\) | − | 4.36159i | − | 0.215141i | ||||||
\(412\) | 5.23579 | + | 5.23579i | 0.257949 | + | 0.257949i | ||||
\(413\) | −11.8852 | + | 11.8852i | −0.584832 | + | 0.584832i | ||||
\(414\) | 8.94787 | + | 6.75094i | 0.439764 | + | 0.331790i | ||||
\(415\) | 23.7607 | + | 28.0857i | 1.16637 | + | 1.37867i | ||||
\(416\) | −6.00789 | −0.294561 | ||||||||
\(417\) | 3.31055 | − | 3.31055i | 0.162119 | − | 0.162119i | ||||
\(418\) | 2.35558 | + | 2.35558i | 0.115215 | + | 0.115215i | ||||
\(419\) | 22.2991 | 1.08938 | 0.544690 | − | 0.838637i | \(-0.316647\pi\) | ||||
0.544690 | + | 0.838637i | \(0.316647\pi\) | |||||||
\(420\) | −0.448767 | + | 5.37966i | −0.0218976 | + | 0.262501i | ||||
\(421\) | 11.3853i | 0.554883i | 0.960742 | + | 0.277442i | \(0.0894865\pi\) | ||||
−0.960742 | + | 0.277442i | \(0.910513\pi\) | |||||||
\(422\) | −12.0615 | + | 12.0615i | −0.587144 | + | 0.587144i | ||||
\(423\) | 2.95163 | + | 2.95163i | 0.143513 | + | 0.143513i | ||||
\(424\) | 5.84601 | 0.283907 | ||||||||
\(425\) | −18.0089 | − | 25.2822i | −0.873561 | − | 1.22636i | ||||
\(426\) | −7.45882 | −0.361381 | ||||||||
\(427\) | −27.5044 | + | 27.5044i | −1.33103 | + | 1.33103i | ||||
\(428\) | −7.78598 | + | 7.78598i | −0.376350 | + | 0.376350i | ||||
\(429\) | −6.84707 | −0.330580 | ||||||||
\(430\) | −8.99358 | − | 0.750237i | −0.433709 | − | 0.0361796i | ||||
\(431\) | 26.8390i | 1.29279i | 0.763002 | + | 0.646396i | \(0.223724\pi\) | ||||
−0.763002 | + | 0.646396i | \(0.776276\pi\) | |||||||
\(432\) | −3.07245 | + | 3.07245i | −0.147824 | + | 0.147824i | ||||
\(433\) | 4.55947 | − | 4.55947i | 0.219114 | − | 0.219114i | −0.589011 | − | 0.808125i | \(-0.700482\pi\) |
0.808125 | + | 0.589011i | \(0.200482\pi\) | |||||||
\(434\) | 17.0365 | 0.817779 | ||||||||
\(435\) | 4.55123 | + | 5.37966i | 0.218215 | + | 0.257935i | ||||
\(436\) | 11.8899i | 0.569424i | ||||||||
\(437\) | −11.3023 | + | 1.58167i | −0.540663 | + | 0.0756617i | ||||
\(438\) | 8.78222 | + | 8.78222i | 0.419631 | + | 0.419631i | ||||
\(439\) | − | 14.5945i | − | 0.696559i | −0.937391 | − | 0.348280i | \(-0.886766\pi\) | ||
0.937391 | − | 0.348280i | \(-0.113234\pi\) | |||||||
\(440\) | −2.02177 | − | 2.38978i | −0.0963842 | − | 0.113928i | ||||
\(441\) | 4.19267 | 0.199651 | ||||||||
\(442\) | 26.3733 | + | 26.3733i | 1.25445 | + | 1.25445i | ||||
\(443\) | 15.6502 | + | 15.6502i | 0.743563 | + | 0.743563i | 0.973262 | − | 0.229699i | \(-0.0737741\pi\) |
−0.229699 | + | 0.973262i | \(0.573774\pi\) | |||||||
\(444\) | 2.62181 | 0.124425 | ||||||||
\(445\) | −0.244329 | + | 2.92893i | −0.0115823 | + | 0.138845i | ||||
\(446\) | −1.68172 | −0.0796316 | ||||||||
\(447\) | 1.05864 | + | 1.05864i | 0.0500718 | + | 0.0500718i | ||||
\(448\) | 2.09689 | − | 2.09689i | 0.0990686 | − | 0.0990686i | ||||
\(449\) | 34.9589i | 1.64981i | 0.565269 | + | 0.824907i | \(0.308772\pi\) | ||||
−0.565269 | + | 0.824907i | \(0.691228\pi\) | |||||||
\(450\) | 6.77999 | + | 9.51821i | 0.319612 | + | 0.448693i | ||||
\(451\) | 3.48745i | 0.164217i | ||||||||
\(452\) | −7.91065 | − | 7.91065i | −0.372086 | − | 0.372086i | ||||
\(453\) | 1.03154 | + | 1.03154i | 0.0484661 | + | 0.0484661i | ||||
\(454\) | −20.3351 | −0.954371 | ||||||||
\(455\) | −39.7001 | − | 3.31175i | −1.86117 | − | 0.155257i | ||||
\(456\) | − | 1.93732i | − | 0.0907231i | ||||||
\(457\) | −0.286885 | − | 0.286885i | −0.0134199 | − | 0.0134199i | 0.700365 | − | 0.713785i | \(-0.253021\pi\) |
−0.713785 | + | 0.700365i | \(0.753021\pi\) | |||||||
\(458\) | −3.05529 | + | 3.05529i | −0.142764 | + | 0.142764i | ||||
\(459\) | 26.9748 | 1.25908 | ||||||||
\(460\) | 10.7071 | − | 0.598218i | 0.499221 | − | 0.0278920i | ||||
\(461\) | −16.9780 | −0.790742 | −0.395371 | − | 0.918521i | \(-0.629384\pi\) | ||||
−0.395371 | + | 0.918521i | \(0.629384\pi\) | |||||||
\(462\) | 2.38978 | − | 2.38978i | 0.111183 | − | 0.111183i | ||||
\(463\) | 13.7072 | + | 13.7072i | 0.637027 | + | 0.637027i | 0.949821 | − | 0.312794i | \(-0.101265\pi\) |
−0.312794 | + | 0.949821i | \(0.601265\pi\) | |||||||
\(464\) | − | 3.87087i | − | 0.179701i | ||||||
\(465\) | −7.98430 | + | 6.75478i | −0.370263 | + | 0.313245i | ||||
\(466\) | 1.30325 | 0.0603719 | ||||||||
\(467\) | 6.28132 | + | 6.28132i | 0.290665 | + | 0.290665i | 0.837343 | − | 0.546678i | \(-0.184108\pi\) |
−0.546678 | + | 0.837343i | \(0.684108\pi\) | |||||||
\(468\) | −9.92901 | − | 9.92901i | −0.458969 | − | 0.458969i | ||||
\(469\) | − | 46.7144i | − | 2.15707i | ||||||
\(470\) | 3.97976 | + | 0.331988i | 0.183573 | + | 0.0153135i | ||||
\(471\) | − | 2.65853i | − | 0.122498i | ||||||
\(472\) | −4.00789 | + | 4.00789i | −0.184478 | + | 0.184478i | ||||
\(473\) | 3.99517 | + | 3.99517i | 0.183698 | + | 0.183698i | ||||
\(474\) | 4.64205 | 0.213216 | ||||||||
\(475\) | −11.7339 | − | 1.97138i | −0.538386 | − | 0.0904529i | ||||
\(476\) | −18.4098 | −0.843810 | ||||||||
\(477\) | 9.66148 | + | 9.66148i | 0.442369 | + | 0.442369i | ||||
\(478\) | 6.58132 | + | 6.58132i | 0.301023 | + | 0.301023i | ||||
\(479\) | 3.99175 | 0.182388 | 0.0911938 | − | 0.995833i | \(-0.470932\pi\) | ||||
0.0911938 | + | 0.995833i | \(0.470932\pi\) | |||||||
\(480\) | −0.151332 | + | 1.81411i | −0.00690733 | + | 0.0828026i | ||||
\(481\) | 19.3480i | 0.882195i | ||||||||
\(482\) | 15.1495 | + | 15.1495i | 0.690042 | + | 0.690042i | ||||
\(483\) | 1.60464 | + | 11.4664i | 0.0730137 | + | 0.521741i | ||||
\(484\) | − | 9.04028i | − | 0.410922i | ||||||
\(485\) | −18.9275 | + | 16.0128i | −0.859452 | + | 0.727103i | ||||
\(486\) | −15.8637 | −0.719594 | ||||||||
\(487\) | −7.64836 | + | 7.64836i | −0.346580 | + | 0.346580i | −0.858834 | − | 0.512254i | \(-0.828811\pi\) |
0.512254 | + | 0.858834i | \(0.328811\pi\) | |||||||
\(488\) | −9.27496 | + | 9.27496i | −0.419858 | + | 0.419858i | ||||
\(489\) | 16.6397i | 0.752472i | ||||||||
\(490\) | 3.06233 | − | 2.59076i | 0.138342 | − | 0.117039i | ||||
\(491\) | 6.83837 | 0.308611 | 0.154306 | − | 0.988023i | \(-0.450686\pi\) | ||||
0.154306 | + | 0.988023i | \(0.450686\pi\) | |||||||
\(492\) | 1.43410 | − | 1.43410i | 0.0646544 | − | 0.0646544i | ||||
\(493\) | −16.9923 | + | 16.9923i | −0.765293 | + | 0.765293i | ||||
\(494\) | 14.2967 | 0.643241 | ||||||||
\(495\) | 0.608193 | − | 7.29081i | 0.0273363 | − | 0.327697i | ||||
\(496\) | 5.74501 | 0.257958 | ||||||||
\(497\) | 19.2114 | + | 19.2114i | 0.861751 | + | 0.861751i | ||||
\(498\) | −9.47097 | + | 9.47097i | −0.424404 | + | 0.424404i | ||||
\(499\) | − | 26.1608i | − | 1.17112i | −0.810629 | − | 0.585560i | \(-0.800875\pi\) | ||
0.810629 | − | 0.585560i | \(-0.199125\pi\) | |||||||
\(500\) | 10.8337 | + | 2.76259i | 0.484496 | + | 0.123547i | ||||
\(501\) | −13.5193 | −0.604000 | ||||||||
\(502\) | 4.44646 | + | 4.44646i | 0.198455 | + | 0.198455i | ||||
\(503\) | 8.73893 | − | 8.73893i | 0.389650 | − | 0.389650i | −0.484913 | − | 0.874563i | \(-0.661149\pi\) |
0.874563 | + | 0.484913i | \(0.161149\pi\) | |||||||
\(504\) | 6.93089 | 0.308727 | ||||||||
\(505\) | −0.300590 | + | 3.60337i | −0.0133761 | + | 0.160348i | ||||
\(506\) | −5.35942 | − | 4.04354i | −0.238255 | − | 0.179757i | ||||
\(507\) | −13.2949 | + | 13.2949i | −0.590445 | + | 0.590445i | ||||
\(508\) | −6.93732 | − | 6.93732i | −0.307794 | − | 0.307794i | ||||
\(509\) | − | 11.7467i | − | 0.520664i | −0.965519 | − | 0.260332i | \(-0.916168\pi\) | ||
0.965519 | − | 0.260332i | \(-0.0838320\pi\) | |||||||
\(510\) | 8.62788 | − | 7.29925i | 0.382049 | − | 0.323216i | ||||
\(511\) | − | 45.2401i | − | 2.00131i | ||||||
\(512\) | 0.707107 | − | 0.707107i | 0.0312500 | − | 0.0312500i | ||||
\(513\) | 7.31140 | − | 7.31140i | 0.322806 | − | 0.322806i | ||||
\(514\) | 26.1782i | 1.15467i | ||||||||
\(515\) | 10.6938 | + | 12.6403i | 0.471225 | + | 0.556999i | ||||
\(516\) | − | 3.28578i | − | 0.144649i | ||||||
\(517\) | −1.76791 | − | 1.76791i | −0.0777526 | − | 0.0777526i | ||||
\(518\) | −6.75290 | − | 6.75290i | −0.296705 | − | 0.296705i | ||||
\(519\) | − | 8.47570i | − | 0.372042i | ||||||
\(520\) | −13.3875 | − | 1.11678i | −0.587083 | − | 0.0489740i | ||||
\(521\) | 14.9999i | 0.657157i | 0.944477 | + | 0.328578i | \(0.106570\pi\) | ||||
−0.944477 | + | 0.328578i | \(0.893430\pi\) | |||||||
\(522\) | 6.39724 | − | 6.39724i | 0.280000 | − | 0.280000i | ||||
\(523\) | −3.18638 | + | 3.18638i | −0.139331 | + | 0.139331i | −0.773332 | − | 0.634001i | \(-0.781411\pi\) |
0.634001 | + | 0.773332i | \(0.281411\pi\) | |||||||
\(524\) | 11.7906i | 0.515075i | ||||||||
\(525\) | −2.00000 | + | 11.9042i | −0.0872872 | + | 0.519543i | ||||
\(526\) | − | 2.06971i | − | 0.0902438i | ||||||
\(527\) | −25.2193 | − | 25.2193i | −1.09857 | − | 1.09857i | ||||
\(528\) | 0.805875 | − | 0.805875i | 0.0350712 | − | 0.0350712i | ||||
\(529\) | 22.1164 | − | 6.31371i | 0.961585 | − | 0.274509i | ||||
\(530\) | 13.0268 | + | 1.08669i | 0.565849 | + | 0.0472027i | ||||
\(531\) | −13.2474 | −0.574887 | ||||||||
\(532\) | −4.98988 | + | 4.98988i | −0.216339 | + | 0.216339i | ||||
\(533\) | 10.5832 | + | 10.5832i | 0.458410 | + | 0.458410i | ||||
\(534\) | −1.07008 | −0.0463068 | ||||||||
\(535\) | −18.7970 | + | 15.9024i | −0.812666 | + | 0.687522i | ||||
\(536\) | − | 15.7529i | − | 0.680422i | ||||||
\(537\) | −3.19594 | + | 3.19594i | −0.137915 | + | 0.137915i | ||||
\(538\) | 3.05409 | + | 3.05409i | 0.131671 | + | 0.131671i | ||||
\(539\) | −2.51125 | −0.108167 | ||||||||
\(540\) | −7.41756 | + | 6.27531i | −0.319201 | + | 0.270046i | ||||
\(541\) | −19.8436 | −0.853144 | −0.426572 | − | 0.904454i | \(-0.640279\pi\) | ||||
−0.426572 | + | 0.904454i | \(0.640279\pi\) | |||||||
\(542\) | 1.19412 | − | 1.19412i | 0.0512920 | − | 0.0512920i | ||||
\(543\) | 13.2922 | − | 13.2922i | 0.570423 | − | 0.570423i | ||||
\(544\) | −6.20809 | −0.266170 | ||||||||
\(545\) | −2.21016 | + | 26.4946i | −0.0946729 | + | 1.13491i | ||||
\(546\) | − | 14.5043i | − | 0.620728i | ||||||
\(547\) | 22.5810 | − | 22.5810i | 0.965493 | − | 0.965493i | −0.0339314 | − | 0.999424i | \(-0.510803\pi\) |
0.999424 | + | 0.0339314i | \(0.0108028\pi\) | |||||||
\(548\) | −3.78830 | + | 3.78830i | −0.161828 | + | 0.161828i | ||||
\(549\) | −30.6568 | −1.30840 | ||||||||
\(550\) | −4.06095 | − | 5.70103i | −0.173159 | − | 0.243093i | ||||
\(551\) | 9.21136i | 0.392417i | ||||||||
\(552\) | 0.541113 | + | 3.86668i | 0.0230313 | + | 0.164577i | ||||
\(553\) | −11.9564 | − | 11.9564i | −0.508436 | − | 0.508436i | ||||
\(554\) | 7.76644i | 0.329965i | ||||||||
\(555\) | 5.84225 | + | 0.487355i | 0.247989 | + | 0.0206871i | ||||
\(556\) | −5.75082 | −0.243889 | ||||||||
\(557\) | −8.12733 | − | 8.12733i | −0.344366 | − | 0.344366i | 0.513640 | − | 0.858006i | \(-0.328297\pi\) |
−0.858006 | + | 0.513640i | \(0.828297\pi\) | |||||||
\(558\) | 9.49456 | + | 9.49456i | 0.401937 | + | 0.401937i | ||||
\(559\) | 24.2480 | 1.02558 | ||||||||
\(560\) | 5.06233 | − | 4.28277i | 0.213923 | − | 0.180980i | ||||
\(561\) | −7.07523 | −0.298717 | ||||||||
\(562\) | −3.28520 | − | 3.28520i | −0.138578 | − | 0.138578i | ||||
\(563\) | −32.2838 | + | 32.2838i | −1.36060 | + | 1.36060i | −0.487446 | + | 0.873153i | \(0.662071\pi\) |
−0.873153 | + | 0.487446i | \(0.837929\pi\) | |||||||
\(564\) | 1.45400i | 0.0612243i | ||||||||
\(565\) | −16.1571 | − | 19.0980i | −0.679732 | − | 0.803459i | ||||
\(566\) | − | 26.2233i | − | 1.10225i | ||||||
\(567\) | 7.28508 | + | 7.28508i | 0.305945 | + | 0.305945i | ||||
\(568\) | 6.47843 | + | 6.47843i | 0.271829 | + | 0.271829i | ||||
\(569\) | 46.8519 | 1.96413 | 0.982067 | − | 0.188534i | \(-0.0603735\pi\) | ||||
0.982067 | + | 0.188534i | \(0.0603735\pi\) | |||||||
\(570\) | 0.360119 | − | 4.31698i | 0.0150837 | − | 0.180818i | ||||
\(571\) | 10.3665i | 0.433826i | 0.976191 | + | 0.216913i | \(0.0695988\pi\) | ||||
−0.976191 | + | 0.216913i | \(0.930401\pi\) | |||||||
\(572\) | 5.94709 | + | 5.94709i | 0.248660 | + | 0.248660i | ||||
\(573\) | 4.53958 | − | 4.53958i | 0.189644 | − | 0.189644i | ||||
\(574\) | −7.38755 | −0.308350 | ||||||||
\(575\) | 23.9701 | + | 0.657269i | 0.999624 | + | 0.0274100i | ||||
\(576\) | 2.33722 | 0.0973841 | ||||||||
\(577\) | 3.64168 | − | 3.64168i | 0.151605 | − | 0.151605i | −0.627229 | − | 0.778835i | \(-0.715811\pi\) |
0.778835 | + | 0.627229i | \(0.215811\pi\) | |||||||
\(578\) | 15.2313 | + | 15.2313i | 0.633540 | + | 0.633540i | ||||
\(579\) | − | 5.96930i | − | 0.248076i | ||||||
\(580\) | 0.719538 | − | 8.62557i | 0.0298772 | − | 0.358157i | ||||
\(581\) | 48.7881 | 2.02407 | ||||||||
\(582\) | −6.38267 | − | 6.38267i | −0.264570 | − | 0.264570i | ||||
\(583\) | −5.78684 | − | 5.78684i | −0.239667 | − | 0.239667i | ||||
\(584\) | − | 15.2558i | − | 0.631288i | ||||||
\(585\) | −20.2794 | − | 23.9708i | −0.838452 | − | 0.991069i | ||||
\(586\) | − | 6.85775i | − | 0.283291i | ||||||
\(587\) | 20.8064 | − | 20.8064i | 0.858774 | − | 0.858774i | −0.132420 | − | 0.991194i | \(-0.542275\pi\) |
0.991194 | + | 0.132420i | \(0.0422747\pi\) | |||||||
\(588\) | 1.03267 | + | 1.03267i | 0.0425867 | + | 0.0425867i | ||||
\(589\) | −13.6712 | −0.563311 | ||||||||
\(590\) | −9.67590 | + | 8.18589i | −0.398351 | + | 0.337008i | ||||
\(591\) | −3.96279 | −0.163007 | ||||||||
\(592\) | −2.27719 | − | 2.27719i | −0.0935921 | − | 0.0935921i | ||||
\(593\) | 29.3041 | + | 29.3041i | 1.20338 | + | 1.20338i | 0.973133 | + | 0.230243i | \(0.0739522\pi\) |
0.230243 | + | 0.973133i | \(0.426048\pi\) | |||||||
\(594\) | 6.08272 | 0.249577 | ||||||||
\(595\) | −41.0230 | − | 3.42210i | −1.68178 | − | 0.140293i | ||||
\(596\) | − | 1.83898i | − | 0.0753274i | ||||||
\(597\) | 9.10938 | + | 9.10938i | 0.372822 | + | 0.372822i | ||||
\(598\) | −28.5348 | + | 3.99323i | −1.16687 | + | 0.163295i | ||||
\(599\) | − | 34.2406i | − | 1.39903i | −0.714616 | − | 0.699517i | \(-0.753398\pi\) | ||
0.714616 | − | 0.699517i | \(-0.246602\pi\) | |||||||
\(600\) | −0.674435 | + | 4.01431i | −0.0275337 | + | 0.163884i | ||||
\(601\) | 30.0146 | 1.22432 | 0.612160 | − | 0.790734i | \(-0.290301\pi\) | ||||
0.612160 | + | 0.790734i | \(0.290301\pi\) | |||||||
\(602\) | −8.46308 | + | 8.46308i | −0.344929 | + | 0.344929i | ||||
\(603\) | 26.0342 | − | 26.0342i | 1.06020 | − | 1.06020i | ||||
\(604\) | − | 1.79191i | − | 0.0729119i | ||||||
\(605\) | 1.68046 | − | 20.1447i | 0.0683202 | − | 0.818999i | ||||
\(606\) | −1.31648 | −0.0534784 | ||||||||
\(607\) | −10.3099 | + | 10.3099i | −0.418468 | + | 0.418468i | −0.884675 | − | 0.466208i | \(-0.845620\pi\) |
0.466208 | + | 0.884675i | \(0.345620\pi\) | |||||||
\(608\) | −1.68267 | + | 1.68267i | −0.0682414 | + | 0.0682414i | ||||
\(609\) | 9.34511 | 0.378683 | ||||||||
\(610\) | −22.3917 | + | 18.9436i | −0.906615 | + | 0.767003i | ||||
\(611\) | −10.7300 | −0.434089 | ||||||||
\(612\) | −10.2599 | − | 10.2599i | −0.414731 | − | 0.414731i | ||||
\(613\) | −25.0099 | + | 25.0099i | −1.01014 | + | 1.01014i | −0.0101903 | + | 0.999948i | \(0.503244\pi\) |
−0.999948 | + | 0.0101903i | \(0.996756\pi\) | |||||||
\(614\) | − | 20.5049i | − | 0.827511i | ||||||
\(615\) | 3.46224 | − | 2.92908i | 0.139611 | − | 0.118112i | ||||
\(616\) | −4.15133 | −0.167262 | ||||||||
\(617\) | 25.6567 | + | 25.6567i | 1.03290 | + | 1.03290i | 0.999440 | + | 0.0334597i | \(0.0106525\pi\) |
0.0334597 | + | 0.999440i | \(0.489347\pi\) | |||||||
\(618\) | −4.26253 | + | 4.26253i | −0.171464 | + | 0.171464i | ||||
\(619\) | 44.9169 | 1.80536 | 0.902681 | − | 0.430311i | \(-0.141596\pi\) | ||||
0.902681 | + | 0.430311i | \(0.141596\pi\) | |||||||
\(620\) | 12.8018 | + | 1.06791i | 0.514131 | + | 0.0428884i | ||||
\(621\) | −12.5506 | + | 16.6349i | −0.503639 | + | 0.667537i | ||||
\(622\) | 16.0758 | − | 16.0758i | 0.644581 | − | 0.644581i | ||||
\(623\) | 2.75617 | + | 2.75617i | 0.110423 | + | 0.110423i | ||||
\(624\) | − | 4.89111i | − | 0.195801i | ||||||
\(625\) | 23.6274 | + | 8.16977i | 0.945097 | + | 0.326791i | ||||
\(626\) | 17.6917i | 0.707102i | ||||||||
\(627\) | −1.91771 | + | 1.91771i | −0.0765859 | + | 0.0765859i | ||||
\(628\) | −2.30909 | + | 2.30909i | −0.0921426 | + | 0.0921426i | ||||
\(629\) | 19.9928i | 0.797164i | ||||||||
\(630\) | 15.4443 | + | 1.28835i | 0.615316 | + | 0.0513292i | ||||
\(631\) | 1.07470i | 0.0427831i | 0.999771 | + | 0.0213916i | \(0.00680967\pi\) | ||||
−0.999771 | + | 0.0213916i | \(0.993190\pi\) | |||||||
\(632\) | −4.03189 | − | 4.03189i | −0.160380 | − | 0.160380i | ||||
\(633\) | −9.81944 | − | 9.81944i | −0.390288 | − | 0.390288i | ||||
\(634\) | − | 20.9287i | − | 0.831186i | ||||||
\(635\) | −14.1691 | − | 16.7482i | −0.562282 | − | 0.664631i | ||||
\(636\) | 4.75932i | 0.188719i | ||||||||
\(637\) | −7.62077 | + | 7.62077i | −0.301946 | + | 0.301946i | ||||
\(638\) | −3.83170 | + | 3.83170i | −0.151698 | + | 0.151698i | ||||
\(639\) | 21.4133i | 0.847097i | ||||||||
\(640\) | 1.70711 | − | 1.44423i | 0.0674793 | − | 0.0570880i | ||||
\(641\) | − | 27.4605i | − | 1.08462i | −0.840177 | − | 0.542312i | \(-0.817549\pi\) | ||
0.840177 | − | 0.542312i | \(-0.182451\pi\) | |||||||
\(642\) | −6.33868 | − | 6.33868i | −0.250168 | − | 0.250168i | ||||
\(643\) | 15.2206 | − | 15.2206i | 0.600242 | − | 0.600242i | −0.340135 | − | 0.940377i | \(-0.610473\pi\) |
0.940377 | + | 0.340135i | \(0.110473\pi\) | |||||||
\(644\) | 8.56555 | − | 11.3530i | 0.337530 | − | 0.447371i | ||||
\(645\) | 0.610779 | − | 7.32180i | 0.0240494 | − | 0.288296i | ||||
\(646\) | 14.7731 | 0.581241 | ||||||||
\(647\) | −10.8512 | + | 10.8512i | −0.426606 | + | 0.426606i | −0.887471 | − | 0.460864i | \(-0.847539\pi\) |
0.460864 | + | 0.887471i | \(0.347539\pi\) | |||||||
\(648\) | 2.45666 | + | 2.45666i | 0.0965066 | + | 0.0965066i | ||||
\(649\) | 7.93466 | 0.311462 | ||||||||
\(650\) | −29.6243 | − | 4.97710i | −1.16196 | − | 0.195218i | ||||
\(651\) | 13.8697i | 0.543595i | ||||||||
\(652\) | 14.4525 | − | 14.4525i | 0.566005 | − | 0.566005i | ||||
\(653\) | 27.5566 | + | 27.5566i | 1.07837 | + | 1.07837i | 0.996656 | + | 0.0817179i | \(0.0260406\pi\) |
0.0817179 | + | 0.996656i | \(0.473959\pi\) | |||||||
\(654\) | −9.67976 | −0.378508 | ||||||||
\(655\) | −2.19170 | + | 26.2733i | −0.0856368 | + | 1.02658i | ||||
\(656\) | −2.49121 | −0.0972654 | ||||||||
\(657\) | 25.2126 | − | 25.2126i | 0.983638 | − | 0.983638i | ||||
\(658\) | 3.74501 | − | 3.74501i | 0.145996 | − | 0.145996i | ||||
\(659\) | 13.1299 | 0.511467 | 0.255734 | − | 0.966747i | \(-0.417683\pi\) | ||||
0.255734 | + | 0.966747i | \(0.417683\pi\) | |||||||
\(660\) | 1.94556 | − | 1.64595i | 0.0757306 | − | 0.0640687i | ||||
\(661\) | − | 20.2923i | − | 0.789278i | −0.918836 | − | 0.394639i | \(-0.870870\pi\) | ||
0.918836 | − | 0.394639i | \(-0.129130\pi\) | |||||||
\(662\) | 10.1247 | − | 10.1247i | 0.393506 | − | 0.393506i | ||||
\(663\) | −21.4709 | + | 21.4709i | −0.833861 | + | 0.833861i | ||||
\(664\) | 16.4522 | 0.638469 | ||||||||
\(665\) | −12.0466 | + | 10.1915i | −0.467148 | + | 0.395211i | ||||
\(666\) | − | 7.52687i | − | 0.291660i | ||||||
\(667\) | −2.57283 | − | 18.3849i | −0.0996203 | − | 0.711866i | ||||
\(668\) | 11.7423 | + | 11.7423i | 0.454325 | + | 0.454325i | ||||
\(669\) | − | 1.36911i | − | 0.0529329i | ||||||
\(670\) | 2.92823 | − | 35.1026i | 0.113128 | − | 1.35613i | ||||
\(671\) | 18.3622 | 0.708865 | ||||||||
\(672\) | 1.70711 | + | 1.70711i | 0.0658531 | + | 0.0658531i | ||||
\(673\) | −31.0809 | − | 31.0809i | −1.19808 | − | 1.19808i | −0.974740 | − | 0.223341i | \(-0.928304\pi\) |
−0.223341 | − | 0.974740i | \(-0.571696\pi\) | |||||||
\(674\) | −2.67770 | −0.103141 | ||||||||
\(675\) | −17.6952 | + | 12.6046i | −0.681090 | + | 0.485153i | ||||
\(676\) | 23.0947 | 0.888259 | ||||||||
\(677\) | −30.4764 | − | 30.4764i | −1.17130 | − | 1.17130i | −0.981900 | − | 0.189402i | \(-0.939345\pi\) |
−0.189402 | − | 0.981900i | \(-0.560655\pi\) | |||||||
\(678\) | 6.44018 | − | 6.44018i | 0.247334 | − | 0.247334i | ||||
\(679\) | 32.8793i | 1.26179i | ||||||||
\(680\) | −13.8337 | − | 1.15399i | −0.530496 | − | 0.0442536i | ||||
\(681\) | − | 16.5551i | − | 0.634391i | ||||||
\(682\) | −5.68687 | − | 5.68687i | −0.217761 | − | 0.217761i | ||||
\(683\) | −30.8836 | − | 30.8836i | −1.18173 | − | 1.18173i | −0.979296 | − | 0.202434i | \(-0.935115\pi\) |
−0.202434 | − | 0.979296i | \(-0.564885\pi\) | |||||||
\(684\) | −5.56178 | −0.212660 | ||||||||
\(685\) | −9.14575 | + | 7.73738i | −0.349441 | + | 0.295630i | ||||
\(686\) | 15.4385i | 0.589444i | ||||||||
\(687\) | −2.48736 | − | 2.48736i | −0.0948985 | − | 0.0948985i | ||||
\(688\) | −2.85390 | + | 2.85390i | −0.108804 | + | 0.108804i | ||||
\(689\) | −35.1222 | −1.33805 | ||||||||
\(690\) | 0.487018 | + | 8.71681i | 0.0185404 | + | 0.331843i | ||||
\(691\) | −37.6570 | −1.43254 | −0.716270 | − | 0.697823i | \(-0.754152\pi\) | ||||
−0.716270 | + | 0.697823i | \(0.754152\pi\) | |||||||
\(692\) | −7.36165 | + | 7.36165i | −0.279848 | + | 0.279848i | ||||
\(693\) | −6.86075 | − | 6.86075i | −0.260618 | − | 0.260618i | ||||
\(694\) | − | 7.88894i | − | 0.299460i | ||||||
\(695\) | −12.8147 | − | 1.06899i | −0.486090 | − | 0.0405492i | ||||
\(696\) | 3.15133 | 0.119451 | ||||||||
\(697\) | 10.9359 | + | 10.9359i | 0.414225 | + | 0.414225i | ||||
\(698\) | −3.41275 | − | 3.41275i | −0.129174 | − | 0.129174i | ||||
\(699\) | 1.06100i | 0.0401305i | ||||||||
\(700\) | 12.0766 | − | 8.60241i | 0.456454 | − | 0.325141i | ||||
\(701\) | − | 36.4494i | − | 1.37668i | −0.725390 | − | 0.688338i | \(-0.758341\pi\) | ||
0.725390 | − | 0.688338i | \(-0.241659\pi\) | |||||||
\(702\) | 18.4590 | − | 18.4590i | 0.696689 | − | 0.696689i | ||||
\(703\) | 5.41895 | + | 5.41895i | 0.204379 | + | 0.204379i | ||||
\(704\) | −1.39990 | −0.0527608 | ||||||||
\(705\) | −0.270277 | + | 3.23998i | −0.0101792 | + | 0.122025i | ||||
\(706\) | −23.0567 | −0.867749 | ||||||||
\(707\) | 3.39082 | + | 3.39082i | 0.127525 | + | 0.127525i | ||||
\(708\) | −3.26288 | − | 3.26288i | −0.122627 | − | 0.122627i | ||||
\(709\) | −0.752533 | −0.0282620 | −0.0141310 | − | 0.999900i | \(-0.504498\pi\) | ||||
−0.0141310 | + | 0.999900i | \(0.504498\pi\) | |||||||
\(710\) | 13.2318 | + | 15.6403i | 0.496581 | + | 0.586970i | ||||
\(711\) | − | 13.3267i | − | 0.499791i | ||||||
\(712\) | 0.929427 | + | 0.929427i | 0.0348317 | + | 0.0348317i | ||||
\(713\) | 27.2862 | − | 3.81850i | 1.02188 | − | 0.143004i | ||||
\(714\) | − | 14.9876i | − | 0.560899i | ||||||
\(715\) | 12.1466 | + | 14.3575i | 0.454257 | + | 0.536941i | ||||
\(716\) | 5.55173 | 0.207478 | ||||||||
\(717\) | −5.35795 | + | 5.35795i | −0.200096 | + | 0.200096i | ||||
\(718\) | 21.0424 | − | 21.0424i | 0.785297 | − | 0.785297i | ||||
\(719\) | − | 14.0360i | − | 0.523456i | −0.965142 | − | 0.261728i | \(-0.915708\pi\) | ||
0.965142 | − | 0.261728i | \(-0.0842923\pi\) | |||||||
\(720\) | 5.20809 | + | 0.434454i | 0.194094 | + | 0.0161912i | ||||
\(721\) | 21.9577 | 0.817748 | ||||||||
\(722\) | −9.43084 | + | 9.43084i | −0.350979 | + | 0.350979i | ||||
\(723\) | −12.3335 | + | 12.3335i | −0.458686 | + | 0.458686i | ||||
\(724\) | −23.0901 | −0.858137 | ||||||||
\(725\) | 3.20673 | − | 19.0868i | 0.119095 | − | 0.708868i | ||||
\(726\) | 7.35982 | 0.273149 | ||||||||
\(727\) | 12.3873 | + | 12.3873i | 0.459419 | + | 0.459419i | 0.898465 | − | 0.439046i | \(-0.144683\pi\) |
−0.439046 | + | 0.898465i | \(0.644683\pi\) | |||||||
\(728\) | −12.5979 | + | 12.5979i | −0.466908 | + | 0.466908i | ||||
\(729\) | − | 2.49220i | − | 0.0923037i | ||||||
\(730\) | 2.83582 | − | 33.9948i | 0.104958 | − | 1.25821i | ||||
\(731\) | 25.0560 | 0.926728 | ||||||||
\(732\) | −7.55088 | − | 7.55088i | −0.279089 | − | 0.279089i | ||||
\(733\) | −7.76852 | + | 7.76852i | −0.286937 | + | 0.286937i | −0.835868 | − | 0.548931i | \(-0.815035\pi\) |
0.548931 | + | 0.835868i | \(0.315035\pi\) | |||||||
\(734\) | −31.2446 | −1.15326 | ||||||||
\(735\) | 2.10917 | + | 2.49309i | 0.0777980 | + | 0.0919590i | ||||
\(736\) | 2.88845 | − | 3.82843i | 0.106470 | − | 0.141118i | ||||
\(737\) | −15.5935 | + | 15.5935i | −0.574393 | + | 0.574393i | ||||
\(738\) | −4.11713 | − | 4.11713i | −0.151554 | − | 0.151554i | ||||
\(739\) | 8.15036i | 0.299816i | 0.988700 | + | 0.149908i | \(0.0478977\pi\) | ||||
−0.988700 | + | 0.149908i | \(0.952102\pi\) | |||||||
\(740\) | −4.65104 | − | 5.49763i | −0.170976 | − | 0.202097i | ||||
\(741\) | 11.6392i | 0.427576i | ||||||||
\(742\) | 12.2584 | − | 12.2584i | 0.450021 | − | 0.450021i | ||||
\(743\) | −23.1386 | + | 23.1386i | −0.848874 | + | 0.848874i | −0.989993 | − | 0.141119i | \(-0.954930\pi\) |
0.141119 | + | 0.989993i | \(0.454930\pi\) | |||||||
\(744\) | 4.67710i | 0.171471i | ||||||||
\(745\) | 0.341839 | − | 4.09784i | 0.0125240 | − | 0.150133i | ||||
\(746\) | 8.03701i | 0.294256i | ||||||||
\(747\) | 27.1899 | + | 27.1899i | 0.994827 | + | 0.994827i | ||||
\(748\) | 6.14526 | + | 6.14526i | 0.224693 | + | 0.224693i | ||||
\(749\) | 32.6527i | 1.19310i | ||||||||
\(750\) | −2.24906 | + | 8.81984i | −0.0821242 | + | 0.322055i | ||||
\(751\) | 12.9246i | 0.471625i | 0.971799 | + | 0.235813i | \(0.0757752\pi\) | ||||
−0.971799 | + | 0.235813i | \(0.924225\pi\) | |||||||
\(752\) | 1.26288 | − | 1.26288i | 0.0460526 | − | 0.0460526i | ||||
\(753\) | −3.61993 | + | 3.61993i | −0.131917 | + | 0.131917i | ||||
\(754\) | 23.2558i | 0.846925i | ||||||||
\(755\) | 0.333090 | − | 3.99297i | 0.0121224 | − | 0.145319i | ||||
\(756\) | 12.8852i | 0.468630i | ||||||||
\(757\) | 22.6178 | + | 22.6178i | 0.822059 | + | 0.822059i | 0.986403 | − | 0.164344i | \(-0.0525506\pi\) |
−0.164344 | + | 0.986403i | \(0.552551\pi\) | |||||||
\(758\) | −20.1193 | + | 20.1193i | −0.730765 | + | 0.730765i | ||||
\(759\) | 3.29191 | − | 4.36318i | 0.119489 | − | 0.158373i | ||||
\(760\) | −4.06233 | + | 3.43677i | −0.147356 | + | 0.124665i | ||||
\(761\) | −14.9443 | −0.541732 | −0.270866 | − | 0.962617i | \(-0.587310\pi\) | ||||
−0.270866 | + | 0.962617i | \(0.587310\pi\) | |||||||
\(762\) | 5.64777 | − | 5.64777i | 0.204597 | − | 0.204597i | ||||
\(763\) | 24.9318 | + | 24.9318i | 0.902592 | + | 0.902592i | ||||
\(764\) | −7.88579 | −0.285298 | ||||||||
\(765\) | −20.9552 | − | 24.7695i | −0.757637 | − | 0.895544i | ||||
\(766\) | − | 6.19840i | − | 0.223957i | ||||||
\(767\) | 24.0790 | − | 24.0790i | 0.869441 | − | 0.869441i | ||||
\(768\) | 0.575666 | + | 0.575666i | 0.0207726 | + | 0.0207726i | ||||
\(769\) | −10.3598 | −0.373583 | −0.186792 | − | 0.982400i | \(-0.559809\pi\) | ||||
−0.186792 | + | 0.982400i | \(0.559809\pi\) | |||||||
\(770\) | −9.25053 | − | 0.771672i | −0.333366 | − | 0.0278091i | ||||
\(771\) | −21.3120 | −0.767534 | ||||||||
\(772\) | −5.18469 | + | 5.18469i | −0.186601 | + | 0.186601i | ||||
\(773\) | 24.0445 | − | 24.0445i | 0.864821 | − | 0.864821i | −0.127072 | − | 0.991893i | \(-0.540558\pi\) |
0.991893 | + | 0.127072i | \(0.0405580\pi\) | |||||||
\(774\) | −9.43306 | −0.339064 | ||||||||
\(775\) | 28.3280 | + | 4.75932i | 1.01757 | + | 0.170960i | ||||
\(776\) | 11.0875i | 0.398016i | ||||||||
\(777\) | 5.49763 | − | 5.49763i | 0.197226 | − | 0.197226i | ||||
\(778\) | −4.23252 | + | 4.23252i | −0.151743 | + | 0.151743i | ||||
\(779\) | 5.92823 | 0.212401 | ||||||||
\(780\) | 0.909186 | − | 10.8990i | 0.0325541 | − | 0.390247i | ||||
\(781\) | − | 12.8257i | − | 0.458941i | ||||||
\(782\) | −29.4856 | + | 4.12629i | −1.05440 | + | 0.147556i | ||||
\(783\) | 11.8931 | + | 11.8931i | 0.425024 | + | 0.425024i | ||||
\(784\) | − | 1.79387i | − | 0.0640669i | ||||||
\(785\) | −5.57463 | + | 4.71618i | −0.198967 | + | 0.168328i | ||||
\(786\) | −9.59890 | −0.342382 | ||||||||
\(787\) | 5.07531 | + | 5.07531i | 0.180915 | + | 0.180915i | 0.791755 | − | 0.610839i | \(-0.209168\pi\) |
−0.610839 | + | 0.791755i | \(0.709168\pi\) | |||||||
\(788\) | 3.44191 | + | 3.44191i | 0.122613 | + | 0.122613i | ||||
\(789\) | 1.68498 | 0.0599870 | ||||||||
\(790\) | −8.23491 | − | 9.73385i | −0.292985 | − | 0.346315i | ||||
\(791\) | −33.1755 | −1.17958 | ||||||||
\(792\) | −2.31356 | − | 2.31356i | −0.0822089 | − | 0.0822089i | ||||
\(793\) | 55.7230 | − | 55.7230i | 1.97878 | − | 1.97878i | ||||
\(794\) | − | 31.4771i | − | 1.11708i | ||||||
\(795\) | −0.884688 | + | 10.6053i | −0.0313766 | + | 0.376132i | ||||
\(796\) | − | 15.8241i | − | 0.560870i | ||||||
\(797\) | 4.54720 | + | 4.54720i | 0.161070 | + | 0.161070i | 0.783041 | − | 0.621971i | \(-0.213668\pi\) |
−0.621971 | + | 0.783041i | \(0.713668\pi\) | |||||||
\(798\) | −4.06233 | − | 4.06233i | −0.143805 | − | 0.143805i | ||||
\(799\) | −11.0875 | −0.392249 | ||||||||
\(800\) | 4.07245 | − | 2.90088i | 0.143983 | − | 0.102562i | ||||
\(801\) | 3.07206i | 0.108546i | ||||||||
\(802\) | 16.3307 | + | 16.3307i | 0.576656 | + | 0.576656i | ||||
\(803\) | −15.1014 | + | 15.1014i | −0.532916 | + | 0.532916i | ||||
\(804\) | 12.8247 | 0.452291 | ||||||||
\(805\) | 21.1972 | − | 23.7060i | 0.747103 | − | 0.835526i | ||||
\(806\) | −34.5154 | −1.21575 | ||||||||
\(807\) | −2.48638 | + | 2.48638i | −0.0875248 | + | 0.0875248i | ||||
\(808\) | 1.14344 | + | 1.14344i | 0.0402262 | + | 0.0402262i | ||||
\(809\) | − | 50.1835i | − | 1.76436i | −0.470913 | − | 0.882180i | \(-0.656075\pi\) | ||
0.470913 | − | 0.882180i | \(-0.343925\pi\) | |||||||
\(810\) | 5.01758 | + | 5.93089i | 0.176300 | + | 0.208390i | ||||
\(811\) | −6.03654 | −0.211971 | −0.105986 | − | 0.994368i | \(-0.533800\pi\) | ||||
−0.105986 | + | 0.994368i | \(0.533800\pi\) | |||||||
\(812\) | −8.11678 | − | 8.11678i | −0.284843 | − | 0.284843i | ||||
\(813\) | 0.972154 | + | 0.972154i | 0.0340949 | + | 0.0340949i | ||||
\(814\) | 4.50830i | 0.158016i | ||||||||
\(815\) | 34.8915 | − | 29.5185i | 1.22220 | − | 1.03399i | ||||
\(816\) | − | 5.05409i | − | 0.176929i | ||||||
\(817\) | 6.79131 | − | 6.79131i | 0.237598 | − | 0.237598i | ||||
\(818\) | −14.2373 | − | 14.2373i | −0.497797 | − | 0.497797i | ||||
\(819\) | −41.6400 | −1.45502 | ||||||||
\(820\) | −5.55123 | − | 0.463079i | −0.193857 | − | 0.0161714i | ||||
\(821\) | 42.8651 | 1.49600 | 0.748002 | − | 0.663697i | \(-0.231014\pi\) | ||||
0.748002 | + | 0.663697i | \(0.231014\pi\) | |||||||
\(822\) | −3.08411 | − | 3.08411i | −0.107571 | − | 0.107571i | ||||
\(823\) | −8.68113 | − | 8.68113i | −0.302605 | − | 0.302605i | 0.539427 | − | 0.842032i | \(-0.318641\pi\) |
−0.842032 | + | 0.539427i | \(0.818641\pi\) | |||||||
\(824\) | 7.40452 | 0.257949 | ||||||||
\(825\) | 4.64129 | − | 3.30608i | 0.161589 | − | 0.115103i | ||||
\(826\) | 16.8082i | 0.584832i | ||||||||
\(827\) | −1.62311 | − | 1.62311i | −0.0564412 | − | 0.0564412i | 0.678323 | − | 0.734764i | \(-0.262707\pi\) |
−0.734764 | + | 0.678323i | \(0.762707\pi\) | |||||||
\(828\) | 11.1007 | − | 1.55346i | 0.385777 | − | 0.0539866i | ||||
\(829\) | − | 7.84786i | − | 0.272567i | −0.990670 | − | 0.136284i | \(-0.956484\pi\) | ||
0.990670 | − | 0.136284i | \(-0.0435159\pi\) | |||||||
\(830\) | 36.6609 | + | 3.05822i | 1.27252 | + | 0.106152i | ||||
\(831\) | −6.32277 | −0.219335 | ||||||||
\(832\) | −4.24822 | + | 4.24822i | −0.147281 | + | 0.147281i | ||||
\(833\) | −7.87471 | + | 7.87471i | −0.272843 | + | 0.272843i | ||||
\(834\) | − | 4.68183i | − | 0.162119i | ||||||
\(835\) | 23.9831 | + | 28.3485i | 0.829968 | + | 0.981041i | ||||
\(836\) | 3.33129 | 0.115215 | ||||||||
\(837\) | −17.6513 | + | 17.6513i | −0.610117 | + | 0.610117i | ||||
\(838\) | 15.7678 | − | 15.7678i | 0.544690 | − | 0.544690i | ||||
\(839\) | −25.5054 | −0.880545 | −0.440272 | − | 0.897864i | \(-0.645118\pi\) | ||||
−0.440272 | + | 0.897864i | \(0.645118\pi\) | |||||||
\(840\) | 3.48667 | + | 4.12132i | 0.120301 | + | 0.142199i | ||||
\(841\) | 14.0164 | 0.483323 | ||||||||
\(842\) | 8.05059 | + | 8.05059i | 0.277442 | + | 0.277442i | ||||
\(843\) | 2.67453 | − | 2.67453i | 0.0921156 | − | 0.0921156i | ||||
\(844\) | 17.0575i | 0.587144i | ||||||||
\(845\) | 51.4627 | + | 4.29297i | 1.77037 | + | 0.147683i | ||||
\(846\) | 4.17423 | 0.143513 | ||||||||
\(847\) | −18.9564 | − | 18.9564i | −0.651351 | − | 0.651351i | ||||
\(848\) | 4.13375 | − | 4.13375i | 0.141954 | − | 0.141954i | ||||
\(849\) | 21.3487 | 0.732687 | ||||||||
\(850\) | −30.6114 | − | 5.14295i | −1.04996 | − | 0.176402i | ||||
\(851\) | −12.3292 | − | 9.30208i | −0.422640 | − | 0.318871i | ||||
\(852\) | −5.27418 | + | 5.27418i | −0.180691 | + | 0.180691i | ||||
\(853\) | 25.0722 | + | 25.0722i | 0.858455 | + | 0.858455i | 0.991156 | − | 0.132701i | \(-0.0423650\pi\) |
−0.132701 | + | 0.991156i | \(0.542365\pi\) | |||||||
\(854\) | 38.8971i | 1.33103i | ||||||||
\(855\) | −12.3935 | − | 1.03385i | −0.423848 | − | 0.0353571i | ||||
\(856\) | 11.0110i | 0.376350i | ||||||||
\(857\) | −5.96703 | + | 5.96703i | −0.203830 | + | 0.203830i | −0.801639 | − | 0.597809i | \(-0.796038\pi\) |
0.597809 | + | 0.801639i | \(0.296038\pi\) | |||||||
\(858\) | −4.84161 | + | 4.84161i | −0.165290 | + | 0.165290i | ||||
\(859\) | 47.8075i | 1.63117i | 0.578636 | + | 0.815586i | \(0.303585\pi\) | ||||
−0.578636 | + | 0.815586i | \(0.696415\pi\) | |||||||
\(860\) | −6.88992 | + | 5.82892i | −0.234944 | + | 0.198765i | ||||
\(861\) | − | 6.01431i | − | 0.204967i | ||||||
\(862\) | 18.9781 | + | 18.9781i | 0.646396 | + | 0.646396i | ||||
\(863\) | −7.90989 | − | 7.90989i | −0.269256 | − | 0.269256i | 0.559545 | − | 0.828800i | \(-0.310976\pi\) |
−0.828800 | + | 0.559545i | \(0.810976\pi\) | |||||||
\(864\) | 4.34511i | 0.147824i | ||||||||
\(865\) | −17.7726 | + | 15.0358i | −0.604286 | + | 0.511231i | ||||
\(866\) | − | 6.44807i | − | 0.219114i | ||||||
\(867\) | −12.4000 | + | 12.4000i | −0.421128 | + | 0.421128i | ||||
\(868\) | 12.0466 | − | 12.0466i | 0.408889 | − | 0.408889i | ||||
\(869\) | 7.98218i | 0.270777i | ||||||||
\(870\) | 7.02220 | + | 0.585786i | 0.238075 | + | 0.0198600i | ||||
\(871\) | 94.6417i | 3.20681i | ||||||||
\(872\) | 8.40744 | + | 8.40744i | 0.284712 | + | 0.284712i | ||||
\(873\) | −18.3238 | + | 18.3238i | −0.620167 | + | 0.620167i | ||||
\(874\) | −6.87353 | + | 9.11036i | −0.232501 | + | 0.308162i | ||||
\(875\) | 28.5098 | − | 16.9241i | 0.963807 | − | 0.572140i | ||||
\(876\) | 12.4199 | 0.419631 | ||||||||
\(877\) | −21.3111 | + | 21.3111i | −0.719625 | + | 0.719625i | −0.968528 | − | 0.248904i | \(-0.919930\pi\) |
0.248904 | + | 0.968528i | \(0.419930\pi\) | |||||||
\(878\) | −10.3199 | − | 10.3199i | −0.348280 | − | 0.348280i | ||||
\(879\) | 5.58300 | 0.188310 | ||||||||
\(880\) | −3.11944 | − | 0.260221i | −0.105156 | − | 0.00877205i | ||||
\(881\) | 21.1772i | 0.713477i | 0.934204 | + | 0.356739i | \(0.116111\pi\) | ||||
−0.934204 | + | 0.356739i | \(0.883889\pi\) | |||||||
\(882\) | 2.96467 | − | 2.96467i | 0.0998255 | − | 0.0998255i | ||||
\(883\) | 0.912803 | + | 0.912803i | 0.0307183 | + | 0.0307183i | 0.722299 | − | 0.691581i | \(-0.243085\pi\) |
−0.691581 | + | 0.722299i | \(0.743085\pi\) | |||||||
\(884\) | 37.2975 | 1.25445 | ||||||||
\(885\) | −6.66425 | − | 7.87729i | −0.224016 | − | 0.264792i | ||||
\(886\) | 22.1327 | 0.743563 | ||||||||
\(887\) | 21.4132 | − | 21.4132i | 0.718984 | − | 0.718984i | −0.249413 | − | 0.968397i | \(-0.580238\pi\) |
0.968397 | + | 0.249413i | \(0.0802377\pi\) | |||||||
\(888\) | 1.85390 | − | 1.85390i | 0.0622127 | − | 0.0622127i | ||||
\(889\) | −29.0935 | −0.975766 | ||||||||
\(890\) | 1.89830 | + | 2.24383i | 0.0636312 | + | 0.0752135i | ||||
\(891\) | − | 4.86359i | − | 0.162936i | ||||||
\(892\) | −1.18915 | + | 1.18915i | −0.0398158 | + | 0.0398158i | ||||
\(893\) | −3.00523 | + | 3.00523i | −0.100566 | + | 0.100566i | ||||
\(894\) | 1.49714 | 0.0500718 | ||||||||
\(895\) | 12.3711 | + | 1.03198i | 0.413519 | + | 0.0344954i | ||||
\(896\) | − | 2.96545i | − | 0.0990686i | ||||||
\(897\) | −3.25094 | − | 23.2306i | −0.108546 | − | 0.775646i | ||||
\(898\) | 24.7197 | + | 24.7197i | 0.824907 | + | 0.824907i | ||||
\(899\) | − | 22.2382i | − | 0.741685i | ||||||
\(900\) | 11.5246 | + | 1.93621i | 0.384152 | + | 0.0645405i | ||||
\(901\) | −36.2925 | −1.20908 | ||||||||
\(902\) | 2.46600 | + | 2.46600i | 0.0821087 | + | 0.0821087i | ||||
\(903\) | −6.88992 | − | 6.88992i | −0.229282 | − | 0.229282i | ||||
\(904\) | −11.1874 | −0.372086 | ||||||||
\(905\) | −51.4524 | − | 4.29211i | −1.71033 | − | 0.142675i | ||||
\(906\) | 1.45882 | 0.0484661 | ||||||||
\(907\) | −24.6313 | − | 24.6313i | −0.817869 | − | 0.817869i | 0.167930 | − | 0.985799i | \(-0.446292\pi\) |
−0.985799 | + | 0.167930i | \(0.946292\pi\) | |||||||
\(908\) | −14.3791 | + | 14.3791i | −0.477186 | + | 0.477186i | ||||
\(909\) | 3.77945i | 0.125356i | ||||||||
\(910\) | −30.4139 | + | 25.7304i | −1.00821 | + | 0.852955i | ||||
\(911\) | − | 31.5922i | − | 1.04670i | −0.852119 | − | 0.523348i | \(-0.824683\pi\) | ||
0.852119 | − | 0.523348i | \(-0.175317\pi\) | |||||||
\(912\) | −1.36989 | − | 1.36989i | −0.0453616 | − | 0.0453616i | ||||
\(913\) | −16.2857 | − | 16.2857i | −0.538978 | − | 0.538978i | ||||
\(914\) | −0.405717 | −0.0134199 | ||||||||
\(915\) | −15.4222 | − | 18.2294i | −0.509844 | − | 0.602647i | ||||
\(916\) | 4.32083i | 0.142764i | ||||||||
\(917\) | 24.7236 | + | 24.7236i | 0.816444 | + | 0.816444i | ||||
\(918\) | 19.0741 | − | 19.0741i | 0.629538 | − | 0.629538i | ||||
\(919\) | 5.24715 | 0.173087 | 0.0865437 | − | 0.996248i | \(-0.472418\pi\) | ||||
0.0865437 | + | 0.996248i | \(0.472418\pi\) | |||||||
\(920\) | 7.14806 | − | 7.99407i | 0.235665 | − | 0.263557i | ||||
\(921\) | 16.6934 | 0.550065 | ||||||||
\(922\) | −12.0052 | + | 12.0052i | −0.395371 | + | 0.395371i | ||||
\(923\) | −38.9217 | − | 38.9217i | −1.28112 | − | 1.28112i | ||||
\(924\) | − | 3.37966i | − | 0.111183i | ||||||
\(925\) | −9.34211 | − | 13.1151i | −0.307167 | − | 0.431222i | ||||
\(926\) | 19.3849 | 0.637027 | ||||||||
\(927\) | 12.2372 | + | 12.2372i | 0.401922 | + | 0.401922i | ||||
\(928\) | −2.73712 | − | 2.73712i | −0.0898503 | − | 0.0898503i | ||||
\(929\) | − | 35.7022i | − | 1.17135i | −0.810545 | − | 0.585676i | \(-0.800829\pi\) | ||
0.810545 | − | 0.585676i | \(-0.199171\pi\) | |||||||
\(930\) | −0.869403 | + | 10.4221i | −0.0285089 | + | 0.341754i | ||||
\(931\) | 4.26881i | 0.139905i | ||||||||
\(932\) | 0.921537 | − | 0.921537i | 0.0301860 | − | 0.0301860i | ||||
\(933\) | 13.0875 | + | 13.0875i | 0.428467 | + | 0.428467i | ||||
\(934\) | 8.88313 | 0.290665 | ||||||||
\(935\) | 12.5513 | + | 14.8360i | 0.410473 | + | 0.485188i | ||||
\(936\) | −14.0417 | −0.458969 | ||||||||
\(937\) | −27.6575 | − | 27.6575i | −0.903530 | − | 0.903530i | 0.0922093 | − | 0.995740i | \(-0.470607\pi\) |
−0.995740 | + | 0.0922093i | \(0.970607\pi\) | |||||||
\(938\) | −33.0321 | − | 33.0321i | −1.07853 | − | 1.07853i | ||||
\(939\) | −14.4031 | −0.470026 | ||||||||
\(940\) | 3.04887 | − | 2.57936i | 0.0994430 | − | 0.0841296i | ||||
\(941\) | 15.6518i | 0.510234i | 0.966910 | + | 0.255117i | \(0.0821139\pi\) | ||||
−0.966910 | + | 0.255117i | \(0.917886\pi\) | |||||||
\(942\) | −1.87986 | − | 1.87986i | −0.0612492 | − | 0.0612492i | ||||
\(943\) | −11.8321 | + | 1.65582i | −0.385307 | + | 0.0539208i | ||||
\(944\) | 5.66801i | 0.184478i | ||||||||
\(945\) | −2.39517 | + | 28.7124i | −0.0779148 | + | 0.934015i | ||||
\(946\) | 5.65003 | 0.183698 | ||||||||
\(947\) | −40.5901 | + | 40.5901i | −1.31900 | + | 1.31900i | −0.404431 | + | 0.914568i | \(0.632531\pi\) |
−0.914568 | + | 0.404431i | \(0.867469\pi\) | |||||||
\(948\) | 3.28242 | − | 3.28242i | 0.106608 | − | 0.106608i | ||||
\(949\) | 91.6549i | 2.97524i | ||||||||
\(950\) | −9.69106 | + | 6.90311i | −0.314419 | + | 0.223967i | ||||
\(951\) | 17.0384 | 0.552507 | ||||||||
\(952\) | −13.0177 | + | 13.0177i | −0.421905 | + | 0.421905i | ||||
\(953\) | 14.1269 | − | 14.1269i | 0.457615 | − | 0.457615i | −0.440257 | − | 0.897872i | \(-0.645113\pi\) |
0.897872 | + | 0.440257i | \(0.145113\pi\) | |||||||
\(954\) | 13.6634 | 0.442369 | ||||||||
\(955\) | −17.5721 | − | 1.46585i | −0.568621 | − | 0.0474339i | ||||
\(956\) | 9.30740 | 0.301023 | ||||||||
\(957\) | −3.11944 | − | 3.11944i | −0.100837 | − | 0.100837i | ||||
\(958\) | 2.82259 | − | 2.82259i | 0.0911938 | − | 0.0911938i | ||||
\(959\) | 15.8873i | 0.513026i | ||||||||
\(960\) | 1.17576 | + | 1.38978i | 0.0379476 | + | 0.0448550i | ||||
\(961\) | 2.00512 | 0.0646812 | ||||||||
\(962\) | 13.6811 | + | 13.6811i | 0.441097 | + | 0.441097i | ||||
\(963\) | −18.1975 | + | 18.1975i | −0.586407 | + | 0.586407i | ||||
\(964\) | 21.4247 | 0.690042 | ||||||||
\(965\) | −12.5170 | + | 10.5894i | −0.402935 | + | 0.340886i | ||||
\(966\) | 9.24264 | + | 6.97334i | 0.297377 | + | 0.224363i | ||||
\(967\) | −11.5304 | + | 11.5304i | −0.370792 | + | 0.370792i | −0.867766 | − | 0.496974i | \(-0.834445\pi\) |
0.496974 | + | 0.867766i | \(0.334445\pi\) | |||||||
\(968\) | −6.39244 | − | 6.39244i | −0.205461 | − | 0.205461i | ||||
\(969\) | 12.0270i | 0.386364i | ||||||||
\(970\) | −2.06100 | + | 24.7065i | −0.0661746 | + | 0.793277i | ||||
\(971\) | − | 36.5063i | − | 1.17154i | −0.810476 | − | 0.585771i | \(-0.800792\pi\) | ||
0.810476 | − | 0.585771i | \(-0.199208\pi\) | |||||||
\(972\) | −11.2174 | + | 11.2174i | −0.359797 | + | 0.359797i | ||||
\(973\) | −12.0588 | + | 12.0588i | −0.386588 | + | 0.386588i | ||||
\(974\) | 10.8164i | 0.346580i | ||||||||
\(975\) | 4.05193 | − | 24.1175i | 0.129766 | − | 0.772380i | ||||
\(976\) | 13.1168i | 0.419858i | ||||||||
\(977\) | −10.4018 | − | 10.4018i | −0.332785 | − | 0.332785i | 0.520858 | − | 0.853643i | \(-0.325612\pi\) |
−0.853643 | + | 0.520858i | \(0.825612\pi\) | |||||||
\(978\) | 11.7660 | + | 11.7660i | 0.376236 | + | 0.376236i | ||||
\(979\) | − | 1.84004i | − | 0.0588080i | ||||||
\(980\) | 0.333455 | − | 3.99734i | 0.0106518 | − | 0.127690i | ||||
\(981\) | 27.7893i | 0.887245i | ||||||||
\(982\) | 4.83546 | − | 4.83546i | 0.154306 | − | 0.154306i | ||||
\(983\) | 16.4444 | − | 16.4444i | 0.524494 | − | 0.524494i | −0.394431 | − | 0.918925i | \(-0.629058\pi\) |
0.918925 | + | 0.394431i | \(0.129058\pi\) | |||||||
\(984\) | − | 2.02813i | − | 0.0646544i | ||||||
\(985\) | 7.02991 | + | 8.30952i | 0.223992 | + | 0.264763i | ||||
\(986\) | 24.0307i | 0.765293i | ||||||||
\(987\) | 3.04887 | + | 3.04887i | 0.0970465 | + | 0.0970465i | ||||
\(988\) | 10.1093 | − | 10.1093i | 0.321620 | − | 0.321620i | ||||
\(989\) | −11.6578 | + | 15.4516i | −0.370698 | + | 0.491333i | ||||
\(990\) | −4.72532 | − | 5.58544i | −0.150181 | − | 0.177517i | ||||
\(991\) | −23.2243 | −0.737743 | −0.368872 | − | 0.929480i | \(-0.620256\pi\) | ||||
−0.368872 | + | 0.929480i | \(0.620256\pi\) | |||||||
\(992\) | 4.06233 | − | 4.06233i | 0.128979 | − | 0.128979i | ||||
\(993\) | 8.24264 | + | 8.24264i | 0.261572 | + | 0.261572i | ||||
\(994\) | 27.1691 | 0.861751 | ||||||||
\(995\) | 2.94146 | − | 35.2612i | 0.0932507 | − | 1.11786i | ||||
\(996\) | 13.3940i | 0.424404i | ||||||||
\(997\) | 38.7536 | − | 38.7536i | 1.22734 | − | 1.22734i | 0.262374 | − | 0.964966i | \(-0.415495\pi\) |
0.964966 | − | 0.262374i | \(-0.0845054\pi\) | |||||||
\(998\) | −18.4985 | − | 18.4985i | −0.585560 | − | 0.585560i | ||||
\(999\) | 13.9932 | 0.442724 |
(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 | 230.2.e.b.183.4 | yes | 8 | |
5.2 | odd | 4 | 230.2.e.a.137.4 | ✓ | 8 | ||
5.3 | odd | 4 | 1150.2.e.c.1057.1 | 8 | |||
5.4 | even | 2 | 1150.2.e.b.643.1 | 8 | |||
23.22 | odd | 2 | 230.2.e.a.183.4 | yes | 8 | ||
115.22 | even | 4 | inner | 230.2.e.b.137.4 | yes | 8 | |
115.68 | even | 4 | 1150.2.e.b.1057.1 | 8 | |||
115.114 | odd | 2 | 1150.2.e.c.643.1 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
230.2.e.a.137.4 | ✓ | 8 | 5.2 | odd | 4 | ||
230.2.e.a.183.4 | yes | 8 | 23.22 | odd | 2 | ||
230.2.e.b.137.4 | yes | 8 | 115.22 | even | 4 | inner | |
230.2.e.b.183.4 | yes | 8 | 1.1 | even | 1 | trivial | |
1150.2.e.b.643.1 | 8 | 5.4 | even | 2 | |||
1150.2.e.b.1057.1 | 8 | 115.68 | even | 4 | |||
1150.2.e.c.643.1 | 8 | 115.114 | odd | 2 | |||
1150.2.e.c.1057.1 | 8 | 5.3 | odd | 4 |