Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [770,2,Mod(43,770)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(770, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([3, 0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("770.43");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 770 = 2 \cdot 5 \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 770.m (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: | \(6.14848095564\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 32x^{14} + 404x^{12} + 2600x^{10} + 9170x^{8} + 17648x^{6} + 17180x^{4} + 6904x^{2} + 529 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 197.7 | ||
Root | \(1.84585i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 770.197 |
Dual form | 770.2.m.e.43.7 |
$q$-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 \(\left(\mathbb{Z}/770\mathbb{Z}\right)^\times\).
\(n\) | \(211\) | \(617\) | \(661\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{4}\right)\) | \(1\) |
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 | ||||
\(3\) | −0.668611 | + | 0.668611i | −0.386023 | + | 0.386023i | −0.873266 | − | 0.487243i | \(-0.838002\pi\) |
0.487243 | + | 0.873266i | \(0.338002\pi\) | |||||||
\(4\) | − | 1.00000i | − | 0.500000i | ||||||
\(5\) | −2.17741 | − | 0.508801i | −0.973768 | − | 0.227543i | ||||
\(6\) | 0.945559i | 0.386023i | ||||||||
\(7\) | −0.707107 | + | 0.707107i | −0.267261 | + | 0.267261i | ||||
\(8\) | −0.707107 | − | 0.707107i | −0.250000 | − | 0.250000i | ||||
\(9\) | 2.10592i | 0.701973i | ||||||||
\(10\) | −1.89944 | + | 1.17989i | −0.600655 | + | 0.373113i | ||||
\(11\) | 2.68621 | − | 1.94532i | 0.809924 | − | 0.586535i | ||||
\(12\) | 0.668611 | + | 0.668611i | 0.193011 | + | 0.193011i | ||||
\(13\) | 1.94532 | + | 1.94532i | 0.539534 | + | 0.539534i | 0.923392 | − | 0.383858i | \(-0.125405\pi\) |
−0.383858 | + | 0.923392i | \(0.625405\pi\) | |||||||
\(14\) | 1.00000i | 0.267261i | ||||||||
\(15\) | 1.79603 | − | 1.11565i | 0.463733 | − | 0.288060i | ||||
\(16\) | −1.00000 | −0.250000 | ||||||||
\(17\) | 3.61043 | − | 3.61043i | 0.875658 | − | 0.875658i | −0.117424 | − | 0.993082i | \(-0.537464\pi\) |
0.993082 | + | 0.117424i | \(0.0374637\pi\) | |||||||
\(18\) | 1.48911 | + | 1.48911i | 0.350986 | + | 0.350986i | ||||
\(19\) | 3.79888 | 0.871522 | 0.435761 | − | 0.900062i | \(-0.356479\pi\) | ||||
0.435761 | + | 0.900062i | \(0.356479\pi\) | |||||||
\(20\) | −0.508801 | + | 2.17741i | −0.113771 | + | 0.486884i | ||||
\(21\) | − | 0.945559i | − | 0.206338i | ||||||
\(22\) | 0.523891 | − | 3.27499i | 0.111694 | − | 0.698230i | ||||
\(23\) | 6.28411 | − | 6.28411i | 1.31033 | − | 1.31033i | 0.389155 | − | 0.921172i | \(-0.372767\pi\) |
0.921172 | − | 0.389155i | \(-0.127233\pi\) | |||||||
\(24\) | 0.945559 | 0.193011 | ||||||||
\(25\) | 4.48224 | + | 2.21574i | 0.896449 | + | 0.443147i | ||||
\(26\) | 2.75110 | 0.539534 | ||||||||
\(27\) | −3.41387 | − | 3.41387i | −0.657000 | − | 0.657000i | ||||
\(28\) | 0.707107 | + | 0.707107i | 0.133631 | + | 0.133631i | ||||
\(29\) | 4.14263 | 0.769268 | 0.384634 | − | 0.923069i | \(-0.374328\pi\) | ||||
0.384634 | + | 0.923069i | \(0.374328\pi\) | |||||||
\(30\) | 0.481101 | − | 2.05887i | 0.0878366 | − | 0.375897i | ||||
\(31\) | −5.10592 | −0.917050 | −0.458525 | − | 0.888681i | \(-0.651622\pi\) | ||||
−0.458525 | + | 0.888681i | \(0.651622\pi\) | |||||||
\(32\) | −0.707107 | + | 0.707107i | −0.125000 | + | 0.125000i | ||||
\(33\) | −0.495370 | + | 3.09669i | −0.0862329 | + | 0.539065i | ||||
\(34\) | − | 5.10592i | − | 0.875658i | ||||||
\(35\) | 1.89944 | − | 1.17989i | 0.321064 | − | 0.199437i | ||||
\(36\) | 2.10592 | 0.350986 | ||||||||
\(37\) | −6.35482 | − | 6.35482i | −1.04473 | − | 1.04473i | −0.998952 | − | 0.0457748i | \(-0.985424\pi\) |
−0.0457748 | − | 0.998952i | \(-0.514576\pi\) | |||||||
\(38\) | 2.68621 | − | 2.68621i | 0.435761 | − | 0.435761i | ||||
\(39\) | −2.60132 | −0.416545 | ||||||||
\(40\) | 1.17989 | + | 1.89944i | 0.186556 | + | 0.300328i | ||||
\(41\) | 5.80665i | 0.906846i | 0.891296 | + | 0.453423i | \(0.149797\pi\) | ||||
−0.891296 | + | 0.453423i | \(0.850203\pi\) | |||||||
\(42\) | −0.668611 | − | 0.668611i | −0.103169 | − | 0.103169i | ||||
\(43\) | 8.15817 | + | 8.15817i | 1.24411 | + | 1.24411i | 0.958281 | + | 0.285828i | \(0.0922687\pi\) |
0.285828 | + | 0.958281i | \(0.407731\pi\) | |||||||
\(44\) | −1.94532 | − | 2.68621i | −0.293268 | − | 0.404962i | ||||
\(45\) | 1.07149 | − | 4.58545i | 0.159729 | − | 0.683559i | ||||
\(46\) | − | 8.88707i | − | 1.31033i | ||||||
\(47\) | −0.337222 | − | 0.337222i | −0.0491889 | − | 0.0491889i | 0.682084 | − | 0.731273i | \(-0.261074\pi\) |
−0.731273 | + | 0.682084i | \(0.761074\pi\) | |||||||
\(48\) | 0.668611 | − | 0.668611i | 0.0965057 | − | 0.0965057i | ||||
\(49\) | − | 1.00000i | − | 0.142857i | ||||||
\(50\) | 4.73619 | − | 1.60266i | 0.669798 | − | 0.226651i | ||||
\(51\) | 4.82795i | 0.676048i | ||||||||
\(52\) | 1.94532 | − | 1.94532i | 0.269767 | − | 0.269767i | ||||
\(53\) | 5.85701 | − | 5.85701i | 0.804523 | − | 0.804523i | −0.179276 | − | 0.983799i | \(-0.557376\pi\) |
0.983799 | + | 0.179276i | \(0.0573755\pi\) | |||||||
\(54\) | −4.82795 | −0.657000 | ||||||||
\(55\) | −6.83877 | + | 2.86901i | −0.922140 | + | 0.386857i | ||||
\(56\) | 1.00000 | 0.133631 | ||||||||
\(57\) | −2.53997 | + | 2.53997i | −0.336427 | + | 0.336427i | ||||
\(58\) | 2.92928 | − | 2.92928i | 0.384634 | − | 0.384634i | ||||
\(59\) | 13.4843i | 1.75550i | 0.479116 | + | 0.877752i | \(0.340957\pi\) | ||||
−0.479116 | + | 0.877752i | \(0.659043\pi\) | |||||||
\(60\) | −1.11565 | − | 1.79603i | −0.144030 | − | 0.231867i | ||||
\(61\) | − | 0.995343i | − | 0.127441i | −0.997968 | − | 0.0637203i | \(-0.979703\pi\) | ||
0.997968 | − | 0.0637203i | \(-0.0202966\pi\) | |||||||
\(62\) | −3.61043 | + | 3.61043i | −0.458525 | + | 0.458525i | ||||
\(63\) | −1.48911 | − | 1.48911i | −0.187610 | − | 0.187610i | ||||
\(64\) | 1.00000i | 0.125000i | ||||||||
\(65\) | −3.24598 | − | 5.22554i | −0.402614 | − | 0.648148i | ||||
\(66\) | 1.83941 | + | 2.53997i | 0.226416 | + | 0.312649i | ||||
\(67\) | −2.69798 | − | 2.69798i | −0.329611 | − | 0.329611i | 0.522828 | − | 0.852438i | \(-0.324877\pi\) |
−0.852438 | + | 0.522828i | \(0.824877\pi\) | |||||||
\(68\) | −3.61043 | − | 3.61043i | −0.437829 | − | 0.437829i | ||||
\(69\) | 8.40325i | 1.01163i | ||||||||
\(70\) | 0.508801 | − | 2.17741i | 0.0608133 | − | 0.260250i | ||||
\(71\) | 4.97615 | 0.590561 | 0.295280 | − | 0.955411i | \(-0.404587\pi\) | ||||
0.295280 | + | 0.955411i | \(0.404587\pi\) | |||||||
\(72\) | 1.48911 | − | 1.48911i | 0.175493 | − | 0.175493i | ||||
\(73\) | −3.48553 | − | 3.48553i | −0.407950 | − | 0.407950i | 0.473073 | − | 0.881023i | \(-0.343145\pi\) |
−0.881023 | + | 0.473073i | \(0.843145\pi\) | |||||||
\(74\) | −8.98708 | −1.04473 | ||||||||
\(75\) | −4.47834 | + | 1.51541i | −0.517115 | + | 0.174985i | ||||
\(76\) | − | 3.79888i | − | 0.435761i | ||||||
\(77\) | −0.523891 | + | 3.27499i | −0.0597030 | + | 0.373219i | ||||
\(78\) | −1.83941 | + | 1.83941i | −0.208272 | + | 0.208272i | ||||
\(79\) | 8.68486 | 0.977123 | 0.488561 | − | 0.872530i | \(-0.337522\pi\) | ||||
0.488561 | + | 0.872530i | \(0.337522\pi\) | |||||||
\(80\) | 2.17741 | + | 0.508801i | 0.243442 | + | 0.0568857i | ||||
\(81\) | −1.75265 | −0.194739 | ||||||||
\(82\) | 4.10592 | + | 4.10592i | 0.453423 | + | 0.453423i | ||||
\(83\) | 8.86108 | + | 8.86108i | 0.972630 | + | 0.972630i | 0.999635 | − | 0.0270055i | \(-0.00859717\pi\) |
−0.0270055 | + | 0.999635i | \(0.508597\pi\) | |||||||
\(84\) | −0.945559 | −0.103169 | ||||||||
\(85\) | −9.69838 | + | 6.02440i | −1.05194 | + | 0.653438i | ||||
\(86\) | 11.5374 | 1.24411 | ||||||||
\(87\) | −2.76981 | + | 2.76981i | −0.296955 | + | 0.296955i | ||||
\(88\) | −3.27499 | − | 0.523891i | −0.349115 | − | 0.0558470i | ||||
\(89\) | − | 6.56822i | − | 0.696229i | −0.937452 | − | 0.348115i | \(-0.886822\pi\) | ||
0.937452 | − | 0.348115i | \(-0.113178\pi\) | |||||||
\(90\) | −2.48474 | − | 4.00006i | −0.261915 | − | 0.421644i | ||||
\(91\) | −2.75110 | −0.288393 | ||||||||
\(92\) | −6.28411 | − | 6.28411i | −0.655164 | − | 0.655164i | ||||
\(93\) | 3.41387 | − | 3.41387i | 0.354002 | − | 0.354002i | ||||
\(94\) | −0.476904 | −0.0491889 | ||||||||
\(95\) | −8.27172 | − | 1.93287i | −0.848661 | − | 0.198308i | ||||
\(96\) | − | 0.945559i | − | 0.0965057i | ||||||
\(97\) | −5.10592 | − | 5.10592i | −0.518427 | − | 0.518427i | 0.398668 | − | 0.917095i | \(-0.369473\pi\) |
−0.917095 | + | 0.398668i | \(0.869473\pi\) | |||||||
\(98\) | −0.707107 | − | 0.707107i | −0.0714286 | − | 0.0714286i | ||||
\(99\) | 4.09668 | + | 5.65695i | 0.411732 | + | 0.568544i | ||||
\(100\) | 2.21574 | − | 4.48224i | 0.221574 | − | 0.448224i | ||||
\(101\) | 16.0748i | 1.59950i | 0.600332 | + | 0.799751i | \(0.295035\pi\) | ||||
−0.600332 | + | 0.799751i | \(0.704965\pi\) | |||||||
\(102\) | 3.41387 | + | 3.41387i | 0.338024 | + | 0.338024i | ||||
\(103\) | 2.37242 | − | 2.37242i | 0.233762 | − | 0.233762i | −0.580499 | − | 0.814261i | \(-0.697142\pi\) |
0.814261 | + | 0.580499i | \(0.197142\pi\) | |||||||
\(104\) | − | 2.75110i | − | 0.269767i | ||||||
\(105\) | −0.481101 | + | 2.05887i | −0.0469506 | + | 0.200925i | ||||
\(106\) | − | 8.28307i | − | 0.804523i | ||||||
\(107\) | 0.568662 | − | 0.568662i | 0.0549746 | − | 0.0549746i | −0.679085 | − | 0.734060i | \(-0.737623\pi\) |
0.734060 | + | 0.679085i | \(0.237623\pi\) | |||||||
\(108\) | −3.41387 | + | 3.41387i | −0.328500 | + | 0.328500i | ||||
\(109\) | 4.82795 | 0.462433 | 0.231217 | − | 0.972902i | \(-0.425729\pi\) | ||||
0.231217 | + | 0.972902i | \(0.425729\pi\) | |||||||
\(110\) | −2.80704 | + | 6.86444i | −0.267641 | + | 0.654498i | ||||
\(111\) | 8.49781 | 0.806576 | ||||||||
\(112\) | 0.707107 | − | 0.707107i | 0.0668153 | − | 0.0668153i | ||||
\(113\) | −10.4783 | + | 10.4783i | −0.985720 | + | 0.985720i | −0.999899 | − | 0.0141798i | \(-0.995486\pi\) |
0.0141798 | + | 0.999899i | \(0.495486\pi\) | |||||||
\(114\) | 3.59206i | 0.336427i | ||||||||
\(115\) | −16.8804 | + | 10.4857i | −1.57411 | + | 0.977799i | ||||
\(116\) | − | 4.14263i | − | 0.384634i | ||||||
\(117\) | −4.09668 | + | 4.09668i | −0.378738 | + | 0.378738i | ||||
\(118\) | 9.53483 | + | 9.53483i | 0.877752 | + | 0.877752i | ||||
\(119\) | 5.10592i | 0.468059i | ||||||||
\(120\) | −2.05887 | − | 0.481101i | −0.187948 | − | 0.0439183i | ||||
\(121\) | 3.43147 | − | 10.4511i | 0.311952 | − | 0.950098i | ||||
\(122\) | −0.703814 | − | 0.703814i | −0.0637203 | − | 0.0637203i | ||||
\(123\) | −3.88239 | − | 3.88239i | −0.350063 | − | 0.350063i | ||||
\(124\) | 5.10592i | 0.458525i | ||||||||
\(125\) | −8.63232 | − | 7.10514i | −0.772098 | − | 0.635503i | ||||
\(126\) | −2.10592 | −0.187610 | ||||||||
\(127\) | 11.6188 | − | 11.6188i | 1.03100 | − | 1.03100i | 0.0314986 | − | 0.999504i | \(-0.489972\pi\) |
0.999504 | − | 0.0314986i | \(-0.0100280\pi\) | |||||||
\(128\) | 0.707107 | + | 0.707107i | 0.0625000 | + | 0.0625000i | ||||
\(129\) | −10.9093 | −0.960509 | ||||||||
\(130\) | −5.99027 | − | 1.39976i | −0.525381 | − | 0.122767i | ||||
\(131\) | − | 15.1126i | − | 1.32039i | −0.751093 | − | 0.660196i | \(-0.770473\pi\) | ||
0.751093 | − | 0.660196i | \(-0.229527\pi\) | |||||||
\(132\) | 3.09669 | + | 0.495370i | 0.269532 | + | 0.0431164i | ||||
\(133\) | −2.68621 | + | 2.68621i | −0.232924 | + | 0.232924i | ||||
\(134\) | −3.81552 | −0.329611 | ||||||||
\(135\) | 5.69643 | + | 9.17039i | 0.490270 | + | 0.789261i | ||||
\(136\) | −5.10592 | −0.437829 | ||||||||
\(137\) | −2.60373 | − | 2.60373i | −0.222452 | − | 0.222452i | 0.587078 | − | 0.809530i | \(-0.300278\pi\) |
−0.809530 | + | 0.587078i | \(0.800278\pi\) | |||||||
\(138\) | 5.94199 | + | 5.94199i | 0.505816 | + | 0.505816i | ||||
\(139\) | −15.4144 | −1.30743 | −0.653715 | − | 0.756741i | \(-0.726790\pi\) | ||||
−0.653715 | + | 0.756741i | \(0.726790\pi\) | |||||||
\(140\) | −1.17989 | − | 1.89944i | −0.0997186 | − | 0.160532i | ||||
\(141\) | 0.450941 | 0.0379760 | ||||||||
\(142\) | 3.51867 | − | 3.51867i | 0.295280 | − | 0.295280i | ||||
\(143\) | 9.00980 | + | 1.44128i | 0.753437 | + | 0.120525i | ||||
\(144\) | − | 2.10592i | − | 0.175493i | ||||||
\(145\) | −9.02022 | − | 2.10778i | −0.749088 | − | 0.175041i | ||||
\(146\) | −4.92928 | −0.407950 | ||||||||
\(147\) | 0.668611 | + | 0.668611i | 0.0551461 | + | 0.0551461i | ||||
\(148\) | −6.35482 | + | 6.35482i | −0.522363 | + | 0.522363i | ||||
\(149\) | −3.64084 | −0.298269 | −0.149135 | − | 0.988817i | \(-0.547649\pi\) | ||||
−0.149135 | + | 0.988817i | \(0.547649\pi\) | |||||||
\(150\) | −2.09511 | + | 4.23822i | −0.171065 | + | 0.346050i | ||||
\(151\) | − | 0.183516i | − | 0.0149343i | −0.999972 | − | 0.00746717i | \(-0.997623\pi\) | ||
0.999972 | − | 0.00746717i | \(-0.00237690\pi\) | |||||||
\(152\) | −2.68621 | − | 2.68621i | −0.217881 | − | 0.217881i | ||||
\(153\) | 7.60327 | + | 7.60327i | 0.614688 | + | 0.614688i | ||||
\(154\) | 1.94532 | + | 2.68621i | 0.156758 | + | 0.216461i | ||||
\(155\) | 11.1177 | + | 2.59790i | 0.892994 | + | 0.208668i | ||||
\(156\) | 2.60132i | 0.208272i | ||||||||
\(157\) | −7.02937 | − | 7.02937i | −0.561005 | − | 0.561005i | 0.368588 | − | 0.929593i | \(-0.379841\pi\) |
−0.929593 | + | 0.368588i | \(0.879841\pi\) | |||||||
\(158\) | 6.14112 | − | 6.14112i | 0.488561 | − | 0.488561i | ||||
\(159\) | 7.83213i | 0.621128i | ||||||||
\(160\) | 1.89944 | − | 1.17989i | 0.150164 | − | 0.0932782i | ||||
\(161\) | 8.88707i | 0.700399i | ||||||||
\(162\) | −1.23931 | + | 1.23931i | −0.0973694 | + | 0.0973694i | ||||
\(163\) | −5.14737 | + | 5.14737i | −0.403173 | + | 0.403173i | −0.879350 | − | 0.476177i | \(-0.842022\pi\) |
0.476177 | + | 0.879350i | \(0.342022\pi\) | |||||||
\(164\) | 5.80665 | 0.453423 | ||||||||
\(165\) | 2.65422 | − | 6.49073i | 0.206631 | − | 0.505303i | ||||
\(166\) | 12.5315 | 0.972630 | ||||||||
\(167\) | 8.05816 | − | 8.05816i | 0.623559 | − | 0.623559i | −0.322880 | − | 0.946440i | \(-0.604651\pi\) |
0.946440 | + | 0.322880i | \(0.104651\pi\) | |||||||
\(168\) | −0.668611 | + | 0.668611i | −0.0515845 | + | 0.0515845i | ||||
\(169\) | − | 5.43147i | − | 0.417806i | ||||||
\(170\) | −2.59790 | + | 11.1177i | −0.199249 | + | 0.852688i | ||||
\(171\) | 8.00013i | 0.611785i | ||||||||
\(172\) | 8.15817 | − | 8.15817i | 0.622055 | − | 0.622055i | ||||
\(173\) | −14.5064 | − | 14.5064i | −1.10290 | − | 1.10290i | −0.994059 | − | 0.108839i | \(-0.965287\pi\) |
−0.108839 | − | 0.994059i | \(-0.534713\pi\) | |||||||
\(174\) | 3.91710i | 0.296955i | ||||||||
\(175\) | −4.73619 | + | 1.60266i | −0.358022 | + | 0.121150i | ||||
\(176\) | −2.68621 | + | 1.94532i | −0.202481 | + | 0.146634i | ||||
\(177\) | −9.01574 | − | 9.01574i | −0.677664 | − | 0.677664i | ||||
\(178\) | −4.64443 | − | 4.64443i | −0.348115 | − | 0.348115i | ||||
\(179\) | 18.3885i | 1.37442i | 0.726459 | + | 0.687209i | \(0.241165\pi\) | ||||
−0.726459 | + | 0.687209i | \(0.758835\pi\) | |||||||
\(180\) | −4.58545 | − | 1.07149i | −0.341779 | − | 0.0798644i | ||||
\(181\) | 1.85701 | 0.138031 | 0.0690154 | − | 0.997616i | \(-0.478014\pi\) | ||||
0.0690154 | + | 0.997616i | \(0.478014\pi\) | |||||||
\(182\) | −1.94532 | + | 1.94532i | −0.144197 | + | 0.144197i | ||||
\(183\) | 0.665497 | + | 0.665497i | 0.0491950 | + | 0.0491950i | ||||
\(184\) | −8.88707 | −0.655164 | ||||||||
\(185\) | 10.6037 | + | 17.0704i | 0.779602 | + | 1.25504i | ||||
\(186\) | − | 4.82795i | − | 0.354002i | ||||||
\(187\) | 2.67495 | − | 16.7218i | 0.195611 | − | 1.22282i | ||||
\(188\) | −0.337222 | + | 0.337222i | −0.0245944 | + | 0.0245944i | ||||
\(189\) | 4.82795 | 0.351181 | ||||||||
\(190\) | −7.21574 | + | 4.48224i | −0.523485 | + | 0.325176i | ||||
\(191\) | −3.02385 | −0.218798 | −0.109399 | − | 0.993998i | \(-0.534893\pi\) | ||||
−0.109399 | + | 0.993998i | \(0.534893\pi\) | |||||||
\(192\) | −0.668611 | − | 0.668611i | −0.0482528 | − | 0.0482528i | ||||
\(193\) | −15.9830 | − | 15.9830i | −1.15048 | − | 1.15048i | −0.986456 | − | 0.164028i | \(-0.947551\pi\) |
−0.164028 | − | 0.986456i | \(-0.552449\pi\) | |||||||
\(194\) | −7.22086 | −0.518427 | ||||||||
\(195\) | 5.66415 | + | 1.32355i | 0.405618 | + | 0.0947817i | ||||
\(196\) | −1.00000 | −0.0714286 | ||||||||
\(197\) | −10.4344 | + | 10.4344i | −0.743423 | + | 0.743423i | −0.973235 | − | 0.229812i | \(-0.926189\pi\) |
0.229812 | + | 0.973235i | \(0.426189\pi\) | |||||||
\(198\) | 6.89686 | + | 1.10327i | 0.490138 | + | 0.0784062i | ||||
\(199\) | − | 9.63893i | − | 0.683286i | −0.939830 | − | 0.341643i | \(-0.889017\pi\) | ||
0.939830 | − | 0.341643i | \(-0.110983\pi\) | |||||||
\(200\) | −1.60266 | − | 4.73619i | −0.113325 | − | 0.334899i | ||||
\(201\) | 3.60780 | 0.254475 | ||||||||
\(202\) | 11.3666 | + | 11.3666i | 0.799751 | + | 0.799751i | ||||
\(203\) | −2.92928 | + | 2.92928i | −0.205595 | + | 0.205595i | ||||
\(204\) | 4.82795 | 0.338024 | ||||||||
\(205\) | 2.95443 | − | 12.6435i | 0.206346 | − | 0.883057i | ||||
\(206\) | − | 3.35512i | − | 0.233762i | ||||||
\(207\) | 13.2338 | + | 13.2338i | 0.919814 | + | 0.919814i | ||||
\(208\) | −1.94532 | − | 1.94532i | −0.134884 | − | 0.134884i | ||||
\(209\) | 10.2046 | − | 7.39003i | 0.705867 | − | 0.511179i | ||||
\(210\) | 1.11565 | + | 1.79603i | 0.0769873 | + | 0.123938i | ||||
\(211\) | 21.6150i | 1.48804i | 0.668159 | + | 0.744019i | \(0.267083\pi\) | ||||
−0.668159 | + | 0.744019i | \(0.732917\pi\) | |||||||
\(212\) | −5.85701 | − | 5.85701i | −0.402261 | − | 0.402261i | ||||
\(213\) | −3.32711 | + | 3.32711i | −0.227970 | + | 0.227970i | ||||
\(214\) | − | 0.804210i | − | 0.0549746i | ||||||
\(215\) | −13.6128 | − | 21.9146i | −0.928386 | − | 1.49456i | ||||
\(216\) | 4.82795i | 0.328500i | ||||||||
\(217\) | 3.61043 | − | 3.61043i | 0.245092 | − | 0.245092i | ||||
\(218\) | 3.41387 | − | 3.41387i | 0.231217 | − | 0.231217i | ||||
\(219\) | 4.66093 | 0.314956 | ||||||||
\(220\) | 2.86901 | + | 6.83877i | 0.193429 | + | 0.461070i | ||||
\(221\) | 14.0469 | 0.944895 | ||||||||
\(222\) | 6.00886 | − | 6.00886i | 0.403288 | − | 0.403288i | ||||
\(223\) | −15.6081 | + | 15.6081i | −1.04520 | + | 1.04520i | −0.0462672 | + | 0.998929i | \(0.514733\pi\) |
−0.998929 | + | 0.0462672i | \(0.985267\pi\) | |||||||
\(224\) | − | 1.00000i | − | 0.0668153i | ||||||
\(225\) | −4.66616 | + | 9.43924i | −0.311078 | + | 0.629283i | ||||
\(226\) | 14.8186i | 0.985720i | ||||||||
\(227\) | 7.17217 | − | 7.17217i | 0.476034 | − | 0.476034i | −0.427827 | − | 0.903861i | \(-0.640721\pi\) |
0.903861 | + | 0.427827i | \(0.140721\pi\) | |||||||
\(228\) | 2.53997 | + | 2.53997i | 0.168214 | + | 0.168214i | ||||
\(229\) | 6.01011i | 0.397159i | 0.980085 | + | 0.198580i | \(0.0636329\pi\) | ||||
−0.980085 | + | 0.198580i | \(0.936367\pi\) | |||||||
\(230\) | −4.52175 | + | 19.3508i | −0.298155 | + | 1.27595i | ||||
\(231\) | −1.83941 | − | 2.53997i | −0.121024 | − | 0.167118i | ||||
\(232\) | −2.92928 | − | 2.92928i | −0.192317 | − | 0.192317i | ||||
\(233\) | 12.5141 | + | 12.5141i | 0.819829 | + | 0.819829i | 0.986083 | − | 0.166254i | \(-0.0531672\pi\) |
−0.166254 | + | 0.986083i | \(0.553167\pi\) | |||||||
\(234\) | 5.79358i | 0.378738i | ||||||||
\(235\) | 0.562692 | + | 0.905850i | 0.0367060 | + | 0.0590911i | ||||
\(236\) | 13.4843 | 0.877752 | ||||||||
\(237\) | −5.80679 | + | 5.80679i | −0.377192 | + | 0.377192i | ||||
\(238\) | 3.61043 | + | 3.61043i | 0.234029 | + | 0.234029i | ||||
\(239\) | 6.08354 | 0.393511 | 0.196756 | − | 0.980453i | \(-0.436959\pi\) | ||||
0.196756 | + | 0.980453i | \(0.436959\pi\) | |||||||
\(240\) | −1.79603 | + | 1.11565i | −0.115933 | + | 0.0720150i | ||||
\(241\) | 3.89903i | 0.251159i | 0.992084 | + | 0.125579i | \(0.0400790\pi\) | ||||
−0.992084 | + | 0.125579i | \(0.959921\pi\) | |||||||
\(242\) | −4.96361 | − | 9.81645i | −0.319073 | − | 0.631025i | ||||
\(243\) | 11.4135 | − | 11.4135i | 0.732174 | − | 0.732174i | ||||
\(244\) | −0.995343 | −0.0637203 | ||||||||
\(245\) | −0.508801 | + | 2.17741i | −0.0325061 | + | 0.139110i | ||||
\(246\) | −5.49052 | −0.350063 | ||||||||
\(247\) | 7.39003 | + | 7.39003i | 0.470216 | + | 0.470216i | ||||
\(248\) | 3.61043 | + | 3.61043i | 0.229263 | + | 0.229263i | ||||
\(249\) | −11.8492 | −0.750914 | ||||||||
\(250\) | −11.1281 | + | 1.07988i | −0.703801 | + | 0.0682975i | ||||
\(251\) | −2.93940 | −0.185533 | −0.0927665 | − | 0.995688i | \(-0.529571\pi\) | ||||
−0.0927665 | + | 0.995688i | \(0.529571\pi\) | |||||||
\(252\) | −1.48911 | + | 1.48911i | −0.0938051 | + | 0.0938051i | ||||
\(253\) | 4.65586 | − | 29.1050i | 0.292711 | − | 1.82982i | ||||
\(254\) | − | 16.4315i | − | 1.03100i | ||||||
\(255\) | 2.45646 | − | 10.5124i | 0.153830 | − | 0.658314i | ||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 7.73349 | + | 7.73349i | 0.482402 | + | 0.482402i | 0.905898 | − | 0.423496i | \(-0.139197\pi\) |
−0.423496 | + | 0.905898i | \(0.639197\pi\) | |||||||
\(258\) | −7.71403 | + | 7.71403i | −0.480254 | + | 0.480254i | ||||
\(259\) | 8.98708 | 0.558430 | ||||||||
\(260\) | −5.22554 | + | 3.24598i | −0.324074 | + | 0.201307i | ||||
\(261\) | 8.72405i | 0.540005i | ||||||||
\(262\) | −10.6862 | − | 10.6862i | −0.660196 | − | 0.660196i | ||||
\(263\) | −15.1292 | − | 15.1292i | −0.932908 | − | 0.932908i | 0.0649784 | − | 0.997887i | \(-0.479302\pi\) |
−0.997887 | + | 0.0649784i | \(0.979302\pi\) | |||||||
\(264\) | 2.53997 | − | 1.83941i | 0.156324 | − | 0.113208i | ||||
\(265\) | −15.7332 | + | 9.77308i | −0.966482 | + | 0.600355i | ||||
\(266\) | 3.79888i | 0.232924i | ||||||||
\(267\) | 4.39158 | + | 4.39158i | 0.268760 | + | 0.268760i | ||||
\(268\) | −2.69798 | + | 2.69798i | −0.164805 | + | 0.164805i | ||||
\(269\) | 25.8212i | 1.57435i | 0.616732 | + | 0.787173i | \(0.288456\pi\) | ||||
−0.616732 | + | 0.787173i | \(0.711544\pi\) | |||||||
\(270\) | 10.5124 | + | 2.45646i | 0.639766 | + | 0.149496i | ||||
\(271\) | 7.45416i | 0.452808i | 0.974033 | + | 0.226404i | \(0.0726970\pi\) | ||||
−0.974033 | + | 0.226404i | \(0.927303\pi\) | |||||||
\(272\) | −3.61043 | + | 3.61043i | −0.218914 | + | 0.218914i | ||||
\(273\) | 1.83941 | − | 1.83941i | 0.111326 | − | 0.111326i | ||||
\(274\) | −3.68223 | −0.222452 | ||||||||
\(275\) | 16.3506 | − | 2.76745i | 0.985977 | − | 0.166883i | ||||
\(276\) | 8.40325 | 0.505816 | ||||||||
\(277\) | −5.86526 | + | 5.86526i | −0.352409 | + | 0.352409i | −0.861005 | − | 0.508596i | \(-0.830165\pi\) |
0.508596 | + | 0.861005i | \(0.330165\pi\) | |||||||
\(278\) | −10.8996 | + | 10.8996i | −0.653715 | + | 0.653715i | ||||
\(279\) | − | 10.7526i | − | 0.643744i | ||||||
\(280\) | −2.17741 | − | 0.508801i | −0.130125 | − | 0.0304067i | ||||
\(281\) | − | 2.20173i | − | 0.131344i | −0.997841 | − | 0.0656721i | \(-0.979081\pi\) | ||
0.997841 | − | 0.0656721i | \(-0.0209191\pi\) | |||||||
\(282\) | 0.318863 | − | 0.318863i | 0.0189880 | − | 0.0189880i | ||||
\(283\) | 19.2375 | + | 19.2375i | 1.14355 | + | 1.14355i | 0.987796 | + | 0.155753i | \(0.0497805\pi\) |
0.155753 | + | 0.987796i | \(0.450219\pi\) | |||||||
\(284\) | − | 4.97615i | − | 0.295280i | ||||||
\(285\) | 6.82290 | − | 4.23822i | 0.404154 | − | 0.251051i | ||||
\(286\) | 7.39003 | − | 5.35176i | 0.436981 | − | 0.316456i | ||||
\(287\) | −4.10592 | − | 4.10592i | −0.242365 | − | 0.242365i | ||||
\(288\) | −1.48911 | − | 1.48911i | −0.0877466 | − | 0.0877466i | ||||
\(289\) | − | 9.07041i | − | 0.533553i | ||||||
\(290\) | −7.86868 | + | 4.88784i | −0.462065 | + | 0.287024i | ||||
\(291\) | 6.82775 | 0.400250 | ||||||||
\(292\) | −3.48553 | + | 3.48553i | −0.203975 | + | 0.203975i | ||||
\(293\) | −15.7686 | − | 15.7686i | −0.921211 | − | 0.921211i | 0.0759042 | − | 0.997115i | \(-0.475816\pi\) |
−0.997115 | + | 0.0759042i | \(0.975816\pi\) | |||||||
\(294\) | 0.945559 | 0.0551461 | ||||||||
\(295\) | 6.86081 | − | 29.3608i | 0.399452 | − | 1.70945i | ||||
\(296\) | 8.98708i | 0.522363i | ||||||||
\(297\) | −15.8115 | − | 2.52932i | −0.917474 | − | 0.146766i | ||||
\(298\) | −2.57446 | + | 2.57446i | −0.149135 | + | 0.149135i | ||||
\(299\) | 24.4492 | 1.41393 | ||||||||
\(300\) | 1.51541 | + | 4.47834i | 0.0874923 | + | 0.258557i | ||||
\(301\) | −11.5374 | −0.665004 | ||||||||
\(302\) | −0.129766 | − | 0.129766i | −0.00746717 | − | 0.00746717i | ||||
\(303\) | −10.7478 | − | 10.7478i | −0.617444 | − | 0.617444i | ||||
\(304\) | −3.79888 | −0.217881 | ||||||||
\(305\) | −0.506431 | + | 2.16727i | −0.0289982 | + | 0.124098i | ||||
\(306\) | 10.7526 | 0.614688 | ||||||||
\(307\) | 6.64285 | − | 6.64285i | 0.379127 | − | 0.379127i | −0.491660 | − | 0.870787i | \(-0.663610\pi\) |
0.870787 | + | 0.491660i | \(0.163610\pi\) | |||||||
\(308\) | 3.27499 | + | 0.523891i | 0.186610 | + | 0.0298515i | ||||
\(309\) | 3.17246i | 0.180475i | ||||||||
\(310\) | 9.69838 | − | 6.02440i | 0.550831 | − | 0.342163i | ||||
\(311\) | 16.8583 | 0.955944 | 0.477972 | − | 0.878375i | \(-0.341372\pi\) | ||||
0.477972 | + | 0.878375i | \(0.341372\pi\) | |||||||
\(312\) | 1.83941 | + | 1.83941i | 0.104136 | + | 0.104136i | ||||
\(313\) | 8.87462 | − | 8.87462i | 0.501623 | − | 0.501623i | −0.410319 | − | 0.911942i | \(-0.634583\pi\) |
0.911942 | + | 0.410319i | \(0.134583\pi\) | |||||||
\(314\) | −9.94103 | −0.561005 | ||||||||
\(315\) | 2.48474 | + | 4.00006i | 0.139999 | + | 0.225378i | ||||
\(316\) | − | 8.68486i | − | 0.488561i | ||||||
\(317\) | −15.2826 | − | 15.2826i | −0.858354 | − | 0.858354i | 0.132790 | − | 0.991144i | \(-0.457606\pi\) |
−0.991144 | + | 0.132790i | \(0.957606\pi\) | |||||||
\(318\) | 5.53815 | + | 5.53815i | 0.310564 | + | 0.310564i | ||||
\(319\) | 11.1280 | − | 8.05874i | 0.623048 | − | 0.451203i | ||||
\(320\) | 0.508801 | − | 2.17741i | 0.0284428 | − | 0.121721i | ||||
\(321\) | 0.760427i | 0.0424429i | ||||||||
\(322\) | 6.28411 | + | 6.28411i | 0.350200 | + | 0.350200i | ||||
\(323\) | 13.7156 | − | 13.7156i | 0.763155 | − | 0.763155i | ||||
\(324\) | 1.75265i | 0.0973694i | ||||||||
\(325\) | 4.40908 | + | 13.0297i | 0.244572 | + | 0.722758i | ||||
\(326\) | 7.27948i | 0.403173i | ||||||||
\(327\) | −3.22802 | + | 3.22802i | −0.178510 | + | 0.178510i | ||||
\(328\) | 4.10592 | − | 4.10592i | 0.226711 | − | 0.226711i | ||||
\(329\) | 0.476904 | 0.0262926 | ||||||||
\(330\) | −2.71282 | − | 6.46646i | −0.149336 | − | 0.355967i | ||||
\(331\) | −3.20766 | −0.176309 | −0.0881545 | − | 0.996107i | \(-0.528097\pi\) | ||||
−0.0881545 | + | 0.996107i | \(0.528097\pi\) | |||||||
\(332\) | 8.86108 | − | 8.86108i | 0.486315 | − | 0.486315i | ||||
\(333\) | 13.3827 | − | 13.3827i | 0.733370 | − | 0.733370i | ||||
\(334\) | − | 11.3960i | − | 0.623559i | ||||||
\(335\) | 4.50188 | + | 7.24735i | 0.245964 | + | 0.395965i | ||||
\(336\) | 0.945559i | 0.0515845i | ||||||||
\(337\) | −22.5772 | + | 22.5772i | −1.22986 | + | 1.22986i | −0.265841 | + | 0.964017i | \(0.585650\pi\) |
−0.964017 | + | 0.265841i | \(0.914350\pi\) | |||||||
\(338\) | −3.84063 | − | 3.84063i | −0.208903 | − | 0.208903i | ||||
\(339\) | − | 14.0119i | − | 0.761020i | ||||||
\(340\) | 6.02440 | + | 9.69838i | 0.326719 | + | 0.525969i | ||||
\(341\) | −13.7156 | + | 9.93264i | −0.742740 | + | 0.537882i | ||||
\(342\) | 5.65695 | + | 5.65695i | 0.305893 | + | 0.305893i | ||||
\(343\) | 0.707107 | + | 0.707107i | 0.0381802 | + | 0.0381802i | ||||
\(344\) | − | 11.5374i | − | 0.622055i | ||||||
\(345\) | 4.27558 | − | 18.2973i | 0.230189 | − | 0.985095i | ||||
\(346\) | −20.5151 | −1.10290 | ||||||||
\(347\) | 16.8954 | − | 16.8954i | 0.906995 | − | 0.906995i | −0.0890335 | − | 0.996029i | \(-0.528378\pi\) |
0.996029 | + | 0.0890335i | \(0.0283778\pi\) | |||||||
\(348\) | 2.76981 | + | 2.76981i | 0.148477 | + | 0.148477i | ||||
\(349\) | 16.4330 | 0.879638 | 0.439819 | − | 0.898087i | \(-0.355043\pi\) | ||||
0.439819 | + | 0.898087i | \(0.355043\pi\) | |||||||
\(350\) | −2.21574 | + | 4.48224i | −0.118436 | + | 0.239586i | ||||
\(351\) | − | 13.2821i | − | 0.708948i | ||||||
\(352\) | −0.523891 | + | 3.27499i | −0.0279235 | + | 0.174557i | ||||
\(353\) | 15.5374 | − | 15.5374i | 0.826972 | − | 0.826972i | −0.160125 | − | 0.987097i | \(-0.551190\pi\) |
0.987097 | + | 0.160125i | \(0.0511897\pi\) | |||||||
\(354\) | −12.7502 | −0.677664 | ||||||||
\(355\) | −10.8351 | − | 2.53187i | −0.575069 | − | 0.134378i | ||||
\(356\) | −6.56822 | −0.348115 | ||||||||
\(357\) | −3.41387 | − | 3.41387i | −0.180681 | − | 0.180681i | ||||
\(358\) | 13.0026 | + | 13.0026i | 0.687209 | + | 0.687209i | ||||
\(359\) | −3.25511 | −0.171798 | −0.0858990 | − | 0.996304i | \(-0.527376\pi\) | ||||
−0.0858990 | + | 0.996304i | \(0.527376\pi\) | |||||||
\(360\) | −4.00006 | + | 2.48474i | −0.210822 | + | 0.130958i | ||||
\(361\) | −4.56853 | −0.240449 | ||||||||
\(362\) | 1.31311 | − | 1.31311i | 0.0690154 | − | 0.0690154i | ||||
\(363\) | 4.69338 | + | 9.28203i | 0.246339 | + | 0.487180i | ||||
\(364\) | 2.75110i | 0.144197i | ||||||||
\(365\) | 5.81599 | + | 9.36287i | 0.304423 | + | 0.490075i | ||||
\(366\) | 0.941155 | 0.0491950 | ||||||||
\(367\) | 6.46699 | + | 6.46699i | 0.337574 | + | 0.337574i | 0.855454 | − | 0.517880i | \(-0.173278\pi\) |
−0.517880 | + | 0.855454i | \(0.673278\pi\) | |||||||
\(368\) | −6.28411 | + | 6.28411i | −0.327582 | + | 0.327582i | ||||
\(369\) | −12.2283 | −0.636581 | ||||||||
\(370\) | 19.5686 | + | 4.57263i | 1.01732 | + | 0.237720i | ||||
\(371\) | 8.28307i | 0.430035i | ||||||||
\(372\) | −3.41387 | − | 3.41387i | −0.177001 | − | 0.177001i | ||||
\(373\) | −0.368648 | − | 0.368648i | −0.0190879 | − | 0.0190879i | 0.697498 | − | 0.716586i | \(-0.254296\pi\) |
−0.716586 | + | 0.697498i | \(0.754296\pi\) | |||||||
\(374\) | −9.93264 | − | 13.7156i | −0.513604 | − | 0.709216i | ||||
\(375\) | 10.5222 | − | 1.02109i | 0.543366 | − | 0.0527288i | ||||
\(376\) | 0.476904i | 0.0245944i | ||||||||
\(377\) | 8.05874 | + | 8.05874i | 0.415046 | + | 0.415046i | ||||
\(378\) | 3.41387 | − | 3.41387i | 0.175591 | − | 0.175591i | ||||
\(379\) | 28.8505i | 1.48195i | 0.671533 | + | 0.740974i | \(0.265636\pi\) | ||||
−0.671533 | + | 0.740974i | \(0.734364\pi\) | |||||||
\(380\) | −1.93287 | + | 8.27172i | −0.0991542 | + | 0.424330i | ||||
\(381\) | 15.5369i | 0.795981i | ||||||||
\(382\) | −2.13818 | + | 2.13818i | −0.109399 | + | 0.109399i | ||||
\(383\) | 9.20017 | − | 9.20017i | 0.470107 | − | 0.470107i | −0.431842 | − | 0.901949i | \(-0.642136\pi\) |
0.901949 | + | 0.431842i | \(0.142136\pi\) | |||||||
\(384\) | −0.945559 | −0.0482528 | ||||||||
\(385\) | 2.80704 | − | 6.86444i | 0.143060 | − | 0.349844i | ||||
\(386\) | −22.6034 | −1.15048 | ||||||||
\(387\) | −17.1804 | + | 17.1804i | −0.873331 | + | 0.873331i | ||||
\(388\) | −5.10592 | + | 5.10592i | −0.259214 | + | 0.259214i | ||||
\(389\) | − | 27.1364i | − | 1.37587i | −0.725772 | − | 0.687936i | \(-0.758517\pi\) | ||
0.725772 | − | 0.687936i | \(-0.241483\pi\) | |||||||
\(390\) | 4.94105 | − | 3.06926i | 0.250200 | − | 0.155418i | ||||
\(391\) | − | 45.3767i | − | 2.29480i | ||||||
\(392\) | −0.707107 | + | 0.707107i | −0.0357143 | + | 0.0357143i | ||||
\(393\) | 10.1044 | + | 10.1044i | 0.509702 | + | 0.509702i | ||||
\(394\) | 14.7565i | 0.743423i | ||||||||
\(395\) | −18.9105 | − | 4.41886i | −0.951491 | − | 0.222337i | ||||
\(396\) | 5.65695 | − | 4.09668i | 0.284272 | − | 0.205866i | ||||
\(397\) | −19.0762 | − | 19.0762i | −0.957409 | − | 0.957409i | 0.0417203 | − | 0.999129i | \(-0.486716\pi\) |
−0.999129 | + | 0.0417203i | \(0.986716\pi\) | |||||||
\(398\) | −6.81575 | − | 6.81575i | −0.341643 | − | 0.341643i | ||||
\(399\) | − | 3.59206i | − | 0.179828i | ||||||
\(400\) | −4.48224 | − | 2.21574i | −0.224112 | − | 0.110787i | ||||
\(401\) | −1.22402 | −0.0611246 | −0.0305623 | − | 0.999533i | \(-0.509730\pi\) | ||||
−0.0305623 | + | 0.999533i | \(0.509730\pi\) | |||||||
\(402\) | 2.55110 | − | 2.55110i | 0.127237 | − | 0.127237i | ||||
\(403\) | −9.93264 | − | 9.93264i | −0.494780 | − | 0.494780i | ||||
\(404\) | 16.0748 | 0.799751 | ||||||||
\(405\) | 3.81624 | + | 0.891750i | 0.189630 | + | 0.0443114i | ||||
\(406\) | 4.14263i | 0.205595i | ||||||||
\(407\) | −29.4326 | − | 4.70825i | −1.45892 | − | 0.233379i | ||||
\(408\) | 3.41387 | − | 3.41387i | 0.169012 | − | 0.169012i | ||||
\(409\) | −31.3123 | −1.54829 | −0.774146 | − | 0.633007i | \(-0.781820\pi\) | ||||
−0.774146 | + | 0.633007i | \(0.781820\pi\) | |||||||
\(410\) | −6.85118 | − | 11.0294i | −0.338356 | − | 0.544702i | ||||
\(411\) | 3.48176 | 0.171743 | ||||||||
\(412\) | −2.37242 | − | 2.37242i | −0.116881 | − | 0.116881i | ||||
\(413\) | −9.53483 | − | 9.53483i | −0.469178 | − | 0.469178i | ||||
\(414\) | 18.7154 | 0.919814 | ||||||||
\(415\) | −14.7857 | − | 23.8027i | −0.725801 | − | 1.16843i | ||||
\(416\) | −2.75110 | −0.134884 | ||||||||
\(417\) | 10.3062 | − | 10.3062i | 0.504698 | − | 0.504698i | ||||
\(418\) | 1.99020 | − | 12.4413i | 0.0973438 | − | 0.608523i | ||||
\(419\) | − | 29.6726i | − | 1.44960i | −0.688959 | − | 0.724800i | \(-0.741932\pi\) | ||
0.688959 | − | 0.724800i | \(-0.258068\pi\) | |||||||
\(420\) | 2.05887 | + | 0.481101i | 0.100463 | + | 0.0234753i | ||||
\(421\) | −25.2662 | −1.23140 | −0.615700 | − | 0.787981i | \(-0.711126\pi\) | ||||
−0.615700 | + | 0.787981i | \(0.711126\pi\) | |||||||
\(422\) | 15.2841 | + | 15.2841i | 0.744019 | + | 0.744019i | ||||
\(423\) | 0.710162 | − | 0.710162i | 0.0345293 | − | 0.0345293i | ||||
\(424\) | −8.28307 | −0.402261 | ||||||||
\(425\) | 24.1826 | − | 8.18306i | 1.17303 | − | 0.396937i | ||||
\(426\) | 4.70524i | 0.227970i | ||||||||
\(427\) | 0.703814 | + | 0.703814i | 0.0340599 | + | 0.0340599i | ||||
\(428\) | −0.568662 | − | 0.568662i | −0.0274873 | − | 0.0274873i | ||||
\(429\) | −6.98770 | + | 5.06040i | −0.337370 | + | 0.244318i | ||||
\(430\) | −25.1217 | − | 5.87023i | −1.21147 | − | 0.283088i | ||||
\(431\) | − | 24.5243i | − | 1.18129i | −0.806930 | − | 0.590647i | \(-0.798873\pi\) | ||
0.806930 | − | 0.590647i | \(-0.201127\pi\) | |||||||
\(432\) | 3.41387 | + | 3.41387i | 0.164250 | + | 0.164250i | ||||
\(433\) | 4.78785 | − | 4.78785i | 0.230090 | − | 0.230090i | −0.582640 | − | 0.812730i | \(-0.697980\pi\) |
0.812730 | + | 0.582640i | \(0.197980\pi\) | |||||||
\(434\) | − | 5.10592i | − | 0.245092i | ||||||
\(435\) | 7.44030 | − | 4.62174i | 0.356735 | − | 0.221595i | ||||
\(436\) | − | 4.82795i | − | 0.231217i | ||||||
\(437\) | 23.8726 | − | 23.8726i | 1.14198 | − | 1.14198i | ||||
\(438\) | 3.29577 | − | 3.29577i | 0.157478 | − | 0.157478i | ||||
\(439\) | −14.9182 | −0.712006 | −0.356003 | − | 0.934485i | \(-0.615861\pi\) | ||||
−0.356003 | + | 0.934485i | \(0.615861\pi\) | |||||||
\(440\) | 6.86444 | + | 2.80704i | 0.327249 | + | 0.133821i | ||||
\(441\) | 2.10592 | 0.100282 | ||||||||
\(442\) | 9.93264 | − | 9.93264i | 0.472447 | − | 0.472447i | ||||
\(443\) | −18.1041 | + | 18.1041i | −0.860150 | + | 0.860150i | −0.991355 | − | 0.131206i | \(-0.958115\pi\) |
0.131206 | + | 0.991355i | \(0.458115\pi\) | |||||||
\(444\) | − | 8.49781i | − | 0.403288i | ||||||
\(445\) | −3.34191 | + | 14.3017i | −0.158422 | + | 0.677966i | ||||
\(446\) | 22.0732i | 1.04520i | ||||||||
\(447\) | 2.43430 | − | 2.43430i | 0.115139 | − | 0.115139i | ||||
\(448\) | −0.707107 | − | 0.707107i | −0.0334077 | − | 0.0334077i | ||||
\(449\) | 18.8863i | 0.891299i | 0.895208 | + | 0.445649i | \(0.147027\pi\) | ||||
−0.895208 | + | 0.445649i | \(0.852973\pi\) | |||||||
\(450\) | 3.37508 | + | 9.97403i | 0.159103 | + | 0.470180i | ||||
\(451\) | 11.2958 | + | 15.5979i | 0.531897 | + | 0.734476i | ||||
\(452\) | 10.4783 | + | 10.4783i | 0.492860 | + | 0.492860i | ||||
\(453\) | 0.122701 | + | 0.122701i | 0.00576500 | + | 0.00576500i | ||||
\(454\) | − | 10.1430i | − | 0.476034i | ||||||
\(455\) | 5.99027 | + | 1.39976i | 0.280828 | + | 0.0656217i | ||||
\(456\) | 3.59206 | 0.168214 | ||||||||
\(457\) | 6.35866 | − | 6.35866i | 0.297446 | − | 0.297446i | −0.542567 | − | 0.840013i | \(-0.682547\pi\) |
0.840013 | + | 0.542567i | \(0.182547\pi\) | |||||||
\(458\) | 4.24979 | + | 4.24979i | 0.198580 | + | 0.198580i | ||||
\(459\) | −24.6511 | −1.15061 | ||||||||
\(460\) | 10.4857 | + | 16.8804i | 0.488900 | + | 0.787055i | ||||
\(461\) | 26.6094i | 1.23932i | 0.784870 | + | 0.619661i | \(0.212730\pi\) | ||||
−0.784870 | + | 0.619661i | \(0.787270\pi\) | |||||||
\(462\) | −3.09669 | − | 0.495370i | −0.144071 | − | 0.0230467i | ||||
\(463\) | −19.6741 | + | 19.6741i | −0.914335 | + | 0.914335i | −0.996610 | − | 0.0822751i | \(-0.973781\pi\) |
0.0822751 | + | 0.996610i | \(0.473781\pi\) | |||||||
\(464\) | −4.14263 | −0.192317 | ||||||||
\(465\) | −9.17039 | + | 5.69643i | −0.425267 | + | 0.264165i | ||||
\(466\) | 17.6977 | 0.819829 | ||||||||
\(467\) | −2.51551 | − | 2.51551i | −0.116404 | − | 0.116404i | 0.646505 | − | 0.762909i | \(-0.276230\pi\) |
−0.762909 | + | 0.646505i | \(0.776230\pi\) | |||||||
\(468\) | 4.09668 | + | 4.09668i | 0.189369 | + | 0.189369i | ||||
\(469\) | 3.81552 | 0.176184 | ||||||||
\(470\) | 1.03842 | + | 0.242649i | 0.0478986 | + | 0.0111926i | ||||
\(471\) | 9.39983 | 0.433121 | ||||||||
\(472\) | 9.53483 | − | 9.53483i | 0.438876 | − | 0.438876i | ||||
\(473\) | 37.7848 | + | 6.04434i | 1.73735 | + | 0.277919i | ||||
\(474\) | 8.21204i | 0.377192i | ||||||||
\(475\) | 17.0275 | + | 8.41732i | 0.781275 | + | 0.386213i | ||||
\(476\) | 5.10592 | 0.234029 | ||||||||
\(477\) | 12.3344 | + | 12.3344i | 0.564753 | + | 0.564753i | ||||
\(478\) | 4.30171 | − | 4.30171i | 0.196756 | − | 0.196756i | ||||
\(479\) | 29.0438 | 1.32705 | 0.663523 | − | 0.748156i | \(-0.269060\pi\) | ||||
0.663523 | + | 0.748156i | \(0.269060\pi\) | |||||||
\(480\) | −0.481101 | + | 2.05887i | −0.0219592 | + | 0.0939742i | ||||
\(481\) | − | 24.7243i | − | 1.12733i | ||||||
\(482\) | 2.75703 | + | 2.75703i | 0.125579 | + | 0.125579i | ||||
\(483\) | −5.94199 | − | 5.94199i | −0.270370 | − | 0.270370i | ||||
\(484\) | −10.4511 | − | 3.43147i | −0.475049 | − | 0.155976i | ||||
\(485\) | 8.51979 | + | 13.7156i | 0.386864 | + | 0.622793i | ||||
\(486\) | − | 16.1411i | − | 0.732174i | ||||||
\(487\) | 11.9629 | + | 11.9629i | 0.542092 | + | 0.542092i | 0.924142 | − | 0.382050i | \(-0.124782\pi\) |
−0.382050 | + | 0.924142i | \(0.624782\pi\) | |||||||
\(488\) | −0.703814 | + | 0.703814i | −0.0318602 | + | 0.0318602i | ||||
\(489\) | − | 6.88317i | − | 0.311268i | ||||||
\(490\) | 1.17989 | + | 1.89944i | 0.0533018 | + | 0.0858079i | ||||
\(491\) | 40.7509i | 1.83906i | 0.393016 | + | 0.919532i | \(0.371432\pi\) | ||||
−0.393016 | + | 0.919532i | \(0.628568\pi\) | |||||||
\(492\) | −3.88239 | + | 3.88239i | −0.175032 | + | 0.175032i | ||||
\(493\) | 14.9567 | − | 14.9567i | 0.673615 | − | 0.673615i | ||||
\(494\) | 10.4511 | 0.470216 | ||||||||
\(495\) | −6.04191 | − | 14.4019i | −0.271563 | − | 0.647317i | ||||
\(496\) | 5.10592 | 0.229263 | ||||||||
\(497\) | −3.51867 | + | 3.51867i | −0.157834 | + | 0.157834i | ||||
\(498\) | −8.37867 | + | 8.37867i | −0.375457 | + | 0.375457i | ||||
\(499\) | − | 1.19268i | − | 0.0533918i | −0.999644 | − | 0.0266959i | \(-0.991501\pi\) | ||
0.999644 | − | 0.0266959i | \(-0.00849857\pi\) | |||||||
\(500\) | −7.10514 | + | 8.63232i | −0.317752 | + | 0.386049i | ||||
\(501\) | 10.7756i | 0.481416i | ||||||||
\(502\) | −2.07847 | + | 2.07847i | −0.0927665 | + | 0.0927665i | ||||
\(503\) | 13.6150 | + | 13.6150i | 0.607063 | + | 0.607063i | 0.942177 | − | 0.335114i | \(-0.108775\pi\) |
−0.335114 | + | 0.942177i | \(0.608775\pi\) | |||||||
\(504\) | 2.10592i | 0.0938051i | ||||||||
\(505\) | 8.17886 | − | 35.0014i | 0.363955 | − | 1.55754i | ||||
\(506\) | −17.2882 | − | 23.8726i | −0.768553 | − | 1.06126i | ||||
\(507\) | 3.63154 | + | 3.63154i | 0.161283 | + | 0.161283i | ||||
\(508\) | −11.6188 | − | 11.6188i | −0.515501 | − | 0.515501i | ||||
\(509\) | 24.7191i | 1.09566i | 0.836591 | + | 0.547828i | \(0.184545\pi\) | ||||
−0.836591 | + | 0.547828i | \(0.815455\pi\) | |||||||
\(510\) | −5.69643 | − | 9.17039i | −0.252242 | − | 0.406072i | ||||
\(511\) | 4.92928 | 0.218059 | ||||||||
\(512\) | 0.707107 | − | 0.707107i | 0.0312500 | − | 0.0312500i | ||||
\(513\) | −12.9689 | − | 12.9689i | −0.572590 | − | 0.572590i | ||||
\(514\) | 10.9368 | 0.482402 | ||||||||
\(515\) | −6.37284 | + | 3.95865i | −0.280821 | + | 0.174439i | ||||
\(516\) | 10.9093i | 0.480254i | ||||||||
\(517\) | −1.56185 | − | 0.249846i | −0.0686903 | − | 0.0109882i | ||||
\(518\) | 6.35482 | − | 6.35482i | 0.279215 | − | 0.279215i | ||||
\(519\) | 19.3982 | 0.851488 | ||||||||
\(520\) | −1.39976 | + | 5.99027i | −0.0613835 | + | 0.262691i | ||||
\(521\) | 17.6342 | 0.772570 | 0.386285 | − | 0.922379i | \(-0.373758\pi\) | ||||
0.386285 | + | 0.922379i | \(0.373758\pi\) | |||||||
\(522\) | 6.16883 | + | 6.16883i | 0.270003 | + | 0.270003i | ||||
\(523\) | 25.0105 | + | 25.0105i | 1.09363 | + | 1.09363i | 0.995137 | + | 0.0984974i | \(0.0314036\pi\) |
0.0984974 | + | 0.995137i | \(0.468596\pi\) | |||||||
\(524\) | −15.1126 | −0.660196 | ||||||||
\(525\) | 2.09511 | − | 4.23822i | 0.0914381 | − | 0.184971i | ||||
\(526\) | −21.3960 | −0.932908 | ||||||||
\(527\) | −18.4346 | + | 18.4346i | −0.803022 | + | 0.803022i | ||||
\(528\) | 0.495370 | − | 3.09669i | 0.0215582 | − | 0.134766i | ||||
\(529\) | − | 55.9800i | − | 2.43391i | ||||||
\(530\) | −4.21443 | + | 18.0357i | −0.183063 | + | 0.783419i | ||||
\(531\) | −28.3968 | −1.23232 | ||||||||
\(532\) | 2.68621 | + | 2.68621i | 0.116462 | + | 0.116462i | ||||
\(533\) | −11.2958 | + | 11.2958i | −0.489274 | + | 0.489274i | ||||
\(534\) | 6.21063 | 0.268760 | ||||||||
\(535\) | −1.52755 | + | 0.948876i | −0.0660416 | + | 0.0410235i | ||||
\(536\) | 3.81552i | 0.164805i | ||||||||
\(537\) | −12.2947 | − | 12.2947i | −0.530557 | − | 0.530557i | ||||
\(538\) | 18.2583 | + | 18.2583i | 0.787173 | + | 0.787173i | ||||
\(539\) | −1.94532 | − | 2.68621i | −0.0837908 | − | 0.115703i | ||||
\(540\) | 9.17039 | − | 5.69643i | 0.394631 | − | 0.245135i | ||||
\(541\) | 25.4990i | 1.09629i | 0.836384 | + | 0.548144i | \(0.184665\pi\) | ||||
−0.836384 | + | 0.548144i | \(0.815335\pi\) | |||||||
\(542\) | 5.27089 | + | 5.27089i | 0.226404 | + | 0.226404i | ||||
\(543\) | −1.24162 | + | 1.24162i | −0.0532830 | + | 0.0532830i | ||||
\(544\) | 5.10592i | 0.218914i | ||||||||
\(545\) | −10.5124 | − | 2.45646i | −0.450303 | − | 0.105223i | ||||
\(546\) | − | 2.60132i | − | 0.111326i | ||||||
\(547\) | −25.4952 | + | 25.4952i | −1.09010 | + | 1.09010i | −0.0945778 | + | 0.995517i | \(0.530150\pi\) |
−0.995517 | + | 0.0945778i | \(0.969850\pi\) | |||||||
\(548\) | −2.60373 | + | 2.60373i | −0.111226 | + | 0.111226i | ||||
\(549\) | 2.09611 | 0.0894599 | ||||||||
\(550\) | 9.60472 | − | 13.5185i | 0.409547 | − | 0.576430i | ||||
\(551\) | 15.7374 | 0.670434 | ||||||||
\(552\) | 5.94199 | − | 5.94199i | 0.252908 | − | 0.252908i | ||||
\(553\) | −6.14112 | + | 6.14112i | −0.261147 | + | 0.261147i | ||||
\(554\) | 8.29473i | 0.352409i | ||||||||
\(555\) | −18.5032 | − | 4.32369i | −0.785418 | − | 0.183530i | ||||
\(556\) | 15.4144i | 0.653715i | ||||||||
\(557\) | 12.7943 | − | 12.7943i | 0.542114 | − | 0.542114i | −0.382034 | − | 0.924148i | \(-0.624776\pi\) |
0.924148 | + | 0.382034i | \(0.124776\pi\) | |||||||
\(558\) | −7.60327 | − | 7.60327i | −0.321872 | − | 0.321872i | ||||
\(559\) | 31.7405i | 1.34248i | ||||||||
\(560\) | −1.89944 | + | 1.17989i | −0.0802659 | + | 0.0498593i | ||||
\(561\) | 9.39189 | + | 12.9689i | 0.396526 | + | 0.547547i | ||||
\(562\) | −1.55686 | − | 1.55686i | −0.0656721 | − | 0.0656721i | ||||
\(563\) | 5.11418 | + | 5.11418i | 0.215537 | + | 0.215537i | 0.806615 | − | 0.591078i | \(-0.201297\pi\) |
−0.591078 | + | 0.806615i | \(0.701297\pi\) | |||||||
\(564\) | − | 0.450941i | − | 0.0189880i | ||||||
\(565\) | 28.1471 | − | 17.4843i | 1.18416 | − | 0.735569i | ||||
\(566\) | 27.2059 | 1.14355 | ||||||||
\(567\) | 1.23931 | − | 1.23931i | 0.0520462 | − | 0.0520462i | ||||
\(568\) | −3.51867 | − | 3.51867i | −0.147640 | − | 0.147640i | ||||
\(569\) | 17.2120 | 0.721563 | 0.360782 | − | 0.932650i | \(-0.382510\pi\) | ||||
0.360782 | + | 0.932650i | \(0.382510\pi\) | |||||||
\(570\) | 1.82764 | − | 7.82140i | 0.0765516 | − | 0.327602i | ||||
\(571\) | − | 30.8995i | − | 1.29310i | −0.762871 | − | 0.646551i | \(-0.776211\pi\) | ||
0.762871 | − | 0.646551i | \(-0.223789\pi\) | |||||||
\(572\) | 1.44128 | − | 9.00980i | 0.0602627 | − | 0.376719i | ||||
\(573\) | 2.02178 | − | 2.02178i | 0.0844610 | − | 0.0844610i | ||||
\(574\) | −5.80665 | −0.242365 | ||||||||
\(575\) | 42.0908 | − | 14.2430i | 1.75531 | − | 0.593973i | ||||
\(576\) | −2.10592 | −0.0877466 | ||||||||
\(577\) | 0.478344 | + | 0.478344i | 0.0199137 | + | 0.0199137i | 0.716994 | − | 0.697080i | \(-0.245518\pi\) |
−0.697080 | + | 0.716994i | \(0.745518\pi\) | |||||||
\(578\) | −6.41375 | − | 6.41375i | −0.266777 | − | 0.266777i | ||||
\(579\) | 21.3729 | 0.888226 | ||||||||
\(580\) | −2.10778 | + | 9.02022i | −0.0875206 | + | 0.374544i | ||||
\(581\) | −12.5315 | −0.519892 | ||||||||
\(582\) | 4.82795 | − | 4.82795i | 0.200125 | − | 0.200125i | ||||
\(583\) | 4.33943 | − | 27.1269i | 0.179721 | − | 1.12348i | ||||
\(584\) | 4.92928i | 0.203975i | ||||||||
\(585\) | 11.0046 | − | 6.83577i | 0.454982 | − | 0.282624i | ||||
\(586\) | −22.3002 | −0.921211 | ||||||||
\(587\) | 14.1941 | + | 14.1941i | 0.585855 | + | 0.585855i | 0.936506 | − | 0.350651i | \(-0.114040\pi\) |
−0.350651 | + | 0.936506i | \(0.614040\pi\) | |||||||
\(588\) | 0.668611 | − | 0.668611i | 0.0275731 | − | 0.0275731i | ||||
\(589\) | −19.3968 | −0.799230 | ||||||||
\(590\) | −15.9099 | − | 25.6126i | −0.655001 | − | 1.05445i | ||||
\(591\) | − | 13.9532i | − | 0.573956i | ||||||
\(592\) | 6.35482 | + | 6.35482i | 0.261182 | + | 0.261182i | ||||
\(593\) | −12.4700 | − | 12.4700i | −0.512080 | − | 0.512080i | 0.403083 | − | 0.915163i | \(-0.367939\pi\) |
−0.915163 | + | 0.403083i | \(0.867939\pi\) | |||||||
\(594\) | −12.9689 | + | 9.39189i | −0.532120 | + | 0.385354i | ||||
\(595\) | 2.59790 | − | 11.1177i | 0.106503 | − | 0.455781i | ||||
\(596\) | 3.64084i | 0.149135i | ||||||||
\(597\) | 6.44470 | + | 6.44470i | 0.263764 | + | 0.263764i | ||||
\(598\) | 17.2882 | − | 17.2882i | 0.706966 | − | 0.706966i | ||||
\(599\) | 13.6983i | 0.559697i | 0.960044 | + | 0.279848i | \(0.0902842\pi\) | ||||
−0.960044 | + | 0.279848i | \(0.909716\pi\) | |||||||
\(600\) | 4.23822 | + | 2.09511i | 0.173025 | + | 0.0855325i | ||||
\(601\) | − | 31.9888i | − | 1.30485i | −0.757854 | − | 0.652424i | \(-0.773752\pi\) | ||
0.757854 | − | 0.652424i | \(-0.226248\pi\) | |||||||
\(602\) | −8.15817 | + | 8.15817i | −0.332502 | + | 0.332502i | ||||
\(603\) | 5.68173 | − | 5.68173i | 0.231378 | − | 0.231378i | ||||
\(604\) | −0.183516 | −0.00746717 | ||||||||
\(605\) | −12.7892 | + | 21.0104i | −0.519957 | + | 0.854193i | ||||
\(606\) | −15.1997 | −0.617444 | ||||||||
\(607\) | 11.3635 | − | 11.3635i | 0.461230 | − | 0.461230i | −0.437829 | − | 0.899058i | \(-0.644252\pi\) |
0.899058 | + | 0.437829i | \(0.144252\pi\) | |||||||
\(608\) | −2.68621 | + | 2.68621i | −0.108940 | + | 0.108940i | ||||
\(609\) | − | 3.91710i | − | 0.158729i | ||||||
\(610\) | 1.17439 | + | 1.89059i | 0.0475497 | + | 0.0765479i | ||||
\(611\) | − | 1.31201i | − | 0.0530782i | ||||||
\(612\) | 7.60327 | − | 7.60327i | 0.307344 | − | 0.307344i | ||||
\(613\) | 17.4553 | + | 17.4553i | 0.705012 | + | 0.705012i | 0.965482 | − | 0.260470i | \(-0.0838775\pi\) |
−0.260470 | + | 0.965482i | \(0.583877\pi\) | |||||||
\(614\) | − | 9.39441i | − | 0.379127i | ||||||
\(615\) | 6.47819 | + | 10.4289i | 0.261226 | + | 0.420535i | ||||
\(616\) | 2.68621 | − | 1.94532i | 0.108231 | − | 0.0783791i | ||||
\(617\) | 30.8621 | + | 30.8621i | 1.24246 | + | 1.24246i | 0.958976 | + | 0.283486i | \(0.0914909\pi\) |
0.283486 | + | 0.958976i | \(0.408509\pi\) | |||||||
\(618\) | 2.24327 | + | 2.24327i | 0.0902374 | + | 0.0902374i | ||||
\(619\) | 11.1895i | 0.449746i | 0.974388 | + | 0.224873i | \(0.0721967\pi\) | ||||
−0.974388 | + | 0.224873i | \(0.927803\pi\) | |||||||
\(620\) | 2.59790 | − | 11.1177i | 0.104334 | − | 0.446497i | ||||
\(621\) | −42.9063 | −1.72177 | ||||||||
\(622\) | 11.9206 | − | 11.9206i | 0.477972 | − | 0.477972i | ||||
\(623\) | 4.64443 | + | 4.64443i | 0.186075 | + | 0.186075i | ||||
\(624\) | 2.60132 | 0.104136 | ||||||||
\(625\) | 15.1810 | + | 19.8629i | 0.607241 | + | 0.794518i | ||||
\(626\) | − | 12.5506i | − | 0.501623i | ||||||
\(627\) | −1.88185 | + | 11.7640i | −0.0751539 | + | 0.469807i | ||||
\(628\) | −7.02937 | + | 7.02937i | −0.280502 | + | 0.280502i | ||||
\(629\) | −45.8873 | −1.82965 | ||||||||
\(630\) | 4.58545 | + | 1.07149i | 0.182689 | + | 0.0426893i | ||||
\(631\) | 5.56562 | 0.221564 | 0.110782 | − | 0.993845i | \(-0.464664\pi\) | ||||
0.110782 | + | 0.993845i | \(0.464664\pi\) | |||||||
\(632\) | −6.14112 | − | 6.14112i | −0.244281 | − | 0.244281i | ||||
\(633\) | −14.4520 | − | 14.4520i | −0.574416 | − | 0.574416i | ||||
\(634\) | −21.6128 | −0.858354 | ||||||||
\(635\) | −31.2106 | + | 19.3873i | −1.23855 | + | 0.769360i | ||||
\(636\) | 7.83213 | 0.310564 | ||||||||
\(637\) | 1.94532 | − | 1.94532i | 0.0770763 | − | 0.0770763i | ||||
\(638\) | 2.17029 | − | 13.5671i | 0.0859226 | − | 0.537125i | ||||
\(639\) | 10.4794i | 0.414558i | ||||||||
\(640\) | −1.17989 | − | 1.89944i | −0.0466391 | − | 0.0750819i | ||||
\(641\) | −25.4359 | −1.00466 | −0.502328 | − | 0.864677i | \(-0.667523\pi\) | ||||
−0.502328 | + | 0.864677i | \(0.667523\pi\) | |||||||
\(642\) | 0.537703 | + | 0.537703i | 0.0212215 | + | 0.0212215i | ||||
\(643\) | −11.8965 | + | 11.8965i | −0.469152 | + | 0.469152i | −0.901640 | − | 0.432488i | \(-0.857636\pi\) |
0.432488 | + | 0.901640i | \(0.357636\pi\) | |||||||
\(644\) | 8.88707 | 0.350200 | ||||||||
\(645\) | 23.7540 | + | 5.55065i | 0.935313 | + | 0.218557i | ||||
\(646\) | − | 19.3968i | − | 0.763155i | ||||||
\(647\) | −13.3250 | − | 13.3250i | −0.523861 | − | 0.523861i | 0.394874 | − | 0.918735i | \(-0.370788\pi\) |
−0.918735 | + | 0.394874i | \(0.870788\pi\) | |||||||
\(648\) | 1.23931 | + | 1.23931i | 0.0486847 | + | 0.0486847i | ||||
\(649\) | 26.2312 | + | 36.2216i | 1.02967 | + | 1.42182i | ||||
\(650\) | 12.3311 | + | 6.09570i | 0.483665 | + | 0.239093i | ||||
\(651\) | 4.82795i | 0.189222i | ||||||||
\(652\) | 5.14737 | + | 5.14737i | 0.201586 | + | 0.201586i | ||||
\(653\) | −25.8976 | + | 25.8976i | −1.01345 | + | 1.01345i | −0.0135446 | + | 0.999908i | \(0.504312\pi\) |
−0.999908 | + | 0.0135446i | \(0.995688\pi\) | |||||||
\(654\) | 4.56511i | 0.178510i | ||||||||
\(655\) | −7.68930 | + | 32.9063i | −0.300446 | + | 1.28576i | ||||
\(656\) | − | 5.80665i | − | 0.226711i | ||||||
\(657\) | 7.34024 | − | 7.34024i | 0.286370 | − | 0.286370i | ||||
\(658\) | 0.337222 | − | 0.337222i | 0.0131463 | − | 0.0131463i | ||||
\(659\) | 12.3506 | 0.481111 | 0.240555 | − | 0.970635i | \(-0.422670\pi\) | ||||
0.240555 | + | 0.970635i | \(0.422670\pi\) | |||||||
\(660\) | −6.49073 | − | 2.65422i | −0.252651 | − | 0.103316i | ||||
\(661\) | −32.1393 | −1.25007 | −0.625036 | − | 0.780596i | \(-0.714916\pi\) | ||||
−0.625036 | + | 0.780596i | \(0.714916\pi\) | |||||||
\(662\) | −2.26816 | + | 2.26816i | −0.0881545 | + | 0.0881545i | ||||
\(663\) | −9.39189 | + | 9.39189i | −0.364751 | + | 0.364751i | ||||
\(664\) | − | 12.5315i | − | 0.486315i | ||||||
\(665\) | 7.21574 | − | 4.48224i | 0.279814 | − | 0.173814i | ||||
\(666\) | − | 18.9261i | − | 0.733370i | ||||||
\(667\) | 26.0328 | − | 26.0328i | 1.00799 | − | 1.00799i | ||||
\(668\) | −8.05816 | − | 8.05816i | −0.311780 | − | 0.311780i | ||||
\(669\) | − | 20.8715i | − | 0.806939i | ||||||
\(670\) | 8.30796 | + | 1.94134i | 0.320965 | + | 0.0750005i | ||||
\(671\) | −1.93626 | − | 2.67370i | −0.0747485 | − | 0.103217i | ||||
\(672\) | 0.668611 | + | 0.668611i | 0.0257922 | + | 0.0257922i | ||||
\(673\) | −1.06758 | − | 1.06758i | −0.0411522 | − | 0.0411522i | 0.686231 | − | 0.727383i | \(-0.259264\pi\) |
−0.727383 | + | 0.686231i | \(0.759264\pi\) | |||||||
\(674\) | 31.9290i | 1.22986i | ||||||||
\(675\) | −7.73757 | − | 22.8661i | −0.297819 | − | 0.880115i | ||||
\(676\) | −5.43147 | −0.208903 | ||||||||
\(677\) | −24.7303 | + | 24.7303i | −0.950464 | + | 0.950464i | −0.998830 | − | 0.0483656i | \(-0.984599\pi\) |
0.0483656 | + | 0.998830i | \(0.484599\pi\) | |||||||
\(678\) | −9.90789 | − | 9.90789i | −0.380510 | − | 0.380510i | ||||
\(679\) | 7.22086 | 0.277111 | ||||||||
\(680\) | 11.1177 | + | 2.59790i | 0.426344 | + | 0.0996247i | ||||
\(681\) | 9.59079i | 0.367520i | ||||||||
\(682\) | −2.67495 | + | 16.7218i | −0.102429 | + | 0.640311i | ||||
\(683\) | −34.9199 | + | 34.9199i | −1.33617 | + | 1.33617i | −0.436441 | + | 0.899733i | \(0.643761\pi\) |
−0.899733 | + | 0.436441i | \(0.856239\pi\) | |||||||
\(684\) | 8.00013 | 0.305893 | ||||||||
\(685\) | 4.34461 | + | 6.99417i | 0.165999 | + | 0.267233i | ||||
\(686\) | 1.00000 | 0.0381802 | ||||||||
\(687\) | −4.01843 | − | 4.01843i | −0.153313 | − | 0.153313i | ||||
\(688\) | −8.15817 | − | 8.15817i | −0.311027 | − | 0.311027i | ||||
\(689\) | 22.7875 | 0.868135 | ||||||||
\(690\) | −9.91487 | − | 15.9615i | −0.377453 | − | 0.607642i | ||||
\(691\) | −25.0598 | −0.953319 | −0.476659 | − | 0.879088i | \(-0.658153\pi\) | ||||
−0.476659 | + | 0.879088i | \(0.658153\pi\) | |||||||
\(692\) | −14.5064 | + | 14.5064i | −0.551449 | + | 0.551449i | ||||
\(693\) | −6.89686 | − | 1.10327i | −0.261990 | − | 0.0419099i | ||||
\(694\) | − | 23.8938i | − | 0.906995i | ||||||
\(695\) | 33.5634 | + | 7.84284i | 1.27313 | + | 0.297496i | ||||
\(696\) | 3.91710 | 0.148477 | ||||||||
\(697\) | 20.9645 | + | 20.9645i | 0.794087 | + | 0.794087i | ||||
\(698\) | 11.6199 | − | 11.6199i | 0.439819 | − | 0.439819i | ||||
\(699\) | −16.7342 | −0.632945 | ||||||||
\(700\) | 1.60266 | + | 4.73619i | 0.0605749 | + | 0.179011i | ||||
\(701\) | − | 33.9279i | − | 1.28144i | −0.767775 | − | 0.640719i | \(-0.778636\pi\) | ||
0.767775 | − | 0.640719i | \(-0.221364\pi\) | |||||||
\(702\) | −9.39189 | − | 9.39189i | −0.354474 | − | 0.354474i | ||||
\(703\) | −24.1412 | − | 24.1412i | −0.910503 | − | 0.910503i | ||||
\(704\) | 1.94532 | + | 2.68621i | 0.0733169 | + | 0.101240i | ||||
\(705\) | −0.981883 | − | 0.229439i | −0.0369799 | − | 0.00864117i | ||||
\(706\) | − | 21.9732i | − | 0.826972i | ||||||
\(707\) | −11.3666 | − | 11.3666i | −0.427485 | − | 0.427485i | ||||
\(708\) | −9.01574 | + | 9.01574i | −0.338832 | + | 0.338832i | ||||
\(709\) | − | 3.35200i | − | 0.125887i | −0.998017 | − | 0.0629434i | \(-0.979951\pi\) | ||
0.998017 | − | 0.0629434i | \(-0.0200488\pi\) | |||||||
\(710\) | −9.45190 | + | 5.87129i | −0.354723 | + | 0.220346i | ||||
\(711\) | 18.2896i | 0.685914i | ||||||||
\(712\) | −4.64443 | + | 4.64443i | −0.174057 | + | 0.174057i | ||||
\(713\) | −32.0861 | + | 32.0861i | −1.20164 | + | 1.20164i | ||||
\(714\) | −4.82795 | −0.180681 | ||||||||
\(715\) | −18.8847 | − | 7.72244i | −0.706249 | − | 0.288803i | ||||
\(716\) | 18.3885 | 0.687209 | ||||||||
\(717\) | −4.06752 | + | 4.06752i | −0.151904 | + | 0.151904i | ||||
\(718\) | −2.30171 | + | 2.30171i | −0.0858990 | + | 0.0858990i | ||||
\(719\) | − | 0.643312i | − | 0.0239915i | −0.999928 | − | 0.0119957i | \(-0.996182\pi\) | ||
0.999928 | − | 0.0119957i | \(-0.00381846\pi\) | |||||||
\(720\) | −1.07149 | + | 4.58545i | −0.0399322 | + | 0.170890i | ||||
\(721\) | 3.35512i | 0.124951i | ||||||||
\(722\) | −3.23044 | + | 3.23044i | −0.120224 | + | 0.120224i | ||||
\(723\) | −2.60693 | − | 2.60693i | −0.0969529 | − | 0.0969529i | ||||
\(724\) | − | 1.85701i | − | 0.0690154i | ||||||
\(725\) | 18.5683 | + | 9.17899i | 0.689609 | + | 0.340899i | ||||
\(726\) | 9.88211 | + | 3.24466i | 0.366759 | + | 0.120421i | ||||
\(727\) | −20.0896 | − | 20.0896i | −0.745081 | − | 0.745081i | 0.228470 | − | 0.973551i | \(-0.426628\pi\) |
−0.973551 | + | 0.228470i | \(0.926628\pi\) | |||||||
\(728\) | 1.94532 | + | 1.94532i | 0.0720983 | + | 0.0720983i | ||||
\(729\) | 10.0044i | 0.370533i | ||||||||
\(730\) | 10.7331 | + | 2.50802i | 0.397249 | + | 0.0928261i | ||||
\(731\) | 58.9090 | 2.17883 | ||||||||
\(732\) | 0.665497 | − | 0.665497i | 0.0245975 | − | 0.0245975i | ||||
\(733\) | 2.57260 | + | 2.57260i | 0.0950210 | + | 0.0950210i | 0.753019 | − | 0.657998i | \(-0.228597\pi\) |
−0.657998 | + | 0.753019i | \(0.728597\pi\) | |||||||
\(734\) | 9.14570 | 0.337574 | ||||||||
\(735\) | −1.11565 | − | 1.79603i | −0.0411514 | − | 0.0662476i | ||||
\(736\) | 8.88707i | 0.327582i | ||||||||
\(737\) | −12.4958 | − | 1.99892i | −0.460288 | − | 0.0736311i | ||||
\(738\) | −8.64673 | + | 8.64673i | −0.318291 | + | 0.318291i | ||||
\(739\) | −8.73064 | −0.321162 | −0.160581 | − | 0.987023i | \(-0.551337\pi\) | ||||
−0.160581 | + | 0.987023i | \(0.551337\pi\) | |||||||
\(740\) | 17.0704 | − | 10.6037i | 0.627521 | − | 0.389801i | ||||
\(741\) | −9.88211 | −0.363028 | ||||||||
\(742\) | 5.85701 | + | 5.85701i | 0.215018 | + | 0.215018i | ||||
\(743\) | −6.77216 | − | 6.77216i | −0.248447 | − | 0.248447i | 0.571886 | − | 0.820333i | \(-0.306212\pi\) |
−0.820333 | + | 0.571886i | \(0.806212\pi\) | |||||||
\(744\) | −4.82795 | −0.177001 | ||||||||
\(745\) | 7.92760 | + | 1.85246i | 0.290445 | + | 0.0678689i | ||||
\(746\) | −0.521347 | −0.0190879 | ||||||||
\(747\) | −18.6607 | + | 18.6607i | −0.682760 | + | 0.682760i | ||||
\(748\) | −16.7218 | − | 2.67495i | −0.611410 | − | 0.0978057i | ||||
\(749\) | 0.804210i | 0.0293852i | ||||||||
\(750\) | 6.71833 | − | 8.16237i | 0.245319 | − | 0.298047i | ||||
\(751\) | −36.9686 | −1.34900 | −0.674501 | − | 0.738274i | \(-0.735641\pi\) | ||||
−0.674501 | + | 0.738274i | \(0.735641\pi\) | |||||||
\(752\) | 0.337222 | + | 0.337222i | 0.0122972 | + | 0.0122972i | ||||
\(753\) | 1.96531 | − | 1.96531i | 0.0716200 | − | 0.0716200i | ||||
\(754\) | 11.3968 | 0.415046 | ||||||||
\(755\) | −0.0933732 | + | 0.399591i | −0.00339820 | + | 0.0145426i | ||||
\(756\) | − | 4.82795i | − | 0.175591i | ||||||
\(757\) | 16.7614 | + | 16.7614i | 0.609204 | + | 0.609204i | 0.942738 | − | 0.333534i | \(-0.108241\pi\) |
−0.333534 | + | 0.942738i | \(0.608241\pi\) | |||||||
\(758\) | 20.4004 | + | 20.4004i | 0.740974 | + | 0.740974i | ||||
\(759\) | 16.3470 | + | 22.5729i | 0.593358 | + | 0.819345i | ||||
\(760\) | 4.48224 | + | 7.21574i | 0.162588 | + | 0.261742i | ||||
\(761\) | 34.4447i | 1.24862i | 0.781177 | + | 0.624309i | \(0.214620\pi\) | ||||
−0.781177 | + | 0.624309i | \(0.785380\pi\) | |||||||
\(762\) | 10.9863 | + | 10.9863i | 0.397990 | + | 0.397990i | ||||
\(763\) | −3.41387 | + | 3.41387i | −0.123591 | + | 0.123591i | ||||
\(764\) | 3.02385i | 0.109399i | ||||||||
\(765\) | −12.6869 | − | 20.4240i | −0.458696 | − | 0.738431i | ||||
\(766\) | − | 13.0110i | − | 0.470107i | ||||||
\(767\) | −26.2312 | + | 26.2312i | −0.947154 | + | 0.947154i | ||||
\(768\) | −0.668611 | + | 0.668611i | −0.0241264 | + | 0.0241264i | ||||
\(769\) | −38.7265 | −1.39651 | −0.698257 | − | 0.715847i | \(-0.746041\pi\) | ||||
−0.698257 | + | 0.715847i | \(0.746041\pi\) | |||||||
\(770\) | −2.86901 | − | 6.83877i | −0.103392 | − | 0.246452i | ||||
\(771\) | −10.3414 | −0.372436 | ||||||||
\(772\) | −15.9830 | + | 15.9830i | −0.575242 | + | 0.575242i | ||||
\(773\) | −21.2428 | + | 21.2428i | −0.764049 | + | 0.764049i | −0.977052 | − | 0.213003i | \(-0.931676\pi\) |
0.213003 | + | 0.977052i | \(0.431676\pi\) | |||||||
\(774\) | 24.2968i | 0.873331i | ||||||||
\(775\) | −22.8860 | − | 11.3134i | −0.822088 | − | 0.406388i | ||||
\(776\) | 7.22086i | 0.259214i | ||||||||
\(777\) | −6.00886 | + | 6.00886i | −0.215567 | + | 0.215567i | ||||
\(778\) | −19.1884 | − | 19.1884i | −0.687936 | − | 0.687936i | ||||
\(779\) | 22.0587i | 0.790336i | ||||||||
\(780\) | 1.32355 | − | 5.66415i | 0.0473909 | − | 0.202809i | ||||
\(781\) | 13.3670 | − | 9.68020i | 0.478309 | − | 0.346385i | ||||
\(782\) | −32.0861 | − | 32.0861i | −1.14740 | − | 1.14740i | ||||
\(783\) | −14.1424 | − | 14.1424i | −0.505409 | − | 0.505409i | ||||
\(784\) | 1.00000i | 0.0357143i | ||||||||
\(785\) | 11.7293 | + | 18.8824i | 0.418636 | + | 0.673941i | ||||
\(786\) | 14.2898 | 0.509702 | ||||||||
\(787\) | −30.7700 | + | 30.7700i | −1.09683 | + | 1.09683i | −0.102055 | + | 0.994779i | \(0.532542\pi\) |
−0.994779 | + | 0.102055i | \(0.967458\pi\) | |||||||
\(788\) | 10.4344 | + | 10.4344i | 0.371711 | + | 0.371711i | ||||
\(789\) | 20.2311 | 0.720248 | ||||||||
\(790\) | −16.4964 | + | 10.2471i | −0.586914 | + | 0.364577i | ||||
\(791\) | − | 14.8186i | − | 0.526889i | ||||||
\(792\) | 1.10327 | − | 6.89686i | 0.0392031 | − | 0.245069i | ||||
\(793\) | 1.93626 | − | 1.93626i | 0.0687586 | − | 0.0687586i | ||||
\(794\) | −26.9779 | −0.957409 | ||||||||
\(795\) | 3.98499 | − | 17.0538i | 0.141333 | − | 0.604835i | ||||
\(796\) | −9.63893 | −0.341643 | ||||||||
\(797\) | 14.6510 | + | 14.6510i | 0.518965 | + | 0.518965i | 0.917258 | − | 0.398293i | \(-0.130397\pi\) |
−0.398293 | + | 0.917258i | \(0.630397\pi\) | |||||||
\(798\) | −2.53997 | − | 2.53997i | −0.0899140 | − | 0.0899140i | ||||
\(799\) | −2.43503 | −0.0861453 | ||||||||
\(800\) | −4.73619 | + | 1.60266i | −0.167450 | + | 0.0566627i | ||||
\(801\) | 13.8321 | 0.488734 | ||||||||
\(802\) | −0.865512 | + | 0.865512i | −0.0305623 | + | 0.0305623i | ||||
\(803\) | −16.1433 | − | 2.58241i | −0.569686 | − | 0.0911313i | ||||
\(804\) | − | 3.60780i | − | 0.127237i | ||||||
\(805\) | 4.52175 | − | 19.3508i | 0.159371 | − | 0.682026i | ||||
\(806\) | −14.0469 | −0.494780 | ||||||||
\(807\) | −17.2643 | − | 17.2643i | −0.607733 | − | 0.607733i | ||||
\(808\) | 11.3666 | − | 11.3666i | 0.399875 | − | 0.399875i | ||||
\(809\) | −0.595169 | −0.0209250 | −0.0104625 | − | 0.999945i | \(-0.503330\pi\) | ||||
−0.0104625 | + | 0.999945i | \(0.503330\pi\) | |||||||
\(810\) | 3.32905 | − | 2.06793i | 0.116971 | − | 0.0726596i | ||||
\(811\) | 2.51220i | 0.0882153i | 0.999027 | + | 0.0441076i | \(0.0140445\pi\) | ||||
−0.999027 | + | 0.0441076i | \(0.985956\pi\) | |||||||
\(812\) | 2.92928 | + | 2.92928i | 0.102798 | + | 0.102798i | ||||
\(813\) | −4.98393 | − | 4.98393i | −0.174794 | − | 0.174794i | ||||
\(814\) | −24.1412 | + | 17.4827i | −0.846149 | + | 0.612769i | ||||
\(815\) | 13.8269 | − | 8.58895i | 0.484336 | − | 0.300858i | ||||
\(816\) | − | 4.82795i | − | 0.169012i | ||||||
\(817\) | 30.9919 | + | 30.9919i | 1.08427 | + | 1.08427i | ||||
\(818\) | −22.1411 | + | 22.1411i | −0.774146 | + | 0.774146i | ||||
\(819\) | − | 5.79358i | − | 0.202444i | ||||||
\(820\) | −12.6435 | − | 2.95443i | −0.441529 | − | 0.103173i | ||||
\(821\) | − | 21.3817i | − | 0.746226i | −0.927786 | − | 0.373113i | \(-0.878290\pi\) | ||
0.927786 | − | 0.373113i | \(-0.121710\pi\) | |||||||
\(822\) | 2.46198 | − | 2.46198i | 0.0858713 | − | 0.0858713i | ||||
\(823\) | −33.1638 | + | 33.1638i | −1.15602 | + | 1.15602i | −0.170695 | + | 0.985324i | \(0.554601\pi\) |
−0.985324 | + | 0.170695i | \(0.945399\pi\) | |||||||
\(824\) | −3.35512 | −0.116881 | ||||||||
\(825\) | −9.08183 | + | 12.7825i | −0.316189 | + | 0.445030i | ||||
\(826\) | −13.4843 | −0.469178 | ||||||||
\(827\) | 6.34437 | − | 6.34437i | 0.220615 | − | 0.220615i | −0.588142 | − | 0.808757i | \(-0.700140\pi\) |
0.808757 | + | 0.588142i | \(0.200140\pi\) | |||||||
\(828\) | 13.2338 | − | 13.2338i | 0.459907 | − | 0.459907i | ||||
\(829\) | − | 19.5827i | − | 0.680136i | −0.940401 | − | 0.340068i | \(-0.889550\pi\) | ||
0.940401 | − | 0.340068i | \(-0.110450\pi\) | |||||||
\(830\) | −27.2861 | − | 6.37602i | −0.947116 | − | 0.221315i | ||||
\(831\) | − | 7.84316i | − | 0.272076i | ||||||
\(832\) | −1.94532 | + | 1.94532i | −0.0674418 | + | 0.0674418i | ||||
\(833\) | −3.61043 | − | 3.61043i | −0.125094 | − | 0.125094i | ||||
\(834\) | − | 14.5752i | − | 0.504698i | ||||||
\(835\) | −21.6459 | + | 13.4459i | −0.749088 | + | 0.465316i | ||||
\(836\) | −7.39003 | − | 10.2046i | −0.255589 | − | 0.352933i | ||||
\(837\) | 17.4310 | + | 17.4310i | 0.602502 | + | 0.602502i | ||||
\(838\) | −20.9817 | − | 20.9817i | −0.724800 | − | 0.724800i | ||||
\(839\) | − | 31.7658i | − | 1.09668i | −0.836256 | − | 0.548338i | \(-0.815261\pi\) | ||
0.836256 | − | 0.548338i | \(-0.184739\pi\) | |||||||
\(840\) | 1.79603 | − | 1.11565i | 0.0619690 | − | 0.0384936i | ||||
\(841\) | −11.8386 | −0.408227 | ||||||||
\(842\) | −17.8659 | + | 17.8659i | −0.615700 | + | 0.615700i | ||||
\(843\) | 1.47210 | + | 1.47210i | 0.0507019 | + | 0.0507019i | ||||
\(844\) | 21.6150 | 0.744019 | ||||||||
\(845\) | −2.76354 | + | 11.8266i | −0.0950686 | + | 0.406846i | ||||
\(846\) | − | 1.00432i | − | 0.0345293i | ||||||
\(847\) | 4.96361 | + | 9.81645i | 0.170552 | + | 0.337297i | ||||
\(848\) | −5.85701 | + | 5.85701i | −0.201131 | + | 0.201131i | ||||
\(849\) | −25.7248 | −0.882872 | ||||||||
\(850\) | 11.3134 | − | 22.8860i | 0.388046 | − | 0.784982i | ||||
\(851\) | −79.8688 | −2.73787 | ||||||||
\(852\) | 3.32711 | + | 3.32711i | 0.113985 | + | 0.113985i | ||||
\(853\) | −4.56328 | − | 4.56328i | −0.156244 | − | 0.156244i | 0.624656 | − | 0.780900i | \(-0.285239\pi\) |
−0.780900 | + | 0.624656i | \(0.785239\pi\) | |||||||
\(854\) | 0.995343 | 0.0340599 | ||||||||
\(855\) | 4.07047 | − | 17.4196i | 0.139207 | − | 0.595737i | ||||
\(856\) | −0.804210 | −0.0274873 | ||||||||
\(857\) | 21.8450 | − | 21.8450i | 0.746210 | − | 0.746210i | −0.227555 | − | 0.973765i | \(-0.573073\pi\) |
0.973765 | + | 0.227555i | \(0.0730732\pi\) | |||||||
\(858\) | −1.36281 | + | 8.51930i | −0.0465256 | + | 0.290844i | ||||
\(859\) | − | 3.49656i | − | 0.119301i | −0.998219 | − | 0.0596506i | \(-0.981001\pi\) | ||
0.998219 | − | 0.0596506i | \(-0.0189987\pi\) | |||||||
\(860\) | −21.9146 | + | 13.6128i | −0.747281 | + | 0.464193i | ||||
\(861\) | 5.49052 | 0.187117 | ||||||||
\(862\) | −17.3413 | − | 17.3413i | −0.590647 | − | 0.590647i | ||||
\(863\) | 19.3724 | − | 19.3724i | 0.659445 | − | 0.659445i | −0.295804 | − | 0.955249i | \(-0.595587\pi\) |
0.955249 | + | 0.295804i | \(0.0955874\pi\) | |||||||
\(864\) | 4.82795 | 0.164250 | ||||||||
\(865\) | 24.2055 | + | 38.9672i | 0.823011 | + | 1.32492i | ||||
\(866\) | − | 6.77105i | − | 0.230090i | ||||||
\(867\) | 6.06457 | + | 6.06457i | 0.205964 | + | 0.205964i | ||||
\(868\) | −3.61043 | − | 3.61043i | −0.122546 | − | 0.122546i | ||||
\(869\) | 23.3294 | − | 16.8948i | 0.791395 | − | 0.573117i | ||||
\(870\) | 1.99303 | − | 8.52915i | 0.0675699 | − | 0.289165i | ||||
\(871\) | − | 10.4969i | − | 0.355673i | ||||||
\(872\) | −3.41387 | − | 3.41387i | −0.115608 | − | 0.115608i | ||||
\(873\) | 10.7526 | − | 10.7526i | 0.363922 | − | 0.363922i | ||||
\(874\) | − | 33.7609i | − | 1.14198i | ||||||
\(875\) | 11.1281 | − | 1.07988i | 0.376197 | − | 0.0365066i | ||||
\(876\) | − | 4.66093i | − | 0.157478i | ||||||
\(877\) | −13.2861 | + | 13.2861i | −0.448641 | + | 0.448641i | −0.894903 | − | 0.446262i | \(-0.852755\pi\) |
0.446262 | + | 0.894903i | \(0.352755\pi\) | |||||||
\(878\) | −10.5487 | + | 10.5487i | −0.356003 | + | 0.356003i | ||||
\(879\) | 21.0861 | 0.711217 | ||||||||
\(880\) | 6.83877 | − | 2.86901i | 0.230535 | − | 0.0967144i | ||||
\(881\) | −0.866059 | −0.0291783 | −0.0145891 | − | 0.999894i | \(-0.504644\pi\) | ||||
−0.0145891 | + | 0.999894i | \(0.504644\pi\) | |||||||
\(882\) | 1.48911 | − | 1.48911i | 0.0501409 | − | 0.0501409i | ||||
\(883\) | 22.3900 | − | 22.3900i | 0.753484 | − | 0.753484i | −0.221643 | − | 0.975128i | \(-0.571142\pi\) |
0.975128 | + | 0.221643i | \(0.0711421\pi\) | |||||||
\(884\) | − | 14.0469i | − | 0.472447i | ||||||
\(885\) | 15.0438 | + | 24.2182i | 0.505690 | + | 0.814085i | ||||
\(886\) | 25.6030i | 0.860150i | ||||||||
\(887\) | 3.94042 | − | 3.94042i | 0.132306 | − | 0.132306i | −0.637852 | − | 0.770159i | \(-0.720177\pi\) |
0.770159 | + | 0.637852i | \(0.220177\pi\) | |||||||
\(888\) | −6.00886 | − | 6.00886i | −0.201644 | − | 0.201644i | ||||
\(889\) | 16.4315i | 0.551094i | ||||||||
\(890\) | 7.74975 | + | 12.4759i | 0.259772 | + | 0.418194i | ||||
\(891\) | −4.70799 | + | 3.40946i | −0.157724 | + | 0.114221i | ||||
\(892\) | 15.6081 | + | 15.6081i | 0.522598 | + | 0.522598i | ||||
\(893\) | −1.28107 | − | 1.28107i | −0.0428692 | − | 0.0428692i | ||||
\(894\) | − | 3.44263i | − | 0.115139i | ||||||
\(895\) | 9.35607 | − | 40.0393i | 0.312739 | − | 1.33837i | ||||
\(896\) | −1.00000 | −0.0334077 | ||||||||
\(897\) | −16.3470 | + | 16.3470i | −0.545810 | + | 0.545810i | ||||
\(898\) | 13.3546 | + | 13.3546i | 0.445649 | + | 0.445649i | ||||
\(899\) | −21.1520 | −0.705457 | ||||||||
\(900\) | 9.43924 | + | 4.66616i | 0.314641 | + | 0.155539i | ||||
\(901\) | − | 42.2927i | − | 1.40897i | ||||||
\(902\) | 19.0167 | + | 3.04205i | 0.633186 | + | 0.101289i | ||||
\(903\) | 7.71403 | − | 7.71403i | 0.256707 | − | 0.256707i | ||||
\(904\) | 14.8186 | 0.492860 | ||||||||
\(905\) | −4.04348 | − | 0.944850i | −0.134410 | − | 0.0314079i | ||||
\(906\) | 0.173525 | 0.00576500 | ||||||||
\(907\) | 2.03831 | + | 2.03831i | 0.0676810 | + | 0.0676810i | 0.740137 | − | 0.672456i | \(-0.234761\pi\) |
−0.672456 | + | 0.740137i | \(0.734761\pi\) | |||||||
\(908\) | −7.17217 | − | 7.17217i | −0.238017 | − | 0.238017i | ||||
\(909\) | −33.8522 | −1.12281 | ||||||||
\(910\) | 5.22554 | − | 3.24598i | 0.173225 | − | 0.107603i | ||||
\(911\) | 20.2149 | 0.669751 | 0.334876 | − | 0.942262i | \(-0.391306\pi\) | ||||
0.334876 | + | 0.942262i | \(0.391306\pi\) | |||||||
\(912\) | 2.53997 | − | 2.53997i | 0.0841069 | − | 0.0841069i | ||||
\(913\) | 41.0404 | + | 6.56512i | 1.35824 | + | 0.217274i | ||||
\(914\) | − | 8.99251i | − | 0.297446i | ||||||
\(915\) | −1.11046 | − | 1.78767i | −0.0367106 | − | 0.0590985i | ||||
\(916\) | 6.01011 | 0.198580 | ||||||||
\(917\) | 10.6862 | + | 10.6862i | 0.352890 | + | 0.352890i | ||||
\(918\) | −17.4310 | + | 17.4310i | −0.575307 | + | 0.575307i | ||||
\(919\) | −13.4773 | −0.444576 | −0.222288 | − | 0.974981i | \(-0.571352\pi\) | ||||
−0.222288 | + | 0.974981i | \(0.571352\pi\) | |||||||
\(920\) | 19.3508 | + | 4.52175i | 0.637977 | + | 0.149078i | ||||
\(921\) | 8.88296i | 0.292704i | ||||||||
\(922\) | 18.8157 | + | 18.8157i | 0.619661 | + | 0.619661i | ||||
\(923\) | 9.68020 | + | 9.68020i | 0.318628 | + | 0.318628i | ||||
\(924\) | −2.53997 | + | 1.83941i | −0.0835589 | + | 0.0605122i | ||||
\(925\) | −14.4032 | − | 42.5645i | −0.473576 | − | 1.39951i | ||||
\(926\) | 27.8234i | 0.914335i | ||||||||
\(927\) | 4.99613 | + | 4.99613i | 0.164095 | + | 0.164095i | ||||
\(928\) | −2.92928 | + | 2.92928i | −0.0961585 | + | 0.0961585i | ||||
\(929\) | − | 52.0667i | − | 1.70825i | −0.520066 | − | 0.854126i | \(-0.674093\pi\) | ||
0.520066 | − | 0.854126i | \(-0.325907\pi\) | |||||||
\(930\) | −2.45646 | + | 10.5124i | −0.0805506 | + | 0.344716i | ||||
\(931\) | − | 3.79888i | − | 0.124503i | ||||||
\(932\) | 12.5141 | − | 12.5141i | 0.409914 | − | 0.409914i | ||||
\(933\) | −11.2716 | + | 11.2716i | −0.369016 | + | 0.369016i | ||||
\(934\) | −3.55747 | −0.116404 | ||||||||
\(935\) | −14.3325 | + | 35.0493i | −0.468724 | + | 1.14623i | ||||
\(936\) | 5.79358 | 0.189369 | ||||||||
\(937\) | 7.86146 | − | 7.86146i | 0.256823 | − | 0.256823i | −0.566938 | − | 0.823761i | \(-0.691872\pi\) |
0.823761 | + | 0.566938i | \(0.191872\pi\) | |||||||
\(938\) | 2.69798 | − | 2.69798i | 0.0880922 | − | 0.0880922i | ||||
\(939\) | 11.8673i | 0.387276i | ||||||||
\(940\) | 0.905850 | − | 0.562692i | 0.0295456 | − | 0.0183530i | ||||
\(941\) | 10.2930i | 0.335543i | 0.985826 | + | 0.167772i | \(0.0536571\pi\) | ||||
−0.985826 | + | 0.167772i | \(0.946343\pi\) | |||||||
\(942\) | 6.64668 | − | 6.64668i | 0.216561 | − | 0.216561i | ||||
\(943\) | 36.4896 | + | 36.4896i | 1.18826 | + | 1.18826i | ||||
\(944\) | − | 13.4843i | − | 0.438876i | ||||||
\(945\) | −10.5124 | − | 2.45646i | −0.341969 | − | 0.0799087i | ||||
\(946\) | 30.9919 | − | 22.4439i | 1.00763 | − | 0.729714i | ||||
\(947\) | 1.69360 | + | 1.69360i | 0.0550346 | + | 0.0550346i | 0.734088 | − | 0.679054i | \(-0.237610\pi\) |
−0.679054 | + | 0.734088i | \(0.737610\pi\) | |||||||
\(948\) | 5.80679 | + | 5.80679i | 0.188596 | + | 0.188596i | ||||
\(949\) | − | 13.5609i | − | 0.440206i | ||||||
\(950\) | 17.9922 | − | 6.08832i | 0.583744 | − | 0.197531i | ||||
\(951\) | 20.4362 | 0.662688 | ||||||||
\(952\) | 3.61043 | − | 3.61043i | 0.117015 | − | 0.117015i | ||||
\(953\) | −26.7457 | − | 26.7457i | −0.866378 | − | 0.866378i | 0.125691 | − | 0.992069i | \(-0.459885\pi\) |
−0.992069 | + | 0.125691i | \(0.959885\pi\) | |||||||
\(954\) | 17.4435 | 0.564753 | ||||||||
\(955\) | 6.58416 | + | 1.53854i | 0.213058 | + | 0.0497858i | ||||
\(956\) | − | 6.08354i | − | 0.196756i | ||||||
\(957\) | −2.05214 | + | 12.8285i | −0.0663362 | + | 0.414685i | ||||
\(958\) | 20.5371 | − | 20.5371i | 0.663523 | − | 0.663523i | ||||
\(959\) | 3.68223 | 0.118905 | ||||||||
\(960\) | 1.11565 | + | 1.79603i | 0.0360075 | + | 0.0579667i | ||||
\(961\) | −4.92959 | −0.159019 | ||||||||
\(962\) | −17.4827 | − | 17.4827i | −0.563666 | − | 0.563666i | ||||
\(963\) | 1.19756 | + | 1.19756i | 0.0385907 | + | 0.0385907i | ||||
\(964\) | 3.89903 | 0.125579 | ||||||||
\(965\) | 26.6695 | + | 42.9338i | 0.858520 | + | 1.38209i | ||||
\(966\) | −8.40325 | −0.270370 | ||||||||
\(967\) | −31.2405 | + | 31.2405i | −1.00463 | + | 1.00463i | −0.00463675 | + | 0.999989i | \(0.501476\pi\) |
−0.999989 | + | 0.00463675i | \(0.998524\pi\) | |||||||
\(968\) | −9.81645 | + | 4.96361i | −0.315513 | + | 0.159536i | ||||
\(969\) | 18.3408i | 0.589191i | ||||||||
\(970\) | 15.7228 | + | 3.67398i | 0.504828 | + | 0.117964i | ||||
\(971\) | −20.8809 | −0.670099 | −0.335049 | − | 0.942201i | \(-0.608753\pi\) | ||||
−0.335049 | + | 0.942201i | \(0.608753\pi\) | |||||||
\(972\) | −11.4135 | − | 11.4135i | −0.366087 | − | 0.366087i | ||||
\(973\) | 10.8996 | − | 10.8996i | 0.349425 | − | 0.349425i | ||||
\(974\) | 16.9181 | 0.542092 | ||||||||
\(975\) | −11.6598 | − | 5.76385i | −0.373411 | − | 0.184591i | ||||
\(976\) | 0.995343i | 0.0318602i | ||||||||
\(977\) | −35.7769 | − | 35.7769i | −1.14461 | − | 1.14461i | −0.987597 | − | 0.157009i | \(-0.949815\pi\) |
−0.157009 | − | 0.987597i | \(-0.550185\pi\) | |||||||
\(978\) | −4.86714 | − | 4.86714i | −0.155634 | − | 0.155634i | ||||
\(979\) | −12.7773 | − | 17.6436i | −0.408363 | − | 0.563893i | ||||
\(980\) | 2.17741 | + | 0.508801i | 0.0695549 | + | 0.0162530i | ||||
\(981\) | 10.1673i | 0.324616i | ||||||||
\(982\) | 28.8153 | + | 28.8153i | 0.919532 | + | 0.919532i | ||||
\(983\) | −13.8746 | + | 13.8746i | −0.442532 | + | 0.442532i | −0.892862 | − | 0.450330i | \(-0.851306\pi\) |
0.450330 | + | 0.892862i | \(0.351306\pi\) | |||||||
\(984\) | 5.49052i | 0.175032i | ||||||||
\(985\) | 28.0291 | − | 17.4110i | 0.893081 | − | 0.554761i | ||||
\(986\) | − | 21.1520i | − | 0.673615i | ||||||
\(987\) | −0.318863 | + | 0.318863i | −0.0101495 | + | 0.0101495i | ||||
\(988\) | 7.39003 | − | 7.39003i | 0.235108 | − | 0.235108i | ||||
\(989\) | 102.534 | 3.26038 | ||||||||
\(990\) | −14.4559 | − | 5.91140i | −0.459440 | − | 0.187877i | ||||
\(991\) | 20.7493 | 0.659124 | 0.329562 | − | 0.944134i | \(-0.393099\pi\) | ||||
0.329562 | + | 0.944134i | \(0.393099\pi\) | |||||||
\(992\) | 3.61043 | − | 3.61043i | 0.114631 | − | 0.114631i | ||||
\(993\) | 2.14468 | − | 2.14468i | 0.0680593 | − | 0.0680593i | ||||
\(994\) | 4.97615i | 0.157834i | ||||||||
\(995\) | −4.90430 | + | 20.9879i | −0.155477 | + | 0.665362i | ||||
\(996\) | 11.8492i | 0.375457i | ||||||||
\(997\) | 16.0145 | − | 16.0145i | 0.507185 | − | 0.507185i | −0.406476 | − | 0.913661i | \(-0.633243\pi\) |
0.913661 | + | 0.406476i | \(0.133243\pi\) | |||||||
\(998\) | −0.843353 | − | 0.843353i | −0.0266959 | − | 0.0266959i | ||||
\(999\) | 43.3891i | 1.37277i |
(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 | 770.2.m.e.197.7 | yes | 16 | |
5.3 | odd | 4 | inner | 770.2.m.e.43.3 | ✓ | 16 | |
11.10 | odd | 2 | inner | 770.2.m.e.197.3 | yes | 16 | |
55.43 | even | 4 | inner | 770.2.m.e.43.7 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
770.2.m.e.43.3 | ✓ | 16 | 5.3 | odd | 4 | inner | |
770.2.m.e.43.7 | yes | 16 | 55.43 | even | 4 | inner | |
770.2.m.e.197.3 | yes | 16 | 11.10 | odd | 2 | inner | |
770.2.m.e.197.7 | yes | 16 | 1.1 | even | 1 | trivial |