Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1050,3,Mod(43,1050)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1050, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 3, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1050.43");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1050.l (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: | \(28.6104277578\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(i)\) |
Coefficient field: | 8.0.12745506816.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 23x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 757.3 | ||
Root | \(1.54779 + 1.54779i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1050.757 |
Dual form | 1050.3.l.e.43.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(451\) | \(701\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | + | 1.00000i | 0.500000 | + | 0.500000i | ||||
\(3\) | 1.22474 | − | 1.22474i | 0.408248 | − | 0.408248i | ||||
\(4\) | 2.00000i | 0.500000i | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 2.44949 | 0.408248 | ||||||||
\(7\) | −1.87083 | − | 1.87083i | −0.267261 | − | 0.267261i | ||||
\(8\) | −2.00000 | + | 2.00000i | −0.250000 | + | 0.250000i | ||||
\(9\) | − | 3.00000i | − | 0.333333i | ||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.02424 | −0.274931 | −0.137465 | − | 0.990507i | \(-0.543896\pi\) | ||||
−0.137465 | + | 0.990507i | \(0.543896\pi\) | |||||||
\(12\) | 2.44949 | + | 2.44949i | 0.204124 | + | 0.204124i | ||||
\(13\) | −2.99455 | + | 2.99455i | −0.230350 | + | 0.230350i | −0.812839 | − | 0.582489i | \(-0.802079\pi\) |
0.582489 | + | 0.812839i | \(0.302079\pi\) | |||||||
\(14\) | − | 3.74166i | − | 0.267261i | ||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −4.00000 | −0.250000 | ||||||||
\(17\) | 13.0622 | + | 13.0622i | 0.768365 | + | 0.768365i | 0.977819 | − | 0.209454i | \(-0.0671685\pi\) |
−0.209454 | + | 0.977819i | \(0.567169\pi\) | |||||||
\(18\) | 3.00000 | − | 3.00000i | 0.166667 | − | 0.166667i | ||||
\(19\) | 29.5080i | 1.55305i | 0.630085 | + | 0.776526i | \(0.283020\pi\) | ||||
−0.630085 | + | 0.776526i | \(0.716980\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −4.58258 | −0.218218 | ||||||||
\(22\) | −3.02424 | − | 3.02424i | −0.137465 | − | 0.137465i | ||||
\(23\) | 2.34455 | − | 2.34455i | 0.101937 | − | 0.101937i | −0.654299 | − | 0.756236i | \(-0.727036\pi\) |
0.756236 | + | 0.654299i | \(0.227036\pi\) | |||||||
\(24\) | 4.89898i | 0.204124i | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −5.98911 | −0.230350 | ||||||||
\(27\) | −3.67423 | − | 3.67423i | −0.136083 | − | 0.136083i | ||||
\(28\) | 3.74166 | − | 3.74166i | 0.133631 | − | 0.133631i | ||||
\(29\) | 24.4595i | 0.843432i | 0.906728 | + | 0.421716i | \(0.138572\pi\) | ||||
−0.906728 | + | 0.421716i | \(0.861428\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 46.7091 | 1.50674 | 0.753372 | − | 0.657594i | \(-0.228426\pi\) | ||||
0.753372 | + | 0.657594i | \(0.228426\pi\) | |||||||
\(32\) | −4.00000 | − | 4.00000i | −0.125000 | − | 0.125000i | ||||
\(33\) | −3.70392 | + | 3.70392i | −0.112240 | + | 0.112240i | ||||
\(34\) | 26.1244i | 0.768365i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 6.00000 | 0.166667 | ||||||||
\(37\) | 30.6893 | + | 30.6893i | 0.829442 | + | 0.829442i | 0.987439 | − | 0.157998i | \(-0.0505039\pi\) |
−0.157998 | + | 0.987439i | \(0.550504\pi\) | |||||||
\(38\) | −29.5080 | + | 29.5080i | −0.776526 | + | 0.776526i | ||||
\(39\) | 7.33513i | 0.188080i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 11.9782 | 0.292152 | 0.146076 | − | 0.989273i | \(-0.453336\pi\) | ||||
0.146076 | + | 0.989273i | \(0.453336\pi\) | |||||||
\(42\) | −4.58258 | − | 4.58258i | −0.109109 | − | 0.109109i | ||||
\(43\) | −0.402550 | + | 0.402550i | −0.00936162 | + | 0.00936162i | −0.711772 | − | 0.702410i | \(-0.752107\pi\) |
0.702410 | + | 0.711772i | \(0.252107\pi\) | |||||||
\(44\) | − | 6.04847i | − | 0.137465i | ||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 4.68911 | 0.101937 | ||||||||
\(47\) | 46.4173 | + | 46.4173i | 0.987602 | + | 0.987602i | 0.999924 | − | 0.0123220i | \(-0.00392231\pi\) |
−0.0123220 | + | 0.999924i | \(0.503922\pi\) | |||||||
\(48\) | −4.89898 | + | 4.89898i | −0.102062 | + | 0.102062i | ||||
\(49\) | 7.00000i | 0.142857i | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 31.9957 | 0.627367 | ||||||||
\(52\) | −5.98911 | − | 5.98911i | −0.115175 | − | 0.115175i | ||||
\(53\) | 11.9515 | − | 11.9515i | 0.225501 | − | 0.225501i | −0.585309 | − | 0.810810i | \(-0.699027\pi\) |
0.810810 | + | 0.585309i | \(0.199027\pi\) | |||||||
\(54\) | − | 7.34847i | − | 0.136083i | ||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 7.48331 | 0.133631 | ||||||||
\(57\) | 36.1398 | + | 36.1398i | 0.634031 | + | 0.634031i | ||||
\(58\) | −24.4595 | + | 24.4595i | −0.421716 | + | 0.421716i | ||||
\(59\) | 32.2897i | 0.547284i | 0.961832 | + | 0.273642i | \(0.0882283\pi\) | ||||
−0.961832 | + | 0.273642i | \(0.911772\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −78.3977 | −1.28521 | −0.642604 | − | 0.766198i | \(-0.722146\pi\) | ||||
−0.642604 | + | 0.766198i | \(0.722146\pi\) | |||||||
\(62\) | 46.7091 | + | 46.7091i | 0.753372 | + | 0.753372i | ||||
\(63\) | −5.61249 | + | 5.61249i | −0.0890871 | + | 0.0890871i | ||||
\(64\) | − | 8.00000i | − | 0.125000i | ||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −7.40784 | −0.112240 | ||||||||
\(67\) | −17.3609 | − | 17.3609i | −0.259118 | − | 0.259118i | 0.565577 | − | 0.824695i | \(-0.308653\pi\) |
−0.824695 | + | 0.565577i | \(0.808653\pi\) | |||||||
\(68\) | −26.1244 | + | 26.1244i | −0.384182 | + | 0.384182i | ||||
\(69\) | − | 5.74296i | − | 0.0832313i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −43.2246 | −0.608797 | −0.304398 | − | 0.952545i | \(-0.598455\pi\) | ||||
−0.304398 | + | 0.952545i | \(0.598455\pi\) | |||||||
\(72\) | 6.00000 | + | 6.00000i | 0.0833333 | + | 0.0833333i | ||||
\(73\) | 39.4074 | − | 39.4074i | 0.539827 | − | 0.539827i | −0.383651 | − | 0.923478i | \(-0.625333\pi\) |
0.923478 | + | 0.383651i | \(0.125333\pi\) | |||||||
\(74\) | 61.3787i | 0.829442i | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −59.0160 | −0.776526 | ||||||||
\(77\) | 5.65783 | + | 5.65783i | 0.0734783 | + | 0.0734783i | ||||
\(78\) | −7.33513 | + | 7.33513i | −0.0940401 | + | 0.0940401i | ||||
\(79\) | − | 0.100902i | − | 0.00127724i | −1.00000 | 0.000638622i | \(-0.999797\pi\) | |||
1.00000 | 0.000638622i | \(-0.000203280\pi\) | ||||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −9.00000 | −0.111111 | ||||||||
\(82\) | 11.9782 | + | 11.9782i | 0.146076 | + | 0.146076i | ||||
\(83\) | −15.9969 | + | 15.9969i | −0.192734 | + | 0.192734i | −0.796876 | − | 0.604142i | \(-0.793516\pi\) |
0.604142 | + | 0.796876i | \(0.293516\pi\) | |||||||
\(84\) | − | 9.16515i | − | 0.109109i | ||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −0.805100 | −0.00936162 | ||||||||
\(87\) | 29.9567 | + | 29.9567i | 0.344330 | + | 0.344330i | ||||
\(88\) | 6.04847 | − | 6.04847i | 0.0687326 | − | 0.0687326i | ||||
\(89\) | − | 91.4648i | − | 1.02769i | −0.857882 | − | 0.513847i | \(-0.828220\pi\) | ||
0.857882 | − | 0.513847i | \(-0.171780\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 11.2046 | 0.123127 | ||||||||
\(92\) | 4.68911 | + | 4.68911i | 0.0509686 | + | 0.0509686i | ||||
\(93\) | 57.2067 | − | 57.2067i | 0.615126 | − | 0.615126i | ||||
\(94\) | 92.8346i | 0.987602i | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −9.79796 | −0.102062 | ||||||||
\(97\) | 14.1758 | + | 14.1758i | 0.146142 | + | 0.146142i | 0.776392 | − | 0.630250i | \(-0.217048\pi\) |
−0.630250 | + | 0.776392i | \(0.717048\pi\) | |||||||
\(98\) | −7.00000 | + | 7.00000i | −0.0714286 | + | 0.0714286i | ||||
\(99\) | 9.07271i | 0.0916435i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −121.663 | −1.20458 | −0.602291 | − | 0.798277i | \(-0.705745\pi\) | ||||
−0.602291 | + | 0.798277i | \(0.705745\pi\) | |||||||
\(102\) | 31.9957 | + | 31.9957i | 0.313684 | + | 0.313684i | ||||
\(103\) | 78.3209 | − | 78.3209i | 0.760397 | − | 0.760397i | −0.215997 | − | 0.976394i | \(-0.569300\pi\) |
0.976394 | + | 0.215997i | \(0.0693000\pi\) | |||||||
\(104\) | − | 11.9782i | − | 0.115175i | ||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 23.9031 | 0.225501 | ||||||||
\(107\) | 125.259 | + | 125.259i | 1.17064 | + | 1.17064i | 0.982057 | + | 0.188586i | \(0.0603905\pi\) |
0.188586 | + | 0.982057i | \(0.439610\pi\) | |||||||
\(108\) | 7.34847 | − | 7.34847i | 0.0680414 | − | 0.0680414i | ||||
\(109\) | 181.318i | 1.66347i | 0.555176 | + | 0.831733i | \(0.312651\pi\) | ||||
−0.555176 | + | 0.831733i | \(0.687349\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 75.1732 | 0.677236 | ||||||||
\(112\) | 7.48331 | + | 7.48331i | 0.0668153 | + | 0.0668153i | ||||
\(113\) | 16.7553 | − | 16.7553i | 0.148277 | − | 0.148277i | −0.629071 | − | 0.777348i | \(-0.716564\pi\) |
0.777348 | + | 0.629071i | \(0.216564\pi\) | |||||||
\(114\) | 72.2796i | 0.634031i | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −48.9191 | −0.421716 | ||||||||
\(117\) | 8.98366 | + | 8.98366i | 0.0767834 | + | 0.0767834i | ||||
\(118\) | −32.2897 | + | 32.2897i | −0.273642 | + | 0.273642i | ||||
\(119\) | − | 48.8743i | − | 0.410708i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −111.854 | −0.924413 | ||||||||
\(122\) | −78.3977 | − | 78.3977i | −0.642604 | − | 0.642604i | ||||
\(123\) | 14.6703 | − | 14.6703i | 0.119270 | − | 0.119270i | ||||
\(124\) | 93.4182i | 0.753372i | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −11.2250 | −0.0890871 | ||||||||
\(127\) | 3.42855 | + | 3.42855i | 0.0269964 | + | 0.0269964i | 0.720476 | − | 0.693480i | \(-0.243923\pi\) |
−0.693480 | + | 0.720476i | \(0.743923\pi\) | |||||||
\(128\) | 8.00000 | − | 8.00000i | 0.0625000 | − | 0.0625000i | ||||
\(129\) | 0.986041i | 0.00764373i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −201.822 | −1.54063 | −0.770314 | − | 0.637665i | \(-0.779901\pi\) | ||||
−0.770314 | + | 0.637665i | \(0.779901\pi\) | |||||||
\(132\) | −7.40784 | − | 7.40784i | −0.0561200 | − | 0.0561200i | ||||
\(133\) | 55.2044 | − | 55.2044i | 0.415071 | − | 0.415071i | ||||
\(134\) | − | 34.7218i | − | 0.259118i | ||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −52.2488 | −0.384182 | ||||||||
\(137\) | 150.398 | + | 150.398i | 1.09779 | + | 1.09779i | 0.994669 | + | 0.103123i | \(0.0328837\pi\) |
0.103123 | + | 0.994669i | \(0.467116\pi\) | |||||||
\(138\) | 5.74296 | − | 5.74296i | 0.0416157 | − | 0.0416157i | ||||
\(139\) | − | 120.042i | − | 0.863613i | −0.901966 | − | 0.431806i | \(-0.857876\pi\) | ||
0.901966 | − | 0.431806i | \(-0.142124\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 113.699 | 0.806374 | ||||||||
\(142\) | −43.2246 | − | 43.2246i | −0.304398 | − | 0.304398i | ||||
\(143\) | 9.05624 | − | 9.05624i | 0.0633303 | − | 0.0633303i | ||||
\(144\) | 12.0000i | 0.0833333i | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 78.8147 | 0.539827 | ||||||||
\(147\) | 8.57321 | + | 8.57321i | 0.0583212 | + | 0.0583212i | ||||
\(148\) | −61.3787 | + | 61.3787i | −0.414721 | + | 0.414721i | ||||
\(149\) | 37.0923i | 0.248942i | 0.992223 | + | 0.124471i | \(0.0397234\pi\) | ||||
−0.992223 | + | 0.124471i | \(0.960277\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −133.681 | −0.885306 | −0.442653 | − | 0.896693i | \(-0.645963\pi\) | ||||
−0.442653 | + | 0.896693i | \(0.645963\pi\) | |||||||
\(152\) | −59.0160 | − | 59.0160i | −0.388263 | − | 0.388263i | ||||
\(153\) | 39.1866 | − | 39.1866i | 0.256122 | − | 0.256122i | ||||
\(154\) | 11.3157i | 0.0734783i | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −14.6703 | −0.0940401 | ||||||||
\(157\) | −125.140 | − | 125.140i | −0.797067 | − | 0.797067i | 0.185565 | − | 0.982632i | \(-0.440588\pi\) |
−0.982632 | + | 0.185565i | \(0.940588\pi\) | |||||||
\(158\) | 0.100902 | − | 0.100902i | 0.000638622 | − | 0.000638622i | ||||
\(159\) | − | 29.2751i | − | 0.184120i | ||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −8.77252 | −0.0544877 | ||||||||
\(162\) | −9.00000 | − | 9.00000i | −0.0555556 | − | 0.0555556i | ||||
\(163\) | 157.323 | − | 157.323i | 0.965174 | − | 0.965174i | −0.0342396 | − | 0.999414i | \(-0.510901\pi\) |
0.999414 | + | 0.0342396i | \(0.0109009\pi\) | |||||||
\(164\) | 23.9564i | 0.146076i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −31.9939 | −0.192734 | ||||||||
\(167\) | 24.3702 | + | 24.3702i | 0.145929 | + | 0.145929i | 0.776297 | − | 0.630368i | \(-0.217096\pi\) |
−0.630368 | + | 0.776297i | \(0.717096\pi\) | |||||||
\(168\) | 9.16515 | − | 9.16515i | 0.0545545 | − | 0.0545545i | ||||
\(169\) | 151.065i | 0.893878i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 88.5240 | 0.517684 | ||||||||
\(172\) | −0.805100 | − | 0.805100i | −0.00468081 | − | 0.00468081i | ||||
\(173\) | −44.2512 | + | 44.2512i | −0.255787 | + | 0.255787i | −0.823338 | − | 0.567551i | \(-0.807891\pi\) |
0.567551 | + | 0.823338i | \(0.307891\pi\) | |||||||
\(174\) | 59.9134i | 0.344330i | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 12.0969 | 0.0687326 | ||||||||
\(177\) | 39.5467 | + | 39.5467i | 0.223428 | + | 0.223428i | ||||
\(178\) | 91.4648 | − | 91.4648i | 0.513847 | − | 0.513847i | ||||
\(179\) | 101.526i | 0.567183i | 0.958945 | + | 0.283592i | \(0.0915260\pi\) | ||||
−0.958945 | + | 0.283592i | \(0.908474\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −138.946 | −0.767659 | −0.383829 | − | 0.923404i | \(-0.625395\pi\) | ||||
−0.383829 | + | 0.923404i | \(0.625395\pi\) | |||||||
\(182\) | 11.2046 | + | 11.2046i | 0.0615637 | + | 0.0615637i | ||||
\(183\) | −96.0172 | + | 96.0172i | −0.524684 | + | 0.524684i | ||||
\(184\) | 9.37822i | 0.0509686i | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 114.413 | 0.615126 | ||||||||
\(187\) | −39.5032 | − | 39.5032i | −0.211247 | − | 0.211247i | ||||
\(188\) | −92.8346 | + | 92.8346i | −0.493801 | + | 0.493801i | ||||
\(189\) | 13.7477i | 0.0727393i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 299.678 | 1.56899 | 0.784497 | − | 0.620133i | \(-0.212921\pi\) | ||||
0.784497 | + | 0.620133i | \(0.212921\pi\) | |||||||
\(192\) | −9.79796 | − | 9.79796i | −0.0510310 | − | 0.0510310i | ||||
\(193\) | 136.927 | − | 136.927i | 0.709467 | − | 0.709467i | −0.256956 | − | 0.966423i | \(-0.582720\pi\) |
0.966423 | + | 0.256956i | \(0.0827196\pi\) | |||||||
\(194\) | 28.3516i | 0.146142i | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −14.0000 | −0.0714286 | ||||||||
\(197\) | −127.476 | − | 127.476i | −0.647088 | − | 0.647088i | 0.305200 | − | 0.952288i | \(-0.401277\pi\) |
−0.952288 | + | 0.305200i | \(0.901277\pi\) | |||||||
\(198\) | −9.07271 | + | 9.07271i | −0.0458218 | + | 0.0458218i | ||||
\(199\) | − | 173.636i | − | 0.872543i | −0.899815 | − | 0.436272i | \(-0.856299\pi\) | ||
0.899815 | − | 0.436272i | \(-0.143701\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −42.5253 | −0.211569 | ||||||||
\(202\) | −121.663 | − | 121.663i | −0.602291 | − | 0.602291i | ||||
\(203\) | 45.7596 | − | 45.7596i | 0.225417 | − | 0.225417i | ||||
\(204\) | 63.9915i | 0.313684i | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 156.642 | 0.760397 | ||||||||
\(207\) | −7.03366 | − | 7.03366i | −0.0339791 | − | 0.0339791i | ||||
\(208\) | 11.9782 | − | 11.9782i | 0.0575876 | − | 0.0575876i | ||||
\(209\) | − | 89.2392i | − | 0.426982i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −146.655 | −0.695047 | −0.347524 | − | 0.937671i | \(-0.612977\pi\) | ||||
−0.347524 | + | 0.937671i | \(0.612977\pi\) | |||||||
\(212\) | 23.9031 | + | 23.9031i | 0.112750 | + | 0.112750i | ||||
\(213\) | −52.9391 | + | 52.9391i | −0.248540 | + | 0.248540i | ||||
\(214\) | 250.518i | 1.17064i | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 14.6969 | 0.0680414 | ||||||||
\(217\) | −87.3847 | − | 87.3847i | −0.402694 | − | 0.402694i | ||||
\(218\) | −181.318 | + | 181.318i | −0.831733 | + | 0.831733i | ||||
\(219\) | − | 96.5280i | − | 0.440767i | ||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −78.2309 | −0.353986 | ||||||||
\(222\) | 75.1732 | + | 75.1732i | 0.338618 | + | 0.338618i | ||||
\(223\) | 86.4182 | − | 86.4182i | 0.387526 | − | 0.387526i | −0.486278 | − | 0.873804i | \(-0.661646\pi\) |
0.873804 | + | 0.486278i | \(0.161646\pi\) | |||||||
\(224\) | 14.9666i | 0.0668153i | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 33.5107 | 0.148277 | ||||||||
\(227\) | −2.32591 | − | 2.32591i | −0.0102463 | − | 0.0102463i | 0.701965 | − | 0.712211i | \(-0.252306\pi\) |
−0.712211 | + | 0.701965i | \(0.752306\pi\) | |||||||
\(228\) | −72.2796 | + | 72.2796i | −0.317016 | + | 0.317016i | ||||
\(229\) | − | 345.111i | − | 1.50704i | −0.657427 | − | 0.753518i | \(-0.728355\pi\) | ||
0.657427 | − | 0.753518i | \(-0.271645\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 13.8588 | 0.0599948 | ||||||||
\(232\) | −48.9191 | − | 48.9191i | −0.210858 | − | 0.210858i | ||||
\(233\) | −97.4876 | + | 97.4876i | −0.418402 | + | 0.418402i | −0.884653 | − | 0.466251i | \(-0.845604\pi\) |
0.466251 | + | 0.884653i | \(0.345604\pi\) | |||||||
\(234\) | 17.9673i | 0.0767834i | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −64.5795 | −0.273642 | ||||||||
\(237\) | −0.123580 | − | 0.123580i | −0.000521433 | − | 0.000521433i | ||||
\(238\) | 48.8743 | − | 48.8743i | 0.205354 | − | 0.205354i | ||||
\(239\) | − | 155.285i | − | 0.649730i | −0.945760 | − | 0.324865i | \(-0.894681\pi\) | ||
0.945760 | − | 0.324865i | \(-0.105319\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −46.6435 | −0.193542 | −0.0967708 | − | 0.995307i | \(-0.530851\pi\) | ||||
−0.0967708 | + | 0.995307i | \(0.530851\pi\) | |||||||
\(242\) | −111.854 | − | 111.854i | −0.462207 | − | 0.462207i | ||||
\(243\) | −11.0227 | + | 11.0227i | −0.0453609 | + | 0.0453609i | ||||
\(244\) | − | 156.795i | − | 0.642604i | ||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 29.3405 | 0.119270 | ||||||||
\(247\) | −88.3633 | − | 88.3633i | −0.357746 | − | 0.357746i | ||||
\(248\) | −93.4182 | + | 93.4182i | −0.376686 | + | 0.376686i | ||||
\(249\) | 39.1843i | 0.157367i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −110.354 | −0.439657 | −0.219829 | − | 0.975539i | \(-0.570550\pi\) | ||||
−0.219829 | + | 0.975539i | \(0.570550\pi\) | |||||||
\(252\) | −11.2250 | − | 11.2250i | −0.0445435 | − | 0.0445435i | ||||
\(253\) | −7.09049 | + | 7.09049i | −0.0280256 | + | 0.0280256i | ||||
\(254\) | 6.85709i | 0.0269964i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 16.0000 | 0.0625000 | ||||||||
\(257\) | 248.411 | + | 248.411i | 0.966580 | + | 0.966580i | 0.999459 | − | 0.0328796i | \(-0.0104678\pi\) |
−0.0328796 | + | 0.999459i | \(0.510468\pi\) | |||||||
\(258\) | −0.986041 | + | 0.986041i | −0.00382187 | + | 0.00382187i | ||||
\(259\) | − | 114.829i | − | 0.443355i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 73.3786 | 0.281144 | ||||||||
\(262\) | −201.822 | − | 201.822i | −0.770314 | − | 0.770314i | ||||
\(263\) | −32.6076 | + | 32.6076i | −0.123983 | + | 0.123983i | −0.766376 | − | 0.642392i | \(-0.777942\pi\) |
0.642392 | + | 0.766376i | \(0.277942\pi\) | |||||||
\(264\) | − | 14.8157i | − | 0.0561200i | ||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 110.409 | 0.415071 | ||||||||
\(267\) | −112.021 | − | 112.021i | −0.419554 | − | 0.419554i | ||||
\(268\) | 34.7218 | − | 34.7218i | 0.129559 | − | 0.129559i | ||||
\(269\) | 109.536i | 0.407197i | 0.979054 | + | 0.203598i | \(0.0652637\pi\) | ||||
−0.979054 | + | 0.203598i | \(0.934736\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −105.472 | −0.389195 | −0.194597 | − | 0.980883i | \(-0.562340\pi\) | ||||
−0.194597 | + | 0.980883i | \(0.562340\pi\) | |||||||
\(272\) | −52.2488 | − | 52.2488i | −0.192091 | − | 0.192091i | ||||
\(273\) | 13.7228 | − | 13.7228i | 0.0502665 | − | 0.0502665i | ||||
\(274\) | 300.795i | 1.09779i | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 11.4859 | 0.0416157 | ||||||||
\(277\) | −172.034 | − | 172.034i | −0.621061 | − | 0.621061i | 0.324742 | − | 0.945803i | \(-0.394723\pi\) |
−0.945803 | + | 0.324742i | \(0.894723\pi\) | |||||||
\(278\) | 120.042 | − | 120.042i | 0.431806 | − | 0.431806i | ||||
\(279\) | − | 140.127i | − | 0.502248i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −88.5422 | −0.315097 | −0.157548 | − | 0.987511i | \(-0.550359\pi\) | ||||
−0.157548 | + | 0.987511i | \(0.550359\pi\) | |||||||
\(282\) | 113.699 | + | 113.699i | 0.403187 | + | 0.403187i | ||||
\(283\) | −187.561 | + | 187.561i | −0.662758 | + | 0.662758i | −0.956029 | − | 0.293271i | \(-0.905256\pi\) |
0.293271 | + | 0.956029i | \(0.405256\pi\) | |||||||
\(284\) | − | 86.4492i | − | 0.304398i | ||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 18.1125 | 0.0633303 | ||||||||
\(287\) | −22.4092 | − | 22.4092i | −0.0780808 | − | 0.0780808i | ||||
\(288\) | −12.0000 | + | 12.0000i | −0.0416667 | + | 0.0416667i | ||||
\(289\) | 52.2423i | 0.180769i | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 34.7235 | 0.119325 | ||||||||
\(292\) | 78.8147 | + | 78.8147i | 0.269914 | + | 0.269914i | ||||
\(293\) | 237.252 | − | 237.252i | 0.809733 | − | 0.809733i | −0.174861 | − | 0.984593i | \(-0.555947\pi\) |
0.984593 | + | 0.174861i | \(0.0559475\pi\) | |||||||
\(294\) | 17.1464i | 0.0583212i | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −122.757 | −0.414721 | ||||||||
\(297\) | 11.1118 | + | 11.1118i | 0.0374133 | + | 0.0374133i | ||||
\(298\) | −37.0923 | + | 37.0923i | −0.124471 | + | 0.124471i | ||||
\(299\) | 14.0418i | 0.0469625i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.50620 | 0.00500400 | ||||||||
\(302\) | −133.681 | − | 133.681i | −0.442653 | − | 0.442653i | ||||
\(303\) | −149.006 | + | 149.006i | −0.491768 | + | 0.491768i | ||||
\(304\) | − | 118.032i | − | 0.388263i | ||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 78.3732 | 0.256122 | ||||||||
\(307\) | −49.8059 | − | 49.8059i | −0.162234 | − | 0.162234i | 0.621322 | − | 0.783556i | \(-0.286596\pi\) |
−0.783556 | + | 0.621322i | \(0.786596\pi\) | |||||||
\(308\) | −11.3157 | + | 11.3157i | −0.0367391 | + | 0.0367391i | ||||
\(309\) | − | 191.846i | − | 0.620862i | ||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 607.147 | 1.95224 | 0.976121 | − | 0.217226i | \(-0.0697009\pi\) | ||||
0.976121 | + | 0.217226i | \(0.0697009\pi\) | |||||||
\(312\) | −14.6703 | − | 14.6703i | −0.0470200 | − | 0.0470200i | ||||
\(313\) | 67.5533 | − | 67.5533i | 0.215825 | − | 0.215825i | −0.590911 | − | 0.806737i | \(-0.701232\pi\) |
0.806737 | + | 0.590911i | \(0.201232\pi\) | |||||||
\(314\) | − | 250.279i | − | 0.797067i | ||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0.201805 | 0.000638622 | ||||||||
\(317\) | 86.6951 | + | 86.6951i | 0.273486 | + | 0.273486i | 0.830502 | − | 0.557016i | \(-0.188054\pi\) |
−0.557016 | + | 0.830502i | \(0.688054\pi\) | |||||||
\(318\) | 29.2751 | − | 29.2751i | 0.0920602 | − | 0.0920602i | ||||
\(319\) | − | 73.9714i | − | 0.231885i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 306.820 | 0.955826 | ||||||||
\(322\) | −8.77252 | − | 8.77252i | −0.0272439 | − | 0.0272439i | ||||
\(323\) | −385.440 | + | 385.440i | −1.19331 | + | 1.19331i | ||||
\(324\) | − | 18.0000i | − | 0.0555556i | ||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 314.647 | 0.965174 | ||||||||
\(327\) | 222.068 | + | 222.068i | 0.679107 | + | 0.679107i | ||||
\(328\) | −23.9564 | + | 23.9564i | −0.0730379 | + | 0.0730379i | ||||
\(329\) | − | 173.678i | − | 0.527896i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 591.123 | 1.78587 | 0.892935 | − | 0.450185i | \(-0.148642\pi\) | ||||
0.892935 | + | 0.450185i | \(0.148642\pi\) | |||||||
\(332\) | −31.9939 | − | 31.9939i | −0.0963671 | − | 0.0963671i | ||||
\(333\) | 92.0680 | − | 92.0680i | 0.276481 | − | 0.276481i | ||||
\(334\) | 48.7404i | 0.145929i | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 18.3303 | 0.0545545 | ||||||||
\(337\) | −383.876 | − | 383.876i | −1.13910 | − | 1.13910i | −0.988612 | − | 0.150485i | \(-0.951916\pi\) |
−0.150485 | − | 0.988612i | \(-0.548084\pi\) | |||||||
\(338\) | −151.065 | + | 151.065i | −0.446939 | + | 0.446939i | ||||
\(339\) | − | 41.0420i | − | 0.121068i | ||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −141.259 | −0.414250 | ||||||||
\(342\) | 88.5240 | + | 88.5240i | 0.258842 | + | 0.258842i | ||||
\(343\) | 13.0958 | − | 13.0958i | 0.0381802 | − | 0.0381802i | ||||
\(344\) | − | 1.61020i | − | 0.00468081i | ||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −88.5024 | −0.255787 | ||||||||
\(347\) | 424.033 | + | 424.033i | 1.22200 | + | 1.22200i | 0.966921 | + | 0.255075i | \(0.0821003\pi\) |
0.255075 | + | 0.966921i | \(0.417900\pi\) | |||||||
\(348\) | −59.9134 | + | 59.9134i | −0.172165 | + | 0.172165i | ||||
\(349\) | − | 450.441i | − | 1.29066i | −0.763903 | − | 0.645331i | \(-0.776719\pi\) | ||
0.763903 | − | 0.645331i | \(-0.223281\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 22.0054 | 0.0626934 | ||||||||
\(352\) | 12.0969 | + | 12.0969i | 0.0343663 | + | 0.0343663i | ||||
\(353\) | −332.857 | + | 332.857i | −0.942937 | + | 0.942937i | −0.998458 | − | 0.0555202i | \(-0.982318\pi\) |
0.0555202 | + | 0.998458i | \(0.482318\pi\) | |||||||
\(354\) | 79.0934i | 0.223428i | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 182.930 | 0.513847 | ||||||||
\(357\) | −59.8585 | − | 59.8585i | −0.167671 | − | 0.167671i | ||||
\(358\) | −101.526 | + | 101.526i | −0.283592 | + | 0.283592i | ||||
\(359\) | − | 405.400i | − | 1.12925i | −0.825349 | − | 0.564623i | \(-0.809021\pi\) | ||
0.825349 | − | 0.564623i | \(-0.190979\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −509.722 | −1.41197 | ||||||||
\(362\) | −138.946 | − | 138.946i | −0.383829 | − | 0.383829i | ||||
\(363\) | −136.993 | + | 136.993i | −0.377390 | + | 0.377390i | ||||
\(364\) | 22.4092i | 0.0615637i | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −192.034 | −0.524684 | ||||||||
\(367\) | −342.518 | − | 342.518i | −0.933291 | − | 0.933291i | 0.0646188 | − | 0.997910i | \(-0.479417\pi\) |
−0.997910 | + | 0.0646188i | \(0.979417\pi\) | |||||||
\(368\) | −9.37822 | + | 9.37822i | −0.0254843 | + | 0.0254843i | ||||
\(369\) | − | 35.9346i | − | 0.0973838i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −44.7185 | −0.120535 | ||||||||
\(372\) | 114.413 | + | 114.413i | 0.307563 | + | 0.307563i | ||||
\(373\) | 415.273 | − | 415.273i | 1.11333 | − | 1.11333i | 0.120635 | − | 0.992697i | \(-0.461507\pi\) |
0.992697 | − | 0.120635i | \(-0.0384931\pi\) | |||||||
\(374\) | − | 79.0064i | − | 0.211247i | ||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −185.669 | −0.493801 | ||||||||
\(377\) | −73.2454 | − | 73.2454i | −0.194285 | − | 0.194285i | ||||
\(378\) | −13.7477 | + | 13.7477i | −0.0363696 | + | 0.0363696i | ||||
\(379\) | 118.806i | 0.313473i | 0.987640 | + | 0.156736i | \(0.0500973\pi\) | ||||
−0.987640 | + | 0.156736i | \(0.949903\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 8.39819 | 0.0220425 | ||||||||
\(382\) | 299.678 | + | 299.678i | 0.784497 | + | 0.784497i | ||||
\(383\) | 161.764 | − | 161.764i | 0.422361 | − | 0.422361i | −0.463655 | − | 0.886016i | \(-0.653462\pi\) |
0.886016 | + | 0.463655i | \(0.153462\pi\) | |||||||
\(384\) | − | 19.5959i | − | 0.0510310i | ||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 273.854 | 0.709467 | ||||||||
\(387\) | 1.20765 | + | 1.20765i | 0.00312054 | + | 0.00312054i | ||||
\(388\) | −28.3516 | + | 28.3516i | −0.0730712 | + | 0.0730712i | ||||
\(389\) | 314.948i | 0.809636i | 0.914397 | + | 0.404818i | \(0.132665\pi\) | ||||
−0.914397 | + | 0.404818i | \(0.867335\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 61.2501 | 0.156650 | ||||||||
\(392\) | −14.0000 | − | 14.0000i | −0.0357143 | − | 0.0357143i | ||||
\(393\) | −247.181 | + | 247.181i | −0.628959 | + | 0.628959i | ||||
\(394\) | − | 254.953i | − | 0.647088i | ||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −18.1454 | −0.0458218 | ||||||||
\(397\) | 76.9396 | + | 76.9396i | 0.193802 | + | 0.193802i | 0.797337 | − | 0.603534i | \(-0.206241\pi\) |
−0.603534 | + | 0.797337i | \(0.706241\pi\) | |||||||
\(398\) | 173.636 | − | 173.636i | 0.436272 | − | 0.436272i | ||||
\(399\) | − | 135.223i | − | 0.338904i | ||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −143.407 | −0.357623 | −0.178811 | − | 0.983883i | \(-0.557225\pi\) | ||||
−0.178811 | + | 0.983883i | \(0.557225\pi\) | |||||||
\(402\) | −42.5253 | − | 42.5253i | −0.105784 | − | 0.105784i | ||||
\(403\) | −139.873 | + | 139.873i | −0.347079 | + | 0.347079i | ||||
\(404\) | − | 243.325i | − | 0.602291i | ||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 91.5192 | 0.225417 | ||||||||
\(407\) | −92.8118 | − | 92.8118i | −0.228039 | − | 0.228039i | ||||
\(408\) | −63.9915 | + | 63.9915i | −0.156842 | + | 0.156842i | ||||
\(409\) | − | 444.181i | − | 1.08602i | −0.839727 | − | 0.543008i | \(-0.817285\pi\) | ||
0.839727 | − | 0.543008i | \(-0.182715\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 368.397 | 0.896343 | ||||||||
\(412\) | 156.642 | + | 156.642i | 0.380199 | + | 0.380199i | ||||
\(413\) | 60.4086 | − | 60.4086i | 0.146268 | − | 0.146268i | ||||
\(414\) | − | 14.0673i | − | 0.0339791i | ||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 23.9564 | 0.0575876 | ||||||||
\(417\) | −147.021 | − | 147.021i | −0.352568 | − | 0.352568i | ||||
\(418\) | 89.2392 | − | 89.2392i | 0.213491 | − | 0.213491i | ||||
\(419\) | − | 550.340i | − | 1.31346i | −0.754126 | − | 0.656730i | \(-0.771939\pi\) | ||
0.754126 | − | 0.656730i | \(-0.228061\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 389.810 | 0.925914 | 0.462957 | − | 0.886381i | \(-0.346788\pi\) | ||||
0.462957 | + | 0.886381i | \(0.346788\pi\) | |||||||
\(422\) | −146.655 | − | 146.655i | −0.347524 | − | 0.347524i | ||||
\(423\) | 139.252 | − | 139.252i | 0.329201 | − | 0.329201i | ||||
\(424\) | 47.8061i | 0.112750i | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −105.878 | −0.248540 | ||||||||
\(427\) | 146.669 | + | 146.669i | 0.343487 | + | 0.343487i | ||||
\(428\) | −250.518 | + | 250.518i | −0.585321 | + | 0.585321i | ||||
\(429\) | − | 22.1832i | − | 0.0517090i | ||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 752.470 | 1.74587 | 0.872936 | − | 0.487836i | \(-0.162213\pi\) | ||||
0.872936 | + | 0.487836i | \(0.162213\pi\) | |||||||
\(432\) | 14.6969 | + | 14.6969i | 0.0340207 | + | 0.0340207i | ||||
\(433\) | 336.761 | − | 336.761i | 0.777740 | − | 0.777740i | −0.201706 | − | 0.979446i | \(-0.564649\pi\) |
0.979446 | + | 0.201706i | \(0.0646487\pi\) | |||||||
\(434\) | − | 174.769i | − | 0.402694i | ||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −362.636 | −0.831733 | ||||||||
\(437\) | 69.1831 | + | 69.1831i | 0.158314 | + | 0.158314i | ||||
\(438\) | 96.5280 | − | 96.5280i | 0.220383 | − | 0.220383i | ||||
\(439\) | − | 380.190i | − | 0.866037i | −0.901385 | − | 0.433019i | \(-0.857448\pi\) | ||
0.901385 | − | 0.433019i | \(-0.142552\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 21.0000 | 0.0476190 | ||||||||
\(442\) | −78.2309 | − | 78.2309i | −0.176993 | − | 0.176993i | ||||
\(443\) | 548.394 | − | 548.394i | 1.23791 | − | 1.23791i | 0.277055 | − | 0.960854i | \(-0.410642\pi\) |
0.960854 | − | 0.277055i | \(-0.0893583\pi\) | |||||||
\(444\) | 150.346i | 0.338618i | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 172.836 | 0.387526 | ||||||||
\(447\) | 45.4287 | + | 45.4287i | 0.101630 | + | 0.101630i | ||||
\(448\) | −14.9666 | + | 14.9666i | −0.0334077 | + | 0.0334077i | ||||
\(449\) | 809.446i | 1.80277i | 0.433013 | + | 0.901387i | \(0.357450\pi\) | ||||
−0.433013 | + | 0.901387i | \(0.642550\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −36.2249 | −0.0803214 | ||||||||
\(452\) | 33.5107 | + | 33.5107i | 0.0741387 | + | 0.0741387i | ||||
\(453\) | −163.725 | + | 163.725i | −0.361425 | + | 0.361425i | ||||
\(454\) | − | 4.65182i | − | 0.0102463i | ||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −144.559 | −0.317016 | ||||||||
\(457\) | −273.719 | − | 273.719i | −0.598949 | − | 0.598949i | 0.341084 | − | 0.940033i | \(-0.389206\pi\) |
−0.940033 | + | 0.341084i | \(0.889206\pi\) | |||||||
\(458\) | 345.111 | − | 345.111i | 0.753518 | − | 0.753518i | ||||
\(459\) | − | 95.9872i | − | 0.209122i | ||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 336.458 | 0.729844 | 0.364922 | − | 0.931038i | \(-0.381096\pi\) | ||||
0.364922 | + | 0.931038i | \(0.381096\pi\) | |||||||
\(462\) | 13.8588 | + | 13.8588i | 0.0299974 | + | 0.0299974i | ||||
\(463\) | −447.621 | + | 447.621i | −0.966785 | + | 0.966785i | −0.999466 | − | 0.0326812i | \(-0.989595\pi\) |
0.0326812 | + | 0.999466i | \(0.489595\pi\) | |||||||
\(464\) | − | 97.8381i | − | 0.210858i | ||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −194.975 | −0.418402 | ||||||||
\(467\) | −185.531 | − | 185.531i | −0.397282 | − | 0.397282i | 0.479991 | − | 0.877273i | \(-0.340640\pi\) |
−0.877273 | + | 0.479991i | \(0.840640\pi\) | |||||||
\(468\) | −17.9673 | + | 17.9673i | −0.0383917 | + | 0.0383917i | ||||
\(469\) | 64.9585i | 0.138504i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −306.528 | −0.650802 | ||||||||
\(472\) | −64.5795 | − | 64.5795i | −0.136821 | − | 0.136821i | ||||
\(473\) | 1.21741 | − | 1.21741i | 0.00257380 | − | 0.00257380i | ||||
\(474\) | − | 0.247159i | − | 0.000521433i | ||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 97.7486 | 0.205354 | ||||||||
\(477\) | −35.8546 | − | 35.8546i | −0.0751668 | − | 0.0751668i | ||||
\(478\) | 155.285 | − | 155.285i | 0.324865 | − | 0.324865i | ||||
\(479\) | 444.150i | 0.927244i | 0.886033 | + | 0.463622i | \(0.153450\pi\) | ||||
−0.886033 | + | 0.463622i | \(0.846550\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −183.802 | −0.382124 | ||||||||
\(482\) | −46.6435 | − | 46.6435i | −0.0967708 | − | 0.0967708i | ||||
\(483\) | −10.7441 | + | 10.7441i | −0.0222445 | + | 0.0222445i | ||||
\(484\) | − | 223.708i | − | 0.462207i | ||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −22.0454 | −0.0453609 | ||||||||
\(487\) | 117.334 | + | 117.334i | 0.240932 | + | 0.240932i | 0.817236 | − | 0.576304i | \(-0.195505\pi\) |
−0.576304 | + | 0.817236i | \(0.695505\pi\) | |||||||
\(488\) | 156.795 | − | 156.795i | 0.321302 | − | 0.321302i | ||||
\(489\) | − | 385.362i | − | 0.788061i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 780.904 | 1.59044 | 0.795218 | − | 0.606324i | \(-0.207357\pi\) | ||||
0.795218 | + | 0.606324i | \(0.207357\pi\) | |||||||
\(492\) | 29.3405 | + | 29.3405i | 0.0596352 | + | 0.0596352i | ||||
\(493\) | −319.495 | + | 319.495i | −0.648064 | + | 0.648064i | ||||
\(494\) | − | 176.727i | − | 0.357746i | ||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −186.836 | −0.376686 | ||||||||
\(497\) | 80.8658 | + | 80.8658i | 0.162708 | + | 0.162708i | ||||
\(498\) | −39.1843 | + | 39.1843i | −0.0786834 | + | 0.0786834i | ||||
\(499\) | 520.134i | 1.04235i | 0.853449 | + | 0.521176i | \(0.174507\pi\) | ||||
−0.853449 | + | 0.521176i | \(0.825493\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 59.6945 | 0.119151 | ||||||||
\(502\) | −110.354 | − | 110.354i | −0.219829 | − | 0.219829i | ||||
\(503\) | 392.689 | − | 392.689i | 0.780693 | − | 0.780693i | −0.199255 | − | 0.979948i | \(-0.563852\pi\) |
0.979948 | + | 0.199255i | \(0.0638522\pi\) | |||||||
\(504\) | − | 22.4499i | − | 0.0445435i | ||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −14.1810 | −0.0280256 | ||||||||
\(507\) | 185.016 | + | 185.016i | 0.364924 | + | 0.364924i | ||||
\(508\) | −6.85709 | + | 6.85709i | −0.0134982 | + | 0.0134982i | ||||
\(509\) | 6.30380i | 0.0123847i | 0.999981 | + | 0.00619234i | \(0.00197110\pi\) | ||||
−0.999981 | + | 0.00619234i | \(0.998029\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −147.449 | −0.288550 | ||||||||
\(512\) | 16.0000 | + | 16.0000i | 0.0312500 | + | 0.0312500i | ||||
\(513\) | 108.419 | − | 108.419i | 0.211344 | − | 0.211344i | ||||
\(514\) | 496.822i | 0.966580i | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −1.97208 | −0.00382187 | ||||||||
\(517\) | −140.377 | − | 140.377i | −0.271522 | − | 0.271522i | ||||
\(518\) | 114.829 | − | 114.829i | 0.221678 | − | 0.221678i | ||||
\(519\) | 108.393i | 0.208849i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −146.807 | −0.281779 | −0.140890 | − | 0.990025i | \(-0.544996\pi\) | ||||
−0.140890 | + | 0.990025i | \(0.544996\pi\) | |||||||
\(522\) | 73.3786 | + | 73.3786i | 0.140572 | + | 0.140572i | ||||
\(523\) | −96.3768 | + | 96.3768i | −0.184277 | + | 0.184277i | −0.793217 | − | 0.608940i | \(-0.791595\pi\) |
0.608940 | + | 0.793217i | \(0.291595\pi\) | |||||||
\(524\) | − | 403.645i | − | 0.770314i | ||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −65.2152 | −0.123983 | ||||||||
\(527\) | 610.123 | + | 610.123i | 1.15773 | + | 1.15773i | ||||
\(528\) | 14.8157 | − | 14.8157i | 0.0280600 | − | 0.0280600i | ||||
\(529\) | 518.006i | 0.979218i | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 96.8692 | 0.182428 | ||||||||
\(532\) | 110.409 | + | 110.409i | 0.207535 | + | 0.207535i | ||||
\(533\) | −35.8694 | + | 35.8694i | −0.0672972 | + | 0.0672972i | ||||
\(534\) | − | 224.042i | − | 0.419554i | ||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 69.4436 | 0.129559 | ||||||||
\(537\) | 124.343 | + | 124.343i | 0.231552 | + | 0.231552i | ||||
\(538\) | −109.536 | + | 109.536i | −0.203598 | + | 0.203598i | ||||
\(539\) | − | 21.1697i | − | 0.0392758i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −199.291 | −0.368376 | −0.184188 | − | 0.982891i | \(-0.558966\pi\) | ||||
−0.184188 | + | 0.982891i | \(0.558966\pi\) | |||||||
\(542\) | −105.472 | − | 105.472i | −0.194597 | − | 0.194597i | ||||
\(543\) | −170.174 | + | 170.174i | −0.313395 | + | 0.313395i | ||||
\(544\) | − | 104.498i | − | 0.192091i | ||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 27.4455 | 0.0502665 | ||||||||
\(547\) | −615.316 | − | 615.316i | −1.12489 | − | 1.12489i | −0.990995 | − | 0.133897i | \(-0.957251\pi\) |
−0.133897 | − | 0.990995i | \(-0.542749\pi\) | |||||||
\(548\) | −300.795 | + | 300.795i | −0.548896 | + | 0.548896i | ||||
\(549\) | 235.193i | 0.428403i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −721.752 | −1.30989 | ||||||||
\(552\) | 11.4859 | + | 11.4859i | 0.0208078 | + | 0.0208078i | ||||
\(553\) | −0.188771 | + | 0.188771i | −0.000341358 | + | 0.000341358i | ||||
\(554\) | − | 344.068i | − | 0.621061i | ||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 240.084 | 0.431806 | ||||||||
\(557\) | −505.708 | − | 505.708i | −0.907914 | − | 0.907914i | 0.0881896 | − | 0.996104i | \(-0.471892\pi\) |
−0.996104 | + | 0.0881896i | \(0.971892\pi\) | |||||||
\(558\) | 140.127 | − | 140.127i | 0.251124 | − | 0.251124i | ||||
\(559\) | − | 2.41091i | − | 0.00431290i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −96.7627 | −0.172482 | ||||||||
\(562\) | −88.5422 | − | 88.5422i | −0.157548 | − | 0.157548i | ||||
\(563\) | −526.861 | + | 526.861i | −0.935811 | + | 0.935811i | −0.998061 | − | 0.0622500i | \(-0.980172\pi\) |
0.0622500 | + | 0.998061i | \(0.480172\pi\) | |||||||
\(564\) | 227.397i | 0.403187i | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −375.121 | −0.662758 | ||||||||
\(567\) | 16.8375 | + | 16.8375i | 0.0296957 | + | 0.0296957i | ||||
\(568\) | 86.4492 | − | 86.4492i | 0.152199 | − | 0.152199i | ||||
\(569\) | 829.309i | 1.45749i | 0.684787 | + | 0.728743i | \(0.259895\pi\) | ||||
−0.684787 | + | 0.728743i | \(0.740105\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −642.527 | −1.12527 | −0.562633 | − | 0.826707i | \(-0.690212\pi\) | ||||
−0.562633 | + | 0.826707i | \(0.690212\pi\) | |||||||
\(572\) | 18.1125 | + | 18.1125i | 0.0316652 | + | 0.0316652i | ||||
\(573\) | 367.029 | − | 367.029i | 0.640539 | − | 0.640539i | ||||
\(574\) | − | 44.8184i | − | 0.0780808i | ||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −24.0000 | −0.0416667 | ||||||||
\(577\) | −479.432 | − | 479.432i | −0.830904 | − | 0.830904i | 0.156736 | − | 0.987641i | \(-0.449903\pi\) |
−0.987641 | + | 0.156736i | \(0.949903\pi\) | |||||||
\(578\) | −52.2423 | + | 52.2423i | −0.0903846 | + | 0.0903846i | ||||
\(579\) | − | 335.402i | − | 0.579277i | ||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 59.8551 | 0.103021 | ||||||||
\(582\) | 34.7235 | + | 34.7235i | 0.0596624 | + | 0.0596624i | ||||
\(583\) | −36.1442 | + | 36.1442i | −0.0619970 | + | 0.0619970i | ||||
\(584\) | 157.629i | 0.269914i | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 474.503 | 0.809733 | ||||||||
\(587\) | −66.4097 | − | 66.4097i | −0.113134 | − | 0.113134i | 0.648273 | − | 0.761408i | \(-0.275491\pi\) |
−0.761408 | + | 0.648273i | \(0.775491\pi\) | |||||||
\(588\) | −17.1464 | + | 17.1464i | −0.0291606 | + | 0.0291606i | ||||
\(589\) | 1378.29i | 2.34005i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −312.252 | −0.528345 | ||||||||
\(592\) | −122.757 | − | 122.757i | −0.207360 | − | 0.207360i | ||||
\(593\) | 744.586 | − | 744.586i | 1.25563 | − | 1.25563i | 0.302466 | − | 0.953160i | \(-0.402190\pi\) |
0.953160 | − | 0.302466i | \(-0.0978097\pi\) | |||||||
\(594\) | 22.2235i | 0.0374133i | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −74.1847 | −0.124471 | ||||||||
\(597\) | −212.660 | − | 212.660i | −0.356214 | − | 0.356214i | ||||
\(598\) | −14.0418 | + | 14.0418i | −0.0234812 | + | 0.0234812i | ||||
\(599\) | 840.233i | 1.40273i | 0.712804 | + | 0.701363i | \(0.247425\pi\) | ||||
−0.712804 | + | 0.701363i | \(0.752575\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −739.213 | −1.22997 | −0.614986 | − | 0.788538i | \(-0.710838\pi\) | ||||
−0.614986 | + | 0.788538i | \(0.710838\pi\) | |||||||
\(602\) | 1.50620 | + | 1.50620i | 0.00250200 | + | 0.00250200i | ||||
\(603\) | −52.0827 | + | 52.0827i | −0.0863726 | + | 0.0863726i | ||||
\(604\) | − | 267.362i | − | 0.442653i | ||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −298.012 | −0.491768 | ||||||||
\(607\) | 776.567 | + | 776.567i | 1.27935 | + | 1.27935i | 0.941030 | + | 0.338323i | \(0.109860\pi\) |
0.338323 | + | 0.941030i | \(0.390140\pi\) | |||||||
\(608\) | 118.032 | − | 118.032i | 0.194132 | − | 0.194132i | ||||
\(609\) | − | 112.088i | − | 0.184052i | ||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −277.998 | −0.454989 | ||||||||
\(612\) | 78.3732 | + | 78.3732i | 0.128061 | + | 0.128061i | ||||
\(613\) | −340.874 | + | 340.874i | −0.556075 | + | 0.556075i | −0.928188 | − | 0.372113i | \(-0.878633\pi\) |
0.372113 | + | 0.928188i | \(0.378633\pi\) | |||||||
\(614\) | − | 99.6117i | − | 0.162234i | ||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −22.6313 | −0.0367391 | ||||||||
\(617\) | −539.699 | − | 539.699i | −0.874715 | − | 0.874715i | 0.118266 | − | 0.992982i | \(-0.462266\pi\) |
−0.992982 | + | 0.118266i | \(0.962266\pi\) | |||||||
\(618\) | 191.846 | − | 191.846i | 0.310431 | − | 0.310431i | ||||
\(619\) | − | 354.188i | − | 0.572193i | −0.958201 | − | 0.286097i | \(-0.907642\pi\) | ||
0.958201 | − | 0.286097i | \(-0.0923579\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −17.2289 | −0.0277438 | ||||||||
\(622\) | 607.147 | + | 607.147i | 0.976121 | + | 0.976121i | ||||
\(623\) | −171.115 | + | 171.115i | −0.274663 | + | 0.274663i | ||||
\(624\) | − | 29.3405i | − | 0.0470200i | ||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 135.107 | 0.215825 | ||||||||
\(627\) | −109.295 | − | 109.295i | −0.174315 | − | 0.174315i | ||||
\(628\) | 250.279 | − | 250.279i | 0.398533 | − | 0.398533i | ||||
\(629\) | 801.741i | 1.27463i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 136.968 | 0.217065 | 0.108533 | − | 0.994093i | \(-0.465385\pi\) | ||||
0.108533 | + | 0.994093i | \(0.465385\pi\) | |||||||
\(632\) | 0.201805 | + | 0.201805i | 0.000319311 | + | 0.000319311i | ||||
\(633\) | −179.615 | + | 179.615i | −0.283752 | + | 0.283752i | ||||
\(634\) | 173.390i | 0.273486i | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 58.5503 | 0.0920602 | ||||||||
\(637\) | −20.9619 | − | 20.9619i | −0.0329072 | − | 0.0329072i | ||||
\(638\) | 73.9714 | − | 73.9714i | 0.115943 | − | 0.115943i | ||||
\(639\) | 129.674i | 0.202932i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −956.048 | −1.49149 | −0.745747 | − | 0.666229i | \(-0.767907\pi\) | ||||
−0.745747 | + | 0.666229i | \(0.767907\pi\) | |||||||
\(642\) | 306.820 | + | 306.820i | 0.477913 | + | 0.477913i | ||||
\(643\) | −294.266 | + | 294.266i | −0.457646 | + | 0.457646i | −0.897882 | − | 0.440236i | \(-0.854895\pi\) |
0.440236 | + | 0.897882i | \(0.354895\pi\) | |||||||
\(644\) | − | 17.5450i | − | 0.0272439i | ||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −770.879 | −1.19331 | ||||||||
\(647\) | 786.052 | + | 786.052i | 1.21492 | + | 1.21492i | 0.969389 | + | 0.245529i | \(0.0789618\pi\) |
0.245529 | + | 0.969389i | \(0.421038\pi\) | |||||||
\(648\) | 18.0000 | − | 18.0000i | 0.0277778 | − | 0.0277778i | ||||
\(649\) | − | 97.6518i | − | 0.150465i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −214.048 | −0.328799 | ||||||||
\(652\) | 314.647 | + | 314.647i | 0.482587 | + | 0.482587i | ||||
\(653\) | 97.8898 | − | 97.8898i | 0.149908 | − | 0.149908i | −0.628169 | − | 0.778077i | \(-0.716195\pi\) |
0.778077 | + | 0.628169i | \(0.216195\pi\) | |||||||
\(654\) | 444.136i | 0.679107i | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −47.9128 | −0.0730379 | ||||||||
\(657\) | −118.222 | − | 118.222i | −0.179942 | − | 0.179942i | ||||
\(658\) | 173.678 | − | 173.678i | 0.263948 | − | 0.263948i | ||||
\(659\) | 1155.72i | 1.75375i | 0.480718 | + | 0.876875i | \(0.340376\pi\) | ||||
−0.480718 | + | 0.876875i | \(0.659624\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 675.364 | 1.02173 | 0.510865 | − | 0.859661i | \(-0.329325\pi\) | ||||
0.510865 | + | 0.859661i | \(0.329325\pi\) | |||||||
\(662\) | 591.123 | + | 591.123i | 0.892935 | + | 0.892935i | ||||
\(663\) | −95.8129 | + | 95.8129i | −0.144514 | + | 0.144514i | ||||
\(664\) | − | 63.9877i | − | 0.0963671i | ||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 184.136 | 0.276481 | ||||||||
\(667\) | 57.3467 | + | 57.3467i | 0.0859771 | + | 0.0859771i | ||||
\(668\) | −48.7404 | + | 48.7404i | −0.0729646 | + | 0.0729646i | ||||
\(669\) | − | 211.681i | − | 0.316413i | ||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 237.093 | 0.353343 | ||||||||
\(672\) | 18.3303 | + | 18.3303i | 0.0272772 | + | 0.0272772i | ||||
\(673\) | −258.340 | + | 258.340i | −0.383863 | + | 0.383863i | −0.872492 | − | 0.488629i | \(-0.837497\pi\) |
0.488629 | + | 0.872492i | \(0.337497\pi\) | |||||||
\(674\) | − | 767.752i | − | 1.13910i | ||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −302.131 | −0.446939 | ||||||||
\(677\) | 18.7815 | + | 18.7815i | 0.0277423 | + | 0.0277423i | 0.720842 | − | 0.693100i | \(-0.243755\pi\) |
−0.693100 | + | 0.720842i | \(0.743755\pi\) | |||||||
\(678\) | 41.0420 | − | 41.0420i | 0.0605340 | − | 0.0605340i | ||||
\(679\) | − | 53.0410i | − | 0.0781164i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −5.69729 | −0.00836607 | ||||||||
\(682\) | −141.259 | − | 141.259i | −0.207125 | − | 0.207125i | ||||
\(683\) | −475.671 | + | 475.671i | −0.696443 | + | 0.696443i | −0.963642 | − | 0.267198i | \(-0.913902\pi\) |
0.267198 | + | 0.963642i | \(0.413902\pi\) | |||||||
\(684\) | 177.048i | 0.258842i | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 26.1916 | 0.0381802 | ||||||||
\(687\) | −422.673 | − | 422.673i | −0.615245 | − | 0.615245i | ||||
\(688\) | 1.61020 | − | 1.61020i | 0.00234041 | − | 0.00234041i | ||||
\(689\) | 71.5790i | 0.103888i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1301.16 | 1.88301 | 0.941507 | − | 0.336992i | \(-0.109410\pi\) | ||||
0.941507 | + | 0.336992i | \(0.109410\pi\) | |||||||
\(692\) | −88.5024 | − | 88.5024i | −0.127894 | − | 0.127894i | ||||
\(693\) | 16.9735 | − | 16.9735i | 0.0244928 | − | 0.0244928i | ||||
\(694\) | 848.066i | 1.22200i | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −119.827 | −0.172165 | ||||||||
\(697\) | 156.462 | + | 156.462i | 0.224479 | + | 0.224479i | ||||
\(698\) | 450.441 | − | 450.441i | 0.645331 | − | 0.645331i | ||||
\(699\) | 238.795i | 0.341623i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −1197.02 | −1.70759 | −0.853795 | − | 0.520609i | \(-0.825705\pi\) | ||||
−0.853795 | + | 0.520609i | \(0.825705\pi\) | |||||||
\(702\) | 22.0054 | + | 22.0054i | 0.0313467 | + | 0.0313467i | ||||
\(703\) | −905.581 | + | 905.581i | −1.28817 | + | 1.28817i | ||||
\(704\) | 24.1939i | 0.0343663i | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −665.714 | −0.942937 | ||||||||
\(707\) | 227.610 | + | 227.610i | 0.321938 | + | 0.321938i | ||||
\(708\) | −79.0934 | + | 79.0934i | −0.111714 | + | 0.111714i | ||||
\(709\) | − | 1040.88i | − | 1.46810i | −0.679097 | − | 0.734049i | \(-0.737628\pi\) | ||
0.679097 | − | 0.734049i | \(-0.262372\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −0.302707 | −0.000425748 | ||||||||
\(712\) | 182.930 | + | 182.930i | 0.256924 | + | 0.256924i | ||||
\(713\) | 109.512 | − | 109.512i | 0.153593 | − | 0.153593i | ||||
\(714\) | − | 119.717i | − | 0.167671i | ||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −203.052 | −0.283592 | ||||||||
\(717\) | −190.185 | − | 190.185i | −0.265251 | − | 0.265251i | ||||
\(718\) | 405.400 | − | 405.400i | 0.564623 | − | 0.564623i | ||||
\(719\) | 670.331i | 0.932310i | 0.884703 | + | 0.466155i | \(0.154361\pi\) | ||||
−0.884703 | + | 0.466155i | \(0.845639\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −293.050 | −0.406450 | ||||||||
\(722\) | −509.722 | − | 509.722i | −0.705987 | − | 0.705987i | ||||
\(723\) | −57.1264 | + | 57.1264i | −0.0790130 | + | 0.0790130i | ||||
\(724\) | − | 277.893i | − | 0.383829i | ||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −273.985 | −0.377390 | ||||||||
\(727\) | 501.531 | + | 501.531i | 0.689864 | + | 0.689864i | 0.962202 | − | 0.272338i | \(-0.0877968\pi\) |
−0.272338 | + | 0.962202i | \(0.587797\pi\) | |||||||
\(728\) | −22.4092 | + | 22.4092i | −0.0307818 | + | 0.0307818i | ||||
\(729\) | 27.0000i | 0.0370370i | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −10.5164 | −0.0143863 | ||||||||
\(732\) | −192.034 | − | 192.034i | −0.262342 | − | 0.262342i | ||||
\(733\) | 370.001 | − | 370.001i | 0.504776 | − | 0.504776i | −0.408142 | − | 0.912918i | \(-0.633823\pi\) |
0.912918 | + | 0.408142i | \(0.133823\pi\) | |||||||
\(734\) | − | 685.036i | − | 0.933291i | ||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −18.7564 | −0.0254843 | ||||||||
\(737\) | 52.5034 | + | 52.5034i | 0.0712394 | + | 0.0712394i | ||||
\(738\) | 35.9346 | − | 35.9346i | 0.0486919 | − | 0.0486919i | ||||
\(739\) | 462.721i | 0.626145i | 0.949729 | + | 0.313073i | \(0.101358\pi\) | ||||
−0.949729 | + | 0.313073i | \(0.898642\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −216.445 | −0.292098 | ||||||||
\(742\) | −44.7185 | − | 44.7185i | −0.0602675 | − | 0.0602675i | ||||
\(743\) | 223.221 | − | 223.221i | 0.300432 | − | 0.300432i | −0.540751 | − | 0.841183i | \(-0.681860\pi\) |
0.841183 | + | 0.540751i | \(0.181860\pi\) | |||||||
\(744\) | 228.827i | 0.307563i | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 830.546 | 1.11333 | ||||||||
\(747\) | 47.9908 | + | 47.9908i | 0.0642447 | + | 0.0642447i | ||||
\(748\) | 79.0064 | − | 79.0064i | 0.105623 | − | 0.105623i | ||||
\(749\) | − | 468.675i | − | 0.625735i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 378.724 | 0.504292 | 0.252146 | − | 0.967689i | \(-0.418864\pi\) | ||||
0.252146 | + | 0.967689i | \(0.418864\pi\) | |||||||
\(752\) | −185.669 | − | 185.669i | −0.246901 | − | 0.246901i | ||||
\(753\) | −135.155 | + | 135.155i | −0.179489 | + | 0.179489i | ||||
\(754\) | − | 146.491i | − | 0.194285i | ||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −27.4955 | −0.0363696 | ||||||||
\(757\) | 698.321 | + | 698.321i | 0.922485 | + | 0.922485i | 0.997205 | − | 0.0747195i | \(-0.0238061\pi\) |
−0.0747195 | + | 0.997205i | \(0.523806\pi\) | |||||||
\(758\) | −118.806 | + | 118.806i | −0.156736 | + | 0.156736i | ||||
\(759\) | 17.3681i | 0.0228828i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −1211.43 | −1.59189 | −0.795947 | − | 0.605366i | \(-0.793027\pi\) | ||||
−0.795947 | + | 0.605366i | \(0.793027\pi\) | |||||||
\(762\) | 8.39819 | + | 8.39819i | 0.0110212 | + | 0.0110212i | ||||
\(763\) | 339.215 | − | 339.215i | 0.444580 | − | 0.444580i | ||||
\(764\) | 599.356i | 0.784497i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 323.529 | 0.422361 | ||||||||
\(767\) | −96.6934 | − | 96.6934i | −0.126067 | − | 0.126067i | ||||
\(768\) | 19.5959 | − | 19.5959i | 0.0255155 | − | 0.0255155i | ||||
\(769\) | − | 103.430i | − | 0.134499i | −0.997736 | − | 0.0672495i | \(-0.978578\pi\) | ||
0.997736 | − | 0.0672495i | \(-0.0214224\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 608.480 | 0.789209 | ||||||||
\(772\) | 273.854 | + | 273.854i | 0.354734 | + | 0.354734i | ||||
\(773\) | −50.4008 | + | 50.4008i | −0.0652015 | + | 0.0652015i | −0.738956 | − | 0.673754i | \(-0.764681\pi\) |
0.673754 | + | 0.738956i | \(0.264681\pi\) | |||||||
\(774\) | 2.41530i | 0.00312054i | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −56.7032 | −0.0730712 | ||||||||
\(777\) | −140.636 | − | 140.636i | −0.180999 | − | 0.180999i | ||||
\(778\) | −314.948 | + | 314.948i | −0.404818 | + | 0.404818i | ||||
\(779\) | 353.453i | 0.453727i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 130.721 | 0.167377 | ||||||||
\(782\) | 61.2501 | + | 61.2501i | 0.0783249 | + | 0.0783249i | ||||
\(783\) | 89.8701 | − | 89.8701i | 0.114777 | − | 0.114777i | ||||
\(784\) | − | 28.0000i | − | 0.0357143i | ||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −494.362 | −0.628959 | ||||||||
\(787\) | 237.837 | + | 237.837i | 0.302207 | + | 0.302207i | 0.841877 | − | 0.539670i | \(-0.181451\pi\) |
−0.539670 | + | 0.841877i | \(0.681451\pi\) | |||||||
\(788\) | 254.953 | − | 254.953i | 0.323544 | − | 0.323544i | ||||
\(789\) | 79.8720i | 0.101232i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −62.6927 | −0.0792576 | ||||||||
\(792\) | −18.1454 | − | 18.1454i | −0.0229109 | − | 0.0229109i | ||||
\(793\) | 234.766 | − | 234.766i | 0.296048 | − | 0.296048i | ||||
\(794\) | 153.879i | 0.193802i | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 347.272 | 0.436272 | ||||||||
\(797\) | −7.28126 | − | 7.28126i | −0.00913584 | − | 0.00913584i | 0.702524 | − | 0.711660i | \(-0.252056\pi\) |
−0.711660 | + | 0.702524i | \(0.752056\pi\) | |||||||
\(798\) | 135.223 | − | 135.223i | 0.169452 | − | 0.169452i | ||||
\(799\) | 1212.62i | 1.51768i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −274.394 | −0.342565 | ||||||||
\(802\) | −143.407 | − | 143.407i | −0.178811 | − | 0.178811i | ||||
\(803\) | −119.177 | + | 119.177i | −0.148415 | + | 0.148415i | ||||
\(804\) | − | 85.0507i | − | 0.105784i | ||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −279.746 | −0.347079 | ||||||||
\(807\) | 134.154 | + | 134.154i | 0.166237 | + | 0.166237i | ||||
\(808\) | 243.325 | − | 243.325i | 0.301145 | − | 0.301145i | ||||
\(809\) | − | 1185.33i | − | 1.46517i | −0.680673 | − | 0.732587i | \(-0.738313\pi\) | ||
0.680673 | − | 0.732587i | \(-0.261687\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −116.511 | −0.143663 | −0.0718316 | − | 0.997417i | \(-0.522884\pi\) | ||||
−0.0718316 | + | 0.997417i | \(0.522884\pi\) | |||||||
\(812\) | 91.5192 | + | 91.5192i | 0.112708 | + | 0.112708i | ||||
\(813\) | −129.176 | + | 129.176i | −0.158888 | + | 0.158888i | ||||
\(814\) | − | 185.624i | − | 0.228039i | ||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −127.983 | −0.156842 | ||||||||
\(817\) | −11.8784 | − | 11.8784i | −0.0145391 | − | 0.0145391i | ||||
\(818\) | 444.181 | − | 444.181i | 0.543008 | − | 0.543008i | ||||
\(819\) | − | 33.6138i | − | 0.0410425i | ||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 676.720 | 0.824263 | 0.412131 | − | 0.911124i | \(-0.364784\pi\) | ||||
0.412131 | + | 0.911124i | \(0.364784\pi\) | |||||||
\(822\) | 368.397 | + | 368.397i | 0.448172 | + | 0.448172i | ||||
\(823\) | 102.651 | − | 102.651i | 0.124728 | − | 0.124728i | −0.641988 | − | 0.766715i | \(-0.721890\pi\) |
0.766715 | + | 0.641988i | \(0.221890\pi\) | |||||||
\(824\) | 313.284i | 0.380199i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 120.817 | 0.146268 | ||||||||
\(827\) | −503.694 | − | 503.694i | −0.609061 | − | 0.609061i | 0.333639 | − | 0.942701i | \(-0.391723\pi\) |
−0.942701 | + | 0.333639i | \(0.891723\pi\) | |||||||
\(828\) | 14.0673 | − | 14.0673i | 0.0169895 | − | 0.0169895i | ||||
\(829\) | 854.725i | 1.03103i | 0.856880 | + | 0.515515i | \(0.172400\pi\) | ||||
−0.856880 | + | 0.515515i | \(0.827600\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −421.395 | −0.507094 | ||||||||
\(832\) | 23.9564 | + | 23.9564i | 0.0287938 | + | 0.0287938i | ||||
\(833\) | −91.4354 | + | 91.4354i | −0.109766 | + | 0.109766i | ||||
\(834\) | − | 294.042i | − | 0.352568i | ||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 178.478 | 0.213491 | ||||||||
\(837\) | −171.620 | − | 171.620i | −0.205042 | − | 0.205042i | ||||
\(838\) | 550.340 | − | 550.340i | 0.656730 | − | 0.656730i | ||||
\(839\) | 1149.25i | 1.36978i | 0.728645 | + | 0.684892i | \(0.240150\pi\) | ||||
−0.728645 | + | 0.684892i | \(0.759850\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 242.731 | 0.288622 | ||||||||
\(842\) | 389.810 | + | 389.810i | 0.462957 | + | 0.462957i | ||||
\(843\) | −108.442 | + | 108.442i | −0.128638 | + | 0.128638i | ||||
\(844\) | − | 293.310i | − | 0.347524i | ||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 278.504 | 0.329201 | ||||||||
\(847\) | 209.260 | + | 209.260i | 0.247060 | + | 0.247060i | ||||
\(848\) | −47.8061 | + | 47.8061i | −0.0563751 | + | 0.0563751i | ||||
\(849\) | 459.428i | 0.541140i | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 143.906 | 0.169102 | ||||||||
\(852\) | −105.878 | − | 105.878i | −0.124270 | − | 0.124270i | ||||
\(853\) | 234.885 | − | 234.885i | 0.275363 | − | 0.275363i | −0.555892 | − | 0.831255i | \(-0.687623\pi\) |
0.831255 | + | 0.555892i | \(0.187623\pi\) | |||||||
\(854\) | 293.338i | 0.343487i | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −501.035 | −0.585321 | ||||||||
\(857\) | 318.679 | + | 318.679i | 0.371855 | + | 0.371855i | 0.868152 | − | 0.496298i | \(-0.165308\pi\) |
−0.496298 | + | 0.868152i | \(0.665308\pi\) | |||||||
\(858\) | 22.1832 | − | 22.1832i | 0.0258545 | − | 0.0258545i | ||||
\(859\) | − | 202.016i | − | 0.235176i | −0.993062 | − | 0.117588i | \(-0.962484\pi\) | ||
0.993062 | − | 0.117588i | \(-0.0375162\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −54.8911 | −0.0637527 | ||||||||
\(862\) | 752.470 | + | 752.470i | 0.872936 | + | 0.872936i | ||||
\(863\) | 814.775 | − | 814.775i | 0.944120 | − | 0.944120i | −0.0543994 | − | 0.998519i | \(-0.517324\pi\) |
0.998519 | + | 0.0543994i | \(0.0173244\pi\) | |||||||
\(864\) | 29.3939i | 0.0340207i | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 673.522 | 0.777740 | ||||||||
\(867\) | 63.9835 | + | 63.9835i | 0.0737987 | + | 0.0737987i | ||||
\(868\) | 174.769 | − | 174.769i | 0.201347 | − | 0.201347i | ||||
\(869\) | 0.305152i | 0.000351153i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 103.976 | 0.119376 | ||||||||
\(872\) | −362.636 | − | 362.636i | −0.415867 | − | 0.415867i | ||||
\(873\) | 42.5274 | − | 42.5274i | 0.0487141 | − | 0.0487141i | ||||
\(874\) | 138.366i | 0.158314i | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 193.056 | 0.220383 | ||||||||
\(877\) | −784.014 | − | 784.014i | −0.893972 | − | 0.893972i | 0.100922 | − | 0.994894i | \(-0.467821\pi\) |
−0.994894 | + | 0.100922i | \(0.967821\pi\) | |||||||
\(878\) | 380.190 | − | 380.190i | 0.433019 | − | 0.433019i | ||||
\(879\) | − | 581.146i | − | 0.661144i | ||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −630.608 | −0.715786 | −0.357893 | − | 0.933763i | \(-0.616505\pi\) | ||||
−0.357893 | + | 0.933763i | \(0.616505\pi\) | |||||||
\(882\) | 21.0000 | + | 21.0000i | 0.0238095 | + | 0.0238095i | ||||
\(883\) | −612.193 | + | 612.193i | −0.693311 | + | 0.693311i | −0.962959 | − | 0.269648i | \(-0.913093\pi\) |
0.269648 | + | 0.962959i | \(0.413093\pi\) | |||||||
\(884\) | − | 156.462i | − | 0.176993i | ||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 1096.79 | 1.23791 | ||||||||
\(887\) | 424.255 | + | 424.255i | 0.478303 | + | 0.478303i | 0.904589 | − | 0.426286i | \(-0.140178\pi\) |
−0.426286 | + | 0.904589i | \(0.640178\pi\) | |||||||
\(888\) | −150.346 | + | 150.346i | −0.169309 | + | 0.169309i | ||||
\(889\) | − | 12.8284i | − | 0.0144302i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 27.2181 | 0.0305478 | ||||||||
\(892\) | 172.836 | + | 172.836i | 0.193763 | + | 0.193763i | ||||
\(893\) | −1369.68 | + | 1369.68i | −1.53380 | + | 1.53380i | ||||
\(894\) | 90.8573i | 0.101630i | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −29.9333 | −0.0334077 | ||||||||
\(897\) | 17.1976 | + | 17.1976i | 0.0191724 | + | 0.0191724i | ||||
\(898\) | −809.446 | + | 809.446i | −0.901387 | + | 0.901387i | ||||
\(899\) | 1142.48i | 1.27084i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 312.227 | 0.346533 | ||||||||
\(902\) | −36.2249 | − | 36.2249i | −0.0401607 | − | 0.0401607i | ||||
\(903\) | 1.84471 | − | 1.84471i | 0.00204287 | − | 0.00204287i | ||||
\(904\) | 67.0213i | 0.0741387i | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −327.451 | −0.361425 | ||||||||
\(907\) | 855.352 | + | 855.352i | 0.943056 | + | 0.943056i | 0.998464 | − | 0.0554075i | \(-0.0176458\pi\) |
−0.0554075 | + | 0.998464i | \(0.517646\pi\) | |||||||
\(908\) | 4.65182 | − | 4.65182i | 0.00512315 | − | 0.00512315i | ||||
\(909\) | 364.988i | 0.401527i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 600.082 | 0.658707 | 0.329353 | − | 0.944207i | \(-0.393169\pi\) | ||||
0.329353 | + | 0.944207i | \(0.393169\pi\) | |||||||
\(912\) | −144.559 | − | 144.559i | −0.158508 | − | 0.158508i | ||||
\(913\) | 48.3785 | − | 48.3785i | 0.0529885 | − | 0.0529885i | ||||
\(914\) | − | 547.439i | − | 0.598949i | ||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 690.222 | 0.753518 | ||||||||
\(917\) | 377.575 | + | 377.575i | 0.411750 | + | 0.411750i | ||||
\(918\) | 95.9872 | − | 95.9872i | 0.104561 | − | 0.104561i | ||||
\(919\) | − | 1703.19i | − | 1.85331i | −0.375913 | − | 0.926655i | \(-0.622671\pi\) | ||
0.375913 | − | 0.926655i | \(-0.377329\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −121.999 | −0.132464 | ||||||||
\(922\) | 336.458 | + | 336.458i | 0.364922 | + | 0.364922i | ||||
\(923\) | 129.438 | − | 129.438i | 0.140236 | − | 0.140236i | ||||
\(924\) | 27.7176i | 0.0299974i | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −895.243 | −0.966785 | ||||||||
\(927\) | −234.963 | − | 234.963i | −0.253466 | − | 0.253466i | ||||
\(928\) | 97.8381 | − | 97.8381i | 0.105429 | − | 0.105429i | ||||
\(929\) | − | 1567.07i | − | 1.68683i | −0.537261 | − | 0.843416i | \(-0.680541\pi\) | ||
0.537261 | − | 0.843416i | \(-0.319459\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −206.556 | −0.221865 | ||||||||
\(932\) | −194.975 | − | 194.975i | −0.209201 | − | 0.209201i | ||||
\(933\) | 743.601 | − | 743.601i | 0.797000 | − | 0.797000i | ||||
\(934\) | − | 371.062i | − | 0.397282i | ||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −35.9346 | −0.0383917 | ||||||||
\(937\) | 684.510 | + | 684.510i | 0.730533 | + | 0.730533i | 0.970725 | − | 0.240192i | \(-0.0772104\pi\) |
−0.240192 | + | 0.970725i | \(0.577210\pi\) | |||||||
\(938\) | −64.9585 | + | 64.9585i | −0.0692522 | + | 0.0692522i | ||||
\(939\) | − | 165.471i | − | 0.176221i | ||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −1676.18 | −1.78127 | −0.890637 | − | 0.454715i | \(-0.849741\pi\) | ||||
−0.890637 | + | 0.454715i | \(0.849741\pi\) | |||||||
\(942\) | −306.528 | − | 306.528i | −0.325401 | − | 0.325401i | ||||
\(943\) | 28.0836 | − | 28.0836i | 0.0297811 | − | 0.0297811i | ||||
\(944\) | − | 129.159i | − | 0.136821i | ||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 2.43481 | 0.00257380 | ||||||||
\(947\) | 659.283 | + | 659.283i | 0.696180 | + | 0.696180i | 0.963584 | − | 0.267404i | \(-0.0861659\pi\) |
−0.267404 | + | 0.963584i | \(0.586166\pi\) | |||||||
\(948\) | 0.247159 | − | 0.247159i | 0.000260716 | − | 0.000260716i | ||||
\(949\) | 236.015i | 0.248699i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 212.359 | 0.223300 | ||||||||
\(952\) | 97.7486 | + | 97.7486i | 0.102677 | + | 0.102677i | ||||
\(953\) | −876.383 | + | 876.383i | −0.919604 | + | 0.919604i | −0.997000 | − | 0.0773963i | \(-0.975339\pi\) |
0.0773963 | + | 0.997000i | \(0.475339\pi\) | |||||||
\(954\) | − | 71.7092i | − | 0.0751668i | ||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 310.571 | 0.324865 | ||||||||
\(957\) | −90.5961 | − | 90.5961i | −0.0946668 | − | 0.0946668i | ||||
\(958\) | −444.150 | + | 444.150i | −0.463622 | + | 0.463622i | ||||
\(959\) | − | 562.736i | − | 0.586795i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1220.74 | 1.27028 | ||||||||
\(962\) | −183.802 | − | 183.802i | −0.191062 | − | 0.191062i | ||||
\(963\) | 375.776 | − | 375.776i | 0.390214 | − | 0.390214i | ||||
\(964\) | − | 93.2871i | − | 0.0967708i | ||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −21.4882 | −0.0222445 | ||||||||
\(967\) | 1085.32 | + | 1085.32i | 1.12236 | + | 1.12236i | 0.991386 | + | 0.130970i | \(0.0418091\pi\) |
0.130970 | + | 0.991386i | \(0.458191\pi\) | |||||||
\(968\) | 223.708 | − | 223.708i | 0.231103 | − | 0.231103i | ||||
\(969\) | 944.130i | 0.974335i | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 20.6475 | 0.0212642 | 0.0106321 | − | 0.999943i | \(-0.496616\pi\) | ||||
0.0106321 | + | 0.999943i | \(0.496616\pi\) | |||||||
\(972\) | −22.0454 | − | 22.0454i | −0.0226805 | − | 0.0226805i | ||||
\(973\) | −224.578 | + | 224.578i | −0.230810 | + | 0.230810i | ||||
\(974\) | 234.668i | 0.240932i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 313.591 | 0.321302 | ||||||||
\(977\) | −44.9724 | − | 44.9724i | −0.0460311 | − | 0.0460311i | 0.683717 | − | 0.729748i | \(-0.260362\pi\) |
−0.729748 | + | 0.683717i | \(0.760362\pi\) | |||||||
\(978\) | 385.362 | − | 385.362i | 0.394031 | − | 0.394031i | ||||
\(979\) | 276.611i | 0.282544i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 543.954 | 0.554489 | ||||||||
\(982\) | 780.904 | + | 780.904i | 0.795218 | + | 0.795218i | ||||
\(983\) | −465.720 | + | 465.720i | −0.473774 | + | 0.473774i | −0.903134 | − | 0.429360i | \(-0.858739\pi\) |
0.429360 | + | 0.903134i | \(0.358739\pi\) | |||||||
\(984\) | 58.6810i | 0.0596352i | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −638.991 | −0.648064 | ||||||||
\(987\) | −212.711 | − | 212.711i | −0.215512 | − | 0.215512i | ||||
\(988\) | 176.727 | − | 176.727i | 0.178873 | − | 0.178873i | ||||
\(989\) | 1.88760i | 0.00190859i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 312.457 | 0.315295 | 0.157647 | − | 0.987495i | \(-0.449609\pi\) | ||||
0.157647 | + | 0.987495i | \(0.449609\pi\) | |||||||
\(992\) | −186.836 | − | 186.836i | −0.188343 | − | 0.188343i | ||||
\(993\) | 723.975 | − | 723.975i | 0.729078 | − | 0.729078i | ||||
\(994\) | 161.732i | 0.162708i | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −78.3687 | −0.0786834 | ||||||||
\(997\) | −814.207 | − | 814.207i | −0.816657 | − | 0.816657i | 0.168965 | − | 0.985622i | \(-0.445958\pi\) |
−0.985622 | + | 0.168965i | \(0.945958\pi\) | |||||||
\(998\) | −520.134 | + | 520.134i | −0.521176 | + | 0.521176i | ||||
\(999\) | − | 225.520i | − | 0.225745i |
(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 | 1050.3.l.e.757.3 | yes | 8 | |
5.2 | odd | 4 | 1050.3.l.a.43.2 | ✓ | 8 | ||
5.3 | odd | 4 | inner | 1050.3.l.e.43.3 | yes | 8 | |
5.4 | even | 2 | 1050.3.l.a.757.2 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1050.3.l.a.43.2 | ✓ | 8 | 5.2 | odd | 4 | ||
1050.3.l.a.757.2 | yes | 8 | 5.4 | even | 2 | ||
1050.3.l.e.43.3 | yes | 8 | 5.3 | odd | 4 | inner | |
1050.3.l.e.757.3 | yes | 8 | 1.1 | even | 1 | trivial |