Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [39,5,Mod(31,39)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(39, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 3]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("39.31");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 39 = 3 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 39.g (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: | \(4.03142856027\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Relative dimension: | \(10\) over \(\Q(i)\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: |
\( x^{20} + 5446 x^{16} - 1452 x^{15} + 106320 x^{13} + 8376897 x^{12} - 1643220 x^{11} + 1054152 x^{10} + \cdots + 2103506496 \)
|
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{18}\cdot 3^{8} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 31.2 | ||
Root | \(4.32919 - 4.32919i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 39.31 |
Dual form | 39.5.g.a.34.2 |
$q$-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 \(\left(\mathbb{Z}/39\mathbb{Z}\right)^\times\).
\(n\) | \(14\) | \(28\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{3}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −4.32919 | + | 4.32919i | −1.08230 | + | 1.08230i | −0.0860014 | + | 0.996295i | \(0.527409\pi\) |
−0.996295 | + | 0.0860014i | \(0.972591\pi\) | |||||||
\(3\) | 5.19615 | 0.577350 | ||||||||
\(4\) | − | 21.4837i | − | 1.34273i | ||||||
\(5\) | −26.0804 | + | 26.0804i | −1.04322 | + | 1.04322i | −0.0441922 | + | 0.999023i | \(0.514071\pi\) |
−0.999023 | + | 0.0441922i | \(0.985929\pi\) | |||||||
\(6\) | −22.4951 | + | 22.4951i | −0.624864 | + | 0.624864i | ||||
\(7\) | −16.9579 | − | 16.9579i | −0.346080 | − | 0.346080i | 0.512567 | − | 0.858647i | \(-0.328694\pi\) |
−0.858647 | + | 0.512567i | \(0.828694\pi\) | |||||||
\(8\) | 23.7399 | + | 23.7399i | 0.370937 | + | 0.370937i | ||||
\(9\) | 27.0000 | 0.333333 | ||||||||
\(10\) | − | 225.814i | − | 2.25814i | ||||||
\(11\) | −69.5293 | − | 69.5293i | −0.574623 | − | 0.574623i | 0.358794 | − | 0.933417i | \(-0.383188\pi\) |
−0.933417 | + | 0.358794i | \(0.883188\pi\) | |||||||
\(12\) | − | 111.633i | − | 0.775226i | ||||||
\(13\) | −93.5895 | − | 140.720i | −0.553784 | − | 0.832660i | ||||
\(14\) | 146.828 | 0.749121 | ||||||||
\(15\) | −135.518 | + | 135.518i | −0.602301 | + | 0.602301i | ||||
\(16\) | 138.190 | 0.539804 | ||||||||
\(17\) | 166.635i | 0.576593i | 0.957541 | + | 0.288296i | \(0.0930888\pi\) | ||||
−0.957541 | + | 0.288296i | \(0.906911\pi\) | |||||||
\(18\) | −116.888 | + | 116.888i | −0.360765 | + | 0.360765i | ||||
\(19\) | −468.820 | + | 468.820i | −1.29867 | + | 1.29867i | −0.369401 | + | 0.929270i | \(0.620437\pi\) |
−0.929270 | + | 0.369401i | \(0.879563\pi\) | |||||||
\(20\) | 560.303 | + | 560.303i | 1.40076 | + | 1.40076i | ||||
\(21\) | −88.1158 | − | 88.1158i | −0.199809 | − | 0.199809i | ||||
\(22\) | 602.011 | 1.24382 | ||||||||
\(23\) | 388.867i | 0.735098i | 0.930004 | + | 0.367549i | \(0.119803\pi\) | ||||
−0.930004 | + | 0.367549i | \(0.880197\pi\) | |||||||
\(24\) | 123.356 | + | 123.356i | 0.214160 | + | 0.214160i | ||||
\(25\) | − | 735.373i | − | 1.17660i | ||||||
\(26\) | 1014.37 | + | 204.035i | 1.50054 | + | 0.301827i | ||||
\(27\) | 140.296 | 0.192450 | ||||||||
\(28\) | −364.318 | + | 364.318i | −0.464692 | + | 0.464692i | ||||
\(29\) | −767.891 | −0.913069 | −0.456534 | − | 0.889706i | \(-0.650909\pi\) | ||||
−0.456534 | + | 0.889706i | \(0.650909\pi\) | |||||||
\(30\) | − | 1173.36i | − | 1.30374i | ||||||
\(31\) | −66.8738 | + | 66.8738i | −0.0695877 | + | 0.0695877i | −0.741044 | − | 0.671456i | \(-0.765669\pi\) |
0.671456 | + | 0.741044i | \(0.265669\pi\) | |||||||
\(32\) | −978.089 | + | 978.089i | −0.955165 | + | 0.955165i | ||||
\(33\) | −361.285 | − | 361.285i | −0.331758 | − | 0.331758i | ||||
\(34\) | −721.395 | − | 721.395i | −0.624044 | − | 0.624044i | ||||
\(35\) | 884.537 | 0.722071 | ||||||||
\(36\) | − | 580.060i | − | 0.447577i | ||||||
\(37\) | 1532.33 | + | 1532.33i | 1.11931 | + | 1.11931i | 0.991843 | + | 0.127465i | \(0.0406841\pi\) |
0.127465 | + | 0.991843i | \(0.459316\pi\) | |||||||
\(38\) | − | 4059.22i | − | 2.81109i | ||||||
\(39\) | −486.305 | − | 731.200i | −0.319727 | − | 0.480737i | ||||
\(40\) | −1238.29 | −0.773933 | ||||||||
\(41\) | 802.986 | − | 802.986i | 0.477684 | − | 0.477684i | −0.426707 | − | 0.904390i | \(-0.640326\pi\) |
0.904390 | + | 0.426707i | \(0.140326\pi\) | |||||||
\(42\) | 762.940 | 0.432505 | ||||||||
\(43\) | 2798.62i | 1.51358i | 0.653655 | + | 0.756792i | \(0.273235\pi\) | ||||
−0.653655 | + | 0.756792i | \(0.726765\pi\) | |||||||
\(44\) | −1493.75 | + | 1493.75i | −0.771564 | + | 0.771564i | ||||
\(45\) | −704.170 | + | 704.170i | −0.347738 | + | 0.347738i | ||||
\(46\) | −1683.48 | − | 1683.48i | −0.795594 | − | 0.795594i | ||||
\(47\) | 33.8918 | + | 33.8918i | 0.0153426 | + | 0.0153426i | 0.714736 | − | 0.699394i | \(-0.246547\pi\) |
−0.699394 | + | 0.714736i | \(0.746547\pi\) | |||||||
\(48\) | 718.056 | 0.311656 | ||||||||
\(49\) | − | 1825.86i | − | 0.760458i | ||||||
\(50\) | 3183.56 | + | 3183.56i | 1.27343 | + | 1.27343i | ||||
\(51\) | 865.862i | 0.332896i | ||||||||
\(52\) | −3023.18 | + | 2010.65i | −1.11804 | + | 0.743583i | ||||
\(53\) | −3139.54 | −1.11767 | −0.558836 | − | 0.829278i | \(-0.688752\pi\) | ||||
−0.558836 | + | 0.829278i | \(0.688752\pi\) | |||||||
\(54\) | −607.368 | + | 607.368i | −0.208288 | + | 0.208288i | ||||
\(55\) | 3626.70 | 1.19891 | ||||||||
\(56\) | − | 805.159i | − | 0.256747i | ||||||
\(57\) | −2436.06 | + | 2436.06i | −0.749788 | + | 0.749788i | ||||
\(58\) | 3324.34 | − | 3324.34i | 0.988211 | − | 0.988211i | ||||
\(59\) | −3959.16 | − | 3959.16i | −1.13736 | − | 1.13736i | −0.988921 | − | 0.148440i | \(-0.952575\pi\) |
−0.148440 | − | 0.988921i | \(-0.547425\pi\) | |||||||
\(60\) | 2911.42 | + | 2911.42i | 0.808728 | + | 0.808728i | ||||
\(61\) | 504.230 | 0.135509 | 0.0677546 | − | 0.997702i | \(-0.478417\pi\) | ||||
0.0677546 | + | 0.997702i | \(0.478417\pi\) | |||||||
\(62\) | − | 579.018i | − | 0.150629i | ||||||
\(63\) | −457.863 | − | 457.863i | −0.115360 | − | 0.115360i | ||||
\(64\) | − | 6257.62i | − | 1.52774i | ||||||
\(65\) | 6110.87 | + | 1229.17i | 1.44636 | + | 0.290928i | ||||
\(66\) | 3128.14 | 0.718122 | ||||||||
\(67\) | 4218.53 | − | 4218.53i | 0.939748 | − | 0.939748i | −0.0585372 | − | 0.998285i | \(-0.518644\pi\) |
0.998285 | + | 0.0585372i | \(0.0186436\pi\) | |||||||
\(68\) | 3579.94 | 0.774209 | ||||||||
\(69\) | 2020.61i | 0.424409i | ||||||||
\(70\) | −3829.33 | + | 3829.33i | −0.781495 | + | 0.781495i | ||||
\(71\) | −3025.86 | + | 3025.86i | −0.600249 | + | 0.600249i | −0.940379 | − | 0.340130i | \(-0.889529\pi\) |
0.340130 | + | 0.940379i | \(0.389529\pi\) | |||||||
\(72\) | 640.978 | + | 640.978i | 0.123646 | + | 0.123646i | ||||
\(73\) | 3088.98 | + | 3088.98i | 0.579654 | + | 0.579654i | 0.934808 | − | 0.355154i | \(-0.115571\pi\) |
−0.355154 | + | 0.934808i | \(0.615571\pi\) | |||||||
\(74\) | −13267.5 | −2.42285 | ||||||||
\(75\) | − | 3821.11i | − | 0.679308i | ||||||
\(76\) | 10072.0 | + | 10072.0i | 1.74377 | + | 1.74377i | ||||
\(77\) | 2358.14i | 0.397730i | ||||||||
\(78\) | 5270.81 | + | 1060.20i | 0.866339 | + | 0.174260i | ||||
\(79\) | −9376.55 | −1.50241 | −0.751205 | − | 0.660069i | \(-0.770527\pi\) | ||||
−0.751205 | + | 0.660069i | \(0.770527\pi\) | |||||||
\(80\) | −3604.05 | + | 3604.05i | −0.563132 | + | 0.563132i | ||||
\(81\) | 729.000 | 0.111111 | ||||||||
\(82\) | 6952.55i | 1.03399i | ||||||||
\(83\) | 6229.50 | − | 6229.50i | 0.904267 | − | 0.904267i | −0.0915344 | − | 0.995802i | \(-0.529177\pi\) |
0.995802 | + | 0.0915344i | \(0.0291772\pi\) | |||||||
\(84\) | −1893.05 | + | 1893.05i | −0.268290 | + | 0.268290i | ||||
\(85\) | −4345.91 | − | 4345.91i | −0.601510 | − | 0.601510i | ||||
\(86\) | −12115.7 | − | 12115.7i | −1.63815 | − | 1.63815i | ||||
\(87\) | −3990.08 | −0.527160 | ||||||||
\(88\) | − | 3301.24i | − | 0.426297i | ||||||
\(89\) | 8558.42 | + | 8558.42i | 1.08047 | + | 1.08047i | 0.996465 | + | 0.0840075i | \(0.0267720\pi\) |
0.0840075 | + | 0.996465i | \(0.473228\pi\) | |||||||
\(90\) | − | 6096.97i | − | 0.752712i | ||||||
\(91\) | −799.227 | + | 3973.39i | −0.0965133 | + | 0.479820i | ||||
\(92\) | 8354.30 | 0.987039 | ||||||||
\(93\) | −347.486 | + | 347.486i | −0.0401765 | + | 0.0401765i | ||||
\(94\) | −293.448 | −0.0332105 | ||||||||
\(95\) | − | 24454.0i | − | 2.70959i | ||||||
\(96\) | −5082.30 | + | 5082.30i | −0.551465 | + | 0.551465i | ||||
\(97\) | 2882.26 | − | 2882.26i | 0.306330 | − | 0.306330i | −0.537154 | − | 0.843484i | \(-0.680501\pi\) |
0.843484 | + | 0.537154i | \(0.180501\pi\) | |||||||
\(98\) | 7904.48 | + | 7904.48i | 0.823041 | + | 0.823041i | ||||
\(99\) | −1877.29 | − | 1877.29i | −0.191541 | − | 0.191541i | ||||
\(100\) | −15798.5 | −1.57985 | ||||||||
\(101\) | − | 5594.65i | − | 0.548441i | −0.961667 | − | 0.274220i | \(-0.911580\pi\) | ||
0.961667 | − | 0.274220i | \(-0.0884198\pi\) | |||||||
\(102\) | −3748.48 | − | 3748.48i | −0.360292 | − | 0.360292i | ||||
\(103\) | 6792.74i | 0.640281i | 0.947370 | + | 0.320140i | \(0.103730\pi\) | ||||
−0.947370 | + | 0.320140i | \(0.896270\pi\) | |||||||
\(104\) | 1118.86 | − | 5562.48i | 0.103445 | − | 0.514283i | ||||
\(105\) | 4596.19 | 0.416888 | ||||||||
\(106\) | 13591.7 | − | 13591.7i | 1.20965 | − | 1.20965i | ||||
\(107\) | −8462.24 | −0.739125 | −0.369563 | − | 0.929206i | \(-0.620492\pi\) | ||||
−0.369563 | + | 0.929206i | \(0.620492\pi\) | |||||||
\(108\) | − | 3014.08i | − | 0.258409i | ||||||
\(109\) | −12077.9 | + | 12077.9i | −1.01657 | + | 1.01657i | −0.0167121 | + | 0.999860i | \(0.505320\pi\) |
−0.999860 | + | 0.0167121i | \(0.994680\pi\) | |||||||
\(110\) | −15700.7 | + | 15700.7i | −1.29758 | + | 1.29758i | ||||
\(111\) | 7962.24 | + | 7962.24i | 0.646233 | + | 0.646233i | ||||
\(112\) | −2343.41 | − | 2343.41i | −0.186815 | − | 0.186815i | ||||
\(113\) | 14864.2 | 1.16409 | 0.582043 | − | 0.813158i | \(-0.302254\pi\) | ||||
0.582043 | + | 0.813158i | \(0.302254\pi\) | |||||||
\(114\) | − | 21092.3i | − | 1.62299i | ||||||
\(115\) | −10141.8 | − | 10141.8i | −0.766866 | − | 0.766866i | ||||
\(116\) | 16497.1i | 1.22601i | ||||||||
\(117\) | −2526.92 | − | 3799.43i | −0.184595 | − | 0.277553i | ||||
\(118\) | 34279.8 | 2.46192 | ||||||||
\(119\) | 2825.78 | − | 2825.78i | 0.199547 | − | 0.199547i | ||||
\(120\) | −6434.36 | −0.446831 | ||||||||
\(121\) | − | 4972.34i | − | 0.339618i | ||||||
\(122\) | −2182.90 | + | 2182.90i | −0.146661 | + | 0.146661i | ||||
\(123\) | 4172.44 | − | 4172.44i | 0.275791 | − | 0.275791i | ||||
\(124\) | 1436.70 | + | 1436.70i | 0.0934376 | + | 0.0934376i | ||||
\(125\) | 2878.56 | + | 2878.56i | 0.184228 | + | 0.184228i | ||||
\(126\) | 3964.35 | 0.249707 | ||||||||
\(127\) | 10995.6i | 0.681728i | 0.940113 | + | 0.340864i | \(0.110720\pi\) | ||||
−0.940113 | + | 0.340864i | \(0.889280\pi\) | |||||||
\(128\) | 11441.0 | + | 11441.0i | 0.698301 | + | 0.698301i | ||||
\(129\) | 14542.0i | 0.873868i | ||||||||
\(130\) | −31776.4 | + | 21133.8i | −1.88026 | + | 1.25052i | ||||
\(131\) | 14023.3 | 0.817160 | 0.408580 | − | 0.912722i | \(-0.366024\pi\) | ||||
0.408580 | + | 0.912722i | \(0.366024\pi\) | |||||||
\(132\) | −7761.74 | + | 7761.74i | −0.445462 | + | 0.445462i | ||||
\(133\) | 15900.4 | 0.898887 | ||||||||
\(134\) | 36525.6i | 2.03417i | ||||||||
\(135\) | −3658.98 | + | 3658.98i | −0.200767 | + | 0.200767i | ||||
\(136\) | −3955.91 | + | 3955.91i | −0.213879 | + | 0.213879i | ||||
\(137\) | 20682.4 | + | 20682.4i | 1.10194 | + | 1.10194i | 0.994176 | + | 0.107769i | \(0.0343706\pi\) |
0.107769 | + | 0.994176i | \(0.465629\pi\) | |||||||
\(138\) | −8747.60 | − | 8747.60i | −0.459336 | − | 0.459336i | ||||
\(139\) | −12584.1 | −0.651317 | −0.325658 | − | 0.945487i | \(-0.605586\pi\) | ||||
−0.325658 | + | 0.945487i | \(0.605586\pi\) | |||||||
\(140\) | − | 19003.1i | − | 0.969547i | ||||||
\(141\) | 176.107 | + | 176.107i | 0.00885807 | + | 0.00885807i | ||||
\(142\) | − | 26199.0i | − | 1.29929i | ||||||
\(143\) | −3276.92 | + | 16291.4i | −0.160248 | + | 0.796682i | ||||
\(144\) | 3731.13 | 0.179935 | ||||||||
\(145\) | 20026.9 | − | 20026.9i | 0.952527 | − | 0.952527i | ||||
\(146\) | −26745.5 | −1.25472 | ||||||||
\(147\) | − | 9487.44i | − | 0.439051i | ||||||
\(148\) | 32920.2 | − | 32920.2i | 1.50293 | − | 1.50293i | ||||
\(149\) | −1317.22 | + | 1317.22i | −0.0593315 | + | 0.0593315i | −0.736150 | − | 0.676818i | \(-0.763358\pi\) |
0.676818 | + | 0.736150i | \(0.263358\pi\) | |||||||
\(150\) | 16542.3 | + | 16542.3i | 0.735213 | + | 0.735213i | ||||
\(151\) | −6003.08 | − | 6003.08i | −0.263282 | − | 0.263282i | 0.563104 | − | 0.826386i | \(-0.309607\pi\) |
−0.826386 | + | 0.563104i | \(0.809607\pi\) | |||||||
\(152\) | −22259.5 | −0.963449 | ||||||||
\(153\) | 4499.15i | 0.192198i | ||||||||
\(154\) | −10208.8 | − | 10208.8i | −0.430462 | − | 0.430462i | ||||
\(155\) | − | 3488.19i | − | 0.145190i | ||||||
\(156\) | −15708.9 | + | 10447.6i | −0.645500 | + | 0.429308i | ||||
\(157\) | −24232.6 | −0.983107 | −0.491553 | − | 0.870847i | \(-0.663571\pi\) | ||||
−0.491553 | + | 0.870847i | \(0.663571\pi\) | |||||||
\(158\) | 40592.8 | − | 40592.8i | 1.62605 | − | 1.62605i | ||||
\(159\) | −16313.5 | −0.645288 | ||||||||
\(160\) | − | 51017.9i | − | 1.99289i | ||||||
\(161\) | 6594.37 | − | 6594.37i | 0.254403 | − | 0.254403i | ||||
\(162\) | −3155.98 | + | 3155.98i | −0.120255 | + | 0.120255i | ||||
\(163\) | −24239.5 | − | 24239.5i | −0.912322 | − | 0.912322i | 0.0841325 | − | 0.996455i | \(-0.473188\pi\) |
−0.996455 | + | 0.0841325i | \(0.973188\pi\) | |||||||
\(164\) | −17251.1 | − | 17251.1i | −0.641401 | − | 0.641401i | ||||
\(165\) | 18844.9 | 0.692191 | ||||||||
\(166\) | 53937.3i | 1.95737i | ||||||||
\(167\) | −17352.4 | − | 17352.4i | −0.622195 | − | 0.622195i | 0.323897 | − | 0.946092i | \(-0.395007\pi\) |
−0.946092 | + | 0.323897i | \(0.895007\pi\) | |||||||
\(168\) | − | 4183.73i | − | 0.148233i | ||||||
\(169\) | −11043.0 | + | 26339.8i | −0.386646 | + | 0.922228i | ||||
\(170\) | 37628.5 | 1.30202 | ||||||||
\(171\) | −12658.1 | + | 12658.1i | −0.432890 | + | 0.432890i | ||||
\(172\) | 60124.7 | 2.03234 | ||||||||
\(173\) | 2780.29i | 0.0928961i | 0.998921 | + | 0.0464480i | \(0.0147902\pi\) | ||||
−0.998921 | + | 0.0464480i | \(0.985210\pi\) | |||||||
\(174\) | 17273.8 | − | 17273.8i | 0.570544 | − | 0.570544i | ||||
\(175\) | −12470.4 | + | 12470.4i | −0.407196 | + | 0.407196i | ||||
\(176\) | −9608.25 | − | 9608.25i | −0.310184 | − | 0.310184i | ||||
\(177\) | −20572.4 | − | 20572.4i | −0.656656 | − | 0.656656i | ||||
\(178\) | −74102.0 | −2.33878 | ||||||||
\(179\) | − | 2972.36i | − | 0.0927674i | −0.998924 | − | 0.0463837i | \(-0.985230\pi\) | ||
0.998924 | − | 0.0463837i | \(-0.0147697\pi\) | |||||||
\(180\) | 15128.2 | + | 15128.2i | 0.466919 | + | 0.466919i | ||||
\(181\) | 44034.0i | 1.34410i | 0.740507 | + | 0.672049i | \(0.234586\pi\) | ||||
−0.740507 | + | 0.672049i | \(0.765414\pi\) | |||||||
\(182\) | −13741.5 | − | 20661.5i | −0.414852 | − | 0.623764i | ||||
\(183\) | 2620.05 | 0.0782362 | ||||||||
\(184\) | −9231.68 | + | 9231.68i | −0.272675 | + | 0.272675i | ||||
\(185\) | −79927.7 | −2.33536 | ||||||||
\(186\) | − | 3008.67i | − | 0.0869657i | ||||||
\(187\) | 11586.0 | − | 11586.0i | 0.331323 | − | 0.331323i | ||||
\(188\) | 728.122 | − | 728.122i | 0.0206010 | − | 0.0206010i | ||||
\(189\) | −2379.13 | − | 2379.13i | −0.0666031 | − | 0.0666031i | ||||
\(190\) | 105866. | + | 105866.i | 2.93258 | + | 2.93258i | ||||
\(191\) | −3688.96 | −0.101120 | −0.0505601 | − | 0.998721i | \(-0.516101\pi\) | ||||
−0.0505601 | + | 0.998721i | \(0.516101\pi\) | |||||||
\(192\) | − | 32515.5i | − | 0.882040i | ||||||
\(193\) | 19216.9 | + | 19216.9i | 0.515904 | + | 0.515904i | 0.916329 | − | 0.400426i | \(-0.131138\pi\) |
−0.400426 | + | 0.916329i | \(0.631138\pi\) | |||||||
\(194\) | 24955.7i | 0.663079i | ||||||||
\(195\) | 31753.0 | + | 6386.95i | 0.835056 | + | 0.167967i | ||||
\(196\) | −39226.2 | −1.02109 | ||||||||
\(197\) | −15917.0 | + | 15917.0i | −0.410136 | + | 0.410136i | −0.881786 | − | 0.471650i | \(-0.843659\pi\) |
0.471650 | + | 0.881786i | \(0.343659\pi\) | |||||||
\(198\) | 16254.3 | 0.414608 | ||||||||
\(199\) | − | 23311.0i | − | 0.588646i | −0.955706 | − | 0.294323i | \(-0.904906\pi\) | ||
0.955706 | − | 0.294323i | \(-0.0950941\pi\) | |||||||
\(200\) | 17457.7 | − | 17457.7i | 0.436443 | − | 0.436443i | ||||
\(201\) | 21920.1 | − | 21920.1i | 0.542564 | − | 0.542564i | ||||
\(202\) | 24220.3 | + | 24220.3i | 0.593576 | + | 0.593576i | ||||
\(203\) | 13021.8 | + | 13021.8i | 0.315995 | + | 0.315995i | ||||
\(204\) | 18601.9 | 0.446990 | ||||||||
\(205\) | 41884.4i | 0.996654i | ||||||||
\(206\) | −29407.0 | − | 29407.0i | −0.692974 | − | 0.692974i | ||||
\(207\) | 10499.4i | 0.245033i | ||||||||
\(208\) | −12933.1 | − | 19446.0i | −0.298935 | − | 0.449474i | ||||
\(209\) | 65193.5 | 1.49249 | ||||||||
\(210\) | −19897.8 | + | 19897.8i | −0.451196 | + | 0.451196i | ||||
\(211\) | 10045.5 | 0.225636 | 0.112818 | − | 0.993616i | \(-0.464012\pi\) | ||||
0.112818 | + | 0.993616i | \(0.464012\pi\) | |||||||
\(212\) | 67448.9i | 1.50073i | ||||||||
\(213\) | −15722.8 | + | 15722.8i | −0.346554 | + | 0.346554i | ||||
\(214\) | 36634.6 | − | 36634.6i | 0.799953 | − | 0.799953i | ||||
\(215\) | −72989.0 | − | 72989.0i | −1.57899 | − | 1.57899i | ||||
\(216\) | 3330.62 | + | 3330.62i | 0.0713868 | + | 0.0713868i | ||||
\(217\) | 2268.08 | 0.0481658 | ||||||||
\(218\) | − | 104575.i | − | 2.20047i | ||||||
\(219\) | 16050.8 | + | 16050.8i | 0.334664 | + | 0.334664i | ||||
\(220\) | − | 77915.0i | − | 1.60981i | ||||||
\(221\) | 23448.8 | − | 15595.3i | 0.480106 | − | 0.319308i | ||||
\(222\) | −68940.0 | −1.39883 | ||||||||
\(223\) | 24945.0 | − | 24945.0i | 0.501620 | − | 0.501620i | −0.410321 | − | 0.911941i | \(-0.634583\pi\) |
0.911941 | + | 0.410321i | \(0.134583\pi\) | |||||||
\(224\) | 33172.7 | 0.661126 | ||||||||
\(225\) | − | 19855.1i | − | 0.392199i | ||||||
\(226\) | −64349.9 | + | 64349.9i | −1.25989 | + | 1.25989i | ||||
\(227\) | 15576.9 | − | 15576.9i | 0.302294 | − | 0.302294i | −0.539617 | − | 0.841911i | \(-0.681431\pi\) |
0.841911 | + | 0.539617i | \(0.181431\pi\) | |||||||
\(228\) | 52335.6 | + | 52335.6i | 1.00676 | + | 1.00676i | ||||
\(229\) | −24930.7 | − | 24930.7i | −0.475405 | − | 0.475405i | 0.428254 | − | 0.903658i | \(-0.359129\pi\) |
−0.903658 | + | 0.428254i | \(0.859129\pi\) | |||||||
\(230\) | 87811.5 | 1.65995 | ||||||||
\(231\) | 12253.3i | 0.229630i | ||||||||
\(232\) | −18229.7 | − | 18229.7i | −0.338691 | − | 0.338691i | ||||
\(233\) | 22434.3i | 0.413239i | 0.978421 | + | 0.206619i | \(0.0662462\pi\) | ||||
−0.978421 | + | 0.206619i | \(0.933754\pi\) | |||||||
\(234\) | 27387.9 | + | 5508.94i | 0.500181 | + | 0.100609i | ||||
\(235\) | −1767.82 | −0.0320113 | ||||||||
\(236\) | −85057.3 | + | 85057.3i | −1.52717 | + | 1.52717i | ||||
\(237\) | −48722.0 | −0.867417 | ||||||||
\(238\) | 24466.7i | 0.431938i | ||||||||
\(239\) | −66829.7 | + | 66829.7i | −1.16997 | + | 1.16997i | −0.187751 | + | 0.982217i | \(0.560120\pi\) |
−0.982217 | + | 0.187751i | \(0.939880\pi\) | |||||||
\(240\) | −18727.2 | + | 18727.2i | −0.325124 | + | 0.325124i | ||||
\(241\) | −34827.1 | − | 34827.1i | −0.599629 | − | 0.599629i | 0.340585 | − | 0.940214i | \(-0.389375\pi\) |
−0.940214 | + | 0.340585i | \(0.889375\pi\) | |||||||
\(242\) | 21526.2 | + | 21526.2i | 0.367567 | + | 0.367567i | ||||
\(243\) | 3788.00 | 0.0641500 | ||||||||
\(244\) | − | 10832.7i | − | 0.181952i | ||||||
\(245\) | 47619.1 | + | 47619.1i | 0.793321 | + | 0.793321i | ||||
\(246\) | 36126.5i | 0.596975i | ||||||||
\(247\) | 109849. | + | 22095.5i | 1.80054 | + | 0.362168i | ||||
\(248\) | −3175.16 | −0.0516253 | ||||||||
\(249\) | 32369.4 | − | 32369.4i | 0.522079 | − | 0.522079i | ||||
\(250\) | −24923.6 | −0.398778 | ||||||||
\(251\) | − | 4768.38i | − | 0.0756873i | −0.999284 | − | 0.0378437i | \(-0.987951\pi\) | ||
0.999284 | − | 0.0378437i | \(-0.0120489\pi\) | |||||||
\(252\) | −9836.60 | + | 9836.60i | −0.154897 | + | 0.154897i | ||||
\(253\) | 27037.7 | − | 27037.7i | 0.422404 | − | 0.422404i | ||||
\(254\) | −47601.9 | − | 47601.9i | −0.737832 | − | 0.737832i | ||||
\(255\) | −22582.0 | − | 22582.0i | −0.347282 | − | 0.347282i | ||||
\(256\) | 1061.74 | 0.0162008 | ||||||||
\(257\) | 62743.6i | 0.949956i | 0.879998 | + | 0.474978i | \(0.157544\pi\) | ||||
−0.879998 | + | 0.474978i | \(0.842456\pi\) | |||||||
\(258\) | −62955.2 | − | 62955.2i | −0.945785 | − | 0.945785i | ||||
\(259\) | − | 51970.3i | − | 0.774740i | ||||||
\(260\) | 26407.1 | − | 131284.i | 0.390638 | − | 1.94207i | ||||
\(261\) | −20733.1 | −0.304356 | ||||||||
\(262\) | −60709.4 | + | 60709.4i | −0.884409 | + | 0.884409i | ||||
\(263\) | 45421.0 | 0.656667 | 0.328333 | − | 0.944562i | \(-0.393513\pi\) | ||||
0.328333 | + | 0.944562i | \(0.393513\pi\) | |||||||
\(264\) | − | 17153.8i | − | 0.246123i | ||||||
\(265\) | 81880.4 | − | 81880.4i | 1.16597 | − | 1.16597i | ||||
\(266\) | −68835.8 | + | 68835.8i | −0.972862 | + | 0.972862i | ||||
\(267\) | 44470.9 | + | 44470.9i | 0.623811 | + | 0.623811i | ||||
\(268\) | −90629.6 | − | 90629.6i | −1.26183 | − | 1.26183i | ||||
\(269\) | 79205.8 | 1.09459 | 0.547296 | − | 0.836939i | \(-0.315657\pi\) | ||||
0.547296 | + | 0.836939i | \(0.315657\pi\) | |||||||
\(270\) | − | 31680.8i | − | 0.434579i | ||||||
\(271\) | −16180.5 | − | 16180.5i | −0.220320 | − | 0.220320i | 0.588313 | − | 0.808633i | \(-0.299792\pi\) |
−0.808633 | + | 0.588313i | \(0.799792\pi\) | |||||||
\(272\) | 23027.3i | 0.311247i | ||||||||
\(273\) | −4152.90 | + | 20646.3i | −0.0557220 | + | 0.277024i | ||||
\(274\) | −179076. | −2.38526 | ||||||||
\(275\) | −51130.0 | + | 51130.0i | −0.676099 | + | 0.676099i | ||||
\(276\) | 43410.2 | 0.569867 | ||||||||
\(277\) | − | 2884.24i | − | 0.0375899i | −0.999823 | − | 0.0187950i | \(-0.994017\pi\) | ||
0.999823 | − | 0.0187950i | \(-0.00598298\pi\) | |||||||
\(278\) | 54478.9 | − | 54478.9i | 0.704918 | − | 0.704918i | ||||
\(279\) | −1805.59 | + | 1805.59i | −0.0231959 | + | 0.0231959i | ||||
\(280\) | 20998.9 | + | 20998.9i | 0.267843 | + | 0.267843i | ||||
\(281\) | −103231. | − | 103231.i | −1.30736 | − | 1.30736i | −0.923311 | − | 0.384052i | \(-0.874528\pi\) |
−0.384052 | − | 0.923311i | \(-0.625472\pi\) | |||||||
\(282\) | −1524.80 | −0.0191741 | ||||||||
\(283\) | 78581.6i | 0.981178i | 0.871391 | + | 0.490589i | \(0.163218\pi\) | ||||
−0.871391 | + | 0.490589i | \(0.836782\pi\) | |||||||
\(284\) | 65006.6 | + | 65006.6i | 0.805973 | + | 0.805973i | ||||
\(285\) | − | 127067.i | − | 1.56438i | ||||||
\(286\) | −56341.9 | − | 84714.7i | −0.688810 | − | 1.03568i | ||||
\(287\) | −27233.9 | −0.330633 | ||||||||
\(288\) | −26408.4 | + | 26408.4i | −0.318388 | + | 0.318388i | ||||
\(289\) | 55753.7 | 0.667541 | ||||||||
\(290\) | 173400.i | 2.06183i | ||||||||
\(291\) | 14976.6 | − | 14976.6i | 0.176860 | − | 0.176860i | ||||
\(292\) | 66362.7 | − | 66362.7i | 0.778320 | − | 0.778320i | ||||
\(293\) | −5490.45 | − | 5490.45i | −0.0639547 | − | 0.0639547i | 0.674406 | − | 0.738361i | \(-0.264400\pi\) |
−0.738361 | + | 0.674406i | \(0.764400\pi\) | |||||||
\(294\) | 41072.9 | + | 41072.9i | 0.475183 | + | 0.475183i | ||||
\(295\) | 206513. | 2.37303 | ||||||||
\(296\) | 72755.0i | 0.830385i | ||||||||
\(297\) | −9754.70 | − | 9754.70i | −0.110586 | − | 0.110586i | ||||
\(298\) | − | 11405.0i | − | 0.128429i | ||||||
\(299\) | 54721.2 | − | 36393.9i | 0.612087 | − | 0.407086i | ||||
\(300\) | −82091.5 | −0.912128 | ||||||||
\(301\) | 47458.7 | − | 47458.7i | 0.523821 | − | 0.523821i | ||||
\(302\) | 51976.9 | 0.569897 | ||||||||
\(303\) | − | 29070.6i | − | 0.316642i | ||||||
\(304\) | −64786.2 | + | 64786.2i | −0.701028 | + | 0.701028i | ||||
\(305\) | −13150.5 | + | 13150.5i | −0.141365 | + | 0.141365i | ||||
\(306\) | −19477.7 | − | 19477.7i | −0.208015 | − | 0.208015i | ||||
\(307\) | 36642.5 | + | 36642.5i | 0.388784 | + | 0.388784i | 0.874254 | − | 0.485469i | \(-0.161351\pi\) |
−0.485469 | + | 0.874254i | \(0.661351\pi\) | |||||||
\(308\) | 50661.6 | 0.534045 | ||||||||
\(309\) | 35296.1i | 0.369666i | ||||||||
\(310\) | 15101.0 | + | 15101.0i | 0.157139 | + | 0.157139i | ||||
\(311\) | − | 57004.6i | − | 0.589371i | −0.955594 | − | 0.294686i | \(-0.904785\pi\) | ||
0.955594 | − | 0.294686i | \(-0.0952149\pi\) | |||||||
\(312\) | 5813.79 | − | 28903.5i | 0.0597242 | − | 0.296921i | ||||
\(313\) | −168911. | −1.72413 | −0.862064 | − | 0.506799i | \(-0.830829\pi\) | ||||
−0.862064 | + | 0.506799i | \(0.830829\pi\) | |||||||
\(314\) | 104907. | − | 104907.i | 1.06401 | − | 1.06401i | ||||
\(315\) | 23882.5 | 0.240690 | ||||||||
\(316\) | 201443.i | 2.01733i | ||||||||
\(317\) | −57585.7 | + | 57585.7i | −0.573055 | + | 0.573055i | −0.932981 | − | 0.359926i | \(-0.882802\pi\) |
0.359926 | + | 0.932981i | \(0.382802\pi\) | |||||||
\(318\) | 70624.3 | − | 70624.3i | 0.698393 | − | 0.698393i | ||||
\(319\) | 53390.9 | + | 53390.9i | 0.524670 | + | 0.524670i | ||||
\(320\) | 163201. | + | 163201.i | 1.59376 | + | 1.59376i | ||||
\(321\) | −43971.1 | −0.426734 | ||||||||
\(322\) | 57096.5i | 0.550678i | ||||||||
\(323\) | −78122.0 | − | 78122.0i | −0.748804 | − | 0.748804i | ||||
\(324\) | − | 15661.6i | − | 0.149192i | ||||||
\(325\) | −103481. | + | 68823.2i | −0.979705 | + | 0.651580i | ||||
\(326\) | 209874. | 1.97481 | ||||||||
\(327\) | −62758.6 | + | 62758.6i | −0.586918 | + | 0.586918i | ||||
\(328\) | 38125.7 | 0.354381 | ||||||||
\(329\) | − | 1149.47i | − | 0.0106195i | ||||||
\(330\) | −81583.1 | + | 81583.1i | −0.749156 | + | 0.749156i | ||||
\(331\) | −134787. | + | 134787.i | −1.23025 | + | 1.23025i | −0.266382 | + | 0.963868i | \(0.585828\pi\) |
−0.963868 | + | 0.266382i | \(0.914172\pi\) | |||||||
\(332\) | −133833. | − | 133833.i | −1.21419 | − | 1.21419i | ||||
\(333\) | 41373.0 | + | 41373.0i | 0.373103 | + | 0.373103i | ||||
\(334\) | 150243. | 1.34680 | ||||||||
\(335\) | 220042.i | 1.96072i | ||||||||
\(336\) | −12176.7 | − | 12176.7i | −0.107858 | − | 0.107858i | ||||
\(337\) | 56729.9i | 0.499520i | 0.968308 | + | 0.249760i | \(0.0803517\pi\) | ||||
−0.968308 | + | 0.249760i | \(0.919648\pi\) | |||||||
\(338\) | −66222.5 | − | 161837.i | −0.579659 | − | 1.41659i | ||||
\(339\) | 77236.7 | 0.672085 | ||||||||
\(340\) | −93366.3 | + | 93366.3i | −0.807667 | + | 0.807667i | ||||
\(341\) | 9299.38 | 0.0799734 | ||||||||
\(342\) | − | 109599.i | − | 0.937031i | ||||||
\(343\) | −71678.7 | + | 71678.7i | −0.609259 | + | 0.609259i | ||||
\(344\) | −66439.0 | + | 66439.0i | −0.561444 | + | 0.561444i | ||||
\(345\) | −52698.3 | − | 52698.3i | −0.442750 | − | 0.442750i | ||||
\(346\) | −12036.4 | − | 12036.4i | −0.100541 | − | 0.100541i | ||||
\(347\) | −183864. | −1.52699 | −0.763497 | − | 0.645811i | \(-0.776519\pi\) | ||||
−0.763497 | + | 0.645811i | \(0.776519\pi\) | |||||||
\(348\) | 85721.6i | 0.707835i | ||||||||
\(349\) | −72786.9 | − | 72786.9i | −0.597588 | − | 0.597588i | 0.342082 | − | 0.939670i | \(-0.388868\pi\) |
−0.939670 | + | 0.342082i | \(0.888868\pi\) | |||||||
\(350\) | − | 107973.i | − | 0.881413i | ||||||
\(351\) | −13130.2 | − | 19742.4i | −0.106576 | − | 0.160246i | ||||
\(352\) | 136012. | 1.09772 | ||||||||
\(353\) | 106752. | − | 106752.i | 0.856695 | − | 0.856695i | −0.134252 | − | 0.990947i | \(-0.542863\pi\) |
0.990947 | + | 0.134252i | \(0.0428632\pi\) | |||||||
\(354\) | 178123. | 1.42139 | ||||||||
\(355\) | − | 157831.i | − | 1.25238i | ||||||
\(356\) | 183867. | − | 183867.i | 1.45078 | − | 1.45078i | ||||
\(357\) | 14683.2 | − | 14683.2i | 0.115209 | − | 0.115209i | ||||
\(358\) | 12867.9 | + | 12867.9i | 0.100402 | + | 0.100402i | ||||
\(359\) | −26893.9 | − | 26893.9i | −0.208672 | − | 0.208672i | 0.595031 | − | 0.803703i | \(-0.297140\pi\) |
−0.803703 | + | 0.595031i | \(0.797140\pi\) | |||||||
\(360\) | −33433.9 | −0.257978 | ||||||||
\(361\) | − | 309264.i | − | 2.37309i | ||||||
\(362\) | −190631. | − | 190631.i | −1.45471 | − | 1.45471i | ||||
\(363\) | − | 25837.1i | − | 0.196078i | ||||||
\(364\) | 85363.1 | + | 17170.3i | 0.644269 | + | 0.129591i | ||||
\(365\) | −161123. | −1.20941 | ||||||||
\(366\) | −11342.7 | + | 11342.7i | −0.0846748 | + | 0.0846748i | ||||
\(367\) | 6492.32 | 0.0482023 | 0.0241012 | − | 0.999710i | \(-0.492328\pi\) | ||||
0.0241012 | + | 0.999710i | \(0.492328\pi\) | |||||||
\(368\) | 53737.5i | 0.396809i | ||||||||
\(369\) | 21680.6 | − | 21680.6i | 0.159228 | − | 0.159228i | ||||
\(370\) | 346022. | − | 346022.i | 2.52755 | − | 2.52755i | ||||
\(371\) | 53240.0 | + | 53240.0i | 0.386804 | + | 0.386804i | ||||
\(372\) | 7465.29 | + | 7465.29i | 0.0539462 | + | 0.0539462i | ||||
\(373\) | −53286.9 | −0.383004 | −0.191502 | − | 0.981492i | \(-0.561336\pi\) | ||||
−0.191502 | + | 0.981492i | \(0.561336\pi\) | |||||||
\(374\) | 100316.i | 0.717180i | ||||||||
\(375\) | 14957.4 | + | 14957.4i | 0.106364 | + | 0.106364i | ||||
\(376\) | 1609.18i | 0.0113823i | ||||||||
\(377\) | 71866.5 | + | 108057.i | 0.505643 | + | 0.760276i | ||||
\(378\) | 20599.4 | 0.144168 | ||||||||
\(379\) | −92136.8 | + | 92136.8i | −0.641438 | + | 0.641438i | −0.950909 | − | 0.309471i | \(-0.899848\pi\) |
0.309471 | + | 0.950909i | \(0.399848\pi\) | |||||||
\(380\) | −525363. | −3.63825 | ||||||||
\(381\) | 57134.8i | 0.393596i | ||||||||
\(382\) | 15970.2 | − | 15970.2i | 0.109442 | − | 0.109442i | ||||
\(383\) | −15911.5 | + | 15911.5i | −0.108471 | + | 0.108471i | −0.759259 | − | 0.650788i | \(-0.774439\pi\) |
0.650788 | + | 0.759259i | \(0.274439\pi\) | |||||||
\(384\) | 59449.0 | + | 59449.0i | 0.403164 | + | 0.403164i | ||||
\(385\) | −61501.3 | − | 61501.3i | −0.414918 | − | 0.414918i | ||||
\(386\) | −166387. | −1.11672 | ||||||||
\(387\) | 75562.7i | 0.504528i | ||||||||
\(388\) | −61921.5 | − | 61921.5i | −0.411319 | − | 0.411319i | ||||
\(389\) | 215552.i | 1.42447i | 0.701941 | + | 0.712236i | \(0.252317\pi\) | ||||
−0.701941 | + | 0.712236i | \(0.747683\pi\) | |||||||
\(390\) | −165115. | + | 109814.i | −1.08557 | + | 0.721988i | ||||
\(391\) | −64799.0 | −0.423852 | ||||||||
\(392\) | 43345.8 | − | 43345.8i | 0.282082 | − | 0.282082i | ||||
\(393\) | 72867.1 | 0.471788 | ||||||||
\(394\) | − | 137815.i | − | 0.887778i | ||||||
\(395\) | 244544. | − | 244544.i | 1.56734 | − | 1.56734i | ||||
\(396\) | −40331.2 | + | 40331.2i | −0.257188 | + | 0.257188i | ||||
\(397\) | 81274.7 | + | 81274.7i | 0.515673 | + | 0.515673i | 0.916259 | − | 0.400586i | \(-0.131194\pi\) |
−0.400586 | + | 0.916259i | \(0.631194\pi\) | |||||||
\(398\) | 100917. | + | 100917.i | 0.637089 | + | 0.637089i | ||||
\(399\) | 82621.0 | 0.518973 | ||||||||
\(400\) | − | 101621.i | − | 0.635132i | ||||||
\(401\) | 170564. | + | 170564.i | 1.06072 | + | 1.06072i | 0.998034 | + | 0.0626817i | \(0.0199653\pi\) |
0.0626817 | + | 0.998034i | \(0.480035\pi\) | |||||||
\(402\) | 189793.i | 1.17443i | ||||||||
\(403\) | 15669.1 | + | 3151.77i | 0.0964795 | + | 0.0194063i | ||||
\(404\) | −120194. | −0.736409 | ||||||||
\(405\) | −19012.6 | + | 19012.6i | −0.115913 | + | 0.115913i | ||||
\(406\) | −112748. | −0.683999 | ||||||||
\(407\) | − | 213084.i | − | 1.28636i | ||||||
\(408\) | −20555.5 | + | 20555.5i | −0.123483 | + | 0.123483i | ||||
\(409\) | −92288.1 | + | 92288.1i | −0.551695 | + | 0.551695i | −0.926930 | − | 0.375235i | \(-0.877562\pi\) |
0.375235 | + | 0.926930i | \(0.377562\pi\) | |||||||
\(410\) | −181325. | − | 181325.i | −1.07867 | − | 1.07867i | ||||
\(411\) | 107469. | + | 107469.i | 0.636208 | + | 0.636208i | ||||
\(412\) | 145933. | 0.859725 | ||||||||
\(413\) | 134278.i | 0.787235i | ||||||||
\(414\) | −45453.9 | − | 45453.9i | −0.265198 | − | 0.265198i | ||||
\(415\) | 324935.i | 1.88669i | ||||||||
\(416\) | 229175. | + | 46097.4i | 1.32428 | + | 0.266373i | ||||
\(417\) | −65388.9 | −0.376038 | ||||||||
\(418\) | −282235. | + | 282235.i | −1.61532 | + | 1.61532i | ||||
\(419\) | −20127.4 | −0.114646 | −0.0573232 | − | 0.998356i | \(-0.518257\pi\) | ||||
−0.0573232 | + | 0.998356i | \(0.518257\pi\) | |||||||
\(420\) | − | 98743.1i | − | 0.559768i | ||||||
\(421\) | 171209. | − | 171209.i | 0.965965 | − | 0.965965i | −0.0334748 | − | 0.999440i | \(-0.510657\pi\) |
0.999440 | + | 0.0334748i | \(0.0106573\pi\) | |||||||
\(422\) | −43489.0 | + | 43489.0i | −0.244205 | + | 0.244205i | ||||
\(423\) | 915.080 | + | 915.080i | 0.00511421 | + | 0.00511421i | ||||
\(424\) | −74532.5 | − | 74532.5i | −0.414586 | − | 0.414586i | ||||
\(425\) | 122539. | 0.678417 | ||||||||
\(426\) | − | 136134.i | − | 0.750148i | ||||||
\(427\) | −8550.68 | − | 8550.68i | −0.0468970 | − | 0.0468970i | ||||
\(428\) | 181800.i | 0.992446i | ||||||||
\(429\) | −17027.4 | + | 84652.4i | −0.0925195 | + | 0.459965i | ||||
\(430\) | 631966. | 3.41788 | ||||||||
\(431\) | 127549. | − | 127549.i | 0.686630 | − | 0.686630i | −0.274856 | − | 0.961485i | \(-0.588630\pi\) |
0.961485 | + | 0.274856i | \(0.0886301\pi\) | |||||||
\(432\) | 19387.5 | 0.103885 | ||||||||
\(433\) | 68957.0i | 0.367792i | 0.982946 | + | 0.183896i | \(0.0588710\pi\) | ||||
−0.982946 | + | 0.183896i | \(0.941129\pi\) | |||||||
\(434\) | −9818.93 | + | 9818.93i | −0.0521297 | + | 0.0521297i | ||||
\(435\) | 104063. | − | 104063.i | 0.549942 | − | 0.549942i | ||||
\(436\) | 259478. | + | 259478.i | 1.36498 | + | 1.36498i | ||||
\(437\) | −182309. | − | 182309.i | −0.954651 | − | 0.954651i | ||||
\(438\) | −138974. | −0.724410 | ||||||||
\(439\) | − | 113397.i | − | 0.588400i | −0.955744 | − | 0.294200i | \(-0.904947\pi\) | ||
0.955744 | − | 0.294200i | \(-0.0950531\pi\) | |||||||
\(440\) | 86097.7 | + | 86097.7i | 0.444720 | + | 0.444720i | ||||
\(441\) | − | 49298.2i | − | 0.253486i | ||||||
\(442\) | −33999.4 | + | 169029.i | −0.174031 | + | 0.865203i | ||||
\(443\) | 92267.8 | 0.470157 | 0.235079 | − | 0.971976i | \(-0.424465\pi\) | ||||
0.235079 | + | 0.971976i | \(0.424465\pi\) | |||||||
\(444\) | 171058. | − | 171058.i | 0.867717 | − | 0.867717i | ||||
\(445\) | −446414. | −2.25433 | ||||||||
\(446\) | 215984.i | 1.08580i | ||||||||
\(447\) | −6844.47 | + | 6844.47i | −0.0342551 | + | 0.0342551i | ||||
\(448\) | −106116. | + | 106116.i | −0.528719 | + | 0.528719i | ||||
\(449\) | −17542.3 | − | 17542.3i | −0.0870148 | − | 0.0870148i | 0.662260 | − | 0.749274i | \(-0.269598\pi\) |
−0.749274 | + | 0.662260i | \(0.769598\pi\) | |||||||
\(450\) | 85956.2 | + | 85956.2i | 0.424475 | + | 0.424475i | ||||
\(451\) | −111662. | −0.548976 | ||||||||
\(452\) | − | 319338.i | − | 1.56305i | ||||||
\(453\) | −31192.9 | − | 31192.9i | −0.152006 | − | 0.152006i | ||||
\(454\) | 134871.i | 0.654343i | ||||||||
\(455\) | −82783.4 | − | 124472.i | −0.399872 | − | 0.601240i | ||||
\(456\) | −115664. | −0.556248 | ||||||||
\(457\) | 104731. | − | 104731.i | 0.501466 | − | 0.501466i | −0.410428 | − | 0.911893i | \(-0.634621\pi\) |
0.911893 | + | 0.410428i | \(0.134621\pi\) | |||||||
\(458\) | 215859. | 1.02906 | ||||||||
\(459\) | 23378.3i | 0.110965i | ||||||||
\(460\) | −217883. | + | 217883.i | −1.02969 | + | 1.02969i | ||||
\(461\) | −12382.8 | + | 12382.8i | −0.0582663 | + | 0.0582663i | −0.735640 | − | 0.677373i | \(-0.763118\pi\) |
0.677373 | + | 0.735640i | \(0.263118\pi\) | |||||||
\(462\) | −53046.7 | − | 53046.7i | −0.248527 | − | 0.248527i | ||||
\(463\) | 156318. | + | 156318.i | 0.729199 | + | 0.729199i | 0.970460 | − | 0.241261i | \(-0.0775611\pi\) |
−0.241261 | + | 0.970460i | \(0.577561\pi\) | |||||||
\(464\) | −106115. | −0.492878 | ||||||||
\(465\) | − | 18125.2i | − | 0.0838255i | ||||||
\(466\) | −97122.3 | − | 97122.3i | −0.447247 | − | 0.447247i | ||||
\(467\) | 3880.03i | 0.0177911i | 0.999960 | + | 0.00889553i | \(0.00283157\pi\) | ||||
−0.999960 | + | 0.00889553i | \(0.997168\pi\) | |||||||
\(468\) | −81625.8 | + | 54287.5i | −0.372680 | + | 0.247861i | ||||
\(469\) | −143075. | −0.650455 | ||||||||
\(470\) | 7653.24 | − | 7653.24i | 0.0346457 | − | 0.0346457i | ||||
\(471\) | −125916. | −0.567597 | ||||||||
\(472\) | − | 187980.i | − | 0.843778i | ||||||
\(473\) | 194586. | − | 194586.i | 0.869740 | − | 0.869740i | ||||
\(474\) | 210926. | − | 210926.i | 0.938803 | − | 0.938803i | ||||
\(475\) | 344758. | + | 344758.i | 1.52801 | + | 1.52801i | ||||
\(476\) | −60708.3 | − | 60708.3i | −0.267938 | − | 0.267938i | ||||
\(477\) | −84767.6 | −0.372557 | ||||||||
\(478\) | − | 578637.i | − | 2.53250i | ||||||
\(479\) | 53446.0 | + | 53446.0i | 0.232940 | + | 0.232940i | 0.813919 | − | 0.580979i | \(-0.197330\pi\) |
−0.580979 | + | 0.813919i | \(0.697330\pi\) | |||||||
\(480\) | − | 265097.i | − | 1.15059i | ||||||
\(481\) | 72218.9 | − | 359040.i | 0.312148 | − | 1.55186i | ||||
\(482\) | 301546. | 1.29795 | ||||||||
\(483\) | 34265.3 | − | 34265.3i | 0.146879 | − | 0.146879i | ||||
\(484\) | −106824. | −0.456015 | ||||||||
\(485\) | 150341.i | 0.639136i | ||||||||
\(486\) | −16398.9 | + | 16398.9i | −0.0694293 | + | 0.0694293i | ||||
\(487\) | −39739.5 | + | 39739.5i | −0.167558 | + | 0.167558i | −0.785905 | − | 0.618347i | \(-0.787803\pi\) |
0.618347 | + | 0.785905i | \(0.287803\pi\) | |||||||
\(488\) | 11970.4 | + | 11970.4i | 0.0502653 | + | 0.0502653i | ||||
\(489\) | −125952. | − | 125952.i | −0.526729 | − | 0.526729i | ||||
\(490\) | −412304. | −1.71722 | ||||||||
\(491\) | 183063.i | 0.759342i | 0.925122 | + | 0.379671i | \(0.123963\pi\) | ||||
−0.925122 | + | 0.379671i | \(0.876037\pi\) | |||||||
\(492\) | −89639.4 | − | 89639.4i | −0.370313 | − | 0.370313i | ||||
\(493\) | − | 127958.i | − | 0.526469i | ||||||
\(494\) | −571212. | + | 379900.i | −2.34069 | + | 1.55674i | ||||
\(495\) | 97921.0 | 0.399637 | ||||||||
\(496\) | −9241.28 | + | 9241.28i | −0.0375638 | + | 0.0375638i | ||||
\(497\) | 102624. | 0.415468 | ||||||||
\(498\) | 280266.i | 1.13009i | ||||||||
\(499\) | −57389.5 | + | 57389.5i | −0.230479 | + | 0.230479i | −0.812893 | − | 0.582414i | \(-0.802108\pi\) |
0.582414 | + | 0.812893i | \(0.302108\pi\) | |||||||
\(500\) | 61842.1 | − | 61842.1i | 0.247368 | − | 0.247368i | ||||
\(501\) | −90165.7 | − | 90165.7i | −0.359224 | − | 0.359224i | ||||
\(502\) | 20643.2 | + | 20643.2i | 0.0819161 | + | 0.0819161i | ||||
\(503\) | −192555. | −0.761061 | −0.380530 | − | 0.924768i | \(-0.624259\pi\) | ||||
−0.380530 | + | 0.924768i | \(0.624259\pi\) | |||||||
\(504\) | − | 21739.3i | − | 0.0855824i | ||||||
\(505\) | 145910. | + | 145910.i | 0.572142 | + | 0.572142i | ||||
\(506\) | 234102.i | 0.914333i | ||||||||
\(507\) | −57381.1 | + | 136865.i | −0.223230 | + | 0.532449i | ||||
\(508\) | 236226. | 0.915377 | ||||||||
\(509\) | −84764.7 | + | 84764.7i | −0.327175 | + | 0.327175i | −0.851511 | − | 0.524336i | \(-0.824313\pi\) |
0.524336 | + | 0.851511i | \(0.324313\pi\) | |||||||
\(510\) | 195524. | 0.751724 | ||||||||
\(511\) | − | 104765.i | − | 0.401213i | ||||||
\(512\) | −187652. | + | 187652.i | −0.715835 | + | 0.715835i | ||||
\(513\) | −65773.7 | + | 65773.7i | −0.249929 | + | 0.249929i | ||||
\(514\) | −271629. | − | 271629.i | −1.02813 | − | 1.02813i | ||||
\(515\) | −177157. | − | 177157.i | −0.667951 | − | 0.667951i | ||||
\(516\) | 312417. | 1.17337 | ||||||||
\(517\) | − | 4712.95i | − | 0.0176324i | ||||||
\(518\) | 224989. | + | 224989.i | 0.838498 | + | 0.838498i | ||||
\(519\) | 14446.8i | 0.0536336i | ||||||||
\(520\) | 115891. | + | 174252.i | 0.428592 | + | 0.644424i | ||||
\(521\) | 314076. | 1.15707 | 0.578534 | − | 0.815658i | \(-0.303625\pi\) | ||||
0.578534 | + | 0.815658i | \(0.303625\pi\) | |||||||
\(522\) | 89757.2 | − | 89757.2i | 0.329404 | − | 0.329404i | ||||
\(523\) | −37022.8 | −0.135352 | −0.0676762 | − | 0.997707i | \(-0.521558\pi\) | ||||
−0.0676762 | + | 0.997707i | \(0.521558\pi\) | |||||||
\(524\) | − | 301272.i | − | 1.09723i | ||||||
\(525\) | −64798.0 | + | 64798.0i | −0.235095 | + | 0.235095i | ||||
\(526\) | −196636. | + | 196636.i | −0.710708 | + | 0.710708i | ||||
\(527\) | −11143.5 | − | 11143.5i | −0.0401238 | − | 0.0401238i | ||||
\(528\) | −49925.9 | − | 49925.9i | −0.179085 | − | 0.179085i | ||||
\(529\) | 128624. | 0.459631 | ||||||||
\(530\) | 708951.i | 2.52386i | ||||||||
\(531\) | −106897. | − | 106897.i | −0.379121 | − | 0.379121i | ||||
\(532\) | − | 341600.i | − | 1.20696i | ||||||
\(533\) | −188147. | − | 37844.8i | −0.662282 | − | 0.133214i | ||||
\(534\) | −385045. | −1.35030 | ||||||||
\(535\) | 220699. | − | 220699.i | 0.771067 | − | 0.771067i | ||||
\(536\) | 200295. | 0.697174 | ||||||||
\(537\) | − | 15444.8i | − | 0.0535593i | ||||||
\(538\) | −342897. | + | 342897.i | −1.18467 | + | 1.18467i | ||||
\(539\) | −126951. | + | 126951.i | −0.436976 | + | 0.436976i | ||||
\(540\) | 78608.3 | + | 78608.3i | 0.269576 | + | 0.269576i | ||||
\(541\) | −38918.2 | − | 38918.2i | −0.132971 | − | 0.132971i | 0.637489 | − | 0.770460i | \(-0.279973\pi\) |
−0.770460 | + | 0.637489i | \(0.779973\pi\) | |||||||
\(542\) | 140097. | 0.476903 | ||||||||
\(543\) | 228807.i | 0.776015i | ||||||||
\(544\) | −162984. | − | 162984.i | −0.550741 | − | 0.550741i | ||||
\(545\) | − | 629992.i | − | 2.12101i | ||||||
\(546\) | −71403.2 | − | 107361.i | −0.239515 | − | 0.360130i | ||||
\(547\) | −383774. | −1.28263 | −0.641314 | − | 0.767279i | \(-0.721610\pi\) | ||||
−0.641314 | + | 0.767279i | \(0.721610\pi\) | |||||||
\(548\) | 444334. | − | 444334.i | 1.47962 | − | 1.47962i | ||||
\(549\) | 13614.2 | 0.0451697 | ||||||||
\(550\) | − | 442702.i | − | 1.46348i | ||||||
\(551\) | 360003. | − | 360003.i | 1.18578 | − | 1.18578i | ||||
\(552\) | −47969.2 | + | 47969.2i | −0.157429 | + | 0.157429i | ||||
\(553\) | 159007. | + | 159007.i | 0.519954 | + | 0.519954i | ||||
\(554\) | 12486.4 | + | 12486.4i | 0.0406835 | + | 0.0406835i | ||||
\(555\) | −415316. | −1.34832 | ||||||||
\(556\) | 270353.i | 0.874543i | ||||||||
\(557\) | 280053. | + | 280053.i | 0.902672 | + | 0.902672i | 0.995667 | − | 0.0929944i | \(-0.0296439\pi\) |
−0.0929944 | + | 0.995667i | \(0.529644\pi\) | |||||||
\(558\) | − | 15633.5i | − | 0.0502097i | ||||||
\(559\) | 393820. | − | 261921.i | 1.26030 | − | 0.838199i | ||||
\(560\) | 122234. | 0.389777 | ||||||||
\(561\) | 60202.8 | − | 60202.8i | 0.191290 | − | 0.191290i | ||||
\(562\) | 893810. | 2.82991 | ||||||||
\(563\) | 50493.5i | 0.159301i | 0.996823 | + | 0.0796505i | \(0.0253804\pi\) | ||||
−0.996823 | + | 0.0796505i | \(0.974620\pi\) | |||||||
\(564\) | 3783.43 | − | 3783.43i | 0.0118940 | − | 0.0118940i | ||||
\(565\) | −387664. | + | 387664.i | −1.21439 | + | 1.21439i | ||||
\(566\) | −340194. | − | 340194.i | −1.06193 | − | 1.06193i | ||||
\(567\) | −12362.3 | − | 12362.3i | −0.0384533 | − | 0.0384533i | ||||
\(568\) | −143667. | −0.445309 | ||||||||
\(569\) | − | 301875.i | − | 0.932400i | −0.884679 | − | 0.466200i | \(-0.845623\pi\) | ||
0.884679 | − | 0.466200i | \(-0.154377\pi\) | |||||||
\(570\) | 550096. | + | 550096.i | 1.69312 | + | 1.69312i | ||||
\(571\) | − | 290046.i | − | 0.889601i | −0.895630 | − | 0.444800i | \(-0.853275\pi\) | ||
0.895630 | − | 0.444800i | \(-0.146725\pi\) | |||||||
\(572\) | 349999. | + | 70400.4i | 1.06973 | + | 0.215171i | ||||
\(573\) | −19168.4 | −0.0583817 | ||||||||
\(574\) | 117901. | − | 117901.i | 0.357843 | − | 0.357843i | ||||
\(575\) | 285962. | 0.864914 | ||||||||
\(576\) | − | 168956.i | − | 0.509246i | ||||||
\(577\) | 127765. | − | 127765.i | 0.383760 | − | 0.383760i | −0.488695 | − | 0.872455i | \(-0.662527\pi\) |
0.872455 | + | 0.488695i | \(0.162527\pi\) | |||||||
\(578\) | −241368. | + | 241368.i | −0.722477 | + | 0.722477i | ||||
\(579\) | 99853.9 | + | 99853.9i | 0.297857 | + | 0.297857i | ||||
\(580\) | −430252. | − | 430252.i | −1.27899 | − | 1.27899i | ||||
\(581\) | −211278. | −0.625897 | ||||||||
\(582\) | 129673.i | 0.382829i | ||||||||
\(583\) | 218290. | + | 218290.i | 0.642240 | + | 0.642240i | ||||
\(584\) | 146664.i | 0.430030i | ||||||||
\(585\) | 164994. | + | 33187.6i | 0.482120 | + | 0.0969759i | ||||
\(586\) | 47538.4 | 0.138436 | ||||||||
\(587\) | −432681. | + | 432681.i | −1.25572 | + | 1.25572i | −0.302598 | + | 0.953118i | \(0.597854\pi\) |
−0.953118 | + | 0.302598i | \(0.902146\pi\) | |||||||
\(588\) | −203825. | −0.589527 | ||||||||
\(589\) | − | 62703.6i | − | 0.180743i | ||||||
\(590\) | −894031. | + | 894031.i | −2.56832 | + | 2.56832i | ||||
\(591\) | −82707.0 | + | 82707.0i | −0.236792 | + | 0.236792i | ||||
\(592\) | 211753. | + | 211753.i | 0.604207 | + | 0.604207i | ||||
\(593\) | 351836. | + | 351836.i | 1.00053 | + | 1.00053i | 1.00000 | 0.000531251i | \(0.000169102\pi\) | |
0.000531251 | 1.00000i | \(0.499831\pi\) | ||||||||
\(594\) | 84459.8 | 0.239374 | ||||||||
\(595\) | 147395.i | 0.416341i | ||||||||
\(596\) | 28298.7 | + | 28298.7i | 0.0796663 | + | 0.0796663i | ||||
\(597\) | − | 121127.i | − | 0.339855i | ||||||
\(598\) | −79342.4 | + | 394454.i | −0.221872 | + | 1.10305i | ||||
\(599\) | −484810. | −1.35119 | −0.675597 | − | 0.737271i | \(-0.736114\pi\) | ||||
−0.675597 | + | 0.737271i | \(0.736114\pi\) | |||||||
\(600\) | 90712.9 | − | 90712.9i | 0.251980 | − | 0.251980i | ||||
\(601\) | 214570. | 0.594046 | 0.297023 | − | 0.954870i | \(-0.404006\pi\) | ||||
0.297023 | + | 0.954870i | \(0.404006\pi\) | |||||||
\(602\) | 410915.i | 1.13386i | ||||||||
\(603\) | 113900. | − | 113900.i | 0.313249 | − | 0.313249i | ||||
\(604\) | −128968. | + | 128968.i | −0.353516 | + | 0.353516i | ||||
\(605\) | 129681. | + | 129681.i | 0.354294 | + | 0.354294i | ||||
\(606\) | 125852. | + | 125852.i | 0.342701 | + | 0.342701i | ||||
\(607\) | −2800.08 | −0.00759964 | −0.00379982 | − | 0.999993i | \(-0.501210\pi\) | ||||
−0.00379982 | + | 0.999993i | \(0.501210\pi\) | |||||||
\(608\) | − | 917096.i | − | 2.48089i | ||||||
\(609\) | 67663.3 | + | 67663.3i | 0.182440 | + | 0.182440i | ||||
\(610\) | − | 113862.i | − | 0.305998i | ||||||
\(611\) | 1597.32 | − | 7941.17i | 0.00427869 | − | 0.0212717i | ||||
\(612\) | 96658.4 | 0.258070 | ||||||||
\(613\) | −92722.6 | + | 92722.6i | −0.246754 | + | 0.246754i | −0.819637 | − | 0.572883i | \(-0.805825\pi\) |
0.572883 | + | 0.819637i | \(0.305825\pi\) | |||||||
\(614\) | −317265. | −0.841560 | ||||||||
\(615\) | 217638.i | 0.575418i | ||||||||
\(616\) | −55982.2 | + | 55982.2i | −0.147533 | + | 0.147533i | ||||
\(617\) | 260927. | − | 260927.i | 0.685407 | − | 0.685407i | −0.275806 | − | 0.961213i | \(-0.588945\pi\) |
0.961213 | + | 0.275806i | \(0.0889447\pi\) | |||||||
\(618\) | −152803. | − | 152803.i | −0.400089 | − | 0.400089i | ||||
\(619\) | 103595. | + | 103595.i | 0.270369 | + | 0.270369i | 0.829249 | − | 0.558880i | \(-0.188769\pi\) |
−0.558880 | + | 0.829249i | \(0.688769\pi\) | |||||||
\(620\) | −74939.2 | −0.194951 | ||||||||
\(621\) | 54556.5i | 0.141470i | ||||||||
\(622\) | 246783. | + | 246783.i | 0.637874 | + | 0.637874i | ||||
\(623\) | − | 290266.i | − | 0.747859i | ||||||
\(624\) | −67202.5 | − | 101045.i | −0.172590 | − | 0.259504i | ||||
\(625\) | 309460. | 0.792218 | ||||||||
\(626\) | 731248. | − | 731248.i | 1.86602 | − | 1.86602i | ||||
\(627\) | 338755. | 0.861690 | ||||||||
\(628\) | 520606.i | 1.32005i | ||||||||
\(629\) | −255341. | + | 255341.i | −0.645385 | + | 0.645385i | ||||
\(630\) | −103392. | + | 103392.i | −0.260498 | + | 0.260498i | ||||
\(631\) | −300176. | − | 300176.i | −0.753907 | − | 0.753907i | 0.221299 | − | 0.975206i | \(-0.428970\pi\) |
−0.975206 | + | 0.221299i | \(0.928970\pi\) | |||||||
\(632\) | −222599. | − | 222599.i | −0.557299 | − | 0.557299i | ||||
\(633\) | 52198.2 | 0.130271 | ||||||||
\(634\) | − | 498599.i | − | 1.24043i | ||||||
\(635\) | −286769. | − | 286769.i | −0.711189 | − | 0.711189i | ||||
\(636\) | 350475.i | 0.866449i | ||||||||
\(637\) | −256934. | + | 170881.i | −0.633203 | + | 0.421130i | ||||
\(638\) | −462279. | −1.13570 | ||||||||
\(639\) | −81698.1 | + | 81698.1i | −0.200083 | + | 0.200083i | ||||
\(640\) | −596770. | −1.45696 | ||||||||
\(641\) | 466494.i | 1.13535i | 0.823253 | + | 0.567675i | \(0.192157\pi\) | ||||
−0.823253 | + | 0.567675i | \(0.807843\pi\) | |||||||
\(642\) | 190359. | − | 190359.i | 0.461853 | − | 0.461853i | ||||
\(643\) | 439463. | − | 439463.i | 1.06292 | − | 1.06292i | 0.0650372 | − | 0.997883i | \(-0.479283\pi\) |
0.997883 | − | 0.0650372i | \(-0.0207166\pi\) | |||||||
\(644\) | −141671. | − | 141671.i | −0.341594 | − | 0.341594i | ||||
\(645\) | −379262. | − | 379262.i | −0.911633 | − | 0.911633i | ||||
\(646\) | 676409. | 1.62086 | ||||||||
\(647\) | − | 562437.i | − | 1.34358i | −0.740740 | − | 0.671792i | \(-0.765525\pi\) | ||
0.740740 | − | 0.671792i | \(-0.234475\pi\) | |||||||
\(648\) | 17306.4 | + | 17306.4i | 0.0412152 | + | 0.0412152i | ||||
\(649\) | 550555.i | 1.30711i | ||||||||
\(650\) | 150042. | − | 745938.i | 0.355128 | − | 1.76553i | ||||
\(651\) | 11785.3 | 0.0278085 | ||||||||
\(652\) | −520754. | + | 520754.i | −1.22500 | + | 1.22500i | ||||
\(653\) | 37629.2 | 0.0882467 | 0.0441234 | − | 0.999026i | \(-0.485951\pi\) | ||||
0.0441234 | + | 0.999026i | \(0.485951\pi\) | |||||||
\(654\) | − | 543387.i | − | 1.27044i | ||||||
\(655\) | −365733. | + | 365733.i | −0.852474 | + | 0.852474i | ||||
\(656\) | 110965. | − | 110965.i | 0.257856 | − | 0.257856i | ||||
\(657\) | 83402.4 | + | 83402.4i | 0.193218 | + | 0.193218i | ||||
\(658\) | 4976.27 | + | 4976.27i | 0.0114935 | + | 0.0114935i | ||||
\(659\) | 18033.4 | 0.0415248 | 0.0207624 | − | 0.999784i | \(-0.493391\pi\) | ||||
0.0207624 | + | 0.999784i | \(0.493391\pi\) | |||||||
\(660\) | − | 404858.i | − | 0.929426i | ||||||
\(661\) | 536607. | + | 536607.i | 1.22816 | + | 1.22816i | 0.964661 | + | 0.263495i | \(0.0848754\pi\) |
0.263495 | + | 0.964661i | \(0.415125\pi\) | |||||||
\(662\) | − | 1.16704e6i | − | 2.66299i | ||||||
\(663\) | 121844. | − | 81035.7i | 0.277189 | − | 0.184353i | ||||
\(664\) | 295776. | 0.670852 | ||||||||
\(665\) | −414689. | + | 414689.i | −0.937733 | + | 0.937733i | ||||
\(666\) | −358223. | −0.807616 | ||||||||
\(667\) | − | 298607.i | − | 0.671195i | ||||||
\(668\) | −372794. | + | 372794.i | −0.835440 | + | 0.835440i | ||||
\(669\) | 129618. | − | 129618.i | 0.289610 | − | 0.289610i | ||||
\(670\) | −952601. | − | 952601.i | −2.12208 | − | 2.12208i | ||||
\(671\) | −35058.7 | − | 35058.7i | −0.0778666 | − | 0.0778666i | ||||
\(672\) | 172370. | 0.381701 | ||||||||
\(673\) | 75975.6i | 0.167743i | 0.996477 | + | 0.0838715i | \(0.0267285\pi\) | ||||
−0.996477 | + | 0.0838715i | \(0.973271\pi\) | |||||||
\(674\) | −245594. | − | 245594.i | −0.540628 | − | 0.540628i | ||||
\(675\) | − | 103170.i | − | 0.226436i | ||||||
\(676\) | 565875. | + | 237244.i | 1.23830 | + | 0.519162i | ||||
\(677\) | 438381. | 0.956478 | 0.478239 | − | 0.878230i | \(-0.341275\pi\) | ||||
0.478239 | + | 0.878230i | \(0.341275\pi\) | |||||||
\(678\) | −334372. | + | 334372.i | −0.727395 | + | 0.727395i | ||||
\(679\) | −97754.1 | −0.212029 | ||||||||
\(680\) | − | 206343.i | − | 0.446244i | ||||||
\(681\) | 80940.0 | − | 80940.0i | 0.174530 | − | 0.174530i | ||||
\(682\) | −40258.7 | + | 40258.7i | −0.0865549 | + | 0.0865549i | ||||
\(683\) | −14323.9 | − | 14323.9i | −0.0307057 | − | 0.0307057i | 0.691587 | − | 0.722293i | \(-0.256912\pi\) |
−0.722293 | + | 0.691587i | \(0.756912\pi\) | |||||||
\(684\) | 271944. | + | 271944.i | 0.581255 | + | 0.581255i | ||||
\(685\) | −1.07881e6 | −2.29913 | ||||||||
\(686\) | − | 620620.i | − | 1.31880i | ||||||
\(687\) | −129544. | − | 129544.i | −0.274475 | − | 0.274475i | ||||
\(688\) | 386741.i | 0.817039i | ||||||||
\(689\) | 293828. | + | 441795.i | 0.618949 | + | 0.930641i | ||||
\(690\) | 456282. | 0.958374 | ||||||||
\(691\) | 64315.1 | − | 64315.1i | 0.134697 | − | 0.134697i | −0.636544 | − | 0.771241i | \(-0.719637\pi\) |
0.771241 | + | 0.636544i | \(0.219637\pi\) | |||||||
\(692\) | 59730.8 | 0.124734 | ||||||||
\(693\) | 63669.9i | 0.132577i | ||||||||
\(694\) | 795981. | − | 795981.i | 1.65266 | − | 1.65266i | ||||
\(695\) | 328198. | − | 328198.i | 0.679464 | − | 0.679464i | ||||
\(696\) | −94724.2 | − | 94724.2i | −0.195543 | − | 0.195543i | ||||
\(697\) | 133806. | + | 133806.i | 0.275429 | + | 0.275429i | ||||
\(698\) | 630216. | 1.29354 | ||||||||
\(699\) | 116572.i | 0.238583i | ||||||||
\(700\) | 267910. | + | 267910.i | 0.546755 | + | 0.546755i | ||||
\(701\) | 77204.1i | 0.157110i | 0.996910 | + | 0.0785551i | \(0.0250307\pi\) | ||||
−0.996910 | + | 0.0785551i | \(0.974969\pi\) | |||||||
\(702\) | 142312. | + | 28625.3i | 0.288780 | + | 0.0580865i | ||||
\(703\) | −1.43678e6 | −2.90723 | ||||||||
\(704\) | −435088. | + | 435088.i | −0.877873 | + | 0.877873i | ||||
\(705\) | −9185.89 | −0.0184817 | ||||||||
\(706\) | 924298.i | 1.85440i | ||||||||
\(707\) | −94873.4 | + | 94873.4i | −0.189804 | + | 0.189804i | ||||
\(708\) | −441971. | + | 441971.i | −0.881712 | + | 0.881712i | ||||
\(709\) | 561910. | + | 561910.i | 1.11783 | + | 1.11783i | 0.992060 | + | 0.125766i | \(0.0401389\pi\) |
0.125766 | + | 0.992060i | \(0.459861\pi\) | |||||||
\(710\) | 683279. | + | 683279.i | 1.35544 | + | 1.35544i | ||||
\(711\) | −253167. | −0.500804 | ||||||||
\(712\) | 406353.i | 0.801574i | ||||||||
\(713\) | −26005.0 | − | 26005.0i | −0.0511538 | − | 0.0511538i | ||||
\(714\) | 127133.i | 0.249380i | ||||||||
\(715\) | −339421. | − | 510348.i | −0.663937 | − | 0.998285i | ||||
\(716\) | −63857.3 | −0.124562 | ||||||||
\(717\) | −347258. | + | 347258.i | −0.675481 | + | 0.675481i | ||||
\(718\) | 232857. | 0.451690 | ||||||||
\(719\) | − | 324777.i | − | 0.628243i | −0.949383 | − | 0.314121i | \(-0.898290\pi\) | ||
0.949383 | − | 0.314121i | \(-0.101710\pi\) | |||||||
\(720\) | −97309.2 | + | 97309.2i | −0.187711 | + | 0.187711i | ||||
\(721\) | 115191. | − | 115191.i | 0.221588 | − | 0.221588i | ||||
\(722\) | 1.33886e6 | + | 1.33886e6i | 2.56839 | + | 2.56839i | ||||
\(723\) | −180967. | − | 180967.i | −0.346196 | − | 0.346196i | ||||
\(724\) | 946013. | 1.80476 | ||||||||
\(725\) | 564686.i | 1.07431i | ||||||||
\(726\) | 111853. | + | 111853.i | 0.212215 | + | 0.212215i | ||||
\(727\) | − | 922269.i | − | 1.74497i | −0.488638 | − | 0.872487i | \(-0.662506\pi\) | ||
0.488638 | − | 0.872487i | \(-0.337494\pi\) | |||||||
\(728\) | −113302. | + | 75354.5i | −0.213783 | + | 0.142183i | ||||
\(729\) | 19683.0 | 0.0370370 | ||||||||
\(730\) | 697533. | − | 697533.i | 1.30894 | − | 1.30894i | ||||
\(731\) | −466348. | −0.872722 | ||||||||
\(732\) | − | 56288.4i | − | 0.105050i | ||||||
\(733\) | 295621. | − | 295621.i | 0.550209 | − | 0.550209i | −0.376292 | − | 0.926501i | \(-0.622801\pi\) |
0.926501 | + | 0.376292i | \(0.122801\pi\) | |||||||
\(734\) | −28106.5 | + | 28106.5i | −0.0521692 | + | 0.0521692i | ||||
\(735\) | 247436. | + | 247436.i | 0.458024 | + | 0.458024i | ||||
\(736\) | −380346. | − | 380346.i | −0.702140 | − | 0.702140i | ||||
\(737\) | −586623. | −1.08000 | ||||||||
\(738\) | 187719.i | 0.344663i | ||||||||
\(739\) | 369186. | + | 369186.i | 0.676015 | + | 0.676015i | 0.959096 | − | 0.283081i | \(-0.0913566\pi\) |
−0.283081 | + | 0.959096i | \(0.591357\pi\) | |||||||
\(740\) | 1.71714e6i | 3.13576i | ||||||||
\(741\) | 570791. | + | 114812.i | 1.03954 | + | 0.209098i | ||||
\(742\) | −460972. | −0.837272 | ||||||||
\(743\) | −671107. | + | 671107.i | −1.21567 | + | 1.21567i | −0.246530 | + | 0.969135i | \(0.579290\pi\) |
−0.969135 | + | 0.246530i | \(0.920710\pi\) | |||||||
\(744\) | −16498.6 | −0.0298059 | ||||||||
\(745\) | − | 68707.2i | − | 0.123791i | ||||||
\(746\) | 230689. | − | 230689.i | 0.414523 | − | 0.414523i | ||||
\(747\) | 168196. | − | 168196.i | 0.301422 | − | 0.301422i | ||||
\(748\) | −248911. | − | 248911.i | −0.444878 | − | 0.444878i | ||||
\(749\) | 143502. | + | 143502.i | 0.255796 | + | 0.255796i | ||||
\(750\) | −129507. | −0.230235 | ||||||||
\(751\) | 167627.i | 0.297210i | 0.988897 | + | 0.148605i | \(0.0474784\pi\) | ||||
−0.988897 | + | 0.148605i | \(0.952522\pi\) | |||||||
\(752\) | 4683.51 | + | 4683.51i | 0.00828201 | + | 0.00828201i | ||||
\(753\) | − | 24777.2i | − | 0.0436981i | ||||||
\(754\) | −778924. | − | 156676.i | −1.37010 | − | 0.275588i | ||||
\(755\) | 313125. | 0.549319 | ||||||||
\(756\) | −51112.5 | + | 51112.5i | −0.0894300 | + | 0.0894300i | ||||
\(757\) | −578076. | −1.00877 | −0.504386 | − | 0.863478i | \(-0.668281\pi\) | ||||
−0.504386 | + | 0.863478i | \(0.668281\pi\) | |||||||
\(758\) | − | 797754.i | − | 1.38845i | ||||||
\(759\) | 140492. | − | 140492.i | 0.243875 | − | 0.243875i | ||||
\(760\) | 580537. | − | 580537.i | 1.00508 | − | 1.00508i | ||||
\(761\) | −762616. | − | 762616.i | −1.31685 | − | 1.31685i | −0.916254 | − | 0.400597i | \(-0.868803\pi\) |
−0.400597 | − | 0.916254i | \(-0.631197\pi\) | |||||||
\(762\) | −247347. | − | 247347.i | −0.425987 | − | 0.425987i | ||||
\(763\) | 409632. | 0.703630 | ||||||||
\(764\) | 79252.6i | 0.135777i | ||||||||
\(765\) | −117340. | − | 117340.i | −0.200503 | − | 0.200503i | ||||
\(766\) | − | 137768.i | − | 0.234795i | ||||||
\(767\) | −186595. | + | 927666.i | −0.317183 | + | 1.57689i | ||||
\(768\) | 5516.94 | 0.00935354 | ||||||||
\(769\) | 698760. | − | 698760.i | 1.18161 | − | 1.18161i | 0.202287 | − | 0.979326i | \(-0.435163\pi\) |
0.979326 | − | 0.202287i | \(-0.0648374\pi\) | |||||||
\(770\) | 532501. | 0.898129 | ||||||||
\(771\) | 326026.i | 0.548457i | ||||||||
\(772\) | 412850. | − | 412850.i | 0.692720 | − | 0.692720i | ||||
\(773\) | −311294. | + | 311294.i | −0.520968 | + | 0.520968i | −0.917864 | − | 0.396895i | \(-0.870088\pi\) |
0.396895 | + | 0.917864i | \(0.370088\pi\) | |||||||
\(774\) | −327125. | − | 327125.i | −0.546049 | − | 0.546049i | ||||
\(775\) | 49177.2 | + | 49177.2i | 0.0818766 | + | 0.0818766i | ||||
\(776\) | 136849. | 0.227258 | ||||||||
\(777\) | − | 270046.i | − | 0.447296i | ||||||
\(778\) | −933166. | − | 933166.i | −1.54170 | − | 1.54170i | ||||
\(779\) | 752912.i | 1.24071i | ||||||||
\(780\) | 137215. | − | 682172.i | 0.225535 | − | 1.12126i | ||||
\(781\) | 420771. | 0.689833 | ||||||||
\(782\) | 280527. | − | 280527.i | 0.458734 | − | 0.458734i | ||||
\(783\) | −107732. | −0.175720 | ||||||||
\(784\) | − | 252315.i | − | 0.410498i | ||||||
\(785\) | 631996. | − | 631996.i | 1.02559 | − | 1.02559i | ||||
\(786\) | −315455. | + | 315455.i | −0.510614 | + | 0.510614i | ||||
\(787\) | −528223. | − | 528223.i | −0.852841 | − | 0.852841i | 0.137642 | − | 0.990482i | \(-0.456048\pi\) |
−0.990482 | + | 0.137642i | \(0.956048\pi\) | |||||||
\(788\) | 341955. | + | 341955.i | 0.550702 | + | 0.550702i | ||||
\(789\) | 236014. | 0.379127 | ||||||||
\(790\) | 2.11735e6i | 3.39265i | ||||||||
\(791\) | −252066. | − | 252066.i | −0.402866 | − | 0.402866i | ||||
\(792\) | − | 89133.6i | − | 0.142099i | ||||||
\(793\) | −47190.6 | − | 70955.0i | −0.0750428 | − | 0.112833i | ||||
\(794\) | −703706. | −1.11622 | ||||||||
\(795\) | 425463. | − | 425463.i | 0.673175 | − | 0.673175i | ||||
\(796\) | −500805. | −0.790393 | ||||||||
\(797\) | − | 550495.i | − | 0.866636i | −0.901241 | − | 0.433318i | \(-0.857343\pi\) | ||
0.901241 | − | 0.433318i | \(-0.142657\pi\) | |||||||
\(798\) | −357682. | + | 357682.i | −0.561682 | + | 0.561682i | ||||
\(799\) | −5647.58 | + | 5647.58i | −0.00884644 | + | 0.00884644i | ||||
\(800\) | 719260. | + | 719260.i | 1.12384 | + | 1.12384i | ||||
\(801\) | 231077. | + | 231077.i | 0.360158 | + | 0.360158i | ||||
\(802\) | −1.47681e6 | −2.29602 | ||||||||
\(803\) | − | 429549.i | − | 0.666165i | ||||||
\(804\) | −470925. | − | 470925.i | −0.728517 | − | 0.728517i | ||||
\(805\) | 343967.i | 0.530793i | ||||||||
\(806\) | −81479.2 | + | 54190.0i | −0.125423 | + | 0.0834160i | ||||
\(807\) | 411565. | 0.631963 | ||||||||
\(808\) | 132817. | − | 132817.i | 0.203437 | − | 0.203437i | ||||
\(809\) | 705446. | 1.07787 | 0.538936 | − | 0.842347i | \(-0.318827\pi\) | ||||
0.538936 | + | 0.842347i | \(0.318827\pi\) | |||||||
\(810\) | − | 164618.i | − | 0.250904i | ||||||
\(811\) | 476089. | − | 476089.i | 0.723846 | − | 0.723846i | −0.245540 | − | 0.969386i | \(-0.578965\pi\) |
0.969386 | + | 0.245540i | \(0.0789654\pi\) | |||||||
\(812\) | 279757. | − | 279757.i | 0.424296 | − | 0.424296i | ||||
\(813\) | −84076.5 | − | 84076.5i | −0.127202 | − | 0.127202i | ||||
\(814\) | 922481. | + | 922481.i | 1.39222 | + | 1.39222i | ||||
\(815\) | 1.26435e6 | 1.90350 | ||||||||
\(816\) | 119653.i | 0.179699i | ||||||||
\(817\) | −1.31205e6 | − | 1.31205e6i | −1.96565 | − | 1.96565i | ||||
\(818\) | − | 799064.i | − | 1.19419i | ||||||
\(819\) | −21579.1 | + | 107282.i | −0.0321711 | + | 0.159940i | ||||
\(820\) | 899831. | 1.33824 | ||||||||
\(821\) | 162224. | − | 162224.i | 0.240675 | − | 0.240675i | −0.576455 | − | 0.817129i | \(-0.695564\pi\) |
0.817129 | + | 0.576455i | \(0.195564\pi\) | |||||||
\(822\) | −930506. | −1.37713 | ||||||||
\(823\) | 1.34448e6i | 1.98497i | 0.122378 | + | 0.992484i | \(0.460948\pi\) | ||||
−0.122378 | + | 0.992484i | \(0.539052\pi\) | |||||||
\(824\) | −161259. | + | 161259.i | −0.237504 | + | 0.237504i | ||||
\(825\) | −265679. | + | 265679.i | −0.390346 | + | 0.390346i | ||||
\(826\) | −581314. | − | 581314.i | −0.852022 | − | 0.852022i | ||||
\(827\) | −542193. | − | 542193.i | −0.792762 | − | 0.792762i | 0.189180 | − | 0.981942i | \(-0.439417\pi\) |
−0.981942 | + | 0.189180i | \(0.939417\pi\) | |||||||
\(828\) | 225566. | 0.329013 | ||||||||
\(829\) | 485612.i | 0.706611i | 0.935508 | + | 0.353305i | \(0.114942\pi\) | ||||
−0.935508 | + | 0.353305i | \(0.885058\pi\) | |||||||
\(830\) | −1.40671e6 | − | 1.40671e6i | −2.04196 | − | 2.04196i | ||||
\(831\) | − | 14986.9i | − | 0.0217026i | ||||||
\(832\) | −880569. | + | 585648.i | −1.27209 | + | 0.846038i | ||||
\(833\) | 304253. | 0.438474 | ||||||||
\(834\) | 283081. | − | 283081.i | 0.406985 | − | 0.406985i | ||||
\(835\) | 905114. | 1.29817 | ||||||||
\(836\) | − | 1.40060e6i | − | 2.00401i | ||||||
\(837\) | −9382.13 | + | 9382.13i | −0.0133922 | + | 0.0133922i | ||||
\(838\) | 87135.4 | − | 87135.4i | 0.124081 | − | 0.124081i | ||||
\(839\) | 702797. | + | 702797.i | 0.998404 | + | 0.998404i | 0.999999 | − | 0.00159522i | \(-0.000507774\pi\) |
−0.00159522 | + | 0.999999i | \(0.500508\pi\) | |||||||
\(840\) | 109113. | + | 109113.i | 0.154639 | + | 0.154639i | ||||
\(841\) | −117625. | −0.166305 | ||||||||
\(842\) | 1.48239e6i | 2.09092i | ||||||||
\(843\) | −536403. | − | 536403.i | −0.754807 | − | 0.754807i | ||||
\(844\) | − | 215815.i | − | 0.302969i | ||||||
\(845\) | −398945. | − | 974957.i | −0.558727 | − | 1.36544i | ||||
\(846\) | −7923.10 | −0.0110702 | ||||||||
\(847\) | −84320.5 | + | 84320.5i | −0.117535 | + | 0.117535i | ||||
\(848\) | −433853. | −0.603324 | ||||||||
\(849\) | 408322.i | 0.566484i | ||||||||
\(850\) | −530494. | + | 530494.i | −0.734248 | + | 0.734248i | ||||
\(851\) | −595874. | + | 595874.i | −0.822801 | + | 0.822801i | ||||
\(852\) | 337784. | + | 337784.i | 0.465329 | + | 0.465329i | ||||
\(853\) | 528758. | + | 528758.i | 0.726706 | + | 0.726706i | 0.969962 | − | 0.243256i | \(-0.0782154\pi\) |
−0.243256 | + | 0.969962i | \(0.578215\pi\) | |||||||
\(854\) | 74034.9 | 0.101513 | ||||||||
\(855\) | − | 660259.i | − | 0.903196i | ||||||
\(856\) | −200893. | − | 200893.i | −0.274169 | − | 0.274169i | ||||
\(857\) | 427769.i | 0.582435i | 0.956657 | + | 0.291217i | \(0.0940603\pi\) | ||||
−0.956657 | + | 0.291217i | \(0.905940\pi\) | |||||||
\(858\) | −292761. | − | 440191.i | −0.397685 | − | 0.597952i | ||||
\(859\) | −110526. | −0.149788 | −0.0748941 | − | 0.997191i | \(-0.523862\pi\) | ||||
−0.0748941 | + | 0.997191i | \(0.523862\pi\) | |||||||
\(860\) | −1.56807e6 | + | 1.56807e6i | −2.12016 | + | 2.12016i | ||||
\(861\) | −141512. | −0.190891 | ||||||||
\(862\) | 1.10437e6i | 1.48627i | ||||||||
\(863\) | 115225. | − | 115225.i | 0.154713 | − | 0.154713i | −0.625506 | − | 0.780219i | \(-0.715108\pi\) |
0.780219 | + | 0.625506i | \(0.215108\pi\) | |||||||
\(864\) | −137222. | + | 137222.i | −0.183822 | + | 0.183822i | ||||
\(865\) | −72510.9 | − | 72510.9i | −0.0969106 | − | 0.0969106i | ||||
\(866\) | −298528. | − | 298528.i | −0.398060 | − | 0.398060i | ||||
\(867\) | 289705. | 0.385405 | ||||||||
\(868\) | − | 48726.7i | − | 0.0646737i | ||||||
\(869\) | 651945. | + | 651945.i | 0.863319 | + | 0.863319i | ||||
\(870\) | 901014.i | 1.19040i | ||||||||
\(871\) | −988440. | − | 198819.i | −1.30291 | − | 0.262073i | ||||
\(872\) | −573457. | −0.754168 | ||||||||
\(873\) | 77820.9 | − | 77820.9i | 0.102110 | − | 0.102110i | ||||
\(874\) | 1.57850e6 | 2.06643 | ||||||||
\(875\) | − | 97628.6i | − | 0.127515i | ||||||
\(876\) | 344831. | − | 344831.i | 0.449363 | − | 0.449363i | ||||
\(877\) | 352595. | − | 352595.i | 0.458435 | − | 0.458435i | −0.439707 | − | 0.898141i | \(-0.644918\pi\) |
0.898141 | + | 0.439707i | \(0.144918\pi\) | |||||||
\(878\) | 490917. | + | 490917.i | 0.636823 | + | 0.636823i | ||||
\(879\) | −28529.2 | − | 28529.2i | −0.0369243 | − | 0.0369243i | ||||
\(880\) | 501174. | 0.647177 | ||||||||
\(881\) | 776892.i | 1.00094i | 0.865753 | + | 0.500471i | \(0.166840\pi\) | ||||
−0.865753 | + | 0.500471i | \(0.833160\pi\) | |||||||
\(882\) | 213421. | + | 213421.i | 0.274347 | + | 0.274347i | ||||
\(883\) | 990585.i | 1.27049i | 0.772312 | + | 0.635244i | \(0.219100\pi\) | ||||
−0.772312 | + | 0.635244i | \(0.780900\pi\) | |||||||
\(884\) | −335045. | − | 503768.i | −0.428745 | − | 0.644653i | ||||
\(885\) | 1.07307e6 | 1.37007 | ||||||||
\(886\) | −399445. | + | 399445.i | −0.508849 | + | 0.508849i | ||||
\(887\) | 951592. | 1.20949 | 0.604747 | − | 0.796418i | \(-0.293274\pi\) | ||||
0.604747 | + | 0.796418i | \(0.293274\pi\) | |||||||
\(888\) | 378046.i | 0.479423i | ||||||||
\(889\) | 186462. | − | 186462.i | 0.235932 | − | 0.235932i | ||||
\(890\) | 1.93261e6 | − | 1.93261e6i | 2.43985 | − | 2.43985i | ||||
\(891\) | −50686.9 | − | 50686.9i | −0.0638470 | − | 0.0638470i | ||||
\(892\) | −535912. | − | 535912.i | −0.673540 | − | 0.673540i | ||||
\(893\) | −31778.4 | −0.0398500 | ||||||||
\(894\) | − | 59262.0i | − | 0.0741483i | ||||||
\(895\) | 77520.3 | + | 77520.3i | 0.0967764 | + | 0.0967764i | ||||
\(896\) | − | 388030.i | − | 0.483336i | ||||||
\(897\) | 284340. | − | 189108.i | 0.353389 | − | 0.235031i | ||||
\(898\) | 151887. | 0.188352 | ||||||||
\(899\) | 51351.8 | − | 51351.8i | 0.0635384 | − | 0.0635384i | ||||
\(900\) | −426560. | −0.526617 | ||||||||
\(901\) | − | 523158.i | − | 0.644442i | ||||||
\(902\) | 483406. | − | 483406.i | 0.594154 | − | 0.594154i | ||||
\(903\) | 246603. | − | 246603.i | 0.302428 | − | 0.302428i | ||||
\(904\) | 352875. | + | 352875.i | 0.431802 | + | 0.431802i | ||||
\(905\) | −1.14842e6 | − | 1.14842e6i | −1.40218 | − | 1.40218i | ||||
\(906\) | 270080. | 0.329030 | ||||||||
\(907\) | − | 122762.i | − | 0.149228i | −0.997212 | − | 0.0746141i | \(-0.976227\pi\) | ||
0.997212 | − | 0.0746141i | \(-0.0237725\pi\) | |||||||
\(908\) | −334650. | − | 334650.i | −0.405900 | − | 0.405900i | ||||
\(909\) | − | 151055.i | − | 0.182814i | ||||||
\(910\) | 897246. | + | 180476.i | 1.08350 | + | 0.217940i | ||||
\(911\) | 93939.2 | 0.113191 | 0.0565953 | − | 0.998397i | \(-0.481976\pi\) | ||||
0.0565953 | + | 0.998397i | \(0.481976\pi\) | |||||||
\(912\) | −336639. | + | 336639.i | −0.404739 | + | 0.404739i | ||||
\(913\) | −866266. | −1.03923 | ||||||||
\(914\) | 906796.i | 1.08547i | ||||||||
\(915\) | −68332.0 | + | 68332.0i | −0.0816172 | + | 0.0816172i | ||||
\(916\) | −535604. | + | 535604.i | −0.638341 | + | 0.638341i | ||||
\(917\) | −237805. | − | 237805.i | −0.282802 | − | 0.282802i | ||||
\(918\) | −101209. | − | 101209.i | −0.120097 | − | 0.120097i | ||||
\(919\) | 217922. | 0.258030 | 0.129015 | − | 0.991643i | \(-0.458818\pi\) | ||||
0.129015 | + | 0.991643i | \(0.458818\pi\) | |||||||
\(920\) | − | 481531.i | − | 0.568917i | ||||||
\(921\) | 190400. | + | 190400.i | 0.224465 | + | 0.224465i | ||||
\(922\) | − | 107215.i | − | 0.126123i | ||||||
\(923\) | 708986. | + | 142609.i | 0.832212 | + | 0.167395i | ||||
\(924\) | 263246. | 0.308331 | ||||||||
\(925\) | 1.12684e6 | − | 1.12684e6i | 1.31697 | − | 1.31697i | ||||
\(926\) | −1.35346e6 | −1.57842 | ||||||||
\(927\) | 183404.i | 0.213427i | ||||||||
\(928\) | 751065. | − | 751065.i | 0.872131 | − | 0.872131i | ||||
\(929\) | −489424. | + | 489424.i | −0.567092 | + | 0.567092i | −0.931313 | − | 0.364221i | \(-0.881335\pi\) |
0.364221 | + | 0.931313i | \(0.381335\pi\) | |||||||
\(930\) | 78467.2 | + | 78467.2i | 0.0907240 | + | 0.0907240i | ||||
\(931\) | 856000. | + | 856000.i | 0.987584 | + | 0.987584i | ||||
\(932\) | 481972. | 0.554868 | ||||||||
\(933\) | − | 296204.i | − | 0.340274i | ||||||
\(934\) | −16797.4 | − | 16797.4i | −0.0192552 | − | 0.0192552i | ||||
\(935\) | 604337.i | 0.691283i | ||||||||
\(936\) | 30209.3 | − | 150187.i | 0.0344818 | − | 0.171428i | ||||
\(937\) | 74994.8 | 0.0854185 | 0.0427093 | − | 0.999088i | \(-0.486401\pi\) | ||||
0.0427093 | + | 0.999088i | \(0.486401\pi\) | |||||||
\(938\) | 619397. | − | 619397.i | 0.703985 | − | 0.703985i | ||||
\(939\) | −877688. | −0.995426 | ||||||||
\(940\) | 37979.4i | 0.0429826i | ||||||||
\(941\) | −746527. | + | 746527.i | −0.843075 | + | 0.843075i | −0.989258 | − | 0.146183i | \(-0.953301\pi\) |
0.146183 | + | 0.989258i | \(0.453301\pi\) | |||||||
\(942\) | 545115. | − | 545115.i | 0.614308 | − | 0.614308i | ||||
\(943\) | 312255. | + | 312255.i | 0.351144 | + | 0.351144i | ||||
\(944\) | −547115. | − | 547115.i | −0.613953 | − | 0.613953i | ||||
\(945\) | 124097. | 0.138963 | ||||||||
\(946\) | 1.68480e6i | 1.88263i | ||||||||
\(947\) | −392710. | − | 392710.i | −0.437897 | − | 0.437897i | 0.453407 | − | 0.891304i | \(-0.350208\pi\) |
−0.891304 | + | 0.453407i | \(0.850208\pi\) | |||||||
\(948\) | 1.04673e6i | 1.16471i | ||||||||
\(949\) | 145584. | − | 723776.i | 0.161652 | − | 0.803659i | ||||
\(950\) | −2.98504e6 | −3.30752 | ||||||||
\(951\) | −299224. | + | 299224.i | −0.330854 | + | 0.330854i | ||||
\(952\) | 134168. | 0.148039 | ||||||||
\(953\) | − | 920738.i | − | 1.01380i | −0.862006 | − | 0.506898i | \(-0.830792\pi\) | ||
0.862006 | − | 0.506898i | \(-0.169208\pi\) | |||||||
\(954\) | 366975. | − | 366975.i | 0.403218 | − | 0.403218i | ||||
\(955\) | 96209.5 | − | 96209.5i | 0.105490 | − | 0.105490i | ||||
\(956\) | 1.43575e6 | + | 1.43575e6i | 1.57095 | + | 1.57095i | ||||
\(957\) | 277427. | + | 277427.i | 0.302918 | + | 0.302918i | ||||
\(958\) | −462756. | −0.504221 | ||||||||
\(959\) | − | 701460.i | − | 0.762721i | ||||||
\(960\) | 848018. | + | 848018.i | 0.920158 | + | 0.920158i | ||||
\(961\) | 914577.i | 0.990315i | ||||||||
\(962\) | 1.24170e6 | + | 1.86700e6i | 1.34173 | + | 2.01741i | ||||
\(963\) | −228481. | −0.246375 | ||||||||
\(964\) | −748214. | + | 748214.i | −0.805141 | + | 0.805141i | ||||
\(965\) | −1.00237e6 | −1.07640 | ||||||||
\(966\) | 296682.i | 0.317934i | ||||||||
\(967\) | −683545. | + | 683545.i | −0.730994 | + | 0.730994i | −0.970817 | − | 0.239823i | \(-0.922911\pi\) |
0.239823 | + | 0.970817i | \(0.422911\pi\) | |||||||
\(968\) | 118043. | − | 118043.i | 0.125977 | − | 0.125977i | ||||
\(969\) | −405934. | − | 405934.i | −0.432322 | − | 0.432322i | ||||
\(970\) | −650853. | − | 650853.i | −0.691734 | − | 0.691734i | ||||
\(971\) | −107226. | −0.113726 | −0.0568632 | − | 0.998382i | \(-0.518110\pi\) | ||||
−0.0568632 | + | 0.998382i | \(0.518110\pi\) | |||||||
\(972\) | − | 81380.1i | − | 0.0861362i | ||||||
\(973\) | 213400. | + | 213400.i | 0.225407 | + | 0.225407i | ||||
\(974\) | − | 344080.i | − | 0.362695i | ||||||
\(975\) | −537705. | + | 357616.i | −0.565633 | + | 0.376190i | ||||
\(976\) | 69679.4 | 0.0731484 | ||||||||
\(977\) | −730243. | + | 730243.i | −0.765030 | + | 0.765030i | −0.977227 | − | 0.212197i | \(-0.931938\pi\) |
0.212197 | + | 0.977227i | \(0.431938\pi\) | |||||||
\(978\) | 1.09054e6 | 1.14015 | ||||||||
\(979\) | − | 1.19012e6i | − | 1.24173i | ||||||
\(980\) | 1.02303e6 | − | 1.02303e6i | 1.06522 | − | 1.06522i | ||||
\(981\) | −326103. | + | 326103.i | −0.338857 | + | 0.338857i | ||||
\(982\) | −792514. | − | 792514.i | −0.821833 | − | 0.821833i | ||||
\(983\) | 180212. | + | 180212.i | 0.186500 | + | 0.186500i | 0.794181 | − | 0.607681i | \(-0.207900\pi\) |
−0.607681 | + | 0.794181i | \(0.707900\pi\) | |||||||
\(984\) | 198107. | 0.204602 | ||||||||
\(985\) | − | 830241.i | − | 0.855720i | ||||||
\(986\) | 553953. | + | 553953.i | 0.569795 | + | 0.569795i | ||||
\(987\) | − | 5972.82i | − | 0.00613119i | ||||||
\(988\) | 474693. | − | 2.35996e6i | 0.486294 | − | 2.41763i | ||||
\(989\) | −1.08829e6 | −1.11263 | ||||||||
\(990\) | −423918. | + | 423918.i | −0.432525 | + | 0.432525i | ||||
\(991\) | −662719. | −0.674811 | −0.337405 | − | 0.941359i | \(-0.609549\pi\) | ||||
−0.337405 | + | 0.941359i | \(0.609549\pi\) | |||||||
\(992\) | − | 130817.i | − | 0.132936i | ||||||
\(993\) | −700376. | + | 700376.i | −0.710285 | + | 0.710285i | ||||
\(994\) | −444280. | + | 444280.i | −0.449659 | + | 0.449659i | ||||
\(995\) | 607959. | + | 607959.i | 0.614084 | + | 0.614084i | ||||
\(996\) | −695415. | − | 695415.i | −0.701012 | − | 0.701012i | ||||
\(997\) | 464482. | 0.467281 | 0.233641 | − | 0.972323i | \(-0.424936\pi\) | ||||
0.233641 | + | 0.972323i | \(0.424936\pi\) | |||||||
\(998\) | − | 496899.i | − | 0.498893i | ||||||
\(999\) | 214980. | + | 214980.i | 0.215411 | + | 0.215411i |
(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 | 39.5.g.a.31.2 | ✓ | 20 | |
3.2 | odd | 2 | 117.5.j.b.109.9 | 20 | |||
13.8 | odd | 4 | inner | 39.5.g.a.34.2 | yes | 20 | |
39.8 | even | 4 | 117.5.j.b.73.9 | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
39.5.g.a.31.2 | ✓ | 20 | 1.1 | even | 1 | trivial | |
39.5.g.a.34.2 | yes | 20 | 13.8 | odd | 4 | inner | |
117.5.j.b.73.9 | 20 | 39.8 | even | 4 | |||
117.5.j.b.109.9 | 20 | 3.2 | odd | 2 |