Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [684,3,Mod(353,684)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(684, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 1, 4]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("684.353");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 684 = 2^{2} \cdot 3^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 684.m (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(18.6376500822\) |
Analytic rank: | \(0\) |
Dimension: | \(80\) |
Relative dimension: | \(40\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 353.12 | ||
Character | \(\chi\) | \(=\) | 684.353 |
Dual form | 684.3.m.a.653.12 |
$q$-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 \(\left(\mathbb{Z}/684\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(343\) | \(533\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) | \(e\left(\frac{1}{6}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.70356 | − | 2.46939i | −0.567854 | − | 0.823129i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − | 9.28650i | − | 1.85730i | −0.370958 | − | 0.928650i | \(-0.620971\pi\) | ||
0.370958 | − | 0.928650i | \(-0.379029\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.28067 | + | 3.95023i | −0.325810 | + | 0.564319i | −0.981676 | − | 0.190558i | \(-0.938970\pi\) |
0.655866 | + | 0.754877i | \(0.272304\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −3.19575 | + | 8.41351i | −0.355083 | + | 0.934835i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.10584 | − | 0.638454i | −0.100531 | − | 0.0580413i | 0.448892 | − | 0.893586i | \(-0.351819\pi\) |
−0.549422 | + | 0.835545i | \(0.685152\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.30958 | + | 5.73235i | −0.254583 | + | 0.440950i | −0.964782 | − | 0.263050i | \(-0.915271\pi\) |
0.710199 | + | 0.704001i | \(0.248605\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −22.9320 | + | 15.8201i | −1.52880 | + | 1.05468i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −11.0966 | − | 6.40664i | −0.652743 | − | 0.376861i | 0.136764 | − | 0.990604i | \(-0.456330\pi\) |
−0.789506 | + | 0.613743i | \(0.789663\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −18.7585 | + | 3.01961i | −0.987290 | + | 0.158927i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 13.6399 | − | 1.09762i | 0.649520 | − | 0.0522674i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 16.3480 | + | 9.43853i | 0.710783 | + | 0.410371i | 0.811351 | − | 0.584559i | \(-0.198733\pi\) |
−0.100568 | + | 0.994930i | \(0.532066\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −61.2390 | −2.44956 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 26.2204 | − | 6.44140i | 0.971125 | − | 0.238570i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 7.10485i | − | 0.244995i | −0.992469 | − | 0.122497i | \(-0.960910\pi\) | ||
0.992469 | − | 0.122497i | \(-0.0390903\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 7.90302 | + | 13.6884i | 0.254936 | + | 0.441562i | 0.964878 | − | 0.262698i | \(-0.0846123\pi\) |
−0.709942 | + | 0.704260i | \(0.751279\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0.307269 | + | 3.81838i | 0.00931117 | + | 0.115709i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 36.6838 | + | 21.1794i | 1.04811 | + | 0.605126i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −16.9760 | −0.458810 | −0.229405 | − | 0.973331i | \(-0.573678\pi\) | ||||
−0.229405 | + | 0.973331i | \(0.573678\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 19.7935 | − | 1.59280i | 0.507525 | − | 0.0408410i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 17.6906i | − | 0.431477i | −0.976451 | − | 0.215739i | \(-0.930784\pi\) | ||
0.976451 | − | 0.215739i | \(-0.0692159\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 20.8849 | + | 36.1738i | 0.485696 | + | 0.841251i | 0.999865 | − | 0.0164385i | \(-0.00523277\pi\) |
−0.514169 | + | 0.857689i | \(0.671899\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 78.1321 | + | 29.6773i | 1.73627 | + | 0.659496i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 22.7792i | − | 0.484665i | −0.970193 | − | 0.242332i | \(-0.922088\pi\) | ||
0.970193 | − | 0.242332i | \(-0.0779124\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 14.0971 | + | 24.4169i | 0.287696 | + | 0.498304i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 3.08332 | + | 38.3160i | 0.0604572 | + | 0.751294i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 5.86723 | − | 3.38745i | 0.110702 | − | 0.0639141i | −0.443626 | − | 0.896212i | \(-0.646308\pi\) |
0.554329 | + | 0.832298i | \(0.312975\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −5.92901 | + | 10.2693i | −0.107800 | + | 0.186715i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 39.4129 | + | 41.1779i | 0.691454 | + | 0.722420i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 82.7526i | 1.40259i | 0.712873 | + | 0.701293i | \(0.247394\pi\) | ||||
−0.712873 | + | 0.701293i | \(0.752606\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 47.4838 | 0.778423 | 0.389211 | − | 0.921148i | \(-0.372748\pi\) | ||||
0.389211 | + | 0.921148i | \(0.372748\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −25.9469 | − | 31.8124i | −0.411855 | − | 0.504959i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 53.2335 | + | 30.7344i | 0.818977 | + | 0.472836i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 21.3601 | − | 36.9968i | 0.318807 | − | 0.552190i | −0.661432 | − | 0.750005i | \(-0.730051\pi\) |
0.980239 | + | 0.197815i | \(0.0633844\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −4.54247 | − | 56.4487i | −0.0658330 | − | 0.818097i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −21.4678 | − | 12.3945i | −0.302364 | − | 0.174570i | 0.341140 | − | 0.940012i | \(-0.389187\pi\) |
−0.643504 | + | 0.765442i | \(0.722520\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −39.6934 | + | 68.7509i | −0.543745 | + | 0.941793i | 0.454940 | + | 0.890522i | \(0.349661\pi\) |
−0.998685 | + | 0.0512713i | \(0.983673\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 104.325 | + | 151.223i | 1.39099 | + | 2.01631i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 5.04409 | − | 2.91221i | 0.0655076 | − | 0.0378209i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −54.2353 | − | 93.9382i | −0.686522 | − | 1.18909i | −0.972956 | − | 0.230991i | \(-0.925803\pi\) |
0.286434 | − | 0.958100i | \(-0.407530\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −60.5744 | − | 53.7749i | −0.747832 | − | 0.663888i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 34.7029 | + | 20.0357i | 0.418107 | + | 0.241394i | 0.694267 | − | 0.719717i | \(-0.255729\pi\) |
−0.276160 | + | 0.961112i | \(0.589062\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −59.4952 | + | 103.049i | −0.699944 | + | 1.21234i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −17.5446 | + | 12.1036i | −0.201662 | + | 0.139121i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −49.2445 | + | 28.4313i | −0.553309 | + | 0.319453i | −0.750455 | − | 0.660921i | \(-0.770166\pi\) |
0.197147 | + | 0.980374i | \(0.436832\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −15.0961 | − | 26.1472i | −0.165891 | − | 0.287332i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 20.3387 | − | 42.8347i | 0.218696 | − | 0.460588i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 28.0416 | + | 174.201i | 0.295175 | + | 1.83369i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −86.8612 | − | 150.448i | −0.895477 | − | 1.55101i | −0.833214 | − | 0.552951i | \(-0.813502\pi\) |
−0.0622629 | − | 0.998060i | \(-0.519832\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 8.90562 | − | 7.26362i | 0.0899557 | − | 0.0733699i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 88.8592i | 0.879794i | 0.898048 | + | 0.439897i | \(0.144985\pi\) | ||||
−0.898048 | + | 0.439897i | \(0.855015\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 43.5924 | + | 75.5043i | 0.423227 | + | 0.733051i | 0.996253 | − | 0.0864862i | \(-0.0275639\pi\) |
−0.573026 | + | 0.819537i | \(0.694231\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −10.1930 | − | 126.667i | −0.0970763 | − | 1.20635i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 85.1392i | 0.795693i | 0.917452 | + | 0.397847i | \(0.130242\pi\) | ||||
−0.917452 | + | 0.397847i | \(0.869758\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −103.317 | + | 178.950i | −0.947861 | + | 1.64174i | −0.197941 | + | 0.980214i | \(0.563426\pi\) |
−0.749919 | + | 0.661529i | \(0.769908\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 28.9196 | + | 41.9203i | 0.260537 | + | 0.377660i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −180.905 | + | 104.445i | −1.60093 | + | 0.924296i | −0.609625 | + | 0.792690i | \(0.708680\pi\) |
−0.991302 | + | 0.131605i | \(0.957987\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 87.6509 | − | 151.816i | 0.762181 | − | 1.32014i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −37.6526 | − | 46.1643i | −0.321817 | − | 0.394567i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 50.6154 | − | 29.2228i | 0.425340 | − | 0.245570i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −59.6848 | − | 103.377i | −0.493262 | − | 0.854356i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −43.6849 | + | 30.1370i | −0.355162 | + | 0.245016i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 336.534i | 2.69227i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 56.4818 | + | 97.8294i | 0.444739 | + | 0.770310i | 0.998034 | − | 0.0626751i | \(-0.0199632\pi\) |
−0.553295 | + | 0.832985i | \(0.686630\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 53.7483 | − | 113.197i | 0.416653 | − | 0.877499i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 8.51243i | 0.0649803i | 0.999472 | + | 0.0324902i | \(0.0103438\pi\) | ||||
−0.999472 | + | 0.0324902i | \(0.989656\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 30.8538 | − | 80.9873i | 0.231983 | − | 0.608927i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −59.8181 | − | 243.495i | −0.443097 | − | 1.80367i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 214.194i | − | 1.56346i | −0.623618 | − | 0.781729i | \(-0.714338\pi\) | ||
0.623618 | − | 0.781729i | \(-0.285662\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 25.7715 | − | 44.6376i | 0.185407 | − | 0.321134i | −0.758307 | − | 0.651898i | \(-0.773973\pi\) |
0.943713 | + | 0.330764i | \(0.107306\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −56.2508 | + | 38.8059i | −0.398942 | + | 0.275219i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 7.31969 | − | 4.22603i | 0.0511867 | − | 0.0295526i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −65.9792 | −0.455029 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 36.2795 | − | 76.4069i | 0.246799 | − | 0.519775i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 143.809i | − | 0.965164i | −0.875851 | − | 0.482582i | \(-0.839699\pi\) | ||
0.875851 | − | 0.482582i | \(-0.160301\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 109.749 | − | 190.090i | 0.726813 | − | 1.25888i | −0.231411 | − | 0.972856i | \(-0.574334\pi\) |
0.958223 | − | 0.286021i | \(-0.0923326\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 89.3644 | − | 72.8876i | 0.584081 | − | 0.476389i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 127.118 | − | 73.3913i | 0.820113 | − | 0.473493i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −31.4750 | −0.200477 | −0.100239 | − | 0.994963i | \(-0.531961\pi\) | ||||
−0.100239 | + | 0.994963i | \(0.531961\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −18.3601 | − | 8.71774i | −0.115472 | − | 0.0548286i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −74.5688 | + | 43.0523i | −0.463160 | + | 0.267406i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −27.3667 | −0.167894 | −0.0839469 | − | 0.996470i | \(-0.526753\pi\) | ||||
−0.0839469 | + | 0.996470i | \(0.526753\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 35.4594 | − | 2.85345i | 0.214906 | − | 0.0172936i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 200.623 | + | 115.830i | 1.20134 | + | 0.693592i | 0.960852 | − | 0.277061i | \(-0.0893603\pi\) |
0.240485 | + | 0.970653i | \(0.422694\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 62.5934 | + | 108.415i | 0.370375 | + | 0.641509i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 34.5420 | − | 167.475i | 0.202000 | − | 0.979386i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −103.634 | + | 59.8331i | −0.599041 | + | 0.345856i | −0.768664 | − | 0.639653i | \(-0.779078\pi\) |
0.169623 | + | 0.985509i | \(0.445745\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 139.666 | − | 241.908i | 0.798091 | − | 1.38233i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 204.348 | − | 140.974i | 1.15451 | − | 0.796465i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 182.887i | 1.02171i | 0.859666 | + | 0.510856i | \(0.170672\pi\) | ||||
−0.859666 | + | 0.510856i | \(0.829328\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 77.9550 | + | 135.022i | 0.430691 | + | 0.745978i | 0.996933 | − | 0.0782606i | \(-0.0249366\pi\) |
−0.566242 | + | 0.824239i | \(0.691603\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −80.8916 | − | 117.256i | −0.442031 | − | 0.640743i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 157.647i | 0.852148i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 8.18069 | + | 14.1694i | 0.0437470 | + | 0.0757721i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −34.3550 | + | 118.267i | −0.181772 | + | 0.625753i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −292.923 | − | 169.119i | −1.53363 | − | 0.885440i | −0.999190 | − | 0.0402304i | \(-0.987191\pi\) |
−0.534436 | − | 0.845209i | \(-0.679476\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −213.007 | −1.10366 | −0.551832 | − | 0.833955i | \(-0.686071\pi\) | ||||
−0.551832 | + | 0.833955i | \(0.686071\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −14.7915 | − | 183.812i | −0.0758539 | − | 0.942626i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 7.74954i | 0.0393378i | 0.999807 | + | 0.0196689i | \(0.00626120\pi\) | ||||
−0.999807 | + | 0.0196689i | \(0.993739\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −149.979 | − | 259.771i | −0.753662 | − | 1.30538i | −0.946037 | − | 0.324059i | \(-0.894952\pi\) |
0.192375 | − | 0.981321i | \(-0.438381\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −127.748 | + | 10.2800i | −0.635560 | + | 0.0511441i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 28.0658 | + | 16.2038i | 0.138255 | + | 0.0798217i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −164.283 | −0.801383 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −131.655 | + | 107.381i | −0.636016 | + | 0.518749i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 22.6717 | + | 8.63726i | 0.108477 | + | 0.0413266i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −368.255 | −1.74528 | −0.872641 | − | 0.488362i | \(-0.837595\pi\) | ||||
−0.872641 | + | 0.488362i | \(0.837595\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 5.96508 | + | 74.1272i | 0.0280050 | + | 0.348015i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 335.928 | − | 193.948i | 1.56245 | − | 0.902083i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −72.0966 | −0.332243 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 237.393 | − | 19.1032i | 1.08399 | − | 0.0872292i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 73.4502 | − | 42.4065i | 0.332354 | − | 0.191885i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 76.6100 | + | 132.692i | 0.343543 | + | 0.595033i | 0.985088 | − | 0.172052i | \(-0.0550397\pi\) |
−0.641545 | + | 0.767085i | \(0.721706\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 195.705 | − | 515.235i | 0.869798 | − | 2.28993i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 119.451 | + | 68.9649i | 0.526214 | + | 0.303810i | 0.739474 | − | 0.673186i | \(-0.235075\pi\) |
−0.213259 | + | 0.976996i | \(0.568408\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −84.2944 | − | 146.002i | −0.368098 | − | 0.637564i | 0.621170 | − | 0.783676i | \(-0.286657\pi\) |
−0.989268 | + | 0.146112i | \(0.953324\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −15.7843 | − | 7.49468i | −0.0683302 | − | 0.0324445i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −257.617 | − | 148.735i | −1.10565 | − | 0.638348i | −0.167952 | − | 0.985795i | \(-0.553715\pi\) |
−0.937700 | + | 0.347447i | \(0.887049\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −211.539 | −0.900167 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −139.577 | + | 293.957i | −0.588931 | + | 1.24033i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −277.929 | + | 160.462i | −1.16288 | + | 0.671391i | −0.951993 | − | 0.306119i | \(-0.900969\pi\) |
−0.210889 | + | 0.977510i | \(0.567636\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −393.874 | −1.63433 | −0.817167 | − | 0.576402i | \(-0.804456\pi\) | ||||
−0.817167 | + | 0.576402i | \(0.804456\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −29.5990 | + | 241.191i | −0.121806 | + | 0.992554i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 226.747 | − | 130.913i | 0.925500 | − | 0.534338i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 44.7732 | − | 117.524i | 0.181268 | − | 0.475806i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −9.64259 | − | 119.827i | −0.0387252 | − | 0.481233i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 320.034 | − | 184.772i | 1.27504 | − | 0.736142i | 0.299104 | − | 0.954220i | \(-0.403312\pi\) |
0.975931 | + | 0.218078i | \(0.0699788\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −12.0521 | − | 20.8749i | −0.0476369 | − | 0.0825096i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 355.821 | − | 28.6332i | 1.39538 | − | 0.112287i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 159.326 | + | 91.9868i | 0.619945 | + | 0.357925i | 0.776847 | − | 0.629689i | \(-0.216818\pi\) |
−0.156903 | + | 0.987614i | \(0.550151\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 38.7166 | − | 67.0591i | 0.149485 | − | 0.258915i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 59.7767 | + | 22.7053i | 0.229030 | + | 0.0869935i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −146.456 | + | 84.5564i | −0.556867 | + | 0.321507i | −0.751887 | − | 0.659292i | \(-0.770856\pi\) |
0.195020 | + | 0.980799i | \(0.437523\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −31.4575 | − | 54.4860i | −0.118708 | − | 0.205608i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 154.099 | + | 73.1692i | 0.577150 | + | 0.274042i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 0.505277 | + | 0.291722i | 0.00187835 | + | 0.00108447i | 0.500939 | − | 0.865483i | \(-0.332988\pi\) |
−0.499061 | + | 0.866567i | \(0.666321\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −173.903 | + | 301.208i | −0.641707 | + | 1.11147i | 0.343344 | + | 0.939210i | \(0.388440\pi\) |
−0.985052 | + | 0.172260i | \(0.944893\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −38.8504 | + | 81.8215i | −0.142309 | + | 0.299712i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 67.7203 | + | 39.0983i | 0.246256 | + | 0.142176i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −115.851 | + | 200.660i | −0.418235 | + | 0.724404i | −0.995762 | − | 0.0919678i | \(-0.970684\pi\) |
0.577527 | + | 0.816371i | \(0.304018\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −140.424 | + | 22.7473i | −0.503311 | + | 0.0815317i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 501.455i | − | 1.78454i | −0.451505 | − | 0.892268i | \(-0.649113\pi\) | ||
0.451505 | − | 0.892268i | \(-0.350887\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −46.8874 | −0.165680 | −0.0828399 | − | 0.996563i | \(-0.526399\pi\) | ||||
−0.0828399 | + | 0.996563i | \(0.526399\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 382.399 | − | 366.008i | 1.34175 | − | 1.28424i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 69.8819 | + | 40.3463i | 0.243491 | + | 0.140580i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −62.4099 | − | 108.097i | −0.215951 | − | 0.374039i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −223.541 | + | 470.792i | −0.768182 | + | 1.61784i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −67.5883 | + | 39.0221i | −0.230677 | + | 0.133181i | −0.610884 | − | 0.791720i | \(-0.709186\pi\) |
0.380207 | + | 0.924901i | \(0.375853\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 768.482 | 2.60502 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −33.1080 | − | 9.61739i | −0.111475 | − | 0.0323818i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −108.210 | + | 62.4750i | −0.361906 | + | 0.208947i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −190.526 | −0.632978 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 219.428 | − | 151.377i | 0.724184 | − | 0.499595i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 440.958i | − | 1.44576i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −13.1550 | + | 22.7852i | −0.0428503 | + | 0.0742188i | −0.886655 | − | 0.462431i | \(-0.846977\pi\) |
0.843805 | + | 0.536650i | \(0.180311\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 112.187 | − | 236.273i | 0.363064 | − | 0.764637i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −339.125 | + | 195.794i | −1.09043 | + | 0.629562i | −0.933692 | − | 0.358078i | \(-0.883432\pi\) |
−0.156741 | + | 0.987640i | \(0.550099\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −93.3871 | −0.298361 | −0.149181 | − | 0.988810i | \(-0.547664\pi\) | ||||
−0.149181 | + | 0.988810i | \(0.547664\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −295.426 | + | 240.956i | −0.937859 | + | 0.764939i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 57.0992i | 0.180124i | 0.995936 | + | 0.0900618i | \(0.0287064\pi\) | ||||
−0.995936 | + | 0.0900618i | \(0.971294\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −4.53612 | + | 7.85679i | −0.0142198 | + | 0.0246294i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 210.242 | − | 145.040i | 0.654958 | − | 0.451838i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 227.502 | + | 86.6715i | 0.704340 | + | 0.268333i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 202.675 | − | 351.044i | 0.623616 | − | 1.08013i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 617.904 | − | 49.7232i | 1.88961 | − | 0.152059i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 89.9833 | + | 51.9519i | 0.273505 | + | 0.157908i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −5.97582 | + | 10.3504i | −0.0180538 | + | 0.0312702i | −0.874911 | − | 0.484283i | \(-0.839080\pi\) |
0.856857 | + | 0.515554i | \(0.172414\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 54.2510 | − | 142.828i | 0.162916 | − | 0.428912i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −343.570 | − | 198.360i | −1.02558 | − | 0.592121i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −100.450 | −0.298071 | −0.149035 | − | 0.988832i | \(-0.547617\pi\) | ||||
−0.149035 | + | 0.988832i | \(0.547617\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 566.099 | + | 268.795i | 1.66991 | + | 0.792905i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 20.1829i | − | 0.0591873i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −352.109 | −1.02656 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −524.211 | + | 42.1837i | −1.51945 | + | 0.122272i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 151.374i | 0.436236i | 0.975922 | + | 0.218118i | \(0.0699917\pi\) | ||||
−0.975922 | + | 0.218118i | \(0.930008\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −219.737 | + | 380.596i | −0.629619 | + | 1.09053i | 0.358009 | + | 0.933718i | \(0.383456\pi\) |
−0.987628 | + | 0.156814i | \(0.949878\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −49.8539 | + | 171.623i | −0.142034 | + | 0.488954i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 524.353 | + | 302.736i | 1.48542 | + | 0.857608i | 0.999862 | − | 0.0165964i | \(-0.00528304\pi\) |
0.485558 | + | 0.874204i | \(0.338616\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −115.101 | + | 199.361i | −0.324229 | + | 0.561580i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −158.389 | − | 75.2062i | −0.443667 | − | 0.210662i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −84.9553 | − | 49.0490i | −0.236644 | − | 0.136627i | 0.376989 | − | 0.926218i | \(-0.376959\pi\) |
−0.613633 | + | 0.789591i | \(0.710293\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 342.764 | − | 113.287i | 0.949484 | − | 0.313814i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −153.601 | + | 323.494i | −0.423144 | + | 0.891168i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 638.455 | + | 368.612i | 1.74919 | + | 1.00990i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −324.259 | −0.883539 | −0.441769 | − | 0.897129i | \(-0.645649\pi\) | ||||
−0.441769 | + | 0.897129i | \(0.645649\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 148.840 | + | 56.5346i | 0.403360 | + | 0.153210i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 30.9026i | 0.0832954i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −79.8812 | − | 138.358i | −0.214159 | − | 0.370934i | 0.738853 | − | 0.673866i | \(-0.235368\pi\) |
−0.953012 | + | 0.302933i | \(0.902034\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 831.032 | − | 573.306i | 2.21609 | − | 1.52882i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 40.7275 | + | 23.5140i | 0.108030 | + | 0.0623714i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 366.244 | 0.966343 | 0.483171 | − | 0.875526i | \(-0.339485\pi\) | ||||
0.483171 | + | 0.875526i | \(0.339485\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 145.358 | − | 306.134i | 0.381518 | − | 0.803501i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 124.052i | 0.323895i | 0.986799 | + | 0.161948i | \(0.0517775\pi\) | ||||
−0.986799 | + | 0.161948i | \(0.948222\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −27.0442 | − | 46.8419i | −0.0702446 | − | 0.121667i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −371.092 | + | 60.1134i | −0.958893 | + | 0.155332i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − | 415.200i | − | 1.06735i | −0.845689 | − | 0.533676i | \(-0.820810\pi\) | ||
0.845689 | − | 0.533676i | \(-0.179190\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −120.938 | − | 209.472i | −0.309306 | − | 0.535733i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 21.0205 | − | 14.5014i | 0.0534872 | − | 0.0368994i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −872.357 | + | 503.656i | −2.20850 | + | 1.27508i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 247.236 | − | 428.225i | 0.622760 | − | 1.07865i | −0.366209 | − | 0.930532i | \(-0.619345\pi\) |
0.988969 | − | 0.148120i | \(-0.0473220\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −252.550 | + | 61.7769i | −0.632958 | + | 0.154829i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 299.577i | − | 0.747075i | −0.927615 | − | 0.373538i | \(-0.878145\pi\) | ||
0.927615 | − | 0.373538i | \(-0.121855\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −104.623 | −0.259609 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −499.381 | + | 562.524i | −1.23304 | + | 1.38895i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 18.7726 | + | 10.8384i | 0.0461244 | + | 0.0266299i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 80.2674 | − | 139.027i | 0.196253 | − | 0.339920i | −0.751058 | − | 0.660237i | \(-0.770456\pi\) |
0.947310 | + | 0.320317i | \(0.103789\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −528.928 | + | 364.893i | −1.28693 | + | 0.887817i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −326.892 | − | 188.731i | −0.791506 | − | 0.456976i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 186.062 | − | 322.268i | 0.448342 | − | 0.776550i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −154.131 | + | 12.4030i | −0.369619 | + | 0.0297435i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 442.295 | − | 255.359i | 1.05560 | − | 0.609449i | 0.131386 | − | 0.991331i | \(-0.458057\pi\) |
0.924211 | + | 0.381882i | \(0.124724\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −176.079 | − | 304.978i | −0.418241 | − | 0.724414i | 0.577522 | − | 0.816375i | \(-0.304020\pi\) |
−0.995763 | + | 0.0919610i | \(0.970686\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 191.653 | + | 72.7967i | 0.453081 | + | 0.172096i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 679.547 | + | 392.336i | 1.59893 | + | 0.923144i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −108.295 | + | 187.572i | −0.253618 | + | 0.439279i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −22.9052 | − | 10.8759i | −0.0533922 | − | 0.0253516i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −561.436 | + | 324.145i | −1.30264 | + | 0.752077i | −0.980855 | − | 0.194738i | \(-0.937614\pi\) |
−0.321780 | + | 0.946815i | \(0.604281\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 270.752 | + | 468.956i | 0.625293 | + | 1.08304i | 0.988484 | + | 0.151325i | \(0.0483539\pi\) |
−0.363191 | + | 0.931715i | \(0.618313\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 112.400 | + | 162.928i | 0.258390 | + | 0.374547i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −335.165 | − | 127.688i | −0.766968 | − | 0.292192i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 230.430 | + | 399.117i | 0.524898 | + | 0.909151i | 0.999580 | + | 0.0289930i | \(0.00923004\pi\) |
−0.474681 | + | 0.880158i | \(0.657437\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −250.483 | + | 40.5759i | −0.567988 | + | 0.0920088i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 798.745i | − | 1.80304i | −0.432740 | − | 0.901519i | \(-0.642453\pi\) | ||
0.432740 | − | 0.901519i | \(-0.357547\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 264.027 | + | 457.309i | 0.593320 | + | 1.02766i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −355.121 | + | 244.988i | −0.794455 | + | 0.548072i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 751.768i | 1.67432i | 0.546962 | + | 0.837158i | \(0.315784\pi\) | ||||
−0.546962 | + | 0.837158i | \(0.684216\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −11.2946 | + | 19.5629i | −0.0250435 | + | 0.0433766i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −656.371 | + | 52.8187i | −1.44894 | + | 0.116598i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −242.816 | + | 140.190i | −0.533661 | + | 0.308109i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −341.536 | + | 591.557i | −0.747343 | + | 1.29444i | 0.201749 | + | 0.979437i | \(0.435338\pi\) |
−0.949092 | + | 0.314999i | \(0.897996\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −332.225 | − | 96.5067i | −0.723803 | − | 0.210254i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −495.618 | + | 286.145i | −1.07509 | + | 0.620706i | −0.929569 | − | 0.368649i | \(-0.879820\pi\) |
−0.145525 | + | 0.989355i | \(0.546487\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 221.398 | + | 383.473i | 0.478182 | + | 0.828236i | 0.999687 | − | 0.0250123i | \(-0.00796250\pi\) |
−0.521505 | + | 0.853248i | \(0.674629\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −397.784 | − | 188.876i | −0.855450 | − | 0.406184i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 246.829i | 0.528542i | 0.964449 | + | 0.264271i | \(0.0851313\pi\) | ||||
−0.964449 | + | 0.264271i | \(0.914869\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 97.4306 | + | 168.755i | 0.207741 | + | 0.359818i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 53.6196 | + | 77.7239i | 0.113842 | + | 0.165019i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 53.3363i | − | 0.112762i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1148.75 | − | 184.918i | 2.41843 | − | 0.389301i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 9.75013 | + | 60.1895i | 0.0204405 | + | 0.126183i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 208.455i | 0.435188i | 0.976039 | + | 0.217594i | \(0.0698209\pi\) | ||||
−0.976039 | + | 0.217594i | \(0.930179\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 56.1833 | − | 97.3123i | 0.116805 | − | 0.202312i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 233.345 | + | 110.797i | 0.483117 | + | 0.229393i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −1397.14 | + | 806.637i | −2.88069 | + | 1.66317i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 467.236 | 0.959416 | 0.479708 | − | 0.877428i | \(-0.340743\pi\) | ||||
0.479708 | + | 0.877428i | \(0.340743\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 46.6208 | + | 67.5789i | 0.0953391 | + | 0.138198i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 263.317i | − | 0.536287i | −0.963379 | − | 0.268143i | \(-0.913590\pi\) | ||
0.963379 | − | 0.268143i | \(-0.0864101\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −45.5182 | + | 78.8398i | −0.0923290 | + | 0.159919i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −67.4536 | − | 82.7020i | −0.136270 | − | 0.167075i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 97.9220 | − | 56.5353i | 0.197026 | − | 0.113753i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −891.558 | −1.78669 | −0.893345 | − | 0.449372i | \(-0.851648\pi\) | ||||
−0.893345 | + | 0.449372i | \(0.851648\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −55.7454 | − | 692.740i | −0.111268 | − | 1.38271i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −383.876 | + | 221.631i | −0.763174 | + | 0.440619i | −0.830434 | − | 0.557117i | \(-0.811908\pi\) |
0.0672604 | + | 0.997735i | \(0.478574\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 825.191 | 1.63404 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 161.087 | − | 339.259i | 0.317725 | − | 0.669150i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 306.042 | + | 176.693i | 0.601261 | + | 0.347138i | 0.769538 | − | 0.638602i | \(-0.220487\pi\) |
−0.168276 | + | 0.985740i | \(0.553820\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −181.055 | − | 313.596i | −0.354315 | − | 0.613691i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −472.405 | + | 200.007i | −0.920867 | + | 0.389876i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 701.170 | − | 404.821i | 1.36150 | − | 0.786060i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −14.5435 | + | 25.1901i | −0.0281306 | + | 0.0487236i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 324.298 | + | 153.983i | 0.624852 | + | 0.296692i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 530.816i | − | 1.01884i | −0.860518 | − | 0.509420i | \(-0.829860\pi\) | ||
0.860518 | − | 0.509420i | \(-0.170140\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 518.783 | + | 898.559i | 0.991938 | + | 1.71809i | 0.605717 | + | 0.795680i | \(0.292887\pi\) |
0.386221 | + | 0.922406i | \(0.373780\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −835.295 | + | 67.2169i | −1.59104 | + | 0.128032i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 202.527i | − | 0.384302i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −86.3284 | − | 149.525i | −0.163192 | − | 0.282656i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −696.240 | − | 264.457i | −1.31119 | − | 0.498035i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 101.409 | + | 58.5483i | 0.190260 | + | 0.109847i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 790.645 | 1.47784 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 451.618 | − | 311.559i | 0.841001 | − | 0.580184i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − | 36.0014i | − | 0.0667930i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −427.224 | − | 739.974i | −0.789693 | − | 1.36779i | −0.926155 | − | 0.377143i | \(-0.876906\pi\) |
0.136462 | − | 0.990645i | \(-0.456427\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 200.621 | − | 422.520i | 0.369467 | − | 0.778121i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 1661.82 | + | 959.451i | 3.04921 | + | 1.76046i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −412.287 | −0.753724 | −0.376862 | − | 0.926269i | \(-0.622997\pi\) | ||||
−0.376862 | + | 0.926269i | \(0.622997\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −151.746 | + | 399.506i | −0.276405 | + | 0.727697i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 21.4539 | + | 133.276i | 0.0389363 | + | 0.241881i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 494.770 | 0.894703 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 389.292 | − | 268.562i | 0.701428 | − | 0.483896i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 863.794 | − | 498.712i | 1.55080 | − | 0.895353i | 0.552720 | − | 0.833367i | \(-0.313590\pi\) |
0.998077 | − | 0.0619859i | \(-0.0197434\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −276.481 | −0.494600 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 21.0534 | − | 44.3397i | 0.0375283 | − | 0.0790369i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −305.679 | + | 176.484i | −0.542947 | + | 0.313470i | −0.746272 | − | 0.665641i | \(-0.768158\pi\) |
0.203326 | + | 0.979111i | \(0.434825\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 969.932 | + | 1679.97i | 1.71669 | + | 2.97340i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 350.574 | − | 116.640i | 0.618296 | − | 0.205714i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 276.835 | + | 159.831i | 0.486529 | + | 0.280897i | 0.723133 | − | 0.690709i | \(-0.242701\pi\) |
−0.236605 | + | 0.971606i | \(0.576035\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 352.313 | + | 610.224i | 0.617010 | + | 1.06869i | 0.990028 | + | 0.140869i | \(0.0449897\pi\) |
−0.373018 | + | 0.927824i | \(0.621677\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 81.3918 | + | 1011.44i | 0.142045 | + | 1.76517i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1001.14 | − | 578.006i | −1.74111 | − | 1.00523i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 322.338 | 0.558644 | 0.279322 | − | 0.960197i | \(-0.409890\pi\) | ||||
0.279322 | + | 0.960197i | \(0.409890\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 362.871 | + | 525.997i | 0.626720 | + | 0.908458i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −158.292 | + | 91.3897i | −0.272447 | + | 0.157297i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −8.65093 | −0.0148386 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −428.705 | + | 349.661i | −0.732829 | + | 0.597711i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 974.121 | − | 562.409i | 1.65949 | − | 0.958107i | 0.686541 | − | 0.727091i | \(-0.259128\pi\) |
0.972950 | − | 0.231016i | \(-0.0742050\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −189.583 | − | 232.911i | −0.321872 | − | 0.395434i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 19.1366 | − | 13.2018i | 0.0323801 | − | 0.0223381i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 686.343 | − | 396.261i | 1.15741 | − | 0.668230i | 0.206727 | − | 0.978399i | \(-0.433719\pi\) |
0.950682 | + | 0.310168i | \(0.100385\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −271.378 | − | 470.040i | −0.456097 | − | 0.789983i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −385.976 | + | 812.891i | −0.646527 | + | 1.36163i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −695.903 | − | 401.780i | −1.16177 | − | 0.670750i | −0.210045 | − | 0.977692i | \(-0.567361\pi\) |
−0.951728 | + | 0.306941i | \(0.900695\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 3.87039 | − | 6.70371i | 0.00643992 | − | 0.0111543i | −0.862787 | − | 0.505567i | \(-0.831283\pi\) |
0.869227 | + | 0.494412i | \(0.164617\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 243.011 | + | 297.946i | 0.403004 | + | 0.494106i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −960.010 | + | 554.262i | −1.58679 | + | 0.916136i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 111.655 | + | 193.392i | 0.183945 | + | 0.318602i | 0.943221 | − | 0.332167i | \(-0.107780\pi\) |
−0.759275 | + | 0.650769i | \(0.774446\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −7.79839 | − | 96.9095i | −0.0128052 | − | 0.159129i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 130.579 | + | 75.3896i | 0.213713 | + | 0.123387i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 188.469 | − | 326.438i | 0.307454 | − | 0.532525i | −0.670351 | − | 0.742044i | \(-0.733856\pi\) |
0.977805 | + | 0.209519i | \(0.0671898\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 279.867 | + | 405.679i | 0.455068 | + | 0.659641i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −404.809 | − | 233.717i | −0.656093 | − | 0.378795i | 0.134694 | − | 0.990887i | \(-0.456995\pi\) |
−0.790787 | + | 0.612092i | \(0.790328\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 481.347 | − | 833.718i | 0.777621 | − | 1.34688i | −0.155689 | − | 0.987806i | \(-0.549760\pi\) |
0.933310 | − | 0.359073i | \(-0.116907\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 489.448 | + | 142.178i | 0.788162 | + | 0.228950i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − | 259.370i | − | 0.416324i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1594.24 | 2.55079 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −17.2939 | − | 70.6994i | −0.0275820 | − | 0.112758i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 188.376 | + | 108.759i | 0.299485 | + | 0.172908i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 132.578 | + | 229.632i | 0.210108 | + | 0.363917i | 0.951748 | − | 0.306880i | \(-0.0992852\pi\) |
−0.741640 | + | 0.670798i | \(0.765952\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 627.345 | + | 909.363i | 0.991066 | + | 1.43659i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 908.492 | − | 524.518i | 1.43070 | − | 0.826013i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −186.622 | −0.292970 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 172.887 | − | 141.010i | 0.270558 | − | 0.220673i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −21.8673 | + | 12.6251i | −0.0341143 | + | 0.0196959i | −0.516960 | − | 0.856009i | \(-0.672936\pi\) |
0.482846 | + | 0.875705i | \(0.339603\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −335.777 | −0.522204 | −0.261102 | − | 0.965311i | \(-0.584086\pi\) | ||||
−0.261102 | + | 0.965311i | \(0.584086\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −1051.21 | − | 499.133i | −1.62978 | − | 0.773850i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 905.889i | − | 1.40014i | −0.714075 | − | 0.700069i | \(-0.753152\pi\) | ||
0.714075 | − | 0.700069i | \(-0.246848\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 52.8338 | − | 91.5108i | 0.0814080 | − | 0.141003i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 122.821 | + | 178.035i | 0.188665 | + | 0.273479i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 929.143 | − | 536.441i | 1.42288 | − | 0.821502i | 0.426339 | − | 0.904564i | \(-0.359803\pi\) |
0.996544 | + | 0.0830615i | \(0.0264698\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 79.0506 | 0.120688 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −451.587 | − | 553.671i | −0.687346 | − | 0.842726i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 1036.04i | − | 1.57214i | −0.618135 | − | 0.786072i | \(-0.712111\pi\) | ||
0.618135 | − | 0.786072i | \(-0.287889\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 47.1772 | − | 81.7133i | 0.0713725 | − | 0.123621i | −0.828131 | − | 0.560535i | \(-0.810595\pi\) |
0.899503 | + | 0.436914i | \(0.143929\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −229.845 | − | 109.135i | −0.346674 | − | 0.164608i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −752.088 | − | 286.524i | −1.13096 | − | 0.430862i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 67.0593 | − | 116.150i | 0.100539 | − | 0.174138i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 197.159 | − | 415.230i | 0.294707 | − | 0.620672i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −52.5093 | − | 30.3162i | −0.0782553 | − | 0.0451807i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −156.533 | + | 271.123i | −0.232590 | + | 0.402858i | −0.958570 | − | 0.284858i | \(-0.908053\pi\) |
0.725979 | + | 0.687716i | \(0.241387\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −1605.71 | + | 394.465i | −2.37883 | + | 0.584393i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −523.760 | − | 302.393i | −0.773649 | − | 0.446666i | 0.0605259 | − | 0.998167i | \(-0.480722\pi\) |
−0.834175 | + | 0.551500i | \(0.814056\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 792.407 | 1.16702 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −33.1907 | − | 412.456i | −0.0487382 | − | 0.605662i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 27.4860i | − | 0.0402430i | −0.999798 | − | 0.0201215i | \(-0.993595\pi\) | ||
0.999798 | − | 0.0201215i | \(-0.00640531\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −1989.11 | −2.90381 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −216.935 | + | 456.879i | −0.315772 | + | 0.665035i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 44.8441i | 0.0650857i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 2.35922 | − | 4.08630i | 0.00341422 | − | 0.00591360i | −0.864313 | − | 0.502954i | \(-0.832247\pi\) |
0.867727 | + | 0.497040i | \(0.165580\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 8.38224 | + | 51.7452i | 0.0120956 | + | 0.0746684i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −414.527 | − | 239.327i | −0.596442 | − | 0.344356i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −113.337 | + | 196.306i | −0.162607 | + | 0.281644i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 71.5817 | + | 889.536i | 0.102406 | + | 1.27258i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −81.6577 | − | 47.1451i | −0.116487 | − | 0.0672541i | 0.440624 | − | 0.897692i | \(-0.354757\pi\) |
−0.557112 | + | 0.830438i | \(0.688090\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 318.444 | − | 51.2609i | 0.452979 | − | 0.0729173i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 360.370 | + | 522.373i | 0.511164 | + | 0.740954i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −351.014 | − | 202.658i | −0.496484 | − | 0.286645i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −866.770 | −1.22252 | −0.611262 | − | 0.791428i | \(-0.709338\pi\) | ||||
−0.611262 | + | 0.791428i | \(0.709338\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 963.673 | − | 156.106i | 1.35538 | − | 0.219558i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 298.371i | 0.418473i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −39.2450 | − | 67.9743i | −0.0548881 | − | 0.0950689i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 869.713 | + | 412.957i | 1.21299 | + | 0.575951i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −960.272 | − | 554.413i | −1.33557 | − | 0.771089i | −0.349419 | − | 0.936966i | \(-0.613621\pi\) |
−0.986146 | + | 0.165877i | \(0.946954\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −397.679 | −0.551566 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 670.990 | + | 972.628i | 0.928063 | + | 1.34527i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 435.094i | 0.600130i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 202.057 | + | 349.973i | 0.277933 | + | 0.481393i | 0.970871 | − | 0.239604i | \(-0.0770175\pi\) |
−0.692938 | + | 0.720997i | \(0.743684\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 646.017 | − | 337.792i | 0.886168 | − | 0.463363i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 535.209i | − | 0.732160i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −564.680 | − | 978.054i | −0.770368 | − | 1.33432i | −0.937362 | − | 0.348358i | \(-0.886739\pi\) |
0.166994 | − | 0.985958i | \(-0.446594\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −709.553 | − | 336.909i | −0.965378 | − | 0.458380i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −47.2415 | + | 27.2749i | −0.0640997 | + | 0.0370080i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 321.557 | − | 556.953i | 0.435124 | − | 0.753658i | −0.562181 | − | 0.827014i | \(-0.690038\pi\) |
0.997306 | + | 0.0733563i | \(0.0233710\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −366.486 | + | 89.6471i | −0.494584 | + | 0.120981i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1205.28i | 1.62219i | 0.584917 | + | 0.811093i | \(0.301127\pi\) | ||||
−0.584917 | + | 0.811093i | \(0.698873\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1335.49 | −1.79260 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −279.473 | + | 227.944i | −0.374127 | + | 0.305146i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −336.320 | − | 194.174i | −0.449025 | − | 0.259245i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −123.979 | + | 214.738i | −0.165086 | + | 0.285937i | −0.936686 | − | 0.350171i | \(-0.886123\pi\) |
0.771600 | + | 0.636108i | \(0.219457\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −1001.47 | − | 475.518i | −1.32997 | − | 0.631498i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −1765.27 | − | 1019.18i | −2.33811 | − | 1.34991i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −313.951 | + | 543.779i | −0.414731 | + | 0.718335i | −0.995400 | − | 0.0958047i | \(-0.969458\pi\) |
0.580669 | + | 0.814139i | \(0.302791\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −31.0167 | + | 65.3231i | −0.0408652 | + | 0.0860647i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 856.714 | − | 494.624i | 1.12577 | − | 0.649966i | 0.182905 | − | 0.983131i | \(-0.441450\pi\) |
0.942869 | + | 0.333165i | \(0.108117\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −471.263 | − | 816.251i | −0.617645 | − | 1.06979i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −676.870 | − | 829.882i | −0.884798 | − | 1.08481i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −474.367 | − | 273.876i | −0.618471 | − | 0.357074i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −256.815 | + | 444.816i | −0.333959 | + | 0.578434i | −0.983284 | − | 0.182077i | \(-0.941718\pi\) |
0.649325 | + | 0.760511i | \(0.275051\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −44.2704 | − | 550.142i | −0.0574195 | − | 0.713544i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 464.596 | − | 268.235i | 0.601030 | − | 0.347005i | −0.168417 | − | 0.985716i | \(-0.553865\pi\) |
0.769447 | + | 0.638711i | \(0.220532\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −483.973 | − | 838.266i | −0.624481 | − | 1.08163i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −231.551 | + | 18.6331i | −0.298006 | + | 0.0239808i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 53.4187 | + | 331.849i | 0.0685734 | + | 0.425993i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 15.8266 | + | 27.4125i | 0.0202645 | + | 0.0350992i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −45.7652 | − | 186.292i | −0.0584485 | − | 0.237921i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 292.292i | 0.372347i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 60.3896 | + | 104.598i | 0.0767339 | + | 0.132907i | 0.901839 | − | 0.432072i | \(-0.142217\pi\) |
−0.825105 | + | 0.564979i | \(0.808884\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 458.300 | + | 217.610i | 0.580861 | + | 0.275804i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 952.821i | − | 1.20458i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −157.151 | + | 272.194i | −0.198173 | + | 0.343246i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −80.9573 | + | 170.501i | −0.101833 | + | 0.214467i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 525.724 | − | 303.527i | 0.659629 | − | 0.380837i | −0.132507 | − | 0.991182i | \(-0.542303\pi\) |
0.792136 | + | 0.610345i | \(0.208969\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −145.938 | + | 252.773i | −0.182651 | + | 0.316361i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −81.8342 | − | 505.178i | −0.102165 | − | 0.630685i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 87.7886 | − | 50.6848i | 0.109326 | − | 0.0631193i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 399.805 | + | 692.483i | 0.496652 | + | 0.860227i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −0.140397 | − | 1.74469i | −0.000173974 | − | 0.00216195i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 144.203i | − | 0.178248i | −0.996021 | − | 0.0891241i | \(-0.971593\pi\) | ||
0.996021 | − | 0.0891241i | \(-0.0284068\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −487.189 | − | 843.837i | −0.600727 | − | 1.04049i | −0.992711 | − | 0.120518i | \(-0.961545\pi\) |
0.391984 | − | 0.919972i | \(-0.371789\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 1040.05 | − | 83.6940i | 1.27928 | − | 0.102945i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 254.141i | 0.311829i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −501.001 | − | 615.502i | −0.613221 | − | 0.753368i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 268.233 | − | 43.4513i | 0.327513 | − | 0.0530540i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 1392.69i | − | 1.69634i | −0.529726 | − | 0.848169i | \(-0.677705\pi\) | ||
0.529726 | − | 0.848169i | \(-0.322295\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −327.037 | + | 566.445i | −0.397372 | + | 0.688268i | −0.993401 | − | 0.114695i | \(-0.963411\pi\) |
0.596029 | + | 0.802963i | \(0.296744\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −18.8168 | − | 233.834i | −0.0228083 | − | 0.283435i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −966.498 | + | 558.008i | −1.16868 | + | 0.674737i | −0.953369 | − | 0.301808i | \(-0.902410\pi\) |
−0.215310 | + | 0.976546i | \(0.569076\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −42.5592 | −0.0513380 | −0.0256690 | − | 0.999670i | \(-0.508172\pi\) | ||||
−0.0256690 | + | 0.999670i | \(0.508172\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 692.866 | − | 55.7555i | 0.833774 | − | 0.0670945i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 361.260i | − | 0.433686i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1075.65 | − | 1863.09i | 1.28821 | − | 2.23124i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 295.393 | + | 308.009i | 0.352918 | + | 0.367992i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 413.860 | − | 238.942i | 0.493278 | − | 0.284794i | −0.232656 | − | 0.972559i | \(-0.574741\pi\) |
0.725933 | + | 0.687765i | \(0.241408\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 790.521 | 0.939978 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −1238.29 | + | 854.260i | −1.46890 | + | 1.01336i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1006.80 | − | 581.274i | 1.19147 | − | 0.687898i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 544.484 | 0.642839 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 79.8756 | + | 115.783i | 0.0940820 | + | 0.136376i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −277.523 | − | 160.228i | −0.326114 | − | 0.188282i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 440.866 | + | 763.602i | 0.516841 | + | 0.895195i | 0.999809 | + | 0.0195570i | \(0.00622558\pi\) |
−0.482968 | + | 0.875638i | \(0.660441\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −1555.26 | − | 320.774i | −1.81901 | − | 0.375174i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 727.761 | − | 420.173i | 0.849197 | − | 0.490284i | −0.0111831 | − | 0.999937i | \(-0.503560\pi\) |
0.860380 | + | 0.509654i | \(0.170226\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 578.204 | − | 1001.48i | 0.673113 | − | 1.16587i | −0.303904 | − | 0.952703i | \(-0.598290\pi\) |
0.977017 | − | 0.213163i | \(-0.0683765\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −19.4174 | − | 241.298i | −0.0225522 | − | 0.280253i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 267.381i | − | 0.309828i | −0.987928 | − | 0.154914i | \(-0.950490\pi\) | ||
0.987928 | − | 0.154914i | \(-0.0495100\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 555.640 | + | 962.397i | 0.642359 | + | 1.11260i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −160.615 | + | 338.265i | −0.185253 | + | 0.390155i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 138.507i | 0.159387i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 141.386 | + | 244.887i | 0.162326 | + | 0.281156i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 1543.38 | − | 250.014i | 1.76791 | − | 0.286385i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −1329.39 | − | 767.522i | −1.51930 | − | 0.877168i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1435.34 | 1.63665 | 0.818326 | − | 0.574754i | \(-0.194902\pi\) | ||||
0.818326 | + | 0.574754i | \(0.194902\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 211.502 | + | 100.425i | 0.240616 | + | 0.114249i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 920.034i | 1.04431i | 0.852852 | + | 0.522153i | \(0.174871\pi\) | ||||
−0.852852 | + | 0.522153i | \(0.825129\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 261.135 | + | 452.299i | 0.295736 | + | 0.512230i | 0.975156 | − | 0.221520i | \(-0.0711018\pi\) |
−0.679420 | + | 0.733750i | \(0.737768\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −1309.16 | − | 1897.68i | −1.47927 | − | 2.14427i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −239.539 | − | 138.298i | −0.270055 | − | 0.155917i | 0.358857 | − | 0.933392i | \(-0.383166\pi\) |
−0.628913 | + | 0.777476i | \(0.716500\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −515.265 | −0.579601 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 32.6524 | + | 98.1402i | 0.0366470 | + | 0.110146i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 68.7845 | + | 427.305i | 0.0770263 | + | 0.478505i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1698.38 | 1.89763 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 338.617 | + | 160.782i | 0.377500 | + | 0.179244i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 97.2542 | − | 56.1497i | 0.108180 | − | 0.0624580i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −86.8086 | −0.0963470 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 324.574 | + | 470.484i | 0.359439 | + | 0.521023i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 1253.88 | − | 723.929i | 1.38551 | − | 0.799922i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 171.465 | + | 296.986i | 0.189046 | + | 0.327438i | 0.944933 | − | 0.327265i | \(-0.106127\pi\) |
−0.755886 | + | 0.654703i | \(0.772794\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −747.618 | − | 283.972i | −0.822462 | − | 0.312400i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −629.426 | − | 363.399i | −0.690918 | − | 0.398901i | 0.113038 | − | 0.993591i | \(-0.463942\pi\) |
−0.803956 | + | 0.594689i | \(0.797275\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −25.5838 | − | 44.3124i | −0.0280217 | − | 0.0485350i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −1088.90 | + | 751.200i | −1.19005 | + | 0.820983i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −33.6261 | − | 19.4140i | −0.0366696 | − | 0.0211712i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −851.166 | −0.926188 | −0.463094 | − | 0.886309i | \(-0.653261\pi\) | ||||
−0.463094 | + | 0.886309i | \(0.653261\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 78.6759 | − | 6.33111i | 0.0854244 | − | 0.00687417i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 142.099 | − | 82.0408i | 0.153953 | − | 0.0888850i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1039.59 | 1.12388 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −774.566 | + | 125.473i | −0.835563 | + | 0.135353i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 786.926 | − | 454.332i | 0.847067 | − | 0.489055i | −0.0125930 | − | 0.999921i | \(-0.504009\pi\) |
0.859660 | + | 0.510866i | \(0.170675\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −338.170 | − | 415.457i | −0.363233 | − | 0.446248i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 1061.21 | + | 503.883i | 1.13742 | + | 0.540068i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 131.584 | − | 75.9700i | 0.140731 | − | 0.0812513i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −38.1604 | − | 66.0958i | −0.0407262 | − | 0.0705398i | 0.844944 | − | 0.534855i | \(-0.179634\pi\) |
−0.885670 | + | 0.464315i | \(0.846300\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 159.091 | + | 230.609i | 0.169426 | + | 0.245590i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −755.091 | − | 435.952i | −0.802434 | − | 0.463286i | 0.0418872 | − | 0.999122i | \(-0.486663\pi\) |
−0.844322 | + | 0.535837i | \(0.819996\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 166.973 | − | 289.206i | 0.177066 | − | 0.306687i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 1098.29 | + | 319.037i | 1.16221 | + | 0.337605i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 283.460 | − | 163.656i | 0.299324 | − | 0.172815i | −0.342815 | − | 0.939403i | \(-0.611380\pi\) |
0.642139 | + | 0.766588i | \(0.278047\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −262.736 | − | 455.073i | −0.276856 | − | 0.479529i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 141.000 | − | 97.2720i | 0.148265 | − | 0.102284i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 87.9770 | + | 50.7935i | 0.0923158 | + | 0.0532986i | 0.545447 | − | 0.838145i | \(-0.316360\pi\) |
−0.453131 | + | 0.891444i | \(0.649693\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −1570.52 | + | 2720.22i | −1.64453 | + | 2.84840i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 27.1290 | − | 2.18310i | 0.0283480 | − | 0.00228119i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 846.116 | + | 488.505i | 0.882290 | + | 0.509390i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 355.585 | − | 615.891i | 0.370015 | − | 0.640885i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −716.320 | − | 272.083i | −0.743842 | − | 0.282537i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 1978.09i | 2.04984i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 645.605 | 0.667637 | 0.333819 | − | 0.942637i | \(-0.391663\pi\) | ||||
0.333819 | + | 0.942637i | \(0.391663\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −173.538 | − | 709.440i | −0.179090 | − | 0.732137i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1455.94 | + | 840.588i | 1.49943 | + | 0.865693i | 1.00000 | 0.000663529i | \(-0.000211208\pi\) | |
0.499425 | + | 0.866357i | \(0.333545\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 117.553 | + | 203.607i | 0.120815 | + | 0.209257i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −1212.13 | + | 97.5414i | −1.24321 | + | 0.100042i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 417.952 | − | 241.305i | 0.427792 | − | 0.246986i | −0.270614 | − | 0.962688i | \(-0.587227\pi\) |
0.698405 | + | 0.715702i | \(0.253893\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 72.6084 | 0.0741659 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1175.42 | − | 1441.14i | −1.19819 | − | 1.46905i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 285.347 | − | 164.745i | 0.290282 | − | 0.167594i | −0.347787 | − | 0.937574i | \(-0.613067\pi\) |
0.638069 | + | 0.769979i | \(0.279733\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 71.9661 | 0.0730620 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −25.0029 | − | 310.707i | −0.0253322 | − | 0.314799i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 788.492i | 0.797262i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 130.189 | − | 225.494i | 0.131371 | − | 0.227542i | −0.792834 | − | 0.609438i | \(-0.791395\pi\) |
0.924205 | + | 0.381896i | \(0.124729\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 35.7394 | − | 2.87598i | 0.0359913 | − | 0.00289625i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −2412.36 | + | 1392.78i | −2.42448 | + | 1.39978i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1452.05 | 1.45642 | 0.728210 | − | 0.685354i | \(-0.240353\pi\) | ||||
0.728210 | + | 0.685354i | \(0.240353\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −445.117 | + | 109.349i | −0.445562 | + | 0.109459i |
(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 | 684.3.m.a.353.12 | ✓ | 80 | |
3.2 | odd | 2 | 2052.3.m.a.1493.40 | 80 | |||
9.4 | even | 3 | 2052.3.be.a.125.1 | 80 | |||
9.5 | odd | 6 | 684.3.be.a.581.38 | yes | 80 | ||
19.7 | even | 3 | 684.3.be.a.425.38 | yes | 80 | ||
57.26 | odd | 6 | 2052.3.be.a.197.1 | 80 | |||
171.121 | even | 3 | 2052.3.m.a.881.1 | 80 | |||
171.140 | odd | 6 | inner | 684.3.m.a.653.12 | yes | 80 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
684.3.m.a.353.12 | ✓ | 80 | 1.1 | even | 1 | trivial | |
684.3.m.a.653.12 | yes | 80 | 171.140 | odd | 6 | inner | |
684.3.be.a.425.38 | yes | 80 | 19.7 | even | 3 | ||
684.3.be.a.581.38 | yes | 80 | 9.5 | odd | 6 | ||
2052.3.m.a.881.1 | 80 | 171.121 | even | 3 | |||
2052.3.m.a.1493.40 | 80 | 3.2 | odd | 2 | |||
2052.3.be.a.125.1 | 80 | 9.4 | even | 3 | |||
2052.3.be.a.197.1 | 80 | 57.26 | odd | 6 |