Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1344,3,Mod(769,1344)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1344, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1344.769");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1344 = 2^{6} \cdot 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1344.f (of order \(2\), degree \(1\), not 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: | \(36.6213475300\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\sqrt{2}, \sqrt{-3})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 2x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{2}\cdot 3 \) |
Twist minimal: | no (minimal twist has level 42) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 769.2 | ||
Root | \(-0.707107 - 1.22474i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1344.769 |
Dual form | 1344.3.f.e.769.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1344\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(449\) | \(577\) | \(1093\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | − | 1.73205i | − | 0.577350i | ||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 5.91359i | 1.18272i | 0.806408 | + | 0.591359i | \(0.201408\pi\) | ||||
−0.806408 | + | 0.591359i | \(0.798592\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −6.24264 | + | 3.16693i | −0.891806 | + | 0.452418i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −3.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.75736 | −0.159760 | −0.0798800 | − | 0.996804i | \(-0.525454\pi\) | ||||
−0.0798800 | + | 0.996804i | \(0.525454\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 18.7554i | − | 1.44272i | −0.692559 | − | 0.721361i | \(-0.743517\pi\) | ||
0.692559 | − | 0.721361i | \(-0.256483\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 10.2426 | 0.682843 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 23.4803i | 1.38119i | 0.723240 | + | 0.690597i | \(0.242652\pi\) | ||||
−0.723240 | + | 0.690597i | \(0.757348\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 23.0600i | − | 1.21369i | −0.794822 | − | 0.606843i | \(-0.792436\pi\) | ||
0.794822 | − | 0.606843i | \(-0.207564\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 5.48528 | + | 10.8126i | 0.261204 | + | 0.514884i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −18.7279 | −0.814257 | −0.407129 | − | 0.913371i | \(-0.633470\pi\) | ||||
−0.407129 | + | 0.913371i | \(0.633470\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −9.97056 | −0.398823 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.19615i | 0.192450i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −30.0000 | −1.03448 | −0.517241 | − | 0.855840i | \(-0.673041\pi\) | ||||
−0.517241 | + | 0.855840i | \(0.673041\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 8.60927i | − | 0.277718i | −0.990312 | − | 0.138859i | \(-0.955656\pi\) | ||
0.990312 | − | 0.138859i | \(-0.0443435\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 3.04384i | 0.0922374i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −18.7279 | − | 36.9164i | −0.535083 | − | 1.05476i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 70.9117 | 1.91653 | 0.958266 | − | 0.285878i | \(-0.0922852\pi\) | ||||
0.958266 | + | 0.285878i | \(0.0922852\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −32.4853 | −0.832956 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 41.3951i | 1.00964i | 0.863225 | + | 0.504819i | \(0.168441\pi\) | ||||
−0.863225 | + | 0.504819i | \(0.831559\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 10.4264 | 0.242475 | 0.121237 | − | 0.992624i | \(-0.461314\pi\) | ||||
0.121237 | + | 0.992624i | \(0.461314\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | − | 17.7408i | − | 0.394239i | ||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 38.6995i | − | 0.823393i | −0.911321 | − | 0.411696i | \(-0.864936\pi\) | ||
0.911321 | − | 0.411696i | \(-0.135064\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 28.9411 | − | 39.5400i | 0.590635 | − | 0.806939i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 40.6690 | 0.797432 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 37.0294 | 0.698669 | 0.349334 | − | 0.936998i | \(-0.386408\pi\) | ||||
0.349334 | + | 0.936998i | \(0.386408\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 10.3923i | − | 0.188951i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −39.9411 | −0.700721 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − | 97.4872i | − | 1.65233i | −0.563431 | − | 0.826163i | \(-0.690519\pi\) | ||
0.563431 | − | 0.826163i | \(-0.309481\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 16.7262i | − | 0.274199i | −0.990557 | − | 0.137100i | \(-0.956222\pi\) | ||
0.990557 | − | 0.137100i | \(-0.0437781\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 18.7279 | − | 9.50079i | 0.297269 | − | 0.150806i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 110.912 | 1.70633 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 60.9706 | 0.910008 | 0.455004 | − | 0.890489i | \(-0.349638\pi\) | ||||
0.455004 | + | 0.890489i | \(0.349638\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 32.4377i | 0.470112i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 110.610 | 1.55789 | 0.778945 | − | 0.627092i | \(-0.215755\pi\) | ||||
0.778945 | + | 0.627092i | \(0.215755\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 56.7585i | − | 0.777514i | −0.921340 | − | 0.388757i | \(-0.872905\pi\) | ||
0.921340 | − | 0.388757i | \(-0.127095\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 17.2695i | 0.230260i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 10.9706 | − | 5.56543i | 0.142475 | − | 0.0722783i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 69.8234 | 0.883840 | 0.441920 | − | 0.897054i | \(-0.354297\pi\) | ||||
0.441920 | + | 0.897054i | \(0.354297\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 9.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 6.43583i | 0.0775401i | 0.999248 | + | 0.0387701i | \(0.0123440\pi\) | ||||
−0.999248 | + | 0.0387701i | \(0.987656\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −138.853 | −1.63356 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 51.9615i | 0.597259i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 42.0915i | − | 0.472938i | −0.971639 | − | 0.236469i | \(-0.924010\pi\) | ||
0.971639 | − | 0.236469i | \(-0.0759901\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 59.3970 | + | 117.083i | 0.652714 | + | 1.28663i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −14.9117 | −0.160341 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 136.368 | 1.43545 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 51.7153i | 0.533148i | 0.963814 | + | 0.266574i | \(0.0858916\pi\) | ||||
−0.963814 | + | 0.266574i | \(0.914108\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 5.27208 | 0.0532533 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 6.60991i | − | 0.0654447i | −0.999464 | − | 0.0327223i | \(-0.989582\pi\) | ||
0.999464 | − | 0.0327223i | \(-0.0104177\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 175.871i | − | 1.70748i | −0.520696 | − | 0.853742i | \(-0.674327\pi\) | ||
0.520696 | − | 0.853742i | \(-0.325673\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −63.9411 | + | 32.4377i | −0.608963 | + | 0.308931i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −46.2426 | −0.432174 | −0.216087 | − | 0.976374i | \(-0.569330\pi\) | ||||
−0.216087 | + | 0.976374i | \(0.569330\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 35.9411 | 0.329735 | 0.164868 | − | 0.986316i | \(-0.447280\pi\) | ||||
0.164868 | + | 0.986316i | \(0.447280\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − | 122.823i | − | 1.10651i | ||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −73.0294 | −0.646278 | −0.323139 | − | 0.946351i | \(-0.604738\pi\) | ||||
−0.323139 | + | 0.946351i | \(0.604738\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 110.749i | − | 0.963037i | ||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 56.2662i | 0.480907i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −74.3604 | − | 146.579i | −0.624877 | − | 1.23176i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −117.912 | −0.974477 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 71.6985 | 0.582915 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 88.8780i | 0.711024i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −89.9411 | −0.708198 | −0.354099 | − | 0.935208i | \(-0.615212\pi\) | ||||
−0.354099 | + | 0.935208i | \(0.615212\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | − | 18.0591i | − | 0.139993i | ||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 12.1753i | 0.0929415i | 0.998920 | + | 0.0464708i | \(0.0147974\pi\) | ||||
−0.998920 | + | 0.0464708i | \(0.985203\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 73.0294 | + | 143.955i | 0.549094 | + | 1.08237i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −30.7279 | −0.227614 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 165.765 | 1.20996 | 0.604980 | − | 0.796241i | \(-0.293181\pi\) | ||||
0.604980 | + | 0.796241i | \(0.293181\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 220.514i | − | 1.58643i | −0.608941 | − | 0.793215i | \(-0.708406\pi\) | ||
0.608941 | − | 0.793215i | \(-0.291594\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −67.0294 | −0.475386 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 32.9600i | 0.230489i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 177.408i | − | 1.22350i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −68.4853 | − | 50.1275i | −0.465886 | − | 0.341003i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −210.853 | −1.41512 | −0.707560 | − | 0.706653i | \(-0.750204\pi\) | ||||
−0.707560 | + | 0.706653i | \(0.750204\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 72.3675 | 0.479255 | 0.239628 | − | 0.970865i | \(-0.422975\pi\) | ||||
0.239628 | + | 0.970865i | \(0.422975\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 70.4409i | − | 0.460398i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 50.9117 | 0.328463 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 233.674i | − | 1.48837i | −0.667974 | − | 0.744184i | \(-0.732838\pi\) | ||
0.667974 | − | 0.744184i | \(-0.267162\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | − | 64.1369i | − | 0.403377i | ||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 116.912 | − | 59.3100i | 0.726160 | − | 0.368385i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −73.0883 | −0.448395 | −0.224197 | − | 0.974544i | \(-0.571976\pi\) | ||||
−0.224197 | + | 0.974544i | \(0.571976\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −18.0000 | −0.109091 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 39.3958i | 0.235903i | 0.993019 | + | 0.117951i | \(0.0376327\pi\) | ||||
−0.993019 | + | 0.117951i | \(0.962367\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −182.765 | −1.08145 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 69.1801i | 0.404562i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − | 23.8284i | − | 0.137737i | −0.997626 | − | 0.0688683i | \(-0.978061\pi\) | ||
0.997626 | − | 0.0688683i | \(-0.0219388\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 62.2426 | − | 31.5761i | 0.355672 | − | 0.180435i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −168.853 | −0.953971 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −12.9045 | −0.0720924 | −0.0360462 | − | 0.999350i | \(-0.511476\pi\) | ||||
−0.0360462 | + | 0.999350i | \(0.511476\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 65.3678i | − | 0.361148i | −0.983561 | − | 0.180574i | \(-0.942204\pi\) | ||
0.983561 | − | 0.180574i | \(-0.0577955\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −28.9706 | −0.158309 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 419.343i | 2.26672i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 41.2633i | − | 0.220659i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −16.4558 | − | 32.4377i | −0.0870680 | − | 0.171628i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 100.066 | 0.523906 | 0.261953 | − | 0.965081i | \(-0.415633\pi\) | ||||
0.261953 | + | 0.965081i | \(0.415633\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 78.9117 | 0.408869 | 0.204434 | − | 0.978880i | \(-0.434464\pi\) | ||||
0.204434 | + | 0.978880i | \(0.434464\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | − | 192.105i | − | 0.985152i | ||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 183.941 | 0.933711 | 0.466856 | − | 0.884334i | \(-0.345387\pi\) | ||||
0.466856 | + | 0.884334i | \(0.345387\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 170.029i | − | 0.854419i | −0.904153 | − | 0.427210i | \(-0.859497\pi\) | ||
0.904153 | − | 0.427210i | \(-0.140503\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | − | 105.604i | − | 0.525394i | ||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 187.279 | − | 95.0079i | 0.922558 | − | 0.468019i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −244.794 | −1.19412 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 56.1838 | 0.271419 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 40.5247i | 0.193898i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 21.5736 | 0.102245 | 0.0511223 | − | 0.998692i | \(-0.483720\pi\) | ||||
0.0511223 | + | 0.998692i | \(0.483720\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − | 191.582i | − | 0.899448i | ||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 61.6575i | 0.286779i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 27.2649 | + | 53.7446i | 0.125645 | + | 0.247671i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −98.3087 | −0.448898 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 440.382 | 1.99268 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 119.359i | 0.535240i | 0.963525 | + | 0.267620i | \(0.0862372\pi\) | ||||
−0.963525 | + | 0.267620i | \(0.913763\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 29.9117 | 0.132941 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − | 169.843i | − | 0.748207i | −0.927387 | − | 0.374103i | \(-0.877951\pi\) | ||
0.927387 | − | 0.374103i | \(-0.122049\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 110.011i | 0.480396i | 0.970724 | + | 0.240198i | \(0.0772124\pi\) | ||||
−0.970724 | + | 0.240198i | \(0.922788\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −9.63961 | − | 19.0016i | −0.0417299 | − | 0.0822579i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 57.2649 | 0.245772 | 0.122886 | − | 0.992421i | \(-0.460785\pi\) | ||||
0.122886 | + | 0.992421i | \(0.460785\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 228.853 | 0.973842 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − | 120.938i | − | 0.510285i | ||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −281.522 | −1.17792 | −0.588958 | − | 0.808164i | \(-0.700462\pi\) | ||||
−0.588958 | + | 0.808164i | \(0.700462\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 168.306i | 0.698366i | 0.937055 | + | 0.349183i | \(0.113541\pi\) | ||||
−0.937055 | + | 0.349183i | \(0.886459\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − | 15.5885i | − | 0.0641500i | ||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 233.823 | + | 171.146i | 0.954381 | + | 0.698555i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −432.500 | −1.75101 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 11.1472 | 0.0447678 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 106.096i | 0.422695i | 0.977411 | + | 0.211348i | \(0.0677852\pi\) | ||||
−0.977411 | + | 0.211348i | \(0.932215\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 32.9117 | 0.130086 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 240.500i | 0.943138i | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 290.462i | − | 1.13020i | −0.825021 | − | 0.565102i | \(-0.808837\pi\) | ||
0.825021 | − | 0.565102i | \(-0.191163\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −442.676 | + | 224.572i | −1.70917 | + | 0.867074i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 90.0000 | 0.344828 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 89.0223 | 0.338488 | 0.169244 | − | 0.985574i | \(-0.445867\pi\) | ||||
0.169244 | + | 0.985574i | \(0.445867\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 218.977i | 0.826328i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −72.9045 | −0.273051 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 191.498i | − | 0.711888i | −0.934507 | − | 0.355944i | \(-0.884159\pi\) | ||
0.934507 | − | 0.355944i | \(-0.115841\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 217.440i | 0.802362i | 0.915999 | + | 0.401181i | \(0.131400\pi\) | ||||
−0.915999 | + | 0.401181i | \(0.868600\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 202.794 | − | 102.879i | 0.742835 | − | 0.376845i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 17.5219 | 0.0637159 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −290.676 | −1.04937 | −0.524686 | − | 0.851296i | \(-0.675817\pi\) | ||||
−0.524686 | + | 0.851296i | \(0.675817\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 25.8278i | 0.0925728i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 18.8528 | 0.0670919 | 0.0335459 | − | 0.999437i | \(-0.489320\pi\) | ||||
0.0335459 | + | 0.999437i | \(0.489320\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 401.734i | − | 1.41955i | −0.704426 | − | 0.709777i | \(-0.748796\pi\) | ||
0.704426 | − | 0.709777i | \(-0.251204\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | − | 236.195i | − | 0.828756i | ||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −131.095 | − | 258.415i | −0.456779 | − | 0.900401i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −262.324 | −0.907695 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 89.5736 | 0.307813 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 280.893i | 0.958679i | 0.877629 | + | 0.479340i | \(0.159124\pi\) | ||||
−0.877629 | + | 0.479340i | \(0.840876\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 576.500 | 1.95424 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − | 9.13151i | − | 0.0307458i | ||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 351.249i | 1.17475i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −65.0883 | + | 33.0197i | −0.216240 | + | 0.109700i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −11.4487 | −0.0377845 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 98.9117 | 0.324301 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 152.318i | 0.496151i | 0.968741 | + | 0.248076i | \(0.0797982\pi\) | ||||
−0.968741 | + | 0.248076i | \(0.920202\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −304.617 | −0.985817 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 283.156i | 0.910470i | 0.890371 | + | 0.455235i | \(0.150445\pi\) | ||||
−0.890371 | + | 0.455235i | \(0.849555\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 48.5819i | 0.155214i | 0.996984 | + | 0.0776069i | \(0.0247279\pi\) | ||||
−0.996984 | + | 0.0776069i | \(0.975272\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 56.1838 | + | 110.749i | 0.178361 | + | 0.351585i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 578.029 | 1.82343 | 0.911717 | − | 0.410819i | \(-0.134757\pi\) | ||||
0.911717 | + | 0.410819i | \(0.134757\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 52.7208 | 0.165269 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 80.0946i | 0.249516i | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 541.456 | 1.67633 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 187.002i | 0.575390i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − | 62.2519i | − | 0.190373i | ||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 122.558 | + | 241.587i | 0.372518 | + | 0.734307i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 332.368 | 1.00413 | 0.502066 | − | 0.864829i | \(-0.332574\pi\) | ||||
0.502066 | + | 0.864829i | \(0.332574\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −212.735 | −0.638844 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 360.555i | 1.07628i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 88.1766 | 0.261652 | 0.130826 | − | 0.991405i | \(-0.458237\pi\) | ||||
0.130826 | + | 0.991405i | \(0.458237\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 126.491i | 0.373129i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 15.1296i | 0.0443683i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −55.4487 | + | 338.488i | −0.161658 | + | 0.986847i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −191.823 | −0.556010 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −320.080 | −0.922422 | −0.461211 | − | 0.887291i | \(-0.652585\pi\) | ||||
−0.461211 | + | 0.887291i | \(0.652585\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 333.046i | 0.954287i | 0.878825 | + | 0.477143i | \(0.158328\pi\) | ||||
−0.878825 | + | 0.477143i | \(0.841672\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 97.4558 | 0.277652 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 655.712i | − | 1.85754i | −0.370654 | − | 0.928771i | \(-0.620866\pi\) | ||
0.370654 | − | 0.928771i | \(-0.379134\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 654.103i | 1.84254i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −253.882 | + | 128.796i | −0.711155 | + | 0.360773i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 97.7574 | 0.272305 | 0.136152 | − | 0.990688i | \(-0.456526\pi\) | ||||
0.136152 | + | 0.990688i | \(0.456526\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −170.765 | −0.473032 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 204.229i | 0.562614i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 335.647 | 0.919580 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 321.057i | 0.874815i | 0.899263 | + | 0.437408i | \(0.144103\pi\) | ||||
−0.899263 | + | 0.437408i | \(0.855897\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | − | 124.185i | − | 0.336546i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −231.161 | + | 117.270i | −0.623077 | + | 0.316091i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −187.470 | −0.502601 | −0.251300 | − | 0.967909i | \(-0.580858\pi\) | ||||
−0.251300 | + | 0.967909i | \(0.580858\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 153.941 | 0.410510 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 562.662i | 1.49247i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −357.103 | −0.942223 | −0.471112 | − | 0.882074i | \(-0.656147\pi\) | ||||
−0.471112 | + | 0.882074i | \(0.656147\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 155.783i | 0.408878i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 622.230i | − | 1.62462i | −0.583225 | − | 0.812311i | \(-0.698209\pi\) | ||
0.583225 | − | 0.812311i | \(-0.301791\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 32.9117 | + | 64.8754i | 0.0854849 | + | 0.168508i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −31.2792 | −0.0808249 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −227.470 | −0.584756 | −0.292378 | − | 0.956303i | \(-0.594447\pi\) | ||||
−0.292378 | + | 0.956303i | \(0.594447\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 439.737i | − | 1.12465i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 21.0883 | 0.0536598 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 412.907i | 1.04533i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 720.329i | − | 1.81443i | −0.420666 | − | 0.907216i | \(-0.638204\pi\) | ||
0.420666 | − | 0.907216i | \(-0.361796\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 249.338 | − | 126.491i | 0.624908 | − | 0.317019i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 697.176 | 1.73859 | 0.869296 | − | 0.494291i | \(-0.164572\pi\) | ||||
0.869296 | + | 0.494291i | \(0.164572\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −161.470 | −0.400670 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 53.2223i | 0.131413i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −124.617 | −0.306185 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 102.386i | 0.250333i | 0.992136 | + | 0.125166i | \(0.0399465\pi\) | ||||
−0.992136 | + | 0.125166i | \(0.960053\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − | 287.113i | − | 0.698571i | ||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 308.735 | + | 608.578i | 0.747543 | + | 1.47355i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −38.0589 | −0.0917081 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −381.941 | −0.915926 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 391.426i | 0.934191i | 0.884207 | + | 0.467095i | \(0.154700\pi\) | ||||
−0.884207 | + | 0.467095i | \(0.845300\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −354.441 | −0.841902 | −0.420951 | − | 0.907083i | \(-0.638304\pi\) | ||||
−0.420951 | + | 0.907083i | \(0.638304\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 116.098i | 0.274464i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − | 234.112i | − | 0.550851i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 52.9706 | + | 104.415i | 0.124053 | + | 0.244533i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 57.0883 | 0.133073 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −585.286 | −1.35797 | −0.678987 | − | 0.734151i | \(-0.737581\pi\) | ||||
−0.678987 | + | 0.734151i | \(0.737581\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 392.207i | − | 0.905789i | −0.891564 | − | 0.452895i | \(-0.850391\pi\) | ||
0.891564 | − | 0.452895i | \(-0.149609\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −307.279 | −0.706389 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 431.866i | 0.988252i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 392.513i | 0.894106i | 0.894507 | + | 0.447053i | \(0.147527\pi\) | ||||
−0.894507 | + | 0.447053i | \(0.852473\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −86.8234 | + | 118.620i | −0.196878 | + | 0.268980i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −814.742 | −1.83915 | −0.919574 | − | 0.392918i | \(-0.871466\pi\) | ||||
−0.919574 | + | 0.392918i | \(0.871466\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 248.912 | 0.559352 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 365.208i | 0.817020i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 180.323 | 0.401610 | 0.200805 | − | 0.979631i | \(-0.435644\pi\) | ||||
0.200805 | + | 0.979631i | \(0.435644\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 72.7461i | − | 0.161300i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − | 125.344i | − | 0.276698i | ||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −692.382 | + | 351.249i | −1.52172 | + | 0.771977i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 280.177 | 0.613078 | 0.306539 | − | 0.951858i | \(-0.400829\pi\) | ||||
0.306539 | + | 0.951858i | \(0.400829\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −122.007 | −0.265811 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 406.297i | − | 0.881338i | −0.897670 | − | 0.440669i | \(-0.854741\pi\) | ||
0.897670 | − | 0.440669i | \(-0.145259\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −457.470 | −0.988056 | −0.494028 | − | 0.869446i | \(-0.664476\pi\) | ||||
−0.494028 | + | 0.869446i | \(0.664476\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | − | 88.1816i | − | 0.189638i | ||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 643.711i | − | 1.37840i | −0.724573 | − | 0.689198i | \(-0.757963\pi\) | ||
0.724573 | − | 0.689198i | \(-0.242037\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −380.617 | + | 193.089i | −0.811551 | + | 0.411705i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −404.735 | −0.859310 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −18.3229 | −0.0387377 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 229.921i | 0.484045i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −111.088 | −0.232890 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − | 168.535i | − | 0.351847i | −0.984404 | − | 0.175924i | \(-0.943709\pi\) | ||
0.984404 | − | 0.175924i | \(-0.0562912\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − | 1329.98i | − | 2.76502i | ||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −102.728 | − | 202.497i | −0.212687 | − | 0.419248i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −305.823 | −0.630564 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 2.77965 | 0.00570771 | 0.00285385 | − | 0.999996i | \(-0.499092\pi\) | ||||
0.00285385 | + | 0.999996i | \(0.499092\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 126.593i | 0.258881i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −247.477 | −0.504027 | −0.252014 | − | 0.967724i | \(-0.581093\pi\) | ||||
−0.252014 | + | 0.967724i | \(0.581093\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 704.409i | − | 1.42882i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 31.1769i | 0.0629837i | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −690.500 | + | 350.295i | −1.38934 | + | 0.704818i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −483.426 | −0.968789 | −0.484394 | − | 0.874850i | \(-0.660960\pi\) | ||||
−0.484394 | + | 0.874850i | \(0.660960\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 68.2355 | 0.136199 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 58.7033i | − | 0.116706i | −0.998296 | − | 0.0583532i | \(-0.981415\pi\) | ||
0.998296 | − | 0.0583532i | \(-0.0185849\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 39.0883 | 0.0774026 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 316.557i | 0.624374i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 68.8793i | − | 0.135323i | −0.997708 | − | 0.0676614i | \(-0.978446\pi\) | ||
0.997708 | − | 0.0676614i | \(-0.0215537\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 179.750 | + | 354.323i | 0.351762 | + | 0.693392i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 119.823 | 0.233574 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 1040.03 | 2.01947 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 68.0089i | 0.131545i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −41.2721 | −0.0795223 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 292.720i | 0.561843i | 0.959731 | + | 0.280922i | \(0.0906401\pi\) | ||||
−0.959731 | + | 0.280922i | \(0.909360\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 493.056i | 0.942746i | 0.881934 | + | 0.471373i | \(0.156241\pi\) | ||||
−0.881934 | + | 0.471373i | \(0.843759\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −54.6913 | − | 107.807i | −0.104174 | − | 0.205347i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 202.148 | 0.383583 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −178.265 | −0.336985 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 292.462i | 0.550775i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 776.382 | 1.45663 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 273.460i | − | 0.511140i | ||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 22.3513i | 0.0416226i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −50.8600 | + | 69.4860i | −0.0943598 | + | 0.128916i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1037.85 | 1.91840 | 0.959198 | − | 0.282736i | \(-0.0912421\pi\) | ||||
0.959198 | + | 0.282736i | \(0.0912421\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −113.220 | −0.208509 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 212.541i | 0.389984i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −130.530 | −0.238629 | −0.119314 | − | 0.992857i | \(-0.538070\pi\) | ||||
−0.119314 | + | 0.992857i | \(0.538070\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 50.1785i | 0.0913998i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 691.801i | 1.25554i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −435.882 | + | 221.126i | −0.788214 | + | 0.399866i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 726.323 | 1.30869 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −665.147 | −1.19416 | −0.597080 | − | 0.802182i | \(-0.703673\pi\) | ||||
−0.597080 | + | 0.802182i | \(0.703673\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 195.551i | − | 0.349823i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −71.4701 | −0.127398 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 829.295i | 1.47299i | 0.676441 | + | 0.736497i | \(0.263521\pi\) | ||||
−0.676441 | + | 0.736497i | \(0.736479\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − | 431.866i | − | 0.764365i | ||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −56.1838 | + | 28.5024i | −0.0990895 | + | 0.0502687i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 706.971 | 1.24248 | 0.621240 | − | 0.783621i | \(-0.286629\pi\) | ||||
0.621240 | + | 0.783621i | \(0.286629\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −366.912 | −0.642577 | −0.321289 | − | 0.946981i | \(-0.604116\pi\) | ||||
−0.321289 | + | 0.946981i | \(0.604116\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − | 173.319i | − | 0.302477i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 186.728 | 0.324744 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 390.357i | − | 0.676528i | −0.941051 | − | 0.338264i | \(-0.890160\pi\) | ||
0.941051 | − | 0.338264i | \(-0.109840\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | − | 136.679i | − | 0.236061i | ||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −20.3818 | − | 40.1766i | −0.0350806 | − | 0.0691507i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −65.0740 | −0.111619 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −332.735 | −0.568778 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 702.499i | − | 1.19676i | −0.801212 | − | 0.598381i | \(-0.795811\pi\) | ||
0.801212 | − | 0.598381i | \(-0.204189\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −198.530 | −0.337063 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − | 318.595i | − | 0.539078i | ||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 942.519i | 1.58941i | 0.606997 | + | 0.794704i | \(0.292374\pi\) | ||||
−0.606997 | + | 0.794704i | \(0.707626\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 866.808 | − | 439.737i | 1.45682 | − | 0.739054i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −294.500 | −0.493299 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 952.109 | 1.58950 | 0.794749 | − | 0.606939i | \(-0.207603\pi\) | ||||
0.794749 | + | 0.606939i | \(0.207603\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 729.804i | 1.21432i | 0.794581 | + | 0.607158i | \(0.207690\pi\) | ||||
−0.794581 | + | 0.607158i | \(0.792310\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −182.912 | −0.303336 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − | 697.282i | − | 1.15253i | ||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1006.34i | 1.65789i | 0.559332 | + | 0.828944i | \(0.311058\pi\) | ||||
−0.559332 | + | 0.828944i | \(0.688942\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −164.558 | − | 324.377i | −0.270211 | − | 0.532639i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −725.823 | −1.18793 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 199.588 | 0.325592 | 0.162796 | − | 0.986660i | \(-0.447949\pi\) | ||||
0.162796 | + | 0.986660i | \(0.447949\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 423.996i | 0.689424i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −353.294 | −0.572599 | −0.286299 | − | 0.958140i | \(-0.592425\pi\) | ||||
−0.286299 | + | 0.958140i | \(0.592425\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 56.2064i | − | 0.0908020i | −0.998969 | − | 0.0454010i | \(-0.985543\pi\) | ||
0.998969 | − | 0.0454010i | \(-0.0144566\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | − | 97.3131i | − | 0.156704i | ||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 133.301 | + | 262.762i | 0.213966 | + | 0.421769i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −774.852 | −1.23976 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 70.1909 | 0.111947 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 1665.03i | 2.64710i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −807.322 | −1.27943 | −0.639716 | − | 0.768611i | \(-0.720948\pi\) | ||||
−0.639716 | + | 0.768611i | \(0.720948\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − | 37.3666i | − | 0.0590309i | ||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − | 531.875i | − | 0.837599i | ||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −741.588 | − | 542.802i | −1.16419 | − | 0.852122i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −331.831 | −0.519297 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1016.35 | 1.58557 | 0.792786 | − | 0.609500i | \(-0.208630\pi\) | ||||
0.792786 | + | 0.609500i | \(0.208630\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 404.688i | − | 0.629375i | −0.949195 | − | 0.314687i | \(-0.898100\pi\) | ||
0.949195 | − | 0.314687i | \(-0.101900\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 106.794 | 0.165572 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 940.604i | 1.45379i | 0.686747 | + | 0.726896i | \(0.259038\pi\) | ||||
−0.686747 | + | 0.726896i | \(0.740962\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 171.320i | 0.263975i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 93.0883 | − | 47.2243i | 0.142993 | − | 0.0725411i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −731.970 | −1.12093 | −0.560467 | − | 0.828177i | \(-0.689378\pi\) | ||||
−0.560467 | + | 0.828177i | \(0.689378\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −72.0000 | −0.109924 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 170.276i | 0.259171i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 904.316 | 1.37225 | 0.686127 | − | 0.727481i | \(-0.259309\pi\) | ||||
0.686127 | + | 0.727481i | \(0.259309\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 335.881i | 0.508141i | 0.967186 | + | 0.254070i | \(0.0817695\pi\) | ||||
−0.967186 | + | 0.254070i | \(0.918231\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − | 762.764i | − | 1.15047i | ||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −851.294 | + | 431.866i | −1.28014 | + | 0.649423i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 561.838 | 0.842335 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 206.735 | 0.309021 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 29.3939i | 0.0438061i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1191.44 | 1.77034 | 0.885171 | − | 0.465266i | \(-0.154041\pi\) | ||||
0.885171 | + | 0.465266i | \(0.154041\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | − | 51.8086i | − | 0.0767534i | ||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 1211.07i | − | 1.78888i | −0.447186 | − | 0.894441i | \(-0.647574\pi\) | ||
0.447186 | − | 0.894441i | \(-0.352426\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −163.779 | − | 322.840i | −0.241206 | − | 0.475464i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −294.177 | −0.431977 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −1233.89 | −1.80657 | −0.903287 | − | 0.429038i | \(-0.858853\pi\) | ||||
−0.903287 | + | 0.429038i | \(0.858853\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 980.264i | 1.43104i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 190.544 | 0.277357 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 694.501i | − | 1.00798i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 86.7045i | − | 0.125477i | −0.998030 | − | 0.0627384i | \(-0.980017\pi\) | ||
0.998030 | − | 0.0627384i | \(-0.0199834\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −32.9117 | + | 16.6963i | −0.0474916 | + | 0.0240928i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 1304.03 | 1.87630 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −971.970 | −1.39450 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | − | 99.1858i | − | 0.141897i | ||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 149.147 | 0.212763 | 0.106382 | − | 0.994325i | \(-0.466073\pi\) | ||||
0.106382 | + | 0.994325i | \(0.466073\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 1635.22i | − | 2.32607i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | − | 396.385i | − | 0.562248i | ||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 20.9331 | + | 41.2633i | 0.0296084 | + | 0.0583639i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −189.647 | −0.267485 | −0.133742 | − | 0.991016i | \(-0.542699\pi\) | ||||
−0.133742 | + | 0.991016i | \(0.542699\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −209.470 | −0.294613 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 161.234i | 0.226134i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −194.912 | −0.272604 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 487.610i | 0.680070i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 12.0064i | 0.0166987i | 0.999965 | + | 0.00834937i | \(0.00265772\pi\) | ||||
−0.999965 | + | 0.00834937i | \(0.997342\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 556.971 | + | 1097.90i | 0.772497 | + | 1.52274i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 291.515 | 0.403202 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 299.117 | 0.412575 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 417.169i | 0.573823i | 0.957957 | + | 0.286911i | \(0.0926286\pi\) | ||||
−0.957957 | + | 0.286911i | \(0.907371\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −27.0000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 244.815i | 0.334904i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 1286.99i | − | 1.75578i | −0.478859 | − | 0.877892i | \(-0.658949\pi\) | ||
0.478859 | − | 0.877892i | \(-0.341051\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 296.434 | − | 404.994i | 0.403311 | − | 0.551012i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −107.147 | −0.145383 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1333.47 | 1.80443 | 0.902213 | − | 0.431292i | \(-0.141942\pi\) | ||||
0.902213 | + | 0.431292i | \(0.141942\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 749.111i | 1.01095i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 776.476 | 1.04506 | 0.522528 | − | 0.852622i | \(-0.324989\pi\) | ||||
0.522528 | + | 0.852622i | \(0.324989\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − | 1246.90i | − | 1.67369i | ||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − | 19.3075i | − | 0.0258467i | ||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 288.676 | − | 146.447i | 0.385415 | − | 0.195524i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −48.8385 | −0.0650313 | −0.0325157 | − | 0.999471i | \(-0.510352\pi\) | ||||
−0.0325157 | + | 0.999471i | \(0.510352\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 183.765 | 0.244043 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 427.952i | 0.566824i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1279.47 | 1.69019 | 0.845093 | − | 0.534620i | \(-0.179545\pi\) | ||||
0.845093 | + | 0.534620i | \(0.179545\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | − | 57.0047i | − | 0.0751050i | ||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 1316.12i | − | 1.72947i | −0.502231 | − | 0.864734i | \(-0.667487\pi\) | ||
0.502231 | − | 0.864734i | \(-0.332513\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −224.368 | + | 113.823i | −0.294060 | + | 0.149178i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 416.558 | 0.544521 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −1828.41 | −2.38385 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 110.324i | − | 0.143464i | −0.997424 | − | 0.0717320i | \(-0.977147\pi\) | ||
0.997424 | − | 0.0717320i | \(-0.0228526\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −503.095 | −0.652523 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 717.634i | 0.928375i | 0.885737 | + | 0.464187i | \(0.153654\pi\) | ||||
−0.885737 | + | 0.464187i | \(0.846346\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 85.8392i | 0.110760i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 388.971 | + | 766.738i | 0.500606 | + | 0.986792i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 954.573 | 1.22538 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −194.382 | −0.248888 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − | 155.885i | − | 0.199086i | ||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 1381.85 | 1.76032 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 347.191i | − | 0.441158i | −0.975369 | − | 0.220579i | \(-0.929205\pi\) | ||
0.975369 | − | 0.220579i | \(-0.0707946\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | − | 154.191i | − | 0.195426i | ||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 455.897 | − | 231.279i | 0.576355 | − | 0.292388i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −313.706 | −0.395593 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 379.279 | 0.477081 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 361.246i | − | 0.453257i | −0.973981 | − | 0.226629i | \(-0.927230\pi\) | ||
0.973981 | − | 0.226629i | \(-0.0727704\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 908.674 | 1.13726 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 126.274i | 0.157646i | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 99.7451i | 0.124216i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 350.735 | + | 691.368i | 0.435696 | + | 0.858842i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −331.684 | −0.411009 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −113.147 | −0.139861 | −0.0699303 | − | 0.997552i | \(-0.522278\pi\) | ||||
−0.0699303 | + | 0.997552i | \(0.522278\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 134.182i | 0.165453i | 0.996572 | + | 0.0827264i | \(0.0263628\pi\) | ||||
−0.996572 | + | 0.0827264i | \(0.973637\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 376.617 | 0.463244 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − | 432.214i | − | 0.530324i | ||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 240.433i | − | 0.294288i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −178.191 | − | 351.249i | −0.217571 | − | 0.428876i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −491.677 | −0.598876 | −0.299438 | − | 0.954116i | \(-0.596799\pi\) | ||||
−0.299438 | + | 0.954116i | \(0.596799\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 941.852 | 1.14441 | 0.572207 | − | 0.820110i | \(-0.306088\pi\) | ||||
0.572207 | + | 0.820110i | \(0.306088\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | − | 30.3488i | − | 0.0367864i | ||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 966.978 | 1.16926 | 0.584630 | − | 0.811300i | \(-0.301240\pi\) | ||||
0.584630 | + | 0.811300i | \(0.301240\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1185.53i | 1.43007i | 0.699088 | + | 0.715035i | \(0.253589\pi\) | ||||
−0.699088 | + | 0.715035i | \(0.746411\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 503.466i | 0.605856i | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 928.410 | + | 679.546i | 1.11454 | + | 0.815781i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −232.971 | −0.279007 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 44.7351 | 0.0534469 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 1376.91i | − | 1.64113i | −0.571550 | − | 0.820567i | \(-0.693658\pi\) | ||
0.571550 | − | 0.820567i | \(-0.306342\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 59.0000 | 0.0701546 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − | 32.6540i | − | 0.0387355i | ||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − | 1080.79i | − | 1.27905i | ||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 736.080 | − | 373.418i | 0.869044 | − | 0.440871i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −695.823 | −0.819580 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1328.03 | −1.56055 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 175.006i | 0.205165i | 0.994725 | + | 0.102582i | \(0.0327105\pi\) | ||||
−0.994725 | + | 0.102582i | \(0.967289\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −409.103 | −0.478483 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 61.7471i | − | 0.0720503i | −0.999351 | − | 0.0360252i | \(-0.988530\pi\) | ||
0.999351 | − | 0.0360252i | \(-0.0114696\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 191.306i | − | 0.222708i | −0.993781 | − | 0.111354i | \(-0.964481\pi\) | ||
0.993781 | − | 0.111354i | \(-0.0355188\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −447.588 | + | 227.064i | −0.519847 | + | 0.263721i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 494.507 | 0.573009 | 0.286504 | − | 0.958079i | \(-0.407507\pi\) | ||||
0.286504 | + | 0.958079i | \(0.407507\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 140.912 | 0.162904 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 454.358i | 0.524058i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −122.705 | −0.141202 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 1143.53i | − | 1.31289i | ||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 155.146i | − | 0.177716i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −281.470 | − | 554.833i | −0.321680 | − | 0.634095i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 454.353 | 0.518077 | 0.259038 | − | 0.965867i | \(-0.416594\pi\) | ||||
0.259038 | + | 0.965867i | \(0.416594\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 486.521 | 0.553494 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 143.493i | 0.162875i | 0.996678 | + | 0.0814375i | \(0.0259511\pi\) | ||||
−0.996678 | + | 0.0814375i | \(0.974049\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −927.986 | −1.05095 | −0.525473 | − | 0.850810i | \(-0.676112\pi\) | ||||
−0.525473 | + | 0.850810i | \(0.676112\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | − | 998.527i | − | 1.12828i | ||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 958.265i | − | 1.08034i | −0.841555 | − | 0.540172i | \(-0.818359\pi\) | ||
0.841555 | − | 0.540172i | \(-0.181641\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 561.470 | − | 284.837i | 0.631575 | − | 0.320402i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −15.8162 | −0.0177511 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −892.410 | −0.999340 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 76.3122i | − | 0.0852650i | ||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 608.382 | 0.678241 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 258.278i | 0.287295i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 869.462i | 0.964996i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 57.1918 | + | 112.736i | 0.0633353 | + | 0.124846i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 386.558 | 0.427136 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −552.721 | −0.609394 | −0.304697 | − | 0.952449i | \(-0.598555\pi\) | ||||
−0.304697 | + | 0.952449i | \(0.598555\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 19.8297i | 0.0218149i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −142.742 | −0.156687 | −0.0783437 | − | 0.996926i | \(-0.524963\pi\) | ||||
−0.0783437 | + | 0.996926i | \(0.524963\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 11.3101i | − | 0.0123878i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | − | 171.320i | − | 0.187235i | ||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −38.5584 | − | 76.0063i | −0.0420485 | − | 0.0828858i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1086.45 | −1.18221 | −0.591107 | − | 0.806593i | \(-0.701309\pi\) | ||||
−0.591107 | + | 0.806593i | \(0.701309\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 263.823 | 0.286453 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 2074.54i | − | 2.24760i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −707.029 | −0.764356 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 527.613i | 0.569161i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 1550.75i | − | 1.66927i | −0.550806 | − | 0.834633i | \(-0.685680\pi\) | ||
0.550806 | − | 0.834633i | \(-0.314320\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −911.793 | − | 667.383i | −0.979370 | − | 0.716845i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 490.441 | 0.525660 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 244.014 | 0.260978 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 759.317i | 0.810370i | 0.914235 | + | 0.405185i | \(0.132793\pi\) | ||||
−0.914235 | + | 0.405185i | \(0.867207\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 84.1463 | 0.0896127 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 36.3519i | − | 0.0386312i | −0.999813 | − | 0.0193156i | \(-0.993851\pi\) | ||
0.999813 | − | 0.0193156i | \(-0.00614873\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 775.245i | − | 0.822105i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 191.823 | − | 97.3131i | 0.202988 | − | 0.102977i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 92.5370 | 0.0977160 | 0.0488580 | − | 0.998806i | \(-0.484442\pi\) | ||||
0.0488580 | + | 0.998806i | \(0.484442\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1064.53 | −1.12174 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 1001.17i | − | 1.05276i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −1361.29 | −1.42843 | −0.714215 | − | 0.699927i | \(-0.753216\pi\) | ||||
−0.714215 | + | 0.699927i | \(0.753216\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 591.750i | 0.619633i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − | 91.3151i | − | 0.0954180i | ||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −1034.81 | + | 524.964i | −1.07905 | + | 0.547408i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 886.881 | 0.922873 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 138.728 | 0.144058 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 466.651i | 0.483577i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −481.677 | −0.498115 | −0.249057 | − | 0.968489i | \(-0.580121\pi\) | ||||
−0.249057 | + | 0.968489i | \(0.580121\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | − | 937.829i | − | 0.967832i | ||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 1427.34i | − | 1.46997i | −0.678082 | − | 0.734987i | \(-0.737188\pi\) | ||
0.678082 | − | 0.734987i | \(-0.262812\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 698.352 | + | 1376.59i | 0.717730 | + | 1.41479i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 323.897 | 0.332202 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −1356.26 | −1.38819 | −0.694095 | − | 0.719883i | \(-0.744195\pi\) | ||||
−0.694095 | + | 0.719883i | \(0.744195\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 73.9698i | 0.0755565i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −107.823 | −0.109912 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 1315.51i | − | 1.33826i | −0.743146 | − | 0.669129i | \(-0.766667\pi\) | ||
0.743146 | − | 0.669129i | \(-0.233333\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1087.75i | 1.10432i | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 418.441 | − | 212.277i | 0.423952 | − | 0.215073i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −195.265 | −0.197437 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1043.28 | −1.05275 | −0.526377 | − | 0.850251i | \(-0.676450\pi\) | ||||
−0.526377 | + | 0.850251i | \(0.676450\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 575.677i | − | 0.579736i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1005.48 | 1.01054 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 820.328i | − | 0.822796i | −0.911456 | − | 0.411398i | \(-0.865041\pi\) | ||
0.911456 | − | 0.411398i | \(-0.134959\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 368.468i | 0.368837i |
(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 | 1344.3.f.e.769.2 | 4 | ||
4.3 | odd | 2 | 1344.3.f.f.769.4 | 4 | |||
7.6 | odd | 2 | inner | 1344.3.f.e.769.3 | 4 | ||
8.3 | odd | 2 | 42.3.c.a.13.1 | ✓ | 4 | ||
8.5 | even | 2 | 336.3.f.c.97.3 | 4 | |||
24.5 | odd | 2 | 1008.3.f.g.433.4 | 4 | |||
24.11 | even | 2 | 126.3.c.b.55.4 | 4 | |||
28.27 | even | 2 | 1344.3.f.f.769.1 | 4 | |||
40.3 | even | 4 | 1050.3.h.a.349.7 | 8 | |||
40.19 | odd | 2 | 1050.3.f.a.601.4 | 4 | |||
40.27 | even | 4 | 1050.3.h.a.349.2 | 8 | |||
56.3 | even | 6 | 294.3.g.c.19.2 | 4 | |||
56.11 | odd | 6 | 294.3.g.b.19.2 | 4 | |||
56.13 | odd | 2 | 336.3.f.c.97.2 | 4 | |||
56.19 | even | 6 | 294.3.g.b.31.2 | 4 | |||
56.27 | even | 2 | 42.3.c.a.13.2 | yes | 4 | ||
56.51 | odd | 6 | 294.3.g.c.31.2 | 4 | |||
168.11 | even | 6 | 882.3.n.a.19.1 | 4 | |||
168.59 | odd | 6 | 882.3.n.d.19.1 | 4 | |||
168.83 | odd | 2 | 126.3.c.b.55.3 | 4 | |||
168.107 | even | 6 | 882.3.n.d.325.1 | 4 | |||
168.125 | even | 2 | 1008.3.f.g.433.1 | 4 | |||
168.131 | odd | 6 | 882.3.n.a.325.1 | 4 | |||
280.27 | odd | 4 | 1050.3.h.a.349.3 | 8 | |||
280.83 | odd | 4 | 1050.3.h.a.349.6 | 8 | |||
280.139 | even | 2 | 1050.3.f.a.601.3 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
42.3.c.a.13.1 | ✓ | 4 | 8.3 | odd | 2 | ||
42.3.c.a.13.2 | yes | 4 | 56.27 | even | 2 | ||
126.3.c.b.55.3 | 4 | 168.83 | odd | 2 | |||
126.3.c.b.55.4 | 4 | 24.11 | even | 2 | |||
294.3.g.b.19.2 | 4 | 56.11 | odd | 6 | |||
294.3.g.b.31.2 | 4 | 56.19 | even | 6 | |||
294.3.g.c.19.2 | 4 | 56.3 | even | 6 | |||
294.3.g.c.31.2 | 4 | 56.51 | odd | 6 | |||
336.3.f.c.97.2 | 4 | 56.13 | odd | 2 | |||
336.3.f.c.97.3 | 4 | 8.5 | even | 2 | |||
882.3.n.a.19.1 | 4 | 168.11 | even | 6 | |||
882.3.n.a.325.1 | 4 | 168.131 | odd | 6 | |||
882.3.n.d.19.1 | 4 | 168.59 | odd | 6 | |||
882.3.n.d.325.1 | 4 | 168.107 | even | 6 | |||
1008.3.f.g.433.1 | 4 | 168.125 | even | 2 | |||
1008.3.f.g.433.4 | 4 | 24.5 | odd | 2 | |||
1050.3.f.a.601.3 | 4 | 280.139 | even | 2 | |||
1050.3.f.a.601.4 | 4 | 40.19 | odd | 2 | |||
1050.3.h.a.349.2 | 8 | 40.27 | even | 4 | |||
1050.3.h.a.349.3 | 8 | 280.27 | odd | 4 | |||
1050.3.h.a.349.6 | 8 | 280.83 | odd | 4 | |||
1050.3.h.a.349.7 | 8 | 40.3 | even | 4 | |||
1344.3.f.e.769.2 | 4 | 1.1 | even | 1 | trivial | ||
1344.3.f.e.769.3 | 4 | 7.6 | odd | 2 | inner | ||
1344.3.f.f.769.1 | 4 | 28.27 | even | 2 | |||
1344.3.f.f.769.4 | 4 | 4.3 | odd | 2 |