Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1050,3,Mod(601,1050)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1050, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("1050.601");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1050.f (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(28.6104277578\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
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: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 42) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 601.4 | ||
Root | \(0.707107 + 1.22474i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1050.601 |
Dual form | 1050.3.f.a.601.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(451\) | \(701\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.41421 | 0.707107 | ||||||||
\(3\) | 1.73205i | 0.577350i | ||||||||
\(4\) | 2.00000 | 0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 2.44949i | 0.408248i | ||||||||
\(7\) | −6.24264 | + | 3.16693i | −0.891806 | + | 0.452418i | ||||
\(8\) | 2.82843 | 0.353553 | ||||||||
\(9\) | −3.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.75736 | −0.159760 | −0.0798800 | − | 0.996804i | \(-0.525454\pi\) | ||||
−0.0798800 | + | 0.996804i | \(0.525454\pi\) | |||||||
\(12\) | 3.46410i | 0.288675i | ||||||||
\(13\) | − | 18.7554i | − | 1.44272i | −0.692559 | − | 0.721361i | \(-0.743517\pi\) | ||
0.692559 | − | 0.721361i | \(-0.256483\pi\) | |||||||
\(14\) | −8.82843 | + | 4.47871i | −0.630602 | + | 0.319908i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 4.00000 | 0.250000 | ||||||||
\(17\) | − | 23.4803i | − | 1.38119i | −0.723240 | − | 0.690597i | \(-0.757348\pi\) | ||
0.723240 | − | 0.690597i | \(-0.242652\pi\) | |||||||
\(18\) | −4.24264 | −0.235702 | ||||||||
\(19\) | − | 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 | ||||
\(22\) | −2.48528 | −0.112967 | ||||||||
\(23\) | −18.7279 | −0.814257 | −0.407129 | − | 0.913371i | \(-0.633470\pi\) | ||||
−0.407129 | + | 0.913371i | \(0.633470\pi\) | |||||||
\(24\) | 4.89898i | 0.204124i | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | − | 26.5241i | − | 1.02016i | ||||||
\(27\) | − | 5.19615i | − | 0.192450i | ||||||
\(28\) | −12.4853 | + | 6.33386i | −0.445903 | + | 0.226209i | ||||
\(29\) | 30.0000 | 1.03448 | 0.517241 | − | 0.855840i | \(-0.326959\pi\) | ||||
0.517241 | + | 0.855840i | \(0.326959\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 8.60927i | 0.277718i | 0.990312 | + | 0.138859i | \(0.0443435\pi\) | ||||
−0.990312 | + | 0.138859i | \(0.955656\pi\) | |||||||
\(32\) | 5.65685 | 0.176777 | ||||||||
\(33\) | − | 3.04384i | − | 0.0922374i | ||||||
\(34\) | − | 33.2061i | − | 0.976651i | ||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −6.00000 | −0.166667 | ||||||||
\(37\) | 70.9117 | 1.91653 | 0.958266 | − | 0.285878i | \(-0.0922852\pi\) | ||||
0.958266 | + | 0.285878i | \(0.0922852\pi\) | |||||||
\(38\) | − | 32.6118i | − | 0.858205i | ||||||
\(39\) | 32.4853 | 0.832956 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 41.3951i | 1.00964i | 0.863225 | + | 0.504819i | \(0.168441\pi\) | ||||
−0.863225 | + | 0.504819i | \(0.831559\pi\) | |||||||
\(42\) | −7.75736 | − | 15.2913i | −0.184699 | − | 0.364078i | ||||
\(43\) | −10.4264 | −0.242475 | −0.121237 | − | 0.992624i | \(-0.538686\pi\) | ||||
−0.121237 | + | 0.992624i | \(0.538686\pi\) | |||||||
\(44\) | −3.51472 | −0.0798800 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −26.4853 | −0.575767 | ||||||||
\(47\) | − | 38.6995i | − | 0.823393i | −0.911321 | − | 0.411696i | \(-0.864936\pi\) | ||
0.911321 | − | 0.411696i | \(-0.135064\pi\) | |||||||
\(48\) | 6.92820i | 0.144338i | ||||||||
\(49\) | 28.9411 | − | 39.5400i | 0.590635 | − | 0.806939i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 40.6690 | 0.797432 | ||||||||
\(52\) | − | 37.5108i | − | 0.721361i | ||||||
\(53\) | 37.0294 | 0.698669 | 0.349334 | − | 0.936998i | \(-0.386408\pi\) | ||||
0.349334 | + | 0.936998i | \(0.386408\pi\) | |||||||
\(54\) | − | 7.34847i | − | 0.136083i | ||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −17.6569 | + | 8.95743i | −0.315301 | + | 0.159954i | ||||
\(57\) | 39.9411 | 0.700721 | ||||||||
\(58\) | 42.4264 | 0.731490 | ||||||||
\(59\) | − | 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 | \(0.0437781\pi\) | ||||
−0.990557 | + | 0.137100i | \(0.956222\pi\) | |||||||
\(62\) | 12.1753i | 0.196376i | ||||||||
\(63\) | 18.7279 | − | 9.50079i | 0.297269 | − | 0.150806i | ||||
\(64\) | 8.00000 | 0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | − | 4.30463i | − | 0.0652217i | ||||||
\(67\) | −60.9706 | −0.910008 | −0.455004 | − | 0.890489i | \(-0.650362\pi\) | ||||
−0.455004 | + | 0.890489i | \(0.650362\pi\) | |||||||
\(68\) | − | 46.9606i | − | 0.690597i | ||||||
\(69\) | − | 32.4377i | − | 0.470112i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −110.610 | −1.55789 | −0.778945 | − | 0.627092i | \(-0.784245\pi\) | ||||
−0.778945 | + | 0.627092i | \(0.784245\pi\) | |||||||
\(72\) | −8.48528 | −0.117851 | ||||||||
\(73\) | 56.7585i | 0.777514i | 0.921340 | + | 0.388757i | \(0.127095\pi\) | ||||
−0.921340 | + | 0.388757i | \(0.872905\pi\) | |||||||
\(74\) | 100.284 | 1.35519 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | − | 46.1200i | − | 0.606843i | ||||||
\(77\) | 10.9706 | − | 5.56543i | 0.142475 | − | 0.0722783i | ||||
\(78\) | 45.9411 | 0.588989 | ||||||||
\(79\) | −69.8234 | −0.883840 | −0.441920 | − | 0.897054i | \(-0.645703\pi\) | ||||
−0.441920 | + | 0.897054i | \(0.645703\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 9.00000 | 0.111111 | ||||||||
\(82\) | 58.5416i | 0.713922i | ||||||||
\(83\) | − | 6.43583i | − | 0.0775401i | −0.999248 | − | 0.0387701i | \(-0.987656\pi\) | ||
0.999248 | − | 0.0387701i | \(-0.0123440\pi\) | |||||||
\(84\) | −10.9706 | − | 21.6251i | −0.130602 | − | 0.257442i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −14.7452 | −0.171455 | ||||||||
\(87\) | 51.9615i | 0.597259i | ||||||||
\(88\) | −4.97056 | −0.0564837 | ||||||||
\(89\) | − | 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 | ||||
\(92\) | −37.4558 | −0.407129 | ||||||||
\(93\) | −14.9117 | −0.160341 | ||||||||
\(94\) | − | 54.7293i | − | 0.582227i | ||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 9.79796i | 0.102062i | ||||||||
\(97\) | − | 51.7153i | − | 0.533148i | −0.963814 | − | 0.266574i | \(-0.914108\pi\) | ||
0.963814 | − | 0.266574i | \(-0.0858916\pi\) | |||||||
\(98\) | 40.9289 | − | 55.9180i | 0.417642 | − | 0.570592i | ||||
\(99\) | 5.27208 | 0.0532533 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 6.60991i | 0.0654447i | 0.999464 | + | 0.0327223i | \(0.0104177\pi\) | ||||
−0.999464 | + | 0.0327223i | \(0.989582\pi\) | |||||||
\(102\) | 57.5147 | 0.563870 | ||||||||
\(103\) | − | 175.871i | − | 1.70748i | −0.520696 | − | 0.853742i | \(-0.674327\pi\) | ||
0.520696 | − | 0.853742i | \(-0.325673\pi\) | |||||||
\(104\) | − | 53.0482i | − | 0.510079i | ||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 52.3675 | 0.494033 | ||||||||
\(107\) | 46.2426 | 0.432174 | 0.216087 | − | 0.976374i | \(-0.430670\pi\) | ||||
0.216087 | + | 0.976374i | \(0.430670\pi\) | |||||||
\(108\) | − | 10.3923i | − | 0.0962250i | ||||||
\(109\) | −35.9411 | −0.329735 | −0.164868 | − | 0.986316i | \(-0.552720\pi\) | ||||
−0.164868 | + | 0.986316i | \(0.552720\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 122.823i | 1.10651i | ||||||||
\(112\) | −24.9706 | + | 12.6677i | −0.222951 | + | 0.113105i | ||||
\(113\) | 73.0294 | 0.646278 | 0.323139 | − | 0.946351i | \(-0.395262\pi\) | ||||
0.323139 | + | 0.946351i | \(0.395262\pi\) | |||||||
\(114\) | 56.4853 | 0.495485 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 60.0000 | 0.517241 | ||||||||
\(117\) | 56.2662i | 0.480907i | ||||||||
\(118\) | − | 137.868i | − | 1.16837i | ||||||
\(119\) | 74.3604 | + | 146.579i | 0.624877 | + | 1.23176i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −117.912 | −0.974477 | ||||||||
\(122\) | 23.6544i | 0.193888i | ||||||||
\(123\) | −71.6985 | −0.582915 | ||||||||
\(124\) | 17.2185i | 0.138859i | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 26.4853 | − | 13.4361i | 0.210201 | − | 0.106636i | ||||
\(127\) | −89.9411 | −0.708198 | −0.354099 | − | 0.935208i | \(-0.615212\pi\) | ||||
−0.354099 | + | 0.935208i | \(0.615212\pi\) | |||||||
\(128\) | 11.3137 | 0.0883883 | ||||||||
\(129\) | − | 18.0591i | − | 0.139993i | ||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 12.1753i | 0.0929415i | 0.998920 | + | 0.0464708i | \(0.0147974\pi\) | ||||
−0.998920 | + | 0.0464708i | \(0.985203\pi\) | |||||||
\(132\) | − | 6.08767i | − | 0.0461187i | ||||||
\(133\) | 73.0294 | + | 143.955i | 0.549094 | + | 1.08237i | ||||
\(134\) | −86.2254 | −0.643473 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | − | 66.4123i | − | 0.488326i | ||||||
\(137\) | −165.765 | −1.20996 | −0.604980 | − | 0.796241i | \(-0.706819\pi\) | ||||
−0.604980 | + | 0.796241i | \(0.706819\pi\) | |||||||
\(138\) | − | 45.8739i | − | 0.332419i | ||||||
\(139\) | − | 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 | ||||||||
\(142\) | −156.426 | −1.10159 | ||||||||
\(143\) | 32.9600i | 0.230489i | ||||||||
\(144\) | −12.0000 | −0.0833333 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 80.2687i | 0.549786i | ||||||||
\(147\) | 68.4853 | + | 50.1275i | 0.465886 | + | 0.341003i | ||||
\(148\) | 141.823 | 0.958266 | ||||||||
\(149\) | 210.853 | 1.41512 | 0.707560 | − | 0.706653i | \(-0.249796\pi\) | ||||
0.707560 | + | 0.706653i | \(0.249796\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −72.3675 | −0.479255 | −0.239628 | − | 0.970865i | \(-0.577025\pi\) | ||||
−0.239628 | + | 0.970865i | \(0.577025\pi\) | |||||||
\(152\) | − | 65.2236i | − | 0.429103i | ||||||
\(153\) | 70.4409i | 0.460398i | ||||||||
\(154\) | 15.5147 | − | 7.87071i | 0.100745 | − | 0.0511085i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 64.9706 | 0.416478 | ||||||||
\(157\) | − | 233.674i | − | 1.48837i | −0.667974 | − | 0.744184i | \(-0.732838\pi\) | ||
0.667974 | − | 0.744184i | \(-0.267162\pi\) | |||||||
\(158\) | −98.7452 | −0.624969 | ||||||||
\(159\) | 64.1369i | 0.403377i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 116.912 | − | 59.3100i | 0.726160 | − | 0.368385i | ||||
\(162\) | 12.7279 | 0.0785674 | ||||||||
\(163\) | 73.0883 | 0.448395 | 0.224197 | − | 0.974544i | \(-0.428024\pi\) | ||||
0.224197 | + | 0.974544i | \(0.428024\pi\) | |||||||
\(164\) | 82.7903i | 0.504819i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | − | 9.10164i | − | 0.0548292i | ||||||
\(167\) | 39.3958i | 0.235903i | 0.993019 | + | 0.117951i | \(0.0376327\pi\) | ||||
−0.993019 | + | 0.117951i | \(0.962367\pi\) | |||||||
\(168\) | −15.5147 | − | 30.5826i | −0.0923495 | − | 0.182039i | ||||
\(169\) | −182.765 | −1.08145 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 69.1801i | 0.404562i | ||||||||
\(172\) | −20.8528 | −0.121237 | ||||||||
\(173\) | − | 23.8284i | − | 0.137737i | −0.997626 | − | 0.0688683i | \(-0.978061\pi\) | ||
0.997626 | − | 0.0688683i | \(-0.0219388\pi\) | |||||||
\(174\) | 73.4847i | 0.422326i | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −7.02944 | −0.0399400 | ||||||||
\(177\) | 168.853 | 0.953971 | ||||||||
\(178\) | − | 59.5263i | − | 0.334417i | ||||||
\(179\) | −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 | \(0.0577955\pi\) | ||||
−0.983561 | + | 0.180574i | \(0.942204\pi\) | |||||||
\(182\) | 84.0000 | + | 165.581i | 0.461538 | + | 0.909783i | ||||
\(183\) | −28.9706 | −0.158309 | ||||||||
\(184\) | −52.9706 | −0.287883 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −21.0883 | −0.113378 | ||||||||
\(187\) | 41.2633i | 0.220659i | ||||||||
\(188\) | − | 77.3989i | − | 0.411696i | ||||||
\(189\) | 16.4558 | + | 32.4377i | 0.0870680 | + | 0.171628i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −100.066 | −0.523906 | −0.261953 | − | 0.965081i | \(-0.584367\pi\) | ||||
−0.261953 | + | 0.965081i | \(0.584367\pi\) | |||||||
\(192\) | 13.8564i | 0.0721688i | ||||||||
\(193\) | −78.9117 | −0.408869 | −0.204434 | − | 0.978880i | \(-0.565536\pi\) | ||||
−0.204434 | + | 0.978880i | \(0.565536\pi\) | |||||||
\(194\) | − | 73.1365i | − | 0.376992i | ||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 57.8823 | − | 79.0800i | 0.295318 | − | 0.403469i | ||||
\(197\) | 183.941 | 0.933711 | 0.466856 | − | 0.884334i | \(-0.345387\pi\) | ||||
0.466856 | + | 0.884334i | \(0.345387\pi\) | |||||||
\(198\) | 7.45584 | 0.0376558 | ||||||||
\(199\) | 170.029i | 0.854419i | 0.904153 | + | 0.427210i | \(0.140503\pi\) | ||||
−0.904153 | + | 0.427210i | \(0.859497\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | − | 105.604i | − | 0.525394i | ||||||
\(202\) | 9.34783i | 0.0462764i | ||||||||
\(203\) | −187.279 | + | 95.0079i | −0.922558 | + | 0.468019i | ||||
\(204\) | 81.3381 | 0.398716 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | − | 248.719i | − | 1.20737i | ||||||
\(207\) | 56.1838 | 0.271419 | ||||||||
\(208\) | − | 75.0215i | − | 0.360680i | ||||||
\(209\) | 40.5247i | 0.193898i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 21.5736 | 0.102245 | 0.0511223 | − | 0.998692i | \(-0.483720\pi\) | ||||
0.0511223 | + | 0.998692i | \(0.483720\pi\) | |||||||
\(212\) | 74.0589 | 0.349334 | ||||||||
\(213\) | − | 191.582i | − | 0.899448i | ||||||
\(214\) | 65.3970 | 0.305593 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | − | 14.6969i | − | 0.0680414i | ||||||
\(217\) | −27.2649 | − | 53.7446i | −0.125645 | − | 0.247671i | ||||
\(218\) | −50.8284 | −0.233158 | ||||||||
\(219\) | −98.3087 | −0.448898 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −440.382 | −1.99268 | ||||||||
\(222\) | 173.697i | 0.782421i | ||||||||
\(223\) | 119.359i | 0.535240i | 0.963525 | + | 0.267620i | \(0.0862372\pi\) | ||||
−0.963525 | + | 0.267620i | \(0.913763\pi\) | |||||||
\(224\) | −35.3137 | + | 17.9149i | −0.157650 | + | 0.0799770i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 103.279 | 0.456988 | ||||||||
\(227\) | 169.843i | 0.748207i | 0.927387 | + | 0.374103i | \(0.122049\pi\) | ||||
−0.927387 | + | 0.374103i | \(0.877951\pi\) | |||||||
\(228\) | 79.8823 | 0.350361 | ||||||||
\(229\) | − | 110.011i | − | 0.480396i | −0.970724 | − | 0.240198i | \(-0.922788\pi\) | ||
0.970724 | − | 0.240198i | \(-0.0772124\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 9.63961 | + | 19.0016i | 0.0417299 | + | 0.0822579i | ||||
\(232\) | 84.8528 | 0.365745 | ||||||||
\(233\) | −57.2649 | −0.245772 | −0.122886 | − | 0.992421i | \(-0.539215\pi\) | ||||
−0.122886 | + | 0.992421i | \(0.539215\pi\) | |||||||
\(234\) | 79.5724i | 0.340053i | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | − | 194.974i | − | 0.826163i | ||||||
\(237\) | − | 120.938i | − | 0.510285i | ||||||
\(238\) | 105.161 | + | 207.294i | 0.441855 | + | 0.870983i | ||||
\(239\) | 281.522 | 1.17792 | 0.588958 | − | 0.808164i | \(-0.299538\pi\) | ||||
0.588958 | + | 0.808164i | \(0.299538\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 168.306i | 0.698366i | 0.937055 | + | 0.349183i | \(0.113541\pi\) | ||||
−0.937055 | + | 0.349183i | \(0.886459\pi\) | |||||||
\(242\) | −166.752 | −0.689059 | ||||||||
\(243\) | 15.5885i | 0.0641500i | ||||||||
\(244\) | 33.4523i | 0.137100i | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −101.397 | −0.412183 | ||||||||
\(247\) | −432.500 | −1.75101 | ||||||||
\(248\) | 24.3507i | 0.0981882i | ||||||||
\(249\) | 11.1472 | 0.0447678 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 106.096i | 0.422695i | 0.977411 | + | 0.211348i | \(0.0677852\pi\) | ||||
−0.977411 | + | 0.211348i | \(0.932215\pi\) | |||||||
\(252\) | 37.4558 | − | 19.0016i | 0.148634 | − | 0.0754031i | ||||
\(253\) | 32.9117 | 0.130086 | ||||||||
\(254\) | −127.196 | −0.500771 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 16.0000 | 0.0625000 | ||||||||
\(257\) | 290.462i | 1.13020i | 0.825021 | + | 0.565102i | \(0.191163\pi\) | ||||
−0.825021 | + | 0.565102i | \(0.808837\pi\) | |||||||
\(258\) | − | 25.5394i | − | 0.0989898i | ||||||
\(259\) | −442.676 | + | 224.572i | −1.70917 | + | 0.867074i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −90.0000 | −0.344828 | ||||||||
\(262\) | 17.2185i | 0.0657196i | ||||||||
\(263\) | 89.0223 | 0.338488 | 0.169244 | − | 0.985574i | \(-0.445867\pi\) | ||||
0.169244 | + | 0.985574i | \(0.445867\pi\) | |||||||
\(264\) | − | 8.60927i | − | 0.0326109i | ||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 103.279 | + | 203.584i | 0.388268 | + | 0.765352i | ||||
\(267\) | 72.9045 | 0.273051 | ||||||||
\(268\) | −121.941 | −0.455004 | ||||||||
\(269\) | 191.498i | 0.711888i | 0.934507 | + | 0.355944i | \(0.115841\pi\) | ||||
−0.934507 | + | 0.355944i | \(0.884159\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 217.440i | − | 0.802362i | −0.915999 | − | 0.401181i | \(-0.868600\pi\) | ||
0.915999 | − | 0.401181i | \(-0.131400\pi\) | |||||||
\(272\) | − | 93.9211i | − | 0.345298i | ||||||
\(273\) | −202.794 | + | 102.879i | −0.742835 | + | 0.376845i | ||||
\(274\) | −234.426 | −0.855571 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | − | 64.8754i | − | 0.235056i | ||||||
\(277\) | −290.676 | −1.04937 | −0.524686 | − | 0.851296i | \(-0.675817\pi\) | ||||
−0.524686 | + | 0.851296i | \(0.675817\pi\) | |||||||
\(278\) | − | 311.854i | − | 1.12178i | ||||||
\(279\) | − | 25.8278i | − | 0.0925728i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 18.8528 | 0.0670919 | 0.0335459 | − | 0.999437i | \(-0.489320\pi\) | ||||
0.0335459 | + | 0.999437i | \(0.489320\pi\) | |||||||
\(282\) | 94.7939 | 0.336149 | ||||||||
\(283\) | 401.734i | 1.41955i | 0.704426 | + | 0.709777i | \(0.251204\pi\) | ||||
−0.704426 | + | 0.709777i | \(0.748796\pi\) | |||||||
\(284\) | −221.220 | −0.778945 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 46.6124i | 0.162980i | ||||||||
\(287\) | −131.095 | − | 258.415i | −0.456779 | − | 0.900401i | ||||
\(288\) | −16.9706 | −0.0589256 | ||||||||
\(289\) | −262.324 | −0.907695 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 89.5736 | 0.307813 | ||||||||
\(292\) | 113.517i | 0.388757i | ||||||||
\(293\) | 280.893i | 0.958679i | 0.877629 | + | 0.479340i | \(0.159124\pi\) | ||||
−0.877629 | + | 0.479340i | \(0.840876\pi\) | |||||||
\(294\) | 96.8528 | + | 70.8910i | 0.329431 | + | 0.241126i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 200.569 | 0.677596 | ||||||||
\(297\) | 9.13151i | 0.0307458i | ||||||||
\(298\) | 298.191 | 1.00064 | ||||||||
\(299\) | 351.249i | 1.17475i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 65.0883 | − | 33.0197i | 0.216240 | − | 0.109700i | ||||
\(302\) | −102.343 | −0.338885 | ||||||||
\(303\) | −11.4487 | −0.0377845 | ||||||||
\(304\) | − | 92.2401i | − | 0.303421i | ||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 99.6184i | 0.325550i | ||||||||
\(307\) | − | 152.318i | − | 0.496151i | −0.968741 | − | 0.248076i | \(-0.920202\pi\) | ||
0.968741 | − | 0.248076i | \(-0.0797982\pi\) | |||||||
\(308\) | 21.9411 | − | 11.1309i | 0.0712374 | − | 0.0361392i | ||||
\(309\) | 304.617 | 0.985817 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 283.156i | − | 0.910470i | −0.890371 | − | 0.455235i | \(-0.849555\pi\) | ||
0.890371 | − | 0.455235i | \(-0.150445\pi\) | |||||||
\(312\) | 91.8823 | 0.294494 | ||||||||
\(313\) | − | 48.5819i | − | 0.155214i | −0.996984 | − | 0.0776069i | \(-0.975272\pi\) | ||
0.996984 | − | 0.0776069i | \(-0.0247279\pi\) | |||||||
\(314\) | − | 330.465i | − | 1.05244i | ||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −139.647 | −0.441920 | ||||||||
\(317\) | 578.029 | 1.82343 | 0.911717 | − | 0.410819i | \(-0.134757\pi\) | ||||
0.911717 | + | 0.410819i | \(0.134757\pi\) | |||||||
\(318\) | 90.7032i | 0.285230i | ||||||||
\(319\) | −52.7208 | −0.165269 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 80.0946i | 0.249516i | ||||||||
\(322\) | 165.338 | − | 83.8770i | 0.513472 | − | 0.260488i | ||||
\(323\) | −541.456 | −1.67633 | ||||||||
\(324\) | 18.0000 | 0.0555556 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 103.362 | 0.317063 | ||||||||
\(327\) | − | 62.2519i | − | 0.190373i | ||||||
\(328\) | 117.083i | 0.356961i | ||||||||
\(329\) | 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 | \(0.332574\pi\) | |||||||
\(332\) | − | 12.8717i | − | 0.0387701i | ||||||
\(333\) | −212.735 | −0.638844 | ||||||||
\(334\) | 55.7141i | 0.166809i | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −21.9411 | − | 43.2503i | −0.0653010 | − | 0.128721i | ||||
\(337\) | −88.1766 | −0.261652 | −0.130826 | − | 0.991405i | \(-0.541763\pi\) | ||||
−0.130826 | + | 0.991405i | \(0.541763\pi\) | |||||||
\(338\) | −258.468 | −0.764698 | ||||||||
\(339\) | 126.491i | 0.373129i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 15.1296i | − | 0.0443683i | ||||||
\(342\) | 97.8354i | 0.286068i | ||||||||
\(343\) | −55.4487 | + | 338.488i | −0.161658 | + | 0.986847i | ||||
\(344\) | −29.4903 | −0.0857277 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | − | 33.6985i | − | 0.0973945i | ||||||
\(347\) | 320.080 | 0.922422 | 0.461211 | − | 0.887291i | \(-0.347415\pi\) | ||||
0.461211 | + | 0.887291i | \(0.347415\pi\) | |||||||
\(348\) | 103.923i | 0.298629i | ||||||||
\(349\) | − | 333.046i | − | 0.954287i | −0.878825 | − | 0.477143i | \(-0.841672\pi\) | ||
0.878825 | − | 0.477143i | \(-0.158328\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −97.4558 | −0.277652 | ||||||||
\(352\) | −9.94113 | −0.0282418 | ||||||||
\(353\) | 655.712i | 1.85754i | 0.370654 | + | 0.928771i | \(0.379134\pi\) | ||||
−0.370654 | + | 0.928771i | \(0.620866\pi\) | |||||||
\(354\) | 238.794 | 0.674559 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | − | 84.1829i | − | 0.236469i | ||||||
\(357\) | −253.882 | + | 128.796i | −0.711155 | + | 0.360773i | ||||
\(358\) | −18.2498 | −0.0509770 | ||||||||
\(359\) | −97.7574 | −0.272305 | −0.136152 | − | 0.990688i | \(-0.543474\pi\) | ||||
−0.136152 | + | 0.990688i | \(0.543474\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −170.765 | −0.473032 | ||||||||
\(362\) | 92.4440i | 0.255370i | ||||||||
\(363\) | − | 204.229i | − | 0.562614i | ||||||
\(364\) | 118.794 | + | 234.166i | 0.326357 | + | 0.643314i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −40.9706 | −0.111941 | ||||||||
\(367\) | 321.057i | 0.874815i | 0.899263 | + | 0.437408i | \(0.144103\pi\) | ||||
−0.899263 | + | 0.437408i | \(0.855897\pi\) | |||||||
\(368\) | −74.9117 | −0.203564 | ||||||||
\(369\) | − | 124.185i | − | 0.336546i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −231.161 | + | 117.270i | −0.623077 | + | 0.316091i | ||||
\(372\) | −29.8234 | −0.0801704 | ||||||||
\(373\) | −187.470 | −0.502601 | −0.251300 | − | 0.967909i | \(-0.580858\pi\) | ||||
−0.251300 | + | 0.967909i | \(0.580858\pi\) | |||||||
\(374\) | 58.3551i | 0.156030i | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | − | 109.459i | − | 0.291113i | ||||||
\(377\) | − | 562.662i | − | 1.49247i | ||||||
\(378\) | 23.2721 | + | 45.8739i | 0.0615663 | + | 0.121359i | ||||
\(379\) | −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 | ||||||
\(382\) | −141.515 | −0.370457 | ||||||||
\(383\) | − | 622.230i | − | 1.62462i | −0.583225 | − | 0.812311i | \(-0.698209\pi\) | ||
0.583225 | − | 0.812311i | \(-0.301791\pi\) | |||||||
\(384\) | 19.5959i | 0.0510310i | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −111.598 | −0.289114 | ||||||||
\(387\) | 31.2792 | 0.0808249 | ||||||||
\(388\) | − | 103.431i | − | 0.266574i | ||||||
\(389\) | 227.470 | 0.584756 | 0.292378 | − | 0.956303i | \(-0.405553\pi\) | ||||
0.292378 | + | 0.956303i | \(0.405553\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 439.737i | 1.12465i | ||||||||
\(392\) | 81.8579 | − | 111.836i | 0.208821 | − | 0.285296i | ||||
\(393\) | −21.0883 | −0.0536598 | ||||||||
\(394\) | 260.132 | 0.660234 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 10.5442 | 0.0266267 | ||||||||
\(397\) | − | 720.329i | − | 1.81443i | −0.420666 | − | 0.907216i | \(-0.638204\pi\) | ||
0.420666 | − | 0.907216i | \(-0.361796\pi\) | |||||||
\(398\) | 240.458i | 0.604166i | ||||||||
\(399\) | −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 | \(0.164572\pi\) | |||||||
\(402\) | − | 149.347i | − | 0.371509i | ||||||
\(403\) | 161.470 | 0.400670 | ||||||||
\(404\) | 13.2198i | 0.0327223i | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −264.853 | + | 134.361i | −0.652347 | + | 0.330939i | ||||
\(407\) | −124.617 | −0.306185 | ||||||||
\(408\) | 115.029 | 0.281935 | ||||||||
\(409\) | 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 | ||||||
\(412\) | − | 351.742i | − | 0.853742i | ||||||
\(413\) | 308.735 | + | 608.578i | 0.747543 | + | 1.47355i | ||||
\(414\) | 79.4558 | 0.191922 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | − | 106.096i | − | 0.255040i | ||||||
\(417\) | 381.941 | 0.915926 | ||||||||
\(418\) | 57.3106i | 0.137107i | ||||||||
\(419\) | 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 | \(-0.361696\pi\) | ||||
0.420951 | + | 0.907083i | \(0.361696\pi\) | |||||||
\(422\) | 30.5097 | 0.0722978 | ||||||||
\(423\) | 116.098i | 0.274464i | ||||||||
\(424\) | 104.735 | 0.247017 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | − | 270.938i | − | 0.636006i | ||||||
\(427\) | −52.9706 | − | 104.415i | −0.124053 | − | 0.244533i | ||||
\(428\) | 92.4853 | 0.216087 | ||||||||
\(429\) | −57.0883 | −0.133073 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 585.286 | 1.35797 | 0.678987 | − | 0.734151i | \(-0.262419\pi\) | ||||
0.678987 | + | 0.734151i | \(0.262419\pi\) | |||||||
\(432\) | − | 20.7846i | − | 0.0481125i | ||||||
\(433\) | 392.207i | 0.905789i | 0.891564 | + | 0.452895i | \(0.149609\pi\) | ||||
−0.891564 | + | 0.452895i | \(0.850391\pi\) | |||||||
\(434\) | −38.5584 | − | 76.0063i | −0.0888443 | − | 0.175130i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −71.8823 | −0.164868 | ||||||||
\(437\) | 431.866i | 0.988252i | ||||||||
\(438\) | −139.029 | −0.317419 | ||||||||
\(439\) | − | 392.513i | − | 0.894106i | −0.894507 | − | 0.447053i | \(-0.852473\pi\) | ||
0.894507 | − | 0.447053i | \(-0.147527\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −86.8234 | + | 118.620i | −0.196878 | + | 0.268980i | ||||
\(442\) | −622.794 | −1.40904 | ||||||||
\(443\) | 814.742 | 1.83915 | 0.919574 | − | 0.392918i | \(-0.128534\pi\) | ||||
0.919574 | + | 0.392918i | \(0.128534\pi\) | |||||||
\(444\) | 245.645i | 0.553255i | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 168.798i | 0.378472i | ||||||||
\(447\) | 365.208i | 0.817020i | ||||||||
\(448\) | −49.9411 | + | 25.3354i | −0.111476 | + | 0.0565523i | ||||
\(449\) | 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 | ||||||
\(452\) | 146.059 | 0.323139 | ||||||||
\(453\) | − | 125.344i | − | 0.276698i | ||||||
\(454\) | 240.194i | 0.529062i | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 112.971 | 0.247742 | ||||||||
\(457\) | −280.177 | −0.613078 | −0.306539 | − | 0.951858i | \(-0.599171\pi\) | ||||
−0.306539 | + | 0.951858i | \(0.599171\pi\) | |||||||
\(458\) | − | 155.579i | − | 0.339691i | ||||||
\(459\) | −122.007 | −0.265811 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 406.297i | 0.881338i | 0.897670 | + | 0.440669i | \(0.145259\pi\) | ||||
−0.897670 | + | 0.440669i | \(0.854741\pi\) | |||||||
\(462\) | 13.6325 | + | 26.8723i | 0.0295075 | + | 0.0581651i | ||||
\(463\) | −457.470 | −0.988056 | −0.494028 | − | 0.869446i | \(-0.664476\pi\) | ||||
−0.494028 | + | 0.869446i | \(0.664476\pi\) | |||||||
\(464\) | 120.000 | 0.258621 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −80.9848 | −0.173787 | ||||||||
\(467\) | 643.711i | 1.37840i | 0.724573 | + | 0.689198i | \(0.242037\pi\) | ||||
−0.724573 | + | 0.689198i | \(0.757963\pi\) | |||||||
\(468\) | 112.532i | 0.240454i | ||||||||
\(469\) | 380.617 | − | 193.089i | 0.811551 | − | 0.411705i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 404.735 | 0.859310 | ||||||||
\(472\) | − | 275.735i | − | 0.584185i | ||||||
\(473\) | 18.3229 | 0.0387377 | ||||||||
\(474\) | − | 171.032i | − | 0.360826i | ||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 148.721 | + | 293.158i | 0.312439 | + | 0.615878i | ||||
\(477\) | −111.088 | −0.232890 | ||||||||
\(478\) | 398.132 | 0.832912 | ||||||||
\(479\) | 168.535i | 0.351847i | 0.984404 | + | 0.175924i | \(0.0562912\pi\) | ||||
−0.984404 | + | 0.175924i | \(0.943709\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − | 1329.98i | − | 2.76502i | ||||||
\(482\) | 238.021i | 0.493819i | ||||||||
\(483\) | 102.728 | + | 202.497i | 0.212687 | + | 0.419248i | ||||
\(484\) | −235.823 | −0.487238 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 22.0454i | 0.0453609i | ||||||||
\(487\) | 2.77965 | 0.00570771 | 0.00285385 | − | 0.999996i | \(-0.499092\pi\) | ||||
0.00285385 | + | 0.999996i | \(0.499092\pi\) | |||||||
\(488\) | 47.3087i | 0.0969441i | ||||||||
\(489\) | 126.593i | 0.258881i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −247.477 | −0.504027 | −0.252014 | − | 0.967724i | \(-0.581093\pi\) | ||||
−0.252014 | + | 0.967724i | \(0.581093\pi\) | |||||||
\(492\) | −143.397 | −0.291457 | ||||||||
\(493\) | − | 704.409i | − | 1.42882i | ||||||
\(494\) | −611.647 | −1.23815 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 34.4371i | 0.0694296i | ||||||||
\(497\) | 690.500 | − | 350.295i | 1.38934 | − | 0.704818i | ||||
\(498\) | 15.7645 | 0.0316556 | ||||||||
\(499\) | −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 | ||||||||
\(502\) | 150.043i | 0.298891i | ||||||||
\(503\) | − | 58.7033i | − | 0.116706i | −0.998296 | − | 0.0583532i | \(-0.981415\pi\) | ||
0.998296 | − | 0.0583532i | \(-0.0185849\pi\) | |||||||
\(504\) | 52.9706 | − | 26.8723i | 0.105100 | − | 0.0533180i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 46.5442 | 0.0919845 | ||||||||
\(507\) | − | 316.557i | − | 0.624374i | ||||||
\(508\) | −179.882 | −0.354099 | ||||||||
\(509\) | 68.8793i | 0.135323i | 0.997708 | + | 0.0676614i | \(0.0215537\pi\) | ||||
−0.997708 | + | 0.0676614i | \(0.978446\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −179.750 | − | 354.323i | −0.351762 | − | 0.693392i | ||||
\(512\) | 22.6274 | 0.0441942 | ||||||||
\(513\) | −119.823 | −0.233574 | ||||||||
\(514\) | 410.776i | 0.799175i | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | − | 36.1181i | − | 0.0699964i | ||||||
\(517\) | 68.0089i | 0.131545i | ||||||||
\(518\) | −626.039 | + | 317.593i | −1.20857 | + | 0.613114i | ||||
\(519\) | 41.2721 | 0.0795223 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 292.720i | 0.561843i | 0.959731 | + | 0.280922i | \(0.0906401\pi\) | ||||
−0.959731 | + | 0.280922i | \(0.909360\pi\) | |||||||
\(522\) | −127.279 | −0.243830 | ||||||||
\(523\) | − | 493.056i | − | 0.942746i | −0.881934 | − | 0.471373i | \(-0.843759\pi\) | ||
0.881934 | − | 0.471373i | \(-0.156241\pi\) | |||||||
\(524\) | 24.3507i | 0.0464708i | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 125.897 | 0.239347 | ||||||||
\(527\) | 202.148 | 0.383583 | ||||||||
\(528\) | − | 12.1753i | − | 0.0230594i | ||||||
\(529\) | −178.265 | −0.336985 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 292.462i | 0.550775i | ||||||||
\(532\) | 146.059 | + | 287.911i | 0.274547 | + | 0.541186i | ||||
\(533\) | 776.382 | 1.45663 | ||||||||
\(534\) | 103.103 | 0.193076 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −172.451 | −0.321737 | ||||||||
\(537\) | − | 22.3513i | − | 0.0416226i | ||||||
\(538\) | 270.819i | 0.503381i | ||||||||
\(539\) | −50.8600 | + | 69.4860i | −0.0943598 | + | 0.128916i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1037.85 | −1.91840 | −0.959198 | − | 0.282736i | \(-0.908758\pi\) | ||||
−0.959198 | + | 0.282736i | \(0.908758\pi\) | |||||||
\(542\) | − | 307.507i | − | 0.567356i | ||||||
\(543\) | −113.220 | −0.208509 | ||||||||
\(544\) | − | 132.825i | − | 0.244163i | ||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −286.794 | + | 145.492i | −0.525264 | + | 0.266469i | ||||
\(547\) | 130.530 | 0.238629 | 0.119314 | − | 0.992857i | \(-0.461930\pi\) | ||||
0.119314 | + | 0.992857i | \(0.461930\pi\) | |||||||
\(548\) | −331.529 | −0.604980 | ||||||||
\(549\) | − | 50.1785i | − | 0.0913998i | ||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 691.801i | − | 1.25554i | ||||||
\(552\) | − | 91.7477i | − | 0.166210i | ||||||
\(553\) | 435.882 | − | 221.126i | 0.788214 | − | 0.399866i | ||||
\(554\) | −411.078 | −0.742018 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | − | 441.028i | − | 0.793215i | ||||||
\(557\) | −665.147 | −1.19416 | −0.597080 | − | 0.802182i | \(-0.703673\pi\) | ||||
−0.597080 | + | 0.802182i | \(0.703673\pi\) | |||||||
\(558\) | − | 36.5260i | − | 0.0654588i | ||||||
\(559\) | 195.551i | 0.349823i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −71.4701 | −0.127398 | ||||||||
\(562\) | 26.6619 | 0.0474411 | ||||||||
\(563\) | − | 829.295i | − | 1.47299i | −0.676441 | − | 0.736497i | \(-0.736479\pi\) | ||
0.676441 | − | 0.736497i | \(-0.263521\pi\) | |||||||
\(564\) | 134.059 | 0.237693 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 568.137i | 1.00378i | ||||||||
\(567\) | −56.1838 | + | 28.5024i | −0.0990895 | + | 0.0502687i | ||||
\(568\) | −312.853 | −0.550797 | ||||||||
\(569\) | 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 | \(0.604116\pi\) | |||||||
\(572\) | 65.9199i | 0.115245i | ||||||||
\(573\) | − | 173.319i | − | 0.302477i | ||||||
\(574\) | −185.397 | − | 365.454i | −0.322991 | − | 0.636679i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −24.0000 | −0.0416667 | ||||||||
\(577\) | 390.357i | 0.676528i | 0.941051 | + | 0.338264i | \(0.109840\pi\) | ||||
−0.941051 | + | 0.338264i | \(0.890160\pi\) | |||||||
\(578\) | −370.982 | −0.641837 | ||||||||
\(579\) | − | 136.679i | − | 0.236061i | ||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 20.3818 | + | 40.1766i | 0.0350806 | + | 0.0691507i | ||||
\(582\) | 126.676 | 0.217657 | ||||||||
\(583\) | −65.0740 | −0.111619 | ||||||||
\(584\) | 160.537i | 0.274893i | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 397.243i | 0.677889i | ||||||||
\(587\) | 702.499i | 1.19676i | 0.801212 | + | 0.598381i | \(0.204189\pi\) | ||||
−0.801212 | + | 0.598381i | \(0.795811\pi\) | |||||||
\(588\) | 136.971 | + | 100.255i | 0.232943 | + | 0.170502i | ||||
\(589\) | 198.530 | 0.337063 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 318.595i | 0.539078i | ||||||||
\(592\) | 283.647 | 0.479133 | ||||||||
\(593\) | − | 942.519i | − | 1.58941i | −0.606997 | − | 0.794704i | \(-0.707626\pi\) | ||
0.606997 | − | 0.794704i | \(-0.292374\pi\) | |||||||
\(594\) | 12.9139i | 0.0217406i | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 421.706 | 0.707560 | ||||||||
\(597\) | −294.500 | −0.493299 | ||||||||
\(598\) | 496.742i | 0.830672i | ||||||||
\(599\) | −952.109 | −1.58950 | −0.794749 | − | 0.606939i | \(-0.792397\pi\) | ||||
−0.794749 | + | 0.606939i | \(0.792397\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 729.804i | 1.21432i | 0.794581 | + | 0.607158i | \(0.207690\pi\) | ||||
−0.794581 | + | 0.607158i | \(0.792310\pi\) | |||||||
\(602\) | 92.0488 | − | 46.6969i | 0.152905 | − | 0.0775696i | ||||
\(603\) | 182.912 | 0.303336 | ||||||||
\(604\) | −144.735 | −0.239628 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −16.1909 | −0.0267177 | ||||||||
\(607\) | 1006.34i | 1.65789i | 0.559332 | + | 0.828944i | \(0.311058\pi\) | ||||
−0.559332 | + | 0.828944i | \(0.688942\pi\) | |||||||
\(608\) | − | 130.447i | − | 0.214551i | ||||||
\(609\) | −164.558 | − | 324.377i | −0.270211 | − | 0.532639i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −725.823 | −1.18793 | ||||||||
\(612\) | 140.882i | 0.230199i | ||||||||
\(613\) | 199.588 | 0.325592 | 0.162796 | − | 0.986660i | \(-0.447949\pi\) | ||||
0.162796 | + | 0.986660i | \(0.447949\pi\) | |||||||
\(614\) | − | 215.411i | − | 0.350832i | ||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 31.0294 | − | 15.7414i | 0.0503725 | − | 0.0255542i | ||||
\(617\) | 353.294 | 0.572599 | 0.286299 | − | 0.958140i | \(-0.407575\pi\) | ||||
0.286299 | + | 0.958140i | \(0.407575\pi\) | |||||||
\(618\) | 430.794 | 0.697078 | ||||||||
\(619\) | − | 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 | ||||||||
\(622\) | − | 400.443i | − | 0.643799i | ||||||
\(623\) | 133.301 | + | 262.762i | 0.213966 | + | 0.421769i | ||||
\(624\) | 129.941 | 0.208239 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | − | 68.7052i | − | 0.109753i | ||||||
\(627\) | −70.1909 | −0.111947 | ||||||||
\(628\) | − | 467.348i | − | 0.744184i | ||||||
\(629\) | − | 1665.03i | − | 2.64710i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 807.322 | 1.27943 | 0.639716 | − | 0.768611i | \(-0.279052\pi\) | ||||
0.639716 | + | 0.768611i | \(0.279052\pi\) | |||||||
\(632\) | −197.490 | −0.312485 | ||||||||
\(633\) | 37.3666i | 0.0590309i | ||||||||
\(634\) | 817.456 | 1.28936 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 128.274i | 0.201688i | ||||||||
\(637\) | −741.588 | − | 542.802i | −1.16419 | − | 0.852122i | ||||
\(638\) | −74.5584 | −0.116863 | ||||||||
\(639\) | 331.831 | 0.519297 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1016.35 | 1.58557 | 0.792786 | − | 0.609500i | \(-0.208630\pi\) | ||||
0.792786 | + | 0.609500i | \(0.208630\pi\) | |||||||
\(642\) | 113.271i | 0.176434i | ||||||||
\(643\) | 404.688i | 0.629375i | 0.949195 | + | 0.314687i | \(0.101900\pi\) | ||||
−0.949195 | + | 0.314687i | \(0.898100\pi\) | |||||||
\(644\) | 233.823 | − | 118.620i | 0.363080 | − | 0.184193i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −765.734 | −1.18535 | ||||||||
\(647\) | 940.604i | 1.45379i | 0.686747 | + | 0.726896i | \(0.259038\pi\) | ||||
−0.686747 | + | 0.726896i | \(0.740962\pi\) | |||||||
\(648\) | 25.4558 | 0.0392837 | ||||||||
\(649\) | 171.320i | 0.263975i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 93.0883 | − | 47.2243i | 0.142993 | − | 0.0725411i | ||||
\(652\) | 146.177 | 0.224197 | ||||||||
\(653\) | −731.970 | −1.12093 | −0.560467 | − | 0.828177i | \(-0.689378\pi\) | ||||
−0.560467 | + | 0.828177i | \(0.689378\pi\) | |||||||
\(654\) | − | 88.0374i | − | 0.134614i | ||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 165.581i | 0.252409i | ||||||||
\(657\) | − | 170.276i | − | 0.259171i | ||||||
\(658\) | 173.324 | + | 341.655i | 0.263410 | + | 0.519233i | ||||
\(659\) | 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 | \(-0.918231\pi\) | ||
0.967186 | − | 0.254070i | \(-0.0817695\pi\) | |||||||
\(662\) | 470.039 | 0.710028 | ||||||||
\(663\) | − | 762.764i | − | 1.15047i | ||||||
\(664\) | − | 18.2033i | − | 0.0274146i | ||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −300.853 | −0.451731 | ||||||||
\(667\) | −561.838 | −0.842335 | ||||||||
\(668\) | 78.7916i | 0.117951i | ||||||||
\(669\) | −206.735 | −0.309021 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 29.3939i | − | 0.0438061i | ||||||
\(672\) | −31.0294 | − | 61.1651i | −0.0461748 | − | 0.0910195i | ||||
\(673\) | −1191.44 | −1.77034 | −0.885171 | − | 0.465266i | \(-0.845959\pi\) | ||||
−0.885171 | + | 0.465266i | \(0.845959\pi\) | |||||||
\(674\) | −124.701 | −0.185016 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −365.529 | −0.540723 | ||||||||
\(677\) | − | 1211.07i | − | 1.78888i | −0.447186 | − | 0.894441i | \(-0.647574\pi\) | ||
0.447186 | − | 0.894441i | \(-0.352426\pi\) | |||||||
\(678\) | 178.885i | 0.263842i | ||||||||
\(679\) | 163.779 | + | 322.840i | 0.241206 | + | 0.475464i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −294.177 | −0.431977 | ||||||||
\(682\) | − | 21.3965i | − | 0.0313731i | ||||||
\(683\) | 1233.89 | 1.80657 | 0.903287 | − | 0.429038i | \(-0.141147\pi\) | ||||
0.903287 | + | 0.429038i | \(0.141147\pi\) | |||||||
\(684\) | 138.360i | 0.202281i | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −78.4163 | + | 478.695i | −0.114309 | + | 0.697806i | ||||
\(687\) | 190.544 | 0.277357 | ||||||||
\(688\) | −41.7056 | −0.0606186 | ||||||||
\(689\) | − | 694.501i | − | 1.00798i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 86.7045i | − | 0.125477i | −0.998030 | − | 0.0627384i | \(-0.980017\pi\) | ||
0.998030 | − | 0.0627384i | \(-0.0199834\pi\) | |||||||
\(692\) | − | 47.6569i | − | 0.0688683i | ||||||
\(693\) | −32.9117 | + | 16.6963i | −0.0474916 | + | 0.0240928i | ||||
\(694\) | 452.662 | 0.652251 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 146.969i | 0.211163i | ||||||||
\(697\) | 971.970 | 1.39450 | ||||||||
\(698\) | − | 470.998i | − | 0.674783i | ||||||
\(699\) | − | 99.1858i | − | 0.141897i | ||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −149.147 | −0.212763 | −0.106382 | − | 0.994325i | \(-0.533927\pi\) | ||||
−0.106382 | + | 0.994325i | \(0.533927\pi\) | |||||||
\(702\) | −137.823 | −0.196330 | ||||||||
\(703\) | − | 1635.22i | − | 2.32607i | ||||||
\(704\) | −14.0589 | −0.0199700 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 927.317i | 1.31348i | ||||||||
\(707\) | −20.9331 | − | 41.2633i | −0.0296084 | − | 0.0583639i | ||||
\(708\) | 337.706 | 0.476985 | ||||||||
\(709\) | 189.647 | 0.267485 | 0.133742 | − | 0.991016i | \(-0.457301\pi\) | ||||
0.133742 | + | 0.991016i | \(0.457301\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 209.470 | 0.294613 | ||||||||
\(712\) | − | 119.053i | − | 0.167209i | ||||||
\(713\) | − | 161.234i | − | 0.226134i | ||||||
\(714\) | −359.044 | + | 182.145i | −0.502862 | + | 0.255105i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −25.8091 | −0.0360462 | ||||||||
\(717\) | 487.610i | 0.680070i | ||||||||
\(718\) | −138.250 | −0.192548 | ||||||||
\(719\) | − | 12.0064i | − | 0.0166987i | −0.999965 | − | 0.00834937i | \(-0.997342\pi\) | ||
0.999965 | − | 0.00834937i | \(-0.00265772\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 556.971 | + | 1097.90i | 0.772497 | + | 1.52274i | ||||
\(722\) | −241.497 | −0.334484 | ||||||||
\(723\) | −291.515 | −0.403202 | ||||||||
\(724\) | 130.736i | 0.180574i | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | − | 288.823i | − | 0.397828i | ||||||
\(727\) | 417.169i | 0.573823i | 0.957957 | + | 0.286911i | \(0.0926286\pi\) | ||||
−0.957957 | + | 0.286911i | \(0.907371\pi\) | |||||||
\(728\) | 168.000 | + | 331.161i | 0.230769 | + | 0.454892i | ||||
\(729\) | −27.0000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 244.815i | 0.334904i | ||||||||
\(732\) | −57.9411 | −0.0791545 | ||||||||
\(733\) | − | 1286.99i | − | 1.75578i | −0.478859 | − | 0.877892i | \(-0.658949\pi\) | ||
0.478859 | − | 0.877892i | \(-0.341051\pi\) | |||||||
\(734\) | 454.043i | 0.618588i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −105.941 | −0.143942 | ||||||||
\(737\) | 107.147 | 0.145383 | ||||||||
\(738\) | − | 175.625i | − | 0.237974i | ||||||
\(739\) | 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 | ||||||
\(742\) | −326.912 | + | 165.844i | −0.440582 | + | 0.223510i | ||||
\(743\) | 776.476 | 1.04506 | 0.522528 | − | 0.852622i | \(-0.324989\pi\) | ||||
0.522528 | + | 0.852622i | \(0.324989\pi\) | |||||||
\(744\) | −42.1766 | −0.0566890 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −265.123 | −0.355392 | ||||||||
\(747\) | 19.3075i | 0.0258467i | ||||||||
\(748\) | 82.5266i | 0.110330i | ||||||||
\(749\) | −288.676 | + | 146.447i | −0.385415 | + | 0.195524i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 48.8385 | 0.0650313 | 0.0325157 | − | 0.999471i | \(-0.489648\pi\) | ||||
0.0325157 | + | 0.999471i | \(0.489648\pi\) | |||||||
\(752\) | − | 154.798i | − | 0.205848i | ||||||
\(753\) | −183.765 | −0.244043 | ||||||||
\(754\) | − | 795.724i | − | 1.05534i | ||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 32.9117 | + | 64.8754i | 0.0435340 | + | 0.0858141i | ||||
\(757\) | 1279.47 | 1.69019 | 0.845093 | − | 0.534620i | \(-0.179545\pi\) | ||||
0.845093 | + | 0.534620i | \(0.179545\pi\) | |||||||
\(758\) | −505.019 | −0.666252 | ||||||||
\(759\) | 57.0047i | 0.0751050i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 1316.12i | − | 1.72947i | −0.502231 | − | 0.864734i | \(-0.667487\pi\) | ||
0.502231 | − | 0.864734i | \(-0.332513\pi\) | |||||||
\(762\) | − | 220.310i | − | 0.289121i | ||||||
\(763\) | 224.368 | − | 113.823i | 0.294060 | − | 0.149178i | ||||
\(764\) | −200.132 | −0.261953 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | − | 879.966i | − | 1.14878i | ||||||
\(767\) | −1828.41 | −2.38385 | ||||||||
\(768\) | 27.7128i | 0.0360844i | ||||||||
\(769\) | − | 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 | ||||||||
\(772\) | −157.823 | −0.204434 | ||||||||
\(773\) | 717.634i | 0.928375i | 0.885737 | + | 0.464187i | \(0.153654\pi\) | ||||
−0.885737 | + | 0.464187i | \(0.846346\pi\) | |||||||
\(774\) | 44.2355 | 0.0571518 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | − | 146.273i | − | 0.188496i | ||||||
\(777\) | −388.971 | − | 766.738i | −0.500606 | − | 0.986792i | ||||
\(778\) | 321.691 | 0.413485 | ||||||||
\(779\) | 954.573 | 1.22538 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 194.382 | 0.248888 | ||||||||
\(782\) | 621.882i | 0.795245i | ||||||||
\(783\) | − | 155.885i | − | 0.199086i | ||||||
\(784\) | 115.765 | − | 158.160i | 0.147659 | − | 0.201735i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −29.8234 | −0.0379432 | ||||||||
\(787\) | 347.191i | 0.441158i | 0.975369 | + | 0.220579i | \(0.0707946\pi\) | ||||
−0.975369 | + | 0.220579i | \(0.929205\pi\) | |||||||
\(788\) | 367.882 | 0.466856 | ||||||||
\(789\) | 154.191i | 0.195426i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −455.897 | + | 231.279i | −0.576355 | + | 0.292388i | ||||
\(792\) | 14.9117 | 0.0188279 | ||||||||
\(793\) | 313.706 | 0.395593 | ||||||||
\(794\) | − | 1018.70i | − | 1.28300i | ||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 340.059i | 0.427210i | ||||||||
\(797\) | − | 361.246i | − | 0.453257i | −0.973981 | − | 0.226629i | \(-0.927230\pi\) | ||
0.973981 | − | 0.226629i | \(-0.0727704\pi\) | |||||||
\(798\) | −352.617 | + | 178.885i | −0.441876 | + | 0.224166i | ||||
\(799\) | −908.674 | −1.13726 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 126.274i | 0.157646i | ||||||||
\(802\) | 985.955 | 1.22937 | ||||||||
\(803\) | − | 99.7451i | − | 0.124216i | ||||||
\(804\) | − | 211.208i | − | 0.262697i | ||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 228.353 | 0.283317 | ||||||||
\(807\) | −331.684 | −0.411009 | ||||||||
\(808\) | 18.6957i | 0.0231382i | ||||||||
\(809\) | −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 | \(0.973637\pi\) | |||||||
\(812\) | −374.558 | + | 190.016i | −0.461279 | + | 0.234010i | ||||
\(813\) | 376.617 | 0.463244 | ||||||||
\(814\) | −176.235 | −0.216506 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 162.676 | 0.199358 | ||||||||
\(817\) | 240.433i | 0.294288i | ||||||||
\(818\) | 144.796i | 0.177012i | ||||||||
\(819\) | −178.191 | − | 351.249i | −0.217571 | − | 0.428876i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 491.677 | 0.598876 | 0.299438 | − | 0.954116i | \(-0.403201\pi\) | ||||
0.299438 | + | 0.954116i | \(0.403201\pi\) | |||||||
\(822\) | − | 406.038i | − | 0.493964i | ||||||
\(823\) | 941.852 | 1.14441 | 0.572207 | − | 0.820110i | \(-0.306088\pi\) | ||||
0.572207 | + | 0.820110i | \(0.306088\pi\) | |||||||
\(824\) | − | 497.438i | − | 0.603687i | ||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 436.617 | + | 860.659i | 0.528592 | + | 1.04196i | ||||
\(827\) | −966.978 | −1.16926 | −0.584630 | − | 0.811300i | \(-0.698760\pi\) | ||||
−0.584630 | + | 0.811300i | \(0.698760\pi\) | |||||||
\(828\) | 112.368 | 0.135710 | ||||||||
\(829\) | − | 1185.53i | − | 1.43007i | −0.699088 | − | 0.715035i | \(-0.746411\pi\) | ||
0.699088 | − | 0.715035i | \(-0.253589\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | − | 503.466i | − | 0.605856i | ||||||
\(832\) | − | 150.043i | − | 0.180340i | ||||||
\(833\) | −928.410 | − | 679.546i | −1.11454 | − | 0.815781i | ||||
\(834\) | 540.146 | 0.647657 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 81.0495i | 0.0969491i | ||||||||
\(837\) | 44.7351 | 0.0534469 | ||||||||
\(838\) | 553.560i | 0.660573i | ||||||||
\(839\) | 1376.91i | 1.64113i | 0.571550 | + | 0.820567i | \(0.306342\pi\) | ||||
−0.571550 | + | 0.820567i | \(0.693658\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 59.0000 | 0.0701546 | ||||||||
\(842\) | 501.255 | 0.595315 | ||||||||
\(843\) | 32.6540i | 0.0387355i | ||||||||
\(844\) | 43.1472 | 0.0511223 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 164.188i | 0.194076i | ||||||||
\(847\) | 736.080 | − | 373.418i | 0.869044 | − | 0.440871i | ||||
\(848\) | 148.118 | 0.174667 | ||||||||
\(849\) | −695.823 | −0.819580 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1328.03 | −1.56055 | ||||||||
\(852\) | − | 383.165i | − | 0.449724i | ||||||
\(853\) | 175.006i | 0.205165i | 0.994725 | + | 0.102582i | \(0.0327105\pi\) | ||||
−0.994725 | + | 0.102582i | \(0.967289\pi\) | |||||||
\(854\) | −74.9117 | − | 147.666i | −0.0877186 | − | 0.172911i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 130.794 | 0.152797 | ||||||||
\(857\) | 61.7471i | 0.0720503i | 0.999351 | + | 0.0360252i | \(0.0114696\pi\) | ||||
−0.999351 | + | 0.0360252i | \(0.988530\pi\) | |||||||
\(858\) | −80.7351 | −0.0940968 | ||||||||
\(859\) | − | 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 | ||||
\(862\) | 827.720 | 0.960232 | ||||||||
\(863\) | 494.507 | 0.573009 | 0.286504 | − | 0.958079i | \(-0.407507\pi\) | ||||
0.286504 | + | 0.958079i | \(0.407507\pi\) | |||||||
\(864\) | − | 29.3939i | − | 0.0340207i | ||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 554.664i | 0.640490i | ||||||||
\(867\) | − | 454.358i | − | 0.524058i | ||||||
\(868\) | −54.5299 | − | 107.489i | −0.0628224 | − | 0.123835i | ||||
\(869\) | 122.705 | 0.141202 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1143.53i | 1.31289i | ||||||||
\(872\) | −101.657 | −0.116579 | ||||||||
\(873\) | 155.146i | 0.177716i | ||||||||
\(874\) | 610.751i | 0.698800i | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −196.617 | −0.224449 | ||||||||
\(877\) | 454.353 | 0.518077 | 0.259038 | − | 0.965867i | \(-0.416594\pi\) | ||||
0.259038 | + | 0.965867i | \(0.416594\pi\) | |||||||
\(878\) | − | 555.097i | − | 0.632229i | ||||||
\(879\) | −486.521 | −0.553494 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 143.493i | 0.162875i | 0.996678 | + | 0.0814375i | \(0.0259511\pi\) | ||||
−0.996678 | + | 0.0814375i | \(0.974049\pi\) | |||||||
\(882\) | −122.787 | + | 167.754i | −0.139214 | + | 0.190197i | ||||
\(883\) | 927.986 | 1.05095 | 0.525473 | − | 0.850810i | \(-0.323888\pi\) | ||||
0.525473 | + | 0.850810i | \(0.323888\pi\) | |||||||
\(884\) | −880.764 | −0.996339 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 1152.22 | 1.30047 | ||||||||
\(887\) | − | 958.265i | − | 1.08034i | −0.841555 | − | 0.540172i | \(-0.818359\pi\) | ||
0.841555 | − | 0.540172i | \(-0.181641\pi\) | |||||||
\(888\) | 347.395i | 0.391210i | ||||||||
\(889\) | 561.470 | − | 284.837i | 0.631575 | − | 0.320402i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −15.8162 | −0.0177511 | ||||||||
\(892\) | 238.717i | 0.267620i | ||||||||
\(893\) | −892.410 | −0.999340 | ||||||||
\(894\) | 516.482i | 0.577720i | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −70.6274 | + | 35.8297i | −0.0788252 | + | 0.0399885i | ||||
\(897\) | −608.382 | −0.678241 | ||||||||
\(898\) | 255.015 | 0.283981 | ||||||||
\(899\) | 258.278i | 0.287295i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 869.462i | − | 0.964996i | ||||||
\(902\) | − | 102.879i | − | 0.114056i | ||||||
\(903\) | 57.1918 | + | 112.736i | 0.0633353 | + | 0.124846i | ||||
\(904\) | 206.558 | 0.228494 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | − | 177.264i | − | 0.195655i | ||||||
\(907\) | 552.721 | 0.609394 | 0.304697 | − | 0.952449i | \(-0.401445\pi\) | ||||
0.304697 | + | 0.952449i | \(0.401445\pi\) | |||||||
\(908\) | 339.686i | 0.374103i | ||||||||
\(909\) | − | 19.8297i | − | 0.0218149i | ||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 142.742 | 0.156687 | 0.0783437 | − | 0.996926i | \(-0.475037\pi\) | ||||
0.0783437 | + | 0.996926i | \(0.475037\pi\) | |||||||
\(912\) | 159.765 | 0.175180 | ||||||||
\(913\) | 11.3101i | 0.0123878i | ||||||||
\(914\) | −396.230 | −0.433512 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | − | 220.021i | − | 0.240198i | ||||||
\(917\) | −38.5584 | − | 76.0063i | −0.0420485 | − | 0.0828858i | ||||
\(918\) | −172.544 | −0.187957 | ||||||||
\(919\) | 1086.45 | 1.18221 | 0.591107 | − | 0.806593i | \(-0.298691\pi\) | ||||
0.591107 | + | 0.806593i | \(0.298691\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 263.823 | 0.286453 | ||||||||
\(922\) | 574.591i | 0.623200i | ||||||||
\(923\) | 2074.54i | 2.24760i | ||||||||
\(924\) | 19.2792 | + | 38.0031i | 0.0208650 | + | 0.0411289i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −646.960 | −0.698661 | ||||||||
\(927\) | 527.613i | 0.569161i | ||||||||
\(928\) | 169.706 | 0.182872 | ||||||||
\(929\) | − | 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 | ||||
\(932\) | −114.530 | −0.122886 | ||||||||
\(933\) | 490.441 | 0.525660 | ||||||||
\(934\) | 910.345i | 0.974673i | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 159.145i | 0.170026i | ||||||||
\(937\) | − | 759.317i | − | 0.810370i | −0.914235 | − | 0.405185i | \(-0.867207\pi\) | ||
0.914235 | − | 0.405185i | \(-0.132793\pi\) | |||||||
\(938\) | 538.274 | − | 273.070i | 0.573853 | − | 0.291119i | ||||
\(939\) | 84.1463 | 0.0896127 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 36.3519i | 0.0386312i | 0.999813 | + | 0.0193156i | \(0.00614873\pi\) | ||||
−0.999813 | + | 0.0193156i | \(0.993851\pi\) | |||||||
\(942\) | 572.382 | 0.607624 | ||||||||
\(943\) | − | 775.245i | − | 0.822105i | ||||||
\(944\) | − | 389.949i | − | 0.413081i | ||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 25.9126 | 0.0273917 | ||||||||
\(947\) | −92.5370 | −0.0977160 | −0.0488580 | − | 0.998806i | \(-0.515558\pi\) | ||||
−0.0488580 | + | 0.998806i | \(0.515558\pi\) | |||||||
\(948\) | − | 241.875i | − | 0.255143i | ||||||
\(949\) | 1064.53 | 1.12174 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 1001.17i | 1.05276i | ||||||||
\(952\) | 210.323 | + | 414.588i | 0.220927 | + | 0.435492i | ||||
\(953\) | 1361.29 | 1.42843 | 0.714215 | − | 0.699927i | \(-0.246784\pi\) | ||||
0.714215 | + | 0.699927i | \(0.246784\pi\) | |||||||
\(954\) | −157.103 | −0.164678 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 563.044 | 0.588958 | ||||||||
\(957\) | − | 91.3151i | − | 0.0954180i | ||||||
\(958\) | 238.344i | 0.248794i | ||||||||
\(959\) | 1034.81 | − | 524.964i | 1.07905 | − | 0.547408i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 886.881 | 0.922873 | ||||||||
\(962\) | − | 1880.87i | − | 1.95517i | ||||||
\(963\) | −138.728 | −0.144058 | ||||||||
\(964\) | 336.612i | 0.349183i | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 145.279 | + | 286.374i | 0.150393 | + | 0.296453i | ||||
\(967\) | −481.677 | −0.498115 | −0.249057 | − | 0.968489i | \(-0.580121\pi\) | ||||
−0.249057 | + | 0.968489i | \(0.580121\pi\) | |||||||
\(968\) | −333.505 | −0.344530 | ||||||||
\(969\) | − | 937.829i | − | 0.967832i | ||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 1427.34i | − | 1.46997i | −0.678082 | − | 0.734987i | \(-0.737188\pi\) | ||
0.678082 | − | 0.734987i | \(-0.262812\pi\) | |||||||
\(972\) | 31.1769i | 0.0320750i | ||||||||
\(973\) | 698.352 | + | 1376.59i | 0.717730 | + | 1.41479i | ||||
\(974\) | 3.93102 | 0.00403596 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 66.9046i | 0.0685498i | ||||||||
\(977\) | 1356.26 | 1.38819 | 0.694095 | − | 0.719883i | \(-0.255805\pi\) | ||||
0.694095 | + | 0.719883i | \(0.255805\pi\) | |||||||
\(978\) | 179.029i | 0.183056i | ||||||||
\(979\) | 73.9698i | 0.0755565i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 107.823 | 0.109912 | ||||||||
\(982\) | −349.986 | −0.356401 | ||||||||
\(983\) | − | 1315.51i | − | 1.33826i | −0.743146 | − | 0.669129i | \(-0.766667\pi\) | ||
0.743146 | − | 0.669129i | \(-0.233333\pi\) | |||||||
\(984\) | −202.794 | −0.206091 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | − | 996.184i | − | 1.01033i | ||||||
\(987\) | −418.441 | + | 212.277i | −0.423952 | + | 0.215073i | ||||
\(988\) | −864.999 | −0.875505 | ||||||||
\(989\) | 195.265 | 0.197437 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1043.28 | 1.05275 | 0.526377 | − | 0.850251i | \(-0.323550\pi\) | ||||
0.526377 | + | 0.850251i | \(0.323550\pi\) | |||||||
\(992\) | 48.7014i | 0.0490941i | ||||||||
\(993\) | 575.677i | 0.579736i | ||||||||
\(994\) | 976.514 | − | 495.391i | 0.982408 | − | 0.498382i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 22.2944 | 0.0223839 | ||||||||
\(997\) | − | 820.328i | − | 0.822796i | −0.911456 | − | 0.411398i | \(-0.865041\pi\) | ||
0.911456 | − | 0.411398i | \(-0.134959\pi\) | |||||||
\(998\) | −683.667 | −0.685037 | ||||||||
\(999\) | − | 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 | 1050.3.f.a.601.4 | 4 | ||
5.2 | odd | 4 | 1050.3.h.a.349.7 | 8 | |||
5.3 | odd | 4 | 1050.3.h.a.349.2 | 8 | |||
5.4 | even | 2 | 42.3.c.a.13.1 | ✓ | 4 | ||
7.6 | odd | 2 | inner | 1050.3.f.a.601.3 | 4 | ||
15.14 | odd | 2 | 126.3.c.b.55.4 | 4 | |||
20.19 | odd | 2 | 336.3.f.c.97.3 | 4 | |||
35.4 | even | 6 | 294.3.g.b.19.2 | 4 | |||
35.9 | even | 6 | 294.3.g.c.31.2 | 4 | |||
35.13 | even | 4 | 1050.3.h.a.349.3 | 8 | |||
35.19 | odd | 6 | 294.3.g.b.31.2 | 4 | |||
35.24 | odd | 6 | 294.3.g.c.19.2 | 4 | |||
35.27 | even | 4 | 1050.3.h.a.349.6 | 8 | |||
35.34 | odd | 2 | 42.3.c.a.13.2 | yes | 4 | ||
40.19 | odd | 2 | 1344.3.f.e.769.2 | 4 | |||
40.29 | even | 2 | 1344.3.f.f.769.4 | 4 | |||
60.59 | even | 2 | 1008.3.f.g.433.4 | 4 | |||
105.44 | odd | 6 | 882.3.n.d.325.1 | 4 | |||
105.59 | even | 6 | 882.3.n.d.19.1 | 4 | |||
105.74 | odd | 6 | 882.3.n.a.19.1 | 4 | |||
105.89 | even | 6 | 882.3.n.a.325.1 | 4 | |||
105.104 | even | 2 | 126.3.c.b.55.3 | 4 | |||
140.139 | even | 2 | 336.3.f.c.97.2 | 4 | |||
280.69 | odd | 2 | 1344.3.f.f.769.1 | 4 | |||
280.139 | even | 2 | 1344.3.f.e.769.3 | 4 | |||
420.419 | odd | 2 | 1008.3.f.g.433.1 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
42.3.c.a.13.1 | ✓ | 4 | 5.4 | even | 2 | ||
42.3.c.a.13.2 | yes | 4 | 35.34 | odd | 2 | ||
126.3.c.b.55.3 | 4 | 105.104 | even | 2 | |||
126.3.c.b.55.4 | 4 | 15.14 | odd | 2 | |||
294.3.g.b.19.2 | 4 | 35.4 | even | 6 | |||
294.3.g.b.31.2 | 4 | 35.19 | odd | 6 | |||
294.3.g.c.19.2 | 4 | 35.24 | odd | 6 | |||
294.3.g.c.31.2 | 4 | 35.9 | even | 6 | |||
336.3.f.c.97.2 | 4 | 140.139 | even | 2 | |||
336.3.f.c.97.3 | 4 | 20.19 | odd | 2 | |||
882.3.n.a.19.1 | 4 | 105.74 | odd | 6 | |||
882.3.n.a.325.1 | 4 | 105.89 | even | 6 | |||
882.3.n.d.19.1 | 4 | 105.59 | even | 6 | |||
882.3.n.d.325.1 | 4 | 105.44 | odd | 6 | |||
1008.3.f.g.433.1 | 4 | 420.419 | odd | 2 | |||
1008.3.f.g.433.4 | 4 | 60.59 | even | 2 | |||
1050.3.f.a.601.3 | 4 | 7.6 | odd | 2 | inner | ||
1050.3.f.a.601.4 | 4 | 1.1 | even | 1 | trivial | ||
1050.3.h.a.349.2 | 8 | 5.3 | odd | 4 | |||
1050.3.h.a.349.3 | 8 | 35.13 | even | 4 | |||
1050.3.h.a.349.6 | 8 | 35.27 | even | 4 | |||
1050.3.h.a.349.7 | 8 | 5.2 | odd | 4 | |||
1344.3.f.e.769.2 | 4 | 40.19 | odd | 2 | |||
1344.3.f.e.769.3 | 4 | 280.139 | even | 2 | |||
1344.3.f.f.769.1 | 4 | 280.69 | odd | 2 | |||
1344.3.f.f.769.4 | 4 | 40.29 | even | 2 |