Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1050,3,Mod(349,1050)]
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, 1, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1050.349");
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.h (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: | \(28.6104277578\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\Q(\zeta_{24})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{8} \) |
Twist minimal: | no (minimal twist has level 42) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 349.6 | ||
Root | \(-0.965926 + 0.258819i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1050.349 |
Dual form | 1050.3.h.a.349.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(451\) | \(701\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.41421i | 0.707107i | ||||||||
\(3\) | −1.73205 | −0.577350 | ||||||||
\(4\) | −2.00000 | −0.500000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | − | 2.44949i | − | 0.408248i | ||||||
\(7\) | 3.16693 | − | 6.24264i | 0.452418 | − | 0.891806i | ||||
\(8\) | − | 2.82843i | − | 0.353553i | ||||||
\(9\) | 3.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.75736 | −0.159760 | −0.0798800 | − | 0.996804i | \(-0.525454\pi\) | ||||
−0.0798800 | + | 0.996804i | \(0.525454\pi\) | |||||||
\(12\) | 3.46410 | 0.288675 | ||||||||
\(13\) | 18.7554 | 1.44272 | 0.721361 | − | 0.692559i | \(-0.243517\pi\) | ||||
0.721361 | + | 0.692559i | \(0.243517\pi\) | |||||||
\(14\) | 8.82843 | + | 4.47871i | 0.630602 | + | 0.319908i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 4.00000 | 0.250000 | ||||||||
\(17\) | −23.4803 | −1.38119 | −0.690597 | − | 0.723240i | \(-0.742652\pi\) | ||||
−0.690597 | + | 0.723240i | \(0.742652\pi\) | |||||||
\(18\) | 4.24264i | 0.235702i | ||||||||
\(19\) | − | 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 | ||||
\(22\) | − | 2.48528i | − | 0.112967i | ||||||
\(23\) | 18.7279i | 0.814257i | 0.913371 | + | 0.407129i | \(0.133470\pi\) | ||||
−0.913371 | + | 0.407129i | \(0.866530\pi\) | |||||||
\(24\) | 4.89898i | 0.204124i | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 26.5241i | 1.02016i | ||||||||
\(27\) | −5.19615 | −0.192450 | ||||||||
\(28\) | −6.33386 | + | 12.4853i | −0.226209 | + | 0.445903i | ||||
\(29\) | −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 | \(-0.0443435\pi\) | |||||||
\(32\) | 5.65685i | 0.176777i | ||||||||
\(33\) | 3.04384 | 0.0922374 | ||||||||
\(34\) | − | 33.2061i | − | 0.976651i | ||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −6.00000 | −0.166667 | ||||||||
\(37\) | 70.9117i | 1.91653i | 0.285878 | + | 0.958266i | \(0.407715\pi\) | ||||
−0.285878 | + | 0.958266i | \(0.592285\pi\) | |||||||
\(38\) | 32.6118 | 0.858205 | ||||||||
\(39\) | −32.4853 | −0.832956 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 41.3951i | − | 1.00964i | −0.863225 | − | 0.504819i | \(-0.831559\pi\) | ||
0.863225 | − | 0.504819i | \(-0.168441\pi\) | |||||||
\(42\) | −15.2913 | − | 7.75736i | −0.364078 | − | 0.184699i | ||||
\(43\) | 10.4264i | 0.242475i | 0.992624 | + | 0.121237i | \(0.0386862\pi\) | ||||
−0.992624 | + | 0.121237i | \(0.961314\pi\) | |||||||
\(44\) | 3.51472 | 0.0798800 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −26.4853 | −0.575767 | ||||||||
\(47\) | −38.6995 | −0.823393 | −0.411696 | − | 0.911321i | \(-0.635064\pi\) | ||||
−0.411696 | + | 0.911321i | \(0.635064\pi\) | |||||||
\(48\) | −6.92820 | −0.144338 | ||||||||
\(49\) | −28.9411 | − | 39.5400i | −0.590635 | − | 0.806939i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 40.6690 | 0.797432 | ||||||||
\(52\) | −37.5108 | −0.721361 | ||||||||
\(53\) | − | 37.0294i | − | 0.698669i | −0.936998 | − | 0.349334i | \(-0.886408\pi\) | ||
0.936998 | − | 0.349334i | \(-0.113592\pi\) | |||||||
\(54\) | − | 7.34847i | − | 0.136083i | ||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −17.6569 | − | 8.95743i | −0.315301 | − | 0.159954i | ||||
\(57\) | 39.9411i | 0.700721i | ||||||||
\(58\) | − | 42.4264i | − | 0.731490i | ||||||
\(59\) | − | 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 | \(-0.0437781\pi\) | |||||||
\(62\) | 12.1753 | 0.196376 | ||||||||
\(63\) | 9.50079 | − | 18.7279i | 0.150806 | − | 0.297269i | ||||
\(64\) | −8.00000 | −0.125000 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 4.30463i | 0.0652217i | ||||||||
\(67\) | − | 60.9706i | − | 0.910008i | −0.890489 | − | 0.455004i | \(-0.849638\pi\) | ||
0.890489 | − | 0.455004i | \(-0.150362\pi\) | |||||||
\(68\) | 46.9606 | 0.690597 | ||||||||
\(69\) | − | 32.4377i | − | 0.470112i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −110.610 | −1.55789 | −0.778945 | − | 0.627092i | \(-0.784245\pi\) | ||||
−0.778945 | + | 0.627092i | \(0.784245\pi\) | |||||||
\(72\) | − | 8.48528i | − | 0.117851i | ||||||
\(73\) | −56.7585 | −0.777514 | −0.388757 | − | 0.921340i | \(-0.627095\pi\) | ||||
−0.388757 | + | 0.921340i | \(0.627095\pi\) | |||||||
\(74\) | −100.284 | −1.35519 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 46.1200i | 0.606843i | ||||||||
\(77\) | −5.56543 | + | 10.9706i | −0.0722783 | + | 0.142475i | ||||
\(78\) | − | 45.9411i | − | 0.588989i | ||||||
\(79\) | 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 | ||||||||
\(82\) | 58.5416 | 0.713922 | ||||||||
\(83\) | 6.43583 | 0.0775401 | 0.0387701 | − | 0.999248i | \(-0.487656\pi\) | ||||
0.0387701 | + | 0.999248i | \(0.487656\pi\) | |||||||
\(84\) | 10.9706 | − | 21.6251i | 0.130602 | − | 0.257442i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −14.7452 | −0.171455 | ||||||||
\(87\) | 51.9615 | 0.597259 | ||||||||
\(88\) | 4.97056i | 0.0564837i | ||||||||
\(89\) | − | 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 | ||||
\(92\) | − | 37.4558i | − | 0.407129i | ||||||
\(93\) | 14.9117i | 0.160341i | ||||||||
\(94\) | − | 54.7293i | − | 0.582227i | ||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | − | 9.79796i | − | 0.102062i | ||||||
\(97\) | −51.7153 | −0.533148 | −0.266574 | − | 0.963814i | \(-0.585892\pi\) | ||||
−0.266574 | + | 0.963814i | \(0.585892\pi\) | |||||||
\(98\) | 55.9180 | − | 40.9289i | 0.570592 | − | 0.417642i | ||||
\(99\) | −5.27208 | −0.0532533 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 6.60991i | − | 0.0654447i | −0.999464 | − | 0.0327223i | \(-0.989582\pi\) | ||
0.999464 | − | 0.0327223i | \(-0.0104177\pi\) | |||||||
\(102\) | 57.5147i | 0.563870i | ||||||||
\(103\) | 175.871 | 1.70748 | 0.853742 | − | 0.520696i | \(-0.174327\pi\) | ||||
0.853742 | + | 0.520696i | \(0.174327\pi\) | |||||||
\(104\) | − | 53.0482i | − | 0.510079i | ||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 52.3675 | 0.494033 | ||||||||
\(107\) | 46.2426i | 0.432174i | 0.976374 | + | 0.216087i | \(0.0693295\pi\) | ||||
−0.976374 | + | 0.216087i | \(0.930670\pi\) | |||||||
\(108\) | 10.3923 | 0.0962250 | ||||||||
\(109\) | 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 | ||||||
\(112\) | 12.6677 | − | 24.9706i | 0.113105 | − | 0.222951i | ||||
\(113\) | − | 73.0294i | − | 0.646278i | −0.946351 | − | 0.323139i | \(-0.895262\pi\) | ||
0.946351 | − | 0.323139i | \(-0.104738\pi\) | |||||||
\(114\) | −56.4853 | −0.495485 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 60.0000 | 0.517241 | ||||||||
\(117\) | 56.2662 | 0.480907 | ||||||||
\(118\) | 137.868 | 1.16837 | ||||||||
\(119\) | −74.3604 | + | 146.579i | −0.624877 | + | 1.23176i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −117.912 | −0.974477 | ||||||||
\(122\) | 23.6544 | 0.193888 | ||||||||
\(123\) | 71.6985i | 0.582915i | ||||||||
\(124\) | 17.2185i | 0.138859i | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 26.4853 | + | 13.4361i | 0.210201 | + | 0.106636i | ||||
\(127\) | − | 89.9411i | − | 0.708198i | −0.935208 | − | 0.354099i | \(-0.884788\pi\) | ||
0.935208 | − | 0.354099i | \(-0.115212\pi\) | |||||||
\(128\) | − | 11.3137i | − | 0.0883883i | ||||||
\(129\) | − | 18.0591i | − | 0.139993i | ||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 12.1753i | − | 0.0929415i | −0.998920 | − | 0.0464708i | \(-0.985203\pi\) | ||
0.998920 | − | 0.0464708i | \(-0.0147974\pi\) | |||||||
\(132\) | −6.08767 | −0.0461187 | ||||||||
\(133\) | −143.955 | − | 73.0294i | −1.08237 | − | 0.549094i | ||||
\(134\) | 86.2254 | 0.643473 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 66.4123i | 0.488326i | ||||||||
\(137\) | − | 165.765i | − | 1.20996i | −0.796241 | − | 0.604980i | \(-0.793181\pi\) | ||
0.796241 | − | 0.604980i | \(-0.206819\pi\) | |||||||
\(138\) | 45.8739 | 0.332419 | ||||||||
\(139\) | − | 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 | ||||||||
\(142\) | − | 156.426i | − | 1.10159i | ||||||
\(143\) | −32.9600 | −0.230489 | ||||||||
\(144\) | 12.0000 | 0.0833333 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | − | 80.2687i | − | 0.549786i | ||||||
\(147\) | 50.1275 | + | 68.4853i | 0.341003 | + | 0.465886i | ||||
\(148\) | − | 141.823i | − | 0.958266i | ||||||
\(149\) | −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 | \(-0.577025\pi\) | ||||
−0.239628 | + | 0.970865i | \(0.577025\pi\) | |||||||
\(152\) | −65.2236 | −0.429103 | ||||||||
\(153\) | −70.4409 | −0.460398 | ||||||||
\(154\) | −15.5147 | − | 7.87071i | −0.100745 | − | 0.0511085i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 64.9706 | 0.416478 | ||||||||
\(157\) | −233.674 | −1.48837 | −0.744184 | − | 0.667974i | \(-0.767162\pi\) | ||||
−0.744184 | + | 0.667974i | \(0.767162\pi\) | |||||||
\(158\) | 98.7452i | 0.624969i | ||||||||
\(159\) | 64.1369i | 0.403377i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 116.912 | + | 59.3100i | 0.726160 | + | 0.368385i | ||||
\(162\) | 12.7279i | 0.0785674i | ||||||||
\(163\) | − | 73.0883i | − | 0.448395i | −0.974544 | − | 0.224197i | \(-0.928024\pi\) | ||
0.974544 | − | 0.224197i | \(-0.0719760\pi\) | |||||||
\(164\) | 82.7903i | 0.504819i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 9.10164i | 0.0548292i | ||||||||
\(167\) | 39.3958 | 0.235903 | 0.117951 | − | 0.993019i | \(-0.462367\pi\) | ||||
0.117951 | + | 0.993019i | \(0.462367\pi\) | |||||||
\(168\) | 30.5826 | + | 15.5147i | 0.182039 | + | 0.0923495i | ||||
\(169\) | 182.765 | 1.08145 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | − | 69.1801i | − | 0.404562i | ||||||
\(172\) | − | 20.8528i | − | 0.121237i | ||||||
\(173\) | 23.8284 | 0.137737 | 0.0688683 | − | 0.997626i | \(-0.478061\pi\) | ||||
0.0688683 | + | 0.997626i | \(0.478061\pi\) | |||||||
\(174\) | 73.4847i | 0.422326i | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −7.02944 | −0.0399400 | ||||||||
\(177\) | 168.853i | 0.953971i | ||||||||
\(178\) | 59.5263 | 0.334417 | ||||||||
\(179\) | 12.9045 | 0.0720924 | 0.0360462 | − | 0.999350i | \(-0.488524\pi\) | ||||
0.0360462 | + | 0.999350i | \(0.488524\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 65.3678i | − | 0.361148i | −0.983561 | − | 0.180574i | \(-0.942204\pi\) | ||
0.983561 | − | 0.180574i | \(-0.0577955\pi\) | |||||||
\(182\) | 165.581 | + | 84.0000i | 0.909783 | + | 0.461538i | ||||
\(183\) | 28.9706i | 0.158309i | ||||||||
\(184\) | 52.9706 | 0.287883 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −21.0883 | −0.113378 | ||||||||
\(187\) | 41.2633 | 0.220659 | ||||||||
\(188\) | 77.3989 | 0.411696 | ||||||||
\(189\) | −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 | \(0.584367\pi\) | |||||||
\(192\) | 13.8564 | 0.0721688 | ||||||||
\(193\) | 78.9117i | 0.408869i | 0.978880 | + | 0.204434i | \(0.0655355\pi\) | ||||
−0.978880 | + | 0.204434i | \(0.934464\pi\) | |||||||
\(194\) | − | 73.1365i | − | 0.376992i | ||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 57.8823 | + | 79.0800i | 0.295318 | + | 0.403469i | ||||
\(197\) | 183.941i | 0.933711i | 0.884334 | + | 0.466856i | \(0.154613\pi\) | ||||
−0.884334 | + | 0.466856i | \(0.845387\pi\) | |||||||
\(198\) | − | 7.45584i | − | 0.0376558i | ||||||
\(199\) | 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 | ||||||||
\(202\) | 9.34783 | 0.0462764 | ||||||||
\(203\) | −95.0079 | + | 187.279i | −0.468019 | + | 0.922558i | ||||
\(204\) | −81.3381 | −0.398716 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 248.719i | 1.20737i | ||||||||
\(207\) | 56.1838i | 0.271419i | ||||||||
\(208\) | 75.0215 | 0.360680 | ||||||||
\(209\) | 40.5247i | 0.193898i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 21.5736 | 0.102245 | 0.0511223 | − | 0.998692i | \(-0.483720\pi\) | ||||
0.0511223 | + | 0.998692i | \(0.483720\pi\) | |||||||
\(212\) | 74.0589i | 0.349334i | ||||||||
\(213\) | 191.582 | 0.899448 | ||||||||
\(214\) | −65.3970 | −0.305593 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 14.6969i | 0.0680414i | ||||||||
\(217\) | −53.7446 | − | 27.2649i | −0.247671 | − | 0.125645i | ||||
\(218\) | 50.8284i | 0.233158i | ||||||||
\(219\) | 98.3087 | 0.448898 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −440.382 | −1.99268 | ||||||||
\(222\) | 173.697 | 0.782421 | ||||||||
\(223\) | −119.359 | −0.535240 | −0.267620 | − | 0.963525i | \(-0.586237\pi\) | ||||
−0.267620 | + | 0.963525i | \(0.586237\pi\) | |||||||
\(224\) | 35.3137 | + | 17.9149i | 0.157650 | + | 0.0799770i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 103.279 | 0.456988 | ||||||||
\(227\) | 169.843 | 0.748207 | 0.374103 | − | 0.927387i | \(-0.377951\pi\) | ||||
0.374103 | + | 0.927387i | \(0.377951\pi\) | |||||||
\(228\) | − | 79.8823i | − | 0.350361i | ||||||
\(229\) | − | 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 | ||||
\(232\) | 84.8528i | 0.365745i | ||||||||
\(233\) | 57.2649i | 0.245772i | 0.992421 | + | 0.122886i | \(0.0392150\pi\) | ||||
−0.992421 | + | 0.122886i | \(0.960785\pi\) | |||||||
\(234\) | 79.5724i | 0.340053i | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 194.974i | 0.826163i | ||||||||
\(237\) | −120.938 | −0.510285 | ||||||||
\(238\) | −207.294 | − | 105.161i | −0.870983 | − | 0.441855i | ||||
\(239\) | −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 | \(-0.886459\pi\) | ||
0.937055 | − | 0.349183i | \(-0.113541\pi\) | |||||||
\(242\) | − | 166.752i | − | 0.689059i | ||||||
\(243\) | −15.5885 | −0.0641500 | ||||||||
\(244\) | 33.4523i | 0.137100i | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −101.397 | −0.412183 | ||||||||
\(247\) | − | 432.500i | − | 1.75101i | ||||||
\(248\) | −24.3507 | −0.0981882 | ||||||||
\(249\) | −11.1472 | −0.0447678 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 106.096i | − | 0.422695i | −0.977411 | − | 0.211348i | \(-0.932215\pi\) | ||
0.977411 | − | 0.211348i | \(-0.0677852\pi\) | |||||||
\(252\) | −19.0016 | + | 37.4558i | −0.0754031 | + | 0.148634i | ||||
\(253\) | − | 32.9117i | − | 0.130086i | ||||||
\(254\) | 127.196 | 0.500771 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 16.0000 | 0.0625000 | ||||||||
\(257\) | 290.462 | 1.13020 | 0.565102 | − | 0.825021i | \(-0.308837\pi\) | ||||
0.565102 | + | 0.825021i | \(0.308837\pi\) | |||||||
\(258\) | 25.5394 | 0.0989898 | ||||||||
\(259\) | 442.676 | + | 224.572i | 1.70917 | + | 0.867074i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −90.0000 | −0.344828 | ||||||||
\(262\) | 17.2185 | 0.0657196 | ||||||||
\(263\) | − | 89.0223i | − | 0.338488i | −0.985574 | − | 0.169244i | \(-0.945867\pi\) | ||
0.985574 | − | 0.169244i | \(-0.0541326\pi\) | |||||||
\(264\) | − | 8.60927i | − | 0.0326109i | ||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 103.279 | − | 203.584i | 0.388268 | − | 0.765352i | ||||
\(267\) | 72.9045i | 0.273051i | ||||||||
\(268\) | 121.941i | 0.455004i | ||||||||
\(269\) | 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 | \(0.131400\pi\) | ||||
−0.915999 | + | 0.401181i | \(0.868600\pi\) | |||||||
\(272\) | −93.9211 | −0.345298 | ||||||||
\(273\) | −102.879 | + | 202.794i | −0.376845 | + | 0.742835i | ||||
\(274\) | 234.426 | 0.855571 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 64.8754i | 0.235056i | ||||||||
\(277\) | − | 290.676i | − | 1.04937i | −0.851296 | − | 0.524686i | \(-0.824183\pi\) | ||
0.851296 | − | 0.524686i | \(-0.175817\pi\) | |||||||
\(278\) | 311.854 | 1.12178 | ||||||||
\(279\) | − | 25.8278i | − | 0.0925728i | ||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 18.8528 | 0.0670919 | 0.0335459 | − | 0.999437i | \(-0.489320\pi\) | ||||
0.0335459 | + | 0.999437i | \(0.489320\pi\) | |||||||
\(282\) | 94.7939i | 0.336149i | ||||||||
\(283\) | −401.734 | −1.41955 | −0.709777 | − | 0.704426i | \(-0.751204\pi\) | ||||
−0.709777 | + | 0.704426i | \(0.751204\pi\) | |||||||
\(284\) | 221.220 | 0.778945 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | − | 46.6124i | − | 0.162980i | ||||||
\(287\) | −258.415 | − | 131.095i | −0.900401 | − | 0.456779i | ||||
\(288\) | 16.9706i | 0.0589256i | ||||||||
\(289\) | 262.324 | 0.907695 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 89.5736 | 0.307813 | ||||||||
\(292\) | 113.517 | 0.388757 | ||||||||
\(293\) | −280.893 | −0.958679 | −0.479340 | − | 0.877629i | \(-0.659124\pi\) | ||||
−0.479340 | + | 0.877629i | \(0.659124\pi\) | |||||||
\(294\) | −96.8528 | + | 70.8910i | −0.329431 | + | 0.241126i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 200.569 | 0.677596 | ||||||||
\(297\) | 9.13151 | 0.0307458 | ||||||||
\(298\) | − | 298.191i | − | 1.00064i | ||||||
\(299\) | 351.249i | 1.17475i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 65.0883 | + | 33.0197i | 0.216240 | + | 0.109700i | ||||
\(302\) | − | 102.343i | − | 0.338885i | ||||||
\(303\) | 11.4487i | 0.0377845i | ||||||||
\(304\) | − | 92.2401i | − | 0.303421i | ||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | − | 99.6184i | − | 0.325550i | ||||||
\(307\) | −152.318 | −0.496151 | −0.248076 | − | 0.968741i | \(-0.579798\pi\) | ||||
−0.248076 | + | 0.968741i | \(0.579798\pi\) | |||||||
\(308\) | 11.1309 | − | 21.9411i | 0.0361392 | − | 0.0712374i | ||||
\(309\) | −304.617 | −0.985817 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 283.156i | 0.910470i | 0.890371 | + | 0.455235i | \(0.150445\pi\) | ||||
−0.890371 | + | 0.455235i | \(0.849555\pi\) | |||||||
\(312\) | 91.8823i | 0.294494i | ||||||||
\(313\) | 48.5819 | 0.155214 | 0.0776069 | − | 0.996984i | \(-0.475272\pi\) | ||||
0.0776069 | + | 0.996984i | \(0.475272\pi\) | |||||||
\(314\) | − | 330.465i | − | 1.05244i | ||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −139.647 | −0.441920 | ||||||||
\(317\) | 578.029i | 1.82343i | 0.410819 | + | 0.911717i | \(0.365243\pi\) | ||||
−0.410819 | + | 0.911717i | \(0.634757\pi\) | |||||||
\(318\) | −90.7032 | −0.285230 | ||||||||
\(319\) | 52.7208 | 0.165269 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | − | 80.0946i | − | 0.249516i | ||||||
\(322\) | −83.8770 | + | 165.338i | −0.260488 | + | 0.513472i | ||||
\(323\) | 541.456i | 1.67633i | ||||||||
\(324\) | −18.0000 | −0.0555556 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 103.362 | 0.317063 | ||||||||
\(327\) | −62.2519 | −0.190373 | ||||||||
\(328\) | −117.083 | −0.356961 | ||||||||
\(329\) | −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 | \(0.332574\pi\) | |||||||
\(332\) | −12.8717 | −0.0387701 | ||||||||
\(333\) | 212.735i | 0.638844i | ||||||||
\(334\) | 55.7141i | 0.166809i | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −21.9411 | + | 43.2503i | −0.0653010 | + | 0.128721i | ||||
\(337\) | − | 88.1766i | − | 0.261652i | −0.991405 | − | 0.130826i | \(-0.958237\pi\) | ||
0.991405 | − | 0.130826i | \(-0.0417629\pi\) | |||||||
\(338\) | 258.468i | 0.764698i | ||||||||
\(339\) | 126.491i | 0.373129i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 15.1296i | 0.0443683i | ||||||||
\(342\) | 97.8354 | 0.286068 | ||||||||
\(343\) | −338.488 | + | 55.4487i | −0.986847 | + | 0.161658i | ||||
\(344\) | 29.4903 | 0.0857277 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 33.6985i | 0.0973945i | ||||||||
\(347\) | 320.080i | 0.922422i | 0.887291 | + | 0.461211i | \(0.152585\pi\) | ||||
−0.887291 | + | 0.461211i | \(0.847415\pi\) | |||||||
\(348\) | −103.923 | −0.298629 | ||||||||
\(349\) | − | 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 | ||||||||
\(352\) | − | 9.94113i | − | 0.0282418i | ||||||
\(353\) | −655.712 | −1.85754 | −0.928771 | − | 0.370654i | \(-0.879134\pi\) | ||||
−0.928771 | + | 0.370654i | \(0.879134\pi\) | |||||||
\(354\) | −238.794 | −0.674559 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 84.1829i | 0.236469i | ||||||||
\(357\) | 128.796 | − | 253.882i | 0.360773 | − | 0.711155i | ||||
\(358\) | 18.2498i | 0.0509770i | ||||||||
\(359\) | 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 | ||||||||
\(362\) | 92.4440 | 0.255370 | ||||||||
\(363\) | 204.229 | 0.562614 | ||||||||
\(364\) | −118.794 | + | 234.166i | −0.326357 | + | 0.643314i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −40.9706 | −0.111941 | ||||||||
\(367\) | 321.057 | 0.874815 | 0.437408 | − | 0.899263i | \(-0.355897\pi\) | ||||
0.437408 | + | 0.899263i | \(0.355897\pi\) | |||||||
\(368\) | 74.9117i | 0.203564i | ||||||||
\(369\) | − | 124.185i | − | 0.336546i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −231.161 | − | 117.270i | −0.623077 | − | 0.316091i | ||||
\(372\) | − | 29.8234i | − | 0.0801704i | ||||||
\(373\) | 187.470i | 0.502601i | 0.967909 | + | 0.251300i | \(0.0808582\pi\) | ||||
−0.967909 | + | 0.251300i | \(0.919142\pi\) | |||||||
\(374\) | 58.3551i | 0.156030i | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 109.459i | 0.291113i | ||||||||
\(377\) | −562.662 | −1.49247 | ||||||||
\(378\) | −45.8739 | − | 23.2721i | −0.121359 | − | 0.0615663i | ||||
\(379\) | 357.103 | 0.942223 | 0.471112 | − | 0.882074i | \(-0.343853\pi\) | ||||
0.471112 | + | 0.882074i | \(0.343853\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 155.783i | 0.408878i | ||||||||
\(382\) | − | 141.515i | − | 0.370457i | ||||||
\(383\) | 622.230 | 1.62462 | 0.812311 | − | 0.583225i | \(-0.198209\pi\) | ||||
0.812311 | + | 0.583225i | \(0.198209\pi\) | |||||||
\(384\) | 19.5959i | 0.0510310i | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −111.598 | −0.289114 | ||||||||
\(387\) | 31.2792i | 0.0808249i | ||||||||
\(388\) | 103.431 | 0.266574 | ||||||||
\(389\) | −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 | ||||||
\(392\) | −111.836 | + | 81.8579i | −0.285296 | + | 0.208821i | ||||
\(393\) | 21.0883i | 0.0536598i | ||||||||
\(394\) | −260.132 | −0.660234 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 10.5442 | 0.0266267 | ||||||||
\(397\) | −720.329 | −1.81443 | −0.907216 | − | 0.420666i | \(-0.861796\pi\) | ||||
−0.907216 | + | 0.420666i | \(0.861796\pi\) | |||||||
\(398\) | −240.458 | −0.604166 | ||||||||
\(399\) | 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 | \(0.164572\pi\) | |||||||
\(402\) | −149.347 | −0.371509 | ||||||||
\(403\) | − | 161.470i | − | 0.400670i | ||||||
\(404\) | 13.2198i | 0.0327223i | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −264.853 | − | 134.361i | −0.652347 | − | 0.330939i | ||||
\(407\) | − | 124.617i | − | 0.306185i | ||||||
\(408\) | − | 115.029i | − | 0.281935i | ||||||
\(409\) | 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 | ||||||||
\(412\) | −351.742 | −0.853742 | ||||||||
\(413\) | −608.578 | − | 308.735i | −1.47355 | − | 0.747543i | ||||
\(414\) | −79.4558 | −0.191922 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 106.096i | 0.255040i | ||||||||
\(417\) | 381.941i | 0.915926i | ||||||||
\(418\) | −57.3106 | −0.137107 | ||||||||
\(419\) | 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 | \(0.361696\pi\) | |||||||
\(422\) | 30.5097i | 0.0722978i | ||||||||
\(423\) | −116.098 | −0.274464 | ||||||||
\(424\) | −104.735 | −0.247017 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 270.938i | 0.636006i | ||||||||
\(427\) | −104.415 | − | 52.9706i | −0.244533 | − | 0.124053i | ||||
\(428\) | − | 92.4853i | − | 0.216087i | ||||||
\(429\) | 57.0883 | 0.133073 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 585.286 | 1.35797 | 0.678987 | − | 0.734151i | \(-0.262419\pi\) | ||||
0.678987 | + | 0.734151i | \(0.262419\pi\) | |||||||
\(432\) | −20.7846 | −0.0481125 | ||||||||
\(433\) | −392.207 | −0.905789 | −0.452895 | − | 0.891564i | \(-0.649609\pi\) | ||||
−0.452895 | + | 0.891564i | \(0.649609\pi\) | |||||||
\(434\) | 38.5584 | − | 76.0063i | 0.0888443 | − | 0.175130i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −71.8823 | −0.164868 | ||||||||
\(437\) | 431.866 | 0.988252 | ||||||||
\(438\) | 139.029i | 0.317419i | ||||||||
\(439\) | − | 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 | ||||
\(442\) | − | 622.794i | − | 1.40904i | ||||||
\(443\) | − | 814.742i | − | 1.83915i | −0.392918 | − | 0.919574i | \(-0.628534\pi\) | ||
0.392918 | − | 0.919574i | \(-0.371466\pi\) | |||||||
\(444\) | 245.645i | 0.553255i | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | − | 168.798i | − | 0.378472i | ||||||
\(447\) | 365.208 | 0.817020 | ||||||||
\(448\) | −25.3354 | + | 49.9411i | −0.0565523 | + | 0.111476i | ||||
\(449\) | −180.323 | −0.401610 | −0.200805 | − | 0.979631i | \(-0.564356\pi\) | ||||
−0.200805 | + | 0.979631i | \(0.564356\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 72.7461i | 0.161300i | ||||||||
\(452\) | 146.059i | 0.323139i | ||||||||
\(453\) | 125.344 | 0.276698 | ||||||||
\(454\) | 240.194i | 0.529062i | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 112.971 | 0.247742 | ||||||||
\(457\) | − | 280.177i | − | 0.613078i | −0.951858 | − | 0.306539i | \(-0.900829\pi\) | ||
0.951858 | − | 0.306539i | \(-0.0991710\pi\) | |||||||
\(458\) | 155.579 | 0.339691 | ||||||||
\(459\) | 122.007 | 0.265811 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 406.297i | − | 0.881338i | −0.897670 | − | 0.440669i | \(-0.854741\pi\) | ||
0.897670 | − | 0.440669i | \(-0.145259\pi\) | |||||||
\(462\) | 26.8723 | + | 13.6325i | 0.0581651 | + | 0.0295075i | ||||
\(463\) | 457.470i | 0.988056i | 0.869446 | + | 0.494028i | \(0.164476\pi\) | ||||
−0.869446 | + | 0.494028i | \(0.835524\pi\) | |||||||
\(464\) | −120.000 | −0.258621 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −80.9848 | −0.173787 | ||||||||
\(467\) | 643.711 | 1.37840 | 0.689198 | − | 0.724573i | \(-0.257963\pi\) | ||||
0.689198 | + | 0.724573i | \(0.257963\pi\) | |||||||
\(468\) | −112.532 | −0.240454 | ||||||||
\(469\) | −380.617 | − | 193.089i | −0.811551 | − | 0.411705i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 404.735 | 0.859310 | ||||||||
\(472\) | −275.735 | −0.584185 | ||||||||
\(473\) | − | 18.3229i | − | 0.0387377i | ||||||
\(474\) | − | 171.032i | − | 0.360826i | ||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 148.721 | − | 293.158i | 0.312439 | − | 0.615878i | ||||
\(477\) | − | 111.088i | − | 0.232890i | ||||||
\(478\) | − | 398.132i | − | 0.832912i | ||||||
\(479\) | 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 | ||||||||
\(482\) | 238.021 | 0.493819 | ||||||||
\(483\) | −202.497 | − | 102.728i | −0.419248 | − | 0.212687i | ||||
\(484\) | 235.823 | 0.487238 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | − | 22.0454i | − | 0.0453609i | ||||||
\(487\) | 2.77965i | 0.00570771i | 0.999996 | + | 0.00285385i | \(0.000908411\pi\) | ||||
−0.999996 | + | 0.00285385i | \(0.999092\pi\) | |||||||
\(488\) | −47.3087 | −0.0969441 | ||||||||
\(489\) | 126.593i | 0.258881i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −247.477 | −0.504027 | −0.252014 | − | 0.967724i | \(-0.581093\pi\) | ||||
−0.252014 | + | 0.967724i | \(0.581093\pi\) | |||||||
\(492\) | − | 143.397i | − | 0.291457i | ||||||
\(493\) | 704.409 | 1.42882 | ||||||||
\(494\) | 611.647 | 1.23815 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | − | 34.4371i | − | 0.0694296i | ||||||
\(497\) | −350.295 | + | 690.500i | −0.704818 | + | 1.38934i | ||||
\(498\) | − | 15.7645i | − | 0.0316556i | ||||||
\(499\) | 483.426 | 0.968789 | 0.484394 | − | 0.874850i | \(-0.339040\pi\) | ||||
0.484394 | + | 0.874850i | \(0.339040\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −68.2355 | −0.136199 | ||||||||
\(502\) | 150.043 | 0.298891 | ||||||||
\(503\) | 58.7033 | 0.116706 | 0.0583532 | − | 0.998296i | \(-0.481415\pi\) | ||||
0.0583532 | + | 0.998296i | \(0.481415\pi\) | |||||||
\(504\) | −52.9706 | − | 26.8723i | −0.105100 | − | 0.0533180i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 46.5442 | 0.0919845 | ||||||||
\(507\) | −316.557 | −0.624374 | ||||||||
\(508\) | 179.882i | 0.354099i | ||||||||
\(509\) | 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 | ||||
\(512\) | 22.6274i | 0.0441942i | ||||||||
\(513\) | 119.823i | 0.233574i | ||||||||
\(514\) | 410.776i | 0.799175i | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 36.1181i | 0.0699964i | ||||||||
\(517\) | 68.0089 | 0.131545 | ||||||||
\(518\) | −317.593 | + | 626.039i | −0.613114 | + | 1.20857i | ||||
\(519\) | −41.2721 | −0.0795223 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 292.720i | − | 0.561843i | −0.959731 | − | 0.280922i | \(-0.909360\pi\) | ||
0.959731 | − | 0.280922i | \(-0.0906401\pi\) | |||||||
\(522\) | − | 127.279i | − | 0.243830i | ||||||
\(523\) | 493.056 | 0.942746 | 0.471373 | − | 0.881934i | \(-0.343759\pi\) | ||||
0.471373 | + | 0.881934i | \(0.343759\pi\) | |||||||
\(524\) | 24.3507i | 0.0464708i | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 125.897 | 0.239347 | ||||||||
\(527\) | 202.148i | 0.383583i | ||||||||
\(528\) | 12.1753 | 0.0230594 | ||||||||
\(529\) | 178.265 | 0.336985 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 292.462i | − | 0.550775i | ||||||
\(532\) | 287.911 | + | 146.059i | 0.541186 | + | 0.274547i | ||||
\(533\) | − | 776.382i | − | 1.45663i | ||||||
\(534\) | −103.103 | −0.193076 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −172.451 | −0.321737 | ||||||||
\(537\) | −22.3513 | −0.0416226 | ||||||||
\(538\) | −270.819 | −0.503381 | ||||||||
\(539\) | 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 | \(0.908758\pi\) | |||||||
\(542\) | −307.507 | −0.567356 | ||||||||
\(543\) | 113.220i | 0.208509i | ||||||||
\(544\) | − | 132.825i | − | 0.244163i | ||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −286.794 | − | 145.492i | −0.525264 | − | 0.266469i | ||||
\(547\) | 130.530i | 0.238629i | 0.992857 | + | 0.119314i | \(0.0380696\pi\) | ||||
−0.992857 | + | 0.119314i | \(0.961930\pi\) | |||||||
\(548\) | 331.529i | 0.604980i | ||||||||
\(549\) | − | 50.1785i | − | 0.0913998i | ||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 691.801i | 1.25554i | ||||||||
\(552\) | −91.7477 | −0.166210 | ||||||||
\(553\) | 221.126 | − | 435.882i | 0.399866 | − | 0.788214i | ||||
\(554\) | 411.078 | 0.742018 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 441.028i | 0.793215i | ||||||||
\(557\) | − | 665.147i | − | 1.19416i | −0.802182 | − | 0.597080i | \(-0.796327\pi\) | ||
0.802182 | − | 0.597080i | \(-0.203673\pi\) | |||||||
\(558\) | 36.5260 | 0.0654588 | ||||||||
\(559\) | 195.551i | 0.349823i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −71.4701 | −0.127398 | ||||||||
\(562\) | 26.6619i | 0.0474411i | ||||||||
\(563\) | 829.295 | 1.47299 | 0.736497 | − | 0.676441i | \(-0.236479\pi\) | ||||
0.736497 | + | 0.676441i | \(0.236479\pi\) | |||||||
\(564\) | −134.059 | −0.237693 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | − | 568.137i | − | 1.00378i | ||||||
\(567\) | 28.5024 | − | 56.1838i | 0.0502687 | − | 0.0990895i | ||||
\(568\) | 312.853i | 0.550797i | ||||||||
\(569\) | −706.971 | −1.24248 | −0.621240 | − | 0.783621i | \(-0.713371\pi\) | ||||
−0.621240 | + | 0.783621i | \(0.713371\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −366.912 | −0.642577 | −0.321289 | − | 0.946981i | \(-0.604116\pi\) | ||||
−0.321289 | + | 0.946981i | \(0.604116\pi\) | |||||||
\(572\) | 65.9199 | 0.115245 | ||||||||
\(573\) | 173.319 | 0.302477 | ||||||||
\(574\) | 185.397 | − | 365.454i | 0.322991 | − | 0.636679i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −24.0000 | −0.0416667 | ||||||||
\(577\) | 390.357 | 0.676528 | 0.338264 | − | 0.941051i | \(-0.390160\pi\) | ||||
0.338264 | + | 0.941051i | \(0.390160\pi\) | |||||||
\(578\) | 370.982i | 0.641837i | ||||||||
\(579\) | − | 136.679i | − | 0.236061i | ||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 20.3818 | − | 40.1766i | 0.0350806 | − | 0.0691507i | ||||
\(582\) | 126.676i | 0.217657i | ||||||||
\(583\) | 65.0740i | 0.111619i | ||||||||
\(584\) | 160.537i | 0.274893i | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | − | 397.243i | − | 0.677889i | ||||||
\(587\) | 702.499 | 1.19676 | 0.598381 | − | 0.801212i | \(-0.295811\pi\) | ||||
0.598381 | + | 0.801212i | \(0.295811\pi\) | |||||||
\(588\) | −100.255 | − | 136.971i | −0.170502 | − | 0.232943i | ||||
\(589\) | −198.530 | −0.337063 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − | 318.595i | − | 0.539078i | ||||||
\(592\) | 283.647i | 0.479133i | ||||||||
\(593\) | 942.519 | 1.58941 | 0.794704 | − | 0.606997i | \(-0.207626\pi\) | ||||
0.794704 | + | 0.606997i | \(0.207626\pi\) | |||||||
\(594\) | 12.9139i | 0.0217406i | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 421.706 | 0.707560 | ||||||||
\(597\) | − | 294.500i | − | 0.493299i | ||||||
\(598\) | −496.742 | −0.830672 | ||||||||
\(599\) | 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 | \(-0.792310\pi\) | ||
0.794581 | − | 0.607158i | \(-0.207690\pi\) | |||||||
\(602\) | −46.6969 | + | 92.0488i | −0.0775696 | + | 0.152905i | ||||
\(603\) | − | 182.912i | − | 0.303336i | ||||||
\(604\) | 144.735 | 0.239628 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −16.1909 | −0.0267177 | ||||||||
\(607\) | 1006.34 | 1.65789 | 0.828944 | − | 0.559332i | \(-0.188942\pi\) | ||||
0.828944 | + | 0.559332i | \(0.188942\pi\) | |||||||
\(608\) | 130.447 | 0.214551 | ||||||||
\(609\) | 164.558 | − | 324.377i | 0.270211 | − | 0.532639i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −725.823 | −1.18793 | ||||||||
\(612\) | 140.882 | 0.230199 | ||||||||
\(613\) | − | 199.588i | − | 0.325592i | −0.986660 | − | 0.162796i | \(-0.947949\pi\) | ||
0.986660 | − | 0.162796i | \(-0.0520512\pi\) | |||||||
\(614\) | − | 215.411i | − | 0.350832i | ||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 31.0294 | + | 15.7414i | 0.0503725 | + | 0.0255542i | ||||
\(617\) | 353.294i | 0.572599i | 0.958140 | + | 0.286299i | \(0.0924252\pi\) | ||||
−0.958140 | + | 0.286299i | \(0.907575\pi\) | |||||||
\(618\) | − | 430.794i | − | 0.697078i | ||||||
\(619\) | − | 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 | ||||||
\(622\) | −400.443 | −0.643799 | ||||||||
\(623\) | −262.762 | − | 133.301i | −0.421769 | − | 0.213966i | ||||
\(624\) | −129.941 | −0.208239 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 68.7052i | 0.109753i | ||||||||
\(627\) | − | 70.1909i | − | 0.111947i | ||||||
\(628\) | 467.348 | 0.744184 | ||||||||
\(629\) | − | 1665.03i | − | 2.64710i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 807.322 | 1.27943 | 0.639716 | − | 0.768611i | \(-0.279052\pi\) | ||||
0.639716 | + | 0.768611i | \(0.279052\pi\) | |||||||
\(632\) | − | 197.490i | − | 0.312485i | ||||||
\(633\) | −37.3666 | −0.0590309 | ||||||||
\(634\) | −817.456 | −1.28936 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | − | 128.274i | − | 0.201688i | ||||||
\(637\) | −542.802 | − | 741.588i | −0.852122 | − | 1.16419i | ||||
\(638\) | 74.5584i | 0.116863i | ||||||||
\(639\) | −331.831 | −0.519297 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1016.35 | 1.58557 | 0.792786 | − | 0.609500i | \(-0.208630\pi\) | ||||
0.792786 | + | 0.609500i | \(0.208630\pi\) | |||||||
\(642\) | 113.271 | 0.176434 | ||||||||
\(643\) | −404.688 | −0.629375 | −0.314687 | − | 0.949195i | \(-0.601900\pi\) | ||||
−0.314687 | + | 0.949195i | \(0.601900\pi\) | |||||||
\(644\) | −233.823 | − | 118.620i | −0.363080 | − | 0.184193i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −765.734 | −1.18535 | ||||||||
\(647\) | 940.604 | 1.45379 | 0.726896 | − | 0.686747i | \(-0.240962\pi\) | ||||
0.726896 | + | 0.686747i | \(0.240962\pi\) | |||||||
\(648\) | − | 25.4558i | − | 0.0392837i | ||||||
\(649\) | 171.320i | 0.263975i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 93.0883 | + | 47.2243i | 0.142993 | + | 0.0725411i | ||||
\(652\) | 146.177i | 0.224197i | ||||||||
\(653\) | 731.970i | 1.12093i | 0.828177 | + | 0.560467i | \(0.189378\pi\) | ||||
−0.828177 | + | 0.560467i | \(0.810622\pi\) | |||||||
\(654\) | − | 88.0374i | − | 0.134614i | ||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | − | 165.581i | − | 0.252409i | ||||||
\(657\) | −170.276 | −0.259171 | ||||||||
\(658\) | −341.655 | − | 173.324i | −0.519233 | − | 0.263410i | ||||
\(659\) | −904.316 | −1.37225 | −0.686127 | − | 0.727481i | \(-0.740691\pi\) | ||||
−0.686127 | + | 0.727481i | \(0.740691\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 335.881i | 0.508141i | 0.967186 | + | 0.254070i | \(0.0817695\pi\) | ||||
−0.967186 | + | 0.254070i | \(0.918231\pi\) | |||||||
\(662\) | 470.039i | 0.710028i | ||||||||
\(663\) | 762.764 | 1.15047 | ||||||||
\(664\) | − | 18.2033i | − | 0.0274146i | ||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −300.853 | −0.451731 | ||||||||
\(667\) | − | 561.838i | − | 0.842335i | ||||||
\(668\) | −78.7916 | −0.117951 | ||||||||
\(669\) | 206.735 | 0.309021 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 29.3939i | 0.0438061i | ||||||||
\(672\) | −61.1651 | − | 31.0294i | −0.0910195 | − | 0.0461748i | ||||
\(673\) | 1191.44i | 1.77034i | 0.465266 | + | 0.885171i | \(0.345959\pi\) | ||||
−0.465266 | + | 0.885171i | \(0.654041\pi\) | |||||||
\(674\) | 124.701 | 0.185016 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −365.529 | −0.540723 | ||||||||
\(677\) | −1211.07 | −1.78888 | −0.894441 | − | 0.447186i | \(-0.852426\pi\) | ||||
−0.894441 | + | 0.447186i | \(0.852426\pi\) | |||||||
\(678\) | −178.885 | −0.263842 | ||||||||
\(679\) | −163.779 | + | 322.840i | −0.241206 | + | 0.475464i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −294.177 | −0.431977 | ||||||||
\(682\) | −21.3965 | −0.0313731 | ||||||||
\(683\) | − | 1233.89i | − | 1.80657i | −0.429038 | − | 0.903287i | \(-0.641147\pi\) | ||
0.429038 | − | 0.903287i | \(-0.358853\pi\) | |||||||
\(684\) | 138.360i | 0.202281i | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −78.4163 | − | 478.695i | −0.114309 | − | 0.697806i | ||||
\(687\) | 190.544i | 0.277357i | ||||||||
\(688\) | 41.7056i | 0.0606186i | ||||||||
\(689\) | − | 694.501i | − | 1.00798i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 86.7045i | 0.125477i | 0.998030 | + | 0.0627384i | \(0.0199834\pi\) | ||||
−0.998030 | + | 0.0627384i | \(0.980017\pi\) | |||||||
\(692\) | −47.6569 | −0.0688683 | ||||||||
\(693\) | −16.6963 | + | 32.9117i | −0.0240928 | + | 0.0474916i | ||||
\(694\) | −452.662 | −0.652251 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | − | 146.969i | − | 0.211163i | ||||||
\(697\) | 971.970i | 1.39450i | ||||||||
\(698\) | 470.998 | 0.674783 | ||||||||
\(699\) | − | 99.1858i | − | 0.141897i | ||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −149.147 | −0.212763 | −0.106382 | − | 0.994325i | \(-0.533927\pi\) | ||||
−0.106382 | + | 0.994325i | \(0.533927\pi\) | |||||||
\(702\) | − | 137.823i | − | 0.196330i | ||||||
\(703\) | 1635.22 | 2.32607 | ||||||||
\(704\) | 14.0589 | 0.0199700 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | − | 927.317i | − | 1.31348i | ||||||
\(707\) | −41.2633 | − | 20.9331i | −0.0583639 | − | 0.0296084i | ||||
\(708\) | − | 337.706i | − | 0.476985i | ||||||
\(709\) | −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 | ||||||||
\(712\) | −119.053 | −0.167209 | ||||||||
\(713\) | 161.234 | 0.226134 | ||||||||
\(714\) | 359.044 | + | 182.145i | 0.502862 | + | 0.255105i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −25.8091 | −0.0360462 | ||||||||
\(717\) | 487.610 | 0.680070 | ||||||||
\(718\) | 138.250i | 0.192548i | ||||||||
\(719\) | − | 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 | ||||
\(722\) | − | 241.497i | − | 0.334484i | ||||||
\(723\) | 291.515i | 0.403202i | ||||||||
\(724\) | 130.736i | 0.180574i | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 288.823i | 0.397828i | ||||||||
\(727\) | 417.169 | 0.573823 | 0.286911 | − | 0.957957i | \(-0.407371\pi\) | ||||
0.286911 | + | 0.957957i | \(0.407371\pi\) | |||||||
\(728\) | −331.161 | − | 168.000i | −0.454892 | − | 0.230769i | ||||
\(729\) | 27.0000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 244.815i | − | 0.334904i | ||||||
\(732\) | − | 57.9411i | − | 0.0791545i | ||||||
\(733\) | 1286.99 | 1.75578 | 0.877892 | − | 0.478859i | \(-0.158949\pi\) | ||||
0.877892 | + | 0.478859i | \(0.158949\pi\) | |||||||
\(734\) | 454.043i | 0.618588i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −105.941 | −0.143942 | ||||||||
\(737\) | 107.147i | 0.145383i | ||||||||
\(738\) | 175.625 | 0.237974 | ||||||||
\(739\) | −1333.47 | −1.80443 | −0.902213 | − | 0.431292i | \(-0.858058\pi\) | ||||
−0.902213 | + | 0.431292i | \(0.858058\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 749.111i | 1.01095i | ||||||||
\(742\) | 165.844 | − | 326.912i | 0.223510 | − | 0.440582i | ||||
\(743\) | − | 776.476i | − | 1.04506i | −0.852622 | − | 0.522528i | \(-0.824989\pi\) | ||
0.852622 | − | 0.522528i | \(-0.175011\pi\) | |||||||
\(744\) | 42.1766 | 0.0566890 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −265.123 | −0.355392 | ||||||||
\(747\) | 19.3075 | 0.0258467 | ||||||||
\(748\) | −82.5266 | −0.110330 | ||||||||
\(749\) | 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 | \(0.489648\pi\) | |||||||
\(752\) | −154.798 | −0.205848 | ||||||||
\(753\) | 183.765i | 0.244043i | ||||||||
\(754\) | − | 795.724i | − | 1.05534i | ||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 32.9117 | − | 64.8754i | 0.0435340 | − | 0.0858141i | ||||
\(757\) | 1279.47i | 1.69019i | 0.534620 | + | 0.845093i | \(0.320455\pi\) | ||||
−0.534620 | + | 0.845093i | \(0.679545\pi\) | |||||||
\(758\) | 505.019i | 0.666252i | ||||||||
\(759\) | 57.0047i | 0.0751050i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1316.12i | 1.72947i | 0.502231 | + | 0.864734i | \(0.332513\pi\) | ||||
−0.502231 | + | 0.864734i | \(0.667487\pi\) | |||||||
\(762\) | −220.310 | −0.289121 | ||||||||
\(763\) | 113.823 | − | 224.368i | 0.149178 | − | 0.294060i | ||||
\(764\) | 200.132 | 0.261953 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 879.966i | 1.14878i | ||||||||
\(767\) | − | 1828.41i | − | 2.38385i | ||||||
\(768\) | −27.7128 | −0.0360844 | ||||||||
\(769\) | − | 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 | ||||||||
\(772\) | − | 157.823i | − | 0.204434i | ||||||
\(773\) | −717.634 | −0.928375 | −0.464187 | − | 0.885737i | \(-0.653654\pi\) | ||||
−0.464187 | + | 0.885737i | \(0.653654\pi\) | |||||||
\(774\) | −44.2355 | −0.0571518 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 146.273i | 0.188496i | ||||||||
\(777\) | −766.738 | − | 388.971i | −0.986792 | − | 0.500606i | ||||
\(778\) | − | 321.691i | − | 0.413485i | ||||||
\(779\) | −954.573 | −1.22538 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 194.382 | 0.248888 | ||||||||
\(782\) | 621.882 | 0.795245 | ||||||||
\(783\) | 155.885 | 0.199086 | ||||||||
\(784\) | −115.765 | − | 158.160i | −0.147659 | − | 0.201735i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −29.8234 | −0.0379432 | ||||||||
\(787\) | 347.191 | 0.441158 | 0.220579 | − | 0.975369i | \(-0.429205\pi\) | ||||
0.220579 | + | 0.975369i | \(0.429205\pi\) | |||||||
\(788\) | − | 367.882i | − | 0.466856i | ||||||
\(789\) | 154.191i | 0.195426i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −455.897 | − | 231.279i | −0.576355 | − | 0.292388i | ||||
\(792\) | 14.9117i | 0.0188279i | ||||||||
\(793\) | − | 313.706i | − | 0.395593i | ||||||
\(794\) | − | 1018.70i | − | 1.28300i | ||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | − | 340.059i | − | 0.427210i | ||||||
\(797\) | −361.246 | −0.453257 | −0.226629 | − | 0.973981i | \(-0.572770\pi\) | ||||
−0.226629 | + | 0.973981i | \(0.572770\pi\) | |||||||
\(798\) | −178.885 | + | 352.617i | −0.224166 | + | 0.441876i | ||||
\(799\) | 908.674 | 1.13726 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | − | 126.274i | − | 0.157646i | ||||||
\(802\) | 985.955i | 1.22937i | ||||||||
\(803\) | 99.7451 | 0.124216 | ||||||||
\(804\) | − | 211.208i | − | 0.262697i | ||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 228.353 | 0.283317 | ||||||||
\(807\) | − | 331.684i | − | 0.411009i | ||||||
\(808\) | −18.6957 | −0.0231382 | ||||||||
\(809\) | 113.147 | 0.139861 | 0.0699303 | − | 0.997552i | \(-0.477722\pi\) | ||||
0.0699303 | + | 0.997552i | \(0.477722\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 134.182i | − | 0.165453i | −0.996572 | − | 0.0827264i | \(-0.973637\pi\) | ||
0.996572 | − | 0.0827264i | \(-0.0263628\pi\) | |||||||
\(812\) | 190.016 | − | 374.558i | 0.234010 | − | 0.461279i | ||||
\(813\) | − | 376.617i | − | 0.463244i | ||||||
\(814\) | 176.235 | 0.216506 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 162.676 | 0.199358 | ||||||||
\(817\) | 240.433 | 0.294288 | ||||||||
\(818\) | −144.796 | −0.177012 | ||||||||
\(819\) | 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 | \(0.403201\pi\) | |||||||
\(822\) | −406.038 | −0.493964 | ||||||||
\(823\) | − | 941.852i | − | 1.14441i | −0.820110 | − | 0.572207i | \(-0.806088\pi\) | ||
0.820110 | − | 0.572207i | \(-0.193912\pi\) | |||||||
\(824\) | − | 497.438i | − | 0.603687i | ||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 436.617 | − | 860.659i | 0.528592 | − | 1.04196i | ||||
\(827\) | − | 966.978i | − | 1.16926i | −0.811300 | − | 0.584630i | \(-0.801240\pi\) | ||
0.811300 | − | 0.584630i | \(-0.198760\pi\) | |||||||
\(828\) | − | 112.368i | − | 0.135710i | ||||||
\(829\) | − | 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 | ||||||||
\(832\) | −150.043 | −0.180340 | ||||||||
\(833\) | 679.546 | + | 928.410i | 0.815781 | + | 1.11454i | ||||
\(834\) | −540.146 | −0.647657 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | − | 81.0495i | − | 0.0969491i | ||||||
\(837\) | 44.7351i | 0.0534469i | ||||||||
\(838\) | −553.560 | −0.660573 | ||||||||
\(839\) | 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 | ||||||||
\(842\) | 501.255i | 0.595315i | ||||||||
\(843\) | −32.6540 | −0.0387355 | ||||||||
\(844\) | −43.1472 | −0.0511223 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | − | 164.188i | − | 0.194076i | ||||||
\(847\) | −373.418 | + | 736.080i | −0.440871 | + | 0.869044i | ||||
\(848\) | − | 148.118i | − | 0.174667i | ||||||
\(849\) | 695.823 | 0.819580 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −1328.03 | −1.56055 | ||||||||
\(852\) | −383.165 | −0.449724 | ||||||||
\(853\) | −175.006 | −0.205165 | −0.102582 | − | 0.994725i | \(-0.532711\pi\) | ||||
−0.102582 | + | 0.994725i | \(0.532711\pi\) | |||||||
\(854\) | 74.9117 | − | 147.666i | 0.0877186 | − | 0.172911i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 130.794 | 0.152797 | ||||||||
\(857\) | 61.7471 | 0.0720503 | 0.0360252 | − | 0.999351i | \(-0.488530\pi\) | ||||
0.0360252 | + | 0.999351i | \(0.488530\pi\) | |||||||
\(858\) | 80.7351i | 0.0940968i | ||||||||
\(859\) | − | 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 | ||||
\(862\) | 827.720i | 0.960232i | ||||||||
\(863\) | − | 494.507i | − | 0.573009i | −0.958079 | − | 0.286504i | \(-0.907507\pi\) | ||
0.958079 | − | 0.286504i | \(-0.0924933\pi\) | |||||||
\(864\) | − | 29.3939i | − | 0.0340207i | ||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | − | 554.664i | − | 0.640490i | ||||||
\(867\) | −454.358 | −0.524058 | ||||||||
\(868\) | 107.489 | + | 54.5299i | 0.123835 | + | 0.0628224i | ||||
\(869\) | −122.705 | −0.141202 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 1143.53i | − | 1.31289i | ||||||
\(872\) | − | 101.657i | − | 0.116579i | ||||||
\(873\) | −155.146 | −0.177716 | ||||||||
\(874\) | 610.751i | 0.698800i | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −196.617 | −0.224449 | ||||||||
\(877\) | 454.353i | 0.518077i | 0.965867 | + | 0.259038i | \(0.0834056\pi\) | ||||
−0.965867 | + | 0.259038i | \(0.916594\pi\) | |||||||
\(878\) | 555.097 | 0.632229 | ||||||||
\(879\) | 486.521 | 0.553494 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 143.493i | − | 0.162875i | −0.996678 | − | 0.0814375i | \(-0.974049\pi\) | ||
0.996678 | − | 0.0814375i | \(-0.0259511\pi\) | |||||||
\(882\) | 167.754 | − | 122.787i | 0.190197 | − | 0.139214i | ||||
\(883\) | − | 927.986i | − | 1.05095i | −0.850810 | − | 0.525473i | \(-0.823888\pi\) | ||
0.850810 | − | 0.525473i | \(-0.176112\pi\) | |||||||
\(884\) | 880.764 | 0.996339 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 1152.22 | 1.30047 | ||||||||
\(887\) | −958.265 | −1.08034 | −0.540172 | − | 0.841555i | \(-0.681641\pi\) | ||||
−0.540172 | + | 0.841555i | \(0.681641\pi\) | |||||||
\(888\) | −347.395 | −0.391210 | ||||||||
\(889\) | −561.470 | − | 284.837i | −0.631575 | − | 0.320402i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −15.8162 | −0.0177511 | ||||||||
\(892\) | 238.717 | 0.267620 | ||||||||
\(893\) | 892.410i | 0.999340i | ||||||||
\(894\) | 516.482i | 0.577720i | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −70.6274 | − | 35.8297i | −0.0788252 | − | 0.0399885i | ||||
\(897\) | − | 608.382i | − | 0.678241i | ||||||
\(898\) | − | 255.015i | − | 0.283981i | ||||||
\(899\) | 258.278i | 0.287295i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 869.462i | 0.964996i | ||||||||
\(902\) | −102.879 | −0.114056 | ||||||||
\(903\) | −112.736 | − | 57.1918i | −0.124846 | − | 0.0633353i | ||||
\(904\) | −206.558 | −0.228494 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 177.264i | 0.195655i | ||||||||
\(907\) | 552.721i | 0.609394i | 0.952449 | + | 0.304697i | \(0.0985553\pi\) | ||||
−0.952449 | + | 0.304697i | \(0.901445\pi\) | |||||||
\(908\) | −339.686 | −0.374103 | ||||||||
\(909\) | − | 19.8297i | − | 0.0218149i | ||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 142.742 | 0.156687 | 0.0783437 | − | 0.996926i | \(-0.475037\pi\) | ||||
0.0783437 | + | 0.996926i | \(0.475037\pi\) | |||||||
\(912\) | 159.765i | 0.175180i | ||||||||
\(913\) | −11.3101 | −0.0123878 | ||||||||
\(914\) | 396.230 | 0.433512 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 220.021i | 0.240198i | ||||||||
\(917\) | −76.0063 | − | 38.5584i | −0.0828858 | − | 0.0420485i | ||||
\(918\) | 172.544i | 0.187957i | ||||||||
\(919\) | −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 | ||||||||
\(922\) | 574.591 | 0.623200 | ||||||||
\(923\) | −2074.54 | −2.24760 | ||||||||
\(924\) | −19.2792 | + | 38.0031i | −0.0208650 | + | 0.0411289i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −646.960 | −0.698661 | ||||||||
\(927\) | 527.613 | 0.569161 | ||||||||
\(928\) | − | 169.706i | − | 0.182872i | ||||||
\(929\) | − | 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 | ||||
\(932\) | − | 114.530i | − | 0.122886i | ||||||
\(933\) | − | 490.441i | − | 0.525660i | ||||||
\(934\) | 910.345i | 0.974673i | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | − | 159.145i | − | 0.170026i | ||||||
\(937\) | −759.317 | −0.810370 | −0.405185 | − | 0.914235i | \(-0.632793\pi\) | ||||
−0.405185 | + | 0.914235i | \(0.632793\pi\) | |||||||
\(938\) | 273.070 | − | 538.274i | 0.291119 | − | 0.573853i | ||||
\(939\) | −84.1463 | −0.0896127 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 36.3519i | − | 0.0386312i | −0.999813 | − | 0.0193156i | \(-0.993851\pi\) | ||
0.999813 | − | 0.0193156i | \(-0.00614873\pi\) | |||||||
\(942\) | 572.382i | 0.607624i | ||||||||
\(943\) | 775.245 | 0.822105 | ||||||||
\(944\) | − | 389.949i | − | 0.413081i | ||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 25.9126 | 0.0273917 | ||||||||
\(947\) | − | 92.5370i | − | 0.0977160i | −0.998806 | − | 0.0488580i | \(-0.984442\pi\) | ||
0.998806 | − | 0.0488580i | \(-0.0155582\pi\) | |||||||
\(948\) | 241.875 | 0.255143 | ||||||||
\(949\) | −1064.53 | −1.12174 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 1001.17i | − | 1.05276i | ||||||
\(952\) | 414.588 | + | 210.323i | 0.435492 | + | 0.220927i | ||||
\(953\) | − | 1361.29i | − | 1.42843i | −0.699927 | − | 0.714215i | \(-0.746784\pi\) | ||
0.699927 | − | 0.714215i | \(-0.253216\pi\) | |||||||
\(954\) | 157.103 | 0.164678 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 563.044 | 0.588958 | ||||||||
\(957\) | −91.3151 | −0.0954180 | ||||||||
\(958\) | −238.344 | −0.248794 | ||||||||
\(959\) | −1034.81 | − | 524.964i | −1.07905 | − | 0.547408i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 886.881 | 0.922873 | ||||||||
\(962\) | −1880.87 | −1.95517 | ||||||||
\(963\) | 138.728i | 0.144058i | ||||||||
\(964\) | 336.612i | 0.349183i | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 145.279 | − | 286.374i | 0.150393 | − | 0.296453i | ||||
\(967\) | − | 481.677i | − | 0.498115i | −0.968489 | − | 0.249057i | \(-0.919879\pi\) | ||
0.968489 | − | 0.249057i | \(-0.0801208\pi\) | |||||||
\(968\) | 333.505i | 0.344530i | ||||||||
\(969\) | − | 937.829i | − | 0.967832i | ||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 1427.34i | 1.46997i | 0.678082 | + | 0.734987i | \(0.262812\pi\) | ||||
−0.678082 | + | 0.734987i | \(0.737188\pi\) | |||||||
\(972\) | 31.1769 | 0.0320750 | ||||||||
\(973\) | −1376.59 | − | 698.352i | −1.41479 | − | 0.717730i | ||||
\(974\) | −3.93102 | −0.00403596 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | − | 66.9046i | − | 0.0685498i | ||||||
\(977\) | 1356.26i | 1.38819i | 0.719883 | + | 0.694095i | \(0.244195\pi\) | ||||
−0.719883 | + | 0.694095i | \(0.755805\pi\) | |||||||
\(978\) | −179.029 | −0.183056 | ||||||||
\(979\) | 73.9698i | 0.0755565i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 107.823 | 0.109912 | ||||||||
\(982\) | − | 349.986i | − | 0.356401i | ||||||
\(983\) | 1315.51 | 1.33826 | 0.669129 | − | 0.743146i | \(-0.266667\pi\) | ||||
0.669129 | + | 0.743146i | \(0.266667\pi\) | |||||||
\(984\) | 202.794 | 0.206091 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 996.184i | 1.01033i | ||||||||
\(987\) | 212.277 | − | 418.441i | 0.215073 | − | 0.423952i | ||||
\(988\) | 864.999i | 0.875505i | ||||||||
\(989\) | −195.265 | −0.197437 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1043.28 | 1.05275 | 0.526377 | − | 0.850251i | \(-0.323550\pi\) | ||||
0.526377 | + | 0.850251i | \(0.323550\pi\) | |||||||
\(992\) | 48.7014 | 0.0490941 | ||||||||
\(993\) | −575.677 | −0.579736 | ||||||||
\(994\) | −976.514 | − | 495.391i | −0.982408 | − | 0.498382i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 22.2944 | 0.0223839 | ||||||||
\(997\) | −820.328 | −0.822796 | −0.411398 | − | 0.911456i | \(-0.634959\pi\) | ||||
−0.411398 | + | 0.911456i | \(0.634959\pi\) | |||||||
\(998\) | 683.667i | 0.685037i | ||||||||
\(999\) | − | 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.h.a.349.6 | 8 | ||
5.2 | odd | 4 | 42.3.c.a.13.2 | yes | 4 | ||
5.3 | odd | 4 | 1050.3.f.a.601.3 | 4 | |||
5.4 | even | 2 | inner | 1050.3.h.a.349.3 | 8 | ||
7.6 | odd | 2 | inner | 1050.3.h.a.349.7 | 8 | ||
15.2 | even | 4 | 126.3.c.b.55.3 | 4 | |||
20.7 | even | 4 | 336.3.f.c.97.2 | 4 | |||
35.2 | odd | 12 | 294.3.g.b.31.2 | 4 | |||
35.12 | even | 12 | 294.3.g.c.31.2 | 4 | |||
35.13 | even | 4 | 1050.3.f.a.601.4 | 4 | |||
35.17 | even | 12 | 294.3.g.b.19.2 | 4 | |||
35.27 | even | 4 | 42.3.c.a.13.1 | ✓ | 4 | ||
35.32 | odd | 12 | 294.3.g.c.19.2 | 4 | |||
35.34 | odd | 2 | inner | 1050.3.h.a.349.2 | 8 | ||
40.27 | even | 4 | 1344.3.f.e.769.3 | 4 | |||
40.37 | odd | 4 | 1344.3.f.f.769.1 | 4 | |||
60.47 | odd | 4 | 1008.3.f.g.433.1 | 4 | |||
105.2 | even | 12 | 882.3.n.a.325.1 | 4 | |||
105.17 | odd | 12 | 882.3.n.a.19.1 | 4 | |||
105.32 | even | 12 | 882.3.n.d.19.1 | 4 | |||
105.47 | odd | 12 | 882.3.n.d.325.1 | 4 | |||
105.62 | odd | 4 | 126.3.c.b.55.4 | 4 | |||
140.27 | odd | 4 | 336.3.f.c.97.3 | 4 | |||
280.27 | odd | 4 | 1344.3.f.e.769.2 | 4 | |||
280.237 | even | 4 | 1344.3.f.f.769.4 | 4 | |||
420.167 | even | 4 | 1008.3.f.g.433.4 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
42.3.c.a.13.1 | ✓ | 4 | 35.27 | even | 4 | ||
42.3.c.a.13.2 | yes | 4 | 5.2 | odd | 4 | ||
126.3.c.b.55.3 | 4 | 15.2 | even | 4 | |||
126.3.c.b.55.4 | 4 | 105.62 | odd | 4 | |||
294.3.g.b.19.2 | 4 | 35.17 | even | 12 | |||
294.3.g.b.31.2 | 4 | 35.2 | odd | 12 | |||
294.3.g.c.19.2 | 4 | 35.32 | odd | 12 | |||
294.3.g.c.31.2 | 4 | 35.12 | even | 12 | |||
336.3.f.c.97.2 | 4 | 20.7 | even | 4 | |||
336.3.f.c.97.3 | 4 | 140.27 | odd | 4 | |||
882.3.n.a.19.1 | 4 | 105.17 | odd | 12 | |||
882.3.n.a.325.1 | 4 | 105.2 | even | 12 | |||
882.3.n.d.19.1 | 4 | 105.32 | even | 12 | |||
882.3.n.d.325.1 | 4 | 105.47 | odd | 12 | |||
1008.3.f.g.433.1 | 4 | 60.47 | odd | 4 | |||
1008.3.f.g.433.4 | 4 | 420.167 | even | 4 | |||
1050.3.f.a.601.3 | 4 | 5.3 | odd | 4 | |||
1050.3.f.a.601.4 | 4 | 35.13 | even | 4 | |||
1050.3.h.a.349.2 | 8 | 35.34 | odd | 2 | inner | ||
1050.3.h.a.349.3 | 8 | 5.4 | even | 2 | inner | ||
1050.3.h.a.349.6 | 8 | 1.1 | even | 1 | trivial | ||
1050.3.h.a.349.7 | 8 | 7.6 | odd | 2 | inner | ||
1344.3.f.e.769.2 | 4 | 280.27 | odd | 4 | |||
1344.3.f.e.769.3 | 4 | 40.27 | even | 4 | |||
1344.3.f.f.769.1 | 4 | 40.37 | odd | 4 | |||
1344.3.f.f.769.4 | 4 | 280.237 | even | 4 |