Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [775,2,Mod(249,775)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(775, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("775.249");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 775 = 5^{2} \cdot 31 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 775.b (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: | \(6.18840615665\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 2x^{5} + 28x^{4} - 12x^{3} + 2x^{2} + 8x + 16 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | no (minimal twist has level 155) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 249.6 | ||
Root | \(1.48716 + 1.48716i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 775.249 |
Dual form | 775.2.b.e.249.3 |
$q$-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 \(\left(\mathbb{Z}/775\mathbb{Z}\right)^\times\).
\(n\) | \(251\) | \(652\) |
\(\chi(n)\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.62946i | 1.15220i | 0.817378 | + | 0.576102i | \(0.195427\pi\) | ||||
−0.817378 | + | 0.576102i | \(0.804573\pi\) | |||||||
\(3\) | − 3.05273i | − 1.76249i | −0.472656 | − | 0.881247i | \(-0.656705\pi\) | ||||
0.472656 | − | 0.881247i | \(-0.343295\pi\) | |||||||
\(4\) | −0.655151 | −0.327576 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 4.97431 | 2.03075 | ||||||||
\(7\) | 2.97431i | 1.12418i | 0.827075 | + | 0.562092i | \(0.190003\pi\) | ||||
−0.827075 | + | 0.562092i | \(0.809997\pi\) | |||||||
\(8\) | 2.19138i | 0.774771i | ||||||||
\(9\) | −6.31916 | −2.10639 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.71539 | −0.517208 | −0.258604 | − | 0.965983i | \(-0.583262\pi\) | ||||
−0.258604 | + | 0.965983i | \(0.583262\pi\) | |||||||
\(12\) | 2.00000i | 0.577350i | ||||||||
\(13\) | 6.97431i | 1.93433i | 0.254157 | + | 0.967163i | \(0.418202\pi\) | ||||
−0.254157 | + | 0.967163i | \(0.581798\pi\) | |||||||
\(14\) | −4.84653 | −1.29529 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −4.88108 | −1.22027 | ||||||||
\(17\) | 2.76812i | 0.671367i | 0.941975 | + | 0.335683i | \(0.108967\pi\) | ||||
−0.941975 | + | 0.335683i | \(0.891033\pi\) | |||||||
\(18\) | − 10.2968i | − 2.42699i | ||||||||
\(19\) | −5.47600 | −1.25628 | −0.628140 | − | 0.778100i | \(-0.716183\pi\) | ||||
−0.628140 | + | 0.778100i | \(0.716183\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 9.07977 | 1.98137 | ||||||||
\(22\) | − 2.79516i | − 0.595930i | ||||||||
\(23\) | 0.127779i | 0.0266438i | 0.999911 | + | 0.0133219i | \(0.00424061\pi\) | ||||
−0.999911 | + | 0.0133219i | \(0.995759\pi\) | |||||||
\(24\) | 6.68970 | 1.36553 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −11.3644 | −2.22874 | ||||||||
\(27\) | 10.1325i | 1.95000i | ||||||||
\(28\) | − 1.94862i | − 0.368255i | ||||||||
\(29\) | 7.07977 | 1.31468 | 0.657340 | − | 0.753594i | \(-0.271681\pi\) | ||||
0.657340 | + | 0.753594i | \(0.271681\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.00000 | 0.179605 | ||||||||
\(32\) | − 3.57078i | − 0.631230i | ||||||||
\(33\) | 5.23661i | 0.911576i | ||||||||
\(34\) | −4.51054 | −0.773552 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 4.14001 | 0.690001 | ||||||||
\(37\) | − 8.02704i | − 1.31964i | −0.751425 | − | 0.659819i | \(-0.770633\pi\) | ||||
0.751425 | − | 0.659819i | \(-0.229367\pi\) | |||||||
\(38\) | − 8.92294i | − 1.44749i | ||||||||
\(39\) | 21.2907 | 3.40924 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 4.50168 | 0.703045 | 0.351522 | − | 0.936179i | \(-0.385664\pi\) | ||||
0.351522 | + | 0.936179i | \(0.385664\pi\) | |||||||
\(42\) | 14.7952i | 2.28294i | ||||||||
\(43\) | 4.76812i | 0.727131i | 0.931569 | + | 0.363565i | \(0.118441\pi\) | ||||
−0.931569 | + | 0.363565i | \(0.881559\pi\) | |||||||
\(44\) | 1.12384 | 0.169425 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −0.208211 | −0.0306991 | ||||||||
\(47\) | − 2.10546i | − 0.307113i | −0.988140 | − | 0.153556i | \(-0.950927\pi\) | ||||
0.988140 | − | 0.153556i | \(-0.0490727\pi\) | |||||||
\(48\) | 14.9006i | 2.15072i | ||||||||
\(49\) | −1.84653 | −0.263790 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 8.45031 | 1.18328 | ||||||||
\(52\) | − 4.56923i | − 0.633638i | ||||||||
\(53\) | 5.20957i | 0.715589i | 0.933800 | + | 0.357794i | \(0.116471\pi\) | ||||
−0.933800 | + | 0.357794i | \(0.883529\pi\) | |||||||
\(54\) | −16.5105 | −2.24680 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −6.51785 | −0.870985 | ||||||||
\(57\) | 16.7167i | 2.21419i | ||||||||
\(58\) | 11.5362i | 1.51478i | ||||||||
\(59\) | −13.2968 | −1.73110 | −0.865551 | − | 0.500821i | \(-0.833031\pi\) | ||||
−0.865551 | + | 0.500821i | \(0.833031\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −0.105460 | −0.0135028 | −0.00675140 | − | 0.999977i | \(-0.502149\pi\) | ||||
−0.00675140 | + | 0.999977i | \(0.502149\pi\) | |||||||
\(62\) | 1.62946i | 0.206942i | ||||||||
\(63\) | − 18.7952i | − 2.36797i | ||||||||
\(64\) | −3.94371 | −0.492964 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −8.53286 | −1.05032 | ||||||||
\(67\) | 2.28461i | 0.279110i | 0.990214 | + | 0.139555i | \(0.0445672\pi\) | ||||
−0.990214 | + | 0.139555i | \(0.955433\pi\) | |||||||
\(68\) | − 1.81353i | − 0.219923i | ||||||||
\(69\) | 0.390075 | 0.0469595 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 5.31916 | 0.631268 | 0.315634 | − | 0.948881i | \(-0.397783\pi\) | ||||
0.315634 | + | 0.948881i | \(0.397783\pi\) | |||||||
\(72\) | − 13.8477i | − 1.63197i | ||||||||
\(73\) | − 0.640336i | − 0.0749457i | −0.999298 | − | 0.0374728i | \(-0.988069\pi\) | ||||
0.999298 | − | 0.0374728i | \(-0.0119308\pi\) | |||||||
\(74\) | 13.0798 | 1.52049 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 3.58761 | 0.411527 | ||||||||
\(77\) | − 5.10209i | − 0.581437i | ||||||||
\(78\) | 34.6924i | 3.92814i | ||||||||
\(79\) | −4.92294 | −0.553874 | −0.276937 | − | 0.960888i | \(-0.589319\pi\) | ||||
−0.276937 | + | 0.960888i | \(0.589319\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 11.9743 | 1.33048 | ||||||||
\(82\) | 7.33533i | 0.810052i | ||||||||
\(83\) | 1.87021i | 0.205282i | 0.994718 | + | 0.102641i | \(0.0327293\pi\) | ||||
−0.994718 | + | 0.102641i | \(0.967271\pi\) | |||||||
\(84\) | −5.94862 | −0.649048 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −7.76947 | −0.837803 | ||||||||
\(87\) | − 21.6126i | − 2.31712i | ||||||||
\(88\) | − 3.75906i | − 0.400718i | ||||||||
\(89\) | 11.4922 | 1.21817 | 0.609084 | − | 0.793106i | \(-0.291537\pi\) | ||||
0.609084 | + | 0.793106i | \(0.291537\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −20.7438 | −2.17454 | ||||||||
\(92\) | − 0.0837146i | − 0.00872785i | ||||||||
\(93\) | − 3.05273i | − 0.316553i | ||||||||
\(94\) | 3.43077 | 0.353857 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −10.9006 | −1.11254 | ||||||||
\(97\) | − 6.84653i | − 0.695160i | −0.937650 | − | 0.347580i | \(-0.887003\pi\) | ||||
0.937650 | − | 0.347580i | \(-0.112997\pi\) | |||||||
\(98\) | − 3.00886i | − 0.303941i | ||||||||
\(99\) | 10.8398 | 1.08944 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 18.2712 | 1.81805 | 0.909024 | − | 0.416744i | \(-0.136829\pi\) | ||||
0.909024 | + | 0.416744i | \(0.136829\pi\) | |||||||
\(102\) | 13.7695i | 1.36338i | ||||||||
\(103\) | − 1.20484i | − 0.118717i | −0.998237 | − | 0.0593583i | \(-0.981095\pi\) | ||||
0.998237 | − | 0.0593583i | \(-0.0189055\pi\) | |||||||
\(104\) | −15.2834 | −1.49866 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −8.48880 | −0.824505 | ||||||||
\(107\) | 5.79179i | 0.559913i | 0.960013 | + | 0.279957i | \(0.0903201\pi\) | ||||
−0.960013 | + | 0.279957i | \(0.909680\pi\) | |||||||
\(108\) | − 6.63832i | − 0.638773i | ||||||||
\(109\) | 5.42462 | 0.519584 | 0.259792 | − | 0.965665i | \(-0.416346\pi\) | ||||
0.259792 | + | 0.965665i | \(0.416346\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −24.5044 | −2.32585 | ||||||||
\(112\) | − 14.5179i | − 1.37181i | ||||||||
\(113\) | − 2.61329i | − 0.245838i | −0.992417 | − | 0.122919i | \(-0.960774\pi\) | ||||
0.992417 | − | 0.122919i | \(-0.0392255\pi\) | |||||||
\(114\) | −27.2393 | −2.55120 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −4.63832 | −0.430657 | ||||||||
\(117\) | − 44.0718i | − 4.07444i | ||||||||
\(118\) | − 21.6667i | − 1.99458i | ||||||||
\(119\) | −8.23324 | −0.754740 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −8.05745 | −0.732496 | ||||||||
\(122\) | − 0.171843i | − 0.0155580i | ||||||||
\(123\) | − 13.7424i | − 1.23911i | ||||||||
\(124\) | −0.655151 | −0.0588343 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 30.6260 | 2.72838 | ||||||||
\(127\) | 6.66738i | 0.591634i | 0.955245 | + | 0.295817i | \(0.0955919\pi\) | ||||
−0.955245 | + | 0.295817i | \(0.904408\pi\) | |||||||
\(128\) | − 13.5677i | − 1.19923i | ||||||||
\(129\) | 14.5558 | 1.28156 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 14.8336 | 1.29602 | 0.648011 | − | 0.761631i | \(-0.275601\pi\) | ||||
0.648011 | + | 0.761631i | \(0.275601\pi\) | |||||||
\(132\) | − 3.43077i | − 0.298610i | ||||||||
\(133\) | − 16.2873i | − 1.41229i | ||||||||
\(134\) | −3.72270 | −0.321592 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −6.06600 | −0.520155 | ||||||||
\(137\) | 6.10074i | 0.521221i | 0.965444 | + | 0.260611i | \(0.0839239\pi\) | ||||
−0.965444 | + | 0.260611i | \(0.916076\pi\) | |||||||
\(138\) | 0.635613i | 0.0541070i | ||||||||
\(139\) | −0.112771 | −0.00956514 | −0.00478257 | − | 0.999989i | \(-0.501522\pi\) | ||||
−0.00478257 | + | 0.999989i | \(0.501522\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −6.42740 | −0.541285 | ||||||||
\(142\) | 8.66738i | 0.727350i | ||||||||
\(143\) | − 11.9636i | − 1.00045i | ||||||||
\(144\) | 30.8443 | 2.57036 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 1.04340 | 0.0863528 | ||||||||
\(147\) | 5.63697i | 0.464929i | ||||||||
\(148\) | 5.25893i | 0.432281i | ||||||||
\(149\) | 7.98654 | 0.654283 | 0.327141 | − | 0.944975i | \(-0.393915\pi\) | ||||
0.327141 | + | 0.944975i | \(0.393915\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −20.8566 | −1.69728 | −0.848641 | − | 0.528969i | \(-0.822579\pi\) | ||||
−0.848641 | + | 0.528969i | \(0.822579\pi\) | |||||||
\(152\) | − 12.0000i | − 0.973329i | ||||||||
\(153\) | − 17.4922i | − 1.41416i | ||||||||
\(154\) | 8.31367 | 0.669935 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −13.9486 | −1.11678 | ||||||||
\(157\) | − 15.0798i | − 1.20350i | −0.798686 | − | 0.601748i | \(-0.794471\pi\) | ||||
0.798686 | − | 0.601748i | \(-0.205529\pi\) | |||||||
\(158\) | − 8.02175i | − 0.638176i | ||||||||
\(159\) | 15.9034 | 1.26122 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −0.380055 | −0.0299525 | ||||||||
\(162\) | 19.5117i | 1.53298i | ||||||||
\(163\) | 4.27730i | 0.335024i | 0.985870 | + | 0.167512i | \(0.0535733\pi\) | ||||
−0.985870 | + | 0.167512i | \(0.946427\pi\) | |||||||
\(164\) | −2.94928 | −0.230300 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −3.04743 | −0.236527 | ||||||||
\(167\) | 14.5599i | 1.12668i | 0.826225 | + | 0.563340i | \(0.190484\pi\) | ||||
−0.826225 | + | 0.563340i | \(0.809516\pi\) | |||||||
\(168\) | 19.8972i | 1.53511i | ||||||||
\(169\) | −35.6410 | −2.74162 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 34.6037 | 2.64621 | ||||||||
\(172\) | − 3.12384i | − 0.238190i | ||||||||
\(173\) | 23.5463i | 1.79019i | 0.445877 | + | 0.895094i | \(0.352892\pi\) | ||||
−0.445877 | + | 0.895094i | \(0.647108\pi\) | |||||||
\(174\) | 35.2170 | 2.66979 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 8.37293 | 0.631133 | ||||||||
\(177\) | 40.5917i | 3.05106i | ||||||||
\(178\) | 18.7261i | 1.40358i | ||||||||
\(179\) | 8.86885 | 0.662889 | 0.331445 | − | 0.943475i | \(-0.392464\pi\) | ||||
0.331445 | + | 0.943475i | \(0.392464\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 13.1088 | 0.974372 | 0.487186 | − | 0.873298i | \(-0.338023\pi\) | ||||
0.487186 | + | 0.873298i | \(0.338023\pi\) | |||||||
\(182\) | − 33.8012i | − 2.50551i | ||||||||
\(183\) | 0.321941i | 0.0237986i | ||||||||
\(184\) | −0.280013 | −0.0206428 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 4.97431 | 0.364734 | ||||||||
\(187\) | − 4.74838i | − 0.347236i | ||||||||
\(188\) | 1.37939i | 0.100603i | ||||||||
\(189\) | −30.1372 | −2.19216 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 8.53286 | 0.617416 | 0.308708 | − | 0.951157i | \(-0.400103\pi\) | ||||
0.308708 | + | 0.951157i | \(0.400103\pi\) | |||||||
\(192\) | 12.0391i | 0.868846i | ||||||||
\(193\) | 16.1595i | 1.16319i | 0.813479 | + | 0.581595i | \(0.197571\pi\) | ||||
−0.813479 | + | 0.581595i | \(0.802429\pi\) | |||||||
\(194\) | 11.1562 | 0.800967 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.20976 | 0.0864113 | ||||||||
\(197\) | 1.02569i | 0.0730772i | 0.999332 | + | 0.0365386i | \(0.0116332\pi\) | ||||
−0.999332 | + | 0.0365386i | \(0.988367\pi\) | |||||||
\(198\) | 17.6631i | 1.25526i | ||||||||
\(199\) | −26.6701 | −1.89059 | −0.945296 | − | 0.326213i | \(-0.894227\pi\) | ||||
−0.945296 | + | 0.326213i | \(0.894227\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 6.97431 | 0.491930 | ||||||||
\(202\) | 29.7722i | 2.09476i | ||||||||
\(203\) | 21.0575i | 1.47794i | ||||||||
\(204\) | −5.53623 | −0.387614 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 1.96325 | 0.136786 | ||||||||
\(207\) | − 0.807456i | − 0.0561221i | ||||||||
\(208\) | − 34.0422i | − 2.36040i | ||||||||
\(209\) | 9.39344 | 0.649758 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 15.0061 | 1.03306 | 0.516531 | − | 0.856269i | \(-0.327223\pi\) | ||||
0.516531 | + | 0.856269i | \(0.327223\pi\) | |||||||
\(212\) | − 3.41305i | − 0.234409i | ||||||||
\(213\) | − 16.2380i | − 1.11261i | ||||||||
\(214\) | −9.43751 | −0.645135 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −22.2042 | −1.51080 | ||||||||
\(217\) | 2.97431i | 0.201909i | ||||||||
\(218\) | 8.83922i | 0.598668i | ||||||||
\(219\) | −1.95477 | −0.132091 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −19.3057 | −1.29864 | ||||||||
\(222\) | − 39.9290i | − 2.67986i | ||||||||
\(223\) | − 8.36574i | − 0.560211i | −0.959969 | − | 0.280106i | \(-0.909630\pi\) | ||||
0.959969 | − | 0.280106i | \(-0.0903695\pi\) | |||||||
\(224\) | 10.6206 | 0.709619 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 4.25827 | 0.283256 | ||||||||
\(227\) | − 14.7147i | − 0.976651i | −0.872662 | − | 0.488325i | \(-0.837608\pi\) | ||||
0.872662 | − | 0.488325i | \(-0.162392\pi\) | |||||||
\(228\) | − 10.9520i | − 0.725313i | ||||||||
\(229\) | 18.4659 | 1.22026 | 0.610131 | − | 0.792301i | \(-0.291117\pi\) | ||||
0.610131 | + | 0.792301i | \(0.291117\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −15.5753 | −1.02478 | ||||||||
\(232\) | 15.5145i | 1.01858i | ||||||||
\(233\) | − 0.0736944i | − 0.00482788i | −0.999997 | − | 0.00241394i | \(-0.999232\pi\) | ||||
0.999997 | − | 0.00241394i | \(-0.000768382\pi\) | |||||||
\(234\) | 71.8134 | 4.69459 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 8.71144 | 0.567067 | ||||||||
\(237\) | 15.0284i | 0.976199i | ||||||||
\(238\) | − 13.4158i | − 0.869615i | ||||||||
\(239\) | −20.0758 | −1.29860 | −0.649299 | − | 0.760533i | \(-0.724938\pi\) | ||||
−0.649299 | + | 0.760533i | \(0.724938\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −3.49217 | −0.224950 | −0.112475 | − | 0.993655i | \(-0.535878\pi\) | ||||
−0.112475 | + | 0.993655i | \(0.535878\pi\) | |||||||
\(242\) | − 13.1293i | − 0.843985i | ||||||||
\(243\) | − 6.15684i | − 0.394961i | ||||||||
\(244\) | 0.0690924 | 0.00442319 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 22.3928 | 1.42771 | ||||||||
\(247\) | − 38.1913i | − 2.43005i | ||||||||
\(248\) | 2.19138i | 0.139153i | ||||||||
\(249\) | 5.70924 | 0.361808 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 18.9520 | 1.19624 | 0.598120 | − | 0.801407i | \(-0.295915\pi\) | ||||
0.598120 | + | 0.801407i | \(0.295915\pi\) | |||||||
\(252\) | 12.3137i | 0.775688i | ||||||||
\(253\) | − 0.219190i | − 0.0137804i | ||||||||
\(254\) | −10.8642 | −0.681684 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 14.2206 | 0.888789 | ||||||||
\(257\) | − 6.73376i | − 0.420041i | −0.977697 | − | 0.210020i | \(-0.932647\pi\) | ||||
0.977697 | − | 0.210020i | \(-0.0673530\pi\) | |||||||
\(258\) | 23.7181i | 1.47662i | ||||||||
\(259\) | 23.8749 | 1.48352 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −44.7382 | −2.76923 | ||||||||
\(262\) | 24.1709i | 1.49328i | ||||||||
\(263\) | − 13.5342i | − 0.834556i | −0.908779 | − | 0.417278i | \(-0.862984\pi\) | ||||
0.908779 | − | 0.417278i | \(-0.137016\pi\) | |||||||
\(264\) | −11.4754 | −0.706263 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 26.5396 | 1.62725 | ||||||||
\(267\) | − 35.0825i | − 2.14701i | ||||||||
\(268\) | − 1.49677i | − 0.0914297i | ||||||||
\(269\) | 7.04340 | 0.429444 | 0.214722 | − | 0.976675i | \(-0.431115\pi\) | ||||
0.214722 | + | 0.976675i | \(0.431115\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 11.8208 | 0.718065 | 0.359033 | − | 0.933325i | \(-0.383107\pi\) | ||||
0.359033 | + | 0.933325i | \(0.383107\pi\) | |||||||
\(272\) | − 13.5114i | − 0.819248i | ||||||||
\(273\) | 63.3252i | 3.83261i | ||||||||
\(274\) | −9.94093 | −0.600553 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −0.255558 | −0.0153828 | ||||||||
\(277\) | 22.9350i | 1.37803i | 0.724748 | + | 0.689014i | \(0.241956\pi\) | ||||
−0.724748 | + | 0.689014i | \(0.758044\pi\) | |||||||
\(278\) | − 0.183757i | − 0.0110210i | ||||||||
\(279\) | −6.31916 | −0.378318 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −14.4603 | −0.862631 | −0.431315 | − | 0.902201i | \(-0.641950\pi\) | ||||
−0.431315 | + | 0.902201i | \(0.641950\pi\) | |||||||
\(282\) | − 10.4732i | − 0.623671i | ||||||||
\(283\) | − 27.7985i | − 1.65245i | −0.563340 | − | 0.826225i | \(-0.690484\pi\) | ||||
0.563340 | − | 0.826225i | \(-0.309516\pi\) | |||||||
\(284\) | −3.48486 | −0.206788 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 19.4943 | 1.15272 | ||||||||
\(287\) | 13.3894i | 0.790352i | ||||||||
\(288\) | 22.5643i | 1.32961i | ||||||||
\(289\) | 9.33754 | 0.549267 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −20.9006 | −1.22522 | ||||||||
\(292\) | 0.419517i | 0.0245504i | ||||||||
\(293\) | − 2.95930i | − 0.172884i | −0.996257 | − | 0.0864422i | \(-0.972450\pi\) | ||||
0.996257 | − | 0.0864422i | \(-0.0275498\pi\) | |||||||
\(294\) | −9.18523 | −0.535694 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 17.5903 | 1.02242 | ||||||||
\(297\) | − 17.3811i | − 1.00856i | ||||||||
\(298\) | 13.0138i | 0.753868i | ||||||||
\(299\) | −0.891171 | −0.0515377 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −14.1819 | −0.817429 | ||||||||
\(302\) | − 33.9850i | − 1.95562i | ||||||||
\(303\) | − 55.7769i | − 3.20430i | ||||||||
\(304\) | 26.7288 | 1.53300 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 28.5028 | 1.62940 | ||||||||
\(307\) | 10.6160i | 0.605887i | 0.953008 | + | 0.302944i | \(0.0979694\pi\) | ||||
−0.953008 | + | 0.302944i | \(0.902031\pi\) | |||||||
\(308\) | 3.34264i | 0.190465i | ||||||||
\(309\) | −3.67806 | −0.209237 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 15.6579 | 0.887876 | 0.443938 | − | 0.896058i | \(-0.353581\pi\) | ||||
0.443938 | + | 0.896058i | \(0.353581\pi\) | |||||||
\(312\) | 46.6560i | 2.64138i | ||||||||
\(313\) | − 22.2994i | − 1.26043i | −0.776419 | − | 0.630217i | \(-0.782966\pi\) | ||||
0.776419 | − | 0.630217i | \(-0.217034\pi\) | |||||||
\(314\) | 24.5719 | 1.38667 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 3.22527 | 0.181436 | ||||||||
\(317\) | − 7.84990i | − 0.440894i | −0.975399 | − | 0.220447i | \(-0.929248\pi\) | ||||
0.975399 | − | 0.220447i | \(-0.0707517\pi\) | |||||||
\(318\) | 25.9140i | 1.45319i | ||||||||
\(319\) | −12.1445 | −0.679964 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 17.6808 | 0.986844 | ||||||||
\(322\) | − 0.619285i | − 0.0345114i | ||||||||
\(323\) | − 15.1582i | − 0.843424i | ||||||||
\(324\) | −7.84499 | −0.435833 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −6.96971 | −0.386017 | ||||||||
\(327\) | − 16.5599i | − 0.915765i | ||||||||
\(328\) | 9.86491i | 0.544699i | ||||||||
\(329\) | 6.26230 | 0.345252 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −15.6199 | −0.858550 | −0.429275 | − | 0.903174i | \(-0.641231\pi\) | ||||
−0.429275 | + | 0.903174i | \(0.641231\pi\) | |||||||
\(332\) | − 1.22527i | − 0.0672453i | ||||||||
\(333\) | 50.7242i | 2.77967i | ||||||||
\(334\) | −23.7248 | −1.29817 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −44.3191 | −2.41780 | ||||||||
\(337\) | 13.6660i | 0.744436i | 0.928145 | + | 0.372218i | \(0.121403\pi\) | ||||
−0.928145 | + | 0.372218i | \(0.878597\pi\) | |||||||
\(338\) | − 58.0758i | − 3.15890i | ||||||||
\(339\) | −7.97768 | −0.433288 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1.71539 | −0.0928933 | ||||||||
\(342\) | 56.3855i | 3.04898i | ||||||||
\(343\) | 15.3280i | 0.827635i | ||||||||
\(344\) | −10.4488 | −0.563359 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −38.3678 | −2.06266 | ||||||||
\(347\) | − 17.7181i | − 0.951157i | −0.879673 | − | 0.475579i | \(-0.842239\pi\) | ||||
0.879673 | − | 0.475579i | \(-0.157761\pi\) | |||||||
\(348\) | 14.1595i | 0.759031i | ||||||||
\(349\) | −20.0529 | −1.07341 | −0.536704 | − | 0.843770i | \(-0.680331\pi\) | ||||
−0.536704 | + | 0.843770i | \(0.680331\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −70.6672 | −3.77194 | ||||||||
\(352\) | 6.12526i | 0.326477i | ||||||||
\(353\) | 2.40508i | 0.128010i | 0.997950 | + | 0.0640048i | \(0.0203873\pi\) | ||||
−0.997950 | + | 0.0640048i | \(0.979613\pi\) | |||||||
\(354\) | −66.1426 | −3.51544 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −7.52911 | −0.399042 | ||||||||
\(357\) | 25.1339i | 1.33022i | ||||||||
\(358\) | 14.4515i | 0.763784i | ||||||||
\(359\) | −10.9843 | −0.579731 | −0.289865 | − | 0.957067i | \(-0.593611\pi\) | ||||
−0.289865 | + | 0.957067i | \(0.593611\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 10.9865 | 0.578239 | ||||||||
\(362\) | 21.3604i | 1.12268i | ||||||||
\(363\) | 24.5972i | 1.29102i | ||||||||
\(364\) | 13.5903 | 0.712326 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −0.524592 | −0.0274209 | ||||||||
\(367\) | − 19.2196i | − 1.00325i | −0.865084 | − | 0.501627i | \(-0.832735\pi\) | ||||
0.865084 | − | 0.501627i | \(-0.167265\pi\) | |||||||
\(368\) | − 0.623700i | − 0.0325126i | ||||||||
\(369\) | −28.4469 | −1.48088 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −15.4949 | −0.804454 | ||||||||
\(372\) | 2.00000i | 0.103695i | ||||||||
\(373\) | 20.9079i | 1.08257i | 0.840839 | + | 0.541286i | \(0.182062\pi\) | ||||
−0.840839 | + | 0.541286i | \(0.817938\pi\) | |||||||
\(374\) | 7.73732 | 0.400087 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 4.61387 | 0.237942 | ||||||||
\(377\) | 49.3765i | 2.54302i | ||||||||
\(378\) | − 49.1075i | − 2.52582i | ||||||||
\(379\) | 27.2996 | 1.40228 | 0.701142 | − | 0.713022i | \(-0.252674\pi\) | ||||
0.701142 | + | 0.713022i | \(0.252674\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 20.3537 | 1.04275 | ||||||||
\(382\) | 13.9040i | 0.711390i | ||||||||
\(383\) | − 25.5883i | − 1.30750i | −0.756710 | − | 0.653751i | \(-0.773195\pi\) | ||||
0.756710 | − | 0.653751i | \(-0.226805\pi\) | |||||||
\(384\) | −41.4185 | −2.11363 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −26.3314 | −1.34023 | ||||||||
\(387\) | − 30.1305i | − 1.53162i | ||||||||
\(388\) | 4.48551i | 0.227718i | ||||||||
\(389\) | 6.23267 | 0.316009 | 0.158004 | − | 0.987438i | \(-0.449494\pi\) | ||||
0.158004 | + | 0.987438i | \(0.449494\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −0.353707 | −0.0178877 | ||||||||
\(392\) | − 4.04646i | − 0.204377i | ||||||||
\(393\) | − 45.2831i | − 2.28423i | ||||||||
\(394\) | −1.67132 | −0.0841999 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −7.10171 | −0.356874 | ||||||||
\(397\) | 8.29231i | 0.416179i | 0.978110 | + | 0.208090i | \(0.0667246\pi\) | ||||
−0.978110 | + | 0.208090i | \(0.933275\pi\) | |||||||
\(398\) | − 43.4579i | − 2.17835i | ||||||||
\(399\) | −49.7208 | −2.48915 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 29.8263 | 1.48945 | 0.744726 | − | 0.667370i | \(-0.232580\pi\) | ||||
0.744726 | + | 0.667370i | \(0.232580\pi\) | |||||||
\(402\) | 11.3644i | 0.566804i | ||||||||
\(403\) | 6.97431i | 0.347415i | ||||||||
\(404\) | −11.9704 | −0.595548 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −34.3124 | −1.70289 | ||||||||
\(407\) | 13.7695i | 0.682527i | ||||||||
\(408\) | 18.5179i | 0.916770i | ||||||||
\(409\) | −7.18252 | −0.355153 | −0.177576 | − | 0.984107i | \(-0.556826\pi\) | ||||
−0.177576 | + | 0.984107i | \(0.556826\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 18.6239 | 0.918649 | ||||||||
\(412\) | 0.789354i | 0.0388887i | ||||||||
\(413\) | − 39.5490i | − 1.94608i | ||||||||
\(414\) | 1.31572 | 0.0646641 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 24.9037 | 1.22100 | ||||||||
\(417\) | 0.344260i | 0.0168585i | ||||||||
\(418\) | 15.3063i | 0.748654i | ||||||||
\(419\) | 17.7997 | 0.869572 | 0.434786 | − | 0.900534i | \(-0.356824\pi\) | ||||
0.434786 | + | 0.900534i | \(0.356824\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −31.1941 | −1.52031 | −0.760153 | − | 0.649744i | \(-0.774876\pi\) | ||||
−0.760153 | + | 0.649744i | \(0.774876\pi\) | |||||||
\(422\) | 24.4519i | 1.19030i | ||||||||
\(423\) | 13.3047i | 0.646899i | ||||||||
\(424\) | −11.4161 | −0.554417 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 26.4592 | 1.28195 | ||||||||
\(427\) | − 0.313671i | − 0.0151796i | ||||||||
\(428\) | − 3.79450i | − 0.183414i | ||||||||
\(429\) | −36.5217 | −1.76329 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 30.7526 | 1.48130 | 0.740651 | − | 0.671890i | \(-0.234517\pi\) | ||||
0.740651 | + | 0.671890i | \(0.234517\pi\) | |||||||
\(432\) | − 49.4575i | − 2.37953i | ||||||||
\(433\) | 15.7991i | 0.759256i | 0.925139 | + | 0.379628i | \(0.123948\pi\) | ||||
−0.925139 | + | 0.379628i | \(0.876052\pi\) | |||||||
\(434\) | −4.84653 | −0.232641 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −3.55395 | −0.170203 | ||||||||
\(437\) | − 0.699718i | − 0.0334720i | ||||||||
\(438\) | − 3.18523i | − 0.152196i | ||||||||
\(439\) | 24.4503 | 1.16695 | 0.583475 | − | 0.812131i | \(-0.301693\pi\) | ||||
0.583475 | + | 0.812131i | \(0.301693\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 11.6685 | 0.555645 | ||||||||
\(442\) | − 31.4579i | − 1.49630i | ||||||||
\(443\) | 5.28067i | 0.250892i | 0.992100 | + | 0.125446i | \(0.0400362\pi\) | ||||
−0.992100 | + | 0.125446i | \(0.959964\pi\) | |||||||
\(444\) | 16.0541 | 0.761893 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 13.6317 | 0.645478 | ||||||||
\(447\) | − 24.3807i | − 1.15317i | ||||||||
\(448\) | − 11.7298i | − 0.554182i | ||||||||
\(449\) | −21.4308 | −1.01138 | −0.505690 | − | 0.862715i | \(-0.668762\pi\) | ||||
−0.505690 | + | 0.862715i | \(0.668762\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −7.72212 | −0.363621 | ||||||||
\(452\) | 1.71210i | 0.0805305i | ||||||||
\(453\) | 63.6694i | 2.99145i | ||||||||
\(454\) | 23.9771 | 1.12530 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −36.6328 | −1.71549 | ||||||||
\(457\) | 25.1920i | 1.17843i | 0.807976 | + | 0.589215i | \(0.200563\pi\) | ||||
−0.807976 | + | 0.589215i | \(0.799437\pi\) | |||||||
\(458\) | 30.0895i | 1.40599i | ||||||||
\(459\) | −28.0479 | −1.30917 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 19.0975 | 0.889459 | 0.444729 | − | 0.895665i | \(-0.353300\pi\) | ||||
0.444729 | + | 0.895665i | \(0.353300\pi\) | |||||||
\(462\) | − 25.3794i | − 1.18076i | ||||||||
\(463\) | 28.8933i | 1.34279i | 0.741102 | + | 0.671393i | \(0.234304\pi\) | ||||
−0.741102 | + | 0.671393i | \(0.765696\pi\) | |||||||
\(464\) | −34.5569 | −1.60427 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0.120082 | 0.00556271 | ||||||||
\(467\) | 9.34938i | 0.432638i | 0.976323 | + | 0.216319i | \(0.0694051\pi\) | ||||
−0.976323 | + | 0.216319i | \(0.930595\pi\) | |||||||
\(468\) | 28.8737i | 1.33469i | ||||||||
\(469\) | −6.79516 | −0.313771 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −46.0345 | −2.12116 | ||||||||
\(472\) | − 29.1385i | − 1.34121i | ||||||||
\(473\) | − 8.17915i | − 0.376078i | ||||||||
\(474\) | −24.4882 | −1.12478 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 5.39402 | 0.247234 | ||||||||
\(477\) | − 32.9201i | − 1.50731i | ||||||||
\(478\) | − 32.7128i | − 1.49625i | ||||||||
\(479\) | −27.8309 | −1.27162 | −0.635812 | − | 0.771844i | \(-0.719335\pi\) | ||||
−0.635812 | + | 0.771844i | \(0.719335\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 55.9831 | 2.55261 | ||||||||
\(482\) | − 5.69036i | − 0.259189i | ||||||||
\(483\) | 1.16020i | 0.0527911i | ||||||||
\(484\) | 5.27885 | 0.239948 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 10.0323 | 0.455076 | ||||||||
\(487\) | − 3.08910i | − 0.139980i | −0.997548 | − | 0.0699902i | \(-0.977703\pi\) | ||||
0.997548 | − | 0.0699902i | \(-0.0222968\pi\) | |||||||
\(488\) | − 0.231103i | − 0.0104616i | ||||||||
\(489\) | 13.0575 | 0.590478 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 2.65062 | 0.119621 | 0.0598104 | − | 0.998210i | \(-0.480950\pi\) | ||||
0.0598104 | + | 0.998210i | \(0.480950\pi\) | |||||||
\(492\) | 9.00337i | 0.405903i | ||||||||
\(493\) | 19.5976i | 0.882633i | ||||||||
\(494\) | 62.2313 | 2.79992 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −4.88108 | −0.219167 | ||||||||
\(497\) | 15.8208i | 0.709662i | ||||||||
\(498\) | 9.30299i | 0.416877i | ||||||||
\(499\) | 2.46320 | 0.110268 | 0.0551339 | − | 0.998479i | \(-0.482441\pi\) | ||||
0.0551339 | + | 0.998479i | \(0.482441\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 44.4475 | 1.98577 | ||||||||
\(502\) | 30.8816i | 1.37831i | ||||||||
\(503\) | 10.2846i | 0.458568i | 0.973360 | + | 0.229284i | \(0.0736385\pi\) | ||||
−0.973360 | + | 0.229284i | \(0.926361\pi\) | |||||||
\(504\) | 41.1874 | 1.83463 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0.357163 | 0.0158778 | ||||||||
\(507\) | 108.802i | 4.83209i | ||||||||
\(508\) | − 4.36814i | − 0.193805i | ||||||||
\(509\) | 42.7097 | 1.89308 | 0.946538 | − | 0.322593i | \(-0.104554\pi\) | ||||
0.946538 | + | 0.322593i | \(0.104554\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.90456 | 0.0842528 | ||||||||
\(512\) | − 3.96337i | − 0.175158i | ||||||||
\(513\) | − 55.4855i | − 2.44975i | ||||||||
\(514\) | 10.9724 | 0.483973 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −9.53623 | −0.419809 | ||||||||
\(517\) | 3.61168i | 0.158841i | ||||||||
\(518\) | 38.9033i | 1.70931i | ||||||||
\(519\) | 71.8803 | 3.15520 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −31.6142 | −1.38504 | −0.692521 | − | 0.721398i | \(-0.743500\pi\) | ||||
−0.692521 | + | 0.721398i | \(0.743500\pi\) | |||||||
\(522\) | − 72.8993i | − 3.19072i | ||||||||
\(523\) | 33.7769i | 1.47696i | 0.674275 | + | 0.738480i | \(0.264456\pi\) | ||||
−0.674275 | + | 0.738480i | \(0.735544\pi\) | |||||||
\(524\) | −9.71828 | −0.424545 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 22.0535 | 0.961579 | ||||||||
\(527\) | 2.76812i | 0.120581i | ||||||||
\(528\) | − 25.5603i | − 1.11237i | ||||||||
\(529\) | 22.9837 | 0.999290 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 84.0249 | 3.64637 | ||||||||
\(532\) | 10.6707i | 0.462632i | ||||||||
\(533\) | 31.3962i | 1.35992i | ||||||||
\(534\) | 57.1656 | 2.47380 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −5.00646 | −0.216246 | ||||||||
\(537\) | − 27.0742i | − 1.16834i | ||||||||
\(538\) | 11.4770i | 0.494807i | ||||||||
\(539\) | 3.16752 | 0.136435 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 15.6350 | 0.672199 | 0.336100 | − | 0.941826i | \(-0.390892\pi\) | ||||
0.336100 | + | 0.941826i | \(0.390892\pi\) | |||||||
\(542\) | 19.2616i | 0.827358i | ||||||||
\(543\) | − 40.0177i | − 1.71732i | ||||||||
\(544\) | 9.88432 | 0.423787 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −103.186 | −4.41596 | ||||||||
\(547\) | − 23.5289i | − 1.00602i | −0.864279 | − | 0.503012i | \(-0.832225\pi\) | ||||
0.864279 | − | 0.503012i | \(-0.167775\pi\) | |||||||
\(548\) | − 3.99691i | − 0.170739i | ||||||||
\(549\) | 0.666420 | 0.0284421 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −38.7688 | −1.65161 | ||||||||
\(552\) | 0.854803i | 0.0363828i | ||||||||
\(553\) | − 14.6424i | − 0.622656i | ||||||||
\(554\) | −37.3717 | −1.58777 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0.0738822 | 0.00313331 | ||||||||
\(557\) | 6.90793i | 0.292698i | 0.989233 | + | 0.146349i | \(0.0467523\pi\) | ||||
−0.989233 | + | 0.146349i | \(0.953248\pi\) | |||||||
\(558\) | − 10.2968i | − 0.435900i | ||||||||
\(559\) | −33.2543 | −1.40651 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −14.4955 | −0.612002 | ||||||||
\(562\) | − 23.5626i | − 0.993927i | ||||||||
\(563\) | − 17.0351i | − 0.717945i | −0.933348 | − | 0.358973i | \(-0.883127\pi\) | ||||
0.933348 | − | 0.358973i | \(-0.116873\pi\) | |||||||
\(564\) | 4.21092 | 0.177312 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 45.2967 | 1.90396 | ||||||||
\(567\) | 35.6153i | 1.49570i | ||||||||
\(568\) | 11.6563i | 0.489088i | ||||||||
\(569\) | −36.6801 | −1.53771 | −0.768855 | − | 0.639423i | \(-0.779173\pi\) | ||||
−0.768855 | + | 0.639423i | \(0.779173\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 7.24335 | 0.303125 | 0.151562 | − | 0.988448i | \(-0.451570\pi\) | ||||
0.151562 | + | 0.988448i | \(0.451570\pi\) | |||||||
\(572\) | 7.83799i | 0.327723i | ||||||||
\(573\) | − 26.0485i | − 1.08819i | ||||||||
\(574\) | −21.8176 | −0.910647 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 24.9209 | 1.03837 | ||||||||
\(577\) | 10.0981i | 0.420391i | 0.977659 | + | 0.210196i | \(0.0674101\pi\) | ||||
−0.977659 | + | 0.210196i | \(0.932590\pi\) | |||||||
\(578\) | 15.2152i | 0.632868i | ||||||||
\(579\) | 49.3307 | 2.05012 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −5.56258 | −0.230775 | ||||||||
\(582\) | − 34.0568i | − 1.41170i | ||||||||
\(583\) | − 8.93641i | − 0.370108i | ||||||||
\(584\) | 1.40322 | 0.0580657 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 4.82208 | 0.199198 | ||||||||
\(587\) | 21.9290i | 0.905107i | 0.891737 | + | 0.452554i | \(0.149487\pi\) | ||||
−0.891737 | + | 0.452554i | \(0.850513\pi\) | |||||||
\(588\) | − 3.69307i | − 0.152299i | ||||||||
\(589\) | −5.47600 | −0.225635 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 3.13115 | 0.128798 | ||||||||
\(592\) | 39.1806i | 1.61031i | ||||||||
\(593\) | − 21.5212i | − 0.883771i | −0.897072 | − | 0.441885i | \(-0.854310\pi\) | ||||
0.897072 | − | 0.441885i | \(-0.145690\pi\) | |||||||
\(594\) | 28.3219 | 1.16206 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −5.23239 | −0.214327 | ||||||||
\(597\) | 81.4166i | 3.33216i | ||||||||
\(598\) | − 1.45213i | − 0.0593820i | ||||||||
\(599\) | 3.72270 | 0.152105 | 0.0760526 | − | 0.997104i | \(-0.475768\pi\) | ||||
0.0760526 | + | 0.997104i | \(0.475768\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −32.2142 | −1.31404 | −0.657022 | − | 0.753871i | \(-0.728184\pi\) | ||||
−0.657022 | + | 0.753871i | \(0.728184\pi\) | |||||||
\(602\) | − 23.1088i | − 0.941846i | ||||||||
\(603\) | − 14.4368i | − 0.587914i | ||||||||
\(604\) | 13.6642 | 0.555988 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 90.8864 | 3.69201 | ||||||||
\(607\) | − 32.9324i | − 1.33668i | −0.743854 | − | 0.668342i | \(-0.767004\pi\) | ||||
0.743854 | − | 0.668342i | \(-0.232996\pi\) | |||||||
\(608\) | 19.5536i | 0.793002i | ||||||||
\(609\) | 64.2827 | 2.60487 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 14.6841 | 0.594057 | ||||||||
\(612\) | 11.4600i | 0.463244i | ||||||||
\(613\) | 19.8619i | 0.802216i | 0.916031 | + | 0.401108i | \(0.131375\pi\) | ||||
−0.916031 | + | 0.401108i | \(0.868625\pi\) | |||||||
\(614\) | −17.2984 | −0.698106 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 11.1806 | 0.450480 | ||||||||
\(617\) | 14.1251i | 0.568654i | 0.958727 | + | 0.284327i | \(0.0917701\pi\) | ||||
−0.958727 | + | 0.284327i | \(0.908230\pi\) | |||||||
\(618\) | − 5.99326i | − 0.241084i | ||||||||
\(619\) | 30.6478 | 1.23184 | 0.615919 | − | 0.787810i | \(-0.288785\pi\) | ||||
0.615919 | + | 0.787810i | \(0.288785\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −1.29472 | −0.0519554 | ||||||||
\(622\) | 25.5139i | 1.02301i | ||||||||
\(623\) | 34.1813i | 1.36944i | ||||||||
\(624\) | −103.922 | −4.16019 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 36.3360 | 1.45228 | ||||||||
\(627\) | − 28.6756i | − 1.14520i | ||||||||
\(628\) | 9.87953i | 0.394236i | ||||||||
\(629\) | 22.2198 | 0.885961 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −4.67198 | −0.185989 | −0.0929943 | − | 0.995667i | \(-0.529644\pi\) | ||||
−0.0929943 | + | 0.995667i | \(0.529644\pi\) | |||||||
\(632\) | − 10.7880i | − 0.429125i | ||||||||
\(633\) | − 45.8095i | − 1.82076i | ||||||||
\(634\) | 12.7911 | 0.508001 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −10.4191 | −0.413145 | ||||||||
\(637\) | − 12.8783i | − 0.510257i | ||||||||
\(638\) | − 19.7891i | − 0.783457i | ||||||||
\(639\) | −33.6126 | −1.32970 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −0.427402 | −0.0168813 | −0.00844067 | − | 0.999964i | \(-0.502687\pi\) | ||||
−0.00844067 | + | 0.999964i | \(0.502687\pi\) | |||||||
\(642\) | 28.8102i | 1.13705i | ||||||||
\(643\) | − 37.4755i | − 1.47789i | −0.673765 | − | 0.738945i | \(-0.735324\pi\) | ||||
0.673765 | − | 0.738945i | \(-0.264676\pi\) | |||||||
\(644\) | 0.248993 | 0.00981171 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 24.6997 | 0.971797 | ||||||||
\(647\) | 7.60791i | 0.299098i | 0.988754 | + | 0.149549i | \(0.0477821\pi\) | ||||
−0.988754 | + | 0.149549i | \(0.952218\pi\) | |||||||
\(648\) | 26.2403i | 1.03082i | ||||||||
\(649\) | 22.8092 | 0.895340 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 9.07977 | 0.355864 | ||||||||
\(652\) | − 2.80228i | − 0.109746i | ||||||||
\(653\) | − 9.97308i | − 0.390277i | −0.980776 | − | 0.195138i | \(-0.937484\pi\) | ||||
0.980776 | − | 0.195138i | \(-0.0625156\pi\) | |||||||
\(654\) | 26.9838 | 1.05515 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −21.9731 | −0.857905 | ||||||||
\(657\) | 4.04639i | 0.157865i | ||||||||
\(658\) | 10.2042i | 0.397800i | ||||||||
\(659\) | 26.4130 | 1.02890 | 0.514452 | − | 0.857519i | \(-0.327995\pi\) | ||||
0.514452 | + | 0.857519i | \(0.327995\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 25.4910 | 0.991485 | 0.495743 | − | 0.868470i | \(-0.334896\pi\) | ||||
0.495743 | + | 0.868470i | \(0.334896\pi\) | |||||||
\(662\) | − 25.4521i | − 0.989225i | ||||||||
\(663\) | 58.9351i | 2.28885i | ||||||||
\(664\) | −4.09834 | −0.159046 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −82.6532 | −3.20275 | ||||||||
\(667\) | 0.904647i | 0.0350281i | ||||||||
\(668\) | − 9.53894i | − 0.369073i | ||||||||
\(669\) | −25.5384 | −0.987370 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0.180905 | 0.00698375 | ||||||||
\(672\) | − 32.4218i | − 1.25070i | ||||||||
\(673\) | 30.2988i | 1.16793i | 0.811778 | + | 0.583966i | \(0.198500\pi\) | ||||
−0.811778 | + | 0.583966i | \(0.801500\pi\) | |||||||
\(674\) | −22.2683 | −0.857742 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 23.3503 | 0.898087 | ||||||||
\(677\) | − 16.1111i | − 0.619202i | −0.950867 | − | 0.309601i | \(-0.899805\pi\) | ||||
0.950867 | − | 0.309601i | \(-0.100195\pi\) | |||||||
\(678\) | − 12.9993i | − 0.499237i | ||||||||
\(679\) | 20.3637 | 0.781488 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −44.9201 | −1.72134 | ||||||||
\(682\) | − 2.79516i | − 0.107032i | ||||||||
\(683\) | − 4.68912i | − 0.179424i | −0.995968 | − | 0.0897122i | \(-0.971405\pi\) | ||||
0.995968 | − | 0.0897122i | \(-0.0285947\pi\) | |||||||
\(684\) | −22.6707 | −0.866834 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −24.9764 | −0.953605 | ||||||||
\(687\) | − 56.3714i | − 2.15070i | ||||||||
\(688\) | − 23.2735i | − 0.887296i | ||||||||
\(689\) | −36.3331 | −1.38418 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −19.1696 | −0.729247 | −0.364624 | − | 0.931155i | \(-0.618802\pi\) | ||||
−0.364624 | + | 0.931155i | \(0.618802\pi\) | |||||||
\(692\) | − 15.4264i | − 0.586422i | ||||||||
\(693\) | 32.2409i | 1.22473i | ||||||||
\(694\) | 28.8710 | 1.09593 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 47.3615 | 1.79523 | ||||||||
\(697\) | 12.4612i | 0.472001i | ||||||||
\(698\) | − 32.6755i | − 1.23679i | ||||||||
\(699\) | −0.224969 | −0.00850912 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 30.9764 | 1.16996 | 0.584982 | − | 0.811046i | \(-0.301102\pi\) | ||||
0.584982 | + | 0.811046i | \(0.301102\pi\) | |||||||
\(702\) | − 115.150i | − 4.34604i | ||||||||
\(703\) | 43.9561i | 1.65783i | ||||||||
\(704\) | 6.76498 | 0.254965 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −3.91899 | −0.147493 | ||||||||
\(707\) | 54.3441i | 2.04382i | ||||||||
\(708\) | − 26.5937i | − 0.999452i | ||||||||
\(709\) | 17.6781 | 0.663913 | 0.331957 | − | 0.943295i | \(-0.392291\pi\) | ||||
0.331957 | + | 0.943295i | \(0.392291\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 31.1088 | 1.16667 | ||||||||
\(712\) | 25.1837i | 0.943800i | ||||||||
\(713\) | 0.127779i | 0.00478536i | ||||||||
\(714\) | −40.9547 | −1.53269 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −5.81044 | −0.217146 | ||||||||
\(717\) | 61.2861i | 2.28877i | ||||||||
\(718\) | − 17.8986i | − 0.667969i | ||||||||
\(719\) | −0.0363678 | −0.00135629 | −0.000678145 | − | 1.00000i | \(-0.500216\pi\) | ||||
−0.000678145 | 1.00000i | \(0.500216\pi\) | ||||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 3.58358 | 0.133459 | ||||||||
\(722\) | 17.9022i | 0.666250i | ||||||||
\(723\) | 10.6606i | 0.396473i | ||||||||
\(724\) | −8.58827 | −0.319180 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −40.0803 | −1.48752 | ||||||||
\(727\) | − 49.9904i | − 1.85404i | −0.375010 | − | 0.927021i | \(-0.622361\pi\) | ||||
0.375010 | − | 0.927021i | \(-0.377639\pi\) | |||||||
\(728\) | − 45.4575i | − 1.68477i | ||||||||
\(729\) | 17.1278 | 0.634362 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −13.1987 | −0.488171 | ||||||||
\(732\) | − 0.210920i | − 0.00779584i | ||||||||
\(733\) | − 17.0602i | − 0.630131i | −0.949070 | − | 0.315066i | \(-0.897973\pi\) | ||||
0.949070 | − | 0.315066i | \(-0.102027\pi\) | |||||||
\(734\) | 31.3176 | 1.15595 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0.456270 | 0.0168184 | ||||||||
\(737\) | − 3.91899i | − 0.144358i | ||||||||
\(738\) | − 46.3531i | − 1.70628i | ||||||||
\(739\) | 11.6240 | 0.427595 | 0.213797 | − | 0.976878i | \(-0.431417\pi\) | ||||
0.213797 | + | 0.976878i | \(0.431417\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −116.588 | −4.28296 | ||||||||
\(742\) | − 25.2483i | − 0.926895i | ||||||||
\(743\) | 40.8980i | 1.50040i | 0.661209 | + | 0.750202i | \(0.270044\pi\) | ||||
−0.661209 | + | 0.750202i | \(0.729956\pi\) | |||||||
\(744\) | 6.68970 | 0.245256 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −34.0687 | −1.24734 | ||||||||
\(747\) | − 11.8181i | − 0.432403i | ||||||||
\(748\) | 3.11091i | 0.113746i | ||||||||
\(749\) | −17.2266 | −0.629446 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −9.73770 | −0.355334 | −0.177667 | − | 0.984091i | \(-0.556855\pi\) | ||||
−0.177667 | + | 0.984091i | \(0.556855\pi\) | |||||||
\(752\) | 10.2769i | 0.374761i | ||||||||
\(753\) | − 57.8553i | − 2.10837i | ||||||||
\(754\) | −80.4573 | −2.93008 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 19.7444 | 0.718098 | ||||||||
\(757\) | − 15.7898i | − 0.573889i | −0.957947 | − | 0.286945i | \(-0.907360\pi\) | ||||
0.957947 | − | 0.286945i | \(-0.0926396\pi\) | |||||||
\(758\) | 44.4836i | 1.61572i | ||||||||
\(759\) | −0.669129 | −0.0242878 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −50.7315 | −1.83901 | −0.919507 | − | 0.393073i | \(-0.871412\pi\) | ||||
−0.919507 | + | 0.393073i | \(0.871412\pi\) | |||||||
\(762\) | 33.1656i | 1.20146i | ||||||||
\(763\) | 16.1345i | 0.584109i | ||||||||
\(764\) | −5.59032 | −0.202251 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 41.6952 | 1.50651 | ||||||||
\(767\) | − 92.7363i | − 3.34851i | ||||||||
\(768\) | − 43.4117i | − 1.56649i | ||||||||
\(769\) | 3.91071 | 0.141024 | 0.0705119 | − | 0.997511i | \(-0.477537\pi\) | ||||
0.0705119 | + | 0.997511i | \(0.477537\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −20.5564 | −0.740319 | ||||||||
\(772\) | − 10.5869i | − 0.381033i | ||||||||
\(773\) | − 26.2213i | − 0.943116i | −0.881835 | − | 0.471558i | \(-0.843692\pi\) | ||||
0.881835 | − | 0.471558i | \(-0.156308\pi\) | |||||||
\(774\) | 49.0965 | 1.76474 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 15.0034 | 0.538590 | ||||||||
\(777\) | − 72.8837i | − 2.61469i | ||||||||
\(778\) | 10.1559i | 0.364107i | ||||||||
\(779\) | −24.6512 | −0.883221 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −9.12441 | −0.326497 | ||||||||
\(782\) | − 0.576353i | − 0.0206103i | ||||||||
\(783\) | 71.7358i | 2.56363i | ||||||||
\(784\) | 9.01307 | 0.321896 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 73.7872 | 2.63190 | ||||||||
\(787\) | 12.6377i | 0.450487i | 0.974302 | + | 0.225244i | \(0.0723178\pi\) | ||||
−0.974302 | + | 0.225244i | \(0.927682\pi\) | |||||||
\(788\) | − 0.671981i | − 0.0239383i | ||||||||
\(789\) | −41.3163 | −1.47090 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 7.77275 | 0.276367 | ||||||||
\(792\) | 23.7541i | 0.844066i | ||||||||
\(793\) | − 0.735512i | − 0.0261188i | ||||||||
\(794\) | −13.5120 | −0.479524 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 17.4729 | 0.619312 | ||||||||
\(797\) | − 23.0461i | − 0.816335i | −0.912907 | − | 0.408168i | \(-0.866168\pi\) | ||||
0.912907 | − | 0.408168i | \(-0.133832\pi\) | |||||||
\(798\) | − 81.0182i | − 2.86801i | ||||||||
\(799\) | 5.82816 | 0.206185 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −72.6208 | −2.56593 | ||||||||
\(802\) | 48.6008i | 1.71615i | ||||||||
\(803\) | 1.09842i | 0.0387625i | ||||||||
\(804\) | −4.56923 | −0.161144 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −11.3644 | −0.400293 | ||||||||
\(807\) | − 21.5016i | − 0.756893i | ||||||||
\(808\) | 40.0391i | 1.40857i | ||||||||
\(809\) | −19.1161 | −0.672088 | −0.336044 | − | 0.941846i | \(-0.609089\pi\) | ||||
−0.336044 | + | 0.941846i | \(0.609089\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −18.5288 | −0.650636 | −0.325318 | − | 0.945605i | \(-0.605471\pi\) | ||||
−0.325318 | + | 0.945605i | \(0.605471\pi\) | |||||||
\(812\) | − 13.7958i | − 0.484138i | ||||||||
\(813\) | − 36.0859i | − 1.26559i | ||||||||
\(814\) | −22.4368 | −0.786411 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −41.2466 | −1.44392 | ||||||||
\(817\) | − 26.1102i | − 0.913480i | ||||||||
\(818\) | − 11.7037i | − 0.409209i | ||||||||
\(819\) | 131.083 | 4.58042 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −36.0522 | −1.25823 | −0.629115 | − | 0.777312i | \(-0.716583\pi\) | ||||
−0.629115 | + | 0.777312i | \(0.716583\pi\) | |||||||
\(822\) | 30.3470i | 1.05847i | ||||||||
\(823\) | 17.3204i | 0.603753i | 0.953347 | + | 0.301876i | \(0.0976130\pi\) | ||||
−0.953347 | + | 0.301876i | \(0.902387\pi\) | |||||||
\(824\) | 2.64027 | 0.0919782 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 64.4436 | 2.24228 | ||||||||
\(827\) | 23.1732i | 0.805811i | 0.915242 | + | 0.402906i | \(0.132000\pi\) | ||||
−0.915242 | + | 0.402906i | \(0.868000\pi\) | |||||||
\(828\) | 0.529006i | 0.0183842i | ||||||||
\(829\) | −23.0938 | −0.802082 | −0.401041 | − | 0.916060i | \(-0.631351\pi\) | ||||
−0.401041 | + | 0.916060i | \(0.631351\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 70.0143 | 2.42877 | ||||||||
\(832\) | − 27.5047i | − 0.953552i | ||||||||
\(833\) | − 5.11142i | − 0.177100i | ||||||||
\(834\) | −0.560960 | −0.0194244 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −6.15413 | −0.212845 | ||||||||
\(837\) | 10.1325i | 0.350231i | ||||||||
\(838\) | 29.0039i | 1.00192i | ||||||||
\(839\) | 43.7883 | 1.51174 | 0.755871 | − | 0.654721i | \(-0.227214\pi\) | ||||
0.755871 | + | 0.654721i | \(0.227214\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 21.1232 | 0.728385 | ||||||||
\(842\) | − 50.8296i | − 1.75170i | ||||||||
\(843\) | 44.1435i | 1.52038i | ||||||||
\(844\) | −9.83125 | −0.338406 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −21.6796 | −0.745360 | ||||||||
\(847\) | − 23.9654i | − 0.823460i | ||||||||
\(848\) | − 25.4283i | − 0.873212i | ||||||||
\(849\) | −84.8614 | −2.91244 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1.02569 | 0.0351601 | ||||||||
\(852\) | 10.6383i | 0.364463i | ||||||||
\(853\) | 30.5569i | 1.04625i | 0.852256 | + | 0.523125i | \(0.175234\pi\) | ||||
−0.852256 | + | 0.523125i | \(0.824766\pi\) | |||||||
\(854\) | 0.511116 | 0.0174900 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −12.6920 | −0.433804 | ||||||||
\(857\) | − 54.5160i | − 1.86223i | −0.364726 | − | 0.931115i | \(-0.618837\pi\) | ||||
0.364726 | − | 0.931115i | \(-0.381163\pi\) | |||||||
\(858\) | − 59.5108i | − 2.03167i | ||||||||
\(859\) | 49.3771 | 1.68473 | 0.842363 | − | 0.538911i | \(-0.181164\pi\) | ||||
0.842363 | + | 0.538911i | \(0.181164\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 40.8743 | 1.39299 | ||||||||
\(862\) | 50.1103i | 1.70676i | ||||||||
\(863\) | − 29.6647i | − 1.00980i | −0.863178 | − | 0.504899i | \(-0.831530\pi\) | ||||
0.863178 | − | 0.504899i | \(-0.168470\pi\) | |||||||
\(864\) | 36.1809 | 1.23090 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −25.7441 | −0.874819 | ||||||||
\(867\) | − 28.5050i | − 0.968080i | ||||||||
\(868\) | − 1.94862i | − 0.0661406i | ||||||||
\(869\) | 8.44473 | 0.286468 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −15.9336 | −0.539890 | ||||||||
\(872\) | 11.8874i | 0.402559i | ||||||||
\(873\) | 43.2643i | 1.46428i | ||||||||
\(874\) | 1.14016 | 0.0385666 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 1.28067 | 0.0432699 | ||||||||
\(877\) | 28.6701i | 0.968120i | 0.875035 | + | 0.484060i | \(0.160838\pi\) | ||||
−0.875035 | + | 0.484060i | \(0.839162\pi\) | |||||||
\(878\) | 39.8409i | 1.34456i | ||||||||
\(879\) | −9.03396 | −0.304708 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 26.8689 | 0.905235 | 0.452617 | − | 0.891705i | \(-0.350490\pi\) | ||||
0.452617 | + | 0.891705i | \(0.350490\pi\) | |||||||
\(882\) | 19.0135i | 0.640217i | ||||||||
\(883\) | 21.4596i | 0.722172i | 0.932533 | + | 0.361086i | \(0.117594\pi\) | ||||
−0.932533 | + | 0.361086i | \(0.882406\pi\) | |||||||
\(884\) | 12.6482 | 0.425403 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −8.60466 | −0.289079 | ||||||||
\(887\) | 7.94131i | 0.266643i | 0.991073 | + | 0.133322i | \(0.0425643\pi\) | ||||
−0.991073 | + | 0.133322i | \(0.957436\pi\) | |||||||
\(888\) | − 53.6985i | − 1.80200i | ||||||||
\(889\) | −19.8309 | −0.665106 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −20.5406 | −0.688135 | ||||||||
\(892\) | 5.48083i | 0.183512i | ||||||||
\(893\) | 11.5295i | 0.385820i | ||||||||
\(894\) | 39.7275 | 1.32869 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 40.3545 | 1.34815 | ||||||||
\(897\) | 2.72050i | 0.0908350i | ||||||||
\(898\) | − 34.9207i | − 1.16532i | ||||||||
\(899\) | 7.07977 | 0.236124 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −14.4207 | −0.480422 | ||||||||
\(902\) | − 12.5829i | − 0.418965i | ||||||||
\(903\) | 43.2934i | 1.44071i | ||||||||
\(904\) | 5.72673 | 0.190468 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −103.747 | −3.44676 | ||||||||
\(907\) | 45.4658i | 1.50967i | 0.655916 | + | 0.754834i | \(0.272283\pi\) | ||||
−0.655916 | + | 0.754834i | \(0.727717\pi\) | |||||||
\(908\) | 9.64037i | 0.319927i | ||||||||
\(909\) | −115.458 | −3.82951 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −33.6098 | −1.11354 | −0.556771 | − | 0.830666i | \(-0.687960\pi\) | ||||
−0.556771 | + | 0.830666i | \(0.687960\pi\) | |||||||
\(912\) | − 81.5957i | − 2.70190i | ||||||||
\(913\) | − 3.20812i | − 0.106173i | ||||||||
\(914\) | −41.0494 | −1.35779 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −12.0980 | −0.399728 | ||||||||
\(917\) | 44.1199i | 1.45697i | ||||||||
\(918\) | − 45.7031i | − 1.50843i | ||||||||
\(919\) | 24.3699 | 0.803888 | 0.401944 | − | 0.915664i | \(-0.368335\pi\) | ||||
0.401944 | + | 0.915664i | \(0.368335\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 32.4078 | 1.06787 | ||||||||
\(922\) | 31.1187i | 1.02484i | ||||||||
\(923\) | 37.0975i | 1.22108i | ||||||||
\(924\) | 10.2042 | 0.335693 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −47.0806 | −1.54716 | ||||||||
\(927\) | 7.61359i | 0.250063i | ||||||||
\(928\) | − 25.2803i | − 0.829866i | ||||||||
\(929\) | 9.10480 | 0.298719 | 0.149359 | − | 0.988783i | \(-0.452279\pi\) | ||||
0.149359 | + | 0.988783i | \(0.452279\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 10.1116 | 0.331395 | ||||||||
\(932\) | 0.0482810i | 0.00158150i | ||||||||
\(933\) | − 47.7992i | − 1.56488i | ||||||||
\(934\) | −15.2345 | −0.498487 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 96.5781 | 3.15676 | ||||||||
\(937\) | 1.74387i | 0.0569697i | 0.999594 | + | 0.0284849i | \(0.00906824\pi\) | ||||
−0.999594 | + | 0.0284849i | \(0.990932\pi\) | |||||||
\(938\) | − 11.0725i | − 0.361529i | ||||||||
\(939\) | −68.0739 | −2.22151 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 44.3041 | 1.44427 | 0.722136 | − | 0.691751i | \(-0.243161\pi\) | ||||
0.722136 | + | 0.691751i | \(0.243161\pi\) | |||||||
\(942\) | − 75.0115i | − 2.44401i | ||||||||
\(943\) | 0.575221i | 0.0187318i | ||||||||
\(944\) | 64.9029 | 2.11241 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 13.3276 | 0.433319 | ||||||||
\(947\) | − 17.9601i | − 0.583624i | −0.956476 | − | 0.291812i | \(-0.905742\pi\) | ||||
0.956476 | − | 0.291812i | \(-0.0942582\pi\) | |||||||
\(948\) | − 9.84587i | − 0.319779i | ||||||||
\(949\) | 4.46591 | 0.144969 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −23.9636 | −0.777074 | ||||||||
\(952\) | − 18.0422i | − 0.584750i | ||||||||
\(953\) | − 21.7642i | − 0.705011i | −0.935810 | − | 0.352505i | \(-0.885330\pi\) | ||||
0.935810 | − | 0.352505i | \(-0.114670\pi\) | |||||||
\(954\) | 53.6421 | 1.73673 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 13.1527 | 0.425389 | ||||||||
\(957\) | 37.0740i | 1.19843i | ||||||||
\(958\) | − 45.3494i | − 1.46517i | ||||||||
\(959\) | −18.1455 | −0.585949 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1.00000 | 0.0322581 | ||||||||
\(962\) | 91.2224i | 2.94113i | ||||||||
\(963\) | − 36.5992i | − 1.17939i | ||||||||
\(964\) | 2.28790 | 0.0736882 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −1.89051 | −0.0608262 | ||||||||
\(967\) | 29.2152i | 0.939499i | 0.882800 | + | 0.469750i | \(0.155656\pi\) | ||||
−0.882800 | + | 0.469750i | \(0.844344\pi\) | |||||||
\(968\) | − 17.6570i | − 0.567516i | ||||||||
\(969\) | −46.2739 | −1.48653 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −4.11489 | −0.132053 | −0.0660266 | − | 0.997818i | \(-0.521032\pi\) | ||||
−0.0660266 | + | 0.997818i | \(0.521032\pi\) | |||||||
\(972\) | 4.03366i | 0.129380i | ||||||||
\(973\) | − 0.335417i | − 0.0107530i | ||||||||
\(974\) | 5.03357 | 0.161286 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0.514759 | 0.0164770 | ||||||||
\(977\) | 42.0412i | 1.34502i | 0.740089 | + | 0.672509i | \(0.234783\pi\) | ||||
−0.740089 | + | 0.672509i | \(0.765217\pi\) | |||||||
\(978\) | 21.2766i | 0.680352i | ||||||||
\(979\) | −19.7135 | −0.630046 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −34.2791 | −1.09445 | ||||||||
\(982\) | 4.31909i | 0.137828i | ||||||||
\(983\) | 44.2806i | 1.41233i | 0.708047 | + | 0.706166i | \(0.249577\pi\) | ||||
−0.708047 | + | 0.706166i | \(0.750423\pi\) | |||||||
\(984\) | 30.1149 | 0.960028 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −31.9336 | −1.01697 | ||||||||
\(987\) | − 19.1171i | − 0.608504i | ||||||||
\(988\) | 25.0211i | 0.796027i | ||||||||
\(989\) | −0.609265 | −0.0193735 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 8.37142 | 0.265927 | 0.132964 | − | 0.991121i | \(-0.457551\pi\) | ||||
0.132964 | + | 0.991121i | \(0.457551\pi\) | |||||||
\(992\) | − 3.57078i | − 0.113372i | ||||||||
\(993\) | 47.6835i | 1.51319i | ||||||||
\(994\) | −25.7795 | −0.817676 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −3.74041 | −0.118520 | ||||||||
\(997\) | − 53.8984i | − 1.70698i | −0.521109 | − | 0.853490i | \(-0.674482\pi\) | ||||
0.521109 | − | 0.853490i | \(-0.325518\pi\) | |||||||
\(998\) | 4.01369i | 0.127051i | ||||||||
\(999\) | 81.3340 | 2.57329 |
(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 | 775.2.b.e.249.6 | 8 | ||
5.2 | odd | 4 | 155.2.a.d.1.2 | ✓ | 4 | ||
5.3 | odd | 4 | 775.2.a.g.1.3 | 4 | |||
5.4 | even | 2 | inner | 775.2.b.e.249.3 | 8 | ||
15.2 | even | 4 | 1395.2.a.m.1.3 | 4 | |||
15.8 | even | 4 | 6975.2.a.bj.1.2 | 4 | |||
20.7 | even | 4 | 2480.2.a.z.1.4 | 4 | |||
35.27 | even | 4 | 7595.2.a.q.1.2 | 4 | |||
40.27 | even | 4 | 9920.2.a.cd.1.1 | 4 | |||
40.37 | odd | 4 | 9920.2.a.ch.1.4 | 4 | |||
155.92 | even | 4 | 4805.2.a.j.1.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
155.2.a.d.1.2 | ✓ | 4 | 5.2 | odd | 4 | ||
775.2.a.g.1.3 | 4 | 5.3 | odd | 4 | |||
775.2.b.e.249.3 | 8 | 5.4 | even | 2 | inner | ||
775.2.b.e.249.6 | 8 | 1.1 | even | 1 | trivial | ||
1395.2.a.m.1.3 | 4 | 15.2 | even | 4 | |||
2480.2.a.z.1.4 | 4 | 20.7 | even | 4 | |||
4805.2.a.j.1.2 | 4 | 155.92 | even | 4 | |||
6975.2.a.bj.1.2 | 4 | 15.8 | even | 4 | |||
7595.2.a.q.1.2 | 4 | 35.27 | even | 4 | |||
9920.2.a.cd.1.1 | 4 | 40.27 | even | 4 | |||
9920.2.a.ch.1.4 | 4 | 40.37 | odd | 4 |