Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4020,2,Mod(1609,4020)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4020, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 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("4020.1609");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4020 = 2^{2} \cdot 3 \cdot 5 \cdot 67 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4020.g (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(32.0998616126\) |
Analytic rank: | \(0\) |
Dimension: | \(38\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1609.31 | ||
Character | \(\chi\) | \(=\) | 4020.1609 |
Dual form | 4020.2.g.c.1609.12 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/4020\mathbb{Z}\right)^\times\).
\(n\) | \(1141\) | \(2011\) | \(2681\) | \(3217\) |
\(\chi(n)\) | \(1\) | \(1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.00000i | 0.577350i | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.145309 | − | 2.23134i | 0.0649844 | − | 0.997886i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.12842i | 0.426503i | 0.976997 | + | 0.213252i | \(0.0684054\pi\) | ||||
−0.976997 | + | 0.213252i | \(0.931595\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 6.26399 | 1.88866 | 0.944332 | − | 0.328994i | \(-0.106710\pi\) | ||||
0.944332 | + | 0.328994i | \(0.106710\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.929302i | 0.257742i | 0.991661 | + | 0.128871i | \(0.0411353\pi\) | ||||
−0.991661 | + | 0.128871i | \(0.958865\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.23134 | + | 0.145309i | 0.576130 | + | 0.0375187i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.84970i | 0.448618i | 0.974518 | + | 0.224309i | \(0.0720125\pi\) | ||||
−0.974518 | + | 0.224309i | \(0.927987\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −5.56412 | −1.27650 | −0.638248 | − | 0.769831i | \(-0.720340\pi\) | ||||
−0.638248 | + | 0.769831i | \(0.720340\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.12842 | −0.246242 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 6.60354i | 1.37693i | 0.725268 | + | 0.688467i | \(0.241716\pi\) | ||||
−0.725268 | + | 0.688467i | \(0.758284\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.95777 | − | 0.648470i | −0.991554 | − | 0.129694i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − | 1.00000i | − | 0.192450i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.69947 | 0.501279 | 0.250640 | − | 0.968080i | \(-0.419359\pi\) | ||||
0.250640 | + | 0.968080i | \(0.419359\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −10.1966 | −1.83136 | −0.915682 | − | 0.401905i | \(-0.868348\pi\) | ||||
−0.915682 | + | 0.401905i | \(0.868348\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 6.26399i | 1.09042i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 2.51789 | + | 0.163970i | 0.425602 | + | 0.0277160i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.96694i | 0.652161i | 0.945342 | + | 0.326080i | \(0.105728\pi\) | ||||
−0.945342 | + | 0.326080i | \(0.894272\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −0.929302 | −0.148807 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 6.94365 | 1.08442 | 0.542208 | − | 0.840245i | \(-0.317589\pi\) | ||||
0.542208 | + | 0.840245i | \(0.317589\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 8.50773i | 1.29742i | 0.761037 | + | 0.648709i | \(0.224691\pi\) | ||||
−0.761037 | + | 0.648709i | \(0.775309\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −0.145309 | + | 2.23134i | −0.0216615 | + | 0.332629i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 2.02625i | − | 0.295559i | −0.989020 | − | 0.147779i | \(-0.952787\pi\) | ||
0.989020 | − | 0.147779i | \(-0.0472126\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 5.72667 | 0.818095 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.84970 | −0.259010 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 12.2342i | 1.68049i | 0.542203 | + | 0.840247i | \(0.317590\pi\) | ||||
−0.542203 | + | 0.840247i | \(0.682410\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.910217 | − | 13.9771i | 0.122734 | − | 1.88467i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 5.56412i | − | 0.736985i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −10.5150 | −1.36893 | −0.684467 | − | 0.729044i | \(-0.739965\pi\) | ||||
−0.684467 | + | 0.729044i | \(0.739965\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 13.6403 | 1.74646 | 0.873232 | − | 0.487305i | \(-0.162020\pi\) | ||||
0.873232 | + | 0.487305i | \(0.162020\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | − | 1.12842i | − | 0.142168i | ||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 2.07359 | + | 0.135036i | 0.257197 | + | 0.0167492i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.00000i | 0.122169i | ||||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −6.60354 | −0.794973 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.79047 | 0.212489 | 0.106245 | − | 0.994340i | \(-0.466117\pi\) | ||||
0.106245 | + | 0.994340i | \(0.466117\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 8.93411i | − | 1.04566i | −0.852437 | − | 0.522829i | \(-0.824876\pi\) | ||
0.852437 | − | 0.522829i | \(-0.175124\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0.648470 | − | 4.95777i | 0.0748789 | − | 0.572474i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 7.06842i | 0.805521i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −0.0306733 | −0.00345101 | −0.00172551 | − | 0.999999i | \(-0.500549\pi\) | ||||
−0.00172551 | + | 0.999999i | \(0.500549\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 14.1845i | − | 1.55695i | −0.627674 | − | 0.778476i | \(-0.715993\pi\) | ||
0.627674 | − | 0.778476i | \(-0.284007\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 4.12731 | + | 0.268779i | 0.447670 | + | 0.0291532i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 2.69947i | 0.289414i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −5.95555 | −0.631287 | −0.315644 | − | 0.948878i | \(-0.602220\pi\) | ||||
−0.315644 | + | 0.948878i | \(0.602220\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.04864 | −0.109928 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − | 10.1966i | − | 1.05734i | ||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −0.808518 | + | 12.4154i | −0.0829522 | + | 1.27380i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 12.2239i | 1.24115i | 0.784147 | + | 0.620576i | \(0.213101\pi\) | ||||
−0.784147 | + | 0.620576i | \(0.786899\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −6.26399 | −0.629555 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −5.60500 | −0.557719 | −0.278859 | − | 0.960332i | \(-0.589956\pi\) | ||||
−0.278859 | + | 0.960332i | \(0.589956\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 8.34053i | − | 0.821817i | −0.911677 | − | 0.410909i | \(-0.865212\pi\) | ||
0.911677 | − | 0.410909i | \(-0.134788\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −0.163970 | + | 2.51789i | −0.0160019 | + | 0.245721i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 3.33167i | − | 0.322084i | −0.986948 | − | 0.161042i | \(-0.948514\pi\) | ||
0.986948 | − | 0.161042i | \(-0.0514855\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 5.52141 | 0.528855 | 0.264427 | − | 0.964406i | \(-0.414817\pi\) | ||||
0.264427 | + | 0.964406i | \(0.414817\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −3.96694 | −0.376525 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 10.4110i | 0.979385i | 0.871895 | + | 0.489692i | \(0.162891\pi\) | ||||
−0.871895 | + | 0.489692i | \(0.837109\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 14.7348 | + | 0.959556i | 1.37402 | + | 0.0894791i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | − | 0.929302i | − | 0.0859140i | ||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −2.08724 | −0.191337 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 28.2376 | 2.56705 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 6.94365i | 0.626087i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −2.16737 | + | 10.9683i | −0.193855 | + | 0.981030i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 8.02001i | 0.711661i | 0.934551 | + | 0.355830i | \(0.115802\pi\) | ||||
−0.934551 | + | 0.355830i | \(0.884198\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −8.50773 | −0.749064 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 4.87634 | 0.426048 | 0.213024 | − | 0.977047i | \(-0.431669\pi\) | ||||
0.213024 | + | 0.977047i | \(0.431669\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − | 6.27867i | − | 0.544429i | ||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −2.23134 | − | 0.145309i | −0.192043 | − | 0.0125062i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 6.55953i | 0.560419i | 0.959939 | + | 0.280209i | \(0.0904039\pi\) | ||||
−0.959939 | + | 0.280209i | \(0.909596\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −11.9185 | −1.01091 | −0.505456 | − | 0.862852i | \(-0.668676\pi\) | ||||
−0.505456 | + | 0.862852i | \(0.668676\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 2.02625 | 0.170641 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 5.82113i | 0.486788i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0.392259 | − | 6.02344i | 0.0325753 | − | 0.500220i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 5.72667i | 0.472327i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 7.26428 | 0.595113 | 0.297557 | − | 0.954704i | \(-0.403828\pi\) | ||||
0.297557 | + | 0.954704i | \(0.403828\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 15.7162 | 1.27897 | 0.639484 | − | 0.768805i | \(-0.279148\pi\) | ||||
0.639484 | + | 0.768805i | \(0.279148\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 1.84970i | − | 0.149539i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1.48166 | + | 22.7521i | −0.119010 | + | 1.82749i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 12.8287i | 1.02385i | 0.859032 | + | 0.511923i | \(0.171067\pi\) | ||||
−0.859032 | + | 0.511923i | \(0.828933\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −12.2342 | −0.970234 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −7.45157 | −0.587266 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 20.9223i | 1.63876i | 0.573249 | + | 0.819381i | \(0.305683\pi\) | ||||
−0.573249 | + | 0.819381i | \(0.694317\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 13.9771 | + | 0.910217i | 1.08812 | + | 0.0708603i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 11.6346i | 0.900311i | 0.892950 | + | 0.450155i | \(0.148631\pi\) | ||||
−0.892950 | + | 0.450155i | \(0.851369\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 12.1364 | 0.933569 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 5.56412 | 0.425499 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 11.2044i | 0.851857i | 0.904757 | + | 0.425928i | \(0.140052\pi\) | ||||
−0.904757 | + | 0.425928i | \(0.859948\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0.731747 | − | 5.59445i | 0.0553149 | − | 0.422901i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − | 10.5150i | − | 0.790354i | ||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −9.33753 | −0.697920 | −0.348960 | − | 0.937138i | \(-0.613465\pi\) | ||||
−0.348960 | + | 0.937138i | \(0.613465\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −14.0490 | −1.04425 | −0.522125 | − | 0.852869i | \(-0.674861\pi\) | ||||
−0.522125 | + | 0.852869i | \(0.674861\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 13.6403i | 1.00832i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 8.85159 | + | 0.576433i | 0.650782 | + | 0.0423802i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 11.5865i | 0.847289i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1.12842 | 0.0820806 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 16.7184 | 1.20970 | 0.604850 | − | 0.796340i | \(-0.293233\pi\) | ||||
0.604850 | + | 0.796340i | \(0.293233\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 9.43446i | − | 0.679107i | −0.940587 | − | 0.339554i | \(-0.889724\pi\) | ||
0.940587 | − | 0.339554i | \(-0.110276\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −0.135036 | + | 2.07359i | −0.00967015 | + | 0.148493i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 5.96186i | 0.424765i | 0.977187 | + | 0.212382i | \(0.0681222\pi\) | ||||
−0.977187 | + | 0.212382i | \(0.931878\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −7.76009 | −0.550098 | −0.275049 | − | 0.961430i | \(-0.588694\pi\) | ||||
−0.275049 | + | 0.961430i | \(0.588694\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1.00000 | −0.0705346 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 3.04614i | 0.213797i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.00898 | − | 15.4936i | 0.0704700 | − | 1.08212i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − | 6.60354i | − | 0.458978i | ||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −34.8536 | −2.41087 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −15.5083 | −1.06763 | −0.533816 | − | 0.845601i | \(-0.679243\pi\) | ||||
−0.533816 | + | 0.845601i | \(0.679243\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 1.79047i | 0.122681i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 18.9837 | + | 1.23625i | 1.29467 | + | 0.0843118i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 11.5061i | − | 0.781082i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 8.93411 | 0.603711 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.71893 | −0.115628 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 23.4454i | 1.57002i | 0.619483 | + | 0.785010i | \(0.287342\pi\) | ||||
−0.619483 | + | 0.785010i | \(0.712658\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 4.95777 | + | 0.648470i | 0.330518 | + | 0.0432313i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 0.207600i | 0.0137789i | 0.999976 | + | 0.00688945i | \(0.00219300\pi\) | ||||
−0.999976 | + | 0.00688945i | \(0.997807\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2.26426 | 0.149627 | 0.0748134 | − | 0.997198i | \(-0.476164\pi\) | ||||
0.0748134 | + | 0.997198i | \(0.476164\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −7.06842 | −0.465068 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 7.58804i | 0.497109i | 0.968618 | + | 0.248554i | \(0.0799555\pi\) | ||||
−0.968618 | + | 0.248554i | \(0.920045\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −4.52125 | − | 0.294433i | −0.294934 | − | 0.0192067i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − | 0.0306733i | − | 0.00199244i | ||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −6.66454 | −0.431094 | −0.215547 | − | 0.976494i | \(-0.569153\pi\) | ||||
−0.215547 | + | 0.976494i | \(0.569153\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3.97697 | 0.256179 | 0.128090 | − | 0.991763i | \(-0.459115\pi\) | ||||
0.128090 | + | 0.991763i | \(0.459115\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000i | 0.0641500i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0.832138 | − | 12.7781i | 0.0531634 | − | 0.816366i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 5.17074i | − | 0.329006i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 14.1845 | 0.898907 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −12.7120 | −0.802376 | −0.401188 | − | 0.915996i | \(-0.631403\pi\) | ||||
−0.401188 | + | 0.915996i | \(0.631403\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 41.3645i | 2.60056i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −0.268779 | + | 4.12731i | −0.0168316 | + | 0.258462i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 9.22292i | − | 0.575310i | −0.957734 | − | 0.287655i | \(-0.907124\pi\) | ||
0.957734 | − | 0.287655i | \(-0.0928756\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −4.47638 | −0.278149 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −2.69947 | −0.167093 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 4.58502i | − | 0.282725i | −0.989958 | − | 0.141362i | \(-0.954852\pi\) | ||
0.989958 | − | 0.141362i | \(-0.0451482\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 27.2986 | + | 1.77774i | 1.67694 | + | 0.109206i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − | 5.95555i | − | 0.364474i | ||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 14.1482 | 0.862629 | 0.431315 | − | 0.902202i | \(-0.358050\pi\) | ||||
0.431315 | + | 0.902202i | \(0.358050\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 15.3501 | 0.932453 | 0.466226 | − | 0.884666i | \(-0.345613\pi\) | ||||
0.466226 | + | 0.884666i | \(0.345613\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | − | 1.04864i | − | 0.0634668i | ||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −31.0554 | − | 4.06201i | −1.87271 | − | 0.244948i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 9.60094i | − | 0.576865i | −0.957500 | − | 0.288432i | \(-0.906866\pi\) | ||
0.957500 | − | 0.288432i | \(-0.0931340\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 10.1966 | 0.610454 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −10.0081 | −0.597034 | −0.298517 | − | 0.954404i | \(-0.596492\pi\) | ||||
−0.298517 | + | 0.954404i | \(0.596492\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 14.4995i | 0.861908i | 0.902374 | + | 0.430954i | \(0.141823\pi\) | ||||
−0.902374 | + | 0.430954i | \(0.858177\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −12.4154 | − | 0.808518i | −0.735427 | − | 0.0478925i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 7.83536i | 0.462507i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 13.5786 | 0.798742 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −12.2239 | −0.716579 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 30.2685i | − | 1.76831i | −0.467198 | − | 0.884153i | \(-0.654736\pi\) | ||
0.467198 | − | 0.884153i | \(-0.345264\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.52792 | + | 23.4625i | −0.0889592 | + | 1.36604i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − | 6.26399i | − | 0.363473i | ||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −6.13668 | −0.354893 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −9.60031 | −0.553352 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − | 5.60500i | − | 0.321999i | ||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 1.98207 | − | 30.4362i | 0.113493 | − | 1.74277i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 12.3548i | 0.705124i | 0.935788 | + | 0.352562i | \(0.114689\pi\) | ||||
−0.935788 | + | 0.352562i | \(0.885311\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 8.34053 | 0.474476 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1.22589 | 0.0695140 | 0.0347570 | − | 0.999396i | \(-0.488934\pi\) | ||||
0.0347570 | + | 0.999396i | \(0.488934\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 29.0382i | − | 1.64133i | −0.571407 | − | 0.820667i | \(-0.693602\pi\) | ||
0.571407 | − | 0.820667i | \(-0.306398\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −2.51789 | − | 0.163970i | −0.141867 | − | 0.00923868i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 5.85567i | 0.328887i | 0.986386 | + | 0.164444i | \(0.0525829\pi\) | ||||
−0.986386 | + | 0.164444i | \(0.947417\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 16.9095 | 0.946748 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 3.33167 | 0.185956 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 10.2919i | − | 0.572659i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0.602624 | − | 4.60726i | 0.0334276 | − | 0.255565i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 5.52141i | 0.305334i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 2.28646 | 0.126057 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 10.6855 | 0.587328 | 0.293664 | − | 0.955909i | \(-0.405125\pi\) | ||||
0.293664 | + | 0.955909i | \(0.405125\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − | 3.96694i | − | 0.217387i | ||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 2.23134 | + | 0.145309i | 0.121911 | + | 0.00793910i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 18.7175i | 1.01961i | 0.860291 | + | 0.509804i | \(0.170282\pi\) | ||||
−0.860291 | + | 0.509804i | \(0.829718\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −10.4110 | −0.565448 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −63.8714 | −3.45883 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 14.3610i | 0.775423i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −0.959556 | + | 14.7348i | −0.0516608 | + | 0.793292i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − | 8.82254i | − | 0.473619i | −0.971556 | − | 0.236809i | \(-0.923898\pi\) | ||
0.971556 | − | 0.236809i | \(-0.0761017\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 33.8915 | 1.81417 | 0.907086 | − | 0.420945i | \(-0.138302\pi\) | ||||
0.907086 | + | 0.420945i | \(0.138302\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0.929302 | 0.0496025 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 5.88350i | − | 0.313147i | −0.987666 | − | 0.156574i | \(-0.949955\pi\) | ||
0.987666 | − | 0.156574i | \(-0.0500448\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0.260172 | − | 3.99514i | 0.0138085 | − | 0.212040i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | − | 2.08724i | − | 0.110468i | ||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −9.66040 | −0.509857 | −0.254928 | − | 0.966960i | \(-0.582052\pi\) | ||||
−0.254928 | + | 0.966960i | \(0.582052\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 11.9594 | 0.629441 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 28.2376i | 1.48209i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −19.9351 | − | 1.29821i | −1.04345 | − | 0.0679515i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 19.9664i | − | 1.04224i | −0.853484 | − | 0.521119i | \(-0.825515\pi\) | ||
0.853484 | − | 0.521119i | \(-0.174485\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −6.94365 | −0.361472 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −13.8053 | −0.716736 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 22.7056i | − | 1.17565i | −0.808988 | − | 0.587825i | \(-0.799984\pi\) | ||
0.808988 | − | 0.587825i | \(-0.200016\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −10.9683 | − | 2.16737i | −0.566398 | − | 0.111922i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 2.50862i | 0.129201i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −20.8020 | −1.06852 | −0.534262 | − | 0.845319i | \(-0.679411\pi\) | ||||
−0.534262 | + | 0.845319i | \(0.679411\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −8.02001 | −0.410878 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 2.80878i | 0.143522i | 0.997422 | + | 0.0717610i | \(0.0228619\pi\) | ||||
−0.997422 | + | 0.0717610i | \(0.977138\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 15.7721 | + | 1.02711i | 0.803818 | + | 0.0523463i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − | 8.50773i | − | 0.432472i | ||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 4.10035 | 0.207896 | 0.103948 | − | 0.994583i | \(-0.466852\pi\) | ||||
0.103948 | + | 0.994583i | \(0.466852\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −12.2146 | −0.617717 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 4.87634i | 0.245979i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −0.00445711 | + | 0.0684425i | −0.000224262 | + | 0.00344372i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 10.0390i | 0.503843i | 0.967748 | + | 0.251921i | \(0.0810624\pi\) | ||||
−0.967748 | + | 0.251921i | \(0.918938\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 6.27867 | 0.314326 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 25.2690 | 1.26187 | 0.630936 | − | 0.775835i | \(-0.282671\pi\) | ||||
0.630936 | + | 0.775835i | \(0.282671\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 9.47572i | − | 0.472019i | ||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0.145309 | − | 2.23134i | 0.00722048 | − | 0.110876i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 24.8489i | 1.23171i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −38.6571 | −1.91147 | −0.955735 | − | 0.294230i | \(-0.904937\pi\) | ||||
−0.955735 | + | 0.294230i | \(0.904937\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −6.55953 | −0.323558 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − | 11.8653i | − | 0.583854i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −31.6505 | − | 2.06114i | −1.55366 | − | 0.101178i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − | 11.9185i | − | 0.583650i | ||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 7.77628 | 0.379896 | 0.189948 | − | 0.981794i | \(-0.439168\pi\) | ||||
0.189948 | + | 0.981794i | \(0.439168\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −13.5152 | −0.658690 | −0.329345 | − | 0.944210i | \(-0.606828\pi\) | ||||
−0.329345 | + | 0.944210i | \(0.606828\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 2.02625i | 0.0985196i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 1.19947 | − | 9.17039i | 0.0581831 | − | 0.444829i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 15.3920i | 0.744872i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −5.82113 | −0.281047 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 24.4327 | 1.17688 | 0.588440 | − | 0.808541i | \(-0.299742\pi\) | ||||
0.588440 | + | 0.808541i | \(0.299742\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 13.0026i | − | 0.624863i | −0.949940 | − | 0.312431i | \(-0.898857\pi\) | ||
0.949940 | − | 0.312431i | \(-0.101143\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 6.02344 | + | 0.392259i | 0.288802 | + | 0.0188074i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − | 36.7429i | − | 1.75765i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 26.6723 | 1.27300 | 0.636500 | − | 0.771277i | \(-0.280381\pi\) | ||||
0.636500 | + | 0.771277i | \(0.280381\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −5.72667 | −0.272698 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 34.3767i | 1.63329i | 0.577141 | + | 0.816644i | \(0.304168\pi\) | ||||
−0.577141 | + | 0.816644i | \(0.695832\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −0.865398 | + | 13.2889i | −0.0410238 | + | 0.629953i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 7.26428i | 0.343589i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −24.4317 | −1.15300 | −0.576501 | − | 0.817097i | \(-0.695582\pi\) | ||||
−0.576501 | + | 0.817097i | \(0.695582\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 43.4949 | 2.04810 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 15.7162i | 0.738412i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −0.152378 | + | 2.33988i | −0.00714358 | + | 0.109695i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 19.0286i | − | 0.890119i | −0.895501 | − | 0.445059i | \(-0.853183\pi\) | ||
0.895501 | − | 0.445059i | \(-0.146817\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 1.84970 | 0.0863366 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 20.4848 | 0.954074 | 0.477037 | − | 0.878883i | \(-0.341711\pi\) | ||||
0.477037 | + | 0.878883i | \(0.341711\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 5.07492i | 0.235852i | 0.993022 | + | 0.117926i | \(0.0376245\pi\) | ||||
−0.993022 | + | 0.117926i | \(0.962375\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −22.7521 | − | 1.48166i | −1.05510 | − | 0.0687104i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 25.8385i | 1.19566i | 0.801622 | + | 0.597832i | \(0.203971\pi\) | ||||
−0.801622 | + | 0.597832i | \(0.796029\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1.12842 | −0.0521057 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −12.8287 | −0.591117 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 53.2923i | 2.45038i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 27.5856 | + | 3.60816i | 1.26571 | + | 0.165554i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − | 12.2342i | − | 0.560165i | ||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 2.47132 | 0.112918 | 0.0564589 | − | 0.998405i | \(-0.482019\pi\) | ||||
0.0564589 | + | 0.998405i | \(0.482019\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3.68648 | −0.168089 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − | 7.45157i | − | 0.339058i | ||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 27.2758 | + | 1.77625i | 1.23853 | + | 0.0806554i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 23.8384i | 1.08022i | 0.841595 | + | 0.540110i | \(0.181617\pi\) | ||||
−0.841595 | + | 0.540110i | \(0.818383\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −20.9223 | −0.946140 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −23.9747 | −1.08196 | −0.540982 | − | 0.841034i | \(-0.681947\pi\) | ||||
−0.540982 | + | 0.841034i | \(0.681947\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 4.99321i | 0.224883i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −0.910217 | + | 13.9771i | −0.0409112 | + | 0.628224i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 2.02040i | 0.0906273i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −28.8330 | −1.29074 | −0.645371 | − | 0.763869i | \(-0.723297\pi\) | ||||
−0.645371 | + | 0.763869i | \(0.723297\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −11.6346 | −0.519795 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − | 7.31901i | − | 0.326339i | −0.986598 | − | 0.163169i | \(-0.947828\pi\) | ||
0.986598 | − | 0.163169i | \(-0.0521717\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −0.814460 | + | 12.5067i | −0.0362430 | + | 0.556540i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 12.1364i | 0.538996i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −27.1764 | −1.20457 | −0.602286 | − | 0.798280i | \(-0.705743\pi\) | ||||
−0.602286 | + | 0.798280i | \(0.705743\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 10.0814 | 0.445977 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 5.56412i | 0.245662i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −18.6106 | − | 1.21196i | −0.820080 | − | 0.0534052i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 12.6924i | − | 0.558211i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −11.2044 | −0.491820 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 36.7097 | 1.60828 | 0.804141 | − | 0.594439i | \(-0.202626\pi\) | ||||
0.804141 | + | 0.594439i | \(0.202626\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 23.1431i | − | 1.01198i | −0.862541 | − | 0.505988i | \(-0.831128\pi\) | ||
0.862541 | − | 0.505988i | \(-0.168872\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 5.59445 | + | 0.731747i | 0.244162 | + | 0.0319361i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 18.8606i | − | 0.821583i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −20.6067 | −0.895945 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 10.5150 | 0.456311 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 6.45274i | 0.279499i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −7.43409 | − | 0.484123i | −0.321404 | − | 0.0209304i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − | 9.33753i | − | 0.402944i | ||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 35.8718 | 1.54511 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 11.1264 | 0.478362 | 0.239181 | − | 0.970975i | \(-0.423121\pi\) | ||||
0.239181 | + | 0.970975i | \(0.423121\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − | 14.0490i | − | 0.602898i | ||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0.802312 | − | 12.3201i | 0.0343673 | − | 0.527737i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 39.2846i | − | 1.67969i | −0.542829 | − | 0.839843i | \(-0.682647\pi\) | ||
0.542829 | − | 0.839843i | \(-0.317353\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −13.6403 | −0.582155 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −15.0202 | −0.639881 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 0.0346124i | − | 0.00147187i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −0.576433 | + | 8.85159i | −0.0244682 | + | 0.375729i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 8.00977i | 0.339385i | 0.985497 | + | 0.169692i | \(0.0542774\pi\) | ||||
−0.985497 | + | 0.169692i | \(0.945723\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −7.90625 | −0.334399 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −11.5865 | −0.489182 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − | 10.0007i | − | 0.421478i | −0.977542 | − | 0.210739i | \(-0.932413\pi\) | ||
0.977542 | − | 0.210739i | \(-0.0675871\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 23.2305 | + | 1.51282i | 0.977315 | + | 0.0636447i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 1.12842i | 0.0473892i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −14.2167 | −0.595994 | −0.297997 | − | 0.954567i | \(-0.596319\pi\) | ||||
−0.297997 | + | 0.954567i | \(0.596319\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 43.1228 | 1.80463 | 0.902317 | − | 0.431072i | \(-0.141865\pi\) | ||||
0.902317 | + | 0.431072i | \(0.141865\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 16.7184i | 0.698420i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 4.28220 | − | 32.7388i | 0.178580 | − | 1.36530i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 28.1240i | − | 1.17082i | −0.810739 | − | 0.585408i | \(-0.800934\pi\) | ||
0.810739 | − | 0.585408i | \(-0.199066\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 9.43446 | 0.392083 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 16.0061 | 0.664045 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 76.6348i | 3.17389i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −2.07359 | − | 0.135036i | −0.0857324 | − | 0.00558306i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 16.9796i | − | 0.700825i | −0.936595 | − | 0.350412i | \(-0.886041\pi\) | ||
0.936595 | − | 0.350412i | \(-0.113959\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 56.7350 | 2.33773 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −5.96186 | −0.245238 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 10.5640i | 0.433811i | 0.976193 | + | 0.216905i | \(0.0695963\pi\) | ||||
−0.976193 | + | 0.216905i | \(0.930404\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −0.303296 | + | 4.65735i | −0.0124339 | + | 0.190933i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − | 7.76009i | − | 0.317599i | ||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −4.96729 | −0.202958 | −0.101479 | − | 0.994838i | \(-0.532357\pi\) | ||||
−0.101479 | + | 0.994838i | \(0.532357\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −32.3830 | −1.32093 | −0.660465 | − | 0.750857i | \(-0.729641\pi\) | ||||
−0.660465 | + | 0.750857i | \(0.729641\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − | 1.00000i | − | 0.0407231i | ||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 4.10318 | − | 63.0076i | 0.166818 | − | 2.56162i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 10.8553i | − | 0.440604i | −0.975432 | − | 0.220302i | \(-0.929296\pi\) | ||
0.975432 | − | 0.220302i | \(-0.0707042\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −3.04614 | −0.123436 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 1.88300 | 0.0761779 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 3.95967i | 0.159930i | 0.996798 | + | 0.0799648i | \(0.0254808\pi\) | ||||
−0.996798 | + | 0.0799648i | \(0.974519\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 15.4936 | + | 1.00898i | 0.624764 | + | 0.0406859i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 25.4694i | 1.02536i | 0.858580 | + | 0.512680i | \(0.171347\pi\) | ||||
−0.858580 | + | 0.512680i | \(0.828653\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 24.4008 | 0.980751 | 0.490375 | − | 0.871511i | \(-0.336860\pi\) | ||||
0.490375 | + | 0.871511i | \(0.336860\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 6.60354 | 0.264991 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − | 6.72037i | − | 0.269246i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 24.1590 | + | 6.42993i | 0.966359 | + | 0.257197i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | − | 34.8536i | − | 1.39192i | ||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −7.33764 | −0.292571 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −25.6736 | −1.02205 | −0.511025 | − | 0.859566i | \(-0.670734\pi\) | ||||
−0.511025 | + | 0.859566i | \(0.670734\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − | 15.5083i | − | 0.616398i | ||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 17.8954 | + | 1.16538i | 0.710157 | + | 0.0462468i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 5.32180i | 0.210857i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −1.79047 | −0.0708297 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −37.4047 | −1.47740 | −0.738698 | − | 0.674037i | \(-0.764559\pi\) | ||||
−0.738698 | + | 0.674037i | \(0.764559\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 48.6927i | − | 1.92025i | −0.279565 | − | 0.960127i | \(-0.590190\pi\) | ||
0.279565 | − | 0.960127i | \(-0.409810\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −1.23625 | + | 18.9837i | −0.0486774 | + | 0.747481i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 10.1853i | − | 0.400427i | −0.979752 | − | 0.200213i | \(-0.935836\pi\) | ||
0.979752 | − | 0.200213i | \(-0.0641636\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −65.8657 | −2.58545 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 11.5061 | 0.450958 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 41.1225i | − | 1.60925i | −0.593784 | − | 0.804625i | \(-0.702367\pi\) | ||
0.593784 | − | 0.804625i | \(-0.297633\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0.708578 | − | 10.8808i | 0.0276864 | − | 0.425147i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 8.93411i | 0.348553i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −1.45845 | −0.0568133 | −0.0284067 | − | 0.999596i | \(-0.509043\pi\) | ||||
−0.0284067 | + | 0.999596i | \(0.509043\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 22.1037 | 0.859733 | 0.429866 | − | 0.902893i | \(-0.358561\pi\) | ||||
0.429866 | + | 0.902893i | \(0.358561\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − | 1.71893i | − | 0.0667577i | ||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −14.0098 | − | 0.912349i | −0.543279 | − | 0.0353794i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 17.8261i | 0.690228i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −23.4454 | −0.906452 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 85.4428 | 3.29848 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 3.54542i | − | 0.136666i | −0.997663 | − | 0.0683330i | \(-0.978232\pi\) | ||
0.997663 | − | 0.0683330i | \(-0.0217680\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −0.648470 | + | 4.95777i | −0.0249596 | + | 0.190825i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 4.69231i | 0.180340i | 0.995926 | + | 0.0901701i | \(0.0287411\pi\) | ||||
−0.995926 | + | 0.0901701i | \(0.971259\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −13.7937 | −0.529355 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −0.207600 | −0.00795525 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 29.9186i | − | 1.14480i | −0.819973 | − | 0.572402i | \(-0.806012\pi\) | ||
0.819973 | − | 0.572402i | \(-0.193988\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 14.6366 | + | 0.953162i | 0.559234 | + | 0.0364184i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 2.26426i | 0.0863870i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −11.3692 | −0.433134 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 12.1635 | 0.462720 | 0.231360 | − | 0.972868i | \(-0.425682\pi\) | ||||
0.231360 | + | 0.972868i | \(0.425682\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | − | 7.06842i | − | 0.268507i | ||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −1.73187 | + | 26.5942i | −0.0656934 | + | 1.00877i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 12.8437i | 0.486488i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −7.58804 | −0.287006 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 7.77478 | 0.293649 | 0.146825 | − | 0.989163i | \(-0.453095\pi\) | ||||
0.146825 | + | 0.989163i | \(0.453095\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 22.0725i | − | 0.832480i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0.294433 | − | 4.52125i | 0.0110890 | − | 0.170280i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − | 6.32480i | − | 0.237869i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 29.3401 | 1.10189 | 0.550945 | − | 0.834541i | \(-0.314267\pi\) | ||||
0.550945 | + | 0.834541i | \(0.314267\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0.0306733 | 0.00115034 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 67.3336i | − | 2.52166i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 12.9889 | + | 0.845866i | 0.485759 | + | 0.0316336i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − | 6.66454i | − | 0.248892i | ||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −5.33213 | −0.198855 | −0.0994274 | − | 0.995045i | \(-0.531701\pi\) | ||||
−0.0994274 | + | 0.995045i | \(0.531701\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 9.41163 | 0.350508 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 3.97697i | 0.147905i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −13.3834 | − | 1.75053i | −0.497046 | − | 0.0650129i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 10.7400i | 0.398323i | 0.979967 | + | 0.199162i | \(0.0638219\pi\) | ||||
−0.979967 | + | 0.199162i | \(0.936178\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −15.7368 | −0.582045 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 21.6453i | − | 0.799487i | −0.916627 | − | 0.399744i | \(-0.869099\pi\) | ||
0.916627 | − | 0.399744i | \(-0.130901\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 12.7781 | + | 0.832138i | 0.471329 | + | 0.0306939i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 6.26399i | 0.230737i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −2.20629 | −0.0811595 | −0.0405798 | − | 0.999176i | \(-0.512920\pi\) | ||||
−0.0405798 | + | 0.999176i | \(0.512920\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 5.17074 | 0.189952 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 11.8727i | 0.435567i | 0.975997 | + | 0.217784i | \(0.0698827\pi\) | ||||
−0.975997 | + | 0.217784i | \(0.930117\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1.05557 | − | 16.2091i | 0.0386731 | − | 0.593855i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 14.1845i | 0.518984i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 3.75952 | 0.137370 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 21.2180 | 0.774254 | 0.387127 | − | 0.922026i | \(-0.373467\pi\) | ||||
0.387127 | + | 0.922026i | \(0.373467\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − | 12.7120i | − | 0.463252i | ||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 2.28371 | − | 35.0682i | 0.0831129 | − | 1.27626i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 29.2197i | − | 1.06201i | −0.847370 | − | 0.531004i | \(-0.821815\pi\) | ||
0.847370 | − | 0.531004i | \(-0.178185\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −41.3645 | −1.50144 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −20.0081 | −0.725294 | −0.362647 | − | 0.931927i | \(-0.618127\pi\) | ||||
−0.362647 | + | 0.931927i | \(0.618127\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 6.23047i | 0.225558i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −4.12731 | − | 0.268779i | −0.149223 | − | 0.00971772i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 9.77158i | − | 0.352831i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −6.34941 | −0.228965 | −0.114483 | − | 0.993425i | \(-0.536521\pi\) | ||||
−0.114483 | + | 0.993425i | \(0.536521\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 9.22292 | 0.332155 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 51.7531i | 1.86143i | 0.365746 | + | 0.930715i | \(0.380814\pi\) | ||||
−0.365746 | + | 0.930715i | \(0.619186\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 50.5524 | + | 6.61219i | 1.81590 | + | 0.237517i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | − | 4.47638i | − | 0.160589i | ||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −38.6352 | −1.38425 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 11.2155 | 0.401321 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − | 2.69947i | − | 0.0964713i | ||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 28.6253 | + | 1.86414i | 1.02168 | + | 0.0665339i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 35.9857i | − | 1.28275i | −0.767227 | − | 0.641375i | \(-0.778364\pi\) | ||
0.767227 | − | 0.641375i | \(-0.221636\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 4.58502 | 0.163231 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −11.7480 | −0.417711 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 12.6760i | 0.450137i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −1.77774 | + | 27.2986i | −0.0630500 | + | 0.968183i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 13.5214i | 0.478953i | 0.970902 | + | 0.239477i | \(0.0769758\pi\) | ||||
−0.970902 | + | 0.239477i | \(0.923024\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 3.74795 | 0.132593 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 5.95555 | 0.210429 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − | 55.9632i | − | 1.97490i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1.08278 | + | 16.6270i | −0.0381631 | + | 0.586025i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 14.1482i | 0.498039i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −33.5271 | −1.17875 | −0.589375 | − | 0.807859i | \(-0.700626\pi\) | ||||
−0.589375 | + | 0.807859i | \(0.700626\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 35.1114 | 1.23293 | 0.616464 | − | 0.787383i | \(-0.288565\pi\) | ||||
0.616464 | + | 0.787383i | \(0.288565\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 15.3501i | 0.538352i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 46.6848 | + | 3.04021i | 1.63530 | + | 0.106494i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 47.3380i | − | 1.65615i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 1.04864 | 0.0366426 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 53.3210 | 1.86091 | 0.930457 | − | 0.366401i | \(-0.119410\pi\) | ||||
0.930457 | + | 0.366401i | \(0.119410\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 53.8802i | − | 1.87814i | −0.343720 | − | 0.939072i | \(-0.611687\pi\) | ||
0.343720 | − | 0.939072i | \(-0.388313\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 4.06201 | − | 31.0554i | 0.141421 | − | 1.08121i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 13.5527i | − | 0.471275i | −0.971841 | − | 0.235637i | \(-0.924282\pi\) | ||
0.971841 | − | 0.235637i | \(-0.0757178\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −19.0013 | −0.659943 | −0.329971 | − | 0.943991i | \(-0.607039\pi\) | ||||
−0.329971 | + | 0.943991i | \(0.607039\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 9.60094 | 0.333053 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 10.5926i | 0.367012i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 25.9607 | + | 1.69061i | 0.898408 | + | 0.0585061i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 10.1966i | 0.352446i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 38.2703 | 1.32124 | 0.660618 | − | 0.750722i | \(-0.270294\pi\) | ||||
0.660618 | + | 0.750722i | \(0.270294\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −21.7129 | −0.748719 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − | 10.0081i | − | 0.344698i | ||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1.76353 | − | 27.0805i | 0.0606674 | − | 0.931596i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 31.8639i | 1.09486i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −14.4995 | −0.497623 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −26.1958 | −0.897981 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 9.64759i | 0.330327i | 0.986266 | + | 0.165164i | \(0.0528152\pi\) | ||||
−0.986266 | + | 0.165164i | \(0.947185\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0.808518 | − | 12.4154i | 0.0276507 | − | 0.424599i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 23.8052i | − | 0.813171i | −0.913613 | − | 0.406585i | \(-0.866719\pi\) | ||
0.913613 | − | 0.406585i | \(-0.133281\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −11.1833 | −0.381570 | −0.190785 | − | 0.981632i | \(-0.561103\pi\) | ||||
−0.190785 | + | 0.981632i | \(0.561103\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −7.83536 | −0.267028 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 4.89479i | 0.166621i | 0.996524 | + | 0.0833103i | \(0.0265493\pi\) | ||||
−0.996524 | + | 0.0833103i | \(0.973451\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 25.0009 | + | 1.62811i | 0.850056 | + | 0.0553574i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 13.5786i | 0.461154i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −0.192137 | −0.00651780 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −0.929302 | −0.0314882 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − | 12.2239i | − | 0.413717i | ||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −12.3768 | − | 2.44570i | −0.418412 | − | 0.0826799i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 0.384677i | 0.0129896i | 0.999979 | + | 0.00649481i | \(0.00206738\pi\) | ||||
−0.999979 | + | 0.00649481i | \(0.997933\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 30.2685 | 1.02093 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 58.9334 | 1.98552 | 0.992758 | − | 0.120135i | \(-0.0383329\pi\) | ||||
0.992758 | + | 0.120135i | \(0.0383329\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 9.97000i | 0.335517i | 0.985828 | + | 0.167759i | \(0.0536529\pi\) | ||||
−0.985828 | + | 0.167759i | \(0.946347\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −23.4625 | − | 1.52792i | −0.788683 | − | 0.0513606i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 18.9258i | 0.635465i | 0.948180 | + | 0.317733i | \(0.102921\pi\) | ||||
−0.948180 | + | 0.317733i | \(0.897079\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −9.04995 | −0.303526 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 6.26399 | 0.209852 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 11.2743i | 0.377280i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −1.35683 | + | 20.8352i | −0.0453539 | + | 0.696445i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | − | 6.13668i | − | 0.204898i | ||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −27.5254 | −0.918024 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −22.6296 | −0.753900 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − | 9.60031i | − | 0.319478i | ||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −2.04145 | + | 31.3480i | −0.0678600 | + | 1.04204i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 50.4093i | − | 1.67381i | −0.547345 | − | 0.836907i | \(-0.684361\pi\) | ||
0.547345 | − | 0.836907i | \(-0.315639\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 5.60500 | 0.185906 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 7.36836 | 0.244125 | 0.122062 | − | 0.992522i | \(-0.461049\pi\) | ||||
0.122062 | + | 0.992522i | \(0.461049\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 88.8516i | − | 2.94056i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 30.4362 | + | 1.98207i | 1.00619 | + | 0.0655251i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 5.50256i | 0.181711i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 43.0136 | 1.41889 | 0.709443 | − | 0.704763i | \(-0.248946\pi\) | ||||
0.709443 | + | 0.704763i | \(0.248946\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −12.3548 | −0.407104 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 1.66388i | 0.0547674i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2.57244 | − | 19.6672i | 0.0845813 | − | 0.646652i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 8.34053i | 0.273939i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −35.6923 | −1.17103 | −0.585513 | − | 0.810663i | \(-0.699107\pi\) | ||||
−0.585513 | + | 0.810663i | \(0.699107\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −31.8638 | −1.04429 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 1.22589i | 0.0401340i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 25.8534 | + | 1.68363i | 0.845498 | + | 0.0550605i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 19.2690i | 0.629492i | 0.949176 | + | 0.314746i | \(0.101919\pi\) | ||||
−0.949176 | + | 0.314746i | \(0.898081\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 29.0382 | 0.947624 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 37.1806 | 1.21205 | 0.606027 | − | 0.795444i | \(-0.292762\pi\) | ||||
0.606027 | + | 0.795444i | \(0.292762\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 45.8526i | 1.49317i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0.163970 | − | 2.51789i | 0.00533395 | − | 0.0819071i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 4.91803i | − | 0.159815i | −0.996802 | − | 0.0799073i | \(-0.974538\pi\) | ||
0.996802 | − | 0.0799073i | \(-0.0254624\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 8.30249 | 0.269510 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −5.85567 | −0.189883 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 49.6190i | 1.60732i | 0.595090 | + | 0.803659i | \(0.297116\pi\) | ||||
−0.595090 | + | 0.803659i | \(0.702884\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 2.42934 | − | 37.3044i | 0.0786115 | − | 1.20714i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 16.9095i | 0.546605i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −7.40192 | −0.239020 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 72.9706 | 2.35389 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 3.33167i | 0.107361i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −21.0515 | − | 1.37092i | −0.677672 | − | 0.0441313i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1.55558i | 0.0500240i | 0.999687 | + | 0.0250120i | \(0.00796240\pi\) | ||||
−0.999687 | + | 0.0250120i | \(0.992038\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 10.2919 | 0.330625 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −52.5973 | −1.68793 | −0.843964 | − | 0.536399i | \(-0.819784\pi\) | ||||
−0.843964 | + | 0.536399i | \(0.819784\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 13.4491i | − | 0.431157i | ||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 4.60726 | + | 0.602624i | 0.147551 | + | 0.0192994i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 47.2466i | − | 1.51155i | −0.654829 | − | 0.755777i | \(-0.727259\pi\) | ||
0.654829 | − | 0.755777i | \(-0.272741\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −37.3055 | −1.19229 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −5.52141 | −0.176285 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 19.6586i | − | 0.627012i | −0.949586 | − | 0.313506i | \(-0.898496\pi\) | ||
0.949586 | − | 0.313506i | \(-0.101504\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 13.3029 | + | 0.866314i | 0.423867 | + | 0.0276031i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 2.28646i | 0.0727789i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −56.1811 | −1.78646 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −28.8781 | −0.917344 | −0.458672 | − | 0.888606i | \(-0.651675\pi\) | ||||
−0.458672 | + | 0.888606i | \(0.651675\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 10.6855i | 0.339094i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −1.12761 | + | 17.3154i | −0.0357478 | + | 0.548935i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 50.1040i | − | 1.58681i | −0.608695 | − | 0.793405i | \(-0.708307\pi\) | ||
0.608695 | − | 0.793405i | \(-0.291693\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 3.96694 | 0.125508 |
(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 | 4020.2.g.c.1609.31 | yes | 38 | |
5.4 | even | 2 | inner | 4020.2.g.c.1609.12 | ✓ | 38 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4020.2.g.c.1609.12 | ✓ | 38 | 5.4 | even | 2 | inner | |
4020.2.g.c.1609.31 | yes | 38 | 1.1 | even | 1 | trivial |