Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2100,2,Mod(1201,2100)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2100, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 0, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2100.1201");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2100 = 2^{2} \cdot 3 \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2100.q (of order \(3\), degree \(2\), 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: | \(16.7685844245\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{3})\) |
Coefficient field: | 8.0.17819046144.3 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 2x^{7} + 10x^{6} + 8x^{5} + 38x^{4} - 4x^{3} + 16x^{2} + 4x + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 420) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 1801.2 | ||
Root | \(-0.234240 - 0.405716i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2100.1801 |
Dual form | 2100.2.q.l.1201.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/2100\mathbb{Z}\right)^\times\).
\(n\) | \(701\) | \(1051\) | \(1177\) | \(1501\) |
\(\chi(n)\) | \(1\) | \(1\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
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 | ||||||||
\(3\) | −0.500000 | − | 0.866025i | −0.288675 | − | 0.500000i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.687541 | + | 2.55486i | −0.259866 | + | 0.965645i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.500000 | + | 0.866025i | −0.166667 | + | 0.288675i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.90032 | − | 3.29145i | −0.572967 | − | 0.992409i | −0.996259 | − | 0.0864153i | \(-0.972459\pi\) |
0.423292 | − | 0.905993i | \(-0.360875\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.31204 | 0.641246 | 0.320623 | − | 0.947207i | \(-0.396108\pi\) | ||||
0.320623 | + | 0.947207i | \(0.396108\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −0.187541 | − | 0.324831i | −0.0454855 | − | 0.0787832i | 0.842386 | − | 0.538874i | \(-0.181150\pi\) |
−0.887872 | + | 0.460091i | \(0.847817\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.453301 | + | 0.785140i | −0.103994 | + | 0.180124i | −0.913327 | − | 0.407227i | \(-0.866496\pi\) |
0.809333 | + | 0.587351i | \(0.199829\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.55634 | − | 0.681999i | 0.557839 | − | 0.148824i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 0.656022 | − | 1.13626i | 0.136790 | − | 0.236927i | −0.789490 | − | 0.613764i | \(-0.789655\pi\) |
0.926280 | + | 0.376836i | \(0.122988\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −6.15561 | −1.14307 | −0.571534 | − | 0.820578i | \(-0.693651\pi\) | ||||
−0.571534 | + | 0.820578i | \(0.693651\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.81204 | − | 4.87060i | −0.505058 | − | 0.874786i | −0.999983 | − | 0.00585051i | \(-0.998138\pi\) |
0.494925 | − | 0.868936i | \(-0.335196\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1.90032 | + | 3.29145i | −0.330803 | + | 0.572967i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.86880 | + | 4.96891i | −0.471628 | + | 0.816883i | −0.999473 | − | 0.0324574i | \(-0.989667\pi\) |
0.527845 | + | 0.849340i | \(0.323000\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.15602 | − | 2.00229i | −0.185112 | − | 0.320623i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0.199364 | 0.0311354 | 0.0155677 | − | 0.999879i | \(-0.495044\pi\) | ||||
0.0155677 | + | 0.999879i | \(0.495044\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 12.4019 | 1.89127 | 0.945637 | − | 0.325225i | \(-0.105440\pi\) | ||||
0.945637 | + | 0.325225i | \(0.105440\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 5.40368 | − | 9.35944i | 0.788207 | − | 1.36521i | −0.138857 | − | 0.990312i | \(-0.544343\pi\) |
0.927064 | − | 0.374902i | \(-0.122324\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.05457 | − | 3.51314i | −0.864939 | − | 0.501877i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.187541 | + | 0.324831i | −0.0262611 | + | 0.0454855i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −1.53152 | − | 2.65267i | −0.210370 | − | 0.364372i | 0.741460 | − | 0.670997i | \(-0.234134\pi\) |
−0.951830 | + | 0.306625i | \(0.900800\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0.906602 | 0.120082 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −7.14756 | − | 12.3799i | −0.930533 | − | 1.61173i | −0.782412 | − | 0.622761i | \(-0.786011\pi\) |
−0.148120 | − | 0.988969i | \(-0.547322\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.08963 | + | 1.88729i | −0.139512 | + | 0.241643i | −0.927312 | − | 0.374289i | \(-0.877887\pi\) |
0.787800 | + | 0.615931i | \(0.211220\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.86880 | − | 1.87286i | −0.235447 | − | 0.235958i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −2.78094 | − | 4.81673i | −0.339746 | − | 0.588457i | 0.644639 | − | 0.764487i | \(-0.277008\pi\) |
−0.984385 | + | 0.176030i | \(0.943674\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −1.31204 | −0.157952 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −9.88296 | −1.17289 | −0.586446 | − | 0.809989i | \(-0.699473\pi\) | ||||
−0.586446 | + | 0.809989i | \(0.699473\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −3.20095 | − | 5.54422i | −0.374643 | − | 0.648901i | 0.615630 | − | 0.788035i | \(-0.288902\pi\) |
−0.990274 | + | 0.139134i | \(0.955568\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 9.71572 | − | 2.59203i | 1.10721 | − | 0.295389i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 7.61645 | − | 13.1921i | 0.856918 | − | 1.48423i | −0.0179364 | − | 0.999839i | \(-0.505710\pi\) |
0.874854 | − | 0.484386i | \(-0.160957\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.500000 | − | 0.866025i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −8.99917 | −0.987787 | −0.493894 | − | 0.869522i | \(-0.664427\pi\) | ||||
−0.493894 | + | 0.869522i | \(0.664427\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 3.07780 | + | 5.33091i | 0.329975 | + | 0.571534i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 2.50512 | − | 4.33900i | 0.265543 | − | 0.459933i | −0.702163 | − | 0.712016i | \(-0.747782\pi\) |
0.967706 | + | 0.252083i | \(0.0811155\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.58963 | + | 5.90694i | −0.166638 | + | 0.619216i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −2.81204 | + | 4.87060i | −0.291595 | + | 0.505058i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −6.36252 | −0.646016 | −0.323008 | − | 0.946396i | \(-0.604694\pi\) | ||||
−0.323008 | + | 0.946396i | \(0.604694\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 3.80064 | 0.381978 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 2.94148 | + | 5.09479i | 0.292688 | + | 0.506951i | 0.974444 | − | 0.224629i | \(-0.0721169\pi\) |
−0.681756 | + | 0.731579i | \(0.738784\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −6.33728 | + | 10.9765i | −0.624431 | + | 1.08155i | 0.364220 | + | 0.931313i | \(0.381336\pi\) |
−0.988651 | + | 0.150233i | \(0.951998\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1.25906 | − | 2.18076i | 0.121718 | − | 0.210822i | −0.798727 | − | 0.601693i | \(-0.794493\pi\) |
0.920445 | + | 0.390871i | \(0.127826\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −5.65938 | − | 9.80233i | −0.542070 | − | 0.938893i | −0.998785 | − | 0.0492801i | \(-0.984307\pi\) |
0.456715 | − | 0.889613i | \(-0.349026\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 5.73760 | 0.544589 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 15.4752 | 1.45578 | 0.727892 | − | 0.685692i | \(-0.240500\pi\) | ||||
0.727892 | + | 0.685692i | \(0.240500\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −1.15602 | + | 2.00229i | −0.106874 | + | 0.185112i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0.958839 | − | 0.255806i | 0.0878967 | − | 0.0234497i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.72242 | + | 2.98332i | −0.156583 | + | 0.271211i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −0.0996818 | − | 0.172654i | −0.00898801 | − | 0.0155677i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −15.1159 | −1.34132 | −0.670658 | − | 0.741767i | \(-0.733988\pi\) | ||||
−0.670658 | + | 0.741767i | \(0.733988\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −6.20095 | − | 10.7404i | −0.545964 | − | 0.945637i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1.93519 | − | 3.35186i | 0.169079 | − | 0.292853i | −0.769017 | − | 0.639228i | \(-0.779254\pi\) |
0.938096 | + | 0.346375i | \(0.112587\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.69426 | − | 1.69793i | −0.146911 | − | 0.147230i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −8.49782 | − | 14.7187i | −0.726018 | − | 1.25750i | −0.958554 | − | 0.284912i | \(-0.908036\pi\) |
0.232536 | − | 0.972588i | \(-0.425298\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −8.19500 | −0.695091 | −0.347546 | − | 0.937663i | \(-0.612985\pi\) | ||||
−0.347546 | + | 0.937663i | \(0.612985\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −10.8074 | −0.910143 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −4.39362 | − | 7.60997i | −0.367413 | − | 0.636378i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −0.0151800 | + | 6.99998i | −0.00125202 | + | 0.577349i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −5.97812 | + | 10.3544i | −0.489747 | + | 0.848266i | −0.999930 | − | 0.0117991i | \(-0.996244\pi\) |
0.510184 | + | 0.860066i | \(0.329577\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −9.02305 | − | 15.6284i | −0.734286 | − | 1.27182i | −0.955036 | − | 0.296490i | \(-0.904184\pi\) |
0.220750 | − | 0.975330i | \(-0.429149\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0.375083 | 0.0303237 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 11.2455 | + | 19.4777i | 0.897486 | + | 1.55449i | 0.830697 | + | 0.556725i | \(0.187942\pi\) |
0.0667896 | + | 0.997767i | \(0.478724\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −1.53152 | + | 2.65267i | −0.121457 | + | 0.210370i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2.45195 | + | 2.45727i | 0.193241 | + | 0.193660i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −5.17572 | + | 8.96461i | −0.405394 | + | 0.702162i | −0.994367 | − | 0.105990i | \(-0.966199\pi\) |
0.588974 | + | 0.808152i | \(0.299532\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 2.08083 | 0.161020 | 0.0805098 | − | 0.996754i | \(-0.474345\pi\) | ||||
0.0805098 | + | 0.996754i | \(0.474345\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −7.65445 | −0.588804 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −0.453301 | − | 0.785140i | −0.0346648 | − | 0.0600412i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −11.9352 | + | 20.6724i | −0.907416 | + | 1.57169i | −0.0897753 | + | 0.995962i | \(0.528615\pi\) |
−0.817641 | + | 0.575729i | \(0.804718\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −7.14756 | + | 12.3799i | −0.537243 | + | 0.930533i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −6.40544 | − | 11.0946i | −0.478765 | − | 0.829246i | 0.520938 | − | 0.853594i | \(-0.325582\pi\) |
−0.999704 | + | 0.0243486i | \(0.992249\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −3.04611 | −0.226416 | −0.113208 | − | 0.993571i | \(-0.536113\pi\) | ||||
−0.113208 | + | 0.993571i | \(0.536113\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 2.17925 | 0.161095 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −0.712777 | + | 1.23457i | −0.0521234 | + | 0.0902804i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −0.687541 | + | 2.55486i | −0.0500113 | + | 0.185838i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 8.58116 | − | 14.8630i | 0.620911 | − | 1.07545i | −0.368405 | − | 0.929665i | \(-0.620096\pi\) |
0.989316 | − | 0.145784i | \(-0.0465705\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −7.06816 | − | 12.2424i | −0.508777 | − | 0.881228i | −0.999948 | − | 0.0101652i | \(-0.996764\pi\) |
0.491171 | − | 0.871063i | \(-0.336569\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1.80818 | 0.128827 | 0.0644137 | − | 0.997923i | \(-0.479482\pi\) | ||||
0.0644137 | + | 0.997923i | \(0.479482\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 9.11645 | + | 15.7902i | 0.646248 | + | 1.11933i | 0.984012 | + | 0.178104i | \(0.0569963\pi\) |
−0.337764 | + | 0.941231i | \(0.609670\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −2.78094 | + | 4.81673i | −0.196152 | + | 0.339746i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 4.23224 | − | 15.7267i | 0.297045 | − | 1.10380i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0.656022 | + | 1.13626i | 0.0455967 | + | 0.0789758i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 3.44566 | 0.238342 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 16.1927 | 1.11475 | 0.557375 | − | 0.830261i | \(-0.311809\pi\) | ||||
0.557375 | + | 0.830261i | \(0.311809\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 4.94148 | + | 8.55889i | 0.338585 | + | 0.586446i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 14.3771 | − | 3.83563i | 0.975980 | − | 0.260379i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −3.20095 | + | 5.54422i | −0.216300 | + | 0.374643i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −0.433604 | − | 0.751024i | −0.0291674 | − | 0.0505194i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −9.91415 | −0.663900 | −0.331950 | − | 0.943297i | \(-0.607707\pi\) | ||||
−0.331950 | + | 0.943297i | \(0.607707\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −6.80986 | − | 11.7950i | −0.451987 | − | 0.782864i | 0.546523 | − | 0.837444i | \(-0.315951\pi\) |
−0.998509 | + | 0.0545806i | \(0.982618\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −11.5268 | + | 19.9650i | −0.761714 | + | 1.31933i | 0.180252 | + | 0.983620i | \(0.442309\pi\) |
−0.941966 | + | 0.335707i | \(0.891025\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −7.10263 | − | 7.11804i | −0.467318 | − | 0.468333i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 15.1606 | − | 26.2589i | 0.993201 | − | 1.72027i | 0.395786 | − | 0.918343i | \(-0.370472\pi\) |
0.597416 | − | 0.801932i | \(-0.296194\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −15.2329 | −0.989484 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 11.0327 | 0.713647 | 0.356823 | − | 0.934172i | \(-0.383860\pi\) | ||||
0.356823 | + | 0.934172i | \(0.383860\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −3.16021 | − | 5.47364i | −0.203567 | − | 0.352588i | 0.746108 | − | 0.665825i | \(-0.231920\pi\) |
−0.949675 | + | 0.313236i | \(0.898587\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −0.500000 | + | 0.866025i | −0.0320750 | + | 0.0555556i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.04805 | + | 1.81528i | −0.0666860 | + | 0.115503i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 4.49959 | + | 7.79351i | 0.285150 | + | 0.493894i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 19.3161 | 1.21922 | 0.609609 | − | 0.792702i | \(-0.291326\pi\) | ||||
0.609609 | + | 0.792702i | \(0.291326\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −4.98660 | −0.313505 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 7.17238 | − | 12.4229i | 0.447401 | − | 0.774921i | −0.550815 | − | 0.834627i | \(-0.685683\pi\) |
0.998216 | + | 0.0597064i | \(0.0190165\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −10.7224 | − | 10.7457i | −0.666259 | − | 0.667705i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 3.07780 | − | 5.33091i | 0.190511 | − | 0.329975i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −4.53329 | − | 7.85188i | −0.279534 | − | 0.484168i | 0.691735 | − | 0.722152i | \(-0.256847\pi\) |
−0.971269 | + | 0.237984i | \(0.923513\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −5.01025 | −0.306622 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 5.33309 | + | 9.23719i | 0.325165 | + | 0.563201i | 0.981546 | − | 0.191228i | \(-0.0612470\pi\) |
−0.656381 | + | 0.754429i | \(0.727914\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 10.2721 | − | 17.7917i | 0.623983 | − | 1.08077i | −0.364753 | − | 0.931104i | \(-0.618847\pi\) |
0.988737 | − | 0.149667i | \(-0.0478200\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 5.91037 | − | 1.57681i | 0.357712 | − | 0.0954331i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 6.55593 | + | 11.3552i | 0.393907 | + | 0.682268i | 0.992961 | − | 0.118441i | \(-0.0377897\pi\) |
−0.599054 | + | 0.800709i | \(0.704456\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 5.62409 | 0.336705 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −12.3701 | −0.737936 | −0.368968 | − | 0.929442i | \(-0.620289\pi\) | ||||
−0.368968 | + | 0.929442i | \(0.620289\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 9.64932 | + | 16.7131i | 0.573593 | + | 0.993492i | 0.996193 | + | 0.0871757i | \(0.0277841\pi\) |
−0.422600 | + | 0.906316i | \(0.638883\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −0.137071 | + | 0.509345i | −0.00809103 | + | 0.0300657i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 8.42966 | − | 14.6006i | 0.495862 | − | 0.858858i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 3.18126 | + | 5.51010i | 0.186489 | + | 0.323008i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 18.6340 | 1.08861 | 0.544305 | − | 0.838888i | \(-0.316794\pi\) | ||||
0.544305 | + | 0.838888i | \(0.316794\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −1.90032 | − | 3.29145i | −0.110268 | − | 0.190989i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1.51675 | − | 2.62709i | 0.0877161 | − | 0.151929i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −8.52683 | + | 31.6851i | −0.491478 | + | 1.82630i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 2.94148 | − | 5.09479i | 0.168984 | − | 0.292688i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 17.3278 | 0.988949 | 0.494475 | − | 0.869192i | \(-0.335360\pi\) | ||||
0.494475 | + | 0.869192i | \(0.335360\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 12.6746 | 0.721031 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 0.484075 | + | 0.838442i | 0.0274494 | + | 0.0475437i | 0.879424 | − | 0.476040i | \(-0.157928\pi\) |
−0.851974 | + | 0.523583i | \(0.824595\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −13.3373 | + | 23.1008i | −0.753868 | + | 1.30574i | 0.192068 | + | 0.981382i | \(0.438481\pi\) |
−0.945935 | + | 0.324355i | \(0.894853\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 16.0177 | − | 27.7435i | 0.899644 | − | 1.55823i | 0.0716949 | − | 0.997427i | \(-0.477159\pi\) |
0.827949 | − | 0.560803i | \(-0.189507\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 11.6976 | + | 20.2609i | 0.654941 | + | 1.13439i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −2.51812 | −0.140548 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0.340051 | 0.0189209 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −5.65938 | + | 9.80233i | −0.312964 | + | 0.542070i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 20.1968 | + | 20.2406i | 1.11348 | + | 1.11590i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 0.343564 | − | 0.595070i | 0.0188840 | − | 0.0327080i | −0.856429 | − | 0.516265i | \(-0.827322\pi\) |
0.875313 | + | 0.483557i | \(0.160655\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −2.86880 | − | 4.96891i | −0.157209 | − | 0.272294i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 15.0220 | 0.818300 | 0.409150 | − | 0.912467i | \(-0.365825\pi\) | ||||
0.409150 | + | 0.912467i | \(0.365825\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −7.73760 | − | 13.4019i | −0.420249 | − | 0.727892i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −10.6876 | + | 18.5114i | −0.578764 | + | 1.00245i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 13.1383 | − | 13.0531i | 0.709403 | − | 0.704803i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −12.4247 | − | 21.5203i | −0.666994 | − | 1.15527i | −0.978740 | − | 0.205102i | \(-0.934247\pi\) |
0.311746 | − | 0.950165i | \(-0.399086\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 25.4530 | 1.36247 | 0.681235 | − | 0.732065i | \(-0.261443\pi\) | ||||
0.681235 | + | 0.732065i | \(0.261443\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2.31204 | 0.123408 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 7.32964 | + | 12.6953i | 0.390118 | + | 0.675703i | 0.992465 | − | 0.122531i | \(-0.0391010\pi\) |
−0.602347 | + | 0.798234i | \(0.705768\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −0.700954 | − | 0.702476i | −0.0370984 | − | 0.0371790i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 2.96430 | − | 5.13431i | 0.156450 | − | 0.270979i | −0.777136 | − | 0.629332i | \(-0.783328\pi\) |
0.933586 | + | 0.358354i | \(0.116662\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 9.08904 | + | 15.7427i | 0.478370 | + | 0.828562i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 3.44484 | 0.180807 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2.55122 | + | 4.41884i | 0.133172 | + | 0.230661i | 0.924898 | − | 0.380216i | \(-0.124150\pi\) |
−0.791725 | + | 0.610877i | \(0.790817\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −0.0996818 | + | 0.172654i | −0.00518923 | + | 0.00898801i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 7.83017 | − | 2.08899i | 0.406522 | − | 0.108455i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −2.38221 | + | 4.12611i | −0.123346 | + | 0.213642i | −0.921085 | − | 0.389361i | \(-0.872696\pi\) |
0.797739 | + | 0.603003i | \(0.206029\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −14.2320 | −0.732987 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −14.6147 | −0.750707 | −0.375353 | − | 0.926882i | \(-0.622479\pi\) | ||||
−0.375353 | + | 0.926882i | \(0.622479\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 7.55793 | + | 13.0907i | 0.387205 | + | 0.670658i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 1.00672 | − | 1.74368i | 0.0514408 | − | 0.0890980i | −0.839158 | − | 0.543887i | \(-0.816952\pi\) |
0.890599 | + | 0.454789i | \(0.150285\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −6.20095 | + | 10.7404i | −0.315212 | + | 0.545964i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 0.264600 | + | 0.458301i | 0.0134158 | + | 0.0232368i | 0.872655 | − | 0.488337i | \(-0.162396\pi\) |
−0.859240 | + | 0.511573i | \(0.829063\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −0.492125 | −0.0248879 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −3.87039 | −0.195235 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −14.2833 | + | 24.7394i | −0.716857 | + | 1.24163i | 0.245382 | + | 0.969427i | \(0.421087\pi\) |
−0.962239 | + | 0.272206i | \(0.912247\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −0.623326 | + | 2.31624i | −0.0312053 | + | 0.115957i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −16.4945 | + | 28.5693i | −0.823695 | + | 1.42668i | 0.0792176 | + | 0.996857i | \(0.474758\pi\) |
−0.902913 | + | 0.429824i | \(0.858576\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −6.50157 | − | 11.2611i | −0.323866 | − | 0.560953i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 21.8065 | 1.08091 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 9.10799 | + | 15.7755i | 0.450361 | + | 0.780048i | 0.998408 | − | 0.0563992i | \(-0.0179619\pi\) |
−0.548047 | + | 0.836447i | \(0.684629\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −8.49782 | + | 14.7187i | −0.419167 | + | 0.726018i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 36.5432 | − | 9.74926i | 1.79817 | − | 0.479730i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 4.09750 | + | 7.09708i | 0.200655 | + | 0.347546i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −14.3665 | −0.701851 | −0.350925 | − | 0.936403i | \(-0.614133\pi\) | ||||
−0.350925 | + | 0.936403i | \(0.614133\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 15.9374 | 0.776743 | 0.388372 | − | 0.921503i | \(-0.373038\pi\) | ||||
0.388372 | + | 0.921503i | \(0.373038\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 5.40368 | + | 9.35944i | 0.262736 | + | 0.455072i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −4.07259 | − | 4.08143i | −0.197086 | − | 0.197514i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −4.39362 | + | 7.60997i | −0.212126 | + | 0.367413i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −5.10420 | − | 8.84073i | −0.245861 | − | 0.425843i | 0.716513 | − | 0.697574i | \(-0.245737\pi\) |
−0.962373 | + | 0.271731i | \(0.912404\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −32.6618 | −1.56963 | −0.784814 | − | 0.619732i | \(-0.787241\pi\) | ||||
−0.784814 | + | 0.619732i | \(0.787241\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0.594751 | + | 1.03014i | 0.0284508 | + | 0.0492782i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 5.26181 | − | 9.11373i | 0.251133 | − | 0.434974i | −0.712705 | − | 0.701464i | \(-0.752530\pi\) |
0.963838 | + | 0.266489i | \(0.0858637\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 6.06975 | − | 3.48685i | 0.289036 | − | 0.166040i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −17.6022 | + | 30.4879i | −0.836306 | + | 1.44853i | 0.0566561 | + | 0.998394i | \(0.481956\pi\) |
−0.892962 | + | 0.450131i | \(0.851377\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 11.9562 | 0.565511 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −2.85276 | −0.134630 | −0.0673151 | − | 0.997732i | \(-0.521443\pi\) | ||||
−0.0673151 | + | 0.997732i | \(0.521443\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −0.378854 | − | 0.656195i | −0.0178396 | − | 0.0308990i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −9.02305 | + | 15.6284i | −0.423940 | + | 0.734286i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −0.0929842 | + | 0.161053i | −0.00434962 | + | 0.00753376i | −0.868192 | − | 0.496228i | \(-0.834718\pi\) |
0.863842 | + | 0.503762i | \(0.168051\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −0.187541 | − | 0.324831i | −0.00875368 | − | 0.0151618i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −7.00484 | −0.326248 | −0.163124 | − | 0.986606i | \(-0.552157\pi\) | ||||
−0.163124 | + | 0.986606i | \(0.552157\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 38.3435 | 1.78198 | 0.890988 | − | 0.454027i | \(-0.150013\pi\) | ||||
0.890988 | + | 0.454027i | \(0.150013\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −9.26912 | + | 16.0546i | −0.428924 | + | 0.742917i | −0.996778 | − | 0.0802117i | \(-0.974440\pi\) |
0.567854 | + | 0.823129i | \(0.307774\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 14.2181 | − | 3.79320i | 0.656529 | − | 0.175154i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 11.2455 | − | 19.4777i | 0.518164 | − | 0.897486i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −23.5676 | − | 40.8202i | −1.08364 | − | 1.87692i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 3.06304 | 0.140247 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 17.0983 | + | 29.6152i | 0.781243 | + | 1.35315i | 0.931218 | + | 0.364463i | \(0.118748\pi\) |
−0.149974 | + | 0.988690i | \(0.547919\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −6.63279 | + | 11.4883i | −0.302429 | + | 0.523823i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0.902085 | − | 3.35208i | 0.0410463 | − | 0.152525i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −7.39831 | − | 12.8143i | −0.335250 | − | 0.580669i | 0.648283 | − | 0.761399i | \(-0.275487\pi\) |
−0.983533 | + | 0.180730i | \(0.942154\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 10.3514 | 0.468108 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −5.47873 | −0.247252 | −0.123626 | − | 0.992329i | \(-0.539452\pi\) | ||||
−0.123626 | + | 0.992329i | \(0.539452\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1.15443 | + | 1.99953i | 0.0519930 | + | 0.0900545i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 6.79494 | − | 25.2495i | 0.304795 | − | 1.13260i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −3.21395 | + | 5.56673i | −0.143876 | + | 0.249201i | −0.928953 | − | 0.370197i | \(-0.879290\pi\) |
0.785077 | + | 0.619398i | \(0.212623\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −1.04042 | − | 1.80205i | −0.0464823 | − | 0.0805098i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −33.5288 | −1.49498 | −0.747489 | − | 0.664274i | \(-0.768741\pi\) | ||||
−0.747489 | + | 0.664274i | \(0.768741\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 3.82722 | + | 6.62895i | 0.169973 | + | 0.294402i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 16.5079 | − | 28.5925i | 0.731699 | − | 1.26734i | −0.224458 | − | 0.974484i | \(-0.572061\pi\) |
0.956157 | − | 0.292856i | \(-0.0946055\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 16.3655 | − | 4.36610i | 0.723965 | − | 0.193145i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −0.453301 | + | 0.785140i | −0.0200137 | + | 0.0346648i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −41.0748 | −1.80647 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 23.8704 | 1.04779 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 7.49884 | + | 12.9884i | 0.328530 | + | 0.569031i | 0.982220 | − | 0.187731i | \(-0.0601134\pi\) |
−0.653690 | + | 0.756762i | \(0.726780\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 10.1695 | − | 17.6140i | 0.444679 | − | 0.770207i | −0.553351 | − | 0.832948i | \(-0.686651\pi\) |
0.998030 | + | 0.0627415i | \(0.0199844\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −1.05475 | + | 1.82688i | −0.0459456 | + | 0.0795801i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 10.6393 | + | 18.4278i | 0.462577 | + | 0.801207i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 14.2951 | 0.620355 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0.460938 | 0.0199654 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −6.40544 | + | 11.0946i | −0.276415 | + | 0.478765i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −0.0576935 | + | 26.6044i | −0.00248504 | + | 1.14593i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −8.38064 | + | 14.5157i | −0.360312 | + | 0.624078i | −0.988012 | − | 0.154377i | \(-0.950663\pi\) |
0.627700 | + | 0.778455i | \(0.283996\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 1.52305 | + | 2.63801i | 0.0653605 | + | 0.113208i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 4.58552 | 0.196063 | 0.0980314 | − | 0.995183i | \(-0.468745\pi\) | ||||
0.0980314 | + | 0.995183i | \(0.468745\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −1.08963 | − | 1.88729i | −0.0465041 | − | 0.0805475i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 2.79034 | − | 4.83302i | 0.118873 | − | 0.205893i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 28.4672 | + | 28.5290i | 1.21055 | + | 1.21318i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 11.4734 | + | 19.8726i | 0.486145 | + | 0.842028i | 0.999873 | − | 0.0159254i | \(-0.00506942\pi\) |
−0.513728 | + | 0.857953i | \(0.671736\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 28.6738 | 1.21277 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1.42555 | 0.0601869 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 10.9764 | + | 19.0116i | 0.462598 | + | 0.801244i | 0.999090 | − | 0.0426622i | \(-0.0135839\pi\) |
−0.536491 | + | 0.843906i | \(0.680251\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 2.55634 | − | 0.681999i | 0.107356 | − | 0.0286413i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −19.3554 | + | 33.5245i | −0.811421 | + | 1.40542i | 0.100449 | + | 0.994942i | \(0.467972\pi\) |
−0.911870 | + | 0.410480i | \(0.865361\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −10.9478 | − | 18.9621i | −0.458150 | − | 0.793540i | 0.540713 | − | 0.841207i | \(-0.318155\pi\) |
−0.998863 | + | 0.0476675i | \(0.984821\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −17.1623 | −0.716966 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −17.0997 | − | 29.6175i | −0.711870 | − | 1.23299i | −0.964154 | − | 0.265342i | \(-0.914515\pi\) |
0.252285 | − | 0.967653i | \(-0.418818\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −7.06816 | + | 12.2424i | −0.293743 | + | 0.508777i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 6.18730 | − | 22.9916i | 0.256693 | − | 0.953852i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −5.82075 | + | 10.0818i | −0.241071 | + | 0.417547i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 24.2455 | 1.00072 | 0.500359 | − | 0.865818i | \(-0.333201\pi\) | ||||
0.500359 | + | 0.865818i | \(0.333201\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 5.09881 | 0.210093 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −0.904090 | − | 1.56593i | −0.0371893 | − | 0.0644137i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 7.17238 | − | 12.4229i | 0.294534 | − | 0.510148i | −0.680342 | − | 0.732895i | \(-0.738169\pi\) |
0.974876 | + | 0.222746i | \(0.0715021\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 9.11645 | − | 15.7902i | 0.373112 | − | 0.646248i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 5.35992 | + | 9.28365i | 0.219000 | + | 0.379320i | 0.954503 | − | 0.298202i | \(-0.0963871\pi\) |
−0.735502 | + | 0.677522i | \(0.763054\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 12.4069 | 0.506089 | 0.253045 | − | 0.967455i | \(-0.418568\pi\) | ||||
0.253045 | + | 0.967455i | \(0.418568\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 5.56188 | 0.226497 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −17.2124 | + | 29.8127i | −0.698629 | + | 1.21006i | 0.270313 | + | 0.962773i | \(0.412873\pi\) |
−0.968942 | + | 0.247288i | \(0.920461\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −15.7358 | + | 4.19812i | −0.637648 | + | 0.170116i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 12.4935 | − | 21.6394i | 0.505435 | − | 0.875438i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −24.3511 | − | 42.1774i | −0.983533 | − | 1.70353i | −0.648284 | − | 0.761399i | \(-0.724513\pi\) |
−0.335249 | − | 0.942130i | \(-0.608821\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 21.6164 | 0.870242 | 0.435121 | − | 0.900372i | \(-0.356706\pi\) | ||||
0.435121 | + | 0.900372i | \(0.356706\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 1.89437 | + | 3.28114i | 0.0761410 | + | 0.131880i | 0.901582 | − | 0.432609i | \(-0.142407\pi\) |
−0.825441 | + | 0.564489i | \(0.809073\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0.656022 | − | 1.13626i | 0.0263253 | − | 0.0455967i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 9.36315 | + | 9.38348i | 0.375127 | + | 0.375941i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −1.72283 | − | 2.98403i | −0.0688033 | − | 0.119171i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 2.15207 | 0.0858088 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 31.2160 | 1.24269 | 0.621344 | − | 0.783538i | \(-0.286587\pi\) | ||||
0.621344 | + | 0.783538i | \(0.286587\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −8.09634 | − | 14.0233i | −0.321801 | − | 0.557375i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −13.9984 | − | 8.12253i | −0.554639 | − | 0.321826i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 4.94148 | − | 8.55889i | 0.195482 | − | 0.338585i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 12.0953 | + | 20.9497i | 0.477736 | + | 0.827464i | 0.999674 | − | 0.0255197i | \(-0.00812406\pi\) |
−0.521938 | + | 0.852983i | \(0.674791\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 6.83519 | 0.269554 | 0.134777 | − | 0.990876i | \(-0.456968\pi\) | ||||
0.134777 | + | 0.990876i | \(0.456968\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −2.15310 | − | 3.72927i | −0.0846469 | − | 0.146613i | 0.820594 | − | 0.571512i | \(-0.193643\pi\) |
−0.905241 | + | 0.424899i | \(0.860310\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −27.1653 | + | 47.0516i | −1.06633 | + | 1.84694i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −10.5103 | − | 10.5331i | −0.411931 | − | 0.412825i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −11.7955 | + | 20.4305i | −0.461595 | + | 0.799506i | −0.999041 | − | 0.0437927i | \(-0.986056\pi\) |
0.537446 | + | 0.843298i | \(0.319389\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 6.40191 | 0.249762 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −12.5231 | −0.487833 | −0.243916 | − | 0.969796i | \(-0.578432\pi\) | ||||
−0.243916 | + | 0.969796i | \(0.578432\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −21.2598 | − | 36.8231i | −0.826911 | − | 1.43225i | −0.900450 | − | 0.434960i | \(-0.856762\pi\) |
0.0735384 | − | 0.997292i | \(-0.476571\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −0.433604 | + | 0.751024i | −0.0168398 | + | 0.0291674i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −4.03822 | + | 6.99440i | −0.156360 | + | 0.270824i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 4.95707 | + | 8.58590i | 0.191651 | + | 0.331950i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 8.28255 | 0.319744 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 15.8140 | 0.609586 | 0.304793 | − | 0.952419i | \(-0.401413\pi\) | ||||
0.304793 | + | 0.952419i | \(0.401413\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 2.28997 | − | 3.96635i | 0.0880108 | − | 0.152439i | −0.818659 | − | 0.574279i | \(-0.805282\pi\) |
0.906670 | + | 0.421840i | \(0.138616\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 4.37449 | − | 16.2553i | 0.167878 | − | 0.623821i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −6.80986 | + | 11.7950i | −0.260955 | + | 0.451987i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −21.1330 | − | 36.6034i | −0.808631 | − | 1.40059i | −0.913812 | − | 0.406137i | \(-0.866875\pi\) |
0.105181 | − | 0.994453i | \(-0.466458\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 23.0537 | 0.879552 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −3.54094 | − | 6.13309i | −0.134899 | − | 0.233652i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −12.0575 | + | 20.8842i | −0.458690 | + | 0.794474i | −0.998892 | − | 0.0470615i | \(-0.985014\pi\) |
0.540202 | + | 0.841535i | \(0.318348\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −2.61309 | + | 9.71008i | −0.0992633 | + | 0.368855i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −0.0373889 | − | 0.0647596i | −0.00141621 | − | 0.00245294i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −30.3211 | −1.14685 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −7.28290 | −0.275071 | −0.137536 | − | 0.990497i | \(-0.543918\pi\) | ||||
−0.137536 | + | 0.990497i | \(0.543918\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −2.60086 | − | 4.50482i | −0.0980932 | − | 0.169902i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −15.0388 | + | 4.01217i | −0.565594 | + | 0.150893i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −3.25510 | + | 5.63799i | −0.122248 | + | 0.211739i | −0.920654 | − | 0.390380i | \(-0.872344\pi\) |
0.798406 | + | 0.602119i | \(0.205677\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 7.61645 | + | 13.1921i | 0.285639 | + | 0.494742i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −7.37906 | −0.276348 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −5.51636 | − | 9.55461i | −0.206012 | − | 0.356823i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 22.3725 | − | 38.7503i | 0.834353 | − | 1.44514i | −0.0602031 | − | 0.998186i | \(-0.519175\pi\) |
0.894556 | − | 0.446956i | \(-0.147492\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −23.6862 | − | 23.7376i | −0.882120 | − | 0.884035i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −3.16021 | + | 5.47364i | −0.117529 | + | 0.203567i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 23.7510 | 0.880877 | 0.440438 | − | 0.897783i | \(-0.354823\pi\) | ||||
0.440438 | + | 0.897783i | \(0.354823\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −2.32587 | − | 4.02853i | −0.0860255 | − | 0.149000i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −7.31516 | + | 12.6702i | −0.270192 | + | 0.467986i | −0.968911 | − | 0.247410i | \(-0.920420\pi\) |
0.698719 | + | 0.715396i | \(0.253754\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −10.5693 | + | 18.3066i | −0.389327 | + | 0.674334i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 0.403658 | + | 0.699156i | 0.0148488 | + | 0.0257189i | 0.873354 | − | 0.487085i | \(-0.161940\pi\) |
−0.858506 | + | 0.512804i | \(0.828607\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 2.09610 | 0.0770023 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −2.34476 | −0.0860208 | −0.0430104 | − | 0.999075i | \(-0.513695\pi\) | ||||
−0.0430104 | + | 0.999075i | \(0.513695\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 4.49959 | − | 7.79351i | 0.164631 | − | 0.285150i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 4.70587 | + | 4.71608i | 0.171949 | + | 0.172322i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −10.1746 | + | 17.6229i | −0.371275 | + | 0.643067i | −0.989762 | − | 0.142728i | \(-0.954413\pi\) |
0.618487 | + | 0.785795i | \(0.287746\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −9.65803 | − | 16.7282i | −0.351958 | − | 0.609609i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −4.83602 | −0.175768 | −0.0878841 | − | 0.996131i | \(-0.528011\pi\) | ||||
−0.0878841 | + | 0.996131i | \(0.528011\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 2.49330 | + | 4.31853i | 0.0905011 | + | 0.156753i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 20.7725 | − | 35.9790i | 0.753002 | − | 1.30424i | −0.193360 | − | 0.981128i | \(-0.561939\pi\) |
0.946362 | − | 0.323109i | \(-0.104728\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 28.9346 | − | 7.71939i | 1.04750 | − | 0.279461i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −16.5255 | − | 28.6230i | −0.596700 | − | 1.03352i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −15.9814 | −0.576305 | −0.288152 | − | 0.957585i | \(-0.593041\pi\) | ||||
−0.288152 | + | 0.957585i | \(0.593041\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −14.3448 | −0.516614 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 4.85456 | + | 8.40834i | 0.174606 | + | 0.302427i | 0.940025 | − | 0.341106i | \(-0.110801\pi\) |
−0.765419 | + | 0.643533i | \(0.777468\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −3.94484 | + | 14.6587i | −0.141520 | + | 0.525879i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −0.0903717 | + | 0.156528i | −0.00323790 | + | 0.00560821i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 18.7808 | + | 32.5292i | 0.672029 | + | 1.16399i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −6.15561 | −0.219983 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 13.4247 | + | 23.2523i | 0.478540 | + | 0.828855i | 0.999697 | − | 0.0246053i | \(-0.00783291\pi\) |
−0.521157 | + | 0.853461i | \(0.674500\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −4.53329 | + | 7.85188i | −0.161389 | + | 0.279534i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −10.6398 | + | 39.5369i | −0.378309 | + | 1.40577i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −2.51927 | + | 4.36350i | −0.0894617 | + | 0.154952i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −17.6365 | −0.624716 | −0.312358 | − | 0.949964i | \(-0.601119\pi\) | ||||
−0.312358 | + | 0.949964i | \(0.601119\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −4.05365 | −0.143408 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 2.50512 | + | 4.33900i | 0.0885142 | + | 0.153311i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −12.1657 | + | 21.0715i | −0.429317 | + | 0.743599i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 5.33309 | − | 9.23719i | 0.187734 | − | 0.325165i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −14.0251 | − | 24.2921i | −0.493095 | − | 0.854065i | 0.506874 | − | 0.862020i | \(-0.330801\pi\) |
−0.999968 | + | 0.00795514i | \(0.997468\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −41.3801 | −1.45305 | −0.726527 | − | 0.687138i | \(-0.758867\pi\) | ||||
−0.726527 | + | 0.687138i | \(0.758867\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −20.5441 | −0.720514 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −5.62180 | + | 9.73724i | −0.196682 | + | 0.340663i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −4.32075 | − | 4.33013i | −0.150979 | − | 0.151307i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 9.42516 | − | 16.3249i | 0.328940 | − | 0.569741i | −0.653362 | − | 0.757046i | \(-0.726642\pi\) |
0.982302 | + | 0.187305i | \(0.0599752\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −4.89435 | − | 8.47726i | −0.170606 | − | 0.295499i | 0.768026 | − | 0.640419i | \(-0.221239\pi\) |
−0.938632 | + | 0.344920i | \(0.887906\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 18.6206 | 0.647500 | 0.323750 | − | 0.946143i | \(-0.395056\pi\) | ||||
0.323750 | + | 0.946143i | \(0.395056\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −22.6558 | − | 39.2411i | −0.786870 | − | 1.36290i | −0.927876 | − | 0.372890i | \(-0.878367\pi\) |
0.141005 | − | 0.990009i | \(-0.454966\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 6.55593 | − | 11.3552i | 0.227423 | − | 0.393907i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −0.00569375 | + | 2.62557i | −0.000197277 | + | 0.0909707i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −2.81204 | − | 4.87060i | −0.0971985 | − | 0.168353i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 2.31727 | 0.0800010 | 0.0400005 | − | 0.999200i | \(-0.487264\pi\) | ||||
0.0400005 | + | 0.999200i | \(0.487264\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 8.89152 | 0.306604 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 6.18503 | + | 10.7128i | 0.213024 | + | 0.368968i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −6.43771 | − | 6.45168i | −0.221202 | − | 0.221682i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 9.64932 | − | 16.7131i | 0.331164 | − | 0.573593i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 3.76399 | + | 6.51943i | 0.129028 | + | 0.223483i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 12.6273 | 0.432350 | 0.216175 | − | 0.976355i | \(-0.430642\pi\) | ||||
0.216175 | + | 0.976355i | \(0.430642\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −9.05970 | − | 15.6919i | −0.309473 | − | 0.536024i | 0.668774 | − | 0.743466i | \(-0.266819\pi\) |
−0.978247 | + | 0.207442i | \(0.933486\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 8.92380 | − | 15.4565i | 0.304476 | − | 0.527368i | −0.672668 | − | 0.739944i | \(-0.734852\pi\) |
0.977145 | + | 0.212576i | \(0.0681852\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0.509641 | − | 0.135966i | 0.0173685 | − | 0.00463371i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −6.51989 | + | 11.2928i | −0.221940 | + | 0.384411i | −0.955397 | − | 0.295325i | \(-0.904572\pi\) |
0.733457 | + | 0.679736i | \(0.237905\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −16.8593 | −0.572572 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −57.8947 | −1.96394 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −6.42966 | − | 11.1365i | −0.217861 | − | 0.377346i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 3.18126 | − | 5.51010i | 0.107669 | − | 0.186489i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 11.2691 | − | 19.5187i | 0.380531 | − | 0.659099i | −0.610607 | − | 0.791934i | \(-0.709075\pi\) |
0.991138 | + | 0.132835i | \(0.0424079\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −9.31699 | − | 16.1375i | −0.314254 | − | 0.544305i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −25.3761 | −0.854944 | −0.427472 | − | 0.904029i | \(-0.640596\pi\) | ||||
−0.427472 | + | 0.904029i | \(0.640596\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −15.1504 | −0.509852 | −0.254926 | − | 0.966961i | \(-0.582051\pi\) | ||||
−0.254926 | + | 0.966961i | \(0.582051\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −20.6145 | + | 35.7054i | −0.692167 | + | 1.19887i | 0.278959 | + | 0.960303i | \(0.410011\pi\) |
−0.971126 | + | 0.238566i | \(0.923323\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 10.3928 | − | 38.6188i | 0.348563 | − | 1.29523i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1.90032 | + | 3.29145i | −0.0636631 | + | 0.110268i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 4.89898 | + | 8.48529i | 0.163938 | + | 0.283949i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −3.03351 | −0.101286 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 17.3098 | + | 29.9815i | 0.577316 | + | 0.999940i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −0.574447 | + | 0.994971i | −0.0191376 | + | 0.0331473i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 31.7035 | − | 8.45809i | 1.05503 | − | 0.281468i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −3.50711 | − | 6.07450i | −0.116452 | − | 0.201700i | 0.801907 | − | 0.597448i | \(-0.203819\pi\) |
−0.918359 | + | 0.395748i | \(0.870485\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −5.88296 | −0.195125 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −3.78721 | −0.125476 | −0.0627379 | − | 0.998030i | \(-0.519983\pi\) | ||||
−0.0627379 | + | 0.998030i | \(0.519983\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 17.1013 | + | 29.6203i | 0.565970 | + | 0.980289i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 7.23298 | + | 7.24868i | 0.238854 | + | 0.239373i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 12.6119 | − | 21.8444i | 0.416027 | − | 0.720579i | −0.579509 | − | 0.814966i | \(-0.696756\pi\) |
0.995536 | + | 0.0943866i | \(0.0300890\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −8.66390 | − | 15.0063i | −0.285485 | − | 0.494475i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −22.8498 | −0.752112 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −6.33728 | − | 10.9765i | −0.208144 | − | 0.360515i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 23.6884 | − | 41.0295i | 0.777191 | − | 1.34613i | −0.156364 | − | 0.987699i | \(-0.549977\pi\) |
0.933555 | − | 0.358434i | \(-0.116689\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 5.50285 | − | 3.16118i | 0.180349 | − | 0.103604i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0.484075 | − | 0.838442i | 0.0158479 | − | 0.0274494i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −9.59102 | −0.313325 | −0.156663 | − | 0.987652i | \(-0.550074\pi\) | ||||
−0.156663 | + | 0.987652i | \(0.550074\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 26.6746 | 0.870491 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 24.8312 | + | 43.0088i | 0.809472 | + | 1.40205i | 0.913230 | + | 0.407445i | \(0.133580\pi\) |
−0.103757 | + | 0.994603i | \(0.533087\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0.130787 | − | 0.226530i | 0.00425901 | − | 0.00737682i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −23.8989 | + | 41.3941i | −0.776610 | + | 1.34513i | 0.157275 | + | 0.987555i | \(0.449729\pi\) |
−0.933885 | + | 0.357573i | \(0.883604\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −7.40075 | − | 12.8185i | −0.240239 | − | 0.416105i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −32.0354 | −1.03882 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 47.3018 | 1.53226 | 0.766128 | − | 0.642688i | \(-0.222181\pi\) | ||||
0.766128 | + | 0.642688i | \(0.222181\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 11.6976 | − | 20.2609i | 0.378130 | − | 0.654941i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 43.4466 | − | 11.5910i | 1.40297 | − | 0.374293i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −0.315191 | + | 0.545926i | −0.0101674 | + | 0.0176105i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 1.25906 | + | 2.18076i | 0.0405727 | + | 0.0702740i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 37.9613 | 1.22075 | 0.610377 | − | 0.792111i | \(-0.291018\pi\) | ||||
0.610377 | + | 0.792111i | \(0.291018\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −0.170025 | − | 0.294493i | −0.00546200 | − | 0.00946047i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 6.51989 | − | 11.2928i | 0.209233 | − | 0.362403i | −0.742240 | − | 0.670134i | \(-0.766237\pi\) |
0.951473 | + | 0.307732i | \(0.0995699\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 5.63440 | − | 20.9370i | 0.180631 | − | 0.671211i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 23.6986 | + | 41.0472i | 0.758185 | + | 1.31322i | 0.943775 | + | 0.330588i | \(0.107247\pi\) |
−0.185590 | + | 0.982627i | \(0.559420\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −19.0421 | −0.608589 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 11.3188 | 0.361380 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 9.16920 | + | 15.8815i | 0.292452 | + | 0.506542i | 0.974389 | − | 0.224869i | \(-0.0721955\pi\) |
−0.681937 | + | 0.731411i | \(0.738862\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 7.43050 | − | 27.6112i | 0.236515 | − | 0.878875i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 8.13593 | − | 14.0918i | 0.258708 | − | 0.448095i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 3.31968 | + | 5.74986i | 0.105453 | + | 0.182650i | 0.913923 | − | 0.405887i | \(-0.133037\pi\) |
−0.808470 | + | 0.588537i | \(0.799704\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −0.687128 | −0.0218053 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 0.138744 | + | 0.240312i | 0.00439407 | + | 0.00761075i | 0.868214 | − | 0.496190i | \(-0.165268\pi\) |
−0.863820 | + | 0.503801i | \(0.831935\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −2.86880 | + | 4.96891i | −0.0907648 | + | 0.157209i |
(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 | 2100.2.q.l.1801.2 | 8 | ||
5.2 | odd | 4 | 420.2.bb.a.289.3 | yes | 16 | ||
5.3 | odd | 4 | 420.2.bb.a.289.6 | yes | 16 | ||
5.4 | even | 2 | 2100.2.q.m.1801.3 | 8 | |||
7.4 | even | 3 | inner | 2100.2.q.l.1201.2 | 8 | ||
15.2 | even | 4 | 1260.2.bm.c.289.3 | 16 | |||
15.8 | even | 4 | 1260.2.bm.c.289.5 | 16 | |||
20.3 | even | 4 | 1680.2.di.e.289.2 | 16 | |||
20.7 | even | 4 | 1680.2.di.e.289.7 | 16 | |||
35.2 | odd | 12 | 2940.2.k.f.589.1 | 8 | |||
35.3 | even | 12 | 2940.2.bb.i.949.6 | 16 | |||
35.4 | even | 6 | 2100.2.q.m.1201.3 | 8 | |||
35.12 | even | 12 | 2940.2.k.g.589.8 | 8 | |||
35.13 | even | 4 | 2940.2.bb.i.1549.3 | 16 | |||
35.17 | even | 12 | 2940.2.bb.i.949.3 | 16 | |||
35.18 | odd | 12 | 420.2.bb.a.109.3 | ✓ | 16 | ||
35.23 | odd | 12 | 2940.2.k.f.589.5 | 8 | |||
35.27 | even | 4 | 2940.2.bb.i.1549.6 | 16 | |||
35.32 | odd | 12 | 420.2.bb.a.109.6 | yes | 16 | ||
35.33 | even | 12 | 2940.2.k.g.589.4 | 8 | |||
105.32 | even | 12 | 1260.2.bm.c.109.5 | 16 | |||
105.53 | even | 12 | 1260.2.bm.c.109.3 | 16 | |||
140.67 | even | 12 | 1680.2.di.e.529.2 | 16 | |||
140.123 | even | 12 | 1680.2.di.e.529.7 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
420.2.bb.a.109.3 | ✓ | 16 | 35.18 | odd | 12 | ||
420.2.bb.a.109.6 | yes | 16 | 35.32 | odd | 12 | ||
420.2.bb.a.289.3 | yes | 16 | 5.2 | odd | 4 | ||
420.2.bb.a.289.6 | yes | 16 | 5.3 | odd | 4 | ||
1260.2.bm.c.109.3 | 16 | 105.53 | even | 12 | |||
1260.2.bm.c.109.5 | 16 | 105.32 | even | 12 | |||
1260.2.bm.c.289.3 | 16 | 15.2 | even | 4 | |||
1260.2.bm.c.289.5 | 16 | 15.8 | even | 4 | |||
1680.2.di.e.289.2 | 16 | 20.3 | even | 4 | |||
1680.2.di.e.289.7 | 16 | 20.7 | even | 4 | |||
1680.2.di.e.529.2 | 16 | 140.67 | even | 12 | |||
1680.2.di.e.529.7 | 16 | 140.123 | even | 12 | |||
2100.2.q.l.1201.2 | 8 | 7.4 | even | 3 | inner | ||
2100.2.q.l.1801.2 | 8 | 1.1 | even | 1 | trivial | ||
2100.2.q.m.1201.3 | 8 | 35.4 | even | 6 | |||
2100.2.q.m.1801.3 | 8 | 5.4 | even | 2 | |||
2940.2.k.f.589.1 | 8 | 35.2 | odd | 12 | |||
2940.2.k.f.589.5 | 8 | 35.23 | odd | 12 | |||
2940.2.k.g.589.4 | 8 | 35.33 | even | 12 | |||
2940.2.k.g.589.8 | 8 | 35.12 | even | 12 | |||
2940.2.bb.i.949.3 | 16 | 35.17 | even | 12 | |||
2940.2.bb.i.949.6 | 16 | 35.3 | even | 12 | |||
2940.2.bb.i.1549.3 | 16 | 35.13 | even | 4 | |||
2940.2.bb.i.1549.6 | 16 | 35.27 | even | 4 |