Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [300,2,Mod(299,300)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(300, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("300.299");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 300 = 2^{2} \cdot 3 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 300.h (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(2.39551206064\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 2 x^{15} + 2 x^{14} + 10 x^{13} - 42 x^{11} + 134 x^{10} + 110 x^{9} + 92 x^{8} + 142 x^{7} + \cdots + 100 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{6}\cdot 5^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 299.14 | ||
Root | \(-0.0108430 - 0.474040i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 300.299 |
Dual form | 300.2.h.c.299.16 |
$q$-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 \(\left(\mathbb{Z}/300\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(151\) | \(277\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.38758 | − | 0.273147i | 0.981170 | − | 0.193144i | ||||
\(3\) | 0.758030 | − | 1.55737i | 0.437649 | − | 0.899146i | ||||
\(4\) | 1.85078 | − | 0.758030i | 0.925391 | − | 0.379015i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0.626440 | − | 2.36803i | 0.255743 | − | 0.966745i | ||||
\(7\) | −3.56393 | −1.34704 | −0.673519 | − | 0.739170i | \(-0.735218\pi\) | ||||
−0.673519 | + | 0.739170i | \(0.735218\pi\) | |||||||
\(8\) | 2.36106 | − | 1.55737i | 0.834761 | − | 0.550612i | ||||
\(9\) | −1.85078 | − | 2.36106i | −0.616927 | − | 0.787020i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.20732 | 1.26856 | 0.634278 | − | 0.773105i | \(-0.281298\pi\) | ||||
0.634278 | + | 0.773105i | \(0.281298\pi\) | |||||||
\(12\) | 0.222417 | − | 3.45695i | 0.0642063 | − | 0.997937i | ||||
\(13\) | 2.70156i | 0.749279i | 0.927171 | + | 0.374639i | \(0.122233\pi\) | ||||
−0.927171 | + | 0.374639i | \(0.877767\pi\) | |||||||
\(14\) | −4.94525 | + | 0.973477i | −1.32167 | + | 0.260173i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 2.85078 | − | 2.80590i | 0.712695 | − | 0.701474i | ||||
\(17\) | −0.828216 | −0.200872 | −0.100436 | − | 0.994944i | \(-0.532024\pi\) | ||||
−0.100436 | + | 0.994944i | \(0.532024\pi\) | |||||||
\(18\) | −3.21303 | − | 2.77064i | −0.757319 | − | 0.653045i | ||||
\(19\) | 5.07999i | 1.16543i | 0.812677 | + | 0.582714i | \(0.198009\pi\) | ||||
−0.812677 | + | 0.582714i | \(0.801991\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.70156 | + | 5.55034i | −0.589529 | + | 1.21118i | ||||
\(22\) | 5.83802 | − | 1.14922i | 1.24467 | − | 0.245014i | ||||
\(23\) | − | 1.09259i | − | 0.227821i | −0.993491 | − | 0.113910i | \(-0.963662\pi\) | ||
0.993491 | − | 0.113910i | \(-0.0363377\pi\) | |||||||
\(24\) | −0.635635 | − | 4.85757i | −0.129749 | − | 0.991547i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0.737925 | + | 3.74865i | 0.144719 | + | 0.735170i | ||||
\(27\) | −5.07999 | + | 1.09259i | −0.977644 | + | 0.210269i | ||||
\(28\) | −6.59605 | + | 2.70156i | −1.24654 | + | 0.510547i | ||||
\(29\) | 5.55034i | 1.03067i | 0.856988 | + | 0.515336i | \(0.172333\pi\) | ||||
−0.856988 | + | 0.515336i | \(0.827667\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.59605i | 1.18468i | 0.805686 | + | 0.592342i | \(0.201797\pi\) | ||||
−0.805686 | + | 0.592342i | \(0.798203\pi\) | |||||||
\(32\) | 3.18928 | − | 4.67210i | 0.563790 | − | 0.825918i | ||||
\(33\) | 3.18928 | − | 6.55234i | 0.555182 | − | 1.14062i | ||||
\(34\) | −1.14922 | + | 0.226225i | −0.197089 | + | 0.0387972i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −5.21515 | − | 2.96686i | −0.869191 | − | 0.494477i | ||||
\(37\) | − | 5.40312i | − | 0.888268i | −0.895960 | − | 0.444134i | \(-0.853511\pi\) | ||
0.895960 | − | 0.444134i | \(-0.146489\pi\) | |||||||
\(38\) | 1.38758 | + | 7.04891i | 0.225096 | + | 1.14348i | ||||
\(39\) | 4.20732 | + | 2.04787i | 0.673711 | + | 0.327921i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 10.2725i | − | 1.60429i | −0.597130 | − | 0.802144i | \(-0.703692\pi\) | ||
0.597130 | − | 0.802144i | \(-0.296308\pi\) | |||||||
\(42\) | −2.23259 | + | 8.43949i | −0.344495 | + | 1.30224i | ||||
\(43\) | 0.531805 | 0.0810995 | 0.0405498 | − | 0.999178i | \(-0.487089\pi\) | ||||
0.0405498 | + | 0.999178i | \(0.487089\pi\) | |||||||
\(44\) | 7.78683 | − | 3.18928i | 1.17391 | − | 0.480802i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −0.298438 | − | 1.51606i | −0.0440023 | − | 0.223531i | ||||
\(47\) | 6.22947i | 0.908661i | 0.890833 | + | 0.454331i | \(0.150121\pi\) | ||||
−0.890833 | + | 0.454331i | \(0.849879\pi\) | |||||||
\(48\) | −2.20883 | − | 6.56666i | −0.318817 | − | 0.947816i | ||||
\(49\) | 5.70156 | 0.814509 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.627812 | + | 1.28984i | −0.0879113 | + | 0.180613i | ||||
\(52\) | 2.04787 | + | 5.00000i | 0.283988 | + | 0.693375i | ||||
\(53\) | −5.55034 | −0.762398 | −0.381199 | − | 0.924493i | \(-0.624489\pi\) | ||||
−0.381199 | + | 0.924493i | \(0.624489\pi\) | |||||||
\(54\) | −6.75047 | + | 2.90364i | −0.918623 | + | 0.395136i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −8.41464 | + | 5.55034i | −1.12445 | + | 0.741695i | ||||
\(57\) | 7.91140 | + | 3.85078i | 1.04789 | + | 0.510048i | ||||
\(58\) | 1.51606 | + | 7.70156i | 0.199068 | + | 1.01126i | ||||
\(59\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.701562 | 0.0898258 | 0.0449129 | − | 0.998991i | \(-0.485699\pi\) | ||||
0.0449129 | + | 0.998991i | \(0.485699\pi\) | |||||||
\(62\) | 1.80169 | + | 9.15257i | 0.228815 | + | 1.16238i | ||||
\(63\) | 6.59605 | + | 8.41464i | 0.831024 | + | 1.06015i | ||||
\(64\) | 3.14922 | − | 7.35408i | 0.393652 | − | 0.919259i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 2.63564 | − | 9.96307i | 0.324424 | − | 1.22637i | ||||
\(67\) | 2.04787 | 0.250187 | 0.125093 | − | 0.992145i | \(-0.460077\pi\) | ||||
0.125093 | + | 0.992145i | \(0.460077\pi\) | |||||||
\(68\) | −1.53285 | + | 0.627812i | −0.185885 | + | 0.0761334i | ||||
\(69\) | −1.70156 | − | 0.828216i | −0.204844 | − | 0.0997054i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −11.3663 | −1.34894 | −0.674468 | − | 0.738304i | \(-0.735627\pi\) | ||||
−0.674468 | + | 0.738304i | \(0.735627\pi\) | |||||||
\(72\) | −8.04684 | − | 2.69226i | −0.948330 | − | 0.317286i | ||||
\(73\) | 7.70156i | 0.901400i | 0.892676 | + | 0.450700i | \(0.148826\pi\) | ||||
−0.892676 | + | 0.450700i | \(0.851174\pi\) | |||||||
\(74\) | −1.47585 | − | 7.49729i | −0.171564 | − | 0.871542i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 3.85078 | + | 9.40194i | 0.441715 | + | 1.07848i | ||||
\(77\) | −14.9946 | −1.70879 | ||||||||
\(78\) | 6.39738 | + | 1.69237i | 0.724361 | + | 0.191623i | ||||
\(79\) | − | 7.12785i | − | 0.801946i | −0.916090 | − | 0.400973i | \(-0.868672\pi\) | ||
0.916090 | − | 0.400973i | \(-0.131328\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −2.14922 | + | 8.73961i | −0.238802 | + | 0.971068i | ||||
\(82\) | −2.80590 | − | 14.2539i | −0.309859 | − | 1.57408i | ||||
\(83\) | − | 3.11473i | − | 0.341886i | −0.985281 | − | 0.170943i | \(-0.945319\pi\) | ||
0.985281 | − | 0.170943i | \(-0.0546815\pi\) | |||||||
\(84\) | −0.792678 | + | 12.3203i | −0.0864882 | + | 1.34426i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0.737925 | − | 0.145261i | 0.0795724 | − | 0.0156639i | ||||
\(87\) | 8.64391 | + | 4.20732i | 0.926724 | + | 0.451072i | ||||
\(88\) | 9.93375 | − | 6.55234i | 1.05894 | − | 0.698482i | ||||
\(89\) | − | 4.72212i | − | 0.500544i | −0.968176 | − | 0.250272i | \(-0.919480\pi\) | ||
0.968176 | − | 0.250272i | \(-0.0805200\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 9.62817i | − | 1.00931i | ||||||
\(92\) | −0.828216 | − | 2.02214i | −0.0863474 | − | 0.210823i | ||||
\(93\) | 10.2725 | + | 5.00000i | 1.06520 | + | 0.518476i | ||||
\(94\) | 1.70156 | + | 8.64391i | 0.175503 | + | 0.891551i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −4.85860 | − | 8.50846i | −0.495879 | − | 0.868392i | ||||
\(97\) | 8.10469i | 0.822906i | 0.911431 | + | 0.411453i | \(0.134979\pi\) | ||||
−0.911431 | + | 0.411453i | \(0.865021\pi\) | |||||||
\(98\) | 7.91140 | − | 1.55737i | 0.799172 | − | 0.157318i | ||||
\(99\) | −7.78683 | − | 9.93375i | −0.782606 | − | 0.998379i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 7.20677i | − | 0.717100i | −0.933510 | − | 0.358550i | \(-0.883271\pi\) | ||
0.933510 | − | 0.358550i | \(-0.116729\pi\) | |||||||
\(102\) | −0.518827 | + | 1.96124i | −0.0513716 | + | 0.194192i | ||||
\(103\) | −4.09573 | −0.403564 | −0.201782 | − | 0.979430i | \(-0.564673\pi\) | ||||
−0.201782 | + | 0.979430i | \(0.564673\pi\) | |||||||
\(104\) | 4.20732 | + | 6.37855i | 0.412562 | + | 0.625469i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −7.70156 | + | 1.51606i | −0.748042 | + | 0.147253i | ||||
\(107\) | − | 18.8514i | − | 1.82244i | −0.411924 | − | 0.911218i | \(-0.635143\pi\) | ||
0.411924 | − | 0.911218i | \(-0.364857\pi\) | |||||||
\(108\) | −8.57372 | + | 5.87292i | −0.825007 | + | 0.565122i | ||||
\(109\) | −8.70156 | −0.833458 | −0.416729 | − | 0.909031i | \(-0.636824\pi\) | ||||
−0.416729 | + | 0.909031i | \(0.636824\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −8.41464 | − | 4.09573i | −0.798683 | − | 0.388750i | ||||
\(112\) | −10.1600 | + | 10.0000i | −0.960027 | + | 0.944911i | ||||
\(113\) | −15.8228 | −1.48848 | −0.744242 | − | 0.667910i | \(-0.767189\pi\) | ||||
−0.744242 | + | 0.667910i | \(0.767189\pi\) | |||||||
\(114\) | 12.0296 | + | 3.18231i | 1.12667 | + | 0.298050i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 4.20732 | + | 10.2725i | 0.390640 | + | 0.953774i | ||||
\(117\) | 6.37855 | − | 5.00000i | 0.589697 | − | 0.462250i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 2.95170 | 0.270582 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 6.70156 | 0.609233 | ||||||||
\(122\) | 0.973477 | − | 0.191630i | 0.0881344 | − | 0.0173493i | ||||
\(123\) | −15.9980 | − | 7.78683i | −1.44249 | − | 0.702115i | ||||
\(124\) | 5.00000 | + | 12.2078i | 0.449013 | + | 1.09630i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 11.4510 | + | 9.87434i | 1.02014 | + | 0.879676i | ||||
\(127\) | 16.2242 | 1.43967 | 0.719833 | − | 0.694147i | \(-0.244218\pi\) | ||||
0.719833 | + | 0.694147i | \(0.244218\pi\) | |||||||
\(128\) | 2.36106 | − | 11.0646i | 0.208690 | − | 0.977982i | ||||
\(129\) | 0.403124 | − | 0.828216i | 0.0354931 | − | 0.0729203i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 19.7810 | 1.72827 | 0.864136 | − | 0.503258i | \(-0.167865\pi\) | ||||
0.864136 | + | 0.503258i | \(0.167865\pi\) | |||||||
\(132\) | 0.935780 | − | 14.5445i | 0.0814492 | − | 1.26594i | ||||
\(133\) | − | 18.1047i | − | 1.56988i | ||||||
\(134\) | 2.84159 | − | 0.559369i | 0.245476 | − | 0.0483221i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −1.95547 | + | 1.28984i | −0.167680 | + | 0.110602i | ||||
\(137\) | 6.37855 | 0.544957 | 0.272478 | − | 0.962162i | \(-0.412157\pi\) | ||||
0.272478 | + | 0.962162i | \(0.412157\pi\) | |||||||
\(138\) | −2.58729 | − | 0.684442i | −0.220244 | − | 0.0582636i | ||||
\(139\) | − | 1.51606i | − | 0.128591i | −0.997931 | − | 0.0642953i | \(-0.979520\pi\) | ||
0.997931 | − | 0.0642953i | \(-0.0204799\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 9.70156 | + | 4.72212i | 0.817019 | + | 0.397674i | ||||
\(142\) | −15.7718 | + | 3.10469i | −1.32354 | + | 0.260539i | ||||
\(143\) | 11.3663i | 0.950501i | ||||||||
\(144\) | −11.9011 | − | 1.53777i | −0.991755 | − | 0.128148i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 2.10366 | + | 10.6866i | 0.174100 | + | 0.884427i | ||||
\(147\) | 4.32196 | − | 8.87942i | 0.356469 | − | 0.732362i | ||||
\(148\) | −4.09573 | − | 10.0000i | −0.336667 | − | 0.821995i | ||||
\(149\) | − | 1.65643i | − | 0.135700i | −0.997696 | − | 0.0678501i | \(-0.978386\pi\) | ||
0.997696 | − | 0.0678501i | \(-0.0216139\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 4.62754i | − | 0.376583i | −0.982113 | − | 0.188292i | \(-0.939705\pi\) | ||
0.982113 | − | 0.188292i | \(-0.0602951\pi\) | |||||||
\(152\) | 7.91140 | + | 11.9942i | 0.641699 | + | 0.972854i | ||||
\(153\) | 1.53285 | + | 1.95547i | 0.123923 | + | 0.158090i | ||||
\(154\) | −20.8062 | + | 4.09573i | −1.67662 | + | 0.330043i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 9.33918 | + | 0.600873i | 0.747732 | + | 0.0481084i | ||||
\(157\) | 8.10469i | 0.646824i | 0.946258 | + | 0.323412i | \(0.104830\pi\) | ||||
−0.946258 | + | 0.323412i | \(0.895170\pi\) | |||||||
\(158\) | −1.94695 | − | 9.89049i | −0.154891 | − | 0.786845i | ||||
\(159\) | −4.20732 | + | 8.64391i | −0.333662 | + | 0.685507i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 3.89391i | 0.306883i | ||||||||
\(162\) | −0.595020 | + | 12.7140i | −0.0467492 | + | 0.998907i | ||||
\(163\) | −5.07999 | −0.397895 | −0.198948 | − | 0.980010i | \(-0.563752\pi\) | ||||
−0.198948 | + | 0.980010i | \(0.563752\pi\) | |||||||
\(164\) | −7.78683 | − | 19.0121i | −0.608049 | − | 1.48459i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −0.850781 | − | 4.32196i | −0.0660334 | − | 0.335449i | ||||
\(167\) | − | 3.27777i | − | 0.253641i | −0.991926 | − | 0.126821i | \(-0.959523\pi\) | ||
0.991926 | − | 0.126821i | \(-0.0404773\pi\) | |||||||
\(168\) | 2.26536 | + | 17.3120i | 0.174776 | + | 1.33565i | ||||
\(169\) | 5.70156 | 0.438582 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 11.9942 | − | 9.40194i | 0.917216 | − | 0.718984i | ||||
\(172\) | 0.984255 | − | 0.403124i | 0.0750487 | − | 0.0307379i | ||||
\(173\) | 14.9946 | 1.14002 | 0.570008 | − | 0.821639i | \(-0.306940\pi\) | ||||
0.570008 | + | 0.821639i | \(0.306940\pi\) | |||||||
\(174\) | 13.1434 | + | 3.47695i | 0.996397 | + | 0.263587i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 11.9942 | − | 11.8053i | 0.904093 | − | 0.889858i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −1.28984 | − | 6.55234i | −0.0966772 | − | 0.491119i | ||||
\(179\) | −15.5737 | −1.16403 | −0.582015 | − | 0.813178i | \(-0.697736\pi\) | ||||
−0.582015 | + | 0.813178i | \(0.697736\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −21.5078 | −1.59866 | −0.799331 | − | 0.600890i | \(-0.794813\pi\) | ||||
−0.799331 | + | 0.600890i | \(0.794813\pi\) | |||||||
\(182\) | −2.62991 | − | 13.3599i | −0.194942 | − | 0.990301i | ||||
\(183\) | 0.531805 | − | 1.09259i | 0.0393122 | − | 0.0807665i | ||||
\(184\) | −1.70156 | − | 2.57967i | −0.125441 | − | 0.190176i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 15.6196 | + | 4.13203i | 1.14529 | + | 0.302975i | ||||
\(187\) | −3.48457 | −0.254817 | ||||||||
\(188\) | 4.72212 | + | 11.5294i | 0.344396 | + | 0.840866i | ||||
\(189\) | 18.1047 | − | 3.89391i | 1.31692 | − | 0.283240i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −11.3663 | −0.822440 | −0.411220 | − | 0.911536i | \(-0.634897\pi\) | ||||
−0.411220 | + | 0.911536i | \(0.634897\pi\) | |||||||
\(192\) | −9.06579 | − | 10.4791i | −0.654267 | − | 0.756264i | ||||
\(193\) | − | 5.80625i | − | 0.417943i | −0.977922 | − | 0.208971i | \(-0.932988\pi\) | ||
0.977922 | − | 0.208971i | \(-0.0670116\pi\) | |||||||
\(194\) | 2.21377 | + | 11.2459i | 0.158940 | + | 0.807411i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 10.5523 | − | 4.32196i | 0.753739 | − | 0.308711i | ||||
\(197\) | 9.44424 | 0.672875 | 0.336437 | − | 0.941706i | \(-0.390778\pi\) | ||||
0.336437 | + | 0.941706i | \(0.390778\pi\) | |||||||
\(198\) | −13.5183 | − | 11.6570i | −0.960701 | − | 0.828424i | ||||
\(199\) | − | 15.6924i | − | 1.11241i | −0.831047 | − | 0.556203i | \(-0.812258\pi\) | ||
0.831047 | − | 0.556203i | \(-0.187742\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1.55234 | − | 3.18928i | 0.109494 | − | 0.224954i | ||||
\(202\) | −1.96851 | − | 10.0000i | −0.138504 | − | 0.703598i | ||||
\(203\) | − | 19.7810i | − | 1.38835i | ||||||
\(204\) | −0.184209 | + | 2.86310i | −0.0128972 | + | 0.200457i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −5.68317 | + | 1.11874i | −0.395965 | + | 0.0779462i | ||||
\(207\) | −2.57967 | + | 2.02214i | −0.179299 | + | 0.140549i | ||||
\(208\) | 7.58030 | + | 7.70156i | 0.525599 | + | 0.534007i | ||||
\(209\) | 21.3731i | 1.47841i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 14.1763i | − | 0.975940i | −0.872860 | − | 0.487970i | \(-0.837738\pi\) | ||
0.872860 | − | 0.487970i | \(-0.162262\pi\) | |||||||
\(212\) | −10.2725 | + | 4.20732i | −0.705515 | + | 0.288960i | ||||
\(213\) | −8.61603 | + | 17.7016i | −0.590361 | + | 1.21289i | ||||
\(214\) | −5.14922 | − | 26.1580i | −0.351993 | − | 1.78812i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −10.2926 | + | 10.4911i | −0.700322 | + | 0.713827i | ||||
\(217\) | − | 23.5078i | − | 1.59581i | ||||||
\(218\) | −12.0742 | + | 2.37681i | −0.817765 | + | 0.160978i | ||||
\(219\) | 11.9942 | + | 5.83802i | 0.810490 | + | 0.394497i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 2.23748i | − | 0.150509i | ||||||
\(222\) | −12.7948 | − | 3.38473i | −0.858729 | − | 0.227168i | ||||
\(223\) | 15.6924 | 1.05084 | 0.525421 | − | 0.850843i | \(-0.323908\pi\) | ||||
0.525421 | + | 0.850843i | \(0.323908\pi\) | |||||||
\(224\) | −11.3663 | + | 16.6510i | −0.759446 | + | 1.11254i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −21.9555 | + | 4.32196i | −1.46046 | + | 0.287492i | ||||
\(227\) | 11.6924i | 0.776053i | 0.921648 | + | 0.388026i | \(0.126843\pi\) | ||||
−0.921648 | + | 0.388026i | \(0.873157\pi\) | |||||||
\(228\) | 17.5613 | + | 1.12988i | 1.16302 | + | 0.0748278i | ||||
\(229\) | −8.70156 | −0.575015 | −0.287508 | − | 0.957778i | \(-0.592827\pi\) | ||||
−0.287508 | + | 0.957778i | \(0.592827\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −11.3663 | + | 23.3521i | −0.747850 | + | 1.53645i | ||||
\(232\) | 8.64391 | + | 13.1047i | 0.567501 | + | 0.860365i | ||||
\(233\) | 14.9946 | 0.982328 | 0.491164 | − | 0.871067i | \(-0.336572\pi\) | ||||
0.491164 | + | 0.871067i | \(0.336572\pi\) | |||||||
\(234\) | 7.48504 | − | 8.68021i | 0.489313 | − | 0.567443i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −11.1007 | − | 5.40312i | −0.721066 | − | 0.350971i | ||||
\(238\) | 4.09573 | − | 0.806248i | 0.265487 | − | 0.0522613i | ||||
\(239\) | 5.46295 | 0.353369 | 0.176684 | − | 0.984268i | \(-0.443463\pi\) | ||||
0.176684 | + | 0.984268i | \(0.443463\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 7.00000 | 0.450910 | 0.225455 | − | 0.974254i | \(-0.427613\pi\) | ||||
0.225455 | + | 0.974254i | \(0.427613\pi\) | |||||||
\(242\) | 9.29898 | − | 1.83051i | 0.597761 | − | 0.117670i | ||||
\(243\) | 11.9816 | + | 9.97201i | 0.768621 | + | 0.639705i | ||||
\(244\) | 1.29844 | − | 0.531805i | 0.0831240 | − | 0.0340453i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −24.3255 | − | 6.43508i | −1.55094 | − | 0.410286i | ||||
\(247\) | −13.7239 | −0.873231 | ||||||||
\(248\) | 10.2725 | + | 15.5737i | 0.652302 | + | 0.988929i | ||||
\(249\) | −4.85078 | − | 2.36106i | −0.307406 | − | 0.149626i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1.25562 | −0.0792543 | −0.0396272 | − | 0.999215i | \(-0.512617\pi\) | ||||
−0.0396272 | + | 0.999215i | \(0.512617\pi\) | |||||||
\(252\) | 18.5864 | + | 10.5737i | 1.17083 | + | 0.666078i | ||||
\(253\) | − | 4.59688i | − | 0.289003i | ||||||
\(254\) | 22.5125 | − | 4.43160i | 1.41256 | − | 0.278063i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0.253905 | − | 15.9980i | 0.0158691 | − | 0.999874i | ||||
\(257\) | −11.1007 | −0.692441 | −0.346221 | − | 0.938153i | \(-0.612535\pi\) | ||||
−0.346221 | + | 0.938153i | \(0.612535\pi\) | |||||||
\(258\) | 0.333144 | − | 1.25933i | 0.0207406 | − | 0.0784025i | ||||
\(259\) | 19.2563i | 1.19653i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 13.1047 | − | 10.2725i | 0.811160 | − | 0.635849i | ||||
\(262\) | 27.4478 | − | 5.40312i | 1.69573 | − | 0.333806i | ||||
\(263\) | 17.9219i | 1.10511i | 0.833476 | + | 0.552555i | \(0.186347\pi\) | ||||
−0.833476 | + | 0.552555i | \(0.813653\pi\) | |||||||
\(264\) | −2.67432 | − | 20.4374i | −0.164593 | − | 1.25783i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −4.94525 | − | 25.1218i | −0.303213 | − | 1.54032i | ||||
\(267\) | −7.35408 | − | 3.57951i | −0.450062 | − | 0.219062i | ||||
\(268\) | 3.79015 | − | 1.55234i | 0.231520 | − | 0.0948245i | ||||
\(269\) | − | 14.9946i | − | 0.914236i | −0.889406 | − | 0.457118i | \(-0.848882\pi\) | ||
0.889406 | − | 0.457118i | \(-0.151118\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 24.4157i | 1.48315i | 0.670872 | + | 0.741573i | \(0.265920\pi\) | ||||
−0.670872 | + | 0.741573i | \(0.734080\pi\) | |||||||
\(272\) | −2.36106 | + | 2.32389i | −0.143160 | + | 0.140906i | ||||
\(273\) | −14.9946 | − | 7.29844i | −0.907513 | − | 0.441722i | ||||
\(274\) | 8.85078 | − | 1.74228i | 0.534695 | − | 0.105255i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −3.77703 | − | 0.243010i | −0.227351 | − | 0.0146275i | ||||
\(277\) | 28.1047i | 1.68865i | 0.535834 | + | 0.844323i | \(0.319997\pi\) | ||||
−0.535834 | + | 0.844323i | \(0.680003\pi\) | |||||||
\(278\) | −0.414108 | − | 2.10366i | −0.0248365 | − | 0.126169i | ||||
\(279\) | 15.5737 | − | 12.2078i | 0.932371 | − | 0.730864i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 7.20677i | 0.429920i | 0.976623 | + | 0.214960i | \(0.0689621\pi\) | ||||
−0.976623 | + | 0.214960i | \(0.931038\pi\) | |||||||
\(282\) | 14.7516 | + | 3.90239i | 0.878443 | + | 0.232384i | ||||
\(283\) | 6.14360 | 0.365199 | 0.182599 | − | 0.983187i | \(-0.441549\pi\) | ||||
0.182599 | + | 0.983187i | \(0.441549\pi\) | |||||||
\(284\) | −21.0366 | + | 8.61603i | −1.24829 | + | 0.511267i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 3.10469 | + | 15.7718i | 0.183584 | + | 0.932604i | ||||
\(287\) | 36.6103i | 2.16104i | ||||||||
\(288\) | −16.9338 | + | 1.11696i | −0.997832 | + | 0.0658173i | ||||
\(289\) | −16.3141 | −0.959651 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 12.6220 | + | 6.14360i | 0.739913 | + | 0.360144i | ||||
\(292\) | 5.83802 | + | 14.2539i | 0.341644 | + | 0.834147i | ||||
\(293\) | −18.8885 | −1.10348 | −0.551739 | − | 0.834017i | \(-0.686035\pi\) | ||||
−0.551739 | + | 0.834017i | \(0.686035\pi\) | |||||||
\(294\) | 3.57169 | − | 13.5015i | 0.208305 | − | 0.787422i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −8.41464 | − | 12.7571i | −0.489091 | − | 0.741492i | ||||
\(297\) | −21.3731 | + | 4.59688i | −1.24020 | + | 0.266738i | ||||
\(298\) | −0.452450 | − | 2.29844i | −0.0262097 | − | 0.133145i | ||||
\(299\) | 2.95170 | 0.170701 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.89531 | −0.109244 | ||||||||
\(302\) | −1.26400 | − | 6.42110i | −0.0727350 | − | 0.369493i | ||||
\(303\) | −11.2236 | − | 5.46295i | −0.644778 | − | 0.313838i | ||||
\(304\) | 14.2539 | + | 14.4819i | 0.817518 | + | 0.830595i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 2.66108 | + | 2.29468i | 0.152124 | + | 0.131178i | ||||
\(307\) | −20.3993 | −1.16425 | −0.582125 | − | 0.813100i | \(-0.697778\pi\) | ||||
−0.582125 | + | 0.813100i | \(0.697778\pi\) | |||||||
\(308\) | −27.7517 | + | 11.3663i | −1.58130 | + | 0.647657i | ||||
\(309\) | −3.10469 | + | 6.37855i | −0.176619 | + | 0.362863i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −16.8293 | −0.954301 | −0.477151 | − | 0.878821i | \(-0.658330\pi\) | ||||
−0.477151 | + | 0.878821i | \(0.658330\pi\) | |||||||
\(312\) | 13.1230 | − | 1.71721i | 0.742945 | − | 0.0972178i | ||||
\(313\) | 22.7016i | 1.28317i | 0.767053 | + | 0.641584i | \(0.221722\pi\) | ||||
−0.767053 | + | 0.641584i | \(0.778278\pi\) | |||||||
\(314\) | 2.21377 | + | 11.2459i | 0.124930 | + | 0.634645i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −5.40312 | − | 13.1921i | −0.303949 | − | 0.742113i | ||||
\(317\) | 29.9892 | 1.68436 | 0.842180 | − | 0.539197i | \(-0.181272\pi\) | ||||
0.842180 | + | 0.539197i | \(0.181272\pi\) | |||||||
\(318\) | −3.47695 | + | 13.1434i | −0.194978 | + | 0.737044i | ||||
\(319\) | 23.3521i | 1.30746i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −29.3586 | − | 14.2900i | −1.63864 | − | 0.797587i | ||||
\(322\) | 1.06361 | + | 5.40312i | 0.0592727 | + | 0.301104i | ||||
\(323\) | − | 4.20732i | − | 0.234102i | ||||||
\(324\) | 2.64716 | + | 17.8043i | 0.147064 | + | 0.989127i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −7.04891 | + | 1.38758i | −0.390403 | + | 0.0768512i | ||||
\(327\) | −6.59605 | + | 13.5515i | −0.364762 | + | 0.749401i | ||||
\(328\) | −15.9980 | − | 24.2539i | −0.883341 | − | 1.33920i | ||||
\(329\) | − | 22.2014i | − | 1.22400i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 30.0275i | 1.65046i | 0.564798 | + | 0.825229i | \(0.308954\pi\) | ||||
−0.564798 | + | 0.825229i | \(0.691046\pi\) | |||||||
\(332\) | −2.36106 | − | 5.76469i | −0.129580 | − | 0.316378i | ||||
\(333\) | −12.7571 | + | 10.0000i | −0.699085 | + | 0.547997i | ||||
\(334\) | −0.895314 | − | 4.54818i | −0.0489894 | − | 0.248865i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 7.87210 | + | 23.4031i | 0.429458 | + | 1.27674i | ||||
\(337\) | − | 0.403124i | − | 0.0219596i | −0.999940 | − | 0.0109798i | \(-0.996505\pi\) | ||
0.999940 | − | 0.0109798i | \(-0.00349505\pi\) | |||||||
\(338\) | 7.91140 | − | 1.55737i | 0.430323 | − | 0.0847096i | ||||
\(339\) | −11.9942 | + | 24.6419i | −0.651433 | + | 1.33836i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 27.7517i | 1.50284i | ||||||||
\(342\) | 14.0748 | − | 16.3222i | 0.761077 | − | 0.882601i | ||||
\(343\) | 4.62754 | 0.249863 | ||||||||
\(344\) | 1.25562 | − | 0.828216i | 0.0676987 | − | 0.0446544i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 20.8062 | − | 4.09573i | 1.11855 | − | 0.220188i | ||||
\(347\) | − | 13.3885i | − | 0.718732i | −0.933197 | − | 0.359366i | \(-0.882993\pi\) | ||
0.933197 | − | 0.359366i | \(-0.117007\pi\) | |||||||
\(348\) | 19.1873 | + | 1.23449i | 1.02855 | + | 0.0661756i | ||||
\(349\) | 12.2094 | 0.653553 | 0.326776 | − | 0.945102i | \(-0.394038\pi\) | ||||
0.326776 | + | 0.945102i | \(0.394038\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2.95170 | − | 13.7239i | −0.157550 | − | 0.732527i | ||||
\(352\) | 13.4183 | − | 19.6570i | 0.715199 | − | 1.04772i | ||||
\(353\) | 29.4081 | 1.56524 | 0.782618 | − | 0.622502i | \(-0.213884\pi\) | ||||
0.782618 | + | 0.622502i | \(0.213884\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −3.57951 | − | 8.73961i | −0.189714 | − | 0.463199i | ||||
\(357\) | 2.23748 | − | 4.59688i | 0.118420 | − | 0.243292i | ||||
\(358\) | −21.6098 | + | 4.25391i | −1.14211 | + | 0.224826i | ||||
\(359\) | 36.6103 | 1.93222 | 0.966108 | − | 0.258137i | \(-0.0831087\pi\) | ||||
0.966108 | + | 0.258137i | \(0.0831087\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6.80625 | −0.358224 | ||||||||
\(362\) | −29.8439 | + | 5.87480i | −1.56856 | + | 0.308773i | ||||
\(363\) | 5.07999 | − | 10.4368i | 0.266630 | − | 0.547789i | ||||
\(364\) | −7.29844 | − | 17.8196i | −0.382542 | − | 0.934002i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0.439487 | − | 1.66132i | 0.0229723 | − | 0.0868386i | ||||
\(367\) | −3.56393 | −0.186035 | −0.0930177 | − | 0.995664i | \(-0.529651\pi\) | ||||
−0.0930177 | + | 0.995664i | \(0.529651\pi\) | |||||||
\(368\) | −3.06569 | − | 3.11473i | −0.159810 | − | 0.162367i | ||||
\(369\) | −24.2539 | + | 19.0121i | −1.26261 | + | 0.989729i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 19.7810 | 1.02698 | ||||||||
\(372\) | 22.8022 | + | 1.46707i | 1.18224 | + | 0.0760642i | ||||
\(373\) | − | 17.2984i | − | 0.895679i | −0.894114 | − | 0.447840i | \(-0.852194\pi\) | ||
0.894114 | − | 0.447840i | \(-0.147806\pi\) | |||||||
\(374\) | −4.83513 | + | 0.951801i | −0.250019 | + | 0.0492165i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 9.70156 | + | 14.7082i | 0.500320 | + | 0.758515i | ||||
\(377\) | −14.9946 | −0.772260 | ||||||||
\(378\) | 24.0582 | − | 10.3484i | 1.23742 | − | 0.532263i | ||||
\(379\) | − | 21.3042i | − | 1.09432i | −0.837027 | − | 0.547162i | \(-0.815708\pi\) | ||
0.837027 | − | 0.547162i | \(-0.184292\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 12.2984 | − | 25.2670i | 0.630068 | − | 1.29447i | ||||
\(382\) | −15.7718 | + | 3.10469i | −0.806953 | + | 0.158850i | ||||
\(383\) | 12.4589i | 0.636622i | 0.947986 | + | 0.318311i | \(0.103116\pi\) | ||||
−0.947986 | + | 0.318311i | \(0.896884\pi\) | |||||||
\(384\) | −15.4419 | − | 12.0643i | −0.788015 | − | 0.615656i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −1.58596 | − | 8.05666i | −0.0807233 | − | 0.410073i | ||||
\(387\) | −0.984255 | − | 1.25562i | −0.0500325 | − | 0.0638270i | ||||
\(388\) | 6.14360 | + | 15.0000i | 0.311894 | + | 0.761510i | ||||
\(389\) | 19.9639i | 1.01221i | 0.862472 | + | 0.506104i | \(0.168915\pi\) | ||||
−0.862472 | + | 0.506104i | \(0.831085\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0.904899i | 0.0457627i | ||||||||
\(392\) | 13.4617 | − | 8.87942i | 0.679920 | − | 0.448479i | ||||
\(393\) | 14.9946 | − | 30.8062i | 0.756377 | − | 1.55397i | ||||
\(394\) | 13.1047 | − | 2.57967i | 0.660205 | − | 0.129962i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −21.9418 | − | 12.4825i | −1.10262 | − | 0.627271i | ||||
\(397\) | − | 28.9109i | − | 1.45100i | −0.688223 | − | 0.725499i | \(-0.741609\pi\) | ||
0.688223 | − | 0.725499i | \(-0.258391\pi\) | |||||||
\(398\) | −4.28634 | − | 21.7745i | −0.214855 | − | 1.09146i | ||||
\(399\) | −28.1956 | − | 13.7239i | −1.41155 | − | 0.687054i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 30.8174i | 1.53895i | 0.638679 | + | 0.769473i | \(0.279481\pi\) | ||||
−0.638679 | + | 0.769473i | \(0.720519\pi\) | |||||||
\(402\) | 1.28286 | − | 4.84941i | 0.0639835 | − | 0.241867i | ||||
\(403\) | −17.8196 | −0.887659 | ||||||||
\(404\) | −5.46295 | − | 13.3382i | −0.271792 | − | 0.663598i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −5.40312 | − | 27.4478i | −0.268153 | − | 1.36221i | ||||
\(407\) | − | 22.7327i | − | 1.12682i | ||||||
\(408\) | 0.526443 | + | 4.02311i | 0.0260628 | + | 0.199174i | ||||
\(409\) | 27.2094 | 1.34542 | 0.672708 | − | 0.739908i | \(-0.265131\pi\) | ||||
0.672708 | + | 0.739908i | \(0.265131\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 4.83513 | − | 9.93375i | 0.238500 | − | 0.489996i | ||||
\(412\) | −7.58030 | + | 3.10469i | −0.373455 | + | 0.152957i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −3.02717 | + | 3.51053i | −0.148777 | + | 0.172533i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 12.6220 | + | 8.61603i | 0.618843 | + | 0.422436i | ||||
\(417\) | −2.36106 | − | 1.14922i | −0.115622 | − | 0.0562775i | ||||
\(418\) | 5.83802 | + | 29.6570i | 0.285547 | + | 1.45057i | ||||
\(419\) | −10.1107 | −0.493941 | −0.246970 | − | 0.969023i | \(-0.579435\pi\) | ||||
−0.246970 | + | 0.969023i | \(0.579435\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 24.2094 | 1.17989 | 0.589946 | − | 0.807442i | \(-0.299149\pi\) | ||||
0.589946 | + | 0.807442i | \(0.299149\pi\) | |||||||
\(422\) | −3.87223 | − | 19.6709i | −0.188497 | − | 0.957563i | ||||
\(423\) | 14.7082 | − | 11.5294i | 0.715135 | − | 0.560578i | ||||
\(424\) | −13.1047 | + | 8.64391i | −0.636420 | + | 0.419785i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −7.12033 | + | 26.9159i | −0.344981 | + | 1.30408i | ||||
\(427\) | −2.50031 | −0.120999 | ||||||||
\(428\) | −14.2900 | − | 34.8899i | −0.690731 | − | 1.68647i | ||||
\(429\) | 17.7016 | + | 8.61603i | 0.854639 | + | 0.415986i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 19.7810 | 0.952817 | 0.476408 | − | 0.879224i | \(-0.341938\pi\) | ||||
0.476408 | + | 0.879224i | \(0.341938\pi\) | |||||||
\(432\) | −11.4162 | + | 17.3686i | −0.549264 | + | 0.835649i | ||||
\(433\) | 31.2094i | 1.49983i | 0.661536 | + | 0.749913i | \(0.269905\pi\) | ||||
−0.661536 | + | 0.749913i | \(0.730095\pi\) | |||||||
\(434\) | −6.42110 | − | 32.6191i | −0.308222 | − | 1.56577i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −16.1047 | + | 6.59605i | −0.771275 | + | 0.315893i | ||||
\(437\) | 5.55034 | 0.265509 | ||||||||
\(438\) | 18.2375 | + | 4.82457i | 0.871423 | + | 0.230527i | ||||
\(439\) | 21.9154i | 1.04596i | 0.852344 | + | 0.522981i | \(0.175180\pi\) | ||||
−0.852344 | + | 0.522981i | \(0.824820\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −10.5523 | − | 13.4617i | −0.502493 | − | 0.641035i | ||||
\(442\) | −0.611161 | − | 3.10469i | −0.0290699 | − | 0.147675i | ||||
\(443\) | − | 11.2033i | − | 0.532285i | −0.963934 | − | 0.266143i | \(-0.914251\pi\) | ||
0.963934 | − | 0.266143i | \(-0.0857492\pi\) | |||||||
\(444\) | −18.6784 | − | 1.20175i | −0.886435 | − | 0.0570324i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 21.7745 | − | 4.28634i | 1.03105 | − | 0.202964i | ||||
\(447\) | −2.57967 | − | 1.25562i | −0.122014 | − | 0.0593890i | ||||
\(448\) | −11.2236 | + | 26.2094i | −0.530264 | + | 1.23828i | ||||
\(449\) | − | 19.1357i | − | 0.903068i | −0.892254 | − | 0.451534i | \(-0.850877\pi\) | ||
0.892254 | − | 0.451534i | \(-0.149123\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 43.2196i | − | 2.03513i | ||||||
\(452\) | −29.2845 | + | 11.9942i | −1.37743 | + | 0.564158i | ||||
\(453\) | −7.20677 | − | 3.50781i | −0.338604 | − | 0.164811i | ||||
\(454\) | 3.19375 | + | 16.2242i | 0.149890 | + | 0.761440i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 24.6764 | − | 3.22902i | 1.15558 | − | 0.151213i | ||||
\(457\) | − | 16.8953i | − | 0.790329i | −0.918610 | − | 0.395165i | \(-0.870688\pi\) | ||
0.918610 | − | 0.395165i | \(-0.129312\pi\) | |||||||
\(458\) | −12.0742 | + | 2.37681i | −0.564188 | + | 0.111061i | ||||
\(459\) | 4.20732 | − | 0.904899i | 0.196381 | − | 0.0422371i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 7.20677i | − | 0.335653i | −0.985817 | − | 0.167826i | \(-0.946325\pi\) | ||
0.985817 | − | 0.167826i | \(-0.0536748\pi\) | |||||||
\(462\) | −9.39321 | + | 35.5076i | −0.437012 | + | 1.65196i | ||||
\(463\) | 7.12785 | 0.331259 | 0.165630 | − | 0.986188i | \(-0.447034\pi\) | ||||
0.165630 | + | 0.986188i | \(0.447034\pi\) | |||||||
\(464\) | 15.5737 | + | 15.8228i | 0.722989 | + | 0.734555i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 20.8062 | − | 4.09573i | 0.963831 | − | 0.189731i | ||||
\(467\) | 0.766519i | 0.0354703i | 0.999843 | + | 0.0177351i | \(0.00564557\pi\) | ||||
−0.999843 | + | 0.0177351i | \(0.994354\pi\) | |||||||
\(468\) | 8.01516 | − | 14.0890i | 0.370501 | − | 0.651266i | ||||
\(469\) | −7.29844 | −0.337011 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 12.6220 | + | 6.14360i | 0.581590 | + | 0.283082i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 2.23748 | 0.102879 | ||||||||
\(474\) | −16.8790 | − | 4.46517i | −0.775277 | − | 0.205092i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 5.46295 | − | 2.23748i | 0.250394 | − | 0.102555i | ||||
\(477\) | 10.2725 | + | 13.1047i | 0.470344 | + | 0.600022i | ||||
\(478\) | 7.58030 | − | 1.49219i | 0.346715 | − | 0.0682512i | ||||
\(479\) | −42.0732 | −1.92237 | −0.961187 | − | 0.275897i | \(-0.911025\pi\) | ||||
−0.961187 | + | 0.275897i | \(0.911025\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 14.5969 | 0.665560 | ||||||||
\(482\) | 9.71309 | − | 1.91203i | 0.442419 | − | 0.0870906i | ||||
\(483\) | 6.06424 | + | 2.95170i | 0.275932 | + | 0.134307i | ||||
\(484\) | 12.4031 | − | 5.07999i | 0.563778 | − | 0.230908i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 19.3493 | + | 10.5643i | 0.877703 | + | 0.479205i | ||||
\(487\) | 34.0438 | 1.54267 | 0.771337 | − | 0.636427i | \(-0.219588\pi\) | ||||
0.771337 | + | 0.636427i | \(0.219588\pi\) | |||||||
\(488\) | 1.65643 | − | 1.09259i | 0.0749831 | − | 0.0494592i | ||||
\(489\) | −3.85078 | + | 7.91140i | −0.174138 | + | 0.357766i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −16.8293 | −0.759495 | −0.379748 | − | 0.925090i | \(-0.623989\pi\) | ||||
−0.379748 | + | 0.925090i | \(0.623989\pi\) | |||||||
\(492\) | −35.5114 | − | 2.28477i | −1.60098 | − | 0.103005i | ||||
\(493\) | − | 4.59688i | − | 0.207033i | ||||||
\(494\) | −19.0431 | + | 3.74865i | −0.856788 | + | 0.168660i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 18.5078 | + | 18.8039i | 0.831025 | + | 0.844319i | ||||
\(497\) | 40.5088 | 1.81707 | ||||||||
\(498\) | −7.37579 | − | 1.95119i | −0.330517 | − | 0.0874351i | ||||
\(499\) | − | 22.9790i | − | 1.02868i | −0.857586 | − | 0.514340i | \(-0.828037\pi\) | ||
0.857586 | − | 0.514340i | \(-0.171963\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −5.10469 | − | 2.48465i | −0.228061 | − | 0.111006i | ||||
\(502\) | −1.74228 | + | 0.342970i | −0.0777620 | + | 0.0153075i | ||||
\(503\) | − | 32.2399i | − | 1.43751i | −0.695265 | − | 0.718753i | \(-0.744713\pi\) | ||
0.695265 | − | 0.718753i | \(-0.255287\pi\) | |||||||
\(504\) | 28.6784 | + | 9.59503i | 1.27744 | + | 0.427397i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −1.25562 | − | 6.37855i | −0.0558193 | − | 0.283561i | ||||
\(507\) | 4.32196 | − | 8.87942i | 0.191945 | − | 0.394349i | ||||
\(508\) | 30.0275 | − | 12.2984i | 1.33225 | − | 0.545655i | ||||
\(509\) | − | 42.7463i | − | 1.89470i | −0.320207 | − | 0.947348i | \(-0.603753\pi\) | ||
0.320207 | − | 0.947348i | \(-0.396247\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 27.4478i | − | 1.21422i | ||||||
\(512\) | −4.01749 | − | 22.2679i | −0.177550 | − | 0.984112i | ||||
\(513\) | −5.55034 | − | 25.8062i | −0.245053 | − | 1.13937i | ||||
\(514\) | −15.4031 | + | 3.03212i | −0.679403 | + | 0.133741i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0.118283 | − | 1.83843i | 0.00520710 | − | 0.0809322i | ||||
\(517\) | 26.2094i | 1.15269i | ||||||||
\(518\) | 5.25982 | + | 26.7198i | 0.231103 | + | 1.17400i | ||||
\(519\) | 11.3663 | − | 23.3521i | 0.498927 | − | 1.02504i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 10.2725i | 0.450045i | 0.974354 | + | 0.225022i | \(0.0722455\pi\) | ||||
−0.974354 | + | 0.225022i | \(0.927754\pi\) | |||||||
\(522\) | 15.3780 | − | 17.8334i | 0.673075 | − | 0.780547i | ||||
\(523\) | −31.4642 | −1.37583 | −0.687916 | − | 0.725790i | \(-0.741474\pi\) | ||||
−0.687916 | + | 0.725790i | \(0.741474\pi\) | |||||||
\(524\) | 36.6103 | − | 14.9946i | 1.59933 | − | 0.655041i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 4.89531 | + | 24.8681i | 0.213446 | + | 1.08430i | ||||
\(527\) | − | 5.46295i | − | 0.237970i | ||||||
\(528\) | −9.29326 | − | 27.6281i | −0.404437 | − | 1.20236i | ||||
\(529\) | 21.8062 | 0.948098 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −13.7239 | − | 33.5078i | −0.595006 | − | 1.45275i | ||||
\(533\) | 27.7517 | 1.20206 | ||||||||
\(534\) | −11.1821 | − | 2.95813i | −0.483898 | − | 0.128011i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 4.83513 | − | 3.18928i | 0.208846 | − | 0.137756i | ||||
\(537\) | −11.8053 | + | 24.2539i | −0.509437 | + | 1.04663i | ||||
\(538\) | −4.09573 | − | 20.8062i | −0.176579 | − | 0.897021i | ||||
\(539\) | 23.9883 | 1.03325 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −19.2984 | −0.829705 | −0.414852 | − | 0.909889i | \(-0.636167\pi\) | ||||
−0.414852 | + | 0.909889i | \(0.636167\pi\) | |||||||
\(542\) | 6.66908 | + | 33.8788i | 0.286461 | + | 1.45522i | ||||
\(543\) | −16.3036 | + | 33.4955i | −0.699653 | + | 1.43743i | ||||
\(544\) | −2.64141 | + | 3.86951i | −0.113249 | + | 0.165904i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −22.7998 | − | 6.03147i | −0.975741 | − | 0.258123i | ||||
\(547\) | 21.8360 | 0.933640 | 0.466820 | − | 0.884352i | \(-0.345400\pi\) | ||||
0.466820 | + | 0.884352i | \(0.345400\pi\) | |||||||
\(548\) | 11.8053 | − | 4.83513i | 0.504298 | − | 0.206547i | ||||
\(549\) | −1.29844 | − | 1.65643i | −0.0554160 | − | 0.0706948i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −28.1956 | −1.20117 | ||||||||
\(552\) | −5.30733 | + | 0.694488i | −0.225895 | + | 0.0295594i | ||||
\(553\) | 25.4031i | 1.08025i | ||||||||
\(554\) | 7.67672 | + | 38.9976i | 0.326153 | + | 1.65685i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −1.14922 | − | 2.80590i | −0.0487377 | − | 0.118996i | ||||
\(557\) | −17.2321 | −0.730146 | −0.365073 | − | 0.930979i | \(-0.618956\pi\) | ||||
−0.365073 | + | 0.930979i | \(0.618956\pi\) | |||||||
\(558\) | 18.2752 | − | 21.1933i | 0.773653 | − | 0.897184i | ||||
\(559\) | 1.43670i | 0.0607661i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −2.64141 | + | 5.42675i | −0.111520 | + | 0.229118i | ||||
\(562\) | 1.96851 | + | 10.0000i | 0.0830366 | + | 0.421825i | ||||
\(563\) | 30.0547i | 1.26666i | 0.773883 | + | 0.633328i | \(0.218312\pi\) | ||||
−0.773883 | + | 0.633328i | \(0.781688\pi\) | |||||||
\(564\) | 21.5350 | + | 1.38554i | 0.906786 | + | 0.0583417i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 8.52476 | − | 1.67811i | 0.358322 | − | 0.0705361i | ||||
\(567\) | 7.65966 | − | 31.1473i | 0.321675 | − | 1.30806i | ||||
\(568\) | −26.8366 | + | 17.7016i | −1.12604 | + | 0.742741i | ||||
\(569\) | 43.5745i | 1.82674i | 0.407133 | + | 0.913369i | \(0.366528\pi\) | ||||
−0.407133 | + | 0.913369i | \(0.633472\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 32.9802i | 1.38018i | 0.723724 | + | 0.690090i | \(0.242429\pi\) | ||||
−0.723724 | + | 0.690090i | \(0.757571\pi\) | |||||||
\(572\) | 8.61603 | + | 21.0366i | 0.360254 | + | 0.879585i | ||||
\(573\) | −8.61603 | + | 17.7016i | −0.359940 | + | 0.739493i | ||||
\(574\) | 10.0000 | + | 50.7999i | 0.417392 | + | 2.12034i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −23.1919 | + | 6.17528i | −0.966331 | + | 0.257304i | ||||
\(577\) | − | 0.403124i | − | 0.0167823i | −0.999965 | − | 0.00839114i | \(-0.997329\pi\) | ||
0.999965 | − | 0.00839114i | \(-0.00267101\pi\) | |||||||
\(578\) | −22.6371 | + | 4.45614i | −0.941581 | + | 0.185351i | ||||
\(579\) | −9.04246 | − | 4.40131i | −0.375792 | − | 0.182912i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 11.1007i | 0.460534i | ||||||||
\(582\) | 19.1922 | + | 5.07710i | 0.795540 | + | 0.210453i | ||||
\(583\) | −23.3521 | −0.967144 | ||||||||
\(584\) | 11.9942 | + | 18.1839i | 0.496322 | + | 0.752453i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −26.2094 | + | 5.15934i | −1.08270 | + | 0.213130i | ||||
\(587\) | − | 3.88125i | − | 0.160196i | −0.996787 | − | 0.0800982i | \(-0.974477\pi\) | ||
0.996787 | − | 0.0800982i | \(-0.0255234\pi\) | |||||||
\(588\) | 1.26812 | − | 19.7100i | 0.0522966 | − | 0.812828i | ||||
\(589\) | −33.5078 | −1.38067 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 7.15902 | − | 14.7082i | 0.294483 | − | 0.605012i | ||||
\(592\) | −15.1606 | − | 15.4031i | −0.623097 | − | 0.633065i | ||||
\(593\) | −43.5745 | −1.78939 | −0.894695 | − | 0.446678i | \(-0.852607\pi\) | ||||
−0.894695 | + | 0.446678i | \(0.852607\pi\) | |||||||
\(594\) | −28.4014 | + | 12.2166i | −1.16532 | + | 0.501252i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −1.25562 | − | 3.06569i | −0.0514324 | − | 0.125576i | ||||
\(597\) | −24.4388 | − | 11.8953i | −1.00021 | − | 0.486843i | ||||
\(598\) | 4.09573 | − | 0.806248i | 0.167487 | − | 0.0329700i | ||||
\(599\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 24.0156 | 0.979618 | 0.489809 | − | 0.871830i | \(-0.337067\pi\) | ||||
0.489809 | + | 0.871830i | \(0.337067\pi\) | |||||||
\(602\) | −2.62991 | + | 0.517700i | −0.107187 | + | 0.0210999i | ||||
\(603\) | −3.79015 | − | 4.83513i | −0.154347 | − | 0.196902i | ||||
\(604\) | −3.50781 | − | 8.56455i | −0.142731 | − | 0.348487i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −17.0659 | − | 4.51461i | −0.693253 | − | 0.183393i | ||||
\(607\) | 27.4478 | 1.11407 | 0.557036 | − | 0.830489i | \(-0.311939\pi\) | ||||
0.557036 | + | 0.830489i | \(0.311939\pi\) | |||||||
\(608\) | 23.7342 | + | 16.2015i | 0.962549 | + | 0.657057i | ||||
\(609\) | −30.8062 | − | 14.9946i | −1.24833 | − | 0.607611i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −16.8293 | −0.680840 | ||||||||
\(612\) | 4.31926 | + | 2.45720i | 0.174596 | + | 0.0993264i | ||||
\(613\) | − | 20.8062i | − | 0.840356i | −0.907442 | − | 0.420178i | \(-0.861968\pi\) | ||
0.907442 | − | 0.420178i | \(-0.138032\pi\) | |||||||
\(614\) | −28.3057 | + | 5.57201i | −1.14233 | + | 0.224868i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −35.4031 | + | 23.3521i | −1.42643 | + | 0.940881i | ||||
\(617\) | −18.3074 | −0.737030 | −0.368515 | − | 0.929622i | \(-0.620134\pi\) | ||||
−0.368515 | + | 0.929622i | \(0.620134\pi\) | |||||||
\(618\) | −2.56573 | + | 9.69882i | −0.103209 | + | 0.390144i | ||||
\(619\) | − | 26.9160i | − | 1.08184i | −0.841073 | − | 0.540922i | \(-0.818075\pi\) | ||
0.841073 | − | 0.540922i | \(-0.181925\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.19375 | + | 5.55034i | 0.0479036 | + | 0.222727i | ||||
\(622\) | −23.3521 | + | 4.59688i | −0.936332 | + | 0.184318i | ||||
\(623\) | 16.8293i | 0.674251i | ||||||||
\(624\) | 17.7402 | − | 5.96729i | 0.710178 | − | 0.238883i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 6.20087 | + | 31.5003i | 0.247837 | + | 1.25901i | ||||
\(627\) | 33.2858 | + | 16.2015i | 1.32931 | + | 0.647025i | ||||
\(628\) | 6.14360 | + | 15.0000i | 0.245156 | + | 0.598565i | ||||
\(629\) | 4.47495i | 0.178428i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 2.65903i | 0.105854i | 0.998598 | + | 0.0529271i | \(0.0168551\pi\) | ||||
−0.998598 | + | 0.0529271i | \(0.983145\pi\) | |||||||
\(632\) | −11.1007 | − | 16.8293i | −0.441561 | − | 0.669433i | ||||
\(633\) | −22.0778 | − | 10.7461i | −0.877512 | − | 0.427119i | ||||
\(634\) | 41.6125 | − | 8.19146i | 1.65264 | − | 0.325324i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −1.23449 | + | 19.1873i | −0.0489507 | + | 0.760824i | ||||
\(637\) | 15.4031i | 0.610294i | ||||||||
\(638\) | 6.37855 | + | 32.4030i | 0.252529 | + | 1.28285i | ||||
\(639\) | 21.0366 | + | 26.8366i | 0.832196 | + | 1.06164i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 41.0898i | − | 1.62295i | −0.584386 | − | 0.811476i | \(-0.698665\pi\) | ||
0.584386 | − | 0.811476i | \(-0.301335\pi\) | |||||||
\(642\) | −44.6408 | − | 11.8093i | −1.76183 | − | 0.466076i | ||||
\(643\) | 22.2885 | 0.878971 | 0.439485 | − | 0.898250i | \(-0.355161\pi\) | ||||
0.439485 | + | 0.898250i | \(0.355161\pi\) | |||||||
\(644\) | 2.95170 | + | 7.20677i | 0.116313 | + | 0.283986i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −1.14922 | − | 5.83802i | −0.0452154 | − | 0.229694i | ||||
\(647\) | 2.18518i | 0.0859082i | 0.999077 | + | 0.0429541i | \(0.0136769\pi\) | ||||
−0.999077 | + | 0.0429541i | \(0.986323\pi\) | |||||||
\(648\) | 8.53635 | + | 23.9819i | 0.335339 | + | 0.942097i | ||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −36.6103 | − | 17.8196i | −1.43487 | − | 0.698406i | ||||
\(652\) | −9.40194 | + | 3.85078i | −0.368208 | + | 0.150808i | ||||
\(653\) | 7.78781 | 0.304761 | 0.152380 | − | 0.988322i | \(-0.451306\pi\) | ||||
0.152380 | + | 0.988322i | \(0.451306\pi\) | |||||||
\(654\) | −5.45101 | + | 20.6056i | −0.213151 | + | 0.805742i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −28.8234 | − | 29.2845i | −1.12537 | − | 1.14337i | ||||
\(657\) | 18.1839 | − | 14.2539i | 0.709420 | − | 0.556098i | ||||
\(658\) | −6.06424 | − | 30.8062i | −0.236409 | − | 1.20095i | ||||
\(659\) | −21.0366 | −0.819470 | −0.409735 | − | 0.912205i | \(-0.634379\pi\) | ||||
−0.409735 | + | 0.912205i | \(0.634379\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −18.0000 | −0.700119 | −0.350059 | − | 0.936727i | \(-0.613839\pi\) | ||||
−0.350059 | + | 0.936727i | \(0.613839\pi\) | |||||||
\(662\) | 8.20192 | + | 41.6656i | 0.318777 | + | 1.61938i | ||||
\(663\) | −3.48457 | − | 1.69607i | −0.135329 | − | 0.0658700i | ||||
\(664\) | −4.85078 | − | 7.35408i | −0.188247 | − | 0.285393i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −14.9701 | + | 17.3604i | −0.580079 | + | 0.672702i | ||||
\(667\) | 6.06424 | 0.234808 | ||||||||
\(668\) | −2.48465 | − | 6.06643i | −0.0961339 | − | 0.234717i | ||||
\(669\) | 11.8953 | − | 24.4388i | 0.459899 | − | 0.944860i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 2.95170 | 0.113949 | ||||||||
\(672\) | 17.3157 | + | 30.3235i | 0.667968 | + | 1.16976i | ||||
\(673\) | − | 0.806248i | − | 0.0310786i | −0.999879 | − | 0.0155393i | \(-0.995053\pi\) | ||
0.999879 | − | 0.0155393i | \(-0.00494651\pi\) | |||||||
\(674\) | −0.110112 | − | 0.559369i | −0.00424137 | − | 0.0215461i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 10.5523 | − | 4.32196i | 0.405859 | − | 0.166229i | ||||
\(677\) | −3.89391 | −0.149655 | −0.0748275 | − | 0.997196i | \(-0.523841\pi\) | ||||
−0.0748275 | + | 0.997196i | \(0.523841\pi\) | |||||||
\(678\) | −9.91203 | + | 37.4689i | −0.380669 | + | 1.43898i | ||||
\(679\) | − | 28.8845i | − | 1.10849i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 18.2094 | + | 8.86320i | 0.697785 | + | 0.339639i | ||||
\(682\) | 7.58030 | + | 38.5078i | 0.290265 | + | 1.47454i | ||||
\(683\) | 19.9440i | 0.763137i | 0.924341 | + | 0.381568i | \(0.124616\pi\) | ||||
−0.924341 | + | 0.381568i | \(0.875384\pi\) | |||||||
\(684\) | 15.0716 | − | 26.4929i | 0.576277 | − | 1.01298i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 6.42110 | − | 1.26400i | 0.245159 | − | 0.0482597i | ||||
\(687\) | −6.59605 | + | 13.5515i | −0.251655 | + | 0.517023i | ||||
\(688\) | 1.51606 | − | 1.49219i | 0.0577992 | − | 0.0568892i | ||||
\(689\) | − | 14.9946i | − | 0.571248i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 18.8039i | 0.715333i | 0.933849 | + | 0.357667i | \(0.116428\pi\) | ||||
−0.933849 | + | 0.357667i | \(0.883572\pi\) | |||||||
\(692\) | 27.7517 | − | 11.3663i | 1.05496 | − | 0.432084i | ||||
\(693\) | 27.7517 | + | 35.4031i | 1.05420 | + | 1.34485i | ||||
\(694\) | −3.65703 | − | 18.5777i | −0.138819 | − | 0.705198i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 26.9611 | − | 3.52799i | 1.02196 | − | 0.133728i | ||||
\(697\) | 8.50781i | 0.322256i | ||||||||
\(698\) | 16.9415 | − | 3.33496i | 0.641247 | − | 0.126230i | ||||
\(699\) | 11.3663 | − | 23.3521i | 0.429915 | − | 0.883256i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 27.7517i | − | 1.04817i | −0.851667 | − | 0.524083i | \(-0.824408\pi\) | ||
0.851667 | − | 0.524083i | \(-0.175592\pi\) | |||||||
\(702\) | −7.84438 | − | 18.2368i | −0.296067 | − | 0.688304i | ||||
\(703\) | 27.4478 | 1.03521 | ||||||||
\(704\) | 13.2498 | − | 30.9410i | 0.499370 | − | 1.16613i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 40.8062 | − | 8.03275i | 1.53576 | − | 0.302317i | ||||
\(707\) | 25.6844i | 0.965961i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 11.2984 | 0.424322 | 0.212161 | − | 0.977235i | \(-0.431950\pi\) | ||||
0.212161 | + | 0.977235i | \(0.431950\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −16.8293 | + | 13.1921i | −0.631148 | + | 0.494742i | ||||
\(712\) | −7.35408 | − | 11.1492i | −0.275606 | − | 0.417835i | ||||
\(713\) | 7.20677 | 0.269896 | ||||||||
\(714\) | 1.84906 | − | 6.98971i | 0.0691994 | − | 0.261583i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −28.8234 | + | 11.8053i | −1.07718 | + | 0.441185i | ||||
\(717\) | 4.14108 | − | 8.50781i | 0.154651 | − | 0.317730i | ||||
\(718\) | 50.7999 | − | 10.0000i | 1.89583 | − | 0.373197i | ||||
\(719\) | −25.6844 | −0.957866 | −0.478933 | − | 0.877851i | \(-0.658976\pi\) | ||||
−0.478933 | + | 0.877851i | \(0.658976\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 14.5969 | 0.543616 | ||||||||
\(722\) | −9.44424 | + | 1.85911i | −0.351478 | + | 0.0691889i | ||||
\(723\) | 5.30621 | − | 10.9016i | 0.197340 | − | 0.405434i | ||||
\(724\) | −39.8062 | + | 16.3036i | −1.47939 | + | 0.605917i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 4.19813 | − | 15.8695i | 0.155807 | − | 0.588973i | ||||
\(727\) | −45.1087 | −1.67299 | −0.836495 | − | 0.547975i | \(-0.815399\pi\) | ||||
−0.836495 | + | 0.547975i | \(0.815399\pi\) | |||||||
\(728\) | −14.9946 | − | 22.7327i | −0.555736 | − | 0.842529i | ||||
\(729\) | 24.6125 | − | 11.1007i | 0.911574 | − | 0.411136i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −0.440449 | −0.0162906 | ||||||||
\(732\) | 0.156039 | − | 2.42527i | 0.00576738 | − | 0.0896405i | ||||
\(733\) | − | 20.8062i | − | 0.768496i | −0.923230 | − | 0.384248i | \(-0.874461\pi\) | ||
0.923230 | − | 0.384248i | \(-0.125539\pi\) | |||||||
\(734\) | −4.94525 | + | 0.973477i | −0.182532 | + | 0.0359317i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −5.10469 | − | 3.48457i | −0.188161 | − | 0.128443i | ||||
\(737\) | 8.61603 | 0.317376 | ||||||||
\(738\) | −28.4612 | + | 33.0057i | −1.04767 | + | 1.21496i | ||||
\(739\) | 52.9271i | 1.94695i | 0.228785 | + | 0.973477i | \(0.426525\pi\) | ||||
−0.228785 | + | 0.973477i | \(0.573475\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −10.4031 | + | 21.3731i | −0.382168 | + | 0.785162i | ||||
\(742\) | 27.4478 | − | 5.40312i | 1.00764 | − | 0.198355i | ||||
\(743\) | − | 29.6143i | − | 1.08644i | −0.839589 | − | 0.543222i | \(-0.817204\pi\) | ||
0.839589 | − | 0.543222i | \(-0.182796\pi\) | |||||||
\(744\) | 32.0407 | − | 4.19268i | 1.17467 | − | 0.153711i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −4.72502 | − | 24.0030i | −0.172995 | − | 0.878814i | ||||
\(747\) | −7.35408 | + | 5.76469i | −0.269072 | + | 0.210919i | ||||
\(748\) | −6.44918 | + | 2.64141i | −0.235805 | + | 0.0965795i | ||||
\(749\) | 67.1851i | 2.45489i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | − | 28.3527i | − | 1.03460i | −0.855803 | − | 0.517302i | \(-0.826936\pi\) | ||
0.855803 | − | 0.517302i | \(-0.173064\pi\) | |||||||
\(752\) | 17.4792 | + | 17.7588i | 0.637402 | + | 0.647598i | ||||
\(753\) | −0.951801 | + | 1.95547i | −0.0346856 | + | 0.0712612i | ||||
\(754\) | −20.8062 | + | 4.09573i | −0.757719 | + | 0.149158i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 30.5561 | − | 20.9307i | 1.11132 | − | 0.761241i | ||||
\(757\) | − | 8.91093i | − | 0.323873i | −0.986801 | − | 0.161937i | \(-0.948226\pi\) | ||
0.986801 | − | 0.161937i | \(-0.0517740\pi\) | |||||||
\(758\) | −5.81918 | − | 29.5614i | −0.211362 | − | 1.07372i | ||||
\(759\) | −7.15902 | − | 3.48457i | −0.259856 | − | 0.126482i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 3.06569i | 0.111131i | 0.998455 | + | 0.0555656i | \(0.0176962\pi\) | ||||
−0.998455 | + | 0.0555656i | \(0.982304\pi\) | |||||||
\(762\) | 10.1635 | − | 38.4194i | 0.368185 | − | 1.39179i | ||||
\(763\) | 31.0117 | 1.12270 | ||||||||
\(764\) | −21.0366 | + | 8.61603i | −0.761078 | + | 0.311717i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 3.40312 | + | 17.2878i | 0.122960 | + | 0.624634i | ||||
\(767\) | 0 | 0 | ||||||||
\(768\) | −24.7223 | − | 12.5224i | −0.892088 | − | 0.451862i | ||||
\(769\) | 39.8062 | 1.43545 | 0.717725 | − | 0.696327i | \(-0.245183\pi\) | ||||
0.717725 | + | 0.696327i | \(0.245183\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −8.41464 | + | 17.2878i | −0.303046 | + | 0.622606i | ||||
\(772\) | −4.40131 | − | 10.7461i | −0.158407 | − | 0.386760i | ||||
\(773\) | −5.55034 | −0.199632 | −0.0998159 | − | 0.995006i | \(-0.531825\pi\) | ||||
−0.0998159 | + | 0.995006i | \(0.531825\pi\) | |||||||
\(774\) | −1.70871 | − | 1.47344i | −0.0614182 | − | 0.0529616i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 12.6220 | + | 19.1357i | 0.453102 | + | 0.686930i | ||||
\(777\) | 29.9892 | + | 14.5969i | 1.07586 | + | 0.523660i | ||||
\(778\) | 5.45308 | + | 27.7016i | 0.195502 | + | 0.993149i | ||||
\(779\) | 52.1839 | 1.86968 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −47.8219 | −1.71120 | ||||||||
\(782\) | 0.247171 | + | 1.25562i | 0.00883881 | + | 0.0449010i | ||||
\(783\) | −6.06424 | − | 28.1956i | −0.216718 | − | 1.00763i | ||||
\(784\) | 16.2539 | − | 15.9980i | 0.580497 | − | 0.571357i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 12.3916 | − | 46.8420i | 0.441994 | − | 1.67080i | ||||
\(787\) | −14.7875 | −0.527118 | −0.263559 | − | 0.964643i | \(-0.584896\pi\) | ||||
−0.263559 | + | 0.964643i | \(0.584896\pi\) | |||||||
\(788\) | 17.4792 | − | 7.15902i | 0.622672 | − | 0.255030i | ||||
\(789\) | 27.9109 | + | 13.5853i | 0.993656 | + | 0.483650i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 56.3913 | 2.00504 | ||||||||
\(792\) | −33.8557 | − | 11.3272i | −1.20301 | − | 0.402495i | ||||
\(793\) | 1.89531i | 0.0673046i | ||||||||
\(794\) | −7.89694 | − | 40.1164i | −0.280252 | − | 1.42368i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −11.8953 | − | 29.0432i | −0.421618 | − | 1.02941i | ||||
\(797\) | −4.96929 | −0.176021 | −0.0880107 | − | 0.996120i | \(-0.528051\pi\) | ||||
−0.0880107 | + | 0.996120i | \(0.528051\pi\) | |||||||
\(798\) | −42.8725 | − | 11.3415i | −1.51767 | − | 0.401485i | ||||
\(799\) | − | 5.15934i | − | 0.182524i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −11.1492 | + | 8.73961i | −0.393938 | + | 0.308799i | ||||
\(802\) | 8.41769 | + | 42.7617i | 0.297239 | + | 1.50997i | ||||
\(803\) | 32.4030i | 1.14348i | ||||||||
\(804\) | 0.455480 | − | 7.07938i | 0.0160635 | − | 0.249670i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −24.7262 | + | 4.86738i | −0.870944 | + | 0.171446i | ||||
\(807\) | −23.3521 | − | 11.3663i | −0.822031 | − | 0.400114i | ||||
\(808\) | −11.2236 | − | 17.0156i | −0.394844 | − | 0.598607i | ||||
\(809\) | − | 0.581045i | − | 0.0204284i | −0.999948 | − | 0.0102142i | \(-0.996749\pi\) | ||
0.999948 | − | 0.0102142i | \(-0.00325134\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 15.8511i | − | 0.556608i | −0.960493 | − | 0.278304i | \(-0.910228\pi\) | ||
0.960493 | − | 0.278304i | \(-0.0897723\pi\) | |||||||
\(812\) | −14.9946 | − | 36.6103i | −0.526207 | − | 1.28477i | ||||
\(813\) | 38.0241 | + | 18.5078i | 1.33357 | + | 0.649097i | ||||
\(814\) | −6.20937 | − | 31.5435i | −0.217638 | − | 1.10560i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 1.82939 | + | 5.43861i | 0.0640414 | + | 0.190390i | ||||
\(817\) | 2.70156i | 0.0945157i | ||||||||
\(818\) | 37.7553 | − | 7.43217i | 1.32008 | − | 0.259860i | ||||
\(819\) | −22.7327 | + | 17.8196i | −0.794344 | + | 0.622668i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 20.5449i | − | 0.717023i | −0.933525 | − | 0.358511i | \(-0.883284\pi\) | ||
0.933525 | − | 0.358511i | \(-0.116716\pi\) | |||||||
\(822\) | 3.99578 | − | 15.1046i | 0.139369 | − | 0.526834i | ||||
\(823\) | −37.0760 | −1.29239 | −0.646193 | − | 0.763174i | \(-0.723640\pi\) | ||||
−0.646193 | + | 0.763174i | \(0.723640\pi\) | |||||||
\(824\) | −9.67027 | + | 6.37855i | −0.336880 | + | 0.222207i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 14.8071i | − | 0.514895i | −0.966292 | − | 0.257447i | \(-0.917119\pi\) | ||
0.966292 | − | 0.257447i | \(-0.0828814\pi\) | |||||||
\(828\) | −3.24156 | + | 5.69801i | −0.112652 | + | 0.198020i | ||||
\(829\) | −44.8062 | −1.55619 | −0.778093 | − | 0.628150i | \(-0.783813\pi\) | ||||
−0.778093 | + | 0.628150i | \(0.783813\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 43.7693 | + | 21.3042i | 1.51834 | + | 0.739034i | ||||
\(832\) | 19.8675 | + | 8.50781i | 0.688781 | + | 0.294955i | ||||
\(833\) | −4.72212 | −0.163612 | ||||||||
\(834\) | −3.59008 | − | 0.949721i | −0.124314 | − | 0.0328861i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 16.2015 | + | 39.5570i | 0.560340 | + | 1.36811i | ||||
\(837\) | −7.20677 | − | 33.5078i | −0.249102 | − | 1.15820i | ||||
\(838\) | −14.0295 | + | 2.76172i | −0.484640 | + | 0.0954019i | ||||
\(839\) | 25.6844 | 0.886723 | 0.443362 | − | 0.896343i | \(-0.353786\pi\) | ||||
0.443362 | + | 0.896343i | \(0.353786\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.80625 | −0.0622844 | ||||||||
\(842\) | 33.5925 | − | 6.61273i | 1.15768 | − | 0.227890i | ||||
\(843\) | 11.2236 | + | 5.46295i | 0.386561 | + | 0.188154i | ||||
\(844\) | −10.7461 | − | 26.2373i | −0.369896 | − | 0.903125i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 17.2596 | − | 20.0155i | 0.593397 | − | 0.688146i | ||||
\(847\) | −23.8839 | −0.820659 | ||||||||
\(848\) | −15.8228 | + | 15.5737i | −0.543357 | + | 0.534802i | ||||
\(849\) | 4.65703 | − | 9.56783i | 0.159829 | − | 0.328367i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −5.90340 | −0.202366 | ||||||||
\(852\) | −2.52807 | + | 39.2929i | −0.0866102 | + | 1.34615i | ||||
\(853\) | − | 37.2984i | − | 1.27707i | −0.769591 | − | 0.638537i | \(-0.779540\pi\) | ||
0.769591 | − | 0.638537i | \(-0.220460\pi\) | |||||||
\(854\) | −3.46940 | + | 0.682954i | −0.118720 | + | 0.0233702i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −29.3586 | − | 44.5094i | −1.00346 | − | 1.52130i | ||||
\(857\) | 12.5099 | 0.427331 | 0.213666 | − | 0.976907i | \(-0.431460\pi\) | ||||
0.213666 | + | 0.976907i | \(0.431460\pi\) | |||||||
\(858\) | 26.9159 | + | 7.12033i | 0.918892 | + | 0.243084i | ||||
\(859\) | 32.1547i | 1.09710i | 0.836117 | + | 0.548552i | \(0.184821\pi\) | ||||
−0.836117 | + | 0.548552i | \(0.815179\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 57.0156 | + | 27.7517i | 1.94309 | + | 0.945775i | ||||
\(862\) | 27.4478 | − | 5.40312i | 0.934875 | − | 0.184031i | ||||
\(863\) | − | 29.6143i | − | 1.00808i | −0.863680 | − | 0.504041i | \(-0.831846\pi\) | ||
0.863680 | − | 0.504041i | \(-0.168154\pi\) | |||||||
\(864\) | −11.0968 | + | 27.2188i | −0.377521 | + | 0.926001i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 8.52476 | + | 43.3056i | 0.289683 | + | 1.47159i | ||||
\(867\) | −12.3665 | + | 25.4070i | −0.419990 | + | 0.862866i | ||||
\(868\) | −17.8196 | − | 43.5078i | −0.604838 | − | 1.47675i | ||||
\(869\) | − | 29.9892i | − | 1.01731i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 5.53243i | 0.187459i | ||||||||
\(872\) | −20.5449 | + | 13.5515i | −0.695739 | + | 0.458912i | ||||
\(873\) | 19.1357 | − | 15.0000i | 0.647644 | − | 0.507673i | ||||
\(874\) | 7.70156 | − | 1.51606i | 0.260509 | − | 0.0512815i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 26.6239 | + | 1.71296i | 0.899540 | + | 0.0578755i | ||||
\(877\) | − | 48.9109i | − | 1.65160i | −0.563959 | − | 0.825802i | \(-0.690723\pi\) | ||
0.563959 | − | 0.825802i | \(-0.309277\pi\) | |||||||
\(878\) | 5.98612 | + | 30.4094i | 0.202022 | + | 1.02627i | ||||
\(879\) | −14.3180 | + | 29.4163i | −0.482936 | + | 0.992187i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 26.6763i | − | 0.898747i | −0.893344 | − | 0.449374i | \(-0.851647\pi\) | ||
0.893344 | − | 0.449374i | \(-0.148353\pi\) | |||||||
\(882\) | −18.3193 | − | 15.7970i | −0.616843 | − | 0.531911i | ||||
\(883\) | 25.2412 | 0.849435 | 0.424717 | − | 0.905326i | \(-0.360374\pi\) | ||||
0.424717 | + | 0.905326i | \(0.360374\pi\) | |||||||
\(884\) | −1.69607 | − | 4.14108i | −0.0570451 | − | 0.139280i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −3.06015 | − | 15.5455i | −0.102808 | − | 0.522262i | ||||
\(887\) | − | 24.9179i | − | 0.836660i | −0.908295 | − | 0.418330i | \(-0.862616\pi\) | ||
0.908295 | − | 0.418330i | \(-0.137384\pi\) | |||||||
\(888\) | −26.2460 | + | 3.43442i | −0.880760 | + | 0.115251i | ||||
\(889\) | −57.8219 | −1.93928 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −9.04246 | + | 36.7704i | −0.302934 | + | 1.23185i | ||||
\(892\) | 29.0432 | − | 11.8953i | 0.972438 | − | 0.398285i | ||||
\(893\) | −31.6456 | −1.05898 | ||||||||
\(894\) | −3.92248 | − | 1.03765i | −0.131187 | − | 0.0347044i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −8.41464 | + | 39.4334i | −0.281114 | + | 1.31738i | ||||
\(897\) | 2.23748 | − | 4.59688i | 0.0747071 | − | 0.153485i | ||||
\(898\) | −5.22685 | − | 26.5523i | −0.174422 | − | 0.886063i | ||||
\(899\) | −36.6103 | −1.22102 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 4.59688 | 0.153144 | ||||||||
\(902\) | −11.8053 | − | 59.9708i | −0.393074 | − | 1.99681i | ||||
\(903\) | −1.43670 | + | 2.95170i | −0.0478105 | + | 0.0982264i | ||||
\(904\) | −37.3586 | + | 24.6419i | −1.24253 | + | 0.819577i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −10.9581 | − | 2.89887i | −0.364060 | − | 0.0963086i | ||||
\(907\) | −10.1600 | −0.337356 | −0.168678 | − | 0.985671i | \(-0.553950\pi\) | ||||
−0.168678 | + | 0.985671i | \(0.553950\pi\) | |||||||
\(908\) | 8.86320 | + | 21.6401i | 0.294136 | + | 0.718152i | ||||
\(909\) | −17.0156 | + | 13.3382i | −0.564373 | + | 0.442399i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 56.3913 | 1.86833 | 0.934163 | − | 0.356847i | \(-0.116148\pi\) | ||||
0.934163 | + | 0.356847i | \(0.116148\pi\) | |||||||
\(912\) | 33.3586 | − | 11.2208i | 1.10461 | − | 0.371559i | ||||
\(913\) | − | 13.1047i | − | 0.433702i | ||||||
\(914\) | −4.61491 | − | 23.4437i | −0.152648 | − | 0.775448i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −16.1047 | + | 6.59605i | −0.532114 | + | 0.217939i | ||||
\(917\) | −70.4980 | −2.32805 | ||||||||
\(918\) | 5.59084 | − | 2.40484i | 0.184525 | − | 0.0793717i | ||||
\(919\) | − | 0.531805i | − | 0.0175426i | −0.999962 | − | 0.00877132i | \(-0.997208\pi\) | ||
0.999962 | − | 0.00877132i | \(-0.00279203\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −15.4633 | + | 31.7692i | −0.509532 | + | 1.04683i | ||||
\(922\) | −1.96851 | − | 10.0000i | −0.0648294 | − | 0.329332i | ||||
\(923\) | − | 30.7069i | − | 1.01073i | ||||||
\(924\) | −3.33505 | + | 51.8356i | −0.109715 | + | 1.70527i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 9.89049 | − | 1.94695i | 0.325022 | − | 0.0639809i | ||||
\(927\) | 7.58030 | + | 9.67027i | 0.248970 | + | 0.317613i | ||||
\(928\) | 25.9317 | + | 17.7016i | 0.851251 | + | 0.581082i | ||||
\(929\) | − | 0.581045i | − | 0.0190635i | −0.999955 | − | 0.00953173i | \(-0.996966\pi\) | ||
0.999955 | − | 0.00953173i | \(-0.00303409\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 28.9639i | 0.949252i | ||||||||
\(932\) | 27.7517 | − | 11.3663i | 0.909037 | − | 0.372317i | ||||
\(933\) | −12.7571 | + | 26.2094i | −0.417649 | + | 0.858056i | ||||
\(934\) | 0.209373 | + | 1.06361i | 0.00685088 | + | 0.0348024i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 7.27332 | − | 21.7391i | 0.237736 | − | 0.710563i | ||||
\(937\) | 16.6125i | 0.542707i | 0.962480 | + | 0.271353i | \(0.0874712\pi\) | ||||
−0.962480 | + | 0.271353i | \(0.912529\pi\) | |||||||
\(938\) | −10.1272 | + | 1.99355i | −0.330665 | + | 0.0650917i | ||||
\(939\) | 35.3547 | + | 17.2085i | 1.15376 | + | 0.561577i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 47.2212i | 1.53937i | 0.638425 | + | 0.769684i | \(0.279586\pi\) | ||||
−0.638425 | + | 0.769684i | \(0.720414\pi\) | |||||||
\(942\) | 19.1922 | + | 5.07710i | 0.625314 | + | 0.165421i | ||||
\(943\) | −11.2236 | −0.365490 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 3.10469 | − | 0.611161i | 0.100942 | − | 0.0198705i | ||||
\(947\) | 38.7955i | 1.26068i | 0.776318 | + | 0.630341i | \(0.217085\pi\) | ||||
−0.776318 | + | 0.630341i | \(0.782915\pi\) | |||||||
\(948\) | −24.6406 | − | 1.58536i | −0.800291 | − | 0.0514899i | ||||
\(949\) | −20.8062 | −0.675399 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 22.7327 | − | 46.7041i | 0.737158 | − | 1.51448i | ||||
\(952\) | 6.96914 | − | 4.59688i | 0.225871 | − | 0.148986i | ||||
\(953\) | −21.9542 | −0.711166 | −0.355583 | − | 0.934645i | \(-0.615718\pi\) | ||||
−0.355583 | + | 0.934645i | \(0.615718\pi\) | |||||||
\(954\) | 17.8334 | + | 15.3780i | 0.577378 | + | 0.497880i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 10.1107 | − | 4.14108i | 0.327004 | − | 0.133932i | ||||
\(957\) | 36.3677 | + | 17.7016i | 1.17560 | + | 0.572210i | ||||
\(958\) | −58.3802 | + | 11.4922i | −1.88618 | + | 0.371296i | ||||
\(959\) | −22.7327 | −0.734077 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −12.5078 | −0.403478 | ||||||||
\(962\) | 20.2544 | − | 3.98710i | 0.653028 | − | 0.128549i | ||||
\(963\) | −44.5094 | + | 34.8899i | −1.43429 | + | 1.12431i | ||||
\(964\) | 12.9555 | − | 5.30621i | 0.417268 | − | 0.170902i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 9.22089 | + | 2.43930i | 0.296677 | + | 0.0784832i | ||||
\(967\) | −47.7677 | −1.53611 | −0.768053 | − | 0.640386i | \(-0.778774\pi\) | ||||
−0.768053 | + | 0.640386i | \(0.778774\pi\) | |||||||
\(968\) | 15.8228 | − | 10.4368i | 0.508564 | − | 0.335451i | ||||
\(969\) | −6.55234 | − | 3.18928i | −0.210492 | − | 0.102454i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −21.4771 | −0.689232 | −0.344616 | − | 0.938744i | \(-0.611991\pi\) | ||||
−0.344616 | + | 0.938744i | \(0.611991\pi\) | |||||||
\(972\) | 29.7344 | + | 9.37359i | 0.953732 | + | 0.300658i | ||||
\(973\) | 5.40312i | 0.173216i | ||||||||
\(974\) | 47.2387 | − | 9.29898i | 1.51363 | − | 0.297959i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 2.00000 | − | 1.96851i | 0.0640184 | − | 0.0630105i | ||||
\(977\) | −28.5799 | −0.914352 | −0.457176 | − | 0.889376i | \(-0.651139\pi\) | ||||
−0.457176 | + | 0.889376i | \(0.651139\pi\) | |||||||
\(978\) | −3.18231 | + | 12.0296i | −0.101759 | + | 0.384663i | ||||
\(979\) | − | 19.8675i | − | 0.634968i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 16.1047 | + | 20.5449i | 0.514183 | + | 0.655949i | ||||
\(982\) | −23.3521 | + | 4.59688i | −0.745194 | + | 0.146692i | ||||
\(983\) | − | 57.9243i | − | 1.84750i | −0.382998 | − | 0.923749i | \(-0.625108\pi\) | ||
0.382998 | − | 0.923749i | \(-0.374892\pi\) | |||||||
\(984\) | −49.8992 | + | 6.52954i | −1.59073 | + | 0.208154i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −1.25562 | − | 6.37855i | −0.0399872 | − | 0.203135i | ||||
\(987\) | −34.5756 | − | 16.8293i | −1.10055 | − | 0.535682i | ||||
\(988\) | −25.3999 | + | 10.4031i | −0.808079 | + | 0.330967i | ||||
\(989\) | − | 0.581045i | − | 0.0184761i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 40.2668i | 1.27912i | 0.768743 | + | 0.639558i | \(0.220883\pi\) | ||||
−0.768743 | + | 0.639558i | \(0.779117\pi\) | |||||||
\(992\) | 30.8174 | + | 21.0366i | 0.978453 | + | 0.667913i | ||||
\(993\) | 46.7638 | + | 22.7617i | 1.48400 | + | 0.722321i | ||||
\(994\) | 56.2094 | − | 11.0649i | 1.78285 | − | 0.350956i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −10.7675 | − | 0.692770i | −0.341181 | − | 0.0219512i | ||||
\(997\) | 34.5969i | 1.09569i | 0.836579 | + | 0.547847i | \(0.184552\pi\) | ||||
−0.836579 | + | 0.547847i | \(0.815448\pi\) | |||||||
\(998\) | −6.27664 | − | 31.8853i | −0.198684 | − | 1.00931i | ||||
\(999\) | 5.90340 | + | 27.4478i | 0.186775 | + | 0.868410i |
(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 | 300.2.h.c.299.14 | 16 | ||
3.2 | odd | 2 | inner | 300.2.h.c.299.4 | 16 | ||
4.3 | odd | 2 | inner | 300.2.h.c.299.15 | 16 | ||
5.2 | odd | 4 | 300.2.e.e.251.6 | yes | 8 | ||
5.3 | odd | 4 | 300.2.e.d.251.3 | ✓ | 8 | ||
5.4 | even | 2 | inner | 300.2.h.c.299.3 | 16 | ||
12.11 | even | 2 | inner | 300.2.h.c.299.1 | 16 | ||
15.2 | even | 4 | 300.2.e.e.251.3 | yes | 8 | ||
15.8 | even | 4 | 300.2.e.d.251.6 | yes | 8 | ||
15.14 | odd | 2 | inner | 300.2.h.c.299.13 | 16 | ||
20.3 | even | 4 | 300.2.e.d.251.5 | yes | 8 | ||
20.7 | even | 4 | 300.2.e.e.251.4 | yes | 8 | ||
20.19 | odd | 2 | inner | 300.2.h.c.299.2 | 16 | ||
60.23 | odd | 4 | 300.2.e.d.251.4 | yes | 8 | ||
60.47 | odd | 4 | 300.2.e.e.251.5 | yes | 8 | ||
60.59 | even | 2 | inner | 300.2.h.c.299.16 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
300.2.e.d.251.3 | ✓ | 8 | 5.3 | odd | 4 | ||
300.2.e.d.251.4 | yes | 8 | 60.23 | odd | 4 | ||
300.2.e.d.251.5 | yes | 8 | 20.3 | even | 4 | ||
300.2.e.d.251.6 | yes | 8 | 15.8 | even | 4 | ||
300.2.e.e.251.3 | yes | 8 | 15.2 | even | 4 | ||
300.2.e.e.251.4 | yes | 8 | 20.7 | even | 4 | ||
300.2.e.e.251.5 | yes | 8 | 60.47 | odd | 4 | ||
300.2.e.e.251.6 | yes | 8 | 5.2 | odd | 4 | ||
300.2.h.c.299.1 | 16 | 12.11 | even | 2 | inner | ||
300.2.h.c.299.2 | 16 | 20.19 | odd | 2 | inner | ||
300.2.h.c.299.3 | 16 | 5.4 | even | 2 | inner | ||
300.2.h.c.299.4 | 16 | 3.2 | odd | 2 | inner | ||
300.2.h.c.299.13 | 16 | 15.14 | odd | 2 | inner | ||
300.2.h.c.299.14 | 16 | 1.1 | even | 1 | trivial | ||
300.2.h.c.299.15 | 16 | 4.3 | odd | 2 | inner | ||
300.2.h.c.299.16 | 16 | 60.59 | even | 2 | inner |