Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [300,2,Mod(251,300)]
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, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("300.251");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 300 = 2^{2} \cdot 3 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 300.e (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(2.39551206064\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.4521217600.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + x^{6} - 2x^{4} + 4x^{2} + 16 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 251.4 | ||
Root | \(0.273147 + 1.38758i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 300.251 |
Dual form | 300.2.e.d.251.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/300\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(151\) | \(277\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.273147 | + | 1.38758i | −0.193144 | + | 0.981170i | ||||
\(3\) | 1.55737 | − | 0.758030i | 0.899146 | − | 0.437649i | ||||
\(4\) | −1.85078 | − | 0.758030i | −0.925391 | − | 0.379015i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0.626440 | + | 2.36803i | 0.255743 | + | 0.966745i | ||||
\(7\) | − | 3.56393i | − | 1.34704i | −0.739170 | − | 0.673519i | \(-0.764782\pi\) | ||
0.739170 | − | 0.673519i | \(-0.235218\pi\) | |||||||
\(8\) | 1.55737 | − | 2.36106i | 0.550612 | − | 0.834761i | ||||
\(9\) | 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 | \(0.281298\pi\) | |||||||
\(12\) | −3.45695 | + | 0.222417i | −0.997937 | + | 0.0642063i | ||||
\(13\) | −2.70156 | −0.749279 | −0.374639 | − | 0.927171i | \(-0.622233\pi\) | ||||
−0.374639 | + | 0.927171i | \(0.622233\pi\) | |||||||
\(14\) | 4.94525 | + | 0.973477i | 1.32167 | + | 0.260173i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 2.85078 | + | 2.80590i | 0.712695 | + | 0.701474i | ||||
\(17\) | − | 0.828216i | − | 0.200872i | −0.994944 | − | 0.100436i | \(-0.967976\pi\) | ||
0.994944 | − | 0.100436i | \(-0.0320237\pi\) | |||||||
\(18\) | 2.77064 | + | 3.21303i | 0.653045 | + | 0.757319i | ||||
\(19\) | 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 | ||||
\(22\) | −1.14922 | + | 5.83802i | −0.245014 | + | 1.24467i | ||||
\(23\) | 1.09259 | 0.227821 | 0.113910 | − | 0.993491i | \(-0.463662\pi\) | ||||
0.113910 | + | 0.993491i | \(0.463662\pi\) | |||||||
\(24\) | 0.635635 | − | 4.85757i | 0.129749 | − | 0.991547i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0.737925 | − | 3.74865i | 0.144719 | − | 0.735170i | ||||
\(27\) | 1.09259 | − | 5.07999i | 0.210269 | − | 0.977644i | ||||
\(28\) | −2.70156 | + | 6.59605i | −0.510547 | + | 1.24654i | ||||
\(29\) | 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 | \(-0.798203\pi\) | ||
0.805686 | − | 0.592342i | \(-0.201797\pi\) | |||||||
\(32\) | −4.67210 | + | 3.18928i | −0.825918 | + | 0.563790i | ||||
\(33\) | 6.55234 | − | 3.18928i | 1.14062 | − | 0.555182i | ||||
\(34\) | 1.14922 | + | 0.226225i | 0.197089 | + | 0.0387972i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −5.21515 | + | 2.96686i | −0.869191 | + | 0.494477i | ||||
\(37\) | −5.40312 | −0.888268 | −0.444134 | − | 0.895960i | \(-0.646489\pi\) | ||||
−0.444134 | + | 0.895960i | \(0.646489\pi\) | |||||||
\(38\) | −7.04891 | − | 1.38758i | −1.14348 | − | 0.225096i | ||||
\(39\) | −4.20732 | + | 2.04787i | −0.673711 | + | 0.327921i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 10.2725i | 1.60429i | 0.597130 | + | 0.802144i | \(0.296308\pi\) | ||||
−0.597130 | + | 0.802144i | \(0.703692\pi\) | |||||||
\(42\) | 8.43949 | − | 2.23259i | 1.30224 | − | 0.344495i | ||||
\(43\) | − | 0.531805i | − | 0.0810995i | −0.999178 | − | 0.0405498i | \(-0.987089\pi\) | ||
0.999178 | − | 0.0405498i | \(-0.0129109\pi\) | |||||||
\(44\) | −7.78683 | − | 3.18928i | −1.17391 | − | 0.480802i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −0.298438 | + | 1.51606i | −0.0440023 | + | 0.223531i | ||||
\(47\) | 6.22947 | 0.908661 | 0.454331 | − | 0.890833i | \(-0.349879\pi\) | ||||
0.454331 | + | 0.890833i | \(0.349879\pi\) | |||||||
\(48\) | 6.56666 | + | 2.20883i | 0.947816 | + | 0.318817i | ||||
\(49\) | −5.70156 | −0.814509 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.627812 | − | 1.28984i | −0.0879113 | − | 0.180613i | ||||
\(52\) | 5.00000 | + | 2.04787i | 0.693375 | + | 0.283988i | ||||
\(53\) | 5.55034i | 0.762398i | 0.924493 | + | 0.381199i | \(0.124489\pi\) | ||||
−0.924493 | + | 0.381199i | \(0.875511\pi\) | |||||||
\(54\) | 6.75047 | + | 2.90364i | 0.918623 | + | 0.395136i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −8.41464 | − | 5.55034i | −1.12445 | − | 0.741695i | ||||
\(57\) | 3.85078 | + | 7.91140i | 0.510048 | + | 1.04789i | ||||
\(58\) | −7.70156 | − | 1.51606i | −1.01126 | − | 0.199068i | ||||
\(59\) | 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 | \(0.485699\pi\) | |||||||
\(62\) | 9.15257 | + | 1.80169i | 1.16238 | + | 0.228815i | ||||
\(63\) | −8.41464 | − | 6.59605i | −1.06015 | − | 0.831024i | ||||
\(64\) | −3.14922 | − | 7.35408i | −0.393652 | − | 0.919259i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 2.63564 | + | 9.96307i | 0.324424 | + | 1.22637i | ||||
\(67\) | 2.04787i | 0.250187i | 0.992145 | + | 0.125093i | \(0.0399230\pi\) | ||||
−0.992145 | + | 0.125093i | \(0.960077\pi\) | |||||||
\(68\) | −0.627812 | + | 1.53285i | −0.0761334 | + | 0.185885i | ||||
\(69\) | 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 | \(0.735627\pi\) | |||||||
\(72\) | −2.69226 | − | 8.04684i | −0.317286 | − | 0.948330i | ||||
\(73\) | −7.70156 | −0.901400 | −0.450700 | − | 0.892676i | \(-0.648826\pi\) | ||||
−0.450700 | + | 0.892676i | \(0.648826\pi\) | |||||||
\(74\) | 1.47585 | − | 7.49729i | 0.171564 | − | 0.871542i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 3.85078 | − | 9.40194i | 0.441715 | − | 1.07848i | ||||
\(77\) | − | 14.9946i | − | 1.70879i | ||||||
\(78\) | −1.69237 | − | 6.39738i | −0.191623 | − | 0.724361i | ||||
\(79\) | − | 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 | ||||
\(82\) | −14.2539 | − | 2.80590i | −1.57408 | − | 0.309859i | ||||
\(83\) | 3.11473 | 0.341886 | 0.170943 | − | 0.985281i | \(-0.445319\pi\) | ||||
0.170943 | + | 0.985281i | \(0.445319\pi\) | |||||||
\(84\) | 0.792678 | + | 12.3203i | 0.0864882 | + | 1.34426i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0.737925 | + | 0.145261i | 0.0795724 | + | 0.0156639i | ||||
\(87\) | 4.20732 | + | 8.64391i | 0.451072 | + | 0.926724i | ||||
\(88\) | 6.55234 | − | 9.93375i | 0.698482 | − | 1.05894i | ||||
\(89\) | − | 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 | ||||||||
\(92\) | −2.02214 | − | 0.828216i | −0.210823 | − | 0.0863474i | ||||
\(93\) | −5.00000 | − | 10.2725i | −0.518476 | − | 1.06520i | ||||
\(94\) | −1.70156 | + | 8.64391i | −0.175503 | + | 0.891551i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −4.85860 | + | 8.50846i | −0.495879 | + | 0.868392i | ||||
\(97\) | 8.10469 | 0.822906 | 0.411453 | − | 0.911431i | \(-0.365021\pi\) | ||||
0.411453 | + | 0.911431i | \(0.365021\pi\) | |||||||
\(98\) | 1.55737 | − | 7.91140i | 0.157318 | − | 0.799172i | ||||
\(99\) | 7.78683 | − | 9.93375i | 0.782606 | − | 0.998379i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 7.20677i | 0.717100i | 0.933510 | + | 0.358550i | \(0.116729\pi\) | ||||
−0.933510 | + | 0.358550i | \(0.883271\pi\) | |||||||
\(102\) | 1.96124 | − | 0.518827i | 0.194192 | − | 0.0513716i | ||||
\(103\) | 4.09573i | 0.403564i | 0.979430 | + | 0.201782i | \(0.0646733\pi\) | ||||
−0.979430 | + | 0.201782i | \(0.935327\pi\) | |||||||
\(104\) | −4.20732 | + | 6.37855i | −0.412562 | + | 0.625469i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −7.70156 | − | 1.51606i | −0.748042 | − | 0.147253i | ||||
\(107\) | −18.8514 | −1.82244 | −0.911218 | − | 0.411924i | \(-0.864857\pi\) | ||||
−0.911218 | + | 0.411924i | \(0.864857\pi\) | |||||||
\(108\) | −5.87292 | + | 8.57372i | −0.565122 | + | 0.825007i | ||||
\(109\) | 8.70156 | 0.833458 | 0.416729 | − | 0.909031i | \(-0.363176\pi\) | ||||
0.416729 | + | 0.909031i | \(0.363176\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −8.41464 | + | 4.09573i | −0.798683 | + | 0.388750i | ||||
\(112\) | 10.0000 | − | 10.1600i | 0.944911 | − | 0.960027i | ||||
\(113\) | 15.8228i | 1.48848i | 0.667910 | + | 0.744242i | \(0.267189\pi\) | ||||
−0.667910 | + | 0.744242i | \(0.732811\pi\) | |||||||
\(114\) | −12.0296 | + | 3.18231i | −1.12667 | + | 0.298050i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 4.20732 | − | 10.2725i | 0.390640 | − | 0.953774i | ||||
\(117\) | −5.00000 | + | 6.37855i | −0.462250 | + | 0.589697i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −2.95170 | −0.270582 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 6.70156 | 0.609233 | ||||||||
\(122\) | −0.191630 | + | 0.973477i | −0.0173493 | + | 0.0881344i | ||||
\(123\) | 7.78683 | + | 15.9980i | 0.702115 | + | 1.44249i | ||||
\(124\) | −5.00000 | + | 12.2078i | −0.449013 | + | 1.09630i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 11.4510 | − | 9.87434i | 1.02014 | − | 0.879676i | ||||
\(127\) | 16.2242i | 1.43967i | 0.694147 | + | 0.719833i | \(0.255782\pi\) | ||||
−0.694147 | + | 0.719833i | \(0.744218\pi\) | |||||||
\(128\) | 11.0646 | − | 2.36106i | 0.977982 | − | 0.208690i | ||||
\(129\) | −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 | \(0.167865\pi\) | |||||||
\(132\) | −14.5445 | + | 0.935780i | −1.26594 | + | 0.0814492i | ||||
\(133\) | 18.1047 | 1.56988 | ||||||||
\(134\) | −2.84159 | − | 0.559369i | −0.245476 | − | 0.0483221i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −1.95547 | − | 1.28984i | −0.167680 | − | 0.110602i | ||||
\(137\) | 6.37855i | 0.544957i | 0.962162 | + | 0.272478i | \(0.0878433\pi\) | ||||
−0.962162 | + | 0.272478i | \(0.912157\pi\) | |||||||
\(138\) | 0.684442 | + | 2.58729i | 0.0582636 | + | 0.220244i | ||||
\(139\) | − | 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 | ||||
\(142\) | 3.10469 | − | 15.7718i | 0.260539 | − | 1.32354i | ||||
\(143\) | −11.3663 | −0.950501 | ||||||||
\(144\) | 11.9011 | − | 1.53777i | 0.991755 | − | 0.128148i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 2.10366 | − | 10.6866i | 0.174100 | − | 0.884427i | ||||
\(147\) | −8.87942 | + | 4.32196i | −0.732362 | + | 0.356469i | ||||
\(148\) | 10.0000 | + | 4.09573i | 0.821995 | + | 0.336667i | ||||
\(149\) | − | 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 | \(0.0602951\pi\) | ||||
−0.982113 | + | 0.188292i | \(0.939705\pi\) | |||||||
\(152\) | 11.9942 | + | 7.91140i | 0.972854 | + | 0.641699i | ||||
\(153\) | −1.95547 | − | 1.53285i | −0.158090 | − | 0.123923i | ||||
\(154\) | 20.8062 | + | 4.09573i | 1.67662 | + | 0.330043i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 9.33918 | − | 0.600873i | 0.747732 | − | 0.0481084i | ||||
\(157\) | 8.10469 | 0.646824 | 0.323412 | − | 0.946258i | \(-0.395170\pi\) | ||||
0.323412 | + | 0.946258i | \(0.395170\pi\) | |||||||
\(158\) | 9.89049 | + | 1.94695i | 0.786845 | + | 0.154891i | ||||
\(159\) | 4.20732 | + | 8.64391i | 0.333662 | + | 0.685507i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 3.89391i | − | 0.306883i | ||||||
\(162\) | 12.7140 | − | 0.595020i | 0.998907 | − | 0.0467492i | ||||
\(163\) | 5.07999i | 0.397895i | 0.980010 | + | 0.198948i | \(0.0637523\pi\) | ||||
−0.980010 | + | 0.198948i | \(0.936248\pi\) | |||||||
\(164\) | 7.78683 | − | 19.0121i | 0.608049 | − | 1.48459i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −0.850781 | + | 4.32196i | −0.0660334 | + | 0.335449i | ||||
\(167\) | −3.27777 | −0.253641 | −0.126821 | − | 0.991926i | \(-0.540477\pi\) | ||||
−0.126821 | + | 0.991926i | \(0.540477\pi\) | |||||||
\(168\) | −17.3120 | − | 2.26536i | −1.33565 | − | 0.174776i | ||||
\(169\) | −5.70156 | −0.438582 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 11.9942 | + | 9.40194i | 0.917216 | + | 0.718984i | ||||
\(172\) | −0.403124 | + | 0.984255i | −0.0307379 | + | 0.0750487i | ||||
\(173\) | − | 14.9946i | − | 1.14002i | −0.821639 | − | 0.570008i | \(-0.806940\pi\) | ||
0.821639 | − | 0.570008i | \(-0.193060\pi\) | |||||||
\(174\) | −13.1434 | + | 3.47695i | −0.996397 | + | 0.263587i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 11.9942 | + | 11.8053i | 0.904093 | + | 0.889858i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 6.55234 | + | 1.28984i | 0.491119 | + | 0.0966772i | ||||
\(179\) | 15.5737 | 1.16403 | 0.582015 | − | 0.813178i | \(-0.302264\pi\) | ||||
0.582015 | + | 0.813178i | \(0.302264\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −21.5078 | −1.59866 | −0.799331 | − | 0.600890i | \(-0.794813\pi\) | ||||
−0.799331 | + | 0.600890i | \(0.794813\pi\) | |||||||
\(182\) | −13.3599 | − | 2.62991i | −0.990301 | − | 0.194942i | ||||
\(183\) | 1.09259 | − | 0.531805i | 0.0807665 | − | 0.0393122i | ||||
\(184\) | 1.70156 | − | 2.57967i | 0.125441 | − | 0.190176i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 15.6196 | − | 4.13203i | 1.14529 | − | 0.302975i | ||||
\(187\) | − | 3.48457i | − | 0.254817i | ||||||
\(188\) | −11.5294 | − | 4.72212i | −0.840866 | − | 0.344396i | ||||
\(189\) | −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 | \(0.634897\pi\) | |||||||
\(192\) | −10.4791 | − | 9.06579i | −0.756264 | − | 0.654267i | ||||
\(193\) | 5.80625 | 0.417943 | 0.208971 | − | 0.977922i | \(-0.432988\pi\) | ||||
0.208971 | + | 0.977922i | \(0.432988\pi\) | |||||||
\(194\) | −2.21377 | + | 11.2459i | −0.158940 | + | 0.807411i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 10.5523 | + | 4.32196i | 0.753739 | + | 0.308711i | ||||
\(197\) | 9.44424i | 0.672875i | 0.941706 | + | 0.336437i | \(0.109222\pi\) | ||||
−0.941706 | + | 0.336437i | \(0.890778\pi\) | |||||||
\(198\) | 11.6570 | + | 13.5183i | 0.828424 | + | 0.960701i | ||||
\(199\) | − | 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 | ||||
\(202\) | −10.0000 | − | 1.96851i | −0.703598 | − | 0.138504i | ||||
\(203\) | 19.7810 | 1.38835 | ||||||||
\(204\) | 0.184209 | + | 2.86310i | 0.0128972 | + | 0.200457i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −5.68317 | − | 1.11874i | −0.395965 | − | 0.0779462i | ||||
\(207\) | 2.02214 | − | 2.57967i | 0.140549 | − | 0.179299i | ||||
\(208\) | −7.70156 | − | 7.58030i | −0.534007 | − | 0.525599i | ||||
\(209\) | 21.3731i | 1.47841i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 14.1763i | 0.975940i | 0.872860 | + | 0.487970i | \(0.162262\pi\) | ||||
−0.872860 | + | 0.487970i | \(0.837738\pi\) | |||||||
\(212\) | 4.20732 | − | 10.2725i | 0.288960 | − | 0.705515i | ||||
\(213\) | −17.7016 | + | 8.61603i | −1.21289 | + | 0.590361i | ||||
\(214\) | 5.14922 | − | 26.1580i | 0.351993 | − | 1.78812i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −10.2926 | − | 10.4911i | −0.700322 | − | 0.713827i | ||||
\(217\) | −23.5078 | −1.59581 | ||||||||
\(218\) | −2.37681 | + | 12.0742i | −0.160978 | + | 0.817765i | ||||
\(219\) | −11.9942 | + | 5.83802i | −0.810490 | + | 0.394497i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2.23748i | 0.150509i | ||||||||
\(222\) | −3.38473 | − | 12.7948i | −0.227168 | − | 0.858729i | ||||
\(223\) | − | 15.6924i | − | 1.05084i | −0.850843 | − | 0.525421i | \(-0.823908\pi\) | ||
0.850843 | − | 0.525421i | \(-0.176092\pi\) | |||||||
\(224\) | 11.3663 | + | 16.6510i | 0.759446 | + | 1.11254i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −21.9555 | − | 4.32196i | −1.46046 | − | 0.287492i | ||||
\(227\) | 11.6924 | 0.776053 | 0.388026 | − | 0.921648i | \(-0.373157\pi\) | ||||
0.388026 | + | 0.921648i | \(0.373157\pi\) | |||||||
\(228\) | −1.12988 | − | 17.5613i | −0.0748278 | − | 1.16302i | ||||
\(229\) | 8.70156 | 0.575015 | 0.287508 | − | 0.957778i | \(-0.407173\pi\) | ||||
0.287508 | + | 0.957778i | \(0.407173\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −11.3663 | − | 23.3521i | −0.747850 | − | 1.53645i | ||||
\(232\) | 13.1047 | + | 8.64391i | 0.860365 | + | 0.567501i | ||||
\(233\) | − | 14.9946i | − | 0.982328i | −0.871067 | − | 0.491164i | \(-0.836572\pi\) | ||
0.871067 | − | 0.491164i | \(-0.163428\pi\) | |||||||
\(234\) | −7.48504 | − | 8.68021i | −0.489313 | − | 0.567443i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −5.40312 | − | 11.1007i | −0.350971 | − | 0.721066i | ||||
\(238\) | 0.806248 | − | 4.09573i | 0.0522613 | − | 0.265487i | ||||
\(239\) | −5.46295 | −0.353369 | −0.176684 | − | 0.984268i | \(-0.556537\pi\) | ||||
−0.176684 | + | 0.984268i | \(0.556537\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 7.00000 | 0.450910 | 0.225455 | − | 0.974254i | \(-0.427613\pi\) | ||||
0.225455 | + | 0.974254i | \(0.427613\pi\) | |||||||
\(242\) | −1.83051 | + | 9.29898i | −0.117670 | + | 0.597761i | ||||
\(243\) | −9.97201 | − | 11.9816i | −0.639705 | − | 0.768621i | ||||
\(244\) | −1.29844 | − | 0.531805i | −0.0831240 | − | 0.0340453i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −24.3255 | + | 6.43508i | −1.55094 | + | 0.410286i | ||||
\(247\) | − | 13.7239i | − | 0.873231i | ||||||
\(248\) | −15.5737 | − | 10.2725i | −0.988929 | − | 0.652302i | ||||
\(249\) | 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 | \(0.512617\pi\) | |||||||
\(252\) | 10.5737 | + | 18.5864i | 0.666078 | + | 1.17083i | ||||
\(253\) | 4.59688 | 0.289003 | ||||||||
\(254\) | −22.5125 | − | 4.43160i | −1.41256 | − | 0.278063i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0.253905 | + | 15.9980i | 0.0158691 | + | 0.999874i | ||||
\(257\) | − | 11.1007i | − | 0.692441i | −0.938153 | − | 0.346221i | \(-0.887465\pi\) | ||
0.938153 | − | 0.346221i | \(-0.112535\pi\) | |||||||
\(258\) | 1.25933 | − | 0.333144i | 0.0784025 | − | 0.0207406i | ||||
\(259\) | 19.2563i | 1.19653i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 13.1047 | + | 10.2725i | 0.811160 | + | 0.635849i | ||||
\(262\) | −5.40312 | + | 27.4478i | −0.333806 | + | 1.69573i | ||||
\(263\) | −17.9219 | −1.10511 | −0.552555 | − | 0.833476i | \(-0.686347\pi\) | ||||
−0.552555 | + | 0.833476i | \(0.686347\pi\) | |||||||
\(264\) | 2.67432 | − | 20.4374i | 0.164593 | − | 1.25783i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −4.94525 | + | 25.1218i | −0.303213 | + | 1.54032i | ||||
\(267\) | −3.57951 | − | 7.35408i | −0.219062 | − | 0.450062i | ||||
\(268\) | 1.55234 | − | 3.79015i | 0.0948245 | − | 0.231520i | ||||
\(269\) | − | 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 | \(-0.734080\pi\) | ||
0.670872 | − | 0.741573i | \(-0.265920\pi\) | |||||||
\(272\) | 2.32389 | − | 2.36106i | 0.140906 | − | 0.143160i | ||||
\(273\) | 7.29844 | + | 14.9946i | 0.441722 | + | 0.907513i | ||||
\(274\) | −8.85078 | − | 1.74228i | −0.534695 | − | 0.105255i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −3.77703 | + | 0.243010i | −0.227351 | + | 0.0146275i | ||||
\(277\) | 28.1047 | 1.68865 | 0.844323 | − | 0.535834i | \(-0.180003\pi\) | ||||
0.844323 | + | 0.535834i | \(0.180003\pi\) | |||||||
\(278\) | 2.10366 | + | 0.414108i | 0.126169 | + | 0.0248365i | ||||
\(279\) | −15.5737 | − | 12.2078i | −0.932371 | − | 0.730864i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 7.20677i | − | 0.429920i | −0.976623 | − | 0.214960i | \(-0.931038\pi\) | ||
0.976623 | − | 0.214960i | \(-0.0689621\pi\) | |||||||
\(282\) | 3.90239 | + | 14.7516i | 0.232384 | + | 0.878443i | ||||
\(283\) | − | 6.14360i | − | 0.365199i | −0.983187 | − | 0.182599i | \(-0.941549\pi\) | ||
0.983187 | − | 0.182599i | \(-0.0584511\pi\) | |||||||
\(284\) | 21.0366 | + | 8.61603i | 1.24829 | + | 0.511267i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 3.10469 | − | 15.7718i | 0.183584 | − | 0.932604i | ||||
\(287\) | 36.6103 | 2.16104 | ||||||||
\(288\) | −1.11696 | + | 16.9338i | −0.0658173 | + | 0.997832i | ||||
\(289\) | 16.3141 | 0.959651 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 12.6220 | − | 6.14360i | 0.739913 | − | 0.360144i | ||||
\(292\) | 14.2539 | + | 5.83802i | 0.834147 | + | 0.341644i | ||||
\(293\) | 18.8885i | 1.10348i | 0.834017 | + | 0.551739i | \(0.186035\pi\) | ||||
−0.834017 | + | 0.551739i | \(0.813965\pi\) | |||||||
\(294\) | −3.57169 | − | 13.5015i | −0.208305 | − | 0.787422i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −8.41464 | + | 12.7571i | −0.489091 | + | 0.741492i | ||||
\(297\) | 4.59688 | − | 21.3731i | 0.266738 | − | 1.24020i | ||||
\(298\) | 2.29844 | + | 0.452450i | 0.133145 | + | 0.0262097i | ||||
\(299\) | −2.95170 | −0.170701 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.89531 | −0.109244 | ||||||||
\(302\) | −6.42110 | − | 1.26400i | −0.369493 | − | 0.0727350i | ||||
\(303\) | 5.46295 | + | 11.2236i | 0.313838 | + | 0.644778i | ||||
\(304\) | −14.2539 | + | 14.4819i | −0.817518 | + | 0.830595i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 2.66108 | − | 2.29468i | 0.152124 | − | 0.131178i | ||||
\(307\) | − | 20.3993i | − | 1.16425i | −0.813100 | − | 0.582125i | \(-0.802222\pi\) | ||
0.813100 | − | 0.582125i | \(-0.197778\pi\) | |||||||
\(308\) | −11.3663 | + | 27.7517i | −0.647657 | + | 1.58130i | ||||
\(309\) | 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 | \(0.658330\pi\) | |||||||
\(312\) | −1.71721 | + | 13.1230i | −0.0972178 | + | 0.742945i | ||||
\(313\) | −22.7016 | −1.28317 | −0.641584 | − | 0.767053i | \(-0.721722\pi\) | ||||
−0.641584 | + | 0.767053i | \(0.721722\pi\) | |||||||
\(314\) | −2.21377 | + | 11.2459i | −0.124930 | + | 0.634645i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −5.40312 | + | 13.1921i | −0.303949 | + | 0.742113i | ||||
\(317\) | 29.9892i | 1.68436i | 0.539197 | + | 0.842180i | \(0.318728\pi\) | ||||
−0.539197 | + | 0.842180i | \(0.681272\pi\) | |||||||
\(318\) | −13.1434 | + | 3.47695i | −0.737044 | + | 0.194978i | ||||
\(319\) | 23.3521i | 1.30746i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −29.3586 | + | 14.2900i | −1.63864 | + | 0.797587i | ||||
\(322\) | 5.40312 | + | 1.06361i | 0.301104 | + | 0.0592727i | ||||
\(323\) | 4.20732 | 0.234102 | ||||||||
\(324\) | −2.64716 | + | 17.8043i | −0.147064 | + | 0.989127i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −7.04891 | − | 1.38758i | −0.390403 | − | 0.0768512i | ||||
\(327\) | 13.5515 | − | 6.59605i | 0.749401 | − | 0.364762i | ||||
\(328\) | 24.2539 | + | 15.9980i | 1.33920 | + | 0.883341i | ||||
\(329\) | − | 22.2014i | − | 1.22400i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 30.0275i | − | 1.65046i | −0.564798 | − | 0.825229i | \(-0.691046\pi\) | ||
0.564798 | − | 0.825229i | \(-0.308954\pi\) | |||||||
\(332\) | −5.76469 | − | 2.36106i | −0.316378 | − | 0.129580i | ||||
\(333\) | −10.0000 | + | 12.7571i | −0.547997 | + | 0.699085i | ||||
\(334\) | 0.895314 | − | 4.54818i | 0.0489894 | − | 0.248865i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 7.87210 | − | 23.4031i | 0.429458 | − | 1.27674i | ||||
\(337\) | −0.403124 | −0.0219596 | −0.0109798 | − | 0.999940i | \(-0.503495\pi\) | ||||
−0.0109798 | + | 0.999940i | \(0.503495\pi\) | |||||||
\(338\) | 1.55737 | − | 7.91140i | 0.0847096 | − | 0.430323i | ||||
\(339\) | 11.9942 | + | 24.6419i | 0.651433 | + | 1.33836i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 27.7517i | − | 1.50284i | ||||||
\(342\) | −16.3222 | + | 14.0748i | −0.882601 | + | 0.761077i | ||||
\(343\) | − | 4.62754i | − | 0.249863i | ||||||
\(344\) | −1.25562 | − | 0.828216i | −0.0676987 | − | 0.0446544i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 20.8062 | + | 4.09573i | 1.11855 | + | 0.220188i | ||||
\(347\) | −13.3885 | −0.718732 | −0.359366 | − | 0.933197i | \(-0.617007\pi\) | ||||
−0.359366 | + | 0.933197i | \(0.617007\pi\) | |||||||
\(348\) | −1.23449 | − | 19.1873i | −0.0661756 | − | 1.02855i | ||||
\(349\) | −12.2094 | −0.653553 | −0.326776 | − | 0.945102i | \(-0.605962\pi\) | ||||
−0.326776 | + | 0.945102i | \(0.605962\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2.95170 | + | 13.7239i | −0.157550 | + | 0.732527i | ||||
\(352\) | −19.6570 | + | 13.4183i | −1.04772 | + | 0.715199i | ||||
\(353\) | − | 29.4081i | − | 1.56524i | −0.622502 | − | 0.782618i | \(-0.713884\pi\) | ||
0.622502 | − | 0.782618i | \(-0.286116\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −3.57951 | + | 8.73961i | −0.189714 | + | 0.463199i | ||||
\(357\) | −4.59688 | + | 2.23748i | −0.243292 | + | 0.118420i | ||||
\(358\) | −4.25391 | + | 21.6098i | −0.224826 | + | 1.14211i | ||||
\(359\) | −36.6103 | −1.93222 | −0.966108 | − | 0.258137i | \(-0.916891\pi\) | ||||
−0.966108 | + | 0.258137i | \(0.916891\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6.80625 | −0.358224 | ||||||||
\(362\) | 5.87480 | − | 29.8439i | 0.308773 | − | 1.56856i | ||||
\(363\) | 10.4368 | − | 5.07999i | 0.547789 | − | 0.266630i | ||||
\(364\) | 7.29844 | − | 17.8196i | 0.382542 | − | 0.934002i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0.439487 | + | 1.66132i | 0.0229723 | + | 0.0868386i | ||||
\(367\) | − | 3.56393i | − | 0.186035i | −0.995664 | − | 0.0930177i | \(-0.970349\pi\) | ||
0.995664 | − | 0.0930177i | \(-0.0296513\pi\) | |||||||
\(368\) | 3.11473 | + | 3.06569i | 0.162367 | + | 0.159810i | ||||
\(369\) | 24.2539 | + | 19.0121i | 1.26261 | + | 0.989729i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 19.7810 | 1.02698 | ||||||||
\(372\) | 1.46707 | + | 22.8022i | 0.0760642 | + | 1.18224i | ||||
\(373\) | 17.2984 | 0.895679 | 0.447840 | − | 0.894114i | \(-0.352194\pi\) | ||||
0.447840 | + | 0.894114i | \(0.352194\pi\) | |||||||
\(374\) | 4.83513 | + | 0.951801i | 0.250019 | + | 0.0492165i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 9.70156 | − | 14.7082i | 0.500320 | − | 0.758515i | ||||
\(377\) | − | 14.9946i | − | 0.772260i | ||||||
\(378\) | 10.3484 | − | 24.0582i | 0.532263 | − | 1.23742i | ||||
\(379\) | − | 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 | ||||
\(382\) | 3.10469 | − | 15.7718i | 0.158850 | − | 0.806953i | ||||
\(383\) | −12.4589 | −0.636622 | −0.318311 | − | 0.947986i | \(-0.603116\pi\) | ||||
−0.318311 | + | 0.947986i | \(0.603116\pi\) | |||||||
\(384\) | 15.4419 | − | 12.0643i | 0.788015 | − | 0.615656i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −1.58596 | + | 8.05666i | −0.0807233 | + | 0.410073i | ||||
\(387\) | −1.25562 | − | 0.984255i | −0.0638270 | − | 0.0500325i | ||||
\(388\) | −15.0000 | − | 6.14360i | −0.761510 | − | 0.311894i | ||||
\(389\) | 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 | ||||||
\(392\) | −8.87942 | + | 13.4617i | −0.448479 | + | 0.679920i | ||||
\(393\) | 30.8062 | − | 14.9946i | 1.55397 | − | 0.756377i | ||||
\(394\) | −13.1047 | − | 2.57967i | −0.660205 | − | 0.129962i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −21.9418 | + | 12.4825i | −1.10262 | + | 0.627271i | ||||
\(397\) | −28.9109 | −1.45100 | −0.725499 | − | 0.688223i | \(-0.758391\pi\) | ||||
−0.725499 | + | 0.688223i | \(0.758391\pi\) | |||||||
\(398\) | 21.7745 | + | 4.28634i | 1.09146 | + | 0.214855i | ||||
\(399\) | 28.1956 | − | 13.7239i | 1.41155 | − | 0.687054i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 30.8174i | − | 1.53895i | −0.638679 | − | 0.769473i | \(-0.720519\pi\) | ||
0.638679 | − | 0.769473i | \(-0.279481\pi\) | |||||||
\(402\) | −4.84941 | + | 1.28286i | −0.241867 | + | 0.0639835i | ||||
\(403\) | 17.8196i | 0.887659i | ||||||||
\(404\) | 5.46295 | − | 13.3382i | 0.271792 | − | 0.663598i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −5.40312 | + | 27.4478i | −0.268153 | + | 1.36221i | ||||
\(407\) | −22.7327 | −1.12682 | ||||||||
\(408\) | −4.02311 | − | 0.526443i | −0.199174 | − | 0.0260628i | ||||
\(409\) | −27.2094 | −1.34542 | −0.672708 | − | 0.739908i | \(-0.734869\pi\) | ||||
−0.672708 | + | 0.739908i | \(0.734869\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 4.83513 | + | 9.93375i | 0.238500 | + | 0.489996i | ||||
\(412\) | 3.10469 | − | 7.58030i | 0.152957 | − | 0.373455i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 3.02717 | + | 3.51053i | 0.148777 | + | 0.172533i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 12.6220 | − | 8.61603i | 0.618843 | − | 0.422436i | ||||
\(417\) | −1.14922 | − | 2.36106i | −0.0562775 | − | 0.115622i | ||||
\(418\) | −29.6570 | − | 5.83802i | −1.45057 | − | 0.285547i | ||||
\(419\) | 10.1107 | 0.493941 | 0.246970 | − | 0.969023i | \(-0.420565\pi\) | ||||
0.246970 | + | 0.969023i | \(0.420565\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 24.2094 | 1.17989 | 0.589946 | − | 0.807442i | \(-0.299149\pi\) | ||||
0.589946 | + | 0.807442i | \(0.299149\pi\) | |||||||
\(422\) | −19.6709 | − | 3.87223i | −0.957563 | − | 0.188497i | ||||
\(423\) | 11.5294 | − | 14.7082i | 0.560578 | − | 0.715135i | ||||
\(424\) | 13.1047 | + | 8.64391i | 0.636420 | + | 0.419785i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −7.12033 | − | 26.9159i | −0.344981 | − | 1.30408i | ||||
\(427\) | − | 2.50031i | − | 0.120999i | ||||||
\(428\) | 34.8899 | + | 14.2900i | 1.68647 | + | 0.690731i | ||||
\(429\) | −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 | \(0.341938\pi\) | |||||||
\(432\) | 17.3686 | − | 11.4162i | 0.835649 | − | 0.549264i | ||||
\(433\) | −31.2094 | −1.49983 | −0.749913 | − | 0.661536i | \(-0.769905\pi\) | ||||
−0.749913 | + | 0.661536i | \(0.769905\pi\) | |||||||
\(434\) | 6.42110 | − | 32.6191i | 0.308222 | − | 1.56577i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −16.1047 | − | 6.59605i | −0.771275 | − | 0.315893i | ||||
\(437\) | 5.55034i | 0.265509i | ||||||||
\(438\) | −4.82457 | − | 18.2375i | −0.230527 | − | 0.871423i | ||||
\(439\) | 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 | ||||
\(442\) | −3.10469 | − | 0.611161i | −0.147675 | − | 0.0290699i | ||||
\(443\) | 11.2033 | 0.532285 | 0.266143 | − | 0.963934i | \(-0.414251\pi\) | ||||
0.266143 | + | 0.963934i | \(0.414251\pi\) | |||||||
\(444\) | 18.6784 | − | 1.20175i | 0.886435 | − | 0.0570324i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 21.7745 | + | 4.28634i | 1.03105 | + | 0.202964i | ||||
\(447\) | −1.25562 | − | 2.57967i | −0.0593890 | − | 0.122014i | ||||
\(448\) | −26.2094 | + | 11.2236i | −1.23828 | + | 0.530264i | ||||
\(449\) | − | 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 | ||||||||
\(452\) | 11.9942 | − | 29.2845i | 0.564158 | − | 1.37743i | ||||
\(453\) | 3.50781 | + | 7.20677i | 0.164811 | + | 0.338604i | ||||
\(454\) | −3.19375 | + | 16.2242i | −0.149890 | + | 0.761440i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 24.6764 | + | 3.22902i | 1.15558 | + | 0.151213i | ||||
\(457\) | −16.8953 | −0.790329 | −0.395165 | − | 0.918610i | \(-0.629312\pi\) | ||||
−0.395165 | + | 0.918610i | \(0.629312\pi\) | |||||||
\(458\) | −2.37681 | + | 12.0742i | −0.111061 | + | 0.564188i | ||||
\(459\) | −4.20732 | − | 0.904899i | −0.196381 | − | 0.0422371i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 7.20677i | 0.335653i | 0.985817 | + | 0.167826i | \(0.0536748\pi\) | ||||
−0.985817 | + | 0.167826i | \(0.946325\pi\) | |||||||
\(462\) | 35.5076 | − | 9.39321i | 1.65196 | − | 0.437012i | ||||
\(463\) | − | 7.12785i | − | 0.331259i | −0.986188 | − | 0.165630i | \(-0.947034\pi\) | ||
0.986188 | − | 0.165630i | \(-0.0529656\pi\) | |||||||
\(464\) | −15.5737 | + | 15.8228i | −0.722989 | + | 0.734555i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 20.8062 | + | 4.09573i | 0.963831 | + | 0.189731i | ||||
\(467\) | 0.766519 | 0.0354703 | 0.0177351 | − | 0.999843i | \(-0.494354\pi\) | ||||
0.0177351 | + | 0.999843i | \(0.494354\pi\) | |||||||
\(468\) | 14.0890 | − | 8.01516i | 0.651266 | − | 0.370501i | ||||
\(469\) | 7.29844 | 0.337011 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 12.6220 | − | 6.14360i | 0.581590 | − | 0.283082i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 2.23748i | − | 0.102879i | ||||||
\(474\) | 16.8790 | − | 4.46517i | 0.775277 | − | 0.205092i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 5.46295 | + | 2.23748i | 0.250394 | + | 0.102555i | ||||
\(477\) | 13.1047 | + | 10.2725i | 0.600022 | + | 0.470344i | ||||
\(478\) | 1.49219 | − | 7.58030i | 0.0682512 | − | 0.346715i | ||||
\(479\) | 42.0732 | 1.92237 | 0.961187 | − | 0.275897i | \(-0.0889747\pi\) | ||||
0.961187 | + | 0.275897i | \(0.0889747\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 14.5969 | 0.665560 | ||||||||
\(482\) | −1.91203 | + | 9.71309i | −0.0870906 | + | 0.442419i | ||||
\(483\) | −2.95170 | − | 6.06424i | −0.134307 | − | 0.275932i | ||||
\(484\) | −12.4031 | − | 5.07999i | −0.563778 | − | 0.230908i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 19.3493 | − | 10.5643i | 0.877703 | − | 0.479205i | ||||
\(487\) | 34.0438i | 1.54267i | 0.636427 | + | 0.771337i | \(0.280412\pi\) | ||||
−0.636427 | + | 0.771337i | \(0.719588\pi\) | |||||||
\(488\) | 1.09259 | − | 1.65643i | 0.0494592 | − | 0.0749831i | ||||
\(489\) | 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 | \(0.623989\pi\) | |||||||
\(492\) | −2.28477 | − | 35.5114i | −0.103005 | − | 1.60098i | ||||
\(493\) | 4.59688 | 0.207033 | ||||||||
\(494\) | 19.0431 | + | 3.74865i | 0.856788 | + | 0.168660i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 18.5078 | − | 18.8039i | 0.831025 | − | 0.844319i | ||||
\(497\) | 40.5088i | 1.81707i | ||||||||
\(498\) | 1.95119 | + | 7.37579i | 0.0874351 | + | 0.330517i | ||||
\(499\) | − | 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 | ||||
\(502\) | 0.342970 | − | 1.74228i | 0.0153075 | − | 0.0777620i | ||||
\(503\) | 32.2399 | 1.43751 | 0.718753 | − | 0.695265i | \(-0.244713\pi\) | ||||
0.718753 | + | 0.695265i | \(0.244713\pi\) | |||||||
\(504\) | −28.6784 | + | 9.59503i | −1.27744 | + | 0.427397i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −1.25562 | + | 6.37855i | −0.0558193 | + | 0.283561i | ||||
\(507\) | −8.87942 | + | 4.32196i | −0.394349 | + | 0.191945i | ||||
\(508\) | 12.2984 | − | 30.0275i | 0.545655 | − | 1.33225i | ||||
\(509\) | − | 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 | ||||||||
\(512\) | −22.2679 | − | 4.01749i | −0.984112 | − | 0.177550i | ||||
\(513\) | 25.8062 | + | 5.55034i | 1.13937 | + | 0.245053i | ||||
\(514\) | 15.4031 | + | 3.03212i | 0.679403 | + | 0.133741i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0.118283 | + | 1.83843i | 0.00520710 | + | 0.0809322i | ||||
\(517\) | 26.2094 | 1.15269 | ||||||||
\(518\) | −26.7198 | − | 5.25982i | −1.17400 | − | 0.231103i | ||||
\(519\) | −11.3663 | − | 23.3521i | −0.498927 | − | 1.02504i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 10.2725i | − | 0.450045i | −0.974354 | − | 0.225022i | \(-0.927754\pi\) | ||
0.974354 | − | 0.225022i | \(-0.0722455\pi\) | |||||||
\(522\) | −17.8334 | + | 15.3780i | −0.780547 | + | 0.673075i | ||||
\(523\) | 31.4642i | 1.37583i | 0.725790 | + | 0.687916i | \(0.241474\pi\) | ||||
−0.725790 | + | 0.687916i | \(0.758526\pi\) | |||||||
\(524\) | −36.6103 | − | 14.9946i | −1.59933 | − | 0.655041i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 4.89531 | − | 24.8681i | 0.213446 | − | 1.08430i | ||||
\(527\) | −5.46295 | −0.237970 | ||||||||
\(528\) | 27.6281 | + | 9.29326i | 1.20236 | + | 0.404437i | ||||
\(529\) | −21.8062 | −0.948098 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −33.5078 | − | 13.7239i | −1.45275 | − | 0.595006i | ||||
\(533\) | − | 27.7517i | − | 1.20206i | ||||||
\(534\) | 11.1821 | − | 2.95813i | 0.483898 | − | 0.128011i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 4.83513 | + | 3.18928i | 0.208846 | + | 0.137756i | ||||
\(537\) | 24.2539 | − | 11.8053i | 1.04663 | − | 0.509437i | ||||
\(538\) | 20.8062 | + | 4.09573i | 0.897021 | + | 0.176579i | ||||
\(539\) | −23.9883 | −1.03325 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −19.2984 | −0.829705 | −0.414852 | − | 0.909889i | \(-0.636167\pi\) | ||||
−0.414852 | + | 0.909889i | \(0.636167\pi\) | |||||||
\(542\) | 33.8788 | + | 6.66908i | 1.45522 | + | 0.286461i | ||||
\(543\) | −33.4955 | + | 16.3036i | −1.43743 | + | 0.699653i | ||||
\(544\) | 2.64141 | + | 3.86951i | 0.113249 | + | 0.165904i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −22.7998 | + | 6.03147i | −0.975741 | + | 0.258123i | ||||
\(547\) | 21.8360i | 0.933640i | 0.884352 | + | 0.466820i | \(0.154600\pi\) | ||||
−0.884352 | + | 0.466820i | \(0.845400\pi\) | |||||||
\(548\) | 4.83513 | − | 11.8053i | 0.206547 | − | 0.504298i | ||||
\(549\) | 1.29844 | − | 1.65643i | 0.0554160 | − | 0.0706948i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −28.1956 | −1.20117 | ||||||||
\(552\) | 0.694488 | − | 5.30733i | 0.0295594 | − | 0.225895i | ||||
\(553\) | −25.4031 | −1.08025 | ||||||||
\(554\) | −7.67672 | + | 38.9976i | −0.326153 | + | 1.65685i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −1.14922 | + | 2.80590i | −0.0487377 | + | 0.118996i | ||||
\(557\) | − | 17.2321i | − | 0.730146i | −0.930979 | − | 0.365073i | \(-0.881044\pi\) | ||
0.930979 | − | 0.365073i | \(-0.118956\pi\) | |||||||
\(558\) | 21.1933 | − | 18.2752i | 0.897184 | − | 0.773653i | ||||
\(559\) | 1.43670i | 0.0607661i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −2.64141 | − | 5.42675i | −0.111520 | − | 0.229118i | ||||
\(562\) | 10.0000 | + | 1.96851i | 0.421825 | + | 0.0830366i | ||||
\(563\) | −30.0547 | −1.26666 | −0.633328 | − | 0.773883i | \(-0.718312\pi\) | ||||
−0.633328 | + | 0.773883i | \(0.718312\pi\) | |||||||
\(564\) | −21.5350 | + | 1.38554i | −0.906786 | + | 0.0583417i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 8.52476 | + | 1.67811i | 0.358322 | + | 0.0705361i | ||||
\(567\) | −31.1473 | + | 7.65966i | −1.30806 | + | 0.321675i | ||||
\(568\) | −17.7016 | + | 26.8366i | −0.742741 | + | 1.12604i | ||||
\(569\) | 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 | \(-0.757571\pi\) | ||
0.723724 | − | 0.690090i | \(-0.242429\pi\) | |||||||
\(572\) | 21.0366 | + | 8.61603i | 0.879585 | + | 0.360254i | ||||
\(573\) | −17.7016 | + | 8.61603i | −0.739493 | + | 0.359940i | ||||
\(574\) | −10.0000 | + | 50.7999i | −0.417392 | + | 2.12034i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −23.1919 | − | 6.17528i | −0.966331 | − | 0.257304i | ||||
\(577\) | −0.403124 | −0.0167823 | −0.00839114 | − | 0.999965i | \(-0.502671\pi\) | ||||
−0.00839114 | + | 0.999965i | \(0.502671\pi\) | |||||||
\(578\) | −4.45614 | + | 22.6371i | −0.185351 | + | 0.941581i | ||||
\(579\) | 9.04246 | − | 4.40131i | 0.375792 | − | 0.182912i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − | 11.1007i | − | 0.460534i | ||||||
\(582\) | 5.07710 | + | 19.1922i | 0.210453 | + | 0.795540i | ||||
\(583\) | 23.3521i | 0.967144i | ||||||||
\(584\) | −11.9942 | + | 18.1839i | −0.496322 | + | 0.752453i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −26.2094 | − | 5.15934i | −1.08270 | − | 0.213130i | ||||
\(587\) | −3.88125 | −0.160196 | −0.0800982 | − | 0.996787i | \(-0.525523\pi\) | ||||
−0.0800982 | + | 0.996787i | \(0.525523\pi\) | |||||||
\(588\) | 19.7100 | − | 1.26812i | 0.812828 | − | 0.0522966i | ||||
\(589\) | 33.5078 | 1.38067 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 7.15902 | + | 14.7082i | 0.294483 | + | 0.605012i | ||||
\(592\) | −15.4031 | − | 15.1606i | −0.633065 | − | 0.623097i | ||||
\(593\) | 43.5745i | 1.78939i | 0.446678 | + | 0.894695i | \(0.352607\pi\) | ||||
−0.446678 | + | 0.894695i | \(0.647393\pi\) | |||||||
\(594\) | 28.4014 | + | 12.2166i | 1.16532 | + | 0.501252i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −1.25562 | + | 3.06569i | −0.0514324 | + | 0.125576i | ||||
\(597\) | −11.8953 | − | 24.4388i | −0.486843 | − | 1.00021i | ||||
\(598\) | 0.806248 | − | 4.09573i | 0.0329700 | − | 0.167487i | ||||
\(599\) | 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 | \(0.337067\pi\) | |||||||
\(602\) | 0.517700 | − | 2.62991i | 0.0210999 | − | 0.107187i | ||||
\(603\) | 4.83513 | + | 3.79015i | 0.196902 | + | 0.154347i | ||||
\(604\) | 3.50781 | − | 8.56455i | 0.142731 | − | 0.348487i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −17.0659 | + | 4.51461i | −0.693253 | + | 0.183393i | ||||
\(607\) | 27.4478i | 1.11407i | 0.830489 | + | 0.557036i | \(0.188061\pi\) | ||||
−0.830489 | + | 0.557036i | \(0.811939\pi\) | |||||||
\(608\) | −16.2015 | − | 23.7342i | −0.657057 | − | 0.962549i | ||||
\(609\) | 30.8062 | − | 14.9946i | 1.24833 | − | 0.607611i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −16.8293 | −0.680840 | ||||||||
\(612\) | 2.45720 | + | 4.31926i | 0.0993264 | + | 0.174596i | ||||
\(613\) | 20.8062 | 0.840356 | 0.420178 | − | 0.907442i | \(-0.361968\pi\) | ||||
0.420178 | + | 0.907442i | \(0.361968\pi\) | |||||||
\(614\) | 28.3057 | + | 5.57201i | 1.14233 | + | 0.224868i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −35.4031 | − | 23.3521i | −1.42643 | − | 0.940881i | ||||
\(617\) | − | 18.3074i | − | 0.737030i | −0.929622 | − | 0.368515i | \(-0.879866\pi\) | ||
0.929622 | − | 0.368515i | \(-0.120134\pi\) | |||||||
\(618\) | −9.69882 | + | 2.56573i | −0.390144 | + | 0.103209i | ||||
\(619\) | − | 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 | ||||
\(622\) | 4.59688 | − | 23.3521i | 0.184318 | − | 0.936332i | ||||
\(623\) | −16.8293 | −0.674251 | ||||||||
\(624\) | −17.7402 | − | 5.96729i | −0.710178 | − | 0.238883i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 6.20087 | − | 31.5003i | 0.247837 | − | 1.25901i | ||||
\(627\) | 16.2015 | + | 33.2858i | 0.647025 | + | 1.32931i | ||||
\(628\) | −15.0000 | − | 6.14360i | −0.598565 | − | 0.245156i | ||||
\(629\) | 4.47495i | 0.178428i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 2.65903i | − | 0.105854i | −0.998598 | − | 0.0529271i | \(-0.983145\pi\) | ||
0.998598 | − | 0.0529271i | \(-0.0168551\pi\) | |||||||
\(632\) | −16.8293 | − | 11.1007i | −0.669433 | − | 0.441561i | ||||
\(633\) | 10.7461 | + | 22.0778i | 0.427119 | + | 0.877512i | ||||
\(634\) | −41.6125 | − | 8.19146i | −1.65264 | − | 0.325324i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −1.23449 | − | 19.1873i | −0.0489507 | − | 0.760824i | ||||
\(637\) | 15.4031 | 0.610294 | ||||||||
\(638\) | −32.4030 | − | 6.37855i | −1.28285 | − | 0.252529i | ||||
\(639\) | −21.0366 | + | 26.8366i | −0.832196 | + | 1.06164i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 41.0898i | 1.62295i | 0.584386 | + | 0.811476i | \(0.301335\pi\) | ||||
−0.584386 | + | 0.811476i | \(0.698665\pi\) | |||||||
\(642\) | −11.8093 | − | 44.6408i | −0.466076 | − | 1.76183i | ||||
\(643\) | − | 22.2885i | − | 0.878971i | −0.898250 | − | 0.439485i | \(-0.855161\pi\) | ||
0.898250 | − | 0.439485i | \(-0.144839\pi\) | |||||||
\(644\) | −2.95170 | + | 7.20677i | −0.116313 | + | 0.283986i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −1.14922 | + | 5.83802i | −0.0452154 | + | 0.229694i | ||||
\(647\) | 2.18518 | 0.0859082 | 0.0429541 | − | 0.999077i | \(-0.486323\pi\) | ||||
0.0429541 | + | 0.999077i | \(0.486323\pi\) | |||||||
\(648\) | −23.9819 | − | 8.53635i | −0.942097 | − | 0.335339i | ||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −36.6103 | + | 17.8196i | −1.43487 | + | 0.698406i | ||||
\(652\) | 3.85078 | − | 9.40194i | 0.150808 | − | 0.368208i | ||||
\(653\) | − | 7.78781i | − | 0.304761i | −0.988322 | − | 0.152380i | \(-0.951306\pi\) | ||
0.988322 | − | 0.152380i | \(-0.0486939\pi\) | |||||||
\(654\) | 5.45101 | + | 20.6056i | 0.213151 | + | 0.805742i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −28.8234 | + | 29.2845i | −1.12537 | + | 1.14337i | ||||
\(657\) | −14.2539 | + | 18.1839i | −0.556098 | + | 0.709420i | ||||
\(658\) | 30.8062 | + | 6.06424i | 1.20095 | + | 0.236409i | ||||
\(659\) | 21.0366 | 0.819470 | 0.409735 | − | 0.912205i | \(-0.365621\pi\) | ||||
0.409735 | + | 0.912205i | \(0.365621\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −18.0000 | −0.700119 | −0.350059 | − | 0.936727i | \(-0.613839\pi\) | ||||
−0.350059 | + | 0.936727i | \(0.613839\pi\) | |||||||
\(662\) | 41.6656 | + | 8.20192i | 1.61938 | + | 0.318777i | ||||
\(663\) | 1.69607 | + | 3.48457i | 0.0658700 | + | 0.135329i | ||||
\(664\) | 4.85078 | − | 7.35408i | 0.188247 | − | 0.285393i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −14.9701 | − | 17.3604i | −0.580079 | − | 0.672702i | ||||
\(667\) | 6.06424i | 0.234808i | ||||||||
\(668\) | 6.06643 | + | 2.48465i | 0.234717 | + | 0.0961339i | ||||
\(669\) | −11.8953 | − | 24.4388i | −0.459899 | − | 0.944860i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 2.95170 | 0.113949 | ||||||||
\(672\) | 30.3235 | + | 17.3157i | 1.16976 | + | 0.667968i | ||||
\(673\) | 0.806248 | 0.0310786 | 0.0155393 | − | 0.999879i | \(-0.495053\pi\) | ||||
0.0155393 | + | 0.999879i | \(0.495053\pi\) | |||||||
\(674\) | 0.110112 | − | 0.559369i | 0.00424137 | − | 0.0215461i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 10.5523 | + | 4.32196i | 0.405859 | + | 0.166229i | ||||
\(677\) | − | 3.89391i | − | 0.149655i | −0.997196 | − | 0.0748275i | \(-0.976159\pi\) | ||
0.997196 | − | 0.0748275i | \(-0.0238406\pi\) | |||||||
\(678\) | −37.4689 | + | 9.91203i | −1.43898 | + | 0.380669i | ||||
\(679\) | − | 28.8845i | − | 1.10849i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 18.2094 | − | 8.86320i | 0.697785 | − | 0.339639i | ||||
\(682\) | 38.5078 | + | 7.58030i | 1.47454 | + | 0.290265i | ||||
\(683\) | −19.9440 | −0.763137 | −0.381568 | − | 0.924341i | \(-0.624616\pi\) | ||||
−0.381568 | + | 0.924341i | \(0.624616\pi\) | |||||||
\(684\) | −15.0716 | − | 26.4929i | −0.576277 | − | 1.01298i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 6.42110 | + | 1.26400i | 0.245159 | + | 0.0482597i | ||||
\(687\) | 13.5515 | − | 6.59605i | 0.517023 | − | 0.251655i | ||||
\(688\) | 1.49219 | − | 1.51606i | 0.0568892 | − | 0.0577992i | ||||
\(689\) | − | 14.9946i | − | 0.571248i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 18.8039i | − | 0.715333i | −0.933849 | − | 0.357667i | \(-0.883572\pi\) | ||
0.933849 | − | 0.357667i | \(-0.116428\pi\) | |||||||
\(692\) | −11.3663 | + | 27.7517i | −0.432084 | + | 1.05496i | ||||
\(693\) | −35.4031 | − | 27.7517i | −1.34485 | − | 1.05420i | ||||
\(694\) | 3.65703 | − | 18.5777i | 0.138819 | − | 0.705198i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 26.9611 | + | 3.52799i | 1.02196 | + | 0.133728i | ||||
\(697\) | 8.50781 | 0.322256 | ||||||||
\(698\) | 3.33496 | − | 16.9415i | 0.126230 | − | 0.641247i | ||||
\(699\) | −11.3663 | − | 23.3521i | −0.429915 | − | 0.883256i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 27.7517i | 1.04817i | 0.851667 | + | 0.524083i | \(0.175592\pi\) | ||||
−0.851667 | + | 0.524083i | \(0.824408\pi\) | |||||||
\(702\) | −18.2368 | − | 7.84438i | −0.688304 | − | 0.296067i | ||||
\(703\) | − | 27.4478i | − | 1.03521i | ||||||
\(704\) | −13.2498 | − | 30.9410i | −0.499370 | − | 1.16613i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 40.8062 | + | 8.03275i | 1.53576 | + | 0.302317i | ||||
\(707\) | 25.6844 | 0.965961 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −11.2984 | −0.424322 | −0.212161 | − | 0.977235i | \(-0.568050\pi\) | ||||
−0.212161 | + | 0.977235i | \(0.568050\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −16.8293 | − | 13.1921i | −0.631148 | − | 0.494742i | ||||
\(712\) | −11.1492 | − | 7.35408i | −0.417835 | − | 0.275606i | ||||
\(713\) | − | 7.20677i | − | 0.269896i | ||||||
\(714\) | −1.84906 | − | 6.98971i | −0.0691994 | − | 0.261583i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −28.8234 | − | 11.8053i | −1.07718 | − | 0.441185i | ||||
\(717\) | −8.50781 | + | 4.14108i | −0.317730 | + | 0.154651i | ||||
\(718\) | 10.0000 | − | 50.7999i | 0.373197 | − | 1.89583i | ||||
\(719\) | 25.6844 | 0.957866 | 0.478933 | − | 0.877851i | \(-0.341024\pi\) | ||||
0.478933 | + | 0.877851i | \(0.341024\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 14.5969 | 0.543616 | ||||||||
\(722\) | 1.85911 | − | 9.44424i | 0.0691889 | − | 0.351478i | ||||
\(723\) | 10.9016 | − | 5.30621i | 0.405434 | − | 0.197340i | ||||
\(724\) | 39.8062 | + | 16.3036i | 1.47939 | + | 0.605917i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 4.19813 | + | 15.8695i | 0.155807 | + | 0.588973i | ||||
\(727\) | − | 45.1087i | − | 1.67299i | −0.547975 | − | 0.836495i | \(-0.684601\pi\) | ||
0.547975 | − | 0.836495i | \(-0.315399\pi\) | |||||||
\(728\) | 22.7327 | + | 14.9946i | 0.842529 | + | 0.555736i | ||||
\(729\) | −24.6125 | − | 11.1007i | −0.911574 | − | 0.411136i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −0.440449 | −0.0162906 | ||||||||
\(732\) | −2.42527 | + | 0.156039i | −0.0896405 | + | 0.00576738i | ||||
\(733\) | 20.8062 | 0.768496 | 0.384248 | − | 0.923230i | \(-0.374461\pi\) | ||||
0.384248 | + | 0.923230i | \(0.374461\pi\) | |||||||
\(734\) | 4.94525 | + | 0.973477i | 0.182532 | + | 0.0359317i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −5.10469 | + | 3.48457i | −0.188161 | + | 0.128443i | ||||
\(737\) | 8.61603i | 0.317376i | ||||||||
\(738\) | −33.0057 | + | 28.4612i | −1.21496 | + | 1.04767i | ||||
\(739\) | 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 | ||||
\(742\) | −5.40312 | + | 27.4478i | −0.198355 | + | 1.00764i | ||||
\(743\) | 29.6143 | 1.08644 | 0.543222 | − | 0.839589i | \(-0.317204\pi\) | ||||
0.543222 | + | 0.839589i | \(0.317204\pi\) | |||||||
\(744\) | −32.0407 | − | 4.19268i | −1.17467 | − | 0.153711i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −4.72502 | + | 24.0030i | −0.172995 | + | 0.878814i | ||||
\(747\) | 5.76469 | − | 7.35408i | 0.210919 | − | 0.269072i | ||||
\(748\) | −2.64141 | + | 6.44918i | −0.0965795 | + | 0.235805i | ||||
\(749\) | 67.1851i | 2.45489i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 28.3527i | 1.03460i | 0.855803 | + | 0.517302i | \(0.173064\pi\) | ||||
−0.855803 | + | 0.517302i | \(0.826936\pi\) | |||||||
\(752\) | 17.7588 | + | 17.4792i | 0.647598 | + | 0.637402i | ||||
\(753\) | −1.95547 | + | 0.951801i | −0.0712612 | + | 0.0346856i | ||||
\(754\) | 20.8062 | + | 4.09573i | 0.757719 | + | 0.149158i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 30.5561 | + | 20.9307i | 1.11132 | + | 0.761241i | ||||
\(757\) | −8.91093 | −0.323873 | −0.161937 | − | 0.986801i | \(-0.551774\pi\) | ||||
−0.161937 | + | 0.986801i | \(0.551774\pi\) | |||||||
\(758\) | 29.5614 | + | 5.81918i | 1.07372 | + | 0.211362i | ||||
\(759\) | 7.15902 | − | 3.48457i | 0.259856 | − | 0.126482i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 3.06569i | − | 0.111131i | −0.998455 | − | 0.0555656i | \(-0.982304\pi\) | ||
0.998455 | − | 0.0555656i | \(-0.0176962\pi\) | |||||||
\(762\) | −38.4194 | + | 10.1635i | −1.39179 | + | 0.368185i | ||||
\(763\) | − | 31.0117i | − | 1.12270i | ||||||
\(764\) | 21.0366 | + | 8.61603i | 0.761078 | + | 0.311717i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 3.40312 | − | 17.2878i | 0.122960 | − | 0.624634i | ||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 12.5224 | + | 24.7223i | 0.451862 | + | 0.892088i | ||||
\(769\) | −39.8062 | −1.43545 | −0.717725 | − | 0.696327i | \(-0.754817\pi\) | ||||
−0.717725 | + | 0.696327i | \(0.754817\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −8.41464 | − | 17.2878i | −0.303046 | − | 0.622606i | ||||
\(772\) | −10.7461 | − | 4.40131i | −0.386760 | − | 0.158407i | ||||
\(773\) | 5.55034i | 0.199632i | 0.995006 | + | 0.0998159i | \(0.0318254\pi\) | ||||
−0.995006 | + | 0.0998159i | \(0.968175\pi\) | |||||||
\(774\) | 1.70871 | − | 1.47344i | 0.0614182 | − | 0.0529616i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 12.6220 | − | 19.1357i | 0.453102 | − | 0.686930i | ||||
\(777\) | 14.5969 | + | 29.9892i | 0.523660 | + | 1.07586i | ||||
\(778\) | −27.7016 | − | 5.45308i | −0.993149 | − | 0.195502i | ||||
\(779\) | −52.1839 | −1.86968 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −47.8219 | −1.71120 | ||||||||
\(782\) | 1.25562 | + | 0.247171i | 0.0449010 | + | 0.00883881i | ||||
\(783\) | 28.1956 | + | 6.06424i | 1.00763 | + | 0.216718i | ||||
\(784\) | −16.2539 | − | 15.9980i | −0.580497 | − | 0.571357i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 12.3916 | + | 46.8420i | 0.441994 | + | 1.67080i | ||||
\(787\) | − | 14.7875i | − | 0.527118i | −0.964643 | − | 0.263559i | \(-0.915104\pi\) | ||
0.964643 | − | 0.263559i | \(-0.0848963\pi\) | |||||||
\(788\) | 7.15902 | − | 17.4792i | 0.255030 | − | 0.622672i | ||||
\(789\) | −27.9109 | + | 13.5853i | −0.993656 | + | 0.483650i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 56.3913 | 2.00504 | ||||||||
\(792\) | −11.3272 | − | 33.8557i | −0.402495 | − | 1.20301i | ||||
\(793\) | −1.89531 | −0.0673046 | ||||||||
\(794\) | 7.89694 | − | 40.1164i | 0.280252 | − | 1.42368i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −11.8953 | + | 29.0432i | −0.421618 | + | 1.02941i | ||||
\(797\) | − | 4.96929i | − | 0.176021i | −0.996120 | − | 0.0880107i | \(-0.971949\pi\) | ||
0.996120 | − | 0.0880107i | \(-0.0280510\pi\) | |||||||
\(798\) | 11.3415 | + | 42.8725i | 0.401485 | + | 1.51767i | ||||
\(799\) | − | 5.15934i | − | 0.182524i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −11.1492 | − | 8.73961i | −0.393938 | − | 0.308799i | ||||
\(802\) | 42.7617 | + | 8.41769i | 1.50997 | + | 0.297239i | ||||
\(803\) | −32.4030 | −1.14348 | ||||||||
\(804\) | −0.455480 | − | 7.07938i | −0.0160635 | − | 0.249670i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −24.7262 | − | 4.86738i | −0.870944 | − | 0.171446i | ||||
\(807\) | −11.3663 | − | 23.3521i | −0.400114 | − | 0.822031i | ||||
\(808\) | 17.0156 | + | 11.2236i | 0.598607 | + | 0.394844i | ||||
\(809\) | − | 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 | \(0.0897723\pi\) | ||||
−0.960493 | + | 0.278304i | \(0.910228\pi\) | |||||||
\(812\) | −36.6103 | − | 14.9946i | −1.28477 | − | 0.526207i | ||||
\(813\) | −18.5078 | − | 38.0241i | −0.649097 | − | 1.33357i | ||||
\(814\) | 6.20937 | − | 31.5435i | 0.217638 | − | 1.10560i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 1.82939 | − | 5.43861i | 0.0640414 | − | 0.190390i | ||||
\(817\) | 2.70156 | 0.0945157 | ||||||||
\(818\) | 7.43217 | − | 37.7553i | 0.259860 | − | 1.32008i | ||||
\(819\) | 22.7327 | + | 17.8196i | 0.794344 | + | 0.622668i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 20.5449i | 0.717023i | 0.933525 | + | 0.358511i | \(0.116716\pi\) | ||||
−0.933525 | + | 0.358511i | \(0.883284\pi\) | |||||||
\(822\) | −15.1046 | + | 3.99578i | −0.526834 | + | 0.139369i | ||||
\(823\) | 37.0760i | 1.29239i | 0.763174 | + | 0.646193i | \(0.223640\pi\) | ||||
−0.763174 | + | 0.646193i | \(0.776360\pi\) | |||||||
\(824\) | 9.67027 | + | 6.37855i | 0.336880 | + | 0.222207i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −14.8071 | −0.514895 | −0.257447 | − | 0.966292i | \(-0.582881\pi\) | ||||
−0.257447 | + | 0.966292i | \(0.582881\pi\) | |||||||
\(828\) | −5.69801 | + | 3.24156i | −0.198020 | + | 0.112652i | ||||
\(829\) | 44.8062 | 1.55619 | 0.778093 | − | 0.628150i | \(-0.216187\pi\) | ||||
0.778093 | + | 0.628150i | \(0.216187\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 43.7693 | − | 21.3042i | 1.51834 | − | 0.739034i | ||||
\(832\) | 8.50781 | + | 19.8675i | 0.294955 | + | 0.688781i | ||||
\(833\) | 4.72212i | 0.163612i | ||||||||
\(834\) | 3.59008 | − | 0.949721i | 0.124314 | − | 0.0328861i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 16.2015 | − | 39.5570i | 0.560340 | − | 1.36811i | ||||
\(837\) | −33.5078 | − | 7.20677i | −1.15820 | − | 0.249102i | ||||
\(838\) | −2.76172 | + | 14.0295i | −0.0954019 | + | 0.484640i | ||||
\(839\) | −25.6844 | −0.886723 | −0.443362 | − | 0.896343i | \(-0.646214\pi\) | ||||
−0.443362 | + | 0.896343i | \(0.646214\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.80625 | −0.0622844 | ||||||||
\(842\) | −6.61273 | + | 33.5925i | −0.227890 | + | 1.15768i | ||||
\(843\) | −5.46295 | − | 11.2236i | −0.188154 | − | 0.386561i | ||||
\(844\) | 10.7461 | − | 26.2373i | 0.369896 | − | 0.903125i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 17.2596 | + | 20.0155i | 0.593397 | + | 0.688146i | ||||
\(847\) | − | 23.8839i | − | 0.820659i | ||||||
\(848\) | −15.5737 | + | 15.8228i | −0.534802 | + | 0.543357i | ||||
\(849\) | −4.65703 | − | 9.56783i | −0.159829 | − | 0.328367i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −5.90340 | −0.202366 | ||||||||
\(852\) | 39.2929 | − | 2.52807i | 1.34615 | − | 0.0866102i | ||||
\(853\) | 37.2984 | 1.27707 | 0.638537 | − | 0.769591i | \(-0.279540\pi\) | ||||
0.638537 | + | 0.769591i | \(0.279540\pi\) | |||||||
\(854\) | 3.46940 | + | 0.682954i | 0.118720 | + | 0.0233702i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −29.3586 | + | 44.5094i | −1.00346 | + | 1.52130i | ||||
\(857\) | 12.5099i | 0.427331i | 0.976907 | + | 0.213666i | \(0.0685403\pi\) | ||||
−0.976907 | + | 0.213666i | \(0.931460\pi\) | |||||||
\(858\) | −7.12033 | − | 26.9159i | −0.243084 | − | 0.918892i | ||||
\(859\) | 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 | ||||
\(862\) | −5.40312 | + | 27.4478i | −0.184031 | + | 0.934875i | ||||
\(863\) | 29.6143 | 1.00808 | 0.504041 | − | 0.863680i | \(-0.331846\pi\) | ||||
0.504041 | + | 0.863680i | \(0.331846\pi\) | |||||||
\(864\) | 11.0968 | + | 27.2188i | 0.377521 | + | 0.926001i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 8.52476 | − | 43.3056i | 0.289683 | − | 1.47159i | ||||
\(867\) | 25.4070 | − | 12.3665i | 0.862866 | − | 0.419990i | ||||
\(868\) | 43.5078 | + | 17.8196i | 1.47675 | + | 0.604838i | ||||
\(869\) | − | 29.9892i | − | 1.01731i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 5.53243i | − | 0.187459i | ||||||
\(872\) | 13.5515 | − | 20.5449i | 0.458912 | − | 0.695739i | ||||
\(873\) | 15.0000 | − | 19.1357i | 0.507673 | − | 0.647644i | ||||
\(874\) | −7.70156 | − | 1.51606i | −0.260509 | − | 0.0512815i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 26.6239 | − | 1.71296i | 0.899540 | − | 0.0578755i | ||||
\(877\) | −48.9109 | −1.65160 | −0.825802 | − | 0.563959i | \(-0.809277\pi\) | ||||
−0.825802 | + | 0.563959i | \(0.809277\pi\) | |||||||
\(878\) | −30.4094 | − | 5.98612i | −1.02627 | − | 0.202022i | ||||
\(879\) | 14.3180 | + | 29.4163i | 0.482936 | + | 0.992187i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 26.6763i | 0.898747i | 0.893344 | + | 0.449374i | \(0.148353\pi\) | ||||
−0.893344 | + | 0.449374i | \(0.851647\pi\) | |||||||
\(882\) | −15.7970 | − | 18.3193i | −0.531911 | − | 0.616843i | ||||
\(883\) | − | 25.2412i | − | 0.849435i | −0.905326 | − | 0.424717i | \(-0.860374\pi\) | ||
0.905326 | − | 0.424717i | \(-0.139626\pi\) | |||||||
\(884\) | 1.69607 | − | 4.14108i | 0.0570451 | − | 0.139280i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −3.06015 | + | 15.5455i | −0.102808 | + | 0.522262i | ||||
\(887\) | −24.9179 | −0.836660 | −0.418330 | − | 0.908295i | \(-0.637384\pi\) | ||||
−0.418330 | + | 0.908295i | \(0.637384\pi\) | |||||||
\(888\) | −3.43442 | + | 26.2460i | −0.115251 | + | 0.880760i | ||||
\(889\) | 57.8219 | 1.93928 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −9.04246 | − | 36.7704i | −0.302934 | − | 1.23185i | ||||
\(892\) | −11.8953 | + | 29.0432i | −0.398285 | + | 0.972438i | ||||
\(893\) | 31.6456i | 1.05898i | ||||||||
\(894\) | 3.92248 | − | 1.03765i | 0.131187 | − | 0.0347044i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −8.41464 | − | 39.4334i | −0.281114 | − | 1.31738i | ||||
\(897\) | −4.59688 | + | 2.23748i | −0.153485 | + | 0.0747071i | ||||
\(898\) | 26.5523 | + | 5.22685i | 0.886063 | + | 0.174422i | ||||
\(899\) | 36.6103 | 1.22102 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 4.59688 | 0.153144 | ||||||||
\(902\) | −59.9708 | − | 11.8053i | −1.99681 | − | 0.393074i | ||||
\(903\) | −2.95170 | + | 1.43670i | −0.0982264 | + | 0.0478105i | ||||
\(904\) | 37.3586 | + | 24.6419i | 1.24253 | + | 0.819577i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | −10.9581 | + | 2.89887i | −0.364060 | + | 0.0963086i | ||||
\(907\) | − | 10.1600i | − | 0.337356i | −0.985671 | − | 0.168678i | \(-0.946050\pi\) | ||
0.985671 | − | 0.168678i | \(-0.0539498\pi\) | |||||||
\(908\) | −21.6401 | − | 8.86320i | −0.718152 | − | 0.294136i | ||||
\(909\) | 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 | \(0.116148\pi\) | |||||||
\(912\) | −11.2208 | + | 33.3586i | −0.371559 | + | 1.10461i | ||||
\(913\) | 13.1047 | 0.433702 | ||||||||
\(914\) | 4.61491 | − | 23.4437i | 0.152648 | − | 0.775448i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −16.1047 | − | 6.59605i | −0.532114 | − | 0.217939i | ||||
\(917\) | − | 70.4980i | − | 2.32805i | ||||||
\(918\) | 2.40484 | − | 5.59084i | 0.0793717 | − | 0.184525i | ||||
\(919\) | − | 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 | ||||
\(922\) | −10.0000 | − | 1.96851i | −0.329332 | − | 0.0648294i | ||||
\(923\) | 30.7069 | 1.01073 | ||||||||
\(924\) | 3.33505 | + | 51.8356i | 0.109715 | + | 1.70527i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 9.89049 | + | 1.94695i | 0.325022 | + | 0.0639809i | ||||
\(927\) | 9.67027 | + | 7.58030i | 0.317613 | + | 0.248970i | ||||
\(928\) | −17.7016 | − | 25.9317i | −0.581082 | − | 0.851251i | ||||
\(929\) | − | 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 | ||||||
\(932\) | −11.3663 | + | 27.7517i | −0.372317 | + | 0.909037i | ||||
\(933\) | −26.2094 | + | 12.7571i | −0.858056 | + | 0.417649i | ||||
\(934\) | −0.209373 | + | 1.06361i | −0.00685088 | + | 0.0348024i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 7.27332 | + | 21.7391i | 0.237736 | + | 0.710563i | ||||
\(937\) | 16.6125 | 0.542707 | 0.271353 | − | 0.962480i | \(-0.412529\pi\) | ||||
0.271353 | + | 0.962480i | \(0.412529\pi\) | |||||||
\(938\) | −1.99355 | + | 10.1272i | −0.0650917 | + | 0.330665i | ||||
\(939\) | −35.3547 | + | 17.2085i | −1.15376 | + | 0.561577i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 47.2212i | − | 1.53937i | −0.638425 | − | 0.769684i | \(-0.720414\pi\) | ||
0.638425 | − | 0.769684i | \(-0.279586\pi\) | |||||||
\(942\) | 5.07710 | + | 19.1922i | 0.165421 | + | 0.625314i | ||||
\(943\) | 11.2236i | 0.365490i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 3.10469 | + | 0.611161i | 0.100942 | + | 0.0198705i | ||||
\(947\) | 38.7955 | 1.26068 | 0.630341 | − | 0.776318i | \(-0.282915\pi\) | ||||
0.630341 | + | 0.776318i | \(0.282915\pi\) | |||||||
\(948\) | 1.58536 | + | 24.6406i | 0.0514899 | + | 0.800291i | ||||
\(949\) | 20.8062 | 0.675399 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 22.7327 | + | 46.7041i | 0.737158 | + | 1.51448i | ||||
\(952\) | −4.59688 | + | 6.96914i | −0.148986 | + | 0.225871i | ||||
\(953\) | 21.9542i | 0.711166i | 0.934645 | + | 0.355583i | \(0.115718\pi\) | ||||
−0.934645 | + | 0.355583i | \(0.884282\pi\) | |||||||
\(954\) | −17.8334 | + | 15.3780i | −0.577378 | + | 0.497880i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 10.1107 | + | 4.14108i | 0.327004 | + | 0.133932i | ||||
\(957\) | 17.7016 | + | 36.3677i | 0.572210 | + | 1.17560i | ||||
\(958\) | −11.4922 | + | 58.3802i | −0.371296 | + | 1.88618i | ||||
\(959\) | 22.7327 | 0.734077 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −12.5078 | −0.403478 | ||||||||
\(962\) | −3.98710 | + | 20.2544i | −0.128549 | + | 0.653028i | ||||
\(963\) | −34.8899 | + | 44.5094i | −1.12431 | + | 1.43429i | ||||
\(964\) | −12.9555 | − | 5.30621i | −0.417268 | − | 0.170902i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 9.22089 | − | 2.43930i | 0.296677 | − | 0.0784832i | ||||
\(967\) | − | 47.7677i | − | 1.53611i | −0.640386 | − | 0.768053i | \(-0.721226\pi\) | ||
0.640386 | − | 0.768053i | \(-0.278774\pi\) | |||||||
\(968\) | 10.4368 | − | 15.8228i | 0.335451 | − | 0.508564i | ||||
\(969\) | 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 | \(0.611991\pi\) | |||||||
\(972\) | 9.37359 | + | 29.7344i | 0.300658 | + | 0.953732i | ||||
\(973\) | −5.40312 | −0.173216 | ||||||||
\(974\) | −47.2387 | − | 9.29898i | −1.51363 | − | 0.297959i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 2.00000 | + | 1.96851i | 0.0640184 | + | 0.0630105i | ||||
\(977\) | − | 28.5799i | − | 0.914352i | −0.889376 | − | 0.457176i | \(-0.848861\pi\) | ||
0.889376 | − | 0.457176i | \(-0.151139\pi\) | |||||||
\(978\) | −12.0296 | + | 3.18231i | −0.384663 | + | 0.101759i | ||||
\(979\) | − | 19.8675i | − | 0.634968i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 16.1047 | − | 20.5449i | 0.514183 | − | 0.655949i | ||||
\(982\) | 4.59688 | − | 23.3521i | 0.146692 | − | 0.745194i | ||||
\(983\) | 57.9243 | 1.84750 | 0.923749 | − | 0.382998i | \(-0.125108\pi\) | ||||
0.923749 | + | 0.382998i | \(0.125108\pi\) | |||||||
\(984\) | 49.8992 | + | 6.52954i | 1.59073 | + | 0.208154i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −1.25562 | + | 6.37855i | −0.0399872 | + | 0.203135i | ||||
\(987\) | −16.8293 | − | 34.5756i | −0.535682 | − | 1.10055i | ||||
\(988\) | −10.4031 | + | 25.3999i | −0.330967 | + | 0.808079i | ||||
\(989\) | − | 0.581045i | − | 0.0184761i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 40.2668i | − | 1.27912i | −0.768743 | − | 0.639558i | \(-0.779117\pi\) | ||
0.768743 | − | 0.639558i | \(-0.220883\pi\) | |||||||
\(992\) | 21.0366 | + | 30.8174i | 0.667913 | + | 0.978453i | ||||
\(993\) | −22.7617 | − | 46.7638i | −0.722321 | − | 1.48400i | ||||
\(994\) | −56.2094 | − | 11.0649i | −1.78285 | − | 0.350956i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −10.7675 | + | 0.692770i | −0.341181 | + | 0.0219512i | ||||
\(997\) | 34.5969 | 1.09569 | 0.547847 | − | 0.836579i | \(-0.315448\pi\) | ||||
0.547847 | + | 0.836579i | \(0.315448\pi\) | |||||||
\(998\) | 31.8853 | + | 6.27664i | 1.00931 | + | 0.198684i | ||||
\(999\) | −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.e.d.251.4 | yes | 8 | |
3.2 | odd | 2 | inner | 300.2.e.d.251.5 | yes | 8 | |
4.3 | odd | 2 | inner | 300.2.e.d.251.6 | yes | 8 | |
5.2 | odd | 4 | 300.2.h.c.299.1 | 16 | |||
5.3 | odd | 4 | 300.2.h.c.299.16 | 16 | |||
5.4 | even | 2 | 300.2.e.e.251.5 | yes | 8 | ||
12.11 | even | 2 | inner | 300.2.e.d.251.3 | ✓ | 8 | |
15.2 | even | 4 | 300.2.h.c.299.15 | 16 | |||
15.8 | even | 4 | 300.2.h.c.299.2 | 16 | |||
15.14 | odd | 2 | 300.2.e.e.251.4 | yes | 8 | ||
20.3 | even | 4 | 300.2.h.c.299.13 | 16 | |||
20.7 | even | 4 | 300.2.h.c.299.4 | 16 | |||
20.19 | odd | 2 | 300.2.e.e.251.3 | yes | 8 | ||
60.23 | odd | 4 | 300.2.h.c.299.3 | 16 | |||
60.47 | odd | 4 | 300.2.h.c.299.14 | 16 | |||
60.59 | even | 2 | 300.2.e.e.251.6 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
300.2.e.d.251.3 | ✓ | 8 | 12.11 | even | 2 | inner | |
300.2.e.d.251.4 | yes | 8 | 1.1 | even | 1 | trivial | |
300.2.e.d.251.5 | yes | 8 | 3.2 | odd | 2 | inner | |
300.2.e.d.251.6 | yes | 8 | 4.3 | odd | 2 | inner | |
300.2.e.e.251.3 | yes | 8 | 20.19 | odd | 2 | ||
300.2.e.e.251.4 | yes | 8 | 15.14 | odd | 2 | ||
300.2.e.e.251.5 | yes | 8 | 5.4 | even | 2 | ||
300.2.e.e.251.6 | yes | 8 | 60.59 | even | 2 | ||
300.2.h.c.299.1 | 16 | 5.2 | odd | 4 | |||
300.2.h.c.299.2 | 16 | 15.8 | even | 4 | |||
300.2.h.c.299.3 | 16 | 60.23 | odd | 4 | |||
300.2.h.c.299.4 | 16 | 20.7 | even | 4 | |||
300.2.h.c.299.13 | 16 | 20.3 | even | 4 | |||
300.2.h.c.299.14 | 16 | 60.47 | odd | 4 | |||
300.2.h.c.299.15 | 16 | 15.2 | even | 4 | |||
300.2.h.c.299.16 | 16 | 5.3 | odd | 4 |