Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [855,2,Mod(64,855)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(855, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 3, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("855.64");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 855 = 3^{2} \cdot 5 \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 855.be (of order \(6\), degree \(2\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(6.82720937282\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 6x^{10} + 29x^{8} - 40x^{6} + 43x^{4} - 7x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{4}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 95) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 64.1 | ||
Root | \(-0.352587 + 0.203566i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 855.64 |
Dual form | 855.2.be.d.334.1 |
$q$-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 \(\left(\mathbb{Z}/855\mathbb{Z}\right)^\times\).
\(n\) | \(172\) | \(191\) | \(496\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.12713 | + | 1.22810i | −1.50411 | + | 0.868399i | −0.504123 | + | 0.863632i | \(0.668184\pi\) |
−0.999989 | + | 0.00476685i | \(0.998483\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 2.01647 | − | 3.49262i | 1.00823 | − | 1.74631i | ||||
\(5\) | 0.746759 | + | 2.10769i | 0.333961 | + | 0.942587i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 4.50527i | 1.70283i | 0.524490 | + | 0.851417i | \(0.324256\pi\) | ||||
−0.524490 | + | 0.851417i | \(0.675744\pi\) | |||||||
\(8\) | 4.99330i | 1.76540i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −4.17691 | − | 3.56624i | −1.32086 | − | 1.12774i | ||||
\(11\) | −2.19869 | −0.662930 | −0.331465 | − | 0.943467i | \(-0.607543\pi\) | ||||
−0.331465 | + | 0.943467i | \(0.607543\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.25495 | − | 1.87925i | −0.902761 | − | 0.521209i | −0.0246661 | − | 0.999696i | \(-0.507852\pi\) |
−0.878095 | + | 0.478486i | \(0.841186\pi\) | |||||||
\(14\) | −5.53293 | − | 9.58332i | −1.47874 | − | 2.56125i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −2.09935 | − | 3.63617i | −0.524836 | − | 0.909043i | ||||
\(17\) | −0.576674 | + | 0.332943i | −0.139864 | + | 0.0807506i | −0.568299 | − | 0.822822i | \(-0.692398\pi\) |
0.428435 | + | 0.903573i | \(0.359065\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.79804 | − | 2.13891i | −0.871329 | − | 0.490699i | ||||
\(20\) | 8.86718 | + | 1.64194i | 1.98276 | + | 0.367149i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 4.67691 | − | 2.70022i | 0.997121 | − | 0.575688i | ||||
\(23\) | 0.422643 | + | 0.244013i | 0.0881272 | + | 0.0508802i | 0.543416 | − | 0.839464i | \(-0.317131\pi\) |
−0.455289 | + | 0.890344i | \(0.650464\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.88470 | + | 3.14787i | −0.776941 | + | 0.629574i | ||||
\(26\) | 9.23163 | 1.81047 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 15.7352 | + | 9.08474i | 2.97368 | + | 1.71685i | ||||
\(29\) | −1.79804 | + | 3.11429i | −0.333887 | + | 0.578309i | −0.983270 | − | 0.182152i | \(-0.941694\pi\) |
0.649383 | + | 0.760461i | \(0.275027\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.83424 | 1.22747 | 0.613733 | − | 0.789514i | \(-0.289667\pi\) | ||||
0.613733 | + | 0.789514i | \(0.289667\pi\) | |||||||
\(32\) | 0.282531 | + | 0.163119i | 0.0499449 | + | 0.0288357i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0.817776 | − | 1.41643i | 0.140247 | − | 0.242916i | ||||
\(35\) | −9.49572 | + | 3.36435i | −1.60507 | + | 0.568679i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 3.01171i | − | 0.495123i | −0.968872 | − | 0.247561i | \(-0.920371\pi\) | ||
0.968872 | − | 0.247561i | \(-0.0796292\pi\) | |||||||
\(38\) | 10.7057 | − | 0.114636i | 1.73670 | − | 0.0185964i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −10.5243 | + | 3.72879i | −1.66404 | + | 0.589573i | ||||
\(41\) | 0.0362063 | + | 0.0627112i | 0.00565448 | + | 0.00979384i | 0.868839 | − | 0.495095i | \(-0.164867\pi\) |
−0.863184 | + | 0.504889i | \(0.831533\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.364199 | + | 0.210271i | −0.0555399 | + | 0.0320660i | −0.527513 | − | 0.849547i | \(-0.676875\pi\) |
0.471973 | + | 0.881613i | \(0.343542\pi\) | |||||||
\(44\) | −4.43359 | + | 7.67920i | −0.668389 | + | 1.15768i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −1.19869 | −0.176737 | ||||||||
\(47\) | 4.34986 | + | 2.51139i | 0.634492 | + | 0.366324i | 0.782490 | − | 0.622664i | \(-0.213950\pi\) |
−0.147998 | + | 0.988988i | \(0.547283\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −13.2975 | −1.89964 | ||||||||
\(50\) | 4.39738 | − | 11.4668i | 0.621884 | − | 1.62164i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −13.1270 | + | 7.57888i | −1.82039 | + | 1.05100i | ||||
\(53\) | −2.26725 | − | 1.30900i | −0.311430 | − | 0.179804i | 0.336136 | − | 0.941813i | \(-0.390880\pi\) |
−0.647566 | + | 0.762009i | \(0.724213\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.64189 | − | 4.63416i | −0.221393 | − | 0.624870i | ||||
\(56\) | −22.4962 | −3.00618 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | − | 8.83269i | − | 1.15979i | ||||||
\(59\) | −6.26783 | − | 10.8562i | −0.816002 | − | 1.41336i | −0.908606 | − | 0.417654i | \(-0.862852\pi\) |
0.0926038 | − | 0.995703i | \(-0.470481\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.53293 | + | 6.11922i | −0.452346 | + | 0.783486i | −0.998531 | − | 0.0541782i | \(-0.982746\pi\) |
0.546185 | + | 0.837664i | \(0.316079\pi\) | |||||||
\(62\) | −14.5374 | + | 8.39315i | −1.84625 | + | 1.06593i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 7.59607 | 0.949509 | ||||||||
\(65\) | 1.53020 | − | 8.26377i | 0.189799 | − | 1.02499i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.95944 | − | 2.86334i | −0.605892 | − | 0.349812i | 0.165464 | − | 0.986216i | \(-0.447088\pi\) |
−0.771356 | + | 0.636404i | \(0.780421\pi\) | |||||||
\(68\) | 2.68548i | 0.325662i | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 16.0669 | − | 18.8181i | 1.92036 | − | 2.24920i | ||||
\(71\) | 3.48626 | + | 6.03838i | 0.413743 | + | 0.716624i | 0.995296 | − | 0.0968847i | \(-0.0308878\pi\) |
−0.581552 | + | 0.813509i | \(0.697554\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.56139 | − | 1.47882i | 0.299788 | − | 0.173083i | −0.342560 | − | 0.939496i | \(-0.611294\pi\) |
0.642348 | + | 0.766413i | \(0.277961\pi\) | |||||||
\(74\) | 3.69869 | + | 6.40632i | 0.429964 | + | 0.744720i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −15.1290 | + | 8.95208i | −1.73542 | + | 1.02687i | ||||
\(77\) | − | 9.90571i | − | 1.12886i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 5.66849 | + | 9.81811i | 0.637755 | + | 1.10462i | 0.985924 | + | 0.167192i | \(0.0534699\pi\) |
−0.348170 | + | 0.937431i | \(0.613197\pi\) | |||||||
\(80\) | 6.09622 | − | 7.14011i | 0.681578 | − | 0.798289i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −0.154031 | − | 0.0889301i | −0.0170099 | − | 0.00982068i | ||||
\(83\) | − | 15.6999i | − | 1.72328i | −0.507517 | − | 0.861642i | \(-0.669436\pi\) | ||
0.507517 | − | 0.861642i | \(-0.330564\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.13238 | − | 0.966822i | −0.122824 | − | 0.104867i | ||||
\(86\) | 0.516467 | − | 0.894547i | 0.0556921 | − | 0.0964615i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | − | 10.9787i | − | 1.17034i | ||||||
\(89\) | 0.668486 | − | 1.15785i | 0.0708594 | − | 0.122732i | −0.828419 | − | 0.560109i | \(-0.810759\pi\) |
0.899278 | + | 0.437377i | \(0.144092\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 8.46652 | − | 14.6644i | 0.887533 | − | 1.53725i | ||||
\(92\) | 1.70449 | − | 0.984089i | 0.177706 | − | 0.102598i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −12.3370 | −1.27246 | ||||||||
\(95\) | 1.67193 | − | 9.60233i | 0.171536 | − | 0.985178i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 3.79871 | − | 2.19319i | 0.385701 | − | 0.222685i | −0.294595 | − | 0.955622i | \(-0.595185\pi\) |
0.680296 | + | 0.732938i | \(0.261851\pi\) | |||||||
\(98\) | 28.2856 | − | 16.3307i | 2.85727 | − | 1.64965i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 3.16095 | + | 19.9154i | 0.316095 | + | 1.99154i | ||||
\(101\) | −5.28430 | + | 9.15267i | −0.525807 | + | 0.910725i | 0.473741 | + | 0.880664i | \(0.342903\pi\) |
−0.999548 | + | 0.0300608i | \(0.990430\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 5.75615i | − | 0.567171i | −0.958947 | − | 0.283585i | \(-0.908476\pi\) | ||
0.958947 | − | 0.283585i | \(-0.0915239\pi\) | |||||||
\(104\) | 9.38364 | − | 16.2529i | 0.920142 | − | 1.59373i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 6.43032 | 0.624568 | ||||||||
\(107\) | 1.30229i | 0.125897i | 0.998017 | + | 0.0629486i | \(0.0200504\pi\) | ||||
−0.998017 | + | 0.0629486i | \(0.979950\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −6.01647 | − | 10.4208i | −0.576273 | − | 0.998134i | −0.995902 | − | 0.0904385i | \(-0.971173\pi\) |
0.419629 | − | 0.907696i | \(-0.362160\pi\) | |||||||
\(110\) | 9.18374 | + | 7.84106i | 0.875635 | + | 0.747616i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 16.3820 | − | 9.45813i | 1.54795 | − | 0.893709i | ||||
\(113\) | 7.74626i | 0.728707i | 0.931261 | + | 0.364353i | \(0.118710\pi\) | ||||
−0.931261 | + | 0.364353i | \(0.881290\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −0.198691 | + | 1.07302i | −0.0185281 | + | 0.100060i | ||||
\(116\) | 7.25136 | + | 12.5597i | 0.673272 | + | 1.16614i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 26.6650 | + | 15.3951i | 2.45472 | + | 1.41723i | ||||
\(119\) | −1.50000 | − | 2.59808i | −0.137505 | − | 0.238165i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −6.16576 | −0.560523 | ||||||||
\(122\) | − | 17.3552i | − | 1.57127i | ||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 13.7810 | − | 23.8694i | 1.23757 | − | 2.14354i | ||||
\(125\) | −9.53566 | − | 5.83705i | −0.852896 | − | 0.522081i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 3.40898 | + | 1.96818i | 0.302498 | + | 0.174647i | 0.643565 | − | 0.765392i | \(-0.277455\pi\) |
−0.341066 | + | 0.940039i | \(0.610788\pi\) | |||||||
\(128\) | −16.7229 | + | 9.65499i | −1.47811 | + | 0.853389i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 6.89380 | + | 19.4574i | 0.604626 | + | 1.70653i | ||||
\(131\) | −8.16248 | − | 14.1378i | −0.713160 | − | 1.23523i | −0.963665 | − | 0.267114i | \(-0.913930\pi\) |
0.250505 | − | 0.968115i | \(-0.419403\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 9.63635 | − | 17.1112i | 0.835578 | − | 1.48373i | ||||
\(134\) | 14.0659 | 1.21511 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −1.66248 | − | 2.87951i | −0.142557 | − | 0.246916i | ||||
\(137\) | −14.2293 | − | 8.21529i | −1.21569 | − | 0.701879i | −0.251697 | − | 0.967806i | \(-0.580989\pi\) |
−0.963993 | + | 0.265927i | \(0.914322\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1.33424 | + | 2.31098i | −0.113169 | + | 0.196015i | −0.917046 | − | 0.398781i | \(-0.869433\pi\) |
0.803877 | + | 0.594795i | \(0.202767\pi\) | |||||||
\(140\) | −7.39738 | + | 39.9491i | −0.625193 | + | 3.37631i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −14.8315 | − | 8.56297i | −1.24463 | − | 0.718588i | ||||
\(143\) | 7.15663 | + | 4.13188i | 0.598468 | + | 0.345526i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −7.90666 | − | 1.46408i | −0.656612 | − | 0.121585i | ||||
\(146\) | −3.63228 | + | 6.29129i | −0.300610 | + | 0.520671i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −10.5188 | − | 6.07302i | −0.864639 | − | 0.499199i | ||||
\(149\) | 8.98299 | + | 15.5590i | 0.735915 | + | 1.27464i | 0.954321 | + | 0.298784i | \(0.0965812\pi\) |
−0.218405 | + | 0.975858i | \(0.570085\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −12.7344 | −1.03631 | −0.518154 | − | 0.855288i | \(-0.673380\pi\) | ||||
−0.518154 | + | 0.855288i | \(0.673380\pi\) | |||||||
\(152\) | 10.6802 | − | 18.9647i | 0.866278 | − | 1.53824i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 12.1652 | + | 21.0708i | 0.980301 | + | 1.69793i | ||||
\(155\) | 5.10353 | + | 14.4045i | 0.409925 | + | 1.15699i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −17.3674 | + | 10.0270i | −1.38607 | + | 0.800245i | −0.992869 | − | 0.119209i | \(-0.961964\pi\) |
−0.393197 | + | 0.919454i | \(0.628631\pi\) | |||||||
\(158\) | −24.1153 | − | 13.9230i | −1.91851 | − | 1.10765i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −0.132822 | + | 0.717298i | −0.0105005 | + | 0.0567074i | ||||
\(161\) | −1.09935 | + | 1.90412i | −0.0866406 | + | 0.150066i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 14.2331i | 1.11482i | 0.830236 | + | 0.557412i | \(0.188206\pi\) | ||||
−0.830236 | + | 0.557412i | \(0.811794\pi\) | |||||||
\(164\) | 0.292035 | 0.0228041 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 19.2810 | + | 33.3957i | 1.49650 | + | 2.59201i | ||||
\(167\) | 4.86386 | + | 2.80815i | 0.376376 | + | 0.217301i | 0.676241 | − | 0.736681i | \(-0.263608\pi\) |
−0.299864 | + | 0.953982i | \(0.596941\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0.563139 | + | 0.975386i | 0.0433184 | + | 0.0750297i | ||||
\(170\) | 3.59607 | + | 0.665886i | 0.275806 | + | 0.0510711i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 1.69601i | 0.129320i | ||||||||
\(173\) | −9.25824 | + | 5.34524i | −0.703891 | + | 0.406391i | −0.808795 | − | 0.588091i | \(-0.799880\pi\) |
0.104904 | + | 0.994482i | \(0.466546\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −14.1820 | − | 17.5017i | −1.07206 | − | 1.32300i | ||||
\(176\) | 4.61581 | + | 7.99482i | 0.347930 | + | 0.602632i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 3.28388i | 0.246137i | ||||||||
\(179\) | 7.68942 | 0.574734 | 0.287367 | − | 0.957821i | \(-0.407220\pi\) | ||||
0.287367 | + | 0.957821i | \(0.407220\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3.06314 | − | 5.30551i | 0.227681 | − | 0.394356i | −0.729439 | − | 0.684046i | \(-0.760219\pi\) |
0.957121 | + | 0.289690i | \(0.0935522\pi\) | |||||||
\(182\) | 41.5910i | 3.08293i | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −1.21843 | + | 2.11038i | −0.0898239 | + | 0.155580i | ||||
\(185\) | 6.34776 | − | 2.24902i | 0.466696 | − | 0.165351i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.26793 | − | 0.732039i | 0.0927201 | − | 0.0535320i | ||||
\(188\) | 17.5427 | − | 10.1283i | 1.27943 | − | 0.738680i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 8.23621 | + | 22.4787i | 0.597518 | + | 1.63078i | ||||
\(191\) | −5.85517 | −0.423666 | −0.211833 | − | 0.977306i | \(-0.567943\pi\) | ||||
−0.211833 | + | 0.977306i | \(0.567943\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2.24402 | + | 1.29559i | −0.161528 | + | 0.0932584i | −0.578585 | − | 0.815622i | \(-0.696395\pi\) |
0.417057 | + | 0.908880i | \(0.363062\pi\) | |||||||
\(194\) | −5.38692 | + | 9.33041i | −0.386758 | + | 0.669885i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −26.8140 | + | 46.4431i | −1.91528 | + | 3.31737i | ||||
\(197\) | 19.8628i | 1.41517i | 0.706629 | + | 0.707584i | \(0.250215\pi\) | ||||
−0.706629 | + | 0.707584i | \(0.749785\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −6.38092 | + | 11.0521i | −0.452331 | + | 0.783460i | −0.998530 | − | 0.0541948i | \(-0.982741\pi\) |
0.546199 | + | 0.837655i | \(0.316074\pi\) | |||||||
\(200\) | −15.7183 | − | 19.3975i | −1.11145 | − | 1.37161i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | − | 25.9586i | − | 1.82644i | ||||||
\(203\) | −14.0307 | − | 8.10065i | −0.984765 | − | 0.568554i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −0.105138 | + | 0.123142i | −0.00734318 | + | 0.00860059i | ||||
\(206\) | 7.06914 | + | 12.2441i | 0.492530 | + | 0.853088i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 15.7808i | 1.09420i | ||||||||
\(209\) | 8.35071 | + | 4.70279i | 0.577631 | + | 0.325299i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −6.92759 | − | 11.9989i | −0.476915 | − | 0.826041i | 0.522735 | − | 0.852495i | \(-0.324912\pi\) |
−0.999650 | + | 0.0264545i | \(0.991578\pi\) | |||||||
\(212\) | −9.14366 | + | 5.27909i | −0.627989 | + | 0.362570i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −1.59935 | − | 2.77015i | −0.109329 | − | 0.189363i | ||||
\(215\) | −0.715154 | − | 0.610597i | −0.0487731 | − | 0.0416424i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 30.7901i | 2.09017i | ||||||||
\(218\) | 25.5957 | + | 14.7777i | 1.73356 | + | 1.00087i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −19.4962 | − | 3.61012i | −1.31443 | − | 0.243394i | ||||
\(221\) | 2.50273 | 0.168352 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 18.7893 | − | 10.8480i | 1.25823 | − | 0.726437i | 0.285496 | − | 0.958380i | \(-0.407842\pi\) |
0.972729 | + | 0.231943i | \(0.0745083\pi\) | |||||||
\(224\) | −0.734898 | + | 1.27288i | −0.0491024 | + | 0.0850479i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −9.51320 | − | 16.4773i | −0.632808 | − | 1.09606i | ||||
\(227\) | 8.19628i | 0.544006i | 0.962296 | + | 0.272003i | \(0.0876861\pi\) | ||||
−0.962296 | + | 0.272003i | \(0.912314\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 16.6619 | 1.10105 | 0.550526 | − | 0.834818i | \(-0.314427\pi\) | ||||
0.550526 | + | 0.834818i | \(0.314427\pi\) | |||||||
\(230\) | −0.895133 | − | 2.52647i | −0.0590233 | − | 0.166590i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −15.5506 | − | 8.97814i | −1.02095 | − | 0.589444i | ||||
\(233\) | −10.5772 | + | 6.10677i | −0.692937 | + | 0.400068i | −0.804711 | − | 0.593666i | \(-0.797680\pi\) |
0.111774 | + | 0.993734i | \(0.464347\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −2.04494 | + | 11.0435i | −0.133397 | + | 0.720402i | ||||
\(236\) | −50.5555 | −3.29088 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 6.38140 | + | 3.68430i | 0.413645 | + | 0.238818i | ||||
\(239\) | 2.03948 | 0.131923 | 0.0659614 | − | 0.997822i | \(-0.478989\pi\) | ||||
0.0659614 | + | 0.997822i | \(0.478989\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −8.76183 | + | 15.1759i | −0.564399 | + | 0.977568i | 0.432706 | + | 0.901535i | \(0.357559\pi\) |
−0.997105 | + | 0.0760330i | \(0.975775\pi\) | |||||||
\(242\) | 13.1154 | − | 7.57218i | 0.843089 | − | 0.486758i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 14.2481 | + | 24.6784i | 0.912141 | + | 1.57987i | ||||
\(245\) | −9.93002 | − | 28.0270i | −0.634406 | − | 1.79058i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 8.34289 | + | 14.0995i | 0.530846 | + | 0.897129i | ||||
\(248\) | 34.1254i | 2.16697i | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 27.4521 | + | 0.705418i | 1.73622 | + | 0.0446146i | ||||
\(251\) | −1.66903 | + | 2.89084i | −0.105348 | + | 0.182468i | −0.913880 | − | 0.405984i | \(-0.866929\pi\) |
0.808532 | + | 0.588452i | \(0.200262\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −0.929261 | − | 0.536509i | −0.0584222 | − | 0.0337301i | ||||
\(254\) | −9.66849 | −0.606655 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 16.1185 | − | 27.9181i | 1.00741 | − | 1.74488i | ||||
\(257\) | 23.8889 | + | 13.7922i | 1.49015 | + | 0.860337i | 0.999937 | − | 0.0112676i | \(-0.00358665\pi\) |
0.490210 | + | 0.871604i | \(0.336920\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 13.5686 | 0.843112 | ||||||||
\(260\) | −25.7766 | − | 22.0080i | −1.59860 | − | 1.36488i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 34.7254 | + | 20.0487i | 2.14534 | + | 1.23861i | ||||
\(263\) | 11.8006 | − | 6.81310i | 0.727658 | − | 0.420114i | −0.0899066 | − | 0.995950i | \(-0.528657\pi\) |
0.817565 | + | 0.575837i | \(0.195324\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.06587 | − | 5.75615i | 0.0654758 | − | 0.353598i | ||||
\(266\) | 0.516467 | + | 48.2322i | 0.0316666 | + | 2.95731i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −20.0011 | + | 11.5476i | −1.22176 | + | 0.705385i | ||||
\(269\) | 1.80404 | + | 3.12469i | 0.109994 | + | 0.190515i | 0.915768 | − | 0.401708i | \(-0.131583\pi\) |
−0.805773 | + | 0.592224i | \(0.798250\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −5.28157 | − | 9.14795i | −0.320833 | − | 0.555698i | 0.659828 | − | 0.751417i | \(-0.270629\pi\) |
−0.980660 | + | 0.195719i | \(0.937296\pi\) | |||||||
\(272\) | 2.42128 | + | 1.39793i | 0.146812 | + | 0.0847617i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 40.3568 | 2.43804 | ||||||||
\(275\) | 8.54126 | − | 6.92119i | 0.515058 | − | 0.417364i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 6.73487i | 0.404659i | 0.979317 | + | 0.202330i | \(0.0648512\pi\) | ||||
−0.979317 | + | 0.202330i | \(0.935149\pi\) | |||||||
\(278\) | − | 6.55434i | − | 0.393103i | ||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −16.7992 | − | 47.4150i | −1.00395 | − | 2.83359i | ||||
\(281\) | 11.7152 | − | 20.2912i | 0.698868 | − | 1.21047i | −0.269992 | − | 0.962863i | \(-0.587021\pi\) |
0.968859 | − | 0.247612i | \(-0.0796457\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −12.7160 | + | 7.34157i | −0.755886 | + | 0.436411i | −0.827817 | − | 0.560999i | \(-0.810417\pi\) |
0.0719306 | + | 0.997410i | \(0.477084\pi\) | |||||||
\(284\) | 28.1197 | 1.66860 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −20.2975 | −1.20022 | ||||||||
\(287\) | −0.282531 | + | 0.163119i | −0.0166773 | + | 0.00962863i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −8.27830 | + | 14.3384i | −0.486959 | + | 0.843437i | ||||
\(290\) | 18.6166 | − | 6.59589i | 1.09320 | − | 0.387324i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | − | 11.9280i | − | 0.698031i | ||||||
\(293\) | 18.1855i | 1.06241i | 0.847243 | + | 0.531206i | \(0.178261\pi\) | ||||
−0.847243 | + | 0.531206i | \(0.821739\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 18.2009 | − | 21.3176i | 1.05970 | − | 1.24116i | ||||
\(296\) | 15.0384 | 0.874089 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −38.2161 | − | 22.0641i | −2.21380 | − | 1.27814i | ||||
\(299\) | −0.917122 | − | 1.58850i | −0.0530385 | − | 0.0918654i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −0.947326 | − | 1.64082i | −0.0546030 | − | 0.0945752i | ||||
\(302\) | 27.0877 | − | 15.6391i | 1.55872 | − | 0.899928i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0.195962 | + | 18.3006i | 0.0112392 | + | 1.04961i | ||||
\(305\) | −15.5357 | − | 2.87674i | −0.889570 | − | 0.164722i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −25.4439 | + | 14.6901i | −1.45216 | + | 0.838406i | −0.998604 | − | 0.0528200i | \(-0.983179\pi\) |
−0.453559 | + | 0.891226i | \(0.649846\pi\) | |||||||
\(308\) | −34.5969 | − | 19.9745i | −1.97134 | − | 1.13815i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −28.5460 | − | 24.3726i | −1.62131 | − | 1.38427i | ||||
\(311\) | 0.193232 | 0.0109572 | 0.00547859 | − | 0.999985i | \(-0.498256\pi\) | ||||
0.00547859 | + | 0.999985i | \(0.498256\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 18.4251 | + | 10.6377i | 1.04145 | + | 0.601281i | 0.920243 | − | 0.391346i | \(-0.127991\pi\) |
0.121206 | + | 0.992627i | \(0.461324\pi\) | |||||||
\(314\) | 24.6285 | − | 42.6578i | 1.38986 | − | 2.40732i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 45.7213 | 2.57202 | ||||||||
\(317\) | −16.6018 | − | 9.58506i | −0.932451 | − | 0.538351i | −0.0448649 | − | 0.998993i | \(-0.514286\pi\) |
−0.887586 | + | 0.460642i | \(0.847619\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 3.95333 | − | 6.84736i | 0.221344 | − | 0.383379i | ||||
\(320\) | 5.67243 | + | 16.0102i | 0.317099 | + | 0.894995i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | − | 5.40043i | − | 0.300954i | ||||||
\(323\) | 2.90236 | − | 0.0310783i | 0.161492 | − | 0.00172924i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 18.5601 | − | 2.94584i | 1.02953 | − | 0.163406i | ||||
\(326\) | −17.4797 | − | 30.2758i | −0.968112 | − | 1.67682i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −0.313136 | + | 0.180789i | −0.0172900 | + | 0.00998240i | ||||
\(329\) | −11.3145 | + | 19.5973i | −0.623789 | + | 1.08043i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −20.6070 | −1.13266 | −0.566331 | − | 0.824178i | \(-0.691638\pi\) | ||||
−0.566331 | + | 0.824178i | \(0.691638\pi\) | |||||||
\(332\) | −54.8337 | − | 31.6583i | −3.00939 | − | 1.73747i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −13.7948 | −0.754816 | ||||||||
\(335\) | 2.33151 | − | 12.5912i | 0.127384 | − | 0.687930i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 8.83982 | − | 5.10368i | 0.481536 | − | 0.278015i | −0.239520 | − | 0.970891i | \(-0.576990\pi\) |
0.721056 | + | 0.692876i | \(0.243657\pi\) | |||||||
\(338\) | −2.39575 | − | 1.38318i | −0.130311 | − | 0.0752353i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −5.66015 | + | 2.00540i | −0.306965 | + | 0.108758i | ||||
\(341\) | −15.0264 | −0.813725 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 28.3719i | − | 1.53194i | ||||||
\(344\) | −1.04994 | − | 1.81856i | −0.0566092 | − | 0.0980500i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 13.1290 | − | 22.7401i | 0.705820 | − | 1.22252i | ||||
\(347\) | 4.71213 | − | 2.72055i | 0.252960 | − | 0.146047i | −0.368159 | − | 0.929763i | \(-0.620012\pi\) |
0.621119 | + | 0.783716i | \(0.286678\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1.55114 | 0.0830304 | 0.0415152 | − | 0.999138i | \(-0.486781\pi\) | ||||
0.0415152 | + | 0.999138i | \(0.486781\pi\) | |||||||
\(350\) | 51.6609 | + | 19.8114i | 2.76139 | + | 1.05896i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −0.621199 | − | 0.358649i | −0.0331100 | − | 0.0191161i | ||||
\(353\) | 32.9335i | 1.75287i | 0.481517 | + | 0.876437i | \(0.340086\pi\) | ||||
−0.481517 | + | 0.876437i | \(0.659914\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −10.1236 | + | 11.8572i | −0.537307 | + | 0.629313i | ||||
\(356\) | −2.69596 | − | 4.66954i | −0.142886 | − | 0.247485i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −16.3564 | + | 9.44339i | −0.864464 | + | 0.499098i | ||||
\(359\) | 1.74864 | + | 3.02873i | 0.0922894 | + | 0.159850i | 0.908474 | − | 0.417941i | \(-0.137248\pi\) |
−0.816185 | + | 0.577791i | \(0.803915\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 9.85017 | + | 16.2473i | 0.518430 | + | 0.855120i | ||||
\(362\) | 15.0474i | 0.790873i | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −34.1449 | − | 59.1408i | −1.78968 | − | 3.09982i | ||||
\(365\) | 5.02963 | + | 4.29429i | 0.263263 | + | 0.224773i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 16.8909 | + | 9.75196i | 0.881697 | + | 0.509048i | 0.871218 | − | 0.490897i | \(-0.163331\pi\) |
0.0104794 | + | 0.999945i | \(0.496664\pi\) | |||||||
\(368\) | − | 2.04907i | − | 0.106815i | ||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −10.7405 | + | 12.5797i | −0.558372 | + | 0.653986i | ||||
\(371\) | 5.89738 | − | 10.2146i | 0.306177 | − | 0.530314i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 23.5158i | 1.21760i | 0.793322 | + | 0.608802i | \(0.208350\pi\) | ||||
−0.793322 | + | 0.608802i | \(0.791650\pi\) | |||||||
\(374\) | −1.79804 | + | 3.11429i | −0.0929743 | + | 0.161036i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −12.5401 | + | 21.7201i | −0.646708 | + | 1.12013i | ||||
\(377\) | 11.7050 | − | 6.75791i | 0.602841 | − | 0.348050i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 7.05148 | 0.362210 | 0.181105 | − | 0.983464i | \(-0.442033\pi\) | ||||
0.181105 | + | 0.983464i | \(0.442033\pi\) | |||||||
\(380\) | −30.1659 | − | 25.2022i | −1.54748 | − | 1.29285i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 12.4547 | − | 7.19075i | 0.637240 | − | 0.367911i | ||||
\(383\) | −2.67090 | + | 1.54204i | −0.136476 | + | 0.0787947i | −0.566684 | − | 0.823935i | \(-0.691774\pi\) |
0.430207 | + | 0.902730i | \(0.358440\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 20.8781 | − | 7.39717i | 1.06405 | − | 0.376995i | ||||
\(386\) | 3.18222 | − | 5.51177i | 0.161971 | − | 0.280542i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | − | 17.6900i | − | 0.898072i | ||||||
\(389\) | −4.69542 | + | 8.13270i | −0.238067 | + | 0.412345i | −0.960160 | − | 0.279452i | \(-0.909847\pi\) |
0.722092 | + | 0.691797i | \(0.243181\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −0.324970 | −0.0164344 | ||||||||
\(392\) | − | 66.3984i | − | 3.35362i | ||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −24.3936 | − | 42.2509i | −1.22893 | − | 2.12857i | ||||
\(395\) | −16.4605 | + | 19.2792i | −0.828219 | + | 0.970040i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 23.1744 | − | 13.3797i | 1.16309 | − | 0.671510i | 0.211047 | − | 0.977476i | \(-0.432313\pi\) |
0.952042 | + | 0.305966i | \(0.0989794\pi\) | |||||||
\(398\) | − | 31.3456i | − | 1.57122i | ||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 19.6015 | + | 7.51699i | 0.980077 | + | 0.375849i | ||||
\(401\) | −12.5851 | − | 21.7980i | −0.628468 | − | 1.08854i | −0.987859 | − | 0.155352i | \(-0.950349\pi\) |
0.359391 | − | 0.933187i | \(-0.382984\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −22.2451 | − | 12.8432i | −1.10811 | − | 0.639767i | ||||
\(404\) | 21.3112 | + | 36.9121i | 1.06027 | + | 1.83645i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 39.7937 | 1.97493 | ||||||||
\(407\) | 6.62183i | 0.328232i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −14.1608 | + | 24.5271i | −0.700204 | + | 1.21279i | 0.268191 | + | 0.963366i | \(0.413574\pi\) |
−0.968395 | + | 0.249423i | \(0.919759\pi\) | |||||||
\(410\) | 0.0724126 | − | 0.391060i | 0.00357621 | − | 0.0193131i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −20.1041 | − | 11.6071i | −0.990457 | − | 0.571840i | ||||
\(413\) | 48.9102 | − | 28.2383i | 2.40671 | − | 1.38952i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 33.0904 | − | 11.7240i | 1.62435 | − | 0.575509i | ||||
\(416\) | −0.613083 | − | 1.06189i | −0.0300589 | − | 0.0520635i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −23.5386 | + | 0.252049i | −1.15131 | + | 0.0123281i | ||||
\(419\) | 13.0449 | 0.637287 | 0.318643 | − | 0.947875i | \(-0.396773\pi\) | ||||
0.318643 | + | 0.947875i | \(0.396773\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1.66248 | − | 2.87951i | −0.0810246 | − | 0.140339i | 0.822666 | − | 0.568525i | \(-0.192486\pi\) |
−0.903690 | + | 0.428187i | \(0.859153\pi\) | |||||||
\(422\) | 29.4718 | + | 17.0156i | 1.43467 | + | 0.828305i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 6.53621 | − | 11.3210i | 0.317426 | − | 0.549798i | ||||
\(425\) | 1.19215 | − | 3.10868i | 0.0578276 | − | 0.150793i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −27.5688 | − | 15.9168i | −1.33415 | − | 0.770270i | ||||
\(428\) | 4.54841 | + | 2.62603i | 0.219856 | + | 0.126934i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 2.27110 | + | 0.420541i | 0.109522 | + | 0.0202803i | ||||
\(431\) | 0.0242034 | − | 0.0419216i | 0.00116584 | − | 0.00201929i | −0.865442 | − | 0.501009i | \(-0.832962\pi\) |
0.866608 | + | 0.498990i | \(0.166296\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 8.28676 | + | 4.78436i | 0.398236 | + | 0.229922i | 0.685723 | − | 0.727863i | \(-0.259486\pi\) |
−0.287486 | + | 0.957785i | \(0.592820\pi\) | |||||||
\(434\) | −37.8134 | − | 65.4948i | −1.81510 | − | 3.14385i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −48.5280 | −2.32407 | ||||||||
\(437\) | −1.08329 | − | 1.83076i | −0.0518209 | − | 0.0875773i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −11.1257 | − | 19.2703i | −0.531002 | − | 0.919723i | −0.999345 | − | 0.0361764i | \(-0.988482\pi\) |
0.468343 | − | 0.883547i | \(-0.344851\pi\) | |||||||
\(440\) | 23.1397 | − | 8.19846i | 1.10314 | − | 0.390846i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −5.32364 | + | 3.07361i | −0.253220 | + | 0.146197i | ||||
\(443\) | 17.4207 | + | 10.0579i | 0.827684 | + | 0.477863i | 0.853059 | − | 0.521815i | \(-0.174745\pi\) |
−0.0253753 | + | 0.999678i | \(0.508078\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2.93959 | + | 0.544325i | 0.139350 | + | 0.0258035i | ||||
\(446\) | −26.6449 | + | 46.1504i | −1.26167 | + | 2.18528i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 34.2224i | 1.61686i | ||||||||
\(449\) | −12.4973 | −0.589783 | −0.294891 | − | 0.955531i | \(-0.595283\pi\) | ||||
−0.294891 | + | 0.955531i | \(0.595283\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −0.0796065 | − | 0.137883i | −0.00374852 | − | 0.00649263i | ||||
\(452\) | 27.0548 | + | 15.6201i | 1.27255 | + | 0.734707i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −10.0659 | − | 17.4346i | −0.472415 | − | 0.818246i | ||||
\(455\) | 37.2305 | + | 6.89399i | 1.74539 | + | 0.323195i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 28.3179i | 1.32465i | 0.749215 | + | 0.662327i | \(0.230431\pi\) | ||||
−0.749215 | + | 0.662327i | \(0.769569\pi\) | |||||||
\(458\) | −35.4422 | + | 20.4626i | −1.65610 | + | 0.956153i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 3.34700 | + | 2.85766i | 0.156054 | + | 0.133239i | ||||
\(461\) | 2.65976 | + | 4.60683i | 0.123877 | + | 0.214562i | 0.921293 | − | 0.388868i | \(-0.127134\pi\) |
−0.797416 | + | 0.603430i | \(0.793800\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 17.9327i | − | 0.833401i | −0.909044 | − | 0.416701i | \(-0.863186\pi\) | ||
0.909044 | − | 0.416701i | \(-0.136814\pi\) | |||||||
\(464\) | 15.0988 | 0.700944 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 14.9995 | − | 25.9798i | 0.694836 | − | 1.20349i | ||||
\(467\) | 28.7791i | 1.33174i | 0.746069 | + | 0.665868i | \(0.231939\pi\) | ||||
−0.746069 | + | 0.665868i | \(0.768061\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 12.9001 | − | 22.3436i | 0.595672 | − | 1.03173i | ||||
\(470\) | −9.21274 | − | 26.0025i | −0.424952 | − | 1.19941i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 54.2083 | − | 31.2972i | 2.49514 | − | 1.44057i | ||||
\(473\) | 0.800762 | − | 0.462320i | 0.0368191 | − | 0.0212575i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 21.4872 | − | 3.64671i | 0.985902 | − | 0.167323i | ||||
\(476\) | −12.0988 | −0.554548 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −4.33824 | + | 2.50469i | −0.198427 | + | 0.114562i | ||||
\(479\) | 4.02574 | − | 6.97279i | 0.183941 | − | 0.318595i | −0.759278 | − | 0.650766i | \(-0.774448\pi\) |
0.943219 | + | 0.332171i | \(0.107781\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −5.65976 | + | 9.80298i | −0.258063 | + | 0.446978i | ||||
\(482\) | − | 43.0417i | − | 1.96049i | ||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −12.4330 | + | 21.5347i | −0.565138 | + | 0.978849i | ||||
\(485\) | 7.45928 | + | 6.36872i | 0.338708 | + | 0.289189i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 1.09761i | − | 0.0497376i | −0.999691 | − | 0.0248688i | \(-0.992083\pi\) | ||
0.999691 | − | 0.0248688i | \(-0.00791680\pi\) | |||||||
\(488\) | −30.5551 | − | 17.6410i | −1.38316 | − | 0.798571i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 55.5425 | + | 47.4221i | 2.50915 | + | 2.14231i | ||||
\(491\) | 6.55267 | + | 11.3496i | 0.295718 | + | 0.512199i | 0.975152 | − | 0.221538i | \(-0.0711078\pi\) |
−0.679434 | + | 0.733737i | \(0.737774\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 2.39458i | − | 0.107846i | ||||||
\(494\) | −35.0621 | − | 19.7456i | −1.57752 | − | 0.888395i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −14.3474 | − | 24.8505i | −0.644219 | − | 1.11582i | ||||
\(497\) | −27.2046 | + | 15.7066i | −1.22029 | + | 0.704536i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 12.0703 | + | 20.9064i | 0.540342 | + | 0.935900i | 0.998884 | + | 0.0472275i | \(0.0150386\pi\) |
−0.458542 | + | 0.888673i | \(0.651628\pi\) | |||||||
\(500\) | −39.6150 | + | 21.5343i | −1.77163 | + | 0.963042i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | − | 8.19895i | − | 0.365937i | ||||||
\(503\) | −16.4214 | − | 9.48090i | −0.732194 | − | 0.422733i | 0.0870300 | − | 0.996206i | \(-0.472262\pi\) |
−0.819224 | + | 0.573473i | \(0.805596\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −23.2371 | − | 4.30282i | −1.03404 | − | 0.191473i | ||||
\(506\) | 2.63555 | 0.117165 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 13.7482 | − | 7.93753i | 0.609978 | − | 0.352171i | ||||
\(509\) | −10.9803 | + | 19.0184i | −0.486692 | + | 0.842974i | −0.999883 | − | 0.0152997i | \(-0.995130\pi\) |
0.513191 | + | 0.858274i | \(0.328463\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 6.66248 | + | 11.5398i | 0.294731 | + | 0.510489i | ||||
\(512\) | 40.5609i | 1.79255i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −67.7531 | −2.98846 | ||||||||
\(515\) | 12.1322 | − | 4.29846i | 0.534608 | − | 0.189413i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −9.56399 | − | 5.52177i | −0.420624 | − | 0.242847i | ||||
\(518\) | −28.8622 | + | 16.6636i | −1.26813 | + | 0.732157i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 41.2635 | + | 7.64077i | 1.80952 | + | 0.335070i | ||||
\(521\) | −6.56968 | −0.287823 | −0.143912 | − | 0.989591i | \(-0.545968\pi\) | ||||
−0.143912 | + | 0.989591i | \(0.545968\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −3.63538 | − | 2.09889i | −0.158964 | − | 0.0917779i | 0.418408 | − | 0.908259i | \(-0.362588\pi\) |
−0.577372 | + | 0.816481i | \(0.695922\pi\) | |||||||
\(524\) | −65.8375 | −2.87613 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −16.7344 | + | 28.9848i | −0.729653 | + | 1.26380i | ||||
\(527\) | −3.94113 | + | 2.27541i | −0.171678 | + | 0.0991186i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −11.3809 | − | 19.7123i | −0.494822 | − | 0.857058i | ||||
\(530\) | 4.80189 | + | 13.5531i | 0.208581 | + | 0.588709i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −40.3316 | − | 68.1603i | −1.74860 | − | 2.95513i | ||||
\(533\) | − | 0.272162i | − | 0.0117887i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −2.74482 | + | 0.972497i | −0.118669 | + | 0.0420447i | ||||
\(536\) | 14.2975 | − | 24.7640i | 0.617558 | − | 1.06964i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −7.67486 | − | 4.43108i | −0.330887 | − | 0.191038i | ||||
\(539\) | 29.2371 | 1.25933 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 2.31505 | − | 4.00978i | 0.0995316 | − | 0.172394i | −0.811959 | − | 0.583714i | \(-0.801599\pi\) |
0.911491 | + | 0.411320i | \(0.134932\pi\) | |||||||
\(542\) | 22.4692 | + | 12.9726i | 0.965136 | + | 0.557221i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −0.217238 | −0.00931400 | ||||||||
\(545\) | 17.4710 | − | 20.4627i | 0.748376 | − | 0.876525i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −32.9435 | − | 19.0199i | −1.40856 | − | 0.813233i | −0.413312 | − | 0.910590i | \(-0.635628\pi\) |
−0.995250 | + | 0.0973563i | \(0.968961\pi\) | |||||||
\(548\) | −57.3858 | + | 33.1317i | −2.45140 | + | 1.41532i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −9.66849 | + | 25.2118i | −0.412266 | + | 1.07504i | ||||
\(551\) | 13.4902 | − | 7.98236i | 0.574701 | − | 0.340060i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −44.2333 | + | 25.5381i | −1.88099 | + | 1.08599i | ||||
\(554\) | −8.27110 | − | 14.3260i | −0.351406 | − | 0.608652i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 5.38092 | + | 9.32002i | 0.228202 | + | 0.395257i | ||||
\(557\) | −31.5498 | − | 18.2153i | −1.33681 | − | 0.771807i | −0.350476 | − | 0.936572i | \(-0.613980\pi\) |
−0.986333 | + | 0.164765i | \(0.947313\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.58060 | 0.0668523 | ||||||||
\(560\) | 32.1682 | + | 27.4651i | 1.35935 | + | 1.16061i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 57.5496i | 2.42758i | ||||||||
\(563\) | − | 20.6856i | − | 0.871795i | −0.899996 | − | 0.435897i | \(-0.856431\pi\) | ||
0.899996 | − | 0.435897i | \(-0.143569\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −16.3267 | + | 5.78459i | −0.686870 | + | 0.243359i | ||||
\(566\) | 18.0324 | − | 31.2330i | 0.757958 | − | 1.31282i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −30.1515 | + | 17.4080i | −1.26513 | + | 0.730422i | ||||
\(569\) | −27.1132 | −1.13664 | −0.568322 | − | 0.822806i | \(-0.692407\pi\) | ||||
−0.568322 | + | 0.822806i | \(0.692407\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 46.4687 | 1.94466 | 0.972328 | − | 0.233622i | \(-0.0750578\pi\) | ||||
0.972328 | + | 0.233622i | \(0.0750578\pi\) | |||||||
\(572\) | 28.8622 | − | 16.6636i | 1.20679 | − | 0.696741i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0.400654 | − | 0.693954i | 0.0167230 | − | 0.0289651i | ||||
\(575\) | −2.40996 | + | 0.382507i | −0.100502 | + | 0.0159516i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 18.0398i | − | 0.751008i | −0.926821 | − | 0.375504i | \(-0.877470\pi\) | ||
0.926821 | − | 0.375504i | \(-0.122530\pi\) | |||||||
\(578\) | − | 40.6664i | − | 1.69150i | ||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −21.0570 | + | 24.6627i | −0.874344 | + | 1.02406i | ||||
\(581\) | 70.7322 | 2.93447 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 4.98497 | + | 2.87808i | 0.206457 | + | 0.119198i | ||||
\(584\) | 7.38419 | + | 12.7898i | 0.305560 | + | 0.529245i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −22.3337 | − | 38.6831i | −0.922597 | − | 1.59798i | ||||
\(587\) | 22.5458 | − | 13.0168i | 0.930565 | − | 0.537262i | 0.0435750 | − | 0.999050i | \(-0.486125\pi\) |
0.886990 | + | 0.461788i | \(0.152792\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −25.9567 | − | 14.6178i | −1.06953 | − | 0.602316i | ||||
\(590\) | −12.5357 | + | 67.6980i | −0.516085 | + | 2.78708i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −10.9511 | + | 6.32263i | −0.450088 | + | 0.259858i | ||||
\(593\) | −15.7236 | − | 9.07803i | −0.645691 | − | 0.372790i | 0.141112 | − | 0.989994i | \(-0.454932\pi\) |
−0.786804 | + | 0.617203i | \(0.788266\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 4.35580 | − | 5.10167i | 0.178570 | − | 0.209148i | ||||
\(596\) | 72.4556 | 2.96790 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 3.90168 | + | 2.25264i | 0.159552 | + | 0.0921172i | ||||
\(599\) | −20.0357 | + | 34.7028i | −0.818635 | + | 1.41792i | 0.0880531 | + | 0.996116i | \(0.471935\pi\) |
−0.906688 | + | 0.421802i | \(0.861398\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 15.0473 | 0.613793 | 0.306897 | − | 0.951743i | \(-0.400709\pi\) | ||||
0.306897 | + | 0.951743i | \(0.400709\pi\) | |||||||
\(602\) | 4.03018 | + | 2.32683i | 0.164258 | + | 0.0948344i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −25.6784 | + | 44.4763i | −1.04484 | + | 1.80972i | ||||
\(605\) | −4.60433 | − | 12.9955i | −0.187193 | − | 0.528342i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 29.3860i | 1.19274i | 0.802709 | + | 0.596370i | \(0.203391\pi\) | ||||
−0.802709 | + | 0.596370i | \(0.796609\pi\) | |||||||
\(608\) | −0.724166 | − | 1.22384i | −0.0293688 | − | 0.0496333i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 36.5794 | − | 12.9602i | 1.48106 | − | 0.524741i | ||||
\(611\) | −9.43905 | − | 16.3489i | −0.381863 | − | 0.661406i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −30.0578 | + | 17.3539i | −1.21402 | + | 0.700917i | −0.963633 | − | 0.267229i | \(-0.913892\pi\) |
−0.250390 | + | 0.968145i | \(0.580559\pi\) | |||||||
\(614\) | 36.0818 | − | 62.4955i | 1.45614 | − | 2.52211i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 49.4622 | 1.99289 | ||||||||
\(617\) | −9.29031 | − | 5.36376i | −0.374014 | − | 0.215937i | 0.301197 | − | 0.953562i | \(-0.402614\pi\) |
−0.675210 | + | 0.737625i | \(0.735947\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 36.1437 | 1.45274 | 0.726370 | − | 0.687304i | \(-0.241206\pi\) | ||||
0.726370 | + | 0.687304i | \(0.241206\pi\) | |||||||
\(620\) | 60.6004 | + | 11.2214i | 2.43377 | + | 0.450663i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −0.411031 | + | 0.237309i | −0.0164808 | + | 0.00951521i | ||||
\(623\) | 5.21644 | + | 3.01171i | 0.208992 | + | 0.120662i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 5.18184 | − | 24.4571i | 0.207274 | − | 0.978283i | ||||
\(626\) | −52.2569 | −2.08861 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 80.8768i | 3.22734i | ||||||||
\(629\) | 1.00273 | + | 1.73678i | 0.0399814 | + | 0.0692499i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 15.7882 | − | 27.3460i | 0.628519 | − | 1.08863i | −0.359330 | − | 0.933211i | \(-0.616995\pi\) |
0.987849 | − | 0.155417i | \(-0.0496720\pi\) | |||||||
\(632\) | −49.0248 | + | 28.3045i | −1.95010 | + | 1.12589i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 47.0857 | 1.87001 | ||||||||
\(635\) | −1.60262 | + | 8.65483i | −0.0635979 | + | 0.343456i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 43.2827 | + | 24.9893i | 1.71492 | + | 0.990111i | ||||
\(638\) | 19.4204i | 0.768859i | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −32.8377 | − | 28.0368i | −1.29802 | − | 1.10825i | ||||
\(641\) | 9.91331 | + | 17.1704i | 0.391552 | + | 0.678188i | 0.992654 | − | 0.120984i | \(-0.0386049\pi\) |
−0.601102 | + | 0.799172i | \(0.705272\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 11.6540 | − | 6.72843i | 0.459588 | − | 0.265343i | −0.252283 | − | 0.967654i | \(-0.581181\pi\) |
0.711871 | + | 0.702310i | \(0.247848\pi\) | |||||||
\(644\) | 4.43359 | + | 7.67920i | 0.174708 | + | 0.302603i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −6.13555 | + | 3.63051i | −0.241400 | + | 0.142840i | ||||
\(647\) | 4.19511i | 0.164927i | 0.996594 | + | 0.0824634i | \(0.0262787\pi\) | ||||
−0.996594 | + | 0.0824634i | \(0.973721\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 13.7810 | + | 23.8694i | 0.540953 | + | 0.936957i | ||||
\(650\) | −35.8621 | + | 29.0600i | −1.40663 | + | 1.13983i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 49.7109 | + | 28.7006i | 1.94683 | + | 1.12400i | ||||
\(653\) | 12.1680i | 0.476170i | 0.971244 | + | 0.238085i | \(0.0765196\pi\) | ||||
−0.971244 | + | 0.238085i | \(0.923480\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 23.7028 | − | 27.7615i | 0.926143 | − | 1.08473i | ||||
\(656\) | 0.152019 | − | 0.263305i | 0.00593535 | − | 0.0102803i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | − | 55.5814i | − | 2.16679i | ||||||
\(659\) | −4.12236 | + | 7.14013i | −0.160584 | + | 0.278140i | −0.935078 | − | 0.354441i | \(-0.884671\pi\) |
0.774494 | + | 0.632581i | \(0.218004\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −10.5599 | + | 18.2902i | −0.410731 | + | 0.711407i | −0.994970 | − | 0.100175i | \(-0.968060\pi\) |
0.584239 | + | 0.811582i | \(0.301393\pi\) | |||||||
\(662\) | 43.8338 | − | 25.3075i | 1.70365 | − | 0.983603i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 78.3941 | 3.04228 | ||||||||
\(665\) | 43.2611 | + | 7.53250i | 1.67759 | + | 0.292098i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.51986 | + | 0.877489i | −0.0588490 | + | 0.0339765i | ||||
\(668\) | 19.6156 | − | 11.3251i | 0.758951 | − | 0.438180i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 10.5038 | + | 29.6465i | 0.405798 | + | 1.14534i | ||||
\(671\) | 7.76783 | − | 13.4543i | 0.299874 | − | 0.519397i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 30.2802i | − | 1.16722i | −0.812036 | − | 0.583608i | \(-0.801641\pi\) | ||
0.812036 | − | 0.583608i | \(-0.198359\pi\) | |||||||
\(674\) | −12.5357 | + | 21.7124i | −0.482856 | + | 0.836331i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 4.54221 | 0.174700 | ||||||||
\(677\) | 49.9003i | 1.91783i | 0.283701 | + | 0.958913i | \(0.408438\pi\) | ||||
−0.283701 | + | 0.958913i | \(0.591562\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 9.88092 | + | 17.1142i | 0.379195 | + | 0.656785i | ||||
\(680\) | 4.82763 | − | 5.65430i | 0.185131 | − | 0.216832i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 31.9632 | − | 18.4539i | 1.22393 | − | 0.706638i | ||||
\(683\) | − | 3.11357i | − | 0.119137i | −0.998224 | − | 0.0595687i | \(-0.981027\pi\) | ||
0.998224 | − | 0.0595687i | \(-0.0189725\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 6.68942 | − | 36.1258i | 0.255590 | − | 1.38029i | ||||
\(686\) | 34.8436 | + | 60.3509i | 1.33034 | + | 2.30421i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 1.52916 | + | 0.882861i | 0.0582987 | + | 0.0336588i | ||||
\(689\) | 4.91985 | + | 8.52143i | 0.187431 | + | 0.324641i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −30.2831 | −1.15202 | −0.576012 | − | 0.817441i | \(-0.695392\pi\) | ||||
−0.576012 | + | 0.817441i | \(0.695392\pi\) | |||||||
\(692\) | 43.1140i | 1.63895i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −6.68222 | + | 11.5740i | −0.253654 | + | 0.439341i | ||||
\(695\) | −5.86718 | − | 1.08643i | −0.222555 | − | 0.0412105i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −0.0417585 | − | 0.0241093i | −0.00158172 | − | 0.000913204i | ||||
\(698\) | −3.29948 | + | 1.90495i | −0.124887 | + | 0.0721035i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −89.7243 | + | 14.2409i | −3.39126 | + | 0.538257i | ||||
\(701\) | 22.2849 | + | 38.5987i | 0.841691 | + | 1.45785i | 0.888464 | + | 0.458946i | \(0.151773\pi\) |
−0.0467733 | + | 0.998906i | \(0.514894\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −6.44177 | + | 11.4386i | −0.242956 | + | 0.431415i | ||||
\(704\) | −16.7014 | −0.629458 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −40.4457 | − | 70.0540i | −1.52219 | − | 2.63652i | ||||
\(707\) | −41.2353 | − | 23.8072i | −1.55081 | − | 0.895363i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 4.67176 | − | 8.09172i | 0.175452 | − | 0.303891i | −0.764866 | − | 0.644190i | \(-0.777195\pi\) |
0.940317 | + | 0.340299i | \(0.110528\pi\) | |||||||
\(710\) | 6.97252 | − | 37.6546i | 0.261674 | − | 1.41315i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 5.78150 | + | 3.33795i | 0.216671 | + | 0.125095i | ||||
\(713\) | 2.88844 | + | 1.66764i | 0.108173 | + | 0.0624538i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −3.36445 | + | 18.1695i | −0.125823 | + | 0.679500i | ||||
\(716\) | 15.5055 | − | 26.8562i | 0.579466 | − | 1.00366i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −7.43916 | − | 4.29500i | −0.277627 | − | 0.160288i | ||||
\(719\) | −12.6987 | − | 21.9948i | −0.473581 | − | 0.820267i | 0.525961 | − | 0.850508i | \(-0.323706\pi\) |
−0.999543 | + | 0.0302417i | \(0.990372\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 25.9330 | 0.965797 | ||||||||
\(722\) | −40.9059 | − | 22.4631i | −1.52236 | − | 0.835992i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −12.3534 | − | 21.3968i | −0.459112 | − | 0.795205i | ||||
\(725\) | −2.81854 | − | 17.7581i | −0.104678 | − | 0.659519i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 27.2259 | − | 15.7189i | 1.00975 | − | 0.582980i | 0.0986328 | − | 0.995124i | \(-0.468553\pi\) |
0.911119 | + | 0.412143i | \(0.135220\pi\) | |||||||
\(728\) | 73.2240 | + | 42.2759i | 2.71386 | + | 1.56685i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −15.9725 | − | 2.95764i | −0.591170 | − | 0.109467i | ||||
\(731\) | 0.140016 | − | 0.242515i | 0.00517869 | − | 0.00896975i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 25.3946i | − | 0.937971i | −0.883206 | − | 0.468985i | \(-0.844620\pi\) | ||
0.883206 | − | 0.468985i | \(-0.155380\pi\) | |||||||
\(734\) | −47.9056 | −1.76823 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0.0796065 | + | 0.137883i | 0.00293434 | + | 0.00508242i | ||||
\(737\) | 10.9043 | + | 6.29559i | 0.401664 | + | 0.231901i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 17.7541 | + | 30.7510i | 0.653095 | + | 1.13119i | 0.982368 | + | 0.186959i | \(0.0598631\pi\) |
−0.329273 | + | 0.944235i | \(0.606804\pi\) | |||||||
\(740\) | 4.94505 | − | 26.7054i | 0.181784 | − | 0.981710i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 28.9703i | 1.06353i | ||||||||
\(743\) | −14.8176 | + | 8.55493i | −0.543604 | + | 0.313850i | −0.746538 | − | 0.665342i | \(-0.768286\pi\) |
0.202934 | + | 0.979192i | \(0.434952\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −26.0854 | + | 30.5522i | −0.955695 | + | 1.11934i | ||||
\(746\) | −28.8798 | − | 50.0213i | −1.05737 | − | 1.83141i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | − | 5.90453i | − | 0.215891i | ||||||
\(749\) | −5.86718 | −0.214382 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 3.72562 | − | 6.45297i | 0.135950 | − | 0.235472i | −0.790010 | − | 0.613094i | \(-0.789925\pi\) |
0.925960 | + | 0.377622i | \(0.123258\pi\) | |||||||
\(752\) | − | 21.0891i | − | 0.769041i | ||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −16.5988 | + | 28.7500i | −0.604493 | + | 1.04701i | ||||
\(755\) | −9.50949 | − | 26.8401i | −0.346086 | − | 0.976810i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −46.5640 | + | 26.8838i | −1.69240 | + | 0.977107i | −0.739824 | + | 0.672801i | \(0.765091\pi\) |
−0.952574 | + | 0.304306i | \(0.901575\pi\) | |||||||
\(758\) | −14.9994 | + | 8.65994i | −0.544804 | + | 0.314543i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 47.9473 | + | 8.34845i | 1.73923 | + | 0.302830i | ||||
\(761\) | −23.3939 | −0.848029 | −0.424014 | − | 0.905655i | \(-0.639379\pi\) | ||||
−0.424014 | + | 0.905655i | \(0.639379\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 46.9487 | − | 27.1058i | 1.69966 | − | 0.981297i | ||||
\(764\) | −11.8068 | + | 20.4499i | −0.427154 | + | 0.739852i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 3.78757 | − | 6.56027i | 0.136851 | − | 0.237032i | ||||
\(767\) | 47.1152i | 1.70123i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −6.62236 | + | 11.4703i | −0.238808 | + | 0.413628i | −0.960373 | − | 0.278719i | \(-0.910090\pi\) |
0.721564 | + | 0.692347i | \(0.243423\pi\) | |||||||
\(770\) | −35.3261 | + | 41.3753i | −1.27307 | + | 1.49106i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 10.4500i | 0.376105i | ||||||||
\(773\) | −15.4198 | − | 8.90262i | −0.554611 | − | 0.320205i | 0.196369 | − | 0.980530i | \(-0.437085\pi\) |
−0.750980 | + | 0.660325i | \(0.770418\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −26.5490 | + | 21.5133i | −0.953668 | + | 0.772781i | ||||
\(776\) | 10.9512 | + | 18.9681i | 0.393127 | + | 0.680916i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | − | 23.0658i | − | 0.826949i | ||||||
\(779\) | −0.00337965 | − | 0.315621i | −0.000121088 | − | 0.0113083i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −7.66521 | − | 13.2765i | −0.274283 | − | 0.475072i | ||||
\(782\) | 0.691255 | − | 0.399096i | 0.0247192 | − | 0.0142716i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 27.9160 | + | 48.3520i | 0.997001 | + | 1.72686i | ||||
\(785\) | −34.1031 | − | 29.1172i | −1.21719 | − | 1.03924i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 43.5779i | 1.55339i | 0.629880 | + | 0.776693i | \(0.283104\pi\) | ||||
−0.629880 | + | 0.776693i | \(0.716896\pi\) | |||||||
\(788\) | 69.3734 | + | 40.0527i | 2.47132 | + | 1.42682i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 11.3370 | − | 61.2246i | 0.403351 | − | 2.17827i | ||||
\(791\) | −34.8990 | −1.24087 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 22.9991 | − | 13.2785i | 0.816721 | − | 0.471534i | ||||
\(794\) | −32.8634 | + | 56.9210i | −1.16628 | + | 2.02005i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 25.7338 | + | 44.5723i | 0.912111 | + | 1.57982i | ||||
\(797\) | − | 16.1311i | − | 0.571395i | −0.958320 | − | 0.285697i | \(-0.907775\pi\) | ||
0.958320 | − | 0.285697i | \(-0.0922252\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −3.34460 | −0.118323 | ||||||||
\(800\) | −1.61103 | + | 0.255700i | −0.0569584 | + | 0.00904038i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 53.5403 | + | 30.9115i | 1.89057 | + | 1.09152i | ||||
\(803\) | −5.63170 | + | 3.25147i | −0.198739 | + | 0.114742i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −4.83424 | − | 0.895159i | −0.170385 | − | 0.0315502i | ||||
\(806\) | 63.0912 | 2.22229 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −45.7021 | − | 26.3861i | −1.60779 | − | 0.928259i | ||||
\(809\) | 28.7134 | 1.00951 | 0.504755 | − | 0.863263i | \(-0.331583\pi\) | ||||
0.504755 | + | 0.863263i | \(0.331583\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −10.7711 | + | 18.6561i | −0.378225 | + | 0.655104i | −0.990804 | − | 0.135305i | \(-0.956799\pi\) |
0.612579 | + | 0.790409i | \(0.290132\pi\) | |||||||
\(812\) | −56.5850 | + | 32.6694i | −1.98575 | + | 1.14647i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −8.13228 | − | 14.0855i | −0.285036 | − | 0.493697i | ||||
\(815\) | −29.9990 | + | 10.6287i | −1.05082 | + | 0.372307i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.83299 | − | 0.0196275i | 0.0641282 | − | 0.000686680i | ||||
\(818\) | − | 69.5634i | − | 2.43223i | ||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0.218080 | + | 0.615520i | 0.00761568 | + | 0.0214949i | ||||
\(821\) | 16.6602 | − | 28.8563i | 0.581445 | − | 1.00709i | −0.413863 | − | 0.910339i | \(-0.635821\pi\) |
0.995308 | − | 0.0967536i | \(-0.0308459\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −32.2499 | − | 18.6195i | −1.12416 | − | 0.649035i | −0.181701 | − | 0.983354i | \(-0.558160\pi\) |
−0.942460 | + | 0.334319i | \(0.891494\pi\) | |||||||
\(824\) | 28.7422 | 1.00128 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −69.3590 | + | 120.133i | −2.41331 | + | 4.17997i | ||||
\(827\) | −25.1591 | − | 14.5256i | −0.874868 | − | 0.505105i | −0.00590503 | − | 0.999983i | \(-0.501880\pi\) |
−0.868963 | + | 0.494877i | \(0.835213\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −34.5380 | −1.19956 | −0.599778 | − | 0.800166i | \(-0.704744\pi\) | ||||
−0.599778 | + | 0.800166i | \(0.704744\pi\) | |||||||
\(830\) | −55.9895 | + | 65.5769i | −1.94342 | + | 2.27621i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −24.7249 | − | 14.2749i | −0.857180 | − | 0.494893i | ||||
\(833\) | 7.66832 | − | 4.42731i | 0.265692 | − | 0.153397i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −2.28658 | + | 12.3485i | −0.0791302 | + | 0.427338i | ||||
\(836\) | 33.2640 | − | 19.6829i | 1.15046 | − | 0.680746i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −27.7483 | + | 16.0205i | −0.958550 | + | 0.553419i | ||||
\(839\) | 22.3622 | + | 38.7324i | 0.772028 | + | 1.33719i | 0.936450 | + | 0.350801i | \(0.114091\pi\) |
−0.164422 | + | 0.986390i | \(0.552576\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 8.03413 | + | 13.9155i | 0.277039 | + | 0.479845i | ||||
\(842\) | 7.07266 | + | 4.08340i | 0.243740 | + | 0.140723i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −55.8770 | −1.92337 | ||||||||
\(845\) | −1.63528 | + | 1.91530i | −0.0562554 | + | 0.0658883i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 27.7784i | − | 0.954478i | ||||||
\(848\) | 10.9921i | 0.377471i | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 1.28192 | + | 8.07666i | 0.0439694 | + | 0.277027i | ||||
\(851\) | 0.734898 | − | 1.27288i | 0.0251920 | − | 0.0436338i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 14.0818 | − | 8.13013i | 0.482152 | − | 0.278370i | −0.239161 | − | 0.970980i | \(-0.576872\pi\) |
0.721313 | + | 0.692610i | \(0.243539\pi\) | |||||||
\(854\) | 78.1900 | 2.67561 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −6.50273 | −0.222259 | ||||||||
\(857\) | 14.4089 | − | 8.31896i | 0.492197 | − | 0.284170i | −0.233288 | − | 0.972408i | \(-0.574949\pi\) |
0.725485 | + | 0.688237i | \(0.241615\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 20.1362 | − | 34.8769i | 0.687038 | − | 1.18999i | −0.285753 | − | 0.958303i | \(-0.592244\pi\) |
0.972792 | − | 0.231682i | \(-0.0744229\pi\) | |||||||
\(860\) | −3.57467 | + | 1.26651i | −0.121895 | + | 0.0431878i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0.118897i | 0.00404965i | ||||||||
\(863\) | − | 32.9634i | − | 1.12209i | −0.827786 | − | 0.561044i | \(-0.810400\pi\) | ||
0.827786 | − | 0.561044i | \(-0.189600\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −18.1798 | − | 15.5219i | −0.618131 | − | 0.527759i | ||||
\(866\) | −23.5027 | −0.798655 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 107.538 | + | 62.0873i | 3.65009 | + | 2.10738i | ||||
\(869\) | −12.4633 | − | 21.5870i | −0.422787 | − | 0.732288i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 10.7618 | + | 18.6400i | 0.364651 | + | 0.631594i | ||||
\(872\) | 52.0343 | − | 30.0420i | 1.76210 | − | 1.01735i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 4.55267 | + | 2.56389i | 0.153996 | + | 0.0867248i | ||||
\(875\) | 26.2975 | − | 42.9608i | 0.889018 | − | 1.45234i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 0.184636 | − | 0.106600i | 0.00623472 | − | 0.00359962i | −0.496879 | − | 0.867820i | \(-0.665521\pi\) |
0.503114 | + | 0.864220i | \(0.332188\pi\) | |||||||
\(878\) | 47.3319 | + | 27.3271i | 1.59737 | + | 0.922244i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −13.4037 | + | 15.6989i | −0.451839 | + | 0.529210i | ||||
\(881\) | −51.8661 | −1.74741 | −0.873707 | − | 0.486453i | \(-0.838290\pi\) | ||||
−0.873707 | + | 0.486453i | \(0.838290\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 36.0657 | + | 20.8225i | 1.21371 | + | 0.700734i | 0.963565 | − | 0.267475i | \(-0.0861892\pi\) |
0.250142 | + | 0.968209i | \(0.419523\pi\) | |||||||
\(884\) | 5.04667 | − | 8.74109i | 0.169738 | − | 0.293995i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −49.4083 | −1.65990 | ||||||||
\(887\) | 3.54486 | + | 2.04663i | 0.119025 | + | 0.0687190i | 0.558330 | − | 0.829619i | \(-0.311442\pi\) |
−0.439306 | + | 0.898338i | \(0.644775\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −8.86718 | + | 15.3584i | −0.297396 | + | 0.515104i | ||||
\(890\) | −6.92139 | + | 2.45226i | −0.232006 | + | 0.0822000i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | − | 87.4987i | − | 2.92967i | ||||||
\(893\) | −11.1493 | − | 18.8423i | −0.373097 | − | 0.630533i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 5.74214 | + | 16.2069i | 0.191939 | + | 0.541737i | ||||
\(896\) | −43.4984 | − | 75.3414i | −1.45318 | − | 2.51698i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 26.5834 | − | 15.3479i | 0.887099 | − | 0.512167i | ||||
\(899\) | −12.2882 | + | 21.2838i | −0.409835 | + | 0.709855i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.74328 | 0.0580772 | ||||||||
\(902\) | 0.338668 | + | 0.195530i | 0.0112764 | + | 0.00651043i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −38.6794 | −1.28646 | ||||||||
\(905\) | 13.4698 | + | 2.49421i | 0.447751 | + | 0.0829102i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 7.28090 | − | 4.20363i | 0.241758 | − | 0.139579i | −0.374226 | − | 0.927337i | \(-0.622092\pi\) |
0.615985 | + | 0.787758i | \(0.288758\pi\) | |||||||
\(908\) | 28.6265 | + | 16.5275i | 0.950005 | + | 0.548486i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −87.6609 | + | 31.0584i | −2.90593 | + | 1.02958i | ||||
\(911\) | −8.87918 | −0.294180 | −0.147090 | − | 0.989123i | \(-0.546991\pi\) | ||||
−0.147090 | + | 0.989123i | \(0.546991\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 34.5192i | 1.14242i | ||||||||
\(914\) | −34.7772 | − | 60.2359i | −1.15033 | − | 1.99243i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 33.5983 | − | 58.1939i | 1.11012 | − | 1.92278i | ||||
\(917\) | 63.6948 | − | 36.7742i | 2.10339 | − | 1.21439i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 45.9834 | 1.51685 | 0.758427 | − | 0.651758i | \(-0.225968\pi\) | ||||
0.758427 | + | 0.651758i | \(0.225968\pi\) | |||||||
\(920\) | −5.35790 | − | 0.992125i | −0.176645 | − | 0.0327094i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −11.3153 | − | 6.53290i | −0.372650 | − | 0.215150i | ||||
\(923\) | − | 26.2062i | − | 0.862587i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 9.48048 | + | 11.6996i | 0.311716 | + | 0.384681i | ||||
\(926\) | 22.0231 | + | 38.1452i | 0.723725 | + | 1.25353i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −1.01600 | + | 0.586589i | −0.0333519 | + | 0.0192557i | ||||
\(929\) | 11.0889 | + | 19.2065i | 0.363814 | + | 0.630145i | 0.988585 | − | 0.150663i | \(-0.0481409\pi\) |
−0.624771 | + | 0.780808i | \(0.714808\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 50.5044 | + | 28.4421i | 1.65521 | + | 0.932152i | ||||
\(932\) | 49.2564i | 1.61345i | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −35.3436 | − | 61.2170i | −1.15648 | − | 2.00308i | ||||
\(935\) | 2.48975 | + | 2.12574i | 0.0814234 | + | 0.0695192i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −29.7284 | − | 17.1637i | −0.971186 | − | 0.560714i | −0.0715882 | − | 0.997434i | \(-0.522807\pi\) |
−0.899598 | + | 0.436720i | \(0.856140\pi\) | |||||||
\(938\) | 63.3706i | 2.06912i | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 34.4474 | + | 29.4111i | 1.12355 | + | 0.959286i | ||||
\(941\) | 16.8606 | − | 29.2035i | 0.549641 | − | 0.952006i | −0.448658 | − | 0.893704i | \(-0.648098\pi\) |
0.998299 | − | 0.0583025i | \(-0.0185688\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0.0353393i | 0.00115080i | ||||||||
\(944\) | −26.3167 | + | 45.5818i | −0.856535 | + | 1.48356i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −1.13555 | + | 1.96683i | −0.0369200 | + | 0.0639473i | ||||
\(947\) | 19.1794 | − | 11.0732i | 0.623248 | − | 0.359832i | −0.154885 | − | 0.987933i | \(-0.549501\pi\) |
0.778132 | + | 0.628100i | \(0.216167\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −11.1163 | −0.360849 | ||||||||
\(950\) | −41.2277 | + | 34.1456i | −1.33760 | + | 1.10783i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 12.9730 | − | 7.48995i | 0.420457 | − | 0.242751i | ||||
\(953\) | −32.2999 | + | 18.6484i | −1.04630 | + | 0.604079i | −0.921610 | − | 0.388117i | \(-0.873126\pi\) |
−0.124686 | + | 0.992196i | \(0.539792\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −4.37240 | − | 12.3409i | −0.141488 | − | 0.399342i | ||||
\(956\) | 4.11254 | − | 7.12313i | 0.133009 | − | 0.230378i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 19.7761i | 0.638936i | ||||||||
\(959\) | 37.0121 | − | 64.1069i | 1.19518 | − | 2.07012i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 15.7069 | 0.506674 | ||||||||
\(962\) | − | 27.8030i | − | 0.896405i | ||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 35.3359 | + | 61.2036i | 1.13809 | + | 1.97123i | ||||
\(965\) | −4.40644 | − | 3.76221i | −0.141848 | − | 0.121110i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −16.1718 | + | 9.33679i | −0.520050 | + | 0.300251i | −0.736955 | − | 0.675942i | \(-0.763737\pi\) |
0.216905 | + | 0.976193i | \(0.430404\pi\) | |||||||
\(968\) | − | 30.7875i | − | 0.989547i | ||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −23.6883 | − | 4.38638i | −0.760587 | − | 0.140838i | ||||
\(971\) | 14.2903 | + | 24.7515i | 0.458598 | + | 0.794314i | 0.998887 | − | 0.0471649i | \(-0.0150186\pi\) |
−0.540290 | + | 0.841479i | \(0.681685\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −10.4116 | − | 6.01113i | −0.333780 | − | 0.192708i | ||||
\(974\) | 1.34798 | + | 2.33477i | 0.0431921 | + | 0.0748109i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 29.6674 | 0.949630 | ||||||||
\(977\) | − | 58.1909i | − | 1.86169i | −0.365411 | − | 0.930846i | \(-0.619072\pi\) | ||
0.365411 | − | 0.930846i | \(-0.380928\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1.46980 | + | 2.54576i | −0.0469749 | + | 0.0813628i | ||||
\(980\) | −117.911 | − | 21.8337i | −3.76654 | − | 0.697451i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −27.8768 | − | 16.0947i | −0.889586 | − | 0.513602i | ||||
\(983\) | 41.6320 | − | 24.0363i | 1.32786 | − | 0.766638i | 0.342888 | − | 0.939376i | \(-0.388595\pi\) |
0.984968 | + | 0.172738i | \(0.0552615\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −41.8647 | + | 14.8327i | −1.33392 | + | 0.472610i | ||||
\(986\) | 2.94078 | + | 5.09359i | 0.0936536 | + | 0.162213i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 66.0674 | − | 0.707444i | 2.10188 | − | 0.0225068i | ||||
\(989\) | −0.205235 | −0.00652609 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −19.1976 | − | 33.2512i | −0.609832 | − | 1.05626i | −0.991268 | − | 0.131865i | \(-0.957904\pi\) |
0.381436 | − | 0.924395i | \(-0.375430\pi\) | |||||||
\(992\) | 1.93089 | + | 1.11480i | 0.0613057 | + | 0.0353949i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 38.5785 | − | 66.8200i | 1.22364 | − | 2.11940i | ||||
\(995\) | −28.0593 | − | 5.19576i | −0.889540 | − | 0.164717i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −32.7546 | − | 18.9109i | −1.03735 | − | 0.598914i | −0.118268 | − | 0.992982i | \(-0.537734\pi\) |
−0.919081 | + | 0.394068i | \(0.871067\pi\) | |||||||
\(998\) | −51.3504 | − | 29.6472i | −1.62547 | − | 0.938465i | ||||
\(999\) | 0 | 0 |
(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 | 855.2.be.d.64.1 | 12 | ||
3.2 | odd | 2 | 95.2.i.b.64.6 | yes | 12 | ||
5.4 | even | 2 | inner | 855.2.be.d.64.6 | 12 | ||
15.2 | even | 4 | 475.2.e.g.26.6 | 12 | |||
15.8 | even | 4 | 475.2.e.g.26.1 | 12 | |||
15.14 | odd | 2 | 95.2.i.b.64.1 | yes | 12 | ||
19.11 | even | 3 | inner | 855.2.be.d.334.6 | 12 | ||
57.11 | odd | 6 | 95.2.i.b.49.1 | ✓ | 12 | ||
57.26 | odd | 6 | 1805.2.b.f.1084.6 | 6 | |||
57.50 | even | 6 | 1805.2.b.g.1084.1 | 6 | |||
95.49 | even | 6 | inner | 855.2.be.d.334.1 | 12 | ||
285.68 | even | 12 | 475.2.e.g.201.1 | 12 | |||
285.83 | even | 12 | 9025.2.a.bu.1.6 | 6 | |||
285.107 | odd | 12 | 9025.2.a.bt.1.6 | 6 | |||
285.164 | even | 6 | 1805.2.b.g.1084.6 | 6 | |||
285.182 | even | 12 | 475.2.e.g.201.6 | 12 | |||
285.197 | even | 12 | 9025.2.a.bu.1.1 | 6 | |||
285.239 | odd | 6 | 95.2.i.b.49.6 | yes | 12 | ||
285.254 | odd | 6 | 1805.2.b.f.1084.1 | 6 | |||
285.278 | odd | 12 | 9025.2.a.bt.1.1 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
95.2.i.b.49.1 | ✓ | 12 | 57.11 | odd | 6 | ||
95.2.i.b.49.6 | yes | 12 | 285.239 | odd | 6 | ||
95.2.i.b.64.1 | yes | 12 | 15.14 | odd | 2 | ||
95.2.i.b.64.6 | yes | 12 | 3.2 | odd | 2 | ||
475.2.e.g.26.1 | 12 | 15.8 | even | 4 | |||
475.2.e.g.26.6 | 12 | 15.2 | even | 4 | |||
475.2.e.g.201.1 | 12 | 285.68 | even | 12 | |||
475.2.e.g.201.6 | 12 | 285.182 | even | 12 | |||
855.2.be.d.64.1 | 12 | 1.1 | even | 1 | trivial | ||
855.2.be.d.64.6 | 12 | 5.4 | even | 2 | inner | ||
855.2.be.d.334.1 | 12 | 95.49 | even | 6 | inner | ||
855.2.be.d.334.6 | 12 | 19.11 | even | 3 | inner | ||
1805.2.b.f.1084.1 | 6 | 285.254 | odd | 6 | |||
1805.2.b.f.1084.6 | 6 | 57.26 | odd | 6 | |||
1805.2.b.g.1084.1 | 6 | 57.50 | even | 6 | |||
1805.2.b.g.1084.6 | 6 | 285.164 | even | 6 | |||
9025.2.a.bt.1.1 | 6 | 285.278 | odd | 12 | |||
9025.2.a.bt.1.6 | 6 | 285.107 | odd | 12 | |||
9025.2.a.bu.1.1 | 6 | 285.197 | even | 12 | |||
9025.2.a.bu.1.6 | 6 | 285.83 | even | 12 |