Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [819,2,Mod(370,819)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(819, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([0, 6, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("819.370");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 819 = 3^{2} \cdot 7 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 819.fm (of order \(12\), degree \(4\), 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: | \(6.53974792554\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{12})\) |
Twist minimal: | no (minimal twist has level 273) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 496.1 | ||
Character | \(\chi\) | \(=\) | 819.496 |
Dual form | 819.2.fm.e.748.1 |
$q$-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 \(\left(\mathbb{Z}/819\mathbb{Z}\right)^\times\).
\(n\) | \(92\) | \(379\) | \(703\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{12}\right)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −2.37607 | − | 0.636667i | −1.68014 | − | 0.450192i | −0.712322 | − | 0.701852i | \(-0.752357\pi\) |
−0.967816 | + | 0.251661i | \(0.919023\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 3.50833 | + | 2.02554i | 1.75417 | + | 1.01277i | ||||
\(5\) | 0.498430 | + | 0.498430i | 0.222905 | + | 0.222905i | 0.809721 | − | 0.586816i | \(-0.199619\pi\) |
−0.586816 | + | 0.809721i | \(0.699619\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.62820 | − | 0.304236i | −0.993367 | − | 0.114991i | ||||
\(8\) | −3.56765 | − | 3.56765i | −1.26135 | − | 1.26135i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −0.866973 | − | 1.50164i | −0.274161 | − | 0.474861i | ||||
\(11\) | −0.184478 | + | 0.688480i | −0.0556221 | + | 0.207585i | −0.988144 | − | 0.153528i | \(-0.950936\pi\) |
0.932522 | + | 0.361113i | \(0.117603\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.17894 | + | 1.70127i | −0.881680 | + | 0.471848i | ||||
\(14\) | 6.05110 | + | 2.39618i | 1.61723 | + | 0.640405i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 2.15452 | + | 3.73174i | 0.538630 | + | 0.932934i | ||||
\(17\) | 2.27300 | − | 3.93695i | 0.551284 | − | 0.954852i | −0.446898 | − | 0.894585i | \(-0.647471\pi\) |
0.998182 | − | 0.0602669i | \(-0.0191952\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.25000 | − | 0.870835i | 0.745601 | − | 0.199783i | 0.134035 | − | 0.990977i | \(-0.457207\pi\) |
0.611566 | + | 0.791193i | \(0.290540\pi\) | |||||||
\(20\) | 0.739070 | + | 2.75825i | 0.165261 | + | 0.616763i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0.876665 | − | 1.51843i | 0.186906 | − | 0.323730i | ||||
\(23\) | 1.67026 | − | 0.964326i | 0.348274 | − | 0.201076i | −0.315651 | − | 0.948875i | \(-0.602223\pi\) |
0.663925 | + | 0.747799i | \(0.268890\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | − | 4.50313i | − | 0.900627i | ||||||
\(26\) | 8.63655 | − | 2.01842i | 1.69377 | − | 0.395845i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −8.60436 | − | 6.39088i | −1.62607 | − | 1.20776i | ||||
\(29\) | −0.185925 | − | 0.322032i | −0.0345254 | − | 0.0597998i | 0.848246 | − | 0.529602i | \(-0.177659\pi\) |
−0.882772 | + | 0.469802i | \(0.844325\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.53994 | + | 3.53994i | 0.635792 | + | 0.635792i | 0.949515 | − | 0.313723i | \(-0.101576\pi\) |
−0.313723 | + | 0.949515i | \(0.601576\pi\) | |||||||
\(32\) | −0.131724 | − | 0.491600i | −0.0232857 | − | 0.0869034i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −7.90735 | + | 7.90735i | −1.35610 | + | 1.35610i | ||||
\(35\) | −1.15833 | − | 1.46162i | −0.195794 | − | 0.247058i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −0.545727 | + | 2.03668i | −0.0897169 | + | 0.334828i | −0.996166 | − | 0.0874879i | \(-0.972116\pi\) |
0.906449 | + | 0.422316i | \(0.138783\pi\) | |||||||
\(38\) | −8.27667 | −1.34265 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | − | 3.55645i | − | 0.562324i | ||||||
\(41\) | −3.11983 | + | 11.6434i | −0.487236 | + | 1.81839i | 0.0825406 | + | 0.996588i | \(0.473697\pi\) |
−0.569776 | + | 0.821800i | \(0.692970\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 6.38504 | + | 3.68640i | 0.973709 | + | 0.562171i | 0.900365 | − | 0.435136i | \(-0.143300\pi\) |
0.0733440 | + | 0.997307i | \(0.476633\pi\) | |||||||
\(44\) | −2.04175 | + | 2.04175i | −0.307805 | + | 0.307805i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −4.58262 | + | 1.22791i | −0.675671 | + | 0.181045i | ||||
\(47\) | 3.55898 | − | 3.55898i | 0.519131 | − | 0.519131i | −0.398177 | − | 0.917308i | \(-0.630357\pi\) |
0.917308 | + | 0.398177i | \(0.130357\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.81488 | + | 1.59919i | 0.973554 | + | 0.228455i | ||||
\(50\) | −2.86700 | + | 10.6998i | −0.405455 | + | 1.51318i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −14.5988 | − | 0.470438i | −2.02449 | − | 0.0652380i | ||||
\(53\) | 4.97712 | 0.683660 | 0.341830 | − | 0.939762i | \(-0.388953\pi\) | ||||
0.341830 | + | 0.939762i | \(0.388953\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −0.435109 | + | 0.251210i | −0.0586700 | + | 0.0338732i | ||||
\(56\) | 8.29109 | + | 10.4619i | 1.10794 | + | 1.39803i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0.236745 | + | 0.883543i | 0.0310861 | + | 0.116015i | ||||
\(59\) | 1.03416 | + | 3.85953i | 0.134636 | + | 0.502467i | 0.999999 | + | 0.00132252i | \(0.000420972\pi\) |
−0.865363 | + | 0.501145i | \(0.832912\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 10.0720 | + | 5.81509i | 1.28959 | + | 0.744546i | 0.978581 | − | 0.205860i | \(-0.0659992\pi\) |
0.311011 | + | 0.950406i | \(0.399333\pi\) | |||||||
\(62\) | −6.15739 | − | 10.6649i | −0.781990 | − | 1.35445i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | − | 7.36614i | − | 0.920767i | ||||||
\(65\) | −2.43245 | − | 0.736516i | −0.301708 | − | 0.0913536i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −12.5870 | − | 3.37267i | −1.53774 | − | 0.412037i | −0.612207 | − | 0.790697i | \(-0.709718\pi\) |
−0.925536 | + | 0.378660i | \(0.876385\pi\) | |||||||
\(68\) | 15.9489 | − | 9.20809i | 1.93409 | − | 1.11665i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 1.82173 | + | 4.21038i | 0.217738 | + | 0.503237i | ||||
\(71\) | −2.10681 | − | 7.86274i | −0.250033 | − | 0.933135i | −0.970787 | − | 0.239944i | \(-0.922871\pi\) |
0.720754 | − | 0.693191i | \(-0.243796\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0.608899 | − | 0.608899i | 0.0712663 | − | 0.0712663i | −0.670575 | − | 0.741842i | \(-0.733953\pi\) |
0.741842 | + | 0.670575i | \(0.233953\pi\) | |||||||
\(74\) | 2.59337 | − | 4.49186i | 0.301474 | − | 0.522168i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 13.1660 | + | 3.52781i | 1.51024 | + | 0.404668i | ||||
\(77\) | 0.694305 | − | 1.75334i | 0.0791234 | − | 0.199812i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 9.81537 | 1.10432 | 0.552158 | − | 0.833740i | \(-0.313805\pi\) | ||||
0.552158 | + | 0.833740i | \(0.313805\pi\) | |||||||
\(80\) | −0.786133 | + | 2.93389i | −0.0878924 | + | 0.328019i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 14.8259 | − | 25.6792i | 1.63725 | − | 2.83579i | ||||
\(83\) | 2.25452 | + | 2.25452i | 0.247465 | + | 0.247465i | 0.819930 | − | 0.572464i | \(-0.194012\pi\) |
−0.572464 | + | 0.819930i | \(0.694012\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.09523 | − | 0.829364i | 0.335725 | − | 0.0899572i | ||||
\(86\) | −12.8243 | − | 12.8243i | −1.38288 | − | 1.38288i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 3.11441 | − | 1.79810i | 0.331997 | − | 0.191678i | ||||
\(89\) | 17.5524 | + | 4.70315i | 1.86055 | + | 0.498533i | 0.999942 | − | 0.0107329i | \(-0.00341645\pi\) |
0.860609 | + | 0.509266i | \(0.170083\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 8.87249 | − | 3.50413i | 0.930089 | − | 0.367333i | ||||
\(92\) | 7.81311 | 0.814573 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −10.7223 | + | 6.19052i | −1.10592 | + | 0.638503i | ||||
\(95\) | 2.05395 | + | 1.18585i | 0.210731 | + | 0.121665i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 8.73810 | − | 2.34137i | 0.887220 | − | 0.237730i | 0.213700 | − | 0.976899i | \(-0.431448\pi\) |
0.673520 | + | 0.739169i | \(0.264782\pi\) | |||||||
\(98\) | −15.1745 | − | 8.13860i | −1.53286 | − | 0.822123i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 9.12126 | − | 15.7985i | 0.912126 | − | 1.57985i | ||||
\(101\) | 6.77353 | + | 11.7321i | 0.673991 | + | 1.16739i | 0.976763 | + | 0.214324i | \(0.0687547\pi\) |
−0.302772 | + | 0.953063i | \(0.597912\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 16.4565 | 1.62151 | 0.810756 | − | 0.585385i | \(-0.199056\pi\) | ||||
0.810756 | + | 0.585385i | \(0.199056\pi\) | |||||||
\(104\) | 17.4109 | + | 5.27181i | 1.70728 | + | 0.516943i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −11.8260 | − | 3.16877i | −1.14864 | − | 0.307778i | ||||
\(107\) | −8.35835 | − | 14.4771i | −0.808033 | − | 1.39955i | −0.914225 | − | 0.405208i | \(-0.867199\pi\) |
0.106192 | − | 0.994346i | \(-0.466134\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.77768 | − | 1.77768i | 0.170271 | − | 0.170271i | −0.616827 | − | 0.787099i | \(-0.711582\pi\) |
0.787099 | + | 0.616827i | \(0.211582\pi\) | |||||||
\(110\) | 1.19379 | − | 0.319874i | 0.113823 | − | 0.0304988i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −4.52718 | − | 10.4632i | −0.427778 | − | 0.988683i | ||||
\(113\) | 2.96252 | − | 5.13124i | 0.278691 | − | 0.482706i | −0.692369 | − | 0.721544i | \(-0.743433\pi\) |
0.971060 | + | 0.238837i | \(0.0767662\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.31316 | + | 0.351860i | 0.122453 | + | 0.0328111i | ||||
\(116\) | − | 1.50639i | − | 0.139865i | ||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | − | 9.82893i | − | 0.904826i | ||||||
\(119\) | −7.17167 | + | 9.65558i | −0.657426 | + | 0.885125i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 9.08631 | + | 5.24598i | 0.826028 | + | 0.476907i | ||||
\(122\) | −20.2296 | − | 20.2296i | −1.83150 | − | 1.83150i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 5.24901 | + | 19.5896i | 0.471375 | + | 1.75919i | ||||
\(125\) | 4.73665 | − | 4.73665i | 0.423659 | − | 0.423659i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −17.4169 | + | 10.0556i | −1.54550 | + | 0.892293i | −0.547019 | + | 0.837120i | \(0.684238\pi\) |
−0.998477 | + | 0.0551724i | \(0.982429\pi\) | |||||||
\(128\) | −4.95322 | + | 18.4857i | −0.437807 | + | 1.63392i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 5.31076 | + | 3.29868i | 0.465784 | + | 0.289313i | ||||
\(131\) | − | 12.0796i | − | 1.05540i | −0.849430 | − | 0.527702i | \(-0.823054\pi\) | ||
0.849430 | − | 0.527702i | \(-0.176946\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −8.80659 | + | 1.29996i | −0.763628 | + | 0.112721i | ||||
\(134\) | 27.7603 | + | 16.0274i | 2.39813 | + | 1.38456i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −22.1549 | + | 5.93640i | −1.89977 | + | 0.509042i | ||||
\(137\) | 13.9883 | − | 3.74816i | 1.19510 | − | 0.320227i | 0.394202 | − | 0.919024i | \(-0.371021\pi\) |
0.800901 | + | 0.598797i | \(0.204354\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −6.95647 | − | 4.01632i | −0.590040 | − | 0.340660i | 0.175073 | − | 0.984555i | \(-0.443984\pi\) |
−0.765113 | + | 0.643896i | \(0.777317\pi\) | |||||||
\(140\) | −1.10327 | − | 7.47408i | −0.0932430 | − | 0.631675i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 20.0238i | 1.68036i | ||||||||
\(143\) | −0.584848 | − | 2.50248i | −0.0489074 | − | 0.209268i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0.0678396 | − | 0.253181i | 0.00563378 | − | 0.0210255i | ||||
\(146\) | −1.83446 | + | 1.05912i | −0.151821 | + | 0.0876537i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −6.03996 | + | 6.03996i | −0.496481 | + | 0.496481i | ||||
\(149\) | 2.13325 | + | 7.96140i | 0.174763 | + | 0.652223i | 0.996592 | + | 0.0824894i | \(0.0262870\pi\) |
−0.821829 | + | 0.569734i | \(0.807046\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −4.15300 | − | 4.15300i | −0.337966 | − | 0.337966i | 0.517635 | − | 0.855601i | \(-0.326812\pi\) |
−0.855601 | + | 0.517635i | \(0.826812\pi\) | |||||||
\(152\) | −14.7017 | − | 8.48802i | −1.19246 | − | 0.688469i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −2.76601 | + | 3.72402i | −0.222892 | + | 0.300090i | ||||
\(155\) | 3.52883i | 0.283442i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 14.6163i | 1.16651i | 0.812291 | + | 0.583253i | \(0.198220\pi\) | ||||
−0.812291 | + | 0.583253i | \(0.801780\pi\) | |||||||
\(158\) | −23.3220 | − | 6.24912i | −1.85540 | − | 0.497154i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0.179373 | − | 0.310684i | 0.0141807 | − | 0.0245617i | ||||
\(161\) | −4.68317 | + | 2.02629i | −0.369085 | + | 0.159694i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 7.35195 | − | 1.96995i | 0.575849 | − | 0.154298i | 0.0408715 | − | 0.999164i | \(-0.486987\pi\) |
0.534978 | + | 0.844866i | \(0.320320\pi\) | |||||||
\(164\) | −34.5294 | + | 34.5294i | −2.69630 | + | 2.69630i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −3.92152 | − | 6.79228i | −0.304369 | − | 0.527183i | ||||
\(167\) | −7.60079 | − | 2.03663i | −0.588167 | − | 0.157599i | −0.0475517 | − | 0.998869i | \(-0.515142\pi\) |
−0.540615 | + | 0.841270i | \(0.681809\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 7.21135 | − | 10.8165i | 0.554719 | − | 0.832038i | ||||
\(170\) | −7.88252 | −0.604562 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 14.9339 | + | 25.8662i | 1.13870 | + | 1.97228i | ||||
\(173\) | −5.36019 | + | 9.28412i | −0.407528 | + | 0.705859i | −0.994612 | − | 0.103667i | \(-0.966942\pi\) |
0.587084 | + | 0.809526i | \(0.300276\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.37002 | + | 11.8351i | −0.103564 | + | 0.894653i | ||||
\(176\) | −2.96669 | + | 0.794922i | −0.223623 | + | 0.0599195i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −38.7115 | − | 22.3501i | −2.90155 | − | 1.67521i | ||||
\(179\) | −8.63169 | + | 4.98351i | −0.645163 | + | 0.372485i | −0.786601 | − | 0.617462i | \(-0.788161\pi\) |
0.141438 | + | 0.989947i | \(0.454828\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −3.96508 | −0.294722 | −0.147361 | − | 0.989083i | \(-0.547078\pi\) | ||||
−0.147361 | + | 0.989083i | \(0.547078\pi\) | |||||||
\(182\) | −23.3127 | + | 2.67726i | −1.72805 | + | 0.198452i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −9.39929 | − | 2.51853i | −0.692925 | − | 0.185669i | ||||
\(185\) | −1.28715 | + | 0.743136i | −0.0946331 | + | 0.0546365i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2.29120 | + | 2.29120i | 0.167549 | + | 0.167549i | ||||
\(188\) | 19.6949 | − | 5.27724i | 1.43640 | − | 0.384882i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −4.12534 | − | 4.12534i | −0.299284 | − | 0.299284i | ||||
\(191\) | 9.17881 | − | 15.8982i | 0.664155 | − | 1.15035i | −0.315358 | − | 0.948973i | \(-0.602125\pi\) |
0.979514 | − | 0.201378i | \(-0.0645420\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 4.24786 | − | 15.8532i | 0.305767 | − | 1.14114i | −0.626515 | − | 0.779409i | \(-0.715519\pi\) |
0.932283 | − | 0.361731i | \(-0.117814\pi\) | |||||||
\(194\) | −22.2531 | −1.59768 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 20.6696 | + | 19.4143i | 1.47640 | + | 1.38673i | ||||
\(197\) | −5.69553 | − | 1.52611i | −0.405790 | − | 0.108731i | 0.0501498 | − | 0.998742i | \(-0.484030\pi\) |
−0.455940 | + | 0.890011i | \(0.650697\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −9.61483 | + | 16.6534i | −0.681578 | + | 1.18053i | 0.292922 | + | 0.956136i | \(0.405372\pi\) |
−0.974499 | + | 0.224391i | \(0.927961\pi\) | |||||||
\(200\) | −16.0656 | + | 16.0656i | −1.13601 | + | 1.13601i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −8.62496 | − | 32.1888i | −0.606850 | − | 2.26480i | ||||
\(203\) | 0.390675 | + | 0.902929i | 0.0274200 | + | 0.0633732i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −7.35842 | + | 4.24839i | −0.513935 | + | 0.296720i | ||||
\(206\) | −39.1020 | − | 10.4773i | −2.72436 | − | 0.729991i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −13.1978 | − | 8.19756i | −0.915102 | − | 0.568398i | ||||
\(209\) | 2.39821i | 0.165888i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −4.61920 | − | 8.00070i | −0.317999 | − | 0.550791i | 0.662071 | − | 0.749441i | \(-0.269678\pi\) |
−0.980070 | + | 0.198650i | \(0.936344\pi\) | |||||||
\(212\) | 17.4614 | + | 10.0813i | 1.19925 | + | 0.692389i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 10.6430 | + | 39.7201i | 0.727539 | + | 2.71521i | ||||
\(215\) | 1.34508 | + | 5.01991i | 0.0917338 | + | 0.342355i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −8.22669 | − | 10.3807i | −0.558464 | − | 0.704684i | ||||
\(218\) | −5.35570 | + | 3.09212i | −0.362734 | + | 0.209425i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −2.03534 | −0.137223 | ||||||||
\(221\) | −0.527913 | + | 16.3823i | −0.0355112 | + | 1.10200i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0.482353 | − | 1.80016i | 0.0323007 | − | 0.120548i | −0.947893 | − | 0.318589i | \(-0.896791\pi\) |
0.980194 | + | 0.198041i | \(0.0634578\pi\) | |||||||
\(224\) | 0.196634 | + | 1.33210i | 0.0131382 | + | 0.0890046i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −10.3061 | + | 10.3061i | −0.685549 | + | 0.685549i | ||||
\(227\) | −5.38143 | + | 1.44195i | −0.357178 | + | 0.0957056i | −0.432946 | − | 0.901420i | \(-0.642526\pi\) |
0.0757678 | + | 0.997125i | \(0.475859\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 0.153144 | − | 0.153144i | 0.0101200 | − | 0.0101200i | −0.702029 | − | 0.712149i | \(-0.747722\pi\) |
0.712149 | + | 0.702029i | \(0.247722\pi\) | |||||||
\(230\) | −2.89615 | − | 1.67209i | −0.190966 | − | 0.110254i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −0.485580 | + | 1.81221i | −0.0318799 | + | 0.118977i | ||||
\(233\) | 19.7822i | 1.29598i | 0.761650 | + | 0.647989i | \(0.224390\pi\) | ||||
−0.761650 | + | 0.647989i | \(0.775610\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 3.54781 | 0.231434 | ||||||||
\(236\) | −4.18944 | + | 15.6352i | −0.272710 | + | 1.01777i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 23.1878 | − | 18.3764i | 1.50304 | − | 1.19116i | ||||
\(239\) | 0.636908 | − | 0.636908i | 0.0411982 | − | 0.0411982i | −0.686208 | − | 0.727406i | \(-0.740726\pi\) |
0.727406 | + | 0.686208i | \(0.240726\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −5.16499 | − | 19.2760i | −0.332706 | − | 1.24168i | −0.906335 | − | 0.422561i | \(-0.861131\pi\) |
0.573629 | − | 0.819116i | \(-0.305535\pi\) | |||||||
\(242\) | −18.2498 | − | 18.2498i | −1.17314 | − | 1.17314i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 23.5574 | + | 40.8025i | 1.50811 | + | 2.61212i | ||||
\(245\) | 2.59966 | + | 4.19383i | 0.166086 | + | 0.267934i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −8.85003 | + | 8.29746i | −0.563114 | + | 0.527955i | ||||
\(248\) | − | 25.2585i | − | 1.60392i | ||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −14.2703 | + | 8.23896i | −0.902533 | + | 0.521078i | ||||
\(251\) | 14.0053 | − | 24.2580i | 0.884010 | − | 1.53115i | 0.0371651 | − | 0.999309i | \(-0.488167\pi\) |
0.846845 | − | 0.531840i | \(-0.178499\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0.355793 | + | 1.32784i | 0.0223685 | + | 0.0834805i | ||||
\(254\) | 47.7858 | − | 12.8042i | 2.99835 | − | 0.803405i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 16.1723 | − | 28.0113i | 1.01077 | − | 1.75070i | ||||
\(257\) | −4.51978 | − | 7.82849i | −0.281936 | − | 0.488328i | 0.689925 | − | 0.723880i | \(-0.257643\pi\) |
−0.971862 | + | 0.235553i | \(0.924310\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2.05391 | − | 5.18677i | 0.127624 | − | 0.322290i | ||||
\(260\) | −7.04199 | − | 7.51095i | −0.436726 | − | 0.465809i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −7.69071 | + | 28.7021i | −0.475134 | + | 1.77322i | ||||
\(263\) | 11.6573 | + | 20.1910i | 0.718819 | + | 1.24503i | 0.961468 | + | 0.274917i | \(0.0886503\pi\) |
−0.242649 | + | 0.970114i | \(0.578016\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2.48075 | + | 2.48075i | 0.152391 | + | 0.152391i | ||||
\(266\) | 21.7527 | + | 2.51806i | 1.33375 | + | 0.154392i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −37.3278 | − | 37.3278i | −2.28016 | − | 2.28016i | ||||
\(269\) | 24.9574 | + | 14.4092i | 1.52168 | + | 0.878543i | 0.999672 | + | 0.0256040i | \(0.00815089\pi\) |
0.522010 | + | 0.852939i | \(0.325182\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −11.9008 | − | 3.18880i | −0.722920 | − | 0.193706i | −0.121446 | − | 0.992598i | \(-0.538753\pi\) |
−0.601474 | + | 0.798892i | \(0.705420\pi\) | |||||||
\(272\) | 19.5889 | 1.18775 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −35.6236 | −2.15210 | ||||||||
\(275\) | 3.10032 | + | 0.830728i | 0.186956 | + | 0.0500948i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −12.3959 | − | 7.15677i | −0.744797 | − | 0.430009i | 0.0790140 | − | 0.996874i | \(-0.474823\pi\) |
−0.823811 | + | 0.566865i | \(0.808156\pi\) | |||||||
\(278\) | 13.9720 | + | 13.9720i | 0.837987 | + | 0.837987i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −1.08200 | + | 9.34706i | −0.0646619 | + | 0.558594i | ||||
\(281\) | 10.7886 | + | 10.7886i | 0.643591 | + | 0.643591i | 0.951437 | − | 0.307845i | \(-0.0996078\pi\) |
−0.307845 | + | 0.951437i | \(0.599608\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −6.96923 | − | 12.0711i | −0.414278 | − | 0.717550i | 0.581075 | − | 0.813850i | \(-0.302632\pi\) |
−0.995352 | + | 0.0963004i | \(0.969299\pi\) | |||||||
\(284\) | 8.53485 | − | 31.8525i | 0.506450 | − | 1.89010i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −0.203609 | + | 6.31844i | −0.0120396 | + | 0.373617i | ||||
\(287\) | 11.7419 | − | 29.6519i | 0.693101 | − | 1.75030i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.83307 | − | 3.17497i | −0.107828 | − | 0.186763i | ||||
\(290\) | −0.322384 | + | 0.558385i | −0.0189310 | + | 0.0327895i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 3.36957 | − | 0.902873i | 0.197189 | − | 0.0528367i | ||||
\(293\) | 4.49081 | + | 16.7599i | 0.262356 | + | 0.979126i | 0.963849 | + | 0.266450i | \(0.0858506\pi\) |
−0.701493 | + | 0.712677i | \(0.747483\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.40825 | + | 2.43916i | −0.0819915 | + | 0.142013i | ||||
\(296\) | 9.21312 | − | 5.31920i | 0.535502 | − | 0.309172i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | − | 20.2750i | − | 1.17450i | ||||||
\(299\) | −3.66909 | + | 5.90711i | −0.212189 | + | 0.341617i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −15.6596 | − | 11.6312i | −0.902606 | − | 0.670409i | ||||
\(302\) | 7.22375 | + | 12.5119i | 0.415680 | + | 0.719980i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 10.2519 | + | 10.2519i | 0.587988 | + | 0.587988i | ||||
\(305\) | 2.12179 | + | 7.91863i | 0.121493 | + | 0.453419i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −14.5281 | + | 14.5281i | −0.829164 | + | 0.829164i | −0.987401 | − | 0.158237i | \(-0.949419\pi\) |
0.158237 | + | 0.987401i | \(0.449419\pi\) | |||||||
\(308\) | 5.98730 | − | 4.74495i | 0.341158 | − | 0.270369i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 2.24669 | − | 8.38475i | 0.127603 | − | 0.476222i | ||||
\(311\) | −7.52888 | −0.426924 | −0.213462 | − | 0.976951i | \(-0.568474\pi\) | ||||
−0.213462 | + | 0.976951i | \(0.568474\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 7.90713i | 0.446938i | 0.974711 | + | 0.223469i | \(0.0717381\pi\) | ||||
−0.974711 | + | 0.223469i | \(0.928262\pi\) | |||||||
\(314\) | 9.30570 | − | 34.7293i | 0.525151 | − | 1.95989i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 34.4356 | + | 19.8814i | 1.93715 | + | 1.11842i | ||||
\(317\) | −12.2598 | + | 12.2598i | −0.688580 | + | 0.688580i | −0.961918 | − | 0.273338i | \(-0.911872\pi\) |
0.273338 | + | 0.961918i | \(0.411872\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0.256011 | − | 0.0685980i | 0.0143339 | − | 0.00384075i | ||||
\(320\) | 3.67151 | − | 3.67151i | 0.205243 | − | 0.205243i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 12.4176 | − | 1.83299i | 0.692007 | − | 0.102149i | ||||
\(323\) | 3.95882 | − | 14.7745i | 0.220274 | − | 0.822075i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 7.66105 | + | 14.3152i | 0.424959 | + | 0.794065i | ||||
\(326\) | −18.7230 | −1.03697 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 52.6699 | − | 30.4090i | 2.90821 | − | 1.67905i | ||||
\(329\) | −10.4365 | + | 8.27095i | −0.575383 | + | 0.455992i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.27846 | + | 4.77126i | 0.0702703 | + | 0.262252i | 0.992119 | − | 0.125297i | \(-0.0399884\pi\) |
−0.921849 | + | 0.387549i | \(0.873322\pi\) | |||||||
\(332\) | 3.34299 | + | 12.4762i | 0.183470 | + | 0.684720i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 16.7634 | + | 9.67835i | 0.917252 | + | 0.529576i | ||||
\(335\) | −4.59269 | − | 7.95477i | −0.250925 | − | 0.434615i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 7.35624i | 0.400720i | 0.979722 | + | 0.200360i | \(0.0642112\pi\) | ||||
−0.979722 | + | 0.200360i | \(0.935789\pi\) | |||||||
\(338\) | −24.0212 | + | 21.1095i | −1.30658 | + | 1.14821i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 12.5390 | + | 3.35982i | 0.680023 | + | 0.182212i | ||||
\(341\) | −3.09022 | + | 1.78414i | −0.167345 | + | 0.0966165i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −17.4243 | − | 6.27632i | −0.940826 | − | 0.338890i | ||||
\(344\) | −9.62778 | − | 35.9314i | −0.519095 | − | 1.93729i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 18.6471 | − | 18.6471i | 1.00247 | − | 1.00247i | ||||
\(347\) | −1.58494 | + | 2.74519i | −0.0850839 | + | 0.147370i | −0.905427 | − | 0.424502i | \(-0.860449\pi\) |
0.820343 | + | 0.571872i | \(0.193782\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −26.0697 | − | 6.98534i | −1.39548 | − | 0.373917i | −0.518758 | − | 0.854921i | \(-0.673605\pi\) |
−0.876718 | + | 0.481004i | \(0.840272\pi\) | |||||||
\(350\) | 10.7903 | − | 27.2489i | 0.576766 | − | 1.45652i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0.362757 | 0.0193350 | ||||||||
\(353\) | 1.36374 | − | 5.08954i | 0.0725845 | − | 0.270889i | −0.920090 | − | 0.391706i | \(-0.871885\pi\) |
0.992675 | + | 0.120817i | \(0.0385516\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2.86893 | − | 4.96913i | 0.152267 | − | 0.263734i | ||||
\(356\) | 52.0533 | + | 52.0533i | 2.75882 | + | 2.75882i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 23.6824 | − | 6.34567i | 1.25165 | − | 0.335379i | ||||
\(359\) | −17.8470 | − | 17.8470i | −0.941927 | − | 0.941927i | 0.0564767 | − | 0.998404i | \(-0.482013\pi\) |
−0.998404 | + | 0.0564767i | \(0.982013\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6.65034 | + | 3.83958i | −0.350018 | + | 0.202083i | ||||
\(362\) | 9.42133 | + | 2.52444i | 0.495174 | + | 0.132682i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 38.2254 | + | 5.67788i | 2.00355 | + | 0.297602i | ||||
\(365\) | 0.606988 | 0.0317712 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 28.6206 | − | 16.5241i | 1.49398 | − | 0.862551i | 0.494006 | − | 0.869458i | \(-0.335532\pi\) |
0.999976 | + | 0.00690739i | \(0.00219871\pi\) | |||||||
\(368\) | 7.19723 | + | 4.15532i | 0.375181 | + | 0.216611i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 3.53149 | − | 0.946261i | 0.183594 | − | 0.0491938i | ||||
\(371\) | −13.0809 | − | 1.51422i | −0.679125 | − | 0.0786144i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 13.8983 | − | 24.0726i | 0.719627 | − | 1.24643i | −0.241521 | − | 0.970396i | \(-0.577646\pi\) |
0.961148 | − | 0.276035i | \(-0.0890204\pi\) | |||||||
\(374\) | −3.98532 | − | 6.90278i | −0.206076 | − | 0.356934i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −25.3944 | −1.30962 | ||||||||
\(377\) | 1.13891 | + | 0.707411i | 0.0586567 | + | 0.0364335i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 14.6943 | + | 3.93733i | 0.754797 | + | 0.202247i | 0.615645 | − | 0.788024i | \(-0.288896\pi\) |
0.139152 | + | 0.990271i | \(0.455562\pi\) | |||||||
\(380\) | 4.80395 | + | 8.32069i | 0.246438 | + | 0.426843i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −31.9314 | + | 31.9314i | −1.63375 | + | 1.63375i | ||||
\(383\) | −8.30637 | + | 2.22568i | −0.424436 | + | 0.113727i | −0.464713 | − | 0.885461i | \(-0.653842\pi\) |
0.0402774 | + | 0.999189i | \(0.487176\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.21998 | − | 0.527855i | 0.0621759 | − | 0.0269020i | ||||
\(386\) | −20.1864 | + | 34.9639i | −1.02746 | + | 1.77962i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 35.3987 | + | 9.48505i | 1.79710 | + | 0.481530i | ||||
\(389\) | − | 11.3461i | − | 0.575268i | −0.957740 | − | 0.287634i | \(-0.907131\pi\) | ||
0.957740 | − | 0.287634i | \(-0.0928686\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 8.76766i | − | 0.443400i | ||||||
\(392\) | −18.6078 | − | 30.0184i | −0.939834 | − | 1.51616i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 12.5614 | + | 7.25232i | 0.632833 | + | 0.365366i | ||||
\(395\) | 4.89228 | + | 4.89228i | 0.246157 | + | 0.246157i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −4.16966 | − | 15.5614i | −0.209269 | − | 0.781003i | −0.988106 | − | 0.153776i | \(-0.950856\pi\) |
0.778836 | − | 0.627227i | \(-0.215810\pi\) | |||||||
\(398\) | 33.4482 | − | 33.4482i | 1.67661 | − | 1.67661i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 16.8045 | − | 9.70209i | 0.840226 | − | 0.485105i | ||||
\(401\) | 9.35796 | − | 34.9244i | 0.467314 | − | 1.74404i | −0.181787 | − | 0.983338i | \(-0.558188\pi\) |
0.649101 | − | 0.760702i | \(-0.275145\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −17.2757 | − | 5.23087i | −0.860562 | − | 0.260568i | ||||
\(404\) | 54.8801i | 2.73039i | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −0.353407 | − | 2.39416i | −0.0175393 | − | 0.118820i | ||||
\(407\) | −1.30154 | − | 0.751444i | −0.0645149 | − | 0.0372477i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 13.9857 | − | 3.74745i | 0.691547 | − | 0.185300i | 0.104106 | − | 0.994566i | \(-0.466802\pi\) |
0.587441 | + | 0.809267i | \(0.300135\pi\) | |||||||
\(410\) | 20.1890 | − | 5.40962i | 0.997062 | − | 0.267162i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 57.7350 | + | 33.3333i | 2.84440 | + | 1.64221i | ||||
\(413\) | −1.54376 | − | 10.4582i | −0.0759637 | − | 0.514616i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 2.24744i | 0.110322i | ||||||||
\(416\) | 1.25509 | + | 1.33867i | 0.0615357 | + | 0.0656337i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 1.52686 | − | 5.69832i | 0.0746812 | − | 0.278714i | ||||
\(419\) | −19.0889 | + | 11.0210i | −0.932553 | + | 0.538410i | −0.887618 | − | 0.460580i | \(-0.847641\pi\) |
−0.0449347 | + | 0.998990i | \(0.514308\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −7.69603 | + | 7.69603i | −0.375082 | + | 0.375082i | −0.869324 | − | 0.494243i | \(-0.835445\pi\) |
0.494243 | + | 0.869324i | \(0.335445\pi\) | |||||||
\(422\) | 5.88179 | + | 21.9511i | 0.286321 | + | 1.06856i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −17.7566 | − | 17.7566i | −0.862338 | − | 0.862338i | ||||
\(425\) | −17.7286 | − | 10.2356i | −0.859965 | − | 0.496501i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −24.7022 | − | 18.3475i | −1.19542 | − | 0.887898i | ||||
\(428\) | − | 67.7206i | − | 3.27340i | ||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | − | 12.7840i | − | 0.616502i | ||||||
\(431\) | 26.2932 | + | 7.04525i | 1.26650 | + | 0.339358i | 0.828689 | − | 0.559709i | \(-0.189087\pi\) |
0.437812 | + | 0.899067i | \(0.355754\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −6.55214 | + | 11.3486i | −0.314876 | + | 0.545381i | −0.979411 | − | 0.201876i | \(-0.935296\pi\) |
0.664535 | + | 0.747257i | \(0.268629\pi\) | |||||||
\(434\) | 12.9382 | + | 29.9029i | 0.621054 | + | 1.43538i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 9.83747 | − | 2.63594i | 0.471129 | − | 0.126239i | ||||
\(437\) | 4.58858 | − | 4.58858i | 0.219502 | − | 0.219502i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 19.9333 | + | 34.5255i | 0.951364 | + | 1.64781i | 0.742477 | + | 0.669872i | \(0.233651\pi\) |
0.208887 | + | 0.977940i | \(0.433016\pi\) | |||||||
\(440\) | 2.44854 | + | 0.656085i | 0.116730 | + | 0.0312776i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 11.6845 | − | 38.5896i | 0.555773 | − | 1.83552i | ||||
\(443\) | −23.0066 | −1.09308 | −0.546539 | − | 0.837433i | \(-0.684055\pi\) | ||||
−0.546539 | + | 0.837433i | \(0.684055\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 6.40446 | + | 11.0928i | 0.303600 | + | 0.525851i | ||||
\(446\) | −2.29221 | + | 3.97023i | −0.108539 | + | 0.187996i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −2.24105 | + | 19.3597i | −0.105880 | + | 0.914659i | ||||
\(449\) | −15.6281 | + | 4.18754i | −0.737536 | + | 0.197622i | −0.607983 | − | 0.793950i | \(-0.708021\pi\) |
−0.129553 | + | 0.991572i | \(0.541354\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −7.44068 | − | 4.29588i | −0.350368 | − | 0.202285i | ||||
\(452\) | 20.7870 | − | 12.0014i | 0.977739 | − | 0.564498i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 13.7047 | 0.643194 | ||||||||
\(455\) | 6.16888 | + | 2.67575i | 0.289202 | + | 0.125441i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 0.658952 | + | 0.176566i | 0.0308245 | + | 0.00825939i | 0.274198 | − | 0.961673i | \(-0.411588\pi\) |
−0.243374 | + | 0.969933i | \(0.578254\pi\) | |||||||
\(458\) | −0.461383 | + | 0.266380i | −0.0215590 | + | 0.0124471i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 3.89429 | + | 3.89429i | 0.181572 | + | 0.181572i | ||||
\(461\) | −8.08252 | + | 2.16570i | −0.376440 | + | 0.100867i | −0.442078 | − | 0.896977i | \(-0.645759\pi\) |
0.0656375 | + | 0.997844i | \(0.479092\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 22.3879 | + | 22.3879i | 1.04045 | + | 1.04045i | 0.999146 | + | 0.0413082i | \(0.0131525\pi\) |
0.0413082 | + | 0.999146i | \(0.486847\pi\) | |||||||
\(464\) | 0.801158 | − | 1.38765i | 0.0371928 | − | 0.0644199i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 12.5947 | − | 47.0041i | 0.583438 | − | 2.17742i | ||||
\(467\) | 13.5832 | 0.628554 | 0.314277 | − | 0.949331i | \(-0.398238\pi\) | ||||
0.314277 | + | 0.949331i | \(0.398238\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 32.0550 | + | 12.6935i | 1.48016 | + | 0.586130i | ||||
\(470\) | −8.42986 | − | 2.25877i | −0.388840 | − | 0.104189i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 10.0799 | − | 17.4589i | 0.463966 | − | 0.803613i | ||||
\(473\) | −3.71591 | + | 3.71591i | −0.170858 | + | 0.170858i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −3.92148 | − | 14.6352i | −0.179930 | − | 0.671508i | ||||
\(476\) | −44.7183 | + | 19.3485i | −2.04966 | + | 0.886836i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −1.91884 | + | 1.10784i | −0.0877656 | + | 0.0506715i | ||||
\(479\) | 4.03229 | + | 1.08045i | 0.184240 | + | 0.0493669i | 0.349759 | − | 0.936840i | \(-0.386263\pi\) |
−0.165519 | + | 0.986207i | \(0.552930\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.73011 | − | 7.40292i | −0.0788863 | − | 0.337544i | ||||
\(482\) | 49.0896i | 2.23597i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 21.2518 | + | 36.8093i | 0.965993 | + | 1.67315i | ||||
\(485\) | 5.52235 | + | 3.18833i | 0.250757 | + | 0.144775i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 4.28159 | + | 15.9791i | 0.194018 | + | 0.724083i | 0.992519 | + | 0.122090i | \(0.0389598\pi\) |
−0.798501 | + | 0.601993i | \(0.794374\pi\) | |||||||
\(488\) | −15.1873 | − | 56.6797i | −0.687496 | − | 2.56577i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −3.50691 | − | 11.6200i | −0.158426 | − | 0.524936i | ||||
\(491\) | −27.7156 | + | 16.0016i | −1.25079 | + | 0.722143i | −0.971266 | − | 0.237996i | \(-0.923510\pi\) |
−0.279523 | + | 0.960139i | \(0.590176\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1.69043 | −0.0761332 | ||||||||
\(494\) | 26.3111 | − | 14.0809i | 1.18379 | − | 0.633528i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −5.58326 | + | 20.8370i | −0.250696 | + | 0.935609i | ||||
\(497\) | 3.14500 | + | 21.3058i | 0.141073 | + | 0.955697i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −14.4246 | + | 14.4246i | −0.645734 | + | 0.645734i | −0.951959 | − | 0.306225i | \(-0.900934\pi\) |
0.306225 | + | 0.951959i | \(0.400934\pi\) | |||||||
\(500\) | 26.2120 | − | 7.02348i | 1.17224 | − | 0.314100i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −48.7220 | + | 48.7220i | −2.17457 | + | 2.17457i | ||||
\(503\) | −23.6349 | − | 13.6456i | −1.05383 | − | 0.608427i | −0.130109 | − | 0.991500i | \(-0.541533\pi\) |
−0.923718 | + | 0.383072i | \(0.874866\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −2.47150 | + | 9.22376i | −0.109980 | + | 0.410452i | ||||
\(506\) | − | 3.38157i | − | 0.150329i | ||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −81.4721 | −3.61474 | ||||||||
\(509\) | −8.17110 | + | 30.4949i | −0.362177 | + | 1.35166i | 0.509030 | + | 0.860749i | \(0.330004\pi\) |
−0.871207 | + | 0.490916i | \(0.836662\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.78556 | + | 1.41506i | −0.0789885 | + | 0.0625986i | ||||
\(512\) | −29.1956 | + | 29.1956i | −1.29027 | + | 1.29027i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 5.75519 | + | 21.4787i | 0.253851 | + | 0.947383i | ||||
\(515\) | 8.20244 | + | 8.20244i | 0.361443 | + | 0.361443i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.79374 | + | 3.10684i | 0.0788884 | + | 0.136639i | ||||
\(518\) | −8.18249 | + | 11.0165i | −0.359518 | + | 0.484037i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 6.05048 | + | 11.3057i | 0.265331 | + | 0.495790i | ||||
\(521\) | − | 13.1042i | − | 0.574107i | −0.957915 | − | 0.287054i | \(-0.907324\pi\) | ||
0.957915 | − | 0.287054i | \(-0.0926758\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 7.44365 | − | 4.29760i | 0.325488 | − | 0.187921i | −0.328348 | − | 0.944557i | \(-0.606492\pi\) |
0.653836 | + | 0.756636i | \(0.273159\pi\) | |||||||
\(524\) | 24.4678 | − | 42.3794i | 1.06888 | − | 1.85135i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −14.8436 | − | 55.3971i | −0.647212 | − | 2.41543i | ||||
\(527\) | 21.9829 | − | 5.89029i | 0.957589 | − | 0.256585i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −9.64015 | + | 16.6972i | −0.419137 | + | 0.725966i | ||||
\(530\) | −4.31503 | − | 7.47385i | −0.187433 | − | 0.324643i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −33.5295 | − | 13.2774i | −1.45369 | − | 0.575647i | ||||
\(533\) | −9.89076 | − | 42.3213i | −0.428417 | − | 1.83314i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 3.04977 | − | 11.3819i | 0.131853 | − | 0.492082i | ||||
\(536\) | 32.8734 | + | 56.9384i | 1.41991 | + | 2.45936i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −50.1269 | − | 50.1269i | −2.16112 | − | 2.16112i | ||||
\(539\) | −2.35820 | + | 4.39689i | −0.101575 | + | 0.189388i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 6.09190 | + | 6.09190i | 0.261911 | + | 0.261911i | 0.825830 | − | 0.563919i | \(-0.190707\pi\) |
−0.563919 | + | 0.825830i | \(0.690707\pi\) | |||||||
\(542\) | 26.2469 | + | 15.1537i | 1.12740 | + | 0.650905i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −2.23482 | − | 0.598817i | −0.0958169 | − | 0.0256741i | ||||
\(545\) | 1.77210 | 0.0759086 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 30.2438 | 1.29313 | 0.646566 | − | 0.762858i | \(-0.276205\pi\) | ||||
0.646566 | + | 0.762858i | \(0.276205\pi\) | |||||||
\(548\) | 56.6677 | + | 15.1841i | 2.42072 | + | 0.648631i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −6.83769 | − | 3.94774i | −0.291560 | − | 0.168332i | ||||
\(551\) | −0.884692 | − | 0.884692i | −0.0376892 | − | 0.0376892i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −25.7968 | − | 2.98619i | −1.09699 | − | 0.126986i | ||||
\(554\) | 24.8971 | + | 24.8971i | 1.05778 | + | 1.05778i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −16.2704 | − | 28.1812i | −0.690019 | − | 1.19515i | ||||
\(557\) | 11.7586 | − | 43.8837i | 0.498228 | − | 1.85941i | −0.0129131 | − | 0.999917i | \(-0.504110\pi\) |
0.511141 | − | 0.859497i | \(-0.329223\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −26.5692 | − | 0.856180i | −1.12376 | − | 0.0362126i | ||||
\(560\) | 2.95871 | − | 7.47168i | 0.125028 | − | 0.315736i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −18.7657 | − | 32.5031i | −0.791583 | − | 1.37106i | ||||
\(563\) | 12.5992 | − | 21.8224i | 0.530992 | − | 0.919704i | −0.468354 | − | 0.883541i | \(-0.655153\pi\) |
0.999346 | − | 0.0361636i | \(-0.0115137\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 4.03418 | − | 1.08095i | 0.169719 | − | 0.0454761i | ||||
\(566\) | 8.87415 | + | 33.1188i | 0.373009 | + | 1.39209i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −20.5351 | + | 35.5679i | −0.861634 | + | 1.49239i | ||||
\(569\) | −13.9572 | + | 8.05819i | −0.585116 | + | 0.337817i | −0.763164 | − | 0.646205i | \(-0.776355\pi\) |
0.178048 | + | 0.984022i | \(0.443022\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 13.5825i | − | 0.568409i | −0.958764 | − | 0.284204i | \(-0.908271\pi\) | ||
0.958764 | − | 0.284204i | \(-0.0917294\pi\) | |||||||
\(572\) | 3.01703 | − | 9.96418i | 0.126149 | − | 0.416623i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −46.7780 | + | 62.9795i | −1.95247 | + | 2.62871i | ||||
\(575\) | −4.34249 | − | 7.52142i | −0.181094 | − | 0.313665i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 33.5657 | + | 33.5657i | 1.39736 | + | 1.39736i | 0.807528 | + | 0.589829i | \(0.200805\pi\) |
0.589829 | + | 0.807528i | \(0.299195\pi\) | |||||||
\(578\) | 2.33411 | + | 8.71103i | 0.0970863 | + | 0.362331i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0.750831 | − | 0.750831i | 0.0311766 | − | 0.0311766i | ||||
\(581\) | −5.23942 | − | 6.61123i | −0.217368 | − | 0.274280i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −0.918168 | + | 3.42665i | −0.0380266 | + | 0.141917i | ||||
\(584\) | −4.34468 | −0.179784 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | − | 42.6820i | − | 1.76318i | ||||||
\(587\) | 6.29368 | − | 23.4883i | 0.259768 | − | 0.969467i | −0.705607 | − | 0.708603i | \(-0.749326\pi\) |
0.965375 | − | 0.260864i | \(-0.0840076\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 14.5875 | + | 8.42210i | 0.601067 | + | 0.347026i | ||||
\(590\) | 4.89904 | − | 4.89904i | 0.201690 | − | 0.201690i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −8.77613 | + | 2.35156i | −0.360697 | + | 0.0966484i | ||||
\(593\) | 10.0628 | − | 10.0628i | 0.413231 | − | 0.413231i | −0.469631 | − | 0.882863i | \(-0.655613\pi\) |
0.882863 | + | 0.469631i | \(0.155613\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −8.38721 | + | 1.23805i | −0.343842 | + | 0.0507553i | ||||
\(596\) | −8.64195 | + | 32.2522i | −0.353988 | + | 1.32110i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 12.4789 | − | 11.6997i | 0.510299 | − | 0.478438i | ||||
\(599\) | −15.7719 | −0.644422 | −0.322211 | − | 0.946668i | \(-0.604426\pi\) | ||||
−0.322211 | + | 0.946668i | \(0.604426\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 18.2565 | − | 10.5404i | 0.744698 | − | 0.429952i | −0.0790767 | − | 0.996869i | \(-0.525197\pi\) |
0.823775 | + | 0.566917i | \(0.191864\pi\) | |||||||
\(602\) | 29.8032 | + | 37.6065i | 1.21469 | + | 1.53273i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −6.15805 | − | 22.9821i | −0.250567 | − | 0.935130i | ||||
\(605\) | 1.91413 | + | 7.14365i | 0.0778206 | + | 0.290431i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −14.6360 | − | 8.45008i | −0.594056 | − | 0.342978i | 0.172644 | − | 0.984984i | \(-0.444769\pi\) |
−0.766700 | + | 0.642006i | \(0.778102\pi\) | |||||||
\(608\) | −0.856205 | − | 1.48299i | −0.0347237 | − | 0.0601432i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | − | 20.1661i | − | 0.816502i | ||||||
\(611\) | −5.25901 | + | 17.3686i | −0.212757 | + | 0.702658i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 17.4644 | + | 4.67958i | 0.705381 | + | 0.189006i | 0.593640 | − | 0.804731i | \(-0.297690\pi\) |
0.111742 | + | 0.993737i | \(0.464357\pi\) | |||||||
\(614\) | 43.7695 | − | 25.2703i | 1.76639 | − | 1.01983i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −8.73233 | + | 3.77826i | −0.351836 | + | 0.152230i | ||||
\(617\) | −5.54500 | − | 20.6942i | −0.223233 | − | 0.833118i | −0.983105 | − | 0.183045i | \(-0.941405\pi\) |
0.759871 | − | 0.650074i | \(-0.225262\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 19.4756 | − | 19.4756i | 0.782790 | − | 0.782790i | −0.197511 | − | 0.980301i | \(-0.563286\pi\) |
0.980301 | + | 0.197511i | \(0.0632857\pi\) | |||||||
\(620\) | −7.14777 | + | 12.3803i | −0.287061 | + | 0.497205i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 17.8892 | + | 4.79339i | 0.717291 | + | 0.192197i | ||||
\(623\) | −44.7004 | − | 17.7009i | −1.79088 | − | 0.709172i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −17.7939 | −0.711756 | ||||||||
\(626\) | 5.03421 | − | 18.7879i | 0.201208 | − | 0.750917i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −29.6058 | + | 51.2787i | −1.18140 | + | 2.04624i | ||||
\(629\) | 6.77788 | + | 6.77788i | 0.270252 | + | 0.270252i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −20.8332 | + | 5.58224i | −0.829356 | + | 0.222225i | −0.648433 | − | 0.761272i | \(-0.724575\pi\) |
−0.180923 | + | 0.983497i | \(0.557909\pi\) | |||||||
\(632\) | −35.0178 | − | 35.0178i | −1.39293 | − | 1.39293i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 36.9357 | − | 21.3248i | 1.46690 | − | 0.846916i | ||||
\(635\) | −13.6931 | − | 3.66906i | −0.543395 | − | 0.145602i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −24.3848 | + | 6.51023i | −0.966160 | + | 0.257945i | ||||
\(638\) | −0.651976 | −0.0258120 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −11.6827 | + | 6.74499i | −0.461798 | + | 0.266619i | ||||
\(641\) | −25.3468 | − | 14.6340i | −1.00114 | − | 0.578006i | −0.0925521 | − | 0.995708i | \(-0.529502\pi\) |
−0.908584 | + | 0.417701i | \(0.862836\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 12.4873 | − | 3.34595i | 0.492449 | − | 0.131951i | −0.00404423 | − | 0.999992i | \(-0.501287\pi\) |
0.496494 | + | 0.868040i | \(0.334621\pi\) | |||||||
\(644\) | −20.5344 | − | 2.37703i | −0.809170 | − | 0.0936682i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −18.8129 | + | 32.5849i | −0.740183 | + | 1.28203i | ||||
\(647\) | 18.8428 | + | 32.6368i | 0.740788 | + | 1.28308i | 0.952137 | + | 0.305672i | \(0.0988813\pi\) |
−0.211348 | + | 0.977411i | \(0.567785\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −2.84798 | −0.111793 | ||||||||
\(650\) | −9.08921 | − | 38.8915i | −0.356508 | − | 1.52545i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 29.7833 | + | 7.98041i | 1.16640 | + | 0.312537i | ||||
\(653\) | 20.0158 | + | 34.6685i | 0.783280 | + | 1.35668i | 0.930021 | + | 0.367507i | \(0.119788\pi\) |
−0.146740 | + | 0.989175i | \(0.546878\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 6.02086 | − | 6.02086i | 0.235255 | − | 0.235255i | ||||
\(656\) | −50.1717 | + | 13.4435i | −1.95888 | + | 0.524879i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 30.0637 | − | 13.0078i | 1.17201 | − | 0.507097i | ||||
\(659\) | −15.0023 | + | 25.9848i | −0.584407 | + | 1.01222i | 0.410542 | + | 0.911842i | \(0.365340\pi\) |
−0.994949 | + | 0.100381i | \(0.967994\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −19.0751 | − | 5.11115i | −0.741934 | − | 0.198801i | −0.131996 | − | 0.991250i | \(-0.542139\pi\) |
−0.609937 | + | 0.792450i | \(0.708805\pi\) | |||||||
\(662\) | − | 12.1508i | − | 0.472255i | ||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | − | 16.0866i | − | 0.624283i | ||||||
\(665\) | −5.03741 | − | 3.74153i | −0.195342 | − | 0.145090i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −0.621087 | − | 0.358585i | −0.0240486 | − | 0.0138845i | ||||
\(668\) | −22.5408 | − | 22.5408i | −0.872131 | − | 0.872131i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 5.84803 | + | 21.8251i | 0.225929 | + | 0.843178i | ||||
\(671\) | −5.86164 | + | 5.86164i | −0.226286 | + | 0.226286i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −39.4906 | + | 22.7999i | −1.52225 | + | 0.878872i | −0.522597 | + | 0.852580i | \(0.675037\pi\) |
−0.999654 | + | 0.0262924i | \(0.991630\pi\) | |||||||
\(674\) | 4.68348 | − | 17.4790i | 0.180401 | − | 0.673265i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 47.2090 | − | 23.3410i | 1.81573 | − | 0.897730i | ||||
\(677\) | − | 6.55217i | − | 0.251821i | −0.992042 | − | 0.125910i | \(-0.959815\pi\) | ||
0.992042 | − | 0.125910i | \(-0.0401851\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −23.6778 | + | 3.49514i | −0.908672 | + | 0.134131i | ||||
\(680\) | −14.0016 | − | 8.08381i | −0.536936 | − | 0.310000i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 8.47849 | − | 2.27180i | 0.324658 | − | 0.0869919i | ||||
\(683\) | −42.6432 | + | 11.4262i | −1.63170 | + | 0.437212i | −0.954408 | − | 0.298504i | \(-0.903512\pi\) |
−0.677290 | + | 0.735716i | \(0.736846\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 8.84040 | + | 5.10401i | 0.337774 | + | 0.195014i | ||||
\(686\) | 37.4056 | + | 26.0065i | 1.42815 | + | 0.992933i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 31.7697i | 1.21121i | ||||||||
\(689\) | −15.8220 | + | 8.46743i | −0.602769 | + | 0.322584i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 8.50701 | − | 31.7486i | 0.323622 | − | 1.20777i | −0.592068 | − | 0.805888i | \(-0.701688\pi\) |
0.915690 | − | 0.401885i | \(-0.131645\pi\) | |||||||
\(692\) | −37.6106 | + | 21.7145i | −1.42974 | + | 0.825462i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 5.51370 | − | 5.51370i | 0.209297 | − | 0.209297i | ||||
\(695\) | −1.46546 | − | 5.46917i | −0.0555881 | − | 0.207457i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 38.7480 | + | 38.7480i | 1.46769 | + | 1.46769i | ||||
\(698\) | 57.4961 | + | 33.1954i | 2.17626 | + | 1.25646i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −28.7790 | + | 38.7466i | −1.08774 | + | 1.46448i | ||||
\(701\) | − | 8.83206i | − | 0.333582i | −0.985992 | − | 0.166791i | \(-0.946659\pi\) | ||
0.985992 | − | 0.166791i | \(-0.0533406\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 7.09444i | 0.267572i | ||||||||
\(704\) | 5.07144 | + | 1.35889i | 0.191137 | + | 0.0512150i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −6.48069 | + | 11.2249i | −0.243904 | + | 0.422454i | ||||
\(707\) | −14.2329 | − | 32.8950i | −0.535282 | − | 1.23715i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 28.7065 | − | 7.69188i | 1.07809 | − | 0.288874i | 0.324279 | − | 0.945961i | \(-0.394878\pi\) |
0.753815 | + | 0.657087i | \(0.228212\pi\) | |||||||
\(710\) | −9.98046 | + | 9.98046i | −0.374560 | + | 0.374560i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −45.8416 | − | 79.4000i | −1.71799 | − | 2.97564i | ||||
\(713\) | 9.32628 | + | 2.49897i | 0.349272 | + | 0.0935872i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0.955809 | − | 1.53882i | 0.0357452 | − | 0.0575486i | ||||
\(716\) | −40.3771 | −1.50896 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 31.0431 | + | 53.7683i | 1.15852 | + | 2.00662i | ||||
\(719\) | 18.6597 | − | 32.3196i | 0.695890 | − | 1.20532i | −0.273990 | − | 0.961733i | \(-0.588343\pi\) |
0.969880 | − | 0.243584i | \(-0.0783233\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −43.2511 | − | 5.00668i | −1.61076 | − | 0.186458i | ||||
\(722\) | 18.2462 | − | 4.88907i | 0.679055 | − | 0.181952i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −13.9108 | − | 8.03142i | −0.516992 | − | 0.298485i | ||||
\(725\) | −1.45015 | + | 0.837245i | −0.0538573 | + | 0.0310945i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −9.88660 | −0.366674 | −0.183337 | − | 0.983050i | \(-0.558690\pi\) | ||||
−0.183337 | + | 0.983050i | \(0.558690\pi\) | |||||||
\(728\) | −44.1554 | − | 19.1524i | −1.63651 | − | 0.709835i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −1.44225 | − | 0.386449i | −0.0533800 | − | 0.0143031i | ||||
\(731\) | 29.0264 | − | 16.7584i | 1.07358 | − | 0.619832i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 14.5543 | + | 14.5543i | 0.537577 | + | 0.537577i | 0.922817 | − | 0.385240i | \(-0.125881\pi\) |
−0.385240 | + | 0.922817i | \(0.625881\pi\) | |||||||
\(734\) | −78.5250 | + | 21.0407i | −2.89841 | + | 0.776626i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −0.694076 | − | 0.694076i | −0.0255840 | − | 0.0255840i | ||||
\(737\) | 4.64403 | − | 8.04370i | 0.171065 | − | 0.296293i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 13.1964 | − | 49.2497i | 0.485438 | − | 1.81168i | −0.0926405 | − | 0.995700i | \(-0.529531\pi\) |
0.578079 | − | 0.815981i | \(-0.303803\pi\) | |||||||
\(740\) | −6.02100 | −0.221336 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 30.1171 | + | 11.9261i | 1.10563 | + | 0.437820i | ||||
\(743\) | 13.4007 | + | 3.59070i | 0.491623 | + | 0.131730i | 0.496109 | − | 0.868260i | \(-0.334761\pi\) |
−0.00448658 | + | 0.999990i | \(0.501428\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −2.90493 | + | 5.03148i | −0.106428 | + | 0.184339i | ||||
\(746\) | −48.3496 | + | 48.3496i | −1.77020 | + | 1.77020i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 3.39737 | + | 12.6792i | 0.124220 | + | 0.463597i | ||||
\(749\) | 17.5630 | + | 40.5916i | 0.641737 | + | 1.48319i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −7.39608 | + | 4.27013i | −0.269887 | + | 0.155819i | −0.628836 | − | 0.777538i | \(-0.716468\pi\) |
0.358949 | + | 0.933357i | \(0.383135\pi\) | |||||||
\(752\) | 20.9491 | + | 5.61329i | 0.763935 | + | 0.204696i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −2.25574 | − | 2.40597i | −0.0821494 | − | 0.0876201i | ||||
\(755\) | − | 4.13996i | − | 0.150669i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −5.08375 | − | 8.80531i | −0.184772 | − | 0.320034i | 0.758728 | − | 0.651408i | \(-0.225821\pi\) |
−0.943500 | + | 0.331374i | \(0.892488\pi\) | |||||||
\(758\) | −32.4080 | − | 18.7108i | −1.17711 | − | 0.679606i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −3.09708 | − | 11.5585i | −0.112343 | − | 0.419269i | ||||
\(761\) | −0.975866 | − | 3.64198i | −0.0353751 | − | 0.132022i | 0.945980 | − | 0.324225i | \(-0.105103\pi\) |
−0.981355 | + | 0.192203i | \(0.938437\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −5.21295 | + | 4.13128i | −0.188721 | + | 0.149562i | ||||
\(764\) | 64.4046 | − | 37.1840i | 2.33008 | − | 1.34527i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 21.1536 | 0.764309 | ||||||||
\(767\) | −9.85363 | − | 10.5098i | −0.355794 | − | 0.379488i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −1.12134 | + | 4.18491i | −0.0404367 | + | 0.150912i | −0.983192 | − | 0.182572i | \(-0.941558\pi\) |
0.942756 | + | 0.333484i | \(0.108224\pi\) | |||||||
\(770\) | −3.23483 | + | 0.477501i | −0.116575 | + | 0.0172079i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 47.0142 | − | 47.0142i | 1.69208 | − | 1.69208i | ||||
\(773\) | −14.9644 | + | 4.00970i | −0.538233 | + | 0.144219i | −0.517687 | − | 0.855570i | \(-0.673207\pi\) |
−0.0205453 | + | 0.999789i | \(0.506540\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 15.9408 | − | 15.9408i | 0.572611 | − | 0.572611i | ||||
\(776\) | −39.5277 | − | 22.8213i | −1.41896 | − | 0.819237i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −7.22366 | + | 26.9591i | −0.258981 | + | 0.966529i | ||||
\(779\) | 40.5578i | 1.45313i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 5.80200 | 0.207612 | ||||||||
\(782\) | −5.58208 | + | 20.8326i | −0.199615 | + | 0.744973i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 8.71504 | + | 28.8768i | 0.311252 | + | 1.03132i | ||||
\(785\) | −7.28519 | + | 7.28519i | −0.260020 | + | 0.260020i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 11.1122 | + | 41.4712i | 0.396106 | + | 1.47829i | 0.819888 | + | 0.572524i | \(0.194036\pi\) |
−0.423782 | + | 0.905764i | \(0.639298\pi\) | |||||||
\(788\) | −16.8906 | − | 16.8906i | −0.601703 | − | 0.601703i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −8.50966 | − | 14.7392i | −0.302760 | − | 0.524396i | ||||
\(791\) | −9.34721 | + | 12.5846i | −0.332349 | + | 0.447458i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −41.9115 | − | 1.35058i | −1.48832 | − | 0.0479604i | ||||
\(794\) | 39.6297i | 1.40640i | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −67.4641 | + | 38.9504i | −2.39120 | + | 1.38056i | ||||
\(797\) | −23.6527 | + | 40.9678i | −0.837823 | + | 1.45115i | 0.0538875 | + | 0.998547i | \(0.482839\pi\) |
−0.891711 | + | 0.452606i | \(0.850495\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −5.92198 | − | 22.1011i | −0.209505 | − | 0.781882i | ||||
\(800\) | −2.21374 | + | 0.593170i | −0.0782676 | + | 0.0209717i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −44.4704 | + | 77.0250i | −1.57030 | + | 2.71985i | ||||
\(803\) | 0.306887 | + | 0.531543i | 0.0108298 | + | 0.0187578i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −3.34420 | − | 1.32427i | −0.117867 | − | 0.0466744i | ||||
\(806\) | 37.7179 | + | 23.4278i | 1.32856 | + | 0.825208i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 17.6904 | − | 66.0215i | 0.622347 | − | 2.32263i | ||||
\(809\) | −9.15672 | − | 15.8599i | −0.321933 | − | 0.557604i | 0.658954 | − | 0.752183i | \(-0.270999\pi\) |
−0.980887 | + | 0.194579i | \(0.937666\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −7.95198 | − | 7.95198i | −0.279232 | − | 0.279232i | 0.553571 | − | 0.832802i | \(-0.313265\pi\) |
−0.832802 | + | 0.553571i | \(0.813265\pi\) | |||||||
\(812\) | −0.458299 | + | 3.95910i | −0.0160831 | + | 0.138937i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 2.61413 | + | 2.61413i | 0.0916253 | + | 0.0916253i | ||||
\(815\) | 4.64632 | + | 2.68255i | 0.162753 | + | 0.0939658i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 23.9616 | + | 6.42049i | 0.838311 | + | 0.224625i | ||||
\(818\) | −35.6169 | −1.24532 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −34.4210 | −1.20204 | ||||||||
\(821\) | 35.4162 | + | 9.48973i | 1.23603 | + | 0.331194i | 0.816926 | − | 0.576743i | \(-0.195677\pi\) |
0.419107 | + | 0.907937i | \(0.362343\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −14.5778 | − | 8.41649i | −0.508150 | − | 0.293380i | 0.223923 | − | 0.974607i | \(-0.428114\pi\) |
−0.732073 | + | 0.681226i | \(0.761447\pi\) | |||||||
\(824\) | −58.7112 | − | 58.7112i | −2.04530 | − | 2.04530i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −2.99032 | + | 25.8324i | −0.104046 | + | 0.898824i | ||||
\(827\) | 20.4920 | + | 20.4920i | 0.712578 | + | 0.712578i | 0.967074 | − | 0.254496i | \(-0.0819096\pi\) |
−0.254496 | + | 0.967074i | \(0.581910\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −2.04801 | − | 3.54725i | −0.0711302 | − | 0.123201i | 0.828267 | − | 0.560334i | \(-0.189327\pi\) |
−0.899397 | + | 0.437133i | \(0.855994\pi\) | |||||||
\(830\) | 1.43087 | − | 5.34008i | 0.0496662 | − | 0.185357i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 12.5318 | + | 23.4165i | 0.434462 | + | 0.811822i | ||||
\(833\) | 21.7862 | − | 23.1949i | 0.754846 | − | 0.803656i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −2.77335 | − | 4.80358i | −0.0959757 | − | 0.166235i | ||||
\(836\) | −4.85766 | + | 8.41371i | −0.168006 | + | 0.290994i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 52.3733 | − | 14.0334i | 1.80920 | − | 0.484775i | ||||
\(839\) | −8.69536 | − | 32.4515i | −0.300197 | − | 1.12035i | −0.937001 | − | 0.349326i | \(-0.886411\pi\) |
0.636804 | − | 0.771026i | \(-0.280256\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 14.4309 | − | 24.9950i | 0.497616 | − | 0.861896i | ||||
\(842\) | 23.1861 | − | 13.3865i | 0.799047 | − | 0.461330i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | − | 37.4255i | − | 1.28824i | ||||||
\(845\) | 8.98562 | − | 1.79691i | 0.309115 | − | 0.0618156i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −22.2846 | − | 16.5519i | −0.765709 | − | 0.568729i | ||||
\(848\) | 10.7233 | + | 18.5733i | 0.368240 | + | 0.637810i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 35.6079 | + | 35.6079i | 1.22134 | + | 1.22134i | ||||
\(851\) | 1.05252 | + | 3.92805i | 0.0360798 | + | 0.134652i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 6.65000 | − | 6.65000i | 0.227692 | − | 0.227692i | −0.584036 | − | 0.811728i | \(-0.698527\pi\) |
0.811728 | + | 0.584036i | \(0.198527\pi\) | |||||||
\(854\) | 47.0129 | + | 59.3221i | 1.60875 | + | 2.02996i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −21.8295 | + | 81.4688i | −0.746117 | + | 2.78455i | ||||
\(857\) | 38.2819 | 1.30768 | 0.653842 | − | 0.756631i | \(-0.273156\pi\) | ||||
0.653842 | + | 0.756631i | \(0.273156\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 16.5870i | 0.565942i | 0.959128 | + | 0.282971i | \(0.0913201\pi\) | ||||
−0.959128 | + | 0.282971i | \(0.908680\pi\) | |||||||
\(860\) | −5.44902 | + | 20.3360i | −0.185810 | + | 0.693453i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −57.9892 | − | 33.4801i | −1.97512 | − | 1.14034i | ||||
\(863\) | 11.6109 | − | 11.6109i | 0.395240 | − | 0.395240i | −0.481310 | − | 0.876550i | \(-0.659839\pi\) |
0.876550 | + | 0.481310i | \(0.159839\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −7.29917 | + | 1.95581i | −0.248179 | + | 0.0664994i | ||||
\(866\) | 22.7937 | − | 22.7937i | 0.774560 | − | 0.774560i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −7.83559 | − | 53.0822i | −0.265957 | − | 1.80173i | ||||
\(869\) | −1.81072 | + | 6.75769i | −0.0614244 | + | 0.229239i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 45.7511 | − | 10.6923i | 1.55022 | − | 0.362296i | ||||
\(872\) | −12.6843 | −0.429545 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −13.8242 | + | 7.98141i | −0.467611 | + | 0.269975i | ||||
\(875\) | −13.8899 | + | 11.0078i | −0.469565 | + | 0.372132i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −5.37931 | − | 20.0759i | −0.181646 | − | 0.677914i | −0.995324 | − | 0.0965967i | \(-0.969204\pi\) |
0.813677 | − | 0.581317i | \(-0.197462\pi\) | |||||||
\(878\) | −25.3817 | − | 94.7260i | −0.856592 | − | 3.19685i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −1.87490 | − | 1.08247i | −0.0632029 | − | 0.0364902i | ||||
\(881\) | 6.22366 | + | 10.7797i | 0.209680 | + | 0.363177i | 0.951614 | − | 0.307297i | \(-0.0994243\pi\) |
−0.741934 | + | 0.670473i | \(0.766091\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 28.9456i | − | 0.974097i | −0.873375 | − | 0.487049i | \(-0.838073\pi\) | ||
0.873375 | − | 0.487049i | \(-0.161927\pi\) | |||||||
\(884\) | −35.0351 | + | 56.4054i | −1.17836 | + | 1.89712i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 54.6655 | + | 14.6476i | 1.83652 | + | 0.492095i | ||||
\(887\) | 6.26961 | − | 3.61976i | 0.210513 | − | 0.121540i | −0.391037 | − | 0.920375i | \(-0.627883\pi\) |
0.601550 | + | 0.798835i | \(0.294550\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 48.8343 | − | 21.1294i | 1.63785 | − | 0.708656i | ||||
\(890\) | −8.15502 | − | 30.4349i | −0.273357 | − | 1.02018i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 5.33855 | − | 5.33855i | 0.178748 | − | 0.178748i | ||||
\(893\) | 8.46740 | − | 14.6660i | 0.283351 | − | 0.490778i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −6.78623 | − | 1.81836i | −0.226839 | − | 0.0607812i | ||||
\(896\) | 18.6421 | − | 47.0771i | 0.622788 | − | 1.57274i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 39.7996 | 1.32813 | ||||||||
\(899\) | 0.481809 | − | 1.79814i | 0.0160692 | − | 0.0599712i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 11.3130 | − | 19.5947i | 0.376891 | − | 0.652794i | ||||
\(902\) | 14.9446 | + | 14.9446i | 0.497600 | + | 0.497600i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −28.8757 | + | 7.73722i | −0.960391 | + | 0.257336i | ||||
\(905\) | −1.97632 | − | 1.97632i | −0.0656950 | − | 0.0656950i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 0.515467 | − | 0.297605i | 0.0171158 | − | 0.00988182i | −0.491418 | − | 0.870924i | \(-0.663521\pi\) |
0.508533 | + | 0.861042i | \(0.330188\pi\) | |||||||
\(908\) | −21.8006 | − | 5.84144i | −0.723477 | − | 0.193855i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −12.9542 | − | 10.2853i | −0.429426 | − | 0.340955i | ||||
\(911\) | 23.8117 | 0.788915 | 0.394458 | − | 0.918914i | \(-0.370932\pi\) | ||||
0.394458 | + | 0.918914i | \(0.370932\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1.96810 | + | 1.13628i | −0.0651345 | + | 0.0376054i | ||||
\(914\) | −1.45331 | − | 0.839066i | −0.0480711 | − | 0.0277538i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0.847479 | − | 0.227081i | 0.0280015 | − | 0.00750297i | ||||
\(917\) | −3.67507 | + | 31.7477i | −0.121361 | + | 1.04840i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −2.86358 | + | 4.95987i | −0.0944609 | + | 0.163611i | −0.909383 | − | 0.415959i | \(-0.863446\pi\) |
0.814923 | + | 0.579570i | \(0.196779\pi\) | |||||||
\(920\) | −3.42958 | − | 5.94020i | −0.113070 | − | 0.195843i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 20.5835 | 0.677881 | ||||||||
\(923\) | 20.0741 | + | 21.4109i | 0.660747 | + | 0.704749i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 9.17144 | + | 2.45748i | 0.301555 | + | 0.0808015i | ||||
\(926\) | −38.9417 | − | 67.4490i | −1.27970 | − | 2.21651i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −0.133820 | + | 0.133820i | −0.00439286 | + | 0.00439286i | ||||
\(929\) | 23.7758 | − | 6.37070i | 0.780058 | − | 0.209016i | 0.153247 | − | 0.988188i | \(-0.451027\pi\) |
0.626810 | + | 0.779172i | \(0.284360\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 23.5410 | − | 0.737273i | 0.771524 | − | 0.0241631i | ||||
\(932\) | −40.0696 | + | 69.4026i | −1.31252 | + | 2.27336i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −32.2746 | − | 8.64795i | −1.05606 | − | 0.282970i | ||||
\(935\) | 2.28400i | 0.0746949i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 26.2867i | − | 0.858749i | −0.903127 | − | 0.429374i | \(-0.858734\pi\) | ||
0.903127 | − | 0.429374i | \(-0.141266\pi\) | |||||||
\(938\) | −68.0835 | − | 50.5690i | −2.22301 | − | 1.65114i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 12.4469 | + | 7.18622i | 0.405973 | + | 0.234389i | ||||
\(941\) | 2.11330 | + | 2.11330i | 0.0688916 | + | 0.0688916i | 0.740713 | − | 0.671821i | \(-0.234488\pi\) |
−0.671821 | + | 0.740713i | \(0.734488\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 6.01707 | + | 22.4560i | 0.195943 | + | 0.731268i | ||||
\(944\) | −12.1746 | + | 12.1746i | −0.396250 | + | 0.396250i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 11.1951 | − | 6.46348i | 0.363983 | − | 0.210146i | ||||
\(947\) | 0.631600 | − | 2.35716i | 0.0205243 | − | 0.0765976i | −0.954904 | − | 0.296914i | \(-0.904042\pi\) |
0.975428 | + | 0.220317i | \(0.0707091\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −0.899753 | + | 2.97156i | −0.0292072 | + | 0.0964609i | ||||
\(950\) | 37.2709i | 1.20923i | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 60.0337 | − | 8.86171i | 1.94570 | − | 0.287210i | ||||
\(953\) | 11.0082 | + | 6.35559i | 0.356591 | + | 0.205878i | 0.667584 | − | 0.744534i | \(-0.267328\pi\) |
−0.310994 | + | 0.950412i | \(0.600662\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 12.4991 | − | 3.34913i | 0.404462 | − | 0.108375i | ||||
\(956\) | 3.52456 | − | 0.944404i | 0.113993 | − | 0.0305442i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −8.89312 | − | 5.13445i | −0.287324 | − | 0.165886i | ||||
\(959\) | −37.9044 | + | 5.59516i | −1.22400 | + | 0.180677i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | − | 5.93766i | − | 0.191537i | ||||||
\(962\) | −0.602320 | + | 18.6914i | −0.0194196 | + | 0.602634i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 20.9237 | − | 78.0885i | 0.673908 | − | 2.51506i | ||||
\(965\) | 10.0190 | − | 5.78446i | 0.322523 | − | 0.186209i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −12.3880 | + | 12.3880i | −0.398371 | + | 0.398371i | −0.877658 | − | 0.479287i | \(-0.840895\pi\) |
0.479287 | + | 0.877658i | \(0.340895\pi\) | |||||||
\(968\) | −13.7009 | − | 51.1326i | −0.440365 | − | 1.64346i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −11.0916 | − | 11.0916i | −0.356130 | − | 0.356130i | ||||
\(971\) | −6.20175 | − | 3.58058i | −0.199024 | − | 0.114906i | 0.397176 | − | 0.917742i | \(-0.369990\pi\) |
−0.596200 | + | 0.802836i | \(0.703323\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 17.0611 | + | 12.6721i | 0.546953 | + | 0.406249i | ||||
\(974\) | − | 40.6935i | − | 1.30390i | ||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 50.1149i | 1.60414i | ||||||||
\(977\) | 3.17102 | + | 0.849671i | 0.101450 | + | 0.0271834i | 0.309187 | − | 0.951001i | \(-0.399943\pi\) |
−0.207737 | + | 0.978185i | \(0.566610\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −6.47605 | + | 11.2169i | −0.206976 | + | 0.358492i | ||||
\(980\) | 0.625717 | + | 19.9790i | 0.0199878 | + | 0.638207i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 76.0421 | − | 20.3754i | 2.42660 | − | 0.650206i | ||||
\(983\) | 10.1688 | − | 10.1688i | 0.324335 | − | 0.324335i | −0.526092 | − | 0.850428i | \(-0.676343\pi\) |
0.850428 | + | 0.526092i | \(0.176343\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −2.07817 | − | 3.59949i | −0.0662159 | − | 0.114689i | ||||
\(986\) | 4.01659 | + | 1.07624i | 0.127914 | + | 0.0342745i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −47.8557 | + | 11.1842i | −1.52249 | + | 0.355816i | ||||
\(989\) | 14.2196 | 0.452156 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −4.87954 | − | 8.45161i | −0.155004 | − | 0.268474i | 0.778057 | − | 0.628194i | \(-0.216206\pi\) |
−0.933060 | + | 0.359720i | \(0.882872\pi\) | |||||||
\(992\) | 1.27394 | − | 2.20653i | 0.0404476 | − | 0.0700574i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 6.09196 | − | 52.6265i | 0.193225 | − | 1.66921i | ||||
\(995\) | −13.0929 | + | 3.50823i | −0.415072 | + | 0.111218i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 27.8354 | + | 16.0708i | 0.881555 | + | 0.508966i | 0.871171 | − | 0.490980i | \(-0.163361\pi\) |
0.0103840 | + | 0.999946i | \(0.496695\pi\) | |||||||
\(998\) | 43.4576 | − | 25.0903i | 1.37563 | − | 0.794218i | ||||
\(999\) | 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 | 819.2.fm.e.496.1 | 32 | ||
3.2 | odd | 2 | 273.2.by.d.223.8 | yes | 32 | ||
7.6 | odd | 2 | 819.2.fm.f.496.1 | 32 | |||
13.7 | odd | 12 | 819.2.fm.f.748.1 | 32 | |||
21.20 | even | 2 | 273.2.by.c.223.8 | yes | 32 | ||
39.20 | even | 12 | 273.2.by.c.202.8 | ✓ | 32 | ||
91.20 | even | 12 | inner | 819.2.fm.e.748.1 | 32 | ||
273.20 | odd | 12 | 273.2.by.d.202.8 | yes | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
273.2.by.c.202.8 | ✓ | 32 | 39.20 | even | 12 | ||
273.2.by.c.223.8 | yes | 32 | 21.20 | even | 2 | ||
273.2.by.d.202.8 | yes | 32 | 273.20 | odd | 12 | ||
273.2.by.d.223.8 | yes | 32 | 3.2 | odd | 2 | ||
819.2.fm.e.496.1 | 32 | 1.1 | even | 1 | trivial | ||
819.2.fm.e.748.1 | 32 | 91.20 | even | 12 | inner | ||
819.2.fm.f.496.1 | 32 | 7.6 | odd | 2 | |||
819.2.fm.f.748.1 | 32 | 13.7 | odd | 12 |