Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [429,2,Mod(109,429)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(429, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 2, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("429.109");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 429 = 3 \cdot 11 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 429.m (of order \(4\), 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: | \(3.42558224671\) |
Analytic rank: | \(0\) |
Dimension: | \(28\) |
Relative dimension: | \(14\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 109.13 | ||
Character | \(\chi\) | \(=\) | 429.109 |
Dual form | 429.2.m.a.307.13 |
$q$-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 \(\left(\mathbb{Z}/429\mathbb{Z}\right)^\times\).
\(n\) | \(67\) | \(79\) | \(287\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.67111 | + | 1.67111i | 1.18165 | + | 1.18165i | 0.979316 | + | 0.202337i | \(0.0648536\pi\) |
0.202337 | + | 0.979316i | \(0.435146\pi\) | |||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 3.58521i | 1.79261i | ||||||||
\(5\) | 2.12568 | − | 2.12568i | 0.950632 | − | 0.950632i | −0.0482055 | − | 0.998837i | \(-0.515350\pi\) |
0.998837 | + | 0.0482055i | \(0.0153502\pi\) | |||||||
\(6\) | −1.67111 | − | 1.67111i | −0.682228 | − | 0.682228i | ||||
\(7\) | 1.37191 | − | 1.37191i | 0.518532 | − | 0.518532i | −0.398595 | − | 0.917127i | \(-0.630502\pi\) |
0.917127 | + | 0.398595i | \(0.130502\pi\) | |||||||
\(8\) | −2.64907 | + | 2.64907i | −0.936586 | + | 0.936586i | ||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 7.10448 | 2.24663 | ||||||||
\(11\) | 2.46398 | + | 2.22009i | 0.742918 | + | 0.669382i | ||||
\(12\) | − | 3.58521i | − | 1.03496i | ||||||
\(13\) | 0.554044 | + | 3.56273i | 0.153664 | + | 0.988123i | ||||
\(14\) | 4.58521 | 1.22545 | ||||||||
\(15\) | −2.12568 | + | 2.12568i | −0.548848 | + | 0.548848i | ||||
\(16\) | −1.68333 | −0.420832 | ||||||||
\(17\) | −6.69098 | −1.62280 | −0.811400 | − | 0.584491i | \(-0.801294\pi\) | ||||
−0.811400 | + | 0.584491i | \(0.801294\pi\) | |||||||
\(18\) | 1.67111 | + | 1.67111i | 0.393884 | + | 0.393884i | ||||
\(19\) | −2.46045 | − | 2.46045i | −0.564465 | − | 0.564465i | 0.366108 | − | 0.930573i | \(-0.380690\pi\) |
−0.930573 | + | 0.366108i | \(0.880690\pi\) | |||||||
\(20\) | 7.62101 | + | 7.62101i | 1.70411 | + | 1.70411i | ||||
\(21\) | −1.37191 | + | 1.37191i | −0.299375 | + | 0.299375i | ||||
\(22\) | 0.407572 | + | 7.82759i | 0.0868947 | + | 1.66885i | ||||
\(23\) | − | 3.28445i | − | 0.684856i | −0.939544 | − | 0.342428i | \(-0.888751\pi\) | ||
0.939544 | − | 0.342428i | \(-0.111249\pi\) | |||||||
\(24\) | 2.64907 | − | 2.64907i | 0.540738 | − | 0.540738i | ||||
\(25\) | − | 4.03701i | − | 0.807402i | ||||||
\(26\) | −5.02784 | + | 6.87958i | −0.986041 | + | 1.34920i | ||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 4.91858 | + | 4.91858i | 0.929524 | + | 0.929524i | ||||
\(29\) | 3.36320i | 0.624530i | 0.949995 | + | 0.312265i | \(0.101088\pi\) | ||||
−0.949995 | + | 0.312265i | \(0.898912\pi\) | |||||||
\(30\) | −7.10448 | −1.29709 | ||||||||
\(31\) | 0.273940 | − | 0.273940i | 0.0492011 | − | 0.0492011i | −0.682078 | − | 0.731279i | \(-0.738924\pi\) |
0.731279 | + | 0.682078i | \(0.238924\pi\) | |||||||
\(32\) | 2.48510 | + | 2.48510i | 0.439308 | + | 0.439308i | ||||
\(33\) | −2.46398 | − | 2.22009i | −0.428924 | − | 0.386468i | ||||
\(34\) | −11.1814 | − | 11.1814i | −1.91759 | − | 1.91759i | ||||
\(35\) | − | 5.83246i | − | 0.985866i | ||||||
\(36\) | 3.58521i | 0.597536i | ||||||||
\(37\) | −5.74595 | − | 5.74595i | −0.944628 | − | 0.944628i | 0.0539177 | − | 0.998545i | \(-0.482829\pi\) |
−0.998545 | + | 0.0539177i | \(0.982829\pi\) | |||||||
\(38\) | − | 8.22335i | − | 1.33400i | ||||||
\(39\) | −0.554044 | − | 3.56273i | −0.0887181 | − | 0.570493i | ||||
\(40\) | 11.2621i | 1.78070i | ||||||||
\(41\) | 0.977956 | + | 0.977956i | 0.152731 | + | 0.152731i | 0.779337 | − | 0.626606i | \(-0.215556\pi\) |
−0.626606 | + | 0.779337i | \(0.715556\pi\) | |||||||
\(42\) | −4.58521 | −0.707514 | ||||||||
\(43\) | −2.55799 | −0.390090 | −0.195045 | − | 0.980794i | \(-0.562485\pi\) | ||||
−0.195045 | + | 0.980794i | \(0.562485\pi\) | |||||||
\(44\) | −7.95949 | + | 8.83390i | −1.19994 | + | 1.33176i | ||||
\(45\) | 2.12568 | − | 2.12568i | 0.316877 | − | 0.316877i | ||||
\(46\) | 5.48868 | − | 5.48868i | 0.809262 | − | 0.809262i | ||||
\(47\) | −5.10855 | − | 5.10855i | −0.745159 | − | 0.745159i | 0.228407 | − | 0.973566i | \(-0.426648\pi\) |
−0.973566 | + | 0.228407i | \(0.926648\pi\) | |||||||
\(48\) | 1.68333 | 0.242968 | ||||||||
\(49\) | 3.23574i | 0.462249i | ||||||||
\(50\) | 6.74629 | − | 6.74629i | 0.954069 | − | 0.954069i | ||||
\(51\) | 6.69098 | 0.936925 | ||||||||
\(52\) | −12.7731 | + | 1.98637i | −1.77132 | + | 0.275460i | ||||
\(53\) | 9.35644 | 1.28521 | 0.642603 | − | 0.766199i | \(-0.277854\pi\) | ||||
0.642603 | + | 0.766199i | \(0.277854\pi\) | |||||||
\(54\) | −1.67111 | − | 1.67111i | −0.227409 | − | 0.227409i | ||||
\(55\) | 9.95682 | − | 0.518439i | 1.34258 | − | 0.0699062i | ||||
\(56\) | 7.26854i | 0.971300i | ||||||||
\(57\) | 2.46045 | + | 2.46045i | 0.325894 | + | 0.325894i | ||||
\(58\) | −5.62027 | + | 5.62027i | −0.737977 | + | 0.737977i | ||||
\(59\) | −2.90188 | − | 2.90188i | −0.377793 | − | 0.377793i | 0.492512 | − | 0.870305i | \(-0.336079\pi\) |
−0.870305 | + | 0.492512i | \(0.836079\pi\) | |||||||
\(60\) | −7.62101 | − | 7.62101i | −0.983868 | − | 0.983868i | ||||
\(61\) | 6.86934i | 0.879529i | 0.898113 | + | 0.439765i | \(0.144938\pi\) | ||||
−0.898113 | + | 0.439765i | \(0.855062\pi\) | |||||||
\(62\) | 0.915567 | 0.116277 | ||||||||
\(63\) | 1.37191 | − | 1.37191i | 0.172844 | − | 0.172844i | ||||
\(64\) | 11.6724i | 1.45905i | ||||||||
\(65\) | 8.75093 | + | 6.39549i | 1.08542 | + | 0.793263i | ||||
\(66\) | −0.407572 | − | 7.82759i | −0.0501687 | − | 0.963510i | ||||
\(67\) | −5.85989 | + | 5.85989i | −0.715900 | + | 0.715900i | −0.967763 | − | 0.251863i | \(-0.918957\pi\) |
0.251863 | + | 0.967763i | \(0.418957\pi\) | |||||||
\(68\) | − | 23.9886i | − | 2.90904i | ||||||
\(69\) | 3.28445i | 0.395402i | ||||||||
\(70\) | 9.74669 | − | 9.74669i | 1.16495 | − | 1.16495i | ||||
\(71\) | 11.6156 | − | 11.6156i | 1.37852 | − | 1.37852i | 0.531396 | − | 0.847124i | \(-0.321668\pi\) |
0.847124 | − | 0.531396i | \(-0.178332\pi\) | |||||||
\(72\) | −2.64907 | + | 2.64907i | −0.312195 | + | 0.312195i | ||||
\(73\) | −2.50097 | + | 2.50097i | −0.292717 | + | 0.292717i | −0.838153 | − | 0.545436i | \(-0.816364\pi\) |
0.545436 | + | 0.838153i | \(0.316364\pi\) | |||||||
\(74\) | − | 19.2042i | − | 2.23244i | ||||||
\(75\) | 4.03701i | 0.466154i | ||||||||
\(76\) | 8.82122 | − | 8.82122i | 1.01186 | − | 1.01186i | ||||
\(77\) | 6.42611 | − | 0.334599i | 0.732323 | − | 0.0381311i | ||||
\(78\) | 5.02784 | − | 6.87958i | 0.569291 | − | 0.778959i | ||||
\(79\) | 0.392524i | 0.0441624i | 0.999756 | + | 0.0220812i | \(0.00702924\pi\) | ||||
−0.999756 | + | 0.0220812i | \(0.992971\pi\) | |||||||
\(80\) | −3.57822 | + | 3.57822i | −0.400057 | + | 0.400057i | ||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 3.26854i | 0.360950i | ||||||||
\(83\) | −11.1055 | − | 11.1055i | −1.21899 | − | 1.21899i | −0.967986 | − | 0.251003i | \(-0.919240\pi\) |
−0.251003 | − | 0.967986i | \(-0.580760\pi\) | |||||||
\(84\) | −4.91858 | − | 4.91858i | −0.536661 | − | 0.536661i | ||||
\(85\) | −14.2229 | + | 14.2229i | −1.54269 | + | 1.54269i | ||||
\(86\) | −4.27468 | − | 4.27468i | −0.460951 | − | 0.460951i | ||||
\(87\) | − | 3.36320i | − | 0.360572i | ||||||
\(88\) | −12.4084 | + | 0.646089i | −1.32274 | + | 0.0688734i | ||||
\(89\) | −5.52141 | − | 5.52141i | −0.585268 | − | 0.585268i | 0.351078 | − | 0.936346i | \(-0.385815\pi\) |
−0.936346 | + | 0.351078i | \(0.885815\pi\) | |||||||
\(90\) | 7.10448 | 0.748878 | ||||||||
\(91\) | 5.64783 | + | 4.12763i | 0.592053 | + | 0.432694i | ||||
\(92\) | 11.7755 | 1.22768 | ||||||||
\(93\) | −0.273940 | + | 0.273940i | −0.0284063 | + | 0.0284063i | ||||
\(94\) | − | 17.0739i | − | 1.76104i | ||||||
\(95\) | −10.4602 | −1.07320 | ||||||||
\(96\) | −2.48510 | − | 2.48510i | −0.253635 | − | 0.253635i | ||||
\(97\) | −8.21511 | + | 8.21511i | −0.834119 | + | 0.834119i | −0.988077 | − | 0.153959i | \(-0.950798\pi\) |
0.153959 | + | 0.988077i | \(0.450798\pi\) | |||||||
\(98\) | −5.40728 | + | 5.40728i | −0.546218 | + | 0.546218i | ||||
\(99\) | 2.46398 | + | 2.22009i | 0.247639 | + | 0.223127i | ||||
\(100\) | 14.4735 | 1.44735 | ||||||||
\(101\) | −6.28207 | −0.625089 | −0.312545 | − | 0.949903i | \(-0.601181\pi\) | ||||
−0.312545 | + | 0.949903i | \(0.601181\pi\) | |||||||
\(102\) | 11.1814 | + | 11.1814i | 1.10712 | + | 1.10712i | ||||
\(103\) | − | 11.5572i | − | 1.13877i | −0.822072 | − | 0.569384i | \(-0.807182\pi\) | ||
0.822072 | − | 0.569384i | \(-0.192818\pi\) | |||||||
\(104\) | −10.9056 | − | 7.97020i | −1.06938 | − | 0.781543i | ||||
\(105\) | 5.83246i | 0.569190i | ||||||||
\(106\) | 15.6356 | + | 15.6356i | 1.51867 | + | 1.51867i | ||||
\(107\) | 9.56070i | 0.924267i | 0.886810 | + | 0.462134i | \(0.152916\pi\) | ||||
−0.886810 | + | 0.462134i | \(0.847084\pi\) | |||||||
\(108\) | − | 3.58521i | − | 0.344987i | ||||||
\(109\) | −12.7836 | − | 12.7836i | −1.22445 | − | 1.22445i | −0.966035 | − | 0.258411i | \(-0.916801\pi\) |
−0.258411 | − | 0.966035i | \(-0.583199\pi\) | |||||||
\(110\) | 17.5053 | + | 15.7726i | 1.66907 | + | 1.50386i | ||||
\(111\) | 5.74595 | + | 5.74595i | 0.545381 | + | 0.545381i | ||||
\(112\) | −2.30937 | + | 2.30937i | −0.218215 | + | 0.218215i | ||||
\(113\) | 14.7052 | 1.38335 | 0.691674 | − | 0.722210i | \(-0.256873\pi\) | ||||
0.691674 | + | 0.722210i | \(0.256873\pi\) | |||||||
\(114\) | 8.22335i | 0.770187i | ||||||||
\(115\) | −6.98169 | − | 6.98169i | −0.651046 | − | 0.651046i | ||||
\(116\) | −12.0578 | −1.11954 | ||||||||
\(117\) | 0.554044 | + | 3.56273i | 0.0512214 | + | 0.329374i | ||||
\(118\) | − | 9.69873i | − | 0.892841i | ||||||
\(119\) | −9.17940 | + | 9.17940i | −0.841474 | + | 0.841474i | ||||
\(120\) | − | 11.2621i | − | 1.02809i | ||||||
\(121\) | 1.14241 | + | 10.9405i | 0.103856 | + | 0.994592i | ||||
\(122\) | −11.4794 | + | 11.4794i | −1.03930 | + | 1.03930i | ||||
\(123\) | −0.977956 | − | 0.977956i | −0.0881793 | − | 0.0881793i | ||||
\(124\) | 0.982133 | + | 0.982133i | 0.0881982 | + | 0.0881982i | ||||
\(125\) | 2.04700 | + | 2.04700i | 0.183089 | + | 0.183089i | ||||
\(126\) | 4.58521 | 0.408483 | ||||||||
\(127\) | −3.77210 | −0.334720 | −0.167360 | − | 0.985896i | \(-0.553524\pi\) | ||||
−0.167360 | + | 0.985896i | \(0.553524\pi\) | |||||||
\(128\) | −14.5357 | + | 14.5357i | −1.28478 | + | 1.28478i | ||||
\(129\) | 2.55799 | 0.225218 | ||||||||
\(130\) | 3.93620 | + | 25.3113i | 0.345227 | + | 2.21995i | ||||
\(131\) | − | 21.8690i | − | 1.91071i | −0.295465 | − | 0.955354i | \(-0.595475\pi\) | ||
0.295465 | − | 0.955354i | \(-0.404525\pi\) | |||||||
\(132\) | 7.95949 | − | 8.83390i | 0.692785 | − | 0.768892i | ||||
\(133\) | −6.75101 | −0.585386 | ||||||||
\(134\) | −19.5851 | −1.69189 | ||||||||
\(135\) | −2.12568 | + | 2.12568i | −0.182949 | + | 0.182949i | ||||
\(136\) | 17.7248 | − | 17.7248i | 1.51989 | − | 1.51989i | ||||
\(137\) | −8.09074 | − | 8.09074i | −0.691238 | − | 0.691238i | 0.271266 | − | 0.962504i | \(-0.412558\pi\) |
−0.962504 | + | 0.271266i | \(0.912558\pi\) | |||||||
\(138\) | −5.48868 | + | 5.48868i | −0.467227 | + | 0.467227i | ||||
\(139\) | 3.08211i | 0.261421i | 0.991421 | + | 0.130711i | \(0.0417259\pi\) | ||||
−0.991421 | + | 0.130711i | \(0.958274\pi\) | |||||||
\(140\) | 20.9106 | 1.76727 | ||||||||
\(141\) | 5.10855 | + | 5.10855i | 0.430218 | + | 0.430218i | ||||
\(142\) | 38.8219 | 3.25786 | ||||||||
\(143\) | −6.54442 | + | 10.0085i | −0.547272 | + | 0.836955i | ||||
\(144\) | −1.68333 | −0.140277 | ||||||||
\(145\) | 7.14907 | + | 7.14907i | 0.593698 | + | 0.593698i | ||||
\(146\) | −8.35880 | −0.691779 | ||||||||
\(147\) | − | 3.23574i | − | 0.266880i | ||||||
\(148\) | 20.6004 | − | 20.6004i | 1.69335 | − | 1.69335i | ||||
\(149\) | 13.7526 | + | 13.7526i | 1.12666 | + | 1.12666i | 0.990717 | + | 0.135942i | \(0.0434060\pi\) |
0.135942 | + | 0.990717i | \(0.456594\pi\) | |||||||
\(150\) | −6.74629 | + | 6.74629i | −0.550832 | + | 0.550832i | ||||
\(151\) | 4.90414 | − | 4.90414i | 0.399094 | − | 0.399094i | −0.478820 | − | 0.877913i | \(-0.658935\pi\) |
0.877913 | + | 0.478820i | \(0.158935\pi\) | |||||||
\(152\) | 13.0358 | 1.05734 | ||||||||
\(153\) | −6.69098 | −0.540934 | ||||||||
\(154\) | 11.2979 | + | 10.1796i | 0.910409 | + | 0.820294i | ||||
\(155\) | − | 1.16462i | − | 0.0935442i | ||||||
\(156\) | 12.7731 | − | 1.98637i | 1.02267 | − | 0.159037i | ||||
\(157\) | 6.61674 | 0.528073 | 0.264037 | − | 0.964513i | \(-0.414946\pi\) | ||||
0.264037 | + | 0.964513i | \(0.414946\pi\) | |||||||
\(158\) | −0.655951 | + | 0.655951i | −0.0521847 | + | 0.0521847i | ||||
\(159\) | −9.35644 | −0.742014 | ||||||||
\(160\) | 10.5651 | 0.835241 | ||||||||
\(161\) | −4.50596 | − | 4.50596i | −0.355120 | − | 0.355120i | ||||
\(162\) | 1.67111 | + | 1.67111i | 0.131295 | + | 0.131295i | ||||
\(163\) | 7.31951 | + | 7.31951i | 0.573308 | + | 0.573308i | 0.933051 | − | 0.359743i | \(-0.117136\pi\) |
−0.359743 | + | 0.933051i | \(0.617136\pi\) | |||||||
\(164\) | −3.50618 | + | 3.50618i | −0.273787 | + | 0.273787i | ||||
\(165\) | −9.95682 | + | 0.518439i | −0.775138 | + | 0.0403604i | ||||
\(166\) | − | 37.1171i | − | 2.88084i | ||||||
\(167\) | 3.21549 | − | 3.21549i | 0.248822 | − | 0.248822i | −0.571665 | − | 0.820487i | \(-0.693702\pi\) |
0.820487 | + | 0.571665i | \(0.193702\pi\) | |||||||
\(168\) | − | 7.26854i | − | 0.560780i | ||||||
\(169\) | −12.3861 | + | 3.94782i | −0.952775 | + | 0.303678i | ||||
\(170\) | −47.5359 | −3.64584 | ||||||||
\(171\) | −2.46045 | − | 2.46045i | −0.188155 | − | 0.188155i | ||||
\(172\) | − | 9.17094i | − | 0.699278i | ||||||
\(173\) | 23.6361 | 1.79702 | 0.898509 | − | 0.438955i | \(-0.144651\pi\) | ||||
0.898509 | + | 0.438955i | \(0.144651\pi\) | |||||||
\(174\) | 5.62027 | − | 5.62027i | 0.426071 | − | 0.426071i | ||||
\(175\) | −5.53840 | − | 5.53840i | −0.418664 | − | 0.418664i | ||||
\(176\) | −4.14769 | − | 3.73714i | −0.312644 | − | 0.281698i | ||||
\(177\) | 2.90188 | + | 2.90188i | 0.218119 | + | 0.218119i | ||||
\(178\) | − | 18.4538i | − | 1.38317i | ||||||
\(179\) | 7.35371i | 0.549642i | 0.961495 | + | 0.274821i | \(0.0886186\pi\) | ||||
−0.961495 | + | 0.274821i | \(0.911381\pi\) | |||||||
\(180\) | 7.62101 | + | 7.62101i | 0.568036 | + | 0.568036i | ||||
\(181\) | 21.8269i | 1.62238i | 0.584780 | + | 0.811192i | \(0.301181\pi\) | ||||
−0.584780 | + | 0.811192i | \(0.698819\pi\) | |||||||
\(182\) | 2.54041 | + | 16.3359i | 0.188308 | + | 1.21090i | ||||
\(183\) | − | 6.86934i | − | 0.507796i | ||||||
\(184\) | 8.70073 | + | 8.70073i | 0.641426 | + | 0.641426i | ||||
\(185\) | −24.4281 | −1.79599 | ||||||||
\(186\) | −0.915567 | −0.0671327 | ||||||||
\(187\) | −16.4865 | − | 14.8546i | −1.20561 | − | 1.08627i | ||||
\(188\) | 18.3153 | − | 18.3153i | 1.33578 | − | 1.33578i | ||||
\(189\) | −1.37191 | + | 1.37191i | −0.0997916 | + | 0.0997916i | ||||
\(190\) | −17.4802 | − | 17.4802i | −1.26815 | − | 1.26815i | ||||
\(191\) | −6.84281 | −0.495129 | −0.247564 | − | 0.968871i | \(-0.579630\pi\) | ||||
−0.247564 | + | 0.968871i | \(0.579630\pi\) | |||||||
\(192\) | − | 11.6724i | − | 0.842384i | ||||||
\(193\) | −0.448878 | + | 0.448878i | −0.0323109 | + | 0.0323109i | −0.723078 | − | 0.690767i | \(-0.757273\pi\) |
0.690767 | + | 0.723078i | \(0.257273\pi\) | |||||||
\(194\) | −27.4567 | −1.97128 | ||||||||
\(195\) | −8.75093 | − | 6.39549i | −0.626667 | − | 0.457991i | ||||
\(196\) | −11.6008 | −0.828630 | ||||||||
\(197\) | 5.93703 | + | 5.93703i | 0.422996 | + | 0.422996i | 0.886234 | − | 0.463238i | \(-0.153313\pi\) |
−0.463238 | + | 0.886234i | \(0.653313\pi\) | |||||||
\(198\) | 0.407572 | + | 7.82759i | 0.0289649 | + | 0.556283i | ||||
\(199\) | 24.1066i | 1.70887i | 0.519557 | + | 0.854436i | \(0.326097\pi\) | ||||
−0.519557 | + | 0.854436i | \(0.673903\pi\) | |||||||
\(200\) | 10.6943 | + | 10.6943i | 0.756202 | + | 0.756202i | ||||
\(201\) | 5.85989 | − | 5.85989i | 0.413325 | − | 0.413325i | ||||
\(202\) | −10.4980 | − | 10.4980i | −0.738639 | − | 0.738639i | ||||
\(203\) | 4.61399 | + | 4.61399i | 0.323839 | + | 0.323839i | ||||
\(204\) | 23.9886i | 1.67954i | ||||||||
\(205\) | 4.15764 | 0.290382 | ||||||||
\(206\) | 19.3134 | − | 19.3134i | 1.34563 | − | 1.34563i | ||||
\(207\) | − | 3.28445i | − | 0.228285i | ||||||
\(208\) | −0.932639 | − | 5.99725i | −0.0646669 | − | 0.415834i | ||||
\(209\) | −0.600086 | − | 11.5249i | −0.0415088 | − | 0.797194i | ||||
\(210\) | −9.74669 | + | 9.74669i | −0.672585 | + | 0.672585i | ||||
\(211\) | 7.75020i | 0.533546i | 0.963759 | + | 0.266773i | \(0.0859573\pi\) | ||||
−0.963759 | + | 0.266773i | \(0.914043\pi\) | |||||||
\(212\) | 33.5448i | 2.30387i | ||||||||
\(213\) | −11.6156 | + | 11.6156i | −0.795889 | + | 0.795889i | ||||
\(214\) | −15.9770 | + | 15.9770i | −1.09216 | + | 1.09216i | ||||
\(215\) | −5.43746 | + | 5.43746i | −0.370832 | + | 0.370832i | ||||
\(216\) | 2.64907 | − | 2.64907i | 0.180246 | − | 0.180246i | ||||
\(217\) | − | 0.751640i | − | 0.0510247i | ||||||
\(218\) | − | 42.7256i | − | 2.89374i | ||||||
\(219\) | 2.50097 | − | 2.50097i | 0.169000 | − | 0.169000i | ||||
\(220\) | 1.85871 | + | 35.6973i | 0.125314 | + | 2.40671i | ||||
\(221\) | −3.70710 | − | 23.8381i | −0.249367 | − | 1.60353i | ||||
\(222\) | 19.2042i | 1.28890i | ||||||||
\(223\) | 6.78100 | − | 6.78100i | 0.454089 | − | 0.454089i | −0.442620 | − | 0.896709i | \(-0.645951\pi\) |
0.896709 | + | 0.442620i | \(0.145951\pi\) | |||||||
\(224\) | 6.81866 | 0.455591 | ||||||||
\(225\) | − | 4.03701i | − | 0.269134i | ||||||
\(226\) | 24.5740 | + | 24.5740i | 1.63464 | + | 1.63464i | ||||
\(227\) | 0.583085 | + | 0.583085i | 0.0387007 | + | 0.0387007i | 0.726192 | − | 0.687492i | \(-0.241288\pi\) |
−0.687492 | + | 0.726192i | \(0.741288\pi\) | |||||||
\(228\) | −8.82122 | + | 8.82122i | −0.584200 | + | 0.584200i | ||||
\(229\) | 4.76299 | + | 4.76299i | 0.314748 | + | 0.314748i | 0.846746 | − | 0.531998i | \(-0.178559\pi\) |
−0.531998 | + | 0.846746i | \(0.678559\pi\) | |||||||
\(230\) | − | 23.3343i | − | 1.53862i | ||||||
\(231\) | −6.42611 | + | 0.334599i | −0.422807 | + | 0.0220150i | ||||
\(232\) | −8.90933 | − | 8.90933i | −0.584926 | − | 0.584926i | ||||
\(233\) | −11.5756 | −0.758343 | −0.379172 | − | 0.925326i | \(-0.623791\pi\) | ||||
−0.379172 | + | 0.925326i | \(0.623791\pi\) | |||||||
\(234\) | −5.02784 | + | 6.87958i | −0.328680 | + | 0.449732i | ||||
\(235\) | −21.7183 | −1.41674 | ||||||||
\(236\) | 10.4039 | − | 10.4039i | 0.677235 | − | 0.677235i | ||||
\(237\) | − | 0.392524i | − | 0.0254972i | ||||||
\(238\) | −30.6796 | −1.98866 | ||||||||
\(239\) | 16.0412 | + | 16.0412i | 1.03762 | + | 1.03762i | 0.999264 | + | 0.0383573i | \(0.0122125\pi\) |
0.0383573 | + | 0.999264i | \(0.487787\pi\) | |||||||
\(240\) | 3.57822 | − | 3.57822i | 0.230973 | − | 0.230973i | ||||
\(241\) | −16.0481 | + | 16.0481i | −1.03375 | + | 1.03375i | −0.0343356 | + | 0.999410i | \(0.510931\pi\) |
−0.999410 | + | 0.0343356i | \(0.989069\pi\) | |||||||
\(242\) | −16.3737 | + | 20.1919i | −1.05254 | + | 1.29798i | ||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | −24.6281 | −1.57665 | ||||||||
\(245\) | 6.87815 | + | 6.87815i | 0.439429 | + | 0.439429i | ||||
\(246\) | − | 3.26854i | − | 0.208395i | ||||||
\(247\) | 7.40270 | − | 10.1291i | 0.471023 | − | 0.644499i | ||||
\(248\) | 1.45137i | 0.0921621i | ||||||||
\(249\) | 11.1055 | + | 11.1055i | 0.703784 | + | 0.703784i | ||||
\(250\) | 6.84153i | 0.432696i | ||||||||
\(251\) | − | 13.8730i | − | 0.875657i | −0.899058 | − | 0.437829i | \(-0.855748\pi\) | ||
0.899058 | − | 0.437829i | \(-0.144252\pi\) | |||||||
\(252\) | 4.91858 | + | 4.91858i | 0.309841 | + | 0.309841i | ||||
\(253\) | 7.29178 | − | 8.09283i | 0.458430 | − | 0.508792i | ||||
\(254\) | −6.30360 | − | 6.30360i | −0.395523 | − | 0.395523i | ||||
\(255\) | 14.2229 | − | 14.2229i | 0.890670 | − | 0.890670i | ||||
\(256\) | −25.2366 | −1.57729 | ||||||||
\(257\) | 14.3028i | 0.892186i | 0.894987 | + | 0.446093i | \(0.147185\pi\) | ||||
−0.894987 | + | 0.446093i | \(0.852815\pi\) | |||||||
\(258\) | 4.27468 | + | 4.27468i | 0.266130 | + | 0.266130i | ||||
\(259\) | −15.7658 | −0.979640 | ||||||||
\(260\) | −22.9292 | + | 31.3740i | −1.42201 | + | 1.94573i | ||||
\(261\) | 3.36320i | 0.208177i | ||||||||
\(262\) | 36.5456 | − | 36.5456i | 2.25779 | − | 2.25779i | ||||
\(263\) | 11.5120i | 0.709859i | 0.934893 | + | 0.354930i | \(0.115495\pi\) | ||||
−0.934893 | + | 0.354930i | \(0.884505\pi\) | |||||||
\(264\) | 12.4084 | − | 0.646089i | 0.763685 | − | 0.0397641i | ||||
\(265\) | 19.8888 | − | 19.8888i | 1.22176 | − | 1.22176i | ||||
\(266\) | −11.2817 | − | 11.2817i | −0.691724 | − | 0.691724i | ||||
\(267\) | 5.52141 | + | 5.52141i | 0.337905 | + | 0.337905i | ||||
\(268\) | −21.0090 | − | 21.0090i | −1.28333 | − | 1.28333i | ||||
\(269\) | 20.2722 | 1.23602 | 0.618010 | − | 0.786170i | \(-0.287939\pi\) | ||||
0.618010 | + | 0.786170i | \(0.287939\pi\) | |||||||
\(270\) | −7.10448 | −0.432365 | ||||||||
\(271\) | −1.35380 | + | 1.35380i | −0.0822374 | + | 0.0822374i | −0.747029 | − | 0.664792i | \(-0.768520\pi\) |
0.664792 | + | 0.747029i | \(0.268520\pi\) | |||||||
\(272\) | 11.2631 | 0.682927 | ||||||||
\(273\) | −5.64783 | − | 4.12763i | −0.341822 | − | 0.249816i | ||||
\(274\) | − | 27.0410i | − | 1.63361i | ||||||
\(275\) | 8.96252 | − | 9.94712i | 0.540461 | − | 0.599834i | ||||
\(276\) | −11.7755 | −0.708800 | ||||||||
\(277\) | −17.7086 | −1.06400 | −0.532002 | − | 0.846743i | \(-0.678560\pi\) | ||||
−0.532002 | + | 0.846743i | \(0.678560\pi\) | |||||||
\(278\) | −5.15054 | + | 5.15054i | −0.308909 | + | 0.308909i | ||||
\(279\) | 0.273940 | − | 0.273940i | 0.0164004 | − | 0.0164004i | ||||
\(280\) | 15.4506 | + | 15.4506i | 0.923349 | + | 0.923349i | ||||
\(281\) | 11.6127 | − | 11.6127i | 0.692757 | − | 0.692757i | −0.270081 | − | 0.962838i | \(-0.587050\pi\) |
0.962838 | + | 0.270081i | \(0.0870503\pi\) | |||||||
\(282\) | 17.0739i | 1.01674i | ||||||||
\(283\) | 18.8088 | 1.11807 | 0.559034 | − | 0.829145i | \(-0.311172\pi\) | ||||
0.559034 | + | 0.829145i | \(0.311172\pi\) | |||||||
\(284\) | 41.6445 | + | 41.6445i | 2.47114 | + | 2.47114i | ||||
\(285\) | 10.4602 | 0.619611 | ||||||||
\(286\) | −27.6618 | + | 5.78890i | −1.63568 | + | 0.342305i | ||||
\(287\) | 2.68333 | 0.158392 | ||||||||
\(288\) | 2.48510 | + | 2.48510i | 0.146436 | + | 0.146436i | ||||
\(289\) | 27.7692 | 1.63348 | ||||||||
\(290\) | 23.8938i | 1.40309i | ||||||||
\(291\) | 8.21511 | − | 8.21511i | 0.481579 | − | 0.481579i | ||||
\(292\) | −8.96652 | − | 8.96652i | −0.524726 | − | 0.524726i | ||||
\(293\) | 22.4031 | − | 22.4031i | 1.30881 | − | 1.30881i | 0.386528 | − | 0.922278i | \(-0.373674\pi\) |
0.922278 | − | 0.386528i | \(-0.126326\pi\) | |||||||
\(294\) | 5.40728 | − | 5.40728i | 0.315359 | − | 0.315359i | ||||
\(295\) | −12.3369 | −0.718284 | ||||||||
\(296\) | 30.4428 | 1.76945 | ||||||||
\(297\) | −2.46398 | − | 2.22009i | −0.142975 | − | 0.128823i | ||||
\(298\) | 45.9643i | 2.66264i | ||||||||
\(299\) | 11.7016 | − | 1.81973i | 0.676722 | − | 0.105238i | ||||
\(300\) | −14.4735 | −0.835631 | ||||||||
\(301\) | −3.50932 | + | 3.50932i | −0.202274 | + | 0.202274i | ||||
\(302\) | 16.3907 | 0.943180 | ||||||||
\(303\) | 6.28207 | 0.360896 | ||||||||
\(304\) | 4.14174 | + | 4.14174i | 0.237545 | + | 0.237545i | ||||
\(305\) | 14.6020 | + | 14.6020i | 0.836108 | + | 0.836108i | ||||
\(306\) | −11.1814 | − | 11.1814i | −0.639196 | − | 0.639196i | ||||
\(307\) | 13.3054 | − | 13.3054i | 0.759377 | − | 0.759377i | −0.216832 | − | 0.976209i | \(-0.569572\pi\) |
0.976209 | + | 0.216832i | \(0.0695723\pi\) | |||||||
\(308\) | 1.19961 | + | 23.0390i | 0.0683540 | + | 1.31277i | ||||
\(309\) | 11.5572i | 0.657468i | ||||||||
\(310\) | 1.94620 | − | 1.94620i | 0.110537 | − | 0.110537i | ||||
\(311\) | 13.0705i | 0.741160i | 0.928801 | + | 0.370580i | \(0.120841\pi\) | ||||
−0.928801 | + | 0.370580i | \(0.879159\pi\) | |||||||
\(312\) | 10.9056 | + | 7.97020i | 0.617408 | + | 0.451224i | ||||
\(313\) | −11.5886 | −0.655026 | −0.327513 | − | 0.944847i | \(-0.606211\pi\) | ||||
−0.327513 | + | 0.944847i | \(0.606211\pi\) | |||||||
\(314\) | 11.0573 | + | 11.0573i | 0.623999 | + | 0.623999i | ||||
\(315\) | − | 5.83246i | − | 0.328622i | ||||||
\(316\) | −1.40728 | −0.0791659 | ||||||||
\(317\) | −17.1628 | + | 17.1628i | −0.963956 | + | 0.963956i | −0.999373 | − | 0.0354165i | \(-0.988724\pi\) |
0.0354165 | + | 0.999373i | \(0.488724\pi\) | |||||||
\(318\) | −15.6356 | − | 15.6356i | −0.876803 | − | 0.876803i | ||||
\(319\) | −7.46659 | + | 8.28685i | −0.418049 | + | 0.463975i | ||||
\(320\) | 24.8118 | + | 24.8118i | 1.38702 | + | 1.38702i | ||||
\(321\) | − | 9.56070i | − | 0.533626i | ||||||
\(322\) | − | 15.0599i | − | 0.839256i | ||||||
\(323\) | 16.4628 | + | 16.4628i | 0.916014 | + | 0.916014i | ||||
\(324\) | 3.58521i | 0.199179i | ||||||||
\(325\) | 14.3828 | − | 2.23668i | 0.797813 | − | 0.124069i | ||||
\(326\) | 24.4634i | 1.35490i | ||||||||
\(327\) | 12.7836 | + | 12.7836i | 0.706934 | + | 0.706934i | ||||
\(328\) | −5.18134 | −0.286092 | ||||||||
\(329\) | −14.0169 | −0.772778 | ||||||||
\(330\) | −17.5053 | − | 15.7726i | −0.963636 | − | 0.868252i | ||||
\(331\) | 13.0175 | − | 13.0175i | 0.715504 | − | 0.715504i | −0.252177 | − | 0.967681i | \(-0.581147\pi\) |
0.967681 | + | 0.252177i | \(0.0811466\pi\) | |||||||
\(332\) | 39.8157 | − | 39.8157i | 2.18517 | − | 2.18517i | ||||
\(333\) | −5.74595 | − | 5.74595i | −0.314876 | − | 0.314876i | ||||
\(334\) | 10.7469 | 0.588042 | ||||||||
\(335\) | 24.9125i | 1.36111i | ||||||||
\(336\) | 2.30937 | − | 2.30937i | 0.125987 | − | 0.125987i | ||||
\(337\) | 3.45615 | 0.188268 | 0.0941342 | − | 0.995560i | \(-0.469992\pi\) | ||||
0.0941342 | + | 0.995560i | \(0.469992\pi\) | |||||||
\(338\) | −27.2957 | − | 14.1012i | −1.48469 | − | 0.767006i | ||||
\(339\) | −14.7052 | −0.798676 | ||||||||
\(340\) | −50.9920 | − | 50.9920i | −2.76543 | − | 2.76543i | ||||
\(341\) | 1.28315 | − | 0.0668121i | 0.0694867 | − | 0.00361808i | ||||
\(342\) | − | 8.22335i | − | 0.444668i | ||||||
\(343\) | 14.0425 | + | 14.0425i | 0.758223 | + | 0.758223i | ||||
\(344\) | 6.77628 | − | 6.77628i | 0.365353 | − | 0.365353i | ||||
\(345\) | 6.98169 | + | 6.98169i | 0.375881 | + | 0.375881i | ||||
\(346\) | 39.4985 | + | 39.4985i | 2.12345 | + | 2.12345i | ||||
\(347\) | − | 16.8397i | − | 0.904005i | −0.892017 | − | 0.452002i | \(-0.850710\pi\) | ||
0.892017 | − | 0.452002i | \(-0.149290\pi\) | |||||||
\(348\) | 12.0578 | 0.646365 | ||||||||
\(349\) | 15.2709 | − | 15.2709i | 0.817433 | − | 0.817433i | −0.168302 | − | 0.985735i | \(-0.553828\pi\) |
0.985735 | + | 0.168302i | \(0.0538284\pi\) | |||||||
\(350\) | − | 18.5106i | − | 0.989431i | ||||||
\(351\) | −0.554044 | − | 3.56273i | −0.0295727 | − | 0.190164i | ||||
\(352\) | 0.606100 | + | 11.6404i | 0.0323052 | + | 0.620435i | ||||
\(353\) | 2.12218 | − | 2.12218i | 0.112952 | − | 0.112952i | −0.648372 | − | 0.761324i | \(-0.724550\pi\) |
0.761324 | + | 0.648372i | \(0.224550\pi\) | |||||||
\(354\) | 9.69873i | 0.515482i | ||||||||
\(355\) | − | 49.3821i | − | 2.62093i | ||||||
\(356\) | 19.7954 | − | 19.7954i | 1.04916 | − | 1.04916i | ||||
\(357\) | 9.17940 | − | 9.17940i | 0.485825 | − | 0.485825i | ||||
\(358\) | −12.2889 | + | 12.2889i | −0.649486 | + | 0.649486i | ||||
\(359\) | 6.07486 | − | 6.07486i | 0.320619 | − | 0.320619i | −0.528386 | − | 0.849005i | \(-0.677202\pi\) |
0.849005 | + | 0.528386i | \(0.177202\pi\) | |||||||
\(360\) | 11.2621i | 0.593566i | ||||||||
\(361\) | − | 6.89241i | − | 0.362759i | ||||||
\(362\) | −36.4752 | + | 36.4752i | −1.91709 | + | 1.91709i | ||||
\(363\) | −1.14241 | − | 10.9405i | −0.0599612 | − | 0.574228i | ||||
\(364\) | −14.7985 | + | 20.2487i | −0.775650 | + | 1.06132i | ||||
\(365\) | 10.6325i | 0.556532i | ||||||||
\(366\) | 11.4794 | − | 11.4794i | 0.600039 | − | 0.600039i | ||||
\(367\) | −21.3852 | −1.11630 | −0.558150 | − | 0.829740i | \(-0.688489\pi\) | ||||
−0.558150 | + | 0.829740i | \(0.688489\pi\) | |||||||
\(368\) | 5.52882i | 0.288210i | ||||||||
\(369\) | 0.977956 | + | 0.977956i | 0.0509104 | + | 0.0509104i | ||||
\(370\) | −40.8220 | − | 40.8220i | −2.12223 | − | 2.12223i | ||||
\(371\) | 12.8362 | − | 12.8362i | 0.666421 | − | 0.666421i | ||||
\(372\) | −0.982133 | − | 0.982133i | −0.0509212 | − | 0.0509212i | ||||
\(373\) | − | 20.2050i | − | 1.04618i | −0.852278 | − | 0.523089i | \(-0.824780\pi\) | ||
0.852278 | − | 0.523089i | \(-0.175220\pi\) | |||||||
\(374\) | −2.72706 | − | 52.3743i | −0.141013 | − | 2.70821i | ||||
\(375\) | −2.04700 | − | 2.04700i | −0.105707 | − | 0.105707i | ||||
\(376\) | 27.0658 | 1.39581 | ||||||||
\(377\) | −11.9822 | + | 1.86336i | −0.617112 | + | 0.0959679i | ||||
\(378\) | −4.58521 | −0.235838 | ||||||||
\(379\) | −19.6483 | + | 19.6483i | −1.00926 | + | 1.00926i | −0.00930684 | + | 0.999957i | \(0.502963\pi\) |
−0.999957 | + | 0.00930684i | \(0.997037\pi\) | |||||||
\(380\) | − | 37.5022i | − | 1.92382i | ||||||
\(381\) | 3.77210 | 0.193251 | ||||||||
\(382\) | −11.4351 | − | 11.4351i | −0.585070 | − | 0.585070i | ||||
\(383\) | −12.0548 | + | 12.0548i | −0.615972 | + | 0.615972i | −0.944496 | − | 0.328524i | \(-0.893449\pi\) |
0.328524 | + | 0.944496i | \(0.393449\pi\) | |||||||
\(384\) | 14.5357 | − | 14.5357i | 0.741771 | − | 0.741771i | ||||
\(385\) | 12.9486 | − | 14.3711i | 0.659921 | − | 0.732418i | ||||
\(386\) | −1.50025 | −0.0763606 | ||||||||
\(387\) | −2.55799 | −0.130030 | ||||||||
\(388\) | −29.4529 | − | 29.4529i | −1.49525 | − | 1.49525i | ||||
\(389\) | − | 2.80700i | − | 0.142321i | −0.997465 | − | 0.0711604i | \(-0.977330\pi\) | ||
0.997465 | − | 0.0711604i | \(-0.0226702\pi\) | |||||||
\(390\) | −3.93620 | − | 25.3113i | −0.199317 | − | 1.28169i | ||||
\(391\) | 21.9762i | 1.11138i | ||||||||
\(392\) | −8.57169 | − | 8.57169i | −0.432936 | − | 0.432936i | ||||
\(393\) | 21.8690i | 1.10315i | ||||||||
\(394\) | 19.8428i | 0.999668i | ||||||||
\(395\) | 0.834380 | + | 0.834380i | 0.0419822 | + | 0.0419822i | ||||
\(396\) | −7.95949 | + | 8.83390i | −0.399980 | + | 0.443920i | ||||
\(397\) | −4.30770 | − | 4.30770i | −0.216197 | − | 0.216197i | 0.590697 | − | 0.806894i | \(-0.298853\pi\) |
−0.806894 | + | 0.590697i | \(0.798853\pi\) | |||||||
\(398\) | −40.2848 | + | 40.2848i | −2.01929 | + | 2.01929i | ||||
\(399\) | 6.75101 | 0.337973 | ||||||||
\(400\) | 6.79562i | 0.339781i | ||||||||
\(401\) | −0.575718 | − | 0.575718i | −0.0287500 | − | 0.0287500i | 0.692586 | − | 0.721336i | \(-0.256471\pi\) |
−0.721336 | + | 0.692586i | \(0.756471\pi\) | |||||||
\(402\) | 19.5851 | 0.976814 | ||||||||
\(403\) | 1.12775 | + | 0.824199i | 0.0561772 | + | 0.0410563i | ||||
\(404\) | − | 22.5226i | − | 1.12054i | ||||||
\(405\) | 2.12568 | − | 2.12568i | 0.105626 | − | 0.105626i | ||||
\(406\) | 15.4210i | 0.765330i | ||||||||
\(407\) | −1.40140 | − | 26.9144i | −0.0694647 | − | 1.33410i | ||||
\(408\) | −17.7248 | + | 17.7248i | −0.877510 | + | 0.877510i | ||||
\(409\) | 6.90171 | + | 6.90171i | 0.341268 | + | 0.341268i | 0.856844 | − | 0.515576i | \(-0.172422\pi\) |
−0.515576 | + | 0.856844i | \(0.672422\pi\) | |||||||
\(410\) | 6.94787 | + | 6.94787i | 0.343131 | + | 0.343131i | ||||
\(411\) | 8.09074 | + | 8.09074i | 0.399087 | + | 0.399087i | ||||
\(412\) | 41.4351 | 2.04136 | ||||||||
\(413\) | −7.96223 | −0.391796 | ||||||||
\(414\) | 5.48868 | − | 5.48868i | 0.269754 | − | 0.269754i | ||||
\(415\) | −47.2135 | −2.31762 | ||||||||
\(416\) | −7.47689 | + | 10.2306i | −0.366585 | + | 0.501597i | ||||
\(417\) | − | 3.08211i | − | 0.150932i | ||||||
\(418\) | 18.2566 | − | 20.2622i | 0.892958 | − | 0.991056i | ||||
\(419\) | 0.159209 | 0.00777788 | 0.00388894 | − | 0.999992i | \(-0.498762\pi\) | ||||
0.00388894 | + | 0.999992i | \(0.498762\pi\) | |||||||
\(420\) | −20.9106 | −1.02033 | ||||||||
\(421\) | 1.88602 | − | 1.88602i | 0.0919190 | − | 0.0919190i | −0.659652 | − | 0.751571i | \(-0.729296\pi\) |
0.751571 | + | 0.659652i | \(0.229296\pi\) | |||||||
\(422\) | −12.9514 | + | 12.9514i | −0.630466 | + | 0.630466i | ||||
\(423\) | −5.10855 | − | 5.10855i | −0.248386 | − | 0.248386i | ||||
\(424\) | −24.7858 | + | 24.7858i | −1.20371 | + | 1.20371i | ||||
\(425\) | 27.0116i | 1.31025i | ||||||||
\(426\) | −38.8219 | −1.88093 | ||||||||
\(427\) | 9.42410 | + | 9.42410i | 0.456064 | + | 0.456064i | ||||
\(428\) | −34.2771 | −1.65685 | ||||||||
\(429\) | 6.54442 | − | 10.0085i | 0.315967 | − | 0.483216i | ||||
\(430\) | −18.1732 | −0.876389 | ||||||||
\(431\) | −17.4987 | − | 17.4987i | −0.842883 | − | 0.842883i | 0.146350 | − | 0.989233i | \(-0.453247\pi\) |
−0.989233 | + | 0.146350i | \(0.953247\pi\) | |||||||
\(432\) | 1.68333 | 0.0809892 | ||||||||
\(433\) | − | 0.335335i | − | 0.0161152i | −0.999968 | − | 0.00805758i | \(-0.997435\pi\) | ||
0.999968 | − | 0.00805758i | \(-0.00256483\pi\) | |||||||
\(434\) | 1.25607 | − | 1.25607i | 0.0602935 | − | 0.0602935i | ||||
\(435\) | −7.14907 | − | 7.14907i | −0.342772 | − | 0.342772i | ||||
\(436\) | 45.8319 | − | 45.8319i | 2.19495 | − | 2.19495i | ||||
\(437\) | −8.08122 | + | 8.08122i | −0.386577 | + | 0.386577i | ||||
\(438\) | 8.35880 | 0.399399 | ||||||||
\(439\) | 18.6067 | 0.888051 | 0.444025 | − | 0.896014i | \(-0.353550\pi\) | ||||
0.444025 | + | 0.896014i | \(0.353550\pi\) | |||||||
\(440\) | −25.0029 | + | 27.7497i | −1.19197 | + | 1.32291i | ||||
\(441\) | 3.23574i | 0.154083i | ||||||||
\(442\) | 33.6412 | − | 46.0311i | 1.60015 | − | 2.18948i | ||||
\(443\) | 25.0591 | 1.19059 | 0.595296 | − | 0.803506i | \(-0.297035\pi\) | ||||
0.595296 | + | 0.803506i | \(0.297035\pi\) | |||||||
\(444\) | −20.6004 | + | 20.6004i | −0.977654 | + | 0.977654i | ||||
\(445\) | −23.4735 | −1.11275 | ||||||||
\(446\) | 22.6636 | 1.07315 | ||||||||
\(447\) | −13.7526 | − | 13.7526i | −0.650477 | − | 0.650477i | ||||
\(448\) | 16.0135 | + | 16.0135i | 0.756565 | + | 0.756565i | ||||
\(449\) | −12.9682 | − | 12.9682i | −0.612008 | − | 0.612008i | 0.331461 | − | 0.943469i | \(-0.392458\pi\) |
−0.943469 | + | 0.331461i | \(0.892458\pi\) | |||||||
\(450\) | 6.74629 | − | 6.74629i | 0.318023 | − | 0.318023i | ||||
\(451\) | 0.238517 | + | 4.58082i | 0.0112313 | + | 0.215702i | ||||
\(452\) | 52.7213i | 2.47980i | ||||||||
\(453\) | −4.90414 | + | 4.90414i | −0.230417 | + | 0.230417i | ||||
\(454\) | 1.94880i | 0.0914615i | ||||||||
\(455\) | 20.7795 | − | 3.23144i | 0.974157 | − | 0.151492i | ||||
\(456\) | −13.0358 | −0.610456 | ||||||||
\(457\) | −12.4301 | − | 12.4301i | −0.581456 | − | 0.581456i | 0.353847 | − | 0.935303i | \(-0.384873\pi\) |
−0.935303 | + | 0.353847i | \(0.884873\pi\) | |||||||
\(458\) | 15.9190i | 0.743845i | ||||||||
\(459\) | 6.69098 | 0.312308 | ||||||||
\(460\) | 25.0308 | − | 25.0308i | 1.16707 | − | 1.16707i | ||||
\(461\) | 19.9560 | + | 19.9560i | 0.929444 | + | 0.929444i | 0.997670 | − | 0.0682257i | \(-0.0217338\pi\) |
−0.0682257 | + | 0.997670i | \(0.521734\pi\) | |||||||
\(462\) | −11.2979 | − | 10.1796i | −0.525625 | − | 0.473597i | ||||
\(463\) | 0.914773 | + | 0.914773i | 0.0425131 | + | 0.0425131i | 0.728044 | − | 0.685531i | \(-0.240430\pi\) |
−0.685531 | + | 0.728044i | \(0.740430\pi\) | |||||||
\(464\) | − | 5.66137i | − | 0.262822i | ||||||
\(465\) | 1.16462i | 0.0540078i | ||||||||
\(466\) | −19.3441 | − | 19.3441i | −0.896099 | − | 0.896099i | ||||
\(467\) | − | 10.9958i | − | 0.508823i | −0.967096 | − | 0.254412i | \(-0.918118\pi\) | ||
0.967096 | − | 0.254412i | \(-0.0818818\pi\) | |||||||
\(468\) | −12.7731 | + | 1.98637i | −0.590439 | + | 0.0918199i | ||||
\(469\) | 16.0785i | 0.742434i | ||||||||
\(470\) | −36.2936 | − | 36.2936i | −1.67410 | − | 1.67410i | ||||
\(471\) | −6.61674 | −0.304883 | ||||||||
\(472\) | 15.3746 | 0.707672 | ||||||||
\(473\) | −6.30284 | − | 5.67896i | −0.289805 | − | 0.261119i | ||||
\(474\) | 0.655951 | − | 0.655951i | 0.0301288 | − | 0.0301288i | ||||
\(475\) | −9.93285 | + | 9.93285i | −0.455750 | + | 0.455750i | ||||
\(476\) | −32.9101 | − | 32.9101i | −1.50843 | − | 1.50843i | ||||
\(477\) | 9.35644 | 0.428402 | ||||||||
\(478\) | 53.6133i | 2.45222i | ||||||||
\(479\) | −1.37957 | + | 1.37957i | −0.0630344 | + | 0.0630344i | −0.737921 | − | 0.674887i | \(-0.764192\pi\) |
0.674887 | + | 0.737921i | \(0.264192\pi\) | |||||||
\(480\) | −10.5651 | −0.482227 | ||||||||
\(481\) | 17.2877 | − | 23.6548i | 0.788253 | − | 1.07856i | ||||
\(482\) | −53.6361 | −2.44306 | ||||||||
\(483\) | 4.50596 | + | 4.50596i | 0.205028 | + | 0.205028i | ||||
\(484\) | −39.2241 | + | 4.09580i | −1.78291 | + | 0.186173i | ||||
\(485\) | 34.9254i | 1.58588i | ||||||||
\(486\) | −1.67111 | − | 1.67111i | −0.0758031 | − | 0.0758031i | ||||
\(487\) | 3.04720 | − | 3.04720i | 0.138082 | − | 0.138082i | −0.634687 | − | 0.772769i | \(-0.718871\pi\) |
0.772769 | + | 0.634687i | \(0.218871\pi\) | |||||||
\(488\) | −18.1973 | − | 18.1973i | −0.823755 | − | 0.823755i | ||||
\(489\) | −7.31951 | − | 7.31951i | −0.331000 | − | 0.331000i | ||||
\(490\) | 22.9883i | 1.03850i | ||||||||
\(491\) | −7.62513 | −0.344117 | −0.172059 | − | 0.985087i | \(-0.555042\pi\) | ||||
−0.172059 | + | 0.985087i | \(0.555042\pi\) | |||||||
\(492\) | 3.50618 | − | 3.50618i | 0.158071 | − | 0.158071i | ||||
\(493\) | − | 22.5031i | − | 1.01349i | ||||||
\(494\) | 29.2976 | − | 4.55610i | 1.31816 | − | 0.204989i | ||||
\(495\) | 9.95682 | − | 0.518439i | 0.447526 | − | 0.0233021i | ||||
\(496\) | −0.461131 | + | 0.461131i | −0.0207054 | + | 0.0207054i | ||||
\(497\) | − | 31.8711i | − | 1.42961i | ||||||
\(498\) | 37.1171i | 1.66326i | ||||||||
\(499\) | −0.181339 | + | 0.181339i | −0.00811785 | + | 0.00811785i | −0.711154 | − | 0.703036i | \(-0.751827\pi\) |
0.703036 | + | 0.711154i | \(0.251827\pi\) | |||||||
\(500\) | −7.33894 | + | 7.33894i | −0.328207 | + | 0.328207i | ||||
\(501\) | −3.21549 | + | 3.21549i | −0.143657 | + | 0.143657i | ||||
\(502\) | 23.1833 | − | 23.1833i | 1.03472 | − | 1.03472i | ||||
\(503\) | − | 25.2385i | − | 1.12533i | −0.826685 | − | 0.562665i | \(-0.809776\pi\) | ||
0.826685 | − | 0.562665i | \(-0.190224\pi\) | |||||||
\(504\) | 7.26854i | 0.323767i | ||||||||
\(505\) | −13.3537 | + | 13.3537i | −0.594230 | + | 0.594230i | ||||
\(506\) | 25.7094 | − | 1.33865i | 1.14292 | − | 0.0595104i | ||||
\(507\) | 12.3861 | − | 3.94782i | 0.550085 | − | 0.175329i | ||||
\(508\) | − | 13.5238i | − | 0.600021i | ||||||
\(509\) | 25.1988 | − | 25.1988i | 1.11692 | − | 1.11692i | 0.124724 | − | 0.992191i | \(-0.460195\pi\) |
0.992191 | − | 0.124724i | \(-0.0398046\pi\) | |||||||
\(510\) | 47.5359 | 2.10493 | ||||||||
\(511\) | 6.86220i | 0.303566i | ||||||||
\(512\) | −13.1017 | − | 13.1017i | −0.579021 | − | 0.579021i | ||||
\(513\) | 2.46045 | + | 2.46045i | 0.108631 | + | 0.108631i | ||||
\(514\) | −23.9016 | + | 23.9016i | −1.05425 | + | 1.05425i | ||||
\(515\) | −24.5670 | − | 24.5670i | −1.08255 | − | 1.08255i | ||||
\(516\) | 9.17094i | 0.403728i | ||||||||
\(517\) | −1.24594 | − | 23.9288i | −0.0547964 | − | 1.05239i | ||||
\(518\) | −26.3464 | − | 26.3464i | −1.15759 | − | 1.15759i | ||||
\(519\) | −23.6361 | −1.03751 | ||||||||
\(520\) | −40.1239 | + | 6.23971i | −1.75955 | + | 0.273630i | ||||
\(521\) | 33.5718 | 1.47081 | 0.735404 | − | 0.677629i | \(-0.236993\pi\) | ||||
0.735404 | + | 0.677629i | \(0.236993\pi\) | |||||||
\(522\) | −5.62027 | + | 5.62027i | −0.245992 | + | 0.245992i | ||||
\(523\) | − | 4.69450i | − | 0.205276i | −0.994719 | − | 0.102638i | \(-0.967272\pi\) | ||
0.994719 | − | 0.102638i | \(-0.0327283\pi\) | |||||||
\(524\) | 78.4052 | 3.42515 | ||||||||
\(525\) | 5.53840 | + | 5.53840i | 0.241716 | + | 0.241716i | ||||
\(526\) | −19.2378 | + | 19.2378i | −0.838807 | + | 0.838807i | ||||
\(527\) | −1.83293 | + | 1.83293i | −0.0798435 | + | 0.0798435i | ||||
\(528\) | 4.14769 | + | 3.73714i | 0.180505 | + | 0.162638i | ||||
\(529\) | 12.2124 | 0.530973 | ||||||||
\(530\) | 66.4727 | 2.88739 | ||||||||
\(531\) | −2.90188 | − | 2.90188i | −0.125931 | − | 0.125931i | ||||
\(532\) | − | 24.2038i | − | 1.04937i | ||||||
\(533\) | −2.94236 | + | 4.02602i | −0.127448 | + | 0.174386i | ||||
\(534\) | 18.4538i | 0.798573i | ||||||||
\(535\) | 20.3230 | + | 20.3230i | 0.878638 | + | 0.878638i | ||||
\(536\) | − | 31.0465i | − | 1.34100i | ||||||
\(537\) | − | 7.35371i | − | 0.317336i | ||||||
\(538\) | 33.8771 | + | 33.8771i | 1.46055 | + | 1.46055i | ||||
\(539\) | −7.18363 | + | 7.97281i | −0.309421 | + | 0.343413i | ||||
\(540\) | −7.62101 | − | 7.62101i | −0.327956 | − | 0.327956i | ||||
\(541\) | 20.0958 | − | 20.0958i | 0.863987 | − | 0.863987i | −0.127812 | − | 0.991798i | \(-0.540795\pi\) |
0.991798 | + | 0.127812i | \(0.0407953\pi\) | |||||||
\(542\) | −4.52469 | −0.194352 | ||||||||
\(543\) | − | 21.8269i | − | 0.936683i | ||||||
\(544\) | −16.6278 | − | 16.6278i | −0.712910 | − | 0.712910i | ||||
\(545\) | −54.3476 | −2.32799 | ||||||||
\(546\) | −2.54041 | − | 16.3359i | −0.108720 | − | 0.699111i | ||||
\(547\) | 9.45282i | 0.404173i | 0.979368 | + | 0.202087i | \(0.0647723\pi\) | ||||
−0.979368 | + | 0.202087i | \(0.935228\pi\) | |||||||
\(548\) | 29.0070 | − | 29.0070i | 1.23912 | − | 1.23912i | ||||
\(549\) | 6.86934i | 0.293176i | ||||||||
\(550\) | 31.6001 | − | 1.64537i | 1.34743 | − | 0.0701590i | ||||
\(551\) | 8.27496 | − | 8.27496i | 0.352525 | − | 0.352525i | ||||
\(552\) | −8.70073 | − | 8.70073i | −0.370328 | − | 0.370328i | ||||
\(553\) | 0.538507 | + | 0.538507i | 0.0228996 | + | 0.0228996i | ||||
\(554\) | −29.5930 | − | 29.5930i | −1.25728 | − | 1.25728i | ||||
\(555\) | 24.4281 | 1.03691 | ||||||||
\(556\) | −11.0500 | −0.468625 | ||||||||
\(557\) | 25.1768 | − | 25.1768i | 1.06678 | − | 1.06678i | 0.0691713 | − | 0.997605i | \(-0.477964\pi\) |
0.997605 | − | 0.0691713i | \(-0.0220355\pi\) | |||||||
\(558\) | 0.915567 | 0.0387591 | ||||||||
\(559\) | −1.41724 | − | 9.11342i | −0.0599429 | − | 0.385457i | ||||
\(560\) | 9.81796i | 0.414885i | ||||||||
\(561\) | 16.4865 | + | 14.8546i | 0.696059 | + | 0.627160i | ||||
\(562\) | 38.8123 | 1.63720 | ||||||||
\(563\) | 16.3670 | 0.689787 | 0.344894 | − | 0.938642i | \(-0.387915\pi\) | ||||
0.344894 | + | 0.938642i | \(0.387915\pi\) | |||||||
\(564\) | −18.3153 | + | 18.3153i | −0.771211 | + | 0.771211i | ||||
\(565\) | 31.2585 | − | 31.2585i | 1.31506 | − | 1.31506i | ||||
\(566\) | 31.4316 | + | 31.4316i | 1.32117 | + | 1.32117i | ||||
\(567\) | 1.37191 | − | 1.37191i | 0.0576147 | − | 0.0576147i | ||||
\(568\) | 61.5410i | 2.58220i | ||||||||
\(569\) | −33.0118 | −1.38393 | −0.691963 | − | 0.721933i | \(-0.743254\pi\) | ||||
−0.691963 | + | 0.721933i | \(0.743254\pi\) | |||||||
\(570\) | 17.4802 | + | 17.4802i | 0.732165 | + | 0.732165i | ||||
\(571\) | 38.8441 | 1.62557 | 0.812787 | − | 0.582561i | \(-0.197949\pi\) | ||||
0.812787 | + | 0.582561i | \(0.197949\pi\) | |||||||
\(572\) | −35.8827 | − | 23.4631i | −1.50033 | − | 0.981043i | ||||
\(573\) | 6.84281 | 0.285863 | ||||||||
\(574\) | 4.48414 | + | 4.48414i | 0.187164 | + | 0.187164i | ||||
\(575\) | −13.2594 | −0.552954 | ||||||||
\(576\) | 11.6724i | 0.486351i | ||||||||
\(577\) | −28.5709 | + | 28.5709i | −1.18942 | + | 1.18942i | −0.212194 | + | 0.977227i | \(0.568061\pi\) |
−0.977227 | + | 0.212194i | \(0.931939\pi\) | |||||||
\(578\) | 46.4054 | + | 46.4054i | 1.93021 | + | 1.93021i | ||||
\(579\) | 0.448878 | − | 0.448878i | 0.0186547 | − | 0.0186547i | ||||
\(580\) | −25.6309 | + | 25.6309i | −1.06427 | + | 1.06427i | ||||
\(581\) | −30.4715 | −1.26417 | ||||||||
\(582\) | 27.4567 | 1.13812 | ||||||||
\(583\) | 23.0541 | + | 20.7721i | 0.954803 | + | 0.860294i | ||||
\(584\) | − | 13.2505i | − | 0.548309i | ||||||
\(585\) | 8.75093 | + | 6.39549i | 0.361807 | + | 0.264421i | ||||
\(586\) | 74.8762 | 3.09311 | ||||||||
\(587\) | −28.9300 | + | 28.9300i | −1.19407 | + | 1.19407i | −0.218156 | + | 0.975914i | \(0.570004\pi\) |
−0.975914 | + | 0.218156i | \(0.929996\pi\) | |||||||
\(588\) | 11.6008 | 0.478410 | ||||||||
\(589\) | −1.34803 | −0.0555446 | ||||||||
\(590\) | −20.6164 | − | 20.6164i | −0.848763 | − | 0.848763i | ||||
\(591\) | −5.93703 | − | 5.93703i | −0.244217 | − | 0.244217i | ||||
\(592\) | 9.67232 | + | 9.67232i | 0.397530 | + | 0.397530i | ||||
\(593\) | −14.1603 | + | 14.1603i | −0.581496 | + | 0.581496i | −0.935314 | − | 0.353818i | \(-0.884883\pi\) |
0.353818 | + | 0.935314i | \(0.384883\pi\) | |||||||
\(594\) | −0.407572 | − | 7.82759i | −0.0167229 | − | 0.321170i | ||||
\(595\) | 39.0249i | 1.59986i | ||||||||
\(596\) | −49.3061 | + | 49.3061i | −2.01966 | + | 2.01966i | ||||
\(597\) | − | 24.1066i | − | 0.986617i | ||||||
\(598\) | 22.5956 | + | 16.5137i | 0.924005 | + | 0.675296i | ||||
\(599\) | −38.3843 | −1.56834 | −0.784171 | − | 0.620545i | \(-0.786911\pi\) | ||||
−0.784171 | + | 0.620545i | \(0.786911\pi\) | |||||||
\(600\) | −10.6943 | − | 10.6943i | −0.436593 | − | 0.436593i | ||||
\(601\) | 44.6167i | 1.81995i | 0.414660 | + | 0.909976i | \(0.363900\pi\) | ||||
−0.414660 | + | 0.909976i | \(0.636100\pi\) | |||||||
\(602\) | −11.7289 | −0.478035 | ||||||||
\(603\) | −5.85989 | + | 5.85989i | −0.238633 | + | 0.238633i | ||||
\(604\) | 17.5824 | + | 17.5824i | 0.715418 | + | 0.715418i | ||||
\(605\) | 25.6844 | + | 20.8276i | 1.04422 | + | 0.846763i | ||||
\(606\) | 10.4980 | + | 10.4980i | 0.426453 | + | 0.426453i | ||||
\(607\) | − | 32.2248i | − | 1.30797i | −0.756509 | − | 0.653983i | \(-0.773097\pi\) | ||
0.756509 | − | 0.653983i | \(-0.226903\pi\) | |||||||
\(608\) | − | 12.2289i | − | 0.495948i | ||||||
\(609\) | −4.61399 | − | 4.61399i | −0.186968 | − | 0.186968i | ||||
\(610\) | 48.8031i | 1.97598i | ||||||||
\(611\) | 15.3700 | − | 21.0307i | 0.621804 | − | 0.850813i | ||||
\(612\) | − | 23.9886i | − | 0.969681i | ||||||
\(613\) | −18.6007 | − | 18.6007i | −0.751276 | − | 0.751276i | 0.223442 | − | 0.974717i | \(-0.428271\pi\) |
−0.974717 | + | 0.223442i | \(0.928271\pi\) | |||||||
\(614\) | 44.4694 | 1.79464 | ||||||||
\(615\) | −4.15764 | −0.167652 | ||||||||
\(616\) | −16.1368 | + | 17.9096i | −0.650171 | + | 0.721597i | ||||
\(617\) | 7.05413 | − | 7.05413i | 0.283989 | − | 0.283989i | −0.550709 | − | 0.834697i | \(-0.685643\pi\) |
0.834697 | + | 0.550709i | \(0.185643\pi\) | |||||||
\(618\) | −19.3134 | + | 19.3134i | −0.776899 | + | 0.776899i | ||||
\(619\) | 5.06137 | + | 5.06137i | 0.203434 | + | 0.203434i | 0.801469 | − | 0.598036i | \(-0.204052\pi\) |
−0.598036 | + | 0.801469i | \(0.704052\pi\) | |||||||
\(620\) | 4.17540 | 0.167688 | ||||||||
\(621\) | 3.28445i | 0.131801i | ||||||||
\(622\) | −21.8422 | + | 21.8422i | −0.875794 | + | 0.875794i | ||||
\(623\) | −15.1497 | −0.606961 | ||||||||
\(624\) | 0.932639 | + | 5.99725i | 0.0373355 | + | 0.240082i | ||||
\(625\) | 28.8876 | 1.15550 | ||||||||
\(626\) | −19.3658 | − | 19.3658i | −0.774014 | − | 0.774014i | ||||
\(627\) | 0.600086 | + | 11.5249i | 0.0239651 | + | 0.460260i | ||||
\(628\) | 23.7224i | 0.946627i | ||||||||
\(629\) | 38.4460 | + | 38.4460i | 1.53294 | + | 1.53294i | ||||
\(630\) | 9.74669 | − | 9.74669i | 0.388317 | − | 0.388317i | ||||
\(631\) | 28.6267 | + | 28.6267i | 1.13961 | + | 1.13961i | 0.988520 | + | 0.151092i | \(0.0482789\pi\) |
0.151092 | + | 0.988520i | \(0.451721\pi\) | |||||||
\(632\) | −1.03982 | − | 1.03982i | −0.0413619 | − | 0.0413619i | ||||
\(633\) | − | 7.75020i | − | 0.308043i | ||||||
\(634\) | −57.3617 | −2.27812 | ||||||||
\(635\) | −8.01828 | + | 8.01828i | −0.318196 | + | 0.318196i | ||||
\(636\) | − | 33.5448i | − | 1.33014i | ||||||
\(637\) | −11.5281 | + | 1.79274i | −0.456759 | + | 0.0710311i | ||||
\(638\) | −26.3257 | + | 1.37075i | −1.04225 | + | 0.0542683i | ||||
\(639\) | 11.6156 | − | 11.6156i | 0.459507 | − | 0.459507i | ||||
\(640\) | 61.7963i | 2.44272i | ||||||||
\(641\) | 15.0769i | 0.595503i | 0.954643 | + | 0.297751i | \(0.0962366\pi\) | ||||
−0.954643 | + | 0.297751i | \(0.903763\pi\) | |||||||
\(642\) | 15.9770 | − | 15.9770i | 0.630561 | − | 0.630561i | ||||
\(643\) | 9.61392 | − | 9.61392i | 0.379136 | − | 0.379136i | −0.491655 | − | 0.870790i | \(-0.663608\pi\) |
0.870790 | + | 0.491655i | \(0.163608\pi\) | |||||||
\(644\) | 16.1548 | − | 16.1548i | 0.636590 | − | 0.636590i | ||||
\(645\) | 5.43746 | − | 5.43746i | 0.214100 | − | 0.214100i | ||||
\(646\) | 55.0223i | 2.16482i | ||||||||
\(647\) | 19.7013i | 0.774536i | 0.921967 | + | 0.387268i | \(0.126581\pi\) | ||||
−0.921967 | + | 0.387268i | \(0.873419\pi\) | |||||||
\(648\) | −2.64907 | + | 2.64907i | −0.104065 | + | 0.104065i | ||||
\(649\) | −0.707750 | − | 13.5926i | −0.0277816 | − | 0.533557i | ||||
\(650\) | 27.7729 | + | 20.2975i | 1.08934 | + | 0.796132i | ||||
\(651\) | 0.751640i | 0.0294591i | ||||||||
\(652\) | −26.2420 | + | 26.2420i | −1.02772 | + | 1.02772i | ||||
\(653\) | −43.2375 | −1.69201 | −0.846007 | − | 0.533172i | \(-0.821000\pi\) | ||||
−0.846007 | + | 0.533172i | \(0.821000\pi\) | |||||||
\(654\) | 42.7256i | 1.67070i | ||||||||
\(655\) | −46.4865 | − | 46.4865i | −1.81638 | − | 1.81638i | ||||
\(656\) | −1.64622 | − | 1.64622i | −0.0642742 | − | 0.0642742i | ||||
\(657\) | −2.50097 | + | 2.50097i | −0.0975722 | + | 0.0975722i | ||||
\(658\) | −23.4238 | − | 23.4238i | −0.913155 | − | 0.913155i | ||||
\(659\) | − | 18.1385i | − | 0.706575i | −0.935515 | − | 0.353287i | \(-0.885064\pi\) | ||
0.935515 | − | 0.353287i | \(-0.114936\pi\) | |||||||
\(660\) | −1.85871 | − | 35.6973i | −0.0723503 | − | 1.38952i | ||||
\(661\) | −4.09800 | − | 4.09800i | −0.159394 | − | 0.159394i | 0.622904 | − | 0.782298i | \(-0.285953\pi\) |
−0.782298 | + | 0.622904i | \(0.785953\pi\) | |||||||
\(662\) | 43.5072 | 1.69095 | ||||||||
\(663\) | 3.70710 | + | 23.8381i | 0.143972 | + | 0.925797i | ||||
\(664\) | 58.8385 | 2.28338 | ||||||||
\(665\) | −14.3505 | + | 14.3505i | −0.556487 | + | 0.556487i | ||||
\(666\) | − | 19.2042i | − | 0.744148i | ||||||
\(667\) | 11.0463 | 0.427713 | ||||||||
\(668\) | 11.5282 | + | 11.5282i | 0.446040 | + | 0.446040i | ||||
\(669\) | −6.78100 | + | 6.78100i | −0.262169 | + | 0.262169i | ||||
\(670\) | −41.6315 | + | 41.6315i | −1.60837 | + | 1.60837i | ||||
\(671\) | −15.2505 | + | 16.9259i | −0.588741 | + | 0.653418i | ||||
\(672\) | −6.81866 | −0.263036 | ||||||||
\(673\) | −32.5180 | −1.25348 | −0.626738 | − | 0.779230i | \(-0.715610\pi\) | ||||
−0.626738 | + | 0.779230i | \(0.715610\pi\) | |||||||
\(674\) | 5.77560 | + | 5.77560i | 0.222468 | + | 0.222468i | ||||
\(675\) | 4.03701i | 0.155385i | ||||||||
\(676\) | −14.1538 | − | 44.4067i | −0.544376 | − | 1.70795i | ||||
\(677\) | 7.87815i | 0.302782i | 0.988474 | + | 0.151391i | \(0.0483752\pi\) | ||||
−0.988474 | + | 0.151391i | \(0.951625\pi\) | |||||||
\(678\) | −24.5740 | − | 24.5740i | −0.943758 | − | 0.943758i | ||||
\(679\) | 22.5407i | 0.865035i | ||||||||
\(680\) | − | 75.3546i | − | 2.88972i | ||||||
\(681\) | −0.583085 | − | 0.583085i | −0.0223438 | − | 0.0223438i | ||||
\(682\) | 2.25594 | + | 2.03264i | 0.0863845 | + | 0.0778338i | ||||
\(683\) | −15.2941 | − | 15.2941i | −0.585214 | − | 0.585214i | 0.351117 | − | 0.936332i | \(-0.385802\pi\) |
−0.936332 | + | 0.351117i | \(0.885802\pi\) | |||||||
\(684\) | 8.82122 | − | 8.82122i | 0.337288 | − | 0.337288i | ||||
\(685\) | −34.3966 | −1.31423 | ||||||||
\(686\) | 46.9331i | 1.79191i | ||||||||
\(687\) | −4.76299 | − | 4.76299i | −0.181720 | − | 0.181720i | ||||
\(688\) | 4.30594 | 0.164162 | ||||||||
\(689\) | 5.18388 | + | 33.3345i | 0.197490 | + | 1.26994i | ||||
\(690\) | 23.3343i | 0.888323i | ||||||||
\(691\) | 20.8412 | − | 20.8412i | 0.792835 | − | 0.792835i | −0.189119 | − | 0.981954i | \(-0.560563\pi\) |
0.981954 | + | 0.189119i | \(0.0605632\pi\) | |||||||
\(692\) | 84.7404i | 3.22135i | ||||||||
\(693\) | 6.42611 | − | 0.334599i | 0.244108 | − | 0.0127104i | ||||
\(694\) | 28.1410 | − | 28.1410i | 1.06822 | − | 1.06822i | ||||
\(695\) | 6.55157 | + | 6.55157i | 0.248515 | + | 0.248515i | ||||
\(696\) | 8.90933 | + | 8.90933i | 0.337707 | + | 0.337707i | ||||
\(697\) | −6.54348 | − | 6.54348i | −0.247852 | − | 0.247852i | ||||
\(698\) | 51.0387 | 1.93184 | ||||||||
\(699\) | 11.5756 | 0.437830 | ||||||||
\(700\) | 19.8564 | − | 19.8564i | 0.750500 | − | 0.750500i | ||||
\(701\) | −21.6055 | −0.816028 | −0.408014 | − | 0.912976i | \(-0.633778\pi\) | ||||
−0.408014 | + | 0.912976i | \(0.633778\pi\) | |||||||
\(702\) | 5.02784 | − | 6.87958i | 0.189764 | − | 0.259653i | ||||
\(703\) | 28.2752i | 1.06642i | ||||||||
\(704\) | −25.9138 | + | 28.7606i | −0.976663 | + | 1.08396i | ||||
\(705\) | 21.7183 | 0.817957 | ||||||||
\(706\) | 7.09280 | 0.266941 | ||||||||
\(707\) | −8.61842 | + | 8.61842i | −0.324129 | + | 0.324129i | ||||
\(708\) | −10.4039 | + | 10.4039i | −0.391002 | + | 0.391002i | ||||
\(709\) | 9.65076 | + | 9.65076i | 0.362442 | + | 0.362442i | 0.864711 | − | 0.502269i | \(-0.167501\pi\) |
−0.502269 | + | 0.864711i | \(0.667501\pi\) | |||||||
\(710\) | 82.5229 | − | 82.5229i | 3.09703 | − | 3.09703i | ||||
\(711\) | 0.392524i | 0.0147208i | ||||||||
\(712\) | 29.2532 | 1.09631 | ||||||||
\(713\) | −0.899743 | − | 0.899743i | −0.0336956 | − | 0.0336956i | ||||
\(714\) | 30.6796 | 1.14815 | ||||||||
\(715\) | 7.36358 | + | 35.1862i | 0.275382 | + | 1.31589i | ||||
\(716\) | −26.3646 | −0.985292 | ||||||||
\(717\) | −16.0412 | − | 16.0412i | −0.599071 | − | 0.599071i | ||||
\(718\) | 20.3035 | 0.757721 | ||||||||
\(719\) | 9.46044i | 0.352815i | 0.984317 | + | 0.176407i | \(0.0564476\pi\) | ||||
−0.984317 | + | 0.176407i | \(0.943552\pi\) | |||||||
\(720\) | −3.57822 | + | 3.57822i | −0.133352 | + | 0.133352i | ||||
\(721\) | −15.8554 | − | 15.8554i | −0.590488 | − | 0.590488i | ||||
\(722\) | 11.5180 | − | 11.5180i | 0.428655 | − | 0.428655i | ||||
\(723\) | 16.0481 | − | 16.0481i | 0.596833 | − | 0.596833i | ||||
\(724\) | −78.2542 | −2.90830 | ||||||||
\(725\) | 13.5773 | 0.504247 | ||||||||
\(726\) | 16.3737 | − | 20.1919i | 0.607685 | − | 0.749392i | ||||
\(727\) | − | 34.6624i | − | 1.28556i | −0.766052 | − | 0.642778i | \(-0.777782\pi\) | ||
0.766052 | − | 0.642778i | \(-0.222218\pi\) | |||||||
\(728\) | −25.8958 | + | 4.02710i | −0.959764 | + | 0.149254i | ||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −17.7681 | + | 17.7681i | −0.657627 | + | 0.657627i | ||||
\(731\) | 17.1155 | 0.633038 | ||||||||
\(732\) | 24.6281 | 0.910279 | ||||||||
\(733\) | 0.126504 | + | 0.126504i | 0.00467254 | + | 0.00467254i | 0.709439 | − | 0.704767i | \(-0.248948\pi\) |
−0.704767 | + | 0.709439i | \(0.748948\pi\) | |||||||
\(734\) | −35.7371 | − | 35.7371i | −1.31908 | − | 1.31908i | ||||
\(735\) | −6.87815 | − | 6.87815i | −0.253704 | − | 0.253704i | ||||
\(736\) | 8.16220 | − | 8.16220i | 0.300863 | − | 0.300863i | ||||
\(737\) | −27.4482 | + | 1.42919i | −1.01107 | + | 0.0526449i | ||||
\(738\) | 3.26854i | 0.120317i | ||||||||
\(739\) | −12.8617 | + | 12.8617i | −0.473125 | + | 0.473125i | −0.902925 | − | 0.429799i | \(-0.858584\pi\) |
0.429799 | + | 0.902925i | \(0.358584\pi\) | |||||||
\(740\) | − | 87.5798i | − | 3.21950i | ||||||
\(741\) | −7.40270 | + | 10.1291i | −0.271945 | + | 0.372102i | ||||
\(742\) | 42.9013 | 1.57496 | ||||||||
\(743\) | −30.3980 | − | 30.3980i | −1.11519 | − | 1.11519i | −0.992437 | − | 0.122757i | \(-0.960827\pi\) |
−0.122757 | − | 0.992437i | \(-0.539173\pi\) | |||||||
\(744\) | − | 1.45137i | − | 0.0532098i | ||||||
\(745\) | 58.4673 | 2.14208 | ||||||||
\(746\) | 33.7648 | − | 33.7648i | 1.23622 | − | 1.23622i | ||||
\(747\) | −11.1055 | − | 11.1055i | −0.406330 | − | 0.406330i | ||||
\(748\) | 53.2568 | − | 59.1075i | 1.94726 | − | 2.16118i | ||||
\(749\) | 13.1164 | + | 13.1164i | 0.479262 | + | 0.479262i | ||||
\(750\) | − | 6.84153i | − | 0.249817i | ||||||
\(751\) | 18.0117i | 0.657256i | 0.944459 | + | 0.328628i | \(0.106586\pi\) | ||||
−0.944459 | + | 0.328628i | \(0.893414\pi\) | |||||||
\(752\) | 8.59938 | + | 8.59938i | 0.313587 | + | 0.313587i | ||||
\(753\) | 13.8730i | 0.505561i | ||||||||
\(754\) | −23.1374 | − | 16.9096i | −0.842613 | − | 0.615812i | ||||
\(755\) | − | 20.8493i | − | 0.758782i | ||||||
\(756\) | −4.91858 | − | 4.91858i | −0.178887 | − | 0.178887i | ||||
\(757\) | −18.3639 | −0.667448 | −0.333724 | − | 0.942671i | \(-0.608305\pi\) | ||||
−0.333724 | + | 0.942671i | \(0.608305\pi\) | |||||||
\(758\) | −65.6688 | −2.38520 | ||||||||
\(759\) | −7.29178 | + | 8.09283i | −0.264675 | + | 0.293751i | ||||
\(760\) | 27.7098 | − | 27.7098i | 1.00514 | − | 1.00514i | ||||
\(761\) | −27.6011 | + | 27.6011i | −1.00054 | + | 1.00054i | −0.000539050 | 1.00000i | \(0.500172\pi\) | |
−1.00000 | 0.000539050i | \(0.999828\pi\) | ||||||||
\(762\) | 6.30360 | + | 6.30360i | 0.228355 | + | 0.228355i | ||||
\(763\) | −35.0758 | −1.26983 | ||||||||
\(764\) | − | 24.5329i | − | 0.887571i | ||||||
\(765\) | −14.2229 | + | 14.2229i | −0.514229 | + | 0.514229i | ||||
\(766\) | −40.2898 | −1.45573 | ||||||||
\(767\) | 8.73085 | − | 11.9464i | 0.315253 | − | 0.431359i | ||||
\(768\) | 25.2366 | 0.910647 | ||||||||
\(769\) | −5.30817 | − | 5.30817i | −0.191417 | − | 0.191417i | 0.604891 | − | 0.796308i | \(-0.293217\pi\) |
−0.796308 | + | 0.604891i | \(0.793217\pi\) | |||||||
\(770\) | 45.6542 | − | 2.37715i | 1.64526 | − | 0.0856666i | ||||
\(771\) | − | 14.3028i | − | 0.515104i | ||||||
\(772\) | −1.60932 | − | 1.60932i | −0.0579208 | − | 0.0579208i | ||||
\(773\) | −12.0100 | + | 12.0100i | −0.431969 | + | 0.431969i | −0.889298 | − | 0.457329i | \(-0.848806\pi\) |
0.457329 | + | 0.889298i | \(0.348806\pi\) | |||||||
\(774\) | −4.27468 | − | 4.27468i | −0.153650 | − | 0.153650i | ||||
\(775\) | −1.10590 | − | 1.10590i | −0.0397251 | − | 0.0397251i | ||||
\(776\) | − | 43.5248i | − | 1.56245i | ||||||
\(777\) | 15.7658 | 0.565595 | ||||||||
\(778\) | 4.69081 | − | 4.69081i | 0.168174 | − | 0.168174i | ||||
\(779\) | − | 4.81242i | − | 0.172423i | ||||||
\(780\) | 22.9292 | − | 31.3740i | 0.820997 | − | 1.12337i | ||||
\(781\) | 54.4083 | − | 2.83297i | 1.94688 | − | 0.101372i | ||||
\(782\) | −36.7246 | + | 36.7246i | −1.31327 | + | 1.31327i | ||||
\(783\) | − | 3.36320i | − | 0.120191i | ||||||
\(784\) | − | 5.44682i | − | 0.194529i | ||||||
\(785\) | 14.0650 | − | 14.0650i | 0.502003 | − | 0.502003i | ||||
\(786\) | −36.5456 | + | 36.5456i | −1.30354 | + | 1.30354i | ||||
\(787\) | 23.4689 | − | 23.4689i | 0.836576 | − | 0.836576i | −0.151830 | − | 0.988407i | \(-0.548517\pi\) |
0.988407 | + | 0.151830i | \(0.0485167\pi\) | |||||||
\(788\) | −21.2855 | + | 21.2855i | −0.758265 | + | 0.758265i | ||||
\(789\) | − | 11.5120i | − | 0.409838i | ||||||
\(790\) | 2.78868i | 0.0992168i | ||||||||
\(791\) | 20.1742 | − | 20.1742i | 0.717310 | − | 0.717310i | ||||
\(792\) | −12.4084 | + | 0.646089i | −0.440914 | + | 0.0229578i | ||||
\(793\) | −24.4736 | + | 3.80592i | −0.869083 | + | 0.135152i | ||||
\(794\) | − | 14.3973i | − | 0.510940i | ||||||
\(795\) | −19.8888 | + | 19.8888i | −0.705382 | + | 0.705382i | ||||
\(796\) | −86.4273 | −3.06333 | ||||||||
\(797\) | 10.8428i | 0.384072i | 0.981388 | + | 0.192036i | \(0.0615091\pi\) | ||||
−0.981388 | + | 0.192036i | \(0.938491\pi\) | |||||||
\(798\) | 11.2817 | + | 11.2817i | 0.399367 | + | 0.399367i | ||||
\(799\) | 34.1812 | + | 34.1812i | 1.20924 | + | 1.20924i | ||||
\(800\) | 10.0324 | − | 10.0324i | 0.354699 | − | 0.354699i | ||||
\(801\) | −5.52141 | − | 5.52141i | −0.195089 | − | 0.195089i | ||||
\(802\) | − | 1.92418i | − | 0.0679450i | ||||||
\(803\) | −11.7147 | + | 0.609970i | −0.413404 | + | 0.0215254i | ||||
\(804\) | 21.0090 | + | 21.0090i | 0.740929 | + | 0.740929i | ||||
\(805\) | −19.1565 | −0.675176 | ||||||||
\(806\) | 0.507265 | + | 3.26192i | 0.0178676 | + | 0.114896i | ||||
\(807\) | −20.2722 | −0.713616 | ||||||||
\(808\) | 16.6416 | − | 16.6416i | 0.585450 | − | 0.585450i | ||||
\(809\) | 53.1019i | 1.86696i | 0.358627 | + | 0.933481i | \(0.383245\pi\) | ||||
−0.358627 | + | 0.933481i | \(0.616755\pi\) | |||||||
\(810\) | 7.10448 | 0.249626 | ||||||||
\(811\) | 26.2176 | + | 26.2176i | 0.920623 | + | 0.920623i | 0.997073 | − | 0.0764500i | \(-0.0243586\pi\) |
−0.0764500 | + | 0.997073i | \(0.524359\pi\) | |||||||
\(812\) | −16.5421 | + | 16.5421i | −0.580516 | + | 0.580516i | ||||
\(813\) | 1.35380 | − | 1.35380i | 0.0474798 | − | 0.0474798i | ||||
\(814\) | 42.6350 | − | 47.3188i | 1.49436 | − | 1.65852i | ||||
\(815\) | 31.1178 | 1.09001 | ||||||||
\(816\) | −11.2631 | −0.394288 | ||||||||
\(817\) | 6.29379 | + | 6.29379i | 0.220192 | + | 0.220192i | ||||
\(818\) | 23.0670i | 0.806520i | ||||||||
\(819\) | 5.64783 | + | 4.12763i | 0.197351 | + | 0.144231i | ||||
\(820\) | 14.9060i | 0.520541i | ||||||||
\(821\) | 24.6705 | + | 24.6705i | 0.861007 | + | 0.861007i | 0.991455 | − | 0.130448i | \(-0.0416416\pi\) |
−0.130448 | + | 0.991455i | \(0.541642\pi\) | |||||||
\(822\) | 27.0410i | 0.943164i | ||||||||
\(823\) | − | 0.0943442i | − | 0.00328863i | −0.999999 | − | 0.00164432i | \(-0.999477\pi\) | ||
0.999999 | − | 0.00164432i | \(-0.000523402\pi\) | |||||||
\(824\) | 30.6159 | + | 30.6159i | 1.06655 | + | 1.06655i | ||||
\(825\) | −8.96252 | + | 9.94712i | −0.312035 | + | 0.346314i | ||||
\(826\) | −13.3058 | − | 13.3058i | −0.462967 | − | 0.462967i | ||||
\(827\) | 19.5041 | − | 19.5041i | 0.678225 | − | 0.678225i | −0.281373 | − | 0.959598i | \(-0.590790\pi\) |
0.959598 | + | 0.281373i | \(0.0907899\pi\) | |||||||
\(828\) | 11.7755 | 0.409226 | ||||||||
\(829\) | 0.226343i | 0.00786123i | 0.999992 | + | 0.00393061i | \(0.00125116\pi\) | ||||
−0.999992 | + | 0.00393061i | \(0.998749\pi\) | |||||||
\(830\) | −78.8990 | − | 78.8990i | −2.73862 | − | 2.73862i | ||||
\(831\) | 17.7086 | 0.614303 | ||||||||
\(832\) | −41.5857 | + | 6.46704i | −1.44172 | + | 0.224204i | ||||
\(833\) | − | 21.6503i | − | 0.750138i | ||||||
\(834\) | 5.15054 | − | 5.15054i | 0.178349 | − | 0.178349i | ||||
\(835\) | − | 13.6702i | − | 0.473076i | ||||||
\(836\) | 41.3192 | − | 2.15144i | 1.42906 | − | 0.0744090i | ||||
\(837\) | −0.273940 | + | 0.273940i | −0.00946875 | + | 0.00946875i | ||||
\(838\) | 0.266056 | + | 0.266056i | 0.00919075 | + | 0.00919075i | ||||
\(839\) | −38.0409 | − | 38.0409i | −1.31332 | − | 1.31332i | −0.918954 | − | 0.394365i | \(-0.870965\pi\) |
−0.394365 | − | 0.918954i | \(-0.629035\pi\) | |||||||
\(840\) | −15.4506 | − | 15.4506i | −0.533096 | − | 0.533096i | ||||
\(841\) | 17.6889 | 0.609963 | ||||||||
\(842\) | 6.30349 | 0.217233 | ||||||||
\(843\) | −11.6127 | + | 11.6127i | −0.399964 | + | 0.399964i | ||||
\(844\) | −27.7861 | −0.956437 | ||||||||
\(845\) | −17.9370 | + | 34.7206i | −0.617052 | + | 1.19442i | ||||
\(846\) | − | 17.0739i | − | 0.587013i | ||||||
\(847\) | 16.5767 | + | 13.4421i | 0.569581 | + | 0.461876i | ||||
\(848\) | −15.7500 | −0.540856 | ||||||||
\(849\) | −18.8088 | −0.645517 | ||||||||
\(850\) | −45.1393 | + | 45.1393i | −1.54826 | + | 1.54826i | ||||
\(851\) | −18.8723 | + | 18.8723i | −0.646934 | + | 0.646934i | ||||
\(852\) | −41.6445 | − | 41.6445i | −1.42672 | − | 1.42672i | ||||
\(853\) | −17.6673 | + | 17.6673i | −0.604915 | + | 0.604915i | −0.941613 | − | 0.336698i | \(-0.890690\pi\) |
0.336698 | + | 0.941613i | \(0.390690\pi\) | |||||||
\(854\) | 31.4974i | 1.07782i | ||||||||
\(855\) | −10.4602 | −0.357732 | ||||||||
\(856\) | −25.3269 | − | 25.3269i | −0.865656 | − | 0.865656i | ||||
\(857\) | −10.0523 | −0.343380 | −0.171690 | − | 0.985151i | \(-0.554923\pi\) | ||||
−0.171690 | + | 0.985151i | \(0.554923\pi\) | |||||||
\(858\) | 27.6618 | − | 5.78890i | 0.944358 | − | 0.197630i | ||||
\(859\) | −26.5447 | −0.905692 | −0.452846 | − | 0.891589i | \(-0.649591\pi\) | ||||
−0.452846 | + | 0.891589i | \(0.649591\pi\) | |||||||
\(860\) | −19.4945 | − | 19.4945i | −0.664756 | − | 0.664756i | ||||
\(861\) | −2.68333 | −0.0914476 | ||||||||
\(862\) | − | 58.4845i | − | 1.99199i | ||||||
\(863\) | 2.19810 | − | 2.19810i | 0.0748241 | − | 0.0748241i | −0.668704 | − | 0.743528i | \(-0.733151\pi\) |
0.743528 | + | 0.668704i | \(0.233151\pi\) | |||||||
\(864\) | −2.48510 | − | 2.48510i | −0.0845449 | − | 0.0845449i | ||||
\(865\) | 50.2427 | − | 50.2427i | 1.70830 | − | 1.70830i | ||||
\(866\) | 0.560381 | − | 0.560381i | 0.0190425 | − | 0.0190425i | ||||
\(867\) | −27.7692 | −0.943092 | ||||||||
\(868\) | 2.69479 | 0.0914672 | ||||||||
\(869\) | −0.871439 | + | 0.967173i | −0.0295615 | + | 0.0328091i | ||||
\(870\) | − | 23.8938i | − | 0.810074i | ||||||
\(871\) | −24.1239 | − | 17.6306i | −0.817406 | − | 0.597389i | ||||
\(872\) | 67.7291 | 2.29360 | ||||||||
\(873\) | −8.21511 | + | 8.21511i | −0.278040 | + | 0.278040i | ||||
\(874\) | −27.0092 | −0.913600 | ||||||||
\(875\) | 5.61660 | 0.189876 | ||||||||
\(876\) | 8.96652 | + | 8.96652i | 0.302951 | + | 0.302951i | ||||
\(877\) | −26.2528 | − | 26.2528i | −0.886495 | − | 0.886495i | 0.107689 | − | 0.994185i | \(-0.465655\pi\) |
−0.994185 | + | 0.107689i | \(0.965655\pi\) | |||||||
\(878\) | 31.0939 | + | 31.0939i | 1.04937 | + | 1.04937i | ||||
\(879\) | −22.4031 | + | 22.4031i | −0.755639 | + | 0.755639i | ||||
\(880\) | −16.7606 | + | 0.872703i | −0.565000 | + | 0.0294188i | ||||
\(881\) | 11.9563i | 0.402817i | 0.979507 | + | 0.201409i | \(0.0645519\pi\) | ||||
−0.979507 | + | 0.201409i | \(0.935448\pi\) | |||||||
\(882\) | −5.40728 | + | 5.40728i | −0.182073 | + | 0.182073i | ||||
\(883\) | − | 18.2558i | − | 0.614358i | −0.951652 | − | 0.307179i | \(-0.900615\pi\) | ||
0.951652 | − | 0.307179i | \(-0.0993851\pi\) | |||||||
\(884\) | 85.4648 | − | 13.2907i | 2.87449 | − | 0.447016i | ||||
\(885\) | 12.3369 | 0.414702 | ||||||||
\(886\) | 41.8764 | + | 41.8764i | 1.40687 | + | 1.40687i | ||||
\(887\) | 10.9503i | 0.367675i | 0.982957 | + | 0.183837i | \(0.0588520\pi\) | ||||
−0.982957 | + | 0.183837i | \(0.941148\pi\) | |||||||
\(888\) | −30.4428 | −1.02159 | ||||||||
\(889\) | −5.17498 | + | 5.17498i | −0.173563 | + | 0.173563i | ||||
\(890\) | −39.2268 | − | 39.2268i | −1.31488 | − | 1.31488i | ||||
\(891\) | 2.46398 | + | 2.22009i | 0.0825465 | + | 0.0743758i | ||||
\(892\) | 24.3113 | + | 24.3113i | 0.814004 | + | 0.814004i | ||||
\(893\) | 25.1386i | 0.841232i | ||||||||
\(894\) | − | 45.9643i | − | 1.53728i | ||||||
\(895\) | 15.6316 | + | 15.6316i | 0.522507 | + | 0.522507i | ||||
\(896\) | 39.8832i | 1.33240i | ||||||||
\(897\) | −11.7016 | + | 1.81973i | −0.390706 | + | 0.0607591i | ||||
\(898\) | − | 43.3426i | − | 1.44636i | ||||||
\(899\) | 0.921314 | + | 0.921314i | 0.0307275 | + | 0.0307275i | ||||
\(900\) | 14.4735 | 0.482452 | ||||||||
\(901\) | −62.6038 | −2.08563 | ||||||||
\(902\) | −7.25646 | + | 8.05363i | −0.241614 | + | 0.268157i | ||||
\(903\) | 3.50932 | − | 3.50932i | 0.116783 | − | 0.116783i | ||||
\(904\) | −38.9550 | + | 38.9550i | −1.29562 | + | 1.29562i | ||||
\(905\) | 46.3970 | + | 46.3970i | 1.54229 | + | 1.54229i | ||||
\(906\) | −16.3907 | −0.544545 | ||||||||
\(907\) | 14.9510i | 0.496440i | 0.968704 | + | 0.248220i | \(0.0798455\pi\) | ||||
−0.968704 | + | 0.248220i | \(0.920154\pi\) | |||||||
\(908\) | −2.09048 | + | 2.09048i | −0.0693751 | + | 0.0693751i | ||||
\(909\) | −6.28207 | −0.208363 | ||||||||
\(910\) | 40.1249 | + | 29.3247i | 1.33013 | + | 0.972104i | ||||
\(911\) | 55.6492 | 1.84374 | 0.921870 | − | 0.387500i | \(-0.126661\pi\) | ||||
0.921870 | + | 0.387500i | \(0.126661\pi\) | |||||||
\(912\) | −4.14174 | − | 4.14174i | −0.137147 | − | 0.137147i | ||||
\(913\) | −2.70856 | − | 52.0190i | −0.0896403 | − | 1.72158i | ||||
\(914\) | − | 41.5442i | − | 1.37416i | ||||||
\(915\) | −14.6020 | − | 14.6020i | −0.482727 | − | 0.482727i | ||||
\(916\) | −17.0764 | + | 17.0764i | −0.564219 | + | 0.564219i | ||||
\(917\) | −30.0023 | − | 30.0023i | −0.990763 | − | 0.990763i | ||||
\(918\) | 11.1814 | + | 11.1814i | 0.369040 | + | 0.369040i | ||||
\(919\) | 38.7745i | 1.27905i | 0.768770 | + | 0.639526i | \(0.220869\pi\) | ||||
−0.768770 | + | 0.639526i | \(0.779131\pi\) | |||||||
\(920\) | 36.9899 | 1.21952 | ||||||||
\(921\) | −13.3054 | + | 13.3054i | −0.438427 | + | 0.438427i | ||||
\(922\) | 66.6974i | 2.19656i | ||||||||
\(923\) | 47.8188 | + | 34.9477i | 1.57398 | + | 1.15032i | ||||
\(924\) | −1.19961 | − | 23.0390i | −0.0394642 | − | 0.757927i | ||||
\(925\) | −23.1965 | + | 23.1965i | −0.762695 | + | 0.762695i | ||||
\(926\) | 3.05737i | 0.100472i | ||||||||
\(927\) | − | 11.5572i | − | 0.379589i | ||||||
\(928\) | −8.35789 | + | 8.35789i | −0.274361 | + | 0.274361i | ||||
\(929\) | 29.6889 | − | 29.6889i | 0.974063 | − | 0.974063i | −0.0256095 | − | 0.999672i | \(-0.508153\pi\) |
0.999672 | + | 0.0256095i | \(0.00815265\pi\) | |||||||
\(930\) | −1.94620 | + | 1.94620i | −0.0638185 | + | 0.0638185i | ||||
\(931\) | 7.96137 | − | 7.96137i | 0.260923 | − | 0.260923i | ||||
\(932\) | − | 41.5010i | − | 1.35941i | ||||||
\(933\) | − | 13.0705i | − | 0.427909i | ||||||
\(934\) | 18.3751 | − | 18.3751i | 0.601253 | − | 0.601253i | ||||
\(935\) | −66.6209 | + | 3.46886i | −2.17874 | + | 0.113444i | ||||
\(936\) | −10.9056 | − | 7.97020i | −0.356461 | − | 0.260514i | ||||
\(937\) | − | 14.2474i | − | 0.465442i | −0.972544 | − | 0.232721i | \(-0.925237\pi\) | ||
0.972544 | − | 0.232721i | \(-0.0747629\pi\) | |||||||
\(938\) | −26.8689 | + | 26.8689i | −0.877300 | + | 0.877300i | ||||
\(939\) | 11.5886 | 0.378180 | ||||||||
\(940\) | − | 77.8646i | − | 2.53966i | ||||||
\(941\) | −26.8870 | − | 26.8870i | −0.876492 | − | 0.876492i | 0.116678 | − | 0.993170i | \(-0.462776\pi\) |
−0.993170 | + | 0.116678i | \(0.962776\pi\) | |||||||
\(942\) | −11.0573 | − | 11.0573i | −0.360266 | − | 0.360266i | ||||
\(943\) | 3.21205 | − | 3.21205i | 0.104599 | − | 0.104599i | ||||
\(944\) | 4.88483 | + | 4.88483i | 0.158988 | + | 0.158988i | ||||
\(945\) | 5.83246i | 0.189730i | ||||||||
\(946\) | −1.04257 | − | 20.0229i | −0.0338967 | − | 0.651001i | ||||
\(947\) | 27.0448 | + | 27.0448i | 0.878839 | + | 0.878839i | 0.993415 | − | 0.114576i | \(-0.0365509\pi\) |
−0.114576 | + | 0.993415i | \(0.536551\pi\) | |||||||
\(948\) | 1.40728 | 0.0457064 | ||||||||
\(949\) | −10.2959 | − | 7.52464i | −0.334220 | − | 0.244260i | ||||
\(950\) | −33.1978 | −1.07708 | ||||||||
\(951\) | 17.1628 | − | 17.1628i | 0.556540 | − | 0.556540i | ||||
\(952\) | − | 48.6337i | − | 1.57623i | ||||||
\(953\) | −23.3736 | −0.757146 | −0.378573 | − | 0.925571i | \(-0.623585\pi\) | ||||
−0.378573 | + | 0.925571i | \(0.623585\pi\) | |||||||
\(954\) | 15.6356 | + | 15.6356i | 0.506222 | + | 0.506222i | ||||
\(955\) | −14.5456 | + | 14.5456i | −0.470685 | + | 0.470685i | ||||
\(956\) | −57.5113 | + | 57.5113i | −1.86005 | + | 1.86005i | ||||
\(957\) | 7.46659 | − | 8.28685i | 0.241361 | − | 0.267876i | ||||
\(958\) | −4.61084 | −0.148969 | ||||||||
\(959\) | −22.1995 | −0.716858 | ||||||||
\(960\) | −24.8118 | − | 24.8118i | −0.800797 | − | 0.800797i | ||||
\(961\) | 30.8499i | 0.995159i | ||||||||
\(962\) | 68.4194 | − | 10.6400i | 2.20593 | − | 0.343047i | ||||
\(963\) | 9.56070i | 0.308089i | ||||||||
\(964\) | −57.5357 | − | 57.5357i | −1.85310 | − | 1.85310i | ||||
\(965\) | 1.90834i | 0.0614316i | ||||||||
\(966\) | 15.0599i | 0.484545i | ||||||||
\(967\) | 18.7976 | + | 18.7976i | 0.604490 | + | 0.604490i | 0.941501 | − | 0.337011i | \(-0.109416\pi\) |
−0.337011 | + | 0.941501i | \(0.609416\pi\) | |||||||
\(968\) | −32.0085 | − | 25.9558i | −1.02879 | − | 0.834252i | ||||
\(969\) | −16.4628 | − | 16.4628i | −0.528861 | − | 0.528861i | ||||
\(970\) | −58.3641 | + | 58.3641i | −1.87396 | + | 1.87396i | ||||
\(971\) | −19.8860 | −0.638171 | −0.319086 | − | 0.947726i | \(-0.603376\pi\) | ||||
−0.319086 | + | 0.947726i | \(0.603376\pi\) | |||||||
\(972\) | − | 3.58521i | − | 0.114996i | ||||||
\(973\) | 4.22837 | + | 4.22837i | 0.135555 | + | 0.135555i | ||||
\(974\) | 10.1844 | 0.326329 | ||||||||
\(975\) | −14.3828 | + | 2.23668i | −0.460617 | + | 0.0716312i | ||||
\(976\) | − | 11.5634i | − | 0.370134i | ||||||
\(977\) | 8.66382 | − | 8.66382i | 0.277180 | − | 0.277180i | −0.554802 | − | 0.831982i | \(-0.687206\pi\) |
0.831982 | + | 0.554802i | \(0.187206\pi\) | |||||||
\(978\) | − | 24.4634i | − | 0.782253i | ||||||
\(979\) | −1.34664 | − | 25.8627i | −0.0430386 | − | 0.826575i | ||||
\(980\) | −24.6596 | + | 24.6596i | −0.787723 | + | 0.787723i | ||||
\(981\) | −12.7836 | − | 12.7836i | −0.408149 | − | 0.408149i | ||||
\(982\) | −12.7424 | − | 12.7424i | −0.406627 | − | 0.406627i | ||||
\(983\) | −32.0373 | − | 32.0373i | −1.02183 | − | 1.02183i | −0.999756 | − | 0.0220744i | \(-0.992973\pi\) |
−0.0220744 | − | 0.999756i | \(-0.507027\pi\) | |||||||
\(984\) | 5.18134 | 0.165175 | ||||||||
\(985\) | 25.2404 | 0.804226 | ||||||||
\(986\) | 37.6051 | − | 37.6051i | 1.19759 | − | 1.19759i | ||||
\(987\) | 14.0169 | 0.446163 | ||||||||
\(988\) | 36.3150 | + | 26.5403i | 1.15533 | + | 0.844359i | ||||
\(989\) | 8.40160i | 0.267155i | ||||||||
\(990\) | 17.5053 | + | 15.7726i | 0.556355 | + | 0.501285i | ||||
\(991\) | −55.8304 | −1.77351 | −0.886755 | − | 0.462239i | \(-0.847046\pi\) | ||||
−0.886755 | + | 0.462239i | \(0.847046\pi\) | |||||||
\(992\) | 1.36154 | 0.0432289 | ||||||||
\(993\) | −13.0175 | + | 13.0175i | −0.413096 | + | 0.413096i | ||||
\(994\) | 53.2601 | − | 53.2601i | 1.68931 | − | 1.68931i | ||||
\(995\) | 51.2429 | + | 51.2429i | 1.62451 | + | 1.62451i | ||||
\(996\) | −39.8157 | + | 39.8157i | −1.26161 | + | 1.26161i | ||||
\(997\) | − | 21.2850i | − | 0.674103i | −0.941486 | − | 0.337052i | \(-0.890570\pi\) | ||
0.941486 | − | 0.337052i | \(-0.109430\pi\) | |||||||
\(998\) | −0.606074 | −0.0191850 | ||||||||
\(999\) | 5.74595 | + | 5.74595i | 0.181794 | + | 0.181794i |
(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 | 429.2.m.a.109.13 | yes | 28 | |
11.10 | odd | 2 | inner | 429.2.m.a.109.2 | ✓ | 28 | |
13.8 | odd | 4 | inner | 429.2.m.a.307.2 | yes | 28 | |
143.21 | even | 4 | inner | 429.2.m.a.307.13 | yes | 28 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
429.2.m.a.109.2 | ✓ | 28 | 11.10 | odd | 2 | inner | |
429.2.m.a.109.13 | yes | 28 | 1.1 | even | 1 | trivial | |
429.2.m.a.307.2 | yes | 28 | 13.8 | odd | 4 | inner | |
429.2.m.a.307.13 | yes | 28 | 143.21 | even | 4 | inner |