Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [731,2,Mod(259,731)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(731, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([3, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("731.259");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 731 = 17 \cdot 43 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 731.f (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: | \(5.83706438776\) |
Analytic rank: | \(0\) |
Dimension: | \(56\) |
Relative dimension: | \(28\) over \(\Q(i)\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 259.6 | ||
Character | \(\chi\) | \(=\) | 731.259 |
Dual form | 731.2.f.c.302.23 |
$q$-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 \(\left(\mathbb{Z}/731\mathbb{Z}\right)^\times\).
\(n\) | \(173\) | \(562\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 2.09057i | − | 1.47825i | −0.673567 | − | 0.739126i | \(-0.735239\pi\) | ||
0.673567 | − | 0.739126i | \(-0.264761\pi\) | |||||||
\(3\) | 2.10973 | − | 2.10973i | 1.21805 | − | 1.21805i | 0.249738 | − | 0.968313i | \(-0.419655\pi\) |
0.968313 | − | 0.249738i | \(-0.0803446\pi\) | |||||||
\(4\) | −2.37046 | −1.18523 | ||||||||
\(5\) | 0.614601 | − | 0.614601i | 0.274858 | − | 0.274858i | −0.556194 | − | 0.831052i | \(-0.687739\pi\) |
0.831052 | + | 0.556194i | \(0.187739\pi\) | |||||||
\(6\) | −4.41052 | − | 4.41052i | −1.80059 | − | 1.80059i | ||||
\(7\) | 0.361953 | + | 0.361953i | 0.136805 | + | 0.136805i | 0.772193 | − | 0.635388i | \(-0.219160\pi\) |
−0.635388 | + | 0.772193i | \(0.719160\pi\) | |||||||
\(8\) | 0.774475i | 0.273818i | ||||||||
\(9\) | − | 5.90190i | − | 1.96730i | ||||||
\(10\) | −1.28486 | − | 1.28486i | −0.406309 | − | 0.406309i | ||||
\(11\) | 2.58266 | + | 2.58266i | 0.778703 | + | 0.778703i | 0.979610 | − | 0.200908i | \(-0.0643891\pi\) |
−0.200908 | + | 0.979610i | \(0.564389\pi\) | |||||||
\(12\) | −5.00103 | + | 5.00103i | −1.44367 | + | 1.44367i | ||||
\(13\) | 3.15824 | 0.875939 | 0.437969 | − | 0.898990i | \(-0.355698\pi\) | ||||
0.437969 | + | 0.898990i | \(0.355698\pi\) | |||||||
\(14\) | 0.756686 | − | 0.756686i | 0.202233 | − | 0.202233i | ||||
\(15\) | − | 2.59328i | − | 0.669582i | ||||||
\(16\) | −3.12183 | −0.780458 | ||||||||
\(17\) | −2.89763 | − | 2.93321i | −0.702779 | − | 0.711409i | ||||
\(18\) | −12.3383 | −2.90817 | ||||||||
\(19\) | − | 3.80968i | − | 0.874000i | −0.899461 | − | 0.437000i | \(-0.856041\pi\) | ||
0.899461 | − | 0.437000i | \(-0.143959\pi\) | |||||||
\(20\) | −1.45689 | + | 1.45689i | −0.325770 | + | 0.325770i | ||||
\(21\) | 1.52724 | 0.333272 | ||||||||
\(22\) | 5.39923 | − | 5.39923i | 1.15112 | − | 1.15112i | ||||
\(23\) | 5.66072 | + | 5.66072i | 1.18034 | + | 1.18034i | 0.979656 | + | 0.200685i | \(0.0643168\pi\) |
0.200685 | + | 0.979656i | \(0.435683\pi\) | |||||||
\(24\) | 1.63393 | + | 1.63393i | 0.333525 | + | 0.333525i | ||||
\(25\) | 4.24453i | 0.848906i | ||||||||
\(26\) | − | 6.60251i | − | 1.29486i | ||||||
\(27\) | −6.12222 | − | 6.12222i | −1.17822 | − | 1.17822i | ||||
\(28\) | −0.857995 | − | 0.857995i | −0.162146 | − | 0.162146i | ||||
\(29\) | −7.39798 | + | 7.39798i | −1.37377 | + | 1.37377i | −0.518988 | + | 0.854781i | \(0.673691\pi\) |
−0.854781 | + | 0.518988i | \(0.826309\pi\) | |||||||
\(30\) | −5.42142 | −0.989812 | ||||||||
\(31\) | −5.78436 | + | 5.78436i | −1.03890 | + | 1.03890i | −0.0396901 | + | 0.999212i | \(0.512637\pi\) |
−0.999212 | + | 0.0396901i | \(0.987363\pi\) | |||||||
\(32\) | 8.07535i | 1.42753i | ||||||||
\(33\) | 10.8974 | 1.89700 | ||||||||
\(34\) | −6.13207 | + | 6.05769i | −1.05164 | + | 1.03888i | ||||
\(35\) | 0.444913 | 0.0752040 | ||||||||
\(36\) | 13.9902i | 2.33170i | ||||||||
\(37\) | −0.561554 | + | 0.561554i | −0.0923189 | + | 0.0923189i | −0.751758 | − | 0.659439i | \(-0.770794\pi\) |
0.659439 | + | 0.751758i | \(0.270794\pi\) | |||||||
\(38\) | −7.96438 | −1.29199 | ||||||||
\(39\) | 6.66303 | − | 6.66303i | 1.06694 | − | 1.06694i | ||||
\(40\) | 0.475993 | + | 0.475993i | 0.0752611 | + | 0.0752611i | ||||
\(41\) | 4.80148 | + | 4.80148i | 0.749864 | + | 0.749864i | 0.974454 | − | 0.224589i | \(-0.0721040\pi\) |
−0.224589 | + | 0.974454i | \(0.572104\pi\) | |||||||
\(42\) | − | 3.19280i | − | 0.492660i | ||||||
\(43\) | 1.00000i | 0.152499i | ||||||||
\(44\) | −6.12211 | − | 6.12211i | −0.922943 | − | 0.922943i | ||||
\(45\) | −3.62731 | − | 3.62731i | −0.540728 | − | 0.540728i | ||||
\(46\) | 11.8341 | − | 11.8341i | 1.74484 | − | 1.74484i | ||||
\(47\) | 0.314930 | 0.0459373 | 0.0229686 | − | 0.999736i | \(-0.492688\pi\) | ||||
0.0229686 | + | 0.999736i | \(0.492688\pi\) | |||||||
\(48\) | −6.58622 | + | 6.58622i | −0.950639 | + | 0.950639i | ||||
\(49\) | − | 6.73798i | − | 0.962569i | ||||||
\(50\) | 8.87347 | 1.25490 | ||||||||
\(51\) | −12.3015 | − | 0.0750672i | −1.72255 | − | 0.0105115i | ||||
\(52\) | −7.48649 | −1.03819 | ||||||||
\(53\) | − | 13.7069i | − | 1.88279i | −0.337309 | − | 0.941394i | \(-0.609517\pi\) | ||
0.337309 | − | 0.941394i | \(-0.390483\pi\) | |||||||
\(54\) | −12.7989 | + | 12.7989i | −1.74171 | + | 1.74171i | ||||
\(55\) | 3.17462 | 0.428065 | ||||||||
\(56\) | −0.280323 | + | 0.280323i | −0.0374598 | + | 0.0374598i | ||||
\(57\) | −8.03738 | − | 8.03738i | −1.06458 | − | 1.06458i | ||||
\(58\) | 15.4659 | + | 15.4659i | 2.03078 | + | 2.03078i | ||||
\(59\) | − | 0.208025i | − | 0.0270826i | −0.999908 | − | 0.0135413i | \(-0.995690\pi\) | ||
0.999908 | − | 0.0135413i | \(-0.00431046\pi\) | |||||||
\(60\) | 6.14728i | 0.793610i | ||||||||
\(61\) | 7.40409 | + | 7.40409i | 0.947996 | + | 0.947996i | 0.998713 | − | 0.0507170i | \(-0.0161507\pi\) |
−0.0507170 | + | 0.998713i | \(0.516151\pi\) | |||||||
\(62\) | 12.0926 | + | 12.0926i | 1.53576 | + | 1.53576i | ||||
\(63\) | 2.13621 | − | 2.13621i | 0.269137 | − | 0.269137i | ||||
\(64\) | 10.6384 | 1.32980 | ||||||||
\(65\) | 1.94106 | − | 1.94106i | 0.240759 | − | 0.240759i | ||||
\(66\) | − | 22.7818i | − | 2.80425i | ||||||
\(67\) | 7.38083 | 0.901711 | 0.450856 | − | 0.892597i | \(-0.351119\pi\) | ||||
0.450856 | + | 0.892597i | \(0.351119\pi\) | |||||||
\(68\) | 6.86872 | + | 6.95307i | 0.832955 | + | 0.843183i | ||||
\(69\) | 23.8851 | 2.87543 | ||||||||
\(70\) | − | 0.930120i | − | 0.111171i | ||||||
\(71\) | −10.8478 | + | 10.8478i | −1.28739 | + | 1.28739i | −0.351030 | + | 0.936364i | \(0.614168\pi\) |
−0.936364 | + | 0.351030i | \(0.885832\pi\) | |||||||
\(72\) | 4.57088 | 0.538683 | ||||||||
\(73\) | 5.70503 | − | 5.70503i | 0.667724 | − | 0.667724i | −0.289465 | − | 0.957189i | \(-0.593477\pi\) |
0.957189 | + | 0.289465i | \(0.0934774\pi\) | |||||||
\(74\) | 1.17397 | + | 1.17397i | 0.136471 | + | 0.136471i | ||||
\(75\) | 8.95480 | + | 8.95480i | 1.03401 | + | 1.03401i | ||||
\(76\) | 9.03070i | 1.03589i | ||||||||
\(77\) | 1.86960i | 0.213061i | ||||||||
\(78\) | −13.9295 | − | 13.9295i | −1.57720 | − | 1.57720i | ||||
\(79\) | −9.50340 | − | 9.50340i | −1.06922 | − | 1.06922i | −0.997419 | − | 0.0717973i | \(-0.977127\pi\) |
−0.0717973 | − | 0.997419i | \(-0.522873\pi\) | |||||||
\(80\) | −1.91868 | + | 1.91868i | −0.214515 | + | 0.214515i | ||||
\(81\) | −8.12672 | −0.902969 | ||||||||
\(82\) | 10.0378 | − | 10.0378i | 1.10849 | − | 1.10849i | ||||
\(83\) | 1.37119i | 0.150508i | 0.997164 | + | 0.0752539i | \(0.0239767\pi\) | ||||
−0.997164 | + | 0.0752539i | \(0.976023\pi\) | |||||||
\(84\) | −3.62027 | −0.395004 | ||||||||
\(85\) | −3.58364 | − | 0.0218684i | −0.388701 | − | 0.00237196i | ||||
\(86\) | 2.09057 | 0.225431 | ||||||||
\(87\) | 31.2154i | 3.34664i | ||||||||
\(88\) | −2.00021 | + | 2.00021i | −0.213223 | + | 0.213223i | ||||
\(89\) | −14.0931 | −1.49386 | −0.746930 | − | 0.664902i | \(-0.768473\pi\) | ||||
−0.746930 | + | 0.664902i | \(0.768473\pi\) | |||||||
\(90\) | −7.58313 | + | 7.58313i | −0.799333 | + | 0.799333i | ||||
\(91\) | 1.14313 | + | 1.14313i | 0.119833 | + | 0.119833i | ||||
\(92\) | −13.4185 | − | 13.4185i | −1.39898 | − | 1.39898i | ||||
\(93\) | 24.4069i | 2.53087i | ||||||||
\(94\) | − | 0.658382i | − | 0.0679069i | ||||||
\(95\) | −2.34143 | − | 2.34143i | −0.240226 | − | 0.240226i | ||||
\(96\) | 17.0368 | + | 17.0368i | 1.73881 | + | 1.73881i | ||||
\(97\) | 4.97145 | − | 4.97145i | 0.504774 | − | 0.504774i | −0.408143 | − | 0.912918i | \(-0.633824\pi\) |
0.912918 | + | 0.408143i | \(0.133824\pi\) | |||||||
\(98\) | −14.0862 | −1.42292 | ||||||||
\(99\) | 15.2426 | − | 15.2426i | 1.53194 | − | 1.53194i | ||||
\(100\) | − | 10.0615i | − | 1.00615i | ||||||
\(101\) | −3.15654 | −0.314088 | −0.157044 | − | 0.987592i | \(-0.550196\pi\) | ||||
−0.157044 | + | 0.987592i | \(0.550196\pi\) | |||||||
\(102\) | −0.156933 | + | 25.7171i | −0.0155387 | + | 2.54637i | ||||
\(103\) | 10.2693 | 1.01187 | 0.505935 | − | 0.862572i | \(-0.331148\pi\) | ||||
0.505935 | + | 0.862572i | \(0.331148\pi\) | |||||||
\(104\) | 2.44598i | 0.239848i | ||||||||
\(105\) | 0.938645 | − | 0.938645i | 0.0916024 | − | 0.0916024i | ||||
\(106\) | −28.6552 | −2.78324 | ||||||||
\(107\) | 0.853338 | − | 0.853338i | 0.0824953 | − | 0.0824953i | −0.664655 | − | 0.747150i | \(-0.731421\pi\) |
0.747150 | + | 0.664655i | \(0.231421\pi\) | |||||||
\(108\) | 14.5125 | + | 14.5125i | 1.39646 | + | 1.39646i | ||||
\(109\) | −1.45735 | − | 1.45735i | −0.139589 | − | 0.139589i | 0.633859 | − | 0.773448i | \(-0.281470\pi\) |
−0.773448 | + | 0.633859i | \(0.781470\pi\) | |||||||
\(110\) | − | 6.63674i | − | 0.632789i | ||||||
\(111\) | 2.36945i | 0.224898i | ||||||||
\(112\) | −1.12996 | − | 1.12996i | −0.106771 | − | 0.106771i | ||||
\(113\) | −7.70604 | − | 7.70604i | −0.724923 | − | 0.724923i | 0.244680 | − | 0.969604i | \(-0.421317\pi\) |
−0.969604 | + | 0.244680i | \(0.921317\pi\) | |||||||
\(114\) | −16.8027 | + | 16.8027i | −1.57371 | + | 1.57371i | ||||
\(115\) | 6.95816 | 0.648852 | ||||||||
\(116\) | 17.5366 | − | 17.5366i | 1.62823 | − | 1.62823i | ||||
\(117\) | − | 18.6396i | − | 1.72323i | ||||||
\(118\) | −0.434890 | −0.0400349 | ||||||||
\(119\) | 0.0128788 | − | 2.11049i | 0.00118060 | − | 0.193468i | ||||
\(120\) | 2.00843 | 0.183344 | ||||||||
\(121\) | 2.34031i | 0.212756i | ||||||||
\(122\) | 15.4787 | − | 15.4787i | 1.40138 | − | 1.40138i | ||||
\(123\) | 20.2596 | 1.82675 | ||||||||
\(124\) | 13.7116 | − | 13.7116i | 1.23134 | − | 1.23134i | ||||
\(125\) | 5.68170 | + | 5.68170i | 0.508187 | + | 0.508187i | ||||
\(126\) | −4.46588 | − | 4.46588i | −0.397853 | − | 0.397853i | ||||
\(127\) | − | 2.25447i | − | 0.200052i | −0.994985 | − | 0.100026i | \(-0.968107\pi\) | ||
0.994985 | − | 0.100026i | \(-0.0318926\pi\) | |||||||
\(128\) | − | 6.08951i | − | 0.538242i | ||||||
\(129\) | 2.10973 | + | 2.10973i | 0.185751 | + | 0.185751i | ||||
\(130\) | −4.05791 | − | 4.05791i | −0.355902 | − | 0.355902i | ||||
\(131\) | −6.64848 | + | 6.64848i | −0.580880 | + | 0.580880i | −0.935145 | − | 0.354265i | \(-0.884731\pi\) |
0.354265 | + | 0.935145i | \(0.384731\pi\) | |||||||
\(132\) | −25.8320 | −2.24838 | ||||||||
\(133\) | 1.37892 | − | 1.37892i | 0.119568 | − | 0.119568i | ||||
\(134\) | − | 15.4301i | − | 1.33296i | ||||||
\(135\) | −7.52544 | −0.647687 | ||||||||
\(136\) | 2.27170 | − | 2.24414i | 0.194797 | − | 0.192434i | ||||
\(137\) | 11.7398 | 1.00300 | 0.501500 | − | 0.865157i | \(-0.332782\pi\) | ||||
0.501500 | + | 0.865157i | \(0.332782\pi\) | |||||||
\(138\) | − | 49.9334i | − | 4.25062i | ||||||
\(139\) | −6.04278 | + | 6.04278i | −0.512542 | + | 0.512542i | −0.915305 | − | 0.402762i | \(-0.868050\pi\) |
0.402762 | + | 0.915305i | \(0.368050\pi\) | |||||||
\(140\) | −1.05465 | −0.0891342 | ||||||||
\(141\) | 0.664416 | − | 0.664416i | 0.0559540 | − | 0.0559540i | ||||
\(142\) | 22.6780 | + | 22.6780i | 1.90309 | + | 1.90309i | ||||
\(143\) | 8.15668 | + | 8.15668i | 0.682096 | + | 0.682096i | ||||
\(144\) | 18.4247i | 1.53540i | ||||||||
\(145\) | 9.09361i | 0.755183i | ||||||||
\(146\) | −11.9267 | − | 11.9267i | −0.987064 | − | 0.987064i | ||||
\(147\) | −14.2153 | − | 14.2153i | −1.17246 | − | 1.17246i | ||||
\(148\) | 1.33114 | − | 1.33114i | 0.109419 | − | 0.109419i | ||||
\(149\) | −10.5675 | −0.865720 | −0.432860 | − | 0.901461i | \(-0.642496\pi\) | ||||
−0.432860 | + | 0.901461i | \(0.642496\pi\) | |||||||
\(150\) | 18.7206 | − | 18.7206i | 1.52853 | − | 1.52853i | ||||
\(151\) | − | 17.1640i | − | 1.39679i | −0.715715 | − | 0.698393i | \(-0.753899\pi\) | ||
0.715715 | − | 0.698393i | \(-0.246101\pi\) | |||||||
\(152\) | 2.95050 | 0.239317 | ||||||||
\(153\) | −17.3115 | + | 17.1015i | −1.39955 | + | 1.38258i | ||||
\(154\) | 3.90853 | 0.314958 | ||||||||
\(155\) | 7.11015i | 0.571101i | ||||||||
\(156\) | −15.7945 | + | 15.7945i | −1.26457 | + | 1.26457i | ||||
\(157\) | 5.84563 | 0.466532 | 0.233266 | − | 0.972413i | \(-0.425059\pi\) | ||||
0.233266 | + | 0.972413i | \(0.425059\pi\) | |||||||
\(158\) | −19.8675 | + | 19.8675i | −1.58057 | + | 1.58057i | ||||
\(159\) | −28.9178 | − | 28.9178i | −2.29333 | − | 2.29333i | ||||
\(160\) | 4.96312 | + | 4.96312i | 0.392369 | + | 0.392369i | ||||
\(161\) | 4.09782i | 0.322954i | ||||||||
\(162\) | 16.9894i | 1.33482i | ||||||||
\(163\) | −10.8126 | − | 10.8126i | −0.846910 | − | 0.846910i | 0.142836 | − | 0.989746i | \(-0.454378\pi\) |
−0.989746 | + | 0.142836i | \(0.954378\pi\) | |||||||
\(164\) | −11.3817 | − | 11.3817i | −0.888763 | − | 0.888763i | ||||
\(165\) | 6.69758 | − | 6.69758i | 0.521406 | − | 0.521406i | ||||
\(166\) | 2.86657 | 0.222489 | ||||||||
\(167\) | −8.98998 | + | 8.98998i | −0.695666 | + | 0.695666i | −0.963473 | − | 0.267807i | \(-0.913701\pi\) |
0.267807 | + | 0.963473i | \(0.413701\pi\) | |||||||
\(168\) | 1.18281i | 0.0912559i | ||||||||
\(169\) | −3.02551 | −0.232731 | ||||||||
\(170\) | −0.0457173 | + | 7.49184i | −0.00350636 | + | 0.574598i | ||||
\(171\) | −22.4843 | −1.71942 | ||||||||
\(172\) | − | 2.37046i | − | 0.180746i | ||||||
\(173\) | 0.538292 | − | 0.538292i | 0.0409256 | − | 0.0409256i | −0.686348 | − | 0.727273i | \(-0.740787\pi\) |
0.727273 | + | 0.686348i | \(0.240787\pi\) | |||||||
\(174\) | 65.2579 | 4.94719 | ||||||||
\(175\) | −1.53632 | + | 1.53632i | −0.116135 | + | 0.116135i | ||||
\(176\) | −8.06265 | − | 8.06265i | −0.607745 | − | 0.607745i | ||||
\(177\) | −0.438877 | − | 0.438877i | −0.0329880 | − | 0.0329880i | ||||
\(178\) | 29.4624i | 2.20830i | ||||||||
\(179\) | − | 9.13551i | − | 0.682820i | −0.939914 | − | 0.341410i | \(-0.889096\pi\) | ||
0.939914 | − | 0.341410i | \(-0.110904\pi\) | |||||||
\(180\) | 8.59841 | + | 8.59841i | 0.640888 | + | 0.640888i | ||||
\(181\) | −0.316782 | − | 0.316782i | −0.0235462 | − | 0.0235462i | 0.695236 | − | 0.718782i | \(-0.255300\pi\) |
−0.718782 | + | 0.695236i | \(0.755300\pi\) | |||||||
\(182\) | 2.38980 | − | 2.38980i | 0.177144 | − | 0.177144i | ||||
\(183\) | 31.2412 | 2.30942 | ||||||||
\(184\) | −4.38408 | + | 4.38408i | −0.323199 | + | 0.323199i | ||||
\(185\) | 0.690263i | 0.0507492i | ||||||||
\(186\) | 51.0241 | 3.74127 | ||||||||
\(187\) | 0.0918950 | − | 15.0591i | 0.00672003 | − | 1.10123i | ||||
\(188\) | −0.746530 | −0.0544463 | ||||||||
\(189\) | − | 4.43191i | − | 0.322374i | ||||||
\(190\) | −4.89492 | + | 4.89492i | −0.355115 | + | 0.355115i | ||||
\(191\) | 11.5950 | 0.838987 | 0.419493 | − | 0.907758i | \(-0.362208\pi\) | ||||
0.419493 | + | 0.907758i | \(0.362208\pi\) | |||||||
\(192\) | 22.4441 | − | 22.4441i | 1.61976 | − | 1.61976i | ||||
\(193\) | 9.01307 | + | 9.01307i | 0.648775 | + | 0.648775i | 0.952697 | − | 0.303922i | \(-0.0982961\pi\) |
−0.303922 | + | 0.952697i | \(0.598296\pi\) | |||||||
\(194\) | −10.3931 | − | 10.3931i | −0.746184 | − | 0.746184i | ||||
\(195\) | − | 8.19021i | − | 0.586513i | ||||||
\(196\) | 15.9721i | 1.14087i | ||||||||
\(197\) | −9.64370 | − | 9.64370i | −0.687085 | − | 0.687085i | 0.274502 | − | 0.961587i | \(-0.411487\pi\) |
−0.961587 | + | 0.274502i | \(0.911487\pi\) | |||||||
\(198\) | −31.8657 | − | 31.8657i | −2.26460 | − | 2.26460i | ||||
\(199\) | 8.19448 | − | 8.19448i | 0.580891 | − | 0.580891i | −0.354257 | − | 0.935148i | \(-0.615266\pi\) |
0.935148 | + | 0.354257i | \(0.115266\pi\) | |||||||
\(200\) | −3.28728 | −0.232446 | ||||||||
\(201\) | 15.5715 | − | 15.5715i | 1.09833 | − | 1.09833i | ||||
\(202\) | 6.59895i | 0.464301i | ||||||||
\(203\) | −5.35543 | −0.375878 | ||||||||
\(204\) | 29.1602 | + | 0.177944i | 2.04162 | + | 0.0124586i | ||||
\(205\) | 5.90198 | 0.412212 | ||||||||
\(206\) | − | 21.4687i | − | 1.49580i | ||||||
\(207\) | 33.4090 | − | 33.4090i | 2.32208 | − | 2.32208i | ||||
\(208\) | −9.85951 | −0.683634 | ||||||||
\(209\) | 9.83912 | − | 9.83912i | 0.680586 | − | 0.680586i | ||||
\(210\) | −1.96230 | − | 1.96230i | −0.135411 | − | 0.135411i | ||||
\(211\) | 4.08646 | + | 4.08646i | 0.281324 | + | 0.281324i | 0.833637 | − | 0.552313i | \(-0.186255\pi\) |
−0.552313 | + | 0.833637i | \(0.686255\pi\) | |||||||
\(212\) | 32.4917i | 2.23154i | ||||||||
\(213\) | 45.7717i | 3.13623i | ||||||||
\(214\) | −1.78396 | − | 1.78396i | −0.121949 | − | 0.121949i | ||||
\(215\) | 0.614601 | + | 0.614601i | 0.0419154 | + | 0.0419154i | ||||
\(216\) | 4.74151 | − | 4.74151i | 0.322619 | − | 0.322619i | ||||
\(217\) | −4.18733 | −0.284255 | ||||||||
\(218\) | −3.04669 | + | 3.04669i | −0.206348 | + | 0.206348i | ||||
\(219\) | − | 24.0721i | − | 1.62664i | ||||||
\(220\) | −7.52531 | −0.507356 | ||||||||
\(221\) | −9.15142 | − | 9.26379i | −0.615591 | − | 0.623150i | ||||
\(222\) | 4.95349 | 0.332457 | ||||||||
\(223\) | 12.8406i | 0.859872i | 0.902859 | + | 0.429936i | \(0.141464\pi\) | ||||
−0.902859 | + | 0.429936i | \(0.858536\pi\) | |||||||
\(224\) | −2.92289 | + | 2.92289i | −0.195294 | + | 0.195294i | ||||
\(225\) | 25.0508 | 1.67005 | ||||||||
\(226\) | −16.1100 | + | 16.1100i | −1.07162 | + | 1.07162i | ||||
\(227\) | −13.0830 | − | 13.0830i | −0.868346 | − | 0.868346i | 0.123943 | − | 0.992289i | \(-0.460446\pi\) |
−0.992289 | + | 0.123943i | \(0.960446\pi\) | |||||||
\(228\) | 19.0523 | + | 19.0523i | 1.26177 | + | 1.26177i | ||||
\(229\) | 17.2477i | 1.13976i | 0.821729 | + | 0.569878i | \(0.193010\pi\) | ||||
−0.821729 | + | 0.569878i | \(0.806990\pi\) | |||||||
\(230\) | − | 14.5465i | − | 0.959167i | ||||||
\(231\) | 3.94436 | + | 3.94436i | 0.259520 | + | 0.259520i | ||||
\(232\) | −5.72955 | − | 5.72955i | −0.376163 | − | 0.376163i | ||||
\(233\) | −14.3015 | + | 14.3015i | −0.936925 | + | 0.936925i | −0.998125 | − | 0.0612005i | \(-0.980507\pi\) |
0.0612005 | + | 0.998125i | \(0.480507\pi\) | |||||||
\(234\) | −38.9674 | −2.54738 | ||||||||
\(235\) | 0.193556 | − | 0.193556i | 0.0126262 | − | 0.0126262i | ||||
\(236\) | 0.493116i | 0.0320991i | ||||||||
\(237\) | −40.0992 | −2.60472 | ||||||||
\(238\) | −4.41212 | − | 0.0269240i | −0.285995 | − | 0.00174522i | ||||
\(239\) | 20.2213 | 1.30801 | 0.654004 | − | 0.756491i | \(-0.273088\pi\) | ||||
0.654004 | + | 0.756491i | \(0.273088\pi\) | |||||||
\(240\) | 8.09579i | 0.522581i | ||||||||
\(241\) | 4.06077 | − | 4.06077i | 0.261577 | − | 0.261577i | −0.564117 | − | 0.825695i | \(-0.690783\pi\) |
0.825695 | + | 0.564117i | \(0.190783\pi\) | |||||||
\(242\) | 4.89257 | 0.314506 | ||||||||
\(243\) | 1.22149 | − | 1.22149i | 0.0783584 | − | 0.0783584i | ||||
\(244\) | −17.5511 | − | 17.5511i | −1.12359 | − | 1.12359i | ||||
\(245\) | −4.14117 | − | 4.14117i | −0.264570 | − | 0.264570i | ||||
\(246\) | − | 42.3540i | − | 2.70039i | ||||||
\(247\) | − | 12.0319i | − | 0.765571i | ||||||
\(248\) | −4.47985 | − | 4.47985i | −0.284470 | − | 0.284470i | ||||
\(249\) | 2.89284 | + | 2.89284i | 0.183326 | + | 0.183326i | ||||
\(250\) | 11.8780 | − | 11.8780i | 0.751228 | − | 0.751228i | ||||
\(251\) | 12.7565 | 0.805181 | 0.402591 | − | 0.915380i | \(-0.368110\pi\) | ||||
0.402591 | + | 0.915380i | \(0.368110\pi\) | |||||||
\(252\) | −5.06380 | + | 5.06380i | −0.318990 | + | 0.318990i | ||||
\(253\) | 29.2395i | 1.83827i | ||||||||
\(254\) | −4.71312 | −0.295727 | ||||||||
\(255\) | −7.60664 | + | 7.51437i | −0.476347 | + | 0.470568i | ||||
\(256\) | 8.54622 | 0.534139 | ||||||||
\(257\) | − | 21.4390i | − | 1.33733i | −0.743563 | − | 0.668665i | \(-0.766866\pi\) | ||
0.743563 | − | 0.668665i | \(-0.233134\pi\) | |||||||
\(258\) | 4.41052 | − | 4.41052i | 0.274587 | − | 0.274587i | ||||
\(259\) | −0.406512 | −0.0252594 | ||||||||
\(260\) | −4.60121 | + | 4.60121i | −0.285355 | + | 0.285355i | ||||
\(261\) | 43.6621 | + | 43.6621i | 2.70262 | + | 2.70262i | ||||
\(262\) | 13.8991 | + | 13.8991i | 0.858688 | + | 0.858688i | ||||
\(263\) | − | 12.1712i | − | 0.750507i | −0.926922 | − | 0.375253i | \(-0.877556\pi\) | ||
0.926922 | − | 0.375253i | \(-0.122444\pi\) | |||||||
\(264\) | 8.43979i | 0.519433i | ||||||||
\(265\) | −8.42428 | − | 8.42428i | −0.517499 | − | 0.517499i | ||||
\(266\) | −2.88273 | − | 2.88273i | −0.176751 | − | 0.176751i | ||||
\(267\) | −29.7325 | + | 29.7325i | −1.81960 | + | 1.81960i | ||||
\(268\) | −17.4960 | −1.06874 | ||||||||
\(269\) | −21.0402 | + | 21.0402i | −1.28285 | + | 1.28285i | −0.343804 | + | 0.939041i | \(0.611716\pi\) |
−0.939041 | + | 0.343804i | \(0.888284\pi\) | |||||||
\(270\) | 15.7324i | 0.957445i | ||||||||
\(271\) | 20.6716 | 1.25571 | 0.627856 | − | 0.778330i | \(-0.283933\pi\) | ||||
0.627856 | + | 0.778330i | \(0.283933\pi\) | |||||||
\(272\) | 9.04592 | + | 9.15700i | 0.548490 | + | 0.555225i | ||||
\(273\) | 4.82340 | 0.291926 | ||||||||
\(274\) | − | 24.5429i | − | 1.48269i | ||||||
\(275\) | −10.9622 | + | 10.9622i | −0.661046 | + | 0.661046i | ||||
\(276\) | −56.6188 | −3.40805 | ||||||||
\(277\) | 0.606036 | − | 0.606036i | 0.0364132 | − | 0.0364132i | −0.688666 | − | 0.725079i | \(-0.741803\pi\) |
0.725079 | + | 0.688666i | \(0.241803\pi\) | |||||||
\(278\) | 12.6328 | + | 12.6328i | 0.757667 | + | 0.757667i | ||||
\(279\) | 34.1387 | + | 34.1387i | 2.04383 | + | 2.04383i | ||||
\(280\) | 0.344574i | 0.0205922i | ||||||||
\(281\) | − | 4.56543i | − | 0.272350i | −0.990685 | − | 0.136175i | \(-0.956519\pi\) | ||
0.990685 | − | 0.136175i | \(-0.0434810\pi\) | |||||||
\(282\) | −1.38901 | − | 1.38901i | −0.0827141 | − | 0.0827141i | ||||
\(283\) | −8.97699 | − | 8.97699i | −0.533627 | − | 0.533627i | 0.388023 | − | 0.921650i | \(-0.373158\pi\) |
−0.921650 | + | 0.388023i | \(0.873158\pi\) | |||||||
\(284\) | 25.7142 | − | 25.7142i | 1.52586 | − | 1.52586i | ||||
\(285\) | −9.87957 | −0.585215 | ||||||||
\(286\) | 17.0521 | − | 17.0521i | 1.00831 | − | 1.00831i | ||||
\(287\) | 3.47581i | 0.205171i | ||||||||
\(288\) | 47.6599 | 2.80839 | ||||||||
\(289\) | −0.207470 | + | 16.9987i | −0.0122041 | + | 0.999926i | ||||
\(290\) | 19.0108 | 1.11635 | ||||||||
\(291\) | − | 20.9768i | − | 1.22968i | ||||||
\(292\) | −13.5236 | + | 13.5236i | −0.791407 | + | 0.791407i | ||||
\(293\) | −11.6884 | −0.682845 | −0.341422 | − | 0.939910i | \(-0.610909\pi\) | ||||
−0.341422 | + | 0.939910i | \(0.610909\pi\) | |||||||
\(294\) | −29.7180 | + | 29.7180i | −1.73319 | + | 1.73319i | ||||
\(295\) | −0.127853 | − | 0.127853i | −0.00744386 | − | 0.00744386i | ||||
\(296\) | −0.434910 | − | 0.434910i | −0.0252786 | − | 0.0252786i | ||||
\(297\) | − | 31.6233i | − | 1.83497i | ||||||
\(298\) | 22.0920i | 1.27975i | ||||||||
\(299\) | 17.8779 | + | 17.8779i | 1.03391 | + | 1.03391i | ||||
\(300\) | −21.2270 | − | 21.2270i | −1.22554 | − | 1.22554i | ||||
\(301\) | −0.361953 | + | 0.361953i | −0.0208626 | + | 0.0208626i | ||||
\(302\) | −35.8824 | −2.06480 | ||||||||
\(303\) | −6.65944 | + | 6.65944i | −0.382575 | + | 0.382575i | ||||
\(304\) | 11.8932i | 0.682121i | ||||||||
\(305\) | 9.10112 | 0.521128 | ||||||||
\(306\) | 35.7519 | + | 36.1909i | 2.04380 | + | 2.06889i | ||||
\(307\) | 0.406775 | 0.0232159 | 0.0116079 | − | 0.999933i | \(-0.496305\pi\) | ||||
0.0116079 | + | 0.999933i | \(0.496305\pi\) | |||||||
\(308\) | − | 4.43183i | − | 0.252527i | ||||||
\(309\) | 21.6655 | − | 21.6655i | 1.23251 | − | 1.23251i | ||||
\(310\) | 14.8642 | 0.844232 | ||||||||
\(311\) | 10.0196 | − | 10.0196i | 0.568162 | − | 0.568162i | −0.363451 | − | 0.931613i | \(-0.618402\pi\) |
0.931613 | + | 0.363451i | \(0.118402\pi\) | |||||||
\(312\) | 5.16035 | + | 5.16035i | 0.292147 | + | 0.292147i | ||||
\(313\) | 10.9733 | + | 10.9733i | 0.620246 | + | 0.620246i | 0.945594 | − | 0.325348i | \(-0.105482\pi\) |
−0.325348 | + | 0.945594i | \(0.605482\pi\) | |||||||
\(314\) | − | 12.2207i | − | 0.689653i | ||||||
\(315\) | − | 2.62583i | − | 0.147949i | ||||||
\(316\) | 22.5275 | + | 22.5275i | 1.26727 | + | 1.26727i | ||||
\(317\) | 13.5264 | + | 13.5264i | 0.759718 | + | 0.759718i | 0.976271 | − | 0.216553i | \(-0.0694813\pi\) |
−0.216553 | + | 0.976271i | \(0.569481\pi\) | |||||||
\(318\) | −60.4546 | + | 60.4546i | −3.39013 | + | 3.39013i | ||||
\(319\) | −38.2130 | −2.13952 | ||||||||
\(320\) | 6.53835 | − | 6.53835i | 0.365505 | − | 0.365505i | ||||
\(321\) | − | 3.60062i | − | 0.200967i | ||||||
\(322\) | 8.56677 | 0.477407 | ||||||||
\(323\) | −11.1746 | + | 11.0390i | −0.621771 | + | 0.614229i | ||||
\(324\) | 19.2641 | 1.07023 | ||||||||
\(325\) | 13.4053i | 0.743590i | ||||||||
\(326\) | −22.6045 | + | 22.6045i | −1.25195 | + | 1.25195i | ||||
\(327\) | −6.14924 | −0.340054 | ||||||||
\(328\) | −3.71862 | + | 3.71862i | −0.205327 | + | 0.205327i | ||||
\(329\) | 0.113990 | + | 0.113990i | 0.00628446 | + | 0.00628446i | ||||
\(330\) | −14.0017 | − | 14.0017i | −0.770769 | − | 0.770769i | ||||
\(331\) | − | 19.6996i | − | 1.08279i | −0.840769 | − | 0.541393i | \(-0.817897\pi\) | ||
0.840769 | − | 0.541393i | \(-0.182103\pi\) | |||||||
\(332\) | − | 3.25036i | − | 0.178387i | ||||||
\(333\) | 3.31424 | + | 3.31424i | 0.181619 | + | 0.181619i | ||||
\(334\) | 18.7941 | + | 18.7941i | 1.02837 | + | 1.02837i | ||||
\(335\) | 4.53626 | − | 4.53626i | 0.247843 | − | 0.247843i | ||||
\(336\) | −4.76780 | −0.260105 | ||||||||
\(337\) | −8.48804 | + | 8.48804i | −0.462373 | + | 0.462373i | −0.899433 | − | 0.437060i | \(-0.856020\pi\) |
0.437060 | + | 0.899433i | \(0.356020\pi\) | |||||||
\(338\) | 6.32502i | 0.344036i | ||||||||
\(339\) | −32.5153 | −1.76599 | ||||||||
\(340\) | 8.49489 | + | 0.0518382i | 0.460700 | + | 0.00281132i | ||||
\(341\) | −29.8781 | −1.61799 | ||||||||
\(342\) | 47.0050i | 2.54174i | ||||||||
\(343\) | 4.97250 | − | 4.97250i | 0.268490 | − | 0.268490i | ||||
\(344\) | −0.774475 | −0.0417569 | ||||||||
\(345\) | 14.6798 | − | 14.6798i | 0.790335 | − | 0.790335i | ||||
\(346\) | −1.12533 | − | 1.12533i | −0.0604984 | − | 0.0604984i | ||||
\(347\) | −16.4140 | − | 16.4140i | −0.881149 | − | 0.881149i | 0.112502 | − | 0.993651i | \(-0.464113\pi\) |
−0.993651 | + | 0.112502i | \(0.964113\pi\) | |||||||
\(348\) | − | 73.9950i | − | 3.96655i | ||||||
\(349\) | − | 8.86653i | − | 0.474615i | −0.971435 | − | 0.237307i | \(-0.923735\pi\) | ||
0.971435 | − | 0.237307i | \(-0.0762648\pi\) | |||||||
\(350\) | 3.21178 | + | 3.21178i | 0.171677 | + | 0.171677i | ||||
\(351\) | −19.3354 | − | 19.3354i | −1.03205 | − | 1.03205i | ||||
\(352\) | −20.8559 | + | 20.8559i | −1.11162 | + | 1.11162i | ||||
\(353\) | −21.3545 | −1.13658 | −0.568292 | − | 0.822827i | \(-0.692396\pi\) | ||||
−0.568292 | + | 0.822827i | \(0.692396\pi\) | |||||||
\(354\) | −0.917500 | + | 0.917500i | −0.0487646 | + | 0.0487646i | ||||
\(355\) | 13.3341i | 0.707701i | ||||||||
\(356\) | 33.4070 | 1.77057 | ||||||||
\(357\) | −4.42539 | − | 4.47973i | −0.234216 | − | 0.237092i | ||||
\(358\) | −19.0984 | −1.00938 | ||||||||
\(359\) | − | 19.9916i | − | 1.05512i | −0.849519 | − | 0.527558i | \(-0.823108\pi\) | ||
0.849519 | − | 0.527558i | \(-0.176892\pi\) | |||||||
\(360\) | 2.80926 | − | 2.80926i | 0.148061 | − | 0.148061i | ||||
\(361\) | 4.48635 | 0.236124 | ||||||||
\(362\) | −0.662254 | + | 0.662254i | −0.0348073 | + | 0.0348073i | ||||
\(363\) | 4.93742 | + | 4.93742i | 0.259147 | + | 0.259147i | ||||
\(364\) | −2.70976 | − | 2.70976i | −0.142030 | − | 0.142030i | ||||
\(365\) | − | 7.01264i | − | 0.367058i | ||||||
\(366\) | − | 65.3118i | − | 3.41390i | ||||||
\(367\) | 16.3299 | + | 16.3299i | 0.852412 | + | 0.852412i | 0.990430 | − | 0.138018i | \(-0.0440731\pi\) |
−0.138018 | + | 0.990430i | \(0.544073\pi\) | |||||||
\(368\) | −17.6718 | − | 17.6718i | −0.921207 | − | 0.921207i | ||||
\(369\) | 28.3378 | − | 28.3378i | 1.47521 | − | 1.47521i | ||||
\(370\) | 1.44304 | 0.0750201 | ||||||||
\(371\) | 4.96125 | − | 4.96125i | 0.257575 | − | 0.257575i | ||||
\(372\) | − | 57.8555i | − | 2.99967i | ||||||
\(373\) | −33.7506 | −1.74754 | −0.873769 | − | 0.486341i | \(-0.838331\pi\) | ||||
−0.873769 | + | 0.486341i | \(0.838331\pi\) | |||||||
\(374\) | −31.4821 | − | 0.192112i | −1.62790 | − | 0.00993390i | ||||
\(375\) | 23.9737 | 1.23799 | ||||||||
\(376\) | 0.243905i | 0.0125785i | ||||||||
\(377\) | −23.3646 | + | 23.3646i | −1.20334 | + | 1.20334i | ||||
\(378\) | −9.26519 | −0.476550 | ||||||||
\(379\) | −2.28196 | + | 2.28196i | −0.117216 | + | 0.117216i | −0.763282 | − | 0.646066i | \(-0.776413\pi\) |
0.646066 | + | 0.763282i | \(0.276413\pi\) | |||||||
\(380\) | 5.55028 | + | 5.55028i | 0.284723 | + | 0.284723i | ||||
\(381\) | −4.75632 | − | 4.75632i | −0.243674 | − | 0.243674i | ||||
\(382\) | − | 24.2402i | − | 1.24023i | ||||||
\(383\) | 27.3194i | 1.39595i | 0.716120 | + | 0.697977i | \(0.245916\pi\) | ||||
−0.716120 | + | 0.697977i | \(0.754084\pi\) | |||||||
\(384\) | −12.8472 | − | 12.8472i | −0.655606 | − | 0.655606i | ||||
\(385\) | 1.14906 | + | 1.14906i | 0.0585616 | + | 0.0585616i | ||||
\(386\) | 18.8424 | − | 18.8424i | 0.959054 | − | 0.959054i | ||||
\(387\) | 5.90190 | 0.300010 | ||||||||
\(388\) | −11.7846 | + | 11.7846i | −0.598274 | + | 0.598274i | ||||
\(389\) | 19.6679i | 0.997204i | 0.866831 | + | 0.498602i | \(0.166153\pi\) | ||||
−0.866831 | + | 0.498602i | \(0.833847\pi\) | |||||||
\(390\) | −17.1222 | −0.867015 | ||||||||
\(391\) | 0.201417 | − | 33.0068i | 0.0101861 | − | 1.66922i | ||||
\(392\) | 5.21840 | 0.263569 | ||||||||
\(393\) | 28.0529i | 1.41508i | ||||||||
\(394\) | −20.1608 | + | 20.1608i | −1.01569 | + | 1.01569i | ||||
\(395\) | −11.6816 | −0.587765 | ||||||||
\(396\) | −36.1321 | + | 36.1321i | −1.81570 | + | 1.81570i | ||||
\(397\) | 9.29444 | + | 9.29444i | 0.466474 | + | 0.466474i | 0.900770 | − | 0.434296i | \(-0.143003\pi\) |
−0.434296 | + | 0.900770i | \(0.643003\pi\) | |||||||
\(398\) | −17.1311 | − | 17.1311i | −0.858704 | − | 0.858704i | ||||
\(399\) | − | 5.81831i | − | 0.291280i | ||||||
\(400\) | − | 13.2507i | − | 0.662536i | ||||||
\(401\) | 13.0237 | + | 13.0237i | 0.650374 | + | 0.650374i | 0.953083 | − | 0.302709i | \(-0.0978911\pi\) |
−0.302709 | + | 0.953083i | \(0.597891\pi\) | |||||||
\(402\) | −32.5533 | − | 32.5533i | −1.62361 | − | 1.62361i | ||||
\(403\) | −18.2684 | + | 18.2684i | −0.910015 | + | 0.910015i | ||||
\(404\) | 7.48246 | 0.372266 | ||||||||
\(405\) | −4.99469 | + | 4.99469i | −0.248188 | + | 0.248188i | ||||
\(406\) | 11.1959i | 0.555642i | ||||||||
\(407\) | −2.90061 | −0.143778 | ||||||||
\(408\) | 0.0581377 | − | 9.52720i | 0.00287824 | − | 0.471667i | ||||
\(409\) | 7.76215 | 0.383814 | 0.191907 | − | 0.981413i | \(-0.438533\pi\) | ||||
0.191907 | + | 0.981413i | \(0.438533\pi\) | |||||||
\(410\) | − | 12.3385i | − | 0.609354i | ||||||
\(411\) | 24.7678 | − | 24.7678i | 1.22171 | − | 1.22171i | ||||
\(412\) | −24.3431 | −1.19930 | ||||||||
\(413\) | 0.0752953 | − | 0.0752953i | 0.00370504 | − | 0.00370504i | ||||
\(414\) | −69.8436 | − | 69.8436i | −3.43263 | − | 3.43263i | ||||
\(415\) | 0.842736 | + | 0.842736i | 0.0413683 | + | 0.0413683i | ||||
\(416\) | 25.5039i | 1.25043i | ||||||||
\(417\) | 25.4973i | 1.24861i | ||||||||
\(418\) | −20.5693 | − | 20.5693i | −1.00608 | − | 1.00608i | ||||
\(419\) | 22.5720 | + | 22.5720i | 1.10271 | + | 1.10271i | 0.994082 | + | 0.108631i | \(0.0346468\pi\) |
0.108631 | + | 0.994082i | \(0.465353\pi\) | |||||||
\(420\) | −2.22502 | + | 2.22502i | −0.108570 | + | 0.108570i | ||||
\(421\) | −11.2929 | −0.550383 | −0.275191 | − | 0.961389i | \(-0.588741\pi\) | ||||
−0.275191 | + | 0.961389i | \(0.588741\pi\) | |||||||
\(422\) | 8.54302 | − | 8.54302i | 0.415868 | − | 0.415868i | ||||
\(423\) | − | 1.85869i | − | 0.0903724i | ||||||
\(424\) | 10.6157 | 0.515542 | ||||||||
\(425\) | 12.4501 | − | 12.2991i | 0.603919 | − | 0.596593i | ||||
\(426\) | 95.6887 | 4.63613 | ||||||||
\(427\) | 5.35986i | 0.259382i | ||||||||
\(428\) | −2.02281 | + | 2.02281i | −0.0977760 | + | 0.0977760i | ||||
\(429\) | 34.4167 | 1.66166 | ||||||||
\(430\) | 1.28486 | − | 1.28486i | 0.0619616 | − | 0.0619616i | ||||
\(431\) | 11.9687 | + | 11.9687i | 0.576512 | + | 0.576512i | 0.933940 | − | 0.357429i | \(-0.116346\pi\) |
−0.357429 | + | 0.933940i | \(0.616346\pi\) | |||||||
\(432\) | 19.1125 | + | 19.1125i | 0.919553 | + | 0.919553i | ||||
\(433\) | 36.3357i | 1.74618i | 0.487559 | + | 0.873090i | \(0.337887\pi\) | ||||
−0.487559 | + | 0.873090i | \(0.662113\pi\) | |||||||
\(434\) | 8.75389i | 0.420200i | ||||||||
\(435\) | 19.1850 | + | 19.1850i | 0.919852 | + | 0.919852i | ||||
\(436\) | 3.45460 | + | 3.45460i | 0.165445 | + | 0.165445i | ||||
\(437\) | 21.5655 | − | 21.5655i | 1.03162 | − | 1.03162i | ||||
\(438\) | −50.3244 | −2.40459 | ||||||||
\(439\) | −22.4307 | + | 22.4307i | −1.07056 | + | 1.07056i | −0.0732456 | + | 0.997314i | \(0.523336\pi\) |
−0.997314 | + | 0.0732456i | \(0.976664\pi\) | |||||||
\(440\) | 2.45866i | 0.117212i | ||||||||
\(441\) | −39.7669 | −1.89366 | ||||||||
\(442\) | −19.3666 | + | 19.1316i | −0.921174 | + | 0.909999i | ||||
\(443\) | −20.6673 | −0.981935 | −0.490968 | − | 0.871178i | \(-0.663357\pi\) | ||||
−0.490968 | + | 0.871178i | \(0.663357\pi\) | |||||||
\(444\) | − | 5.61670i | − | 0.266557i | ||||||
\(445\) | −8.66160 | + | 8.66160i | −0.410599 | + | 0.410599i | ||||
\(446\) | 26.8442 | 1.27111 | ||||||||
\(447\) | −22.2945 | + | 22.2945i | −1.05449 | + | 1.05449i | ||||
\(448\) | 3.85059 | + | 3.85059i | 0.181923 | + | 0.181923i | ||||
\(449\) | −7.15280 | − | 7.15280i | −0.337562 | − | 0.337562i | 0.517887 | − | 0.855449i | \(-0.326719\pi\) |
−0.855449 | + | 0.517887i | \(0.826719\pi\) | |||||||
\(450\) | − | 52.3703i | − | 2.46876i | ||||||
\(451\) | 24.8012i | 1.16784i | ||||||||
\(452\) | 18.2669 | + | 18.2669i | 0.859202 | + | 0.859202i | ||||
\(453\) | −36.2113 | − | 36.2113i | −1.70136 | − | 1.70136i | ||||
\(454\) | −27.3508 | + | 27.3508i | −1.28364 | + | 1.28364i | ||||
\(455\) | 1.40514 | 0.0658741 | ||||||||
\(456\) | 6.22475 | − | 6.22475i | 0.291501 | − | 0.291501i | ||||
\(457\) | − | 7.77735i | − | 0.363809i | −0.983316 | − | 0.181905i | \(-0.941774\pi\) | ||
0.983316 | − | 0.181905i | \(-0.0582262\pi\) | |||||||
\(458\) | 36.0573 | 1.68485 | ||||||||
\(459\) | −0.217837 | + | 35.6977i | −0.0101678 | + | 1.66623i | ||||
\(460\) | −16.4941 | −0.769040 | ||||||||
\(461\) | − | 14.0654i | − | 0.655093i | −0.944835 | − | 0.327547i | \(-0.893778\pi\) | ||
0.944835 | − | 0.327547i | \(-0.106222\pi\) | |||||||
\(462\) | 8.24593 | − | 8.24593i | 0.383636 | − | 0.383636i | ||||
\(463\) | 22.6758 | 1.05383 | 0.526916 | − | 0.849917i | \(-0.323348\pi\) | ||||
0.526916 | + | 0.849917i | \(0.323348\pi\) | |||||||
\(464\) | 23.0952 | − | 23.0952i | 1.07217 | − | 1.07217i | ||||
\(465\) | 15.0005 | + | 15.0005i | 0.695630 | + | 0.695630i | ||||
\(466\) | 29.8983 | + | 29.8983i | 1.38501 | + | 1.38501i | ||||
\(467\) | − | 5.71487i | − | 0.264453i | −0.991220 | − | 0.132226i | \(-0.957787\pi\) | ||
0.991220 | − | 0.132226i | \(-0.0422126\pi\) | |||||||
\(468\) | 44.1845i | 2.04243i | ||||||||
\(469\) | 2.67151 | + | 2.67151i | 0.123359 | + | 0.123359i | ||||
\(470\) | −0.404642 | − | 0.404642i | −0.0186647 | − | 0.0186647i | ||||
\(471\) | 12.3327 | − | 12.3327i | 0.568261 | − | 0.568261i | ||||
\(472\) | 0.161110 | 0.00741571 | ||||||||
\(473\) | −2.58266 | + | 2.58266i | −0.118751 | + | 0.118751i | ||||
\(474\) | 83.8300i | 3.85044i | ||||||||
\(475\) | 16.1703 | 0.741944 | ||||||||
\(476\) | −0.0305287 | + | 5.00284i | −0.00139928 | + | 0.229305i | ||||
\(477\) | −80.8968 | −3.70401 | ||||||||
\(478\) | − | 42.2740i | − | 1.93357i | ||||||
\(479\) | 6.53308 | − | 6.53308i | 0.298504 | − | 0.298504i | −0.541924 | − | 0.840428i | \(-0.682304\pi\) |
0.840428 | + | 0.541924i | \(0.182304\pi\) | |||||||
\(480\) | 20.9416 | 0.955851 | ||||||||
\(481\) | −1.77352 | + | 1.77352i | −0.0808657 | + | 0.0808657i | ||||
\(482\) | −8.48931 | − | 8.48931i | −0.386677 | − | 0.386677i | ||||
\(483\) | 8.64529 | + | 8.64529i | 0.393374 | + | 0.393374i | ||||
\(484\) | − | 5.54762i | − | 0.252164i | ||||||
\(485\) | − | 6.11092i | − | 0.277482i | ||||||
\(486\) | −2.55360 | − | 2.55360i | −0.115833 | − | 0.115833i | ||||
\(487\) | 17.3700 | + | 17.3700i | 0.787112 | + | 0.787112i | 0.981020 | − | 0.193908i | \(-0.0621163\pi\) |
−0.193908 | + | 0.981020i | \(0.562116\pi\) | |||||||
\(488\) | −5.73428 | + | 5.73428i | −0.259579 | + | 0.259579i | ||||
\(489\) | −45.6234 | −2.06316 | ||||||||
\(490\) | −8.65738 | + | 8.65738i | −0.391101 | + | 0.391101i | ||||
\(491\) | 27.3151i | 1.23272i | 0.787466 | + | 0.616358i | \(0.211392\pi\) | ||||
−0.787466 | + | 0.616358i | \(0.788608\pi\) | |||||||
\(492\) | −48.0246 | −2.16512 | ||||||||
\(493\) | 43.1364 | + | 0.263231i | 1.94277 | + | 0.0118553i | ||||
\(494\) | −25.1534 | −1.13171 | ||||||||
\(495\) | − | 18.7363i | − | 0.842133i | ||||||
\(496\) | 18.0578 | − | 18.0578i | 0.810820 | − | 0.810820i | ||||
\(497\) | −7.85276 | −0.352245 | ||||||||
\(498\) | 6.04767 | − | 6.04767i | 0.271003 | − | 0.271003i | ||||
\(499\) | −12.6629 | − | 12.6629i | −0.566867 | − | 0.566867i | 0.364382 | − | 0.931249i | \(-0.381280\pi\) |
−0.931249 | + | 0.364382i | \(0.881280\pi\) | |||||||
\(500\) | −13.4683 | − | 13.4683i | −0.602318 | − | 0.602318i | ||||
\(501\) | 37.9328i | 1.69471i | ||||||||
\(502\) | − | 26.6682i | − | 1.19026i | ||||||
\(503\) | −19.5149 | − | 19.5149i | −0.870125 | − | 0.870125i | 0.122360 | − | 0.992486i | \(-0.460954\pi\) |
−0.992486 | + | 0.122360i | \(0.960954\pi\) | |||||||
\(504\) | 1.65444 | + | 1.65444i | 0.0736947 | + | 0.0736947i | ||||
\(505\) | −1.94001 | + | 1.94001i | −0.0863294 | + | 0.0863294i | ||||
\(506\) | 61.1270 | 2.71743 | ||||||||
\(507\) | −6.38300 | + | 6.38300i | −0.283479 | + | 0.283479i | ||||
\(508\) | 5.34414i | 0.237108i | ||||||||
\(509\) | −24.5577 | −1.08850 | −0.544250 | − | 0.838923i | \(-0.683186\pi\) | ||||
−0.544250 | + | 0.838923i | \(0.683186\pi\) | |||||||
\(510\) | 15.7093 | + | 15.9022i | 0.695619 | + | 0.704161i | ||||
\(511\) | 4.12991 | 0.182696 | ||||||||
\(512\) | − | 30.0455i | − | 1.32783i | ||||||
\(513\) | −23.3237 | + | 23.3237i | −1.02977 | + | 1.02977i | ||||
\(514\) | −44.8197 | −1.97691 | ||||||||
\(515\) | 6.31155 | − | 6.31155i | 0.278120 | − | 0.278120i | ||||
\(516\) | −5.00103 | − | 5.00103i | −0.220158 | − | 0.220158i | ||||
\(517\) | 0.813358 | + | 0.813358i | 0.0357715 | + | 0.0357715i | ||||
\(518\) | 0.849840i | 0.0373398i | ||||||||
\(519\) | − | 2.27130i | − | 0.0996989i | ||||||
\(520\) | 1.50330 | + | 1.50330i | 0.0659242 | + | 0.0659242i | ||||
\(521\) | 2.34848 | + | 2.34848i | 0.102889 | + | 0.102889i | 0.756677 | − | 0.653789i | \(-0.226821\pi\) |
−0.653789 | + | 0.756677i | \(0.726821\pi\) | |||||||
\(522\) | 91.2785 | − | 91.2785i | 3.99515 | − | 3.99515i | ||||
\(523\) | 9.63657 | 0.421378 | 0.210689 | − | 0.977553i | \(-0.432429\pi\) | ||||
0.210689 | + | 0.977553i | \(0.432429\pi\) | |||||||
\(524\) | 15.7600 | − | 15.7600i | 0.688477 | − | 0.688477i | ||||
\(525\) | 6.48243i | 0.282917i | ||||||||
\(526\) | −25.4446 | −1.10944 | ||||||||
\(527\) | 33.7277 | + | 0.205816i | 1.46920 | + | 0.00896549i | ||||
\(528\) | −34.0200 | −1.48053 | ||||||||
\(529\) | 41.0874i | 1.78641i | ||||||||
\(530\) | −17.6115 | + | 17.6115i | −0.764995 | + | 0.764995i | ||||
\(531\) | −1.22774 | −0.0532796 | ||||||||
\(532\) | −3.26869 | + | 3.26869i | −0.141716 | + | 0.141716i | ||||
\(533\) | 15.1642 | + | 15.1642i | 0.656835 | + | 0.656835i | ||||
\(534\) | 62.1577 | + | 62.1577i | 2.68983 | + | 2.68983i | ||||
\(535\) | − | 1.04892i | − | 0.0453490i | ||||||
\(536\) | 5.71627i | 0.246905i | ||||||||
\(537\) | −19.2734 | − | 19.2734i | −0.831710 | − | 0.831710i | ||||
\(538\) | 43.9860 | + | 43.9860i | 1.89637 | + | 1.89637i | ||||
\(539\) | 17.4019 | − | 17.4019i | 0.749555 | − | 0.749555i | ||||
\(540\) | 17.8388 | 0.767659 | ||||||||
\(541\) | 6.96161 | − | 6.96161i | 0.299303 | − | 0.299303i | −0.541438 | − | 0.840741i | \(-0.682120\pi\) |
0.840741 | + | 0.541438i | \(0.182120\pi\) | |||||||
\(542\) | − | 43.2154i | − | 1.85626i | ||||||
\(543\) | −1.33665 | −0.0573611 | ||||||||
\(544\) | 23.6867 | − | 23.3994i | 1.01556 | − | 1.00324i | ||||
\(545\) | −1.79138 | −0.0767344 | ||||||||
\(546\) | − | 10.0836i | − | 0.431540i | ||||||
\(547\) | −4.62998 | + | 4.62998i | −0.197964 | + | 0.197964i | −0.799127 | − | 0.601163i | \(-0.794704\pi\) |
0.601163 | + | 0.799127i | \(0.294704\pi\) | |||||||
\(548\) | −27.8288 | −1.18879 | ||||||||
\(549\) | 43.6982 | − | 43.6982i | 1.86499 | − | 1.86499i | ||||
\(550\) | 22.9172 | + | 22.9172i | 0.977192 | + | 0.977192i | ||||
\(551\) | 28.1839 | + | 28.1839i | 1.20067 | + | 1.20067i | ||||
\(552\) | 18.4984i | 0.787346i | ||||||||
\(553\) | − | 6.87957i | − | 0.292549i | ||||||
\(554\) | −1.26696 | − | 1.26696i | −0.0538279 | − | 0.0538279i | ||||
\(555\) | 1.45627 | + | 1.45627i | 0.0618151 | + | 0.0618151i | ||||
\(556\) | 14.3242 | − | 14.3242i | 0.607481 | − | 0.607481i | ||||
\(557\) | −0.179965 | −0.00762538 | −0.00381269 | − | 0.999993i | \(-0.501214\pi\) | ||||
−0.00381269 | + | 0.999993i | \(0.501214\pi\) | |||||||
\(558\) | 71.3692 | − | 71.3692i | 3.02130 | − | 3.02130i | ||||
\(559\) | 3.15824i | 0.133579i | ||||||||
\(560\) | −1.38894 | −0.0586936 | ||||||||
\(561\) | −31.5767 | − | 31.9645i | −1.33317 | − | 1.34954i | ||||
\(562\) | −9.54432 | −0.402603 | ||||||||
\(563\) | 4.44720i | 0.187427i | 0.995599 | + | 0.0937136i | \(0.0298738\pi\) | ||||
−0.995599 | + | 0.0937136i | \(0.970126\pi\) | |||||||
\(564\) | −1.57497 | + | 1.57497i | −0.0663184 | + | 0.0663184i | ||||
\(565\) | −9.47228 | −0.398502 | ||||||||
\(566\) | −18.7670 | + | 18.7670i | −0.788835 | + | 0.788835i | ||||
\(567\) | −2.94149 | − | 2.94149i | −0.123531 | − | 0.123531i | ||||
\(568\) | −8.40133 | − | 8.40133i | −0.352512 | − | 0.352512i | ||||
\(569\) | 27.8668i | 1.16824i | 0.811668 | + | 0.584119i | \(0.198560\pi\) | ||||
−0.811668 | + | 0.584119i | \(0.801440\pi\) | |||||||
\(570\) | 20.6539i | 0.865096i | ||||||||
\(571\) | −5.48524 | − | 5.48524i | −0.229550 | − | 0.229550i | 0.582955 | − | 0.812505i | \(-0.301897\pi\) |
−0.812505 | + | 0.582955i | \(0.801897\pi\) | |||||||
\(572\) | −19.3351 | − | 19.3351i | −0.808441 | − | 0.808441i | ||||
\(573\) | 24.4623 | − | 24.4623i | 1.02193 | − | 1.02193i | ||||
\(574\) | 7.26642 | 0.303294 | ||||||||
\(575\) | −24.0271 | + | 24.0271i | −1.00200 | + | 1.00200i | ||||
\(576\) | − | 62.7866i | − | 2.61611i | ||||||
\(577\) | 13.6386 | 0.567781 | 0.283890 | − | 0.958857i | \(-0.408375\pi\) | ||||
0.283890 | + | 0.958857i | \(0.408375\pi\) | |||||||
\(578\) | 35.5370 | + | 0.433729i | 1.47814 | + | 0.0180408i | ||||
\(579\) | 38.0303 | 1.58048 | ||||||||
\(580\) | − | 21.5561i | − | 0.895066i | ||||||
\(581\) | −0.496307 | + | 0.496307i | −0.0205903 | + | 0.0205903i | ||||
\(582\) | −43.8534 | −1.81778 | ||||||||
\(583\) | 35.4003 | − | 35.4003i | 1.46613 | − | 1.46613i | ||||
\(584\) | 4.41841 | + | 4.41841i | 0.182835 | + | 0.182835i | ||||
\(585\) | −11.4559 | − | 11.4559i | −0.473645 | − | 0.473645i | ||||
\(586\) | 24.4354i | 1.00942i | ||||||||
\(587\) | − | 15.2874i | − | 0.630977i | −0.948929 | − | 0.315489i | \(-0.897832\pi\) | ||
0.948929 | − | 0.315489i | \(-0.102168\pi\) | |||||||
\(588\) | 33.6968 | + | 33.6968i | 1.38963 | + | 1.38963i | ||||
\(589\) | 22.0366 | + | 22.0366i | 0.908001 | + | 0.908001i | ||||
\(590\) | −0.267284 | + | 0.267284i | −0.0110039 | + | 0.0110039i | ||||
\(591\) | −40.6911 | −1.67381 | ||||||||
\(592\) | 1.75308 | − | 1.75308i | 0.0720511 | − | 0.0720511i | ||||
\(593\) | − | 19.3137i | − | 0.793118i | −0.918009 | − | 0.396559i | \(-0.870204\pi\) | ||
0.918009 | − | 0.396559i | \(-0.129796\pi\) | |||||||
\(594\) | −66.1105 | −2.71255 | ||||||||
\(595\) | −1.28919 | − | 1.30502i | −0.0528518 | − | 0.0535008i | ||||
\(596\) | 25.0498 | 1.02608 | ||||||||
\(597\) | − | 34.5762i | − | 1.41511i | ||||||
\(598\) | 37.3749 | − | 37.3749i | 1.52837 | − | 1.52837i | ||||
\(599\) | 4.21393 | 0.172176 | 0.0860882 | − | 0.996288i | \(-0.472563\pi\) | ||||
0.0860882 | + | 0.996288i | \(0.472563\pi\) | |||||||
\(600\) | −6.93527 | + | 6.93527i | −0.283131 | + | 0.283131i | ||||
\(601\) | −30.9038 | − | 30.9038i | −1.26059 | − | 1.26059i | −0.950807 | − | 0.309784i | \(-0.899743\pi\) |
−0.309784 | − | 0.950807i | \(-0.600257\pi\) | |||||||
\(602\) | 0.756686 | + | 0.756686i | 0.0308402 | + | 0.0308402i | ||||
\(603\) | − | 43.5609i | − | 1.77394i | ||||||
\(604\) | 40.6866i | 1.65551i | ||||||||
\(605\) | 1.43836 | + | 1.43836i | 0.0584775 | + | 0.0584775i | ||||
\(606\) | 13.9220 | + | 13.9220i | 0.565542 | + | 0.565542i | ||||
\(607\) | 13.7380 | − | 13.7380i | 0.557608 | − | 0.557608i | −0.371018 | − | 0.928626i | \(-0.620991\pi\) |
0.928626 | + | 0.371018i | \(0.120991\pi\) | |||||||
\(608\) | 30.7645 | 1.24766 | ||||||||
\(609\) | −11.2985 | + | 11.2985i | −0.457839 | + | 0.457839i | ||||
\(610\) | − | 19.0265i | − | 0.770360i | ||||||
\(611\) | 0.994625 | 0.0402382 | ||||||||
\(612\) | 41.0363 | − | 40.5385i | 1.65879 | − | 1.63867i | ||||
\(613\) | 18.5457 | 0.749053 | 0.374526 | − | 0.927216i | \(-0.377805\pi\) | ||||
0.374526 | + | 0.927216i | \(0.377805\pi\) | |||||||
\(614\) | − | 0.850389i | − | 0.0343189i | ||||||
\(615\) | 12.4516 | − | 12.4516i | 0.502096 | − | 0.502096i | ||||
\(616\) | −1.44796 | −0.0583401 | ||||||||
\(617\) | −24.0671 | + | 24.0671i | −0.968905 | + | 0.968905i | −0.999531 | − | 0.0306260i | \(-0.990250\pi\) |
0.0306260 | + | 0.999531i | \(0.490250\pi\) | |||||||
\(618\) | −45.2932 | − | 45.2932i | −1.82196 | − | 1.82196i | ||||
\(619\) | 11.4724 | + | 11.4724i | 0.461116 | + | 0.461116i | 0.899021 | − | 0.437905i | \(-0.144280\pi\) |
−0.437905 | + | 0.899021i | \(0.644280\pi\) | |||||||
\(620\) | − | 16.8543i | − | 0.676887i | ||||||
\(621\) | − | 69.3123i | − | 2.78141i | ||||||
\(622\) | −20.9467 | − | 20.9467i | −0.839887 | − | 0.839887i | ||||
\(623\) | −5.10102 | − | 5.10102i | −0.204368 | − | 0.204368i | ||||
\(624\) | −20.8009 | + | 20.8009i | −0.832701 | + | 0.832701i | ||||
\(625\) | −14.2387 | −0.569548 | ||||||||
\(626\) | 22.9403 | − | 22.9403i | 0.916880 | − | 0.916880i | ||||
\(627\) | − | 41.5157i | − | 1.65798i | ||||||
\(628\) | −13.8569 | −0.552949 | ||||||||
\(629\) | 3.27433 | + | 0.0199809i | 0.130556 | + | 0.000796691i | ||||
\(630\) | −5.48947 | −0.218706 | ||||||||
\(631\) | − | 10.1732i | − | 0.404989i | −0.979283 | − | 0.202495i | \(-0.935095\pi\) | ||
0.979283 | − | 0.202495i | \(-0.0649048\pi\) | |||||||
\(632\) | 7.36015 | − | 7.36015i | 0.292771 | − | 0.292771i | ||||
\(633\) | 17.2426 | 0.685334 | ||||||||
\(634\) | 28.2778 | − | 28.2778i | 1.12306 | − | 1.12306i | ||||
\(635\) | −1.38560 | − | 1.38560i | −0.0549859 | − | 0.0549859i | ||||
\(636\) | 68.5486 | + | 68.5486i | 2.71813 | + | 2.71813i | ||||
\(637\) | − | 21.2802i | − | 0.843151i | ||||||
\(638\) | 79.8867i | 3.16275i | ||||||||
\(639\) | 64.0225 | + | 64.0225i | 2.53269 | + | 2.53269i | ||||
\(640\) | −3.74262 | − | 3.74262i | −0.147940 | − | 0.147940i | ||||
\(641\) | −31.1467 | + | 31.1467i | −1.23022 | + | 1.23022i | −0.266344 | + | 0.963878i | \(0.585816\pi\) |
−0.963878 | + | 0.266344i | \(0.914184\pi\) | |||||||
\(642\) | −7.52733 | −0.297080 | ||||||||
\(643\) | −0.268561 | + | 0.268561i | −0.0105910 | + | 0.0105910i | −0.712382 | − | 0.701791i | \(-0.752384\pi\) |
0.701791 | + | 0.712382i | \(0.252384\pi\) | |||||||
\(644\) | − | 9.71374i | − | 0.382775i | ||||||
\(645\) | 2.59328 | 0.102110 | ||||||||
\(646\) | 23.0778 | + | 23.3612i | 0.907985 | + | 0.919135i | ||||
\(647\) | −39.7977 | −1.56461 | −0.782305 | − | 0.622895i | \(-0.785956\pi\) | ||||
−0.782305 | + | 0.622895i | \(0.785956\pi\) | |||||||
\(648\) | − | 6.29394i | − | 0.247249i | ||||||
\(649\) | 0.537260 | − | 0.537260i | 0.0210893 | − | 0.0210893i | ||||
\(650\) | 28.0246 | 1.09921 | ||||||||
\(651\) | −8.83413 | + | 8.83413i | −0.346237 | + | 0.346237i | ||||
\(652\) | 25.6309 | + | 25.6309i | 1.00378 | + | 1.00378i | ||||
\(653\) | 32.2637 | + | 32.2637i | 1.26257 | + | 1.26257i | 0.949841 | + | 0.312734i | \(0.101245\pi\) |
0.312734 | + | 0.949841i | \(0.398755\pi\) | |||||||
\(654\) | 12.8554i | 0.502685i | ||||||||
\(655\) | 8.17232i | 0.319319i | ||||||||
\(656\) | −14.9894 | − | 14.9894i | −0.585238 | − | 0.585238i | ||||
\(657\) | −33.6705 | − | 33.6705i | −1.31361 | − | 1.31361i | ||||
\(658\) | 0.238303 | − | 0.238303i | 0.00929002 | − | 0.00929002i | ||||
\(659\) | 30.5606 | 1.19047 | 0.595236 | − | 0.803551i | \(-0.297058\pi\) | ||||
0.595236 | + | 0.803551i | \(0.297058\pi\) | |||||||
\(660\) | −15.8763 | + | 15.8763i | −0.617986 | + | 0.617986i | ||||
\(661\) | − | 27.4724i | − | 1.06855i | −0.845310 | − | 0.534275i | \(-0.820585\pi\) | ||
0.845310 | − | 0.534275i | \(-0.179415\pi\) | |||||||
\(662\) | −41.1832 | −1.60063 | ||||||||
\(663\) | −38.8511 | − | 0.237080i | −1.50885 | − | 0.00920744i | ||||
\(664\) | −1.06195 | −0.0412118 | ||||||||
\(665\) | − | 1.69498i | − | 0.0657283i | ||||||
\(666\) | 6.92863 | − | 6.92863i | 0.268479 | − | 0.268479i | ||||
\(667\) | −83.7557 | −3.24303 | ||||||||
\(668\) | 21.3104 | − | 21.3104i | 0.824525 | − | 0.824525i | ||||
\(669\) | 27.0902 | + | 27.0902i | 1.04737 | + | 1.04737i | ||||
\(670\) | −9.48335 | − | 9.48335i | −0.366374 | − | 0.366374i | ||||
\(671\) | 38.2445i | 1.47641i | ||||||||
\(672\) | 12.3330i | 0.475757i | ||||||||
\(673\) | −29.1269 | − | 29.1269i | −1.12276 | − | 1.12276i | −0.991325 | − | 0.131434i | \(-0.958042\pi\) |
−0.131434 | − | 0.991325i | \(-0.541958\pi\) | |||||||
\(674\) | 17.7448 | + | 17.7448i | 0.683504 | + | 0.683504i | ||||
\(675\) | 25.9859 | − | 25.9859i | 1.00020 | − | 1.00020i | ||||
\(676\) | 7.17185 | 0.275840 | ||||||||
\(677\) | 24.9876 | − | 24.9876i | 0.960352 | − | 0.960352i | −0.0388918 | − | 0.999243i | \(-0.512383\pi\) |
0.999243 | + | 0.0388918i | \(0.0123828\pi\) | |||||||
\(678\) | 67.9753i | 2.61058i | ||||||||
\(679\) | 3.59886 | 0.138112 | ||||||||
\(680\) | 0.0169365 | − | 2.77544i | 0.000649487 | − | 0.106433i | ||||
\(681\) | −55.2029 | −2.11538 | ||||||||
\(682\) | 62.4622i | 2.39180i | ||||||||
\(683\) | 0.459703 | − | 0.459703i | 0.0175901 | − | 0.0175901i | −0.698257 | − | 0.715847i | \(-0.746041\pi\) |
0.715847 | + | 0.698257i | \(0.246041\pi\) | |||||||
\(684\) | 53.2983 | 2.03791 | ||||||||
\(685\) | 7.21531 | − | 7.21531i | 0.275683 | − | 0.275683i | ||||
\(686\) | −10.3953 | − | 10.3953i | −0.396896 | − | 0.396896i | ||||
\(687\) | 36.3878 | + | 36.3878i | 1.38828 | + | 1.38828i | ||||
\(688\) | − | 3.12183i | − | 0.119019i | ||||||
\(689\) | − | 43.2897i | − | 1.64921i | ||||||
\(690\) | −30.6891 | − | 30.6891i | −1.16832 | − | 1.16832i | ||||
\(691\) | 4.21161 | + | 4.21161i | 0.160217 | + | 0.160217i | 0.782663 | − | 0.622446i | \(-0.213861\pi\) |
−0.622446 | + | 0.782663i | \(0.713861\pi\) | |||||||
\(692\) | −1.27600 | + | 1.27600i | −0.0485063 | + | 0.0485063i | ||||
\(693\) | 11.0342 | 0.419155 | ||||||||
\(694\) | −34.3145 | + | 34.3145i | −1.30256 | + | 1.30256i | ||||
\(695\) | 7.42780i | 0.281753i | ||||||||
\(696\) | −24.1756 | −0.916373 | ||||||||
\(697\) | 0.170844 | − | 27.9966i | 0.00647116 | − | 1.06045i | ||||
\(698\) | −18.5361 | −0.701600 | ||||||||
\(699\) | 60.3447i | 2.28245i | ||||||||
\(700\) | 3.64179 | − | 3.64179i | 0.137647 | − | 0.137647i | ||||
\(701\) | −19.1236 | −0.722289 | −0.361144 | − | 0.932510i | \(-0.617614\pi\) | ||||
−0.361144 | + | 0.932510i | \(0.617614\pi\) | |||||||
\(702\) | −40.4220 | + | 40.4220i | −1.52563 | + | 1.52563i | ||||
\(703\) | 2.13934 | + | 2.13934i | 0.0806868 | + | 0.0806868i | ||||
\(704\) | 27.4753 | + | 27.4753i | 1.03552 | + | 1.03552i | ||||
\(705\) | − | 0.816702i | − | 0.0307588i | ||||||
\(706\) | 44.6429i | 1.68016i | ||||||||
\(707\) | −1.14252 | − | 1.14252i | −0.0429688 | − | 0.0429688i | ||||
\(708\) | 1.04034 | + | 1.04034i | 0.0390984 | + | 0.0390984i | ||||
\(709\) | 8.89433 | − | 8.89433i | 0.334034 | − | 0.334034i | −0.520082 | − | 0.854116i | \(-0.674099\pi\) |
0.854116 | + | 0.520082i | \(0.174099\pi\) | |||||||
\(710\) | 27.8758 | 1.04616 | ||||||||
\(711\) | −56.0881 | + | 56.0881i | −2.10347 | + | 2.10347i | ||||
\(712\) | − | 10.9147i | − | 0.409046i | ||||||
\(713\) | −65.4873 | −2.45252 | ||||||||
\(714\) | −9.36516 | + | 9.25156i | −0.350482 | + | 0.346231i | ||||
\(715\) | 10.0262 | 0.374959 | ||||||||
\(716\) | 21.6554i | 0.809300i | ||||||||
\(717\) | 42.6614 | − | 42.6614i | 1.59322 | − | 1.59322i | ||||
\(718\) | −41.7937 | −1.55973 | ||||||||
\(719\) | 27.5168 | − | 27.5168i | 1.02620 | − | 1.02620i | 0.0265562 | − | 0.999647i | \(-0.491546\pi\) |
0.999647 | − | 0.0265562i | \(-0.00845409\pi\) | |||||||
\(720\) | 11.3239 | + | 11.3239i | 0.422016 | + | 0.422016i | ||||
\(721\) | 3.71702 | + | 3.71702i | 0.138429 | + | 0.138429i | ||||
\(722\) | − | 9.37901i | − | 0.349051i | ||||||
\(723\) | − | 17.1342i | − | 0.637229i | ||||||
\(724\) | 0.750920 | + | 0.750920i | 0.0279077 | + | 0.0279077i | ||||
\(725\) | −31.4009 | − | 31.4009i | −1.16620 | − | 1.16620i | ||||
\(726\) | 10.3220 | − | 10.3220i | 0.383085 | − | 0.383085i | ||||
\(727\) | −29.6948 | −1.10132 | −0.550660 | − | 0.834730i | \(-0.685624\pi\) | ||||
−0.550660 | + | 0.834730i | \(0.685624\pi\) | |||||||
\(728\) | −0.885329 | + | 0.885329i | −0.0328125 | + | 0.0328125i | ||||
\(729\) | − | 29.5342i | − | 1.09386i | ||||||
\(730\) | −14.6604 | −0.542605 | ||||||||
\(731\) | 2.93321 | − | 2.89763i | 0.108489 | − | 0.107173i | ||||
\(732\) | −74.0561 | −2.73719 | ||||||||
\(733\) | 4.47182i | 0.165171i | 0.996584 | + | 0.0825853i | \(0.0263177\pi\) | ||||
−0.996584 | + | 0.0825853i | \(0.973682\pi\) | |||||||
\(734\) | 34.1386 | − | 34.1386i | 1.26008 | − | 1.26008i | ||||
\(735\) | −17.4735 | −0.644519 | ||||||||
\(736\) | −45.7122 | + | 45.7122i | −1.68498 | + | 1.68498i | ||||
\(737\) | 19.0622 | + | 19.0622i | 0.702165 | + | 0.702165i | ||||
\(738\) | −59.2421 | − | 59.2421i | −2.18073 | − | 2.18073i | ||||
\(739\) | − | 35.9843i | − | 1.32370i | −0.749635 | − | 0.661852i | \(-0.769771\pi\) | ||
0.749635 | − | 0.661852i | \(-0.230229\pi\) | |||||||
\(740\) | − | 1.63624i | − | 0.0601495i | ||||||
\(741\) | −25.3840 | − | 25.3840i | −0.932505 | − | 0.932505i | ||||
\(742\) | −10.3718 | − | 10.3718i | −0.380761 | − | 0.380761i | ||||
\(743\) | −6.21792 | + | 6.21792i | −0.228113 | + | 0.228113i | −0.811904 | − | 0.583791i | \(-0.801569\pi\) |
0.583791 | + | 0.811904i | \(0.301569\pi\) | |||||||
\(744\) | −18.9025 | −0.692999 | ||||||||
\(745\) | −6.49477 | + | 6.49477i | −0.237950 | + | 0.237950i | ||||
\(746\) | 70.5578i | 2.58330i | ||||||||
\(747\) | 8.09264 | 0.296094 | ||||||||
\(748\) | −0.217834 | + | 35.6971i | −0.00796479 | + | 1.30521i | ||||
\(749\) | 0.617736 | 0.0225716 | ||||||||
\(750\) | − | 50.1185i | − | 1.83007i | ||||||
\(751\) | 27.4042 | − | 27.4042i | 0.999993 | − | 0.999993i | −6.52405e−6 | − | 1.00000i | \(-0.500002\pi\) |
1.00000 | 6.52405e-6i | \(2.07667e-6\pi\) | ||||||||
\(752\) | −0.983159 | −0.0358521 | ||||||||
\(753\) | 26.9127 | − | 26.9127i | 0.980752 | − | 0.980752i | ||||
\(754\) | 48.8452 | + | 48.8452i | 1.77884 | + | 1.77884i | ||||
\(755\) | −10.5490 | − | 10.5490i | −0.383917 | − | 0.383917i | ||||
\(756\) | 10.5057i | 0.382087i | ||||||||
\(757\) | − | 18.6277i | − | 0.677034i | −0.940960 | − | 0.338517i | \(-0.890075\pi\) | ||
0.940960 | − | 0.338517i | \(-0.109925\pi\) | |||||||
\(758\) | 4.77058 | + | 4.77058i | 0.173275 | + | 0.173275i | ||||
\(759\) | 61.6873 | + | 61.6873i | 2.23911 | + | 2.23911i | ||||
\(760\) | 1.81338 | − | 1.81338i | 0.0657783 | − | 0.0657783i | ||||
\(761\) | 17.8310 | 0.646373 | 0.323187 | − | 0.946335i | \(-0.395246\pi\) | ||||
0.323187 | + | 0.946335i | \(0.395246\pi\) | |||||||
\(762\) | −9.94340 | + | 9.94340i | −0.360211 | + | 0.360211i | ||||
\(763\) | − | 1.05499i | − | 0.0381931i | ||||||
\(764\) | −27.4856 | −0.994393 | ||||||||
\(765\) | −0.129065 | + | 21.1503i | −0.00466636 | + | 0.764691i | ||||
\(766\) | 57.1129 | 2.06357 | ||||||||
\(767\) | − | 0.656994i | − | 0.0237227i | ||||||
\(768\) | 18.0302 | − | 18.0302i | 0.650609 | − | 0.650609i | ||||
\(769\) | −50.7843 | −1.83133 | −0.915664 | − | 0.401944i | \(-0.868335\pi\) | ||||
−0.915664 | + | 0.401944i | \(0.868335\pi\) | |||||||
\(770\) | 2.40219 | − | 2.40219i | 0.0865688 | − | 0.0865688i | ||||
\(771\) | −45.2305 | − | 45.2305i | −1.62894 | − | 1.62894i | ||||
\(772\) | −21.3652 | − | 21.3652i | −0.768949 | − | 0.768949i | ||||
\(773\) | 25.2039i | 0.906522i | 0.891378 | + | 0.453261i | \(0.149739\pi\) | ||||
−0.891378 | + | 0.453261i | \(0.850261\pi\) | |||||||
\(774\) | − | 12.3383i | − | 0.443491i | ||||||
\(775\) | −24.5519 | − | 24.5519i | −0.881930 | − | 0.881930i | ||||
\(776\) | 3.85027 | + | 3.85027i | 0.138216 | + | 0.138216i | ||||
\(777\) | −0.857630 | + | 0.857630i | −0.0307673 | + | 0.0307673i | ||||
\(778\) | 41.1171 | 1.47412 | ||||||||
\(779\) | 18.2921 | − | 18.2921i | 0.655382 | − | 0.655382i | ||||
\(780\) | 19.4146i | 0.695154i | ||||||||
\(781\) | −56.0323 | −2.00499 | ||||||||
\(782\) | −69.0028 | − | 0.421075i | −2.46753 | − | 0.0150576i | ||||
\(783\) | 90.5840 | 3.23721 | ||||||||
\(784\) | 21.0349i | 0.751245i | ||||||||
\(785\) | 3.59273 | − | 3.59273i | 0.128230 | − | 0.128230i | ||||
\(786\) | 58.6465 | 2.09185 | ||||||||
\(787\) | −11.3665 | + | 11.3665i | −0.405171 | + | 0.405171i | −0.880051 | − | 0.474880i | \(-0.842492\pi\) |
0.474880 | + | 0.880051i | \(0.342492\pi\) | |||||||
\(788\) | 22.8600 | + | 22.8600i | 0.814354 | + | 0.814354i | ||||
\(789\) | −25.6779 | − | 25.6779i | −0.914156 | − | 0.914156i | ||||
\(790\) | 24.4212i | 0.868866i | ||||||||
\(791\) | − | 5.57844i | − | 0.198347i | ||||||
\(792\) | 11.8050 | + | 11.8050i | 0.419474 | + | 0.419474i | ||||
\(793\) | 23.3839 | + | 23.3839i | 0.830386 | + | 0.830386i | ||||
\(794\) | 19.4306 | − | 19.4306i | 0.689567 | − | 0.689567i | ||||
\(795\) | −35.5459 | −1.26068 | ||||||||
\(796\) | −19.4247 | + | 19.4247i | −0.688491 | + | 0.688491i | ||||
\(797\) | 18.8984i | 0.669417i | 0.942322 | + | 0.334708i | \(0.108638\pi\) | ||||
−0.942322 | + | 0.334708i | \(0.891362\pi\) | |||||||
\(798\) | −12.1635 | −0.430585 | ||||||||
\(799\) | −0.912551 | − | 0.923757i | −0.0322837 | − | 0.0326802i | ||||
\(800\) | −34.2761 | −1.21184 | ||||||||
\(801\) | 83.1758i | 2.93887i | ||||||||
\(802\) | 27.2269 | − | 27.2269i | 0.961417 | − | 0.961417i | ||||
\(803\) | 29.4684 | 1.03992 | ||||||||
\(804\) | −36.9117 | + | 36.9117i | −1.30178 | + | 1.30178i | ||||
\(805\) | 2.51853 | + | 2.51853i | 0.0887664 | + | 0.0887664i | ||||
\(806\) | 38.1913 | + | 38.1913i | 1.34523 | + | 1.34523i | ||||
\(807\) | 88.7783i | 3.12514i | ||||||||
\(808\) | − | 2.44466i | − | 0.0860029i | ||||||
\(809\) | −9.87247 | − | 9.87247i | −0.347098 | − | 0.347098i | 0.511930 | − | 0.859027i | \(-0.328931\pi\) |
−0.859027 | + | 0.511930i | \(0.828931\pi\) | |||||||
\(810\) | 10.4417 | + | 10.4417i | 0.366885 | + | 0.366885i | ||||
\(811\) | 22.5590 | − | 22.5590i | 0.792155 | − | 0.792155i | −0.189689 | − | 0.981844i | \(-0.560748\pi\) |
0.981844 | + | 0.189689i | \(0.0607479\pi\) | |||||||
\(812\) | 12.6949 | 0.445502 | ||||||||
\(813\) | 43.6115 | − | 43.6115i | 1.52952 | − | 1.52952i | ||||
\(814\) | 6.06392i | 0.212540i | ||||||||
\(815\) | −13.2909 | −0.465560 | ||||||||
\(816\) | 38.4032 | + | 0.234347i | 1.34438 | + | 0.00820380i | ||||
\(817\) | 3.80968 | 0.133284 | ||||||||
\(818\) | − | 16.2273i | − | 0.567374i | ||||||
\(819\) | 6.74666 | − | 6.74666i | 0.235748 | − | 0.235748i | ||||
\(820\) | −13.9904 | −0.488567 | ||||||||
\(821\) | −7.39357 | + | 7.39357i | −0.258037 | + | 0.258037i | −0.824255 | − | 0.566218i | \(-0.808406\pi\) |
0.566218 | + | 0.824255i | \(0.308406\pi\) | |||||||
\(822\) | −51.7787 | − | 51.7787i | −1.80599 | − | 1.80599i | ||||
\(823\) | 20.0101 | + | 20.0101i | 0.697510 | + | 0.697510i | 0.963873 | − | 0.266363i | \(-0.0858220\pi\) |
−0.266363 | + | 0.963873i | \(0.585822\pi\) | |||||||
\(824\) | 7.95336i | 0.277068i | ||||||||
\(825\) | 46.2545i | 1.61038i | ||||||||
\(826\) | −0.157410 | − | 0.157410i | −0.00547699 | − | 0.00547699i | ||||
\(827\) | −15.1447 | − | 15.1447i | −0.526633 | − | 0.526633i | 0.392934 | − | 0.919567i | \(-0.371460\pi\) |
−0.919567 | + | 0.392934i | \(0.871460\pi\) | |||||||
\(828\) | −79.1947 | + | 79.1947i | −2.75221 | + | 2.75221i | ||||
\(829\) | 2.07180 | 0.0719566 | 0.0359783 | − | 0.999353i | \(-0.488545\pi\) | ||||
0.0359783 | + | 0.999353i | \(0.488545\pi\) | |||||||
\(830\) | 1.76179 | − | 1.76179i | 0.0611528 | − | 0.0611528i | ||||
\(831\) | − | 2.55714i | − | 0.0887063i | ||||||
\(832\) | 33.5985 | 1.16482 | ||||||||
\(833\) | −19.7639 | + | 19.5242i | −0.684780 | + | 0.676473i | ||||
\(834\) | 53.3037 | 1.84576 | ||||||||
\(835\) | 11.0505i | 0.382418i | ||||||||
\(836\) | −23.3233 | + | 23.3233i | −0.806652 | + | 0.806652i | ||||
\(837\) | 70.8262 | 2.44811 | ||||||||
\(838\) | 47.1882 | − | 47.1882i | 1.63009 | − | 1.63009i | ||||
\(839\) | −28.8183 | − | 28.8183i | −0.994919 | − | 0.994919i | 0.00506777 | − | 0.999987i | \(-0.498387\pi\) |
−0.999987 | + | 0.00506777i | \(0.998387\pi\) | |||||||
\(840\) | 0.726958 | + | 0.726958i | 0.0250824 | + | 0.0250824i | ||||
\(841\) | − | 80.4601i | − | 2.77449i | ||||||
\(842\) | 23.6086i | 0.813605i | ||||||||
\(843\) | −9.63180 | − | 9.63180i | −0.331737 | − | 0.331737i | ||||
\(844\) | −9.68681 | − | 9.68681i | −0.333434 | − | 0.333434i | ||||
\(845\) | −1.85948 | + | 1.85948i | −0.0639681 | + | 0.0639681i | ||||
\(846\) | −3.88570 | −0.133593 | ||||||||
\(847\) | −0.847082 | + | 0.847082i | −0.0291061 | + | 0.0291061i | ||||
\(848\) | 42.7907i | 1.46944i | ||||||||
\(849\) | −37.8780 | −1.29997 | ||||||||
\(850\) | −25.7120 | − | 26.0278i | −0.881916 | − | 0.892745i | ||||
\(851\) | −6.35760 | −0.217936 | ||||||||
\(852\) | − | 108.500i | − | 3.71715i | ||||||
\(853\) | 0.740344 | − | 0.740344i | 0.0253489 | − | 0.0253489i | −0.694319 | − | 0.719668i | \(-0.744294\pi\) |
0.719668 | + | 0.694319i | \(0.244294\pi\) | |||||||
\(854\) | 11.2051 | 0.383432 | ||||||||
\(855\) | −13.8189 | + | 13.8189i | −0.472596 | + | 0.472596i | ||||
\(856\) | 0.660889 | + | 0.660889i | 0.0225887 | + | 0.0225887i | ||||
\(857\) | 4.22965 | + | 4.22965i | 0.144482 | + | 0.144482i | 0.775648 | − | 0.631166i | \(-0.217423\pi\) |
−0.631166 | + | 0.775648i | \(0.717423\pi\) | |||||||
\(858\) | − | 71.9504i | − | 2.45635i | ||||||
\(859\) | − | 23.9653i | − | 0.817684i | −0.912605 | − | 0.408842i | \(-0.865933\pi\) | ||
0.912605 | − | 0.408842i | \(-0.134067\pi\) | |||||||
\(860\) | −1.45689 | − | 1.45689i | −0.0496795 | − | 0.0496795i | ||||
\(861\) | 7.33302 | + | 7.33302i | 0.249909 | + | 0.249909i | ||||
\(862\) | 25.0213 | − | 25.0213i | 0.852230 | − | 0.852230i | ||||
\(863\) | 36.6324 | 1.24698 | 0.623490 | − | 0.781831i | \(-0.285714\pi\) | ||||
0.623490 | + | 0.781831i | \(0.285714\pi\) | |||||||
\(864\) | 49.4390 | − | 49.4390i | 1.68195 | − | 1.68195i | ||||
\(865\) | − | 0.661670i | − | 0.0224974i | ||||||
\(866\) | 75.9620 | 2.58130 | ||||||||
\(867\) | 35.4250 | + | 36.3004i | 1.20310 | + | 1.23283i | ||||
\(868\) | 9.92591 | 0.336907 | ||||||||
\(869\) | − | 49.0882i | − | 1.66520i | ||||||
\(870\) | 40.1076 | − | 40.1076i | 1.35977 | − | 1.35977i | ||||
\(871\) | 23.3104 | 0.789844 | ||||||||
\(872\) | 1.12868 | − | 1.12868i | 0.0382221 | − | 0.0382221i | ||||
\(873\) | −29.3410 | − | 29.3410i | −0.993043 | − | 0.993043i | ||||
\(874\) | −45.0841 | − | 45.0841i | −1.52499 | − | 1.52499i | ||||
\(875\) | 4.11301i | 0.139045i | ||||||||
\(876\) | 57.0621i | 1.92795i | ||||||||
\(877\) | 15.3288 | + | 15.3288i | 0.517615 | + | 0.517615i | 0.916849 | − | 0.399234i | \(-0.130724\pi\) |
−0.399234 | + | 0.916849i | \(0.630724\pi\) | |||||||
\(878\) | 46.8929 | + | 46.8929i | 1.58256 | + | 1.58256i | ||||
\(879\) | −24.6594 | + | 24.6594i | −0.831740 | + | 0.831740i | ||||
\(880\) | −9.91062 | −0.334087 | ||||||||
\(881\) | 2.57557 | − | 2.57557i | 0.0867731 | − | 0.0867731i | −0.662388 | − | 0.749161i | \(-0.730457\pi\) |
0.749161 | + | 0.662388i | \(0.230457\pi\) | |||||||
\(882\) | 83.1353i | 2.79931i | ||||||||
\(883\) | −29.1580 | −0.981245 | −0.490622 | − | 0.871372i | \(-0.663231\pi\) | ||||
−0.490622 | + | 0.871372i | \(0.663231\pi\) | |||||||
\(884\) | 21.6931 | + | 21.9595i | 0.729618 | + | 0.738577i | ||||
\(885\) | −0.539468 | −0.0181340 | ||||||||
\(886\) | 43.2064i | 1.45155i | ||||||||
\(887\) | 3.46375 | − | 3.46375i | 0.116301 | − | 0.116301i | −0.646561 | − | 0.762862i | \(-0.723793\pi\) |
0.762862 | + | 0.646561i | \(0.223793\pi\) | |||||||
\(888\) | −1.83508 | −0.0615813 | ||||||||
\(889\) | 0.816012 | − | 0.816012i | 0.0273682 | − | 0.0273682i | ||||
\(890\) | 18.1076 | + | 18.1076i | 0.606970 | + | 0.606970i | ||||
\(891\) | −20.9886 | − | 20.9886i | −0.703144 | − | 0.703144i | ||||
\(892\) | − | 30.4382i | − | 1.01915i | ||||||
\(893\) | − | 1.19978i | − | 0.0401492i | ||||||
\(894\) | 46.6080 | + | 46.6080i | 1.55880 | + | 1.55880i | ||||
\(895\) | −5.61469 | − | 5.61469i | −0.187679 | − | 0.187679i | ||||
\(896\) | 2.20412 | − | 2.20412i | 0.0736343 | − | 0.0736343i | ||||
\(897\) | 75.4350 | 2.51870 | ||||||||
\(898\) | −14.9534 | + | 14.9534i | −0.499001 | + | 0.499001i | ||||
\(899\) | − | 85.5851i | − | 2.85442i | ||||||
\(900\) | −59.3820 | −1.97940 | ||||||||
\(901\) | −40.2053 | + | 39.7176i | −1.33943 | + | 1.32318i | ||||
\(902\) | 51.8485 | 1.72637 | ||||||||
\(903\) | 1.52724i | 0.0508235i | ||||||||
\(904\) | 5.96814 | − | 5.96814i | 0.198497 | − | 0.198497i | ||||
\(905\) | −0.389389 | −0.0129437 | ||||||||
\(906\) | −75.7021 | + | 75.7021i | −2.51503 | + | 2.51503i | ||||
\(907\) | 21.9163 | + | 21.9163i | 0.727717 | + | 0.727717i | 0.970165 | − | 0.242447i | \(-0.0779502\pi\) |
−0.242447 | + | 0.970165i | \(0.577950\pi\) | |||||||
\(908\) | 31.0127 | + | 31.0127i | 1.02919 | + | 1.02919i | ||||
\(909\) | 18.6296i | 0.617904i | ||||||||
\(910\) | − | 2.93754i | − | 0.0973786i | ||||||
\(911\) | 22.0011 | + | 22.0011i | 0.728930 | + | 0.728930i | 0.970407 | − | 0.241476i | \(-0.0776317\pi\) |
−0.241476 | + | 0.970407i | \(0.577632\pi\) | |||||||
\(912\) | 25.0914 | + | 25.0914i | 0.830858 | + | 0.830858i | ||||
\(913\) | −3.54133 | + | 3.54133i | −0.117201 | + | 0.117201i | ||||
\(914\) | −16.2591 | −0.537802 | ||||||||
\(915\) | 19.2009 | − | 19.2009i | 0.634761 | − | 0.634761i | ||||
\(916\) | − | 40.8849i | − | 1.35088i | ||||||
\(917\) | −4.81287 | −0.158935 | ||||||||
\(918\) | 74.6283 | + | 0.455403i | 2.46310 | + | 0.0150306i | ||||
\(919\) | −4.67940 | −0.154359 | −0.0771796 | − | 0.997017i | \(-0.524591\pi\) | ||||
−0.0771796 | + | 0.997017i | \(0.524591\pi\) | |||||||
\(920\) | 5.38893i | 0.177668i | ||||||||
\(921\) | 0.858184 | − | 0.858184i | 0.0282781 | − | 0.0282781i | ||||
\(922\) | −29.4047 | −0.968393 | ||||||||
\(923\) | −34.2599 | + | 34.2599i | −1.12768 | + | 1.12768i | ||||
\(924\) | −9.34995 | − | 9.34995i | −0.307591 | − | 0.307591i | ||||
\(925\) | −2.38353 | − | 2.38353i | −0.0783701 | − | 0.0783701i | ||||
\(926\) | − | 47.4052i | − | 1.55783i | ||||||
\(927\) | − | 60.6087i | − | 1.99065i | ||||||
\(928\) | −59.7412 | − | 59.7412i | −1.96110 | − | 1.96110i | ||||
\(929\) | 15.7587 | + | 15.7587i | 0.517028 | + | 0.517028i | 0.916671 | − | 0.399643i | \(-0.130866\pi\) |
−0.399643 | + | 0.916671i | \(0.630866\pi\) | |||||||
\(930\) | 31.3595 | − | 31.3595i | 1.02832 | − | 1.02832i | ||||
\(931\) | −25.6695 | −0.841285 | ||||||||
\(932\) | 33.9013 | − | 33.9013i | 1.11047 | − | 1.11047i | ||||
\(933\) | − | 42.2775i | − | 1.38410i | ||||||
\(934\) | −11.9473 | −0.390928 | ||||||||
\(935\) | −9.19887 | − | 9.31182i | −0.300835 | − | 0.304529i | ||||
\(936\) | 14.4359 | 0.471853 | ||||||||
\(937\) | − | 35.1355i | − | 1.14783i | −0.818917 | − | 0.573913i | \(-0.805425\pi\) | ||
0.818917 | − | 0.573913i | \(-0.194575\pi\) | |||||||
\(938\) | 5.58497 | − | 5.58497i | 0.182356 | − | 0.182356i | ||||
\(939\) | 46.3012 | 1.51098 | ||||||||
\(940\) | −0.458818 | + | 0.458818i | −0.0149650 | + | 0.0149650i | ||||
\(941\) | 16.4475 | + | 16.4475i | 0.536172 | + | 0.536172i | 0.922402 | − | 0.386230i | \(-0.126223\pi\) |
−0.386230 | + | 0.922402i | \(0.626223\pi\) | |||||||
\(942\) | −25.7823 | − | 25.7823i | −0.840033 | − | 0.840033i | ||||
\(943\) | 54.3596i | 1.77019i | ||||||||
\(944\) | 0.649420i | 0.0211368i | ||||||||
\(945\) | −2.72385 | − | 2.72385i | −0.0886070 | − | 0.0886070i | ||||
\(946\) | 5.39923 | + | 5.39923i | 0.175544 | + | 0.175544i | ||||
\(947\) | −6.83298 | + | 6.83298i | −0.222042 | + | 0.222042i | −0.809358 | − | 0.587316i | \(-0.800185\pi\) |
0.587316 | + | 0.809358i | \(0.300185\pi\) | |||||||
\(948\) | 95.0536 | 3.08720 | ||||||||
\(949\) | 18.0179 | − | 18.0179i | 0.584885 | − | 0.584885i | ||||
\(950\) | − | 33.8051i | − | 1.09678i | ||||||
\(951\) | 57.0740 | 1.85075 | ||||||||
\(952\) | 1.63452 | + | 0.00997432i | 0.0529752 | + | 0.000323270i | ||||
\(953\) | −32.7614 | −1.06125 | −0.530623 | − | 0.847608i | \(-0.678042\pi\) | ||||
−0.530623 | + | 0.847608i | \(0.678042\pi\) | |||||||
\(954\) | 169.120i | 5.47546i | ||||||||
\(955\) | 7.12631 | − | 7.12631i | 0.230602 | − | 0.230602i | ||||
\(956\) | −47.9338 | −1.55029 | ||||||||
\(957\) | −80.6190 | + | 80.6190i | −2.60604 | + | 2.60604i | ||||
\(958\) | −13.6578 | − | 13.6578i | −0.441264 | − | 0.441264i | ||||
\(959\) | 4.24926 | + | 4.24926i | 0.137216 | + | 0.137216i | ||||
\(960\) | − | 27.5883i | − | 0.890408i | ||||||
\(961\) | − | 35.9177i | − | 1.15864i | ||||||
\(962\) | 3.70767 | + | 3.70767i | 0.119540 | + | 0.119540i | ||||
\(963\) | −5.03632 | − | 5.03632i | −0.162293 | − | 0.162293i | ||||
\(964\) | −9.62590 | + | 9.62590i | −0.310030 | + | 0.310030i | ||||
\(965\) | 11.0789 | 0.356642 | ||||||||
\(966\) | 18.0735 | − | 18.0735i | 0.581507 | − | 0.581507i | ||||
\(967\) | − | 50.6195i | − | 1.62781i | −0.580995 | − | 0.813907i | \(-0.697336\pi\) | ||
0.580995 | − | 0.813907i | \(-0.302664\pi\) | |||||||
\(968\) | −1.81251 | −0.0582564 | ||||||||
\(969\) | −0.285982 | + | 46.8647i | −0.00918706 | + | 1.50551i | ||||
\(970\) | −12.7753 | −0.410189 | ||||||||
\(971\) | 42.5150i | 1.36437i | 0.731180 | + | 0.682185i | \(0.238970\pi\) | ||||
−0.731180 | + | 0.682185i | \(0.761030\pi\) | |||||||
\(972\) | −2.89549 | + | 2.89549i | −0.0928728 | + | 0.0928728i | ||||
\(973\) | −4.37440 | −0.140237 | ||||||||
\(974\) | 36.3132 | − | 36.3132i | 1.16355 | − | 1.16355i | ||||
\(975\) | 28.2814 | + | 28.2814i | 0.905731 | + | 0.905731i | ||||
\(976\) | −23.1143 | − | 23.1143i | −0.739871 | − | 0.739871i | ||||
\(977\) | 26.4066i | 0.844823i | 0.906404 | + | 0.422411i | \(0.138816\pi\) | ||||
−0.906404 | + | 0.422411i | \(0.861184\pi\) | |||||||
\(978\) | 95.3786i | 3.04987i | ||||||||
\(979\) | −36.3976 | − | 36.3976i | −1.16327 | − | 1.16327i | ||||
\(980\) | 9.81649 | + | 9.81649i | 0.313576 | + | 0.313576i | ||||
\(981\) | −8.60116 | + | 8.60116i | −0.274614 | + | 0.274614i | ||||
\(982\) | 57.1041 | 1.82226 | ||||||||
\(983\) | 6.82777 | − | 6.82777i | 0.217772 | − | 0.217772i | −0.589787 | − | 0.807559i | \(-0.700788\pi\) |
0.807559 | + | 0.589787i | \(0.200788\pi\) | |||||||
\(984\) | 15.6906i | 0.500197i | ||||||||
\(985\) | −11.8540 | −0.377701 | ||||||||
\(986\) | 0.550301 | − | 90.1795i | 0.0175252 | − | 2.87190i | ||||
\(987\) | 0.480975 | 0.0153096 | ||||||||
\(988\) | 28.5211i | 0.907378i | ||||||||
\(989\) | −5.66072 | + | 5.66072i | −0.180000 | + | 0.180000i | ||||
\(990\) | −39.1694 | −1.24488 | ||||||||
\(991\) | 12.1164 | − | 12.1164i | 0.384889 | − | 0.384889i | −0.487971 | − | 0.872860i | \(-0.662263\pi\) |
0.872860 | + | 0.487971i | \(0.162263\pi\) | |||||||
\(992\) | −46.7107 | − | 46.7107i | −1.48307 | − | 1.48307i | ||||
\(993\) | −41.5607 | − | 41.5607i | −1.31889 | − | 1.31889i | ||||
\(994\) | 16.4167i | 0.520707i | ||||||||
\(995\) | − | 10.0727i | − | 0.319325i | ||||||
\(996\) | −6.85737 | − | 6.85737i | −0.217284 | − | 0.217284i | ||||
\(997\) | −32.4500 | − | 32.4500i | −1.02770 | − | 1.02770i | −0.999605 | − | 0.0280966i | \(-0.991055\pi\) |
−0.0280966 | − | 0.999605i | \(-0.508945\pi\) | |||||||
\(998\) | −26.4725 | + | 26.4725i | −0.837973 | + | 0.837973i | ||||
\(999\) | 6.87591 | 0.217544 |
(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 | 731.2.f.c.259.6 | ✓ | 56 | |
17.13 | even | 4 | inner | 731.2.f.c.302.23 | yes | 56 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
731.2.f.c.259.6 | ✓ | 56 | 1.1 | even | 1 | trivial | |
731.2.f.c.302.23 | yes | 56 | 17.13 | even | 4 | inner |